From ecf66a43013efbd6157f30f9e8de0ba321bafecf Mon Sep 17 00:00:00 2001
From: Roger Bivand <Roger.Bivand@gmail.com>
Date: Mon, 2 Dec 2024 10:59:30 +0100
Subject: [PATCH] update docs

---
 DESCRIPTION                                   |   2 +-
 docs/404.html                                 |   2 +-
 docs/articles/CO69.html                       |   8 +-
 docs/articles/index.html                      |   2 +-
 docs/articles/nb.html                         |   4 +-
 docs/articles/nb_sf.html                      |  34 ++---
 docs/articles/sids.html                       | 119 ++++++++++--------
 .../figure-html/unnamed-chunk-20-1.png        | Bin 0 -> 58588 bytes
 .../figure-html/unnamed-chunk-22-1.png        | Bin 0 -> 70554 bytes
 .../figure-html/unnamed-chunk-24-1.png        | Bin 0 -> 70865 bytes
 .../figure-html/unnamed-chunk-27-1.png        | Bin 0 -> 77673 bytes
 .../figure-html/unnamed-chunk-32-1.png        | Bin 0 -> 133313 bytes
 docs/articles/subgraphs.html                  |  10 +-
 docs/authors.html                             |   2 +-
 docs/index.html                               |   4 +-
 docs/news/index.html                          |   8 +-
 docs/pkgdown.yml                              |   2 +-
 docs/reference/COL.OLD.html                   |   2 +-
 docs/reference/EBImoran.mc.html               |   2 +-
 docs/reference/EBest.html                     |   2 +-
 docs/reference/EBlocal.html                   |   2 +-
 docs/reference/LOSH.cs.html                   |   2 +-
 docs/reference/LOSH.html                      |   2 +-
 docs/reference/LOSH.mc.html                   |   2 +-
 docs/reference/SD.RStests.html                |   2 +-
 docs/reference/aggregate.nb.html              |   2 +-
 docs/reference/airdist.html                   |   2 +-
 docs/reference/autocov_dist.html              |   2 +-
 docs/reference/bhicv.html                     |   4 +-
 docs/reference/card.html                      |   2 +-
 docs/reference/cell2nb.html                   |   2 +-
 docs/reference/choynowski.html                |   2 +-
 docs/reference/columbus.html                  |   2 +-
 docs/reference/compon.html                    |   6 +-
 docs/reference/diffnb.html                    |   2 +-
 docs/reference/dnearneigh.html                |  12 +-
 docs/reference/droplinks.html                 |   2 +-
 docs/reference/edit.nb.html                   |   7 +-
 docs/reference/eire.html                      |   2 +-
 docs/reference/geary.html                     |   2 +-
 docs/reference/geary.mc.html                  |   2 +-
 docs/reference/geary.test.html                |   2 +-
 docs/reference/globalG.test.html              |   2 +-
 docs/reference/graphneigh.html                |   2 +-
 docs/reference/grid2nb.html                   |   2 +-
 docs/reference/hotspotmap.html                |   2 +-
 docs/reference/include.self.html              |   2 +-
 docs/reference/index.html                     |   2 +-
 docs/reference/joincount.mc.html              |   2 +-
 docs/reference/joincount.multi-1.png          | Bin 15310 -> 161040 bytes
 docs/reference/joincount.multi.html           |  76 +----------
 docs/reference/joincount.test.html            |   2 +-
 docs/reference/knearneigh.html                |   6 +-
 docs/reference/knn2nb.html                    |   2 +-
 docs/reference/lag.listw.html                 |   2 +-
 docs/reference/lee.html                       |   2 +-
 docs/reference/lee.mc.html                    |   2 +-
 docs/reference/lee.test.html                  |   2 +-
 docs/reference/licd_multi.html                |   8 +-
 docs/reference/listw2sn.html                  |   2 +-
 docs/reference/lm.RStests.html                |   2 +-
 docs/reference/lm.morantest.exact.html        |   2 +-
 docs/reference/lm.morantest.html              |   2 +-
 docs/reference/lm.morantest.sad.html          |   2 +-
 docs/reference/localC.html                    |  13 +-
 docs/reference/localG.html                    |   2 +-
 docs/reference/localGS.html                   |   2 +-
 docs/reference/local_joincount_bv.html        |   2 +-
 docs/reference/local_joincount_uni.html       |   2 +-
 docs/reference/localmoran.exact.html          |   2 +-
 docs/reference/localmoran.html                |   2 +-
 docs/reference/localmoran.sad.html            |   2 +-
 docs/reference/localmoran_bv.html             |   2 +-
 docs/reference/mat2listw.html                 |   2 +-
 docs/reference/moran.html                     |   2 +-
 docs/reference/moran.mc.html                  |   2 +-
 docs/reference/moran.plot.html                |   8 +-
 docs/reference/moran.test.html                |   2 +-
 docs/reference/moran_bv.html                  |   2 +-
 docs/reference/mstree.html                    |   6 +-
 docs/reference/nb2INLA.html                   |   2 +-
 docs/reference/nb2WB.html                     |   2 +-
 docs/reference/nb2blocknb.html                |  73 +----------
 docs/reference/nb2lines.html                  |  10 +-
 docs/reference/nb2listw.html                  |   2 +-
 docs/reference/nb2listwdist.html              |  61 +--------
 docs/reference/nb2mat.html                    |   2 +-
 docs/reference/nbcosts.html                   |   2 +-
 docs/reference/nbdists.html                   |   2 +-
 docs/reference/nblag.html                     |   2 +-
 docs/reference/nboperations.html              |   2 +-
 docs/reference/p.adjustSP.html                |   2 +-
 docs/reference/plot.mst.html                  |   2 +-
 docs/reference/plot.nb.html                   |   2 +-
 docs/reference/plot.skater.html               |   2 +-
 docs/reference/poly2nb.html                   |   4 +-
 docs/reference/probmap.html                   |   2 +-
 docs/reference/prunecost.html                 |   2 +-
 docs/reference/prunemst.html                  |   2 +-
 docs/reference/read.gal.html                  |   2 +-
 docs/reference/read.gwt2nb.html               |   4 +-
 docs/reference/rotation.html                  |   2 +-
 docs/reference/set.mcOption.html              |   2 +-
 docs/reference/set.spChkOption.html           |   2 +-
 docs/reference/skater.html                    |  18 +--
 docs/reference/sp.correlogram.html            |   2 +-
 docs/reference/sp.mantel.mc.html              |   2 +-
 docs/reference/spdep-defunct.html             |   2 +-
 docs/reference/spdep.html                     |   2 +-
 docs/reference/spweights.constants.html       |   2 +-
 docs/reference/ssw.html                       |   2 +-
 docs/reference/subset.listw.html              |   2 +-
 docs/reference/subset.nb.html                 |   2 +-
 docs/reference/summary.nb.html                |   2 +-
 docs/reference/testnb.html                    |   2 +-
 docs/reference/tolerance.nb.html              |   2 +-
 docs/reference/tri2nb.html                    |   2 +-
 docs/reference/write.nb.gal.html              |   2 +-
 docs/search.json                              |   2 +-
 119 files changed, 249 insertions(+), 434 deletions(-)
 create mode 100644 docs/articles/sids_files/figure-html/unnamed-chunk-20-1.png
 create mode 100644 docs/articles/sids_files/figure-html/unnamed-chunk-22-1.png
 create mode 100644 docs/articles/sids_files/figure-html/unnamed-chunk-24-1.png
 create mode 100644 docs/articles/sids_files/figure-html/unnamed-chunk-27-1.png
 create mode 100644 docs/articles/sids_files/figure-html/unnamed-chunk-32-1.png

diff --git a/DESCRIPTION b/DESCRIPTION
index f8f7035f..d45754b4 100644
--- a/DESCRIPTION
+++ b/DESCRIPTION
@@ -1,6 +1,6 @@
 Package: spdep
 Version: 1.3-8
-Date: 2024-11-25
+Date: 2024-12-02
 Title: Spatial Dependence: Weighting Schemes, Statistics
 Encoding: UTF-8
 Authors@R: c(person("Roger", "Bivand", role = c("cre", "aut"), 
diff --git a/docs/404.html b/docs/404.html
index 52123013..40180476 100644
--- a/docs/404.html
+++ b/docs/404.html
@@ -20,7 +20,7 @@
 
     <a class="navbar-brand me-2" href="https://r-spatial.github.io/spdep/index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/articles/CO69.html b/docs/articles/CO69.html
index 9e3c2a9a..f3272d50 100644
--- a/docs/articles/CO69.html
+++ b/docs/articles/CO69.html
@@ -20,7 +20,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -548,7 +548,7 @@ <h2 id="measures-of-spatial-autocorrelation">Measures of spatial autocorrelation
 <span><span class="va">Prop_stdR</span>  <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/lapply.html" class="external-link">lapply</a></span><span class="op">(</span><span class="va">vars</span>, <span class="kw">function</span><span class="op">(</span><span class="va">x</span><span class="op">)</span> <span class="fu"><a href="../reference/moran.test.html">moran.test</a></span><span class="op">(</span><span class="va">eire_ge1</span><span class="op">[[</span><span class="va">x</span><span class="op">]</span><span class="op">]</span>, listw<span class="op">=</span><span class="va">lw_std</span>, randomisation<span class="op">=</span><span class="cn">TRUE</span><span class="op">)</span><span class="op">)</span></span>
 <span><span class="op">}</span><span class="op">)</span></span></code></pre></div>
 <pre><code><span><span class="co">##    user  system elapsed </span></span>
-<span><span class="co">##    0.11    0.00    0.11</span></span></code></pre>
+<span><span class="co">##   0.117   0.000   0.118</span></span></code></pre>
 <div class="sourceCode" id="cb47"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">res</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/lapply.html" class="external-link">sapply</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"MoranN"</span>, <span class="st">"MoranR"</span>, <span class="st">"GearyN"</span>, <span class="st">"GearyR"</span>, <span class="st">"Prop_unstdN"</span>, <span class="st">"Prop_unstdR"</span>, <span class="st">"Prop_stdN"</span>, <span class="st">"Prop_stdR"</span><span class="op">)</span>, <span class="kw">function</span><span class="op">(</span><span class="va">x</span><span class="op">)</span> <span class="fu"><a href="https://rdrr.io/r/base/lapply.html" class="external-link">sapply</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/get.html" class="external-link">get</a></span><span class="op">(</span><span class="va">x</span><span class="op">)</span>, <span class="st">"[["</span>, <span class="st">"statistic"</span><span class="op">)</span><span class="op">)</span></span>
 <span><span class="fu"><a href="https://rdrr.io/r/base/colnames.html" class="external-link">rownames</a></span><span class="op">(</span><span class="va">res</span><span class="op">)</span> <span class="op">&lt;-</span> <span class="va">vars</span></span>
@@ -780,7 +780,7 @@ <h2 id="simulating-measures-of-spatial-autocorrelation">Simulating measures of s
 <span><span class="va">Prop_stdSad</span>  <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/lapply.html" class="external-link">lapply</a></span><span class="op">(</span><span class="va">lm_objs</span>, <span class="kw">function</span><span class="op">(</span><span class="va">x</span><span class="op">)</span> <span class="fu"><a href="../reference/lm.morantest.sad.html">lm.morantest.sad</a></span><span class="op">(</span><span class="va">x</span>, listw<span class="op">=</span><span class="va">lw_std</span><span class="op">)</span><span class="op">)</span></span>
 <span><span class="op">}</span><span class="op">)</span></span></code></pre></div>
 <pre><code><span><span class="co">##    user  system elapsed </span></span>
-<span><span class="co">##   0.063   0.000   0.064</span></span></code></pre>
+<span><span class="co">##   0.066   0.000   0.066</span></span></code></pre>
 <div class="sourceCode" id="cb67"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">res</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/lapply.html" class="external-link">sapply</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"MoranSad"</span>, <span class="st">"Prop_unstdSad"</span>, <span class="st">"Prop_stdSad"</span><span class="op">)</span>, <span class="kw">function</span><span class="op">(</span><span class="va">x</span><span class="op">)</span> <span class="fu"><a href="https://rdrr.io/r/base/lapply.html" class="external-link">sapply</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/get.html" class="external-link">get</a></span><span class="op">(</span><span class="va">x</span><span class="op">)</span>, <span class="st">"[["</span>, <span class="st">"statistic"</span><span class="op">)</span><span class="op">)</span></span>
 <span><span class="fu"><a href="https://rdrr.io/r/base/colnames.html" class="external-link">rownames</a></span><span class="op">(</span><span class="va">res</span><span class="op">)</span> <span class="op">&lt;-</span> <span class="va">vars</span></span></code></pre></div>
@@ -843,7 +843,7 @@ <h2 id="simulating-measures-of-spatial-autocorrelation">Simulating measures of s
 <span><span class="va">Prop_stdEx</span>  <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/lapply.html" class="external-link">lapply</a></span><span class="op">(</span><span class="va">lm_objs</span>, <span class="kw">function</span><span class="op">(</span><span class="va">x</span><span class="op">)</span> <span class="fu"><a href="../reference/lm.morantest.exact.html">lm.morantest.exact</a></span><span class="op">(</span><span class="va">x</span>, listw<span class="op">=</span><span class="va">lw_std</span><span class="op">)</span><span class="op">)</span></span>
 <span><span class="op">}</span><span class="op">)</span></span></code></pre></div>
 <pre><code><span><span class="co">##    user  system elapsed </span></span>
-<span><span class="co">##    0.08    0.00    0.08</span></span></code></pre>
+<span><span class="co">##   0.083   0.000   0.083</span></span></code></pre>
 <div class="sourceCode" id="cb76"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">res</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/lapply.html" class="external-link">sapply</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"MoranEx"</span>, <span class="st">"Prop_unstdEx"</span>, <span class="st">"Prop_stdEx"</span><span class="op">)</span>, <span class="kw">function</span><span class="op">(</span><span class="va">x</span><span class="op">)</span> <span class="fu"><a href="https://rdrr.io/r/base/lapply.html" class="external-link">sapply</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/get.html" class="external-link">get</a></span><span class="op">(</span><span class="va">x</span><span class="op">)</span>, <span class="st">"[["</span>, <span class="st">"statistic"</span><span class="op">)</span><span class="op">)</span></span>
 <span><span class="fu"><a href="https://rdrr.io/r/base/colnames.html" class="external-link">rownames</a></span><span class="op">(</span><span class="va">res</span><span class="op">)</span> <span class="op">&lt;-</span> <span class="va">vars</span></span></code></pre></div>
diff --git a/docs/articles/index.html b/docs/articles/index.html
index b798b17f..45dc4290 100644
--- a/docs/articles/index.html
+++ b/docs/articles/index.html
@@ -7,7 +7,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/articles/nb.html b/docs/articles/nb.html
index 3a8f1a60..12580ecb 100644
--- a/docs/articles/nb.html
+++ b/docs/articles/nb.html
@@ -20,7 +20,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -105,7 +105,7 @@ <h3 id="introduction">Introduction<a class="anchor" aria-label="anchor" href="#i
 <code class="sourceCode R"><span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va"><a href="https://github.com/r-spatial/spdep/" class="external-link">spdep</a></span><span class="op">)</span></span></code></pre></div>
 <pre><code><span><span class="co">## Loading required package: spData</span></span></code></pre>
 <pre><code><span><span class="co">## Loading required package: sf</span></span></code></pre>
-<pre><code><span><span class="co">## Linking to GEOS 3.13.0, GDAL 3.10.0, PROJ 9.5.0; sf_use_s2() is TRUE</span></span></code></pre>
+<pre><code><span><span class="co">## Linking to GEOS 3.13.0, GDAL 3.10.0, PROJ 9.5.1; sf_use_s2() is TRUE</span></span></code></pre>
 <div class="sourceCode" id="cb5"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="kw">if</span> <span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/utils/packageDescription.html" class="external-link">packageVersion</a></span><span class="op">(</span><span class="st">"spData"</span><span class="op">)</span> <span class="op">&gt;=</span> <span class="st">"2.3.2"</span><span class="op">)</span> <span class="op">{</span></span>
 <span>    <span class="va">NY8a</span> <span class="op">&lt;-</span> <span class="fu">sf</span><span class="fu">::</span><span class="fu"><a href="https://r-spatial.github.io/sf/reference/st_read.html" class="external-link">st_read</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/system.file.html" class="external-link">system.file</a></span><span class="op">(</span><span class="st">"shapes/NY8_utm18.gpkg"</span>, package<span class="op">=</span><span class="st">"spData"</span><span class="op">)</span><span class="op">)</span></span>
diff --git a/docs/articles/nb_sf.html b/docs/articles/nb_sf.html
index 14e0273d..cfbfe407 100644
--- a/docs/articles/nb_sf.html
+++ b/docs/articles/nb_sf.html
@@ -20,7 +20,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -203,9 +203,9 @@ <h3 id="comparison-of-sp-and-sf-approaches">Comparison of sp and sf approaches<a
 <span><span class="op">}</span></span>
 <span><span class="kw">if</span> <span class="op">(</span><span class="va">dothis</span><span class="op">)</span> <span class="fu"><a href="https://r-spatial.github.io/sf/reference/sf_extSoftVersion.html" class="external-link">sf_extSoftVersion</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div>
 <pre><code><span><span class="co">##           GEOS           GDAL         proj.4 GDAL_with_GEOS     USE_PROJ_H </span></span>
-<span><span class="co">##       "3.13.0"       "3.10.0"        "9.5.0"         "true"         "true" </span></span>
+<span><span class="co">##       "3.13.0"       "3.10.0"        "9.5.1"         "true"         "true" </span></span>
 <span><span class="co">##           PROJ </span></span>
-<span><span class="co">##        "9.5.0"</span></span></code></pre>
+<span><span class="co">##        "9.5.1"</span></span></code></pre>
 <p>Let us read the GPKG file with valid geometries in to ‘sf’ and ‘sp’
 objects:</p>
 <div class="sourceCode" id="cb4"><pre class="downlit sourceCode r">
@@ -232,7 +232,7 @@ <h4 id="contiguity-neighbours-for-polygon-support">Contiguity neighbours for pol
 <span><span class="va">eps</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/MathFun.html" class="external-link">sqrt</a></span><span class="op">(</span><span class="va">.Machine</span><span class="op">$</span><span class="va">double.eps</span><span class="op">)</span></span>
 <span><span class="fu"><a href="https://rdrr.io/r/base/system.time.html" class="external-link">system.time</a></span><span class="op">(</span><span class="kw">for</span><span class="op">(</span><span class="va">i</span> <span class="kw">in</span> <span class="fl">1</span><span class="op">:</span><span class="va">reps</span><span class="op">)</span> <span class="va">NY8_sf_1_nb</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/poly2nb.html">poly2nb</a></span><span class="op">(</span><span class="va">NY8_sf</span>, queen<span class="op">=</span><span class="cn">TRUE</span>, snap<span class="op">=</span><span class="va">eps</span><span class="op">)</span><span class="op">)</span><span class="op">/</span><span class="va">reps</span></span></code></pre></div>
 <pre><code><span><span class="co">##    user  system elapsed </span></span>
-<span><span class="co">##  0.1720  0.0089  0.1818</span></span></code></pre>
+<span><span class="co">##  0.1810  0.0094  0.1912</span></span></code></pre>
 <p>Using spatial indices to check intersection of polygons is much
 faster than the legacy method in poly2nb. From <strong>spdep</strong>
 1.1-7, use is made of GEOS through <strong>sf</strong> to find candidate
@@ -408,12 +408,12 @@ <h4 id="k-nearest-neighbours">K-nearest neighbours<a class="anchor" aria-label="
 <div class="sourceCode" id="cb40"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/system.time.html" class="external-link">system.time</a></span><span class="op">(</span><span class="kw">for</span> <span class="op">(</span><span class="va">i</span> <span class="kw">in</span> <span class="fl">1</span><span class="op">:</span><span class="va">reps</span><span class="op">)</span> <span class="fu"><a href="https://rdrr.io/r/base/warning.html" class="external-link">suppressWarnings</a></span><span class="op">(</span><span class="va">NY88_nb_sf</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/knn2nb.html">knn2nb</a></span><span class="op">(</span><span class="fu"><a href="../reference/knearneigh.html">knearneigh</a></span><span class="op">(</span><span class="va">NY8_ct_sf</span>, k<span class="op">=</span><span class="fl">1</span><span class="op">)</span><span class="op">)</span><span class="op">)</span><span class="op">)</span><span class="op">/</span><span class="va">reps</span></span></code></pre></div>
 <pre><code><span><span class="co">##    user  system elapsed </span></span>
-<span><span class="co">##  0.0217  0.0012  0.0231</span></span></code></pre>
+<span><span class="co">##  0.0238  0.0013  0.0253</span></span></code></pre>
 <p>Legacy code may be used omitting the kd-tree:</p>
 <div class="sourceCode" id="cb42"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/system.time.html" class="external-link">system.time</a></span><span class="op">(</span><span class="kw">for</span> <span class="op">(</span><span class="va">i</span> <span class="kw">in</span> <span class="fl">1</span><span class="op">:</span><span class="va">reps</span><span class="op">)</span> <span class="fu"><a href="https://rdrr.io/r/base/warning.html" class="external-link">suppressWarnings</a></span><span class="op">(</span><span class="va">NY89_nb_sf</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/knn2nb.html">knn2nb</a></span><span class="op">(</span><span class="fu"><a href="../reference/knearneigh.html">knearneigh</a></span><span class="op">(</span><span class="va">NY8_ct_sf</span>, k<span class="op">=</span><span class="fl">1</span>, use_kd_tree<span class="op">=</span><span class="cn">FALSE</span><span class="op">)</span><span class="op">)</span><span class="op">)</span><span class="op">)</span><span class="op">/</span><span class="va">reps</span></span></code></pre></div>
 <pre><code><span><span class="co">##    user  system elapsed </span></span>
-<span><span class="co">##  0.0223  0.0009  0.0233</span></span></code></pre>
+<span><span class="co">##  0.0242  0.0011  0.0253</span></span></code></pre>
 </div>
 <div class="section level4">
 <h4 id="distance-neighbours">Distance neighbours<a class="anchor" aria-label="anchor" href="#distance-neighbours"></a>
@@ -432,7 +432,7 @@ <h4 id="distance-neighbours">Distance neighbours<a class="anchor" aria-label="an
 <div class="sourceCode" id="cb47"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/system.time.html" class="external-link">system.time</a></span><span class="op">(</span><span class="kw">for</span> <span class="op">(</span><span class="va">i</span> <span class="kw">in</span> <span class="fl">1</span><span class="op">:</span><span class="va">reps</span><span class="op">)</span> <span class="fu"><a href="https://rdrr.io/r/base/warning.html" class="external-link">suppressWarnings</a></span><span class="op">(</span><span class="va">NY810_nb</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/dnearneigh.html">dnearneigh</a></span><span class="op">(</span><span class="va">NY8_ct_sf</span>, d1<span class="op">=</span><span class="fl">0</span>, d2<span class="op">=</span><span class="fl">0.75</span><span class="op">*</span><span class="va">max_1nn</span><span class="op">)</span><span class="op">)</span><span class="op">)</span><span class="op">/</span><span class="va">reps</span></span></code></pre></div>
 <pre><code><span><span class="co">##    user  system elapsed </span></span>
-<span><span class="co">##  0.0585  0.0013  0.0600</span></span></code></pre>
+<span><span class="co">##  0.0618  0.0018  0.0638</span></span></code></pre>
 <p>By default, the function uses <code><a href="https://rdrr.io/pkg/dbscan/man/frNN.html" class="external-link">dbscan::frNN()</a></code> to build a
 kd-tree in 2D or 3D which is then used to find distance neighbours. For
 small n, the argument <code>use_kd_tree=FALSE</code> may speed up
@@ -442,7 +442,7 @@ <h4 id="distance-neighbours">Distance neighbours<a class="anchor" aria-label="an
 <div class="sourceCode" id="cb49"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/system.time.html" class="external-link">system.time</a></span><span class="op">(</span><span class="kw">for</span> <span class="op">(</span><span class="va">i</span> <span class="kw">in</span> <span class="fl">1</span><span class="op">:</span><span class="va">reps</span><span class="op">)</span> <span class="fu"><a href="https://rdrr.io/r/base/warning.html" class="external-link">suppressWarnings</a></span><span class="op">(</span><span class="va">NY811_nb</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/dnearneigh.html">dnearneigh</a></span><span class="op">(</span><span class="va">NY8_ct_sf</span>, d1<span class="op">=</span><span class="fl">0</span>, d2<span class="op">=</span><span class="fl">0.75</span><span class="op">*</span><span class="va">max_1nn</span>, use_kd_tree<span class="op">=</span><span class="cn">FALSE</span><span class="op">)</span><span class="op">)</span><span class="op">)</span><span class="op">/</span><span class="va">reps</span></span></code></pre></div>
 <pre><code><span><span class="co">##    user  system elapsed </span></span>
-<span><span class="co">##  0.0434  0.0010  0.0447</span></span></code></pre>
+<span><span class="co">##  0.0472  0.0006  0.0480</span></span></code></pre>
 </div>
 </div>
 <div class="section level3">
@@ -472,7 +472,7 @@ <h4 id="k-nearest-neighbours-1">K-nearest neighbours<a class="anchor" aria-label
 <code class="sourceCode R"><span><span class="fu"><a href="https://r-spatial.github.io/sf/reference/s2.html" class="external-link">sf_use_s2</a></span><span class="op">(</span><span class="cn">TRUE</span><span class="op">)</span></span>
 <span><span class="fu"><a href="https://rdrr.io/r/base/system.time.html" class="external-link">system.time</a></span><span class="op">(</span><span class="kw">for</span> <span class="op">(</span><span class="va">i</span> <span class="kw">in</span> <span class="fl">1</span><span class="op">:</span><span class="va">reps</span><span class="op">)</span> <span class="va">pts_ll1_nb</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/knn2nb.html">knn2nb</a></span><span class="op">(</span><span class="fu"><a href="../reference/knearneigh.html">knearneigh</a></span><span class="op">(</span><span class="va">pts_ll</span>, k<span class="op">=</span><span class="fl">6</span><span class="op">)</span><span class="op">)</span><span class="op">)</span><span class="op">/</span><span class="va">reps</span></span></code></pre></div>
 <pre><code><span><span class="co">##    user  system elapsed </span></span>
-<span><span class="co">##  0.0321  0.0002  0.0326</span></span></code></pre>
+<span><span class="co">##  0.0340  0.0000  0.0341</span></span></code></pre>
 <p>For this smaller data set, the legacy approach without spatial
 indexing is adequate, but slows down as the number of observations
 increases:</p>
@@ -482,7 +482,7 @@ <h4 id="k-nearest-neighbours-1">K-nearest neighbours<a class="anchor" aria-label
 <div class="sourceCode" id="cb59"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/system.time.html" class="external-link">system.time</a></span><span class="op">(</span><span class="kw">for</span> <span class="op">(</span><span class="va">i</span> <span class="kw">in</span> <span class="fl">1</span><span class="op">:</span><span class="va">reps</span><span class="op">)</span> <span class="va">pts_ll2_nb</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/knn2nb.html">knn2nb</a></span><span class="op">(</span><span class="fu"><a href="../reference/knearneigh.html">knearneigh</a></span><span class="op">(</span><span class="va">pts_ll</span>, k<span class="op">=</span><span class="fl">6</span><span class="op">)</span><span class="op">)</span><span class="op">)</span><span class="op">/</span><span class="va">reps</span></span></code></pre></div>
 <pre><code><span><span class="co">##    user  system elapsed </span></span>
-<span><span class="co">##  0.0281  0.0000  0.0282</span></span></code></pre>
+<span><span class="co">##  0.0283  0.0000  0.0284</span></span></code></pre>
 <p>The WGS84 ellipsoid Great Circle distances differ a very little from
 the <strong>s2</strong> spherical distances, yielding output that here
 diverges for two tract centroids:</p>
@@ -537,7 +537,7 @@ <h4 id="distance-neighbours-1">Distance neighbours<a class="anchor" aria-label="
 <span>      d2<span class="op">=</span><span class="fl">0.75</span><span class="op">*</span><span class="va">max_1nn_ll</span><span class="op">)</span><span class="op">)</span><span class="op">)</span><span class="op">/</span><span class="op">(</span><span class="va">reps</span><span class="op">/</span><span class="fl">5</span><span class="op">)</span></span>
 <span><span class="op">}</span></span></code></pre></div>
 <pre><code><span><span class="co">##    user  system elapsed </span></span>
-<span><span class="co">##  0.0655  0.0000  0.0655</span></span></code></pre>
+<span><span class="co">##  0.0685  0.0000  0.0685</span></span></code></pre>
 <p>Alternatively, spherical distances can be used with
 <code>dwithin=FALSE</code> and <code><a href="https://r-spatial.github.io/s2/reference/s2_closest_feature.html" class="external-link">s2::s2_closest_edges()</a></code>;
 although running in similar time, <code><a href="https://r-spatial.github.io/s2/reference/s2_closest_feature.html" class="external-link">s2::s2_closest_edges()</a></code>
@@ -546,7 +546,7 @@ <h4 id="distance-neighbours-1">Distance neighbours<a class="anchor" aria-label="
 <div class="sourceCode" id="cb79"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/system.time.html" class="external-link">system.time</a></span><span class="op">(</span><span class="kw">for</span> <span class="op">(</span><span class="va">i</span> <span class="kw">in</span> <span class="fl">1</span><span class="op">:</span><span class="op">(</span><span class="va">reps</span><span class="op">/</span><span class="fl">5</span><span class="op">)</span><span class="op">)</span> <span class="fu"><a href="https://rdrr.io/r/base/warning.html" class="external-link">suppressWarnings</a></span><span class="op">(</span><span class="va">pts_ll5_nb</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/dnearneigh.html">dnearneigh</a></span><span class="op">(</span><span class="va">pts_ll</span>, d1<span class="op">=</span><span class="fl">0</span>, d2<span class="op">=</span><span class="fl">0.75</span><span class="op">*</span><span class="va">max_1nn_ll</span>, dwithin<span class="op">=</span><span class="cn">FALSE</span><span class="op">)</span><span class="op">)</span><span class="op">)</span><span class="op">/</span><span class="op">(</span><span class="va">reps</span><span class="op">/</span><span class="fl">5</span><span class="op">)</span></span></code></pre></div>
 <pre><code><span><span class="co">##    user  system elapsed </span></span>
-<span><span class="co">##  0.0515  0.0000  0.0520</span></span></code></pre>
+<span><span class="co">##  0.0590  0.0000  0.0595</span></span></code></pre>
 <div class="sourceCode" id="cb81"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="kw">if</span> <span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/utils/packageDescription.html" class="external-link">packageVersion</a></span><span class="op">(</span><span class="st">"s2"</span><span class="op">)</span> <span class="op">&gt;</span> <span class="st">"1.0.7"</span><span class="op">)</span> <span class="fu"><a href="https://rspatial.github.io/terra/reference/all.equal.html" class="external-link">all.equal</a></span><span class="op">(</span><span class="va">pts_ll3_nb</span>, <span class="va">pts_ll5_nb</span>, check.attributes<span class="op">=</span><span class="cn">FALSE</span><span class="op">)</span></span></code></pre></div>
 <pre><code><span><span class="co">## [1] TRUE</span></span></code></pre>
@@ -559,7 +559,7 @@ <h4 id="distance-neighbours-1">Distance neighbours<a class="anchor" aria-label="
 <span>      d2<span class="op">=</span><span class="fl">0.75</span><span class="op">*</span><span class="va">max_1nn_ll</span>, dwithin<span class="op">=</span><span class="cn">FALSE</span><span class="op">)</span><span class="op">)</span><span class="op">)</span><span class="op">/</span><span class="op">(</span><span class="va">reps</span><span class="op">/</span><span class="fl">5</span><span class="op">)</span></span>
 <span><span class="op">}</span></span></code></pre></div>
 <pre><code><span><span class="co">##    user  system elapsed </span></span>
-<span><span class="co">##  0.0435  0.0005  0.0445</span></span></code></pre>
+<span><span class="co">##  0.0475  0.0005  0.0480</span></span></code></pre>
 <p>Using <code><a href="https://r-spatial.github.io/s2/reference/s2_closest_feature.html" class="external-link">s2::s2_dwithin_matrix()</a></code> requires a second pass,
 one for the lower bound, another for the upper bound, and a set
 difference operation to find neighbours in the distance band:</p>
@@ -569,7 +569,7 @@ <h4 id="distance-neighbours-1">Distance neighbours<a class="anchor" aria-label="
 <span>        d2<span class="op">=</span><span class="fl">0.75</span><span class="op">*</span><span class="va">max_1nn_ll</span><span class="op">)</span><span class="op">)</span><span class="op">)</span><span class="op">/</span><span class="op">(</span><span class="va">reps</span><span class="op">/</span><span class="fl">5</span><span class="op">)</span></span>
 <span><span class="op">}</span></span></code></pre></div>
 <pre><code><span><span class="co">##    user  system elapsed </span></span>
-<span><span class="co">##  0.0845  0.0005  0.0855</span></span></code></pre>
+<span><span class="co">##  0.0890  0.0000  0.0895</span></span></code></pre>
 <div class="sourceCode" id="cb87"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="kw">if</span> <span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/utils/packageDescription.html" class="external-link">packageVersion</a></span><span class="op">(</span><span class="st">"s2"</span><span class="op">)</span> <span class="op">&gt;</span> <span class="st">"1.0.7"</span><span class="op">)</span> <span class="fu"><a href="https://rspatial.github.io/terra/reference/all.equal.html" class="external-link">all.equal</a></span><span class="op">(</span><span class="va">pts_ll3a_nb</span>, <span class="va">pts_ll5a_nb</span>, check.attributes<span class="op">=</span><span class="cn">FALSE</span><span class="op">)</span></span></code></pre></div>
 <pre><code><span><span class="co">## [1] TRUE</span></span></code></pre>
@@ -578,7 +578,7 @@ <h4 id="distance-neighbours-1">Distance neighbours<a class="anchor" aria-label="
 <div class="sourceCode" id="cb89"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/system.time.html" class="external-link">system.time</a></span><span class="op">(</span><span class="kw">for</span> <span class="op">(</span><span class="va">i</span> <span class="kw">in</span> <span class="fl">1</span><span class="op">:</span><span class="va">reps</span><span class="op">)</span> <span class="fu"><a href="https://rdrr.io/r/base/warning.html" class="external-link">suppressWarnings</a></span><span class="op">(</span><span class="va">pts_ll6_nb</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/dnearneigh.html">dnearneigh</a></span><span class="op">(</span><span class="va">pts_ll</span>, d1<span class="op">=</span><span class="fl">0</span>, d2<span class="op">=</span><span class="fl">0.75</span><span class="op">*</span><span class="va">max_1nn_ll</span>, use_s2<span class="op">=</span><span class="cn">FALSE</span><span class="op">)</span><span class="op">)</span><span class="op">)</span><span class="op">/</span><span class="va">reps</span></span></code></pre></div>
 <pre><code><span><span class="co">##    user  system elapsed </span></span>
-<span><span class="co">##  0.0354  0.0002  0.0358</span></span></code></pre>
+<span><span class="co">##  0.0397  0.0000  0.0400</span></span></code></pre>
 <p>Minor differences may occur between the legacy ellipsoid and
 <strong>s2</strong> spherical approaches:</p>
 <div class="sourceCode" id="cb91"><pre class="downlit sourceCode r">
@@ -608,7 +608,7 @@ <h4 id="distance-neighbours-1">Distance neighbours<a class="anchor" aria-label="
 <div class="sourceCode" id="cb93"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/system.time.html" class="external-link">system.time</a></span><span class="op">(</span><span class="kw">for</span> <span class="op">(</span><span class="va">i</span> <span class="kw">in</span> <span class="fl">1</span><span class="op">:</span><span class="va">reps</span><span class="op">)</span> <span class="fu"><a href="https://rdrr.io/r/base/warning.html" class="external-link">suppressWarnings</a></span><span class="op">(</span><span class="va">pts_ll6a_nb</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/dnearneigh.html">dnearneigh</a></span><span class="op">(</span><span class="va">pts_ll</span>, d1<span class="op">=</span><span class="fl">5</span>, d2<span class="op">=</span><span class="fl">0.75</span><span class="op">*</span><span class="va">max_1nn_ll</span>, use_s2<span class="op">=</span><span class="cn">FALSE</span><span class="op">)</span><span class="op">)</span><span class="op">)</span><span class="op">/</span><span class="va">reps</span></span></code></pre></div>
 <pre><code><span><span class="co">##    user  system elapsed </span></span>
-<span><span class="co">##  0.0280  0.0000  0.0282</span></span></code></pre>
+<span><span class="co">##  0.0295  0.0002  0.0298</span></span></code></pre>
 <div class="sourceCode" id="cb95"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="kw">if</span> <span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/utils/packageDescription.html" class="external-link">packageVersion</a></span><span class="op">(</span><span class="st">"s2"</span><span class="op">)</span> <span class="op">&gt;</span> <span class="st">"1.0.7"</span><span class="op">)</span> <span class="fu"><a href="https://rspatial.github.io/terra/reference/all.equal.html" class="external-link">all.equal</a></span><span class="op">(</span><span class="va">pts_ll5a_nb</span>, <span class="va">pts_ll6a_nb</span>, check.attributes<span class="op">=</span><span class="cn">FALSE</span><span class="op">)</span></span></code></pre></div>
 <pre><code><span><span class="co">##  [1] "Component 20: Numeric: lengths (6, 5) differ"       </span></span>
@@ -660,7 +660,7 @@ <h4 id="spher-poly2nb">Contiguity neighbours for spherical polygon support<a cla
 <code class="sourceCode R"><span><span class="fu"><a href="https://r-spatial.github.io/sf/reference/s2.html" class="external-link">sf_use_s2</a></span><span class="op">(</span><span class="cn">TRUE</span><span class="op">)</span></span>
 <span><span class="fu"><a href="https://rdrr.io/r/base/system.time.html" class="external-link">system.time</a></span><span class="op">(</span><span class="kw">for</span> <span class="op">(</span><span class="va">i</span> <span class="kw">in</span> <span class="fl">1</span><span class="op">:</span><span class="va">reps</span><span class="op">)</span> <span class="va">NY8_sf_1_nb_ll</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/poly2nb.html">poly2nb</a></span><span class="op">(</span><span class="va">NY8_sf_ll</span>, queen<span class="op">=</span><span class="cn">TRUE</span>, snap<span class="op">=</span><span class="va">eps</span><span class="op">)</span><span class="op">)</span><span class="op">/</span><span class="va">reps</span></span></code></pre></div>
 <pre><code><span><span class="co">##    user  system elapsed </span></span>
-<span><span class="co">##  0.1534  0.0023  0.1563</span></span></code></pre>
+<span><span class="co">##  0.1675  0.0024  0.1708</span></span></code></pre>
 <div class="sourceCode" id="cb101"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="https://rspatial.github.io/terra/reference/all.equal.html" class="external-link">all.equal</a></span><span class="op">(</span><span class="va">NY8_sf_1_nb</span>, <span class="va">NY8_sf_1_nb_ll</span>, check.attributes<span class="op">=</span><span class="cn">FALSE</span><span class="op">)</span></span></code></pre></div>
 <pre><code><span><span class="co">## [1] TRUE</span></span></code></pre>
diff --git a/docs/articles/sids.html b/docs/articles/sids.html
index 218ccbc3..cb404411 100644
--- a/docs/articles/sids.html
+++ b/docs/articles/sids.html
@@ -20,7 +20,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -95,7 +95,7 @@ <h2 id="introduction">Introduction<a class="anchor" aria-label="anchor" href="#i
 <h2 id="getting-the-data-into-r">Getting the data into R<a class="anchor" aria-label="anchor" href="#getting-the-data-into-r"></a>
 </h2>
 <p>We will be using the <strong>spdep</strong> and
-<strong>spreg</strong> packages, here version: spdep, version 1.3-7,
+<strong>spreg</strong> packages, here version: spdep, version 1.3-8,
 2024-11-25, the <strong>sf</strong> package and the
 <strong>tmap</strong> package. The data from the sources referred to
 above is documented in the help page for the <code>nc.sids</code> data
@@ -208,41 +208,58 @@ <h2 id="getting-the-data-into-r">Getting the data into R<a class="anchor" aria-l
 <span><span class="co">##             ANGLEUNIT["degree",0.0174532925199433]],</span></span>
 <span><span class="co">##     ID["EPSG",4267]]</span></span></code></pre>
 <div class="sourceCode" id="cb9"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="va">nc</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://r-spatial.github.io/sf/reference/st_read.html" class="external-link">st_read</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/system.file.html" class="external-link">system.file</a></span><span class="op">(</span><span class="st">"shapes/sids.shp"</span>,</span>
+<code class="sourceCode R"><span><span class="va">nc</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://r-spatial.github.io/sf/reference/st_read.html" class="external-link">st_read</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/system.file.html" class="external-link">system.file</a></span><span class="op">(</span><span class="st">"shapes/sids.gpkg"</span>,</span>
 <span>                 package<span class="op">=</span><span class="st">"spData"</span><span class="op">)</span>, quiet<span class="op">=</span><span class="cn">TRUE</span><span class="op">)</span></span>
 <span><span class="fu"><a href="https://r-spatial.github.io/sf/reference/st_crs.html" class="external-link">st_crs</a></span><span class="op">(</span><span class="va">nc</span><span class="op">)</span></span></code></pre></div>
-<pre><code><span><span class="co">## Coordinate Reference System: NA</span></span></code></pre>
-<p>As the actual CRS is unknown, <strong>spData</strong> reports
-missing, although it may very well be
-<code>+proj=longlat +datum=NAD27</code></p>
-<div class="sourceCode" id="cb11"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="fu"><a href="https://r-spatial.github.io/sf/reference/st_crs.html" class="external-link">st_crs</a></span><span class="op">(</span><span class="va">nc</span><span class="op">)</span> <span class="op">&lt;-</span> <span class="st">"+proj=longlat +datum=NAD27"</span></span></code></pre></div>
+<pre><code><span><span class="co">## Coordinate Reference System:</span></span>
+<span><span class="co">##   User input: NAD27 </span></span>
+<span><span class="co">##   wkt:</span></span>
+<span><span class="co">## GEOGCRS["NAD27",</span></span>
+<span><span class="co">##     DATUM["North American Datum 1927",</span></span>
+<span><span class="co">##         ELLIPSOID["Clarke 1866",6378206.4,294.978698213898,</span></span>
+<span><span class="co">##             LENGTHUNIT["metre",1]]],</span></span>
+<span><span class="co">##     PRIMEM["Greenwich",0,</span></span>
+<span><span class="co">##         ANGLEUNIT["degree",0.0174532925199433]],</span></span>
+<span><span class="co">##     CS[ellipsoidal,2],</span></span>
+<span><span class="co">##         AXIS["geodetic latitude (Lat)",north,</span></span>
+<span><span class="co">##             ORDER[1],</span></span>
+<span><span class="co">##             ANGLEUNIT["degree",0.0174532925199433]],</span></span>
+<span><span class="co">##         AXIS["geodetic longitude (Lon)",east,</span></span>
+<span><span class="co">##             ORDER[2],</span></span>
+<span><span class="co">##             ANGLEUNIT["degree",0.0174532925199433]],</span></span>
+<span><span class="co">##     USAGE[</span></span>
+<span><span class="co">##         SCOPE["Geodesy."],</span></span>
+<span><span class="co">##         AREA["North and central America: Antigua and Barbuda - onshore. Bahamas - onshore plus offshore over internal continental shelf only. Belize - onshore. British Virgin Islands - onshore. Canada onshore - Alberta, British Columbia, Manitoba, New Brunswick, Newfoundland and Labrador, Northwest Territories, Nova Scotia, Nunavut, Ontario, Prince Edward Island, Quebec, Saskatchewan and Yukon - plus offshore east coast. Cuba - onshore and offshore. El Salvador - onshore. Guatemala - onshore. Honduras - onshore. Panama - onshore. Puerto Rico - onshore. Mexico - onshore plus offshore east coast. Nicaragua - onshore. United States (USA) onshore and offshore - Alabama, Alaska, Arizona, Arkansas, California, Colorado, Connecticut, Delaware, Florida, Georgia, Idaho, Illinois, Indiana, Iowa, Kansas, Kentucky, Louisiana, Maine, Maryland, Massachusetts, Michigan, Minnesota, Mississippi, Missouri, Montana, Nebraska, Nevada, New Hampshire, New Jersey, New Mexico, New York, North Carolina, North Dakota, Ohio, Oklahoma, Oregon, Pennsylvania, Rhode Island, South Carolina, South Dakota, Tennessee, Texas, Utah, Vermont, Virginia, Washington, West Virginia, Wisconsin and Wyoming - plus offshore . US Virgin Islands - onshore."],</span></span>
+<span><span class="co">##         BBOX[7.15,167.65,83.17,-47.74]],</span></span>
+<span><span class="co">##     ID["EPSG",4267]]</span></span></code></pre>
+<p>As the actual CRS was unknown, the GeoPackage <strong>spData</strong>
+version has been updated to <code>"EPSG:4267"</code>.</p>
 <p>Next, are the geometries the same? <code><a href="https://r-spatial.github.io/sf/reference/geos_binary_pred.html" class="external-link">sf::st_equals</a></code> returns
 a logical matrix, so we’ll check that the diagonal values are all
 <code>TRUE</code>, and that only those values are <code>TRUE</code> by
 summing and recalling that <code>n</code> is <code>100</code>:</p>
-<div class="sourceCode" id="cb12"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb11"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/warning.html" class="external-link">suppressWarnings</a></span><span class="op">(</span><span class="fu"><a href="https://r-spatial.github.io/sf/reference/st_crs.html" class="external-link">st_crs</a></span><span class="op">(</span><span class="va">nc_sf</span><span class="op">)</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://r-spatial.github.io/sf/reference/st_crs.html" class="external-link">st_crs</a></span><span class="op">(</span><span class="va">nc</span><span class="op">)</span><span class="op">)</span></span>
 <span><span class="va">xx</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://r-spatial.github.io/sf/reference/geos_binary_pred.html" class="external-link">st_equals</a></span><span class="op">(</span><span class="va">nc</span>, <span class="va">nc_sf</span>, sparse<span class="op">=</span><span class="cn">FALSE</span><span class="op">)</span></span>
 <span><span class="fu"><a href="https://rdrr.io/r/base/all.html" class="external-link">all</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/diag.html" class="external-link">diag</a></span><span class="op">(</span><span class="va">xx</span><span class="op">)</span><span class="op">)</span> <span class="op">&amp;&amp;</span> <span class="fu"><a href="https://rdrr.io/r/base/sum.html" class="external-link">sum</a></span><span class="op">(</span><span class="va">xx</span><span class="op">)</span> <span class="op">==</span> <span class="fl">100L</span></span></code></pre></div>
 <pre><code><span><span class="co">## [1] TRUE</span></span></code></pre>
 <p>Next, let’s download the GeoDa files and repeat the comparisons:</p>
-<div class="sourceCode" id="cb14"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb13"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">td</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/tempfile.html" class="external-link">tempdir</a></span><span class="op">(</span><span class="op">)</span></span>
 <span><span class="co">#download.file("https://geodacenter.github.io/data-and-lab//data/sids.zip", file.path(td, "sids.zip"), quiet=TRUE) </span></span>
 <span><span class="co"># local copy (2020-10-22) as repository sometimes offline</span></span>
 <span><span class="fu"><a href="https://rdrr.io/r/base/files.html" class="external-link">file.copy</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/system.file.html" class="external-link">system.file</a></span><span class="op">(</span><span class="st">"etc/misc/sids.zip"</span>, package<span class="op">=</span><span class="st">"spdep"</span><span class="op">)</span>, <span class="va">td</span><span class="op">)</span></span></code></pre></div>
 <pre><code><span><span class="co">## [1] TRUE</span></span></code></pre>
-<div class="sourceCode" id="cb16"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb15"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/utils/unzip.html" class="external-link">unzip</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/file.path.html" class="external-link">file.path</a></span><span class="op">(</span><span class="va">td</span>, <span class="st">"sids.zip"</span><span class="op">)</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"sids/sids.dbf"</span>, <span class="st">"sids/sids.prj"</span>, <span class="st">"sids/sids.shp"</span>, <span class="st">"sids/sids.shx"</span><span class="op">)</span>, exdir<span class="op">=</span><span class="va">td</span><span class="op">)</span></span>
 <span><span class="va">sids_sf</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://r-spatial.github.io/sf/reference/st_read.html" class="external-link">st_read</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/file.path.html" class="external-link">file.path</a></span><span class="op">(</span><span class="va">td</span>, <span class="st">"sids/sids.shp"</span><span class="op">)</span>, quiet<span class="op">=</span><span class="cn">TRUE</span><span class="op">)</span></span>
 <span><span class="co">#download.file("https://geodacenter.github.io/data-and-lab//data/sids2.zip", file.path(td, "sids2.zip"), quiet=TRUE)</span></span>
 <span><span class="fu"><a href="https://rdrr.io/r/base/files.html" class="external-link">file.copy</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/system.file.html" class="external-link">system.file</a></span><span class="op">(</span><span class="st">"etc/misc/sids2.zip"</span>, package<span class="op">=</span><span class="st">"spdep"</span><span class="op">)</span>, <span class="va">td</span><span class="op">)</span></span></code></pre></div>
 <pre><code><span><span class="co">## [1] TRUE</span></span></code></pre>
-<div class="sourceCode" id="cb18"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb17"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/utils/unzip.html" class="external-link">unzip</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/file.path.html" class="external-link">file.path</a></span><span class="op">(</span><span class="va">td</span>, <span class="st">"sids2.zip"</span><span class="op">)</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"sids2/sids2.dbf"</span>, <span class="st">"sids2/sids2.prj"</span>, <span class="st">"sids2/sids2.shp"</span>, <span class="st">"sids2/sids2.shx"</span><span class="op">)</span>, exdir<span class="op">=</span><span class="va">td</span><span class="op">)</span></span>
 <span><span class="va">sids2_sf</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://r-spatial.github.io/sf/reference/st_read.html" class="external-link">st_read</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/file.path.html" class="external-link">file.path</a></span><span class="op">(</span><span class="va">td</span>, <span class="st">"sids2/sids2.shp"</span><span class="op">)</span>, quiet<span class="op">=</span><span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div>
-<div class="sourceCode" id="cb19"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb18"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="https://r-spatial.github.io/sf/reference/st_crs.html" class="external-link">st_crs</a></span><span class="op">(</span><span class="va">sids_sf</span><span class="op">)</span></span></code></pre></div>
 <pre><code><span><span class="co">## Coordinate Reference System:</span></span>
 <span><span class="co">##   User input: WGS 84 </span></span>
@@ -261,7 +278,7 @@ <h2 id="getting-the-data-into-r">Getting the data into R<a class="anchor" aria-l
 <span><span class="co">##             ORDER[2],</span></span>
 <span><span class="co">##             ANGLEUNIT["degree",0.0174532925199433]],</span></span>
 <span><span class="co">##     ID["EPSG",4326]]</span></span></code></pre>
-<div class="sourceCode" id="cb21"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb20"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="https://r-spatial.github.io/sf/reference/st_crs.html" class="external-link">st_crs</a></span><span class="op">(</span><span class="va">sids2_sf</span><span class="op">)</span></span></code></pre></div>
 <pre><code><span><span class="co">## Coordinate Reference System:</span></span>
 <span><span class="co">##   User input: WGS 84 </span></span>
@@ -282,12 +299,12 @@ <h2 id="getting-the-data-into-r">Getting the data into R<a class="anchor" aria-l
 <span><span class="co">##     ID["EPSG",4326]]</span></span></code></pre>
 <p>It looks as though the external files are assuming WGS84/NAD83 for
 the datum, but also contain the same geometries.</p>
-<div class="sourceCode" id="cb23"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb22"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/warning.html" class="external-link">suppressWarnings</a></span><span class="op">(</span><span class="fu"><a href="https://r-spatial.github.io/sf/reference/st_crs.html" class="external-link">st_crs</a></span><span class="op">(</span><span class="va">sids_sf</span><span class="op">)</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://r-spatial.github.io/sf/reference/st_crs.html" class="external-link">st_crs</a></span><span class="op">(</span><span class="va">nc_sf</span><span class="op">)</span><span class="op">)</span></span>
 <span><span class="va">xx</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://r-spatial.github.io/sf/reference/geos_binary_pred.html" class="external-link">st_equals</a></span><span class="op">(</span><span class="va">sids_sf</span>, <span class="va">nc_sf</span>, sparse<span class="op">=</span><span class="cn">FALSE</span><span class="op">)</span></span>
 <span><span class="fu"><a href="https://rdrr.io/r/base/all.html" class="external-link">all</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/diag.html" class="external-link">diag</a></span><span class="op">(</span><span class="va">xx</span><span class="op">)</span><span class="op">)</span> <span class="op">&amp;&amp;</span> <span class="fu"><a href="https://rdrr.io/r/base/sum.html" class="external-link">sum</a></span><span class="op">(</span><span class="va">xx</span><span class="op">)</span> <span class="op">==</span> <span class="fl">100L</span></span></code></pre></div>
 <pre><code><span><span class="co">## [1] FALSE</span></span></code></pre>
-<div class="sourceCode" id="cb25"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb24"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/warning.html" class="external-link">suppressWarnings</a></span><span class="op">(</span><span class="fu"><a href="https://r-spatial.github.io/sf/reference/st_crs.html" class="external-link">st_crs</a></span><span class="op">(</span><span class="va">sids2_sf</span><span class="op">)</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://r-spatial.github.io/sf/reference/st_crs.html" class="external-link">st_crs</a></span><span class="op">(</span><span class="va">nc_sf</span><span class="op">)</span><span class="op">)</span></span>
 <span><span class="va">xx</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://r-spatial.github.io/sf/reference/geos_binary_pred.html" class="external-link">st_equals</a></span><span class="op">(</span><span class="va">sids2_sf</span>, <span class="va">nc_sf</span>, sparse<span class="op">=</span><span class="cn">FALSE</span><span class="op">)</span></span>
 <span><span class="fu"><a href="https://rdrr.io/r/base/all.html" class="external-link">all</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/diag.html" class="external-link">diag</a></span><span class="op">(</span><span class="va">xx</span><span class="op">)</span><span class="op">)</span> <span class="op">&amp;&amp;</span> <span class="fu"><a href="https://rdrr.io/r/base/sum.html" class="external-link">sum</a></span><span class="op">(</span><span class="va">xx</span><span class="op">)</span> <span class="op">==</span> <span class="fl">100L</span></span></code></pre></div>
@@ -297,7 +314,7 @@ <h2 id="getting-the-data-into-r">Getting the data into R<a class="anchor" aria-l
 given in <span class="citation">Cressie (1991)</span>, and the parcels
 of contiguous counties on p. 554, and the aggregations used for median
 polishing.</p>
-<div class="sourceCode" id="cb27"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb26"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="https://rspatial.github.io/terra/reference/all.equal.html" class="external-link">all.equal</a></span><span class="op">(</span><span class="fu"><a href="https://rspatial.github.io/terra/reference/as.data.frame.html" class="external-link">as.data.frame</a></span><span class="op">(</span><span class="va">nc_sf</span><span class="op">)</span><span class="op">[</span>,<span class="fl">1</span><span class="op">:</span><span class="fl">14</span><span class="op">]</span>, <span class="fu"><a href="https://rspatial.github.io/terra/reference/as.data.frame.html" class="external-link">as.data.frame</a></span><span class="op">(</span><span class="va">sids_sf</span><span class="op">)</span><span class="op">[</span>,<span class="fl">1</span><span class="op">:</span><span class="fl">14</span><span class="op">]</span><span class="op">)</span></span></code></pre></div>
 <pre><code><span><span class="co">##  [1] "Names: 12 string mismatches"                                  </span></span>
 <span><span class="co">##  [2] "Component 4: Modes: numeric, character"                       </span></span>
@@ -315,7 +332,7 @@ <h2 id="getting-the-data-into-r">Getting the data into R<a class="anchor" aria-l
 <span><span class="co">## [14] "Component 14: Modes: numeric, list"                           </span></span>
 <span><span class="co">## [15] "Component 14: Attributes: &lt; target is NULL, current is list &gt;"</span></span>
 <span><span class="co">## [16] "Component 14: target is numeric, current is sfc_MULTIPOLYGON"</span></span></code></pre>
-<div class="sourceCode" id="cb29"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb28"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="https://rspatial.github.io/terra/reference/all.equal.html" class="external-link">all.equal</a></span><span class="op">(</span><span class="fu"><a href="https://rspatial.github.io/terra/reference/as.data.frame.html" class="external-link">as.data.frame</a></span><span class="op">(</span><span class="va">nc_sf</span><span class="op">)</span><span class="op">[</span>,<span class="fl">1</span><span class="op">:</span><span class="fl">14</span><span class="op">]</span>, <span class="fu"><a href="https://rspatial.github.io/terra/reference/as.data.frame.html" class="external-link">as.data.frame</a></span><span class="op">(</span><span class="va">sids2_sf</span><span class="op">)</span><span class="op">[</span>,<span class="fl">1</span><span class="op">:</span><span class="fl">14</span><span class="op">]</span><span class="op">)</span></span></code></pre></div>
 <pre><code><span><span class="co">##  [1] "Names: 12 string mismatches"                         </span></span>
 <span><span class="co">##  [2] "Component 4: Modes: numeric, character"              </span></span>
@@ -333,14 +350,14 @@ <h2 id="getting-the-data-into-r">Getting the data into R<a class="anchor" aria-l
 <span><span class="co">## [14] "Component 14: Mean relative difference: 0.9984879"</span></span></code></pre>
 <p>The <strong>spData</strong> data set has some columns reordered and a
 surprise:</p>
-<div class="sourceCode" id="cb31"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb30"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="https://rspatial.github.io/terra/reference/all.equal.html" class="external-link">all.equal</a></span><span class="op">(</span><span class="fu"><a href="https://rspatial.github.io/terra/reference/as.data.frame.html" class="external-link">as.data.frame</a></span><span class="op">(</span><span class="va">nc_sf</span><span class="op">)</span><span class="op">[</span>,<span class="fl">1</span><span class="op">:</span><span class="fl">14</span><span class="op">]</span>, <span class="fu"><a href="https://rspatial.github.io/terra/reference/as.data.frame.html" class="external-link">as.data.frame</a></span><span class="op">(</span><span class="va">nc</span><span class="op">)</span><span class="op">[</span>,<span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">2</span>,<span class="fl">3</span>,<span class="fl">4</span>,<span class="fl">1</span>,<span class="fl">5</span><span class="op">:</span><span class="fl">14</span><span class="op">)</span><span class="op">]</span><span class="op">)</span></span></code></pre></div>
 <pre><code><span><span class="co">## [1] "Component \"NWBIR74\": Mean relative difference: 0.04891304"</span></span></code></pre>
 <p>so a difference in <code>NWBIR74</code>:</p>
-<div class="sourceCode" id="cb33"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb32"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/which.html" class="external-link">which</a></span><span class="op">(</span><span class="op">!</span><span class="op">(</span><span class="va">nc_sf</span><span class="op">$</span><span class="va">NWBIR74</span> <span class="op">==</span> <span class="va">nc</span><span class="op">$</span><span class="va">NWBIR74</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
 <pre><code><span><span class="co">## [1] 21</span></span></code></pre>
-<div class="sourceCode" id="cb35"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb34"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="va">nc</span><span class="op">$</span><span class="va">NWBIR74</span><span class="op">[</span><span class="fl">21</span><span class="op">]</span>, <span class="va">nc_sf</span><span class="op">$</span><span class="va">NWBIR74</span><span class="op">[</span><span class="fl">21</span><span class="op">]</span><span class="op">)</span></span></code></pre></div>
 <pre><code><span><span class="co">## [1] 386 368</span></span></code></pre>
 <p>where <strong>spData</strong> follows <span class="citation">Cressie
@@ -351,7 +368,7 @@ <h2 id="getting-the-data-into-r">Getting the data into R<a class="anchor" aria-l
 <strong>spdep</strong>), and add the neighbour relationships used in
 <span class="citation">Cressie and Chan (1989)</span> to the background
 map as a graph shown in Figure :</p>
-<div class="sourceCode" id="cb37"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb36"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">gal_file</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.file.html" class="external-link">system.file</a></span><span class="op">(</span><span class="st">"weights/ncCR85.gal"</span>, package<span class="op">=</span><span class="st">"spData"</span><span class="op">)</span><span class="op">[</span><span class="fl">1</span><span class="op">]</span></span>
 <span><span class="va">ncCR85</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/read.gal.html">read.gal</a></span><span class="op">(</span><span class="va">gal_file</span>, region.id<span class="op">=</span><span class="va">nc</span><span class="op">$</span><span class="va">FIPSNO</span><span class="op">)</span></span>
 <span><span class="va">ncCR85</span></span></code></pre></div>
@@ -360,7 +377,7 @@ <h2 id="getting-the-data-into-r">Getting the data into R<a class="anchor" aria-l
 <span><span class="co">## Number of nonzero links: 492 </span></span>
 <span><span class="co">## Percentage nonzero weights: 4.92 </span></span>
 <span><span class="co">## Average number of links: 4.92</span></span></code></pre>
-<div class="sourceCode" id="cb39"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb38"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">gal_file</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.file.html" class="external-link">system.file</a></span><span class="op">(</span><span class="st">"weights/ncCC89.gal"</span>, package<span class="op">=</span><span class="st">"spData"</span><span class="op">)</span><span class="op">[</span><span class="fl">1</span><span class="op">]</span></span>
 <span><span class="va">ncCC89</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/read.gal.html">read.gal</a></span><span class="op">(</span><span class="va">gal_file</span>, region.id<span class="op">=</span><span class="va">nc</span><span class="op">$</span><span class="va">FIPSNO</span><span class="op">)</span></span>
 <span><span class="va">ncCC89</span></span></code></pre></div>
@@ -372,7 +389,7 @@ <h2 id="getting-the-data-into-r">Getting the data into R<a class="anchor" aria-l
 <span><span class="co">## 2 regions with no links:</span></span>
 <span><span class="co">## 37055, 37095</span></span>
 <span><span class="co">## 3 disjoint connected subgraphs</span></span></code></pre>
-<div class="sourceCode" id="cb41"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb40"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="https://rspatial.github.io/terra/reference/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="fu"><a href="https://r-spatial.github.io/sf/reference/st_geometry.html" class="external-link">st_geometry</a></span><span class="op">(</span><span class="va">nc</span><span class="op">)</span>, border<span class="op">=</span><span class="st">"grey"</span><span class="op">)</span></span>
 <span><span class="fu"><a href="https://rspatial.github.io/terra/reference/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">ncCC89</span>, <span class="fu"><a href="https://r-spatial.github.io/sf/reference/geos_unary.html" class="external-link">st_centroid</a></span><span class="op">(</span><span class="fu"><a href="https://r-spatial.github.io/sf/reference/st_geometry.html" class="external-link">st_geometry</a></span><span class="op">(</span><span class="va">nc</span><span class="op">)</span>, <span class="va">of_largest_polygon</span><span class="op">)</span>, add<span class="op">=</span><span class="cn">TRUE</span>, col<span class="op">=</span><span class="st">"blue"</span><span class="op">)</span></span></code></pre></div>
 <p>Printing the neighbour object shows that it is a neighbour list
@@ -388,11 +405,11 @@ <h2 id="getting-the-data-into-r">Getting the data into R<a class="anchor" aria-l
 object. Finally, we associate a vector of names with the neighbour list,
 through the <span><code>row.names</code></span> argument. The names
 should be unique, as with data frame row names.</p>
-<div class="sourceCode" id="cb42"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb41"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">r.id</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/attr.html" class="external-link">attr</a></span><span class="op">(</span><span class="va">ncCC89</span>, <span class="st">"region.id"</span><span class="op">)</span></span>
 <span><span class="va">ncCC89</span><span class="op">[[</span><span class="fu"><a href="https://rspatial.github.io/terra/reference/match.html" class="external-link">match</a></span><span class="op">(</span><span class="st">"37001"</span>, <span class="va">r.id</span><span class="op">)</span><span class="op">]</span><span class="op">]</span></span></code></pre></div>
 <pre><code><span><span class="co">## [1] 11 26 29 30 48</span></span></code></pre>
-<div class="sourceCode" id="cb44"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb43"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">r.id</span><span class="op">[</span><span class="va">ncCC89</span><span class="op">[[</span><span class="fu"><a href="https://rspatial.github.io/terra/reference/match.html" class="external-link">match</a></span><span class="op">(</span><span class="st">"37001"</span>, <span class="va">r.id</span><span class="op">)</span><span class="op">]</span><span class="op">]</span><span class="op">]</span></span></code></pre></div>
 <pre><code><span><span class="co">## [1] 37033 37081 37135 37063 37037</span></span></code></pre>
 <p>The neighbour list object records neighbours by their order in
@@ -401,7 +418,7 @@ <h2 id="getting-the-data-into-r">Getting the data into R<a class="anchor" aria-l
 nineteenth, thirty-second, forty-first and sixty-eighth in the list. We
 can retreive their codes by looking them up in the
 <span><code>region.id</code></span> attribute.</p>
-<div class="sourceCode" id="cb46"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb45"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/character.html" class="external-link">as.character</a></span><span class="op">(</span><span class="va">nc</span><span class="op">$</span><span class="va">NAME</span><span class="op">)</span><span class="op">[</span><span class="fu"><a href="../reference/card.html">card</a></span><span class="op">(</span><span class="va">ncCC89</span><span class="op">)</span> <span class="op">==</span> <span class="fl">0</span><span class="op">]</span></span></code></pre></div>
 <pre><code><span><span class="co">## [1] "Dare" "Hyde"</span></span></code></pre>
 <p>We should also note that this neighbour criterion generates two
@@ -435,19 +452,19 @@ <h3 id="probability-mapping">Probability mapping<a class="anchor" aria-label="an
 this reason, the high and low counties are plotted separately below.
 Note that <code>cut</code> returns a <code>factor</code> labeled with
 cut intervals.</p>
-<div class="sourceCode" id="cb48"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb47"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">ch</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/choynowski.html">choynowski</a></span><span class="op">(</span><span class="va">nc</span><span class="op">$</span><span class="va">SID74</span>, <span class="va">nc</span><span class="op">$</span><span class="va">BIR74</span><span class="op">)</span></span>
 <span><span class="va">nc</span><span class="op">$</span><span class="va">ch_pmap_low</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/ifelse.html" class="external-link">ifelse</a></span><span class="op">(</span><span class="va">ch</span><span class="op">$</span><span class="va">type</span>, <span class="va">ch</span><span class="op">$</span><span class="va">pmap</span>, <span class="cn">NA</span><span class="op">)</span></span>
 <span><span class="va">nc</span><span class="op">$</span><span class="va">ch_pmap_high</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/ifelse.html" class="external-link">ifelse</a></span><span class="op">(</span><span class="op">!</span><span class="va">ch</span><span class="op">$</span><span class="va">type</span>, <span class="va">ch</span><span class="op">$</span><span class="va">pmap</span>, <span class="cn">NA</span><span class="op">)</span></span>
 <span><span class="va">prbs</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">0</span>,<span class="fl">.001</span>,<span class="fl">.01</span>,<span class="fl">.05</span>,<span class="fl">.1</span>,<span class="fl">1</span><span class="op">)</span></span>
 <span><span class="va">nc</span><span class="op">$</span><span class="va">high</span> <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/cut.html" class="external-link">cut</a></span><span class="op">(</span><span class="va">nc</span><span class="op">$</span><span class="va">ch_pmap_high</span>, <span class="va">prbs</span><span class="op">)</span></span>
 <span><span class="va">nc</span><span class="op">$</span><span class="va">low</span> <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/cut.html" class="external-link">cut</a></span><span class="op">(</span><span class="va">nc</span><span class="op">$</span><span class="va">ch_pmap_low</span>,<span class="va">prbs</span> <span class="op">)</span></span></code></pre></div>
-<div class="sourceCode" id="cb49"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb48"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">is_tmap</span> <span class="op">&lt;-</span> <span class="cn">FALSE</span></span>
 <span><span class="kw">if</span> <span class="op">(</span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">require</a></span><span class="op">(</span><span class="va"><a href="https://r-tmap.github.io/tmap/" class="external-link">tmap</a></span>, quietly<span class="op">=</span><span class="cn">TRUE</span><span class="op">)</span><span class="op">)</span> <span class="va">is_tmap</span> <span class="op">&lt;-</span> <span class="cn">TRUE</span></span>
 <span><span class="va">is_tmap</span></span></code></pre></div>
 <pre><code><span><span class="co">## [1] TRUE</span></span></code></pre>
-<div class="sourceCode" id="cb51"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb50"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va"><a href="https://r-tmap.github.io/tmap/" class="external-link">tmap</a></span><span class="op">)</span></span>
 <span><span class="va">tmap4</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/utils/packageDescription.html" class="external-link">packageVersion</a></span><span class="op">(</span><span class="st">"tmap"</span><span class="op">)</span> <span class="op">&gt;=</span> <span class="st">"3.99"</span></span>
 <span><span class="kw">if</span> <span class="op">(</span><span class="va">tmap4</span><span class="op">)</span> <span class="op">{</span></span>
@@ -472,17 +489,17 @@ <h3 id="probability-mapping">Probability mapping<a class="anchor" aria-label="an
 based on population size, have values in the lower tail, and those with
 higher observed counts than expected have values in the upper tail, as
 we can see.</p>
-<div class="sourceCode" id="cb52"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb51"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">pmap</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/probmap.html">probmap</a></span><span class="op">(</span><span class="va">nc</span><span class="op">$</span><span class="va">SID74</span>, <span class="va">nc</span><span class="op">$</span><span class="va">BIR74</span><span class="op">)</span></span>
 <span><span class="va">nc</span><span class="op">$</span><span class="va">pmap</span> <span class="op">&lt;-</span> <span class="va">pmap</span><span class="op">$</span><span class="va">pmap</span></span></code></pre></div>
-<div class="sourceCode" id="cb53"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb52"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">brks</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">0</span>,<span class="fl">0.001</span>,<span class="fl">0.01</span>,<span class="fl">0.025</span>,<span class="fl">0.05</span>,<span class="fl">0.95</span>,<span class="fl">0.975</span>,<span class="fl">0.99</span>,<span class="fl">0.999</span>,<span class="fl">1</span><span class="op">)</span></span>
 <span><span class="kw">if</span> <span class="op">(</span><span class="va">tmap4</span><span class="op">)</span> <span class="op">{</span></span>
 <span>  <span class="fu"><a href="https://r-tmap.github.io/tmap/reference/tm_shape.html" class="external-link">tm_shape</a></span><span class="op">(</span><span class="va">nc</span><span class="op">)</span> <span class="op">+</span> <span class="fu"><a href="https://r-tmap.github.io/tmap/reference/tm_polygons.html" class="external-link">tm_polygons</a></span><span class="op">(</span>fill<span class="op">=</span><span class="st">"pmap"</span>, fill.scale <span class="op">=</span> <span class="fu">tm_scale</span><span class="op">(</span>values<span class="op">=</span><span class="st">"brewer.rd_bu"</span>, midpoint<span class="op">=</span><span class="fl">0.5</span>, breaks<span class="op">=</span><span class="va">brks</span><span class="op">)</span>, fill.legend <span class="op">=</span> <span class="fu"><a href="https://r-tmap.github.io/tmap/reference/tm_layout.html" class="external-link">tm_legend</a></span><span class="op">(</span>frame<span class="op">=</span><span class="cn">FALSE</span>, item.r <span class="op">=</span> <span class="fl">0</span>, position <span class="op">=</span> <span class="fu">tm_pos_out</span><span class="op">(</span><span class="st">"right"</span>, <span class="st">"center"</span><span class="op">)</span><span class="op">)</span>, lwd<span class="op">=</span><span class="fl">0.01</span><span class="op">)</span> <span class="op">+</span> <span class="fu"><a href="https://r-tmap.github.io/tmap/reference/tm_layout.html" class="external-link">tm_layout</a></span><span class="op">(</span>component.autoscale<span class="op">=</span><span class="cn">FALSE</span><span class="op">)</span></span>
 <span><span class="op">}</span> <span class="kw">else</span> <span class="op">{</span></span>
 <span><span class="fu"><a href="https://r-tmap.github.io/tmap/reference/tm_shape.html" class="external-link">tm_shape</a></span><span class="op">(</span><span class="va">nc</span><span class="op">)</span> <span class="op">+</span> <span class="fu"><a href="https://r-tmap.github.io/tmap/reference/tm_polygons.html" class="external-link">tm_fill</a></span><span class="op">(</span><span class="st">"pmap"</span>, breaks<span class="op">=</span><span class="va">brks</span>, midpoint<span class="op">=</span><span class="fl">0.5</span>, palette<span class="op">=</span><span class="st">"RdBu"</span><span class="op">)</span> <span class="op">+</span> <span class="fu"><a href="https://r-tmap.github.io/tmap/reference/tm_layout.html" class="external-link">tm_layout</a></span><span class="op">(</span>legend.outside<span class="op">=</span><span class="cn">TRUE</span><span class="op">)</span></span>
 <span><span class="op">}</span></span></code></pre></div>
-<p><img src="sids_files/figure-html/unnamed-chunk-21-1.png" width="700"></p>
+<p><img src="sids_files/figure-html/unnamed-chunk-20-1.png" width="700"></p>
 <p>Marilia Carvalho (personal communication) and Virgilio Gómez Rubio
 <span class="citation">(Gómez-Rubio, Ferrándiz-Ferragud, and
 López-Quílez 2005)</span> have pointed to the unusual shape of the
@@ -494,7 +511,7 @@ <h3 id="probability-mapping">Probability mapping<a class="anchor" aria-label="an
 values than one would have expected, suggesting perhaps overdispersion,
 that is that the ratio of the variance and mean is larger than
 unity.</p>
-<div class="sourceCode" id="cb54"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb53"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="https://rspatial.github.io/terra/reference/hist.html" class="external-link">hist</a></span><span class="op">(</span><span class="va">nc</span><span class="op">$</span><span class="va">pmap</span>, main<span class="op">=</span><span class="st">""</span><span class="op">)</span></span></code></pre></div>
 <p><img src="sids_files/figure-html/poishist-1.png" width="700"></p>
 <p>One ad-hoc way to assess the impact of the possible failure of our
@@ -503,17 +520,17 @@ <h3 id="probability-mapping">Probability mapping<a class="anchor" aria-label="an
 observed counts including only the intercept (null model) and offset by
 the observed population at risk (suggested by Marilia Carvalho and
 associates):</p>
-<div class="sourceCode" id="cb55"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb54"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">res</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/stats/glm.html" class="external-link">glm</a></span><span class="op">(</span><span class="va">SID74</span> <span class="op">~</span> <span class="fu"><a href="https://rdrr.io/r/stats/offset.html" class="external-link">offset</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/Log.html" class="external-link">log</a></span><span class="op">(</span><span class="va">BIR74</span><span class="op">)</span><span class="op">)</span>, data<span class="op">=</span><span class="va">nc</span>, family<span class="op">=</span><span class="st">"quasipoisson"</span><span class="op">)</span></span>
 <span><span class="va">nc</span><span class="op">$</span><span class="va">stdres</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/stats/influence.measures.html" class="external-link">rstandard</a></span><span class="op">(</span><span class="va">res</span><span class="op">)</span></span></code></pre></div>
-<div class="sourceCode" id="cb56"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb55"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">brks</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="op">-</span><span class="fl">4</span>, <span class="op">-</span><span class="fl">3</span>, <span class="op">-</span><span class="fl">2</span>, <span class="op">-</span><span class="fl">1.5</span>, <span class="op">-</span><span class="fl">1</span>, <span class="op">-</span><span class="fl">0.5</span>, <span class="fl">0.5</span>, <span class="fl">1</span>, <span class="fl">1.5</span>, <span class="fl">2</span>, <span class="fl">3</span>, <span class="fl">4</span><span class="op">)</span></span>
 <span><span class="kw">if</span> <span class="op">(</span><span class="va">tmap4</span><span class="op">)</span> <span class="op">{</span></span>
 <span>  <span class="fu"><a href="https://r-tmap.github.io/tmap/reference/tm_shape.html" class="external-link">tm_shape</a></span><span class="op">(</span><span class="va">nc</span><span class="op">)</span> <span class="op">+</span> <span class="fu"><a href="https://r-tmap.github.io/tmap/reference/tm_polygons.html" class="external-link">tm_polygons</a></span><span class="op">(</span>fill<span class="op">=</span><span class="st">"stdres"</span>, fill.scale <span class="op">=</span> <span class="fu">tm_scale</span><span class="op">(</span>values<span class="op">=</span><span class="st">"brewer.rd_bu"</span>, midpoint<span class="op">=</span><span class="fl">0.5</span>, breaks<span class="op">=</span><span class="va">brks</span><span class="op">)</span>, fill.legend <span class="op">=</span> <span class="fu"><a href="https://r-tmap.github.io/tmap/reference/tm_layout.html" class="external-link">tm_legend</a></span><span class="op">(</span>frame<span class="op">=</span><span class="cn">FALSE</span>, item.r <span class="op">=</span> <span class="fl">0</span>, position <span class="op">=</span> <span class="fu">tm_pos_out</span><span class="op">(</span><span class="st">"right"</span>, <span class="st">"center"</span><span class="op">)</span><span class="op">)</span>, lwd<span class="op">=</span><span class="fl">0.01</span><span class="op">)</span> <span class="op">+</span> <span class="fu"><a href="https://r-tmap.github.io/tmap/reference/tm_layout.html" class="external-link">tm_layout</a></span><span class="op">(</span>component.autoscale<span class="op">=</span><span class="cn">FALSE</span><span class="op">)</span></span>
 <span><span class="op">}</span> <span class="kw">else</span> <span class="op">{</span></span>
 <span>  <span class="fu"><a href="https://r-tmap.github.io/tmap/reference/tm_shape.html" class="external-link">tm_shape</a></span><span class="op">(</span><span class="va">nc</span><span class="op">)</span> <span class="op">+</span> <span class="fu"><a href="https://r-tmap.github.io/tmap/reference/tm_polygons.html" class="external-link">tm_fill</a></span><span class="op">(</span><span class="st">"stdres"</span>, breaks<span class="op">=</span><span class="va">brks</span>, midpoint<span class="op">=</span><span class="fl">0</span>, palette<span class="op">=</span><span class="st">"RdBu"</span><span class="op">)</span> <span class="op">+</span> <span class="fu"><a href="https://r-tmap.github.io/tmap/reference/tm_layout.html" class="external-link">tm_layout</a></span><span class="op">(</span>legend.outside<span class="op">=</span><span class="cn">TRUE</span><span class="op">)</span></span>
 <span><span class="op">}</span></span></code></pre></div>
-<p><img src="sids_files/figure-html/unnamed-chunk-23-1.png" width="700"></p>
+<p><img src="sids_files/figure-html/unnamed-chunk-22-1.png" width="700"></p>
 <p>The dispersion is equal to 2.2786188, much greater than unity; we
 calculate the corrected probability map values by taking the
 standardised residuals of the model, taking the size of the dispersion
@@ -543,12 +560,12 @@ <h3 id="probability-mapping">Probability mapping<a class="anchor" aria-label="an
 GeoDa, but uses the <span class="citation">Bailey and Gatrell
 (1995)</span> interpretation of <span class="citation">Marshall
 (1991)</span>, rather than that in GeoDa <span class="citation">(Anselin, Syabri, and Smirnov 2002)</span>.</p>
-<div class="sourceCode" id="cb57"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb56"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">global_rate</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/sum.html" class="external-link">sum</a></span><span class="op">(</span><span class="va">nc</span><span class="op">$</span><span class="va">SID74</span><span class="op">)</span><span class="op">/</span><span class="fu"><a href="https://rdrr.io/r/base/sum.html" class="external-link">sum</a></span><span class="op">(</span><span class="va">nc</span><span class="op">$</span><span class="va">BIR74</span><span class="op">)</span></span>
 <span><span class="va">nc</span><span class="op">$</span><span class="va">Expected</span> <span class="op">&lt;-</span> <span class="va">global_rate</span> <span class="op">*</span> <span class="va">nc</span><span class="op">$</span><span class="va">BIR74</span></span>
 <span><span class="va">res</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/EBlocal.html">EBlocal</a></span><span class="op">(</span><span class="va">nc</span><span class="op">$</span><span class="va">SID74</span>, <span class="va">nc</span><span class="op">$</span><span class="va">Expected</span>, <span class="va">ncCC89</span>, zero.policy<span class="op">=</span><span class="cn">TRUE</span><span class="op">)</span></span>
 <span><span class="va">nc</span><span class="op">$</span><span class="va">EB_loc</span> <span class="op">&lt;-</span> <span class="va">res</span><span class="op">$</span><span class="va">est</span></span></code></pre></div>
-<div class="sourceCode" id="cb58"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb57"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">brks</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">0</span>, <span class="fl">0.25</span>, <span class="fl">0.5</span>, <span class="fl">0.75</span>, <span class="fl">1</span>, <span class="fl">2</span>, <span class="fl">3</span>, <span class="fl">4</span>, <span class="fl">5</span><span class="op">)</span></span>
 <span><span class="va">nc_miss</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://r-spatial.github.io/sf/reference/geos_unary.html" class="external-link">st_centroid</a></span><span class="op">(</span><span class="fu"><a href="https://r-spatial.github.io/sf/reference/st_geometry.html" class="external-link">st_geometry</a></span><span class="op">(</span><span class="va">nc</span><span class="op">[</span><span class="fu"><a href="../reference/card.html">card</a></span><span class="op">(</span><span class="va">ncCC89</span><span class="op">)</span> <span class="op">==</span> <span class="fl">0</span>,<span class="op">]</span><span class="op">)</span>, <span class="va">of_largest_polygon</span><span class="op">)</span></span>
 <span><span class="kw">if</span> <span class="op">(</span><span class="va">tmap4</span><span class="op">)</span> <span class="op">{</span></span>
@@ -556,7 +573,7 @@ <h3 id="probability-mapping">Probability mapping<a class="anchor" aria-label="an
 <span><span class="op">}</span> <span class="kw">else</span> <span class="op">{</span></span>
 <span><span class="fu"><a href="https://r-tmap.github.io/tmap/reference/tm_shape.html" class="external-link">tm_shape</a></span><span class="op">(</span><span class="va">nc</span><span class="op">)</span> <span class="op">+</span> <span class="fu"><a href="https://r-tmap.github.io/tmap/reference/tm_polygons.html" class="external-link">tm_fill</a></span><span class="op">(</span><span class="st">"EB_loc"</span>, breaks<span class="op">=</span><span class="va">brks</span>, midpoint<span class="op">=</span><span class="fl">1</span>, palette<span class="op">=</span><span class="st">"RdBu"</span><span class="op">)</span> <span class="op">+</span> <span class="fu"><a href="https://r-tmap.github.io/tmap/reference/tm_layout.html" class="external-link">tm_layout</a></span><span class="op">(</span>legend.outside<span class="op">=</span><span class="cn">TRUE</span><span class="op">)</span> <span class="op">+</span> <span class="fu"><a href="https://r-tmap.github.io/tmap/reference/tm_shape.html" class="external-link">tm_shape</a></span><span class="op">(</span><span class="va">nc_miss</span><span class="op">)</span> <span class="op">+</span> <span class="fu"><a href="https://r-tmap.github.io/tmap/reference/tm_symbols.html" class="external-link">tm_symbols</a></span><span class="op">(</span>shape<span class="op">=</span><span class="fl">8</span>, size<span class="op">=</span><span class="fl">0.5</span><span class="op">)</span></span>
 <span><span class="op">}</span></span></code></pre></div>
-<p><img src="sids_files/figure-html/unnamed-chunk-25-1.png" width="700"></p>
+<p><img src="sids_files/figure-html/unnamed-chunk-24-1.png" width="700"></p>
 <p>The results are shown in Figure . Like other relevant functions in
 <strong>spdep</strong>,<code><a href="../reference/EBlocal.html">EBlocal()</a></code> takes a
 <code>zero.policy</code> argument to allow missing values to be passed
@@ -569,7 +586,7 @@ <h3 id="probability-mapping">Probability mapping<a class="anchor" aria-label="an
 for rates data (to shrink towards the global rate when the population at
 risk is small, here as a Monte Carlo test), lists of local neighbours
 can be used to shrink towards a local rate.</p>
-<div class="sourceCode" id="cb59"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb58"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/Random.html" class="external-link">set.seed</a></span><span class="op">(</span><span class="fl">1</span><span class="op">)</span></span>
 <span><span class="fu"><a href="../reference/EBImoran.mc.html">EBImoran.mc</a></span><span class="op">(</span><span class="va">nc</span><span class="op">$</span><span class="va">SID74</span>, <span class="va">nc</span><span class="op">$</span><span class="va">BIR74</span>, <span class="fu"><a href="../reference/nb2listw.html">nb2listw</a></span><span class="op">(</span><span class="va">ncCC89</span>, style<span class="op">=</span><span class="st">"B"</span>, zero.policy<span class="op">=</span><span class="cn">TRUE</span><span class="op">)</span>, nsim<span class="op">=</span><span class="fl">999</span>, zero.policy<span class="op">=</span><span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div>
 <pre><code><span><span class="co">## </span></span>
@@ -592,21 +609,21 @@ <h2 id="exploration-and-modelling-of-the-data">Exploration and modelling of the
 <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>4</mn><mo>×</mo><mn>4</mn></mrow><annotation encoding="application/x-tex">4\times4</annotation></semantics></math>
 rough rectangles. Just to see how this works, let us map these rough
 rectangles before proceeding further.</p>
-<div class="sourceCode" id="cb61"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb60"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">nc</span><span class="op">$</span><span class="va">both</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/factor.html" class="external-link">factor</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/paste.html" class="external-link">paste</a></span><span class="op">(</span><span class="va">nc</span><span class="op">$</span><span class="va">L_id</span>, <span class="va">nc</span><span class="op">$</span><span class="va">M_id</span>, sep<span class="op">=</span><span class="st">":"</span><span class="op">)</span><span class="op">)</span></span>
 <span><span class="va">nboth</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/length.html" class="external-link">length</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/table.html" class="external-link">table</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/class.html" class="external-link">unclass</a></span><span class="op">(</span><span class="va">nc</span><span class="op">$</span><span class="va">both</span><span class="op">)</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
-<div class="sourceCode" id="cb62"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb61"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="kw">if</span> <span class="op">(</span><span class="va">tmap4</span><span class="op">)</span> <span class="op">{</span></span>
 <span>  <span class="fu"><a href="https://r-tmap.github.io/tmap/reference/tm_shape.html" class="external-link">tm_shape</a></span><span class="op">(</span><span class="va">nc</span><span class="op">)</span> <span class="op">+</span> <span class="fu"><a href="https://r-tmap.github.io/tmap/reference/tm_polygons.html" class="external-link">tm_polygons</a></span><span class="op">(</span>fill<span class="op">=</span><span class="st">"both"</span>, fill.scale<span class="op">=</span><span class="fu">tm_scale</span><span class="op">(</span>values<span class="op">=</span><span class="st">"brewer.set1"</span><span class="op">)</span>, fill.legend <span class="op">=</span> <span class="fu"><a href="https://r-tmap.github.io/tmap/reference/tm_layout.html" class="external-link">tm_legend</a></span><span class="op">(</span><span class="st">"rough\nrectangles"</span>, frame<span class="op">=</span><span class="cn">FALSE</span>, item.r <span class="op">=</span> <span class="fl">0</span>, position <span class="op">=</span> <span class="fu">tm_pos_out</span><span class="op">(</span><span class="st">"right"</span>, <span class="st">"center"</span><span class="op">)</span><span class="op">)</span>, lwd<span class="op">=</span><span class="fl">0.01</span><span class="op">)</span> <span class="op">+</span> <span class="fu"><a href="https://r-tmap.github.io/tmap/reference/tm_layout.html" class="external-link">tm_layout</a></span><span class="op">(</span>component.autoscale<span class="op">=</span><span class="cn">FALSE</span><span class="op">)</span></span>
 <span><span class="op">}</span> <span class="kw">else</span> <span class="op">{</span></span>
 <span><span class="fu"><a href="https://r-tmap.github.io/tmap/reference/tm_shape.html" class="external-link">tm_shape</a></span><span class="op">(</span><span class="va">nc</span><span class="op">)</span> <span class="op">+</span> <span class="fu"><a href="https://r-tmap.github.io/tmap/reference/tm_polygons.html" class="external-link">tm_fill</a></span><span class="op">(</span><span class="st">"both"</span>, palette<span class="op">=</span><span class="st">"Set1"</span>, title<span class="op">=</span><span class="st">"rough\nrectangles"</span><span class="op">)</span> <span class="op">+</span> <span class="fu"><a href="https://r-tmap.github.io/tmap/reference/tm_layout.html" class="external-link">tm_layout</a></span><span class="op">(</span>legend.outside<span class="op">=</span><span class="cn">TRUE</span><span class="op">)</span></span>
 <span><span class="op">}</span></span></code></pre></div>
-<p><img src="sids_files/figure-html/unnamed-chunk-28-1.png" width="700"></p>
+<p><img src="sids_files/figure-html/unnamed-chunk-27-1.png" width="700"></p>
 <p>Cressie constructs a transformed SIDS rates variable, 1974–78, for
 his analyses (with co-workers). We can replicate his stem-and-leaf
 figure on p. 396 in the book, taken from <span class="citation">Cressie
 and Read (1989)</span>:</p>
-<div class="sourceCode" id="cb63"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb62"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">nc</span><span class="op">$</span><span class="va">ft.SID74</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/MathFun.html" class="external-link">sqrt</a></span><span class="op">(</span><span class="fl">1000</span><span class="op">)</span><span class="op">*</span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/MathFun.html" class="external-link">sqrt</a></span><span class="op">(</span><span class="va">nc</span><span class="op">$</span><span class="va">SID74</span><span class="op">/</span><span class="va">nc</span><span class="op">$</span><span class="va">BIR74</span><span class="op">)</span> <span class="op">+</span> <span class="fu"><a href="https://rdrr.io/r/base/MathFun.html" class="external-link">sqrt</a></span><span class="op">(</span><span class="op">(</span><span class="va">nc</span><span class="op">$</span><span class="va">SID74</span><span class="op">+</span><span class="fl">1</span><span class="op">)</span><span class="op">/</span><span class="va">nc</span><span class="op">$</span><span class="va">BIR74</span><span class="op">)</span><span class="op">)</span></span>
 <span><span class="fu"><a href="https://rdrr.io/r/graphics/stem.html" class="external-link">stem</a></span><span class="op">(</span><span class="fu"><a href="https://rspatial.github.io/terra/reference/math-generics.html" class="external-link">round</a></span><span class="op">(</span><span class="va">nc</span><span class="op">$</span><span class="va">ft.SID74</span>, <span class="fl">1</span><span class="op">)</span>, scale<span class="op">=</span><span class="fl">2</span><span class="op">)</span></span></code></pre></div>
 <pre><code><span><span class="co">## </span></span>
@@ -637,7 +654,7 @@ <h3 id="medpol">Median polish smoothing<a class="anchor" aria-label="anchor" hre
 <span><code>M_id</code></span> in object <span><code>nc</code></span>.
 Next we aggregate the number of live births and the number of SIDS cases
 1974–1978 for the grid cells:</p>
-<div class="sourceCode" id="cb65"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb64"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">mBIR74</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/tapply.html" class="external-link">tapply</a></span><span class="op">(</span><span class="va">nc</span><span class="op">$</span><span class="va">BIR74</span>, <span class="va">nc</span><span class="op">$</span><span class="va">both</span>, <span class="va">sum</span><span class="op">)</span></span>
 <span><span class="va">mSID74</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/tapply.html" class="external-link">tapply</a></span><span class="op">(</span><span class="va">nc</span><span class="op">$</span><span class="va">SID74</span>, <span class="va">nc</span><span class="op">$</span><span class="va">both</span>, <span class="va">sum</span><span class="op">)</span></span></code></pre></div>
 <p>Using the same Freeman-Tukey transformation as is used for the county
@@ -647,7 +664,7 @@ <h3 id="medpol">Median polish smoothing<a class="anchor" aria-label="anchor" hre
 function iterates over the rows and columns of the matrix using
 <span><code>median</code></span> to extract an overall effect, row and
 column effects, and residuals:</p>
-<div class="sourceCode" id="cb66"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb65"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">mFT</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/MathFun.html" class="external-link">sqrt</a></span><span class="op">(</span><span class="fl">1000</span><span class="op">)</span><span class="op">*</span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/MathFun.html" class="external-link">sqrt</a></span><span class="op">(</span><span class="va">mSID74</span><span class="op">/</span><span class="va">mBIR74</span><span class="op">)</span> <span class="op">+</span> <span class="fu"><a href="https://rdrr.io/r/base/MathFun.html" class="external-link">sqrt</a></span><span class="op">(</span><span class="op">(</span><span class="va">mSID74</span><span class="op">+</span><span class="fl">1</span><span class="op">)</span><span class="op">/</span><span class="va">mBIR74</span><span class="op">)</span><span class="op">)</span></span>
 <span><span class="co"># mFT1 &lt;- t(matrix(mFT, 4, 4, byrow=TRUE))</span></span>
 <span><span class="co"># wrong assignment of 12 elements to a 4x4 matrix detected by CRAN test 2021-05-22</span></span>
@@ -679,12 +696,12 @@ <h3 id="medpol">Median polish smoothing<a class="anchor" aria-label="anchor" hre
 of the Freeman-Tukey adjusted rate for each county, and residuals by
 subtracting the fitted value from the observed rate. Naturally, the
 fitted value will be the same for counties in the same grid cell:</p>
-<div class="sourceCode" id="cb68"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb67"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">mL_id</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/stats/model.matrix.html" class="external-link">model.matrix</a></span><span class="op">(</span><span class="op">~</span> <span class="fu"><a href="https://rspatial.github.io/terra/reference/is.bool.html" class="external-link">as.factor</a></span><span class="op">(</span><span class="va">nc</span><span class="op">$</span><span class="va">L_id</span><span class="op">)</span> <span class="op">-</span><span class="fl">1</span><span class="op">)</span></span>
 <span><span class="va">mM_id</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/stats/model.matrix.html" class="external-link">model.matrix</a></span><span class="op">(</span><span class="op">~</span> <span class="fu"><a href="https://rspatial.github.io/terra/reference/is.bool.html" class="external-link">as.factor</a></span><span class="op">(</span><span class="va">nc</span><span class="op">$</span><span class="va">M_id</span><span class="op">)</span> <span class="op">-</span><span class="fl">1</span><span class="op">)</span></span>
 <span><span class="va">nc</span><span class="op">$</span><span class="va">pred</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="va">med</span><span class="op">$</span><span class="va">overall</span> <span class="op">+</span> <span class="va">mL_id</span> <span class="op"><a href="https://rdrr.io/r/base/matmult.html" class="external-link">%*%</a></span> <span class="va">med</span><span class="op">$</span><span class="va">row</span> <span class="op">+</span> <span class="va">mM_id</span> <span class="op"><a href="https://rdrr.io/r/base/matmult.html" class="external-link">%*%</a></span> <span class="va">med</span><span class="op">$</span><span class="va">col</span><span class="op">)</span></span>
 <span><span class="va">nc</span><span class="op">$</span><span class="va">mp_resid</span> <span class="op">&lt;-</span> <span class="va">nc</span><span class="op">$</span><span class="va">ft.SID74</span> <span class="op">-</span> <span class="va">nc</span><span class="op">$</span><span class="va">pred</span></span></code></pre></div>
-<div class="sourceCode" id="cb69"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb68"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="kw">if</span> <span class="op">(</span><span class="va">tmap4</span><span class="op">)</span> <span class="op">{</span></span>
 <span>  <span class="va">out1</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://r-tmap.github.io/tmap/reference/tm_shape.html" class="external-link">tm_shape</a></span><span class="op">(</span><span class="va">nc</span><span class="op">)</span> <span class="op">+</span> <span class="fu"><a href="https://r-tmap.github.io/tmap/reference/tm_polygons.html" class="external-link">tm_polygons</a></span><span class="op">(</span>fill<span class="op">=</span><span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"ft.SID74"</span>, <span class="st">"pred"</span><span class="op">)</span>, fill.scale<span class="op">=</span><span class="fu">tm_scale</span><span class="op">(</span>values<span class="op">=</span><span class="st">"brewer.yl_or_br"</span><span class="op">)</span>, fill.legend<span class="op">=</span><span class="fu"><a href="https://r-tmap.github.io/tmap/reference/tm_layout.html" class="external-link">tm_legend</a></span><span class="op">(</span>position<span class="op">=</span><span class="fu">tm_pos_out</span><span class="op">(</span><span class="st">"right"</span>, <span class="st">"center"</span><span class="op">)</span>, frame<span class="op">=</span><span class="cn">FALSE</span>, item.r <span class="op">=</span> <span class="fl">0</span><span class="op">)</span>, fill.free<span class="op">=</span><span class="cn">FALSE</span>, lwd<span class="op">=</span><span class="fl">0.01</span><span class="op">)</span> <span class="op">+</span> <span class="fu"><a href="https://r-tmap.github.io/tmap/reference/tm_layout.html" class="external-link">tm_layout</a></span><span class="op">(</span>panel.labels<span class="op">=</span><span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"Observed"</span>, <span class="st">"Median polish prediction"</span><span class="op">)</span><span class="op">)</span></span>
 <span>  <span class="va">out2</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://r-tmap.github.io/tmap/reference/tm_shape.html" class="external-link">tm_shape</a></span><span class="op">(</span><span class="va">nc</span><span class="op">)</span> <span class="op">+</span> <span class="fu"><a href="https://r-tmap.github.io/tmap/reference/tm_polygons.html" class="external-link">tm_polygons</a></span><span class="op">(</span>fill<span class="op">=</span><span class="st">"mp_resid"</span>, fill.scale<span class="op">=</span><span class="fu">tm_scale</span><span class="op">(</span>values<span class="op">=</span><span class="st">"brewer.rd_yl_gn"</span>, midpoint<span class="op">=</span><span class="fl">0</span><span class="op">)</span>, fill.legend<span class="op">=</span><span class="fu"><a href="https://r-tmap.github.io/tmap/reference/tm_layout.html" class="external-link">tm_legend</a></span><span class="op">(</span>position<span class="op">=</span><span class="fu">tm_pos_out</span><span class="op">(</span><span class="st">"right"</span>, <span class="st">"center"</span><span class="op">)</span>, frame<span class="op">=</span><span class="cn">FALSE</span>, item.r <span class="op">=</span> <span class="fl">0</span><span class="op">)</span>, lwd<span class="op">=</span><span class="fl">0.01</span><span class="op">)</span></span>
@@ -693,7 +710,7 @@ <h3 id="medpol">Median polish smoothing<a class="anchor" aria-label="anchor" hre
 <span><span class="va">out2</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://r-tmap.github.io/tmap/reference/tm_shape.html" class="external-link">tm_shape</a></span><span class="op">(</span><span class="va">nc</span><span class="op">)</span> <span class="op">+</span> <span class="fu"><a href="https://r-tmap.github.io/tmap/reference/tm_polygons.html" class="external-link">tm_fill</a></span><span class="op">(</span><span class="st">"mp_resid"</span>, midpoint<span class="op">=</span><span class="fl">0</span><span class="op">)</span> <span class="op">+</span> <span class="fu"><a href="https://r-tmap.github.io/tmap/reference/tm_layout.html" class="external-link">tm_layout</a></span><span class="op">(</span>legend.outside<span class="op">=</span><span class="cn">TRUE</span><span class="op">)</span></span>
 <span><span class="op">}</span></span>
 <span><span class="fu"><a href="https://r-tmap.github.io/tmap/reference/tmap_arrange.html" class="external-link">tmap_arrange</a></span><span class="op">(</span><span class="va">out1</span>, <span class="va">out2</span>, ncol<span class="op">=</span><span class="fl">1</span><span class="op">)</span></span></code></pre></div>
-<p><img src="sids_files/figure-html/unnamed-chunk-33-1.png" width="700"></p>
+<p><img src="sids_files/figure-html/unnamed-chunk-32-1.png" width="700"></p>
 <p>The figure shows the median polish smoothing results as three maps,
 the observed Freeman-Tukey transformed SIDS rates, the fitted smoothed
 values, and the residuals. In addition, a plot for the median polish
diff --git a/docs/articles/sids_files/figure-html/unnamed-chunk-20-1.png b/docs/articles/sids_files/figure-html/unnamed-chunk-20-1.png
new file mode 100644
index 0000000000000000000000000000000000000000..59e419563bc95fe0eec77c6ff8763bae44d985eb
GIT binary patch
literal 58588
zcmeFY`8Qkp_diYt+N-MfwyHJuwpy*R6G{xX?NvolRLnuuJk}I3ByDwgmExjilA`Jw
zV~QY&p^BPIN)U;82qGjRBFOjj^%=fvegA;(PjBlCYn@2WbMLc<$7An(-aj@o6#Y%|
zHvs_wQKN@{TM7sqjSvtx?0QTHxZ-q(2mww)PfZN}2F}1A_dX5*oQ?-Qv<ndska_oO
z7ff2%bQch~AYk<O-6s*bYZPdvGR;YLt#~dMZzP4W(DMK1pCi9r{ZpBI==TrR$wr+*
zCo+{|xm7oW{94aOkBx1(#>Td~y#D=|;DcxHFPu5`hj9)@i_z`sq5YH7MbjpGhTj`}
z#0d>U@tP~OZiO`ARw|GyznK%*QK$dArvEwoj|Ton1OKCe|IxtzzZ%Fi!d&ZPxm#r_
z0QY4vVu%3(0&8_LViCR=`_18u=G&Nw+ciL95Lh&|IKyof*88X6YOdFzpn)voRx&-@
z3QdAWjshR|<-=Q09<|q|k51>xyC3}}M5e`|Ux`QH#rezA|DOvZx#5Qet`to%6pDqR
zI;$YyzgqF9HV%c9kXDO`wDR4to>pk>lpt`u^j@n-Ul9b2U34?B$YsaW)=M5ki=Prn
z1U`IG@dxmo;;V7D7S3N$-~Vvx6ls<1k8!Jgx#7cap?H6gv^)&_1o6-5ql*KP1gK}X
zy&w}DB^&sx_T`pG`}E9|Va%gXCpKQgEj|-zMa0!&BE5+G>sU-&72QYZQy^+lob_%b
zL8N3P#onicloDAHzRR(<H0QEtT|Ti>s|$S5`Zf$R?0ySlJ{@Ms!&mebgUkHObaP_-
zE5IfMh`GfXPeMIp3dpH5&yTH{2)Y~`k9gT=mG%N!Y-Zf$UQ0-@QJwmn0mTeUEDW~K
zZ2hZH1LEQ<kd6{YaZi6J5gx{!xfVzK)0|5{<#*XcGsKYkd&PET*DwnE8{d*J*0Z_s
z9E=sYb1DY38oxURTI!1gSK8QBCyJuueGm8(NfnMF0}z$Ce1whO4K5cNa{;lNj1wYC
zm9Kj0i4`MYvwT$M(rK3DfmRtGF}lN_Sz0Q0eh_i6_+@-mf)*Y{3*~uY5SKJ{Ii>hn
zHY%BVq`u#MEQ)e8in%DICd1ppy5as@i>#0G8~`tp0<czPBg6FYLG9*i?Ndx%&krn_
z{$+|$Jnr{pJhVqxfHgps%~aZlBNktcD2~xmM=Na6w>v-g27hSx7nWe*u)5*l$8yA7
zNgJHI7px61_DljAHj%hJOaAV&x&e-zqBmE9%ksQUsvms1llX_S)IR@#gzKmeStUvB
z3sFf!{EAt-KSvj7PT60s%dxPN<NhST=t`&zD-m3$9{uLS7S{CpGvnj31gUFrPoMJY
z;4O&7TiDZGlI^`ed@w2b@nZ%SI<!~e=eO(aD{e9FqDiMW4z+5v{#v#*jgWJkb5Rm&
z=e?xtu(ln%G0&{axp7vc|3T5AJj|m)=<^47mm1<_TMf5-i(X6Ygv6ti`HkuhZ_Rur
zd~u0?b!saCg>vhqynod4F!)(X21`Qnbk+fw&D($f1`k;HwWunqKLf`>*b$#RT0ag<
z?r~Rjwn~Qv6(1Jp!zPH_5$yX%@hHAs!QEQJ<nESoPBAvZrgnFg-53BOBPkU=Z^C@F
zqSt=b<vfNdNMx`M^traGe&*|ek)(W|1DPw0Vyc`h(C^umCrUIG8?QSy{kzw=0&Nfw
zATON|&6Kj%d3nA$ueP+5+HBEx?=PqQvxxzBTOGW~^u{|%f(Lg684szvHV0N9Vo!z}
z3ni#koK^^S=_B~-NAr`b%>r{5|D1QC*G~Fr5WUI|pwbX3b4gKFPEcU3=<ma=udNC1
z{L;u8rKK%h-O-ovBK_mbGq6g)>)lEWDFILT1%m{RK61%9>Uls5!$np%`sqY})^RLl
z|6u@+(SrJ!Vnf)m<CbUWDH-~b`N~s>&};h_OKd_hS(so^DN&@x9zNlq1%fUntsajM
zoR+=-c>V+Hr~<H7MDBZ+&?B`~Cpx5o``$Vwfb{J=@1kCo{ZkarzXV+rMr?D4^gIaF
zQ-}T4F?gm~S|{=*c9J#bn07zwKeM4|DhIwX8a;@`UwgMp=0!1_y}lISrf%)-!zB|s
z|L(byaBJTGwxp+!6}fcAE&oAbvRQHANi~7o!ya?8Ixo(H6PHC<_ujwdg4ufq_fZX;
zM-4gh*eS$y#6fjbFpHA3ut&f#hnIBK)nEfwAufYopOCdg;4~RTI@m1=wS<ly62En8
z`RVy@W=|*1x4&70pfeU07W|KPD3L!sIxLVYwFSuf7I`h_mKqT0I&=ucLsYiuT!{Jr
z3>;$>IX^a=og|~(oGBK~JdigcfO}b$ggX*z<UC<n{d9Bv2rpp=EvfY;#%7&_1koFV
z-P*Nrg1V|ss!J80c2^ty(AdS>*y<We#ZECiVK5j)8|Q1M(yE$)S?f3<&{sTu=i=dW
z7S{KBncvWg{y9%{zj~MS@S2e4y=K2pkk>XfkJnb6eAF|BRWV48RH4~ysptj=*R_r8
z8YG)j*~?i|YPcZhO2XbNWmPC^EctX}5PyAbe8jjA+#8HVnW0g-BK=!&^UIr7jf^2T
zt?*#)S0<K%m}jn2>$$cQ(X>~GMf&k86D)<{a-*ClPSoeWya|ZvpQjjTyPAB!B*y)a
zumk(c=OhyzG*Q+a=`6t)3V>&axHUk{Mjk!AkY16E4a&&Fnut-2v%ZD9o8yw_9FFaW
zf1N4x<xD#b-WN_<%8%_D+=EYDGSrOjudQslily>)(id&iF+Z7<sXbT;HoHVrReQvz
zd(L4GgcylOYM(ATZ>*$$X&=sibU}MyaPSU?vmoGI0bVsKLXJwk@E;3u_&Ia*1sBMX
zi=Fa9=I0d@z)SVs!o0aB9e;>gH$>bt->zFp6O9m)k*g49+;I$bF;C$hi)cCMb<S%y
z(6yr;9BsCNM7a)3sq?Tr^U`PSL8erCKt^1_9jluBwQ8IlJ5rYbQ6oSCdx=0kt%&sW
z5^#9JexWITKFFVX?|MFWz^cIYfL=O1b;l@@08d1YHP#%L!?BW;>y|E^0`Z6AJ2fhn
zoNEI8h^4P;p0zh5u)YRh$rPr5pF7<N$`EMXD_tA{wO(OI60(j*TnW3VrKtP9*iB<}
zVCd@5b^e6-z7)#dkvhbc(Z_t0Lc(c@10j}?Zj*-V&Y1)%PKplgO%a`=>L&ret0h48
zh@A*N0I)-*^N3EQ@YrX&Wdg`=;!pI847!(Qx&CTaTD<A1_edF6QxE3jd6+8C9g`7T
z5+^z5>Egh0Yd+x6&O1KTN)L5X68i(QQ917E#k-6<9Iku!+W;)CgmfGx=+X=%;Vcq^
zGuVAP9gx{$<70?cRbHAqDz=aDK{4IS1z(yyBd6aOvT)uwzL&B$-nHIc`NjjXy;o+5
zO7<VH^XU!_)RD@M5$Vs8bgZb$Le{n4Wi)Kxm}{=Wjf;?bZVR+VhrAW)!`rPAaOc|z
z{{bgvQh@t?h;u?VBt~A;7Slc9X?nxZK=Q0&=7C*tS6S)##rM~a;EQ4n%@$%%4VpGi
z!4Sw!UvKefV#OFP>d*ZfF%MM7$+Eqn9&O-lw3KNeuBZN^zf{<6B#@t?bCN7By$AtY
zoC%TIsML8$UjAGj9X(n2@|G+nYmHUk^d@f9)BQu-Ma*xbiF)wh=M$#iDPnR1zjl#I
zoV-aMBml?Q^w#vgk76;G68-H_dJ#AC;KSK%{eO)sL2K{&Hkwm<eBY(1Z(yaiRF##>
zwdp|W{8GGb>>l{6OIYAK%46fliRt6D((3^~i5_JNFBXokMS2vKx9ODFKdzUtt{Ciz
zpnKZ{UZ`+W_(F<>79{~lWHNkeu5r0_-CNWB{$SL>h+7UgdET6%ce|cOucNQ=JGERU
zeq~4NRYp3LU2d2q1lYwPh|8D$$X49M`&s#@>64u4tZk!}Mi1m6YU#*y#qiO1?>cwO
zg=^bSs^S-iP7@hzILlf)!iDIuW`c-T@@D;}IYaxS^Um^pt)VQ!ryv}Uq`0P!qpYW<
zyM3Jd(_K=)1#ZpwF5~jI`@a@NL7uhX?RpuT1{`GCN)Jp`{4HlF;Ai3CK+L0+5PaFI
zqC1JQXh<vh-yPvumj2S0(8xKlExnkHXYf69Mvq#|+KjZLj+3Mdc>5Yz)T{R&s1or!
zsntKvY^i*od$sGN`#wZaO`uOs9k56+a<cC}W&F8Xdk?LmoTo5Nv18plW-ESQ|4N}#
zTiaHm+4FxenA?hQ&2M4mEf<9q#)#Y7U1syYcA5mee@SmOMTgybZ+HJ73#};GwH;9w
z2J02U&HcMXriBg%U<d2mKhj24*;|piT>=8vJ&)j99na~xmaZIMu<x-HoeO}Dw|ni#
z2Vj23_Ad3A2-sP(nCq%f_QFFui{miqVsd3*F{;Qmz2|U}OkVh{(a`QUypYehTMj6Y
ztbQ_x%Ax7-W@EUMo=z#fVr#}iMTdK;u)p!Ln6|EtT_O(S?~+z$LtCcw%M=(_dtN{Z
zg5v@&#xG4D^%(6zD!4ziD{2ki+3p8OM>n;raBJln>XsPclal{#*_^HNa$D5EzfWl|
zFLjxl;*NX52Gk{%07rpN^xG1poDugUL3lO%!q8kJu*2Hig_*ma5C9yj<R1SczTl41
z2F0jdLc5C+71p52@JQ6}A^9&6#@1|)w1-6;#S2{52Xyhs7fZH-K=fAmZx8o+A0f2s
z#)6S`X$l|P6|$|5TfbWswE0t7Zlt^}OvAph`i%$sUJISNqGM+5(;IGmqX)6)g*imM
zq);|e7*W)V#@`msD86-$)+MK%ZLSl2Thr+|1j6|cA2Nds_rcg__Y;fd3@n}j*|Y$a
zF|)sE53Ty(D~D%}x!poL!0<O6i=j%ou_ORcJN`KOLQ5V{lRdyF%0`TfiLhZe;!0K%
z)gRS<xZuf9keHWk!XKhbDS&@F<=%<jdLpY85k1j=XKq-8vzUs4hyKzM#s>27zSVC~
z6NBWvk$pqvkZ|H+hYb=%(wV!a6=<V$eoYA=b=r9Yww$4M-4M;D?+%bL=_S2DB|@;x
z=z>fD$K#9o3TuTO*+i+-#?Nim$)g`K^W{;-mL|*<c~r){mXX;NZoGU;$}__H!9u9s
zKlABr>h(4XFsl^L%UYT9<|+7F-R<|$<g|HFqk{)2zNtDI5mdCiR?S^9*$9#{Uz@6<
z-~CcvOmt#npsnr-VN&43`xg?Ku!IMffP7A-SMKhVZ$HXQH_F{G8!oTI?5ap7+#Ma&
z6j`11SPM`OuDM0|rz&){SS~yK^Z@gNl4?)8u=yk0dEZ?JG$H>cIS+0zf0!fN^NyjP
zn*oWr3)!zLel~TFRsIjOwnzwUm4+;F7(ZFg$?l&_{<+H5P$vBFx()D|H1BgsHu5ls
z6n@G)Id#u9Wzcamw<Tx3D`n3sg|E=<qvWlXhcaVQjHo&DU&IHwOnLoV$1D&^-3dkq
z%H34)L0*r%e%d@Hw#$Z<F3;C6@=fb%R_z|V!kuX27^!LsxXmhy{+r9J@9*g7P*zp-
z@b<oDVqyYV;{cNxtes~DY)zB^0J=O>cpF*bH=s<gsr}>Meq)g4a6sQcQ`<J(+j{Bo
zrW=;3Prs78FkS7F7H>=2Gf~Y9KaKoMR%0$fW%?YZLZaZDQNv)Lpv_MsKK@Ex(yHE7
zb_;n*b5G1dq<O>rqe_s~r<^J~nUD3e)PLqVsrakiVxp0?)XaGiVS?kWV*!ZZSlV8{
zd`rfBmeBz$Wl-`FYc)k$N@qzkHQFvkOhGGqepOiaxpVG3D0NGyjn23-PUwtI6h*QS
zLjKW^6wecpC#G&j3?O8-WU22Lgj{j}=&D$B!v9@DS$W$Xp<CxWbdJDSRVN<31uQz<
zN&L46{hbn@qj(8vTP00cO=Ly7k}4I&lhx85(nt%40N}D$iKH&thDc+xkRaJ!9z!qF
z1_HH!!085dUKq==kq5tBeJ9EZpqPCJ1uRr|HmqMz%m^%`eZ=f*{#H>oOok;orq1`=
zeHcml!RLpiKreH-@_}Yd;L+VraUf+5gc%{T=U2pw&K)Rr%ZU-zB~qiGo?1C6ahTtG
z*ZZ};NsU7HsxZr$hPc8ly8D;TTH;+7UQo(@tP58KR5dB!XBCz>@iN4I+!tD_5T2vn
zV>B2}Q^D7IT>gMe_6YF0`~GcMKiLzJe^IwyOiniqC#!Rt?vcCT2Gz-3Rdpt0_*JCq
zuu4T(ObN#{3EfpDfQ$!XlBE0Nkzw4#I(is7`XI5-6L%K3zjxrDv{-?Nc97Mr{^(Jg
z1@^^&I#K7O%hzI>r~*DY>hB?VrDEMgnx<qzoqdI9v3gJS6FaI8csu{rEZOFDZqdP~
z41XFb;Cf!5-S6w^0S*?yGjix-P!ojS6Md-r`0L?W#hC!wlN7%C4!2g*%eS)u5HPm(
zw#y1&p6Ti7;pGb5X0P$Av&_Fr6kp1L3a!zdQ#c<sG<ANgyGSQ^`ER{duFWEh1XuzD
zW&zoLRmLpvbV}aGNd%J#!mK5^7EQTkcAGQ+7UdiFn`0Z-zQ&~b+p2iWWp3znu01Qx
zm}=xEKRcyUPo~$(szuS#UDtbFem5o`S9-U~PWn}J!BNbBD2by`x2p~9oUxPuG>Bkv
zkHN%5ZYGWdR<g!6?<S4Qb4x|Pu*j=A8qynZue_!G?rEO7RG+VkrdYGH#@CQ8%rC+I
z5N-W=#^A>GP^}@xYC+Otr2K@VhRNar<w?QJ<nX@_TOBaFxT4eXz1(>7N$4VnydD)z
zS(4Lj{Md`E(NB`m%?g0t<e_Zv%QUSfM+)<VFR*yG#<|VYuw8?w!6Su~0M4T-P#k?7
z*V)KWiXxvRufGUxUy$hG{44z|eBpK!0g~O%HfOJ}cOS;q+^7-OjM(D{VM4^@$1x8W
zWO>-LJnvlT=obC%NGDA1?-vZUrqE(NH`dH+uJ1%rkD-+kd>aMFgmfcbmMn94Ks-VE
zv}%{Yq#B+r^*u4CX&vtqtqBjHZIxD2!4(JV;ggYrZm{kUq;@r}W$p4Ha;#2)j@4%e
z?Z#RMG}N#E+i6{fkRDwzAp2l6PCzuX*Q@L+>V5tK8UJU}>$Wud18G<&X$rK(ItW8z
z@dIuP#+ZYV&k1NHhA}hEhzdIQk-qUM1}o;ngHwdiavGID0QkjSzZ4K@PYN=Y?+EGJ
z(VqoP^kSTd0SNKYgy%UKMHU6FF)R#qG<YeW2Ca)+n;z;JnW9v3V)m#yOWDQqi#R!{
zneoChlJB)}hOu@nDOS@+R=Yk^Yzlfut$AgyWaOO;Nv9WyDH}NxppjED;zJA7&OxsG
z=!V#cgv1w&RYBK-vfdhHR9>_jnhPgrMt@8T0(I|&2p_JNIk$I^FW&+>=R*JSNr<6u
z%)Cs_?5eWJ0N5K)vjkNVX}RjN?AwQvYeW~`_j{OMWsg#t(iku;7c(yJ>gC%W*B<5M
zrB|AZ0en0vN5f1Ewf5QJC7q1k8!-GrdHue@g}+{H&I-gcVOlo|0pH>TM9Gt!;TQTR
z7WEA06mhp#4m{5Q6pkGkGx85+$m=t>%pC?J3}lyK1Kls+z=0Hi*95eJbROrufGTGj
zjhfKa&hNtPZ3eeb9HQtN0YPiZ-t8~!s^;$-17Cv=_vuCjyBGqXy4LLP(xCVlSj`iv
znbwMtnN~JOXQC%qRCqy37p;>o-TWpjLLl#h?LD_IR6h6no}yhW6mn=p(QaKKNqQ=p
z@%4Gsa`Gi^g8u$IPzC!v)iyA&X~x?PwP*$!p)G8t_U6D5om_ZgNGpa}u<g^M-IS9@
z+BkSlusl)tQw{vZwOn;_dQ(bxDkD{z@^ZU;ktH+}kP>|$2^@1<-h2PA#R8TqGeWP_
zl>J-%qpscPYQOJ`dSVYXu3a~<S3vW=!sG&{KmD7n(sk9Pu$4q|$g&t*-}|<uuZERU
zi)K!VX0}lwe34^cm}Sq}nky00M{j;x&FRng&V$2aHbN}WD0s}=R&-7GX(sIbg)-X$
zS7c;A_%2Yr#U<<TQ*>!tamwtt+~uuczv`SKnaXaSNy~md?3(kwyqI3Nj)cruURM%Q
zvUlt3*=(&5uPcOcispzf2G4zCvlw?6r!i6+_6PaJbF*5Y7y$&LUEA|aRkb8pAF&MY
zt5HBLdn=vrACe`S<T*R$_h9nlJjGWBEcFv_nxc=Kb!`)kWf0o_^7n<cU-_aX(kptM
z1HjZo8avYbH-j?Clym|V3~B?B+9@*v*l4-8Q-ve1HfOXEIn`9wDmyZ9f8iZ-1BCFm
zB1&gW#9i2VkIE^@xVw=R)R>&HM^WohLcuH|jUo+nDL;o*gq%x?$mk*~`CfyXNpum>
zBt7m~iA}Gi#j}ze<?YlWNN}n1v+A7Om9yit8&zlR6HXZ7UyX2szbLp`d`3RYf3E#g
z|3|<glTf_+b~_G$95p|6W%gwA9&bcV#R{|5Ia3<jG;qf+%88`V@w2;Stb7OA@59XP
zd-a;l+i#WogBl!6m_?d;>Vu8*Tjw4Tse>owg#EB8`*3|q0JOht1c1#G|3#<|S(2*6
z$3Uss2lH!NWg|n&t>3o!vj0#m&VSTyyT_An(LZKxv-?Wk<|O<84VtWU6&9Y7GMex`
zvAq3N9##E+%u7(M$_>1Isw5JPtMPaL1gbnuu&V(FPWB&Au52O!FZl^gXnDKvZyZF;
z0Im6TdZ^fm$Dw|7>NV7WKlKlqQ1`j~+Fqq(#Oeg1C>>sbgs;$w!gtF~q{Q1dl@ycA
z)8p;6_di?x1XSwY==`k2x!1Dgd$7LUTHeWz5;y}hcB&QSGx&^ec*`|X+Dw=S24!R4
zsAtL=^&3U#$KTx`S1QoMRe0onM~!1}p208;wZ0iuL+nkqB8$Kg2by{f3#5U#)Z%oO
zryNcp!?8*&;V?#LXRKPqeD$q_V=5&oJnsPX%ZQt_swW3$Km45EFIYu?XJ?>fS>CsJ
zAB-TOGL^?$#=|Rq{<ot;@=_VX{GVBX6Bh68Q`tSLAHl0xWB>_!-L7e9*!jFvDX!|d
ztb1l7fXp^Ja7YO>4UX7AVC2ze%<VP?N1n^RR=-KOua7WKk&~9JszA<%q~hHk8_%>#
z5^cTDrc1f30~HvVA>g^4k$j>%t&*mo+s<|!JlgIqQM&R<bFW{Ax!RIl^p2$Xr;Q9|
z^tBJ^tbygn8|!C(3ON_%l1MAG`KGY!;BccvHeA-gPI1Ag|J-kJHtGD#*IA`(yeRp2
zPh7#niWBfv%vzv&2o346t~=U2W0k|mid>>3E$Yf~x6&tW#>;}DFXGPD!)*_GB=j$d
zscffqq?$*T+o9bV_io{G5^k>+$L?G-h`UIW=%Ar^m@TW^1H#o|rMN9&zKuyRt@%x8
z+(mZ5!xi@DbAC5h49t?=fXy2POGTXyDO!RE38kWeaz4dNc5rySeI+3XsyEl8U<?oN
zaHu}b`<EF~J%01PQkZt0GEh(9<$}x7{2n`KO1<t^GST?($425GinWyvDSKV=eAwfZ
z>4Cfd!ibM`$){s~gk-DVI0$~MIHPXVtltg2!X?P#Qli5F$oYcfe1-e%7%?YpK`1i{
zsFWD?MaE!jgagys2cGA=aj(FV8)wT}uAmNv<dET38c&>;<|93RhBre=KC3gIN&RUk
zc7I<WII>lgGoWT#ATd88JORYOTw7UP9mTkLf5vX>7}*jikIufDg!9{eM>aOu5LR}j
z9U=P+5?w+oxHR?B>dD}iX52|#tvj;COHTFt@+r+))%E#ipN4@w@S?*R1At>@or0=V
zfR!-z{uH<3nVX_Y6(=I%3m&3LCWY0zZ#sbrI*`@Y^UnG$|Cczq#abR2G`p#@GNX2d
zTQ8qvR-JJEXY2l?ygoq4gkP>ph{=MI=W|l_5V0mLh0&)x-5UiLsnWUrhpcUoxBHqx
zRHpO9c>$3#bvf5l><jf~8!g}TKa6N}TKei4Q{2;k#vr*kujL<M^Uz_sLLLO@{pshy
zlMf^VH!GlenJqit2&V%b(j24PsG^6d9)-ww)yWJIv9)fl@b)u)v(q>hYNOh+wWr=r
zv3ov*tQEdc7JTh9{Vm?z`wiynsHL4ImS_jcboLd%)Ksnq@c<t8mbDg+lX^Q??#-Cy
zq2ys^DXbL7kDpWL^V>M=y}fDQOZwM$CcfL86b-1i)a-UhiH4^13K5`5S76Z{FMF<H
zW&NRzg6B>Ps$I7*u;`0sP=*`F;-P1^G9Hw@1o^W&*En&CTWi@;AgNE{jnNFncexn*
z^hg6)Eo%2n2a)%_;NbxoG}RL8U-mWtI@i(#jp@w^u42va59&<XB8I36ho}`Fg(he*
zAr@!6f!;>sPypC230g?4Nq8{#=sRwL>3{natp|c%9T~3}@sT?Dz4MFo`Dkl9weEd4
z<f5{&W~-yNX49;IRV~C6d-HnU<=Rnd$lYrEgussxtDJZ$8iYHc`sL9B_nwDm49>1}
zTMOI6+AiZlC`WO@Bqy<jLagp>dOE$~ofzu7ryjqwF2@&|xf-@O_mt-IHfkf_^7XvY
z=0-|DAdU4T-RGRae~~{V>^w;%(`K~-N4+tAM=0g6z?b5ShC8h~k{C{a`&S_kON6%u
zAX&l-@D07Pko>qdm`ZmuSS2vJ8v|Ql+b9@SHm>1wTM!&tm#<OC$;dYJ0`lF-rG20#
zE4-~bFRs?0&Ex36E>tdboF5<cA8vl*aW>oB&!MydUirmu34EUlZ_#JUm;sjE{|{89
zjC~5?-%6fY@;ur3NZ>_C8o(&NeF#o@OpVjhnKn<0O6u!*zts47xzBj{hVbgZ86mrz
zw~B$W^<@yWO*q#~_|g8}EGOo9^WHnS3V$xD`2yYJ62L3cL^up%ENM`4ZzphpBG=$H
zVValOm6+S-W(c&bf&99+TgGfon#u{rhRn`euHeGWaqrzUP1w+PqS#tWz^^V2(O=C(
z{lg!pNIn=K0_Ccsz-5?qUz>FA?-%C%D{n4)!cNp%ToV@fl)cvY^8HmqKWZO~w+}Ds
z)%dv@CKz~B{1SCh+keEdOp_*kECP$$&+61D0Q&I+wuTSF8td8~+pNBV*&7Cy55R?=
zKHVKlbhAQ8@4d2Q{x&7h*Z}&wTNv|a@WGxNXR%`t?jy-2ibSuCm3V9VUi46(?vEQJ
zf}@xL^<91dr7Ik|!@?l@KYE{|!k0Tl1Zq7G27kUN85`)nJ6?!2E}dMZJ8CM$mKSBl
zvWp=VgO`ibB)-2D&MqDC@r)EoZ!=9(v-J1K;eYjn=nd6B=@t%b*4NZy{bJKS$!-e8
zl-&2{WL^Brc;ns`Bqg%LTXZ4tRd0-a4l=N8M3NR(mga5CIJCEs_r#h4e)1zY<$f$W
zq`R?cQXmcJ-*i?^F#=0D>pnfQ-quyb!VsG_WfjJwk6!<dEM1(gptU)8x1-22xQjiO
zcdQ8y)hDB%XPgfjH6PXKTC-*VAk^Jq2IuL@4OSpvCIe`;6>5eZS~MezudQQrOVa%@
z_I9?m4*@;Yjz20KvJJrjz~@SH|M(*{>dagvUA8OlK3uE&&Hr7JI^WZ$HBpLG5o4`A
zRA%WA{#E&n<Nm^mFup$~3LqZUR~HL^d~+-fW=tmdg-5YC5Dq??=|7c;hRum!@3fSk
z{|6j-0eg|#&Y|SWal4`J2n0MJUv9k(HxgrR9l4R-Bg^XdU_F`!N$-xXvQ;ud$I3?*
zEg*Y#jK*L68x<kD*brNbGXU4}44|u+KYZH~IBKsTT5Ih6b|vS{AEN#Hykg4h%{#)8
z8#T4{O$oYzjC=46Uq~uqQyi6ND2D3WPm<~V)y+?$9t2VO-MrwX*mss^x*ZM<dRd~*
z8?(1pFt;T!KP^ov!Xv-8Peo4Axug6YvfcU?iw|c>F~8X8fao5&a?SMoy*UJ@QYU(2
z=kIiwG?k0c&m=W(*4`}4I<Sk}S2$as2wnf+bE}QH@qE-wF=+{0k0Gt<mZ-FM#kgO4
z*Z(nBK;VmK7w+0mA54MtjkB4^U!2RFY+sQcjw8^3s(#@^n~_H8^?~6U{R4-VtSH2;
zzA5hf>I8qyb6#s|OPm<cSuZZEYRb7rS|8i{Vj=5}W94>em=ixwK+bdrV>8~2?#?_Z
zCJhD`qxPdFJpEa5@+}9&*m)3~NwHf8*DB0$qE~Z*|FxNs?Yb1n#YikB3=-D*7!JCL
znWIZCuCDn^D4{&84{J}(NKYRqT_99dRk_h8EB`y1lT~oFbYEET#qob?zG?vj8J^zW
z-t9Mkb7xR3#0_pF2SFtjOx@LT?2g|V3?sN10?$QMeS1AG{B-A>^tosLXJdy;-<kMk
zJ+pgnuOjspXEf~dvldE94fHCz%q_6d18MTVYA(1Bwgg}FpRDXi9chVjJtG%0?X}yn
z9kpq;8ggBP`~ed=Qwe_S>aGUqx+id5>InY2Cjip0<o@Ad%d-*^gV8D~D(*ntv$wbR
z66(VTZCiV-7RB5n<zSzuJ7v+)D(=(QMHKv&Y7T}iPx6Q4=C={sGO%e0ss?@0?_Vti
zK?Yu|MkDcsmn1n+(JxA~%vfS*)c04g!6Nt>Pj1dT*=Hwd;}z0zjr-N7J>e)!ih#9U
z5~+5ydeEmULg{cgCPL6fqmPp%nS1|jEWoOHpZ{?!%Xcp(+Ofh4w}q&QGpAE#Ho`H}
z8uxqc5~ZC-k3h7t_w0$eZ%$)E>=+v}Ivch8%c#9l#6LLr+SJlcv7Q$FO2X$xPYwV(
zWDikgvN}Dk!Z0yX`~53yd+Ncyb4o_bbg7Il@#;Y@f49(a44KrzH<Y~-yttI0`VIUm
zr4<fkW(`jJv~hiOLv5Nl1jwL4pg^Wz?eo76m6s?NUGM%B*6`#$?B)+zsK$s?MA=*6
z7g8q!ZA1dFPZw?%-w^n%kfx@xI3Tyv3}9-;Lrz4Pu)e*iTfiae$~#qJJ+bYlvXEM;
za(|V0VI44OwUE)mXUwOOoC%lwB|E}wbT7XHkRRRSLx+N#UUt#?>AQ2_?REo;N6+|9
zvJ$s*`hhYckUXA|DxJKsWFT7J3hDa+%zyX==rnKp^cG5}2|StVjDmfti6l_Jtjq^k
zw@eMr&d%ELv8f8Tfsq$+rdcFJY00MO!mQ)=P9Xl4LI5FbqJJ!<b6uAh@HOICgpxa0
z*rv=fN0TKx>RWuDYKBD_Cgt{2aP-o}sC$1MFoXkoRiOHMGjFd9M(r-Zx=qb{#mxy<
z^B&yl%7`i%05$67L6Xh&qLtO6S76=K=iF-ZpEkCrCYjd<8x91)iedO^vY!Sp%|;@C
zd@*ws5VWS{of86&l62Mk{>41_8)>ufzSAtt!uI@Hx&my;c-o=E-7#|GrMISQuO!aH
z^9+;S$7`Lpc4Uxl#R~?G7|-}E==!OzHqI6he(kV+Q_?(Ye?P;$gxE`JW^1y9<(fj)
z{G-Q3Q0X@K#V^u~+><(D?36y&q@E<5pq=s;(6S!3uY1Y6nSG8Ad)G5x`P&_!A5ll9
zhid1k>&GkUO91^4(rUkB%rk*I8OI`Ag~D)@E#7{~+eG4T;ynvgn!Bvt@lyN0o>$t!
zw}yVLbn)`E>Hg%gzv>I|hh2ur#fqYq8l{T$Fh@l38}KD(UZ+HY?lfVu(Pr_MbI4p)
z5EMz-+<7nUw6fTGkM(G|DUa=5G55M=@++P_K>6^$BA<sEZG;*n$XKB^F|t76*LTzB
zu;a%MSA7ZLd>8U~G9CiO?A9*zbQ{BlZ&WPEoFt8FvEPh~8m;0cem&bh?gihuW4zJ4
z2Ns{9D^IkObhE8c&9~yAlSsek$l5V-m5;wHRAoBc7e7N19c)kz+`|v{JT11*-}!vT
zfLWd2HhKkvqW`z9IWRmttmW(wUU7F8%qvgt$`$xaoz^CD>+{vPo{#QhB@mz0{+4o#
zX2R*j5g~+IjcPPyHDpJPs!8|oGa~3J2nLpl|41O-!Fslb{nhJD-OigzKaHJAf7+oD
z%~2;U&T7Wo9YFN^S~-uYr*myA#G@FA<ge!rQ&}9w0Gj_JWAS0}_dz@#S#644Iaqml
z3DyxNaoP6>er|FpBlaiIS4$SY0J13;ujEAPN;C+5Dp<>RJ=D`S*eTPw{_TZNj>Q|Q
zE%5{xXjT$qn^qKb7U-2_F%{cm_JeBtMI~RU_17_KFz;+02gN1qe~gEQ9*`{p`;A&1
zUJmYk{ty)-+uRO-FJ&r%pZb*|uNB5|YFtv_-`C@gIA^`1ZtD-nM1PG9Gc^+5mQYFn
z1vPKiu)1#M*{g5~ay+JTon+%P^IK{yi?6C5LC@+$gx(O7b1;4@q$4%T;B?7;8(j@6
z5(eAS&s~U}bC9SL{FGgq_ptQ?P>Qm%w+A|sMgVjBZzvzOHM`hbb7EDCbh4={CW?+%
zoGPBFkySE@E@zMV4E9T6M0<ZgBU-cBuNK&^=0}i3N89fsQ@b)HSTd|r>>x*n(bA$q
zH&M+R#x-fNZ%j4ms)HO0Tm$r`4D=~;U8ERe&e)L7);2%Se6Jn-U6+4g7{W}?!8$hQ
z`;^*ZqyLat7?{HTLn16U`I|3E9CS!5#l>&uarZ-z;dh(ocY7DPyFGS#+E2c?y1M>J
z59b-Fhjjh^ebfg7gfhUxj3F;F>%(y|qoknkA_7m6UPyF)Dqk9<g(A;9{D>6@FibPP
z^~5OcD@t*6LFMpp-f!TZAJ7I*)`OYNt24}vkdx7)y}@%J_$3}>=e$uxdNIFDZY<fI
zTp8(W7O<Z;cj{RRIhERNWpra=scM-MvZ0Ik=+MF<2lMoKiPGFu&gW(D>Uu(d>2Q7I
zFnl&=>Yu;^5Gu>lIb<ju!cTAEGl7WVi`?Q5#`GYgNoC0NV&^*OiHh=iAau-^`${c*
z@}h@>aN%_0!l8#{BNL-~*decHuC8|nDW+GW%tRu7J-oCBtskz%Qh*_{u={ldSL?(6
z!jHU&7}mAy(XJyt?x5n_zk^CR&l)_}d|2n#@8%qzgyY3iBh=pVS42pTIb|(ehc3OO
z=VgON{#{QKeK*W3`QP5l8&!<=7@+x+Yp@BTVI*ZUM?cM+zbv+7#b1_N9OARKw~}OX
zf=s&5apV=F(ZkKa=*J#QvqcB7Gv}PegR{x3ZfuMjb$?WCPz*s?dd65EZ9>OT;wyWx
zG2Nb(+z1>J&wXpc8bLjGSDkdRuU-58Q~@fZUA;KB051YMnvrrq7$*i`i9Y=dp60a$
zgE_h^vF6f%33J~_FMFOU-;zCF3-z*h$l}}~<5ItH^#Y*>67t++d1qY5_95}QIZvR-
zSg{<AOIxK0<ydV0OX(9_2McdpUF9bFG<12uF6ecqu6j>Kg8JJi57bw9mO?cPA@9t=
z?=nINe-%Xc`!Kre0u!huEhEEu(D_BiPW}6>Q2c=eLJJeQ-;L|D=b9(4CtuRqEHPjF
z5jB-lD0lE9HJ}19lf-w)?xzW_lSf)+8)<ays!Oa1+8|ec3A!=>3MK(nXGf0iRF0E5
z;(-}_cCL|)o2sGFev;{qTUzKr0~G)0cuYSgZR#XA%t5z;{uCgG=FM}luvPv6OF=ih
z!)kjeMxU+jt?@u#Pp@IDUvBdGbxr*mI5){|YgTD+P{Ik(@pe#2tuCnmXpmInOc!`g
zLJQVbqh6|UPrC-5PyGt<^~q7ao8$*}mA$ExDbElooXd?W-4a){{+V|cJJe?3AO62J
ztI+M6x;J_SQfp0&Mqxqx40&#Bo9|TKd|-ep_vLSYY<#`qcX_OTS{@2Gp$W^u-hN_h
zwP%nN^aIqLI-aLzhYa`9DrHYJ-W<!b0iEC2N|GDw=Wj{X?2Q$=<#@OaQXTo*&Xk|N
zK1NN3iSs`JRWHBO%Zx?r@ESLT`LGrCxLWNnVudyAFsA?Y78YGPGY#H4DQ9d?zrBrY
zCNwW|Sl#GdVVbmd-GaAl1MN-Yj!5%Wp7Y+U3_3xlv^1csm=HkV6msT!;nVNw#<do`
zhVXUN{HuLj{cS=KBw37#xQ&QjnqyhkYl-wnHZO$@nw3>=mKdW+pw$My25_{{!ny4J
zFWNXaODd+ms_Jng=SgdhJhxU}&73(akI>p_d60rKXSy2&JYteA4FuN`CwlN*<5V?c
zW{8oh^d^^lqn`sSLzi6UrpxOm&&wD!+qR0Zin2YAJifc|!rP%y1sFAdP;Z}|Uv8tl
z$Lon#R1(H!i`SlstK>9igt<e%-sU%hU`(4StXf9Qcutpg|ENI@y3kJEI~NMsCTtiq
z&ic0KsqGXw8_`?2ZvLdLwaKXv1yY{TVA=D7qn<z>DH&O9oUU~yRCvqoe|KI;MC`{j
za##7!Wf3G05!AS?LMJ{R@n_eyQ{-VI2{uc+#ZHlnoT;4|%|NY5)08(4RM7Zcd^B09
zQpQT8IIx5~sFIWjPWe3Km8*Vk?CaNiXV0Fk@g-HRO<;UYill8FV4B(0e=5@KVt+7-
z-`;DHr(Nd0Z5!0r&iD3rr_T8WrbM%^AaOFk%<2}OuXPNH@H%zqaEOOq+@Y_p{hzo&
z{{V_>wo7)Sy-us?eDA!ifbeGPJ6cm8ZqBR3&Gtp<nb1+{Q79fhOwPGst7ffvyJ_pJ
zc~MJ*;(kZbmRa5-#Pb{bR>i}N@IgiN4|vb0kg<J9`pQu!ha2cWyKmPkMIjG9R6p|E
zd?_5v7~Bh$jUe;CTTwT#!9!B|`t)8kx!yW#VJUf~v~HCIUp5I@jS(iUvP0&GYUg`z
zD^=OLv8#oX7LR7o9~qr{U=w~~nH}kK-ez!BcnT4o)|DvF&AS`e|3+Sla<O6jzcTwU
z++%Bw1R4*^{VY(4fu@k(!KZTOS5xs?-KIve#!RKyY1Vq!;tjuS1}l7#KNssBlOcU<
zF;z^%?-Oa&ALK<@>wbnM=h+VaCvRQ12?FY=3L!|=lo346nl_zfMtZPy$#L5YHlIhm
zKHC-+?>9>Ye76P?vXr@31VQ>fE)D|Kd#jK`d;yh2^)DF8onPIGEH+!1aYh)*!k5qs
zdl_&KRX9<?gCVMEwh#y&q2fw@YzJ`w)K~?o`~gGYlCja-VOpW3IVj!_f}7VuC}Ft=
z*2r=_0QiHlni?>#UE=GgqAA*ph)n3>KRdPOgq*LuVeYHMlC_C)zI`m57u#MxBeS+a
z|0m-L_ovH?>M1j3tWl*Y(>x{GAw^T3O9@-F%3kE*^SFp-8%O)D399+INGmuMniXD+
z10eJJyccGQ&nDMy+X!LYzvG6C0>mSo{K3|*675cQX%>$9EWE|GT!OZ+rxrGN2Wx$N
zP0o7nWdz40WTwm+H2d1e?Rfa$aspxlOUoPt^gz(gkd1b^d0I728qRl~-{A2t;?Rv6
z8PRPLi+G!sE9^HF83JSFrCTXZ-UrxNgK$k>@3p*rNSa#X%Bx>9av+VC)I5l+Zu3VL
z6dO#f+{7c=p^y4=Y9s=&WbqBK2~3J;uO8K-q;HdSN+;mIVYOj`M~+3KAJ*tR`Ql=$
z+l><YO36uy4qdJeJbwhmFbj51;gPaPcgTbh?}U(pR_Wh2z6ymaPOAtX&tjwwVh#@i
zE)aDN9X;s5{)Sh)YbZWZW#uCx(zqSPcQ=dPbJGgzqBl;bp^e={Fri%&Uk(<1p*BPK
zN(0b7cUeX+_da4*;WTQn1jp#1@HZ8P_Za#ao_jx%o{@+sy-gT+p<vXfv`GdSxh>~4
zKw7eUwMs=ebu26@igs*pG8fYFy)CsDw)HJo7F7MQ%j^VPulZwY9+AAPG)T@vBgQc$
zfj2(>a?;Joja@M08)Vh@Y#JfLMk??{$+cBhd6<-oR?X7U)0v~-McskzfcXU@Wcqv;
z_%+TbSh*WWF+nN7m_dcqBVWK18kWTReiu|*dr@!|7~ld>!Ju}g8XplcU2j+N1~)>g
z<V?=EV55_I7}laEJnmZGTg<EH93^@3MK!^06xvE#?`c`CexNzRyRasDj;I^14BcOD
z>Ar=SRUnSlLSNhXIay;ht^IAhbN$O&&j$AT7&XtoRT>WPQ@O63lIys>I5gJ_3q3W9
zJQ<u3ygVPQ(bLQT1uHTd=c@7B=OvQ#2JeoSu~moBP~nlF9}YkZ_>19MkQy}{r%PW9
zns@-B1z(mf%GvcO#-zcLY6()Xk!c=iGy;DjrX}?C3+VqVqo0f8%#R>b3iGe#KiY`r
z%B5TVRdVbWgY6eMcJwxfqr?*$Uu6D$6m?+!uQ90J`$1H;|1$+r>VR9)V)9fpDX|}2
zx6^vKk+07$cHB>AWRFc%_wX=w$0E8gsGJ2^JQ}}V;26?|6h)C#qUL0sBQ29AI|jDb
zGk4m_a=o>{G*&SZ8*Z0sagSml`mV)&aLOY@!)yp>4Ybc)yKbGN&=~MI(FG%R&yF)c
zcI3<d7N_y~#y(PAmZ8uX@}n24dzD?4?%g~%ht$7r=rOk}*y#o1zTXc!UsoA+fkF$t
z0<H}wK+0>+c?5(q9aV|ojEWP<RwX|Y6CQz{lzd(Ct~85;2HA!C5XNa?TglD`MQ5y5
zhGKq!>wQhiM-e@aDDb9Doj#*B;Aec16m4K^^FD2OUj(*atE$C{N}k`b)J&3f)+UNz
z*OH@_e+FN{l(OS5wlGPYr5wmXU7e(7AS=8e7mOtX@4|UwN~gG$_*)eK1%Gr^cS#R9
z-(j>}{`<Pqjh%y?|107(n;&dF{DRT!17Q%5u)1^+E{S8OL(J@a1!{peH~^9XK4m5Q
z4W(2c^|a9<0+g7Vf3rNNNFe_=|2&TdyEhA{rp8FIaMkI&uBsqzn=o?>hwv=*Z{QU3
zL&EiWTH|4CbvIPFwb~<aqvxhE(Vl@~e~f`Gk3CIPt*{<`&a5Q3m>*2n8!~sg%}yd6
ze-+<j-kF;gsQ{w(Feuv(54J;8bx$v^&);y>8cgf@V*L}S-O$62;zu?}v5bt$-}flj
zci;@gB!B4tMs~?L!c%HSH4|5hG4g}buklhNkAc9ev(7yn@(r08(ithd1WdI8WxRfm
zTfp|~HH@r`?5skmlaH~%uNtYxL(d;1mc1J;&)g0+!*LX|P|OqK<A2~;qp?sLGAejU
zY_IH$)q&1-Mn=dICnivpFYKJfa^_9^%$}oNwq5Y=SEh&5hZLL8zB=_scPXL!OU(4+
zDR47oPH+LScXI)9616f9&;nue@L<1^98VqhK<ZX*d~I=9)1rUNL-<Ug*y8$qkX(5)
zA9>#s-s}Pey)&zTzT29oFuxDs*C$v9h;6ElaY|V;YyVriU6hSAlzk-(+f+2F`seHG
zxG{P8Q!ck%s?O_(=|s$o3(dv$2X(?<xL<PXe9@oT7TbS|H{jw1zVug;>DRONKd2S!
zV1`K;l%AGVJ;^cbP%-fI^f2(~48F7qA1FC(m-Rd6V74=yp$X@3dMn_69>Lg)c0K=S
z_SC~}G+6I_!8fsW*8q_WO#$30y!NHdq14vRGd(Mx*X8MHw?W6<J&3+9qa^p5FHdf-
z-dOowo0nSYTsX9K%6@vJTyplry3XLGW3RrRI70mEq#{V>lqOkK+l%f|<;3VH+pShi
zsrpAqaV?6f@h?4UM3sQi^nN^!lZXlx-CiCGei+{<of%{He`W!2hykht{}94eFOVhh
zuc;YxX9|zHgyNo&g0Ou$0~_*v^EDZ(<>HFu(f`P=$%H-<%G)-$OMKz!C(~~*op!GE
zAu12o$}6v!YaBJt`=0YULeY7;w;5sy!PfixzO)gA3+f!h3-2gg*!=-JeEkHzY`wqs
zI9_k-$o^9a_b^MS0=e#~T+sRJwl-(;uST9}5Z?)P+BtN1CuoN|dX7CmK9CnsIOGKu
z%u4!sqWu(d>DvAkdt%O!yFm~3oYE{hPM2DNvi&8*L8+(oti6lD<>4=FjxzOx-nzax
zb?!e!MaTX+a_+0)j^2ammkie()vsvR2-U9@Pj}Qeel~d?C8OIkBYg!>^D%!%$Z}e?
zM|MO+GGk)4P`IO>PhXXQ)&=s{2|lwOYBRZf9tV_IUCt!fx|8jbiz%#tRvw~GEu%>@
zVatMb*lb`4!Qi!fqDaXPkwSUD;fKBN4ty#_oV8C+vn`+U!DQpG&rcl*z5?-Zo8;f9
zyH$I#le`$-F^-OZ`R?npr&s~umpLz|4uuQa{CsmELUE&Z19-th{uw=eWPLX;fcOFW
zx?l<V68dh6e)QxU6zasD&Kc;GIGlO}FCKArW2lOH2hf#KU5;o&EB2+7+j{MTLJMhn
zTiKA;ABK^%2X8RDRboc}2{3x(ZknUhVIcn6R3+furv971T$GP{J$SYuHFs^&_QLj!
zR|3CBoO>zO96u9PBJ%Cte~=-wrc7z4NrDK%Rq(|pOIJ8Yb&Q}?%_Po#(`>oRPh_1(
zY?{jWqtUGS?pjlGwZ+r#NE)JMDosx)dn~yvQ2NbT)%@v}KP<l|{MMv2!_&KW%(%#s
zq+zTEp?^ySi5<2PM2Q?V=`MbuseWp|09j6S`ad#r1Tzky4_At`;PftTP({}S^n{|X
z)=++*wt1;mXJLb+Ptr6b6TWl}9YTAIe2PqoyK336cKd9AWvCVQR6$W|#uH`8hyg^U
zYSDa%?8?2|eg052MW@G6M)c@xYuBm#zt(uC8cbxrLHxZNl~3W=Z;GnkC3LSenK36b
zaZBspdU~=C%W<zSRFKc%*O*0Wum2N<w{GSa1kGa8zO$OyJE50HBQLpwhCch{khZGz
zyMCOqP`-tqQruYkN3Czwt{bGO8vND)dlCJiLy3pTc5IYrkk2ih63!LMb}Em0k&u7E
zR!yhg0j#hJZ8E*2GfjG_dFYbso!7fk6Od`{U&n0^D<2Ax`8iTaF~WuvlOO8HKurp1
zx^=B(cIsy;YOe_w!A>HHvMyJw4~(A%Bj>$ssPyEeW)rajukyAL<NGhiKJa&ve*1Q@
zz51`;Pv0D%?z8Zw%jafzYcYc=<p{1)X7gO}M~#4IWVseMgJhe9xx%KMaz!y&-;W<-
z-dDrlt*Y8~4Pf?dg`%T4*WlqUipi0>&Uqo;l`GY}`HK=CI1B#9_mgZ%VL4Y$uD|~L
zH-y%a^Tf~Dl+^bYq4Zq2tw!6ah3GG7an!85%1otG`+0Y59*FV)h-DXcX=QfSXH1nZ
zc#4e#kQK}7!Q&3{<}X7qze$zBrid35Pf4ARsw;{aG-En$E-ht6Ew}yM(<2fXnca@s
zyCcBD$+|BymF%L3COMVpT@1KxDdyvzpXMEHhYFq$66dC36DX^v<ku!D@nLRP5GsfC
zwx2~q8sF3B_LZ9iu?*djAWHwG7-{7DC9Pa>=a`Lifl=GA#-(dM@*7{C!yhJ-p64d=
zo}{~rUzvIXtk~-|;q6I);+_$>#`G}NEGRi~BUxNA9-r-(j6`M6T77nF+-TiD_NHUN
z?9R?m(qot(lsIL5_Hq2qJ)5IvCBL;0XtQh`PjdE`8{W>5n@2J#<a~B=1atMNN&c-t
z-Sb5f6?54khJ&`A(VxC`A7%gDW<Xk+>E@pE{bB+>q&A~V3Zqo^V3n0D7*7-ayPnM-
zzwG{pY4lC;t8w(VuJbF;%TuG2Ek3dg3hj;)Z)dnY&i(@HbpA4nK9+vO@%P(XPmwA?
zdlZjjgKmrp#7lid{r5Ds2|oN<PrTqrrenm#_3&|x#^AZ@=G33Ic&7))AkjmAx1%a2
zbY9s(uR`!4xyAnHi~Mr@WLCRG4wWLa)eM_=r#Bt<p*bB>rmTthoKF?!)7`Jp$I*bg
zBu&u;_iuZFMJrc3ZB3k>B;GQ4c0CXJ^bT#)^W57%4u8-|%<5S(0za&FeiQO3<NF*w
zt~u8ij8OXhbJ`CDL=v?{vf}V{?g%<~LyixP>3C87F}}ob5VJCLNqUbgRz+{w=iHjz
ztlW-zG%-KYy!7ECtcw-yBK5!_|9EbsxaRzM2SX`1qHRL(V1N4KO{0-)i+a-&6Tb2C
z-NR9uM)NGFIzALJO4RVQ8TZH4l$rc`#&7P6;Ipk?GI(#6PoZBcesv;b4wpbf?Rggs
z7QqFkYK1*8OD<L7_js1=>6{x118ugr<8EFFW)o%J@pqPj%Op&mW1U@(Cc@WmiM9wQ
zyW7q>-r1j%t6t<yxosU)dwu8|wL&6;3Ev!3g;Cop7RVt{Y_jP8!`53y#nlDdqPP>>
zo#0MzPtXwDAwc8qK^rG%aCZsru7L&`4<SHshei^DH`+L_^WA&KIB&f7qv7w~Yp<#`
zYtC7<P&Qj^T719`f6s%LwkbX%QKv4Md}CiC2LUlb8;cf3q=ozSSYZbL9*|NG{?#k?
z31lHaz@{ye>>~2v{i{A|FBX2oDOvht;TlFi+eoYj4iM$(=>vXWbk9r5@3VwYGK<4v
zqQ*X!rq8PH{h(w)cVAl&^mH%sZwmK;C$utAA~IRVPaN)t51riDAdYn_rZ>9sa7t+=
z;BCtArloW%N~QxuNq24EmClXrbZP;KR;u{<x-BR$bW%>eL6}$%!u*N$$ekVDh+8^i
z9Zu>eB$c!eM5SgEVpW;0ZbQp43J4iLxK|)w_Ko8h3>Cc)9h7+(iLK(<p;=Gxbr-oA
z*tjx-QOZ~MpInsgYkDD=Tp6y_w0>N>+3OEtbtC#@cheUD&jKD%(VihdLfoO(E=C9I
z=|>LD>{2XfD%1t_vgC)`Ssn3$CTE*go{`Ya-n-fBZ;M4rj~h%W<BMDqKh}u<iyD1Y
z|IPS{N&?v{6P7KI_{|2>{1+CbADqGs#Lrk_rkW_(?Wo6*bKC|x3hSs)Jjw1I@y#$(
zuE4vYn4zS1=u6d-m1W=4I{(h&=p`z5*6CaPL`V!ehy&)ONDRVq`uF$06;59mF-H8o
z^*1;Wqi<yYW~R_T3V+7!mY+wB(v=o`g>S*rcxra8#yye`Abzxh!09yGeFrT`KckUp
z-2a~O;%xxb(Lc9@Ro_W5s8WV|dfpzXL>+xjJ5)zuPn#RlSjrY+F;B|p6sMUNeJH6*
zmKh?_Ve-X&73Mcd8V0)^YF@muQ|EtaPqIkAckehImOj(|Nn?<o^0S(PgSKC>iV5Vj
zT6uB1i_s`j#Oz{`ojmuAy4Mc&qn)^*k2WYu<Z_h@X?k7!hd^iI8~(q732l9DHG}gd
zt4nEClqLb2hMTrm5#XNO)OxsuEI~0%<ldq7z)1JzuTxePtoF(z_E|ZpOb{({1EaVm
zwyFiUm0Vtgh6yulo5zwje^fdMe}DP4=tD?i`x(#AA-sV->1;8Ns4i@Cq4S-S(IIh%
z;d!R#pVc=V)p}JY&#2g2Pm=9tLBR^|)G~q=uB6jm?s<WE$r3{bCIcBoFN{uw*ZHbP
z^&zL%STlASPra&Bk{l%lXZP=-uepa!LtlHg<8U9w=kaclD+_1Q0kJ^J+GU<y(T2z%
z>@G4<gg}bFS7@8AMjP`|XphX$Jet*9Az+7Ry3Z=Na-I-nf~9?!!CWixLVyUzpARLn
zt^%o~Ts;M7ai{a)SD#6xZM|Ow+=xz%2c^G~iD^BPX~J8N_PElDpNlpR#<KLoq-<rK
zzE^LLzZn=XHFYstd%~_Udm+~)&27*r^Q^TG_fU(VhYWZ2rF4?qS!CzGu%7Kb8gE65
z@nstgmf7EC0J?(9;MudKQ~&#Zqw^);Jd~^UYkr40XluK~8yT24Gn>})o)+}ihzr=n
zPJFtF`4f2yxdHjPUvpWdwa)c0m;)*b^?_u#tg=%exE{K%`M{6h(zZEQ<<+_wd*U(?
z|2RrD8U@ul(gcm#!LPz!?)8c?vlO@#Yu|+T!g%WB@XYg<vFFC{GmP+Quv*$tRYeF}
z-o4{>5V7@(()Uw>wcdt2lUW|hGYUI&SH3Ut*XBCiL`4nAWE%Od)3B{<_V{K<BV?3f
zs}e{%FM}R{xB~bTA`a|RvMZ>1R6Rir{{2JkgUMy@PA{iX!gLb#9U&i%39=;7ZGWf-
zq_w!o*CrNTCUhc#P;V)qZl<RXxM0>EuGc)k4gs1D<5XcMK}yt_UU{`*jL!&LFymLr
zCQBoiAX%KxCE-FO@*9FNqaeK$ANjvNumLYJ{v>HErT~+As~-Ny+;L=u`p>?8Zj3f}
z0+oihhe}YoUMhai!}xc;`V7LUU&$Je76#9GL)hJj-i$TTOohO>kNsdpR#!GeXA&I8
zwjRCK?6j;0z2pUYIuX+9QnFyvXxj_nQf4_ZR{gXpdg!5@0mC;w;!|myb&|VH^iAU6
zV7Cu8-XCFOVR%R(uO2_DuH~NJ^K>Su6rON7bZ(@!8I{hk#j3Z!jYJelQ?RF~0yQzd
z^l-K<SXQSF$pX<RlT-muZk^i5Q-c46V%nyrFRel)YhxQ-h1rn!1s@7KMsvHuu~pKJ
z3n=1k`;BA^9wD)YeEZ-IEK6RvbUs?BIp;zL5Yv1BDnBEZsuUbi>f)&kxhMrqeovpN
zlnK9l{@efV+qzdlSwrVvPd+@i4KCTWG9x8|vw)<0lf7FLAvXc6Fb*U)EkK!L<~JUb
zXSwjLiZC}s5hNS)^0?-W7V-LrCoox9qj#~IGs-3|h#F(Ct0lD)x##r@9#TIph_nk!
zlydQ9fN%aC^@X#Ya?eR-*(5xLXwCbn)z8Q$uapIC!H4Z=)$1EanIr>x3-`I>daMPX
z`iN3vT-M^5&^MJ|C)LJ|G39pgP{NwD0!CNxUPGG`rI7&s<JQB2I5#s&vjoXK;I)_c
zjy7>0QO|zSlJ;F=e%2Ygg6O1iL^)U**6vDm8F4gUN}c@%$pGzCJhD*a>BKyl&xRcw
zux%W$zbg>=AtTBxuK_M5B{hrnE))A}*#!+ECv0`9gUNYB$~E;Xy|;*B(>L6`*^be+
zZ2~1P$kg1M8RFkPEP?qUnS7vuGlYjwvXMI8X`jrtwf`Gx3R2|?t&Rk;n)UiwFD6ST
z)#QQK9=Egf>;s&Wh!KY#z};EFs|XDD#Iw(imnas>45SroGy(F(?zoI8w>_MT+O^tu
zf5t2<gs-~=Ysn`{+Jb{N^~<J~Jqst`Y4A<Bfi(M#aDk+qE`blTgVg?Bux)cvOM~LL
zk)G93wSv0+*@j`;;cF5p`Eb%Io&8yNv8_EA^7bbuEE{Gc-=4tNI08)=KO>5M7hU}j
z3M)deDqaTa{JnlaGnZ;YzZG^@kH5cg-d7*LytNn1jc4ooQF4G8fe*LN4NC+AeVKlL
zt<4dsihUn2SN8r~$CyB>;lfa&^5!*ZMQf{t2k8S;E;}sCs9+L9ot8O!nx)T@Po$UW
zVsV}n$A4SWtUl&L<l(j){1m0s50N2zUNCDtIXOcZQ?93Fm#kqtR#d*Xu@bBZCY84<
z`kupDGYZ=BbmVs<!jh}Kto)1A$l_fFvuRb|K5!Sylr>UbEI^w^@rl^%fh|4>!|}}H
z;~4*sAMnyc;d&Piq6pu@LEgHu%KD^$uw7vexCb*lIb(^y+XEO7Mvw8e17mLNO{1~y
zesiK^`orEV1l*u{bjgy$_fn2Wa2!An3tGCOy~JBD>cp((e;z#QdK54-hs;ihuL7oq
z?Y&<zd3$vegfs?`GC3YNjtov#{H;4uJ29Izi#I;@;*38$9+J|C$aw3EhuQ3o0c)3B
z|9jx2sEJ0wJJZ;{#zZZBcxlUCLq`WcTM^)#&)$cRJ3Iu4TCd);(jTcpCSwF{8(395
z3<$4-Pf+Vtjz>0ZYOt5%R)DWW1~vGfUFXCrHCmu2)0%gOTdxyOCqTh!XP<VQUf>V$
z#R~70$2t0QX1!Ywm0}j4M=NQD4cG^9&SKgbR7xAEmc3fxcz6fgLH}IZ>Nwq@nP9K}
zg{>DdP>Z^$D@MVSXL=>K{YE{$)@R~F%c)?pN6d}LofO89pfkz`&h!jB3E$YmF{RQO
zrnhcY9J#UtD2VV7X4O<_EhQ`Hdmk%X!ZGMd?4UwjEQ04@z?h`9iTulzKN3$z3=0$r
z6z@OSQ*<GK*{|;njqlP(fFET-(ho&s-nk#zyZYGsqiosT%LHe3l6+}79nEsTtCUgN
zn!+aHm7qk{FW)z(?*3xh_z8o>AuVw95BrrmPuFdjzso#^-Yc8eVFn|YbvphIX2f#p
zQWW+V4}aW&E#qe!=^54=4)m=R9hA`T$KN@ni2v<zt*3u`9L134pjhbJ?t^sS8Rzfq
zS#GUHnhcmqY~`f*95A*=tE_-yc@}f=*aQD=m50OAFoWW;FXiXa4W4wx@b~477mU+q
zC3e#*>wG6b48NfNA1v9o_@Op7mPv()A5}RXa+z~@Xm4_bOrZOnvz<Xo9KV;w7<pIk
zc+4U?tU6->J)8_lI<zHM%|MaSk2Um`_7W?Q2WkC1qm1kJ4E>-Ahr)KZ+~F=>6Ic74
zFF>0v$zPC8*Z=cTj6#=?qp2QU5hUbNe9PI<;c%w1DmV~cks-msOd2MfMdSaQ2H@IQ
zCZt)eZqo3m>J-SuP%KAu)LOmdl1I>S^h?N9q8p(GM9WCN)1>@a2jGo{;!G0E)82`-
zZ@_l)dx$`k1B28hZ!|QGzP_xQjdtI{+fS>tveRB}3P5V_BXAqLa@5@XtZaD&WA95E
zXnOR%w6DeLE1#4I<hBs{CrvN$d6ivt9O#9KoU|B-bw*B5g>HEFuYftjlp%iqr6du-
z0LT-c2>^S24g%xe?l4QzQu;40sQ<+UBRnq363-q!c<*%+_{H%xImrta=fvjxWL9u8
z_|of63Hlf>BtQ?fxF=t{;y=EiANY<k@Jk%&wL+K@N-QRbp)cv-cE~QI@$X%u7BX`7
z<D$r=a4BbgGrv#Yes6k*^CVm!*&N%A0VxnP?p}G8$hv)eV0xfgIw9Zfrokm_o%ltL
zgz~0r_`(3Axh?jQtBkd!`3fL}uVRdf^!Y75{b2b!e2hQ_=<A8Mp}Z)7rmKE3j6gF8
zVj(Z|Gs2u;dJa&FZvP`{UaD-NuL9n5Iek9@Ey^bHBM~3n-3cz358BWT<7R>0|Ej%=
zGfiJm-cWAE>%t+gt1Z%mNMfyH1$Ofgham=vJ_b6)`~SCVxBu<hbT}EtqKCwg-PpYx
z1=gh(;8zp>J}Ew}rKM|Q;l*6?@Ks!a;;o8me-wX?+3|{g%%SAy7hs)EwD|-Himmt;
zkC8o#&m;H2ZQU_Q1!lR&)ie^Z&{)CpN7bmtuFsb*kGukxt0&B5*^5=YZ{>;g3Vb9}
zfB&ptl2acpJRrVPyTPCS%K@L+bv4j7cf=|0l6ZqmHR6~!DxMhbkZYLft=M0uM>hux
za$a+-O)PugDm^FYVQPR48h<UT@iSVM|BMtu?=Ao}2J=A94m*HY(4_5smz4jAQ1}vD
z9%zCeIiRP|o?b8m7!`o@NbSc&ED-X_8EF$s68o0TUFrX`7(yt}<vmHAI2GjIEiSWm
zc{o|zqd)Gv|61dSi&Zhqe#v-Q@&&~ua%{4Bu*DWM?O{67twlmf$if539&WAXg-vut
z{MD;&k$VVv1@ue`CVPpnyj^?-=95CwJ27cm|KyrkK1gg8{P6Chv}f8OIVmqKD>%}-
z@$SARPH-){d19=6(DE|NU7!$AHWPFUw=r7o2wLp8E^)hpNuCaDFfo{X(I5O)!AXnO
zfFw<Zm6@u6=;nxTCVV(9zF}i@(oiILhRlNsKsO-^_6=f#BCY@b5uxnB|4xfHIWk(f
z|7h|9k&fEXUe^7bd^bs#Aj_uVsCS&5f}}I#ZM9*Hm>`9g1+ivyTa7&zMd#sVF+Zz)
z7C?jV^oi~%m-<ibQn%0ngMQTeXzj+@svXVO@U;2y9DEdv>wD<6Y1=mW4{`wALZS&h
zIpe(O+#=#NjN9ZLuf6;yJ9<n3K^%Ig${y1&{{Y+}aL38=_$a*N;?I)aHxqTWP!iev
z?c#itclhRO!m=?xqsV1~wmk(T*rvNqZhT-)<bRRXkpXen!Vx>0x=1$O-NC8pVJUpn
zvgPCA%;vaofZ}ar_AdzlY5yew!qsqtG%R#=USSenMD?FbRd>SsuhzarxN2Iw{pz6F
z%HC45{gak69bQ}JOGhk-L~P0A+JF0VJ1Re+LZxN&_2P+l4z}}BB1I!)2bum!ti5g;
z@Pz9eG+~^9?|Xn4mK6`uoGYX95O-aU0-0r!o!ri^aYlf>O#`>aJo2Mxf6Yu^jL7AS
zr#j}fN%?t)NP622^=F7?ni~}~6fx<Um#h2#59!G~{SSF)%l6DT67GLjjVx`Q1Y}AN
zc#T*|kHI2W<4jC-iyG|oY$3yapvk`&m&;b!n5+>3OQb3gROl<oSQw-Ln5V@S%TnPr
zxGv?p?;^YA>^Cy$44j~2dwr@6^;95f{N;LZBgSDhm|L;J=d2*O{uWTh*DG^65wCxQ
z`tEJ}$8zmz&1&5${n~j)A;)&ghNB%IZQ=g*!}F&+k%zR;?u0=mLws)zI3N0o{AvE9
za_Z39&>JhPP~5G%2LmUEu2Eg_A$OnYT}v>B%<0Fd`4nhFJ5+f6bgDle=<z3!aQ$&k
z2M<a2#jRGTfZy9gghfAVohs>)rLptAu910SS^PsoZgq4itWb)f)c-g_?o>TgVHU(q
z1%R1d2=8*mz9D-3VS!9nav=B9W+s!IwhJ$+3Hud^*tRnz69cs39pM<8>)#kxJ{;sN
zm_YS^gk3H`sfW)|eDE5XR!n%J_&}k8)bx)Ntq^Yv_bF2R)rz5Qa3PrjrC)<^I*lZn
z^kTEp0IyFKhgQyzSP<U;A#R;_9w8SmRm7Rr6P(sVl_|`Ps9G=#boSlUAO4ds@@T+3
zVye7Zm~q0VLv$>yXY=Bff!Zi?kER^ZsVF6{SHiY$MEjKM+UwRz=%**y_>T`MWoLx%
z%Q<0By`+t_%dWl>MiZ*5AG$v?*eu746wY|<KJn_3T?oIXs7N%2;qKzbGi&F!y9#U;
zOMOYtVBXxbh+pdq^_;}k{=!_hDz=W>+s2!a9kRC#Qj3{f+zJxd<qcMbhhZ7Uz6w3c
z7#Whf{3kR?X}#Z{&!zKe-NQ7`#a5lXQcbuyyTxuYZEP3|C&VSEhdlD<k5t030XON#
z96cvD$A|E~UrM!YIGe~Kj3g>;{2P1_DR23t#@#JiF)%vtSYb0R&)6%Ckb1rx%Vb;Y
zW0HUHn$P!*n*ia6=rj2ru`D9dAk!?H2JS-i#^H?zgwsuQ_bD;D{a8D5*B++k7Cnh1
zp~;-b(f&U!vRoZ6Giyed>-+mIqp?-b>mJC<GP^CB5(3YaWEeNo^UHms<II@Oso%-F
zYiPrnz6(&t9Kw8u_?ld(rY~1J<~mv_7(av=u;k9cpE*HsPD~0?^i`RP!TeLhkEiI$
zm7?S>PBDJ7Au>mtuhwtA0Mz;_F6iaG>qgi`zsa}>q_RSr)mhTGrpULF--`ivX#L|O
z-GXAx&z^vJB?tIGJhumFT9o|f8N9hSocunI2R&E}r!`agoXg%dpEA2RjjHabbIuZm
zH7*o<8dL2`+C{H_;G+QHDJ;`QizjQ1(7E+uv%CS<yG7_f{;pdN&fnz{Vhrq=B)o1V
zaRm4m=!7GD7a?uD8cb%aIs{M@XttG!)WA(Jr;LA^cZPpElWEbamQh=IA*mAigLRzG
zZyMipolE|uJM69lO>Zs8_g0ozkT;KH96mp(xC!Wu@GajJ!ru6eWB`q4No#<KScqd}
zL5b4~`X;dX&no>cZ#E4cv-%VQo;y_lg+Dl04AS6d?`Rwk`;C8LXGwBy28;(awiwO;
z!S?_GTX3UZnrJY+=o_8wz99k0V1EWZ4>C<lEbGQs{w3KJMqN+N3+Ijgh%lOb3;!9F
z`C1Syd=sPe9_bO{#ItHATC6NfK}N9YYvOd>USurHDREKBBSZ*&Bk(79WA!ion!*)B
z8|)r1U)SwZh>oa-LCKFgax-urg$R6g#U$q>l$Uh-qk5SA>+RYbwJJjuum3EZy}>E9
z=t8~=s@8S%H?>^}*6J}t-LLvj`EV$e@)NS-(>eEZ{`89Xdxe~1j-$^X-6Wc29(b^%
zzT7?aK3;A_BaolAu5|b$V=v;JM=uo>8PY872wHjwH(#U=@enZW4aCI{NdTFeFD{0I
z9xaZQPDi`{9)i?n+UOIr8uANf4y8qXHm>8PV8EZ70eDK%Ps*e|Qn@7yF6P-L7rrlX
z7mF_N<>zlXDQ&f8GLp(8m0XrF9k^aQTEj4Zxze5$GM+sB;Ot*-HW%|(Z1Ff>r3V1i
zU{u1p$&hqcn=8}hfTv!gb71S$X2yG7J8me;4@yWqcoHlM6@Y}lWo?cT=XS#JlYo*#
zXK+p?Qzh3{P#RDH*pehop%P)!2r~9N<xoOMB)7Al2;W@T2|O|g-h`x5MlncE>x`Dl
zU82m9WNoni!F+Qi?9P=Ix0ESR+i2=<!>2o6os)2UgFN6%D;sER_CH<#$$|PU`~36g
zqL4F+cwDBms#338M0p#Yl$LaBXQI>P#o^e?vlsR_86L%w8c}lfoG^oa3M+d-H=R#P
zBLOkQ$g9nqr@<)Lmp|8mtkE)e8uN*CXFsOY`JJOxWG=Mw6R13^WpEEsso4+bqm@6T
zj*o=CZe3{jLC$65Oy!Xt#J=&$2&)J<H!fB3_x*VXjpVdk;^gXvFeaSRg9Y8+cWc~I
zq9As-yq5RDlvWRf;t5C$uslPaJZ_wbpcs5OkHpKUAS7~3RFH4GmQAIN6iFBN`so@t
zfnr4hL6Yv)pK8tPL*WUC=9a~sz+K$g3EL0Y^+*mKMPoc03l(W=vJ&`3RY*xW$)Ny`
zUxe(BUMo^!SwIZgCA_NJUv@UeZYH{4kn>O!*6|ongv_A7QjCH<?4tr+sd~H&P>?zT
z=3IPeiuSXnjsVH6q?P{0>uP+G;ln0t60*dh?zQv5P?8@ay@+jgDcW8f>%+Zxxya%1
z(l4n0eqCv-*>?vTV)u8`JL(0e%YS_MCTw^f{*E<`F4=0E>C3N4a|kX5$SA%fxvqU5
zYSaoeVn88BOVU`#t`-gf4BPbmxx9@Z06I~}Hk|+PYgahJ^OBv<>m&m#jumU!M`a|R
z124r{O90ck^0(S-!~o=Vl3+W;B9u+cK-4bY@)jJ(WbyuiLFh|*bFT=(3%NhILJbbI
z==|UJ<KG6$f9H<gxp9jq1a&Sfw4!F?cDl%)jh4;X>tn7abf80#222)q_W~2-=HlSl
zBP{2`BjV&iWZ<yr__mS3!TYS<UkA>DhCE1}Qj+5nGFLjmF9I-VzuVT(^i94a`zcc3
z$>wV{fzr-!?|aQ98@7bskgQbfX$13lSSA=7LhFy?VePhQYk&CnDpHSiEuCet^~Q#G
zzeOV`lT-TIr~`E1>oJ;}kkCCwNxs*T6jZW5yx~uY>H5aCg*Ygj-tf8hrT_WCzu9j9
zmyp1h`BEq;XijJ~{^BcB?Ys5*N?i^Mqga0;rU;ic8rbE|Fo#B*<k9In9+X1NKv70w
zLM&f5ESY|hkrrv%*q(pH?dS~>s4v00hvCd8nD46N2~d#bDui>10R4gH?Sgm{X(MtE
zKdDfa0-&TQy!g6OMX^+xU$|-kp<DET)AJP$<~3`}rk~vdgv<}eiD_gQaLjU3kUy<w
zUeE|s)q|HO-JV%2z~S<vC<&PQ`DqBS>Ey&UWDi9I(3i4*Y_jGhW2}ZLjDx%#pekmS
zeS=|(Zw|3QgPU9|u;8^7A2MDzQUD5Wz1k*c`+AaCTa>x0_{t~G(KQ(U)E^obHv{>`
zJKMcp-WkK54Zq!Xs_3?0Qzx(Zc9GtHKb*5G2iwzIOeGl@g(ItmkF|!>)L-(f$0r%{
zS1b<~3PLT=D%IB+;J`_{Ew6-=QXAEBGqp}zq2b*GMl%G_#Bi6jiDtV1%ptx{@X<8H
z3Z8E@vyTRU%Lv}OP~Pg3^AuCZhAC%V2Seh(OO}T?$}2tmI5yBv^ay>_cPA&{)9)|g
zV7KUIr$(g2DB%!%Kgp;`<<$)}qe&E_gW_4X%kvI2Krh_(5zXeR@ijW<qnD9a5J!W?
z2zFIhu#)n$BLECXfv?nf-^|)sQJ@K#LC_Ez==T0Juf@D>6;k{VWY`^&CI0DcW%sXu
zrQHIJNLo6sg61N^Z;jUvG$ct8_~su~@tn;+_1z3hMx&k4;eZ8kRjm&8e={S^q3B?!
z%9+QS9|UY$kt3;~sK_?sXAce$BSt~9`ix0adzl%G{K(m<OU?Oc@Z_B~Dhi4GHl$#?
zlDo{}s&eY`kyT6)e|$RJm_t{rtm6A`Sw_tQiJs?)=X@W%l#dG}XHrb3x-og4zANz)
z#>iER*GT*BG-+P01a$wnX|{|5)#6fE>0=dlxa<OH`_9Pj1Jk_-bKjA8eQuZk#$h6y
z=YKV%$+b@G|B1zPQEJ<4@diMH)${J}3?**inWD5C0xgytaUgORswmzq4FqoxA8%{?
z*J;@V<JEEb6je6go*bP!y&?sCZNI{KA_magCfL8i*)_g>t+XH+7ib>Mm=k*?JJwI&
zfYtkQek(}kMr~cSe#iZ%5V;^OB4~=p(U}^rT=Ajb<CkTFt(HgLv>~CzZ08>*a&5F%
zFK#om*R_fvZ@_|-7~@gI$#Pmb%nU17k=C9@?}IHJFz8fJmVa-Ptd$ehwdc9Rgw#U~
zbU)uwd?rHYUve8?OE0XH?r_yzS39I7AtCyhv67hWoRIh?csGus|9s?jPDgbMh^{1k
z>9C${=?1(MgCEg!VMuX;9^*ee1t*nYpO0Giy)xkYm8+CI2<5Itr*Q5KMFx)d%n=3y
zRPqdmK~Qxx@{BCNw#6Yg@|6d@)DNLA?hak~ZWleou#QoD>@+UU6Y)NR=O=N^xCr4G
zOC%Z0k&W8WfY<%KV#F2wxcOA)pVijj>xpzb>3+A+efE28*E4h};z61GbldLj8=Vw5
z*lK{UECIYgNm85Ax%Tf*+lWb!V<ukk4Jc%a+_Y-dd%o!yyWK8LJI*HG>22(e#~u28
zb4>6#0B`Ez@61Z#$zR{@q*m5pZ9`%be5Ak`)%U`T6SuM#sD1B3urv@nH~x@2k>G`#
zg@1&o5wPDYj4TO8f-_Qiy>&X<ZPU-mHoo7+xegcQ*#4Q45W85>(2@uSZQnnwb$V{2
zOQWC`0_qtZVDNNQ)T^V{k(8NU6vSj#H4o=N%e66O@s>)k3$DK}H_X^b_0qeNtpt#r
z4CD#s4cZ7y(~3#)ObIqHP5fwmH7*cF12$Xw(i8Dz41oGbeQO2b=1ebllrSTRT`0nh
zTx0VgU);9YHk0a%z}$#EU(_z05tL72A%-kFXCUife~485o+>?N*;VE`#&fouW(22^
z!|)~jtY1wCiiTK*rY@|O$|B6g(W0w!yPpkENS~*TWk~^G`PsX^(m=eB>zav`Z_mem
zsn|kE<6>E9mpo~ndMx{n)J4@7X&bC!Z+e#(`qGb2rz;hBP4SvQV&Z2lL24J_vQ~9k
z-y3&!PrlLZJMhM09CEgPJf%^_cVQJ<o|g5){0xc5=Vs#KGJfqu-t(*wZ~DUcm_uRv
z{G^^3{AUghKT*x0J1Q%8o3M9DtRbn^-X@r4q!p7TN0-Y798}RCaKzC_G$3f7wIV-Z
zwRPiRGE^-%rhj0j9vkq;|9#u0(Cs_!<j2h4NuaPgt>~3zs7BHT&ST>gDwEva^+JGe
zziDx%|0NSJKx>w#h`=Y{U`PUPa1q*K<nMf}kxfE(W%3u8#*jN{=Wx@1iXy3>XBixJ
zWq;helI4b@HJjb!(q3Or>%K#erDuv@&;ygqiqyClIpc7%D$ly;&+<H_F0VO0D#ahv
zISua6D@OP_e}eye(BNs(bfSIU-80G9db*N&ywJ<bsrI8Ts^=3k-W_(1jQr?dD9edC
z=TUVfTXRK9&ffb~L~)capK$P`{vlV!6U*a}eDrn{q;|lb8~Ne8wpWS(*=(YUYeGEV
z&EOG5!1gstYwOR=ATp=IAnv-7>T#pKtM7-zHU5Z68hV*8ovPt8pFDQhuo>J<eOJ<!
zTDZ6-7%`CGXm@r<FN!Hy*0plyYwW|~D+P@@mYE&bl6;hoXq|3K@3!bcn|y~)%9$B<
zG^wnS6HjWvc%f3oS#In&*S~NUR)K<7(!!yYNZ4wNc{LCHq*!Z9a7%6xVu%r0r(x*~
zam)@33+po-hHWh^96Q|QP6sX=v3Yz<p*Zs;KkCGvZB^t_R+UR!rRgaN@NL^s>d`oV
z3A_%A+Aldmmvpz!MSta;#aFv?ANai0ny`PyL=R2OR7<2(WC551f7w+saZs=<uB!Pd
z?XocPyn5b5Zw}CexCnN+-k3@tpJ$vF%#=lQ(Dwpco5rYVZI6Mxn&LAyv(^W_DvGqA
z1Ss-A^#`z@+4Eq~`lT2KlF5>kRZYJ`Zu*Dv-{kFumFhg`?6STpGpL&-(Y9{`&MF3;
zz(U}+MDH|5XJU!mgvMJg>f{)`lk~~@h`kNO+4UUvg^If*kWBQm%z1d?!26+F2pxz$
z5^QpCbvl&PPry>+!}we**uH=0+mO#j+QpX_-NMnj78m6vyH9<rW`ay#&nzkU`2V^)
zH*`vBG0T;+y1sDYHXMc|0f=snJ+ftRWg`r{Lp`tO-aQgBN_NWQhhpFl%oc4w#DL}e
z5K(Bu_8BF~w*4XBPyo0!LP(8R?HupwKWNs=Cf9?_MQwh1=QS<44wDyvb44rb<@r9<
zG?lINGEEM+v_@D?N_XBjEWirBu09FX?wJu9WjUTClNy~>e)n+wRh+{S#@5;(W0ulc
zAPfuYFIK90oa%6~85CjC3rRr*Otknj^5>BH5$*T6e=GiC=x5UvzY9#UHUcg(q)_}X
zRi(3A)~KfK@;%#WB4QRYy4Cy=4#kmySu&+s*bI^zn(EY&etlPuN7v6`Eadzyipk5b
zRmf*uK6H6T)i2trTmm_L<K4k=Y1oPyv5?D#vE<e(jF=;bmE_f(RPY)-r<~vu6`FbE
zVULv$x%#AG?v!f;=I=~wK#d7KJw|4QEjps?Ertxj7W$Ult@I!azmN>;2alyWxu=)Z
zA1L`KnC}YLJpCTrmW$T>{v+}Gds-b{UD9*fOd+GV9xZFX7{)j?kMH-AKOaCvjd$O$
zK__q`Fv>#kIx!*24H_iVS>~)vZM@`-9W;3@YmWv`LTLX48cIKlRWRpJ^{od;5}u4E
z#B;yFUjDa0GrfGOK0%3g8XMCSZ8^UXOEqNEicboM69~k$`$lhT0O04j$wA1K@Y>kD
zKCv%zOKXD!aD%~WR(ZgjIZ@3(-^5PHin7U~D!r4Uny)uIUc`Ac6&FRtk~<g|MCrFs
zF4G^oy~Gz0{UzD~%`h{}w591mWmyhc)G3NRAxR4$^KR?U<dxLHfv83R|DuA%z%mF~
zk@c$^{*3JUq_JSEoR&Pc-YLu|`jveI4&F@d_kHcmJsLn|RkT1N)FGE8aaWTk%TxJc
zVe%Uj(Zp|Nb=I(5Q7O;<zt;g~uO5;7@cr;Ki?(lZi`o2~OktBam49A7AlcYhxN+V@
z0_yGTd;x^oNm0M+>mMc&q^X1ZgqVBMoc9?ZTXG(-mh7EVd+f9IrHJ2w{86wLxIH_2
z)9<O4FF<2z7xooq#))IT-yOWF##p~&{0KsS@<<8auY%Ji5k-J2zgv4kG3@!l_kON3
z_A8JG8|}+D51!%j!#HNt5*32sCM-(iUwqK9&bD47EfBX}QP9`VRW*z?be)VTzDu<`
zze9q3{Sy`(g+7$e#`4A<4T;?LHC}mhk8CiSSyec&5QZ3%=pH|iQ4{zFN)yLMbw<qH
zxS<7OFQY!1ZU}22KJ!0<xOWCtl#Ps**J3rIWe*Jgv!dgoYLfXWlg~m3Ag0^<YVfHA
zc8GMSr|-v4nbz)vAtmllu#Tq7UNG|Zz6er3UZ5lnwugB9*#jk{qDk%9DL!b)UJ$Dk
zbu-<t>h4&k7woK8P)2M7F=Qc2gjrA)co*ssYQzfua?Pkx@>h~aB|!w8t@UId4E$m!
z4IlSk&y5<0Vu(hb>xId#;bmIl`i4t@3TM}q<-MiZTi?8M1~u)H7revg!lvU`ucg!~
zdoU=hnpfBUt2ti5^j+oW^jdi5Au5;OXG96Q^P08G@7|_xXS(w__XHHT;5bW_$>7SV
z)<9N39v;#=k~k(LER*;4dk_EQ8AvgO+NNHS(YKA3mZnaU|0U224_&*OqeJ;2aw#W?
z2>n=r3=01?LH+i{EVPlLC<X(xg)#K@(E+(<6Z4VeYo(8)AZjJdA5#o&QjV_R%+Hp%
zls4(WS%15Cs+CG=Ghy!hb+|j2sB}VkP2nuC@(XcB89u%Ua*v6IIaEU?IDd_<z<T=2
zHyp01!t<~_sSiu(YU-k-B%NJ4;#AvcpBrexRIz<`0*}LCBZfw}5pzjPGOKzNS_3uD
zsIj&-y7>Hhz#MXgzP+D4E~!k7R`s$(g&(gd$fqi6H(YvD+?GClTVM2fqpLd)p9i+P
z<qCX<uUShXW8v7yq(5gp*b8RfzIyKaW!##xG(&4{#m2aZoph2(GU8;VZCdFqSaZ1~
z=eCf-=U~)p|BcK~S`%pzA?|HucnN3~sDs`iO&+^pYp8^2h!Fd`xOm3?V+raeO7*;?
zPf@<zj437Gs|+p{G#WG-c7IB0GpMMr!J|40*sp&G{?(cH)Az*BW)NLd(7rja#HQJZ
ze8?v@E92|Brb>d=KP0iZ7JaCradhLOL`Pm0+-rh)xnY8^UEdZhJeg~y-xtsKr@Pl9
z#7vU08UvW3{8CPhfQ-FgF9{9x;ECzeq5^Ne3b5~1b35{0cf@8cIecNeuEO>G&SMIr
zTlM_&&+N7#k>P^Xvj^!0<HwZ`Em8rPG=&UA|0DlwB<s@XL58u8<}K@pvKZSvf61FK
z+6zj(b-O11G<+$EA<09|Nn~!G&wppY#k+)OsEUIF!G=bHuTh1}G%t~B`pjppJ%Ugb
znfVQ6?5!#V?Z1pB*+k-_I1q@K$ippX>A$G1v7Ghv*AeG@X(cx=cX+_d=HmPo(bVAs
zsUv~)zVe&eo#zycF$4VZNEjeXYpK4Bz#Yj2NnSk?-qJnh3(|qLkLB(P8_AWL1->z8
zvb;M7HPe1(H-IeV_Ffzph-iU~aVyT2X43w(VpW@D>PmS6+|~O}-B2clGnJwHKszt`
zNfM9|E=mVt2cpd!!Wf2~3W8`#JD7~m>@vp$YG`QT-(^FY!{X(s`dVvxLs33*GqA!h
zwj#Vt@yle@<)5^*MPKtH)FVZ2CT_<UKiD|DbSav7-W!n^A1x+KD$q6?jvq1~xBRZG
z385h$5e*V;zL*`LH}nNKme>9PR;O}LvUP{%u+$W26eL%k)POi;zCqq>W<CB)&3J#Y
zdJ!Z;fH%to|4t<6G-K?6eo+7wI4neJ{EtE&hi^5WYBJw6t8wII;mn<o2KFq3@EYFi
zYE;#!9>0{S2ltg7kdO@yvShR1wSUcyK!!FU_t*!s^@P-{N`qED3=iioSZ$LimPU%C
z;kRm~LDiX!Sg+ZKAsIN!d?p<MjKCfF!NRFv2aLHkdd;OFBWF<P*P&rY4=v?no$*Y4
zYX>{6Re5c}fYQB_u(}@;;jv^*f8T{fNu3H#!Br1vP{;~ZCzVCR927UoqRkWz=tL8B
z{_^2&_-WL}=U0FIN8Kl|P+aM>W6u)#<}t7t^Ub(@8t;AsZ!9n$^P|gC`r%B+jjZyy
zB+`7DfBB7bE0BrCZM6Mq#aFmA2i|xqQT@)TEuIUl1m4RJ*M>C1Qa*J9c&MWNt-fZM
zdqpwhAfxrDm}IgHvhU(GsPz^~p6MtsbK>!2$l4E=+utaTuiZSSiqj?uv>y*8mxbXY
zO<(>eEw;<cavNqURO^<Q@Q7S%XE3^aGdX3`4YM(dOfXxEE2dzAt7HGH?77zLwr)y@
zEo8paqw;+AR5+`XQbK42UTC7><$;lll9HYm>R9vKL~^f;M<2v~y=Fkm<<GyEh?d3{
zzNVV5A(6xhR0V;-L&Ih_y#{m>s*CEcp~WSxjDY5You4R``o*S#c4-O$B-fj!dxjvO
z8M3j`2b3`LirkI5&uXu2qNvl-uz4y;v+iS#&}f8lKB^!B1(;5(+u<k1*nS3}eFL=q
z1_yb}V+wkhu}z(dk7y&N%o?DQ22icj*WkqfSuOQT4y|q$S(yF{3wFxh4X5{C=rKN#
z`R;0eFdR<FH-s(=rzWvl0X#5&(@UJaa}s&n#O8sVnB6OE+Lrw=XMb8-y$>dGx|kV7
z_8CH%lh0n9Wx|}3CubRK!jDom&&I$(8WO+sWFviu`jQmJD|=2JjzFXl%E|?bkl!ma
zn^|Usg&8Y%&0FIS9YIfyWz(xt-Rs#H6$OdaDL?BHq}Dj3Dq#$C%)EK1sQGEjbn!}@
zC5SX%;MjfYJtnU?JB3S>Y!E9$dA9;qOF@KY6)R;QgF~6in~=|s6Ayq53^*JX77YI{
zTynjBA-N@`EykVa#45RbXJA#@{Hd^5^;Xk5siv|}<U`PvH8S~OD+P@^ITc&0E!d)L
zdK4R}?*Z%)h>9*<PySv^9{H_#7T?&^fT%b0m`(v9ICNX)oRIB&LNoSz6v-Wzf;BP$
z)~E_&OPIN`;VZr@1?xP*WL4vwFg)xzxGst|Fr0XNq`PO6j3qp*FqO&{3x_)ME3ZFL
zD={p;(cT##I+!+LUtxKgc|@^fFLvGh9zZ}rO++y`a0!wh-fW9mRUD==dj9Q_w<{_>
zpY(rTssnzqqgO3zxr}(l0yqQI4Z5sNLwLfw>PFJ;yJN*6K3r*MeJ3APk;^=NYg_O7
z`}ZtgsdHbn2P9prNWkoDYz?j|i8IUKw@<#F`so4v^nHq3!CIU+1%1qY()&veQ8uaN
zCG&DL9g<nSys)L*{g;K@;?G?*pK(u;uX@|<AGUDx0OW1q938eZb^@UVRzcip(-lED
zzk`LleXPmTxgNN+nwJD81yJ-B_|!a&G$-eJ3`VhdW<^VNydF*e(;8Ei`e{!QhWN1N
z*u~!D6)x}Ge?D;RL$V{KeKm<Dub^6CO^%lME!}(~h8YWMisocjZCWacif1eNOTtEK
z1~|@vVbOK6qJgP-;`V4-17x^;wd>M{!WCJO{!#c@^WPI|4F^PEF)_b&aDzN*Rwt$3
zP-u4G@_bxMa;P)W`FKLe3i?9KbJ@i@ZrGdg0d>hcBUp^5H^4@_Q@a{Ys8@Hw7hE*4
zbiO@}1#a2;FKGeW(A}bm2hu7?L$f}y`oHK#PAtOqcj#Er1swd#>U4clB!N8%a(7B1
zCf{MS;$cU%y^S`kJp;8OU76Zj{PH%!t>QgH;4OE=u#`j$p8Q~t8krRx5aaQ2H$Co}
z%(`IduQSyrVfwRsiSo4vN3GL|6U{Q{TaN3LRN*0nQFQ9jdzX8c(t50Jmo(dx)hV$Q
zo9|JIOcaeG*t0jMLTa9Rm_3Bt(2A-5CC7pBba*EIkNhSSkLtq;rGTKTZGP)T@w14#
z-@^UrW$sJ5w=m^3^MBpGuP<3^Ey!inmpC|NG2jN6P20Nf#Vf2WqLt(K4AHpAcYU1i
zotg-JlWS(pJ1CTwZ|9^cGc;yz8r_0fUI(odB*7aCj(#EMEG&^!U<M6A(h2k_jtK|A
zlt=<bjmD)N$^GA*KKkvOrgg(MKM-$ker4QfGj8kz637EGoUbAWX1-Cvk;FB!iJ5s0
z+7NSGSgLZri*}2uGtnPM!~hKubyBfKw^oO);na$?ySs&hJNC|6w>8%(U%kXMoNe=5
z+hX~CS1Xu!VyW|TY}>gcZ-%`8|G0M4na;xKtZ%^0ya9mxr&Sb5BphTJR3F4f1V!1I
zGgBAc6?LPvFgGMJ#LBQW*)Z7e?F%a~6;%v~4tev}VALcyCHv+T!Zdo{=BTvK2fzsz
ze2V`6F~7&$Ku!?0rdg;wMY!&*8BdXZ>OZZc0uC^f_rQG{VM#wqWVOTL<EzMbV?CFk
zap8w7^PlRR&1g}7Gt_ynnO~f%9-YL{8>&aKC}AxA5*@fN_@e*%1M+Pi?}+%LxhrF%
zA$%Z+2bsbtHplWWo{K_&U{CAUm~+3&K|UO3<S7ck0dpn-;t(^@n&5QqQ(I775`!Ik
z*vHPv&68%8i(4fksy{$!1yt>Y-D^dMKN~%>q89D`CyFz$M%_DYHi+r}TUCo}xesgp
zReSY7z|cvJ)zDAif3c}=Fh*)Fyxu`@f&+3xc;>%SRm%gd8qF&AFgyI~*-hT*p7|4V
zh;;UubvfwGQ~V6!gl=hg?w(hp531IRmR@^np|#Szl!#fT&X1amW}MeO<RF6elmwK0
z6Eq+8%kCaq3(7f_U`1KT)vj9~N*y)enVjYMEosn0hL#0>?O~7uvv{*Hb`hmAt3W^m
zzO&Kga1h9v!bE(AF1BZ!USXkYvnBxmV7=2ej-u4Gu{9M0H17YVJ7ndVS?&!A3YusR
zI7(`ES%b4ngPU1GKRg+rs*oW9#3aq*0G->rUiOS@^S?s(z2dwZj^u<0kPO_z6{KVA
z374y-SB-9-PwMdY6Xuiu+qt2jRVrdY-!fIT#&cN+Y1T=oB&&$5*JKs?g2GrZTB9da
zXgK>NYVm6AaT}M6MIVs*Sm`u1PG7EW^>~5*oXKg?v=ZkP$%jKuspQ;^;d``z;v<&f
zh-8NlGRLfPZ4;Bd+z<h4P`_B9If+%Tt?tz$+$;NKPd?gWUp?6NqCPUsFa}Bef;eTW
z^QXl7$&h`$uY}*k7_+xt{;;gqRZkV`00=0S-(;(Buv`=V{VC_uxA<MriIPUR{d6gE
zBE%lLCJ5z*jQ*+>PH4%+Y=N_krSX$%p-=qB4kL<?vmtkUr%+y{XPzo!U;JA+hztUr
zC`KTC8@zj^Q-G%J|8%b?Xw|YBAn4v~7F1*2SaY2svF(6+R0)+;#hG(K@+7nPlEHV%
zRCn`k(iv(__k_GXQ~>{xQIjJ)9BkjANWNw%Pb~pjG|Q(~kC%m?dxBX3FMqX7Hi<Dm
zAoKC%I?~u#Lh$M*oBIA#F$&jMD)oG4pVpRij^t>TZ<UYSSM&1kmju-0yKO96P`$^0
zeEJ_Rz~|<coWQ6KG{HQ?bS1{Nt|jA4zrsqdEs0mNJqALEQoOp}F@Fgfu(AU39(jly
zTz+)bO>SQ_bf0m5#S_IZjn_B9McFPwNK|@W|L#vU*!@f?infmQNClNB7CDZyT+H&7
z@SXji#)y7JS0WOL99M*ZN)FxLKs3FY2>WEOGzUq{l(*%o`wpwk-gQOOFE?|yOAm?g
z!B_rF8RDx0f;dygBFUW;2wg)*&ApVP2Xg$2Q^^BbpyDq-Yf0ps`2T3w=`3}-V4!}E
zsrrQX6^zs<zq(bYrgu(m>Qd#EC?b1(*#`h8_{*k!j&?QC@7}xsdvDm_d8nPkVL^=v
zCC@(m-B1VWi@)aR8TC`}^nZl)UJ;9-`{BB~-oi!7>CiOJbj~})TiDTCZo*IWv6zoc
z@kRk8?rwXXBFHd=tyeCF)yPHv`%SSyE?-y88NiTVstMH}{O6VwAK)hu_8h{RAYTIW
zyCobc-$|$^U~VUG20l-@3{Buuja6ZIsk1!ZfJ);!c(s_&?PZo%yP;NyH)xgx)w-8i
zb=yjnZelII6<-Y4freaaNS?FK`j~QEy+nY%P)G*cN=l_aY_9qE@JAt&Kl*5-y`)G3
zIQv&Jvq(>@Q%@Pp0>3yXeZqzt=LUfzGW+1&zdnkA;=nap)<Q#V8&d+Tsv=y}@Bd4%
z8ShW+!jvLfCh$MoG={BlK{+7%U^-+sqvATy+P5?xm04RjFk!nt_^8Q37DOxBmz>)r
zVc62;{Dfc}MYDLF7Z1ycPsfR(4iCouK`P2(h=DU7Kt$JhNuEHFeTBes=I3KXoAxio
zYXJO}ZLfuPvWh@rqaRnyr;4K9Hg|<Zg>4ntR7J32;9#RI!a;C%{Rh9ZLwU0UhLMV@
z&Rs{BBQC2~6J#heGHQ0j2h5R<n9K0#e{+7r@Zs%Z`EmrSK0<K&kd94xR0dgenwAk<
zL9wV?77@M;qBKOW!&6Xs9gi5GNB$b75hnA+!il;8H_OZct^o#_(UktbUeWPtS<uCT
z98JmAsXE;y2W>wI)@;=lu`)WLO(Nl_ZSF$6#KUn|K_S4$n<9ee)=Oq8K9JW~J8hMW
zi{{?PxJ`lZcwxTDl0OM%8*KYjD~)|-5yG@Z{xkPD8EL?g_|u*M7w36B8K_^cBxb*!
zqZt^9-_;PX2rJzGudQOcn`gl>!?C?)+IZ4YUVYN-#+)20tCb>Mh|+(U608#z$#SHI
z$jXSh>R7z&@6t6{#LOfv%?`imN|h8L06tc&oaBdgalx8PCzA`Dn}~%M#KLSJqa}Hs
z635{jOQw(wkLl8MXnmpK8v6`l)8m9Vf$Ac>Ya4yHvD;su|NQtQXX&A2LWC{jSVQy)
zQk4;*k5fO<{%lVFo5E~&pO6jGn^$gNBT;3qBT}b7qlM)>6QnUm)lhYk--*8xCvSE6
zM;RZ*E(RnU6LrTQf$vvnDc~TOd-YAmMEKG_d2VB8xZ|Xv?w=Mx7-cU?TiWMO8a5qS
z)al(6B=ttnrZzhF>g&e?h7$O7c_l_Y%%*TquZ2$&-iaHyWnkI#I>Nlkn%~S=Y}<HT
zn4(GTo;t0?M!N;ac@F$$FReEC*H#WjvTt5p#NiEdB-VHo;N>UxPhFF~D>`(6+RHz+
z)8lmw%Q%Sx^E04&!$Cgig8)X#ug~DNCbUKHpclvQhf+tTCq2FQdJ7He2klQ^<OHUt
z+fV=`_Y#!t$qd>T(jst^FdS8^xw7y4aAyR@%~GmGt&{PH2%Zna?}4PXhZ<|!Bt-0-
zlDmujnhbqA8mYF!0CVp$!J~GC_8=bPC~O{L*;N0Us<)qab(n`2%*62Cbp9{?7;sas
z>zaK|G%FdoJJ-ESnsk6N$XgY8f{!m=KZR|sS?cUn2&b;7t<l#X!OzdwK77U=cQ;Q5
ztds(waf^5(h62W)2imje#@>eQ4nPbWwken_?YR}PkQ&K1<iE0()y4dP{q^~q@$^2G
zNkK%f_g6q9z}}dIkoJQ`X9~>q$-jK|Lu<W|0}%>h-x>T*W=2RzS@bt<lTC!<hKETs
z0H*5bRn<vZodu*JrYoQ-E(o!U-$WR@_E(H8>oVTZ?{=^hZtxbN>%%p<_uj@7=S<bc
zY!$p`h%JhiU<?cka%}gq-1Lcc0oxqiuk=+6kG{*BX&Dc7fn=L^5c|R}o>X5lNzhTi
zh5W0>3VQ{fnh>UY{g6}!By!AX2e<r5;#K!tKCqm-?I!DIN13bA;JIcr!T|W0y4mH)
z=pOP*u983-jMt3C2_=k$EMmGJJ}%;Fxov`CJb8a9BVNjlD!^}}hc~wUM)B))f9Cwj
z8;TwVL%7Cd*u=+b>RbdqWP{xh`e$v7<iP#WJEu1MBO5cMo8KBSC+;k9l0J_2{R;2W
zdK14ET3S4LO=I=HX4!ZxyB7TWl30p=q~P|}h<#v=<a+s1y^RqKuC{f4qhfdsNGeA6
zd_KOUL@gDRWT1b&-&=Hz0pTv{NeZ~pDAyl*d7Rex^TRVrhf@YKeiiAa82#;@yE6`v
z@7luGP;}l<qk<vnZ+Kcc8fB9FEwpZ?Hy%ZK#j8SwNryM}5vo^Zhth3%F&|>BJ$@wg
z6q@*!U+>n{UU>GBD75!feJ8^=>HtcNEeoohjN}n$Yi3!xzW(w1lOu1^XL@jlO9XyS
zf=4fUaPrC*H?td%=z}*uRP%2yP=%av+ZNIpYHFdnUIm5eLhRr@8{UATlXP!Zs7i5+
zp8@v6CblGga4;400X#N@k5oBi*wl#VibRWf5|?*-L{l7kXA0Ta_6>M#d6_l@C14Hn
zjVuy@-$qf08YsBlDGINw;N?xvHJmj1JkyHQi2oUWLEZ6;r4eZd4KHKl&)GFcgq$VF
zyX%4anw@u>KK1%xWMDGrT2WV?QWA4fdi!+q?H@Wx>{<kM+o`aCfqHARbBO3^RKd#9
z8Wuy-zPfq-I^MvK=3(RQA{a4}PJz8#4Yo?n8W~x}skc^fNm@t7no=c5Y2v`v?C9ZR
z3*6dBUa4(7rttgH<T}_y#2VPpW^7QcJ6l-FPM|cOFuSyrRm1%ef(lW#D5;Noy%mJz
zN5p5)dHM>{483I2q*LK^HBt&q;CJqkCN@XpL48K+YH%$`18*UPptj8cJHlSb{7lpC
z5jv3RkP8j$9*p4=Zw>}>l_chDdfIj1nU0-YiXEyrveDh$?DD{+5&l<OT_s+w5;^9+
zbMYEk>=4aQD~UdbOZInISS&Ip$tu^0&-hR{3y;j2$jDlsyIH)@+AgnaU;h3vwFYQi
zkc|e2(JY!4G=f~(MaBE0Z<9PbEZX}J;inh*sgpg;>HTGzaIKSW*H)XX_rp%=zEmTP
z#)|p`>-t!RWxVaXnJEgrlSv6zm)!5d(<OMzr|0cl*kc~r?GEiT4ON`{IN_hZ<=2>g
zgh+*3eC54@{y%KJbySpH+dfPqB@&VYC?F!;EubPODIuN0&<x!TA|NFq-5@0$Gc*h!
z4T2y!#7H*?3^l}e;e9{P`@X;Rxt9O9mb0(D&pys$pW8kw-s#C7?fcfkt2_|BOw$jm
z$w9a|2pi*7KCLc$qTE`XGE6Fpdm=}+>yTOQ;pLK_)-KN(>Wki6v+a@p8B+P^AzA(N
z%wss>nu?+2WXaSN8sD9xFmbf<-Tsij?C}S**N-32FoOG!$};ehCoG;n{QAsv7H1n~
zepk&@ZSO^$ja?PQz!v5n`fVzgm6MFkVI{x<;KNZ@*r?xNNjT<ZwWm$WG0<$8Oy-aB
zt9-oJe%Sv$@Rzvwt0h>j84UnuJoTh_{-MoI=T}VLvX9jd`=J9o=Njf-?ox^nJjU|*
zH~%y6rZltJrd}wnNIt(mGK<{HAhOx!UT?aH#F>44ZE4==Ymmjd@m>48%%hg?TgLQn
z?#Hl<M@1%|TU9pH@h$OSc&K7k?!UX>d1j2|N*r={4?3J|Hp0*==KVl>8joM>W91v`
z5A3grKsKYC?~IOV6Hczb?m`j8(r<s{ZnzrN3d9&sj)(fkTjsgX%~+y-zs{3m07=-0
z0=KR}3Pc|Xe(usJEy!>y#rR>|f|x&#nQdcZB_G&1>u6+yo1`VnhU7C@U(!72Q}w?x
z6^o07Z9N~fMIuWqaE*Hf8tup5<bexgsxo%Wm)_GraW_m7G<W&=iCcb?q=ed4tL}!U
zPO9F2Hy=Bsy#3OrJ1RM%FI@<g6>1|j5+(P`Twg|WnPQg|H6W}Ioh<kB=n+896Vlk2
z0zikb?>L(l(cm;Tp!A~YIRpqow@mdWVC+PCasz$2jA9ygb{@&yEr;P*kHqiu%nbEk
zXIz<Q_%M_0>0Z~hDDxd1<p|pmoqZ!}d8lMY@A2M@p3#v8_KY}oiE}4DIyN~=Ts^*i
z-2Y<_{BbYsWA>Asj~X(93gMq5(k*u%B2<7!%klKGnP%-oy_ce^^PX2wx&Cc_^v7l0
zQH1KZ*d8DEoxE|lm*^H=|B8_Vt;Wr&ztD|)v=9b*A(Z0*TCl`fHEVILl(lap&wE#4
zLuTK=mngCCb#O26Ab0<uwfVF_qs{genZCQ<!-ktPEWwG%T*<E~lvdevkz@ikp9u57
z3#iKX#FCE?22m1fqg&Jc9-N)-Q-t@?`7j4fj>Kc{lm{{2jc6@9oI#2O<UnP9%lD8j
zfdu}A1rPJBq`Z6?o<6F1szu@X`b;X3VY7jDauuT`p24}Lthw3<<5}m_Mr`B~K})br
zLNdtFYa+vT59CdPuPW06E3Gaf?drz{BI4s$52w2`Ng39l^?qTt!^?Z~3f_AOFtgM@
z+o=YIimYP4O!TiS?u@WaI7spDAM%oBBM+2uyMl<ONSueoS?rm1^HXErFe&Ef72_tJ
zw!T`J82;Q<VX3_p`YOIY!l6JvQ0uXV5`Jn*(}JXqtH@q#(W*npUvxGHcVQ_<P`6j%
zC2&K3WW0F2!i;7b7PIdCx4EGI!--3B#m4)*=Y9yaQMPC6lFJ$gW9|L8nUBrKjdbUR
z&Z&CGPFF#)citnT!B5v?QAIUstskofz0*gjP*YVHbHeHT3L-(PrmXBA`!Kgf_oh{#
zYnWAN<m<M8UWoDaP-gYOJ*?|9mU{IXZs`MGURw^SZxP=JeggtqMsn55c#sE*TVP4K
zyo*&(9pazdcN%WYH-tJzNH=?jur)fq^zr!SCAFlHo&10Y)u~PvHsTTQ@V0KbT*E}m
z=d*1S%T_#Zs}o6AjuuDvwEkcHj^VHlu9q$TRib@=0$*`{c8Z+~Ak$8tP$buY^-|wM
ztc4;RkLOKiRvzg<_P+5v#D9>Bw4=ovYpjueJ*YT%F`{QSoITW{8tHW5Qrc{!Z^RO8
z_Uz1H&aOnyP<!*~<3TYgao3*x{hLd*#?4J?A=FZ)Ua`QmPNx8g^q*by8Sum{G29h+
z99_rQ*SSmL?MtXvNAJ3w-|p|%cSp3+DqMYjt}c3HB7NgjT+Tn3Wz~464702X`ZXKL
zz)x}gwSy^7u`)%=BM4!`-}M_~iDSqLB08-e|LPUmLtUv5p1U-&n|;%IDS-ow@6$H<
z*QWn$L_YTBCH|nDmy9Q&Uu;ZEyUZmK<|?cfC%6){`03_lz;>rmjgfQ1a`a*_so-M?
zSgjo)^8w5?+m2OHexDl^^7?qzhLxS+sk>#yl99V{3(<Y*UYOHPfs6D(nB;lqDHC!t
zIdjm#b60O+Z<pzuN5`lt_((Laz@;+kgMR#~=%B{p7W(2UdEveHLb^X7T{v<5zBqIT
z+PowZj9g$5ob$E#01QJT=>oIiDQ4)qdAqq}-S|zg!J;V#LtCjWcZ8Z^^K%9Acy;L1
z_k&gF{ll4iuw(Zsw-yFDrjsV3c8pm$w#bcj3N&mcPI&+Nk<CYSaD#i=UD9m9Tg+#Q
z%pXB@8?hcDugG#V`E%lRobt`>aPWExfwR7m@%3cnRWMpd-@Khb^t*ii^wf-?qY5|p
z6|*VLy)O=(eTgs0C~@oKX+@m^#HKh|B0Ak^lhxlSfGa`?^Z14y+~Ejej^HAAcrU5y
z{k@v~$Nl0($=?>4&L?xnHVc~6Jh|uh*Oz~mNE-p;p|vN(Gq==$3G28;@3$#)wXm$F
zMiyMBo{(^dBJvi&l40W%H)-9&evzw8WqpD4ZGod)H#N{NRtH#qM@j8`9$K+C7vr^a
z=LbhEyTz$~r<#FEYz{|rrSvm3{z1(*7oCvpV^XSy6?)G<GE*775pxHQ3@0J)j7P2N
z$L_ngITfRPyqg!c)p1iM_xg^uCG?t6_ItcljqUK-wy7Qz>yg0Ye#`}1f5)}c0h7ay
z8(*cF#k!l*8Kws2yzL^(`b{CP@aL3E2flh-RLvJk`<9eZF9FUA<VMYBD&sZ!xg79^
zLuu_XQ?{6)HOwG`_qf3Mx=eCESG_NxKd{X<t67V%N7dVZ=0QyJk2eQX41_r8CFe7!
zn;jyW=58s<LsPvkg$yAHv7UJQP7BK%<x?9sL}7Vdv%`o}ud8z%QI`&CM}~{@DblBL
zU_HO39nqujHNtNZzza6+ew#fqN2{dSl-B6g&>-)YAYIAp?4$ba5yHFZn_r)|52+KN
zh^-Eqaai|8bj{`GipwaWoBi?|rEy#A5AtMOOnV}O_=M5eH_0~6Z`djOENhz}-}1FM
z)VZiU(aq|3ZaOqXhJ+co(fEv*ZMagSYcMJd$I73RZ{b;s#r3duGh1-G6$TTYDt-<8
z3hoX+dYiNlGv{W;d>`=ELN96C|7d|QcKOrDy1|&X;hCU12l$(ozO+s7o(D>Nufque
zdtEd>AQ2Cv1A)G~gSe(TpvzYedG79;l!`*E78C-f$3(b^7}2M30`8Z^97oIdTb@w&
z_-^WJ+Igb*YCP;xg(P}=7g{_GW+C+rHzwLjDgI0l?mcb0-bHuA0g>;&TbnY#dMhsd
z93A9Ihj2*!+{3jA3J)XEx{-#ftE=2AvuGNA=Dq+G>?~}b;C76`AWtlF<<b2CJdqh|
z15pg>DQicGs-~DL27(Nnxf!^`FtB0jvkO1`Dr~W?x+{Jp{{6|w3*D$!#7{y+@dg|d
zx!b`ozf{}$3AW8HQ*yKvs6-2xD_*WlK@bQ2txvdzS8X|-HPhU++H|n~h|}xzb@<zi
zeO@5J->tw#4@^D_fLXsq>NgM5$h<pyB*3~5V*J9ZePp+7&$>5R#Q6#0UhlTZl=~B^
zC_2zkFVi%NRK93?q~eg10-la91u<3v=H{4SK(MpyH4V^M{&3^Bvz*Yz_99Ffk<^mi
z$!`H_q8;-EaA!Exkq=b^!I|^{dsUTvYjGSj;`<w`z!-Y-YlFkqG-s&vD|B+CujvE!
zK!;Y<6(il#<Ks{L77{)tkBpbDo7Zslmky=1rQ!Oe$GbzMBpce-5zUIB_0WOBYvy_`
zz41vT58RmLGyQSo;G+EFKNZ=ti5=5>$Rf{SN-&-!s1mU>nOzL<l=1NKpHLDuR4B0}
zJWL*Z(wKt=;SAwdoZ=qvb+joB9aYv<m-`2=TBa(-d7Mxq^YD@wVzo~Y+ec{s4x=Ec
z17p+22d#wLFa672vVI_ELaHo<Kj7`kPYj;*2(Sibw;H?2r;=>UU#vZ?nb{c)gT9&;
zNIkRU!FwV}0eef2o*mnJq1HN^<k2-2d!vK*@ou|r&4=LU1tW~*!WEC(0`XC-e`b3q
zPTT62TOXGVX$OANf7Wc&bOm%DYYj{RvT)5zneC28Wy0{W!u>S|+&vLt<IrCsHihN1
z@Q-&cBqzS`i;e$EX`MJtc?;WNM+zYMbMBPkwAoxRdbIQF^<pS-4AJw^_A8`c9Y$>d
zY83s5msyu>kBM~vDtL#scj%*!{>*wYc1x<V<wpE>(`L83yuMP9JkUg2(geMMNggIL
zE-G2H?s6pXhVtez)VC2GpFBI3T`XQPSguxS-WBV#wML!cb(Mviczh%C*@<Cnz#P;K
z4Nrb>uX|rn3sKId>Q7*h`{qIR$i7IBzDWA+mO1kf|9Eog&?(+n+T;hAhAio5Up=CH
zYhOLcoRO#M$0_?+Qu@1#(@MBL(iZ7i_+!@v`RfyU7Zq6(aKSC0d6R>s&S*y#S$*~r
zgO0LZ_8GSs*z0>i1(@XnVqJ_>o0U9Fi{oXrZgdm<izT`_T;1_PjQ!YaEIX0iVu{f-
zt98@(ql(M>MA?hNR6Q~6{+~?@Q9RdcG3dGi6ZP{eB?B*;@gJkGdiMv??KktRv4P9G
zR1?y^CZEIoNmjsQ3jXsG!@)xuC2}Rl7n%2fM+K8ib`&=((`}%$n#QtDG8CisV1uV?
z>#e~@82ikYPY&)>RmWVl4odL|6_D_hR7I0WS=dhgz@$R2`ICELHS`{%p>znq?lH4)
z?}}W_YMHf(rgT}jaz&o~71;Fv`x7SC&KCc;_ZFjGEttz`t#9I*l8R1$E3&GF;CXhP
zy`fnL%wbDq_sLHTzEhT)9|k;)!P(ak0z1+D?}0dkFT-VIpr5;Vn*!Jywj0;usb?pP
z*tzsuGutbsL0clCr{M`t<`ge#1VH6JydN(vLhlTU$h9uA?&#Mi8cr3w@p?MLn?B6Z
zz{$vqu9<zAbIRll4Q~7}u08w9)gK?2eBpl7Ks1fvN5+1W?*I<mP9+7I)_77U4{u}t
z5FX(r9o6PU`=_S{<aD;Y2v*{3VLSy~IN9sV30V*i-!_3{{$y!KVx97WrSz{4srPqD
zS1tmzgLIY(rD}`F2WvbyACFaZw0}O3uCslC#%jUfoOD>NUA%dky?S~aJM`yzJkFv&
z%I<u8N#|R|(RO&&`W9){^khI7xO?*1o)5%-12LaRyzq+kw`1G=C93Gt3-aTpzM8UJ
ziSpGcfosf%rI~|b8S9W?Br2rYxYfug^rKp<3EqC3$gB7ZdBiNCvXG3U0A^nqfyVWn
zhR!b!8=6$E%GYrOTgwOhcsI}xq^A2UAU;PdX>7kP;`b*?nzl=n<8cN-r(eJeJy(Db
z<;eZPl&CN;OXr^5=hzq%7V47SyL&$F?!G=geXA}OwKKVN&6{p%S{wzzs;nNM-Wl%N
zqR)U90~fV-yPPHQETdj{0Pibq!^-7eJo1;sZ`^|^*y4F&PC6_+lYSrEH|uaD8*h+Q
z))9$3HB|}>PPw_*Wg`gWedg9F&8jzAO`=iqYm@<Wy-mw|klt?rthwSME|5xGqQ&7c
zB{@%n<fe)eixoV+@tXS)DfgpUxP6wX*IJO|aM(l8!2xqJJ&2{yu=5>-;k=E2(iL?^
z`HtgLg)|#za6bt7NYK;(rfN{W<B2IYNqp?_(23WHiH}+g$7_tMzQVp$j0rH-S9z7u
zpAQ}~50KhB)8EO@l8=2WDPYw?Dm-JKl$Dj0ODe?tT0H<^Db9;1(%`F~z^?7il{UX;
zaDmrPy-fS+>ePfcx{2t8=X)XZs*QuF$5UfW>N!m-4Lj`LZ#=8US$AjiX*2IdllsIC
zV7D2I2Z`ZOEsuutHC8B<XwfN(+$%vo5oFK<U%LsGYvn^T9Z=~SSQvt{bum6IQFHp#
zc*YJzK8`%)d!8~*w4+4P0{%}KbO}J_NqR;_B!LF%|84=k?B~1-elEv=ypz^Xh986D
zY2d!snxid}&M=^{c}!Y3)@VDgy6x|+zJ1#KmT5MDe6C;^c<6R}Hv2jiWzb3grHni<
z=J-&d{7@)%+XXR(DqG~I@yWh|5&!yO8J8etGTz6dPHa6HZTrk4F!f2VGdoojP$Q?^
zcz&sMkfg%)abKoBNCL+Xt~R+WKH}p=xGE-|E2M0ezFn&?<@OUczM{Tcz97#%lD4_R
zam0<3rC2HV{4-V&(9DLOL|aN>b7AbA;%0|N+@=(A<P7~Em%|?p)_e$|ciuE90*@1)
zHux~9wiu9(Z@MWkFl`!_XnkA4m*GV`esv&{Uhb)*@9>&%53B5MwbTnio~D!b$gUgK
z>$HsP*^G(nz{b;p;g+iES=r&=Ga@u2J3ER?F2kcFY3Iy?XczG(>-}iNafQ-VV39GK
zb+zu-H|#*-MhgO2I5~atlUB=pLqmAo;~dx;{f=y=tJTs+Kg`<(2@<@cbH01M3n5B~
zSJaDqukDDPGb{RlG-Z?E?b^QGWUC}xWcKI2;t$bh3zZ@b#=5=wa_`uFs+Ttyx%t%Z
zbn`cm^-3q&)m=kaE}zYd%^S0i*<LR?AYk-APX6GT*vXHDG_yW{qrVf`oz0u`zMPLq
z1I(|S@tndAc69KOTiuh0Tx>M$+T<hCzNaK)Dg)&;mA_CY^(SX+Kdrt@=1fvdOxJVt
z2VcRs4X)?QZw6RgxE1{M7ic4UMGV7j`Zq)rq-PHfD$HQQ74kNrM?qaf81JrkrY$cF
z23<^*!(e=vKZFZg3BX5ONS~w2Sqy~Ds&j><v=jD$S6GfKDE2mSsyo#o(H!G}<x`y^
zqo`T$j44#|Sd=efB4EPz(%cw$Ww*st$LmK6HA-?x&!2T)T@|EFq%ScbalOn|*;F$<
zWq-{V_jBUcnOVh4W*afNdw#H=P0b)DscXPd|FYCZ8uNwa)e>62^nO(L(~5$;hKi3b
zZ0^LTxT>(N39_YlLQ9r?s1DRkX`PH_BwT};($@w3^s-}MC^IAlTuoU#2q0r^d&6nr
zuJCaE(MA0LORSW7Y@O68V?1NQ&{S>=s<bvkn=Cb8Bv34Nz#S>jp);NsBYRrVjxy2^
z`LuAqNc&Dx&u>5_i632XJlSJ<u+-CR#QTFuI|R?W)zze}jC%C#8=WS-^WBEwJ_`Zi
z{Z|K5Ca9XO&+L1&Ef|j3l7d@2zl0BE2~_^W1<(zFN*>zNbGaM`EPI_L4r5N*wm-6i
zIbU8c)1)iO4=Wl?y=Up8{_fn$!bw=Mt-(dbGMq61uV)T^N;Jfe?Qk`EdZ8Aq#PKT`
zMfwfuPUA2ShTOF0Jx81Hf${KeH`#_agtvg7VQ(zijpKz$g^8asG`)W|Y2bkMtzM|A
zT$^z{4ukq4z}Otm2wg#-oE+6vO%+c=_!P?$s9V5T#8YtDf>Z92$9vC=>H6Ls+75aL
z8<E*COu6^3ANgK#v;BU`T6|Q|lqe(9$PEAdQ|~%TE&g@y(UpUaX+3<hM&l0R=w(1V
z7h`Hm?c-CIA7%-8d-A54pStN!{fkc+lfFFrrJtMXswMrVNM|57bA6Vxy1-6~ptISx
z-+g{mdimt^H2lO;^xgLe`O{MB4Sw1zs4bNWe@Cl6Dlr5GP6q>o$SQflL;QL9r{bF5
zaw`>cD8}2XWo7v09MR#v8JdML(VI$v@ZG<1i)IxG6@@T?K2si8f2Dj5N{n0KVcz|n
z=-an`^g<@#Q`*9_@)^o2SyL!T#8rbUv>E%6uFk`%ZQ4wgqu3eEbCjT6#6|md!S+Q;
z{RoX^^zchWe9#gjh=e)vDh`3s=&S`4kE_Nvl81OFTvSn%QRR`O@2|RnIU5?5Rc<xX
zN5xhSL<koSi(<U{ZuBT(EL0o#2fi*_@o&a;jZCDEu(Q}CGdas2^e>t>89eX=8m^e}
zKc!#&EIbgfehYzSlFx<6idX1FE4A*c)_k%GqEZq2s3v-02G6qqbx$)<>_^G>5rkZb
zX%pdw?bmu#R;|twsanUYE&)fEc!~t)^SfW$s~Zm6HVT1!C47)`;>{2G@35I|fg9O|
zM#ETTw(%3Y7LAhcNaTaC=QUeyQ4tXlS_#v4^bDmj9tn^4(0?tv-$JTzt>B$ho*bio
zeSkM~AR~}E^rjqYFQTNTMhb*UAUSAiVkSGlgT7w!HRATa3f%!koQ9*B=Bqyi`yI1P
zOI8e)`r{@!fQsp-=N+E*t_CuQWd5A7cBIj7_x}`Dx@6**N_BGsDrndbrCw3la-VY&
z_6_)!Xi>!#1+2oBK=8|hBXM>)3e6W_)iU-X?75k>4CNd(8CksQr)hGM6vxZ((%F}`
zZx--FixsFK@2A>*{O?|*MYu^<YQ1=j`+U+q+S40P*%Xxqggf4VgYx(jvu+r(f9UXh
zh!K}~hTkYFB+%A<5Iq@zHlFR<>CdN0jJ)wg%+t9Mr&CWWEoJJeb5Ifj>CnfcZ;1{O
zT`2?;im%TEn_dDC$Y+jfOyhkl4LP~l$`(e)$GWxRw6vKrZLSZq#n8jbbfN;s4$V9*
zvr~Rfr>GCePyPAc9!74xepMSzi%RL|&7qIwCc|?i9yX+Zec)bRO>h}3Gv!WEtG2r$
zraC_h{hNIW*BO2xz=~boNvbwbUDpCum3a0JyM>vVoQD_vP3vQug)C>;LP|6SFZ^-4
ztEi}vvj>n|8oSL*%D(=fe>Yp=!}^qCZzNw*jrD}~f>3L6t1qV&Q%{&qxOBf>!E2(l
zM0{@tM34LY$8|WT!s=!Z+_730#Nn(S12kqI1?cw&mTf=v1QqQqs*kn{?n`kZbS{(1
zw&R+Jn3<VBt<c?mNm~x;e!_#-m<uvb{}7gnhM8#OwU0Idqfb{{Ix#5>CXH+N^k5Ii
z9=N^%$dgi$`xMtrEwRhLhR%+$!WUdt&F`@~-_WZ&z@Z*MVN6U+%*V$EM<S7<EZHNZ
zPYJ_1N4q$C@3DH(3(4+7Ie}%#75cAM9xyY<7i;_S+f3Rkss>Rb8}HLUUtE)|hSGke
zkhi2APq48`kMVKX#!#zJ>1kB+`6L<%>b2nz+r}jr3~kHwy9O>PS?jIsO2?v3^53xU
zQ2he5iYzkyN9z_PSv>4u>kr%fHxhq!&)kPm#<~<2A_l1)L~mRSRefH3*K3LG(h2nA
zZEtXV^17k4Z6+vRsPgS9RZCDM^~Ub^BN}aayDyjv@2VRNZ1Pl}XtDwyo%s^en2gLu
z_X|sI{lHdCKjFbbyOZ}XBWnU8n)pcTPg=ddBk{9V;)qO^YW5ep9^dRjE<Enak0;}~
zzjNZNXxTw%!`8tl5B;1edZ+UFfo;Zm{SvL&^2^Zn<4~E1`HH4aU=`-B0!~U`8O5<s
z%GZNP|I72Y4Lt9?r+ZJn>bB>j>RI*$J#Yp^-W#%YIO|;^6Qo*J5_6Lw=y5?Veb|S6
zBUn%uX$lAuNQbQaGwTrQ{j$KQx5@7w@NhaiQy+H)VHg&GzHWH_GKp(Q)F{zH2!3c?
zHr(~{)L`)0v^Eb`3a$<M180HP2jQn#+u<FUA>AGj&5;`7OPQF>;KC7hb?*18%7?E=
zG%0&$u-X`_hO;r$E&?DYml3a?zYhp|2Lz&+7C^@Ri6iS222oXkRq!&RHhOnaI@r#7
zwy6bA%f2N#iig*p&f2?q8%BCK%9*ae0C^ibm_RDs|00Uh>Y3G;h>jn!-0#3~{XLzm
z;|B*s<XN+lqKqAZIaABF*^NgFhE2g#$lW_s7R_cE*@rof=lNuR5j(`>l+V~^U5%&t
z4`<NWrclN9hZEK7KF;*#=#$kA+U3xlDIuhI4)qyP6|vW2z8;)|3VYK8q9DoPBgr5J
zIBnr>9HtDr!8IOoiEdW~U%S4#oh3NI&mU4$99xTv<9{Sg-7s<LD!8s7M=q!HgqeBl
zi<s4yiCT}N*y85VFBA0jM;|tqpCc9`>Rz&eHQAve_k=v;B7`#-k{=0&G-Ch=Y5V1w
zG^1`yh@;=7R?q1P;P3Ffu`9cudZn$LhVyx^|71EiR+Kn9$8Nq}U8*pao#oUcV?EpE
zrtc0wz{-&otlgE$rcR6p4c^?ib9ekO8_Ky#YtuH_HX10!?oPim9>EgDT*PO@rMj4$
zq29ng`8H-*;KNhC#S6EA$Ek=oG{1Dun8)DHxWQV$yv*G}S^kKNV2v2Feku2LyKLsm
z5XOE@;zP?;I&+uu%4A7q22~Q{DR;fYQF6vIvN;qQNM~IJz@mp!R@%^3$FASF-pk7M
z)uKH_TRu>qZEmG-ka^_?zybX?5eIz>-=2VTCo0BYEqD&V^TzJq#ahFjLWjhrz~>*W
zo$Fx1+~ZT*7OCBE`mpzLJ+Kxz4XjK|8)u9Q6eQ8x`>xF|{WD4#7RmW$a6BC`M3Moh
z`J62NedK8oHel`LtQK)^Ykkc7P$mZO8f2fI=JWYA*?zEV;I^G{;q!(IC!^#dCjHJ(
zpt(QlV<+OUp1~Q=u^U*SWy~kN#JHkzhz@=H1C0dt^qhN|Hnil_%bXc-BtBoXnwU?-
z5uZ^G)G}MpMnW`~g{gDO$A{crhk0YOX`WbXhEED&>ykYSEJ_o=vr4<3+wvXaFz}#s
zqCKE_gQJbLDCAGtyeQ<IVb?gP+-_)QoPVn{g|3x^z)3qSfzIx{Llv&zdbJ+`7p>@J
zIO=v24Rx!9<HkR@8oA6$>1Hg~9Oo9D9p&|eG&2Gu+x8nt?Xsv-U6$D8?;;13QvvR2
z4fq#`heQ59ECh@^{T}^XOR<68T()$y7vfqEqU9UkfUlVa=Ml=9vZM#L@V2qeYew+a
zm_*_G4vEFC#hWLEfj5L@xD|K-R$FsC_^Kq0i$cyBcC^@jv&5q(8Z#|_H6!}t>&S>#
zUAHKuF5bT68q;^ZUMA4&iJ|E#3@fzz<d?U*Ve;$znli+~2h0ReasjDKH+Iy33_{3K
zAuvlV01XL1b-TU}k9V2-T5S7ylA>2ynBxf=iF=VSw)nePh~239tHu+J5~qRwh`K&|
z!E){J0iwNKE37oA6cNaN3#$E%)IB9tRRm?;x`gt@UdKeIWG7?AVbCL{7n_HcpKHz{
zKNAj4!(Uhiu3<z07D^z6IcI)xr61z}t@*p7b9})o!!YmR3?{PIDQ5xifFNO$@Roil
zGj&tc8yFz9J|0L909HF()ecpt0@}+$nE3<2-qqB0>F#W*ySxqC-p4ajXI-79DBpbY
zDdHbr@#zzif_IuAOBbLoK#avM^LGE(HC?#1r-<cEn?G@leQH~yO>Z%{FCus)8|EF3
zm7LU?B;szkh&e~>H!rn^C4ymsGqCtoe`e8V4I4jYXTBSJbOB5{JR0OIGvFCmHdOgR
zymvx=;1qWL?^pXX-y@5kR`NMudlFivM>XfXdv5W3=)vw_bD52Tr9)~YOD(s<h`Uji
z|BB7^nU`Hib5?kk@yyuC>_bQa-4cxxL@OiK>P^hCIKlpJ<2O^K-Sn2(wKEs{YGycT
zFX^=QRp4kA!o%He6?g(%bm)PJBetp#)QAZe!awLutz{4#$u=(JaPe7irX~(k2P50j
zJaAjQL)o!ZV3FveO;XlCopIfE!LG)Q_tasrGWCdsnIPek(}|3Xz=%8q8_N19^faAG
zCexn{^#Rt}@p<rLd1$V^om++b+dRXm)kcLRmm70lSeeR*NtQ-qll-Hrt7my&y~#H)
z2xYqx3h%9}QS!U$X)+UwSG|8AwUsA>;<L(Vth%=tvBKD&jPA@4&EXH>-sOMxS~=5T
zgvzwFpR)UllCFJ7siaC$vCPKI!1bi-*Hl0#L;N$9n!!Gc2Xg)yg9SmAX}ecyF{^Y>
zWtcznH3<M&>4!(+K?%G`y6umyX<J+^RaT82Gt$kTfTqCRu;&JNZ%bLH@@A7Nwrh6c
ztr~8AQtOWyHx?Ni_a-s?#%T>-E^(LiT7d%3BU6!IFeV>IYw((GH9;(TWinN#%9^*E
zc*34PgL*%z$PyTjf4in8I-Y~lMh6cD8Jm9Tzm)nHA7ZG=Odmd?b=Yy_UZ@{{F0i*E
zlDEJcJ-cGO7;GtAbGD(-2}D4_?J4I!o0OCLT3WVPlfe2NBJH|h@O(ZCtVgN%8#ltx
z?(A`gyOFWiG41uiMorRjNt!~IUU$in<=&sB<<5&tT;mx5I1E$s<H#(ke-!O@=EIx=
z-4?bxRf|p1v#y^iqdW4j18(=xd#vcy*>Ykm%YPNOzKqb`@z87nS5-C;`dlL1vo2FB
zCu&SveL5CST5Wz|+TJ$EN&|&lK;h4GWku3eEC@(935{XvUpQv+6;f>S>kAv$y2cau
zpLL`CpZ)Y{X{x)H$?`zef3_NS6R7&u=|?0sx}(<W=)UZh!L7M~iTr?9zpk?hBp99S
za3HfFQF6hs8ZO*b_k8&2Jba&i>x9eHO{9A=_~dTI+7n76Sj#0H%ppNhZ@Pq1dw>m$
zFg2L=Ae01~&rDW4uo~!ra@h~|RC|WKF)=&?ol1`_05~_$P#FNuWvQvk%qn=*08h8A
zAbT|(P0RiTtL|PFB1?a;+x66PpxAn^Mk`3v2j)O3Nd%J$(tDD#N%|`Z-)=BlM_*KR
zi{#sy*xhr#Hpn?%e8jw6VG-tPJ@jj^>rjwB6mm+s<VWFmX^Xv`0V%vDC)nL^gdShu
z4;|wmBMFaAg|`=IO@R@+KaPU+;PoH$2J*&k<D7bsj+`7FRXyo?%&SfeyFk~ofMbi!
zcH9Qh??4A46MN2Y-5fBbhJd330RXw}Sn+3zPZN{g+WV!&E<Sg;Vk<4=$Ruy26<MnH
z+CT0nq#PCUDKV*pvI;d)I;r}&7?=&1s7Of|*0f45_s*1{in0OkED((C`WI@_6S<R2
zVrUT(+D=>*bIzuD?2LpgZZ8kX8YeDL{=mK~xQnhePv3Op9vt?Ne@pXa$Jms_iTj|o
z=8%BOsnt8cA!t|5J7ds)Sh?M}sP&(Kf&~;DV_)>^7kg&5V*ZREug=63>iy~OQb`gv
zLn2RpSfp4%{GSVyU}{$^_6(p9eHK~kn%Q2D5l4RpX1VJfa{9QHCS88VYxaHZBsuK4
z+Lwt??R#EPPnx(k17q+`eb4@NeDfQ2p?Al;&+VQ%g=g|dQZQB~3S+nR;0nQDxI1`z
z2sgk!YlM9eDFr}AIg5WGBlsY^1e{F5geQ%8`TYyuw7u=mEc^^iDSW?T+^h0cE4B?E
zNvA~bT`*EuGu;ETYV>$j@yL(P>4_8Q;05w`3X>Huw%s5|a!7h|Z0J^WKNCMjL<n&u
z55Ala`*0RY%XHD)m~nd2^@Nh)u$#R5UF7rr+&5h6>=Kk8?{;fMwwyOwukGqj&Oq&R
z<#LZNE`fj8fHoTVR@U!xH`@iApR~Fw4n4KjHwaZWz+=!pU40_)6SrFAk!en|OIS!3
zOgO!&H!h}$)4df2&6dnU^y!7GG7m`(BrwtxyufOChTivAUvGlw;CX76XidN!fGkay
zYm$5M0lDA^mg`WCp3HIUwI&cwY16KiC(FS{(pZKYXzv(W;+^LEct=fxU$`3n4_ajz
zlC_VmDpHxbL=?b-b(b%-dht(r{Va}_qm8M7I)hca-B8_Siq6;$a2hxStr0-9gjDO6
zU8pnyPz4S(>!)QCHWL@U_NOB~ndfit-*VPFA9*aG8?)tMSC%o1iOXF~dT?2O+Kws;
z(iHd~!A^o#o{D(Zk9QP4J%GwIAY!-%zg>U}k{hGWpKH2%CIA$$f0BNWPDXFArgfmK
z!U)acMgR)yDVss9_Eo_Xwg-&`JE$)<EZFw=7ufdWBHI?jL1r<2>GXB&sFfi8LeO()
z4w#C@?!=~{p7N!0M!IkY;AZ)Yh=I~C9*2nB>wtIMysOPO##GTU)@lmHPotjW(rKJ8
zelhCrwUU|`Z{Mzm@FZS3*$pCN$=g$WaN1rMADJ%zl5n;_)K5GK?o^$Lb4dd4QvKTf
zbw$jPKCJCG@0^i~govcSb<+7<#*2g-*p;>zf4di5)?4x^mriT+dQ$LCS!J!VG+f}>
z|N0~$ec+RLzNjET5(T24JLaT{hGoQR97ub4uhEqj8vO(pbJxfE+Nf1TTPB2*rYCZ{
z>4oQDVzQYN2xz~*g+7}A^*+pAMAd7Qic|suc{R834FE;HDuFdb!j<>H7IM!P8pHS1
zc+y+aBPZ>r71eUJ^;*21NbuY?oE<`U=|QT&RcFp1d<3jnI%PXqu>j}+ebw-7TW_q8
z{L*Of@6UoZZ4H5+jRI>>;j3+ewM5b$>`(uE8gK8}0BPS=-&tY(Q{!KCYt^6Qs`gwo
z+%#l=5gmF+@>UseyH2?q9iB^7Y}>vO2J*JotVVw#BO=@y>l~a9R*dD>I|p@Ljm{QS
z0^iLS{*HAZj{y%(@lUF1KX7ti#JIT{!khiMtxE9G<6Z09US|%=GLKN7V52yh27~f{
zww$rKzykd4L$Coz%3Ek~($NY5cfzZ@yGBaNy_(g|V~6&b-8?<zw%j9d1+dT;Sw`)d
zP{irGt&K@AyMEGyI_84v47Cie)8<6-uA6aW*aJ-T^ISf+AKSPgF9+tYkGG1O0h|MC
z0C^u+CeA?*BxWOI?mO%2d&tQtdRU%*GdJn*{`b$vCT7n?ypuIX9H)PdolxG3k^#^!
zp5*O~qt#vWQQ7iku`i0vwwiYToPvN+Hz2RRd%S&;5INtF7D+Vz`BMAhi`;2isOinc
z)Oz0D^R6rh=b$NP5ZB<=2Hb4SoA%q^7LNqaCmVzafc)8u(4U>Y3H=5f=c~t?Wu=n9
z_tA<BhUif!2nJZ#*{MrZ40;BhJT^9HFE7}Y-#jJd0sBel1rJ00L+v5Xw0Ec6!);SU
z$Tv_)^*|R1b4itJBxwKAt7gVt0Y~U6cwRnqvilv`lzX*<!9S}kJ-LnE%)V7zVx~*%
zY_YaRpHAyZrG}Xp1FONi-Q6RB=T<c(7DgIRp)jak3nTBR4N}+)?CJ3VR+BN`l)(aE
zCK%O$MmLA$#2Cr-+o;NfMEpvisg#G6zPkQx2F@c3%v!jeVXB=M8+@zK!u>Z}#sJ_p
z+lghVN)rawD_fKnD}x#9S7+^CE_EcKxK)$dVZqn#^siN>IkzfsPLQ1GVtxbcJ*c{M
zjnUHcE!_JIk9A+i9x7|z9LZy~8dps(%0oS_WYFk2n-<q4K;^5r?COJiW;-OQQH7{A
zXvlUGWmL1kv~Y2nTX8kK0Imo30;U2Pz_C^8gt5=~oFqQs?%`KpXPt7JW15goF91^v
z{AGAC7L3i$OM@B~PAE>CA>9(?JGBwtl{a*RlE97K@2Zz;S%Gax^nV<d)I&@ee)2@e
zVoC?>mY2;;PaOtyhdCHr9u-(s+f)IA%dpag%_#T9-zg$^@f;9$LCBai;93Pe5>;c&
z`Dg2=wuIWVkjiIR_0H<-l<bL$76P;Y4D@S0o(f3V+$3VQn{uy~{P!w~Uifx3Saz5_
zJF%lX0F4q|;_BkHP|%o%6zGUl_2a@b*UlN>cag;7C%r*TDc)4~j#aJ=k=lzRw*(~J
z0EsFIQ^dd634833)07Q38(_P9>9|z^_ucxbSN4PNP_W<+ldguzfz5y77#QYooj}Qp
z*C)=g($05PpD%^-+Rt^k(qD*MEJXmrj$<*~^jn4&Rf!KLXCDvN0JN_c*lY1{SL*jV
zX%7<>pEPi0Zt1WEiIRHFwIpFdaN02Dw3D7047*Xt8WMu=?fEOMg42WcvE#6aFhykz
zf42vDVg$1L`kUmC7JCpWvn-}%;ayH!6v7NBd%eZB>uN@r$u$-80lSTtJ)sp1Y3&uE
zBEB5HQaT%7N=8f;iFw=ia~`jR>kKg4-?X}M2YT5EB8bXIs!)5Aii#(YB2L~w^~iQr
zm&Y7bQQw+5Gj|@CN;|dk289!RHhz~C_{h|NI&~B6k16*bN>Gi1mano%$2@(|Fc>jI
zt!r#PFK<X`nyMXfC??vh%8BM;<}bjwb=5c`{`REkSR$$wf3tJ_3iPVU>_U;)Om%)W
z@p|#9(p}QFn$$qwgZst{V`*)^*k<0?MX#m2IuMYz9EkuR;-)Xkr`Rj;Kj22?{|j!6
zL$d~lj|cCs4P$8ISm!5|6tZ@t7RuCLFxCzvG2j~FN#RijC&EQlWI{e(h>6zz?~fC*
z*h&GW^9k3i3HVE10FLQ~s%Q|)kD~Csvz7IBqG9sOQhgnHmVUkFifxZMT{7s_z6X&b
z@x4ULPj^Lnl}qPEmPx(}bITfN4%PjGVKl2sng^++W5SI&(vz`#f^@Kti<0t{Nlbgc
zMCq>ko}p#B?YB*Wq3{X#zVh(wD!c@<o*Ly0vCPyy(UW_pXkrHRMqYKXovu}J>9*Od
zGai9@SLtOM<J{9d<;LoZK@B%6awIj{dyOarEtl$pWQcS_>Q~H(rZ7eFmaJC9ZtpXR
z1pu2k$*!b+H9vwQWamvKHvOw-Ud!y-%u-_JS4jC9)6lW&{WVm|<^tRsF1@y10D!1H
z68^_?U`FaR0o-IQ-5xwf0kj~#?oRsYYa{`ZaXfr#%bs^@d2Z+*bJwyeczo-%tl46I
zIK$toe_1^C?`5JoN`BPUx-8(WD*pSRxS5aZB>+v3_~Pw^Zhb{Uigpw@5}A_+-Q8{Q
zlusZWiCYar_VEJ7C*bM<zshR|DCY1bL~xu`E5(!D$tFm|#qyvcIVhZSNG+YNY99lF
z*9Kwq#H0`6?PN@*8BY7Z9Gl82NMmuFtKh%3&@=#qi1<Pkn#5HS3KP;p>C+|Kwm^e|
z5$8<Dov#lH?kqd}*^*A<{`S)b<&gj)uDk63l}5j%n0vcxv`LN%$z4cy`y~1yJ?L?;
zV+v;T0$v6%$Xc3k?p;!;d+85fm88AZHV3o=E?b)Nc->~;4~uDOJVQ)BX<3s{vHycL
zFs)lo{`Dt?pM6(30EbdtHPy#e%NAn^_{ECr-}@U?VkQr2tyIiiLk0!CwCy+7MMoUJ
z+Z=#qVe`(I3tttB##dY#<?xFQ0J2KFYEiRvlwMPa&REVY(+$8-(Qs<T0NLR^Xuj7#
z-9VZ`1bT-Rogz`6_!Ynl900sv*B)T6C>twBhIO+&Xdbut17qIs0^o(_);|8!9spjz
z9n6>hF<dr2ARYBed2>JwaNZvr<|2sgj15LUln*a1Wm`B(URPl#J?b)M5fCCL+WtC5
z91y$A%E7(?-sR9lxpyyBG{?Iue^rtK7f#4O%Y+m@vqPL<Cu6q4*%QFN5>@14JzTX-
z15HFh1Z+h0v!<pfn18LebbcfXc#;MSdR;q^Zqq7yEe2YbpR#ek^}Uq0IY@kx7`i;1
z-{HCAulb1Y8-MzFN082j^|^WBnHi1gUoa|bJWf}dc)H)IgE_vYd!?ppejAeMR5mFW
zXs4U9828bG(Ne%$7pW;xwaVuhLG*NUN!dEou=|eR|4R?4l?ip9{W$0hvB>m50p=&C
z6AXxGjJ#3#BhzJ|)#pJE9oQUM_|9-rhwX9_>qu86B=-#=Ro(9K7_sxBD9}7zbs2cW
zy^QPWfY2T_XzKqT+J=`Nw1)6mrXyA)@Iisnd_-rHe2(Wb^UCzJP~o?$D4>{r&+)gE
zW&lcQ@gFf|6xzVnpEoVts&10_-oe$`%>DJxDmv)s32#*?hzHQVDakx1S1X$__H0z;
z9!3HMl0Ei&pmS$0lAgk~T-8u92sBs=G=TBkGyb9h|KS3RIV52y1=|fdpaZDW5$BcM
z^an$D(sx=oks@p9WpllDI4{~Q3r#A=CmZNy8rLzyG24khsc-AujV`I$Pr+EHtG%HZ
zSkr@}*3O}rFpA{mxju>EV?8-?d6UyyXQh<s_DlJC+12V#Fz=##^{*LBSuPrW2=V#d
z0VM9(ZVf7Ws8Gya1M1@cX9TjV1>hb17L?QFod5-G$cTYuQ=p>%yI&8^QH6-G-Uya7
zAs2Q9fUENym>>Dc>%n&Z$o|C9wZdA*+Q&4;Q!OVa&LC;QZNT;_R}GXQ_QN`heDbgg
zaBELV#jw5Zp1r|F-w0B`TNoM!T25*<6*|7~=vvRVj!9+X-G<i7dtPF2k0qxJdZVIL
zK;t{#2TYg)eV}=PM}Xinw`1|MmtWkRwzG?8(%;EA?V%l#bXNT}Z%ss`>(plvn<nBD
z=RN<am0lrL`GeLs-<sugAWXSsG<{kY`#Nr8I7PB6xVOINBT;vQtk84P9leqmBYxu%
zu@BA0O2$~Nw*q0bSZBpy!!FjY9y{gkuM4kD-t14(i0yhH12J8Ly4^3t>4AqEU1qlF
zg98N-bj9NzOz6%?k^XH{s+a-$Xz#*)m#05ZXKg7~S_?XeC)sa(p3tln*=rhHuiJ{q
zA;A4++;3<5=0y>kZ@@)Y5&!5og}dnN)^RA?pS4yKCaIB{vWmfl7>S(nGNbqlO62?t
z-cfS_bGvy<fo_Ws$P?eE;Mu+uq)8yf{M}9wM1LA)mj`ieYsQm_Q5_c94BVbHe>#Y%
z;KyaDIai9h5$4YiIDP_k1G9tcUSxPY@0YXh^?T7xoaI)}Jciiu4ht}d9#8F?Ov4{0
z$d9G(E=2bgW6c8jy=qZn3<vY@29a3b%q&M`G6xO|qT|V+HABTSQ~ylxA!ZT*$NyU6
zpX>(Kg#5yCHY=k=*C0M~H&r~$fq`)jmtBH~lxq<sUPE8&$&a~ERcobLLOElv-C+cn
z5?P7TZ7-C}rkOO$nbPE<50SqoujGJOcx3~(FleylL=dS0FvC+bTrciH=7j!Y)=(g_
zMc@?v&0gLwefDG=zE7P=W7=<_+X|ugNX9`niB(9lMk8T09=DD8ue9I(W{SDz$IT0!
zrfq#Xf!FKB%>wp3JS+ktl1(|v*zi6#&vjfcFx@QK2CBwG_)hh!n#;YPiRzxu<m7Pv
zNi@xxFGH5kR~mce=VOxkJQT2a8|z}`AEEV?Bo*0!z5{R>Go%?fX67*=qt^gf^QxGO
z=z29T;cO%IC~t3|YQ{*T`N7ocOmmjD<-UH>OOf<P3H^0tDz`_lsoJD}OJf+-qcS}D
zsoAjMxCmt59|}@<<>$lR*weFr_RQORd2Bf4@Vd}JB2#;^;`RvYqANIn4YHCa;hLa(
z$Hi_|Zc&19!m#JRjP498rF#JXS(iqYsxldxu4+d^e7lkj!(TOI6@Y>N?5c4icPK0s
z<`X}F1#L9)<$;}zUb^(tG5WdF&#QmQlW?qp%0ICKKtrJJd8v~EY>ph5%HVuuwa`K9
zD9*lBA++Le#iV2c3^@iSe}q$u95@E*b$qzqV^>jEVZk&;z!HHTy%`;mApsYjF)jo*
z*0Ba)hEKrr3tJtrfxrTBJJ&uHRR$1$z9|6ZdUFd<$}uOuMqF-WFZP!>X59yhkp9)N
z=xk~6Er{GZglzo&)0U9tWQWep6SoBk0HOi(NUxchJjsS_`V1GC5{i$sK&r9P%tYYA
zU64m`Thk{_{0E?eQ*Pb1iQ8)oKamo{9}mUC8)G9_UoD>|0~1b@R;i+18f^eV>tn<_
zdikS$EBW$I<f^)7!8d1fd6ym=N6VdG&PGhgp#p~mNh=B8Q_K84#SH*4(vO>hIS8aG
zYZidyzKR2VW7Q&O;Btjbi>Qgan)MBl)J52M$j($K+|TqsZPpA@5P=kJPUa@uj_r;Y
zsH(dq3m1a*18)tBDBTeFL|ieVGk!j4<Y5=tg!5fj2EcQ?)Vme4h|7$S3_960^`^%^
ze{X<MKDy7Pr$j-}{0F_aSGPx!RC~NV5tbM1euwBDw}7r&!|&?Exh6M;ZXRL}9YUm~
z04+e)2UL_C7OFh@$H!!pEC<K%e-#fMvi~U_%(xb}t}oD|kpIZ#FK{gP4lKvhrJ~c8
z?j63v;I4!5sz@{A<Rm}Ee@I=b8T$RC!^quJ$6<4Q;bm#n(Oq$qPm{0*=6Wkted3><
zH0g#uI+P?lc3?E!on>e_9-zwd@^~6(SohJFQSY^x!ox9tP(^`Vy(_?l0l<-B!zl(j
zr(u|bJ%TNHFkZ1BZx5jH6#e&_0dV2Q1#?znSUFiMMbuOP94F##ovzoGc$G<bi6J&#
z7g)NlZhUI<zdEQ;o6!GAJzC!P9$;+Kv`?7_xlQ~;t^D`csM@R8j(3@^3iXsz_+s67
zdM_}OsbQp8zIbN%gpc<0S_p&e2YPBez)+Db-a!$kvEQ1QuVzF-wQI)A7Nza5j!t)f
zjD%He-%Yf*M;18>67+8zxWrdRI;WL%>km=_`Tp+mZ3h)cnBEBZ%%_A-LtVI&=WFL^
zL0m7qX`+TfViA}OFyeNc?al>)4)F)Ty1NX4F0VW-fN?XEE14^x4oZ1j!@Dd$NT$s2
zD=_r+?C56gyXrNW1)&i5*yYK*;wreF{J~3$Tz)aPe@$dgICyy$l_#B@BLj0zGelK)
zXOTRX4}<|4C@Y?2`erQ0k%{p56;>UpEOqZK__q9L>|ZsQS!`Cec^_b!?!EWanE$pN
zS{Ud$WNNRI`mBcyn-}vm1;gs;|Dzdpe*1SI=&^H9-TwPgn7H%BuTj|BVWn+Pr}gE^
zKXXb3eG)v{#MrG=PCw`TQ=Zyb{4yd?@iv-QW_uw~PQN6_N>!L@Q$27wY^l%Px9<60
zE`E5UUn$yP#1DyqGztE1XA`^b{_4M`@sBr~WQ(Qm-<>jq4{es8Me88GMz#W6xW$uQ
z9Mo2iQSd@hlEduVLD8+dv`>h5#64tA7!m+%I~PdZUkG~$rbch=etebj3(eb!F68Uu
z#uvp@!&>AEb!;UOBRdl~V0VhrgD4~n);G1IGE58W-=^;4`Y$r%lmo#%W&1y^B<5;S
z@TK)NI*n-BQPEck6ZG`-jiTyh4fxh1DqdDrpEZ(vjZ*y@yg){qu68r5%oe@THUvP4
z0AZ9)Sw(KiIzLq#9WC?!+l=gZ?uUW^nlk|q`(Ftfse{|h2ZWSyxBOjc|L;kVon#4p
zKvcE{ZBqCmU@<BMUijQo5PGC&l=h#qF_f-1zU0cQ{pl>B?2L99mT~9)N3rtWC3s}<
zG+qPBr4z%ckV5*>Az*s0A>J`o{t(7)5jJPA`H(<qc=fF$qE54Y%b%Zn3znbaF`@pE
z!M%TEz;CHc+j}d6l~#FZ%dYu4<4{wZDfYLQ4$HC60-C+<2O8Df#Z$^P997vL{u9@`
zrvOu`WE4(Gi};?A941~caLF=sJi&2P>KvRY+kcsXNriEW4#^wlTCBL%ULq0DcDTn6
zbn}iY7s6x>WB(pJmfPl|CLj>9PSBq)j@+*Oo}Wd3Y$0VKzGc}l4&2-4%x%M~Y;bXO
zxz|4-)nGxgCmX4iE}-P9n;~MyT*9MbIALnb{2AjkZPVudT0yXD5D9k!$&DWc<>eM%
zvZF#^>BJ9jxUyQYK%hzO-aICZY-$;_Cc#Ypg7Dxr#4mwb7Udw#Ygj!od$ih;=zYP+
zt98(iF%?{owNjD@hCl@V$IF0z+w0@+93Lg4>b`|MpRAd#g5b9Y9KV(JSbolEQVkU*
zsgDP4BztW0INzQI>vwV>WW_Y%F7Cf`wY!G4J%jW82_nVXCv1p0hm*jUF++2qNsfi>
zP%iu)Eo&l*FGl9G>2E|vuqs4HDoLs`#r_GVDTGf+yK1=Vb-7^2od!TyZ5q#8*KwV^
zX^d>k98T00bH1kchJLa0ZqG|nLV$dctnw(!Ck-*Abjh9X&@fC!p8)JwM}I_3!^&6D
zgFWwY7KV*-^8MMdTO7F4;a&R`@K8iT|3=zd)`tN2pQ*as1hIBhb8Oqn8kJx5J0>c^
zovC~gWHn^^PAC21+wBnZB+T&S#0Or22N6JVX@9R~IXF)*fX#{LfDs8cWvnW(N5laB
zD$wqHk!|C`7s+unI|#R1J5LV^D-_vFTss#+Y9Pgs;g-$M{^K3x{-%zv>wsQ#zj$_g
zY9@BrhpDUP@wnfq!~Mf^<&P6;#QheXqjz2>C>8a6<<_vVn|ffD^pYU?^Y&7j(sM+J
zMqoUCwvk$3t`>A&(^BnswrYBJgtD)I0l<TF2HD?|A#+X3Z!Ug1d&DG~>ouSBq8nRc
zEP?y-BI&ovLy(8D|A{3yUFF``ktUMd)OV%^AA>h-eHr7%f$oOjZ_}$W=B8P;;Km6s
z;MD8M&v@6^UfKIlO=b9$;J8Iu)`qVGl;Ch-Ocv&pe+Bv1p8vI~Ka7SoA)Z%*yfpSX
zL!H5BHSo|iy0)ObS!PNXo)S;%<11j##9jlos^ZtSRM}ijtF;t#AKIoJec1~}=X9N^
zH{-D!Vb#W1jB5|Hp{&*?4Pf!-6O-yrI;`IRlor_bBB|*U%KUnn1_Q=wsUiYwrZXm1
zzJMg`1GoEAHAwv7vWegtxbAqbd`Ms7d;fpplAO9WkWRjCS-!g%mu=+CGvihjJ*Fpk
ze-70EpUlM7hRo86H4q(i&Pq#PCWJ}V_!03OY#eeM25gT<GsJf~gFwBs18q<)&Vyuh
zB38}+*WQ)JL%H_<+crW&D6&6MDqHql9g&o!g-}^q%m`yA+sIgwB#w;i)G15FBvTW^
zgrqRWUX}?{YLK0fDF5r8Ii2S`Fa9r|7tiN&?l)ez?(6#9zw7>O-|PFE+cnbk_L8@@
zr8k`fQk3q!-*HPEu|?j>+%g<TnM+F?aWQOxB($gP1!g!u(KH*8Ga?OtdLSgP3J8)i
zAMW2nFKqnm7^vN_dVW&nRGrQN6n#o3NHO;^w-EX$ivC?-y+`$!W<YQXlFnQG;bZtV
zKcPk52uj)DnTCN6c*nWLR%32YWk4`%aZjMIQuDNmy>W0-YWUjoaL32Pg;Bfr)<htf
zwFZ92{hv4KV&p!3i&NC_?rzSZ!Y5S&09ldEu5>M)_2;!*T#T)K2FgwlaKQ{apRiGr
zl!cU0L1yGeu;Sa9%0lC)z<!r6VPbQ2;?ljHhOT$|0R1h-Wp>Ho;kHjUB|Z0h$PaA5
z-R8Hf9Eoss5zrn!iCMTRFSo(Wuc7QO4&AA|mT-3XSnH2bI$Fa}s_bWgLG)_E<%jl!
z9qBE<AJyse6HXJ~_#W2l0<s<sb`@%uAH5*F`IFUpPe^D_I(3dD%A6a#LnDEIpY@zd
z+&tEvFB_uA86fRZityLXMH<iL!WD;Q9{b!yX7VGCpL{xXp4c=Q=6hCl`_Fop${O#E
za0Q*Cvb;>xJc(><wyWBiFfGvtWR{mde_}8e+#mdOg%YJZCS#)T#W(oA-n3qdp6%>S
zvJ?_<-1)&LF2D+h*}10S@S$j}bRpSj&>AwX?^qCi$%^hB%FqGzp9-t~3zl~I0J~tv
zZ)@r3fQBcnpL{ZIq|gf~7U(mB#d=%L7=fA$S*i%HE^~zCCMNjB<{sDyF{i56EQT^(
zNu?c`k9q!dOrLZQ@z{s%u33(>xRLm(*NJiToW`7zzp_6z-G>Gd5VAVcQBwM)SE&Fv
z&zs^|cVj3tf?ypa_RdiL))sao=&Qg{#id_L9JWm*D_;j#)wMLQre?2gPPgB7tAKBy
zY<<5i%~ylQJ@W#Zf__4Io7Y>omnEM-PJ&ojC!`9G8lr&f=L;Tq2_1zPElFpOs^QJG
zoLDjN+qSwn1|H|j0YT?h3Ym+g%}Ui9%I(I<*sc$u#~xoN8(k0T#Ji>pM?2F80Xw^B
z8bv&fe5fct^wIIRed>Q6Vra)u=(ycnPqk#Kdbphd#F5oUthcFOv3WiHQZdu-a{d`x
zt}C09g{s#5o$3Lqntd^1S$)upnRoRWsFV^lS?I-N|Lvwz9y0A`g$krY97V=*h(ZD=
zqw?mD;Jn$K+-zEpWkk3^LjPG<#5n$~u$VG5{VttQn8ldM#4TRyveg<>DGM>*d7f<>
z1UyOg1$IVQdNG0TMCdM!_UszH^hhF1O5q|D^-PeE{fZ#^?#`V^RcfR2zenZ?e&T!@
zl9R3WK;5t2y;au7i>yn;5-067w|(RAFFw8OFmlmhpz<D$ihF~TuMqiG{DA9yqF>gu
z3&-X$QaZZ*v=f}cjX#8Koa~^BT6`AT@u5^A^3YI5KlMIF&0ro^S|e-;knwznU7ErZ
zN<nR3KPxTDsrPtt4CY)YzN)kcj$Vds)JCQZGo(?mWr7UONvu#b-Od_07|ru8CuZmh
zFSf0hWB;@E%j*Tu%%yXyUcWZ<9t*<=epX<e<d?UhC^%9Q6@oHq*fy(=$0)rI<Rwh%
z)~5K-CGBm@$z2$&p%bW|kI-Z{9H~I3$7|#YpvfxgRl`pkn7LQ0QwXEgL3yK$mXHc-
z#(1YlBu^`8-J!cPb}<T|hEEROe{N+m%$kw!Ua~;<U?*em>AMeRmDY$zDQNB;UP$1>
zev9X-VovD=el!&|n>D+)6r@T$32$yjX4L62&1hmaq8j!2FE*lJ&?>sm^BqXg(<wDo
z7*{!eLim+%f#(wDzcw~_HV4@CrcQb~(`YuA`sT{Qo_z$mY)I%q4YYZJ!CK12<)^M_
zTgj&3(TME_l&H-Z{>apRuhD_0jc+d@9wSbPrl~p1(mEo|kPE8)HuWCX<pXgzH}EOo
z5~z^Vmt%O8y2&S)B?TWk;%vsMYv;-knttB%*W<F@T=V273YyrJsGtGAm(8U$-IvoN
zBCAG4{XSUD8si002ChAqt`J|lDc3OWT*UCzmgJiQ?ZomfzW;wt&QYLEE%y#&Eu4lX
z|IvzlgZIqhkJq|2u13ovR=oQ~xH5m`@p4?c&rLsdV${NXD1&rnM6bR)^>GqeN)=SL
z6+SNSk}Mq~LHZqKW-w%}=aB72kgM7}&SQ~X6Mc-=f%8ok%0cKNyih{uSf$;??Aq*v
zRh#pFDR>tg{7#}5vSbO-8^(%DOn?H>fuZL8_;{eg`S<#A7?(1Wc>Fi`UA&(U-_{{<
zj>Erh-yXxf&$%uo!oxV<w+IXo$3-I{&Q?(F{PmJPIu9a!8h>%BRKv>f2Ksd>|DrF=
z-`!4E@5hg>ww$dSC%2lms+DTTC2snABE2Wv{{>(Dm1j1<sR{n}uyyj^J&`pH(@4i(
z^0O>o_`!ubK85O;m*L4WT?V5mUzy$O3%4$2=_*PLw3x;|he;3TVMf_&ywO}uKi;&8
zgn4Bx1$Qpu=vhMVA!Awf?StbBGy+$J^me=RBO0J>5xub+Pb1<cX^Y-c{jLfRWyXHl
zdwjvnxzo4Ls)&W`Py@=lK0o!vXT33c|Lf(33%xD_G%3ZK7lzyB+j6vXJVzs(Y6F!I
ztS$yF6t$udyO);d3gvR%lwtx2jg<o`tJo!@V1P_!T3J+_F&}*Mi#N0^5xO4heNZ6L
zhddc%x;(jsA)%Gk|F-z{G@Cj00kvz>@Mhx+fI21>KNWW8((OXNJb_x?Fo`T)j1v9w
zJytB(pmVE73pt})BPGIU#?hh`oxR!r2Fp98ODu|LxPX<c?+qEfhV3^Ch%k=E&5ofv
zal4eC&&^B8mDC;QuLxd~(JsoAyTY*9rp8opb*hUi{E6a;4qINTQT4Fi-jcd6$4WP&
zED!<u!La*NCmmAmfe5OZ-QH3mmd4yu59&q+TC{U<eQOnWzbk2qqy7eSRsY;0zu{<3
zRv+O}MQk6pHdTiVJEZjgOmcY(e<iu@2=Ct^zw%M*xG|L};P`j2x1Vo({&ViP-VX6w
z``$?=*8EUmMDI5!d}1<@L;Y-}ma00^7S&NcMl6vtAGCGw7Z+uyZspgv{d}>&w&X~O
zw;ZqV1eSkp=C1fShi<OQfLC!=8%-7UxC9*Lh^|jQCQ>Zm2p17pY;Pu~ejJspqW%uE
zudE*ZY;;QeYu=$JDWC{txkY(o*te#eSSIt()`xi0O^qXUA&Rpm=#gfUT(Ps-VL%FT
zDqEM(&ZT`JpEQR>Pa_nw?E@jbmcZv6G$Y*4f!OfMyePOwPNA6imY)GT5^xRKI=+Jc
zA|oan(yPBuH7W=!%$N{%-<q~4I<uuONxd0<6Xiw3SqVj=_6K}p@xrQ>kU&(;0G^g;
zz2frn6hBibl7+^)_a&ynqr2nli~<egu8O!-PiA+L!r#Y;n$aEd`bjpR8)#YwHJ4<G
zw-*Pud_3qW1mDo;-(DNF`t<?tH4<eM9pd=I<yaBM1&jkeI*~<*mDj|GOB=<d=4&hC
zePj&F_3+cLZnAYFpE2>!3B<|!JZk%YLTcZ0vwcR|@fy`6KZTT5sz#|XD>G|WV?V)D
z9FOw?i7UKAW9^xb6s1~wz<vdxOG$QtNxeGwczDH4lJ0PFdp|^l(cL3>zJf95Cg4b_
z{lRnC+B-b=$gLK4d^JmZC)qfdysA4#p~>iRF=-7-(R4~{(dszg+ViKho#5kz<JD~Z
zT|V+83r4=*grR;+(h?e-CYC%cqs=<2U$Yj^^Z-dP@Mf*-*UmEz?=#;-6dVIdJhG;I
zMYcu`9Q|UB)B&M@Sj6}O1n5Ene&QOU1-@~@ef5t<4`0_;Zf=A9bL4D1ZEPf9&u$rQ
zVSlc&u5bXb5~L2@S9=p+S<+KQcyv|<Oftz<Yd4zfsz~AY)q`S`N`pDWv9_UHD_dh6
zCNmQS!``th?3<j;*7T14?0pNsa>pL@k>0s1-%gdG_G%0q|Gq60=+=^zb6V>4ysZQ(
zwA=&-@-@ogfX?3G9O_M(G*H~J#OJhQ>0#$iiiyOF#TV6WdD`SJn%8U}%RpkV5`^df
z9AF-Kvn_DwYS2LFdUMj^$Z>^lbf1$C@U2?#7A5xHRYrrsX}{Y@=Z}&F#x#7U5>1#g
zhCbF?U6Nz~d&XV!M5r0O;?8BZR<GChJ~44#`B`oKg@&Y%`bt&a$m#FzzS49^_mLsX
z2;@!KN)btmT9#}H5pTcvIISi&yRTr;LVJCUz#yO|ELn?l-({spmhsDl`bm>&dDQE?
z$I#36Z%06B1c)#!8^CqiDX35bZ#4a(_8u;@u>4ITMHhB}^MY2APX>BRTCskLnPL9x
z5SOBj8;O>EC-A3WVG)`W_Kv)Is?;xEe!$&+!k)L;%Gc<kNt6wdN8rgp3msd4WMEUw
z4Zm5zK&ki`C`nQpeE-a?^)6?i-rhfi)4CNW`o}3qft^{ZZq0T_zi!`nh`;ba5`xyd
z_C`Pubfwjx1b>q3ni`-utG?O0o>G@GdP$E9f@*(b@IaT2w;Q}Y(_`Gxb+3#RaCu+<
z{-i1hsvp}_3qd!@KJmw>m9<ON9j{N{6@#F`-E*9f_SBm3Fr|4dx9-yO6$rwOZVBUn
zBpr{Q?)bdqs0u+9yTG8}dU;I<I+wbS2S@<nZ27=+;K~;PW5Hzzj{#S(l6%XbwvFxq
zAkLiFvv=dd(7&wBQ6{{#qVUW$=0fnOf3E+U1`>8SxIhs1o+IX__W!j-{+ak64g8~l
f|9K76+r5AclNX&i>sG$N4|C*@tvTV~x!C^$6q8#(

literal 0
HcmV?d00001

diff --git a/docs/articles/sids_files/figure-html/unnamed-chunk-22-1.png b/docs/articles/sids_files/figure-html/unnamed-chunk-22-1.png
new file mode 100644
index 0000000000000000000000000000000000000000..165f93e429ff5fd050dda650ab72f84bd3bffbd3
GIT binary patch
literal 70554
zcmeFX_dlEO7e7vyw%Y2ewAAcSqqMa4?zBgZP!vT`yJ`eM+G=SjilRhl&59AD#7IP|
zC^2frN@9-$A;if1=JkGmKfiqbfX`3wJRVoBJnqMR=eq85o%1~BJkR;?$lT!cN#T=R
zTwJG(3?Eo=aUBik;yUbl{21qo)1hH!&UDPp#NYvE=6nwBw}3g*i5G_U!CYKo@&69)
zl*KI%F0M;lMi1`Vgy*i|ygwC1#0c(^w-+n{(H0iK0iC+8HB|X|2XDJ`$NxG!e#Lz?
zvF(`2)5CFXEAI}QzCB#+A)uP6*m>sHr8d_)Y5yF1R{hwO_hV7Uc!n*guPQ7I80Hxk
zwy~O**9vPP{h5zoT&atMm6KX2D+AI6SLEQ!2VQ`s^n<AFJqGK<fA;ymum4Hle-ikg
z1pX(1|F;q_Epj_TVkG}l!Oz9@YIV=IP@IcPwBbHqcw)hKJ;p3wsf>Q=jl*1AivGmr
z{!%^W>PV=+0spI(e#1j}XLwevJRfM3vt!e5FxZfv>QN-ubVgCde_ny#xQ+MUABx|O
zApfrmIh<A6UVkqiN!*t0@w8G+>)iaYiMsIb%{oVrZ8oq#XQOCV_J}WBrU&pkP^p8s
z3G^3wqH3*dd(-8_d$ZnCoLfKgaVsc7mt0)flxAZZV2FICKcMD|R+R!qtsP&R?G~y&
z{d_vYDdDaRl9KLr_BJ6bX3-$@7U#)or9;k7X*-%_f>mO@wdL2#G!gv)!e<AdhA4G(
z`}v9!Zxh}A-ee}<34dW<6JUs3Vq_vNIur6ta5*i}%D&e#v3We4ztJ~o<28jwvgW?W
zD?SPYNFX<$$M&X{oPc$4NjnlzU|Oh`2tsuHIs>=H2!r#>97dK^r3V0tvG8FyaR;V}
zf*GS>!>CaE3}=8>!{{Hs@>~1jfsHyh?3giAi$=A(v{UHAy)zU6qinYnXu?=4dKCC1
zdRfa6)o+Gqc401gAn=K5;awHveUJG;H7_gj>~lzDd_HeNfuVh78Hv_F&s-dH{|+OL
z-9}~|YTM!8JY-$k+IklhcOQ|zMdJ2t7*+u8W>$w8gqCVmY1P-pHal}oKW@!)+nQV-
z?TK})XqFdwl65+uj>yO%B}{G9d0zC*vO7iBBwIO21BiDwT%@U+d$1~NJ~*7DIl2i}
zY-B>vSYMW!<NAsqDc7DXUb^hizO}x=Zp~W8OfJ9KoST_uG0Lqgb^CI*%Wq0(8z5TO
zXL6{v$gK+@ixe<3gZJQ9IW_>~|7_HEZj3ZP=5BAl9GSA+CpY%{Eh*1lhuDmtT~|Z)
z5x0;BAOQN}!p4Hfc5-kRg=Jt~tohYH*j^xF#W0lsT>GWT_v|eh9Nd-OLE@=f%Pw5S
z(;G%S=AUMw_3bmg5mT}WS5VFh%oz4qsN5{MXLa%~0!u1}!IU9=%8;-FuBVd`2%Zwm
zT-1=0I928t(P!l9cmr|aaH06GOxr_WsBeCD&ee}#Z;Ij{hegI0^adx<Ddkz1(8J@z
zF|yn&7Q#KMem#xxA@Cx6+0;H0aed5oO?4kfVkQ(cs$@>RY4<;}PLDXSb@}C|+^}4A
zv(#m=?afanWv;$M8|>{m(k|pUfQ-2+5xJ8mFaDQZ10x|r>dd1HvJ246LcKH7bJSSg
zh^)X8YA1GBi@s~q@iQJ-j_|G=n=z@+_=Kn;O&uasoQ!s?9INzqLlXoy54Ab9wdg1U
zI!ko!r_s)av35;VfG<bxk3(SSB$1>?PQ}Bd<;kIiw=9UanzZ}9HcJ~puh{B{7Lxjk
z@&5W3@6Szx65CjtG!YY&C7<gWb6cS`hs^%l-ZY`nh#sX<o|}KPZiC$Y<Jc=^5q<V@
zpx5QT#DNmv?$&+Y2s>EtzdP~4Q%6FheW&VP=4b4lNe<zlj_O6wbFL{%sx_fenP`dh
zUX4tcm@gFX$RuVLmPs+!pH3gfC-FVVH(c+0tLL(DXliw^DK-1ViOuDsNJoc_-R)7k
zs>Ox1pQ9nj5r47q+Pwm2?Y6y{ezzRBUV5$O{_@PELSlnYQ}wxpsvm)m121y5?PPzn
z*yNgeq~Ijc(r}zg=_^uEBD(s)G!JIJ$5#XSYqm9YMy(Iww;G@)=lXh0|FHLHR=|<_
zUyfTKLsaw*$`uxZ35~h7mJ5$T;C4K`KZV>-=`3tR5r4m7l_QvMW-qq3{Q`x3SvO%?
zSQA6tBq{)HWBxsX9ms!IUVD*Nec#f~NF#65Ob)g?$dM<xQ-0iKU}uDUGQ4ZlxC8Ip
zo@?tKb-3lcf>UFvl1DawWw-Y`B_9PB``&@5jYY;zsq>#i!N4WX7Fc0|nQ1VMR+ndE
ziCF7isQQ<8@V7`NlQ$x<z_4)8kh6^zoOuflzZvG}baUqDtClXIlFM8zBSOPw4uRer
z#eNjJ)*Espg}RS;{zdA>!N&N6@92ilJpSA4unX#o1U;Kzh!*xk;ltQl+EMJS9S4to
zg|O1H$E-Ue?J&Hwb90UaBf0A~8i`OnYyf$faBD>jl^q$RJKBUOZQL1RSsceYnQzZ2
z#pWTCsO{tHKFY!fDeI}qQSLy_{t#26@q%0%hum5Jh(G1&RGC@dOWU3PZV*)Jsl~MB
zONtbryI+aiG#^N&7Ma#|ZhUrU*)SPcLgV=jsqWxq__AH=rcVr2Nnx21Z1=LkZh3Gb
z%oC6kxGLBhdAU!A)edGyW9Sk&;;&%Q@+clWgt&sDqc@$UIr>?&c7yDFiy5N_HTSYe
zzfpBM2(Wdi4d-e)eD;--45VGRbl%R$M%kgPPMzqAERz{(A>)SmH7A2~Y#fyR0u*L@
z)hmLh5hu5KMI_FEL%*fFu!$t2v|1TTRlLPgYn?&eBdI`nYA5@rSgjrWX0emN>N+KQ
z`+jM<HBOGMTNV3=4;;CtowhV+E$hOjv8uje&9>+2R-w@#*wR{+pfv!X3GFY54pXxd
z=xF8+1OUolK3$l@TvG9`1i#!&@~llkZSI=j><x32y2Z;uyC!TFu=IL~OcCV$N&M=d
zaQnFd%eS!k0+|G6G$RyRYY4l=Oz&6lgFF0yk)o)@<p)F)yL8EA^S&i9zI@|(LpfgN
z_28r{N!QDo0T;4bR>R6g^(M{TOHu>U<Zv;Wv|;9=Wopsr^>ioge)qnGt4elhTLi`#
zfsV@4LGWnpq<Gy=6o$3z?zYl>un;9LLL1<_cRA1ryBgNQ*?N2CX%G972|s)@Q~!pL
zaFTu`D(|E-*O!+ZuN-NE+B!|6q3*h4^nDk&Lqf@gt7@IVd%0reqz_-7`R9C}5mTUx
zZ%SqRtJeM%8(3eh7ipP_YmEt&g}dmW3+Yi^2%XQoCLoffmTJNRj~?ZDLV;-1qK$x&
z)AHm^3Bn!@om-&9s=R1h5&dB&Q6I*G&+5z&w8kTmU^(L65OUv-wk&P|=F31{Z18)0
zBErt$MuiN9l8hOvvl=buQ{XaH13hmW`3^_v;_te^)0Kt0|Hyfj`Yi|KvX{$0df(z;
zjL7_+=sAZqc+;&sBQjA{E`0C4dyw}14cvY!pYE3fb3JTkOH;!%roQ;+YCsf5=b?E>
z)dpRNulLwg{9R0(fi*OGid6+C7H`p%yhHZzIb~I(5KZV#WDC2%_1f``z0&1_Q(V&l
zQF^GuYY&`CTN~<nDpFVElcIjr&vh23R)NtO>F1#4e-sh-6XRCZk}t=k*#MxV#CV{<
zZ~g&i<6z@fZFSWa);Ctm*8cQ@&4!dwLLX>g*VDX+{g)@r6T}{~rw%vn`w8RTMcY4t
zW2dM`{Nzx;dT$O~Uz<5vaxZ$D^7UTWIeCKVlKDqJY6m506*en|Z4mV}wPuV5(DoJA
zJL^w(&E1qU2a=Yo)cE>M4Gij7x-lnSB1O^8dk|Qpw+%!ONPBn{_pdqb6w({<%+nEe
zQctJ6AGKKhl;eQZs!Coyo;&P2-qoce)iKxN7Rc{exkCAgDGkDdRHF%3Xx`&!QMvH0
zZe<&OwXPkPsNf^a7kbopSc+j`>aHpcnp}t1?axsgmPk2qA6U@1OUy)+k&1u|A<cYX
zMQS&F&#MEF(McL88Ek4&NSyM=9J|apU_>{o=;S9!6ScHr62}eouNMiDdoKTanEJzu
z$8~o4Ly<<h+tTA9-P$^U0%3giY1jDMx8Bq*$2?mu&p>15X$q|of6gO~YDd<Wv(TG9
zH=~$V;t+rTk^az%^G3~dflYC5sfXZu$zSY?kr5G7H=>CGtKw)qRD7%K=-@EOCBmsV
zXp2O*?S?q*43Cy@bCp0ih91s82m*>tP4>w<$}X8pK1_An4Nu4}jMZ&@m@3~djanSR
zsHOGa<G4;EcToH}3xEXvg!iDL?A@KPkMj)2;YTW3=AA0PkrD5iKy35N!gLo}FJ`qh
z>}pDHy)=y6<5!;Qlka?Wuc2$FyXN#_9~89*c$kgXNhx8^(5=bT?~rEWc}gNEMnML1
z`=Mn~6-lcB1o7tqaGY9*NV}8rE3uVOD+`~;_JK9&qq=ED#whiC8vwDGRF)Os7fy&=
zjkE%Euc^}L0ZPa7j&#_9yKY%pSSH2=tq=6*!n(FEg50+@<-)O%TXTI3N~udvDhZkk
znLvNQoEbvshWQXOsYCam=A@O@8)U@{JC}*k?PeF%VV&)8+8!DdNY2L<D{F%E=AL_c
zO4ZfX$=XKqTVtsuv;LL>vI+M%$%u82xUk|N(N|Ckal00aYcvg5dOqYh84>E^bb1n?
zteSlSDQ_*N(NwpXTxV1^1HH2JxJ9eCL6{ToiFIC{aoSqowWE{`wB{D}ZPB$Vsbh8Y
zscmL3Z&xRx7o-#leHpRG?Tglcu$bhDDWL?EjtdOtfM5pz0FL6_U(MP_nm!e!FMPA)
zJMwC<F7cRYRkN`U*mb0E9EE>*8^q|xcqL0gJMOA%RE@|^Dv?}Nf+b}|ypdaO!Z>F3
zrpHLa2@Uhe+xks9mA4>%FrmV)-U99#-**Lq-M=ijxQL?h@OjP4xP+^fo);qN^oQfi
za7jH7^T`E=DRsAJy`QsOriYpIhgV0V$<tIOsS{t`3PRz<F0Y40QhbILLmk@lZxK#%
zzYyvqr)#x^QJZCRl#GI76@$;o_m@7_xjWfASX5UXN{_q2(X{lJ(Cgovft%@?Nr?nQ
zjo18()2>$6!%HP+{Z)EC$WKE&dCp%SQ0^p4=%5vw#gQViU5uk!5JFI3Gm}Z+LLomf
zn08B);KY;#$_GS|dXVZw{3hk=d1inxYEkD#AyzXDf0dBS!G-QK92;_u*6={>?NtUK
zKqL&ba#E?{@hU-XMy!c!`jY*fhr2E0pUp$*<ub?adZLxSy!Y#cokWyZ#l<`Hi;Bdx
z(5tUH17c51*!ni4vtTcZh{Xq;!Lqxq2Ej#Ak~5WE+D9g<c7@_%L_dxRvEXopkAy6%
zdDc+O%*gcXo9uTaD5KCzaJx=0Wr?apwmA61V>L~GejDiK$IFW;hp$Ck1VDF^bItdD
z1{&vR9d8g^9!74~D@U4u9KioNJs$F^-0Sr)*a4<?+E$C_Os{F0h15aSzk0BGTc>V~
z3z(mQA~uVgJ{Ws`E!ZHv17-2_<#&z~ERQP|p*t+uEA;b8`IMIz`4!3ZjG$Cz4S}+i
zYI!E)JOe8guRVWUytkE<JtXs-Gk*n6Cued0UGTi^PY}^i%Py;{RAJMhH2Fs`^Hb;E
zP<;n-r?>;Tn0NJH*I-~_O@~hkphx{x|7_NW_^!Nra_{Ru-;?vrq8ZbbUxVR9$<b^?
zsWy9Lmpno$3YuLN*wf9yuWd-TmBWY)#`tv(5OBgK002kq#(bkSSn_eagXGLnDLczE
zlV>YzUhKAXyQz5(oQB0|@)k-E)&>QPh%j>+rhWH#d7yRC7ai5(?tH&s=$~;dV2s+o
zLK~6Zu-F@)_}M7k{q_iQ*h>D|3<~tol{>I1+5RY*jt|p>Cv9b^p%>TpN;DUe2Da@k
zP#78Sv}4GFQ452hm$dQKh4Iz9Hv+v}&+g-qX_2e6Z~j80PE*)0UvZ8`5D5)fn{Nj7
zO(=_p2M#%!N6fn=tRqXYfF89x3;OTqRZ%n;TRbzhifWl8>LL%}ql1;Z1I;O|l3j7>
z`Ozxf%jp$)n=`K^^=>nmTIon6v033-Q%!%ZS9%mMEzo$#gz_NG<sz$fLXQoJ8~v4k
zF;6dJVNWtbzB|~6HJCG%WrSC%kZ+alt~1h2U8s)^pXL%h#33@8dh`?Mglt-UX#l}!
zO`hYAC+5pQCcrotk8YJ`LUz*#hPQi;It65k^a)f>jL7n&`l3NEW;e`7LKA%9#i$q8
zP<4S8fMl>lhoe-{!}cFSUG2Mx1wxSaq%LoHkV*`Db%B_)buwHDYns_v4hydz?wV?9
zP|i6y@1=n2#d1bVzc?mdqDflX3t~k7^Oejf<FN|KvPSKWRPL?CDt;eBDKIJhPI=8$
zdzA@lMzo}`q35M}8ktKNmuZ&RvO*Eg$&|d~UY5{#X}>a378Z~IGY<5Gc0X3DhWcAr
z3eahd-QdiHz`!BeW_$Z5DxdU0eEChbLY$s&AYzhiNC`HY^t}m=7CMX0S?E1RVt$Y$
zXitA;S4m2k)TXVlNh;jrt41-GyS2vb`%|P3zDfG#D^5joBzTS^!NG*9(&@p07SXd4
zT2<v)ReUhZW%E;$5~8-nULaMfzW)^(YJ^EWsoePhDBDMZmj+Y5S*ARr|BC=T_0xso
zoq1(5D9A@_T^P$#8tyXXNEl*<Y>fChI}wY7Ff!T^n<Hy~e&NoCrj_2r{}~RP?gb5q
zVGuemuXjzh<5I><d*bm~#CrHO6FSzRETF%rd3o0dmt+H|C%g36$XemHU-ZZ+1kR7$
zPu%uy-5tFvfJHOGV~u3!Dk9l096L3J>igRukJ*VtaWdqm>B{(Px@ik!DUJMv6sZHZ
zw1Bi=qZr>bz03vP_9+&l`ra;F>HuZLYEgMj-uBI8`nO+FHHwk%CS0`L=RBxz8e0#&
zK0(M>U|&4e2-fK?mMm8*Dvif9OLv1I3lfq|c?-DquHDjfd8vcomZ<+<jCn+wEqT0B
zpljgNbyq^TD|FGOo5O(Q8WEjq+wWfl7RvP0oOlqn*eN2L0yR<LuKOmPK3w4Ha6DX1
z?Z#+}oTsD5g_ij(VGymDLni+6$1}%uA|gJPUqUl0_W~jryRI;zriF839^4t3$~O(v
zmWbT9N&X>hRG3ZqwpXOf_9H^F_8K#<j7A4qz(f7=^-&;Zp_i32NM)jXyU;=JW8f2z
zO2-!6Dl5tVD2f>a#*FbM>0d=TTR`GabiTM!a1=lYBAJ!0t#azFol95*;1gY>eX64L
z@p%@jSdz_zk#0&Iuq5^Be3+1fCQ0z+Zg%xgs-DUzAbTWdi{+C>7K&>Gt9BC%Ybkd@
z(kUXZ?q8WX+G*i+dGsAz8l%Rev)ZF?rOLB@+LjqZqTnfG{%0aFv3TSt<u%V6st|cI
z(8Q@U!u<^_T)N~9Q1iz^3os*lY5xe)qV+}S$o)n$G|n)yb3U*xuduGKH)Z0;3nr{z
z&>1q2E?Bh;k<iW#jM#kUnd6bbgHL@DrAw{nZE*;|<(ROiwT|VV4%-(;5-NpjZ*NUb
zbXh-%k$nhExgnDoQ1qlZ^+!q(cmwK)M`B6-7bh<~Of8T(f&?M7wW9~Bjl<B|%`m55
zY-B$*G))5U*+zemCV`u22BkALB%zYvKqv_=eE>0HMWqomDz5Z%>jrS`wgm_)>Jl}n
z8Fp5vo#MNVT1a`O^N^D<XFcb}Oj>6#hyN;SrT7p{6wZVlM+~>a>%O>og5otcjL0*z
z6XH4VwoY297Qfkh#4)ax-sC|xecJ`COuRf@GBL$!D3wVYUT-fi4`-~^)bIlBNPtjX
zI%Sj*JAnE;fQ(Xs#z5!R9IdD6E6G`a{6+;7osi+f$NyIR!D2K#R1!zWXKY+WbHZlO
zUTa(bJz-R(<L8l3RAse;1U`BTe8z(9kjC~-k7?AR{+wMcP4`oF-&C4<GUhV1ptZEe
zXTe^4G1NefiV3Gp**b+i;+(aPP`<@_8?LhM6LC@6+9h)Jj@M{aRzT4gt)QnEi`&l+
z59a8Mhl>8tS(A}yKEa6+FRU*e(NWWXI!Uu{=z3;_I)Fft;Xz1R7I>p9QA4Tj?sG@!
zWlzV5AGn_Gj+lPEXpMa4v|L1Z*!mMAp85MJP|eTOH2{bEvsQ5Kwuss&eqz5?(zyIn
zU{6Qa@Hh5*a-KQ+8($HSw9H)9*?Apep<TV4a#{|6<oQ-bTEH8mXBUE;ZG$6pD{Xx-
zHM^0H@pO(kggRL`IcDGA&5)E3+x^9?Yu`Pg2U(cfQ@2=jj4RE@FQ{VLPfk_(jU2mD
zeh5z%iEAS<D@;4X0!Eo<h(U*|c^s6v3IW(Mcxw)gg5eQf!#DJF9Q^$4>sTK;9$PSI
zj1$Z6eigR%DlCNW?W?^<^~Ur7VEWP*2D+<~9gsHtcx|a$T4AA`jMl^5E+al`fCc-<
z$POU2^OrBQ0H>EfNDnM;?d4(W`+owk7mS4a^k2RrjR%^buIGodUdE6?8zMWSfj_MB
z!I9O`oEZwzMs@aPVkS%;N1Wxa%J9hctkXFDOd>LnxNTADJkAVmYK@Ui0!f&0*dzb|
zL0hQ;07f(UzgNEfJ*m7lp>Wz!jA79JVK|1cxtuKtemd?8EVVtOHbr!-Jdo@{H1<J7
z3e+l<D_EVIL4Hf+zWoxv=Z`(*<CG&-DmLmt;}@3GC)~S-xB+jI45Vs7=~h3r?#5@C
zo1}iea2l9(s~gx=#okDGSM03In#e*#(@BZAX?3tp5{P4xcSPO=M(#fgFn`q8GIt=y
z8?id+Ca$58HTS1mfDfg{6tNr93iF(r8bBTULBF`EDxCDgp<GJthKQ_qIPm3G)5x|U
z5b+mJnF+?M)qM8I4r_rnR}GV>LoP}m{Llo8x~79FXZy^loX<%&Zb%<|kkrdwa7<??
z7_};O3&sO#UGTFMTTjtx7^2H|cEi?|hG&4=jmE-!&=P8V!Q!j`rx$<=^i<)r&<EB*
zU=e#ROP_zEYDHdh{qXbRzt2l`zt8MfoBnZK^0;MGw)%`=hHy)(Z!tj&r(nk$sRUf2
zmvi<&G|#?QG~vE9U%)KS8b6_t;rT@?SQ+K+1>9L2cW$46!FDSF?Z)TV{S&TqaEL*5
z=4MrvBcYL5|L9+8Ykjf}s3Vurwg%Dc_DW-9x{hbN^2S1Gw9TCswWdD5G}NxB<0_o4
z1A5XQqw`;Mda**>c$pcq?llZzW(=Mwf*p$ot2$0KZb?lVr0qUQXqxX{+Y+eU75MC%
ztol*Dd}Egt$3K$iI+Xv9+>htu(>ByP`2?ggdSVb2KcD1l;*JFa;ksMJ+fCrG6tWIU
z#=0nHrm|0j7aFxlz3Vt=NsY(BL#u4YsyMrUkq{g>H40jve5EGxwkgyp@FJxuV7RRn
zmd?P<k^`NBaXtE>b;PNR8S0kgp8pF-Abws*X{~t5g3<tBhVQx6b)9bG=G0~4tG0im
zjZljD8{01C^+_M@oUwsJ1d=%R7Tg6C-&GZkHRkZy#12yT5VaeQ@0<Pc{Q1o%=D}OW
z!nlqinANV9H?Hx^F3F<wfS5JhN}C(w&HnldXnZn!SUBAX(K)JYRvYGBlaCiVqQ_n%
z=;{$Ki@x9GewHN>Go@p{mdpY-2<As_8EZ0qy1u#FXVTC0Z!Ev{<#^ZjPxb0SH#=g<
zlMw@S=jG&GE0Id~^6oKCk;ziv5FQ8eN=wSQ&;B;Ms!-9yNNgY0Ywnhgl{1R*+^6e3
zF0Gu~k_3aZ+@1YpyIn+CtZgIlshO~piiq5n2u{SIs1yGB{wSFFE+qe8ddAeLR1d7O
zxT;hrW&>R9J2BX!e;X)oKdo=ra{Fo+_^rRxnI7{)cv$}Dq|c#xi$hV7b<%1mu)UqP
zbIfJ?sNjO^&=&TMCnn}+GEuXN(%&6kzKLrt3tIcB1pw5!7dQ$w{ZOP4alBcA6n0Du
zT_-@=$g2iHF20aL0BU2iq~Yuh9}Ma`HZ!ux%hL;-%bY&5#*qRpK+VIxioR$Ov|y9)
zZ;Urun#S6738W^O$a?Z@yZhS~J7TGs{?b3Z$I~T@DIC@H<79YEpBA2^5%L#W;?ln|
z_jBkB#^w$}>YziCt=Qe|dWrT9fS{)v#emWX*$W-69%~{-x}O&Gj3^4}$cBd^@$38L
zM)<4+o^<W}1%l)OqTOd2A$b5y*UnvF&CXA)&mWt4bt3$AyEWFHHH~gvFX&8l7r{qK
z!eVN}uXgm-jG#K674|?T_{*}E_@cw(Jt2ViNs9-{_<jAM9J6K<Bd1baj*)QX-2!{n
zVZDPpw7$FWd41rmB$EL?se}n*r(zwp4{^!VO4X`V$VT(L2TWfJ5Ujdwp_heaZJ|vE
z{fhiDWrdRjD)kfeuX@yJsQaTLoF<+$RUy}ZJk}ui6v<#_*L!|aJ+f;7B{CwiB8xK=
z{hCDGj^TgqCA%laF>{4J{3O%?B+2SJkN`mGu*C%sARr`ib(e3C%t!$rh*)ng{&7%1
z$LL5)=w?GuOpSBja58lxkhQN>@(GM8AQUrExXvL){R!kt4czpm-T(w7tOdo&P%^OA
zWw31EIvF7s5cNn-m?GeHtRs^{I}bkh6WZCOGtCa;YvmCYJ0ADh>fJ!egVx!BgzMb|
zk=<{oh9zB29P}bBU*uRLIy(Gduc`@`;Yxao&RejMJeZwb<d`;Cr8}Px{|X^)%MbQz
zoF>~3r|%_6f<4spP}%`pXU4ygi_br_+>1m-Yweu)B8n1hO)Iuw^!jJ@MehSYk}vlq
z*$(+goA_Q2SvHqUv=-%5F}9RebDx0EeW@iDuiPwIlP~(Bhei#J6qZ^eQi>XBJ-QjS
z7s|*HG6SsNU6dX6zS^E^M2pbfV4*7rhxXyw1JB^_m~c%b&M{^NbQ{>50rNWp7G4$X
z+lenl6`1NJg<w2s-bL1*S2;9(Pe`I?b7=OW@=zHjBtbuubQ{`i%Kk*?0dL0g70DAn
zKTNHau^OTNSzeICy!5;NSN~Qf^T~40Zg}C-a+w61(4lf-2<%yn<DzG2*5cvgF)lGo
z{g{<5y?Qc6OxnOR=U|h*fhkADM1rPOWA<A5mwpePzW4jYmKGu6CRtrcUDMOs+k0wH
z>$^h4Zr!`Pobps%laap}`oH-TmUCv5*}ZFZ2t<&R_lcS?q>_>nBxcOP+1b2&G-sb#
z_n&S94!h@ymaC5gG%6WgNPi+02ZhL{O)DV>MrWC-L#8iPjTE{UT?x~%x3xs=;xZZ`
zVkHfbe*xF>C$DHS%y>Bw9X|DNvAb?wWJ4;p{Tdx7P}gM*yl^bP!z)=bacb%y=Xv`D
zUXM|;2}k2Wd&3%};))tFw%stWDMF*84?|aP)9lE|8kRQz9*@A0N(m%sld13e=9DVE
z{nQ@{;&<+vSe86jwN`T|!*IGBtksU`0VYhHRISeU?O;4%1*tKGsj%locFMzY!mGvE
z0TV)RF%NI4=ii1Z56kw15cM@>YoGAlTNH%j4#E>9J?u~2CrqCN2lBpAl4-k{c*Wy(
zqmxD>($LB?e5%%vczy9q!)X|B59<jYXs)uB^v;OQFYLSRwKN%fR^AA1+|1NW<bYci
zXm#!KKGQ$~9Dv<}3h-i3QH*W)!gTk9_Rj8b(-<x~V0*W&YbYSIj9BC{YF`DD52f4Z
zeS+b^%Ueo_UpVLy7|%g*PtSuu`mKu-#;-APmwo=5ytQun5k(x)E@vi{r^WvbW0ZxH
zw0>>HpwZrqNQzqS&MV;C=5}K&^n1MPde~0fy3m>Sp)+Ik|2Y&6ffrvur%GEnp_##c
z^CL~ENnX+%_Sgt?b5-69ytt7NBfXBzGo{T(k1x3s=r;~J*;{umxM)-`^Kfzwi$6!|
zM*zeC=~Ye)OR35Ym_~(Xm0uS*=yZ%(>BlG?|4gG#$IYQeF|t~Tv0*|FZ|%>`HVj`W
z!}?~`v<Fo*Md193fdhqz{uHX9CH=X=-HFN>grP&<f?-`Rs%||OJ%M3R`tM_wIf<Gy
znntVYy!`?H#ibtwI?kuJzuEod$zyc!-9q`7MF7u|2}6yF5HSYg*sMp!ob4xjtdWZL
zy4NNsb)h#kED`{{LY*-wmV9{YasT9ce?qfi!mMw3{|hK}bI}%ya1H~c@uUnapqBBc
z<bagoKG&$9b(H3D*so|gjxSPD66rHjVf@-)0VM;GpJ>Dbvn&9o7(LhPIED)F$Hc84
zK{B1yCMtdjaS8e2J6^|PNhRCGF0J!(b1Pe+fx4NRiU0CDZ>Rx}0PYf;+Ruc~5)Qn?
zxA+0Qi8avqd?O?2@X2sK>xe%RBCr@MG1hjqZY0^CyWjj*u2I=5M~$7R`q=MpqGle;
zp|0DH-}UfulGbA;a_Yn_la6GqhEi2QiKvCVCyvhS_i-_RW!g(UEbyNn@Nkb9`ue%B
z`K@7t04;R-@|>&fCN?yhR9^?7j)g)w;B8x8-(8t-_r+AM5wnw5giwLKC~Bz;T=puf
z=l-{TxJUO^9%E0!EicGAN8gTEiH=qH!TsvP)tRGbo-F&K^CGu8p?2~Ll3f-b-3(i-
zJ}1d$OZhhE9xNe}Bacs6eNJbu$*LabDe3PWv`m?4Teou=tQ-l2#-|`Coo?CAfKt2B
zRa*cJ0QHH@`aP`Rg7L~nwItI}<lezt!kk!%e7be;dhQqhrEya^15aU%$$*8O!R*uR
zIHRDKySr_{Pa=KbUhvE0o+2-ica?Gp)_jtEVMN}6fbo{r)*#sqP3}PZOyEa2Cp|~@
zyD7f*j$V&Ss7v3<JIOU|-o`8Xy}9noMwVXFMkvZ;d00D`{Vl~CL0l9uDopiLv{oq`
zB!2`K2gT`lNju@jD~NsxKRgX|-W&!tayvkkf=M>2f)6#B3luknZA>gSh;u4b-T~3M
z@y_<%Crb8{+C|LQDcYI77+?T7(t2}rzN|?NaYJtXO4!_2Df=lyC#<)!aO?%amhc;u
zJM%ag(<EpOFOXyl!{#~fJ&*g37nN`X;@4{B$=~O26$1gcf|aR^4h}8+a^Jw0iwmTB
zvFo2h{N<cbsbr%{?*t%}O0~hAfN8==MLNuk=)>v!LN>VW<Kc;JFIgobWqi@4U}bP!
z^MrVJBp+t{N9uRd4~*uXg#UtAsTXDQL$)@X7?l?_OZ;vSwvxx}%+S`HGImc#!tvi1
zB2MP!Mh8#TLfS%XqHCwtcdMK&<SK<5JT@Nm#1pcVv8%W#a)A04DRQ)#+1L6tPeXHM
zRTm5d3><FzA(U>h-=+)`TpB)@ELB7GQL^+he7wEe+xfcskL(oV_|k3sCS6Jk{6)`a
zGkVC)+S3<K7xw(-)BB_QB;J0t(dl8@)xHG~9;`}W^(z^r8T5<xbr;4~qh!*SJXe?B
zf>x6t2m4;m{fmK5`U)#OJw<>q56ElZ49MzQLq0_);#TtfcCe1z{IvfcM*tua<=+af
zUp{u3+`EoS2sG1dN~T_aOJ}k=!30;|9NOekdJ8w#ym#~7(^siPMyEpH#rI>FM0?sC
zyy*ErNzl^I&s}7*?FF6m3`O(e?gJiE<HWd;`6=s{QyXdGNb4su*|qXr4QOxsOe4S|
zm_97gozIv;=Si^BCCtn17br;q=3@Sw#x%-u%-jdYT%c(nSLiD3r7r8h?&Y(R?7--O
z3FLHnfPZpUBy)9zTH7f}B{=z0)u-0OIIRiEU9CefS4ZxkIw*(2E7oO)5a0P4-CoJk
z0{OMKRQL~na{V*qhi~G2+$$;~sx;_ijC!Hck!r0KDbLmRyo_VK4^-It%>&V{QwX@0
z$tsHWMAL<Cn(4AX`8wGjyOb;qeP@~SMuoWX%%=0g=(CT(*1)@oan1FJiwg#p(T}mz
zN*`3^8Gr<q_-8b|Ri$SE%pTB73#&6sUBJ7?jvZC%yUiv^u*W{GJZIdmub#%hqh{-K
zS4R=L6$<heKUJTJl`aJks!WaBAS&=uoGm4wg~M-i7<nE%bZ&n_pmf6`Xl}YhjbI6h
z^OUn+t*c59<dRB$C8&NDs=yekn!358fc(^-IPlR<WIVf2WVgxv2Mq(|wDdR<Sx2Z4
zyy1NHVSKv<g=hww?Huh{Fe;bMxt=g*>oH@z>6p3rm<Ks!y?i(Y7u;5OQ6fKvNX>mh
z^eVAj=p1@0T3LO+)E2P0p*k%#x*fS5&QbN|Z$y1g{#9Pz-Yu7SrGrD11})Xx2yAwS
z#5Gr`or*}DaD~J{?9w-e`a6$uef<1Na2&`~b2cIu!#BJyqOh&08}G9A{7pd|7Lz}F
z8qle9#9=`4$8(tkx9c=Di7-BV>T`*S&ZN#^;wRs0JC(5Op-u!%y<}TEazGb&AA&g3
zP}04e7je~v`RjnO)76?L9Wx)bl=j)$rW4uxu)Q&cyC#*|IptG-TS+OM!&Z3KW$PE#
z%nAx|I4VB=-~QwnE!Z41Vw<;$Hu=senU_oGD7V6=W(0cHW0@CSt$<l|K{YC1ChB%g
zhaexX54KpUaB~N4?=Qr~m5+8fo!xBs7x$blE)%CK*OX^yt$cc)Eto5NOM0xzK-?lt
z^^Bp2yLPIhle7eQZj_OczaQnm+&V=9&W}t(xXA(S{Xu0jPBm7y2!5)8M_bG96Kdsw
zxFOflF~_c+EIpu*`HxIV4zjJTi1Bd&Po!7;bgF0$x&|F!mG3x5Xm+IX%UVE9A}D@6
z*2_cc9A2M)ZzDXLiEYhey<6V%h@w(f=(r2P(pC!nDUm`~6<aTNIWYV8?d%X1rg&F2
zNpp>ZCo5i4&n0M@WX~4p&id~sO5iOz0m7ybz`&bM<b`^<!~@!aNCc&${9qcZuy~ND
zW{vIUV{QN!Q=)hLy+1z`Ui?~0Hjdkew}xM4k6P%Y2Ecn#I4!$N5OKY9frrl8U>!Zi
zu*Jd<gTm6AiKYzbv62`diRh^#V!kysESUXizN?$l7Fs7V?GVNqrgHwmW6AXdGT~OH
z+tLbTpbVBpqlq}~9vtQBjD01zq0e;IbYVT<jAyrV_sg8WSb$x1nRfYRX#(p_q6a!)
z&5r3aZ_1kcDg1P66eQynqDl#NG4$U$R#w2rXShN&jhdg5J2U>!FUcqI(?@Rz!`x~Q
zm8=zX{8XRtU0gJ+>y6#(UHS>~-2R5ZrR(iOQ%+?;LTI6$IU;Cq6q$#NF(9x}tGnep
ziMQcSWJ!+SCTnG)*<NTlj>)*i?BvJDqHa}WGAB*!ws{h+@bWv<qb50Znm^1guK*~)
ze+BLQKH{(KWd2%f->=!{%ECa?r7`l}Fh>U@Ky^A_p8Jny!dfGpIjsWxZj@cOSL<cv
zj<f4Ns4R5myA)<+Nb8Oq$r()AfOg2UX#@VC(9tA0dq#1-d8mhkmva?qr0}>fM5((s
zb;JZKmZ#3$j1Az#9gaR`CW&$P;Z-7ckCKl7;BcY67v5KSCTt62YP}m<3PxpK7UBLd
zDC<)+n0YJJ$!i<TEKXU15W;A8Ived06Xyweo?3Y^^PaFsG5}c^DQ0@l_j8g|j3Zny
zum)y!Uz1nr%h6XSzP%AFF~!*%@2w7$(Cb|+P$5dPJpz4WU#}O+TN98C>mF2&?&6kP
zzl=@kHf|-su0u<8Gx`Ig7<Z&nVRS&kk}7aF;YujokT~{)LlNNo_{71Z7Brjy)0r3}
z{SXb|6a#m#wlNoEmy%Dj0#I8z%6pGK9-Q$-4-fdFX&K1<ftbs7dEqZd+9#|?<I|i@
zN(G`@v!3dR5{Pfk;GbPnH|mBuKx~h=uyhQCBuVN~40J!Um!$Qw6tsZ{f4ds87tQt7
zC%WM<m$lvPq0wUPuz{yqP0sbJ>g6z>HAj<*AMuajX7}rwJX>^wmF*iNNq+xEP)+mk
zDkC4ZODW^819sTv&R=>1H@Vb9hEb)*fT@wLy8pf>UMb%K6?w0^*%;?!-rT|~ua(a{
zP$q+YIc39*#;WEWpUfDhds&s}v?+#3!dm5NLX~r3Hyd=al;dapCxo9kD_aS+U?daW
zUUU^0Cd8;MzVovFJ}EXOj>OmrQl|Bo#mF5n8xpcCT?+di8gg5D!=YT4W9RWq<=hF-
z`=Igo59Hk!Vfc{3x&wAOjKugOaquW+Us^9;I<F<<`TS%Lfi<D9tiUQI<d9HFDV^B@
z7EZ_@xfz_yM^QC7lz*4bv{Q}q3ui19%1tGn#7k29FtU-*yWco%^9@IkinFi-lhv35
z{#9Le@d8&Eg~Z`Sb*T!s_XZ^laipTwh#S;C-&GVVs@dhB{xE!JO_$kZ6Bq&R;ebjX
z-xz*T(KhT7Nz-V;m^uR*Lb4(g%HbOUuSLJGUMl1t@Pg&Atve&%<7?fMt`7gRc_ChG
zQ~YJCHDb^CCuscVNMrm{(nZ80+9YLcv;g3=tiVnU>~>+54J-${NTht)^XJR^(_zA!
zt)o$w<d}k3zDY1G1qV(h-TnJGbFq2-uqr2;f31zMwMcHDg$z~L5CZ^WPQBu&=wU}}
z8K<_a&iwQ9%vr8+er^TRYP^Ys$AKL?g6O<=2RjU2Z<=OE>#2S}BJPtLvH$nXJXw$Z
z3}yl^KEUaHY7VW|sttvPaH^FNJEjR6ZV4UbvVqR{A1+%V!sx#%BJ4S=)a_}rw6W=s
zBS>pPEJDNn?u4X`MwM4?Cvw^%6Ewwpq`bKw%sh;ieV8Vah(o^I@@(DtH5x^c;~e}!
ztWLpKnY2Ca$m<d@1JMyHt?owUz4w5T_$*GMw|rA!0q4cT-?E`P<8&gT4l{Pm_x`j|
zSwF6d;}mP<hu6c@V#HLv()70*8XT$hSnKKSN4H<6KjL(ta(b5dVcQF6GY(M^@|;wT
z{SmIdcE6rP${J#h6AVcR=IqFxZpaL&JmI#tgcu_?O2&iu8CSfpRQy>Duf9o5!S5eY
zl)K=p+h}`<r!wf7@fm-ewUhY!wklF2_d&^H$az~72-UJ(Gh&q7Ur*^buvmnq<n`=<
zv5r<F-6^be!XLN}mDZZFHAMiq=+dAmo<Tw@H;c?mWTu_AMmj_gN0BY{6ox|?(y8Vg
zmsbMpC9qH)^J8i~gbm)sYni5zs`gm9Fru=?z*@ilJ16gqLJxb}>P1QPc<0?C{Gzv>
zG^!qRR#ezOq>x2NZn|w#<`PfuPpWqxJ7unZ8DrUyR#R&$=WPc8N)POWRKbEbB%E}#
zl%|x1zcs@mccb#W^76{6G(&xwTbhZW)@6F#x{6-nmB9}^H_9hwCcpQ}7l33MlR3S{
zN&1CliM!3|gU^+}3UtJy-{opph7Af!!9LwBIh=P}SpT2f#nou~#frqh2Wu^|k4{)!
z`BWpY<KJ#dbu$+`^@8kr7A1oF^+37gq1u~_aZwk9v0uPzY|53F#$|WjVr9<DmS=pY
z+RHwc*|+XBIT6lG45QuLbdF(NLZDvI(;8c{HFWc(9bc|~gqRfgDv`4m-)y`*)&BTp
zZC?5D%kR79eOrq7p`RS>Kil0fef}E3oH)u5-MltaCX8r0)W|=6M*GzC(I4&a>Bl!u
z&RqY>AKt08u}t(UbxLt59L$Z)ZLw1oHiNk7F}ZeG^cT`8bLJ9VQ0+IS1DD)R^v=#u
z25mfVR!3KMPOz`$lA}(}##wtznT5;;Ody(YAO8tCD%`yr`cwGB<8i0W_*X~&`DaBj
zSr6oBHx4*yFF(`Y_ee8Fh(5l38ay^R=r2^SyX^E%jtNTXFa@WOYsHvI)-JEih|uN1
z4Vjtj)!rdO<+-QDpFbO4OXzUJ-8u_7J*-^L&bK@7aQJKW@eaRB%%LA|)i<4Hz~KcR
zHyE0m$2YG(Jr>UQ;#^~GGIQf_oXA>mA>*C&FIJiK#)a2=hXxLjVTEFP$((n6e#kxe
zae{JA@R97iZ~H5Va$URRN5{>hEQ_yP8IA2JJv_CXz#Pc?#p)rP1synAibcOB6IAB^
zY+-KYUb&+4I@R9==-r~oN)WsqG{D!sp@0AJmeAkHinU9R?k+1F`%Z@WywNZ8zk%Vd
zJl<N$n&XoZ)p+l4P3BrdK<V-|;NKvenb6j54_8(E_a-3s&_giYJ)3o!Mh)vcSO7U2
z_Gd(~jM(lH1wF6JPTBddzf(EltanxSv(<P*lK<4>%zB%*rt=S#ZS1Qqm|xZJ=lf<L
zEU|AgWBJr8i4@4KdxUX$(+giqIL11<uUTE#$qN|>pCbYxD<D+V>3!|ZnOYC@2?qb>
zKLhVtEMGLcbip|a{rVgHnR3pBndX~T#&6HEaEdYyw^#~rnaH4B&7Yc<ACtwWKOJ$F
z@%r`7UcgB9op0wiu$FBBzx(d<=g||#5jMY|x`431CjxbA6noqcB^3XXU0i;sLA!ta
zt@q`(+;OiJPk(m(%)a34{LS@qyXYasr6gzI<r=*B+B*v9riSJN*8&~Nr=)SIY{j~4
zCsOxK7l`AHdl^#Z&}$oq1T4heiNoOdgLf?}O$Qz!1j@@^Jhuz|+|hzeLHYCYnGERB
z+hh5ZVzJ9Jyl9Zp36oFNrd2|urNIk=L5U}=C(bD~or@LQDt<D(NEVU3mgzC8&O(L7
zxjv=I^aq}FGkRbk0ke8)Yb4`onW*&sCv@?OUryMZ)QsJ0-q+ZX#y&?bEPtGwp+$wx
zq3M&;sJkK{Z3IdEFX;v*eEnuAA@R<iL-FO>E()W+pPh)}3cp${67CnP%21EtAjSy+
z=6c28{(DlhdUD;I=kHJ_x0=Vp)~DAG^UaxyIReGbhdg_Ie&cj%Xt&w-Mm@EWzAIX^
ztJgQLuT6NbEsJ~muf6fUT%rE!<7<!06+&Nby*+=mX4%+++ty?8P(K5;L(gWxu4A}P
z9m!%325xTBSuRz~8M0EyXh18ygm4Y`5*FIE$nO~y{GR8v*CuR6H2*q&@K@*gfSYw2
z*8{>*o8WAbU;^U`4m)i);19pjN_yjwpS^p{=iMmR?FI_-^Ye~V0pnV|Or9JqX(kii
z`l_Z?DK-lmxbD`d)TzVcb@ef82z<uWqbbNsBTYKh@KW)UtysYufBlg6JkB~Nwv7Jc
zsNis57WGo^I^vbF#T6PNZd}O>8p7?eRSUGh*5Jxtfso;`i=xzNIDGuhOqALt7EjK1
zZeR${NaM+|&Nnv_Gj&|J@W-MWl3T}&i;aVC3~%J<{71N=H#U8gbuShF4$6h8RcFY)
z`tV@h+`38KWGfY<>O3f`f=tnW)N$`C-SPGL`)jDnx7AwCz1E7-T^jlJbU6e5IxX$j
z>cx-KM>cx9$H;#}A5{hKraIo5)4I9oujY=0c9pj>_dF2IAx*on<axRteX6ydaQ&_K
zgIWJU<?C&yoL?WhI9+kXqv7Vf{RK)rU$tTP-2J`U{lBQ9{;B(9lZ{Ie9n|-#dAj1)
zmIK~}l&O#_36ad=s8v?sGy<G<|8!#jcs?10Tq&sIwO`*b+srI)*sQ!CEb4fCt3{3L
zjHy@nY(MK-(4gYS^RWvU-ixZ5FP`Q|)r?DZ>+>DIRb45+dDHX~4e_8>sJ!HQK3D5e
zhTNlpzCY*Ny2ipcPR!JvZeUk07exz%^KSwIBOWT6McxbS45sPw6}@uVx+37G;Q3Rb
zAtII6<&gPEbxhrVp<uWb$SZ7i<gvxLQ?k`bY^X@^2M!vvo-Vj}y*$$vzw-fq`Hw<@
zaXC*u^KQSz)15O{1>XQ4bvo}i&urfTA71YHKfM5IZDt{b4Nl1#pd+aec%XZ+Y6vl7
z$o@jUX4{;##V1jMKK3DKRh00i`Xhxd3B3l~QE!SJNCoY3)!IB;D^}y@-4gFL45brR
zYGu+kww!N**zm3W{FrezbN{`o@L6-SJKz(4&4iWSoIjc|p;=?F7|eAXQ$TNq$cXEi
zZjH~LMqnf&;~3w(s%ghoQ0ssY!j9F0c(moYN~wemCxd%c4-W-u2T)2Nz-`WOKQ1$o
zw)*Z6PqM;hDqQRm+Fbs3A6<XHJ`1jM$@4_`;sMiiL9}&`A<x^<XMaiFIz+wc(Nm<F
zJ@vr2ruDJBewhu-m+PnEDS3>KJvYM4tQJ(Z`=+P=vZk8L=U%CW({29FjJrBQclfGp
zx%Pu*Xs0KuU)z)Syf2}N2QHMCen3#osqp@BzHoo=q5UgKE;`w5F5I^)DsbFLiT&`?
zQ?wukCkWwJcbFM{E__G!-Mo6J8K2+C&u4nuXE$v8t=WKE@fx-KK+170efbZ!-M>$8
zaHd7--dX#H1R0-az!`ewQBGUH+OM^qr{-eQf9t)LPxdnRU6;r$f^XXlB^BpRe0*^3
zYTg~mIiam10jl>|2g{iaa(SBlzf#Cu@1+f)=&Yet{_$Y10d-8@vlX$EWc@M21G`3_
z8(~O>aHIl_H)bc3&Ff8v7qqTHz$uEqZ`Y;mC2FQCTN-<1M>90cnO!Mgn#s~$sEvO_
z5}$v$bXC}myG7SA!jH3>U-;)iAnQWSdW)<MBA;Jkzc2>@T=L33_~rG5xd;BX9Ot;w
zx}NbHvGLp<%)FAoL8uGsPid0pA7}m?f6C(?D>fauc%k(L`5)Gn<3L{h#$%TRKGgPP
zPUj<iE%^=Pv$r8el$j680|S*~W|R4)rAodhk>}r@HMtUa<G0%_v97<8ZcjyszpWMZ
zxE*GaG~1nffA%>y_+PCEtqpnQS&BlA@yC=Wg~c3c<X7hlFZmE15*ZnP`eS$jWxnmO
zN&ul}9?M|_2!n^<`qn&2$6Mqv5#@r}+2uEKTrX~nSbk(#zRhTZ>YS*mySGCX(a?K6
zh(4-;z4uSV`5F;$WS?Bs_nFR?rx@MdbPL;PeE&i=XhphL?*%#Gmr0e=FI;ss`Qo!O
z!!Y(_=#|?%c_m&eX_Sz?vu8hCSjxFs2<+lQfSK)4>^?NvcUGlb=^@hHJybPwt!TU0
zu9{hF_sZ3(XIx%XyMF|g@`6!L_<42^Qh-0peZfBQ0~hYYuji}MzlrN!Br;n=AI6Ay
zpN|kMFXfYV${%)_xOO4tg&MD3BP2OdL7_|S$xFbq;K)MT$CbbCT^3y~x7utLTz^JL
z){WV7=euzOVfquz#3$B#q&auxHU3<0q06kV&6kyl>gm>0Urc+-6&|38xzWO-#>f|n
zyDNXeG04d_VgMj+HvGG`;@UF2<b;*ZC*s{j!L!BM4~owG(&&99=vAFd;5rjwd4#R^
z0(^Mg7~VGSFkDU332L}lbxi!pd{aW5$DZaPvO|}1(EY}?sVp7A!>nmK_{kyddUL{?
z|M=o9v47o#%AC4+I{*Sn@O-h>j7SgWm%GrEZlD<7Fl#R1;^4V+>T(*?gZ?e8aadYd
z;n(@6sznj_j6XIOPwBqLu<tL&4Rn3cZ2ZyNzwjk`vrAt41tFU_a^t~L@OW)(<KXv*
zLZfp(ag2_0Z+Hn2(kbjcG_|sCVP(Spi^vtHIk98yS?f>tYsJ>+3h?5Pg^Rh?bt-<M
z{%<}$tT`mm0jRC7;nBAs!;T(v!s7oh5a_WNkS1nI>J(dOEA>`nKuc`D;51V5lELfm
z%|PC&f`zy#cw*R2jTbWB%e;uYk%Uqk#14i(Fr0oRXP`B%^<{22Wz_n<Z1d+Q-Lp-i
zf~Nwsd4DULt@oZjdrL7{GgbdauKp>5VAWBLw}-WBeeA`<uWsI(fjF1=zw5~w<iw4O
z;ELI=9l_02Du8DxS(Q_#ibH?A@8O9=@h;XUN8j+9*?YBjh|Cq^8_TMv?W+hUbpn61
zl@E^GDYH4r&>z*^{0gsf1jZaH1aUPzzL5PuyS^a$AB%6sNoLyur#&a^-CNFXN$%Eo
z-5K3vpFgynkfo1DwTMa&npJoS(D(0pO6=d_)oYbF6r<o_Va6}P*X425ElE(&@9k?0
zR$*nVCiL?LFK}*wx3TF^z_(Wr%>2Sh^(O71FuPMBMf%4e<j+<r9?ubnuixRxEj|=t
zFZE`iK8d_(AS7#+=Sj=g?OYQi7wmN)hC?xO)p7dK-Ypjkh<GRYcLeD&0WfQqq^<$I
z`u{QY4eWIVOt-OZ+qUh-w%ypajkd9kHg0%=6Q?m6+qQjA-}n3Oz0Z^UfHQmc%$l{<
z%r-+{S-+Snw0e>~V4YI7vB&V??xj%gs<h;_b0uJJqnyqn&Tf)}y!_eNiOYxlc2d2c
z=Kq-i&I*=PLwOZM>Jyl@56>!4v^;YM8?w6Sb0Ku;+ExDo3ZF31RGy$=e@BhTKQQy(
z>?GXkaGKk3GU9EQSM$4D{gMA>rtvC-I1IDci?@c5l$dL>e-k@cC?4AC)T@q1Ro4kk
zi4I#9lXzL~u?IH!NAlDO2k<dJ;sr=e`DQ`-jP~3=#eI?D^zEz(_K2_trlA(Sm^;R&
z9^Hz#<Q;BIjDLRfd-$T!(0<Qt(<!gIYZZc8(4PP_0<A>+)KpqA*gE{JSFNFisTT+6
zi(frWf>sT{wbqZkcK>eqL#xH<*KdMyXYEu!o}xhcm=@;2P7uy40XGyaczrv6T#poV
z9LGLOoxys6+Wl0uX(%*n3=KU+Jpkl8*_*2zq?fwXU0R>Xoe=dA{rLq9daCzj*=h{B
z9-FV3$@^gr2nbaOrA@DS6}Y@c<i0E6KyFyEeI5?w1z!aFY_DeR*@gdmx{3F9s@WL4
z*||=CqxxU@%@$jxvNGYyUf7O?tXkmFq*wV6^nPZ&@Eb8C;CIJpXN%OwekV&9s)%N&
z&|Q4_^V4}SW_S`Vf0nxYmSQ}#*%?Dh7S&;O(S@|X&nT1n^R1~U763NtN(UN)zB0lw
z>V__|85)1oBy)JJA~U8BcL=s0t@n&XUOpWs5~?-6Q5r?4u&D221$?D-fJn53n@zTb
zX1!YZ&YUe@hqXK$H2&xF^78<sE)h41zVS3_Zt{2N6=!>9d-tZz+_W>83S4I3)yidt
zeOSJ}^0E-0Tk8b7q*6l5y4f{|4NZZA0aQu&>a3#FbI1i=$d)7Z9dV|AGxmTH!3Oy+
zH%5olfp3C2K@SOwKYR!F{H5zw_J!W~fLhvz@4`0t;1$X^TL%&YD{%v_ynzZ`c(F1f
zLV3W}P6|i=PA_jr=ZADsa1q?;YkMvNrNZBz*o884=3y8<MvH^|u4s>cdyy9%;g$9l
zs{+oSYh^akWSD{;kdr;+3_X}9$G@&sS+q4Vx<}ODb`>#K6bNWwa{rq5`=!fw>mB(O
zy4zyxhv99-rR71DpsvpWoPl#!x}^!lTFzMrbW3`}7vj!QxCb{m7MA*_@2~pZ1v`H%
z6oXzUGfkej3^s0q%vTKxGVrw?S%4DkxjS}*>^ZH+D%9+O0y-V&2}7098>NFv0GI&h
zMXk8Vu>ODz>&aL8PvhdPi5I+c`KzI^7E>+(IWt_fEPPFCg1C0hu^PUCZ~IHdy0fps
z@C{H<0Uy_hGd;+jCto$4z-ML*`f;-1D0PIjeITzEfx`LhiV&pw)Dcd9FB~@>ru@f@
zAp(X0e4WHk7F%OuZr-S1ygukCiK<X25CvfA$s5*Px{;!_-{x2UCndj5F(M?EPpHao
z^PxnUkwxgb@oJ^BY6Wk&fe$4Gj+C5YdpRN(#~wkJc%!wd=8WWYK0%W$(h(h|gMcgO
zuTzm1Qg38CJ+3lef2XlHS{S<<FnDs@uij3ua7SvUZ{M>~BSjCxx-mMf<*ybwI8CfM
zyTOFAv6Y)8111f}2z9IoBlkI+0g-s_(u7YV`l93DyZJeHBjKPnv5^KByq+cEPGMvz
zn=Hyn@*}Q1yhGcm$22o@`N@XE88FTg+iDZB7Fpc2ZJ8abnEENy0Q6javD+-NC_wi_
z%;H|457m%h{+^cJVXlj&@B@1DLR_libH|GjEibTAik2xChWV-mQJOW$l-t|40s1Ga
zJ|YkhVglO{GKh>&ptVcRirF^2`gwy$LHGo@^=>@VItvpyYu9`I^2SmK8RLIm>rKA)
zA8eHkoCaa5Ch#EsRHDQ2L@VjNnuQkM^Pg%O!>Z5HCJzRj$T;$lE)~kA9uMSAx2LtZ
ztKO6&1kUwkh;4Y+y8M%7A9!W?HI6#t{a@#~&IFG5KHsjqNNzM8t#HQz;WS(@hRUmg
zN+A@zIKmkkt)KRDej$51MLk~zQ38e2|MiTACQ_@Tn$Kpdf-yRPH?9K5ENOpO$p|3j
zW}C4#kGNAO`LVItW_JWjhXDt{25POnbE5On+cgpCLErakNl5TjJ;9>}({WFr@{EZ|
zx#Z@!{2|(-@Tf3OZ)6+@<TE$*cXxz|z*~wE@B}l%9doi&0u*<?EjPP_+_T>BIt82M
z9qz+S@ya_vnzc&&{72l`LWm=FX1gcNax7{}+cy6?A%$LTG1!q(m#<l_#eg`47L9yg
z2Lx<hc5rb@t9H<h>FdZfv4B#2+jC?bYv?WZ<uNsj+<1Hk=|V>T+#M4g8rIpaa4aVa
zN5~HOr<`dUwN!P*GvSpr+sdj^YZzGaAlwL5$+z{;vx>gH#ZTn@h+Qh9fFomdTqF6z
zMAolgUe!D=AxbF;rs{Js<E2@S6nKd3F`IL@_3_VQ-1{Fsu*Vvyy`_Kj85X_ycWnJu
ztj~~leQeTr8^_+&9h>r<m9{!0<4hc7{_U`(I*}h@PQvaNv<KTPZ6nGs6DqGl2IC#E
zP7LaoGq#goL0E&oqTUfu4H)q>+PQv;>tm}u&5u=v%Lc2U(Q&CrGQUeCJESFCF=ke@
zNV@3D;|qBBevM`5Lk!kvU&$Vt;ns`M)V5>{;XHz3OqohW(}(U2Z?JZ+N*<7}jS=}7
zW&(w0g*JU!zSE2C=2ouUbk*+<v1-CyF7n8}17M|U84Qj#)m#U(FsZC23#j)g_FA#w
z2O#g|1=5!{Q8$u*6tp~0wSO)VAwoxc^bVng#VYbW?>G78ye3b&&P|GFdUZ3MSRX>h
zzp5?k{k?`5O7BYb9*X;Lto$Px6Y3ax@EcT$LBCZm7RQJC5J`QM8`_`@YtS5htg)U6
zu?(w)Si;E`S}=l;pezMZBeQ>1b&!Zd*uWd}Voxn0U)<8qdLOe)Xy<QJB{MDs`be!=
z!nmfzyN6_e5dkpY@rp07_%;ktG99;swfc9il1D$G<!>8R{7!~+1WVC}s$Io^r>QXp
z;}|-?z;VwrDbm~DJP*T1^8o@*-IGDKgb{?!_%hpvp9Gwsg=I^O68K;{m9;Hg7SfU<
zdHGrjX8;zF^n#ZjQ#(jCK=h6Nb>3LQ`iEKYRW94u5p2tTYSPV({pmDiSfwEA>&*9<
zR2G;F4Wq>VIm9(O)F_T46fyc}p$|TD2ULoAOl49#F%RTI>*Nxg3UpygGjCZ?0)Qx7
z91x_R#J9`hIpIT5ADynqtTyL^Zcs(=KH&o!0xmS>v@VPr(g_;;U^slP?U-r3e5Ghu
z?8ddyuk2>GRo%jlls1nF#h~Gsk52Hp|N65cSzV-b5mPSlZV^v(0U{!#-tcM+-hb4`
ze=@yRzHo3PY;@~>nOH}_73wDdw*=r#f7(+2$xidJ9X^6K1wH0^V4eB47ajZl+B5wa
zw>aawtB{T3*Z;9$m>kIyW1~CyM>@xGeWHtmULmECVeZx5Sph5~*(;Lbilu_lECr<%
z(Qv+^57V2m4drAY2oC@@!+j*_&r_WeD$za}j<<F(#)Jt%?%9IA$_SlxB&T*?UxRUj
zW;6c14l5D1jFbe4$uR`+qf&jLnoNJ|)$LQ8XxXEOTq{oFHB#c6G9_12ZokvnWW5gk
z9@Q#ULd3<SoDa99!fpN``NItkIKrw*AjEnnVSI{CNK(e-%JCx*v7gE*$~)SDDm>?<
zTVxwSg=1dw?EaHh;>!;YwAy$#1-N0EGz3#z)j=UF_sRem1bj=8#1Uo+#O*<QO-bk@
zSX^;_pTx{y$99&AkDDHHMBfCdZ%<3wzdpn{l0W#~LZcX#n&uP(A4+~Ck(zBCZp>V@
zbB$iChat8QPIT8uPkPbI$4ki_d=@ExieTPztl?MeF(^mXTtEm~K*tP}lFw(}n$Xkj
zt42!GS&k<Ew24`k9yo$lGLh9X?8L$$-!gRnPqE;#`Zt(Jq0P+Wdf|?89WA(5BvYyz
z4HyT|-XVoy%aUu4I5avFT7Og>yy)msrRNP?5IEN6;b0IhLkJO#c548pWFzoW$<)!?
z{~+q=VrmmnL&;~FX3`-RmQ<e^whz`mT_lWhl%>NDpo})4JHcx)NK~nMy=UCi;Kqa#
zDZ(FlYDhfsz?hQq$1v@Irwl?wQbuo$kOvbulmDBnpB{`nx}L0%9Z9VoojMYC@Y6ZJ
zyDzO^Pg=d0%O%;&p)p|*%PT+C>GegR&|-S=rdQGz_cmw5w(nntC31voS;PF0N-$co
z%uNxyOD;K3p&X*PS^r1v6HM?&{ik{~3;2|TtazbcZxb(pAi&?Vs;ie&=eGlyea;xo
z$86{sL(U|01+wgMLY&(QHq7<5hRQZ+9dqPJUZVz!Q#iDILPIJ+$<;>$MMh0r?WP8p
zxW;-v88T(D;trbjBC#_8xZ@w|_escJ+X-TZ<Nn2BI9UpkB8d#Y60qQAdvi|liYQli
z+N-R`b%^;t?{+`9aoFYxUhx{3SLF;{Tzx~;x#3^bye{R-<Zw@7@Z-?FFm|3@Xk@K4
zItyBq*GVtS2<+w}@Dmh=(Tm~3P#|15GrD^HP-MPXBT!rB=etKTAImS7GM*8R$rX%s
zaj5Te5B*Q^bgwOjHlE;@6ol^t<CqEcU1g=9DH#5k!R@DKvF7m(Wx*{sCC05dA&?m-
zcD5r0I~X_ndt_Y7X0I!#`>Uv7`hi$w)MXBSrx&YE0Fj(5Ujh%O`Ufi@vu^<IG0-<%
zOc4TOe(-S~;(C^Y8eJZJOo0xD(uYVZ(9m-7_uU#TCTJ7*;8FC%-e0`9bZlTVFr+(U
zP5fadItDqB<L=?nf$m0TxhuyTnxpUCAXzE~;<9MDxvAJ6gNAi!VK`|63MTGVndxRA
zLiBJ64$nJdgn!?CTDiRcLSE~!Hd`o0|E|uNfftpwK*nKtb-+7a?9N%bj1~=YHQ+So
zUsd4BUIBrogIozX^y8cvyUNt{0h3!Nd6PHOD~*YXg9v)|Hc!aF8QPh3db0`QGOqg7
zf`<SqCRk^;Rb@qNCuldyR3w|>SQI+T5{*?R%g|Q6QHX|6eR&QznMhYOrc#;X2`*8%
z-!%4c>xpEy{5R40*EL;iE}UPjyWjZ15M)ultu-ar=9qLJ{Cl_%OuwuAamjG9yBRYl
z^Moti&KF2n2rkI1w7Xl!Y{GGqym#B;Dk>I}!hHv!Arl^{=moxg3bpHcuBT4&eP6b1
z^JZKVwz_%P#*>I58Zc1Wa&&vp;MNpL6lf>4IF+6@1vi-CjuCpsl1P;85b5I|_+PCP
z<_Y7<kl4`>d=1{=kz@D*f<}MIrbo_i_{02isQ~N)xzgLt5<t=;Q^F4mKSfeFV{0cv
zK(o+|3)^in6TxO><j2W?QwYp30FFjo{?<!GuOm^Lu@mr0h;H26kD1qy4=+xUrZO;?
z?;r_F;I`#f1~xv!FGn`&dy}ZKe;OVP9zO7D!_oICe%=l@Bn$T(+^UhVd8UzRAh3pa
z>M>E~-pUloQ}s>&UfS(`xo5QjzTsY;?Z16Aiz=-8VPw(?F!jcJ-?{u58NGFPo;4Q<
zGY^=F46hbFbJCpJ^wg({!sQsjeC>6-x<`YU5eBi&FYBC2?;rtG3M7EK{I3AokZ1x+
z0&WaF4t5Ey4570ylN<<i2_K%OtGj!7r8oUq;rkZ5__%s%JDmKVVfr85KFAf9#|NcO
zBHCfJ3-b&Rxg5lY4H&=X)IUb0dwdm6Xx|-}qZOAqEZ@i~fVb-TGkK+QNr8jvxH(GC
zqsKNRnvG8vOCUb1CJ&XhM>c>FBSlNGY~<BM4H&&JVBE-67_Z(HuI`k7kk`snQnTHC
zTW?ma9UBl0K+6*KAMG~7OZ`xuSUP8JiS~TZXZby(6pjcBqPFUL$>P;JZDpP3D_96l
zgidvx))pqLN{j}S!kO3MiQvoVEZ4QSSHHu|B7Lp@)_mhl&BvTuq%odONk|~&fhz7b
zxybUBV8<Sa7-E!P`08W|d*!=D36z<?Y5^mK_&{r0!Hk}Q?1l><uH+s*=LAxV5UB_+
z0ZGBbfm8m&q6h(`Pj-ockEj1gFB&!vsqll`-WJJx^F=C#^Z_D4)JKmH>}7lG5hP5D
z*TKw;&A2%42tjTU;V(kG$!D8M-{E?`H5tNv(9rVmh0)&@sU%}*$C$7uCCYhaAWlUn
zNkv$Tx=6TGT7Q{##8vyXtIKI&I)GNLmh>HnX_;n_6o$T$3=s-eBo@jaOw>f7&T#x*
z$=RdO{M+Fnl{WL`Bt!e6^#&i)e6HP_aY+MnJm7^Asb{x~agtsQ#~ZxSk?AV^b8P!9
zSXN-S^Srty6UK8;qGq43JK(n;(&$4zm5QP@g@&dhv$=J<n3ZmfohOn${e^al5?^&B
z9qIsfQ}@u8?a2W^EB(tBB#<z49cXdt@QDM2{&1UrxP(puYlZN3o{kpIU-cxaOn|WJ
z^vamKlqRzb?bph$%kb|k*lz<CfN$POUE1*4_Ww88#6ZOPK`zj9ePlCXA<T8TrWc`8
zt2{m4l6GhTkzK}1ViT^kL(N#*VExmqVoQa0%C0qn-802UmQ;C@Zx+ruWjzaVqj%MJ
z!wGF00J0XI=g6(nw0q_bjKIZii<{^D!9kp&;4-sh{!0VmH1OX(y^Lv=>NSh(!|hA#
z@P_S=;E=+z{69+ME$sGpX{c|%za9r%!FqIVS;v?@)au_mHrq0CNJmFlnc~Ax>zK>_
zCD%{1WD;8JQ6qt_dJQ+%M)$EO7k8emetBLJ&2x-To*<^=>4TpkQ)Lcr)w)I+`^r_^
zE9rq+a-dB18%QY4fNxA_RM<U=`9-H^I|(A*xcl4>;t&wp^APlT*SNn3CVCx2ddCrJ
z^84%=;)-XhiJL@4Sd%5m9-sQ_!++Aw1q5l9@94^0a*wP4++ip9eR7_Zx8Us<I_rU1
ztE>`+pV>DWN<5BM<!m?=*$!5aZnwITT#eq0%7=x)((5NcWbrMf2da?fpM|iY1E$wi
z!>V4f;~F;QwK;i4RITTwyKlG0J#M6ZI@cOvLg09Ca}xV=A}#AsIhE6j2;R%Xw)=Ww
z_1Cgz<K=|8;@Zt6zo?3}ASJj>Z4^c%M1H@^h7Q7Z_fTEQSONd0#U(&;@&lM?XcX1c
zO*ss3_TrLCkFcQ?2auS|R9)6oVHi$|C_54C6HBnl(b~o~2p1jBYhU!H_~ZI-XFi1-
zPeasr*DAqNt1$v+!XWHzwt4975Y>`0T!`83&#fbt4hB&I;Q1PQJ9NNE4R+gUL&kWP
zKKk?HpVYRLjJY7jpyo<x@2rI?E^oyUp0Mjuvd#y;JpHj3%5Y(xH^})PJ^4Km6i~h-
z%&Z(WQMS4c;^z`psHUd<IgAOsq2{`WK|*|m0*O)(pUh~*pTo-=z1l<E8VQ|KZ3fG9
z<#o}OnF*(}2JK>rVO8Lm0-{<PVe_f{x4yW+qBibVTmTihw(6C=B&mbQXSDJolS3JP
zNUzHU?(oKj>&RuSFWdB8$k2_8-nc9o!R5V$(xyHWY1`-=T^Q-WAH=iV`r3R^^(a-?
zF!n!?m|=<Ua-9RCB;xg}p&EY>vbm#Xw!X14b1CH<D(ffKTJ-ng*~Gb6&$vJAMQJF}
zemi?Jf{3%Vo$W;=>ws0uT6UwUqhV6qs_X1rV(diPc!VU~G!=wA0;gH@`QUSThjCmI
zD_hy%s`t}8%;@|$doahp%55OMTKR~`@IK8@u*o=N_}C|)Ap0MeL+(Ro*k4;aDf-CM
zC{e9-ouNt8N%Xce8WFGCyh@mOX?Wld>R)GE4Rf#InBEy0<L3E6*}5;9h0;q2dn;*!
z_D+=fh5nb)Nb4TE9jAjZQAe9<Wh-8ASO>f~SxvC{dn2MjVQaDQnq6V3r(!}{EFD_o
zV&qL!7c$7$VeXySF}8mWdd+ml10Pq-9w|J2c+iWy>sCURw?tHR?o9`TX61JEG3zr@
z>qHTR))S3!u|<$M5qJzJVdT5>I<*|~mxx;VCbJtic~_ofsn9QprXhDa-@AE=dMs@R
zRm3n{BTdtw7<cw6^~bHGoVLr+PH)54Qs&qDIVP^wdb%EfO=!;s*3iC@)ZVPgc8U}%
z?ujsXKyE^ILj+VOo$LGllWlheS9*Ug|NZT6)?AI{t_!FWv$D=OU<brEO@}SPWM%aq
z5db?cv?@cd30n9F895`_duEvGx6qE^ciMf|LeJZ-Ytt`TeK(9}MPHOBPKRM(kCxh-
za&>azEGj7&G9Jp?(~s7=a?Wn23YzoknWAc!qgA&7-fD4c+mzfjb}A}vXQZFFGS%U=
zT^ZBu-l)QdmrE{al6W-LnO~DvhbAy)(9Da9*yx!pRl!jZq;bg6$^z&hoWJxr^imsL
z{Taay#gtuRt2c`Mn$8)fuwlUDguh1=iw#*aF-feG;ORc7%lrPteZs8fyI#(q`EQFR
zMQ}PslZpTJ0xVYGyxk)6j1oXNqv3asdIsQUV-X9hjvt%b*H{4KIdvzU!KQqB0RN-h
z5w(%FLHXDvdX=@F>(9r%{y&|sWMkLKw5Cdukk~&GWlLlW>ne(%2mJpN_;{HA@c^kj
ziQiK4qq4qNX6=p~?^-oDb4!?_I7%MORsIT2!kiII@ZBX;MLwv2*DM`ar_QA~_$v;A
z{g&~Rggb{ux}NQ9NCI9LRNUQZJ|?`@ie&P7nlqTT>%Jqof!HhV*ZI{Dms^O=z__qB
z#5RgZVS`Q2y75Cf(Hpd5SrQ8Web0ohoiaH4ye~BNnhwcS5>gVXcG>QlTY3IhAN2q<
z0pdd=;M3F_lgwIm6-S~8mSN@}K}&@Xgfp`OVJ1n_?67Z8Hd@!M-zc-je`K;l1%8R&
zhzP~@ing~TYj5E66Tp2BeauLd8%N{pVf=Nxg<L$6eRu2$qAz3V<LFSXMyjn&p$%7o
zm*AJs8{lsX0;eJu(sY^@|4+jEW7+jRn0Yw=W?&t{<)`;s^X$q0Rj;k*X45Z>7RAT&
zr6zLe;@dfCRhunq=pzLKi7YHDoFVEwmznDip_Pu+Wquer%bQJ*6mbQZDL9LmTdc;Q
zCZ`Y(lCyItb~47IvFzb=R>n|Z#i>>*K_=)W(c<On0bXavz6{=?r!bFV<#e(tgJSmZ
z#$>R0CGg8K?X8z5Uf4GJ*B^bfoPDtqG5Gjr*b77e;WjzcuJeaghnFKG;+ryje{-re
zWcxCAaY!y?ldsLX;=1)CI@KTD<(ceOBY|BSXjvy8hg!|?JqK&I={&Y$1^v?ERHhlM
zh8Wbz`@t<CcHED`T<mDwW^mhi9{f&)0Sq!?)>`ph&aYd6o=&?yDD&IM3$G$qFAQUt
z#vXl}3+<cpLSSp%L+)v|QFhnJ*gOIcSXYuNYh8o>zoNBCL1V+rQxb{#yo0=@b$J)U
z&t++!1M#)GV5ryEf_~o{*pb*ndr;xqK6L!PG#}uqyIAis%o>gp2d<<xifJOWK5G<H
zMVVmS{yl$&3cev`L|NRrWt+$}&7jbK3SY-1z%rq`!LrmG?4}}nN_Ub}WMn4zjcPDb
z@g95S_?9>?qx{RtQSb%kVAk@3U){6ZVSaqu)#GPMZJvQnTPrev`?*S9yrY!wTMK_G
zON-(fv?_Ra26Ge9U`neI68T8_S_fh$GmcRbGZz217CpMEsK#jS=Ia}DLh}AeYu%|X
zdsug6_0b+b=#@c2?%I2<kp1l&2t1QA<N$&t7{d;`*G1ptX3c=wHb<DBLXWPjCtKNC
zW6)QEz^_}X$gh<$7*C;xM_uhOuB}@C^%xcRIC7tdt5=>8F$lvydpuLLuGncrZ{IcP
zMn(bwx~#>S;j}%;ulK0CLLcj#bGL*;!|@+J_a}?@I|!KmV<MWGw~MpiGY1K7;>+U6
z^E#Y-2KuNb15K{pt$zhydYN~1#rWhFF|z1Zz)0a`?iD!S`2|ovjAO}uF3Rfhxx}ao
z0B$~Y$HTSO*9p0K5^>y7WVpsR{GCCam&h#B;dS4;{(O?xJf>;NTV}>2bTKXN`P<HO
zBt``%wY>7_rVX?K%r|F7DgLQuilb2)6&Pt*j#T>Vw*b8(M_#P@U;zR(3Hur9K3s3J
z^S5=e9ejqT<DGd3=V=d!O^A!T9VnSDp;cc0v1G6UgO(3gu;I{6<CZh>Eqfp@$P4GX
zr39o64X#oP$b)DE7JvbSidx+yuaKvx{drxY7l(y`o8YX_LFK)OhW(h{b>JeXokORO
zHwE*P+uFqcQV}XHpRpuX#0$NdFIHZKSxLd5qlR5Eh8n%W(wD)2K6!L9y&zjK3GZA2
zA3b+2(;&o#v`^%&G8hFOtbikW5Qt;)u7nWE*$C@?!6#!qI-LIAn=2fab;8(#Gs=vp
zH*55)(HpmmayF3YOs0D{$0zzGWS1BkW3Ac_-O{-SgMbLFh+Sj1N1b)oOqMo&$oKwy
zBOH@@Le?Hg8_v5fHJomSX6-u)l1H=;ArAGW!ZC2-RdNl`{nuYvEY2!|2_S78#e3@E
zx+X5iw8EZ?#{xFs*HRhMiYcAG-SV$`b64rwKai)H7ah$KI@gUoQ6f@XyNj3ewX)jt
z`=k+<0_`()vANFW(D~p3`rMneNBm|Wf;$=Nv}^r-UBPVCh58F^YyL;jtBr<ox^1b$
zO7VfeBEIyx@Ty}qF-`~ggSGX>yVydFxzj@ixFmX#fY<8JtLVG@$9_e3?rBxI{6?pR
zV_zE2U`;L@J6f|lkj8@5wC}02yQ16v^{jR#-K(7ihemBmD8}C*SivE1l(sdp{hY#N
zMGs`Dt8gY_oC#%jA9#Go>GLGhuux;Gh~R%_lG)_*T2#G%e)IzOy*yNV=H7u05M!Q9
zA;6QiI_oGA(*F|F0>kSOJ`#|$#`#K5Bs`wf+MPEbhB_cvgk=`GxFl6u=04HOC<X^v
zMv+T>f!Wu%^q}BeVR4F9i7cYx1uoexH?y==#cbA1m&LkN)Uj&NbvoH5-4c07BM4T}
zR6qy)={ws)QO`_?u&Zl-a0zp|r8RpkY9?1DCoS)2PPApTp#qEc7?)jRRn#*U@1UD!
zpnbLS<XMQQyH<Fm$4yc!#I&>vKQ*?C;jo1o@(8(ZOuER3p@Uck)7S7{7=(!ja<56j
zR>TNhYw{;A(Eey1f_9r8Cz2)c0rNdERq&=fq($qJtc)ZW9JRxvF<-P|1`NBZzv~(Z
zuqg`@rwUdLq21EP;NrUa4X0YajU&gO7G8W(aI6p5t5T*d8tie<3BJW`(n(KN_(a{O
zL<$XydgBUiyo?PL6TEL14bZ$~3lBpXlM|amhW{w11<_~<$K7x8L&moRNc(?<u55p}
zjYxSLz0!ZlWNs@(oWV<>Ut)oQIKF*U9mmS-v#n}F++rB?F!p<eoI}f`V+t4Bp*`6@
zGLKyjxQpME*{+tN0xSe^*uvIr%F%Xs;`6Y!dq%7yAn-L$-lDK=N|9pK8++xiZ9Qwx
z{ioq(i!Dic=V!MJu~4YIFkV263<%)<sga@23?T8`0tad8q30THDAloFPa872kek!p
z2WW{nL)nAq7Y0I2tHoR60tgrjSZu}yHP95)1n&4Q_GW+`g*fHx9WT9X0V6I>D8q8w
zOi=Fcr{fcDI|U+BldWBxE8OG1l<v4sHJ}s$WNGbHgGQ7jHme33;&!FM7K;}rj`8@F
zYFo^0Y~Q^{TKG_kjDLhBWr{Bhn>$stefg8R<is|tuf&#^1GDO9u8S_nPND)!r`W;|
zT7)R9&Ouw{4sQ+fXa=$EAo5u${=dI(@F5ovWb%7R16hUK5rH0^wxCzoMbu5i$5qVw
zfIZrKOL?A^W60^<S5qfg;iZ{?Uh%9UP<IX%J#s<m6cviPC{y}imTyXw<mtl78l~i?
zs7GjPCcHKnQ$F9&cJiA_lv6POI-phBeWjwo*U3_vs?)JIRkS@ntD@_;>%dRO<X&Ei
zxON?zNf{#p#pw{uiOF+e4q=3!EysK0m9Fq5(Zq&H5>B1HX}@+|pRWCz#aEC{!)}f)
zAComHz1d|z1F=b|44<Y#scsW(1WWMeFGA>If+W2O3D!T)9|+zvg7P{-;pc!+h<g6h
zaYbPXD(`YQ;i;`7w#jgmg$f0#P|SFgVEk~NK-`QVlKeaoHX7jLQw-V3-gh&-1kC0M
z;#cJNm^&#D6$O29cXCv_m6F9jUgX#|H!OK7$pR(*i;KJW&s0#{UeYaI`@5IAK@`Mg
zzn@g&h($@R1v;|(<2&6M%TrRSV#9mQB^m#;QLDW-w7j@A3@2we0RZnSbvh2~O5Ado
zWEC=p`E82=gVQ(XKBL^<iiTwr<QLlYMt>SSV%Gz|AQhoWkV$%M0p!`gJMJzEn1Nt4
z1BCOcEEgWkC^Pv#1^yqc98>~rtW+--%V0gK)rN?#DPojgJI|1dQA*1`_dPQzRxlt)
z@8}*A05>HX_Bt+EBuJM*iCYfF7VQlZWEUrFn_1fNn*&Wkx&*`35db!b+MSRVFV6%m
zF*NcFXBM!1=aN;+9au_dgz<ed{YB?JE_Z0Mq7RQA=YWJ>1816Lll>t+q~E~RbUL$C
z;VaFh^{cdQ+_jOBF_Wm2k2oIf7c7QlCA9&5L&dF;2RFYAqA%lI_3JO2n?}au&2%IU
zl-LN7>ieYRQnnJ80lkCBO~uB9#f_YB?e_cLG4`<jBu<gxxT7pz7s1`#*P@KCMsM{2
z;lTlo&FBAA1?#zb{%$?)RN1l$Rm6&-OvJi~NDp>Sjkb5ez^}?6A?z?H!T*YuPOxJV
z%lm{*W=hpFlsCVx<IZ|1P#Vw3AoTm$Ai+u`J8{0;64K<GBBFDYon*NU8*IzgWYkuv
z=We3X{X^EcM)LRNPpGcN4d7NHFWRa8K1Ov6u?(AgMr4C;xAh=D)fJ8nuL?7EQ`7fz
zXMft*e3UD_HE1&4<dKQ*P+s0B?y5*+S`m%lJixR#T}4%uZxL1mx>019<cm(+=>@5b
z5_M*H3O%rc4pIoG^AT{L{zyWSQeG%CT@KpvDHld!UjWph*c8i&qvOAXc>XJ+DK+_C
z2yxFyfB8F}Iz7lrw;4kaxSBn7FfrNRglZ=GscXMJEYjGg=a8w3yB^YT%3)beJMNSh
zsdzUn(g@`E(FecWWguQ&0ea^P&xG8980z0~%KMpuIuXireU3zCQAMQ=HxyC^DU_|z
zd7EN#j4bawolBiJBYQopH28feDFUFxUbbcXF2Y#vHa!sgTi3&E>yNCvs2VlSl(3eZ
zVF(}Rn4k@2)9OdCct1ov2b4fOlc}sXu!PfzW5Y^|ShbGNCmhS~@CLo@<7cW|-abx+
zX%<{{7*o9rB5|k0Z<-JB|4PgMmJ9Tg^mCJ<+7$E(+1%YnCSeRA5x-a3kPHa7^qfba
zXpLH2bYtv>{VcM9+qZDV7ftO0>kkVVfa`H-jIWg7IdcLlB=WBU=FiM0A02_r@`dvD
zvL0ML8qyEbMGMWFWTUPlLeI8ov=DD^Fnd@i5$=P%_L<|NSN-+=Gg#W*sH>X~$~#7}
zz^RIIjSwE9#StvxZ|Prpt3+HFBMSRDMtD*e39*Q|HFXSF?phdHiZBpe-xpYFH&?VA
zBX3Hog(^9Nt8YrsAj(Fksz#3uIx?GN#~`>N=trr^$}r@B(uHVkjR7^3=xuPNP`EB>
zbfTj-9kmcTp(Q{z#rn=ErIGL_(AI{Fyy@T=;=cfa^kp%sj?v*o^i)3T|KtM?$SOVm
z8>_4^#fXYUF(PhADRo4#*DloiLbJWt*=BRp6A}OK!0pH`Y)VB5t?7ImC=_ik`!jCk
zzd}z)WSD-d-23f!EKLdHc=1+KaJr{tNe*blSlWz9*~)tCSmPSZdNHbsZ~S&Hj)9S2
zn#H2>YQa16AFvUa1cW#`e>?*X0YBA>vA=hO_o^ZEqm5|s_k9@~NQ-k2=0_pt_}+A^
zLSs)b{!RTQe+tmq<w@N4Gaqw|G-E?14x1mmSO^YNg@#Oc*--Z9@z&U|L?n1Qd{iV_
z6t5|*5V(FCY*(p4l8CFlzjI8I@eu(Or#1_lLq_lq4Jd$1dgU*W6XD%pEEtMtW?DVN
zv6`?PH5??g{_|^GCn|XyR>cw^@Nr~N)<ltUORZs1A%Dpj=dAak>P%XeRuqgUJdHRL
zI%&Av$`8N+OFaVO5y^TyP|zkbVKdl!4=k9Lm%N68HV0ecfsELLha}0Gu3dJO>Lex3
zzt^U4+H?@J9<uG|<9pi+H5D+BBq=DuJ!-74k1P5wB>Fur)`y?+oRO5)9KDHjX3=^7
zFuNan4Kcf+GncmDsP|SSOr%e)u-s<gn*V%ThZ}2k_Ph(9<Bn_QTVKh7mJg!@_g`N$
zp%PScLWZo=MoKdXS%WC{hhzV3Up2in%Nyx28dhh-ga{n#kqk?+4OzgE#I#;cGjyf1
z*B8g|fxa>aEf+#O@fPMIo->9BhMoiaL0=7$LVP{rg}H*Mo7${%Uu~^@Lt}Bpc#2Ya
zpZjN;2ep-QE24s_?<~3KLGmDHGs3Kg>RDGxL*yZYNDPo2x5AZ{WXSg=6dR<hk2A-1
z<;1pN_|#agj$bh61(5J>mWI=j?Y%)A94W8Cf5PfW<?ufoT)c~Py*`+GQW<o!He_-5
ztjh1$p^<04ZnXAaNK1N{1W_B9yk<{RIz?y{Gj6A-o%_aSF}8aQG0WEuu#pj7OW4^r
z=z8GG560j(2RktqJ9IT5N8w7(RaZva$@NR!Cy?PN!?sK{s}>K@kuX9lKX>RdD`!w5
zM0t~Uz)bzJ&`qgFi=AwG#QYtOtK#C63S<OvugCBMz=!nTb=zsc9(84!XKz#VC(JEL
z;8=+B{Pa+r|EVZa0ICn_RR)k-tj6sAHH7|>*48hi4vZJFpju;#J0uyLr+x+hO8B3d
zJ)5pEwhx?JZAY^MXz1jav6kTI`petdeQ+|HyeCBHN$%*`PMo|0w(mk>f=*1Uy&;z1
zVGU_A_7Frh8?|A|vca^zY&bDt-*!!CgWfj&_e4PWpPicfp&nvBSPFttNM#<7*Wjf5
zas{{ko?8^Vqs_o9^C8xuDh`Yudk_v+eKjUOLNB8YkSp&H-XI>;2I?o~E-5=s(5?1R
z#cVMLfBE9AnjsgP)hY_4^8{RIOms%wuq4^zM<+5Ox1KdBvn=2^qvRgMMqj^pNjCm`
z%RCB`q8$(<OTWAPoE^=K@_}U#-1PEfUV$TgqBKQ&^4&55R?@l!VJ{u+IL6ane2}|v
zUm0%+ZN&o@?U%ayY(f+Q`11YQk@%3tAyv5R14sQkiI4Q}Z|w?Rt3j}(dpiFCL8&xr
z94l+o;fzCWHEb}69drW{;&>6^$G}P;eOU!5QqZPZih`u`>3UpHQHLzr;9>v8Q1*xf
z$?I}K#Cl?s>M=gZBn;wQYn0|3>SAC*&OU~-04}KS8Rw42L3UnV&5(y;sm<ftXuIJA
zrJv;nc<tv0a>%+~Scl{rq@Zwuj9{AMR0auAsvAf~u?H;IjO>U}X1Unys(Lt4l>j38
zgvR<T6Sz9ea;?e9^%x%n`R8htsxw3W4)D*(CQv_S;NqV)*R|?xOM`<<%QHGQUw9f6
z-k5ST+?on;h5&@zmos+{8ho;5Fn`aV_J?Z2Zu1WpIRmeS8VZ%)avQSu=6^Sal3KvD
z%6XSi0277!fbkKXmTO3mw;EZdc`XLTDYPLL)aJ!YLShFgqHUUlc+<9zW2N)?(hfX2
zq7aSheB5-%JCDy7fG)PLC`6=#on)%94D&6NVID+rucUSc!?BI=aEuo}PyhUo9-lk{
z)ar2FH?wNwIycPKPwX%*>=U8+90pyj*8@~>Az6L#DO<bw)OT1yTo90Awi;{S$*l1`
zh7wy6Ep;a}7YaUu%T)CTYYa55f0MyK6ET`MBj?8_nxp)<yC?b?r-wEX`&R7zdmrU1
zx&lx_aIoD8fx!fiFptW3AAaDck)Ui>TeOZt{W~BO60}<Qko)`AxZF8Xe9Krx3bY$H
zi5U`HJ87Y>guVn0QeEVE-HMN{Ne*+);{Q=8|GYEE+j4_N$4r><(6i9dx##L`)Qw4q
zA0!H9Ep8`^GIFq#%jPx`nzo#wi`dpw6)lWqbi%K6)takhGMcH!U&o7FKMAnHo+>|Q
zP-|rPc`ADDtTY*oY|#TqdB<szZBsI_l!;IQgxs8O)dl8HL#LFCov4)$&l|@H25q(G
z4M*SNq)kVAP?u^YUUc^wF#6H(LFUhqLtU+SAX7r)76FyKL~*RWA?P0H(A$}s=PxLR
z0^_;$Uti(tu5%j+1GkMDlz;bP8bkH@1^8rTzS0!-zgAg3(u5ZHT&xQl?@1=(!n@*L
z4GARMb59^NrG2GaH|845w<`Vz^rgQ2>tyh84uAHSs|Fvu+v%jw`hNCZNR$1x*yh7;
zKK7G0BlSng%7+Kgc5f+@3=*vz82HDAifpbReCxZW%zZiGr5|s$j;p&-GlkEKL5K}f
z;}a(K!nLyo;X2E$lQBx+?__$p!!bT)BIJdfW~t2l3Xp%Pbuc)2hxe}o$n_^L(x;0d
zOu01_KAeg<bHO=UU2$8F@L@PZ0^W5Yz{-p|#T&-l7d|qO&C!rl#trSO_gzg(5*YpU
zI(xZN9)lQ2qfBlLTk0N)DTt=<-@vyDLRBJ&X!T-$_#p5dwWs2SM0fJRgPL|MQO+)c
zHYOZG<|Gb3S6;7IPS00^dguzj$EVp=8FoQH!<z?(3>LpHlxuYtLf8y?O`prd8rNji
z(E$W+SZ)FE=ted((X&Nm=++L0)IXCl_*InuVakNeeaQy4BFPpm9XU>-X80}q@p&ap
zyJ6pELvfSZztediZg&MKYbNg;jT3pN+*Ny{mJvH@iHLOlICny^2w9|6Y0D!ShEhtq
zKVd$-=cfe5iV`Awi_I6Q8sg9+L|g47Y*;a7WoZ^WYs^{X0MsXhE6~Qj-YL`$*fq`T
zt-i{Wu;G4tvX9f|ZT6ZhX8_0wjd!y))CHU{{x#sfQS$F0BY=7dj}(38M4FGaTk3a2
zXcK388wbqc>c_r0*&kHhhYa=Rx&~8}p6`qeUgwB)qRa!nclj%f!m?oaD)aT)Y;EmK
z4^61i>&TmGNk+9T=aAY$JLVe5d->~Au~Pxx2E&Kn>^(RurBrb+DbH{s8&$U)x{z#E
zu`2}z;i;K$3VeQB8QsQTn*=Zl<DMab-i5hK8P4(|N++_k;v>yP77&K-Um;RM202YN
zmU#+Xn^Dv=+aLucmc5mp0oo98?PMM9I73%XQj1_iNsMUWtM-#~*z4iQF@1^T43A(S
zQ!&plQdI~(Sa-w8VHm@yC)gu+MF{U-HVHc6Xy-?QsYm}E2TnueUs~rcm5*)ydFS@R
z4>D@NIbcG@aSlw-7IsFwKZ@nQEWsk5vY(a0uflTY&-tT>zUr6<Ip8AMeeI&)Vfe}6
zLM(<sx(Xi2Gzq#gRNhU(kP$VAe}qb=F#%f&fvrGxHs4GPaS^?%y7H-78E8vQaWSQo
zTZI7EFXadUJ2{}!Eq0=_5jj8e_DOS+Z95?)6s(iQzSa<*!69q42v=;6$0-=j-rB$j
z_+5{8j;jC%nnQGs@lNZ^_K(oUrYy>2TqrQKC_<9jv@`}Z7rc&txvp0>>3S@$V8<H=
z)vC0`Iwfqd5A+>}JTi@im!7uyM5c-H_nHjHbT_zhK^f;eeexCiLvj0KrRD1fuYQ1W
z-e(~G$+>%9HqW)nYQffqC8!W`ZQY9f-rONf@<@SI-7w4;xA5P!Fxvq?+_YvQe@4EO
z{a0gBU^i$`E@%1Y(MGJo;#|hi$f8JccppqhU-;X+&xD(mMium7#m8AeZs|Is^6RI`
z3=ar5%nQe53hUqV!+wXK83glHulAf@QHai$;6K+w?k3UfCACQf+p#d9%XcWC(6ZmQ
z=2UzeZp8~eC!P>=k-oE;T?|7<4y<JuO#mIH@Lmv7j|3hQNqC@`9ays;B-PN9VJYV$
zl-41WLkR}o^U9(8vMP;ZljpG8<0BXBzkn|f$+TLaUOJFR`I9N$oAdxC%j^&~H{G$c
zZh=P}p4qM^WlaD<xAPOhc$<sS7{{%wsZm$A7}F|RRcJhp9Hv?-LZ5wL<T+-8eebUs
z9aDaD+|gOMPY85Oq*_vki(}06cnuE)NL<c4)BvIiyFTJvHfVRFc6N{6MBwIKwIbhn
z^P_^b)?FJ?XBX)QNJb_mb!ow|Hj*Eq{~NcK(THaX^~B4M>VwTwHI60NcAPXTSOuxo
zb=GmbSOfZ39x0YQeV5iN3DXP>rrQ=tcH=R>i15rz$=bAD)h)Yr+q~vfoZ;Mzv`_fI
z(|j`;iM-Dfx=+C)xT&eB|0DEF2Rik5Q&bj{zk5Pm{0tbC-*OT*09_11+44Xl8)ngW
z&)bNf-0c&6b57{lC#GtR<Xi_ZNYuafbhio*8YOr4eVxR0zaz9k{XuQfJ3v-yP9p(_
z;1vitir``x*$iKsPV0`sP`zj<LOy}#^+;FN5IC}Z8-|ILhf!Uxi{s6Vn0i7VUkW<z
zA#rOrur+zVi-(bix5^@(V5FOrqTB5l4ChJTDe@P~x2P(*6qi2bvC(1?(;J$tTb}TV
zs~)+{W4@#AmZV2jl9Yio#Ll;w^s$(vwrVzG^BPK1lx4uKXyv+Y5V7;~TnF;#pJn=Q
zq}P>Qx-OFdQT_ysfaECJ%>55I^4QDv>{(7xcmU%BIh6SrwBzwcs&(#sD;)+O5Kd(>
z&(#c@_|I2aHvz=OM4BVj55Br{N?6doS2dn6WLso{^ZB4(pZD?epFN#!so|$O^iw-S
zswFOsVoJQ3LUZ`snRvU8Nw;yR22XPnr2T1b5s5|CPY88<%Y4CsyLFS{{G8j?U2Y1b
z@9RC!s{`uifmJlQ81#o+yFhJ5W%ik|&LbL&a=Im!^sgyw$nv!gUx+ky)+pwr#=|JF
z;m5?}BOS(^XE|<tqn|tb<qkisFDJsO{+tL-P5EDt*lg(OW$8W6XwB0iuZwvj{+(8$
zWPy)BlLM@Vhn8lg*8G;!|J|61-<ay)W#gr2J5(<&VewO30)h)8K@3ixZDL-D5-qU6
zLq|tvF;HhiR;umQ|5et<Qr249a%fw}vMX6n*HR`z^wT$jbgJj_v0F5HJGa?)QYq0n
zo7U%ly#Qzstb!pR5NF~?Z;Wa<CF%diS0(-pthlGSS9^vRq+gfVOcqzDNS4E$BK?w$
zbm2IPGo){`hJ(hB0klGV(q3J_6l9?w#DcFOzEOijMpBqMVWc%&pVbY-PPjLzt9I7k
zblt{KIH96oB+v(tMZWB|kK$V&h3~TA64pJ)ozx?INk4CAY+paA>O-E)w)%5WcV2e4
z{9nBk8}N}}B**R^jKaye4&+IOD|WHH!G)m5+RbjtES(B@`$&j~30LB>+fzK~@=CZj
zBu#)Fr^a+B)Wk{#wl!5)GHtr*x%W4@%m%pzH&wqVAq;1wy=J<Ar>x8m50@Jd0+xsv
zf&l(FjCs|4jKhmp0m04BraV3F5v7y|TrzbUhng6GqqW>=>Uzv=H1At3R$M5gKOWyx
z&#oVjJ8OaELHB1Uujs1u-x|t1B>&*slBKMPG*|jg1pZ43OvAl9pt!uQPj?^U<ng?s
z!Bv`Z);6V73M{MG(Y$~0f<W8rqOFz|#P5YCeGLzXfEoaXxBU-c>B-bKk|$x71Y=!~
zKg-|N4g`#NrQi|0Jw&szz8{rkmG;MykfT|g&X?N#R-7pCW=eIifaCB{dT?4=0@{c7
zd}@535(4j}c`~T+t-Ti6!UVQL%;<s_K#8oF6Ct!Q>VE8RH3LE~p}tdHfCrI2$>&{O
zAOg=rBP9*FRz9Lbk|Do))+s@fB1&!DB?b^8Mg7cQx+ID~Te%h5qv^O-B2f9tkY9Yp
z$dI30!4=LQ-R)ri@(#kI19$46IRGKu6m;obgO=<UnPYm8i^;5-N8%ZwME5nMF!c>d
z9{p|CF6SvihyAjs>23NNf3D{#heOE14;0bRZ1|~eGRGK2lJj&4X1n6ZiK^FNJbnMK
zW{1(ik$o*Sj;s|mNEdtesRLNN>41p&Fg60*kEEQdx{=FGJaVYXWt$>o6G!LapQ^pT
zl!Qgcc6LQAU%Gqxa}uph)ejoaUMG^x9nHZfGxUr{E@h>cu8(-!Tha9lcIXpH!y~nR
zU=hckzw4+ZMgRDg;Po@B`Zj~NhOz-~BMHwD^bskyyEA^>Y)M6uvkqp^qK{)qbJ97<
zV>{}*VyWQY``~L-SBH2o8VG|3nN<tOKyer+T4D!qB(QxNZFGzyRD?QeQ^T%{2b=IS
zBi<1q9z3L|zi#(;7k)%0Uq?MDoR&2}&wWq>x#<fFtM-WQw{3~2?J&uq4t3SXH0#<u
zH#=+onc9nQby*jigClR(P$jlW8&u)wc4jd5iK6`*-kdwr=SKk@!o(^QI!_BTRV^9*
zUnh5gOX3eW*yayR=Fg*5-vkUI`q1?4_ue8qDEuMvE{D_j(`lT=610HKl${*2jO3jh
zKNRFzq0*=$<i$gQD5;VLSFE{6%}PbWXGQ3pSr5UjTuoOysYy`AXG$KiN__TexKT5a
z;(KKlN1?Gv14eesd6a;97NW1mw;xL%*si!@cc`=8hpR_`TgS?F{Pg^Q%;UO1cCLm+
zmWPH%%AVLCIfCrA9elAjCF>Q%wq0lRjiKbutnr=kwWxhx-rABt8&%!k`w4nr*gJkQ
z+)WyVkaS0xgyu;nP;G%O`S*n-{Mk~%L;j`X_!qL{OZXztPs8*t%%$vv->L};2~2oz
ziXYF+`r(0D?VdUU)LP@A#<iv_^b|w)&Ran2?Jf07Bab?qP?<|$Vufb)%l)Bes(99*
zI(=tQ`H}w#LCux1ACYkohX1BLTC|ho;mfzAYI2(cgQ<E01rdwgWt@Zy$zt?0>4^P8
zCRpYLAJhj&X*+0%!V?<qA2*na%r&A$YEY37&;;=Fo<(T-l-H^9<ju*`A`;JVo01Hu
z+d63Z(W)%7KQ%wS6}GgsBP`YE$=9stSY;`x{I{(^ACFH;b`}Wr{>Y+T@;f9xU*#J4
z7xem(Y!bX-;>=$pd4UF3urwWZDps!zrO0;g7Gl`Z*G&_!eS1K(K+$LIm!O-P%4a=L
z)FX~xyJL6*+e_Ncip(B9R_Z7LS%K4#w&ZQU5NAvbDQ})w{o}^V(R{fFl|15BVph(?
z&1}#NyeMV73J+NdZ6;gNW(u?imPpWqvs1Rx5~ag?P1*2}$X&2K&u5eCxM*$Cvlt^U
zLz`8TWX9nU6+-?VpP4$dzz%?wT_p)2$QA&*4{!#07j>HSC3nWd#?m|I+1xv|CRseX
zMgQsu>A;Qrja@>P;n57wDW1u-Y@nd`pNM3h&=-|avmv)`)sAn4jsW{ZK(0qux&U`h
z*(^~lK(6O2*TX=iunE0sKux7E6{#^5g}Fw+AsL?I^pVZW*?%*Le`656s;}%!5z32#
zNbJaeWGE`(%b4|OXNhZUR{A2cg?xS#B&@&d2p~DVX^6uAP{lrc-(F{KrGJGz_TM!)
z0{yGrx-*I1!)5e5NWUE`Ff$h{H>R!ky!@2QyRi4f8^@(_*+r9~%q=py#?n)updv;F
z()Ml?5w&Q|cSTl`z=Ep84~eq+81p6Dnrk7{Vb^L_IYf3Y__TdH9%od_xc(S(|HTT;
z?R2!~(9#l6NMXW@4wr?z3xp@Xow}RbRWaAiObloXN6Tr*Uo*@S=)lpDUS9QI&F<>H
zI*XHZAm{z@URx{v`Bb6dPLyM8U7E6e{u)g$a9)*5z}I@@=2~>?;3NoTfL!Bgmn2)$
zYm=Dr>oj7|&!}Cx#Q?u?m;{+q5iD1N=Z<F%*q2JV*V<j%6}d;lp_Zr%Hrv1I60b#w
z1kPuZ-@Dm}D~h=R)DT99C0LI>XCY@L>7vM4Bo&>$&N6vGRSoE0$J%t^^)t%{(RF4g
zKTUu+c1#ZkG%Zc1CLbK;;R!nveOC5(oqV-FXKG8%bfk^_#P-%jQU+7~_8F@@TLU&}
zzyA?S**<yAVe~hIQ=3?+@i&fVVWz?`u!W0VYNS1;>yQ9gMa=nba(?yNxLv^!nTH0|
z-2X$>TLr|qL|vj-fZ!0^o!|rwPH=a32=4Cg?ykYz9U2KvaDq23K^qz;=ycA^KX>k1
zzjl39yJ|1lYrfqPvT6|up_pE317#yfmPZ+C=Gho@I&y4Z1Nlzaa*BcZ8Jn?>q;I=q
zyJY?;RVx6ZCUZI}USv530EotjL+={0PS>m1UFk%dRb@y<0dH82{T5;KFX<IIF%8=H
zoN@)G6B<liLdZBHSJ~!&dZxa1h(1pI>RVkLJ6P-kX2*%_w1KASRi}mT;J$kT+L?3V
zo1)phO4_X|g_k*Z9D2TF6miYclece12?nBl@vZNEE3$vo{0fUx+)%hj;;91IXSv-I
zkW&&Ky<O=G@~z7GlC|9%nNRkzqd|3%(HzP&N_l}b`I6h*;KU^J<-5wgAF&)|xbc^R
zJ%>%Uq?TOWFOYYRI)fQI0rA*RXJWtYu^YgWrX;--;(SV$FNAQWiS|+4rI2h7{k;!c
z(}&!i>V^#|jmB)Z0=dT*Ef1BCF)b}L7F3O9$29HLYue@S9x;X+cAsXn_RVAR@&VbY
zBL>6`W}gifoK7e+Fzo0p@GmFXG@XtorT;L-tfh?Et<?x+0^D2lGxZA_08Y_oV=-y|
z)1o8jVfth|gXgQ7VJGpQD+H)&^vuM^^2%h#?a(wF)Tz5Xomq`aIR%v*O7E;oyR}|1
zh%lCTb@3v=QXX{-W|C7kw46KlO2&8b6y=J$4~bH$ezMrl^jmMVF&+IMdpku=vZV-C
zd0m#GdZ5(0u53uI@#nsPB<dlmBFlnnv97nUaBMb}#udTh*5%Ino|Fk&9o!7_qO`#q
zfciR*G`$unmvaXdLu{|09Aj$3y8JD>u6_L)%YREl9R;xth+0pJu6<v-)2V)B>Ipcl
zxDB6Hp0OaeEef@(J8d!D+3PA5)5E*mm@gHJic{;k*wMR(PFrrAswN^avYlZ~<J}I|
zfKjig7jhTcqEE`eFxYOr<4=(jRqxMLkZ$KBQy3CWA}B0%+dH&cS4tYeOHAnjE!DBk
zQSsEp4=1-ZRJ}mOfskD&-JP%+e1FtXHZCs_dDPXw<RZOEA#e-aU4{xb({WwLurdv2
z2sW9q#F&!#H}t@=^ueiMtH@In<eRU@US>(#^k1i!XEmuMkMJky7;V%+R=|Bz>%|%t
zlPh)NN1NfqsRA+=X1AWtW<gN}a?O&{B%+$}^uPKZq09#3D4&;=Q0}G63fXGepE=K>
z<X$F-8fS$IXBb8^;yo|C7F5JX-2zZFWMTnWq$XxWx}qE@9bK)hyotcUWtsDbS2Q?@
z4a2{`Y=q()vbbV&xi?}&9)5|Dy<wg%Oq{B(?7Y@>IDFgoL2RvE=2cx{`hvQ{nAR{a
zTO^2nh%j3p>tT>~R%C$JuP>R-SSd>o2npt8DfxaMnYKo}mhU@pz8cQam%lM1__)sx
zt-|wHZ*dx~;gdwTh#p$=40?CA)2j2m4zg99)_Q|cU`u~)A1(2C1b?_DVsf?hj_NP%
z799WVpJe@LH3E_D&Npb(%ULXTRLg`eA1`!caaeIE9Vvj_h^Nm&qKJ0BcXi)DT)=j<
z@7oybPni}&)^yO~@3`UtY$t5pl07tRFb)4*i$%t8TliUq)%tCF7uxeCUwZ;Pg0ZkX
z_xR3lA~7Ah0duXHeO1wQ<Q)*kXH`4Pu+gWZa>QpGgWU@{qB-RxWnepO?S8Vp*jOWR
zdg<X8*H6{jm!6B|XO`3J>~hCguGz(v(A1wp(ARL8)I{UZuc(Bd5P|R~Kf=YOk(rs{
zU`XVzR-&rGwbjL~_gw2*R)-}5WCCQ{4|DaAE{x;MJx;WqrilqAsAyENuj78CCj6)!
zdL4`~?clY>k(4%3^956RR*a5Ly~IKi5tK`D#X@<rSLYwe@+W?dN|BDKoKtV(x*!8&
z!C5iHc~1WJt-hZRufs9T?*59uk^J9iZWrXWDMn&jF-m$;6DWx{*v;Ywh+wh2$ec*M
z8siUzHiqY3P#~_j{n!-6j^5Gf0feCZf&GD_(00h}N8yei%wr09pxvJTxh}R#CxO*L
zV!kjT4CZl0e7^o79>ce>rQQvq(%dy`GIGZ=UAeQe{{ENcjp{v$@6PYH1n&4Sp{ZY(
z>v!f4cJyEKjHFFGyfddV1tncK-{1HYiD2sH>*c10TkaWG-q+*d4smLI+zD!JFGMz8
zAOX5Igre8Q(~_n094(mE6FWGf)NlFTBPw<cVR`*oR>Ue_jPeHVQs3+LsZsBANY>sC
z=iE2bMa`!x|86fg`}l7s-f3Uh81zN*J;R8bt6{^MnjQV2m;IBD(KTOMvU-jJ^$xZ1
z@kN7(vI0(s#I1YTBaF;SY^RsB6JKDj{I`9>mF)l>tjPoP4iBUU>wr-b$8Le_C^z{;
zBA&9s)Zdd;<9kt`pwCHc3?Rpt%Ztjl7^%iTY=D1WpI8A^5%=f<eGl-=V?0|k*ZeeM
zJNa$v-XX8>$y|K**P!y@3tQ#}_C|1dUH}5I?M*%dV;`DCFh(}%G)yM$bvaK*Z`QJp
z!7dfExb-szyfuc#?+D>mSOa`nzBuVlyODka8P8sQ)-|Zo;}^L~bp~dVLayfsJMP&1
zuP4Gh-R6rYmcF_hG<xDF33Mb9UY+JnKCNW)L>q9#uogi_>-z2YLmRNSb>0BTyfz_(
zjk!PFLq8xv^I0gvn~BgJQ2igyVf#>CzO%hgK`M``#4lgd-pS^(n}xEG;n$VD(TtQ=
zsxF&lX#^_~bj2_dO-pG60~zak_g=4k4P&oj?@^QY&-eTRI7fHFy*6EB=l*nMVU8jt
z<d<Q&Dh%Pqay=zDf};2{pM2iy#(y@k4MyV}-FtfG`PZiDP8iEETH|^B7S(Nz`UsB>
zNESR+p!HxniqMhY(JlGZ9_o~i^y;&S=AV60uUCK8?rx`@Awio;kvb8k3S}?I$7eAa
zTd6iHLSvw545A#nFQ*a|pl*dchIya0>B*5HwnS|37Fv17-G^B<gJCBOFRn%sd=%1n
zMU0_=nxI#OEyqlU4w4<QATqP_W#!;Ge(2Uhnt$aN^Lu?I#XkLXR~MF=T#aS(L70++
zocezBkf72i7RsOV0mqJ>T!wx}6kl#{Te$r8V#kbd{~Ns|Ux(_acte5UhsBQh7Q7+=
z+?wcb39f;evnD!p@bT_G@$Xl8X2+THt`L&G<K-j7=JwK!l7gveFt%CuOLrKE-0=N(
z<@38hZ6l@BZDKJUy4#YZzeg^{pjm0V3}M(3wZCU>5p>`l#(lQs&u!wZSGBb|F0FJg
znP7*)QZ%je>x25Xa@DG&X$zn(3)*vp2k^HX$FXaq-nF<Ahp92+!ISQz8G2Ln@F}(`
zyvGNET29vn-N^OZe#PD!As9c($LALJhHWGP+!sNl7eR1D_k-L3D|F!IuFppkAoLcr
zAEOmSGcq6map1kNm~ukysktvOj#28k7GL|ICaZl=>5&SVO_M|TV>Jv#_`PQ=={iff
zrM?6g<xN}tM2pZFIs-786ph|f{h6Wo6<gE>WEpHv$|kNJVKVG;M;~+sEA`{s5VLEE
zZ#{7j4+n6DqytmydYUf&vO(I1c9b(pIP^T7J*O&s6cI;7Buq2;=pV*ARcmejfGvx)
zn+dlXFbql@1%jlCYvvFlqsuu@AFDd3f|k4VTkAQFjn16R$69M_PutI^Tf=RumIX3f
zmOtbK_$T8s<;#5u`?}0m#xh`7gGKX~U~D&4K6!Iw-@mTg-lN`$I%bXKEq9k?Bl%pw
zJPl6LuTgamG-H<Zq$E)43*ebJF6&}c73B`n4*hfuG*&Q%Jqqf=&3wm(%w(3?c^y~@
zS+UJO(I>xUfy?e=MQF!(XZURP2gc}}^35T(dxO{ugJ&;$0A}#t`3uMN5))O*A1&aU
z2!LY%BCLzmXT#HOnA2`#uH}G+I@li}6Kl~}aLw%)bX7--i+}TjItr2j@i;1xYm@gw
z+QO<qpIIp@l*l)-M!2@=Twm?e3cQRr6LnU$5(L0}ZaWgEUO2b&bl`$l(n@Ydd1RIR
zYFc~oceeYQ%Wvo!%#1m@Y^{_RFsurhU;V7BdcAy-^ef)TiIf|w@6jh6*foYq$Uha2
z1ZAzF3zCC%eH{~qk6Qms=i&zQ)a{uI%0vTtlkDrl!i58vm%GU5NMyC-k2*>|@tK$J
zN-q*NCxmAP8DxHsR)$ARQ|+ve-FI`~vHst$LtRYY@8A9&SE<pj5p|2jU99_Q!W(|f
zn@+xMmLWhXSb16zf_Wi!atS@$<nxV`8_*3*Lx<OC_l0fH51CpOhA~9<qXqXU3|=b3
z6HMXd00J4J=Krne2<;g?b!dT5d_lFrK4&u^;0j*HPy~MF9O4BLEoMeA=l#q$6vD)&
z5KPk+U{Q>Xgj4d>Zj7x))|y;RJkdyN+CufpaNoQysAV7OqKdJ_1*Ekdy6VfJTc6R@
zmLDA2Fvk1H*Xcy;{s&PSnF*PKISJRs8UF5Ct)bTPA%1+N?<U4Q%v;XIue-zlNSB5z
zSVAnmDP%f&ZJGj%OC0MLr3J;?MfMI(9JFOa3LEgb6HGpAU@TKjAIUA(&Pnzt;*#;>
zkDbE(ls~b6N;rWHQn*BSf2Ci0Fc8l6*AMG_?YnF+JMa+8x<_R;2g@S!dLz1@>dXoH
z)lb}Mfe5$>)|rWdc{cq%b)t3Ro2^-d)-KONNd?)9@K8Npehl0Gj=J@%wgda^4|tbl
zd7gP%k(ktYVHOo$>=g0_%{)HgIG!XzHEsu1ih7wdHN<^D;TU22kuPv4Pv%-Yp7v{Z
zY3<{kOycI@C&V%^yFZiehd<&4I>I?Hg$XpK(^1Mn!rmmyCzgBD!^%Q4kO^PA&cBp|
z)%_I^^Lj2M(3R?mq9q5G1*7VG>%Ej<n!koUOobZrYp-l#{?)v*Y)BXq#4}OJ&HFGC
zH)2}$AhET}wqziZXeaiSpf#8M@{})c<sGGZXwarEg;s@2p{Z6X&-wnBr>YqGrAVGH
z#R(gqY5iB3lux7!*Nj?z5;N_ey|4TUM&uulcxP|G{(&?^9l4?j`RhE06zfKT?NRvs
z<)=S^CF4!KGLaal4j)xe0wt$4Mx~7{m1i3eVC*`qcK&w1PYyhU?3s>*qHMfxNIZ8y
zO|!!)!p-`wV0x8oc;H}bpE+K?Igu+8K>+mXPCo3ys5uVH`Anr&@Pre_1v{^2HZk5B
z102Kev6SCZA0wG3Ee9GbI@TwDqp(ktCtU)kd6xi>niVLt<hW0RqVk5Z0z@}y8g)%b
zACNlwLl5c52D_dO)$7;p`cTm}6a0_wPZ_!$?Zq5cbq}Il&nz<?;n^u3(dx&ve{NyJ
zI363NwkGXAgOvog2P5~Tup>>5+LFoaWPB&@DV?M1dmnoq6`|?t?m+>n1I_757N+(=
zG#>(BwmRY)%>d!0PeWi$$Dn0G$Z`pw(;vpHuA{bb+t~9oJ05!&6g$F6dPWo`VZxeP
zxolE)3&v0Epu(binNHiPD6R2hJ_0>#Rg`t4Vk=3`&kSCQx9%%ok)tJvQ2^nnkSC`G
zesG7_?Uc@K+5Sg(<+hMx#@QA_!OajB*j-N)WX!*L4q=w&O=I^E%p*SVaDB}Cx#5Qy
zr_Q{JTH}XMo!m8-5YLS-NiD^jJRDe~we0DCdHp6w@z7*-y%xTGMBb#rDJnzZMc!sE
zDW8p4F&tlY^fR)%tA@C%eCgFVW%eHXd{j1Q9vv3vJPy?TLMKdiX*WjHWmB7|)A5<H
zkO+{Y2Q*@uwG14$nm#`xMT?B2X$d5?CH?$@v*cWsrh9c%7v0c|Y~)D+m#|;^>$Gl-
z*DaM9u<!=<z`*r!M#?x+OWW^7%N8&-lY;bWk=I2dd{`0XQ_%0Uf81jR%)$DZpcf7&
zrPPP}53>-U-bTC^gbr^wWIF+W^(qr~_7AB}VAEPco11Kzi0QFUy372A)&ZWl&tmYl
zW29|)_F98J53U>Uvgmu5|IvOfAyZKip3Conc6~>6!Wy=OsyIvlfEr2|^?h_Cv|N%w
zHsQD84{aoFH4g;^xec_dXx=%RuNm`xwniuba_g=>X2hd~eK%UK^ugryLK725(}Q10
z4213dO5{?rOYXTHbwLzu?{7`txy%@10rIW(w=@ZK>{V8`7gRSXrTegj#IAxltwuNo
zGnUfycL#|=8xdZ`UM{5xZn8dcS>wu+K4Ohb4++gGzM8+jc<bFZ#7+tq$+oh?5s~N%
zXE1&a)L~Jkg^4wM?^oD9qNna|2^0l&<eKQM&wvd~L3Z+hbaEJ_&6cyrndMGq46puW
z(Vn(Y+t#1HfoK4-P8=^c1*U!y#BpcyTL_gh3quC&09R1;d_D_5YZODz4S`*(2&ljw
zK^V<=qpvmM>guLN=li(C#K}`UMbBdtlEGR>2v;skrp;Ve<#-=LL9p>>&}Q~BGbslo
zu>h(GT`VKp1bOC>j5~bX>?jT|=+7voWIlphiGfaszQ3fj{3_E33+N7VjuNynlS#td
z=Gsv`{@`Hh!0$QdX8|ZFC#$3E?k-{J@?fNko8tm0%3#tkv^!qZ&yUVqvGwJ|Q0i1$
zI*!x5_C=v>-0;{X<to{n)SRN-{1t?#zF)y)AnISH$KU%&^nx7p4I+{O60hMs9xRj*
zgRXbDXeLp;$rSeD+n;aaHEVRz@aAJVj>`x>)7Y7tL%`$*Dx}bfQA{q~Z+HaT5p!L5
zkc0%!AYl~4=hOk1-N<iW+62J3JBgt%cH0g`o3R6wV1(c(e)P1El|E9li7m3)cNJqc
z49{&CK-GsPUM52O_n`s*Z+Q<etT4iueiz7JVrC)G%^bVr4hW8}&<&26;|N8<!&-n#
z%VJxZJ2}_cNc&0yFB2<pa!Vsxy7#oj`r}X5?Pk<q$;K<}SDs4()B5w9mol1ybIf-`
z{_^J!{yW^mO%?N#$XB(E1uPO~kn6GOXnk&QK3iZpzd!1ICr~OgQ`D9RC2yq<Hh&I#
zjx(ypI;x0dP^ja6{hnuNGI0m{4~86vOymNVuC^EbRe!uKG2fYV#)?XcTtT9}3?QmG
z8aZL)J|I%Eq?wB-?dvnM%Hy4+WP8*&E+!T5=R>vVr7HR3)76@8bf3!bs$pY&2#{mH
zKbLzk$1>>urRnB06={(=ksoovF5vae0nd=!B;TNIgg(`yo@W>*U*la2y!dvq9sdEk
zkVkXy8(nbXD1I)avuu?=7dsV2G&noIV?RBn`k{JZ&cIwSOA^;QI&mM&^pTfKz2a&*
zUt-F`7P?KyW=~h3$C<8mMSRO)@AcwJ#}JUma#fGn@3j9F7856{E9BGcp5VqWl(t)P
zq}SC4KYWsr_@xb+7le00gM{ursaUh?ufjKh)O`DtC$8cPXG$s4?I4(V*ZVc?4;6}4
zU;T+aJZMSaF?zW|m_HBzO{<!(E*CPJbgXt=K?{mTOeg!4DE(WHbIQ8nE49SGFj0?X
zA-XHP`F@(5d$lOTJZO*>N0k_4<bgfVs_uKwSpNGtnfUtjasR{iXcIF`7NQ;IvV#)$
z_?CO<6i^XJ2KDP3{G~4S92vHuT=A!_t@}^ZBX=JN#(TBy7LD2Txo$--8S=w8+jwPv
z{Y@T6)-KFuq@yjcs&js(1CODLcO(Q~mG7~*uUYhpbO@z+UXTvT0y!t)zdCC&ZhH&5
zm^Fu^m%~vsI`}Ga?y(FE;MNwtNQl#tv=Bpf43#r~erbzTs$pP-o3EjQ?r;oD`~aD7
znj1dz?)u4B1gM{O=}r@TxFfX+%Nbs>9n=>v26%pFle)FN!ym0|fAm_cC8gPiTt2Ha
z;QTsdFE}cDA*LZ;iNs$E-teY!xvY!2vaK#QljaZ;55VX;`%@#k@nL|GLLS~RXD;~N
zt^~FjWy+1>VtKvLp7H{og>~b9v;bIUqcgPB7tKHKVZDBO8V?&lSTq|Sv20nQKIHUU
zOLjx7*W?B<ShX@U$727AsE$|KR+9ST`Z}hqozXpm-u_Js$zt!bw?`xmciFrr7EyA?
zKK@Z0k7)Cf0$;?})s@|`?Z|y4Dp?9(9!i4A=3nF}`9a9Y2iVjVY9cWt=?<@jJcqrD
zyJDNOT{#4<ZvGQC?%}ot4n!81LhrE@#?UlTbtA^Fxc&sWrlXX$axvL|iVc=Cu-S1l
zu+t0*N1CP9Y#oJb9%Jkxxgoc6ti438|4^64N>|?R0IfdFDYgmd)0}XzE`3Ocy7L_H
zG^>>ndb}Ny^)+b2m(gVmHEI`>#N57}krc)3ivet?@i{iK$B+FF6vh`lVqo(|A`=X(
zDjL(t(LT*J)*W#TZBxF-pQZuwY7B}h=|>8>GjS%0ayd8F74l9SCYqSHfQZN0<}(jB
zM0wLXiw9yfc0WkAf8V~P1yqnldG_Y-bXDGrY4)1g^9ObA_wLqPIx*fu%F6?!ylCan
z*ow!xo&i72Zqd*jg>w$iv2e}K8OHLX0bbY?O}Li=0QJ(5#_4U;lLd)JM+i)n9=n9m
zEq#m96w0>uJ*Mq8H$TL(aLx6U9XJqbg>ApgAE`^|aQa5J00ayqPpZKi^mpN?sRGMs
zs*L_=i_dq<7%(ocQToEBZggJhe3x4~%8*F2HA<HkLg@*+Oz}A+vtNPV|0Dl=P*Q&a
zp?xky7bt2cO`TIpY`(TbqLP|E&jmqH>9qF6V+X%^pRpE??`g~OTWpRS0XBht&ze1m
zDtBUW`Jo-VfWLtf2hV#(o|%=%V<skiw;t}~*R=mo`bI$jrORd#d@y_6QCa*k^+k;Y
z_Pyl2dds3(6e|Z))B(qhom}x8#M#IFnfa7np>JkrGbKcH)U@e5lDocN`%0@hoWyqD
z-;dn3g&D(BYY*lg{ixG|dUDy%lQLVC;mU5y=U>|=SEW99vvA4N8<PJG#ZE$=Sp34D
z+2#2zYS%uAzV;~#Li}$y?=LZ55JG^-pT<#eYG!o?8AlM|yaHcLIn%BEeimVzdp@jA
zZnUY7<SuAra{MHfgtfsHwo~ukz15D;pR6S6<nJU+pQnJIN~4}3*VdRlu%v_5I>Jfr
z5q&$7&zHIhUsqJRcH(t>ljldrMZEfFERG}R{u?cfeP@&HCy&*e>ec0yxYj)M1uUta
zML$u!_+G7!7B!|rlYDR56SmKmPxGS1;iaZHU+EB>)OJ*}+RTBtNN}*>-eWLuI7Ykf
zC%HYCyi&!S>V(7Vg>Cg1o+Z@rV@dYFRgXlauPDvF613=D2Tz}^MUD6(R<RUSB?V=$
zb#9DazLg?Wy6+@x5tng6SV^(-Tdzd=fZL6~rD9fbty%Q)F0v!r&hmN<L#zpumP($q
zpFc)#7j??zlR4(Fj~7QBuFn&v`tQH&C(BKB@UL)+q9x$!KB~J}(M1CGd$py=#{5r#
zO))vl6ma*<j$(GgVIIv*+W5ys&IgZ%i))z>ajQGg$OVy_$!t=_jfn1^Rpxr@l`ie2
z4=`EMgu%won(78N>ac6rH0yMGnxOvzQ1e?YWK=C5^q@PWN>dQuSSC&>qRx?UHgeD>
z57=X|wLvO91nhc~ibmb)ao0*EZQ3G&4H_3r_DvyB8~l*PAR++t1INdN;pB7u5B=3a
znJ=O;G{67GZ{E1Ua{iEfAZI1D_tj~;gW8mZYpY7I#vm$=`_9JrcZ6und-s|hom5UJ
zR|{&0*EjTIr!ySo+_U3P7Umtn_aU?II-$hd$i9X+&pgzg`b4<{w%dL@y41pA)XYav
zs?>{avdnK5+b0$*)$J4?eY9t=I~s63)g;$FpW|p&1&?b{QjjUCvjIr51+&V_vInc1
z$6j(UEAE)0w-@KaLpB>&)CN&Y{{X`X1qf{g{PuUL7>fRz`7<xb&Ro-+@^|Z#T;_x(
zZlfRiu0~S82e~f9hPYdXr4@GG&cll0k3Ym-Hpmxdg0!r?3AkEOXFra8s?+SGp2#iH
z7Dun+<xDBriMzhTW0mTuNA2{e%>r~1k#Asa$tBW}jN**vuh29be(_dt-*R0v4abP;
zZBQIBOyXAII=NB7Fa6TP=DmjrXvL6!0Eya=jj`_kLaDeDVLH1=<GiHOk!$p2>p9IS
zYm<c1`M4G*FYwliZCs;Lr9N)aB6vpc;PnBNfw^{zh6WLVLEd&XkVcI}mFfbC<^FOH
zVD#h6?Kkbg#s}KO0CeX+;E2Mdpw8X+V{G?jh@R^EigEt)Rd;a;3rZ2f=oQHCxLA3C
z(lJjHlmD4xqt`LakxYSQ==G_|)bz|SR>&V8l#z<|olA7^;7we!E}zN85B+pwGP!=N
z?@G}PsoJGty4;*&zVgSR#$N+l1&a%mLDmuWAI=s#<i8!rX=C47<I1=sN-a7sWv>%P
zW&-F&F#AO7-cvH5i)G71X;ZsI50-TIAz@y>(&de);41JtQ2eQ6q)h(Xd*wrry_Xa+
z!>nFmR*-0=Te?UJoDq`wGmie#vDc@m&k4oDkW5BCe@~C#HX%1zjV>v+0WpzJPaIXT
zm|enc7;O*&c*)edzAI-e%uu|Y9LU$6)g>eOMi5c~QxbNN4u*xCQgX5AA)BvjfU&-d
zi`h4b!gRqb{1cBV<9XHhMggtOZP!=joJ2eSBM1Ucd2x?uO=`BryHmO?Y>H|<QPA+Q
zD|^c3U32zES+<Uk43WZ#cx;ug6w83bje9s6ZVMp~fz-}*EjJh)ia&TPcoqS43$r=;
zwo7|xF#~0U{zVZ|KM_Arf!l*|DM`F3Oe|=u6qfa9k62QS3d$cB(C1@8&sC=_tQ4xW
zV3^OSHePu517AC7)E%I3Ty;8YzHQVw4`~;~s0z67Z50b6NFqm-CQkamx055m9+w@&
zkkyT>d)pUpD=%`RF1vgFFu%@hZH-B=#_8dssoQp4lx~Rg|9e;+X&(QJU0bouNo8E0
zcy)}1=kI>Cz3Q9>&~6cll-B>8zRbx0Z_HV9@A{Q7cF!83*tkUcvYG@h@8Lf6Kio|&
z%w+>~A<FPPLeMsp5ZVTkz`QBZ3M^izRGu4A51bHc=YZ~PKSJDqEgSxVH2VE|>d;U~
z-HNe+*OxVsG%1xwrqlQeN?@PdmI3+M%=b(@=U+G4WxNLq0>zwKI6qGLPV=|Wt6Zg;
z(n8WKWW6+TYwZ?H#1#o+P<t%^(rao0{s9#2?pvK)g7+v~we~AJB;HIXY}L}pg2{1$
zVh}wD)tE;S3vps8B((Bg{g~GpNA)+MR)t+V$oj)c&nh08)*19-iGX;06q?RX{wZ+8
zyMd=6HzR85XSJ=s2am*4Jucy`QVGND2TW08Aa}uvU%L)-&5GGoc^v8HyKh=9%$IB5
z0atq#egec&GT67mowh_6Bd9mbRh+0oqAT8=j-X2qjKGR8Oy4@TNkI}b!GHJ@CFJBv
zXtKkxONejd9t@UIhniG$kDGjvY;P8?Zx(3>1Q}$HF-%j*-Hey5o!%;RcqccpIVQI0
zNy-;~OT0jAS^`VoxJ|RkOnPkf^%ka7cwJqqGMy1kS6r&owv&aFC>hd^QU`H0q30ch
z6L#&dOT!tS<><|4eDdkZjW3nRZd_#o&a>Q4Rh1uoGSCgPBTMTc)=tGWLxR|Z%QPuB
z@sszkw_1?X2SPhMWkSux6jtridVB6&X=8alr2Uyk&YVY9iz=EZE$Px7huKDWLk9Z}
zsM)i;Qw*Rt8`@Ti)C!^j2s#5pxzS)6;M-wCf7&8{>$yWg;6{oaXoA1&ki&0!_%J(x
zgZ~9mrnzMb8B#?3wvEy$cF;j08Gi<BSqdcMJN;q=mEIM8KcpTz)IiQc+(2%%JKaR?
z1Iq4G&UX$-F|yp2rbwS4_nA~Y?|7HHZ9(593#6UbKA1UErErh3N7!j{4BM&)yrEXD
z3aJJFD!A%Bq=%TosT(J68U=dZA_1zFny8{8?NK5>CSx@y;PKt$rf?p<)c7dH$-Da3
znQJwje?uCh0Tz1*$+!%ZrQhW+ZNbq`m*ADpA!llBbI@p`?=X}Qn^iBzd~fx&@IwIC
z{mA!Ggt{33a%0E{|9{-gVtHpgOdvX-=;9R%EH_}(LExCx^hsM!`Qi1Sp7(TZu{S^G
zU9*CxO_m<gz0{x8+lay1Fm;{G=-M){3TCf9<rXQC!TaBBdO3>Q^X+RyE(6@R*?><a
z)5HoTf<s7up@(g^qy1+i2V{>O40S87dM9dqQTg-+`pyEy(BdPP%Qsv<t#2^34_ol!
zm3b4{ke1a6i8IQUUMK&i<9W-wq&P=8cp7l{mNtzI(O%gsJ6J;-<QVy*uEdZWs%aNL
zz{9K7UcxvzeCdJ<Zmf!~U<OT6EX)|s`f#H~Bte#hl|+if7X<=w-%hPDVwr|@S&Yf>
z>>W&>t?~(cS{1Gxs|ewS+Cs+;k(z$z#zX8K`c~fXDXN+bIi~2<FQn<y@P|3{b7WKE
zRbv83ZIn*C-J)@iUe1v%3pw&;oCUGyRjKF14E2#TThWNi@tCbo?9WaYW$xYZ*yFUZ
z#eaSBS}=joG=K6DBv)1AXkn+4Q|iJ=r9%lfVx}J2z(2uFwD**%#<Pus;~oc_?=a6?
zj;J&&XQMpfSen|Uf^yuTEBmlzKKC^*(WrDO<~~ibwn2@%L9lMoluqZ|bzG4R`~{4c
zgK<Za)WI`_Fw~kU_#JAMppvO5^Ju_vOBl-`+F$?Ti9aSEn-KuH$2~tw935a(f+n3w
zGeL;I+V-b0FqxyeYark~D>>|!8`0DUCFn?QtD(9Uo=!L>gv9lqk3Y$W9t{R!gYe8&
z-Y~%(1D1Sw_QaCsi#oCb2mm+$)D#Rlf(I7l;!oo95h1WH%n{M+Nv<=$hGf^;10nhy
zBnf5DAwA!^bj2UbKVnM8NA4Z{+)NO;*n*o~8!h-6#Hl84qE3DzHlT?9cxo4MhC4h^
zA<P0A=U9YvLgoPVf<*2t78*sT8(3tW%i4`9P@w?<&rlB}XhzhXw%blQm-|{2F8+-e
z?@X+q=ac7zurU9IpIZTlcT=#BV+9wL1hz+Q$95FA;BE@k4^hihpsO}ng@d~Oj4_$s
zA3)I4%DqJ8rv@evglF_zZoDpP_6zrqE*Avmo$pDEJ|pF6o$xI$i<Ms1B8dEKTAjaC
z=TFX!Tlc0x%gynaHOVk9vr)EEo0|$Sp~|!C7F0*Ewf6YoEz$vrH~)Y6lJi|O;3fCH
zBg_gk9_;pxT@t|y!46_0s*f`q1jMkj;LacD(cCb2E;x(OHt!BZ(Z%s93nyGpU_dE3
zbre`0uEMB1hmuDjpSMz>TVE3DR%}<;^I|!@a-<C0J4#8Qb{}^BohliOXWWF<m$jJL
zv?iDZ$|pJu3zHUfWl6qk51GNm=;(v>omHr$>x<5@&aj(@Bz^X%>A*A8jhV!Eif2_;
z*-LEzRX-V(U{BZre>Zg!v45AV$YwqNE~E1g9FzGa<s0Fm-R!fOtLstqxU}s;Zu@2J
z==R0ABcp9hY&BH6?K_}AvtR5V!j13D!;}_Tz_-~~sTb*VT@>k_&VjW`uy}J847G;J
z@L6?v``~p~Bo7p!7evP8eJKtGc#;Hr_S&OUd7ugyJp>Xw8Y=$)c_jtE6zW-xL7vT~
z-_<?>&Z2u%cGh^$qivJ%4DAfp_=KZK*CQN{))V9?2xGLmH(?mQl+2KRBlX5_;s=lF
z=RowPC9@<F8;`X3Yq-AhxuA&Zm8=FgJ(LI8i#6d5{yi3QmkF;AXV>h-twA$1-!bR0
zO8ApJ{W1Pte|nr1it^y;b8e-5C}}>~C^sBW*+hY1{pm@PIZkA;?7%qg(Cj%R>3x1b
z0|smaD_VQl>4MW}sZ7YJ@W;(W5P$X2TG}UkuP?{}cYE~M5Zn{x!`e>rH0xE8Smu*D
zs>%|NMQ;*${od=T<PeUyR<)eeQ*@_Qd)Hn~HUN3K7qoK?Ry(}785hk(g^F~1Fkv{e
z!fcx#zH=a72Ht=EE{y3#)ZZ7&{ZEdA#T`FD1knNwwYWyv^Oz_UimT(!Wy4Uai2!xf
z+uzgeHre)1gH18FQn!QY`a{o&B$?$K04xDunp)3S-P)#71FJ5=Eavc@SzS@KWm}r@
zPgq{ix98zDyJehIH0S*ve8<`<EBa#tU$WhW9eSVYs;0I;INWl$tnQSKtF_a_wSVJA
z!<S@D+VGoXk%@m59;OHmnhWPT6!CmhX*i%q@-P^!TsAXjuAO$CnjdUmv|L?jS;mb=
zgx@6@``PS61q9H688n<b7K$A{GmE!tgFMZis|V{hL3RORpZ){|eo_IV!^D@HS-_r!
z37<5-2Et!hUvKs8bS3+X#ox6H{#un#CTHnYJAm|v8ghyB)bTR18wNVUJE&v(Z7d9v
z5akDi3~^Ity%6PsC0AUazHrFM?N-dvMSJihW4zyq7fms2;=nWZGeRblC(UOjH+)t+
z?`;qj3=p=t-@_?{)afFmll#98T%pV|+^MVTtk)jh3T@UK@o<%$O|6OAG21P^ROg2}
zv{~jGGs?fvT)*9NG!)Ypuc6Aw&c@cyN<#)_1+5F^+~0_14f~^H*KQ&@O;&Qu2J1Pz
z^kF11Q#Si2As29rMie1n23MS~@m;R}Z(8D1YBP}A>rE9IwCn&SNd$N}8h8%Y3zk|L
zz6J&d`Lqs!ta<Jwf!lFFnBWInl2HptuaewEFJHAcQ!Rt^#h3J<rcgW`Hx;eydn?(S
z`m04Lh?e1;D8cZTa`s1^olRZ&!XJ&8GCG`4$JuG}Hx7~WB-$&z&|U64+V0<z+e6*Q
ze5rH}9}2$?_P==sPQ1VTbWLt8<hG%7TUXJ&S&+|`@O-`TR*<(b&$SWFO>;?)w5k(M
zb}OU=2@>vVjI$P4J`7^kKPWb;%_L)<bZya2T=P9!*Cjc!5__H{j~3Ur+ow*L#dQ+V
zI(&40T3gz4piRWb7mEW)TmU|HUEYn8@KBE4lRu5cbpm@fkn>=KbRX6soWj5g?DiTc
znEW|&08ba&h!rMwfDFnPrl@0?;>{<?+E*B?Xe`jE^w=<<7i47h&CXu3r-^6%O&IzO
z2V8CZ*ET2+RR9~?_}L@!Kkt&6T@K3Dbb_+b1&?s58~*0+;hL{@3$zzl*8#epJj>D^
znWO%2QIx0<6TNPqw=H89#o|zfZ+-G|r|m*9?ERYiXJRp)_b>6qkP&PhW_W;EJ$m3N
zQ#ORPo&Y0o_q~H%0S_JTjAb#CkaD!o+~JQ>gNkVp&;%zE_@(1omsLM^fpp((Vn2Al
zMPI*`Jjg)I+X0`kxo+FKTWLiJ)sa&{fSD2!#wL4-a`5XHWoWtteE7g5n#(-tZu2i%
z63t>O3JjuEyhZT^&dbR7N)j#WpV+F%1a&n!UFkH7;U!V}fm~udD+p_p;!dwzr7&%O
zx<;Ral%Teeu!gX~6I`OllAtXdruY9tOf*gX|A~n?RM7C2)iW845SsjQFE^?m%Ht5r
zu;o9vEpGMlZ#cwr1W@KTg~+a`UGDgvsvP(GAEg&e+~Qxi5+&Ea$(KMruPukC;Ox*1
zAbrJud+gyg9i^?Z*-sBAM6isPuUCFeP2Epo4VjcN@EP)BLhVsjYsA<9bZ1>h6f<<$
z=Mi@$ni#KSAQb+v*)|fe|8qS6!})o(9Xyfdbn6TlyX@aHw>@(>2-Y)klWGh4-eDF0
z)fetPob0*>oe5m!DA0SoZ1l3-KRDZan1P!+|FY2k>dKxlT^Mj~RLelTh`gsjIGZhN
zThP}zMOAU6jM_I8oHvd7-JckLBDpQc(|n=Rp2)<S?Ckb8vmbl@<KJ%qOuDS)HgXfv
zTZ0)`6xAfZ<>YW=4UfhYjYchsQuKR6dWU$4o19<nU@?0|a}ww$o1OBuh`<UYzr<MO
zgS8+~X5G`F&4=O#ao7KAQ(6hULP$0|u7mX){y#(rp?xCiE%Xf$wvb-KEA$VPG(rGt
z@Y@ftuC~OUO)J*353umVb?~P6Wn3R2!~m8;swPeN8<}U$gj|Z2zq_~`733Qg1-Hey
z>BU(Ld?Z|B|Cfc{@A6qM11Hv9ti(Dg-f&VH0vA2Q80m&eHc)3qrLVZ_&Dy>v#HR`;
z1m<%+MWpI^_7J~WLU3@a$BaNo1bFzq@!D!fKLYK&<HpuvwoOr{&#d8gXzFZ{;o}ib
zA^3MojYP;h*wScU(6hJO8u#*ikljC=DI@J=ZQDQb-8s-5460u-m}Kqi)z$9Os#mbS
zK`vnM7Qi<HaeuErxC%|>csWipezyufYd=`)rfu0)TRH(}lm7mk)_QVC%xhx#^=sOY
zn({qYEKcFyn8XH6GW3!UkwvxPOCpGyf?4L>wVjP~eq`E-kEQveoqeO$MUe)RJ0OW7
z9+@zV)%HyeZjCDOzsDoi+MQvBIbtXZl#(6*)gO%rBL-qx#{+@w1f+BEUjXnHE8a%-
z-~gWg*7<*&N^t`~D(OSDzw=tDXjItL@h$AA4UlBICgaM7bU;o8xu%4H^9Uf+;pKiE
zCz8MJu}%=reQzyc{~UK-IAygP_)Yi*>J6EBYWzkJ5ctG@uD1={<5<gbmXRFGQMt!9
zH~~TJPOC0=$Z9M^bs;gIp?Y(!nJT}J=4_Eh^Rjhx@7|HeX09K$y-jIiJ)OJcN1L3_
ztABvWg#F11pV!g7hiuWn@t6H6_J4EVuWmMcULDZR2@|P9JGN}fmIGQC?#_DqG^ML`
z2&laUH$U5UVD>E&_qC4i%Eh7_*h$`?iSb5uHIG3&6kFcL$onH(r>9nRDkGQ&d+G~C
zZV`t;%d0SUL^16n%c6IkS8XED2`G}FoLl(TWfXI`ks@NcKffMj)uyzWdW3934ZgST
z%oR3$?m=Ru`02K$hJC)=uyVKZw-v};O3~g4-^@dztHI%p$5N7MQKQrC0pA4D6&KnJ
zmxJg%AiSrYyyNB_Ck1N$bmbN4v!oM8>qoF)l$E5xdW#V^mWmAzvsOzI5#62I34f7_
zrqj^2rtk4e-zQK;&7dh5aIsDCR|A<JwuE2QnvuOVg04UMePQ38d0)_lZ285!l4-y2
z<x8Iy^B+1S*d2|zbS(?$Cp@KrkxvS_kXdxQF)MG|@Aq8r&o?h19@0M$sxYr(%Nh0^
zgf0~KUGL@bSf~65_wOmJQmw8<mHMt2*)!+%%e#;)#Y!)_HFHY??bBl6J~yG0_T^n0
zXxUIn);LG^-U~eZq|-z6Me90?(YwaN^Zr5i$svdZMT`|0FujG<os++@cX22^{kF?w
zYTobegfo@l&%)ZP3gEE)*nV$5u19I5-{Sars7oTV%jLzj5cd~pNtZluaw*}G(|oak
z2G#!}XDRoDu`NpTc<lxv$J#*{i$5fXr^OUYtwGNI-wesIj?Y_6K}3SZVpNx0<^C)+
ziKJEK*rn9Q{Y6c?vY7v}0jQ}xr>BUg^1XNY6?E<2c&P#6s(+!SbTSun*3QJ8mvbd&
zuH||2>t-fQ6BYI$dy78e(*>xEHW=pE)}U$)bxmrq+`LR$dS5!eWTwCOzktRtM8Wgu
zeeqI-{L8Jq6-ELRm;Tq2FY}J?qH<?OdT_Op3RdxZd|KNM{+do3E9zxjN(S10<~iyt
zLG3X#AG|B1KKy`-W%r29pzvfq1FX6y5eVd@9)OrC{`@*8__e&|w0J3&6J0zlvixUJ
zAJAeeb-fvH+Q5vR1#fc{-8u}xbhG70Z*!N$7;iTuZf~u@AwOFn1ez1^Jddf}KSS3~
z<5ja;zhtg5>~z^90^uq#TPDws5ba;*q!oXx=N|9IP$JjNP8*4t3DgF=&EH=rt*xf^
zJ@C#zUr{{o-+6bU7=`vg+OuH{`a>6jIzO<!ldAso*2A3e6Vh8YRdj^&=(O`bT>*NV
z0tMXc`)j|Yi(TW%vo)6EGS*lZXI$;(9sUGA;If-Jxs`;g-AJ-PVXmVGdGV1#fR1dk
zTY$My@3TcYMqVDX+I<Phz&JlHKRmH`R49&hlfCr%U>T+;V)Gid(SC}k?d^-i?V>gK
z7ddrtATs11Hjk8+#HLZl)H1WOO8FQc+<0@u{6n-OGS~<J^de6z%>s!`)8DKEmKN=x
zzlxQ7^#mZNh2WSdYYA7>@azOs$^V@g4Ub-k3jBk3|LI|f*-?ovO&gM<2W(d;kERd`
zlW*&+*+hDZG!ixVTHy9M?`FMFwii>^w(n*fdE>brNYvMmCVO{Rv$fBIG{e%p;rZxt
ztkZLMYw6n=t9G#|y2&@X#tSiU!)?9$Ml|c|8rp*}XjKPhpy}NB>snX27n$@II6s%Q
zjott>!YvvcIDOvOeNM4EX`Ec5n0qi`zhih<^#14Rh*&hKznA&p2l;e00_c;jONy(K
zkKZEHJ~8rU%QPhYM!8)5y&CBdxu?8PBraN~oYQs1HmpF%QFn^zKydfU`h%rVh7TKR
zhDC}>dYYA`LKek3(nol!F`Myu<9$KB6rv9hY4@}b60Z`>O;%4{AYjn7m2^!BNj*HU
zd(1%XiEv3?mX!{*7bA@MQa^%{rv<?ykE>FZb?Pn79X2EJS99F7|0`|yrqubpU~XwO
zx)z+U`w4wN%(Fc?HqRo6*D2kDIk@-eNqId6wQd)jC~C_xk(;3F+`3McIsp-D$9LLF
z!;M9w+D60tj~1XZ#so3y8tW}IFrUyFZ^uo1B4yk6)`=5!EKHTbjXyi4;qU0Y^)JI)
zm?aT(OK{BLTB+DEe*Sg6`4*B<=$5L}cx#rz25OsV>}bn7PW}DmH&(?GMWJvZ&rXJm
zb)AC*qPR{7PX4d8lD^z}g}coeIFm0#QCKtxUpAxl6e|n!{A2Y9k_z)Yr#}yEK&Of2
znW)8`Y>sQFr{F@QXtXDqy-7hc=bChVM1MoIG2uIr)^xTI%DFrN3fnX|Z5a6-J_}sE
ze7xv-g%5a|;f}q&gOauFySql=n4FhSHj1tAsR>jTE2f%;i_atdyuq2{+1ZId6Oh#g
zSK`gM{AQKXj%wXv)0y*Z_%tYY+!f3C9y>^G`U0gb80c$>nE8MC4%j0-{re#WoBKTI
zK2n#w&ADmr1u>vC<gcAA+z194VtM6<BR6t>+C)lIvY4fCV)VjOlISR4Q$c#~DI5wI
znk|VO<#(W+9*IGTpl)PhG=RAr#D05tgYV@mbfeaC@?atS>1<LpwHDi=fLynvtzQr3
zAo~lKC~(6LRrt2>@EED|M(fypXH4x(Gm<#N;$p)R0zE@JrIq7FSVp{i=drtLc$|J`
zS*r|Z2z^dCMZ1ir@T<KjLn6<u|EwC<^N6($*Hfw;;`gOi5e6nX1fV{ek^2Ziy}*N=
zcQkjRQ8Us9DxmSSeNB9RpzhxI?3jY1LLAzYF*<%j5EQJ6BVWm0O0aJFhhcdXwG{ut
zso>mXv0e@?xlCN={%79dH7XKjvUDZ0nnj0tlnBoG>P}mr$AKoL={?Mwr*NSxWOLn4
zshZi7`8-@+S3kUx2EIL@J6~LHFkDUE`H_0vviWYm1wu|TSKpHe;{$c?5OSuRfIrLD
zc3^#8F?0fM^7>f!>RQ{}9G{1D?>0%Oj`(1ThbrXj9S0h<`LlM!_2KJtl!j*sgyFAQ
z4;u{W(!%cEd>>#QaD;viVugK2v^zLTM=!X9ep(jTT9PC#gmpMJ<zFrV+EWjM{#gu$
zqkHMd!{!Q(!nsck8AdWu7wH!oj0=TP7)EmyCW~%wg^T|D=ECuzI`<WV3$2U&?QEX3
zD88{iE&lp0xx-b8y8Yn1dDrqg4C8A;iwjG=I>S7%oLa>d*%ReDYJa7QHsDW-E3q&S
z&SW=yjCa7{(Zxa2krH?_GH~P8b-yGO@VNAjAt!%^Im&y#Q9QPSW)uUcT-S|oLA&e^
zkgGjA$31#MM)c%`SkVTzeV~NZ<oV(t6ft=4@Zu>^%saR4?=8-??Oj$KPDt4|GAa7D
zYb)A=a*EIu=e%_LPMbMG_a~jt%p&bUd0!C~SxzcdAwz(H?en^0%U_HP4HItnGG>qX
zH#4?Bypbrwo${OX1nmzfK|eIKynJ;+>-^|dK7@}3!wU5PV}xp`XQj;T_q9<=8!my1
zl`-JMrUMm)eFdbBmWC9}>?nxc4@7(p_y4O6q2+@vQ+iHN$Mq?;?mS{`{AKMIdGIpK
zA*sw=`U!U2a<r)sM=QkE+780mHlVs7TnJOO5p!N?W@=tLuMTeijMNexJ9b6-lB*uu
zBRjM<>DpB1=-{0Feyg>u4axoa8t9$T4D=<aw9RgKe3{K;8DqJCnab=fXhg20C^{N3
zfa2Yx!c{TY(GIB#ck9kuvLoUiY_3fwAijIe&H<l&MO(AWu;cEbEG@6=cjeOMg!lrK
zbs>R%-!3}mqk1ClydVq+*C5@%M`KbiAp9gc+-&|6asV}kC$tbzE61nD!)5#rq%h?{
zbiq`?P%r(hoe2&d$r$bb4vngq(nFjoE7(TC;vQSQIQOlGB_RBq*%JcxvY$DAvK?z<
z6IffYECJ`%Y%W5~y)IoFOW6db$JVXOXE8kx)IK;y@-p0diF}6Sr~h&6PK91+-Zh81
zDnsepl~Ex73C5hRC)26A-!zY5PWd@a>fw>?baUo)fGEkrnZI+UNNM{X>7qlbLwBO;
z;KffnN4!B>F=7M8M+<fWJD_6tYHkF+X&E5QurmxF7z+`k(;*QOVjWui&}mz-42fI1
z!$&K4h6RR(x|>=t`c*4V`3ox}l5(L}6N9xI3qphQ2StoKAOUVidfHMQKxxGPieXhz
zg)h7{u2<bJ%Iw%klP?9<{nHo$;V)+p)oy+^Eu(aF=haMx5JMOusG}iTH(TC<M()sN
z3h|2_+H$U<9uYv>@g41~+#t^n?V+%5QByKNHP8JwKh*tm;S)PvdCDF0vTjM6q^$SI
zcR^pmGOleQ?x9;3&JX9h=0zzEMNOpU<|$|toZ{vbCm7s6T7-s`Xa3|A5wjn5?Y4dQ
zV7}v4lcg7!9eQ|mZy>QvRvq2j?8DSLgz{?-+IS@#Ha?PwM%6-P$Dn8B^nS;7vI^z4
z!7(j_HAHH5whWGh<qwZ{3Z2pqk{fUVSH?dDur;cB;ejc4KIn7=!o4tqvr&--Bb(w)
z?EX6n5e1sf3!lNV+cX^h#Ak!C$}%$C2}Ts}-M%RarUqe$>c35Oe*m|8JzTHfTRe}P
zQ<m;}-;FG*${tR#Pu6@Q*0R2N;4fE_lgCVID2o(-5iiklX))Gs-aL+{?Wfj~_!N)F
z_D5EobIU5Em<j$Hfyf6lvNe+kllwADAD_BvwWF7}EJsu>K@9^9gGt_sr&m9L7@L_V
zK|$b&r~k~6p4aW1yFqyO0xt0w{a-Q1qBd!+U3+#N%kkU2k^|C56}xI+yJhj~?n=+w
zLASKH%!nXwtgmYZati4x_piyJ-G_0q=?EZID{kLm&?nG#qDHLOp%7O<(&0Kc<DXLP
zxs$1{#13tPg$k3+X#Sto04#;G``)DgbL=7RI>?h`;?N~>aQpL?EgnORL}{_hJED(B
z8Bt#$)ELZ-LYqCAQ@wQ!7~tJ7HbVQjscyP?SHAA4fiqThL}>lfJtnGEzE-WSa?_13
z8*_t1>8JKBEq6;TR8I;2xk(z%0sG^_w!Zs_QC+Z|b0tyP7_tOm-Qz>MJ+M@@Du*E-
zDYapGyyanE@Y;w2$U_YjJN=<n7g@M540;g4yk{#ve10=|9WNxwIf%}muiPP?knE2E
zWNoXxQkSS$Nc2jGp#o>l<QuDnW!Nn|r@mnjKarO&hFO<g1S0`)Bm1-EBm9K;0u%IC
zG&&itW4Z=FYKBs|a~zKAXlV<MgG(oHkWqJrzxVH<oY0*LJ}NfUx}Ki}A^fTZ+HGkm
zwgghuC*$f@L`hE$pL^UnB_n&$p^IS5+Z2(LH$9a$N_}AtyyRYW^3(uo{>EEq2T9+@
zeX=eW716U2WKZ3`Ib;Z)MDlyQ^8wIRKi?41041rOJUx;vxj~4&h&VVt#g~(h8#k(M
zf9QFWqCMumYRs(}jcCr}dF{6UsVvO_j)i@1>K2{`w36h~Vdae60H`jyhB^ylL~Rk1
zqpswYfO}fIm<x3B$YH9>Ij4)+t9G>1{H_ttcxDyWKb1Q_*4>_{w$vxX8~*nXo>=H@
zpdGDJt28D~PN<x3=?@A5TVv{mb_E|8v2Nf$!dEzEt3S4N*grQ;EF*Dz!_!KQp5j&`
z8_SOtr*y8&sVR+yZFK$gb0+?gp9k}xT+x^q9T?GKf?ib2)A#h)7^$qX9NGJcv_vOy
zAJ6S(c*e;W;eWOFmJd-z-TE-yAt0c%h@g~ohX^Pjq0-&W(9Mv7lz@N^T}nvz&@h64
zNJ_&HgGkqqL-XE)=Q+P~{(<+?;RAVd?^=7UYh7!ty=kQyd@?m@y~eVlde>&!lk*uR
zVhw`ouoqNlJRhxVNd9gaCQ-hF<C{(Euu{g}PW@y91G#2BS&qM;Z{hc=PNvcO{aT$W
z*E@gNz;@=xQ}R_K>3Lcg?=1$KU(oqxv9j_|CFJ=2iW-mexuYP1=pIf^Z3u}MT+s9C
zfb;owG*iDQ$;jj-2$N5KSunOCFN^Vbj=I>iuf0tUWB8JC4_b+k_LMy18U7(MhdV97
zkZ7_oCU*X9UHx0~vH68ww%Uc@2P>&Cj8$(oF-Ln->HtyG1@gvVN1@JD2OPPO#d*A)
z>n|qX4S`Ets>S@B)5V`i8lY0uUT+;!vs-fMfLu`i(@-^mG_6Liw=MLc1u#NQh^fVb
z3#Wk%CUA2xwrv{X5W)%NxwL$}$qc1erH>dZ<ZcK_$S^zZChB#W6n?u5>@S7qo|^4M
zU%Z#IQt!nKJ_JKZi!F!A0`6JknvmUG?@{>{aBUG?c_#O<6>G&Pu;wX`Dx{k^$eM5o
z#s@F@?2D8o3@-Y7cA}>v4j>qlupbmiay|-+EB?N#Wk0nvN9_^a`4aS$EUq??dp300
zym>WJI;>g$%r3Yii?V}1<%msxA>~JWADe^u&lR#8FE56*5v%$*3;juR<~iUrk-~*#
z#o~@CrFYT<a}MVR*|wd7{h=-xi&>P}?X=Ta;4-_JdRSyg@<97bY+X!LdUW4zi3LeZ
zC_iEhMnrYwo#xe$K{O{B(tts%W*AY4QHfuXYJ*k(!r1a_g{A@<r3L)U0~O55Wcpq@
zfAMYe@gEx*^e1-;SIGCi`yFw(o*Tl#n<Gw$ONOZJvpVrP&lu_VcRSL|1ZG3+c*0oB
zwsx`2$t?}mvfD+rA26^lca4PiDiyjvw!mDgOz)M>I7#H1+We{*)b5w+)9S$FO>%wp
zlVf!M>Zpz7PjVRr4)?lxm7~y0+fMT;j?e<LhA+=c-xr5gY&DC;%k!piEl%3fML?gI
zgRx5a5{;IW`4UCEo*)$w>YCFl*rvP`?&q2d{FrOPus>g{(R_VQDJz(VVGrza9cMFx
z3)2|vx=V|dgXPS-*>XYR3bkJv*>-dqzg_hH;L&PsE~HfDuEz4=*(Jqi9P_F`a-TK9
zJNpiw-@3z1SWyRpg7BFdn0J*Ez7sw}!@A?zXRr8xQ*Y?ImAk<^Oy_h(Rr6dIdhZ-v
z-!jIvdr}nt{*fh`wD@L2xye`jqmTYR`SC!<Z!i>8eN_>h|B!mOY(MBumE&B_?|f^*
z-qrS$6aJ+L!zZZCudA+?m%f()Nz+#hI_wL~g?}Mgbj9S$uWGot`&kLju%q}?v$}F=
zinU6d?iey;s&kZyQ-!gJu|_$2f3B*F-@5?vfbZb&T&M~2^Zy?2SeKBHpmXEl9U=Yj
zDXnn;izW?9pjpX*>zV3JEO-^!hvgqi!l!T1MtYPQJ!La1S(@#bFE{msm9j(+zctRc
ztYn<jjz=_o_vg?%*>L^4fs$O?i${CsLL5~fS4spMffRYL6OPlx=iGX+%=-B+BVH<Y
z^zS$yQ`l#kfy4I=D>;5Dbl8IGvj;srPGms@0r#k{61aE~g27;YyESsGX^~ZaNY+_L
z6U2JIHZFi(qQc-2V+NPH-m~WM!!wFy8#1%KcoaToQ$f*>LUw3&m0-nY)9Q26xeed!
z$hEeE(2v&ok<xM0?~5%tU5y*^K<sQ%M81j&RwA(=7#AyR`3fiy(w7s+v289iF#LWE
zIaDb_cfwb4aLJQn{(UYRk|RoBc9Gg^$GGJD{nZ7>Or7jppOUHYNVj;uzdWP7FgF$@
zJc#j12Y(C+$)+q_Gw8?7UiP~;e8vWf&9_Xfd#6`-{w;subqindj%OGPOU`hl%vt%~
z#b5WP8tv}*Wrj%?lRvL8E2E+YY*h3W74kWE5eAgKnSjNmv$?PW2icsDnBF)(USk{{
z`{+t*cHBC2M@C0xZmgwuTAJx<L<q*(v94`S{#8aU^UwUd@2~StSulE}rok+|kR=lN
zWpVEhHZxM0OJ{-lCK4YldwsL7W<sK+PR(z6$mE1U_qh9k!%^NxwgC3p|ExWDUE8<0
za)iC}P^xBzd&bFowpxeYlXi%Mm6erJ(Vt0KL7@a9aZLKxr#-wQSa({!7(V&?^fEVS
z>Pn*;gbIR?4A^h@37Raozcg7`tLqMwsslBe_hv@txQN5xQv-3}qP*6fPMAaH{L^sh
zPxqsj^R3(W-dR`siAnD4U42+f-Ur7N*?EFu>l~BaL8BFFqwf{yQ{LQVH*(ZoapX;L
zRC0vAB{Fv_U}@$<y(~Dn3v`Ut{55(hCp?TsE89Np!`q3@)^(q&+g>QO_S}re!VQ^`
ztMv3?s6u1^B(jI3B}CcL#$WGe&x`i)dyM79<r$o5k$W#%lr8O;lNWf0l20BbAYZ<{
z^U-}fU3Lz68S>ldx+(^hZz<T&RUj#6Sm%{mG7^+W4VrR-I~%}a2~kCk;%}t*4c+P+
ze%8vTRYkI}vSK;>20qu<T;M5XT^CkGz5#6cvatDFWl&r3%39_Tonger1?Co>A^lqo
z>QhY9(*)AFBbW}SlsOY&Q+5On<L^Cssn684G^E|<l5|w6wuds3FKV3_hN_<~H&}B;
zzD<S*%hzI0Y#2QC&Gyl2oEym1S5Q!}D!hw~iBcM*d|BD0-zotpY3r@mjZ{GsoAIXC
z659`iUI4@DYPur049Qu%5kNUj_n8K5y}91*>AjaV5Fr3D@IBO_$TyVjGm#Fvr*S8x
zCXZ{TadWwqxhjCWm-vExMsOoJ*5xEH{P`Z-rk1<3n5ur|(2t#iqt8mfN+3<XEueO0
z+x&rdUS(BORFu;AV+1ut;{EEkSpYWSHAFFdvnXBnb?xeb=w_Y>@%`n5=9V5ybHBp~
z+K16F`FaoMS<9YJ(D1gb%4E+`?ko~xB1jqH76tE|ye_fn1`Cw<F~*Vahhe<$@o<{U
zK?8$6q9!}`U?jCd>w#!Wf8sv~U1FTUe}Bf4=Pq5r_+L;rWwe6kI~xiLio~?HXh{*I
zRE>Wx9e$r4#dyLPrHkuw2j_!^jiLY0u9b%~)v9-$2txYaZu`L1@V1P_{OY{r<tpv&
za?kNo#b#@H03rpxJM~B)3V1vb?S}jG*=*<#dms#xFKK^TD$~6G8?eQ?3iA)Er-gwU
zr6rQ5q_)1!c1g4+wle~o)wZk&%-<KkMW~nzAClp=N5o9OU2@@j=Sa}9SH9Jpmmmi$
zVm^bkCEIN;e~2RHHxz@z%HKkF7KYQm($sB(?eQt&6?qq@pA}0^H1{=xVFaBaXm*3o
zf4Vln`Y$f$gPjm-!`rKS3myU<&6GU!rsb_eO^wlH+gZcFj@wxIx_JI2DLcQ*H<<&6
zVR-fa@Tzi?$dx@U96BwW{{4{rMlc2S?j0O!IlC*#nN}1pA|L3ayAxbyJP0`EYz`_&
z7`bH)hZ+bfjc1Xx66@hfVS(wV^;g>WB9jt`oUol;kYZcb*eU6bhNjEy$KV771y&7a
z`PitRAAX1<<{{C}A);BfBD;2H;w?#W<ic;&W1VHezKHKUmj}hh+Mw%NQc1sF+o{7+
zT9k00-7%7q@h`px_u-+hkY3Ow$Cq@v8WGJNNwEiTDE7<uEt+bp2Tn{w0y7A5lg`&A
z2cpS+3_4eaMrZUdaLcXr*(mofMdfYc(C4r&kZj}1ICaiwmP}9Kwc{C)gYAE9B{<yc
za(h;LL2!&E3s60$W^osjhtiZ3(YUxk`RH3oS&ffb1Oayip@9O;-}S^H)^3~C<$+SN
z8RTMoGp8?ic65%aj+U-XK`U$8?^|#sQ5px5rsv`fGOca)@{ZxHD<7Hls89HQ5rz4p
z5Z&PwZ&uDQpOV|&@9UQR%TqK$+#q&2xOT`x?l<A1%j(RJv<40@l>lym=R{n<K+g&^
zI3xxxBA%f>O&L1g>um^G-fE0jQO6O%ya?rRoNHLvON>(DzTIT$xXG62O$N6VyR5vP
zxVUG;S7g0*h&?T`DO|8<yWp~0_eSmx647ONcBUy9a3DZ{2o79xgOVs-$bSHrM6%4&
zpYW*=Nt|~wJ)f`PDMMsMV@%5=Sr6wkZ(RS5oBXA+03h1-7D}%@>;ssvVn3M5f){J3
zv?{p4kGaH>#8K_hHp_^uNr6BAF*XNgX@A*M4%|6>BmCBPU2ur**MD7Ik5^PsaG+T`
zA;EyZ_%p$L#8@dC=VR>oqJM}ML$XJz=4@4q?_BO#@Jo+#eLOkXJ95zSg6Y(hj*Hat
z{@Nn=1Neu0`{m_lV5IphGxtyKY*ONUjCI9zsm|MHfcGv-7aP|*!F!+}aK~APNc=KF
ztbB`>S3uqcZx=^E6XJsRA|#e`+w}C4>kY|pu<&a;qTsLMLqTJEP%|diO2R~D>}>oO
zp+35P@g%Nyktyt{<;Q}5{5xK<vR3DY=mK3|)##B#%r^&bN(XuJWKQ*VfHwnqq}SR%
z4BI7hq@*vVIh^vpV?pSWyDYa$bj^oFn$GplYd~@`d5FN=m*46gTq#faJGuw(>r<j4
z?1hqxNDU4kR{E29gp=S!7v;uMV1^%ZXpGgEy|V}LWd$8BSkBUv@el=;x*5Mo4G<r(
zH%UmhwnvzIWY-rmKCiS-L4pu9oWp`+80mQE&1Ugn!DkV$)-jE`NasaSrjt7*7Wy<k
zSN%C3T@7^=MOJaQ?>h!Xc$hYSUsA>(mu<}o5Eb%%zKx%=2p?G%ewVWONC_1#{Xsq~
z+h(|S4D99vlHApnU1!0QW+cjU&ZBkV>djPT=W-s4$<@!tf`=EZqz}4a#uvMOcrKg8
z5lX8nyvv7VsVa-%{~I$axsAy_P>RI=tD+frp@R^I32N8oh$a^VGTIG2l*SkS6Trqw
zNsLBh`8ICkz74zg2?GeUn|70RYn*=1L9(8%b)C@ESFWoHA!*n`BAI4-&PgTdd{mc1
z*S;_#DXVozgA^{XrdVma+^4IZ0&wCX){G^Sqz|Jigo+K&-fYoAE9Ik=Yh(bhm$-tk
z7>EZ%C!m3_ro!^h!__t>+6;t`X0+E-hQp$c)cd!?C?y3p8c$mQR0zj<z%q_`ymw=R
zU@g0i)U9iSw)NX!0F{G;ramc8sJLa}&4=M2e}0AQ-zY418HW@>Nd%=RuC5D*_lEZ$
z$96H{VYFwE1rT^S>fCJD(DkoaPUu*aJU64mk+Y-jsn}A7`-l=?xi@9{AF61b+8k85
zC%7JExOz!oB894^j=o7_%vrKCy-FvV^Do0@dR*&V>*un{@hR?<DLU%Mb3x|FI~0i`
z)IS>W_bR{=GzlCx!{n{?1#5s+uGfx@6VnD3w>hhYd2u1+-DlJY@kJvd{2`nS2Xnjs
z?~F{k^muLKYm}|qsSqFJtkUa;z~QlZfB8cQqqkG3FW0na+VaM{CB_kNYA<JJsRY^E
ztZK6R#5EK-MwOphnLiH7m&9yWkDTZJj^Q%x*Zz(t=Q@2xyl37Z1;nVPcy7KXq9Lw$
zQs3V?>ULJ1lW_ac*S`z|i)U1wL;_uai;0{tX6yw3u1jYSbiUY%R%7}9)L3^@n9oZQ
zCaSf}0DnirPW@-PqvmX5=?)V{3%2l8b0>NRc#oTt6TH)#+o@k-+p!<3zZxcSdNYmR
z^|d#9dgjQLb}SMVMukTZa+S;kf9c^w-&X}<lkbVuDOh6+pltP!dy0J>`g(}jv$x}h
zmml;SgHI@}=;_YKDp<W^jzhbdLx?`-2sfES(ffMM4&Hi~Pg?0(gQ&oo8K>?OQq~80
z<gK+o4nEljy6%u9IHo~Jk7bxVWL?eEydr>G2xdiv-qyAQ`Xcemt-hdH3-P(II$|yl
zoZsmEs1Ci(S+58mR4No+qs#hva1(U?+)-VpND`=j+Qm-h)*pX0d>LOADabQS-str$
zwtv-X{flBps$!UyCwo9fF~-jq+>Mo!N<Efr%S*E~To*~!R143=3?1}~X$V)aX1?Lp
z3kn;%W(=<ZOd>U0G%Eb>3xop#$4vhB!K;A_HN}2zGs3FC^z1rZ+q4iAgtO<h-GXU}
z=^iO;1!fPE*X%iPqhjgM>lQE3-lTIpLrWUOAApoUKj;;!A8x`_yv-hs;hRR^)nScZ
zVXvOUX(V)=d-oJBep<8rZa6LSHDSFM_j%}#-k>!#HQART-Ho&iCqxFPu2&1#<>bt^
z4)77N2AR6gl{csNC8&Or`@X1^X^1C7{64QfSC``aTa-*rHzvoX+Gg)F+hIcdz<IwP
zx&tM2a$IV5o*^6~T5>KxuYvy^;6kDKqd`WY&`r^hJ#|8jMPesR8J)Uq1K=JjWt+vX
zp`{@KgE&q;+Whb5VfT>sW)Xz`Ed$MPHQXIWAdfMkkf&2OWC~kXi$Y}T%ee650ovyC
z%ohWobx`7IQ?nnw>|H(_MHji~<4Umc(QDV=H=h>PP#!WJR}aXC`;!O#{<carJu#)d
z>Cm;f8V7l3GZeX&ISl!&5^`lsKBO{Zqpfn}ekJom=Bs=;C$)2K=31@o)V-{$-#H3S
zQ@-(%RIz@R4*egP$0|QBPAt-3n)7CNw?uBJX`xC@z8R2)u^cfqn!7R-Ik|56F=el5
zJ1w$MVy0l3;_M3H8p$A6o;=`Clylf;J_!hQL{#ZZpfGbVWOS`hH?h|;4qb%$c`<?<
zoO^h2WN_z<#(hxt5l&;Bd5J2<4~1{7MCnR_Cd3*yd+qa8z7YUAOLWz8bz0Si$nVh&
zSG!2X(ptb;P|x0zUv^37Wd#>Dj}cxYr2&$u_aTX-NBiJ?@576`*nepm)MRGnlRSjS
zLY-jozn!MLQu*OEdJ{RF6|W<W7<PwVK&%s03REh%w05!b-#$5>k0S))g2pK<1O_L>
zC)1NxYFF5v2Z&6Aif-KI&_n^M6nz-$7>)U6qvo?n`vyLdt|fzKPd{R^zbb18WfI(<
z{XsJPX7JuG<A>U}!+7<i6j-qj`Vj4XYxqf??k_LBxeS}ZXQIlYt?&@PwkMN}#wEt4
zb#dyesSI%%$NSg;;B3pFS3}fn5{B;CHvK)GVf9$D1k*C<lB_e2_e+xs{*w!E-I8lm
zIX}aerV26Iy|~VE6-`s+ock=cA96K@lM=e2X1GZn)Uz!)=Gx$Txg@Z}Tj=237`?<x
zU6II%RshunXa!(Jqar3!3LLae#Q(Pq`RP$!RtwXOckf}NH~4vuB&u<{>O4Jw65ib~
zy9^bW!Ye20squTyPHxgWE<)12H@s<<V$ZI97?|U9Vs?Du+2#kpCxtIBe0Ts0Rjbum
ztuNh?;i*IwS#Btpqea5bli{$|PFQwN*kSMjvw_r$-$J<3$8}^ZopVViDgf8z`@%j$
z^4SbLEbnfwn^M7Bv7yA^JsdgLZ|*+L3jp3_Wqp(Xuh$-+*onjDb%KX>q`8%X*~zr?
zN42!kW6AL4CaH$_frl?Wg0kKXT^BMmOklClCtv@Xn3hO-wAk#OpQugX-LJiiC-+Pw
z;}HRtS_wPw+Uop-LZIt5;=NEk;mX)JdCL#BhGP(30z{5WV7hVFiovlW+{5tw2F#+h
zQ$goVjqTiW{14WJq}f@d<yzM0mFhA(Gs9)u4DUe@4Ddtsr5mu<qLf$Qrg@YNZ<*)+
zxHcHMm?Xa4T@bo^atD~BXVmE7Jb&{Op5-uT+aVk1N$(@w-u7tC0djNR-4EbL8~R9T
zZ+&S}X`7GhEV<Gp3YO!3U)jHk2kYRbeCG6yU2$)c2XU9om;i5Mi$VL<Q3M!J>uL*U
z4rw(qKhZsgm081V=S^{grSG=hzp4JPc?s6{IXb~!q2_v+o+>nnY;;IYDDVQcJ3xR1
zO2$V#r3ZSwbs=+h`Mrons5l*Pkbk7@S^%&A`|;fa7uvRs)uUX7Vc*NE4%zrA_CWRE
z>uJCiyso9~rKd;gUqJutE`~AI6}G(;w7xna@g*+T1t`DID)q)6?cpMQR!LR@`d%UB
z$`imF^Rw!v=Cgnn#s_Q6{DL_=B<Sc5&gEdovi|8i^2?;s&Z$8Mr97VS{gS9T$t8X#
zFQKE<lXa%Ka*dDoX0^OV=y4FZd})zx<UMUHNAW#PB4-G5&S7%07O0iL3{9wwTa}@s
z-HsoV+#NGGlwF$&aIU9gZ?e!$3T0Y<ueny|b_@$#o_Wu3$UzRWyn27C-KujC2hU!K
zX<(o#bw$oxG7MF5&;=Pef@ODq@SQ#CO>Q7tuvrbvS=#>2Cz^ulyZCq*c<`vidaPpb
zatJ4D_d7Wb7WXB_B?e`D#C!<BG&xq4(<KWGH7Fi}f&6p$O0PEBC_DU6g}@*cT=u$~
z&MV^ATxWnZ5B0&B)EStmzvk|)iez=@tI#aiIUP#+zAtSRi7(D6R9t<0;D~OK{82`?
z3*f#YP8AfMe?{*C1(li*YY&Mko@q%P)1NJFy#%IBJlBCful($L2`;=7eoHr0YgZ2*
zAz#C0L)Fj2*tInAF^8ZW)if2MzuW#Ehy;}RY41pEoH>bqeA2|bq{qFkVrEE#iMYTF
za^*`M#K&w8Mmow84D@rJpCeAr%+5m^xn|lMdZ?N%Dav&jdd2S^;8C}W9;ea`K>{l4
zDk#EOV24s8`3|Ed{-MlRYgmhA{Fj&5h<^6zHu_UOS5j9xq}}IUF|uip$)LcPV_j$^
zrnuSW;J`e9u=9=U_KeHW>+{3R6rYABphpGY<?{!%zo&~gd;3Y$89RR*8>9wJgAkrC
zYWCOVx6UxPde;u1@$B{e1mJDPVTQ|QOF4P6w0?Xi>5){21NYeiQO_sKO`{#6#2_;F
zCWiLlzsI^%?K)I*FBJ2H<yjN$T1<WjIA+;}{R#*H+*O}yLLXVo%X0k_enbll1bf4N
zul%ne>}5#KpxNcbw>3KAoOTnjcfV`^SsF2p1G=hJm;ZDyY*%aW;!F;9bGD?pJ-2x3
zjqxT4h3%~0kw~zrZw+GV+n2&tla5>~yr(h*+7zdIl8jPr+VKmJ;vbA82mFCe>kO3w
zK-uMw*^h1<<=to$yp4n^vr)295*kf)dl}!JB7W;Ma`(qrH5%FtzP?wfM6ZO2!kog~
z<D0i}*q32(;q)d3Q%#~h-aq#oLp4L>a)(=0t}wUo)v<I^^i9><rlvs)kq&bj3T!&F
zhh#c{_|Q4OaY>Jm-bg<=+s8IMJ=1JS7b$$~x1J`gm*%U5q?xOqTB1FB^x;i_uW8@)
zZh=&a$)GE*zucndoJjd*ro?Z9CvV7X>AxRJ9nXLEPUhE!2HS_t7~CM+?>CMy6iwTh
z;WU2hyw=5Dbt84gImwvnQ-lv-?+RmXS;7uskCD5ay?T4XC+Vmw;av_^O0FG0e1QF8
zRjaPz=>D^?`FvrmfeBG68wB03j7h5A_f^%?{@9N%)haqH>Ww<AnOOX2X_F-Fv@IRa
z6QscnceiQ<4{pdY9OchLNh?beht~+hFs8I4CF~`SaZ&)E^#Jf$<M^_+VmjygL)8yC
zk9O6t$ul<R>z{SvROIkcH5u!yh;23XbjmtQ!#D-w7l<wZ6*#or){j;n_wTQ(^G}Oj
zg<E`G7MD5POIQ|l`&0PXpemPZ`@ujIGmezF{>}8EcbHnS^#{NGD=*Y#NW4P8JgW~o
zBLwBsQxc){)h{~|1a}x@IUs`LWUVmO&R{WUF5PSTGKn7$LU_n2#p_y7+#bk<WI&|-
zLJVWykb&E953!EZP-wrkd;ivN?OUUvuunT_4xk1)1xcOyY_*X&`k-<TAH0FzVS@_o
zgCuaNIzmpmZIbHWip2X`ZC;88*bZ~LpPjyMskF;s6WWm|%Y;Wr$Br3m@5QK=8tu`L
zD^2=s$EqP)ihne3snze5NDRN}(+IH)JuCduNG>*27w@~!8XNT^8_NWsDbo_0vXtXD
z_oP^fT8^&=rI6d%A74;si)K^oJ<n}rMq&x(+yT{jJdkfXX{^sg9*B8gV*mCtR@Nc+
ztnaQL2P#A4lVQ<6AGD{Ll@|@12T=`8S~4P^rFmrxUi<=DR>qJb-4?zAlVhM#3I8S)
z{?b!mJMm0;2*`$@NYTUZZ#+y1{c`;LQf~r!Jsu=*GI*@1EkaqzvgtBr{%ZP3e%C1q
zjL8i{n5{S(Ju=RiIBdDMy#-6_{@jx4syorbYAtPU@c2{Bq*mkPLrFE__noFS=F;ai
zGe;-Vg87HBQ9_??hgtl}RO0(VlktZSE2jfK%(jsFd0a%}ipRad?gnZ3@A3QzIsWf(
z<Uo0dq214*(ex$iv)nn&{@)@aSr$9bM2(ek(^F4KDz+>J4{{CjKODo(9zlv!x56(r
zrLM1F_pK+X4Fo?qERGOC>}RST{?CRDU1qH>cHg{zAz)7a=q_z$wGcp!t5#<9)|8Mt
z_DbO0JNRR`V=!bj#If;XO-Fo3f&qY8-EABC^DYgkYkn9d3)JF2vG9tlFhsFlg;Etd
z1w{LG6vr&D4g?hUiaGO@GpTd&LlQDvkGttA@{-<8=?&?#Biaf=*JvpS)xf(302E>y
zT?krz!_6tUZ_ttfe=)^4&i6fauhGd3FI^&=?~%nFqyelm`>rEi^M)$abVNo|?he9_
zDf-92Y<yH*9tz7aB!L<@vFX+i%4fvk#c#(1H~d0+iSprr>GaIQ7I<rSy)_>JCF?Y1
zdG=RGYQ!;&dQA0T@|$BT&FLN2q^9=&c9MjVm#nOL(bvWRm<FhY(fYGa{2`Xlsm2e+
zluK6yM)7v;6EQJEk>7TwTy0UD?m+?dHjg2FFI&{)Uv`=UXqz}-^qU=uI>L1d3Q{X$
zKOhSJ74W^FFy>gDDn1Cmk;zwsv{!oZ=wRNC-G=L^o-~9wbSor7t$SAx)&!ejzXavK
zo$`H(e1hQj2pq-?CI@5rYQDn;?7&FfrOrrAS*~l>BS1QL*0MQ#4!++UdblrapQdee
zr2x0#&X^>Gba;n$_fgMM#(R-e{Z3!3;g2YIxWq?Mjj>o`_C_Q9Y`%DMap0xV9ULnG
ze8X<EBeIaC2wWWDWgKRZ5jC~+3e`3}uF+T#G+6S&Bo>!j;DKYYTgx+1K7p?2VeVYo
zpBTxHCgIN#(tJS{c)gY0Br6sCK!_AVX{jdB5v64JsRlrYO7dAAbI&W<Hk}w+uHI4i
zhb^>gO?TNfUU=h6y*isDZr`b?k24g!8*3m7ugLG84Q0Z+y9;oCG*FPEg>d3ST-XWV
zMTFpQ=a@Gdie0;=xzcJrk(~SCnnE;{%0E@)s;e-Ybh~rx8>e#WQiIR;Z0iGmwm1)h
zUp&;ApCORL@Y$}JfpsQr`J9xo!F$T@$Ef{1NF?wB^;=X`z618DQd4t8PW-Z1x}F+f
zpKPe-8PWaLY_*?f$qBx>51OYxn$t`Pmkuv%4xp9l`O*c6^BS^saXtyR4Z1Tz;hsC2
z?5^LEo8f2N_qvyYHeRshJR}y788mf6kyz+=k=B1Y@VO{L`a@wA_xiSd#|eq%l?C|+
z1A7cG+`P1wW&1(Bk=}ehBiv#plT2r5i*;iiY7BHmK_x?ag%((1%9wtWwlLM9wdBPh
zw(UHj@!0~8doEqTdsePO@I4O27UzFe>}p%J&HPT!n^xe}=&bHrF{C{{DWKxs*kW0#
zb0ch38n{9%m79|T!4w>=?`V@(jx?+^?B?K=eFDUJ$3yp>rseI@ir!0kdvn_)hz2-f
zC-FFpA!cd%FC_J48Z?(GfH6gBS)VKv0HafSb+sGe_|sn|2cYz)<?W*w<*BA25zKYL
zijEj0;#YjH*mbxbtqFJd`>6MRFEMTy<lwlAjyCn&Mw?i94g*{y-mCHs(*_@D0U=Yv
zJ2?3avC;aYHD=J4@iVO&vtFqH{)9YSnkG5%8p)U}Z$dXeuI`fvbba)#?oGpT>cGm`
zuY?@ZfX7}QAjuz38Vxwi;eT!2j-5lt!hg*I_JRggnBne3k*4j0cx%Q{)&Bl!!E{xy
z6$INMWiXW<g(<?spV3xfo@$r{koJoGH~2j>iH@qfjdcJmL2!f5<Ei@og0GJ&*1DL~
zjl(Xt38anT7T!i1N9=7<5Zt)+Ux}VhkfDuS$pW|=MX}*iq&&h1ks*xJDuNVd!B+)w
z2m6p>?zzF74;|`6F>f&chB9M5gcXH8#dg66dfUx^4RgAQYN{Z|p28@?Ob{_208)pF
zlqUfZ$Y0?mmN~0P_8V?0?PO9hZe^FMU{<6u$qxSt?`dToNp#(m8M@rP>qzU#HAkKJ
zLX2V>XB$7e%x#hEFzCUE^vdxhUHl;r;*@UKxSRp03zI@f!?a<~sVo+;*f_U4ro&ru
zFeWjXF?BE(@tsR8f+-U9MzWfLsSfX~K~ye!5T&&F`%TNIRXaI*1IICRC7VpkN40%&
z^f<b7h8z`E^VD12No+0%xd_<`@ktfucl-??zRi1G28g?6ch&_f-{yq>C-kwVt_jNE
zGJxP;(<otaac<wp)Lz}jOpee9(wrOM2XE;Ch3A%rG{HCUqJ5|!BtrUA`Xfq_jUg*Q
zZKUBh?AoGyCyyAj+t_RT=IAa~3}9h^LBRK4SDiG)<Yu+73i%q+A(Urbp2KhqfILB|
zn+cfUDsV`Q+et=H1MXo+fLhe$J){&LQER~aHSWjYPKo;ZA6hOV58P~i9Sj!EcPV<s
z%LAD`HYmp1X&9>Jk-51ZYg!+F1cbubJFa@_KMW_)km73W(ygpzpeC3e)FomlJu2yl
z*i{l^kRBQQk}bqJOP$D`YA+UBT!OpK4<eqViD;i_tav=o#;`6_`P>vPgsc)DHW(wz
zo2q+tD&nfoXc;WYhv!sWHQzT@S21m7U<4SQf5?Y0Yik<3@y^!mIyx2*0qwVhk&3Ya
zolGwtv$sn5xG?-#!A@=*+E(Rm<7A(z<<=X|SY1DxC*6Q^v5w*du3jl4a5dv3Nu&t0
z4(-$`zO{8RnRT{;YqwQ2%`g8GeZU8zeCH$_L8j&<k-;6`k{a&9aelS@DqF;25PS!q
z6NUI&9UC1U?&z_jZF`t*Necu{?T@`V{CaUq(=rvW00+>`F7uckl}H|@uRD^l4}R->
zR=TSyQO3A#F6X17-NH&~EsGhCyPDwumq8ef=`8sjnk4)`{O3|$TYiG!gDs2GuD>D^
zl(v$+vCPFv8Gw$1D6k0tqYl2l()CzPKQkv^Az)OFj5VnZTj?c1!l356!RAlB%g1I^
z->mKC^`FV0+UpY5B75AjX1omT4MjGdd~O0riu_x3uiR9-b@70;`YwhBc7R&KEH+Hq
z=1+BgF|52-0ud^(C6a;qEX+_zb&6ZX*jN`6{31|u$#6F@BZ%r507e&7nSc-j1%-V&
zaP{%cRo9g33hmxfBJEb%bPK;x@2ZzAxAo8A!@1CC`ThoS4fic7xVXy>2BSS{WLre%
z4g*+57Gsed3C_txr**K`$}H<AR6AuSDg)Ooir4t%OqDa5sr!Iqqo53_Y&)|gCxu;1
zD*dXdM7y6XmnB4?jC|8m%I*-{dDc;gNXA0D?WAAkwosb<5><@@bL0l!(r!Lsu7~z6
zD%_sx4G>(|&xlgmesXJxer~9=%pqS^uC(3wlGB^aPK|mP>Xk`)hcpG+&wc93{?OY~
zU7YN~{AnK?boo~uU=-p&j7B=8rtOU>#3uDHhF(k#lfzWTj;f5%AvU?WS4p-k$*2wW
z7Qn_tO;n~u{S@LJt1*9>)!W3}ST)f6-0}U}9s0sej9tN{-K~Lu`bq3P?rJIP9#;@)
zFF-7Ff4&E(86~!3Z}wB5x~snwa-v=BwVdfahjr3K^YnwYuZ>-1o8?T&N&m{#{fL&-
z+*2s2WFx4H%sI%3E1{z<2X<)ryKCv_QQ*K{YSt1j8XCSM@=;_v=QgYQMS|d_LN2`R
zhDNB&zP<8y;RD_I2S72-fb2z$3@8Ovp)AsK$+_6El|qjwlg}ECjs{Q<J^ioXn*v+S
zc}o)bFkyIUy?bSLO?aU-v;vY<nyD7h+jzFWBUR@X1s>vvvKzffU%B#pl*I{kBCiPa
z{m=pkT7-0M5l=+akJ*4w9$0S-#F!XNAl8TT^<S1D;q-3FpT_^rGNieF&^E6%vVhr&
zt7kXM3dZ%7cI_6T$~8ZT2~d4@DUH~Ht!SEbQ+F0r?8_l^1R;k5UM6H<>{DlI%vvDU
z{Y~*5Fp~<it=V@)gZ>&-G_E?E%nHwrdkp3zuXbN8t4Y7)fo|uR^<NXxpbEr~zlk>z
za?pMLLeuJe)+&<9ULiv4KWfz~C2y$@Irb4KdPs5d5n#VpH2ivTnx-&fV<9`(GMM0s
z=cfkXxx-M&(ErK~l%@RN*@1kFv|{t%s|W$O6j7$cps)qI)y0?lUqO?>ekymkSt%WP
zZtj1tDFf&lC&TV8z>dFd+qqzG{No{O*}t%gTSePu(``;wtT_10CuU4{;6WP6p5S@7
zrQ6Vf-`}gW`ma&7;*5lV56G5+QnnKiPE^_tWS;UO49m5aU2eb5*|py+GV;0pEgsiO
zL#$^t%c{!g^XsT-FwJ2ujj4n7=O_EGX4t@HueZ69mz)>2z*=@T%YWZD55$M%d<xMx
zi#YZ|@^td$u=ShZmzwb|=G9M`cShV%cJJXL+g4X&EorF(=Jk#HAluF*FD@I~Mq)%N
z4JlgU-eZ{sq#*>cw<{mc@h}AYrZY9Q>n{#yyeVpVfiY}U)M-p%FWD@K287dkA|0_V
zfq#wg{OK1_M@P$e(}EEDQ@0HBMPJB`zdNmubX&%LG=mN?)341vSHI($Aa@G#?-|y)
z7YHi{pqBt2{f~*WuwLnOcD`H}Kk_M}b8pQaVsr7|QRx}m&qznW6yhbbXS*3Y7QV0h
zR@n1buHcuYk10Asbar_+w#?k9WVFy~jKUrVozlTdDd|Xqa$kNqlvgRJKjjv0Fy3{b
zON!h^icvM4%2bO(_8Sj3j4w~48A%eXs>^#6+C-}Cryef`d(!8$9O{eg#X1N73G>S$
zT=fyLIS}j*Te->_*elsXr2&E&r6g#dBn&hbUEV9Yv)p#$O8zyu>Hf~mtR|$2hk4Pg
zArrt8lQBW7Ck1Kt84L3l9H%Qifv1Z2Rosn##tSm5zjSPfCRTu!CtmYQjeO3P-FbE=
z#CpH8oy0GARXPR$&fRnB&CfGO)D=o-d)OSgWRKbkMV>F74yV*#u6Y3sbIezxLA_H}
z-Itu;wsT>lv+jWV!@k0Mi}P9GOY6D?lbp+EWx+vDD=ghEzsNMdCEEy>AFWpwqk&qR
zivu^tC6ZstOM}Z<%&b^@1D}%c>wozoPJoakcUfAwqA~*iu`ntUpXoAliQ%O^2<=`_
zPPn4N4+f>26e_jQJe-jV=somp5B9AxB>4I+<dL+p2~)Pd#!9$lt-A?_{gnM*>uB^m
z2}S&~vh`l2Yx_@wPaPI+3NC(*kJy+Wn=wn)3YK2R5kF-{0uiDyXG=`!4IJqwDZk5l
zkqRq&eSuGRt+%cT7lKdR{bT%TFXW!tcG|dU5cOgWlTQoo@~4+yPZfx+j98Ox=wT8|
zFi03>e6mcg!)D2SYCo1zH@F@fHqXjP27qwYb|_X$-BuOQHNuw~8R(uVNv#iQ18CG@
zZ@V7*@^J44kFcTHFhl!Y+Yy<!pwydy36~ba5Ws>#$uzX6cWIpH=+@F(vMt9J+^`S@
zd2a1zFdE1)yRsgp2&OVU#IvO=EyG4m_e%+sjH>A&T;Pa}n`#$A7wGqLQ2EU(-KyPB
z{hMdTz{UdFWYhWQu7H*@mucMRwQW5nygE{$s1lI=5&20?<$FF&75cQJ)6w~-d<|TE
zBYKdhrvA_S?o6?ossFN3ml({at@02ugw}|x;p0FegvVCDcdwCR=?p3#UXECGgVsFR
z^hAo1@dh<G(0glC;1+P?gN$59Ev`2@a=MuVkFRSU>@{1`^5wfW<h}2yx$ODXRJN|6
z(P4h)qqmu#DJ64kUi77T2Mr@(h9BdE_PI_!yP0)xdfdgY$X4w6Cp0LXdo58)LIt6*
zAs!*TX4uFa*a=;{n*fs6>^_nJ2{N;#>NP6GU8U0yo;u}5Vk6Gz;wg?D?@|=UX3L^^
zK<GiC*E{f%&+uczXmP%giOmP~(!{4fo46cid)du`A_r%i?Bh3IRoghHTT2s47^|F&
zm%r>J(woiTY;tyUF#w#m9}^iNZ7|W$N2_ZW8rbj<;!>#|W{d<Z7m?ocs+pTlbUkhi
ze0*Jw-~QIJM_tiV?b?JSU<_mGYWsb7Ve}P9Mfiszpoah`-%sPxkhSpBuuTG4erBFZ
znFS-Zzpkqe96=Avv@7TTP7-ACl6XEMyXvt1{^lx+#508~NKwIp1^<$okK8wbP>L37
zE7UMVA>xV_+Z0a*vrO>&#%*$!_O>Y!a8~e)G@dkI*<x}H92=7|;DX5;nbwP|g1=V0
z0Vtx|sFRXm^Y%plS;nFSb%<8yQe34>%;#P*zNEfL={o3WiaPRyiUvs7DLE=~TJ>xc
zgLMCDG9K6%89oNAkPp^WYHkAy`6bUsp}cj^1zTuGp<SBG^ASaupY{jy^5Sqtob!SH
zC)LKXu9Q{H1Ly8Rcv5`UY2@Gqa9d61bzI{Mio~Cq=&VUr&{o5caraHo;znkpGvRQ8
z)xAM~bMoRH@SiwGI(PZ|IG8%bHe!Y&8#VqxwDV8Y6d$mHN|DMo&`$6FxE!#kjR484
z(ooxhDN(G8!L7evK&zN2EP0q^q025nSkqP7m&hHqH*|U*n*i%@o7o0P#7V`X-jJla
z3FQgj?5Of9e{pX)+v%=v$^wZjS>FnLRTbF07sx(f8ge@M2q3M}yy!!yxVD4;cfOQn
zTgzmf{JQWCWjm>n&axLZw=jq{2*ato3e-0B7_f(&#(<SbgrauGAOagJXOr)qMoNEz
z9u(1*Ijrvkfi^oNjw6stiUTb_$D^=!<WjZX*}JQK0I|rZ^3qK^HVhHu%H*=;^uRp9
zpwgT)wLf2}z!6EaepuMnnFgCudpf6*FeL_)O$|A<@)*#-64jcnq_}OkxeIM8^_K!|
zdDdz)@k*!PmhA5WC-y6gLUmxMt3uo=bRJs?;POHzvFAuH@0{9vzBsjp1QaH?Nb`z(
z-z%itst}!Mp9p$8Z4Dj9Bv$nW|8*)U5I&?+RA8064TK7C>A|!sjg@=)54%VuJDJqW
zyx16m4#&II#JvSMeSz~95=X)vSVt!%LQOH?K#WW!IPJW!v*ADVv2irvC=uFSfYnmR
zC*#Y!KDr@92*RF*E(7&VBQe1CjmFVNhe&^xnPcj9?Ak4ymf!;9>g4sG&aZCiLd@yb
z`lRK5>bYM5+q15PjA~aMYb}j)%0bF}mJy(eRiktgwuKa}BVKYAIzD`(PIfAIc#O~G
z1mC`W^{wF+DAl6@UmiP(xeQ)bMN+;hUGu4St}^1+x&oLyRKK*EVT+YOw6*Y)I2sB<
zQ+(GPLLXDdh0=N^u?}>;PL``_mSqdG*w_ES^^&DDqIsY=P59z=p3ph?Q3DcC>-{ws
zvG=-_I#f6!7#NhZ$_jE?nY1UbE!L7<^v047g}%h-q6g6=<eHE+w>?L+RDnyP-iP6g
z1Hs}@ojIXA4AP{we5^&Ba*ltDH-@)VM`?K`R)y_b9pmxIy}1d}0tC(PqgUSVR{dJ(
zxPxLf+Bfd0%Q~n}%SXpGFm`-AGcHf-%v&IwGMWO-hJ#pHDa<llQ9_6S7(BGUsFjy{
z_PPy5gRoTWXTovDbrvmW#2XA+#Ar9PK5eGIhb==|#wX{JqVLmEoZE)&OI$Tlr+7+)
z^hd<lvp?%%SmS`T3<MFY4KFMT^qXR}kA<OUSxT)29jdR@>8w6GGK^n-8g%N&v?#%F
z;>tSc#T|qiC;-X~I00E~ZXN_=aW$P&C*<j;nbkK4t;2fRl{Um%L@X?eUFanAsRp5P
z(Q*b2fe#k_U=49dPI~mh|IS1)m$;9>MQjxsG?|e!PBQpd{L)Kzivw7ZsRP?d?tUVv
zVNJydU_BIid_{(H7F$C(d_DkP_|NlL;wfZ0HIQ;yWUY@QR}hULw?)UkYwRs46YUQE
zA4aaY96>o;5SP55zd5V<$LWG7RN~<1ER*}{U>nRf_D?($oSk_713w(89!=_w60!|m
zFOPl5OG7V>J|_sR4fHDoH;_IqlG(Cn*Lc}*X*yso@*Xa^cK%^9sjrG$xw0RUaZpdo
zNy#Xh3<0XN(V6DGKt`h`CXi%x%v9Aew5)-8{K3>b@X_)ZPD{6?-KsE9Mh3aXJ`}l<
zD+g(@8i=o=(nE!9pM%~zkpn1)D&?rgJ2#fvLsD-%`Af$`xtE<iGGCm_>X&$5dmLBX
z#@Z<oXOwQ`HR^YU_t|zg2lDp~IE?4Q_5jBoJg}$k-sO@#eja2j{Ou6}D7Qo#``XWR
zOThk&x|;@1`|FXC3H!3(Np09WmHnGr^u}KoV4Mhg-Gn;O-c{6qK?&N8rbx5MmFyM<
zo@Ku2UEaRm|6V#1;C039-82C0`x8jA4c-i2f9d>?b=1L-sqxYF1K@u{IMF1Af{G!)
z&7}KeDh1nKsLg)%bh=)NN!Ax{c(|RXrKJYPt+zpA^28a{+hHi(f3@a`Y>L&$7oC?O
zm-Z?!YCqXc)|+NbKs2W#b#7G{t3XEmu*U6J)T%5@IC7d!ab$wV@Oo-Yrn|%ke)%zG
z3QYI@YRcl?RI4_>c)aN6%QXYufZ!drBpU^65PGuzp^DNWa?x)4Hy_6Rdr>^Ml2(A0
zv>(5cC10G5F*}(Fq>u+Z#wg2P?3OigcZ$vs2hvrR!Kmt;vS9P|kx?Kc;B-_nf#byt
zF9uNN2Ndn!!Fe<#886RDk>FrOVbAp62~L8}e?Fm7u49Yk+!GdZHL3uLlk;}VE0i2f
zPnuu<Sv5^5{|KTcKAm*QQE~Z|=G|f>gGemLZ}eG~kpT}8W!_r|DtP<Ey~$`MdJ-M0
zK7O74(@8WIdjS{VbBmwRBL4v>b+7*cuNdWBpwzIIK`$AATXJgw?05PPq=+dRUNUfy
zpX^V$NYhLaHhkOk88R~9pTkuWqp@Y0=zVEQJM7wE*4&9fO&ax+`$V7W?R6ZXk0219
zUkfQM`7Z#4cY?)?2gNKJ=Zjws3B7M3U!DXT4(Slg0}0dJ?%zU53-r3uWd>=<-fXE=
zc9K=2w(MVBJeTyjhek7>Jh@yU#dd8(jdWr}r%bNWBbw$n-LRBU4U8>Su~wo}8CUw(
zpqmUA%wAE1e~B9@QjZiax{21%YCb>Ef-LNR{LAlhSd>X#@BZGO1y3;!GUcW_x>RM+
zKe<tYh|nkfV8r3-)@SOIVCIjadG`C)%$PKoYd|7keIcdyEl-<}dh{<vy|TwKbWu>w
zyZ&G2i*B<%tnh|_Y^ns)s=}2uH3<=WpA+1Sf=(kKmK*g+$Zi3pGrc<q%POpwuO0;O
z%+CM7Go_7Qol*!Bv!7ZEGUOl9nVRd@@q+A5;BUHu{^6PR3O!&QtlslVct2p4aq)UJ
z>^FHJ&LeHA^@+$s8wgdnhZht+`c58FP7RgzOIQ9Sg2ACPebfAf59OXa*2*N@KMLzA
z^!F*Zj~sEFeFUa&EPKCoE`g*%$U00%;-RrCx7{yu^a@C{?u2(+N#$(q%}*yCX4SWL
zJX(vUgG2k)4qtLpQKYRfAedEs{cAS9UnnEq6J5-(JI!m`T+tu~h<bmf{W1!XhW+?-
zted`H_7BBG{77T3yOKd@iwzgR&R{h}aJ7jjwAsL&r$&c>#y0@$;&-FpZ|GhjjGe_J
zt}zabi5ggPj1g;2TMrl(Rav&lN;|-IGJP!bF#7MzYyQd-*AJM8MWF7~Qjp=LU?l*2
zDgXIFqZoVQmiLoQvV#NcUTF^3=1NYCFTb1^_a<=|W?{v$!Kx;|dligzN`icaIJKXp
zI<;BM7TCH_6EjTkdc+>eH4T)GV+})QdPK_E+pQ{!bjs0iR_XN&TFWV6>%sP}dx#eN
z4w4G9zH+T3rFQ$cM8p`wp>D<#PokneeZ;;V0AGD4g3J7iXa5JJ#QP1W=qGIazMwBG
z?~05u(akv4O}#PYALLIDMBA`jNlWw!;8lm*xD9a%WDoOnR9GkNZMH6@o{`GhWCDpN
z+Pg7PTB~WB69E4BPl>g9BXr1Zj@(Gk#u&(+DLx^^4TO;)P=(x2|K4-K7{W5iUKJZ`
zM-KqFV-%<^V`YuA#S8{7{082O3uJWJjxPDAGdr#GFS7u3)}}y=grfM@#;WaAOAJIG
zhWJE+cwzR$we!=}Q~o_sZMTX{zZ_kQdD24CPJ2y=A*@%;_u`LG?=@#t;}6GT{TsQ%
zn+D-C^v2Wpr=#EL|ASws^&aiHpc7DUQWdppOcX(C^h6L=YkwV`p56J(HAMfK5}EY{
zsNMRPkPDD_2ycWGRs25|F9KO_){u6&JyxjQDJ3W};5LQrld3#QlU^N!>)U2u{n{C;
zF3oNdZ6&h}gn(s=5()(li5nJWkmuby1T?W1<JJMdrF@Z{ud0p)2w&?E+K@`@?we;H
z(xBKmSnM&73(W;$UfgzqIeQ`)7}2l!e01X!c4l+)kI4&#)!Ciib@h0&IBy#Q94-|3
z!r`_xlm7l^x4=VENclZlJS6*917*&>a`>&UTnX=ONzgFM-q@M6Sj3-+`<*DWCpWv?
zO^o>$LuRp?8E%Z$Tv#0MNcBiqc)e5aiKPrAyZferxXlvnV_!SW@s5Dlg)*G~)Vg!$
zPT>sy3n$-SR){{10}73SZNxp#gWg6$Z$_)nwi=jvm0z7Z%<h4DpZ;yptyr$-I=2C#
z4Y~Gx{1XkTU5o1nGctp+kF&*lRNoC_+~Wm)RbmsFac_6@7RzzpB4$=Kh&$-I<Hnnz
zmv_6^;i9tb!m8pt&YF$k7!VG$jBea|x)k=IL-}2cZCAcJ!+Yu8E$yCRxW>_txL1I(
zQc(D#CVgwt4eWebdtbWvho!t%kyQ>juMr1te)(!BQ}OLBxd}z_i+i_^eR=NFkCsiI
z@u@_F2W<|_%(VIMIe=yiWeUH!Gras4TUEkswxj_%U|-#2tSsZx7tOt`%vimfiaXZe
zn#u!sTZykriEewSa_a*}g`3G~#0(p|vmQ1lMM4HQlw3~^+F$olQv=v9ru?>_3jf4Z
z3361>w3<Y<u_dNgeBLKoVSj}~NbyOPy_!3a<MzRlyjwlbrqF*bc{=xq1DXEWL)_-s
zm5=e1_M-7^t8{g(LcqZ|0DU{(h+dYveSUriCcN9`;lH3D0J|jK|1UoF*~$$otH9P{
zYxI0ZhlFnpY`Tusl<5avp(lY=@L!aVjn&2jcgv~G`S#`h|0X^94ji3^27u}U%INTa
zxQ-(2f#^0S&|uWhB_IgFlH!<<-3sKe5xEw%!=dF(_Z6;hPIg%$<n9sVeq&)OSzz{m
z(&ag(LPNn_ugbay!p$nr`G|>e8VV!E7|HX?E{aNpg8G@Pb$e%Ys-$BYF)&~^1g#ht
zS^h5JIVw+5+EGrK)DD;!xxrXZF`o6xp!T7xd!j{lTeiTHfwxZ@LaaMdriu+PFmi#r
zN-#)ZtOCHd-8sOaX}~kNI40<?A##MkTY-;vz;V~;uXvwptU$)P89BgDjeyBZz`(E<
z;M{t+lmYy4Zc#7*{m}n?{ND`x-wgcU4E)~={Qo}#>VBAy2gCd28Z;p2#+4P-6)K*a
Gh5dh4zSd~~

literal 0
HcmV?d00001

diff --git a/docs/articles/sids_files/figure-html/unnamed-chunk-24-1.png b/docs/articles/sids_files/figure-html/unnamed-chunk-24-1.png
new file mode 100644
index 0000000000000000000000000000000000000000..198b8ebb62d498a34e5af8288298eb92302adb85
GIT binary patch
literal 70865
zcmeFY_dA>Y{|1a!b#k}8QMKAyRa%PL<L=a$MN6%ynz468jJEDpTdPfs3X!%}?JbBH
zb(aRA5~D;Cilh-q?AV_4a~#hP&p+_|^mX8JTtTk)>pI`Bah~V(=7E*zspIF5^YQVW
z0^Gl2%f}}e&Bu4h{pb<i8CL-!kasxp)ZFwA@5uYux{XQT9gc<EcMRv_lTP~c#h*UE
z?8V1-fe&!!=ELZ`MKY+ulNlqsc7XBwd7G2JGr&FXCX)R<EA+_R_xFHjhu{D8`NGAc
zw=`t`Id<p5-_KvayL;iU|NfG{q;Tf7+MVOEe8>2YUA%SS!G()&7A>NVd^<GG-QLb4
zmJBi6x%qzMH9+Hskz6+0DE$#8!34yus>1q>I)_&t#Eh*f{_h(9@7w=H;Qu1<e-Ze<
z2>kyWftq)HqAv7wx2{M5KE9B>z4>w(K0cQwbCGCs<@Mh9#a`RKN1pw>YjV+P9NS&9
zK8WzE)YjsUrn>+-4P?@ZT6izF8@!jtACQ_DQ5XRr9|d4*|7Q))1Qn(Q|NQXy0q^Yp
z_XL^uE}bvG1TN6vg+z0Ga>fMb@14d!zr(!UdBVj!a?eJQy48X{c!1!&&WL~qsexLn
zg*t<ee63#v3jU|){io8=lAeh-XH6=h*au0IinHXA<)AtYeQ~y`nIU!hXvb!P4&$nI
zwweL}U<Q~7-=4Qd7?tqz{w~d$_Z}t%Hy3(llO4eZfJwlDFSoItd*XHfo;7S{@L2UU
zeu=wIEXn|huC(7==Kr+ppH0RrN-{wRBc?BmP^g9XKS+p_;Qg;BGDoAI`<KM6Ogs{~
zm~*eJxB6s!sbZtdW82u3b?JjTudRCvPngjvD$p0yVt{h+kuIoJ$LTX2jREysu#eak
zo%#iz=Ng?SZU9JQ4UNT>kXbI1j*T8yQzoLP<coNLxjksI7+k+PG#k|x|7-m~Y8~=O
z#N}ggDXYA3u|<~Bnr|2PaZJaGUC&MoBDVL-Rz<`pV~a*`x)LHjKHAFI{rBO=M~0tl
z{|2`bhwS*Koz5-^j9XY5eKG3xGKfAAv9D#hz&=)%>Tf`@LdwJ8fpz(tK*-gTY>Pv`
zbZ$?xZ3$^5p#PGu%(dye+HULyZtOI!Zd^O)fk4aiM4Y^b7%OA*2+&TN<`?Mx1oU8Z
zJnZeZeN#xp$B;X=cEWCDYygNdpaqodm3-dk{Qi4>s7zZvqOedIU}uIXwn)fkK)$6t
zJ7EJKaq`(gF7WO^5;D6xt2{DlzkF4=m2!Ki6o(!MuYRMk`^Qb=wo2lFC)Bbh4vvd_
zpG!MOT-^0=*^JIM^38GRVgV>7!5f%~^OgkQ4<8#lm{9rN?sp-b!K|G8dJ@tmXwhZB
z#;}NF9@v|s@LRlUEsGepw4PB6$8E$+cG2={*X&}<m9g^^oTBktRNQvK$Z!xs5=>}W
zrxc}#^EK-W0H>WwbBAoLr^IGnWI%q7808b(EXnmVx(<Gp3!Y+%=^MdGwRKso;Y*v<
zyYDY6Bs!z!9O*RYn=H!W{Kt=31!UIAdW~rP9V*2$CU^;h-d=j<)yM3YZOCt{&9C#x
zA+u8h#wh(|ed7GCm61)|Goz2NKerwLf%tMi+{A0QJ#3pHy^%O!2iki2w_2GR_ef&3
zP(}5N@r~3~_=Fd27tm~cZk{ptyDaHCTKm;(Y;?G?h)z^`?HaD}2BhJJ1-#LM_FLLN
zj$rNzdDn=n9*iSL8k#XS>@)+%BZe1z)ybcn5E1P7jEaQ!Q9D}!s@)^Y>Jt;uExTH4
zu2%FxA!TzNTT_e@337r@Rh3^Yq_V-9UKpbTP-I;fL!6C#-qVWO!ijA-_)kuHx7{Cl
zb6cy(<?*9w(2YhiJWJNaD%z%if}t#jnHaG6MZZDI)vZInZ-io-H;5HjqLx}B1)|-i
zSY495HcwO6*+vGOQoEKSH9EKC&7aNLD$K2D%Wg!f4gI-l3&xslu8Y-o1F1sQN=1M^
z+T^~O5^IdOmmN3Ua}iJ<E61Y28HIJMJGn>rnrSrF&bdy8Wl!l)d-H-#+lVpr1Hlcu
z;4W23vL=(;7i{wI0{_~WHr;-F0WZ~b`$Ng;QN44P)ucRq{UEV9(##XpX`{Zvu{8q)
zuKkX9l=Q08-Mv@>u4iFKypF9ef#1ft#rjURhd#8Wk0nL~QA|R%2rSD4ZkF4tR@Uc)
zo<n@5PVcIh_)N=5%xqiB@H4FXp^~^|+RwIhku<NgTl?iw0A*ZQHGEj&>(HRo;gR0!
zwp~zFYj6*w&S=1_1DB+eUEdVZ{%H<8CPZ&-Uv0P^v=Tdi={6;dCc`uZ4jBiQAR3{d
zps9%i0kVU8e0{`hXCyB(CySlxTo3J%bS%-xDYT-gM8w-kpGvPC$#Z@!b~gDmLb_K<
zY>BqEUPkAXU5VZyTPZertLx7~2c?YLgC`}%r(7BIttWZN<=Bqi!DOU+E^<aI1&blz
zZA;)uxjvksodBPVVr7sT=vOU#GEb{iMRsmua7%W^judKEk{h8<=Q>g&2x|_u+x^OW
znHlVT19$WK18_b8BD$0{FNqsm{bph&#HUM;D!#~9GQx0OKf3Wq2US#2<+`rEG42Ma
zy6rV2^(a{8%e8wUQBq#QXDKUbLT!6NO5Ned_38BdDJro`-ehM90-Sq;&Vo9!Zb+m|
z8cGiMV4gu%BYg5a^SI+#E5B1Na>CF#J4*PmLeIdhD1D41z5RBLRq@4OP)sRnB0mAY
zz={ZxMgNLEFu=CicVQ3!vjtDBO5J=S2f)`k0UG9Wk%a2_(fT}fSub^h5ra<;7xX?5
z|NJ65`G)Dxyvp~E-0-$RNacUAGs}aQp-G#u>V4g*WJAdm0!Mr6NuV;PdY$N;;r-RY
z*F)Wkn_`_$-E1U<>o9)BBXB`xcGu=Gw~#4zc0*Dhn@CIvll{>V+~#kl;k0qWa3Xjc
zrC4OLxBuy_IA4_xHTF5PfQTIO=%srSigYsBwi*a3<&9DuAAc~CNT-1YX0PUyTyJz(
zipaAVRC|)ktqF?0&mqq=<Hd6^kOsYh=D=`pQMSl<R=B_8{IB?^9=Kt1=(h19HMRyZ
zXo%euw(+w>TG;j$WbF5Cx!p9ds$?<wnaU$GRy}TUN~|ZVbK*hzYD)G{$XK0m8{g8k
zAD{V~f%;fa!vrHQ=61F+nvKW*>|4Q)boD$Enca1{`*}k+x7V;_z~;MK|Ge1WU<7Pf
zul<N(IIs&kg&XyQl^7Jr6T4{+P~?;gyBImLm_k~^SjHe>w(uyi0I>IHMR#a!<;>g<
z^{v)(DQQ(=<RP<aIH#r2kZW)lcsWu7>Nv)`JhNcENJB%a^uMe%eX|mjzFs#yj^w?v
zwmLFOVob%n%Ru{wA?78OEj3wtq%=Dvc*Y><?C;DXNkF?927_Eh0!8>fDDiUr_J<VM
zMucRUc#wug6G}<NA9r0C+jidz#EN-|aZEW*@%NHBOVRTi{sCN(9swaNCRdTZ70!qh
z`dVZow9jvzH7rkpDt$D#w;u&9%3en@iR0YF#`vB<n5~_yt=(!gGXl-giLX0XDFOTv
zym+{@pey1<0|6k7n)R5nvdu*hSk{N;>MQ)9Mv=|%L8ORXOtphkHf5!D(j+s;q==Zi
zF(b`tZ<OJij`@pM)$i?W5?iX~DljDCek_?XdIaVbs{K8^h#^mx3aWiZyPQ(79(IVb
zy4bN3hD5>!82fcIn=3NROe^@hIi@LjeFi^oIHikfGBgQExPiYFmo*Ycl`F;unVSVG
zL`I}tJvph}m^P#^S2^p>1Az|GnM<5%hL%NU%uAL!57{P>c%5Ez@!GUtRgx1ieqF`E
z=&jr+t33VqU~8>j0<A7@%_+C{u}^+o@dk|ZDf#l}yz#8zK%+Jx4g}h!88gx3J{%}A
zq*i<28(4emYjMVHV->#z-^n`n4*R1e_9WhJ$Wx3g&oMl>GOL8jU$|f74Vp|slSh+y
zTSA3bjINHXo1V~ge;l_zn&UHR3}5zjx*O}dNDL3T=9-@3>zDR*#DP}w0__r|AH(mU
zQ*AxoA0%RkXlUsOli??iN}^`-pT+ysYG0g0G?<qsU9&Sy%qZ5Q9{UOWw~hYrhBFwg
zxxL~*5N@)HXd$=(%yKLnw6lY!`8p-8j-fT59cplkqn9OxTw>L$*={EV2LKBRt`!UA
zxAFd^GdHx;m;cEr0DcUFwhZBto164n4cx*fMu!0_(LNtUg0B@}rm2Xb@Rc_2Yg9pD
zZkyCzj<eD%<8T0Zzjm7>V;*SN+r8?a`ol^Cvh6roS<>5Kp$y8hFY%DL)-xEwH|;65
zTYjapfpwD{6E)hcTN?vAH79=2TNwa`OlpQ~dGo-O_-nO7*Gb*$rg5K`ny}tuWcOP2
zpp6K{d=RYm-x~_*+VEV)*$N~>pM*$~#4xmwu_580pz_>w4gHcaF>^8uC)F+_<%MAt
z%4jxJ&dxM^Mx!H)uZsB@QQzqRFnhaq`m-H#Ux7r`_(I64J@(f-FN%HQvg7+g1xl@g
z&(9SXs#aU-{OCz!e9B5p^)$4Q=H+l?#(ZO;9%U*gvJJW+sjeng`~qy#18HbUiK1N&
zX<gJ75O)XC%cWdr;xGpJbIGaXsmBYnuGDXSq#vNZ79+Lbt5<`PQLMq#vsc|rF~lcL
z9eD)3*{PAnLB+#HB%hm%>cX|G;<Nu@uXp`+H`?g$H*O>Ow8ry2F+LXk{G0ZqW!%P6
znQ7>i^)G&9`+aL6eO*0^T<?V^;ZZYj-iKrZ6dRF8u%>!LZ#=6e*KwBO_Y6$k7tB|6
zi_ODMqhk$Aj&Y)e39EQ=X#3=O8pY29oFy)|*oFy<pWO}f*UfDRSgt^m?F1Vmb?+lB
zfE#s2l^_#}CR^&V0$GR(rzBBPTGcT>#&Npq@0OY(T8U4hb${|Q8eh%Ns$ntXrE7k&
z3E<E~BpH85=Wp|b8xpMcN67HP$ztIqVbq;UhD)_fn{nSYY94kD0qH}CX>Cqg`&6-i
zmO_r_qXI-$1JwHn0v5VsdUX0cdR*v4YjC9}8k~asxKmcY-{!Eh<p@R-gN!HWyLh=o
z5=b<7G$~t06w}WyM%_)26V$yQSi;YFQI=R4r}K9|!EfQWs;KsjBIrM;u6;9tR;huc
zviW#naBxn2!?Lt`uxJ|+VwP8J*J+T1_R<m(Z3{+lW6{J6LyGa{k3HgMQ7>t$MXkw}
zwxk!9;lo<VNqfpmdkrvd!{8_J70=ma=h0TyAnpC$uw>x*Xp*%e$j5|FwMJ7LF3@}n
zZi66kN`j1X?JKW++`!R6?1Z&CM6oLQ!^Vh_$1{5{x;QDQ-I3o=LJ2+`ku$8$*nr=T
z*|_?mRsF6~vc_O{rY$W9)~I34&k;2o6mLrR5bnkdi(1r0WfW_LBU7i`SoC4q7T5J4
z4Eo_<)!BMwxN`o_2vI+!JRy;)nbZAOe03;nnUESGBv}INZGfS(wa626?y;co5<uM$
zef3x>%E*G-#kFv@YJf97q<#3WaxEKPthtxp1#z@oF}14Mm9<_$dH~}y=4@bYfE6@s
z_m@k@1Ybze;kHfz72?FloqlB<c43u?Sx-T^%*e6P5&U{#M?}yJJEAeLk1$!DkIk|A
zxp8UAQiI$a(7Gekb)s;jg?TQd@`geVIwde)|CkHl?yR8eydk+-ZNQ_`fMa^vCF0v2
zeMo3)ck6;I*=aC%b1o`KZM{zOypKBX6EQTDwcd)@(TnTMmFJBE8fJ_LJJQBaQ}W0#
zTPuUL;my=7ih|*YLqzOBV}shxs_fol9rJP!SlgS*uWx#7=zSJ^S5oQmenPa|v=MGz
z2e$hVc5v&*iOyW!s(!_sE*wFe1lx|Wiwg@~51xKH)1f~F2w&ZASlEyf0t)5w+QN~^
z;tVT7#t2SQ5<W}L*bnn#SwZ)&eHMgNh<ko8MI8CC8tISFJ8zBbE*mEz>Tj{+aZ6Id
z!6w#wLGa3%*jFC_1b>9#M0=hz3S}ZYH)Je3$3#1<Fil#JB0-hKl{XTH<qf)*ryg=Q
zFqSY_*9uZqBp(ThBfcTp+nO3EwOW|v#P8>Sk`0nRr7^L2W&PWG-QJ@){e)CcA30Wt
z5<XPXYhHdIBcCw;+N(Y8J9Xa^)}d?Q3R{E48sV(vxA1@<#jUe|cwHRFq&M_X$SEE(
z@a>U4fGDq~NX|*IgKL3Hu8J(sh~?65M9XmIO}`Sry>8GAR<2}N5ujyfI3g_L#DgT_
zsljgTQf7!c`G-rpUT)$1f=;Kk=U_P<i0E)xdq}G#|27nCD;>W)jV#%T^adNc@pG{A
zKpEgaJBh1d!HwB!*C4S}S1JxX4qm~69afpfEl7iYY{f=Nu2cbFM`MvJZF!9)F_r-X
zqH%?l5`+1-XT25n>fRUU8+}ZuRO5JRoeD{B`w>xBPjG{5ImVr5jpe`F{vg^0pYRMk
zy_AnWxPn8Obk84*T+B{*H+NvQavQLpDSxnB5qXGDUI6&y(+x|6Nc;s>w_9vrL2+6X
z+?HUt=`=}ChieAtB6&So7#-``ma8wJSRdG1*MO*?n1N!5r!Y}kMusbgADM_3kMWwu
z2BqM-$8ivABMIpejU>@Byy3b|e!-`_QNyU)AJE4sGg1!=WoTEFigq@LtXMiDs{LR;
zb$2p7m`=0R!CJv7W+rI+Z3%Rsj1d+0TR@f=Ujk58=*G!of*X=QG~94j;f9Cr4C}er
z#Yqsd#8Cyk*trUD5Hh7C@T?gCq)&V^jiB8TZC}?#C0Y8Mzmn@4I2@Zfhq7ML@i{mM
z<yYf_^6JM+d;6dw2nR|u-kwMA^D>ZKR&Zej*>Yzw*_^5AJjRxhx?<f^?XWT6%ponS
zdqG&EGx>Q1%=f$a*~-h|BX5`V8+|_vIDXLg^KYVmDPj6m!<9&@JHQqKc6)hLzGE#~
zg&I?rDH~gpCA;@KDrl`F&JAM;7YVMW4X+{>(}p;qag|Qo*Yu^HW}F{b0lB=z^5xa$
zH_mFj-MjX>(9wDqOFe5=ZG!xJU6&~#Tx?*}Khx`^Wv)|PDXlmQGI=8QO^vO$M-g>7
zaDpWm;(`GySiliLydv%(e~z98$s?pXV%|^@bGh{pkpyL&+x?XTdB=`_N&F#Kx9$kh
z>?(;U+V4YO`zQCb;5L)J9j!w#lZ;PrG}W9O3zG_$V_4{u3tby<6ksXF8GuIXo*gTl
zj-%rp3iaIz^vbR5XrF`qU;)B(W@Eg6i;lzd)!d-Ui2C~Lva|mFE30lnwCwiDzG_Iq
zRg;yO%8E68kQq)0ZNEB7vuaA}_4N<=HxsCnxV%~ENA9lR2GJ>cN7`@^KI}I;D-A-1
z9saz*6F`!|t~NIDG8UnNVjNLh*M<lfi2AphqQ8Hx#jhV~B|Fy7ZOfGJ2-a>P<+=?V
z<j5yz;oQtu3}CU4?=kUiu!EInLDmQMFcbJ37`6J7pCZ9SI-56dEM#{W8pYORfbN<T
zkur5ZBZ~PK79&8drL*n}gR9*R`ZC2WkOX@iwCiG5bo|bB8S_eI@_ap>9rtD-?_X<9
zir#=)u3p(RvR6#Z=Q^)6)pt!C>RgS;e^eswu8t@e|29xKwu@BL{$C`LjGJ?0x0dX;
zk%}C$3l3g+Q~OBC&J;sS0a@%h)ua?8XYxTFV-BusfNmTc2Y!JsH=O$F%N;Pd==N`G
zZ{XgKAR`0)Y1Xx(h}P0>)}2nw{rKK|V#4yf`9V^L&JM1Eu#v8?HCAz+D{H=D2Z+B7
z;{iSqAj7FoGimdY?l3$Nlc0?=gC&HF#s5lo{S_$C9L3A=yI*cZ?zvBvps)+2&di20
z-rCP6oyGNV3#J$lJ3en?xkOx_^oR_}ubV!bJu=MjS#OV^tKSsv)k$BTkG0&5+T#AW
zJDB{K_WSgK-{9m$)ku9nn)v-Jd7W)?K>qE_h0uztk#+HXHES9vBm`<_7qU+&!0#?4
z>8y5hr~_EZeukE1ejqA93DiNt6$WZbp&4L<lJi3`jyR~7(Y%zKg_@F;zrM01eV{UZ
zAzGI;YM{TnU&`xYHNc?tAM<^L)P_WS9$RJ>Ryp7#w~L!NNU(;jlH@|0Wyxm;_Gjb|
z_9YVz%<KCoZf0RRxC1T!uA1>`QhnNiK8|AvBx&xHz;{3C?Y-r%QRfB3CA!j&d#l>V
zV1B>1G~EQ-tRis=-njqN^5I7D-R-w=?-^ryPAN9miXjVKP*Jt~WYzQe*)Qg7oa<{1
z+(g@~qh7T%PW7)IdND%k$EtD>7K%5RnArf~UP#SkN5;pPN@_oiz027>Z#B7_YCXOR
z?)dqgvwMR_y_lJhi|5MmXt2hHzJetP*q+_)`%Hbx4nWRZ+0qa4Z_1MO45Zf-^jnuA
z3mvh@C@}MT$j0TO4um%gIEgPwV!sYVql&`sbdpr5_c2)GQ)$+^*QJEEH33b+TRYU)
zg5zAv1D51f;cbBN{jh|M0~6#N6}gVVsvZn4a;p`$<b+gLy<iFYxP$j|vSurCfc-IJ
z=B5^|WA|P&CcD~<&*uVfL>!BMgb@#HhSS(dAe3=iGxIW8{)E)hprhs7CtBd=R^}jW
z{L{iQQqUj<(xSXNmY`D~Qm42zO|yM9s~u>W1w}Rl=B{_?G81jasNbjaIcfEiOqXa5
z1yA0pq>zW$&G?~Mu46n&q&-{G92<dvnMx*(IN6!uY)f!Y3;|)Adr?_*<~<V54~?Qp
zfd{iFVftvQHREcLBPMs5I5gBChY{B1(Z3h)D^3d`N^pD$v3)DpSI8NpSdd}GnXX-T
zfZG<2whK^J!@@Vh-$6}X_Tdvl@y5vY7VN<7ifzFDn+e9j;=3o>fc@%;pIJU}5Vyl^
z=79K}#Wh)^W!aHVLEhZ%K&vZ@;$qp$>hrY3k<{vIwBvnk|6MAvGt0?+LVr-?_yI6R
zEBtF^fL8mYbznIBBQV!A#t$gNfiOFEzWNeq$*B&Ha!ecVp0k>)*nmo;kQ&4z=oBCu
z9|?Vx7z>V5LK(@<%{uoxvLjb#Dn|{;GM<JYpBeV`yqRm2Hyk;RWhYPmzg_@xKY4j;
zaW~LDxFmcB>%iGB0&pq4ITa>mn7IGi_=QqKHS(>bNX}NgsS3(t1q>}PTUsp1@Y4;>
zOdh)uveah=U{qV}EK!=n%a)h2Og_vFNw07VyjOP)1-rD%JLax8?&0JQx)yypw1vcH
zW{pY?R!;Xf)wg$cT*aBR(RZ=W*WHZh%ltLH0-3)2;{bAe{>Cb*0~W$9f@Nf`qFnya
zy~!ipQSXr((Nik5_dSe$=FP=b=Tt+Z+V6$iuM$4HQ?@zz-|CSz6lYBHTU;jPS3LHB
z!7+|&vHL^~)CltLQTi|!9M<zA)(5tDP1^n$BsLPP0`Xr|K$2t&9SzFftv=xmAx!_p
z4dSAvjT5Fmeopv@_tw2hGEy(j$L&6^2ymoURx9PM9n=HjLx+ac<hPiB{T=xOPZ(9t
zne8@JBF?@WoiM~O?R~s|ca$x{(hKGQU!7P?KhpUt{?K7D2Lr&)DB3PY#lawLQgLsd
zF(jeIHMR=p6lCn63a7R%c(K^K8Cax!_%~S*OM0}P<8`BfqTKF<wU)AJ?2CWaKFhqf
zB6{k!Z|_9u;-=QAM&)YSQQ<yY)7|u;r*S@^oN^wYw)<-q^h^)r-vfsm9W3a@ZWyci
zm(DMuo=0j7dhR919gMX=On7U~3&JL*q6huK6l1kO%)u5kgGYx2+9mlgPYo1ph1UZH
zU~?s~6DYZ0PVPu3<uP#a4QWU4ppeNooxw|XMgFK=KMk2;VQqLhduJ@oE@%qSasWU;
zWtH~Mz8b{F^MnPYu2(bM;$F4)AkbGFX**iTP(o7HloT2nik3PO!nWfbhGnC_QqpVt
zqh361HP=+STZ|KJ^lkp)zo<3uB2Zty&0b|f?)+!V-KBQ0t2gSyr=pI8FH|SA<_{O*
z*~fxSJ4l{k!od#;n!KTmHPI$$V<H~yq}29<*Ix1<OtinPwDj4syIgbO`OP5A`r?ns
zOe>ut5~>OG#Aa8mo{A3;Xi8p-7-EqA+%kh#*vwX_`QXq&jUFGc&g-O0nf}lFar;kS
zOd|-ct-nqyNQl5^1{<o$eNKI~WqxLTm0ZG9Ea%LTXhAF3IqXl}Km_P9bnZIYQX|Kz
z$^jL3eQzQ<kGGFpc{6LEDLFoBt+lF^uqmx2@|>Ex@DhE|@D1c`u61zBI4(r^#aA)_
z56*W@LV9NxU>*eeZ=el=R%5}jzn*aosfhe>;3O^fN`(^Bt=MXV^Ts7Bs1SPKPb{#v
zdJ_DR#14}F`Sw#<k|{glTE7kf=!H?W^5cl3lB=foMvY1mmd^Db6i;wE>ga7)cMcat
zZ07r!1Q>f}{zx`~o2pr5{7<x{0kR0gyN8o>H-&;d5ocAdN&d^P<2Rypf%hNiV;h+1
zw%aPD-8XGX8I&*rW3Vg&3P@0f)P|B6mWiZUDPbp4VPFaKibAPZ7B>s@QAfgB>5Zdf
zu1vxH)9=Cg@r_@Nl(?!7nTu+X*0&y%6qOZOso68jJ34gZZZ*23YbS+&;1mzce!NE1
zqwbD+!weF8OOZi5sLV!aS|}wp!Iu?;eo`Gf+LO|PQxzQ-v?h$)C0`_J70odQe_2*F
zIoQDx)^=p)_WevmP_iZwi{K$N@_yxwp==I)a6`|c*`8#PZ<KeWWv4CPELfQ=<Tf;i
z^C_L3T}M<U;^)SoYHHM}W=&*sAnGHU9FsM8(NyV%xsC=UMmsJXm0e7dqJcSjaW^#u
zJJt+wY6@G=<quq7CUM{ExbRr&;@UwgeYY3T1e?0QGNiawFK+1l44lQ&tF<DTIA?g-
zs2(z<LKtitG-ah2xX{C-qH-~^K)CkFl83w=MU%xr@B5yA$A-8tecvtO&o#m8qSSap
zxlg~W137kk`@k*jQ{hyMNs(5m>DswA^`Zgq1r?~3PZPh%i2}Dg)Z7@mzM>Ics8w22
zSX`*BaKq9MG4~Ck3^Lc;Lo(_D@oQj217K3$D8W`OL9Ak4!^%L?&e?oYV=pd~raWEg
zaQa=|?4u3yT!U^UfB_&Ug@BB6bcqiQ2qXen7UhzrmO2Fyn!dRy*QWK<KQwHOt}}Ol
zm=*)8YUQmZT3Gwkq)|BZ`A+#>Y)j+M=bOR%J&Cb<gJynVpO3F3N1ym9qr~b<a?A}V
zGBG64Eu@7BLB>WQVT}Yv5f8-@CVK&`^=n_&d177nO|t~OBBD8c49b{_eHX<W#W(6f
zq%S#9H96iIR*c1t35V@|;t*<PFaq|NHj%Eh<yucnFvfYc-Q4ezKbTdW-V^bGe`C>2
zP<t|qAi4Jw4rr6CIVxZU4%mmwCvea7oLU+@y(ExbFxFrVL>Z#jvVf$cIR<cs%U|>R
zN~J?G3d*1$vbnTc)XR}KTF4B7#qFu#kjau@L&MOnC*;_$_SrIC^P8Ljl|^!5taV?3
z9&z{+;%5(v7=;o6?2aYJ42?ke^&MApxNTnq?4#p@-Cy89;LCnoM2>jZvX<{){{slj
z==rMZ!=PLq&ecTDnZgNLYD!9FUScjf#C5A`uy&e!Ac!!=fCN^8>@<{#UcHTZHRBv9
z!8Qk}DAZk@8zPEB-liH-ACZL(@Cc3jK4QC+0cIDc*+L~AJotEdr?O<V<<OF0>LicY
zP2^2b%1BRW#CCyG{L;Qz{4~Yv2wdB_J5>8sV7|z`iSvUK?=^%r-*B+m!Be?MQVN#m
zetrt9w&StDSAOf9Qp8=*scWdq%4J1uW0)ntanIRMvxLa=U)Uv#LMX>S#}N8q;~Ywq
z^+XPd<z)c;LZz09j^_3+=junRO{5`0%hvR>8=1TTlpu^I@(6{|bos4JxvZ@Ku@`JQ
z6F`|dQDevq+=0S&bD@I=*@L=cv)d^6ZUl@sl8D20H{=s;Kqe$Xk=iq)4)vV_4w5~Y
zfKNcoxtWJ4;SO@=P>8+w>kKCyoQT5KWWXgoKC2l5`j(k;q@hg7u+C|U^7>XbsAGH3
zpPo72$Z&sk;$uX%T`wkFRNl3a;EZVc@`0<4(NacJp`!v%)2<R$_x>p=bZu|bv(2xF
z&zSMdavi$$%Ta5u?rEz$Xko@K7rR$xv>Q1E2=m#Eh?0(+bSqe7)z-S1yenmS->@dF
zGRP2@eyr6IpQA_Mg#f%zq|v-#df8>m{Hx@lDCmmzd(y0S!aSx#geYd2vpyt^tb5C4
zg0of=!CaG*2{G?(LM8%f^O{i`YgWq2rPV-DD2i4e_qZE?cW~~`C<fTU1{W2E3kx$~
zwhR44OGqSAEzLc8;(T*P_NhB=Qqw<1U_oe{DH@oX;GsSM_pp}(=PJ%_gl&g#4HUqp
z=|nwmm6tl1R%&E!JN^5cQN^JS!?D94GPk4lU>;=@8~3ZR7*5%t>Mp%b=WW3Pe2HTW
z2bvbHNwfc-?WZ&wQ^KNDoazeQE0#~#I+>l2H>U*K#h!Jcshi}?S>vr_BRa@=f^{Yu
zI|m!8b65<$ZQx4m!4H1sCT&rJ$EO6tW1(VyCFmM(cud;((2O>J8~ovtfOvHi2o)bS
zTA&NpmyzEaos-T1wKl=GM8KL%qJe1=UDl5$6@2L@s~H9!szsZ{aN?pvxpY5Gy}e<<
zej#pao32uaT5BofU1fG$ac)#z%Fx#9xB7uxbvAjZCO@EeADs`Rj-A~3Gi+^7uW?$a
zZRnWk!>@^BGu8V|-1&#$-=W0(dZ^{fFn+(Z7tJyA5xUt>>d3;j+j(*i8>mj2#|BGV
z`L!=lh7t|UePUPWzQ_~}#{&(dL6S9XvSl5})4*}7iOv;PB(255MWP$pv1Kc!lVn9;
z2NXJz6NFq@SLxOJU%{*X4jg(<s-#j2z@^Ow7K|_RIY2w^BobNfy4Y0tj%&CM#GJ^`
z3o^Bh&f(E8viDaslPYG#y+vD1GUvEMt^2Xm{Eh=Nm`V6^H2?G@&*vjvRh3ZtmuQx$
zvL(cH0W4nrpe4w}+!2UbaBq{mhV57!9k3W5VwCfXR4cTfD`^?T;HRHDy=p5(&UMW>
z=7WR1Y)dLlCY?0&Jg0ICw9~cK3_6;f`pJr>qbgvtIs(VDhzQ`dT`i<SDk#jqH2g_3
z=5h>j9L%?v|Kw{!(-`RG3Qy#KH_`eBk!@};+TUj@n+%5jP-J?)!pmDibwI5-6$znF
zj#7oSxyXMi*Bs!E)w|jKK_&+3)2s+62%(6I-v+gB;e+!xwXw7Ld7&J-qgsOf0e+Ew
znU}s}?Y*E-dx)Xg%C}<zbUI+4H8Hd|5u*smAKX9EDZ!&)lSk8t#s*Ks7I4uAtMrFt
zvXwshr6jk}!76@}oB4Q&&wHT`eY2Wo%$#4VURIG<K33ge2cxhRtgLipXk(i!v;PPT
z?-5u0J;%Pmd~M+aDjYm}{|z?H?&Y>~dngCdmflv0DTyQ%Rw@Ox`~aEt!22=5lTP)}
z*_-z0cEeH6TKKw}ZA`zARqV#C`Y_ERB7T$MQ~k10t+%%R{a_`R(*A@e<c$-8I{F59
zPPERqRQVRjs(1V5ujE)NH_olqHTSjD7e$Enj$U%FQh+6Y=jqs(L*ivT*{bsxbiw!C
zS{8hDaVz@0pCzNR(CXUtb1fRlXD?;EWH8!wxs2zCZ^(ZZ<@MK9`8m5(Q*i%u<FOA_
zX2=vG(r}0@55|~FL^-T5f^^c+;s>wO;pbCGJlRj#El618B(%2?NK#{y2g}Ft?9I8o
z!u}#z*LNw30PemL&!4b1cQKeJtuMN_ayz2tJ{NVs*n8DJD|5sV9k4nYo=DPCrN&;J
zwuD77C)!0j0Ci1GS=H^^S43ou2gci@)|x-4n8bgbH?5Cv=5vu7Ux!{&7wPHdiMUB>
z#5B9@^3r4isVPpU3|vj?+_ckwT8DtxsDaLWOpa(-9djYWYxL~QbNWRPR$-}@e%sx8
zQ-B*3%V3Q@{Jh8tPl$615(zJ$;(Q6-y5$3^^OIsV-X7q*RB|YfJD74@n8yvOcjK5G
ziCIA0)uY&J`j&utrH@8{1G0G4Qz|h;17N0k3WAEw(l>O(yy7Vqyh#^7NtVmLN{-j(
zcI5N)5Xx^6pl|@vF3TQPygF&M@xQKwf)3lH;Tcm7f1qo;H3wHYhS$sV9y`R9mr>mM
z{i5ekrzo%C5HF6~o)~`gl*iCr;<XAqnJ8m~T-ic?iyE?VeRj9?6aGbmukLNP@s?1W
za$ly=si7aQ=Ib<<;6OUkJ9^qi)FBYc2zmua$nJ$)HQD**9lzGyI3e!>fWu&jjy+!$
zRB-;PXGplGI%00d7Y4LjnZXwsPDMvLC&9J*k#`{-2JJzs-UnnmLld6k@u^mj9Xx};
zE8w$sFWca$y~^h0JR>1*wa6ge?aks5A|+P~U=cwbD1x)`?=$sRDC6mc!RT>f3*?}(
zh{tOf7#Kjd*FbDC2K<@yHM0~DKYmOtJdS#YpW@E5Q#?&MQYtAlw7;7b1=Ig&2IGyG
z#J3c^6Oeu$yW(YGrX?a)8scM9mO@+Hiq$_6=7zf2QR?I879#p`GSInxidk41h=|I#
z$?|UF5G%bQS}2Y?yf`~`(%P0dhDey+lLV0*bUq^$qD|KJQ~jlv+SUF1Wr7xI*v5FC
zGFv?6sa`sf@V4Sx6Zl1=6MP0FKv8)BPf=n;?Ec|6czE7h^xBM>YP8U9=M9WXz0R>>
ziq`o?W(Zm*fC%)pAKMU#9%p0MCnh*tB8RIfCA`WgK^>14H?>^xsgC)J&jtHUw@UP}
zE(>mL9XHX6$*gP8cW}35RJR+<1c|ApxV#fP<pA47VzwZbz>N4ov1_h(1vxx;^6t<*
z4AMEVdS##89cu{5ORsy+MIfjA?lH2p!3dkM;*GQ7KH-dgf2@y4j8Iu4jopW_LoM+<
za$JWU#tntUnaF4nh%?x_(;&~n>QM^x5$bXE%i*FzD0fz?-@n)GCJ{g%+fiy8gYj%6
z8z>hRUSUTi813P!1QOaogCI8Fb~cx17Z>v?&P(t$JDsR|bW#<@TS4pkS^)E0K#?j{
z7kwQGAOeuY2XkLlAGBk1Mca~P2Q$D=V2u<BXOPQi`+Hmem~JD3PdsvL#y%!-z2cM%
zy^CE?A)N1mpH5R}S9&uKw`_B#CK6y@m<#2V?)L)mYDN=%Y9^9}u7zB>$4}=j=;Q)9
zQLz}~8@vIqQf5r;UB-&EtC69o!tm92#C&5Mlv11#!HLTwuv~wi>tDh1NDFj63$vK~
zOb1}RvsiyZTAVMWoySSE2wAV=s`H25(&Qgr#TK<l^cOi6N(G<35-skY(i@6@QM4B^
z<kSVdtCsJK_YHzFWxTM^ojd(hH#Q9&PsPU0vKLCLS3jD9C|vQq6(VwXE7-(nwmzbL
zk=2FKSu}cs6D^{2FY{AT2&+DVAJ2RD=W=;H(|d{#^*){53mRh=sa6(4xdpek>G>${
zdDh!s`jcd|+tTD@xtGbo?y802I3wo>-#7^qo+7!_G#tbePhhRs{D>W%B3g)s5!|dC
zf#z1VGdAG-5_aCuNmit=Fess9o6T<g=O$1Yzbk?U!E{uxV#5aNI488x-eLciucd4D
zB>381o^0YgW&)YF`@X7?CJD}3+2dwug5X`v_%UDDde>#Q!1THsc}MIL4iY7|wpsIx
zdQjAjz)Iz!xrryRj^!nYpYv*gEVVB&lie`RYR0?mEJBV5y#$9(2Pf3#$nH%auH>UV
zCa;>gEkxP%;Z$b)D?w&0Yi5*TfWVL9T<?}#mz7~a5ju~+z(&g3VzBvE2kU;DSkboG
zW!-ccqdrsFxCoGkAfFY_kInf!Ssb^azCJ;(Zu-nC0n6&R?FhSaM)B&ptd+i!K}3zQ
zamfPNB~CEdu|21CNB9*6_d=n~!RVRC2X0-b2j&`j_Q`w-Kj%?fSXQpKmwNLHf8*Sy
zh`RiFO|pNWL1hk*kyR0afz%N2T&gS2d~9px7f58+*Vl|8NamLDOdWRdSmAhJodM!i
zq&X6X+T3B!;Wl*t*b1%Qo47Uik_tvLGVaDy8+VSeb<N3E8qjhVc2vEl{uZ-_n9-2E
z`^0h*0dOYftZv-!n)hCyF|RsJB2%?=WZTA!pMpTjSfE<L@Y>FJ2`c`|wBR$rP|Gw4
zL5eN2T|qsP>8MEEGbpt-F=)F}EM2m<Lh9{k=iy-};bLU;;3H4G=wi~s27KRd;fY7B
zq9oLGl+dzpQK~yOcvqGh*&?0v;p9-na*SYo1-U9&Pl7PEvUkFup}q1(AW3FR%oyZ9
z>10QJTodTeRt2x5$Ib%T)xd!C5#l6P*i=w{LZ-c46Wo%}%3TY)%dzej^!4~r(MC?v
z;U#$;R^>19)YQQCHi`Efz^bXBnu`ugetoN;f$1jCt6fsXTJ<PcO1dm?gtg9NuWf^j
zbv-{JTKDhr)F9UZd7jm^&LiIdTS(+-5djz4e@^?CcvQ019&G7Pl(=~T99!P&|I{De
zi;%|0Rgtxnb*SbHt<nO)qiDq4qo304t1J~(_G5~ScHkWu=2vF}%?J`ft`yOHcvF2I
z9v3?z5rGJMqBhzzw!1A7Osh7T`aa9rTKL9WGQn|oe6FyPXWXbK<OXF`thGWA<g?ZE
zGD`lvS#6co7Ln;90;?oqr(UiR2;vnoM+|oo30|e)4IwLKlU$;;37$n#V!}`Hxft`S
zxrooYPx3lBopy^2nKUP+)_~!BhAL~8Q(PbB?=-soikB|8=fQ&=e&BS1D<bG!hQ_Jj
zT%N77Sm;8=1j}EEND1S`tFqfOVmFrO$t!{rK(ONMR!k!wgQjpfocHuymTeF=I|U4n
zinzG*_qDI<y6?8Por4DVFGt#H?jKA*iRT;%ZEaj`d##tf*H~DVeq8I0D$zoOc<8o>
z`ZKNja_?$ycDK8DI6f9giNgz#zRJd$T<nySNKcJ?uPWzS`}=8U)5)Hru00q0pQy^K
z@0>iO+2Hd#hfzOXY6lIfZ9CYxc!}xh<z+vACg*g{`u@m-jZ${BoJap_dK`srVyZOr
zYGI%_Jg{d`DEGcgTEW+FEu5a<0?cA=@8_&XzIH!xi`y$Ayoo@&>dhJh@0>@{1*+-3
zQk6YX;32!|M`kky=c%Kc?57da3_s-D?+J#I<%|E^oh-Bq&_B+15=*QZ5&DO3KKu5x
z_OWW#%2PpLve)pNNl-p}xqjj(T(Qe=PimWHU^}DBE_~t7JQ}{Fd$6(nZsYXf(T8oR
zw=WDhT-Gezyn5^(NhuN0hjyR18g}=v{}}w<&diCrJdolQ+CDge)DJeyxt1XQ@$*@I
z-0rpNE6cy6MUYQYqX7T8K8rql@%rhRb#cGgwmX+NF{86J@CV%fnSb+Nd7pEazh4j6
z6z7Ec81_a49HvGdosE?{>w-Mqk`I5|(q0gX{N_xLi9CD#2=S-E-YsgQNAR6Pj==Tq
zBoPRSMA1(F*6>(WEcu(pMf>T-$71I|i|$P(2I1VS24R3P*QeytsfS)^qZorqt*DES
zZ|ZA`X~K>IE<Jo8$hrhLX|uD^5@Ws@x88F~-l^@DZH?h@Bd9%KYa_KS#4E=AvgjLn
zIHa)*HiB>e=QTm9Y?P4a;bM9={ezePooH_AqlT*YN42{D#YX*CQ1H6o`nT_Z=JsE!
zgqY5I-@5JIdh#Pl-G4o|KUaUg&{617g1~bfQd)k&u-UML-S0=oV|%;8Z?w<my>5+p
zqyIav(f{|8m(d5ILpR6_k6PQ(yekbymVOV*v8P%R$C8x-od2vc%&|tG`di({@B4BC
z?8L1bx)-XWs^mkjG}$wM=p!KE1O_hh(eZh(Aoa3nY&P-?W$104PS#6JpExk(%tv@)
z;yCW6yiBHkGMy55#NoB~!^eSVTu#lNH%>kMcg+IG9{Vht$?v3Myj<7?pWPMYW{+KI
zV@@8&y}5kNC_zo6mxsLIZ@GpW7yAAMnyR=|5}ymfT5B+uYRV%O=ZdRbh5+BD`kx)Q
zU#g;B)Qf%r5=kp68}(ac8G*N7xqs&&u_bi2Cog;K4-&=tzdU|E{?t+T@am#*1R^Kd
zUQ|w>cHv)(JIte^6_-MlQUgB-UAn*Nvh*l3=Dc+6K*j^Z2j2ytrsiKhSpOGh5S@v;
zIh~5wjL-ZrV6VE8@ljm0N`6?z^jD^z?D6ooZ`FCSs3YEW8f$YRnywrQhJZ}3zd0>c
z`NQmV^We{GQ@}HFK6ROyFFL~=%cGTYI<n8OrUTkv`^lV)Z2?xJ&P3zhRyscCs<P7e
ze@zJw_Kn95)wx*w0h`wmm$WLsWUn{x5(DR^j}eS-P4<@lIM;a7AUxIb-IwN*U$ta)
z!bio1<99B*j`wQ>g#YC=a;C4@LattZrw<mJ`bl2zWWCNY2iWW<HUA42yzjoOP~U<?
zSiUS;e65#0JAI}2PX8jts;VE(y}M3(+lvVv$@=_y@{872dhfK>HH!P|e+*J4j02WK
zI=XBOS|2jeve>$`<MxAwR8;qgkm%^|!^1Fe(ElJ)*Xi=B%0JnQ|IK8#hs0nhpYd4>
zfhv@!vC1>~TNWv0Bkwjsu6x<v-_aEvO}z5-%<s_6Yl3C5I&H9|P5Zy<RKNbNi%sX>
z?3+{ku<!+EIm8E(HakKF-5Sv+_7uAnNe9%?N7OwQFC+9&t0nR)_MnV__p20SWSZuh
z^tWuPOZWKOjg>nr;QfNLwf4&w`)7=Nk?lR->t8!%oQskS+{k?!^UcFU;k#FR|38)5
zKh>9}yADyd2El`IkUxljTI-S`8htgZ?extwRMDVQ@9p5J!^or)ch#*;!0|U5^)L@I
zW-s17*5*k?f4`)usCPR1k(Ve)=dE*A@>2O1yB&A%7p&R0sj8ZhIH!|+Zv2O@PsE5F
z>Uk#rPQJ7Td56(KuVLb5g#B0xtAi(tlF9oXA3eKHeRs{eS88njafO`yFd@Lo@MmcG
zSFzEWyN@vcs^l&j`2Q>Cl3ywqE-lmQ|1QHPr_r|M*h|;4p!hUmb$k8u>#v${4kM}t
z?g6jQB+`8a#=Az}HY?TZnVpnW;orgUepZhi|CHr*;AC4idc~p2<s#tBox`VRe*b>W
zVg<HOpJ?YBs%Q59FJ0HU^U}3~>0GpUJ(uq@T}K8tthu(1`I5QLpvBb~y|9ZM)EN>K
z$J%!JiH$!HfUQtsORmxH86RtMDl(BygHG-hYx$n?&9Ki2$vggnfP34Vx2P8PwN8I;
z4U(YJdpCujbpapuu(3U)dqf<e*9#j6CvN-o<WR)tcM#_eHkF+h-&F*J{H`KC=$3w&
zEZ>M$$&E0RXA4B9<zJyj{&nx9^9>YhmZ5Llu`s`Gmw5T}e}6>_BfqqDXhI0T?<fUL
zW^4QZTl-1+Tf^rMR(T(vIZcO7<pe!UDiF<85w$-AHPCvkwgpquTj!)F?9MK-Sj)Vm
z7esA${Tb%?KLALiU_aMB4*SO`={q~FQ1j!o<r()V<MePQ8J;XhzpJ@sd&lCo&E=N^
z<=-cd-XFR5$p60oe(32#Hpk~5*$J@?FRA|bk3G^Q27IFET~B;Go==wourDj~^St<~
zEZcm_>2F%j_`-KpZb9ha-V5TC2i!<|PxO4I%3}SCwY_-Nw~6DIlMY=eGC1Ph7#z23
zpNf8=ZJj2Uruf%|j-|;f<rK!C-RVzf6{4$p&fOn)n&R>y1NdCL6MUncS#Q67`uX>B
z3r=SR^Pc7Wzg_?Z@2BtEfy)z*mxufFicp$h4#g`tI6X;3HjFuTHNzGBKh$R&S6OmW
zwYz{kQn$kglFmQq(Y=!fez49w+ZgVybsG%X7If%19;zg5Z*oXJ;DrMqxeYHNIzl*?
za^_;CM}`9cS!dIpIl><jmmzr}^mQ1)Z0(FTiX>G(eme2rtMUQf*H7HlIFt>x7OU2q
zx)~ghX@UaZ{I5AVhk6Pdx}sJSArtfJS}fV<WX20KY0;$bm+AN#oZnB+(dDBKRW;>f
zudVfF`mGDXG7CM~t~zIhd|n(yj|&7<3;I_6_1x-`RD+yxBU#><j*cy-h5KJUcg5JW
z_NMYtm!!+ri>^G*R;oQcX`@l|9br3dz_=cQ1<nuOO#CmUT_$#XX2I_n$|JAG%RMd*
znVNcPgUf|%EJ}=5xvIpxSM7Ebia)v;HGO<3snc4Z!ypMVKe5q<^O(4?6hF-oaO2nQ
zl;t}(z4`l{EJuVdVKxu4e=ej8U;L-};Z>WQlmQ!+RP1|`OQBltwKSZxZr?joaAp1M
zj2%d5%Iu23;L)PBU9Tg(x4**fXs%tfF^C*WTcAa@J^Y(3Rq`umj3HeSW(&3$zvyxD
zOry0%y29XL&mx<6(d#yo?|-1)R3xVkf56II{;;R?yOH@lMe4(q$Joaf{daWU6g1d<
z(=hUD&%W&BJr20wo57Upy7H6|%hZ&>(%;|NG_{VtX{1mURKp4UDE7~^r3-4da60@4
zpH$^*`jZzoa+ZGk^O}p$+00XH>4<0#`Xa|+G(39m9_v=E?Y~;Z7tY3<J^jn^&8Q%6
z*Buh10HrFMfz>N>H4t}Mg#Fvp%x5v*ynC&>c{I}2&tBu6L?MxiPG?|{KrmnAH1~Nr
zKlMngsp8-JzfaOLeMl;u;{qMmdwhy7rh6qwE>WMW9o~4B?kT|G@|*DOx@faZJmMTS
z^4)j;<>h9v{>y(tE0HAsb<yaKFt{h&y2UtV_T@4uS^ooh$0P2}q-m+Y9aBr=*2yv_
zQ>Xe+jM>jSf+~r#%HIEmC0hJ-RrykBuFjWJZdT*BTS{worrxM3T^IT*wJGV1o<nDL
zP3GJG?&@J_8N>i#)Mxu~;^r&E6V=K$;s@(zKf9P19XSivpUVCQ(&;_j;+-Z?ed|L0
zr%sh4%MMoe>|VdI6W?zh48Putcde>Dar0E@UcH=-*`03coj!PB_$|X%vzpc^r-5ZV
z0S^uLr}tNXpD&t@Lyz@_eU5qwtUG$>WuK8<^L>Q-fM|>E#FY@~s<ARH{nM9TobEb0
zL1jeTSo-O5ETkdz?+;l#sA_9#|0IzLCIaf}Y}YPd?B|PDIIB!Ou?yJ9JG3jXB-dFj
zkYHT!2eIRaOmg)=^qVsMKtXLy9X4leO7%$2gT1{RI9DzXg%OnULP`I(k~hVRu7xtH
z^6OJ&ImNC;;|mbx+3z#N+N7R^b;+~GTnp}LuF1J;M(%l|GRJIaw-&pqKbA#4EP7Q|
zVO26UQ2%rC4XJVWKK<OIQdB%)*(UQmuUlLkblTJee7b(hFYWC|EuKjvCf`D%L;jvV
z@2N6rZQ|ur!4T)HQ<}Z2Z>zoA;_hsxMG6vSvXLGSJ;bFOe>i1VEh2`EQ=47-?<l?!
zL%KV!-jFo1B5=u+JH?w<kIrf(Yd`+{lV9$Z%K1w0lTq+QnL|r$(^vfZBjDuY`FZ?#
zboEGcc;jHB)3>)6y)gQqG@p#&xlh{vdQsXAMawSP8C_Dy`DZh6f+~v`Zd(bEoQC#B
za~kFv7g2|ShvP9E?^^g>6TVpbvmvs8adxB5Z+BihDfg#P&fhw`x=H-LUw}hCKRad7
z*9CXc^i~LX&TaF3L%2rJ=QV2gG5mJ(u2#{rbJe%J0xQzhoGe8^vLyoLB+;k>i&#|2
zw8NBHE~W<ZKG()SWN&RInh{@(tbjl5jOn}W`8RI-Q7quE8z!|^9tZ}Y+Vtgq{dFGt
zd+?&u^ZeNugY?-a^%>;zUYAcQTx#Qf(|3#Wf%6&yz`OC$%?g7nGz*Uxmm;$!>RVcH
z+uQo-vL=dY=Dx!nQ?ahvdpZ2o(tI7qVsFzf<Do!E<DS6M0Us6S^=p4Tzn8Q_!5rV!
zoKAm!u32Q4+KD{fPSv8W8@_UV9R<A;bTXPHyfpT@-;WoF+qJwAA&ft4Enw~Bl>6#A
z6}X)`hI@U8Z8=Jtm^iQg;<$ZhweahQA7~NkG|M7^g>m(?B%9;)VS-o6#S<!QZ-3nq
zkH}3MXc14Eh}Sxh3^^vb^#<UfV@#*%<5x)$i4Xru?v99#g%y6T`9MEW{;;)OO2@=K
z%JI^9+Up#T_y&i6Zz={4|36IqWl&sQ*ENg=0>KFm!GpU8ceh}{-Q5~@cMI+k+#$HT
zYvWF1flh)$aLKoG-RC*=QpGQ-x>&2{UUSSLYwr+PlZv|HGb7o~O8xecYnB<pVJ*2W
zZWOn$=#Rp%Ms(Bt!~A|<^1=W*c(Nf?h_}|g)%dR#lBxD4QfQ@EV-C5_C&~&)u6)|G
z*JeIUGuF5Ep|Y(@1fAx~IMsvEc1bUsf@%8^g8#xi7f+)-wMpM67+mQ)4SBKWyvprd
zqpM8x{)3N-;WNNs$YLxA@<5!Ax@KcPn#hs0ljeJri=x`wU2V?x!kAn8kl13E3F%fy
zG0uH+NIit|-o~oA>e^!HCaFT>gd^%($nPZ*+>~!eCwpm1obfh@Rf&IiV^ihxmTci>
zbl|R7*0_sdov*C|it@6|^c*q88k*eP+rFv>T`}y|8&hT3St&HB&7K(SxXWjK$;qhX
zWfwQa67;-$A!><{SuWUdh{60QkD9R3&Nsp*sZ-WleKQy@+!@6PblTR|e@C^~<p{pQ
zUR>Loi#mJ$8ZS{T$?m-9Z{D-OrikPUy^><wN>cqP3f`IGu-kd-*9~n6OvaUcV%|L@
zg`Rl-=zv6AzHj_he<NfxQN{|hlgG@dvo%Bp3#PFL1Nd6Jrr)kXUy|d+;CDDhgIwZ)
zmF%^%$Nrg=A}5Z2+`i;K{P;I_+hnfBfqDv)<G8u%5Zi2<PGh<;`tUhb?T=-!MMx#?
zsmS_vt11ETlBFF>2Y3ooDIqcZ%p4qJV$wbkgi1BG;=zpas11yk`3<qEV^_ZSR2v7p
zAmk6V&X|XKMX7Y`aQPCnlU7gDoKJpu?FmPdlXR4YV-i8U?2^%ZSsr9GL>7Bp=sc^m
z;IV}G!ue>M2uzc&dRz0z;Q4ml1IsU9)%FBw)(T!9pn`-iqm{q+^?{F$zHg|c^DVk(
zqCcr_PL&nge+T_*ZupnNyJ^!sPnW%`2|?$uuQ>P6ei0HN+HH92X*GBqI2pESxW%-x
zm(wI8LN*=KopwVzZQ78E_z#fbCx!Ma5S!kT7ConNQ4HKHLW{YNoQe2+(vfrJgSF(G
zCZTci$K%SkI(_^uhTp5|C?$wzO!wVBY`wYEQrVC)QK1nde0nSL#YY`UsVM=$gq_8d
zzA7^b(d7ci{pOIXsK`2<Ce$+@9m0p)EyuMgKs%G`n)Ny4H!&q-a{3%oZ-6E_^;}q;
zQA%6<&M||RovyTup>@TA{csSfU#(H*5=JAPAKQM^5k*9cPv&Zp>pX|7Q~zkzvWiMc
znCDd?(S2M;%B3z}t^V_dcqHb$fkOs*#iiflljhSi`#(%T%EIs5Nt>y9r97IamG59Q
z{M7WT9^Jc#@$vN(6CR?&^5ni7X!)T_gl+fc?XE8O`SuCb-rIVMtbUPPsV{!cA+12q
zqBdi%BWFr4Vv}>M6Iu7Ye{S6Xsn!K@BWO|0s4mTpj1*m2#-NJ+A})vDVu>lz))|W<
z)=DC$;nT75IVB`MpAGC`f|;x)mlGSYMTQu<JfnuBnQ}U(8Bzp$24wPeY;bXSsSm`d
z=t?vNp;z-t`le+`8xf2hj;Aj69Cu}VD50<GBoY+v^F1&fz%q8*X%zJL@JeV?xli48
zIv)rFQLqyp0d*mSzqyBO6kG!A@od>XIUg_wc|XPh)dlRB{dE6;APPXf3>iI-7|l7h
zRjM;k`VDfJ<-<5lQJ}s%&1|vfk6|?1`q#~+y7NCr;?i*T=VVQ-f{RFJ%`~TallY=>
zFK|TzVNzLM@Zn8p)cVNQU|!)b>K{3xnDJr{QDey#EE?iM38oLg#-u&L-p@AEDPVHn
z_mMFoN57zpri$Jv!*649-HlLG13vxbwu(mlT@)3Wh89=Bh3x{Xh(p0hG+tCoBu{>V
zOV5JGWG`Qy*0~>Ro_(LvSa?LcHNzOXx_XUEnI;!=>}*X^l(&BR^>ZL6KEiJ%Sv+!@
zQf%sW&Mje!F;_04<;6iu(=d-z=cR--JGV7}STODz(Cd;B+;Y13Q!x_IBvFh#ADvP;
zvdtnecFGx9i3x1dny@X%=`PbM{#KD64PE!6@>kss{|p_M(~VEIErjn$<FH(9v)%?K
zeU3bgb3^fuPd?^91G@PWMJG+mH48@<k8`oU;<V}dDksR3Io5iO^q|Q=w?A<9wU=`M
z`mcnB_`R4jkgrcj7ofSxqrz1UksCgTsoxo7l#@msVH9-Yo}@R>E~>HLA7*?HuUbNo
z`9w#HZ8xnRQclIbVZ_YjXiRbR6O}k>MV5D(jSXQR3l1X^9v`|`g~K1nGXAWjbiKg+
zELW|d6r>5?;puBb{7rMk^{X=b#@<?csoQyHf-t?8h9%q;z2>I@8fTJtcD0HM?MvcY
zJ(B%l45GI<_|=%y5igdJ0Jhe|S^O#4T;$~lEwv=TCgB1gj{@uCPKRqG55z09%kzAn
z7r(2Xne!0b^eg_O<09)s+1<Nt?$iJF<CP)D5#~KYcU_PcXOd@XVW>CjlP=AfBdihX
z7TKk1=+C3SEEj920LRHX=|5uJ@FR-red17gs1b@@CPIPaEm`S$o(W1*%Gk|V7>-LI
zHAbsy+Hy3>*9E?Jp8ZzTVpf<KSmAV@f9$(BnY7uHz0qGt!>+2rN3o;mgZuTo1P8HR
zmSz_R1XzQ$W@JRwbS2j44By~}{^puXNI8Bn<!o2e9V@KHhk8=Rq$E)w&lac56z`XQ
z?RQ1o;&SPC=c@BDT$^&|>OID=ntzv23_^L#6S9>dZWYfqiNiz&D+-@UZtVyh{Zfs!
z<P`z6DWnpRl5i=IFpD4UqlE;Wp30%dq~|`!a=$#n)OYlIT1vditZN_4GJ;#XPz64`
zI&%B}O<Z-dD0rE{+?;S-KkhI16V<f{Q3;UXCc%^Why7@o<_*dL%!4n*9A)f5W=#5u
zdo*E$&xDNYp2Ad_!ed(;vV0kt9{Vj770={rL1AtU_W+K>iWKTnz1S(?zT!t5Fp9y2
zXtX#yD7dIGP?=e}p(sU{9P~^4sGR}o{?5Z?Hd=Fo4_l|WIn<V9mgdR|Yab)Qb6yp@
zwjAFl{&%P6)CAo~%cP|J^iuhmQtn*Bf()(v&tW8!+>$eG@BA-Bv`49l*;HjX3G+pg
zM}~r0_z)WtNiUbRk`G6VI)o7)0hPb|;V9?d?*q=wmly%hv$f0!mkXrbl>R<A%_qaB
zUPZs>%U&Z_G(VAxKt;ZKxeej3U<;+SSMMaG#;;8e2B*HCVMNkiUJfW*Kb<wc*R%Sx
z`;`N97aOFC9uw~x5Y{J<17`jDQ?gZ?DI@pFFkX+zo3qG{tG>wgiz+O3svBX2vHQu*
zM^yw39jQT0UADSdHM-hFI4av>VowUsYO2eL->Qtq&d<#_$94phprrP1b{v4xqk>~G
zk&pYuI<V|p|IHVKa<$4z$$3v9R&tu2b-WZ(0UG+?r}nRWF)Y_E7q%&8v|&NEBtdd2
z^2Ob6=Fz#(uk0w5_c8Vj+}s_irVlJFuv1d6B?0bpPiYP$7l+Y~o)?ndHO~C23w;#v
zl*7IW>vSOnafV{>@{&C=GLo2-)Wz9Zw9B8rv0~ftdc&^%GYOi@%cHyST?ZKC?A-tO
z_^5u}s2FbUxTtIqa){967375Q`tibM7w`ZbO$8Usy!I|0;E;G4rZoGL_N5}#^}T!6
zzTL9ooacfSP8=cchIzKWz5Bcy8C3r+fbiakQ`c!|WnCtSb^7SC&~@Vp<04~y2bhV?
zcA-rbQ9Vr8cU{3w)4e-8WM(}&Oz8^$$jgk#I$t+Tx>z>uJ@~$6qFtZwKA+-GxR8>m
zFmBpciJgA?=|)Sa18whA@l!#T+HR|QfV&raA0K%Ym5!ejKy*v*uY~Ca!;Zm}at3Rc
zgY$@Uwku06IZQ1XFu-j=D}EabG_$qThrGXhXiv52nnNv!bt8W+f1ZZx=q}<K8)eKO
zT#>jGo|}+G7Ieb3$k&KTsfa34MIJ1Hqi~fT>AJt;LLI_pZ+mM0nF)bFMhS+xAUAa>
zbhUCn-7j^6+nisKy_7X`kIQ}Y|4Qv5An=O$qD0=@Nhb)@gLVQ*|Gx9WzYywQwE(}&
zkZPS2z|_AHL3r-U2MfWzqF)$|TH9?|khRV_S}l57d^LHFBn`eB(%~9@f7b*30L;XF
z?~qw&fTtKQyu)aazLYBAppu1xDLq=&G#MON^RtuyptaPXR!I_DJ;;(@^uN>?j7dsF
zP%);(Xz-za^}r}`=e_Z>9GDw)Re*4pQ1qUN(AW9D!Lfbe$H|1RVfa+yudjX#MI2`6
zLB?1Rh1=^8%{AY5E)Zq9IUdh7eV0(Z%BN_#DfbPxd(Jy|=eapz6oPop^ilp}b&ieI
z76BK-DleUlVCZD-)%9uScqB#MSaD}0K={Tq1XuqWJ|t-QmMX6>ly1BOYB?&MSu7rv
z0YMXn(ipYwi&!6vDq~8b5d)vc0;iAb`x4Iau?sEY2HXuKkF+qGU*?T+H<i>Lvd=%<
z`7Q^`A0Z2!i~p3SG0xY5cU$uQ{P=1Dr=vbJ&nI5~zUD16`B#)W)pY+<cW!ikyH$j2
zQKX1eU8Z!Y;#{pCcvDQyTYntu;qZ@($@31>Q!AGi`%ttUKh@G63*LQ0oV-qSek9U9
zXs25ZZHM!&e~|^DlV?fif`cpX3ZjWtDmG~D)0#s|cEvqM_=ygGJSjKh$OoSx52JGg
z54oyoZgg>lFeiVo{G>k47szv#x-`ZQOHr}%k)fh+pSwtC8lDnEl0JdH-gnhACYCP~
zPiQP8;$;|04ArIg(@M(x<DXv~?J~*BvS>&}0hj+J2G%NctE=E~soaIxwzaEkidOg%
z3G#C0smyf6P}=VQ#0{9)egK}Q4(1#ShJ;3dr(Pfu`Q1(9|Cf!wf0tn$j3na)=8bDS
z@fIMMeuK~g40>_lE%Ul8_^~*PqTIu6{$W=krW*wuhN3L|BR|}DXyroGd9Jc_W@TsL
zbET!+M`pz7EpzLujO0A)zH7jOGT=$6@<;Tj*oRH<c-Tacq!q;T);q(6(#nl%6K6vt
zIZ!F13p>7sIarffz^_FtR_SL|z7b(QG-!-X3YjHJ(0togdCm)07aBE}fU0VW5xh1Y
zF15~(577T1_WX!D%VE@@bB|xcNJ>aC=I`FZL2R}<ht_s>pa*1sc|n2?=SM3mc)q^A
z*dsmv>6xZk=)k<ef{(vdla7nDSz)Y#x&DFkGlr47zoSIQ#Fba2L5`j;<rnoNCIdgK
z2pp>V@jdj(YP^M8;~0FzEAbg`DzTQHSRRSskpkPLpEe6WE2YwL5azZNiiO^h%ezvI
zpbnA3%T$Lm)~zV0hQ{Z@YzjD&3{n+h(^}m+V-64u2+;a4bBm`E@T-agx~$NP;p+S_
zHPZs^po*AJKB~)w2Y(Yi#0Sut#)NO#i>w>bO-pfjoFL{_<-;wQ|1tMEYB7BPBXJbQ
z^<GV8r$}vh8$t!^q$2Tqm0o;>OAhX)mMfu{35Tj#o<juWe=m;XIpmmdC;z3!IY2I`
z$qKR~^-(|Lt)Zfaw-|ayA))>%Gq;=Uwj5&Ww{i@Pyatk6XtPG5USL_&H~#qGKKNSW
zrlqs(Yq&9~Zxtu2kXIadN+~u1%%#L*c<}tNPys$>k>mw&yk<=QGWp?nCyAthyfeyH
zhJG!$*(q+~^DarMvcI3-Gz9WPXP?J$Yj?fLin4q0KdDk7KUEgKLEAD4@o2rLD8rNi
zpxlW>1&LNi)#=E!;RC6etGH#Ljv_Q?->U5B%)Vu5ZHG>%`Vc<Yi0hLT?cZTjOL=<*
ze~+$mvTT4IQTypL{(=76v2+%koVeSH&E6ZU&d<$nH>8>sinyftBzdVy!jri|Ld6)x
zqQ8xNW8+O0<$*0{bc-r^y-wM8g{8p9QDI~P`P>eF+(1)0yo^~OKFD|!$iZUWq@&_H
z+(_82lN-^Z6i?=Jk}+A+nVpY$CD6kZvx%2O&1>J<l%v;Jv&M-S=KMi@ChY&18XEfc
z4AK*OoZm~GyELHCIt$R4yu!j|n$?HjOAbfZ+YSFv{8y8(fW)qk_rsY8nT0nEVe%%a
z2;Q)EKu=Bz^N<`dS+WulE1v#jmabPc*^Qvmuq&Y%T{S!=@4C&2fhW^Wa8%`);qkXZ
zr3zl;oDF&2k^QFrH}M#h=&Zg(zJ*?UEH<Q=*@^HOx;+@mK<v^&Z^P3R>K*8Y%+F=U
z%<0lCbnYmH69}4Mq*CfGAAh{9EEXO;mbx9X9z+hM49#VifgrnD&ls(v0a4$;y0As;
z64m?gymiwdj$KkUwYp#7Xy5<1wv8nm;5vZCDEt%BEgs}dry)Z{85H<b_Bg&!XuWan
zbW7SWn@vEeS|uW%+5EQTM=!>TZ|}ysMxxl@w?<;<#Z1^szpQ%KN1bb_q-mrcm)AXR
z%RD$@m(CIKhy~MWAm6btCEb?e{O<n!JM@Z3Nocu`V)WNDMoE8&_r_(+)FKNK!&wQ7
z4UP<4=~_dJ+Px#;$8WgSrHkFGit50~v`=~((~~!j^Lv~aUP~Yh1@D3VJ6q22+=s-_
z6YEbG4~=`apUXu-_}}(t%lmaj7LmJk?HJOKRdM#bM^@p!|NEW}IgH^Arxwg^$yk)R
zi`XmVNo>ew`W#9Vjp6ryu{^309(r-&dn#ju%Ar;T;4a&Utz{~A(Vl|a_;72cA=Cns
zF83NGoW=$@KP0`DwTy;OM8c7-LY5!he_YTbRy?+F@h;p<QT}G3l*eai#EXs*pw57^
z`Wp7RqGqwq9`6j|-aP2erE0IVmDcl@Oj7H_oj5-8%CfhyAD)A_Rw>M|c6sh)81T5j
z>SyrjvJVFd;&0iDoLgzaulQtX?!vEaY?xYEMb_5V>Zecq_w-FYF#Y~iGQvTqO2p@-
z`$z4^q<$pi4)SKTjsiQTYZ9aqfP1K==4k=Lj*TTlFc$uJvjpEGOXt2HAcXIkF!&%9
zr?RU!h*uQ=uhGZvA;xv+^>ZetqMEgouabt|33G%R6cEEd*3&g@jbKxN4|bLtcZvFP
z=g8i!i|qx#&OEv-*^<v#p(3JOjIc6{scO7Rk3D`o26a-*(`(FgD=&r<iSyDRHA7HO
z?D_9OgVA7~wMf^bP)}eLGG9qe$_P$zBf#~acKohC2fVBX=7ok{&W7sR5s!V)9-sN&
z`SPlbP;XHwhf>YF8eaOQ%7dB&Qsc(&*5S{UlB*Lv)NH&u=|kwr1~XYtZbFpo66HjL
zuF6RClS)k26~ke4`-K?)@ZM&gjtY1A06px~P1BIAJt$l4msOd&HZ&}*Q^fMjpvB|U
zOr{cr`QKk7jCDjX4H!%leAe^)(k|k5o;KWj%~T0SQNF9LT)L%0kJrxX>0+YpEi~LT
z?maXSB}CMPpO9M;LHoLPuzASsLove-brS7wE>SI_GD%bWrVwGBs+WtFZ84=VS^J({
zbje*5JJBJ^fsc!Re~QVZBzgJyP5u4-YaZ+!9bNqV6nhNGd_Vk8-j9m}5VAsSGkTJ1
z>^{>Q<O|J#>YxL18YPq{YJVOXM|cebFmlWxbQkATv@}AI;jA-&;Vd0h4hySv?iG1j
zn+nG@VfXi=4QZ{Kjhh&;I97oGs$mC2^imzZ8Zb4~kK`wqQ2g=!BLkRA`FZR*Pd;Rq
zYjdSpBFg`g(mj5_Oe=P+k{zxFKARhJdVc)0%SLAPySPD$T61r8n*5W(^!mxhI01#(
zKifz)FZ(cx3;GA@dQJSEE17TmeBpSS0y+sW4_$HO7m#l66yLkEdB?Vnz`w7O6izr&
z<-<Vs=dP#w`D)5+CRFiHfuwP(;tc<VM1R{`tsoJ&0Id6Mc4%?%-P=I?d*lV9Adxq(
zlo#_bLThAiUPt+^pV)VuL(Vx_ue6;~>O#9)vqnrih5@myF*nNmY#Uy}22gq?Bt@bR
z+`QVN7svQAD?;m*$XSEiI+Hqc%Rpi24@HJ>ms)CKe(4fFi<N$dtf0$x{c8Ch{UwPT
zeJo)s5vIedN{#Vr`zG#fxpS(*nz&PU5T6gXI-RB|p0vGw_FkohaK2TT3o)<ZMZ%y>
zrGb>9%az`4SA>dX7b}2vFtf52T_G|hQ0r8+Fp&5zpJYRaN;5Y_bJO{G7y97!J}7;?
zFm19&!UQY#<3ksPi^;qC<Ib&4cRPlpJD|Zn9~!+LMz=p%7~NW6`@aveZILG)Yp?4$
z&Bf*k<_Y4zc<LVua(dfKiH#rVHvG_yc7NWF59`}6!x4P<6h!tWfF<WPU#*YP*PlRy
zJ)*x0){psuh_W|O_e$3(r6#m{<KMJP{G?!~BR@Tma&-hk7w`JsnRHZovn7ik104vP
z-DbgRRW+oZ*<vmnr<Mz=G6*kTKjdNzq;@Tfc!&ZNc6T?=a6cY8Db<!Q`g0%Hk+E7-
zt8?arN$Ct()f-spAxP;6w$r&kEOt2ppe*|ui<rdzc`A$yG&mx6x9T+JqZCbG;k*N|
zYTHF7W~iDi)sVU8(EoV>GVDYQ3O4}?B|?b_WecQ!c6dwTPf>#}XCeFQNDx8k@MI$i
z85)ux6$wCPYiS3XSj%*p(L~tb9c*B-5cEyon`gv}>i&YSYy}M8vpQ4*%b~ky9P>9%
zoV4dMKEkdjypzH_Q6TiXdV~OO*QVLf?v+idWAgg{DB7{teO){R%o6V);#2ZdO4)a@
z-;UPx0F#A!DfgWeG0|#d%W<YW3ARjSy8!M3$wHaPJ5%w0bin&ums{E_-mu?@SuPu5
zN{t|y;aYPkuuE?tF3e%chv_PFsqW@k)^tjwj}=8cj^9F-zr3w3Z73iWiR~XmX7{gv
zC(z5|u{ajYLO`xClIS+xMGO_aV*XQ^MsY#hti<UNY0-8hmq}H@cLJ6#O@iAtbzY2V
z1esdPymMC)wp*tU_V8h`c=(jZ71)+hH-795i5~Y=-D@!f-QBDj73glAno2=BF41@W
z`;~7H!_ABK-&+O-S`T~sV|iiTpZ21xE8$VUxybV`=z#ZQv2&U;BkuK_zEhUSKX%x1
zPqf+udT8<&rI8WSU({#D2_A_<c}+!iD|BtimH|GvQM#2EDM+!_{*DP&s!>{E8Y^sa
zye$f?PO}fwBWNxdIlf2ukv5XS$6rb0*xtu^%-t}n=(JY5N%4ge@G*bmM`uX*=I{2Z
zXu#_3I4kZKFF@Cq9WzTEWBEqK5ce0?RZgKC2G+$}bqnel^0Vfo0|RRkvG2*pz5Ljd
zRQ<}qB|S(|tfN~h2`JZe!`d{@3|P7Dr?>l5CM^EZ+aG_b+S9nSD1{=z)fHibJpykH
ztY~&-q7tcMJ(*bKgIhS*Y+fBj4tTwNN4BfA>aYGWChdRHVIMl}A35I|3cLxxzK@s=
z7m!b1`Tq7+jJs$4?m16b=A5cKaRkdxVFh|+<ZJlU7X<$E?2CIZ(iFFQ_vUM`(QKog
zh=_EKcU>E3RSdET$R+xw_MTOx`ca}-5=&x)zL_#Wg0xnd-1qA{0grgGL7Ig%iCeO~
zsIE6u><rpj$NNT6eXw?VQAEa;7<!3Xd-R7|u32Du#gO57`y(M{nt@>w#U-&KE_|(I
zI%dmN+F7||<J5@9mc3G+W+ml%3H>8)audeWZn_*s%k(<ll#(;!F)@u}K<wq?o3V;e
zTN&sY*H5pn!C9&|$sMTM{xbZrH{Y+oqlM;zI1ZCv)n(r?Po!zP9oLC_-!a1+2Fy6(
za6DqF{mO!k*d6!t$0@#Ny<v|$7x{G{p(GxkuDOYqGWW|#;%XOsm!s19Z0vgTD(Lqc
zT;mN2I-_)?E}CNv$eH(_vs9kO)>q~WxO?&ok)Xg-KI^|L1P(_n5E>nX>kUhw&ajM0
zy3?;PBB|c*$Z|?w7cs3SrSSu&2-60AjIu%4uqxqa_W0^A!Mvo?!#0evYvK>fOc@>^
zc2JmZSA;E@#F9^MJ$<-KXosH&QqHf=xWR=V-SUP~ud_o`m9Cx<us)7-2H6grLK#x0
zib+(`Hcsq7()&USz=9trpL*mKqj)qq0Z%GJya}Bc8si|Z7-L%3&x)48<(S(zg9+)d
zepfZ49`kuv=_mz;BKSJaC;LNUx*;7Ff_;dEcyPu?C5WS<T=BfIrzgJ8umQPeuok@(
zj+7U~3yMCa-OZSTP9(pKOX_4r@w4PP)c(;<2&~cgOQGNMEvwbvS1Q27(}W3q**m$s
z3;Ir5_6;BH*)ZMpiFEfssQx9TMt0rFV(P-UANn+5*Ymj%{itOIu#HmpBX_5}V0g-s
zzMlJyY<ow4hN>FK=(F~KW*@rHB({*{TWIjpZ1pNJge0i!Ek;%c!%2HtR5OpRI$<V3
zs@74PvUW?b1AI&pYvSH8rk2M9q|uOlrzV={x$2xK4{|1uQq=<X@N8PD!qKiqUEdZa
zn!MO415Lsh%gG0f!6?}J^D?F3@2FLd?~`$tCcn6${&O|CKGlU14?1#JQL^NW`*tXi
zeE~s)*MBJn_^+^Dd6*Hti|(2h-Gz@jSVQh^Dm}g;){ORG%|T~;!;O4CE4lPH6)D4D
z>m&sFKh+UA;t=HGLv|s51bOk=v6Jcdgb74`cHJ#VVC(zu3^ykI?<vCqv|IZ8_7px(
zSC6>Pfi219FLdyXIZ<k|9Ix@$&9Yd9wpx4EzR&Mh>r3Y`U3W|Fvw5R*oFj8(f9Gow
z9?_lUbCJ2Lfm)1%wK^dB0vc3jLC3`m)i(MPALe~*{%lW`%~doanR~10NNr7O*KHea
z&9bw4MM(6BFQR%7y#oLMecty?1;ZR|`m`=>LHY*vUl@V4(NLA|j_Pqb`v>$^Sd`7h
z=ElH4h7QTgBN=r5V`mM%jykwkR}4LWa^oi<754MG+JZnx|FJ>uW`{t;hJi2cbp~DB
zE?wIm*)ueZjMT9zdZa9mg=eHuDOD${!GDpu;h#l!>=61}>>*uQbH4!f@u3k=ADR4|
z2U~r;1G!(8Kh}Fn?eqy1_2;bm<d~C8`{ev%WB=KeMzGvvNoPd2sBsfOJ<W(Yz->*O
zGlS~rHIC%4rV;Lgvk2J#e0CKTNX5uT)mm)uQS;Wc?%!tFI!zsMen}^6R2YBSfwekF
z#`(T8W@G7+eOj|{(5=q&m5yQRT0>fVa1_g-2eq^?02e!ak))pD=l6kkXvxO02_;IR
zX}Ak9Qt}@?3?(zEzQ`Z|nl+2F!EDYjVuF%ukkkSi_DI<r>J~@zOl&`hmQZf@)9ClM
zHXe5-8G;Ba$^8Q$4Iu2#|A+I&$KO796-3ORmw@YKHO9H?pc6LmEk%tv$54gdi<~Hn
zQ4_`p2DNi{<NV1pGrIO1!6PUT=DE6;X<N=qD5v++5BIm-Ssi{a_I$IH;2Z8U{>($}
zCIBg+0-V!PZ03^9DxdVmueY2-IYqoaXDYvuqrFi?H^P_WmylG$`ai)%OGtM7e8l7O
z*dw0TsjW$wb`i*pl*2H?6Uor36yNG9r?VwW_Hf4Oc<FSgHvV*KOs^0*fHgu$r*309
zV-@crxYRhp3HNEZx+H6xuhAwUnxsIoi<q!pT^vd$87+3)Y<bwOE@*Y6)0L7;Ft7{`
zx2jb);cEv-#F~BqycsrWNhKGT3CXqBeQRAiz$_}HnJeD3ZXWoz`Q4#6saCzAP_zR%
zwzCuP7iZFhgNyxGR&+lH9DBU;>3fvjp8iP;vF}~;(lbM+jrq}CcK!Gk@Zixx_-Cu#
zr(l78tI=ma5d*Y?Zfu3SF~?Mt2A$eA!-(2Y?`DSvZ5AYe1(}BD+Ym!<OH!(CpR}Tx
z(6R^lSJasyN0|`(E1qhiisHN`Rt5ykl}6hwDS4jleLGw#CSD$IajvQhL6hhWy1-Hl
z{A%PXo5;@tZY0wT6(8lSE*dJA?6;qLJ~OA$bqbo^NL5f{9jWq9ZJ=3U9TXMQ1f=G>
zK7X72qREERTu*>0Sj!Im4Ob50vMyC%Jj?%<U*NBJRCP-nE{-{?>b$JWtg1fahk*$=
z*K9BJ;Yc)%nGs<_$O&wE0ojChzYgjxsTy|NDXBXA`YH^}Y**3aU4YkQ6LQ<C->b|@
zL_}oo<m7rV8ovc~*!xelG~LTEU-W%zNHqF?;$(sIdZ$jK_p|7;2KP2BDY};dOuZ$=
zIi1jJleSYRK{NW%aw{;f!2QI8m^COy5=;aB-9;vCNh;jl++UBtw=e3Ca!_BwGmWA`
zrRYOKhOF*R@_Utixn&7WExl%<k!h@*?%S8{b~&vdwM+f=cs+FC6nSQ{rt06bM|s)@
zCK~EPHo^<QXg!i5O}1iR!E$t+qE<>3zX=-~vtBi4V9H&G(R2i%uBn;9Lwg8&0_YS~
zO9|>)cFk&TMNLx#)Z&>0u;79DSju4|K+7l>FfXJ3E=_YL9Pmug7-CzO^Gf6B;IQXS
zdg_t$ba!6R9%iL#9uE-lF-4VT)J$*xAIXv(rkLOP|0hgF#qA`1jvQe?HC>B-@ND|^
z6xkiX_;liwu%-k#b|45{8Tj8+^5z(*BVs-u&HSIRn5kM)$w;Pg&$ty!i4`e$p1M?u
zuxW(%jFks#R812?`B>3I9i5EV;&$a1uvWBDe4qse);D9y2Pl@gC_><UTS`hbdm8re
zI~yGuF@ZUK!K5pkjo@WQDiH6rSsz)NB#O8DdIFZ;>PKQM6O}S?Tl_t1DL*k#ms0At
z)S`Vpw<2?za)#A;UitZ7ApYu;z^bwS+by>G&cDHefrb|43uk>J1o@CB{ac;z1qKq<
zLiOKxv#**u2ztL|HRi4jy<QDd<zq`25J?bJ(d7lgJ?C1A!`2WTX@=jsUL=V3wfo-u
z*2tb&@;>K9Z*$z<hxGW;Qk+k*_6c$ZXE42*1O^t&%*<r9faD(FF64HNVE?kt`C|U@
z&oX{0_Sd2%yoXE+Jx&RMSA#?*hqqZ_Ne$+1r8Uj%=YIX@YVv-*ib~K80$UX5oIa77
z7yUHb9Sb)49m}fHuWS+c_dd!Yz6%mj+a$L#K=rR_YQJj?%Ggbp5{Dbqd@I98M?dy?
zUKG@-CXoz>n>UMr%OlGv)RGeO)nej?82hl@M$m3O!^nIOxsJXz77QT?k<4?;5pc}L
z6=EzLs~@C*(t?vqImVfnGd{$uoQdy9M{B_ZetMZ<2$D)@lZ_K&bT1>wf?CI=Rwr(F
zyA=}@{dgwPk+haUN?765MZ;|y8*#<aEj9J}Tc2S5Hw6-^IQt9&5%rFF&}h#h*M7=}
z0u@*XJ!ogCgYNONY}}|MgdVi-wpU=vM3OiG1Zm50O|26KkwmU6|IF*z&K+T1)J@g<
zFNoct!`lJ+t3s4lkWTkwMRaGwn%dgS)xeik&D|NY3F3l+Ny(x2mPyDv=+6?ni~W7)
zPtzHIE%n8}e9Yhxa~GxQ!S81-w+P%b^~KwMk#_;Yu_S9#S7v=g_tLv)yXRjo4Fc$~
zg#yv;8%{dFu<sjTEy%`;C?Vr;b0YALup)4NpDq^r|7Oqo5Vg(%csIqK6Y%4Ghyq$L
zrv<cKYOx2|P7BmB_(h!BvC&7{I8KGQ%)2lTZ(l=Y*+*A(%N?UHW<e=ChaM?;I7%*t
z*)R<uL5mb0I2Yjw7wSZ197;}(xucsXJSOZ>-+UR(pDuvcJV*YqfLi`}lBd%|eYifv
zi1{yHWeJt^Y`fQ#zU-+WT(}y?LQv)~0oL2#<HRToWdf1CE<#C6nu$cyi-!iEn|D6G
zPm1#mg6yMnzuZ{jq}RG#(&97D3<djmfBZ_J74*LfBjRzqxNYkrsoyUM_&V-7&%<6W
zFQZ6tkw9_g@eAMke7j2q=tS=B?k66s;`HGMyl(t?N!Ovwl-FAQzKtP<BHP!`tgs@y
z{bHNP0jDIr3$@?x>Q30>{w5-Ilg*mG3-IcH4urd3?dKJ^?3>tlA>BQ0guYtRT);km
zxIn&e?e9B&*rMD$fAiNOu9d*G2TjikpoTzg05#NrYJSFzQkpsp@~e`sw&3&j*b+`5
zTPdwGTe*WUDO#(Fp<PyIQt7ty0s?%UQD%;vK9HTUh!$vn6Q8=$BY>z;OIeGwFUOMY
zRGQFyU2r}<=g7a}N&2MIg3hT8l_I}6MsX$0A}F0ZmB=i#=Hh(DjRW9*<d3G^cO*Lc
zv`!<gQ9xEs@2F-wHd8&ft{vUPbhceC5^(N?U>IPaB=O8xef7S&7(hJFWoCu+Dts5#
z=RIA3Y#z<OK;I#Nuf1-TwbnN_2rKhM9*aea<_Uy6eo}z$fYYK`m)UW<Q>x`ruuUYv
z3=jroaHRCRJmQ@m%bW)9UO2A{(*K8!vh6<dn4#7kQ*iWQtNdx$$=-|)yUVX9`=7u{
zB~%YRm!_dOQ|^c|zl3-1N63D=k2^{|j@(0%M~U&&&p!uyMHj<9=_BBj_qhpOdK;M0
zMqDDKnhbRC!g{2wD%w$;&GnNR>l-`nR>LKEWY_ww?-qC;O5k{&iz(z%`Nb8^L>J{H
zT%E!^(-CY)3ZFHorui~jsV*5Q%}i7KI5HC8s9oe{Ii`YLo=0#z89&7xq=|3AYkzUb
zpWMgu!BLG8ZH{^pkAPN0Q&Mk$LW*&Nk8>x%r?k!_ak7r{=m%=s?Fn5kVZ1E2J_FSW
zN6y>6t**a!RB<jRlmn81_>iIhjYbGLxg1sz9sdpDP$FH-h2Yot`1q7HI843|I`c1j
zl5C^jo0>QqUE2x_Y0qb8(aByfA|Lt@gcG~Q^{SV>4&r&*U7-n|UZ)d^Pe7Q;F7}Im
zI&{lR-wO8Z3hg1De~46F+4MfP&vs|~{SP&!a{`QHvH(JD;?V5~OTA@L#Y$@hsX^+x
z$Xm&|gi)%)_7C}=<ONWuugX{;SIFIypuPKbKw>AuY8$w8C5h;zOE@;9vS-P^ZnriE
zjnt{qD`-CR0&P6nMV?yG7li$1AE{eD_?*`b84vYZlrdhhL4;OXRxt!xGN@Od(m`~n
z;zrZpLacf0j(!_+Y=0xj%50sD>9KJyb~yc%>=Ei==dAexth1}DE0Is7{P5x;kycsl
z)J7lF77LJ(J-!(LP2bSdGZQKDY|?v4)Q1VaE;H;kY+gAzIf*+l1vo^Y3OI;24Q#Vw
zLN&*4RbyokK9in&^0K?jd^xga7n2v8n{H}ySKJ@LE~T-Y&&8xpn3<at`*ck(pou{v
z#z%O?l#M0xE${h=hqlBO)$w&mNtuUZa~+&!@yH^PDHS%sq`K^mRXRo6JBG>V(=hC^
zI<KzZ<~+~AdKHr%g(Z<n0J~baZ$q4itIR0p7S6)k*4Nt_pcZyA02P@!e-8W`KXxY)
zc;p}dvh4~ri<@9p_5vny%)Lh-FcjTo0O)&DZGKa2D)p=D5Xcdv=lR%5odFk^y)vKt
z05c+h(&GLp5ENLHC&X=K41#JJ?+i*5np{zrZ`5L=Gt#brdl93uOFz65q6g^GG{S{h
z$}%P?Z<qy}BksNq@(?vb)yaGWY2)=Fn$+WBUGD^jJa$GRDm4gt1EB+Ohghx+9-PjR
zeeUpm9Zjxl`Uw-8ORMn~SE}ayY*Uj9Y*ov~#7?dBW6lOI|F$X>#mV`s(-JtIh(|U#
zEW^+zIy7`*)<)OP(B~Jm-wsr-??&(887cxk-E5P&|KSC!Bwx^5ym&rSj-3Zs3jorw
z0gxW|nO4cmXNiLSu)C7@17@=tB|fH(wLF)bC)IFCh>3b#QA0LC(Pg!E2Br-el<}%+
z#PtI9Uw}+=Q8rQM#L2={Q)wu<fN_}uX{|b^qvORgoQPZX44LDvPcLP0(6@RFom|8O
z&Dg+rSGjQk4rBc-+tb0j;rO@7e9|HAC}rV$Kk^O%MO<)V%RonGuVvM6%HhEWDTE8M
zzc&=w{rJ0@)5dJ2;xVlVf8akA=sPA_I*89cQc&3X$mL*>D?4<Cb=;zZ#whCTA6Rr|
zGW=+X)Ie_Rx+NUJlSZ;yoaQUn?sS-6T&{6+bZu*HqzjIsOJWa<6~@%(9Z<nOSRKS*
zPh@tGD)G;1EqT^6aYBSItRThEYMi=aaGWFug|$XII~V>S?|`TK<5NpXjo~(f;*T4D
zvh9>Ufw)ksk>Moo{4u}^#KMqvS@$<p?H_G#Ikl|dxeoBrf?Akc|NiTAixPe0n9@{4
z=dEb3?>olzN%cdg<Ly*uBlu&S5~vLJA+V*NvfVmUspd_$8`A0CiP<6G@p*a@n5rlV
zlMpw;@mOMUCn;g$>Yt1gn$_{mR?DhC^u;dFffb7Jy4m5;#)6$;;2;~H6r*S3@f#>Y
zW94x_@A7B5y4V&=Ubyn};C&__YBv0~^9q`0;W_W-Sfl|GV-F`*A_~>@vbqiqFN0ut
zVvw7c*Y6I?rU@&NCmr;sd@yz?&bil^03bH*Gxl9EdLO1~IZJPqw*fN{UN~*(rcyE$
zFaUu|KmS)x>1os&jZEI;urjBKk-lj8ByCojD#dfe5c{ZBbiImE(q?p(8UH1$P9JJH
z6{QA=4`X8c-*LjbQdj15#R1Es;XE?Ps(~M4R;&o`hg;2fBkDCvmuLwWV56gx+-Hl2
zIKL#xu+a6qiPpHW%QSC@3H=RdG>r!305sqKG3ZsMl&f+X^A~M0l$TxMbl<(|ljD{j
z$nu(J6hjL0?tDjt`YM}Bj3vs!mMov8ZpEJ4`~KpiD$dMO!{dSitLoHMaLdY8uYXSc
zV^#frIKCmTHyAJ|t*x!`M!Wswh^^T+aib(0Z;bixC}>ceh25IhK8nZOYbOD%p+l3!
z%1huJOCUvt6ctKuFBwaDYT`q$s%5p6c$V2xk3a71zDT6fTxo*#xf8PTeijyUHzE!d
z(n?<aHpZm4aJ-Vtgu_)&)E{o9UiXxrTjxlvYv0t$ZFq7z^xAEQ7W_p%v+hm=w1$eB
z5n8ZVSZB;y#=ZbP36Ru|*C1{sp}tR`$yG(T69hF6QYpBpE{;vM<ZNxXOFubhY?p6-
zIRxLj9!}y8vi$%Kc3@DuzM5kFQmeVXvuP3Nl<`f?#OxXwtKfA;R(DKrGr;BQysq6Y
z?q9eN7&*4m8}N7TIsn<OAG!mij<102y37Lmz1vkZX#xoH*_O4e175Fu0B%@?S^ifG
zOb0;HXo`MARaX?aZ*oljm@Znty1tQVVOl(<3m>H2qeQ8>TUV4exVXzO<a0fNSU`$a
zN>b9Ie|(CQkmEGZdkUjKegV5+^Nqp1#Gh-h3v43Ck5E!0^`}|-SJS>DYqDgbBwb%f
zSm>Rn8J7ABA+lJuOht*Lsja`*$adWF&o^Mb(qQGqT*y~JE$opd5outoW4E-X8uF%U
z6qH&Olu>R*$AdrgQLo?H9f?04o}tVa@|La6QvM^q`mn)z1?#rqkT2*nK5)kQW^fc!
zpy2PHO6!OK&>e71UI)`EIpp=W?VxkW>GJmtztLl<(d6wdw^Q!}&FSs+^}gVCm%)F2
zgNDXr&v&n-mL&HdcQ=C>`^jKMke<&nuOHrA@XUI@j0L^cBz14FgxI7Tz=*J$3W&Ua
z_6GOS>VW?Ns&@d-q+~6{4tU00Ym2{V`r`+!z;t@RH^HqJWhQqmM$DZ@$f-70<y5xk
zm`MJlniEr9G;~ZbBxy;X81{d6sF7qY4|BbQI^`$&^=lZKvk*Z$Spt6wHRhMec88V}
zkHK8Zvs(&PT6c=~6W`N#<-dCNA)oP2QqA!*ojq3uZQ#)uo+x3<nRfpOLNi_jMRzkW
z!-^j+Mx)iOv?ov~CTIPL1n4KGRY#F%OhFmSm=5;<a7f*EqIUEKc7>1H?<H*Fwe+CU
zEu)LzzzAu|0@zAubaxL|!q*BoFiPg^mo4CK7jrv1yOKMAK>z`ccmT1E={faC)oPmg
zzwGPpbpvq%E<(V|TVGV4k)P8~BuaAcziZat2D6id6fVL)+TDwC-|K4lH(Gd)9o(uF
zR1Y6u76(?8Af0*zOWPmcJ;Fgit4;qf|1fel-Wy#LnzPxC?O{Y!3zB+&HfXvGAnVnw
zu%iS}QjLCVj+|zjG^WXf+d?k9Ma)CSWFZ;q7*aH=k6Fxm_5E$(dCn0k?$MY@f+WHI
z?hrsMTLr16bwZY$l7&;t>xCq#3zV^4bMcs$GK4eapv-_Bd9=fK6}(}$1JA_k@}=<0
zc=}tXGRXuyd_}XE2#h>GzeU9t+U?(vAe8n;!QddL;fc*W;&+z5;(*^XPc#Zh`MgRa
z3L>PirL}KT%cJ%dN6(nXcK<O)p+!-zaZ*b?aDJKHyd?F{f9dJbKjNzz-?YfzuTzWB
zGV*t?0bAF0xI)ocyDwl>)u%t1mZ}x%))q~!CADWh%hRa!;@_v7@FCp8@5%%jonqsI
z5AdAfP^Ykei6s5_|K~0Tnx|MOtr`EK-CORqJ>`>m3ITT|Oo`ejwNUp*%|&AaGc;iA
z-<I~RA<DKC0~Dd2w4C)*T_koSrtnZ67-~8LKlFXxX2u*r5AJo7w4vd`wDEAB)z3X4
z6~B}nY$qs~XLs9WGr@DqENXKzdrV2+qmgN*;ipYRn9!&h8_S5DisH<p1r8kWF)>0h
zLn~_rHt=d3XSq|fZAv`QI1{{jj0wgHvvRk~|8wL?Mq^M%u*o4Fgej#8Z}cqk`U6^f
zYUXsBEnC)FY{~UhEE_v5UvI2Z_pna)3*Fe>=(ZN{_LQ9|071E6Vj6kv!LO{WU?g#d
zuli(_w=3Y)v)N3GVZhN!tsi~X+HLtUC=diBdzUHIl99qhGGAT_*^fL??)7gU#J=jZ
zzVw)Ndjf*`t;sPxOe<h1hX%cpmV;LQtG*F_FMK%4Uo%R%nJGkBbeQ|Ys5spT8<=$~
zOAMsd!Lij~$Q&W2uF3Q)DB(jcHU^Ej*{Ox*`*Yk*;vtn}rf`)MyhSw|QYWmm-U^j5
zBePYwIK5wWX>S-=ceA2w-NLX7w)?PGX;(B<b|Ymf@=g9k>q!y6ul=f;|DGa>03(IJ
zu&IxILcEJJO-n4<FQPWzc>fnA+GJGrpK_PW@NX<q0@VxRHt1NbO{M|ZuZ|x$HEA9y
z?_!KQrQjIdn~zJO^S34eB*D6r)mme&G_2&zPOcvp6^e#;`H<sut!bU?rx&1?w^*Y{
zaJYuPr=JYH4{^_S`oO^TGje6TjtG3-zFBSUdX?(P6X2P*V<7ui$AJGg%=z}>Z`0kG
zSh9tuKNJewX<=?@p{dc=WmUG!Nokpw$e89S`F~yjOl(*&a=zwcHf}gWGc)Z2{H{?;
zhXb_G2Q!n<PcYitH9!c(>+?w+YD3rnZ=4CzTU~Q;!|q0Q>33YA!?K}Vgz=VTzK^QQ
z8aip-1<(_+J4<&>cMA>SvmWoJ#{h~dCl5%@U9O<F5!5#T`gC2cnC<-b-g(5rXoeZH
zmj$f;bZvIrOLYHd?eA((ANn)=F5fQRg=>e?8MLg%Gs#^f`g}4Y@NcGjQ?sjtgv5{}
zVQ^anYH^sg;&eQ1RC{?6!O)A?_=}kA)H2;fa+rBwndYK{=MtgAX%X^-t`QsKR<tic
zPAqQ6T+VRI4K&`(?u^|o^m~r2$1+WTo;9YK$}nBgWkSacTy8oRDn^#Q4=Y|>J08g`
zXOfcJZF$1v%)^$6H(T2MfN>Bxg5Ff7N*<VUlvEM{8PCrCmiQ?#F?YHOq`WSB=yoFI
zi`|`~g--<jFjMR10It_*P{_TYOo;r9J*+!?i7)Kofc4p;;9~+0JG~yw?GZ(d2$t`n
z{z=|7j~2Rz!}WA*7x~G-te}?`{{GTFLz<p=&5`FD6?xLi_V1@+vSXeX{snElH?>>s
zpwJv1r+*?kX2kWcPcl-Fn;Z8x`@ELEzFiz3{M{_8e6izfnjyh(a>Q&z$i5egQGmzb
z<JTYJhb@Apf2g?TV9VnB>8nmW4+rZeoN(I4R^mmB4PgwY9ngdkyUDz;?uq($W|>J}
z9Y)*>hJ6gnjSvil8y#0X9IdUbGi50+RuIjYJ?~&6R4+qBF-hGlir~}@!V@{EFA~PX
z4JX1Oyi8ml)PL3=NI%gD`~~3`LGj*<nxPFXVUcz&kwD5@*aR&*f9H6_kL6-0;pj<I
zoL+v)tGuOH=QNxbzxwGZL_xLb9GJc_b0MTDvhnh9fl8tK6YzSe_2^xx%BvSEsgD~I
z@AzDj)VuMxk(=yRtozMW6=QfIg)XFZQ?hUJ_nCyLZapwhDQJRC0v{i3@i*6bT|+6y
zFdvDiaPK!Vbj0l&e>jiUCD1w@b=kf5izy!dzJ7_cUvdkMk}|Hb@WpU3sf7<Z;MMO7
z$Qv;3pUL5YLeAUAySj1?MStHtY1=Vkd$JmKkB6h+%d?g<MGSq+$;p|j8`as1y*ez3
z>`schPp1!?)a>;mzNaz9DSLhDcY?W-XLt&I*x`9QpD8uS%b=|8!Gdp9K&E$h>K)Sj
z{?I+(CG}j#e4F-?=lbxDxat4h?l3yJj>Y$~Rr0%PoZQLV8_1QdWj73P0xW-8uc9FE
zjqw7c0ub*IIQ_u*>j|Mh#PilktCYI^l;5KY6r;m8BvbKOsg5<@3oucBJYN?ylKi#a
zx6Z!8%c!uf+p-u!HB5t9<nHm=MemCq{q!VV3=h#RGHIuE)M7TP%jO0G(#A8(zE@Pd
ziF3%>vDezlBjv|4Sbznkst(MPjT@LpZqONA<3H$n)W!q`ERZ{84&lywirc{-ibB`z
zx_iKT-Wc^|_DHbzHqP(Je4KoJpVsb_#qIo!AB=0I>^>7j{2NNYoSOkwJ<Gx`^dtCw
z1NhT_vN|#0#LVVZh*yCvogYcMJ1#LdJmBs4dt5O6H{t44@L}y|k*fK6`6cPD%`O=U
zrsqUTnm^@*KnL@nr(#1N$MG5T^bf~H&R9)BOCAv+AtB8IV)v(SWRmvhkzY?VHZ{b3
ztzLgdHzwicU2$WtSbj;8N^0h5kc-29KM{wbM5DnnYJ>S3&;P*qI>FbT$ukc{KanK&
ze$U)cnoHBSWO9HmQj+VPl(9QC5CfY}TfSWrLObv(wf3-b_vwhY`fKP?mOrW?tk*~^
zc{1SUnNy~N)zXMfa`aZeh}hYUI|at&>kh?a>l&3H(``0fgaE=@n-z!PHg2uKb`2`f
z3St$OCnFt=92$^ikdcj(Vho23DG|nONKli+rf`dI**bgQ(Fxgm){UJ>un>t`M>9>v
zy@D>wUo_83>4zU%>(?svjFs9<zP=8@_`U=bkZUuENM)CC`aUz1TH<**ZMBP4FK3%h
zJz|Zq=R=vh2(7{w(VyniK-o1@0{tU?o3;93e}dYehAlfedNkdAVU5ZM{ts99G&N+=
zy@4L`!EMu>e@6u6@49HVvMe2-5x`G07wkEfT%3uoh`CA#^$<ft{>hT=y9RhK;gt`R
z*=y(Q>dYbPY?bgf9}V9tqp-XKOIu^7Fl0y)V{svgn~s*1mkIt6C>wQ=ahP+sla*q_
zQ)8sMl{NoUcx3RbO*e=?e^7(MLLF{SqiVVMJ?2BI5=HzK-QoxS7X>B7R^+IIH}8j+
zF*T6$SE!7!hV4S-Xg9f;G$%9HHYJF8h(w!OORj!T^lsKp-?dbg$1D*@>ss5Ysc+Bv
z@^vsLFFBWs{FwAXpcbz`oVW8vJqQcH$S@^prDN7wyv<cyT1Kutvb*l-=`o{BuQ%!w
zPGNPzfZGBvVWGc4ub(%~rMqTQ)8a4Zm&cnd;V(Q3Tn0MlyV)-9y%@;SgwAX?XEGKe
zDt1J!{?g$q?;vc!zp`BP9l@H<TNDgu{Fsvact!Iy)1Mz-L7AwOwfc<ke(%}!?@`#P
zrOp5CtdkUh9nwK6n_M(N%$2niENF4rF_cOOyW@sq_9LIZ0te7W^jg!8V(+lI9rLMH
z4(3_s3I+T3&vw)W20y^m!@73A$`2g0gYQgXq)zr-K{1kw)$&;~Exd-@r!R3I>tgey
zb`65<B5~vA(KT&qtW^j@-^!b$jYb*IYoD45B|f`hOgxKAzk)d|DMQx$1bi=E2Ru6J
zYkxq~xan7>a}qnX?YSiN13%_u(<@9;Z1>z|#e0dM7aP1Q>vT2Mu_|atPcOE^967fB
zq(SAFS+ccF<WhM@KCiLqZrz10XZsU@-Pc5)sBbR;I%mgBddYV+Eff=_$UKey?!Tx&
zOS)#Y6b9UVuQEXdu<?<!`CdiMaHe3vYgF5j+MsMWyYOq!?o`k$9Q##+Uq?m#F~)sH
zzY&b%n}WLU_M=>JDJ;&#L?>Krp^d*^Tl&KV2Q~!vPe7+zb8~ZSNz%KuQNF$dlth)A
z>8Y+0=#pce=BFF*=HJsS$m@v`BAI)d`UFi68%0T*H`FBYxj16hjK<JBkk|BHzRQ~l
z<h;jfk4MPeKsXojVj}&39@papZ?P|kxjjzKi~ssOyB2BT2YvYal>qtwqw1}q>e#w)
z!QdpgyE{RHdkF3U65QS0-8Hy7K|*kMcXxMp+vvvW%K2~K9$jO=!+xt(Rcp=p*(5+P
zxM@?Nj``5=Xqi!7$vv|fLGG-HTO?MZfjijyfaAd9$bL&<xH|d}T1_tb49XoAAzVG@
zE@pP{AfRQS<CPI&j9@6wCOoR-w7p1c<23y^B-o<K^X4pra2R@5eTdem9m~<{WQ2{`
zjAFO!g2|z`W&OjWQ~eJn9wlA*$BxFId1BP~(!|E7R8}b8CY)bHF8MU<ZN^P&cdK!z
zZv(^JhVPNYpe5BT0nj$vV00J}7HY$77wH$Pm6g>NH?lD5)Va%*ch35{Hc*?^D~WE5
zrZ78RXrZb687)L}LpTifayJh6{y5?F_-ME=K5_(&zrI|`@SN~?{RK3@dJ5x4jpJT~
zC&rY20r_I~_C#a)u%;N@@PErY$orm$I4sx2pWnFFc<oyn<j9XQ1G|~x7Z}oqEf<#s
z49N4e%6PnUxsB^7gs2sN#HU)%9@L!V$VDP2AQTy<tsa<jeE!N!cWgH;ncO5R9#H))
z@z=+p>ng^8y`H-9%|=d~qS~REDeJf+?BZ*dJSoux@&XlNY&3>{h!19(YaK+9`4oBu
zbA`$vJj-2c?0j(%`9-GGJT^5L!bQ{c%ZYc8*ixfS|KPSm%%jE{rwRYCODI~j(ya!{
zs%!*&d$LUBK6)SBE2+jx?Rg$#C2I(du2&r3ENBMX|5$5x*#88+5P-jE^|+(oQ|u9o
zY|}VRQYhmz;3njRw5|5y*7dn#oz6xEAw4F(ufinWaXdO0C43iOPI%!HjA!12^Eykt
zTfCWk8%f+xR0M-R=ze%v3TVKTSZ)6O`?o&1sq%U;8b!{!L>vNr0l`|<NaQRvYh7zv
zt_F=!uvho>FVK#g8U{s03^$E}K7T8uE$g$C-;ge|i77{KdLHk=&k-li48a`g*uL1H
zCE6}=5i9Plkmn`6OVDOj4AF&tpwB(d!DZ+(bj!H)A-d*_;o#G4R4)rwo>PrqZ2D71
z!yK8^HoIGq#?H?`Gn5Plu%LAUOKm83zG!*WiFI+Z7yev##NycWf#!2}aYrkos$=ou
z!Ih(BS!4T%cjzpP&9yz@&CAWC<KaXWuwt1_o`it3#@O4N$da+L{T{zppEXcYLEvsK
zO-dRY8X`;Hba|dz=7ks#ZKFV1N-TIIOhNe^4PhzmV}E!*k2~j5a2tB2-XiLnj1n7~
zP`;OHgDfMdWp)t0SLx_PkXZN#+I>7FNv|nWKNTz<A9#%OdPGs6^Zb9SU5swcFW~!t
z6}RM{q5BbtQ{7g9Nt|-s=cLYQCG-KsV(=4mVMf!sQch;+mw~@P=dx|w<aI?OR2u%3
zTqt7Mj+z69=`IsG<dg~IrdOVFk?>$m9Mf9jA-MAsmb)j)vU+7tTc*ec?1d1qB@km+
z{Ftx7GT7X*+WePU;|#Rp&uW_U6Gjz!#&i7>mZ|u$M?^<c=B*PCxJe#&)Fs6TN1~kZ
zhDjgHSrqcTf|t{Ywm=wRR8S8BGYc-_0h6bOy{qVST-&-$${>la*Tv*w6m>wOofWb5
zlL3=j2Z<ZfgU41Sgztx!S&E!Tr7fE4MXmvIu}-W9%`Sy~Y}nOioO3P+U&seckSY$t
zGo=qTj+QUlga1qWBoGGc)1Zs+BCiv3IjO4))q&y041(C=lCfx%vgX{0^s9vSp{u-<
z8e5q_0xk@5=#BU=^xk{YzxD9nVKuhmm&L~EW;7CVR|uB2ue}xePv>$YxnUMe(55ij
z0<8I=3)#@PJy>Ae8l52$%DTWAXlQg}c@SM{`djyAMUn1z^XU6V(^Uw1AKC+EN5P9Z
zq}j@$0B1G&Q|+^8G2N}(=TGH9_<L@=*l21fmrSkrED;+~mgty<h-NU-s<B7qyy%T0
zsSB5cbQyEF{1QLO-G~Rt1Nj#;Y`}0@>uSA<MG}V*Ul(1EpP2OHm$}YD_mPPIIKnRi
zrPStg`zA$tEQ$fX36`q_Cf)VFuyRSFo?ZlUDReEczD#UL@B<}CD?9TP%JA}?9b`Qy
z8W0`R5bfF}n5v2Gb;-KwO9JZcnhxz$9~BHI84jN5g!cORwn0LGA?u6d#tUwIr7_HD
z{rJMOr91w8q0BjF&V<5;MVHvRbvL!>zhXAJ@R|l1ty(I+%xhs$s$jsu7qte5IJ(Q8
zmC}7Ct2QjqSgxo{thFjProusBDa-dnOW%pp633fShwt=(04h4;5hnxl%FBwqpDkgx
z_OODj4%r?lFLLB-sbQNk&cJo*@<c*-7Ey%s1*J5_^NlB-irmRV+p;$>PEYg0qM}~#
zU-58qAZLBe5wTqu4cqTVd2!EVr%Bz&d;CJ^re?Nd<P9CUf4BW_>AvXXMf??^T%F!>
zg^Jet(U@^}EWV6T*b>67(ixA9){$KMIp9LgdFZ2&#Ay;&pt#s*b&UbAar^Ba7$z-l
zUQ0rNgzvw&U?TsLGUN%snjIj7PP>cC?-GLd)iGCVj+0moLWYRZyL#p2WxYvW2l+|b
zWm%0Ko(q@rP#W$(j->LLR2?90-dIn6bdaFnewd}!No_cr1v!?6ynXyu1ZVX@M9<d0
zMqE}IoUmd=eDJ?w77FN{A;ZD0O$6|Y6&a0I-zJekdD@g~gDs3Me5yyY8ZJK(^yLa~
z&psrHe&0$|!jSlT0b^Aa$}o$=x&+n9=ZslNi}T}xMvF4<i|xQ|6%3SOys@5Z+i{<E
zVe@4fo8+B^DD`AiBIq>;(7tFW1=8({DaHC3$whDrGAs`|X*{)`I=U+phmKQtB*9A;
za0Y%8^X{xUqWQ#|l0tnQu~<^rG&+>9Vci`e)=wf)q6I61Z~C{l7?<jJrUF5%52LSm
z+eT<>#>4X<47EIHJbF@m&=hsxHn8b?^{N_Q63FZ3Kn~zG3xiEG5JP*L$z5X{*yF(f
zcUz}1d-qXmaUYn7kX^dgf-Z&z6#VUjmfw6wpmlAtt0rW_lo(6SX5sy3$$j(a8q$Kz
zPkfXz#(UfTtEKF|Qh>07);q#ie6mL28|p&}V0U_nb<yFh&b*?XeUb8Of1QgrQ|3wa
zk)g?1aY&sjKNvZk1EX!&n#^V>Pq!L8)h!WSYYL=)8pId#n(REOQD)@X454R)Gq9Yi
zeu+{#9*bc`RzM}U!tUpT@o${yD*Hau#G?pleDslTz}PxibnKWGq_JDCl4qTF&vP%$
zjq<A=V1Ub{=B(Nv-?m55-6a<1H89}nqgb+oe|Ls!CwFNE`pY6bL~BU1dn@K$v&b*4
zAT&*7F>?$1acmloyN1Unu9KRe4j{bq7FW}HUkfnEDFdKfQn0nt)9YK$&PAAgT;t}Y
z0wYN9^>)^DVkGx!(;5Iv%*<$$#kUwgc)nAccpAYO#cl1Sk)dDYFPl=b^0T`zek#?T
zLKgQ7k`EOyN6Wf)q(cljDPz73P(hs4ODMx2J(n}GjU4fe=w_PP=px<?rL{qjeTx0g
zg03ZIIi+J#Y=>$b&s@$!ITo=SE%vrjrkY9}Ox^YAEZ@E*<ydaf)#Fy>YhNbpG=2sq
z4w;!)dDm2;U8gsU^feUHZXM_Fcv<-%=H2WOO$0}w;!pPp`eFPc<n62?y?nBxe(#!;
zV4%*Kz{_EE;2o_Ik^a;+aURSXtzuQz9(=#clOCxpw{o?NP+MSiv%)1yp=VkCDB^pB
za@E@T+=@Uo-fp)I37k9fMQmWffo7oCIXyj9j%)?~!}WmF$>9UUxBkx(#Y%`=(V=<1
zW1F1T?WNXU%o!~}ONE)_Ag?-oIBk%8VG^ky$gV@C^0ke#(|_ma!~fMNzSppv!YML>
zckY_2B&3ufDtY<sVq8<-bhuzhkKovf_=HdvL)~~5a|WZqULzJd?Wi=9pUleLtU5+i
zs8u$u+Lo|Ihd}-6FYkv$*Xt`DiUqZTgW=!zz%fG4v#gvYYQv~>{j(5PsVFcaBDLS0
zw_du06DDu{8{AU~rImH^PCGB7^G5>(W#urE3kGiKILx&VU^ud8eJ|7~KDq09DKjdo
zIswiV;y~KpB%;b<JeE|q8pPV0VhZX$m5aOQw!VD-HoSw%%7x(YR*FCCIboU2eHIiU
zz1!6~{r?V3;JTTHZ$r>?-RQGwS5bFIhikI;8`WMAt9rw)ZWX5_UVqJiQxvpt%UJ*k
zGV0mB@`4MOLY4fYOFDYZcTneB;a?*#s?-slSO4DgQiFRLjaIDC1O76kH$ryXjUyhj
zc`L<->@F*6bMinz+HQM`A?UybSOm4Gv#yv*lqV54;}w|{hbIjbGxd)d^o@Krr@dw=
zHFMWXpv{1&fkYdW2sf%Wn-sIJLrvk&Wn=tl=_rkmNNP7&y!}SH_eNT<Z?WK&5`8$9
z6l5(r=y>FYtO#^?XwUjDQ`;L39PP;xgBg{p4#zW8*&Zi!g3rs76WWu;R}Z@}v*#`;
z+EGeo<Zk~^8+`l-psP6SyJ!n<20v1%kk$r(0tDnwzPVFFYqxcsGSe}QQKDI#L!L2{
zEzjHGtS?hCGCY;8nD@}*Z@H}}UAa|!hRQ#F6v$*B^A$;W{l)3|Iz+B?TJZh#ZU?<I
zOFT1OgHlV=NZKJOXlL4?jX~d3YL2IPB|MeA($jmgT&h5(V-eSKS~^a}jo2-E!fPu^
zpi08Np1k}aT`#JC{u4r>`T(@OG-{F6M<@Oij?Lfa6Px9rx}6@4NT4`tCpBUIW!{Y3
zo*Y?<(@4^4zYD8j`A--#F)`88(Kg5$QNu{T;$m$bMU&%I6YD)6M=52OIe!_Eem_uC
z3UsEx^&zT@kHn>^Rm<KLHj~{C{o3O0iYJDlUvn}Qdj8}mF&(WB4qsD@g){4s$9RAC
zr_n#3nk^4x5^LyxpwT(!aN^9g@4|SXp$d!cf4sRaaR0@q{|&yJNb?u$hnhm7$B=~|
zqAJwof@nL5edlsdSk$=e3k&2CT=M7f6*IN0vWz0m*(wrC@E3V<)q`=|6Vl6H`1>N@
z?<AyBylx8z^01O3+N8Ow@Ta8h>c}Hz8J0D~q;Ln%NkwU2HH;X~LRp{nf2la=ZEua!
zjnJbltP-ChJiQVRVkq!;1AoH*Ngf<8Hv}3Q8p84nU{in~fU1R>>guK~a36*O=yp~i
z|A%ukN67)hiah&&7ej*hRu-IkRwyG~u`&j(*p91x50%`Yi{|{Nwu+c2*yU3_l=%%>
z!+XPHx8V<Sy^xiXoH?4s)$ob@=+)c$-%7(?iEXN$K_gmW^~S_xp`v>)=}x5NGH<8L
z7+$yx1_)!U%%AdJ^X^r+!J4YlX%$}R`bsfDmMyT(smY|(xbNhLfvbP>&@CcHe4erD
zxN-Fp%&79+PPd|C@gpy3OSoYY;fI$P{O8nWSQW0nkc-C{wh>y^TE-ok#m^-Y3uoew
zUa%Or;%=Kelitgprf6bC@7e)h0+V)2P<?WH`@g05XGnK-b-mb>wrsB|D!Y7cJGZvo
z1#l09^P&q}!>N`Q|HXfpTS$n6Kd>55_Np|H4o4|m)@Gv>_UcH<@jr$OSa%v?>Hh>p
zl9Df74FPfEC636-vt}bexwz9pKig8)zrwIGb%2(yPV*o<DE_%yahZLR9;1)p+t2i#
z<a0Z*b7q?2r2z7pCc!^LVd9om<;3W>D8M(@qxT9dc-9~1SoS(}mAyF_QfbE4a~UgS
z8>|{3`?dM#jqz&xRPU5@@nMqwyySE}Ydmggw88|123l4#F>`}jl>n7*iTqk$6AR3!
z+@y2V2Fb&fMA+e%iG%92Lpg+QR?0Q!{)A1P-W}a}{Np>gqfx}b1NP2`Yx|=q?gwe6
zcI)(7!znVmovZ(SA>a9dPXuMfKixDE?yLDlY5fdlB{Y1SvqrZI4@_oIy;^0UgV&i|
z(Oh1^d_QtbI5x3W{=$Uei4Wng>P21!FWEy|^j$Q`3YAi{Y0bDlu^PA@1a*Ps7M~d4
zr;!_=(H8KbI56DH&0L&Nk}28e$+uTNSy=UAE{HJ`_P0hz%~Km#1BP_`kBem$abKzS
z8y1Hm^zolzR8K_|+r_3GIP?u96`DGW2IAunR{tasi}!Nt<I;q|TW0sBU(Pt3;<X>Q
zFr_f-9$fE_s#zX`pREA?9{3`jUL8!Ld7^s(FYhRD<1)*>M0m)dQC<J%rdfcSrrCK~
zva33?$dsJf=u6BL_a1%VKX`~`Ap15_P~dl>9rU)Y6oFdl*w(~n;7g#+7pe^r$K||w
zMiWVha)*OeVzTO1M}#6Ri~N&2kCd^fBW<WP8qu|zL3fX+OsL_Ow#R7LV6CR}onH+h
zu5)Q?dxZKYA4JB$X9^9P7Pt4gX1Z;jq1jJ`d!%VAb$Qk`TaVns_f)Cft6X7h&$!*_
zs%QE7<;Kio=zn<(ecHt+6+c6v{S(0ej8(SRwG^Nh#az#zjNAlzeZE1!2EysJ$y_i|
z`VAF2*bR$I)(GlBe(Ti#2B1%bV7-h+CJ{g=MQis(emK{QK<_z?(eMhfh3i|pVvqb_
zv&Gg0ckuASf8Kdyy8yfv-(L}x{_BujX8hR6yzd@YB&Myb`TPB@`P2oHrVvKZ)QZFi
zNtQS1RemVZN6raaOPA4FnbzKuU%EWw_rmZwGD={~d3Au@0@CP@N`mgFNZyqx0?cg3
zYH_Rxg%y2@@(t?5VfkdT_VvW<EpO7K+qe|I9g<IdQIE@=6saTHUfVj*%E21!|6^{A
zfzA}sWNoEo8^>jqWjHz~Qf0xDKBrMOENlI1JRZfOe2N_IFti$*@yiwQ;mH`-OObii
zy}emGYgwmBgD4#<H&O4PZQw`J!#O*@#Oxgrug>d>2Mw^cuC8Fx7FSza+dq?^3*DZM
zi`-wX1}#lB6=8DTZj0Pcii<vhw>bs?;BFzAaQln+?SM?ux_<j$cGiKXHk2UDt=~KJ
z3k0ah|4vKq^^NYHOg5)|i@-l;Qumz_#7JZHjLUL9-VXJGwx#-Kt%G(0$&1^z69qz-
zZTIld{GHsV_TLsn9pFlQwz0kfPVT)(k_Lvapo&$-$5R_7pz@xk(bx*d&F?f+Z)1k%
zmk9@G_g&5}Byim>;$XW%^vunDtKtnWL0|s0#D;vn0BiHT;-@5;T1M7qL!-Fpeix8+
z`ZrG~JSK%bA{P?PmL{2tQT2huGj+Qp@)8llu`ZTsD>FEb()G~4WAXWa7I(<2r2M#%
z8~l#CYa|PZV^S(6qF?g^%3uI|zYb=Wwc9mQg(*k_aEuZ4k990j*e|Ndq!xsh=@O#l
z@t7_J*+(4GDj6nwwEv1vET=TK6e>99aq>=SIQ?$At}F^j*Ypex1B<dfB3KYn(Ce*j
zZF6wfSI=GCpI0|0R#r3$ohvZp;_H<j7n{F77<btoUYc*^KyAXk^r-cnQ=Vb+cE2ON
zNNsIKwYw4>9imkYvX0JQmip%m<*S!|^|PJKH}QpdU~{}M&Aw;e;j#q!2fg54vy{-~
za@RVYx%M8Sc6D`krFGKB@Fn(skA8jznNq&2CO&dGQhcMGZ%E5Y1}ps<krl_Tgo-Z7
zpxq|JmD|;nuk#{vsW1c*VN4wx3k6H};@B{{tSXqTEt>Al5`?)yg8x?w@Ef~h-a?Fg
zCmOw_R$&usuy>)0xZp?GxD}iQkjf;DG5>XIUYccL!byQ;VTTW;LR}hqavIuRBUMTf
zl|ZZ9jK`zIaTX85RU$}=ddwqQXXzdY7+(0)p&YYoj!U(6jN)$X8FT(RFBN<AEC@vF
z?-E_Q!CiV^db(dUAG(cdZa7HxVWHWqHFf`sf|Jl#qq2<*QF6m}Ljmm?ej{tHda`~z
z^<~-bn8A2sI^4NXfZX+wUi4R$e^_I9*~e?tP0ShTU+;u_dE^1JDm>#nW^k~x^Y1Xc
zfAs3F>L%{%t|?`Wt8z`^E74H+OvmFt%&<iHjW>g(N$6dk&{oiQpHlR**oj+xO({{s
z1O^VSJwf5|HHL&-u7zia{Zp~Yk=9n;dH#;avtuA>HVS8?4>QFve)EuwClTISrPG4Q
zRC|llrRMc+HS%mu$|m|vb!6x@Cn*0oZ&$THrvd(p&;~ZA#@mhLNnKSQgiM}*i&+Bo
zsL)B`kQNk!e&$XqK10DkqJu)Xa_`W~@capB-UDs43a(?DB++;*%N={okY41a#f}jx
zLIn9~9f2sRU4=4AYm7M>8YdUm^4i)S(6Cb@iu_Z30q^22U&btaTjABu$Lk!TS{t~B
z`89_wIBY!O#|p1Ua7>#oMI)D5P-!z`_u@V$nvhV#MXSF;%q!rmIqlN@kPT%6A(Vnp
zpOaC&Mlvq+EQ4T1c~j^6vr`>VVNiS(2su@SZ}l`?{>e>Th<8t1s<j65og)FI%<Ld%
zktS@$QQ@+F8r67ag_d5Ny%lql^;1F_RGG!SU&q-AC48e%*5CSO#K@as)Ji1jDn-Aj
zz?ooGOT-;jykg2T-czh(t~5&Rj;7HFY7L4?u)vCybA|rx@M3js>W_1FE6hZ6Zy|)h
z1^0~~8EeVJjmBAwvnAtKoVEg1OxGb&Ep|?4=3z#P1K6X}{D#pgOL!EqI8?us6D7;z
zv(J$!?gNw^$mR$)!R}|(gZTDbG!f+dmEz&Jlh~8{qm%M#Lefjl*8X1>{5z3ectO`o
z&-i8#Il6kAA1+6NwG(vXZDU@ebP+4|j9)3X<hEYB0Q{69hWu@pE%~`xYfU@IeWf#E
zv+VcpZM5IvTUjuc)z3GkcTAB5j{c07gmK!@DM=NP>1l>?0cBaC?VfDDDjM2WQ@Ul4
z-NYre!bDF^z>Uqs*BHg{1~^9?WYO5m;jM8nGCjl6l&R+F*}oQs=`9pjP~hBFVB=Q{
zGCT7zixxQep5(!!k7i8pc<791*x~S83-sC78u`aij$-TtEbv@pJVmfO3$4I(E28B6
zV&j7s-aoW3I8*Ao?lZbGZ%*S7BWh|S*)kIwwdU8Hgajy_W2a>8sM-;n{ZT1FM~bUE
z#%6e46kj%7pUF6|=Hs>fR)!zV_4~UZNVBVss21hGcN0<6kP~K?c8klQa`VvdaB#uf
zlWD<+wzBt>&8Jf=wdl3<VI1h@h|%!<U9n}`YaCWpQmo&Vl4Z*a1iyyD;{?{wjo@R#
zc9SlU4&;{k<3I7?TPkYwBBD9%R5CJMMB|?2E==f;T}P+PT^(mQ@QLIHF*8aijPdJW
zRjAa1_+ad+xTme~>ObpCWoHfGVk(92)$Eoj<baz+Pgwfh2~|rAms2qP>jCi(?AuSy
zvkyXJ)&!#a*>xNb(<#En*it>Y&d9-HY0&wE4YKV;<BRTJMLr8ht4ZQohFj=avyz9+
zVw_Wy9LW0)%}2?X=S3167;+QNoHK3Gy#M+Vah<u>&Jpn=JrVkx{e}N{akR^pSp9IX
zquTe&JKxCj%_O${Z%-7E6LI_VOPsSeaKvs7ms57+`(6Jr26p@Bf4jX~kQwxb`d>LX
zr6o<@fM=zRqeg|E;3Fmr?kw={V=I-DYIl0-;0gDoR>y0@pi_#KUg~Zusrf(pz6A9y
z#D>WfC1)*%RajU=b6@x7$>)sG4_hKEoZ4~8mW-r)vKGjFiXI%#;I~(>cJSGszqIGl
zDE8VnHA_0IhPbr$inm2!e<_WVh+dOu&EuZWy2rXlK{oHi4x}xOP)f`BP9!=z8>Sox
z|8Q~r+V?;GLBq8B5HY<J68Ij9Ut*UBU-xsSID7@8Fe=c@6dJ4UmN~4f`#8<o9j?9W
zj!`&wo~9B^A=|NTf>i(?QP--Y@ABn1Bld=n>GEzHv+i3@&>h7zcv6J{G%@>T{B8n3
zATg-pvy%)AQhz<+3#Bn!u|h_Vy_wE^TrBKyzRt5`G)j?MfyoK)-kr1x=0&tfc32`;
z<fP+a;a0;ce5AK^p3!?FP!>t0t}^%Kau`-W+hfCWc)?;Unx=J-Ezk+A*bY`o*@<Mq
zwmMj-6$az}N%mj$WbfB5L|q*9s>^4&nP-agdA?3<YQ>-9@lU`OYk}OkfVX6mp`M&R
zqKd(!D&D@o0R28)o?sylQwB&t*JlwOAOrre@!rBPVb%`Ul2LlTa??&6cbQbyVoUMp
zmR}j01JwIy`aT|HeF5d_V4t#Pu>A-KOFsBElK#Gyx!y0uSjgZXd9YymqT0`Yu6yvW
zlm&%NuW6h9W`eZsHYlN?BO;$j^R7VB>0kA9yg%x#W2#OF1#~Nl$hS<!c@>KxlmoEd
zR$9X3N|tfmuhO-?NUMj-aw!yb;!+Wf(88<pCtX}s$k5`90*})o4C)}-)f!T*R>>dn
zo3{*28ff$1+oUE^drr;u8B^Cyz2^ZP)n5@Xb4F0^NHZ|2lzCb~^-{6A<ND&{OM224
zvps1F|L|%1D;yMGIO|y`iclcFWwVeO`ov-!FG^P?gkUx^jTodrGV@`xzYn9GJ_EWd
zc1Ty}nC@n3{#pJn;u-~yE&Q|_RrjuO;Gw_$_t0@Ulu1vbmfbPT!BxFfD7k6SIYD;7
zEamQ<_^lPp#R0R7+*w>>14%>5sECi}5wKg%maC;-q<+zl=(-;C$Qdu|{IaReV&XcM
zvzi%swW~+Bh(|c^>od=vO-F2q{K1xMkG`<Si4>^h(s`=uhRR$cda`0KryPi0oW%v=
z4}(A4u`Y1oq}?aiFpL?6(L>yMT>86&p*Pi1RoC4k7H7fGdARepy^B5$U&ca7!zNkO
zK|Lkmm1ST)BC28Vf+hVy8O~lhwLk`^kbwBRsqGnC55nX1NKn|M>%r(GN$mwC^uzSa
zox+5AV_b?A8cw&u!RTlg!C)Dn-P77DzlLxFHiXmvHUwyZHZu<oS$aJ`^Vx3DOPl>x
zzW>cBMsvfM-_nk%oAo0T>j>pvcJV^i0!3%VL2B=*$1*aRtWVS>HQ6S4DLK<?D`gmJ
zg+m03L)rR$UmtIcDzP1R`|ql!uZwCl2Sd@JH>$k-t2k4#_un@X?CN<jl#{uBh9Rf;
z@~cKWkO{nbnyMg`_fI-1hV2G&(5h=gXwyrdaHE8?h7Cz0XbWfV95FZ_)Wm0OkOY}g
zoe^QQdpfm#KHc9hGvfyMTEP4EPpJXqN`n9>hoM#4G!5l&v=Ua(+b9dl3(5|sNnqCp
zm>mHDGDJ{=@sjJvG%B?tOb|Ey{}bK6oV5~xQ?=}Wr)mM3n?k?AGnhrQlH`TNu;w^c
z29vEm+}-N1urSG&&_GVERau?O)|{0MD`HgqSc9^Ybs+#kqI3ph_=n;E|E+T9RBNC6
zy&@G24qujs=r24=nJbtTOI^SVVY4pvtGxP*gNPAsC9vFBHQ%AnI_reXD#2~S6k`}Y
z`oIN+lNfSJnquWmEW`vRpXAhjm@j!wO{0SP?`mBF9^SfZ%A@vuz{4Et9I5=r9fp&p
z-@MTgE&30nVKuYn&|vgO0buSC3G^GY-V4O7rXMlrRe~4>6O`h(eSb)O29~(q7vleY
zHqJl2VsE<71#vk97P1yS|NLmW5bcHHpm>W7q_|BIRx_h+4c;sYu^X$`ekmS5Fn@O!
zoCR85I|ftDEjbLUcjOu$cP3w6zP0`hPb31OaBdk20QrFR?4NhWPVD(JjY*&)%l@HA
zdo+4p$yD^u$2`I^DQV`BxgnKRwMaEPQR%z)Ir7BKnj19rent-`4I<9o*3s~T@<4%J
zc*|<bL&fRbsy#KuXRZB@Fba7S!tTYab%b(NJ&J9L^g$cEK6R~UC4`ZHvdD6GE1P2Q
z7t4VyZXky}r<vD|JeI8EJBxX;tRmmCRr>ATWZ16hB!(2UJ;-iyT4SQ0FKFV?_`ozX
z5??TckX#y({H{YsRtB}GDY^$&Mq}Im%jmD5EPcsQYtjB19;rE^qID)N);)^oaSB1*
zF|l4SR3(Hi$_vL9il48?9-Ho`7tyz;0ammIU1%>VkWAO9?13f_+xqguhOa8?dC&&~
zMB}Fb;p-f7dCk^*^cdNNvUlmtSt*j~3HdJHvHAbwwoPemv8n5q`Ok$WP5&X&(feng
z+RSA=Zm7aS?B20Y)(nT93Xjnf`ymcC4yyyR!ZVf%pu0uqj)%wVBHgUdszS0>DZf2x
z%Mw}RC$B{+4afe#ietYwlI{NZfKA1LU5=?iTfUo8=6B7)k}kK;K!f*tmw8d?0DhsM
zU`4{62={`4A0uzG<45U{w&5ue6+w9uPGxnnr<0m(;}P=ZTwY=SUG1|gzOlh^S<WJ|
zSr!bmdIl0~ba?HKhq5L!A^un#|MISx-)j09b0@ak9q^@TIo!J^)TebWekraUFGnBt
z-c9j6!xqalTEyD?8D#%zGRLmiwy$4axOwULe1DE1wvI;rt#rPm%qNC62ReH+A>CW=
z>@^3r<2)69<?3j0m$y?WmAMm~=pdB3ib%MAK@9TlLV>E~kA0J5VtS|AD!m53Eu{{<
zw06xl(}0BVp4a5ICL!J}LTXI*3pg|CUk_hp|0%sie!RgmkaJ4KI|wKygxww#ZJEub
z@BW?;Le>GorPC-eaAx*|L+PWc1J{pvqjdN%Vom$+(9VsCgfkALnrh$->{oL+I0;Qo
zuN{o$$ReToG<(HIv#$jp6sOb&=VYCfAu~yrRQ<L2LIoI=EFr%6CV0<N|J5&=cID9j
zsLZWuo_@+v8<oh);`C|f=`MUrAOd~_Kh?2|{+`RN*0~;J!6>ah=&4xdfq5C0OkoA<
zT3hfNi(+N;VqQv02P{nzR%=W}of-VP0OKP27?>!w&6EB&WUz_iQ)x{>sOd*EkW;c-
zdBo{vnenX#(;=^qb%I_6er-g{Zr!SN$Ij=Dyt)=VLpwq^OKW2xmw%v*fSYHG0N*M2
z1frZj{l37QNYw%D>Mh_WWh3(u1ThQufR4V3m!1G1YM?~*?1E*1E=f1wlgp4>eT($@
z11N(aCXAqM2~Bn`>=oIif|_5Kdm_-!Wl8ub10J%hq)pf}X`7bZQssEjgxln?^)Zl8
zQj`x5l`Ui0A&S)#MZ<ee>cS+8t4%yx<WlDp))*0}z9lleyJn^HSQ$igWq*<LELMvY
zj=gaI!QE;t(&^ZYojog2?2vxVA0(yG;w+5?9ljs!8i#O<EU)z&zJz_@4{DNGl95uG
z6dOS>eigPgn;kRys>e8bTHhCvgcrrczvE@NRz8QW&e%LT3wEe3Xm#kKdtFRqV-&`b
zxL#OaBflLpSZD7=(_AHjeaeFnEE!iemQODj0x6{))(!;+0h_KVy7Qp<86JI+kg-x7
z7XmO|ISe{G1+~d>gmW5m6?2^3n$!B3`6&%Ruwc0zA#Dj`JFbdH{s^z?lbD0QFmFf^
z?JL&Vu=l~TA?j&7SAj1fIDW7X07!zxxz@q5DH44nQY?EPclj7WmC~MDcc+CkcA7KN
zA9{s6M51BGxe?JzNZe@*Wr!3_yL7qXiY_P*9V^}%Yctd7Hf1degU-ROIb|zprNGOh
z;#acL0Z0vmVLV(^=_q3vTRXC-X=90NdN_MRNo6aTNxWG~l~P2*CNr02IzZ_ub&fXr
z8{S>@bDff?R7=eQZGv55kAY-#*n%*>Hf1F#x5jt!wDOSg3WWs?r408c>V+|^-i0f|
ziOTw^k_kn$QV~qCHb5qHc0P_nc<fFLu(Dds4uzl=05JJ?8D--6FN#Brji<=V(JQ$%
z_xc>z7h?jlWQaNXNIecZPJB#3ftDV1iJRKatior9HYodf$aqn;N@->x;f%k8lY41&
zjfRIyn8_4m+0uB)M9x@~)cT@~my5;CT?qM^%CH*k#a0COysDN03qM`SXk-ziRVYpM
zO56+>_}*Y9P&OHEc|WhfobN>_2gn&%{n&Q@!6xJx4prgadRC0=?Px+wf^c|*hgB59
zJwCxzeHR1D!3OfSi_^IM2nOh~6Hq`h*#4G`Y77G=QY7W|!JcT5@P~_DEpI1k5p!8A
zi0*HXhj@s8GU$HSn*eyUPNhWUBA`Gg+N>P33i=0WhJ@6PExUbF_%=q6qoHGJrp3?x
zv7zrR=fQHx-OD$ne|l(HS}aCut=!+2Y!9uCidtBCVNP|6@xgUbTBRbvD*5P@rbNp#
z_FGy{1KGXD*&@4#t7vBW%9CF-w~R}o@Tb+R&sL(Ef89;2!oCqQ=Rnz1n`eq0Gf}V_
ztmnB7#+rSNfjC_ubKtu*N1MCS(%Pxcl20v9*!zeqAW@#&KE)aaFO~kWjz;kgd`mRm
zZ-XGQ2ujsb3?SWlJj^lW=I^-totU?JPK@pd;FG(q|3t1+Q&rFtL0y)CuPb6LiT-t-
z>U|)3!%~l>%CshgFsZMe!RHFLI{hKfsV}Kh)DS0l)k<w$rIM;=nF?hl=2xFNVyFd>
zGybSmMw#IdT##t-mC-h|#)y0rOeXPtMDDyL5gJ$ZURG{<K98iaEp6>XrMbiTEdi)1
zS?OqC2vIQL=iFPYdo|opoO?LF5nlQ;yQCWh*dW2ow;0SqbFJ_5w{ATI$!8GlCd^Sv
zb$tn~Q!-Q}AKU={suvB{eiRM$L1K&tDD{jiYUw&j*g%L$q4yWE&h`5GdML8S#nbAB
z1{Ir~v;RH3kYXMTNL$92pQ8iT<sD5jKffuz0!e{4#7wkZDz-Xe^`5|O3=8BE5s;O<
ze#eOXI_eCn;{`R;8Vb7R(<S7Ct2lMRTi)C+9)DVrQLS4e{K<~L1jmfPsziv;Aw6p@
zvmQ5vS?K3Oyhas;Nu#>zzKmtO#JoTB2HB5XwmYQwzIDEEvAJ_0_sX7`J)_7w)I!?N
zIyc7K-AJ~@QAHjao%2a0HhdNOdDfbuu8MZ9M<9&42=jTlGG25^Lx`(v35Mz8RYL42
z{KDy!s`Y)c&34rq=bSVPjaE?rWxp$?y@jPOGO^favNA>JntUvrRz|O)Y_?PtBtt}L
zx_?&mxgx=SU=9gcD@=KYi{J>s#tu}^f2sl`v8po~(6_&#ofgA=5N_6LRGuN>lHope
z*w#BM;jLc}rq5ikUoHX!U9sj*Ox|aaTRgMtd{HV}hn;<+gcGYssLaq-vPD+sgB6l$
zB}BL2!WE;#dL9uBt>01}uLK`_-?Hm**+w|t^n4ROe?MB}c`j3nPm62v{EBWE{(D|5
z4IWNRDQrF5coz8x7W~k4+2Iq5dbH1VaYLf>!2dq)Xq#rkjP0{$`p#B?{dU-Sn*;}i
zTB=78Utm&VBsrR!v}oCeCDBu%@<|mz(STZ9dP6~5t230~OfUb*yHhIcw9<^dS}f1I
zrNUTYq3A6U`$+m%Pi_@_m7#z^Ym1`4^v6txp<pSK<?o9(w&)cV3b!_kt~{LwTrM9F
z;weA6UaXNJid1N~hFm@aM=^jyyE3*~{BPxu*zBmGHzddda8ReCDx5#%5uVWvrzMAq
znFmW9p5qc>y8;?8_aESw?)OEnl=}FD$Y1Dxe!VIKVZA#S`f=PCNhpznzsg59*-$o0
z(>Yql{Qu6QNhkj8-MQfICSKQzsi1v2Rj3kqo_j4{jumC!UOJZ#-_~kT_}mn_C&jYa
z<of`A6!Lw9c?0oPD*W0ZLNxT+6#l%O;=7CTu;u%P_~Fv$+0bh~W!+EtkHum*i~JR!
zapRqvoBrgFAyzPltCXPa?ImGYMkTnjN&4lQT9@%G-pe=g+iK9@8E3Iec#@16QHYA8
zQ(Jx!`ob7077}s#x}%i&eVgMMlK{G#;Gg!-_<#xFb}LoL0}*KOwI&kbaatI8H!O%r
zoPqS0f6y~<?*2>r0CZ&hk9!Gl2JVKf|Lr|fRUVm9H2D%=x3DUMk-z}FXfTwplvrb_
ztRHg26KnS2$tebyN%6xJ>S_gUHauzZ+e^LliMr~*oe^Vz&Q~o#)L@jp&EB3W0qUNI
z*i`;r*0R35{MY8wr@y(PdR5*}Aq!Kh?pW<_+?w%7Ze|REtYl1d0ftB^JFQ3h4ML}t
zalDL9=;T)*vdw!<Fv?`~!`SI+Xr5ajcemmRsr#gY_tEalj_(6h$BXsi!(B|f2dKI8
zeYUfE)i(3+N=AUNP?DNbD?L=Pz;HF_FFUlNS|Mv5Yo6p3CGC#ZlxsCNB{y!OlwyI}
zXGG_W4to~ELxof$yvyCW>~!v8+33g>fscG9o4H9niVk*>0NrhIn(lE84fxh{#;qyk
zze4YzW(Aq$!dQJUL&?|vMZ0Dc7A4=Ln~`W^m(sAgi)@LD(1A<-+5Ok0kq7<nEadQl
z*Vw;WShdL+dp$Oz)1t>$ipS1m<-+TnygC#Y6T<0#;PNg2UF85SkX@2>=|%IOMNJ1N
zt^ZZm0h!@N`4ZiE`j0WQ{fgNgpT9ezt%*a-oa@Cz?qCVmx4`vWbg$YZuooaE!owp(
z_U*=XyD;S8e)%o+0WQ);7t*i`zl;N}vKp4p!}{8J0n;@;EMP?fdPQrkU1+w5x3zM&
zLR)khQ((<~i{s2K&5w_IN4hBnLmqqC)<(eU^x9w7$6sglP^9zjOXvM+&aU@m+r;MM
zWhc7CXC0qiLB3});O9!hr!f}U2fp_+iWidiS&~89X9kO($Kk(e(6T?qvA7-CkQzb$
z$^O!x_rdbYkE2j(4Y_rOnk9{tkP24y^RH^-y(&I52|CfUZ_1q#itW2*wI$@oBf~R>
zvSBYW6hH8Po4Ea%*3T*B9jc6>qm?^pz>|!8Q*)~PoQ(AGYR5aQ=5+n1X%{d})xWrd
zF@cA|K9Eu@e9FPu+6px~et~r4;ms%P@@T--Rr(ie+tmQUKO>u{qKll9cFO5u<qZIN
zY_;6UPW_LrpJE{>Wd@~FVn|Q0%v@weL0j^~Q>#t)k1q5`6Cwb$({z|i?VjR_n3hnj
z&UZOe<0PPjW8s;X6}N53(&TH$wTiBgsWOKo58E}^#YYKPUL$v_Vp|+se{DtS<T2bc
zwAvbfMnP!H@$t^+d^CK&-+J$SnodFUw|zTd-g!*9lwI45tlZf3eeXYfjJAELQ66>q
zpsGYzZN?B?Kx_ED;4h_rUBTu=0k?k6&24qG!p?&kMt%=!zUEqbw}`Xi2zssP*UGaG
zpid~L*yk&3f?ti5oSGzJ1YQ=XUF9N2El6mVJe$VjQ^)t1&KIb`vh`4f6)JFX`?UsE
zoKxEt5CxnKNF52wL2}Y|YE;-w?R<MHCU8a7=&50>A^!}mC#99>A<Ol4Ksg48)iY&M
zm^e5QV_*;cE@1_sy!0l#tv+mi^a7$a9~id={bDfdytTh~J^OWjXyYT{d!Ov;{NUp~
zKybrvT~%@pfTrIm=qIH~|8<Z(#PooNq3!KC_^gx|-VCl9J3}-L{x6XgI^nxxIKQNZ
zN}#!;^6ZI0A6*+p=`6hFuBg+@@>k9Z(({d(S}(3l?Hw+mgz%0$V$u2qGzeoQ_+$e2
z_kryF(f17rg!Ll$munPnC>&1S!3tZt-amM`c^(tIxOGf+n~4PT91$x~GM{i<lI-Z3
z)JHl-#oJuUFO6vwjn|bsBeM+-qV4(Clm!elFT7Ptt)?m^6&GANq%4xN>!!yUO;2tM
zjxG8Dx`A_Q#m=ujS+mjRs(I2oniT%Kv^|hMLhSou-?Dyz>8Ymui<LV%u%0UC%&^VD
zwXtS)XE^e-)~nJLiUii93z#F8mOo_KRdntBLIWTpLP%v$z%1kUfYlsPxCdZD^qAtM
zy8EXGUq5E(h8vgJuEqV)9Ow?`k?2!?>+eRb|7g^nG9T#65|6nk{iFmc4oUJeJ+8<O
zg7VRnorZ4PKshqGYU&V5p40#af|TxsRo{D5fX`|do}NjVC;nb5U#%p0NpA7_iQNSO
zDJfRyeNlZ)tOg<tv^}(3(p<0V#ix!y;(LtrHmADgx5n|Kigc?84SjAkp&4V{bh24e
zY36I<q1jG+Ld!8V_xTuGR1-q(4n)ci$xS}jp_Sie5!itJlawCqWi7`;y>DP{f|pz#
ziLW=zG3#JCLTjlVnC(>AcKxY$JJzLjTyyhD<=+9nTjrBesc!-OaL@mAgX1Su+tu;r
z%*5-12U>mf#0TcHg7=?&_5IHkcK%1vkN(M$;ColxdM7#!cy8``QN5PjKvAf!bYICG
za`}(GQGdOdq?hl+9R9N(8K4Kx*H{hS?7OfwO~x41+a+_cMQH5|M7k&agz_x2pfQxz
zWe4}OZc;Cc0a=U0d7Jl%Q8%Cklq|kx{rA_(GiPM(Y!&tnQ&+hUPXI7dXzJs|^v4D>
zIL*2MYmHuOBP{fbw8Tgyd8cZX2uemF^eOfJ=bf;08boa=S!w2`Q8BE<n&;$FnObF*
z1@r;BXr(3@!sekeij#R~GY0%G`d~nE^KVYZem{;bC89{S_r0_a#Lxd%3!vWdGTNC5
z>|$Iy7x{w<`#Tq#P;W1g&+h*t<MSxKe)7_Mdm>?|dNqI9hdB}a+=;>u`_f9G*rIQf
z@d1RSd}f->N!zmikMh%3d5i9JQ2!$)Tops-_LO&Q`<s(V-!ez`7@m`EqU7t`Onlk!
z3eOaBffRQ6VtZJbH9IFFl8mse7IpJYv&Tw9Snlozf)t9HvEK14hl-5%<HA<2QB@r#
z<ISJBJ>CnN)-DLY+<wGUk(3#<H1|eC6p$|&^<V7o&S|NEd$bcz4L`LBdCGIdl}lxt
zcDb^Lt4CW04xcSlaWr>6Oyo0yfULh1RUP->_V%;K#(9gYXxFwtoyx|u5)OtK5*Q!k
zheDX=C*36G_hr^o7eC!`Ymyf&_$=pVDXnqqj~z^%doM3bEx<M<aR1J+Re9LaJPFZw
zefehCb!hU^k-)T5c{uu6`OFYlkdl83f<N&M`jY-*8}>{Ap)Ic^ORFneoP84f6O7o^
zC*F_AF8o7JRCE0Ve?QxbX+J_5S=XYu5+sM1;jFg<N-zE(rGN<7dURI^n~P+}^@kyv
zjZ6>C&k?>?)2&{UlbvIg9cnoR>4N>AqN1_mBjUx=u)O=w+IR5IEy-Wx`tVyyxLH*`
zla+IKTc#GMAutv_smqvKSWuLF+B(4>Un@yf@VQR#df6orLUo<Y5t>Z#IZgrM>3atq
z>|GVJM^kdLs(cb(PFFHl6?U|ntAL@_Sc7i^B+?Zha^T+3K-3_gEg;GPq7Cxpimqdq
zoj;k`_c`%AwH7JDqVZpEHXpO4P3N!5v-Gw%c8XxAWaUfHk`Y!MBe4>$h5!IB&eb<A
zu?%L?=o3X^<!{Avb`9UNkY?IF>(Mk5XVindkt&xPT}Fy$eNyc#Nh&I`YP3rpZr)dY
zw+)#$p|*<NJ10T4zRxH(8$~OHbC#SDd_E=jsB(qG<a1+l!xm=5^w@ldzpX`F5Imq4
zq{HG*I%}(wNu})TzI{wuAPZAoTa)li17<-hj#u6vWY{{KE|dqpZvq-bK%e_%^muye
zJECqPGtHy4x1eqZ70wUSbsuz+vG)$VumP)21BzX?d;gyPWK8+<z1H3vDyUBl`l9Ux
z1#nImExG*P7eIx*%^0zjoVYDd;7mRo@DH$ubR)YY@rIfILUj4=D6UUSc0;9u9j)s-
zIU6Do?F7EZ+^NX*#F;w9ktvU)Me4R;?AP|=Y8WLTe7e4T<k)zA+uSM=@`&LA!|+k_
z4w${|nuhX&*E?NEFQOl&5E`SGHSZ*ap`bgIy#xNvRcug1H<ho5HBF9vI+BrB8sph?
zxC17o*~ibJQmOwaSDEMNNW94N=5-FItVrLs8<JsehXw)>ysmJ3Spo0e4~h#;%yC)+
zr})ijmkxfe!}~}O@zycF2l$cV^r?&Mpt94l+o6LS=a(-h_*ftc*da&$?U3BNWiCs<
zIhqg6+pDDwpIu8ovqZ;k6W1-OkjKMbZ#vi_9A^*ynT`A)4GjyHDaR*I3o9j>BIdT?
z3|47fw(P8ZLQ_RD{Z#8q!p85O-pNhuar0@Xp=J^hERB{dYHrlzNK0q5-qiflrlxUn
za~;SWd2)Rq&RunQxO_Wpyzco7eniR1wAu!Je&6SKyU6h<ne&hnL38jwH0z-feWDs&
z%rP0DR<zE$I23QK_vNgGd4O)!__@={$Ea_B8fV2~9C0%~9T9z)o0Kayb>jb(keW_7
z6TNR(G-s2S@XrQ11ATH-eeyrQC%fFSOKTgTaLQe;=(UOoVH+}!`H)}QHKb~`aE`P6
z|5@p=AEJ3io1kAjw|;JE7QKuC2d?qI12@xNMRTj%oP9|j`r~~yma7Y3t`_y*tnlth
z5E+YQ5&efk?9Yjq7u5QfWr?huM)|E)eOWS-Z1KGIi$Ae4QfxJxE&$eNI7<~FE1p?{
z;u&n|jr3)~;nb%Y@{-$AxF_cQq)2}KV#4OD5l1$I=2wj~H@n1=F-I`%sN~mr_#L;>
z6z+T6noH7P9hnHz>LCRxB?SK)+69fCwTA7wn~Kv`zzSlx*sL*q$Hqt|k0hMA7hoGv
zJdFb;5%vcssp{yvx~2f*<Uwb(lX)ciC_5oD&2aolx-2oCxW@;hZ<(viJ%IOJm8OiV
zYt%ilGDTBhtcM!J_c(sG-c^SZaZ@Lp^skb$8&E%Pmb<%z|ELy;1WaBYsNNRr+qM`>
zfi}DQ6J4Sxjm3On!6lRIa));tb@)9cM|@#|1K6=n^pxVyH4}od3hgI^LN=PbB-e~F
zr&sxO)qW<<486IO1D{a&haD<~>g+zax7Wj>r4lVC{M}Kn^L){-YU!j#5cx4URTjhQ
z&5Nm+R~9y!bzMJPhGC`(2G|PZpIq{tXCv|}RBkoig*;t}O;&%VJiqaoG`48WFIKc;
z%%lgQQr<$MLB;8j3!ZepJ^6j2mzbz-&V>^Y97G_Dwo~NsxQ%<J%_7&SI&>3*5LSd{
zp9!X>q>TNVzRopYVKc#VLBg>xu~KjOv%JGwXtMT;>H(qUgnE9uz+&sbOH^2rLG&oL
zDfgEYQ?eYqr#+Kw)}S}F&M5QMg9GZp7?Q)5(~4dD7|+Ze?c+w~CgYCb`=>p_B0j6l
zs3+3;*EiI~zyO!`t;uFP*M%fA?&$$bzT-gQ`;0KzrYquZO@j5O)&Z32Rf44xyPkDk
z&6TdbLo$%KCrcFTR<IrlarpsWr>iku4<dD^AKjQ?P4LynUa|XF6`9xz??%6rtmTg`
z;E!=_Jw5WpAxxGTU}q=q7@}3e_1J?b-#alMP+Ce&CeaSbWmAumR{(oD**&C^VU<hK
zlSu^GfFa-dvnf4DphP4)i0+D_&1g;t(M8<MXm9WIZ1ZUfTvZX&O<PKJoLz{Y*Hv^P
z{$TUdV5B~E3JmW(DYxKa*D30+fcY>NpLlL@-gW;PA35;MC`)5vV&Zndmcw&48+&}k
z)2L<r#p71I(W|QWe!Xdx5d|XVta|;!VoPjeR^*C0&IQwlO?dvf19#^cxWF?mv@|<I
zZ)f%h3b*n@!<`_fe0S@9;o8+hP=w5qqP$xa9JMuFki2!oV*jE+9{(Q}lwcUyf)?X1
zJZ)!)oO~iH+{d|BAX8P)buHXw7w${&&mCnH7edZEV<&GCB5jiM+ykojNt(w~RY4-Q
zy|^hI=L8c&ebX<snN`gQ-)d#KAEf5*<K4EGFw1N0jSqX}VcK6858!nS5f!(h`X-%9
zEu=iU;Z<i@(go#}N~r&6G=nZ9F7Y5Qr@OeU+|D@19@{>p#TKTWf#km$@p>&W+Cp8d
z)-!(Sz~P=}>8W48FE`_)-_EyjX9Fz@H0T}xlb<=Ge?kk+qh1KE4OpJ?9tZl|0<T8#
zRY#+FAEeH1Xq68>U%<9_i@Qsc>MooVhV1A*B?GmE3(n|<tP8B|@t2p;Y(H=+0SiJ3
z?OIa!-emcOEIfQFtxT1JyXAI;VF2RWnuWyR#z)u5hA9Up!d2Y!;oJ+aEku$QPwS<k
z>dM@j3A9%6z4IW6Wj*#DZNH^o(}zn71_7+}bk#X%D8<$Uiz514+XQT1gl5a7%L|hW
z4oT*@+jE&Jm-A8Lor*#(O$rB^&p**{N%K3{M2=tgQ#g;uUbv-?i!)3bId>*WUb=P3
z_+M_;zuk0ccb)q8R9G|H`yUbDp9IvezLBCdq1Cs7gAv4HnqL{uS4{l4S`Tf_uGHAN
zI$Q0)SByce?I*SJx)kI!MXVl&wV_P56c^2aE6XE+69&VNXye=ou6iC_hiRoTb>^`_
z7}mmAGNWz#3v2@8g>1Y^>So%!rV+jy@!QLG)@D&!aI}rsy@Qxly=cq2L6uqe&Dc_K
z>xaPwaj>nyy7wTb`<r28uV9pSnnv0_rHMf6*a7@{M>adr3tOJ}W8jjD?ANYSJdr)m
zM2Vxr=9HC3DZW;1G8~wPjr>adftV97!C5B*ZnWbiW&g(JLsfQJEtB=5Y3Ak+*UlA2
z-3b0E5Map8)v6qqRg%3J?W0GXt$LgFS0=A=2xhx|%nJye-E0yFo&Tr3_YP<C{rkof
zYVT_8(xS9gTGXi7s#3dD?LCXwd(+lx&8kgQ?M)RSMoJshNbOCmQY3;R#CR?~pYQ$L
z_j4S-zkmPS`6rG<uIs$s=Xk%y`@Al2kSLA`ZEh?x78TyrybI_wm^t#G+Nj{Mgb>E0
z+u~#3t&)^iH9RJaEC?4UGRv@|h==3V$1$88lS=Z*{PRKwqRGVp`oBZXR5h~dAuh#G
zmyi$-z6u71<QNargy#qL`Ze{G4SI8)@YReQFty6nvclh74Y4rgF(ty5I6_c@gKhsd
z$1Pea$lIqsDFVk%IZ`oK-aURRVKq+GKjHWGEZC(hnylq_82f}sxK?%%BRh8JcjK-4
z)Vk@bsq8<wzv@&srlnFE+I=~yF)N^B<KLP(={cQ6B!?Zq5MQyTh~9$|*J&5R$+46h
zF^(Ip*N8o&$#;?`Hlb;`hR=x{zeW;5jvp3}_ii$tLv!}G43o69ZeEN6kEHO>Q<vCU
zcaE)@pVKr>D%dmKYRz&oY9G(P_OWC*yR_P|cx(<Q^3CzFW^^Dus;id?*Fm0~HSJ#+
z{r9bg<M-k=TIN0`*X`JGcnodSX4KrF*y&2uU};8MTJ`Z5=B?d>H${?tb({m*@%N4o
zc-fCWDlez*XVXy?S_2~^HRC#46J5>p??axGJgv;zZhdAlciPO}_~^=gS}Xo_P;wJv
zT30pjyC*Us#IMaX?jigopC-Xm)`8llGt5eympOhf{R(U10}YDTASVoBZb{C~G1$Vj
zq{;+}86U4-SNMJ+gnjpjNs{WT&V1SIe!q=LX(WxsmNpqZ*z*y^1Z1da{AkcVr%g%m
z5;EY@R!RRm48fWKOH{B?e1A7exteYRLYX2+?im>Qi?7c@gro%mW_0{OlN2Hx^6Y+S
zIzBe*(*(;gFH&zTD%erh^Dm_CfHHp}viG;L$V}_?iMV^G(xz26ZHPm8l^&&DzNJ{F
zI4XSDl=Bv@rF0z7t>(zwuaHC$?C36ab-|^00Fv@hL|@VzdV`B(xr4~5@Xkh|qgEu%
zB`7c{mOH{AEPv~-C^`xjI;!8uPx>aZXLMK)*ePo?>O!!)gXkfi(lvfH>~ykr(X~WN
z9Ju(QHKwJgf>k8Ms&`0Ak%uE5d9~&KlXqZioQS`AQOz!{Yrjj+W;0zK>}tmV52k%F
z_nnW?gQ^Ms^l&W$W0{L=b7>B-ohWt-fAe})X+`n|BVKpOX6@j8g+EE^B!c=x-N@}x
z%;#DQ%mA)eTX2+KKcjcdK<x>UHSTyjOVOFdQRQbqQ^4bECf3xuhtv`3-5HgXD@Fw3
z0g>=fxskZn-)3U!U&cIyn<9;_;NC??cPp~Y7gUIIgR8fnNuc6gn%?k1Y}u0q6eKL;
zwteOhth;NT)W2WvF}qk-JE!MNX8Uf@y<xT!&NyCHm*EkKJYKx~=l7o&N?)*eSt{n|
zt56NsvtPl-Y0M^12H3Ht0b?u!w)(eka<FWQmwl(m+e#`(^@_GM7p#Y@GTr{D+4w5}
z2GJprpU8lDXS336u0<9_{A8sJ`EF-mBg;A8yP)YEU|6qL_B@)1=&a+q_+ME)dryeI
zHPCY^`?sepVs9|Zv8{`1&W*X&^RD#i9lpLSGAen4lFwqfB|17<y?(p(vlwY|R`3G@
z+0biE8?QZ35+4bz$OpQ7;;RYX+xt1*;u`lG@-)=+`-0mNXYCJ=RM*LGL|?ySK@@8L
zxnS0^!u_!zbG1Cz*t_l#oL&{LKfY?4E{Ba{n(c({w~o_c``K?ZGlHo;4Ths)TQW;l
zv8l77Dz$(|cza5TEoo2TSR49kMA$6)+U~rVwNg;a*Lr&W^q6w|B*{RLHr2gMj-t*D
zNvDNAy@)4ufm+Lx6_6)rf9Y_S<z$*8;{eNhV^c+iygw=Zo+>KZ5XCwpoa~r{MS(@0
zh9T(>y`rCh{s&ID>xBJ~XqUK>ua{-MZxCKC<mgbp_KPocNS`UebMoa+6<=-Bo0{Z7
z39x>ZoPgW)sr`MIJ(un;7-h!##Jtgq?Jp=!H94ey?30@8aQeA210m0)R8(4+Y9yhJ
z`Fm&7s-a9c;?-6oL!2$}#I$siEA&U51pkQ)>MDh7?8!l~j+#%=gUbvI46N4H?7*Pv
zw#Yb^vD>Hj3GQ=@m)Pz;!p9~C{g9ULf}buil9|z#e8|Zkv4t5+P#y$BZYI)Ey{)gb
z%>CI0(fOfh2=V^P51tuMPtl|7-QbA19G}HqI!och=ybs0k0o%n3Hy=iP^n~MjXzjC
z@b+!9Z~O_&+&Q`VRRGs{wq9d(uKdwV2dS7nJR5m!yLDDQa#@vZghZ&(AoOAV{_!;m
zZtpX<vq{U`*U{1Bx6oG^l6?Hs5^e~(T9g-B=BkdzSH(ROJYYKBHSK!X?C?-TbYclv
z<eNs3uTut8y4w1GCpH5a3tE4kVL7Xc(??KQlo?k<3iH1%3=Y*y=CwW0n-|4HeM8XR
znNvkPO3Dgp;Ghpi1J3#ecd6~xHhSVNPmi7k-O{IXIbgSiU<Mw7DhAAChKv<~-km_M
zoIV7CNP_H?_S$2a4Vj&(tskuZF}2p))j$@~=SW9vX3`Cxk8Xcl!k4P!<505t>yELY
zWk+9)R=(&`+7^+8<5lh{I=kc%ojArj^=}=s>5Ff-Z6(p14080%ya9Kyudt1RgDsM2
z2-18jpR`+wXTL*i4^FP0cb(YM8Lg?JBB{X71wm8s&APRz!TRmylM_*M_G9Ny^_+B%
z)GKdNM+W|}tX!Gb{1J3hh<Z=P$aaYhIZmVhMmKgm@JlYQ%I)#X)RB-ix|7a0rB<nw
zVdFQ4(wXm%jG6LUv{<9+by6yS=5vv|=pl<+63*u*9Z3r}_mH?K{B=)1E#X14$KOrA
z*`w2>dmLPNVFH8lOGgU3XOGkBQ}5*nZT~XL(BeoqocK*GCcT)ZAWqT?+!ZjN(XK(D
z#5oyb2~9UrYf81KwRyrd4{S|q;!L5gLf&RyIZcC8$W&J|);sH4xA_FTAwxlSa7}{o
zRnDG4!C8##H-YXMXxxpp6ldPY$N)W|C?!UupU%xKl6t%yl1%8%_?9NKhP21Z$6dq8
zPd^;aW&7O8^4+O+Cb+q;Hcq)SlQ8ahj48cqKQt)x#$uSo34>2{VtFE}vbFKR82*Ct
zx{B|*wldkJ)Vy{^$9>ynS2|yRA9%<1p0lQFs-eKk$ttAo(#Mf~pT#DVku$o7I!-ak
zA01m>#OHl2$8LEDtKFvrw?6aa#F+q9p(s!;@f^|2(1PnJ2aXM`iGGZ}7v}oMlAtY2
z+`@wAK~rJ3UC{7wANie)0y<><yrRw9HA-OhkV=l#r<qnNWUFv~Y4qx$R7C{FrY4`e
zE||Q@EgwzVW7V{(n~~4XJg?cNt>Jej+&Mc6Mp=wkJ@|%vss53DKSMpDr1>#&YaZor
zQ?sNwrd8xy#ALWVbq1n1wP55!&ZiMkyJF`xI_FD4qI>9oI-R8%pNM4kn?Rhm(HR<?
zQt+PIdS^}N)Q63xmgPG6m-%@e2n()lC~rSHk+k>SG>06Dv~E}3m~jb+1Moppms(gT
zXl}}`JMeo%Ts3LKjGPO}>10IGY{R@3Cq7=>e7Ka0bO5w<2?`Ek!*k<I5rMOZjchwU
zLu9SzOw6iTm4P8?Al4lb=vCgx(@VO74~Q#gCOw#h7|ec0F-cQe?@PeK$~dudUzB0S
zX-2*LT4R!WcX#?GFB>X-MHbadGgd!+2=V@|7CUhod&*f*QK|iBx6ngy@(=&~0lA5r
zv6{{uINy$H<xP#dyz~K_rFrG^y^l{w)OFN8@G%F=!mdl>`VV)g!nYXw_Evs`@`zN$
zyH_idHgYqQ_N|J&Hd8XAH2^_Z73Plasge3|;dIbvByuy0r>7jZh_s01R>lrpK5mqU
zw|nutm3D5=oepaRzZY!SLNbRRfZEA9oDH^!LqRR%cx^OBaI-vFZq2qmru)h;xfuh)
zpXj(Q3AAk6LulQnP+-a+5;DY2$X}2${xWbn-1&3TIjcnHta~`k$iP1YnMYN!HyCxi
z%@2-GzAk){GqLg7y6Ji2WqvZ!^!f)sjGD_-rqj$f#0$rC;$AeA3j;u@SfZE1eE#=B
zT~^RZA8A7N^x}7=m^$OD;y=Yy>(e*sm41;zyF9epT}7C%L_+R7kJv+d1rP!=yIaog
z=Hp-qu&WFCHSlHh3igm4{wg$)%PHTv5ql}bMj!TG`oP==)m|KN;stai_Pi_4(_caG
zn1a;jd=6tbui)c>Sr*v#&Nod6bCiF>@LWQ}weRFIPJ-rgFMcoVjdjd6V~je;5{x*b
zsZONop*8g)d^&3*T0P|Ee8porYC2yYN8R}Q>ZLy{x?Y+mLv1vD&m%?D*jBS5?bf(e
z2bgJF9HA;Kjr$_PZTf1TV!zX+X=*XV#k;o=TkA~YC+`Mlzc!;nu%jhzU;W9`*JSi{
zuS*O*#T2GblzYhveFH5KE?{)bW~^QPa`dP3?VP`ltB*8*d01`oRMEyO&fT9hEPrFk
z_q2WQL$PNMNVIF@;NcR=l0c6{2Db&y8}+u@3phu?<4!R)9jVtaF_)YxUvDe@<>0?g
zUml0JHU8$~(p&Y3kZ$R>cgSRujMO-aP2<d5x)g4xjW|RLi5LmF_iA1HRfSb?@efVL
zaC!IgTx)RseOpLfWA@fEBTWMGedA00#(fQhJK7sDPb^O&0}3*xGPf2mL#Kw$Dokr0
zebPVS<NnNczBtQC{|0Z>*00xS<q6Jjk96TW_ywsSq!_-ZW#B(~2(4#Ai5AFKV+gNc
zgkMI!VvbIwE7ne|E;;YFl@>zwTMekf$ERSQA8&LX0D^s_pL$!Qs^AUEpt8V`rW{_<
zXrhD>IU_hM7Z4t-d=%v$F*wX?HLnC3Lqgvei)T6SJ#K87At}QE?RTAB`thhfPyI0u
z9UfLLam=f4m4~$tM-g#>IEU|hG?_j`lbO)WB{Z!(280N+y{zbHB>;^)BSXrdWt;U_
z_iulN*op&Br0JHReK0fISNVMX1<aV)ueJSB?U;u-9WZJbjm6@NnxLEI=8($Q6v~?%
zao><jdpCZ%jB!=NEz8|sH+Fru>5o<RYVF*;&VJ+v&AVJoOyT=v-nz8r3>9{5De0Gp
zHx&IE<qMZ;tt?4kan>7NuP_$!nrLH}0PDjC;l9|Z25?Yr;Axro0YQYh1WM8nE&-c@
zOKk0Wi>(*XkxsgDi!7W&^JfI4-)ph3{8g!T@6g29@UxRLd&UQXrQ?AqeH<GqXRazP
zJntP<92e&5u5xZ_!;F0^q>dWxr(v<%%Bw|p8Euev6<Q1gqa%YUot=sy-z2a60)nlM
zPA+<0b(5EvO&i17nP){?r<K9rB)DQELy_{#W~UN#b}8r@K1STk_m`IM3G)}ZzSdbl
z`I;0w`_i)?utp$u#vV8!$imw_^TQHgN$_gO_Q0y<kwqdfUKlmO)zQ&kU1yYW&`C}p
z+{+sBM-Mn(aG1PKy!3D&k*m8lfOWKhsm-HmrY;E{7oUc_Uh<WxkKA-f<I#Fbx^U3F
zSwMv-iI>@ny}@{NsZCi-vy?h-^ZSr`szq*%jEW$z@HDx3$>}mUSaIUNQZeLWl?ofy
zzZ#1ZY}4I)<7lUSmttHF_xPq?pvzr48hqp`2_W1OP+6`;x`QwdGbfuH?AZ7(0h1v>
z;yO3?l2x`7ZcInAN&E=B#aL~!On`ootXVQ#a_39m>Md{#<f@T?Pg3}*$@o<rEC?Yo
zbmA!U<=-8gdUU6ii3)z@2rEdDHdHo-An&y}m3w`Q9!;S=$r)^BQY%cQr~5?RX=dli
za9DD9AgB2P$oCojar5M^8B(4?GdbQj*)+c%9s#mzomTKhazhTbCRk#<y?}6%S29kq
z{+qGuGL8x{i+CUQM(8InrvKGl;Q;__U0`1Vt>RO!O%6K6nQiBc(|M)m)TYX%&9*+e
z=hCPt7_?^+Lq;(1ShC4p5dQXqi_(B<wcD+N3Aj~wFrCAF3!#Bu)Xbz#zX!*d+ej)y
z=lk=WIZvvCy;_|bIN7n%jk{(Iu*~^g6EY+f@`(6T^LIaMeLL>@)L#cilmUdj;vW_`
z**C%#eFG?;;77hEiQ**hZ<0V9RVuGNGo5{7^CUMSXtx<YD!H<37n5Q|>q?|l+N+r5
zy?`ac#UY+t+g$Pl7FC<SYjG}z7Eu_ud!sQY5$B{e99-pn!}T7YDLxP#a8RE!S!~K5
ze7_qIjwp)5^c5ASB#_{N+WrMHib~j@bwd^ljA@NxTcOOSO(4ASuH(4-EY`wEv?Z=@
zz<DY?XF4`k7;g}3kHD(KY%0Jg9KtB3n(h;HXS)n#{W>SiaaM_={3%B{V!QIK<A(;x
zgP#`1y*(eNY3&W}cV;~Mb?HWfl+?*!>6G7b1}yp<?C{q%ENRz};$%GKK2@H{i7RDF
z=b|=)3{t0ZGQXDA8{FLvb6nZ~u*I5cpQ)v1P<1nV=2q>4<eQH9W3}D%SHiW#-ooj8
zVYzhh6=y^+ynzI9Kvc}8MA|srcD3In_proxZqsoE>yr_PAxue*g+PC&7Sp~OSK<1b
z4?sE9+vk*}VNw`sgPB0CMQKTxhDKLN;HQ!&zp6G>dU)rkRjj=4k|6V_a0w0;$ot4t
zYM2lOY%^UuJ?<)9;nF$`B7D&rpgy&KHKWvu?T@v6Mv+}@xWRS*y`|NQAe4par>r7r
zE+|@Qd@Htw3njPqT~&DeD+);Z#p0@Dsjl>_;D4n}#2}N|Db3I9|I`93f#rWIC7c>|
z9-)YR!PUNuan53pz!<6z=EJzC&$Ihv{)k|j2vb5w#OJOs2~cQDc~CfbZWG#`_rtmp
z#GeHr*r5#(vNX;CqZj&+jn+Q^4o`FT)?gpD|25Dge#%sfEVMPi%lR+yTyERRR2vu1
z9<k%&g^m>B77Xli0xB@2(y>EN>>EpW6nMIR@RW6`itl*1>29MCgpnHW3(1y0E>%0(
zuC8Va;8dBCL2JDbIwEWY%8lMocNB+EMNns0Y=ysOU%6x7aA)~**kSNbiRjp9I^qQH
z@CEh*hXW<_d+g!=qmG`m4x|M5-N1>U&CtH=`;#t&H^;S9vh!3eW0mmvxMx*>I%<0h
z>keKk4(CA#nA{@#qmELbmk@z7r>a#p9lqduK98}!558`_%-uWh=XW$MVIPH&NcY&)
zKl^+P43qC$Ee5>;hcyUfMum<Yb~pLrUzEA4W&^<cqfz$r>4UT3-81tzUq0~E#+lQ$
zCIM#2m2lc_oHk;fcDd_zJ#Q2GOnzs5HSu6LQX!+EINa|x{Cj5HvnYdDyvf6bVde2C
zpJUC+0UOD-huJ%1m}V>S#mOIW;ij7z*E^7-Oh)kys&=Wv4U<6<OE++>sj3hBko5RS
zN0}nA+sz*ni1gkCrr8+?yacfQjlZ(AsFjz#zSIQ{s`Qr(oXGb30|@P*&K75hZGZph
zbNuzbMnc<IQ@%>f<$<auZCiw*h@Ie5a)Ttf;}R8t%s3B=>S?zr=XrHdOQ(iQ!?-`O
z2}#Q}KbOwte4*u&VR50%kOA4MsrnEqKYpA5T#4eK86_1Q7u^kPkpm>H*et$p)vXq-
ztuR4)>xqgEz521_m;tGmYInI#j+*kWwZCX<6pa~yU9!?LiT6{mtM)ezK)rnkseF)V
zy*KRR6XWS1xjDR+?(SVdcXUD<{H8uq@>)XfirMr%*lfj!WUC=kG_upvUtx6i8Wp9V
zbi+Cy&-5183U?yOK!br_+qvpFQ{WEVO8hf{;r^=9oDXB9QdM8Xd`H`Vq)*+?j{(9@
zokPbflzmu|;u~_KhF(FK*(0cRWLr^vmNK|g^~U1zm|q-TU8h&|MrUo@sTOvO$`@KD
z5(q<FJ;h#*Jh{*M*b;&y>`WNpPTmvGA$D;sIWg43R~#LNaCyJHgpoBmeHd13YMF4c
zgl|ZDn*A3_Ut2Z~*S!A7z^~`htnPkkg0a4Ho`ygfB7<pqKmQ_#<S?QIZh-sR5}}rG
zn{LWQrXtc%F+tSFGBQmoF;%$`nFX(@)i!ZE?w_I{Uc2La3FYpp;xnZJ>?EAX&DfDj
zB*lu6f|yGB5QNz}ldLgCa$))Rz^%WBL6O;fFBt(!CM<laUjv+Ch+$r|V&Hd7<dq#E
zo7c6JsvBkQKRqmifEv(>6`tat27=#GDusx;s+A<)s06JpAnQKKb<EbpJeyS_y=BKE
zl#_d-UHP1a0k|D71;w{aT!KQn0II8aF%Hy)&yT+nli9~T@0uapdg7nYA*$&ql;TLi
z^)R_`tXi$zeLXgqb@9en5w>16JCSv0YyVb8Po&A0=N7ezle<p}dF!(c=K0Q(o&mIn
zc17m=*ivH9tuo-fz+T4MAg7;3hP-(Tl7TT2`DMNT(?`(qro7orzJZU9K|wt8xjFnx
zhru&~G@nz8O}WU%uy0#LGq!UcRIvlfY~d~mU^2YsW0WZ#^8l0x$$CGeTS<DSdLJ3n
zc@GHc8mI#28Hj4(7gzmAM&AsbiT8h1IdZV{_r*ib_UF6b_So$0Mee4nZuzYHPuPg8
zZ;c&C$Ef;Un-}HC?00v}SC=ALVcXG00KSe++%~|@99_Qjq*$d|sBhg#T)=lG%*k)Q
zpl4tJ#{pS|AxX-bI_jOjhh?bz*=)R^xlHZkxHWZ0z)ic-`yo6$Tor#C8cMeLi}f6=
z_*R`9bTxE5ED;M$3z`)Zu7|hK-6r8FR#k=7b-M2-D@H&D-S*x4hpxGR%JZyU9eWiD
z{PDG)#o+eu{p`0T%pb1Eg$8+ADKQlN!O#9YLF>8NGt>bzt=r=BcC~S4dQXMEv3Gv|
zlldj!4!I_|A?;B&nMpY^dh2xh7)UBxTU9Do{@Ssc+>SETDB}a7WvzaWJ)=z!ECxcq
zZ~c|L^aassuL^m&1jYKM52Th=^u_86&eg4?YfMky??qmP)W=dNkQ-A4RBk_eLtXzW
zQq>2lYFAafIubMWmb691QDtV?eNU>+lac<F-IH8ky3_Xmo`T-m0fbuKdc|;*j^(j@
zHW0g{KjMa5^Y4MH)MD{bFsn0^3#IaG)P#)t+2qe82giNr_fTI8T;1@Ce?ur|g(m(9
zo;6_~4`bu|X<05UmO5O5XvpOkmWvVNWxCuOkq<K+kC>FH``G;vWf>PG1|Hj0iHl0p
z-5$n<G67AEOW1D7S@kP`lHm)Ig=>PeMkSjpma#!{PgwBTb9aT;iPz(V{p|R&_hY{u
zQ2&4^if`UcoUcMcUOM8TmWAn0J<DPM(I55#ApitTL$H7IEf@O=_I16E;7S!m2^^lL
zlU-xf=N6P7#hA7?$viLuJ92yW?Jr-;e7~Mr`YkdC1xV0XasYi}=m!He!QvhTFZ^fc
z5S#SIX=#U=ZI$gBmI`5MH5r{(24tlqPQE+VaB1B(^jlvh!zJ*Nguj`<9XOF$n8FqM
z0Vc^NZEj7%E;s@#gMuaQcYGQXB}Gje+Ov(1PQ%9cL_#$xSNg^V$TWII9};OvJou@Y
z0X8EKV#nDuVs{aNVeNm=bTb?{%0|>vG%dO@EMdRo<Q5$4cg^h{PR+TcDp@YQ0Kknm
zv@foeV0708+^N)5$B^qz=?k6UIMjYUE7_)PDaY<sCBwPG|6#<VD<IPN_Yos*QNav!
zJU4R+El3?+o*AH%2~h5e=Jz9at?wb<y){wV8|YZ4*yQ8Bzx#?Fz8i$Pz8}N_7ibZ)
zTUP3V&fQHeNd2MEu*87i=2?#lmj@{@tDXuZf`O-|-2hU4zw_G`<*>joZX5-=4iO4!
zBl8o)WeQDi@zc!^wN%HA|J5PIClWHTua>+4<=`GcL$N5G2#|Cb9{#er@y6bwa>T6L
zDg0jUq#ax;BcGeSaPzI<(q$X@7Q>~D2%<DH<6vo}#R!Q1VJ+(w_ToPiDbufB27j(^
z#X}c<L7<M=58lG0Eit@+>IfJqb|N=^K!9||@TdM>b5ip^suCQ1@D!0i<m&1k8j4lu
zDhB5|PK<Mbt4U8U<4u?`2cGOWafwWCmO1KdcT0cibGCh65h6UB%nOVv!3>mrI;v43
zZ(_TWtqWP=^;lx8S4__y>GY*2Ay*v_DSg(nAHr*W8{XaHmNAt67VZs|FwC<v{V)}*
ze2e`$BmQlhGCCuM$`=eMvpCsKE6Wx>r7I4DIf#T!N?&&#pU_F!Gbq!6_cga<Dk=HV
z8ac2T7TR9>exK~HR(xuIsuH0#o1X)AKNnv9Z}=Q0O@yrSekA%zYaR~09h-HwQzzYm
zG8d=b%P!r~SAKHA{6#6gWcP3_K-k2p{iQn=DL7iG65kUYQ_xf!*S;*(R?}hHG3>h(
zInGU1GG8{h&IL1`-Kh+O7!%LY&0tkoy@uK{IuTn<UoLwh%pb^9O^!BzS}x;x>51vU
z?Gz@1i{r4ghv-%zw^rhG=cW38l_AB8wd<?BIP*10BB9z;=>+F^Q}kq|s<VtE4x4J!
z8*DtQk5!e;eesQG#V@FRSH-dCQu50zF-CkvpG}~Y;iP0OqDd!39sQ!aL?K7LkQugO
z-Z*jkkN&gQ(;g295WvIL=%u{doB7!|<DM?*hm(a%fV*aGUWL*fU%`cC*;JX5;u+B&
zvv9HEyC43$0>nMkW+mRi()p)<=jn7s1Y9fS7Dm`|n723TbVB`0Lt2!$qwaf7?Ox&*
zp@t;G8!AYNnH<HuE%#UA5~KNg61`%JytcMg_cvcKuzuyh5m%9Jb<KRaDglsQZVX-X
z%8Jl)=f+^s&<)Oeq-8X=lx+Sk9WWB+#JR~DjQuRHEuiiY%e0_seFBrpPY9B}n?69T
zP3yV@1H(UAYoO0YA@!i-A)xXixBLH;z^7k{OV8zI@sI6T0D{$qK!#xhAMbFrmbf_f
z-DF~?=V1)qNXk~QBIQn>&6CfMT!U@ywDgg@u@84f(^Tza`>Q@a7Fg#|%Bq*&NTs?4
z$gLWPQJ25i9C(8>XnqyiUKST@w%)O&5BBx-Gt2q=?K&{T__C`!&M|>Ckk?hW2d65t
z>OaD@H1%g^n{}Lzof<<5Cs{rd7a&)&GqMMhn8>>%si}h!Mki(7M{Mdw!9naPcg8w`
zG;iLubqu1xU&r~nJlJ4hHfsYO+T=%f)T!P6l4ldp23&l4+aX_CIgd^sy(jF3w}a&{
z3QL;*ReQ7)xN--WfINVm&2i`Vv%5jq31p3y{Vhsugi+I&LhqoDRXMWV`Kp7j%h$LW
z5fv%JLe?SSlK?=VNb6haiA;W}3}Y;<uW$xjW#t#L-?G(n=s@zc$M<nI*XdeF@ZRWa
zg4iWMZt116oAJm8N}~Ke8;7*^>|eo`Wz`5eT86fh%Yg9%;(U42YX5__D>kRTC%R0%
z;&-fE>+@OiF{4EPrBol%V7+|9hQ%H#l%vYKtvFPn$66o<w6`u1rS9E2s|46pZT7e9
zjC=eP`Sd98B>Dm9rwA*m>ciK@;^otxF~-mfz2ppy_5G$@ofr6vt8*jVoMi6zz{z@K
zmsnN5LTB^IsrK4`R5j#k*-N04l%_`2NOlIj;@M`Z;<uI^;q{Dz#X!$UJS=4Op*q<n
zS6%gBQ2tG6^ZL*6$+ViI;6~vcs))XDiiGZu_&}f{EDy6v`zkQsSZ>0S;4<R0%<1^$
zq9p9#69pKGO}$6l_GQDpdfLaivw232@L!@HpFIr7z0uSuuGFX|#~8Y~K#xV2@p+Uw
z(!N#XA$Uu6^|FhB7@p%;cBW5|u`8L-8lODKnZ!vVrzUF1ZEh{j_QT=lluwHKS~At1
zkMei_Ok=2H9wusbM;zT|I!%NQoDI<gCi>NWx!R)(8G(B1LPju>M9PEa+fdtQq<-Xh
zmBy+TRNH?_wQifz0F>z&ibKfGe@;x`g;?!y-&>MrE0Qa7>)-M{%C(dFDem_Fx}_;N
zNFM)AjFf4IHNFpc&L9?0(K+SdKlBQbR%VRlJ-UXI_R|u?C?YIaQ@r9JERATsz5HY~
z93D1K3_pA9NAdj9+^_o-25=1B4(L9-tIaKMO}MeW&~%y_XLoQ+BgnC8i9XTb+zZ1e
zMS82y5h{kqqoX%f^xpyldgw*kfZgGktAU--?*~(5H#_AbpoEc9HoEWqPt2TT2K+@e
z8nr%X6NCpY$pIbL_gh!r=U(0x1Bu)Z6U9$B<Dy;);Q6H}&^&1n6>y^o>F`i@M(^OR
zs&Sdo(cF_4=$**Du{h2gZ}74fsF4`BGhmy5ISy|6Rlb`Gz7iO25AP~;F{SYfFE<A6
z%{7eBz~Z^Q&6kYBLNPU5bVKEG8-K;Pxq-bPV&xZ<T|y~Y?;Q3LI3?lz%54FZ(%+Ue
z-%W<a?JR$^pTMw2DOAx&+%sy28rzDp*00scuQR4j-Z;C?ZViCuTXvm!&@Rb|Dx}Sm
z&@wD9{j=eZ*U4+fXgAr<vd<2a!cQ#m#rkpwpQ<-jXO_xLHyTa42?BxYW8U@Uf>ihE
zDlk*0ifCCEkuS}Fsz4@m+Ld>*-+u`qJyYQ3jUtm9!JX-YUCE%+HP~A?O6Iox#X#$D
z=`i~T6&v2U-bZW<NmS>yI73p~;d+MP>7Vjs>BHRxt4M2hvi=2;IcURWkKn&+gkDG8
z<q@cFzh)JXbYh|;bflR{?+)0Id!5`J`badl%WZ)iO%$xBr>|=6=^nrg7m?e9*F6%*
zb!?b!%ZO#4ZLZZinI=zn+IGUEg#0xut_E0$#+P#>f8w=g70w$G>Te<PWUikg)1)#3
zmHn>i_(P&hy|S99`XFxr$miJ#ovgLNEt~Y7S0h!?Un?lH9r91MnWi8x<??goz*fH>
z-TFVObIQJ*Bi<7qj7PY=Y3(_|ZwgwjGt6l@g2Qi)?HpF#1+h<FUAzsT4uFP!B18So
z4^#V1Md^Fa`IaAD6krr=RhefjWC<Cw>^uC`6?yu2HF&iwn`*VV2#Yo2p6BXz4?+Q~
zyH=-fL916i0yrP{(AAVz=PV)I@7OWvyOG@9uaKJ?NadTF+kIZT0yT)#9?MAGGK(wJ
zR?8kY7{3^Fzw)>bKs^SB_ZN_lHJzOf^`RgYCHEz8=+E{?iXheco_oU}bYNmpr`-Dm
zz$iu>L?_Srz6JzGN<)t%q5h}H9@$*{VvQCcF<knm#^;ml;fIGGMs^OZH#+4~s-Ct<
zTm`$L{R@Wg>mGu_?V|&aG0>jKyUSvZfWite+zX{ukreBYkioAa=$pf`)$_UYc4-nD
zet6rPvw*FbMgPlZ<M6Fo-R=)GWG|*Ke#MvePmAB#o3uT$5<JMB;n*+r>dXCrt}{`)
zkF>yeB`j)G-UJGonmLftS#jwoWtO<9^V)+X&gT~p{mE{H024s$=3W>B&5UO$;{PPA
zubJNK2NbU5ZSXD91}79|+|78D?{nTK1-@P>LO_I{Sckc`S;dqy?E*h)@FyJ;s0Zq(
z5JBrnV(~7z#cg^JF-@uUH%%trlbT+4n4Sms&%=M9L!Jn!OPgcNNXPhq3mw7Bs6nUO
zEvQapbC{*%Ue46wX}t&v=9PN8RI|4D7VcJ~WRuwyzq?mG6vL4(qr0EafLdr_%=kia
zb7`^`BEK6o<TK!7Cfp!rJ=fKHAZR0Mf1IdtfO=YmE7l3{Wyx9bg-!oTdfev`<4iH?
zm7no_M>ehsw4B%<nMfnkU`&0;H~5muzsj)hL&30qn#5mON0nw*c54fvG@w91L;D6@
z(t^r=mIQq)?%)iII0bPM>dt0*##6vpvUu1p9IJE7KDis+^Gk9IM2lyjzGlR(nCZE1
z4kPh1XRrQ)oDNUhtUI}kenmz2Q$QDRZaV$=_~pDF>=`b0A=TC3_lL>N8ZBG%q%C(F
z@h9GtZ~B!Ea%X>YZOJR&%xDWKxp_N${#Znc5zmn!aKG41Uomo{AHj;&C96L1WR{Yn
zfl=VKC7S=vBFe+r;gEChT7Dg!E$z)(vw(G*+Za@ZsYM0<>OC(AEjrir6_p~lSb_C~
zGU|N>Pz&@l2;~OQ*q{)<N_Fx3S43y^;gmAShAQXmqM*%<RTx3nVI4cL(>L&JP6^4v
zM8yh7j`ybcxJ4`)iSBtP_?*=?4@AVdlFI!*<N(!ZoCc<Y?apotz5_7sIN(~nP}he7
z!$?Gj2<5gRCQxxjiD!9_x`IjcZCh7uzsO5pr&GI|dAe!_IX(BYXiDwBw%K<_$$2&<
zt|)w8SC8!cK^<lPg(I`4MwdLJH*y&$J`w$Xn<JAouDbq30_0=U+2&f>*jk}uHa2#7
zPv%RWvd~VGjhvP+I}Kq(QSo=!K{Fah>kAK+{_p;>0C?~pf0-;Ojlg#LdBMHEs(}QZ
zg5VEl0dlwo`ki>Y-i%Y*+_w$3|G?q%QW|cN0EPLb=_+H(+w$2p5Mkz8qdtJoC(;nb
zyXx*|>k4QJc1Z|Sq&fMq1fdcOQUROXs1#XRc?bBEW4go*Qr8#LPg&gPSdroc8UL`m
z=cMKQa)8U#{h7I^1ZSg2XUgvI;i;(R3x)aB=fYa|ZS&Kg+VHZXwM+~n^<mzaQ}=)m
z#&h#Ffx$b~|Cr8?);XCZ2XQ50UyVsPFU?)z@J;SMk;T1m;l(!A<HW`eAB|zE+5aU%
z1sG#7U@Rz-a_`8xz_Ik9z9{#BR7b&<&l0IS48@J*&h0|AKC75lWQ!vnLHQo1XRBXs
zB)Lj9jh^~bPrVSzu$5b~F0Q_E59HYteR%8@In6Ed!ED)aLXLLrFIN)#j7K@(VzLA@
zQRz-Q&-cwYcfFr&Y7a^f=ft^Nd?P9F6^9TE0ai{H)&-*5@~mhMSU6J)=kls1hV{mU
z$jx@ht<}&4jJk4jvt6W<d;vzknbV0UefFK<*M_;m17J=oZ2XO7SL(n~c1pgATXjNN
z_Hs*fga@R^1EJ$dgS$3Yu<yEWHC@3IqhBIsO*f0>tRA?0Ir;zah?x$UVVRBd6fI<U
zngcvgFn81r*B&GTrtJUqiGeBGODfkWyH8&yoBnI_dIn;3#HTPK^-ZmI{KHy9TfU__
zsbtGbU+h7#;aSy2*O_CxDQLP)gg&pyK>$^=Y_2Lg_A(cq9X%{`yor1qI<s*A8IcbL
zINATC8^*+`;ZKA%#j1W|l1+l=&B3R}7mLS#Z%KD=lw6~{PfCVdR14K)qSqxg8i?NI
zcvrn{5^(ts>N)!4xnH}mm9ihD6}vBE7@4RHg-p})5(f#+46L^S?(i*6Q3F1s-+K3P
zU5f=$P(ljWhQi-$Tc<Lpb7AP}$wx?&Wqa}XyRY29dRgu?u>Sy1|H=RGpQB?V6qY>+
z-ch#{PXs7xw6B>|&I59s6)*w1@toy9HlN-kJ`&_Qnh9Ew88&ij<g6eg#`-cO5u4B*
z-@%Dr-%@26;TngDQ_*bD{sgz7QxEy3@45F5158lqWcSC3!e#(w!R5>#&18}^On~+k
zu)b4&0W6!2b8C(vsaCu1(oD$gou-<D8(TUztjaUL{_?=9x_4~HiG<r52-;DQ(Mt;1
zJaK7;&`K9BU?D<QwTaGoh0)yz*;zqz(jeRMC9_7%RHSzk@&3X229z%+|L#928E29k
zv4OjrJ6&CS+FuxOZRX8s9_Bw|p=cW`1>`nX>$=IX>1yfk^Ru4W9y1uz68a-fwZrJ)
z=^RaQIhhp66}(bL_kpBIpIbn=svxFK%g4C;Y0#1*)JwH<_J@Mfp3hU8k0-=9j7Gz#
z)2`g5;{s!SIg3y(pWf*(f{!y**p@eAV$NDkus~+;2ZDBE3oCw;bNZfVb+9>m*Axol
zGFic^2$;6NE~@<t87@{OpWmK08cltpySK19Mf4;r=n16^qalKY*Yh%!pS5u!77tDO
z5;23z_M#bKz`8oAlOoM&WM3zK6nuqLPWx9D!yFQ*$T`n5O0%5^LYB<><5eD-jrGRz
ze|KlJUzm<$l<<buOSgzzU!`BFIJX=@>9f}6u;+i%r{{;NoJsxa0#75E62#h3YcpJz
zIO&cJJ71yA_AcP(<S>FNn$;S@(d7sIVtbAf27q;O>ue_`zH{=4D61x9f01@za4|44
zMd7>A?V>A<=04nv_`X#lO^BY*twyIXc0GH8{)5oh!q!s)ds!4g74^CRJQL*|^Lcq^
zLNpTCi3Q>M86N#?tMEU@80W!7{(jwP9lD<jKWx71Muv+u-N?m`Ejjjy$Lq9m;y)N4
zNJ$XkBdVysx4I}assi%ct~s#x;>JIFFS<$nL~suJS^HwxLk9F!gaomxdzbT%dmwq@
z<2->3x3ST-lgDW3us{>}QGTfn+uXh8b9?dMvFc-0*Fn}6^jgySEO`F{<R=r_dPF0C
z1U<8$W_k1DLs8<yN6A{<<hLHjui6ixmN&WF9pTNcp=RQ_E9^`j!SJhh8IN?A-gY0<
z8kALCQ5MJ53Y7xjV9W^ES>gD?F{bquSBjCnSV}OeMk<Sc)8j2HnmV3nE?A7pui8h<
z-<`*B+{ZcebC%8KQKa`4kr^!n>z?g1Ex`!d0-24}U=M|Gm2kjh!_7o`E1Px`ik)Kv
zTETd8L?wJImo$VOUvGL-Fktq=F<vJ6r%ZbD+Vrj6Z-H7LzB24E<%ea~f0U*M^Q-XT
zqJt6~txCU2F8a!`@5Dt>DxT)2C65`&%=0V-O6S|t@Rr_mv3~2lmL=P1M9dsi9ScV7
zKFi#k7L{Hdb(uv2E>KSY5}n1O6vLlufFo(_&7+9Apf<B>W3Y(e3u+@UT2revizZJe
zRyB>xgGz6aPmnh3J4`41!xBH8*Hm$fP|z~h$!uk&?B>lqwiBWBWq-N&F-~>H14iXm
zWwJESWoVz@%vj^12Y~MxIj-+|i*JFVDNUWv2%cdp)0x(tDaUM+zpY<Vixz~0CiY~9
z$6f(dx1N5Q3suqTDNAIRQea_wHtc!Ua7<Py>||5ow#jJyAD;rJb)_Y!%=MW<t>Cdg
zPKt_;E`&$*cWU-^K^tPd93T5xeUwt}%wWuJY91a$jpN6o#+sHEJWU!+uFqOu@doN~
zzEc4BC-Srn?C6MjTF4+(SqK<#9ZYXlgn#!Ifk0OnR1_cUDqI1KEZ4&)MCWKbNjvWX
z;qf7DJs(0n_e2P`Uhfa1KXlAOr>bsp+_od9gMFzW+fZ?gA<BKFpSTfdR}A2B*MKS{
z#U!!9+$7|?hj8N-Dh}Y((cL9F7hHjH<!6M9gn9jpSKz1VEyCiqKt#io{t{5caT(9q
zbn7~0OAbg<GkSQ;X}{q!2fs~c>yx<%g~$knqT(*Vgap>f0*eWLp!|n>$Vva+Z<V2&
zrz_#Z%oTLO33V$|zXqIif|nd?F+F|ji@Y~|9=pn?I8gv~@#gjuAT`m4l&q$-@1NPv
zo#eW(Ow_s@)`edKtU6@kdA%91rJ~uV2~k&Na0ww1IhsL@9DS2A7ZcQ(q%g4;5@48`
zm*MyUSd*c`fJrAXb3uS&K9w5*ZOSkhukN#`3EEHc26AR(uoUAThqQsDzt?j#hOW$u
z@&>98jR}msCOHSYncW)aNXf?J&rdzzoo~uo|D6o>x%))1aFX5*!^3u8vA9-npGSjk
z_nm)F^10mj{3L!7oEa-I%D*Fn*%((TqU_gJ{H8-tp^XOJ;yI9i5BksgP>TDgw(56W
zrnIyF)4TT&$~;hsyq)n$9t;s?*Xi>y7cc;plI5_+!FR;Ftz)9qIYuv1VCl9-njio!
z;aV=V1YM+&g^W;c?}vSuSrrLHtLxHMccdIu1O#;;z%61GLJOObJ-cc_2-_D$IL+?D
z!y6w!vPcGq&PZoQig&LeYk_O~aKS7y?x0$%k|gVAd;^>&ibWcr0S>jR3obeJi4;M1
z+=r4+NZPtog_Y0B3Gbq*XX%LNm!b3E;~p@koy@N=@HE^MT)oQKB$wlq|Cm!v(T2NJ
z@eMGb)UOiD5PsgQGU}rP+By^@Zo{`eZ~C>Kw~&orHp8u7H1f%hnMZuCj0~&{zQh}d
zdyT*L^}`axCVgnr$)JNvyX^b_t%*`dM8CeE`(X<yRsBYf^1BJn@wwT4BFkSVw(CG4
z_u7VszG9IojUS_%^^>N^RueK4;^Tce=dmzHt^xOnuFDJ=lFf_fFrsvswbQfRGDFS&
zWmf%5eZghn;F2VGnqzh%jWpNomgn7xR4?Py6^jPAaZ%XA1k5m2zWF}BQ=>r{VGh%7
zgPVen@1eohN#o%S@-SuAZoMgSX}#bRjVg>5QLZP!pB_&mvD28*8|Di;YRf|8Hlx|m
z7{pmE%IT>h@?BK`z_4u`50SXa@e16*0TjsBz^)|Gp&;V%yEZCEG69VPQ#s1~fO}Lo
zSu$SC%Pm6t1u-6mB9;e0R1Lhu|I#rvPWn+(Pe_n{eq)W(NgN_a=)uVow55a&J}_(*
z6gu~K+ODgt8c0)YZuR8?$7u+v+3^D%=4Gr<#hDE{+2#3kpvj+it{$tqo(Q#>L!hTF
z{ljoZ{~>BYxVhx)3El4LzU25mn!7WV8_RAP2>aSk+LPQO_3OTW+Bp3hsl?=K%lmi3
z=<z4C`)5*(Ek9FUmJkdreDu?2G^bCFFX1%NcGtZ(%$D}g=4X~Y;uyb^AjnM3WjJBw
zmeYF(=4m_-3gm0m2j^?g2vu;xsyVzv$1GoNgJ`K%DtX~(g-8qTl^Ov#<I{6OHW<=!
z<7D*SJ$z7{8BKncYkZm;2q9D>^uq(CCR|&2JIr#Ut9%FduUEe!_uZJ=OhwJspH3pa
zu<r$qS2_C<pXq0HF)^_E|HCeb6x+I-$FD7JVIK}m>HynaMd_1V4Sp*3**|%gq$RXN
z9{a5`ae``IxtN%<74F$LHqB;jkkP*os0xTyCOxl#BGfv0tm7}D3ZnT%Rd%n%N*7*C
zd(%nC&;Gbc=joGdH(NHJ@@nI$`cr?GLw$|?gB$2jFE>uWK~Up4-*BXutzN^pGhoMm
zCW-^n%WevljLSn*QbuA%cPCjzJ#z%Sb4atKMJD;?j<<sV_Yk^qb_dQr);b}0_PI0o
zG%0IyGXOmwUJa68bUgDJ_K}AxFN}#1lozEMA$rya23cLqz{NIGG6BnyLn2kMOS?;o
zmED&oa~^^V6Te?2=r)WE{q&nr;JeNRG)_&ifY=wb8fNZuwgqlq=DY3GsHl+N*t|n^
z&xdgQL?USlW7^<cG)r{I3LJh(!o@QbxDu_46xS^j(Y@NRL7S97YVPavocg{zDNjl#
z8ol+nC_<c@`^7Di5Mme@cG<5?z#f++JK;;=mzMPiqxXsO_?nx4nseZSlS>oa>xpTV
zR@YSqR<?_g$Q^jgj;QUV`K8Cgazqr=9(Gvv^s_MRa_s9jS|aCZYN$_ocBjzg^A{R4
zqwGvOi5zuMJK@a!pu|~X-F&_-6B25Y8xO3453Jn`@14T}j&tl@C9PN#k?3yn7TV=m
zZGzZ(1<m@_izka}ENcZ0Ir0W!A8zi&SapJwE2J`F5I4;A?R{~r0aJJYUvWApIoKdR
zYrSY>=3x6ht@9KS&E#<bz7OU-UptDhB`1vb+dfI%W%v=REQEWgU*?X=a31p7!ilpV
z$q;s$il&vduVA_6BHN;bD|OeeGGrLJf=<87hAO8Kj>vJg=ul!h82v#8qPhvOpDP8K
zR$C3rC7ZhxM2o*CwARMqCss3ByacSlaTm*W67k&?9%v|rk_*2>vB*H7yjpid3tsTd
zkxMq$M0jziiF#$i<7`rdt~zbNRX|A&1%tG7n1bg0@X#9$9&>k4*SS4DwY&GCV4v#P
zLpPO>rxR6sTcoGMRTP6$4%1F&jDR3wif(l=t+)KpM0Vr{0n}D@yc?NyY}^tHYPizt
zJhEo-&L0oat^8S$ac};%lrz`*obBS`7EHtzCX^yJ(sp^==P&_%9n{5*KR=cQY6Y}C
z@4lZEM;c<rEn+nE;3hdyMLls~0s**pX96)HKcH8zF?Onw(*NMuZ1m)bi@QUyb2Y2Q
zKuWR9#yZG+foN_V1~O8#*}QFgp5Gk?7pziOP3vAuEPntc7-u}ZKST1YqL3xP1fI^`
z>((e#hq^Ue62aCApb^jMs=kg4CZcJdsr^jvydBm94m4Y1i!Wjo_)_8m;3`hJ{eh$!
zw^?Rb+O?=1+U<_1a|S*~NIzyo#{gE&142|Mnb{UJG$?G9hkHoBnfqdX4X^A1=xcNb
z?PU7UFmwbvg5jTj@SP^ubuGUX*p|S1B8u}tlg)m2ksz9<3A&8uLsyn{3UDVYCRd!>
zR$l0`A2ROE-`i!}0zP%^$-J=*>J{|r5RL3UDB)wCn=Gdo12owfd2cZv^Dj;(OgP|i
zY_xw`6cvvY{yo3~HaRP3(aE0Fr$z0ZVU_s+&8A<c&!3=h#DQe%OS?J~xJ4G90b^3L
zrTP~>>pb#4q8l}H_XjfpKs9*2rG+6$$fRB5$p<5>A8zwee4~`8X}H~qsUIJ164<M&
z&j>WL8!SHaMA7E614|{)<Y#G|?MBPD(*|gk4eBQUP>UU8zS21VH{f;QaWMRe;pfa)
zLh{rF%WJM_tj>19`E{ute9JulkBi-b01M11Hj_fpl>cbM$p4iY@(NHRQwmQIjx@P)
zKNm$!@B$_nAYQ(9JV$=fe}9Pz8DCd97r!?T+wSF}_JeZs2gH{r0S7M#MIDlA0bB+{
z5<}4iE9REn2L$iK$U+6J16DsyeGN;*wB)4!CxGPwuVwCkIy;~bglhAM5n$eton8g>
zB%b=S(7=O+VdT{aupj23ALPxq1+-qwofPs2vRAGh8VQd6yKQRs?!44i)ag^dN3DGu
zO&=}0)OVngD(K495M=3mW@c30j$s9X!r&BsV36K*H3s>XnFQCOeE#;a?NiC0Q0SE6
z6bMvfq7`}v1gbDg)j9sVa~--RQ&q13<!%dXW1PqC*NPE?Ksb6LGf>#opLJK-Ik=GH
z$?M5b-@gzJc`nQkmlUUd5C}A*hM)q~SUpW$9AD~`oMDq$+m`3V{22WDPVHM2Ck=22
zhVw&+-P*ky5-9e*b$ch#H?g?8Ad?Hv3j$d@1m6Q8GO2g&hJ=c}|5MU(Aly54bgRA<
z3<9l5o`1(i^Zsc!{KZw@sx4ijIj5z^3@<YpTY=-QJ-GO3T(8W4rd_Qp?AnfI6j49S
z(V@0o781w~0{!woKQR-8=AEQ;#t*#w)v}jRs{k!q*Ib+1KNf7R7!G{`&LXD-wEx!!
zm3ngjs2_{Z_D|l=matp@plyiK{vBU>9s$h(5J+(9TB^Ix&dZjGQmgcGgPizsmf68(
zA`l2RJr(-2;A7@t5T_xZF)0YPk6jcw4f5pFND%N-e#32-tUWyq5`S(wu6^a{1C6Cz
z5m12gPfE})aHmMZq|KFJXKCZ#h8!$qq##hP`gv0rfG^%)PG8pWJsAao(1Vv+K%i?P
zoL5@QZNzke>*hpVq5_4*PnP{G$>KW=AhcmBWeih?7C#79?Ox$>u{V4t(o6l47!=0u
zmPra)`_$t`pXSXNntL|9uLrD@g)quj!*OBaXQ5$%tv=qlMO45*FglM^d}e%kNmjJP
zmYjKa7I!My*Mm#2sU;%NBZ>1-Bn5FTf7k4=h#|Z;c9OVbw?*@63EBME4v3JgA%Q}^
zaHMZ_w_D`R1E7WL$5tT%2oj6Ds*PLkxHF5kSI8f2m7qyL6QKN|THqRB8mxlA*a0CT
zFXMn9f<Ta4Kxh7s4@&fkytAQDC6UAPfsFd(klD}(0#!Qj*apvb1Oh+8tq}4tz_I@K
r^}iAL-w6C~1pYSy|35?kcm0g$FE0yan7k#$`RP@jYARMKSiJr}_vbJf

literal 0
HcmV?d00001

diff --git a/docs/articles/sids_files/figure-html/unnamed-chunk-27-1.png b/docs/articles/sids_files/figure-html/unnamed-chunk-27-1.png
new file mode 100644
index 0000000000000000000000000000000000000000..625e71f07f53c275c51ceaff3b7200ef5cc66fcb
GIT binary patch
literal 77673
zcmeFY_g_+d{03}8EiLWN(#+IK&CFHK+-0RXDfiag8#gW_^EPiYwcMMu(46EzMFq8T
zuiT2_NSuhcP;tO>{65e3UwD4{@`A&89XP;wf8Oi5-WRd2^ffQD++<;3V7RRH^0@&6
z17k1)!?`yXn1CbJXNPToCnkFx&F8=~aHBqJgaJ<%eO{XTGcfSRoIcJZE^aw7Fx+O)
zdj8ZXIA<Ln@+l|8g8u-_7pVOJzdwmz3oC4N32m_a^>F&e`_{QPy%Ud_eq3x~`?aC*
zwi07A73q6pOvf(jOqAC{wuiNmZ9k@eUHTz??%Avgey!1R?V0APiB?JDgT#}s2JXei
zLZhFJGmUqs|4PmD?jK;9b)7Jo)TV)><E#Jk3;%EPe-`*Z3;dr2{?7vc|60H-jYWK7
znc4CO2>4zTtfnRY41<}w4&R*kH5N(?f5hWxby52s;I%RtN~j7*dF%NarGY<-A-u~?
z>usGu@i#Lu2};Eo1_rZ8ca%l<VikiVgKg4tbKnRALz>8$(?Z1X)=B#<*XfR3=G8gI
z(;c(I?(z+W7W?msi7v;I{Cd7#wjZESkqYbdpE&F_MI}qTEby+kh5yVkntZENqXqQS
zPsokl5&5N}Z78V7Zn>T>3D<to^K=d+vPVJu$*^6wR6==@Myk|pZCRXR^nkO!K>ssh
z5FOe?p5SVBhzkqFd8)}ds?x|HRtzTI&PU+N^nS(dt%g9ur+=~7YvV{zzL~CKw@5&M
zATO`su%9Li@8UH@MWnTfgz$@0plmX{ofH+Lvav>oA`G-%UpZ$cI7*}CgdaRHK-Sgp
z=O!xW#CE_lrZf;kMqlcx1)}{rP?7Tq+apc=8lMif1KOPyi<7P`7T?}B@}ZW5n5OA5
zX2)Sl4J7YHZ)_A>nwqlURYU>;h46Th0Ek{6dF3UG4sGiU!^5u@<!OHCoKVb$4hw^=
zpX26P(f&^QPPRDv#yzc)(GV{~q)GDDmKa5P<+vp(Gk9$^8)<f5ml4)@^USQqoV>NQ
zNPso(E$oB)(}5I4vc=eNvO0)t6chjkvtU$2cJ~T@xQ~w1e031XQ++a3I!??iGd3(9
zH7M8DEAk#~FHh4(rMZ`9g<?L1=BF9tXQ=0YvOm2~WY`3X+NglD7NhMyw5fl{w5WS^
zzgOYeH`P(<2+zQLR!6bCYE@AoWdvMB8)>pamF0yRz(cKcpzfiICOYMLBWtL3x$)h#
z?uElfzU30oyy!lQR=I^vd1bQ&CSp|8->F#(+U`Ut<+Gh}xf88>k{#;A8h>Otw!4_n
zH|6K-`VgF_maLvM)89Yc;Hwj==*(yMC69m_7B&#ORvoBkd)N@RbfCt>ASQpdsioVX
z)QK<-!;E4w3^Fy}*1cfCluA*5##LLQZ9q^@F-m16;cr{phJ}Gd(ZukDLmO;)!>vns
z4XHsSebUb-EC_?4`s><=;v}y0>H^7G$<!o+M<Q}dwpds-72(H%D3&W+lHVA3*!(KX
z{p+8p?7t0xJKdq!tJl7d8X#rgokMA~6qtagZ}!~W_n;IXQE*Dc5hRO|6>k>0RwtUc
zeBF6wN&D^JZQ7bC1-W&w=0p*NHis%+4-Rp`<BS^9;ik|BSNuZofcf+CDt32+5Ou!U
z4YRrZ{cN#|dL~Gh2md`b?;|)0C8xFrR3&xAYTx78DYA@knps?ZzL*s#A&E4RWX9h-
z(*R*48#K!?1fy+>g;T>C{mVit|M6_Rb*ZT-0($tw?quzY^-0#UBL2AdA$^U*hr+FY
z-=-1imfhssA&oLG9Y>xAyWqwHYWK@~GV^tcN8GDtoNHOMKD61_R+wi?KTG$%@yXhK
zpEQvhb)w0IAmNGf&UV4~pK&b24bd9$Xs56U+7vx#jIz6wXcH;{S31@n3O<1#XET)K
zz&*T{wWrHl4ci&pm3xPc7F457f)-KI!aL(+*yGv#McYQf6GjFL&9_`;uiN=ycT?*U
zYZ`d8k`8}AFKvA2!Mi_`94id>43sZ4E&e9=IO7sqf4%m2q^1;YVnGL2j=modwA2R*
z2ho1~Amx5pUVOX0IOlm{9f{MhtKq%Q5?xE2qA3L}mCNfFnu+N;-QX;$Vn^!o)D>U)
zt=rd}6L0p?0dMb+RXXM+*6i2p<HT>eN2xgCkt^$u<ye-MQ~X?68T&Co&oSKdE(b^I
zwYcaMZA6N8TS|}NFvL5)W3hC@7FDK<KlZ@gm#xih2u$hW=H(rDE>N%d=ylic--J{<
z;>ZGI!<Oy0i3jRqyxun{bGNv-JI+$*QhBi6CE!}Uh`$l6A$H4o%3)1Zcq~P5)I$7(
zi@C~obS;O6&;3w!iD*Y3oNjgi<q^TO9aTjiiN-PSmn_kj;uB>tCy=m{-mZ_j`rqol
zO4E;dXci{Wy~OPpNtN`_B!P3wevWfiGy<wPxjI^~am=e1GZnPN4<%{(+s)FNf|eZf
z6!w-1_Bj|_RnFMhz2K%&W?cihD(+X9kFH7dT0n#AN3G31g`%k3?tMn^jLyzKuKfw(
zPuq8{u54^{uDFKfw%otQQe2}oc1)Xs5dIKP<juZTtw8Ume%Oi7lk;BdnL~Vjv1%$E
zKR&fUZ_LF6ZwJ?wnP(42#X;65XX+}-&o*goThTvH*ExXLB-B6cPqgh!Rt7;oM5{~0
z$ID?(N=MfyO~HT7_;CInz(HE8Da_CW60|IzhoSxJtkN~ex?Ew^<zq+oqNWPd?}Brb
zl3BkBn2!%Peun~%)$`J&<-=?KTiq*UdPHfXZ`;8FsBq^Tdu;=cyfLmpC|MFSvgR$;
z8@|RXiMnp2_NBD+GVyNR>q58kvBUoLX|&tS8M1L{L-q{3?V&-oXCN1D#u1g3myobN
zTjTW4{?Ot6Q2^T>f7gl9o|yI&uy8|DgP9bSIN06&HC=*wQuBU3vTI*?J5{=(ISl{)
z+v}NmzgPR24q)+6wKH$WfD&r*ajOWf4-N3Gc3X1aj^;9$sjC~s*XM7S*P$9%SxwE4
zKXyi2Dx8@~=+9){cS}`QV*F!iHvYxx!D50E1kp^NZkk&0>|mhDw7d7rld+T;RhV2%
ze_nsPaj8E&L1l8RuC|!O-yED@Op+b;KhgA?-NVNX?RB-rt=><su7pquYG9Lb!U?uJ
z^`8jI{0CLx$F!J2YuLbHydm*AONb+RWci4TG5CyKn_<BjvqvAG9v1j$;z&ok;Y7Vi
z2$5t0aneY2=l~8fmV#<v_iV$K>ia-0F2$qP_4*#~{j+S!U!0jy39EB-brnNm8h$jd
z+UK7P(2>nv(1zL|!U1B3`-b_9kaJo$dOlwiac$3gA_cpVr#$;_YbTS&`_uHVf7!-e
zT{4?I7yC72U=JU%^?R_8Ur3+brgzEMqsnbGD~C4^t$%D)Mz&7f_nZPAv#DWq<X+zF
zTD`^@-N;2eQO*Vpvm?`vw?qe)GaX1ryyqEQ*#Nh1yYD^mXH7!4G<4<9$RgG2vBm2S
z-a40U)VL)+p0QMN@V_P2*WjW{!;BBoagr@l8e4dyQk~gM>qhzI&Z(m8Arq9IJNJNN
z&#$R%Gm>kGaFIKhY*BZIC(LwtXyWCJBCIxdhQ*6W+Hpx1Bu`>RC3DOsE=B@Aq+1)p
zyUV42t4|=zyJtr@(dk<koXh1sb2SkBo;LV&>1V90ez4uVqn&fMl+V{(wnAPP>(R5w
zHuQc-KKnXa2x0$7Si-t9R)?z!1IE8QWM-&A?tumwG7v$RH^(GwbUR3Obqze@B4swY
zxZtqMDYCW{p&NbSttR^6@(8~pDD?aIlyHj?xV0-MZ>FLUB`Y^J(-A$7wJ0%VtV^(d
z3|~G>B=qgLR5z3=?R!sUhSiaJ*ZP+*_e4jx;?Au;kSr7Ipy^rqM|{IDnP>NB&bRIc
z1vrxr<EzcWy!$V+BMi!&iCNL9%?DBGc|GhW{jh<|{A`zVrXIua|Imt25Mvk9nMSB-
z0h=U4Sukmz^|D>w2ahp9QigfPw?E#k%l40W>t>SHrbHL2`VL=)joRetL%FT?R4v;K
zj#Sd+Zj7&g2xXNDmb7-Y$$ZzEzefwZi5##BgZPAtN#-f%ae?>-HVMzY@%0M(<cZ{5
zk8w#i{`9!W&-2r0r=zC2X6R0>a&yb2IfT^fV#4~SU4recPN-6rZ92p*;ITt$m#1yx
z53xy?ME<UQ8cuR)U^bZYo~WnKF=su6PX>I{V~Ka7Q4MHq-(CmBGTANOzh*G~Llq_M
zVu?>C8reiBAgmh=yplufa@nD`ITF<d*Sux)8ZTGKmmhX(&5PH(QS>XvsX8$}kaips
zPm}cs^;;WxGK}MClF6~J%)nhre_Mxh^$L=$BT_<V9z&M87vf7zTr_77b&W*P4;6EO
zpAe9$WbojclzAz_pcGN`HOF0?JMTtcacgU#ZU1ZnkVbnw8uJqRMP;GsQG?w^&Y=jC
zo>tmdv<ESv2}<+S5YA4ojPMN*q*#bIj#Ug)#_iCvZ{6bWVW$s*7r*W+e<IVjkvfnL
ziuo8nmeOCgy4FwqJm2o+ifd>}T%Ur|H`8Hhl6+xGlu!(Y>DzgREDfNXKXT`iEL5Gy
zQ<L)mcIr#y+bBds9#@;&&Z;IBKJsn$YYrsaf_xh*1+|i?N2-55G}K9(ueGeCmGekF
z4sLQIjS{;W0!yVH{>gdzHOuRpRP)>E(Ws9?nWJCq!p6b9Q|FeKP|ZQRGo(f-lT6(^
z(brhoMu;e&s1cfQxMnwxJhjTrr?|B4&fh3<wy8eFrDqN6X@R+?nSB5YcMBIog{p*&
zfqOqQ)*dlSs$>K0&CUR=yN<BeH_lcYw46q&?#9kkM>w3eMnHgVx1*)eUc+gOl#2|m
zAQB{As6{#cc%MEv7Kyc>$6k~7*3B<+;q;I!l>68({^X4@7-(R0NE~mizMG6>U^3l#
zoHk9;gIkK*9z%YF210gtypr;TdP_(|bBT`h>_%|MhBEB0nT?wN17xm3rYUHDK&d|L
zXle2KGyva*o!9dC8d5moURAwuwO4kDiK&A8DrBq+-2I6Tr-NyJ5et(Y%Yp0Sf<U_V
zij}&|@T1@&04|;(lJad2CCfM3^o-efwSl}Q+&0D=QK~uhRrh)IwZ<v=D}ks`r9w=<
zAx}HRu)GGO5b5sZX8WZrc*z>i$`kA{c#VZS)2e}ioL^luY;M8L)s)NcZIio{m#`@N
z)>^YNW#|&TF<nP)8WX4)s-&1*JMcMnD~GQs#Zpc}*`d~;bWtsQeqcK>f;{f;&36vR
zJ5h8R>j6L)|KZ_bF$jU1on7<p?f&i0JWP#bwydSEb#aJzP07W{rpKs5N~H^$ca5fg
z$ay%$Ry%_o3kOMDJ@(<5qP3fXBk=+I;$C*X0rtvA@?h&Bs6^UU_qsdRK)V^olm!dN
zsP;yKmO@lIh*DHkEe)iv$(oY{eSN}jMC3H?-`n6MW$12SIGKLXrhGU?^v7*P=7tR!
zZ*&5|QCu^>#lv7$zjwUH_E7U#^CsL9AFYrX{I@FrONWY2!Q3D_npeP?6^oy>OeD*4
z5~tk}(C#}{ath{dKm+C4G44`Pf|Ao6)*q@2U6qbwhpWh5zn$&;rF7A;Cidy1|1Xj`
zoT?!aKil;0Fi`ZGfW|1Oe9FhVZ;E;|JEwOmZrT5+a4F}0{bRW-*dcRsrY-%iL-kBy
zwNZam<GxdX-(6&m1)uP*GjGx63e9qnlI9!(s@btcdG3MoOBMcmkzMNOa3>2aW$c@g
z_Hv}A0j^RYcOL^OS^t$&<Fe_j%3|Hu_$|n{Jm>1=(XPE7hU^?yI0M)zw&#UdyY0@w
z#4(eUr6+G`nrf$_O)+6|L37CX!7`TAXlPcrXi`}EREgi3mv{V<NuAX#-pBGpU7Q0~
z|1w2d82H)clNj$`@Ag%I^U5Qu^?2vj4Ux)fMHKe++y}#(HK)#b7jVv=nN3Lv<T}2`
znd9z#&*@JUnrr}CUkzW$515A8J^(j;R!0LcoDYO*R^woX4-h<%MLYTI-)h`~&NUb%
zmgOimMc*6KwbB(8{+6d}gcHsPHCF<HEbV||{xNuA^N%YKWA6;W#ZE_98M&+|;RNTY
zEEIa@Uiwj8cE17I4PiVMBtBd9*qYbBwCMP7(oi9EK73=cRyy0H-24w#xODUq=wne$
zOQ{0i1X{k%3zuXV#pVAdfRN<`hN~$p1Tk4S+{{kSdAS``zHxzpRk(#!%wsfJSb96G
z`P8R%Frf>#Uv=a{?ky~E!;ULQG&QBS2+5hjhndA*9Y}sh*S}pw20VQF;{u7(;mi1*
zuVt;CBRb`*2fbZVeTUiozk|a@XT`21X=kUrxX;PzrEmdnW!?06Ixn-tx}3fi`gbV0
zDfIC99vGLTLX@v<P^zv1FDw<J0z+2}yeI!O>5d?FyNfw?SVph`+rbha*_N@njl-z7
zPxtk08tUh=`g0Kmv|(YaFl@8=_|;)W$y1nj@XGs1bhat7%PYH<u$bH-EjMY?;bT#l
z;b@sO`ahRBehBVjV10Pp)0|ZEMsD77L_bgW&HJnb-u>y^?#}|n?0sG%JBKT-?eNeC
zh;r$1HnB4E)C5a#u0L$bIKN5xY!l_WQNf$=0*u5gdEFC^`;IVa;^&$#H!d9=uB)x1
zUY2}?sfN-L*m6~J0Sr?W#C>UZVvz83r@KwPyJwMrGhU;F29;ULBfUgX7HoWKS(aR8
z&Tsr8qaLdI65@}?i?E;6ll~eDzo8w+n}RLgFSN{@7!EA_9%Q7PVQ^IgQcsmJKTppl
z>}1pg;xO|-GZC@V%8bmO-OAf9^gD<j(OeFR4M1gWi-#3i8)1(&u7#Pptna`<9hm)I
z<cZvHn)&<T?_4HNEL?san1wmP0&8A>YPNE3H7z~-dwjXf93OFJ26vn+%%z8(P$f67
z2BdZ?gl_~GPKBSW7nhOEQyc3x%;Y-edTi975Aduv9+DRgPtf3wyb!S3<Di|^8SkZZ
z_`!~H;BKGC5|p+n%H7=cB$RniWSD_LG?hW}hv%q1Tq|T?BLzZs4>Vo!I<D*(@+D(T
z`5-eu=peCDUKih^GlDnlK9nMx|5gMY8kH333yr#$XeJca_%FZP8)i!bIj?sgbduKA
zTpO>R=ViSxCS!?aY+Y*mfD8<*vxO41EBj``wY1yzRGIL#A;bc!B$)GxfsN`YTuB~0
z08!b^4_~m}cX~!HDI^z7Y6uJa9W7-d{W9Z$Qd$*u(%$59RG~0FLL#nV3u}Ick0c+L
zg6R7C?AF>zRyTON03;$Elx#tOfbp59&Az|U+d8ceTD8LH@U>#mu5=+PPLNCk*`yNk
z1#RJk4MAzBS%3^KXH~DNu<}>~+=S7>N^}XtpV;6x;@Qkpv}WLhU-5FdqdBG)S(A38
z-kgr1rUJ(RukPaSt^nR(!Dv|${g<C2iuIgUQUWtyCm~J}G4n6~U&`QMK-2P!$5N^s
zSf4aah3qLk&Hzd-)4TNKpHkdd&(BF>=~kwuM~o-kyriAL!jX5EX4(!}UEBQ8nO*8(
zBNkYT%C1HBta1y>X$OL6(b0}5DB@00jKrcQc6EUYf-Qt?L(~q8fd$_1(7sTUY?v+~
z@z^ggV9v_sv9B19X}SLREqy6oRfr-l!XQZUN5l@Ia`3pbC_*XKT^6?0?om8Wl<%7p
z=VS>99w=7`*fWwyKrKJ{(9^plc%sGUdR}8dkgA@frd5?+ssE^}SxYK~5Gx4R-!@2!
z6r6pimkp7}9TTP3clc$~K&Bqw>MF@~N#Xap9O6%Cxq|#|p5rQgK>}LX=E{v>E!A1q
zg;BwtuYVph0D-b?d|y7|mGJ{^*!tGB?%dVzgLx<U3}aI7Bv1%jbyex%YkFnE$^ad+
zT2I_a0Z*nUgpsw}1}Nz%CW*W{zEia+d-}FRZ_Him0*1K75^ZLzTuhIw1#BhiKyYpG
zl^%Oz`gidkCM)(gO6yGfD6-ag1(o39QGCYWT7ShY)i6J;JxXt7-FEZI5|WV4cNBig
z1VpSkz<bHzWOjn4>b4hkMP=V*XARBnU3<fOvR>$vRGjhZLmw{h{y|KmLXL83737su
zlG7!`>e(gXYXbxHMfjqBjICDEN4#K5wjlE!36!K9woYOsWqX8cCTS)g+iL9zqs6;o
z+pBDW^sYsF;qau|IR5s=f|hD3p)_kEQO(_voo*-aaB95sK5br*PGy=pu}dQBZQD7t
zpeR~2o204a<2M{f%q@4_;kM5i{Eb#fT5m>6Mq-MX?v`G@<oGvM*Z@na1!!q$YIjdL
z$rb`pB!__w#1N{gd23q^0LAT3Qamk)n<qf^i2Y{b5z6npbJGau<GL3Epqo$b<we}1
z$niWOI<JlHv8wBNWab8EXlZI5K?ConPA#LnwA%mPCHdJmVcr#MNm+Oy4+oCqy!&@f
zNJ@62<=Jw}cJxXi{IUa>zx(uIy3s5OJDNv!#(*)>r=9*ta#J8pH!u7sUO9r`lSfv|
z>b@Jkq306lV(L9rBkS^BVzEy{<u6JFv%0#{>B>=&6*5n#Y=U%bTuaWm)s$gaec=#f
zQW~;Fs66F&0AH6uh2)hTlcGS@3g>$ZuXQ|Y1Z(BL>Xh!7IsJAIn<IjvS_a|k@cCze
zAyu>@B)Sr<Wa+8xhcU^=K>{4X`OMSIN#QS&;CkE1rhPD(E>k%vKbI=Z;CN)|(n*ov
zYz_e_*R6g@;s=aDtZMHlmFb~Qv~g+G78mS}OY=@+QmK@!XbiismLh*RtOQ8=p$+J$
zo@w1mq$Do{pBl?$(|N!FvZ*esadXga3@Z9FoQwPI=<d?*cs$sVRs$O@F_NOKI2g)?
zh$a{3S>VP!pL!eke_C2|{pvZ{qm9_(CX~nmDRgpq?$wd?PZgQUABTiKIVtSsnQG4A
zm#m-(=*AyW>hZkk4h7OAJbSX4?h-cJFkSV=-+S_h0z7zDKtUn+5&ZxHQ_+;nv8+*@
zuJ!c~Rczc|TjdC;pm)mlNF*c>XuM$+*=qcw79{O2u-W%|{<u9mfI|a#^L{q=C3TFl
z*8ge&h9+DUbr#FWq`tL^ynqz#kVPZ9-c<dqn|XRn<gAUnCYPyxWv?$N=TP7Gy5nGP
zU6^y06NgrWau-M#T|L;Y9`50AI6N#C);LJR42$V}_59r;v!gb8VblBC9HT2tTZW;>
zV%#+RF%h;stKaDPch$w9F+jwcU-^@|>39;QIDDCx8}>JLL{p=}(nKXp;<QWM(&X<U
z41<b79p}}=vWr8HgS&gmte#1`b4o@pO5d1{PwgS?kLFKkL|LK2RL0Qt!EfrzuMULC
z?>XCf)&ty_{X&T`P)~cs#ysOGm{Pw3PY=-8D3KC=IJ&%JO(&@>39B6y=WvG#Yt(r4
z;f{MdnycLqS0ya*lc`6L^{xbLAaJ_wY4S~$wp!i#+2t@fCT}e=ObsI*PflaJI&x}5
z7N%E?JWypDYyHnrK;xJ0cd%aE<X570B=40Qs3e)IoHy8&%?vcPQ*c_`IR)8ZU;PtD
z4S3cYTDokZ^yshPibt5{i_l=0LumN>#l#uAsb%L381>RvH`VT(S?jH`$UUQC-Bg>5
zHlaAo>|SNr$uiv&=LC!{KB^s>eaMzCs;@w+{dG2Q{dK7WeFL@>C*oy2abZEnZ89ar
zwdm#K*=staePx`;cMGxFyV=3MA2!F_QDv({>y+AMhtYD<>tB>AYmce0^?ZP|uhAos
z-OJNv!?xn61SBn-c4B+1#iUVqmIB4AP-DR-3E|Xoh*&Uxv><sFCAl!FokvtlqUmrs
zk0NE`e9j&mZ@$uwM)Rh>7jBo9(bEV<nDkj&LI`Q`md>N?@TSn6=YKT!^hf8R8l2$j
zUZdoNZLWdL{^z!;3xo18(7xR}P1r}dt2%>J?j>QZqa1~Eb~9;^YiG?q-?I&oJ*T#L
zE>rm+{B&G1p8gky0;Y%AKXE<#<A{lRTZJI81>1ujo?3I2ATeIZOy*%{X94qhkFO+X
z*M^?)0}=96@>(&1JHsV^ZGjZnwWsS&*<=0Kuj!lcG!F5~we-@A$$H>c9zAOmgAUj_
zEd9sgO}N)d`<)L$LB3@t+GbXypE9POYj6OwOQ%jJQ%|_yeH~=_6I%Nbo1>m7gw`e>
zVHvTs1Mep{ZT2?dPPrfP(j%#dQc@1JfFA*v9q3{{r@Opnc~c88mE8avOz3Qxy!26G
zojzZF%KHJFea7fvGv(Njy0qU!ey<sA38dn*QE150#1yp?-}jQwi78zg66SK@tZl`z
zuREJpe}MDqc6x0E_ZqbV`!t*6Cvo8|<CQr^oF*cv6@Em$M9YR{A1-D!q-wh_4-^GO
z%r~zI+d^e?$uQe{dDOo@k3!Fl%FkMj?4|!)RBZ40IU#lNdmZSK-y7UR4s>qlNYc|W
z&ex_8&C*7nwyoG~b}Lj0FlBSbcmpXpZPdeA_P|8i)4EztlZg{qOHz+Fy|*(9kC18J
zIhLmWKH}@@Aj9s{k4z(;)t0UHNGcyrDxgrX;jtWEzFwjWXfe-AX?YYb{VZx#ELHlo
zmyO<j4+?4u33PEFmo#Bo=!p(o11|I>pr2W4uWYFsfcJ4FVp8|XIQa#|Xu-twM)Ch?
zed;D31w>PK1ZOh|34$QK>f>ketD|n?=>xCIa`XGx`ySF`1!waJwSvq==Crw6hnHKV
zMk3rEx1@jTGPUVjZ9Wu7@51N@O0D=854U=`hC}9B3Q%xCR2-KfuG;1Ge&tGcZuv%Q
z*(mOzj+de+f(eYd%mHQbx@IJvVzD*qzC{Cddr7^uCb!Sz+;T^T<^$Y%cRz|)WNq@Y
z%H`xeP}(3HxGEJqZ!VAoL?B+1SV8F2n7pCqcMO0Zmz$Mo)Z=nnDjLAa>EvKK^9~5R
zfh?5KdvKgb;qf0I<3&64>;ZJ7=IN(EyeIR10mf4o(5ZFE6EZkW=y~P-rP)fB0vrp}
z4^taihT{0lCfK+*HJzUtyn)rSg&oZWRQ~pW`pnWUeY~_>zC*Iq3}rls*J#-*Dx~5u
zce>Pcx3!bTky)^UM<)qxxG+%Ce*X{TthX+`OQvT}D8!NPgxQW8U@<L94Z7w)blv{&
z1<gWjDX~ZZf9s6@iaS!NYl2coe&m{TY@=Ho8d}$J21mbda}|yONGB-N*VKXu4CM^`
zldj%4I;$t(1Bq~ad`flKc}^!`i1JGS?mWHHRnmI*=g1v}378BrNA>eyY_Wk9Q0E5P
zN97v~8Wi;V3uvB7XaKC!4**V4kb0;zn+!YYgTDlIjKsEA_$izYBEJGeL#p9P2x&LA
zDYQZD^n*-6@cO0Qc6I$HnBcWwxpMc7qxF9AsU3dREyy;6kNV+wqz)>@KLPD|hdY|i
zPv6P6BzF$bDCGX;qY2@iR_IZYHCb{tTt(P>n=g2_9|O4TPVei$V6MS7!C8D~!%4EB
z?d*jiTAxOm7bGbWLlnbPHI~Q#NRiay)8BrQMAq4!xRlwV<yT)xo7LU!iTB#@KK}u(
zwLNrI#f8D*`CBg6OpmG{VV9dQd*6?06h}oeT;yWGMV#P$Dck7&#m}vlD;pLXNJ{sG
zW8<k!ig)^LN1Rx8J$HKt7x}{n^bOl7ReFahPi{^pt8l_%pMTNLUJLq`as*(=wSmpw
zyQtO};r8m1uS$zA#KxLjPTGY;83%O}v4QtN^6%o=H?Tr#luFPNKyjUN`OHU&{cGg#
zDvRuW8o+Y^!-ggXvL+d=rgpSNZb(8;0aGmgqa_f5hl~Z!c;($}$}k0Jv`++#QqZ!d
z+98RGARjbRMIkmv(89dwnmk`qv;cVuB|mU0?C3qQ(vB|PWhyk8O&He718u7%HRTY}
zG?>VZP=_SII(5m)d4xEvh%f)#rZLM;jPJ`;y`wujWTz(`m$uW?F#iqw^H%P53v12q
ziDfmo^ein_s0WA9FHh?lXG4S&%k{twHC|!uT<CtXy=Y3hCKEUxvL!vA<rMv~GR?w?
zb|$55C@;S`HNUh}C4rG-0)yO1xRld}-zmGU#6t`<5x1C%BP};?78T2$Mc096vQBv&
z?_k%lsl?tZX7F-=F<jp3W0gdF5(M#uNDCy7v#nW3aPF`-FMXwM#9+f`ND+H~P+Kif
z9yx#^w^DnB<Hzn=wR`(*AGcsnLN*SjipOx|daQ1adk*F#UEZARACIdqy&3f_Q0^T{
z)7cF6?KP<GYb9+>uueEcrfZq!D9799gGCbj<<Ri`GnI!WSxuPuzzSMtlQ|t$TzMRC
z-o(jJlK~)q!dlcb^k$S=O25*EtCyOFreSk{2%<0BxpJ?!8#0@kphVVP7GMXMvKWB#
zQ!)Ro_*18#El^&^vR1JAf)rP1L)tgBz8?neoBH~-vtf-h8m+OZDXop(Cu_G9{2E5_
zool?MQx&ugb(L9|Or59Mgv&qxi&jGI)||WiPCI&-`Zc|%J?7>OZme5oB&1QMb~8yO
z%3(p|Iwy@|6#!hv1Q)eH{KfC;N#uxwU(|dgtuQ1tfV!Taj`Y|WMq+*Nq0bf^sLA6t
zP2RLowsnlSKr%-NWjB_mLUZ_|%-QN{jA!|f87w&As91<Qcs$7Vv*W`qDeg?pw`gEo
znl{}AqkJvSd;EC|5C%}~97n5Nl7S%zfQK5`Ze_5D^*;sVL`F6tvdKtn7NFwk{GAMP
z{+r2T%Za`v_JRov7zaTFjDvN6vEZ#mNYkGy*!f;k)1Uz0%I!b$wo(83XB4w?La<2o
z3f?Xl(+G^T{Abp>jODt=*sf!ExLeP%E-`P$ysYN9Y<0seG#elWvmyu4?eB0sk}5Pb
zFpMX(C3h^>;JtY29PI+;&&(u8ac$?3`nrD504wZdnie%1tY&Wj!L~OD20=7Ca&XEj
z0V0y{&}CHSca!bOXOf`C4KRQB+I!Q-rv>;(&a+#(V`Sd?&Y^P#Jy2`IJtdC8F8b6O
zBL`m-oeoT4foo3zzN){C8x<-602^ljuK*eehvN84r<`f8dt?6*8RWK{;AC_zXm1TM
z2~)my^BmLl@p7H<XY2@{Wd71NEH(fjkM8loq!vJ`ncW^S2K?}slweppKU6GLz9_;~
zAA4ZHf|qBT<7{x;lt6WDxdWX;F7E7_x12324bJr@y>1pOt(lnP7V*o!CJ17irvj@P
z#hVHC(breZ?@@-qj=)&1L-G;<Vd&4gDOY`|-@`@U2@3Mp7dzfvR#kDhxBV*&+yjEH
zC!5bI)m7buLr-$0E+=9`T-&n-P6a~C2?IuqcHNQCBgSCU1e(Uh7=G_d8+*C&Up8El
z03sG-fq%-t2@1Prat<pq;*LI$M2hbi^LQe4zaIYaxtACIfR`M08|aF(Nk4bhx*PaH
z1Q!z3u!IxK2ho4mwPga70a$Gtd<TIEGa!N;oygOl|E|dvn?4Y!ut{Cpd|491CZyF3
zSqGgAy}FmD6zuhE_<R?jM*~25E97iDC3FqtZcttrx)ELiZq8K)L4a@g_Rn0y;W+dJ
zr?qgE7FwRBj!6qGSCuUvO9~Y)9!s`xTJtSWGAb!HE)_Z5ik@ywOS=e;YpL1>xnZCD
z5jjjZc;Fdr7CJ;7Y=mR-tkqPlSLbAPdR5p!T0kJ=Ua?Dn<K1)1Owv*fHKzLsvxAw3
zElC@GT{+x0yKx(NR=0S(w8IwdAH@vRV!ySkr+jET?v#%ZJI#FXlemH2(8eh_ufF-}
zqO7sR!LHcp+F}LnRv;>=g9FFjG<=6@=8#Mj5nmZ%8L_u8n@V5Uj}Xw5?5${OUuJ90
zX{P5RPf`4-*k@s1Ed_)L_rX0OgL%WH*w=HY?#1WA_Lt@1VNwgJT>+`fX?nU-)D1zH
zXcs+;;CDI0H2K&yi62zu_aXC~4=*r}@A^n<<+oD$Zjt|~n}?*}{foc_*YiC&3{X9#
zJfM47PS%OaO$AYnT1h+~H*KbCL>6<E3|B~92gx9zRBgcU$#;xYX5f$*H6;M%4-J0q
zD$2`a`P4u3dl&?2{$d0Oh|X!fc_12IsmG%xnqH)Bo}wd?qGWJCJ!xoU;hK(NVjSYy
zhqiA<{UsF!dmB?J_W2q1#Se{3QLkQZmDC56+kn=zFgBo5d7BLg1#B%qC<7gYg&smG
zFuTl1O5t_pXy<lcO~gW0S>{SV;ko!iGDqeOxGtjY9MbrKSBmj;(ns17$sd0>%6*fs
z@6Vho6B85C5*w-q8bjLVZfsPHB!5hdUp_{+USgM5+ictz3k>nI^ES`v=>levL&Jla
zr#QB!=urB#wHY-TSU&49lo6{IZ2)<c7Va}kDmE$&p^U7<d+cv9+X6VZ4vfnRO?t+9
ziLV(L1w>F*n{#}9P$VdETbiHVe>|*q&<D(*CiJG1q-8SF^?3&XrH~UqO@!0aVb<9F
z7Sp8x8<+^4yfZ)mhCIl!qiA{Cf#TM<$p&XqjTgSr%cY@*H)Q^IrE>jI8l$ofu7&P7
z?Kf&pPW6l6ewz)zmbB*>gDwQ@WMRBllsuK*oei!n1IZim-01w>@<fq8^nS8rbB=mt
zMnWUG`@m58Jg?~|b%7R3T&-*yNy%V+LmTQS2&ha9l)~gVTn74!F|kG2R_XN?eFqMS
z2x1h!r+1_O>td^mCId_3!&G(}stH;X!tI=XJ+3VvD9v!=KH{sDb}?`_(nee9R!-EX
zvWReg5V^+U_B+)O2|76}Ey@dpKB%`sjuxKnMunD)x<5$8jRaI>bvueDr)nQ2TGL^+
zVw^*hlbQV$eu|3PtLyiRtRxU-4-iHYg@8))^1YD*v^hA%xV{PQj!Nrxl;ucH)zvqV
zQdQ0Dik)O`Eb#*79>wQ2w05**c6S31Mh}*Lw*2`>ymVQg5jN{JTC!0#`{N!SpDV(d
zG*}s%qa>g4nelu?3|K_}GDpq3cwlykrU^{`X;f@ezvB{vWG@*Q1LFIXTyv*{-g}S?
z4E_h&20vfw^PxsG0;QK)7)~KUgtge<N-D&+`vBem#@KCLRuPzgCh&D{3>$iKLly(*
zO;d+R5bXsY4yv;;DF=nl0(|`O@45)hh;`}aY&F=zXm;)X<TE5;#;dVHdE)_uAOM+#
zBhe>$;p^!%>-Kv^YcAtN%JBy40D&B_Sz6>(WF)qfuTn=?bpT)7tPnff$Y5)KJ~&e7
z(Y8l(TDRr+Sg@$~WKNCm+x;p)-=|BhoiYd^mVZ>E0kXepL6$|o55zG<=(bUba5jI6
zXBsfq)OMSyH3H@3wBgESUuRfP#-V`);^xUVOY*IZYg-kFMOmmgI4p4Uc-Y)7e)TeF
z1DE6PA}RN-tt~~zaM-@`lR<Hc{UecUg?wau9i_XL%vPn(SdCl@n?GDMC9dChvaeE1
zb<6!}9JyuBV#@x_M9hlIQoP1K1$FOtUC*MuoTpXt!tnV`7l+{B^#-w-ii!kJe64Dc
ze!q%#<9vU7NVpxXwPw*7kc|KXooPQn0~7MMbJz5DKw7u?)Nr;e9=|G<W>7j_<Xv23
zQ(9z!#7HAm1CxNAB7@RGlTyU1`v9AgE&aM!FuJ%o#y-jZgQ>oRl`701J$9f3V=@%}
zv=)Da!i{JlWcEzKR%oBu1U$eT?AxyHSTUKEiam`@tLq1ySg!-xqp!&v0Oh@-^(k{?
zjdHx=5+UEbDUTJ#<PMJ~k{_h+{F*(eJe~$9pa|lep}Z%#I>x4dAG+d!R9XV$B-{Cx
z8=Y|M-rv-aX8MpnwIW6}r-FONfq8FZfWP_RdD3cB3&WEmjyXn7YiNK>6n#k;Y5PY*
zV0Kn_adSRk8YoG&nGxUCQVVU$`^{kWxg)~DhSMm2^Yg*NtUWNR)8)WjJ;9F=wF0ZM
z1_u#HY9qAcea?!S8q#Z@3~p`tEPZ|k{0(9ZsRhsaAOt%*R}Pw@8l}1U;k})kW@F{H
z&|hV9#A``AN~Kyy{O_`ymvIz@pf?d@wBTyfQ=i}hi!MOUsvs>x-_B+};(~l>MAnn~
zJ@^I+bz7azeeElLqs-GG0RT^c91iTm<=kv~yi5XFHGG0ofegnFBgqfc>sP+&+=m?y
ztARHhA9K+H+9`mdX)&6kV|#|T5ox(6TQ}>k_ZH&gDFZvi#Ze2xHk!Thg491VcxuBq
zRu;YMq%~{pA7R7rgeXq8&3-b)bJ#}DSz9Ga!o^ZJg}?e%UNez(c}`mVg8f*rUW$$Q
zK5Ctj+U3l)HFLL3h?ZT>WwE2WPFl^|uPwjN`3PQer7_5>d;ZypLU_FzxXJgfFsN6p
zK3E_s>Z{20xJk5!p&ZyeokAS@R#z0(?zt&A88A@T6p;@_-ZHyH3^Tz8<N|`@QEU8U
zRj6JNa_SRMHo9^xYnQRSVcUn9izlHZt43N@hkw@`Z|)5csAK3dTab6~<F6bGlbDEK
zO||p|)4Tx}cKm^(@13qXwM`!y)t2fZGCNm)MDP3453u=NYZV@e4$UXWhSCvL`$0&(
z{ORmlv^I0)a|~a2fti0?NzlCdd)mo>USnD4Qg70}%bk1hFp0K6q6I!)=(U-~WMOp0
zs$`&-`~u1FUeHW80&&@(&atUV5V3uBhOXm-K4|QdWt$nD{44;L#Bc3SqjeM_);;@k
zu%9AXqqw<wb;?Z!aHvxMquj=-kR9WWQFTB2p6&14Q@W#veY5faJ(HKeRhh$gvloz#
z`X8*Xo=(sK1t)s7mgK#RgS<ny#4!7Z`gl*a6P^FL4KCCHz{-22*=(gcPx$yAeXknc
zy=v}g1OpQ5vM_d0se*OPW{>&{se8GfDzRv=+EBIv5ID<J9w&Qbqol&NM;BpQIvLP<
zTB<hBMLM}{y3nESQN!#v4Hd#4FIw)2hrpLgZHm8zkLOmK`7^p2J9?>}{%Io0Jkv@;
zNXyy4?3?0GY4<@LlVYP~3@M;BtxazH<B`fytsKf`I~>phq>S6Dq)EF-I1<Mw=o7jN
zx%Za<x;yN|gffHM4;1Vx$Q=9#ao!64SXp`c2S2$RG2&cj(RZ%g_SD+w!`!*}ulT1c
zNz>VLSI%P3@OUy`nrS_f+WV*y=Q8X%?&_r_PQjYs)f!|4+$;<vM~(4AA@Cx2T1ja?
zwE?)TL9jbVwWy(n(%47^ukyPeBDtI4aanR@8Rc$r<@lbxwC)}5rc6h2e{~K+7O20!
zfjR{_VN<$kz@=w-(f0B0ad_~<@|`xJKAwXaFa82-+3~w^=d%$B@d!>Y<W$wdJ16!s
z0?{&r`*+mCgJENbs~66njePPdxC}4)BJzpd<E_d^$7%=r*T-K^SDOXd1alaC|6WZL
ztVaAdeO^$<ccM%4ug8<QzMn+Yjf;oXTxyi<`!>&+_~RzUq|=0z-dkm4_zZ_RU%TfZ
zWBGvL`zO-GH^NAm?2hiDz5TRO57FUQiiMXIZaS^%Lb}y+X;G>CZu57;ei2_bo^zf>
z_Lae3{8Cmi<VZ2|3g5AY`1u-ov`_K#asQneXZwco4hs~g2ON>B(6teRe$`?QvIyGc
zrZPmlc89%3vCEOZBwWENQ0p(6Eb&s{tJUo*z_mSnQz?hM#(4JW(>dxM<kc@xR-x{7
zvB3r5Pdz=ARuSB_n6S?*vI2%_aiZ0MxwltWFd3|$&9-JAW(V}&mbuHrY3D2#_0CS`
z;q$q^FFgtIdIwFB;Tp-Z*>y7hL4RKKa7&k`u}Iu3|FTn`D}RKWRC)Ew*dac^taQk=
zI5_h%(_<;ce@jZNhML}d4nkH8&cdyZA<K`n4%t;N*BAXK!lECS3ZC{8PDj<aOt-VM
zDeKjVV(#Y43L(Px@%)6#JaT!KdmZC5FHN7V{Y<!LzJwFEj!P3M>6WyG$p$i~rVHgk
zp%1A>IP%l~?{aUSw~2i6iOXI^<@^R(o<zBx7_;ILbCLh?TZD(w5X<$}_@A{9_QBzz
zc(!L;AG9^EoJD$fD#qQ{aP&+|!(EKIYYs-<m}^y%C%O>FOlm#75NHHvqY4G0o+MaU
zB)uay8aHIX{Oeh)eNMHssy4eu#;shTTOS@ytMr#mbr9;aKYaE5Ri?Bncq85?ARvP`
zUVIq~sSMtNKQkC?Xo1P!Oe_))miYZ&>lZWS{!d{y85-Muj(bN)Hgf)lbVKFeKc3P7
z6=AT$?h79Bv#nFLw!NhEjU|$GdPO}gFqf<U(;;Q+*Ym%XtfsZ{Z&fnyOdp-p{I3_^
zxDaW2`wD?^KpvYJSef7X`D=z`!v&MgyCXb32@*dg5%Q^i;<v9Szq`xT?^|_s-t_~|
z+TCA*#IVUv#dT$zMn)-1HJE>-v#l%48yW}h>O54GdU5|6qNL<wJP*%gLwRaKe7uoy
zTBWa{z((ds-ipTXgwYGv$RB*R8oig!|CBN73HaD+mXMhEqa1rNrcK>5UO(G*r8%r!
zR$nX+%^Y-}bM$e^?n-Xf<Ndlm&v{XKOiZb~mtNQrOJkH;=z^ux+OSwp`08Oc^*4=Z
zYQ103&bg+|1+!gJe;N_C^nC5|Qgv_#KQj!b;d}8kY;Qm0ytB!2{%l`t)85V27{31E
z_?7uz6Ei<_sx$naN=Rz@>RmUtASxETWjdSoELE`J^IxuDp=2y~lScT$t%PYY`>KD6
zYM!JywQCd&oREXUR>}NDN4w@shaJ8Hp{qn*X~Ei2SI@G-<z81D5nQMkj~ZhW7S_0^
z@ihRHP+3`+7nf}j$nV)D%qo7fs%u8byr%a;Xpu1230O9hT3R>TFBw6u4&TXzY!70<
zf7kRZi^b7CuYNk$ZlbcuUr<sz3+CGX8qtDUJ)D+0Ara+S0~bv4!HYLp&OT)uIpff>
z{E_WB;MZeUqve?`ZeLl^f6UqLjQ#ON$K?BiJY<Aka^c^KE}5}zwL-n@|M*lr18y`J
z7}+E){p1RE=)d~)*`M>~%f4>}5}qk&&g;s4&#=+dJO_nFi_BHL&v~<@Iv(j;fgkx$
zdZ&A9^Z89nv8UG9hq)J{gU>9h?Fuut>14_I1b9xY_{iitMZWm;UhKC%1LP0#&GXe^
zrPM=3MDK>(`1|-cF`mM6stv*&k7XaVuXa81#t<%h+P15i>QoTd|IYl1bGe=CtLGEG
zF2*G;&Sr{k*?u$UJ+b9t=SNV{Xl;1LbTe|gu=g|#+x??Hcm2ZHqvRQ_h~1&YV6OvN
zcWrmqa(6xD2bQa4<Zs0VA`5cQKx)qp+PGw6L0i3UL;4bC`x|%s=A6F%`ors{K>5lb
z^1ge!GRg1%z4%KrPR8}hSK}AcB6$qsyXN9Kiy1qY#QS#lzQHj{125sMhjS%`8n=vt
zjAC^ET>T{;eIqU;Gmi1;yB@E;6t-tFR|Pm@|6%L+?_Yt(x8%BmOt#cLKRtc`7I!1;
z=+U`!T>o7_$ZsuTg9-(r!}xCP^xxGo@V(qF{!CYao{O#zIVV@0=_6LXpl~hzZw>Ck
za}$a65?PEPhiE*PSV6maH#R|kFEC*3%4A6GnEasC>$a7gu)%HS1YRrix%mFp&4Diq
zzZ73Q=zM40($|t6|3BVvzFh#wadx~{V>N>}JEN3?*Pj+_{R_s|z_Q%vGMfE-XTFS>
zbj#12Tz-(7x+-6GKbWSGy>89Wrc!EdIcYc57}M!N6!qV~)kdIXyxD{Q^V>joKwNuw
zW}N9i(=#w{Lrm&-+H7t^1Izmu>xTVoQIqWG*x2d*or;n~R<Hln0z87)7m&}cMP5#j
zdQhU1k(tq!u3oc$^z6Wv&%xAMTrMWn;{nKiYoFnV|Hkt4u+cAYFZr+KiSh50pGqC|
z;Wj~XwLanDzgJ%QE!DZ`|4Hoy#-+VLWo++x2Ia0ZT)aPMJ(qi#DdXb7cVABLy9MW)
z(A9B`?ARZ!)M1sPgWnNk`=bk*924$$lv59y_a#;iKHZ7(dRKFRA&7uZYr(s-c~SSS
zT=2VF@jF%|PTJ1Mi0v}(U!8qu>=FAcOn+K0T5^4%VwtSn*!kMi=f7h1i2qi$78E)n
z*j_xXDEm`^k$Hrw5&TfX8_X?xRm&j`rTJ*_-{KdaT6qE$<Jq2a>|)zYFI@@7Z%lvq
zB;Knr64zbw^Ln~T0S0phF8?XL_E+nLWC3scQb)&udgYIo^?XD6O5@UcKD*6aJvh^h
zJGh;0bR#(xb2IJkCO;@<Hh^Ck`{h1yqgKxxWoX~mr>10?R_%6Qu!7k1C&u)(aRl|y
zLnlo;t~z)*;n#=`mHkKX=g2}vEkn7v2Xmoz#dR+fd}KGBzX-+G>LhVDfX~b@i1CVe
zGthWmWq*7_`~0B2*3rsTn66Lp$L?ZM&K$kvc}sFzVIp+}?%#7@{vkNkySsfS8ETwv
zwJ+Xvf}qDoJ-L15+J(DOrnk);4t_=CJ*J#byahWC>WtEodm}ydBhxFxk;4#MTr(94
zL~5SOj@WpBP4&8>yV!fWZFA!C)a=vCZnlKy72ls^>J5}UeUuq17kI_ZQ@{xS{CiDW
zhUd?lm+dcxK4MljJNEANA2!2F5GF;wMW0RT`qyjU`z{iz9scd0y1=iXrRYT4L^MrD
z@+l=aw#n!~9`4Z|WlH|3ugL#?aZz76Z~DBZPz9I?IqL2l{QaN`QtHvYLhPH)x&!by
zALcLI(xqm}{^_eL#f0Z6DJYtny(=-8C|a#K?N4N;2lDp%7~;Y`q+8wPmTC(j?nx@<
zABI9JD;p9L)-0HuIc?9;)($+vUB_u{QH-hSEx*D2^jQek$j0y^TtNZb4aT5zESn=|
z@6=wup~dnQ#vC5nRXcDF%$%0+pu43ma-eVpdGQ9wd1EHkDo9W2ee~1-oOkBpG4qcA
z#hEvA7IyQDd&gmDw)$HK{YhR-ktbdIHCKc;d%k_gd`dh!+#;DoJa5<pM>tj?Z?&AX
z#EamlJae$ZK{&8JWg`E!h+ZlC$N5-VIsEudMA%{7zXi+DWA#^suUx$HpQEtF@d|>!
zvN}XqR!EksiBlo`-$}`c*p*lgg*NQf!oqv@QO~~1G0%_b{Y#X;QsyaWWT5xQLW4mm
z^7}`%E5dUZ;rjxY1o=Oe&A&=Ns1~HU>JvC7ZgG|cNe7kcqNLmRn49B5a-B&M1y2}l
ziW_bc$Mg$2KvzP9P`3^L`@QZV5M>I3n$9l#XetnNi5xe#7rtf@5%lj^O`y!5Ve9a7
z28)YAy}HY3;^o)ttSYx@($Vb)K@<?RAV4_Ag;kTFA}6Qo;&slYu<E{ysh#o+^f;$w
z%EVg7+KpSn*101_tAis2Z~w+nPbJ%9ZPH@=yJa(abE!Y~c&=qQF0GI0-0na<XLC$R
z4=4EXw&;Zfp>>|~JzGjGMM*aG`}Y{fLUuA>=T$#nb0RYqw4}B;v`BZYPe%(xshw9n
zfBejEYSr;+m9>^H*PL2pOtL)@{8ow6vw1Vd|JH%x=CGqO=bTEHDwg@1lo^)C=S=z;
zl`gLh1{!1Vm3sTGLw4a8O9Mh}g!?}KY$h{iHmxRgVGlJ7rlCBWVpnvWrJFB4PI}V}
zv@t*K0Zr(WSA>s!@moD#n+epJ<=Evn?miE15{?F-aJ7&r_?3kBnR_7V#q0u_OJaWb
zGXK*qaIM7w;@knmy2t-AxJ^F&S_Nju;lMrX;+dW=>W{Ao-TLpZo=qPc`A976T+H`~
zHP!MNbzg(GoJ~o6?~5C<Hg%YX%o>0Eha1zl?uTc^tt$Vqt6NrWYpm%lF7;W>?MZBV
zs_N!}bol~Pj+fm@6f6$F!J~}teaTRFIQAL^9lSe?U>mspUR*a&>mpl}=f#>OG<NuW
z!9O{iq6R~S^Z6W^ZZZ<^ba51A*VQxgkC{p95-wD3Tu$&g9v7O`Bl`K<-)#hRb}?-0
zebn*#=HH){g9l0Pf`CqnVdTax{YubrCfjRHarim!vwRj+;T{G*j#)ON7<=IQ&h<07
zHC(~>(8qtj)gL{ZlV%-*pW$>iJReE*{1;6i76&U(GlY|_y=lJC#D9Rl=I>;Ybe5zZ
zwF}eZ^lub$i+l*DhM5~opL94bk(7ad*^fnD-<vd$!kdCY&Ue*n?eLY~GQ@!rLcDs~
zUcTsUZH+qK8K&z#PMa;b+o6%LwZ#w1vD<CRIBXo&4_Y#x&MhL$88)FeF2z*PWdvLR
zHG$~d#VtW4H>|&W{FYnE`@~mUxayblxBeyAKY!44$%c46og<=hlXS!2pGrj*1DSyv
zxrwZpM0N9Xt?kYz*Q+{;GIb+B`(17cv$)+O6#?H1Qk|?qihfi`$z!?`(@xdzn&l`b
z*|k^2K1D@3(6sa5m5=@(nyx9j&bHgeR%0}_twxP)+qP}nwj0~pNn@w6)!24&cE5j|
zXY9*;wZ`I{bFCL;wC`A3T}w__le-dbe@nB>m%q%nxBICIdRHUn=vD4+$rcN|-dp$(
z?CLlNFQBzjOR8E;PR_&()QB~EHDhv|kMVd((Wu3AL9Wn<IrACVgs*P4M%D@35U~ah
zKB%}<)WkGlRI8#m=Ibwg39o!|CoB*5j)IRUM|6>i>SL}@)BSB5JK|(Sq2JE(S*kU1
zw9<oc11mE*JQK>(BDtKtlTg~J(IUF;1&S7tsh0?4F4J=@hf_{^y@)ddec-RFNN5R(
zfp+&4gy{wo{8m(S8%^4`V;=5TrkxKzq#Mxic-maI(hS(cHN5Ki3f_A1OC&8`>ee5Q
z%|m300-sbjT64#6MMT0a(L9~`UhqC^KW|akuIT#sO%|HH^`4-_BSOoz$_xe*ywkk8
z;`I?L^3X4);)fYN&-Wq9R-3IqlbM%IV&RT)c&!gPGr`i(s{N?P#ew{|0epZf)t~L9
z(Twujqk%XV^xrvD)X*Zt9A0?aeF&!38PN#@{-q}Gp)e#e$??-Sw!d=ElS?Tn3i?`s
zLnaiM@yz(wtS5H`l{62g2R5~q2F|v+w;g$hQ8cnpo^ZLkcpOg4xrF=LeZCP`(9<PU
z2$^)v94`wmqPx`Co+upM;#UsQq2g(peyX=G_5r2(Tb}wG(~uKe89qz5WUF~G#@c`C
zCNrDaHR9CMH2M88njF}yw`vW!^Ruy7Q9M{T)qzoi@`ZXVy=J`8Hd`S3Z>Yfg*KJ23
zh^juH&<d2ASBBHOYBOa|dIS*+9}c@bRDEYy^e@m++Oz36I#cPp(e2jg3{PO}%bd6y
zG=|$J^&4&oxU+KG_G7kv`uLqChnWC38?26adgpl*oH5kN0kIVWZ+H}zXG9&ao$g)s
zc|3}4YKqjo^=|f&p0a}Tor>XV@xMuWO)h^1vP!d5)AvU#yZXo>&)9{lx`Tn3cK)B?
zTdBh!P~Kg32QbZ0^%*3lizh{8C8^9QIdxxFN{Ys(^t{Kn%tyw&2V>^U_U4XU9)|7T
zcpNqhFEMIdDnD|34$7XctCsbp>8%(sJV3p!P{FQl={Rqd@_jhUuZv^B1fVeGWGkik
ztrZalklxjmCNHEhd3bW!xV?oN4YX-kGHKehx+gTnOGxH@+0*Hu+<pHn?TQ2X!2OYY
znwX}Bfl~`n-@mDwiiLpt6Q<AaV;PIiT?4;awZ+kEubIISVc1N8+}P|^UEmGg&Vp~c
zzlwkQ*}{(=kKt#iIt9&j@7Kh6`_-BCa;G4D_nFa{4%bjD3%M0TugpZsaW0^$7(gqz
z<95Wq$%g_nzcrVkw3Dhp-7u!YO-_SPBuyhOj=n(WW}_@EJBOieZBtovBx5#zcsIu5
z=ABqnVMbyeeh`#7-O<pZLjFr^Ika8+_U&_>mD1zN)Ei`Fvz3`LkP~ChBPaN`@AvPQ
z#XXf_?)r_<Z8lvn;ik48IOahR8%}cv75dek_XDP^b%66kcs?&kT4w)&H;b%+llNb_
z#=UDINbkBz8$E~~24mKoWFLOYiDSrD-I<;Ap^M;SG$SWTC%q)pd;EDmHd2^zZ(6rk
z+cO3Bz~Nm34P7i11_;(*8ao?rcpq=2)IpL8>NcH$%@O6*#&$lmp|7tJJn~)lt*({j
zZyyNBAr8GfWPd`B2wbOo)U~VmAJEPm1GgJ7oo+7oBgQiJRjltBX-c*oH54_a=*naZ
z$NK{vv$U-&Eo({(3!}2KoO<hDu=5%H6Ta+v<9SE~j%u6*j>1;oo`v27?XIGBCa+Pb
zTPyy`$}U2ZUxJ-m^Oae8V>Z*eXqkoe*?UC@*lX$!?GOrlyms`tx7l{?JlH<SW|-L8
z=|gSKzkkffJB=WJCHi}xSf&WQZ?Z;>ODi#6ee`Z6qVvd8<TFY+f0!rFXtN$0cMt~0
zQ$)wnW4N<MnzJ9mx7+F+K5&}Ms+GN2QTvVwIn00%%D=+HLxA;n3Yh>)5H6bf9`E)W
zFXgbj!pX0{OVaj3b`3`xwM8`VXU<<zYy`S)xfzvp;wR4-+P}Ew>a6qO6N?Q8D!I9x
zrTqs2smh^tQ|@pd`+P}bk-xf#9ZQ0r5SQorKD@}-6KSa=;eHVn2UU_3lN1J35*3nY
z%Vf0mVkq;*P~#4Khc$qMW)6MN2=bEwMJ@}#T0QFj`$VL>vs=zLS3Ckl5fynOGZSv2
zaAll_6b)$1SQwKxlyr{m`m2offxWpI`{+(CP*7ks_m#vJ*VwGZS0IBp-_Mj^O=VnW
zi5!oh%EHq2%EQP(FO>vGTVBwrQ^<1PU1r-VVICNlv!1B%vP>V|Fq2!7oZQ{^692q<
zjGGBr4+q3Zft}rohVDq~E5)hwM5fLT5AWZ+LsIYB-P-g#t%h8gm95!HAbh6d5=`M)
zS^|!{h0p-<%Ta+O@_cjmZFjE^!a8>D8zy`o#3$sl0AS0ML8BB>z`ainlkSbdVTy(W
zT<Q<5VMofT0}Gml)~&PGxB8f%d}d^jZLm*-=UnnSSF&yAPLs~Mv|h%fudd{E%+<OQ
zU`PHp4#fi!ELK4^6&xJ8{b{yG#$)=8gn#{xuFwDB%GuJ|PI--h=LUNdZIiaPDd{;I
zS&Vb3QFfUCi`DtU76Az>OjJmI)eScmi3BogY!YCbzkeM9?&`oU&1oq)Abb+qbXGkk
zKD0MvR)rHSI&8#l$RVvUiAs?ir3#f?5>QDZDM_rUnphf=!OKV|9Tg>V>rWn6LIcaJ
z6-y~%K^|94wL%BS{`Fvwu<<IMgS2#;cGMSa>DG{-79sMth4}h3w}K${(0|8(Ae-J_
za|xA3%Hja0TxwR@blbjNIW6*XV+h_EkITgk@-2)+$%E70vaGGVzR`WVWdt&+wJ#IH
znX#eEim<NTS^E3iTB{@Op`Y{RmwbjFpq2jWpo))ObJY_aPd<l#dgMtrS~BfrEc`1W
zuR;<D@yYqvMnGIVoOukD^P)XPKYx_It7A=bfKbmDeA)F<1KOKinQW!6B;m@rjnc;x
z`ZBC0pP8oK$oTuS!ym#&i0i(<%aT$-tm`g7ctHQ(S6@lw)jF~!&pt>QiVr7yNPhUq
zc$+G~OyCo^Kj=HeFF8!fXmEE>e}s3^Yxyz4>+C=QNCF7Ext)&(3SWDHB=qbr25LI}
zwDUWNdQ$nf)0e+*9xNU4;{oe|?&MF}yPmN?5K=Jj8?bjT0IiGfot8)bO!=&UZ_+de
zZ`ycx*Y!E#+wM;~V7qXf;d=VsZNB(0py(T|@Sr;2+WF`~uxPZuIL^nUiaq2+DfWS|
z^{Kf=@SMl6T3uDBWixr%o0p8YHMkNXa21KrAQ7Vh5hTq<m#j%apnZX>EyaJx`mXkw
zx3cw)6*5BlGvd<SC#m-9ePSbMIZz_dl+i3Yj{zqMVmATP)hwobgQ4`wx`s*vO7Bp%
zd$J{)huiXWuR)Jhy5-U+Q_ikMGb3Ym`bdqIp~8!tv1RG2`4hwMvO5NAQw<6%)Bj4K
zn;1Ya<IkXneRp@bg1p*w0rzQjtEJ~y7kfA6^j`MHMc8#KE0GjJCh4-oKC8J5$W_;o
z<ia#Iu?t&gSe5;nL<j2ppN><>BDER)zzH|K5y_Vx5^-u^b@gRnx_t!#rsV_4%mC$M
z@ySJh+X6!MFS#7H!TR0u>cIE_oM|hx-@((&*x%g?@SmM-1zD^)k=|hy;NJ~zK^>T=
zdpWGguEBihs7L+Ssb`bWE9+$8`cB}wP1@`HaworkW<yT!0?d<&TK~<<JT8RwX=IYI
zLq?;xFXpfiVt+UnNBE$xb|2=Jfrzv5o4~N^I!n5+s_H=<;p<s*RC(&^_;uLKvWZ27
zjp49>FjH0^-SP}CTEW3hu&1>@H`LZ0H&QHcPeqUrH%q#GZ<LQqzAtMxt->seo}&GQ
zM9gh_K%qSd*F5I%#(07Ei^z!zL;|9d!Q5*E52uNPnFEIyGfr_`Z)(ASLNumjNb!>B
zcx?NIQWEuTJlyj20r_?*9P@qe>624j%&8{bh&NYTo2yvakg<GTil`tTu)Z}1*a3*(
zTARsfrw)3PJ`rcqg>ZC(hWjH7v1bgY!TxQ;9kzDAQShgp{~Yu*nm?p?^%}WFtxL1n
zT#|Y^0rtBM5w<nV{O%{5w_EX6HT~AxlkFP=kqY$Ngfyhs`k$}v?y5O;>6@YGy1P2W
z>s&gocD;NX0}=)ohq-=7OUMqI((6%YGSEKn{XJjP%>usGsldAUe$&F)*iwsfw1Eyf
z(+jUN)1N93cIb|cKLtq@6|`z2rn)Hf;iQqQTx=A;7)v*wWCCRkqEWH7_wMB^$?QU$
zX5wbe6#BE8+{wvL-9#|4*<TWq$GIBSpXSe|IysQ};I7V{N%{v-5&wgzMuYwZ89`?{
z_y_c#Ei;OQ+|kFCv5`Nh?x5X<jO%!9&Q|Z}Aac=Y(jB4wCxQ#SrVjj0#*~D<dqhcb
zV<w4*NO7IC@J{1zgTL}evbM%d({;qxKek2Xb~`!}9L_Mk>RyO8jU&CkMbjI)8nljT
z$QY!l(lts^F|ab9hBtwLZu~@EXS&*!RPMoOQ}5@*lUmZ}&rdUR#n#@KIAub+FKIAJ
z`&Bs(?_8sE|M?|)#HX+A>Tmv=w(pJ|UDfQ9NS;iNq1T-*l~lz$?AIxOMDg1-q>-=7
zlnltym9NIdD_l3f{pY1O?RO#`Jdc<vZYLd6eQ|j8#9ly^M|s5)|F}4v8W`5aVViPn
zNb11MPR%bmYA$Q2fNVy>Kc=^}=$U1_EV7=BMt`R8Z8z{cG6@lR7&Y3a%WfA>p%cKW
z5Fn@x8SdUw2-VlI?fUZkGdITJ=dG`tJ|i!e)iFG*b4uSI*6oj2kvC-7dT%E)QLAF(
zFS^pS-Sil`-JA>0q+tWwuHGQ2uQ5Tt5hde+eStNwtv?juJZ92M{rPeuUIy8s8`Nc4
zQ9rpP{nz{5MIh(}5`mimGo}BtUmouVnN;VzZQyB=)#u}5-;mj~4b4u7dys(dj(p_c
zA1rP%Nh9G!s2ohn9_1d9{W;Mhd;aG^!PMA34~|&&mfcb4UZI&vzsBLF(#`SGuPgu3
z$w|Z(`(pR6w-W+I#l070+-fA+8w)zb?2vbbd9|VY**|9=@3Wo#W3}PErIx$wi-$X(
zoBER$c-|GUVKkX*D{QLf`sL@>&hPirGxMxz;-%V@_mjgmHq}NxI{C)pa$fROo~W{T
z6XZdP8SoTqoRT#8RsL{8=^t;(+HOuFtK;_GR2uqA(=|0YCk)l+x{^vS<?DVi)ND2y
z2z4pG0Rks>Kc4zvL-TFD6QyRNHCvA8w||2N>b{TE7aPQf$~bD-ZagK*8?)9i=m~fp
zlEvry<^E)oVZtRwiA0g$4>wk{Tj@*|Sn=muoJQ3((!b+%hL`C9vG@Eo-inJqMG{36
z>`t$g*DR(njtJNXd_nRX{?z%0HeLQhn-ZV`B?9#E-!PB~{kcdRT=S4GKZxwNUmjyx
z6;)H~_}^9K;_@fk`&3+(+?~vBCp*5fX|jH~s1?!BII_#tRdJHec@e)&+IGLqTrQDK
zFJ7Pb=8f3Cxt>VFKQ45vUIU({KL|J4gSV<K|4wR>*9}|>;kGTXZn0KK>q}d%=!}Te
zNw<AIrstR55MP|*7CqFwJDrI;TM2WFJ#%WE;4Rw={Ee<z=a}`?A~dXa6~;FYe^@nV
zXFrgUKcfYF^@}Q}+zTW-^Ej!Z31g(+Da7N~^>UokD(M}Pp&+0|<6KGhCUEM0|NCLP
z&CCIl9Q<|pDLnm*mcIMd+>>A1@#bW=r0Ph2#nU1k3<4kA=ds@9IiGgH-BS3ga&%=e
zYs`G719%c;J9whk(uFM=XffjF0QJCa5b!aXExhER?cpSX?ojhV1|V8tozTKrE=@Fx
z4V<Kx_P2|?i+IjBgytsADfqnh6sHDt1Nt)saVPL_o??Xm)II%Od3lt+D18=M)l^r7
zYRtyG>M{|yNn#n-^CPLLc&N15b9mD>?DjA->S589UF~f%c8+y0yTZRm5LbkLXh|DQ
z=M(>tA@hoKIHl6sl+<KYU706gOshl|^c|K|^mm33Xo&<i3GrVI8^vMQ>S~swjFfhv
z5`ajpjiM{vxoN|(I-tCHvak!lLqKcZ1a(1m$*i?${4N+7+)?B0Vbq+~Yq@`chnrQ!
z<*Y^6cPP_d+r+cGU_o|6<iCB34SuV(SBBbY=7i-An!@g;`K59-mIJ9re0do7$|*EO
zfc;8+{;qF8&H95Ru;JZKY4Ss*@fRN8#AL3;o*{XY_8&3BTi;p>0U5-5Z8Ouv9oYqv
zymjA1iJ`g+1bT)U<3Cx-`O{G&MI#1DZ7MfK$S@5Z%o@Im7j33GFS5oaA=HOV%&uE!
zoID!Q$!mAocdfR#Ua(E;YI3GHyzWLEF%sLQl~8#8JYtqjIsbxMm6Ab}F>cY03_&>F
zF1ea|5LuB+w-HiOg0Jk4<?)#GoVrDnFks1M$~2KN<0gK5b=tO1)YyFyH4iQ+)+jpK
z37D$vQ+Ey3)J|1|g{D69&T^MVy{VPvM&B582CpPmew3ERN4P&IH_&C^s-}s(*=Q<j
z0qpXLVU7GuDl|cR26|c(gG<U=8#H$n$IZz+e%7ER8K+&};4umWb)vx=*6zy_g~-+v
zA?FXGz=n-<pLzqg`kUgIf02sxjUN`QpT>k_`fx1_$W~>?`zkv-y6541A^0l$=H&88
zbG2&d)Mv8XLF-8@DwxgxdfUDe)x&qrYodaACFNbeRtw5z)N;%AFr^nCsL>p;Krc-t
zmx-M`&3b81@sKGjs~Jz|eL#l*HKTavb$?U8xmxM5=rD5M>-_Y+ck3}dfKrJN-xm>5
z4C-YPL<D-W1Y4yfk65ueM|+-{oR~>RdQ}zr{5YoS5SvQ|U+vq=zd?HY+fYT5-{yjn
zFq@V~FfQjso^TX~21{mTz-q0evXe*Bc*oJI#HCTg+(!2u%VVo`;(i`QB2ETBh#+Fq
zv~SN2H{^}YsWb)`;<Df(#_Ze2ATu2bnL=p$Kj#@HX7PXwQoRmy>Vwsn-9Z!;<^_&c
z;^J{mHh(pyKTLx)r$1d37IS+k%{_!EM<^};dk7N+j04U*0)V01@?Xb(kmB28qRSDR
zSI=bqg#(P$t?1&V`1$M4)%y~F4Bzs@3X4T4nK(#~>PrfSj{T{WsW>L3w&2|csyT=6
zP_dcW_zXWAXz|E&1>`=Upa%?nA)jAaaMnkyJ^SF*%EC@Ea1WC)N_nk(@x;aNzCeFS
zpCdfRANAzhtgJgVGg;Tn<VwhR=KE<T9~vn=g13hLRQ4p#U-9pGM5O(8jU3Ph?PH!a
z!xwopDr1yeIkCGY{&V~`i;4;2_tWoHXoJg#yNQcfg-%$h9|b0)DQ;veZPGk|q%Mqv
zPl?$FQIB1Bzyrd9zO~EGfAR>FYVZH(p&-VbT*eEb4L{DO9xp=t7JQcl7X@9V*pR_?
z^PCYm-eFerJYsA_qqHeDbvD)?oRyO2nF-MV@4Y43)w_#(UI=-;yX^=@(ne3SAYOSM
zwzmBhtKwRzGK#}8ww*l_LkuH%yei$Vifw7f6rK$JGma8_QD%xJ@krY51TAyTu7t*$
z!}1u&b(siy_-}uh&o<9skC(6jHTVn*{2x$wDFyLutNI1ot&CTpD_YuTF0_N`u(6A9
z2Z30zNXDK%9|mqe=`x&^nH$@5Sa4yV=ke_N4aXk&exc++**|&SxarM4AP03u5q7?@
zbA3G3f54x(<75RieL<REg=Yp&RI}!J$n-euS_8#nLH1`|g)jIgPqt*S_JQNlXqw&s
zU{D~A2XOe$RzHbQ3(OlSkK9yLE(LtPI=-ZBOBYfX=L8n}EP66fNzvhV>$zaWocqQm
zAd+)@1&j3;CL3R(Y!|w{yoMg2?7ZQ7exFpp3+iVO6CxNwbIdlk5G(`O8YB`;g)n~x
zrdJ-q1rhkhmwTpUG$?cODeK9YWwr-8X3$X}NSI8+d;N$#PW`aun3$YC<WERvz@sr8
zht{9<MXK5(*eA^nf7yy$>VCQXf$s(d4ae&Jq}w$tNWZfkUk`s;3#JYS$|Ou8N_V~G
z_>!u#krIZVj4Btgx5X++{50t)$oV5(8-=pZRj*qoZWJNr6E5rueEF^e(O=ZO-<Ru#
z%iCW_=khf<M8H{)RB$<cX9$^M@Gi-%82mqxoPjP-cF^BRf*O6@Q{F3{&zZIG|5^Yp
z++iCQV`fc@I?JQn^zOSL1T~CQfA7!jj7NEEf^f!jZ4Oos;OwMsj72#jZ?$zLr6IFw
zo+Y-gc=-V+egB*zkZD+0WiH?L2N&4DG42zmc=tIpTGx1jIB+!$h#D!)$4;ib8Kqej
z@)|^8X9&yazuFc+E9j_7oJ$^#lryt_45kbX_iHqvtBuE2S5*z0NG&Ex0c~rJDMZ3f
zp0maA3Dxex_1H1-g8(eG4oq%Au4vw{9B2Q^<(_8@b_R!VS`VKi!SLWzTfRx`vDc{=
z37s`j>gH=A!fT^63{7CXQfG&%dk5`)kz}I37LR)|xGxO(7#Os_<1}zMweNQZbNe7<
zN<S<|uCegKQ#lX$^be2jwQ*tlUl3XY9ZN%f<KuR-`^WuhktsAZ^6fZ))@LtEepYSM
z&F)3HJb$nBGaVt~54N0qPFYQ5Eb)_q+WHgpu;&eYoAbl+RnJa~Mn!VIju8n#EYr$@
zIO(eD(_?#g^SK2bO(5rA*4Fl@A-jI|f)66mP7&c@ZL~p`M|It(RV%Q4_h5?SOjq1R
zOM{}4g~Dt=SB2a#vq`lq;ILt2Wy=G;e7NO<&DM=JICyxyuw<_&j;a;lSo~W9pB!qb
zG6!<Yrnf>}ZRF%(qJ3a^>PJV3C%Aymi>BDoM$Giot-I@!GK=->)6hC1WiK4hC#4K;
z;^+dtKl<Je&8irF2>DHzw@bO_M@%|N#x3D|NfZ3+?_$toz(fv&Hbr5&gIs?nHi<t^
zRcx2|*jkuH2mo)X+~rMd|CYtt9$eYL{<`_&e@w8?>*XasUHl8q+<fNG>TD$CvEe}S
zOYCdigpSK)Ur5+dJcE|qBV@Z}cS!ys1kOFutly2<z(^y8eM}qgXb7OX0nC0X%xZWB
zo3c|RXc%jlbrkCPd*foa8-yNy4+Y5&Q-5vxR~<OlMd=M2PfT)ybI=Mg(hVd3tXh2a
z+p2lB=09`m>t`qYx*29CSM4SSmbx<orjJxA`k<_JWerYNYlj4T=Ih-aB~sm$!Q4Y}
zJZ8o}%uHE~%t+{1QByMEe%I233RrSUJZv->1ZOnmGRkZY&vAd46TI&|++DqlpSC;h
zUGfGCga#4{vppGgY3_2v%5Q;q`@^`Z<Dm)vVCw<@t}l<Ce)b$NH}@}D{j9eG;!Xye
zOb6LoHxKQoM|r|e4i?WS{SpZl8(g9ky;|QAcng6BqnHM%uW&>AeYqR+D6A8CH^2Vl
zWuZSgBh5ti^7RtD`}Kn7_#u9GjbH4g;kDZ6e&*S7b1npKGG-Drhjmz+L-*X2gM=7d
zRBlY;ZrK6g5vVS&$bv!PT=+(177!OK|1FoL4kLDZewrc@r*E*G(r^0gF-w-l`-njF
z=8gS=RvY~aJ-fSauL-dQLG9uoP`NcHL@#@B;5tEi0)<^z$h7!nb?=)8D44N9<3S3&
z*1l(2mI~u&0O?DDOr*_r$6YYeA%Mu8O~%osmiVmKc_?In5>F0LZAeT;bry00K0J)#
z_}jUyKkrI-qRYvi@mvZ$DBF+x=4<*ZlNZV9XA)X(fB6@|k1c%{@SFdIBgVgQ<Wxyl
zDR0Tc6kT*8uf_JKTm!;Dhn-XRonEYKc4Rwyfqk99+PybKtvE9s2T_YMnskoi+y~ra
zpO0ci!I|cbQ*quI`0~x#^J=1_Xe?y=+(1LQ@iG`U`kN$AP9`|IkE)f2N&uc0R2O&9
zx3u2a^yz#-7Y~23^F(G|44UA5vk7THQJaF;!vtf-u@@P}1C@t44BA1a^`wnRMfCDp
z79#d76AEYh9>6?7a|I(1go;e0zN$!@9l1)&gb1Yn)AcQosGOB;GTzt;w|n!yoV)qY
zjB9+2h5OB}dS4n*oIECvnOI2K$~601Ff`4WI+O{ZV!nB7FQe{}K91B+yW#!$B0=Bx
z?<0EQ9%^JtP%DCE+&)n^pm@1PX3(Q#Lg@O$`FnoG1TyOcpYtv@Al_+aZ)b~vW1g+e
z{$Xf?&!^2L@cPf7R5bsyCwEm060xllwMQ9w8C}y4y*LEtL-{&G_3E&uRu~3yfQtnt
zd(Jh6isH>x*3b`)JY}DGVLL5%HpfSi-L39y+hL5AO3SL@#XhG)FaCxfHju>E!~4TX
zAS>05DVcYoTa#nqzC$%hw3?<S-qb5nfKwtnIbNg2*m@K4A}!boGcabfzziIHmGP>d
z)kk>?KbqXQd7al(w>rB;#WE$E%SD8kR>hf9R-6%dXD)c`_KqlRaO|yHvT(SqH$2VQ
zYd3vRV_e6_kop{hUNWp=+O@6JUVLA~B|znIt&eb$>51bo;auO;^(oJ#qB@|_jB4Lh
zBkG*4^Lq&Q1XtediOfGg1j0>%F7m^-x|VW*svKaP3Kjz8$o-wfn+RJ%JNJW@tqb=3
z2d>Om3w51uN@l^U=Kh_(383(BPx6lCUtZ7pjn6CmNE<RY8rP=tz8AOlWL5NM=B#N(
zYg`N?p=;oW-k|MMwHR)+!O)d`k8>0ig!Lez_K?7Z9aLNugP{F3CZy0n2C>%;t1mK)
zm3AG{kFNsD@Gat@xof4pA@Xv*12bC-r)n`~q&U}hU|I?p{iNcT@$<LGmcD4LWLQ5`
zE3IJg3p_k-<$~2Na<|mi6;`qEMEq777!&n-HuX3t>v^rZ=`t&=lnc@t{t^dJAngw+
zJ=WU!vl4n5amPlxn=bc!!v)71TkoAn=cRZfs-&ft$8a7c3#7{tlkk7hrw+G&sZBH+
z$fAuyv8sad2z@fkx*EJ_Q(9FKeHm#dyw{pl!)?nbJ>eY>><>zE;drx^u?mC?I3j8m
z<W|%{IE|zu!ee>1HjKr_vkV%sle?(0O{~@`8&)RU#m#U8SS=;K-)YD&@Bh#jB+`4}
z*g{BJ3^8E@^`@>I>Q5fGYfM35F{}5_`J=?s%j;KHMKh6^u^^XNgNSsJbx=)SiF$Mj
zKy%S+PJjK0tmuvS<zVzXillDH$jrw@Ynh96H;vCO0we6oad=ejcc-73*~@ORS=Ydb
zmU+997mjy*ynlp$&KK?k@trd$=ZYSrZ;qxKC1$|dgaOSA2hK?XjrY?mrQtLG#cReh
zefKs0%2U1p!&EKe7=*R};>Q=LuKphej(@E?41{Gv7)>7x1TCqglHw{Gh=|cQxwzbt
z!fwzp5JEZWxICNPm2se0tz^m@ZW6M>f@;2mz6KUDrbD~Ns)CHEYIEVvhAA@^N4Waz
zSO22G&~b%hklwzie{#olxB9%O>K+v+^7tgxsR*N$jKD;!1DTYu^EiuQ)-K(mSO(ay
z`rs@&CCzH!pIkrUi{<W(33x}n-D}U~H+maD>)IUPbuaC>Y+PVgjT7L@jjGB=+S;9A
zQ;}Ps+RfjHFKb`KYahN)x~?Dwg?-lE!R@N`U%IcCbJ2JgUQh&1eoU_8Db;zKOGmKG
z&}Q|f=Qt9AX?v|sdX{p80?uZH-P+DPJuclM4w<;RcR3vRz@u&;)s|tk17$61wGq3~
zp80mP3Ygw^{#C*P9AE=qji;hwV|HP8_+aAVmJ-{7=X$klGR_a~tb9QMRR+ZtYfet#
zt;^=le!8UJIY>Hea-F8~muX6gREEMBJt|TUD^~jy@q`D%Y|Mkus0K#l;X~%lORS<|
zY^uteoDSD4^U6vUuoL8`HP7)*mEKzNIXPvPIp(+@#Z@b2ZJYCF2ekP2XkI&WaB$P3
zEf(F|zAOPh>X-THVP3aFd-Tgo(Z#l>vhHan94d|X{*2L6Zh_$=Y_CO6v^xjA-F{^j
zHX-Lnc&oh#{GK7z8QYJj1u%Oe`A2qE=-pLq;-rH~s4;|#tMEB}OZ-d&X4GqQfaOlI
zW%U<^0jdXbJ?JxKfdKU@PzWDr5c^-k*}c9t6f+Z#K_az|`30~`W0?WiR9F?(bjJ2p
z@T=rf(#GfEmUmRmIb5xVuCPs_OhRnCfXYZOQ3><l`6%;GwhlNDvq%pa!Y3p7<t8_x
ziypiVTlUWSB?xS7O;EbY-R?&FZZz@@_aa5cva>9GXIt~&{kW@?RAQ2(L5&<y`f(9z
zt(rh@#XGF+83#8Kx_uBQE1UI-Wj)2?9vcYSm!0*E`OpJbMQi5cf~_C%f!QwV(`3lD
zBqMxAr5tnK-X_8ji2?gO_T{Deg<)&+ds%<&tvJ5kXXCqG$uIRT&O&lv-(Eb{{+U~&
z(752wiBNcR&^nsCTFi7~^0;pA!5AY@Ybp{nlmZeD@)k%~+A)Rp6Y<(`X96G!fVn>M
zj8pv=U_X?w-TQzHUL-a1=k~<c%rTRbk%3o0=bs-s{ONwVWfe1$Ng~RkXh_k)dg}JQ
z#aaXyV)AkO)eZ`aT4N&dac@>QF(}y+R?-={R0%@tP`lZPv+XT;H+IG!?x26!Q~J-~
z&#stw&YS8Dtza^Va{|zQNl#0MinMTdG{d!&g#D@sDyTq+KLy~o>>*_~WUAy~hN3zn
zgrona7^$!PMrVbc{3pJdKB{^!F$G(R7fuSnNHId3m_RUgM8Wvmx$QbEVvff595Qmb
z6x3P$L8Co5swTAewm84fU6VI%0X@w$M_Ej}$J&r_iV+a>3pz*GAmgz6jZ%Wc<=l~a
z(cy$6(L*+yL3~H|@q??H)BPZt^ahapN}oJ|Js9j`<$O#E?V^HA#RWar-60JFwyzJf
z?0$G6?E*J_A*$MLk%?arusMKvz;eJ9L({Y@U~!C2KcGCVyB6#Tr0s}X?Ozr<jsUXZ
zXF-&5{QWCA%$(9%O3GTrRe<bq(q*H@S%s~iku4Bp*P%W#UX(bwQ|DpANn{zRNy`~)
zs2T9U-=F#pr0p2OzI84}tz^lsNYsM|Q;+hPnQCR#&{tVkjSI7)L~Q;x!Y>y;0eHzY
zh15Z2(-3=Cn!hd!i6s3nflt@%gQ}RGLpCx)M^O2AtO{v9%_b}Hodc^9t=usAvb%Lv
z6m2w1<5reN1YW7`cJ{ki<*49lc$}Pb-enGEgQKWa@chBrT}3f`9FbiwH7U0BiibXk
zO<qf*D6GHrkPBgrJ0Ei=t$3tePJ>L5l7+gyPEyXKQ428J+u;>lJqNOvsH}iTN;G@V
zaWIptp*+`f9bUVHcBYUScI?$OkI*C&pBOd#ew~r*C=l$S{p;)nfoh`q!<$gwji;=z
z)G$O7125o;kQ^28BREv5y46~2X`Fkv9b9MA7h<b)*{hsSVkF{s**6?>X9Gs8^M4ix
zM=O|xMX*H|`{om7o}1Z|R|iF|&~J|S@I0#Kr9^$X)xtC9l+m!h8+Q<mp<*B&WK2@n
zlyVHq9XP^SLuIJ!3n0@c$e3x-rXy(3&CZgm>atOlNJZaGlevz)M&l|mdf4thC)wDF
zWX=&=+v3>JYr{O^vsQlz88odS+lZ!-o0Y*Chy4u2x7$K3Sak(i)Eo-%g$~zs<B;c%
zgbNW1hm8%2X8De{C8t>>lX(F`!GKN*59gh02xi|pnrJ!MC<R=d82WIq2BA*c(`Z=i
zKmX<nJ_#jGD}$%=Tq7s`wHX@XJh}s!Py_27If|eWI#mVgLv&KtwE-yse*LWgM5YY#
zUsb^PR~0-j{V)8$zU{McwUD7BHuO01ln=|F{Mi=T)=$o1>Wrc7Fx^<0<ams^qI8nT
zKbf3!h)GN~R%uZws-$Tu=2i)x1|tWLm#4S*kFdB|LT9&Cm3h>qDiQ(vrUM>%;EHE`
zBjW)B&4Tq4j|UI?DiZ|blyi|J+XOfSSOi9N!Y3}Y7|s!C+HPRJcM$vH+4>cTEQbNN
zPHvASY0kAPY;B9$Mz|XA3mSCx4&69YNud?qJ|g#jAC=|uuceO-A|WB8d=FdAie7QJ
zF_b}18X8Pmr8`6=4IV>HMJktyXC%J1qgD2Z@0Ka7X{=!~HBhtZTsb4QFgR>0hLl=k
z)FGe?LeL99Z0jGbGYED7WeVVCU=z<Af#S_;wm+WZX80GQf4>1$u1jpBO{BbjPPQ0c
z8Mi0tp3MrAn_7LT$@{Cao7HYA^Av5$hm~Z0G9)ZjeLDLDnW9N#TAf)L$Ijp2&sc5s
zlAPNtm^4ks&n6nuSFq3Y_^YZ))*`)S^g+G3>6R9I!gW8CQ<hQ`wiJf%6L?6OdA~;}
zEb2rS4-Oy0y_KLOq>N@|^fPAHP+{AD6mpg&MJ+rcoFS-2HuVYb1_VAbW}ljDEiuWB
z&4MoUTBvPTjow4BIxj1#-~1#XnM4sM72z|ekwm|Z@-)0OnbXT_<H7LqVZoORy;|H3
zr%sUio(kAD|LKCG<jLHw&(0Cn`B4!~{2YF}?XD4QExQVp));~jo+8XH6PTuvw0AiV
z;EX{M`&S~?lycM)zy!12k0!o4sNh}cQDVhA+7FCK8eo#>h$~Rh@?g!txaG>F11HXk
z%1Xix$Ias631%u|t9+MHJ!M3d$Vq5Bbq)ztRdKkv#UxvjD-We~K3=dUlvl9pB8n&F
zG;OIdyFxv9<s3L7Mh<@SC5>`aSx}iXh=Q^wYYrdQ@8wg+*gSNM-IqDMm3=&yeP~>$
zRdTA5NdAc;dF16N54~YcE@3!R))<w_AaTgj!5Fh){{bOf&*6r0P9Jpg_eXsP9YDDJ
z{t2V6S#)nLN^nv*yg+~IMO`Eb&R}$C4z7^7evzVVV@AG<aWjYNoP1qyZX`~Uc1wM8
z=B?7u_^+zW#43!6F4!g57r$g#$ci0X3-vh;h!WfpZgLfHTh-M*sAIYCR>^h^?QamI
z2R0X&&)O`!(|?Wy9O2-W{sZTq&kcbM60BsB1(kKdA4N%>SfG}D0N=sc=I;vRnd_1}
z3x0;#aCz>mHM6FJRxZ|kI>S^c{n6m2(0~9M(O+1_IgRNJ55FEV@CkH}WU|QHSEcV5
zNI>XRf+@^>O?(!O<XHE!thc(1tQ4?5t2uK#Hc(GVWluGdOfsAr5keA^p9xXW&;&$c
zfvNB|n6<GZqA}3O+SselM30Zwn;sPzGho)3>2Tajh8$z`cOA)%m<m1|w$!ilZK{S5
zCtS<FTv|V9M$Ll5b*dK)s^nz8^iNyP&SZJ%4itb405p+BHMv-)P3GIsDQ#vHz^}**
zS*FLr1-;_KojQrc`fd_g4JO7+Z-WoXM=hcYn4ju7{^2*WsOozgzB_h6+h9kJ2|0_h
z%2g#Bu#L8xzi$|mtEe7K{>5qKv|E<h+0<#vG<;&3|2${BttveYLUTWg96?t=dxWNi
zjqG6I*)41y53HFC>=_IzstoBNKBVZGlqDm`+{wJvt*@?VDl`DHH;uUF!(dlJ!!t5U
z^ID<+e4=CIavgD+B5yS6v{ycK{IUo4F@xG_QWh<U`LVkQ<2%!kF!^uUvIu}?)okpX
zv2E^ovWo6f<%6P?Zwry1-S@;3Kj6C$*85GuSBn*T;JY^?`_xHJ11qplmG7%+LCB$;
zt87R|@vR{zO*xGvmA_9Z{BhiMVy}(gA<UGt3c%I*o!Ttyf<%X*B|;$)FAvHIdIe&#
zQwSsruRv|3m+&E%#2P?=uB35P-Pgt5pCvAOFozb;!op+ZLS?yM&vpFkWT*O#E|@h~
zvyId;M-^j?`R>~Fin(*ED>zD@vj7TCJ|R2%dbY7AGEv#s^Q_oVnLZhO{&_=CcI{5a
ztHP?1>!?LrPe06Bp;!hl76#h6Paeo$lr?vT+@jLvjlqjvdsJV?l^-Z9M*(Q-`lO+(
zb>SN{_oFd!14}!<tzMF?ba_xrmOdy#nK#cAv}Ny>O~YjS)D^|V9J<0#9=9s3ri>tA
z?pcKFK!|J_xDDJ-;BXY=Jq6KQN~3Q%5e9k~uH2Z&1?G26xTA|b+Fh`Gb`?4*xc(w8
z5FtL5_BcL_8q4d@PbE^{g3&?F2>7uR_V-pL>{d5`e=+-CnM+V#+TP46u!y8}jEnnj
z%D^RV>`5AX5UavPiy4_!S$Vq;E^r7mS!1amJYRCC?)TOWJvnDn){prQO)MsDiOcDb
zBS+7cZ|rhja<lJ`+#EgivByCAlQ=#H7icVeG+)|2{iem3MMGlL7}V$zcW2dAo&L#D
zy2_#pL|eKt17|Iu8<I&%@euIUuS`uMSnkK1W#1UPYFKV91-OsLyTAH8-cCkj->&^h
z!I=sT!_~zDtFxgY(ME`km^xKoXf#ML$;oCU=JEh@JsijctvRGF5Nx`nId_;y1Cgx-
zrxLcie@?xAKrCQOB|7S|C>Vn(Q-Yy*GNuz(ToOp}$dE30tTYL;Py9xcvr0i7i8cDN
zCgC0CNix3%(@h3n3wzsNp04=`3V<67V766i_-8bQV_=V^aNX|1kay}ARo<09jITlW
zeU;t~cO2KE+5$LY2hOc3A|Vk#7#P`sg%1fbRmvWgq^YE<DeG&=*Hxt}@2??djiB3x
z^umclI`?zSu7P1c#O`cf?B0Izg~Vg%byTcMB2TU3Dx!ya$Pg36ev2QB6x|aMRwUUC
z`GprfNLAsY1k7mnv*T*m<co3xy)bk2k9$?i2c>4h?5(J@#pQ5kW*uh258RBp^bruG
zF?n(xDq0t6G`Lcru**AakEpb2<*5<{^?Y`V61%y<jY4|*V0ERnp%K#IMq-d5rDc#~
zM#QsC-TuBOI(-yi_QoB9Qx|qL;z$LLZ?50mjueXx-y3MDS-&Xy@Ktr-SToJe%LFI=
z3*GIRfpKhxgo`igsNn5-dhkj7VH7c0(i(|^4&Lxr_+L#tg8`;>xTtp25yBg^7$}?!
z+?}yYN>AUv52mcj!gDCVXr#791gfrdV|BAkhOI=6MM+ItS-f=kvM`0SDRJkAg{oSc
z)szF%{~q1=oGG7I^<*6<ho(xPJci=%<>o1z<|Cp2d;iYj$R^4WrD=|qA2mRF40tA%
zcAAZkSJ>7Y5wk1P;+I41uBq}T|GETKkhKF;)uvPJPd#06`r5#OsYbSJRh80fDE3C7
zwAi?x`g@KECJONOhk=KqEYq^-sOJJ<xcV<XsQEahy)tHhvN!!!RVbZ}e{)S2g8%YW
z{7rH0O({ifJ*Iw!x^OvRA7<OW0-*;x5b9maFAu6Av4U6Vf@8>DuwS68Vf;p^3W}aE
zcv1czX!G*(eE<$FjCvbg-}9L^OB1}nP|Ug(xDH^*l6jneYM%3Ms)N)OZdqY7Hs-I9
zM21c-5F`e~<#Qe^w;aywWcpl4s6)x`%c3hQbNHCWHixxH0-5q82`jVOso643$E~F^
zwa9;~!<RvoS6Ee$>^!0|B+xCbHk?OSl}eML51}^hR6C$|Kbz?aHz|=@`oeZAK0#23
zQ{VjjgtCGIwf3bYLOb@Pzp!PnkGlQE*%WgrtxZ;2gFVRW0`uC!hCYtuuP-1ajl+WL
z-}~rQzj(CG4@^W6qY{w=+BXI)P40B=v=KhQnm75K<wq17Rlr%&sqVx`VU=j`@G^4}
z!Y)qzqSbosf3^Sv%4P}_9A0#M9t!LBZY{MZ%_fuk_B2oaF%okgDa393%BSe6#HjHG
z%$gCyO%sO~z$I_*BJH~sOed;mIBolNu_@9iD*j^oyQY!F{82F$O_`MCv^}aO(o8Zj
zxl{A(9Rf$?RfRa4Bv>!u&WG%%@iI8Gk>;s)J)|$2fT%LK@1>zN1wYQk#0!YeswLuT
zEJ=6g_<_|HFKH~scwQ93JKi+MbjvOm(n{?LJhh64%uQRKH1>P=>UXduY<7YntWEKb
z1Lh0dnk~pJy9{sLE)I1PRc0n}Gz}VJu1a}?6B5msxB?G{zATiBQuJUdL3~KP8deX`
zqAhmH>(9kl|7zP{f#>eli+}eD3^wa~|2RTGMoygV(IWebIy<)YRukw;e1XX{lFhHq
zN(y^|19cq;U9R2O@|QERE!mB0tyK-QS3quPb8G&-?}03>bx#0ssMvAC*x94ZHwJqr
zl80xv|Fju5&qGD&WTB<6qk(&4UoY!N3+;0WyPCD3Ikx%W4>S)`^Nu;<zlhetJcp-H
zVCG2Xro>A8_h9*J+~XK{N`z<>k_W>zaQWN+sW{N~>_GSM=Pd$8&qK0$VEtDuKFyh{
zB^(e^sJPZ+VvVU2c_Tt!3Q**n`xPDd@?Y6|qN^=qdx)7~NPy`9m|&enpy~h$6g|m4
z2fKAl7xSMaPJehLOPi90Z^eWfP=r~9J(~zX>NDtUYS$-A%#&Er%x{<Ef8^wG$x55T
zM^!R$r0ZecEe+RnzG1|_joj#+9z<pJi0IM!5m$HjB5b?lRW&mH-UtaFo`wRFdPfu3
zw<r3(8$1`kc`k}8OW~3=jjWiymasDoT7D@IiLN?}(!d-D3mCD6ssa??$(kU=N2b4K
zw!BBg-Iks{ujb1t+-ugX)Yld{>fATsTZuVV23?fe14GEjb}3MVh+^?z9Ect6NI}7<
zLmWVVL!zP*ku|Rj*F)`JZnpI3{;712WlJgpZX)eZJ}z3ZIj@Z#eR$=ji<wV*=3O-_
z^UplJ_(&r1YA5wXR#b(A6YP@%l;#;{1*}^z5_h*QxLX<cVww3*IuL(rkwL#{TJ{A?
zo&3CsRRMk?4dyO>9Y@R3#GF_Kd5RH?9a0G!Gd|!j@tIB{p}Sd42!Mh8f@RVBQIuNN
z1!lh#cvtZ~_#R!wwyp0X;J=5(6$rrFq0ywD*f}REH<NR8IwYeklTR4uKEi0r&@y2*
zoq|QAHPo`!X4FooK`)X@nTpNEiH~>oIc=}8O&@sP;{pTorT2|th)Wu;{p7c|-H`fn
z>8rZQCC-$-ZCV1~xc{Rqh~GB(|5|`K0;+ABEeE>6$$&OUlSauaI^2N<l$!>~nOA-6
zwpY8YH4%nf*CF_J6rsXc(rd4)tWyH1-xLd;_Vj+|6wQ|KW*owmUkNoAy+sZA6^F7R
z=$UC_`9=tg3Ua?)mF3A#dMm(Jb?k3wKymE@Uq-4=?)^xypy`cepP&^^3vMVfyf;3C
zj8Zr2d3Wschm2lLh^+Vee!gLkVjL}*9{qH`3E5LwY9ab*2P)(`-Ast`?_GnDqj-Sp
z>;fvlH~jDYXrq^kizGDJqe<3}K-KXp%6eLJ`(Fg(<X^>C_z2OG(dH>Fs%*Qe0aX%k
zo3Wb+Gl<@g9SMxRj}gyIjGbpl3(&q!&Mk6Top{(hr!_>)Oo;`a(xj~An^;+AJf|7F
zC%&prnf;n52Fm)h(oNE2`{{mHqLPENn=ifLf1Q##mjFJyFx^hN6Jg&xAjxH1?&5&U
zlppzpY)%nwbaPz5dqS)86B(TXa5<PkiE=Ef{uuat$uQ_t3u0O|2&)~cWpi&~chlvk
zV3T}MsXatt1}DF~4MT7PS-yFE1f>N<UI{HT=4v0AJu)DnYw`&HmSuXZf!Ejm*<b_B
zR)F&Rc?!V(laC4F9YLZC#rP-i1xTmZck29HO_+D~xfrWsW)t{Z5dq`ib;*{xJD#*=
z@ynv1t~6eSVW^?P*hKZK{3!QIlnw@L6LHhVel?CvDkqCyRBpx-cN?ed%tsBq>?fI~
ziQhuk`Qn{shDM34I6NZ$rP=WFc-~^j7@D$48Vj4fZAn8_-f0>QNva`)V1cW4lXc-}
zBQon-)X@HZTQ+uuX`OI=sDd`5k|<)u=kHpW`^?YZAzGdIS0i?RiiHQ&^%Pfz5tjq=
zT-1ql8Rz5_Xox@mmd@1NYd3Iifb3GZ?|lnek1fJ}Nr(S(*WPh08pRFxrLo%2Sl}E5
z4g>HGKm)8Vt*Ai|fFOY}f@%fCgE;>Tm%f350KWF0z#9-dTmlzg)Dt-V8+2!3a^kw;
zifV8*>@_N3G&mV}2K<^7LqfN7=IJND&I(v`#-0bbgztp)!d*1Ol7!hpc$k_FQmI!q
z<_G`6UNxzME>sT>I?|@CrCHJ7(q!P}QD(a+3}O-S_a5uKi56Kyu?DA)nYk&(sBtJj
z)xCg??W7tlno!Dn<BLf~6vFII<Cj36w-{4F*p6veWf^7qzoO5r+Y?dnI=&#5U@u$-
zzNqFsq0Lc5)Dc5X3xFyuG-gH!K!$-IMQC7&XwUSR2U)z_<msA7d!x>1hr<~8@szwD
z8~WiVxq_q*1Q>G5!W2Dp6a7WL6#A6^Y_L3B&OU<T4teh_%hNXp`+*HbwV3uZFIrou
zH+_;9;lwebRr||61qeH>`7*sRvGuKV@N+O=060N0o|Qn?@c><cq)S-%w_sQ90mz_z
zyAIu;{~p6Pm~POxqEni9B>pJ6af>j4GMj0J8NJ5Z;@04pEJFs*-B?T6=CGwxwMMO_
zwjvAS1@#5i)_OgE!6!x6)Y(O_RmyR3iOTBOh8<x?Gy_Mk$e|N*5>>+@cEvxi=4N|~
zZOfjgeP`w-%%eN>oI*9(lF0l=uGpfa%UU?6dJ$b9K~$c9?8h=Fl%Y*I^w$GS^w=V_
zd%&9yZc*GpF_DB9IW+W&cdGKjI`Rdp@k!`W{D<>CY1;&UtywX$JK6PE{*5QKI`L)O
zK)4Z?wm*`JFr1*|P(f4*HMJ%F+qWGC<u!~N=nNkkT{z|bbDfrW32N-y*@q<35g~H0
zSFe9JEa?}N?^W~XgU}8;qB%=Fo?Xb%79LFZ&^K@-5JJdLw^Z9pNWGMqTS$*bmi2cK
zkEUS9|M{Z~(KQrTnBB3@t9bt5@n1z?z%&#kW?3LMk~tf_hL}4}Q68PtUYSwxiwKK?
zw=@86TF~3Kk2{c0sZLQP4H$VPo|Iamo`je;tcfbCqTSIRB)aC<=nIvx;UTsqn81=(
z*0Y@G6#nEHr8BoYucU0s>1R8~nkioVw!ZFy+CPM@Cwe~uNW;%~g+i^W`^nuWR|;Go
zoGPT}$?$B0@~co(MOga-rd-_iXX`Wng-&4(74<_)!j@eIA7K%dDi+M9L}`CX$-RYK
zjY52B>&R*09D*1jngM}<E+2y0D6(44(1e)PlwQ5a&L4;pmkf=M=W-jo%v^pjh2S!5
zh{<XMUE%Dib6u&?pELrjan*R`(1p=NXleQRK<7B#*0)zC4_O`R2Coi9x1PY$rDxIu
zw;_5D6=MGLI|7spBS@|w%PgPE#F?A>(RuT)eCcUsCQd-)3EH{E=5FPv6LVB`eUmF?
zq|07)JA8eTuAzfn0<Z{V=-rN_c=Je@@#dMeBMn2O+Z#yz%k=Qc2h1Q$oT%lt;?csu
z^Y6p#fQ?b!xvXEbzLI#<!EG_2GeY0ULeEWzTddy2e|3P9W<RQIK+dAwQMFvY=&Z{&
zexXNqcoR3mR=!mWSsjpF<`Hv4JS<n+=ZF4I$f~!&`x`azRMmrP<tDtB!L!GpK~U>@
z=Hn|zjKMXkx$1oB!+q=Ov4e^I77ssDD22Fi8QQ82Xl)a`(w^Zva)V+-T4!_V#+2JW
z(s^UF*@Cg@k=VF^(1Y*B_W*n5xaK4n#{O3o4Oj)C>;o<`GJGD!>Ta(q!qqnqpBEgx
zaJ{iLu>}`xGb-EU!Vbd|M8-H<zsaG=dwKuvBPdIrw^?t-bN#bD-_PS_XLP<&vTRr#
zeN(L5e9ytW>0co$No}!uiz?7K_FYyR7r&{Ri}0o~lJy|cvfaPhE!)8xIWzIWyV+az
zR|}r4Bj#_)U{5DwywkmyWy6#Jq*oTQ@iT0H(A0H<LYN6i<t7_Ep@-Re=tDw%-}O#w
zLG7TS-{hfMY>`JbMoy<vpm;nIWq^=?Xx8E;=j%ajgZpj6FMVyCUM*ZF=Y-h&x9r>|
zhzkc&woNa+ev#i^Hm7N(5V*&csXe*bkc(ljSgSAHOcx;RT|1fXfH-&UM=Vgcq*2DB
zd8mzK#zwXLr`wv&Nw@#}$W#g#g)7tk_@9iuPw!7l8+HbE0b7T9uja41k!L<Cx}{wW
z*~;_Q&-1n@Rz>V&&Y$f!j1bQ8P|2UU2D8nji8uS!GOPF0@cXbd|3}j~hE>{rZ9LoN
zw6m?LCfl~{nrgCbPquB_wrx!{*?#vt|Kr_9ANtnOb*;VDxqj<h_kB*Q8NT5v+=<4R
zbG3|XCO<RR-H>!+Jna)hf^Uv8w#Yect%)eez#mV%xE#sB9}@5Uv;37?@!-ha>vum~
zmg_Q_)JHE?hK77NTdx%C%J;Tb@=G=Q7K(TJBWOMd*t41jk*VMkTlf~LMe+$Xqdro9
zT!FH{B(VC=3fI2*xe0#G7w=S`(R#=^_}WFPpjUi=UcPyw68I9&MfgcQ3_#3a-*ff`
z5Bd#u^v=zPSikOiq1V_ik;w5su@DIXW-l=JCuF)M=Yu1#A&_hyHkn15&NO+{GT5{d
zIMuP-V;s144JpkM5x$fWZ;5ofAXs{Kim*2|h73O?mucv<ft`+%J}Iq?BpxGaH=D5s
zw8fENz{g7`sW+dge9^JftCAJljyh^Vj?n@4DWp=Z+GzEx3#OA}MG*vA8)7#XEoGMU
zcUbB9L`$18HdS6QD69V17%U*74!%HlAq{;?j?w(AG7AT1m8PufLFCjDvbTC3*X*i3
zxH0&7wA>$LS9CT$gT0^B`3(y>P{-C(16z7VdpV{<#RxdQyYufo=i|Pv>r}TVWm50u
z`|tMoMtZ0nLA%YEyGF%*uNAv*CON-<_lWCj6FgQshQo3N<yf(&DDX&eVEe%@qe9KN
z*PwwRdBYv#%>0|%_6X}4fr|`i^H_sT!$!~1C@fmh1MMm<`vG^56<d7<lOIOK<w}Dw
ziAWZ4cJ$GuAE{u?xqch4Vu&GQawq4A4&IIKIs;H$^dJ=KW7}Dje0wZGJwO(`P}K`H
zMs5o_I<msPiye3`P*bGiCwB9yQwVGF!w4R1uoH1YB86}2h}_YK6Q0qAU#%4}B4m1l
zp>tRFdV!owJ9C+SQ-%Cb@(2NgyD}qjf%4_f{)=m*IL4h&O41@^`1o~7FLV!%n*GQb
z=A5Le2=?M8rymI5#f{p7Y;cH}9lRozZ6Cusr7GWxo5AViC@jwGa$S_0NG~GsC3e|4
z+@NYyP6dkGLc?s<gw5`QYHV2@l}iNgpG=FXCTx7%;hW;$1my!QHG(TiGCGl_D1Kc*
zDwLr9_|`j(vAdwtv2wfYobd~GD1ftP?DpL`U8CgT=^iLQ&x40H{I9h6aM%vJT&-`P
zK3QtvpTVvf1zuik{`-$~uzdC1p`YOf*q;01iLUpqd{c)Ojm9n>W*!>~Ohf7GFei53
z0kW#H*~7a~q<5tEY+Nd21H|<iAI@EC-PY&};E!08cj+(j-<PI1WP27T7V5zaJPeYD
z#>nwH@GVa3p4<Qy9P%9xD9R6C)~JK~Lv*}~-&j=&c-0eexxx5aaOV?YNeDN(kc?IH
ztD0=QHIsk7j$re}YeTg4j~mdrVj*b<S7v6LU6IpLRt5ajLn#k60p%bABJkb*ho1x3
zfaRv{4+z-iuBoz8hQp{{o_EIFm-F_T$u`7R)~lup@GEevyI9rT@Xpq^3O#7N|1vs}
zKeT;sI`G~|KVq+QW<DvEr5~~6xcIy?$0f*VaqSs=oV1W6;}pn(i_0l!29ivc=mu^K
z<@X&D+-PD*s7pQEP4;9%C@hRCRt!OA=QjqQ=UA$XyWy<V3YLo}Hx}!C;eKFFY|j1w
zsoKa$<K{A!FTfvK7C`aJqK5;7kWxKdq!#<*M8x4zdnJeKY=~4Nyu1E8k#E<vxr-k0
z@9t@9KV_j2A7TZqFuyL6d?uWh)%6-g>z@f!eg&RouC$hzoaEW%sA5dpmN)mm<9&$n
z5IYQ3g-sKO)qd6F9n-A-;=KPN&3tw<B(WMf&+RY5wKIp%vxOY)hTO7uEZK=3;8D~3
z5(7Y3xEnq#cdp`tM)f8W0{{R6V>A<Bh)c=MIDE~$xv%u}M9zHPH#A3fn2&m7VsbRG
ziHf!cgb%^W$>o@kFbhgMN0u;i^%+^!Rn{ksB#Wb-ckzoXHL9Qz(efH^)dU$m%Gm3s
zYq~5>EX(d2M~YOCJhGXoi~fp5#qc#}jfjUkY?n2mgdUa6qF{B5QgEV-ztn}is9|g5
z`DR=u;`x-4(h6@fB1arz^Gd(w2Y~&xwIwF}0G?Y#>^9Ah6y4H_nchGaDnLyHpWxi^
z6DHkmY(~r#RXDVq-Ar8dS3BlZ@cnx;`DMb>!i6Vg=U>UycUtQndG89#5G0iI?@w;v
zns_fDh^?zRvNIdZ5c_t(%-suRYP=Z@y(%R(b)9w6J;2lRDR=4lm+x5pnDAU$;96Ad
z^d%X+yxJ(;Yz>n_JMv;`BTeI8)8RL*ff0#r(<{c|&q<S+EX}iZ1eDAMXcSXi_Ja@C
zMQWCbN0_(}JB6)A=3>wjC9d+nG<fPz%}~LB@y`bhEE3Gors(98bN53tu`vWfQA-QT
zdgs`rxn{hOORrpVl=Cg|_OD!^h`?8#LVFCC6>iN-$o3>7StG*gUU)}W&|L-iUxnLs
z`k%w6exyC%;oCdR)En*r=#T{}x6WE#NjB=*y=#AMW@$`Q&V%vnIK4cq_~7|mhR*(6
zIC`@6PV3llr}mgWZ>eAD@&O0?_u&A1X7XU~;)+wo-nJlr(9>$V(xLZDrAD3glx?w2
zumZc<>9Ny9y-*`~9?pxyRg)LYA!)XuaEBNCrj^f{L>2ZAsxN)a_H{AGyewbu9B(5b
zY59eayDi=v4cXr>bC4VBk;@_)nNq9E*(s9<({s%Q!Qltw7-gU`MBjEIgl<m!QZTAS
zDy;yVP3=`N-2A{Fxkgu_(@)`)Eeh{fE}<#i(WQsO;?TL|i#OfhQjO+}WvcrO(7+{%
z{I0jz6zoyioF^_=u=qz?lVN%P)5=iSt!$3;btECjtc7P;L>6TfyMVt?-?10}28q1r
z!ehvIjBEW927!MO$iy?RIN9y!4ZPLMJ&03kSt7f3%aL{0T-zS4S`T=b9&Oz|!PN}=
zSnoglX^Hg&D$(nm6i$(~tN#a_9RHz|>D$d`r}wEq-vcW#TM4)qrCrGHT;2)W#Xvdq
z)`e6=1|e8mM3s$=a1yfW9^Xql_VX>{-~_k|I3Y0(Tb?1Wu+ts=+{(Ma=2V8bpVJQ4
zWXoQN_BgeOJ`~MPZQ?>DC+Zz#^1iPb6Ks6UF)SmYsC2CzQ-M(-R$fZMshn!=VRrak
zsS?f`b7yID5~eK;6$PUIqAM&OC+!AwGD<wy7b4!`$!;Ee#$%yJ)?&h;(NtO^$qEmK
z-NmRd(NEIsFPV}oX<jkXVwz$j`I|X{^X8hQj4z0zXvApScNKeRUe#^U+-Z}9<%<@G
zE*p0YOgcE_&}Ze`MJ>%dS_ZulQ}ZrD1dDb=ZhiIM5U^jJP#jy}C7+;jKK=E-H0T>v
zB#p9ae_@bhY+h|Z$>|#3$z;uJZ0P(`PrdM=0=tMHySsk``CbO(^Kmb+<}{}n7StAo
zMf!7=K@Y+mtZ1z?Ws*w-;0)3!Xwxw9Xz|jdlUES8lw88gyTG=lEZd)k%Fc0!33%Oc
zwd<U0+9+hbeyBO_(09qoJlXq2RnZ!>_+?4k(+TQKl`b}_VAEfZ*N30pm3;-1JWuBD
zRkrf*s9p1!F$lZeAt{wCkCwB_)*mDT$RyzEY~Prd2-3nqCo_4#69TAEPuB%s@13ge
zPp~|UvVZlXITUC=9j{Eq%S~$Hc4c`3q;O8j0!T<DSOTa5sr&&XFaf5!#&`zlsqHbA
z7HXgZ?4fzbOis8_I_VJ?o)&A4VASrur~ZstLFIg-QGsW&iW(al-(jL#>}>p>5Y9+a
zhli<CTd?xM-uRmN7>%gGc(x(8diJxJ2+xBes??k3U}66IXe0{k(mTn}-Pn0prk5R2
z7pD|!PSZJk9G|Z>S*m}U{Tctk{*ICJI#)8wi$Wr^Ac6u^IWn19`I-o)I_Zz;kM&q?
zWALXDm9q+Sy<YQN@}?axOV--01#f&z@Yt&^UC$8W$bU(@RJ5?{Ioj$5$0Ng4Lehxp
zT=8D#{|;Bo^Kt%=S9S$&5I+Cf3VPQ~vGJDpY}Zjp=NUyH)P3>+8nD9lV8oi4@|G7>
z?-$|LZj@o9!bXpEVFDyv@`(nB>(o&&`w6=WLu0<rcN3u$V48@@>$J|ZG3u&=#YbQk
z9xgODjoiYPu0tKOSx7%NokNcG*Kcz|tfS#*x{V>{eX%k<%F+(FlGa~bEW0-1kW?-2
zL)K0AX8$X706;I)yYmQEEzOusLRk?tMG8floD6Fl+n9+_0+0mEpA{+l5q*CIiB5{%
zth+$6+i~Fm{)+v>-Y8*`f(s~XXFd-baE{N0Dl^Tz95TC?`Q&8QT#d~sHEoSCBqJyf
zB=SY{t%+ErS?LPj518G#^qM--csPg*y4rmUZykItWtm(`lk4)3jwu-)k=V;DSu89h
ziD4)TC@V%y?~G~<W@{x&+9m{KV-?gH^Q_U*Y4VRCR8)l~0@BgPOnaGhs#k4EA1<6_
zGE?iDrfgWmMQx)Fjc$^me8@1U89dq19(Qt8>tMdYcLKk{h2`Ayfis%jRiZ$|BSs<F
z=<3@CIbqcGHvPJjZWS|GyHo?972&u7lO*HZ)~_|_#1f(sDs79L9EEz6ge1AxAb7&W
z5`p&dohYFLr3WuHrMoR2$@QS5v;BLuriq2rw{O_`$y$5jJ^Lm9^ObLQ{0IJ<7x3$S
zu%#!iNZ@FyU{K}O435XtI{lIEhwuLd#bHOj_b*jq;{Y28Rv8(j7y^@DhQEOqQH+*c
z+L5X0Yqq&LPO$U+8L`{_I^*wpW26PuxRF(S@I6?#O20Et2rV-j5plT)BdwZebjp6q
z7O>R{FGH8eAB;&Rlwpufka%mLTJCP%@5yNsNnczAJv05&>H^*Fg_-bMWN~<m4k_O>
znb_C9yNFk$@r7n~!DK)1j}??H*jbCtK>w+EoIjIas_#!dwPJvjgcOD%5-E)#1alPN
z<ST+01p}o&bu^XAFTijVCnU;pJlU;M8mB#~Ivg8j%t}pQLXd&f==(M1qT}@YCoLWg
zM`mvalco-oFBO7K+(0NmD*J)(ay5jTGbXPrh{INpaSol6lRXSTo4THKWhp$BRVdHz
zyLKWY%S-tv1-Dn76_z05(n(Yxv17`t<gc_M<zi!u@uY((NY;U59lh^h;b;1Sq4KCf
z3E327{zS#DC%(%d&IfT(6J)`o^Uz~BLew{#LjScE)fJeP{qx}ql={pWV<;XEmc?x)
z7UUiG8g=)e*JIHe*9~VCbP?>c6ZL=jgA;f+qzP+eIWJ@8Zf1wL+8gZ5Tr8(oW!ZHK
zQO_O~+8u*pXl^sP_}n8Uv80hKJld`--QTB`hP!PFJzY6(Mt4afPxlkSI8?EG2a2-P
zWhmJ_3BGrqHHRdVaygu`Z3pL>hb_Ct#ndo}q=v*K>-yW=XbKqlwB^UqjY&8jR>sju
zp`r-GD8UHA1Y&?;OtMCn8Kkp>P;2kkG34b?lAU{mjV(;SZwu{3yJ|_2&$InnV&$*z
zexj>Pt!1VF@jL9~%*QDcsJ7~zb+T|ce<Ip)#7x^O0RFA`I`drteMuC%t09S+++jxF
zOjHa=WllQ#6?P`)Bpbd1wK$Ca3|Bw|+}fC66xfgjwOX)-ro4-zK~_!id)P1Fb9-F)
zoK#Q<f4J5lWZof6z1*!Iq2bv>u^VDWD5ntLR3=Sv-!V-RTyt}ujM4YTBM*GWYJbr#
z)n3>p8}Q$o))df2%RXsHw<QqNM+`t>NI_mtc^zM*M67;+_sZV^;lY1m)aYO<JcT;Y
zDbVXIPoBA>zAloxO3Yi7_m1}SKIB2UxM2&}#{dToK!O>wOc=!&)sRWQE#A~pm(a46
zuSEV8r2gQ1Qx}?XnxmcbObtWf`ox|G!%xeNM5^B2lT9W*N>MCrH-aRiE4*-lo&d`2
zu{}O2`PSggW^3$$FGjO$Us^#m{BHsi8o49V?vg;rFKXukQC5s9s2FCqEnF@@8~l(!
zcr}Bqup$0>A1__+PO94>flQ$1+EHAcK-diR8$yy|z71SZaa0DusG8(4BB=?eK+Y!N
z2e6&1CM`QqAVQ(d69X02Y<V9$MmOBxCv}fAJ#MddhrVpx=aIaS#JZu@q0;<`M-`d~
zfv9h)`h90B#jeG`UMcuo0=4zE0GMI$#`e6_yafCQ{lI(0{d;sxGd%sVL9f~@KG=I1
z!TF)zli}<BM~Ni>*B(*fV;|yIC$#cjLy08jKDlM(;h(2IH3J$+VFWka5F<d4exN)O
z9!%2dbLCR3e(dJ>%fHg&h`JhVRt>$NhHJd(g2Wq9KETplQ7Y=X#Fg&urNs62&ukHA
z4?Ak`lr!_X6^0fq`I#|=a~%PFouG)+o$)eDQRHnBy|!c&=E<EV(&EbdZ&W=i&yKQS
zL=q$&5hITe+)HB91GnpRNQ}R9u!7$+=qo6X74X&xfmFlbjHXOEH11q0j@D}QunLtV
z%Ud+OBc-_}9+y}C@5MT(W7y^)h}b%sXHhy7grZnh231>+BVch+(q%L2uB!mI(_8~L
zzyg0!-yXKRPA;yW>8bV38(Zo~EsWp!<-`&GdX#Y>(ii0IlYjL?4>(K3c{bP3tSKr9
z6-lSRY4&*HB5tw553_zQv8LA0@(z*LtUZVYEFU>z6vbyX@D2D0rA=wG>V)r1MRs06
zPpcrtfbC4d_Y}Dk{zn;}69jf2V9*oWlDN8G2i4t;{=n7@-24Wj`G$$lDV=H<bvMF*
zf<;l`&8~u&4_n~#_9#IruBU3Qlt*!OCyRlx3(uT9ds?2fs#3LpBCCk2C4g0eGI{q-
z!8qRl;pE?<^M=5<(Vdf;kD8bmR0xq!3sUSPl$%V;D=Y&yWD`Er5{8YP(-2zJhWWcT
zDt${M?TYq>%-ObyP6p$$txN*{gcpSX%`IuzWl&;BllUIt?7fxrLl?=`5YN^y{ZBIQ
zpD~EDfDfO{;_7(ZvB<7`k-`RKW-UP%4;<S*B38&vf%59WHAVGTw4au<KX?u4LDt+A
z$~RA2P$0%wz&IT%>=S<gU$_Ws_l7*toO|MGaBkl>8B3SvdM0@C9u--13iOK$I`i>x
zZff+({g*nrbgESz`kQy|xFhCg7Xa#q%1~f7htUEb?)wbA{Gh(D2!}cF|8n%I0R&i$
zw8<g@ut{V2&N;ff2`D*{+c<MSbA{M#u0q^gB+tu;TM%4=R1rR&kbmQmHepsB7FAi^
z#eQOUdRopog1^>_l9C|E?K1LvTw=Qvx_p^L$V!T>_U%ENZBTDbqmN5E1tlX7s5Y|+
zAG1$Y$`D2rc6P$ND}bMFydth!|MLo=w`QI{dZdsaCN=p=D~@`|B!LPcS;vAZiVFeB
zsv=lgGVtmriw*%U1K!8R#7rMQ*tnclZ1`c115+GhXtiwoOGX!3d4SDX1XPCpAS2)C
zG_N3t$79Ys6B8gSOv&mI@MpOzxBF*AigaCh14#=$Oul%3R(oeVdB6tnl$1bOjrQgH
zm3!bh-}NWdHBj=7<g7Kh5CgxkLwdl<<*T(f^gwxgbUk=(SX#_mUyT9PJA9++WPxDT
zNb#+uZtD~NRlOO!QPlrwLPIeB6-XJG&%Iv$>-*87;7mOjofXXqdwqWYMyb4tF8Yp_
zUT|Wp`JzZi7iIhkQ!7hw6?MJfD(6a)%VbWi>R$&7I*$IYpUkTd|L+CJJ`YF!VJR)+
zLrRctC_W<$laG)e29SaYu=&6gMKPIhRgFV|fQ7Kezl{|X5fG}j5R{fPbQIfN07<Nt
zg)2r8Lc#neH~dter$qYL$bKpJEs7%O3N4WTlC6*EEh8zX$*%xw%M43~WT!R2xiov0
zsF!r^k`s-VY9tXBJ)+xMan5`wz=S}Tq3u{26alFeU)~8LK{<2(XoG@e7*k@IiWJ?A
z)Gu(~qq%du@`pV!U5y}yB&{+`e~A_0Wc~%Nyui#xs6r^L%IsLKns2HaJ$JYX6>PGZ
z<KV#%B_U3Fyvhl;y=|G#>nZs}<XF{nzuN$lAk%narA<ftE>~JLvh<{WeY?r=#OfQ?
znb+RmLii>B{g!z3?h}4R-Oj&@C`9+lf38MbuS;(O&%|cbgA<Wfx=rWQi<fQZ5}0EW
z@!%lzPRhW$!EEmIxqbc>M!zgz+{3>gF3RiG?q60svE7Y#msEcz>=EMY7r#0^Cgm?T
zH<{D_%%WGNH%;s7Xef#}SeUTZ8(I?Kkbo?WoNajQtR7rt{w;xNRs7uV<Rdy$xtfrr
z({rSyMj_4LE%|bkfO(>60G}UJD1vf`l8@2+8S!GH3>1J=fFLGFTo_O^C}J7mekKzc
zWw90DeTXfH{+c>t#+t|tN|4xR35f3<9a3CyDjoB}a$MF*a40?ZqQA#>@%`OlVOOXf
zw4pU7H|aKe_lg2JS0#CGjdrnpQU2@(rMv<xp3SdB-1{D1)x;5{NakYtQPx<96?>6J
zrso70JTKIxe*)-x98R4agPVLNY6kw2GF@w?zIT)VZkKHyJjlpyVo5F`s;4D!ji=o!
zM|LL+<|PZwBcZB2X6ni5Ir(~YKcAkQdPBWN-$nirLH}RWivgqF&`jN|?W*pr6KTL1
zV%N5%xxVITFM#3G)G+L6EA8-#Xk$F@W-xuDBiQV>yo<F;@^g`Q^yVtFoP<|G<=hB%
zPT9d&{1W8Z_-sT4b9->JRMYE2zPWnoX<N*5FAb#Cc<Oz=tY}syL$~v{;=BUW#5nqo
zyCna1*$vI?AK}^g2GkaIr;2z*8G=vtXi?mp_TCIBCeUy2)R~W30fAn7HIsvWCCtDU
z5Y28w%B6oNS#${PbY0Z!kGuLC21IO+uF&4v-<bFe{V%@IPl$ZN*>){dxxU+8TMyJi
zF~e(krhD=VgA8pGsnU%&?b;uqCqxabB(7^8Cn%OT+;E-}NP;8QT`@)lcc#00k;~3t
z`e2_>tGxx0|0WxZbY4Fn+8mf=6Ma3Nb4G0xkY|?S$o-MGbtk%$iL{4!;Y66sU%K$c
zD=laE1h7oS_DS_Z>nJcICUbU{dQ0@#hi!GCVZzmdZ)@EGTJ)YEh}t`1LL#JTCGE?@
zQ4-(3UYDa`wHS1JLxStRd!_zVjfd3nib~faQL!93r<v)e3IG_Dp3mG*lNB?0z5}GI
zW8#%z*{hAMnxRE_GR7W!SI(J${V|Re7VF7{`}(5l;xil2P9%Tu6K-MH*f9^L!ZWs2
zc==%8Jph7s;CyF>Z8v-;XvlnJn`0T)^Ak+(^M}rxW$Bi-O6hsAMr6n$41t@wdt?W@
zdf)QSJvZE&1QIkB;`Fu4?%PXb<3evNqt<k$UyoCB`+vhOfi-lPP9&fqW-zqp%P>Zk
z@Qxcpy(}{1IYV8dQ5D1WhK^-y=E|y>x7z4W<(0_NhdPM(_k)i#%A&GgD+C>-$^Ezp
z9I8LY^|yE@?Y9;^T=+qs6E{FPav%J#n%SM^W>t(3b(@<`DD#_&%t6S-a%d->O6(@s
z$xb3r`29{#Llxf8V7AbNMsvVglr(`um<kdaI68vsZ8!xK1w5WvtPewTLz4s`Zqd*@
zccyAavpOR=7Y%9Ly+O!a{JyAnr2AFJz!cF)JFj%z@CAB$)8CvzQv0I5d-5%SryH8E
z2E4CNGGIu9jqY0rQ5Qn8JQr%b=ie`D^BwJ$F?ylW?Q<#)k`_=`y}v$~|0WEzb!!6Z
zFrR>Ux$B3Lo@xI?=-VO}I*uigRPC|+S2rzt>P9uuR!b*##vQ&O5lhWH#tY5;4!%@6
zjN}j1G>v$O?b@0&?G7=NV78Hy=DV8EWL$lzhJ^Ecsc?P6D+tb}kJOKvwXs7-@T?`$
z3al<#*C-nk%(@OYtWadssw)5?QA3k%O}tQD!p7_pLO>)3q6<pIQazjA`;-1eB@?d+
z<_W4v+F3K9%0ejDVZo%{SWixPUb%#Bi(#dkwgLUJ6FW7smupQ>^LOD=Q&ua619!DL
zT?y4Drt?o5RQbrtEW!J0Zjw!ev4x?loU{P(Z3Eb5sXTBoFt$w#`ZVOeQ^x*XY+~(z
zqJC53j3$<7_@=&8ACzxjh&j(BDFRP5LLbh0;)bNfNtSxWto~m8|Hcu+Ud#bYNI^Hd
z(a8UVjT<n*M^938&rp7QWf*`@M%L6<#&o?3n_u}Zs_{Ka4tj@gdFm-<%`5L5wZ-0c
z7qf$9F=QAut-fkY>P2(g<^00yY89^J;L)uNYrw+mcP#-$1!gj6Lq`#wD3;9=N_9BZ
z`?|C9Ut6vigX{^Iou%(X&{qkgxY{t`){z(i3eqA{3&3?P?Snh~biAf6*#$Nj)g}Ay
z{wuQ=)M6=__!L?@a@=|b%_$=)Z1#qRe{$(<)7r(1ZrzpUP_>L*4U2zJegB1fkLe4K
zOAGF#^4N{k^p%l)PjtF{!Q=3R&~|D_qRTTDm3>|8mlQ2gXT>tGJ!yglv2;h~fQ78R
z7T!jS*vlP6_^nr3oW3I@qX#a(zT2C$s`hRs_ez)P(-!BMV9@rqfs<VU8?adW*ev{o
zjMNP;Lxk9iDO|c;Kd>rcVg_huwzc%~bAfc={Fmkp0?}YPIr2>T#EV{HJFmz|EW40J
zrAYOE6H_yfpS#4|Mi6djDpqKYg=kEU4l08+&_X3ja}A?eVkvRWTuH+1W%EV9&MqJ|
z+SK<PfxKx8u(z<Z&Q7P~=$ToqZP^r?FpN#h@^Epqy-t;Zbb6ViGj23X6upxfBmkeD
zXiysd<>rHBONhGx27m*rCj&%+(W|2RnCkz&Tn{v$P;XOQn(?@-4sQhd8N?TFS=-NK
zhE<H7HEA+h>RB2bA^_p@Mcb1@Xl1ta@cu3JZ6h2GPhN}nXls}5LX_`&-Wgeuq+uk*
zd;0!Ai+s1y<2e@>_o7XExksZ2NY|a%PyGk<LY2_=n!hQ1Y-hScEI_Y^<Ow|>rM{)T
zd0R_AHnM)85WE_<9-|MDzlRh5c^9?T{0;%06I^HSA5TkPJvq4!R+AiL{8jP}d<O&X
z)sCAQ)EIH;-y80T{~>=wVZimeU-Ao>)iKfC7p_PVt$9UIP~u`}E+2$$O2z|45c4Fr
zN<+Fybvk+j=8wf57Y<+%9kpn;-v8;n=*}#T3UyjRbok-=a4Wupm^j(y8P7*RRNPga
zbrUSDe_o@r&`-Ek68}5~d0sHje0j<>ywx>Dkg?U52MaC<CW;Yv3wCLvbW{>}!s20f
zS$#mi^26f=@b^_9nxxz^h1kO`OH=H;S59!znuL9dOzfh<s-~oCqL~rLAHLG*ubJ7i
zVf(sXEc0Ght%((0-m#b?tCL=+qo~^JNw|m=6YJx&mj+@*sa7@JUt}OkBwk|6r5wLs
zrH=s4Uw)kHp*U`vUxO8jb)B|gc!osczOty;gmk+mb5wNL5$QZ3|6KZNUMG0}QAoMG
z69Wj;6WHTx1GD>tBY1Y7{rJkzPkKG4k3EPMQ!w~XkpOzt!2DZ88vlBiru8(mD6&S5
zVi+1m{KT=lti{TbD^}xnHxoL}Q@*1!p9#<E;8eYV=8Od-7&EU-8FZ#oiaGt@#TsF|
zXwk4Lg&{uJ{^czC=S0}`>L9kqICn!sz?xoZ4MUTC0*Fiqa_U*?A^Q$_T{-HSUVAa0
zFeh<c*r#hNZX9PK*i<{i?0GqbHBjA-<W7RE1;bwV^;RsSDxE@`ipCC9TCR*N-%E|X
zTSY6oBi;IofzGSjd+NiV2=wRr)_$+_D`-T&jFttzEtm*$%S6|1VD~2|sqO*Ugh2I`
zV3ynPOU$k4Qhfns=G6p}OyEyt$}$#Aw*p-rNo05PQpQw1>V$N>;B?-&T6+OoS);5+
z_z7`71XBIbYW<LE{U8g^8{1&~yenkGx2u7{CxhJ__zA}tJD@tWbDtA~qeIj3WY_tU
zzh2FVj9rn2VAj{L1z#SLLlQif?uyAb;Skk*w}t*^Y=F@52Tlq=>EFH-7IGY`_`?;~
zX~ivfkZLv=5;;6@^(@S6BzLRnL#MHl%Ms~+%F^mAz#+43PxpLl>=AmV&#<<!ccL#(
z67GB|YPs%v+j^*9K+FOnl(p^7tg<82ZO;-B?@|>a?Lf~K-u|u)VFRqVU?X^Z%C~zd
zi}D7@K<B2Y2EXZ%V+W#z*)oe$V&>b-F2s!>v<fr#`IocP3D%O*wPtv^*F2YSA|nla
zVy#>SWs<t>3dyY7lB-KA6G|vl5y*w>aE-QaWG80I7y%S)q-md}?gkQ5t<*DRw@ssy
z0E5_>SIuPk{&-|fBm0G_*#{^KU-HqUp(e`F*-sj4NrE~r5Ahx!%VyiVi`obJ+S6~=
zIS=!Xa6lkJd+Atk;#vtB5G~<IHM)!V9~`ZXNBmCk7fI`pw)9lq4Hs1L<~tAGx8rJh
z=;??K?1hEhsIUDPGx2oY#Od*z8_$+jQYf9tvb4m`t7*Km0hj2-bB2fxgFhoEK~^iT
zcW}JtmAx66xP^urvML<*<jbp)g~e$Kl}M7|$&uN|Fph-@HvOM{WF4h8Ya!{)V~LK4
z#U(@msZS;9wrvPDtRTGV{u&E=7DVxvTc(tkV1LTUNitmB2*ngrwZgwukh6TMuygh4
z`p%gAX$iZNtRJ74MyfUWy~6Br=*l!mk&=&+it7W84zDkgWdExa8QshmPQHh*djnd&
zd+GL!e(0&ytmWwL?e+xNQ3yRSNN;+b8eiwzYm(S9?_c7+Zo{hkV&K_>_N|>mY?NL$
zz%ALTG-4`j%H#ZR6t!9kf!ir+U?HDd%zx>O139O)7ge+OLFstEMW;zpG@-NbihjB7
z!-|~!%XR$>C;^3Z|A6E-!VB{tJ-4{c9nGN>>d8z6m(70L4=Ikz{6><JIWo&QRgQjy
zl0YD)avNC)7>5fe1w^1ppalTHzybh%06$AGief_pJnrH$V=L~E_<>nf1oqJCW2Soq
z4+h(rd*6&Ixqr3g`)y^F?YgMwof=li=G%5fnyDinRcmrahBykj%)kz0h*Cj=0P@^p
zhQXdV4z*|Og_Lo}Rb;s?EN|CeXBbgKlTJc|*<@^7&+_0HYgwUIWdhcUOQRbT-pEea
zwp-3HwqnUg+ElTa!uxX-Tq36*Au4}XMyItX`|E;TXKO#Gme$2>*zS8^c)<(4?C9go
zDpIvp7_|dznS;&@Ha4n;)F7mpE?)>0(3$RxQ$0|Mzxh@2vve^6IZ|c6mD1q3L}md-
zAK$<F4gl<;1+ZEx26Z9j8i@3z8S#fwqDNJ2N{AOhC*?7>ntP^0%eSu_Y|FB5u72XA
z8d!*<9(m(vy_g234KE($pa{W;2!t7+iD6*KAjo*Hwq*!~&N@w(%$X$@m+m+c-Ylee
ztm0`Q2~P+Pb15EYh7r^a8fywB0EtEbKoTZ^oCH3=VrqdY`2EDf2#*4I?tdPs_wqF8
z$J$Ug)*J8@QEagrSB!v_hMV&P?6}ZX`CN7Yu(>YdGTxK6bdvZjhkVluI^Yq+Y&v@<
z7Nx9rv8kS_ycw^pj5uGrhJ^Qz{9EGEY+|Hds9$qu@8+{=V-pYKHJ%ar*eORZce52O
z4K3~Mn$sUgFMib&+DdC$u*ildkY$IF#b3uUkMU>kXtGIH!t;a-9w}-5%D(pW>>c!Z
zEqB;(PZQ4YMNsSdw)Dk@FQoFkAPdMs@6^^=>LOZu?LDE#*q+#d_<wNYjDe_mdJ&uv
zEZq-uH@<=Yy=e`}Vt0O2{XZmO4RrjW!pxi12ven&P^SA^im!j(lhVE~Z7uonEM(7=
zaJ>KMiuMGOc!$oKTDsc~&M80l>51uCB;xTEBMT%f8%HqGXet-u1kn0avtbWiGo(a<
z)Maz`<7F`vE5Y>u0}AF}*q9G!vrd<rspP{slq#C?c0;=I7B(pH*4!@fI1M!lIt)z`
zm3ipIU#s$qF8Txck!v01%(7TV!r9n5iL^#89Y49HT+Ff~=$~@4K3nGT(INU}2~Ea}
zO4l(*qq0RTEyS~kp16MpppfBu52fLXoDV~u6QBpD9m(f1RPy~yPFtL{dIFqJW0=er
zc1==z{+_%q!jrdJG@*M%O>f?om-)yi{m>WMhxze@ef<tiS66?Yl6RpOmw$P$PZa>u
z<XL4p(m{+JdP<~ebhU^~e6nv-7qime9jmE1iJ!FyqXO~SAqspq>Wp8_vFN%hD0{Eo
zt`v5WkWWu62od!5h0)}HPD6&>E=dDi5*T*VJyR<<#m|p8C+y<8F#>tHOV`Q|TBGCV
zh7EbgE4vfki_hmFXR7{F>1F)&g|OSDm?wM6fKJ>2oPM@qrs&{K=<Bn9QcDISD`@6>
zABeJzC5=eYiFVTKvo?gf;al9lT*9s8@rUoJ7Z=6H;_;-aREl5Er{RvNi<?C~x-A;n
zT)}JS4p5yFX%jASc#)(bG*Why>rM|LK)bvQJA6QR?(Y!<lD2Vvup|I?#r4@d*71E0
zC42W{oB5DeA}KT7*p+ePm%OBWrQJw=343wOJAu=yITPfFa`=oPUNZkxqJ7i5M~+X&
z(ayPP^4}zwCE=6vy>{Oq&)7ccZ+=<6V9rQ-S2RmMKg{<+X1bULbpybx$!`I(An$nB
zpa#fHNS#k`Zz>@CAa;=5hennEJ3U|@AW94f19}OKWX%%P8#0}S^Y;*PJZ+#5YecHa
z^){ZAKkvz>U;<c4hPQa|POJ5{Li%U3g;6F7L1I?J^DxijtpKTJnglHOm7YEYk;2er
zHVirV7=phQXwGH{XgHE1V$sS=MZ;f>K`NWiX&h<cvxiaiJ?0lan@ms4xmKggtVS<5
zlNQAaJ+V(eZyV;?(9Sj?;-@e4LKRVjCi%g6159dqt@GnxyV6^)9fq;Hhp+39>whSu
z%AegX9w#V8s2)+s>>0)D8+|^z$TZbD?aT{A)us7T(C(=IA`mSgH+;6fPE;R2e(Z}!
z?yHYAhlWL4)CK4H!qB?~Y<l*i`S9pLOI7iDv+W?cek`IT=}VA>g8R3)`FJTh+oC_K
z@4lBuJb@AMUVY*G1aUhmPip(m6*d0ttAd?xkPVyZ*B7?U%O&i|3He#^m@mP_ug;t$
z<~6k^rW`NTuwoid)(kw_{`daN18cWgywu~LnyW5hLZ*_zdkDrjirePaGIF^`n-4!Q
z2U*I75!L!Q74xe-`JJ_EN_-}of@scdFG#sKqm&dw(HxkC|FQsqs^hX@&luS3R_UuN
zWWAGvi0BPlh|%oBeou;&F@9Tkv?YD&H?Nq{<*t9|Noi1gJ3S8zSm+giDc*<`U;u}C
z_<KWQ{3}uPrY3dFJNqWMCLV>q(~4E|s7S`VXY_j1Tjs}?2bMfrLYD5%i<qv;SjZ*A
znW;%q3iI~Y+hiesq`MwHjO==dWu<+bw(cmi!}}DS6cOYP?$Dx<y+O)7|BO9x*Zy8}
zVxALOx?nWBplba9{7+mx2e8ZMZ}%U0rdPFkgG_%vU^ZV7!<u<et9m4n1WjXC6m7^J
zK~CO=KkT++h<|_ia@bEP_$+w*XF`LcxZb4)<9*8N<m~e0YI4Jm&2}lFxt=Ry`|DU#
zp;{J~eZZ){K53r4I?ifb<mm_3>#0XVk_x$LlWNI?24e(Yycf0OPzE!Pgz%v;c7gM%
z2vG;SaBVnr`a^74SJ2k|4C6t&hScZPaz{RNWeGtVeS}d%eW7i{g=lYalPO6yxhV9^
zpstNpamBgmA<a!j_~2nTKlp$=l_GE0gC+6v2S=5dhfRz{BNA^{H-b$?X?l#}u;|h<
z36BRsQ5~W4bdOJGz@ON6|JmXX6D)gkuh(QJ+Ti!yC-M<%Oj~!_r3`D}C<}cP0&QL&
zg?~8%TS>a(Q(LYlz4kuP`65yE(!_Chg}EMY4Annv+P9eNbpys^uCP0Qp9wMXxz0tY
zO24@6k~GF09DA^z*xLQkd)6a`JimDxJRz1|5&{>`t}%J*DtPku(HhSO$mBcDB5mfI
z)l<K7j{n&{Uk9RpHe}l`+H4RIEx#R*=B$>>=ocZI?HHE-`hwO7{_5TdICT0q`kKI2
z63YFS8+GKVb`BAI__qUVGL`}0Sj0L~cffvoR!H`bLElEkF$sXU_0(FO2`nJ3v4om6
z5Ws!qsY6!`I>z<H>bD;#uh>);tDqWq?wv9|J_!=f{YG!DW)=#g%APAiV{7k851~kc
z*|KBq)+HeYVY&DgAY?T8hO-=Li6ddliB)^#4g<D#jMNx>i`K9bS$5pZgd!Zg2G$yl
zQYIkpX^%*<@<gK2jYjGj53o+JKpH;9jV8ZAp82#7vy~~jGXB(<X>Tx5H@3{}AID1O
z3!<p9z4@JJZ|=BDkCWz9L&^oGJfUv@d^usU+=r6njY%=vFx1XK#4R*=lQD4DJdxjT
z#23B01w7lEG4*ndAxWeVvwa7K(+BmE7qaDx(#98B<?2UEG(Zcthw<|YySY{RvkRs+
zkm(xa`djW-=L2kS2MNS~88{myQ+FjikFcLD<e&FBW_oLS#OJS_i>b_wJV`4F!ZrV6
zOY-9IWwMpsrI*pxTiP&0z$$`JsbAHWaNLt2PC;{%IZ(Zs`pTi|W&a^hxgU0NcHjSA
zT&=WFH<I|d5(to5{B@b<a<`P)E@);rAMcaUARJVlflB5Yi`t~?IY!or{erh{AN(5`
z4i=XWxIf3jiZ*_XjoInlXik(CAFZfjOTYL`miMSvGXNq`ZBM?q7(QR01{{V;NQM1%
z^9A+fj+}p_xIcWQ_uQxS_?J*HUyyO}zrIty$>o@jO_xs+ZA^~VeGQ51SCoz)@s>D^
zSIHoK&cF|Du@+LYD;ZOSAa>u0shJ;-HccM#<+RjYgPx%QZOcEt1Zzk&`SZb|Tl%w~
zv_IP!eX$;W3GBXNk}hap&$;KkWhQpM=c@efZ1n_rrmYG5uf@2|7TDFL)SAv&>nKJ!
z3J>3Sc^+V`ej<c_Ik&#wzeEo@+BZ@n^KaQfYq7zO=$(Z|8M6I+v4mBey&&r4Y&=0J
z^6s9{$mZR%EzSpWcjm_*z*Ov{yGREi_`7t&5z+Cxn9;pEkgpnBXo|ndOd}|59UB!V
zfTWRM(Tf0s_J^%9YBt&&+V-l+?}+x!{_)zN#fQkzCSCPSj(T@sjq5kpwSizM$q}z+
zv=wMj$>&us7%CZ^ipiHlPUQRev0mR2j5uR}!PN>>&a}cTtm01v^gKKrnhIo%zb6-0
ziSi|}k&w!7qh+#vcwS8hbxSmG6M)C9%`$$jbM7Q7_rZ(cJ$6ndMY@ipy=}9`1)-rg
zq4<Se@yG>t?Y+x%9n-7*9|Q#XDpfcVLell_JqIud8E`v;6S@7Q%<-P|cEASE@aRw4
z@`lOWB;(^nu0O@<Z~Bq^PIfo>BaU)ZA#F9lAY!S$&DU=ygYba@c%{f#VKY1~<%grC
zN8l5^IR4NJb%0g1^`^`8fnvX?-lZJBe4$!)(UV<=enddb;xuG<HMVkK==Q^5*omrJ
z97QNgvJLXk2OlqLhL95GX_NGQf7}xL-AS8^4fN>%fnD}P4_3(K)ub~unoxB_F1@(|
zy5_Ll7bAsww~)>=1nu}0EAzYD{qGJ@VbDg?q;S$2;%Q1os^ep7=r0_zZ;#v&ARRDp
zl}Y2c4o?z*%l{l8nXz9=lU`Al6n*!x>fY<CeJR;xM`Ngz5I-XE+s`a&U=>jVG+>M(
zBt<yF#-WHcNy)5&OusrQ&0C8fn4IUP=nCN@Wl?1GTvg$<t$mE7zd~G46uY5>J%^JY
zBLq?KnF$!ujnZLdE;MKKX?w>PvFfFZuoD`<xwNKkTltN+h)!AdQ}HWhvV{J%m+pPa
zvRtk|bdc+UWpVguhH>p|0KAt`n4$Qo>BEj+V2&5MBGzb!AyvjrIAy(ToGyw@wEN4u
z;Q+KP4@?|x4~9UDh=gx^`*J&?MpmDgZbce6#AJEHGcO1DxY73zg_a<AAWuVEcbY#m
z<=apB(lhw{^LZ~V=~D52e44r4d?++k`4NJ7$vVPVz1y1~DU<Db0s&?Y6hrnlOFX|@
zCt)l0^NRoo5)gT~?V-SQp7-5PAQq1LB5w}&5M>V!;xZSslm+Z`NET?hH|AbIo-y5w
zG|EImTy>KULw{44yI-oYer#E}z2h<EP|pz=)VmTB_JmU0j?Ck=w(bZffyrP(bcKt-
zU1x>4^^uwCpq_W4d^g5c+*+4@Z)^#88iL6m96ywle^pzUSp4;ugxO_r&c}+U#>nBG
zOZ<&0s6ED-8S0(%5-dzH$7DY#thsgaHeaIh92+G$N30ql5tsMUS)-aX3{L5(V$OLl
zznyy;1vqIvx7m_LIZ}l$bC1@+g;EsJmT@N>Pd71lilXlf46z+4UH+Qa&XUj#$ms&r
zbL0<VptC4vC{F#@ZV1x0hOsXv?kvM9;yBhU1+|VN@NZW4AQWwzN7zjA^*Upjxq^rR
z2M&XdAq{<X<A8AO1)6{A|GfYZ5Z}cB*VUmU-kP@JVK?@nS=0cGByyiGQA8ViHyhox
zabRzve3#e@UsX5q+@Wr}*BzMQ_KV8L<zqPnPOqUPpgRPW?3)uClrT>K)kW{@7A8RC
zMGN7=QvHpsNjU6Q6(=1UECZHR{6qPjso^lDw)<Q8hD!pD6Gy?Dltjec=cpEgX0O_`
za@tnFX~P?}@>8g8kZz%vS=rf^eDPO?Ug$ozQX^8sr(8l{^2)EJWS+6C&phJ~QO~FN
zOa4QRH#tE2&rWJA=E}GX{TuG60A}{AHscLRXRq+$@*V-l-jyDM1mWvHHGQ@_5I38-
zOZx>MCSu29QIk2klwufKzBe8u7tY@x@oQ;{;SxAmBRD`3)tda--APfjL^r)d!5#i*
z8S(?BbLir>-~1&W8JI>!IVahG)L+Xg^QuI}ErNT=(}`gOnqSgvAJpGQ`z^N}r<fQw
zd`J@~;5@a9!^7<0a=1f)qk0t$EFuQL=$j6<E4>WD1=T;I<jSFZXQXDvnW$IG3EqLB
zbVnLgkumz3ySjoavZjr^40O9d2oADkrE%yk)MX5&J}D1Zq_-Hxyh?9EDqtsfBK4{D
zS3Q&lejPdERFkgQlbc_P5%Rm*NXm`{(PS{G{pH^t^mvM=VRgV3fPq}ga7n~t#f|(V
zm(?Z$6#Mjb2pkgyns39de1HRT>5DYoFO_zjNek+)6BBJbgcVjNU19nzO5iO7kN;an
zfsfrq=s;@xyMl7`k?k1`cg(Vp;qjfT!v#vhR>ja-7?O~kSgRtpZa$YHGfzm9n2dph
z#eCvrhY9MI{q6mayZNl9bLzBIY_V{<rA%Me>0H2Sz-c^rP;iXlJ*m_N)BVI0fm2A^
z0ekg>Dpg$w!wyVmeqrrlJnsOmW0@#0a%$Q3WH>tV-VXT0kW@Vh`%M+G(Iw_!Jk}Z2
zgoj8&FbX$`e+_8IDz(I0@r)IE%&}reJa}*i*1inY-r6@mVsEv#&<*K=2)=%;b=+M`
z+`dlVUFj3JpN%hiC#jS-RCG*NL$zlNvl$>j1?J&~3=AXh!v8hw`o{m(TW#(g)AiiT
zIx)#-%|ElsV~lM4w~n{F^~R4YD(|YIyy9HpluucSCU$f*?D>Kytz1d<R6;ThH@<x5
z-2Gl+JSyrrNlN^fvis%(sx^Rfy%ijJt8-uyK6c*mk7^@+k6+va;i~(<YL4In>i5q(
zI^Pqx`HfZ@V*YkN_IMJOxXL%QBv}dhsb@6|QN`bQilFwvg`Su#&#D5smZWakIp`gP
zKDS8>UnAI%(224H7Ll_nm2-24@nNfM!3`q!Z0V`uixpKtlX<7&H#)w;g;Ox`0#Z3(
zdZ=KUr89XV_zCNcSEZ?qH=VFSd{Mu|&wu_%?f7Z_5VMmh1SQLPqw^(PdfaVX8TGc3
zZ5WLjvtrUS)g`W(g(L>qavy-oW=}T1Ao;l7x-+rb@SGdtJv1^g_%Z)Zvw75pcr~t@
zQz2CWg=#fS;D#Bq6+v6?mqUr*DxVtPD~DO1QV*jnjuq&Bq)a}qo`1OU=~w;9Pp0!;
z&mZY_v$KyEs_AWZUa_9s?GV2G)Lm{jp~L~;mEc86`~s)=f<p3Lyuzf8$fp|bE(F`Q
zb#Hy#QEL3makPdCCxa(BvzFgBX&m)^&x6;tSGiK>%rBdUuFOP{?e1Dd7l~8Zo^i8>
zhL<pnn+$A$(c*VYWam|}bMV^~x(G$MSUg*l7SU=CBYV^M_Rs<+w-9(!!N=-~8C3du
zO)3jN+=DCt)u@Z;*Y#WMkB9KnK{TSXp?;ZNkrgQnVpqu0Ieut|wIeH3o*T5Di#cy^
zu$d7;Cs^4-e1?pnZj--zkRfpEE2IG>Dv^?hIBFNFQ?FUTgejaoyWHS>mxcj5P0H7A
zaBgMp_=7~@YlpV1grKm(zD@S?m1Nm1Vl=mWzp4U1?@~Wy`*wlz${O#+$yD`eoUyyP
z{Ot`Pr|j(WUz~J^|J1`=@%uf|8r&m*`~@Gh`eNFUeWx4oveQvOqw3LMG0gR)#U6&E
zH2v)KmtMl2rqvcN$ajFCP-dl$(e|fLVUdm~40@wop?XL8ez0_(_ncYLN$tGTAW!Hh
z<J2zKL)oF8JgZP)NdW5X>Kb{vXUr})M_ce2!jSdZH$&6<Zr+?0v_rV<{ad)3fdLc7
zmAv|HF*qknqd;V%*ssJL>9x2ycQE>GMLZn_wjdM<h+N{}5CQN!|NFRL$j%|@)|V>i
z-&T3w)yi>K+vyWCS`4n6f)Wy2PnkE9s^qKFyv>O{Qr}hZtS7<j5aWstcEb(~fIDEu
zO^+yIgRz};Mvw0_{j+g$AUTW|e)nW$kspU1pQ+V{_C|{iqgH)hq!lSN*1k>m(bD(b
z@~St>oAh~?I|4pd2N&r`OP;2{xQcL8hmpfmF`d`Wjr)L^?}|`<Mvoc|Wfr=sF6~!r
zFTkks4b^@h#(E>FxQ$>(*|V((2$smT40YJLQhj;$r0l|FJMhVY^0GBQhl^dWSTTL=
zJF}+f!Vo$a3nNof>(Lr>axTs(dz>+PFg>Y3w><CDs{RU3JKiqvx0tClb3Qf=nw5yj
zq~vu59a-PF7VHwUC32Y<pPbL%0k>m1hpq}g4Y?dTKc-h35oROup?pm0dGzir0h$JO
zxI})XzI*xiztc=A^UbyCx?zLL88&jDT1Dn%h?+Qn+Mm+cy_zxQ6S<+kOeCou9gmz$
z1TG*K1YZ&Vwh)Xx|3eZ>N4LLb*?3%_0gsecc2Aghc>#AfF^JrQd2;Jp^XFNR`2ME>
zxE?Q_P;785c1updELA0LXn0ZVg7e||;9vgI0aQr%JEF?xHdP-P;PFP?8=S(XYE&$4
zkuB<yvV|cpSv&vljMq{?YwpdcOnmT8lROZm(uz~Rcr*KRjKugNW@G(iNRQx@ih+v^
zU2LP6g*t=uKGqx9X7kzte@G=<PrBTK{|Ns%Di=!=PGEenNOEVhg=kbO^u(oB2St=6
z0-b}~CduZE7%b7N$GqOeM$w|2hadh~mV3RKV!fTH#(F6_-W6=x1nAOa`|v5${_t~s
zT=N_&>DGSuSPnqFDG3h04^StjC=x$AJ4n6ZKpQaE#PhaNe+zd-sAEy<iKvqThCWWb
zLJw{r&%PGqerU*;p5-Qup5M|$q{y2O&iqdAgbkt6a=@B9LHgA|`cy*NBq)z{WNmgs
zLZ7B4{M)Zx7>|3hJQG&4NU_)b%TI5;yfF5L*2`p+S<nWaH{HyxAM$szq^m2O{HKK9
zJ-neZE`M*Mi2|NfTj2o+(F)@5tTR37kDjlV&c0>EBiih~+5I|4l+)VNh^Uva+f2(L
z&eElCoN+sXwAHJivtaXbGK#?T@R;U}eJy35PjD$`|8s}U<#I>mLZirEEs13=%2VL@
zW-}#zdf2>`_sWV(n`8FAK*AnwrmL&R;u<Uizc6?f8H#Z?=@YqKh|CW!gl1l>9aJ_+
z<UzVjho`@(2HL4~M+{*hr|j}Y#nuyWCCc0}sq{#l?iss}Nna1oQ!$J*v@xnywj|76
zq?SWQJ-yU}>=Eo(aFA+CkCC$A!)Pjhs|=5G^9Ji0yEoab&~jjPgG6TyVczZHd$QRn
z>N5{Er~Qz<)DfQ%iE4K_pu1Jf%?JpJ1+~8y;F*5_k#t}VwNCQ5#vl96Vt;T5e(hBl
zabFt#Ez&?XSu2`O?|Ycj;X-3%?1ei{(EsuDmH|<B&-*Y9(n^UmC|wFjhae$H2+}Rm
zuyl7zmvpyuH%o_<bhGTz&C<Q>v)sS$|9Q19_k7OGTr+cBbIu|DM!6{vBM`-a>99(j
z`Gcahb|<3D?Mmy{zvfIv*FV<EhbkixqxNTR3Oy%ElAx<=ZMZ(oy8unptZovBF3F?H
z(aw8>7t5nAX(CrU%d-6RYXhw3?}|hhgJXBa+V{ajs*M1GX&>^5rD0yH-I%qm!<dfp
ztNF-XJqezFbf6RkAFW0}@JA#^^wU$<Z&w{m^ijVfNo=$>O>^fyLSNSEocJggRy=J(
zh`^!|S+-FJ`bfq$qWkR{5qBiL99hKE$in+|{|+wS1sA6*fBf3{OKtIqHAJf}r>HjT
zQK>R#b^7&j9|3JO`o$ZE{kGKb`A`CP<V+j<DC4n3b_2kTdPCA=hSy{}O>Rx$Iy>jW
zr54gukMH?rkHDwR9gd%1slQ`}v?zoEcCr>vkDVOx{Jl#4DzZGDB2l6lgN@gk$v+r3
z{^mylTRcaP*|?fF@L^0seKenHw4ojW<y75Mu^YdF1OPNKGXW<2n_H3s+V)NvKENip
z&|s|d%-N3G-g|Wp9g-0A+Z~gdy3u6icuu*@AXI4S^~i}#7rr;;Ev`Mutw%120J@E9
z_#l9~fH@+cH`Rye)br%s(U@$!<Dv08burfL2Q*2jEFmZQD1A8LnWH#}J=@E2#tH<a
z<lmD=-9wW+{N%~QA8PYrN&_77i#y#Fi3=;KvTh!3=X*oGCYhuwE2nI7w9<on^N}Ig
z4;If*2@1e>M=sn=XuB84a}WFst+ieG7_8eijNT&TvE&n@p>zw3QrxbJCOX+K<R&_T
zM#>AYkw-m2gC603tdtEzJqQb2(3BNa#@x4dRBLo{RP-#~064XdQ_s~d`a{=3b_|BH
z9}RMY4Duex4qC4(!9mx(tn3x9tn4KBP?&V##u<%-CxE=vk#!P&YWB2N0OT4*XFJ^0
zcXn_09W10l%v7@ZGm|59>{twotXOG?;-u*A5>j=Ox5_Av2lmFS(74rGwg~LkmRmFQ
z%n`txGLV?{EOLviM(V<=_$>}6fe3eVB?qloiOL`V!IJxd9+I^7)^(>u9_9=a=oI#-
z|DaYi-ypBXbJA08OtWy1AZNGJq<e7N%P6<biR7Ae!vp|6zVGI0Dm|Yl&axfih|zS(
zX=L<ygilF5HH0nV3AYDl>F2lJFjv{e>vq)JO7Tt&oiFlqR#dB&*QZ!eh=d@H)jeXN
z<e}ddPU34P;vlvqT<?jgBPpCp+~Bj$dm&}oUQkQZ7h^F+I@3=hc_Mt3Rr#3r!_gQ}
zH^kF;l!OB|cb|IojXR3W9Z2o$7)X%Bu5X=rC=6?VaG6aO&`IiZEILK&i&lr=W;Qfh
zwzM;fZztq<Uf4Fb&03)tv{Xk|(Fg^lVa=b8hbB`5*>#}SWprFmN=|yxyq!o2T<sUM
z5c>Y6xOjGC0q~%Ql7mjI>$ajha{OAXHfRXphs<~YL$r?Uiw?VWfT-mlY<px83DaXG
z-UVCuGqK_!fl3R`Un>n0%itefQM!+efHQ^dl|UVmLb`2v^cD50nrRF)uE)iQ-Fr90
zJ1V#bH-kGGC0tV<okQgm$k>P`Hc1uo!YA=~c>*uXXb5?4sHF*p;$y}~`q#YLNKHmx
z-}2~HznY)Lt<6JrTyUfQHJ>=in=ge*tfoM$slgB8bo0T_qbb@yWn)(ICb6_V_mbUv
zoi#)_jw$icgo}*1P-CP^^}vH<az|cNFQ`2ApUPKrf8Sow608A^%zY?i8^y7x`V_if
znZc49g4fZTHQ~0}5p7Kpj>}j(h<e_*9HOGkHlGTwtOgJU_V<NZdhKCJs;TFzC$_3$
zyV+f?kW4xrnW+OdC>yd>q-Fxw#USA>Ievwd=TFn5B#h1C|M{K$v)`Tn3$S{Kp2R%O
zgq`xY;L|Nc+w*IwODBv6g=bA+4fx`TUNZ7-id0>=#G%s~0`MGlQ<)_927|C*_IF|w
zEI36HEsqBB?U#NGkrK6!t!ka)GHWe%yXt=>6=;D6orDe3@nt8~)Ez(8noWf728EH6
zUyF^NUzx{EGfXclc6bC|_D8-A{TJ7E?|v1_?;M&mjN`5pVBrXfLAg8L%bUI_v<6qK
z)gO7Jqfnlr2$X9F7t;ZaFe27tTqpS)7X~G;5c>`pR`i;YUogEor}w;6@5d)6uJ(Ds
zu@;jo63V^eaQ-Hw)fC%FI(0O~*A63UlD8o)NA#y#F?YQjGT}XWejk;^^(b*k6QEYr
zTJrYcibtnl(JA9`Jmr<Oh;*TN05GnHjaS3aK-5Y#6?-t85UHL+W?|*utCMmkoEq3j
zy+VNPJ&MSkQ=AAvcn-7rUQ-rlqoGP*F~u#d{ZEiBl#4)p<tY3?CiXe|zgd04atFd_
zPUYQD6vbavM9k{*jI0}T{E`T5N19ehde}NCI#*#LhT}P3;2~jEQt&*|Ma)A@KKqh_
z+|dDNGz#j#d~%RCG06ShFDw0gE(Out1xZ6nEi(KR0NYxNqI^k*A_j}5T?dy>M~~Oh
z`P1l-w(y#5#kNex<wRE*J<s&fO064%prd$cIlr=nHe0<GTYUpwR*#cSl!bzeq&2c_
zPzj4pIo5c$lRT5`dFhK+Qs&xi1|D*A(_XkNXrl$n;1-T%5g8)Po6di4>eLka3Gfnu
zo}wzY2EoNIDah&FY;pIK{mkXRbn4mKG&R0Dkc-Pn9~cFZPq%qQ&aq88Z^3>Vbjs{M
z>iDzbHxrT{F?bby(|HeitDmyE$6kvX7BJ%H+Mq&N02SGbp9ah2t^X5?X%|xKDd5+R
ztd^Sp!<^g9m@-L^vEK7G1fy(+PgtjBFzBp)*4s1gdLc&w=QuKj=ZS^0Zws8l>JsLM
zmhVF-j#UlI2eYX)kzsV|0S0QG1|~+@eA|=6{uc=w<WnHT?U%IIUzFd!EYmIzRmJix
zWqeo@CKwk8**$U<Nd3h8<d>HbyXI-V)%QA{rt7Sg+LOq0Pti;7(CqUax;ycw%N@nl
zGvlOT7vt)oczz+=E}=*hQ|6tSqMLcvn53Rz#IBNOp6@oV=1f4eEGgL{EAA%Sb;)1C
z%M5sVo{hpP=;%9x4ca~|I{nVm+km$^bl!hG(~;pB1KHB7(bxg37Lzkp1~CnDDT4R5
zttnfs;6plD;JOG+0{-=7^0+t=_w3om>2#vLU9C4huaJbBgMV55_2w=&S@>BU^@@V}
zt+<#A&)2JOE%j8q(MQ|X82~jsgS?iGz)6=M449|q=oR}*x=k;OU*2k9Qq=ASz05vN
zcIMsl#FR;lVRZa^^mbq%CAX!Mzp|TBAeNUPA?Is64F?K8biu^@7rrU80et6#l+OEv
zOMjh4YQm8@ssyW%KY*|(zy_I#3hpPnH$_NgC-&vhA{MM*sW+gW`Xuu8kz~w|D&`TF
z5)L*x-ukuXt|<=+8FN&5aDgQ9c}F2S!D)n1y4xREV`cIzG0!rM2uR9)cmL5QGbX<z
zTrICSP}%Eyo#&QMz8k;hB65SB?u!lbb}y(b?;L}?+-_Fgt}+Y8YVOBsc0K{PsctN`
z>Y^BxP$H34I?`rxVfJgZQR0H%ycQ0z83>yh$0}DNb8DWr!csBa(P+YUTe!$XVN2vn
zKw#FiMX9O^fpmD&Rf1u5ZzIQ;7LKBR7+@8=>P5^m9i{d+PB-)C{&HgT(G2hy&Xbc)
z>j1%3Fey^e=4WsRoXJ4J^G}-<O2E$@PPc;}k@knl!rwg%7cp8My#A!5@!kj*XK#V|
zwbM@xPLtqttdNz-D@NRx(oVg<@{t9#v5Pk$Y0@GE{+p&Oq%&A~MCPxn6zuJM4Yy>5
z!tpOvQ+2!RVXZ&C`^rGJatrU=8hL+B*jNwP*vh0bPCL{V7oSxO9*Q6DoCmiF)$Ec!
z8jMt7&E#_PNv#hGCVeEVre9r(m?D<kqn_`OHl{}%1GEtEr!YC`m+Vh=<qBLktFY%X
zg*l`Q8I3-z1ggMM1*CEEhT_Cb<0-Ddpa@_pGVO=B+?Ke3#xl|0jh-Dy6_v+%eXOe>
zJbnVT9JY|QdN`5+az5~MGDm7xW`ZjTi6>wJbpnZ|yry*ae}!e758<hNhmT=TIbF!A
zxL=s`9~n3?DvB;pcf+H=;(lFGM=p3$s(J`ZG}J7!m3;MJXp*9Y%EW{ag@JMiYbd<I
z6>3E`?c{*nsw!>&WQKmGgTx*z!6RuQgC$Bl!1B|f!bXtt-)}L_pCjw%Su|csE(V_u
z*O~9O{oyghMI#GYm-9)}CYF~h2@JdO*$STLC~2+bNWmGxrxEkf_9^F+O_hsF!qq?7
zf09~|3j~-2YiG5|9d-jNzIOOu>gfr~PU)C>JhtjmZ<2CMMyV#*&j3l_ULP5joja=N
zwaufF(stt$g|T8jvS8?Kd>Px(NDw6;)UlEJmvWt!lgc<d6Od>yFgnNo8qbaK)1I!z
zF~GdC%uUq1@to-Wrym~?7twT=+o_1My$iWB#l8?;(cBrKG+Vi0h{O;1jxXx@Th0!r
zm%2#c3`ntJS&JXliCIf(<njS8k?h4gqF`ZY&qW^dynZ9=;(^k9|0|t-+)KibOu%+O
zUB04D*LZt7w)lWTL{#Edp)WjP8Qi<6FvAUAxOJb(uK$&#E9{KHGvoN<gM8ac71}QB
z@n2XP9T?m*1;@o~=336}=dqZ+vEH7-ZnDu!cfg<Us0-wv2r33g?sk5MiFMHHQKOL_
zDL5*?pK!1$3G(oA_ffHqxjpxyv8E1g&VT!#Qa+e5caT1jjv$}i$K4JN@q@AVJ+RZH
zc|mXI9gJ4&XOtypEU8313SfbT)^XG2f2Lb)_lT7^6^&g2@{^XF+qZfy`UeRlTo1vr
z^ksB9&Of#2r8u(zo8c%iDMKSliP|k~<$g0t4VRQmq@w=nnGEgrX~i)n{nfbhk1Z9|
z%Ro=yLC{*TF>RL4l~;A;;v{YB;ifN_iRMOF*swvB55anJ-#9TRoGPy`Homo~!FaBD
z(j`4Mr$;eFViw9`=T7^{_=jE4-?5*Ryq_G5FTgxk#N=|2rGGnpn+IQGL-*jdVeglJ
z_;S5#=|G8kdZG77thHTEl}ON?M<4}Xk+9CZR!lk<A?V|dQ=LD?d;)hp5R|=1e&X`G
zPSmZ`$LvIEK!vUud0u_LYsx`iLwPj1J8zc%zn-imv>F2PgSqkX`k;Nb_Goka8HxM{
ziBZy;6R#zq$9)<|HQ|FiE)cM*R|fdYhGVhJolQ2o&Wi%_=99SvS`6NuJMl^{r6O>W
zoKEtrKZfQZ34ZY@?o}Q|0KOYvUt#M_YV|s&1ao#_jgGeE`uWv}r$vcO4lVT?8GvK&
z7w6Yn!`h^SUD0~i%_XLuJM@--CPM9W_rTkAx)!~aMAP+uZ&htT)^1#5^JYf_zz`eX
zmof}+pFhe~37sAC-dp+=25XPznr)o>WZASIy$Q3#MB1CAt!32EIIK<tSJ9b^<>z+e
z1JDKrZ~<%J$AR%Bfl)!jg_`V)=CnI#?95F8L0$;O)Am;v59!wr?0Sz>f1^|G_wnIa
zQQohYmF|E-rgm-q{J+K5EY7b*yQLv7Ay?aE6j>zy%l>%qC<}44j%RLAEce&0{?h5W
zPu>-617~5w%W2634)nHZNlzBuP0G4}GH=mcY2Hoes|RfBFIYO=Y(HM-H5&(mgC-Bu
zNJ>^g^Q@{_9IRhq#bNaQLZMpZU|$uT%8(zGB$yo}iLZ7g@IkDaa!D&ka>&X2eH;C5
z#(XWBa{oBJlTL0An=2*OD)%I~<}dXW!`k*09V{mOQ-lZtD$0beAO9It9_@bQ_rxpk
z$i9Vq$=qH>o0KH7Fh=$2Y-3uf41d>9^UZ37yLL-g`RWI&!j^>ayq0|^(lSmtyWfLp
zLhRb+jcVYhHtr`f`?F?RC%g^J^{wij(}!-G3ojRWm#>=cq{lFcKYCx(_D!BSY>W~V
z1My$X>8^yIU+*h20Lix)gJk9redr)}D?|oGcvEnK4na^iUv>GIKjxft$XLK$uixZ`
zt%VXQ`f|y(MmFHDjy@{1XNnnOnl+@^D=?L-aoqulkuL3RInNr8z9bJ)I0=}&?~;7#
z#+^!OFYC19SqcTlm07mn<fcVG5DzKwn?a36V8cOwwa055*M%E01%ld%EAOBBP>0h)
zatwNU-Y6S0{=n+%&aSpGvToGgWEqPo?rw-i;?_}*#3;m6^TXtNVyrM=Z8Q*gV0r!Y
zjd0E~yo8ss<Q{nX{E4~NtD54bcx0y$uO%BcTDde_nzJt`(|w7#AX0;X?SOeqb!_(#
zi&94|JwZglP4`N!6{Te_k4BQ;Pz~T!#C+wlLDlt_-*@-eUC9U2RGpq!*+?d1cx=A2
z*`|n>;d>&CR3k|6ZK-Oc3E0ejPyg@XoLBT8*<LI<`^sfMyZi5ZE#~Q#s(Lo7P^yU+
z_E)vPe;W7(Xf528k$wsD)HzgL($QmWl>2qb#KLK6?=(j~sQsQLzA1>C_ou{DP9M<i
z;t1u%j3GOEJKJ`-@ekC~5jbu*k1v<fbD!~BXay4)8U<EZe5pt?=u}2=l1zNo;qWXo
zq0Z+U;neA<chE->9=jXZdI|!Du(~M5-9xyBG=8rPEMp3u59X{FP56vJi&p8Ur_s}u
zT#d(|MYGbrrfsvF1%VMVJj;?DUT8xj#xfb&)IMdrx8vqYyg^EZLc&CWDzXWWpR<(4
zKJKBH=Eb1RUuGioDL(BAr@a=bY}<lncY)D4LFDqG-WIm2V?}Gl;z`M;23z}S()fV4
z^TBW?x?n~um&RKlE?ng7eall?Mvj{}Ho>D<@G?wqPJdSs1Yd%_d*%SJkHXG-Wy&CP
zQ4iL{C&|Mi?vYrP)viN-gfM?1=Mg}SX^MKBeM8zMJeafd(S{)9Yx?ygv!Gw^9^$9_
zbnw@pHWQWO>QU1!7E~<+dA6e5<)yn=>Eu5=E-gRsq-eEWqlE|UTGbV2m6`peq#-Xe
zY-yjrZb7!J9qim%WkVB&pxc9z%8o}Z@E<-Pjn|LbQs@)}x1}F?+E~*|w+z9J_+~*7
zlN3)yV<%DYyUO*GGeiF{F*#3*rT;ezP~NLAjj&d0<Z%%88YBdrV(OB}-Q{&4<2I{g
z@H1mxem<G|Cf<>}LnPgSCcFM3Kq1|s?!Ir?Rl)*>Rk_f-$u>e&xE0d%s4ilDm@91|
zB-;ruu#ou`=?8D;(^XR2<#u%?7jD+8H#rKiUZ}bUcpQ<B$q}8M^wElHm>Uc>ULbu=
zME$(tiD(!OVpzdH)^eybniIb>L84=E6M?GWas?6L+fSRv`9UzP%|t{(R1U`S-FG(j
z3{+A3G4T*iEtf!Z(VWoO(lOse_sKypGNW?l#s^6$ceU}DysqGMmg~3JM_ot&oXpd=
z8>;@S8Afc>58}HQh5YWxiPN|G#I4b6-Z!oL*#e05N-hw7g)BjOnz{ROIpBPu>_bu6
z9+OoYFSmlBawQd=5TVY{_>B&xq<8?~lV%<BNcti8zWS>;td*lV+zsF99+*?;aw=B1
z`{80WMVs2I>A>3ZL{QS#1A7SjWb)6CD$hA@iWBfijW^5^i5FB@1Q&314e_=L^tSrZ
zH?&1MB!LB{7?!WS@#kL#O92|5Yz0?se7G{IF}y6vC#wATEcnunUmShsR^F*79b8yE
zvY;2I&fL|S-+I+M8;<){-j<@tm~o>&_9}O%uc%oIOO#q>?+rpYe7r(GUm$a+r??qS
z&W69RYiS;bzMIX_42Htq3Xod>2@I~_pB{6;<*JC#C4PtWMhIg2>#3bSiZ+<(Q20^7
zbH-vBxscu8CX=icrC{T=-ps^2=PHSV^TkW&i*L@GbcE49!xfG<2rEY5_&w<A0-PW{
zH};Q}UH;UpiV0-t|AyV*Z@`bhp*VFL&B<xMz@t_5)qM3vpZUP7QbY9YUD7Yg2CJ^Z
z3r)Y=C{KZgwU^h|FhVQq0VNIw;Qb8|XH~^KEY<7f$$mcfObgI$fw<W0Wm}AMGgS1L
z%=qMZznb)8T=M3_i`13jd<A1Ga-Ns%@8fKF#+fiJy!K8*Z_<VZ#!E1fYsfxmZP)ON
zH~lhC>T@7Dz2EF*qPs$)bmz~65$}EL(k#4Xc+v4@53LFbjM60R#D|v2Chkgn`!TM1
z#*^e3)-3k?7ZN|&P2}e751nQnXb!0NUJOoN_PMVK{9RUN2eT=55lmE8NK09+l$3jV
z(<SWfSWk_~PK{$C)t5bJ{?=iu;5?nBfmdhXUt#k%JDr2Nly=V+Rvir0ZjAA}o=QCK
z6ySNR)|SHd5tm!&BK(VUzw)$Dgvl~lJFcSsz%?<p9Em=!2%nL<QO{e(bMFZO)^hv}
z+c;$uc$C`S2O1QxD4oJp?IwnIeo=`?oaoqxv0$6r_<=(h5#6w{B6_{Nw&yEjo2N^I
zy*JZWSU2jVF`+`~ST4L%j&N?dFUB7geVviLIHQ57r5ht|GC1VH%bT54U^2FezJ9~r
zG;nA<!N-%gUreigscr>M$sw$#7ZPmt*o%8njTqi9TWD^Hj4*D$K*S)gYtD*3KPx1C
zmV5sEe-ZT|OdvrW+zaB%_97o|!JKGCLu*dQz%8t(Ft3?xJL^zTxAdTE2vAL`x?@gv
za1<Y-`hN05VIey=ZtZsW&qL>e6S&<sO+}=2e^b`rW^+vB<{g4HJ+`C@U$193^eZky
zZL>lQiIOh*yO}<EEMq9wi9BW6S^xcK_^w31WOFYll|CR2h0f&^t(PcnA&!S4_*Rne
z#D+;+Y<sBAj(ejv^o2Wxv4Hjf%37EvPZPCw3weFPi+%S1Jhz3#3rqT-FBNCH_1X4r
zI3ca-W1pkOLRc!oiOuL^(xOZlH!R|91MTRrZW>;lSQe#@BzR19<v<tXPrChb)b$U2
zPEi|kcJt8IH2uLC^Y;oc>{BWT*{Ct}SOj8-%2na@{+6N}jNFCcT@z!iiHJfgIrI*7
z#s;O}y{eX1jnpE$DCrIu6QzIwYxQuIySt(5!mmNAK3bLgL-GO7`{gUAF2VdDGcn9R
z?RBsCRs14^qIrM)HPhPD3ygnVCM#rp=>SIrKyBrS!PfMf)#WHfCZ-#Q5Q3NZ>pUY(
z|Lqj>NvSD{pruDz(UiMG@apB$$);VuH;e12VDoJrU0uqd@ON7V9o~(bSFC1=6ZvV3
z2JaWup(HQ5w;yzu%6eTkkNN0<wp&9msy|Ic*WT$WUPP+$lf1zg)A6+L28t+k{u*7S
zo#|2+3`rK%@Gm(tT=FG4NKz@fJ;De>{h0bQPL4}1I7)nkJM(Xktebr}113;nE8CAb
zwn_1GnEg7x4NQ^w)0D3Z{TGL7$aW-__b)`CAEwJIUNvTm?4k!-$c*@Fd>E#by!;*3
zYddrCZD;DTz#UMe9*TmX(Ey$Jh%zegO4DQ@;+2S`J=CPDfBLGVHrZSbH)nm;OYBR9
zPws|3f^FYk8}bb|hhGwr*!Yxh{q<1Qq+mik3m|FSl~PmGdms`Xf5DD^dnn{}tk8g;
zRcLyK<v7Ri@l_O}P2b*&mK4IDdgkRR;8xoEXu^f0Z3g>-roAAJ7QyzsUVWqq$C^qG
z9p>N@?-!6Ao7GI8p}3|P{;b07u>f5FQF}$;TKPOC{`6Cu*GcDrzVy<vPxpP#TN;+I
zjxIDCXOCaV-dMMGE_wxsOr~nW3aMm#i9$ZBz#fSOGx+IW?k);tO?M!j@F)wclv+WX
z7fL@v^4xRT8?=6@<CUaY&fN1;Mppo~rd;QI<sf5lLxg3!%hme;^`lTIP=5cEC0=gf
zMaR30zovX}aN}D0BPSe!=|BC#*BmjHwp){4vJdscyi?dD5y@A|gfzcs4LMP^(6G%W
z+Dca0#$L0{uCjcYs3JQ<WxVTKo9NDa)fm|yd!0KZ$xj27Lbp4Ah?%;E3<j+eZ*$J;
z1M2@rP^;;}GXR7F1eYm&pe_vGg|I7D1aR=>qpVq-2Z9n6+fo$N2Tvjq`mkE|1#!CX
zs|irsZsD#N0X>3@VS{-UqSHqKM7{&MPO&6!#dGDpJ;qTADm!jHW?wsO9Mdp~o}sW2
zaoM>06&6KWJkU;aB&4<XsxpMOZ-3JJRI;Ck-E^+0J7l>WjakFR^-^?F8NmCR&JOV7
zRY4=V`McvARn{L99Jj#WvN&Wro?1|NwVWZvK+#bro*QzZ?%goK1Z&+b0oU}^JP$vh
z+#0=_(D|twajZu}x`G)S@!0vc25!m%sI#t07Md;wQQVdgc+nrQgV&^ni1Rn!Q87D|
zx^?I*+}8@hk&6kx$qOHTun@asSGDZg0zKADgZHFHY(w4tQceRy0i9GJkywBT7QIfj
zDeFjQF}d+SU&zhvJQNuD!&hH`k=ElBIk`$SASwI8DO`PhSrFl}9M-1u(04YhQ@)`;
z_mHs*E{K^!5?iMn{u^01>rxD27kXBQU$|#|O_sAGn|C&W+jxY4u1>4S^7biWEayy&
z$C@l4VSm(v*pJwQCq%@*TnvB8mnve*4`$r+9fGm@UP)&<+j<7$NHKZV1SQu?^~(rZ
zJK{=P8kq^M!h}wTv76w#=M?_<-fbe8$JuYH)eu!@X<{gzdl5g`AOAYu{)+dEE1v%n
zg)KrLsA-s@FAQF9Wu-7$-@oU5E-_y6!q5mG6)H%IUP=?eGJU~zXSX!IXodYz%`a^a
zZO1flGnfH$1s{-l6~8!^Lau%)I%m>ZW|r9d1faNO+l(8K<9+>`K|{qPG^yZAZ=?yc
zk&MOkIyFQb_N-xZkK8B0-JI{{{t(xntqdkv=RB$s9q%Q}F@f||w@$4H`BsE2$}uT`
zJI6-E4L@lZw`5PfdguBla&etAU+S2zlK2`Mzjd^p7gTP>!;CkCCPpBF>W%wR#JrJ&
z?Dp8PdJW&mPfzT5s3^r6;?FO@HOmXLXr*roaPN5%<^+A=-6YPwVE={Hb~d8=$66$6
zvhC3zJAai=C|108eF0AF#N~}=?UIbB2D(zdtGk*_A&ki~J1tE|l)0`n{Lks_rPH>N
z+hG^O5?eukDCTgiBAuw8u5pV8PM)P4mjF{J{|xiopl*Cs(BxHjlLX7y_{&y1G^V0F
zep&7xbQR%{$IQ6_PP5-6YTC(NP9gn${JK8aYD{-NLl$C!-MuN<OyX@9yD96PAAf|k
zhtr(U&#LEK>!jhRJ=^`~RMGzDoHxtGya|o=H|UUE*Ow<%`)pm+iZ42!5z37f0%FK}
zhpMTl_hN!Vc7|ZHHHB@_li>{(QGm8*Hl1XV9g{IVR+1ghNZ;gF$PSF(jt%5zBA(w-
zP0>vL>r{3!YKAsYbl>3Hb$y@REfxZ$60<w^ZdA+U5vl`epngxgkV|}V)yoe~nm+nr
zRYR{2JZY}?u6s^A5iU;e16nLK6&dX^cDUYnb=HSDY|y#0@`hDC)v({jwz#EkiEwH#
zSGHGR3DP8??X&-)mx}834pzvLQS<LVA&so7SvpVGrs+zT#*BbUUj9S}Pw<6&9a)Kj
zErkX@JRPx1t~H4WKll;WHo1A_6{Gpp6pEFPQ*YTTTIr%2lz$X}?_ISjbu-g_99>%C
zPk&n9t?N(2Zufw6s@!dLH$7C)O@r)*{nO{Z`MIN1pRYmYO0^hd8)4$$_bMRn7`e)+
z_BjGw-z{eta9U4}*yVeZuh=#xfvt52R5@2&#aDjI*l511S$Jsnw7{i%g~jnghYTa1
zvMilHXwmVO72xg7<4wZft2amb>DvjZB)`B_HW-qT<H<Cz`qb(zxSB~zcIuyUz5rHk
zBQ<V;`4GE)OT#o$9DnsJq+NN=Ei@6`ov}m}Gb=IP4#?-l#2|)98tt(VVyNc;{oTH0
z#gev;(rRqt2bh6s*6~Sep|dDy=OqddeojKMMkBta;9QuvZD(k<-L7fZV9Tvjz+dLf
zfVu2O#SKknZ_8*(s2Nmag{Z%gCOZv1AL6pJhyVWsSrg}}oqyQ8Z3?;=`lD6Wd?jLs
zW<P<dWnW3k4LMBmk`N-21aCqsS=S(u-z9>0D6rCbP_FrKmk%EOBew$il01}C{@}nT
z+TRmHpz?afOE<?}nJk3dFDz_;06!kMV>hW6Zf`DpJ&ir>@GMD$cnPtLp;^8@nb$cH
z3~!(I9y(s{{Cp?U)m<M!oKh!OQd_mWEZ4&I$=J$rAr|WSpq+lQzv7s&@gsC~TQHv?
zD_98nxIC|Ly{%2!b&m3HWRS^iL)L50cNgYjn4;>Fy=(j$Lv^GLIOwx)DB5weGjmA!
zaM@f|dwp)2P$52Aj2iElq;@*t{G9xR=etQdo~vh3mn?S<DT1z8M6Ze9Q%bSNqY#-W
zLOTsTxOf4WVyg_LVAd;Dop5DQ@ZmI7H^hO;T`#-Pi|T8MVUDk`jB&jZcK2UxeBYH)
zXPv&LMN+$uGx1W~8S4meiWc9gv6=}q#<FVoJeARF(H5%f?4aowK*R3V4s6QQe;kSI
z$9K(_{)jjbxsqXFYqz`-0APsZ%-*E8CEIUtmu_~}z4O^O*&VbE8Gh%e*(^3?6kP&%
z@?8!zC#fal`Fu~L4&!H$#}n9YzS5hE`Sgw0)K3k$`WY8$H|=2Ps+u(BF82wDfl!_)
z3C#p8g_*aZO7+gLv^Hw~3OCiCMXV33WB-W6c|TuAbdfZCK>FnL4k5b#q7sv<LcYha
z`<&W_V3=x;lGr|DU<YT!8Y?2sZw`Lhb(n4@?cT2?^i&`Q&7SEI@SAV4V>U|<7!Voo
z>(XAua!s8LK9n^TR*pT*5&bkwFCFd#bs#z(y4hNfq*`ZDv!@LQr293vk>Y&bb6iH$
zkwsq|Xdsf-S(aI_;KdX8lU?q?g5vOC+nCN?UK@=X+xKSdne=q&*!u^dT51-PnB#+9
zy3vR}`8%POE7Q|}ISD3}`Fcji$pT>laZqNoXuYJbh%};6H5Uv+WRnl6pI`Ujw3j;|
zd)*Ho5*HuNq=*X5ew%^mZkBRDbKsBlTAM5tXT%|C2bq`uHR;l&jOsn*h{YYrsol_>
zc&rS0JaPFhL5q&U4~ZWQdShB#Vdco6cjavlqq_aFp?~iM>=oZ&kUcDaY2cf>+=}d}
z+Ddxm<r}Y3hbKIzg^C}dar2%)Ju#;%PzIWPQ?IdK9->I^W4m}!-r~{DYQ0)+1%tAC
zuM6J$9?kK=;W1PPW&2MT3uKmp!VT*_3SjTFv5Q20F+_Ec7h1={Pw8_Ua&U4wGY86g
z&U`m2|CzncB&gb(jAz0pJVXI}?Zwi*qeYIWP#83p!#ZpE{@T<n3{FZiX6wVVi>A3-
zo*-X}Q%KX0@I@SB)}W%X$pnB!s1ACA1zLS&(uO0dI{r!HaCz)G(Sls2Sd^$?mTQth
zo}91EOJj@A7_S8OQIwX!*LeBz;;SJ`y!%YDmZE+&tPd+uQ*YkQPDKH0bP{3aTuM$?
zi8)d@6nig;DjykfqgS^xy1W{HeK|yB;L{F5tQ|3BZt%xn6Jh)%K{_nHcQAv2?8S0j
z!vqT6kV_F6fl#$ShTMfNY2QoHp^B<Mni{{Qu6Uk)Yy8q@bkvjhl?(LfN29<|<9t9k
zWTwe2%hc@Mk%PE*Z?Bely%T_~R`1JILO+dTZ|aPGH0O}p*0ou<X{`7=v`PAY`80y_
z`f(?qXzAM<m7NNmzrDv734siVntF?K{KwlLso?@<y0`_81~{6~BAFw5&2bb1W*FeS
zf<C+PZn&hXIcvZodLDrH?7{iW?S&`?2zJL*6T2M8m&<s8m*MMFnX!rrL;Pp)w6v5%
z*AC}(X?pdR?=V--icaKVofhFnXY)T@>Eq`=6@Gacctj*a#mE+u@c^8$nl<4xlyALk
zSE1WB)jghiU{0^&cgrU}q66P;mHud{6(v*T{WA+LRZDGK3Y3a`oq9Y@%$R~0Adr>Z
z8#liE70w5Yat^$>N{W$1m}`&}+M*mA!o57wV<(7Y@SqoaTv6?Qq(U|dZdDyff_~kY
zll>L#eDCW0%vOH;UHLzABuTb8psuMn3C~aeMsU2fD$W-y(8d~p2Yr0rE&{hkp_H=f
z(%s3@%4g1D_e|0?q*F7;_%tnLYP!b;OsAi6)QBj8@e_cK<B0DV$5TRTWmBb(_8upw
z*XXfs`21dno;I%~75Huy-JXMDf%OWC=vWJnH-27EGqj5_eOS$m&ZxJ0QL|t{hsxtn
zzr66ZUqQXw_I=dOUn*O%Uf7F<U#+Ggww0d=Toc@H<v_9J%o%bh)fhqnY~6^LA0CaI
zQL528Tl$8cX-VYb|KB`U!2ZtkF)altj1H{Is<1@4%PP4!RD=EbeMcvKbMFj$H(+TI
zv4ZS_VC|2Wo=aVy>{o^jT4ik9<5sW2yEP~km|8f{S&OWVDa(W{?0KwFmsr1jHJxIh
zlg#2+yx7;L;=%&+Wgn}gDypRdFTk|UwtXYuJr&`l6tjairGj_zi18v`XG2R<!#fwm
zwe05p<=qpgmEA143F598r?K4*xzPvwKb~R8JOBR{JtQ(zoNB$gfY$c%%<Dz_#+)Fp
zwY7LSPiH%lC7V*ybyEDE&?Z5S*$0<h(@ouBT~g)X^~)u%U!v;U`+MrYDX5ryZ)ulC
zdn&fBP~M0@gD(%fBu$z0MhEL7gE3zbGbXdTe>RD)l0{rZ;BYo?<;h_~cwjY{U9KES
zm1phTwMpseY<~QfxG1y}<?*`B=vvbsiqxfr@6~)U+RZ=uf6x<)c9T|)h=f;KuEn(&
zzd=eoUlGt_G8}YMFLLb+iXn@6`(^9j#?oAu=ZtpM*)X!c`B9$Q*CXy#eW-LqOI8o{
z+thZkm^6zEFLH_x8;FEjW1dZN^pR*f5wXBuxQuQF`pdb<9h&ycoMtavnr64%kL?6L
zweY8kn~dlmS~shM<RSIj$vD;s`E&;(RuuD50it<Wql9qkqJQ7J{{wR^1_CYAZX8#8
zr*`)t!qLr%IjFxR_vF1&#OPf08v5xGy_r+={flb#6OF}WW1fK@@z%1K@yMO*x};Q>
z7To1iAaAO&25Y%J3_vmD<^$`G=n@1ab+Y$9Iu(koNVu<T)HLJ<O8>!>esWl{eWWrT
zTfnStPjlMeHX*JG*sSTi6v2KJJ!Q;o^GSIQHHrU++tJjgo-xM=?gt?)x@W5`@X=5{
ze#16tgo%ID$tdem(>H(2oAD}J)wlCCP3!gPp|1F;I8G?edvx;wkQee5dnS6NfP(h7
zg{)_EVjyX8%GBoi2+gF#i|Q$2#t(}zq#tV-Qx2xH>1LO{?h<6KI#TR^DV)(_!b$Qe
zMGUf?`c=0d!@99*p2GW}sPHC{--^$89QOZqjSjT99<64PxskNfxw)m5=pt-j2PaVR
zZoQs!&~e8!{*GQq_*KL?J-p~3xZQfX5i7r(U0f`DNh3#Lo(;h&OSV-Z0ECEVYW?Pw
z>)6*pwlxi2iB5_W%XiZ&p^1&PgJcdDb9Q9)FF9-`VgDXp7I*G{%sw{KH<WmNQ1pAF
zocq)iLe#zO(p-&nNYT*MN_qPvOM{pcLsYEco*K{ad!$vMdAi(c+LfXb-+!u|EPJ@%
z*8I+aVCSb#V6WAVf+`lHp-<=;Ygjvyf`N}@5fEW&Pk+xftGvNO2OnXEH<{fXs?(Jn
z>EAIL0yS~=KVu}muKb40!=^Pe>Qepj#Cz0otbfP2HKShpsf6uw=o{!;|GMhbZTp+U
zZl>l%PUJ^T$g%p<%(IuFMPa)?lW0`dTmG6BLarZg)pq+3Pd+el%^thAz03pNVs}XT
zpp0AL*|CMRo0Ef0CP3qb)0Q2@kl>OG?IZa(-_r*0DAFHo=#J+r8E!8MyP}rVQtw5b
zZWIHCrO!WU11{x7L$XNxJO!G82ZUz@q8V#Y_TAKnl@d#zfltAtt52&Vo#rSxnAyl;
zO^Wsp)kvtf){u<t=IUhVLr!;B^-TKn0^jgF8u%l2Z`%EhAOw%^9Yy{CVt(n@?A*|y
ztH=b$hS>pGnLxQ0w16eV=pf!Hs>JF6W)X|~%Hz677&^(D*<(-#JYEb%mP12{lY1fg
zTg>cuvr(ne+iCy0F=eN&1MhDm?00ilYevR{A$&2jl&7r$Yk<;RiTd6BYEincXwwf~
zeq*j#Mw@CjOQh)cKW(Em?Xg@wnoQWi>(vvVdL?ti6hHS%ynd5zNz04pOsGm5PpjZ#
zEjlE%j6dz_fFqsx9b;(MF5_>2>#J(PrhVA8P5M%oXW)t3S}Zl5ZCh6U?4nM~1Inor
z$@lH2_ouPVppRIOWDvK}hv!6hjZAX-f4#t8<Z5yS-p}3E<_8(Ba{E87n^a#{PAm+5
zG1u}v#qGVA6bV1=m>#MMv)2zkOj@ICzVw(vUid_;|G5?`rf(MY=Do(IJsB<N6_ctj
z$uZt#+%fdWI~(ri^g&Kix_Z?MzV8PfAOry^Hdf1G7(;VnGo(F!>v&{!ejdFfrN!gi
z>tpLKn6cpqxWH@v6&zfZCymQH^Euc#n3J$AhA{t;TiXhAUA}O0<N3Q!vGJ=+gXRRJ
z*cbK`joZM!t}|t;k5|%W@N)+tuy=%t=4K;Q<r<IbmNE`a43Dzq_=zPK>yiDG6oNSl
zbgu?A>DN6zK}TT!DK0(|=+Ax7NDQB(L>oB+@s-z$m58RRxU_bio6Ti2n8B_GhXZE?
zV479xcTV1G2`x6a-^;nx)_9&LfS-f^OvD{YxhTyX&EC|p5l#yF#B84aaKmBJthZ3O
z@&i%Nu2l)s^R9k1QHNI57AwF8uKsAVo~>=c`|53?cH~MEG*Jvn-|Fo_eqy(1Q=|;y
zSh-1A1fI}z(uj7RL57Y7_8oOYUv3O}9d?RIYnR}-OWkdz@VCIJA@rwMr}vJuN3$N$
z&-It`|DZ~qIh)-u!k}}$<FWJdU%P|giB5NouQ1DKpMPOTt9}+1!!2rV{xI_SC=Z{g
zjKH)~K5TWI;(&6jb-1aG+K#KPm2ycBpAM~7D@qR#Ir10j@AieB*!%wYAuig3Sv8Mn
z(S?>dn6>0FRimY`imaI|&&lnMCb9qp+G70E+xaaqi|SgbVOc2Mhq%Sl&P$>KcEl5t
z2>L><bH@U-P|Vz%#+icx`u7kpNxBXw>xDg6j(DH{X9D20A6(VewL|Pt-*094s^6OK
z>^Lb<6;RJ{D0UrJ6?sW1Qu6CE!o4cUd0|c1Jv+!bqUh!X<EDM!+;u=#-0-IMQl18U
z`xx^O>CPYH;MA3U2od~fRzb4g>eg|bBr)j+q1q#&TP>fjG&~T}I3md~f#{IfkW;G4
z>*(sD(ww5OS5**t4Sc!pI{OJS7zk?<x|Z$E*h3u2lx$Z86xZc&aQrZ88ekc#SWQ|7
zJi2pL5>T$5c5XxU=nz$N>ac*mxO4G2vTMYKxUBjKBDPk2{?9IGVT4$DV2^sP$QO((
zK)fKZJh%q^ZkI_b+hcISPuAUvx-G*;zYj1rF+qeKQgaM3>=f&4kUPrbdD{hZ){il7
z;ysS^U-;FiY6J1td@YpS=(F7vA0;(a#O>tP1mR6|5b`^n4ZW!p6IME~CYzGP5RJ`}
zjYNZw5d2ruo&XRm$aBKQpbrk6<ePM(5on+ilpeCC**GYH6I}<2t9#vhNBk=Y8mnf1
zaC`(gQiiRq85Eb4zzpQ24dl5T4#pfdlnpEHYCF77rJ(XyqA0v(1O`a^Ew6_Ks<v0B
zJqIiz^M)j`q-2-z5$8>&&ze>jdfsxo{J&WM-*;cLPTaC(aX@#f%x)ercN5~65{N?3
zsEPlsM)Lm(@2pa<Z@&p8g<^t=Ew98Hp7R>>A+hGP-UET3obh~4o=4gPbh}k@FvSEa
z%}m^TAwpU5zRG{jCCjN?I;wn=PdJo2S~c<*<1XFiox={^qEnAuUv1W3#NdTi1VUGH
zWsPJ%0S=7%BF?u}HD@o`8>REL_Fwuvm=|s)xNk9shsEC3$(Xu{O!RT%7XEheiq6m#
z(wqwg)%GVI<iA5K(p2;NNZIqU+*s-xL*ip$2#$jqfoNW5AKHA)6=HJhZ8KtG@VipJ
zy<c$g5F_ui2D`_7=L_~~yOD0efoMMzl+C?ScqzPy5JD?^^(FS+RNfFcK}rmpjazi}
z#<(wb!BRq;XC|U=sfCV4pQR{-(Ojkei;oCLGM@C!DDR`8aO%D4hg$SNd*<&qn;KF=
zSu(tnlSLh-4*QEpA5=4{o2i$XMCC(5Gb~rHahpeDIbNMq>(_v>f*CEuocw!oJUNcR
zeq5evw=uSv>XG{szGM@uuMTXA5%Soa3g3VK`6lAO9FEXYN`~?&AJYh43cKg}Vv+=g
zV=Bds?jE|0v5sszI=i^s0i&q2<x9x@AZzJpno6FH2M?E00!smxWu60#)rE)OQuXq;
z#~>gwE$mMhKB%~lTh{yDGhd>T_d+u~(8JQiA2^kSVoBfc``T=-bws?PmFgDuCqS*n
z{P?u9w)oAcFx2{4$M|0-ApLE!;3dBAWl(?Y?5>O9Jqc5q9LM~&R%3!)x4ow$O9;=b
z=A6$PMF;GQXqaE?ppEs7*9*Qpe(61*8&r$+c7~QH8mQ^%kfGGBuChtfK+~%08I3`I
zwjny*-qX6%3ZR-<Y}%g-RT()J1=MYagwx&qF_xs8$v?$Er}Tdkz3PAUem*mj#X4c1
zI1D)*DyTEFNlbw6NC&<p$=P>K|MyR+E2Y+C|LH)3I%Bx0>|{b&reh8<67kvCGi0wv
z>E7>XF7+5ONLFIDA=^fNJIPR#+Z5<$esUmEKJh!0ph?^_bI*SBa$e&^p8B*pKnY@k
zD72Eg;b^|LkwXIkTu20{@S>Q*=ZHQ)2)WM*Ab&MCjZsSc%vVQgO)U{NTKt+!DC4vP
z_WtjP3x%EgTxP`ycf;f2+xRuW56mVuS{yOsqb>Q}!EdSB$lYHD_u<`r{rLPEUh&5W
zab+Jd&bjY<B$8K^96`OQExjXt!;YkQb3Jp9?K0OkO_+@ifcIUXLpoh@y3lXOU2=x}
zt5L<#DrPOS5NnaoD*cbo`1V^Ds}Is0wx)2{ny3z{MjQM`&5$vw?$YHeU!;n+6uEF%
z1t`kr6IB4%JdaiFshEDM=Ed!(ay^p5{F@^d<8sbyAtuh3)Ydgr{gPj|Te}fyviBL;
zN{)N_e7USA=rNb~AL23hJ#N^rZcZu^yw};dAZF|ccHFtMwXN%rxF`k}BGsLPka-!p
zhXNW)(=WEIz_1x3Jw#l!_JO8;DLe<*Z>pDV{~(xa(PpXaJ~zW<M^4-7C8;{{>ZXRD
z>e|{OEYpc2rMps8Ym=mc-kOn>bsBonp+_q8<Kri^YqVYJi+>o?(?roFBQAUkB_1Zj
zCboIlK?SLbZ#HRW8wu#XJwH+)d_h<6?dRJlvKJ=ooOIJ^Kn@kGLQ9FaQBlG1bVPQ?
z<GjBFsUKX3(?sh7rzlx`=+TCu!ZLr#)9$+bNcYj&U+Jd`=`4Q!k4F+E&EI}n*Khv*
z*C3tl;_<B~`{x^BsO;+po<+^;%1;oHNke?ZJj^Y~<)({94&|EkK?U)V*W~|K?M2kl
z<yqo(z_YMsXs;@vCzgiSd8m40#pO*+w8Og>mzS5^JUkchX19{}32Qf5i(TsapqU#%
zA4hk50*5gvdX{*4SxWq{t;}Q&BYymDcVIFeJMLd4q%Ma*0q&zk86yD+Blb9-?Ey|w
z6<oA%2^MD~%sOC%DNFfca%mE~c5-7viPuR%Nqb4j;a{A&ujze)o@Ql-`<oZY*mGBu
z@LhhM&-Dko@ZB4(w%>dY?E{e>0B>HZl6g9NJKnlWnBP}$0YQnYB^{aY$lY~FqyFyW
zqxTc*mu$~d)CW(ulM$knLl$-GQa26NYUe_OeYr|KC163OPU&wQmeQmItAeuvSzxvf
zFgr<yZ%&7Ujg8Hc7r+}{napeDVP?)iq-z3fA<)Whk6RmJ1UFa0htr&+ugy>VU<9QG
zdO6al3frn9psWRyWg3`X>)j!R4OfybS^GkA)z&4=lcM~#Dx>(7H*1h?JqM=l^4A2Z
zap`%P3{h81jYh+kToTmoYX%595}@k)h!1>;N$sR!>oVu@P9N_Z&CvwEtk;Z|P7abK
zLuy9G=-<C`|FVQNoms3^D>W{1vfXJ3a>P<rxlcRzqdi4&{BD3Wz}JBBe1k{@g}c$W
z`*Nz)PZj{3$lVecWMt`UVRd5=fKc<{)S%khk^2UA0Tevz^5IDFv)3myWaX2Zr@*YH
z;>WS7hUqQY*PAHAbD%{{?(c-bo~)poSW<ob)#z$o8p|h{N8nq(_@6%MyQnoRSnkOF
zx@<`wV5JN!F0MPXG_ZZDtYx`#m^t<M#@+Z!@3lxzV76+hb0T>@#l-5JQ=0cq_~p}8
z^ZfCftDdLK%-2f)05O)eyPVk*)BSRuN&uj6MvD0a*x69lPO}((K~^u~wGImaXv(TC
z3n{XZc8aEi*o~V(mL7O+S24}Q`xw6~oC}Y4whJdVbl%`2WduskBl)i&mgI6Y{*~He
zGe)WX^o+n9KoQ*j#c{ni<g210iT)tfos8wXk{hv<`@bsIn4C#<w~w*g)ifEy1RuY&
zc+CyRM}uOo0du6)t95u%r3INM`V9MTXyi<5n6{~sI7m*4r~WR9!&bgywAEik)3CL@
zu_#L0xtIqkV)(DTIz>UUR%12Yn0)#Q-^$~o^4+e*yr@**&*76hE1R?Gbb9*wl=C24
z|ClGM^TEv4Qv~d@z4Ul>UZiJW02od^z6^?FnqHJ_-BAa&Gfhu{^_|H>S}&tFwFRA6
z3aZ7^RCfohD3Gmr=Z}EGvyYU9U+S2Kp-gu+2_ZWUIbY5Jb*2kZXb=pv4y10XrMr8k
z4;RY5kI6&4p%~}m>)DDkRk`Y%hMjuOFWia@s&{AmPeo&A_6~=^tNiJS8SeAf+uPe?
z;I4wb4?1NJo$+6vwwyThD{OcyXAcB#itI|f7A)>_GPV22Yv|?@9<35C#&a|iyc@|+
zo-WHa#p1Ul>czQ`R)VRY|DM9@s_3^c+ugc3{Dy#YTAg#(OBuRG>f@$)czg`vjjRCu
zJ;T{`GBi|{$8qyZfv!3!o9(aeSPk1V)PoerSLrWk+XgW|Tq%pURhn1+^Mhe(3wEW3
zD~lRBv)FU}WAZ2>Uv*_F1s8Jkt$b-q_-<DNO<7i9LPB4B1Jy(JZ=$%n#c73?z%Avs
zZ@RJsZqCe|eq@BSfBC>WyCK$Ot5H5zce{1cE(SkOY`-ATrCn7_@DuT(Z_FO2`GxPh
z)id@;#)X)3*LG$JvHWf=c;g4x#}IpzaQ%vp2#5yB%B7ffGw`5#B70LSBNDb51{ae3
zLa3qp$0GT6;<pPqiUkG}=R~nvx@7-I^)={{lRv`mKh_Hiom-S%_Gm9PPwnmh17Eu_
zD)6UsH{H!1US+mdCuI3G3zF#_Qtpr5u9wWfy0xZ?h)*`)4=`TD1tmUL;rR;4NLu`6
z2rs+&xz{J2jOq7u{L`BqUhC)O>$VC8=UnXa!vh^lI5Q_!*J9sp3wuSnZ-j_yuc9E|
zSczBI_4-YyvPf}>CFtio1>5s~fywjjc0Gckj(kL@fcnxYs7N({rri>5q}(Em?0c2A
zk!ZcA=`IBLO5)<;ZcP^{NT*D_0?pl1jYELvd0`hoj_Gvc#+ls-GmovjBY|dB1VT+W
zI?-;*<_yQ|dl|CZmA9PIJkf2hRpE-kRi=t+q+!E$fPW!;$cvt12=LR{m|~(<HZ(Mx
zG9~`u;BeR=Z1dI{-<<*^d|ugea>ZH7UBVPm1-V9Gsf>XK`wi^KVEu&kYLu<@Gzn_9
zOW~!;ni9c@iDabz0s%+KdwY9-pI{F&Q?++wC2d5gsHm;>>ylHZ4P)YZ+FuKtY$F}B
z9{1F=7bVxPuY7ClS>5KNTY#=#@wPktI{6uL+(nA;?GCHUvJJ=5xO{mK;8(P}ewIIq
z*mbwH7br*^JUl#!L6`)^-eID8{Pj;yPx%TKrK6*xt+(+6pz9VkWs%G-akn-OK9cR}
z4M|ey$~R|n8kMr&Jon3CA1)>gzAW?`O>NsSYbs6bio+%h$BMe{j0f>Ww4DW!kZfyx
z#C(tuKZyC|j=P<V6~-+PE6`2zVQ1Q#RLt?hzG4cL)J1h-X{{)ocG#ur`~o@ywB~IW
zgIR?dE>~W4<2fHw{*BpR$MrdicaE`{NPchQLBM$TJt0TIk#<<empqp7?&n43LPEvy
zM?9pD(Z^^1UwdB~)#SDQ`vRxXisJbnd!VSuX$??CKmkEOz}hMX6f7WM7?pX(KnOEf
z4|px2B@vLh4qz$skT52os2GMIG6V>dB_SXrfiT1{-siRFtaa~N_xt_Qe3Q8L-tT^%
z=Qq8J1w$V3E0t4?J1(bi@Ipx)Mdr8X&!2<yRB}Dvb#i}NT)g**W!3oglntBsl@b@6
zlV7asxsT5q8wX5McZ3ZCBkB2}rWx7w?v}jYrbG@Y=5&*G9dlfS^4kC|Ch-ABhrD2;
zo6V^w<yqIvEAqC)SZj5O23BAr(jmuHDz8gdokMAau(a5|*LP=o>s(fK1$F%~UZ~~T
zoqV5W&Y_8hzn2Ia^^yk%LIwj)@`!|g;=b=~pKb(A;Jw%=N7mXd!fLLVnq}Y}i)M9y
z9sGbzFk(cJ+yhdYb<`!-Ns|q)q7(DHjxo%wM1j}>OVNGoHrrrGq0M+7Ows&IpM`1<
zJ$~b7ZO`$bS0l}=4K_D<z~Xk|%Jq(Waj|vvv!qc$l*Nf1CRf0`s~T_6Z@yY>pF*{;
z+C7y?FL)X`PBjlop*pHu60u9&cCe&D&6@_KO`V>wuadORw#g%9r5XiM-^7XqT1|H|
z=jZ3yq%C5lW9cAX)Nu$)%G;bR=nf?h?Jn)fH_iCq5$pT!HF%bd!~}QQ0{UP+tIfa>
zE1JV3Rt2ziFp>;Rebeex3C2C}`*@`8PHYyEM5y=eEf@%(#7Vl`wVNJfmJC)D{y-sY
zwM%N1<KCCVi8n_cTOH}1E3qxsuGk?M$28Y0mp^+ael)k*`c;+kcp)blBR<(a-m4}V
zzp^nIvc{r~>`EtN6AT!h!M`gd8NlxfBf(26{Wi}WO1Y)(TLFDVbuYPHS$5i4c9pDD
zZSQgDlWv7IOjdn@)z7(-=c18|-X5-%eLJ3F?}aqex!EIBo=(-H9*ohz?f?t&ikh<1
zV9NU!1TAF;cAv{{{8nobF}O@QiJ%U6Fgnw&x*Zlk!O_<!<u`o&h(w~Il2WSn6Rph5
z%%8O%T~?aW@$tv|##kS#k6Y+GLySBWV+>S@Gc%~-#uZ5}knUkxvp71W)6u!h#<}kW
zh3XPjlof)X%IP3)9eT}o;tJx|Mjm(h-KnVHpXje~(GE>bXs-{y9#zEkR7m)Eb75T)
z|H5@DWPr43P1>tA5}i72Om4~LRFXGs!ylbQsDIakmZiony;8C(9TZK(3jgWaX*##C
zaIERyQ~;n06dct0#n#jd#%ZUCY+Lyze1wA7hxgw1-SU)^rlkzE67)h(NNvM@LBe51
zBE0e&&Oxzo*OI79hsV$eC0fkA9_s7+G2)Bh>Y5r-dV2cfu5ZUg8C;jRUpERml-Fn5
zM^?itcM)%zocMnV0e{)1A|LtNJ5NSR#bVOwUpUXN+~+T8skIq+08L$fNQ)I0Lp9lx
z+mU@mV;Qz3_OMm0>*$YT%plg;6g=^H0?#S&_5IUi!N$M2Z7QW|l0l44<tX(RPU1z;
zd?_{l8^%qa29p9#+RU18%%fX_92b~BFZ=5r5FTf)fumdFv$JsJnZg8d^SP{W3&;nw
z-CCR?l!NsQ4YQV(mW~}e7L=RJ4dHwoAxD=H9gP(O1I?b<YkPkz8dnC<^uT!RjNDkp
zGS<yswtgJ@!O*{JF_Kh)8N}4~WVaweHzux0BgscIEJs=s6A#7AK6-4`czEBweOH~F
zoZ8c!J4)=H)xg!w&CNmgU!=M9j%*B>SzPbncnCJKY0A;7U%c0TyNfc@J)XNdR<1rm
zpL`(|WH;dri)v<dMNg+0irQrMe(Bno^Pr3SCmw$7;NYNZVv<{3T@7UTrK|PV2~MU&
zwx^{E_pTuJ8$I({Ls#;x;1YQxiI0WJ5Bi*oHwvXod<4xxIvlTv$z*nScXK*3G|y$(
z{-)>4^tyKK>;C@!BU$w<=T1E(rg!whOyEAkq#;VrKctv%`&oJuEr65hE6^SWckkW1
zckp!7aUp#p#K+e+Rht(N7oe`Lj$dDy+g!YD-rd%ACMG6E(6~3W$QDa;v!S_#UM=U_
zR<iWq+yLzGEP3XMbilM3lf&}SPixI-;X8?M-9Ie6nWgXbo|VXvgX<90Ajjs+#F|%!
zw>uQ?%e6&*jc)$HvWWEkZ3V8p`^U4^1t?z~$?D2}`0$NnnHRqKaVe0^<MHfD>~&2|
z^IyGs<<b&$BJKR)3`;eW$b}2OzP`pLCV&`~Jz=!{oQkqCFK=(PEFE`i3a$rSW{P~B
z@a3yiB|QU!OxuzN=b!u-VHA9VxMn|tKYDoY9^TE)3y~*f^&~U>CA-CnuKN*$eK$!7
z84iP0!#Qu#<F=Ozd*}L}u@knSI*>#a_4#rBc$J!+o7?>U#$doI?l`-zFCCT+pyUKl
zVk}rDgb((`#l;nAS6>!N+%8_c$m!13W2=w3^2c5+XHV#nvmMPcNmrW@<jXT?Eibsb
zy0Xqr)cW>P`Awdlo<`v_-71BE<AU`ZSU>)2(c)rQQ&W?{%iS~V?3|p=JNq=K-VM2!
zUQ@A)Th#mH$6W~Gae(cnc^yG=Edkc<9Wu>%|NcGIwf4!AC&8?y>}6grkHa7<A3WI2
z;du3N#|FB)FV4)&P%kyG`}>#aES=WPnlL55dO333QAV$t(JxPZ^O;f}`~C+I`T)+x
z#^#=iNhVa8(CR=Wic<pahb{f_D(}>dZ$JiR=jDxE)<WQsCs^btlaFsK%t)rOYfoLY
zd8;h<UOOApD-qbXwI8iT7T9fF#x@2RK$9_tX~so?vAWDQSAzyPPr=cs!=EE<IG3h~
zBf^$t>lq%8#orI2=zwwE0-xXW_U&csyi@5hG`9<Tp!-dTg0V08hjGDT!MIV_)ERBp
zrU$5I>XLFOVa=D=ANAMYAG~pQW7T~#6c@AcLa$ZqTwl7CjhVbq)1>j1N6xbp)oPuV
zOS*Kva~Be{Yin!ED00DReSIA~q>{FaQ+>7bwHr51)YjIHRC`)LL~U16M>I-?N!z`5
zZ)jJTVGsSS|91W7my;^pl?K!qs_IwcO`i8*TH|l?kSYeM883Nyc>Js5o{CjyXlPf*
zAyw7h7cb6sb-3=eva-s~&%b10VZr`sqM)Dv`m~Plyg7|C;#=4=L5oe*mhqril58|2
zx2~`gzGhTn=9+GWBf}ijd==~J>pys6alg2^xmj(RKp=R-V7B*8(9%(d#bg${X#4v3
z%#7~tcQ~M;atZbZd~DF34vl~+<K5zxUhNr_Q68oWLbV^RWn<hgi5fAj%>g@X>>(_k
zs{myuqxvP63CRH3Nh&6hWBsQbLn(#%`8^q$jv=v|=Ly`-jDzM0r(q7ELgGy^esF5a
z<8?<z_}an<V481GP?_3v#WR58g|Wt3HBUlB1SidKqUz!Ps`PG*(F0Bz<_UJ4w7YCH
z@oR=yuy_zLFp|<is*a?krE%Y+9~SEeQYtG$?c|zS&R4H8mZm#^5K#bt+iKqbthw35
z&dx5ou&@`<nB?=n;$Yj0Ha7JQ9}YD4Q}<0zPb(`cGf<?itBdHBUymdZ&{d;3=@tV2
zgGq`TmZZdVjs|(b`duMMXXrg_|3B#V{%QB`^A_K?6UT3@xqaW3_B*cJCo<9iR5*%9
zD=QJu2YM$@W-u6xyJ>0OVPT6hdhwbWmOef{ke;9fbbfkE{-q(v7ADgNkH@=iY+Kvd
zJnQrG!sB&e8ij1L6DQK|+_@9TDufkbvaR!tGs1aHHLRkdqOOrqG>avipYO8Sd}&js
z)h*j#MZvU^Ip1T4V&-3r=gG9mvL=eMq!3&Xtan>Mr4tAs7sp>uei0ht;W35#SHqP-
z@O!7DMbr-daP?snTYQj7CSV5IHUX4%dh#5QC`>B}18PD=MWr!f&K4aumt`0+0RKu?
z4J>?Zdo-gW*hcTJKqzdTD-;5Tp>vR#mBotV>u>B)HH$kHA0JPQICSPapPXK+`8WmS
z!0=EWRT>G>gq|>pTAa%9<tQj9`22~-ZsJjcTWE*&_D=Rqb|lLy0gK|xC;5;*>772E
z2Y28NSFK@F(7mv*K$)Nc<p$!O2KoEX$#mo!6F$Vh56P*0pyS#U(SM`DrIAFZ(@k=U
zOu;qTB#6i_Ts;o&4_xb02}rnCi5Vet#N;>w#$YJhjLaFw6q%fYNw-Gf_KW67ey4LN
zjle!rX@9f`SH6qrJO#vQ6u%w;gM<=Z1d%woC|rd{Hi{N`!4Gv|6M;bBe9uT%S40mc
z>gvT(0Iw^epHs%0iD<)!2l|ygRQ|8vV&K2Q1?k?OyQj(`9$isWH|6kCZ8tZURCku-
z);ruz8XM;TVb{^9<?yUWZr!?tQVaJ+YHI3L7nh5TF3guNe+ZzAZft9zCxM%iSJJL4
zqmngjd}3nOW%QC9V`s8`MSrB~RQRWyIP=~A5nsG|@hQF#PNCz4N=q&7``fBau(6>{
zt$=Lht3gWn`T2%>1}lja!^LbpU)@uu9=bM1dItp^`xB&k{`lj%RbXy@K5gj0#~2;j
zimhABoZ5Tss;dJz<^K#(9B?4J>{zWt{ulGKc&P0OtfZ~o<U{j0CtRa^0~|QES~i=i
zq%-qzX_`2ma;+T5NB6{u8+-yh-%S}gQMX=i**rlC@u2zlAxIGRzWH_(8fvW+=@bE;
zL9_cZ^B5u#zON|w2vEPgyqIbYBBZyo)3Pg|2~N)R^76vS%gaa4m)AqRYEx>Fkh0Jj
z?qe$?=?Ap%-mz;7*b@6r7U+NHH4m=f5>PXoM|_$Iuncz#Sdl>dJ1c+!o@evp{hg@S
zuU`-GjS=LnHBKKvoJYwvX4%gQVt$|1r9Or3V{4a1YBV)BI~xq80fn`!e}LaaMiA<k
zD3WmFKenqf!+T8~Bb1%30faxS#&o@&|L`GT#K}<9safd<tlgH0rnJ;#CAX;OKjF0M
zU<UGx3BMP478nzb0>EjhEdLHv>eX9dI<ISR=78x#jvY2Zn{g9kN{rf$B6(tsStVx3
zu79Dcq-D9qVBfH$x%g;T#nMvNd?TJ~+0~Jsoz3Xdao+vK@IWVa`&)*)`beRdE+bUU
zDBp{<zvDNIq!uH@%(?Pnr2Gz}CogY-<3(>Sb);&0+U4fub#HENHl>-HnN8GG%gV_u
z&*X*{yR1=_h6lh9HyX)^vvS@GQnB=h9K)eguPfCg?~GYroRMnjhckixe-OX1<_#o$
zF01CqD)3y($@T#7l|4{0+`IerrKOrEjDfzu*&aCa{6D_;Voi)%-xF-YhAhu4i}Q@M
zxo*t*{EQSze^k4p88wMJ+oxCFeh+KT?N(4I#+6shpM(oOZ($+yzYBZH$SHV5MKyR6
zq=JrTU<$28a;4O*vn0qg*PUw$Fz)d82N`Fj2+~!|PfOZsXNAK|E{sx!hLS-G&%C^|
zFSv0C_yZ^>p2cfjd1uwQv%TSr+t(%=mKdH+>BUF_NdGam)}jlf!96`YS4fi=MdQ*R
zKKtZV+Ngt|3+pFh<_ms$$$tz`<Iud#oLU7Qd*`Pw_%Mc=cN_Dqh^|2CVZ<j#@5bZ>
z-JGX7jJDsmlt^)*gY)e@ZDM!D%bG~=H)wq+f68QUJicbu)}Rh3$fY6dQ8}w6*WvHb
zD<jQBVbg$2l~kM>qxFJ_jE&Tovk@s78bx9ltyZFaSb^Yx9%AqrT4FvSGI9n`YosyU
zx34JZE6`IQ<di|63=G&a3ryK-`vv+_e4(&6H<X?Y-hfd0g@;Uunj{~iYKeccb93u@
zt&NaJiYt+PY|Yt#(kBLl(~vT<W#4Boy?=wjH^Or+nC(b<mHy$Q_~^-#!@w1D0)aJ1
zp8aX(VY0z`*ETdflt?6~1#+0|?Ci|BPcz;J?`wQr;YK`AQZXDBhmto(2y94oLUZC{
zTl-Sh5kDDtgfn)i&OK;EB2Gj<<MTfsEw8QB12W6{Jv;_M6!Nh@d}rSnwRHWHH8e7e
z0KIbZ;OgPZ)@`&&Sd>Fa(rIcEKa!3{cIZUfMign%Ml^zv@0kX=@FN}Wach}u4#_KR
z{nmVPfhFIj`0F_tr0pn;MngrStgP%%*vbqAT;QWej~;h56lG*&oTNAp(_)FJVWbZH
z?eZ@;lKUk*U9xORsx)XHFLWb}X^;+Hc<i{R%>XTDgEb_RsHz4ad2DsnvB<V$_8%dE
zTD5qsU*v*hc;uFME%No|*wAH3t5r?YH3=J=Qpu){j$qVkiBeQWxP!JmXmUDS?de?e
zED(SVY6r0Tvo@DHRI`}>YAGrB=}=Hd*pq^0f7#~L;EFGjegajBgk1OY`_|(Ap-XUs
z5V)WW0~Bm{4jcvOrg~E!&~9230H^a9^qk3keSHUw@EEA+xh#>?`1rW;fdgG&BTy-1
zW|q)Jl?Mv>kK7u?@n{X>3uE9uA|fNH<%bYt*zf2$B?PJJ<Bv7!-QKIpRH82?+m{*!
z1`fNKnwpjj2B3y#gDM2I0-we>37%PKzC-83m#U`{o<Oi=1qLKDGbGMXg!B0*U3T02
z&{hWu>o0e^AxRYQAKj0>zx}SS`h=po5PB9gs##ThbhJ@;c(_sGc3etIiY{n2^h^W-
zO=ofZ7_=aG+mI&r9Tcxk(7W8<1O9pH`K=>asqykB&CKY<2Eel}4T@{b-ro8mszadu
ze%PsHE&={G!p;YeIHdr9p&8n;^ja%+yrMo$H?=_p4O^0&QT;sj==PzQZ_$Rk_O&n#
zrx)aH=zN+f9oS}ISio^2vA4d7JI(-Pb0NuKV@B;&|D5s$c^G3Rq=usj<A7s8nbfVO
zbKqql1nPeC=8fE1HcdXrGXs;D$;rpi42_EOIQL1L-lQ$8I(gH9)Q^p%G`b-}>FD{i
zO}9Tz11^L*R~iAYgNPUkR4nQ9!}OdJRA@|nMy+<Y5*4uz+S!P@da~)Q1G|at7e%iy
zt$oGDQlG}G&2+fd*9I8Bi0WEdFZS6-p%#})3DedWcSYR{{?Ldq&)~4&?T8;~(rtBp
z9vi??S-y=e!14C~NhWQkF{n0qA+J-%#W~9K@*%feG&9B0f8ksvB_CMWNyfC2p3bZD
z;8l+?L$xeCAF2DXXjU4k@)NHhRvU8J#8t;cN(JjG4u@kc8Ro$5f7;;+t>cEEXe%mm
zxk`xhP^+aV7fa9eT9JjMF~ps=pSOi|yMTAs8{2XrO$K}RAZ2<eZluO7c&b`KHV`YM
z)oV{@b#a3!Z8(R|T8eCsfZ_!0)dk-8Q0zkWV=EcI`gSlyBE9-kGiR5pM=yrI7JBJz
z@~w2kZcQV@Pk}oStrbYt(EKuYa?=M)9@q|)*~|pzsZDCHN-OC(6B82;x|;4vv6&Z0
ziCLU#3~{uSr`cmcioi(Fcb*&u;kSKB(hydIsuxbsN*qchOd`F%=0q1455W-5V8W-`
z7)4{9I>jXEt?SFn8$5^L`9QP86O2|Hk$c6pJRE7#f9=C~HfP0nQ2xvTbj)#O_D8)Z
z>G3dNl8x4#jm*17Mn>5qBO{r2DcM2w=eS77ACu~m+IcDjwUhcAa|zQ5uXFs(LMw{}
zi1S0}9}g7>by~L9=g}p$#jS}pp5V@c!TL(OC6&@yab=MNV8Y4|&o;6#7UYBef}Kx*
zYGZ3H`Y)gcZ|fmd*80a~5GM^Zvuas7AITpjIP$VAi@>n?CM3|glwd_z&_r|xBbP&q
z48$g!WJqRuHL>*3-NeME*|So9Dxh7Fp&x-ffKJO>HU!N?eR*O;ggylq%w~?!EZgM6
z?0m@&D%fkEl02WP4NJWRzO^kYQ_3Sy_ZB=${*|K{2aO}XMO}q)0;(rLgMbMc3e!hi
z>@L+rjZ<;8D!0OvJW|m&t##i)u%w`BmItAa^C8C)d;A|S?@$LRec-MDdXS_&{B^d`
z(9Taqwoh>7#V(mzG6=gDvg>80iI6ka7;ZRbe*Ab<d91)qNG{y;0z>t)w#@Jph!hCc
z0Dsu#)6!@9o|eI@nSt@~eDL!=;3iWxhzrAgYdHqL-&Rd<YLG{edNd;QtA!>yXcBo0
zQVP{!#}X$QLu|_J+smVYmH%{=1;&k%1|*bT5sP_12XlNrm<ihwCnqheqobq3q0<i`
zwLstRCGD{RC4Bi8NOI8C0L!r?G%?k>%GpG-8Zdx;-hlkYsG$7zEesmUP(T0>^*o-%
z?-Fk=_wsJa9s0IuHvqdn+W((H#?XVdIj984LkDi{HG2q?TQRE(p_Cn(9|a+B=cpZ|
z?uovgl7ebCP|Kf=bLku$r|LU2x@@~C!`9}2^Xq<oORj%#@JhrHAdNY6Dhz%>k#u8?
zui12$8pEfszy!HOD8tuBuKcVGwGhXGS`7z^-;@;YL__Rc3(pHC&KI&5R)OQrX?=aK
zA5S7kgB*HIduB_X6?B4?03QI?XGwZ$TN3xLJld78*wsdt$o8)gq)Y>)1ld)1TwmZ3
zAx-So_4-&=SD=Egqp;MzCHQYhQra660xY&Lt-2Ehu6Q|L7{`leTNS;dEUpH875k)W
zZ9N`{F?s7MoNy>`;~zah@jsS3j917ZRp(b@OgrwY+BiD0D8Euc0~gt{Cp)ErF2K*h
z-K3pw*Ex?+RZyxya&wZDlK2-PrGift7M*SQ7##WZCDNv@2DO6E@YAE`TvoVQ?$i%@
z@K3EiKmDJzrI1~AKXk4yNmqOUWgQZ8A45z1_4(@t{<?v`Zs4yQ`2TPN9+$SwzdSoB
UEuA0Kjc$)UXZ=IPS&yIoH&we#1ONa4

literal 0
HcmV?d00001

diff --git a/docs/articles/sids_files/figure-html/unnamed-chunk-32-1.png b/docs/articles/sids_files/figure-html/unnamed-chunk-32-1.png
new file mode 100644
index 0000000000000000000000000000000000000000..b3f8812a5c35e378f6ea414282fe7767608d7fc8
GIT binary patch
literal 133313
zcmb??by$?`+vbo1NEwu*Fo+-}NS8<sA>Gmf(k0!XAX0*Ki*$F#Af>c)&q#N7%|7$K
z`rB{6Kla#TcjrKc86KXw?<>ypysqmuRQZ(*0p3GA5C}v7m6cQlfw0^`APi$1Y~USz
z^ic!g3EM<oMiO`i9v2c#e!vs1gRG7-2t*x%`iB;^a$p7m(Se|n;_B|H+w&fY55^nL
z5A4ra@vm~}=&T&V>W{)!t-^7w#=;z#I$wXI5AB{~m6m8;pkz!YCwRO_s;ICS^Y*nV
z#Bs9dwbWhQz>oK^f}YZKh<0p?%(sa(ny*tdS~PlD#Ru=Ld0ZAG>kbO&tBvxUoEDt<
zL!dGLPhSO}B^w*RtGyCfSuHJ9i^)zew1>BH+*}O#`O;<h3<)3gmuYHfP~Y_}f<Rdm
zxGe^+4czL)W3o#pR?rsiGDt%PflEqDHDj`A*1koFW;Hi^?-uJ+5%yUi50-k`xNN4%
z{U}8|-<?N%ffT^5f%}?|7i#GHMm>e9x;@?9#B-Z61`qNth5vgGi}paQIXAcuHOtca
zw<z<uddIId(3tF(C&!~oRaWDLyLQ14s6PA5Ji+Hb+g|AbmHqjV<OxReA8V**;_u7-
z`?G2Q7wqXDD`EBiFBhwl&6FEsY)zIiMa#Z(Q>$gJ&<;P@npD%!7@t>+&Sqa(GwgZS
z<uYxJoDjBWgvNX~^VjNCp^rAYxjbRjZ;b5<BdhYhI4rhTekFGEE>h%F+sevHuqAEw
z3!{9z!*)fF)2Je!i<=sRq+Xj<T3?^q#l_`0FRyuvp@f9Qk?(<fv)XK8Varfkf`Mmf
z2(9lF!UWq^KcPd=)!?dbV!~r~e684zAqHZpr#uJj7*ER7lmT$TGGE&T0VSW^oYl>O
z*WLh;-?>D01mz^#&KHQwoW1W6<?VTo7&@o%cTC^Q(Tv(ACHiQ@`}?m@s|L+^Zk14Z
zu76Eim^ke;dFHzxL<`za8uAX-cbl(iN>S$&cAfuL6xGyb0gb6HDF>Iue%Rc!YP~%v
za~|NCEO%UzjubwW^*#PZdoY@D8@uPT=SAfJLu)=76iW5Gy|~`gYO5ss2(iUTcVEP{
zvbLU`-%WE{uq50)g>-dwdG9)Bn2zPEY*&xInx9V%T&&olF{V9p7al}yqPMTFDO(h9
z_pS+%K>_uFd#b(9mL98KZ8!!YzyDTQTY3NnxOQqa)p^kP;&A1)Lp#=-AM$3qekl@o
zOJIJ&9ID!*kjNRpl<ppgGO1~#K<<Dotvdn@^osvCCXL_q0lSs4t6lR!_paT`_QNTc
zD9)&>tG%|NI~>ihv(~c~_5!6CNI}z7kd{@?sFK)#81h2N6^Kx~hL!k|z$V4+aEj4u
z?Y#j$c>hd|brp+PwCr+R*)y7`wOCp%;CmVw*JPt$lVXK-zrje1;CLugIu4B5ZSL2q
zYfVj!@a6h9D&O<pKxEM9B)~^Sk&6fJ3oDQB;hI!v=T$RjSStzB?8TnGDSQgwGPPK?
z+I{OaGh3IJR;RdTkXxAn7<hPdbKPTH$BzjJZqzE_Y;|+!uxiWE_4y{Zl-Wq~XMt);
zB5^V_9`D-#r=fgeS@)EM#pGbIYtD7nwm*e03NSZ~*LM5z&o2VI^-CWm=`GKS^79et
zUc0}6g<1Q~l@}L>cMuAN-&Ycj9`d_AVmpoKSpxE$8<m>PClh+a%Xp%|OM%<-rBLa*
z+sL)=cR1eE&ATpTg|TO4Wd&}G<{fQU4c&|CNqT0A4J-ySnx|y3F_QDzb0cTFVJ)3v
z*7KJX*{>ok4&R$CL%zv4r4*dNCvJ0&U?P!Y;<&gt$!{u=f}2m+8`tUO<mG3tTVz#B
zr6V48{SKiWOcij}Zt>*l2q98xnh)b>#eq#*WDGQW9L=y+35g=voA+Px+As72mU*e8
zqZ3xkYS5f0L+cYeU1d>aH!lcsoi-x_AO|0nw4XkG8j0ugJbs(|Dy>&&uek%|+PMa2
zG{ByGOc~x>WUn32fW)z`(%<N%=COK^@Y)I2zWD%qQr}Jg=-ER7Cx}|E!td-auX^3X
z7Z3P{#E`;%7k!3_Vt%5aAZ!AY@9%L@!HG{T_&o1)xVxh7L^suHy3*|Ww64wUbbGpU
z$uXFKvim*m{X{M^JfF+spA9}2G*vdGCyI@i%>(b|)MmM@Cs=7b*B_CxYQGSsVR{(h
zwEi{ZFavp!5l$@>4*-_)R!JR~^Qr;}*u>1@ol7|K_H1CsuBg>}sA%v~C>jFo?F5yL
z0iVOW|C1@>1?RamZ!&r_k=V6EH)v0SNTid1Zw@AUwcXJfdVd;##47WF#mYYRCE()a
z%dIl_X0YW_cSP#D5vaPBmNN_ui~<*v3i2>A4)cj(oq>jc6ks1HFyXWqq(bc{$s!#J
zz|KZqhWSjjWq&eH7!VWo8bga+VIIhvvm{{;uDnzyJPi$v?V3pgV$5<hLV;ys)Gl|M
z_C#|PQ{qoW27$kl3L|wqowlgM*<BsY?d_Foy&Nx7H82<?6xxR2GNrx%z!)%Ms{3Ln
z3J!E`>>$i~0E$-)3Wf<dukN2OMRA+;##YbHJN8h=#>F}Aw}bh>UZWeOLu~+htEs3|
zXq5FuiQOjJdoNKA2*?5f?lw`X-v=a77qGBCAQXTQmYz8@@Y>-yowXNZZ`$TMoiZhQ
z{3=yeQIP;;soSf)wSv6##e*K&JgqW=9jcZ1mD?p+q*2?=sVT5~RKP1FKM!@;ns^4d
zvb1rNCEfcFYS(fyQGz}Mz#M=+pS27;K2%n6p-2Rq;9(~a&GlysUJc0GtA?%8CUPNH
zn~9yD@3x&<Nb@|e4|<YBeFU4fEAQl`x#}K0YXUBDUrn-b2LhvUJJHO!Brj!fR$+~`
z-M@}Z|J_~Z)qXT1xX+o{RJk#VxEh?-oEALR(DqkT>{V4%#F4i*1;xd0VE$-qffWU4
z=L#n-%gvj`ZTA5%RsfjPR=dH85!4Y((ASu-Zr8Mf4Qq7S$}cNZYJw~B&39rD3Bv%l
zEi@N5HYTGC*?fK2*PklzW%QL$NtY<F503Hi@z)+Jaj6d9aoHxuCni+Y)J9FF?ftIw
zR{N7Wv|0~IP@KX8_r5`Z#f&z`3Q!?~LNNe^eTq&?v?~Jl{E$~D>U!<iMRL3|Ti10t
z<g@Dx00jVM&)8dzN2>QKnDx5=Pt5%0)d!M1HX(r<h||*g#ZRj@sQgAnI^fhMjhmRU
zyMWytm%3GSb$jRC-~#{{*5R3y=+=A!A|QcTEmv7xeQb4UM`Y*7K0)90_k^Ck8K6cU
zklA0jIRMK;MO^dwVp#F(hL~su8M_*LTU$2ZLJGG94<>+7{EiO$INJUtFx~2pJv3gd
zJ1048CnqNgDZCL)d#x!xr_*^J9#T?R7HKY|Wi6)<QLu3i@aK$48>L-+04g8=33YUo
zfo$&LvHbo0Ln?4@g(R*I04&9{2Z7hdawkyXkPL)E9o$z4Oyh2JR5@mP3Ix5q%Z|NL
zYfm_9>B%wd$Q7Wi{v_@YV84zX1bo%&CqQ_uu4Y65RF0x^_SSO~1MdSVAnhiukvg@4
zo(3)x@K6X;Rd5v%H#0oubq0|AyNRo8(S<tTCe^dvYeI0#yK`9Uqj^Ma=Up6h<on-T
zL>ow+YJ#fkp|U01C#zXNEC}t^2aSxV`kr^t*5b$ku3~Syc9MmPMZaPtHN8CEu(Ut-
zJlX6@XuCE8nDB@ptU$B$^-n+v{U~kP?Op%%O=v8a$9iHPu;u*->5GFXzd4gOS;+Tn
z=ohC}%P-kB4@gKHyD2P`b##8lFv{2JBJ0|22>ib&i8c&4d2X)3zlPAv(AUd5uvy{p
zvl+GuFSP<_J-z9v{`z&lTk8=u$iVkvrFrJKWzVNfD)XKZkO2xAqSXF|$jeE#(kK!V
zk~y!v7GUANr&SrYCm)vD!L<D!$P8pzNtXtN_WFwy3!EBA>s)Uy)&PhaQS4#W(3`wW
zcU{m_SKo(W5D`a6*WvA=A8$=^m^Oa&-o#t_n^qI3v;tBngw9a6R@I)Jiy+sr^R7&`
zek+j6s+yY88X6?l6UCMlyHy!Cte7HVx@Fco8OUoU%oYnhcryk*jd0@a%@u%P?SR`x
z;(uM5m)7Jiya1AIPjf5XbCVg=dJtj%u3izvR-hg#XNB$_awWly?C_n~>`4BVST#^R
zfG&Eh_BJ-l0Lycmc841S+RQdy<!y$aVvB20VIh|tx9|0Nbzcg)8?E29qk)S>qv&qS
z*+Oh=tTK?msb{2!ojQ0hf;^{h67Tt0wGV(yM^<WuuS>g1YTWvh1A7{JPZD#iwshg6
zgR=nOVxUy<YHAt3mT{U^+KC%IG-fQB`C&Hi^Z6I*nwsV<N>+q*3Vgg0!T3Mxk>X(L
zP5^*)s>}%h?6EfR{f^7T>2+#jK9JnihP-M67U%w0DZPKH!nE#Te@;Q(G^KrW`^ltX
zMs0d7;s~&dF23+cwhPhH#OaJRM=(Ccci?sa(q;Q0ZwK~}fZ{<zgc)9&gv=fTj(tv>
zP&-2pO*01a*m(IzwD8H8+BG1h?QXyC0XNOd&CTs1(@8oW8)}oJZwC}bCrU7UB6*sh
zpP!kV8$4;~*D~*;c2u3a`Ie}c+I8yD&LI%2sE`5jO}olm@hH<xvF8*KL^P<qnkgPc
z$6pKJA~hc2suSDbX-m#(!H`Vpe?o{|uNI%{IGs>WdriaQCQUX5Qe*C~WhF5>Fq~rF
znsg#s(4vivPyX38rS|ZGcSlWMf8NAHMdj|Kffw5yGWO+eO8YkeIirBoxFgtcBPXGj
zyv7SKBnYL}2lym69*~h)c-vI9q;^EhzW@1!2?zmv1NYxpt=B6Y5)K%eKx`$n9_Ntq
z30>3{WM!e#*%CKG8)f7fnORYyr?9Bh1R!53uk8xZoX^=j@$#jOlG63HUb&IDbGo|!
zGt+KPlTMt=)16s!_TP^g85upsXVc$_NToc-8dE)*Gj|Tp`t<~mJYNB*Xl!gG#Bz5A
zk}2Mn9r=32v%k_-O-aZ;rFZ8o&C2WlB6~|HP?&U_XeA{jHPPY=#JdOxkcM#wv{%8w
z!QoeYBKJ~C&+H-hi~+#D1~B8zN^jhp^N@(}IU?w__d!>x@8!nznIDobJ3BU!*H+gV
z!K1ZvB8koq$XS$Lb(?q5auxx=5eH;=H8ZJelVYEe9O<F2uitH3i7PFu+8QZ(`4&av
zyUj<hP>jvO!r~6tH<8o$r6#kt=gb<s(yWgkd4042sK~af`8|FB447G1tPGHoZMShn
zWvz_^T$K&d%il`2Ow|mo#<on`d~Y(--rWn844j$K#bN%Dyi>zJ@0<2$(lp*S#dF4E
zHkRdU3EV~dyI`5%mK!@NZ-&57TXIe#5RkZNC>5l$a|A#Rh|_W;JAAe}uC9#PZT^+e
z&X~CfgG}Udj6D1AUox~gKz%QKz28x+TZ5;H{Xw4ZiE<(;G3p(c+yP;x0|;wCKP7Qn
zjI{ar0fMKEbar(%7pUPV0%;_Zo)ZK!LDRkh=|cse6{<8-61{kjyn!RJ5aHZ|Kdg}H
zrx$L3Hb!$;iPPe;o2w^n*LPBoe^3j^REyVV0F8<l^(>^Q;#a$b10r2Pn8tqBks`OY
zv`e26*lGy?ox4C00s>UZ^EDsm@%gnlfQCu|u-r)$bYTH$>APrjqy0>71`=BMY|a@#
zB8M5vJhM5wg=P=S1mK~jqXTtxbnH&`EQtWBq0swGFMA0_0f<05zk(wdgq2@gpwuUb
zqj?`4(65h4!yG4cENtTp+2OoASf4TgUJk#&HFW>|fv_0^Y6S-z<^n<q)7$+JF-`{r
zY!#&Kg>v!XO5Y<!qlp=y-QmQ}&05xaX*IJ#>wEqP5VgRvINz-gudV>3Oa}sN^rkyN
z(a>Xs1Sef^qnIXc<G<{e_ohYUp!2@Y8OZL^r*6DYAT8a=0BBg4^#PhaQi4$6eFu?P
zYI5?!LD4H4QNVR2wNS{t=F80@@3SWOhfFPXy{Mf9ptc)m*hxmo@PjZzkOLr^?Mdj^
zI5?D2IQVFy_~37z=fsi=zI$SLIg*fHQnJD%b^)ECOp&DjWnPwHL+$kA5da6=Koybh
zu}a}z9pwbL{ns}cZu5Tfi88~XAR^KFaZ&jM_7$Mm+S$MQoLx)hz26=iAAi^*b{l<o
z=ma2f>d6ZzpqR=E+!n7dj_P#J04cH->n3W$H~;Rw^<=4S1uJ0gi<JZnhuwy?TK-*B
zg*1{4RoBn}z#_b)^vl*n$x@!!4Krvh!_PNlHleSkzGxZ1f^mR90G;Io)E;lH^)d9Y
zvQk<*6NTLDUb(oOc;p05P?Cclm{pWOplRJy&8kB5(KtX9Qlk{vkjNPoAd?>gAMks>
zgUABl_+o>WWHJNyuNSLUfIc4x+Rx^G^Me?uDL5Z1B*IW?6fhqx%hRVGhyXBv8bsvW
z=J;zs5@=rCTu!!`10^V`7}^G?@OWc1M59Ra01zG#Ir0fk%h58m<d3d;pO(Gp`a~jp
zwO!SpCX@guk|aQqerRkIjOQ>M1i+|=tnK_C!S!`XO;z<fP<WxVzD}#RfN4)8N~c@a
z4df{TxNKe45)b|I_@Kz}<`dA=D7ZKu%n-{!wK%GVL{r3WHk7D6X=BFXv$E(>eYDk~
zWZe6Ym#h7hF0WJg9qE-sP9A6(`ta<vAw@GT`Yp8Ed_@2u4cDo)p-{_vwW8H_sqxAz
zc;$}aIlAHPVS>O;_2?APRnY;iJA?a)6={~3^d~+8bf;O7530f|cliC1#(Q5Js77Hx
zeb^81n0EEsyFgzGLK=3^L3>*+;POId*^_M-?}Dnz<|O-w6cJ2mX9T!e7(hXk4h0s-
zX#@jlmgsh&EaBF6r5_1M#nqiC09WnWZcrT>X<nNt7*JUa0c!U<P)07;iLRCkm#I5s
z!QA|jXsXVIEqLBEKT7)QA<##hu%~8Uv$Nj=H72+Hf-un4AY2{FfM0)n+76@5OZQ}f
zU$64bwp65W8lwY#e*~C#1t@*&XfnUm*CzrH;q?0hSuS<z4k}(t>K0};gWsa0V49#y
zQEFRGPR<-qKB88SqB#_muuaecT`vzJ*u)I5w!xb-xDucUf!_?&>$lp@*w)RvAODiM
zm>%-&1{6n%*J3yTMF5zl-JH%2fy%O9x%D#V?E`@x3e--VYcdO7BWrM!+zF@P2FjJE
z|I~hfltbe`9+vO`VrqS|%&-p2Jx?*E8$jy%jog%EFTY#^+OV*?+sT^h>R7Mch7eR)
zf%*_YL6&;Vqk4lm2?o7@5ozVFfJ(vbgLkA(t>=h`yhAF0Q^r66s(A~vAslCI>v+m2
zd2PruF30k8ZQ1|@;dnBx<=jQ0^?Z^nLRtV2LRFr7`Yr|qh&e(9!c|It0vIRVL}>f`
zEev9W?tsaOqYZ8*XvP#q>nEBSUT%WramAiJ_&gKWO0-{vKg)~l!UiTqN21s6zJ!lR
zBFd@Y3^217it)43{&4gr>^-4WN=hh;vVJ<J6+l8ta~^AH`uZgg3V~MD>OhL++qaoO
zORCl9YE|PEeRO7JWsEj!HxPK0p6@GLThj{*S%B6{i`Utpr%@Ept_1py%<SyB0MqFa
z6pm6KTB`Z@hyYC`YQbGqr3#~Vbf8#mZ2(I5-nGXcQElqOnlhgqIM75T^IaM%@ch1J
zxXF`m*yg))`gU7EhS~)vGe}U?9+2#L7lN}>Q$Jt<7*(&HeU^nJmkp&|q#w4BhA<bK
z#)qXlEbu}_{JhR~=gqB(-GyHP1s<mO;_E0ytu(F8dLVQX02%DIDzX~@+iJh|!)U`t
z&+K|3W@K8<jvkAN20sn_x+6g7{`^T9n?1%=_VqR0ejNU+uMkcoFU37f$Epg#bKLzV
zUi6tZH1;2r&FVq^wP2CyMeocFy>x7tm;!W`$7^5C<D>L9d~(jrjulDz=+r)DHnxGS
z?kuGYQ4zb?HSZa9UESnKqh~Q=Uyk1owRx9{>odZ)Y#{eg#GW>itA1e+CZwi~OsURc
zO083L67c)>>j?nWo67q7js^vE*It|@SfyCW()Yr1Fx}8z;RIF+p%n=!!^wgcYC$XF
zMkhR(EI7ft7^$Sk+cz#nK1^65&TUxzIPuhXt__7mBKGh-vF>9Q_W3`9xg(5>-YQRa
z!J=WGo}2Y!*3#5NTFNk2CeX)qcB`z3=OTnkKSLM+&4=pp7x;u=k6Ne&Hf^NdSM_Nl
z%H2b|0td{iI|s(z_2D{xP)exE_gp7Y>S3rDmN?=aHkugTAyE|CE$(*G<BvD*_N|oE
zL{0rO%##+g_!-x4)DWLoPouMK)8VfFObEtWsRK8dY;DvY9vAN9x5H@KucJmW-PAPJ
zJ~!1e@M7Bvu$(uD?JIy6@s<Kq+OO>^=hm2Dc>zuSYlp>JF|`7x|1OicN)=HhZm;1#
z1hU8}HpFSh4JY)B<HZsl0xu{{+cEE3#k-u!Cm}O~c8F$+Gnw`{0x$x{h?LAK46PLl
z7<?yLx}+Y1!59^`IM~rb!cl^ZmML%iwSb=Q{AT{QNT9TCl)(q-J`pxoO%QnYgE?hJ
z{sci6C;kPA=1Np6e=@2mhU5(a*;~P!Uw@AL%G7{cFGzm9({_lnA9*LR12p-j!iQpC
zlGE?y@VADRfHjC^lkuP118u*p-Nz58qLRkUNI^YVM{O9QSj}@RXIo7#sP`EWpXv6Y
zoUrM`*qspq*?1`9K4CfEzB3}4>TJ*E1SSG&Xg6}mX|J?VB+5n37A819uEPqN7yudI
z#wR(c#-L-n19KDzRL)*X&d9}#7@<#v`B+bnq#0;O`pI*Hbl3+8J+BFI(7WImx8#^#
zyaLw(K^(A;RI1Q$v`E}lBvaT<6j5YX6D-H0RwJg?(s${f`>76b6P;Ue8a_NWDZx>F
zxIHsqi*e3x=G#McdIjb50Vl!-YlHklf-aT<f~jVoKxaR&@3l91U!X+G-1xX$%-9m3
zK`LhLnq2b3txFq%0jvq0cnpof8wcwD$$7<fd?IY-M|Pmc*Z~XjL6gofDe<VqUFA3~
z!}t|ZA?y}MTx=`(>Iz%T^E<=fbJ6`W!fMp=^l1<g|7K!QQ5>Y82M})f51&8Ty8#nC
zl*|zIX)cwEc`#>f_e~RIh!%|1{!2dKE9@7HQruvsU<XrPNMbMcBANB<!kBX&M|gU$
zRxR-CoNIqe_}?uM?W2GU)ocU65&{(&M2#^b_!g$VasdMi($@VC9Pj_#gmDNpiinz;
zDAEe3&NYaKMX>9srzq<A*LOS}$?DeBn2)Thrdkb$t;rBQFNz~<Wib43u<e9$C<7;B
z)Rk+e%lQAX^9*)ZfQ7$^|8#q0SRhTS{>I1Hi#Qz{KLg^RkKmv#GgVAsntr8TE_YVw
zYz<)Ie+O@Z#f1D|ZJKLuSvjNXDiRFEpsoHvlYJmbEZVQjbXWFlcZiLUMz;&Ro_q1w
zqxX!Qdk=kestsdmng7HKivn#<KhfTI&$hdmnz-n-J4ratBk+X2rP(qtANf?;L@^A?
z&6NHD31+H-7R4rdMiVRh@o{}+T9^Tht^FFTbNnze7c+piH!H0S<Lb??$TE-^fvV_s
zO4n&j^}wGYp(;O%+Nv9dW=)0dvwbO}`}<LvTl6}FtfxD%7ajt&JX$IUd_*aok{uQQ
z!?!jTZKnQr+pkG<#?&yH)4E*m1X-HK&&rSR_K8pYGnB;Z>80Dpb>JB;im<iEOea9E
zVye@1!`|mZs2i!v31S8!HrF%BcE;N);po;QW6_>Nw9u;7n)x7gqK=@<?OgyKnZ$=?
z#lW@&1WqfrMQMlhu#@&{ZzCwF?Pti!51M}mo*%y5t*1Ko7#6BScNhI}R}bsjtGCur
zAxVrCXFXSt*`3D{2fgS<&(;mR-=f*~7z?A^huLhp&0i+Sf9o252Pr|icOZ^HH<BQo
z^~ENq>^F=7Y?3Vu446<e)a?D&_c6IC15^?2h$C@--tqp}3k%&6FPeG^?S#r=2xC1Z
zI32r{7~h@Lx(0a`fLr2udkVf~&`vL5F>)l9yd^RMBZ_pe-OzHuqZ+U~0%K31y#XTs
zB7qhBu8v&-$QQRC<cc@)yco<|JG1MA2%xjy^D3DrAq=dBgM0l0US!a%h?@}uV`QCL
zTgJC~yc?8<j_OQtclNcJYV~69KB1vXCSXK6iBtU6)Q8HQA<W4tC;<YsOv(~R{Q~&H
zi~VyEFv?c`6IcMHy!aC~z(&!50q_6Q#l0%!Du2%c{D1ls4b<otwSj^>`RC0^>xGT<
zj8{^Ph3rt(-&NrMi`n-F3pxj^a-4G<ck**@H$E0{P=Fz5&BaXuQZW3NX3N8I0vpB9
z3jNmtO#R7%GVR$fK}_#dg}4PU&q3!Lh-3CrJ%H~1W+$s3+9gH?8X<TPEf{o$B@V}M
zda}ij*nMSVU5MlGh?B^@Hf%E%;MqS8!0Ry(S3c83)Woht!0Li7HUwh%1eQ;0R-#}8
zFb&vbW4QrzCim}R9H{OqAU~VWKSnSk+%vU=R<<$cuu~r_ANlaF)W{UsUZIm=90ic?
zKXVW%w~n;UxI5-1Ks@AV2vx=YyFe;1*60~maR#-5OtsozJ>8Fo;CnATdW#;JHT@QE
zg>U(f!-fKn@yI}X7(J`Qr;`CP&Qk_4u^$$9?fyMt(K|C`q#I{^Bh&safew`N^M3ml
zYo;h;i$viQPB1wYW;|I=@s%%exzEEX3hn5%t7wSJ=RXn7LZv9;Y)Ua<kCPiDk-z0&
zq%iE|rc&e*2kSJtjUnEQfvo)eb1dNl!^q&JBqtm0*HVU{4MXl?d%Vk6cwYfmr~f(6
zpw2&mHL7rSbQ5T4hT}p_t{~Q5E=tHsgl+Sb;HxN9mF7R!E#T++a23;1C`_7ZXN2WC
zdMyIFhE`#AONSM@3Hgs<>@i1wQ%ukjD~R=$i;~%cM~x{aWc)>f=<M}zPM|S|M*n6+
z_V<I=oFeQ4jV6e9Mr_LI5=l}N@k4~UGUnQ1f>UP&RKPYq^#9$4>9cao`iJYYR`U%n
z{1C~p?GrOcqMUS!I+*RtN`Z&LwYp?zb_A<sKbL%DV_us4{fKBB&kcb4Ti}?HU^@(7
zFe`@L&#%p5;L#-5-F9pB@?x|^;^iwJ@HxAKyE4)Sfr&VS&AoEZh{<Lpv8agnC(Abl
z7O)A?cZtx86?f5E(@aI@4AD&k$}oB``&u!JaaPIDP5p)ZQ`AoNuu{>4$-kpK<^MM<
zhv<zm=olp^%F#ZqsJz1Gf4Yt<49dr}(z89H;iP$jg^kVwTP3U&BhB{s3^@4jpJ|!x
zZ{`acDGJSwp_Wk)mh>-h{%<hn&lTCO5MH*;-N&*qvGISx<^L9u3LFTqebG`U=Lvqk
zd~i;`FJ$y+AA8@+NSJtIw;QVZ^)JC03;s!A;l6c@RAQ&5k&6fAn2A^lm<t33Yv@B5
zew;s^LNA{EduT@0I21&Ne&lZ<q&?vXn}1YO#MTnD&@F=@5l{xoL-Pq(^Jj*s=noS@
zXI9DoX!P>yyY*=Gc;~v{zGN!Zl$k0_a*E>##cb9x40gQLqn!_cIN<qnREH#<0tSVx
zybvDZaz(eh(@TLPoO(F(ZM@beAS~eG1^zjCJ<SwPk02#CtKnURkhKF*K&x8(4VXj0
z{kPygax%=2CGn`4!&oheUe}I*DF1)+xtjQ&e0D9T#uV{FGr04W6*{x~z|9TgpFmMf
z@S=B5!y3bYzp7Gvka&N2Py|OiwsQAMJoCcRXf4*D{(_$)ad7(uMNIX4<sYDxTl;V6
zOE^~HN6gyF@naO=wCFzp5jz;&eq2T|!H4C;w4!qx3A+Oef$<%&O2pK9{YgAkK`{0x
z5qEJEMqd!xtei8e7jZf0BPawkPHj^Jv90U>Bb`PpKT&kfPUVUwN;^GqGa{a&25nQ~
zZ$F0ie)$tGs)GMZ(#D$+;siDY1>E>YNm!xo^al{CeV+D~d%JRqaCKb%YHw9C(^2vR
z@E5Tw;{hnuvA_ITYq$q)vAW9DIimt}3jt^Kcq5L3HK(5<>B%w1?OjZ_Gc3*b!$7qp
z@GpJOl-^L(KTO1ZO~LBLfdk_O-4Be#+XHD~9x?cb`46GBfmh8{hMZvwuzN<Hl(UN9
z1-y+G=!k3kAE=lu`=99<JJR9$h!eXWqh7$QO#?;&3(}dWlINtRZ05T70+_Zp;y($;
zDw{AIeKUmKN|9~#-}94di{e)RuUyQ`ALxRNqgl^P=Zc2e0!PRC{|K}HO_u%HnbnXC
z$2+$>K&{gEM`b}{{?Cq;{ZSC=nV*`P(EfSB%%p;lMTq%J_|qda5C#aOzoZ)<XOJ(f
z09FBOZ?Eiv-M~y=nDW&r#o)#Khc+_M<3Uyap|Ga*t=9+-1knpf$RUb`O}tXB!R0jP
z_xE*-(Dq3k?s49Ce}<zjALI0IjTn>t{TC%UJ{18zRx5fc_AypEMlMKZMR@^8;IyfQ
z$M#qvE;8s|XcicTSlFO5Pzc7_J8>b1Ws2$FysCiU#E8OKNF=BoR5<-S30D*e8+?*j
z@d6u*blL1NZ<!LsO2U9q+3bV=q_IMSl@>rHI<Xb^9rQla8`JGO^jb%0&YohiW3OU7
zLzp5wjV1|OqaJItKc`Xkh^f~9gD@kt#&0-%*urdku+YZchws-5uZ(}LoOeJlAOwwg
z_PG%{2z11a5v)2gnOFfy^HK*$N9NsKY+xP+C^qF(G6f6sik*M>nC9Fy*)|K7O1HKr
zE}s11F&u0F2vgTr8zQM;3or<R9kF7>0;K6*3wvLI#V4-<g<FjIsmSjiFX)e1=`(UZ
zOKgLLa19Z8V%mcW1FQq*nq;syXdzI6{~+k>U3au|;&bzlD>M`e$Yf(5wP80^LNi~G
zForP2F^J~w@m$MPUN|GOn6LXkrx4ZavC;1M<2c9;KjmfppNVhKnj>Bqaw<&SoP11p
zczMf}zgJ8=!v>ut0a`ey?WreXW4F(viGK<{{M={1`GC~kG$l9F4l*QY<zE1sg-r%L
z@`z`E&a(Y=LpqwcgBxc#?Y<+^*nul2b-b|;<`g&1;e<<hsYTGnJ|XIA>c3aV-@>e!
z+vlSMwGC8)SE_<GqA4b#2v2<qgHABKA19U)pb)e4FRVNK2LRrcH=hM9z<frFy$H`S
z>#@matn@MKc@o<mhk3f%n9i^Hclf*c^9WSy$1KxX|C0eEv1|S<0gSL?-r5wx<~S)2
zKkQO$b9622zJ)vJJp{1#bR?ZZFp~Cb97Gl!=arX{9qCCdhO_@wP^DGiJA5WAj3Nzm
zrZ*n=5GeD1B#tX?u4$0gW4~T5*i~O<>c1o(JHqY$-%zCX3Jm)IQ!I(sLIb*H;0ZIG
zcnI@{zhKhy@pE4omdM+-|Ar;lE%tnC+CvfTMbBlqRbnj!VzM>=d~|jr>mht1<TFDZ
zjW)cU3s@7?8^wS2`QNIH+_%a@8W*IY5qG}k6Gdk&D339@=L~|yWaJy0YGNQKuS5Am
zqxKXHIKnQ8fny2Df`-_VjZIysTU7$dETU<0qE_x<>D1a1@r_Y$K3^JpTPn+jSTal8
z;^c`W{fk)HFtd`}fup-0A7Jq{FmEkI04>R_@K~E9>1|>T=;l|J1X$zrfLN`Menj?b
zHMP=`uA6}F<(g-zn9+-?mf0RUTP_>Eb|Qvzhsh7wpbfWjszisY*SmHBK;=Y%&=^v0
zs}-nEiF21Y99RC;{N$Gxr{u`mu05YostWo<GeOOYUfHJyHH`wc$s7cB2J&hKErD9h
z(MEFBWXCkvQaR$80{1Yp)eIB^)>bq0%A&HjDL=?s_E9cN0$Dy~HRI_a-0@77nd4qR
z)4iXjqgkoBT#G+X*y0&uPKX0ye3fT_&NZV~gj5#uUJ*v}rlqL)BUuRD!i%i0k&?xP
z53Qh`o3hWxc!x%nW#~2Uv>&40G;Q~?W6!@x)R-huscWdbSd*l$SaIjkN_jhtt=enZ
z!fGZep1cx@8QM)A+Kqj$BA9ek7Sc;7bSg(v^7c7Jc_=Akl=1V2sY@#Kzj9aZ_7Vyt
z%fc7fW~;`%gI)7%?uW*HmK`&jD$S8Cj_!=H2z2I&c6!BFn`%EGW-p+`@U5o<(E@Gu
z03XAXeth;ZS{EI5W70mtF7_lL<QKC|Q~fGmobjb^Vpu!PJBMYHAc809^oJ6B{_Ccp
zrKTjEZfbL6O>1ecf#Gapu5@2ahQ@&5K55QtQ(d3-*~`8K+0BHOU(2m}BG1MyotaJ=
z6U=p_OUhKDHO;UyEZIcii)?v{TUj}Jfrq~;5zay}U(=}=7k|Ib&`U`AD4u29hjdar
z3e_&kP>W}BBYf2?*?Yo?zNLwMR4^H+Fqw@%nJU@HE!a`RdzWa2=FUv>3JEi%T$by6
z{87OL$+ZE!6kEKE+-3CJd^r!lP|c%__#CPrgu5j0Rz4i(z&+Wt`~*oDJrV%f<jrnN
zuhpKYmVjJz4c^s?c3<MnpMUY@N1pKyQBHTIC!10xw;Z9{0(Y@}Sw`&*f%4%8sLV5a
z&Q6m1Z86x>qQaQnOnMaT_6UcU=Vdc*9=+b&%kXrNy4eE1))wD)vD<3Kx3d&-moFq-
zNGWR>X6`Jyuq8<8!r$=C6X!Hs*y(D`Q5I@Su;wWKTBK7}#+PCghqas(VP<tnO7ALV
z6{9Vlv=iuwKw^$6HUrd!-Sv9l)}Ky(>Fb;gefSzbeb=X(R_UPEL&x4w*z*Y^1NdG2
zf@Jms`W8Ba>DyXR)6ShL-=tBGwEQy2VGjH*#f3d&)gZ2!8T^Fu<#N4{ED!+E6&4bX
zI^c!SF^sN4qtUF$g!^oL<cI;i=0_c$B+E<D9#(ObcJb7_A%1SNZG@q>!NYpN_^vV2
zSo?AZEd@^SHC4p;s4^Cd*$}ht{3XAOP9H}YgO4ktN)7%)>mUyEX{Ui4m$IFAWsA!R
zbrrpAljD*;4z{-VNaU9hm2!mr@3=|v(8@<Y+meE}Z|&}N`2?EISD40t$ax8S$==lY
zl!^c3n0+eNTara!aew;C8j^mcbZ>7^fjvwz)ce#g)055nIuM1DjUR_%i!5e{zb`3S
zBhjLLjjPSWW)y$NPwGOJdsLRh%VGwBLrxFQaPv}Q4D>kUJHNCTJ>2?Q!A?<an;&>7
zmp_YHLz(F+GFJRyb6oiZSKV)ftNzYUE|Z$!a)Ab=frt6Jam~@w$22zD*jw>0ZanWv
zrDR$OjCtd`6n!<8;Nrhm#xx^zz1L~t;-X_S?jq{G;b9d_qwwxrRL2%xzD)aDJvBc>
zlKO!e1?w(J&^Hb!_F7fVZN^V$<FhZJRKCD@Oval`<lFT&?qb|WIFC=Brx+-0oJ^qs
zP2Az~2So3asW9XkKE8YDdn?JBGik#Fo%MPi?sQMjv%i}%#;~y4`U~2RZkCU>udq!h
zSz-bXf(alGi@r?4B;{gT8hWg3%MGOtb#>Z!J?4w`ldfAd{XXN9Yc(gOmg&dM<$k57
z=nUt3@e}5-VC_8XsjV9|bE3?PA55K!pIOVKNr2&YCvW!<>!)XxO5L*yKMkb5bCKyz
z%COgyXj4BTj2=h=<KnP2XS9mU=X1yvM>r#J%AFiB&dZ8s4aceBXK|9Hj833&HI0eL
z`s^trE#JYM_iTu+JCVU?@|Q9a+O0@0^$1f|^}(JKXNTK#w7#exD~9W|$XMkOiGBXs
zlEBcxU>HYLWfpBTnov!H&-S;v??u8YL<bK)=HZ^^sf~bSZg4)$;2uVv+f=UYZVcJr
z;_SI2;!iLFDRu3ob85#+11o?1j??08cE-p_dj_)BZlC1c!r9Qh-<{BO(F&J+esNWz
zJ8|kN<#Y5@tmK~d2^zi_d2l4b9`aLU;Wen2?6KDYA?@VtY1bpyS5FLa7(^+vkybK3
zSYstYXgipRVV-v{wxdE*51(v{FgFyxd(oHPh~fG{B}3lVat7dEzDEFC0`m(IHAh+G
zzLp<;G$;CJ+<bgbC)ZrrDZWU32L|0(GtSa^r<aX)`_Aj_g|G=M-QcqH@6{i$;f2R&
z*CZOO98oNIVR%tDax~Gp2zL-(v;G?S9BB<!FS-0&xcJ-FZgj7R?1P?V7TQFA$Y%03
z`W?m-hcUkzpW9;3xK0`5WaXOi=APg>8wtgU2Pdq^Rz-VK{VnoNoJ|}-$mUrG^V2VH
zKej|PsVd>^uU@@TnU>8Txc*>S_4XsP<6_J2FCWT1jSmY_aX8=DRFYZmQFjzE8HSR_
zwxPAS{b(M5JuBZGaM-f7kzGyRn>{6~1&!GUCm*u4IF80^$t-4^K`_1-P~T53EsB17
z7@Ao5h|}TBK}b(FCOf>py~y@8I*XQg+au~bt`l8GYG}7XGgt@upI&Z0B9Zpz(@pip
z6w7EdwVr{OR(yK9*V<|Q67RT2H`hYeMpx?HC<``v(CI@wiL>{T7|{dPP>6{nc6fGW
zX=0o+k|XtUw!CkxO%fO#YN<$ckLC}xWyn-35&nEuHLi`ZwJHvO#_6v0vHE`YlhO~S
zzL-ca{lg0QyM@+-&dm$S$a9aw?i%D<dL|@+)ue61^uoc5{A+%XQQet?=I<lCmPc2^
zUTbe2rg)Q_1ZyjD5n1PLhWj};A-*RMxv-|ml4lHgw8G!Uo6<>s-?koMA)nVK+Dfpw
zXn+s?e2#mPl4*x={1C4N+;Qn9*p{#Xd#23G@4-L$=0}sE`a`+f`DzwXg-Dh1j@xoq
z$Jtq4b*52mf*A~6^B-9H2WX*rgO8ks-HbE1zj(M2T|v3@HGRyS_bz_qGspry|FJ*x
z9+{3gOvF#ZPx`jEr-Hnm);&CxE77f~0ygAt2FsbBCx@~~o&q9Dt%)TGgNK!J!GDJE
zc4;9=z(#Mq(DUVk35L(n#CDxWwtcW@owI8;nrZ2>c&e@~F7T)O1T_#*9R-t<+0LSg
znEVCV>o1JQVI`06xt6YK21f~{8myG5G<u4L#w9tA#7As}Q`UCI!==WZ&foaD)-nCk
z<u|u-8g5hIWo10*Oe#O-(DNkUai=?`B#BkQXCPFZV78UGw`D+BQB6Kp7GyxZes_8b
z6!A#xZuG1C_Kww;LSOqeb&2?s%Ov@*-S6v&D&Ci)#E96rw&V3n?eA*!Fyqqyz8Ymb
zU_u_FKX^eHI{tlgGV{8oAE`z-&o^EB%34B^t6s?a^_5{^Pv8=_ds+W%rzwPV?#1H8
z-s2wLbsik-J%WPvITe}nHwtSPL`EX}Oo%ENI)V)WF?zgj;sog|K0$l6-g#P^L$==r
zvxJ@7Sp`8zgfW^o9q(CZ5VZ~SILAco*64WzuP{CmeK}=*V+?k0%FI*I<{NInkB_Se
z7pCnQc+_L`E0W=;h#_reKwvK>|Mfs#H?53g2ImoJt@=#fO~6r>4>pLxv(Hr)6MMU5
zrAM2w*c**y;)SWunr=0AWGlJc><_~!Z6%Wh9*Dtp*>O$OWwVESjcvixkWa3j+be|?
zkEfR^T85C}hK*gBtYJM}LdD#-13Q6RR;K9%!Mb4~#KHqtJLVKPL{AeHIm>NCttM*I
zV(9Q)D66LOzqAVH+nu~0*~I#3v>geqZZRw-WmyP$lws%9q)`^*zFkz#uK4QqQAY6Q
z;WAwv-mIRu(tI>9(3*y61)u@r*55Dzfmk;x2REkLI<`9O_RX4k^)`s@ef<4G3(Mlb
zld^ZOrcY9IZ&N{=4`Uic`HBM%>x@>4lv7sC8It|qYAs6=TtEv;Wq%ESLvK#w%zX8<
zD<~vbQ!~p|ja1LJ<ZYL*EAm*@^>*%;WY%xLaG9_fqFAzsDTZUuloQI@lS)N-qwz51
z8r((OIZPQV#E-pNecuiLH&($jCqFZ`RDFpUh(g9s5#zNC6|S0VuklS%GV{k1m~(_)
zwuyY*OCPqFe1jLf(Db70xd3o)Bz-}LAcMgKV^Hz<d-Yf31vH1$Z`k^RXzx7RC+j=%
z%O7}ZG<x_3R>kdfBArFtm(}BGk;6KD{cA#eX46UgNZN_Bx)!}Y;smHA>UO-Zk7os@
zC6Y8J$7CN!Q`MTKeXo9kvsr3Y(|q?l!|1k}syBtoWY)<MpOeu&NmMmP5C$mFco&Wp
zF<DJ7t6sg^=8gMLGQRYmG<YzNm3(k#D^5zmKhL!ae}6@8tQ)<LtqEnWJo=yxg}iTf
zI3(C#9qwZu;Yj^e!oX+-F}Z;EcNI<i^4fWMDtP@_dFD$Y*$(_8FRP(!R_hn(CsEyB
z?UPlS??;s1x}3kUn~hqGuXVO8Dx<3$()o#IRH(@)b77~-iz#>c_y|YtLum!}OU0pK
zxu2PAM=fpvQ_@q-_=WM}C*YqeJhU%wF5m3eL93r5+nbz57|Gflq~yPQB{Rh$^A2t0
z;{$$cOS!k@MV@*a97$K^?F_qm7Oz_USkSR~Alx->X{c^d&#vhW+JXlggUuFdDrh|O
zE*5z-RLb748~78YTUM|ng-kM;HfpO8mfPI=y8(?_RUv##npYk*x4dl}4$nBnE}mf1
zVoYK*txgXHhzo}51$c<>nf^1jD6}X5G!at;x6LgX#FJ@HfVbGc*KKCXbtB#&FygNE
z3HtHCnO_2{l-&0{vvCrU2>M6kccqmO%`yr@w<3~#-y1GI9n+A@350$k`5HT#Z4;6v
zTWm0L8yt#B>3fnf)>8W(Q%L;za_rrk*>f-JV#U>G#eMI%;W$lH3+4x*0%B0Y{L|k@
zdIbHX05zX4(_U2TZt4^+*ivW{=oNEayp!LXkD1(4K<kpEl2hHC_1XcA)4tsJJZP;~
zxrolpEtRNr$1DY0$9CWiw~rT}m8AM4@oA&;yL%hKPjOI3><(QepjoGh>6@s*9Y{ld
zC0-t#Hq6VKXp_Qgm#N<`*2M&GF0&SEkxEYuUo4*JeX;y3>R!9jco&JiLV+ExW|0K6
zwbHw4mjYin2%q~uRr1KWRUrV2qL*T5f-$m0?z{#y)8Ze;hvDqM_#FQ`%P6S=7rF@&
zlN|pBvC?9~Nb@;cPfh3BN`Q4o894{51gMqx+}T`GuHd>r4zBt!(u(X9=Y`0<Z2h{<
z@)avu;@oG=i#xVM@8g4zu`f+p{Aj;qrxD7%mR#Q3Xw%47_i+o;8zTrNufgL(t+H9`
z#PmKr;y*t|Vr`p7DBnJV%&fCf7b%>=%I4}%I5_VH-H3w08A%?<-~ot1^ZU*#C8i_%
z+=njjQ5Y%PnR#luE`<H5<3hFILok8l<qlR2Z7mX0Zro|TPV4Z}po(R>DG}$`YVFrv
z<a#)VK*yyj_ZLo#X5(W-#In~w-|u9DIk6!@T}vEGL~A#(8l$AV@y*C~U70~zGyAwL
z#A%8|vUUII)X}^3+4j`&pfftIeKlMADpwUQT1TB^4g*b&_u^jSP|CKVx?TE%DC@80
z`h6>mKAASkl{PN53*rm&O#ul3O_ft?xQN*o1j={&`C0;Ho_$1j_HT!Yw;S1Lp|7EL
z_^-f5Vfj=umnU?4dj~I=R+yr*cf!yNPM$=6m4O^pXtdmE2^QZI23G?Gy^ovH!jqGS
z>HXj-d!@Je?+5y-o_@0<C{9n?9+-V|#Px)F>ab$0{QbP?`_f(#a#h_>PMXPxWlF@r
zBPj{ejXRZh37BDeaK27)xPPTPjYq&z#Mt1?eM;Y3DZn);l5fQ5gP87ZxM>p>@ZD2Z
z!IEF?II8<jNd((u9f8=q#(ZipFK8w~Pbjp5xs>;PUBY;qxqQu$t!{e%l@oB*yD+{l
zWSbymVJ{0Zp~|$`WO1mgTSK)t{u5-~8s&dBO)VGlILOh*HK^4~yloz;&N|4I^Mc+(
zq{P#$53YG5m~Z&S#v*S$d`vEl8bR>%L{Zi<qjAxcvpCb$2WN6EW})0shr9&(u#vCx
z@JB)Ofg!}8HN10CjF{pEi#|_OZn?7!;&p0Xlr4r&3BHkT4|anVyEojlFPrcvH=zYn
z*Pk>J*fRyy1f2!8dok59+r`OW&C3K@TlL*%;yQE|r5N=XB=VfF`%iDy^1*ipe$L11
zElv63jdDgNoPN;wl?c4Rp#+e9$e1)R^8p%JX9b1{_=yvx{=o!4qhmvS34<}CG$%`f
zljDXtqS{mC+};=ZG4>VfrS*gBJ#;G5IcM~f&0&d=o8cgPt+}MGj!XEn_qD6D*3T2X
zLn2Z_PdCr^SVo?v(#UVcTU>mQBE8%Z4n9vNoSWjEP`g^(n>s&Ah^!g>dlmpGbFwt~
z`7M>?8`v*m%e7Sz?B+w9=4-uk#0R#PyouZUCOY0p_sW74X|u&bdheCP*Ni9Ujfa8|
z$h0brp~}vXp_&<H^q@0^)yJ`TQuOKgnVM}xE-ODd<WY^oo$KWU!-L@E%eNWFLFqMl
zj?RadWJL-SDmBk9-pG^hl=_yL;f0iUO7xngu>AVz;d6A8RasMx-jybL`$AUWoEdM8
z+iTz8_bFm$oor_d{`lbf3@Uu1n6Iz2oNw4sx+9EhIF|C`M@Qg0={qq&KUN@UD`7@2
zl3$;X7a4bqER$seFMp)#<*66yU|7R#8v2<`1xLX!ZrB&t7VIOPyQkyFDC+;xD<?H0
zL5o7W6X;(7VTMGi7ubFF=RwMtj2n)IlT%F#%2r*>zbX4RARxRrQO+I~A($!HoT*!t
zRk`1{{Rz$dd*fX^2GTTp!Ud`=_J;z&=U(<JT3TvxHF4B4Vqe~>+zmRNN|+(AE?_rI
z8f_KYZXhe(J}1!5Y7I_av(IuJOgp|^^iw^(sQT*4-l--nA0-o$XQ4=7ql-=nmp7aO
zhZ&tI)rh^49ryZ~GA-`)5*mCYdN;^e2sWi=4DA(>yZF9Lu!R6lkV{EZqZJt_`UO2b
zd0vz8`FuU<XL{pKsBPd6qbHjQ_%r53^?rwUMh8EC6yI=on~&2rH|%mqmiHA?D5!mA
z(S@3WX%A%2j`Vv^{Ly}!b`bGy!?(puBJ+&!=awWp!24j%I~~bVkaQ7RY47+S0r1Da
zEXc2q(%H7W2;^=D<*y`6caRo)108eqgF^FX>c(JC_|zL`LrIk^NocLv&q~r+UDiJN
z?gk2`3Lk3t+?&c*F)2xNNevC5U!YV<!2g?zaWr4#U*ey<FBI7fsaTY%WV8QeqB17^
z$-3(2V=s8cH|4ckM?B1j5jn~lAgRKIwf51sW3HeFg@YGqdsjZP3~IAkrYrdP^YyLu
zZ$&D@INga!qbAqO^!i2fP80M3y)Vw58s4%lMh2~%G}cL2&0PAI!4^ZxY+B7l<Rsbr
z=EN}VFoC;1lY2D3w#mxJmJ+Q0B0qHHyFCaT@XX%#S`_tQyv8xe7>r4gNWXk?_}yab
z9qAT+Y7A5CN}zsttQ=!YOu63sZ;XP(?OQt8VPv*0f}D0GeiY<RmSLG-=D})y<>HRq
zXkyd4wxk`m`JPs<U6Y{zMSRYm6D@kfFH3S-g1Jj@zYlz#<{2@(!P$@z{j}adgnm=_
zx~Koh;rA@(g{`*xJ;|Vt>-|&^TWJNE9^xP(@oZ@08P6HR!fBgP4@N>(>&n4UiJ`@4
z$&YD<)5xtQ=Z4RZ`+ccBuHAM*n;7xri505X^%m@ms|c=a!eF!J&7Tk?3lA_|O53U(
zTHPN>S_p53^^1TR_}YgboqUX9`RcrZiBI*`*09A(q~EDB(evKL`Va$QGwne#^3HdW
zcvxfcZo*RwI**D9+JntbY3mQV>&Bffv@hna#Ks&qD;ypi46hNFU7S>E?KjBqdG4O>
z2G<<9!V99DxnN~_6W~3p=6rLVMoykax>(=$5v8kF0dNda+)h^U`r{`#Hm4fRtJWka
z<Fg?QpZf^P_~LnNGW4>v<8C;994pw>qyOx$OpAHdTw$6YVu6u|*UVZx0!?-A8~+~m
zgL2^O%i+a}f!L;XJs)?Xk$s~VcYee%XWbdPmwfx^aPiKM=1bB3i_z`ICA-<Hjd^F0
z)sbu_+rr0JLw-_@cIaPs{5N_Y8J^7AoO%hKVSF9{f6Ll)Azl~nGz|MlUD#%FD}1~o
zF?Zlq=uQATXZT#SPfOT6#@`)wG}4ntEqi|u$#b~aG5EfJ`?+Ly^3$T<cS$IwT$Rpv
zx7!THzCN8{d*_w?PKZrVSCNU{z2)uJX6%(uY@!G0YGl4lp-G$dng*my{}atgRN=Fc
zA8Vq7SAOV=dR8(^tCYuTPJO+U^%V27M%%B*8_^t*NOgnO8qPbMHxIUvj-4$T<p$iJ
znP?5_lBW)(6Ax`43jW|LZZlA?Wc`puG^xYx-xB|0Hb3Y}cWZA5lvhNPgSNQvX|i+}
zZwzJY1h66EWCOp_UqJ**qONf&1Q)A_Tt5316L&K-RHj?b>qAm-Q1ru~WTOlX5$}Xc
z%7+W&#@p5V11q_RaZq>IUY{{$nWZ1hpg-!f*9NXdPsQ+eT&>wzDFu-*(sDkBUAW*x
zYjC2}2=bhEOE2Y3^2d2|wAGY6yFTX(_B?kPBD#BZldS_u6fSJhQco`SNRJBn6|hX!
zrL~18j_ZN-eQ2=HN4K!srQWC_p3lY09e3KnBY2{RJ^D6^M}?7qql0I+D72+ej2Mnl
zv9r0*Xq=&y3ER?mQl%9QGfxq5KgnmY+QOd33Zo&FE|T#jXsn&q;~N2oExg$rTOLa=
zKFDYB)>O2S^;qFGITet7j+>n5fgS0qE3&r`>5fq2bkHBrSb3kr7=MeN>h0d5*txIx
z;{zF=-S#NEf$2?}eWd~8iQovl=5|5H;zHAUwv2Zg$rn&J;UWB{gj?r8xAsHr)%p2(
z^X7qwyN_UCKNS`?R(-fCn>jF)e*bWeu}9;>V>X=MkBS8AWPW856da6(+G_oJ+5Ji5
zy`mP<TKtEi?J;p=WI=mDIg7rvG0v%8T-noZ_sR#q82$%MU%?hv*K>_)aRzsa6ff>>
z#oZl>!$5I&_flMnySuwgaUa|%6d2s~<9^=j%P%<B+1bg;+AGO8t1Ps5MP!BiNhV-?
z(HLuz0`Wd5shNzA2IQ?PI&_g|%SDDpl_PzDk_CHrfs|P@f1Uf`?KT+$3!lRpN7=L?
zKEfxk0`v+mGr9u$!<@@69i8bfVs2RVw@8#oRq?ILEi*8oKp%2;H{ZPmQT(nK$lvF5
zJ{Tcj_>A1ETP)Z9qcWxY>(3|EP!EbGq#uw@3a}5>*bAKaXOnw@?VB{p&QQTiuc4s(
z6d|_Ob!eP~Mbeq42Lo=DanQd2mBaQm+>2PvbOym9T1h$K&iakSFJ9&zeP^Xl1bT2(
zg(?b_K1I1IVS_&!F;6$r(TXCf3#yiil-v;p1}kQ$0K>DPWxT(tF2UZQu|vzpTBJa{
zW?>HrWF5=?&S_9%!YVbZaVb_;i{q%cBAcv)AJ`H)R+DkOFbu=Ye^!?`C(&5bzqS2f
z<izbf^mOO0+5FleQNMCyOEFfgBg&dZ5h*;y3K(K-?6toaIjf)lt`~VjefCNYI)4*r
zyV$s8R1(S;&g$`F`w@d3!GUUv?KTQ)ODa@!Ry*fvgbObHNtw5a|BA59z3my|R>6mA
zfH)MSvDh#gXtO=oXB9a1p#>Ip6nb|`HaDmvi)*u%pufBPu<{_*i>D@X4p?3J<v$&<
zb8Vp-A)ObPa6Z2hGiwf?w-7i<%{mv1IZ)fZWVJPb-1bd0>M7`3-Re>R@5oPxCh9yY
zh5YS!8nBvJO>oQ`PnDXILeVH2Iu+6TCFKadQtD`9Q^M5<OF@xDzIM<v)qd0qR-c)%
zH1$G;W#L>EA(hr>@zk%FWtekI#pPPUtq3b6&{7hwTxiYY8#{2pq|SWHsFo<I3I!3O
z<UunaHWH$6QJ61#>AF#0g(QykjjK9|vB(3%8mCtO1s)AFo^~HjX1{3pC3#$g>mz@<
z9|VzE%m(`E>B?I3BcV}NxeQ{@#LSN-Nu%c@F5Fkcvk0Yi#LvJW<x_HzQo5SmzY~ii
zo=Nqn6!sdOswHE%^IoQ3U92_Xz_=lRD_Q&3TTPG1ZUdZf3J#6-k6Zhz(qlotBOdH9
zd0w&CFB(CtLPaQj*#RUi-QTL`o6$0IFUR{Ix^@#ej8(ytM_M4yeVdFd^#b`_A}-T(
z{(03H?EJ8#%kJal5tMzrUtIGv3^#CvBa+HrOQRc7k%lM*{`qBg;Z-=iQgC7}38}zU
z7yRy^L9$zNG2Ji@yEQ2Dv9rO}mUF8{bJe}KJ~66*XA)DWT~58?o@0uc!Cf>K%9os%
z*FY&Tdu94zLq5=yi$9LXrQ{b2IckjRPOSQRNe9E=EtshCTgDLq#f|oU!ZH1^q>-E7
z^br@XV5XULiT1d*6yEd!@0JhG<={Dcrs`Zx=Uzh*xytTv@p-A*rNnj9pyNID%{Fm4
z+;fk-Z#+Q#`J)AB&4*Qf$%n9=FjZ*@&-**pWA}TY=LLuDhA6J{y-bqwD|B`hy_PM}
z@mu>dByzH~Kjt0BYhO8u^&PF?^979AMcx(1*%q)iPB<<d-XF?$3Ht{}D(Rp=)qt&C
z-<sa?mQ~;uVh@}z$lGBZ+XA&Oq|fw3r`JJ<9NvEs`<DoGo4oV&f8OmJ_Mdl?W_Z;L
zipuh2H8~`$lN{AgMR)3G)^sar=e)7lcdlibQPU8iO-%+b8rwNv=o8`Fmi1fuPaaFO
z^eLVPi+|f*ssf$i4ms#J(A-s#4{2i)z|(R2#vv3$3CTgRFiGSq4SP{XQACl!`BjSg
zJU{C`M<@ez6v;PZoX-dm(Oe_!RZ<L5!;j9{zhv8VE3?GC6lW5pknivlQj*ZQ9vLzm
z*XWR924g?zn?5#qpLU_{a@`?<Vge$LIuNL|z6y5Z&$^KRxYbu_l7!(v4bw%6FDom6
z+z*WZmLhv+`rrS0&sylvD{6LsdT5GSXJYbI7P^1x`c;CxJ|Mx;rA<oKk*+7AdW=V1
zY)@R#Xtl034c5-2Xgu2p$M)&BzRV>e3ho+2-kpKkC$`AvZGkH1;41MDvrx$~zU?8l
zp;v9iRU{+R&_Zt>dTO_cfVc!Dm9z4~e%geZS8nMswh1)ltY?FFo=lLS2+pph+|PtZ
z3hl3ZeCA?jb0OHxTKw$gX3D9d%KbPIAh!N=UX5^c?B$E=wcnePC31;2bk<rK;NAm>
zfB7=ei-gLW!eJ_Hj8WRNkJ`0)!PwV}@MgDo@@0EEaH}f1$zg;X2C-_u9$0VG*-Ev0
zr(1ckVhj_YR=<IJLADJv>>>Z3r9C`;6^0bIA*`T$t+6Y;AC>*BKAVzLM7mPJe*UUF
zXYX;d_`NNZGy2Z;rF-EqyD2g{UOu5!qltAnt>_*0Jpa9PQ+W$9ApFeZ4L4{uC-UN;
z9AK*Dr+hi<VBm61c4yccwb6;4?&1dLf-!^WQDNP<@NbpT8ojsaaun<Je#wXyZGVUk
z?DKB(RdTvpZicx!l~wsu6y&~=j$^tEsTzAn4Agx7;iEPHzT1PVeZxxeJVO}Lp3=FR
z=ZevL(OQ%=u7Ph~1$h3Q1$pirC^3s37Yj>DQ*v#t4*5D7Df*wNYR*&i5S!`upN6#;
zPOTn>tAIz|7H23cc}oNJ1}f8B9n?kAy^}hUf>vvJsN7Ungclf#+^<Y|jcrOlZ$DvB
zIlil`ER|WzLt$>gN$|i>Bm~rS>H5NXov8w=2aLL3>S@}-gP<#+^zaj*{ClLF@elY0
zp93SCYw0hn7y0-4gqFU_kFI_4ohqzsgEGLi|L?wex$U8L2|Gwx<{Ag|CfxR2kYa9}
z9;ouOUT{Z7x`u%@$JR)LXh@C3*Y~^di61tbRhS%J-Q6Sum$_5){#pO_qNl|g5e&)&
zbZlLsQ-O`-Z<d}Td(N08(KmMNd(mfD1&6s>H-=Kdy~z1C1m#>43k86nHKV3}Lnx3&
zcjUcz4%i_tfvTme^sZsz^N(Zs6Js1oNw5&+rjf0o*UF4oWTmU+<CWETE#gzsN-`M$
z`sUL4n>S1<qhOcId<96ybz-fEsnOllSHJ!wY;#Unh+AjYU<u2UX6`}=8JOZB^ocNn
zP<u`Tt1FD=BZLcMTtXkMA^4ny8v;X3B4|~w?J8(LARA^YEm~Nhcn637qM^R2LqiXS
zQ`zW>e=<JSy<dSNCEw%Fxqa+MQpem?3@8|asDL|!=V|Q18;wKk|Iq2uUwZ7GOsyWN
z#|YM0dqI}IaoI&>H`hwP>3U%#9Pa&RSUr6w^TM%GAkAX^Og^L&wl@55;Qe3T`kV@E
zPdb~lkJeiq$sfl#V8`tEfF>2cEI1wlUHTh+%@q&vGUMW6%bW+H1yO4gOJoQ3$g^|W
zj^3<gw82n!(i_WnZZ>?nNM=&g>5Y38&}RXhD1@WbK7F3x)}!5L1Ab_Udy1Afi<|>x
zM}<;6A}VJAsyBYgmy$8~x;^1r*O#OpxIZ@w3r?;zb5}m_G&G;);Ff@!oL7fT#3I)m
zv)+u~4mX|a%sKe$K)In9BX88UgN%TIG!woSmLd2{R^dh2s<vxqL)T^S0~shgynYh%
zn>Z6Jc<X$!2cj}Dc-ok#EI!S0PKR@x51%5+e{b;W27_J;D^EwkT_w4BMoOG^s8vzm
z$t(?&TEG7`WJn%%r1E$R0oFf>jCl8MzS&hrEhymvZ~k-FORwAQ|NK>=gxFOWdVo@P
zAs)L<F;7N{&5dZKB)$s_yY7xLmxFGd?eCl4GcryZ;IEaGvHvZFKhs#_-6!RZWUKh4
zfK}66ThcfHQBOPhexD0J_xp4+_0gcuETZkFZ9!@B)#6PLp#YGX9^l9&(4gUk81YQf
z;2vve>UT&|t2nqB^Hk#WX_!AaEfAE8*4ih}jW$e@{q)1jup2+)c6oGuv{ZA+D7@MH
zHqDAfeBnR{K+$6O_~M?~qQmJ)+W(9K@Z9K{mJY7WvM+uiVduyfymnC^8y7xE+K3}#
zxqoG#YdB!A7v7)zda5Sde+*Zppd+=os$hnSgx0=P)>bfh&fJSoP8f+!wRy)Ai6|WA
z3F!?p#1NZST7FepzCT-CyMu)6R7?xcVPqMh1`1w2%KNF!_LAcz^uNe|psxS9<DNQB
zFDNs?&q55KFrKR_#SY^axvW?*2jmJPr00zB|Ak2eM^bWPV~R9FIiEKp)j6}u$+O#B
zJixeE(Em@?2)GM4lBP&N1b4!F0$xcX%a1yUj)Dliw_c%s3Qu%N(sIZaiaMz;@cUy?
z69#GI_Kl$uJkkCXc_Fj(UervsU{Q2_A_#)C_KEuxZhfaLl$=|3l<hI_DLzxIJIW)K
z2P}d^x@TOFX7|jTwt6u-S}TLu>E7_1A<7j;g`y%B$_zf3uk4=5PX^spq!LCC*&Xgu
z+|&qXfoCUnRrGc;=UVEngrtO9hP{#BJ1_Y|!nh?{TE=t#FgtEq<@ZZkR=?#KnhBWX
za3$PKg)=musnPNDI97=VKuME9VL=au8W8Owvn3z*RM44l!M6)m8EKq5w~zGbiQ!Rp
z=Gi0d7A9WNKbPWJk|jpwOQ3nHu?Qa)?=gt$VDxW`5eOa~-(atuODGAISCLK$AqbpB
zyxD0oCIsMpeIPeH-5C9!m12KX*5wKHNMSaWAwVjQ(Y_`I0%AV4zez}vFI*?B<H{83
z)5`+VY+BE5`4V~ZQEiq=XnKr=3TA7Ry;W4HEU07&L{dly#(RE9$t#vY;LFi%&a2ix
zG~+g^?TU!`GbNGD7k@`o<t@?sIlZCiZ6c)G)jTOOVP?_hui?^5@53F6{&M~(-N1ML
zicc&B<t1@;F(|otAtrebZ6OrI!+oT%Z75KC%0(g#1(fW&d)^LH7QLcU@JDRfj6=Gi
zhRzTQitL>#G=J<mrnfZx_vQOzepsU2sL7*~mzN_#hG6{iyZ(va0qQvDPj9`Il!fIn
z>%6(`PlZeh7Y6Sh&MzgS8bp3Vj44Xn&4_-UNU=?=&#u&-tHZO0+pY~<P+`)^`z*AL
zl@RAHDo&_>w1+nN19aSx$E>OJw3G#dEBIrFqaa1L>ng;!<S~Zg92nqL0YeS<k49`$
zI{+gGkpW_6y({*}*^k8`H+vr(!CO-{wEfFzO80e)C{-l4!6BaQRAcp|9&OB+2vUTS
zj~e{Lng~A*WkuE$C4;Y`z$q(92s-~O(kHR6Q4@lwk9d+`S&SPJ4cIL+F*K!^FKj<m
z${5HfIcKPCDHvSYSS0oxky+=3WzGVfG|-;9OGuv$S_2|NL`wG_EV2GTN2E2)Zm3v?
zjM`cZ5%*g-cD)Gp%K5UPtZ(b>b0xdLwQR+HbzUA>onjmLUC_oBwCP5A5w^;B8ymQh
zAi`gyCiZ+s^>pWb=0oq^OX_uuny4!}B^bBt&2zN0&B23SFJUV_GCIl<rn&!O&i3BM
zfV~)LM&$K2A8FWI#AKF=UI{Yn>?sZd9PvXn<PGU_AWF+YD$}(R<eJ#5v5+t-IG@I&
zv|)f0&_PC^mYvMaBqSp`JT!EXPN(1B$u$s5{o8l)J2Dt+X7>_}omw#p?YbXCu9-fO
z2Dek!WXXIz@N@29*ngmo%qKQ|uuS(h+e2BQNfENJ3YPc?PL4-w5l3qtf7JRp#5d~h
zH=JHv#(3J&wMR+X@JezuHoFi5R@cm*{&xsna+mN%zflw{u53Wfw6cE|f#vb`c^I+9
zco-R>Lr_)O5emsipKU6pDw4w21w&;hmJ1OYGQOOD4DJ=XmerVp!9;0Nj_f80`*FH`
zvuB5!gMjJk^eyHlXqJWCYU7n+TA^<Y1Kg_x!aSeE3fOZ<4<d{HM`fohVkr>J*LK2f
zK`HNir=dT*f&Dm$fzy4jO*vDoW?hNJ;dC96$j~>&$&?*jkdFesfoO(I^>oWEqqVM3
zQP#s>woI4X?i6n+e<Y-aKUDiuq80%@YuhfjiGo2S@8_vU=E;j`iPNtIa&!r?E$+Z%
zgeuZz6qOv<#u-mP4y&j>#ypu6<F*-!UbQWrP6yAFo?gPA4p$R+IrN4*MWD<<_kYfL
zNqt$`uT|lyJzPjP+<5Uh*c-E5wbl{CM1%q^GQS8i2*ONYeyS%n5Z29fOWe}TxzsH{
z$0RozM}S}W&8{6ldN4q5gkV(~C}LgE1Vc>dGTY5rbzALO$eDw~?>5ZZR~|MesK*7F
z1wTy;v3LIun%C><KN|N)XGi;gQ2lo$;k)CpIc3rxx?ju^CbG!!Qk|sUc5G@2`~pq1
z`5vgDh$cHW&mmdsvEC++K!na!j=ZucnGeUB-DDUrdIT*E|2y2i5Ym=$(>9+FpC+i%
zNs{nJD(Ftst;rcdsyoq2ylzfwr))u;v$C&R4t32b`)(tC3`2xJ6DYbx8yiL&q6(ew
z=aD4x*7oe)EP56ZAb-Q$i?V@eQa@sXOCeIJW`j7$<|#CEPZ7TLX@kdIR->F^E~4!@
z!K4_Mulh^>fQ|+?T9VzWPRr(Dh3PHL{=y(bvBB0{=8;Z^J7VTTJeb-IMSM_n*1yU8
zYvU#dSADIYxQ(LV)wV<By)Rvj6uK~CX&SYF)Smd@3A~X|2|HaZe=?pPCc8u3I~G6g
z#^W?B1vQ(tl^I7bO3c#Na9|7Fg}X!81W8p3c-o)zQM2vBkDwdvfwdX@#loaz*H8M%
z1iXd?egQJzloTQ@-(s2_VOq;6;Jtz?a!tJPrUHmtdW#1guKtIC+Mh1qH!Cw1IGK7r
znFH;G1%3-5w?|LeI1%WPQvZRmc4pI$)L@{58!9l_M3P5W+eaC%fF<0hL1<JO{)+~g
zqimU+qb`18Q~=y!ld2~nSwh#nWv(ot_#LE)$(P-=NU++bA#T#}ThHdnWR((UdM(%E
zEW^&K%Ibxw-@KaK4Lsl^Rz<HPM}YCQuVI*>yjUg8p*ij<6zrl{tPA#ByKlRXLN@l5
z1vi(x!fc~mO21B#Q_lEdwm*bo+f!!|7hTB7=19i>4&8ai%z7XGj;RqAO~HaiqKRW{
ziFc)rxw^h{_h8^&R9;{{NX-D>jg`7M@bs-butVE5`lagN;DpUk&`aEboakaHi$}0v
zZnV4sZ$^CVZD@kgbhXJJ$ZS=h^NgF>Igr(SG-RQUSUcH*p2}a`z<QIOslmG9JJeEn
z&Z>SOQ!$#QJi<@eLaaunz`HMgH-##2Xjr7JNFVBxx1D!>0>k&F94YV)g`Jhc3Viq1
z5j1)im}KdX`7IeA0PlSMTjFB~`x>e!Sm*Jv51J+(-(@TdjPL2^`=1$nlvUc)D>VBt
zze8~XN+m~kBqE>R3VKA<6sYDG3n~V&!tvZbG-Z#gH6$)A)vM4Jv=sHDVt|Wd=sK0>
zFID2UUH$IO?!}cswt1rsMwm-^Dvi1N7&fnlg4KeNIOdplyoxmtm|BU@kZZ=}we?=?
zu@enxR{VKUBKNbvK8Vw$MVQkn!VX)<cveu^3T%dyPsDmVs*3}>xlPC4X&&$KEF|>r
zVkQ6l-lvmajz!ESTx(Qh&oZWQ9+I|X3|cXMj*2Ew(TQjqBVnLXjrfyv)Sl}Q6H}V;
zh@VP>6e$`<KMI;>2JwM0tPhf$QUIPRaQSsSv906{4_~-fbsuF!U)hbdiqF1L$`h2c
ztfixMUoV>Av*p7a9_c7mq9j_A;uENHufYtL^p(Z{bu!awk(u04wWl`|Vd$PgApIqK
zlnRJQn@Q3PHr>j%9(|Ljm}bY+-%^%SF6-S9`#zgOsQuedKn)VIQ4w$m@524;I!^cN
zc3{;4Vo#qh;i{s`9_np!K{3(0tw;=U+7U=prrNxeN)NzFjUQa%+II=i^6|^>=Mo8T
zyFB~_KYT#@5x%Eb%XjSp-l;3v^tU$0HyHje+%Xave>|+R%{iTNfC_(yi%S*lonkFQ
zSFbq#1T7>J3)EVU$jOt1?*5FPY7W`BwXNqa?Sk6)DOg-!7l(_>AQS{2yB>D58pesr
z@O^87+H7#FvPws?#0o3PA4z(_>Uu7~;q{@ROj4Q|0p4eqBrh~%2VBYNCXfz;;$_$O
z9eF_y38sK4uSI{`jl^c3B3dz_xh<&V<@2@t!L?{+Mf$1=Zi^rsW925sGOW<14hK}#
zGQP&mV%pIrR&Y0%vM>vzz>+9bOzQ}ve~&5DMyTLsIJ3{W0jzZA|5z6Ae>(#FV5N`!
z=eAxEMqHoO<*%pxgB}Egix7_eT45;M@2HjiEndACTnT!}zh32a-|Q&iY$9af=d~et
zgAW|zlsmuWsz^;SRHGIJ89WFV<o0zwQ8B%l?49KMv&B>cj3*|`o->kzHS<jolXJM(
z<|;7ttN*BXqf%utC4IEpQ~gS0Mngg`ldq~rSh4vW9zq<!<O7e-Q4Ls*J`bIMf4(1(
z)D-z9M`Q0X@rG=Lhn6W3)C!n2LjAI1pfVK?t%*a)Q`=yV-B|_FPH;#Nm)Mj{0$(-N
zMkHyrpo*&}mCRDo6s1lT=Z91Tpp7+pzri2aRKlC=ls&g_7p6zJB=qNc^j}ckiZbNi
ztQVeuN!!q!PkOagdulnGpmslq7v&e`-KBS@c72y-C#VO*?avnh#%Ci7J7U|DXsH26
z7k$aYABg^N@q@cGLIY7{dlEbj&{611sE~A#J>4yAa{Hj5a1a}_(u%?5w?XM);NquX
z;vFGoR04xk4C=cW^kWIw;i{J9rCOydv0)756d0=dK|+!J#A5VYQE@+Wkvl|P<8<Ej
z-*7`(``7Ptn#B^DQlEf-O`e>WUDJe;c+!F&OYK-=V#{P2VFVnL(1%s&Hv6japuZ(B
zit*I9${n?WlqGNz#Ujtu4`Xc#cU?IK1{3*h%!g?~P!qiMjJguIOOb9N>wd6d|C~F{
zx)Ea;REH+8BL5!symO`h4Pkn}9o=Ychqn9?^b$3SY^a|UPDm<o`s|^#3RF^LawApw
zvR<nLN9EmpwHvqfqn&tfo}~dl5x+NYXq6~3h-YcDCS5G|{bY4q%_^nT(OVp#Jg!uJ
z(iBOL)v!5~HV-4K2kP_<;HVthcrbGFLv^p*va#*DysgoTb@NfSb;IW4La(n*Y}rAs
z3|m4?OF6>2^_N2In4C+BP(8`A&R?P$;z&Nut)R1A^T*{FTavJr)8V;Z@`C)F>3c%P
z<5{?F0)}#$Lb|+v6}UzKgIBD0YC0{xpAGRyupx{?nA>Pa$;D2+w1*jCoS%V%XRVCm
zk>YaS(d~O%uZ`}i>rN<n?+6c=NsfEgtJ~+0VH02q`_!2oiD5t5`R7VnG_MN#l(}@?
ze)|Q1KOCXd%{S=YcDq=aGJzA*s!0VxKRkfTZde$iSHPLbz`~$x6ga>HhY*NB)_OZa
zD`ny~R-t0h-ea#!x2zK~i-`FO)*Em<A@!N{!2GAN?Uq@RuCJ<DDUVxJ;UB9KB2TH|
zYTF_WIKo~b1hlWZlSCsbQ8nuW!XPE>M2sICi{^nB&#aypMxjSsXf(wSF<-WXt{sO+
zTjy46n}UC+u0jt+OJtAl2Bfuwf5#R^@Ts#F_vEO$NE=uyT^ewL6O^sKE+x{vtMA?1
z>Vfag@c1tA(U`D46D)Pl%a()I&B(5B80MN)&OP*G(q~~XH_9E)%Q;SBV!Sl>>oX^c
zGCAerB>MX$wf=TRKQZ$+<tCyxsIlXVVpM+nT%~cl9FL-pIObR64FmjI8TxpPwB^1%
zRL~#giGRw7U(qa4Za7?Yti2QyooczV%D`UHkil-1gWrpK*Miq<i2s~>=avy57S;Ml
z+o6735PbpJM5uIV5|^9Sv~bpiE2uk&zawoVwH6!VIuDu;zySB$|7iUycevL_b$1QT
z*iQcNd1fozU9%CO1N(H$1hi^a_z3d9EAav>ya5zh#lbX{RP;Z_*`7bMw^$qJF=|9d
zDI$<JgezApm^>lMEz9Qw<%1>Y%TQ7e6oCbTwiMoX2GOf-l5EGjN9X}Y@-ls0WM;65
zxe@!G?PcE>t^3hEFZg4(xg0$IX_=1(wBorVrdWyrlA!^YnmTqHoedqUZNzwXk@?kX
zvedNxP&~ajS7`p`mO<N2K7~HPoj|%DC(7K$vz+uS3M$z`#bhp}qH@?GcQUt9vFo3h
zgyJT$wKuzWC=Y~)h}33{m8dCBs4$cK5{V-s&j~#jld|m26f?6TmX%J(k?lqk=Z%AZ
zDgIV5*A$XF%6}pxzokVr7Z?w=urKXU-nZ23=%JG$v%@^DW({5yXXu@al?Vd=>6XZ>
z5EiviFhoURoT3&dl>)a!;v{&}!I^Cj0T>0%j0vXnK5}~+;BsTv!oN)U`<|y5YVIA{
zH$wyCz(z6`ts-D2oKb$cwV}Xk-8y@fQs1%e{s*h2MDZaV33sgO?nw$m-IB<C$2<BU
ze$yMuWn;_5Z6J{i8?Wg5JONns?{r2hvm>?kn=rnZZGeZ&5QxZ3IQODCqtg=pkN?nC
z*D$_kE&cvTd^Ts62iZIasP-lFYV)U5`a{Q+Z0Bof{#sCk1xLTaIecToHLGd+fU!0a
z+q2NE;6egY0!5D2qhmOkE7$|n7D+T~;Hsi+6uN8V0c$f0{jNr5tV@5)Bwh{>*~8xH
zUy9iek~@rxWq=-W)W2mpM<|dqIU`KCgU|LRa<>O&lWmO1YG5fPK3s|z@>nOA54%y-
zc>Dj{eObv|9EU9gW4B*hjkE6Kn?6Q>ic5JkoQ*y7P|!MRWbEI+APP^RA)SlX_~Gw-
zAV;=hj^g8<%q+*AgRtp=x#Y0`_gi?7l7wr-bqQx?C}@fS!=O>z6&<K|{!Opr&RPr!
zXv9k96Ln@ehjT03z(QM_ZOMh3I_`&AnjE%0LEfrK0?>7F;&5M;ar!~ZwX`r;V<;Up
z6X>xb%j~(zvjrw3;D>WjwEwlrN2$U*lL@bhStAGf{=Lg`sNUd%VO-nN8NRN9l;(=&
zz7k~z7<d8GmZ~>-=Mp?$fdk7qo89C>q04ucZ4c9R2WXp+`$Y+i3mV4Y`!9I_fPeCV
z*E9MF)xFbj!xj{SmE~^VG>ix|2~0`QG%Pu+UU_I6sb^K#?f-zY{Rh3PjgsNDue}M|
zu6eXpY6<bVr{CHD5GT>gk1iJeL@mvGE?HVrQwZKf8|H@v4UkwHn&@Hi<FoedyRhjM
z+5-KtGK@oqgbz0Uei?B49BW{2VrqK$;3yjhzH4tBXRH?mh_;Q6$Z5i1A1wUUn(55O
z_xYog@=6QAB)vT&nS$%ixzOoG`a7v5(nTgNg`yQxsTX*`#q(3-7Q10v!2tQpkGg#@
zAR@zPg!h?qctsuLY8P^MBl3pc-`!e(n3g23yu#W>t*GNi=CwN*nbVsG$EQ4lng8{`
zl+2gL2jO`^!pN7vk{q5nboqvxpaVY^upicI*HfRQF>rQ_dH`m((&X>JVFfZ9yn6$y
zM14ITv%xTOeQ0r_HF8W`sEHX)tV2tK5J?q_Mwb&L=A)^>)^t@oR7cv6MH`=*o(YsB
zP3cCFf$ls>8O99(A{aNGhutR&^F3IMR=;{3C^Z9ey!~d<HL3HpHa-c!nO9I;p#Bz}
z>MaXh-w#`w3Tghf&p|F>-;3{cSLt+?HCat3XMvxz^~N=nZyb0cvTazuDkKu@`$Uao
zyzKyh_MJMuc&oV8V^pQ((I2R>*$8Er=VoN>pzixRuC;?znYf0&Z4BLOrYq>XF>>h&
z_#=wiDD<DONZ9?Oie(I&Hx93&iDV*^5WX^6zE<LWgg<=#Bu(OI&EU+#miOjJ@2z%h
zVtf2JL*I3S!FJ_6bL>hM$2sKT1<r{0p$RONB~7)%U#^cBmnFApBc4Gqlv>5*fJDW+
z%Pos7c-D<>2C^-eZnoB=%sNz;hG-@8m;16O#W_gAIDaI_AU=$WFm0F96Q_%*CwR=5
zZy#$)95Gdkkb($RGA4rr31TFTT`Kp)?H}>qk<G8XCYt#U_>Q4$_OY&wMe+16Vyiy$
z#0Wl`4xJe{zwn%p$pVTPYeX%S_r9um(y_b2{dbkg<^oqfdKxX202=yUO0P>XXmDAU
zy!Dt+G@A%Mi`0HCcUQ~k%@dpy_3Fs3w`!*`gj`~pIya!+h20;UayMm&VG@QYs^YC3
zQ|KsRtHa+GN|OhQ-KRA3#XL2T8+ZKg4}T_Uy#5>#md&+!;gb%h{HMB5jhK5!45}Tt
zm}K*5d*g4MW)uif5%=0VUXq;J{Yo<;jaW^D%KVXXFai_+s<}R!k3Kq{$R9ipG2@ar
zRl>`c&vcrcz>P%(9f8u-l}=)Wn#$f9GVz-;%@Yp?m*pC5n)BwNMLTG^oGO{B(dQ~i
zK+On0(FLshx)7Y8cKvBu5Opf^5W&oZM=dAR2F#1R9dTfx)=hl`5A%QNRvW*k&!-r(
z{Hl`&)oDQbmnt<1Ay*<MI-=kR3|xf9kR#V$q9dWm%flo)jxkhs8+e3c5=MdYH*dl}
zjEa>ayKK9(y?@mx?o2+PjzlQHjcs;&OBRpVn$i%(<gK>OjH#NdRfrXE{t7g)T)bbB
zrQjy*lA#+u<jk72?$2%D-PKxWPReMS%O!q5mu~U&+;s0h#^_$rrWqF8zZn@`nuJkl
z`y7Ncwg<#=@)thIs>$c&In!B(pTX`%nm4`d#2!8!DQn&(BDj_{CyVuxhicul+o7Vm
z96|VZO++;VYl+g-*4gstiicH4+s9Dg0Fe#@Z<N;1`k<gguu#SotB6>rK7#&OwjK{p
zEp0Q3TfvSx-Qo}C)2h1f%%L$+^7#^X1=o<~x@(8-f^=1UDJ+%XMm#kLw%F|(i(f$T
zv#qMogzuy3s*EAO#jMFFt8hcPV0(r$W`<FWncfB~W8qvSvb#W|c0~k!?p<@b08Bpt
z?y(=Y8gl<Fm3auV6%4EBmaxYz%P$DwdSZ3Q8?GALJJm#QV78ADpoFpeUG$Ul^r*>x
z>eKVuH4E>XZd*;Vd!06?exNe+JDz8I+-N)LGQ4k--1;y>>Rn-<X(j1<$DbaUrR`J5
zQeoy6y#GlGAZPdEoyq0<|H65_>G{3aoql3=5bV9^x(z1~7P_G=xXTkRl_}rhN%ts#
zG!g+eYvId*-|<Kx(2zJf4!#-zRBV105BXexu+YcWBae2a#zoa`e_pa1hu=6EgTQ4L
zB1!_4PwiTGy9qx1x_sqM-*iE`hSd@Fcf(6PPFLl(vDxn@{eO=YqZ)2*wXz*?Dt3Wq
z>n(-pOuwh82q?XuVc}XGEFp{-<}9gUK;}*O@SqGvnTROsT1IF5K80GUTj9{15qtrp
zdI%Kg1`Cvnup;^}W-M7F6o1sw=x^(7O}DS~JiJsR8QeXEqO&A{m!Gbl)c9|HYVL0g
z8arS@a899i+7%gN5#Ljc`I=pz<Vc)8-hO2}Z3BBCtdE#TB_VtKTfv;4A<>xn(w8_m
zGZ`w+7@S*g+)u<w$KGgm%(b#PTB(F;I$E-T?x+hkT*1sDn&awHKN`KfptdzQAvik#
z;c*o6SVs`mgw{W+{IgpsXEP2a@4N%PD<7i-`lx1kx}>f50Fy^oKf@_m>fT5B$j)~p
zX=7ub98tJ|ZidEbROqK;X~ef#Y%P)1zvd~Q(oTxwQ<YZ98!0bpph843b()4Y69GXl
z_<caVCCuIv)93$^v=QLpyId{q>f)aa5ftUO<`^X-ST7(K{5SxMV9uUp;hQ?LwGlw#
zNA^^C|8DYGe0P7xz+Jc;y=+`(R@Yqvit|@Hso2S~$fX-y*&JzZ>=WXzZdy`ns}6-Z
z)9mcWhQIWfV*vm+jdbl<DVhRvGBWMHSYrJ|TDY9)e}o)zLvib#h<+lEj#O)0u3r_W
zJ2#{7Sf3d@x=;LWdJY|i&U_J}f~q6fri39qkdkj_p)p4yDp=+;`P>2d^=<kEY;gv!
zTCa9RGrvUVk%3C&z}Xxnd+xr8FZB#P<12RsVp%t!k?R?y64~Qe?40htMM+c8MtzP&
zfWa!anPIOX-f4v@)EpK~5bsB7-<Sx!`bfO4v<0Pf3w)(3f~6tdcT0AhJKOMok`wvs
z-(D6vyK*>hSLb_vmc?wx45hnmVX`@idL2!XX|<q-Ada65^L%k`1@>}LVm4Hf37Wil
z(cpFN{Ot1~Nmb^0uZrQ@Z}o>S$t~-hihtfQ3po&`@rUKLmg;Zmgs~_uFz(jn$Kf>x
z*f+Y=8zcN>m}9z5mGz}dMDQQQ4*VaY((6mu?iNp!5!vX;In*+BN0%mfkk!IqLBsj^
zjn@aRge00jj3(vpD!tz{ixM>+D&IXUAM<XPY^FN-s2lGmLr3_JM<A$q*1i&+@@u-8
z>N(tIS-#_CCM_LV9ddJD<rO&?oO}<;xWymaKX*(&8&StLG2mK!PN_?C$4b&ttjC|=
zzMIWKxe~P=CCE1vNf<fqpi&!1r|WvRWS{m$WhRlrU>2MG+(0d9x@(DY_|Z2mheQ$Z
zf|Rt;%D4Gj)<FGj)V|+pF<t$<-H21)DMpX(NE4dpcS|z=zv@FDt}uQh@Z`*(=E^h7
zK**SFK4<&i(4R-yS#DZ&4U!bc6FXQ3ArKTS*Rz1EZm16q!CiM=rej>vI(jDC>K(~Y
zm(d1`3%Oio++Bf&vi=5>=ri`x>w@<$+8su^N_NtUAdRceX$1y-q|RZ*EUKz|ny&iE
z3fgrvr2wU2rcawlj{qHBy?W6a5kzc#3NAExR%&UW1Pf^dAmNm;2)Uk8mOon%jrNx&
zTp9Q3FcZae0IDiabnCu0Q#a$b`)xh>gV6SLQ2O`ZDh0Sgv)Y$Wx@lBS-#DzB66WCN
zCeu=(g;9Mmm(e`|W9J{?^tz(&qtbyZ$qoH;-gHl3l^dAk!P`csfB*RB+Uc*eEEj!X
z(<>T9<DFnY94<jAWrrr3bdL0fb!OpPtbrR}8`7=lyB5JRTBxRTLis2}s(|)R4<>cc
zOpPYno3Zsrq$pf_W5;TJ*`q709-NLQ{A}!!5aW0I&S>ur5(`#w-%=vM&f87qyS^(F
z*W12f{QShww^xSM$?D$CaC1I<cg~WNw_i<;05m+m!H~3qX_Rp>6dbhZX<iEdEdj9>
zw#X`4Q#8r%J#JW1e*^hpYG+RLc^|r9l0c}xf#;Mzt}ABDD^uZ$=@(5B#w`9!rjRef
zd23*Cbrwz0&$9N6w#&3T5rh%1oK6MY&s{1a#fj$0OZ6>XOVxhnFDdv9sapHgI0;jW
zr*&Q%ns+R{DqGaF#L<}Of@woa$Ox7=;<epP6<vSzGdx$Ls!tqy3rco6QdCjsdq}SP
zyGy2~*e8W2dS&Kk+HCPmapT5~&h7@?!2I$zYqlBi*T|{o6*QSfyZgODDyGUl`CDC5
zmdRr*!^B_p7_eSIz=-#P8LLY4uWwK+43S1x_oN86Ic)>{M!8Q1A`msAo5$mxgoFg;
zm<Q@PZT^Nx-;#|Mxw58;MO@cmyHE5)`4a3HtZ#;pvJNMnPvn7~FfilQTa_G#DZmnQ
z<w1neWHqU1IUE>3h}K|e`KX?t5<m#7HwvokiAT5Z#L$`^9Gi`s?T_l#lDZ*GX*fcL
zoa6sVM0bvOZR^U?*s?yPiaF*PFeHvOO6Nyo)DmkRt5^M_UkemrYQI=PbrZWsza?g1
zYGvNgl6S@G*+CyzlSqTxT>l2_{e2Mx&OiAWm!^klCa`c_5b{-tgBZPgnzhBfxb7je
z^~<)~m+utT)f=5u)N-=b9)3~rUoLrkRHfdV#lM<+Z6uT{B>7h6E}@+<imMB^2C;yc
z>Gg@LwsP^85ZVcE`TkliNWd+0bMQ3Q*BN@k!60+-WoJ2?f;GalpUWfgf@4w7{dk%N
z8;Stz>NCywOC(B};ZKyyKwVkQ+d>q^u{)RZlkJPGPCKi6bj=4HB1jYp0;swSX{pDr
zLY7c;nnmZ5_k;q|Eya|YA*Q&Q;o@)RM|+RinZ0g}e-Cn3^Hjr6p7RerSFd&j;tH03
zf3CT`SK5}1JJ7Fo=rz0Mjq~h#Ix&sT{y4npO4#?QN4dj=w5niu2T_cE(1()j(+)*Z
z{Ggl~TI^G8m}qi*<u5j80;4ChSM=RGu(<VbgWiuwU6q{M<+~-sgD?^}x9>D2L?AP*
zVm;zY05=j*!Lv8xuBJ@x<1e4ymLm#K1q_oVHn!i48&8$e;Exort-yTP+Q@eXC*qY|
zL72(py@axU!+K3dG_)&2ryUyE*Sg1J$AY?B`kPZ7@*JGVzCKH&D$l14_-8e^=Wwu>
z4BnLB$;um6@bU=|VNfdCqiP@k>`LLvbA1Bn2$1i_W^)0Rv$g==`;BNgkqx8bsq*|s
z>o@M^regTy_baK-!oxL)I`tcpD;$y(6CF%<i+(xeM^N$>)o{qB*d+gEl_93P6Pv^K
zEL__#u9X-}tbKZwFBGIC+A0*Zm-oZ!ob9g83tJ`cXXH1j*0^rV<iT2sM=q-(m=8+x
z@=V5NP`9EyH+8jRe!8y|eypGwi17Ik59p9aRLKV%%Kgw19r7K16__iPQ}-I~bE~`f
z+3BZ&(p9}GxNjeeYDR5hv2cH)J_&y^8yVB5t-pMzyUkBwM7?_d)r9DQ?Se4xhr0?C
zd24RK@`$r{wYXg~f5H2l?ckwMB;0>udauQu1ZiVc4KKw5%fv&n%Qv<x^nt&ID(Ure
zzpTJM#|M@az13c(t<9eW-`ht{CX@&M=Ht=E6DQ`X%<{Wa8-#^VD2iD&f8%c{=TGeC
z{c$yWn-ZNv(KK?djhAPKDGm%=IoGdk7qEcrxr+KihQ8XGdOHd8i5;c#+<c+=9Qx#d
zP9KsO)fZ-!RZ63^TSTvVZUmZQ{Mycc`{S(4dq~>k21?R}muI2s<Nbv~aVO)PMf9`<
z@nb%Rq3EwuLhIRp*3g__d!>1>->PJDKw)S`t?sNZSwTb!sf4?h)R^}3x!kV@YeZ(G
z6@(<G5%wYXl`UiHqI_BveJqydNbGvlaTR+C&O`iPfh5<W>%$E~6?mSE-*VKFCLiIs
zF0~XYTfDt$k3##_kk4QABwO9-E4mSqCIQ39`t%3{8x{VW|E}-8Q~cZZ#U#2pQ+*v8
zu87TCZ(xX}b=4%81nGp0bmdh99JmEk>cTm21Unx!`a+6VG7(w1;WtHxSWQ-Sg<)TW
zKPLD~EZOa)CK^DI!J)&B25q(ECcyNfbU{DBnUwNxD#P}|y#Ow{zW=FP!S>j)guK67
zU;EsCoL@V`CH&@i9Miz@H7M+SVAYw1AS{AX5Kdlsu%wzzlM!bGdd)Gc-xQ==j&c=O
zmmJ<^M&0ak*%ocP><q<;F*m4g^{X%3M#>v^F_3Y&8i6itP82>?2ujLlmW17fDCu9w
zcYGrYnvUA~on}T#l0b+1kWT{>_hazVf`vFRz|NSvCD8=265Sbb;>cJ%EOWrW!u}pw
z7$DpdoPp<vE>@dXWw{I@B?s7d`&VwzJV)It`jKt7?j%SN*<v$BJP3t()*+7BU`7+q
z^Lzd6xp*cYaS2_I;W}gRI@6CGpSp+XV<RjwEevY-N>)+V7#=XDQ2tQ)MEhTygod&g
zO=4X?r0y25BaNk4RA-dm*=uio=rRb8Moqqv>B;O7TH9YK2@9mi)5`b-!qYR}>64jr
zVr8l3H<EHrC$zKCt>T)O_k1Att(Sys_rLgFy%m2;N;oMg0)0s;C+lXGq@feK^UAgs
zd^>v)$2R|&S_*G`wuNfDOT|d&rtbdklVb>B`1o6=1-^bO>mQai#sXT`-etYR2Z?Q{
z3!`o3CA)hqNfZ$~fWx!=wlYIY7R)B>OZDWQAj~?(i{;`8Y9A2#{ZAH%;(w$7`3EV`
zE}K9-{h9)RSEmf!xBSq&qg!+Fv?c@!d5C*_x^j_QZ(i)VPCP2_HIQq&$e#3@9Ej3f
zc8NF`Jb}>-)j%7MUeCrJmJicLaI~*Z4dhHRBYeW>FOU}#>Y4QKm9$*!$l8R8G17N-
zrRun2N9wZd@dMP`QC2O??w1q&w#k8xh#izeXA$0+^7-)(F0=!JHuQAQxU;0Bp%4`|
zp9g^#f})(y`bL1fV&%W>FJgqVqUOI@gJjg~a#Fiy*QzWJqPlu1P0`VSFxq_v>u+0|
zdW@pniCJUL?IqfZS;WOJ_5`FvLae*Ge(obT``;Bjm(AIe*6Ul#$+DCz78NJ8(4D2q
z=BUCL{mt&A7ZkGH67HKQzo+H|?39Of$LvBvk-S%;x!fPT0fg%Ax{JxU?R;EOou=3<
zP*J3b#=#41o#wz*E9Gspp**0ni*svc{)vW9u_-|AHm{c53CdEaNeJdX*k&vD>RRj7
zqyFhS3>WSMm$iBb^u&!;y|<6b9eA&c)w0p27Y9Ab>x6*`;~n^E#`f^CjE2Onj4cH7
z13$w}{ZGC~9%MwTW|defTr$U&<>hIMbwp_QO5lxD(~j@xjVh@ox9$+O4pTJ+Hln5J
zy71Gnr9_(q4U8v<uS&~IefjwAyoKOAfyldLsmOb=f$zhcc_Gl53gYjMfY%d1PGn6t
zNx91`b50CNyrb&kDI;|(!yg3(=%UaSv}-BPe*$d()YgZe(6clX@t`&TcwZhY2|*>R
zv%Qh>-YW85;-(A9WxEGuV3@HOE3uC9SCKM{cu-xe;<Yr5TTx!wN)dq?f2$17pW>n=
z|DvAOqvWhAP(vMO$mv?7?>?1EK~{+YX=##F0OqVxmPxGH2u~1f7@%1=$|ZTsCr6|;
zi$=$X(Q>c}9SlDwmt5h+JKQR9LL}j8ldtDcKP5QGALobtTGVoH@V}GyR8d?uzYW@Z
z{?(Qyc#ubLf_CHT@?5wngc+?5;}A0;jMzBcx9-B`s`7ma&Jb_wra(3yZ18e;<w6I;
zy4+edR%_UkiBYTcqt77OI;E>QJ_`gjf3=%)J#6@&J^}c_qADe2gth~z=-yzwp3Lvy
z17DczH{f`BCpRtZ%TUn;kr20_`e`)9R=+T^_TRXeXpm^j@jeO~c+RZ|Px}(%*#Ij%
zJ_Ql{e=We`HYGlBRz+X7x;X3<3a@EYmr$0;ngpf`#W8T%7!d(3O=24oI$dt5X*F$N
zFPO*KC<hgFE`}?!eZ*t>qzgo(iW#M-Z@+68vOHS-#1XMUJ}NtS<K_9!Ien53&pWP}
z`=v$bf%m{{*raJWoXYNG$<2mtXFl5uAr*s~)%QQvylzh1RsSg#JM$DJVU~GJo?FCD
z3PwPXGKP?bf8@Rj|7w8R7JKQ>EhkT5RrG*cs5vXrZ8?mV(zhH{@g{Q;BlU^w%<TES
zV-AnC^BMk~1RuhVgZ`e|408xohoT?;<f+2kp~mIfP&0#&h}*!*zPJ#|xYI>-a~iTD
z09~IC_8%TBwe8pYuH!UR(r|P>5kw9*7#0?~7}m5H(N;Z^>d=kY!Xv1vTo?CG|DC}H
zqlwicB|*pb6O<e<(;=cs^GLYt&#16)S(AX)cg7Rg0ynIiVzCDw_FZ<8;UpvjIo+2?
zjfGL&_=WPOi|~e9G8V2=%whvs{0CY~x1t-Z{_Q@*g%VwxEWiZg(}wjc>-PG`M0;h#
z0)rflE_eCOy|JT3$<bfhr5k4cWiTRY_;m-gnzEDfu~pG>;NX*5%0ZrTlx3-e=(nT%
zADok?sBEQ!Eo=GXb>{($@chubJX>gLRK*&H`MMgVg`D|1l5#kNk>b1vVI*@P>gwKo
zm-H|a+=j$yGa^3V-;kwvaZ}CW4LQW$x{RvrdbrVyd97a><`DUAY0}?Yu1RqlCu@`H
zAq+pJ)Te>vD8XUji?3r7`bGsTj(XDA!LVd4_0cnVa&aE9Olv|Gw01>XJd|Lw%a55w
zfLkQAGFc0b$|_>LTSPokOixxBIH2c@A)6>iQ)Fh7QcL1(N|xA1k?>ie11-pJ1b*3B
zAiKH_Cpu1)4S{3Y(<6IF-{g(YjWk05W@Bx!yDLT9eq)Vt9d(uxQw?5E*2a+IbNZ5-
z0$#P9o@%$&(-x<Ou_BR5lVD5n&bPcUl6REd5@Tupxb0@f3zQ8#kIu%u|0z%(y5v6Y
z6?&r2Q*Dx6u&6eY(6M;zzb!Z%`h1=xM0xyQ#iAY}xK@2#NRXK|_R5RXQlU*NGC>bJ
z%({PZ4A@J|?8t_%GuN2eK0`e^L}!{X)z1jOsDrp7ddzbow;jfj!GR!J05q7z0KoE-
zp}3K>N~tWEwlN}w4hT-a_xBwZ41G?q;$AXw-tENv7XoP&HTmX64weitz*i8C$j#7p
z+m;%Bs83~?>qT|+i|`}2!fH?};%bg!st7uM*+DDsF*_AQatIP9$}kRG7u-KIg-9K>
zPrX^GePhJxqJsO|#d^^avmT56TA*KDV2n<u%yFn;s?K5O75sPcoFWm*{13y-B0^|M
z&G{FMLRuI6HTCr`g1ej7xRpnG{$kDbDZvFvlXtHkkS1tG>cJ=nNtq$=xQc8=hGsf(
zFl@!|ndmnCsN_Gqoi}iKb~sgvl}D?^dt;-U^05ovK4F?Cne471(cTWY8EcKG!K&#2
z$cvAy{TFd#R0HUiJxsQU<_wi$NL=MzPOh&V8*7+@t@HwAH%#na&_D4_-lP^q99#Qh
zG_6@0^9sEF$8!1l+U}xuInX{o1kl|cylcNw!`1t2Dq2jKS`<5D8C@493ZYI6n&^1V
z;p^2RZDGqh$ZqKKV?>Do@A<sb<QdC|((URVh1)JPeNJMymqRlMkJ|CH;+tCx>EMib
zRR1Z>bOv!FcU^X$RnCq2blXl!TVhaiZ-pE1wm4rL0KCx>{+wcy1ZV&>2saS)zW296
z6;V6wu<h$rfx0~r*lCw@dJ`XSL;RqR%nEt2PQ`5r>9a$R{3YKZsfeZJ2u&kRayY3{
zY&4Mt-CNNa!0Ml^O{?q3@=4k_VKn>yL|F7oC8hgyG{vKF2B^ozTdrESf>X~=(+h7=
zv-pOY=zCXgyw2|kWp$FK$TsDRpu+$&ICoWQEc&zcdjC}(O+9OJ(4AVyXqDo&;W7TY
z{@;*KARt+W64Plr)2piJ8VAIWejMQrRj3>vG8nAyh+pqto_aLixfsMf{)h#9=Bh3*
zge-Rx=-!rD?x)7pN+Beb_8?tPQ#(F05A`7~DApuuiM!S34ViIZNGrWI?-8#@_pJq>
zWxo=gdiK3>JM8XX^1sdg@7+&0Ekj#v`mv%v-51?uhh$_J|Bvrp!We4N=T`_T_S<DZ
z&<v@h@CVzGw!=8T>NJtkSmzewLH%zt1R{{t{OM*3CWd?NE_(Rx(~NhE#Idg(Y_Yp^
zj{(1Q1pKBrYDkb)<hiO;@;bIX*owvE$kO7wYO;GC7d=&ztDI2FI*O30Y?jkb#2Ib+
zln^X<fk0tZDh7z_`3z);fzB`oRUKgIoZqWtCL*JY<p&)WY|dvs70^+5AW%I+fP3o1
z)a8;o<^aCu+uNSyl`kGi_bdPIq}i5=6z}+`c6WL>HM=J5D2aakwsrl)UjCP(pr(qF
zC{ftX@LoTX=|6;US|=r8!BM2tYT8?P{ISfhRdYhrzLa6<kjs*XBw*~hY(s9KTh6sQ
zEJ@QHvp%WeRh$wnW;BPKm8*~{KzoXJOQvQ_SP{--<(QoLx3vE)EGD7Ku6^ORw`I(t
zL*n-lANQ6SwxDbuvijG}spaDTi)IEv4=}Z9xTr;MJFS2G52sIRun7dV71o(eUA-w#
zhC0?7w|sHM$&k8c6=%B3yMrwYFxayw=0AIL_QLFNYpkXc5_A)@_-;ghZVKACU7x`s
zMv5`{&G2LY3(Rh(9`Qa;K^;<7O~gO^?iF$qTcOXT(UFhyu4paPl3l@7ab>?ym4mf2
zmGj|^*YpUurg~+;PvQ~owWz}*4p_6W)y;}A)QzQ>9}RNx3pV>JB0#}*b=RF)U7g?y
z%kR!JUr-n!QF5Gu*-$a(j*}5xn(WDUp^v+n-!pcc-O*E}WGvts+~IpF*@9b1lhKmC
zYI4rpSi|&^{{B{jIOY4%I@F@QJ;_o5nwKtc@E%#?ZbKfM8DxMe{2BB*7M&l;NoigP
zW$2BLP!kr$zhdS0{{a0!0>67<^X)A*P{8DOVe8#3Zs+6U<KyG=>fka|bGSM&CZ1vC
zzrC}exC>yMdx89X*!h977u3Kj(4&e4bpkyJ;V$p@oAjW_njVIso7*3)DhtX3wHfI)
z`oppYV|T%(yX>vr3Ht=Ek74uzb)wM19$R_{UHLG29lf+^k7v6o1h%tsbQ0sjQ3~gt
zC!KfT8`%o0XJPPQ=TwHtr$D;6j#dBO5<Aw5yRD!F5sBMDtI-}U4&fGyy9ixfmkRB?
zCS1i7Gcf%X<f;E`BXZyEq(@QtPliWa?#J%o(&|3$HMuzmdf@xqZgICn@`UnHZbq=b
zJ;yimO5BZZ>s)`T(*$}TwypLup+m-@cWOPN+f*S`uf$zYwj;WWe)BqluwcT;$Do)~
z5vGwgonIxAQ!PfSy2OpZ+p}}y#JwH6hdPLB-wWICtG(>H547CZ5Q$ObiO)N3kB^U!
zkB`sQjxX@KK}rgzzQ^jHy_=OkegNa_)3!D<GcLu*^n{9P(Gs2Ur;`Op412%d`Ipyq
z?xd+9%@$9|EpGwYh6>BIu%jWQ&$ahwCG!vz(A_L5Fwh>)x=I?Q^E)Ba4KF_m$DV?<
z@J6Ax=;44-3#t_1cBFmEWzbxv4@$_Gdsut=d&qP-MLGN8<K*-<2t$?3zW_0h#q@ee
z6Q1}q6hh8^H;FOmyRrOv_q7;hTY-qb7Q#Cay$>N`H>|t1is-e@L~kvw3V8Y0$4DZl
zzKlHj?~v1fZ|^#0xGZd$n^E6yZpK;hEhn@q5I;1u{(r4S+lG=SamTRnyYfujt3&3T
zO>w`?_f%BB(lbJRDpEXsPFW^ItIqAnsJGXr*bWth;Pu3>G$3MQBB1Ghy5Q^tOdT%2
zmRp8!Uwiw~`Bi1r&?y#<!thPX`k__wt7_Yl=$+W?+%jVOy|Ci}#2Y`1xc@Jq|Jw4h
z#1^%@RpO(K3)A`d`1ttvyvp${8k|xrko;f2K<?Quw!Ep(b-+bxduet(KMRSy?T@s{
zMq!~19&PzG)!`PaAR+bC1@b4KMC%<T@uoWo#G43uUAsZHA#JlBMH_<_(@+tBPNN8I
zA)#-ls%&0Q^wdK33S77%2zWG*ODEvWH`ViE9wxpIp#<!^zWiIs&8o;US+EKTIUERU
zAqWqviIR3uOv0hJLe7NA=T!=DeifGN{Z36SL252UVd9%Lm#3e50{zep1PqTOuPO=k
zLLjapdfUzN1U&j-=-v#k``=siF-}6F7rO3I19a2jWKU!d1gy&3A^_3r5#e3P^br+-
z8{Xw?zgishHe^3st*jkGj{jNf(SKePvMU`kH>08+4G%I*>Jc7-bQ|ueprVmWM8_a=
zK^4-9jM?)U*Tb$N_F6)ZKz6eEdYx!bYTUBxY2aPjMt2;~4-)JH(=4CIS?hig-&;Np
zGLuT=4J1?~ubrZI^@#6Q6Q=E&Sk7KlZI?OqzVxU%ckFun=6m4ucUAwQnw8Tqbf|rW
z)<B7*Be%fpk<OgYv(Ku(gV)3IsoKTVYLUFC9$2*>Rwtc(r-2yamR~FXKXfDFt)GVR
zN086{3F5%}o%!g-N1?mLY?`Z|2Z1*?SpFfP#VWWRMFZ{v-UZwW^s7qZyazaUxf|!>
z<KuIs;S0RAkS6Bp48{3zwC+vlL+c0k(#Vti^iPw2@t+*+zHsp(;msaJ#3oOwl(<YA
z?}2flB6yP?`=3h4jjxcOn#7nqhRmtKg}HQr!c2z1t|k$Eeb<6?8M)O8D>jSxbRftF
zGYy;Wh6`V-y<7{nza4tOn`30V%i?Y&`6Ohb5VgKzGh4P(i0xEDTrp!60kSzL)}s*Y
zRRi00lAl(AX=6L#==aqCDX|%%!|J&#s)?Fn!Kyl)RUWY6epa77iMd+ek5A?^ti5=G
zuIu*_Fxr&<zkJeJ^p6`>FT!IVLA>R6kfAJ?E%=Sgg7boZB8-R~+W5K_Q<e=f=RCSg
z_XXZdm^o!3P)w@gR@I;B>WfO;b>iz?Scc#L6c%i(+=OBVq66&}cyn{@o187?)#qDS
zE??)086{k6p~l|q(JfXMN{5JSv1gIvHbUDj|37<g9wk>=-uHjrTYFXS-RhRq+PBe2
zvq&0XRs;is83u+e7!zz9_&LPH#>Pux$Bvyqa%}7Xu@hrX9Bg6|#>X}uuP`uX28LOg
zRkKPn+ShJ%w_3eb*Lv%|zdxQ^>gw*Q>bq4-Bi+wAb*j6Tdv9&`-uL@{pYKx`7J<9b
z#A&OmVj!3kh-jM}W6V05PU)<D>Tmzfs=}`_pnbbMuW$xT7tJ%<wm|ksYZdTHZcdoa
zY?8lK6fzruh)ir)mh3;YDc^H#A79JeaPZsBmp}HrI9IE}XwaBBX{gqB&HOyuR&(xU
zS!cWxh8}bG+$ryq;OhFHh4g}Pjxu1=dr<4%=KYwOSq1F@xVbMcJ_LNC$^Bn+A@HVw
z+kqv1FoDqn+z-3~7ze%si~s{bYMHhnBqSu{vf|1Xc&!TNiD#&c9-(sXD3!4zRK|{A
zojZoEY5o)2bQAGC{{qlh(<77*J&JkkNzbb-?SGW==6^}7JD`$tw<VZvDNn$rEx=81
z=wZkQ)5xV5-OB8v^&QZ~r|&1V<CEg>u}p~Aj#MLRk0B~>_-QC+AsQD!Ga8foBT*^Y
zjzsPM4f}6H{#FJ=m0TMNl!FpcBL!K9179<@Jin|+lfjgq3^u1IKM@TIX5x@e!m&pi
zKkUr&ux0D~L9Y=P@uF-;7ew13xl%-od=s%Znt@2$+<<mDn5_{7YMn6+(DAOO;_ijV
z<tA*AcRNwDMa`jdBha-OCR^n+tb?}DKl)#&_xu%@L+JbgsI*XM15{>ra|fvMULLND
zR50$+*Au1lGT~SpK^I3wSS*f8W3ejHcIdtlm0Ant6uLA4<Bxc6+NdiKO9vzHVhgaX
zCVNO6wi;(HR;QR#_N3Rs+ow_OSEIElV*7>fwY|So2Fi$|jpW=hQCE+TS}t14zF1o#
zrcooPX;Vt`t&;Q4(W#TMcuoYNRyXym<i&~FP;_37hz1|)NUoCKmaa5@4doeIkX_JN
zG`$&SUbX*Gl8tO6rTL)Qq%vYTs>o`Iw#`L|Xj7cmOObQ9Ul`p71G{0QMI!IT;@r!q
z+kOZ3d<K2s8*ud7t#uK1ZGo#k()fNqdDoE`s-r=s^p(q6Y0^P=gZtfl*zW}X%obi-
zO#;{ltg>Cm-(9XciI9+xkjt4XR^YW}#>jr-Q<M)qyyRocM}I{5=#K(jzb|d<Vqlek
zA=tJPtR6V{5EL7`YRb{Il=D$i@l&X}gEE8iMC0eHOs9iEZzr7ip^F#M03!y`q&Rn?
z2@w#Z2@#beafrrIZ7a~t1l3yd=b(KV&W&^tI<A80I{9eJ@&$8QUT3wzbRIfWaBdPt
z9As7(CSYg+R;>YLe_vATV76v(YR*8`zAxHli@inLy=H%Au?~4piY@Gxy$Az_Tn-dn
zlq~ApBr`AVr~TR;!HT?zZV}50<A6f#`ZW6R-$AyHXcQ#MfcACLS$p~<bZ<ieIvec1
zcOKCdkZ5J|n`LTNcS)dO{89Ajzg${~GiPAzfnY~+L1t*ST1c!?b=aoY+MVf}{Kkv~
zq}PL)m2&lZqz0QVLtCY$j#-Ue<>0jJy&+1Dqee{jyGGRhd?K=sQ}#q_$?4>cmRO7B
zn4D`Sur5bwy<35|ZJWG5R#}97C+|`2q&#o-u&ggJ0J+*|3Jv*F_TRSH8%aR^?EDyq
z%r<G1x11zaIg1*p#d7hvjkHMQ?cXC&3F8M)*L?~-c@R!L)OuHVyaT$o!R%Sd!@c=G
zq0c-b=T<F3z3DevXEK;MBj*VrwX6k>yA*O8@$mqb;gsJ1)&VyIEj-Z+2?+_gvbgdD
zUaLa+(8FZ^;?r0&0Y?rvB);t?qHO^-j8e-{HfUoODNmortZcx_PZCKdh(>Z~VpJ+I
ztYU@A>@?+LQVM1c?jW&h0LxP7as{hUz{+Q-oIitZ(#S=n9h5ca0&1>im7!F&C&25Y
zl>s|%a5lL-dt!M6UVx4b4FulhaPYbicy$UUrlq;bP|RHumh*>T;s~t275Z1t7k3w8
zX6Kwq(Kbk|lmS$E0!jh7`<zm0mzW7xxN9_~^V7^c{{rz%yHUy@oeH45I<peaACSK%
z52MHSq27Bh4F3rI>R-ZeK<DAzSHZv@RQFaHfOc+L)J#d6t^CXss_l&}7GbXtf!CZt
zpZO+Cc&}{nhmzlZP{caLiM(8tr=>YsX0z;9t)fKIMA9OV>WXCUXAjE0y=|*~EHZ32
zZCPS_nhC@>5D(+M0qrNX{Th}y&&h0qvcrZ+(M$l_<$%Iz5vS^9*e{3h??&*;Y>_N^
zUAEoT4yR14l6;rqE5xO%3r)o9g<|g-sjNaRzqm^jiXKFMx1Za{K5?N&(@@UBRFhn0
zCv<Ov(YeNM`jxMt-toWThF?V=`Wra(w@?hAQYD&(HGA!2s(oBd_02yH&7N(kxXb4E
zLVumeqoBy1mb~PUTGj&(`dr3JJFEA-cB#U>HTV5GP<!H?0e%+vD6k7S3w#s!L%?aS
zM;!Pq;E_<=4G9Se36?8H;5Cmw&FnvYmdcrz&?Ud_6n7Y1{j|U9gBU3-CtA@CC<K^S
zR$M-zI(HyP;hDd6{CM-se#|rbU9TsSaUk$^EYpAwAk{5pjf(^u`!m!EVkt;=OG#_2
zZ^3}eT2SIzu`}Z|sEYdmh-HZ=U6=*4b8frrYFd>y(PnMeX5Bc7V&T^?)dop>0C(Z_
z+Jnw&X|AfsYe=mIZP?4Mmh;*orK)-U$=6`mZeZf2!?w0y`V@4!82p-9Fb|7p5$&9d
zbXYFVdMR6V-*iNm@)Tcv9F)Si;cX->ALX)%?m2O{%9+Q|&wLT}rvHE%d^1d+K)?3a
zaP%Lc>>{Ue0c!h4WH8te4doV=$|tXaNUJ-WyA$kRUug8Hdthe&@=u;%=Wtpj*$){}
z$*>NJc<=HFys-|6uP8edc(m!gBz`FeYH3{DoXb?{po};=vvu*YN$Z+JtsK;p5l6Re
zogWi{WxF%&<B_h|%}`4s(7JNmD)}rTX^8beWmdLJR}W)K;#Sf%v5@n&dx`ToWypB~
z%6>_D?s>X0m(7kP*~H4QA6I*P<-$HiMN;T#pINS@F*}mtl!FJ`+nPTu+tRk#&iW6i
z(W(<N>z!pbFQno@n4h%utj>)hoVv**UPx>~lxU@de(0A`cYYnU>(g-Uzk%cTqhI?=
zIR9#+r7TUlU!oYAG4ibU<u66N1GW1XTep0G;v}S&$w2Y?AOa)-r$6FG?6FVu?ZFDQ
z1IyYU`2cXhj)S-l_^-eQ;8Vaa*%1%_>|lM@+uQzSpW7W05)u-!fGa}a)x|8?d;Tqz
zaqkTSyb{~EgZA5R0(102PYcXZNN*6QNIjQ`8(K9OORW``MtO2x9-%d}JdIdYs%_~9
z8B@@EHH;rv`muh=+qsgBny&!#+yF6K)GfOZ-7ky_jhgb+h&`~g|E^f@{I_6s6mnxw
zu5mB-T?gl0tiMPvthoug0(2@VL$=!w@eHiL%3H=}X&lr9B-cX0?>VqTDqS%BjQi&q
zJ_JFnG0#tdAI-9DB^2uj;RpXl8k=1GQ_!&<^~Qe>yM7LiehdBDU%|A8eQUnSXQ?ab
z?Bh@gChvO@Mhca_wl&MHqRS$HT&|2hAi230gL=82k%YJlgJ__*l=IXJ5j!g!>?#C%
zFCA$U2k&y=WFj%r;!OV<v@R`OZlCCb;yI7Uv}#mDR8DuRQ4vN2h@fI!=+ZgKm^EkS
zgm!HOe_j<yOQW!W(3!3N7vecTS4*W#dV@HKmn$~Yt4qJ)qjG)fm^4Vu`uObfbta1n
z6X@^%0_x5`ml%c3ccV7H2gY8M3Dgtca~}y(SmONX%p>ThKJRXsE>OEaEhdLnq9RvL
zWsEbbJM2N=CxA8f|NDWb?8aqIxX-?POlHXVw{;$40FT?^?k?bkn)`kcc;0T9wgy-#
z)9WVt`bFfd^=E)vY=QY9;2xkwCx9U#At9GHm$SVHs#&}D{M<zmcT;=bO8Z-OgIVVo
zl{*fpP5xIB>-4{jDpfHevsp^=vWG+*YugG&l1ed7`S=S<EhP|C%3<@={#C8s6hUi<
zEa4i+o%R`xVA)-ti!u<jvQU`@a{`V%3qw!A)baV^E<o<AbV>HpxT2Psv%xH<itdML
z9~rSq!OnO1YoMep5#19jyf4EI=e=#K_Bn7d$4>ei{6ri7?)0;N04E=qyCIf=t9}CY
z-g{AR{|c<x>uTM)(4aJ17tzxXLaB9Pyvp3r`kd-Y77PcK2(LRdOgxPq{`=)$wGoB%
z#`>aEr6?1U%I9f~5r<qrnby_gL1F-`SrId54@qf!a!~Gz1hn6Ff_C7x%$=CqwpQar
zNRRrNv9hBg%votZR~i@LHa{fI{jvuov(}uRFH#mq<h&=*=VRRq2y$7`cA0SYLvqlY
z8@86*afyjo4pM{OMR&h0<Ft?ShDf||e*N?b^h3W2m6Cmff)&@JZu=e72k(RH{tcvh
zov*7jQ?slE9J&|%(64|QV5LJXy*pvc2U@f2TKw+cFF&Go_U_%lUjkpWFZTiGfd3Mp
zB7O_73HZ_iaThz|?nCz9zvf_B+wALWfDz!Q?d|QeUA?2g)d6jHNJvP?6~$$Jq%@EJ
zfXOetg-Az|&QE=Twhw-$ahZBR813D3y#Et){i~lNb!{J5P2wO*qtf-b6(k0nAJfz8
z>~7u`q&LlXNoWhQhbWy@Onvij(8YjqZ<j#D9SXdWX;`_t)te(!mMEVujDXpKpH!g)
zuie-9{@f^>dszgI71#M+-}FgOQ2`B!6`_5l_vi0?H<SZ#<yDF@_=$D+UshAnF!H>|
z=la_}Su>-Qq8q#~pwfIGtRMSr7<+NStqNA%h<fWEpx*xvu;XJ8cOY!mbMRKO=&64O
z(_t>B7h<a*z6?!TtgN^;FDD8k=%Zgo4}DXF*0!y|PBJzky&f`K<^9YZYy3Df3+c^^
zvYg#vK%~z8FV^9F-x2GOCRQpc!d|p}ezt09R3`LdUClGagQk)AvykO7$dw%!wDPCj
z<-I#4-q&1U&K`o|IY_P!<_$3dbVi#q(rnZ#u}%@ZgJ|$Idq{qpt;X>2oAwgXP)o_j
zd2idA=I`_9bLb~Nx7Y=p>O)=kv#1YzTVfZSp4%;Q@oMz*UqL_lyRB>JrVP}Lzp*^x
zYbfw8WXcvr`)#pT0SVh-`wZ~gcGhhW?6t2O<@8lW-w!)j)_{HeHQUX5y`AfOJFwaQ
zK|Fk=R2qkbgoFgiWxM0lxqU?1hw1)>-@b6-6zSbW&yGI=9YdR-%O*NsK+jB4eDxWM
z`yQARIFur~VlC#VJC{Uq*KI^Qra(K$(<@KPC2Hrs6+Jj7b0;p8FoNyAEl-NmA=U+n
ze!DEt08DYN#CsrSmr<G1(oy-s@)kFf(2-uU-~FolZS#SVNGynbYC>-(j2Nx$Myw)W
z6qfE$J97-W0(L*W`h+tFimr$_8%sgiN6xgiz{-FTP}y*K0=C=$`@Ze|x$AGXC-(!w
zoRW_9tt^S2v3!)Q`X9WM&dn0{YI@5pk$GFq4*apNN>j9jv<;&6{1ROEDLDQeY05U)
zK)|Y7erh(K6!VRN%Dkb4%dbIKTJI8GP6|Wl!(S3NB)TRuR!Kv{NJc~~BPN4z%Y@R|
z`Pr3`v@{QMyRSB9oM+<B9+LHEwk}=%Uk|GwdF$0D9x0vx03ZNKL_t($jqzR)#Hvj}
z)0=AY(~-&ob5;ahU6D-K!bvFG4XBERx#M#!Dh6c_4Ws;^9SXepGmzQ<`NoY<10mkG
zboQ`S5HZuQW3`s#8klw1IIA$^{kv3)<?y|C%IqO|9R;_OpHcZ876Sb4%^s45re4lr
zolyJx^Mc>^e)6y#)8N6`A9pYTcKo~O%u3X*pIbbcVZ>m=ov00W!ubOdiFEw_`ja(A
z49o?`Pp!R0D7j(Vk3-Kgm@Tz+dB+}kXW>j)$rfAp*0^|o&-tLLA=lg2jdsQsaMX7B
z#_jEBMBKjqD6ntAeMf=M1OFM=S;s9L5)u*;(uB)W;MKW(kgw*lE)ZJm=2ps%Vj~rW
zo<5@M?<Dii_h97}=7}Rj2G<j5*FciO;}4Vj!99-F9bL5=aM>8BS{@j+T@`MyigL)#
zY!q>*w&boVAlH)KD1xtx(mbWJ7^w_aetF!x04kAmelDW2F!)9|-NFv;Z7ZC0`<^)r
zJsX1?%uP(fu!}6$;v@|0fsyANJh%yEB_4pFFvl8qCT~Rd2Iz_`=_++i?vz9|6kF85
zYxEV*PgR%~8s&L-GH58BcmdtF6J@$=5*2Tk63?Y5PNM(m$6??G)TVdCx;rGUp_XV8
zwtN7!<^3?a5B=(2!Kv@deQWljw*5G)eAD7(N4ijLx1wi$=x*DclG?F+uG$t?i!3XJ
zA@t$@-XH^0+YJpH<YOjQilbFqB1Wm0lv~%COsq>Z<G$gUwnTJl+XmT#?w$*C`Jy1A
zRc#Zwh1(tPh0K6Baoq^lzFfv0ag!}<&EkD$6fi-)SITgov0OMMlNeqzV4*cl`<g`R
zG$ga3HLme!23inZ4Tw>}X%oVF!~<x^+dk+`;Elx{JP3H@&(TNz5jNf>$JOp_iyzZ-
zHR|Ti!tT$&;lD>8{3hf^plvm3>%V}_?^~RKs|?gFpF__M!MOW|$4ipzL0w-juC)c&
zuQkLmc{{e@{{z+oet-B?&7j$Vt|o7!Db>atPc*pyd$z!PO(^h&goK2+<MI=D3kPe&
zUALGRDTr@hS2L(75ZieJI23q2yGYF$5uGX?oTye2&Yp!-V(Cw`S$S)d<)?3ZH`(v~
zwfpCKCFb(0*^`2S_uHMR?ehwaxU4M8zS!=niYbm*vm`Eva>>qbEI=tI4v2+0WeJC(
zP|pp)iMy7DmzzX0G-C95X^1uBBf~V84OZaQ7VLT#3>}BFFD?D}cm_6jY^vsjSZ8Yl
zULApaohD@tQBw!$c=NlMe)u~sp9tM=z7@;pKw(Og!V#B(Lf1B!IUxh6Ne6DVk!R5(
z&%#r`2WxMaLFuZS7C4X;^zT9S?~%co){t2ut|LB(>be`sL+H{Fm?Ocs^OM_9sh$3p
z<Cx1t;H?yFao2(PUytJ1#m>ImQ4#H$HLbjW64#cO9L?-OyAhNJ_g{HRs%w^-lq!wS
z7l0iv-}`>T6K>zb;uxx9C)%8`8-Usulzn<+i@!?S$6ZUVb;Z7zcBXt;j)_*e&V;*@
z3BPEt6&IP!?i-6$3i3QZ0<SqOlS>tkzoU8-hTTnKcy6lZfZPcYdClcB0yt)H9Tc<f
zdja(ChT;??x?t+0eE;1Xi{c$H`hqOy+{;V<{tD;ez&Fqbz5!iZP@CQZ8}EeFf(+nf
zH(c`x)XtxV^RGeA_U6$A(In~}{~OLejUIXo&O8dU0l2N(*GhbZlSrl@$ew|&Wrzd0
zyr>>%f;b_0)xPcr>iw7$u+<iMmpZt=Y+tu8(Fm@ErI{fiAt9G1m!H7vw(G2uMNT_+
z4rIUcO}c*kZm4)T$t{jaeqhdJ;|r?`PCOtE$*bN15g$&62E_V%=zQy4C}jZ_N}Hf7
zSft4xKT7GuYk{s$MO|j@Sy_m!ZamOYcC2g!m{;Ltch_cNqZ_;Xwu*rfMI{E%SqHDt
z%!2B2IB;EpQ^z3dp^Q>n{vA&<L(o0o;DIhE4Z}be%=E+TX!FPJyaUQhHR1I^_6Vd_
zOJqr)_*ccF9-51_zv;(N*;nV1ldUz)pRkbLYhYr(M0@1NVc-UtC~&ert(4&S{pjQO
zL$U`pzN^N8R5PYXyZAmu+97fkDtVRsmdYdO@(`4UY-gbhj1;QvCduAiRxT5P*NA&N
zo;4%dW=97(z|4Ag;$oNh6P5T6rzis=Nywj&s+ZjH;GL|+acHx@-`cV-W&4;D3*KdE
zBwUN+diJEmI=FSbHbO=12#*-V+MNmG$_lO#U9`=6)Whr%ah~UW9G4P3kPA@YHM8=&
z$ZUhzC4L{N)&85RHA9;aUkj!O6Tworsr;#jISH$FxD$AjU64IJKeniMhjSNfvI{b+
zVEh1#?vqJ(a6a)qc^LiNAHu%>2`k?uV(;3w&UbCAh-{M+qA97KS+iI6WmCuC%wy;?
zkIMGB9XoCNki;>0aglqaGy{oc$b7%NxYNFNv*T+t0DHu~-V4-gG_lrxu9G~rhwSTj
z1AkoS{%V$%_ma4fkdTlol*>=xjRa7NH4jDZpTFVw(N=bn(wP!*uRW!5M_mqP<8bU*
zd*vn^egd|>2@D@jlSL@h=@*I2EY5n10BwW4Opdl;<%3(NYk?R0y^D6(kr#fkyKhs3
z=nAycfzh-r0(Y%-*0H=1<q90U-~00?4@2*E7=P8lgX=JT8uTEj0EFsVDtTD92M&C<
z@nd$ryS3sj*cqbP;2lRgfP6S(@ow2jx1&o1v^n>kimq5ga^rTQX#-<s!Tut98amg*
zRD<ljXd0pkC`>@#HR3Lsdl4}5tUSL`c2|~KI1dNzK_9pWx;EPmq<1ZLAh|(B#nl@h
zgbYxbg3^!(zU9&8!drYDs_jjn9G1xjhQ54ym?}du+r79{8<A`>8CMTK`}V?FiHWcZ
z&YF4wWVXz0U+!3IoR67J&}`B$=yiI@gRaa3lRsNUn|8yiyhK|#al~q?Mrijb9=iSB
zEyCxdjh{wg%_uIBQy=RP7j!H86wt!oN)Wm1)`Hir42c%1jU_T-(6w2PkJ(d;GwGLV
z_E($JYa~S6tuk{;mhUz~OItAfBlPf(WV_bAO(swW-r%F*n34?r&P}KtAA|BNoPA2f
z-ZPIuzDadcvPWVf25<GaZXbjV*6Pt^H(INABJ>k>hV3^UIBKgLx1W;%7M>hG2%NR^
zaqn5+yj8$g?7u(nU_CF{BJmf2d+p^`$=HqIrhyjZiiCuOgk0WSb^@<11>3a59L-^#
zb?17>K5#ERKlNUZYt%9TNo|luElZt{pUclL2`}g1=u5D92dIFW6_q+*=IO@w7shFS
z(_5JOp@$|~4Nwse11ZatQaY;`oZ|@FS&fnijq=pe5e(C>$>X~Qy*qi&9Gl;q$P0ct
zKcl75S_|CZB%2J9*53$f33qQ$nA6g{CrE)e2tB-G1KoSu#W{&amByhkK{>gDna972
zk!qvkrrR*4_Jes)PJ!zY?*?^xu`?%{mY4)HC&H`IK>VCK0g<?rmyRy%f#HD3Bk1S;
z2kiSJSoucVfpoin$4{gaQk|&O)iQ}vJ}XfU<)JwtK*dm*H$q~Azjb-V%C}&$@gh+i
z30B;Vb}lVQEyOY*HQ;^nu6PzADM+n>{1Q#6l7ou{s_Y?WE=i{taVRdapUa;LwxmB2
z_ts)(_L#Hx%`LfOQfZQ0yR=*Rg2?MJZUZ|b)~`V9SD+2@yrdR$s)@TeD*K`!o2oTq
z_6Q_b1-m}K$7r2|@zc<~RVF%0(-IjJNr1}9F|zj>i6}bXWKw+MH9K#+&i<?adKi5X
z`uD)hNm>3vtg?u^-P<8QDifk^FmrJ9Tj-<Tl8TsWwM@N+r*4R4BxY&t?Q-rnaY)>~
zLyy7O3v=U;b#Fu6_#fpw`(m(^z<y=&uYq3xz7D)-M>4Fo#oc!UuK_>fVtMxfzYF|5
z@HzXoW55}^G0I)QbM|sSYyZ6p_+{W$;H$uo9IQtJAF!8m5co}d`?uLm;reW+aKJ8;
zkdTm&%b&|j;MHX)1=lUs9LqEPr@!I)c}6S%7hnGP(oTp{C!Bq7@$H3iICTQn4F=FO
zH3lb^Zt@kGd70GqH;{kTMMJPgC@`Wq@RGKXKPk>2)#YA9Xhv#K1OlgxKBiv<!+>@V
z&c%uaN51d=d9}DHC2T}lH!jrjwcHWdb_X1K(9UkO=~@R}adG)B7x|O^%D+LJnr4S&
zCZF=z3!-Zaj6PS_Cl;%mqT|*(iK=m!a`4%XJulgK-CJPH&i{*~?2O$SL8X~nr&1De
zxA$t89fpEK2V^bUg5f98!%sr{8q}R%4{m^{Vh~@8ireL{l}RX{h4?x!0xIkFLM02)
zo{P8s0MX-*2Dh+Sx9y(y@ICTNB`-ozvmDJx!j7Y;V}_bN=q*C29;ppWi^Y`!q*p>d
z7fke2qyzABOf*F}Y};m^j|3D|5p5SC(CIN%Te83QDmEtveeUP+UmX<WM9Cu5oKv@!
zRy9>?gtp|j<~U=!0m)ThB&Av9tiy(kjTjz-^L0M^{5j~m79vp?aWIKlDT%n-wME|V
zYF7P<>qOi|!>9vy?!>EdZ0@@j&N=8wP><Y*G-i9{&qZ|I`ay5YS%i{!rS5I0Yd#@j
z`0$hRxo-HeiyJ)@3cU5W4|pf=+Y4?Vx0{sxH=xkqx%K!0umkuh;12t?ch~|iz&>CT
z@HOC%YMwU?d<1aQtmQbc0r-Clmh~d=KA?%SC?q5#B%~3Sm%v*(6HN9gNeVxDl-&2f
zF<*dM3Z*bo?L<}v<Qgjs+qrplPLg#7jx-r~PoIS046N(`<zsM|jY*S<CDEkPW5nNj
z7t@bEh&H{S*e7<}1Qj0xsnWQ7wPS5khVK`z0^sC+=zO>21H0kO$@yi2UZ@1n=q)z`
zN&kzfOMDV`-33EOVdMbB)39*|l+U$jg-!6|4$=xnb1?Q)FxwJuYkXgMhG^NPXrEdk
zqHOmz$rLS3J8Ph}knsZ|%KDu+m^qF9;lD$@{VU=q44O!nTrN76L`z%_Oa$=VR)#dG
z%Aa;WfujsL4ypiz#qvb+$brP5#6dJ7e@tBeUUOWr8$9M6I!SZKWx_I&^q2jL-!gZ*
zvM8vy1|uoo1GmRjZF!5Dh@_+mm>>MOhpU)b`TU)V+HT07mfuO+R&mj43);3ob{WOp
zD&<LkdBsjE*qoAU;+A(Suqyl9(#%P9i!$sA7nl2|(u}No#r5Kt^--~<pZYyi`x;pJ
zCeO=gNW25qza#kNdLfKxsK<U=fHmxfWpN-^CtkrRCh#%a8QcNP)Deh}0k_-h>XghK
zybiX8Z6Ue3tgOAfkdTm&5RY6YBTyUdW|Fc#mGKf&fA(uob|6qHMdt3GCvojHcB4;o
z?j&#YWoe?~2Qw>KfVrb{C%U>FvL=kYxU@TB`~W0wfNt4V*XTAl^|+fS5Sf0N&fDI?
z<Rjm=v-aGR*l``;Q|L?d2It`Q)9t)eaQ7>-EI9mt_w`}BKqmtj)J>m(p4I-B(}?m2
ztZ0MP@00ImDc}-dC#Z;&?z%07E_K4OCnU!<@8kQic!PplRQEQ?{WAkPS1wM<rGK}G
zyk6Z|qx;ZL{toJv&&umP{$2F+2~_V+8KAa8_+54`lLl*O|E|Sor{qdI&E<@B*_pp%
zcHB-`#6TU;ds-ZlxSgWyT#uy0-Dwq?i@VqYV{sG`1Ky7>@gA6UA@G&PMYv0>f}+Q=
z_h`nyKn$P*iWo=@dT;nuI4uzuOGPEkTi;s$?p;5b`nANmTO;sdM?ho`$)rG{zj?-U
zD@m<!A5jxYNzQg9FQ0LcdBH(UcvH>j-6GX7K{57%#4Ti2!jwm+vaX<i`0r8g`Z{!M
zfYJ>5`7fh-u9mFcc9%_8FGb3;;(88ggk@*(21OBQQr-nX$-!fs66CT%LPA2WXf7{-
zH#_EgTwOl=QbTdqXzL=n<|-ls8;SI+B(`lkDq5_cUEg&zj08~HI(rxrD^SxG`s~Xv
z<1zwa=vm0T9TF~&`#J%~_Io-pHl|;t>&<sC`B0NaT8&T;Z8!a=E|tzTc0aoz(Kjaq
zcwurs^lfwg_@Ofn9n(#S1yq`z9Rk(|5cAOtE$-c*n)tZENJ~y__Mq*~awzbcU2y38
zG5{_6%t>B|mx-80#L~fuyS0q&lb8o14$~eTZAZTa9qVEHN72uG2@2=YfO^BfgYEw^
z=q<hoTqXjqIcvKueSFWOZBS?=E-Hw%L!?dCV?@LySuet&>@u&i5#}sZ3aE}9XfrQa
zw{A+<tpZd$X0dv$2C<4@PC|Tz2;Xi=t`4U0l@U-$ho8s^s|=Zqk`3$xBO#x$9})w>
z2;|T>^E^l@vydNZeN(l1WH#Gb$7=pWN;8bO2;T)44L#iul)#(pf%69(JkTY%5pk#X
z?-B9X%jZ_kqJQuii9kB|H*oN8#BP#Vg?iuLi8%dwCVLt>)?Mta2nh)Z2?@F6xqJlP
z+$j17pM^L41avehb6$e@?psjF43X}BR7WQ&l|;oND5FwG=xQP!2HAw5IEEfN4YOw*
zJh%>SVkWATlg-Q8mcW?aPv=|S#ni*!aaFk%-?m!@vVPGOyGyyxL2axDiay-L`C%~j
zIE!hpG#vJsy^GzDC@9PfL|d4b8Siyot{gO}m2=sCx#RMEX_obuTrEzxGlwtEz}YQD
zpU%r>WQWB4JaB{E5#0SgMnC_@s0EE?^eg`dwe^FN-}t&iLwO8cI*E#OL9G8`Z;($k
zdgR*>@0Uz?uM~%+Y@F)Xq$2sUm7KVP%hQW<L+eo*x808cIOcT)T`Bu$y5;fr@262&
zB`@XS@g69-6uT?_tDC^CW{I^!*++y>B<Wvpbu)pIUhm(%>m?SV5oSP5^O})Zy|f#>
z6(m>L$I$BWAksYZ+DMC=+lax8&z=E|&{`%1f*>~nUE5$Xpk|A;XiM^YJ2%S2te5ls
znbYV;|Kt1^rP*OP@=pO~^e!{`aX9%PdiV*{TmRr<Z%s%@NJvP?CC}?a;63}4l;^B{
z>*5o8GY|X!AA0}S!7RWF{{Xjr)Uy-LNVk)?etXR=WseTVeEo(OUUA!PciyIC-Djy*
z{0mr-nOEqz?OjYi@*T&|NnY~?yEi}pWDoi8<{X5WFmXuA`t%Z!SZ9Z&>4#r}Y(#PT
z0Bl$tTw|Sus2CU-umY$oORSW}J=Nd7ws#j=i@;GnH<$mJTDMrtEu0l0s!|lUpqUjx
zDX~JtrK-EAw*$^~LB0jTcTi>M0MjR+Z4j~nInNfND=_k`G;u3THE-5dk9a%!*aDY-
zejE<n3)?>$=%%)gIZ>C=skxlf_PrN-!<u82;M@<O=N9?REF^mfJ@n1F+)_7=$%VuR
z>>SVl_92NC!R(Xq>6Wj|O7w*3X1}HUH;^=E><9}NIj%;!iG$iD#W9K7NU!&vX`A#B
z&roId<ovAJMi{YxT%iF@nihs3z0t?y!cwT<vPzA#-R#VeV^j4fqqR)bl&9>;2K!*E
zt@*$6;#qO@YAq2+rSr0!%sRVi-l@6jomS-q8vze<f~t^e#MCi}rl5ZpjCzQIuu77(
zUxR-6&rqB1e*L(3tD^472j(V_S6qLww<;tgBqSu{b-|@C@Sc7c{qV2J4E&1gQ5${?
zN?CMq3QAKj{M3A5A$u0Gd1$Y55>_a~@NpPF0_8l!Qn30uNVmhe(=hTf-1?zl%4@X=
zD{q5S_xWEIaepOdL(f3>O?JeQ!}U!BGa!u4zCvvECdxxgyGe}pZldjZ&*rGQ6o%!b
z)~kcVZ~i2}^g)<83<G;19;x35(9&@D2maSZz-9i~Gf>>_KH|eE#j_Ae`x6Y>wn;8#
z@vK~$5$kH~fUD%@JH8_c5t9}QO6D|de+%sU2XEWk6dxj3s!t*#%p641QqFk()gU*n
zK9#ZzdgGg%X9y-bp=0CXEW>z*h|-rd8q9O(;)(g9ZY`0Hi?LzOs1(pgzbwMa+52F{
z+fb1dx-u*A1*I{VS@6AS^tDum{C2gL=mK4VXqUVvk(7uHM$&tB>_T!UJP50e@NuBg
z79<BC>tZ`HoBRu#*bS^QTbv8L={5cxthHFC#2$DhkO@dr_SK0Mb_7EMXLNdfFrr~$
zMB;o(0ZlHLQ_Y>NzR(gmlGzOT6W%I%Qme&%TQ~!`CBCyp91?w~XfJxEPQ$X=@4PZ3
zhNWJm%<OUJkq&OqKEH3Zlcasu!uZR9Y*te$McL;L?1qu&ot+m%;?TYhMqgNb--=yw
z4tyyKyoK{3>Yn&s{i>iao*^V8BqSun5tp{Wd*XXiZdA={8+!pgR_EkpAurz#*S!le
zNfFK_CgJ1@aJJ4#!`Lfxe;d(&vlC}w^&L>kLb_MPmaK;Xp6Syupe@iTP!0uNZNd5A
z280!dgW$G1KLl1l?%i4<8L&LMEn_R75<v4WZNb@xL|h!Wd2z$pu`%xv91A)3vNY|;
z1=M8j)U&W<d$2C1S}Hkl@}$-{FJX?hNggGZJMp4CX}bU&d>@)M5i6g8tM7yZ9&)Bz
zMcbf!_FdZ`)eXZ>wtk(xJ7DSvm_-r9dw0OZVMwo#Qtnt%1RY(0azUI$g>#ZKy-?g;
zbtCGQ&p~QM>$lr87CQSQDAtKAPzi|kK(tpfWiLf4v*;uLQzA*Q^JGWvTUtKIpMcCZ
z+ij<1KNjm1;dY_3ccDPj<|2c9DXb#I`(*tpCWmV;;-wMy-{`8|L|rq2oOpA(tY}+n
zoT7e&Nx!-HwN$@rnN3g{g>ubtRYjoSJ!Wb?TE2Hd3B0BAklEVW?D^RvcDB63cok(x
zW436A9FLv4&8-rYCeTF($5d^BZg3u|O*#LLr2ISG=i$@MTq(-rY3D{cz6KeARgYK(
z+Sbk;ANzL7F*TNkL^s6RAQF@BWTgnD926&{0qVl$y0JFYjlTgK?riNg`(@-=^bbC>
zxMzSepld7i?hps^CBzd$0lDNI@j8eE3keAc3AtprbOqkA7txRYrniB_<WYF^Paxg~
z1sB5Jrnk9Y*HT2vkV=5gLi<|x0&k@g4nE|6J1WY-r>$&v<G6IIEd`Jjry^L>&P3Zt
zyU`jAF_LyB=+z^d3U*sc=i$`1q4R3#Y^+LPS#an<M^D!prp#`-Voe5`+7huZD1o;y
z39|{v1pDD=OQ8&1{YPRE>gC|7h~$9A+T?Miarrz=2f4=eC<gStM9#skJHSlAnHON<
zr2l35(SQo)MM#}I2$T5A$8|*8piEj-_tBN&T=t)vScpg*wfi%0)rW&CEp7$cLT4Wn
z*RF~}q#L5Ws8}yVE@4r(27T;*ITw89J<)>MgCZDK3bG$_k^>v-3a&X?mD;$0n1`<F
zMqDO`{Kgho4s&heebV&vVl>`MtnePK(G(v|(t;96YneSNPVx4uVCJCg^D>*Ai~q3>
z5fz(N`s9uWD?S#_$fQ`aiA2|2$WV~0+;MpyiX)4Um(fm0^vE!vl9R_2&H^4Lnp1<p
zIHilDvTx07l#`wON&hZqzp+Q@6)=84;<MV;f-VO)8DEd8kX+^5D|Wm~5ehDTI|DbM
zZuu{eS=o}!42+@2(LelEsZwlT3%xs0eLJCdCv;y0(SRB|hJ=KKgoIonT)G19`2#*(
zBBncWw`~<{y~g|c9O1H5tkMau{V*8EfVGs!qfqNV0m)V9gTD_O-wDU=ht5r?HG4(y
ztrWp5qANui2wA3FS4uVim!xFdDuHF9RgB20BsxDOmtx}_TBUt-YH!AJbggzvr2=Oj
zgznuid;(@1<OFuF<I$%LUbz1Oe&$oxk%}ySzlLU4u{tyCZXn=<lTX0*n?MEd8QJ5u
z!V~uqTYnw#t2PqvE=jb2c~mn0q8;K|FlX)fh2f?>4IPtQ<*f^SBg{!)5(fKW<8^TO
zIhd~VS;kWG8!AjTk6ZDx&&v+aFZ&&N7J9c!o?R~BvR8m)xBq<K?yFF@{#WSQ9Mo0?
zPi01`0LnwC_-aUB3z5!?BiQ*u`*(A?om7c+w=ioIuv`j_L5aJt*lkvi%vRLqPot0h
ziDVt8)`)Ysa~CSTUR;Y-8LTo|oASS|h=^oW?Eh;n)!U+7;<l{h<kD!r5oB|)TKu?h
z&6#RAdXQTrztQ~goC~#C!^|qmfV3TDklt8d5Ki>Taj24)#+<$z#MziR$r1M32)0UM
zg@~hO4iW<rPgR)_C$AAlwOxhAZa7vxC*Q+BqE3KHfRn%4oST%0w#hNO(R&n4%h#yV
z?7YNhL_?%zl0SP&9JVX2gRvL=Ew>(>o92tV7jW@gF`}qlpN6Y{^3t6!EzgR9Boc>-
zL()90cZWnYg@lBJgoK3n;*u43^=v?yeNHLoL<BWjIB0iuvZdhozTnEirq4s)f)ib3
zNS2>Djaqp(biF}tzUIHlVCjwjp{|JG<{eT%*Bv!CSSC6@Egj6YRddm(R8(A1mAqs)
zR&r3uqbqs2t@cuLzjO$1a009h+dXv&(YAGNAbI{-NGQ1Wz3|dMO6jfEA_i{V3)5%i
zB)GdD%0mqO<+GTD9M2x^;<l^i1~o?}*DyJ)c=X=y@S#t>gTbW3>|mu}<u&4V&rd*h
z6msVwo`Lq2knVz!gK{!{<Q3R_Ehvx9S)h`SGyCK#m?tHxuXN~1N{61r=o%z(?Hh^p
zrO}h;iFBG6ss*AXk=B)1md?WVy-+GZF%Of&km`W0UMLUC_dK=>hEBssy^i4uqCO@g
zw7Iyc+W4y?Y7N{V1Ja<ni33dd%oE-6e$*R(UB2I!8kK1%oj{wDsMIx5<{MvgvA4<}
zW;WQ*-w8oCI9iByDe$H@1eZtfAHq)n03ZNKL_t(ro{*S|@`4JLM8Al+ku++<C&5Ud
zHhxMf5mdCM`{R7PpLu9|Vzp?O@@l&YmX`OYdQ81=S#Vsn7T-rD-#miC@ZnaEb_6FZ
zR!I)X_uHJ6jP&9N#Cz?^kebQP^m<Tnd0ebbvURmRA)P-t-%%Uy5rNU1l?I-<W6m>7
zqZx^JqHJ%|jJ^MFhe*4`6cooqxNO_z^E;{RhI2>fKC^1ZZ)TIMw~`mJf2KwGu|dXe
z)KcANRX;afmh-(>hkSPCl>Pd**&=YA^FZGY&;^qx<ykqFc5jhrqM3jMe}H5c`1xrh
zdr)uxW9SYr7AGjoJe+w1eeyw6?=^D*^v-{Ev9~NFBqSsx<g((D6?j>0fp_P7rBiS#
zaU*0{?T`<!wDs)s(EDaEN{|>pb-zhEsK@Hem`5`9A1x5OjVLP9<60zcj+T@Dd4pA3
z{50bB;5RP=H!F{>6zs<p<Z|Kfyge8$$bco1a#n`y=9OeN*Kwn0&_l52ZgJdPcugbF
zsbr8?7SS#{CSvvT4?Ik6=0-+Np5{I88RWsgeTv+K-1nWody${|g?ExHER4ob(AEp7
z9%%1}&OXT|u4H8$?QPKC25QTEM_Bi@5b1|=r=Vm&d!KvJT#HGn@c7@M&BcR3Yw`^F
zN6t|7#C3l7BhZS<yyDQ@ccK+krokK)(@<|5C_t%3a4nyQ{&vac#(-i3jywWeZ-<!u
z-EDh29CQ}hv50t`l69*jZr=2OeD>o9yuZFGJy%PWg&)RW5wZPJ5_ruqbnZp4W>JZ)
zsJ5GJQSLGz(0!Q$5(B|B6>El762YwEFixnc)6WBmZV`B6o#NK*+iPbIFF0z=Yf2XM
zaaGCkT{b>jax1Lz0`WI5@3)GIFjKjG-mz0xkDV8eqxOAP&28F}??sRTZ)#AEM+>74
zO5-BXrq)RGK&)eaBhTu?ll^jCDTt6*Dahxkkyw)Ivf8%QckdbriGhly!AOHOD^6l_
zVHApj^0Zt)MB`W+l(VSzYtUZA*Q#r`o<OXvc`jxhZDE8=tUb6!iVIOuX&P6{yk@Fe
zUVp4xzK@AjQdtvelS!4_3E1;qc=b`4ymm{uK@`ixVfh{O?}3R|#U$c~WVioi6wbr+
z$xBP%EzO`0d;<=C6IR`f+WB!ge+UT)2?+@aX$hC^$TizyfwyBdY}yNb8>C@DJZ;a^
zN9^iB6U?Bq;<B*n4j6u5>4&NS9TABx*!CgRmJdK?;B{D9ycBk0j)=3oTqmzyAN~VT
zBufD`eXDkxUpP>yrPTa8uQkk`lYxy{$g%&2KLFtW{_zpCH7CesM~B(>+&OOEwOZEO
z)&~RYp)^$Ea4A5!K|`~J<-S%4tkbsGJPm5VRR?gZ6eIiCE10L84`7XWtDJ_)z3a~n
zmV>fwU75>-Hh>+sh{Lz~lH*0#{eF1mLFYNx%7C7$nv1u&5xMm4uwxs1WDy6EO+9f4
z{rG=Ez2%Gkm*p389G!a!6sXkI5L<Qm?I(lUmo-8eQci88Ma+w&Mf_3`aq?<f&{Rsx
z1c6FRY5G#Q6hWKPaSf{P?XYRfr5OX{7b7N@sI#)^C4Vi`FQQL;eNHqDg7i9xB534H
zH?woGB8?_EYE7S20k}A__!Z?&*x%{6e5Yf5a!f5}WkR^T)cN89cWLqL1(8`7hak01
zT*OYvY=zuW7soT7Q3XwDQO-Lq8VXk5|J*V8&X$Mg9L=R6*mfP9%fjhroUgn08fhZh
z2yMaWbK<=1+6qpZKsUmO!_)}}4{VNp{6C>O)<gGJ-^=nvIR~%)1^VOzsP#VvcmE9}
zdoJ!aUH%xrTY&ciHv&DtIp8Be08JtSLjg`t{JsvfAP*%ZBqZeW<<b>+b1i6MpbWU>
z=b^I`bXABc+hueM28YoWorpv$;uu+~yR*_#T4p+I<Wfs4EuwC`9d*@Dz=n5SS}wWQ
z1L^gUeKnY688Jw%_TB6zHygpKlXX`s?pDbc^RRCH+zq7wGAFAPM;vzm*A;{8L;En#
zIv>;<9RqXC*McVA7hIFIdQ?38Uh6fXDxZd(H^U1LI?EaD-z_d(Cyeix{Xzd87=O8W
zCU7Ipy(A51vOddGb3t{v_lP-x&c6he8C3gicDC+iO3=;Ds-#wfN{Bl?zr=nfu|i7I
zgQPSr`y<ndc<iG}C*CK5QRgmH-|djR#G4mgY9!Z4G(k{gHbU-H^C$^NG@7Vfa164F
zkm!ZHov|LYBfdQ4yt*W_*~4T>i=v4j;6`x^@i5V5)`_Sxv(Tj=`4%|*!=;yz8Gz}d
z&a$=(lXB_YB!c_22cb4M0xNdI*gp5qt))_glEa9uR$vz3;5X6x|1aw5pG4htk4%V!
zw3;5^e&7wjIPe`{1Q-C^%*dyK+ktPla9aU>#o^-~4+Y+kkdP2}T$%!Jr6dlspt<cA
zpe<S>?l!?Z57B-pw+<8w`rinr?{AU?8iAoPZ{jY%;9k^izvE{kuXxnTccafgQGcM|
z1|uoLK+eB2Bb#+DP8@&cMfmXMd4peVwDI&mpT@E*ZhGeme@<4bakIR+6>4Um9d;$|
zR-e~0qV25{cvUpmjMMUY7~BP?mJn`xwmTPht5izjJW8#Abic$UxWOt*q>YOB`yTbR
zy0K*wipSB}$05EB)%niLCyJo~x)l)(v2G|$ND00ZDn*EO%{kbEB7Z_k|C{}`(_Tce
zIn>sFC$Bfe8}T00z`M}H|KNXFnay_mKmf-IH~FzfX7O!pTWoPQE#E`0m{SrrvD73<
zYE5e!7kZ(UeGURWAJAg(SPB)9$c<T-=L%CtMUd{_4U>nU<g#DE*gojl0q5&w^gBcu
z(0h?05X>C<zK=m^3U%A(VdWby&URdRB!GRuD&Q{QyFPY~?*#tL7K~ekcA!7}9dI}B
z{T6OVNJvP?Wyz&EqHTqH_nHrixa$UU6k`2Q4p`*XSy+1~oV>4onfq7~&bt_hstBa|
zE?m^cy8_+ZE0UR47l^wG`hQH^xM#oRY#EWXlnNFaL?O5&JL%kkGd()SSAY4h*z^87
z*|cW^GvhfP`r6-e{-kWn4e$JQV)$^<)o~3kB!AeX^y*{o7d<nIwhWZvECRwYQM;*5
z%g_)>dUNqMqH`5AGsz~pVb;g~GCwAlo*hs)x7bnJHVEx&A=N7lWk#NXqAku%pOCD-
z3GXG>s&|L?ZTCYZi=KT3mDvNy?H6YomYbj>8jPqkZmPJ5GBT&7`BkLN&i)Pvt0X1b
zsWp(Vv%gKRgS<;oERvDj)>x<Hr8<l%2x)*-Mo&IB|F-06)ZmBF$G-{{2a|?Wo0J9^
z_2G1K0y|<P-VgCEpdu6Oy;oFIU-T{-L_npf2uMfiT|uNtQ4mOI5~M>AX;LE~y($8N
z)X=1cDjlS^P?Q?FbO^oo4xuJz`#a~1aUbu)eYg+*^}xs&+3c)6=Uj7s^ILPxZLBZl
z%2R>HSFdw$I-1QaGP*vDd={yr_RgZ3h@qkEZtgvDbsnj^S-M6-ROxAhK<(fn)1aSp
znBX`2Z*3f$Jd=EMy;P;Y&&OAf#aFZjcc-}*k6+8lUK4$*$=E#$HOB?>(>4<n5jqh2
zE<5Y9P<}{`&rB3~7bmdmOMXj|@994uSH3p%z&)UU&e%n|2(#E{t-~DW(6!><19`gA
z=CV*XZT?mvHb?o>@1&aau^9?JI2qf+FWKUuGUruw_@%}?7i84uoRaihSl*mnPP|_5
zvNTOVa?y{(PiqvZsXrE@@khEZ4*h86#5{j?&D*drm{Gspc9_=_i0J5&J*b(bH3_{3
zCN?@v)SG-kI4M+rBVX-zC}rQ9pxEd%N><47mG8PyGq<6B<N48GgY&NA)E6|{lf!48
zXFS{&FR)GA6tM9AMt_?*J}P(JJ1<F5`6shUd2t=>_9_w+Lk@*E3;G?ONU%~#sf512
zBW(D_xFOv+;Vtaz&990`-1qa&K5Dmgoko_hAKy@1Ta0-$L)FE;@=s-Ji-&l^yDc6C
zYU0UXBwI)@+)jL}FT7QAk3i#x&g~C38V(K%J-P@aJQD7QdAXk5b+hGG`(BHw@WDOx
z{3v9zw>RKt=Xggk?RDe}^2tYjTgB2aA+B7OAZ5mrh|-{?=oJo%E1Lap8jfxp`x5hw
zr~Qkwz$pr*JZX=9kSwY9g9)M(qNdwdkLH_=?)mmLQK)Fj13OeNK3d;FRS?`pMYE$e
zs0L>igmQ~t5dVceA!KAtfPAkIbs<S{fQBRVZ`;C^iW`|O+yd)#iZjI}*ZyqR-4;EI
zt|NBf{bGPE9VGE9J#gclWwQt*uu|(+7yl$KF>lz6&-Fg+LAK?&Z(G9B?qb1CRm%pv
zgrRFKDSuMHQC{;f5>o3h?I<KXeO*V?q3}`HH{uT|&6p<GqC&u3w?fs_D5KfLnERL~
z9%R>lbXjLP)C?uZUUqt}Pk?3&H8HZGxP?+rlewhE!6w1l9k;MoRdb&A#=N3$^JYG(
zgOoIWYtRm5i(<TKJCV###{9SXB4>+ttd`8=b%u{rfwR~rn9x1JN58X9Qfe8t6pQiV
zm80ToUJhT;R;Kmfk@uLf`Suy*?$m%9y0{`gH^<#?SAt<b1QZmv!C;QW0pHBDX$8&N
zM@gSU1BioRPjlN&SSD_27vcI8$#jgkb}_6xs>&{@!mNJ@;%;1AHs4~}db2ZXw&|&d
zeLeylu$=e~RGxVn>hcFnUHpDmGsgo|?~ZLZif=WQ*Uj#xpIIP#Ce272;-!<JQs1?`
z-b;ZPLG_<6{qc9~Kr%#E2&RMm0h#KoR#?A$izZ9YfBf3}I(8x$Q*6s+waMoXPyIO=
z{V9HJ)3Y*vHb=(3HhHHg{Pall&$~6wdoJUR<enw<SCS1Tp`VNh3EeWFwi&hqi<erq
znzp_-d^XeCu^c+zB=ys7dsmcG{f>LKmRrH-VI5!W%e&m8U-vd7`)_oWIZza4e_{Jm
zD^WDW<=mj{{h?JG!RV7qNzj*x@sV<%itqieMT3VvGUBF1@deI2@V$h?HPdyaqed-&
zK61m=k?A!S>?iLj&KzUP!=lE_s8bVK#MsL2+_4I99H#D<^CVo3xHO@0rONT7&@g-H
zN5@9MG@dEx_Oi1|;0O4Q{#W5QTX<2=<A%K7lq%kTuSn9z{1~sN_V{TIV;`NPi}S+1
zRg!S+zt`}5c-!y2jp<8bxMhW^g1O02jr|IUP17dCm1s`f@sT2-<{0ToCU1SUa+XDn
z{;7J`Xxpn5#g(cs7XOUS)t%R)On4Px+pOF0E%0gj?5TxU%3UWS#~7dM$Ad&yWFNl^
zjL6)aCKSKj*bJO!BI72&SNEHdHEihD>`WK;v7Eo2_h|Twp>MIZT0>Tp`VB7~{abz|
z?t*=PtB|T_(!3z5leE0vSCvAwj3R|Muf@J-F8$G_e-2l)$I}9&iee)cHZn7(uyY~7
zb9ASD#zMZ>)5OQI2C|o&vG%hLkEw>-lyfZN06<A^-MeJ=6AI$|^bS)<*6Eza#pafe
zQ1RJe(|mHVwU%UE4I<t6Pt^_hIE`|tfAksvamKP>@pET<AC(uy-r^nH;%<hh*Ph1Y
zCF7m-KL1L&x#IiX;tO9~heLntox%20X?6)zRWI|GUY&K!_o?HfJlm$PQ~Tg`Uo-Aq
zK`wM$o(oGU+wPQta2~m=lv_mHdcd*by*BS>owkq>HD?d5o-ML5p5$3>D%!Zjj=f~9
zZmK94%Se3RLiR#|$qj0E+X$)X2V~np=vG|Ty%cDki6~H1fqEvZR(w~f)C?$Ye${wn
zn^Eg!QQp_oMEsDzmtLIYc(P<xlQplzs|J+pFC=i+?OyPGmU29<N^-#E)s3@(YUgoy
z{KtRzg1U!eW1gHn({!Lyj>HIInHDesiY2re$*%Zy!Sv+#?x$@z7hv)J{iS;B;{U4n
z9Q?^q^=qp|mvLVN(H3H3o#Ju45XI!J6kqz@FFrkwBpn*QZ*=Y+6%lDGQfP@+d|yuT
z5A4+uP0EKJtQo-+>Wzsrd@!c$^Fx|SBgnTympJ9j_tiePMw=O~kN3n}WnJupev7G`
zTh3MW8#h$6t|#CgxD3MsV+?(7KTdmu`0~C*qRCQ+@x-@6MJPSv1yARo9_=R>SLf*Q
z#lF<BCu<|Dz^q^P_Bqx4%VEgdC_xbG><$}SP0%s1Bh9#CM4Q(mgg+v3C0YNTc;j)_
z2L)ff_w>CwcNz(pYxsr-o1pY7EB(e_muv!@lQyV+;kSedE_R#0>f&!)59tb}==QP2
z2WbOw8bzlwcL(iYRX7%}+W*tjbY}+#Q|!ulRh2w5ZYKucq4kVm%H97pQ`-v<(H9NK
z(hLYMSidx#7h#Ua$H)!Qd?R#q|BoP+_y@32gq|hU*uAOQK3hzc<=#=153>A7_9=UX
zD&3&OtpKU*PD#cQiOmsP|LD)=4UJ8=-lYo`$-Ym{EW|v>pR88y+o{6xtv5ED{Lxb0
zf9N<e6`4VabJ!Zsc_c+|)cV|CE7)?fcCzzEk-GSq_>b=@Mp<<UKs7zE9qf%<YhOd2
zSuL{EQnAs$+kW{p9i6CnQ(!+SccH%V<F?$d9v9UB=WQpN>uo=!nNumC{liIw?7xGo
z$ZJAw^*=4-kJl-h=%$EgiidbxaqzDBYUo!c*`1-k56W-Z_t#+yI{O1Vhe(lCi0=h3
z2H}jjhjIxW>}Jztdi8Bfu?h`&ZM>D*QA^pOU+%rm&$}vq{J4$o)Tb(;zUFm%B7^l2
z&NtBLg(p1bN4U=Owxau=6jV(otV-Yyh5}B^R3J;jj`!@TGR8=A933l2HouKQ8_h4e
zmSLf+h0;aBc6yX?%o8l{f*Q4wP&C(v<8K&dc_xpgWFw|N<}zw&$gp<)74^~#fCqh+
z-Zk!9x@_lo(Zuq+S%dR~ydX&d(~e9%&_vqxkMFE&`)<)vy^BiKi#_vzO98Lc<n0|N
z=U0pbxa6IiI3*;84mfAy^x7F*5V|Q~f|^Ladw(%(nRjGfX)qTDSJBnte)uEjopXBg
zQBLVWzU+Byr=o30(4s@!`nK=lR!QckAw$>nehsY&zqDf)rnEE@TIUWwwiL^C&=F%{
zY^Uipao2In$U}Co4Dm-LOl+K!p(66dA;i|J$C5bXi7S|%OBS~a!>$7P6mg_pjMMv`
z2lpm=zf0vqe_S?*2l}oInAR)KKlE`ZYmt&7OVsu?nTeBM6GW$+fcd0<Wi&rmc#<t?
zdHTUWyo&zrrx7)dy}dKU<b;v8s1<w6cwr0aVpxQWoX6CqFby>ACL7N+iNUKDFA`${
zGcwmk7T7uSCwR>Cxt`+tkjmTVj#AZ+-m#gAm{vny$)0%S)!@retH61u*|~%!#{8z$
zJ$Y;T?g}SH(W6sGZNZD}n2-Cjb>q;!sZtJEiUZegZM1W=PCQ!nL8l4<m(5nBsPUVu
z`#PclmQwu%d0VGSUbKU@VtR%_5ncZsM-WQLZeh58Sf7cd`7ucuGf-(qJ()Ov1W`GE
z(aI$nAV?k$`jP*0QLt-XqQY7<N2}C>nT;Ce9(A@FdB5)_cZwyY%C1#Y^zGjyQ+Iw%
zqk<q5p7)=?{GDBM&l9zdSYkE<j{U_S4m3Upb1ze%DEHkw0-BzjOsD@!{AHLU9@vCU
z?H4m$)(4oX-kFaV!RxucEGIa>ThEgL@V`97ia`9d3vM2qLOB)^NxtgubZiHsfZBd#
za>(!-Aw3RsCM9%UAY3I-Zr9wFw~$GD!lUH{IfDc6j`^`>S%m-T%Mj-u5)$LyBa|KY
zOAZ#e7S67JE%eu6pnUO0MZT*lKpAd-wdrcC06nHhlyp7V_jc7zr^V3o<&(CaQx~a0
zJ4OC)OxB}^vy>yG#X2oIhRZH7(Ru!O2mEyvs9NM-f)ctqWLHiDi11a$7|vX!BF5?`
zVQ+7t>2_^r*NvV@R&_O&M~z38@Ga1NhSEopPIr4*8U9#vhrjgRcp1YLMkDGlM6EZR
z{n;3o@=T7w>!tANg_}y<FQNFe*}jxl%~w{t#3%W%^_hjM11n~E;GE>TkKaupAL{FM
zIKXxGOPDAEfoSV{FXwvm@NYt&cU9?&e|RCd3R=}*?T1az-V$+9{`R0Q>SS}fF;#uD
z2IW!tBtj(G_Qg|uo<GZ)jwqV`*3hkVvw#6=L23O`<T*mz$vB;OZhQ0KB4hyV3A>tG
zXTgOkh{YNVvx;Zuyf8OuZuor-|5a+@Sk|j(GNiP<)kwZ;Vk?Vn5F87fLD`e;2fHfB
z|Es<EM)`^auB?1lVdx#ZfvW=|mF!7ybx@2@Q%8xRbgV;Xsuc3E@hoveh}t+pUo&X>
z0ZQ`5mP6p_{X7t{R~$;bb!f}t9X)&WSG*2QxbiZvxtqfQ`Q&Wo6k?H%CH^6Er`>ve
zjw704RCuH;AxWq+Bnm%-%%r>`sx19{S~b{2JlaGvwT&OX{$3$S0*@icp@Iy5T!-aR
z9L0UEzxI2TIXw9fI>8e1+}&)Yc771l>)D35K<qvnA_~{UbZiySwyoMkOVr}FN-pZ9
zUrsPDi9XFDq}l&??`AWae94Rxbm;!IO8#+sA*aT)w<K+&4r0{4RQhVoQzET^TjBi^
z$J#n^Tk*UO-V`PL35K=e@Q<T*RUeaywF%o+k;RGHF8w;WG=aQE?{(8y6LkqLuVO98
z2!gu#g3|k5Ep49tSTunz=?`MYw2zL{{abw?QYkK(4?_5(7HLw();njR*Vr}VrXZn-
zaZ?$ye*y=6y#dIZb$yJS=JRC8SS_{2w%6?uW=g`m6fzmh1cxh{kUEx3uIIb#!&d!n
z)@j~k_0RvzOTHoav|Sx4eAgcHxQzVe-|h*J1w?-ZdIKJJ$R8%dS4N&M^U%W;cMY`k
zIS%ARHn;xHObiGKaME9|5q>|!`cv|ay-5J%Q<i30ioOk2sHKIx1W9}U{-GpW*Tc_&
z4;|4w_M_#}(gUUsVzkR&n~R;F-{}x|Sb{d`qiFs7bmEFe*&V%D+PbZ&Typ<2#<`-7
zNSs=r@xGf!uM8YZ-Bt8uL+dCKxj`LeL^4dCDaj~yI*bsNl_Il3!o0IpPba?Y86*Nz
zV53<28|YKb2q@m=$f}k7c$|y=475-G5h#0~fBlYO-^5=A<GA&yV}*I%?Q=7UjMbbg
znYfwN(k#&ntJ1xS)44)_6JiIVraM<%?WcPn2Vxu=_K!zW{-*Kjvlu)3t)ln)b%mn6
zs+Apd-kk$}y~$EPM{Za23kS!osE4W9O@J)}i7Zps)R<$4jgw1VC(~>084zcO5O8~j
z73wJ$Dg^LSD4e|3<6PcEHAVXjy|Z+!_4W8k?GN-CR~dfR;5Zfd*#@6>(FaQ^1Ku;d
zWQMEZ0Xz&sDVZQ7;^dpF9FM>1XrKc0&GG!N@a**U%zUG^oE9mE-}@Ec;Weu0^qIrw
z%Eat>v_Uy^)7#PS;;ky(^Ps2PtOFE6O#))Xf7y?X3D;mS?`E^lZa^L8ity>5>8GN9
z1^&PnP)92Yi+PPEQN*^7N_8U$8T|1iSDJl0LO1pZ(_G7ngeEe#Gzi=#Y8tZ?y=O@5
z$}5~~$3=mP@iW^546fny1m55c`zI@9!armH`^oxoCEHQsG$q(+fMdd`hoR21hNLEc
z*S}RIR%9&wFe@VbQ3$zi4Bg-fP!fH9`wTzXa3n6Vd(n^IgP(|E!z>lEF5~%o%GojH
z2Lk%lcJj3;Eu5rZTMnND5y{g`M9ERG%IQUbZoB!iPa4_X+U7I|(~$jmXXfCo5>JUP
zx6`L*V(XLk8O36iMn8C3dRo?d71TE<maZ*5joc_HxfrWa$|}is^VvF*W|$X9ULtV2
z%LNOe;L++pYuDMePRC&4wtA_cm<zg7+CRl*sk9Jd!<-n(_!{Fa-b7oOCmykyO(`BP
zKnjo_o!VASCuplE1A~_y#B4d9kYsavBUG5?A0J-kT^h+xrP-jZPD++z2rJQ}?R%&V
z|H%Bhr$W>A+i5t1Hw5sEpw~l)9#r|gm9Gtm-niyH<7K7<jbOv0ho%y%B;`DQ_bWNU
zQr%>3E0M=O#dy;}wtUSYx7?zm%4}((OPjb#qaj_svz59&eAaG;a19}-*WaJ^)~g>i
z2nfBTaYt9${b$uR8?WJ0+Q0c1$%it6doY4x1!tKY&LyjX4H3F*u7bIQ^mNYzXZS?>
z?>fb^Q4h7*FWK>?xRRs^`g&R3Wpn2!rTI8u0X=fc-}4uvGm=<v<X;IFhE$%B7Kvfp
zA9D48HsybGj_Tb)=JX{)3Ns8pH8|P+PH-Qs98exe_*fI39Op!!aW_eVN)G*)EnNHK
zI7FhO`_@>`-}3UVKcF5~{(8C1S<alxoY~7B3b(3_@$3_!M0c6}Fuz>N9Qw!nY#Z6x
z=ddc}%bi|Vm8r8PND&<|D32KO4D|BWkq#6r&-F$6_vB@~F5jxoM`(;XIBR8YEJ+Uq
zscTA9Va?Ww3~u0v&wMDoG57j8{}%nqMND@pQ_S?i;Gk+s){g@c*Tchu@gl6j#e(0P
zqmzbMy=Re{8K#lXx&uEg#?eJhjf1bX{)9~4fGsJ9=)i|+^a37ecyJx5+r1|X?(@n~
z>9BfS8YR~KVOSwK5?AHsL~q$>2CAZdZ+zJzM3Gqg?81(N0g^?ndYp(XRER!M+?6ru
z05vV#v-aMFVE8Q-p-uZgR>#%Eh&mrh`G%dy9(S5lAQVY*j0`sOe{q&Aj~+33H68A#
zJbm!S<7a-Taa+n3R&b0xCn-m-B39YsBt^~0i4kqEN0K}M*=TYW-Qydod%b!%m+0<$
z_{e&H68%{S1p3B!1IBvmQN*)u%djE&-_^|*UtIBjyb=*{L_fj{X$#AIzKiu##zd(a
zjkR5aEf^EasB(fEmefyekImJyuyfQC%EK9ZS0+`B+Z>@fm)SS|Z!Li6Tj<=ldlgA*
ztbkja3!P$wigbc{T6RuZPx44#h*yons#5lLo>;e})MJZ_#?mLo`w;8v?~R@3mD`cC
zLe76}8w~<LG~5hM8(IEvdAI=wx$YBBT^$=e1Kh3I1>cPjpV_CQ?5Mr6uUP$^wj84l
zhG_i=Ee++eV(4Bgj3+z&8H}q+M=x1s7WxNrbPuc860|VF2F2J|@7IO=ay$E>i_}Gc
zt9mG~o)!t^tuUsmt8dSQp_6k~Igo1f_Qj6}M*-Ni-Dv3x`9!`ss#zHVkev42{TnaW
zYgK=GG`f{r4v?FqoR#y6XYd>S<l#yhHgPVOXuKL0icap~MfP;{S*%z(uQ9Jx=)?5|
zwf4mey`MYpmL>P3dZpQ@^Zcz=DF4n;HyaY{a@~2(GhobPo5L3A#iq#H=prPwJ~}GU
zWx6I!Q-yumzEl{%$Ht0|Ah+I^!WLY=9`A1Jv8yq)J|lojwn;6NXALV^A!mgI>fX}t
z@X7MudNr<-n7Vh!yw+j9=bPNyfyplUUNA=s(zbYhtsZSw5Xz{#(`FkJQI&KqYL?yZ
zb!`Ug$HT6A`Y-CSN#M$!jwH?qWMJpp$q=(bqrGePshs1ZxCGWNua(Ff#b_B%h~yPv
zzP<e~f;|!0SixE_MCWeys?wJ&rKi<Ay&XAkgP(mgfB$#iQFdf6ey36PEa}2oSa=+G
zy@&p;wDgt0Bq5&L`6z+A4+LttA=g5B^U>c0pFmbY>+4;WSJn;eV{!Dj$n61~(n?ku
zeLWX)`6hd`bmrL*X{?k?q#<?g#{tICL7&LNm5Xp;b-F#VvCRSJdzsO9xjx3A{?=#Z
zHd0+FWQi5zVL#u0PWH0E=Y4E+U(f8N7j!&6<Sz<D^Mp;bxY&gYXi->NzF4M;+|H0K
zy~=#|exzYWHZ0^xO!4oU^JQ!fDOR~m_!W$c&etQzsLN$K*sBp~C7&QhmlXYJmB-rM
zr1mlueJTd&DLr6jxeVF9_7gn%(@c@eDGCDRN#1~gDnuea{pPb+3@?}U^|RoLT~Wtr
z^0J8*!7?&HgfMWo%u$r$RKo}=E9<!8^p_GnT2`NIIE2JJ-bCQ?D)P_FKv7ubZlEw`
zj$KqJ&fLQ9(3A%mU$<RjJ0S$RrChFMxzu1ziPI0P@*0L>X*SGny<EswY8;qd0NLUV
zbtTWVtcTUnWC_)3t>t$(k$hUuYo+`{={MpeYm~1^az3{%?Aksr=Ci1tc~tBbjlDYd
zo%EVxt5_R`4o}C-zb|)_c{uj<76{Z!sTD=Y-FHFTV}!kjZtI?_ev0zUM{mDum((Si
zb+}k)5Ou9=i&W-XnR8(H8LNwZ{#NI7LL*01EEt8PE1KmyLX>tJT|UYm#f$kY_dxfA
z%uDbrao4*9a?+tS-FDtq7Ho0$6`y`0lA1Y01w{qOn<jgsj(fEb0te31iJi-KIS}22
zKX!9wLqmM1d#KT|N`=(|*;tPa{OPXm(}-u@s;8Imgt}vO>w}0*>}?R}Ymh&!+{V~;
z+~l<*JhKw&V#0qi%K}4&#Tqp8#Qq$PjGx$3D12ahD~EDzA_^m0gGBWrQiXM!YCJ!0
zb{h)|;X->$A|Xr+obgCc1y}qWdK;(3Gb&?93c4#@#+gXI7nLLyUlz?KjSY(>eVVe3
z*&B@{pBmIe3pg%TKIzs_6{SC9&sYMwrg;3FQ%R-OvGNO_5!Ssb>FvS4o^nqXJ4izz
z^REv`vbDt^$uP~-CJ@NK;L$wMo3ywF3x~6jHnQFdYuMwHVA1Xmuezm+^sq@Sm_DR<
z_SJ{mdm=s%ClP1`%QHi^e0?WOj#2Qlu~nb^uy@`CytDT{XzV3CZ~T+&&e5x>)Ke1c
zu`uV}tnvN1hOYoJ{`&8wMG210T2q`r1~g(+^wP2wlM{cxwb@r`lk(gZ@7+<@&K&gn
zzREK)mgDYc*)*4=^z4{bCM}Vjp^p{I)qSNxY+S1~KKVhB-~-}BLmbq=%hvr8?9#RE
z9o%b==e5V3Z209$AGo0Vx{VH`7ETC2pb;`rcY;{>`KYj%ug>XZv-A=FAg5qEeU4q1
zix~&q%1EVe6|n}9Nh$o(+>uQk%4?T;Cgs^x_DH27J$>})b@Rp+dlKrlZaEut%PHTi
zE_MLy0P9|BjIj~pTM>r(s&?mGCk}OHkIfTq)164K`s~%cU488*bQ$0V@rl&XM=OU|
z0$$88Tj4ua{O_VHJdUT@`^qu%b?Cqg-btA=3F{NJq0PpHCS6dTC>KWsPJOb~B$k*t
z)uT~0_;}l`a5y)H($np2iu6OfhR)rDsZzmWn!Smq@EgNFMTg8}<A{;TP3lKbw3=7v
z&`JWN!@YCKdsZrKwE`-*#iAtwot6D*sgwhB@tjC}H#euMF1vcY^JykH=QVAY%>LvC
z)p!R&D<Ux_vh?Tt8BlDAS&TE~w%pgB?8IxX#tS95(b526nhfwLar)(2t3L<Ov)9jg
z43`y(t&&GB<womcx|lR=da59@t|sX_mZx)B$K7*pY{1o(w*h(<Y}FCk9M6=Pm*sWg
zxL5er3K>gJtCGc~GWQc|MF}~t6svGOf&!}SCiNlJkX#BEK`Qr;Z}>p*rtljNLE<dp
zw-a6P+Nb*oIk@+o{gxYpl!cgFqYl1Nv!mZti37@=8p=I1;O^L8xb$atV-z)L{Te?C
z*S2C~#}jPgaT`ZBU}$AS6QPPl$vvy5%)OijkOq;0$2zBLEOB+G0Z@5&=f{BcPh~0)
z`gaS=F3fZwQ=F2`-CSB{91m9Ca_>;gooJI^AC64(tx9Ecv79J!2WHs2i0`OZo!wW1
zR4kE02XdgDitx&}nG&dvx(L9>2<xJxMtneWGfy28tKhLT#!pv>lq3%;#SSZzg3^uz
z*NJwH&4xacuuJJm!;~bWqba=IRvQ9Wm$tQLXB17H7op>0=pM=E5Mx?!abe@2Xyr%U
zp)w@c-u5RJFlc`66luaA$bJD~F?_p1@z`n(6t5+^0a<<PUSnWMG0i0=g$a2FkvyZ~
zk-lrd^6b+yRCVWx5pP9q8-0)I`gM+*;m57+scjaJ4Z6)-r}^b3%JTgr9hgw5U@oCw
z4SHcGZoj6O6D`3BWl)B2F;iIK5wUb+ev1|EF}*H+j|Ccpr>}dvx|z>Hdr!qiKj1;2
zbc0*&1if>aYB1xP_!ZcbALORleT+rc(9<rqg`Ji@KA#Wq`aK#HDv25Ur$Tt0kq9SC
zLm_#T=4z;$m#I%?n|?o`l?C!Fska@T_ZLTyPVrF5@&pc^X=uFN9)T-*e*H}>7=t@d
zVwaK^aII031h#A+RDX5ht=#5KOu)tHYBcGjH7HrGlx(;e5P<xNf&mx&WNNJ22>*8~
zOc)XSoDUVE{VI0Lr{t{e9q>vHpC=<eNGip%`fW&J!c|P=xtNV1&B8egx~LWwDmGd|
z33@{t*4wQMmgi7ar0L#e+Stzch<)m*Sl+%%69QIZCUu)zx}dnp;>&4hQR3U&tA>nA
zN+80xN)+*VEjw5*m5u@T0Hxaia=Dqi_1GG-BRc7F+D1n8>n1mL+P7|!r$Pf0dwi@R
zKZljDLXwquzbe;W-Nd4&k0s#8E&@#W#O;NKY!{&dds$Gr!^6a$IpgGzG8$u6i;LE|
zfe+E76#=)c*Y(aW<59Plzo0}cN0}27e2u5}p>fYeY?Tk`CRzOCESGxnttde)9$(mG
z{N)mv;PHZ<_S)Eu4ud$K=WUWcGRZw3*3*KQSMS&yq%j|Co@uMN>TOQHz`N?qupSMS
zf*D{sn3zFFbtB88Qs>8aK!H<ZUE9~0v733jzGfn^>bIsASUlZ+hgIwhiD0#@=9W4x
zR_7Gub9+x%{)NB%GO2H{J`H}JiVra(&ich(06Z`FDq;;H5D`weu6Aqii!<MbqWhof
ztH?PGunf-6P%4jka^-Zg<aPUUq1X84s!gMTdqq!P-_Cb*jA~3mruF<-U;u?~Ot4m9
zkD%pMl9wV+^YQOoPA!Z#4)(xx6nmA+U7tU0Ez*d51R$UG`RSH#J4022CEUm82~*9A
znC%Q92=wOlO%&+WJ99z&-cSdopuFa4P*3~R*}<<9`F7PEB59Nr0`F&xf`0FwbJ!uh
zju|xE++u$KdeZPZxzR~7gm;7+4uj4}X_@C_kz{AYK69@Oy%ZRH`<rOsCv&2-AE)yU
zNzPlZhmFAVa_ghMx`5KXJEH3ju@*B$pVsGI&BVnh$Ntj!)hmaLWy-to<?w6M>XgjK
zs#<S}opc$U!>rp+OtEC3yYVH(|Aj3tc$`z#!VZ_n0~khx?gejnN)gVtlbrDsax>0T
zZ1AVa(XP%NvqdeymEC#rg;vfzjLrGvG8+Iv4ao{8vfU{`^d>9}(%Ms=41S}9RVuZl
zpuaWl!M$m+qz>hM?}Z6ri9t3t>rsaro4XZ*dPuRdX(I!juIVd|L_R;{M_M3^QUeiS
zLHKE+tt@+S{i8PHw{<XN_Vy%w_$-syM+F;0>7y+HKJ!ywO#mIu1G1t)a7Y1QB6j(!
zI~G!<LJ^i4os^*ChSZYC*M~hDiXZPnEf)eLL*WDuFzX>8wYi0)N~qgq8#=UoWi8`n
zDIV);C2}}ODH^Z;NOa_5^>*gv^P#}fL-kh)FwFpU0??}(VD%fbkXmKiUwXn7Y^yAk
zvfD9*&2x@c%rW=FhZAZ_V>}j2dbYiD9|#>vf<SUitN_SiD$DNO)wszlX&JK>=W&6P
z!|;!GWyy|BlBB(9a<NrAEyc;h`dS?AZ7m$GRp4Kw)L#+2Gc~MJS-pr<m7(a>Eq`sZ
zPFB+BWKNtNLkZw3aJXo#d(wb1Q!-at@{h_L*F=-^(2>UCi)+AJa}&lC5#*)mK~{q_
z(6c_dpB8_6h{mb#53h%Wm22RG-}h82>y!s{T0jM$1=^gG-0k;;I}TvZ72QlYk9Tm3
z6e-DU9Ltq#m62l%;+%^R?x(X+0qrE_ndJTF(|001ZVBH2ZT4&?o0nXtZ&TvshF)}2
zw`)Pi+o5v=8zZeid>Wdsn6*XI@XXG~J$dpJ{Se)!;&a*f=Gh0}Z*--aN_O<@JO-(T
zf0@4~jCM44Z7Qs+M}a^f7l5>pb7^O=IK8Ud#?C%Y^{m|PQ`%9qppY%ON<^j^#><{g
zwB2d73U#nTgomEkA%@HK>dY=Jlm>Lh@Q<Mk)qER_35TCW_3M9IS(IE-S&ydCZ!?14
zINO?V#|(7g&IniFm<a(6O!k5qfXun#k?!vn4^(43tNF1uCsU{qtO5}e@^gsF4nvMs
z<jrx*eBl6SrY4{WkBsMlJ{16~$!k)m=nY2#h(0;HsZ(XPmp7w~usMoJ!0(GlGMzTA
zEv6gk4&|K8YYVcCmGza|-M`u-dv5GqMNh8*p5z_CHM$4KvK%Qs6qwYX@gW368I<7h
zXm3CUI_qj*m@|8)hml-*&j$<yd7k(vb=l|RIu$C<AOeLpRJ$d9W$b996D33|&wT(S
z(cnA@-Y}qb5|d?wE>oqlD@atP*r^N!qztC&E6NfzEhuryoM~_0UyF7ly&=2vA>|nB
zI`2rtsWs1De}jgFic8n@e(r3x4G3hk4@vYkI88wE+xsjjUk}`@*sIX+n8S>Daxn4M
z$}8nlz!mlrK}v)P-61_j$CCMG(w*8M&|R=<IdQrxlu6jDnY*eu(Fb@tI?&(g^zAQE
z2YbP+?F<$)lSJ0p1)qgvd|b6DfBw%NSYEc*n{v@xZn{Q%&ND#UDI$<+^@^x)LX-XO
z3BrChmDMaaU<Th}3b2F5D;lagi;e|8sUw4e<ToFPC$RlxcV4nWC7m+r0tAJ^JwPAD
zLFz)w_Qn!RybdVi0NDoJbCH3-;b3o_I(gYRCh?53dRp!=QRjI^6R*0Ic){>#yg<15
zc$}ZGp14SD%zjhy53vk24E<iV*K-DVOx=PO6jg@0z5(i|1aO>vv)QT3)R=ln1w-X;
zt43i`fu8I%71WZ^)9~*(yG&60FjR0S&Wc;9T-)gi{kk(UA2F_uJ*`uDDC*iXeQ065
zLE4Q0cqh5k3;^*>*=|NpUcR1ea7YM>)bNr>H8e`~t@T(*!zHq#+hT;(QiaKjh0&Zm
z(Fi7)tmy@l6hoiwXcq2f%U}Z<EAzwF^6%B%>{_!$i$0gRk-Nr~`jSVrVtj6yuO%A?
zlB>Lz&)Py<2XaJ^pWw~%mX}OnPi}yEyX~6gpCjW>ultT^86<NuvPL($>LeRG8vGOO
z;uia$FIEJ$yj1C>H;SdaryJZSeagh{)Rr0An6T9$h|}UbLPvVx>xb1QDD6$z#~jHy
z3KhDf?(6!cKj8)P5ZXk&D*NL9;D`#!iv)lm5&v{T+1CTOW;Cfsr^YF}#rv&i7e@_+
zvrNf7T@;K7#6L;;1Iq_qWaFBcC74u3#=Ietn61Xai5)fAu%9yhkp{mr+bs6a#h2XN
z5uO(Z{%)9UbTDT;oziMI7Q)~sn(jsd(whkD&4C}inkB^R{hEkgB&UkW(hiRkCY&9&
zbIO9%VmvZvN0{+BHPhlSG>MqN2{ofURrpZLuaPa2hp7fmkEM94gifaVXjOyi{{<$E
z0iSWQe@pyLCV|}b2V)+9vqAlR-E^EUp-#NzFXjG9tx#8)t&xgUNy9@V#wrNa;)<qj
zSGr3r;_Ji*E{p9YN3u^7fnw2JM!2~gwbCDYBV}d83l2m<Y1mzNIxFMSW%)TOXwRL*
z6<w8`t;Xnj=MBH9!cyC-;WTY8Kw6*wg*|?504Qv#VCYMY<d^OMcFN;*mT~`iL9zR|
zQ+q{lX!H6i>Tm6NSS%fX@ylc^XVS(jr}L4CGG7U0Wi!bCC@|XN_Z|SFcwLOyErM-k
zGKMNkv4T-FBA?!#o(<$|f85wfo!uK<Zk&%3Zjj+@hkkaU29(D9&#}oeF)YJQ9_1jt
z-+3}&BuC2a8)6xfeR85FRistTj1y_EN_4;91^Gh&MF5P1fsUftu>)obZ4nyk=nU0L
zJUPecc$wBL90O*+|Kci;FkP@+*G?Cc+{7DWQ{tj)Ia=$HoAUYExm4T}x;bUw)UcW)
z8!uVYTj~q~DI-GAMwc(GN6D*p(bHi|quZ%HMzlJl0<({fzF?n#fuODT3qZFc#b-%9
zqn?+#=J$asA&%;*<SGzU-*7!_BM@qXvu~C+sBoJFFxNaIm!R{EQud1Ocs-Yhp?8Rw
zgf)+1gcnt5UyesU5RsM3mQfABRNs{TyKNQVu179{nu~j=D#rL65Okg;$K)3j?o`vg
zmM5@8dw7c590>G-Gd_0m<hC`s-vDb~uaNcZW9{*Yh&&7((y^O39wOE~y`K+`sR3XZ
zzrsI7!rmV-S2f{E*|}g_B`H+4ThKo;hPWWEU8F=2tWtk939H3&7j!qxJpeGDcp7-A
ziw37*<!cC10G?bn48<hTnLHo&ePi(H_thmaFx9n9E&&36efFB!g0Z=)Ok(_QM3O3M
z_1QC?*$T)(M0;pWC3n243Ly!fE&n8Ecv=#wC_@WC0+53axeHQIOW1uiVK1D~X#@Op
zS1=zqpqQVb5-JAnQ08JODq=E3!Ak3v1%?U$Y{m9}!riy9Wey=-6$e#$le&t6OXE+i
z;lhL(VEVXE3iL5p?R<rvW&d$;;RgI$8yLNU8v*EtA&^-79O&^~3m=-iBc!L3dHH^$
zmulAW<7Rt5q;_(nM`tfi(6{vp13b{TTf2nBcX{%A{N(%a8&ujD<nS0rUE(_i`|ZRl
zl#lWC3@<52?+m&lEaqc6CQS0#83C1PS+e1OY9BqhFAV0a^#O3hhy;KYqlZ79Y>jwh
zf^XQ1%+@KW%O5RU%<zqr`DFDDM$2I>B*)ZYgLNE(rvv~*HcRN86;c-9`(i7S#w&9^
z3G6)?9KQ?|RWG%lYj*@zM2ZRbUl1#T-n9|@T%;h{55JF^a!kUEmYD@SbA^P~@Xb}e
zOkCoMV|h^+FKR#3Rn~Iht&XV&YmgHNfzsoX;(@f~%eHZi3P2!@k0DY4w2@;p#XvVb
z!E+)jP*t4ZNl4+w0oK{9SC(8D-?!h4rk9kT08%))>-RT>{JU(XFXu*Tu}nucSu5qX
zjX<LBWEM)ktz|ZRyNVyJ%1>#q1wr%FHgzbof#iy-ilQbj+s^~DLdHVUwE?dk?a30=
z(N8Sv<d)(BG{vGCsQYjS1nQRuZ1QpO#_K)J)?G1Oln;MAMWrmq)2G&dR}Z*`GD!>O
zfc5ax#&9VRm4Dh@4L5!?={?w(6cERA%blE7jR45(z5x)ek}hjC;kt~z#KXrTIg*(i
zrQ%%fVO{1YJk_KVDyGv6JjR3JvX_7rsD#8H)~G#8_yuj5zKXqvqW$knkf>q{DeFa;
z<`JJv!3Z_JuBZ>uGp;fjJy<WwX82_4n<1D0bn^4)6##7b+LOC6g0eI^k(Q>7^$lt&
zsN8>{|G$Z}{CUS%b=8p@hgz;ih=KV{7;F+OS0T~~-A0Exi92p1dB9A1Grf`l_pVZA
zzJVbdTP%5~i!iUA5v<tCf||LVTmt6v#taY(4F%WFv2kx0`n$<9Yyo*6M3hV?$8fmT
z1D^f29Uf(%JNonA%`DLBi8IL96ouPcFwUF-oh;p$bAr<6*GZM0@DnU>#Tyd9oAC3O
zeKqji>VeqJiY)P}n|+@usfW>T6x)n*PSEerg8YRAngL_5eJ@fv>=FIxFxuwS=8t;|
zDG2nDnQflv*ZdE6Xfb{T9y{@|uW~#|uuh#Rp(sJ*S2L$i%-aCE4q%l91Jr5BWt92P
z6iIeW_U`wbrfWoUvDzH)>mbm-DX0PvbPR)kc_5mgVUT8{Ywz%g2*lbwHvJgL)HsD~
z4cP#Ats@P%D*s4-+LkXsLSWOd#6oRS)@L{`E^KCHgUR2u9||?D+5r;SI6eIRL|T;9
zq6bfvN2@twqRK23BlB<V5ddqCG|Bp(pKmUi7$O~YIuD0dD^eALp};EJjZ6?@lK_EE
zmcQtB|4WQ)V~HuoEBRItHISZ?0&5oF7MlbFLjFVp&)f=jnsIOrL#sqq&SUj9b5|cD
z8zZ9z;8*T`6)26aJ1!p5GugTL<yl&J;!=f?1r`evz#@NyeKhbgclA@X*~~}d`l$Ef
zY4-BaO$4A@(}8&Xsl()|Nw-eoMB7;|^oS)u9)VmqVOta+xzS4ggt`sqa<>`5oXY_C
zTpLP%x}zB}>o#1bSwBzxdyf+2pY&8%3ZHCe3G_ZHUD$s7mp?}mI6|MjR9Lq^3Ptgx
z_yFQlxC>1GNafNqkwKR2GF42aE}Bk97+O9mm9H9(eCx^e!*VF(C%&F#nfGtohsS{F
zwsjeukd!CB+?d=OKpCJ+7xfbDfZ~oFXhD~w%avofnv=Npzf_LMPn19$|H(cMnC8%i
z&#?NlxXq~h0*H(+<RFkUkQ;B|6g&^NpeV;fN0%2x;W;)lDu6nP!U27rTOYXY0S46z
zup!20n?U~u5NICNeizuT`EPvV2K4qnA3^^khyO8x|1XRnqjYWk|JDNh&(ivT>0<KS
ztK8f#jyI0`Q>E;yu%sZlMzlGAB783MAvJJ2yB98NscsP*G3a+v#2~qw<P;Q12LHAs
z{{J&Z2()&XN=%w%?2C&}9sZjd>5r$1!4yo8(Rv`by)_&qgqelS)WDI9o%yFF|NDxl
zt@^2Ym%^edZP`vDQ2Ln7{ry#^e;^hZa;!$<+Ao;7=7~Tl3CjBa=V@6p{|oH@F8H61
z|D^E$lmq8OJSph$XMZ4n28KdvbfrFY>jh>bcKO0Y_vVNg=oU4A%KwdT^<of7){WY1
z^I|DN(5S*c$OVi{heCWK80r;%c>|<PUFrg$;D2LvBL-2eazP2^vYnv=<#GO>h<Vp#
zKzT}QOC2O90FVX$`%=*3(0l(VOb{p*-k5F6ajiPEgaZ}KAYhyuH^4rK-MC|Na3c{$
zRJmSzNB}Vgkz6Uoih{45x3_2!%rWLyK8*@Pfe1zR>o)k(WYk<PdvW}+Bv@A&qH^&o
zo8-G4MsQ=CeFrhZw&BtI^$$Mo*^?d_Ca~^>Y*sPC;JTdjl4E8G&nPT%tcAciL|`i?
z_r|FKekK0c1>a!UF+dF3{E~k`5nfhjq#n^aZ~AYhEmw6Vh3+o|ZS6$|98LH(;2b_L
zhxRUhFL8(zUET-dIjw`UFWE(D^|`hZ9@fI+eXawu-IVJwlycwC^RltT58p=YT?Qa<
z%0q_iJ`UZIx|amb8B**%)<MsY5V)9ZKf%K(Ua)Lbr9-@o#noWVlVzs8TuZbh0)aCa
zDztLHW<bocZdBs0h!DOqD!{grU{pDPQUDBHM+>=#$W}x6Y7A*31dj;&U;3rOA)ayB
zm)FsS@I$3YnBa!7?|fp^r-bYd{Zp61?7fQ}zb=;c2Kga-T%OLk>5<hdcO(OQ;}E4A
zP{P?z8h?EHCAx8GR{!oUPD3_qcAjKn4)Gx7*zf9IeINqCeAqfe=zGgMqj|>#H-L@G
z7NVv5Ek(N&$;eFU*1Q_Y-!zDq@P!TaSlvn`NH2N%<v&xqYc0zBn@`rxNIK_1z||l&
z<jdOS)f+dvZqM-tVbeZ|EDHUVrKs$11ciov=Ya}U7|D<1-0cSF(xr?*e%~I(HWU@?
zxW&PA%+d@Snp5?dQNHkMMzSI5?@ZOd9Kv2>CmvaU2=ZaSx;M~%kxy41VR-#fA9rgl
z@`1ipq^zVTBbz&c!VMn2e=-9d9i2X2C}EeD$XWigBXToK_R#jgCVq%?X;zbcI?e>K
zphh&X$Dc8`vVN#EfV<!auJvib<9h!6lRg-J!XgH)ubZ!G$6@b*TPwEBY-$ZdWlx(~
zj(YSS9QlCpu$LIn8?Aqtl3;SF3y|r6KKlL;c)(BQ?)S9E6MHc?-dk1*??0T1%EqtA
z`pz)!yj|?WtxqMkkt*Kxvxz_Hhe$5UHf6j!m%)1#vLum+K5js>g!6&@B$a#?g@`LP
zKzT{-#Zn+pMi+Ae(^<S5Qx6!z$&t9+maya_7L!J+AH4Mr_}L$r5PcZKK{HESY_dh;
z!M#G~)LfS2rIWq06JHFwXz$ahYNHCG5kzI>Jmq?=N#=V_uIq9d-3R<$y~wcLc7)6h
zN%!8V3g25{o0?xHOTOZr^_Q#eOrTAQe`yH%C-RV`4k7h?X|Bq(BuEwY;mHe}g{sX|
zIe1IEc?3vhKn3vX+sz&L<rmUQ49+;~O_hOziwdGhLqZC7E52k_aL*lP{J?#Toq)UD
zHGP{O`-Tth<_G*{bFhZ;#Wq>alhyLt`2!;ivN+ubl*jWgeTwXZB)+#m^IG$*`J^(q
zKV4awtXAWXD{n+NUVSF(Z(Bknv|mMuuL_Cag!f#uT)hH&uByY?csOlQ)!~abhk;40
z@NlH07W2zR-BG$t;v+R>v?rnuw6KAYnMJC4>_R-7Wxrru!G7zJia0|2mIz{2d-dC_
z!tbRzpyf=gC}@P^-#j!{tz~12pV~Gyf429{e5;?oBn+8(?Qc&mDmeNr;&OnIjw&V^
z%h7(d=D2rWH@>(wmaNxF8A4hu#<|-F`xSAuGF$$&nGEEgS5Bp5X`3s=ci~Bp#Y3xS
zHk+#8#5Km!Jn{X=*gGPsJa^tPD$7mfsowq>6OP?EPI4=9>N?gW7psM+274xF_ptBq
zvON>p);(g}Lc{=Nn=-W^esS0B{QF}CK_Ao(pIi3Ruy>Rcxmb`6Fx{ZY%@y%|$A~<X
zetPZ^Z2?Y(_SWNAsh1*EPn#o!q_EQ_&o}CL#I2ueO>vKLa*gL4{2?=Z=rHleA|@ab
z-BV;2?ceqzn~}ppHFKR=Q%$F&j}PwbWbfLsSCXtXYZ+IgU-w*WqoL~jOJw|?IU?$-
z5>=GWS;GT2`q;im^-HEBU;8`bLheTVZ<9w#EU$i5i1^%^+Sp4!c7^D5ddgbqdgv!3
zPba!fEUztaN20~FHr872ht?7#u!-Dw5x2#IGbb}klg=L2#?CSkeF^->8m!2#Kv}ab
zd<~P|wk&exB!p$j&i+AARt%<Uth?>K4eIo9J3aB$xDmd`@5S(d_mEZJv0u2OC7Q<C
zCE0wNjKHDgevieJL-e%f<Y&0bIl<l>=PXZqgZX=7C`u(%DCxQKaN0F3nkn9TT2R!1
zG}kXLr(Z&`V|TyVik<vzzQ$6TkUPpFjbN`9mA!Yqx8=s+qcBv3%eI!~DGUFD95(=K
z^p-n}zqlj?X)CpmzB5H*Rq7^JYx8~%QvGeoj+t@V$*0Hu>E`9Ltyt1f8A~+b<#I-S
z6%BZ1$ZhnHzmp>uTxXuEn0l=6(4v?&TZ3Gb6p1-lb2u0u2uu&e(CWKw4mfpq*PoGE
z23b|7BdIRm#_h_9I;lbx!4jPLwHt3?t-k)E=RGM~M{Ugm%O`KmC*4_p(oOMw(CVOU
z?=Xo(SDCH(B8~A4+WnM0jC&1^{nFTYIzRm)R=s5IcH!abpXm?2ANcKs`Q2-sN@2-d
z<yb+j9j19jIwM$U3_MDuJyxTfo{LCCxj4ss!JzuOiVsrn_l306_oo$EvusWd6Gj%~
zIwpi|U}+wlb8{D@$m@RB-kkTH{96Zc(izwn^Bnc=QE!L(0Phoyl;K{2@fTa4$f~@G
zms;>ilk5|=Z+<N0o)Ehg<CL2{o&Uv;x0BRk$yoTnfyd>uE+^11)$UY+?#683`hD<R
z+JY$CM$HvaA{8L3tZ^CBB5=f|d}--#ZwO{N=@I#KndPoR?yhl`l?cSVS3|}XMPAx+
z*F^tS+5JjaRV~pWQT-(Ie%O&J=Y?lIo#IL$N~`&*<G6izd4QLp$9kkV<~yYYuJ-3z
zYX~~4!S+vgl{MIUrI?+oq{tAR!uMN6T)KPgcXQQKu)Y)~MYf%MHNu9~c#BlV+1b9>
zk7R4k%qP;u7JCswYW31NETu0w&Tk+0ajMk6FU<N3Bda^yr^`JnKJKkUUFo;2NoUMn
zym1R}Ns$aZe9qZ>v~`rVSH^Y=HhX$xKyutr$jx9(f;XmKj<XKpy6qn;y-`J#(F}fr
zh*Y`QC9C<~Xfy=DAK-OYe9`!d1wup<_eMKT8FP8VZtlVI!<8#8z*_Z(Qhkl*u>HRp
zm&Wl#{>r!O=OsZSQGBCXEy>b6?Nhch-zD^8-b@k84&^6><&ULsL@kfMEfIRq_k-Wk
zfbWhQN4~&cI(NT6axGFdpY4zr9Y%hKy-{{BY8ZyPd@?Mk`C4m5vA)$BKjFKv(X=^T
z6eV!WSq=Jg$C9V){pv|4e)pTu373}3_nUw8K-J(2J}?tePnb#WDe`JfiTzq7`~sVR
zIK7PAi#}Eat7(mam8S$Z%n*0*@0!q*rU}&6VuBmeM0=N)7N=YCI5(xCNRHyfL(kmo
zQfhq)kjp>P?oYJzqq?lB-PZ);ETS>|rZZD?DguY_xd=hCth@VyDYu4xc&6NiFI;)A
z@$G)<HxjD8*>^A|cS#kWqS9g*+Bq;?YLepq*2gTu{7dutkC_q8KL(;v1OGGzb>+^E
zs=@kyT8}kvz1}XX<5>w-HTt>3$s-~EONMzr=|`;IZdJ52jSY*YOQectp-Ip}SayK#
z;N+U0hBAG8r6IJ~W@Gs(x`E`XcR}b%Mw)9wv$>QGObNbVf-C-ZHsJ8-C|&XD5PE$;
zEz7M=`?V5|?GcR48fVew2Pd;Loi;b|ZP58C?DcT$9CNu7`gZ}v6u<mOOk0*HE@O}*
zrIl3IQS9^t@L1b-sx+G)S|FpNe)y>?8A;9@g(4-18jTXBg4)y|clq?|JM!{H`a9?n
z&&%LaLw&Jgu6~(xBx8fprMhfkv|S9N$T<694qCv)++ge2fqHzj%NWZe^-DZ<bqCFr
zo$DDu>7fRJlpw69c!q1Uy6!}%dV>$tNOu{9Z{r28w~t<rzcw$9J@x=MT>Wxu1W5NQ
zn;u>E;-i2b10b$F^UY#OgACmP8*+r>9k0@}rPxns?c9)fT*npm)Awv$aQ*Cnkngfa
z$!X%9%ac9dS}9n7Tez%^dzEZ7hFI3U$%}c92~<$B=||0AW+#{svlJyjcuTLz<aAqh
zyq<PA(Gop2aPwK<VHsztdc;UQ!%?+3Mlfbe$h2>Y&VK!GdcKeG7;9Uq;L7y8tzo~?
zkbb6W>d1V!)J%8XXt61SNU>8~NiDy82FiYXz-#Yzwu!0UEDC0e@m!wLq!Z;?>Tt0+
zj!k3mg?iLfQ#HT-{&!TRG-kBrDyd9|oaH=iI!o!xrXIJ!+}W1X1@rBd_sJUuLiPrn
zi5}IdQ|!a;j@B!wiY!1;ChT&ea)y`VN(wV$Iw@ju6z|s5O&US_WZZ>1veUx8tF^#(
ztqOq~^D{bQ#&EcRyCIUhex*u%xV8_DV0m9qN}7ewQge-~U-CV0?hRi*azy+E3t8@!
zW(QD+;39sL1jPHcluOW6FSJVeyjy7`(1LrEe{!7!^_oknP>OWJyMkG0Xl(e_#%APv
zcp~S@%<p$o1)YAgH~0*7&{eak6*_DX@uBk7?0B)gs6ra@>|mEq>ruqze@g_IWeRgi
zki%1B)gDzt?gQ2<TQ8>L*sW&nCz9%P$(+es^Z&r}Ep2beBU~(=7e}Rdc+=z{5iUvQ
zNv^T`5>l;eszvj2!`AWdzh__3@p!31N{UhNJgaLh#g?(c1!2OsTfr@+@sNjw0nz=S
zySM&<v0$yvDu>k7dQ$h`<al2D$b?^(*CNmFWSwsE`2R1e-YOu@uIC!Y-3!HCix=18
z?oM%s;_goIV#VEyyEDk(?k<D7I~4t<_xnEw{}FS@-q}f3*2<M+k(QuAZ#+LAYYJ^O
zK`QcCocP|bS%%qAYx3e}Yxu}oD^>meiu;4Z(#>SAH5OHfNw;to|NiXhYEB1KuNzy&
zC={7JJoa|z0J~A6+)oW&V=-nx=5rL``Z{8?cFE89@-w;3D0xr)8DLR76K)0`&f0j9
zl9iIa#Hg7u+~3*FjYO>_Q)p?{Fl2_{Ipv|1+UBo0%OZM$3_)h}uSCEYA{?->1gup^
zu47*IS11M#&xDbnvcx-TnZP*QFYNl1l|;0(`+bdKun8gDGUKFCvlN;Um9&@fYj9Ua
z{rbbrCVH_^zq(_sl>OLWkpHP@@TM<{*Qp7-1c$RtdLr`kfV_O)3VHTK)^vJZ;-LbW
zE&W@nd)4ocE7SdkTNY$h)WN5Z9CvjK5LTH@`dODx$eV)D?XNRPEsI-%FI;h(x$813
z4V&>lx^!f#SlXi^Jw|D?yc5UT3xD%#Ha3RHR3{PpEfe-c->!I`uR0T@HZm5yLqI@*
zbt@xCr&I3V!|1Z$MD5Xj;5Sai&uLYz3+{V$`?jNu<X3QiQr`Eds$`tiwD2ZG;=z}M
z+IUb?u_&GjSAVZz=_UFX*R@h%417jTX?@g8GkMv?Se(jjeLP!5o|7Ls^o2OTf6Tvk
zL7ylsolfQZX5yZ!i!o9!>3nFLnaP`bxO2a5CEX|qVtSH_nIf^&wyS0`xa?Qeqk|Y?
zV71*FKEAI&d!<jD7C#AmOSRQ>KO*_!qyFbF{RkCJca9#vxp*~`KPGS2GT<qj^oqtm
zo39u55Sih)*xX(%oRS6tf*q`=)H)WS%R$PsVrQ&>`7%RkZo@yL$(&L-!n9}XWLsGP
zguhkZhiKrqzvb7zTRg_VAAoXb;A|@Ohc-yeJal8@r(S1jmNcjr(^>M)Cz0Re&dpwk
z;jGeaq)SfZ_~4h>>GW#*z)F}!`E4eD?UkMdnLbwiThLScL=bQN9WEzT(8!#5oo?XJ
z%U6~(Y2v|~ns6uD^81WDdeBfRt(Nq$nCb&qh5F(DCZhgbX0y_b76M|stee6cLYbVu
zxqDGRP50qvlD6s`GnGprCn#W=2<%9yDxA%+qVFy(!CDGeK|U@WoL5{SMpP^G2E#V8
zt@k`eofKo40B9SA>#<$c>i5emyhDyDHtU7h(Mm&_1~;wR7FraNM8T`pB=jw)U;I>S
z;6~0PF`Tym?#SfdRC4KIrDM{3y8)08tcc($GL+n-mynzgcE#Y!hFSw?sNoHn9{XPM
zsvyHwKSi`G_nXGcp{ZB|8Q~6UPz(M~^~$#LkHu=@nes*Ciso)dSWnD7?d;f#oFIM<
zs?2P!UbY%DF~x&&-QrjXxmdKEc#wziD6G?{xw#ZcJn>VCmUTYS2zVla0+7(nFnRv?
zfByz-PpqWToqhhg%$G%#1`sWWA4N*3v%ET*IkGuX-bn+MB(VZ`dRr@O*Sa7a(=j$+
z0q~H4)e!2st-Uf^wosK>(X|Oo-|}ZUuRBthP5<kJcpp3wIG%#a#_y1v0mUbYo|^=E
zOiMyNGBIn`dN|`Q8h0snFjY11g7;7#h36&*HxZPQs_-(v1*W(4sUD>3JQm0=@^5Fv
zX@_%T@zja4?I)`%Er;G-UoMv>CD!C({<+mq+Q%5w5K_;UNVd5ObGjxoC?Ulh(Y~jR
za6Ye1;pRRnF9ytmTI)|<(B<n8Tj`CQHSI5NgBmpy3P0SzY!KF>Yw=#*I5oeS`#K%<
zfmdZpQNmpP%Y#gMpr}D+0<m9frGotI2gn>7%m^Z@X21VMgD7q=jgw#(VBk!Q^pLw|
zb_j0n#~Pt3_AE)de3Vr)^P&F4P|@tb25>yN;!D8CCrtLAtXfTsNbX%+K-jQWs{br7
zG(R=fpgdY;ejMR%XM4GbBj;X0T~`|RMwh$W4+UV|&2p!1dH)7|kmQjps4RJ`nwgw2
zXja`SX))&Zn|<ozN1@;B_Tj<D<EUq3@p{>DekcD}onV{nZ?lFO<U_FBy$+^-#WN>l
zOsUu1@g)>T35zrNsrMCqJ~f*AP-iAM`z0!2ff^rmDm#m2(PI_D*B<HF67XY)dZIDd
z%e${?x+HO=J~mfZXWBdH5~5&PGn@@7O%5uX-Kv(TK}+=CZ{L$FoB}E1Zb7kG7pn^i
zxp6ZA&lW2l9m9W$(X<ZAJJ|@CbC*7leV%`;Y<q3E&DMVZbGyKH-p%&6VbG%ZtbyGD
zSC@)+LiM4QTNeLcAJczk-<ehN3bMp*Yq(qcaV2@2q|3mvd6`_v+ORYwPYW2eX^F*G
z3m{il;i7nB461m37P3?q`gFdaW_Zv?Uy~xPTLt*4z@|z1NnB@t9)omtGDmJ6!=~KL
z<DjwNhk|3wz%SP^&YmVMi3?z$b8-rLbDye`s>K@W?P<Sn&Bw2AJ4%bIf`7Gh1yA(P
zvK5?*abXS%IAut{91<beOA#8t-?~MN=3ZMLDeiN4Q{&!*BsbYKsM>}>EOAI*+jIU=
zVo*_K>V3w|#zLJTUErOBQy*ie8=O}u)k*C7c^i<&`90uM(@^$vd7IsN8dlx&J0qua
zQWU(;(%>>@wAsd$EHCl>BR^YeUBLUrD}j~FSS6rxXF>sDiSBH=bM9TT_PEc*pDPo_
z4J_Jgm;N(xD*suGYs`(*_xE3W*uUP{CJeL_NplPV7sA)mLsT8V(d~7J(|-~zXlbh=
zeo9EF!#qC7>cA|&|E#$*by*iV4jbOaxwMV2(OT9$^`b4PZ$xKeK1TDM|Fdo3AYEsJ
z!to>M&r@~_L))Rbb9*WrATE9{hmXp`ET^zKm2*tbJ$hcH$LAX-#fq1I*y^vd>Br*h
z)m<)H^W4OP3|qE3dA6@7S5OeO5DS}zBM{1LyGz-2clH{;C^GLQ7i53mel$EDsQlKu
z&%Qhy{B3h?<M3Mt5dSkC1`8p`7KO{m_VwxkWy;?mM{vmBKd#5$1!!sEYjNO77#lbA
zFupu45LY)Lz_R-l&%p>tCd?>G_&a{Ss#uq)$-At&T9Bb7qP6=`O5DxvyGEO&xaOu(
zE?+t^zSpjWg}B+^qyOb2H-u~mv&Tj?a|nBzSNdq6fyZm9QTo?_%Z`n^M6Nm~+K2F~
zl81;7>0pil3aYu(4I*eSz;dEHe~)ZFF!Rq_4JLe4=O+Vd=zXmpngK@`lQnO0Z~<>|
zUpg+|T3a?y6`v<@Z06sOGqX9#AkE}Twe+LgUx=rB{lBmXBC(8%PH%UeO;J{$hdp*S
z<PQV1>SXo<UC74olvd<XLVAo?@ldi8NXDYUzZ&ITov<sRDz<)w4=4w#&Jx?8cA`8O
z(LJ0nw^zPKZ;?O*aJ_c36Cmvn)^<ey`Z`hIhgmhNUR3U--hBk{qZGf4mEBc>FIK&K
z7-ZR#i*qhzcYpq7Gxi(XZ!y1B_d$1DHV$*m*|BmV7PZiaT(x9RNYRT*>Uzyk;hKLF
z+712VY1dOp@aN-R$WgkM_gW-P9UPovwE)5*!jYm7Kco-7+pgg7bq&`?Wi*Sh7o^+V
zMEv;{pyffJRc%;jPxMnk)hLlj2m6*G#G~@d8W$c4Tu4tm{p{ly2z<;8^V3G{0A_5h
z^&eNbvnsw5^kHAIdPXPT>cYiTblNi$5cn!n?Dh*zR@qUPoICJof}tu_1S;+fw{enb
znhx27zwm275vmMYSu1OvT`JYYLN3YXp00})CSLTzHKM2@)6006N>vkh;!qgauFa{M
z5BQ{Me0+(zuo>QT=f1FW2z=}$_1i|-Xd&r+S>(Qo6AYUN5E0hFr}I0|zC3UnDIF;z
zoF5!*rA4=2*cUZIxUhsQ^*?%fp?U3)w_dxIZa=(WwR;wtHsNd8A0TPJ!R=&=;Rh}K
zvtXEC2&N}0oY+SJTWN2$^xryEWNK_S4Y>6(M*@>G?flF%h}XZY40u3hNiTpV-N6aH
zwpf1jpHz-rq($?nWVW_(Y~%+4?;4_R?0j!K1$J9<zqy$?PKj@bDvjK0jp|5K&^`(x
zap}=bp+$gNhQz-rMqeJzt;=dv1LEs(5j!WFwAI2#y6y$dHlIoQD|Q7RAok<@TT4W1
zI9Y|?1uubZ_ZXwhkoWhHX+~cdT~}i+jmr9pLNc;`R#c01T^}Fh;LdNQ*YwUT^#;lF
z5N@kx1~vmXOr=fdzRvW2wLuLOG(oCzi~O7G>0&D+I{5w+bQjZ(4>m73C*Hpsxa0o2
zCajg`Z3~`+5WZ8*36t^(smf{lSJe=OEtNLNK%go!0Yx8JZD_>9KM}mJe4Z(*O7nC!
z{@%(gmzvft=}pv8=KRS+T02dyn8tw0=5VHHh^ZoJOm0kx1{6a)qRq>wA$vE6T-5LU
zR#EA_X+q`#&--Gf9W^}>@Aalz_Xkbw`5c{s0Tk0V-0=`QUByo#UcE?MkQqEs`((wf
zKe>n{Z-@+Du<9R`<&B+EE!yT)q#1m|Hm@oCWj^~+^v}p8Z@^bRgU6??5u%_`wQUFL
z<R9(1;O7gr?(Eom8`4)ilvJj2Pj0hVE`Mbf@EQ4Wa)E!Iea^<KSd0=jc6fAE$}(y@
z36C*G`2I+F)ew^(A1BHdv2?Dqz~lzAPbWG`SgQZ87od4<+vqw&omi@idFvEg9P%8v
zAjVBuWD3C;Z=PapXj1*$G9R4E!sJoi6`3FKhFMwGr@x~3!1Va_b^B4x^OAVkw5gL4
zxrhX9)E(b#;=bzRK-&|s&5<a@AZXROwI({O!DXxBAgcZtYyNSPPxB(-D%PW`=^Md6
zhcuFAdaDuzzuC9QC*!kVA!vHScDYJ<ypg<KUG;}qwma)1;0o%c=&uCSHwvDMz<K;d
zzr7t!v<+<;N#J_OU7CCX44bD<n**xF5Zw!dpiMW<ptC8^c^1^#Z`;-*AA|ihgHW0(
z$C%r<6KHad+`0$@eUWW;CI)_@_|HqE`FH%Jy+U4<k(vZXx+t%&al3kgSduJ_y{opQ
zpb0-4e78H!;j$rqdznc==tE%zJ>(^&%TE7$JbIUb3x+neJhljr&&h4|yZ<{53FQ?5
zN|@{R1X+b4V)Sp$JW5bM0OBHOgI}|GkoAtdS}WLgw$lo2fg9@b8+j<2LGdg*xePVg
zo*X*PzKG>de1ntkFIDjkA|>L(@WZ?VpK~!crNw)QWs~u`aFh(q@*lplEpiNuXPd#5
z;6H6$);}i%ggo{y=~|C{bBz!BI1N`$SIu;Sp3O|>hL0{4+e8cs@jVrx^GI1@#8oP&
z{)R9~5;DB8qP*7}?(uyD>M?#~oAY06G$u8MF#tzMv_(C@f~7Zr_|o?=s{HJy0W3pm
zyDw-_Iw7hacS0SN+cl2kg5b+ZA{E(HIZ4-hhuV?;E>nEdt(8o8qG!xZrQG7A8ZyBl
z6a(WQBrVotA@LbEmGVIsWEOU<^UhLt*DIR5#oKdNS^X*H8vl%6erem|ekdIuOJBe`
zg7VAkrk(B*0Rh>E*k-gd(R6U0N=m3pADMJgUB&7+0{Vf^)ta!dW)GCx%UXQ+JISje
zTM?|L<n|W!e9q=QK&gC4d4T(DHDgpSC`mDhSqjz&H5C#X=o5GebrF%`hx~-Rb=h|U
z^b3bwhwngdWhjSvLEV}PWchQ78w_@@yU+ibZ*QfqY0WLTtv1+o8dSiXSqt}~vz3g^
zOYvCb0JHJt6f+~&VzpK@te*8Vq$Slscu`S`#AEfw1M(-Ehaza?`fnoRqUek}eE@Z0
zXb4IxZ<3BgKlJGKGZc5ML0=#Ht!I17&Z#3!^j#1TASuYxSN;eSk`DOt`qT|1$S%4W
zi8JsP__%0E?7Y;;>v=4<_01+eqx9x=y>Y+gmuM^PwITPQJlW8lMt_qkZ8W^om=uh3
z19b=Yo+}H+s>cR#cq&=52yah<h$rlme9p2%&YJ8VN2a+u(4S0!usQG~R9O}G_FGbc
zH4>sf8YmnfJ&~`_1uq`$^-z5YS~0aDzL6q!2qC_5T+JMD=^K)O{dAi07tn?k?>8m$
z(na$*T!LvaUb~%-h!A2C>T%q=uF1X9fm4*T2|uOZrALPNp;_a>MyLOfY`Aw$^DBr`
zTy~v@50*&Sn9?%=;kyKZFQbm^`nSK{BspGrmbq(=?pQM0K25mhA3U&+G`5`L7cc%$
zoP08G@7;M<YL|obm0X`aT4s+F96syAdJuFl?@s~3m7yQQx;Y`>(2YSaa$qRa;X&RQ
z#@Gq7|D8@=^qsSGok`gTvg})@SG?Y<^4<if!$nsUEo+1|d<mf=6<SG35rhs&Sc18n
zaP?9MjFT#`V(%b+63cthK+2>={{`g$d$H-LIw9G6t0bYgF-5y91rAmbG4HLx+;}K2
zaW}AL*A6?l9!v4wY1FHl2Ad>wxUZA-4_GBiFxF!yB~GKR2<F*|Bwz2bzR<s>h>MG{
zJXSUOuC{SmZVZLT_Jca>7O=QuHdY#P^f(>;rdBVQGLoMuQ{PiNFZEG;x56o%T4ea#
zHoY5+P+b=Xi@RXf3elY@wH;o`tamidxqU8X?my_@ow@VjHk<uAPp$>yjFNdxoIP1c
zb0FRynRb{HOdky;AG^ClAN&iV{cKV#1I2*2&1YwvTet-;Lh;I*{}QJA^Dfec5$hR?
zcwzTn6*Dg5a24e!<~=?Eoc1~6Yc5MR*ApJo{J{08qS|;(N=BKXyXyn#X!S*Wies0n
za)YqxX6XPT-idriPj~Wskyg~bGn11W4}NnFhF|+=cSYwWe*zwRb*|X%$>@L5lRPmE
z;!Bs*VG~p`YvA2m=G|1Ck7W~`Tzn9^nLYkm&yH`1vo+M@Z}S^4!auQecNiDMnzTYn
zSv`q1-mK+{njOb|h1}|voI&dY4spNgx0r({uA+gIf#@AjuUw8AxG!C5Mg6OjLZAUV
zFdPso{|Z$Dwiz+6n-F8xPuyGxq3t<kR#K$;Nvh?-sxkIaxDONUj)`1UO44@DPIeJ-
z?~gV!d@{<+is?gqW5zU#a!n)gOD2ChRfp3x;g2Y0Ld@i@@m-F{$=}0U(he{e#qAR&
zcFnYQExih+Eti>)zd3&f9=|43x9}$j1y|w_ovLYeg!fLZ<=ULPv;eRHds9K|GhY0G
zN!|GGlFL#1dG;SN^Y@z|??O42zLP-{N2sPxF)fCI%|5!5JlbBnJDip05dmxc?H-b%
zwXtZ^$b|1)il%9BiqPG#;}G3YzGzS1x75{-s#1xf>`6hUg5W2*%zZbvt{Ku(OG-CI
zG4#RLahaU(m(QAhTWw}An#G5T1DZqQis@5S-^O2q2WI?L>@qghqUwh(Ajtx}qYe9Z
zQ;;);4@B{4-V*Yrc?X%i${K7%&ES{ENMY(9jP=<hL0aHx<Bt@dMZfmf{e^Geu&=;g
zC%<vG>n0M+q~i&tS+tH}fQyBCJ9mG$7s%-fJT<g3IY%wsful4DKXT>?T)Y0O7(bh;
z(zi)C$ZaQ@Z~tmY#vLYbU&6ExKh`Ftvee1`8s`CdhgQ(#LF0P3+Q-j*K!WJv>B7y~
z>DSjqj{fSH)bp}%<j(R9=j{zo8Q#CThfh<z(GI&+Fe+So_YJrUv<##q%xVT5SQe})
zJ(T+WLm9+xuI9F^cn^@yXS*1-5iG-hY@_^Y@eG#Rd|IWlzbN;-V|(ag{9<DR7IF7#
zI|j-)L?oQh@AhC9K0}!Ha8N!&q*MZInUalrbAeUahPVO)Qh#S&x-j)k#s7R6rt=CL
zVGEQa2}hxSepcnlpBqg_$d;bOTQ<!nTqA+AK{yLy<?EyWDPgY8JZ_-rK5iKD(%-Y@
z8g%|7t(MS4brT5aln5sZF$nXK+!&sKZuy!m__OM_)7U15x9;3Z^PA-0pRwE=3Wt)*
zC)?x#AHr(Rm_~}LRp{w*vJS#_qRF#kxE{9p=jmAVii!)d&Wpny`z{*bK^h!l_lvtu
zi?{Dmv-&~QQHy-kWMP=W%@l>@Ig~P-Kjr8~Crgyd5u5`|b>uog$=1sj_NnLS9Ujow
zS=GUZ_4`9$^cai|!p5L>x4?g|>pYQoAD90~l$XwWsE{W(p8g8eXlg-<o0Q&rR*18y
zJw4mrYDy9_2%}pZ%ahCOl0SP6Rp>$dq#2vRF9It6s$CUg&#LbR&$fV1U~r=Yt67iF
zwiCFCnxHQcx?jokSQzY5Q1EDW?u4^}bo#ge=j1TAyZxSxtfz+-h{X|%5HTA8l|a_P
z5-eG$0YNW(O4gA}AwEmje7<X1hu@wiVjDS8nk)7fcLefN^A4X6mh+rdg)nMnJq#l(
zHS;11+i5oKbmxi`{5od6Ca>KlhQ65gPEN?<&CRISWRk&AYp2+N&2&<xHhU*_Rwlk<
zA(X2D@-<mGgez}GZ!RkP!&~U2%e~E%*a3nWfmB@i@tX4EtI$#SJNta5qY+DP*aALX
z7`RpC3eb~_I<Wp+HZi%oimcq)5ER1GD~R{G<kW;ClzgEB#+S?avWwn%`P~US|B7E9
z%j+`QUZ}2b*QVeS9r~jKd2MZ&>WX^He5(Yo-VDYiMFjuhk~ECHr<6^vP!&g2#_^}y
zZP)~U9K|4*T6pr(Gar#3g?T%rDBtnP3iTPQ>fERqm8B8~99)xatJ<|zMQx7QLXweo
zK4)sT;ZwDfp)tR;tSw(ao;4G1YHBkHV&zDzoIchGmrc8Mx<^Mf9!#&%(|6EPL|}>k
zXvBybwh|Xr`K}&l)mc(%TZV#!n}oAZCe<P<VZyV0w`(<8r^jai1rs9;VFiPZ8PK<T
zK688vkc~p>YU<Nw4Z9&kv>}j79hNEww!$v$(U5V6Hs8!UX(tEn=k-fC<gBdn`X0;E
zB7gudfTzS^BrOzdUN%S4%?zKc`X&GCnGk5LEp0MYDLKw$`xnqKKR0Vy8~>|P?YwUf
z2VhzM@qz&BXZrIfYUqX$rt6EudeI%{{ID5MW)UW(mTBj4>h$IlhzTFS-{|o$GlAbV
zNo8$>bw@nhJH$Qy`&u-C`>}iw^$T}a(_S_^ltVxw<hNO)zwpg_&Av3xx|F1mfNsPN
znka*#q$TkdmdmSFI7Lb3O?mA5=?DwMIRZ+c>CAitfFiseY$!dh|4PvQ;BgW$X8RnP
z(lB(I#oRxbEZ82P<LL>XboGqpy7VjB+F)7m2DSm&gF3R(EfY_t3|Xz?&pN|e>#=CW
zW-6Zu-xdUsVU)Ry!dpf~5gaT*1JZd_9x4be%A-BKkmiP1G2tCVDf5(=gnPd|JL=NX
z1Dk_l3S<gn&mR=+3=B<GoH&9-s}P&(zaoe-3ra!Yc-K>k2u9MyUf8-YrVU!RNf!;y
zR_q1pQN0>u6NjAfba4)+YIVtsIDo$MW@Y!+J@d;o<6z4Xn@6Fyo0`qDy~A-g6|>PL
zOC&_bGBs@r6fvVpRw{5HJnD;-SsA9@`{_V-8Hh_Xe1btn4vh#^MJlemcULL3%Dxv=
z(_dBUyUr~oMr^Ux6+<z<_#PmF3XktzFqF!^BOzKt{QmjMVvTSwnLyPWg7Z$FpR^%V
zrqV~~r~lJquSp|-)8isxP-3+*Xgc{cTi>w7n{jm6u0ubWH+bGqWZw|96U|nH-~;dU
zAm#((q7@hb*@65tGpw?99M{zp;@kplt}qWeN3Kj>;vk9yhyj^YX1Ku_p|z6rA38V^
zoCS6w4{s@d6#e#QH;z3u51tLSR{zUyccil?a1zeAhutQhX*@C0A)@}-TtvyFfs?{5
zn5m$yN~+iQAniJv{6y17QFbZg!aLyMk6W>R<N(>HQaa84&!K9U2ToKx-svxJms>8;
z=sQh32rj$B6-K!L4{j5cyuGIGnoS<>Q?8bV6z{_sDBWcqMK>AQlxFuH1?+R^OxK*0
z8;|1EmBGvn#l0i9L5grELbM;3MCv&~uT1<kiTM5AeJm84uMWe1hdc}%{^HPOhX<W=
zLaRSmn}q=7YKf4#F182lR^YeOyTkc6AXf5I41SYys#6Tv0DRF}5z{V$fq;XfG^j}~
zPd&&bDT+(`<|pubR;Id$g=&GSX<TstU(=C|d;%vJ{=4k0Q`XKKrKDW2_l%K9x5Ho0
zD9w$BgckWsQ~BNHT=bKyjDu*?9~rIkmuK8}gld{@nNdfm+D>5WoAB$K(wU<Hr{KG2
z`Lz+U(A&kH!yi$+8b^O5^~xowi2a!t0PNXW;ITuKE`rrXwKtfSeXp(_@R8Y_3gN{2
zd}<5*MTnrej?f+Mel=Hu`0W9-#`kEo3(uxy=c82QZF?BDj%jwxcyj{{cpR(E_0o4;
z8$EhgT;N`EFM4tJe2qG4`&jO6b~nNBbPZ|sX-BpLa}Q#MCPW=@A^9!RfdVhwsHCdM
zxW>+aTdJlf<ZbK;cRhYTsZGy{7puzpDL4)S@(0OH10up-PP(U0i;7E?$Kp+x9|?Ap
zT>1LWJy@IUuKaX_D$Kz#k}5+xu6`+pV?)z~27PXQONN>k`hlvQ^@n^Oik*>JOe!f&
z-NjqR0qA7Bi*QS&^SY$1YF_aR)sHq(!4m54oW?2*77f8H`3bYB%3zFS0bWjAuiVmw
zd$T)S7sst9G5IaH{aqh5Co^c=xYS{~{iNonq5&X5Oe;UEM%>^T>!jU798)mNZ;+~X
zZg`{<C<tr-R5m25sbGs@E_+}3k?^3u!d;aB*TaUeuU=-}Hm!EuY|S7%d9XYjASd0H
zbN*GqoRa^ty`Y4_`)KTdsM$NUx+B8bH_Wagv`KY`s5U&lJS7-|<HR>#+?~|;-}qM3
z<%zhN{`q#wG~`y)yN!fa7%^DrIK)k8j)l9<eZ%^Ua<QM9QcEf6+`J+I5Fz$KGiM^7
zt@%$s#n#VY1(?YYEn9~iEh`GdXG01}2H|3q<%ewsF$U0#A31~?A$}1GrtdP2!@)UO
zZ4tA__IizLMrW<b3QBfiZSDLMG^!Uf&z*^1>`kQ60l5AXR`WA@DB(7)5Us1ZY02~m
zo*BXr`keyHnL&l94^Wu3mP{Ak^8FqA$!#kU*d3kHiI4>;umvbw{%IK$KnM~-con6h
z`+&SM3a>f71;zl`fnc8GvJW^%Y(EC(-&EuN<5n*btcP6!T5fl-$fj~cL5|p2{+Qj*
zd1+c&(%sT-h~_XG%MoiUt18Cr57+!WlZnSpHlm)Bm-fsyC3O0xX#^e?lG<NL3d$|x
zwX=6d3g;=fV-?BQfyc>nS^6LYqcL2CKe;qo9FeNbDWg>^RyG(-wA)*NU6w$>C<2{N
zUXSj^4h7ys>y+`l^@rsrSD<)8Ns@QLEAHqK)viEmva8>1CNGtRtGCLnl#Gh)$=emZ
z4+gKnn4XWcq!CD^Z$nIDT0wCT-5moz0Jz<V>qIyfKDv!({FFhsTbV#kpj6OD<F?mf
zASvW~ecuwaqq(b(%U#PSQuco_vz6#5vBCr#6yk=XbHi6j+5+Wj$l`?HXb<9}3Ca~m
z2L=@Dd0!&^RWYB<>C19m;rS$=t-Gyq1D)Zg6e&Vl{<>HsASUH1hTAgni%8@SG)qDt
zFXi;s4Gu5QZRc{voMi5H3Svj=@$w7{!f%Yv^k~_6k0U=ELKGHqNx?}o`~}$b=b)p(
zsKiza1`~MGYKNv|#xK-xoWE=Aa+`o&$cJO9SpX+%%5ya<+lb7qTDB{B@Zicyi!`>e
z{_kNQlzrIS;H6}+&1bwgq&!r~ukat1(L2mDaT%o0&MLZITe;1Zw-i??R+%<y{4lR^
z%x}v=cyC6aQwN*we?*y~$v>iOn((Az7+GOa@oIE9)N=bTe1d~NK5won`FJ`^0L`%h
zUh@o#q4^82hY$cH{4k26!)0PpY}pXU%5@1ejWMa{&B;~iQ7U2AOp+KuBaZLN>1&Si
z?1A+aR1!=>{J29&(U5Pis3T)^$xGWlsJlPDYsy=wTzWTB6M%;D=f5ULMCjNFimk6a
z&zIh_tHZ0Prl>G<@PF&+({^~K#uGr<1ut=aOVHQSTB&I9@F_8|3H{<IO52q6Y;x<z
zc1P%D^lfzYToTWR$=arcWzrkB#qytYKzx+?pJ^?JBb6L7C6_r^zWo~iBmc7&38QH4
zevxqYtYAa5J5Bac%&Ch?&-v>ve-+^B_u!n%lXp;%QD9k=$t<D8dalKPRgoqKG5-|8
zs7;-xhJ2EX8Vq5S8LW5lws(-hpla%vJQCjMyyv}V+FU!h$tMPOF}RrZvP*+1Kgc-1
z|E)_fg1{esIfRKLPkH53XU)PM`*Z`{r1Qb@kvZ&uWQAl1gE7dXSwssPB{bHM_m<2v
zd)y3s0x(yF!Tn$O0+q1Ebv%Vmu6k}04(sU<#UWM7``~83$&wxe{BAX9-h?{&AcgGC
zbWtkN2KrzcQrP`*rs)C@*D}e~vW@fFf#NHsU<RNzWzr?B*(K>mS8a+!H1o)}k|WL5
z!>vvt=Ger#Ka?d8?>(A?Ff;DaX*90>$uUqYft-N^?*{W*9>VWjj_5ti&{)=6IjjsV
z8d(Bn89Zo7sObzXOdBHu6_UL~2ElyJ&o)(${~`-GC7GmA*nm^gDLAyiw<FtU+?E)>
zmfO3Qv4d5rNm@{}=P_-`pF0u5me1|Sx;vlec0X)G(2z%(euu9q-2BQ59>~_3K6cwp
zt`~~{cc%Z4HLHa7bjFk!ZNq1$poS?uWnJ2+8@zU_NJu~KUpd;cQ-7_%*I{y8WD5R!
zKBf-Grd7a&RMErs<Ps5p863Sem4DMB`Vf}mp<-Sw*?e%Zs3cZf53&>Jc+Zqm1jV&K
zSH0c)0RNMm#_;|XD5>mNWGw!Wyf3WQTM#HD!99JYL1OWwHkVR<$3!=>sd}V8(nyYe
z8TjwmcN>3^?sT`FgU??76!|791PNa=OKi`D5AQ&JG_?#hMV!AH+=`r6tf)U(s2=u<
zGX{df4T^p^<<(3Vr>;^21CpAIKt!2N{N$;gsERwH7zyDUeN?A3dp!$Vr`Y`9PVq(l
z13`i}8}tud;tqae^ibZ;R5mB-F38Gpa^>&w6PTo`g0b`)O+V5Jx}4wcv~naYazzz7
z`EvaKPnS4C`0qep*d7^g=5u>S+pa#MOBP8f>G!S=0$??5N)UP9N3KNM3FkF;IuTZ*
zIOkp6PT!;q%{hul_w@`gN%birDTVSHretWz_W1W|PbZ{^iXwkA*yY-bpUj)PY|Dkl
znB&wA7t|t}!LlrS#WR~Kgs4V5d3tv;EfGk`#R$)S|3o*9%(IBsWv^-^|Fvn$oXCdi
zHEuMR9nzohrD0TTJvWs(^csVSKW<k5@IAg0seH=LK+lH+sm0;K$BE#Kv2tH9x1IDC
z5WvtU<f!IL__7PXvz7u*@OaO$-w>HO@KE#%+XDq2J}3-7s^oU;#WW|$rrzyt&#g(l
z-qnWxI=B~S+SnEFXEK9GKDWa6BDWO%@uN{N1p5!GpKFaM&s*>Q)>d&tI<(ALOo%tn
z*F#5Ib>}(HS<p_hsBoUv)t$tNcbKsIhrp?Kn75<<8tvgRFVuHxQ-wn5!)u!vi!71R
zQaIfm==HvH&iNny?f{OcAJX{rE)x%-s^P06Obj}#9XW`MxH-WKTrLTy|0!VoQBL5O
z_L30#X*hC<yh$P{8xe%3_&F&i%f}X!UI*`d!(IyA(q|Qd9HOwsAL)P7-8Y(kaTh?@
z70gw=(l}a>O%xo8g)S$czLo!gC31!d<gP<`%eyLv;t|_op#mk+ER*h*VLhH6E!qas
z%+QBiO#fg)<nh#ZpnkA(kD^P}u=$EpLQuR;oK-8TKeeU33*-GYVai?W*~qp6-?#H;
z$)RJF6NLH!tEyMQeVDpvD(5>C&)kSD;QRWI+M6}Fs$y@HWPsBg8>cTd+ehy+UrAR)
z`+m6TY570PpoBgAD@<w)F+`Ysk$JD<YOlk+!tG9mJ`hg34B-GlqbFJky8$uaI6eg<
zQf9{@Ty-uGlq{ml9JEh{1jRuR7s#hmj=*UIh_7<2Rj26~h_z=*3XB$Oo`p_mCzWY%
z+>#Homk3}c=ABSTP=wDjW)D&eM583Y<_cbF`gT4LC?9yy?HRVP&Z9H?HU6Mfr9<C2
z&`&T`HeqS*cDcN^M6Qjr^qJO)Js%j&j_H5hBCz~h7*pD(R0-}1+bmY}e)(XahXMxK
zD6X1?a6@lhQ!xO?ZTB%$5)xcafX`PpfY1Ra)?Mhgch(2CAaHc$qNSTJgy_R&p6TQC
zxgID6cEp@#m(mN>rcOeEH_lhW3*-G^)(nCm^}wd?h|i7YJ+#ZkC*FT}CXL*1_*?ZF
zJSa`v6}e*AVf{%JaY3{i!=@frg95V{uEtR<#Yk3>m#+!8YTlI>!IvniGzvr48^OMG
zH?f#U#q$vz6eKB}9YQc0TT~$(Tv&2Uj_9Iq#ft>r$9j`VP-;u%wOtoT#3WjlDM#AE
z)`a&RB*3i?Q}+HwV-5uhp^Ff&NX`d@r4``m7XP0<yIL6FpA5F*d6MM}`iFtTPY@~?
zC81Y*(Mru@L%+wt<6ZS}!WD)(v+NelcV=f;Qg{^L%d0+2o3fxAhGY}L8Pb)M`7qbL
zkX!$9HA{um)ccO%xf_6g9hDkX#kWy}v#V6`3%l;MZMk`gNp=P0$hBW~xjdpIGurF=
zUZ9yXPy#dbXGm;2cEy%W1w{%01htiZ@2S|MJ7uGKDg5EcayW$Yg>jKa&{8fktbqqX
zaPdQQ(W+QxsGcQuWzfT_>?ci3&R4~vR~YpiJ)v&<w-|Ou3|rh_w|u>SA^&9J<q&Xo
zGXQk~y#c?DqrmbEcV#Jj`Db@vi0+Df3+4)5#$ym{=AFTRR?ekxnWBh$#l6zpUD+5<
z%*5r0vOOYCPt7%UeJ5h5@ey>hX)9U7Dr*?^(zH`<j;WAz8rgX!sqT)LJ$7`sPvLkU
zygWo6^H1xwL1<SkW$b!uq=Oa~*n|WXq-5viP^ipmhQQ3e`rsX5K^9NgX@@LhU)>Gl
zM0BQ%8tGEPc!vsW>Yg|VsURxqVR?=aS%Vkgp?9PY!wTS##O(wbu99>Ytg~hS@x`hT
z+a9b8+njZWL~$-49x+s(*^V@p+o$M}!>R*AQDK)gCxPp?to~wWf?TdK6+ueih0n;q
zL&~5>+MryxZv-H&7wB4u4%nw~l1ISziztIRvMc=mD7&$Qw^!srqve)i216-DKSVh6
zQ2W(c`Lp0Gq?0<iK+PXP+bjWLH#VE2Cq@Els-c1Hj6YLDxwI8ij2$qRqI)`Rm&ciB
z2#!l~2aer#;;bT8de)5J?UyBavF?0MUt9Wns~*LIdfddnC!NWb55_@#;jCLEu{*+n
z(j3;Fo4=RWdTt8q9Z-es$TPHL;ZT|gKpg3S3?<~VI44I~C7xbbyAHfK{9iACrLT6|
z^ni7o=zGdUTSF@01&8(COZ@Co3%@5Mr!P*u$`<V2Jg&0j*16?PLf?HA@Qtv`s3Af6
zMJ*xm@m8Vv(R~X&sE*{J4Ilf;f6F6K31TzXG2oxl^z~Qqu+b5_*~5>$YoXwQMAi?1
zq{)y(i5MbOVqB;D!r$?=d7-_1AN^Nl8kJQGOC~G6F%p)c*6wT%c0;oC?4EPWB^E2B
zP!6yCFX=C?-yE@zaM&KywVoRYB?i~%M3Wi!*Uie;OJX@^ae`X3w6&KP$-24(;ILtH
zGXlK*f_z#5gwq;Vhw-b(!?QwQaUMPTmwt6AiuKhRP_Xu`ZW|2Be&5E0f7K83-^bs=
zxC&)5to}c(Y+BSuXlDPtX)ITK=b{GcQlXt4oQdM8{-Mlg#O`2$>pHlxis79vNtw|#
zEKSso(bskk$mxkntT)5#t=_B;cF2%pi;QxiPUS0K#LxTGeh}PC@6&)n9%Oc3R^Z+k
z>n=l^8>CaC*cU?Z*&c$frZNVb{@^2{v2Dk&AEUBsFtBP&uxhyBA*017EZzzd*8ygi
zTBqG(*^Wn%HC_MmH;fHnONAgJiIC<#uI6E7wYnN|VtJl3`yEE3FIXlFC{c{%hCUzr
z`G>8A!X;o^Kb4=KMoJpII}3m-fv9XYvq|xmIfX_ih^HDLAjo)Ym+-xMt==B<Nn#5V
z2yXy}8&<U;O%nkT&o^U&xqPPJDE?(g91I@>jTQjlNikHsmJwyI3i>u$Ie&ANK?A%M
zrtkV{c;Ur+>)H>qu<KD<)J5z|X0aKt^ts0U3`P9SBIZE+$ZEqSW)qD&U2Tamv%Y#;
zZSpL#4vZAC_FSX)+HQ=od5=D3*YCj9%qJM!O=fY)KlWtvA-9<+JpR?jGqffCIhexy
zyXtz{cB(KMet#sAoy8&))y4xQ$UttCvba+UV9mz;O`zGi%mR5{L!eGvMh$(kpg6er
zCZWM~jMtFEtR{3d5|r^H#^{@K-(_M#t39hH1|$64ffbe4F(g=*`}ECXSxJ0*NnrJ#
z0ta6l+f~G!v&<d)TM>GwKs!PSvKxvB*8lU9F!uG;3iI9D_0beK@-h32w>0!jON_ol
z4dH&9I8K&gM*IYi)Z%#h<U`lKOWefNFh#}^VE&lw>alLAV0yR<+W7oB!a#?c*nNak
zrsf`wAN%**fxr^m)y{{+ShsZgypTxQ-SfK27K4FtJUB`m*o17JU*BU@$}A!DGq_&o
zQ!4B{bpn3U(fv!M*578l!5hnKHp(R8@NH-BC{BED;a@7`K?|lOMH_;OJvWDR&&sv%
zrTh|_^Ae4#cEZI0*al#<ok8z}t7k)`H09o;Ae7dpitidegD){SJYT?Qc#ZdPQ`st}
zuHk_E>ko83L5Flt8-7v<ffu)@W&HDZZ~~|)SPzk|Me)b|*1aAB?oa3wQSRd#9elpn
zM4sv?5P?6cc_m1iq_iXzA@&lR736SD&5g7dTIp}kje7TIEZ2K-L0zl^w<GLaoC7}*
zlK2Er4g16K)b|L2H9M3rw0}bGH0((a{S=dbEN*Id@Wzg#fT4eeb!~48@w@QL1x9z2
zzzSK0F)~(v=1^&4YF>YycIRJBqc3$Nwna3!*Xs$cZJrV$7WCzG8%>gZQF{tX=313J
z_1E3RsuY>&c{DC$qP#*1`Lmz`NkMY(lF};5IzrD~Le80#lXMH~$j-6x<%!ZfaW1+9
z4g8LA7-}2X8WAo>Azn|p>LTU13;*z+5K9^T$QB7SLYGx$MbdSetMfuQjO^Ijdkyf~
z>bMw9-Iia~-#+C7k+<csd|;9R)L9}sQ^D%s&5R-`?`W>YoiRM7r8|OKXSV`xu@P{#
z$*?IQV5V=F`vZg5tsBhT;MT;7FA2ptdjon1gKPpfS1B%_Dj|dr1mJuzo(}a_|A66@
z-oshnmUIaDH>k4P^<K-r>&J%s{j;gfkpLUUMS}y;{kG;7%Bfckmr$lxrnvxiXu)h}
zx-k|p`y$KpOUbveCDoQW@{2G8<VmcG&>#ILDqMdMRO`3y=-JSpbQQOu=84R>0uLw2
z(fy!hNBH#ImRwvyGxR#B{42|0eQDo`4i;Bfg5`aYYC;Je#Kq8sC~bC~jBp4n4D7{D
zTAT1C8E^*QWNvJEmmVT}bw?DoWilogjLJ}QE)?oYy&XwJOm#zA7tNA-1cFq3rabGC
z`f5wu>2gY(Y!1_}kg&}fY5kOtb8>9-v=vv3ZN(1gv|+(@cBB87LOu0s`}wO!Jf{|k
z`Fubg4{S6`SU}ht@P8`W@`c~bIjy^=ufpBiHnaWQe~$VqWXZ@1nhBDnN?^DFIXC}v
zCC7bM`pumDzJslouJg6_tprnfwDJCKaVn&82)qb3+h$j52g9lq4o$puN416%dr~Y4
zv>l&^cUUbw`}|D^%HsLKdIwZ}r7~_ohvFJ)!#NQlBViq5EpgH%IXi8By`#(xR<UxS
zRKkpmx))A*0HSqqlZDs;gClEOS&4~d0lu%Gwc!b4Yj3=uNb@4$S0B#qx`ScKAQye3
zhNi9Oisc@~^!YdP!Sm4mCqCPCCMW++>LZ=^3-{h7)smb{GnENeI<>uu3CYh0&D>*o
z@X(V88nj|E`oB!%XJhEXHEh1P0lKRsXJ+LNyD`8Rf$QU&<M|h;&ft{6O?}f1R{CYZ
zkngb6a8Pu7l<LH(zcWs)9~^W_;b`$|FV_92EwMNq(N&+VU1BU^3!*&2Lm0yrRWy%w
z{9fbY)eOZ!{%*5^Y_>GezC}GZ=;GBYRlmfUbzs+FQU63WPT3T!rFwYkLDN#EUfK&`
z>-s5xv#8^DQ!ts94-2zxd+Zd;<Qt_?<Mnk!lX(d>K<bq6u44F8!0f8aXhUfoA;vl7
z*ddUiXPC3rv;O{^JBTqW5R6iHT%t7Xeb_}#`ay2KoxQ=((38y9kQBqeQA={eXUB7%
zrTT^>;{W0rzYh@SvfwJ_p=~5-U*my(snv<W#8ID847@@{CEqFt6yji4aFD}%-!_jZ
zc5X%4u_oj$-F}kGy!nYbVLI^oi8_7*=NC4n=1qutf!~j0-kVWGWW46U8{CnX_!eg)
zOW}RtW?XwY<o$KexX}5Bc#^2UfNfY@<yMvVOAB%jbyDC>hERarI<A1nPaGS}+`9|p
zD%E=>wyll2M-Q!s=UNEM^S10bS|1DzU+C6wpV_4`M7JmVy|!+t$#1{f|H6~cp|e{t
z6Q0rGdN7b$lZBy4?Ob3uj-`nH02!Sl`?k!KaH@E;gmfe?{UgFs1^?lb4727NMy06_
zLAfR^9si4_zD>oAAA+O8v3?zGR$(!o$>*`4WUbyGZWV<7-R5v)LU8^}zuZfkctbT|
zl1U{@uslPyzl`=>TcEbcMI!U0tFYaN-iJcf!(@GfEXIpMOU5-?2r}{Uiq9_4h})qj
zs2%mnvh~RBFzy$>eF1+I$XPzG{)AdVL?{)*w)bPlht^x>7bYs!rcx4cl3Wmb=%l>y
z_(KO4W|FFT$s&PHAJ&g6tNubhoVSQiAGWo>zN~a$KE`g@I`8`KBMn2KQC)dC)!7@~
z9IIvVU@NJ5XK|AKkL^i1G@}lPWKT9sSa$v%mTmDa=d^qWq};*(9DKjzvNM4EaVak;
zA%aR=XglwADW3C+2iA&8PrLY!N$?lT#ABB_@uK=cDqEU)_sE%@yd)q+NJ~P2>cG=N
zQf)v?E9XnbKVH#@%@Z~3;AwH4_Gz{4V>YD~c}u4)C6^L6j*`W%tm@p3vNYrY_&qnJ
z6b>y^1+9WTzxC9W)x1t&LW<3+f1>#=>!#w;7T~GyiZG^_4rKnhl#NWL^bL8a>vLQy
zV9?jOH?H4T<$MhU%F)g?M?i+mVI<?<b9p5GdeF7{^<5nC?5V`o#~s%o7iMef=T0>{
z+@v^n`yvkgicBNbZW0J}jX=5`8Af%mjt0y?+*tqitwQz!Vi}$KIp;)zOLiUKFsS`7
zOq2&lPk~nWU#)BA^9kI-{zSa@)JGwuczrZ*K~mfifD(RNhmw%fpreN_ViNF2YZpT9
zt^ayxSZ#qk;0q9JRrX3rltbsJJD99|23VfhNq~t8ud{Bq#tA$1&&qvT6vej~p2H`f
zQ{%EByE~tleu&+c8G5l7pQ7cLC0s|L2t1H2o?KMZUzY2ZS<LRMt|2pN@a%%)qbRo>
z)bRLiX<rL1TTw}sC-+Gih+X$I{cB3L22eC#c@$2Cj!`&23CTf1f)W=>Kdrsy*+SWb
zWrwl;b0N@X;KOA&g}FP`p9)Jyq85%U4W0NGB3X(8Zzx!TBcoQdR0^NL2^wXMfY#@c
z(pEJEd!*Vo>SWuX345c8{33vn)zAIB>HylCy^rv5fmps;Db0FvCKL#Cu%9sj+tAkd
zahlX%n%|Y51sqA9P`8wVVsJ%~p5Bh$9bA{;|L=ytRc{{&qq>sYy5x$D>K2ZO!4vk)
z+2#XPgId9k%`)?Rv)&%x#YJL~JEhfmWE0_~$=_O^vK+AqeaX!?@38J?YIVQxAG0Y1
zuIJ==^H0}FJDzBZ(S}ORpA7K7Hz|i)^V{t(j>0N0-6q}4VcX!U=&sx9m|xj>G*md+
zJbKTA{OKYVP@McTu8}(E-M^|fv9m3rcyqq0DIOWjQzPsMI)q(-?j&HB7x98Ff_0mt
zt;*CU6ccRPk2WUh0`Qj%2c0CpxN-d@bJDZPDDaW1T*Ky|2wvbEs-a2=*t7vZ7>cO?
zB!dnxtGLGEOVWzz3HNlxeCmhi*&g}u{}a_B>5Ke5uwkzmuN(?r;DZbyE@0mwJZt4@
zCjPNN|6<d_pK5-OOU~Ub{pwt?-1gl3!>;A)hX*RFtrJyZJ=DcaTy(0$LRU|W<~@CH
z>(FGMuI!*8k{+Fv3xV>E=ZPmjnhU7bmy!bo-H0ed9tL(XCM~n+sVx|D>vUu56eWEY
zVRqO#@4(p+o-Y8!8u1ah{xmodjE25dEW)A7x<qwfZHCqTU*V!P7k*~JbkX%Xvc*12
zy$Z#t{@?Y<PJiXSUYJ44<<i!EAqs17I7#O@IYy$sgeraxy;{udboKGvLc7TFHH5E1
zX6%T_^26hOk;W@jO%unV&1Xd%_@eGA=Uy8CYcwXJ|AMwxCL~ss6(phttVVBTYwzTJ
zUW<(5{BrefF+Ujx<q)0XXGwJh<@>1>?uqUymrLN1=!z0(*!-98U)-sM{_nQ(NL-n(
zQr^6nHFGR^eDIcZro6FdvRH&BM)p};>TaM`<P#jm(0^A^DdROKei=>g`4iovVej)P
zV^9Ty(<gmZpWDcZusU_%i-yyIMXeTdJs)Pb@-k|cEYcnfe>8#g!NeTkv+@OTP-VSU
z%}y(LCVuaQTb8Ntc_zxnQ*56$tbs<%{VQ8P%n=?u;cJ`p-gzfbcS5m%Iz1=}q`ds}
zoB8oVQkEIzS>IazzRU{mYg!wjE~@){Sj3;Rsk(Zatwl=;%txpueWLRcEs_JHZB4Y#
z4mRdCwZ3q?FBr}b#&iz&^EIjQ1GwDP#3q*ctaaaCvpZmsjz?xUP~G-Bw<{aK7^Cw!
zK(3uXtdn<n|G{@_C@?n`sin%+#o=e{MvHjpY*=Bzk4{&cr#F6U6Yw+3{)aA%abb)H
zPG3be#BUc|jMvqB@GYr)eg?CTrZ3QzKApBza(0e#*YJ;@=F;EWKVK-is$P|}LnxBG
zj#gK|7KYQIpEI#qmCvu!H>nu8!VK`l5)35bAt$;amZ&PVBbP>2>}rg0#rukMaQs5j
zrmAN3h~%N<-VuO@Ywvu$cCYQHQM-&)YoLB@W3BHw)prdxQfbzlby~LT0c$a?-rZvK
zjH-?$wVjhMbbgFi7Uz9?*@PJe-6WL;SoU%op~}-$hIwaG`D;YlKCe55Y$<?@%FgiN
z4sS@_Pm%4#Ts!h11eIALnv;4uRQ8Z=heBcs7Z$bhh$)2ao^b(CZgW1sm~QQ2a-8|V
z6~V<a?z-52G%Q~~LPyvb$~L$-xOPL8<6Ry#rt?XQTyH{M^7p^KWn7r#@U7GzeJ9%2
zry#TlVefDSDG>R+YiqRtXf@$6QJc)?kD7*iCvj@tuKO4}4<v0FqH9uhtPK#Z?qKz7
zunbu!?xtKlDzI`L8$Yq}#mY)M$&B^@!fJ4xst^UT^?JyQvyN6RgfI$$gmYWMMz{%f
z_r~5swf$!spa^d02LzZ-%(RL&nPBX853%1QwyT-cmg!%Gpl7%LiaxU!^r(IhV{-tH
z(UJp}2RMlp^?Fx|a$9`2D<-MDc{=;px`%&{JGTIi3OGMt?wyI%YA)qvdYbR$Z-#2U
zk)33;6mR@0t@d>RBiH@Y(u&OtSC9V^d}}4R(%i1!8Q8D6o?oYJVG`oIleEY8;f_u2
zY_#oqrWiUDB6dL+JJE!~wH&h~<8SPI(n%cdMZ^<CLSBoWjm$JZ=H$*RGnspDlvA4e
zT~|^D{{si3xo{K_JZAp0%x4PR{Sx3rsx3S=h<-T{&IFs#gkBzZc?Av@=o3<`xBe{p
z$>sqGaX@T8*fk)p(l+_`w{-%OG9rV~s0z;B5?Mi?K=~&2RJU$EPvl7^PwyPz6vR8E
z61f^j_j?|52ee49+AH6`KMV}K(iq?`!&Z@;FA}E9_&-E1xtW6nZiS5h;>_C#t*$`$
z*3{|GH#va2;N$q7iTy~?|9K0Xm=M@s`po-e-+aZKaJS}fmeQ&OhKLg{%>_JA-SiI<
zkV&K8f=y7lrMHk)7{vTx2CG8`)biF4pc(aHS`aoY>cqV`>yuIbA5Y&HUg!5j8{4*R
zG(2%~k~V4B*tT_IG&UNWjcwa*W3#c@@Sgte|K1OI&gbmC-&t#B&8$iGK~*#uRELGK
zT3T5(z(=>{(NY$VA%z793;{tWQm0T(!$_ZuMG-p-Xu450(@0XgN#i_>Bc{?sQ4+H<
zNg(v#ELd>7Kx0&P$=2?X6vdo^u{`U1&_PirLO&ibm@NGrXRrSd*8N1BwZz4EzeOkt
zRnLrLro|ihno!10p&l!Cpy_;w=*0n1i%)x5C-(^L#9w#kvBrtKvAq)IKY}~sgWBf7
zvIzCV=3iA--J(|i(IuWV*7s$qp!%72e^8VPKNpcZ`2Pw{G~l)g)Kt`l<ipwe2Ftb+
zy?thj5ALOy&X7b<ploWnR!a~u&8MoadV+T|IKwN9N#U)GmpSHq=~$|$wGGFi5wbkL
zOJNw*+6ARGs2V)<5h7?PpRUAr+i&#5k%x$sCch(OcLgC6^2FJ(HlF>kJoaz|l432k
z=E@)G98#gEyQ6Nf@jy#gg@N=ISVeH8;Sn~Ks|Tv>Ajn4Bs+S-3veg5I^zA?A$5cTW
zjmfA?K@9lHXerg-(MShmmmD<<EEVf26LC)uE5r+S*?N<kj7%TWrCxgbzuZChgt{%w
z3|y&gSp8-W18zwb{?y;_^md1Hn*#Mk83aryZL2+Yat>F$iAS$-{d*rh;2EI-Gs$VI
z;WvuT+NTf#uLeNuR+Y-CoeF#3x(kOZf3&?Nq?Qou-jdAjm0-C#-8YvqQ)Z86s+94@
zgNwU+FTXk)`90cXvlW^|a&fi9%*3kD^FbJey0h-lt}|gg<`AnS2GxD>mPYA(Wh}#E
z2wIVp2c<HMK@gof-yIvY^TuFF$69(ht~g_3vLrLHo%qjg7*_MRk?-USolZY{9SmlX
z8$iFcL`T$vSP#4D<$+V*M!y;@c~jKOLa2x<uQ*-JpwiSa2aDNG*DQLN@%#~lLFHGK
z9SaA#VW#_&EyVURLlrlS_J7gjCmgm)=9LOqf7YL$YjIr%x-GO6D*E85<%IN`j-3A+
zIP5dDBn4Ob*@$nZKmXFRB$6u`NG@NO@OGYFzb#FuD3g!fLr2Bj=YnB-Qa?Jw_0i>#
z?;0=`%E{@gqq}w!41t9h!~fwji$)5?*XH}Bf+gN3p{=!E7bL+5G&>a=98NozhcgH%
z*2Q7NLz7)$sH;=j5nW-y(80=c4frQvCT+@m_xfrK5_??F)`AlYtAkfpDsYh1`-|U4
z7LwQ1S6Z(pzsk@<-K<7~pq_XkJ&|;V^hJIgKY22TxtII4MDspzMozteVKP^)oj6r#
zkB_%yHv<6Lk)k=uf$=|d$r8Fh#PBG!>8WTy6V#gLagbE-#dNzxcU$~VMMep225Xf&
z^^_JRd_A_zaj|U9-`>?ogq=u|#V*!}RP46yX`<Lwy3XmWr?Ea^DEVkf8M$S-kc_H?
zrFVDHGVK4r_8dm1Z8C$9D&AwJJ4VshUWKM{ZeEhSyj9S<)TBsJqR@9ikBY-WZ?brB
z_qjCNRxtGLBI{Jv69(-UBe=3J@rr!<Ojs#&Br7*lX-<FTCR;#HgmDy%tk)dDI)=M=
zQ)xP#j?4Z7$q7I2Gu{C${z4OC3q+7iGyB#=_8N`zSq(*Lp}mKOj2jyGj`Mn6nM;Yc
zP~Dp&EdJ{xF+8F>Zhht@Fs86UFHmB{@O~Ix;>j8BoIKX4*<Ij<EW}r!|BYGEaHa&_
zQEb<EZK7=r9x&7o>ks%$YKAMuR2Qi@wR^}#<Cb16jWm03d{~uNwcl-w!xoF%{@|N^
z2lUFq@{fYLZm!l^gE5w4QKiAOQHwk0(5cfPyspfVj)qYH!D`We=GQO5c11lis=dwQ
z%7f|bvd~I8e|m^ecdF#{$wup|Rm+0$FIaj=13L@Ge`ni<;lW#H@=Mjd!ml{S+><LG
z9}l!46nfPCr6(S<1!3KA#WeE)?Yzs~(e9!np7WxEU|p)=>;FPk^FvbaT6%v{vXpsi
zJ=yPnFFdC^UD%StHL}>Y{=x9qhGj&tVM@){$=f^DF`OzTQb7(kKX!N-P(QLy*XQA!
z3t62FItCh5!wL?hHq%>OAnom{o(&Y37O>>x06#zYDn+EU+2F>c5CtY(nI^R76f!la
znugYA#kmDkR*yfWm*v<GToz1xH8T49mVDnHV~F_O^J*pt1esN*r%_`@e?==?u&&OM
zoQ2%{&GyStXTI)<^-Eq@Ay@S1ryrXf1If7St0?0Jri~Zd@oP<Ekc1YhirkeYPNSc6
zN0!hIC+OQBxZ3+n29OPl4atc*j9%)aMmp#&swwG3f`snzNpXLx%4~h_yfI{gU;hsP
zmM_6A-HuubZqIVtdV57###XO}U`=|vUm87Dd8*323DBX8KE0>i5rz3>8!)E34`zhz
zba^dN>SMNBzg;xdITP&oe&)h#ZX~2ttg;KZ<YzX@!05TAADYrM_d8xw<V_f!vwTlI
zzr%x7UH0hH#kTqRqp1GLEhz9xh&oyg3Op<^pCXQen?!J5zuXai{8wym(R_5#oS@3W
zak*0wR+GfQ12MaP&tiqC!SyPmr~^~bqlF@Q^K8xe#BYBrt|?dV5>E-6ukRIk<02#f
zB^v63>?yqn@QY@kw+A){LIIi_K3Z)Z%nEr8|AT+$H<F2_hA*H(I|b5p%G115&8l1~
z@V?g9_7*Pxr3%bl+#o2%9nItN%`=)J|53}EAVR@>3E_N~Q5uZ<(AGFBbanvb#iv&I
z-gK0xK&_CA#;qao@T@z9a0L{-5K=ff>vSifFEu7Bb;I#6)YgJSiP}_asAp3zb+o+D
zZshKS>&ov~)P8$g41|n%o%g%GObkFOhok5Fp+AGWB(&_=0@HD*dNA~TLRu{lk~%ja
zpky&<j@tRTVsvuPPSil}O?^MP2Gpb&TJ3^=g$357;a6=7Av!B2-c}=m5=vhj0@SvV
zd)ETkWeULkj2r}$xV1Ys;vUu)4$oBnAbR}-?oK8Rnr|^PxE(yVc6@_VN?ivrNh9KN
zHbAfTkQ6~}bEhgNC`S6lxEReQ7+p<!$mBSUaGP*h`xNs${Px7_bzIet98hzj)Ov^v
z>XOaA`ZptGj%3(_fcgPa1*mv01_fDRq6zl_Ld4X?1~JB)RXY09Yc?D5<iuK{Y;Bji
z2<a711g0I?g68wp6n#U3-I*|`mlUDRdh8-EJoge<p&!z)V?O>`SRCagb&bPV>}O$T
z+28DrpHsfaQ345rS<}0jH2ca>uS`8d542B#eY>W~OoDvTYVGl(4-3opwQjYI&GX#@
z&05yX=b}rjV)i)YQSrpb<~1nUg#nMyJ<vW-Pw!}}UVy7GF_Pbh???nN`tU+TtPO!5
zWD(uD5INEL<Y4@Zw+4@ewz8x#lAAQ&*#6o$LSPkPH}Fh4&G8oOj=4yJv}Am}W=0rB
z-$6&;IkfdDA;AM#AAj%RI|(Q`RN^;1gPspEWhcvqfzju2l4nwZya|*KwK_>rl&{*B
z6W&Cl`9rZO5eckSj{p=v=9Q~ko-M^t!ML*`G^rO=;o)JfN!+4&!}=kXI_Nt8-JS}b
zKBmB_JN@^%99{$MVyIO5no2Osc2DmFV~BU+LxM><-F=%A6guc-`9yj;{7jslil2>7
zhV%lK=Bs;|NENH0QFjR$MjX!;0L&s~v3~H*&&;JZTboU6gzf#{0YbP}rYq*1RFkz=
zDg2ivVm=557(f4@R=H2bM~4BAP~>o%V7C}BF`#S$$Bf#`IjpPs^(~r>m}*BRz)X{D
z$VENDayzabiTU4ZzHOZY)NAD8VdhKmVL>tQ5X-K@RT=zYT@@t`QysET1>Og+Jvt^&
zWm~`Dq(M_<1U3>v9n<a*ktMTStwiFHG>*`QC`p2b;&W7Kg9Aw?)59_@M6Td65MedF
zYqof=mk?UC>$^FN=5%pzteT7px8sf`HG?h=Z(wDC8SWKg(N~P%-JYsQuudMxhF#Rk
zuujAl!Xp_0Hr}Ry_#!2)isqIIGrNWiR>K1goz`x|7!@>r<<4bL4<vBc(5%Aq`0X{D
z{TlEHm751RUO|~g?${!pe|(&Ec{b9l=xzON<4alJ>Q)1(X@Ks#YgQ9XDG`kf`A2Q>
z@(A~gP>ABRe9U`Y{!B*mJf(3rClH?YPNoeR#!ndzCdAXm*TQ_3@RsW;tMIBisjfaa
zzdXpPTL<`?c9v_XIgCAWQBiZ9`c02TY7nOL`K1%Cy=`v2y|*8tNvc0#T;&ER-sMBH
zK#;?9i?)yYxvsSvKsA%E({7gpl0%b0u}QCeG>uXf;BVrx`rCxLW%lMmZ=vpoUJhD;
zbD(SE>ekSN!>{)ar7y={tD-X1H4k>{bOdfr@&u*VhA_q768Lr|-T@=kS&FLb8w#c6
z0lmq$Pu6bRInnjP+g8m70#dZl<55kLBl<k?<#jwpIX?D*Zl0}gy;!so8@R7Uj*t<w
zOdi%wTaRc&!g-MCMG4E3t`AI|ty_meqmPaYHfpQx%wc0zB%I&n#dh1UpS&QTev2$S
z!{y_4w{zji;UF#~@2Zv(2hTx>n^)>Q^ezr~cvsf~V=2ak@U&Hs+;f0V3M()G(|L=S
zC5=POY@7zrd4JP;2SgR*S&y&z6;wF!R)D@2T-}ut3niiPPQ=k1dYlv~46a^f3#h(%
zCMq3XL3(Ii1lJ5@3*{B%>Na6$z`|>Ja}mweEA`$W9A=ZcH(f*|6&yKHga<s}tvK$Y
zOER*wKU`Oh2FKH{FGwfFlu{e+1wmc0u`V7?8j)Ph4EfjJFm^uWXb)lmi_!>e4@KCV
z6d{rYN-sDyjRe907cdEsAA0FqEo7;`+eV|g2QnI*u1=2o`*CkAUGKb^lDc_=Scr>q
z<w@bO0QFL>(-?Tc$H*CFg~GKZmV(C@zhcvXh;fFgw;rXBn=-ylSg2g)7969=E*LAw
zRuU}2S<px+?ubVa-;W)M2w5(lz!PyR>>hxMVM5VIiE_^HW71a;WJb{F_PN0}E%;TP
z=I$Vg;0kY&|Hbn)3|soVEtk;xf^oIq>?TSaF_{aVa6Noj*%Y30Zm|-wC_Iq=SD`~$
z0)T&_Kh0G66ZsFqL?mB9HBq-HA$}_0fP=cLn4wW|lq|*gX<x`KEb}JK$E4}XL1GiA
zWLMxyS`#M0`UUHRF5ljGLMy2nRSE-Tc-RR&qv&Mc@Q?Z6AWM?$hO5RL6lq>AT7LJ0
zD%d3lz6~Y3<1WXE@eS7;3fW8^dzn{Wd0_4LHy$r?`=2lw!e816rUT+TJe}hN7je$0
zRP`K!)yWi5^|P?Sy)h`V3s?8fC=VFNmlG2FpPfG^jC_+z&2bq*DUE&#BahEw+m5Fv
zw=U|r<!p$UXixPGd`vKF(W&K>cdxa8$V=|ji+(t%BcV0E;Vsn*81GfVMp@aO>P6hv
zsKEk3TKA$uZo&9rKDGI-uC98zPrxkSykwkln}ahZ0xvLR5NMseW0h1Gd<8^zWA;kC
zGw`*_q%}t3xWaS#6?@Rx`_Nam%(DBSet$yJDjW9Hj_V4NE^}f4KP4gY)}%J;KY`lP
zkx(kF8~u)myD<W-9o4u>>Ed6v5KO+sgZj|6Rp2rrFM`--H1S6+f&MSIOU<r(Z!2w0
z$*>6M+x``jrnQm80a3jZGYymv*bZUz1M<kpggw9fFpNFAT_ig#X{P!~?6k;jC2|~{
zhG+sed(p#8#Y$vII73SC5L-}vtk3t3fkKG(Rv8i$qi*$f^mW-j-u{3};DU?Uz<lcl
z;Cn|#w@mGFSuar@JjK;;Vjprmagf4;Zw+eQZL{TH`i{yiEMNa3_&`ukU1$}cvP-B4
z3>!P`z2LH3!a@2%Twxf8%QPk$AFjR8X14iP{?>NH)ywJctHrWB?U2|M7hc%U={>Qu
zv4#))O)r-;+gE&lo6~xKuT&;hxgyI<=egErA1Y`mr?@{pxSkLgJ424+j()*7x9j)p
zcv)6NAYs>k(LF#QAqIF9cNEn!`Fi}cUVotab|GZ5c=0`UR18kPrbs!B1(9YTU2Pe^
zzw08Z;_oy+j|}!vR35=-ZyJVY)~LeB?=J`)LBblc3DBQpy+4m@{#pUSeJ@eJrqLXt
zf>op3(vmzmiz<9EGJ9ROqio&lZwlFgi_H$JGXYf2LXU07$Zx|kd=;OC1mGKFhGshk
zet3r+`oB9j_x5^lXm__yc)@m(nEh=}SQxOcglds$Mh9#tB^Ms#i57x`k0}~B_m)o7
zegWcT&io`D4&>M8@6!u0+3&Z0?3Up}--K`4CGND}@Z^JhGt=|1#$3u6nXvq$wiM-b
z@#}7xrWS~JJq&UOKFO6iD32U-5Cv6Bc*30|aM&GUg4R<|w>DUfuSlD_hN{8iY_Y35
z4Q8y&K8m4^c~&x^^Z1SIm0u9*J>O-CSlhKaP`f;aIPD_p2H}QTl>4xNLQPpm+j(Sp
zqYSkeRADM^wgU2{i`QzGhrvpGWl?l7ok0D`Z&%vOeOKmEt5j=Hm((#Pqr+p317cs#
zcY973C`kfl$-OqhnqEkXa-1SJno+)(0J~c?Zsi!mb9IOY^yxdQvW<Iw^mF%`h&iRs
zI7v2kcFUN66BbG$L~epm_>Iuo=Et}1pit-A2@+Nka#PbVDMy*VWbY62YaX*z@yLA7
z%%67#>3g3PNWSL}BjY>m`<N^8b!!h{9gyjJI@<1VT_DfCoHf8ptv?FJ&%Iq`$9>PF
zbi#);5?WFGWnd)8uybP5kdkaq5o#K(atT(;bw_Paxez&D34et3f#@{Z@vM%bmSUx7
z4Ht|i5J?2&N^O+QZR&%l^7Suw)UFM6eg~IFN@JETNTMrPNoac|@RW>8J7LXa#|kfs
zJI)cWgZv485@k0^9@S@l*t-M}sb^_*a?(){xEJG^4d}mp9ymNuZOmFT>w>V4liGYk
zYcDA{cx5{!4^OcGX*qzgd<k`64#2B>XnDn6ur?F)C_8`s!!Wsz2wEVtcDUU??DS}O
z3DTq1G5YpgLz&YQdpHK?yY~dT^N(-CNH*}d%p1teWSD9P%)!Pj#!c`e8d3btiAsD}
zxvSnvpC}O`sQ+L}xHh5W&uIrJ<*Ch6qR$CRMGECtU%UtuHK*N0g{KWpGh<|i%XA~B
zq!_Z8ytME@8u^fVV5+7gw0C!pGhxa`wO8((!o_CwX;iG#{al94cF)gA!&uURtC^JK
z2(Z2<l#q*(whyI?>aecV9-$9daV7$@0HVsH5?6Q~1<X=Y|E(hPS`RN$JH>7DQ|ET}
z(^i&d#S+qCB?@zQJP-KYo{kWW%T?yVem4OL58>Lim_Gc1gS7y9cTIm5uS<IG<zX;-
zc?VQX)!A*sQ)2?!jy=G%o`VKVU*q*ukp<cF0PIp)9U7IvwX42oRF|4YF)}0iGfR9u
zg7J>teR#a+>STZ5CZtRMpygI58n^qS;oC=)<l8-2lgcI4O2sN!Owci_s`ZndGf3#k
zL_#%Z(JV_Qr6JK{ihuutt$-T4mDP2;_iJN?vdTaexlH@BVLwwthD!$?F<~>rim|GY
z2e8@g?g{hnDDlg4uS-ek3fYcGPD|jbl;M4o0l*lIb`^%Hi?E4m$4e+SYZ&>*Z(<3w
zQ<ogF8Ml<*Xh!_Y3;y_)sP?m8yzf2Cw5keURH+|g5iA0{1F;<4)JH7>qk3x~$lJz6
z#36bx-`<#oZ4a%swYGDid%PE#{jf?QK0e(RzWqBA2rz7oq6tdzz5mpim4?sD@HMD#
zldcEdst1ORqjNJ$23uc(4fG96vB$qDUDiNvv$E(uM8qU0@nP^Q|2eo)h3g?I)?wHf
zPDb`P(as$$b0j-P7js3y>q`$4x2@3VH{Z>~Fv_-aNW=w*9or&1N-SFn6XBs6(~FKO
z)2&0KLnkLNt|8_Z1F1#jz8RcdCsx!Q@V`Sg7{KDi@<^6iKY20US9>h|6sO5U47Y<;
z9P|BL3~+UB_<TUE245x^j`HGLW0hL`klr}3jGz4w+m`ylCTR=aAqw*}RZU-Gg!A;7
zrri(a$?$I7YFl^T;ZC@hFYu5G@*%Sqa~nUP1)>Mhr#S5Vh(Yerl;-Z8>x$?~f14bF
z9ik`a$^y)OLi7KDmu;S;>$%HzZdB8X#%c$y11XA`cQp8bIDj2Grp(9PsSlWsU1V>`
zisbDkE8UM%pQ5g#I&>^wOIuf_caN^}uIGV8qu>-aB1l>piPiS9f4lz*zb_ryU*K&Y
zRtthB?aUUllAG3|ObaV~Y?lTS=HbZW>L+P$ULDi*O#LXqM&$<Y4kU60;+*#mEhPyF
zr+nTLcd}hgV;FS_b!MtZtrQ|9Nv9*nQnP%U&rl#^aMT2W$+=tb_~K+BvQabq9$P{n
zm1BEDn|JIf1uM}j%mwUQ3Z{olm_On=^efC&^-&v028zA6B>=nk5`uj5p&Pk(3-<j8
zVoeZM2<Fv@2F2kTz8Bu>>iXZ2oI-&i>X%H|(W*tCD7iyJ{b+rvf`#*V_Ceq;z35|U
zRYRMAaHidymb~1z-N3Drjc1IezcgGK?#n6d;U-g<!OUT7f<IuBF7l`pWf^tX6_9d=
z44}O6z9*IRjMr5+jR(|rnlX8$l<N)B|DD_!pm1+0A(n7`?jI3L7)rqPXsRv4|7mqR
zB$<67sWy~w3uA4jQ2|GZ#BWSuP_<2}Bu0kgM3x(yMXhvdNt)~bCO)@XIDnKH!Z@sx
znU3Yjw^z>NC|vuOX?|M#VAw_-bv=mBo&|rEI6gPL$8JCz@%e570bDK+g^h-6BK3(;
zfW8cm?23^I*+%Oy5k_1m)#BO@yk`J^K874px*$Y>(CCEtR%D9Ck&d66<G#u8V>%(r
zYg-Z2e+xTpPV9VScBF?@aepyYe?r?$00phR96mU-W}jTw1)2vw?_i~nNJjR(ihSWF
zQ*b{A{-V&lz~h%o?z_B9>6tX`7%0jZ!CI;K#X5L|&`EWUaxMNNDOq9Mb=_(a$zEe!
zm?qzTw*nYk8?Rw@t6lJ&`Ea&9sD#a2Fla-gLbKqP0d@aSLc^0aVhp*4rSDD|5AO{w
zly|hbQI3K=-Gaxb+MV=g8F=xY=84IBqh?EpQMEjyhY-v{XqHP8?Mq-ygh@#`(9Y~}
z_n(r+Xaw#R3X%!Ks1EE2eo&B92`P0I<6Pel4#qy{xY{R(<I6Ewi4y&B^k>&@J-sJE
zw-qvdR7E-7hJwtSnuTwU-N#OGhc~M|@I+5$j&afvX&z1mr*@w|f4m<A;)lT+Q55h?
z_`|5@E-d$3EQ~)J_%kHxa=L+0U5Sc0-KOwUtQV=-)i_CT2fi|ibdqB!KAqLbk$**F
zm<=n&2_6=5?bU+wA0(@bP&yb$3G!;oELQrt_Mn=24WY>;;(2HAF<{cP7Bh~Mk^=}{
z9exi|DoGm8#be&J)lgk{T_)>yidVc4;Cw;o3_t@Q;0Ao!Q2KYp1iOQ}TBt#kn&Kb@
z$=Z3=0^TdezepN(jt<9Y?@YXb8jcpn_6qyvj{Q@2gH>I#q-k{+KQ6`n&u2hBU-&s^
z{zyLNsbuX|yCUZc+X?_3d;5j8@(V1)inEfjDvJ(@trf-MZyZX5v!<!I>&4bc3&C!l
zFC?^4a0v+o$<X2o0kZxd5m5^Ep&4p2$4@iLI(`jE#5xMYn|{B7%R{LTJ0vV;Y;jd4
ze%=q#Hvb*-vX0@AQF1+GY+g+8awI$<9x%O3Ox9c@K1%);zT(X$$~StZmx%2#v|n{p
zY=MD{PW!9--+zg+#0<{!P#|Ke{VB22t4!J>s7ZW$pRAHp5H46nN9ElS<rcWF+a89x
zZ*EU~BBra*=hCaT$CyledsMN}ng~*Exf8RCfJ@+Ue&R~t=ae%{)hM41;B@)+8W095
zpGSf@7|m)evHi2<pI)A5CAdqsqDwSC3@*YX$1?n3tJ8x)e^L2>nv}5mfS)yZPWvd`
zs~?>lM-tXy;*mlr4A`X=@Ht?i>2t@nipnj{Y7pUIDbu%)Bc;v<vt_y~w0VF0S$*Mj
zPhtg3?E!(be?$pRG6gJrQ+mGMu3(Bc%?KaBd(=NX1#Vd*XTme1y9Ak0t75BirK65*
z=bw|jN4!|g%<Kx>TMAn9ocC5!%oDCCqJ56AlH%W<%-B#`sOF{Bbu<@if_Hf>yF)@g
z4@IzP1(<T{JoqqOqW~my>5*z`+o5SB6##s48|4LehUd^w!dZ)Wfz?z%$YM|~)D~+|
zbBZ-(lYXs~nc^Bkv9Psqg1S?5B)ijVkvRpT_FsWNreWzfI^t3an;D}EIzf0kAF!xI
zF^f=2mZV+MmUqQ&Vg!l)=OnTSIC;U+U&O;D5S6s^i|BCjny7Fxl$eqhgQ=wQ5ra><
zb825&)L|0LWYlNzdm<40NX~p7BgCT$5Y4WjHmGcxZk5_7+w4%ni{}`qjld@riun)Z
z2Is0uexdCk**8WBc`mp#*CM*MnnbQvcJ$f}>7-#I<*!O=dyE+0pF2p|kdIb}mp6v7
zjv$7PMrl|_8OO);3u@#EUlpFQcq4s}*{{bkBkbQHydp6D&@=tQdX#!PRM3|ZUKt#U
z&B|*1w=B@~{9@A4yvpX>Xl#rWR-cl@mNPK78C5YZxIGdq6>kDucxTlX?M6FXlGfBr
z31+_Hu(E2m5o#Amm*TTuhH0F~Q9aA(UQ40VTM?UQKpOuY(%kLhD#hC$?q#H^B+=wW
zV8;518!Qq`dX>4&gC_FL{6T+k{(PG+uPxHPO3bBrZF3=5<hh>@b7XV<&EG|dTal{M
z>#lIfpA_5WvC!a&X1AI=yvy#t5KyfF=1HHEdOYrDp3YW8ExI`deEhQ7d=dar0<nU}
zxMKBc$sy}8x@TDfSa@+UU9p~+c_Co$tIYAj>Ws<Ny(Gl=a>RCl`QJYzy`i!L9*wa+
zBc<cz*O;rwQ-6>4Z|NiAN8YCYRJ_cDsv+&o^|qi#pipN+A54b2_Wg};Q-_+>mKWK?
zgAwnI=#O}eSe49XdukQ3EoVqU@|c8mN4_h(%=8)amHnK$oU3jo)h*82M3~58lcVLI
z63YnGd3Pf|$P@Zlr7sfO3zV+qvt<u>-QUEL9HeR<F`}}Anhxhq*{Lu78Vw4Iy8iV*
z)SlH9=hNtruy=vgX0G*wYlhhrx40^Y_&$Arvddpbg0P0s_`_=JU(g6Wjo&#RBH)@y
zW%J1q_5BOhBhL6d1e~F3i>6-UdLm@Tj~Rc0@a&6?HClgXOO(TH5C({NuI>kVGPZx)
zkO_|E5$cboqSkK~=E%pZHD+E-<#->e=5vS-{>-WSJr=t$K2|DXM}Vz9fZ&gEbr46<
zp&u&=FB0u*60%xodkhYnbpWt)cMuuB@Ov(C>!R+@F89ZN4QBpD62Ij&h$6bYKB{wx
z2xm=-rDI_oRm4<vqeQyXqu`JY*45(pU;TQcQ6-66%lc2O@xo~PYO#IKQ2}v&CtCx5
zYbeP)L~$(o*m{>a2bb&gwnQw^^~38ueqb3Ml8NQMFzr6A{r@wFp8LYeWg1DJLVk#z
z`|(D)6vDI(QuGg;u?yC7Xu=^V8QO5~X1>seZ#=j{zzbYGdmb^*!us8s-G@^e5#vZ&
zDf@bkR-dMW5?(vrnnOA}Ed2$i3k}A}25SC-tWpbzn0hY(X+VEa?3HI(J7l^leis5^
zt3{~ogntxy7M7-kc><T|91`>EQ=s1FZPWPpH}=Vf42@5BR9?LWe&>I*FpkkVtZPOj
zn);Ft@w%Lm?w81=a^KnYUcxF6-|QDJ{!|<tSae97KGjt_*jbSw{f;NT#A9v18ejP`
z8>TV29wPE_e_Hju<UgE<_{Re3T&&-;{2o{Qqc%rsu1zd@CX;T}$(V{AO-jJE%dl08
zYYI(4nciB{Z&tRP(s}S_JRk^Ny@L5NRD%*J_>JP)U0kzA2H7MvFzOBU<H%!8yOY%G
znJQMpN5Q3s?GV+7X?gPA@QR0W#VyS0I#h#642(6jJY3fTdH^fk_52PzrEt@D1~sGL
zZPIE*c-1L9hBh#x4au%6nyxEQp@yJ<-a)!DTY(j>2>KrRrKg$$w#j8lgxu@M;REye
zEEThjvr*$RvRuFG^xk{h!?u=WaGCS&<QCrl!#()y8IwLFUJp6EDb?@<Y?$?LGz@OQ
z?O(@??{)vMOQ$wKeyZZzW5xU%5xcFB%yOZJs}Q@2s#s-GGr)r+yO7%2Dr}CMYv2cR
zQ8U4#87SV60MW*9Mm(##&q&yB&I2L|z$)k&rbN%UA06AzTpfm@zhFYAFO5(|MJynm
z#)*C=R%H@_l~0zV#iflbA&iI;w{)Q&EEwx6F=v|KPAT(6eg}p%!=939J2k;%$X#Wl
zvy>%|Z|35oefN_WJNm}Sibpjb69jHv#bG;?H954)?(h;Q<QN8X$m)*SKZFCyVLckU
z2ci={4XPXNmFOy@5&AUY%XVr&YQWZ400B7W5#WI%9zTvOvxw)PJ)b|xie&9EIwP^%
z=|A~wTQS>`qPs1PP}9>$6-Pc1(hV?5@$W;4)xtao!El=EkIA}zMa3*13KpFx&tAVw
zPeGNZLP-zsH#EiUKQrySkg-f%aa1!0s>-Qy5w9(H<PY3t*32U290neDI929_fy^?M
z_-YSe0#80VD_z4fG@;;USBO{^Reqj8)l~JrvtvQ&kvslu*a{fKu6@7B&%|iyreBPA
zFXD(1c@qE!F{CyamZECKScn-&-0g{8>|S&TfA}YgD@AYH5`<1@ejkfV$4;~-Tbz%Q
zn12SaC|y4`J_$&gm%X_8?Ufmv%B{oltIP5-8yYmiyN`3CAn2f`j^doqrHpRIyccQr
z-h}C{Z&2w%G7p!fQsEouKo8!erYj*MWX~Tsw#Ie|6S@WRP47_}L3Q-E6JwauMmfVv
z)B}`SvaLsU$`(q>yeFQ@$B;8?^4*@htDPvq?mB%aDwE)A-^d<r>oW7WpZcit(L|Lf
z|Bwfd$J7lsP={E}Qa+#I|JYi*A0U_6Ju>Od4E&%Q-+hbg{Xi3%H33{gy0eugqCh>h
zF|0kY!?o)DyF$W$SBO!gs(8!ZeeHj>{@mc(a=(P1vrTOE_@Rm|)&BbhF7SXg!9wVq
z11*?V&MM3i)=W6)H{s@Yz*62oHNAuG%Lm3OrTrmQL(W97b}yZ|xM`7(jg0O#Db^b9
z7NNz!d7dlaT<L*E)y+12<1}{hyUTrm#Zr%W9-DWzdKXZ?iciMa@n0RTGNf_fbJFl!
zSv9UWktW;xV-Gt9<4{SL;O-Lu?fxx%ts9V#R!vzSFk9o}H&~ro<|IRN@(y?P)O;wp
z4L!H@VG(Ed)&;Y>7PS>+OY=^6)eY&e21X$1f4Qiaaa+@%zsJSn(`<`h$i0FPFyd2&
zDE}>OhEe2rytRA9Pi)+rdJFMb^I^Fm^6CLS+LI_R4rf&cci!J<)PAbiXAvH&zrq;c
ze$c8Cx40yfr6}e+aS1dL<fENpm|pQl-hPU_Wk?rYCJsUF^HMPy3O!V)-}$60NhK|Z
z_5?r)7hB0%)!emxTLV=0%zET3JUD6*pNEp`4`RAlg(VQ2tAGtpPgPc$8Q9O*Wd&hf
z-TdP=X)qpN5q94nDYqVaD9taA-(tSC4D45Z33W$Q&boM?(+08&bI04o@?S=#^fV2$
z%WuyFUWN+GG~fq(;6J^OPCOQ_kpa?aQv>`_e4r5mmIC}yNkk3L$RnHo_UPlkdx8_x
zc!+`GCjz+XkYRy;!Fqz-|J;9P0>3*T($iJXDkS+qpMV7vqE~sbHEM6+KZwyM2rDd<
zf|I{0X4(tTL<-|nlnjMA)QqrUa^@$|&wME?^&lerVHRZm)Fl)ViEN(j<&+buUzCrp
zHT8Es3YnooCU7oi)MxnTp+bX|+MJ{-8<Oh--0(^Fzz=5nm9wm^TQ_!lp)bG5V+cjM
z^(CSmS7Krcv4lO9SQ+6eNy2@r^G#$rLT2Ei)4IT=+no!4CO(SIE0^%44{C;~%a2WQ
zvr8<kPquU6bx)`F6OwZ`cWkFEk(Hz?g)uTzfoeef;bObE3U;yEUaf77K;U*NwRcD^
z<TS*VTflNIgosnX67fGlf=T+(er6WGW`6oAUE`fwu}Uc6shLFe`L-j-uDiS(_5lTk
z*-9D*kPncNLz$Uspc_p14HiR}G%Q&k&UNl5OgT7TfeQ~bKgEg9gVcx+^EHBbhR;10
zfha&HY18qtB=w)HMAkzB+Rrza#fVlXQH{D^z?Jc{`PzQrS8MKzZ<}LNO35}ylycT8
z?OijTK8}{CQLIDhCwyMs!jXr(3eH=1di>5$@YY2vnB`}P7j+acHt3t5oemiOx>#VI
z)}Wa-c%8#KMuv~a9L)xu*l0|<I*!jO<Uf@*f(ucX<=!@dX&vO8E_~0E2Kl)kFfdg%
zTRLr+oS?03V>cwjLrP0YD_8C*_)+!p2YWsfo#TBzAk>+H50h6X`Bk$PKsN@a8|JHY
z|ILrJ#W!1;Wj`W*q%6SxA=siHZUFLMdmIw4;Hl64e9xXL3Ry?jwl*7=RmcSg4D<G6
zkmz>#2x9)3m3q|<Hsj+szqSpav-K|wtoQeN?k|08Dz&=9F4tx)2loUid_G$`GYIhC
zJy<l_&v74)zM<eNSR_aoeaCxqo0g#sN*#=xy;sy&-|)PWEwnraYFFnK95OV52={;S
z)E<hrP)?>GEKbj;;4-JraBQN+L`rSm+rT9SJHjO<kXUB^CYGyoN8?rN#^&{Kx`hHM
zP6o0_@Z9{rUI2pWOMm1jA=yu1Owg|s42bsv^1c@gZNpBohZUNKiV|tH*%4c3NL>)_
zWXb}uixfpMn?lgwS~D1L-p)6MRII2KI+303VvY_)V*T!KH|FBbFG($bg&dh*FHTdA
zzgXZCKbSFdgIY4<SlJ842%7KBx22N0UiQ^a|EDE#GUb^6W6{B5_Hk1jj*DwHuLg>*
zQGsATIRWMYb%Z{o(VepLZov2Q-$b%b6sCvK9SY01pky?wrwSHcgZ;1fj0)BM(71&d
zYG~Y@{=<Phm^D-B1XY{^k%y0V@_AvsEzS5v(|;UvHYC@(u;e8dXFG6-RqPP(I(Dno
zF3_&b@@7q#MP<}j&=3B4M~PMKRj38mI#mjg2n6-^W8uysjbseqIa#6te&6Zk=zCuD
z?q1+!X5VI2wS+zML0rvKK?RyjQA@u*^n63o>gbYso8t@6BUld&;`MqnTlOIAdhof~
zy-~oi@NUp_oCtsM?>wCWxPb092?tT*XvuaL!gpO;Fm#>Fx7WzTAHE&7D404u&2+MA
zzmI{xY^g2s2qT?;g|?$W+lOToXp7>e$*|m4jmjo?KukTUhibCnSM%DvBFXr29Ur?=
zAkkFoWxX{>$+%TSrquegGKH$0cE0>?^yNEVt;;N#^P9{@$;^Tc{}QGdf?wpUnX!X&
z)QMH?z-7aJZNsV69@%I6Ba}5F5}0&x@lx%K!YZ$pY~^+!phX7n63?jXB@cj5U`AHO
z8*kJx6OJz3P%D-_aOtfjX@f3$=JyDNEEkIz+9WrlRS-=p3*!Zii))9oj9>(mBaV?W
zq{P@@Jd|)hK+5m%+m*;~jD@SF!6#zw?EH)Bn!9_}Hq2Pmno2zGz8b3Ho8K6Q1P*{u
z-9*{GHhkI#7;i@=s@?bUSJEc#V}9W;oA5Uft9l30gT(%1c)2HDu$R0DDKsI+7m}u1
zr@jc9u=Wv&t?uoRj4~72C~ICE+82K!3Ib9KSq%8<z5lUU$?pV#AgNjHhMlU0U)lv1
zOKmnc`bfg&tSmhEf3JRgM8-^SGl##7@0rNiye=V+nO)uiHOUbx;4p1DhCVS*uPT{Q
zdgc!>Hvty`7Rq3cYMvU&xr-iTeY6KA4k0K6<bHy4LWubzw>-N`sy2y`Y075_D0p9a
z;lv%OqPgR(AZe$-2TGXopSF&9KHZK%()NKr?f1eNomVL@?daGZc#&>DNq=7NB8s7F
z9Z%((cazYI3tp>s3!)P{g*YO4`n7;I>|w>-EeK_Cx+Q(=&9Chgs=W_8i{f5OCBIsX
zah-BmSP%1j@BvkI_m=lVg2Zz_{=E%~^TQCmMlQS`r~m14c<4Ws5g+q0)RJ%{u(p``
zj0e|NZl3hv_rIZY6j<qPQmV#9TQ6epnP}Ow*3WC3f@y}cO+@k{R$ntySFEe2$Aj{w
z>pq~>Z8w%-?LeE2clvgR-aolKHRo`fFQsRSn0|Ab^l!9zdrY`NHi~-sg4wEjLdK+D
zU6aDm&HVU};AcbV_mT=l<>sw^DUlWnBXUYx7_27Amum3Fjm6p`F>B!rQ1PPaYY2=Q
zaxgOd>r}mhGVbxHBtmCD8DY;vV~MNH4hBChi9^sV+wY^XlpSq}jlAqk>aFARH&RgO
z&kLlgZv6rH6E=S1#4PtQ&rD6usIHh@C{*G0UA6#f^DEFBsvFCQd|K~hrb~=PU<ddh
zL0vUOa8ONww6eiocW?*p1+>$NJz!?;;0OQQzju@>0-ae?M5^AY38vbTg4iN_aI||p
z#Mp|!iNAU<oA3n(J3=<q`(P0hdit_fAEHHu%7H%gzs_<a@PJ*WIFVoW(4V2|@U?X;
z=MLlQrNZ3Q8lmpyC$oQl=12{le(zH_XHaSmKja;LSX%^@YnT;pcxQgOkvUYjQB+uu
z$R47i^J*<mxeP%##pxIHtoXXdsDizM>%|9n4;<QHwUyhhP%C0EoZw8dr*_0xwuDNu
z2dBtHfvhF*{1jrx5XHoeYB42(a<;DRj}<A7wMD=6kcg4t<yJNO`}>Cz>pO6`yc8%x
z2JxVfBZ^^D<~3*EbOMGJKX6l2HMLQ@YrkM=9(W+Pm_Yz6-RSYj;v0c;{0V}>oO0l#
z)mcy6u0M5tgXCxcpUqm^?xxFD<4@VjJt?=0Z&$bcSvEz9%YG-3dTWD&N6mcHZ7R%x
zvNSUL^%#wyg8#K$mQ9vKR0qF0nSFxBIG2%!FG42-&j<6@!ya;{fzx)8h6?sPgLf3K
z>oT&<Y~MlB4_us|ztHv^8~OThG^3(sq$eIB*!7#H;ruW(A-&Ea&JHrKLoEOD8kQVm
zjTAik*N^<$A`q0X2)+r*PZ>QzFZe#M2cptL3{2IHDSzkF<3<+svF1AkyF&@g7wN^|
zfQKS&EO)VU&blX5n_m@*S&I;!u`v0%26RF{Qx@=Rdl=coX;?$KRS_`Ku5)tE{H{RN
z?xV|pKpfcT=B&X<%&yk-`J&p~j5vnZjPco&h6$v{$jVAhsby#tLt98I`23L)Z!6xK
zFd2s7G=DydM^(9d!j;3HR?6^jhL1{ooRtOL(f^Ye>x2n{*%Q9%B~y#&h$&`QXlRkk
zIL^k7)j<0AZ6>CBvsL9x&C~gvZZYRDhqPHEtFSn14XqU4RzM*SOYp;%ditfbLcl;Y
zWD(@}tu0`5-*=*k-x-gRM*DZRa+M^~Lw4i9?<34iw>s>=)x6`}qNDXS;avHxz_f1Y
zoOguh<Q@e;=X>dT0RQ!LV<ErLlo|ic=T+rsBt_^Ms1K4SJ;N7<X+<d9ZScPNHUa2$
z<fLkAi>MhW{6GUp5$ELdAP7I|=NFCV*RTJ<87B3Wd9eBHK6Qy-Sc&@XZ4@!xW}TyG
z2n(KekZ)yiC^4owW2jQ?h~>%~a+mgiHrRjner*!h{*Pu`0Kb%a^RF9~2XN=S@sSfU
zCRS;mLJfIzJWH)vY)k58aZ)%(!opswsB9R9#|je!4-`#y%o$*Bo>W{6I+N?il$#JJ
zQoh4|$n~vND2CW8!9D*gt)o+y4ZJ6~1}zv?8+dgO*WJqU&@L#mSz&UX&d6AbXJJMD
z%iVYx!<gg!kKoP<A3o7cVOw_QIM8$$s4t_iQ*mIEv&3M2BPvEOB*)D!fU)B{`&oG~
z;m5KwlAL<AR*lV}N(8gQ{+p=CI_!AH#BdOwh-*@@Hy4(dKcNSz2m2Lz0DgeMWnERA
zl*IK&0J`){He53r5&07t*t*pv!SPjo8{rDMS0`W#raN)=pE3(KphghL2MsR93^@3|
zd>B=cHjw{`S89xUt#aZU=$}3M+OUa=smcfkKE|>&Jo!4Wys{E)NoH4pZ@$UpOH*Qi
zEst1t59}6&uO{b|iOi_7YcSfoAsMJO)5d#d{USmHdq*~)ev<AJhjusKIhgXPFFoTX
z_MGp37A)~D>joYI6=4gL`ZDjHG857Kl2}h0$jln5X{-~lPXvka_T|8J>&($w8%zRC
zvy+04XKtPJt{6FEhn!B0uKr<h<S$Jez6_k61PN4e<Y<5NWsdhR8QFOC#mcbPRnrGk
zAY~DK&f^>Ee_%3)$d!V+Q(&!Q${+c@?r(nS>&9m96yxUqLNAoL<6WPPsk!WYb0hiH
zXyVJhJ~WaxY8QSD|1(`$yYM;3vqTFYM#ypF00FH6Bs!!&0b-@jE96xm^wZ9}+&0-Z
zeE<kJ)8(Dni+sfj_BjLehP4R$Lq2u%k`G;Zg5v~uMUM2gJZ8)v<iqzwQP1NzgcjV-
z9h*<n)Q>-AY#-PtkTHI01lwb{1`icrvGC5+&0l~Q!8#t6?b9)=2p~20CsO7+A2D1(
z$ph{z!D@zhvU+XoYJT37_KTWe1*&~n7R4+QJIZxZ7=E)=1zmQY0=@0vW&%$A2c6BP
zCC<odjQVnTB+JNG%{VxqH1n+<3^Bg~W^PdUdm%SJ4OT{2b+8<>C{X58HNUwIG>*`k
zb%ernapfPz#?-O{Th~e0_G%pO5hu4C-Pxjxb`OB5dMr~j$p|vMiDdquAyNxllfHSe
zopLR`<&({RB^LV3reM6?<9FI&(B$Su0d`K|iElFJqkQWkrtT?1e)VspoI+foxL+$3
zF*HC(nQ6m`vd@#*gDEEP<eOF5VUWx0w4vXm*587xWah{P&o&z)=GyelgXsf1sO3V1
zYSBm<8wepT;r);Zq9U8mKSlZzdBAU2!|sV8^LHx0AJ|#=*aw5ThbcPs6<WOd?7r=}
zntoOG&cZ68epz-~b-g=s%7n@97EEg({hbwat`hQQ&heR^VQ|;+qLar@w;Z?2ex9B_
z>qC}`><OTIajiR!(_`UI&CR6t$BHAoxaGzp8PA{CoYXV-;j@TfZFPzfF*R&!QDNEk
z{!oIU$_tx>RSBf1(ytU)#Ff_*{cpvStBz|QEj7P|vzID{kaF77o@vEw;xaUgzKMJ%
z*Z=IQ)4e%pfi2n+fFJ88-ZU{9s10Gs)0!=N93Q&XHSN|fIMrKhS>k_b7;%#WP93VY
z1#Fe`kJdrQzGjEYveS}{L8;U)p=UTVEC6)n+RL*J(k>^u6pvpL>-YMjF~y|P{*8+m
zLo1Di1ZLKAh2(-_?9>VRaW&lkD69mS!ixEvOy=HLSiFBa=TI?PXT1(w+Z@O22wJvU
z?czrFlLoZ)2X0>tb=OZvB56H(-L?xyw`Sr=Fg#~xXEq4o$+o!ET}$X1nMKO_MNjE6
zJ{y>hQo<ZneH>5ll4?uok8d2#&0&d);3)4jSCvTdxhyd0`U$VWiZ9&XQJlS3NnjAU
z&Q9%*S^lZ1cg}-N;R#uOMjKT38aue$<AP$;B@u8@lY5~pI&0jEw6g)}_jIYrA?q&q
zsvk{YB2^VGcgWSzj-PNm1D;V`G2TSh;{FcM?Tt>nz)(GRy!e}?UaPuSf}6~uQfpf~
zNZC8XX-6<WL-DjPrL%$)G|}EIz?97*cg5Cj&R7^@$8lt*3J#*1!-)OV2b@aEm=2$T
zmx7^ktwV|7R%}g*<ukoiSWS^%j{379EDFf%t=MDrOVIURc;;q?JC1K*CbQuy=)c*Z
za9Hs33*cTz{d=n+lHg8I<|t>D<L^2lx!m6E9h%~gc_x66(vUi4BQNC?LuZ%l7plxP
z_`9yBj(^(t8=Zb7J!*zg(9J^jeivGg-r_+TbdTcPpU7sQD$DQ*TL>=V_r+uhO0HjO
zKn;p+n)(yFb6|RrVDw^$UcMGAg~Ti+QAGU>LppU5udF+1VKM?DqLM3u8$i~uEqrS5
zfMqZ`ySf>}Im5@hR_nH-u;9{)`8VjL97?N>v3W?7i7+yMRSE%KP8Gqe=ZpG^^rP(y
z0lF1Zr!2g#Et^XwAV(WTm;0_kbYU95_6A7eS+)IVRAAV}Mb-7kAKI7DwBSW(tl?Tc
z-#_eg7Cks}LP0VV<WCWEwLD;xn*VL0Oas@?`#p@p{QYlQW}z7#5_mTGUEnV}b_gUc
z)r5tpG@)#W=FO9YQ!ue^vcIBe!Pr!u657Uy*J4HJ0DdF=KF*?56ncp_`AfpOF}3pC
zVq(QESJ}kQrO`?mnzAb*U0|#K-4s?8HDAqi>O9Y?e_^w|!yfQ*7@Ri}-PNefMchK6
z(rO9i`W0Fd9%w@z9E9VUL^eki;%uDvfC6DO4(-APy_>mf_+Fn8A2WTJHtx@!QhN48
z#2A^B9mXhtK8vWIPndN!21ljvjFr+Po%_u2Ts$*K_)83vuZMIvu7p%t=##qPLr!Di
zzg#iMh-Os!(mMF>@`V4SGc(|u68w<2gO~7S8bhymq)Tvxp`v7b@+3C}Nn$jUcRRBX
zEOQ=JzHAd!U(2%ZJ5v&#YS5X-$xv80kBd!r(xJ})<@%VuY52-fCB@)%b?ZF5;EUH`
z^}Gx4j&0!p1a8{lcP270I}&okl?5SGL8+&}J62*5tMg8as;DBUybDWi3?`Z&kQSgb
zjH5zBfwtFF84(|JTvY+(4oPHPtK7CS$GoTKJ%&slU7r)y?%klGI(@%)`a&60&7vs$
zLR2V(H{5cx4Ag)<qJJlSeqGu_vvS;L3J3U8oHOhewnY=%plsIY`f#0N`~yJ4fCQ%N
zY|hTw0e_J<&ThvG_TOk`c?d8cR}Y|@SSQfT<eVO&dY^2Iq${FLCv&1XsgWDEI|#!`
zdFtZ!VV-B}^j3Bb1uj#W2f_Au@C4m5D!?SU!^DOiU^yGotz#8V6y6ub_qN;i&Gl|4
zQa7|ch}DAYt<AS%exTx)go?{Kv;{t0pv_bX+l4)5Ia3M=aU{!i5QUWAHen9<uDh?n
z<rvrgyGS?ff?yHTgk>d-l_Q_(!%BCVX^xBT<n;bHC3iCM$ld(rHRdoZk2ks#<`1vd
zAw9A6w}EY%mp3%5jg{b6(^aE?H{Hj9l?EPNpR*)0cx58@|66G5D&1o_?mnDNCF(u0
zWvs6LV)GfVAwhuorq_H`SvP_uAexEp6fKxok8&etV~v?#^ECF5|CZ(DR2L;9%Ss4P
zTMHjyb711&(roEetv{#%Kk+arm;+TZV<e*Z$?A_eV{_O@g*Nh+sRuMW$b47Q;?scM
z6ztE=!R-pmQKVA=2vxQQo2=(W)h2?@XzaRQ`NAs@=9#LqM!u~?R*;hj<cvR7sy>H^
zYpmJXGZdSAVg=^cxFpu#mAQA1dR*8EqYHjcDA^Yh8*7Vme_~?&Fr|9A354BTWICz%
zfIA6dE=WW8)<PZIO?l2>ERB*&n(?2;Nl3dU+)HUv_JGv$(J#aQ&6luXZAZoh*(Z!=
zx^5WGCdA2aO>|_413)DvO2RsQm3<3x`Ig_GL~48rH(Sy=p^kS+5X{-QfDWJ4z5%59
z<~c?L5AOE+J6>rlfTzWAM^$Y#?RhGsPkM2d{N`x(p;e|~lFzT-_5+`<2iJSe>ep4~
z*E1357K;<(^n%GiB3sPjfnSp|SSS2a@V;Xj^NGo$HB`iYr`@B@kU(Hv7u;XMlU+xx
z`8VTYRn;ndp(cJVsv0r0b#G7<2ejWiJ`uZ1kq5j4%6lh;)JMNFKq%%wg8>jna+RIf
z>BjAOY7W&T&CL%4crfzj+Q^45ib&kWQ|bw?;er5!#I>Rf5>%HTb#voakC_N9S?)Oh
zJ`0X$u-#1zV%IARx50<oyOC9f1`<eF%B83|x{@7I4}G(3nCoM3+Qs}vAtl6I-kYU@
z7k>Z_zh7`C9@p4=OFqtNvJ3>=;Fnwy*H~|orI^_Gy6~wIrhoN4y$+%u(gsPjONVhY
zBfwFZtZpLb0!g}$2=EZ4+VpZ1h^xGNJ=Jq8`ZIcOoB(HnG;P{Ozanl<!F!uhS~VIN
zF5yiwG10x{VR>MM^^x?dwBUFEmD5h(y%yFt<CFh?xcaKFxSD8L7~I|69TMDKf<p-I
z1Shx*1a}J>2<{r(8Qk67-QC^p<UjX3-1~j|Wgd6W?(Vg!YE{+WO0HMXW9NQn>`#UU
zkM6`dKQg`y%o;2@;fm1Y@Y|vpKp1i@-LlZGc3s%;)B3k;i3HOOW1oU)Dj!`XuxnLH
z%?<t8CQNGAUkMK=!>HWgK4F0Uq?q@f#3qWbNigq~UGZwN8~)X_o<GII#=lM_kU}2Z
zs=(e3Gu$rtk|f0FwhW%tuL(R-S~`zhBdt1(5r%`ON$eme#%JpEj=$D0V;f#2c??Zt
zuJxod#Vcwc5v{@b389H0W=O6bKmR!2{Z1!ul-NQru<~6Ek4hkjPsLzC+8D`LYJTBZ
zF2+O~Iwhukf@NwfrhaoZc>K~L@Gjsx4b>%LPLs!}n^L(*=9ibi{zMOR#HRO>IQu**
zuAWWA#X<E+egXjm!*WU~(t?%nI$!j<d-yX<jaW0|Jf>^z8%&ybw$VB%9#0;k_7+c!
zVpr&K6+C^l{DbdgB|qRF<)dh5SO5Ck^C*oZmpqs;tM=F1@wyOw-KFP$P<1&kz-kA7
zVc~e0A}*decE;h=ZHA@?U<Qo-Iedff){R}v2h;K8p@2l{^l+a&VSfg-=RbK#To-(+
z_cRVr1i54bHCfu7i?}ibD#1^C6L<4YR4duIiL;M`ee)*c=0}JoB0SC3r3l{u20%$S
z-ah0+a7|lD!FNoTwMpz*5jOH4Ghr0RUIq--(>}yyU+K;~diPy$$9~jJ(OfCCJ*i6D
zV{%&KR!`_NiSp0-v7c2`BWNZdOq`;(RqDu-y{j;DS<8lcHV}UGVuA%8t8&WNp5K&`
zzFK8iMgZgWgk-u3=Hi<$m*r(htq_Qszh+2dH=1l%HiMT2Yu3@CVr<4N#_2$s%zU!N
z(?sdx0a8$%ItR=KyfHQ?O2tXJ=qFDkoJ1KDagFwQMjH`S7B80av9-~0wb2;GiaK4g
zI$iQYXr|ysB;sBlB-BqH-HvgLH_7&{P4>Ac5_BQcrDT4|ub#>jHiTs*^Z8f-&;i{F
z{c674bs7l04*QCK$=?ZRM|_3btYqKuHv`}61Yk4kx2k6^%~h1&9afDxHq3SNS`h0r
z)Mvw=4My-h^yWO4Hg?HQ5S(oEFE&E+LfwX6uX=e6e`G`oWy%!Uk+jC{umx}-ZTUs=
z{gvjqag#S{IG|h!F}UDxbI&+;S*a^($+eGt#ok*%<Z-UJvEE*hC6eI}UxPw~9AIj^
zJYBv-YOQc-*53Y{<KkCS6f4H<tth4feC<`%ZP)3>RfFb#yP$~e*_t~%CO(4<T4pKX
zCI<Hq+Kj6}73Qr%>v(eZUG?T=J7-fcHph%uZJ}%f(CK0TKg^${yV?`MSHAo=)U`sE
zfxjU8{8K?WCa<_c-*^>6n?ULyiLU0T0B^hoVv$R?-V70lyU4@Ho`XEL{c{Os!E`tL
zp-H`vJbML!2-SVpP78m;%Of!6Dz!<{Nrx3-FVG0#3%iO?CgZ5vsSFT-c~z?8r2IE?
zeJYl9H&gk2-ayp*Yy(+xwGFm>P;<g@Wg6-Aa2V$OU<|kExPE3eXk*tWPT?xxr5_K|
z3TW7^UPTAnp-&Rf5th|~5K!QL&i1X=rVHK9#XA(sJRP?I|Lt=|zQ|7U$>&Ug_(N`3
zf0i9QBFT`8mb73GfI87&L)|62Dm>kwOHTdBBIDD=FlOQ?uKG%(%3Spxczlr<ktA>6
z!5HNG47nP_?CG{+`Oe#zbl$)0=2O17v${8me4GC1Tvs9Z=1az}V&Y>)*ALyYI^kiR
zmkCRli9BFU%`pZAam4-FDE9h@>G|4jSsuiqQ~c+Lu~A%~poo_ciSU*wSah_Hw+a=;
z&_m%tC-jFlHmrr;l83VtjWJ^(Tc6-J5Bw@2eWzr=N(CR0e$ag`x*1UiRx+#){-eND
z{`>^Mm+WyIvhSbFSYiZyZO=69*k&!F)mVdnq9u}1CcyOCLWyUgsWDc1PZ!1*OA-M#
zeQCD^t1PlM0TC%drza5x*6$wF;zg#skoiR*Ub4D?#K!!%9-cG>^jq!#mJ=5~Tsk*c
zl442+tevEQua~w`45O6<H`3YS004jl(~`^(=5cvofwcX6lL3wGbkl}Swdq@g`@jS3
z9Ds6g-!Z2QfKtt0)f%HR=eQ?mAlFyWFzAz0&)U#9n9jV-_x;D<<3o;}Dp%rBuC-@e
zfx>KH?EORe((cp}&*kH_=2bU-MCN^`;uBHI6v{cNXL2EP4Iw9=^-`EaMonfRYkbyQ
zTwcI!Qe0=9dd@!lGG)_tcDqjR1Mc4|b*K5y*Z1YSWkhHx5|j?*M2_V|s$lKg(<7kX
zDQrO44_@f@*tzPK^XHM3rMZjr_@m-r=!Y)-{rAu~#~^(DD}H?+G<T892|q(vR8PRG
z=jVZXya@o0gRSflDi~8!>qL__`Oh)H4Sd>$ih6S4t61b1A{ubSxrsQxBdiO*34Qxg
zF;m5~3}u1&+J(@nv-r)Htgf(2%G4)X-1D&{jm)**z4<^hGAA9uEPS`9tD%=)$`g0Q
z5Z1fNb9&|v+noo@rgV%xx&}3+Zjz*FIZXr$27x$=oJ5#-4!p}EPP}VaB@}=Jy%-_}
zwfz`zDD%2X(kp{8O;CxhWk5nmQ|zRx{{T!)4(6%d?#w+xyTJ(HE9^TN7Sq}l4b^cB
zl#pE5b1_TJx%Ft4E;^-)qVyN>veqem2+P(ENpRS2+C*k4d+7r3f4gaBP73!q{LbC{
z8Wo~vsY=$V59Aw#TKjGQX7I&jg?T1I6x=#xv8GWcCQ&EIr7~Mxkvv|w(<RKa2N=)o
z2AnXQA9_~b*0kyF`YI+{z-xXN%!IUA=#LIou)u+DFjUQkE3ql-IuXNWFZf60PCC@3
z1w#m7crV}GfrlyE6CVWktCEEzu)|xcGueMr+gzK8P(Q#9r}iT@lizm1$VQ0wC(U^Y
za=9A`D$h2(GEsIywvLZswbzFM<$Seo469)YHC;biG}0-*B}swBQPRyEyRExz&O5#H
zuB2(+MB;9>-T4p{-x>$Wo}K=rp+fpko6QS=aU>xb0R>B$h!hZq8ZghCCk4LDR3MOF
z65W7;@}ajNA0Lu;D$l{AP2EI_(?sAWV7bnz7Mq_bg$Vm{RdyK)7Z_fHNAfv1%c-lr
zlMy+zlgRi<USTkJk=-NoZ}IZEW!=3PXbp0lg5p>G;KCNhXH@gEK3&@N0HSl&Zrv`%
z>1x$*ZFU6OIpROS`q)wjfymKCwI94J0m*G1K=C8)u}y05(?CpTzlQsC_Xl(1z6)K&
zKr{hwv$q99j0mh+{F8YU(S8Prhrm4UR_j(7+Wo!Ul^(U|Z4~`d@|KqwJnYSkvo>qn
z5#IbWVpY(Ay+-r#Tf%2Aj!TZt2^ns*tRpJi+))F+ftMcx|Aa%NRPiD^u>Y$CxFijE
zrPfm7e{X>k`y#xhe=<gdS5#7YRpLv=!^fZir9o0fE7mAV!<1d;>|8fD2Z$@Qw*9pA
zYv-}&xBA@Zn2B@2Vh)v%9i6sP7)s&wCw)+8k)}cJd66bYo93<`{|zaM7Z9?D!*n~Y
zs<@du!kuH&#)-hm8Ji!DK{Q#=RX~A-*pS6|<nOmOLnxca!j9&5{$8UD>yZ=;bYM#m
zSdDLSb>|oPi!{EjcA-*~&KKZbbq%lfqMdsfTa#MExIK|S#v$E@7iRR(U{=-t?QnW{
zOcg7T=oWF7*7c6p^}`ViV0xTrT+d$(^3!}@^yuxDsJc`EPPVv_w$a>Iv@MSDE5bX@
ztbl8>Pm6(fQA$W_dLi+$gQN6W5u_Jzf}2n+tx5nxu%m3KA6;Yl%hDIqcTNWvUEFiy
z$BW#(foIEq6<Y<8LR@_hd9TW9!Yr-bc6|^>qtDAN-V}R5+LS{Z6ZMkXkZm`kYONbC
z7Z+rjQraXVZNnR{YIlLhmk*J0@AHgik^AI$BNgy0QlTDX$|UD>&>@JUPS#u{mo~|A
zuXYD-acB(vR3*;4Dqq)fSfuXGAfgzR=6U3_Mlx8%wiov+?&TbNMdF($8iYLdPxm>a
zNd!HtAI8qQM@sA5Pa5s^*DS<IZDYHGFmGl?@@+S^FIp|(@IQGgZDPbd!;c(Lhc;m}
z!0`Iq3*|`pM~vddjr&%U0t&oAxZiM8nC?cP*UU%QYXuqw>6=w=bz`qCKC`A+>$$I}
z;3d{V6bMPw8Adf#UI0<Tx0Qew^7U99oLR0siYDdzVM4Y762Xl8_`W;yPjVO{^ogJ~
zRP1ST*oW(!jgN6jN3HW`(fE#f%)oSUqjbVhsh|UHXN-tiX{z&-C$_U%bB}bzsOgB5
zx!3WJ+E3y0p%cWICco1L&i54VJ}fTA0;z}2`6nhkeR@e!;()Fs`rdzAN|o!MRT}f9
zYvO{We`!_BS!;!>eKP7tt^%vc%c_z3QQ27p%!zHP$OFw%a6VO40eUGuv!FMpwzsHz
zZ^)>dneSx~B#~X5k)3NNrX<Qp7RrER=3nZhWD;b8Uf3w91XnvQUfMf~u*#XN@((wL
zaw)U-qGRpNdjB@yb&F9JA0q%T&@IuFXR(C33~*}0UZJ0mO~3J!k-MIW9=YTx0)%+4
zkco!ixbNObbKrs5X(eYNc$ou#dY}pLDy0y&x0DX`iCfKDMw11k#z+f);3VJed$hN=
zg~T=@uIe?XsJ47jD)&bfb>;D+4v^9-3TuoxW!44FwhFeZ8CeA)Ef&5UqK>4QDd1|4
zC0b5@OvKY><Ftx1xx+9Z?w;AuYb_X!=xo>=;TMJRUZaAap!urneJS9@G}DVyMC9KU
zj7A^8s+_XiIA_$&Cs*BNb$rzRx2wCX3x|*9!xz;}x`*m_N3g_{sFUtNI}cm|>S=&c
zX|hA-n82(v!RhBqg!ai(+6A8vud7w7^Vaji_8&H$F4X7C-_cnEm89n?@Cq;Q)^i<;
z7qnQBIaU!d829#x1<)7G2oZK;4OB}U8Zu9GWv<`IC%xxxHF}vVgd&h(v%`PiJ1)<p
z<tKG!n0Cpz4PQni2Pa5@0}r|uj?j9SazlWA{)vIP2neT)Zm|u&n*_>?FpOpE4%Z>i
z!Vupfc+^)&g6B!ac~x2Mr7;Ln$Z3OnKt)gYTfpq#Kum7L@JT}5MsD~#VfrkJ#(tzb
z`GMeQyo&AnRcdh_3c*DqJ6ZKhQ{X`CABSQO4@pn}QN^d$9II3bicG0Bni8>sCF-m+
z6V>tj{e1Oi*&Y$a9+4;(8T!SA*v1NJ^Fgq&jd<rILNEAnC4=pV7XDC}Ew;V4y1d8N
zs&x)a6At0^A=9TlB_n->1z9yoAR|;)Om<ZFydk>NxIH!NpBIPt4{Wmy>fe^-{Q|Ez
zF)KI=jBNc;ZW-rvc==M+N48CDF?5yBFZXvGgIO2x;to2oVBRFqdiF>!;pz^P>FIL_
z;nI(04d6|crmztl{o3w+T#Lu4mqrH^Ky311W|q$)GnFfNM(KjuqhoR1W7Uhn?V46*
znbLl3KIKs@hyffM<JI!X0l>DL*NboC(x@y%tT^XJH@rjAv#|8q26<02N*6VYn<qwq
zA^lli98Sxxe#Lo~kSD=@YpLG8UmhBWwl;=sknofR5#9J@EF+g8jihhy%hsoD93H7p
zpfdvNCWbl)I^IFQ(tayt4m-5kA8_uJ!I_9e@Uwu@bwH_LfQ`P`RC{K+E9G1&e>Vd~
z1qi7E#N_nA+7X@kM*H)glew+o31qaZvwJ22-B-=Yq(nx+X6X2GSye%G+R$T&=i2i0
z9j$NM4hLi<|NCEZ@TXI-yuGDBI5N{$_>9rbwB8M;1G`mP_hCX-r)ss`)<!wt#t20M
z^uZ9S!&}CCR#CK4e@9%}C(9UhyZUowtBI-(3mc$klQ^`UILi6FgMJZG-L3jfF7P$d
zDOJ2(y3Zz1&Tw`GYYUT?D|NaDtIaAi>CfOv6PH(pkA$d9^j7Ju6i5_xU)F^J-ipry
zz#l2<h^neq-*!1iT#??Zw)EVFk?Y42@o4;fuv6~<y#*B6^ek7)RcVUUT&Z*dKG8bC
z@n$aKp6Mscs@4xbx`mrH`7P6`$!~u;PDJl2;G$mIRD+gB4&}B5#+#)CPbBmsO>72R
z;17Evd7PBgAsrJ_7(G&(fX9Ap$sp}<yx*;og-{Z|huH|@N2Vq5d7ma39TH6REns!J
z>9@f+=rdot@nfn-^{o*)a9nBx+!2Ba>6`&#W0&ypDo>!}uC>pUZ++!9tLW5lSRgP1
zij=n!*ZRe6jq48iu6x$MA&b+-ZJIA3wKTL4RN>~izlt{?cf{|VY7!Uh<>yp$GK!Gl
zNcf~WegK7AMvy9m30%;|sI~M26|F4F^$hhZ>uRtY3E+IG4S~lcunI;l9TIxr`crHw
zoWyM<$Q6lw#O+bH_vz~{Mz_>vwks3I6}|>YWT9C_F<Lg}0Xv$O?c9z=ug7ZQ)3zq7
zRW@xk!QIG8M2nCZ-0m{RFPI(G3VUfSD_<N#5-)QNYY<NF6p(WLUADKLj2-++lh8#8
zZa5+1i?-7}&$3r<0;|4)KJOc@pmM~^Ls-X$F;<&@bHXE}&IwZ}IyoE9KbO_@#8rq7
zZm{ScVJ>K1vH2VD%1$}eAj!2LY<x);b(<V@;6_WzITSgPqQ*PNUZMS!e5@PhS)`p)
zfutU2^{a8c3mt}tO3wk#*+ToLd;lKLwexy?vvuK#)MS|lM?;KTNAy8p$Q3*JCq5Hu
zj)1&M&B;JUMoY3rp&pQC?%?2k3<hg92UYO{T81?Thpq;KD^!85<yp>EEskp5OicJ9
zmM6dz;V(|!7Cjf2Y&gab#9y#Dl9L}P@Y5m_Uv$5k_ztMb<{@ZXi-;zRjwVo0%}z)#
z5Dg54=zFlZ&7SA?i$EwqWd+E);R7DW9`B3z7c~gnd2xaEfN|m~H}DPvF@MHDSwrW{
z$;gP_U1qr69aMeK>W_SkT2CK@&t`T;mQ9lLV%S!R<Cda^p-7n|IDK!4+2_bnH=5H?
z+I@9VA2)8w0~!1j|NRHowP|_f#<pz~rJky_Nn@+L9`7e8r;T7pIfuguKp(qkT$9ou
zi>?Ke{h?jvS}oln*orbR9@L*7JSs_o5z$H7ef2Q@GRjD)m$wSGj2^FPYaUAU0)cPe
z=);|ZQA`|cVV%Y*NrHkEOYf?X??MF=wJFUKl2OKikx;{w(4mKze;I~M-_Mcea%X?U
zITvZgAE;8UJ$yaFl|O^SAM(bhU^i#{<Pv2!N+GvI1kIz@ZQ*YSD-8E)(t0|FvR#Vi
z#T)(2o%AvI@g4*0Uj>BBf+RgP(nW(<fSQ2FTHkZbg3VOgtOpB~dUC*)&T9_Y(zruT
z=CAxd3!Z^bKkcvmSSTL-yH`MFTZ)pC5xzY@^s;=E-#`nShISoD3&3mJ8Yojhe5AqZ
zqz}3!p6O3HPDlo0be58Hp0piufoE0$IOx)#0`ssmxuRqF=IpGudU{U4SNcUkDn<;J
zoxbra-Vw5jM{aaOC^r|vF^oS)g5~<HPqk?xIn+`M5keWU($|(oa9-WbFKF&|fxh_k
zKCtU`H?wKTeO5$fCnB|c%|mw^6W!(Pv#?^e3zp&^m~Z!oFTZIqPvayByYC5C(#&TW
zYmeo07?4rzs8u4FJwCp$Jg~85_!SGe+z<o_5h5Ja#A>93C|Rb5RufHEbXW0o0MY@%
zsI4Lf_x>#B%LD$U{u@v}-+Qi|I|uwkjvRDP2yBYBN0eUu|3x_m8e4$9>`{!l(;1h?
zZ#uX<7Y@(fyB*uxwsuC_7niWU`5F8Ulj~P1eARZKrAUTr^Ej@!K%Q}Ps?!ob3eM!s
z<`f=@mQqZtdOqF%anN5pBQhni<Lv7COY~`!Yvw3a#f^rMDtd@KP_3_C=oj5|Br<#%
zKq&@hJ!Hqcn~TXc^OM<UQ>MUWOIuwRznRR!eNtn8XDiL$h+JGaJWH6^h!UJfYrv5u
z>T}EiV^iJL#N~jpdCM5oAW%y*{6aA|&C@EjJo_4Lh=F^E`h_v$xlr1Lr4Z5>9qakK
z8N#Wm<dI$M9yTM_soW%>DA^4s38@Q`&>Xsx&QG~t6{WPww)ms8^92GAKca}tMWBFH
zz{CC@yVZ&B--uK<9QGzl`(c6ADQl5@@q6c2x^L6V0b98!O(5LVJMti<Ru6QYWs8|k
z8Rl_8JG_`&qt<XDft5D=T-I;J4FYqidyz(EtC*9J7)<)C0yke0SBWOagmEP=ISJ;k
zxZ~});y=M%GDok$04KCt${!^|&T2`74?n*3wobB1X&V7b=Q6Fgjfnzqi9ltHa#V?A
zn_5$3$%n}jPiE@6OYhUadYD0;KU&dQTEjt9=8SFUnflo?h^9z3*2GJa${kl;gJGFR
z8mTVEPPq0-tOV77gylNy+WYUU)nc&NSWt(T6;uYXkq3$J_&*3;s2jdjze*#ytLYwf
zHHlQd9yP~{k$u1#j}C$6$e}=}7o)T{-+@4io!C0UI4yml)4H;AdAR+C?{1YSY=?)`
zC>9i244cZ0)P(+Z&=Td2P^TqKIQ<7>ip7#uuG%o^Y;)h=<+=3C2kk4o=Y}<`J)7w<
zrdDW0OSJD#OMK(yBVbN1Q%gcuy;oRZ<wB~5rSSS~Jpvm>JR_<&HVXPD49g48<gCqc
z6Cz|FoggXnUl!>=cFM)qW+~8cmC#V`7dN9Za6e$p*P{w2Kvjn$BX5R&gu1PZ=!cAp
zkD#C0<ftL_v%|i0T|z5YZk!*n{6Or&L2%UvA)=8G&wl=2?C5{X0EV_ma$O<|KZwhj
zN@vacV@nw_wP0<1c!4Axgae#f;trz~PNR&@lDPPNxrI5z(7SK2Zk{+>JbuBC(@;9{
zlQk4sidUjTUJ*}am`g>{;8{y>3!`rv0m~D!)`{g@WOd8n3p(XJR6uCm)CDk6JqI*|
zUdgg$8fSE}Zr+M+qLhE7U2W<8y-*w8-x%u9_Kwne8_}6@Y6GpPfj|8{%;;s|tj=Nx
zFT|1teQxuZl19Hk@e5U;BS!|gYY0p}^4RGj-g4d~f6R$el_guY3t<+<Sj|JsFVIHB
z9Dm!$4tDbub?$40@VxmV?p~fnR)}*9*fD&0?mu4Ff&MeV9uC?%Mg2pJ6H=$=Sm50B
zaKsQgBNJw)WS%hV&w%5K%@=!^TWjK|1k#@cQG*sYR5)@xT>hGfbeU_jo^@5vH5qLx
z&Esd^8?O&f^Xhum5i8X#pfjpl)%<WiM~+9SU7lnU{+-`mIqK&qn~6mU`B}ZLN5H<F
zio;(DV4JmdsKub^u&+}$lQowZy`b~Z@3XqVeardlp4z}P^->kO++Bb@?;wGO!3;nl
z*6tl?f%YcMR=|ui3pD~E-$O$$MLHe9f_ph;`s!4s83khqRU5K7FJ$>M43QZh1jNPw
z^&?HI5LfQ7=AZk2={@n#fvcHrX8%!@#Bw!%`)NY@H4hwjd)qV1UDBFAprbaQ6xFbW
zn#6DBfoks8S(s(@y3kLF93+AjF{4?5;X78E)hu%P52~8Yibk5%f$Nd6j1qM9a+OX4
zkNSdwFDL<|`<i5>dMiATZMqtJ9`kxb=)Xbb+SA7n4YV~BevR6F6N=mJ&ao=LzF6W|
zn)kLLN%9pF%(;8Fi3;#YR|s`Z!HQD`M-Dp_R$;S#MG~dl{+I+%KudlAP)KcxQJtNc
z{8ybnD7tY%=BP)&o<R5SKC-r|CJB1QvG0H%u2QA2J@5F=_nY1Z&`VD&tAC6Tf)W>f
zK5>1^kW-7DP^_l6cz!0b_&spNzw}_^a>KB*eTIi8xh6Bkp=^Ne%0nslBEUAn_;D9?
zdg}*1C}4Z`#wc*zaYoK6ClL+%>I>-wfZK!B(V2e{tez*TaRtNIyPBp6ht$4+wxbC=
ziALLE=jVauM~b({iD7d0-FpcNU|;;fy}$QTn`0WVHRdS-bmx0HOO-i4<KGzYotzJU
zA-47gY+!OI3<8SZ2fkRgNQ=6qs<I3dq<i`2WCz`%u@ZARt4}VaR8*>^RIKvZXhafI
z)^~*jQU=gSizof`N#MV+N`k6Z(aD!ql4bTq;CE|9tW%fL_7G>dytEwRn*GD@Dq#(n
z%2}BKSGKU^k@Tga^tR$TS5j#W1`^@1lzG?yBqlBJ^$L*lji%rmsu>*zmSM58UGmo#
zBb?@l?$i|#G=^$72nkMQ5im&@yG~48z$~+gZQ)jxw6UIC=R>Iiu|gI8*&>2TT_$2V
ze@(2K)pz!@OB9G!ht%N9o89tK`WB#3IAXTyvc!z^k(-NdqiVA(m3y?xg)kve7*}^3
zLs{^VK3OBn*G+wAxb;VT9mF~qIZO1-d7Sgo3F9o^o9&Zo{ebU0n~F+Ptc=4Je;jJ9
zi#?vKKzG=KKf>Yo&4ls_#?@*fw2Uv5yu?fWhV$)eNB=Hoq-TB{^e%YS{AB!ng}jne
z5cx%7bL`8H0co$)(IrK>dwiNogst~&oP@-@zqR!o$ajR%#9f+8qs`z$J*u0!ZyzF3
zemQS8eP9gy?L1r&r9)tb##d~G@Z-uo-0;nYIlwUKbpiCU6{yEUG!STL+EsR2y%l^l
zQSz<HA>jt0a3Hq)&Xw>dJe+s0ah4edL|rA!VGNA@U6Xs)BH`n{FWOY45}kXPO86Ty
zS4M^*wakw=u_`CT2!9}_d*^eg0y9?87oQ9?E&lr$&4zNY+_@;^&)Bwtllt-Mx;3r1
z3}q0B5=9Hsf!nZ%`tYq=m(*uA_Bq<>SGUvh%70$jXYKi-^OUzLV4<b(CMxm}{6G?3
z$y*HGV^X{eetCbN(i&+LyqD|x8%Kn2+%=u}UXl3-crZ(L_16GHI0eQD2J&8OZKB_Q
zhji$KM2(&wos3SoP)ppun-HZo5$Y6CU7ktr_iHswqRV3k1>#?tE63S51W8#$`MvM;
zB2wr1{Qa(JyHE`K$Jz)oT4*Vl3Iuh3!?Qr4j<!!yns*q=j4oxGA0&hzE&&1%-53WW
z)gX&Cz!soJLx5=&OG7=YV6CRl^O7}{GdW>Vk>z^V84=+S!D$%5jWXNKTSk^qncj%w
z!V#Gsxz4IUs{XcrFe0qP#NeUT$NS_Xb3Iun5>Q}EGd!#XA_^ni_0ASlDcE!qnBUp*
zjH;ulFximgKMpNyShlSR$?EzV&WzOR=W~M~dA6qV>tt4RCLj^^7f$E7Z;(W?Kket7
z(=&vkU<r-AR0B?(miGI5e+;1PjBF{Ps<{<xJJd=}kcsN(=6>Y2K+Ne2W@Sx;B<cRu
zmJ?`eNL^Hn;=MZgCES7)PQ>2{giFNe$FLa8D&K={#!U?K?*!H5#85GADIS(eL}Q~m
z;@~w28Va?lYIw41gcuN8#r0echZ(i{EHCBi$wv!oeK+9gen!2AOa!AcH0)P9VKI-4
z!;0lQII5Ep;UOXY6|)Zh1}R>@<DMryFfchKCm(k0*_pCDfW)B}pm9j|VSlT;vG~D%
z3NU&77O(z4_V0_GIT-Hs_gX(bgxZe{Ye}Rc_kPnL$_Psy#Z{6oPjP<FV8TRI+{^%l
zn5z%it?eq^)`LY*R62QCuZRgn=n^}J!5ovnl&!~=DeamHEBDH9XgRiioYm)iIX-Px
zBYa5@=->#@Ss(XWKax&J$iKrIE@elFvo-F@>q=kC{t@-{R@bwin-hsD#pS}FSFy!U
z-|CPLQG=Agyir@bD9p$ogKsDx@zrO&P}CsFp)QzY7Q<MC%DCo^pr*|##96Iu(BqqV
zC>B+a(&t>`or`##a8~ptJ#}xjnRS0@T(L!TJG`fyp?ZtId$ih^2abc^fA@5E&12@^
zd<}*_qxi<;_Lq(qKBa|F^{2&dDmO7PNiNxk{_T<szi)J%@gcOyA@!`1^g_XqB}DI}
z4Yh;FWm~7dAIvMqWoV~}xqGfE!K2b<VCTw?*#`7G{-a>5ZRl@sm1XKDL2)U)eU5jj
z&X1y*+Jv)w(M%MsNWV-ZS+uJki3?L!fXuD65?ya~yNnB2IA<ucqGKEZyM*rlEk^m+
z)I4S(`<(6t$R;3RDWuh%fP3`jt(R`+rTn*scHfFOp2CyyIJRB!M<6aLN)3w^-0?qK
zAoE$X3WUGl4uuo;#Ip{ofv3m8F1`SY6YBRerE+5Wxba^Ig8A<UMjy4c)iUIR(pXJV
zpfjufAgM!z$r`{h!5e7=rxbO44{$gO(gxav<eM8&pxdviJp2fK2QU&M@o>K4y|63Y
zZFhdWZhzt=_H-!YOE<i<hCq?+1p`Klkh6YOFv(EGElk>10N!yyq*~CVVKD1t(836>
z23~7JVpbULWS0xx#V?-z8!_K^453M(ojMz#$e`LuBj=@e|KTM1yx1MBnW;*Ot6*O&
z>8bOh<l;QWZ)EQlrfrR5Oh4tw)&^{XhepBMngXHY{&j_13lw``!62paG7L5vhgmNX
zNIiUh7Au}{w$+yVo$BpQCRvR#gYBG`;LYk7R*q|9ndtR?q=!W+II}x{B}f;7%8IUC
zBZ+UWwh3c-On~TyBQWTb*A2@J6QEDG-f~9JUyi6aV5WHLtq_|hu7p>Oqg4_N51vxl
zVvgNnD?_br)s_>L-M`8(CalT)OZ$T%y2xKA^4g$r1RD)cbia!*#KA9S?-b!s9rn)0
zu`u@wthQWBe2>JUw8*utDo1@3whTs(X4j;w<QZdeCWJteMq<bqwjbdoo1gC@`R=|+
z&V8r}-31g$*@>?I28{GiJ&w+qYPAOoe`lgUy49C2j+-yv{g?lh^#Ts`(CcOV`SHDl
zy_1@xqCtTiG~T-3(8+9W=k;qf((~i|wL+rkF<nk~?L`yL{f$uDh*8Sq_s-}q<+e=1
zjmagka$WIx&UHK1S|A-MoahrzpXKdndN@WK=n{@nQ1h)Vbl8@o1=WYwb#`592dJhb
zxvci-Ebm0Y*(8BvPc4<#&%?|Yd~Q@9190}I$4`v!ymr5q=NTfNGiv@g<BwlX$k9Vj
zz(Q7*2}uq8bu@dYrpxbNGnNj5*JJ>*7&2PU03FHgdKSIwl7KwhvQMHRrP-Q|wr;5?
zu%?8y)?46$1W+dwWPhNIH3FS~f~-8(g#=zghfsgTxrlA}bc9O|+IY7h=){7HC`s%M
z$Y8a=n>GUI0Nmpo!_azy-d>ifsf-hi>5B0xjtL0OA3H9#P$DRTFkZk=zy;cEasQb+
z=3~3<pU}>UKEMT#;6I78+kpdoE8~&Z#3_b~42rVRSe9Z-LSUYxaz>#|@M(BUZ&VZ}
zg)gFNvp}<LjKn#iWyi1YhEgm%QcPaKZjbzc&~(>;bXUMas?i0HevWE2Jx*?TWqrg&
zWYW>yORm`=%7d+kAia12pDLsw7n?yhZo4&RG3`$>aa%E5|E}lthp&<wo-2X%rEDsB
z(<K8<zeF8`hrhZ+PsYoKTfcC7lx(4Qyq(Upwqu5~7<!y&D`j<LrVR*esJ=~cjKEVo
zuB*)<jU<e}Tg<B6aNb~H>nvfV?mK$qzO%cEL_ik5APMfUU8Yy@X@LGPWgv1buSD>(
zYh@FP_6dc+Cz0zx)!=zlvD{nUuf~y(2birIrBGO;d$b7nFZ4@U!%<KJ9L171fGk!q
zA4998SmEkmI)`e?hqXuPL*AjEjXO@B$Od1vUF0Vj3S6EesrS2f?_-n-ap*n!^*ve0
zb{NJuTujEju*LStkWeOAJY+%~lkF$6;;=CRV6*k`LU`nH9PK{q<h(5EtOQh&ZMv4#
z`g}@!Q*{P|h+k5=_)j+cN4mO@Hc5Pmf_um>DSz&_BcCFousdy6!zhLw%saF}DL}HW
z{-R%RvWlZ$BkAK>!~((V*&w=Gzy+LZPy;-yJ|dx`Pd0>o78*vlQdR1&)UlMgRQa9U
zZOV5%^FAi|abxp*@y-MrzFD5-)rIy;Sdm4A&KtCj#@OwEJxfshol0UYYy0d}pb`Q#
zO@hAKm^tTBhDoA-5Oa~$360jA?S!|%eEZ9i0J_zqlSy$>>AgPiBN*rA7MS*V3CDYk
zLR+0w9aA2Ke!W2RMqr=@D)<BuN#|V{6cfP{yYv%%EsxN4F^(|dAd2ITvspMutUu!*
zOGI_gyCSxSkT}PtyOH6em0<Qhx`<FY>%yFXfMquHV)}!Kk3e@-(2s?({Nv+Yo_P3Y
zklrE1YoDTG1LHlsyb_j3)a#Dq;pGF5R+x|J*<bnyTBr_n&zi9ZW}NHhYPaG4)dCbz
z9#r609WiL<Hu(v^z(1e%7&Q$xetg0<scx-Hg0;jKtq7|mTibC2_L`JLC@*qH^V+S+
zDgq|@tI>U-UNIdoA3tvvZ6}Aakyf3f4J`P2bl&~zuW~FL#-D*=`mlgXYMJ+@&}mjG
zf`lMaMNRt_@GOQcx79MYolI0N3}^s-9GhP+yyp3oLGtQsMUWHjeje)TSICu}7<rW$
zsqQ|5%E{Ir7i!o_q|WNc7FCF7$!(SgL#_RRINX<kyO|L_^}s8~?6Lv+2Hbm2t1zQ*
z<HYYYJd!qeQ>`U*LydT1yO$Y^{_xfHzX}iGZmPuG`879Q1+JCtg?nb4?RN^R&o){o
zgxk8YIBHj2`=~o^dL`(~Rrz;)UqdUeWHzoyhq=GR$<Q#*%f=00&RHfa3?Ax~B0&-6
z*crHgKw~l>!pBJ%QK4Is&yFO`*7tKZ^UD5>JBL^zW>uay%smHkqc@x?-sJO)aj;Ls
zy~;9b#6={`)^Dft4Ag@ZZd;Fo5KdI153|RWFfmusx}tl?F}Rl*v4)BLXX&x|XsTa5
z7L6OC;BkwCS;tnPOLGNyYOzr@mQy(O5$Xv8j_A`CD$GP0#DFg7Gis7Ytb-c~ZUlj{
zHVEG57~mqu=n4lN^Qs|+yy7j19Cp{JtIE)ay8V5XH0CAk@jBdn_iO;@p8hK>YtH20
zykB+67fuk;3zD~?OK24ZW;4$b_F`e%=0D1;I|tpp2QnGfQ)SqKC~V%?BcsjPm)J$e
zqSET*CddteX>rS*K|Tz8V*^PBDU-t;5h&2R`?`fXiAq>OL2ME2>o9Ov<~-G*qLOq<
zT8q26t5RnJc=kQE9S0TV+(%il7gAC&YL;WJ?Y=6uB`m=iL{cVkNB}V9+8{@tB4JHd
zEgYrg$$JJn&RQz40IJ)XvKM&=d|b8hT<$HTdA;vxx^IMIy#jfpmjac?GY=vwh5GOe
zS6<V3G{$epI>74oR~Aj<5#!d&%?d5~Z&i{QQfZ<rXAFe$TL3`8%GAXUO-CF+CK__H
zv<XT6<R`3pdiL~TM<+I77l%)0>0Ri<otI%fcw4U0jM$H$q_+}%9t2!yII6>i86mW+
z1S*}WT8?e=?@a0Rs3)iw+R7d~Vbq&-Xd8u@#10_ti)Mwh+XeQy=v9L)ssu{FNew!)
z*@|Yj?$QPJC6i-C80YGE(Z7*Ns$OBAgF7TAyl%EHew-2RMs1)_Efnf!<UFimMppP@
zAKcP*d3Vlr`hvsbG2vEy(Jt}9njd91&^Q^44=FuVk7G~$1>n6~lJnm#Tt{y0EJeTs
zelbJgDU0_!N3u$a!~dBRmAt5Ey+kGl3Tlpf{Q0}^NQ1r-skJ*IwOWfy@?6IuhESHL
z_DlXCBwyLvYxwHg`D_wmdz$3tVS|PMLNC#Kn-uxo^>0oo?(g#R1YdveF25A3zF_O7
zIjc)mt=0pTt#~y%W<Njg@nmgz`#u7ER#&fyEHY&x(5@>h7@U9FS#S(*w7x<=7<}#n
z>McZ}Q({nt(&$Mt2P2Trmg2EybY!+cdwYv5CQ`<*gii8{Zla@qWm8Z+{;t<Uj0)aW
z=Zp0#3;;1PxWFcPMIp(12<p|%(d!9A5Q}<b02<5|xcAOsz%4Fzyv_-Q|HCt|`B-a|
znCm`xISrY<?&SACuJ<bwoF|QesvT}yWi$1QLIg^cwZz}x4Kw$d0v*biaYk2TB0KAY
z>Gt;fR0j*3<1K0L(1X~W`|=#Ya}V#O*(S>7Z-k16_s8c6Ajnt$_RSIxaB<?8F98Yq
z><0VcL;QAG>d<-Q0!HK<1_>VXa(fny6d4CAb$D%r#nx$o_e+`01~20yXn9Rcj&YjS
zXz~f{XNP|%W9n!z=2p5&de480eIr92qRgc=G10^U)hb7zYW?sg)kO$GpXErEZBtTI
z+&-0ARg8r()I)b{tZ{w%c)nx1PN54;`Fp{N|8~vu?*EYW${itaz7HKuECWVo%uf;R
zF%RF(qZ!w_k$BMJpW*c^;0G>j&0Rzj>R+tAU&_`3zgC6D1~MibLuN9Tzg(sjdNZDx
zovuQ|*b6(g+R13em}3a2y<yM><8X-xIgAEG6Q&FiYhe*sHCtFntm@MxOH_K}s6OF3
z6W5d65!@pA1`FRf+<Gu7l2>@KZ9jT%;vd|Y^*Ws9;&keZ#w#VSY@hJBfeaxldsz*E
zYLn07UKH(RYGHkAhT)A5;n2t2;D$kBq!Xz%l*(80x6Se{o=|!dU+*>%x^y%OUMF~i
z*-VK`@}mRl0zQd`l0vi4M|XEeT6M&ZdpsG}xzpuFvfgEEs!&pU0xDT-u+P+X&q^_@
zET9NcdAez{!|9f-G;8R%{>dK<Kk+Uc+s$tnfEiy7%bR)*VY1ee08#STtEa@ycq#Gv
zh{_uB<sYHub5pZk;JB4vgRtC&l^x<#U*_vu;^Kv7Yh54G#c&FbzMt{uPaf|I<Wm|?
zlSXaBd_#MPnzyW>EVd3zg|XqqJnD8KbOoTN!wE2%IRAPe<Q&K`x^`!qOqS?)^Z<A7
z5GW?s8oW;iy^DW)*X}|_Ij|#J)He%R#-`(q^ko*$M2+=l*DgXU5neqvSNviIls1FC
zD@MTW0jdxb+hqt8<K?i*SFNDeZg!`47Rz&|c%q+&eMzjZ&Mj(ms>CFMF&8$<or4)h
zG<4*=h&lxPK4aPgV2Wi+N6jk91oSI5H*9(d*IlNY;Rl;HI6zddmWSj0^^@euJk87g
zr%^kqL03SVc%F<Z3S@jJq5b{0RTz40sMD_}1@KEYF48g50Z)S%HZjtTzYCML4}SIr
zaS$9J7A2IDvPz9@-v9o*%Avqa2Qdb7EAJcVvs0RlvwgT0cGAJY?uXARQ&J7mg|dTP
zKknk554@oBt6f=T^E)w#d&m~C_C;HTP$2xDihUm)zIDmj<~(BlmvCcHx)1BrZ}K%>
zv?j(nj^%{!0s*)`$0ZbK?>=L@e=UeNHx6fnNaZF}>}vj#>rC~h__hPT$4t4eDXq^<
z!?^_}Z;Mw$x>w(?wtPK|CT2W+uV+DT?YHYgAb;)dDZ5+js%VMyjh1IhB9yZ6Mq0oq
zTJa+l`_!QIhv}n`=GnT!L6RB#OE%vl2l@38pH)3xQ$j8E<??qc%~;m6#4n59Z&{)+
zs?G~(A6(nJo{BDgd-5>uE`gvH=NZ4YCEMjK&FzyHf4YXI5BJyC4&l!Gg(i;n%#|I-
ze@BP5Gd%Qq7e7Kt+ZM%yP}*yRuDl8{R3p5>JyDeY=Ge@qcehwLO*75NojO;3HMr7q
zA<+EPw+7o!Kl<vURjMir2wG>m@?Jt`<KrB#m*5;Li3*9@FqqztqLMb-$6?l;ZD_{J
zxIu*)xql|Q?bCA45-@SxvyixE$~7@{H|)a1aCl4!zTNAu3*>UFL&?;463Tr#7Y&Gw
z1I?qkFh%UkF*Q&m$E5fANMEm=jV$DpY&;@9ABnW1pGf=QKSh%TE^neT6QU~ouQ-6j
zNWZf0gubic35W(U(^=#<0U#=phTr7bS;;y!(%tENB02ZOb6~rCWsUjIehXZ4zzyzw
z)rnnX6IpIS;oQ#_gkcOa5-kKiqufSXpf8ZZ*nCjhxADrV6#;7~Bw6ciiI7)R-OlrI
zS|iLu_a(fgts~=%;0a7G7GL$+cmhpoqqyo=DSOXP@IYSsLmaRDd8$;_44W6i&j_^g
z1j#w^+0xI2H6D)Tp&kCZmPhwSr2B*2Mo6s$O9!VB%+z$hmUqze9bT(RSB#X!7Y`Og
zj7UuprtMsQpqwqG-%i%N@;|5fy61Fd<F}DI4#Y^-J|QP@{6A#>`gi>-7$1U1;>*aZ
z8ciPF0PoEnN9^94PPX307zhy(q}qQ9f$Veb&67^DffMU~N8}As9u3_n=YL#xR}~VJ
z`+h9}7dZxs-Au0g^VYh(r7dB}K<<f8lPv0Rx6NVE0y@tsyxjv`2v}Qk$JwV({T2J`
zN_$ro$=GH=bg%wGGe9<4<I#G;I<DJnmW?vtM}J|4&8?Dx=LFe%$Lk~u@Fu5J*+Gi0
zl{%#2Jn5;L%`3dfoUMO{0mb)ey7YC>7E7qKRIN@)dP{#2Rk=babFi7e0E4rOuqv5Y
z8?dI(5)qgKC%UOPOl%ZWNOf*Uog6NyWC3{Q5)g+onw!RRXIpR&$&UJY%7NFnX48)2
z*aMVSa_ZR|4}X0A=Cu?qawxj_mgr7G2DeVe_R{%hF!cXd092i4MGzIgJ^$Hr-E8#B
z+So=1Ulp)D+{mELQh3+<9e7jn;!Gck)UOL@8tdZ7hQS6tBrYMfm)u{oBt-7$x9<fy
z&s+E1?0%_FiO6JQd*suTOJT@k$L5NT^Mk#Byi2=`7LnM}&Br#@7#OPPTQ0IKH^7sE
z1~#yBfp6eYSRH{-Enu2iY;DxKqN9Or<72(dd$^$|^bd+Bd$8Yqj2@81zM|~P*ZW2_
zGi}3w_<5UY!a{sgiday%$bYQo&O+52_nmM{hggdDixxVn%Aa>PEp-(F5pMb1@QhIj
z4MJLLHcVi7&f!J|=yxzypWvX^t|hKV5HkcO$*7+%>a1NL%2678uNmXzanT3<ajnq-
z*r$zrdyvE`$#f7^22)QHy~RR=fX7xBra>UZ8^@h&6ChFj(y*dhXBf$5N6cY-<}CEz
z5yLSFu%|vZuhYGO;jG8Q!zg`obw4c71YfO_k!%mHEpXlT*=dtjhU^=Et10n3?+Ida
zzpV3%f!B#8G>($Y3~Y8pAPpuf*G0~s+p6~9CC=X#o$w(j^h(a#z%c!nI^0moo=izo
zt*U9u@p6`XGhKg;*Qwf=E13!5hJ){hT7ogOF^l(lCE#Y_f{@(3_zL%|>O-kR8icHX
zqLfEb%K5m>ntyS83T^CvkJf;y9aJ_Z2cJacEeZ0J;ohy3!M<3%XYIPfTR6y)csZc#
z0`Bl*{lIRuXO-~R%<{&6+h54`g7!Fwk(v4dD`9U1O!hvZiH$pfBv`5br(@gvv<SF>
z*u6l_m};{snTPy&W!5|BdKiqSw&b($4IIgq(FBBQ8Ld&1p*w}Il>|>((eRysODZB_
z<4z+8&WM70k=)zyT%)0;;CN>N6Z!AE>8|OmuIeVLC>5+6r+;?~#UH}vL?<sfW-)xA
z&@yZtCvcAD(IX(DBq!f~prZ($m)FF9<tP-bzp9I3f+c7712yR&io0)vXU$_wm0wqT
zA>nK?7%q!`GtwHj(kB69E;6bFk|~T({JDY#H_*NF0;Mh|qysADJUbY=2xXf>glCdv
zMDDUMG*`nxcQ0MsZ)E?boxyTl(`=Y^=7Wo6f1|@hoL$`_wQ>ot&jR?M68i8eadqic
zUl50*+m_qccH?5q389Q8rn1N&x6lt~3B}Yd>WYOe-^B5%_lC`*k^AQSuroYFl4a<4
z(Pfh%brh&*IIe0oXhX+=(marEW7Zkm0QGTy@eyF}weesQe(Q50$TcBeEvcGV)q@Lm
z$DfDC7Kec+IX%4bW}Qv9DHMpzr=UJ3=X|52iXO~IR|3mh$9-z$g0ajd%r#b{t}Jr-
zdsu3*%H&)Q*_@{~(?m$5tOrftm~i48>|@9gc_ctV2G4qx23_lmd2v`TPTdUT7av(U
zyw=F@|Ghdst1<Z9RV*e63XKob`@N4G;cKSor6xqs@)o+hLNZ$I5L8b`DGFhN;4mLx
zD!63Fo2PdV2vKo7UKk0xIH0YKN3Ly(`5(yd54l;TGD|$k<j;H;fhaH`f9nX}&JKMb
z#<^!E;#R}m@UM^Hly96L3=*wLaw=*Wk5@=P!*6{>VcK0z^UP{3ATiMM%=eW#7nSI_
z%swP182@{oI(qPNA%R~vAXY9uStM-^M;n$gO!SURiPq%-FIGC=H<4cTJ*Sb7&#m10
z*1i<c1TLxg%N2Ha2?gVYy#0&S7It3bf4UFw0SF$w6?1Zp9Ohu7)ZjQg)$(9+Dl@&y
zA1UoQk$0$RE@J9J)LqP#%NCem#MT1M<A9N7_w*tgu&@{!7rb+s>)sI+!?0O#9)z#w
zhoTqaYAf<BvvM&6XYTGJf2r7&OOnjP1s$0;tYv)cEe$;NDi-k?jP?6%Y1G|o{kchq
zP)i`3vfrRYRW1XYX;?vU))5ltrQLUuhHRq4w`mK_gGBLA4N@Y5CbE4|^sy-PqB3SR
zsIQM5Zfq8LH;V#!zfutrukO;|HGNTVZ7^>u+|8_~L!W!FulUb_9sFN@It17^P!h^<
z*eqcKAzx{cGlKROrYlTkZkvj7ev;(|eyLAqMXze<WO5kP9vEEGjQ=fzp`FEU{fXL-
zCG;-{IEA=jH0aIq)#c(I{A;_kiDZYgA@4u<h`Xf^)~|N#2VxP?QzV|@KHYkp6aEG1
z>>a0%6?Ws&Zcd_oE<5Elk2=vV1j+H~?jK^_8X<>iN6A1A421JQa0GF!E*0O@)?lbz
z-pPh2@&`{^@D=Aa#_D%4O*i9;Mue>UI5QKtea!RkvNE>Fj)|?AH&v{-Ey8+fM@Wq&
z3ULcr6JryGZd^lpT2n@qA0r?J1~r#o-Ss`_M+owr@baC=>75MHMCF48r~U!nP%tmg
zP^P!CA<h?O?RQBn+&@NCbF$?Zjs0#9fTJd3>@!iPNUaw_jx<$~D!(D2apBX<*K-z&
zCsAv!Uc4&qXnFor_LC+|6b{dK-n|cjI$IXnRdK~|J4JfC6?sx7w%9q9CAQ`xN1j<~
z_AA5^He4@Z|5@$+V<SQnAcf_o32bT#F_?~A5HFIS6=rWOK{rRs-ZC(U2U-3O_Qu0^
zxW!z!1k>OSqo{aKxYvCv@7o#>JmyQ_xZsfDT;*}}6`R1R!))aa+cgTIvRB0!r;#h_
z_5k)P*pyn=P_ZRQsHx)5+LsjicXP~tp+6xiY|cA_pQHa&Dz<P!=xiafg=pgu@qj~G
z1fiQQTli!+x>#RiEZ8GP;P-((qsG}I9dUNT1bxDKqT=uU>pU-*tk`x^2^&I-MJ)gK
zJ%r4SNLu9@CkdRwu#-+lIn`HiIuPV5yCxH>UVkpn{ZRf+Y9N5Na5_t)<;UUg5FP0G
ztCdT^Z4WKb*uk-!Dj`Ea>xQhYs;saO%%MRs9om^SuY3Ff68^#&-aTbTF_(sCCbmfz
zW!VZ&gX2lO=T)tUZ?xOn+bjB7>X?yqGU1T>Q-G!hgQ%KL!{aieH3iSTF+9F{c*?js
z>#FOy_t1%~Lc--uO!5v24>x>TD7FPv|3kXwGwwV(XdrJ#(4w`m+YUr*JMr&70ZSn}
z3AFrq<Wc6+8}ePAr%*{#NF@9B2!vh$-!{VWV_*!nq?c^QKRd*b=BA4WQmiDTr(Ml4
z8}p7-8H&Raj1g?mSr8FKmqE7gG^epA+Avo+?Be?ybRz-ZnJvZpk-*j>JjxRyvkQcc
zxh{i8_kf4plE3p)pHuK;1VlrZgs0*6sZ`nYqI)GQD5Jj*jswddPJ28~vLG+G9C${d
zYh}<S$U^Q%4*RLH-J<W72oT1pyM<849jh2$v}BTsxm@0|D3WDng_mFc^H2nTXt&9b
zxbC%Ec5#RyN*#y>RA*nC#o0PggE1^wZ{6i7tsR`VO#EH8Pa;Qxs~QByVJF0PmBh}q
zE=Y*Mivb6%{vZ^V$VS}EFro+}U;aae^K}VH`3ehY5NITlD_aAaH{D%S&k!JHQc4q`
zT_4-2HB?kTPP1wob~#rnWY0817OlcZv9@MAlS2)0V1Fn4Mm&J-=L>?Z;Ln|*wb7lt
z^Ofe6$?Lf2OB6fT3GxK2xg+aLT(F!+>Tx<;kis2A9CB=+xxkmt9PX=Ki9)O1N{UFD
z1?Gq(_+LN^!?y|<+$(Oz_)nmTetDKwf&`DT!@q{sMS^>ukTQ-cfPDfu;@Baz-zpCR
zx~Fm$!=~0~Z#&Rzs!QyK^x?u|)Z6cFh0lR0Ob<rC39!Y(hNHoQSe*o4IptKXnvKJ)
zb<Z7BFL3eA_7gsPBsOcpxft7rts9BQ%cdU3OQl)$+-{|z&ZeQhu0lQPLhABdb<2tK
z9wSdo`|tnL-gm_{)qL#+QBe^=q)0PL5$OohOAzS@Nbg0YhF(H%O7Rt>H$jSkbO<$+
z&_$((9;A2ay^{pa4)6c_zVkb`=jL1-ZW3Vj%-U<#de*bn%<S!if_(8Zp5Ap|q<k9A
z8k2H)ccardbt&QG1(`?9jTvVFWG7=Mdx3oif;no&+5-;Fri+%{yK8u#8{k61HS=xC
zkan~)Mbq3PBHzZ7vnIp6emPjE;RU*_8rZS>F?8of0NB}F{qW^uB0sU+=Rl@|V+aS1
zocp($o@8xrbrM`s3Sav!M%f8i_05p?lwJ|XDim8^YwG2lkm#?fOM+ARLXv+ME^llw
za#71n9pzGAHoZ4o>;Vm}v_pX)(fQ}WKMRvgp6DlUkrEGwD=w4E{9;LsakKAw+^yhs
zu9pkjqLv-`3!lr^Pkhjws1e)^6Af0cNvY3b_kLTu>HZ9&H!qS~l0(QnnX*dy&>LI;
zD&<o7eKRfiZfk8u@RWdAv_oKv1Z{_4W5}^dG=0mqOUyFP>ELmJDDuLYf~SIHBJ<@E
ze8X4&<||S!QIGWtPG`q<R}QKG$UQ&EuJ3=Z_Ui38VxN|iMU3LnXf^1)aNk-K?7q%5
z^7n{&^A2jFC-foCz_Erq)NH^DUL%r42H%x0u5@|%%aH?%>B-MS4O>%`8p3}HPd*G<
zJD2)KdAYL4lUM0r7&TWItY$iPeM;C>nNfftgnBF^OXSwO$u{g<;Mh&sITn<}J?iYv
zFqp;j^V<E#;^0pWKf;X)P!{eL(80==OHy(k3<5fnFqUhsV*t(gh>dKb_JrL+G6+1o
zo1C)~10n1iUd_F9l6RpF`ZoNBM&gu&jO1fF>-(Kape`-u5y;()GiHEq5Rt=6>1If=
zZ~SP!fgb?(s6buSjxSBW`glv`EZ}g+REBkk5LIt=USE?AlrO<cADu9gcRT{=K6hV_
z<k#SIY4nqDf=gun5p7@@dDQR4(b%pcw4cp{r74$xtk8et$9q%dbY#z0l4kneUq;WJ
zypJJd+{U8y<3&NwWbPYJM9WAe?)fiC@_X@+^~$TxU?UZ^t2vN+HWX*yf+MH}XCy)M
z&_kj4+-bW4$X#UUv)RCM0DIQTB}FU7C}P>>s2BB!ZeYj5FacCvwmpl=tu3DxpEwfb
zy@%Wgp!D(w!|oAeMldvz5)ckO83oLBXoXDlDp4Qcx45q!pgW<>{NoUGyAj00b=+c-
z?rgHP*ZokZJF0`fk2)nsjU@eENSL#O+8|rQ-PMwOv!{<**BPHO8HJh&lK&GNsxX!4
zUCw$BR#WUK?ooJahAE^x$I7eCh`F*@;7w_8M8n3ZZ=IK6zw`!;O$)kq%$}FI_v7M5
z%M^aWPE3k&^3Ynys7BR4_4>^9iwC?9gk&(ja~(lr3vy1=kAp6+^%6iBc=&xn0i<>R
zXZ$UY5Cvz6O+AQdd9uZRuebi(Oa<ZZ<M`EY;8Bi(PUjn+NKGbB79<Kc;J$zT7<9{N
zBBD}*h;7>}9XMP)EW^wT`eqQjN(YxaYxXdBo+K9Yb5<U+>XYdM7U}Ro`ZO874nFxC
zHdZ)Ly5eIH(H6rSD(razAvBGs^734C3IY?QwkrAg;wlGYITrIA5P#}14iyI{MDK6U
zQO*&!4st_rUTHYYlgI7GqChR=$yeYdm-x76%oOe^dlpaFJAUpu!Q%ca*m`CYBZyGF
zz!q&@S4hc-IH{=sXos$zJMD{ucm{DMOW-jSVZBcbA-7Si8;v9@Ox9%r*N?qiHzdez
z-`<_Eo6A(RGH!Sq{ekn)5x1o~z!CV-1V?l@F*XqSG3$)^MW$StzxS(|aw%bXAKi~_
zF?S)fVs_N;Z|)Wf`<`4pn`FMfO$d*gZcuZqccMJaI6dxnuWQb!IK}b@(a7S_-QNsF
zh0n?cBz{cP2cHKy!<!R4ZX53%@$;PEtS95zKb2`NYPt>I*Kwk2*pZH^cxs{DTdqMb
zAMsge?cU$Eq7R+<#)>Pe1RlH6PCtJ-i;zcKvO$Mxbd40%7GK9jm=4;Re*F7jAV9>&
zzewJN54AT_l3X{K0U?>$7zlVy?m-tVFTE4?@RoWbA^x?Pl4XRZ*Dt8Nt_hPz<X^t}
zAmN2>FSzvkh#8ZejrJ(#CO#G4)#H4Kf1|)#@ZGsI2%ZF5d;pHXA5x|{-AxLvWeB@o
z6vTyj$dwh}H)m}9OsLy$!(I*D^q@9sTE4CMu*q)i;53v`yXBun>r?*w-0wL*l*qtm
zN|<~O#@FaBj1B`%%pv*fgR*sVpXGm)K^+4=^WSbWx2UFMiK$oE9evB3{V0L?hL^Uy
zP{yCe*TS*H20Cp;k4vD3;|TUa43d<n!Z|u?l80H>v$n1y%h}CmQs|-R3h|z0x^!AJ
zhNIP?m6iO@Z->1jI<cv;g)d>n1fJ2Ip_w-v38G-sL5_eKg+>0yo-nV3#Jt`JrZ}+9
zN|k^)Ys?z|v~1mg61<O8wU@J&>EdQZHaFG5Hci4O|7q9=LAGUcv5jjcqz?O+mU3t@
zk)t+aZMp-K2H#Fl(vwlv=lP1n<TiB*gny>3T)X*<M90x>n5U^yf4`hH+v*+B;7cEe
za&!QeCQ>s0>v7GGiO0t}_tEEDcl4Iit=Wa;7cd$FfhBjcu^DX+k8J9uY_DBPqPlRx
zyYbY`X&7t#ssM34_xkqnuX=*hXyBcezx2pVto^OuOqOE>n63eH)_(k7H}<Z0(LP9c
zlD^k1cr1wys0*FdasK+Ry#NAFqUbwxZwucPim82IV?O$%_VbML;I_<n&5@MfJdqj>
z=-8%ItAIDvU=gwOu0BSyzYlwN{#cz0-1?p!W>2<8)AooPXC~M!HAeDg3+GTNzl}xJ
zFvvw6@`iVf8-4mm#zdchgDP-wvQvq9|Cs5(Q&W*D8{2G=x&r|2{z=6*(UhRphKzVI
z0(&7AdC=G|#vMnoq9ar>gx0iXQFLzk)Pv?>33ol-Z&(4V#ZQ_4H{ax{KSU@*9PImX
zM56=CAF!oUi1QoKvx8@bhw|74%R>_-RnL2`)%vPp`uUf1U9gE6qaM8YbICdCl1@~L
zno_Utq=zX?&kMHydbZw58_xI$$x<b!#UL9KQaqR0q-9<UeSF}L!`;vIWg2U2<2{|C
zG3|$)o=$&gZ6P<E1+QQom+{5>nRj%i*DjX1Cojc!sdkz6D%&JZflwFr=-qV_yt}wZ
zLyrchlf+k2G44&doh{9K_Z(?<cB(y<wQg&XUY8lf98?*~&5k30b3sE~I`m&-2c!$`
z%99j4z2&R<prF_J;Zzg`)^SWc`p?D1u@_%`W3W`+t?Y;Oe(i`EC!R~ePUA_;*2BA9
zy!SS%`Mv&AM<4IBYgLi5CF<BD1h(0*%~iGj4!%KvwerJg`r5C&_8X6^YMq6>sR9Hv
zLLb&L)B;}~-XkKU?+5WtKjb9r+=E75I`2gKQ;r(j6$veHe?!Q(6&+ek8<BaE9@7B(
zsqM}Ne?r%97u~P-;#Uj{-BVqA?<?WrPWGt*rIp-IH$Wh&f4zZRHt~?wmqNWU|77y{
z!?<@;r?k6H?@6!i5Hu5=63!L3LettOZ)Zl9L5Lc~n(3#VTY!Ues6PKkr?=-M=NjI5
z?$lnLoNL>-TG$qRNOX191!)~bS3;2HaM*U1NT$&W4p?H6x`cWxJv8|<Y4r|)74AES
zE^IV;A7&5&vGT<cr+0qXBG1#x=8U<1i>ft)FQZ-&_txC*w!Q~yOgH@)h%*VF?gBfU
z?6=I|wUIk$fY9zY7d)AQKU++GZt>~=s5)0qN176-{!$sgs#8<dZY{bTRQ+!!)kNkt
z@XHvlsQ=@B)BJPyX51p%?q>!Z5Y8$Jj6qz+$StoSqF?uO7uL0Zs#UD_K77=zTA7_@
zz2basMkP*GlwMkJvzSUH7i=N(wl(_^ETMzWowig2bgj&p@vZJCMl$FL`|P#KMojPr
z{ql};?YOpq+bvY4Q*|^cH(s2GNYjHdL6Wz%-kt1ti2c%ifAVXRUbOYtgR$z<Jm5z$
z0=+T#seg#H9=I`cZg#5?+%)g8Em4yk%qbF5J{XjD5^mMS_7vItRc=SsXzIppX!5D(
z1NqS^%F)NbAvb5|C6Lvvoi#xQG7HMIu86+tm{?#z^oPS7{q!;cZEAj7QK}}}E1kWd
zP+_~1Z>HZo8Z(*#%$h=K@H^kb{LQ13uEL;zPtXmM+_%V#inYy2UUkj`$h0qe#<eN1
z{qxU5I1wQ?3s>`z!q|pF;U?REmN!`3KOm07rG$3VKG)r@nn^2Rx;gNI%Hx6ePzz4U
zTA`ek@ub$^Q^@oS`Zbig%-(VO&e#*5t>QT&0>;_?Zv2SAEqnaB+9VO2<$F_aF8x5@
zeRlw1L7?YK!^=ab@VeF?y0{0;T(O^(Pe(e9wWeoohtq~SMbG(&wFouyhs2@stc}wM
zcor@<ybK!aPQNhJc<p(M`eaZgbI#VmrI00EvSeIP<Y$KOHs8qag($B%K-k=mPwppw
zqczhOrSQR!4L-I99(#p+vZe5o(lxk6CRj)Pm85nwBk7P#5?SKOCg-*tY1282%*DCz
zgFk@0fY?vO{@apTRnU1~31cK~H=g{IF|`(jO4IAN>*BgpwUNO7e!E-RQU!$4*FFre
zj!3@WzrCxjw8btXyWqIPMBz92cG2ouL--2CuIxV@cMMJ>tLm6ua5iuw24vS0vRRPb
z@B4Udn*xbslNgDPOpZ3VkAtaY3|Pq>Vjs)6mwuXVWv8;k6%2meXC&H25)0Xd%`3;a
zXd)Pl>WkiATuwF&uXMr>nipGErb?*~ul0TylvB?}3@0cIW<S$slntk4tJxF|pu~}M
zffHID@5C#08Ek6FvdODb^eE|nVlVo`-N5W7Ow6m-fZ=B4q2*7z(Q3BVobPmUqA76W
z_3Y${xYVnh2ykWq3KjkRuwCQ40vSOF0(m{XW&&zG8?A^qOT&6ppQd|**UE~M(U%f}
zqe5b%oM^WuYkPC|5q<Hk^9Tz*ZwN{9>%8vF6|OaEp+N<>zj1CZ?V5ykfcy|jdRtTb
z+<&WjOhA~^LQ<-zhSSZgm}Up0myDfWlOL1t$^Ug5LYSn`b(E7iFCP%omp5M$o)aSo
zxf8)Uv~W4>{TA)NwL~)9jTv?pqU{td8!@H@fm&0@cCUd@Wo=Bf7iZ3UE5R3Ebxq20
zm-{x`^xm&M3{pCRamk@|T*9~&%l22d_RlcS6Uu}P`*64%hZT)+Z&5H|$|=_tLTFU1
zPWy5}g+va#JP~;zq#8#7Qw!t@pHzcTna1unxN+G%vE)%GRbvP&spD!nc-LiFIYZZ%
z*7vy{dE|7-1fc*0g-W#&gM@|Xu=7mDrqS0;F1k9RL{<hnGBzLi3L73Oc8DKq4S3Y7
z_;2O-o_pf@Im(olEwdWgwX|}dYQq;|JNApTTn_gt4!Uy=iWXM)a{9sIEA#Kp+U;I<
zFI21~^skm+C*<KMnD{FTi4+$0j4$<=rP-CP1au9$_w*BaZJ{FNV_}K>SAoj#ro!#F
zkqBgz7I)jtb#&6mZqSK1e@J{^PQ{(0KCH>ZL1YQ$e6M4FwtMFylsW!rMwC{Y00b)k
za?6VVv_efHt?T?YvrZKEKx4V7oAtx|3E`qN*kI!spW^<$5AVmCxRVQ9KR9eYI&Bf`
zkNpHlI@b967lf@WYHhAKcFbN-zu0hl2kbzO*nK67C^HPND(?O*(DxH&7x`#*KSnuK
zBC3_KP`I7bAtKl2*>c1snDg(CxSaZi4y>rwR7zMw^OvxOL0*|q5C~)~2k2F*FD=E0
zg5%Q<?5wj;fMWc9?Zl(YGxzJ#AXx;LwOx^4m8fJBm<={2P&h+u+?}#n=TO?=|Ld13
zNio;OX?T_GsTkZ}WUE_(yAFYN_X}pxK-ALHEf~j?`m2PWtAU?+E_nuulX!}m#tf}U
zClG-^&fMJYfJ(jv*dD$lG2H1)NSoh0`)6zXYYA8OkkHB&#w2t*KeVVIjO4Hzb6}ct
zZ-vIGykOr@!_VQ|+x1mATmjB<7OORt?)bar?&1sXBHY4Wn*;1w3npi+F8olW5O+p4
z3Jj1&N5BIDaj?ULs%OrVI0x*zevA!ji~8oyYA;;tKNJ2q1YQk5CwUHHsXm1b(Fpe0
zg;<`6c9+_ge{JDN^wf3xy&azo)8BE>Um4AhKJ%m9PHND2k>+tK*z}bS1S+`;xG+dZ
zZvk#A(ZFUc;O-@vwNDgYqKQFP&1r{l&l|b6lun})&$#9c4jMeBi*N&!y<t3g3=Qi1
zV$0U-w4FXq-C=>uxnPmMAy84b+B#N!pXx$`I!_^BZqlf)gy(kAt<LZ_M6HvoX?VWM
zb^4oUB#S8h;}F8VXe4(bu~qBTyRy(TbhK_TZ04@7h0zemh_cm_RadJy78u_(Ra!e>
zbzky1Yr14#zU1t(XcCIb>>~!uu@!HQLFTpaqfIea0ocfI$5-*|UsS%){-ixU-tuoM
z=1bkPv#-#y?>|n>;?!i_CzMQP0h^S1SHd|q0%QfT57>O?57mitE}0@PRpTtud6c?7
zt`|Q5fz0Htx@KncAatm1&apv#%@naK+$V~|8jYpYHX@5VkED}b92ebx3&;~Hj@p;e
zD1GxDIr!VtP>JfPocTH|6`)^VQ-VpgKP~%?X3fMEtJX6G?n3f2t-+a&&A@ZP2BfYx
zf<SXwojwLm{_?SXJ6zo;(ITv?{V7Eu12V+zYn@*WHK*ry3r*LfewU0UmL>u2ZB<BK
zf6w`)w5zgU@|Zy-s<?7KQ>nCH!6S*}MiX{MjoDObFRTQUNPFi72=pbIr6~gVq^8u@
zr7Lyf@CZ&Z6^nE%DA?}9BC}o>O@<p){e`I(acNg=Y8}-l%%-B?DuOJY7x&2$EsLn$
zihtmFrOOLmMq%9I7D>kENR!`jm*rNXI4X}I=^nEg`C@0g$r>)cwD(SC47O2Lz=Rw^
z!H=x1nxEYfk*~Q6YGo|ODi|(;3kqtiT$_G6JTuL9K6(F#L`&=BRk91WL`&hZjR}8@
zCR_J+SKYWJ<2-Q_%{6mvtNp*)MOwMiiBH*at2RG_H7DVP{LN(rCAIC7Jza*(D-*-K
z?zi<XC)GlbiP($4WVx0*dZRb=*%6XVc7faG?*zIX&bBTeclDeLB{OY?6%}dFckIsy
zIZ26vK*=%yT7Xow&MIm;AQ~pq^&_xe13qu<0P(5`D#dj{I)tr}1%m^<szvjc{%de9
z{ipS>A8;TT(s3&tO9_A8nB=l2?z1oX!+(;DLjEM4Nza&jQ>#Ey#m;TyUzT=#T@oOP
zZ+d}SEzXI~ZA=`FX4gK$&flF6fT@)3ZJqh4U8_PBcl3W@z?q)mGSR~F<9S&n$}Gxx
znUG`F*!qski>1A)NHbwYmcUDh;xA+U6U3SV5$6qjoMmU417<USKOnnwFFH|o$9VTn
z-k(yQQJXN<6!Mf`McB8i8mN*Sl~M*2Bq8HF-9%LC-bDU(co@d>Rq}K2+QG02I!bdY
zZWh<C0SiN|u@dT@oX&0yE^gPw2<|=$X*cZzV~x5cpBQ4Ge++mv0s9Qn{$0)nU>$pv
z)<&skwZw&+O1Eb}4*LQLR~%2<Mn~*+Q%-(UC)jyEqnUI!Vd;Q@Csw}8s0^YUzYgy%
zC@ru@ZFpHNv$eq*+35UqX)jwA#jL<2(2X6^lyq0+i#ciyKNU32brlMLg;iJ(H3%dg
z&o;>GD?ho|GVmSSmy(%W$Ds_~mW<K$OsFePeq^l<E=&JDl4`6jnBqSMy<ZAE++JX>
z&j%;JCN<q|dDqJ`pRP3hMHL#Bd#nu8)#hlq<nOYd=<+LkP6~_>5h`*U@VeKpW5dP`
zyR%nN?#)#-N-bh1NGjzj$5N%1e9WNn^v0p~&!!Zk;jhC1n6R25LKQ!LIeu~I=CO1#
zFL==2WcD|^qvDy9#a43OTS0(jklUi2o&YI*fo&%y&j1MNE_v})uM;yzw8paw>~f06
z*|AY_YxdG*TgPuOKDy0?vk_1=Z@#<6zwH5#I4O;9@YD^0oZ5AjDwe(zOa+*gjW8aT
zomEwXH#eXiEp7`mg$;Sx6L3V)Kri_+$&7;Ici;WwMgeh~**7z-@M+e_cux1*RqsBP
zoS>kdyMJ2}_YEtzi$4QS2~z%q*Q-%bVP=5#)~Ti%gW{BcN|9BcaeC+<G~Hwyhhk!;
zO`L<#>6v9?p8s@)txDGCY8EGD=dbjoJ?FEr3lS~wo>njxkuU`WzgNlEKp<XfW#^SU
zAkYuqqv5g9PY}#*Y^NwY7WYj%bU{0edw%G5tnq2Rm~AD+ETP1$hGCAZp1SKm*^iSh
zz;n6XSmi>UeY+c377D)(K&|7#0ASZaRvWpdarz~}SSQP*PF<ob<)ZW|Em;I5^0PAC
znV3@L1~htBZ0z9P#Mf?|E6gF9u`o86cA>ZuQKmHLv#LZDlngnoA33L(1?IVY1P|Y>
zxuq;+ofZ>4f%lOKkIm_z3;opL+)vBI_o11KG?r7N&D*^ddAz?b;OxrFsg>&AWGjz3
zG%!_h+%un=w0;NjXk!30&*A{0@D~ob7l4c@HXWI<rK^EraIFyTw^nice)DsVsoZ@w
zVIA7E2-=~el&Kh!3q5FHl=DfJ(#5V*-aK5Ok{XD!bG=s*y%x5!<??57r$M-(4Z`>C
zlG4k4w3a;i)>Qb(G@}fs_>L}=d)_^%6Ilj;S8f3qnfi<G{OC|O9X(9<5>Pzn*HQZ_
zKpwZjPY{kBx2<Iesj-rS`36syS6JbX9cUWh7tOxw-j*YS&8m?6HP=8>*(pt<%`om|
z+pdomcBZjLLhdXPxs5z62kmP%VHYar`hWo|J;p-||EP*2Pnibh?DCGW5?7;X1|Z+2
z940*DzWsKM0Y^pFjPMqxPODuZ5Z4l#$dGZr4!^~V_^T>Ok|6=I9b|wf+d(OY$|kWV
zx%a|N!?-QsX@~@jZ&uHj`tIoJbRF71ZxowxBYW+~FqNX^H3P}MERSkliOMy3%V{3v
zZSl#uQrdWgB$p+a*!UI*B;^2|4Q=c7Q>So^s#PWcm2Y~mLPlTi6%SbUs?bgkeD@P_
zr*V6y^y1lAg6d2rP|9JLR(A7VerZ=cT;7=NPVP(}YNr-FeV8*3wV~*@a^ol{V*lmB
zxg)_N2{KzAXahpQ-@N4Jr)3%+f0eyT=A%vof8>4(Z*<-I`4OohQ(2V2yj3&7@jP{2
zJ%?FC^met^@rM!&OIM}TjTiUN9)Uo5T=*z%7WEo;$g$5Zz<$B){+xfgq%?a%v^}Ly
z=PdSKr3#GHX{{Vls0ib5S47b1dIGORKBH|&GWJA%GT6^LM*}_}#dII9IuU-7q1j}=
zT=g^3tcVmE9xyUwg8om^P+ggXry9qhC1gn(nqaK%t2I0|kIuIQ=t|N^6(9wOHWKgR
zBdxYE{>A}DP@@aYRdcH!JZD~E^4^fafEsSotq^XOFBLrkC#8Ma%_SI0w)*EgiNKZR
zGJn?Y0+;@@jcF=;VUSdt=37sh8ew2dfeiWfG(g#MBz<^P1={kA4tsx|8@K@V?@+%f
zY`^%wvaP0nl2rPp)lkPbOZk>#!m(B0pbgOUeaS(QMPvOvp#6$GKHx$v!v%V0bQa(r
zxtE7t7e8kj)n_l`bEj#GwD%0tb<@BcRJM8Mp03|50~!Zuzq-1{TB$mtDd(qv*dM+K
z>Et&N-D(u|BJO2^uh&izS=)O|pEUz7DbPiG>l?&o0`Lp!CB?JNTR%7lc`-@mwSdzT
zS5YDpT?Na|s`~hpxSuDrGwQEs15D<-jen9Q;6`Slr6?yB;B#JB8Ij?yT=Dg#t_3JD
zGlV-!P}bY9a5ByDR?QE&i8xQ{Rb-@)WiTXZg2$B@xUZm;BHX>{e@&Cl5I{ujvscq}
z{-(LJw}JG6WjlO--Eox<O5FftaEaP(CdK+2x?>}>vyzitNu8pm2?m)4XU_Cr@{5Wn
zIw~4Zu%slQa#sa?0+5t5YGT61-!N9d8nsd6D5|41$zCjx>*$s%rzH-hKdVar;`c@n
z`>ycF_J=Y4rb!s^7Wg(HK+P~`r}z+)r7WVo?r5XYM2Gx5$GFkOsiW=?%AISKR~)Ye
zr_Xd2PK32ETefI=zHRN!4yFc`cjJd`{qc{z%0}r|SM)vO?h1fX|8W4iDE?_2zjm!k
zFIi#DQ(MbWDO)8aZeV$&bK^1HBS?ghzbZhXucR0Wy9dOpa_8{%=9=HLy36ue%CXF{
z=;SIbZ`jIShq2ne$HJzWCbKnH3XA+(XXf~LA)c-tjE2S&O=WLbabB5~q`A-=^(_U_
z#nTTgW=Tb*FvL@$@M0r0t};OqjN~+983epl&+^LMo=}b^)%*?wN(sAyry_hJB8EV?
zjbkgD5j*m;E=()!ve;)|#>pgtGrd*Is*c;eYZ9OCOJ;VBsV8?L<EnRa1pczP=pr(j
zx!fYgz3-J=`yYBm%u%)twZjs6Lkb=GI(^u2CgrMHn%{pKYtGkF=LMg=sGuv@&w2b3
z%czh;YV)O;rAnJtoq+Svzdcw2C`!zM&vu$LH~hvrMPGK@^-4_D+Udp^6;2ufkHr=B
z@$ZHPhW?oDaLds-Yz!M0y6p)VA{hnVboFdLHRQeB_{#Uo&9sMt?ZnW{bcHkT<qns2
zK*@-MBz<uCGx7#_<3yY;VA~TVEIb?@baCH3uxuoiLOKCC5`Z~`bo_%)E^fu|XCfpn
z_EJ_ROk@_|5Vsje;XGz!UXiHQnrE<1oZQ#cguWSyZN`bc{88mVwZ(n#Xt*R5k{%Ro
zCPN4^ON^}q@JJ4Sk1_u5;I%v^M}6lKkg`TUH6ZcagtK`BKh|a*j7+@i$x?VI#wQ!n
z01U483_m^Jo>#86(^@&9mQ@sDkF>NV`CGQdDMlSANBsf6Fc&JZ)z&08)-`E19QKJ|
zarsL7-6@0{;5;C&J4`?rky`xR-7<#T3rrcevZ-)T&?zd|?qBkOeMN;Hu@{N-k=AHc
z9BFHL{&mCMNR|bUKE{Y1c)Y*y8@TUQ_OF+YfIEZu(czL$a}&4K0$d9>gq4@=Rb*jK
zI{GeTvM@E#J3cBJ0f#3&Zb~_J@@+0ptO51D$g%5}w=XnGv@yr<*PF0jeD+yOmOhjP
z`T|)?<I#w=kh0}*nTA+=OXIEp;|7OmHhknHcqZ%hUT$*@U>?gSVANzORt9AdKJENO
zUjJwJNO73bQ_tlbncDasQ#USe?dhdo`uNfT;IsJIwkh$zDtaeQq+>@zGn|xtI1V2N
zMH-pLB9{GGc8I+x_fre@7awHO)sv*KFOP2JM`;Iq?^a7dZUFYwS9(!{M(8LkJ{!&0
zE~s=puQS!n)AFs!k^UI>UC-gD=lue<W-0$|HRYs1M44@W#sw|vw{1*-cIjzoioXgV
zLu(^1;QXK$GcPY{C;9?C;45FuWgQ)!G^lUPamMR2u4r~KD#m^{@`jzf?pK@otA5K!
z;@Asn*Ig9FC_>3zZN0L=sOqoV?!tZ6bx5FGJ-N=lA1k`((52RHl37x$QB+WOuv^g~
zV?3=&x|~_Cqu)zTGVJs$Qql{)LU1dB2A^EuD>tB|9|0G{0Fi+V*AF|_3bm+o>Bww`
z$s0E@iS$s6ziHpgD*5Am$vmc>aag@kqrJL>nkOPhAOgHjPlMHU*-10+#AoIz2*G%e
zu)hcC2t-DcTeU4i(9<UXr77Xl&;ekH0@<}Ps$wEKTpzpfU>nt1jj7ilH%`{gRh<Wu
z0tPJlhOap{vfW5Gd;^LZZXY)KxIZ|tNScIMx#!8kmN7L{j&!MUo0g(0g*=`DTwH4L
ziaI29Z!ZO|emh<M)bVaiSA8qZi=O&{VP51b#r)nA|5kZ_m4zgaX$fuiM`CCV)26Ae
z@bO5Lu)XmZJYAe$*kufeh)GrUR(974r~wQQ(ymDpivS`^BHkf23WFDPJ05wWV`W;!
z>~Q9%&hb^&6|VC7^*O);6ua`|xOLYxS$<`dq~Yv_A5E(dP7GvC`>yLzN#wsg4tqV=
zI|j%JT9+ci!-}*CV74P~_crpQWNPw;c5W0x^${bwm%HR`C1UGor5V#W-?vHY0UX16
z4WwXbN2U(MpX(>r^B|g>{|OM}e89UW3Md1C`eg;(GY`6u2DgD8o^hN(B+FR3wn)dp
z1Crl~<_H!=yDpCPeAB1@DhiL<pd`KA^sYcnbq9_z$B*1rY)4oaLY}q1R)SiY1(MQ-
zP@P-MdOA%#8Xjm3-vIqb8*<%1f|2w^lgHl}WspUzucZ2EBAy1-3)>nu-uTW^sYbR9
z5Mr~!E7F;3<w|Se#2zX65Sft6Um*A$`l5l@K(xV*ffW-naz5oZ2518W{ny|!*oJt0
zl?x~D8g~zMj%e~_?EQ&=GXK)G_U$8D*r?o2UU72(T0ee_&%w&cUsnJqomgj=rL2Fa
zNjy=j?>KvO+rI21XrtT5NztRLZw_c2bmOY9pcAH_{q{KOihRf!9*ix8H@G2vnCod!
zuWR(szP>eM0NVpm-MT`1Hk3xG^{mEbSeCLa^9mE}Dba!9w>p+Hs8wxY%`uGa=>Py0
zt^164ZqCu6ue>p?B8vw2{^B7{pl~8{hcSRJ{ta5ROkvH9pAATBL3&zO;gLne&aMfj
z8Cwd3{pT961XZiXiU~!mLO9QJ9uZ94NPuk;B@lB!#8-)7Nl7Qtz-c<6N_AC(Hp|qV
z*%V!+SI^qTeLQtqRDv1R*Tsv>$$X`ZA;yiXI-&g!SSlRex$FrwL5N;z8p)%5l`Cx?
z-MH%ZBc6<wH2xuplAd|t&PLq9rlaf+dm4XE4RNY1mmPK<8;m6ZR5t3;cG6^Q{*vF6
zA~cQ35Qtk5EM?m^_~@JYkvmrhMQ+)gQ`b$=1H6Es=u?SkLXmpik8DJaI*IkWCZX?#
z@7%a<x0)9fDY?-1_?lvN>VWWfHN(6AH2MH+2;5zK%edP}Bm%~=(-rRDMYM{NAXe@-
zF$CBqs^<WHtMvn3xBr4fkUaA?GHiU3kL%>_ST}XIaZTMk-2HeWPDOu(_y7(F2hvl(
zs~4p9pQyOzl&F;M_S@l>`ejPK-hLLD(`$Sbqx#``i3Tjw`KA8hTaqfFBthX#j0&Q|
zQ#yIieh<N)=9U|!1hfkZ1uW*}`3frtM3ki{^HK}A<OAn<!OgWX>E!2b?NH6qK`uo}
zceZ|uy;18-3VenDGJ{=xq-9eE8sQF$vwDO>*^U@s*f4YDOz&eK*sHZu9j?SanMRj$
zm$5{nVmS0_qz51I)ZJ_lv8dKrJg~h~CY`(=a}W!skkEHA9cmi{=d;%rsWWelPv?ue
z3w5jfiuVj2^?L&6(dRr{I9>c~4P4zCepP=G4pzm|c$-3bF7;P6m=y^FRdmE@&^oSX
z3^3QiMLx>CH$;O9?^=o@_rtRrU#2%ihnFdx?E#w*uf+fLulVXh-s&1zO<1Q7=s~np
z*C|bU-KgH)Qqp;xMd6aunAUX3*_xak>-EOoS-|#Ni{9M?V60WdJ)WoFE7oy<)<7HM
zr?wmKov1;`6H%7#_XW>BK_yp3lOQ((<>mraY>L^2yyYYNt#bz0?xPMEvnQ$?$iqQ;
zd{>i5J)qnIFsH7^b`7pVoyfMjnk95bK-xB*QU~Gfcg`Hh>0pS3=rJU8U5o@=@2onb
z26;66tLLU2&<2F};8vC|H`jJJA|wqa!&8umQpCeNf-;tl&$ed40{`8QYue3my6$Y!
zu}TAt(uu9fE{4X>HuxU!1pyFu-_ncD=ByXzty5#+I=14$hXJj04&nhD>k~k^4&Mpo
zRRYCJn5WRb>A>RX*1SQ%QPVaN95j}FBIdyrTS@&v2aolf;llU@2~f`u3Ofl*Ud?aF
z8<Xjjvm^c^<`#2;onRF-GhoTU>R7W<CSXY*=Mb@XK=(9!$}f6n)Hl)A0b3@qec05<
zI6sB(GB;uXw?X0`8m`*7B>`Sv_=m*Gqpx{3p~rfbvhlPCU$p^1<SHLDyO)Nj&Y0G+
zXi_%iI5I~3_O#Xjln4r1z9LV&tSC_cW3()$iA|X_O@kSe{GJa_q_$_y(*uqEW7NIs
z7Is%abS#pYY?ITN)iw_=se{y>Q-Sfy207E>At*>BqNMC-GcOH+au1j_9ZP(rDej#d
zG+cH%MhY|%C&agvA~6>l@j2#7$<5EOc7;aH#ACnLOi*1drTkYvsXrYTpDn4Vin9)m
zBmMB2yQ;{8j+CafNvfQ>DHwdk_w}~~xJqoE{nC}z#kb&maV0`(uA^rA=GMDcGkPvD
zsZ>$9l{1DzY||*9#lN%q0e}c-Ow-xOmR@mZ@MyJy{g$1^2&pk1Map-tCjMGib~M1P
zjpG#K&I2@c>_2jI2m=MOT=4CyRs**hiO7H$^bJT75|RLdR)jtcSatoO3}Hl=-Z93j
ze&FGiCBH{3P$%fb6#+>rOGyEQq0f0_5Xk63bK?&O@xy_P&OekKKv(&GRLG!x4J%)`
zvjBgV%E8A?z-W#mG=TcB?){(cnuwRHe89hge&eYVNbfQFEPLeKVwG=wG(b@)llb33
z6?(7!$&2<kZcbH*4+IeQvq)ENoMjv$FH@dSe`R?f6tAjCSv<KbcYck=AhD|4%PqH!
zd-piwjgC*{dn}^;E)MsY-A93TtwV+W5$5~{vg(~8d9Q#!q;*s8i$M~?PyW`1u~6T#
z8z!rb1vzK`SE9Ul9i%66b>k7eYD=CMui3ZL12TT8-KZv&tbK6Js6K&<2K2ud%=O$y
zv#_gyJ)9C1lR8wPaB|Rxf2kpUD)EZILy`^+8wdV3;OE6vD)#@s{y(e-Eqe389seC)
zzA7?he8>eQeLj(N2N=-x2aJ}uF#>!^4Y2K&Krj;j<^T3axbKqaTqYd7^fCqSIv_<^
LRT;Rn*@yoHm%POp

literal 0
HcmV?d00001

diff --git a/docs/articles/subgraphs.html b/docs/articles/subgraphs.html
index 88923e51..12732a73 100644
--- a/docs/articles/subgraphs.html
+++ b/docs/articles/subgraphs.html
@@ -20,7 +20,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -126,7 +126,7 @@ <h2 id="no-neighbour-observations">No-neighbour observations<a class="anchor" ar
 <code class="sourceCode R"><span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va"><a href="https://github.com/r-spatial/spdep/" class="external-link">spdep</a></span><span class="op">)</span></span></code></pre></div>
 <pre><code><span><span class="co">## Loading required package: spData</span></span></code></pre>
 <pre><code><span><span class="co">## Loading required package: sf</span></span></code></pre>
-<pre><code><span><span class="co">## Linking to GEOS 3.13.0, GDAL 3.10.0, PROJ 9.5.0; sf_use_s2() is TRUE</span></span></code></pre>
+<pre><code><span><span class="co">## Linking to GEOS 3.13.0, GDAL 3.10.0, PROJ 9.5.1; sf_use_s2() is TRUE</span></span></code></pre>
 <div class="sourceCode" id="cb5"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/args.html" class="external-link">args</a></span><span class="op">(</span><span class="va">moran.test</span><span class="op">)</span></span></code></pre></div>
 <pre><code><span><span class="co">## function (x, listw, randomisation = TRUE, zero.policy = attr(listw, </span></span>
@@ -179,7 +179,7 @@ <h2 id="no-neighbour-observations">No-neighbour observations<a class="anchor" ar
 <span>    <span class="va">w50m</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://r-spatial.github.io/sf/reference/st_read.html" class="external-link">st_read</a></span><span class="op">(</span><span class="va">target</span><span class="op">)</span></span>
 <span><span class="op">}</span></span></code></pre></div>
 <pre><code><span><span class="co">## Reading layer `GB_2024_Wales_50m' from data source </span></span>
-<span><span class="co">##   `/tmp/RtmpzEChJG/temp_libpath8ee3b7c361c1e/spdep/etc/shapes/GB_2024_Wales_50m.gpkg.zip' </span></span>
+<span><span class="co">##   `/tmp/RtmpXVTJuL/temp_libpath3b356d487bad39/spdep/etc/shapes/GB_2024_Wales_50m.gpkg.zip' </span></span>
 <span><span class="co">##   using driver `GPKG'</span></span>
 <span><span class="co">## Simple feature collection with 32 features and 19 fields</span></span>
 <span><span class="co">## Geometry type: MULTIPOLYGON</span></span>
@@ -371,7 +371,7 @@ <h2 id="subgraphs">Subgraphs<a class="anchor" aria-label="anchor" href="#subgrap
 <span>    <span class="va">sc50m</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://r-spatial.github.io/sf/reference/st_read.html" class="external-link">st_read</a></span><span class="op">(</span><span class="va">target</span><span class="op">)</span></span>
 <span><span class="op">}</span></span></code></pre></div>
 <pre><code><span><span class="co">## Reading layer `GB_2024_southcoast_50m' from data source </span></span>
-<span><span class="co">##   `/tmp/RtmpzEChJG/temp_libpath8ee3b7c361c1e/spdep/etc/shapes/GB_2024_southcoast_50m.gpkg.zip' </span></span>
+<span><span class="co">##   `/tmp/RtmpXVTJuL/temp_libpath3b356d487bad39/spdep/etc/shapes/GB_2024_southcoast_50m.gpkg.zip' </span></span>
 <span><span class="co">##   using driver `GPKG'</span></span>
 <span><span class="co">## Simple feature collection with 119 features and 19 fields</span></span>
 <span><span class="co">## Geometry type: MULTIPOLYGON</span></span>
@@ -654,7 +654,7 @@ <h2 id="unintentional-disconnected-graphs">Unintentional disconnected graphs<a c
 <span>    <span class="va">tokyo</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://r-spatial.github.io/sf/reference/st_read.html" class="external-link">st_read</a></span><span class="op">(</span><span class="va">target</span><span class="op">)</span></span>
 <span><span class="op">}</span></span></code></pre></div>
 <pre><code><span><span class="co">## Reading layer `tokyo' from data source </span></span>
-<span><span class="co">##   `/tmp/RtmpzEChJG/temp_libpath8ee3b7c361c1e/spdep/etc/shapes/tokyo.gpkg.zip' </span></span>
+<span><span class="co">##   `/tmp/RtmpXVTJuL/temp_libpath3b356d487bad39/spdep/etc/shapes/tokyo.gpkg.zip' </span></span>
 <span><span class="co">##   using driver `GPKG'</span></span>
 <span><span class="co">## Simple feature collection with 262 features and 3 fields</span></span>
 <span><span class="co">## Geometry type: MULTIPOLYGON</span></span>
diff --git a/docs/authors.html b/docs/authors.html
index 5035c6a9..85ffa634 100644
--- a/docs/authors.html
+++ b/docs/authors.html
@@ -7,7 +7,7 @@
 
     <a class="navbar-brand me-2" href="index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/index.html b/docs/index.html
index a6dd0b70..133ab279 100644
--- a/docs/index.html
+++ b/docs/index.html
@@ -22,7 +22,7 @@
 
     <a class="navbar-brand me-2" href="index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -63,7 +63,7 @@
 <div class="section level3">
 <h3 id="spatial-dependence-weighting-schemes-and-statistics">Spatial Dependence: Weighting Schemes and Statistics<a class="anchor" aria-label="anchor" href="#spatial-dependence-weighting-schemes-and-statistics"></a>
 </h3>
-<p>A collection of functions to create spatial weights matrix objects from polygon contiguities, from point patterns by distance and tessellations, for summarizing these objects, and for permitting their use in spatial data analysis, including regional aggregation by minimum spanning tree; a collection of tests for spatial autocorrelation, including global Morans I and Gearys C proposed by Cliff and Ord (1973, ISBN: 0850860369) and (1981, ISBN: 0850860814), Hubert/Mantel general cross product statistic, Empirical Bayes estimates and Assunção/Reis (1999) (<a href="https://doi.org/10.1002/(SICI)1097-0258(19990830)18:16%3C2147%3A%3AAID-SIM179%3E3.0.CO%3B2-I" class="external-link uri">https://doi.org/10.1002/(SICI)1097-0258(19990830)18:16%3C2147%3A%3AAID-SIM179%3E3.0.CO%3B2-I</a>) Index, Getis/Ord G (Getis and Ord 1992) (<a href="https://doi.org/10.1111/j.1538-4632.1992.tb00261.x" class="external-link uri">https://doi.org/10.1111/j.1538-4632.1992.tb00261.x</a>) and multicoloured join count statistics, APLE (Li et al. ) (<a href="https://doi.org/10.1111/j.1538-4632.2007.00708.x" class="external-link uri">https://doi.org/10.1111/j.1538-4632.2007.00708.x</a>), local Morans I (Anselin 1995) (<a href="https://doi.org/10.1111/j.1538-4632.1995.tb00338.x" class="external-link uri">https://doi.org/10.1111/j.1538-4632.1995.tb00338.x</a>) and Getis/Ord G (Ord and Getis 1995) (<a href="https://doi.org/10.1111/j.1538-4632.1995.tb00912.x" class="external-link uri">https://doi.org/10.1111/j.1538-4632.1995.tb00912.x</a>), saddlepoint approximations (Tiefelsdorf 2002) (<a href="https://doi.org/10.1111/j.1538-4632.2002.tb01084.x" class="external-link uri">https://doi.org/10.1111/j.1538-4632.2002.tb01084.x</a>) and exact tests for global and local Morans I (Bivand et al. 2009) (<a href="https://doi.org/10.1016/j.csda.2008.07.021" class="external-link uri">https://doi.org/10.1016/j.csda.2008.07.021</a>) and LOSH local indicators of spatial heteroscedasticity (Ord and Getis) (<a href="https://doi.org/10.1007/s00168-011-0492-y" class="external-link uri">https://doi.org/10.1007/s00168-011-0492-y</a>), with further extensions in ‘Bivand’ (2022) <a href="doi:10.1111/gean.12319" class="uri">doi:10.1111/gean.12319</a>. The implementation of most of the measures is described in Bivand and Wong (2018) (<a href="https://doi.org/10.1007/s11749-018-0599-x" class="external-link uri">https://doi.org/10.1007/s11749-018-0599-x</a>). Extra measures contributed by Josiah Parry. Lagrange multiplier tests for spatial dependence in linear models are provided (Anselin et al. 1996) (<a href="https://doi.org/10.1016/0166-0462(95)02111-6" class="external-link uri">https://doi.org/10.1016/0166-0462(95)02111-6</a>), as are Rao’s score tests for hypothesised spatial Durbin models based in fitted linear models (Koley and Bera 2024) (<a href="https://doi.org/10.1080/17421772.2023.2256810" class="external-link uri">https://doi.org/10.1080/17421772.2023.2256810</a>). A local indicators for categorical data (LICD) implementation based on Carrer et al. (2021) (<a href="https://doi.org/10.1016/j.jas.2020.105306" class="external-link uri">https://doi.org/10.1016/j.jas.2020.105306</a>) and ‘Bivand et al.’ (2017) (<a href="https://doi.org/10.1016/j.spasta.2017.03.003" class="external-link uri">https://doi.org/10.1016/j.spasta.2017.03.003</a>) was added in 1.3-7.</p>
+<p>A collection of functions to create spatial weights matrix objects from polygon contiguities, from point patterns by distance and tessellations, for summarizing these objects, and for permitting their use in spatial data analysis, including regional aggregation by minimum spanning tree; a collection of tests for spatial autocorrelation, including global Morans I and Gearys C proposed by Cliff and Ord (1973, ISBN: 0850860369) and (1981, ISBN: 0850860814), Hubert/Mantel general cross product statistic, Empirical Bayes estimates and Assunção/Reis (1999) (<a href="https://doi.org/10.1002/(SICI)1097-0258(19990830)18:16%3C2147%3A%3AAID-SIM179%3E3.0.CO%3B2-I" class="external-link uri">https://doi.org/10.1002/(SICI)1097-0258(19990830)18:16%3C2147%3A%3AAID-SIM179%3E3.0.CO%3B2-I</a>) Index, Getis/Ord G (Getis and Ord 1992) (<a href="https://doi.org/10.1111/j.1538-4632.1992.tb00261.x" class="external-link uri">https://doi.org/10.1111/j.1538-4632.1992.tb00261.x</a>) and multicoloured join count statistics, APLE (Li et al. ) (<a href="https://doi.org/10.1111/j.1538-4632.2007.00708.x" class="external-link uri">https://doi.org/10.1111/j.1538-4632.2007.00708.x</a>), local Morans I (Anselin 1995) (<a href="https://doi.org/10.1111/j.1538-4632.1995.tb00338.x" class="external-link uri">https://doi.org/10.1111/j.1538-4632.1995.tb00338.x</a>) and Getis/Ord G (Ord and Getis 1995) (<a href="https://doi.org/10.1111/j.1538-4632.1995.tb00912.x" class="external-link uri">https://doi.org/10.1111/j.1538-4632.1995.tb00912.x</a>), saddlepoint approximations (Tiefelsdorf 2002) (<a href="https://doi.org/10.1111/j.1538-4632.2002.tb01084.x" class="external-link uri">https://doi.org/10.1111/j.1538-4632.2002.tb01084.x</a>) and exact tests for global and local Morans I (Bivand et al. 2009) (<a href="https://doi.org/10.1016/j.csda.2008.07.021" class="external-link uri">https://doi.org/10.1016/j.csda.2008.07.021</a>) and LOSH local indicators of spatial heteroscedasticity (Ord and Getis) (<a href="https://doi.org/10.1007/s00168-011-0492-y" class="external-link uri">https://doi.org/10.1007/s00168-011-0492-y</a>), with further extensions in Bivand (2022) <a href="doi:10.1111/gean.12319" class="uri">doi:10.1111/gean.12319</a>. The implementation of most of the measures is described in Bivand and Wong (2018) (<a href="https://doi.org/10.1007/s11749-018-0599-x" class="external-link uri">https://doi.org/10.1007/s11749-018-0599-x</a>). Extra measures contributed by Josiah Parry. Lagrange multiplier tests for spatial dependence in linear models are provided (Anselin et al. 1996) (<a href="https://doi.org/10.1016/0166-0462(95)02111-6" class="external-link uri">https://doi.org/10.1016/0166-0462(95)02111-6</a>), as are Rao’s score tests for hypothesised spatial Durbin models based in fitted linear models (Koley and Bera 2024) (<a href="https://doi.org/10.1080/17421772.2023.2256810" class="external-link uri">https://doi.org/10.1080/17421772.2023.2256810</a>). A local indicators for categorical data (LICD) implementation based on Carrer et al. (2021) (<a href="https://doi.org/10.1016/j.jas.2020.105306" class="external-link uri">https://doi.org/10.1016/j.jas.2020.105306</a>) and Bivand et al. (2017) (<a href="https://doi.org/10.1016/j.spasta.2017.03.003" class="external-link uri">https://doi.org/10.1016/j.spasta.2017.03.003</a>) was added in 1.3-7.</p>
 <p><strong>sfdep</strong> (<a href="https://cran.r-project.org/package=sfdep" class="external-link uri">https://cran.r-project.org/package=sfdep</a>) provides a piped interface to <strong>spdep</strong>.</p>
 <p>From <strong>spdep</strong> and <strong>spatialreg</strong> versions &gt;= 1.2-1, the model fitting functions previously present in this package are defunct in <strong>spdep</strong> and may be found in <strong>spatialreg</strong>.</p>
 <p>Default branch now <code>main</code></p>
diff --git a/docs/news/index.html b/docs/news/index.html
index 2d9898a0..ebaffc81 100644
--- a/docs/news/index.html
+++ b/docs/news/index.html
@@ -7,7 +7,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -41,7 +41,11 @@ <h1>Changelog</h1>
     </div>
 
     <div class="section level2">
-<h2 class="pkg-version" data-toc-text="1.3-7" id="version-13-7-development">Version 1.3-7 (development)<a class="anchor" aria-label="anchor" href="#version-13-7-development"></a></h2>
+<h2 class="pkg-version" data-toc-text="1.3-8" id="version-13-8-development">Version 1.3-8 (development)<a class="anchor" aria-label="anchor" href="#version-13-8-development"></a></h2>
+<ul><li>Remove remaining <code>spData</code> ESRI shapefile use</li>
+</ul></div>
+    <div class="section level2">
+<h2 class="pkg-version" data-toc-text="1.3-7" id="version-13-7-2024-11-25">Version 1.3-7 (2024-11-25)<a class="anchor" aria-label="anchor" href="#version-13-7-2024-11-25"></a></h2><p class="text-muted">CRAN release: 2024-11-25</p>
 <ul><li><p>(temporarily) remove <strong>rgeoda</strong> references until it is successfully re-submitted to CRAN</p></li>
 <li><p>add <code>write.swmdbf</code> <a href="https://github.com/r-spatial/spdep/issues/171" class="external-link">#171</a> to complement <a href="https://github.com/r-spatial/spdep/issues/163" class="external-link">#163</a></p></li>
 <li><p>modify defaults for <code>licd_multi</code></p></li>
diff --git a/docs/pkgdown.yml b/docs/pkgdown.yml
index bf48a05f..42246122 100644
--- a/docs/pkgdown.yml
+++ b/docs/pkgdown.yml
@@ -7,7 +7,7 @@ articles:
   nb: nb.html
   sids: sids.html
   subgraphs: subgraphs.html
-last_built: 2024-11-25T13:37Z
+last_built: 2024-12-02T09:55Z
 urls:
   reference: https://r-spatial.github.io/spdep/reference
   article: https://r-spatial.github.io/spdep/articles
diff --git a/docs/reference/COL.OLD.html b/docs/reference/COL.OLD.html
index 9366104b..85b8fbe1 100644
--- a/docs/reference/COL.OLD.html
+++ b/docs/reference/COL.OLD.html
@@ -17,7 +17,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/EBImoran.mc.html b/docs/reference/EBImoran.mc.html
index ffed66fa..7063ba3b 100644
--- a/docs/reference/EBImoran.mc.html
+++ b/docs/reference/EBImoran.mc.html
@@ -7,7 +7,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/EBest.html b/docs/reference/EBest.html
index a043778b..ac1ffa66 100644
--- a/docs/reference/EBest.html
+++ b/docs/reference/EBest.html
@@ -7,7 +7,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/EBlocal.html b/docs/reference/EBlocal.html
index c7423877..bf06c712 100644
--- a/docs/reference/EBlocal.html
+++ b/docs/reference/EBlocal.html
@@ -7,7 +7,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/LOSH.cs.html b/docs/reference/LOSH.cs.html
index 0845239f..f46be0bd 100644
--- a/docs/reference/LOSH.cs.html
+++ b/docs/reference/LOSH.cs.html
@@ -7,7 +7,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/LOSH.html b/docs/reference/LOSH.html
index b39dd3e5..395ca3d2 100644
--- a/docs/reference/LOSH.html
+++ b/docs/reference/LOSH.html
@@ -11,7 +11,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/LOSH.mc.html b/docs/reference/LOSH.mc.html
index b349e8a7..2035890a 100644
--- a/docs/reference/LOSH.mc.html
+++ b/docs/reference/LOSH.mc.html
@@ -7,7 +7,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/SD.RStests.html b/docs/reference/SD.RStests.html
index dbc0b2a3..cb492eed 100644
--- a/docs/reference/SD.RStests.html
+++ b/docs/reference/SD.RStests.html
@@ -7,7 +7,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/aggregate.nb.html b/docs/reference/aggregate.nb.html
index 271fdad1..59bfb97d 100644
--- a/docs/reference/aggregate.nb.html
+++ b/docs/reference/aggregate.nb.html
@@ -7,7 +7,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/airdist.html b/docs/reference/airdist.html
index e02e500a..f18869b7 100644
--- a/docs/reference/airdist.html
+++ b/docs/reference/airdist.html
@@ -7,7 +7,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/autocov_dist.html b/docs/reference/autocov_dist.html
index dfc3bc73..6fad1b27 100644
--- a/docs/reference/autocov_dist.html
+++ b/docs/reference/autocov_dist.html
@@ -7,7 +7,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/bhicv.html b/docs/reference/bhicv.html
index aa1bf4d0..bbeaeda8 100644
--- a/docs/reference/bhicv.html
+++ b/docs/reference/bhicv.html
@@ -9,7 +9,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -90,7 +90,7 @@ <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-e
 <span class="r-in"><span>    <span class="va">bh</span> <span class="op">&lt;-</span> <span class="fu">st_read</span><span class="op">(</span><span class="va">target</span><span class="op">)</span></span></span>
 <span class="r-in"><span><span class="op">}</span></span></span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> Reading layer `bhicv' from data source </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span>   `/tmp/RtmpzEChJG/temp_libpath8ee3b7c361c1e/spdep/etc/shapes/bhicv.gpkg.zip' </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span>   `/tmp/RtmpXVTJuL/temp_libpath3b356d487bad39/spdep/etc/shapes/bhicv.gpkg.zip' </span>
 <span class="r-out co"><span class="r-pr">#&gt;</span>   using driver `GPKG'</span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> Simple feature collection with 98 features and 8 fields</span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> Geometry type: POLYGON</span>
diff --git a/docs/reference/card.html b/docs/reference/card.html
index 77ba481e..e6ce7968 100644
--- a/docs/reference/card.html
+++ b/docs/reference/card.html
@@ -9,7 +9,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/cell2nb.html b/docs/reference/cell2nb.html
index f597fe50..74d79109 100644
--- a/docs/reference/cell2nb.html
+++ b/docs/reference/cell2nb.html
@@ -15,7 +15,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/choynowski.html b/docs/reference/choynowski.html
index 5bf220fe..febe122a 100644
--- a/docs/reference/choynowski.html
+++ b/docs/reference/choynowski.html
@@ -7,7 +7,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/columbus.html b/docs/reference/columbus.html
index e24444c1..5eeadd10 100644
--- a/docs/reference/columbus.html
+++ b/docs/reference/columbus.html
@@ -7,7 +7,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/compon.html b/docs/reference/compon.html
index b66247d6..52976684 100644
--- a/docs/reference/compon.html
+++ b/docs/reference/compon.html
@@ -7,7 +7,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -189,12 +189,12 @@ <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-e
 <span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/base/system.time.html" class="external-link">system.time</a></span><span class="op">(</span><span class="va">udir</span> <span class="op">&lt;-</span> <span class="fu">n.comp.nb</span><span class="op">(</span><span class="fu"><a href="testnb.html">make.sym.nb</a></span><span class="op">(</span><span class="va">k6</span><span class="op">)</span><span class="op">)</span><span class="op">)</span></span></span>
 <span class="r-in"><span><span class="op">}</span></span></span>
 <span class="r-out co"><span class="r-pr">#&gt;</span>    user  system elapsed </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span>   2.461   0.000   2.470 </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span>   2.112   0.000   2.121 </span>
 <span class="r-in"><span><span class="kw">if</span> <span class="op">(</span><span class="va">run</span><span class="op">)</span> <span class="op">{</span></span></span>
 <span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/base/system.time.html" class="external-link">system.time</a></span><span class="op">(</span><span class="va">dir</span> <span class="op">&lt;-</span> <span class="fu">n.comp.nb</span><span class="op">(</span><span class="va">k6</span><span class="op">)</span><span class="op">)</span></span></span>
 <span class="r-in"><span><span class="op">}</span></span></span>
 <span class="r-out co"><span class="r-pr">#&gt;</span>    user  system elapsed </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span>   0.786   0.002   0.792 </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span>   0.729   0.002   0.735 </span>
 <span class="r-in"><span><span class="kw">if</span> <span class="op">(</span><span class="va">run</span><span class="op">)</span> <span class="op">{</span></span></span>
 <span class="r-in"><span><span class="va">udir</span><span class="op">$</span><span class="va">nc</span></span></span>
 <span class="r-in"><span><span class="op">}</span></span></span>
diff --git a/docs/reference/diffnb.html b/docs/reference/diffnb.html
index 0d598302..ee26e13e 100644
--- a/docs/reference/diffnb.html
+++ b/docs/reference/diffnb.html
@@ -7,7 +7,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/dnearneigh.html b/docs/reference/dnearneigh.html
index a7ffc72c..8f6238b1 100644
--- a/docs/reference/dnearneigh.html
+++ b/docs/reference/dnearneigh.html
@@ -7,7 +7,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -222,14 +222,14 @@ <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-e
 <span class="r-wrn co"><span class="r-pr">#&gt;</span> <span class="warning">Warning: </span>neighbour object has 11 sub-graphs</span>
 <span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/base/system.time.html" class="external-link">system.time</a></span><span class="op">(</span><span class="va">o</span> <span class="op">&lt;-</span> <span class="fu"><a href="nbdists.html">nbdists</a></span><span class="op">(</span><span class="va">gck1b</span>, <span class="va">xy1</span><span class="op">)</span><span class="op">)</span></span></span>
 <span class="r-out co"><span class="r-pr">#&gt;</span>    user  system elapsed </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span>   0.007   0.000   0.007 </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span>   0.006   0.000   0.006 </span>
 <span class="r-in"><span><span class="op">(</span><span class="va">all.linked</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/Extremes.html" class="external-link">max</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/unlist.html" class="external-link">unlist</a></span><span class="op">(</span><span class="va">o</span><span class="op">)</span><span class="op">)</span><span class="op">)</span></span></span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> [1] 522.4464</span>
 <span class="r-in"><span><span class="co"># use s2 brute-force dwithin_matrix approach for s2 &lt;= 1.0.7</span></span></span>
 <span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/base/system.time.html" class="external-link">system.time</a></span><span class="op">(</span><span class="va">gc.nb.dwithin</span> <span class="op">&lt;-</span> <span class="fu">dnearneigh</span><span class="op">(</span><span class="va">xy1</span>, <span class="fl">0</span>, <span class="va">all.linked</span>, use_s2<span class="op">=</span><span class="cn">TRUE</span>, dwithin<span class="op">=</span><span class="cn">TRUE</span><span class="op">)</span><span class="op">)</span></span></span>
 <span class="r-wrn co"><span class="r-pr">#&gt;</span> <span class="warning">Warning: </span>neighbour object has 3 sub-graphs</span>
 <span class="r-out co"><span class="r-pr">#&gt;</span>    user  system elapsed </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span>   0.012   0.000   0.012 </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span>   0.014   0.000   0.013 </span>
 <span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/base/summary.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">gc.nb</span>, <span class="va">xy1</span>, scale<span class="op">=</span><span class="fl">0.5</span><span class="op">)</span></span></span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> Neighbour list object:</span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> Number of regions: 48 </span>
@@ -251,13 +251,13 @@ <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-e
 <span class="r-in"><span><span class="op">}</span></span></span>
 <span class="r-wrn co"><span class="r-pr">#&gt;</span> <span class="warning">Warning: </span>neighbour object has 3 sub-graphs</span>
 <span class="r-out co"><span class="r-pr">#&gt;</span>    user  system elapsed </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span>   0.012   0.000   0.013 </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span>   0.011   0.000   0.011 </span>
 <span class="r-in"><span><span class="kw">if</span> <span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/utils/packageDescription.html" class="external-link">packageVersion</a></span><span class="op">(</span><span class="st">"s2"</span><span class="op">)</span> <span class="op">&gt;</span> <span class="st">"1.0.7"</span><span class="op">)</span> <span class="op">{</span></span></span>
 <span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/base/system.time.html" class="external-link">system.time</a></span><span class="op">(</span><span class="va">gc.nb.dwithin</span> <span class="op">&lt;-</span> <span class="fu">dnearneigh</span><span class="op">(</span><span class="va">xy1</span>, <span class="fl">0</span>, <span class="va">all.linked</span>, use_s2<span class="op">=</span><span class="cn">TRUE</span>, dwithin<span class="op">=</span><span class="cn">TRUE</span><span class="op">)</span><span class="op">)</span></span></span>
 <span class="r-in"><span><span class="op">}</span></span></span>
 <span class="r-wrn co"><span class="r-pr">#&gt;</span> <span class="warning">Warning: </span>neighbour object has 3 sub-graphs</span>
 <span class="r-out co"><span class="r-pr">#&gt;</span>    user  system elapsed </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span>   0.013   0.000   0.013 </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span>   0.012   0.000   0.012 </span>
 <span class="r-in"><span><span class="kw">if</span> <span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/utils/packageDescription.html" class="external-link">packageVersion</a></span><span class="op">(</span><span class="st">"s2"</span><span class="op">)</span> <span class="op">&gt;</span> <span class="st">"1.0.7"</span><span class="op">)</span> <span class="op">{</span></span></span>
 <span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/base/summary.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">gc.nb.dwithin</span>, <span class="va">xy1</span>, scale<span class="op">=</span><span class="fl">0.5</span><span class="op">)</span></span></span>
 <span class="r-in"><span><span class="op">}</span></span></span>
@@ -300,7 +300,7 @@ <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-e
 <span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/base/system.time.html" class="external-link">system.time</a></span><span class="op">(</span><span class="va">gc.nb.legacy</span> <span class="op">&lt;-</span> <span class="fu">dnearneigh</span><span class="op">(</span><span class="va">xy1</span>, <span class="fl">0</span>, <span class="va">all.linked</span>, use_s2<span class="op">=</span><span class="cn">FALSE</span><span class="op">)</span><span class="op">)</span></span></span>
 <span class="r-wrn co"><span class="r-pr">#&gt;</span> <span class="warning">Warning: </span>neighbour object has 3 sub-graphs</span>
 <span class="r-out co"><span class="r-pr">#&gt;</span>    user  system elapsed </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span>   0.006   0.000   0.006 </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span>   0.007   0.000   0.006 </span>
 <span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/base/summary.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">gc.nb</span>, <span class="va">xy1</span>, scale<span class="op">=</span><span class="fl">0.5</span><span class="op">)</span></span></span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> Neighbour list object:</span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> Number of regions: 48 </span>
diff --git a/docs/reference/droplinks.html b/docs/reference/droplinks.html
index ea781a4f..c97051af 100644
--- a/docs/reference/droplinks.html
+++ b/docs/reference/droplinks.html
@@ -7,7 +7,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/edit.nb.html b/docs/reference/edit.nb.html
index c1f79110..bfbfa2cd 100644
--- a/docs/reference/edit.nb.html
+++ b/docs/reference/edit.nb.html
@@ -17,7 +17,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -100,12 +100,11 @@ <h2 id="see-also">See also<a class="anchor" aria-label="anchor" href="#see-also"
 
     <div class="section level2">
     <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-examples"></a></h2>
-    <div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"><span><span class="co"># \dontrun{</span></span></span>
+    <div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"><span><span class="kw">if</span> <span class="op">(</span><span class="cn">FALSE</span><span class="op">)</span> <span class="op">{</span> <span class="co"># \dontrun{</span></span></span>
 <span class="r-in"><span><span class="va">columbus</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://r-spatial.github.io/sf/reference/st_read.html" class="external-link">st_read</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/system.file.html" class="external-link">system.file</a></span><span class="op">(</span><span class="st">"shapes/columbus.gpkg"</span>, package<span class="op">=</span><span class="st">"spData"</span><span class="op">)</span><span class="op">[</span><span class="fl">1</span><span class="op">]</span>, quiet<span class="op">=</span><span class="cn">TRUE</span><span class="op">)</span></span></span>
 <span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/base/class.html" class="external-link">class</a></span><span class="op">(</span><span class="va">columbus</span><span class="op">)</span></span></span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> [1] "sf"         "data.frame"</span>
 <span class="r-in"><span><span class="kw">if</span> <span class="op">(</span><span class="cn">FALSE</span><span class="op">)</span> <span class="va">nnb1</span> <span class="op">&lt;-</span> <span class="fu">edit.nb</span><span class="op">(</span><span class="va">col.gal.nb</span>, polys<span class="op">=</span><span class="fu"><a href="https://rdrr.io/r/methods/as.html" class="external-link">as</a></span><span class="op">(</span><span class="va">columbus</span>, <span class="st">"Spatial"</span><span class="op">)</span><span class="op">)</span></span></span>
-<span class="r-in"><span><span class="co"># }</span></span></span>
+<span class="r-in"><span><span class="op">}</span> <span class="co"># }</span></span></span>
 </code></pre></div>
     </div>
   </main><aside class="col-md-3"><nav id="toc" aria-label="Table of contents"><h2>On this page</h2>
diff --git a/docs/reference/eire.html b/docs/reference/eire.html
index 72fdc0f6..78b28462 100644
--- a/docs/reference/eire.html
+++ b/docs/reference/eire.html
@@ -7,7 +7,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/geary.html b/docs/reference/geary.html
index 48eb11e3..921e45ed 100644
--- a/docs/reference/geary.html
+++ b/docs/reference/geary.html
@@ -17,7 +17,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/geary.mc.html b/docs/reference/geary.mc.html
index 5828cfea..4065838c 100644
--- a/docs/reference/geary.mc.html
+++ b/docs/reference/geary.mc.html
@@ -7,7 +7,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/geary.test.html b/docs/reference/geary.test.html
index c64bfaad..9ca0e4f2 100644
--- a/docs/reference/geary.test.html
+++ b/docs/reference/geary.test.html
@@ -7,7 +7,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/globalG.test.html b/docs/reference/globalG.test.html
index 6faa3a5a..1e17701e 100644
--- a/docs/reference/globalG.test.html
+++ b/docs/reference/globalG.test.html
@@ -7,7 +7,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/graphneigh.html b/docs/reference/graphneigh.html
index 681776ea..175a91f5 100644
--- a/docs/reference/graphneigh.html
+++ b/docs/reference/graphneigh.html
@@ -13,7 +13,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/grid2nb.html b/docs/reference/grid2nb.html
index 24100edb..f185ce52 100644
--- a/docs/reference/grid2nb.html
+++ b/docs/reference/grid2nb.html
@@ -9,7 +9,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/hotspotmap.html b/docs/reference/hotspotmap.html
index ebf98b1e..eb4dee67 100644
--- a/docs/reference/hotspotmap.html
+++ b/docs/reference/hotspotmap.html
@@ -7,7 +7,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/include.self.html b/docs/reference/include.self.html
index 7fbe82f3..b2f08c5e 100644
--- a/docs/reference/include.self.html
+++ b/docs/reference/include.self.html
@@ -7,7 +7,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/index.html b/docs/reference/index.html
index ff72ecd2..f6e25287 100644
--- a/docs/reference/index.html
+++ b/docs/reference/index.html
@@ -7,7 +7,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/joincount.mc.html b/docs/reference/joincount.mc.html
index 3c5b638c..c6cc57fc 100644
--- a/docs/reference/joincount.mc.html
+++ b/docs/reference/joincount.mc.html
@@ -7,7 +7,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/joincount.multi-1.png b/docs/reference/joincount.multi-1.png
index e2eb87243ff7753a416c532ffd71182d22b68472..b3529e49d03b508fa9c1e4eb88934139102e3b5a 100644
GIT binary patch
literal 161040
zcmeFYRaBh8vIaUcI0Oyu?oN>43GNnL6D+v9P9PB6-6as*8Jr0Ox8UyX?sg|<?{i=8
z!+kyf`k`UgqPx1g<g2fWFjZw4bW~zg004k4Co8EA03dh*0B~QB5n-P!Cg+{O2E;E4
zGLo<n_S{Rf2EYasM_FAL0Dvs?-xn}u``jD=pajTCe)!~>d9>`2`f2(edVV@=>u@yT
z<Dd?Y4UeD(|EYYgK-#pFjb1Gw)nbZP+BBRiZ2ap~Y7V`74~|dOoR2n^>b@Jef~QmL
zX1Im54!se)I(9i+=W;5tyTVh~TIaL+xN;jvD;NL&`<>Vc53B<-1TF@42g>SW%Kvx9
zg`i>Fn0o1(sG0Eqo9HYfo7ady$%?+)^gCj@|Ey}&dgU4pILL}R@-YkVK*{x>c_^A5
zzkTFgxcXHvvc%?F@o%b+^xt9M8!`ER>OhQXUU!8GqpvlH$30BQ4k;?m+w!CN=%VI2
z|GNvjTj|+2y2UE6zglj6bVtdz-Uc#lnbj-3V|8;viYB}&?f**GNV4w+uNU(*cNHr5
zKo?jmZ3cMdm+F*JuUCMx0PezBg1Q?w8veVN3HRMN+}|^0#Cw-f-k>%V6Gst08t4PA
zpR(1??0+{Sx7ePb4zI7x_jh*%5!AL?TI^t$P<;G%xT;JPo07*2*&(9u$9KOzJ(E?r
zI4yyY{|H=IQ7=IToE>$mS1F^RG;q1^@Q#KAguf&)f%4*F<qRHcjL9CAru}83j??mP
zPBqp&2TVDD><H4l8|~InriC~N^uQEg&aC%oGTba^k{CNuiT9<WVIlGj-8;S+f!--L
zQpkT-!cW#>Ax!ff{#EeYk88*A^-r*sTuR|rAC++TI6=^uScPe4$-*nMEeU4173HA-
z&|p%$*UpBtpfL~n7&Yerx})_CNaucW2(?pN%NM*6YC+jd`p?u;gC}y>Q?1p}jm6W}
z+NhDT<DHeZ)8CmE{CT8WcaYE6LA}%1(8@z6Kao=n*o;N{N^_Q`-!4mf#TaZ`%d?-a
zt+qV>dyEZWha%(yKUJB<Vw;9mu|)b`%dd}25BO8q;-vBUb}sOqkSnf6^q9DJzrZg!
zaCmOEW#u%C8P-qcR1uI4Q#?LSt^caD-B(94aQhPM<`JC7P#0H98(x}m`_c?#0=d#*
z6CrsjfG@#*5+OFFwKxNPtBYrZ1DjL+VhN|ypLykl{{)6XYjN!;mcO0PUibg9EdO7v
z)_DhyX@hh_KV{7?DwVO^-MIR5E?Kkebxgg!xgwg2*D~;yCs!j}RO9e#XEk~Zuv(wY
z?|`|TvpV{wJ)QGqYqQkxiCi4}Z&kL_f3?e+!CnFTNT^OL;}dWJ<MU#<H2e=^+3}qw
z!QRPC;L84W+sUW2+OSx%Mf^TMlc3b%{q+&WS~RX-v{l#LY;Y|WOtgj3pDljMupbsX
zKBd(o&FYCZ&Rq0SampgE%rrVg?WR$|H8nD12#gkm!>LTwJy#0O6i?T5@J2g%hP(0e
za)vyrmuJk0=cHSJD0uVQVfWgorgSg!&sr9vi`B~)$z+iR!NMkz700h7=e}O4cV#kB
zZhe4Gj4=(RLM;&M*N~c7OMAiqL*l_myJOQW;62mKsea!>;iuo1z$oFJQ0QfpEsI=y
zp<O1>2sRu~e#3ICFyx0ABLkup#*5u&_5!Sv+z83(t@Vv%`1Z-D9vkS|7oaz_?(UHo
zZsinY<Vta~{q7~T0WeLe&#ILSqLrJtVZvC-{_?E6en`&L*sf)BpN(r55>oY8IOi_&
zwy%jU+1|9T-@ez6cV>f6pa{0Bg&+S}eKr&KuqdR8$EG3xjj^)fWE=O{1I74OspdG1
zjnGtsS0=>XhP<Gb=yqC%ElY|GCb0V-K-Iq$5BG5oEka&_46}N#Ik<MS!Oj@G$3Wbo
zUlgt6I`v7Lc9DPh+#`A2%Ej=1@SbzE6ZOI5Ej$kX@4CfQXL^&ICaU4Da1`aH6tlB>
z*(h(6$4_>&P&@2x4p7gc-=sAvdELFhl*5V#@t;{V8i!$dRvfc1&9v+GiJnw7ED@z9
z<u7OHb9Qh9$*-;B9;#sIHp6aeLW>IuJK}mj1<lagjD}=mc)pqO&YM3r0ArP!lV&!;
z#granjdB*ysI}QE^52rQKG=!;zoIQJ;T}Fr>viO1zmNoKTUU^%+IaC+d!qH-nxBc8
zNQGbT!UX^Yi{_H?<v(Yl_#$R5pl&9@7Ug5Cs6e8GO@!Yd0B?eJXmzOy_jt!qts%1L
zP%CQNJ_v>bTdLa%u?geDQ2^4Qv9aqgA!&L0-~5jr=;wpq7zTO}&l%0a+se(X+RfEL
z`48q-$mYoAde$mo5~g?k=j2aMyc<P;iM)Sbj}aTiIuT4CxLfGqowV&ftPbK6#{AP+
zxc?kjz%_!2gT3TyEf%t}`TJ^Hw7zTet55wi&+=q+B-RT61N0+AgTL~d3ID{WpO}G*
zh5d2Ip9!%2=lll6+;>xoMsVc~jWw`O|L^_36ZpRq_`ehQ|2P4=k~Apl+Ur03EB#-e
zF;&eD9Rtf#Vv{FW+l~QxiLU+&mkMvFkeV=>=**7k)rBVlm%#+x7kJ|J6-ey=bvMTD
zV^eQ-q$lcdq>!Ek#&7vuG!VRPM3wCh!3r?PnWX*eA6T+;kWWzY&h$rvdwBv%)%lC-
z6^pv2I;p!A==fWPTRaCwhdxm^AMEiF+PI`)kgm)GePw6?K!7aZP;j=L2+U*a#k>8B
ziLjZxfgAvlmK<NU_d=sfW~TG`5Jux0l=lUeSaL&@M(V>1V#HGU`K-XBH*FIZG^^aL
zK$XzlT_6FFWWiI>Zl8TEka$QXMD9lZaGwU|QiuMzb{KNVPyv?#`26pdEJ%2~V`x2!
zpMMmZ1F%L03rub|kx@8bmk{56RxUk%A~iv;#%dxY{2Q`qjTQukbFQUcx@$FXuA>Ro
z8xpfR1k1%wslPe<2biqKyaB6l;puZ6s8}PzR-ZPbkzNyZLhS*YfyVq7gxz2ga346s
zIuW!--pG5h7Nw2L?OIiN?k^b_26((7?%&I24@TMYh7$vbB8nn~@LlRGlvRO-vy(@G
z8k6^@2+af6yC7}Q^P;P3JZ%F2uI=A-E|d*GZJ=~{*#}qjSI20vGc_Is#4_A2jG0bf
zoX`8v%{q#Jbzn;{4Y&k~P33Y&v&OTQ6)WXKiDlE(l;8~R?$QqAf>N)gKxe_tP+jN;
z=->Qd)|Zwc(WU0uxHgeT$rnK<hZZx<zLZwD)9-$^HuD2Y*m8)TF)I*eA)hM4iB!(o
zhvQfLGf_vMJ97E>dPB~Cp}z2D@0|(8-{uOWd@TY5!I0b&)6ZSyg`pp{tR=$ZfeZEd
zy<=6HoW~gh#rsgdYj}w<v=3cf?H)>&Pd}74AaG#W9DB8{!=|^4i2i71GcI?8XE9iW
z<mBJ_Ai;87Er3>9o^J)3mQE6ZXka0LJL{3W-drr1!e-!#gr|Gw+a|ZMZfo*Q%{4X3
zvT+Cb<zCQhr6zfPg%SwS?Ud9!=3Mi9Q5OEB{ap-+f6CB0&jiZq;=DMdk-VH%Zlvd5
zRF7ZC_zcbYXtBX2F0GF#TVWwwO{@d-jgh6T=#G55f4$ji-Pqg&J{lqmq@#LFsn0ix
z67{4_R$jf#QDMhG7*!rG$GWq3UN`O>Tt6?nxL+FuMT=1eVR&Jaw+Y8U99Y)c66*G*
zdF7FRy}X0>DWGyR;JIkiNJTypqH201<rK8dKpw{YVBX=ONME(2T0NhOvBzUp=T;*d
z?3C5wavE9X_~{jU0B}YQz5dMIybpch{kBKeb(rzyNT+Y{9efj&qNE3@BT==(=E^$0
z2PIUrwFtY+sVF0hXdPOz|MYTo5V_MpHKYf_SzR~2KGCo(H!8V&bmZR$ty$U$kT+yI
zz-a@_Ff%?DcaPB(+#&-u=z505+FK%zxYr!kKZ-k5_`N|Cm1Tc(H`FINk&#^8au7gJ
zcTl;?K%jz})&M|&@<98amXL2>MPj%l_$xYMWj~om&0Nhz;2j0%U30bqLjfspm?0?R
z7!_H*lMtW8fb4|s4`Mnha#o-~Y&cV4XDRagW^7asV<j(yOhI4Eo4uJ7lq{0bPyVLU
z>d{_bFnaLJ8~A%9u$lv+oIZs_uu*)U^;1nPKN12EjT4%m51PGp!WHug1Sa2#ti`uw
zBF|>!bPvnzXV^Y<whjsGKcNSkJWMqb7s4)m<Ug055Cj%-o|qU=P_VQbKn&!!G2^j*
zY*b;4f(9xOV1?PI|7v|n^3i#}`*ASEH_@O$AW_tlaY{=`n$#H4eQ>V<u07z~aZ)Bu
zwt6dvq2^_~6_6Yfwz83Tb37gNDA{}&FZ^)*bqPJrCj9MHW;1>B9XDsbMOv^9uJU{C
zgrMS|Jez;MpkC7a+j{py-`!WW%-NMHT86hbnX%GZ($h=^r+zcl)^^{Fj|9FuU=U62
zrQDpP<2|ic?51kBwX{f|q78{LWXl#>`(to2oAuh`&;?j@R&jaE7iYe7NdRs^kG$Sk
zYzz#F?vMal(Cd>qhA~QmCjomH&rW|sqE=6%3QAgEe4~-x-BHCeRXo`Vl&SK3K647V
zr@cAe*?ZZO_u}cr(t&7|VHx-@2OD9-v2QrVvWKXM&b)K%nqg8@PrC1pOVCkkiL(*)
zWoxeRX*xDqgpitui1!5r$gg)4+pSQ?nQT6))NSmzFg{*orR(#7szN7#%}}SBw&<(J
z=M4RKv7T~VIZtM+VH4;8B*1O(1(uk==@zTMr|)F#H;$&3;8g?N+WCjhXWGybp<=FI
z9-7s6>&<v?_Q=dlsvd&+c8!d>POI4RY_u@6l|%#Mz8f~)ZJj(fu-t!LW_CZE$dHBa
zUAZ3{q2_(tdSxa*D|$6LU?~p~bsZdD*H>8`p@|TqQk1`aobqvS8^=n0G1q%z|7=Rm
zLto@{Y-pZ&v4}pvhX8G9BrB>PVR}PnBn?N?-IGI=*LYXz7<b&Ry6au6x<h~ep^*yS
zJED8_0Rx@XX4jERQJscp4Hj(GT@DECXGKe+k9!)vb?{OMfi#3Hch0uTHyJA#H~0EZ
z*Sg)xkl!jDlhradJQKgA2hmix7(cu`Gz*f@4=UUr#nhD;wBk~$F>Cp^=w@8m!|l7A
zXy^;4PGcGj4la%%HR0W<rQVe<Rs{5$uMX^^pXMfyCHJIxE(vN?%EhK(Xy>F19a$-@
zVv0*4xGvl9{#=hAsK&^;JDr-xHMf0!vfAx<pjF{8>_5ZEB3i5=dAuf<j5%skT3F&d
zwex?tC<q>I^IzXk^l`>ME08Og^t=lf7S+MBoGIz??GVOrq;Yf&kCc$pbPm*|N^tkQ
zTU-%RL~IU|CF_)}kxeYuiA2ZS&afK`|2fXW5Kz}=e%k)$(MB5wG@w#HSC-Hy@juzp
zlz|24736KvH$ey!;c#$BN8f00;jAHg5n5*6GtuPGtG$<^owQU}ZU)!7<f7z!i2`jv
zkEG&&2lK!Ct9(3(M)jBxnccnbcS93(LTKEXJ|X3x-gu@YPtYNCzi~UTddz}*bbif7
zuGmvLrgK(z4xkg4y1U<47DC;dv>VzfQ>HZ;pAc9UlpdI?owIKsSSelmvueB6ey=$z
zGD;$pw29Q9%$tyq)0*-q`b@ZHvDUBk{_Ers(o)@KEaBLT5Jey+{+~48F2NZGML;H^
zfpx6*f+WV-(Ai_0hKs~>VU!4={!~&PnIKnrE=|xyM8C3vrPl!B4qlbTO3O4B7@Mqx
zvp$z5t%mSi@>~2MYB<Z_ysDb?2XA_*w0Wi=HDjLx_H3Qnz_Ujmhq88SD<Rd@qdJ&X
zs+(>B2twX|bU&HO5>rn7(7B{^3RMIg+93GOCa2Uk9!2aXv|N>9oPb;h2J?)KkVKh`
zB>E}k(GqBsP`1g9P$40s@X;ucsN@iR88O>ykB|B`rWbPamZ$21r{>&9kv5<DzS>jG
zcNfKq*vi+T(^vdrNP}}Pa$QlFwyHt!!uIx9u3cmQqy%mJ`FnkVK2mYBcXgZV=2wH}
zqkYd)7Fk3K9bB7G@I%@>G+ec=Nn{Q?S7L?WbRf1v?d7G8w8Q<zJFqjPuPm?kET50G
zY>K=P?iFpmE^>b^>e(Cpi+YL?uDRJb6Hi8F{gn347PIZYbS$BU>WVjnQIh>~3YdN_
z>NhHba%C85&j_BVO~js~-fimL|AW)4Y$B0fFbT;cB;T8Ev1banlGgO^fQyi0Q?fr8
zc_U`zfMzOsJ6>?DZTLR5a_~&s6)w;Z!?~-lmv_86xC-qb@R6yGzZBOUj7I!2s0$9~
zRUi}*kPfFf<>Se<OdNJ)WDAvKp)VkxaS(WY*>l5pFc4$*T}9R%?Svb(M@p-q00`g9
zBLuY8B%YEdp+I5S!|OGH^~KRnuC}d5XAQ&TOL$mrAxDB3(8qOTa6R1c)>N_2zCtvR
zNCffh@9t&Ek3J;0pzbUofW!A!em)K}c9f^Sf38@c5&cdV`NW+}{coI25h?Vg9qFyz
z&Ym_a&i1sX0%J)zp#LC8yMO&Tgr~@qe}Y;qoV#v6DPe3Q>M+6Z1o$#j9;9kBfPkUI
zUg&Y6FdEHMqI1qv)0WRir0P8j#65b^gaLp=-!oQNAbW42C7lsTm-H1^t4e|Mc0_)~
zur9L-lYH{1GpJ;%=x3eE7`Uy)8O8iuz_89mS6_=5o#;jdNCCN{Jh%mNf(Xxt%aStP
zUFr9&G*5?4HYWrQ4|OwrCFy5ht0J#S_EDBFSnW5t6zt3i)&{S>CfXE}{+Z)LJ^@8C
z9u0ehocv+W^0|;ZC(e&!g!u(P3y9%6_xscD-Y@aiUu9;q{}FLfgrFyqRQR)~-==rt
zzvRq%h&^29mLo*h2&#mYcZW$a4tRo3PdLFL_BvIHe{^;AKAKa1fE+E2yo4DVwSZAP
zv}X^V^^k=jZisp5>@<m1b4N1yvnr=Fb*IsGJj^D~hnUq{wQmWhga!}!3F_ws)JuK^
zM*EZ(absYf_`M0bT%;#_fp{2i#W;*0c)m%Up%41Sjn@PsM2yWwj3D0=H@ev=?)=_b
zRn!Lh7<l-7hN5(e{Rv6n;ZNS?-N2sVqBm>C-B_Q)`K2~_S#zmyV(^2^VwAjfKzi{V
zj2?>bctZ^h%d^-nJel`0fIR-r6tR#m2x<iskN5@hn*a2zx5p#sd={1wb+-xf`x3`!
zSnIr(P2Gg{_dQSO)73%wpbdDei<WJnF%jrdw4mDI>VFth6mkUK1pY%E+N(Ck9v8(w
zKkVk0YP4!=)f?g*e0~mL$T^u0*-aM$VgkFpU89}nu3YV3HH-$=PW)6-7=l_o4<Q{}
zMIh1{2Oa$wQ=Yyzqyv4SS%XnNq+R7kLC6i?IFK;x4{PL(!{~@%dzd0zhGj*Q;H#j=
zH`}GlH<q#=`Vylk9(+ZOy*Aum&SnhQy>`7`o^CFMTc3DdAbS!!+DfTf$Cpt(O9HQU
zA-JxE0Y(zrZimTa3cKf}^AHq>Q!<=Oqi3i!3m!CX{hrwbJ(ghTRCaWa$d2!qtTbQQ
ziw9S1u7X;kh`YV<WLn#eKb?c$r-Aef_2|7$i40iq5DCiI>6CDiB7z1%yNEL;KhC^f
zow;#UHzI_bQ^h7_BjzkEg1arvICE!rYIZzHE&M!0dPqv&K99l8ILxRnyj&xW4ycT+
zSr#z7wNjDl4MP6Q!jSXqgGtXuyghH81G+*_sFvdn`e(9Hj>u>9)y6P?9x!k2@X|J<
zC}?J8KjSDN^}bKUi(%D&hdepSHkZ{%&OG1xptyNRbbGuf=MzN4{x2gtDSuSC4sis3
z<?f-%a!)40slz#?3Sk=!2kDtxi}^Oa_Ht8?kcNH>dMXzE)PCxdsJ-VUHV&ShP@MNp
zU>4xcQ>{&@FK#fVGZ_JDQ<hvmPe=_t>X1l?*o7<jc(w;JVLE%~i0-J1{3m-FB+-xX
zab&rLWaaYH`y7s{7tv_Y!bwy@x&`H#jfptVu>%ftE_zw-r~mDYp#R^!tx2ce`a+Jo
zp?~yi3vRH<u$_1@li{P|>u|yQ>ao}nV$lvW;M<dqbTyaCwUVEjaz3F~WWCQkF*~(#
zb%ZN<Zvil125%y6M70|^pH+YuxfbRZW4dYtCkGJoT>oI7ddmkmt<?Qp9%{c9$|1V6
z2h6!xdS+$PRY^732k&^1Oby~dBcKYO?;+6q@T3SGr=j<Dg4NNFSwQFrX7c&&p@Lj}
z0rS|aPbu@=GCu?kZMJF~h7T9bNMTAV<*qr9EE3575&u*rF#pBt`|ycS<i5xQoEeB9
zBywdZKFRlD`uQLS`E=Q9+MKTvxMJPQCChefyGHPty1Qefy3-VxZBQHAu>EtSx;44M
z#LsQx)!OD*!T9TIise7W$1e&An|d(s{qp2`WlzfQ=sI|m-Iv0;MxwH+BrMq);<oo^
zOh(1x*4~fUulmB1&h)e;9Gyzyvhed}(^Gp&86>B%+jEqV%c;&EWo`8P>E)kzgiOw_
zZ+6>n;5js>DWA>z9Vc!+6RgQm798?(&^Y)mCK(w#R82Bw>ud5ql)5<I4R%~3;ph(;
ztuk4hkl>jW|E%MBB3C+^Na$2r3LQ;*Um=(rGgGm#5M#7Eqq0)KjcuuS>+fsRuY9yr
z;^USf*1?<7+5SlV`Qx9>jPtWuV4pI1MlW2-_VoPT^eyv0)br88sY;btasj_BBU79+
zkt)3%?=c*}5=b5R`(8@8>6UARXAoa~vu@LQZL5(yX3B{0f55R)8nh~q0vM<E-LT0s
zCGE{9hy1+f`a{FfHT3$^pH0P+g$%LC9Oc`imLTS9-D-a}pQYOXCWzDz$JOBiLcPBw
z-i9E7(`kn0n}S&lH!sB0HYqqYpL#S$3e`{5yR-YgQ}=d)sblPdvGHCUTz+4OJzl(q
z{8us-d8#xWw_;}NtdEOO?8tcP?w{}Wulh&L&wH<r=G%?Svfz{ZSi%@6c^dDhIJDbd
zQ3=}4-{ght@MoM?BjnlhT%PQU&qkLR+ff5eWAuhX(KZ1*-G6M=eNrg=J7{2;`(P<r
zSu1GF?stbYoF#x^%Ana)P5VXE%Gi5*i+?dUV^S?<b@Xybj7D+rzK*lz;G&T{WojnV
zObO;I<O;w(V2Oe_*{!Md&HKq<BG&==tY_^sS<X%HYjsC{CKp-j`6&~UT54QUt(~cB
zfB(O{X6b1_X!`Jl(_gS`Q2ySvTaY>qd9vjeE|;3zvJ+-IaXpuZ3x+wIR`HE~WZ=HQ
z%6Xcb!l7{j9J$rD7Z)4(Q@&KUu@z{W$|mlXRH{JfF@wS3q{tu<Gdc~@|Mmj(nR7Y0
z64w>~d>hrJPth~4qx(AxZFTn{X7$Tx*KL?2wc^1<nPx9;grr<VQ6;KCrzbk5FJH`A
za~($NqGG5L+6M~xL6e;22@Sq*$+dwL7EcHNOwRQTpphM#JDl=fR>BzAFXZf@^e2Eu
zBDOAXV@)j=%~A4Kke?_g{u*TSW@~+{>?NC>Nq20QBqD9vMzuB5(avihG25u+2iDkv
zkm8HCxaV^Y$WX#>MFl(<a?5B(v9Rh;1~WuG{dbv^&-nd&DT`n+rPSX|#1M_*i{<89
zm$7`z0VRdq0G^JIt4rVTiI(V2+n_nC{@IaVBY9+$xAY}?FAfIjNN?sU2Ix~j0qBql
z`gS~eW$RK|&-!atJu9f>nh=%#;iK_}UJwH)#qwq~EL$vHf_CBN_oofK;l~w9oTTkY
zQryk^!v)KtMfBUG^N~wF+eUww)8jvKLN+{X@|+}Qev9INy^!$qSim1&b^>PvxB)2x
z)r)rcCla8zfhjKuV`spOUET_vtlZOb-hrM?i4x?Jb|LQf=Vt!ih-%d3C8Zgy)KBOJ
zsD+`ePTb%(ltS?Ct<#DZLkeSSe>=JbyrHro9(#WlYPm<fj-5`B6SAUV7|W`gq1s~%
zcx-*qfVSe9%(7C&yk0K@=@9NP`(UV)5<IJj3@>&?_aaov0p$5t3+z~W0762=zZ~rW
zY3}<f>-I8c^F}dXN++;2p5f&_Ukos)zcf;`{T&JYjF9DdcX`jsvJBNwAaEXHIK4PY
z-)1dO|GJH^7VGHjgQkkQgbSJ>$#6_nrt-NbUd!Z^TO^6vn_cn-T7J*HjtS(V`rGP_
z=J4At1~H^1tRUWvLIQC&H`Ysp%FHM!)Gh(6>m_t7Gy03jPT+``TJ56PH;EV1aI{tv
zMG#MV&MWlYg4!GSe;iXAPgT4uZI{GrKSP}C*@RG1IXg?9FnO_xJ#c?qXAlRKjg6T5
zLI&4;XMhfkDM}jy<89qF0-}RClovA<!Lg^p{OP6?r<U6U!lg-o1WWTc4}LV*K7A1_
znM^PzD|9~*F=4Cr&~1w^K#DeV(`70fl6USp9mRnDJ@Z<?+(UQ8{7IJook%y5`Kaqw
z=BVq`V<n>92cyuX>2Cs2M2$n$2eaM@Pm6tO7!Fv=mZDHMFzO{=&M;+%RA}qz{w{Gj
zEfyx<y~1vF{5?9EI&FjHg5RMsmg!54-LIrzX=;wJ?n1dQU?Q{joBqXt(vD|gzLOH>
zOswg!*UF%)f!~zV=KtNxktT1eUzU+xO{!^5Q_zGboz*y_Wz<5F13J;-Mvx&a@7APf
z>lIrGNShc`I%&!zuDx!Yv4>7J%($V=t5%qM|B_iC$dxb(=IzO#B_SiAk6lQP0+C~y
z6A*8*t?`&x{GQs}_r3bgCfrtZe{_qaadD0YF!1na4?Rk1Ar<$*j*)oTn$9SXkft^e
z{!EW_O*CP#`QU5H72vgt01Ni+Bh&gWmEP~pau!&$Mb%_21QV0Gx8Ba2-}FuA&}9?Y
z=xaRpt#?bPSio4j9fGRQZn`Ki3J~`0kAI!M)QN=c6UOb((=0Sayw9=M>8nv0T~F93
zJtTJ^y|TNQSakn5a46=V0CRfp=#ubU$3{27X)+1MeW^ImjI!kO>*CWdQv3AhOG!}U
zz*dRg%ZC}_&Z&tf33|EstL;gqVNpK;=!yuE^Y12+{nRu=hvG$owlPd&-yfdTzoAbb
z{}Jl2)MZJ}6mhM-8PoALA2U9p7%pI?%kUcQ_k;^Lw41HMykX%F7(@JgCaUFwAvgf;
z5uiv&w3%4IJ#RVdn(g24jmE!z;C|O+tpJ}~Md1P45nKGFQbw)A7l=2st5I`si713m
z=14E~m@`joY8yYsA^I)qRBYr7$i@C_#rIaGp;K`s{lv3AQ{hEp(C3ncX(ctc7Kh$#
zzbBx0)c!Ef>FBMCr^S5!)`renL&cooX>8OhTOf>+-)$7z(F$<b@gugJTDL(-;BkX!
z6*qF325JLWgtiK$k?b=zw5vo0cqz0r<-Lw`9n}7QYZ%i`PI8=yh&j9O{UX1a^k>tl
z#bP%eJL(+vJAS3Hf}Exnd%MfU{m>u3xe`+d;%!E~<Fj7J>l0jCt+U**5?WwN7s86A
z1fYqw+~H7NNj;%H2&DB-ccmUfSjWkmt@bm8+?hkKNmkZ0UkS8XcZLbbX@N%zKM7J!
z1<RyVZVuE<wN5uGkWX$v@pW|~xbninZ&=}4U|8;*ZV)Hx5xG2neW4B55A}jN)60Oq
zm^?|&-D29qtdnWql|8cB*UhbV=HS7-9=(a0Xf0~nqiE=y04|o111y^;tEb7Q<@;<c
zzti5op%8;anVu%GGKvJ*ZaSR0FC(bgTPkT2s*2xVWh&D69K4#DK5~v!Z`Y`AXrZED
zc~kGY;Y8?hrT339JE>KHQ98=XdW&Y141t)lm0MZ7LpGI0%}K3>iNdQQW>v10qWm5S
zP@mUqwTIhC?$<g`%e7q9QfX`S@1OJQY8{;%6b`!FL4>+<Kc&940^SPVmSddlK-N|t
zy?V;#U-L*3%<)S74BGZ{S~KfiJ9y1l88As?w92jW%0-(Img@WR3~pA2gxhVY%H$R9
znml>&&OKKhXNRd8TFT!f_`HBTi=&t2kL86r8d+gz-Xf6%WK#@?JY5PBi^}<sBdr*z
zl_pz#xvX7NRG!%0a=Uq9Xc@Qiks%RXw+V*LRszV*CG)wLb~+owTK51??21d88gy8P
z=}FxQb<vh{$0@T*H_oYBM<o>j2pRi8-{d6h^(g&|{du|;-5~qPS=BbG55G{_Owl6q
z8t4Grk5NBoRbI3my05EN6z*%iwoaW1YcQh5W~}YZBUZlL2l#&+XiEVw4#%ABup!{$
z)vr!g=u@!o-Wh)~4~=0z7(AZDV3-*!>4Q;f5)`dTvwUNvK6rChEFPWwj$%-a*{!<C
zvk|d6_SWV^iWe&yDi;T5p{zhAv?gZwEB~zg#K=Z62?=oz#k&srXJ%gqmV<r$MRKU=
za-B=FOBK!j1n4b2zIGy)_h=G8nD_85oj@mJdep;sWN;$t%^=4HEItl|_x!+Ghb6Iz
zpS1oZhrs*qibqRz1K{O{PxKqZEJocdEcllbgFS7{)<h&MLooiN_hRB;fGMK;RcSV3
zyzFN5KP@V&?4P^x^Zxnj=+u5l=*iTc$!Hpf@SpTrbyS|(yXCv~1=gkvz{|r)#Gkh)
zU1q<9;9~e{eJEfolYw&&N1x(4f0dYFduNuQ`{u0B@dxR5y=u=gj+;*h-np9}vsNpq
zh9K{+0fZAA>D)~U{Y`Br+1%+=1vTvg1Oogx5ph4XvBGBj<l}|hwaPGT70j>5<;Eyh
z5zbL}vP2`N5BZ!o;mk8#Jr6CL`DeDcjGxGjJ0E{nkS`%HMrjwJo{R#>=LZdCz!AV3
z(wyFC35@^?G7oXY&gR<S=|h}W5J{kApb%K0@#1b|pLmUB{azHBc_wtFCxkBR5P=Bj
z?m_@3d#iW=N?(7Op{I)v$Z*gS1fWDBV%T(@?}E?>91K=>14A9Q#{D`Lj)?BOtcWCk
z#8UnyDNAmU4ZM9(5&L4kFI_u1aSx-t*>HYUDzM_1JNjb>T}BAxzhX=uzJ=yr+uT3v
zk2%eDVP1SxePMv+eU2BJuA)@T6nqEY8$c!snd(x1C18Tt#qkGkWO!k?H)MK$<K9n3
zufZ}kVzS}p+sT+Fm-R;g%vX5`S~ji>XxrVgJ_Kg$YA-Vpm85$fUemjZHCZ^`{=-cV
zYg}#okF=Ewb^$v_ZtxIgp-fom0?_2RYbD%xs(s&mx6gZf&V446``)tP0Ojw`Uni%1
z-+HFyBzypt4oDvBhA8E1_jh#3&yR0pZDqJhzY^=hF#yiyYj2)g=yOyx^;$S-A~Ne6
z2ObBae>!dab>h{ILf%$y+!<-b(t(TYABlDxqHqqIcACjZAzROUTh~7nhQ-Z%i~7?z
z#J=Y|W08D-AuiIk%W|IOGpL`X+Yn`e8!k}4+f4r!6kwe<HmhNS=n-)vmXIx$DRG<d
zD#Z$6Y<`GUMQf>%53~X(DDbJqeSO)QsP&Y(uG;9g_yy_A%lA!?Q)hv}+{a!X0O`1c
zXBnc$;ae0sGIkgz!oK81EK&wqqzPnbOlbX@J{h+jTDW7X)bH-kZ}6j&#sI2{#`B-v
zGGcuDZ4m}g4GgmkW%-cJ7s`zr={F=!?ud$m1PV_%F%BjhxnctR?xckIfv+H~cX^N3
z>p*DkQ)$9M{nx~H?<>o`{K|~1>D!@WD2(gkY0zKYDqVpRK_8)Aj!#1$MS9YuK}eug
zIQutlPooIY2#C|xt#6_IU^h!C3L%>Wy~<8dv`yEcJ;sRN=oyhCK>U13pYhT4k=Y@Y
zv8<&5A|kW?>ZeT<q5TOV_~w{5R;Tb-8EuTXokfah+M}$K3<RG5arBUa>WUk|s^68b
zcFJxdhb_Ll)r!f&OJImS8zp~h%dvfwz>MhnC1n}59i%r4koN46e_EBDXA)EOmSqq1
z?|Vhc+mDRe1x53~I{`CudNH#AfWg9Wj+Yg5H6HCgAv*VKCj}t3Zgb_T{Y>)<f?<3{
z=kg!FDkR3iVe6apyW-9>%5H~Ond_uvwsx0Yn3wW>y+=xQyycC|bV2AoZOS}{IWsWk
z>YqfPD)ZkDrOXPUw~Kkd{TdpP|COYL1unnRdmKwNMeK5!eAJJrKsOJLkZ)eE%qJn4
zKfOMiH+r@0SYZB7KO9G#D#r<)$;X%@;mRDrjGR+}v|*i1mA|8&>r@tE&OAwB0-J(v
zyWgB97lcjR2G7oU32cz$NorB=n9oq4rV(ORu6;0WxPP%uWlK!M(nY6pePFs>LUp^)
zQNfFUZTB<Z3BS$Kj-OdSR0yeweQ8CPC&648+C+Bnvf}IZ`UX~uui7aED)}DkZzje@
zxj6OP3KKOk!GCDn@n7=;ObFi4xBIxzOF}9<rBHre8Usx(<{FvICt`bsHZ#3HXkvN8
zN)b=)OZ9wYD)6Z*1p&v?DnNZ_vAdS71dY!4fnm9*SM1|ep26`)En~$JqTnCFM}x(I
zJy0a7p}UUQ@zwZ*x@)-^G>)uSRF+)>*>zZJfyX+_)k{xzp~t>TQ^DE~eA4cludXAJ
z3*@Vh9Lp-tom;dq3~;Zulv)#127g#kKXgiTTl%SmH>S|#xIW(Cx!y0(snX~W%PACJ
zs_ilmjFp*Ez|e4YV|n5=-nP=-O!a%Tl`4#rXy&7jDdk0d+Z$o<eZpL!LInP*bwz9}
z^86P&2j;9RO&#9LAr|BTE`xFkyD)B6#a|ikI}UeW{dJSxIGC#XS-DBPmHWw9^|?-v
zv-3dE!(LA?<*1fFAe}R4$Rn!<#^qJER|Pa&%yoWRczAV%_1*C1kVB`T9l_;`E`28}
zg~Qo{l9?LWtvN`dkA#8wk*wq^yE@_AwLjp-SPf-ivFL78WRX_Gq-%MWRt2{&)WllD
z&iU|`&4;{qG%MX%o0WA%XZWxz*?FVxc4o2C<#VtDMY`MvqhMIcd@FBvP`5)6c=qL2
z!=0|DtJifeDCDZ*kxXO{sYh5C;{B3!<mh9s5D^@<EIl*1W3pCBzoH&M>BtbrDAExC
z2P<v8>sDP1O@ch9Ph%QMLzLA-+v)<p3Mm$+UFy8=d#Y!yc7~CeM0$U326A9(%E4|t
zEGFie6e^mNV(=WqR{s5wl@lfRF70Ewy53zYf&E(gd-LGj13YnMMkk&ka3un7(9p;)
zmTI}Ujib*Rd*?wJ03D}G4&BRsF`z%Oyhc4iR<|MTSYvls$qOm{2z+keJ|tG8p82!S
zW~)l=-KjB+n$btN(|yB%RxE2>68iHeZBKtBPBO}ZK2GmfZnuFu&wcNm94^w0BmjSC
zPJ1oqz8<TY)$DcJD}43icOjL{UoSN2cUpxvFk*%Dsec4Oy5K-a5Sbw@O~dU;V5cL~
z7g>Iw2aREW33d?n;~$p|X7O0eS#G_dCl0HHLG=~=)^GgUY?}_J9mr7ANB<=M=Hu1{
zSt;SseHa9RRa#^#1^MB(AxLmwo^H$C2}h(k=C!L3_FpnI*rI}0iGq;6w<w6qH@E3!
z^q?{R%{e@Qf%Jck%<GP86ykkdk&2_MRw_4#B298ao^IPX{^x_6Z4E8f<TWrR_A<rr
zhMs{fYcr=Up*V$2URhR}6(`R{3!}Nl^<mp>ZE*R<;an~q#-7Y*Cejn^POr8obIg|a
z_}s9>Ty_%4@Rn}2TySe8C7oS_k2Twjhi2GDNas=VcWu>JJsoVZhFn((5>?(Ov+Chk
zK7{qa1_}!0L4`nefS=D48H(?H)?oVY<sm($CWR&?e_H4rHkXlaE4OCGduXqt`dn&y
zKU@MN(?j@<VNu1A-{^O3K+f-$W(c6#Oe!;6zW-||aK+DEfq{l>aPV^u((5Aow>DT|
zJj~FWyGB6;!}pGUrTpQIU{x4!<wzCLoK-xuttf!JrxRJK7rfkk$`m|Yk8~><0yF5g
zwl7?-X}4M<C>y;YVT2ir6ALWX$?urbZsjlbBe9xnE5;B%;vb&meNrNiB?2vXf7}mm
z!;)>Mnm+t0(Mq4=DzeTo{o63`XuWmvSV+6}ZekPpt%Qg=3)VDI6aE}WGj)8N(oA5M
zTw;pq#d!n*^nP8fVlR+FU0}0N5D9l=_~%|AkFMLURIu&Q0@1uncaw&pY%BWQ^N8k<
zfOVbZ9UIT%c<ERT22olj*OxB^-&$i>VG1Sc$G<<$_<V^9!?uI*@ug^TZw0SSs!pCu
z7jMQ6#c#_ElmlKq05Fbt3YU>QQ0TJ$6-Q8cxSLNl`B8u?kKo+}Z(FxL_#?7GrY*Rb
z(AFP=-MiZz>&lsA;M18Fm(Q!|Lg9F>c`!+F<i@Bi|78E+FVEX5AkcANPJ?0LjqAcT
zm>y<ly9p<pK6^M%8zd;{hx|_~yq!MMTGc>Hxkl^tcK*4~I2#LOTu8@It4qp3v=9Aq
zrBu}CC_brM%zZgVhqmh?9$mQE_4D*YJ~Cd?zs?-G^_#(%2yLE?=m5u&Ex5S~o6}^^
zC@hP`O0Ew>>1=a7xiH0nU9|H>br#9dRf>nvS|h^gx!n0qXr?Gv6iGnJqDhuY;L39T
z((A3TG<hR_uJMQ+4Tj-RP|7Y>_3TcutXQY3=}6Bcv9RjpJ|?G+p5W{&UrNBLVei1M
z!&)DMSxpV?Z)1mF7>$;pCQDT4M-K8MlsfAx#f@8Y`b!H8Ri@L1oix~0v>pD}7K;>K
z9hrU%{HNtNBUCJKmG3!HOarv8A6v(QUbkTw_HMjiPE!AlTFLZip}~V2sz2^{Xl<2e
z*7Ye+`8ziIy_#}Dt%r?V)%)=U3^GBN*(;h-8$8TWjxXLZFOi*(2WAOI`o4uBeKjS-
z306H3Wkazlm;`zlfRp(y)9v8fHrBSAoKW?5{2`GO3olsKfZ1J~wR|iy?|g8hQk>S|
zZh-=_qY6rn1jp>;E$f<Epsd!41&NEaQgOG@s>KM6cG33;wYMKf+`8-zXn+&p-hUsD
zWWvnM-iB%VW$<-8(kfIw@tvdFl-;I`n=-<vk?}P&=Jabg9FmCnyLA^y9%osYV%K<c
z;js{4bCZu@&i`(B#bQHjg6Y|NpW#Gl1XB&KwK}g%!CO&gYlH13*A3CD!IDn(!D)()
z-YR3CQtxIM0T<N3QkLSgv*prL`RFin+IhKZ0ps3a7Jb>PxSY=g`3}>RDvyPrr>i&Y
zKBwk^tHEfjc6Mfrc-+j1lthH=E${SJg6DCM{DsYPIwWBEt6U;}!ng|(H&PS>Om|fa
zw0z2Q(aI>A>c<~X(h|mgb+HeO-Lz(04NiUi50WzU39-%Z(5-pr&*#l;O!lsH+zK0(
z;p&TdrN9W>5KVKs;PPljEPbt7@NdX-R!1|!bV4p*xV0EA48HBziSBeX#$_yFTlnV7
zdj)N+i$_TI=1pZNWXk4ezzV%fnxELP=L#+ZLymCUZOt_A=0ROverCk#3pJPp|GN%r
zS7eygzfRSfNAs!0&c<xR{Qod0-(cNYaY;Z-Vg275+fM%1F*q;RWlEOVDzt0++NGO>
zB;Z7=dNvaQ$M?`sv@+$p7+8yBTEfKM3X?o7Xg52vXRmwqe7;s-U2E%sRKq2{byUW<
ze@1e3L2v&_TlajmPL{Sq_LoA$Z+;8Qi{Ibmzo^Z*DL#r!r;D&<8E2>VAZRD48Ua%}
zZ@J&sxGFDx_NDQLlw*?#(&f09c5c(ND<gWmI%{F{ounvhNlylJxZi!L?S_-6zRCf#
zx*a#nOS)!p*AZnJ{|P<R!uD@;_<8{(Nk&YZc{62p^^*TZ{#K*PbU>_AVm|-CxfT*)
z;-W#HyF}82vq$o+l_D76z}?iQ-6U`mamG(w!jR|g1cUXWhQzy@Dx0o{xZ4D)gBw?3
zwz>HSlgvDctb|Rx4wA7LzHoPb{RYn#I<L~df|T!!G6|y}Wy8mY`#v6T@uV1?+o4+e
z<zP&9O1x{$ZTZkA;XnGIefsmucD_CI8y2SzPvQqq?j={}Vj(8%U#m{5ax8z3^<r}@
zi_feX?wvnp5I=7Sl0QT!CBIGDX1yCw{)Asen;3a##W?Te>PZ%s?omhjxJ7Eeu=$rw
zKFXlp|Cs*wGK@V{+*_(!5rtKoS81C_fG6qxw3jm#c@9QEKNmE{VObHRbt=Emi?Z45
zLRg`2Jj4yxyz$E5`^X`zo8g}=>1rGCi5PGSfOJ;EC4PKY*VO2K0txXIY0$D298g5)
zz#v6wMBjHF6)MZCH?<*(AWEBlTGX2-@1Vzpvz_kgu^9g+_saA(F)u5(SCw~7xr{_>
zez{zxnv)HyuY#~b&Zm^}SYBsDtofQ>ECed4^S=VkCt7W^9RJ1pjqtIAGIDgtiJdcr
z)yUdO;kcC~wWd?ET99cZG3n+R(f-rwGK{ErL0r*mk6i6Ie<Mb+oQkrSVK4c4H$7t2
zMluk>36Hme3=ZP~-W-f~j-O7$DotfM9>;{{D<TNjjSjNXg2E4DzM}g0mKUj|x0lzq
zEc4ekhfUjg+@m5)5icU0$h1<_oaP3^F`YUe`V;*)Gl$tqP6d>((0(uV<XLPbVu`2W
z*&muc{ovs4@^*dsVvCnV8`K)?G;LnI@V3nMX-yZkh!k$z?$Xt)XT;J0XGvtUNwMSk
z^(f2I6W4q(WNbeBs3;+rmUil|PZf3UCj=m#u_`v6kBrpOxArd|aIwztKCuSoUak0?
zwj<z7JkF$@_6?s{$SsOvd3L^!p^<U7%ue&NaJO*Z^*(uQK_Zg-<xS?zo!GU9q!{TB
zmF!z@J`&y7xP;3HLq+~WC%;6jpCGG|OJP&udt<4oL$i-AoHq^K2*VeA*Z$;U-S;5|
ze@+Jb2H=^iJb>ReJ^b4q%zs(SugCXY9L}86fmwX(+1S(Kpuh&(>(x`8UNn&BQaJpV
z?y?Gawj5XSNZ%~|H(8#ygBaWgFlhDlvqYk&?)%XoAVe$*aqUtKcy;irkFF~(ft`42
zDt}zO!kQQ(+x2{7_dDZvDhcpL-pR|`f*&o%Nw?ieFWIcrC;3ZbS}aurMzsO<Mxf02
zJ>snUvE8}Rlb;8hV%`?0f^ce>z61ATNUaRVnkSz-n>%Uhv=ynUoz9_3QA}7G%h9+;
zh9O(d&1euq{BK$+4UpORPCwE4A%@K+Pf~MZZAOGDdXN}XSKDX(1%%NpbB*PVoMo_~
z>%~lE18Kj!Y1Nkzc+TR*taoTJ?AnY*X}*J(g5qVS{xPj3WVq4=fBT&wevJCj7t^R9
z-lwC}YsnwK`)S<t&*oo77-x4$q}sDMf>z|!CUfv|Uc3e=XDzlp6x(p*PCivGA4t(W
z@q(#R^{;w96_e>H!1vzuewD}{TG_zEd7gWx9^i}E*OOo?Cp30E6kusy^_i|QDUs3X
z`=xe+>1#|gSAbf{um3zxuRn=6;l7q*!)I5nrWYSTq<1ZOi+ziO&XF29ujlL`Iriby
zxDIO6iSmUK8iqA{>iiWX)?7pg<$Q4iGVT}M<AzU@rpVV4%s7F&6jIdTn2D303WT=^
zBCLsKmtI}}E`0c0ANgxA`pV4tl0{vn+||0r%D0>_ndzk^9v)$4W6|@q1RyA~R<i0E
zLEWn*eOG40R5(#on09UbHI0)#Pzzn&->e!Q`RXXwazGj>eC`6w%>vp(bk!vHB{6QX
zeQE4$QjJv_o)pvWvVVFc+{iEyS+6+PR%Mj2T>YU)VpDYemsAqlXr7$_ESQ}!Kr&Jp
zC3f-KHiqwgPt1-RE_RH}={uviCVi8nJG-#<y+VONEo{vaE%|hBY?jP2-L)gyvmcL9
z>{AfNLaq)jlv9VzCk9CC*g(j(4sO#u@*ar^&M&;;^-u_?guGxKDn~GF`Y!u-roZ8p
z@bzb4@o0n+9=IWk+awu~J2?oUu0Y%<;PrjCJQx{plqtx8AC*5^5lrn$?sOX+?9D1K
z7(KoHr1E~~ipjjCP=`Dc(a}IyvmDG+1NUuZi@gc)Onm$vjNX#mv@u!L_&bR$rgL7|
zzR%m2rD%a}<;(L&8w{GeqDPby;l#Hp^tf5mfIImb=wDFqUeu=&D0G-dKe<+5KX|Nu
zHr+kn%X7ag7v5H-HBbX*|E+e0wnsV0MEs+nHPZL{2E$fH=hKBwz*k~?so0kbsWY2_
zAh+~p1fxXo?5?t&8^Qnf0t_+<FazEu9!~lNL;#bSX4&L##MQz(Zkaqw(PFxF+TR1w
z?Wuotiy*fI%;NNaD#JTJEoX4~O<*?q8m!@^8@bRDIku2^q@%WWMGIi%r~wb+6`-~;
z|M%fX)T0Ak8;Tou;|vnm*)v^!C}+f}K3n4IJu%v4_oZgWBz9nqqeKEc{}n~-@DYh!
z@(nYogN9cqmj<K0tI}?%G7i$yiylU|cpB5{9jm62$MH*k9vo(eW1ddnZ|1D}D(R#|
zC*onj^!<BpGVRGtSecUT`|NL0X>JDqp@{_G-b&*|fMC_q&Q_Ge_B%O+T=8zbo*0))
zZ#{ga>a&+mEH;fkN5l(^Nz>0C3M9v*K%c{BEdY+MKR4{Z#)@lIO2U>;_O+oBF0>_U
z{-J93X+mmMm3l`QY3NtVSX@6RI(8n29!@dGviJ<j%>8<wSnbd8&`dImsd?f>Vfmn|
z5`N$jFz0#vS);k{(7Vvc4gIpC{%m3P`;jQMOtn#2z74yanMV<WfZvz*Bl@k+78&%`
z_h<8g&gm&ifof-&uK>7>!wdDzo8YAQFWHCHm$%IYClGC+?K#B$WWZ0)@&nU@W`vcK
zK}r){VPs(xPKUO%XsIK~1^)B)F*ln6)5(CKJz?q;Q_CLu@YxEYuY@Eed4_Kt0y<Ky
zHaGWI7Hg*2^CVN0&$^B1QB&czSp0+vei%)Ig_br>?iwN7lpX9IT2-gmC_+*_buSz9
z6ElzBslORDnYA#$(Ry#)(y@R2Q5ki-<PSP<>;2S<ezRrz^$n2F<{eFw%>dI;C8>kR
zdkICu`VX4&w%Shc^KhCtVWgtuQR9lErTe(#x~K0y1RVJa?V$ef4Nd%=_&|mIRBS=B
zAk&-Vb=*oDCs?P@!P=^Q-PyHhN<y#}F9~w<?yxgXM+|s=`)l&jd@)<N)f`1!z!9>c
zYe<ZVUlZOU71nECflJFOEqfcv^=C$g06&7g7BOFQlyPD&YOiYpD{_{8XhZ#*;7jQ6
zeGZ_Sy7|ro1v*bXZ^EpNskx@9_MfNur3Cn-U7|DE-ayP#BqsxU_Kg)vO6kdHovG&Q
zxddds$<#pI^DVo(2cC`B0l)Ir{zY<B5PJ1zmkvga^!cbfeSF>Ygmp1j^!;dGtTz8q
zkD03Dqk<nD$O6^T0Q;T4Ix5>V(}JU9mIW=r&Ny{GGbRJyt&b18+(yK6?W=tXzM%i}
z-`6g;my7dvRfM(ndiz~2DanHPjrE*o-+ev)9N}z#s1f(7e$%=YQ0Tm}mn8c~U93Mt
zZ~yMuln2@Qlf9IqH(drKQLLVLUTdQWUr-P-HGsX6a+eo^h!UA&MRR#N7MF?9g%nxx
z*S!iUUs`c($p_LDLHQY_?fj1+|FYiU-BS<1TbSCoHEdRPEz9W(g%^ep)XKzzNNE!n
zQ~h$J!tLn-OmvKgsEP)Hg?G!DFG7a-oA>$073LuWuigiMduPc7d6O}7dp_0ql!Bkb
zvv5_+a8B?Ion=#a2n{5PCn3fka41wOdlc|gD!8kQHBk$($@0#zJroQfx@*O^!>)de
z1g+g9N>69vL1SL4?G@26?G~(JOy3vc6a55=e{|<C!zp9p?-%GY&F$RWzE{^XM*K6>
za4IOJY5Hh~St}xvc6(Ealq>g@mZJVZx+0fTbOjQ(-*=NMsk!pAu!$h5k`&p*-ist;
z?t#vJD2-(iKNV*Yd&c2Ya~}#+rvRZbK?wOo@Eh}O+wLs)3uSX=Hpu6pKRwkN@_Q+t
zLN}s=ezOV_nJ4w@&Tb%w{J6Tu`d^O4n=2btOYPns^<B1h$9T$i@J-zIEQzo-C6WuI
z0!LvwaPZaW8ItO8!&m^RVier3QHM7ot5y#4_uwh~8q}!yWj>x>h#>gJ{~_c-*)>ya
z%j;Ra0E4bkt=x9WAWSntp6C~-D*Qjs;B`c9VMhQ0yi_{qzDd)=zEW?w>U#w{!&}VL
zwZ-nm<sJ>v!PCyt!5kGSx&$ywwD{4|(&J_A-)+`9J1LaE2c8vH45AB=@nXVAbwEE2
zC%(DnsZWW0hj4%xFcw#Yl21M;hn)~_qaludhVh%HyU{&9mT?qD?g%GC^SwIbSw!a|
z3OAbMca&fRH273_P$UQ_t(zKPpSoY$GZ2bIeCJaUbYy^1f%yM0^%h)l1>3qP79<3>
z0Kwe}8r<F8-QC?SNaOAhBuH>~Cs=T4+#83+3I00woc+#TKcL50y=K+?Y*t+yJ8U;c
zDu_p9boaO@!8t#Lj^^T^enhJdgU)Dvw2Pr;%{)p<k$x&?Awc<NfC>K^$8fEfciK#I
zIU;srdwD98a5D~&AQwcD?eD$oLmO|J3U2ohV{#L0H7+mtvoDzE{zupTP*_tpYxiQT
zi?QeOr)377jXuF$$g6DlEA=q5u|m@0d9cide0W`8G2-cie+2_Om1iHi9-7~rh)8tc
ztAPw5H{EO{8Z-^I(H3hrDsGUT>9%n+hr+`3;zS7ljSI9V)x7T+B}1{4H^OE|)68sr
zRy;~)9_?(K6^@8c?%Y0>apx|lZWVc%3Yx|*>u&)fJ-sy4)}w!tq$lVfH$OXmGJb0>
z&Yhb0U9xz!#r!HD(Y<NA6!FxL(bZr^HU5>A?)icmj?~n-z7_?_m3wL+jR`qBoh$4`
zP;r%XC7agju1OZh`&<SA&?UIt9H30zu{ZhlJP4LoI=E5*K##|*GRe+@H&(dO4uEP1
zI)OWs$1S3PLLP}*N<`)(=V)mJcNf%)x=_K2Guz3OO=<ehZhpRO$Wugn_9Ce5sC<~1
zMQ}ghDO!gXO04WBRRO(^VRD#{&S1%(Up77nxAlvE*Dt@fG)^?7+5IV@GJzc?IdQqF
zApHrIW)550)cIR|h=@MzXzBdGI}9oA)mtxyGiYMB+OXKfx>}N|rQRn9&5^D?M7Ff>
z{}2L@CaLe?g0^_mrP;ezg1eVNp;lgS^5~p_A5Hb6Z*}2Le0T@P$LdhS;^D$sw!I<4
zd&{4u&0>qhD}SDr<$;<R59}&*@bJQGQ4I{vMyQZY^zdy}VaBfMOj^nEcXYrX0k^iH
zmU-R{&y`)~U`cfE9uvObXWC;`!=A3!lpQT|R}<uX1Sp?+H~L0JB!!mL*@Rxr4x=Bs
z3#R{OX<Bw^d2*=vH+`qVV){gwqNLvTea2X)2?bg8jiFX749>KeL)!r}?$jEI!+>a~
zUZyC0?}ow9Td^3rRns`iPWh4OIfItJ10(UFbfdfd>~(KE=F&iJm2;NOE#&2?dc)4U
zQwL9eH3;l7d*bS=`Wpwl02_1U)63=%uKI@s<1Y@?Q&+=~L9pK1DF)nV9ggaeE2i@J
z+q=(`@+@@KBdDsSnB1~OL;Uw|*#mJSuODo~fyQZ=W1YHVOXX;VzmkRb>y(hnje2Mr
zn7edU$S#>BD1kT_YIf~b@f};@rlP}=)fb(UeTBrn-(#n&K$<@9N=E1v#CrxxKuzKh
zuVhv9lerlnPU^r3NoYB4waKh6Lfnb9O*Snc1MKf~r!CY*iBV1J1eOm(y_p{GpBD1$
z>CUtUGSsB&ZO17$5J}SOkZerMi>kgq!$5^7I7*Nl_r3;8g3rUOC&kRJjl@|{{N|vU
z{pk?=voY7O7IuiI`L$~FQ<dutuK_Hmjv}JutL6s)^1uqc`Kg<mG1zsrVzP7cfZkrB
zA^^A7So0|a5a^1lmr96h6cWl!7wjj+T~F?LD^geg8cJ<{70uumtvef#G2Cj8LDTiT
z=>&twpp_hT)laUpecvc+FJ@+b%6{S%5v!Sxm#`}QP8HtKzq792%!_0Z1^S?fkl>(u
zG!}INLD$o3>#||(TkSdWY8Prs41&|df_4GOUX%+GYN3S&l!GTR{5iEBTG;)do&TbC
zJzoOxm6Ur<di`)zJ{aQs&y#kV5GY%s+oV%wWq(uismgG=wo(`G<IU$zKPEs7w&E-z
zjDV@Fvzxm|$B25FZ7>+ts@K-z@5#0%HPMQUV~F@x+4aon_M@Ld*Vj4qAES#sN`4ed
zn+__j7}*RKQod~OI_#}OK9+g;0kFh$E}I}{tvL8E<BEqPdw$w&oBacK`Q&70{OY3-
z>e1XJ-Cfd!kH3hBlNuE$n9PW8odguHnz@@2qsXHi`A8A0pD6SVYT>-v6aM&+knx=7
zN@E_sniB{4+t$=A4&MpC*ZAf?N~1dGdR#+AHq2+ORcj}LGzQBTucS9{<#{@gRg#It
z<4=2<RQHaHobm}=A7L4(FbF7T%3IO{M)VnZf(FbGoar7G9S4*~9+LLzejv6{MW=J7
ziCR)U(*F(L<*F^S0Geb#Eoi*Wz<ozwxA|=HYIwP3$L`<9Al>4Bc8In&E{D)o*3?of
z=<f5t<QCkwWu#NSNt4sW7%h~(ito|uWiXA(*<hR(wjrgj5$tnuT+44gaFK{z;OYG!
zvw~{<2e?_ddMLzXzVd+kHb2sOwB$Az3n_btaUCUGIhCyq1mL?uu%gn>N!c!*sI=}2
zss&^6Ic#nB!W$lm?Yl2{^{gWXO4DLHvna&e2yPRB4MC9wh`zOWO+S<QRZ|4dBKMm@
zFkKjr0J#rE{v--?f2^#08^}A-Czm)@;{R@>8wm6wcv_Y?PiMDBB@Y={q24H)x=C`{
z9^&u&SUvE@@0+K#_2`+|sZL;yM?+egU{f3kpOG%jpA4f;)P12}ho&Ap_3h)0mNlPk
zmS7~-aS+=<7)@leh`bb`h5eqMEFb*Rx5pLC)NGTdT_vVVsZEl)X6lFxerY~DZlpoj
z#P(C~N;)%1uW@&h)9QmH?7!0gm8=8{2Rr=9D&zi(Y#v+8Omo6@epqsM;escSB9v_#
z6HEEpSh8ktssWkUY14;_OSJ-9Jw!|5e;&|Nf6-qo!I<5#d!HP=sGDNiOf~E*UwiI7
zG<z4Rbe%Nouee)J1#BdYe|QDVvfcMXcolrS2ZbP#%ivCULYbaS2QAw%$~&>DQ0~cH
zN<g=bl`VY4Q?tIra;|TWxC^)Nue}0dG5UZUU6Jkc1A`-7&Je2>MzU#>GA(;1+=7e`
zw=#_mIGEl+I_8IQNY^g1QAs33Bpri&TE(>qrgZPP0B&CC4q9^SCT-nK&+1OM6>E81
z+rWSrET!LJN2cefG}8g9qp93ZUDNDrf4nFmKU=N3_B1$9viIV94aLWv?9=2ZN33Wc
zucGH$FA4p5zJ$UHXx*olgXc!e_p0gw98{=w?|RLQK8hNDP_Wq&AL%h;#?9q3tn4Fn
zV4LS)jPYoob+-xhLuZBehGxx<g`q$om^t2_kx3$`Cs3V}NOy2aPN6YD!p?m1B*hA9
zW%p@8fkXK^{Srf0PZZi>x-<5@4StCK9igVneJbvBNA2<#?Or}&8~OBZFYp_G3sM>L
zU&-@x-rZeM-7D#y9KGYCIn|LMU&3Xt_2F$|_$GoQuax{08FJYC2{YhM@^BA2AXt&X
zFEC-VCv@_4AI9o~qSJ5bp81`7@q^S|CV*<H17u0`@O8l!CM6SL#baJoCDf?d`{B{}
zARsYSgUe^?$JVY|AL5je4$F>iqdGMTUXaZ0ECm~x&cWn<!{$(-C?GU%e-CE{%?vES
zW}m_=QvNZd&M0KBt>~fE;xA06vIe_WOR!o;fF=jg0r@Q{ythm(n;0J1SHEi(t7Lcv
zAEZ1ltvAw3@B2$;eN^vBs@Db*!nTDj7@-t`OVyuIAcEPxV{SwtdtrSz*+HopUpE2-
z)#YX#uH<BmN8JU@3$n#)5qK5KXk(wU<nI*+5Uv!Y#T3qxAAQ<iM)q+#q~COKVOLtR
zlgJ;uzzEv#U$5i~s|4PN=VkmZDC-hzDaBFk%BNlKOx<^iG>dhLJ+Jb2yp3mg<fBk7
z8>I5NK;p!fBS`xdOn+JVzv7%eNt4>gh{ahuj;@7r0W@l^hlw0VxmBOd<@OFpKm<I#
z<rF7IF@fy`z{E1%0TYWY=OqpFr3FDH>JNnZ+LT!O24HTjHRjVvd8u&r$%lUpo{i&6
z{;cmSWY3IOK(s7h$yxAKffvJqUWc^PYBJY!K08v1y>SAn7cgajx>2cV1w2P{W95sJ
z{E@Vf^~zL4sY12zK3a3d?$C7~$E|xFnyUjC_TQ86Gely?TlTqz<q;iAU54i1exs17
zMzZ3$(Iw2qmw9QJQ53K1i-LwfS)9?N{0q*WuV|0IgJe@{FbDVUWbv%Wi~5eYe}%36
zeTy3LOjdeu+HF-s$OOJRijHIafXGo-rwXvg?YCCU^hp^)@$7DwB>?&#FtZp0@SgKV
z&3mgo(dl$<#$J}P6%P8zLsPNl4{IpnLB+dSZ}Gb>Q;CM~zXeRlnJe4c)T~pSc`btM
zQxQ+b8XZWZOXP`VoXdWM-v=SZ)$As<K%~?~p>>g`0yB(H(B@1pbL`-~Lm2Ptj}!$3
z$~8uLxEE(TaV;C3eZzft*K|#?a34ONJuyXjK7f+b>FRB2Q>K{QIjTxaO_*wfH9E85
zi(OA!cw`^QNNx(FT~eyeCsgKh$EJ5S1Wx&H!gx0+@Ul9?<C7MTKI_DhB%HgT1v-AH
zME0f7ASw8+Jn-<nFy%o83q5wf&Uf=UjPFU6a5t#Gu>l>h%$S9_hL__6sUm7txO&nY
zfh@cVgWnGUt|o#;UlN&=3(A2X#W2Wb0}Kc_b$@f5k4E}&Cp$8jFSJ;6wK-&!Z9EV?
z&Cylr)_ZK}b$&%oj<5g98IAVfxF51QDN8g1sb*VB3-k&@>59E?84=GN3lTWrV!{A*
zg#m;v)m?roPqqrRf}fY8@LZ+TE+gYYtf#m6{jegxC=S|%Ad02Pi4x1@Kd_}!3=P3i
zm(P<8T8$;2v^Bz??YMVN#nzytU%`;mZcr;Pp{9Ffp3c0W`FEN7n7(q#+4J3%ml;~d
ztCDJh=v{DRCH{9Ul$Wcchb8aol^III-E?eCj&?AO<9N;6e~4Xei6#4W*fzXjChWBB
z=%rgHgi{TGysYurMRWdxreD@%KwD=<ew}gqG$!U)gwNTyw8>+H8h^KiO4dY;lEBD5
z1z(om0iqCXgj`Ir3B!KPVxye?eIr+^dUjjRVV$3Nsk$9B$@!Y}q!7)F+c677S6AAb
zkybpk@FCA5?wknvA%0Z~cX?IyViKPhdv=Xn^~zFb(waiE$<nt2CuSc|M3UoM-KlP)
z?q`ScbJYR*uVs3irkI<L`FdQ6tsjKOdJc0H%c;LuRGTS`<9D#+A7gl}an8<G{$RZR
zS1ygPIWMwfs9!%n)<~yruM#P4ezw`Y>Wuw#V)(f082Dpo;0~2~x~1MR!$0q*E;6ly
z_o=gIhu$Smsd!1;2SxgxV~sVAxdzvUhzci!blM9TxX&LFAalXhaq)OyZVYQobmWFH
zUEU=2;#$%Ul^JxG!?o}S5(Vkj$bA`@eH`gCes>F-tM-`g<2f*+y8{#2Ox4ED{?dpm
zWCaXK*?ntf4X?x?I2-pGUE9)$KF^xmEFNwp!e=I-PzmoENCro2tc|bLx9jIJj9N%_
zNEy?VzZ!^dKKNt>Fz-(58Ib6NRVuxO|Ii)#@MC5?v_?BKjG@#0$Gd7SPencu30(Ey
z*WNILjemxnW~!NC>bQy=tkfOx9;34D?!0!b1GRu0O^eI3MpMIu@f*s%2oP5xbJn}3
zazY!{AR&}=uv3Z*oaggv{F<ICq+*&AG(}|g3lroUlt*1!bLvX#&XeUUkBc=q>1(jW
z>rSQ-?epffyJc7`E{A;GTr+E2IiGIpR5PGn#w0@Y9esIUlTyZXsG}Dnq?iYPS)zVm
zmsuD`tuWymi~b>O!G)U&1>#UnSbMvz$7%-Y3m|#uZ<yYOQzR_avwykz$I8B6MgQ}-
zp1X7u{P^kBk@o}=Z)&5A#;3WTHM^RI%$0oZgYWvl0gcNb;eWAU!@-}r+$BonW4|Zr
zX*r74#B^f!2oif&n_S~ua=9)*Us7apq{Fa8q;<jP9szhiGd=h=hg=8GoPaCr<!*io
zQfG!eHhG|N-4ZD>$$^&HN_3Hr8jfgI-`V5(f4!Bwh8|xu8O9%&J8R3lerYsIv%;@{
z={Oq#c8wVSJ>QI~>w<}1T+1tEyz3R4lSuM2V(2@DF%wm*?5;0T{fKVB0#R#+dcNTW
zn0rh&72vHt`j~u>l);9SqssIBmt9}Wc^7Zy;$BAc3t5CIHpLW@gVhQMJ8+9+WF%@R
zcXi|P>dBl=oPF%Ns>V?XUx)F2Duy}PB5P&$8ZELE;>mkGHFD5CzeY09rMhiM49;j_
zq8ZLsDwO%>2v%j9|4?JERlb_P3UJrshqb~V_Fn%Zc&?!1sQYkI%1FY$Q#AP6zW!(`
z_z#lZ`dlAU$*5MmuBRScfn(v9V4a}8La6tnOKuiUN~rZ(n<-2jX&+xg&No4!OeG^k
z;j$0)q=a9=<9CUL@$b-}Ku*u(v>qi;QZDuN*~kYRK_M!nT;@mq=(to+c&dBS+ce0;
zOIS4ad-FVFW~$zLu%mARk+@>M`1Ht4jK%lZoc&3A>(_#H%vQbT7_E+P*(v>9jrm0i
z>iG9x^)Wg5jz<*>Kr~*ArVNF%rm=R~CxRUfQ?SN1ZU|46(WNA@ax>UO)>Tz1h;dU`
zXtqLLbwkuYx(lF1w*5tzpBq)>>~98VH%iv__w<=qqq1o3*}-QjiiZ=xUP*Lx9J&W%
zO#%Yr<7zRT#b-lPSSCba6gla7QBR4l*cem=E2^%A2W=at`~lWlrPm+pS0(Tss$T*2
zohTy36jfk1ttP<$cZXd=9qBlhc;)j+jfJPDPxZwIMG30*h;SjJenKJ;?`guZw1o|w
zUwbUD<BOrqT>s6}3!WD_55wEWRV}GZ8+M4-p#xgu&xe3d6|;##ibVU)io9jl4ceLR
zxvgH+por=T+C+pw)sSQWO}RP&@S!gFKPu%rnz%8^%!Rojt_JL%Qm*wJpCq7XjiuAi
z5j_`-OKfL-A18QA=m7yvg7o&9<ZpS0)hH0j`*E{3qX;N6TlME(mnBvU+i9MNUs%yD
z*&e%Emru_Z8mq2%?bw1q^Wjycvzf^6WE%AAy>p4dhpo&M6U@(hxN)ekGam^qDrcdB
z&m|7JZzaee{@(4mejuESc$8Klt*sSwV(vvR&hNO<`bP3rp%f|Ejwou@@XU-iuY#N1
z5l6V~1po@hP2*>tmf+Uj#<|kccseKe^k2`pN;p1m^P<z+BAPV-2*LEf`GwMrS}AEg
zI+ZeGZSFL8YaiVOvvnh*$_UjZ0Zrupbx?OVcxd<&5@hid*qF7{7FjCO2JG2p;MX5E
z65I9AJiQLgp}UW#9JJBESQ{Emj8`jKzBn9;nh<+cy@dH}fa&YAyK;nL5W8M^{YdmA
zFyafavfBHmGKBP^QGwgeB4w7kJ%Ln-=z#Zu)#NzT@7=n>AsV8!vx&y2WaHS<`o^rV
zSSO~mr33r>6#0x{!K;fL>#K%Jz0AHH&9eseHF)+I-Y?7)?|DvE(<*pnhPIzVgUMP1
z7Y%#6U~a$LqD1>zlj8+>e+ka@kLG=KOQiHMF7zYJO9<A*ooM}rA<@2^y$0*^Mu6Z6
zQrCOy9v+!~>;%F*UNj3&l}0rYWXmb`3}pzd{oTd~2Lpxdx+(Ci)Wo^YJ?46%Yt`!=
z%UUPHPP+wLLlqMW*;T#G1x!O8_yto6&Kv!UXQX=^fhmVAjDtz8xo#x)R685HnuQhY
zMv|&8CKTZJhUJ%r(KTvd!kpBSFs+sHywRBqf^cyXpu$F0u>E$nnRRGsB;P%ef(M`D
zW87_4&=1yxX*BO*zYL>qAbe?@;GV^kMD;|up9*hpgod3JWey&0h^Nn=YMp!K8VtYX
z6;xvjhv^s~q@T*^Ve|;LP2OyLdHt(i9$YP{V=Zs_=_{3=i(Oc8l>fGzDz#9IdB*Tf
zfKCN}y$!}z3)o=CVFObwrDhhXN|7h*Zu#fOwJ`k{z9)UNB!>ZpiEEK$eMCfQ;Yy|g
z54`Ei{exi;)4fQky?&|ufAeZ%w3!QKPXZ#@I*rkmwZCV5)Rtei4iz)_5%`h+v{Qz$
zO~0DTr^Mr244q#^%k#B#E;N}2{q+g?;(<x{dFW3L{NHBzB>F=r{{U;kxIyx0q`Ed_
z{8>)k5IUmg9}E)iS9qOAq72sGj1uL_`^9583uw5QcFQp({Qa~9Jbu|BvG#SU?IZl-
zWNeS4irL>K9{J7WFxT%?1u32;BIaaIS9j*g=ieKAHkDpB4%mC8*4{S?K%EI~NALE;
zHaeID#aV4yxQ6MqM{$x6S+echD?X(knGBvppn>_}=`1u{_P8cg@5{<}$`Gz^$x;1I
zrhMImYbycYRO9zXWkB{ZUaX`HK)+*TU##>c*cmC{@AVVUDk*Lg2-Q1Hx?5)XLPvc;
zfR$~`*VsBF$k^$O$=nCQhSA&z^V~J4EF89gMG)nLBgMdH;X*}lN{m0(7T>qjWHR3i
zGG3xj$2P{&O0amU5cciaAjFWC(ZX`rxYX*M?jl1DQN{t&1>1{6zxcUmq2>=)Tsq7X
zfYr}=g3srI#6iq>Iz3d85GXeLt9WYUu$l5>6=p&Y1E6yeCM*-U=QuDPrRd(s1!9Dt
z*Q2J(wGm5S&o<t`zQHH_Wp=}8`!q^Ot&Zt%r)*CRGTQ|}Ue4LVfb?~`{zAj|4UHge
z`a8)4$;?FS02X)x#-J9J_jcUjG@-PiW33};32V`hZn20H68IS++`_$HWa)tcci7<e
zJPrTuOaVPRoZAiqU4Yf_lJQKAKA1fExF#(AE*Vz3^L4a_4s#XSVKaSo|H%TZtyNN~
zZhRRp)Ck&^7YchFz%aT}#2z!?77Jvumc2df#{S9@cDu4yXY?)fJoO8wedT=3I_QP!
zb=rlrgO!?ts_;#rw8f3?9z7}JFHkQ}@gSc^wJJc~7#%eOz@Z2Ip38T@Udvx#&uw+%
z_V;cdnz(u`**GjjW2_8kM`_pDlNWrhqxAk){3JrWjzVCiOxV^vID+VS%)cQBD}tE@
zvU{;LSyJ4Bus`!9r-Z0s+k8GD+Qy-ZcEWzwRjcNL<LW7m<y2=5iE|>`>8{2;(+PcD
z7i`c{v@n@-xzOdz`L}?1qBJn2+(4t+Zh$~*m{68qO3Bs1fcbpNpw`+Wg6DyP2JkD6
zs<$yt@{xG$EV{|3{jo_Qqt$&zXKd}V7wU~_U+^2>3-~Qr{Xb4|{W7fcw>54eEf~oA
z{_*o$>YQiD>%)sVG~1*)Ju<vikO;7$G7h;e^r8ygOMh(`*^LO*zs~h!3=}Us>!hr9
zcRG;ZW&WE~yLLBJN{gWp8=}Q{kv}&5<NbPzKf;%pYMJr!G}3k9=BkmLM80v?bqr@1
zKn?{>9Rl-fz18OCti)30&r`Yg&@E&EGJ(hFxHcxwxyM4U-^r8Vh$1KGfT3i;f9nZn
z;k69+@9tvTC4_8Sjz+S8YkTrSVzu#4uEQIUVwQhV5abr~69SZ;8#6i}Ot4GfMMMI3
z#$_Z3G2_@zVN6YkrI}$)yhQMbBY*GX9N%hGVl9{;LQTa|Lc~}yTywLkSr`NDPoYy$
z`%OvrH`eGJnI}zRt~{fLyci-R!PYE&S)SRAk39ZC<_HWaN-p#)gq^fTTkvt3SBCPW
zK$F8(waweB;xYp&RLob-&4KC!P(6f)t(2iP?wDd0k)P3jsFO9%C4Xt3wI-!i?z2rf
zS`krl?SP!d&D`KhWmup*dWuyj!o;Mq14F{k1URY4A~z9%DT2GRv&~{#n}W376wQ$n
z!G~v%!4bBE;W9m5F2U-EaBaL+E#jP+7r|G2^WF=app{3vw6I)I$~c~Po@Xu(-fRTk
z!yw0!ZCsBnIrJSbmj8S}iM;P;sc|Gv5|`Pti!WT$i1*qIXFR*RfGo|aGFfbGs*lx}
z2ui*Pc=`DBfSsUf*E+*1ru-+(6?}?3J#Vm^)N~Xj^{CXw7t%WKFh)$N@Q;EReNa{@
zprb9h3eKHR*6z}Zk<+)wc}^^M&$Tkzl+_fb%c<Gon+HOOy?Yu3j~A!pbt(^-84vw7
zhqu3~lfLvET3HuZO&BdH+0&Ts%+2{iC3n{?L@7etlxDZ3u`qW{{-(Sl>6=Hjy6EA6
z1QzUlwkAyq_#q%Dvbb|4+cRIDDr^`O`7jfd00y0J*d<X$>y)9^H2}N$n|4S_$oD4y
z$#mnh25`qH`@H_=@F#!XaDR**-Co3E|0LQNl#5%NZ`IAi46wJ#T^=Fi(}JzrPA6MH
zi8o$YvUt%Ls-Za9ahf>yvnXy3$6B}|hKl9XOM2RCw3q7@exPE1?0nwPzI~J0IiMRE
zbNHpI0%;9ahE9NAaCRAh`2w<?jY;Q-r1^G2a~7*e+PRAYn~bRo)T*u`lyZHp|Dt69
zbqL$Wp4nCdNx7dOI$JiA&EZDM5{we9Co0trl8G%5hT0D5KCgZL?U+@hVPLogP?NXi
z%#EC`qN&$|Nd1DXRYPtc@_hgbLYZlbg~^(khaIj$yg3s(m2J-}$k6=!GlcExe1?N7
z5@h^WfzUK5;;z?JiqvB;BUoawUC-uF3Ef(KRl}~mZ-#rur-3wn@g2(zz=$zK6gwNA
zoyGyoR)oaN!ksm(*9RVEWR;Qy#9h1L^jE`K=KF}1cc&o(5=tHY_UEO!;XWh0l}ER%
zu+ki&HgVQPTM6fkXMaMQCOD2GUmb&)h>;)2Ecy7PM+*6f(%cfQ47}C*)p;UMB;Yn=
zo={2TBIM4aU2jL~5jOx{;M|EUUPDHp6<LWJt|A^K-c!5^63k~57?F^f;=Fu_g}qFK
zt|lRjUa00q6y|qivnZ@}rvGjg7dGZ*&$vNZ;D!L{*WLqseaflJ(kO>&AiEVvewv12
zn1vx`=ky@Ol7V!HoYi+|F-{a{bG4oTL8g#J1S@qSqgo~uMok+EY3De4)K+&1CGS_b
z$@7Z)-36EnHs#a)YSl|az0IpPg4b_Xx$h-Hv|RKU290gqzw$l!^2`rXnXfrz7Uq5?
zr33IWDMoNfWv>HzJ^fd>3tQqmtl`k9v|Cn077<}d6dP4Lv(sT|_NVv8$Tt1zXa~0O
zZgd)ERqPE2+%k8SkV7@4Ac>$c!>=EL4dsGN<a#lnmL)J$u#@1NqnR0fi>0=i_?s@0
z(`;vS2b?Xb%mg&odv;W>ADC~VI>}o3zwZrT#5U^{Cse6iG`x|og33XVPB^N|7IH!Y
zrc)_oA6gg;++kgt>o&Y&SGr(OS@%$*q0NPaIc$D;?^v!@?|-vb=Z;L>pxNFFAWXt0
z`?jGeJ@1nOJ(J0pskfo{*5VU|${?-!)dd&__t~zgFLNe!9i`WqS16~9i{<+y<d__f
z!ZIVw%cYvd7x(q&c^b%uc^ak{Fk~R|OA1f3exM;Ou5?nkiA<$L{!9OHmwonBj(nja
zq@8wjtz93uA|!|2!n=Oqa@ABMtJ|3j^yA@6PDuU=rnvTEzLY0aDWk*93#m;zvb2)K
zye|>^T$y$ubdJ_CzX|Qs34XjQroS-Ms}W_3{$EBHGj4$nZ=Tu2+j39X&mGyq4mx7i
zPmWT}-IdrblRNv&Y(Y5laeIa+!DQhH4~HHa4Aucht1coYcJ7RS%<v%08c7dmm~nNz
zOerjh$se8A%}9Cvdisffqma{*YMdTo=R{uzYo~5G5fA0EM?O9d1$Ic%uy)^^Yb~%~
zqiyhMy&n6Jm|}Q4W+s(gd^KT9Wl9d@-;ji`cRydB;f^lR=%b63QWo`(L2<1!&1u||
zkFLvZLlVG9H-Wbd$3Sm}L_c4xc!Zs_I_K^%KBGTUGshK=cgJ=cd3FPk&bT8lBnOH9
z_4x7x$4~kTUEbO!g>P;mI*C}3I^GI>uGHw7Sy>!N@=XS)5szqhGHG0-tG(nMA4=z4
z!PHb?bEG@F|M>bZfowgoH<1y5AjeEaC1yS*Nt5)WA;Hc*RoJ}z=Nvq(rlZ^S(vWBi
z$t6zfCtv4pa?J7HiWJ#5?U&kbJ*W%ry?dt!oqkAl{vu=mxeq)9t!j79kA*fjTpD41
zoqmmfJu_s(3yjv@?nbkb$BpIGMHe*w^qZg*Z!J|HRh3#mzCXWIaQ;JeeBW;YR&~2@
zV?^PZ9NOjX%z?qvs83kmnn}ZfG}za}p9mo>bL22G_4$!VkZI1wn>m6jI%MPSjQ8yN
zQ#SPHJ7*V(@{!)hQkIX8_uO01JYxE=96w2mh_hmumw|ToLwlP=1_iC{5zt6?)|~GM
z39Y<+g(r8%SbBgYLcGGSSru0i;J)3lGCNY9^UtOyst^GpH6k--sv^T8=y6%a?dzhA
z-aT~NCrE-a_fN0TU03bhc{}EZ%_^#`<gbSYyD(vO?fT{`)zZ@W*6WvV#a~;Ag%7&W
z1PuGRwW_Ds@AT%$i)<sFn&=-nC{pdn$_LS1xyLc`vV)Du;k!j<s8kMo^xn32o2>Z3
zu!Npscm{y&n!&H)Kxhlr<AIUa`n<cCw!EUsEB`@H4#eofS)-KkbFJHAA!EnQGSO$(
z<~kZ8N}qx5Z|vQn&l{Wsmny#+C<Y0qUN=)F(U;yW2A)!l7;B8ds>!`~cQS$PE(pZ3
z_KMv+SOW79>KPs6mc}pb^+7wqf!c57LAnS40s0V`eWxWb3u)a?f<ddD{J)9b4x=*D
z`e)(q_9LXwSRufWT@%-yb@)F(JC1)@?dblUKqn5!=5g9v=DT_7k=T4c4!4<P*1fo*
zb^AqfvQXLfji<j%0b&<9v<e^wi@DF*Z>E~stkS>>$xKrTxiNC5XytgCnwuVrN=Rs@
zx`&Q%Gr^ILGLpt58qo?NB8M_QUHs*YI&yx;F6%TLx9aDu9bfHC$-iafad=VvE$CQe
zg&?4SS$jryT7mX4ldE=rwA`1I<Loc!`sJBE1=38`pEAFc;&c0oWQoqd(?>{gC-Mg(
zCLf8`hJheD-D2PK3SRSN)aMu6khsp`+H7wWKmW&)_cz=X25L1L!@-NKn%Boj%oPUf
zOKj0U<7r1%(#(;HI9l>sHi206A-J~Mq7_)!2U&p-YpZ9%9K+6<1U6->D!1H^TZpBp
z(Ig`UMq=U%#IosUIdFNYYE95ZSznhNxt=W5(}B~2BLFTnn6$RW6|yVeoT`ED$<BdV
z^~5W|^`3<CoVugLg&{pjx$UQx$-FmIn5G<Ga*5>M53jX*R>qDns5kvf&Y}*^_@fB|
z8UZMhV|m#8mCu)JDEU?2m&Dw7yj6Q5m$JQk!aoGm6K~0$#NxS7P82z$j{T9KVkqT^
zc}nJ0jd#00XNDT;?M4l7uV%}@L3aJdSt$r*(%LPp-HSJVz6Wx4d79sMc*Ao0^(HR#
zVi4_++>0;S|CSs^^PxJw4VZ2kRRPe>6dU(KgQz57R)OHQRrxAml{)^iJnEn^*oJ-s
zsltSsxVuYU^6y=d%vJkmKNboklR9_sLOTV{@G0q|*C&G#I}d28Xj;?0LHzty*a#`E
zCwb)aM@q;jLZ;sH;p4j#8SX)1YXGqgyAeF;y0PgqBtF(I|BlmJ&pmIaqj9=c!dCn*
ziYD_^hnB4N#xzr_OO)?0lRmV~`jcpFaCyT{z+unOAoOdG3)NW`%Of9NBHOV^aBnal
zeE=+dV6iU8f2<*Wl6B}I7)O@}R%epB#RLnA5IQIp&I@HS7d#2;Zip1GNi~6yp0EWn
z3Q245elvu$>hm6R%V>u=hY0>&4?2&~fk#M4=Bx-gudtuaM<T9MYx*EF8HSk9xP3RU
z{TN3J(AGzq{Lyu6@*yB9l~M<eK%gh_*lglH)&1rog&JbHv$;_U29WjbP3n{dq2j3q
zM3ii$^LiKdCfzbdvyYKap4u?zmmKTI98p}rdwdRs2!v-K*Hkr&6+wME1whoY49OkU
z!LbpdwYLu!EH^!LG*NVr7uMl#&q0$(vwq&lgua}tJpmzz9X-o{;lNGaZ*V~c@x|lw
zaPWDl3o5{w0{Jz-m_Y7FU9)g_B>Q)&Oh2OutErC&Fr<huMU+=dHJtgLdBwXvm4SAv
z62BqQexLl~f^KwS3&^U?reeF!gGqO~!f^;PGL=$yl-pQ4Ia*Yi7U=$@j+EwveKBC|
zcp6$~98w1Udi~cxGL#AC)N{;m%1w(mG1s#JH%P&{wrt`|Da~(_rFA-4ZZm&{(s{pW
z0*h>;DDW{%12P3c71OCg(er!Gk`&)<i^guO_2t{vlv2<dBxMsl${G?zLsn-q?FvLQ
zuH5+EmT~BI@<GSl1JJqS)g`NZXj0<;K)Pg>6OcZp`+}l@6Vh6qQFH$1LiK~8-}u+5
zpc#bOpHU;B!KE9<y-(ge-_)j|3Q=Nco8u^PN$L>W?_6RR2}~;Im-fc0kPxX4+PB8G
z8Z%SD`_M}gG9xZAMO(xV5`Y#+pg6YPQcko(K>L6#=^@~s$TWV3@zK_cM&$frC@U}>
zLL~Zq{Q*)(i<yj&`~=Ov_^#jM10pr@k5+z3XCT7M$wO}(HEHHR*rwljaCnDB%m1^n
ziM6>47U{070^jDLhxqxB`;}jM%=kJJ_G=@_dCtS}<?T<nVZvPfs};)<+6bQq&VG?!
zz$~Yrwi*3Q+fW7B{?|YR5FsHXL10Z@XxJc?cI(J9sh(fGY{kOCAEMkrVh&-nGEFw_
zAR&ysV$SeLM00bzgucgX5Y*=5rmSR(dR50m)R3jTV8i@Ppk8+FW;qUAhd7nKOYb^j
z-wUyq8wZUTt~YuVN>idO({?8X-@o16!a{u9K(?DecS)YfFk(|#T(5yv;>SIaThh!(
zj%)yr=f{ND8_kqjwp)tO&ULAKHl7AK^umCY(><#mDrMt|Skl!^hUY@VOx9RktSN(2
zM*|Ig9-DoK9Kh>(pnUV1x4-g+sdCQu9#idSYF@*(>7hd*9SF?E7n9#GrJLgZ2r)mx
z-Te~J($xO(>ZlqWcZbqFa4jP+Pv{mBA^)SZLn;k9^2e7c)7hGjSw@_}n%0?D+v|#v
zP%Y)?GtMEg`(7G?0-PQ_4N}Wn-<M=&Ux{{+jXTIrp6=x7$|aG%S(l#fv&S?H9}EY5
z;O}_QO657%NOf^))rU#zd>cEOsC6w<UbzEF0%UfoYO1pz1P1>$Cu=*6VmN6m`I}K7
zhtUq2<%cK;qKq&BFSJ~(76n+{ihVn`fi!SiFNI}M#((>OE+DI<&NnM@B*Dkolloe^
z<;Eefpsl>f5ry5hbXsvbETIQY6HpCGJnrxJeW&j~P@;ccCNc&_Yu2K<tLR}Hh>vY?
z7tN1Huw2~6bP5mk0cW);F1$z>L|3bT_4$cGAK|zzRBSsTJV~`Ki0XGZ^=G>laWh6U
zXH|4o?o)-Awz%8?G2B)mp}L3+!qySGm}LpA3W*cfGtW(x@WGkQY2&Jux%a$^J_TVs
z45hPjo(6$G3uVqAeah<)mb7z01#55v0%Hvxq{Sun?m4-Ke&^2dxU$P~T6_5U_(Jzh
z9OE?FVZZ7%I*~ZR`@rgtPsTb*qcf<~@27xaZ<^HlhtG}kgp+xfo9UPUW=-6w+s2Cw
zy_!`?^_ShJzo4@JwMC1r8?J?fF+3-b%jW2CQBgwrp};L|_zDtYA~+}Tk#1IZPcNP)
zq-b4f(?lDhwbF@@==hf$63AF!jj2SuZ_^?cHtps1+6Te;NnU{jpq)%8&$1ewo-pa=
zmm!*JKXm)@b>%+RuralvVFi0*bTK<FOO?53*_Gcv-{G$|z@G4TGY|x!R%CTCXogHr
zdHKc){C#q+hz<vX$%kH!z1h%&Fa10BAyFJJh}ny^P3o~|qF1DNRTo#OY3B5bpU3{n
zw+db>I+w@~%QO%ds+}-Mj1W`dK&T*$a<-y<3TxwB68nc7G82|1(()N5{*6#NLxa%|
zrQK%o-5M9j7u(%cU-9$1^Q1XmAx|;^0<A7Cl;Q_}cceB#?pef9hGdu7+$aBOe@j0{
zcZV|(6uJZ(u0Q_5!SR9){9+|poD_xwJa<pdWu9vc>-lr^*6H`O$(@aM<;yeucLdl&
zbq)kdKi_fwVS2(8a8->Ktg$c=XvsPQZNVn$kph~MOkmc6kgmNC(toG&aOFRX<Bok0
z2{ZmAPND(0?5}-p0(`!Of9%Bdt|5tJ`%P^<(VKxotgUdcRWLqamvp~M>SQ8i;GH|7
z#q9@Dp9}Kapn&U~%@l*!U!$4q@erII(CXqXFt)WBY2F%2s%&v21=rk(ED{9LVWDz4
zh(rB0zyF5-f?D9X=r?*7(ScB6`eAH9nrKCcOur+~7p9%LHxJgtn2i-`OGAom*-54h
zJmsw$GOd26BpRlRfy_W6opPVV+)tC-CUHg+zD{dwO)ZkwNf^ypB@Aj<K8DMs&mQxz
zUAn+m{mp}fW@O$Wmn0%7utHM&zV^sEay@rVD076~Eh2ivvbRL*TdDMV*@(V-8j!!Y
zsbA$HL&c(1y?yn+hbQ`p`;4%<Xtxp3VZ22}q^feJ|3zz9n`BqyG9c4+I@=!Yr0iOh
z<on}r_{GH8i;E4HgvemUdQ2i_*7C@ZY!`weirar-zn~@Fa?DDTD|m!QMT9)um(kSt
zSN@2Vnh%=82->xs*V5gPxwZ*3Z<3;%rNxFoUskb^eV5x<#!GRj)PUS~UC?$K3o`zU
zg3_cm3X4BAGS!dnd}>J4HQ#eJ(HbUaUH0ulBKC`3U!NlgPvEI_*-Ks#gzFAcuYV>H
z{==f{tVHfJ5RmVs*(si5(q3X2v%fD#^|K0@fGC-ke7z8c1=3w7g+HQIk$cU9;j+U|
z71uu;ZD}YC>guBAIz!?^V^)SKb<#`s?FBV}Kys;Q-R@>FkRUH1N<-mRPjoz9B%we?
z1gUUFdRlAs3~5M}er;Q7uN_$tCz?WV5b+pfwNwZRD7{?_=iBI_G&xk6y=mdXjL&kZ
zv57-^;=&vA077rXl4?U-A_P1U6cAt1rNeuZJIfUtPh%$2;3~}nb;+Y>hryh6GH8&>
zBhpf&&qD4YtpeXb!BMu*1OdsbMq&^senN!TF-HkJT)F+rE4T%QZrZK1<YxCGsr5yP
zA*{PTEv>GpKfQvt7zlu5u=^zl8Z6k`Y9-*-v4Iqf$lq*((aEMt>pafQWY#Q+SStQl
z>FuHyD*l<l@f`BeKl-t;z$89x;Y9^m5&7i2UsgF8fS<pnv2`Tt(@Om$v}<Y$-F%K@
z9-tuQ?m8h<qf0pj=V<<K@KvIe|0A|b2KhUWR-#-ls4-@R`0s=rUpLO+U?@G<Y8Mg;
zWz4ePfebZ$I%5_>htGyHBycocOeKB$yKq*|4GFRc92WpT=FlQ{W&cu-Z!=*+c_%tl
zC{R$udc5sjQe6{bs|ki+QKNTLh$01L5|DrAKr4eyY={;-c@fk!)7$^H*U)EIwQ{2C
z1*%l7bIQWhMss0#S1{hw^FMGB+TPuk!L!ln*{xan^1XB;Ph8-ZXmL~DXAhYsIsE+A
z5z1Zn^S!Mgm3Fux`xnK(Z%R2MFnvV~#3CfNtZctdg{PnUi^rLlG*s4sM@JZvPwthu
z)6bEu{@txoLdN7aGKeXgmx>7lZ>3wiHTz9&Z#N?QV8d9_J_RO^T*J@uQ%}n20Y*J-
z09O(Z;P^+97t4xWN0s#!6xz)n5bC3C`J75Z{LqDaEBVO<CF;vP5)#Q7t%uQ_1moxH
zmOuB3TKshYiNP3h(;r{R4DODzv^3T~@Z(}aA%Pv!5k_hf*W-G93<)c#pTu2yd%ePx
z)(r6JIP$o&B!d)+4wJJO<$0$f2KXBwM_ag^zG<x&yrXHSf%nsQG#I+h5STjao%*ER
zL*b=XZKi?*qjEjip+4)h`c&*PZ(pgk5O0Vd3|wVw1O?H$GTp*C&LoY!qx=_R|4o5*
zsb0xO<yrXquUWqO0wjH40U13BtUYrN<N_osI_uL}TCyR&`zBg+6A;M5>!_TQ7zL6g
z|B`t{fBg2d1W;mWNTg9|W55I%tP=jk|FN5MHl|$+cmC~K;aAHlS#4pPHsQ?+Nq!Ln
z#H(u3sdYKHYl+faK^-jb?SZk_F#L1h=r_8?)w+JqO%DOJ(0%JgEWZhu%AbZ3)E}oK
zt>r};qSicFF}xCrPxj_3?w?$3{arE%_7YTIQ@X_kE^*SAUSDyyYOHdzWR_V*VHJ2D
zF(Kpt5u7~?>CAQ;oKO&`#d^{x>PeFHjAg~#9&GlSh!}W6j;xc#gE_&lJz;>`nC@MB
zgVI@hmWjPeX^*NSZqPW`8uUT)v4i~x<oAp0Cvm!`7p`6;15H{NQxK#+d2D)nB$tY6
zzuoBSDGD0EK0k^bdDNZxAtTdhmt*SI6HcUeZ@yyPzUk=y#h#oyp_?xg#ZJn-zWQ|G
z&%)WuE7J_jz*_LpUV)_w4Q}@#fl~VTJWQ96+-OSxbzc(pjlC;rqlj~)SpD?Z!lj*1
z4cu3)8Z8`8J*pK_Y0MgZCzPt?uYhvS{=Ga|*&kj|gX(g`Q4=1^bk4lr@^e60We}eN
za=mrv>Xre|>l4X{ul~K#g;w>w1(VYf{%7^>{OJxjxToJ~2C;7UlbfgfZkr<+%??4c
zQj4yB%2H70H7CE-$HkkimH%TCe$|21hcXp)^1+V#ns`ETvHfBdR+qp0o93BomZrwD
z-6jOD`h&X>KbFdMOcZpQ75gza@)A!yJ%&TVQuh;GL@62cDfYAilCyz?z{wB3*w42x
z3Eii6<bfxHFp{4xC2g5D_EByYzKdgh{j0!O4Zg(SzixR2VNk7iJz5XXi_}ts1#tSl
zZzwWb?z>$@(xBfoB3<yl=z9H{!?*#7BnLkk@E53DDm-AV`(%D$^2#D!;U<7Ip8`=W
zT9w8yNsycIeKTHN96b2&(so|)Q>}ro$K#aBl{iAC4Bel@e64F8wpmfYQwClMS3rK8
zR&RZ>!4R9te&IyIAAbLFiHZ09^lwT~@LS}_x!ldk&vr^Y-_2QWKcTjdW!^Bi=LE8N
z@M(y0W*D?xjpBnzvnW7t5Eu+%R%=rDedaRMqy1E<{FLiLI?iqD2I#>#(Gw1<*$3-J
zQGh<<mGMh%-aq!7zMXp%k)(jDr_KQR$3>iY=Ni`=clLwKR(9G6jx~_;^oVu$I^Whg
zI54h`$aev_W1?mpST`^BuE5E@v<#7*evRd6l6&l8H;~0YwE`{=gAzkQ82uo<RRvU2
zuZ*Pf`(18X5q!T6tF&*CvDU*OXuFvAs$+9DE&IXP9*`5ooe@CdfQcIo8CN6gh%o@C
z#gn2hcX6*w^dPk1Ei1o?(rbmCTI(DA|4k!Q8oT<XdKQDvmN}Fx@k?Z!ie5%qXDDmf
zETpBK8V_Xlv1POq<hF0)K%Y!K##8VdTeS4*+RF%l>!beJpNsTb4~N$Qub&w6t;uL-
z7`|B?cnc*2=H0<%fqV`uyX%_pwdE-}s9IQBHm9vp9Uq;U%884AXs*8p9{l7B?XWKS
zLW(E<90WOV1KTCj(dj=~fZ<BWE&<6u6)p|khzqfO2%g6?2k+P^oPO7ZiM>9Y{mO<K
z_S62#RkU-{8V+JaiyvaNcReYXWSz^IPGjIH1!x~(co8lxHCWoByQpLYCE&Alv^j)J
z!m4edQd&sRIuMLK;}F&Kn_~;RCv{$FRnfGl)dhX{e*-HM!dg^6!khh~KXtyiwH}dX
zk+t*~O<*@u)DdqDw0k*`S%DTz&l}Pe-2t+29>kKugE<Tft-&2c(9V{WNv#2fSAn0q
zlQzB|@ivqr?N{X+{y101UaQE1BuQXNdFUZ`&3Rkr9eSj7juZi+GK|n3h3=>L_+xD2
z2El*s?Hi7fkh-~{k4d{@NVOAxE+cbc<M3&9dt#`Z;nXw4L=;Kmlt^c6${>c{_T)^q
zWId1AdtxOE`@(o_9*(7~tgs*EuH<FqJ?4R5dhot_;Y%oQ$-tqt=Sfc2h|QeTed<Y@
zVIU#9pQYmPyFpYi+5)ssfTARa6=gj65(Sv~m*ic6K{D%N)h<83{7UaJoEc?XViIz>
zj;^8XsT7Yw4i!F}sRWVe@!FHS?13p9UjpPERPKY-$&}7t<S@J>P~!4+RZ3eX#FC;e
z=!A*Fk;?yT+7geWAF7CMv{f`+9|E?aqgwNXOvPzzk4Q@Sk2VDQh3~h>^f}w^UxmP3
znqYu_T2i||=)wKz9LtFMXq9|xFCp{wMB;{LLKAOe)dqiQjfJ(;>iGk!N;ob`nx3Z)
zy+E!u;cVMbN34C;7rSH8Y|8#CHO#W)Qnm?o?sww*%V|T4C+{O1G{e-{PN+~7jPM4n
zu7p&h$Ea!mw1|@^UWL2`w--^|Z%iZ!%!@@TVkCV>&@vk2PPCIcKW|vg*vwryV;(Re
zLXaapmDncFUyEvF9eBv04s+wiErCSh5BE4Ex6-m1bt@Lkd8wyz3))eJ2!w)YrgI?Q
zKUN>k?@r2_(%xR@bA19B$H0nIk70V!-VKDmaRvNAEkR~G-82d>Z;pl2k^a*vXi7Z}
zEUgKy`b9$)+=sK*<NEop${2%Tk?V$JPRB)o8&gBDB`moTvPt5$s)q1cLcQC5L~Og8
zu0Vq*=8jTu8yu?_k=PK5#Lq@Qed)&-a19?fegFkkr1}!rY3b;(8en??R(m+P>S%T}
zfHMSqm`LRFKZWIuBYnDf6yLn1-oY{wCM3{1xzFx%E&{*hTDqapEwKZ8HUB8-cy>zr
zTVS{4l{&t^i@v>amN0umDJg!0nuG~^bQp#E&SkA@7x4Fd0iy@7h9>-X2yaG0Yl?W+
z-n<Nw^+H)jdl?=Z;Z3=|%4=g+3IjH-&XlkVBRYFDbCj!^r~}~tGq8w^MPV$tKuYkc
zB6+;UAJ4#v8l0m`Kd+y#Z+U$X!ZgZu8yi(>;QUQ8F1^NNHY!xOTm-2_yS3Z*g^EEe
zQD=LD2FBYsCS)yt!U{-+rrDZ8cN%0e9Cd2rfK;6pcpGOgJ>O@nsOx4ez#KV*)6aQf
zvG%^Ck2=Btxe4w!d3{n$<@I0zv!R}H-;TEgIx>B-cR6jSa)&hb7j3qashv>jVpsp3
zo=~W*F8dl6m0nh9{TX~Dq6hD|7L5!JfA_C6B;e4qrj%YMje2vHcd#|1inr^$cK71s
zGcwVTcvLK5NpX;tLp1`o6==LoASS~imM&4DqHHDCGh0B%W=OBm<}><GD=fecn<-3G
zhsz#QAbpBv(ByF5C|5sF=W#kmhQi~Ip|Ws|hUFD6p4y1IKkswi^x@4p3Dt+Do$lr)
z+bWZ#Ja|#2Qlq+_K%U^8`KqCUq#2tJpL|Cf$J*8vlQ;8s8GtQW($BcEB`0W&lk(o`
z(U^hHd<dPWKH8W5eLPlNqimnL1f~x=4WfS7WVnLM&PGQtT8oE#*YeZ8VWA~A-+Ej>
z)ZAC25#30CRcTsBg!#!8Q17T!<OS<zsP;#5sKe~*5)lBS$+uvd#ZaY*y1QXG7#+0B
zIPp2#Ko|4`*>KiZ#-NS}^MsymauH#m^CY3r7p!1HC8b1On5Vh~QCE@@*g@W7a2|N<
z$>L85)5f+!P?XWB362ll&9CEYQ+6pDSY2MDK^NFJjWsYj69*7NrdaRMVlYuh@&bT=
z2m;hwD1|cTgj1NH^;P#hEY8)*MkxQ^SS)f%I#kEy?_oBRPB)x_KI`JFkXeO9^Q?#~
z1nqopm|&sl+{-i~-1%6b-zPKwc~3?jk5n}}kAj091vL}~p-=mhwM1RF6>OY$9lf~q
z2iJu3FNIBHci3(ZPCLKT^V)vOthuFoc=Ml)%9C%M?{@q=_cnXSb#-8C6|~y};MsB|
zKS+1Iy9K?HVfEH{TwTAw>|(v1Hk-t;axe_$Xro*I-FLlyH;CusPV0)>f~oT_2B^Ho
zAS-iEH{i&vQcqmocHR@<d8@If1z-#T)_#h7LKI<zBkyc<rY5RBy;vYLZ$;K>NOnJ8
ze0-xj1hcqbu5U;Zcei_5-EskNq7gBqr_*hoCnBjfmFhsQq%?V`o8bV7ta-C<t&aMt
z<Udv(t%3T3Z6dt5wQerpiATs;3$bT<Z#T?TV)Pp822YBlV!pZW^@9A`=D>$xi809h
zt7WlUK<(Y??ijw*1F-&SPneqDmV#aC0Bqn`6U0`)S&*8a>Ub*14dl0{;8T*E$%)E*
zVQUzPU^qsE&XY>_Gg9jQw$N&C%bl2s&;z<f7IUE{+PMV`zP!fSh%KCxsLLpGcoBtp
zJe!J#;hUXq9uYKA-ehEaBua!z+)#wegH~|nI8Yo!>O83+Xx4Y3CWg|HoWY+NQ5QJ2
zo*g}$sb5TOs+OMPUpd8#Eq{E+^a?p!gis5hzw0}_BiXgf)~p9aLJvOy=qp*Yn~qd6
znyuZ?)Ra(oU$b3mvtRC)m<o0MSlCq!iCdVy_%R!_M2m!hBMCzk46Ct*l@?R<f9DI}
zQCDACviyHcon=&9(Xy>^4esueU_pXwa1ZY8+PJ$0x8MO1+#7cd?(R--cbB(w&pmfM
ze)eFDhVHd%Rn7TT6?0_4yXp!28)ZRP|96}X%yO>yePuDo7=%D`NJs$K*2=<Gj4QY%
zz^`~<nK%7f9cjphpvx|{kLBU4hw8=j{PQ@Y;cxPpsO&AiEYqMQ6+#DmDLC%@Z}Zym
z<se%tn~I0aGvOI%BbeaSJ7syVf+)3$hpD>v>EI&6okQo^id^*U8|I?!wS%LgymRVE
z^@k1;mCTOFI2!`|3>Wo6$>AEsO%kD*Fgs_dYNv>jL~t7e735Hgyl$?Tc8Zv(<=DwF
zFh`tLu<#_6w#iyB1P?0c-l)YP@=QFCF`@oMe$o<w)TwnMyms|F@ZiRsFk9I;xaC{e
zks~<l*Td;wMvkH6i7kJ@(`xTyStcCj-q42qxc}peLI1A0&&bF~BRGw~#ha85)vIZ%
z#OKXNDBgaz&Pr1)AH<45Ikg1^JY<x=kd{46i=|RI3EjvpX+I*<e}uU`%-@~8G9>j9
z$cgiJGp<j4^JUUI-!6P#bny6Msd6j`bDO1F;@3Qb)pfiJ7_yiM_=1l#iR(W%8BA=a
zveF2Ip2Yfxjn6n!Xu&sP95Cb=jFwP6hzFn3UZ8EJxQ>Jk8>{hkZvRZSNrp1gmIg5Z
z10?6dzLcg&88tf~g%)=&=H6^{$t;|HBDc!E5+E8O3~Bp5^!z-cyg)W6Z6Rh$lRI1%
zSaIlQQ-*cVnZNWC`ukqIv%QMcTVQ>@kB3hBd1gH?E^0>#YB$E>8Z)rJQPFRnz-%va
zM5*qezO+l{xtR3-Mp@y}ra~O#Mj^NDRpucQy_4nGiN?+ZQjY-5SZ*wJ4(8&YBN&3x
zIrZbn1E@z{l6^1(%&Twd5LKUX3E!SLzE8Xp2{+ymf~c=VB+4HO#g>Gy;$|$C_HQ(K
zbCk+DiYCsHA0|4FFR-Oa_Y-LLNEU~?b`374vtxWbeONBn%jZES8{1g!W3-S;Are!R
zwH9e<0(pB>4%2M1NVFoU@`YO_vJu&wWGbz1`#?u21wx1(`^Y_;iy@~?`#cdd*N%5i
zCrm{w+`Zo}L*uj5m^f%4E8)VUEUxYGl+dQAW3$>ED!%a%o|x_(h*_%0umg?2!9uCQ
zouEA&J0ACo7ot-ZAw8RIGFG`+ftN(z#2MkOugokyD?0ytb&iIcs1E16!-X8RfwU7z
ziE+*pEYlbo!TCt_lv)l>Lj#j{Eh`3D5>h1^kUO7JsVjI;-KwzfVrI99FL}=jLAl#T
zgvKD3(w^bg97d7j@`I`8`BMkZZu4+tBYs40hw9pUY$ZVz^8fzcI@X@Ob(i<9dcgfL
z|A4c*r|2<7-tGy*sV~@4ln{N=kshVcU&G9?5#3HI*!XMd&L}(>M|2Pe&DeIWaUK|@
z(N-Y@`G8rWhNI^pY9?|;&hv^0l_f1X_-sLO_i7_j`cqt`Uvc6wg{p9z$6_feuntT{
zVWbYK!DY}NtNhRx%z2k!V0Gz7Ns+pN)};gAaQRp*;5t2E9%zAb(g9dg6Ma9`hNHvi
z^U{r2$I@2YpxJqEwnyGfc)Z30PFjzcH%8$A3RTiq5;_R{W|;N6s`R+jIY)IkoUr@<
zn#+vX(CJf%i{j(A?hV&!5caKTJhmfNqWL{DG3+o%%+5w3_QpRL9?fv#zVCib+^RhO
zKyy?o>*Y2(S(_JzNOd#nH8HNU!OfkJ8ly@rBLbzr*0{u#e&?VN26}D<vpd{=Bk_*&
zTJ)anNtMm|S+jd}I5jQKRVz*ID(}E_qUD&;mlEAPxN;*vkw;oQ%dr`saG&@%5(UAn
z=dkO-0NrA}bOB!34=qEC>|M;|3!}|)q&_hk(dX*%UKq{mrm6S=tvE^ex#7TX{R)pa
zaBaY7?YD<lOKsw3j*6CWbG^S;5~@(#n0HQB5wcU7xd@~_$SER?Da~1S`<Tjt>FTy?
zYj!P0lh*0(h7525(FZEe(j=FW6&0D-LibO4rMq!4k(RArUO%)`%FzCtjv%CrhRny?
zaeny$KS?n%EF4Dv!%q-TJTI_fL(|gV71c_MEvs^*K&xEpg+QE}WX)iJ0WHmPuE|5-
z+{eJNx~}bnzxexryz%gv_x+tV3<z`Z$A^dm2Mp<;GSZr-mlgQ?$r@9Aa+I)r!`hW<
zvLz|uf!}8HT7;oPT`=tlRgQ|--YmAOe?#Vi!W;Qi2rgzqxk@e@WO`;BgdV-sp*E!!
zRnpo@rxCQ@LEcAn?nXj2L!h$FzR7Y16fy(#-(Cel{7wrD80CbrruB=`vlcZPe!}bh
z=MaNWf0=B(H3GOEOMY>Egf7<*h@hhjZS(ird0g|q9*giT$M^KDkWhbPGvz-gTkqcb
zDK}q4y(uFU!AD1+*V~K*Y`0T_ez5M+T-N+Ev7-K7-0w3F`jA8Nh}Xz?X|%zB-}YkT
zq!-I9ENSRpf0{PzsYK<Wruv^BW`4>*NQi!5Sq#&rj38WBf!&vv{qb!;v+eL3k~`}M
z0ILv(h5B3BO(rq)O(FM3s`?g|$7sP$7Q@AyjmfiAG@pbfFR%iKQAjqE0qkWz6)l|0
zoYT1&G#Nih*PA%5eT%Z<{auD~9^8VzIzTbci6x~?cm7nF&{aSBad$O&F|=z5^@?WU
ze|{C!3P}?Fl<R}cKG*r8)y<Q4U;6cVFE^28@KpFy)w~?lZAcx6w6DPe)}tsjvo*T(
zm{|=`(f(6WHj(f$9vYP4v?T^C<VPWRjVmRmg=9eig08GA-LI>#+$x4<>wy&z(PV{m
zY;|v=#7+J+?}Xe|Yb@L&->r#>D-dWVd^Nik;VWSDQ{;<|oesU7Nza@#*I+U>cMsoe
zw0}1tUp&L%LEDdAM^qM6AAh@jI>cUXIu|(lc+E>5X^5!YQHHCrH+^@sYP@}hl6TAK
zO^2?eI_?P}xmt;I-`8?$0Wq4zQq<3`n-a*`h5-Rf*Dxpj+%0-8MpSr1@p_!DR>^Wx
zO6NQB_^h6a?p~5#AUA##=R1-T$ffZcSfy3cB{RRh)KR?l6$yR{C5A<W?D+N(4~DXE
zoT4}<vFXA?A6M~AQ>E+`Ws1nNR7GeSsVzk@Hw?&QDRSs!`2G%9Kz_F5sQVP&q%$}P
zC;w=^srK^ufbi?Bganth*2Da5@;YL&%<um%pCVO+>JN|&`(6FxhGXpI*36*)oaS0a
zG0d6M^@do_KH4jguTrTu)z$*?qZ<)j`4Z3@`z@+#RZ`Bh0<F7&Cj@o^{vlT)YMN1f
zC%6b&Q%LB$f5!*oSD(&bL<FBED?QhI5JVsyT&hEp{51zP@svlCYHL(pP~>@MZf@H{
z6n!v6%6b-C(6;{O6kH-_S~<Kg2-={HbP@TkoCv71(~g=aZAM9qZZwukEEl7hGJ0jV
zp=^-1VjF1KS=z?X8keF>;|Z$RW_ZMpcfC2fJA!n~424q!G#gp^lX2tt_z0H%LTORH
zt_(<f)aX>V^mAB?7fsUR(h*-)WO}N+5~?n{4zdIwbV=Ljm+WRAPj57~nV0!z>Xt=o
z#)4n|ild(S4YAY^+(M~H96ox+rWb!s(9ImZXsuX%RTg|FRUaQQk$u61dIgP{^mHa?
zDjN{KwmjtB3q3ZUNNv%9uA`=lRH!#P8f|E=wq_vTg4QR5-IB2}C&H<W;?DigmLK<-
z46tC(I*A}wI{gE5pGl`6P)NVE&5{(|sWqc5$HRr_mmu^3AsO+=ADTjgUuxFw9P4`X
zE4?vOQtKP?wng1uZ+p!5oT<nemY7~Y7c7fC{gDW7V;)Dvau#cijbHWPn9Y&%3T3im
zss<8SDX(kZZ8B@oc`^`1YqB%dP9%K9PhNPHR>%;2o}@)dJSxlEj#HQz)DehxP?;+H
zz_%c#R8gMvbySZ*{kI0=zAbq|kGsuk_Cthbq7JytM_G6^X?o(hNxBQv%CBEOB@6$5
z3b_M%U{OFgy4VJ^juJ7V_u$*L9)varHX?FI6>MSdXqFWvkEk)wQ8)7Mit`>7b1>`!
z)_!7i{(4*-oBO+~sbx&{8mHnvftI^4%YR39Z@5y8Z!$7W*M~^zMAR)htdN%2c<8-R
z)1&2#_B%`4iaUecXyY9(P@uB1+U*GGqfqM4IkJx|FiM^e=MF|fD_&RAL+|%!5QLdb
zz$J-Eg#KNrY`0-v&*S|9Rd;AW>h;8agA@43VO&V1&o=!0_qDQ~oo$Ypzju*jzNmC<
zc+HBfn7jV%)FE6!^T2mY#WbqK5`XhP6xP;}x!(fTwwd6>hzv6G)ktFSy)U1cTY{a1
z%<*EnNcg@D+=Cx|eeYSOr);d59V0Lem|U;sl+CK_Em@eH$yhHhh$1bY4ku8b473H}
zu1(+`?)P6qQ45oe7TA4j0&!8q_ultR|1xvgBT|aOH29c(<dnj<WNahVcxhogi2i2S
zmrN-6^he9%iXD+e<(7Uv((sHQvn}Chyf^rO$hCOx4)SKI!e^xBL<GI`PA@#x4`C#r
z#4?C70ja!6Io8N>KKaGB3=&-oB|R#eZsoWeiJa%kF?(HddUe~a^l(EU&}>t_uhKEM
z!QNlAEb~NYgX+3bLztO#nw0gCCg@4->t`7BS?~#j+A(gQBo8ptr@&s+x~<cK-Q*a_
z)KnWL)Pa(PC}8Iv)Ia%vNnCVCVOa-r*A^B(h4vd6B)5#m4q=IlKiX@4S~h!E@OvsW
zY7J6gv;63-_(z-<Y1!}p;wal@+*QyXkRs&9)5v{^xH!r#N4qO=@IO4>ze-U3K?A4r
zH1vL5tuZvHvp4Hq!xQ|t`KFO9#;buk>v*33gd@%E8#zsusbN@#Xqwu?)i-a8dEhEN
z*5~)(pm5gi`Tm~JCXX58Rw5^@040L<pk@e2L1$eXKZP?Ub^0?&U(-@}>xLZ0l#{tq
z4Ge4y<WfXVV%dMjuwwM{#b|5z5IW@x;a-2(f2!|@cR|B$JN0enuIzY$2hS2}h_C-r
zH#JbsYQ1{2CYKyNSL2DyZ4QgWpKl#+jQhQ@hRQIDIgMvwJXL?H!HlXptqB?3FvM3#
z>*2IQnAz$OuWP~9^%+Qa%fb&z6i72lPZV`?T@+eVSfO1QGfZebT|Xb%1oJ#Z!JcZR
zqB;jSF-xHmot>Ccdoz!-hYy?aVDa3dK=H=iw2!ach!)(Jd^#{$`FIL?tX5x<H+c9!
zcV;&j;ho%T8B~~2IT94mj~RMBDxx5`oY1?_k1mw=W$1hZX8pYM+bRmF6Q8`nn)peN
z(6i5s{3#rE8S`1UdXw^B>~k&h!_$uioX6wRzc&|CoM{~yxS!C942UJBGqI{pHJ#3E
z{l9#t^1}l@N$0C6*}<1vnw+MxIJ@xQp6(gr>%nG|6$oM1t2)x8SM5_Z8eCSv9jJv;
zr(+7xoAvghQHTw(D$fw{0`^yLj|uF~m9(ziE*rMLJ=-NxluRBG=ZP#au%Qegc-5M}
zCOhRx{NLc7S<o^h2r3Vv?l-HL?mHo5>Iatks%kZmm@`5mQ)b9ci>Fknl`&=MUDeGc
zB|Lasqj0JbRJj#i3zPEHl??r3#l?M|VD%8ulB!f_Demu%{l-;w!Iw<kv!^Mq?ANLQ
z-LmAiF(LF>cjcG{jbqDOvGvcHbzqAik1avtW`GYq;^~af!+;U&u>J4@lc3J>!h^Gb
zhOI+dM@&g9k$Rn{E=w<ch=WxpZ8;a~H0V_@7Px62^#jkva>bNe#CnRKut2kw&0*xV
z!rAhLvYOJznKkIqf#i{zaO-lwLr-0pLW21IGT<ioFvS8P<YTf#d4I949d?hpopnyk
zf9d8}7Tg692)S0u_0%jbS|F(S<;AwnrqXC>gV||;iQIh+YQxJ;Q}nCEy5zTaB6N-d
zx&`C|{-6Mb9$zR6J)<)>8X$~d6EEqOo$kFqd$Y=hZ5qv>mmX$pkMqlKmznrX?Irf8
z=SFjuV;C(6M3Gxh!AN59U32k!9{!I+t1RVX_u;IZeQ?|d)1duNW7g{?uhYDr#6|oH
zBv6%*5JY854r}mVi3g|CvVcTCAbgxMzk+WhUvf_NinSFZn)*TezNSfYPQOyQA^rLy
z2opo9=OUY1<Qv3U_rSV4&MiJH*@!i1M%^83Pjz|g*pYALA$|%s(^+z{e?BhPn@kAb
zb>l{ZwKdOCmbmR8iy6o(px2Xkh=I{#l6qq{{A3_qy>ft#*_~zA;xy22=HaALZU2lD
zAU(!A$y4{T(BX_>g2Wh2%={QyHj9sUwif>1F$jH%?uIz%l!VZT%|5){J!h(gRVjgV
zTsT98asx!OdhK(3L}hw=zj^$sO^+8`lQd6#LbS2HV@8PyB)0<zF+B9FhM_Gzssaka
zg4?0xp&IoH_A5Zdrc7DRmxyfv1K#U;RSB)%Y`yM&9ng**vPL7A9KuVQ)P_o%ce0ez
zNAl19)<}1KcN;!$Z@o+E@}fDzHRk*X1y)6EOw>)q3}qn1$+`Y|zSuuiFhT#Y=S~Om
ztN7l!wrt~Ztc10;lJia|;2RlusPdtF@nk#s5jBGY{bAFJ9deGJ%I~ke_zf}=dg;l~
z+v1qS`g?can$k<Kiv?}s+p9{`G!_EcyWA2E_GP6T@Y4OnSKtyT*Dm_>y}H1Okq`3@
zC^Et-Mar)2RX$Qjtlk<J9&zLAnL5{D$U9nOiELB}Ow9<2;!V{pXUOPXkk_mP_G3!V
zo}T}e<1ZJpm$4TUC0{N!hjAm)(VfH=%US58<<0=k2A$24E+G5;NvImwzekI|oN-Rm
zz8Bvph9*GH`AADHi%N7E=R*EesmSV1a;kGKwfGmy-4#XquZ&<M-z)W@5Wjfu4-JNP
zaC&E3$cYnqD>1jio9r;%jOD|kvOi>FQt!gR){u0!qcz#m$Oi1tzfQM!rI|}WpCoYd
zF6eayo{}3@J3t3E+Pj<c5!fu1IhQo^c>a}0>|mQWZ`nqG-Gf4_9!*bbCQ!di<Kt^g
zMkuoRx}JxRvC_8uME-E9brgp-@eX;U*ZIFkNai)4s0tGS@qj;ZkZ3~~%j2!QzuBKb
znhge$G~H%@4qmR#Uim%bN6Y57pW$Z<&q=g;Q;Hhkq!Ap6>Ex8lHeQF`Qy5TC^YUgk
zBHa4pcpx8pLJ$_8kBUDF?g{(?^fw0|q6U&ER(CRu1-;VG;-tgPxk_bheQU#$jNc+K
zLDRzJN__Fd+b$oary)LMTpQr~L?pG%G$C&%UzbP@Oy8fLp1&lt`cHr#x~2y^cqQ(b
z1di%Un*=Uioy3csn@Z36Nbn&tJ3korpZGkvO|h8=#Nx(?8;3JY0ZkX3+>KqxnsBQJ
z*G>x0M@AoFcymFj4R#W)Ce|xxc2XbCPN+}9xn`q*1(MVqyfT+!bA*<H=iG(r?H{>Y
z2!^u5nQOG_IsVG=NGu1zJNBMK0T+K%+VV}$Y@tEH5i-g3=ierz5^g&tEA7PYZfsg3
z>%wl!(mr+^7%CeV5v@jlNhLYL<KNbjAo6{j=wh<<_OJ2BwXb*~_Lx(#JV*F?g=XO(
zmJ$pOUtNp({>sF$G>l_3CIR9iwecThOU8tJzf1C(G6=xRbi;WFIqJ$@K<B?1muW-^
zD5mh}70CB}M1MCgRIR8)N<4R~=8~<p;EqokPgs=$Ds&m9=a&L#&q8N^>S8w{M5S-A
z>n*=XH>Ur0oSZ5Z)Mvy+h;nGk;}+3RW|&B;aJJXXSc`u@{VYP;{JtUH9YL}fXG`tB
zVQt&$H{fTgQjL%ifEtWZ$7@QE0&=;0&9Sye4xrmxii&7e88~>fQh2R3r#Br_=i>2<
zoOG)Eep+g{QX<CgYNx?xtb;vrQt)3EAkQ-4vIl!(ax}-FIGNK1OXCP}!>K=a|G17N
zxvxbpy_5k7s>h^MQumXoqy!rT;t*y!PkoNso6k?_q(PQ=V6Leh<35=j1GWD<Aw8v3
zsFn=b=jPlTgP-yvr3QCAjuCHfKHOzqVz2Y^VkzxJgXMfNE_Ou}izn~8!|awgf|ufd
zD!sl&{Q5yX?VqN`^jeAl*v2e3=@s^g>*?F~Vy=8uWb49r!}pMrVO*stocT};5iBvl
z_X(&<#%Eq;^|MU)PzWckOcYe-eQcW&5T=bub+9w9X3>F~Pl_~Gg<Q!vHFEP{@WcB3
z&L`u1<_40X^YzU#uB*c4<f9}id%7Y6QpB3*YBlh7XHLz(J2c;i7iCE;fRiHy?%qda
z^acb3keKEX`VBu-91&F)`OK9*|M%Bc?IT7s1LBQio%O8rKXW#IrY1*+Y$G<})e`(c
zUjTubZnpEc%KuJ>&Di7vcj*ku7;-oiqCV#<Cl+>*b}74<9lbn{w;DZ!>;qK{U)bIn
zaNuDs(Hcda7A?{B`KHouv*cS}5%mRs;&jEBlyZqExz?Iz3K1j#SizTRiLI`#783hP
z-$jY=6v~MWlhUc;y%FZQDhC>=hVl%X{0zsUEa1$@AjN`2@0tcTT9KCi0)7y}31`ZM
zG|Ru6iqwscK<E|E6tVl8KRnua=r6VLs0n5w(Wc*CVoa?AeIcEGMx9)T6F9FfFz|Do
z$BF$6qCX_Pm{;*2eC2d56j<CXvWzB_6iZfYm-aj1#KY$8e<m~HISbH>1TM&kfP<x}
zY|fVH5o8QL$dBi^OHUpl5Zpp!w|#J$_X#>-=JV8(Hxz1vRE)*+wX$~Bs-Ms5xDZ-&
zV^r@Q`-286<>g%imJ<%An44C=%Q>fP{V~B@wctTX+o{TQn=OB^C^;3@8{cf&px71H
z@mF+IZvc1{i_fWbtu9U9S<y6xFELk;37KH&+#n3kIG~;{E7G*@KJN7#%S8PhJ=UPG
zbP-$q#)c>IFC!&eLeMY!S-c_$5f?SfLi%fSao*Uh{x>U!-x(;!17s~!tSuB5APXih
zo`Ct6a)K34{vM9MPR{@N@%wBG1!4LS@RLL4c6VI-NV!0ofAaTEn>+Q;jO7Bqtiwa(
z3Gr<9C7(8C|6jWZo}jkjXLRJIwy9?AO}j3X5br)+-nz+6rx9ZL_!fxpK>q+JL-;DJ
zD(Ip>ll2x=Ycg4$;UDCHs57|Hn2~n45mYQ<5+N*8TW!@C&Ihh|Q_z=sY3uLn49A(;
zO+GC2VmX5Xq_68oSKg$!-*Hwdr*<%C?MdZA>)Ub}z3ChgLR_M;YK5Z6DBw|+U((PC
zsb^eS3nN;Io5vejV&RB@GCO@o$)K@U;(kILnQDn$P%M{Qq8#p-<#6=aT@Wc-Go!FB
zgj{X^9`nmj1%bd-sM(*XD;YPO;gP;6>sQ75fVL7~KSO-|Fo*S}gPkfplasN3&y51<
z;sh{Av#rZh=jp2xWQwS@_VT~LN39E2t!p0rSeS@Ay<~c(d>j7ut@he<{?wt?73_q<
zb`+J$m-C=aO3eK53c{mP@UFrU{%eVms<Zd-F`|c#hV$*%{0LtFG|q9k1Xl2S9*K~^
z_V6eL^4vONz5=mQb;+Rm=|%t5o)Z@0j#VS2#tx0jQ~u_Xo$^N*2$hw$FEh=`4i-Nt
zAJ>R{Ppx~1a{Q@=VyK%j>h}fRsU-!QZG^7dW7~{SpCnGDebg=s<_790PL{P`T!^*j
z)*!l8T{(ap0j{gX6{E6_`w!TY(B!ydPT8L#w_EPw!V2cL6H;<jA-ckg>L8L1gQNaT
z^p5Nr$Q&rn{Q5N3Q!ki=;Pu3?fMcuK_#Wo^41&2MRs7cZ5uZ>$h{}=73fX*fNEV*_
z@ij9d{f(sX4q7Bp>Om2-njQfGqs#X5B4Q#BB?gilFfV+4>A4${gYq(2UGY^-5|%=9
zBzIz*fiDTCaix!HMS~T*Fi2<vj@QSiJ|QU5l=Co6w^?8|R#ZpY$X=W{FN(VyxESIn
zhD}%~za7&o&WS)}R{k#xTi{0l(H`I(u-@fFj`*;^(7)$30t?*;Jr;NzFkSQ12I&K(
z3kg$i%~*3cBV5jzP5@rfs#(WDzz!4oDPS;x$_TR#f7KoY5<xj{jl62tKoFf_=2kd^
z1K}RG`Qu{Fx?|Sl^OvybZkfJ0L#pATGphofQQcVAKP+=&nZB$FHJ_B<-bNhfC>MGY
zW#~sTw}{8oZC#pku?)W$L{X0p-F-H1Nd`!hv>2J~g4$4?BIInZfpK`DPf(VCPghA)
znCFX(vPA(!<lg*vK?h%w9$BM;FG`ca65YFe*Fyx{oO@?~KXV)bgbz)28;6s+ZwLcZ
z_NpuLpkCvz#Rf;TMyg*kpD97v;l<#65xE*Ug#;Lzgs{^4`wD0s&*w=uQ!QHBucqC|
zkT;!meu93a{99X<c(2(x!S652jf@b`d6`we-ZeK`OqwIn?az3Z=`fqwldUEJ8`j^>
zJt>8z+BzzeOrynt`_-`<Rw3Pyy}Zsge+!Tub9==95l~`MeJs;8AAn!Je&FYOj!Pxw
z(H$I!A}(Ls+qMic=+k?Qiz1RZUaFGCSQ^L8DGN@L#`Lux?s-lM5o{n?cA`a<eKigP
zElt+R*56l*y6ta-pSb;svec%WO1&PXaGD>N#GCpNk8vMBzs+AC$L<UkcUt`3vTFzB
z9di#NZywUWWgQP$6I*?tHO3eT0O)~h@z^j$A4o-YObQdyujTy&5P&!t(Q&N8=I;rq
zu`EsO$j8I(&JPIMSZ=4~)^^CCX%Us@z=95qS%uPXi%h+XEiC=&zEba7Rt7tDt|OG?
zI=IQjk|q&<k}_rPhS5IPlMSXf(mwR+jRX)yG`-ccJzLn$A)A!dB#Edq<iY_@*&<q{
z#brre+melG3A6;M7UjY&wW>k8n;ejAH~wC@bpAs@y3~+iTNFIg(58*);TxO@+|5z5
z69$_9b2lfyD~fH}{IbkgaT8Ce&{w+mGZdae(c!>8^o+obliVv(>w^NF!yGIr^#D#f
zA_pQ&226+l*y!6|(!?3FnhLheH&^G+>%r9B8+>aJw43JVWWux;m>0e{wj`tL#oG*l
z^yj?r@u<WwxSry>qcZdUtX0U|us^7Dr98<$0JlD=4lbR=ry&a@1zS4c?xF@!XP>=4
z*q=vux~)IzW9&1Zm;Ei`+4Cac@!))p^^}rQo{j%bWUlck%H1>mDr$uq5O22loe^Sa
zF!fZCkz(ycQj7+(fHjKVmbeTx_mZ;J6Bn`X%bIn|{$o5Ie|nJVWRT>81R?kpHbmQB
z2loh<ijI0QI-~L%X(0>&=l;MO_lJ}V{;W6Dl8s=0%OSk(A)N^NBuvO=wHZY#Qq`$$
z7~d&1N{+UYq_>hF5JOF|FU3*8UrjUDPL2QYcGC0!dV`?%xb8>DT25|<KcW*vS27)2
zS-dRJ$I6)a%~yQ-C%oT*0A%W2)Hb5<-c(dAt_UcuX}9{){#sL}A{^n{3POloM@;tW
zAf@q8z^|Lr(Uogydzo6V`9Q|xbg>l|YaCQz`8f|Xji~5`^qsQhdm->4B-YwP*39Ua
z+ZqWNuv|yko4~94V>U|1EyYt$iZ^z#ZPEgqQuHqYf4;<?u-7hwfSQWt<237Y9W8D}
zG6>;~9ZaO{1}dt@#2}guwqZI|bFc@VO4<72-NVFr9oRgv{R$fRGhZkR7e+KTim56&
zcJa}ngIF7GkYl<<?ZMTr|C1&jTmG}vkK-D<G7rWVYv=;otwE7-)n+XJ-kiCH2U1Uh
z(h`My<a-zdNB2}mM|L`2c2FLTKNU<&>|o~JwoD8aP}k~8hYvj*@)&5@Su$>6*(_}6
z4Nr8poLU4uDKLMb<UVS+=YA|UmNs_gL7YzJpRlmi>m!R8NSiMt;%aEi*M`+Z{D(n7
z@P<oF2~ZX;9|4x>oeGYJO~TV7!+)G;<xWIsW>`09Phrm*O+;Ws&63XgK}_2k%8m!T
zo(A+7L_f;(RBnP)fD$>4=yt7vEXa5pK_JzjaCh0r>t=nwz(R=LaKjM|OY%TUD&;#8
zR`VN@Z*xe;e*q;HtAcLx)F>K5$eIAEE(ybSt`_dK);Lno&H2(nAXz}!#0+dE*U<wN
zI8^L)q*vvd<I0P=k)bRANNq!6eLwj2+;zB~jm~H`zRCcQEl_{`Y-*$!WJ9*dBw+t#
z&IVp^AN8&E9cdWDljybdgXADc4ql@$v0lhYgU6fK)ZwuaqyUm7UvTF55?C$?1r+VN
zudFP@K=AEtP+lUtbAZf@V@rvs6Xfta%2uJLNF(uarHos_b|A|WFbm*W$$$LnzycU2
zM*yIs9zDwYP7)*>b&q9ZyHOha5WYgOlzeQo_@x$sz!Q{iM&r%g?C&31V(0%szIAg*
z{-0e5K$UR97Z<IF?Z$A%!mo9O@g$GEW8YxPS)Sv}gk6$k=CD9xMp6j}KqDdB)xp^9
zOd=#Xk6!Ms<~vBgcPF))OgD~}J2GAgjWQ!>Q16)_J?a%Bup;PdM6LPX1hanv-QpL;
zV6JqvKPmz~1JRbKB6v$bs~qE=DG6zcvg%;b5<5XSH6tvj;o%4`kNV`N88*XTR<@IJ
zNJc&M9!qe<FnniZ5iR)wCadF8KGecH@C~h0r?uT0P-KV#wF2fpd0AQ^6__Q`WK`E7
z0kfXFuvG{?l`#2e5vwuO6Y>0`dc0U?gQ{xb%iMZn4Y#9#Nqi)lY6KiR0+e!Ky>+rT
zJZi4JZ;?knh-ph|QFNOj55n^0#LERmd(Mk&ToR~h^L>2a69rPk;+Sp`i-IJ=Im;<x
zn@Fg~Np*}{0k%-jZXS1cw^yKgvp&?)VI!4h-94M9_Yf~E7e_o+U*(CqLe}pYKU0T*
zehz_>sIn;nu5deHt}~1GtG0;X0@t~eFb|v*lBem)CqD)5Xst4nr7CF-ln<4gr0TJ8
zae&Izo(ZuINm`sNp*D-~Z<9xIRCI%Wx03u%HTDq5sV+_shqY1|gg=fa3F_)DP7o2K
zZyQESx-i^iOSwdc&(!FHQ6FgCT<#0ou^!(DR}22M?7-T>q1BwG=yezk+0L7{;%=db
zH0DjlQJis&J<{dwo90tv6iX_%R%1`h7<0JSDU}yAT8^4Lssr*xnR}<VSDq^v9`4BX
zV#iK`*{<xj4IdMvgw#ml(gQg2JcUoIb<7UV+~ZxrBXmb~Q;WPqna^#@v9z2EiWil_
z<s=V3LtlGaz)q9uD|6>Y=N}t4?n_o8b`YD>K)n~C<bq0aL0FS@RqV!FOI3OPzMopa
z8U<AbquAP=A3)VEb7<?CvhTKY`eKYxNHy5Xox<lLMs@)<_WDCjfDl(R!e^v>GwGlF
zc^}@IYA47Ep}wa*_@tj&^$<>-oSK-vy|9J#lh`;+l*Y2}rYROj{d|H0;3ZxQ&nZ(1
z(|jR<T);>GP(3z(UjhJs8!ts0(z-^hX7>ZK0L7U5&RlF-TBz^9%&)GwNOs57Ml;W9
zSD-f8G)?UFR-9MNOq<hro#};cjp<`Mz-0`!|ENxDItvZZiGP5xga8H0ld>P@gGTBV
z4$|U)o8IZGFlEUJueR${4y9EBQ9f11`GS$*x7ljUyjJ4}4&He8_-&2%MbMt(yborz
zd(?uXHqZvy$}jJ9CM~Ua?>}!pQdZV`1$h}remg&|vVV+tX=lKINplR&&L*)@$3#HG
z9UN5hi&GF>FIfF!u0-+0y+@;-_5#2#)#O&^xNPGX9`OMsyj<5Xu1pvm<3=KStOa9I
z+Ocg|>lLwb_Aks`2dZdo<zTFjZV8=KmVb_NI3w1iCrqHgaX)eAMN1)yRRD8~S=P;#
z55A5|(IErh2uBeo$GO76LHMB11zxTogoZZpo~)#iHP<g-iB-(WpyXs`<kHp7xsLds
z839&~V+p_?rnGeFsDaS_eew*>P53~nWeh0XkFJBRFvlqCu59cLpMu$-pc)(RR+7v4
zu?CiRl2+#m835G$A18hLv8V~G=MD^#zmol91fhS%ng5Tn;!LUf(^pwPUmW?LeF(Z@
zE)aL#sa%k+M@>R_ydvT+_9H#o;HLFIM8CbU5ts^e)9xoERnvf#i*h;R+J!M(4r7yv
zRM$*|kv`9n&Dx38KSJrhN;EiS^0@sPUx+2A2M?gmQjA2Bx1Ohk$F#25E*{dJMT<GL
zsHXj-!GC}qgoBD&w+YdPNf|}Xx8akob{nG&G_Uru$FBf}+oFMd|87pmGuK@2;I2<#
zZPFSNUX-}^FZGRj{R+7<w_FYdLW|0o%pba!1-vYt{Sl}=AFVF`GmfiXySd{_^_<5m
zarW-l<O5dePXbjH9o2>rm=)kSD?k9wl~|ePvJCz$O$S)mtQ_swQ#*Kf94YjK0*`d0
zI-EfA`{Qu>d11TStomH@a*z`sWw#c_KWSv<&U+|eG<C#3B~Y%W^M0T$-uQ8y!h#H_
zo(h><K}uJEh{0Kn_O7e9R?hiTTGD4^ELi6G@G9xph0Xr->uO?e#z+wm^z_$j6CNeq
zsdBy?{@D#<N#Sk=B?ivRb5K*ua)9V_OX&8u$AgEf%R#e&#e71a+T+O$&v@aS7g$50
zy#i)fP_Nt7xGUPwS-ZY2*1vyre{LBx2fR8Tu>Z#9_B~1;d_mAC6rw-Ov&Es0X4kf>
zOga$X`8u1taqp-yA@J7>H2wms0K669K0hLMa%Ws#N9|&I)V4)*Lm<Vz1-}kT$k|!n
z&8xfdNxcbUJix}p(t=Nfv9JRNG9qqsLIVPRi@O7g`LG-|f%<U$w}oFg^82K{u6v)y
zcmBe-5UM+KIq!F874!xGMv?1$xRYacM`*0CYJ?_OoH{(FH&qfyjzozFkDnQl9W7|L
z$K|N)_c2HHm?g2WBiJA5ArktheSz7%%z$6mIufS1z5GQ812ks77zt`BbtL)|Lz^4@
zmX<gR_1<ji%9q~o=x%DLrc7*bM>Y`S&(cpd;^XJSg?cXB2RP3J3r(X<iG(6I{{Gf)
zvD*2hIaB|$^%TdHqpE!HxMMwE_tS1sDA$$S@gq{lwFd+RZXi)kLsso-9v6|-nwVHw
zpkP+L>HbHw&V=7ktQbI#M?G!mN+kLh4){zx^JQ1KJwfHS@cvQabapGuo<gnay=Sru
zc(;XVa@~AII+VX~$KNC9H&lEBRm}U$xk%AQpBn<~o_&L+8}+O2Sq)(vg1Hda`oyZ8
zAM>;z<-A$RL}n*%#;9<-(%kp+<FD3ZxD`&XD_XymBb7o+2TcYpH3>|T>+U>EKk*23
zpi2i;i7Yj(qO-s1$dSM;_~g}u?9`<)Oeu6%GyU|;^T5^v9NmSH@3W=kIGPduO+YtD
zOtyY#hf=uA!mbQYARk@C&3X2pWFPDpnnWNc5LAT!kuTS;-p<-^pnurF@b$`@D*?zp
z{$@6qD8w1<Gx9k+YW%GE_&4V@kFb`GAz2qpXJ<HJgV6f)5vUPa>rW+L@=_lfW{!X4
z`(Q~PJ-&3h=D64ceI?MK5z)kMAm9U{pU=7-wGQVc`|E&c6j~{#k<6zmpi+qFP?7|K
zFs!0IAp&JC>m;5PqQfhW7o5vX&3jt7yFb0$6W!!?Fw*kRLAIjo<2Z&dv1k^s4u8|G
zp5N4yCD*I2w}1@?p{!`ky|b16L(E>fJLg)`!*uSCZ8pe=WbYrkd(JDX1!b7|F45?f
zDyH21LYj4?i2{%jhf>7nYnowDnh*yrnRY7QG2<P7F2|Mh7#bJ)>n!NC{gQfq!noq}
z)3DV8dQWhuiY}I>*4lg>h!S;MY8Tz1!G(&ZJ;ulDi=ClkRz*t*3DFYhJZ`4~wo(Fp
z6+|i9DI>9F!1~Dp5{xL(t18;Vm!y?D16PeuTawaXl#-&R%kw@DyVY6xb?vV)|Fhe)
z*@K(!xz`S;Z=o<eW{)W{;SSoiH($GYYdDW)q(_9j*Tlk*T+V;(hD~`@-byU#xAMS9
z2LWV+;a$*n@a#W$PhJDp-@{s4!an$k{0s{J*07dgssV?BQInievuA39arH$`Frox=
zhK{J|a(GyPpYRsyFWkqR%S931j@O={(PlSWw?{AVnka=u+s5HfnJ=pM2LUPiznAyg
z5${N%pj&N#Iza&Bv%5Jcjg}turbC%`-#nQiIu+9Y%X!(cfEd2ZJe4)`Xb4iH=R4)9
zZ&skYze9Y6+B<ZozuxhmT{!t~F#XCQafBl1BU$2Wi=|xh`pXh;9crd8HwJy8H^egv
zEYw%`6@QXa1Dp5N@_jEM2HBp{8q_e|6KLwTVy46!g>52wfs;F=FT)0|mGUSgJNwXA
zBF>@px#38Buo&J(^~9By0i(@?D2s2{#@{VNakcLm9qkw52dbOlbiif@2B&k%VX(ne
ztf$5gAEL+!Bx&F8=Q8&6fEE)>X<FEfx1)BK6*!*Z2RTxTol}@JeEWrOVz65i`&sO|
zv)nL!gE@!g1E~}4#^kOzeJ2|IxgYQ1w)J0tt6Z%~K=O~hZi(Y}K)Y4<27+zA60e~4
z4!sK+rPaC^kWGh2=NR-RB?bMKwlIxDw%G1wJ08@#7mq<|%N-8^HXeDedX(RCZ<J9d
zy!FfgnLvTu^1{KSCM6;uy92BPY$MiC`b5b-9Dsx;*51`(s^MoYjBif$1)Vq<KHsBV
zEK}<)HQ|tmQa07fbBS$s-w7O&&84NUXe4OID^7gJpQoXN_?$1IvJ4xZbjnCB2BKcr
z-JIyfYV)>i1;5>O%Ro)MDa9=L-*R;DcBHCFJMJ|91bVHioAoSVFya^!4y&#uw=b2S
zml!Bh(n-A89oJYO05iLMzE3Y;FR;VL?4en<RF&>OQ(v7f9S+JD+`R-0)n0zco$4b^
zZBe4hv0ijxi#8VmJIVR^#s)($csq2?#Hf%~*+mpx9zyASZccN}4!r=8SnUjQ6_fsA
zWc4aSd{?|IFtc)YCO>d6?XZBB%ai0gBx%Wfm`xZtSUeoo;}64LikHyc<29r%pK2Wa
zA5j&Q)oW!z&rE;7WgOYPBOKJfr2vRuTpf$r;AUfXFBVIvHe<K4{@ZsS-P*ZKQyO|G
zk@B3z!{w?lz~kJheII-{)Zz%-0+MTH<E~IF66Pi6Azgl==eN0z@;eAC1A&ukFluw|
zm8TKF<yh>+4y1cP=y_o29?B3AUN@hj(X)lNRAs-km;KZGyDBw|&sb5NQyEGZKw>G5
zMGRlXqJGtMiWX5j_B?GseC9Y56W$;B$lZaXk~sqOp`uJ_vR!+3(e(VQ<VJq!T<(||
zuHCWIVHRj-)hDJ?)p}$_ox-n%z(yf-?Fra7oH+-RPi}UAKizoZA_eS5JX9d$&VLsy
zv`fIDOyC;tTP#IO@9co7iSEaY;G=@{we`*&srkVTe;4czO+Iw-hK6dsZd*LA$4%GH
zYrS+Mj-K<jy;*C3UCn!Yeb{kNg6QotqK#t70VTj^iO(f9z)ptyZ8LsKf}`@%&zdS@
zTZSk0^+Lj|D>r*<oPVsu;`td)0m-qTFX3ff6{Z4m>6G62`Rk~j<boj!i{L*$>uULw
zxMk1&ra+gyC7jFfbXUa}Tx9najANlt#ra6Bmr76RUH0pn!m^Wt^xHGwczyQ6-^n4#
z!xOg$tres#*i#I-F@!s_H9zMF(O=N(ujbsgChi4xYw9uchKT*bfI-#s<zi!#kY8Js
zHRbaaVc8eLS1XNq^4u@}2cRhvaHiB$esrk$ar++ErgkG<G*5U(dVAd7*<nS?tDEm^
zBX6~m5{1gd(dKX-TJcjn{G;Nk#q^QjpCem1fH`**L09aw8Q4<o4U}*7MRX#C%Yf$c
zqB1%rqP$4wg49drh{9<uk4jk}W5dAQ(Ga55tK5H#Lz0qlkFWP3{hdelNh2@zL9b6g
zj^Gy++s!+b7ar)xdal~A=*5_cjpAT2BOPY)^|;Ac@p0u(tP=7GIzVgx<OXeJFhLC<
z5ywpy`*aq!k^n>dyLT2eh5wzF9!evFZB1?Rh_#+fwS?1jNFHDz9J1AIFOmE7Ai5pw
zZJ>rS4rMQ}U4h7E5AW&k|Id}ybZ72vaYhVmAHZ@Q;RD22I`2MjAV`KZA1@_&3@c8(
z!5$9B9{p@P!*kL_<q*N(XgV)*60ed_WWeO1Z>~OjNCpxh?^v&c>B6hdMl%X&Ah#r<
zOQP1b2Ri3~<+>kD<~afdz!Cr+@`BQoHK?ytATzawLtcC?7W9<DGgSOFZ5d5i^A4_N
zWvG^Hd8uw??7nvFz(yM9U{$+kB@Xs;OHS-1d(^vXI4m+hci&))iK|#R4&DSmCjVn>
zdq}YsR@yR3SF#iF%6P#bGkj2`->aMH`(yUGGXgR${*s2I>Gv+a4F+CqtL-zaMnccq
z>+RZ6pttjD&p^sA6tL&i%U5x?9e@c$Nff~IHR)WFi(Hd2xqf8I5j^sSRXoug`SSoR
z=zjHwIwnw?WGwh=+KdUl9pf&Vlbs<_e&EM=_~m=UyAJ=!NXpa@F-+H#0kDY5>%u~0
zl|avac0-8*-<5yZ{}x*OKRDm_-q#l22n{P261(@`P1mr4$mwUqJ9W-XO%3dt+l^S<
zv^kXR5t62lbGncntaMOD)-NR^hS)|u*2arExi9=S)Iqt8k<^1_3NVJ{Tojmx9V-82
z0d!>zqwe{Mk7L**z`-doUqW<XNSoG$TlWZKbFMzufR<DaKJWq<ePGc>eNyca)mLzu
zQsqTs?vVExA!u_f9q$f8Oq|C}X8XZvSJMw@>Iu7>oo<E`D>&Lt<8sm`Te)j9JH}QD
z{xt=#lWDEde;T}bfB>T6U`+G`XNLiO1YU3inj=I~(8ZWC;w=GxOKkmucaKzqf)E;r
z1%JP<L{y3}a0D9d7FTnV+Ry?tVHh19EKI_8X_l>Ob3@y8k{FuppBoiFQbk@&vLMiJ
zAn|qX#E1xG|CR8kx-vlX&(^p?f6FNzBQ%I&H*Y0*$36V5AL!O#MSJ^ZjeYtE41FdF
z_|~3)?t3VWfBv?Q=4M74TugB^@6KSM2*7M%oV{6&k(~|AW#XI3X1i_DLq9ZI$HrE{
zNIvT5eHonL#@0(%ihi8qD$fbTkxlrn$KE(L-^wIEAV>^PP#jhua`;?L$dJ&vhW<V*
z;PAEMA`lXgT;C&maITGFDALio6zPl0Ed5-X6FXZ^0Sv?MJAmYk-gk`p>|M{Wq&J+Z
zGZqr<_kFdq6KY5l_-{TXEZ_D;_McLNlC~ke->IR&V;Ap*8y*GO@D?jW^+R$51^ZVc
zb+${#znzIt)>dqqyo0hEJDslpyclSb&0bZ-G`}r;Z2f0S3WatGZVyRs&DOpq5OV_J
z^ss9icCP&HJ-UDWGy0kRN{nf1j8tBPI2{@*V<FF450PpK_;Q{YLZX+0h2m@;9_jSs
zFoLjh3B{ZLSMGnECd__&kQNhkC=e&EvpFpi$62^LtqdTb-}UMq>K#mp&meQn3e2;T
zi6;1EvUPG)uU#xH_}bSUTpLAl<a$Zd2&)fU$$UE2KSg;j&-vNcX*W0UP2lAB22-TJ
z#ecNdbI-<zoF$-}a*V}!Y#%$GMct`_%?><7vv7pAfd$iaO(+23$NW}NyILkQWzw{T
z)oEhsWu@nS__Jwx8zUwVAy*xPhUPu``=HJ`ZSlRU>vCt!cmI3=Wk1v@_lbekf^E{m
zeJYzn;+m8(HGKrApmC{-Nj^Xpj&KIiOaJsKZB_h6|79qfG3nt+6R2clE52f3i_9!}
z%lMw_=KDW$1G2Dq>!!mSzTi^h+YhGH4FwXT^+3Ch5TOK>ee~J$C+Ar=d(5{PJohK*
zbx;0)mCDLC_>-#`W;fESf6d4w@Uo5unBuwT4+wgy&UFc6Q8Yy^7FiTqC8Q7>K2AJ<
z<iIfN)*WF--Tnn*X}4?EkDT@1AKLhpg!>cnKSc8J0Ttcwu{H3+fx5p*XP9Dbjb~hD
z7wO;cEw4R<AQs>msCsQB4v=`)3Kne88{<51OXPl*AuhTHx;T^I*gGU=Q;2P)fq?|E
zAp&V1puGJ)P;%Bd2^n*Z*IZs(i!-7faAT_sP#jQZVoVxcz<M%jzys}tj^^WPH1knG
z0n&MWdnCG(5tNdZ%|)nQnm@H#=P$<)X#&s6->coTx0F=v@H;FTEVu+H(7hn6lwtD`
zaAER`1A<_2#D%;ig_Y1-zr%_sb+4nVszwGN<pyAjMBZe?1LHZ`M}36Mm(VfE<JYJ+
zR~P#F&VD$rFP)5z^Y05xth`}La9WM&v~t$8(x+N1-{;z?`o#3P{mKvU>-32c>i&)R
zty;Mf)5ZE+P50ltmR&hde1EqvK3|P`Ig_$ok5|Foz{lU9IIfcIvyX$rse|Jhq}%6&
z>g|0RrNeqX9~QGNW}^cJS1=cKQ1tHMpCIlZ+g+<e5cz#m6G%_%%a?aV5)C(Lc$dE{
z{7l&2sT37tZl4*x=-{nvRvq|pFN<}BBF{kgM#69~TfXIg9mw>D(%~jmigw)P;?bBZ
zlxA4<bP0LYgC>pVx0`9Z6ed5X{Nq^$A4=sdu<4w+LweJ7^b1y%{SzX{k1(+v;rQv?
zx}eME*@87uZ^#StD+in^EtWz`!Wt@4>V%lvQUoa{hLXmo<v~)s(9ZEc9d@1s?^9KG
zuftKT^g)j8@Ez2D*K{07*2@{E2}-;-=uA7@;X4v_S4;SY<!CBD3_Mkm;i3u$t_(HF
zGiatK1o_w+SCeD<9}|V#H*Jjy#$zR5dqa<C#gaWydz`A!v5fQB2PKk|6OMi_L}1jb
z?DG&|DVUs<o|K?_8h|i!+7}dmMU)+<hci*uz$AMQyjcj_TzsW#-jJg{E7Y)7OtGM0
zbteodnWN#pD>pj$%Xy_PKJOxhqin0ep9DFo_lZ~tg}0ik0~6gt@8inXPZwTJs7ZpZ
z2#NCPE$94A2|MA5=p5QGd9X1wDHo(%xn&Fd4wZtAnOo&RnZcsZQR}I}`jG(hE{mc1
zTo>`}*z2VNWNbSnASLN;Z@5t%H0lmwsx8-Z;die;7&Jqa|2}!Vl;-_o>AB%^m0vAk
z)U^kxtt$qy^4;czr>EmHq5f(IZI%6C<l~FO<E=}yG=MOc4=EJb=u+-k(>LrT__Wms
z#MeEye>ziVIZ~+vaL?h#;OO_g(Q^v=XFH-#YMLkf{ZJ<mghGC0TR-myQD_oj5PhSn
z_{=2kX0C^>>qTF9vFv@9`-7561AI0q49Vh=iD4^mSGYziauq>({wr9Dx{lYv0!inr
z)1QA^qdoPhrz1;ZCuwM|bF(?FQbtP`f&G}YuBA!cDYQ{`UNJ)NI!i9$;>`e@hDAdt
z7yHP2#~hkPNR_V=-d&;kdd$h}Tjk}foh79;^L61TZ17vqDwyt9S&~@K{=BMj+)<BC
zn#j?P{vc`RXL{@6`wK3BtU|JvtO+r>&+%|Vr8<zqetRO#9(@fI?9smMp1or$C+ZkT
zZpr(J=g@2Bj_&>XLq#F|4#&*#rs6n$4b>RrLEsz?N$hJvKMqY4LGXmF1WgJxG%!WL
zwWY8WxziBLNM(65sE=o42kx4-<6d5rI5^^<F#8H0Z`NObI=+1aee!V>8KE^y;&f7M
zp2q9KM2*zL!GeVR^>HMgrewMnNrAE7?H<{!<EhyNVrAMD-;v5dm|rwA<b}+j(BYBK
zp~m)5=3AYU!mmZc9UONIzU@bL`@BNO6Ft%Xn}mb9Z%r+3xYDDe$(C;Q+b!60?~uk}
z0(wlZh0&mJFg2R!-`H9ItNl$*W@(Qr<%_+-MAkeGn-1w*sjDd!9aF78Fv_XoxoAP^
z_b;||HjN%1=@XVbzj^9T_J5(gOn9{XOQ_Z!tQ`xcPF-zQG+t4Dx^HhWLN<3fHpp{S
z!v#}cE|0tVG=UiC)|rrmCjdZE<ELco%($5=(X}*~f+Ei9&tCGV;(E-+rwYC*zMZU6
znEy=SNWKm)3dFm#xOpHmZhZ2UPO{-`BHT0DJoN^1UGy(5Qyhdu2A5#AqCPj}=Y?rq
zul0%{ae#_{gShMp3iH4(D<gAg3{aX=8P1B>j5Wj2>BbgI%QH_mOz_MQ4bQMTc|ynD
zr5jxL+MRPjGdYO--8lu%9N+qVY8(X;FkWw>2}+9`+e<ARm^2T!#y>U$#O41&gU*2$
z0Z}{t!Ms5nW0)JSK5S$njIhnZ>z;2HEJr0sMFzT^e__C0MNuEUg})SK*{An1L^*gG
z9=9QAbCf=sxO<bg#3`riq{fT&e5{wn7r>I4pP<{Xm7MD1D%`q0w&wlGmf!BcbC%}~
zydqN9OV0_P8}^`MK-cDtQ>&~P$msb|>y<{lOt3%6^Vh1E-WslEi*6JxKPoFDrflk!
zN(h7Kk#p+y(5m8W^8Ge%4at6B%wS?8rnh?ZZ!3#jcmavUP~VA`7_6Z*N37U2e~8Jt
zj=}hK-q<~<6G6tU%i-A=tixGl(Fi^BdkVx%l|8Aj5D_%0r$d5u4arXLaw#^k8-fY|
z&kY<+&#O9rBAK$JxQxh|Tmbn>Jj*ik4aI$0F!60iw*2g=mb{JlMbL&6Hfp1Hu?`E@
zKdgO+{{J!c%~6>~{o2{KjcL+k+pfv3iIZ*HoNP?CU6XBFlWq6i^S<Yt^|kt^)oS(B
zy`Q~*`y!RQm1Ues3|%A%d)+~GI40^sJ4&p2Yq#|afWWv<t0(yd2bYlkG<BG+fCtKU
zN|hM~)Dx6VpYe_4);&8xr2@uz!ymgH>-YR(0Xx~|=Vb5_G*v-Qz|zEB>z60=+DC%q
zBjz$3O(;2Iu<%&#SO!v>qxX5L3jA*B*Thh;%dJ*7kU)Hu3!-xNTHbe*%Zm-!(_xJ!
zOym0Il3n3STIi_!Qc5Rqt^~Tdy+ef&m(}Ynkxz`eNtLgnnE!DhPZFntg?`oe0JXD4
z>{rfcA$EJ5%=0jvPoP=J+b*KErh6;+VaUQOYp}XUWkXmoWDz=r-L6s7+t&^4)xyUN
zNT&31q86&c3_wc9$il;UA8jxxU`;2TYmK9!+m#Ol%S6M^DJbWs60!*!c-=$eH?tar
zM)J7^o4olwVi;gMVozL&nfj=+RJ9@D^$QG+oj^V~)_XD`e<wBeO@Jjpu!qV{A!%I@
z8s_#v;^8f!&twfj>6JITwVwExfEW!}!EdZBy!}CH*&0o!k3d;E8bCbM6LZuYOmq#}
z6%Z&ko=B05L34tgFy}OJmXlBm=|g50esC`p@Ih_!pdZO}2I?hF|JX*x+dXDZLy?RD
zr(Drftits{v7zLNuv=_A4xV#Kn+D|=g@B7tuHABY2j6D@O?SszhxoHMkPH_&k*9-i
z9RpVt9UvGO-kn>SC^}P@2IE1F+9^&NqTV&@DQ4W|C}Z%|O?7&3zIaB)SG|>R<dnkt
zyFy2BS}G3$$<C(2r1@t+uriIt3p)r?Up7_QC%9@1jmmIBN(1%_RNY7)Lr20gzMdfV
zQfgl;yM)Wi^J_WGD#e1l|I%^DvP_cyH^;;BQkH|PIBX~$=34m8fC97o4NgpnEdrvJ
zhwWxG58EF&OL|2-$G;6;eTd=J+;CR(B{B-9qdPu3=f+eY*X-I%Sd%r-sOiM9mpF~z
z7g!VOgZ77h^`>+qw**rqul`haV5gH47>+0y0cypNLGER-)R1t3mC)N>v$<ZIu5P-0
zL5;zp{ifB$RA~BIALonyAu|qNn?R^1^EyD5^+m4dvGl+P<z8~)sfSc_NZ-72-@|?Y
zPD=T6nJ~=oNHj@)trrwx8?2hueFx>%n4#Rj;tN)0o4e<0O|A{*k>k-rG(u9lFS@%u
zsNwocp5JgG7j5o;xCSgR%<X_7zJB)t-si249^j1LM-=4hD;!kc4eV?Q>$BnH?5i@t
z(x?I>z%I$FpNMP8vw2P*)-|Ceee)RWs?XjVa~E>v3$)3F4;S&0#~TdTvwWMw+mW7+
zxTR62GZwK|u60G_LW5dE$+Uuu@$5?COfsR_<38tTTV`Fz+Ryw|^Jj$Ltml9sNu_`^
zdpPeE4OEh#8O7*3wsCACIePnU{Xt%&rDz}aVop=^YQ&kn!_&@9nhQ5QUE0q)^`Qvj
zBS&}>Q{PLnUNRJHnmBzrmOV@CQq6>2OG^X^hcC)|kkQHFjMl>Fn#H|MUq!A@7)M@R
z(0~vjDrV3XYl)QU%rO3D()0qm;`81vXPV7jf(E7gZ|s*LzsDNg>W~w8F8}pEt{!<%
z@Hc^2d)bLnyAJBjW_J@n_zzaw2%#&r?#Xywd|&seWj!ei4QqWU&Fx1=Gfu0Bz36Ll
zH*8g%2_#0wfXwuYjfZVs+T40aRakyn5#TBQcoM@&&)zI6`AXnZ0$aBvw~H=dXtl^@
zeqJPh;XW=M4V*b0_d(%DVXL>E?HpqHht`yw8_fA!5m4y9V))A4MSXCv*%cy%@~sel
z2dFb|tCwf+l8fwhSuPCvACxZDp<g=VDZM2Ujvh6U*$0TQ=UgfdWqfBi3^=buB)OHj
zDA{tFa{sL}G}#x>W{}AD?1C7h&5lodEzkxlhnQ!?Oj0RCQKTX%UZ(<oYH|GV7?kNS
z#UF`jPceb9zE050n%ZotR`^v%Wt9Bl`zg*uCxa2JwiL7MQjYSb7ug5}dbz4|v)$gp
z6_T+JcBgT3*a_`>T6_tG8Umuh@T3`-ZJ%MHL--Nkmjy2ZiY9*qbEY#x7^{l6ht$8U
zTxHc&_*mlc)`J~>+=ms}^<Qz`9Po$l^*~Wb!19j_ZSi;$$R?U^?Y{BouTuPUbBKyp
z7jQ{P)4oj^G~0y5fTZ|H{>g?XV{&awMDn`#iut*`H$BKo;xW8jhP?v^I)pt%qxDQW
zSjYgwO^%upn`bb?3enffS1&S+%fxydM12afx*XCn=K^{)gK;Yb4BIVV{KH+7G4Dcj
z^Y(U1k$m*_V1a<+x~WL-A={uwZck8({6~7xyRN^5rxWMUD11k?4r4$bfZ;JShV710
z0~6w8+h+t!1NGQwx3uET(z;(udAKaeZbBllvK+amj<GDU|Lrsth^g$i9f!V_=3kam
zO!nBhmKo_OP!GiMZkO8F03O|1WxIl~VXM!f-0h1ROv$|Yb{7ZVF$5)|E71h4x*dJ?
z3DT+`4ZgjmzoD}Z7#+zGge<$u8m#E*uE*?FW9h`}FcV&^6w)VUOOI=W1I*zh^t;(E
z?luU%Fl?_>mb+IOU8W<^enEIU$3N3UzVGXOE;-!JjcjMgiLFMuH2AqH<brXqedi9k
z-eXkOqU|{U_TNh<W$HfIoF#XdRtSg_l=(uTi##6!*14AXvvX&Pw*<v*zI4*CU473u
ztRXM==<o*y@j2u4uktQ0rPEu5ad@nJ$>DlSz0ZyYvJUn#o9T#Q^MVsp-&chEYTQ`w
zC1TM#mHy^ET4Q2?`@89PM8V{+Qn3}$KL>-L9(wP~;bXeDV3*Kav}yB9BGmb|(@jNv
zr5FRgK3FKOke#qA=O98P9k2I|-`A6LT+VpZAT~325MVl7ep^9y!?;u>az02<G-v&)
zjfg#~f5aJsHBQRY%N%Z=8>iDe->GEOML7HYH<(MFS8w>)g13$i-F~D5h2YOmlmX!X
z^2BEj3d9P?84Le@82Q{W0U={(4F=8{;gXQiJF`gYS4F|~&YK_fu1Kmu{qwTn$i8;y
zz&>oqf><qJLslv@u|a+=Kz2PkB!BQ6Dd%&Q6?wmg*zuGL8z?`s$#HhId!xXAjb#$b
zTV%wd>lK_PWX-Xgp!9Sz2L|ZsJC1XWWDxmQmxz8AX^O<Rhn}W&_C%lEZ%-(|k36f-
znbR@hWavln=$3-3O&M1m$CZuS;)b@`zB6|uFuz(I41k;CYO;A|p^rGP;I^JXBWc6O
z>UV(QAitr{PpV9YtvX`<Hx(EbG0Xquez*UYKd@OUpKKHpL!C~C&5~rc0*ZKBWwg${
zIaaEk;EW&WvEBOQKo`a9M0@izvX%{;i)2oKsJjtF!PeyiyBv+yV<l^_RN~XzYYk?;
z^ghMDwb1DEu?PWgSAK3Mrgd{-*p^p+d&`I7mE6btB!8`!ushQd`!h9HYppFGXr`9g
z6n!Gf%fQoo@t%XaSf#(+NyQ6fwsAWzyf}gil^2-rjQ6}k+g50aZ*OmMLp`bmjU~&m
zu7CRjRTt#^-podR6#}EMDCEadmwly~1SURsuwl{I0{^S_$o=@wELnXuuhni+sHMcr
z3L&)DU28oB$tK)KsagF&`_q#IhZf>;rb8NprAQyV2vJJwJ4nSRU2oel^^XvKNa3rC
zoc!uEkbJ5*A@2<h{B|r+6ihu&DD^Eo>_Kc9UQQk67(PpwOLuZf{*LG42z4(uj5c^m
z;8tne;RwIkp#swD>~Uee(puD4#_amp_{&J#ik|Gp5sLRi6Zg>Gox5g&iyt+6(rdIY
zQY!KpoV3JORpI{*pemEpRZv>smVQ4-5ZsWrSI3-4ujMM`M1yIeH4JA6lC=JuUFx0*
zkj2jn?uT;_nk>TN5gMMqW;tys?s1m5#feM6;N0i=+Ic>cQ!{#Nq_^sH$4Itg;jK1L
zLwqQdF+!bpWPKz>7RT0$mSC$pVh5!;>W-(D!%U#2Z2AN5*60C;B1wkdl3DCc{OMtC
zCwxzo&jMY-JB*jR@>>(}#qCOu{!=s5O=UBjEL-@|?^|17(p|YThE_8L<Ls#3HU-A#
zOK!K{<1^Jn3x0>>S8{K@u}1iOe!1cw$LVl%1EvtZRZGq04NrM*b=p8$cX*Jt7OJEz
zDHNgPZ|tX7Z9M@&XN(=xFm{Hwt8Bwr$|NlJ=+y9P9(Julv=Q@6>1i8AB-*$2ZicUT
znKt^Z?@sp7W8=cGnD)(G{`WazZntw+SjIrGmD+=QT&Inw_i`zuqExSX0=`@M49a{!
z<sac{@KE?0Z25t<V+n%xPY6Nmt)StLNAyi^ihzeZ7xl*Yj>{b6uy(AhY%y;M0NhbE
zRn`+1TqoRYp=5MvLtugt?w9~1wwGJA-JIR|3(95d{?gO`lPsBZ8*HZFl89=EisS2f
ze$4@oiHQCyqs5y>THHJ<)sd%t*UM-Ri7~eG;!Cs6^vO?NXWAbcD$)JUQM+3LklPVe
zdF_06Zb`igm%fKz$uGbP&18U2I&JNAdsBAU2J51*PH)D=glu{y(-P1?c~oem!k4dn
zmG_A`7(#68barDTeARqfEGw1?5Q%0qTi`OyJN+A1Kcf5Xn}%&DU6|;^HA%wy5j^p9
zJF)hC_&@=W?zkGM@LDDVr7w_&zM)Qo<HOJU)%Jr|@UJ09-B#yc2py3=m!nf%KOQ6E
z72-{q4e0KQc(*{I3l8-7&QVvd4@=b?Q@XJlr^--o8Z?%Jw&BrR?2HbZ?@4P_a-1$S
z0ZA;a2`tnx8OJ0?mJ(2BrPI&QTE@7{j+7^h+dYfn<8OnQsY-^^<{AP=F8Oy6)J|(9
zZZ^_war+6v`H13VPEa0<@0kdpNk`>5CCN`Q-Fg_G&$z(Jpw^Pb<IVAq)vf$?Xa@R6
z(I{qc-Q>%R$Y6eL|F1Rby>ooKGi`Xm%So+GJWIHfT-lniaEvc?qfZfab{Hm*$({}g
zBkvZx7r)N?qdh9cjd-<V1bi!rIC$V3%&lT7W>U*WUp-~2jY6g2Ry0%l#A@%$cnyEf
zpXA6>T|g~$i~b({pGuF>=U&wzy;M0cdnGVPN@f7yQYZ?FN742qvJe()hHr!kAj?1J
zIxCQmdSTJmjx$Mp&@7!QX6S;=rvaNGkb9$_v(Q<G1VheHzlW2<o4Kpjk<I?Q9b<`T
zwY~#M@>Pe#S(Ac@xMKZiC&gKh{rtv(Q!YPObnqZ<rKN9dkWi2RP3ZY8+igxLg90&h
zmNJtejbkvq<?$r~+Ag{3{_2^Gg9qt}^A`gtOx&9z#UP$6XZk}cdNX!^jpVMa=V@m8
z!AU*l_JhJt4yq)2I}G4`Fj!b+JlTP(U;{U@w`SC84rAZk9bLkfT{u8OE(IWAIFlm2
zuSRFWZ|5x28b46vQ2#b#L;R57RTzxIuf2RDRKHO}kmFWUs1Txf?elzJ8HF3Fz?@9p
zFF-4xURiD^w|XdKuVPv~nlod{mT6(Z7>mEUAphDN_=OCQUQ(X6>Q|)+oqz@9_v0<Q
z3uffljqfah8wn8F4=>9dV`FXS{4NAnK<d>`tM12cN|FmA5r~9d8DIQ!pLSTeewvO1
zO5(6TBP#sKm2d`Ybr1k}2gF?t*1FO+RSJ-|6LKQk{s&y?;@1Wp@bwbDCeF!?w3Hpc
zGW+I=R}rL<fc?~Y4luO4xL6I1w5{Ad5i3}FnR~|X-TYqsX<UhY0R7u~EJexE;Wm+?
z!O%rybi0}};X`K6(GkW$&9zPQxgGMiAFua_C`V&1FN<ws7fmxh9-(LPjZVBmOHem4
zIMxHHNKR!PxB2kO{h5zE&H7oBx(dxtG?#)iz8nJnenjCvz`xgycP@`lWB{Um&|JgE
zGvf)7f>3P`U7&c7e5J+lT(56ju&-N-Q5|7%cZvFX$<M~gzFF<eKx0~<QP($i8m43I
z;rU7mB1p?`fQ2rM3`Z1aS!Sqbum3Lxzbo@IpINXqAtOSRcc0Lf4YwBSSH7*=NaO7E
z<LxoZ3+C7Rv)oE0`^RQPz3fjxuA*VuOQGrcUar>S9!Do+Nqz`#oYkWn<UeiPa^aoV
zCUpWG&?7$w+T2kuDnwY_UY0Dv8I2AmB3fv}M1h!@8TD8Z)=ch<h50t*1Np#OYfa(B
z%+Hyl-`(Yuiw1_kLpnVO_J0Hq{3dw22Bjdlz934K8)+@MPG4P6?J5N9B-St<EODV#
zHh*K~Ql<&iN7W*HGNMZ-Od4N!vHGN0&~n_Dggl!1Ph-_>53ZG22tZ}hBU(y-YM%sW
zZ4wP!s6uQ8P}&-7+<~WGxs7K*<tdoQ?AOKL@9=RxR!e*f`u8<e8H3V0v7r7X*cp#H
zaFq=+jK`>cMzg&@m8EA?!ov~+a`{K}f_S`<vn$>uiHh^3U$2dcsoopQF|Reg+T!O$
zm&rU)Hlwg@gBp)Wd^}Dm*SRp%O$AbO1Xrwl7F;(F0#_4>>{IX$<DdoN(3}YgEo+MY
zu<=Y3HPaQb$~-CW_<g6pw=;w66?sQxAyoND;d|JQPkG-xlQTZvKr2ZcBqEX49fhcg
zHlE-)*saI5p(ZR@7e^f)A+yYXgzxSkj@dtV7pEc7eqtHt)b?bYH#pu$xEu4FV^($%
zr($N7s0M`pm##0#Wb}e61n&mpy(-JfG0SfEi7*pM{{9$z1mkaa+nR{!)>Y?R9qW47
z`sDGmbl6<><oh1buj2f@;{=^fHzYs03|eq=of_19Q;~w<E9(~F1gsHKZG0~cG#S+0
zJS4<s&Q>i7I_bBc$>4!{+b8_o5!TFmo8QmC*w61~^W*c^xpkPy2Uj#cs}m^K56S2s
z^=xx(IS7+$5?$2kd3jac72zyBxn{tL%2o^}!2l`qNMDNk|7rmuy)F`M&=(&Z@D$dB
zHs7QG3IOa8U`QA|0R;F@zjmew@Y3vwR)eZJp&|T(+7AsbIBRCD`w@Jh){-fK`2bVt
zkl>qDN{4(*mlx(ml()Z$qduFX)KHngCgH84dK_vLR)d*hP({<8{D#oXC|4?D8y0X*
zf)pk5(RTW-PgE!HJEO#STheH7CZ!rq1$|pB0}R{q#NDX?TLf~o+03Bly&Tk(uHttF
zcKi#F%B}bDJTo~n-ZBzS1}j}-+UzBFxV;6G-}XQO*a?VYi<Nk*wMh!$QvA7{F;9$c
zxnOdf_ol;|yF-EkZb~k4U#b%-fMEfzJigOLY#kE<NIC{U{h-FyD1ay%bBlo&T$if`
z9*V?AZ>j%Zn!Qo1kPNQ82W_uRg!(OcVU$MF_9k`c05yd<+)$|;ZWz}W8<38={!DM}
z)Ov;ML%qZ-@#Mb2R4hUZ&ehQwfm#~RkPUdjTgdvW5$5yB+-a?%zR`YPwQEn)(d$Tk
z=$J=wF0_uY|8F%Zyd5ysHND2l{k1)qawU8BaIwi7XFTO49qU)&;!0~p1LmFFWvY6c
zb`C{Mg4_|y&&5>g<LiB&2b@JYf%wmNc${<>aqKyewZ-2cz-*i4@>&0P8Dm~M^a$4{
z_@V*Qx9N;#B7qq<R~H^ppi9+d+Vn*oXe*;cdS(fCfH(2j&=b~5zUh)n2>E>(WSVO>
zOGoXA^!juL$zqsfN0Q1pCnOybl*@wR*(W2EA+D3P+{74)UI#`iJbe=0=>rD<<+~$t
zq@Ts=VffF&l0QaY4~}~tu}SJKH_Rw5z=nx@i&{#!r~!vT6h~EGRxNTT(gmLBc6<gR
zt0av4S&ClaZ{Sz!hI#?Bg*}EzB6Ant%o4wtO84v6bqNQaD@+2hlxeyzOhE~E93jBg
z@~h&Ly+(FgbyK{5x`b~gaOiuDIbLvgm&EvVv1Q{z1OVlq2(<pXQ%|}DPI@wa?z^qq
zdAjfzav3u_SDVT_eOE&H=BN!&N|&?&U$+`=V*))!;`6OhZC%=?jwilb3XfTP+{S#G
z%>G&dlA|b2Wa}b>9hDA9i6m!3C3CtNNd}%LUKlODP2mCl`S}wxAgYL!`|QI~M>J=q
zKgNwn$aCHM*S=~5liKX}QsehGxD<FWFOCTUCmssTs;=st%n?H%buoa>-JW<Ou=aUi
zVa^@~#R=*kyrVD0pjrQkjl;{CjonneGog$BRC5@oWxW%3+HgCbEP#{bMB0gtmyasy
zRTqn)JwwCd7Rkr3Xj)ub{w+lT$*S)Fab8#ho)_v3F{-?3Pm#;>e_Y;wy^LJtpcR$p
zBe9Pcl*U#o^)B2NCyT24O4TFb$}%s9nR!1#0)u^jVZqJ~a0~!{6&XW&fm&F*Ag<wz
z^AoX7s7$28-33Ovwn(uy6|F*T$(7qzGjKyB<!qH`4}TkMH3D_v3PBI{j<@(kdQY#n
z&N&&IyxCZio?o5;r|;b7EZ96qZd_g}Kk9wqJnKot!pK-9QD~Y*MYSLXH*EIXx_%G2
zu@<vN(z`qvJ6+4kuS!@Cwq1LIcu~3+c5}zQ?4@L?pkUrnkySkryWi&I8Q)_AHhM|7
zSo{FI*nJm+&qwSlY_>ATM*>-Tk4$@>hsrUK=>ax43$MK1tTu4<8!S;!Ecxc?c1OFZ
zwI_4`Zhm+(;3{#vf;PwRSbG|m@&?IhV6|8|@2i>cMeiLFQl@zC7TX}A+Z$>JTOT<g
zrGr?nH?fu&urdTacF>eCWz#Q43y`#r%5z~wV>Ku_PnBd1k6jc3$XT3;jzp88xlVg$
zMl2%^79mmFYXDmN_vu-Sl(gq)_+srMCEa-Yg6MT_(b$WY>XYtQ@3*$ezy(k|q5akv
zZ~4tC30(RG>ZbfZg-L%GW#lc>jOG`l$U4@(MSQ-28I9>BHDOB;t>FR3X|3i`9UvSi
z;Un+%%Be*0i`25j*;J36qg3XQF9d!IZCjELN&>{nGg`Ip#g8!}Vn%-RiW)a_=@8K$
z9XL-2Cb&q2(r+EBeRtJaoEzUfzvHMs!oF{RR0aAdZI}yf<;o4emLsw5*i*!)Rw2_U
zxQIGvja4+e^K~@4I^z0sO#R)i)WttiEhYs&<uLLTV!usrtz{F4v<l5KjAk_W(XMAk
zFxETo-BIfZKG9q7+_Dtsa9XLyL42__m@xmI>g@63PTWcl8Mu<#$?*Gdd8Gb9Oy7Ax
z_F3=t!Bt<d9ZWw{(cve4Y&z?2db9c%=l)4{A>EDGx5<K}_gh@)zkLKrx5?LYgi&2u
z3Tvi^dPVCib;d=(g`{G@!PoH|9QiXgt6dpnij7};A8>s~v{+iKM25-O4y_v+RF1(!
z;osveM#F<$N+8bGyOgH@Q+6`~QkRgmUY=~Z;lOfM#MNqz&0qf5C<01&b#eY<_JZog
z+bNrYBEw^?zx7L&d6xs+0HL%!8X4$X&U1;)p}gt(OIy!Md6$-sW`dK5Z$!M46P}Of
z%ljo)#gh>{H#h(l5H+NhWi0O`(mXxW>(H#({kH0RnGyzugKVeQtH|ntqvl6|G>X4{
zHga?P9@b^*HN89Xyf0*2jj!v4jwh=ZoXgjKS?#@a36i?1huW|#EcHN*9MGMrRWq<*
zbks0CX8ZW<&Vg^n8>4o#)fSLW@i8WmCweB|l21I}89H=lgZQ1PO=7=JCZ)C`h|MpJ
zU&eDVVh&|5aJszz!vXyNwgs8uB(|Y!o*uA_ZbPEP(!!W-+$mRLyE!{2pdgx3q(m=|
z!5z;_i<B4Pnet&`HRP0JL3``Cq_EjlLc?&t)4BD@o)*?U8lE<J;@ah4<`jmt`y%4W
z1zqezZa3}It~9N-M7-<8V!O&<TZFfq#jx<eXol-n^_V@%GU+d;Bp`0p0!Z3(^>K-3
zub=0QQaJVj=d-D%=2(W$qn5itp}*NB8`?p$u$y^VR;;f|)2U;8@~;9kJ>o*Mlq_e*
zJqY~Paxx}d;gr!+r@m#5BuAc($I7t5)pK&MBAAeGC;Y4_XI!6v-a$&^)yJ(4X?KKM
zwA({&%<6S{P+v1EYg9edMQwQzIOdPBQihYL&s>?;6H;h>(`3pjas0@ee)w?Kr5HwQ
zK{ZL$r`SE$F<y^S=h#z{*K<}{U3Z%tLxWeFU2Lk%*l_hs`HZ!1(PGv}SBm^EO2rY?
zLrQYJ;m*LXe@6A5BFWk)V+4=OP2cfS6W*?0!(!PL=|a!C&Rz&rF8wZX<!0EsHVUrL
z|JxPCbx($ka8?TS-mrh`g^Ej`7pW(!?`}LBBV-Ib1cl;b{WF5^s^{~mQk)8CK_fMJ
z1Eyl9to4he_7L0_L%-}P>{iXDMG>zkU}u(PEyG?%*Gt&$N*Rr4Hx&1Wi4-)g5_Jj^
z1pItxKg9T7{sb!ofIe!wAA_Q2X<N1&icuOVvZh+zt6a>XE_Mn0(4dgm!hs49Tn<*x
zcJO4POL##~j$;<OW}thyoy&#o00zY6CYrS7e@vOBJ+@+z8Etg{n)a8G&+ET_Y<*8_
zff;!|%oLhb>vRB_GNR9^dX1ShhSaexFxw*`&|>E<9lX)<g)~m-lKY9HXpwqq8Ub@N
zpDsrB0`j}&8kMyyIG((w_XDEkeUK}$(8vo=sBNmkH?2qx12FM&JJt19FWZ+{{2!ag
zMk`v#t~!<mv!78(SRR!wEk{K^W*sT$3;|l0pV(hGAGVeZn-%S+uYZVy1g>Nh<JMJ*
z%=**Y%lvK^d8rX^V{EyaBE%1c1Ak>3bye169101h2SQqyOa6RmYq5v!9AL$QPM@9p
z5Pw)Qn(rgd=)_nvhKo?Z>A(O+PSln2?JReO&9uXOS896p;&Fj?8OTEc4&qN;EELvs
zW}?3DN14eWICr^8WaUxjaMUNGp2BOIh=#IlVIhpx{k5+O2#Aan=YK&#8e(bg>pD-X
zDJv%B>6@$Bt564vvT8rx$w3|~v`4EfF9&mJ7&}dtE2H$<!v+r|H_v@Af$xX|%eL~%
z?)@j}A<?F$__nv<+KFGwt9gdak!ZYd3VNix0%1WKu>ID5WeJ9qc&Ov1#nc}VzJfDg
zm?mfeaYI|yzgLj|UG#sOE+Y0cNDBfG;G0N8mmH3$v{SM=Tq5LgK<`@rqafu~zsZQT
zXV|A~7+<=BAGiARdCc9;sFHCWWAj#AdeJ8upmzYeVgT9JLIkJ{so<VOehq%5rIvJ$
z@$`uf=e=*mC!)IQL4+b|+1X#wS2YA4Ujfys{qsPioPO|JgMXM3qk-#J<m3C(Umuk@
ztz*Nvp%rJG+k2&HL*c#oAtgewp%jA_BFQ7q4s;+PA?IHw(|JJUM0tVYD7y=N2@Mn$
z<9dM(Y~!?=CiP4;bAG^5A4982Q)Fb}EH%9gk2%CFXOd>|s>^Z$i8WPYcRI%&W1JiT
z3HTh2XVv=VT=D*?0zIoy+rgX8ZxhmJS<c`H0c{t^6_$ybOa=A#t3DY}dv*0<n&hfJ
zCiZSl&bd*@za7{O3*-&zNvS(i23z-@xv3a}^8VwNIo!vqYJIsfqn|Lwe`OH7dLq`q
zAEUorU4jzdCb!$aW`#*x{U-ZO^5ucYme(f#=ezRf$8R&*SKX}^wn{PuTYV>yxkWD@
zJD%*bK42@$lab_36scx4B!p4~iXWEQ87X9vrCLrqd$yis0q~h@w~ptF-aRbHt#7GY
z!|Z$+hqFyixOs%&H2%ozgJy)<B&flC^36SklXC_-+cxQy`!{`F0wqg|=UOaDd3+Ga
z0cKO>t7^mqhyv=h<!wd-JjaPdbF#^t-AHP(Fs;8FGB>12UsR*EmRmss#RDnEDuxv!
z?r^o8s6Dm|G&tVF%n_&`UT8>Q`eVG}f7xS`jWBb(U4yT|JCqn9?4^s-gEb)nOqstz
z^0I!W!Wi);{N4M-063@O_nrpA(`O!zKoxB!#0gYm&I<osvr8RbKVaFa<Gd~)YTG&Y
zVHtB-TaAqEcHM*KylD2Y2nv}C@Fk`HA3-2typ7z0cqDf?Sg)@5{Ie~%>rn&fMo4Kd
zT7GuUN(pzxQ+S>J?cf5aV&`(cT~Dj<Tr^}6Wbp^|4|P``*T_q~9UT|)d%|{C+|~dm
zRHRnu;Ao)_VSMKZ{~$u;8%ZA%6DCQw<luTioSK~I;FjTj$cG0~u?%Y!b%>6LYn$P|
z8$Lhm9d}Ddc?^8IIT#CAZ<MeB+&R;a0*udD>P@F_udlNw*ND{BWs6`cF`brI2Sk5n
zy&(dqI8Qo_KJ|eI3>tUUgPpV{l?<$8Xg}vYFfxy=5a77{IzYMtcxb;Y`Z4vDscnxY
zb>WZvh9Pf?hQGozHaO-jd~h=*4h2s7$}Q^Uy<h;La61Q@(fN*M#ruG}0Kh9q?0JyM
zp$#zml!0I+`VBz5x25=OX;J@N_8tzct}%tsJ58np>EF16L-iJiZag;%NH_Qf-MFFn
z{c^`PE>jIcNo3Pi8BFtP2x_5Af5&i<7rQkWEde2P?zdpwL#-wzNc3s=csfqV6tw#Q
znzNB;ItLo<_#z*XRDk}X`;&8LJ_>b+Y88xW#xSR-kYIv|PU&ZeEWqTt3JjF<i#@c}
zyw`_`JTm4V-+{w~D4XHrM77}Sk=@iWVN}0BxIU0lc%lNJ8Z3Z+7+Nz(AVh-Ho`qxZ
z>~i(4K9YY9sRN2ch-fSYA8wGrLBi74Y4yJ^;Y2qO?pu7&JxPxmNw><y2!8x-1*8Vp
zDwt5~wtuUwN3q2aBKyA&ARIbE2|+|dQP^@#X#oJjyr&ycfSS5ZNPy#Ide5mf<O&F|
z@Wxk~lK>41THajBSQRFufB3n_i~v)(3lc3LIDpQbs;ld6h81T4M^o@cqQIFjeyvva
zAp#T5+^hVa_<w-7G+1tI^jF57H*6FLjcfnlk4GAgeSJpf+jlq)g-yf#c%{KO6U&d3
zR_Cy6;3|W<X9eJJ<gS}6|HultQ0MPX&OmL)aTM({F|fssye*BB+9Myi)+Pf>6qq*-
z&h3+KJsW~xfg70A*jI0)l|(wG15F-ReoKi5_)=&rK+pJR!)i9}N8PPVa5O;mXTg)z
zs4&w?llMA4;%e3pi~+i5lzt1^ih~IS>dSVsTI*+Azug6WK>mr*5v)1PKnrM>)mIrB
zlwd`5*rBYQC}{)6nBBMJL3^Bp6dF*klU66%+?CQE0i|v^-4#}4DtKK~o)XX9y|#KO
z{mLmqN0W_SnDec$!y%vC`Y`t7dN&J%TcqO`oj2|#dYLQDTkx^d!El62?M`fmdMQpL
z{Zjz^BdD7E6K&K|j|6c>2B4JC-Qb$2?ZzqR4H=7AKzXS7+o4TwCvhTk9(mWURXRn)
zc;+ckw)NM0Fm{GSh@#Yg_=wb_s{OmZ{B|`$Z1;}AWWcO{^+$NpEfr+gBL0XYO@P^#
zIO!Y7jCJ&t)35dG+Nqk9LYgVlQOhhH*xwpEf`Hja#p89j>(Rh`HLai;nUYP0?7n4d
zQZiD}#NTyri2;D0*nnq*mdvoEW&t(i?oVQH%$}Lxd|RvIB-b+t4)G&IK)DMihxoK8
zM}EbswwSe`J)ANEKcnfOZLl)z7MW_EMN?zO7X#e)l}eHB9LKs~ZzlV|^dzh@Ra^ZN
zh<nPZCRSbNoBF>)I!PQP`m5&ju@_MIvGhp)R=YCh&A1{p66baSPVI=*a=fHFhWLK3
zvntk!2}7lRKg)D(k8ZSOr`T~~G@b=*Xfab?)W=P8U9d%V-YWC#9vw<lAcNyrnT-#9
z6kY?NaGV85d0Y=#uRL~!w)m2;eydG3UG--m?G`}#tZh?L?rF@h1$PLi5x#ah*$`%4
zUj0!CKh3U5&?Qk;`M!v6e~@UHgyl*JTjkTQHJDCTagIq6(z0AYr`+&^{W((aHc|^L
zjI8RHb%dD>B*q6byz-dLv}pg%gbaB_A4o65nG7)U*%N+**084-9@~SjmbA67JnYJ^
z!3Ie7ewwOtS0prkSg{C+VsE9Ebh)ZO10_1Y#=j_^%9O7s1JFzV)&my6uy(lr<V5}q
zq;?c&z0LlUkt05SC8c_?7Zumh!h)Qypu&r-Ozn&u_6rYn*GTk46#nfgIW1^;_49QR
zfM3TxZxmbJHm1WWihB}^G*H6^fpiFaA=|ClJt!;f6vMSP4Bd?bK%u|GXDf=YEO6u<
z45we4p!xK7%Eokp7L&bz9D=BAMsTS~i@SLd1(PUqD=5~7?tHH+IqN6BYO8;~oICD*
z>#y6M=^9<dA6)U7j6+a$&#|bRr$t)U%}%@k-^A+SO#5IxMx()snX{#~y+|@|==N-6
zLPGbpdm4V^sGYRNvlK?m7QK9$EygOQV&S=R`lt4F%3+N7=SC9pgLR&a6<<Pc!PDDz
zH?S)K;;AAy$hE?&FJ0Yl+z(iPm6nVLFYa$%Chw!H98UZv&LLNH+Hcm-vAfl;7r!2&
ze|G+&`j@(v^a)4q_q?Q2W^_@0IC(ds$ox)=J>|U(<8}zz@s=ANYRjHE=A2_eSckwT
zky7K`onW5_$bM}4Z-KZMaSUfpqzVcAHI!0Le8-eLHbRD0eT7_rCi2gh0#vMFw9Zku
z7P&I`a!K9zbqLAX!60YPqyZtSI8M)=#j$MK9lW<yH@TnZtd7B5@n*freEdb;2gWnR
zM1|-Un}A^Xuq+#pK~#AWZ+)B`Jd8*yvB|j+0D?5?j-?6JuV8Apyj&xN@@i1%4Kv{s
z>+huL!)|q^ThXV(E`X@TT16M4k_gbvR_y~Mo8|9Sc2<i}o>LNFYGiLhjn>oAFMa<X
zwelF<+)}$ARHAy;0BUl=n<zeoHYx0*PgHB4s;WgfK|<`h`;;QUx`I%wKf)e7fCm7@
zC9lbn?q%p*y97}aj8qS8W>UV^--ekVV_C2E2?re~6+TXX+k8BB5dORHbT-s#y-q&A
zF-b2@kXM}lo%gPJYj`lQJ8O4C@P1#U;J+phSQOlJoyv=@5Sj0h5T1QpA!|Jg3;AZ;
z9M~88YpP;W3s>_Pw35YS9E0aJnKmslwAwTG`zyfEV*`Ca!p-P1DV8OUhp(jJ^rwM5
zwbr^?J8gs2m!d{7NK)N-+it}AYi%W8o6RoryoM0vc$9tLcE2{e>XFMB`@RX11U}Za
zMQbLd2?JzZH&nEEf(b-7p-A?azgYQDF4rxnfmE_oBW8X5w@|NU^lFOuAGEu3;A^z2
zUIbSj3&`@nn+l4~Oa6UiR<rgA{8kj(nNflw>iE<1NW0O&u{8jw-DJHaP)CVyG1I|R
zKgA$G_1t>;BOM6<&@r_7OJoHyZ5697BQKKjSUUX~hU={gpy(F?(0vUKuh>4N{=>)(
zudZdecC7S7)BEIQ<K*hw?^a1Orx>wXiAviy3|e%CqfP9g<1?Ax7w(>Z7@LVKHQ{kL
z&O$(Jx^~;EN^QRz)u;SH)&y5WK*a*w=d<YOq*wD<gMLdFX*I8Q#|XnAQ<bGog9@tg
ze9|FFxeIegf93rD7N;Ma@;0RHCOKa17i~|-0MksojtlEfElfVv$ew5&<}UY*tpTwz
zfbWG349swZ>`Jew*<|gzsI^S}jHiIZQV_vkf*C2oxL{^Kc5<=Kf>RO^z0`gKs|NCf
zUh0_OljVohGr|1;Vq~@$39bU31O70x1wJmRI8z7M<B&E|!q|)W?}@Tv8M<ziZ>K`m
zpA%^`IgmlT0SV8dLII8C@ar|@KQxMXBNEUCjKnsIPM^eej+&PNJ0*}+gsh2>^e3q!
zc()Nq9(_Yv@kJuKoY(-e<N)T}Ri_*|tp)y@Q3nml6}$Gg$P4@X=d!6r>J2@xD$QrY
zU>j;Y8HCy;0qnYEw2NmL*Fk=rP>z4QJRs%=KfUSB5Pmyq7Fl$yfxYA>Be^0%UjXE?
zQemja%isHyUGc(s0#BtfOz~U@?{>J~kQ3%!wtyUNcp!EWAI0@Foz83B62{l0cy^c|
z9K<{ZpDmV6WmAN2L$7zM75D7RxT%C85)Zs%t;bh}^}|CM5~yWZFO4Ll?_92&j~8hF
zZO{5Tq%Rn&kd16)+&yhNnN`lqJ~4R)Y14qGan}^gk6pUg_2&S17xF(%4ixEj!7VMd
z?&;EPe9h+9SLSs2kpIYEvLjp}8a{z^+hr#Y^t2qIO?Wm<%b+ap<kWF!eYeHWKkO{V
zL~i|qoYeT0vw<QYD76f^4T0Fw=vkkLyK&ym#Ffw{c6{Gc7H4W(<<l}F1^bZm*{B|E
z3lQSD@3I>uneDZ8qHJi7xJY|>2{pp<h;{pl0u&ygY-7!CA~!#megFn0h2Eq(#1#{2
zz=qKf4_mxmY<#Zc&_&=md%v?Gk(s7J=FY`jO1=5k&_ibJ^aGcaCzbP|iqz;u5~4G_
z$d(vEiWoEgeWp``gT7ENGi-rW`G@jkHB4kroh!Xl3rRmaF{uG?fss-39HnCcW*(2&
zN#vj1p+x2|K3md21jc;l=k4gLTn;6sNd+*Xe@pLbRG?W@L2OBAR=hiXmDHoYxZ`t!
zkAdQkL@z}r|8}p0PF^*yJ|>$D5I|0Zs^3jlnk+BKgw=iGo@*N8W-PJdEojB3k4hew
zU2!s;5xwJlcr~G=vSxX%_>Vga78YGqX>>jq0Fjl`sP*8csqtAQ6dA4I$Q^KRBmUI*
zN;SCg#QYC&{iQL*5%KvHv~HUXWw2HAI<2}>L^fw=V!sNCRZM80?V~1^VGQyKa{SRd
zTl)c#a@@0CF94V1h<Pt1|6f7DZ_u7WU+<_h^|`!x`AtB|w$<)swX$b)w5P`JMiq5h
zeoT7V-8%t(zs{>TB_Yt3)~z!Vw$ZjU)OH?Ga<qJFR*CK=XU$mbvo;3kyKb;M1g|ZA
zd)%Jp@VLL<)~$)BLY@r5x_KM83Yup3U;5GxHT_Jfj%q1i5VR7tgNV_E#;pA@rbn#(
z@U?pDV--M7(vP?H_HjGwyIq-nCZm^kR(#v23J$3iLU9Fk!W*Dnp!QevH%GMs?nIE0
z`p9ot<Jh|B^A7_xUryHfZ=)WV^jRSQUW9ig^jl*WhRh?Xn<J9r-Nb26&W^E#Cs%T!
z#;@fjhJjj3OeXRik$F7(Gd*4Lb;xh72z6|I_JAq`OeyfpWt)Do)JdqdEWg|n6a?`!
z!t2QjhnB;`JdVV{U7cS1z17{&=U516qWGD{I(A7;K%_9=6DqQ4+nee-@^Zu<XR`jY
zUD9(0F1@3by3jksl{maq)%H8}y&!8a`BBtA+E&-aYw<1j1;q1quGU7!uXS#l8L|f$
z*$NftFP-UN6gku=$eW!){*=e20+T6`BMgg+LZKKrV&WzH?oH3U!Y|ofBzS@SD`#ZI
zZI`-l&N%`yOraR%38jojeUdG=ofep`psa?!7omz4y~`Re%gDGQMmv@USq0}a?948Z
z={)xwso~XIHE(}D{j6^q(y{zPes$o(g6cTr54b^$S3<ikAWJx6;S$D(+`QR$s}SBC
z?oa@RW3*^JYEON|Z_7{4N69r(AIS27{oh{qLvpejtd{FeTU~$!@|8E`SB0iM44T_p
z{P92`v(CRVX_?dJW|<i-!(G-4^JgD0(OeLenXPNb__e?rSg6)NAQTI;YK67Ce_c&|
z!Jy0XKT{*py5l~Y(;NeK%j3<eJI~#FVU--=@AVW~I?4o+AJ!WxeZdoAyCE;H|EmRn
zdR#0(oLxFukdTc^FTv>JqACKT`<PRf-=3g}JF?GcjH<DZD!LaVYF+7x2EQ{i8B#<|
zP{E6xQbWlUR}k8<y;Qz?l>lm}8z?UZQ$#iok5Qs`{>j0{nSpVsml0QN1aAPI?X}>Q
z=Hne5ut|JlKNbZPa4PJ-D1gZdvMvfZtNyVWRBd{>StTEjd(vxS##<5A3IYDc>da6k
zBcU9p292;CFa2sDfSikxRDAov65(iaN2Zp-e}m@sP~gKdn`HW_@urC|ug7bKjY8K6
z5s=vhI^U83@a#W5IJV%N_(H+)xbYRTim|sHHAwK-7AXKe{dJA|TaPwa$Bz?uI^4bg
zc?SnFh_x|8%{uflmEXgzyJm6Z7#~yqdSt#NjDUa!$m_$RF#^;$&t<278uk*3gCtkp
z*I4H;3ocoY6z_9d|7}8UuVDlXH%OWI3*p5iop;U$K4OK<{VJXWW+LNkd+~e>>&NY3
zcu(d%T0`ooQlrXQ;A?=~SxJ#DM{WBYU{VGnzUY09kKpIf_Iiybn$SD2qB@rd*pRNa
zh?8;^X@%46O)f_=<fYwY?A()RCT+dfqq=^MbN8O|EZy1)P1cIZ8!&w%)&N^p*a#T)
z&2oH77W%hwiTy2%g0|s(Fr5xm%Wj_<PPIfllxEtu5UCFC?vB`Ql48fIx~Vyhi?t-G
zy;&GDg?jiN#N4i|bkZAT;Ucc8@m3tFc`HL3#^H9rad*EqZ!Vie3Ya@k5e@ezb7TRd
zi<&Qi-j0hFz0=Qv9RO>OIrtS(T2GaJ<YH)N%N43uMeeFf0fI!$+95rnX0cY`L~{7N
zA`h5U@^f1{qDAYW$g25&lsWh}MNFIL{zt|WUhy~-_tYPYgXfCiA@BsbzpF|N4kZ1D
z1+|-o7UmeB3RvJBAb}5ish9R%@ZNEN05AgAn<NWFrT;MPAVh`GI_~T6=ME*DuRF(d
z$nRH}A193nKQrBLv&A1cXGHsrtQP4Dy$NHDe1BfI1$BwRfFT@L?q!r7>g6e>Kr?hy
zwTw6RtlJwj4xu`}V^m~d&ai0UHq<RuJ}qU7r}9x<eC5fqBTO(k`}`1pFheFkkpre9
zYQW(v!`E(tyA*E?Ag<!m_)Lwh1m2xkKqjzZJOJ7y{hVy|<(qsri6ov(#}Uscya`;J
zz?+Z3&&w&&HfNS>bs<J~ZJfFP)_4-gUyE7Pl=4r#6+K{PK2PLWEVSJ87S&7wZu@7(
zQG8o$9*rk|zIwUI1lD~^?hk-O*v!GyE0)@agng5os8~J$?@`Z`yXYt`eeJ<kjeI8%
zdT<}kdc~l$>=s9eESx-Q9(ncv>mnPF{^JD|tg6dTJY}st0Vr)^=|>^-!1%$X<vW`r
zq-jnP)BknYj6M&0_f()`H(8V!ZkX*H1y&ztVr!gFd&)Ase*XpSAf)&qg@%I|u+=N{
zel?jK>*I8LH9xx_={PdQcpAtAoFaQMmiHaE#>+I#jXZ{@dW;#a&*qDY2;pHKWP8Ot
zZm!v6+4xS|*8xre*|Qya!=Y2@$Ft(-H)(~qTxeM~bb0*@MzSZufGH^0_{9Q%7{6#S
z;REW=#3fg?AF*0~bhP%>nSl&dObPW6Ic(kE+ZTzufgJisVZ3bWQ<PHWU*j)O3ZD^O
zLThmkuDl6rLML;&V_rl`J7CA%qH5X*fAVK~$Zp`05*1m~rCKc6fq%Zb!eN5wWQx&0
z!+Nc=Z36LkIt0KeBF+gu^Vbb<+hH(x;}3N;x-lbz<VITt<@w+PiV1KaSlXn?m3TvB
z6<!_0;Mf82y1;CALS~@Ln`<%<-~LQL)|gQsn%`sEDCiMKYB3b(JG^mx7KA{xRsq`#
zm`z&&*n&7+_Dq_!=^!yuu81ov)0+o3bXUakPDm9>Dcnq2y7+&uh`*LC{{2FXb^gsy
zd}Otn=H;Cn*j+$toCu|}csBVCtzZDd*c)I2)M9D}AZdF5;2CqB8!sjtj_quKDQ<7b
zQpn+$tE-iaor!?@X+9tGqCk(li#jh)(5@EGbbA1|1REeYbOdp5N1#$lW^w$0cA@vk
z(hlbcs?$^7Bg>|({@04Lxk~Xr>4{&H$dQJ*R-}PTVPfUW)ZTrs-)p7S@(%qY9ni`C
z_7;=IVBKIrb*D)(HvP#@>uarCL`xl`9mGV_@MB?QIO`E%(fKw`hy4@0T<~r|0fn!|
z%b&z=euNJwjsNDI8UBe_?H%CXM>z-l@aGvrj_y1#<|yRA7pTsiH2&mDC!cXJXG(wo
z%wShGeYHBgU?O`+LO-{(<AhEMFNXP%oi8%)eIF)Scq7UX`yR(1tUO351drs>{c@cY
z6)_+%>B7KrF#F*mARz|=;9#%>YxD90$jA(S2j-K=wK;+PETmo=8-Fxn$5$f>qR2o=
zeQj$=^_WbXxERko>^O9vIx+LiBa<P55bDqJ&O~Q)5qZeoT_Vs-T%D>W^IqKGM6v}X
z@z|~xeek9@I(H!06h8Td4{HAH79z=~K9Pb>JB8#(WH_~wf@!sxGn4yz;k3x|qL2b_
ze#t`q{7_v@t8;RnuuvW_?^Mc?b2J}E-sk9plyEpB=Rfo2eAdZsMy%|=bLzJ0X9t(~
z7y*PNg6pC^0KM+h=g9d_asU2kml%1y=W|GrL*$i0VPZQCDRp;sNa+ecQ-dmn$okW5
zRWgURaypRIHg!0OEBO{koP&kyeNzyx(L`rBeDA@Zu6X08qpExv;>GOv_p3M2M@j%&
zPC}zWhc92nsp5}IH@WcDD%1TB&ggZMxgN7UrP~i=)V?2aeDbrKxDHzLkGYmk9XB=M
zh3RHpTS2ZPx7sM61X_6V6B_ZS654NSbf`<bg5$ZcNy#eTaE5KDaf#O>tslScUZjg_
zq>ye$1~I(tSz5KLKgULMr2lgr52HyP*cCY+O<*#?QvTADji`)UTk=tes6^RDu`8d_
zRu}s%TY`o7pT&tyUMaoW>Rg@TGNG!l$&$CwJIa+OiRMN@*(;8bckSm@=Kv_+Y<KFQ
z@CG-n4eW^dwC;`Q*aAR^<q&r2wBbM`Gwf;ax466}Z@=OV`FFp~z2upn)W~is*rGdc
z^pRLxV;DPlc}c`kI$cL!8Pn<oVV9*ej*!$?$m0N#r)Qs}$b)+}C(GjBE{L_GP~>QP
zqC~BIJ!|@0@fGg-)gM7`3pt98^Jb}9ccLhbe<Pr1*RR;>mZI62^H#&#{T$x?7@8Qu
z6+ZlK`)zu8kpEaR3eJa;93jjT@FA~NB?UE{=<+)A4da|N3K_-pT24^<P7I0ac>DgI
zKb63E_f?o72sfTETI08EM0Z=`SgJ9pPMJn(R<Y=$79jeI?F!o6QeM6A_BNnPV*5<z
z(B+E>GD9Hdc1W6<?(!$;fw8Iq9OI)E#5jDNc#G_DsQK5PFj?4<?ip&<%^+fn{28bq
zI$m_Gy_ql%LjU@K$0vxeakVGc^WQ{`j~97VSIGEfZGDQ4C2tT(BIpOc({B{418Hx_
zO<A-sr~GeG`6X3qEX#F4QD<}BLyQy^E@|UBVh!w6Nl&Y4t#8z$YmPTxVgm7**gEa_
zZl}WNfDSMyuW)koA-bDOv<4`&Av!X%Ys>xjmu%lxSK1A)=2^MO5Inp^EcaaoaO;ep
z?|R#v+~%6KN~jK}lo9h$s$Jc#k4yDF8E80h-3~~km9GXCv%ejxn-PZP@ipP8$zaH4
zIAR|K%x=^tuOnO1ZU^(jqo6gZjO4d(b8XBaEUVh#Lx)7_=yRxcn0{CBOxPF>w+)Ex
zUWn&1#;Mn;mpGK>{ZA*QP80%E7i7un3wy=qoAlz+6a+zywGXG<iCQ(1qiRAj&5UPZ
za6#z+;b51plNUQp&@{@u^RCyEOKT)5`mZ$CosA2sjzd1lMIE?BpNKP;{O~Hdv&zI@
zfwUS~<8Gfs-P`_*&l!D?<)066=`?xKr6RM10#fev0+U8-;FFkQ!y34G9!xpZ&sb?A
zIh<~fmWMxIg|+T_=PP&s%yC*giD4HSM3d|}Sl+EJ7TtT!jSLVM)kb&q)6{hVAuA>*
z;uUYHI3p&9M@ERCZjZ+(7p<jMi(sk)(}xvwdgp`7HRRz63{}6l;XhwO#;1O1!i2n>
z+Y_zqZmB=s0|6tuQ{}u0dfe1h_o8*!23Ag#;YQs8=Q!%4M6+g}$O;ekCV?cG&R;v8
zZ%)H~ulCSR?+(niM>&J?Y_$8o%U<%M2m5-79duBGa@J5}_P4;_>JDA}3O_GhRsmLi
zY+SOsx^p51P&;U%{N>4;XtUSq)AS#^A3_-3efe%-xUkLpfJ{@Zj~pNf?4j9gN?9tY
za({B*?aT;(Tye<F-X2&xwtPsSe??xU#gF38d!iMFh6z8=lm0{lx{HKOp_3Ro2Ji`@
z33?k&e<ZFC-d~8gB9r<H^VAVY%C-`Xz3y_i(hFdeZ;43UYd>Fk@=4;1kq$4QDsg67
z5KUTpo!WzW78wpw*@(AobCKhGFIZGnqz`(#SxWzlZ3-Cq0hVo~qQNj%yWj6);Zpva
zzSbEQPu>@4iDIRhS?IWE9K1hvrtQU!*l-~?-NySn7i7IkEFy{+0X3B*iMdni+8yOX
z%o0kUG%>CN6>pk^RQB{rw~sb4Uyl5D4>J~QPF#+@DwRr>7xL}w&Y`d`y=|35RTjVh
z4#W>SH12%w+X*-&`fB{C6b^Q}@{SBDE60uQ_(}_!Wv6*VLgI&m!)5(`h|Rp&4K0d@
zxXJgO5^R4UYX8gr5xO*4^D6qHic~)J>%~H0CkKY#4#!E_{dzFp!bkU8&EQ1V)K{!;
z!15^lb^ItnRC(FVF6m)HJ~E|$yyZ$Y<v8+_(sv;g*y;1mZAA6Ux$4fuP#T95Lg!04
z_IT?cXE5YDOFbv~wyE6X2-ss{=sytgPn!GIn}~OGLr6kYV)%Yh-{Op*b3ZT9<C8IR
z^3DDY>Eh@4;@4jrY5$wJ(BM8)RPPbyqQVHH>XksG52=4k-+6?b5Sk;tahuB*f?e?c
z@${AfQMFy$FdYKYARwT$ba#k!cb9axFmyN4-AFgmHFS4(cX#)<z3%t<e*0qvXYcb|
z>&R6Okg|GL+fRe_dmeM!^`K7}g01H6QuaY4Hv5&SLY>Xympl2->#+DU7?0*A2VABY
zzgh|>Y!mV#B*|*G>4aA=VEo#w{INTQ9n?A5@0g8>7l^2C!hF@)-{rSlS1o2XuWg`*
zv~4SfJF{ok?R#S3|6(7Y>?AgQ$4*d^Ux!oqFGfw&1_r@=kpRN;htd}D0~%<KDP63=
zaJBjO>2vE#b*Iq!*ir6<M-d@I^=+wLX0pk4Trd5}#}u*kzv#qte~)ZY!&RF@qR?Hh
znJ{lHLdj;a7#bsuRj!AL&wOqN7$K9iQl`LOX_dK~;Sh1HHo%-=uvm{Qq(}fxv=TO?
zV)CajuvmKqAI+v?d|hg53PPpCK@ugkWxIH0N2OtR`^y#oag~kGiPyWG<bWS^j`u;C
zi*i1a)@b-!TgP7gJSONKnamyX&fB}+-VU=qWB3xsM1Q^AH-6AFwAuc14ilE?m4JE!
zt;hs^k^Om@51FipZsy+He94v#8d_~H|MXI09<{lDu`BBPRUp2v1_rd-!NIytf3=g%
zRKdqD&I`Y~Dw^qvoIX6EwRfb|ZMYuEu0}WwD~?#(Qt^u?+M5#fre(<j2kWNfGp^6e
zx(UXlJDF>HTX2((w{WXOC<G3hB#eW(iBgDWPqbaE?sMA9?m6b-Jv!?qo1b&5sStr0
z$IsQnM5ZH#GWg5>@C+~e`I%az3e1)P%?n-#N&(LW?{w2+W-={)1Myihd{*`&@zYD1
zzc$aIzq!J6`U0b2Dp;{RO{#~zh$usaZ-^v>&to9e*%|hB`cdsUMYj5HZA3rPFZ#dN
zNSN3Vni{X8GXTMSS6-f|$BFqpDDFs}29Cf~vpL8mD15GfuvBu(O0Ukt@qGo>&Xnku
z0Tfo+`!J{T>FrsuI-@u1j~IQ+ZK&22^VN7(c+V<f+klSBib^pfeHl;de?6m;kD)-e
zYL2QB=%`}alfXE1JI)Qr(H4ImW-WVGkJzH4xo<VvKGxIT=RMmEmgeQ3$)+&5Hby}`
zR{Y%B0#e|VKqRRygE^(wJvBLS><#rW;Wgem&RTto{7bArb`-=UeCr7VBU4=dS+Nkg
z!``LF+jEkYW!{PY%*eB5rT3j;0S$JchAN%gRH8P=!3M00a9;9KZfN7461~SaF>Cd!
z&ydfxIB&F(5Y+dF<qUT;W+vq?oQw+!P$5hvu>8@-ZTjvj@N#pUk_XZ{?p%rjE$ele
zudqUj$3wRMWcE8%Z~%##)oNv8cYc(#@r_2V;Ous&%+PbRZzi*mz37%J4itO4tHc=x
zf<SXzrV+kr?r&eOc12vg&g!+Kn^OW<yv1XFLsy8&2Jm;IECoSp5F;lq^<+Ev{`sPY
zVzh*sV#Jy8)Db>)!t6+PvG)=&1G=Y9DYSXhKF8*>+MzWswpyQ{EVu}{WR9pEO6^GZ
zGdw%StT%0>P#W-5AU?mLBr~*UCTmfCH7oT}jhjy$uA<a}nD}YpkOBu?&f`UHc=rzR
zaJee)rmN7*40sV4cUdR}-Z%Mk4JEpAugBe^n@Ip<I5O%yWIk1@GSx{V!;AK3yC@o`
z%dpT;RY$sa!_{17#0+YLkxdeT1Og(RQfuYuN=NW>17sc~p)V%3Js&l-h_*V&?H?P9
zolrdunGEFtYxY~Fg4<A$XwdvtOi#JLs0b;Piy^>neH1Q-H2%^+A;6yWccILtyMAJZ
zK)w5z;!wVjYUXDkC!CC&DoaHn{#vH>*NNt*v0>Dd1y+XN&$di|kGkbm#}Icf|G)*U
zZ5*>oVl)jG09ho>pIyr!6~B@GG6-(PMpJO^XHoqiSM_nhNj_BCd|o>@tOZ+Kc>Fy>
zWd(LZltOX8_f}Y!2Y>Q&AUg%3<FRFEt0lgHI7}>CR4pi&WD#jV_kjc=^@3An1qGvG
z##3@8?MseSnYKIJapd|y@->85AFJRU6|~uFv&uNt>4La#MG}oQD4+Oy^$tuOzmOu0
z1>ZALU!NLebgLc77^&9a%L}3`cqurJI0_j6$qmjupoKCLA(vV8s}3+z(dLZB>##tV
zA}qL<on6zf?WL*9PgKx2x>6s-6@3J*9PfdYSba>x;BPGAAKo6Chn6$~_}d=dJhx`o
z(qC@SKX_&JSD7xwUT*pW_kd5smpDJCEXS8#8zWDyk8-+h3H6I-QWzBYLc{#iLe!C}
zbmfgm6IJ<%wuQ+l*Ig;)#wX8n3FUm)!ktS^F6B)D7PljZzx)jXe|=a}QZ`5bv{*~{
zY)jNz=@}HSv9g+;(I*Bt1R;TBrV2^MqD)()|Lx+wR#%8%uaQ$5-qSB~s?5dH@Y{o2
zzM{~Tk!=^eoh6t#2)0oymv@|)fGHpcLSd7HVa3+yR23CfuHK$iCC8C~POVN=kITdp
zb7Ao9C4oimx=c^XXk^uQ`b#A+JCvvnnQ}g&WAdHR?1+a=UB>d!NAk^nFwBhvUe4x&
zrJhy3Q`U9W{YmRQ=_aP^?z!xGiZ2qnCXv;ZBHbO1Dr3YE1)S@#*5jJMFv`8p1&rI2
zPkWb;%hEDDj$8Rez)C@}8{zdv1q@gGNSezGPGDF{NHn1?^tyx{o>Ti6?pM{%!S5dz
zJk$jED1>e^em#y&Q!Jr;gXyR@W&1-258FDHn!9iROByp8oCjVM_^Ee*4IPUAK-;g^
z_yNZE?-&TpdDa@s>H&XzkTk#<jOTfZBWP>*SHi^#5&(+szeMbHJ-?lB7pc!9@NZtu
z9IRG#BY(Pua{uU_a@PcH>jf8Eo;?I#+vUD0)p^81IXE34N@KvbF~~35d46s8c~$iE
za+szmp;!Fwhu-!O(JRAZyx`#knr|Eza|^2LzviV-w1Z`l;JeS2A3(a5g(5;Iwqs86
zq>?|+6mjV}c3#=Tfi=FgCr!;kb5M_;z$ZAhPK+jucfA>@J)fumWZ?M`Yv-c951Yr5
z6!2dRwySN$Md-o5l}vn4R`w`rrTg#IKN_nhu~);ym${*1$c`upES4zr@dr9|Z#23u
zcG5eH(30PSQi7aj5PHK%C~_WZutW}=0uymi*gnf7m@SI?pJ8}!bEZ-=8CPssFXy%<
zir5Ak&~77-C5!v&nFdZ7{q*%tJE_)RuYrSr|3a!@_`vh_dNx9u2cATQh(OR;HaAz+
z+R0ZafQT|`mDSJyFOBkSe|HakUmcP<?!$juJSTr`{R1E(@dv)+=^(u3g=R9|H@ada
z_@`bSYh{ukw<P#Kz0_DD*s9g@CQD_ToFCsKzI2qg-u^pl>f<75=u6l9>6l_ja*BS_
zV81<D=Och~z6SiIfmeFi=XkS@ndg&MFI)z4;(DA6I3WBso~=Y;E-Hll*D8jDvy^ES
zLAJn(HK3QA&x^_y!^ZWvXc!WN7Pc}}$1nIKEPDCV=qjMJ=(Wq@GyEIbc_E$)QVoEt
zq!$rnmDIBLuiY_EzV?$eWtequeaEuTKM}0fVq`x;@G+v<=o#h%hDVz98j|;X>W;KZ
zWM#zNqV<_-4nHb`Dv6o%B;vo7f^;$FhBDgA#YT`#GMFfOZ3Qb*j!2u!yF()Z>EyO(
zEDycR4drE6Wv|GU<nT4B{r)o8ExGRa4V#&L)_#gvYKi~Gf=G>PNN1=xKgF1^|5w>l
z6z|8mfz<KA>e|?Y55mmnQ^&@2EH|Q&n!_?ow%(-VRH=6s8-7O$7+P(~3!<I@A@`1p
z8L~7!>n_Rs!M-)ERScZZ`LspBD*XK_(B`H|Qq9D^A><*s<NQ1qgumc8FuX)Zv_kav
zr4CI;TIWY4I1rQJ7WpDs`%REat)BOqW@B3j#p9+m&Ldp9g$HTjGQt8<o@ft@_9F>B
z&;=ZQKg{#*pk2C5yr%D8_zSJ@+8_PA{VN*iY_nIP{;YlS0K3Mr@B#xX(bcAQS@?Rz
z#sclGD$u@KgHG`6;whJ+Z}hL>dV}m`5VmkMxv(P{69=D|`g{vDc&$;NC4}gL_R(@5
zW2r*miM!XYkmeKu!mrAWY?vB}YrS<#uPqu5(V6(_sz;dzXbE*W2F^uerAuiiL5L(R
z(Nc6XRXu-En96_G&yML5Tztaw^e+c*ue1d%N_4NVc?U*xArfd_`rA7C=kYf?jI37`
z^HN%czi*CREvS|8^%-IRPJEQGy1)uif99lIl&IW3f8w~u!*219Gzd`mj##>u^ubDG
zHr`7^1D$YIAH_qk%{1kNf^kx7+6;lP`Ey*CQ}_9VhtI&U4kO5G&93Mwp93<5WNco<
zPS{d=8l7xC8Q=>YkKGjA=(?6xXfpf1*bGPetN7j6ctk{Xq~EuQoe91IU{bFgN^;rT
zDba6;Vla>vJt0^N8v}?8)~VW@gjwMcD^Mbn;F(+y<VeBR;Zt91oP5%Ua=6UK;f|<d
zJ}}FeFo#~i+?%29(%K*C;gMH+{3ZceB+m2sMN?eR<>Cjd7&W_~5i06^kzrB%EAObh
zeb2y`)@1;-J7PuzLnypv_NX@ynzNkuxt<UM_oA3fLkkUflzL-O5#uc6YfOToUZ0p`
z-_ro2@7pQ^5%7#nHV}N`*v87T)5CEaObvEgmJ>vGfn<%j6h`%Uigz>qFz0=CUo}Um
zT+!}eyv18P*#2^PFWa7Ft@3qv!dUq0`-#A_k8Oy;#$KsYz$ffZhT;P8v1V~@WICWS
zdKV0Q&@uP1`b8;2XDMw=>qW05ri+w6J8$HK^J|qAV5pxT2jn(lC#RLlMe?rn4&Ir*
z90JfjskwWJrL>O6$Bc3UJ~YOtON~z<ZkU;V(u%sr{xt7o=N^PbYI9Opi|hiQU-4{=
z=?HMzy&Dzp6&mfoy6|DW@T1C@Ay<LGl6Uu&BnVJ*gu|1f^CX*9ux6x|iO2Y1RO)J2
zt)=&3=WuCF@E|O@Na)A}kJ>QFNBI`*|E_a#^k|8W=$Q}umpWMaJ#1uk0Ivl2=KJH4
zzLH3_`k-_yci?Aj&_J<g=gj6jhvEFt)Q)J9S;s)V+sXH>j6<I-=bThoHo^CLXQka(
z`29H)3TY+;Cj>!-bZ5wq44cyVaPn=+V>Q}Xy?JbO6B7g2D5H%<zPGmM!BT-cXmVx1
z%-nWban1O1-Wa0y?ntjGr9v`LN`1+nCWOR{78cvb;bY04_zWPkCV1Z3O0Z$*Dez}-
z9^D)6S-oekduOgJerVqJ)f;kY=<!8d52yko*S6olf)~>!XEioN9D{}$W0lP_`f<H6
z1TSA#$R0_CcJ+I(-P^+1=7xQ!nt;PYL;pwbmZ_!a)&t`!H83g=lC0kpSc#N!kd{Sx
zn!y8+Tr<#{+!CRJfAM|{*Pyo&5rK6fDakxuNs)%gmeH!OiDLCY8$TnR^6;tC`y@|6
zRQGkDbAMQS;3|+qs;G~z2B28}t*yYU_NQ{TOp(+zBbWo1fp|Tz*!A8a$<?B^8hA{a
zE3GN+`wtiHZ6P%JGMtcY1u4Xo$i39Jx90c@1(JRUZS=-a=z8ekT@1dQRQbFPj#nb6
zg9?eioR({edpOvC_gkp`!ehPjUf^;bX){-$m;;(V#ks@Xfxv=7qWL44AeAmv)1Ut@
zfKE}ff<aT<<%K|6riDb~8u)rS;kH<e<&xEVF}J5Mv;?^LzJ;FeyltkVAAiCzHuwds
zY54$9fCc}rGb5op&*Sk%&t-lFV1qYHCv!NZLZYl8*UsE}jnRifMP_Ea6jV9kCI-&Y
zZHK)jj<EmJ0??pyMSW~y6=*5W;&Hk36ziy`48}v`b5uP1kgMZ}@=pKJw95*<9N)Zg
zo12i$Q0i>xg!>@>Jr{@B(YR{_Dy?1FTADh{BYXrzgB6ZE7^`Gs8JLRdHB?o&yisQa
z+{sWz4H@|NZF;_Rs^7vqrYYHx+;k#^dUL#&_i)dD$7-?(+Z>c!Q);v5ttCCc3l!Hr
zA-z8gF`Nb6HzzGD>sHh@mqICBpC!{DhkB0V%NmKRoE=oV%2gpe&*SQorEjPFqNecw
z-o4}-QAx;f)$Z%YueS%K(bv2UWGPpcPp~H;DUfZ327Y$ma{xb5UK$Zr##<1=zvcXV
z#Rcy6mt_ZUkJ2A7Ytv|T!mAHh3WZjZ8O|&K_WZcV!9l2LR-E?bsU4(?xc1c58Fjqs
zyNdwTjF0j{bPeG*=Tl)qx`G!BZ0+RdNuZFXQ|uvsjMlW%@HK0_ifYN>tdwse;l~i5
zL9x=Jcw&|RI-L~0g{Fug^}!KBppC|a>`fPzhwX`5{B{YxpckT27eEE>XKhMnTs~7x
z=q!i~UwFAXRVrwx3!O>HmA{AisdqSYt_aoBLDu8=tolr5q?mU3#67M?NYKO$>9=4&
zaE*$?t>Syn`|q_ru}wHwEes+U<CHm9+)%dX=%JElQT@3RGW19^Tk`elvS;esp!fM5
z^MySUfEE|o`C4ChhlDHku7-6O_&>dVxOk|INM6>ZZyzEFn{hQJ1$MpI_AO}Iv?Mh9
zQGbAWpz9r^&hK0}kfcq+iMgEg|1>{FZgY@!utfluUr_`pXSiAo17N}TZDxk+_nRTO
zhvVnl=Q?@mH;XKsRtZYQ0IuKUS5}z-6Re+M(|*vqN|N6HcFCZ23p$z^xKVAuslKsh
z$<R!a3lk5ap=UL`Lon{#4<s|Y?fIA@t-k+tw<H&gz}?F|(!7le<fTPqqpTst@Em_C
zwuRM%Fz?z5!RMqmb9%!y%%!payfPry-tu?|0wT<`=e`TQpK;GwUtT=lDUnd2G0s@a
ztXwnzGLX)COV~i~5z3PFPd9Z5X8Ol>S%VK7x*z5|1%VGdux#KoYz6M~vm5^bS(-iy
z9ogq}<H88=dKehAtR{Iw-*K1zJEzwvK{<bjJo5i?Lr^-Cexm4D>A>h579<c5fVvhM
zF(EQnSd9t;PedwzE;oJ7D*q88x5L*`qR9+A9(&Fl7;}eriWzwkWfC`|+o5f)VDGf~
z*wIjlRwxoeVE#dGJtMCk7y9ffeK@hNWz@W`HGl%-n{$nX+{G8}Gk7<er|13ACqz$z
zzd4Faa223lbK$t1x}3R?Qu-tit<4*x&yI+ET)F=y800{yR%$k9d&_trL8ICtJ^Cr8
z{JL9NEA|5ksaVb`VIZdtv!ANiR<g*aBQ@!nXfuSbCKE6x?(@LC8E!m`p|Vl_9l1{H
z=VC1aM8B^9*P9}$g`BoOf15(!Jo%9fS?ddKFmbuukVGhHF$RjIUiydgT^Y86+KoFO
z&vkCHC};%&uxS7#M*^^%Ux`T&#A<%??@EG-4KNyo%^rhgB-k$A6n*2`Fh11ea1I_x
z9nEw=0y}MqB(@O_MMPy>aUWh&0Lv(I`=@aB5>>k#H7N;T{vXich6VNMYkzBDnrQ_q
z9-)}81}`k@i4f?tC?3&}xNWeQbz4R^7_bA#9ItK)Aw2kmQ~q<Ob<rx+v@u^O*yfkd
zxU2Z^T0rdyp?oI5RZR9$Y>r7%?A{(v&RYGhFfo)KZQhdQ@nLx+UO9w+4P}A^tR})Y
z;NZU%K>3-d(D$2)iYYJ%l9otq(m-@jtfWX8*@8p)KV6R1Lpc_i*kY|ZK>k0_VwEj>
z@9j{cer?GBJ(Up*0Y*|xG^JV$@AVVrx>5vSkZ{s{!&DpM2SC?8xYO}eHqT)q2CX}n
z#pZD-tGtbCPnxyLS)YC+{jX4b6%$vB!+S`wBc-%+)(Rx7&2`hNhw&37J!kPu2c3sd
zr8*{e4S)#en9R`FXo3!3a(K$gCaC>q@1b8FObne~Af|))(Ixhn*g6j$%V^|05-`4A
zqIzlTZ=Dqb6Z{77n^Qgue~VQ8MyH<<{ACzp%<%o^YBRD?C?><*cfC@)P{X#;haF2z
zzNL^<m#Zl=kQgK#fw{|h3fdBTOCv3ToA#gG13C1WW_DtT{kL{TojDdNCyB@(itFIX
z^Y+Tp#pIsCM40>vq?p`o&Br8$fF4gxy3aD-h#stFiwxS9fzFe|8O`A=p7{HZ88|jg
zqUUm5iFadYT^0D!Bjs^uLL}6AW7l7gf++tz0ucS1bb{C}B087QyZ{rQK!1h<*e8g{
z4>QR0S04#dvIKljs{e!*Nx0l^3hO>kxF!@vl!x=s-~m2~glb&1A>A@9*>}2NGp9y!
zM35I8mw+^d>EQ9FquL(%N<!FUESiSN(Tbwl109Iqc?PRxDSkzfe1k^e7M=g5xcrVC
zsYuZqx^c|K{TJPVu>cxl27sH2D*J7Q3W<{*OlixvAwDSyuoBsb;dG!hNkGG!^rAv+
z0MKT0rviq{ms-W+o=@JQ6ufrkCB}QQk{B&|CV^Asr}-R-R&~QxtH-<IB>{_M7mtdR
zH0;zF|E3?jg&GT<<tA9>ZIgw^Bh!57m9or%K87x6l4+G8u^;CiAIg}4Ulq|17szkI
zk9VtXcMpBRCjNg^9jYW@5_e`g7Bhb%yy=zf1^I2+;|2IbWq-XTHeSuy73ycvAjFe5
zdT>uq$ZP^+l$Ltaq|gjX6sD7*T|v~cGcBd(ogEt6jH^9gbEBJJ@&1qQxFpf17SN{T
zDiVK7<|$Ga0+Z_NeNpd*A4CjjH(kEM0y`ak9AI&g-PexvaBJO;+TB^HoHD|<8E!i=
zya1L2(?U)iGoIV1GHvIQ@N&--2xpnesv_<=dY1=%UJ*X3O@l~YC?G&!JfEQdh)q3t
zD0I~D)65@-6*;`GXmTUQcx|aQ<~;IrJFgpGJ`pHov>Psx#O^qIHN-2Oih@LjNK`eL
zrB0$!5zrI*?*;vlFEr^_Jeh#4nBAu8NMh>(HoLX_NjGsD5802FooK6p#0u5?%<KNT
zWz%~2><>IubsT4B4G71-c-X|e!oC)(bi9S=-YdSJ3eBX{`UX(8k?++fy`C=BpLY!(
zeYWb8uDhJDWY6hJ5HMX2rlr;OJlu^x;92^yK8YjRYOy`ZVRgc-yz-}YZ>Z$dj!xsa
zU^N=5?P)O(LVI1Le_aotQbeu}2-tyNG6dfuLJytQ9#;>B!Do9zlviU=uykKhlt3qZ
zfS~VTUS_lzE<Y2XO_i=g1HHy4fDyqfN`0YzoPbel$KVT_Qqvb1;n5A1E%#Ei+9#<W
zD^5hKeN}~;u`gEc?SQcVMbtBN>+DQOx4`S{3k%1CUUj7&i=$KUR&c~8;r!DA-S^9%
zw~cm0YoEa%q`sVu%|qJdpNctXj=Oqj0Fjc9aYCYZcuoo-EwRJ0OD!O%3F;C!Qv5m-
z;qJMz#yi=*x|5#lJQMI#1tlHHHlsy+h+X*?#)@4Ps}l}C9cbd8ipxZAR|XLUl2JCl
zB;W1@)c$vr&b}vA{+HTJn=XQs*p92VaI;l(Oe8pyGVr`h2%cN9>2T{nQunpf6F$e-
z2vh3O6>!p94>Ch8kFHP0_4~dRC-oN~Zvk-m3qpWXGqj-X4_q}=9c@182%eZ4GYklH
zm5H8`ox=51kBf|}H#ZB@EC2KKLZ@1K=R3l0IKQqx7*i>8kJVX(B$qOVS)8!)oHHnU
z&25_aGU&2Rw}ip&ha*P82etm(4Q3n47Co_!dtqnm+)`d&-NCI;B*FHNM?O&$ok@Ec
z7C{vA_bs+J1wMG2yNbZ{>SO);asKi9hbC}w5C9Q}MqrhCP7U2^@tyFMA^YGH=wa8o
z3CG!Tx6Px(D&K1K`Hc+9iNZfbZ`GK%{G3R+rflT9n8W=@F{%*jE1Q1$#mQAzo^L^m
zWAb7_p0xC>9?b;jV1mSDJPYsoGvx8pQqrHwWeT&~1mUG+&_j}lryXyquu`)3;!K&A
z{85n=vq{u<=S6X3#O>U%SE#!P>cFT9jneHiIJ%U-*5!(se4JZu62eEX?d{32QOXL%
zpXkphGyV}%lCBqpdSiO8_Pq(z79j_(Uz~Iw{~?^=ypyc_!1KB?`aL_5f)+<7;whl^
zK;#9QSkc>rIW^=V%yQV3<N!IK792ESDFz&!U%jt_NVLB_NAra>I$qBvB|_R-m{b*+
zJ7S4J5y~aeHy_kEPUif%a$|E&j)AwCbkv~)Lfet_-%&SJjwHa(cJ|7TmwF`1_6>fn
z7R{p!XZS}Al;Hk%Kixw9D!ffT(TDkKuQa?HZW`$Qs?!}>H<8PV_!1ZP0NOZ!H-5Kx
zD$^INWZtZLG|R<!JzjplopSjOsjzy@nWEHcTSUx2|Ir9ZbgG%;7h(i@t(#G0|9QJ>
zmBDfy6v(9NwIjI&g*Ma1q?5p8D`)Iw;_<+}P;Z6KU^sK*eXeVC2oQ2jWCm-vGGm(1
z%mXAr@%@>;MU<XzcJa$3y4n%HQRR7)e4+6Ky(Vk&YbUC%l=Ht|<@579%uk1w%o#@2
z-;8a14GxYOvy7?XIQ~3Kr8!$do;7O!LW{Wwyry*wyThW?F(UMZZ;7Rp->U|6IRNk4
z&fg8`wNRr$(X0h5p;qV4V@McZB~q%ACDXd<&<Nh^<jWYWQ0r%Kt)-VeITCf~0RsBP
z)u{unJJ7Igu4k-ZmhkA=5`4eMqtQOQz24?pNolqgoJ8%IgoUIQYKW_%*$SW^LE94)
z+LU+79#@q=NnHmuxMAlnGkT)Z!*{5@SiU{@z;HiljxseI>yeMfk)!r!T7?=hP}x-H
zG9KK9eT^Y&Es&-hf3>G}Z66bMrkT7SwHey4@N%m-E80$t)a)9W-N!?eZ%@1`13D29
zEtJa**Plq*y+4aJV8~v;YnOxpqBN+v^{1{uEj>>2Me*)QEa1=Z-T4*Tj7Z||cKopZ
z9h#ut9cm1b>BBDz%$NO}ZKZf^rO_kUeOvGAPc-eX8dfOSZo5B)t!H<IsGdGT%`|$;
zUQlDe)K*CVbj4Tq&G6*qJDOezT>4mYc#W%UY!UAM1O^T5Sgv%VQU}!b^C;rQnfFY|
za0gzIWLerraqNUJ!T(kJ0zb`LQ#<fK1z$%Zm@C8@m>VGp=%~26npcX|e<+jM<92vn
zF+%8nHMMQ%&X?Y$uitIvyjaXaH^BPD^o7xF(Pa-W2bUZcCq<8gDr0!3w&aym;JQA8
z+w&UlB`<+3Eu81tjZip9m%GyEoha_$y(o~Mly2od79}kgi!uSSf#HG9=3zO3=$q<H
z%DCPoe?_e~P2JfPAZG+N+6$a?VFxUO<*IbU@p?*NxBYvn8^PiVPbq+RiU|ro|MOVN
zUlx1U3~)Ba4(ky1xL+(frW2MTi@f9%-!n+P<YWr9Lj4Gz(h~|euo<0GGY+rQ8~OHW
zkNmRDM8z0A?N>GWIUhA**4w`Wv%0_Pe4r11)goTQIrl-YL6U^5TBb<<6dAB`OO$rP
z(rV`O7XIdcrb`q0*o<1)3-^AaW)q)w@ACMxA67@c`c?^0=h!!219Y6U0_W`M$+Q5$
zj_y~(G3dNjPx#pBt@bQz*B!X<#+Cx8jX|06H-?n9PGU$%87_Fg0$qEQZhUGkR-i9H
zcd4!IN2)shQSz(*%P38`VuBPt+pqr(1Xft>gsLom>PpZ?6(H0Jnei4eE}488^260y
z@b3JuE9DTT%sP$(J6oMR?y4W9MN|nQ)8*Uft74#R`S7-)OswX$g=*YpS==~w^LkJ%
zSF~p(3DA5`esv!M5-rCHfBZ?P@m0$_CrlK)MP^J>+|uCd^`hqX!?{-7wTw#Pm%tzd
z7ji~|&EY|lW?ipC@LLn##95?)uT8hW#NSBqq~SVRjqL&(zk#}pU##UmX3T=}Jv2(w
z8)Tc*p+#*`G55>TMuibKpdk6<l&sR3u>u5*tLW$MW6mg>ejq8#wsWwC$ntp~7g+1Q
zdF>mviD~8X4~}a`ZcnUpMp+dz5<g5iTuqB%wcjcsSPS?7$FiCY55FtI@OrO*8Aa~*
zLREbBlZ#l}nAf%?hViPnnzOE`jj<7xOzihM&JuAzf-2<9GZD}yZ~0<tM#^xuIBDNq
zU}&`j3wja+)|!F>9bjitYBWcWWrN?Z0wO=5#dX2;9%PpE5PqWJZMs^Y#p)p@9ONMd
z+HfTs>N{OUUGl#}KE4LZ25IZ@^U!Dn34mNUV@a4^rSy&v6aYyaie$Wt@s_>4hrv7q
zgVA%F)7x(CeUPH<kuHq29UKITg!M$ge211D#&V|0za=l;joLqFk;-N;y!*H_@7pt|
zTF8oo&;YZEmO0V1zRYB8Gvl|}LfDgjXS-f~_$6iR$qrIQ+1^mgP~cepb<lsqh(jC9
zy4eMZP}T$%u-O6oed@a6Kvh=v>m;~11p^e(0QWG7gV>6s)`&N=JnBO<J3pu2BLkP2
zWlYJXV*u>8V%}jtm-$fv6H2MIO&U6;mDPh7VmQH^-nbI!Z}4k=TvXfrKJkuG<Vlu;
zW`Hidz&LWbB2qw=?KkTwi!X-8!U=V`B^tFyHwaZ~{K&|go_9JtmA~09A11B>Q*mGG
z<FYK}Zbrv*D;Ga`X5c{TmIw-A6|;De4`T9c4@&JXuvixhu;Bf{U@2~4iQ3|B!vs`r
zK<z|t%iXX&mQAvrNAyMu-T(%Ge3?Z83|B~-$XlnrPLP4s3_66+>aac0s%T$7Y7FNd
z4`7k-rC`N3+?ExTt1pfy_NQ?o4sx^pN4CZS&S_ryBB#tyrQTJ5R@^-go~*41A^Qi;
z{?4?5Uhhz<e5NaV_<}VG>oHCjmJK3W$BVx*jzU_FT!%n7=X%M(1%)HDI9!-7kHz<l
z#X0(IV{(&9=^nMU5&r(#7-`dOZ-k^fnDmKNTsYvv%92=r!*BxCa;94Rd&YjCh9t~$
zF<EPK@zncS<_ebL+JU!bPK#1Z2K#Pi><l$$1R9KRE}ku<OSx-jac(Tt%P|4OuN*i-
zuAWt;rt&r8muPU70E^P6%YMbVyH=i`?{_Q6IG-20F_UyO^fTKL3*;?Qe@HZFk@%W)
zWPbRjF0xBo^i|`(b<mVFe}JW=^JJ#PMyjqe!^<cB8+5eQBM>-qznZiEY8zfSegv>&
z99G<Gezavg-nkd|43K7uYTfmZ`sBD?zK-YN?0fG=ITAW3TJ0Z8>wVXOEw8R}m|?aG
zAKjuq{PXo9Q>}T<=6=c_!BJsd{C|uSpsM=q=6h0?l-SW?os~p9*Xa5)ny3Muz9oO7
ztY0(`X$NNj_yUw_BJq}tIkV-kpZV?G>||#m<j|eEF^w4>c&XH%@ieZpU^`~O@R#@A
z*&*ef6`)sKBZf~=C%3@fn&0=n*4y?jcje^@kA`s0^x4q=E<o4*+PtkaSZw~1QW0}h
zVaDCD@cq+ZY<JZqVT=yDus`15;jkY)!l&Z~(z^<C09k<9P5toxkUHXOD2P_fVo%rn
z5F}V!NJg91w!Kpr^)Qc0hf-*Aa;P^|dPZ-wFSyIH(!`h^j~t4p$JMlJK?o4)?b&C&
z|I<Ex%n5>HiBfZUOpHL{;<{HrtDAB6Brr%$1;4e6Cw@i~@s7`<6z~Vgz8v(;he~uo
zPp?s(Eu$MFo<Coq+;M?&Z-u+&Hoe`wipx14>!kxtveqXMY;ElgATf$&Zen<dZSIXq
z4KJ23B`d@pOq4sD`sU)G1Q?iUi`E)}-8r@&1Oao@>WQXc`$1C&&<ZYcJqa5|lX3UX
zZk3*KWL!4-2R0cklxyRqh1AERp64d=R%r1PC++Nx!O^+YS<Ah*J*|K9|E(#w^T*`0
zseN!az+yOy@o_Vv{c1bZAL1UGIH3hl6k;^`^n?DB6qZCU07=@1yX_^-bh96HM*Di!
z?;#<a3rAY?aKl>wlD!An3tgzSKA`qYNH}UMkKwgN?OlTHoIh8X_e5Z?*P^m5WsT#E
zc5&otNtU~Q47LBslnmBexY|^Ka~-U2vR6aF?t!Da3&is7h{*upo!wxbiS7#v6jB+p
zDo-P?-KalKfyZ9<U<cGxHQ5No?zw%hG5&}55TnaqENOdz`ip3TzT}%d{UHk(y-KUY
zL$P>&$a=n2&J~Kv@6l)Y87u9Q=^&jmr7!SM_<u22Z%G8ygjMJ3z)E`JK4*8e9b@Eq
z%UZ4WxC&tQ;#quMlxIJb-zh^{x7mL1eB^diq|0hVLVMo`hU^ddGuiWufr%a3;x`6S
z{d@ZYM^^esVu;{%K#vPv&PFp(S4+IqGCssmV{4~Bm%8?3%3!%h)jV9`i?`<v9#C<E
zw;dLk-YKVf$g|W10I9AU#snx&`;Pt7s%~p)1Md_|c2BgD#u`lm%Is=5qgK)RVfTm$
z07v!hNn#<vU)lbi7WfK~h<Mh^UQiu0o$$M0)XeaPcEzFga}&=dAPrYQRsw7OrwQ|I
z!FlB`pxx%DN|i~{#R3$d!-WPaHi0E0lz=@WpdSZ@?@~jd17aZk<pT0b%?oYj$xq}h
z?EdvW=)MAcR{Pp=#f*3NjPdkxhYc!!_idxui`%Zv`ja<ZjEg^rWQ|3T57gC|to_k>
z+a=+x?%{EN-y3tnj`Pm*tdbGh|L{#-Bp>Gga$?&NzEk-8@p1=dTb0#Ji(tSiVqoiy
z-D9vmm)yyqXgUQao%EOkYm@@st?5XT+S&~+G0p2O4oHtJdTMCrEn7U<G?Kl=bc+bu
zlHIqSKN6Re*G)op^A(cnete^2kvWEI`*C|*Vc6q?M46`TuSpUS7k|DEJgsEUQySu<
z@t^L%35YeHy|m(#0MUrdspYlAL7Z3@+asrEP6BN=8>;$?Kgv94@@v?{J~bg7z6BZ#
zBOc7zS)uSjx<#u3&e1#uS7V;~gTRv#XU=(PeEZY3LxLwi;I@(lple{DI2*~$lOdMg
z+n3wm1j8=s*yHVe286+PXBmKW6S70T0VT#0>#MReO_niWJ`uikukLZEove$$KCbJX
zdANDA6(25Tno)A_5?#Nc1$-et0C{<K=^_G}9dPU2b>T{QRqz#0+w|GnDFte0QGnrM
zTE(C?c-z7;8T2Bo=fggHYpKN|cd6krnzQD6K7R<F?G4R;<HLU-<w_x~`IV8@4sr)L
zC*0>Kx0KiNxQQ{>o|^&F0Txy5GZrj-vL%jrG~E18s>EK69}{KPRn!-OKL|LFe7>Nu
zxEKT`xL4(pK`FT$Lc<3u`EgLW@ai-Xud72QDlfYBp5qQ;HgE9OB39C&+6tO94f7L^
zs3Bi4xL-{HGrtnLP?+iQf^#{U`=->++k<LCU11qQ^H$QJo)W5K_80g{+8WMBJ)jdc
zQ)`~qz*E%z=KW8X_T8RoLi0-teyx#9_Z$THuP2?*9G%HaJzF7R0}lg|94zt=9imfQ
z7n*r--QC!{BO&Sk;uh#x4Z>m80F4)Eo>Nwdja*%?<zQ!<DGD$G%1XHyz3!_quc?u^
zXtB=xHP^kZH>K)Y`8IJsYK5_Iq46o=NI8pXH;G>!qX-h~4PC;bpl5}gUUa>Jk{ax$
z-QPy4yR@!>&@rHeB2A$53Wt`NWxk(LnJ(^7)qV;{FA5^)+7f~OAz&#<$3b{lkcYN?
z#yC5uy;wex=dR~<jDN}O*5yW4;V(TeNIhK6_vq^OTi2FOIW}5XsBB*?pwJO_*;;l;
zaBma;h=f=39_;x}{AQi=?Kc2fCoax?chCe_rhx3}xS9*{^!|i{LO_s)K6PaQkVm3(
z^I;+Z*^>(1eUO~}SZec^I_mZGq)&a6e_+Oc4sL&+!G~_pa2R;K)hSE!MnF?#{WJOL
zsJ=5U&MzCabD@Y7(94NUq_3~fWw^#~W6Gju!1}teP}?5W0H&}3z!viEcJHjY=FK0_
zjOcs+M+d$Y*==gbhlrc~^bSa?OM>M4<?)!Bf=#f>%QQPSsk|%Z0P^P3qeZ$Y(0$!p
z^d|27xq{5Yg8Sf=b%|1ZZP05}caLM_aB|4*^W8tCU-E^&7>kt4+GwN+^_fUyCza=0
z0DY3B#P8CFeVvHX>#8N=IS(w+V4Pj4j%KTjwB@Y&O#3W=CHdZ$mIMb>?WnCu_ORXO
zMpWojaF6%Jh#ir-rvqAuSXNg{`6EusYT?bGN36Ho2=DA+U<=+7^U`EH{YF}`-NJdf
zR7Xyf3rvvg1s^}IBPXmv6Mxy^jh%Nj4iybIfw!{6AR6t;^k+0<y?MHoQnU^P&s9(Y
z05H{d0#)9^hr_4qeTaTYHVaYmBIPLE|0$-8w}|0D1t;{6;t3eQ;(-b1lBR1GrF6-)
zz&W^o-{QiBR$xCZC<TkcL{zSu)D6Fd3>|%U&OE^dEwjykdE#}>YF}5k29EO3b6hbC
z3*m=dRF3{>f7}G)s!nVW4)enx3#fiPiEEuJg?~I$jpPf{COlHci&I#js4ux)VuJz$
zqj`MHJP|t+ps4hBKbFJ-LDE~w(=sDd|9N#x;xuRe>r<QsEBYjf0e%bh4|+ukIY{m2
z!?Zr(%L!=#WXk_68?LXp#t&FS!Dh(ho1wN6E)P<AwKRbEFz;HtZJV<(^yHi(rsdZM
zz{}*|VW2j(P9V8-qXi(=E34B8=B{iId+eUC61z#9!~cIr006MxEWXoJc|dq(Bm(-I
zy>x>W?_M1brBOpT88Y)LRSY5qoQYPTK)gi_u<S=&FE|5!sju6w?iZTXQl6(kCz0Ds
zO5<ERJ<ysJ-r~^vIyPecgt6Ajxqb*(Pzt=f+_0Ph;n17T=dpN7>9SX<-!Hc@9<R-K
z3d*#`6^H6Ci*ITx5y+Tk)3pwP6Kcflmv1h;Q~eqCAvgDDC1@>hlUNn%E?>4K1=Jzw
zT3OLhzV@s#Ew=L;_(jm1(<4jjh}^Nsf*#kAo<Q?eXSC;XXE)G|)2Jj|W#V(ZS8ARE
zm$)sk{PNUj)>ec?TL`)^F@NbnIh7i`KDeOqvJy)<yvg}yWB`x^mLAskDh;L?TQR_&
zNG9`yxoCcE%TNw)i;geY^Gouo{tt>KbKx~gz~Rk-2+Al)yqmZ9n%>zl6E4y??)Y%q
z5NtSiS@A!F`buvPi!OlmShbF>Y2dHTdkWxO0)&INwsFP}r*fb`X*Dp~gGDu-$B&g{
zbLS=2$%!2O$DCi(agXgd;l!&;s^jxy8mc5|VaZJ$gCnrAT|a>4;Uv14g@`Ck^_t%9
z?goP77qje++j&`3V8x6{{8n`zlBANxtG#;pBEXXbZ}Z7ou+-PTKfE`ys{6P0s^BmH
zI;gjgcGr>8-I!JG9?uJztLl-lD}JGo+nfCAYwdm`3oXyR{2Lw)FZnuyWaaIqC5@n&
zx?N1d55SNB&Z%>EI)SpymXbzq>sCx=<h{4|VDJutL5YdX571#^&N)#%^_c9xaw)SG
z;IxLIMqP^uA6n`;k2wMc6oBlcI4&)e!xa`r7o5pK3?~QoBXn`2UY<`0_r%>SnUpPi
zkr|G?F5H!E_LR03+mDxJlMB&w0S*lmlS~LQ;GeqyZP_nG8M~ABxUPtG0B4Q;je16I
zKSI*0)esL{i4RGn6>aY~&_;-$JNvS<q@Ro6PlLMRU8H(XBnZQDC(-jvY^Rca!Ke`F
zlLb5NX7AV6Y255EQMk@THzZ-vDKw5FxRcK>ucF8aFAtOEn|H@IK;6>d7_{y`*M{VB
zaNAr{dzz_8;-C&Y_Ts7V1m5H`9GkLaFna}kfywIMbETZ(RqTzExJ2^HK?7Vs=-+3B
zg$C2hK-i%nsM@aowRe~yg4y1f2E~)Onkskyy$OV^(XY%37?L8FIkM3vpF6W>?D-F5
zUC#iRv2!6il?ytA#7UPr)77s(kOf$zdrTl%eryrHL<4-7VB%r>6@k~GC;XPHQM^Z~
z5V4|F;7a^Vz$c*%cbVk_7u9^i-SZRHxdO`RT$4p;TRDjtoU=4RJ<l8><r2aY5&wT@
z;*fXDrHr?vo3Wuv!*0&k{b#koXKRxV_STPXP7{}_%Ga<7yI_)sD@t5caG9`L9zCj!
z>RA}se_o772w>^dAMMvaC=DHJ0V4I=L9VW6IxX#(uX<-q65}m$!RhwI{DRl*P<Fn6
zp#NLs(~QOU*sl~nfSRU_4yJF}4F(fPJ7p0Y9*3-D(S-0&v!yLhhmRYs`K?-aZiilS
zKb048E0a?m+A_K+fn;-FH!(JzDP;$gK0hk`>xcs<n?r*DjT_wS2U#9fv}`eVI!ksM
z>JSQ&%n-}7{*@9yzvs4Z4U1+4V1r`))LR<mrrw>=Gf!pxdzBA9>F0WacjN+?wQvB1
ze}IXf8zDmiNE~2Jn*y&##)%3qDs3SEUb&dVSS&#%1q6(HLunj-wCFrW%$uvhNlz<)
zwz}$6JF;prfh_Ws$YZT>%}*LYwKUejKG)(K@h8!9o<&?oH6L1ox&Z=V_?RCt-}AcK
zGg0f_?ZBxWHVPMD>8npN<ZD$};r8tYdv4^<8UTC@6Oe!~CmAm`M#niOh(7{?X|%<L
ztK2;XxavItF~BUa;!zjrT1gFEkCQfX_o@r*`FEpi`EGg=qw!|$?q3sY$h18@ihTRe
zSTS(P<DXymua=QGqiHWMd(cwnrYCN_d&fh8Tije%uN&a|Cwu3}pAvyU%jT!wEKoy3
zo0D~~=m&LKdZBHq*B@wFXkF;I$ONWw7LP^Mav|&b7%Ew{Qhsg#oE2a-W-m$f)>^Zz
z8F+T(j?HzM8`UCob97Xkc1)sloeU>mztN6ODp+qv?EswH9?RE>%nbs==DFR~a*!W<
z!~ta#BE@Xp@W10SM=|sT<yT1KQ(K8mzli^d({mgx$^j6<m4*x)R(y0rM+RF#6}`9(
z@5#zGm90Z0?1~#PJjh_4^+AE>)}Ff&!=G}5#IlTrw2P9pl0dX9LDm}@=WVlwC(2jR
zPfQ)(MeBP?iMbwb;Bl=}%^J`5zWa{t`tEUHM`zLjni%0AMB!khmpj2vmK^XVKd&BG
z7e=%Jb8>#x6tH#-zbi)4gp>C-;@wU6tS()WpnjybF}2z`r0!T9hu5TTTp8++&~Vvi
z!pvfD+;k8s+zjNk3(q{1!w%oP#Smd1Mau1)eH>u+vgarp&gfaY#P8w)o0MWOktv31
zCgfvm^ZXN1y{<|PaTVAhJ26nct!V(u<i3t6ApQz)YDueYuvLQDvo9~cf4XyYyMluT
zc6woLM}bEg{x8oh5`a93mZ@YEka^Evt|q5~?w@1(R@p||1psG7Bg;qFbkYN4K!xja
z&GPqDJ(9(hGAK_K+Zl!JEMs&qDuK*-^}H&&hW-jnYTNLBd>h_E;oq?=mr^3V(ra2g
z1@;YU4Q}1V$#zJTh5S;x8j+6y(xG(rr_HSd3T{W^vV0God2~x$uBRXXdU+TS5vR_~
z{sRV_36;;rN#PDs*ynnFyUI@082@%dU_uN?gFQPcq~w#@s^U0>ROSAfbPJ`>Q*W8?
zz5JUYW8`6Ku$AM`wJ<=iKXw7!KMW?;`7Ey5Gh3&{TWhWQ5;$k^a|MA^OfkN`r6w|l
zX`i1JoegkZ-!XgrD8yW|{se2e4;B41M>q5767YMM(0d0`u%<?{dsf-#ggx)*NAj<I
za!fl8X}Ol^c~>XW7RP#dBZn;&fLsjUsr{<q2$TjHMIix(MQ*eJ7EyzS@Zv#Z^eR(Y
zwOHe~AxZs%W@4!NdDay3PdFmof2pQURWYRh1RVX+)~O-lxt4v3YRUEDGQk0|t6t{5
z^C;V^kuNAm+2Q|Z(HJ5bN%}boA-}zLKPgH{f<FR)N9e*RA^3psZ+nb4i1L~9>||TK
z-lJ9_6d*Nd^mT%DCw_>jY)C#QVaB=rnf?BDo+R5}rSC1m_+s`0L8ziqcRiG2pW6l0
z7MJd^tFuys>*87)6Kq4X8vhRXiAy=$%~a*`WR$GsbA8AW4czuNuMYoii+;j$Z}6Rn
z-kRst2vVqAd@x8s67*Tz7HVwKyIkM-Ufr|XkVRBnGEF^MLeHUXpAyv29|&02;5AWd
zEy_B#6{`Q}0YW;n{Vl3>V9hVab3Ze`=$|GBSZ~AW3IiqpkcI&&P5}~xLg<oB90S>F
zC~TD8kQKp8un8ef@QdZ>qu9r+p=p*Aa6@+EwTlu1A;71+4v!vNCclJk`BJ}SwO%7f
z<ydrI@YQ&7wEi&rqxMZQhMpvc1m}A`RTxSFYL$=T$(Jxmh0YHMAE<HA&|^MM@l5f2
z{Vq=GS>w6)%rr<L1(i3w*G5n8T$t`?!qVb6=D2nZhC@Oh_lRh^Jk2ku$q6Bx#s>}I
z)&7|c@wi*|Qvf=iisw@|2f3quGAcPrF1jR}oNLH#mHiQ~NA4m{J1{(y2XZ6|*G~gz
zE`jWk=pwZ}TzvC=&Rb&pIJd7n)(G7GYSI&MV){jESZa#MV~s*<+bENCAs#jqOC93T
zWClST!qvtGWvgLDn@C9Udic!q<K*UN2<Oj2NKi$p#RtxqbkC*^7kR-2PHY|mV?S1p
z)YjC%eXECLg@b1Pxkaou{TN!VJEENMYfQ-#Yqok<>YyVH*(h_A0byPqXsPQK`z(Rc
z!-l1=!x+9gnG`pFKvFZ2mW0n$<vlVU5I#hNPAe<lyBBOdJ+my;u(`YnvP~UYOf(}i
z?xK@(csba7(S>>0@szgdAsWZCD9*N@FBe#%Gn}Kzb8?06-ihRM>UEQ6ZWq_!C|WHH
zUTrwgJE7QegnzsBcJ1HFS)cG0h0H-fX24<0op)o*YJIxH<OzA+@rou#p0&*xD#|xj
zb(XN}B__9@WBgor6<{T3n%zeUUom91#&W(Ibge!4YU7kM@Qz=br)1=W4;Q3Aft6mo
zl$P3avhBW*_*ty1?&o^}C(IGb$f1h>3bfE9R`(YC&$CdVZN`$W1NnPIrouP1|A%Xl
z3oL#wcJu1w)BXCewrM<{bL{g1UC`|fBhPj<gjz!5SAc44_wu_(YaHLzQ+|;yxQvPn
z5$E;TV8)bPHbV)n1|>&CbsV9iEcg_D^@R7}k7AMdHaEVijeXV6gm6AFJ|p92ICBK3
znR5E-?S3B&*A3mU#qe}6BR@fn!q0WvH{l>0U0*T3!nMJ@`Q5Mq9`~}qHJt>s4qGqK
z#T6y{fP~+4jbrBDl;NlI7tfqr`km`6!rw2--*Ro7Vpgx|`OL-#g787Rh||z#lh>Q!
z6hENC=lE{LqwREa*2QU-QC(cJ!y}uv=|s5i4S?qZ%r)9~k4u(w#e(!%<5Pz}gVtj8
zctjsVfW>w_3BDwbt24P>&k2c*gRM~^q0D!f*|kSp!5IUddOWo*`<20}wFJ0?;J1Kc
zg?;8y9?)V#HiweoN+J!82u0IrI?*(ooG6ChnD|9&CC0+-BCiyR28qp<|3Z{)i<QRG
z231MavUZ0viS;3?;+xC*v+g!=kX|V~qU!|;IaK*YP)z-mmb8<t$ixx)sIQq&2@dZ_
zrpU;!E7U>u^Nlp2O0B!ygqEt8#@UZj-#V5TbKUnNbrq%~7J{tTypV&Zq9<ifN2jXc
z=v7(Sj}dTRvWJxd_;~9lw#nRa_9<?=@IVNQafX!`XtEKg&geV^`Eq_`LkzEB#a_=C
zy0djMz$<KI{kUqHmahS_>aTwwGslYX0(uQ{#zJ;3bYv9F2kw*8R_rIa9bj7}^-211
z6LdEskkJ<zm!pP~lGT4Te`$<!h|FeDysp6{FKJ*@#FZntt(1c(x_O};kvXTWsh0BR
z;YytG<|lXTmV*coctU(TebzfPc_fht8-<;y(bQQ2!kxaL=`$NnnVDnb^cLjRyd=eT
z%!@fseqoHi*IL<=2~f@E)G)d7Etlr2<$K?o?!fCn0mFQT@A84;dVhkV3t!r~L!T`=
zCEkgEsK7*%4wzIdYP>s*(fPgJg1(`(vAE^MOHJLo$*udj<iBxBntKlyL=zmIXFN1e
zeIjFH&HiD55bg69J1J5WrxJ5BWvM(>l^7m4Q%Edss@BP>GtCpvQ`;t{Jyn6{$+1fo
z41DybUoG`HAV+kO#&>o?Q2i|PAw2xH=>iuP>EpwsE^;~Ck(i~pY@7rq!`I<3mEOHp
zn<X}yw6poa8jM#ljn+B1(^PYM>a$qV6|d(+yh16HO?+I2-{XB}jF)#w&ST{JB8IR0
zlRp}?oEldcPjanH7#yx%go32PS|Eg;@i{RWn4B{GbE_~k7B@hMr{*ue($rQ6uR?t9
zbr}t2a9^MQpl^Dlj@&^H-7+jIKb3vg7lhJ_WMV06_tkpZf8=cATL@8w)^Z?;=zfxG
zEa=g3Ad#_@UJyDdO1m^7!?>1&hKZP?`L&x9UZzv9MgRThyy>8}0Q_Q#%+@^v@Km50
zYkDc5*NK+2wni$ErjfRs<k7lh{dN*Sb9rVtpqVH2oc;B$V6X&PPyA`fb`nO!plR1@
zDoLi-%YicUHyK1PTsE5Arq43mBLX;c#Ar&*GyJ3)bI$umr>F!*Rj$^itlY&S?ZN0n
z!?Dx?>Gsu<?G5Qw)4BMA1sa3^y*)aH(SGYb1D`L2#KrIxSp23`WCiwNLj+TR!6`PG
zgj6%k7B<!!N@e2U1Hc3D;OMWua%e0gi7LA@$NoLjIs*!k)1PnjUu-=;O&$dACO$LH
z*{Gb<>y!rEzK5K&(!^9xqY0yQ-bauXJ)<e&dP*Oy$Dy-wLpAdrVt(^{0xEN24ImiV
zPCO*+=QCmgSl*~0y5VuGRYvluO2*rD;nUjg3r{<wjpW9<#S*`TlOfdmzq{$_Nw^0g
zO$Mp-SI+wD`p(bf9Vgf*LT(lE?RoMwsc^6czVLC2sTMjKIq6!t9G-6;WLQ2N?z|y!
zw8KdMe>7cXP+U>6#zH~}?(S~E-Q7cQhv4qcAVGozcXxMp1_<u%?gV#-ce8JIia*p;
z!PL~beY!vE4~%k3DVbz9jIfmZD~u5G{^r?4-@5R<MYk<D$TRPjOy~c8Vom<Uk^E^2
zZ|W22k}cNCMAis@{vpXQEiHxEf0r#mXhE#6Tl5SIW$mpc8C`<82~320XRED){Es2~
z1m$whkJWB?9!^|X*=hB8;%Bx39X5dFy7G#3p6U~RFOJrWr=~Y5CejDdov@bb9gSp(
z^05BQig+ce;>Nw`cqKS8&bG$IQW3+XN17}S(x|Fr;;oI-(*+5Mhz#}X=ilCy)G#X@
zP;klZkLAUWJ^5c!6EL(_lfO*1l||Nw$_YSgw4rI;j9r-WAR!`$p;J`M^xQO!m9M4>
zt2Lg;2PTb-XT6jVRa_GCy5y%o-XFF!SWGSR?^}>vtG9&6#umG(<7ywkptpW`+0_i4
z@Exub!RGB%u@;=_JJ#WQ(bAh;ob)Nc`s`@&P5ICBJ1cNs#pyL2d%TfAgBd5D39VlK
zjFeY~iLpJQ2-tsy+n_EJbL!I-HWR|qgO@jei3uo7^yp~4Fz<PiC$<<bTST-Isx>3Q
zeI0Jk%q32Rj@I>%9bX%&Nq^rPYlnvMkJhs@D4vTA(ei-Q?LX**?s9eKKigdlm*@_K
zWlae7R(z@VfAo&(_7Ns+)Il{vq61<E2FI;yIo`L)E}+cmg+JxOYF+`nqTI{+c<e3X
z{P@LycTARF=AYX3DtK+JELqRQ-wI`N`)cI6T1UxEvzoaDJ2dcu7o8mJC%?&Dkt}2d
zD7-dgD3r3Da|)pq`Ll}@*b(vs)Yb5fE7PF6PAeLKrq!g!%{AJDg>wv=7<BtZ4uMzc
zu`f&3Az=YAcU|n(Z6U7l1RknYAa5}WqMKh5dDTfQ=RgeMJ&x6=jhNd;OyK&KVkF7>
zD6Bdxw!D^n@DX!JBg_Gu$yc`eo;#E^bMD-e;T%hwmzZ1SX^}NIiXa%<>dun7IgDM(
zL3)yN-|n-0c3lK_dW~pCwF>R`x{LU`Aq@YE)>(Sm)z{sZ@q;&pD#{ZoAjcw`6`l4B
zGl4`q@#-F@sv#Ny`_qfs&s^h8aJnzNQ?Az#iqES*tx$#c6d1ujc*#~>s(i(TnKvZM
zZ$j4F0SJTG?f*pf{htP~1s{hy1JmbevImqAUR3YwD-eF$w)W6)CN9Pu0=>X<MAy0f
za(<4nNQgsPdm}4Y1!3yeGb)JxQrF!#HG^7na0R>l>+MtaGW(Cy$zpZbqH$^GHq`;U
zER9NY)T~;{8Co<nDy6zGjeP0odbyNCuW5%C!$)-=@v!xdZ_VUXSLX9x!)A}K`U+|`
zE^#*M63u1c+dNH>O%2R6RzF=#%kHN+{ogE8oh^-Wq@xSAZcY>5#J|-h!vKs|?T>JH
z-|((U$uG|4IeVEon(GOW9c_Ofd~`0$F%Spbn_Kkt0#BKUG!Lh00+;3(14b$|G}<}D
zQ3C1>*^32Sm0M<2mC`*cXn?Bw!h1v2zVRzaA~%se_RlcT9`6iEiQ%beK7OeR)NiAA
z*#2NrAibyV^QX}l0q1z1xXt=74;OX)UGxU)2`vfgIMamO`w<3$y$D})5bH6c!;I!q
zAMvWww?xT`uv{-|!L9s<)3jziiE7E)n_BIC1u^Jx;joN@6llL4iu#OrADE;!z`OkS
zM<2g<KY0rKJHN@O`x^%ew%ct*&TBzAQbybn-cH)ZC(K-;a?Z_F+t(8DBDP+#!q?lB
zGK516$X;#9@fv{}jLJRWm8uwM=UXZt@_OYxuoX#2J$%lN%kykl8ODw+4ktxg3Zuuv
z#DCYg(wz)6O*KR$5)EjFoTTcR<Gc|(p$Tlp{b*1uApY(O%Us0)u{qcSQ7VQGwyU#E
zN^8>_6d@Do56(T{SZv(*W20#HWDVbbDlNj4EH$K933l><>3~ySYXn+8(OR?IOL%ct
z-sqFzIz{yoMifQwup9}eXcNA9bhdqBWV&Wia@ln3?+C^?Q|LlB`J&=nB|kzv8c4po
z@?_PY$eiOMgn@igXT}3TX%COP{x50lU43SC!@oB1SAMPfk{WzOge;<MW}xMywuGtr
zhf;oS*=FPp$lm_JOp_-_)8;JwrBWS=2eCK7{d?$sET3_?dTtQv_xN5lm$L9)su5#T
zeZH2nsu7*`D~%;_>O>6Ns9F^PbqMU&mTh&qPhTw_62>O=2p_azY)iFo!k4{9fdk|%
z8D=?lG3HHC+n~$J@OnOfJ#_E-V;h|}_$36&n|WF8n6mGDJOb1$)<|Hfih*<4+)b6D
zX>qjreT364)x*`ALoIEzR$eC1*Ryc6`RER6K+(7Dp|b_+GZX_}(nbV_L488s@zqPn
ztJb={t&1u;yTEFMv3$ihCY>pRoU6%}UeFc9S-lha7#=97m!&(6PaaDRdImZV&cndD
zWzMv8qZ@C?>#Be!B#~Hz2s^;{7bN*OF09aVNU8VQ9U;9Ifp+ZnV!E>$x27Z7wIhhU
zjZ|tW(i*6D&Knnf_-fWJ7}b-CG6~o>kymYomWy!DTL?e|*Fe8UiIS$VhA;F8N86*B
z==y8NarCdhZU=Db*OVH~O>u}t@aeWVal%5%{Z0`Bj=5pF(p2G~%F6G$xq5FIGv}^1
zK8!%0hcmw+6vu;`Xy+PZ5tIar?fo*baO&vA@WU~$ENwwuO)p&=$jU#pwY4gtxJ&OP
ztJ3CnQ6RM%@fLY*cN<%()3FJW5IlF=w$4={1$O5^nf$CRE|Yb%nA7+p@4|k<pNh4l
zs{sRI#JaP3UaK%0^2D-8;i$c@y0X1D&ba3u#{jfFM0$N-c_J2$x8HPc)WL_CDjpza
zjPT7@J*mdBx~R;R%B>akAJ@$u^=fgXSzhF1L1!br!{8&Y&Cqn})i6r-gN-S=Z%tvJ
zcSmXeli9YqSU(6-`p$foaS-p4v-GSM&2=oEf6|kuZ>s_mkW&4I_UZT@(hyo8cRtBM
z#mkI8IF%FHo=xp4tSy(~lX3tejI$5a2*bU{i2KR<Rj2|z;x8jUU`1)fO6GX}ZC=W3
z2UEbNf`v*8YX;oLQs_zQc#$COwsF;p%WP?`D=Q+tI&4f|4c}6yK6jCYE<(WBLY-@{
zpyFx~6_*e(i^^_cD{f&VTb-{DMAVvg?We&>Vt>u^6pv#~qm;0=mYct&J1Kgwf9EE@
zF?=_+CxXrq{&4*0Rw(#{y1MLR>JJvYzos<C6Bts%9AoTS5*wmBOSSte@nD1o*Wzmo
zRM4D|Z47DW!m8!u>^2M~R;Qf_4L5YciWC-K`Wm}N3ZvUm7Q29*SzF^IXdut_gN98A
zEGr38<Yi}4xdr(cL3ijuUVD$kz@VjuBWm@j^cY&&s>P+$ot)fbTpb3m0}vbjktUgM
zz<&kdsTfwpbIa=|5q8DHE<7o4)wHur?PIvPB>Xk7b=HOyoEBv!B=qi+u`gmHwNs?}
z8|hqYZIYKUSX)cFRYbvkM@8}5c2<18XZ67q;>mTP?uAb9>@=T@M`joJ2J}2ezY(_-
ztYn;jr$Bnc^dIn|CHmo))%DtR^yx;K@}_b8l8RIeFgt{fXa-k(|15?Qq5l;^`wpXi
zvKb#olf}1O?JUJXG%Tyj<w?5}3S{`R<MhH47)2>f-7{VO3^1i7za^%S!9zcs@w2)$
zsXuZ1$~C&5XS{Gt5bnOb)HFN31QRf~wG*ym1QSy$^>Sk(sFMZ%9c!=Jc(v1wnHX{A
zW<qzvgNo88aZnfED;4^$RQ&R;y#KZ8;mr*~{@9|Jh{2Id0(fBT4tuPSS9j)Wt#@30
zG1g+LO3;&<Oi6MX-Dg+L!@Rq`P6kPOMGa|O6U-C%LLr~%v(-57VRG7mEOyMxd)>}c
zWjm~2t#f;ybZvcf&wfaEQdhm?n+>(!%j+4N0!MGudqLz!n4CuRHv<DuUiEwPFLg@V
zp1c*^n@fqZ{(len^@t-?6~7^H0*#lcS!W~?jEqLG<Ae={KW%KpNmr$svlGWbQ(eK{
zsP@P*GB#ON7C0~<9J{u3h<Iwoy{{*fTbM)B(cqNX&Zf0~`E+uHzVxha2&_*C#F;>e
z#h3kdPZGW3l=5<{J&4$c$McxPDW&_w4RoaG2Z%<t-d-g(ek^aVghH3O<;3A3*|rmT
z2)~J~2C|ILHP7m*9KLZ)%-)XIO;b}VI@_Y6kLNX{P3FlEjA{{p`|*u;$LAmdvE{5g
z4;*Z@d6Jq><PiIS7V4-_9J+$DWvewKY@l{8F%#JKExeXVRlITy{8fdQq$scBP;52?
z@H`R}aT`H8zSd0J`6&}9@2t+6C8nvU?v3|-gi>#GVhbCoq11A6@3+9ILJA4d;=^MW
zpPiM_n0A;>CK5pPXy`Tf_x&bK|2Hk{ghOdmF9(fPl4q59#7IjE)^)vv`Z#09hhDFu
zkQY^m`E=8I07a26<v_D~x^J?x4~<ZfN~(D^%tc9Bt(vVQFUO3EAl&gv@>9@*e-S<Q
zd7PlXH{B{drT?$CBM&Zps3qQI>LGY_YX{a%LVnY{u6tkZ#pV@Jnc&?BOhNWqZs6h$
z)<0hFBa4iI|6eYEt(!D6`{8EBqRguoOZR=dj-d-y5P+tLjE>ww*vpDLsY<yl;xxZa
zyrgOEYLFBcuTB;dw*N=wx;ySF_#W-As7LddT_C>kB{DtstBRdWg3^1u$+N9g?L8ya
z8@vfJAwKbBeq(Tv7mh~5oVZM@T$Zh;LZ635XWtkD0();}TrzlAJy8CUvv_d5oB-A&
z)?Tl0XG{xqT=s;29~k(nzLvm8^;gLg-KgT`h8K(9`My(YHr$%#pRk=fNObtE(KvZo
zG5E^e(Opw?EI?(w?i$RRg>^kI9QZg}Xx96iTLz1b5z0U{AdWTACtH_X<V)@a0m}tm
zxbS?-9awDQQ{LQ?<P74-&F{qu-BM07Y+UG*RlLi7<xYAv&zZrsnZr?fcS$y*M(!;9
z6$aqr;ez#JoTXE8i@R`Rn~9XJ)_aVf=RTovO!E?V%>a?`yFtrPu%^Rr@cZ#~@^`p8
zJwbUT(F%(qCO7w#xXW|vSl{8a3htXOCv3J(k)u_#XDOFu9G$8Ut?;>8?|h(mLtv@c
zv^n=hmjMT5hG7>N9u&F6!Rf~eN9YN*6psaZ2O?(n*0BTZ<1>my;Knb%U&$WwlKO|?
z-bHYHSY|M<59IqAd<_P}3;Bs}cD+FSgl2qSsW)s&<IS4LbwOjG>%1eQ5wGE2^yz|z
z3MmxIKXJZM#Zz(_4I4>JBBJ5VcwizL@Uf=b<)fRRN1#{35ic-}az<4)CWQs*<v^|7
zO5Al~$e{M%k2AuP4}uRTng!L`u)i*c2_w;1g`a`b!pVhuPmdPyW!?+_Chq~=@!gpl
zMaJ%ETSkX8H5C%)r8yF)B=gU?V$*fE951l!3-ccN@#F?INfkZa3~5_|JD_EVz}QAx
zXxr`m`mBuQFVPp1LslOWpkL2Ms0;+&T)eB2z*0rBu}_fAjC*c-ajlEwQ#zQo32)N$
zuwE01G%19_|JVxIckc#_Mu;r}68|5cRv=C}uy8fl<A;g`3>|6D`okhvY5|rD?x?wR
z5vP+p<Dhl$<d@Ap5)cTPqwV*Mc#iC@)8iHs)kH@YXzF!8?TmQ0n;8Iuz=zC58@5&M
z2>M+=r7_Q}z4jO=X;G8#miZEgfU2;za+EAs<G#J~qN)Jf852SO$A+O{bwP7L_ta&!
z*c+O5F9>KHE~{YO8<R5On9`<_W?Jh-srdO=Iq-nOP$^2tQsEItxIAg8Lex~?P20I1
zLoxn-$9PoM3Ban84?)`s;gXYS#g|)*V#*Mizr|QMUqyzAb|8VbzVGaG6qIt9baPE7
zg8a=9$vwBbSz42~W1beM@)<LMAT_U#D6Vjd3o1n!J2)k5NTJ4{Z414{7bK1-ygZ4K
z?vJq0)g+f+@?0zTofYm}mA*-M#OAx7t37St2a-}w$E~_<3pC>in~}a;(zw^g*4S!G
z*-xOP<1Y0aq{LUVT-4sN`c}G3+2uD(f_@g0Y&I4RKDc4lu7vuw`2-4b)JUC<QkZOg
z%zwS+&V@i)D>(?C+7~&c9sWr|WXyW3NcB@fcC4gkPkG2?eCg6{o2z5uxzmIULALM_
zLzXY2ZgFVSVTl6sS}{GLxkM566KO+XKc+^EgW>mvKvn;T6d9&8py|qx7NkbG++&d@
zmUS<;&~Rg*d>mMSEN0vN2+$LxHjnE0RS%ybKq{cp&X!i|W7t(3>E1|d$Xe7OI`ewH
znD#4K@Q>1s&I?oCI&SWAM2G=T{wRrNcfkQN*_&rKl9kvUh`WQ3wu9l9A1W%9N-E*7
z|42U!J4M=KRO!wz5!?LYfy78ER-6c5jS@UJvLC$F5-4s=LX$W`iBm8Vxd;`(tgcA7
z@Aj)l2LS1U3<DD}PPNTYEvlzt6Ap`O8rATvt<>(|QKz=II_kPtSGMl#u#B@0^!DYu
zD=xrui0e0?B;_r);Xy>ROc?Pt2IZgYOVpZOO@5;LL&Q0q(~`(oVf(vs;6xk|ae!Jx
zY5-GfJC1@j2tzmh)TNE^7~B2r)q39At<JP9ZA$rc6tpp_dum5t)Bbh-Z1A#={j(gQ
zQYTy#?(A%}ZDH)MD*$<Yz;W$-lD|xK%@T~@<rmgGtNP9d6BGS$qpS6pX|?2_ecQHx
zM36W&K2!pr93V5Yh;5Ek$hBep*D{%08gePbXm}6a>4Yyj{tRi{Lj#EEKK{mlY=jn;
z=W0B(_T$Ya2gJI?dd$WTM8gpjIm@RHBnM*0^-;ycf6t<78A%d_@!mvY6D+iqJML6G
z&)P`C+aPl1rRF%*cN8MU9W|KeEW#P<d5ZL|BTB92G?a^*=|-Y$k^q=u8_AXOb(6ZC
zFi%j43@fhl1m3s_O*oINedFUIVwL1<+E?`MO5s|Q=$0cai1qiZP^{;qssZzjGf&gk
zBeA<?04)DqARgsdaqdYDZuUBif+!Wo^qpo|*#85@UcY<fj=i>)NEC7mNaiGquH6J>
z83}q0sZatc`ndb!4yg0Tje*3BE;<jXM<*x?S@`9JUPZ4jFx`?m?DIC-9JhKxf3t`@
z`*geL00cMf3VFF2SBy{K!_tlfn?^JRQomMH^u-wK`c8Um;1Q{8C%NYSEkT)6-x_*0
zo&Dt(4_aDIV$ObQ+5cGDzpo}d=X%lP(c4+%ix*+oYtBfezM>|)aTd`pyZwoIx;H+z
za;j_lI%g@pnZbnq_!1|Y2TyNBNyYm#n?)c;cxLsd#y$f6mokpMq~a=4A2Rf3(Ho?`
z>21O<Q)67OrrN87oJ8X)u<TLJ3#_jU*DiL3sT&e!5f&WlkINE&m$PN{n&|1Ka)JJD
z$!S(J8Z4Bgrln@13M=jUOYVG2%_q|!$E*lXeRr&J<jb>EO=t08$UZR0gjS_uuSzP0
zccwt3zk8s^1dIsaEJpZc&!Id`YD_1}b!$`+KoY=am#HiqU_aN40VFL<L}E5?CY?*h
z(mR8Hy2;{@U<7IT#>WE2I&v6S0=eOz4x{1RgLSuB2J@IN3hyra$@jOsZ3|P>)OOQ1
z2A(W+k*@>UJYf-?63ERJ-x2ierW4_w<1yG!0t6(f3)Rbc_vkI&y(RiviQ*lh$zo15
z*I!#hw3<;Bzp<9uzpnv9ok}?tBXRyh8kgehFPD4Nmt_Hw2eKWZvVpkDL)JHd8GTlu
zT0KY@T<l_0M0>jMO0u>Bh=YrKDg$P?_6z$*s%T3c-VJuFDLRz`djXF=6;i-rNoIx-
zR0HFCm6gcl@zl`{XCr;(o`-)z)fm%go$984mD<H3FJd{Cl>QA%&2?VDLbeDK+3iEX
z(y>V-y%BG{-csch>hwVc!0QRlXZS*1*gK2%v)N39j<Wd(c=&lRe}u57%KAs=2>=~L
zeYcOC<_EIRP?YjpuZlSC=iu8HpTEdL9QIYTXQjpH|HIhlp`?W#re+H2pugf7E+t{M
z^2G(64#ENt{Uoe9V_on%HMUh#zmHDna+v!KnizOnJXO`p7q8Ok7xP?4!taJUdy1@n
zA8))!<+i2zfrvF4quB!lEfMI1g`eZ!EFCxnmp5rua5{e1gNrt0BKsUHIj<9WmRtt^
zoYa`6&NFEC-&pyZdE%G@5~h42eEO$_pcRCBgpuu-wi~{A(NN4Qsjs(G9}~!6I9?A7
z-(;wUERv#f-$6mg!I<tv6BB9e4~GSGafiiv2nd3T)sy!wWwC6sj!8#u2NFHN*`{YW
zYdQ2;%HvBi9#a0h>k3?`CseNP8)h%Oc(UPy$+*tcsx1^Ghj&HNuTD^xjr3=l%u$Nk
zZh!tdT<Xh^f-KpHSIs5Rz55EFErtZnUmHGPR0cnaZQeB0eFBE-m}Rmy-Sp=ZloLtL
zXX^<J192zhttds3%d{fMYHs7kGpCvQ%;4KLz7y{4ty%68zh*oEdzLpFq86zF)W-BD
z7PaR>30Zx90`+Y;(vK70GUbD!YkU|X0E~1}t!se^fCqpdc2Nm5eAPhKN=AI<HmNs{
zFOUR8ePB?xstAUEHY;h{$*Skf-n#*zbd6CpuW{y?$%W@*)^FwB+rw}<7M<S_?=7HS
zT^J?lM5-2PUA~l22C#?Q7=ay)vO^O7aiI?Ig=|VI3Ms>u38p)EsIjVU=mgCR;!g>p
zKLeFvCn_gAgz|PG${~G8c2bv#)H0%=@>-<aE0J_5UU~vW-j+hhEZakhd`y(|@gkAY
zS~k+?Zw|pr+NPCFEKv8XkC_j1_Y?(N)0PJAA-McMLd<<s5HCQU%`E<h2!>%`BaW`S
z6yKyA0tpA(b|{1OJpaT7r5$x=xdE&RJ#d}p>@05?5ylhSt7afLA~p=ro~O8gJ|1!;
zhtN<j;iNduZ{CTMgVE=;MX%XE@*oz?*9szl%K--5%URxGzX2n8nro{mNp|9Gi@tjX
zm#KmLH~ti|BEEWp<RM@t@V>8X(HK&#q&!hb>5!zz?fH<~BYtJY{4?7dtJ72TPi)(a
zgO|arD`#0#Tc~0pfEW6QZmf9RTWx%~#Z?NGu~E|(Rcnl`>6Ddah`OJh*-N3{jwS!A
z(l-7li%InLu>DwZj6S16&f;)NSkf;`NFwp0+4nC`gFNcx3=6D<o;Jd>e!JZn&Yx}E
zBT$nly!bwOq5%P6oid_8#~jP%1~XR`Xx6T#*ju*|`!GkWpgH4V;F8&VGZvH4{_Pzz
z(v%uJWXFCy*vx+%W4!0H5K8(7x3N&sIRL89wB?FYX!`B3d=Sd+?kz!J+jf&6fSL19
zY*;_bpmZTJI+M&Xc7;aJIsDC~=1_k@e1vu0Qd$Fy<Q=Q78?swX%4?HkK0~Vz(VB9I
z<c5){F_Aa>{s7uDZuNrv2?4|cX?89Jxg3!GZeX+{b7&yut_@9F{kUX7b~I}%C*S&G
zttEL@oXD_rA#w1aQ#o=(VP~|N*S?5qbE6Px3z|y5@#IGgtMpE%nA;3lckzU^Tw0RZ
z`BY^}VydbbVrKlJuN-%aX2&)^ysvhQ6L_DTk&XQ@#AV?JQMjK@pyOd;y?Hbz^C#qI
zS1(KN>bUv>Wry_D&>B5$dIrzzDB6dPPV`g=adM7X^L?kvnzIV*<Mq#e7GjSIKTO`9
z1MXc6Gq)>xa+B9c!mOLZ$-OvGS&UpO4V9-gf8I!Rw%*!`d<jxq92ay+zVzbQ?IeJp
zXR12>rqnY3-zD7`et9iSwY7UAl=3b3$EHs+`%_==Y0L&!*`oXupu_DGWf*@-NSbH4
zNvB@ZM$SBQUF%_$w!dKkfF=c_vVH@z59d9()d4ART0D`OYAqTCk-(;Xadp!wZ0JlV
z8V+!0+)(eXAnyC4Kh3cUHP&(AR2xI4>oDO9%I8|$TR)$FX=;MC;f6}Ib&aRXOl|E>
zy-0-Lpq%=(7i$;B`qu~>Pn@o&ta<U?o$9QWGr6|yFdud?(2zDtB=x22ZNHa_>BL_B
z@_ZP_<MhPJ_G)WCCSskFIImRSzeX0X#{R%kYs_bH2`oM|2|jT&c(tR+9YT7Jk>?KW
zfFXC=@~IRT$J0r{MRO%Pluv)RU>mRdm~ePZ7g%tVp@Mq{PXh)Y-%?_*X-%gi_MfjE
z^4osPDC9$5^XtY-vj57T;*sH{#7W#N<N@bO#~OKd*SQdk&Obamo1Hh|^?Yd)c;}Nw
z8`1V)9fjK&-J2q6Pw_}OI|~y?=A|Pw&-U{SUt}=Ah*7)9{Dx|K$f9{WDhDB|fBJ<{
zEKd-)ilkFtS;n1y#gvzjzp}+%3{XC%AItEC4y1k-%3H>`hbTeKxrv%q_X&7?;P`ol
z{TtxaY0KYYV}W%=0zX=*Ev28mP-7XOk9}op2sFa8S?%8zn(T}EA){L?2+wA@0Qj?6
zd3<x@4yETQl1Y^pMmXRLmo8RT`ik%B4#3u1FYgpyD|6sK?xXWGQa^3zCT<N-aK{mG
zheFwWoHyXD?)Q>YX&!7b4z-LS9Xn2%_?(xS;mo%pJHdIKF&JsB0G>lsOk{~M;;oID
z1yiCvO?qjhZUnvdD!kYpd1y9hI#OfOMk>E=0rNCRzGX}O>vt}+NN9Vvgykf@@$xyP
zKZ?@7IrCmS@TCP6^RmA>=bj&A{H?y;8G7}u^}P-fe{tOcrkVu4%9^eCe??e^duyy$
z6>|jtSPkoFSz=)0SeN{r4HY<jD4)ZD4HLjBPe4pLb*Rs{_Y7zp?)=#`+!&#Z@r&-0
zWHvv9xc`-PR>g~LJv6!_xV~6M#~b$!D4@-IqXGS43gD>6om*cKyHX?@dbsyWv~|9G
zbLKtgQ@@ji4gWKx5xSwywdA`hIwwP_K&4Ve?)VV@>t91KMQnGWq@nfz$VRF_mPXI3
zKkr2+6nH#cr)vNxb3V#6)+SCflkCjZuFS~X7n&f=is^A}<aX;rvG(gzLnAe96`!fW
zG!ml109}upihG{~`v{A7)8tT#F&qq}=xHK`*88o(_KBf}+sjcML-tJ9j|$^v>=y7+
z<RU-BgB$j@zbvu=B|cuIzx9IS$*w~7iN~3+W&8i8405BCW)ZITha+e+H_g0aF&s!q
zeCAgh|C6zUU{&nF8WUiqbMpX?f`DlW!jXKb9~fM3LLC^&Fh1Az2k;Gn0i4`4<<ky?
zf3VJ5nJ|DY_c|(bl4fNU;BUHO654p7ylC-j7^DGA9PO(eVvUg&aO^J4U^-H&CHp<1
zq%%2TjZ>CY#i52dCvuVQyzlNJlXc1Ed=U!;fAtIEJJp>9-sAbIE;SgJKStiDZg`4o
zpWiWnH-}_yI|c7Oz#<b(1X>3m8^Okg8-!sLy0xTa^&0fp*^@oR&k~-zI>X>q7_g)f
z#i&Fvs?vprfzzO|*0tE4ma3RS`q;ISPi54<o?dD!8twwESt_%N#qjDAtFN8C6QyuZ
zT*6Ocp)^V@j&oIk_-k-y-=jW8md=t%TXUZ@;*)phUhY)Y3$71bJtRtVoFa-Ly=S(c
zbY6jGNR@bBY~8@WNfEIqi|Hi(Y6!6?*O9=%sOnPr9|=CRM;!eL*{Sg+R5Y?*X1B>}
zaJeyi)<lniYl48}@qjtqy9Se)X@Sb+QjA<%B4vSWiN%}6xeYZ^@9Ke+Bn)Qb6*Y0+
z4f<lQN+$3(<=0rPnelA+D$OUJFe%`=n+jHeG#Ka(3(X#>A2v3|_>Jp%K*u{qG-Pnn
z<hozwc)1jX*!eWpeOSWrPulc$!-p4C@w_UqeFiXwCHRHTMTnWr52-WyiM)>nrh42g
z$hg!jzOg}!3``7XP{|R)ew<y3U1#l%jW8HvOJZ<oqNYa@SR<TmQZlNQpvhN{MkY|O
zHj|RbQd|th%xMdKu)?=;`Fj6^;l7y*i9T0@2=!GA$Hb?w#B3J%;Qb*PAU{L;WoM((
z-moke<y8b7?4m?of4?&Oa)aI9Y6Fq%Xh0V}q4R=cPs$oW#raYY()LqoFUcoo*vdDD
z!5?h)fR<%gJP+d+Se4m&=<pAWBB=YRrJp{A=9Z(eeO7?%B7uArT#935x*akUs*uRX
zrEmsA{MP=v4l1C!=nLm%pE>KhSFh08UysvkW6GEoAH*SWr?Nu?4b;IwR9^!6j(qzv
z^LOd9gsbPpbSjitgp1op-#X2Ym@c5?VM@VNm>{nvee6A5R7a3j9RUlVGCR64rnG8m
ztKl|Qvv!C}r>vupJe<X5`;=R?hzF9?Q+X04D-U#*F<N8fBpOx8+_^oQFt}0C_BZPo
z$|h&9nGqYgYk50)W$=sAW0@+g39j1s%1SaY!OxZL-M6O0F@Be4=f>Z}F~{PPADXc7
zP-9~&<ZrMBR98>3NT%SL%3QC{xD2`6#e8WXrB#bz7?IQ&pCu!vT`^N!ctxVExl=lK
z!)w9EzBPIS_({?Myh0(af0Q<p`ovA{zY;o}K=~nr8h)cD%4{WJun|B1<YpSnvml1z
zpUUtwYa*K8BX0=!cRzUBV?zAnhL$g>0C8d7P!hU);_4!jT^C9n-g{)!;|bjtH%Iys
zSwSkRk@LaI^vK%c?&<aciU~Tzejc0Zv!|8k_32#6k~pk{z(KRly^}yM0DeD33sNSO
z)88~$l$3#)R5uz`DI?!@9+FGlF<2XK2NzL`v=wTNQg&PAe5?4rZgxFIFOJ@n470CT
zI|%?vz=V);Tg2k7Ad>(Ghc3m%l!HP-DrS6&$QiIcEPIkW)0209n8H(fXlQotI!*E^
zthxEUS!_gN!595J3Cx4dycF#1pGmOG^mR8T?EW^<<iW5ePSMxd{xF|qb3Ry&?B$Z>
zuDHE>X!WM<-erttAbQnRtj1d1&)DYegQjENB|JmSCoK|lXR(f2zd*apJ^*$qBv|g&
zRce^pf38UMxA@h_dOC@CLdf}3O)-H}Eq)kD%LtD0;Z3Pmk-(2W$)~3&pWNpibr2P3
zt^lw2U0xdZy@z0~;5t%n@Ss_d(^;Kl^|J9(dum@+mYUpdE?9i?GIRKq%i7Oh*v`bO
z!V}`WcMn4{Rx0_89!S>$^3hs6IhEI#Abcw_UEqp3et~B02wTPH@?T@mLr2tl7ld6>
zNg(jfJ@EYi?s*%y0W{P0QI-!*Q5y$Dm&2+$a<72%y1sGe6>R#5pK7(F^4ch~dgD$o
zZlg$fU5}v|Yr$GeL-^}gU0PhU&hV?p0(|FzFV8~v*&o8UH@@>sWSECz)(tP?L9$@F
zD|!;MpKkrUoghDn1~HEDtD=E$&3x0rK^CA3F^F0MNrMk`&Vh~Qoj>3N*J#WjFLWNd
zI$^A~6`7rnS%@|+((!f)Hl2uXx6R6mi_wGsn`*oJ1NJM9Y}G|3SDte#L({6{xBK^;
zs_*TADC%T)acxq%<?axcqNUjg<$?UBRD&$Qml^_6mNq6i{L(zL4Kzjp*C)a-6^Kg}
zpMrpJz(G)zer;x83X?lo983p_uDJ^>zhIk6Xb@vB_!Z*h7w4u-ST|T#AL`t_a&(vx
zu~o){R7|Rf?d}Cv=(IEleryJd8oDu<ot>?`WJ@mBF>1{-F1U4$eKCW@wuvQV1=RZ|
z#XVFT*W#bd;UV98|1IM{{BreqDQG^Xlkt<%=uE2}Fww2&5nArmTimGN$#PKdc|Rwn
zAdV&2&gO5K`e>h#j!>e3CJLxn6XmY+jNolTQJZ%o({#>`d4DeK1-pS8nLQM?e9A0R
zY86#nR!lKwGBTc<;tsCYcmdFpx`Al#)(-$j(u?kmiha=fd72V=cw=%rS!)~Lk0RFT
zqYe*88Nwp+eA_xr^jtO3-VUjZ-<twOj}AOco<B=)Sjfg})}$mmICG-i(`g=x=Me#;
zwyNd3{7|O!bU79zGOhVGlhGRf$**}5Sc&KwPuSEhDZV2(h`<|se~$dmfMwx#e8zYv
zi7GJ7l3VtQkY>Gw1=@YA^K47wm*iusP_IGL2NuJ~f^Uo#NRS9%X|~OUp6RR}V`QgS
zQPx9O5mDx_m%r7-#2BXxSaF)14T0)ESI8|4PeFJuyy=+|K1U_tHd4NGat&pU#iSei
zW}dLc`V#8qZgePDaSp^KG@a-rCPd2#W@O6g`y;7G>aE+#vED%Ph~Pa+6s%viOmAo{
zx*;4<#ZRp5#3PIO^YE8BI2+OfWqpLaNKE`67Bce=Ln=LKYC!oh(yN+i$z91`y|&Qd
z?cU949Zr3mkemu-U*9b9$|H>zo}YX@v9G_k4qr}je<1F8$n}}rV)aWo)Eh*js!E-z
zN+sw2JOWtao9ywGtS7E?Lti1FmTzwvZ`=2WLXCk<lciB>+p3U81NB!Dj1c)u@2GBC
z-s={RJk{ct5;KzQ7oXd6K<i}LJ9#FaI1strCvEw6p8=61VE^#wfIRmW2#3Cg{(2by
zWrfvIYz>fquEQ7wZJA*X4g;ZuG@rxf{E4ZjvH`s^*vFd2AnsdP*dTBK8_!%=Ih6Nj
zTEaHnCGi;UHxjXIttYz$^)(K8xZr<X_bj7Zs-r!=q6ubEbo3d%U$#@Ewj?4ipaHTH
zZ@>r#h_*i}xO2s2zjP3_sYj7_UyU*95gP0^CTcAUWFGM|0h*Bjz^L4=J3p$I|KiX<
zq6!R)`0v_8mC>G6rl@8eQuB%J>6}lr2yjGPA4G4{J_`z88LYKIt#tcNiO*A3kHmdI
zbf6dz;idwO>JsE2l<L^J#AD=g`%Mbi#l4JZ)ANAh8!l_S*Y_2~gf|1y#jO9K{wG@w
z1^S^R9$dGUM!V^~PFqp(G~u$%<SA+UG5<!V6~{hZql(02Tvu3OVqh#IAIFFCV?86T
zv8&JN4_pJ}c$>d@#U>0j)3s1F&Q2MAPxz{3A_V`HM;U`u&qsKSN$03-eEH0MyezpM
zZ>CH88S0$ve2{kx*!1)FL*T{MnC|EJ240Hp15p36rj#a)7~d;Kwpemu)dTKOVkn^H
zAeZC-Tm~?%UWg!L0^^~8_=KOvbX<?zb$>dX!^*oE!cEaz>wU)tPgfuN`fSwC-yb>7
ztt3;?I>3<+HbeNj#V^4pf?GNAaaPJ_$l~TYvb$XlNPyxKo?pVXO)8yz_PO)#VFAWs
z4?cP5_4UT}vefJ)5+(4obk>uPo0`S$*E@0W#*Ilk^cojnsP!Oj;uxrlbLxukdG0R1
z^!=xkr9pBeb(d8i#M9rU==nO|(J&j)sx=u*+v!rfBHX{60^{s~>lY$C6Y~Bed*K%+
zu;uj<UKmdcVc_VMxMd0$fR|YR&7_REn6(3;ot8#0@|hag^KN{1MrjTd>BImRHn_|d
zRlM+CJCX1|EdZwK!>t<n+<+aG(W_4EK_sz&=JuZy*L6Z`;}cF-fyd5GzbfH+DV<o<
z1hP-|jGDB>XJJq<Pw;@{V7++Z*ZC~-B?fEwLfheju71Ap&xsqBYWs-r$1)v1(pkaR
z>`X;{I`fLjT>r$nk)K@7)1oSYLfKh^oM3J#nYg1RY1!lNh%BsE6u&H1c>~S|G!NGr
z@c9{N{mQLV8hBUfS9VRGpf=2PD`5K(n3?PKyZ7pVE~CZ<{L72i^3gsS2lU~_l(m8d
z?_F7}s@i7<o;<S^W$3}JF{&AUlg}%<j>x%a9?J|qVpm?DHSQX`&v1DMZa~T%Qb(Q<
zr`25iAo>V*zn|6`lX<~j;;TrRjU4l6NtQh_V=ht_$7jZclQQ&W`2tHK0#iDXdEQpn
zG-elIV{gOS43VP#RJnA+n48E?r*C~|#3|+M%Ww>iUbpi)Cj+Y?k*2<cW^o`x45bd2
zsN<1vqa&T|vZb{6^5WPl_E9?Pc8rZNjl>TTy(5|kl4zrD3mzXd#4fwN*CjVlc&Yt^
z<B!p<d;1s@ay1EvMCT&~Yu=h*fG|l%bR85U!Nw2IH4I4%U?*b)7z6c*B6}HB;uwPw
z)7?l_YdId-)qV2ua@lOlfsvJBcO6tK30o>t4?UKaAwjMOkDdlPH<hw{NS$U@)X!^K
zHJ&_x=*@HExQwl|Yo3OD%p+k`{<{4<%A|1G^U@8Amk(YeZKtdZ5)lHdqN1&;VhdBb
zrqB0}_Drblmy6_5!xea^8OW>Gbc0!QiFTJt9Mlj@x=GleKK}p-nrkmMHp-Y6Q{)LW
zo*;b-_jhNBMUHp_G;^zIj}N=mJcA0HcShP$+I%?bS2X93iKc6z-i%eO^yar>9WT5V
zbe)u-J<dhNvo4<>c>P)xv{$8c@qUQVQravZ+=ev;QccXdX{iPj=upygr;tQ5<`?g)
zBoa*&G82*ohoV-rXmzore?n97iAh>qv<bOIC?+P?E%rGf;j}*!9xL5+`vOE26g?D<
z8cqeKo^Q|KVG*N`V%nF<T;X-pEr1ZrXwnDFbFlaG*SF_k(O)kR=-y1>-5NVu#r2v#
zzUiHl(o1FQ3eW}prca47U4dWx%6IFRS!v_!Y*RsZaX)IZ9(Wag(vIDRbRhoCtM)r>
z`&${}km%nHkEx8K<DboD=9qYn?NW+hH@t2)guc}mTd|HMx@i-eTlwZAJ~x;MUu-}V
zb<P2lX2`Ge?JcXRM6)33l;eZ#As)q^1w|BYcZrrcRW*&&_0YXP8UF;s04_g#WvV1v
zfHiE(-v9V$1c^N6k3s64<pECPyqcJ;MoWO5xS^a^p1*i@l^T^lBYuj5?){=3Sgzy1
znPfIV`@={)v^_;F#Y=zm+84om11$2l13wbm1Y<IrXDp22Y?;q?KXY;5DR8D-KIC=@
z%c6F&Oaio@#q;~b)kB?{9VwK2)SxhSsHZ(SAOwnwkMJfJwodIA^{0HU_@Vbtc|l@r
zS8gkS)$jN#g+;0!I%JGxB7|w<`H-m9K^-T13<i^J;cW;d+h6_XT${)Zhs=Trn;Xxo
zzhWp!<PImJ3D?n#@VR;M&l_=>Du-_`+nzU)UUULUKgl0M+OX_DX?!GymhLJ{H`iV0
zQ~0K&M8jX&Rrb#;wH>eqxz93bay!RZD|U}dX7!v!{$BjB{~4DcLGPh+a?p6{P;!>;
z8lFi^4YoQ3&*%F(eD1<kH;!9#*A~!hiFkp7j#p6tIciU<)1?c;1(aAvW5}WsgK#1j
zZkaa+FoA`5s-gt4%#Tw(9w>3?Od6SEKKmjO^T>#y=SXMtfUxL-LcjR7JCh#g2tolO
zE%~H*p5GXF*lK>#f5ui<q!lL&!?M4+>u?NUeb5Viao0o4yttUOQp-FA@~9^>FETPN
zS>vTn8s!_z*`pIFoHm<3Dt6Ym9aC!gJPyjaU(8tu*4X%FcBQdBQ`C2>ex0-P6<=|t
zkbXU2J!g5c$dfZ~xR_uQB=n{TS6x{JaM9T0ogK?!4|o!!-(q+gI0GeX0(-q6Zz2f5
zCK$p?hO%Tq<+bq{;zkveHw6gu$V|)(ikF~r;sxSx!N?*+9$EQIf2z;)L{{_H9~zqR
zoMz6}=Wx|2auWgDY~0m=`*fl&T<ot!=88~H8<eNvTUqr+dasC1XuGoHV$*|^*L9#1
z?Tn#1>k;or7nenTYZ8zHD&3TNrKC_26*K4Go+CFN(j^vb<~}t;sPm=Xb|Pl*d`G2J
z?Q~DHli0O?L%3NCMp6cFa<JUvDq@T-fs|et7|(@b#gWP3-{z}{x-^%8cw@8hpGbs~
z?pFjG#m&-VB|{k(s5g{xxRNqLrSr%Z4f6lQo^z*V3{^3I?0~ZK`GSjZ%_BHSw~}~0
zv4m#*>Q0n6Y-;IDv-;iSJ$*-t5w4?nt1r0XP&ZG&<~?(4N|_Kb{bI6sz9A(Z2tv35
zjoLi}+a9=nxaJ{*US(L*1B-LS#ax$$G<bQl?yHcPpf;dBBpCn;qvLrO5|5kz;R7-r
zv4}8$c3R3$e~1t%7Ut~~BdVg*u3SvNzz~PC=0#fnlKsHf7Yoop1oA&IOAEG#y&h6R
z<WdpR#(?#fr!DedE(IU}o>~Rxk@Hgdqk&)zG*CK#OI>mj6F-`Aj6it*sYPZ$7a1~T
zkP6)8I07=UFHk1}z`^v4NoWY=ym1x6r?`o?IyBGC5GCv7@hXJgVlZ<X^9&Xj_FW7r
zLc@6zgpO^BOB>%!i>PFFmJndrp{8E%wN=!UxVp-o^OHkN|JECbQ1@b?rTzy`e^H}m
zNxo2(lH=_PMWqUf<!Zi8-L3u|a1X-%9;X!0Y#|iAEo`3IfrK1Nlot9087QD~XmH>9
zCoZ9<1SQPgcv5s&YXe4V$rby_kmEX$n}$BeGvQN=w%v5KeFc2e^Y*QnB6n~y*~1cI
z`PS-zjI*(Ql=`R6rp?;7*y#V9JcZk(Lij3SgC-IgwtZF7MU3E`S>ImY$3W8ha9q-?
zC#aDzep#K&lX{eE8IW-lo{c$sX;j+_>T@`WNkKH*fhsZ#e$gHA5(`QMrd$LM+2L;u
zH+m7a#~qnr?XmC2Bh9jj9^A3M-Wh;b(B4TD0U&vjO3SwmEXr;?0CydbF5<I#FhRUj
z*R=x`fhnBVrvipXQ3Pok+VEVqlcq+tmoNkzWALNC%>=Cc!{i`dEjbF!8hGjvm~^K*
zdy<{JiR{kwWTV%+wkxCD<6!kd$Va{aYox&w_@c96H@Zs%qS<!(G`Hrk;jra>JMj<K
zcfVR_xbXdKM|^fQOlbk5y$0`}EWmHFa@RIx@!<?C@5b)i&~ZaxVKSvfvDt7n0yZq3
z4yoVMM}HU_?yK5+4HUej`B`X9#bw+CZ?-C2-uBiHaPpCHZP6zwk4QtX!O$BeJ(U2O
zwbzf2^Pi39=n}NZ&W;YmC?o(k`O-Pv*TorM;Kp9mm&h|*n#+B!DQNw10kc(+O)DhR
zyS~>%_KrT??9Qls1{Ol{gmB!)9cd7?(DSt922Au>Lkr*yNFDl-tEfo*Ivx2-I~xjn
zPn(w=`ic57@WWfA)i(%g<woglV@@>rX5}Z!?-^@--eEVVnAI@Lzr%t6(f266?|SQ;
zcsU1Pp_|<OqQ{SV^2qMDtUBVu_Pp{LD+-*_B-Uz~F9qOTfDt*(LLtxJ@HN6*>=Ocd
z$R`Z*HH{Hqn2P;wBEe@^j!d*xoBfKGBH)V95<=;lONH^fAG|)e`a&mN_se5La9MO>
z!4CaR*SXd3o`h4BYLUxTtLH3Q*iZ9Z%e^=)62N<LZq$U|$8}zSWoZEW1c*qvpM~AB
zKm{1kPBDOb-iH%L(UnJv5Wnc{`V39}4G{f(n8J4+VyPt0yn)#Udwx%OK!y3)ia@g4
zJw?ID1eD^cfeHYi281Q3lb1C=d|`o)64Uay@FT+r@Os#oyTB;*PPcz73?={=#-GOW
zJF~@@gNz?H+AS)-5$V0(Sx6;i44@XXpQ5XL%R20ZR~1T3nYk2LmPF?#1z9=bN0saP
zQGYrCpKJaWXD(xcw3W^s+dh|aSZ-l&|19X@xtTk_!$;^@`4p6gLo<6$Am7HB=5f!>
zszdK>jG%c?TVe}maH<>SaZj;aXA!sa!An^e;W^Ty9Zi8C)hdO3-g}OU{?)iKpb1=y
zu{FpC#e+mze*R2Rs+hRijAjIoXj=+^jdueTkTP5vqg$fHKm|e|LBPwZ<N!4?CGYe9
zOOPR^x}^PjRsA*OfI}yjxw9EzA!Alw4!gM*aZ(%CXpOs1sf*E#AvEg_f^?cvFO{8Z
zg2(ce4RaYFMJ+^v6*7V=>>qgkOkd|z)Q`g3T5u1V4H3t-TKisj+Kl<{Is+Q3oQ3Xn
zeduCb4;Q4-;W)2frZt|=6e2`SLS!OWsl+$p)j#;~cL3s!Q4TgF40*~DJ!@#pi~pr#
zU3^Ci7w{r<kyRbQwNd8z{h@gd!MCxUzPd9Yiy<MMQthR)wNp}SzmEXyAT*FN4W%KU
zpzsCBNK&CgGu<z84_aaswiN^-O3o_2N!7nK_yIWD`0r;yuLA-?@wvM#FH<j1k<TQ^
zB30jEP+(xh(UCEP#e{3Ni>^vFs{Njp@n}Eag?-Tf@ByCq)A#&)(vCpnPbB$vuKyA<
zj40FSX#%5RM?tzRl^H2c<LOJI3Xd5FFPYo^NhF{zFE^(41!P;1CQ{A(lR5;}&6mu)
zz7@B~t4FxoZ|CriSn^c&_f52OYBMyvQ$b>?r$V${aVa8q<p-}EC=T~N-_OnD1_`NB
zHU#}`0)C(vTdb(3@RNCjwjKqs5}NbBo!O^<oPSLE&=F&LPL-v^c756OYm2Yme_Y9-
zSNkX2G~OXT&Om>;bFFUBznz$C+Wr_t#M3VUvohy1F7B)rcDlc)g}PIhF?P@0$HymR
z`Rc7nS@Ns=5yxEE!cgF9yZoNfc{65oiAv$^^mvZWBY{r`)pf2Oxtlw<D6^2{Up6<m
z;NuWFdZ>IGaxqi0Ek^5BsfIfEX8-urvyVJp`>rft#lz#7R?bjDf{EzMUyB-#CtFwV
zk}vI5xO|C$s4-oVCyzJ!4<I4lZqI=CcCQCDv?@Uzr%?Q|@Qz;;j4flh_P%q+TkjId
zK&s8JF~&G#s%rCyD>(z}>6rewH=aC@)Hsym0XW=d?c|DYpMn@88HpY$RyAsEIxhnk
z7uRK&8<i>N-%ANEgj5yN4U$4cwy(wxBas7CT4Kg7IzLKPQ~6yF!ttPEM}Ncn3B}RJ
zm&^b+J;(47PM}oAzUerG>xs!DT%gNrqR+!TK(Gf(h;|eS*^LaA-&+{)+&A9Juq}?M
z<1v{#U~N9V!K&HbqFST4Un#Jn^(QZ8&@*p4;7PKQ7xGyen(IR+{ieyz{zl0qRs4<W
zUy><P-#|bWMr^v81NHJ#hMok!Dm~-<aiQ6IJ@S<e>Vjf*olRDh?Wr^U1MzM<ii_;k
ztgh*k+YH)*P_~OQK>%UB!(nnD_tB5`dAZe+_aD~NkQ1TM#_wD>LpwcYBO+>XTi8ER
zQQ2QSPPF$?_)Wt$er9)W56R`&uVg(~bML<1l4Oe+Qcb`g$OSyhyxE%IylItvV(3m<
zg~*K@1QdAh3%{fkc!Qf0v3F9Ho82gC2ZES8F-Z7rue8_D&vZo0C(_EUzd?TOB}Z{u
zLH|y5FLdWI$thKS2U6ku*)4aHF~iJZDLY<OwYAuWI<TGqvCH%v)*qJ?f5loE^6=|T
za(z2$@YU#Zab{NL=pXEDnGNWSkDS0Kq}+`){PgsLNG*#2&o3>l(a8B4@$J?~8{O;L
ziz1XhDZsla4y>3TZP|1+v$ZxXq4|BUf0(2!Cncdu3FLk4_;n^T77iX0s^2X9M5nlK
z*NPk5zKiAd%xNvNasg|mq7MPKI}7`*(zs_jNx@Pn@w8lJNXl=7s*#k^KeD2JIpCKz
zm9RtR1&ULXTj_}LE(`a~TpQi1qL~n;2@i*cdwO|f==Ow`tt6BemHj0D^AFB)Ge*gs
zH)(_^;jukU2C0z+>pj|PY*hQtRxa)F^u{r<w+w>*kAf}Oo-O|TLjn>=9H@FdGGoU9
z7Xo3bQquazGg~~h2*<<cHFi%G#yvfGT_l^>_7D#kiwG({Dw?9AdE=8XfbtG_`5A1M
z7ddQz@?z9GzvZrco*ys0hq8-l*8VMIp2bWYCWeqEHd`%CEX{RS&XsqRYbFBxhF+c)
z#Pm*nN8p<iCDY|$58a61^ulxmVW_?;JBy&WAVoC(A*>yjH$IMjPb{%_9wgvc!NPgN
znLZ~Z4m#*Wp*+JwNuDeRImPfhLBHl`vtumP4h(e3ChVG0EO{*s_~)Un+&{XXf5bvG
zdt_?kQ9?P0%>Nh$K24(&VH7e>)+p;tatRuONODsq%%Xs6EOkYAYTnNmSPNp2H<R5Q
z;uGmFy7$AiQMdik|Kztz2Kp=S?gVXSL{1T6Mt_z$JRZ>Jum3Z9-OU*`wY~cDK=*B6
zJO(?R^zO?Y?jTFh3g&!BSGc9Tft-0b-K~E5uX!Vxzu(E8OVnWeL#*CJ-(nSCw=Gcy
z^g6=!i3(JC;NlFvqHymjfxF=CZ~8_o>}TKu^|=ut6rUhjz+UJFTMQ7!KF`!}6ZF0D
zi*OJnlb?l(b6%7PJE*58QRPHszuKsfTov{<{?^HPp(HmGE~p^EZ%g#&vHx~ho+(yi
zCgP6c0iW9wo>fGTg+SfVAxEydh*_41KANG1Pmzv|ADr{~^tYVlz_`tD{L26*{noiv
zze)*H!q!e^z@fl7-QBL)<^FhsT<c*i%ZPZ|PxlrpLBjP5tY4V;dAA{jy{=)o*UcQ|
z-nQZ3^tI!huAQ75ak#4tpQE{g<<Fd{gU*;N#cmXZ^|NTPxS{Q@#i%x`VC|#u^WKs^
z4#fVz8Kix#IL<iUcLMx2=#$QQ2u0|!zvks)z%j%9-!Yqou`(l=s_qEnG}&#4$^cba
zCQs_+0SWhL#Y(b;iTubBMRH4M;`9WS#Zx}XsJu!K=crd$zH)Ed)1ex<!Th4V>_~Iw
zM1OgIeB**}O7dtvh9%=6C|^9GAeS;2=2Upo)5q7@cKqnDfN)^=aEQa=Sslahe`I}g
za9#fw?TyvAaT?ob>@>D*x3O(ojcq%P-Pmc^*tVT_`u)B4*E^G$+{|R|J@<UH_gZW3
z<%v(Hbt0OK;XQPeoW{F0LMhNbTFH9r06{2Qe>q=6(AGG^Tx)(+kWbbdL9fSfR$Ai>
zR>Xh3<^}j2I!rV&e6-2fyY32-7F07&S7l|#aA>~mfdR+lmdtus>l68}<%{b}Gs1y7
zU&P|V>O<iINl$B{^;IV)l1A%dfXE?4%>%zF&dG|qup7C>uOK@_4J4^`V!$+X+Oju|
zY^Pc@n!%6Qtu@-{Leacl2%Bp69wTf~`he<L-TpJ1T*EQUl26_!vFQw&^(z5gr})Y~
zVz}lgI-&*=kl1cH`L6tJ_>f-DnMH{*>)`rcG+NTh58G?dhcb&VR012xigdQQJV=j9
zOU>XK8&i@;9)ymBw=n-fYP1PaB4AaM@w%rEW@oRh+u6#FgNQ;%pO6j6Y2_Fx_9ruh
z&tJ<x*hU$KM@%4ZjYhP1>Og}=qSSz}t|tr>QIi_LpH8f!b%>d~@%K^-1aLpwyNja@
zeR%;LG<TjdH%L}vBL+6d{P<nR$jdr8?wKhrl|V-+ItMuNtD86NR`xuox@3cV*<|>E
zBSdAFgocfXBB3im^RV@vX7B0}RSlEYyX#fCdff<YTnv}@Pv9w;d{~~gPb06uhjKk{
ztPc}>ymf;fKRu$Ax+9|^B1Yqiqr0(v1ujq<h;wwoi)KO@=nssFZIm$Crpy-Ix>p1k
zyTi?(g%o*rbDxOE_f!!1QRO2?3Sr^ODhyRHP}!?HEDt}w!}V3;V;P8}@*QLR(Q8jf
z<mvp{z7Qb?)6`cFLxx#-Z2`_WeM7RxJf%iu{A(--5>Dr#Hj8Z~Qh%AA!hZ|mQ^$)N
z3NiUAIK{dl&3rahAI91*@gWkah+o5Ko$ZHdUa@IM0&OkMwec06$8d-Yn5b&rU-~k;
z`T9k|=~fO6&y|oVyWRZy7un}0z&;a8n|OI3-=9UkRzPNf{Vma;(pk`)>WdXFw|0%~
z)b+}d@Uq9q@4Al2B&L8<KSomU)<dUwS3DY?8zp+-HF=YlRKomo*5*j+(F`k;yA`+r
z>`gu(Oy~4F_FU=7Rdpt|v!GV@2l$LQZ-UGhHRYBY+v^l>%{it#K5-gWS-Ef|2Gxz7
zKJN|<%H;&_fJ8YSMEWEiUlXEngWVvARq-a(a=ESQB8lK9?AuFuz6{an`f!p<trQ>4
zEx{Nb?{587sLM>=sDoWB)8t>(ss08`K<jC+6H!Ol0B%8gcyQ##BdsF-6UcaJV_aqq
zXF`g#G;vTnIU!y{Ov7nE>VjEu{Emadrv1*Pd%V=AfV0Ul8dcY&`kc2MQdu*jiQfM7
zKnqN?ULYm~K`Q17wZqmw>?@}piF}4E)^ou4meIKH<Tzce&%Lq{3YeWp5^^pzjt!Me
zLDzX?r1Xd6`-Tj*3g#)_Q_^I$kAL&m-S3BKPJFyxRx(9cn4ma$8H$e-ebLFqP`HZK
z`u1%nb9=Ql;JXEI&5@DjdG%JZ08PnuHWf|bU3aI4Dr(Hxf;cW9-6Q7?3x9luEf?O6
z8$zMa!`{|HnKKm3dMIHSdACPvn&>uOdF26i3o>3d!nyCEbq_vb`>wHDc2u*zs3LLX
zkbq@!nkc@fGf^pc%@9He!YegpX^`x|<01l%YrzQPd3rQBZ8s9o#S~#>>e0&0pfEhv
ztd-M4*ytEtXw|(FRWZnCFKn|a<Jj%lMwF?wEhSq(-P3-bV5sW}IiP)Bho#^e8172x
zZX(agF;g2>+|6S>=q`7z7Oe+ur<|GK0itZf{Kla0?!?zP7Pmw04k*{<Y}V@(zArJI
zv{!%YQE$bJE*J#Rs=JIVmdbaH^f!$*rT^}9(7vs01>F-w7s(O^wCic_dsBEWIBEbi
zok14E*ND_QW#;Bnq5TK>T!a{rja;~AXxZuDAw$&ybL|kZ>*ayBw8Xa9jaULf5JR+$
zNL1_ffqYX%+?yKtNTT<_MpC)4_6Gu}ll$mot;%r~7M-@)qwYi7{!hg=m>!h36Um^M
zbsRqXr<rg-LQ-AuvCUooWv<^NSLE)v0C#6XO2}ckr;N<mvutedHpW_M&qsSMZ0EB!
zKVai<gn}BVeN7^1!0<a~FX;E+HF_BxUwq$j;t*9OmA@Xd^4xCMRS#P^RIQwD%$PIR
zfKE!H_tW3Xan9o!GF(xlk0OycJdt=thW6yK9h!qA-9J0cD~I482QeJfQ=g&vtTJ)L
zD*B(@^?#abbW8?L<dF$van7T1PQyMr%>F!LFTd(KbxwRbgS5i)rKh<@xP(?1B8>#H
z4YppW_v3>9(hVc<mYp`%NRL;yrpPEOa-rD^+6cnKZ=TWR?*wY3)ubyDzP_ImzPa~s
zkh@f`Acd1`LA=-4yeP=mTEDM-v>uu^g>6=UgFWYlJlLv&%?~U4ZVvCtAVl~V)>zn6
zL>fDR=Dj%Ur^F8x0sTKeBH3j{&vDFl$Mo06b&m~q7zTs~azjrsww%{G9SMZ|26BQ7
zT&dzc%!Ly<<F%`qnRZ+`o@mYH+ImhJvUmGKjo)T!OZj89ec_G!w1dBfp`>}$w2Gna
zneI~uh}fm{n(I95MukEo-!aQpROy56Wk>IZR`X#n%qS{LOx_rKO5R)yXzU1yfT9h)
z1>deagqHY4S+d3<*xQ*1P72R8u<dGMittBDpKpY?hyj8Y7c)UR4x|CS_(VwU2^`x}
zZz+LLt&N`|x9=irHh)Fd<kDzaHd2RSJEEjb3P(jRXE$~1)+@JsLzUO}n08pc{x!kY
z`BUBc?-}F>f~iJC%j`qq&50!lmYYv@W7Qv9r|F^A`ZuFQuv%1j7Ly1EaAH6N`0ds@
z+&+z6{{3v<(X+Fk6Q$CTATpH-8E|X9&*Ax9hV<hg&v&Y?a(3s|9o0_&dQ~Pg3>&0o
zhQD{Fd$JVoc|Awr0z&W${z2A?L8bC5RAe5Ps8i(WK)$R7!bqjA8Fd=01xn(Y%R64w
z45$t<dVLnX4Y!v0Xes_AZKZ5Dca`to%ye?8$G_GcY#a<#)a2PQZTd4w(-z8c!Zbu_
z{mxl5Pnlwvj_FMtYf8ou(h5CD(3R-#0lB-EasQ?SF8?F_ebr55|C+D?$)#cyp<hUd
zSe4?`AlH9q=yBMcV66Iwv0-28ALR!5qG`C;F5TgWo3)~*fwd2e-Yl4T1&%3#5kvC3
zG#d#9o&e^srS@WVNsH-HoCHD{ST}7+FKg20;h@=tn@nDr<%~rV44SS$9O>V1T(Rg?
zs+c8sTAwD6FBff+iRy0-YT-}5&+#ItxnpxFj_44$za;`C1PZh-Nqh`3-8}f}qiPBz
zGy*Kk<B!@h*p^hcJA&o?>fNoJ@zkuAbq*U6Uf<7f5E?^2X6J0b0M1FQBA?3nUvU5K
zY!54E#o<Hsf0&y^d)6#Mit8T+Qj&5RU?|*@Z$Nq>eU3ecCD~G6m!5N$-{!0hK_`rX
z%AM)opgBW41OB{q6$fXDZMx|FeKt9%{JhR~^Tfj!99A)e?!2=LKju*%V|UxCcPLU@
zU9BVBv|K!Yrxs%_6}FFJWaF8!iAFHHo@rdz$qcD4gqcqs6=aU7_IG_WBWbjb1Dg0R
zM5pV}uX8P%>-vaCgA0oFzrVWXo-4K!v1dC-1&U714AVb!Xd&N~wvuPk|DP5>bWOnD
zSd}|$6cynUOf@(+xOD{k>TEe{KGF5ld)4Yf2kArOv5b<$--CgLQ}lkVfV7OZ*cepi
zuki3&=>r1K&GKzS<GY?G3)5Vb`uhtdXO+wQdvz<a9WT1Mv05j^B-*~83Ko~ZUGOiH
zR**I!o<S!++NS>D9+8;675_FOuxSXQyCA3K0QGfq<F{`Aa1OdEM$*QMGf3wSv>Bal
z-b*>ruTZ3|pB2d~r?6#LtK=n=%0yJN6R9!aJF=s`70MF^a`0e)vS7PAv9_^X$t5L^
z8yQ87b{H7p>PQyv+2UN3jCyI1Ido0QXkK420w%=lI3c=cyZNj61yrNU6PIc^h3DFg
z#HwIBfL)LCYUayhW!j;0?Rz`ZGJ8d<#QcP(m)F;^fz=`#9r8g4sLnE}nP$;#n@5ZX
zm5LUGIJOf_GI6kgUN1QSYymK_5a;=ame{jCcMDQM^xVTi8<1HAxUIYaUA>d^`$kT9
z_3sRO3R`GF!X!Jf@DI8w24(bmS>wrgZ*%&~{dNpgX~MsUji!+aqVpV<AqiezNBX=O
zu^d>2#0Ie*&^zoI>>qri7t=>(4m?R;c*Bwvwh7;!Djl#63(zG!EGb(f`H5`bdEPf7
zX4R?NgOqrui}6y1$hQ+sZv%#JJMlEVUYVr-C~G8SE2)gbczxp4{#n_K$qDC`{|@#Q
zA_2@nM{b{x2e#*7geNVnBT)#BzNLF&z$qdM(W1~YFa-2kVqM30*Rr7d=+(XbrjvHC
zl}-W}4YY+?gXLRG+Bd6H@@2Sqx_?LxaQdD#k2*Hf{T9gRq|>`FJbnN(x?D+bsmQZ8
z%!TU!<^V44yLth!H%<0nvvW<&&lWt-MVO#lY(2-$3ON(%9`Ia)H!IvIuR6K*Ld7WW
zlUJn^8Tz&)P0U<_HM)8;IT41fhlkrWGX|Ry;{giBF%D06%aDfEXAlk-%T#m)<@ZHP
zSoQD+&n#G;`xlGPj_0xh0{X*~iLED4JiaxIUCGD4@fKcV$O(@w)+*hc!Hq+(Emc;b
zQom00mRpb7ANTD{Lj~{rGDCBIQ#M~s=BRNKYi7vz=w{5hBZI2=fDsIgXH>OZ`4wJg
z@0oAw9=!`Q`dM56>Rd6nMf7;1y$9d?+N?XgjDs@zwOfGnG@>1KwDvPq<R#e7ur_Bj
z>AjcU-@0^Z-2R<}h^Y%3#BE7f_@e0(!<j1+6Cw?B6TyPw!{BYl>3#b|D`gS|XT_47
zR^s%eUYfG=#+F%@+7kaWf#9pxAvyk>oxUz_)F#C4+*rBm$XZ}8HIB0Ox#vL_C4mu$
zV$P$-A>4rLnI5c?)2^Zeav%pCB$wT66Js@QOBRR#hX;raFjiH<wYFWROAe-7?ZA-T
zwk$dUd&r-K-q`}PNI35@JR-shRNh7z({x`mC*$pP(7wdV!FIgMwv{&PZ@&3-WdMLI
zFYohh!*Y4X6D{AK*e*Oc-BaVKkd}}F@8*m1;w+QaZrKBVDaq^4^s_qPWbhXHzsZ#r
zM34q#bxYy)if{(mm#sYTC-P#?_SiGAE;p+B#bA@MyO*bVak)u1?3EC%chiw<7(I?d
z%N`4*ohbWL{V%n2(BeeLkpt=@suKGg=uG_-sLpS*CO*pC+gJ09nH|rf1Nk<REcGXK
zEDEx>0B|{ACTevh$+Qi}^VWWHw4gT?NE-b$YN3C9+2o2_zOIG#csg_d#rp)0t=m}W
z5~w|&oja^a-!-XrsDVA>N=W5d7pQ0gz{)3qP^a##$``eSS5y4}x;%tP;>ru_`DGVf
z6o--81j(d`7HteS>3U7s!F$ThDYcZh8w8V&SMatts`Rd3-y|(G!P?@WgYLdWI`1`m
zxf|f=6D(oY>Vj~gf)iXKF20XVOJM5rEqA~6-6!p~;KM?r_kOA2J+nV1#U)Aq7MIE1
zbn!6L>deP1%NJaW;$J4Oq0uz+ySD(1vfBrC=Cg?1BJol)!@s2hzc7*iBt9hfqMH&<
zN80{Hf&nj~V%l~V<p-0)pYI1HKi3W+Q6uGIMN5V%7k3g((7yH6dh+7a4U?~^4)a?g
zr6KXO-!yP-)n>I}5!OOJqNJ7_mfS(Z^fYLz|I~SaX8Pg=*&<L?OLPjn)qAvcA087^
z7Y=gMS%|3m>*)#`O-vOR4v3d^&3^{=gQHKSLUFqQ2JguxJL4BmN56Qa7cW=XgE=>I
z1|)yB4p+^Q`+z$$1;k&rzxqHD{v1eg`Qu-LbP5HO&^nd4*TAxTI}WgW*V)-R|G-o_
z{5hiiin@@rLE@=9oFMW_Dq!?|tv$I-&s`_988WQhhXyCFP%+SL&1AwoIKWu|rZV}|
zy^wbuNml|QzuGq<Q9oK-t)TB3(|eOK<#v)_8b=~+`cJnUQz|n689N-o2DE<~L|MTf
zN&X!^bv}@h6j4Kj@b|=Qq^&3H_9h;RkZOkChS90@?`XVJ_+CZ_-Nx=-gT9W=jBe}z
z9SRnC910~1(7ATdKK)Qz`SwK5YvTLuV<u}llD?@)cn5jTBUb1wb8bzrv_5cHzQjIW
z?we*hYu{TVyybMZ9swH39On#B_1u@;x1!xI5%}D7TFaG|Mi<X0LtSi-m0%+^)r=)>
zG<K-dU)(_0P#PewCVYS(NG!$6<~rjq5byRUuIBnH(7ma@$WMY>Lsqwut}L|*B_SXx
zvYOxx?l+t#uXesp7nYjPwz<?Eq3PRtwA%Jgt_8uFMtU>0VKa!tcKw9U0q_H4>csa|
z2;ien@b%Nd1Ia5flqay+J1>`+GGfyiweL6d=eOQ_$&8mR?iO$Qs%K4zOXW!5m0<5+
zlkcHAtR1-&4kxgU%4ZTT;6wf;eg`VF^?Kz+znx#M8}Kg1ruG9nGg6o8DBrfxz7wMU
z&ZM>3E?txQ5ZxdhVTtYD$@S&nv(A`b-}Dzku0j)CIQK)M7lFQ?W34sct4d;VGzCZv
zffcKYmd22f!Ka{mwSS?7z2S}AOen3V%6W3`;&0~^JdGz+s&54K@rjIE)TkKAd@tQ!
zvpWjM+W_h0>CJPA>H<x^TzFJG1SvZL`>PDV99VV>;QGYy&LZZ>!ZD%B_G07y>UDNQ
z04W*r13x(Wuli}uva;<&(9~Rk3F|z5&I248TK9mnre|5bk;La{0%ehRbi#GHt;z1A
z)nXqpuX#u@zSCE(sHX~EnU~&yL0vugQ<m-;*jtO&Q**2pANX%`U)OPo`L#^?K@i=q
zXT%37>K0$Gntxd9-?#jG)DEACxDYOZ%)7}ZdBfP*K%TFm1XBHkf2?mO*!_d*Aldk0
zw83)xWYFD!zEll)pT%cGRp{Ph`1M{f&MP(DiI*|o73@z*G`H%iwNHB4En2P6Te~!d
zmn&$OJ~M_tpV;v2ocqk@H_U2@1~1)PW^wP<I3W|fACUfddE4;_kX;xFzYqY2Ly$EW
z&Qd4AV3lUim@eZG`I7}I=7^y-!TKp_62BTycE)*My`4jUXIsm_BX71V!gJ!9yv8A9
ze!22hL+e2d3s<>3YAQMKW*YiB#Vg{*;Hc2N#14&0Vc;(|k@7F)+6w<UA@cWhu&eT(
zZt1E9ISkPU5X@ZZnxp?j5B6Py&|TUjP2Cz|rP2q80({I*8dQ9$GxRg-!~%WYFC)Fl
zRKv*f9<e>g=BBIf*xvrKRHXvEhOD=bZPeZVp>|YTq=ol#;-WgCAvJ;RLKiU_0YP?i
zetLSkh3N=}PK_`KXLY4#$~NaOg71nM$;eF~XkgY+J|edLLp$tc$p*M(sYlfaq62_4
zdT9!FV?p|7$0uZ4IJ4u(Owm{ozC(khJUiJR<;`KB)olScu$qsVfAIAu)tbIuUzamM
zR{&ZAR8h~v&>^#OZR2^c@dgc$LCJY3XxT}+nW3KVcrx`j^{k#6eR#}#mg%2IRx9T@
zH*N=6s7Eqd-+?KrKwDI|ulkYo0x3)CP4hL$_g`axk<-pJbNII*GA;5S@V2s-$5?Vc
zirtP6;cxTHO_Zc*I~Pa-s;dx!pEtvK#$O*kehfK2XJeg`yD-p{i>itvity!gVUK(t
zO3Cp*FkuO4!8BhJe`yl1FF6Avdfy_PYU_OVGrpj~_l$I+TL)378gjpNmlL^RON>6-
zv+O7H(K>I$;6Fn?jdg8?@#V;B9ytLBv8e@Fjmz0oh3*SPE%QlB_iMuKZ#qfjxoq$9
z0YOtHHg&IM<iZ8Q_AKENnQ;t^1AK%tE~U5XE)lFheqok_FeZ^V7$%0g%z+)jvvJ-&
z{!8WXE-xVTX)w;xh{g?2=wxk$FkgdKDH3l<Si7mAdX?mI>Bg3<U^f7#AnL8vr7wQy
zeruTtQkC6yeQXg~mfU+yzYmNgiWKx}?4e)8hC?Xxxd<uS-~qVKf<@|wlhHT_9V1}6
zwkN(#sjT>ETQWao0pSW?F2Mo*zX>v3Y6h8`n65HlYqQu~ksVB^DlcNayXW3AZ_pDb
zZBy7=s?K?BQldnX%}?Vm7CTkdMBS7$kdo6IU(yba;yC1~wQED4aCMcn<f_7}s`527
z;VYY6+fjJzMXueD5s2>W1)bwuS;X;B^KPK)NS&q23nfz1U@DWzh~(E$9!Y>Fb>HZ$
zYsS>euA{TiF<iI{ht}JeJ+haqU5RCR)f@1bhM#1wZV(aCm~e@g=%ycx_@<&+XA2F_
z!tVdNvxEm?=n6FkCEVUuH#GgeG9x6v`zs9wd*s7c_u%EQ%#A@ZX5z!+AK=`;+|OPx
z5?Mj3Se8vXMka75FUO9@xstKE*8>mwrh}0F>MB~qYZTk<NIDsK(#pag&dAu_G<Odm
zS*|WM=4RJ&Ag6$^n*LK<#|pi#9;Yc%&I<Jh@ho)^!z_5_Av0a>Ylt$kFFBEfSZ!Qh
zI(<KA7i0^nGbH-s#7A@i9pl)v+qDt7hdK&i4}jmEqTJ$%10;KHEU}wo$adeBAjg%^
z_cWz1Gz)N<z!$+?!N1X<!(w5QFg@w9B1e7ATG+0v|92Dvd5HuIuVZtXIjue6y7TZ*
z?iIVkwW&()2lb{p8;d@G!Ga5W7R&$x%lUyi2T4<;5>%uAX}iq_ny&b`^$X|Pv|&pU
z`j2fIW-9!@rsDVRl3^H6&qYMlzWp(?<OQ)75{c>yq=z(ESqi#8#~G>-!byJg-=t4#
zBbZEj1q7%HfTni`=3(=Z0Coe#37|W34bJ3&BuD5}cNXG!gn%-k0HmvNR92x%el}rg
zUu3oCA5XFFQ|aTuz5q4r>vVPdf&{8=9q-9>{o#ZA5gbDI?I5EHpSxIxG;mp8=y#}@
zn)b_NARg!YBoibU`^2XL>xMSeb`u;iK2!5|Ddd0|nTChNilViI#fyDH!kXICBkt6z
zC(iCAOupx;o4)KkgLxSi^JniMp0fBBbLm=KVqA>5Eh*g9+W<5^U7-c)hj0jd&pJYo
zFJecMnxUd;GVLu5T-S0iN6+5PjP<&D3pwF)SO{5HSJ9s@<Bz)xrz=>hCw_NnEN3tP
zPUH$%IV;Xi@?*(F*kkojpVBjPsd@Z&+cS*LNXE~@RhH9&If=R89?zaX%Utk?N!as!
zMp3v>K!38g<PK^Em}iLF!_tEatN@E-yZgnJiub9(<u7^+Cza+`lqCWwx&()g=0b|Q
z=fazq^gq<U?evK@So~Y1oFCM83w9?4q=bCvL3QcBR2xu%$}%w%eR6mO8akiBPjCV2
zS$8dKQYw+BH#G5`zvwR6-M=G>=X8Hkv2Cv;%wB+8*CHx>Ve0NV;jK-cUN3+Pms4rd
zWr+%_Af#i>*Jetc0SW*T<}$oL``Mf^(0PU=xOLWgw5JSMc3Lg%?QJTCe{wb`cE#c&
zl>ZZSQNHao_UMITMNRJq2mX4m2mA51)XV7WNwwPfX(gl;41D^pfsH*JfZ?|&HU069
zO6u)I9QWeGHl`Q2LI9V+Ha2>f0?bttC93;=e23|Ip5g$5tJVo+-#nY{UNBF}M9hvd
zAu|Uu3M!}gD-a-?Fr3-1n<qQZhu3Zf7r;E%!qsfCq<$V2J0#tKJ7)=sleVQ{1DWgI
z7k%6eV>q__(uB!AoJL=x&aV}<?IDVgS!oD|`VM1X(cs<TPRYs3kNVAv)(J2%&Cke>
z{T@NgjrvVT8UQ{aMbJW#TaaJwMJw0O2TqFA&|tGiJCX+U_6@ylDNiFjnFgDo1(Q2k
zkgWT=&g9`2KB7Kb2oYCopW|-2vT1SPaC#uQZ)V$?l>6fOiK`kmgC3>sN`2tnq-Av;
zuR^lc#ZuNZd$6Wp?5#H%Jd5e!<J|VoNBJH)UegLBR{20tpz;ghG9cEQ%oF`DPsrTR
zkm5fzrAMx5vRIp)*=YiI`9kBv(OOy*!?qEGwyf=5_x&*^4br(KU+vj}CVTudAgqbD
z4otA4J@1-=JJ<5SEfZrSkt7qCo3mXc#+DI@^=Xjnzq@@92NWU+g<>T3iU6uKfAhG6
z@H<8@!Qj-<#YcBvh~c-py@D-7!v_2UTBT|{kOZ$@c@Zbb@1G3?w0Nf0jXSierO9z<
zkBp?ioq5wTH+L$VwU%#A@JsC@%Wo}p;;US&K@kQ`KWs0nb`tmw^#ZiAAPU@xH?5u}
zh5Zh{=(IZj_vx}i-UZB&ym19vrfc%PnvQ0vv!79r4B-}VqW2zgoi?|MaAaMLO~+lm
zY!X{B1DTJHF%c2i^RUy$WT<W!*pMPvRi6X<!f{xGHzPyA<L-9IDrwDrmU~Gz+;_NK
zVQ_X3u$z`NJnu5UbNi%z*7jRUgZTO7TpL_h;&XD7cWvWYXpye|Z9JThWkjMhDQxxL
zRhcmknso^Ef$5I<hZxoj%FCdBovp6lq6eD(Ivk)n7@^7VllRL}-I@lq{AgapRozwD
z*oHNLwu7L`Zq@I^7Kv;9F|~XJ0eH@u0KBEtViN|k@P}uQcnuGHoGDpubFzZ$w{PG6
z2Nq1qqs{NqG-FnAwtnpx535h#wM*~s@Z}xX+ulEF|NJqO-Av2KmFGQ(!fGZ}b$_5z
z|Nig^!25fDE`<YN>B4t?21tC*cVh2l`T<%<K$G@G5NLz9(&9Zt!otrm3A>RO9D}%#
zlT~v8ka*~AYd^^Eg3yTPn6wIw5#nR$opt7v#D|i(fmZhO;(RBWf(f}}rA9AMe&$1I
ztsfNV@rM43>m1!K*MH2Vif;h%P$<9*`<>PAiq`Luqy}8>7sfxW8Dr!9BKEk=fK9rp
zPcl7S!Hm25%LyV8hWhgkUy}_{MaJlJyjz7c>F10ZNJwnd^AXSX;_hU~EP~_%IfJHl
z#7<rk{Zm{U@D9`0jO`LaHx){@$JYp?HN_M9QeDYJtg)>9&Hl@}a6!25=7dz9!CfpT
zQYAf`Y!`q+GjY@igmZRseP3#xq<lHRqM^AbQ%K}cN5#&C@6`39MTOixf5PtlJRTl9
zsAP0&K~W3ihRGC)9ks-FuH4{Z3ht;<=h%wt{kli};st9_{q76_E?gxlovQ!Hn6J(A
zrCSb>n5JVt$CLl<?||_I)%_;`i&AWHlpN`|5Iu$12NNg<uNiy_1o47(ARQW!Kw)}+
z7S1R%@>ffybz%eCG>MUEuuMv`ExFm47*4j}pYxscg<sXD7taS)xLm>iK*IyVXurk;
zT7s_m{uAWIx1W}w2>CBq;wPC&p+;;5E4Mt9-GI5A#V6T~WrA9I*IpGMCC<0?X`Os_
z<=^ISiZrf4f)xA;m3X`E&wUi?JTG&NDfc_W`)38i{LPA|^UjKfwgj4vS49#;85*$=
zIH4@OQNQ2vFLAC7&DMc2Abx;U6jvzmUuvcf6cdApA~f9|fT4RA;r(zgh^z5+q(ul2
zyorrq1dN(~*QM0-C)&e`d<mHJJ5>x)a=ft-LGlKdZuc?06%?vJAjYPLg;o|cl3Ym-
zn}z>0FKJdSbHRh~`uAY0516u#;^r_Ea&%}gV@H+VC*Umn$|SDe7+T|(+66=$Fypv(
z41u#2jEdlbv6{j4Qo;p;1OSAE2J)MylA~!&X^j-fG&ckQ(p-Ret(x?HU7nU-L9)-@
z0=S!84c;)1+xbHrB%tpxz7OF1UeVx>H$OZT^8<1NY4h#Jn)?83k7G|HD6B1C6PFR}
zgI@96Y!iV<<=2-b=vPEK@OLn&^1M7jhFl&~0dj$6aA<J#GD+j#QX;C*nVdCI&35xe
z9$J(~O!L#^7te6)?|Otphf+QIJ<Z1-WO$s4te%Ud;!!GzTVQrONzfk7e;RiDV$%>-
zA=99;znJf@<3*c_J)U!J7A$Iz!)`ZOMteP5DWvgG<1knMf#g(!7y?L4`<OiU|Lytu
zUlkMSK$okWtj0C0f2fLmf_62f#>eM_#ne?A)h_pF@*}W6V+$qod{_g!J%ZmPzVPmy
z{JiAHBqdo5`pR+6<=^@@R{Y=9Ej+bRzazZIyksUA2eCJb#a_@C%s&mbVB-6_a(-A{
z0jGFs^ua~TL#?<qzC;pJ2IRgh!d3zjR`rLStf3>-bAkap#ra1U$wMr)hPoHf5q@ay
zLYHoBvq;~SFGaud;4YMI7h@RUK*2Nzlj<>)6G-|!<OtOIbwMMcbWav23~^bEJ2LAs
z&yCt}CysbC&0R5c(o*?SBjQ`<fRX)FuH6Gm!16=M*5if!m$jn{eQSVpV2%er=|bGg
zq1PLfsZRmkxGiuT2N~UU1B>W*SpONS^=5q#kklX!`9@mMWF0cLoS=M|uMD;ZA$$2n
z#a{GeWSr|?Oz`*{Uq}UT>+0_NKq)JfQDFfHSpc^ll;Ey2`pBadeiQvo_$a>?KDiF~
zfxj~#){FLD2>^AwL;4?TZ&WrFS_2iU$BumRx^Hw$vRUh~#~9D5T(XBhrpHvF_0&ZF
zQmWWL&~|TD*yZ3ldlJ^_VdT@)$5JVfx(Fzx=rbDUyv%na&p-TC>oM#pgI`0gcrV>I
z7jU{f4Mia!v0FqGBf$QiZ?AL5i|+1?vQF7!M1tie8?7V9*j+s6K5CU)^}N#Iajq2W
z5UpMZw7pB)-%R_CH28`6dez%3{U;|Dav>&ih^}5tQ4HPhLv!%z67}!f)j(#4dT@~u
z6#~FU!9&J^e(?p~)*@?n#rVREW8V^lrt!YB^A*XxZ1c8c?_5xgM3Yn##9GhRxH<j-
z2O|A&#u}cIgo`=xKPBry#vkc^&XTqlK(Vv$5f<ltRbPhV_{SS1Zzo83mVs@BT9U-Q
z<Jx!PktZ`Q_vWVVP@+xbWlO4YD%KX-acvLC3uWzC#EbWwpB@VZ^=(h;YlgGm@EtUZ
zho~0&C>U!*2~lHD?Gv8Xc9z&D$tjc!22%1Wmv&8W4M=mQoUi)ZW0dXy&2Obnd%aTR
z%G^<1<B9y%B)L=?cdZ4Lq+N{>YNfansn4-1>CVEqxn!FI^1rkX(Z(mZVCqiTfqFZ*
z)!h}B?@Bvu)XANo?F!v2{_3bx0*RKGF9aQ6W>imV=@Q@9CGcMs4XjrE2NSVgIJjKs
zNpFTE-5O$kYU?%z#owN<m!B=4^g5g1;pA+DG73O2b8gQS>Lf)koPc#8-l`UO#g?kU
z5^VnHf$z|EP<W(6nR|2hqc5>)SHnn+1>+ej)5j#8;{_M^nMBuwCQ`1vC|(X%ss(l^
zLSBD;RcFTii@V*wI&__Gw?co7T>a=*zXk5`MINnPod>~#GN~u4s?frR-7J;ZZWSD6
z^@+K`YGm-Z)+q(GkjdhdsrI5w=J95Mrce961sk^x5LZBa^;ZXe?Q|G%Oe3)=S+3fl
zE9aDYYKJJhJ4q4eOepGwrFYd~=(_1--Iws@5tYu)OEg(!j%3UPvlAI^^WHMcT6X##
zKrHO(C*IBO0*AJ`fP}_I-M{@}ef5vp7eJE&+jdApQr*@)e%N~41FX%)MHsN!J>NVq
zANK=vRv%a9cV|&-FSo|<k%!bNZRU1{;o)RXCz-w<i8xn5By#ELPGp9E^xs+5PYZTm
z-zflWIDTzFauShwLL#*hcBWDz$mHW1?Ma#+Y_kZ4p4Z3IK$t}`Ky6X`Ep0(Mf3eq(
z06N+Fc9Vfw`*oDS!^exXZ~<K&!=6Msf6b282DxMP7hyBo1?&&(ec$Hl&Gy}Ew(i2R
zm$waB$r#=>41FK5p0?VqW^}%1SwN*||GKsXa1nrv!AFdsn;bxg6i-b|;EW4gB;+i6
zK)FQ6u*Y7A#r=~S%MXB#k1r-`>~&;{1e#xB?$Vt07vqSg;6iNTRpG_&MEAm<IdrwC
zZnzp+Bj?R9P30pCazhzEMC_<%mu{j6dLZW+gel>V?=JNmlhBOZJ5Xjg1l_uuKV29g
zMk}MvS=`G@Ra<2fv24?jDt9TKx*@$1sO_J&qXn9#U;JCy)W<`ay8qP3(Z`!?en9x9
zp)NWnZI5Me+)w0N-#mUnx!~*yd(MJAN8O&6vKCOL$sydfA-LL^gXZ|s4hzlN6<`(9
z>470}@bY3i5!YPG8Npz7s<M6lfvY~su9S0vLv)TLWzlP^9@9@0;nomqr2EbW$amov
zw<g&BFxu+Xk>?jh;M7b(+29$GPz$;5W&qGrb@S)in_Ns2mnM9<#8jpMp?18gPaPY8
zs~?z&{^mo4?R3ymJAdxq7npGD+gjhwGR;L0ScBb(*T;c6ziX|7<tCf>=dEd=f3q*v
zXtX*mEHZ}0jE2b{J~NgSai)VcgZBq9ro~&9>6(n}r`d0hJ8y01uATgk)~ztjF!>Wg
zKK59ud#S5s@`CPxRM%J4^nL$N3$Q5YYoox@o#h80`{#{(VEN`FVOoCBr21q)xC%<u
zz6C)7ZQlUp7R|$2>U0b+Cm=TYyC?-$+1QRG60y|(9XKMNJYbcLC?OSNTb&ulC)&Z{
znjc9sVK{zvLud|mc@vKye<j(QVP69BK-#;F{2gA+eBfLEVMTFegmD2IB#zdu-+8vD
z>+*0C^grN!*ot>aA)=X?kq1kp`IyLTumXtzrM_P!#XM|_BeR>aY8}SX)>aU*SU3c5
zm}J)>ymZ&TEO0W$tJ*JAirw%d#br`F4e0toRe<ZtTwAlqcO3vg986Tryq=|nMJ9S?
zw=L^G8XAj$$1k$9WZ@He+DB|?MvjtROhWNFf=sRQ$}o$PVON4xNmN-6KyVbwe+dWp
zA7d{|T!HQmxi<IegqN3$-FMB*8_LFmiO-cc2Smh^XyfLcA=At(3j)WPCoU{JrpPrP
z6&l<CnUnbV14>vDgBnNk_4i5d>h#BJ6T{<{JjafnQocA(^FrNz2KVb)R)NXhh)k-|
z@bVXaIg_NAe2fWV5#5i*?e20$0XG)g87DxRE3)=z<=2z(tTP3wfbx^8a(aE%W3pGg
zqhv4!)D8rUd+%ne1lVrAU>Po02y2V%HX|@8dgux^qGCV^%rk^vHqe`R`Io@NH_{g0
zwH!JrX(TFIt-gOd%C|<AMB)3kOAM2|SQ%KV6t)xh%CRmG(NQOa>GPu+=7{M~n-O$C
zsW=v9G{aYDKq(iJTIg`%<~S>vRT$P0KpkdwaSp{iEkB#qfpb#NSZn=URY@TRa+D@R
z<U!8{6@ws;5Gx6IlVJ;R{K$_&x%4cIof?o1MfY^HT()6dYqDV!U_0`)xK(yzfl~!6
z!ScKQ-pse?mNQtpDJD`NxJ1EpcwXE&e1GE9dH0>-+~k>u24vwhL8X`!VEo*O1)`Y@
zIFXV>e3w2q5$UT6zy?nW`X9c}DS#sV+%@m&pMo|!jvMo_kh4_WwGA*|=!9!Ar}ltG
zSGDhXL$zb(q*`IPb(-r{0j+*fcfSdxGv3!0Tis?24iEEYW#$d^HNyqF*MO$kN|p0!
z>+JLSE1qALK<Erz-aD)Xo2c6cZ--vXgBbdSfTlpfE6}^?b!)$OF@hfRHa^<IZp?Ct
zW4yP^8m!LMTM($=nQGCson!{YdcWIVX*=AD99iMOmlo#UoYzi*?HO0n?$qlTQsyLf
zH~t!ik^As(yq*JZ7THY+rop<4gsT-XV3k8R>$~NOPfI5VN)U&HE`0l0AIkBrE9*ZL
zD6iHZUF+kD<~?SKanF2KmDhqq%U+8p))jWM>9IQWK!TwazZ!f<XLv}mErbHVzNGgt
z4}zuZ8(rRGye$0P@?0)~X^){kJ*(xE{Mtwh7_7rtA2A8^lBk>q;2-7N<rNWq)dU(<
z5y>FBR*$dr!ld%rS9Q_SsTplG7WU=G2l|PhFbzu~T{cH>*B6hN$``Pvz(d$2x!>Ic
zQiGPRr(jC7i-iPymH1L{!^`sQo4$e<S15L3JdL`|JIZB*0Fl08MExx5e=KmO<)f^W
z`V?n#{xxvx^Pc{Tf0~eq*FqI*?<wmKI)YeD5&lU^HCcs{0Z}P1l%j#CA5|yS3q0fW
z483)>&OL1|TQj%emgBQncMQ$zslGnOvS#)KdB>QpSwN{8A1~usX*W^7t_rfcpC!XA
z0a!)fLZ|=5-1_Ry?&~$0te%eQ9{UZZEak!C;@en05fg76q5vVa+#m9>2;Zl<a3R(8
zslVG!-~PmT!Jqm+8;{zD%lo)oZBC5Z-X6kH3$9wD;SXl4Rl}mVD#o(*=YEPA=|Pk>
zXYCwfBMYHg9xN?%iIVyOBlzI1AAjbca?DKx%*`3oDF$!Z`!@KudpbZq^xbY}_s2s3
zGN6#SihUJ%ekq9KlLHbPS&3LwlPRG2-rk2z7tA^gyXtR-46N{WMwiyiI(mk3rvX=n
z)`(s}(gUn`iTc;lbU$mz+8VU^iasAWHE`z)Q`KI;o%R*{wUKdP(Xhvx{XG>^xT3%Q
z0?so5f`po9UQL{B(le%_n`dq}0Mo$lxI`CrT%|c{t{*sOqpw?-*3JIu<tJ^?q`Ih_
zzdPEHMI5h*qNY0RcSXD`owuD&epmGRB6QzUTlE2@|2~orOJ`D(5unN{Kid~9`AXUl
z=DRD7maVm^{~+-qo$91`0Z%9#gMs;Ct+jmjt(xM)7!d9$5m--LxrXj=my@}U)~S&T
zy|fPLTk`q%b1Z5l5eY?WL*pFINr~@p#xGHU34x|YOcDq!`md<X30k#V9KZXuc$$yN
z(P1-1P_Mzn@fz`ZhP)91PYB;{>Yz=tzU$nphvWQK$smRK<hEnFh|w~1b!($o*>^kv
zlFx<~w)DX#*8eu*yG}VD*kjQLY`1Pt%xdDT{w-f9yn}R-H9@%u<4W^5Ei1LL<fpoU
z5vDs-#D9RF{e!pMj(JMl<DeR@>}&MqWQ1x^E^97ABv%7teuBpGJ-Nf-4v6!<hWO@X
z2oO;g^iXZy|3Gtv+APTr)=vK=urmsQ$F>6$Uqq@ogYL`ubL4Z(221qrUVoKwzcKFp
zY*(H@H-JO}697M%EG=LgW0*g2Tbub5u4jzEnV|RFrEvJO_3nH3!#S9NueGbnPCyUX
zE~vpDOLZk_=Qt<%lQ6J@>NH;d7cV(tDS884%lo?Sa~#b_@1`z-Py__)zEf%3Kmhqd
zQFXftF>$BZHg5;qL){woj<&JPX;iBzGEm*{uUS#-oHN!5Wq@DN*`6C~?4$adlN-n4
z*B^R@zs!hH3zsqC7wgQS*2hT!8GELSYcNmB=28RN$oFq9%YX}lP!<g8vN0!-!)w;o
zu-*Voow4+n7bUM%x4mG)I{U<QNUJ3bXd4_Aukm`F;<rXIoZAkGsb$+pbIB;*&N!TI
zT1>LZU0F94WaF^!YG!M%<T-IXzBD1J#r*>8Ff;hVleQ5pct%Y1ZkttLiq+r-3rDS;
z1EPTPdK6$LJJ^1YsHTMc{Oco|m{s!$o(wwFUOZAxgKr?YV2s^evv%}%*JrpBYSb<c
z`kdcmy3fpQ?x9N7&_{??-RFAz>&?N)_cp>}W<Z$=fTpwNW@_Hm-T|l|cNq^rkcQ#B
z=%wkk0AOx`!5JM;lq5)qO4y=!y(PC2=>0;XKx$pFlATBP3>{96#R0nU=cwqdnTKrz
zKL?$I=YwTmtilwy?FV)M-I`(xU|z@axgbZrBf#jXf2>0^mBj~o5UG1ZyCYM%$Nio^
zD~V8eLm7ycP$IFbJr30^*e##kLFUqN&>708v`WX3$|&5vxT(Tnh%uA+i4ydmLig)2
zVtUVix(OSSQbnfs=9P~qmaE~^<E%lw#9^g6Sc4-w)2#a<7TEmk)RlEOjg*@eJkX&q
zE{c70@^lMHOt)*|M}r=3XYL<9?raR4fstYw*5G9z;Q>Uj^uN}-tclY$_(S-4G5?<A
z8#WH7;}G|=p+pAMPI>z19`}|&7xH<h;3)ci_?+&Z*=B+5F&yO<0CK_<*V);U$n0qY
z*{7;7>R2so=U?$~wmeHI+oZmK7ezK+mC78*-?DYZT^&x7zySCg*Y;i!L;yHmQ6mJB
zL<H%9l)nH4R-E&_;tii=StM$l`bZ^Ve=O}2(t<mh%C;S{h*A975jerB18{E&TV1(I
z^010+>BtQs4+tz#O!1lZ^^V5Qo<`}K{Vq0yrPQiNbRJ|IqMcb!K(w(@#6x=wcgBYc
z`nywTFcAx=9{SzgA~%wYU;%)oW%mAGwI4QqICUL*$YC*1f<~M=*@yHk`JZSBfMxCp
z!4<v~_(5+*D|<T>$Y2gOpAG8L^Qf22P;xNd`NrfhApp^|5`m?5{csSg#Uz9mSS3`K
zqUhF$gpw5>rfXy^#F?LoB+2%+HUj6PIQG>HiKVNXyKV7@2bUbi|2M7<fI{;j_+>(-
zV`p{r#(o9p>MRbRNj0-wDi|*dPaqMbnS57y@%~LXlZi~&o)av6`{nDK7!2`59Q0-4
zba}#GhrG4y23#yMn<4Me$(0Wdbl<LDY+^b_1$7`qO}Z3F)IV;Dw_n@=;_Zv}af@|*
zmVQc-oI$sJN^Eqym&{8JLZYGpuz;a&ryT)+@WZuOQ6^4v^V-J4=8MT@u)G)N!#f}h
zF`g3ev2TV2#xa3V3S5#z!*+AO_>5+Cs@Q5E*<ikDIVbDnuCMtf0-YR5vE-VAN%OI7
z%K3DdYXsGkKVFP=LYTzj3+BK8A}$F$c#XanR0`uOl3(D$Dht%QFN>19!J05=SzH9&
z9F9SiqR+xi?PIGDYuU|YN8f5(YACBI^mTwRkjTJh9vwh#z?{9FaPWN(#CX%d)N1OF
z&A+R3(&4qnUSI$bNOqevo%IXa|8!zyb9W_Vfc}BZ{JcUmG6y_1TM?q@2-XX#5tJXH
zhGe}OVPDm5r)Xl8#A;rGfys0bX4H(wb<0d={S1n`+$GF>w4+OCkK1JUW=CNw?0}hz
z5H8G=8o!1V70t6bCSB57x_G&dPYTSui1beNH)#mWq*Og0hPVoklSy!o7@y*}6apqz
zK-oyJckqx$^DoB%t~uKOi*c+9DI}J4B1J)m!DDf@F?CeGsFFtn!Ru;RMa#ukQ3EhJ
zFHR^3_K2^zx?TAKuHEXV{^o=|mxV$3l3f43V!ya@V$4^s!%(TS-+$Qc2Cb@9&GaMs
z?=|yI1xV@)ib5g8$tg0w#h=fMcFDr25^$_ay!QBsXnyZu?NJki=?A^}fiX0%o|K5%
z_-O48=7z>YL?1d&(+L$iT7FU2G3wC}M=iQT{1Ei7zAgA={jHAvC=3kxysfu?I@J0-
z%GI^;P^6{q)lmt$l0ekJ8dtx4aTKS!-F;gZ1}Vj%YaGvx^$STvf%VG(`5#7xy4B~r
z5F^^S@1E>NGbcE+mBxafeIw`zB@v5a`DN#<ycA%On~nx`HE%$}**Ep|LUX8|LoWa^
zkL0&opLq4RQ*`?r@JIOBuQyUcMg_0NXTAbfC+M3?i*oV5LUEI~%dfpzHN?ArP&I(y
zWID<B56^ui0R5$Kx-imeu|b!vLRDf%(!g%ONgPveB9|Zn7Uvx4scXKR_WOT~9@AJp
zQqfc@00F`7FZsvCjCALMqm_1=wHWFv65J@a>{ESklBG}xJXL`i$MAw4#GYcHa8MRH
zx*4M?M_D$0>0jQ8i#s3lKY3&(-l5-yKQXzwi>>du-e6>L<Vz*xNgJ&yFo95_Fin~R
zUquN~+}HYN7l5{kG4ibhWlXU^t!!Awdzsder8m*Z(8&7~oKPM{@`N)FmtHB^j|gmD
zFkK6$qI*L?3ir|A3dm~abwNYj9FmE}?M1=K;HI>ALdnA@knzO1Q~?k$+v_d%$ReWN
zswyI%?TM%&tWZsmQB5usm%)o7V+toGy+4L!m;VTfFE{QzxDyaKK3oh&?XNmceSf?q
z`IO<))3SqX5*l6Qc_x!%xm6VY?qsFPgNvdT{JcdoY08OXms7WCMXS*Gf>8;r2h9Lc
z4N=|jxAnaQV?kIl05uN{c`e^qgHS*?knA{E3i7x}nu4}1SFqFJPfR{e(_mI4*x{1Y
z#BB*g7;MtNSL?<|WSe<ofKv3r`2cOWVMRf*)<NuUeq*g=Z1T6VZrX;BkJeznuG~uP
zH5(bi?DH%OXXZ|bj0_S_&Dr{}wkJF5O?lp@Fc-FO?VawPliD(`7t`HV5|X<+Ku3vu
zYu71$6QU`b-{($fyCp@wPWZ@r3&Fu~;&vp)&YZ(_ni6m4_9|e+O9`>@4NsI0P%S2#
zxa8W+oUKyUt7oIPFQdMs{)#<c>L*qgfd>=C^Dg-1v(RP|DcrdadRwvj=PoG0WXX3E
zonCKwdUHE<rSzK45}k4S?Jl*ff1fU&_Q`fB<H+O3*LZs@-3KG#8gIW`n}U(YJJl#2
zOb8ipXeuG6lYs|?f<hXw51by9qK^IoEFB^gNFkIU+#R%6bR87PJT-d`B{;};#foc)
zf`_$I<5BN-k&yYx*lWXBT+L=u0qj4!6V?_a(vy%C;Y!`!kURGqag847Zx<qEC%CS3
zB-WG0!%*OY#BUeG4ptL33<va@zTUm=<SRB4n=2Ls_-fm2zZdB?1=Z5c+uql5+*xi$
zcW$*I>aw{+V()PmyfB<3p$X{OhbI!B4q*@o-wnF#>_5lp4eI_<X&cOeZldnpAQ@27
z{;FjE!bI=-X%P)w^M&Px_Bhm3?cA3ZS=Iz!cAd`a;eG@L4>SFJy9h+!wSvL<=6PxT
zm3FTa#N_jvq^US7Pa2O6ubcX9JB&lti!aulwkqi4Rg>rOUa28UdMC~_W-rrR@(=U=
z03p%r4>Og-1+O{lIP<KaRjcQkS1>=S4-hnmm0SmLq?<A35hgmjxsMFJ%!&NXCX*JF
z_%sPwrdsco%xXP;=qcU#<st+v?bk~$`%zt1SE{rw(Br%<fK@BcG#??<%M8}kB)mN=
zo)5hF<==5jEucQ49YRf0d`&Q4c_3SoA8Kl3ElhWGul8oFfp%F-XUz1koa2gZ^X3LS
z>r_VHNN7p<S#$2Vm_`6i_b?jcO^QE^+N&!B3?xN6r0+3o0MQ)oV$$vJuZE%)Rfwl;
zS+b6QuFL`t7WDo0b8@Ox_i!g=I+3Ke`BlL3zIyu-mPSmK%Dr!B$b@oWw$mL?#=@Sn
zHARSPv1WQ4J7gB)g9h0x#~jZ*P^)RRcsvHTvb^jJGR(QXmS%&HecM)tSih_YUx!xj
z+f=2OPJbs)A1b%Nt=PVUxpnU90E}<O{Uo7dC^6u@tW{ZN*1==cj2_UK6h>?+N+1P!
zZS}G+2|DL<LTzUB(0+M#YgufKAj?SL($_Io_9uHq0pFW=g<f>Q+pRJN=SKGiIl6<;
zSN6!&=vL#NzRXNrkh7^P!d4G?^LSF#_dzUjiz{=?uG8gy&5lqAYLs4O&KmFCKzjN6
zAe-gTN!Cj(KY9G!0ov2n?t7$lI?R&)ro*d`Bn&Q<DN=_JI5$KyE!c*I%8&fP&PaVH
z+DSRWJ-rKP14*uXcaBR`6eanRgS2}-9P~wKXEvR9hfx-KpO;nEDx?^)^UhAa72o~(
zBNK+ZuawbXlkV0B0Yt!1d{%n+*v5nuD)mmMPP12@$MTXwKF#ZGA+KD3aRtK_E0cKR
z`KetqhK!pUV|8_uI{Mqoizm6?8^n22FX_>#Uw4v*WPJ(g8t4&4T)JYhU3^AdxUmK*
zd}G3~l#;cjJO2{DvmyGY4ZQ7U2iak^EjTr@wdieYtevG!)raHJ&jrJ>uf*0F1MCb2
z+>UN$<b4MTv!?lKL>?0td1T+K$!o@Yj)I-XYR&SX2M&gCoNd;_M6P$!hTxKY8n2}x
zp;z}O&w)B^T1ULpnnG0q^Hci({J;P5azk?MOb}O!Xg0E9Q;t!Z)o9Y@dfNvnb#-+w
zZJwX1LmbZZVq_xDKI?yNLAaDlu{<RF5~^0TFH@d)Lh#k$_m0@9>Z+~v>)lh%gz>`1
zU<50r-EflUl*n`Y58J6o0l^Oe-`y_yF$8E=YpKpvoE~&3$$T|IKL;%7QYAeGvDUK>
zRMWLz<Ub7_bFc#2scN2dduFpe9_3)Z3-EsfmKdf^O=IPw0(t3**xy+6RK%c9KbE4L
z7uP12imfZiTM%*+$ezUyQq1hI|M30F>m)Ax;De$}Oxmx#>u>=9t4Roj_lIwgAh4{?
zEy_$_-jwY2A5Y%g-h}uN3y#m(T8H2NrqZ$8*|<keTb@(@#_V$4vR(usQcRFsMi>U~
zlk+aZiOb>kb`GLBABbl^)vpcyMHV*>|3D_gAoe~da#)@Ffzw{Iccw2pn({!zbK0@!
z3|cF|%~yX>+}M~mILa{gbaT8g6QtNZUJ1t+h>loLx6`_oc-be;WJdso(_pC$bn;z&
zC-)f@ZHyl=-}<KSmpf~{$@^d15=*>a^7Zmra*x|s2;Hxydlmucq39&SWNpprv%jK4
zg!ujsO;;UNW%qP1-5?;+rGzxn4T^Ll-6`GOARyA+-5t{1-5pYwj!Sp*J^KE>wOBs<
zCuh!?nLT^<oWss$QzoiP2E%=x7TcmbWVqb^UZKOs7fI4B@Gz|U2AZQO7KzOq&!sJ4
z$mL<C+HUocp4Wc(^8_!NnpNQ5x}d0-R&9ufm<1BDZQD;(%lc2>?HRMZd7Rgoe~%7`
zbKtxAymENU@j(l<F$Z7kBFxa&A7)J8q*{h~3E&3V8@k7KzA12QP5F$L>NX$kx6KDL
z1=WQ+MwCqI6SeoMscAb;4mQz?pAIX{Y3P&^!p+}>eBFWW#}SHdrqJO~pedI>6E@0J
zw9lqyR=u|t#Mt*Gqr`5KH}cU~fLeL$;#LRej51uWk%a5xYxby}FJh3P=KE4z+E)Mi
zWj#K|5mh}xiKWyk--;UWP{c3yzd)6Mubu|dCNn&2zO&B2mfjmVbap73|KPwCdl<sc
z{<>LK8RVc)y(;;XD+4vje();~rPI@rFlIip(ab~PzJ-9?`1zh@4_8JcA0_XcFjXOF
zmZ_H1W1d^FJqbJn8-WK*?{s0@gTqR6|3t=qvZP({Dbn?)VnavX3Bs<}gOL!q#1GbC
zTGr>OPL5+b?K0z-tO!gAUx&}Vgb}V7E!9m)zAvS_WT97kuP^d3#oYVR>pV1Yh%`k~
zTWk-(tJxG0L*e&nqkqqNMxz>SR5`4i4%9o9fh4InMMnA&(AIED-UO}?On!{jGGXO`
z%~qr#*%cRUyh|gjm~<kp4T_JTS#zXVk$$5DH=Bq+zM8O1$+4*^jJQWG$T;QMc1P(@
zb;{I3*ROVOtr?jfI^CpT)L6B9w>N0-TW_}uGF(`Ue<tg`R2$SadGobSp3^qZSqu&!
zG}N#kqpB2^>T5-1CcNvyls^8GIU;<4%}!h$+i+{WvApH6QWGX=dzDDrcqXswhVfP=
zyMo}^&&7{q_=>YLv-4I`#RF3#K85`Em>E7%*ROsCGXf=d;@v}LyAhUoip=+U>)Kz}
z9wHWQAcJER`u4oH+xR;MGoYP6zJG%+qRxBhR^ZdFYEZtKB#twX7@+j}t7OS=<|3(W
zFocI91lYads=!lYMsEydTmCPP>)|soBL@u#`f_q#7xG|!Gd%_0Z_5IS07=%Q*l&5X
z?=-q;(=dv{AXEGBaMT;gc6TT0%o4#!>_9?GUzmi_5&T@_|Gw43Qy3nJ$?>!EVq-z-
zPhtdOJbRP@LU)(>s>4vSN|IZHUB)_h0$ZBoaJi4_zpUbgrj0wvz};`{v8zyB8v~Z-
zyvixhsuf9oR9MZn-sWXw5SO$klre4N8K<C+^(%IdXi`e7tUn-USgn_Sc@#`F0oR9z
zavP7*R@2KfML)Qh2Ht3<ygr-m_DzJy{Zf`H`64r}6w}M}Y@H|7W_oeNL9$r?Bb-L!
zBQA*!%vz;Ce%f(dC~)P{_kd4ZDRo<Q<6h$Id-~POzfh3-Xh!aem5MCX+U_UNPxT)B
zd?q=}#c~s0E)Lseg63nNhPZCGJ;BQ0U#b}I|Jpo}3loe33%m<kF^uuWJB47dj-L(o
zkf}U!&qH@)YfrFTUW&yv)G&B`C>cZ4Zw88%J%)mu_h?`9mg-?DGfHyb+uOQ7eH)02
zgY4MBtvli7qzz0<tP^??i=iJ_@q@_GJXDZ(w=_R18cOjWsLL%h@=rxR?IT~5v?j`0
zEIwhI2}(2Cxecet|A3~zn&1vDuiWfTS&Y~J?e|Hwe<PsCcIca*!G5mj{Am@8CDcQL
z{fN5-W!78RG<gBxvNb~eczifdsIM?9Y?G0kr1RLg-)eqn$6r6Lb6ES(;D$?z%w)+M
z;n$k8ztFM+#Y4uaEsmA&2Rf%PhXO4sEA8?2(ao*<aDpPPMrPPL+%*<#-3i0B;ch0T
zbd9mPPh)s<dF)<<Y#Xh8y)R{K0s?nT2-Va3L{q-H537T1nhC$jDKW{=@X#zPo_?9L
z4W-Ao8t=mzT+Mkz7v*^KxcMeJmkVRBMNyp|ot=yuC)bdM^?FthdOyd--~h(|L8hd*
zDxC^suOjUNs9KBc??$hi{=QD>Lz}~CR~D1q3&O?B+BFqlS3jlKo@RgwVelvWoC><0
zbrbPc;HpfTp#Qwc@WwaFYUd+GieQsy9<j`1qZvJ4!xel;t)e)l-e{6FCDf5Us*#Fz
zgwo;mwmm%`RAKEW4wXk(5MH+?OXywAn8y6}Jqfs!Yp%A;f{-1h5CIcM=cx}j6m2{Y
z7;H0c*EBbNwL|FVQ$16GAS~bV+VW(pim?aDa&tSf2wD>sC7Ld&iI`UP{!GtM8#u--
z7IU9P37_`VkDg9D=GMFDX6JaNB(&t?8P7C1nZ+bh<7BihUp$hOJtm&}#jP4y6l3@m
z0;A3c{tns<S5Iq5YI2w{xHzgX%#^j8_LfEu@~(W+CZlU;yy4EVqg&fwNhAv|z3?p%
zN)I>ndNcJv7O`VwPezC4KQ<h<3IXs(Wkr7F(#0=W^hWBO)+=@8IeK&i)`%lmA;RVU
zM}#N}0$H7a>lHhe#8$DBik%Zmj%Ztozn-v0{$KRrd;{(b4!KDve%2T$h9Z=$!Cd+-
zdU1Js9YssgxW}+vmL5)NM+$&~tThIk_humsUHcn@l2DyY&C2ZI)y|U*2chjUy3#=$
zQ5SPwTx0NMCK$0UwpP)i&heP`WBdVcO^-|_TKloV>DQXxNE7KnL_lr5yE<?^SPgk@
zcJvST8XzX(JJ|jj10#k{J9Kk2_y1ae;Fp^Q6H4AFm?C=_`^Ajhz_nM1pQ}x}A)1lW
zF#9NUfreFBroh7JtrSD6dq)QEPm8t`2JO`}*}HE@zanhb+BG7U=s$*i|6FC!+xC>2
zF?vk+3KH7N@3?}9i5u+>IwDreCDm_Fm;}*Z_6$9PV9lSBNPXVq_YPJ`ku{=B$`nIM
zFINqIfjUb$GL?llxkLp4*dI7ewgl65c;nato-8^vNeso4{j~*MUb=P{*`jcXj<7c>
zFQC7N-PWv>*vAPl^{iFs3WjWY`8d@r`#?C17Jfy<(c5X<)+5M<lH}1PU9g7_Y4ld1
zHULGl&@Di|JH0pNc-qIgHZzF@q{Qb&@%Z(OMblem-G;%9=f?8IXQk^zGGFOSgj8Yj
z`XE-GK&~yas6Ma@^5Zl~R<E7!pMpg|r)G(QO@r}Pg4R%lG4ySTvqvWO^@wj?_7mbK
z(;9k!z^%ZdB3PGA$Chzp`7OsetS7kZ>~0jhX|Z>8Ch*U>EY#Dtq~r|gnBUiKWu;%y
z<JaYF{`oo9S~J5kT{3%BvHq(?v-t$kbZL>7Qijc3H70*m{lO(}$odi%`F1xk!WHvw
zfexnlJ_V*0Jy>t4^LIOmR5Cjna;{ZUsgd}}2~OU)_pd9s$|xXXRWFQRtoa$?_XvtS
z2+aSSX8CJA`K@400|4iGR`OTLoiasN@omSHc0io(i-=+r)5M!WDeXR>A-O#WxpHV2
z98+wYbA2IqsyrX$04B}b;|(ahpsYA$`InU5%I~DvB@8XDWmr!POXwSzpm?`0ed3*J
zVE(L6oq4H_t>;-j@rhP=_W{v!uZvR;pPvzNwtkwr-7peEz3d29&<n3jS^_UmrojHJ
z@*X5sX4wr*ZZyWXh>?SutStSxcX~rj(>G)#%;Y^)%(dZFQ}qX&y4KS~#Zxis<U#+K
zpj1<+0G5+9Y-{!m4MA=s!OL#_*&}cukc1g-v7n9bTo}8K9a;5>J-BBHpJ;>|Luiow
z7RzlUHGZvwQlHagjo5wT=&cLC^*_{4D`s?t{DbUH1yqGV8G5aVb^=|Nv|;}BgXV=T
z-o&Fj*Bn(*Vd>8TN;AQq43_{TXKWtJA2egxmUE?>s}7SE<9M5<h1ObWw6#_V>*f*+
zw$2~woai*}T=sn~4Sd%e##-eWTRx1QViBWWvl`D}S=V$p-~O7OJZ^}VCdKqhjHCNx
zK>lIm`oXhIhO;uVp{yc&Xo5(mV`lt15-<7cJIOkIbzJjmpo&%9l%*Pn3gKNTyJK*p
zE4{VO`V<`Xw?kLk2EUl}R;7DBM2L0=rZ8dM)pg^rOs=Ax!wiS#v=?(JeE1eTrI1zd
zYvuIg_-aiI>kM-IJa=L1f+202!#^ts{bz&~uTE9a`N)@IQo93hdfxOmE4(Pa{gqZ_
zb7%|0bjI@(_OF_U$tnl_Q~g>$85p3JzUOSrbmUsiju#qU)#WWb=t*(=QN2$P{Wh;B
z@SFH~$7@6hK9_|h(Mx=H8e=7P#&@su%J+w+7}z4efQA$8YRkV6y7dLWX)DX$`<7s`
zc+Qg09XB*K;{4EBRjA{e1-oWD3gc}%NCP&g#{JB-GNP_kfVb8E0O5s(t<sQ=U2{+8
zDJ_DE>%dM7eIEMvHT56oy>k}$aued^F<uYO7HY#dUma~W_&Yf8Q2lBXRWr?T_xtGh
z=K7#&7V+VcjmX|y*!%k_%J=X-bw9^3(e`JuKKbRdfv@t3@rPDgPdFC>@^bD?kg{mS
znlRM+Q#@fIOCJU~Sj`+V9htZ**`l<HwPrB^r-JR0`Wnj)eAkiT_a`O2BoJJ>=6d>c
z>GbP|lhAcFpw=E-yd+aH1q*};ffCd%1vN?T<cxko;~wdndi?4DuhgIaL-3UwQ&#c9
zuPO+s7<NMDN<Ml?5W^1a&7}#~_3RD^_8L$4xkaG3`dsUcs~~Kvk}(1{W36iO*yG2u
zn{M`cU-o5(q?^W!<)7x!tygwUuZ?s~we3D+`WikbmQ#MZvcv{HDg<_)DA)IQ9lI+&
zpsQHdPu2MUye}<#YFts4oYgHqceBL>M~_r)XOA>rJP&zs86|VxT5g&eELF!)`^4=b
zop2x{?%t!TekvnUFSZhfG?5bcl_8^c6j+oQov(*XZ=Vbg;$hj>Bsmyhl#cfs*5WWQ
zv@o%bU2<uV4lbyo<!Y-bT}QN{dh<IiUaC!-MyI3avB0_-rzWrP`^4}(cEzZ;p{s4Q
zMFT#G_ybJ!UrN0Obp~K6rv|EN_I{P<&5V|Ky%(`8K8JP03#eBhoc(+~T;+63d4Is?
zCs{~?FtZ`Eef)^h1N6QYS!2EUfLY<)RS5qMw>`(G$Ta+$mCNs65Tq#{y0|HP?CBDE
zpT0x-eY`0zb~*WECR>M+6SY5<66`Au*sxay6Lk(qei%+xhj%-Bw%Pe@nHxT#i%Q0q
zccGx;;@co%+i0Q_n<al^l8=e4%+~3#pXYzOtEP6QdhV62@iX9ZBi^5upV3A^0t;Ki
zk)kVUEY*WUzkX1Qd#%%0Mmg;0bb!JCvcrSLA#LUCE8_rG8s3H0Q2bVE!`3m~Ln0&z
zh-C}6miBV(Xi05uvh1B=orZ8yt9^tujaEIRxD_tQi|A=k)$u+t(`t6x+~2GRcsUrq
zPx+>rVc{trQ!AvvKL~+lKV$aFEPpFF(%!lW%zJ$@*s$keT!(s*bW2@QW;OWd|6kE`
z{+`__P&uf%{#>^3@{jdluKUE+QHM$NQ-`LwYXOW&VPv=2(DlJ$NvI_07ch=6Qp<~-
z+&$Fg5OLl!*V2M;sUm(yyGq_owdL3clOC5e?>44{0RG<gs+i6S&bJx^?l<!BVbsS#
zg($M3vt4A$R`$qvIc$(&_0}~}fN8K?v#Pv`ScO`vxW2F$(IBdLHfOw3%Xlq}r?X*w
zOSpoz@NnssNqA>5>B<wZ&>A)hP_$p-`{RQ)iRm>gwoX(p8*l5LQr0<T#<x0z(dBG$
z^}gm_a3ViGuF$ynS71vr*H#46ZWv6!gI&N*S?rV2X3aNoET@J$_pWgJ=w+j|DNQDq
zil}`?j}OyXKPw2v(YM@23neSN=$6a#COrIRZAhIETwdWw6f&rh8l{FDUo_&3|558D
z4rc2Z^uTe|9P^De$4S$~*2s=HcA9E(r2arMv18i`W8#<jBYJC%GVe6Kok*juCO^Hq
z>Hwiy#S2|17gsggYGrMq=Yj{a)RX3BK~_zFdExcK=M*G3!trOZeSN%O)%k^YTS(F3
zSM#NhTFgyMn>&>d)f<votGCyu54E1x<Rjp1f3#JM4!D!^!|}jjQ}|IB_aX{cyBxuZ
zwVlZ3FdCF<)Q&P|xEV)ptSwzzZ7vO-vv(8a7s4v9qtQpGIUkgXo)}=$Nt4Q1t{;p&
zZZ6&T+QV$-(c>jW>@)n5e8B{n?9o<rRh+ExhCeTlMx+fDHZegw^(r$JO(|}4+7nU$
z#ba%=mT|LjeSm|bd9uaVaB1@{jR*D&`mCa1BKM~}-F5aOw25Cw{A+?3VilYzLRHnP
zjAOCOIhFIAeqS;+U#%4-2s2mb{ZVsJsP;s1s>nsy@@n{EnWRL#`uixlzYu#)?ko0R
z1hdDfcU3N2JL=8exnNivedLS?Ne!eI2FjF4cE}+BU<B2v4#K?`$BD((>jghWzHCD<
z-LxNC_lB036Zge&#9k3;-j=bZ7*%*o4xW6VR24f5HJ9Attar8Ii%3(#(rv|BiXU2n
zTimHjM_B_Sv}Vs<#yx0d>)%*F_0D&={&L!4<P|1id6z;>Zue9W#0T{U@{%&3pbAeb
zlcUVXBRkMc?3`fbh?DPCDCN`7UivJ9(IHTu+Hgsj4aH1R&plJwn&2zR_L@><hD4}{
z1w{pNpc9<tDNj}Ghw>Ff2+wsA53mt~<*Ran^U2^xiurmu5u+t?5gN^LE8#+u{WX7M
zrDKj?<)80rnY&l}0lb#>H5s!;WvuJDj*o6+et(D{<g3bsFPnml7eCQ@6vYpZa5zfM
zl5snpPnOysp-VO8Xz5Y1w%%$vf7dG&?O=9QE3-l&M$OBjYOW5~6yC<i2E>zjaSlpe
zM`l}VV7>e&%&yQ?`EDl8-udD3g2XT8Xh3Dlc!hB8q8h1ZYKiisL<<z)Zo401P1d0Z
zI(RUFYnK*FSVIw3zMMXUpMNWEYEY&YICb;N|Iq>>?t!$B%F;$jzo${J{G$H~-Lr!2
zVx`f&afG@aAzs{uDmm<dG)nyfxLkQB8RiPWF#rJyOJ*MUmShT^aSKW3eGL`e)X<bT
zaUF7cto0c=acZB^FjI0@g&`^IbDeUshz$#@jIG(=HA<!1pKtRzKhLbv3w9x0xIEc%
z-=(j=IGb&K58*;RC=x!zZSiu$b9wU9zvR2!CX8RpmXB9~N%uWvao8qr;7c8;ak>BN
zl$4Z2(`4OsSt7Q0r3mXPM?66N`2C9L$K1ho+q0%xjAI&6DqPFV&>aufiWB4wNgsxn
zbtlb85yk1sB4@TS!gu23z`l+Ba-%|LkYgtn_$SNJreX~dB50l>HLR^d_nGz61KH2s
zdhnV``Y$xZiW{i8TNie9Va3l#m7$j%9XsA!Xj~dr{(rpyHe2m|C*T(HZBL+BkIhr{
zx!0a@jv<!j>L6$y)SGL0PsyEA_w+%P8Ic8`F|;Qad*v=TaSwY)Dd6+THx*uo&w-h-
zAG?Vcz1C5Vf^Pv|dxq|pm$iCR|K{LWucPUQ`Zz<pddAL-=xv=Vo~m{&UTjZt<sn~B
z<fNN5q8f9cs9$e=CuFNP)fuN?MmArAT4!8Gi}Q^~XDlv4)nm6@PGbB1b)JQ}nMMX$
z`0h~)`jO>Z@YTW$1#?`6!tYv)Qa71-#(vE%ZC`P1knT-uhJ<FKp#x7PeN|EN0=nXD
zlJ7>RW~bE<mEmB+!0p-bIlmUp+%Kq4GWggo+}Rr1b*Q^SDg>az$p=b!SF7UllOSD{
zk*vR#`TQ{+@h_^6V+1wgyQ&vcs%eR4>fGCLpx+@Sq47Z_LA7AbTEVl?s72bo)C%Qv
zi_lz62OvmMq{CdE`{<nsx06In6kSz-DrXeg9O~xnc(@;5#N}*V{$RUPp)R~545O0;
zrs|-dC@)6sM^F;gW#ijYejMz-t6muGb<`_wArk(){t-$i+u0VH6x8AeH^RBp{V2o6
z;-f)Up7K_9=h!hh1t--C2&8liP(b%t&hj->*+dSSS@1<K7{Y;$x&icba+Hgwif4(2
z$H}B26Z=%<!IKAct|4_&ulro@v>jM4H!;qDD*I$f*ps(};FRwyYPzTl<qVnG6X<}|
z=cVsL3|sE1ma~xA+vzHwC4E&1l|7}`qGNydM4e=?Dc$@2vsB~9fBfCYBc%L_EhW7V
zQ7CT+=%cNoTHe;Ya8a6So?Tw)?C1u&JIyk;+Uy(>=^(EJ3oBAue3^I7z(Q+EHY$G#
zs3MQNcNfR`zH$zTC5%7`UIbrX=|*k~e|4z5pV0Eu9u%!CYumq>pFtS9+rg0*<Cj@V
zlPq6d6`~{4C?=+D?pzQkjW1C4A>!UKUAQHIaac#zlb?8+h;(MqG8U5E+l_N8d>7;|
zp_x!a!;VCm<RssuhYNEAB>?;0Hxd+M@8IffGPSUIOMUy>608Qz<Tp`c$i0{Btw%`s
zjUWH~n=flSv2yu_{NYjr=n!TB3L}$s=LWAsACo`Vz^zQCffnhC$0*t5#`^pCc^d$;
z8;cjOrN#Kh?o~qnwF<~)QUCL_#U1lt@u1N+dj1~Y>pzP&5o_f>-NpF5p)_oeHh`2y
z87Ey!3N`s_B$oJ76N6xNok}Z%HorAf5uaI15@`-gRIB)?m%_9*wWxw@2W+hZ*AT|L
z^%o+2saLV9#}p6ie~t-8zg&h6I@1Z&V<n{`<;8iBeUWj3-iPx{jHQcgKQGo=^HiJI
z+Hw-df<<Ul;jv+N*qOGu0}uOMMMlusnV>HX`7f(9`nMDd34*H>zt!hs9XWN-3aT(-
z@gcJ*o@^Es!ukzR;MJtoy>8LTVb|b!z2VOxu(y(CeeVRthKx!zE2mmukHivXSO<<u
zXJ@3lQyX`))@pf^3-O|YvGB!jCsAdHNA|=R{q|#f!bXZWcR9m5!KL}i#B!!yhktRK
zxKurEpSG~{0^@z7>iK$G!X5ER5TupozaAT{^jAFK*dcqYkk1gf7AF}W$DJIb=i5nF
z{y^#Q`r!Ksrj8<?OZ_=AJ+_c|@p!Vl?Ps>C1>za*4&Ly{NyurA)nfmG@Hx%U1gTf5
z_oAZgCa$_Ya|uTk#R*K7W=qI3Qcg^kL~Tf~gDf(<3)Hwbb4(S4gmQma;f~!@$CP(w
zY7FS5F7b1txV{@KSyV@4PlLjPX+4T_JI<ewKH}d6U*cY)?w<_YLF%4ryCr}2^#b;^
z*PDHgn?1aE#C}xwV1yzg#w&t#fuis9GvMHcf9nFbYoSLzDKKFT0}ddM#r`Sn&7<zh
zSuXrOX{CaC%)f_Ae=yI(NVvQ9WqXl+l&3j$b?@6^a&*{`z8G{xaKzS*tm+Kg$1?kg
zltk&Jx;5ezZB%L4VO0#_j}gSKGEKkEa=s;Gx_R$u$nFuimS|(No-c?PSj%REtz(N{
z6%-r300qxUP__<N?O#S1QHLxC4fymyFkDZ5d)*88tfd(<I`<)cs2z1B&&m^^_yU()
z{$@!KMg8aEUSe)2<Oo83A9hq5d$)qa6^1|C;Q{{{xFiU0=mf5Ogqtvmm)o+8;9R<S
z=KXaT^anY5dsSO#`Hv6Ur~QdjU;CrmzEkaDzrNF=SSwGAP>_T-nw(2#f8t|^I(rkm
z?MU5r$`TW^v7OHNjK5H(9gSusi@={SK|W&uk5>#!PbZ943l|d~8d&b98K-#$#S>Sn
zKXCSNG$zg9v?q9lFA*m2i`5PO${bDmgJH>Ypf@vJy1vCO%r+=I{uOzR6X}jfUe0tX
zT9x;<`05psj=zUjW1Vf%yip@{Zlj`QOv`nzCw$wZl=YbsgW<1re&GH>1!^5e_Hf^|
z&P?2)HBAI9q$5xfX|}<7C3#+ki#^xc&@>u{Mqjb3S&ramcTBnx<OTtguL+;052t1=
zHX$2#aR5pn>PMvrC;hA%admA=+b3AT+7B3NX;04pZfmv%7e_N>gNM@MlHoQiY<-R1
zx@{GQw?tlwK~dl`(dLg;B(ZBpv<NBObXEp(`Gsm#rjlpEX2z(Ji!Clwn>A5qJM_#e
z?Q4cYfv_(#m{AWJEFs)M*4Uy|jGGCI3QB-lX+MvAkC3+N!F6k`gWS2HfRXjBw9S@)
zayd=c!KEGXM5VaWcc$}nJ$<nhZSJrUz+GRSXq~4}v%a}Lf0;SV`n9PVXAImg-9j<m
zy{U@z4^1@3JBp?J!;w}!57TPkJ%a=ZN&k#eD4!h_P0*p3I9sIhU%H^hdh!B-;3w^+
z#Pp*@+4S@iHRxJYt}8nI$NimPQiOGXvd6)yawc#rKz^#IOy>zpe>xp4QTnw<vV^>L
zLiVTH2d@ukIx)dk`5fj5V6&b1GYYUOCE|Bjo$?iR#JWkH{Jim(4~0ZmnWjeFaasU5
zX{tnPZ8}}D7|w{8K=~2BSeXVv9Ci()@v)&p5Kda<@L?S0C(T$x1P!}4CzJyS+g6-L
z?)O}qFknycg@~@o`B~S|S!?Af%-Xk<DI{gXCi_pma_G-e4f*RVkbTB9`@RQZb0yjo
z*k%HE^X{DUP;-qV_v)jMYNt=f$PwCqi#%8+Y<!@(sAWE%E)#D9|I)124ojq*vJ3J=
z;sd=YN^GnzylX78-sp;ofjYPhO%R^%bE2|;YS~Y5yc$|8NgZCl&edFQY^w}XWGRdt
z6%_nDy+63zK;V@s5TN@SU}E=|!S!axj05-VLwVx}%%VL%xw`YHY2{1n!mcq?Eg~PO
zzIdqxvtk`4P-J18X-fXQOra!96YoS&MgLk#`*O+8L3Y=zo;>$y652ja^oMn3eAW2s
zaK{g<P!w?+Ntw;V2W8yC6M*0%C3za)zejxov!Y;(@OGDGM}Xuv5ApNbQbS<J1m&5;
zZP(X(gg7^9{CC()PYnsZTB_4d;;$&WviC$w8J6~i_LhGk)*Ex*KdJCQ=R^LJ4NN-9
z3KnF(P{<bdugM2opwAXUq*sUU4mnW(|F3e_T=GF#`_#IvDZ_x&GNf_clqjl-@=?8|
z->T!mor03*whxvCw`1UbeXZBik}f%Py~oj(zo{i5x*cq+Xd?KFegyR>o7~L!W9;cw
z<)obveu`G+G5QG!OaU~GlsYyeyL#svF!0_bMK*1=eKG22DATlX`CVLpN-+|%($E<Z
zIKyqAzmHym=jYr3*^*JOLYL)4jAMkUP^~}_xD2D!9hA-0LF)zc6NYAadfXNe)&Mzj
zq}4xIGvRz;$rV)lsT_&W)n_W+D0xMDMBMXS@-{6{@*ime7y=X>LxtF#UqN?PebG~-
z=I^e;HzN<sCzkQuw<GyR%k6F!`t?uICOk3yDnOHJALr5!NND(;3{13J@9zzCvj_V3
z#FUs@NX%2j{JC~w;I+`Jj++@T9y+#5(Ms0++gwcFq^*p8I%xb-I*$^6w_7Ll{tKOR
z*S1!3tc1-DPFh{zCJZj4f(n=xEF45H_;PonY@{)^vXo=%Q}b9)Zzyw7jMA`*umYkl
z9*0ux4uOs|fxd;|tM^jQju&Nb3ai(T*20|fMc2QcDw&HnU)-s@d1}R@TFad?$Dc$}
zONmQ$*a?TcV=25v<OvYdcI<JW%H6ZerSb7#q#fp9U9#vP_ZX8V;x@yzzWLE02dHQO
z!C?qC6cA_+tMT$Tra$Yse;T25!DjbWkx}w|k_PpVjJ;;h)Zgc0eq~b^(mh|J&wtQQ
zuA8hKL#LMGHFNof&Ql(s0^{xzZ0Hk^MRQjEmgIeOJL6kWDcTEvlCVKFoh_bgpL~vW
zha*<ck4l1|`#WcV5o{-s!~|p+*RU=FT95%38~Ezi#!|qN@3G&KP4UQzeEro+JpuOy
zU*-2?^w4{Ut(m4H?n9v_<rld8sVK6zL~K_qF1nstRTrC1(}s&lV{Irk?+4c|@Cl6`
z4zomZ#N}KT-2oIB6TE~1DPWZ3>(1%@ka6IRmcqPuh$-R>jxt6!%K!a|5-GMvG}rfy
zqdB{|gh>6|mlAH=cnZ7W{o>d)jbdy%rOdZr0=*5lP_wggLT{6KW#J~;5`|*IwwWD*
z6NN)|&6&-qfUnUFE;z|jg@#gcjkec5@l-z4B`0iuL(%7tOn*UpcE!W|s^`~FUz!4c
zXE{y`+rTpCRFb-<_i|Rk*-ltg(0664F03A{R{Attj9X&U;8$omLINdvnb7j}Vx3Bf
zy|un)%Q&#}^C}(DePH7f%(?|!A7Fe<TwcP*4mu6uf2(yxQO8Da<$eBoj^Cys$aSTO
z_}jl`h-DD$NM?48Lm+3BXW<?Q@tgVlFu{c72H|Zd!K$xyRs1g7>%JRhvX=Nwi=A}2
zL8->Vn|b->&%v^Yu)lkJDI(>_*&<skZ=(m+K3ZDo5jSEYo4Ofv0@SEGAS9At0K^W>
zD4C@96K&&#l4Oh7Mjh}U$41TRc+b$8rObZZu*=JFHw>)O0TpKNt|Pc`g)%xWwa0K-
z)sAhC&+Ud~UF3|ksumT3v}U68vU|@lVNLitIUoPT?Mj691cOpe0kb?aUcEVrbYoQD
zx=ZcD24DCIW=Y>=Vpx%2!n-1_!CvJQxFhy&&+J`JQ63qhlLA7%#Y12O6q;|4FX;+v
zop)3d`Dl$|!e=Vys#0g|y^&eVjBj~UvgHlCq=X+b2N@I_9RUKBgz!{yC;iTy1m&fA
z(>jC%JKtb!7Svovr<=8a9S0}7cEyYpWzz8bL<<_@^^zJC1KZD_kGq6D`ZU-5ZAOMn
zqPMMu&}p#GhQA!!h`QK;q^I$j6M!9K0t_(<%H?U_KLj&r`OTzhntGqihrSAy{gU&k
zKYM!Rv#XP(Z0&%{&Y}8<3zx5%TDP-z=MUQRQ|ml}bSY!=pTRTZg9rB!CQD}1##n7n
z6O4(*$89TJkng@VbxteY%hu7(3<)t;Y2HWR)cy97%8#?cn^qkfX1wdMISKY^ZT1kB
zSmyCV>-5yCH!Yz0Yb*B5za_UkZk?(*WrD;_0W%w}l7T5dOAu>u1x0+?n0^sNUP>~k
zXD*L+gbW+^tz^QSbp0H(5QGb-#T#9JK_5YN-3mmewI^55hqGlmCEmBD`(@av)w+R@
z%eDKnr4X}4Wy@GB&P}(E#Xa{687&T<OQPVn6FSYA@_ylJ?o5U))eihmk>kSHOL=J%
zLdS76-slH{9lwSJqkyjO<*HDcY>W=XpMfEx$Tm1Q*XhZla~$YaqC&p0<DdGqRU^xW
zbZ7^Z*jC0&9VQgS-P_&SO3%sUr@8dDXjgWfI9}YWjU{O%rxp5I#G|@nHkR`fKtKAO
z?ftnmP=wGWd0BFv9xW^W;qZZWp@Z`HFGU7R<u(H6Cox57=VsCl6d5-6>DrFpDy4+m
zbvpPH(`&=Qd{bBN*LUG-&K8xTm9dSF@Wk4GX3HaoJ#;6G_s9|SHHf7U*1BV@JSLfV
zBH#+qW1<<baTw1Zq*=|9S;l^JFFHP_YXNWDT(D9Pjz)8*fc36G$0CuJPt;VR0?|?$
z1(17=#WLU#<q&tCIC#$2|JMSjngtH=&g<E6-Cc3>M@BMf0(tvzoM89WtS2Ql_}LQ+
zfVL&QH3}YiV_sN6pZq&zg%OVwYX!d7g>My_FcYu+>X0?q2_v({FEd_w!%)6ea^eL<
z896LtWZQ$cy6;M67%5TaR&813lU>x3t;>x{G^Ccqtf*n8gevET3jfkU&PzyDn0TmZ
zH`ky*d)AM}T<$iq{9}7!&eZ~xzrprF7o0Pgl%da<;19;U|CuwICoUE^Z1RIxE+6p2
z;oY4l&lX*Y0i9P=3;XD0rD5r&zal@c>D`$bze{ARD_ISPn^!?HT&b3eM*E*)jOb<%
z1vumv{K{GmKS<77Zxbw`I{hcsswFpu;wOjsP;CVa=+3Dw+%h+81_?oq=M&vV1kfB?
zdGKVsRBih1$upt2zxaWmA;(xez@*vAlmf)+!=T%m=iz|{F+qTeYPn@1YD&iO;%OCj
zHsE(aY&xo=85uJh?s7l*2+|kMEUVtqawPixp}!mj^!IN}*HC@#i_Ap|#QLaPash*!
zSe-11&C;+QpH)}}+iC9`>Gw{6$WYmXkSmK%2SZxvM@z8)Nus=6B@`*NXiJU!{mKNC
zAmz7bNxcyJ+t|TLKzRHnKtp_G_andt@7_l%D%X9s2)*V#=Hp-O&309-I{K>=ZqlCk
z0>QIXfiHgue(S(!=a(%F;qfI=Ktm~KHJy_q;(Uu<WIp=_lQ!C2;FVL~x8rNZ5<7pk
zh*$<>5~Z!#_IQm{_GE8I8v?aIt1;HR)MYxNwzjb0TP2{*Wo&A@F8##RLg1w5>Xs2B
zSyM<IQ=`w=PuyWRAuak(yY&*l!!->Vus14<I%_SR((p&<psd<*(h(F@&l`7pyCsMc
z9BLPT*jQB?+>mcP?AXFE5DSNXrCf~!mrd(cV#JbAkfB)Ez<2@EEh67AJ_X_-lY_N`
z0}e>`3Fcpjj_9;FL0A6uYUKO=2T_2tGbkPB^ZIOyOSULCvd|XvsrVY_$$czb1R$Ze
zQX1&kjtdnHUBE~uKOs-rGP7}D>nPEY-ud)Upv1S1u;>}=FNa!mnC)s=k1J19uy2kP
zT`=BK^3Et2ZO-i7<FR{*EH?hLrWs?hB0H~}X*l5+Pg4shr;b~wI}e^?(i8HYVx}KP
z9$md&jg1A`iG2}lrj*@m7rqBQt`9pPxJ<wRnt=*=84`qdT1M$<<^-Wki(hRUWUFDC
z-Z%bhdN{=n{!8{34hxcT6wKC5Y^<(Kr18RvA&`X8Pj-o{z=CRN<*Bk;jlh*P)Kf*X
zZ0Lvu>hgGm-(m-=Q_SAJk!~3LnV00Sl;QlYO;otS9Sv#jP;y1L^;0O6&&z&tyIT~g
z!x|#J6DmOQSG~HPf1d5PvFu_hF$<iiEIUdbqG(^liTXvviDT6>!p*y?jKWnlf(ZQw
zqZ5$qudI$l*ShDBri4<xukRkH$)}FGvS*5-Nb&LR4>eJAmX#tY%rHgj9MAmG)T%xw
z>Z<!N+B+bq0jl<k5Zdf(z=Ewjhw+B_=@Mx<_~f0d?zT&TVXX<J2X6qeh5xJ5{hNhH
z{?+V<v~pJmbB`lyouw7{?41*ru7LhG9{D6k3x{Z>iW??p%M=I8Pc(lsWuHrwvnk9v
zx*}{H{>ATa@Ut*Xi6>Zr<BE&dF?~qvuuPM+OK21jdP;uU!NOv4Yz#4Nqx+Z!0IupD
z(cNkciDY&ppnn|CwH&jg7|{|@IrV1xR`yBLSqul<{445l9cy}5K;rLyOYsI?kCMj-
z68Q69TK1t+@k+cZ(4f#hGM>{~>`;U5%!)3+Cnq1!1@4ES!LUDpy#~W@fc1Tk4@`z?
zmhrHb)7sHeKzA^)p8P`pf*kB;+y8(wt=zD6DlNL`oYB_LZO-74+Jti0FHVP~!~<h8
z%ahzWekK`XIu9HtJZ*qvc1cnq7-Fc+A36T|DSoE%n$qC_Vf&>auC__eK<?Jta<Wa%
z$u`bJ=c;Etdm15k8ZIZ;6mY~CFo_{B++%rwL;;|nAo8}jws(}vqiJrp?$SY*blBTv
zss2D!pXTKQ3lwEACR5b(F1N@rg6(i4#oF;a6F-!iK_H&E$)w3t_jP02MDX3)MXeo#
zw*i~s@Qu|vs89q8ebp_R&W=o}Ik4`3ofP=#+8bUR7X|!vp8Lp~xhzumz+zq@Xe<4y
zWdS5q_zV8){#84PA|@1p;2IE^_*%l9eLUehNg<YhGj@bOdPZ`V;pYAmJ^1+X*a%-M
zx<mJ2T^t~dK+*@ZL1;7*Y0O3jQgUZymBE&Z#nXtCpE7Oda-1~m`7fVRU2+eC#6rpl
z1vc?x*7hSAj^A=a_TC71+9yXE$_Ru|+UaJy9bD>;k`4@|<GpHr*;=@O>0Gk-9&-+X
zfYP4zD8kp5f~hD%hGXJUU|)&tqf8Qz&MH%A<pNV%zqJL%!(~^EgZvFsJ-%xxcSJwx
zlTFrwUBdr6#$<OP|2&y7#!nvTzdVp@=gjp}`y>U8p#x;$UH$DDfwrS|<#}$MqQE9V
zM*=TW($1aTc~EJfPMjKF^{~*fOmfi2piA1~?u=MogU>yeJ-8<7PWzM<D#*fgpLerL
zT>H&#)@#H)o2Z*SUam%KOfvfJPESFwwS=})UZ#iaRF;FeSw`~-K^z6_F@K!=a>P8)
zR+lY)1=ByxSxIq!o*$Nj5>LHMqHaV1W)$$|y}nf#z8i2fVpaF?K1^Qo7<~-iUP-X5
zY9cLwrcrh#`}|Rx*_Ku4vFZthLadtK*oD=1OMoEtf9rkwp2ZdJbCE>`E!X*KYCh*t
z$w;+>c5(&K4nkU(KjICh1kaExoG;!e6Ag`jtUc2DiET(ywytlu#i+{t10YgI(RtmS
zHY$I=OxXeacCMU%KdNpGXr{~QFY~*Q#hq`LVn3+$g84F5+1p`^q4-^<+tV`D#O==t
zHR2PPOdN}*=0wbS5zwyAc9@7Jk25)TQUE+dB;c`@W`)Bmh~qJiprr%kf_j_c&DcF?
zTdob)9DkreY?wJ>yyfG}lIZhQ{&ouQ<-YC=ogx_gavOJ`CcEV}-pUCrCQJK=ig-%2
z0r;O?j9TJrNvZtlv9XIc`#hcx)+!EPJnt@4LmxK~l%3yvZfrEAluD$F!(vJOCdcYF
zV19cc=ok7n?w@oBNZN=0w4<}^HqE5HOek$eH7-y($$2KTv7+;Z6na(aNH;SH`gH4N
z#8_P+7B-Y?Q6l{586UXu!?aI_<E)sOODCIU)%(>Ydwy%RP@}ws96aNqoqexN7P&c0
zHe#(=+!=4Ryg;w$b9BW{xJw7Yx^xte?iEbK0cs;e4^gb9mPBlh{cIMiL;y1nR;0iI
zssZHbQe|89Z>lO6SA|!O9jm^UtPUrkEqu%TEGh#gmkeYhd7j?XpCZRD+5G4t08~9=
zqaA9=4y7khk8}CEeB1JAtwy#og5X^%uJ~8exwc~TbjK?FLgG$nPoHxJ*z92<1R`Ia
z8FSGO#jbkG$YC6Gor0Z)?Ic<MJ3NiSSOASZ%dXo<3NZ19%h7jgq6u`&rVc!IgX5tU
zy4d1Ez%bsII-X`Rj_q9Qg=zXhoTRWRgioysbUMegLCXI9m_;;A^%pdT^?P=^!*bE(
zRKTWZ3CS-;rv_7cQ>&MLk7}}XkM;uQ+Cq}3z0ajHACH`?Reg|z&gL4hxxF=-#u?5+
zvO(MNxzhfu6HX+z5!2H}pQkF1>c{57n)|Q$)Z|EE!E=w#`0h?G4u%qoJxh`Oaqekl
z#-wgPT7daDSIgE2h{xV(t{n_chqruP*Xk${H89JM^*#}_S8}BH!`3bw<W!_02J9wM
zY68%=S@vz042J(-A}GTA`ZonSjTv>KwqC81^JdZYP&v&sg+1vN4CxncKaHhWD8-I6
zX4_eya?oY}sebJsnyE!|h&bJmcjf`wZQ`yKtg<zJXP6Uj1g<1(dAJ^55G`q_`Ip7b
z(Yo4fdORIbpol9dJ(EiDH30ejkosetN!wYr9G1XlvVEr1ey4;{Wyar;2%}W|q0>!c
zR{CHMP~*X$&6-L|r0=pwVDTT(!qmjD2$Isx5@Kpqy+AcXuVZ3($obuJPZqGmnF5pR
zFfWmmqkTABy9cZ9D>|=Q^;*9$pvG2L-mI9Q;xCmKb$-i?tOkhLZ~~@9Kx}6iM&Az2
z(2WaoX9G##wEn1K{FgQY2*hCjMw8GRXfAWHY4dpem66Cq0S9B_6M@Vx(w0$`K}zJb
z611v7bi9dk){j2PLY1w7@;&NkCp-Fs5S4!OrE9fQc0s{rrN#6M;oBwEZ3de+c3YuF
zF9PvkorWx{*@`cF`infIppK#f@s#TH$UL@RGl|vi^1i*gy0GW#<Os)_C47F15#_UG
zF7doVIQz(_%M+PY_glXgSz`d@$rrss;F2{5gp?{g=t?}<HNQDPEU(K@TV-DpzAlKm
z-9~+d!?Rvpz1+kMsG%_$v3@BrE+T$$YFT*(&j`OZlfF<8ydwQYJU}@e{a-nK4ZT>s
zH+|xBIg8*1Dx$>U|6u6FpJpCyQDb*K+@zL{p7R6~Lhq6i&c)EQsJO*{`J;JV{JBMt
z4ru#@3tn4$w<#L3S^^WTU>!rd?Y#HAN2c#3Ute?3gS#`FA{IK>YL04RV6HaEv0yyj
zK1&MP56@-EV81&qsd;o4Gzx-v=>tN}%i!ZQUB2*s8*55~ZHIl$>#xp#xLyZZC^Bl8
zxAi}e^5Jv>boFF{7G`dDbvVmyM?BDdy|v@-g2EzwHQiOqVSUs1PVMmd14_5ZD!eV*
zUaQ9+*w&31%>OO+3({9#)i(jn``*459!j6TmL%NSHN}UwX!*4!^5}>(o^0-b4u6Cf
z2OFttBV{7N9iBlKIr;^lyMvr;DezHrZboly{^V=)f1i+s2S06^rRg4(tV7nTd9STK
z@qzh=K5J}_JAK9Pf`iTJ&fl4;ZBL7;O;||f>@S`bcVz7)ME=~$ec(N+HLKX&d3?Gz
zOb=gwtv9Gs=jQcdySe&0QBUi|Ts<bKQ7{^i=unJHb^e0w-mkOQChFx+!u+lokrg0x
z#rhAUD7X?&w#U@J`%VG<;ydwCxS2>$vH(Ho|3X@vB%3-mK-)!ws5`3!60Ln3yrk;(
z>?(^y1&F1bG@N-l=F5OV)Ct3Qfq+H~bS!}*GmzXnI-v(9rY$9cFy(w-bePalR?_td
zy8%*4YwX2qcxYZ-0EVwd*b`4|ME#~qRg*miQXnD71$}{~x`PxDXmqYLKtmzJxlkgd
zQNfUXFmnVX_xS28*z1EmyZL!{@u^mUKU$78iteBKKot3-r)baor>le@r{BDo0VQ?6
zJGVIfY&^N%{Vyc_C#;ZPxP$To$>cDtMmEZp&(&I;goH9k@azKmdqS77RY31Ic@_*8
zfad<|Y(sA5E}TI;<;k~0*GTI{v^wm=rDc31!$Woxo2NTwbN?|C>C0OHi(rS>>!&I<
zd_xd}j>=GO&zT<K#32n|^`IA&=WC55#fTi6KqdiP{?0gig>Nvvm~NS2&{_4Jt!Y$1
z0ao@rAFFh-zQM|6Q&@5u3ZQPnv1mu$%sll+DPJx~PTBoU8%NOEM(3^cxu^=)m)Do7
zldhd4?Em*=cRJh~C^J-LzMApP{l3mmzgwuug*-(PGN!kLoSIIN_yVjyfRo=_r+vAr
zDpWuad8;vD@9y&wK#^Uc%FiD1tm#aB)2AGOk%~&I>dU#+zzK-Q6RTz9Krg&nH>kiv
z1Ly^#gA<Y}2y-w)*YT&iS;Idlx@rfmS9p5a9p+RB0k#3q4uDPtDyZwdUow%fMNMBP
z*0h7f?7Yy3UdJUlPP$fCS2b!Ua~Sdi-BD&&eVo>4om8{Fz<sp(ZP2&63cTV+9&krh
zdinA@R)#~==tJi{pB$<4$x4$$(2@0iGV5M5t7Rx;ot>iuLws}V;N5OTb#z_cpSXqR
zgZV#ECR!qX`b+AqAEcaB$R+!rr4bBh-QRyfBoBD=MJoi>HSmpUN(-n&B#v?U%zn?Y
zdnKL&loIq+>B@0<OdD-E>mxE3F&D!w^kX2pd+)Qx)PWsUI#VJ3cND@0RFJF#OX2#F
zT=$WL*3+X5)}D_q|3O+y=J+;kZdA1T)$c7VrCUf*i$M0tqsL_O6UcOZwC1Tjr!#Kh
z$xLzK+V9>bmN*v*7##0CQUBb^GnL4sbGBD5_7vi1-9n5NQ&SU;TTy3s>2PpjkBMe+
za0jLl+)N0Z%vbJ`f<lFCp`S%eOIH3{3h>Wh(0{A>X^JAPJ@&4w&W>E7Pt`_G%U=bD
zKiyv6=}(hS&le?SIFZjL7fe-^x-~kp?oM!~*RB&@PA1&rvy_gL!m|(SSdIlCq9Hqq
z*IP6RsrL7FU1GiMya8d)bit1|0-NnE7{0O$q22?)fbUVK+2+bn1+Kelr{k(DZ%N8+
z5}|ub#QlDvbcF|V_>7&br`Owzj)6oE(YIE1b%O8IgBv-5dHlZ>Icc-(VWq7+Hk)KU
zN8Uoao_)vmdkGw{Y^i6Fr__QfLa3#gh6Q%$@7gwLDWG)7d*el+@TNxwFEhW}p1GdC
zD`>_lTQ%F;VbY4+Te!f;39;$&8>j2rT+FRaeuR-4CxYpGqk^4oBcDBh_oMWC2YRW(
zuES`g+_B2+qaG>wGxZNy3?AZ-JitoRo;`^UcyV)hj_^>K?}KxUCv%K<oad?ykAqFb
zUrq_TD}1ng@k7hY))E>7PEl?ju(0-#n=4k$3YUuBl4NSxzH_t|GfWH1G;%gMq$((4
zBTD%q*-V%6^b+e$|HwG0P57Yb$b)y7+(-AnCA}xb0^@wql4yq6FpUiKIS&dPZz#md
zbiFpZjPUrB4k3|tFkyBHDbtzyM(cp@Oo(Bl@uM%Ac(g&6Pv-C^ejrI=^MTwggciG<
zX@>jVFj%;Ef1&tx1B$@Y`-etlh0rG>CeNGAwswkg^n97E%{d}B<DAMzC*Yh0T&4Q{
z*7yKwzn_UI^vTNX{tef~$1(ra_1BM*?l_;aG(O1vy?V=xtfYY5`oJ1%Zpmb6x*yIu
zg2Bbm_+<Kv3J4?o(^R=r7bX4$t2A`$e~yG`C-L8cPDb3PxEAY*5@wLDE9A%<O|T}s
z(-aneC+0773>nRSJ0Oa5G8hlw)>zf{RmoOpoozM=9Ixb~=W##{O5yyKS$p<P$z)Ah
z*>^Nov+-_$0u-ijJ#`NschAQpvPTHKY%MTH@a=Z>xFSpkTn~||Z&Y6&hmRy^kU$aa
ziash~Pm4>C3y1Gq5Zg!}c;ad&3n;k0Dx!64`w%Yzu`FA%F1!H)(pcv3!{^wfi^#yn
z(29=R%J1rG#l~>A2m3sy{h2VUTM<VVqqm-k_A=ClDl|bHLjG82@Bg=Ps$58C$mA7o
z-LptL3$@{Y8-djhVPRWbc+#rAd%SeDSI3zJp4%iX5gxB9VlJaE9ysXIp1#Hn#h`Kg
zSx@P%9$V^KHRR+UP4ni&Hl^1%o*hx&%Ce0-7Rtqd7YRD<mKf!I8M{pi6ShzwuDBJR
zLt0N5;R_XZS`<Rj5DScdQoUX$g_~@QfZT;TP;ZTjLuIMNcMq`bYY+Sk`j}Txx^gAW
z<4-EPWnk~DclZ02#ne_98EQ4w^(OZyl{))#g=uXi4KHoF{*YjnCk@pH)Pn<b^ho+C
zvj5-4z*tb_n@!1cTzSFKfkbk4?O<=#3j973ZTP7|b7GLeW*Vv&Tln+9aDkDqK}ama
zBcK1^gs185t%yqVYV`2A+G(0gKNg+WiHza$%Td<vG4uw3Omrbg741jg3JSB##BAVA
zo>>%BCmUVe8gdwmSp+hx<rTi?^yK2jEjdsYMnrd^^NwZ!qt!B>ymE=iJ|evc(#|AV
z;6%oyiwWrQkv8nmWII|@CXpwudCsXUnV@$cN@S#6`K{}*w=UI+Y4<@uJN7hae|62b
z!)9nbl>6`u5D5M+L|!Pg8n}KzRQTNuB}m30ripm=o|#BbeheP3PHegK9*(8V+3<#1
zSI=pMCPq<N#j?&}f$qQ(D3ReBLkvd*cr%}^^~aG3(WyPJYDsS+o#7^5mba1bN`yLs
z&4`k*M<axt=TB^_%qr8L2Z%gxLwuqwV*9CilDTMFK!=cHch(|N7;BABsWtd!f1Ff3
zoBS^7kD8a0NZJr;dir5xc$s$w8Q=Aj^hKwDrzWE9fx;8LGuj=>*VkE?*0evcCY>8r
zDAKvFv?VoDfEcYT1FLr}7q~Q@WfSu4O3$K=fXDlx18BniJ{uLo=VSiUThW8gapc@q
zX+wO}<FtyVgtjnMUJe!eE;OBEVYmsUf{<XnRjXO#1^$*f>tj~Q)$Gfv;!E+}{|<vf
zumoT^yCy^!bQsJ|L^3+|OT;&Ddb0<~vlVg~Fq!64fsE1YNv$q02(j2)&dpcJwJjLD
zcMi$n2PkE|l&%rCFB9)h2+a(7vCYy1GTTm{M5y(>Vr+NaHJ&#b#w;KClb(QZF#Y<%
zcEuwuuJT*021AEqpMwCliA5C`c)rPLPtM^_+HjRdxRjSyA|bJ@N$&i~F~Lj4L*-4t
zw<2`HkTo1P>Girr;+1Qgxy(V$wQ<%2R#vpRm<WM9^QJLDPBC*n&_>tVQ1{8CmR!&-
zCB{2Jz$^^@o`@KBV<r=r2p&1aVffqr<eB=Z3lrW#A9?yE+6X9p^gd4NlCvn03n<K)
zWnR}%l1TsW1XT$Ai*t<7bzsI$A}}3zq73+D`m^Er)J`}DzLWcdN~u)y>Tqsq0$52(
z1%quQ*_E3AM3&M5FIQG9age|<xU6g7k<)>EYN%A#q!BlLc&PYG<51+!&-zDlA=InZ
zTifb5EySqsszSHnHmp@@T???6s>`2DcGFK+!~Xz<G^k4yTiBd~e$Gi-;z7AIRH3jZ
z!8IXHSrBX51{#!Ls0oE=%9&JhD|gK&?i5pdMHutW>!-Oy;h&xk@WST*5%m>dQ8n+|
z3kV2EDBT93(%m6~NQ-o%bT`Y=DJmr(odOa|ce8*3F5SI!H!QuxcX<E$`!2ZP;&67(
z%$z6h=boAAuZiNhp1X4M)rpY8UGGc%5XH8jtObHS^eX$JJh$aQj7}k*VYOj}GYCdL
z)sJW5Lul`m{%7VF<*Who_mU?~GyccJ1K$!KLbRTtz?7NLIa!4NH!18M+&{W@2a{fF
zQYbR>Rn11PqC7o!v+ENuSM%BZORZ9DU9s5#-&)XMt*(JPKK(#2)9xmTPTC7Gd*kgv
zuOvv{^R-jzAZ67*W%*T&d?6cZ%EA!}X5;UvU9_eW>wm93oTb%+F-Gz2_wukc9xC?O
zGp65;wdM#MNQbe582Y{F^B8H7=|6MqZt(p534XoRKgWTy<krnoz;AteI$-m^lcEE+
zTpdr5P9+`vFD2hal|T2yaKcf3BcAl>gquY^6Z(ymz}G?7yr8R)YLS3li{-@lf2Ofs
zSaac_l)gQBfMzR)uH(dRkn%MIJb=Zn-FuHBTy(GsgP5weD+hMGyk5Z1!m+CjZ%TZY
z$tHNRsOCE>)SIUr>vhrdKs??4htY|r;-*tj<MrEa87#JIM6+0hGBFc)XT1a`HA9Fi
z6!KvPmz#F#VN(Oz6Mem6cFjDD!jV^QFiCrd$*<5BEh9U`u=VkTmY_N*%)I#za1K(c
zvbQyFmpV+WVA~f%lIwD59!kF{a)X&^Xndb}I0h{r=|{~aJznswo|)}3HOyrW&91!a
zA_H@{MQ79IC_aH)qQ`N5V^Zi@VyBzDuL`7{fd|G`g+7a?h@4{$`5T8FF#~a!wAmx{
zSpsj>ccE{M{N7C1b#65Dac&-u;{JiT+kMETnd<QJngGb|hg_0NR9Xc=KoIzT_=g-V
z?I(2H$wZzXCmSUFjDnDSE7^3rxHP%#cN)S28S+_tv0s#?k=})S8{ZZD`bxfpEyCFp
z<jPDzW!{5=Ti79_sD|J?-o}V=mlmWY(q^3c9bB-Ef8OK@|BbM$x`oE<3lO?U#N(y$
z+97Q9-hp3D4nj`zN|M#)M2~VD&E*z#w&K2w;Jgxx1!+M-6J;1PyvCJC7yMd9=2CwC
z-|(dLZx~uxg7X!R*v2WhmK9?7Zo8TaQJ57smyKV2veZ-J_+4Pw#whx>*)vaJ5dvY!
zLV@Y3lE}tSNgkHrI6-JT?&pr4O!QZ#ZK(xI*&~&%K*v{bIro)CRRS4<TE@1>Y{Xv<
zn%(dM0&_L&CD;rdWk2P^QQ6;_Y6XYZdQ~NDRdqUB6I$-mR#ElY{VL>a(lo&u%^xT@
zCMhuxrPW|TWFql8OE36>qdd?|;x1QxX@Riy(b=v~qBjY9NrN|flh2-l*^KXm#nu@Z
zgTgnW{I`kEO=t+YcpvEefyb;@CCUFu^XHxn)(WQJ{O`gt>UnzVN?<GWl##Z>D$`uL
zsg7`B6ymzyJcmnQjq{g{z>D#7EB8Xw$sgunLAQP!$;_cp-jui?=G3Nh2v%%MPmViZ
zh)KEfjxK2k)y*sKX^3(90=r~N*~^aPP~4pcimuTO1O2kPE%Z`R@O$*8pDXV)%u^?^
zB{k+jOWY%9vuy@J%3WD#COD^Xz4UBlNlsL#%1Z4r>U^cu{5{Y6xAWqJfEnjYzbs5G
zy?2#-=G2FP4m(=nmMZc(ojI!24`d5|>=#0`AvlbVIW!!}`^gdz|F{4JZT}+fkQgAa
z$r`qzH;mJnnA;dKAKkQiMAP3$i#n1H>!(ptT59|yqD>3_DgZ9cwuqZP-^9Oiwk4F)
z#1kg5cNqM-byLFH=OcG$Doo=V?${A370whG!SvpiOgYWv<LKsj`2=T!?ATK1GZ7ug
zDFZ5INv=j)(0e!zu7lwCCPG!Sc8XPepPQ`I-oaNnhmp&<BZEPYjc%9UqUB3(7DY@^
z67c8q=S8qZ`#D5qx>4j_+YjNx5$eQg7wwid1ZxWx#u>kT4<cfQd->e=rq%~DX(**E
zEv!?!ST&$44m0fq$V6St_K;aHVPRzv%spAv)i%L#k+3cLb=h<rpI9P9BsBh}@;%$E
z0Zi+E<~%y=yCsp7I@V2VSF5yt!p!kfOQ#(NWH4}KNVLMrDF8)Ek{tSmC^lUR+80+&
zy=Ai0F)l`_Rw~4!ykl`R7jayuncziT`xEjur|S@~c{T%GWvlHv)|c2$TEE6ATp5j?
zzs%!v;+m~@FOf|#RP`v)0Cx&lMS=UBPlS_`|M)YO$c$z=coQ|hZ-5P5R>JN*-YQYS
z*>bPcTGOVfaT#J@y9w-F)+_Iz#gNPk0@ly3&P9uleunDrQ{)i`dNKZhIy!&2AN}Je
zYQ6IZF@bQn5~kn--ji|Be<n-*@qZ?ZlPVE&P?RC2{@R}X{o}C$Xj8cjK935`<B<>G
z+OtB#sCx=njqIKEGgrr0J5b`3kvN_6H;v-6Q)O;b`brOHTg=(F`@28~Hv12&a7v{z
ze;g-8wy%z*6`rqd7=nB^oG`8nCs+=(EqI1E4);}n1rja-(X}nR)ey1->)L3+eX*E$
z@6{ngHmNS!*FF?tt#1q8T;iq}DFg8kun9o96B8Y^O_pa)BoH@Bf7;4_WZ2~A%kUFA
zO7s1}w=A~K=YP`=sb~KUXMr%s!j1;Ex%iRLvF+npxKM;=z>|B_O8Kq1=h`(!qOzH7
zq14;F9Y3H|DQ6g#j8yIf^!tdy=btj7_7<zt3RV4oWz!w&nwL4&`}EO_r%B+q0tpFu
zBfqmUg6wLeWRY5EPb|=Dez6)7|DDmC<BQ8&Ta!bGY@;$Z+(xS4fkU1^OP}dc)CEVR
zhpjKC#<Q>DavC8AHu`8Lk3pPXc3J;?W>Vq3TRfoi--X@yhF4Soqi~PfAWY?jWNm)3
z=xEh5Fu!ddV08fNhCujf?{@waGb=D1JHY3?)aR}fv6`Too2qQfW*f0zFR4aS)O(X@
zva#s+PuVZmnxJOe5R%!^KoS{3heQsEJ<z=rA+*&_%%iIy2L6>VBEeKQv1=xX%HkQb
zm#LQZ{n@5f4xE+rr4g~2^B$l;7&gu)D6=64m<%i0(jB~Bkzhj2Cl-r!FQ;(su%Y_^
z;_#YGhZs-~E6GPh(+q-5ipmEUZEOrW22;Uy?a%|i-O?AaND_^4eQ(zg31t}DBF#t^
z7~|W=o|QBLA2f=xV}Xx-1)!!z3)<3}U4u23l3rlL6$yGo-;CF|SCwoM`lQE`cx--F
zhLI2J(dKC$MG%X#n_D|0_<q+Jnj^#NQ$U{v#hYF>L&urm)=u-Bp!++#?W9&kiX<VK
zB?82^BgCX)vEId(Pd>Ylr&dwMejUM~B%44FEcJ<%Gfk9|ijjZ&t-YESU-5RL8~DZR
z@a@(j%Q{#pyl_k2ZNa17@bh2Sr~dIStX0QyH^x0UZlyZuS-Gb}nFc$de07$uYvvre
z^e6e3i~`p7Kt`@?+||14P|Tw5b=Tqb?_{;9Xvaw2#y*5No2S6Ugtc_u=dD#vWVco4
zmusL@<iG5p8*@`L<}!;<zd!$=)uc}Z2@hb~Td;3#eYc~Go!3`TB<7b~J&j^y_G-5Z
zAES!f4f*a56`n1Ph&!nDtbR+op3vC6771Zb!?dye%_vBDt?1cuO;2s{^r`d@Eia6|
z?QI+!SIjX3Mp_!sShvf~U)fWg(ulzp3Ly%t0oncPUfZ-ui-%Y>Nq5>ptjHd{nzwdS
zt@bP*sm5$`o=JA>H}O)^4;QJMVS_ShcweK{K~{}=qrR|*CTS_xT=l50pnlzW+?wkS
zT&Js48*{W4*~oI$&Qsh><T8T=tY3!>zV*~BP|D<L^n80+B4fsVHtd*V_;_z-M|W7*
zfU$?O-)wCKl-`7hBeffR-JC4!ta4E~&)RhA#&pe`t9tv%)SbrFxH3pct#9iopyB_g
z?SEbYhWc~2Bw8}sDDM52vBXs)=v^?n9*J+d55@OHzu8nj-Va3ytW9N@*B+T1v){p%
z4KqHjo^)2@U*<2vSK?}#4@Me?`RQkx60-}wta@O^b*16!9r{FVU;OC8r=dClsd*A~
z<eY`?@6kgfRBATRC6oJbCHJA#I!*{X>EtUMo(t|DP9lajGbxzY4j-%swylULw!{tH
z07qsEsS{i`=xt2!k8k$6Rr<+pVX!vmJsFja43yKR>~4_=65?g9Yi%K8v7NHW+YeUP
zv@OTTZyobue*M36T<HB&Fp*Ycd@CM^kZ<?xyU2#TIcJ8Gr+UQwSy|3rLF16qys2Wr
zw3otZkv}aWi4&rgcl`q~ROS{61qSo1?OK2>GZaIE3Wgdt$aG>k>5T|}G92vwpxvpX
zkVUi-tsOTe0eC}d&s!7gfgcZw5fqq~k7(NJE{nBY*C+trF2bH}VtXBLCcNMMwsgai
zh~!OB=DXvsk(U8K5|6RQe|OZO?g3|A<>)X^%c?KCdcLei4@{bNc^<7x=BnH?kY@U4
zm@>8RtxK&;xCh#6?Fi?_+^n)LTE^v8YtS94D-v~~as2%&!=RB92NpR==0R(pxVI=G
zP#GJVjNo9^{;()aowuy+AKUuY7$VcB_jh7mW_Mq+<`FGf9};q+KmKjGloshjsh%zF
z*&#wmDX1Q&jLeHM?fX4%Y&!q>3mqyC2-<FU4O7<Z+W4rC+-lnllU{##Q<~aWqyLk_
z*)vOqoNl0;Q`=WFRRrF=y=F4HDJZ(t#+|sj%G_c8V>^%@?pnv~;7~l@-uxEvvnoR%
zgu#aC)1WoQ(`_P1kKXwxlqSH%Yf0z*#O)`p3U)NwP?x0w^L+k^ET1+sT(`pQ#4{a`
z>Ic%ZZ_2qEGO8qsolCUj5W5PmCpG%M_vo<SH}T5+mFc>VZ@*wYk(NRB;qF~-;WNyz
zidH#2e3o$grEjzDcu3};Ki!Q%he!3DN3q?$D2fo+B>1fEwx5Q1zPrTm)TMN>X{dzo
z1pW1)K;6@iI($Lf*q@wjuE`Q;o;{v$(&8aKN3Og|M>NdR&dTWJlsxC&b&n}3@we(r
zh=0Gl>Gx8}Q2=s5_`7K~<o5-=^G#ltQ;tDSzg`NL^eEP2MgudIsvxd`Bo^Dqyndkq
z9>I_UaXC?x(<j+Cdp}o*XPZH@_h+BA8T`{vBSw7(z57n21!%Td`P3Bc!vV`1l^YiQ
zW;vAtFX#$Kbhc!M)EBxo5TMzyGCq?nzJZbTp|!L`r*_h-l*t^iJJS*6=ht2${6$VB
z*Ix2%!J6ZX8?67lBA}<s@6vLni-IrDV;0LyhBw1Vs@$wqc?~ed5*Od4^$I(EYnD4K
ziU@04a?OOkTx60UU@!tb9$pzJKG8cc4P)OR=}1%E%^t}{hYQsxm~4meh&H<Ew4iQ;
z+!C+l4n>Eu!bB3&XKr_$%v@0F4uRs2o77zna{-)RF7d?LJqYT&)j=Q~?n`?c?<1#k
zUFkKEbbeIF7cCL{aF|DbzpK<-_p^$6(&;CO1W#%(jE4_A@_vEfaY--JznEJKbO)Bc
zl(I1<USOxtMQ{*hE3Xr5%#CNpiLg}jl00r->AFzlp(GH|%%i1G3#jJ`y>PuHLk~|!
z>oEA@l&TD7#HDicv`%nx6cA|6dN$fc-rDS;tD35)fVHdJlft6Mf9r3pZ{C19!3;~{
zAh2Hz3(`Z_i3^Jr|H^tt5>iaw?@2TBls86%y2>0t`GT$dm}Q1|8PNTL9#$gaE#_nO
z;?WPTqtj+*^4Zj?Wp=1ALxx^dV5!vZbk8#rq7iW)yke(}V`Uz%3>B2veF(aA=jY5U
zj816z1A4qTFd=q%y8m&ZQR`@&l$}H4nJa+xf4d<zI0>_0t9Bl6q%YZ2KR`j&-m^4D
zd6@3Neq3vXUm5*V1YwQHTNj`PV5N(G9iY=X<$Zcv%oZPPICN;=)iSGIONl#Ze5#e7
z&kEb)-@^XnX~u0tGus`C;;*j_3Ks_i<Knb<jl8wc&I>u%DWiUfZ#;qz_A(<dv%9E|
zovpPO4|qd=`XJ+-{d$_)5@^5<sf~Oor}tp{wXxVcS+6F#%!h-`b?cm)C*g(jUxD0P
zt&bz~ZP#R)vbacH$N-@&o78?2N%j{{dOGPBL72B+y8%2hM<yedvKgmm^Ey))hfq~e
zT;g6D0i8!rF92^Z5o@4dlfKcnS&74G87<Kif^rlC^_d3jO7em*gGW-9?{02){-}DL
zfftlp(;a00&I1wTEf$cNu__L>sphe$34s02o)12@Szh>q;@YUdc>fh0x`o@_f@tAj
z^4X-Dz`nD^f#Kp!EiU-}vW~SbrudiY#eL<Y4Do4VZFd0Kb}5$Ulc2gPAT<-8u1!kW
z;{WNU9fyv(u=ESH;%C|J&&aii(=`*X9a&R1oNak(Gm>Ryy53(Wid*!joHlbzzXX2=
zV;l|PuiJ|L_#v<d*8>_5mL5%H01(@8T~E^OS&has>$=vPx>vr+TP`3ou%gus`9gie
zmY<@*@^F~+&&>xG+z+qQ^UD@Wtot6DAsiUku1I9JFu`7xp2ENxU_?Rgn>soT%FG)t
zWfdo0TQ{uhedr()$-Z2@P3l(l0;k*q|IJ>qJQ#ws?yHhX`P&49=n}E@T(=77Py<n!
z+*y7y9rme#Xd1C@eSq%GE71`s^)qXM!|og)xs0~2Ex+246QADi-necac-yd={3~jx
z5n?hy1qgUK085mnHs;enV@(R=cI3j>kwJQJ*GZv-#qL0L|AguPl0YO4nEzP>-R;f2
z>2}+m(#GQ6^#;z<=Y)3p->WH0FfDqds29wPc{4|G?ypU0BI<r<E<e3~lmb}-Q7@Uu
z)#~YZuGKY)jdoQDz^!!%6|u4^r?*>R*gnS6lm_yPz{Y<M&k*-)*Y!tm@ZWnt0y#{u
zD8Jk<2v(hynngmBk`yW>ZpgJlKXx;>p!RjC1thlFS5=j)_i+DDYNQX}0?4!~83|ho
zQZ=(YzTg6VLHSig%i*hI`8oeM#O4a>naBkYu-PhWDfO4A@_97KXbH=XA57m{|4p-&
z#Te8`UEPP2sT1BK0T-uXPcJzTQ`cJP2gMtTfbCx%tbf7qb~na5B;z3q%^tj&ccpK4
z<D*)!f>|KEHPc1pNR9k__xMtCpUe@y7uJY_sn9OvWj9X6Qe?PjL9WC%A6#W(dT(m{
z<lhHx8Ld>{ClQGB-Cpq9AT1W|AFvS-hNGE-Mp5US!t<>ajbFV@X|!dID)u?|T^L1B
z6pKUUElt906KUmM^^|8Hg<UkwCtl47h$MRQ9r>=g+zYg@dFB02dphp&+u+&@^ulUm
z{g(I#Gz!ZL2U6JO!fCVB?(EddCTRJzM7_{9@b{jCaUg<6++O1p@`wyxs;&owLzmMO
zmso+$`H<gk^$+$f-usq?`CDSldg>H3hn5I<D2|%FMW@yVWFEwF`6-}L;2Cm*(&bOO
z5wkO2#ue2y7<*T=R$yHkPI(@Vzoe3br5#@vztN^~kMiska=lkWe!Zp8dtVg035Vz-
z@1bf!000=&wqiu)G9AHh*m@;=7%Y%!tsFu%8R+8b;Vq-64I+7=_;p9~T<0Zt?%u8^
zpKH<8lW+NDJuD^ywK?i>$w4uQnVS~eJTlB>izDwdr9{)U+7QjE%RWB;@S}|4e@I@-
z9g=rY<K9Z(pM3L*7w=2!4``7n_)%I`nfU?j=mFu&BjW*Eoz5LKY_xo0qF%s?j=(&d
zD^i-*B#$tGtW8mSA3Co)BJnwH0<ovcQO66Yi#sy++gknP4F3W<+p>@ZT=KxBxB+QA
zLa^s#uX{n>$iC(Sy$13)OCZ09dRe`}>F~9y1w~c6`jfx;=$erz!)k2=LvN4;7f1os
zCe3z6edp9APtDwnaXF>)o-0~Ugw9Y^9c?VAYwYR4{NvV@*T7BeTFu6!kMq~Hv+Qrn
z!t?fC_@KO(S~Bjp<_%mp?cZ1XSyZ6+=nh0MXFja((&WUqff&vLr0j<Iq~vNH6}=pl
zzagdc!@FY6qFr@>8fZvBJlOCBVj`T_!*=8&S*rUOL-Eq~KrZ#(VZUOS@kEE<-FOJb
z;3I5}M{g^Y4JpqK`xFwXm;0alykVgvGCBunxhpfYB|l$#@BvYW@o-5sgLPQ@D#?eV
zXKnARr2k}i;pZu7lRhe@R1BN*Daf>s-wwc=ergsP@TC>{G;Pp}WPxv2g3fX}z(UXc
zbzbv2V2J}IBKHTT{Fn}eGA9CmCAHe`Qi=C(jV=^wPgwh{GMw(d(*Ah5v|mUBdzv%b
zuSYi>DfdLUb92rY`9Xq?)}}oZY<50(=q%hL;8j!*FLJ>C7c*IU#6HsPEA?5v*Pv;X
z`U!WMrgiI<YuRzHQ@=&BYR}=G`pf~87azyMZx}P`2>WOCd2e}9LZ1J}pW$~fwBL*t
z*>s-&!XC*2kFi#Nr^rM<n{B>ZD{HZOFhQLX3w`;!8KY<cT#W@cwq<0a1A(0Y;6x3r
zM`8iAP$;O;4^6=43=ed3kIK4K58cFtAQ|FK-Gbjl{0Bw?R4ZiP;DQL&85@n<=R5|Z
zW^UFEB_k4Gy$jnqWaGCazenhkfu$6%_=S?cqD?YSdPI~@l=aAod}0jp0`F)&+e_PX
zO%TNPI=fpe%W`xR?LP7lIh|PiYj(S@k9Fw@t}&K2g%_^{%4y*t8_NkLTiB`3f=Fg8
zS+9C^_{^bhClvi2C=V$#AiN;+SbKXy0dFr0^Q|A++V{2To>txktXA>WKgtAo`oD9|
z>ip^%WP$ZmT*j|UxIURR0|+EL6360;&za{AxiZ?pk;lBVhy#RjYT{2N7-Fck17UUx
zWk9a`)ui?{`-gUW`Tj$O7{5IL441$QoiHP@%(2gGFPMSir}AAshnHjyf}$|Ff3D-t
zC0RXG5~}DinCEW|!*duraA6h}7;OpL4WSRf4M!(ix75Qs?k~UoAU@S9K+c)2!;%+p
z>VkKVM(5Q^&!AtcIO%lBSCNk3&fUbpI@)>qDVzg*PEOf~1)k|FHzE99&&8R1n|j4b
zPfv*&mlAGTeCth*EdsUr)Y_(M%MB-v3(%mb7P&;R{-?jQ|M}53DuD9fKy{CmfGb&>
z@0>u&`zw8!FreDE?!{*CBolzQ2m(MvCVs1d-%PuQXCJ?vya(*bvF<q!sKpZl`_0^b
zb@@bk)M6yx-tc|uYJU?|I+cB>SrL`LrhoPQE`5ADY;pM1Am{UNAY~Uy!9}H!{}>~A
zGeli*cKCrLd;5C(ZR6*D0iuqD<uM!!8r_~LmCgl|;NN3E3~3v)3SQdIS*)*6GM_cA
zwOD+^2}bAh_wu(iru(LSZuxiapWr^Dyc>k7KQr2%{b=rFn?WU_bJu3A4EZrtq+6$B
zA_Fi)AA!7B`r<O7BNgxDe2sB$;!PTuWx5JCBFo1^!@aH|s1dF6DVB`@8e5Za63Z|D
zS^WCI#x4%0CXpa@w@JYp?Q2n5SKqc#PpcQ7K2JkV<AVF=Nk^-vTQ~1<z&c(kIwyBG
zm!{}c^~ZZnMEJ{~beeRzDvAHEi=SDd?x;+2nU*I8*w_@|v$`;k!>-s(_yZ&Up61Uw
z>wl>3GOCF&OaC9}*@jQVr>b9LYd9=aI}KPQZ#Ed~?wL1FC_B1QCEIuvk-ZJS2b}Jg
zASh1j@lJ1p#i&1=M7eqA<vh{g4OZ6PIZ>LC;}_=C79ToL8(KH%!`Zaz(Qf)MyCTE~
z=DwZi@br@FX7(57mj7HXBjX(gYsH6sYGKzjoJ&4dvE5@hoLr|iTkDI)pBMYw$ggFK
zKT-MNSdVo{$I-iyNLC3ibpPpqww<?vT?1XG2m71ZlN!tbuR>#|o=KM*iMN-FCNBBu
z%-nD65R(9-%fB%omXTtadO`0oRzA)Zf#Nu~iV=K@%cl$7^`=c4k>0rC#6M=<=KK*G
znA(l2prIu6SE`P{>c)(l2b&^fz!p63_Tzo??*k<~?hi4t7v|K1#FOuxDj)rw-ol_!
z0Pg!fTHX4rRY?aQ$U}bt9+3PZ%&a@wpsCu6_T|gI*H4p%kyudjXM*~4_WFkwnv@};
z(;-@``z_f>L;^i2MT;$ySL{+{vM{>SG`h`2hV=JZU0r|j1+xXV-D+8Rs5ocpXT3S5
zvJuCqAPqgH$f_`H<(<cSjW`LSNw89>-X$V$j%AAd^k)Pmlo?+;G>lEj4tUB)1+|7;
z{)s_h0I+-O6Zxgr3k9k8YM!%_u&tA?qOCl7@m#3US0F6)(gA>k6TgjaEyLI3P7L-J
z80|^`=D$BtO|EuEFfsLAQTbXI4IFom3GF&y*Nn$T71zR_yox$AgLL%8af2+*j$m&#
zo82}|zY3&Gn;C^#_U{p{^ExVu<r?^DfeH2-CR1VQ{uuC2bDE^N0lDn>0rEq8R!Mb-
zv)QZiZR-5gjK*?A&yFAX2wsAK?sOlB46?Oe?oX(?T0h<7XDR*#%~T`t6{(3za4!O!
zJx%lB5A-M(^bFcbsq9wHPviE#6E*xQSKBH5)iYN*^kif<aEkg66hHzR=rt>U1f`eL
zNy<BZQ>B^WiT93LFu%GK+tbu7nIE1p>bfzhuaeSv*^^7>0N7g$`nLdufVuTeX2y5Q
zhksxAkrw3HO8`s!O_+%H;LntY;|fONafcqYZTqF)#r}>H0D094>;Gaq`C9u}Pi7{T
zV&L;Ck1ATM;Xqq7A;~28kDp&%rT4zgZ2SvZ_tjauQF)%vJqjkp;|?FTY#0S_@!U(s
z0y`n$lpDXQ<ZgbZm<iRbUbwE6*8IQ(V`IQc#hCwUPaTyUfdBmd8H@q3epp1~?NuJs
z$fHcN0ITdmJFl2=)7Q!lI5XEF05B9MRI*UMKdkMKY})1eW~Jci^H*<(qZ|y|F%{gs
zIS@cGOe3%{A@7+#og+z^AFpH9{pHzW%&*8<%e4AY`NmvNI#{3j<y3q$u*bSi8-ll(
zp!WY~R)PN|5EMRp3wwCQjXW(*sE-Nif=TJU3Nu=P@qM24m|(O=tdu#Ete~qQ3lacN
zm_@C1(wN^xI@(7n(==KzMn9VQjOq(FNUzp+N{h%=TMM>7kjz9AX$+kX3fJjGrOIx>
ztNpMCB($RZHAk2bJ9m#$lQYznTd{rlKX-zAhxSUpdKz$E6w#FeUi(63ATK%@L`@DL
zJRs2tXd~EMyI=Ryn;{0l)L$>iA&@S4@m=oEQKt?c4SOGg>5ZBL6hm2rYM~Awr=(5L
zj#9%nmwdeXF0zDTHbaVE1=o=K_s7T<m&Z!E>&i2tbv0PDROiNKcBH!m(IUxeh|>Ob
z<Vdytrd0L5YP=^pp^boh1G*8Y8E>Nyl;Xnwoe7}yb8_}xUk3T4)ERRnST}tgeo-L|
z0*aiQwH^&3b%mfae(RowCtz;aErs~TXvWy<J;~C#7V|U9u<lhN?Kv0n1WZ^FIll-m
zZBqM&#jukgo<zQApV2bAz!CPhywiVWh|foiVMRDjZk#X6e&vtURtbyAhb9NOw`Nag
zuW{)bpFOer@qEvAG8w2;{?2DHY(`u)mDyqPDA#q9Y><S6CcCcy;rCaAp4z7oMlgRf
z3o(VF$dZ}x57pEo0DCRUJr6qU0545dWGNHfv@~{~>eJN!6o@Re5J3fju+Dfjd&8aI
zX=n`!oi-6?h9z(({>{Usz6S#Cs80BKE4uMpRl>m+xUnLq%ef7GO~TPy;1YA-RR9It
zy&7?i?E|~BC+AzuYJ8nPgn=CRUY}HZ0XfB199QKXVj)3`h=8?yj#3^-^z4I_yG5a+
zx{}p^BbKa{Q`F?jbp=zR<6X|4v^M&+Ey)imH!dFWEZk)NX2pFXn)A`mZeMUCb3&}Z
z(hY30{+#2VKgzn3<<Et(7{%sHK&C2HBouc$Q_ZiE_cm7Im$krJQoO;Tz;}br1r=E^
zvVZSHyDEGMuv+y$4PD-hTIp_a<n9yhFYJnKqj?lwSBKjS4&(8-1KZ~8G*QTg9#~Vj
zb`&}z2MS(`)~~{flt}C7v{$O(Us#417UGH`HXv>4QAKrI^81Q?D}DPsXf2p@`DI`J
zCLO_!cXUFnsPWdlcl1W?4;l$Um54V`ggoiIKQ4+}o5t%qwg9`-7_dlfK5$*njk&k0
z_P0rYgi!l(N<v+2)ckQ7xw)<|kj7FrUS<^a`2`3B;FF55I3>Mvv1h$}`E71DEMd0<
z`Yop9(If2!mCHZOBRUO3Se#gi8qhW%{_hjYsQbqS_^(eMApq||dNmh&%c`0k25dN`
zVwr*XFx`?xMfk3dqZP5>!1=x!9UxgvjM@IFO8;d^tcmGQ*>yI8oX>z*40sOPjz5Z+
zVr6K*ZcvkUEA6Z1&6U~j_k^I;y$Wp1q7e1fk`Nclp2QI4pHl351;4s5+8mb#jtnmO
zL!<@`_?wYPc|-tyO%*bmkLfIez8i2Yx&M?#3q#QBi?~<-pZ}3;hN^1>bn)j4uZf*l
zY>3yHFuU~$gqhdA>vsB>^;FR7(EyKkJxjggy9g}rS%|+@kCJV(V>}$iUjcZKsMGtg
z^b%)O%0N{r$~|-|XUNEC-4^-`jayYwzTdNUllrTn-n4n>;G7(t9mm{uPY?0e1jdZ-
z(DxRO+yu<-kI~=07zh3Hc-_HwT@|{AR(T?vj*Vs67MlgsPKEV9`rSJq&J>+3GWiK?
zEPsbrx}c(*98%=VHj+CQjk`Jo&rV}_x;%Vma7+7~fIsaGPqglcApjMII=(OSW{0Cd
z0;Le2A@(YUFV?AWePwg28s|%4h;Fd>#k6~CdfskYLDI!3TW>|5J531@QW)od=+Ek6
z8sl~d(a$(^Q%n^KiSFO~VMXCPHaS2w@C3RI;LH9)Am#yKox1+c5&8!D5pnfDbpg7~
z6Q6*?-XTSh^$J+b`$-DFPa@-Wfj=HHNdS;u?xcxmlhwnX{`3ROZ6eh%7Np4c)Yb@=
zo8Bp25<!B*st23?sUrJ8UhYLzZC1%bk&5PxeRV&vnfr+opOb{s2+Zct*9~lIZ+!Kf
zSmMggsWyV{-BtLhh8|*-mW&K#{7+lW-T*~C^;9lhT11L7e{Kn$OkR*m2D0ZY6QHw(
z)0-{j)oZ%bJAqiysMcZ^$w9qX4WmbdALXNdoNpYPc?kV<8Bgt;9P`6?C-68p!;6r4
z_WSMps}KC0T@6Oy&-tCbHgA4t$={Z>M}|4o2Q}^nqzTnvph@hmPXTMpjCGGoimoLr
zPhvx!mmH+(%n#+IhMe_xSo){$o?IP(-Djd=(cfvj`>LA%VlNBDvgTOM^!TsPW+~oz
z?w6g#tq&I5*`D8TZJ-YtBwbXq8vNCJhJa_CR8KeS$P!@1V|WF;0w&dWQ*746sk*{l
zd?b8K=lJnx1~Y+U-;&Yn%w5?d&41xz#>A52H~RrYY3tK!fjHs1LUg1GJ)Ck@BOufT
z6I^Ku8VS%sPLZdmq!7t0s($tyM|A+FccnTG6sF592Z+UZERHO(jk}AEUnhxc6=D3(
zSigWTkY-(p5{RPnc2DI$KY&;I0u%dk+*sq6+r3McoFonZh-s7C7n0RQ;!42s<ffj-
zTbN`%uX2aqR+u~YKw(0u&e4vs^fRC4yx=CMj2+0GnpF@l4uOR$!hH5UOs0Im4lG;`
z8QXc(*I35YRch1<ty2?9dFKE7Da{_<3ajhOsOqqoWb7hLPqf)1Z($gWSaQ2lrsogG
zhG7^&^%y6SM}vR{3=+hxtN$k#fE5RD@YQAAg;;>SkidK%)4*N@WM&}xXRIjxZz$Q6
zd;<;ag$$lLkt$7-wbRC=&bCFy<T7Fpw{`1W`WXdPXD31?=D`nhBtWWuZy}2@`)${1
zZyBwA<rCuMs;<(+u)=G|(c_5Qn`E&shkG@uZpma9=fqZWw&77`K*@kczTfb6CnNC}
zfLWAFMmz;JnPiou;Jjz~V2AxEIQUN?;Q^B_lU-D!8s(`6m8=T+%?kxZRVzQ6xsyRp
zFz3NdtPDp$)&$Fj{wj^D&^8+0-;w2e97$M7eQ#zCh;kONPp6aa`7~GXr4afpxg;hL
z%DuA4tDNq3q~60WI$g9925qh|Asva@#msb<<h;eF3X5XDZQX_+n_jXfr{~>2hzVG>
zq@i(#yYSs?+w4GN4<lv{->0M}>|~5wjmUbqj>L%WqTVR}o_}{P^?s<}3*dG60LcH;
z(hn-51-QF*zOY%dXY8PA7qb;y)j5((%mbdmCxwThTGx~!znN9m0VbR9Y;s^<I)V)L
z^q${*%=Om3v)4;hq%bHQV~%5r@t<ou;J*_yTc2;h8>uLbzN>oc(Qg5?VBMt91<4RV
zn}f0H0|nHgzKecvJ%tBdL4lC+<FJ~g*g7_UX9m3X_L}-`59kR+{H067lGd$*Rh~QE
zXOXg3OV<y~&|N4C-eG5h%s>O?+e#gXS=UyPl15MR>fReWcFNg^9>w)fx8|mpV6}j;
zR&IYFB3!z>z4<eBZH2S<RbCSF6fLbP5B)u;Q-vFelCnwf2aM9;{XKDTEeBIZ7B*Oe
zl%2tBzNX%<3MCf=Z{^K2w_<<uZ*1VZh@wJG5AOjwXHH(U(L6z>Zcd3d%LI8Sw7uk4
zNqh252dm4sk#+3aEOZmB3(oae$*r-$4{pK~wU-V|_U99beW~1}8wKChcNK-KznWAq
zHV5?wZpBs<073@<I0O8#yyYe<%=DhjI7`kAR{)`99T&}*zND8MSM+D|r=vhC6L`@w
zxJ(0;uf>%3=q3zOMt2La@ki5b9!U+WF2*<|xA`dbosCrcXWWfHdSFxZlXTb;^KGJ>
z;{XG2zLnU#zoT;3$FzH=Z?pEknL<w$a@z(;%-K%`*X$Qu+n)U!>2nT%_|opRg)V@u
zR5e|=w^VGCi*>k;-Jy5U!obZsHRTR4@9wg+<mLlOWqWe&zPsXMCd7vpqk(GjSb+%m
z^)3LQCLmYhe}?OvkQ>~jbpq8W?{Llw9EnReC(O8%v5Csv+Q)QM%iZS+m3l%p$~|Y^
zc*?RE??yQCwfRf{P7q6fTJLo4XrQ4NT4XMnA=6pZGRoOLvR^~%Olenz#gSpw^b&jH
zeRu(ms$oBdMkPP+R!6+mag}6q4{lVFnvOKyjF*hG4i!bf5@skQ;EIxG4DNK@jl<KM
zg3QIT78AQlJ@39KI99k@q$_&s*ed-U{!27~ASn$$>G8~=pS<tdQ>wNe@2Po1q|Qz}
z-7w$AclLA5>P&!wQn&Eo8LzcM<+smLT@>ZsWR1iF7=y*t0cP`<4QFD9zF70OW``T|
z1tICBMn`!vK~0Rzsmk}alI}?Yg{rG@3)6J**9m>5M(;&EWu9DihJJOb=44*uRIxSu
zN~Tzf7YvdEIaI^qAG#$IeJfNCdhIs6QCeEbFF<<WVgq8p7z?1AUf!tjzQj?btio_7
zskr4@aIt&RY1q1yDl#%2+K}-QAcuE9+c*D~zSyF}i!NAbRu_fYUY+vz)>7cj*NXV8
ze|ZkK`jJIlNL>Tw>ixa<?|_pOI?h&!XE8136$kX9&JTylDbFd|pdk!>?$iK1(0Ck<
zaW!*0u7CxpbhY24tV+8Ira!USNaUZ;m_c4MU(cSnBeO@^f&@~|J>x@oC@(AyK3&#T
zc+*0=lj|rV^B4~&3SQ^T6e;fW1VURdEyM*LICCs$$~Jz8L;sDT3UI`~bXcvYzp)dG
zyjZT2tq$SCeBh&q;(5ZtqWxLkHt$qgnRd5vlW}331_c|u;l)s>8tB$HrjRV&j=2L_
zTe1mic3doub1mI`E7803s*;!f1#T}X@9dN55*oN|5=S7}Qdgx5BU?$Z`gd)(Vw~jd
z*Xz%Wc?H0VAy$OtdNjBXbdSpCJbwg)HJ-mebSACK?XYXu<!2Fv0c>LuEiu<4Q3r*R
z)JGmju-ML?!d$&iuudbIBvcF%r<e(kddJN!=)C-537Q5QyaG)8Adb}ZJ2Q#Z^>0~f
zInmB3j4#}3RV6q_mlK)!In0!M7mJi)HNU?4%%Vh^DN%+ls3n;}s!Jpw;agFb`S(rf
z(*d>5&r4h@zUmSmH14+uY35GYaIgs1;SoK`2fiH#?$ZO*TkeZ4#bH}bz~qo;D@XNJ
z|Dg~U_8AW}0l8Y1thc2oVMgku$}D--@DOd3elxEbaXd``;waJSCgLdG?R%|d(-9s(
z_H~wJ&UYR3nXj>1(N;-NZDTTfi}%CL<}(^aWe~-KaI}x0c5m+jVxrV_3W*?;jYHHu
za0ls*=mCoH@_2%bv`JichG5r);eX7KI>kRvZKOz|076;Km-O#$Kj_*J-8*AnTCR{z
z?r%!iWF;rITr;0@mZd}|#bRiSF@ClYhOFPHs3*4nsx`$9D^|v)-<t_WY`#QnX7iN!
zOg4LuLO|Q0vmL0k%X(B~;rz=1k9nHu{$D9%E^QxkKlu^CPEPZ;8+8gv<@5e*ZNxPh
zIWbpZuK14|)=NHNH&R|OFV5X7oW?IAkaU$%`L~)ydPoikI%L)#!VSdu?q8d^hDoa$
zOKLqs=u%Jm4)$wtT&k7kMh;4bJit>AQ_p{>!B2jC<Y6?;KZKmCQgo+v&+Lgq-^u3T
zget3n>~)1^5aL<N#8JKk8mrCC)S&Y-SKd1=MQtd;M!^p46oU`cAT##+hwz2zEt#z{
zvr6?&V3cxH#@u!FnMRU+5m5p;&w;#*%0Cg7h66RL&si>|Of}bMj~`sNi)g+1iXH|d
zVBj-gWUag6jshHxQ*m@W{z(;WY#=&?D<lZ6ykHyIF?q_Ao@eJVw&O$+0ty;3=wJNh
zlTzWHhWQ4aty%)->~I+<>u@7~qk-P<k{MbfV#l1gbh=hxTPc6V4`6?qt#EfskYq{m
zVQHG#1!Eb|nNc2@462m?yZSc|5s0G@?fJ|GTpFR!k7M$@E6023CwmiVPYXx5dAm(u
z=-xvo4Ohyl1~UlqK@8D)vjUO2FtP*M7H=|wF&szS^L8(-|B-s{t8(25yMmhkFCFS-
z*`$1`CueWIK4t2M=Q!|O*!@`7HAiGwFU7J12@EB}N1utHd9-MNf$G_lc`lTCvD)C~
z8afAgRpp0w&t=t!EBQms**cm2<(l`Mgc`j^h(exASocR9<NqKPi0%0dZTClwOxAVn
z4V9>o5JY&lW=sD%a$$y8Bj3l^k?97%0rqO6IF@fSQXyxfbWN4ugBggodbP$1QIihP
zFX3eRT9y3sA;Cmh6?e59TrxBu+%7vCSinu`?Jy;6#DE4H(Vdx*6_o>dh(p!(FMyX+
z!M6CoAlrJi03X>MsR6LRK#JC2r5|kwWRm$M$3=A}q842RZP_16`xII(awvMb<4k03
zTtUwMuZ#&i?fo|ZQ@{*UBU#djV{Cm4a>@1F%x*G<V^QNxOdayI6;vumb_q}U{0@Lh
z6+?vqV)fFZp5iKZLQHaFcQujj=O_+<c8m|WCf$our3&)~BLIWBu$*TK7p9#*siUJe
zIJI^+Z;U`w@MY{<W53|U6vR<Px0S3K_a(}25L?vOg#7~cpr=`Q9@InnPgH~Ri7uZW
zKU}gV#d<JEcLBrVyr3Y(a_5QPl!K*y_;5vSUPB8k42%i_)=m6oti$NBda(%|7>;m{
zx3A)|DTv^$l+PoJ+c#8l4Ub*b+W|`Gdk({N*(D35DN5uYh2qlDTeBv!e<!NlVU**+
zmEk2by@-9qH&pYqbJ5io!Uw!%ROk23_3?IqV&25Mpp0zsn*D|J#=oTK{*&%6MI?;U
zZRtbuyxxSYpvfB8POL-*is9M%+Ip*pG4G%{o-jt4Sw>Kt-md7$2Q2#QkFSbNfAqxT
z8yIomE;LEc7l?i0uJKg>R@_9jF94X#h2uOED5jX~lH>GwUm081w&`Q`uG0ib>IJfe
z+nGk>^C{@1;lljZ-VB&7`o)8nLAXylDZf1a!j+ZzQ0AddzglW~6EoGjhokFXRcYRF
z5qwdR33|=@TkzY${ca+ed(!W|y)q>#)!!36ez#BPZa}Ey1_r*gCUyrbign$T$HY-r
z?5QIfC&dOR))(2{Xdn>CT@b;Q#OykE7E4oZs>%kt-8-_HYHKyFSSo9j6`$Rqv7=f|
zzdd9WI$o@_VA$WJpN~27aaW)#GnHw%{Z7nOwVS5LzxoF`08j27#edc$1gCtnf(|t7
zlJ>A^FqxhK{z+*hmYD!w03U3`BafU&K)J-S+KQg9z-GQ_!MxPQi&AKl){DV&Joaa~
z_+Se}joorh>9ko}*454?M~}jppGRdLq1=)9B0JEkzdyOI+oG$x?~WXGVc{(Y{5s}p
z<awV&vS}W}fPBTzUYQhzi&=phvw=LI8n7*r;gfz)b+g+Ob=e79iR`0hn(ZpUmUuES
zx&7)HeT(bX*xelLP}~E$N)2ek?BET=gQL;BtijVaMk2BjZV>mdX#cIVbPSk3eRkPl
z+#EUXd2{WB0hza`1&&O_LL!auSNj{y+0Vt6hI}q&p6%5?Mi~1DM%|8EAm@zqMHhYh
zy?0_|#d%?3q<7QeD&cY<wOztSF5J@@rd3tFtmi9{8Y=2yU~=LjXUGdLNl#cwEvIT)
z48DMj;E|iIRwM~sOB{6+3tjYjvD4IM)^bdUA~nvec+^YRk0j=zWp}D<JZ;Xd=Qf-4
z9R3t?T)3N@%rbN-f`KJHAP}PUzM&=JOGHR9#_q01sezYsTV4XcW|ZQv2)v|4&@hMx
zR>tS&JKLb|WrC7@DuBFP?;C)n);yQv78Gr|KFla-5d$ZL<u@b0;vrM%ec3WDPX=Nc
zwC1lvn~-1WS4Sp{qTMj`DtiKD#@N9r(d~Eh+29Yn`UWrq1a%GGhjYMcigwcoA21OL
znH%hBi={G@${)ey+)p|fy5d&n<5ar{*~pn2pTk3AX_6U?F1tE}w#p#&TbDm<soxSz
zmonpB&Y&z7YrzlJaX1V!Bua|c4@LH){lu=4AOjlY>%_1do%Fixxr;&s{kIWc-?r0J
zFE+z?J^m8v;>Iz#Qx)e7mf^c@^~#_dQp|hBT=|%+_Utz^li1aIis?Yk5tMZn!gIH8
zk9uqNSLj$`XTRrI$zNaPovtrC=zX8#kJ$G+m7{i<i^8tR^7CaE+v?cd-|WGFd1|tx
zjK|t4R^$}TC#~c&NZ6^E{Ws?-t#~FPoba)TxLBix#|~Z>fup&Lz4coSKWL8HPd2xe
zutJ?xV_=rIhBc^4hT6!ng|m6RbQz@0W|GvP$kVF+poG%y<YGPN^>`)XO>;qblAN*%
z_tu~x(7J#9ADX5EW>jS2yqgo>Z1YB?g3A_5F7vEXOjt=BGiLDwvWo$hoZf5;){7B~
zN&UXE!GMf8X1qvv6J&5}ZFjSWAjbW;pRK9jZg`O=!2{FvnrLoEKz!gMgc%9Qe%+We
zn9~P$L;>@@XJ5PbNq7fjap*e2Tukl;9K)iJ7Pi;O{9iZV_YLd1=B|-PzXIA=OD9~k
zaokl@oONTGP;PiGOE}29YJcWt=hy7@)|_&4Nh=7s8l`Q5l)|`&l`}p-t3pQ{OcIP8
z4*L}SS~p&L{Wohhq8m5OkfSF)I!$HqFmFX8ci8;oJlF2=@9L?F;<=rI*x0M(oUl73
zntXNNW09^W_KFEU%#g<fafmsKdsw1#woGc55?hl*nA*&j=WFW{^MG-R5pFP2TkCWZ
ze~ZP;s53i}a<!hM;C!BaY2Ng$vZad8;bw5nT*XHOK4RYV_-<f2Z(8yED!?)13>VTd
zfcPjnE5tNyY+heX>P?IAwC)y$BHIQW`Yt0*y!WVQu(w;-<rK6Yr=V3c(90jeG}#MR
z+f_LFFwQn+i`XZw-30;VI(^|Wpy>Ru>+78qCNkb@;;bo*q4~~G7(a0|C&1c!sIp7%
zS4ft66y0}m0JAR^cZI~r*8D`CZYmwo%S8$sXUuuu#wt{}I$7M<7U^gWq^s!6X!~f#
z7`f&U{nuw{K;rbiuQbXLSc#Uc1(I$$e2|~cFyQ$fx;K&1GPeTbp!-t{CRm@Q4s{tK
z4Jw$3WhteG^23DTl@<$2*0JTRa7H--!9}a<i<N@3`p&7X#_jrBwOZ^Z2j!yyxpCJV
zivOM?)rz;gt#Wk9V8H+{j7-ZQY;s!6kAQh?8mBugebPkTc*d+VS_u#BupWKmZue*t
z+Sf_75Oq2tH%KWG(Ii~|Frbs6q*r6)x*N}3j0H5=n##BkGJecFC7#g^*h5>tkCuWL
ze}wd0;Bi6qhc$~=OP4>)XB^&gbHJ}Ed|$_?#dt%otQ`_2m@f|I8c$ZBetPjOb4eTv
zpY%dqj*?Q4eR$YZgkmk>?02mv#sY@D!GQ^)8{>VvBBRq%6`zpS!Zm~S#?DVF1_7vr
zkO-VsE}lV0B37nW)gh*hLFg<f47u{!+?T{5<^dryil&+0Pg_kT2FwWYlEwY+1!CSc
zsvEONHbWP?GHX?mN4zEHJY7h((#K&qSpJm2d%R)R8+Ce1iWh6Usm%rS14KJIvWcD<
zHX1AH`r9NT%-bh7RfSN#;v+UbILd*Q<|e--lC<31pqXlq364g~a@Y6FUx1u&!B|IF
zoAQI}3%mc!C42{+H!#?U7_9IL)s-LQXxaZ+ht(H9lkr{-^y>R^c;kF10DRD22u^}8
zS-8ds(R1scsg}^?S|-;MS!APj**n9ISy`4d6sz>Y25w9=2w%X|<@>f$#SqFzcRqb)
z?oP6AV6z?JC?My{n=SI+Jt6m+TBWb6$`8i&AA}<+@UgIB!QLMg2)s5gcidK*&0&+g
zyZ?9Rs^SnxvD0yRzw4(3N8c-y(ts#_&}(=(vt92+!YuRKmY@3icFR>ecaoH;K+%S$
z*qI&?Vl>CeYbSEC_Y-5x@oY-&^hMjzT)P2q3kYrBc06GPDc7$&oMF1|tXkk%e*$ih
zTr1L$6Q9r)x;%i4)MNu^DHj%MG1NOvyWdUPAkf`P6_uFRu~#E8GS$!G*`Z>baFZDC
zr|`m;yX-s05xsWvTf2RW5pgnjxemDr2AYV%{p(yi*}EqiKubq39XYTWA@VUiF{ZzA
zJ!5vFS7eo@4f&SG+QitYsJfS9R_G03j>BoQt}~7`w#61bHKsi^p8U4*B`v<s0mkSN
z;5YL843E+junJRHZC>x*H7r6xuCv{Q&0O#PXl6HUC6XcP?NK8`t<r0|!QQ^r^PW#(
znmPP!u%{_CqsVTsT{p~cUz}XIF@Z3>it`o~-WM@;#vo)?fr$aMwUd9ZDXmtFH6=@y
z;Q~T^8E{ynRAD=Iq&s)DgbCSoS<kaTk8N%`-%UA+L)L20H!#8tmu+i!;h*Hj@qo{l
z{o=-Uu-J`WNwC}6&bHga?nLG@=<Vz34Ztnz`)mC~Pv6c$_YH-$@xc<Yrng6!U4aZ;
z2@v-vs`4ql;KsY*^d$w=x_HK<W~}%-P1`BISE;Z}b)UC1vEz*2?g_aqQH<g6w$Y0e
zwl!3sHuU-R&g8IyfulgQnh#FibL0@is!~xAzDH~Ca(&mB$b)Ad7UQqGzdwkQAC}Op
zLp7_gS+TM!I<HvnTFYH}+H4lA(#t<LpT;+D*O1d>hWlL^KTa^<;oZXmetuUIZ}L$_
z^mJLZl%%r!Cpi9G_kjjyyu3ydR<aoORgThzsOS#-=eD+-o~8S0#(;Al?9$ReE$Y%4
zbYfR_Heb;0Ef+_G{4#3ro$cfh@iB2bnYDuA-1RNDZ&7Zmxw(M3fWuIm`Z=W?OD#Aa
zMI0*%(@B|2f51F7DMdTTJ`)AoZfPlMIb0%Da>#48es!WP_G3im?q#)_(x#dE;54wy
zIV*>u?TgFN>0Wxs#I6f)Y?LA<6Uj-<|M*0X_1w5^0zUXe!ccYo+E*-M9X7fdcxP&i
zUv9~Lin%INj6RI!l0r0gBiFU)P)ad*%onaPw=bg75=;je_U#t4>;{!(1w`CoM=c#Q
z7<0Fmd5mN0@$L=AKpUXMuYA?I{0tD27_F#BJ2#y0{#7YkfvDl!L!Pr_yuzUm*K(SS
z^(CI+_H`TS{%0e398kJi6u3eA|2`}uN2eJdMZwtQ;|jS!i|8`+?Y+9Z_4eKT<36yv
z0K-TYDs%FlJ1$;5Ay!G0I7;;K&BMC~eAM6F%NqywDOR-N=-es7cqek7wbY@>L*{zf
zp?SjcPl|{(Pq=weeU6ui0nOc$dV`mtZIe2AtkdFoR;!29!UhbyPOoB(&%knYBb)7a
zx485Aq_O+wMk*b3Y++#U`wg^qmEJmLULK57mf-0g<}gsl_9|4ofU}#?-rc?yoWYBN
zpqg4xqNlCO<hXa&TAQz}Qz44ma(jEO(RUX>E<<RHIR*(i@urZN?ARjK5p!0>qhi%S
z#I52{jq>f?TLhZQn*Q8+O0Fa|t0YHfI8CPu@xE0iC%pR?XF|jSkFJJYof;i|`@0LE
znG@Frf1&*Jl~%Huma<s~);p^V0-67bVHi-VsDisBj9D*7E*K04B;UPc&|1^hY`tEJ
zC`@Jb;&n=JqnB%@`Q3F;Ow$XvF^)}WY*XIRY!-u7+`4957hUp-h1^ZO=zkBF3_WHR
zVuh1?dR9~i*K;UW7{!p9DI+{%OhgQx-!(CqW}U`vOfbm?-<5k`XjbNDSYwBXPhi$b
zTzMj=OlyXFXXJst1&meeVp&%|I2q{alQTqY2HsuO36*36frxwMq+h9nEc;?(y_w)`
za*@2w|F69(|7s#x+hI{=29ZIoB1B-20K>k6fe47BF+xCP-%$+0U_kaoHbuZ0A&ea%
zAe#<IKv0m?KmZjrB*-FL3|mkVkR1a7lMuMA_doc~`OdvRO#Ra5RQIWV>#et{p67Y1
zPb+-8`%n4D1OIs7|IGuHmC>z`R9KIz;uj94>-ajjPW}*;cIr-w7c-i$*q(9n&i?iw
z4ACz2>H8LnBDcdQbX`GA*S+nL*+#$LI9ZR{>OdELhxL7agE5@}lU^$5JT`y#%d5EG
zxw>iXN!$(xy2#|E9oMk<hb~?1X}$pu_H>=3X7qAlBtxoI@l%QXaq=~>hPO&#0*Bej
z)tzEJvA}lWCU5Z6^(B5<m!*$H)SZ^jkbVaO#3$fQ_?+KxC%xD=!2gK(ltob*&h(mG
zzG8yKcOVCW;8myhd~?+23!>jREF@J=?VpPOZGSX5$U**Mfq~;4wZ<&J@)B^M+Zx8v
zpD<#^!Q;DiI#uzcd~`xXOb?ltCTZa#vDJ(f+9b?vRkSd-<{ElwP2g62L#BDZ6sBju
zKX0plHA*wfV4yR&XM0bVZ$RK(P<d&4R+70gUf3SPRWSCt`oX#1T>r=!0E%B4nome2
z^=icUo5jrzQj{X&uv4$ni}h|<d+g#PbE?C}8|#OnA&|dxJl)$C;f^c25yZu5$L3Jz
z)b^Y8y?SRNLWv<Fvt}atkTPBitlxq23?>)bdN`lGX$J}vOc=a<=#7osvE$SZ)YM%T
z-$72SVPXbPR;Rk*kBrY>0^@Tf+yO`cX1-0i8z*VJ2ozEBhF&-der5lBl*+&!oc>%7
zyjV{>l|dD^`WDa-pR?cx`Cu7%Bu@Tz{cluc1rFW5?jO}Bmw$L}Ut=E+R7&h=$*3Ji
zU=L_(tBo!-1Vm#)={AJ8%kV28E)Z{hag$SWmFXY{KKfrQ2FQ&V@ZS-TR6`KHg#pFD
zK6S>}cL?I&%2fklRmZykz0Z#IuMMRw%aefNo@KB@dm;YK^NUd;kj7IW-vf@6vZyE}
z#3$Yes?Uy-3uB_|pPh`hZL2xUsew^oyu|}+u1_>6d^#SaEjTcvG`Tc{Qu^!iFH|QB
zpM6oJsuIWS<wE(hoJ<&9gH%4Ta{p302p9KR7*M5h-=k+H&A#5u(F17|QT-a(JQNw#
zdhN5V8)5y5SLUL@O@iV}=YC?f#@E)ZVwiNudZ$RL2TdX|b!Br5ru?KP>@24MCI=%u
z%37M#rpf~3%I!qqhEb+URACzJS$jR_LptU%zX>&}=5Y?kqo~FE0s=LUQWjFN1_~LQ
z*Ue>n0_mttJ-@&eAElHFfHt12LG{A#i>-78Ny0w;!-f}Tp0I6A%7X1@>f-i>+=_wM
zB^tgzHr1JTc`LlRN{wMny=d&Lx)hW(oxT}N|6%G&GxL%7i;=C{R|xdqz%~vs;$K6z
zI+vnO7-SzJ#Fs-U0%mOMFZrsV)?sCQaLo+i|2kx@TAkzvs=JyBkk+AsTsA1iboL5s
zwUjH})EM_!6-Ml?IP29#O>5bAw<Ss3yq!%g)iWz+IE65;F>iCridZ#9l}?Hl)w;Qg
z`5s621d{NGI`4gRbW|v`tkhbYvh{bw`NBn@ruetx_<0H(X<p!mTc7OFcNm57ut1x}
z0OcHpRC~+4jS$Iw3yaM&keqET1P~S8L=}`(9?MP^!33iyIHHpll-0x*i)=#}QrTtR
zH38^?_1GGHiR!W%zFqf5YsAHtz@!qFS2~A#KheI_KRXcE+|@l}irViG5s9C7ybngp
zD>KXH&hs~GT<sqz&m9@6QdEr-07r6J*8{xwEeyh><;!vw!jtXi*O%3n6dCkd;p23V
z-z$)7W<{QG>nQ_j5=b1dF}Cb%z9x2|A&(`dY6X+deGqc_+(rY;?({s7ud+Q2n{yd8
zC!B{BA~#|uk3~utw;XSXs41G7?Wm?KI<P;P^u8j_nJ_l9WU!%{DlXiwQ+X_znPG#G
z<f2G>VvIQ1Q89d5Do_7_e%OHl+#!x@&iYJGt*gS~A}wU3yJN~U{r*LZD6Q$qClS6A
zi2vBMSw(|#Gn=aV&0YCq1oZ@)$dqckSGs9Bwte~ay3~mD$JktfF@9;Re6n8)>qoCh
zk+3Xrbj9J*#wND92ZFpjb_7OEFJHm53$qlGF_^a6yz^WsP#*r9^QL<i)`MiESn|XB
z42#EP*7~%aipW()m@`}w9XvJ=T#--|rn99%2)?C|03fWWtJ>I{65Gjv(Bhxs@T^T*
zyx|yO<J+ujt>>sGHBJW|eXMHv^vSk!d%?o5OoC~A2VaF;!rH~Xr*mkxtD$d$C=)SQ
zcHHlC8~cJI$f5T2yT`_BYL2upp)-$Jna=#<0SbcewnX1;dXHPph@`~(K;w%_El&Gc
z5=b+PYD>|*GJ$s-_LAqE`%074NhzQ<mHk*bf+850_;X?6YG(FObFI<YwWsO=Wu8jn
zmt(@DromCix50sRN0d+MHZIH0nGJT&aD#Q1W~6dA1=&NJe-4I*6hLDw{^Nv$Yq+@&
z;T6G^N^@y5i82L7)?sDBfQqWX{7UexyXW8<N|scin86)WL7mu(B~#97OuJN42YEtT
zjTBVWoW?$i)>QqOqOga<#Qer`*Q?gak+V14+He-_mC|kWbHmL9wm>P2%~({&<SQ#*
zj}<o!QgTtVpZ=B*Q@$Ow;lwT~^P2SaP+C2jI@k2`wIovg_ORyg9?L(`x$G|;zlc1L
z<WUdU#L6o@^DVs8ZD~!N!tib$LZW;xcqF?6%&fr`ita`eseZ{0dHS)^_|Wky(*)0B
zgjqFsosJ*=a)0=k8}j*T0c+H3%NU5ng`U&))6>zZJ+Y2QM2L?2P1zPMq?apM{h@FX
z=_IrbTR*(~9R{YZL?SW&V&2s3IA5C)NN;}L3)<8EHptxb2NzSLx{SvO@{E@2KdK5S
z@}w<5eHCjp^eO03h-XkkV|}7K;N|(D;-N*#wKl#y6;8R@bRCcd5JV|!>0PWOw%Iwa
z5Y2-`qPa&OrF`~RgxJf9=-X_O>JO}~SiQNU=8{(Hnk-ssBpuY{ZvCiu1r9BMCg-s#
z>&fHCKK8lYN5r_^5ed_#EN;szis@c8E*567iUOMFQJfu^1}<)!V`NHQFlwTSpi16f
zD)sUTa?<w;+_3L@BmWSp=;_hXkQNOwKyRB!KM-s`s89TSc-iy3BD>M)&baf*$tI@>
z>#VtL8b{W`9eG;3Qd#q5cy)`i{Yh(sahI;iRaktGyg#QKlnOZaVHz5|X>tBlOlzJe
zJF<_D8kVvIl4#Mg0PC^Ls_=UrM5NV`YkN)=c?#`p`T!ff|Mf!p$kW14I~NfnGs5!y
zqj!x4>n>`oCp1?p=l8}`kxvT|)Vru;IL&)?U43A6O1H79&z#@$<A#*w-{!7)*26C?
zAo-_7eZc|30Hzq;d8Z>I$BI}fG)`&DR~5k;jZ;gk3k!M^%_dHuIJaRbBQHJoYDKzO
zU;N4KXqcO|LE-V%`t6l)y-%c7alWwU&={h!K9M2L&rs|=fhkX<h4d3Fy`>>TV9sJ7
zDFaV_Sii%CRaXo!k=i{-+)&I3z>NT=1)=uD1i;OCw6o-L&i>IzSJJAcT-HLAwSkvz
ztxittd7_)c113e?!_c9S;Fi~~T&B3xy@`&vh!Gx?eLe*O8UwKeV7vU59~ai50lx+$
z_1bX+gZ-^E1XgtfNNld}FT3B!Aab@PJwI$gwU&toE;P&tyxH!IzgU0hhQ_)vW@pv=
z(Hn7S;1T<%BR8VcPjcJ@D$jiSeetdCd1h1~`Bm`(eAGd?Y*JEtd7;c+uCf2NnX-IY
zr-aMc<Ru%)hHmFR;vZK#wWyZJBID9RmX*lo10XPlq@v^<IORq@T|)el>(tj>Hy}rY
zcM52;`?akxD-K~oeTMRNZ4NnnCc++2CNy{Il$Gk~+z9gnBnYJ+cCd_D0jgu<VTxts
zkX=tviKFIv$j$?Ao!OHpJzcjwOivvB4QfXR)V*~=A{7_$2yLo4ZTKfTm=OT<@9BGH
z0PpnWbQ8Vdgk*24tBy!(1KHW!$ZH5ORG(gt+r63R=G0(}uu!e&u^Pje>IH23z%!NU
zmvln_^3$wO$J-O*joteMs`$i?!OgFngdZEIm-~p1r(`;xFK9npxxsG#ScYuewE@i0
z&p;u|UqM$(<b0B7OB!;1v67<_PhRfVb}}^yFi{z*(x6t!BBr1%G1=4DxE1kD;b!m>
z1x|@-O%SDAX{YvgmNLtGebl~UYf7C&Yq7ex=}9=1q&v(RljnztKe@laGkL!Z?tYu#
zfH!>T0ut*J4<BC6-oc`#Ec<T1^}#3p{yKB@?Xnz3JPez)oQ{5Xs~BJ8e7YUC_3`V3
z5uYo9<`<lOQD_vglLdn!8N17vTOUJ*KIBB==1oRywAg<KnVSX+G9%uZ`8p~1x#AA4
z?KIZVX+Lz2p!vd&zb4rb(N|uyJr!>)MRS1t{Vvir5?Ndo#ncriZIKlkXMN@60fi^%
z`gl>{#=W1h@jQk=k*yS1xQ89*=Q-Mv7mz$7p2MrE%&m*Uz+=twG%uLNR4V6Z=jH0l
zK+EFj_t;gQ1*~ND+)}JMV>rX=yI}Z#h3ct&yxoHz9ix?bU31^sK%H{<?WwK*&3^+`
C>`<ft

literal 15310
zcmeHud012Dws!y#Emdl{6_iPj0jwg32*|9~N+XlV5D)@rR8(d#3<)8$QmK`p4Jyd2
zRDlGN2r?yv;1r5XTG-4<P$o%`$Pgk!;O@QgoO{0SeE0VBJNG{4{&Dg=l019Ad%f#j
z?^?h0TkG9kKk010>67iBAP|U6sBey)LLd}l5eS8|8`gtY25#Sd4}Psb>tKHj{02V@
zU$IEw*T(Q~yrU2Ztz_t*T>9wrc?4ny0(I<&du;9`k61Q}CJL6M(<udvh#x{)-|vW=
z)-k?xeIST&9W}UF{+5!0hr8y6uP-SgPkg)KsOr&A<UZfA9C53=E@?+($W6<;?nlsb
zd)UvBNWJw*QCP?Q2di#e-5B6D9HhY@8fz2gWr3-WY|dY3f65OmDCiLB${sZk#1fxz
zLi@Jnq7DPPzZ|UWzyAEo0{^nWKW>4>gJtDRx#+yrs>M9vh=;j6D6;W|i~~4Ot<bz*
z-8aVeg%;5A9}4xLxq6LPYJ{oO(6f|z8uU~K)o<>eS`}$^#X|}|`Q!3yos}~^m>3MO
z3(ae}xiQxJx@<`*y}|i#gBq#;ib(uoVKUH;uzTpda+(hgx`IFirzNUE-vRg5)kEJ1
zRox*)=sRn-oDuZhcx+=V9QS%B8kM07`(5Szpzp-%pTCDDMmXO5T@mjv@N|NX{{DW7
zPwWqU!PUa8(bgOjL~la$-!0{D6d|B_jfPd8c^-LgHV^TqBv%0xpa5tA<-k6`31|bp
z^)TNAX*g*h&wnQ=5dwe)#l$RJ@K~q-5GbO|ULEM}{+($Tdu{2OR#Aeg$Kf^81iXi2
zLHHFg?I7F&-Ou{WDz>J{ic-_cZm3?oDvSa`01Ob*<jfnUs5XTP?9ncze!ez=gG;{&
zTZMJN)xC=e&~u4ehZ|Y(<89xw3bf?jIW^Ue=RX{fhEankEysJ8_(HO<4{I-8s<{h6
zKO!JG^4QZE8CN~5%+S}qmVm558<pA~@Z%7V$YA?}8-t<Q0MCmOh`4|oqBe?o8eVXS
z3*YO#zplOoC-jv)S1exu>K0oS%Qr$o9e*;3%?vU_8wmq#bY2jC-Ht%0_*C`<YgP85
zmfH~lOMQ=7zA<Pedzq^8>De!%B<5<5U~k)hM4msI?Lj&yl)4v(MX*&VE%verA%7oD
z36`6c7_-2)<=T6gqch!`!opK+028VPC8~))_YN<BhBQ7qbTwunw9L;(=8Ws_eMMj_
zc0N>=Qh|`+L&-|Vvj`_7S;CFL0-(&D;(e9Su(<pQM<04HK<Tshq3Kdjk{hws5<8ij
z&|Yiy=C<%TVCo=Lg$87OW`8iafJz|(vs^>|Qg@ty2YfO7!!`X+VjyEAel<D7^HXt0
zrv;VcpT)lKZxD7xn2Eoge*Y-UGsaWkjq3z5sF?<Db=GNf5=|kA2s!bIw&On$!X#B5
z=24$={A68}9QcOziN+RuebwTVSj3>GY$o;xP3SV?Yk7X2XbT{qYh!pGvKpb!Ug0QL
zn5TSN1gr&z*Qavgd2gy=S-!tb=^|b-J^j8)X>*QrFTmn-Y}cXsx$>B)L^uSkZYIVM
ztRt<x-fc@}uX2SgfFhtZ%#QI~9orzXE@sx@Pe|_TN<W1ro(yj)XMT$rsugw$^apK5
zCWV#2G%!5&gcp{wSWF?=sJ+cUDSMu!0uMe5?jhlbq^M}+3T~?R)l#qU79ayuJXXt?
z=USJZ#fo`AGL__$=O+8@!}3GG0X-*!o<mqAfxGKx!p)(`05uAMvg%4KTvQsK^{4n9
z5@vcRZT1QDlzB@0xuTv>w^itg#?6p(Rtfux5<1VQxLJ){6Se_v)Ibk(`tY{25e&Az
zu)i`XAKsqppS?HiK}FdOi_#8=uSQ93HF?c)+JWM*yXK&zq21lx-O+=J;fLhJk!@lI
zTfBQVG>;l)$<3Cw0_lV2{NeeYCML$zO%+hnw{o?!tfHjt*fNV8YP#TP7<~KL#@I~J
zO5N-g(mAats<t(^UUf_;4uNMt1iS%*Mf%XV;p`DnTLEh+?=QguE<1sgVnop<-Ha<n
z>wBVguxySwnnaNMj}UBd@g$iG1vW40mzr?z)kT;C+>Wy0LvUCOopA&sUWrPw;I7s_
zuW~N&vk*#+3ZZo&0-k`l{VnE=D$pRD-$#o&E@8ToV&#Zyv8^}6v-Q~&Lv3(n$H<AG
z@dy=#w2SbMKY+wtd=GdshHBe|N{<>uxZ^*7u74cn{|2D{cZdMf1Z+rAWpy=}ceKx%
z<&-lOdnJ>9IMYG)ZIt3JOLhT8)Flet(;TfrV;V!!1I9mlKV?wtzDkh%D4y+O13pdT
zDrFz{J~;xy_E1SCkdtmKR-$O6eKuwGL?EEhN}c_Ve#FZSv6<p#F!=kLvZOx?Hx@Mn
zO?DF#B=y1&VBc_MvFB>(X`e^|G*{zh{UP4Agh%+X5_*|7nq9Q`HddwqMRrrxtP6!y
z|0DqpH7Eg@ERU$GxM!v)QMINX3;jKM(tE;sxhs&EM6GYY`_@4znP{ozdHz*^p0@aX
z0tvdsU~SwGbFDaSnu2SU4f+zf<VDy~^&pA4)?A++V`*C5;v-!NjA4$ApkWSs#H8|S
zRcP3$U>d*jSw1|&1<=;mtyaxziGKs>nsx#R&)Y)Phl{$6r8nyqFOExK7NHUq{XVpS
zbUN=O?*MIp0z!4W7At(-vO8|lSN2X<0+mt-M=<P{a$VWW>QVXlln$z)`fv<|p!O1`
zFd#AEkFv@Zk4kEV*N6LKlIjY)oA7j<VUB-5I`nkoIuI7bb}2#p)3|ua55k{^CwZMz
z7j1004sGRi2`LOEgH=)8IfO~|#;w*ico0MKq%!H2&0#fQwo#iq*^r^efJ!*Tj-m5;
zhUI=0Yve33`SbS`+N-q1=&C@uAla<&7sWEzFs%H<7<_xVp|*roGZC~hTD$f2_kWck
z`qA&`?bOYlJst&pjoa!yT&M|AT?1dNF(Rv<z{H?w-u_Vb{jT_xW?>+O9vrm>e@R+3
z!u8SDrCPd!<;)T=MPRC`Q~v@bn1*7sow+c~9YiuTNRIs3Rm`yXgiDggiZ-oq9*NCT
zeQzibaX*v`bA{>lF9`%(h$IbUFJEE#E@&O9v)7r9HH$$``Nnu95+~g<Ht54H!vnFh
zG9g9yEaW3O+M(j@L(8Cc9+#EkS~>O1`->MPDMF!8$3x%~346A|<6tu%oU(N*L^fsv
zClX@vq`nr~Oi$dmc`)Z}{281j$hM2vx_)ZO9d`y7o<bUPgh}R5IJl>H1~Z~dO$$5q
znpT<+oK$b;N36F@*l4r1SzzXAXleTJz$rIw84YyW|4ML`=mV;^U+#id023M3*_1#}
zI{%rh$8$WL*SJLW_Ya5N93r=w;%eb<uB*|wMZNA?8oqx+9PH^Q8d)KHcVa0%6gRHd
z^Fbu67dC!JfHzg|a#7%u3JU=>-@5%b-jAXt%W=aJBWSjOC+q450;#X3cKU0>KFMgY
zxCe{-Bm5e|tM_(3;0LFyVw}_F$%9uaNY?rvr0Bnk-EeMM?zm9dNAZEys(lU2)Szn0
z7nI<&|F;whzpKUH)EZSWz@|oL#$O{lB0y~>=1+*&4+E%GB5|R`pRZ*1;ju@Jaoiuz
zhL^<@jo$m+luAkzMc>nflEAPm#TPP*m{rXC%u;5ZB}4cC#@f8E8(C~^4>lA36^^@p
z%F2sah<CxsK3`gMnP*!z4UFHy22Qce)Thi6T<8>Ae`1Mc0_vj|pH&ji$J$G7*Y)&x
zl1>t7%yK4majLhJ;EQ|H`)=v2@JrwZbv%XOe>%_GrUoDWwLk^h1cm|>p!Id((#l<h
z><M-0ph@)7N(jyg*SCQn@WGt2Axyp{uA0rkqbE<MUG!=Ys1K(C--|ZHq>s!Cbpd;>
zsK%(o4w42rX-icxGq#IP-y9sl_Lgv6#TreApnC`w$W!Z_^QfHKLQ{?<x}dJm6khno
z&p|#HO!MoCYntVlsCYx`O~kZ*)qPtuB^=sto^)^Vg?xAX3tw5AVwt^ZPFuIJGGgd;
zo8USE@t|q*KVD|sJM+J^%qZ&6@qcNzA(xS60U5B-aziXS(CoWG0+n9Qyo3F~78cN%
zaGf@EcU^s1lTwrOu#K`;5C;RtIYV8ZKVeY=?uMBEfWGi5V&9Vxz+3q=T!lxQf(1su
zc{C#*tyM;&+EzZ^wLRZcHda!zca7CV?*IoJqA?#W{sY;=y#1~X2OoqJd|3W%`f%mf
z*8lzK1El$RzIkRsmvZdNC@_0mmLj~o69$xUB#8alb`DaOsDAv#^vf!W^5h8In@Bs>
z2xgMIQ&_N;FQzC{uVR-?0%u^5Oa>EM&s89`sNt=8luC?~1iNcQHZ2?mtNFKU)%<Qb
z@eIb6YwkfXj}`lSxajN@e+?A4yLcT<hj$4k2|pU=d$aMXQh%R3yJ!V5J%RZ6uS$Rc
zii5pu0GP<}8fFSF?OIa`lv^F=Cb<uG0P=Ethw0Q=ih}YK+<(X_NzLEbG8RwA&m3}y
z*-O(A<+2JJpxF{Ps)DSi{2D7cKF$}O-f;W}m|*;o_R8O&CYV7E<3e%MB?9&vIFBOq
zuv9s5!(|fA5658A79Ay3o64pi3C->It+|U=aohU(CXY-{PIyv>owv+Ua%<lltVpA4
z@cgIz|AT5Y)8U*3-q9N(;w4c<E5{}Ggb{!@SkC)Um$>7Zo;qdo28=*xMF_KP?;Ao>
z1eEsDmDqLc8g!4RxTL+z_TZT8isYd%NpT*w5knNBH^h!j;rQ~1NfuI1BdVXNpB<G+
zv5d$d!dn}jmAbxOA6=Zf=qAb{#YyU2?TVPEe}%(=p{}thcD&;^*_5TYF4Fo+xlrC}
zEst--7Ria@OO~=W4N6OePlQA2tF3p|@~BVct3>HzA=lOaN=jWa>%ro~Ei)^zl4;?G
zO|-QIGVUao{l9#r_ZW<)2p0c>Jby1Y_JTy{G)M};t@LiH=PXK`%HYS>mQ>EX(#65#
zHC#8PQS;4?u5E|e856m%;n-_N9v$UVgCpBXm^`#r@5oyH&FVki@zQ350Aw_IGkqdt
zUgLxNXmA=~h=R?ALgfB~Um!FXeY?P}4*2nUSPnAl5_@+N2Y&^JmIx?eA;UdzT^j4v
z2htf&j29Tprz8?E8ax1n<hG?-LY^QnHQj?=63RQO15083c0qw}?}_&8I5a6UPn*4B
zR5GP5W>+qn+k1^$fIT%gicv@f%xw}emrMfRYom#aOG&KcTnw?=vH?HnTf3C%y6P^W
zkIVB^DIE1#*c709t*bXGNx0HgKx@~s!t403E0~<cyTSsG%#^qSa0b?5xFn1kMe*NW
zU{{Tw_^ttN1|?!ZLy3d9v2InI#iKYEi5*47eKjC{#Q{*ZmsJQG&xl$n0?JBDtgPQD
z;p3+Kc3gq~JH3d<3Giy8%ORI)<3;gY$B5yyh8gvsm7coAxlQwH<_-!uIFu(iLlC%*
z@hs7TD=DVpJ5-&zzkXWU0oW^JRa*1v2;;`xxotpG7y~wCA|?n_{qFzWgZRtMBDpZ2
ziTmM4Mah2B)KtvYwZ>cHQ^=(RI>R?8O*-fK6To!<Xz~(^+W-Oo7@VXL;1<dA|BEgJ
z;u>h{KQ|%hq@$7-t{l>hAb1}p_YlnE1o~j_?48f@VxT)+Ly}xmyA?7<Bdww@u|_e8
z<sm5Hvl4M@2Fh#Gd<Fk%+`Qvsxm;4N`6|5D28?zsK&DYE9uX>01}J^<OLr>Vs5+%!
zOAJk{0&9|RAQhg|s_9<z`+QfPH}ABJ1k{P@#eLWnb4m_HRjsSTJ?|98kB5=j0jn69
zH;A4CfW}tM7qIzNt4k84iom5Jz8m`jSckpvB}Pl;6eX1z%YRi$Q_z~PXWc+2plxHV
zb(k=ru5x05*8CzD$CsKXvm4GIkxe39Xol)?^RME6!9OVxQ~0OBSn!in*A=w6QCHo|
z_tk|#%M3{N=~|syRRhTu$rs}<Td@=q+$5tyQt1j^7zXOwwR}<1>gw+;8#zR%sgv?O
z*!0CdVL?iPMBlT^2ok|iFxWGc=dn5twk=sem{CdcmrKpY+9ie-24KeyEWuN;2JKqo
z)1Sa?^#C=Wt}UB_+bX%SakviGF&i(Lu*CnZ6pmX~PGWdqtWcePx@oYZ4G1(Sg*_`k
zeqFuQ(`IZvPAf{BMRoBx1v^ILx(%^0*I3*SLzZLhV?rATAuJ>d>~6M)KULSMN~<ew
z1?;WpaP-Dz4Y0r(@@LXNRB`8QjP0N~V~!em^cY>@c`*OW>Kg+1GW^)*c(9T28<RSx
z!!->n2QlNA<kyJ#sR=+o{b9EXdNsU@Q}fGO1LJ!5v8R_?DN9X~a$ykYI2`)!b#^q%
zz#}T7vw@o-Yi~Vga%RA4Jo<eD*h;{isv1ATRLI2pOQNWuaMFk^0fT{Ldz4?}&hf;!
z5{Vnx52NBMnBhqud?Zh!r=dZOXM@cy5_}}-TwL1+fmDnM51Z5^9in|*TW%S21P+`=
zT6Ld^hl(eNh9%nmvT?<{4!9xFXc?k=lg;Y46UqRQS{K}(Mu-?d<w=g0EEwl1$yb!D
zgY;~)G<f6neG7%;s^!&q8oGig>-3Cy9~m5oE;hXMPL%n`5W2Wu4sK%L$H?7&ppl?U
zjq42FtZ@Q_XCug$3FCvC`Q~Vya%akX@3(OJ3;rH#U9Q9@)rXZPlr!%wE>d#f)j#L}
z%Z}j?0Kkq<nF3!@LpMMIvuq)1=*0%h7<{~>KsE`5X=3^32SN*2R9O+<pPlf0EfcAZ
ze+nL)JQoI1Z&0LV%x%!q0sUZ_NyzkAy$9Al$Du2UmsJ1%&v4edA&J-fL2pDP=3NR2
z0oz^H&)}8;DBCLSpI`JMCLO^u6JQ^xPWY#PyoCG*&dvTp>|_&{z#gW?S?FDWKOe(=
zY-=*M2L%ODLtpP)tIV@Bt^V+N9aKY4o(cjH-2zah>U-FE<+<CO<hk-r^G@;HdA?d+
zxK3!J8{7W`9<8KP{4nghmRJR;R+;Tdb}=*I`bTd3=7($VW?wuskzzDHjnUu~qdf}f
zw(eS-U$kKl+xYNm457XV-!do)qS}?%qIsS?4`R$@mkrG_Vsf5%MRF57=8596jmq20
z@_lS-?}=dq>y-n`(ilF-Ec&**<X=f4Ol@NkSF4#1n88VGak*h>zD@L814&~M9v!{g
z{-A*%EM=N2e1c12*+&v2WZ|x1$$(lHjGl0tu-^@1E$l%nRoC*%@WUn2RIDbnz(fql
zlYEQY0e|0@+5UOd4)6<JI8+qC=V<lA3j&Z7LhETX9NQVxf{Ve0Cso+F63@#8*`BAZ
zjLCO{$txf;yX}G~OR>@Uf)aR+L9yE|Ay7JNYWW+1QRp~EytM~TaeB~!L72{P5haJ}
zKp8f#<>m|T0GoiiVRnx}tqU}Fz*)^#jCgZTdU-;zWys`PFhflAe!m0=t0QusD(q^t
zxsP|0Bng*=idgB?PCI{M!uJ9ghoIg-O%s92DYf;@Gmdt)3-r~9aFDzaX6s7UP6vP3
zwY|E-13Zw3!>WmiAihose*`<#s^7EVMehVVvUDZN-li%~o3qxjA^tewp&V&rY;3<d
z)ru-EV@|y8Qj}e7?3eF`#v|6%?={spGQ|dZJbA6g%NHcnKZ7uMmMn@ONXn-XAfy6@
zFb4*Y$c#kOVs6!j8jrwz7oq4v^a9rB;A-H%XqUzP+CP(r$z%RfMfd+RKtfHB3gI1x
z(}WO|2u40tkga$nR#oLm#QXjnyodqlKvtYP@OWuVSOlIGYg>h{K_7S|B`8S$NxBc9
zd!XI@{c&!PHjQ&@ZPps_7%PvpN+L+LgS<Tia?6AZQ;6BaBf2{_eBpDmG|i~7B=M`e
zd&;}BPY1cjC*HsOTj4R)Tc12M3qciDAAJ6A@xNR?c>mI)6J@DI>uzR#V*6uB?{`0Z
z_Su=wl6TAw&8etGL=kkx2P?%q0&i&nsUOJe6VYZBwsHtlG4p*(*+>z~5XSA2g2b3h
z*103Ps3}xrIN3qQf*oE@_nfaK=bMVU6m$JJpC$>UI^tH;CjNcgS7bY<NMAB(lBo_|
zEDUWQ!r*mI%q$|Un1*m(D#=+pye~ZU5r|KG#GE}J-vcQ5*m3*M2XwjjC?X7$p1x*?
zJ_p}1xVT^a3g#$1E`5FDiJ?#7txo*oLVtJG-yN`~*0X^9Z<$H<+cqa-GQpI4n12<4
zXkR0;zrV8Io#T%WaKd2_jYmICeoAwQz4<ucC2k|Tr)Kp6xH$~XLswyD_Mcn&k5Bh^
zZ>A}LlWV>B6?s?2WWh)#Dj|2|Hj>3O{4}dC{Lmy5a+LtZ&)?6tEF#sA7PxCz6{H1A
zQ_y!L1oErH9ks`vzG3Zeu0pkE2lD+;4R#K-IiIiO7mQ>hgVgRiLxTzr$n&2|Zz7wJ
z7V-IU1<sM*Yzx~LC|dC&XJq7NjLb()_MvPu&M|&ndo#sGf9PFuv98746wXg0(<pwy
zh+Rt$>COlPsg`MB<T&%)W)a*A!XIuNP%$#<up%!<)IIFK!Xnq}Hpjf^2{b%IgmqKd
z7`ycP+0625<iJ=~&E95K%ZK|bOE7@HFauYO9Az?5k$oGYIDP8koRO)oDWwx3qn3>!
z>s}D5|9sf<F12cOA#KYTzf;}r!gYDR0@*rxqaPf8>Q@tMbgFMxM#QA<kLgvX`#sCf
z=I4#jeJrm^e?;b-_JT)wTFZsm#oIN{+FLtB6S3Ak68ymYjoaPZbf3Xpmg75yFqTFR
z6+YyFmSGwa4BN2b3gzT<M*ES}=?=A0PuPU=^8EXiVdS26lkvV;O&2ou#jFgaeeo_#
z9YMbV4SW~5ng`lz^S*S2z&ixV1`)g5dez~EDU6C=fW6uVm)rK8JDNdQAy0bK*en+^
zy|uD?3o750tG4eH8@8G5x_X|vUZ0<~RJShVnV40Y^c1>|koOBnxO!xD#qZ1^&1eiH
z^6<DP=+W>;dDlN7uG}zch&ci5quhh)pE3<!uRcsi6cUL`cf{j12m_nIHEQbqk%gW7
za_zOI!{8e;u-3OezQy!EG2j8y5RrK63<QWzir|<B-<n#8TaWl>M!N3MebvDHxC`sA
z9tqQC41#L$Z9q#T&i~z5@pos2-^D8kqYvw7#*O?8qO*bVssJQKS48szVPa;|`7<wZ
za%G2fTxR-dH=wO5G<SBIc}2TXaw{>@(Aub(k5PO4W6VXea>n4D5h6xSVV}kQxn37!
zU4`gup`wVKTQKq%85oWE^wG$9lwa;h6v|eBGk!@{CYPZikCWd)PsAP}qi@*~&-6Sm
zL)7Ti-4*=_QPROhK1G^GV>Uc``}DkjK{syaOESA9pWhGuxX0PEv}gq8&eL-NeLX=e
z@W)JdMe+A6_s33aB<SzYo4;$FKRy7;E{E->oMytwEJ(L2(no<MysIc}MzQyWxy!eU
zSQ*xO&1p2{Z*RW^5GSt}WoUNcw!FM2L7C}$^Pu$=>&Bh!`TFpUXqOo)RJ4fs*~M33
zdVRgnpi-nh(z^$@6Aqhy>Yv89o-rWkFwU(<%{x|@HMb+5(v;=Bj(h5R`{&0vGt&H=
z3LaI_?;3R@y)(~IzPBm&@6@<TQ$~3Gi9{ahIG(#?hjR8G!3X%}WaMJFVa}1A>H@+s
zaum6KPcwyEK-$?%$cQf*J$=Sqxvyu@f>=Q!_vl;fYj)dCN+6Lt^y_vs1G{MV(Vc1`
zlR@n42CrKqy~wa{W}YCG%+qXgM_N!TUp5D}^c20M%N6b#&*ZpjjZU}GZhU{uV|3HG
zsC3()6tNvK$!693hL>IIIWn=lpi_yZZxQy47(4w45uk@RCB7VM=%!9w9nKiEeq&p|
zv)OM~S*d@g0|a=CW7_`tHF^tk)={MTb&|&2W;ZK0I(rRCIXjx|GN)yz73*d+dGec?
z0n|!E?wwg0vIbdK^1T0yS;kb5ESFY(Vy2vXCsm4E82HU!>{ww>9?vWc79+#<=<tXw
z2BHaI?#RH>Y5IeprQ4NJI&}vp#>w%>X6Xq!Z&$MkIX7pd<^)GZM|R{4JNn7CBP^rO
zFAQ|K;4m9fE@H{7mImVPW&+o`GXh6uy;xpq$r+sJM%Gog_T4&H@b!oB#0MxTZY~P{
z=9dZ;fo&7YM1wro-8-z*vEQElz@@*x=M{D0I$E#pVDrwX);lL6<FGC|<}KFXMEIef
z&F_sv^9*%yb6Ty));pUY7++;%Y@hWvZK{8&G25Px)pn$$618Nx+S^9eq!}87Wm6N)
z9_mDn**tFU@}A0v4~skU&Zi}8Lf9~<5y$1{c*!jZ?E2g<GmuRw+meX&#w2Onn4ia3
z2u{IstE<M6<)Xzci^7LZcKe@3u(P+f)zFL3Zg+60HZpo;>nr+1)q>%?3PZE((j3dm
zil%scdJHMv-LsqLxe_d~7MSo_T4pm}*uNg1xjwVpi&RQmu-s2Eo3Bc64v9A7vMwB=
zq1}oW=BxaiLd*_w?e2i8Ing)9etRn*1iRe1S(NDdZg)&U{=4-mv)(!9h}-;4pDd5@
zs09a_th1i|0%`Y!<s;*U(0*ff_UX1NNV&Uerd%ITuzx23%-FiUmBtOlPb~vV57G-_
zL>p#vIPqGRP1bL-K^3y^J_b6|CV;NXG@=$e`-SGuBliw8=r*ebW)=PUajJ2GKY1^C
zxh(#d$!}*Q7NZyJ7@C?d)zfEQ{kpV$SbyJ9o0nT<x!Gk7GyDS$dz#Z9X!TG_U&Sw3
z;!VHs$^a>w_{7XrB;lrmiFIJV?l;<Z{S^+YXb#lwScy+>c~M0!49mCTww3t3%pxpr
z2r>^dh&bXPd9s_^*Ym2Qw6$sb()9anX(FKOVgsb3cJ`j0Rl)6ZOOI?~iDY!<%NVmo
zQ?@xs<q!@-6eP$QX}<cCq!zFvd;%<!+E9G=gc2~uu?r>b)myr+*<N0WFPJb$n#k@s
z#=~wAep~%^yz31P<^1Jvj9y*bH4D6H)wc8gpf478cg&1SZ<$=t$sC#Y9(&sZLZ$>|
z7_#gnYGN90c;NkZTYXb1BYM{0s<ID7?YQyOw)&!%9TWYiR9Os){McZ2?(*dW!UpYI
zer>0=-{d&<=8il=(sySD)&}?Y)sMGFe(45!^_~hsoo(+fyA+*H+>w|2oj;3q$4)ix
zDr3iBSC$~T57p(u=AtaS20Jr5X0M~beNL&QH{C^dDk<sp{nnct*tXxE^FTUyZqrbY
z_K8TpVNt49w|vG$ew{R8S8JHxQfPJhgCkCJQOxiwWcuytDwN-$4*NLC<;(l08nl!B
zoOHkp`g~L`2sMK?@ohf>$^zL@dNc-W{X!+|Z4p6Z_^abt9Di(l)1SH&FfTj2PuT0$
zJy=e_VHVWie>EGQ?&l=fcg{cEf&M@x+L^Vj|G}juNf6$pQThGFr`!*ZK`%xHJ5*Gq
z6qr0&E;i$u?>pth=$ebV{lcW>PAZigzpwcrD#7B36hxlBqf$xj+~vhL$*I!`plkNb
z<tM5Qy-K^3684U<Ijf74Ij*MfZPPJmx2Hp;Bf>toBsHP^R4krM&lFH;&XLPmJF~zQ
zIWb`isU@3neFDKyP&lmXdCUCvQ>04D`>Ptaf2%bwvaB{<jTz6X3B&U3eab*HdzpK8
zc6fi1^P&l#Ji7fp%P3$I2=14#{^=*^4~*8M8V250F13QTUZ0qzW&9-917+L$;mmTo
zZizD2IP|mb<@*!e-U&xEkPGLqyg<XFy#1LGQZUf{txcQfE1GEER1C;N;FeJhg}aXC
zL9VuK(L=SG)&sD}5SN*E$S}vqb9K~-?3qK1_|~zURGnu6!=^%)t&tCgU!{uc?#8pL
z>-&hO$PU|^RzrRkCErP5(IrufLyY4a%p4<~$!_-X*4S$j(13+)#B$I@iZd%;85sr+
zYUiFy|GbOlT!D_$iM)h0vOU=0)HN4`czbfTO&FiP57mvs>~9UYt8?Bi<QY+{wwKBH
zDG_Z~9AvZ&tK&?{wQ0%5n__~Z{6)ar;|c84FpF#*mxPmm5`N_(S5F$=wi{4+?U0ds
z($-Ufc(A$Zg!!%X)9rJ|=gVnv_Q_lxlt>wnCttSgUdwG&C}&jUsP&Rmgz~c+(?!h%
z;q6TnJ+mdF!-q7;lP4lcWWozA=QDLanInlvH`J7Kq<@d%<8`3p>}6+<9s|8iyAJs@
zfAqj6D{`<yWLRCw)1wnT|5R@Bzj|^;5=@*BKbfMsb?=<0i24o(b0&RnxJWI;=VZj!
zS*Kl$;CZ0ZTxNbo+Mx~vTSx0IoF&^C%#Kx($T7$T{v%vM{)ihYf8Z<+UM;(3PqRg*
zd}m<Qqxor6Xnys4a5}hsrY)8*rNJ3$8ymnyZb|>ONbc0!PmfX)V+4^CN%q~#!4_`P
zX4K{rGtZDlE|G57c2kq2O6r5Whf9@_Tg6diP0wyC(`I(6g--BY_{=tu-=8%y_4yCB
zH%Dx4gs&Ix&G5}0`N?9;QMaysy1%Jy|M)MFlkd*2IGQ2r${)5r-X}AGm7IG~nz~~y
z4e9bt#icFseAkfR`uV!b*1o_boO5W|Z1(M-b%;VN?J3w);LI$~#D86Pw?70muO5|p
zq>ekKkuhn0#>Vb)3JH7LLYl^Cm!wX+s&=mfTOY0Su3-7?b%~!l!bR$QGZVg031Df{
zN+?@5E@yXO@04$VjmGxj0)y~WM}iEa3ceV6Sj7Tr^(36PC(mlUo;s>2P#51BY24V2
zcg5D9{|>h~B!!+6poKu-zk!<l?-rb~%i(or29EwEJL{K}Zu>WXo5z;$+C1W>vdq16
zPDCEx7+7FC7F3Rk^diTY`ps4&my8(mAPFA%wxatMG&T4+nHQnJk8srO^VA;Dpqm(&
zA1B~867{Daa<h|b+|3aPn>U|>P1u)tl2K!uU)e^@awu){$NhAN$P?Q*Ce3ZCWpLx=
zWZrY@t1&;Fi;Bz58u?;$=F?0ks~qW|Vs2K%so^D~FX`|o#yx`zjaHco8Nrw8=e@D<
zVU=SoE%$f8YJ29=<oP!P=Bv3Py3T7tnsWuUm7~`@<#19T{11?ko50@T+u}Tw;l+6N
zrThi^TPI^Y$f6hbb+k{9Y?nj4&4N0Yiy|mZM70twkb_#5mgu?`X3a*Kg|-NUr5@Oh
zNL&HA5#O>Uw^)Ax9~VZ#k%!ls+X$W?sQd^kwMP(m%_8T;ea&mA24Obb_(pKdLK|83
zWR63HZu5-`hZ0VbdB@}5nQW)C&tDsMajIZza?YlJbi?a7RN*5Kw}0*=*RxYx94mG<
zE2It^IYpi!r|Z=rn^RF!Umkf^*eb{xDMNDn8v+Srb4NnnQ?hTtIj4n12b7=H+0-8W
zh3=%)T-YRRbC5!en~teuXj;GfFwvRTA+6opoDmqCmzh%MJR1@1uo?<lMa~?2%`S0%
z*&e$*jEr%#TA4<I+XGmO;)`;tmXeTmUP+dqdV1@@VgZ3@X??Am#nx;7Dyr2d?;IUT
vxE&;&`le!EGkcVK37+;}e_#ugty@(>UFa-RRy+Xrtx;b)AEO-&`0n2U5Ku(w

diff --git a/docs/reference/joincount.multi.html b/docs/reference/joincount.multi.html
index 9d72fb52..401fdb58 100644
--- a/docs/reference/joincount.multi.html
+++ b/docs/reference/joincount.multi.html
@@ -7,7 +7,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -139,96 +139,30 @@ <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-e
 <span class="r-out co"><span class="r-pr">#&gt;</span> high:high    52.000   28.138   18.342  5.5716</span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> high:low     28.000   61.170   25.882 -6.5200</span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> Jtot         28.000   61.170   33.190 -5.7577</span>
-<span class="r-in"><span><span class="co"># \dontrun{</span></span></span>
+<span class="r-in"><span><span class="kw">if</span> <span class="op">(</span><span class="cn">FALSE</span><span class="op">)</span> <span class="op">{</span> <span class="co"># \dontrun{</span></span></span>
 <span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/utils/data.html" class="external-link">data</a></span><span class="op">(</span><span class="va">oldcol</span><span class="op">)</span></span></span>
 <span class="r-in"><span><span class="va">HICRIME</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/cut.html" class="external-link">cut</a></span><span class="op">(</span><span class="va">COL.OLD</span><span class="op">$</span><span class="va">CRIME</span>, breaks<span class="op">=</span><span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">0</span>,<span class="fl">35</span>,<span class="fl">80</span><span class="op">)</span>, labels<span class="op">=</span><span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"low"</span>,<span class="st">"high"</span><span class="op">)</span><span class="op">)</span></span></span>
 <span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/base/names.html" class="external-link">names</a></span><span class="op">(</span><span class="va">HICRIME</span><span class="op">)</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/colnames.html" class="external-link">rownames</a></span><span class="op">(</span><span class="va">COL.OLD</span><span class="op">)</span></span></span>
 <span class="r-in"><span><span class="fu">joincount.multi</span><span class="op">(</span><span class="va">HICRIME</span>, <span class="fu"><a href="nb2listw.html">nb2listw</a></span><span class="op">(</span><span class="va">COL.nb</span>, style<span class="op">=</span><span class="st">"B"</span><span class="op">)</span><span class="op">)</span></span></span>
-<span class="r-out co"><span class="r-pr">#&gt;</span>           Joincount Expected Variance z-value</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> low:low      34.000   29.592   18.895  1.0141</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> high:high    54.000   27.224   17.888  6.3307</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> high:low     28.000   59.184   26.233 -6.0884</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> Jtot         28.000   59.184   26.233 -6.0884</span>
 <span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/utils/data.html" class="external-link">data</a></span><span class="op">(</span><span class="va">hopkins</span>, package<span class="op">=</span><span class="st">"spData"</span><span class="op">)</span></span></span>
 <span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/graphics/image.html" class="external-link">image</a></span><span class="op">(</span><span class="fl">1</span><span class="op">:</span><span class="fl">32</span>, <span class="fl">1</span><span class="op">:</span><span class="fl">32</span>, <span class="va">hopkins</span><span class="op">[</span><span class="fl">5</span><span class="op">:</span><span class="fl">36</span>,<span class="fl">36</span><span class="op">:</span><span class="fl">5</span><span class="op">]</span>, breaks<span class="op">=</span><span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="op">-</span><span class="fl">0.5</span>, <span class="fl">3.5</span>, <span class="fl">20</span><span class="op">)</span>,</span></span>
 <span class="r-in"><span> col<span class="op">=</span><span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"white"</span>, <span class="st">"black"</span><span class="op">)</span><span class="op">)</span></span></span>
 <span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/graphics/box.html" class="external-link">box</a></span><span class="op">(</span><span class="op">)</span></span></span>
-<span class="r-plt img"><img src="joincount.multi-1.png" alt="" width="700" height="433"></span>
 <span class="r-in"><span><span class="va">hopkins.rook.nb</span> <span class="op">&lt;-</span> <span class="fu"><a href="cell2nb.html">cell2nb</a></span><span class="op">(</span><span class="fl">32</span>, <span class="fl">32</span>, type<span class="op">=</span><span class="st">"rook"</span><span class="op">)</span></span></span>
 <span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/base/unlist.html" class="external-link">unlist</a></span><span class="op">(</span><span class="fu"><a href="spweights.constants.html">spweights.constants</a></span><span class="op">(</span><span class="fu"><a href="nb2listw.html">nb2listw</a></span><span class="op">(</span><span class="va">hopkins.rook.nb</span>, style<span class="op">=</span><span class="st">"B"</span><span class="op">)</span><span class="op">)</span><span class="op">)</span></span></span>
-<span class="r-out co"><span class="r-pr">#&gt;</span>       n      n1      n2      n3      nn      S0      S1      S2 </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span>    1024    1023    1022    1021 1048576    3968    7936   61984 </span>
 <span class="r-in"><span><span class="va">hopkins.queen.nb</span> <span class="op">&lt;-</span> <span class="fu"><a href="cell2nb.html">cell2nb</a></span><span class="op">(</span><span class="fl">32</span>, <span class="fl">32</span>, type<span class="op">=</span><span class="st">"queen"</span><span class="op">)</span></span></span>
 <span class="r-in"><span><span class="va">hopkins.bishop.nb</span> <span class="op">&lt;-</span> <span class="fu"><a href="diffnb.html">diffnb</a></span><span class="op">(</span><span class="va">hopkins.rook.nb</span>, <span class="va">hopkins.queen.nb</span>, verbose<span class="op">=</span><span class="cn">FALSE</span><span class="op">)</span></span></span>
-<span class="r-wrn co"><span class="r-pr">#&gt;</span> <span class="warning">Warning: </span>neighbour object has 2 sub-graphs</span>
 <span class="r-in"><span><span class="va">hopkins4</span> <span class="op">&lt;-</span> <span class="va">hopkins</span><span class="op">[</span><span class="fl">5</span><span class="op">:</span><span class="fl">36</span>,<span class="fl">36</span><span class="op">:</span><span class="fl">5</span><span class="op">]</span></span></span>
 <span class="r-in"><span><span class="va">hopkins4</span><span class="op">[</span><span class="fu"><a href="https://rdrr.io/r/base/which.html" class="external-link">which</a></span><span class="op">(</span><span class="va">hopkins4</span> <span class="op">&gt;</span> <span class="fl">3</span>, arr.ind<span class="op">=</span><span class="cn">TRUE</span><span class="op">)</span><span class="op">]</span> <span class="op">&lt;-</span> <span class="fl">4</span></span></span>
 <span class="r-in"><span><span class="va">hopkins4.f</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/factor.html" class="external-link">factor</a></span><span class="op">(</span><span class="va">hopkins4</span><span class="op">)</span></span></span>
 <span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/base/table.html" class="external-link">table</a></span><span class="op">(</span><span class="va">hopkins4.f</span><span class="op">)</span></span></span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> hopkins4.f</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span>   0   1   2   3   4 </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> 657 215  98  30  24 </span>
 <span class="r-in"><span><span class="fu">joincount.multi</span><span class="op">(</span><span class="va">hopkins4.f</span>, <span class="fu"><a href="nb2listw.html">nb2listw</a></span><span class="op">(</span><span class="va">hopkins.rook.nb</span>, style<span class="op">=</span><span class="st">"B"</span><span class="op">)</span><span class="op">)</span></span></span>
-<span class="r-out co"><span class="r-pr">#&gt;</span>       Joincount   Expected   Variance z-value</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> 0:0   864.00000  816.27273  116.05233  4.4304</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> 1:1    94.00000   87.14015   55.25216  0.9229</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> 2:2    18.00000   18.00379   14.81562 -0.0010</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> 3:3     2.00000    1.64773    1.55539  0.2825</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> 4:4     5.00000    1.04545    0.99845  3.9576</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> 1:0   503.00000  535.05682  227.76750 -2.1241</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> 2:0   213.00000  243.88636   97.21769 -3.1325</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> 2:1    99.00000   79.81061   59.01930  2.4978</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> 3:0    61.00000   74.65909   28.58592 -2.5547</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> 3:1    28.00000   24.43182   18.99976  0.8186</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> 3:2    15.00000   11.13636    9.82411  1.2327</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> 4:0    40.00000   59.72727   22.78583 -4.1327</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> 4:1    23.00000   19.54545   15.26564  0.8842</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> 4:2    14.00000    8.90909    7.90051  1.8112</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> 4:3     5.00000    2.72727    2.58616  1.4133</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> Jtot 1001.00000 1059.89015  273.78610 -3.5591</span>
 <span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/base/cat.html" class="external-link">cat</a></span><span class="op">(</span><span class="st">"replicates Upton &amp; Fingleton table 3.4 (p. 166)\n"</span><span class="op">)</span></span></span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> replicates Upton &amp; Fingleton table 3.4 (p. 166)</span>
 <span class="r-in"><span><span class="fu">joincount.multi</span><span class="op">(</span><span class="va">hopkins4.f</span>, <span class="fu"><a href="nb2listw.html">nb2listw</a></span><span class="op">(</span><span class="va">hopkins.bishop.nb</span>, style<span class="op">=</span><span class="st">"B"</span><span class="op">)</span><span class="op">)</span></span></span>
-<span class="r-out co"><span class="r-pr">#&gt;</span>       Joincount   Expected   Variance z-value</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> 0:0   823.00000  790.76420  144.44877  2.6821</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> 1:1   101.00000   84.41702   55.98143  2.2164</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> 2:2    19.00000   17.44117   14.61542  0.4077</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> 3:3     3.00000    1.59624    1.51444  1.1407</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> 4:4     3.00000    1.01278    0.97111  2.0166</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> 1:0   497.00000  518.33629  234.93545 -1.3920</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> 2:0   216.00000  236.26491  104.42142 -1.9831</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> 2:1    81.00000   77.31652   58.70829  0.4807</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> 3:0    58.00000   72.32599   31.49151 -2.5529</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> 3:1    21.00000   23.66832   18.85316 -0.6145</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> 3:2    17.00000   10.78835    9.62487  2.0022</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> 4:0    48.00000   57.86080   25.15973 -1.9659</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> 4:1    21.00000   18.93466   15.14473  0.5307</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> 4:2    10.00000    8.63068    7.73708  0.4923</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> 4:3     4.00000    2.64205    2.51686  0.8560</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> Jtot  973.00000 1026.76858  284.51030 -3.1877</span>
 <span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/base/cat.html" class="external-link">cat</a></span><span class="op">(</span><span class="st">"replicates Upton &amp; Fingleton table 3.6 (p. 168)\n"</span><span class="op">)</span></span></span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> replicates Upton &amp; Fingleton table 3.6 (p. 168)</span>
 <span class="r-in"><span><span class="fu">joincount.multi</span><span class="op">(</span><span class="va">hopkins4.f</span>, <span class="fu"><a href="nb2listw.html">nb2listw</a></span><span class="op">(</span><span class="va">hopkins.queen.nb</span>, style<span class="op">=</span><span class="st">"B"</span><span class="op">)</span><span class="op">)</span></span></span>
-<span class="r-out co"><span class="r-pr">#&gt;</span>      Joincount  Expected  Variance z-value</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> 0:0  1687.0000 1607.0369  303.8034  4.5877</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> 1:1   195.0000  171.5572  114.2057  2.1936</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> 2:2    37.0000   35.4450   29.6821  0.2854</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> 3:3     5.0000    3.2440    3.0687  1.0024</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> 4:4     8.0000    2.0582    1.9674  4.2361</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> 1:0  1000.0000 1053.3931  480.6959 -2.4353</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> 2:0   429.0000  480.1513  215.0360 -3.4882</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> 2:1   180.0000  157.1271  119.3987  2.0932</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> 3:0   119.0000  146.9851   65.1029 -3.4684</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> 3:1    49.0000   48.1001   38.3268  0.1454</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> 3:2    32.0000   21.9247   19.5237  2.2802</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> 4:0    88.0000  117.5881   52.0312 -4.1019</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> 4:1    44.0000   38.4801   30.7868  0.9948</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> 4:2    24.0000   17.5398   15.6933  1.6308</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> 4:3     9.0000    5.3693    5.0994  1.6078</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> Jtot 1974.0000 2086.6587  582.8326 -4.6665</span>
 <span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/base/cat.html" class="external-link">cat</a></span><span class="op">(</span><span class="st">"replicates Upton &amp; Fingleton table 3.7 (p. 169)\n"</span><span class="op">)</span></span></span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> replicates Upton &amp; Fingleton table 3.7 (p. 169)</span>
-<span class="r-in"><span><span class="co"># }</span></span></span>
+<span class="r-in"><span><span class="op">}</span> <span class="co"># }</span></span></span>
 <span class="r-in"><span><span class="va">GDAL37</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/numeric_version.html" class="external-link">as.numeric_version</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/unname.html" class="external-link">unname</a></span><span class="op">(</span><span class="fu"><a href="https://r-spatial.github.io/sf/reference/sf_extSoftVersion.html" class="external-link">sf_extSoftVersion</a></span><span class="op">(</span><span class="op">)</span><span class="op">[</span><span class="st">"GDAL"</span><span class="op">]</span><span class="op">)</span><span class="op">)</span> <span class="op">&gt;=</span> <span class="st">"3.7.0"</span></span></span>
 <span class="r-in"><span><span class="va">file</span> <span class="op">&lt;-</span> <span class="st">"etc/shapes/GB_2024_southcoast_50m.gpkg.zip"</span></span></span>
 <span class="r-in"><span><span class="va">zipfile</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.file.html" class="external-link">system.file</a></span><span class="op">(</span><span class="va">file</span>, package<span class="op">=</span><span class="st">"spdep"</span><span class="op">)</span></span></span>
@@ -241,7 +175,7 @@ <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-e
 <span class="r-in"><span>    <span class="va">sc50m</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://r-spatial.github.io/sf/reference/st_read.html" class="external-link">st_read</a></span><span class="op">(</span><span class="va">target</span><span class="op">)</span></span></span>
 <span class="r-in"><span><span class="op">}</span></span></span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> Reading layer `GB_2024_southcoast_50m' from data source </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span>   `/tmp/RtmpzEChJG/temp_libpath8ee3b7c361c1e/spdep/etc/shapes/GB_2024_southcoast_50m.gpkg.zip' </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span>   `/tmp/RtmpXVTJuL/temp_libpath3b356d487bad39/spdep/etc/shapes/GB_2024_southcoast_50m.gpkg.zip' </span>
 <span class="r-out co"><span class="r-pr">#&gt;</span>   using driver `GPKG'</span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> Simple feature collection with 119 features and 19 fields</span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> Geometry type: MULTIPOLYGON</span>
@@ -250,7 +184,7 @@ <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-e
 <span class="r-out co"><span class="r-pr">#&gt;</span> Projected CRS: OSGB36 / British National Grid</span>
 <span class="r-in"><span><span class="va">sc50m</span><span class="op">$</span><span class="va">Winner</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/factor.html" class="external-link">factor</a></span><span class="op">(</span><span class="va">sc50m</span><span class="op">$</span><span class="va">Winner</span>, levels<span class="op">=</span><span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"Con"</span>, <span class="st">"Green"</span>, <span class="st">"Lab"</span>, <span class="st">"LD"</span><span class="op">)</span><span class="op">)</span></span></span>
 <span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">sc50m</span><span class="op">[</span>,<span class="st">"Winner"</span><span class="op">]</span>, pal<span class="op">=</span><span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"#2297E6"</span>, <span class="st">"#61D04F"</span>, <span class="st">"#DF536B"</span>, <span class="st">"#F5C710"</span><span class="op">)</span><span class="op">)</span></span></span>
-<span class="r-plt img"><img src="joincount.multi-2.png" alt="" width="700" height="433"></span>
+<span class="r-plt img"><img src="joincount.multi-1.png" alt="" width="700" height="433"></span>
 <span class="r-in"><span><span class="va">nb_sc_50m</span> <span class="op">&lt;-</span> <span class="fu"><a href="poly2nb.html">poly2nb</a></span><span class="op">(</span><span class="va">sc50m</span>, row.names<span class="op">=</span><span class="fu"><a href="https://rdrr.io/r/base/character.html" class="external-link">as.character</a></span><span class="op">(</span><span class="va">sc50m</span><span class="op">$</span><span class="va">Constituency</span><span class="op">)</span><span class="op">)</span></span></span>
 <span class="r-wrn co"><span class="r-pr">#&gt;</span> <span class="warning">Warning: </span>neighbour object has 2 sub-graphs;</span>
 <span class="r-wrn co"><span class="r-pr">#&gt;</span> if this sub-graph count seems unexpected, try increasing the snap argument.</span>
diff --git a/docs/reference/joincount.test.html b/docs/reference/joincount.test.html
index 2856721f..cf219164 100644
--- a/docs/reference/joincount.test.html
+++ b/docs/reference/joincount.test.html
@@ -19,7 +19,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/knearneigh.html b/docs/reference/knearneigh.html
index 1d1d7376..28cee9a9 100644
--- a/docs/reference/knearneigh.html
+++ b/docs/reference/knearneigh.html
@@ -7,7 +7,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -166,7 +166,7 @@ <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-e
 <span class="r-in"><span><span class="fu"><a href="https://r-spatial.github.io/sf/reference/s2.html" class="external-link">sf_use_s2</a></span><span class="op">(</span><span class="cn">TRUE</span><span class="op">)</span></span></span>
 <span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/base/system.time.html" class="external-link">system.time</a></span><span class="op">(</span><span class="va">gck4a.nb</span> <span class="op">&lt;-</span> <span class="fu"><a href="knn2nb.html">knn2nb</a></span><span class="op">(</span><span class="fu">knearneigh</span><span class="op">(</span><span class="va">xy1</span>, k<span class="op">=</span><span class="fl">4</span><span class="op">)</span><span class="op">)</span><span class="op">)</span></span></span>
 <span class="r-out co"><span class="r-pr">#&gt;</span>    user  system elapsed </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span>   0.014   0.000   0.014 </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span>   0.011   0.000   0.012 </span>
 <span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/base/summary.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">gck4a.nb</span>, <span class="va">xy1</span>, scale<span class="op">=</span><span class="fl">0.5</span><span class="op">)</span></span></span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> Neighbour list object:</span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> Number of regions: 48 </span>
@@ -186,7 +186,7 @@ <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-e
 <span class="r-msg co"><span class="r-pr">#&gt;</span> Spherical geometry (s2) switched off</span>
 <span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/base/system.time.html" class="external-link">system.time</a></span><span class="op">(</span><span class="va">gck4a.nb</span> <span class="op">&lt;-</span> <span class="fu"><a href="knn2nb.html">knn2nb</a></span><span class="op">(</span><span class="fu">knearneigh</span><span class="op">(</span><span class="va">xy1</span>, k<span class="op">=</span><span class="fl">4</span><span class="op">)</span><span class="op">)</span><span class="op">)</span></span></span>
 <span class="r-out co"><span class="r-pr">#&gt;</span>    user  system elapsed </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span>   0.008   0.000   0.009 </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span>   0.008   0.000   0.008 </span>
 <span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/base/summary.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">gck4a.nb</span>, <span class="va">xy1</span>, scale<span class="op">=</span><span class="fl">0.5</span><span class="op">)</span></span></span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> Neighbour list object:</span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> Number of regions: 48 </span>
diff --git a/docs/reference/knn2nb.html b/docs/reference/knn2nb.html
index 520edf40..a799697e 100644
--- a/docs/reference/knn2nb.html
+++ b/docs/reference/knn2nb.html
@@ -11,7 +11,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/lag.listw.html b/docs/reference/lag.listw.html
index 5513d851..54985964 100644
--- a/docs/reference/lag.listw.html
+++ b/docs/reference/lag.listw.html
@@ -7,7 +7,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/lee.html b/docs/reference/lee.html
index 6759c52a..277538a1 100644
--- a/docs/reference/lee.html
+++ b/docs/reference/lee.html
@@ -15,7 +15,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/lee.mc.html b/docs/reference/lee.mc.html
index ac5af6c3..811887ca 100644
--- a/docs/reference/lee.mc.html
+++ b/docs/reference/lee.mc.html
@@ -7,7 +7,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/lee.test.html b/docs/reference/lee.test.html
index 229f6100..8346e928 100644
--- a/docs/reference/lee.test.html
+++ b/docs/reference/lee.test.html
@@ -7,7 +7,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/licd_multi.html b/docs/reference/licd_multi.html
index a4c43a9e..cc260f8e 100644
--- a/docs/reference/licd_multi.html
+++ b/docs/reference/licd_multi.html
@@ -7,7 +7,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -164,9 +164,9 @@ <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-e
 <span class="r-out co"><span class="r-pr">#&gt;</span>  $ local_comp_sim  : NULL</span>
 <span class="r-out co"><span class="r-pr">#&gt;</span>  $ local_config_sim: NULL</span>
 <span class="r-out co"><span class="r-pr">#&gt;</span>  - attr(*, "timings")=List of 3</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span>   ..$ set_up        : 'proc_time' Named num [1:5] 0 0 0 0 0</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span>   ..$ set_up        : 'proc_time' Named num [1:5] 0.001 0 0 0 0</span>
 <span class="r-out co"><span class="r-pr">#&gt;</span>   .. ..- attr(*, "names")= chr [1:5] "user.self" "sys.self" "elapsed" "user.child" ...</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span>   ..$ processing    : 'proc_time' Named num [1:5] 0.106 0 0.107 0 0</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span>   ..$ processing    : 'proc_time' Named num [1:5] 0.109 0 0.11 0 0</span>
 <span class="r-out co"><span class="r-pr">#&gt;</span>   .. ..- attr(*, "names")= chr [1:5] "user.self" "sys.self" "elapsed" "user.child" ...</span>
 <span class="r-out co"><span class="r-pr">#&gt;</span>   ..$ postprocessing: 'proc_time' Named num [1:5] 0.001 0 0.001 0 0</span>
 <span class="r-out co"><span class="r-pr">#&gt;</span>   .. ..- attr(*, "names")= chr [1:5] "user.self" "sys.self" "elapsed" "user.child" ...</span>
@@ -221,7 +221,7 @@ <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-e
 <span class="r-in"><span>    <span class="va">sc50m</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://r-spatial.github.io/sf/reference/st_read.html" class="external-link">st_read</a></span><span class="op">(</span><span class="va">target</span><span class="op">)</span></span></span>
 <span class="r-in"><span><span class="op">}</span></span></span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> Reading layer `GB_2024_southcoast_50m' from data source </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span>   `/tmp/RtmpzEChJG/temp_libpath8ee3b7c361c1e/spdep/etc/shapes/GB_2024_southcoast_50m.gpkg.zip' </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span>   `/tmp/RtmpXVTJuL/temp_libpath3b356d487bad39/spdep/etc/shapes/GB_2024_southcoast_50m.gpkg.zip' </span>
 <span class="r-out co"><span class="r-pr">#&gt;</span>   using driver `GPKG'</span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> Simple feature collection with 119 features and 19 fields</span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> Geometry type: MULTIPOLYGON</span>
diff --git a/docs/reference/listw2sn.html b/docs/reference/listw2sn.html
index 734f3efd..1ea2f8b4 100644
--- a/docs/reference/listw2sn.html
+++ b/docs/reference/listw2sn.html
@@ -11,7 +11,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/lm.RStests.html b/docs/reference/lm.RStests.html
index a0e8ad8a..016d812d 100644
--- a/docs/reference/lm.RStests.html
+++ b/docs/reference/lm.RStests.html
@@ -21,7 +21,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/lm.morantest.exact.html b/docs/reference/lm.morantest.exact.html
index 22462940..d9811fef 100644
--- a/docs/reference/lm.morantest.exact.html
+++ b/docs/reference/lm.morantest.exact.html
@@ -7,7 +7,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/lm.morantest.html b/docs/reference/lm.morantest.html
index b4dba0f2..9261b1e1 100644
--- a/docs/reference/lm.morantest.html
+++ b/docs/reference/lm.morantest.html
@@ -7,7 +7,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/lm.morantest.sad.html b/docs/reference/lm.morantest.sad.html
index 99b0dadf..bbebc76c 100644
--- a/docs/reference/lm.morantest.sad.html
+++ b/docs/reference/lm.morantest.sad.html
@@ -9,7 +9,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/localC.html b/docs/reference/localC.html
index 47e6fd56..b98fc6eb 100644
--- a/docs/reference/localC.html
+++ b/docs/reference/localC.html
@@ -9,7 +9,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -199,7 +199,7 @@ <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-e
 <span class="r-out co"><span class="r-pr">#&gt;</span> [37] 0.86422915 0.38817470 0.23425755 1.26191610 1.34455327 1.80707481</span>
 <span class="r-in"><span></span></span>
 <span class="r-in"><span></span></span>
-<span class="r-in"><span><span class="co"># \dontrun{</span></span></span>
+<span class="r-in"><span><span class="kw">if</span> <span class="op">(</span><span class="cn">FALSE</span><span class="op">)</span> <span class="op">{</span> <span class="co"># \dontrun{</span></span></span>
 <span class="r-in"><span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va"><a href="https://rstudio.github.io/reticulate/" class="external-link">reticulate</a></span><span class="op">)</span></span></span>
 <span class="r-in"><span><span class="fu"><a href="https://rstudio.github.io/reticulate/reference/use_python.html" class="external-link">use_python</a></span><span class="op">(</span><span class="st">"/usr/bin/python"</span>, required <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></span>
 <span class="r-in"><span><span class="va">gp</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rstudio.github.io/reticulate/reference/import.html" class="external-link">import</a></span><span class="op">(</span><span class="st">"geopandas"</span><span class="op">)</span></span></span>
@@ -210,7 +210,6 @@ <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-e
 <span class="r-in"><span><span class="va">esda</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rstudio.github.io/reticulate/reference/import.html" class="external-link">import</a></span><span class="op">(</span><span class="st">"esda"</span><span class="op">)</span></span></span>
 <span class="r-in"><span><span class="va">lM</span> <span class="op">&lt;-</span> <span class="va">esda</span><span class="op">$</span><span class="fu">Moran_Local</span><span class="op">(</span><span class="va">x</span>, <span class="va">w</span><span class="op">)</span></span></span>
 <span class="r-in"><span><span class="fu"><a href="https://rdrr.io/pkg/Matrix/man/all.equal-methods.html" class="external-link">all.equal</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/unname.html" class="external-link">unname</a></span><span class="op">(</span><span class="fu"><a href="localmoran.html">localmoran</a></span><span class="op">(</span><span class="va">x</span>, <span class="va">listw</span>, mlvar<span class="op">=</span><span class="cn">FALSE</span><span class="op">)</span><span class="op">[</span>,<span class="fl">1</span><span class="op">]</span><span class="op">)</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="va">lM</span><span class="op">$</span><span class="va">Is</span><span class="op">)</span><span class="op">)</span></span></span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> [1] TRUE</span>
 <span class="r-in"><span><span class="co"># confirm x and w the same</span></span></span>
 <span class="r-in"><span><span class="va">lC</span> <span class="op">&lt;-</span> <span class="va">esda</span><span class="op">$</span><span class="fu">Geary_Local</span><span class="op">(</span>connectivity<span class="op">=</span><span class="va">w</span><span class="op">)</span><span class="op">$</span><span class="fu">fit</span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/scale.html" class="external-link">scale</a></span><span class="op">(</span><span class="va">x</span><span class="op">)</span><span class="op">)</span></span></span>
 <span class="r-in"><span><span class="co"># np$std missing ddof=1</span></span></span>
@@ -219,16 +218,10 @@ <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-e
 <span class="r-in"><span><span class="co"># lC components probably wrongly ordered https://github.com/pysal/esda/issues/192</span></span></span>
 <span class="r-in"><span><span class="va">o</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/match.html" class="external-link">match</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/Round.html" class="external-link">round</a></span><span class="op">(</span><span class="va">D0</span>, <span class="fl">6</span><span class="op">)</span>, <span class="fu"><a href="https://rdrr.io/r/base/Round.html" class="external-link">round</a></span><span class="op">(</span><span class="va">lC</span><span class="op">$</span><span class="va">localG</span>, <span class="fl">6</span><span class="op">)</span><span class="op">)</span></span></span>
 <span class="r-in"><span><span class="fu"><a href="https://rdrr.io/pkg/Matrix/man/all.equal-methods.html" class="external-link">all.equal</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="va">lC</span><span class="op">$</span><span class="va">localG</span><span class="op">)</span><span class="op">[</span><span class="va">o</span><span class="op">]</span>, <span class="va">D0</span><span class="op">)</span></span></span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> [1] TRUE</span>
 <span class="r-in"><span><span class="co"># simulation order not retained</span></span></span>
 <span class="r-in"><span><span class="va">lC</span><span class="op">$</span><span class="va">p_sim</span><span class="op">[</span><span class="va">o</span><span class="op">]</span></span></span>
-<span class="r-out co"><span class="r-pr">#&gt;</span>  [1] 0.258 0.448 0.123 0.019 0.123 0.021 0.294 0.439 0.155 0.001 0.127 0.131</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> [13] 0.149 0.256 0.456 0.191 0.111 0.293 0.001 0.037 0.027 0.098 0.059 0.279</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> [25] 0.150 0.028 0.114 0.277 0.484 0.001 0.067 0.099 0.091 0.243 0.299 0.001</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> [37] 0.301 0.488 0.307 0.209 0.248 0.269</span>
 <span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/base/attr.html" class="external-link">attr</a></span><span class="op">(</span><span class="va">C</span>, <span class="st">"pseudo-p"</span><span class="op">)</span><span class="op">[</span>,<span class="fl">6</span><span class="op">]</span></span></span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> NULL</span>
-<span class="r-in"><span><span class="co"># }</span></span></span>
+<span class="r-in"><span><span class="op">}</span> <span class="co"># }</span></span></span>
 </code></pre></div>
     </div>
   </main><aside class="col-md-3"><nav id="toc" aria-label="Table of contents"><h2>On this page</h2>
diff --git a/docs/reference/localG.html b/docs/reference/localG.html
index 6865c4dd..19fcea22 100644
--- a/docs/reference/localG.html
+++ b/docs/reference/localG.html
@@ -19,7 +19,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/localGS.html b/docs/reference/localGS.html
index d95f7c38..b0a93e7d 100644
--- a/docs/reference/localGS.html
+++ b/docs/reference/localGS.html
@@ -13,7 +13,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/local_joincount_bv.html b/docs/reference/local_joincount_bv.html
index dea4a62f..8b489b0f 100644
--- a/docs/reference/local_joincount_bv.html
+++ b/docs/reference/local_joincount_bv.html
@@ -7,7 +7,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/local_joincount_uni.html b/docs/reference/local_joincount_uni.html
index 0394ca7a..b9fb6851 100644
--- a/docs/reference/local_joincount_uni.html
+++ b/docs/reference/local_joincount_uni.html
@@ -9,7 +9,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/localmoran.exact.html b/docs/reference/localmoran.exact.html
index 4545f830..2c6f49fa 100644
--- a/docs/reference/localmoran.exact.html
+++ b/docs/reference/localmoran.exact.html
@@ -7,7 +7,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/localmoran.html b/docs/reference/localmoran.html
index eefa6b15..e327ed9a 100644
--- a/docs/reference/localmoran.html
+++ b/docs/reference/localmoran.html
@@ -15,7 +15,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/localmoran.sad.html b/docs/reference/localmoran.sad.html
index f53ca9bb..6956f1bd 100644
--- a/docs/reference/localmoran.sad.html
+++ b/docs/reference/localmoran.sad.html
@@ -23,7 +23,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/localmoran_bv.html b/docs/reference/localmoran_bv.html
index 1b5d245a..0848fb89 100644
--- a/docs/reference/localmoran_bv.html
+++ b/docs/reference/localmoran_bv.html
@@ -7,7 +7,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/mat2listw.html b/docs/reference/mat2listw.html
index a46d0e4e..acd73ec3 100644
--- a/docs/reference/mat2listw.html
+++ b/docs/reference/mat2listw.html
@@ -13,7 +13,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/moran.html b/docs/reference/moran.html
index 98eafe90..5258f180 100644
--- a/docs/reference/moran.html
+++ b/docs/reference/moran.html
@@ -13,7 +13,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/moran.mc.html b/docs/reference/moran.mc.html
index b76ac2ef..4316d7e1 100644
--- a/docs/reference/moran.mc.html
+++ b/docs/reference/moran.mc.html
@@ -7,7 +7,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/moran.plot.html b/docs/reference/moran.plot.html
index f5330dc6..2d438ef4 100644
--- a/docs/reference/moran.plot.html
+++ b/docs/reference/moran.plot.html
@@ -13,7 +13,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -142,14 +142,14 @@ <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-e
 <span class="r-in"><span>    <span class="fu"><a href="https://ggplot2.tidyverse.org/reference/labs.html" class="external-link">xlab</a></span><span class="op">(</span><span class="va">xname</span><span class="op">)</span> <span class="op">+</span> <span class="fu"><a href="https://ggplot2.tidyverse.org/reference/labs.html" class="external-link">ylab</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/paste.html" class="external-link">paste0</a></span><span class="op">(</span><span class="st">"Spatially lagged "</span>, <span class="va">xname</span><span class="op">)</span><span class="op">)</span></span></span>
 <span class="r-in"><span><span class="op">}</span></span></span>
 <span class="r-plt img"><img src="moran.plot-3.png" alt="" width="700" height="433"></span>
-<span class="r-in"><span><span class="va">columbus</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://r-spatial.github.io/sf/reference/st_read.html" class="external-link">st_read</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/system.file.html" class="external-link">system.file</a></span><span class="op">(</span><span class="st">"shapes/columbus.shp"</span>, package<span class="op">=</span><span class="st">"spData"</span><span class="op">)</span><span class="op">)</span></span></span>
+<span class="r-in"><span><span class="va">columbus</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://r-spatial.github.io/sf/reference/st_read.html" class="external-link">st_read</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/system.file.html" class="external-link">system.file</a></span><span class="op">(</span><span class="st">"shapes/columbus.gpkg"</span>, package<span class="op">=</span><span class="st">"spData"</span><span class="op">)</span><span class="op">)</span></span></span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> Reading layer `columbus' from data source </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span>   `/home/rsb/lib/r_libs/spData/shapes/columbus.shp' using driver `ESRI Shapefile'</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span>   `/home/rsb/lib/r_libs/spData/shapes/columbus.gpkg' using driver `GPKG'</span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> Simple feature collection with 49 features and 20 fields</span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> Geometry type: POLYGON</span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> Dimension:     XY</span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> Bounding box:  xmin: 5.874907 ymin: 10.78863 xmax: 11.28742 ymax: 14.74245</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> CRS:           NA</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> Projected CRS: Undefined Cartesian SRS with unknown unit</span>
 <span class="r-in"><span><span class="va">nb</span> <span class="op">&lt;-</span> <span class="fu"><a href="poly2nb.html">poly2nb</a></span><span class="op">(</span><span class="va">columbus</span><span class="op">)</span></span></span>
 <span class="r-in"><span><span class="va">listw</span> <span class="op">&lt;-</span> <span class="fu"><a href="nb2listw.html">nb2listw</a></span><span class="op">(</span><span class="va">nb</span><span class="op">)</span></span></span>
 <span class="r-in"><span><span class="fu">moran.plot</span><span class="op">(</span>x<span class="op">=</span><span class="va">columbus</span><span class="op">$</span><span class="va">CRIME</span>, y<span class="op">=</span><span class="va">columbus</span><span class="op">$</span><span class="va">INC</span>, listw<span class="op">=</span><span class="va">listw</span><span class="op">)</span></span></span>
diff --git a/docs/reference/moran.test.html b/docs/reference/moran.test.html
index 17dc9773..d418c08c 100644
--- a/docs/reference/moran.test.html
+++ b/docs/reference/moran.test.html
@@ -7,7 +7,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/moran_bv.html b/docs/reference/moran_bv.html
index cf6a872b..d24e8932 100644
--- a/docs/reference/moran_bv.html
+++ b/docs/reference/moran_bv.html
@@ -7,7 +7,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/mstree.html b/docs/reference/mstree.html
index f9d7d5dd..e1ffaaf2 100644
--- a/docs/reference/mstree.html
+++ b/docs/reference/mstree.html
@@ -15,7 +15,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -115,7 +115,7 @@ <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-e
 <span class="r-in"><span>    <span class="va">bh</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://r-spatial.github.io/sf/reference/st_read.html" class="external-link">st_read</a></span><span class="op">(</span><span class="va">target</span><span class="op">)</span></span></span>
 <span class="r-in"><span><span class="op">}</span></span></span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> Reading layer `bhicv' from data source </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span>   `/tmp/RtmpzEChJG/temp_libpath8ee3b7c361c1e/spdep/etc/shapes/bhicv.gpkg.zip' </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span>   `/tmp/RtmpXVTJuL/temp_libpath3b356d487bad39/spdep/etc/shapes/bhicv.gpkg.zip' </span>
 <span class="r-out co"><span class="r-pr">#&gt;</span>   using driver `GPKG'</span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> Simple feature collection with 98 features and 8 fields</span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> Geometry type: POLYGON</span>
@@ -137,7 +137,7 @@ <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-e
 <span class="r-in"><span><span class="co">### find a minimum spanning tree</span></span></span>
 <span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/base/system.time.html" class="external-link">system.time</a></span><span class="op">(</span><span class="va">mst.bh</span> <span class="op">&lt;-</span> <span class="fu">mstree</span><span class="op">(</span><span class="va">nb.w</span>,<span class="fl">5</span><span class="op">)</span><span class="op">)</span></span></span>
 <span class="r-out co"><span class="r-pr">#&gt;</span>    user  system elapsed </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span>   0.003   0.000   0.004 </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span>   0.002   0.000   0.002 </span>
 <span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/base/dim.html" class="external-link">dim</a></span><span class="op">(</span><span class="va">mst.bh</span><span class="op">)</span></span></span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> [1] 97  3</span>
 <span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/utils/head.html" class="external-link">head</a></span><span class="op">(</span><span class="va">mst.bh</span><span class="op">)</span></span></span>
diff --git a/docs/reference/nb2INLA.html b/docs/reference/nb2INLA.html
index 2bbc8c6f..f90032c8 100644
--- a/docs/reference/nb2INLA.html
+++ b/docs/reference/nb2INLA.html
@@ -7,7 +7,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/nb2WB.html b/docs/reference/nb2WB.html
index 6bf97732..d63c6123 100644
--- a/docs/reference/nb2WB.html
+++ b/docs/reference/nb2WB.html
@@ -7,7 +7,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/nb2blocknb.html b/docs/reference/nb2blocknb.html
index f50915ec..3c6aaa0d 100644
--- a/docs/reference/nb2blocknb.html
+++ b/docs/reference/nb2blocknb.html
@@ -13,7 +13,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -104,98 +104,31 @@ <h2 id="see-also">See also<a class="anchor" aria-label="anchor" href="#see-also"
 
     <div class="section level2">
     <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-examples"></a></h2>
-    <div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"><span><span class="co"># \dontrun{</span></span></span>
+    <div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"><span><span class="kw">if</span> <span class="op">(</span><span class="cn">FALSE</span><span class="op">)</span> <span class="op">{</span> <span class="co"># \dontrun{</span></span></span>
 <span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/utils/data.html" class="external-link">data</a></span><span class="op">(</span><span class="va">boston</span>, package<span class="op">=</span><span class="st">"spData"</span><span class="op">)</span></span></span>
 <span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/base/summary.html" class="external-link">summary</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/vector.html" class="external-link">as.vector</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/table.html" class="external-link">table</a></span><span class="op">(</span><span class="va">boston.c</span><span class="op">$</span><span class="va">TOWN</span><span class="op">)</span><span class="op">)</span><span class="op">)</span></span></span>
-<span class="r-out co"><span class="r-pr">#&gt;</span>    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span>     1.0     2.0     4.0     5.5     7.0    30.0 </span>
 <span class="r-in"><span><span class="va">townaggr</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/stats/aggregate.html" class="external-link">aggregate</a></span><span class="op">(</span><span class="va">boston.utm</span>, <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span>town<span class="op">=</span><span class="va">boston.c</span><span class="op">$</span><span class="va">TOWN</span><span class="op">)</span>, <span class="va">mean</span><span class="op">)</span></span></span>
 <span class="r-in"><span><span class="va">block.rel</span> <span class="op">&lt;-</span> <span class="fu"><a href="graphneigh.html">graph2nb</a></span><span class="op">(</span><span class="fu"><a href="graphneigh.html">relativeneigh</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/matrix.html" class="external-link">as.matrix</a></span><span class="op">(</span><span class="va">townaggr</span><span class="op">[</span>,<span class="fl">2</span><span class="op">:</span><span class="fl">3</span><span class="op">]</span><span class="op">)</span><span class="op">)</span>,</span></span>
 <span class="r-in"><span> <span class="fu"><a href="https://rdrr.io/r/base/character.html" class="external-link">as.character</a></span><span class="op">(</span><span class="va">townaggr</span><span class="op">[</span>,<span class="fl">1</span><span class="op">]</span><span class="op">)</span>, sym<span class="op">=</span><span class="cn">TRUE</span><span class="op">)</span></span></span>
 <span class="r-in"><span><span class="va">block.rel</span></span></span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> Neighbour list object:</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> Number of regions: 92 </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> Number of nonzero links: 240 </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> Percentage nonzero weights: 2.835539 </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> Average number of links: 2.608696 </span>
 <span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="fu"><a href="testnb.html">is.symmetric.nb</a></span><span class="op">(</span><span class="va">block.rel</span><span class="op">)</span><span class="op">)</span></span></span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> [1] TRUE</span>
 <span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">block.rel</span>, <span class="fu"><a href="https://rdrr.io/r/base/matrix.html" class="external-link">as.matrix</a></span><span class="op">(</span><span class="va">townaggr</span><span class="op">[</span>,<span class="fl">2</span><span class="op">:</span><span class="fl">3</span><span class="op">]</span><span class="op">)</span><span class="op">)</span></span></span>
 <span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/graphics/points.html" class="external-link">points</a></span><span class="op">(</span><span class="va">boston.utm</span>, pch<span class="op">=</span><span class="fl">18</span>, col<span class="op">=</span><span class="st">"lightgreen"</span><span class="op">)</span></span></span>
-<span class="r-plt img"><img src="nb2blocknb-1.png" alt="" width="700" height="433"></span>
 <span class="r-in"><span><span class="va">block.nb</span> <span class="op">&lt;-</span> <span class="fu">nb2blocknb</span><span class="op">(</span><span class="va">block.rel</span>, <span class="fu"><a href="https://rdrr.io/r/base/character.html" class="external-link">as.character</a></span><span class="op">(</span><span class="va">boston.c</span><span class="op">$</span><span class="va">TOWN</span><span class="op">)</span><span class="op">)</span></span></span>
 <span class="r-in"><span><span class="va">block.nb</span></span></span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> Neighbour list object:</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> Number of regions: 506 </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> Number of nonzero links: 15234 </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> Percentage nonzero weights: 5.949945 </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> Average number of links: 30.10672 </span>
 <span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="fu"><a href="testnb.html">is.symmetric.nb</a></span><span class="op">(</span><span class="va">block.nb</span><span class="op">)</span><span class="op">)</span></span></span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> [1] TRUE</span>
 <span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">block.nb</span>, <span class="va">boston.utm</span><span class="op">)</span></span></span>
 <span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/graphics/points.html" class="external-link">points</a></span><span class="op">(</span><span class="va">boston.utm</span>, pch<span class="op">=</span><span class="fl">18</span>, col<span class="op">=</span><span class="st">"lightgreen"</span><span class="op">)</span></span></span>
-<span class="r-plt img"><img src="nb2blocknb-2.png" alt="" width="700" height="433"></span>
 <span class="r-in"><span><span class="fu"><a href="compon.html">n.comp.nb</a></span><span class="op">(</span><span class="va">block.nb</span><span class="op">)</span><span class="op">$</span><span class="va">nc</span></span></span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> [1] 1</span>
 <span class="r-in"><span><span class="fu"><a href="moran.test.html">moran.test</a></span><span class="op">(</span><span class="va">boston.c</span><span class="op">$</span><span class="va">CMEDV</span>, <span class="fu"><a href="nb2listw.html">nb2listw</a></span><span class="op">(</span><span class="va">boston.soi</span><span class="op">)</span><span class="op">)</span></span></span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> 	Moran I test under randomisation</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> data:  boston.c$CMEDV  </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> weights: nb2listw(boston.soi)    </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> Moran I statistic standard deviate = 21.786, p-value &lt; 2.2e-16</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> alternative hypothesis: greater</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> sample estimates:</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> Moran I statistic       Expectation          Variance </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span>       0.690285059      -0.001980198       0.001009685 </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
 <span class="r-in"><span><span class="fu"><a href="moran.test.html">moran.test</a></span><span class="op">(</span><span class="va">boston.c</span><span class="op">$</span><span class="va">CMEDV</span>, <span class="fu"><a href="nb2listw.html">nb2listw</a></span><span class="op">(</span><span class="va">block.nb</span><span class="op">)</span><span class="op">)</span></span></span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> 	Moran I test under randomisation</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> data:  boston.c$CMEDV  </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> weights: nb2listw(block.nb)    </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> Moran I statistic standard deviate = 22.455, p-value &lt; 2.2e-16</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> alternative hypothesis: greater</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> sample estimates:</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> Moran I statistic       Expectation          Variance </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span>      0.3122905961     -0.0019801980      0.0001958827 </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
 <span class="r-in"><span><span class="va">block.nb</span> <span class="op">&lt;-</span> <span class="fu">nb2blocknb</span><span class="op">(</span><span class="cn">NULL</span>, <span class="fu"><a href="https://rdrr.io/r/base/character.html" class="external-link">as.character</a></span><span class="op">(</span><span class="va">boston.c</span><span class="op">$</span><span class="va">TOWN</span><span class="op">)</span><span class="op">)</span></span></span>
-<span class="r-wrn co"><span class="r-pr">#&gt;</span> <span class="warning">Warning: </span>neighbour object has 92 sub-graphs</span>
 <span class="r-in"><span><span class="va">block.nb</span></span></span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> Neighbour list object:</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> Number of regions: 506 </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> Number of nonzero links: 4868 </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> Percentage nonzero weights: 1.901295 </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> Average number of links: 9.620553 </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> 17 regions with no links:</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> 1, 55, 56, 57, 58, 65, 196, 257, 284, 285, 286, 287, 342, 343, 348,</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> 349, 354</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> 92 disjoint connected subgraphs</span>
 <span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="fu"><a href="testnb.html">is.symmetric.nb</a></span><span class="op">(</span><span class="va">block.nb</span><span class="op">)</span><span class="op">)</span></span></span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> [1] TRUE</span>
 <span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">block.nb</span>, <span class="va">boston.utm</span><span class="op">)</span></span></span>
-<span class="r-plt img"><img src="nb2blocknb-3.png" alt="" width="700" height="433"></span>
 <span class="r-in"><span><span class="fu"><a href="compon.html">n.comp.nb</a></span><span class="op">(</span><span class="va">block.nb</span><span class="op">)</span><span class="op">$</span><span class="va">nc</span></span></span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> [1] 92</span>
 <span class="r-in"><span><span class="fu"><a href="moran.test.html">moran.test</a></span><span class="op">(</span><span class="va">boston.c</span><span class="op">$</span><span class="va">CMEDV</span>, <span class="fu"><a href="nb2listw.html">nb2listw</a></span><span class="op">(</span><span class="va">block.nb</span>, zero.policy<span class="op">=</span><span class="cn">TRUE</span><span class="op">)</span>, zero.policy<span class="op">=</span><span class="cn">TRUE</span><span class="op">)</span></span></span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> 	Moran I test under randomisation</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> data:  boston.c$CMEDV  </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> weights: nb2listw(block.nb, zero.policy = TRUE)  </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> n reduced by no-neighbour observations  </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> Moran I statistic standard deviate = 21.145, p-value &lt; 2.2e-16</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> alternative hypothesis: greater</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> sample estimates:</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> Moran I statistic       Expectation          Variance </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span>      0.6188830566     -0.0020491803      0.0008623116 </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
-<span class="r-in"><span><span class="co"># }</span></span></span>
+<span class="r-in"><span><span class="op">}</span> <span class="co"># }</span></span></span>
 </code></pre></div>
     </div>
   </main><aside class="col-md-3"><nav id="toc" aria-label="Table of contents"><h2>On this page</h2>
diff --git a/docs/reference/nb2lines.html b/docs/reference/nb2lines.html
index c69a8db1..c8336b70 100644
--- a/docs/reference/nb2lines.html
+++ b/docs/reference/nb2lines.html
@@ -7,7 +7,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -132,12 +132,12 @@ <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-e
 <span class="r-out co"><span class="r-pr">#&gt;</span>  Max.   :0.5000                   </span>
 <span class="r-in"><span><span class="va">tf</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/paste.html" class="external-link">paste0</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/tempfile.html" class="external-link">tempfile</a></span><span class="op">(</span><span class="op">)</span>, <span class="st">".gpkg"</span><span class="op">)</span></span></span>
 <span class="r-in"><span><span class="fu"><a href="https://r-spatial.github.io/sf/reference/st_write.html" class="external-link">st_write</a></span><span class="op">(</span><span class="va">res</span>, dsn<span class="op">=</span><span class="va">tf</span>, driver<span class="op">=</span><span class="st">"GPKG"</span><span class="op">)</span></span></span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> Writing layer `file8efec6591ae67' to data source </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span>   `/tmp/RtmpGWmmWp/file8efec6591ae67.gpkg' using driver `GPKG'</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> Writing layer `file3b434754c9c27d' to data source </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span>   `/tmp/Rtmp2GWLZN/file3b434754c9c27d.gpkg' using driver `GPKG'</span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> Writing 230 features with 5 fields and geometry type Line String.</span>
 <span class="r-in"><span><span class="va">inMap</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://r-spatial.github.io/sf/reference/st_read.html" class="external-link">st_read</a></span><span class="op">(</span><span class="va">tf</span><span class="op">)</span></span></span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> Reading layer `file8efec6591ae67' from data source </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span>   `/tmp/RtmpGWmmWp/file8efec6591ae67.gpkg' using driver `GPKG'</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> Reading layer `file3b434754c9c27d' from data source </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span>   `/tmp/Rtmp2GWLZN/file3b434754c9c27d.gpkg' using driver `GPKG'</span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> Simple feature collection with 230 features and 5 fields</span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> Geometry type: LINESTRING</span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> Dimension:     XY</span>
diff --git a/docs/reference/nb2listw.html b/docs/reference/nb2listw.html
index f49de9c8..01df63fa 100644
--- a/docs/reference/nb2listw.html
+++ b/docs/reference/nb2listw.html
@@ -7,7 +7,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/nb2listwdist.html b/docs/reference/nb2listwdist.html
index 9c7d464e..7cbd3a57 100644
--- a/docs/reference/nb2listwdist.html
+++ b/docs/reference/nb2listwdist.html
@@ -7,7 +7,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -146,84 +146,29 @@ <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-e
 <span class="r-out co"><span class="r-pr">#&gt;</span> Moran I statistic       Expectation          Variance </span>
 <span class="r-out co"><span class="r-pr">#&gt;</span>       0.473883371      -0.007042254       0.029994057 </span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> </span>
-<span class="r-in"><span><span class="co"># \dontrun{</span></span></span>
+<span class="r-in"><span><span class="kw">if</span> <span class="op">(</span><span class="cn">FALSE</span><span class="op">)</span> <span class="op">{</span> <span class="co"># \dontrun{</span></span></span>
 <span class="r-in"><span><span class="co"># Moran's I (life expectancy) with IDW with alpha = 2, no coding scheme</span></span></span>
 <span class="r-in"><span><span class="va">world_weights</span> <span class="op">&lt;-</span> <span class="fu">nb2listwdist</span><span class="op">(</span><span class="va">nb_world</span>, <span class="va">pts</span>, type <span class="op">=</span> <span class="st">"idw"</span>,</span></span>
 <span class="r-in"><span>  alpha <span class="op">=</span> <span class="fl">2</span>, zero.policy <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></span>
 <span class="r-in"><span><span class="fu"><a href="moran.test.html">moran.test</a></span><span class="op">(</span><span class="va">world</span><span class="op">$</span><span class="va">lifeExp</span>, <span class="va">world_weights</span>, zero.policy <span class="op">=</span> <span class="cn">TRUE</span>, na.action <span class="op">=</span> <span class="va">na.pass</span><span class="op">)</span></span></span>
-<span class="r-wrn co"><span class="r-pr">#&gt;</span> <span class="warning">Warning: </span>NAs in lagged values</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> 	Moran I test under randomisation</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> data:  world$lifeExp  </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> weights: world_weights  </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> n reduced by no-neighbour observations  </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> Moran I statistic standard deviate = 2.7769, p-value = 0.002744</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> alternative hypothesis: greater</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> sample estimates:</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> Moran I statistic       Expectation          Variance </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span>       0.473883371      -0.007042254       0.029994057 </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
 <span class="r-in"><span><span class="co"># Moran's I (life expectancy), DPD, alpha = 2, dmax = 1000 km, no coding scheme</span></span></span>
 <span class="r-in"><span><span class="va">world_weights</span> <span class="op">&lt;-</span> <span class="fu">nb2listwdist</span><span class="op">(</span><span class="va">nb_world</span>, <span class="va">pts</span>, type <span class="op">=</span> <span class="st">"dpd"</span>,</span></span>
 <span class="r-in"><span>  dmax <span class="op">=</span> <span class="fl">1000000</span>, alpha <span class="op">=</span> <span class="fl">2</span>, zero.policy <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></span>
 <span class="r-in"><span><span class="fu"><a href="moran.test.html">moran.test</a></span><span class="op">(</span><span class="va">world</span><span class="op">$</span><span class="va">lifeExp</span>, <span class="va">world_weights</span>, zero.policy <span class="op">=</span> <span class="cn">TRUE</span>, na.action <span class="op">=</span> <span class="va">na.pass</span><span class="op">)</span></span></span>
-<span class="r-wrn co"><span class="r-pr">#&gt;</span> <span class="warning">Warning: </span>NAs in lagged values</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> 	Moran I test under randomisation</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> data:  world$lifeExp  </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> weights: world_weights  </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> n reduced by no-neighbour observations  </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> Moran I statistic standard deviate = 8.8557, p-value &lt; 2.2e-16</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> alternative hypothesis: greater</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> sample estimates:</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> Moran I statistic       Expectation          Variance </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span>       0.601498970      -0.007042254       0.004722063 </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
 <span class="r-in"><span><span class="co"># Boston examples</span></span></span>
 <span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/utils/data.html" class="external-link">data</a></span><span class="op">(</span><span class="va">boston</span>, package<span class="op">=</span><span class="st">"spData"</span><span class="op">)</span></span></span>
 <span class="r-in"><span><span class="va">boston_coords</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/data.frame.html" class="external-link">data.frame</a></span><span class="op">(</span>x <span class="op">=</span> <span class="va">boston.utm</span><span class="op">[</span>,<span class="fl">1</span><span class="op">]</span>, y <span class="op">=</span> <span class="va">boston.utm</span><span class="op">[</span>,<span class="fl">2</span><span class="op">]</span><span class="op">)</span></span></span>
 <span class="r-in"><span><span class="va">boston.geoms</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://r-spatial.github.io/sf/reference/st_as_sf.html" class="external-link">st_as_sf</a></span><span class="op">(</span><span class="va">boston_coords</span>, coords <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"x"</span>, <span class="st">"y"</span><span class="op">)</span>, remove <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span></span></span>
 <span class="r-in"><span><span class="va">nb_boston</span> <span class="op">&lt;-</span> <span class="fu"><a href="dnearneigh.html">dnearneigh</a></span><span class="op">(</span><span class="va">boston.geoms</span>, <span class="fl">0</span>, <span class="fl">3</span><span class="op">)</span></span></span>
-<span class="r-wrn co"><span class="r-pr">#&gt;</span> <span class="warning">Warning: </span>neighbour object has 9 sub-graphs</span>
 <span class="r-in"><span><span class="co"># Moran's I (crime) with exp weights with alpha = 2, no coding scheme</span></span></span>
 <span class="r-in"><span><span class="va">boston_weights</span> <span class="op">&lt;-</span> <span class="fu">nb2listwdist</span><span class="op">(</span><span class="va">nb_boston</span>, <span class="va">boston.geoms</span>, type <span class="op">=</span> <span class="st">"exp"</span>, alpha <span class="op">=</span> <span class="fl">2</span>,</span></span>
 <span class="r-in"><span>  style<span class="op">=</span><span class="st">"raw"</span>, zero.policy <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></span>
 <span class="r-in"><span><span class="fu"><a href="moran.test.html">moran.test</a></span><span class="op">(</span><span class="va">boston.c</span><span class="op">$</span><span class="va">CRIM</span>, <span class="va">boston_weights</span>, zero.policy <span class="op">=</span> <span class="cn">TRUE</span>, na.action <span class="op">=</span> <span class="va">na.pass</span><span class="op">)</span></span></span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> 	Moran I test under randomisation</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> data:  boston.c$CRIM  </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> weights: boston_weights  </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> n reduced by no-neighbour observations  </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> Moran I statistic standard deviate = 51.34, p-value &lt; 2.2e-16</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> alternative hypothesis: greater</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> sample estimates:</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> Moran I statistic       Expectation          Variance </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span>      0.8845114518     -0.0019960080      0.0002981586 </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
 <span class="r-in"><span><span class="co"># Moran's I (crime) with idw weights with alpha = 2, coding scheme = W</span></span></span>
 <span class="r-in"><span><span class="va">boston_weights</span> <span class="op">&lt;-</span> <span class="fu">nb2listwdist</span><span class="op">(</span><span class="va">nb_boston</span>, <span class="va">boston.geoms</span>, type <span class="op">=</span> <span class="st">"idw"</span>, alpha <span class="op">=</span> <span class="fl">2</span>,</span></span>
 <span class="r-in"><span>  style<span class="op">=</span><span class="st">"W"</span>, zero.policy <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></span>
 <span class="r-in"><span><span class="fu"><a href="moran.test.html">moran.test</a></span><span class="op">(</span><span class="va">boston.c</span><span class="op">$</span><span class="va">CRIM</span>, <span class="va">boston_weights</span>, zero.policy <span class="op">=</span> <span class="cn">TRUE</span>, na.action <span class="op">=</span> <span class="va">na.pass</span><span class="op">)</span></span></span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> 	Moran I test under randomisation</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> data:  boston.c$CRIM  </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> weights: boston_weights  </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> n reduced by no-neighbour observations  </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> Moran I statistic standard deviate = 18.976, p-value &lt; 2.2e-16</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> alternative hypothesis: greater</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> sample estimates:</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> Moran I statistic       Expectation          Variance </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span>      0.4392852330     -0.0019960080      0.0005408065 </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
-<span class="r-in"><span><span class="co"># }</span></span></span>
+<span class="r-in"><span><span class="op">}</span> <span class="co"># }</span></span></span>
 </code></pre></div>
     </div>
   </main><aside class="col-md-3"><nav id="toc" aria-label="Table of contents"><h2>On this page</h2>
diff --git a/docs/reference/nb2mat.html b/docs/reference/nb2mat.html
index 5be37856..fd452f39 100644
--- a/docs/reference/nb2mat.html
+++ b/docs/reference/nb2mat.html
@@ -7,7 +7,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/nbcosts.html b/docs/reference/nbcosts.html
index fc572a10..66b45454 100644
--- a/docs/reference/nbcosts.html
+++ b/docs/reference/nbcosts.html
@@ -11,7 +11,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/nbdists.html b/docs/reference/nbdists.html
index 69c41c58..5221e9fe 100644
--- a/docs/reference/nbdists.html
+++ b/docs/reference/nbdists.html
@@ -13,7 +13,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/nblag.html b/docs/reference/nblag.html
index 112147dc..f655e992 100644
--- a/docs/reference/nblag.html
+++ b/docs/reference/nblag.html
@@ -7,7 +7,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/nboperations.html b/docs/reference/nboperations.html
index fbf007af..943a37e5 100644
--- a/docs/reference/nboperations.html
+++ b/docs/reference/nboperations.html
@@ -7,7 +7,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/p.adjustSP.html b/docs/reference/p.adjustSP.html
index 4d9d3593..7a2056ec 100644
--- a/docs/reference/p.adjustSP.html
+++ b/docs/reference/p.adjustSP.html
@@ -7,7 +7,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/plot.mst.html b/docs/reference/plot.mst.html
index 70be7009..3f926ec2 100644
--- a/docs/reference/plot.mst.html
+++ b/docs/reference/plot.mst.html
@@ -9,7 +9,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/plot.nb.html b/docs/reference/plot.nb.html
index 5948658a..66fab66c 100644
--- a/docs/reference/plot.nb.html
+++ b/docs/reference/plot.nb.html
@@ -7,7 +7,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/plot.skater.html b/docs/reference/plot.skater.html
index 9f6b4a7e..f1eb88a2 100644
--- a/docs/reference/plot.skater.html
+++ b/docs/reference/plot.skater.html
@@ -9,7 +9,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/poly2nb.html b/docs/reference/poly2nb.html
index 9dfc514c..63f9f529 100644
--- a/docs/reference/poly2nb.html
+++ b/docs/reference/poly2nb.html
@@ -7,7 +7,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -156,7 +156,7 @@ <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-e
 <span class="r-out co"><span class="r-pr">#&gt;</span>   0.041   0.000   0.041 </span>
 <span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/base/system.time.html" class="external-link">system.time</a></span><span class="op">(</span><span class="va">xxnb</span> <span class="op">&lt;-</span> <span class="fu">poly2nb</span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/methods/as.html" class="external-link">as</a></span><span class="op">(</span><span class="va">nc.sids</span>, <span class="st">"Spatial"</span><span class="op">)</span><span class="op">)</span><span class="op">)</span></span></span>
 <span class="r-out co"><span class="r-pr">#&gt;</span>    user  system elapsed </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span>   0.059   0.000   0.059 </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span>   0.055   0.000   0.055 </span>
 <span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="fu"><a href="https://r-spatial.github.io/sf/reference/st_geometry.html" class="external-link">st_geometry</a></span><span class="op">(</span><span class="va">nc.sids</span><span class="op">)</span><span class="op">)</span></span></span>
 <span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">xxnb</span>, <span class="fu"><a href="https://r-spatial.github.io/sf/reference/st_coordinates.html" class="external-link">st_coordinates</a></span><span class="op">(</span><span class="fu"><a href="https://r-spatial.github.io/sf/reference/geos_unary.html" class="external-link">st_centroid</a></span><span class="op">(</span><span class="va">nc.sids</span><span class="op">)</span><span class="op">)</span>, add<span class="op">=</span><span class="cn">TRUE</span>, col<span class="op">=</span><span class="st">"blue"</span><span class="op">)</span></span></span>
 <span class="r-wrn co"><span class="r-pr">#&gt;</span> <span class="warning">Warning: </span>st_centroid assumes attributes are constant over geometries</span>
diff --git a/docs/reference/probmap.html b/docs/reference/probmap.html
index 08b97160..66efdb8d 100644
--- a/docs/reference/probmap.html
+++ b/docs/reference/probmap.html
@@ -7,7 +7,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/prunecost.html b/docs/reference/prunecost.html
index 72657200..2fb7c6c1 100644
--- a/docs/reference/prunecost.html
+++ b/docs/reference/prunecost.html
@@ -17,7 +17,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/prunemst.html b/docs/reference/prunemst.html
index 724c6657..556b0170 100644
--- a/docs/reference/prunemst.html
+++ b/docs/reference/prunemst.html
@@ -9,7 +9,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/read.gal.html b/docs/reference/read.gal.html
index 1ff234a2..10688add 100644
--- a/docs/reference/read.gal.html
+++ b/docs/reference/read.gal.html
@@ -7,7 +7,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/read.gwt2nb.html b/docs/reference/read.gwt2nb.html
index 91223890..a57a97dd 100644
--- a/docs/reference/read.gwt2nb.html
+++ b/docs/reference/read.gwt2nb.html
@@ -7,7 +7,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -259,7 +259,7 @@ <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-e
 <span class="r-out co"><span class="r-pr">#&gt;</span> </span>
 <span class="r-wrn co"><span class="r-pr">#&gt;</span> <span class="warning">Warning: </span>region.id not given, c(MYID, NID) range is 1:100</span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> Reading layer `california' from data source </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span>   `/tmp/RtmpzEChJG/temp_libpath8ee3b7c361c1e/spdep/etc/shapes/california.gpkg.zip' </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span>   `/tmp/RtmpXVTJuL/temp_libpath3b356d487bad39/spdep/etc/shapes/california.gpkg.zip' </span>
 <span class="r-out co"><span class="r-pr">#&gt;</span>   using driver `GPKG'</span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> Simple feature collection with 58 features and 2 fields</span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> Geometry type: MULTIPOLYGON</span>
diff --git a/docs/reference/rotation.html b/docs/reference/rotation.html
index 9a46c461..b5e51ca9 100644
--- a/docs/reference/rotation.html
+++ b/docs/reference/rotation.html
@@ -7,7 +7,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/set.mcOption.html b/docs/reference/set.mcOption.html
index 8ba69907..51b75b1c 100644
--- a/docs/reference/set.mcOption.html
+++ b/docs/reference/set.mcOption.html
@@ -7,7 +7,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/set.spChkOption.html b/docs/reference/set.spChkOption.html
index c9fc2a48..e5c1eefb 100644
--- a/docs/reference/set.spChkOption.html
+++ b/docs/reference/set.spChkOption.html
@@ -7,7 +7,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/skater.html b/docs/reference/skater.html
index 577fa1b7..e610f640 100644
--- a/docs/reference/skater.html
+++ b/docs/reference/skater.html
@@ -13,7 +13,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -169,7 +169,7 @@ <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-e
 <span class="r-in"><span>    <span class="va">bh</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://r-spatial.github.io/sf/reference/st_read.html" class="external-link">st_read</a></span><span class="op">(</span><span class="va">target</span><span class="op">)</span></span></span>
 <span class="r-in"><span><span class="op">}</span></span></span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> Reading layer `bhicv' from data source </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span>   `/tmp/RtmpzEChJG/temp_libpath8ee3b7c361c1e/spdep/etc/shapes/bhicv.gpkg.zip' </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span>   `/tmp/RtmpXVTJuL/temp_libpath3b356d487bad39/spdep/etc/shapes/bhicv.gpkg.zip' </span>
 <span class="r-out co"><span class="r-pr">#&gt;</span>   using driver `GPKG'</span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> Simple feature collection with 98 features and 8 fields</span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> Geometry type: POLYGON</span>
@@ -340,22 +340,18 @@ <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-e
 <span class="r-out co"><span class="r-pr">#&gt;</span>  1  2  3  4 </span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> 22 23 33 20 </span>
 <span class="r-in"><span></span></span>
-<span class="r-in"><span><span class="co"># \dontrun{</span></span></span>
+<span class="r-in"><span><span class="kw">if</span> <span class="op">(</span><span class="cn">FALSE</span><span class="op">)</span> <span class="op">{</span> <span class="co"># \dontrun{</span></span></span>
 <span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/utils/data.html" class="external-link">data</a></span><span class="op">(</span><span class="va">boston</span>, package<span class="op">=</span><span class="st">"spData"</span><span class="op">)</span></span></span>
 <span class="r-in"><span><span class="va">bh.nb</span> <span class="op">&lt;-</span> <span class="va">boston.soi</span></span></span>
 <span class="r-in"><span><span class="va">dpad</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/data.frame.html" class="external-link">data.frame</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/scale.html" class="external-link">scale</a></span><span class="op">(</span><span class="va">boston.c</span><span class="op">[</span>,<span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">7</span><span class="op">:</span><span class="fl">10</span><span class="op">)</span><span class="op">]</span><span class="op">)</span><span class="op">)</span></span></span>
 <span class="r-in"><span><span class="co">### calculating costs</span></span></span>
 <span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/base/system.time.html" class="external-link">system.time</a></span><span class="op">(</span><span class="va">lcosts</span> <span class="op">&lt;-</span> <span class="fu"><a href="nbcosts.html">nbcosts</a></span><span class="op">(</span><span class="va">bh.nb</span>, <span class="va">dpad</span><span class="op">)</span><span class="op">)</span></span></span>
-<span class="r-out co"><span class="r-pr">#&gt;</span>    user  system elapsed </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span>   0.047   0.000   0.047 </span>
 <span class="r-in"><span><span class="co">### making listw</span></span></span>
 <span class="r-in"><span><span class="va">nb.w</span> <span class="op">&lt;-</span> <span class="fu"><a href="nb2listw.html">nb2listw</a></span><span class="op">(</span><span class="va">bh.nb</span>, <span class="va">lcosts</span>, style<span class="op">=</span><span class="st">"B"</span><span class="op">)</span></span></span>
 <span class="r-in"><span><span class="co">### find a minimum spanning tree</span></span></span>
 <span class="r-in"><span><span class="va">mst.bh</span> <span class="op">&lt;-</span> <span class="fu"><a href="mstree.html">mstree</a></span><span class="op">(</span><span class="va">nb.w</span>,<span class="fl">5</span><span class="op">)</span></span></span>
 <span class="r-in"><span><span class="co">### three groups with no restriction</span></span></span>
 <span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/base/system.time.html" class="external-link">system.time</a></span><span class="op">(</span><span class="va">res1</span> <span class="op">&lt;-</span> <span class="fu">skater</span><span class="op">(</span><span class="va">mst.bh</span><span class="op">[</span>,<span class="fl">1</span><span class="op">:</span><span class="fl">2</span><span class="op">]</span>, <span class="va">dpad</span>, <span class="fl">2</span><span class="op">)</span><span class="op">)</span></span></span>
-<span class="r-out co"><span class="r-pr">#&gt;</span>    user  system elapsed </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span>   1.743   0.177   1.929 </span>
 <span class="r-in"><span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va">parallel</span><span class="op">)</span></span></span>
 <span class="r-in"><span><span class="va">nc</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/Extremes.html" class="external-link">max</a></span><span class="op">(</span><span class="fl">2L</span>, <span class="fu"><a href="https://rdrr.io/r/parallel/detectCores.html" class="external-link">detectCores</a></span><span class="op">(</span>logical<span class="op">=</span><span class="cn">FALSE</span><span class="op">)</span>, na.rm <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span><span class="op">-</span><span class="fl">1L</span></span></span>
 <span class="r-in"><span><span class="co"># set nc to 1L here</span></span></span>
@@ -369,26 +365,20 @@ <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-e
 <span class="r-in"><span><span class="op">}</span></span></span>
 <span class="r-in"><span><span class="co">### calculating costs</span></span></span>
 <span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/base/system.time.html" class="external-link">system.time</a></span><span class="op">(</span><span class="va">plcosts</span> <span class="op">&lt;-</span> <span class="fu"><a href="nbcosts.html">nbcosts</a></span><span class="op">(</span><span class="va">bh.nb</span>, <span class="va">dpad</span><span class="op">)</span><span class="op">)</span></span></span>
-<span class="r-out co"><span class="r-pr">#&gt;</span>    user  system elapsed </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span>   0.047   0.000   0.048 </span>
 <span class="r-in"><span><span class="fu"><a href="https://rdrr.io/pkg/Matrix/man/all.equal-methods.html" class="external-link">all.equal</a></span><span class="op">(</span><span class="va">lcosts</span>, <span class="va">plcosts</span>, check.attributes<span class="op">=</span><span class="cn">FALSE</span><span class="op">)</span></span></span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> [1] TRUE</span>
 <span class="r-in"><span><span class="co">### making listw</span></span></span>
 <span class="r-in"><span><span class="va">pnb.w</span> <span class="op">&lt;-</span> <span class="fu"><a href="nb2listw.html">nb2listw</a></span><span class="op">(</span><span class="va">bh.nb</span>, <span class="va">plcosts</span>, style<span class="op">=</span><span class="st">"B"</span><span class="op">)</span></span></span>
 <span class="r-in"><span><span class="co">### find a minimum spanning tree</span></span></span>
 <span class="r-in"><span><span class="va">pmst.bh</span> <span class="op">&lt;-</span> <span class="fu"><a href="mstree.html">mstree</a></span><span class="op">(</span><span class="va">pnb.w</span>,<span class="fl">5</span><span class="op">)</span></span></span>
 <span class="r-in"><span><span class="co">### three groups with no restriction</span></span></span>
 <span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/base/system.time.html" class="external-link">system.time</a></span><span class="op">(</span><span class="va">pres1</span> <span class="op">&lt;-</span> <span class="fu">skater</span><span class="op">(</span><span class="va">pmst.bh</span><span class="op">[</span>,<span class="fl">1</span><span class="op">:</span><span class="fl">2</span><span class="op">]</span>, <span class="va">dpad</span>, <span class="fl">2</span><span class="op">)</span><span class="op">)</span></span></span>
-<span class="r-out co"><span class="r-pr">#&gt;</span>    user  system elapsed </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span>   1.764   0.192   1.964 </span>
 <span class="r-in"><span><span class="kw">if</span><span class="op">(</span><span class="op">!</span><span class="fu"><a href="set.mcOption.html">get.mcOption</a></span><span class="op">(</span><span class="op">)</span><span class="op">)</span> <span class="op">{</span></span></span>
 <span class="r-in"><span>  <span class="fu"><a href="set.mcOption.html">set.ClusterOption</a></span><span class="op">(</span><span class="cn">NULL</span><span class="op">)</span></span></span>
 <span class="r-in"><span>  <span class="fu"><a href="https://rdrr.io/r/parallel/makeCluster.html" class="external-link">stopCluster</a></span><span class="op">(</span><span class="va">cl</span><span class="op">)</span></span></span>
 <span class="r-in"><span><span class="op">}</span></span></span>
 <span class="r-in"><span><span class="fu"><a href="https://rdrr.io/pkg/Matrix/man/all.equal-methods.html" class="external-link">all.equal</a></span><span class="op">(</span><span class="va">res1</span>, <span class="va">pres1</span>, check.attributes<span class="op">=</span><span class="cn">FALSE</span><span class="op">)</span></span></span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> [1] TRUE</span>
 <span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/base/invisible.html" class="external-link">invisible</a></span><span class="op">(</span><span class="fu"><a href="set.mcOption.html">set.coresOption</a></span><span class="op">(</span><span class="va">coresOpt</span><span class="op">)</span><span class="op">)</span></span></span>
-<span class="r-in"><span><span class="co"># }</span></span></span>
+<span class="r-in"><span><span class="op">}</span> <span class="co"># }</span></span></span>
 <span class="r-in"><span></span></span>
 </code></pre></div>
     </div>
diff --git a/docs/reference/sp.correlogram.html b/docs/reference/sp.correlogram.html
index cbd51544..006dbef0 100644
--- a/docs/reference/sp.correlogram.html
+++ b/docs/reference/sp.correlogram.html
@@ -9,7 +9,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/sp.mantel.mc.html b/docs/reference/sp.mantel.mc.html
index 9b4442e4..7e5d3ec4 100644
--- a/docs/reference/sp.mantel.mc.html
+++ b/docs/reference/sp.mantel.mc.html
@@ -19,7 +19,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/spdep-defunct.html b/docs/reference/spdep-defunct.html
index 27e4a3ed..cc7c0a33 100644
--- a/docs/reference/spdep-defunct.html
+++ b/docs/reference/spdep-defunct.html
@@ -9,7 +9,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/spdep.html b/docs/reference/spdep.html
index 73fe9115..d112b3bc 100644
--- a/docs/reference/spdep.html
+++ b/docs/reference/spdep.html
@@ -7,7 +7,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/spweights.constants.html b/docs/reference/spweights.constants.html
index 89ffc64a..0ed5cf07 100644
--- a/docs/reference/spweights.constants.html
+++ b/docs/reference/spweights.constants.html
@@ -7,7 +7,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/ssw.html b/docs/reference/ssw.html
index 8762d495..b53220f2 100644
--- a/docs/reference/ssw.html
+++ b/docs/reference/ssw.html
@@ -9,7 +9,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/subset.listw.html b/docs/reference/subset.listw.html
index 9451ab0d..cc3ffd32 100644
--- a/docs/reference/subset.listw.html
+++ b/docs/reference/subset.listw.html
@@ -7,7 +7,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/subset.nb.html b/docs/reference/subset.nb.html
index 8d43381d..7b0bf100 100644
--- a/docs/reference/subset.nb.html
+++ b/docs/reference/subset.nb.html
@@ -7,7 +7,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/summary.nb.html b/docs/reference/summary.nb.html
index fd330fa0..d02880c5 100644
--- a/docs/reference/summary.nb.html
+++ b/docs/reference/summary.nb.html
@@ -11,7 +11,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/testnb.html b/docs/reference/testnb.html
index acfa8c32..de24d925 100644
--- a/docs/reference/testnb.html
+++ b/docs/reference/testnb.html
@@ -15,7 +15,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/tolerance.nb.html b/docs/reference/tolerance.nb.html
index 0f0076a2..06d94a97 100644
--- a/docs/reference/tolerance.nb.html
+++ b/docs/reference/tolerance.nb.html
@@ -7,7 +7,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/tri2nb.html b/docs/reference/tri2nb.html
index b0dd073e..7f4d04d7 100644
--- a/docs/reference/tri2nb.html
+++ b/docs/reference/tri2nb.html
@@ -13,7 +13,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/write.nb.gal.html b/docs/reference/write.nb.gal.html
index b8ab4425..30364db8 100644
--- a/docs/reference/write.nb.gal.html
+++ b/docs/reference/write.nb.gal.html
@@ -7,7 +7,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">spdep</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-7</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">1.3-8</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/search.json b/docs/search.json
index 3e7f82fc..5d320c48 100644
--- a/docs/search.json
+++ b/docs/search.json
@@ -1 +1 @@
-[{"path":"https://r-spatial.github.io/spdep/articles/CO69.html","id":"introduction","dir":"Articles","previous_headings":"","what":"Introduction","title":"“The Problem of Spatial Autocorrelation:” forty years on","text":"Cliff Ord (1969), published forty years ago, marked turning point treatment spatial autocorrelation quantitative geography. provided framework needed applied researcher attempt implementation different system, possibly using different programming language. spirit, examine spatial weights represented implementations may reproduced, tabulated results paper may reproduced, may extended cover simulation. One major assertions Cliff Ord (1969) statistic advances measurement spatial autocorrelation respect Moran (1950) Geary (1954) general specification spatial weights used. general form implications preparation weights , calculation measures. look spatial weights first, moving consider measures presented paper subsequent developments. , put together data set matching used Cliff Ord (1969). provide tabulated data counties Irish Republic, omit Dublin analyses. shapefile included package, kindly made available Michael Tiefelsdorf, used starting point: read SpatialPolygonsDataFrame — classes used handling spatial data fully described Roger S. Bivand, Pebesma, Gómez-Rubio (2008). need add data tabulated paper Table 2,1 p. 40, form text file added rainfall values Table 9, p. 49: Since assigned county names feature identifiers reading shapefiles, extra data, combine objects: Finally, need drop Dublin county omitted analyses conducted Cliff Ord (1969): double-check data, let us calculate sample Beta coefficients, using formulae given paper sample moments: differ somewhat ways skewness kurtosis computed modern statistical software, see example Joanes Gill (1998). However, purposes, let us reproduce Table 3, p. 42: Using tabulated value 23.623.6 percentage agricultural holdings 50 1950 Waterford, skewness kurtosis reproduced, comparison irishdata dataset , turns value rather 26.626.6, yields tabulated skewness kurtosis values. going , variables considered presented Table varsvars. Description variables Geary data set.","code":"library(spdep) eire <- as(sf::st_read(system.file(\"shapes/eire.gpkg\", package=\"spData\")[1]), \"Spatial\") row.names(eire) <- as.character(eire$names) #proj4string(eire) <- CRS(\"+proj=utm +zone=30 +ellps=airy +units=km\") class(eire) ## [1] \"SpatialPolygonsDataFrame\" ## attr(,\"package\") ## [1] \"sp\" names(eire) ##  [1] \"A\"       \"towns\"   \"pale\"    \"size\"    \"ROADACC\" \"OWNCONS\" \"POPCHG\"  ##  [8] \"RETSALE\" \"INCOME\"  \"names\" fn <- system.file(\"etc/misc/geary_eire.txt\", package=\"spdep\")[1] ge <- read.table(fn, header=TRUE) names(ge) ##  [1] \"serlet\"        \"county\"        \"pagval2_10\"    \"pagval10_50\"   ##  [5] \"pagval50p\"     \"cowspacre\"     \"ocattlepacre\"  \"pigspacre\"     ##  [9] \"sheeppacre\"    \"townvillp\"     \"carspcap\"      \"radiopcap\"     ## [13] \"retailpcap\"    \"psinglem30_34\" \"rainfall\" row.names(ge) <- as.character(ge$county) all.equal(row.names(ge), row.names(eire)) ## [1] TRUE eire_ge <- cbind(eire, ge) eire_ge1 <- eire_ge[!(row.names(eire_ge) %in% \"Dublin\"),] length(row.names(eire_ge1)) ## [1] 25 skewness <- function(z) {z <- scale(z, scale=FALSE); ((sum(z^3)/length(z))^2)/((sum(z^2)/length(z))^3)} kurtosis <- function(z) {z <- scale(z, scale=FALSE); (sum(z^4)/length(z))/((sum(z^2)/length(z))^2)} print(sapply(as(eire_ge1, \"data.frame\")[13:24], skewness), digits=3) ##    pagval2_10   pagval10_50     pagval50p     cowspacre  ocattlepacre  ##      1.675429      1.294978      0.000382      1.682094      0.086267  ##     pigspacre    sheeppacre     townvillp      carspcap     radiopcap  ##      1.138387      1.842362      0.472748      0.011111      0.342805  ##    retailpcap psinglem30_34  ##      0.002765      0.068169 print(sapply(as(eire_ge1, \"data.frame\")[13:24], kurtosis), digits=4) ##    pagval2_10   pagval10_50     pagval50p     cowspacre  ocattlepacre  ##         3.790         4.331         1.508         4.294         2.985  ##     pigspacre    sheeppacre     townvillp      carspcap     radiopcap  ##         3.754         4.527         2.619         1.865         2.730  ##    retailpcap psinglem30_34  ##         2.188         2.034 print(sapply(as(eire_ge1, \"data.frame\")[c(13,16,18,19)], function(x) skewness(log(x))), digits=3) ## pagval2_10  cowspacre  pigspacre sheeppacre  ##    0.68801    0.17875    0.00767    0.04184 print(sapply(as(eire_ge1, \"data.frame\")[c(13,16,18,19)], function(x) kurtosis(log(x))), digits=4) ## pagval2_10  cowspacre  pigspacre sheeppacre  ##      2.883      2.799      2.212      2.421"},{"path":"https://r-spatial.github.io/spdep/articles/CO69.html","id":"spatial-weights","dir":"Articles","previous_headings":"","what":"Spatial weights","title":"“The Problem of Spatial Autocorrelation:” forty years on","text":"basis comparison, first read unstandardised weighting matrix given Table A1, p. 54, paper, reading file corrected misprint giving O rather D neighbour V: file, counties represented serial letters, ordering conversion integer index representation required reach representation similar SpatialStats module spatial neighbours: done , can change representation listw object, assigning appropriate style (generalised binary) unstandardised values: Note values S0, S1, S2 correspond closely given page 42 paper, 0.846886720.84688672, 0.018699860.01869986 0.122673190.12267319. discrepancies appear due rounding printed table weights. contiguous neighbours represented object match found using poly2nb. However, see reproduced contiguities smaller link count: missing link Clare Kerry, perhaps Tarbert–Killimer ferry, counties contiguous, Figure plot_nbplot\\_nb shows: County boundaries contiguities attempt also made reproduce generalised weights 25 Irish counties reported Cliff Ord (1969), Dublin omitted. Reproducing inverse distance component dij−1d_{ij}^{-1} generalised weights dij−1βi(j)d_{ij}^{-1} \\beta_{(j)} eased statement Cliff Ord (1973, 55) points chosen represent counties “geographic centres,” different centroids yielded applying chosen computational geometry function. distance metric given, may kilometers miles — tried, results sensitive difference applies equally across weights; miles used . Computing proportion shared distance measure βi(j)\\beta_{(j)} harder, requires availability full topology input polygons. Roger S. Bivand, Pebesma, Gómez-Rubio (2008, 244) show employ vect2neigh function (written Markus Neteler) package using GRASS GIS vector handling create full topology spaghetti vector data extract border segment lengths; similar approach also mentioned using ArcGIS coverages purpose. GRASS used create topology, next proportion shared distance measure calculated. compare, need remove Tarbert–Killimer ferry link manually, view summary original weights, well correlation coefficient reconstructed weights. Naturally, unless boundary coordinates used identical original analysis, presumably measured hand, small differences occur. Even though differences general weights, identical contiguities, small, consequences measure spatial autocorrelation substantial, use fifth variable, cattle per 1000 acres crops pasture (1952), see reconstructed weights seem “reveal” autocorrelation original weights.","code":"fn <- system.file(\"etc/misc/unstand_sn.txt\", package=\"spdep\")[1] unstand <- read.table(fn, header=TRUE) summary(unstand) ##      from                to                weight         ##  Length:110         Length:110         Min.   :0.000600   ##  Class :character   Class :character   1st Qu.:0.003225   ##  Mode  :character   Mode  :character   Median :0.007550   ##                                        Mean   :0.007705   ##                                        3rd Qu.:0.010225   ##                                        Max.   :0.032400 class(unstand) <- c(\"spatial.neighbour\", class(unstand)) of <- ordered(unstand$from) attr(unstand, \"region.id\") <- levels(of) unstand$from <- as.integer(of) unstand$to <- as.integer(ordered(unstand$to)) attr(unstand, \"n\") <- length(unique(unstand$from)) lw_unstand <- sn2listw(unstand) lw_unstand$style <- \"B\" lw_unstand ## Characteristics of weights list object: ## Neighbour list object: ## Number of regions: 25  ## Number of nonzero links: 110  ## Percentage nonzero weights: 17.6  ## Average number of links: 4.4  ##  ## Weights style: B  ## Weights constants summary: ##    n  nn     S0         S1        S2 ## B 25 625 0.8476 0.01871808 0.1229232 nb <- poly2nb(eire_ge1) nb ## Neighbour list object: ## Number of regions: 25  ## Number of nonzero links: 108  ## Percentage nonzero weights: 17.28  ## Average number of links: 4.32 xx <- diffnb(nb, lw_unstand$neighbours, verbose=TRUE) ## Neighbour difference for region id: Clare in relation to id: Kerry  ## Neighbour difference for region id: Kerry in relation to id: Clare plot(eire_ge1, border=\"grey60\") plot(nb, coordinates(eire_ge1), add=TRUE, pch=\".\", lwd=2) plot(xx, coordinates(eire_ge1), add=TRUE, pch=\".\", lwd=2, col=3) library(terra) v_eire_ge1 <-vect(eire_ge1) SG <- rasterize(v_eire_ge1, rast(nrows=70, ncols=50, extent=ext(v_eire_ge1)), field=\"county\") library(rgrass) grass_home <- \"/home/rsb/topics/grass/g820/grass82\" initGRASS(grass_home, home=tempdir(), SG=SG, override=TRUE) write_VECT(v_eire_ge1, \"eire\", flags=c(\"o\", \"overwrite\")) res <- vect2neigh(\"eire\", ID=\"serlet\") res$length <- res$length*1000 attr(res, \"external\") <- attr(res, \"external\")*1000 attr(res, \"total\") <- attr(res, \"total\")*1000 grass_borders <- sn2listw(res) raw_borders <- grass_borders$weights int_tot <- attr(res, \"total\") - attr(res, \"external\") prop_borders <- lapply(1:length(int_tot), function(i) raw_borders[[i]]/int_tot[i]) dlist <- nbdists(grass_borders$neighbours, coordinates(eire_ge1)) inv_dlist <- lapply(dlist, function(x) 1/(x/1.609344)) combo_km <- lapply(1:length(inv_dlist), function(i) inv_dlist[[i]]*prop_borders[[i]]) combo_km_lw <- nb2listw(grass_borders$neighbours, glist=combo_km, style=\"B\") summary(combo_km_lw) ## Characteristics of weights list object: ## Neighbour list object: ## Number of regions: 25  ## Number of nonzero links: 108  ## Percentage nonzero weights: 17.28  ## Average number of links: 4.32  ## Link number distribution: ##  ## 1 2 3 4 5 6 7 8  ## 1 2 5 5 8 1 2 1  ## 1 least connected region: ## E with 1 link ## 1 most connected region: ## V with 8 links ##  ## Weights style: B  ## Weights constants summary: ##    n  nn        S0       S1.5        S2 ## B 25 625 0.9083144 0.02191845 0.1427746 red_lw_unstand <- lw_unstand Clare <- which(attr(lw_unstand, \"region.id\") == \"C\") Kerry <- which(attr(lw_unstand, \"region.id\") == \"H\") Kerry_in_Clare <- which(lw_unstand$neighbours[[Clare]] == Kerry) Clare_in_Kerry <- which(lw_unstand$neighbours[[Kerry]] == Clare) red_lw_unstand$neighbours[[Clare]] <- red_lw_unstand$neighbours[[Clare]][-Kerry_in_Clare] red_lw_unstand$neighbours[[Kerry]] <- red_lw_unstand$neighbours[[Kerry]][-Clare_in_Kerry] red_lw_unstand$weights[[Clare]] <- red_lw_unstand$weights[[Clare]][-Kerry_in_Clare] red_lw_unstand$weights[[Kerry]] <- red_lw_unstand$weights[[Kerry]][-Clare_in_Kerry] summary(red_lw_unstand) ## Characteristics of weights list object: ## Neighbour list object: ## Number of regions: 25  ## Number of nonzero links: 108  ## Percentage nonzero weights: 17.28  ## Average number of links: 4.32  ## Link number distribution: ##  ## 1 2 3 4 5 6 7 8  ## 1 2 5 5 8 1 2 1  ## 1 least connected region: ## E with 1 link ## 1 most connected region: ## V with 8 links ##  ## Weights style: B  ## Weights constants summary: ##    n  nn     S0         S1        S2 ## B 25 625 0.8437 0.01870287 0.1222501 cor(unlist(red_lw_unstand$weights), unlist(combo_km_lw$weights)) ## [1] 0.969543 flatten <- function(x, digits=3, statistic=\"I\") {   res <- c(format(x$estimate, digits=digits),     format(x$statistic, digits=digits),     format.pval(x$p.value, digits=digits))   res <- matrix(res, ncol=length(res))   colnames(res) <- paste(c(\"\", \"E\", \"V\", \"SD_\", \"P_\"), \"I\", sep=\"\")   rownames(res) <- deparse(substitute(x))   res } `reconstructed weights` <- moran.test(eire_ge1$ocattlepacre, combo_km_lw) `original weights` <- moran.test(eire_ge1$ocattlepacre, red_lw_unstand) print(rbind(flatten(`reconstructed weights`), flatten(`original weights`)), quote=FALSE) ##                       I       EI      VI      SD_I P_I     ## reconstructed weights  0.3203 -0.0417  0.0225 2.41 0.00792 ## original weights       0.2779 -0.0417  0.0223 2.14 0.0161"},{"path":"https://r-spatial.github.io/spdep/articles/CO69.html","id":"measures-of-spatial-autocorrelation","dir":"Articles","previous_headings":"","what":"Measures of spatial autocorrelation","title":"“The Problem of Spatial Autocorrelation:” forty years on","text":"targets reproduction Tables 4 5 Cliff Ord (1969, 43–44), first containing standard deviates normality randomisation original Moran measure binary weights, original Geary measure binary weights, proposed measure unstandardised general weights, proposed measure row-standardised general weights. addition, four variables log-transformed basis skewness kurtosis results presented . carry transformation variables, generate additional binary row-standardised general spatial weights objects — note weights constants row-standardised general weights agree given p. 42 paper, allowing small differences due rounding weights values displayed paper (p. 54): standard representation measures : =n∑=1n∑j=1nwij∑=1n∑j=1nwij(xi−x‾)(xj−x‾)∑=1n(xi−x‾)2I = \\frac{n}{\\sum_{=1}^{n}\\sum_{j=1}^{n}w_{ij}} \\frac{\\sum_{=1}^{n}\\sum_{j=1}^{n}w_{ij}(x_i-\\bar{x})(x_j-\\bar{x})}{\\sum_{=1}^{n}(x_i - \\bar{x})^2} Moran’s II — paper termed proposed statistic, Geary’s CC: C=(n−1)2∑=1n∑j=1nwij∑=1n∑j=1nwij(xi−xj)2∑=1n(xi−x‾)2C = \\frac{(n-1)}{2\\sum_{=1}^{n}\\sum_{j=1}^{n}w_{ij}} \\frac{\\sum_{=1}^{n}\\sum_{j=1}^{n}w_{ij}(x_i-x_j)^2}{\\sum_{=1}^{n}(x_i - \\bar{x})^2} xi,=1,…,nx_i, =1, \\ldots, n nn observations numeric variable interest, wijw_{ij} spatial weights. order reproduce standard deviates given paper, sufficient apply moran.test variables three different spatial weights objects, two different values randomisation= argument. addition, geary.test applied single spatial weights objects, two different values randomisation= argument. order conduct 8 different tests 16 variables, use lapply list variables specified order, sapply list output objects name generate table row column order original (save copy six columns comparison bootstrap results ): values standard deviates agree Table 4 original paper, exception proposed statistic standardised weights normality untransformed variables. can see happened substituting weights constants standardised weights unstandardised weights: Next, let us look Table 5 original paper. tabulate values measures , , since expectation constant measure, square root variance measure randomisation — extracting values calculated : values follows, match original exception initial version Moran’s II first two columns. write function implementing equations 3 4: =∑=1n∑j=+1nwij(xi−x‾)(xj−x‾)∑=1n(xi−x‾)2I = \\frac{\\sum_{=1}^{n}\\sum_{j=+1}^{n}w_{ij}(x_i-\\bar{x})(x_j-\\bar{x})}{\\sum_{=1}^{n}(x_i - \\bar{x})^2} crucially inner summation +1…ni+1 \\ldots n, 1…n1 \\ldots n, can reproduce values measure shown original Table 5: variance term given equation 7 original paper case normality, randomisation; reference p. 28 equation 38 p. 26 permit reproduction values second column Table 5. variance equation given equation 1.35 Cliff Ord (1973, 9) either, time possible say tabulated values computed. Note since standard deviances reproduced correctly, can reproduced second column values using measure expectance, just matter establishing formula used, far proved possible.","code":"eire_ge1$ln_pagval2_10 <- log(eire_ge1$pagval2_10) eire_ge1$ln_cowspacre <- log(eire_ge1$cowspacre) eire_ge1$ln_pigspacre <- log(eire_ge1$pigspacre) eire_ge1$ln_sheeppacre <- log(eire_ge1$sheeppacre) vars <- c(\"pagval2_10\", \"ln_pagval2_10\", \"pagval10_50\", \"pagval50p\",  \"cowspacre\", \"ln_cowspacre\", \"ocattlepacre\", \"pigspacre\",  \"ln_pigspacre\", \"sheeppacre\", \"ln_sheeppacre\", \"townvillp\",  \"carspcap\", \"radiopcap\", \"retailpcap\", \"psinglem30_34\") nb_B <- nb2listw(lw_unstand$neighbours, style=\"B\") nb_B ## Characteristics of weights list object: ## Neighbour list object: ## Number of regions: 25  ## Number of nonzero links: 110  ## Percentage nonzero weights: 17.6  ## Average number of links: 4.4  ##  ## Weights style: B  ## Weights constants summary: ##    n  nn  S0  S1   S2 ## B 25 625 110 220 2176 lw_std <- nb2listw(lw_unstand$neighbours, glist=lw_unstand$weights, style=\"W\") lw_std ## Characteristics of weights list object: ## Neighbour list object: ## Number of regions: 25  ## Number of nonzero links: 110  ## Percentage nonzero weights: 17.6  ## Average number of links: 4.4  ##  ## Weights style: W  ## Weights constants summary: ##    n  nn S0       S1       S2 ## W 25 625 25 15.84089 103.6197 system.time({ MoranN <- lapply(vars, function(x) moran.test(eire_ge1[[x]], listw=nb_B, randomisation=FALSE)) MoranR <- lapply(vars, function(x) moran.test(eire_ge1[[x]], listw=nb_B, randomisation=TRUE)) GearyN <- lapply(vars, function(x) geary.test(eire_ge1[[x]], listw=nb_B, randomisation=FALSE)) GearyR <- lapply(vars, function(x) geary.test(eire_ge1[[x]], listw=nb_B, randomisation=TRUE)) Prop_unstdN  <- lapply(vars, function(x) moran.test(eire_ge1[[x]], listw=lw_unstand, randomisation=FALSE)) Prop_unstdR  <- lapply(vars, function(x) moran.test(eire_ge1[[x]], listw=lw_unstand, randomisation=TRUE)) Prop_stdN  <- lapply(vars, function(x) moran.test(eire_ge1[[x]], listw=lw_std, randomisation=FALSE)) Prop_stdR  <- lapply(vars, function(x) moran.test(eire_ge1[[x]], listw=lw_std, randomisation=TRUE)) }) ##    user  system elapsed  ##    0.11    0.00    0.11 res <- sapply(c(\"MoranN\", \"MoranR\", \"GearyN\", \"GearyR\", \"Prop_unstdN\", \"Prop_unstdR\", \"Prop_stdN\", \"Prop_stdR\"), function(x) sapply(get(x), \"[[\", \"statistic\")) rownames(res) <- vars ores <- res[,c(1,2,5:8)] print(formatC(res, format=\"f\", digits=4), quote=FALSE) ##               MoranN MoranR GearyN  GearyR  Prop_unstdN Prop_unstdR Prop_stdN Prop_stdR ## pagval2_10    3.7851 3.8779 4.3142  3.9016  3.3307      3.4159      3.9276    4.0292    ## ln_pagval2_10 4.0965 4.1074 4.0841  4.0343  3.5795      3.5894      4.1278    4.1393    ## pagval10_50   1.0899 1.1316 2.7511  2.3760  1.3348      1.3882      1.5127    1.5738    ## pagval50p     5.2011 5.0555 4.0178  4.7194  4.6604      4.5247      4.8823    4.7387    ## cowspacre     5.1969 5.3907 4.3531  3.7709  4.1379      4.2991      4.7274    4.9135    ## ln_cowspacre  5.2420 5.2455 3.9211  3.9085  4.2007      4.2037      4.6532    4.6566    ## ocattlepacre  0.5565 0.5593 -0.1707 -0.1668 2.1366      2.1478      1.9219    1.9320    ## pigspacre     2.4807 2.5393 2.2928  2.0802  2.8312      2.9010      3.1908    3.2703    ## ln_pigspacre  2.3015 2.2724 2.0520  2.1893  2.5171      2.4839      2.8460    2.8081    ## sheeppacre    1.0188 1.0630 0.8689  0.7387  1.7398      1.8187      1.4792    1.5470    ## ln_sheeppacre 1.2930 1.2827 1.5156  1.5767  2.3708      2.3511      2.0374    2.0203    ## townvillp     2.2759 2.2681 2.5475  2.5902  1.2148      1.2104      1.6275    1.6216    ## carspcap      4.4927 4.4015 3.2247  3.5992  3.8897      3.8075      4.1826    4.0934    ## radiopcap     0.3156 0.3153 1.2294  1.2348  0.5915      0.5909      0.7857    0.7849    ## retailpcap    3.4985 3.4524 3.1303  3.3497  2.9291      2.8888      3.0346    2.9926    ## psinglem30_34 2.7349 2.6895 2.3382  2.5519  2.7541      2.7065      2.7078    2.6605 wc_unstd <- spweights.constants(lw_unstand) wrong_N_sqVI <- sqrt((wc_unstd$nn*wc_unstd$S1 - wc_unstd$n*wc_unstd$S2 + 3*wc_unstd$S0*wc_unstd$S0)/((wc_unstd$nn-1)*wc_unstd$S0*wc_unstd$S0)-((-1/(wc_unstd$n-1))^2)) raw_data <- grep(\"^ln_\", vars, invert=TRUE) I <- sapply(Prop_stdN, function(x) x$estimate[1])[raw_data] EI <- sapply(Prop_stdN, function(x) x$estimate[2])[raw_data] res <- (I - EI)/wrong_N_sqVI names(res) <- vars[raw_data] print(formatC(res, format=\"f\", digits=4), quote=FALSE) ##    pagval2_10   pagval10_50     pagval50p     cowspacre  ocattlepacre     pigspacre  ##        3.8836        1.4957        4.8276        4.6744        1.9003        3.1550  ##    sheeppacre     townvillp      carspcap     radiopcap    retailpcap psinglem30_34  ##        1.4627        1.6093        4.1357        0.7769        3.0006        2.6774 res <- lapply(c(\"MoranR\", \"GearyR\", \"Prop_unstdR\", \"Prop_stdR\"), function(x) sapply(get(x), function(y) c(y$estimate[1], sqrt(y$estimate[3])))) res <- t(do.call(\"rbind\", res)) colnames(res) <- c(\"I\", \"sigma_I\", \"C\", \"sigma_C\", \"unstd_r\", \"sigma_r\", \"std_r\", \"sigma_r\") rownames(res) <- vars print(formatC(res, format=\"f\", digits=4), quote=FALSE) ##               I       sigma_I C      sigma_C unstd_r sigma_r std_r  sigma_r ## pagval2_10    0.4074  0.1158  0.3477 0.1672  0.4559  0.1456  0.5384 0.1440  ## ln_pagval2_10 0.4444  0.1183  0.3825 0.1531  0.4930  0.1490  0.5680 0.1473  ## pagval10_50   0.0877  0.1143  0.5840 0.1751  0.1577  0.1436  0.1818 0.1420  ## pagval50p     0.5754  0.1221  0.3925 0.1287  0.6545  0.1539  0.6795 0.1522  ## cowspacre     0.5749  0.1144  0.3418 0.1745  0.5764  0.1438  0.6566 0.1421  ## ln_cowspacre  0.5803  0.1186  0.4071 0.1517  0.5858  0.1493  0.6456 0.1476  ## ocattlepacre  0.0244  0.1181  1.0258 0.1547  0.2775  0.1486  0.2422 0.1469  ## pigspacre     0.2527  0.1159  0.6533 0.1667  0.3812  0.1458  0.4296 0.1441  ## ln_pigspacre  0.2314  0.1202  0.6897 0.1417  0.3343  0.1514  0.3787 0.1497  ## sheeppacre    0.0792  0.1137  0.8686 0.1778  0.2182  0.1429  0.1768 0.1412  ## ln_sheeppacre 0.1117  0.1196  0.7708 0.1453  0.3125  0.1506  0.2593 0.1489  ## townvillp     0.2284  0.1191  0.6148 0.1487  0.1398  0.1499  0.1987 0.1482  ## carspcap      0.4914  0.1211  0.5124 0.1355  0.5394  0.1526  0.5761 0.1509  ## radiopcap     -0.0042 0.1188  0.8141 0.1505  0.0467  0.1495  0.0744 0.1478  ## retailpcap    0.3734  0.1202  0.5267 0.1413  0.3959  0.1515  0.4066 0.1498  ## psinglem30_34 0.2828  0.1207  0.6465 0.1385  0.3697  0.1520  0.3583 0.1503 oMoranf <- function(x, nb) {   z <- scale(x, scale=FALSE)   n <- length(z)   glist <- lapply(1:n, function(i) {ii <- nb[[i]]; ifelse(ii > i, 1, 0)})   lw <- nb2listw(nb, glist=glist, style=\"B\")   wz <- lag(lw, z)   I <- (sum(z*wz)/sum(z*z))   I } res <- sapply(vars, function(x) oMoranf(eire_ge1[[x]], nb=lw_unstand$neighbours)) print(formatC(res, format=\"f\", digits=4), quote=FALSE) ##    pagval2_10 ln_pagval2_10   pagval10_50     pagval50p     cowspacre  ln_cowspacre  ##        0.8964        0.9776        0.1928        1.2660        1.2649        1.2766  ##  ocattlepacre     pigspacre  ln_pigspacre    sheeppacre ln_sheeppacre     townvillp  ##        0.0536        0.5559        0.5091        0.1743        0.2458        0.5024  ##      carspcap     radiopcap    retailpcap psinglem30_34  ##        1.0811       -0.0093        0.8215        0.6222"},{"path":"https://r-spatial.github.io/spdep/articles/CO69.html","id":"simulating-measures-of-spatial-autocorrelation","dir":"Articles","previous_headings":"","what":"Simulating measures of spatial autocorrelation","title":"“The Problem of Spatial Autocorrelation:” forty years on","text":"Cliff Ord (1969) conduct simulation experiments, although sequels , notably Cliff Ord (1973), among many others. Simulation studies necessarily demanding computationally, especially spatially autocorrelated variables created, Cliff Ord (1973, 146–53). book, also report use permutation tests, also known Monte Carlo Hope hypothesis testing procedures (Cliff Ord 1973, 50–52). procedures provided way examine distribution statistic interest exchanging random observed values observations, comparing simulated distribution null hypothesis spatial patterning observed value statistic question. First let us define function MoranI.boot just return value Moran’s II variable var permutation index , function Nsim generate random samples variable interest assuming Normality. make easier process variables turn, encapsulate calls boot wrapper functions f_bperm f_bpara. Running 4999 simulations 16 three different weights specifications parametric permutation bootstrap takes quite lot time. collate results compare analytical standard deviates Normality randomisation, see fact differences large, expressed median absolute difference tables. can also see inferences based one-sided α=0.05\\alpha=0.05 cut-analytical bootstrap approaches. indicates can, general, rely analytical standard deviates, bootstrap methods help assumptions underlying measures met. assumptions affect shape distribution measure tails; one possibility use Saddlepoint approximation find equivalent analytical bootstrap-based standard deviate inference (Tiefelsdorf 2002). Saddlepoint approximation requires eigenvalues weights matrix iterative root-finding global Moran’s II, local Moran’s IiI_i, analytical forms known. Even computational burden, Saddlepoint approximation global Moran’s II runs quite quickly. First need fit null linear models (including intercept) variables, apply lm.morantest.sad fitted model objects: Although analytical standard deviates (Normality) larger reached using Saddlepoint approximation measured median absolute deviation, differences lead different inferences chosen cut-. reflects fact shape distribution sensitive small nn, moderate nn global Moran’s II, effects seen tails. consequences local Moran’s IiI_i much stronger, clique neighbours observation typically small. perhaps interest differences much smaller case general weights unstandardised binary weights. addition choose use exact distribution Moran’s II, described Tiefelsdorf (2000); implementation covered R. S. Bivand, Müller, Reder (2009). global case also needs eigenvalues weights matrix, solution numerical integration function, cases, timings quite acceptable. output comparable Saddlepoint approximation, inferences drawn chosen cut-analytical standard deviates calculated Normality. Li, Calder, Cressie (2007) take challenge Cliff Ord (1969, 31), try give statistic bounded fixed range. APLE measure intended approximate spatial dependence parameter simultaneous autoregressive model better Moran’s II, re-scales measure function eigenvalues spatial weights matrix. APLE requires use row standardised weights. order save time, use two internal functions spatialreg:::preAple spatialreg:::inAple, since definition spatial weights, eigenvalue calculations need made. notation using ::: operator says function named operator found namespace package named operator. APLE values repeat pattern already seen — variables, measured autocorrelation similar irrespective spatial weights definition, others, change definition binary general make difference.","code":"MoranI.boot <- function(var, i, ...) {   var <- var[i]   return(moran(x=var, ...)$I) } Nsim <- function(d, mle) {   n <- length(d)   rnorm(n, mle$mean, mle$sd) } f_bperm <- function(x, nsim, listw) {   boot(x, statistic=MoranI.boot, R=nsim, sim=\"permutation\", listw=listw,     n=length(x), S0=Szero(listw)) } f_bpara <- function(x, nsim, listw) {   boot(x, statistic=MoranI.boot, R=nsim, sim=\"parametric\", ran.gen=Nsim,     mle=list(mean=mean(x), sd=sd(x)), listw=listw, n=length(x),     S0=Szero(listw)) } nsim <- 4999 set.seed(1234) system.time({ MoranNb <- lapply(vars, function(x) f_bpara(x=eire_ge1[[x]], nsim=nsim, listw=nb_B)) MoranRb <- lapply(vars, function(x) f_bperm(x=eire_ge1[[x]], nsim=nsim, listw=nb_B)) Prop_unstdNb  <- lapply(vars, function(x) f_bpara(x=eire_ge1[[x]], nsim=nsim, listw=lw_unstand)) Prop_unstdRb  <- lapply(vars, function(x) f_bperm(x=eire_ge1[[x]], nsim=nsim, listw=lw_unstand)) Prop_stdNb  <- lapply(vars, function(x) f_bpara(x=eire_ge1[[x]], nsim=nsim, listw=lw_std)) Prop_stdRb  <- lapply(vars, function(x) f_bperm(x=eire_ge1[[x]], nsim=nsim, listw=lw_std)) }) res <- lapply(c(\"MoranNb\", \"MoranRb\", \"Prop_unstdNb\", \"Prop_unstdRb\", \"Prop_stdNb\", \"Prop_stdRb\"), function(x) sapply(get(x), function(y) (y$t0 - mean(y$t))/sd(y$t))) res <- t(do.call(\"rbind\", res)) colnames(res) <- c(\"MoranNb\", \"MoranRb\", \"Prop_unstdNb\", \"Prop_unstdRb\", \"Prop_stdNb\", \"Prop_stdRb\") rownames(res) <- vars print(formatC(res, format=\"f\", digits=4), quote=FALSE) ##    pagval2_10 ln_pagval2_10   pagval10_50     pagval50p     cowspacre  ln_cowspacre  ##        0.8964        0.9776        0.1928        1.2660        1.2649        1.2766  ##  ocattlepacre     pigspacre  ln_pigspacre    sheeppacre ln_sheeppacre     townvillp  ##        0.0536        0.5559        0.5091        0.1743        0.2458        0.5024  ##      carspcap     radiopcap    retailpcap psinglem30_34  ##        1.0811       -0.0093        0.8215        0.6222 oores <- ores - res apply(oores, 2, mad) ##      MoranN      MoranR Prop_unstdN Prop_unstdR   Prop_stdN   Prop_stdR  ##   1.6470091   1.6241614   0.7681895   0.7170636   1.2615083   1.2723149 alpha_0.05 <- qnorm(0.05, lower.tail=FALSE) all((res >= alpha_0.05) == (ores >= alpha_0.05)) ## [1] FALSE lm_objs <- lapply(vars, function(x) lm(formula(paste(x, \"~1\")), data=eire_ge1)) system.time({ MoranSad <- lapply(lm_objs, function(x) lm.morantest.sad(x, listw=nb_B)) Prop_unstdSad  <- lapply(lm_objs, function(x) lm.morantest.sad(x, listw=lw_unstand)) Prop_stdSad  <- lapply(lm_objs, function(x) lm.morantest.sad(x, listw=lw_std)) }) ##    user  system elapsed  ##   0.063   0.000   0.064 res <- sapply(c(\"MoranSad\", \"Prop_unstdSad\", \"Prop_stdSad\"), function(x) sapply(get(x), \"[[\", \"statistic\")) rownames(res) <- vars print(formatC(res, format=\"f\", digits=4), quote=FALSE) ##               MoranSad Prop_unstdSad Prop_stdSad ## pagval2_10    3.2903   3.1711        3.8283      ## ln_pagval2_10 3.5346   3.3982        4.0441      ## pagval10_50   1.0883   1.3219        1.4791      ## pagval50p     4.4402   4.4258        4.9377      ## cowspacre     4.4366   3.9164        4.7406      ## ln_cowspacre  4.4758   3.9760        4.6493      ## ocattlepacre  0.6030   2.0748        1.8642      ## pigspacre     2.2611   2.7154        3.0775      ## ln_pigspacre  2.1158   2.4271        2.7417      ## sheeppacre    1.0250   1.7040        1.4476      ## ln_sheeppacre 1.2669   2.2921        1.9731      ## townvillp     2.0949   1.2079        1.5872      ## carspcap      3.8500   3.6840        4.1044      ## radiopcap     0.3750   0.6094        0.7906      ## retailpcap    3.0663   2.8049        2.9245      ## psinglem30_34 2.4649   2.6449        2.6089 oores <- res - ores[,c(1,3,5)] apply(oores, 2, mad) ##      MoranSad Prop_unstdSad   Prop_stdSad  ##    0.37142684    0.10779060    0.05650183 all((res >= alpha_0.05) == (ores[,c(1,3,5)] >= alpha_0.05)) ## [1] TRUE system.time({  MoranEx <- lapply(lm_objs, function(x) lm.morantest.exact(x, listw=nb_B)) Prop_unstdEx  <- lapply(lm_objs, function(x) lm.morantest.exact(x, listw=lw_unstand)) Prop_stdEx  <- lapply(lm_objs, function(x) lm.morantest.exact(x, listw=lw_std)) }) ##    user  system elapsed  ##    0.08    0.00    0.08 res <- sapply(c(\"MoranEx\", \"Prop_unstdEx\", \"Prop_stdEx\"), function(x) sapply(get(x), \"[[\", \"statistic\")) rownames(res) <- vars print(formatC(res, format=\"f\", digits=4), quote=FALSE) ##               MoranEx Prop_unstdEx Prop_stdEx ## pagval2_10    3.2895  3.1660       3.8261     ## ln_pagval2_10 3.5384  3.3979       4.0430     ## pagval10_50   1.0798  1.3131       1.4745     ## pagval50p     4.4568  4.4430       4.9446     ## cowspacre     4.4532  3.9268       4.7453     ## ln_cowspacre  4.4928  3.9875       4.6531     ## ocattlepacre  0.5967  2.0611       1.8596     ## pigspacre     2.2486  2.7033       3.0740     ## ln_pigspacre  2.1031  2.4131       2.7380     ## sheeppacre    1.0168  1.6924       1.4430     ## ln_sheeppacre 1.2575  2.2779       1.9685     ## townvillp     2.0822  1.1999       1.5826     ## carspcap      3.8593  3.6899       4.1037     ## radiopcap     0.3696  0.6054       0.7873     ## retailpcap    3.0616  2.7938       2.9210     ## psinglem30_34 2.4533  2.6321       2.6050 oores <- res - ores[,c(1,3,5)] apply(oores, 2, mad) ##      MoranEx Prop_unstdEx   Prop_stdEx  ##   0.37187539   0.09751723   0.05419300 all((res >= alpha_0.05) == (ores[,c(1,3,5)] >= alpha_0.05)) ## [1] TRUE vars_scaled <- lapply(vars, function(x) scale(eire_ge1[[x]], scale=FALSE)) nb_W <- nb2listw(lw_unstand$neighbours, style=\"W\") pre <- spatialreg:::preAple(0, listw=nb_W) MoranAPLE <- sapply(vars_scaled, function(x) spatialreg:::inAple(x, pre)) pre <- spatialreg:::preAple(0, listw=lw_std, override_similarity_check=TRUE) Prop_stdAPLE <- sapply(vars_scaled, function(x) spatialreg:::inAple(x, pre)) res <- cbind(MoranAPLE, Prop_stdAPLE) colnames(res) <- c(\"APLE W\", \"APLE Gstd\") rownames(res) <- vars print(formatC(res, format=\"f\", digits=4), quote=FALSE) ##               APLE W APLE Gstd ## pagval2_10    0.7702 0.6628    ## ln_pagval2_10 0.7615 0.6655    ## pagval10_50   0.3954 0.3446    ## pagval50p     0.7519 0.7313    ## cowspacre     0.8329 0.7408    ## ln_cowspacre  0.8148 0.7487    ## ocattlepacre  0.1468 0.4092    ## pigspacre     0.6227 0.6205    ## ln_pigspacre  0.5582 0.5887    ## sheeppacre    0.1594 0.2841    ## ln_sheeppacre 0.2046 0.4550    ## townvillp     0.3442 0.2644    ## carspcap      0.7140 0.6166    ## radiopcap     0.0083 0.1376    ## retailpcap    0.6376 0.5307    ## psinglem30_34 0.4094 0.4889"},{"path":"https://r-spatial.github.io/spdep/articles/CO69.html","id":"odds-and-ends-ldots","dir":"Articles","previous_headings":"","what":"Odds and ends …\\ldots","title":"“The Problem of Spatial Autocorrelation:” forty years on","text":"differences found case variables inference using original binary weights, general weights proposed Cliff Ord (1969) necessarily related weights thenselves. Figures plot_wtsplot\\_wts plot_mapplot\\_map show values weights sparse matrix form, sums weights county sums identical design. case binary weights, matrix entries equal, sums -weight counties many neighbours. General weights -weight counties close , neighbours, share larger boundary proportions (asymmetric relationship). impact using boundary proportions, boundary county exterior subtracted, thus boosting weights edge counties neighbours, even . Standardised general weights -weight -weight counties neighbours, chiefly edges study area. small data set, n=25n=25, possible edge configuration effects relatively strong, may impact inference different ways. issue egde effects really satisfactorily resolved, kept mind analyses data sets size shape.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/articles/nb.html","id":"creating-neighbours","dir":"Articles","previous_headings":"","what":"Creating Neighbours","title":"Creating Neighbours","text":"vignette formed pp. 239–251 first edition Bivand, R. S., Pebesma, E. Gómez-Rubio V. (2008) Applied Spatial Data Analysis R, Springer-Verlag, New York. retired second edition (2013) accommodate material topics, made available form understanding publishers.","code":""},{"path":"https://r-spatial.github.io/spdep/articles/nb.html","id":"introduction","dir":"Articles","previous_headings":"Creating Neighbours","what":"Introduction","title":"Creating Neighbours","text":"Creating spatial weights necessary step using areal data, perhaps just check remaining spatial patterning residuals. first step define relationships observations given non-zero weight, choose neighbour criterion used; second assign weights identified neighbour links. 281 census tract data set eight central New York State counties featured prominently (Waller Gotway 2004) used many examples, supplemented tract boundaries derived TIGER 1992 distributed SEDAC/CIESIN. boundaries projected geographical coordinates UTM zone~18. file identical boundaries used original source, close may re-distributed, unlike version used book. Starting census tract queen contiguities, touching polygons neighbours, used (Waller Gotway 2004) provided DBF file website, GAL format file created read R. sake simplicity showing create neighbour objects, work subset map consisting census tracts within Syracuse, although principles apply full data set. retrieve part neighbour list Syracuse using subset method.","code":"library(spdep) ## Loading required package: spData ## Loading required package: sf ## Linking to GEOS 3.13.0, GDAL 3.10.0, PROJ 9.5.0; sf_use_s2() is TRUE if (packageVersion(\"spData\") >= \"2.3.2\") {     NY8a <- sf::st_read(system.file(\"shapes/NY8_utm18.gpkg\", package=\"spData\")) } else {     NY8a <- sf::st_read(system.file(\"shapes/NY8_bna_utm18.gpkg\", package=\"spData\"))     sf::st_crs(NY8a) <- \"EPSG:32618\"     NY8a$Cases <- NY8a$TRACTCAS } ## Reading layer `NY8_utm18' from data source  ##   `/home/rsb/lib/r_libs/spData/shapes/NY8_utm18.gpkg' using driver `GPKG' ## Simple feature collection with 281 features and 17 fields ## Geometry type: POLYGON ## Dimension:     XY ## Bounding box:  xmin: 358241.9 ymin: 4649755 xmax: 480393.1 ymax: 4808545 ## Projected CRS: WGS 84 / UTM zone 18N NY8 <- as(NY8a, \"Spatial\") NY_nb <- read.gal(system.file(\"weights/NY_nb.gal\", package=\"spData\"), region.id=as.character(as.integer(row.names(NY8))-1L)) Syracuse <- NY8[!is.na(NY8$AREANAME) & NY8$AREANAME == \"Syracuse city\",] Sy0_nb <- subset(NY_nb, !is.na(NY8$AREANAME) & NY8$AREANAME == \"Syracuse city\") summary(Sy0_nb) ## Neighbour list object: ## Number of regions: 63  ## Number of nonzero links: 346  ## Percentage nonzero weights: 8.717561  ## Average number of links: 5.492063  ## Link number distribution: ##  ##  1  2  3  4  5  6  7  8  9  ##  1  1  5  9 14 17  9  6  1  ## 1 least connected region: ## 164 with 1 link ## 1 most connected region: ## 136 with 9 links"},{"path":"https://r-spatial.github.io/spdep/articles/nb.html","id":"creating-contiguity-neighbours","dir":"Articles","previous_headings":"Creating Neighbours","what":"Creating Contiguity Neighbours","title":"Creating Neighbours","text":"can create copy neighbours object polygon contiguities using poly2nb() function spdep. takes object extending SpatialPolygons class first argument, using heuristics identifies polygons sharing boundary points neighbours. also snap= argument, allow shared boundary points short distance one another. can see, creating contiguity neighbours Syracuse object reproduces neighbours (Waller Gotway 2004). Careful examination next figure shows, however, graph neighbours planar, since neighbour links cross . default, contiguity condition met least one point boundary one polygon within snap distance least one point neighbour. relationship given argument queen=TRUE analogy movements chessboard. three polygons meet single point, meet contiguity condition, giving rise crossed links. queen=FALSE, least two boundary points must within snap distance , conventional name `rook’ relationship. figure shows crossed line differences arise polygons touch single point, compared stricter rook criterion. : Queen-style census tract contiguities, Syracuse; b: Rook-style contiguity differences shown thicker orange lines access GIS GRASS ArcGIS, can export SpatialPolygonsDataFrame object use topology engine GIS find contiguities graph polygon edges - shared edge yield output rook relationship. procedure , however, depend topology set polygons clean, holds subset, full eight-county data set. infrequently, small artefacts, slivers boundary lines intersect diverge distances seen plots, require intervention keep geometries data correctly associated. geometrical artefacts present, topology clean, unambiguous shared polygon boundaries found cases; artefacts typically arise data collected one purpose combined data used another purpose. Topologies usually cleaned GIS snapping' vertices closer threshold distance together, removing artefacts -- example, snapping across river channel correct boundary median line input polygons stop channel banks side. Thepoly2nb()function asnap` argument, may also used input data possess geometrical artefacts. Similar approaches may also used read ArcGIS coverage data tallying left neighbour right neighbour arc indices polygons data set, using either RArcInfo rgdal. Syracuse case, exclaves islands' belonging data set, sharing boundary points within snap distance. number polygons moderate, missing neighbour links may added interactively using theedit()method fornb` objects, displaying polygon background. method may used removing links , although contiguity exists, may considered void, across mountain range.","code":"class(Syracuse) ## [1] \"SpatialPolygonsDataFrame\" ## attr(,\"package\") ## [1] \"sp\" Sy1_nb <- poly2nb(Syracuse) isTRUE(all.equal(Sy0_nb, Sy1_nb, check.attributes=FALSE)) ## [1] TRUE Sy2_nb <- poly2nb(Syracuse, queen=FALSE) isTRUE(all.equal(Sy0_nb, Sy2_nb, check.attributes=FALSE)) ## [1] FALSE oopar <- par(mfrow=c(1,2), mar=c(3,3,1,1)+0.1) plot(Syracuse, border=\"grey60\") plot(Sy0_nb, coordinates(Syracuse), add=TRUE, pch=19, cex=0.6) text(bbox(Syracuse)[1,1], bbox(Syracuse)[2,2], labels=\"a)\", cex=0.8) plot(Syracuse, border=\"grey60\") plot(Sy0_nb, coordinates(Syracuse), add=TRUE, pch=19, cex=0.6) plot(diffnb(Sy0_nb, Sy2_nb, verbose=FALSE), coordinates(Syracuse),   add=TRUE, pch=\".\", cex=0.6, lwd=2, col=\"orange\") text(bbox(Syracuse)[1,1], bbox(Syracuse)[2,2], labels=\"b)\", cex=0.8) par(oopar) library(rgrass) v <- terra::vect(sf::st_as_sf(Syracuse)) SG <- terra::rast(terra::ext(v), crs=terra::crs(v)) pr <- initGRASS(\"/home/rsb/topics/grass/g840/grass84\", tempdir(), SG=SG, override=TRUE) write_VECT(v, \"SY0\", flags=c(\"o\", \"overwrite\")) contig <- vect2neigh(\"SY0\") Sy3_nb <- sn2listw(contig, style=\"B\")$neighbours isTRUE(all.equal(Sy3_nb, Sy2_nb, check.attributes=FALSE)) ## [1] TRUE"},{"path":"https://r-spatial.github.io/spdep/articles/nb.html","id":"creating-graph-based-neighbours","dir":"Articles","previous_headings":"Creating Neighbours","what":"Creating Graph-Based Neighbours","title":"Creating Neighbours","text":"Continuing irregularly located areal entities, possible choose point represent polygon-support entities. often polygon centroid, average coordinates dimension, takes proper care weight component triangles polygon area. also possible use points, data available, construct, example population-weighted centroids. representative points available, criteria neighbourhood can extended just contiguity include graph measures, distance thresholds, kk-nearest neighbours. direct graph representation neighbours make Delaunay triangulation points, shown first panel figure. neighbour relationships defined triangulation, extends outwards convex hull points planar. Note graph-based representations construct interpoint relationships based Euclidean distance, option use Great Circle distances geographical coordinates. joins distant points around convex hull, may worthwhile thin triangulation Sphere Influence (SOI) graph, removing links relatively long. Points SOI neighbours circles centred points, radius equal points’ nearest neighbour distances, intersect two places (Avis Horton 1985). Functions graph-based neighbours kindly contributed Nicholas Lewin-Koh. : Delauney triangulation neighbours; b: Sphere influence neighbours (available); c: Gabriel graph neighbours; d: Relative graph neighbours Delaunay triangulation neighbours SOI neighbours symmetric design – ii neighbour jj, jj neighbour ii. Gabriel graph also subgraph Delaunay triangulation, retaining different set neighbours (Matula Sokal 1980). , however, guarantee symmetry; applies Relative graph neighbours (Toussaint 1980). graph2nb() function takes sym argument insert links restore symmetry, graphs longer exactly fulfil neighbour criteria. graph-based neighbour schemes always ensure points least one neighbour. Subgraphs full triangulation may also one graph trimming. functions .symmetric.nb() can used check symmetry, argument force=TRUE symmetry attribute overridden, n.comp.nb() reports number graph components ~components points belong (enforcing symmetry, algorithm assumes graph directed). one graph component, matrix representation spatial weights can become block-diagonal observations appropriately sorted.","code":"coords <- coordinates(Syracuse) IDs <- row.names(as(Syracuse, \"data.frame\")) #FIXME library(tripack) Sy4_nb <- tri2nb(coords, row.names=IDs) if (require(dbscan, quietly=TRUE)) {   Sy5_nb <- graph2nb(soi.graph(Sy4_nb, coords), row.names=IDs) } else Sy5_nb <- NULL ##  ## Attaching package: 'dbscan' ## The following object is masked from 'package:stats': ##  ##     as.dendrogram Sy6_nb <- graph2nb(gabrielneigh(coords), row.names=IDs) Sy7_nb <- graph2nb(relativeneigh(coords), row.names=IDs) oopar <- par(mfrow=c(2,2), mar=c(1,1,1,1)+0.1) plot(Syracuse, border=\"grey60\") plot(Sy4_nb, coords, add=TRUE, pch=\".\") text(bbox(Syracuse)[1,1], bbox(Syracuse)[2,2], labels=\"a)\", cex=0.8) plot(Syracuse, border=\"grey60\") if (!is.null(Sy5_nb)) {   plot(Sy5_nb, coords, add=TRUE, pch=\".\")   text(bbox(Syracuse)[1,1], bbox(Syracuse)[2,2], labels=\"b)\", cex=0.8) } plot(Syracuse, border=\"grey60\") plot(Sy6_nb, coords, add=TRUE, pch=\".\") text(bbox(Syracuse)[1,1], bbox(Syracuse)[2,2], labels=\"c)\", cex=0.8) plot(Syracuse, border=\"grey60\") plot(Sy7_nb, coords, add=TRUE, pch=\".\") text(bbox(Syracuse)[1,1], bbox(Syracuse)[2,2], labels=\"d)\", cex=0.8) par(oopar) nb_l <- list(Triangulation=Sy4_nb, Gabriel=Sy6_nb,   Relative=Sy7_nb) if (!is.null(Sy5_nb)) nb_l <- c(nb_l, list(SOI=Sy5_nb)) sapply(nb_l, function(x) is.symmetric.nb(x, verbose=FALSE, force=TRUE)) ## Triangulation       Gabriel      Relative           SOI  ##          TRUE         FALSE         FALSE          TRUE sapply(nb_l, function(x) n.comp.nb(x)$nc) ## Triangulation       Gabriel      Relative           SOI  ##             1             1             1             1"},{"path":"https://r-spatial.github.io/spdep/articles/nb.html","id":"distance-based-neighbours","dir":"Articles","previous_headings":"Creating Neighbours","what":"Distance-Based Neighbours","title":"Creating Neighbours","text":"alternative method choose kk nearest points neighbours – adapts across study area, taking account differences densities areal entities. Naturally, overwhelming majority cases, leads asymmetric neighbours, ensure areas kk neighbours. knearneigh() function returns intermediate form converted nb object knn2nb(); knearneigh() can also take longlat= argument handle geographical coordinates. : k=1k=1 neighbours; b: k=2k=2 neighbours; c: k=4k=4 neighbours figure shows neighbour relationships k=1,2,4k= 1, 2, 4, many components k=1k=1. need , kk-nearest neighbour objects can made symmetrical using make.sym.nb() function. k=1k=1 object also useful finding minimum distance areas distance-based neighbour. Using nbdists() function, can calculate list vectors distances corresponding neighbour object, first nearest neighbours. greatest value minimum distance needed make sure areas linked least one neighbour. dnearneigh() function used find neighbours interpoint distance, arguments d1 d2 setting lower upper distance bounds; can also take longlat argument handle geographical coordinates. : Neighbours within 1,158m; b: neighbours within 1,545m; c: neighbours within 2,317m figure shows numbers distance-based neighbours increase moderate increases distance. Moving 0.750.75 times minimum -included distance, -included distance, 1.51.5 times minimum -included distance, numbers links grow rapidly. major problem first nearest neighbour distances study area much larger others, since avoid -neighbour areal entities, distance criterion need set many areas many neighbours. Distance-based neighbours: frequencies numbers neighbours census tract figure shows counts sizes sets neighbours three different distance limits. Syracuse, census tracts similar areas, try use distance-based neighbour criterion eight-county study area, smallest distance securing least one neighbour every areal entity 38km. areal entities approximately regularly spaced, using distance-based neighbours necessarily problem. Provided care taken handle side effects “weighting” areas analysis, using lists neighbours -neighbour areas necessarily problem either, certainly raise questions. Different disciplines handle definition neighbours ways convention; particular, seems ecologists frequently use distance bands. many distance bands used, approach variogram, although underlying understanding spatial autocorrelation seems contagion rather continuous.","code":"Sy8_nb <- knn2nb(knearneigh(coords, k=1), row.names=IDs) ## Warning in knn2nb(knearneigh(coords, k = 1), row.names = IDs): neighbour object ## has 15 sub-graphs Sy9_nb <- knn2nb(knearneigh(coords, k=2), row.names=IDs) Sy10_nb <- knn2nb(knearneigh(coords, k=4), row.names=IDs) nb_l <- list(k1=Sy8_nb, k2=Sy9_nb, k4=Sy10_nb) sapply(nb_l, function(x) is.symmetric.nb(x, verbose=FALSE, force=TRUE)) ##    k1    k2    k4  ## FALSE FALSE FALSE sapply(nb_l, function(x) n.comp.nb(x)$nc) ## k1 k2 k4  ## 15  1  1 oopar <- par(mfrow=c(1,3), mar=c(1,1,1,1)+0.1) plot(Syracuse, border=\"grey60\") plot(Sy8_nb, coords, add=TRUE, pch=\".\") text(bbox(Syracuse)[1,1], bbox(Syracuse)[2,2], labels=\"a)\", cex=0.8) plot(Syracuse, border=\"grey60\") plot(Sy9_nb, coords, add=TRUE, pch=\".\") text(bbox(Syracuse)[1,1], bbox(Syracuse)[2,2], labels=\"b)\", cex=0.8) plot(Syracuse, border=\"grey60\") plot(Sy10_nb, coords, add=TRUE, pch=\".\") text(bbox(Syracuse)[1,1], bbox(Syracuse)[2,2], labels=\"c)\", cex=0.8) par(oopar) dsts <- unlist(nbdists(Sy8_nb, coords)) summary(dsts) ##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.  ##   395.7   587.3   700.1   760.4   906.1  1544.6 max_1nn <- max(dsts) max_1nn ## [1] 1544.615 Sy11_nb <- dnearneigh(coords, d1=0, d2=0.75*max_1nn, row.names=IDs) ## Warning in dnearneigh(coords, d1 = 0, d2 = 0.75 * max_1nn, row.names = IDs): ## neighbour object has 4 sub-graphs Sy12_nb <- dnearneigh(coords, d1=0, d2=1*max_1nn, row.names=IDs) Sy13_nb <- dnearneigh(coords, d1=0, d2=1.5*max_1nn, row.names=IDs) nb_l <- list(d1=Sy11_nb, d2=Sy12_nb, d3=Sy13_nb) sapply(nb_l, function(x) is.symmetric.nb(x, verbose=FALSE, force=TRUE)) ##   d1   d2   d3  ## TRUE TRUE TRUE sapply(nb_l, function(x) n.comp.nb(x)$nc) ## d1 d2 d3  ##  4  1  1 oopar <- par(mfrow=c(1,3), mar=c(1,1,1,1)+0.1) plot(Syracuse, border=\"grey60\") plot(Sy11_nb, coords, add=TRUE, pch=\".\") text(bbox(Syracuse)[1,1], bbox(Syracuse)[2,2], labels=\"a)\", cex=0.8) plot(Syracuse, border=\"grey60\") plot(Sy12_nb, coords, add=TRUE, pch=\".\") text(bbox(Syracuse)[1,1], bbox(Syracuse)[2,2], labels=\"b)\", cex=0.8) plot(Syracuse, border=\"grey60\") plot(Sy13_nb, coords, add=TRUE, pch=\".\") text(bbox(Syracuse)[1,1], bbox(Syracuse)[2,2], labels=\"c)\", cex=0.8) par(oopar) dS <- c(0.75, 1, 1.5)*max_1nn res <- sapply(nb_l, function(x) table(card(x))) mx <- max(card(Sy13_nb)) res1 <- matrix(0, ncol=(mx+1), nrow=3) rownames(res1) <- names(res) colnames(res1) <- as.character(0:mx) res1[1, names(res$d1)] <- res$d1 res1[2, names(res$d2)] <- res$d2 res1[3, names(res$d3)] <- res$d3 library(RColorBrewer) pal <- grey.colors(3, 0.95, 0.55, 2.2) # RSB quietening greys barplot(res1, col=pal, beside=TRUE, legend.text=FALSE, xlab=\"numbers of neighbours\", ylab=\"tracts\") legend(\"topright\", legend=format(dS, digits=1), fill=pal, bty=\"n\", cex=0.8, title=\"max. distance\") dsts0 <- unlist(nbdists(NY_nb, coordinates(NY8))) summary(dsts0) ##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.  ##    82.7  1505.0  3378.7  5865.8  8954.3 38438.1"},{"path":"https://r-spatial.github.io/spdep/articles/nb.html","id":"higher-order-neighbours","dir":"Articles","previous_headings":"Creating Neighbours","what":"Higher-Order Neighbours","title":"Creating Neighbours","text":"Distance bands can generated using sequence d1 d2 argument values dnearneigh() function needed construct spatial autocorrelogram understood ecology. conventions, correlograms constructed taking input list neighbours first-order sets, stepping across graph second-, third-, higher-order neighbours based number links traversed, permitting cycles, risk making ii neighbour ii (O’Sullivan Unwin 2003). nblag() function takes existing neighbour list returns list lists, first maxlag= order neighbours. shows wave connectedness graph spreads third order, receding eighth order, dying away ninth order - tracts nine steps graph. distance bands graph step order approaches spreading neighbourhoods can used examine shape relationship intensities space, like variogram, can used attempting look effects scale.","code":"Sy0_nb_lags <- nblag(Sy0_nb, maxlag=9) ## Warning in nblag(Sy0_nb, maxlag = 9): lag 6 neighbour object has 7 sub-graphs ## Warning in nblag(Sy0_nb, maxlag = 9): lag 7 neighbour object has 22 sub-graphs ## Warning in nblag(Sy0_nb, maxlag = 9): lag 8 neighbour object has 52 sub-graphs ## Warning in nblag(Sy0_nb, maxlag = 9): lag 9 neighbour object has 63 sub-graphs names(Sy0_nb_lags) <- c(\"first\", \"second\", \"third\", \"fourth\", \"fifth\", \"sixth\", \"seventh\", \"eighth\", \"ninth\") res <- sapply(Sy0_nb_lags, function(x) table(card(x))) mx <- max(unlist(sapply(Sy0_nb_lags, function(x) card(x)))) nn <- length(Sy0_nb_lags) res1 <- matrix(0, ncol=(mx+1), nrow=nn) rownames(res1) <- names(res) colnames(res1) <- as.character(0:mx) for (i in 1:nn) res1[i, names(res[[i]])] <- res[[i]] res1 ##          0 1 2 3 4  5  6 7 8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 ## first    0 1 1 5 9 14 17 9 6  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 ## second   0 0 0 0 2  2  0 6 6 11 11  4  3  7  4  6  1  0  0  0  0  0  0  0  0 ## third    0 0 0 0 0  0  0 1 3  5  5  7 14  6  8  3  3  0  1  1  1  3  1  0  1 ## fourth   0 0 0 0 0  0  0 0 1  3  5  7 16 16  5  3  3  2  0  1  1  0  0  0  0 ## fifth    0 0 0 1 1  3  1 1 3  7 13 12  8  9  3  1  0  0  0  0  0  0  0  0  0 ## sixth    6 3 0 2 8  2  5 5 4  8  9  5  5  1  0  0  0  0  0  0  0  0  0  0  0 ## seventh 21 7 4 5 9  7  3 5 1  0  0  0  1  0  0  0  0  0  0  0  0  0  0  0  0 ## eighth  49 6 5 2 1  0  0 0 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 ## ninth   63 0 0 0 0  0  0 0 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0"},{"path":"https://r-spatial.github.io/spdep/articles/nb.html","id":"grid-neighbours","dir":"Articles","previous_headings":"Creating Neighbours","what":"Grid Neighbours","title":"Creating Neighbours","text":"data known arranged regular, rectangular grid, cell2nb() function can used construct neighbour lists, including torus. useful simulations, , since areal entities equal numbers neighbours, edges, structure graph neutral can achieved. Neighbours can either type rook queen. regular, rectangular grid complete, can use knowledge cell size stored grid topology create appropriate list neighbours, using tightly bounded distance criterion. Neighbour lists kind commonly found ecological assays, studies species richness national continental scale. also settings, moderately large nn, n=3n=3,103, use sparse, list based representation shows strength. Handling 281×281281 \\times 281 matrix eight-county census tracts feasible, easy 63×6363 \\times 63 matrix Syracuse census tracts, demanding 3,103×3103 \\times 3,103 matrix.","code":"cell2nb(7, 7, type=\"rook\", torus=TRUE) ## Neighbour list object: ## Number of regions: 49  ## Number of nonzero links: 196  ## Percentage nonzero weights: 8.163265  ## Average number of links: 4 cell2nb(7, 7, type=\"rook\", torus=FALSE) ## Neighbour list object: ## Number of regions: 49  ## Number of nonzero links: 168  ## Percentage nonzero weights: 6.997085  ## Average number of links: 3.428571 data(meuse.grid) coordinates(meuse.grid) <- c(\"x\", \"y\") gridded(meuse.grid) <- TRUE dst <- max(slot(slot(meuse.grid, \"grid\"), \"cellsize\")) mg_nb <- dnearneigh(coordinates(meuse.grid), 0, dst) mg_nb ## Neighbour list object: ## Number of regions: 3103  ## Number of nonzero links: 12022  ## Percentage nonzero weights: 0.1248571  ## Average number of links: 3.874315 table(card(mg_nb)) ##  ##    1    2    3    4  ##    1  133  121 2848"},{"path":[]},{"path":[]},{"path":"https://r-spatial.github.io/spdep/articles/nb_sf.html","id":"introduction","dir":"Articles","previous_headings":"Creating Neighbours using sf objects","what":"Introduction","title":"Creating Neighbours using sf objects","text":"vignette tracks legacy nb vignette, based part first (2008) edition ASDAR. adds hints code nb vignette use sf vector representation instead sp vector representation create neighbour objects. .","code":""},{"path":"https://r-spatial.github.io/spdep/articles/nb_sf.html","id":"summary","dir":"Articles","previous_headings":"Creating Neighbours using sf objects","what":"Summary","title":"Creating Neighbours using sf objects","text":"summary results : general, need reproduce results using \"Spatial\" objects spdep, coerce sf objects sp objects constructing neighbour objects (particularly polygon centroids used point representation). However, new work, use \"sf\" objects read using sf. spdep 1.1-7, number steps taken choose efficient approaches especially larger data sets, using functions sf approximate nearest neighbour (ANN) implementation dbscan rather RANN.","code":""},{"path":"https://r-spatial.github.io/spdep/articles/nb_sf.html","id":"data-set","dir":"Articles","previous_headings":"Creating Neighbours using sf objects","what":"Data set","title":"Creating Neighbours using sf objects","text":"’ll use whole NY 8 county set boundaries, challenge implementations just Syracuse subset. description input geometries ADSAR : New York leukemia: used documented extensively Waller Gotway (2004) data formerly made available Chap. 9 http://web1.sph.emory.edu/users/lwaller/ch9index.htm; data import process described help file NY_data spData; geometries downloaded CIESIN server formerly sedac.ciesin.columbia.edu/data/set/acrp-boundary-1992/data-download, now possibly https://earthdata.nasa.gov/data/catalog/sedac-ciesin-sedac-acrp-1992-bf-1.00, file /pub/census/usa/tiger/ny/bna_st/t8_36.zip, extensively edited; zip archive NY_data.zip shapefiles GAL format neighbours list book website. , zipfile now new location requiring login. object listw_NY directly imported nyadjwts.dbf Waller & Gotway (2004) chapter 9 website. version New York 8 counties geometries used ASDAR included shapefile spdep converted original BNA file using external utility program convert MapInfo format converted using GDAL 1.4.1 (OGR BNA driver available; entered OGR 1.5.0, release end 2007), contains invalid geometries. found mid-2007 included villages /excluded -umbilical cords boundary enclosing tract, underlying BNA file first converted MapInfo (holes exist ). use GPKG file created follows (rgdal also used output; GDAL prior GDAL 3.3 built GEOS, BNA vector driver use geometry tests: BNA driver supports reading polygons holes lakes. determines hole lake geometrical analysis (inclusion, non-intersection tests) ignores completely notion polygon winding (whether polygon edges described clockwise counter-clockwise). GDAL must built GEOS enabled make geometry test work.):","code":"library(sf) sf_bna <- st_read(\"t8_36.bna\", stringsAsFactors=FALSE) table(st_is_valid(sf_bna)) sf_bna$AREAKEY <- gsub(\"\\\\.\", \"\", sf_bna$Primary.ID) data(NY_data, package=\"spData\") key <- as.character(nydata$AREAKEY) sf_bna1 <- sf_bna[match(key, sf_bna$AREAKEY), c(\"AREAKEY\")] sf_bna2 <- merge(sf_bna1, nydata, by=\"AREAKEY\") sf_bna2_utm18 <- st_transform(sf_bna2, \"+proj=utm +zone=18 +datum=NAD27\") st_write(sf_bna2_utm18, \"NY8_bna_utm18.gpkg\")"},{"path":"https://r-spatial.github.io/spdep/articles/nb_sf.html","id":"nb-and-listw-objects-copied-from-the-nb_igraph-vignette","dir":"Articles","previous_headings":"Creating Neighbours using sf objects","what":"nb and listw objects (copied from the nb_igraph vignette)","title":"Creating Neighbours using sf objects","text":"Since spdep package created, spatial weights objects constructed lists three components attributes, old-style class listw objects. first component listw object nb object, list n integer vectors, least character vector region.id attribute n unique values (like row.names data.frame object); n number spatial entities. Component list contains integer identifiers neighbours sorted vector duplication values 1:n; neighbours, component vector length 1 value 0L. nb object may contain attribute indicating whether symmetric , whether neighbour j implies j neighbour . neighbour definitions symmetric construction, contiguities distance thresholds, others asymmetric, k-nearest neighbours. nb object redundantly stores -j j-links. second component listw object list n numeric vectors, length corresponding non-zero vectors nbobject. give values spatial weights -j neighbour pair. often case neighbours symmetric construction, weights , example weights row-standardised dividing row input weights count neighbours cardinality neighbour set . nb2listwfunction, also possible pass general weights, inverse distances, shares boundary lengths . third component listw object records style weights character code, \"B\" binary weights taking values zero one (one recorded), \"W\" row-standardised weights, . order subset listw objects, knowledge style may necessary.","code":""},{"path":"https://r-spatial.github.io/spdep/articles/nb_sf.html","id":"comparison-of-sp-and-sf-approaches","dir":"Articles","previous_headings":"Creating Neighbours using sf objects","what":"Comparison of sp and sf approaches","title":"Creating Neighbours using sf objects","text":"First housekeeping setup permit vignette built packages missing --date: Let us read GPKG file valid geometries ‘sf’ ‘sp’ objects:","code":"if (!suppressPackageStartupMessages(require(sf, quietly=TRUE))) {   message(\"install the sf package\")   dothis <- FALSE } if (dothis) sf_extSoftVersion() ##           GEOS           GDAL         proj.4 GDAL_with_GEOS     USE_PROJ_H  ##       \"3.13.0\"       \"3.10.0\"        \"9.5.0\"         \"true\"         \"true\"  ##           PROJ  ##        \"9.5.0\" NY8_sf <- st_read(system.file(\"shapes/NY8_bna_utm18.gpkg\", package=\"spData\"), quiet=TRUE) table(st_is_valid(NY8_sf)) ##  ## TRUE  ##  281"},{"path":"https://r-spatial.github.io/spdep/articles/nb_sf.html","id":"contiguity-neighbours-for-polygon-support","dir":"Articles","previous_headings":"Creating Neighbours using sf objects > Comparison of sp and sf approaches","what":"Contiguity neighbours for polygon support","title":"Creating Neighbours using sf objects","text":"first generate queen contiguity nb object using legacy spdep approach. first either uses pre-computed list vectors probable neighbours finds intersecting bounding boxes internally. points boundaries set polygons making observation checked distance less snap points set polygons making observation included set candidate neighbours. contiguity symmetric, j contiguities tested. queen contiguity found soon one point matches, rook contiguity soon two points match: Using spatial indices check intersection polygons much faster legacy method poly2nb. spdep 1.1-7, use made GEOS sf find candidate neighbours foundInBox=NULL, default value. contiguity symmetric definition, foundInBox= requires intersections higher indices, leading slight overhead remove duplicates, st_intersects() reports j ans j relationships. st_intersects() report whether neighbours queen rook, step needed distinguish two cases. spdep::poly2nb uses two heuristics, first find candidate neighbours intersecting polygons (st_intersects()), second use symmetry relationship halve number remaining tests. means performance linear n, overhead identifying candidates, back-filling symmetric neighbours. , spdep::poly2nb() stops searching queen contiguity soon first neighbour point found within snap distance (identical, tested first); second neighbour point indicates rook contiguities. details alternatives spherical geometries, see section @ref(spher-poly2nb) .","code":"suppressPackageStartupMessages(library(spdep)) reps <- 10 eps <- sqrt(.Machine$double.eps) system.time(for(i in 1:reps) NY8_sf_1_nb <- poly2nb(NY8_sf, queen=TRUE, snap=eps))/reps ##    user  system elapsed  ##  0.1720  0.0089  0.1818 NY8_sf_1_nb ## Neighbour list object: ## Number of regions: 281  ## Number of nonzero links: 1632  ## Percentage nonzero weights: 2.066843  ## Average number of links: 5.807829"},{"path":"https://r-spatial.github.io/spdep/articles/nb_sf.html","id":"contiguity-neighbours-from-invalid-polygons","dir":"Articles","previous_headings":"Creating Neighbours using sf objects > Comparison of sp and sf approaches","what":"Contiguity neighbours from invalid polygons","title":"Creating Neighbours using sf objects","text":"Next, explore possible source differences neighbour object reproduction, using original version tract boundaries used ASDAR, invalid geometries mentioned earlier (NY8_utm18.gpkg created original ESRI Shapefile used ASDAR): can see number differences neighbour sets derived fully valid geometries older partly invalid set: Using st_make_valid() make geometries valid: also see geometry type geometry column changes: checking \"sfg\" objects, two now objects different topological dimensions. can remedied using st_collection_extract() get polygon objects: However, making geometries valid, change geometries, new sets neighbours still differ made valid geometries ways imposing validity: neighbour sets old boundaries without imposing validity:","code":"if (packageVersion(\"spData\") >= \"2.3.2\") {     NY8_sf_old <- sf::st_read(system.file(\"shapes/NY8_utm18.gpkg\", package=\"spData\")) } else {     NY8_sf_old <- sf::st_read(system.file(\"shapes/NY8_utm18.shp\", package=\"spData\")) } ## Reading layer `NY8_utm18' from data source  ##   `/home/rsb/lib/r_libs/spData/shapes/NY8_utm18.gpkg' using driver `GPKG' ## Simple feature collection with 281 features and 17 fields ## Geometry type: POLYGON ## Dimension:     XY ## Bounding box:  xmin: 358241.9 ymin: 4649755 xmax: 480393.1 ymax: 4808545 ## Projected CRS: WGS 84 / UTM zone 18N table(st_is_valid(NY8_sf_old)) ##  ## FALSE  TRUE  ##     5   276 try(NY8_sf_old_1_nb <- poly2nb(NY8_sf_old), silent = TRUE) all.equal(NY8_sf_old_1_nb, NY8_sf_1_nb, check.attributes=FALSE) ## [1] \"Component 57: Numeric: lengths (4, 5) differ\"  ## [2] \"Component 58: Numeric: lengths (5, 6) differ\"  ## [3] \"Component 66: Numeric: lengths (7, 11) differ\" ## [4] \"Component 73: Numeric: lengths (4, 5) differ\"  ## [5] \"Component 260: Numeric: lengths (8, 9) differ\" NY8_sf_old_val <- st_make_valid(NY8_sf_old, dist=0) table(st_is_valid(NY8_sf_old_val)) ##  ## TRUE  ##  281 class(st_geometry(NY8_sf_old)) ## [1] \"sfc_POLYGON\" \"sfc\" class(st_geometry(NY8_sf_old_val)) ## [1] \"sfc_GEOMETRY\" \"sfc\" table(sapply(st_geometry(NY8_sf_old_val), function(x) class(x)[[2]])) ##  ## MULTIPOLYGON      POLYGON  ##            3          278 NY8_sf_old_val <- st_collection_extract(NY8_sf_old_val, \"POLYGON\") table(sapply(st_geometry(NY8_sf_old_val), function(x) class(x)[[2]])) ##  ## MULTIPOLYGON  ##          281 try(NY8_sf_old_1_nb_val <- poly2nb(NY8_sf_old_val), silent = TRUE) all.equal(NY8_sf_old_1_nb_val, NY8_sf_1_nb, check.attributes=FALSE) ## [1] \"Component 57: Numeric: lengths (4, 5) differ\"  ## [2] \"Component 58: Numeric: lengths (5, 6) differ\"  ## [3] \"Component 66: Numeric: lengths (7, 11) differ\" ## [4] \"Component 73: Numeric: lengths (4, 5) differ\"  ## [5] \"Component 260: Numeric: lengths (8, 9) differ\" all.equal(NY8_sf_old_1_nb_val, NY8_sf_old_1_nb, check.attributes=FALSE) ## [1] TRUE"},{"path":[]},{"path":"https://r-spatial.github.io/spdep/articles/nb_sf.html","id":"finding-points-for-polygon-objects","dir":"Articles","previous_headings":"Creating Neighbours using sf objects > Planar point-based neighbours","what":"Finding points for polygon objects","title":"Creating Neighbours using sf objects","text":"knearneigh() dnearneigh() require point support, decisions must taken place point areal object. can use st_centroid() get centroids, using of_largest_polygon=TRUE argument make sure centroid largest polygon id observation made one external ring: st_point_on_surface() guarantees point fall surface member polygon: indeed taking centre largest inscribed circle (function returns radius line segment, choose central point, point circle): need check whether coordinates planar :","code":"NY8_ct_sf <- st_centroid(st_geometry(NY8_sf), of_largest_polygon=TRUE) NY8_pos_sf <- st_point_on_surface(st_geometry(NY8_sf)) if (unname(sf_extSoftVersion()[\"GEOS\"] >= \"3.9.0\"))      NY8_cic_sf <- st_cast(st_inscribed_circle(st_geometry(NY8_sf), nQuadSegs=0), \"POINT\")[(1:(2*nrow(NY8_sf)) %% 2) != 0] st_is_longlat(NY8_ct_sf) ## [1] FALSE"},{"path":"https://r-spatial.github.io/spdep/articles/nb_sf.html","id":"graph-based-neighbours","dir":"Articles","previous_headings":"Creating Neighbours using sf objects > Planar point-based neighbours","what":"Graph-based neighbours","title":"Creating Neighbours using sf objects","text":", can check graph-based neighbours (planar coordinates ):","code":"suppressPackageStartupMessages(require(deldir)) NY84_nb <- tri2nb(NY8_ct_sf) if (require(dbscan, quietly=TRUE)) {   NY85_nb <- graph2nb(soi.graph(NY84_nb, NY8_ct_sf)) } else NY85_nb <- NULL ##  ## Attaching package: 'dbscan' ## The following object is masked from 'package:stats': ##  ##     as.dendrogram ## Warning in graph2nb(soi.graph(NY84_nb, NY8_ct_sf)): neighbour object has 2 ## sub-graphs NY86_nb <- graph2nb(gabrielneigh(NY8_ct_sf)) NY87_nb <- graph2nb(relativeneigh(NY8_ct_sf))"},{"path":"https://r-spatial.github.io/spdep/articles/nb_sf.html","id":"k-nearest-neighbours","dir":"Articles","previous_headings":"Creating Neighbours using sf objects > Planar point-based neighbours","what":"K-nearest neighbours","title":"Creating Neighbours using sf objects","text":"K-nearest neighbours use coordinate matrices, can handle Great Circle distances, demonstrated , data set used planar, case dbscan::kNN() 2D 3D building kd-tree used: Legacy code may used omitting kd-tree:","code":"system.time(for (i in 1:reps) suppressWarnings(NY88_nb_sf <- knn2nb(knearneigh(NY8_ct_sf, k=1))))/reps ##    user  system elapsed  ##  0.0217  0.0012  0.0231 system.time(for (i in 1:reps) suppressWarnings(NY89_nb_sf <- knn2nb(knearneigh(NY8_ct_sf, k=1, use_kd_tree=FALSE))))/reps ##    user  system elapsed  ##  0.0223  0.0009  0.0233"},{"path":"https://r-spatial.github.io/spdep/articles/nb_sf.html","id":"distance-neighbours","dir":"Articles","previous_headings":"Creating Neighbours using sf objects > Planar point-based neighbours","what":"Distance neighbours","title":"Creating Neighbours using sf objects","text":"Distance neighbours need threshold - nbdists shows maximum distance first nearest neighbour: dnearneigh can also handle Great Circle distances, demonstrated , data set used planar: default, function uses dbscan::frNN() build kd-tree 2D 3D used find distance neighbours. small n, argument use_kd_tree=FALSE may speed computation little reverting legacy code building kd-tree first, general differences small user notice:","code":"dsts <- unlist(nbdists(NY88_nb_sf, NY8_ct_sf)) summary(dsts) ##     Min.  1st Qu.   Median     Mean  3rd Qu.     Max.  ##    82.85   912.85  1801.11  3441.04  4461.26 17033.11 max_1nn <- max(dsts) system.time(for (i in 1:reps) suppressWarnings(NY810_nb <- dnearneigh(NY8_ct_sf, d1=0, d2=0.75*max_1nn)))/reps ##    user  system elapsed  ##  0.0585  0.0013  0.0600 system.time(for (i in 1:reps) suppressWarnings(NY811_nb <- dnearneigh(NY8_ct_sf, d1=0, d2=0.75*max_1nn, use_kd_tree=FALSE)))/reps ##    user  system elapsed  ##  0.0434  0.0010  0.0447"},{"path":"https://r-spatial.github.io/spdep/articles/nb_sf.html","id":"spherical-point-based-neighbours","dir":"Articles","previous_headings":"Creating Neighbours using sf objects","what":"Spherical point-based neighbours","title":"Creating Neighbours using sf objects","text":"Spherical point-based neighbours may found using Great Circle distances. used many years, switch sf 1.0-0 use s2 default opened new opportunities spatial indexing sphere may help.","code":"pts_ll <- st_transform(NY8_ct_sf, \"OGC:CRS84\") st_is_longlat(pts_ll) ## [1] TRUE"},{"path":"https://r-spatial.github.io/spdep/articles/nb_sf.html","id":"k-nearest-neighbours-1","dir":"Articles","previous_headings":"Creating Neighbours using sf objects > Spherical point-based neighbours","what":"K-nearest neighbours","title":"Creating Neighbours using sf objects","text":"input geometries geographical coordinates, sf_use_s2() TRUE, knearneigh() use spatially indexed points s2::s2_closest_edges() (see https://github.com/r-spatial/s2/issues/125#issuecomment-860107442) performs well also larger data sets: smaller data set, legacy approach without spatial indexing adequate, slows number observations increases: WGS84 ellipsoid Great Circle distances differ little s2 spherical distances, yielding output diverges two tract centroids:","code":"(old_use_s2 <- sf_use_s2()) ## [1] TRUE sf_use_s2(TRUE) system.time(for (i in 1:reps) pts_ll1_nb <- knn2nb(knearneigh(pts_ll, k=6)))/reps ##    user  system elapsed  ##  0.0321  0.0002  0.0326 sf_use_s2(FALSE) ## Spherical geometry (s2) switched off system.time(for (i in 1:reps) pts_ll2_nb <- knn2nb(knearneigh(pts_ll, k=6)))/reps ##    user  system elapsed  ##  0.0281  0.0000  0.0282 all.equal(pts_ll1_nb, pts_ll2_nb, check.attributes=FALSE) ## [1] \"Component 52: Mean relative difference: 1.466667\"   ## [2] \"Component 124: Mean relative difference: 0.0251046\" pts_ll1_nb[[52]] ## [1] 15 38 48 49 50 53 pts_ll2_nb[[52]] ## [1] 37 38 48 49 50 53 pts_ll1_nb[[124]] ## [1] 117 122 123 125 133 134 pts_ll2_nb[[124]] ## [1] 116 117 123 125 133 134 sf_use_s2(old_use_s2) ## Spherical geometry (s2) switched on"},{"path":"https://r-spatial.github.io/spdep/articles/nb_sf.html","id":"distance-neighbours-1","dir":"Articles","previous_headings":"Creating Neighbours using sf objects > Spherical point-based neighbours","what":"Distance neighbours","title":"Creating Neighbours using sf objects","text":"Distance neighbours problematic. nbdists() works well s2 spherical coordinates, none tried adaptations dnearneigh() work adequately yet. argument use_s2= set TRUE s2 > 1.0-7, using s2::s2_closest_edges() legacy brute-force approach, calculating distances j copying j symmetry. distance metric alway \"km\". permit s2 methods run, without arguments set, s2 > 1.0-7, s2::s2_dwithin_matrix() run: Alternatively, spherical distances can used dwithin=FALSE s2::s2_closest_edges(); although running similar time, s2::s2_closest_edges() depends additional k= argument, , mis-set, may miss valid neighbours: Using s2::s2_closest_edges() respects d1 > 0 without requiring second pass R, faster s2::s2_dwithin_matrix(): Using s2::s2_dwithin_matrix() requires second pass, one lower bound, another upper bound, set difference operation find neighbours distance band: Setting use_s2=FALSE falls back legacy version, uses symmetry reduce time: Minor differences may occur legacy ellipsoid s2 spherical approaches:","code":"max_1nn_ll <- max(unlist(nbdists(knn2nb(knearneigh(pts_ll, k=1)), pts_ll))) ## Warning in knn2nb(knearneigh(pts_ll, k = 1)): neighbour object has 62 ## sub-graphs args(dnearneigh) ## function (x, d1, d2, row.names = NULL, longlat = NULL, bounds = c(\"GE\",  ##     \"LE\"), use_kd_tree = TRUE, symtest = FALSE, use_s2 = packageVersion(\"s2\") >  ##     \"1.0.7\", k = 200, dwithin = TRUE)  ## NULL if (packageVersion(\"s2\") > \"1.0.7\") {   system.time(for (i in 1:(reps/5)) suppressWarnings(pts_ll3_nb <- dnearneigh(pts_ll, d1=0,       d2=0.75*max_1nn_ll)))/(reps/5) } ##    user  system elapsed  ##  0.0655  0.0000  0.0655 system.time(for (i in 1:(reps/5)) suppressWarnings(pts_ll5_nb <- dnearneigh(pts_ll, d1=0, d2=0.75*max_1nn_ll, dwithin=FALSE)))/(reps/5) ##    user  system elapsed  ##  0.0515  0.0000  0.0520 if (packageVersion(\"s2\") > \"1.0.7\") all.equal(pts_ll3_nb, pts_ll5_nb, check.attributes=FALSE) ## [1] TRUE if (packageVersion(\"s2\") > \"1.0.7\") {   system.time(for (i in 1:(reps/5)) suppressWarnings(pts_ll3a_nb <- dnearneigh(pts_ll, d1=5,       d2=0.75*max_1nn_ll, dwithin=FALSE)))/(reps/5) } ##    user  system elapsed  ##  0.0435  0.0005  0.0445 if (packageVersion(\"s2\") > \"1.0.7\") {     system.time(for (i in 1:(reps/5)) suppressWarnings(pts_ll5a_nb <- dnearneigh(pts_ll, d1=5,         d2=0.75*max_1nn_ll)))/(reps/5) } ##    user  system elapsed  ##  0.0845  0.0005  0.0855 if (packageVersion(\"s2\") > \"1.0.7\") all.equal(pts_ll3a_nb, pts_ll5a_nb, check.attributes=FALSE) ## [1] TRUE system.time(for (i in 1:reps) suppressWarnings(pts_ll6_nb <- dnearneigh(pts_ll, d1=0, d2=0.75*max_1nn_ll, use_s2=FALSE)))/reps ##    user  system elapsed  ##  0.0354  0.0002  0.0358 all.equal(pts_ll5_nb, pts_ll6_nb, check.attributes=FALSE) ##  [1] \"Component 20: Numeric: lengths (6, 5) differ\"      ##  [2] \"Component 28: Numeric: lengths (7, 6) differ\"      ##  [3] \"Component 112: Numeric: lengths (109, 108) differ\" ##  [4] \"Component 116: Numeric: lengths (109, 108) differ\" ##  [5] \"Component 122: Numeric: lengths (105, 106) differ\" ##  [6] \"Component 123: Numeric: lengths (108, 107) differ\" ##  [7] \"Component 130: Numeric: lengths (108, 109) differ\" ##  [8] \"Component 134: Numeric: lengths (106, 105) differ\" ##  [9] \"Component 158: Numeric: lengths (101, 102) differ\" ## [10] \"Component 165: Numeric: lengths (101, 102) differ\" ## [11] \"Component 168: Numeric: lengths (101, 102) differ\" ## [12] \"Component 179: Numeric: lengths (89, 90) differ\"   ## [13] \"Component 180: Numeric: lengths (96, 97) differ\"   ## [14] \"Component 188: Numeric: lengths (46, 47) differ\"   ## [15] \"Component 189: Numeric: lengths (55, 56) differ\"   ## [16] \"Component 196: Numeric: lengths (47, 46) differ\"   ## [17] \"Component 210: Numeric: lengths (106, 104) differ\" ## [18] \"Component 226: Numeric: lengths (88, 87) differ\"   ## [19] \"Component 229: Numeric: lengths (55, 53) differ\"   ## [20] \"Component 235: Numeric: lengths (40, 39) differ\"   ## [21] \"Component 237: Numeric: lengths (14, 15) differ\"   ## [22] \"Component 245: Numeric: lengths (16, 15) differ\" system.time(for (i in 1:reps) suppressWarnings(pts_ll6a_nb <- dnearneigh(pts_ll, d1=5, d2=0.75*max_1nn_ll, use_s2=FALSE)))/reps ##    user  system elapsed  ##  0.0280  0.0000  0.0282 if (packageVersion(\"s2\") > \"1.0.7\") all.equal(pts_ll5a_nb, pts_ll6a_nb, check.attributes=FALSE) ##  [1] \"Component 20: Numeric: lengths (6, 5) differ\"        ##  [2] \"Component 28: Numeric: lengths (7, 6) differ\"        ##  [3] \"Component 112: Numeric: lengths (62, 61) differ\"     ##  [4] \"Component 113: Numeric: lengths (62, 63) differ\"     ##  [5] \"Component 116: Numeric: lengths (56, 55) differ\"     ##  [6] \"Component 119: Numeric: lengths (68, 69) differ\"     ##  [7] \"Component 122: Numeric: lengths (43, 44) differ\"     ##  [8] \"Component 123: Numeric: lengths (50, 49) differ\"     ##  [9] \"Component 128: Numeric: lengths (65, 64) differ\"     ## [10] \"Component 130: Numeric: lengths (61, 63) differ\"     ## [11] \"Component 132: Numeric: lengths (45, 46) differ\"     ## [12] \"Component 134: Numeric: lengths (46, 45) differ\"     ## [13] \"Component 136: Numeric: lengths (61, 62) differ\"     ## [14] \"Component 147: Numeric: lengths (50, 51) differ\"     ## [15] \"Component 154: Numeric: lengths (56, 57) differ\"     ## [16] \"Component 158: Numeric: lengths (49, 50) differ\"     ## [17] \"Component 165: Mean relative difference: 0.02823018\" ## [18] \"Component 168: Numeric: lengths (54, 56) differ\"     ## [19] \"Component 179: Numeric: lengths (77, 78) differ\"     ## [20] \"Component 180: Numeric: lengths (85, 86) differ\"     ## [21] \"Component 188: Numeric: lengths (39, 40) differ\"     ## [22] \"Component 189: Numeric: lengths (48, 49) differ\"     ## [23] \"Component 196: Numeric: lengths (45, 44) differ\"     ## [24] \"Component 210: Numeric: lengths (68, 66) differ\"     ## [25] \"Component 226: Numeric: lengths (82, 81) differ\"     ## [26] \"Component 229: Numeric: lengths (48, 46) differ\"     ## [27] \"Component 235: Numeric: lengths (38, 37) differ\"     ## [28] \"Component 237: Numeric: lengths (14, 15) differ\"     ## [29] \"Component 245: Numeric: lengths (15, 14) differ\""},{"path":"https://r-spatial.github.io/spdep/articles/nb_sf.html","id":"spher-poly2nb","dir":"Articles","previous_headings":"Creating Neighbours using sf objects > Spherical point-based neighbours","what":"Contiguity neighbours for spherical polygon support","title":"Creating Neighbours using sf objects","text":"also turns sf functions used find contiguity neighbours, s2 spatial indexing functionality accessed finding candidate neighbours intersecting geometries. timings little slower st_intersects() hands geometry predicates s2_intersects_matrix(), results , spatial indexing used, scales well larger data sets:","code":"NY8_sf_ll <- st_transform(NY8_sf, \"OGC:CRS84\") st_is_longlat(NY8_sf_ll) ## [1] TRUE sf_use_s2(TRUE) system.time(for (i in 1:reps) NY8_sf_1_nb_ll <- poly2nb(NY8_sf_ll, queen=TRUE, snap=eps))/reps ##    user  system elapsed  ##  0.1534  0.0023  0.1563 all.equal(NY8_sf_1_nb, NY8_sf_1_nb_ll, check.attributes=FALSE) ## [1] TRUE"},{"path":"https://r-spatial.github.io/spdep/articles/sids.html","id":"introduction","dir":"Articles","previous_headings":"","what":"Introduction","title":"Introduction to the North Carolina SIDS data set (re-revised)","text":"data set presented first Symons, Grimson, Yuan (1983), analysed reference spatial nature data Cressie Read (1985), expanded Cressie Chan (1989), used detail Cressie (1991). 100 counties North Carolina, includes counts numbers live births (also non-white live births) numbers sudden infant deaths, July 1, 1974 June 30, 1978 July 1, 1979 June 30, 1984 periods. Cressie Read (1985), listing county neighbours based shared boundaries (contiguity) given, Cressie Chan (1989), Cressie (1991, 386–89), different listing based criterion distance county seats, cutoff 30 miles. county seat location coordinates given miles local (unknown) coordinate reference system. data also used exemplify range functions spatial statistics module user’s manual (Kaluzny et al. 1996).","code":""},{"path":"https://r-spatial.github.io/spdep/articles/sids.html","id":"getting-the-data-into-r","dir":"Articles","previous_headings":"","what":"Getting the data into R","title":"Introduction to the North Carolina SIDS data set (re-revised)","text":"using spdep spreg packages, version: spdep, version 1.3-7, 2024-11-25, sf package tmap package. data sources referred documented help page nc.sids data set spData. actual data, included shapefile county boundaries North Carolina made available maptools package 1. data known geographical coordinates (longitude-latitude decimal degrees) assumed use NAD27 datum. ESRI Shapefile deprecated, replaced GeoPackage, written reading original files spData 2.3.1: shapefile format presupposed three files extensions .shp, .shx, .dbf, first contains geometry data, second spatial index, third attribute data. required name apart extension, read using sf::st_read() sf object nc; class defined sf. centroids largest polygon county available using st_centroid method sf sfc POINT object, can used place labels extraction coordinate matrix: can examine names columns data frame see contains — fact columns examining , others useful cleaning data set. Let’s check different versions data - sf spData NC SIDS files, GeoDa Center two forms: actual CRS unknown, spData reports missing, although may well +proj=longlat +datum=NAD27 Next, geometries ? sf::st_equals returns logical matrix, ’ll check diagonal values TRUE, values TRUE summing recalling n 100: Next, let’s download GeoDa files repeat comparisons: looks though external files assuming WGS84/NAD83 datum, also contain geometries. Now contents files - sids2 also contains rates, file spData contains coordinates given Cressie (1991), parcels contiguous counties p. 554, aggregations used median polishing. spData data set columns reordered surprise: difference NWBIR74: spData follows Cressie (1991) sf Geoda follow Cressie Chan (1989) NWBIR74 Chowan county. now examine data set reproduced Cressie collaborators, included spData (formerly spdep), add neighbour relationships used Cressie Chan (1989) background map graph shown Figure : Printing neighbour object shows neighbour list object, sparse structure — displayed matrix, 3.94% cells filled. Objects class nb contain list long number counties; component list vector index numbers neighbours county question, neighbours county region.id 37001 can retreived matching indices. information can obtained using summary() nb object. Finally, associate vector names neighbour list, row.names argument. names unique, data frame row names. neighbour list object records neighbours order relation list , neighbours list county region.id “37001” seventeenth, nineteenth, thirty-second, forty-first sixty-eighth list. can retreive codes looking region.id attribute. also note neighbour criterion generates two counties neighbours, Dare Hyde, whose county seats 30 miles nearest neighbours. card() function returns cardinality neighbour set. need return methods handling -neighbour objects later . also show new neighbours lists may constructed , compare literature.","code":"library(spdep) nc <- st_read(system.file(\"shapes/sids.gpkg\", package=\"spData\")[1], quiet=TRUE) #st_crs(nc) <- \"EPSG:4267\" row.names(nc) <- as.character(nc$FIPSNO) sf_use_s2(TRUE) plot(st_geometry(nc), axes=TRUE) text(st_coordinates(st_centroid(st_geometry(nc), of_largest_polygon=TRUE)), label=nc$FIPSNO, cex=0.5) names(nc) ##  [1] \"CNTY_ID\"   \"AREA\"      \"PERIMETER\" \"CNTY_\"     \"NAME\"      \"FIPS\"      ##  [7] \"FIPSNO\"    \"CRESS_ID\"  \"BIR74\"     \"SID74\"     \"NWBIR74\"   \"BIR79\"     ## [13] \"SID79\"     \"NWBIR79\"   \"east\"      \"north\"     \"x\"         \"y\"         ## [19] \"lon\"       \"lat\"       \"L_id\"      \"M_id\"      \"geom\" summary(nc) ##     CNTY_ID          AREA          PERIMETER         CNTY_      ##  Min.   :1825   Min.   :0.0420   Min.   :0.999   Min.   :1825   ##  1st Qu.:1902   1st Qu.:0.0910   1st Qu.:1.324   1st Qu.:1902   ##  Median :1982   Median :0.1205   Median :1.609   Median :1982   ##  Mean   :1986   Mean   :0.1263   Mean   :1.673   Mean   :1986   ##  3rd Qu.:2067   3rd Qu.:0.1542   3rd Qu.:1.859   3rd Qu.:2067   ##  Max.   :2241   Max.   :0.2410   Max.   :3.640   Max.   :2241   ##      NAME               FIPS               FIPSNO         CRESS_ID      ##  Length:100         Length:100         Min.   :37001   Min.   :  1.00   ##  Class :character   Class :character   1st Qu.:37050   1st Qu.: 25.75   ##  Mode  :character   Mode  :character   Median :37100   Median : 50.50   ##                                        Mean   :37100   Mean   : 50.50   ##                                        3rd Qu.:37150   3rd Qu.: 75.25   ##                                        Max.   :37199   Max.   :100.00   ##      BIR74           SID74          NWBIR74           BIR79       ##  Min.   :  248   Min.   : 0.00   Min.   :   1.0   Min.   :  319   ##  1st Qu.: 1077   1st Qu.: 2.00   1st Qu.: 190.0   1st Qu.: 1336   ##  Median : 2180   Median : 4.00   Median : 697.5   Median : 2636   ##  Mean   : 3300   Mean   : 6.67   Mean   :1051.0   Mean   : 4224   ##  3rd Qu.: 3936   3rd Qu.: 8.25   3rd Qu.:1168.5   3rd Qu.: 4889   ##  Max.   :21588   Max.   :44.00   Max.   :8027.0   Max.   :30757   ##      SID79          NWBIR79             east           north       ##  Min.   : 0.00   Min.   :    3.0   Min.   : 19.0   Min.   :  6.0   ##  1st Qu.: 2.00   1st Qu.:  250.5   1st Qu.:178.8   1st Qu.: 97.0   ##  Median : 5.00   Median :  874.5   Median :285.0   Median :125.5   ##  Mean   : 8.36   Mean   : 1352.8   Mean   :271.3   Mean   :122.1   ##  3rd Qu.:10.25   3rd Qu.: 1406.8   3rd Qu.:361.2   3rd Qu.:151.5   ##  Max.   :57.00   Max.   :11631.0   Max.   :482.0   Max.   :182.0   ##        x                 y             lon              lat        ##  Min.   :-328.04   Min.   :3757   Min.   :-84.08   Min.   :33.92   ##  1st Qu.: -60.55   1st Qu.:3920   1st Qu.:-81.20   1st Qu.:35.26   ##  Median : 114.38   Median :3963   Median :-79.26   Median :35.68   ##  Mean   :  91.46   Mean   :3953   Mean   :-79.51   Mean   :35.62   ##  3rd Qu.: 240.03   3rd Qu.:4000   3rd Qu.:-77.87   3rd Qu.:36.05   ##  Max.   : 439.65   Max.   :4060   Max.   :-75.67   Max.   :36.52   ##       L_id           M_id                 geom     ##  Min.   :1.00   Min.   :1.00   MULTIPOLYGON :100   ##  1st Qu.:1.00   1st Qu.:2.00   epsg:4267    :  0   ##  Median :2.00   Median :3.00   +proj=long...:  0   ##  Mean   :2.12   Mean   :2.67                       ##  3rd Qu.:3.00   3rd Qu.:3.25                       ##  Max.   :4.00   Max.   :4.00 library(sf) nc_sf <- st_read(system.file(\"shape/nc.shp\", package=\"sf\"),                  quiet=TRUE) st_crs(nc_sf) ## Coordinate Reference System: ##   User input: NAD27  ##   wkt: ## GEOGCRS[\"NAD27\", ##     DATUM[\"North American Datum 1927\", ##         ELLIPSOID[\"Clarke 1866\",6378206.4,294.978698213898, ##             LENGTHUNIT[\"metre\",1]]], ##     PRIMEM[\"Greenwich\",0, ##         ANGLEUNIT[\"degree\",0.0174532925199433]], ##     CS[ellipsoidal,2], ##         AXIS[\"latitude\",north, ##             ORDER[1], ##             ANGLEUNIT[\"degree\",0.0174532925199433]], ##         AXIS[\"longitude\",east, ##             ORDER[2], ##             ANGLEUNIT[\"degree\",0.0174532925199433]], ##     ID[\"EPSG\",4267]] nc <- st_read(system.file(\"shapes/sids.shp\",                  package=\"spData\"), quiet=TRUE) st_crs(nc) ## Coordinate Reference System: NA st_crs(nc) <- \"+proj=longlat +datum=NAD27\" suppressWarnings(st_crs(nc_sf) <- st_crs(nc)) xx <- st_equals(nc, nc_sf, sparse=FALSE) all(diag(xx)) && sum(xx) == 100L ## [1] TRUE td <- tempdir() #download.file(\"https://geodacenter.github.io/data-and-lab//data/sids.zip\", file.path(td, \"sids.zip\"), quiet=TRUE)  # local copy (2020-10-22) as repository sometimes offline file.copy(system.file(\"etc/misc/sids.zip\", package=\"spdep\"), td) ## [1] TRUE unzip(file.path(td, \"sids.zip\"), c(\"sids/sids.dbf\", \"sids/sids.prj\", \"sids/sids.shp\", \"sids/sids.shx\"), exdir=td) sids_sf <- st_read(file.path(td, \"sids/sids.shp\"), quiet=TRUE) #download.file(\"https://geodacenter.github.io/data-and-lab//data/sids2.zip\", file.path(td, \"sids2.zip\"), quiet=TRUE) file.copy(system.file(\"etc/misc/sids2.zip\", package=\"spdep\"), td) ## [1] TRUE unzip(file.path(td, \"sids2.zip\"), c(\"sids2/sids2.dbf\", \"sids2/sids2.prj\", \"sids2/sids2.shp\", \"sids2/sids2.shx\"), exdir=td) sids2_sf <- st_read(file.path(td, \"sids2/sids2.shp\"), quiet=TRUE) st_crs(sids_sf) ## Coordinate Reference System: ##   User input: WGS 84  ##   wkt: ## GEOGCRS[\"WGS 84\", ##     DATUM[\"World Geodetic System 1984\", ##         ELLIPSOID[\"WGS 84\",6378137,298.257223563, ##             LENGTHUNIT[\"metre\",1]]], ##     PRIMEM[\"Greenwich\",0, ##         ANGLEUNIT[\"degree\",0.0174532925199433]], ##     CS[ellipsoidal,2], ##         AXIS[\"latitude\",north, ##             ORDER[1], ##             ANGLEUNIT[\"degree\",0.0174532925199433]], ##         AXIS[\"longitude\",east, ##             ORDER[2], ##             ANGLEUNIT[\"degree\",0.0174532925199433]], ##     ID[\"EPSG\",4326]] st_crs(sids2_sf) ## Coordinate Reference System: ##   User input: WGS 84  ##   wkt: ## GEOGCRS[\"WGS 84\", ##     DATUM[\"World Geodetic System 1984\", ##         ELLIPSOID[\"WGS 84\",6378137,298.257223563, ##             LENGTHUNIT[\"metre\",1]]], ##     PRIMEM[\"Greenwich\",0, ##         ANGLEUNIT[\"degree\",0.0174532925199433]], ##     CS[ellipsoidal,2], ##         AXIS[\"latitude\",north, ##             ORDER[1], ##             ANGLEUNIT[\"degree\",0.0174532925199433]], ##         AXIS[\"longitude\",east, ##             ORDER[2], ##             ANGLEUNIT[\"degree\",0.0174532925199433]], ##     ID[\"EPSG\",4326]] suppressWarnings(st_crs(sids_sf) <- st_crs(nc_sf)) xx <- st_equals(sids_sf, nc_sf, sparse=FALSE) all(diag(xx)) && sum(xx) == 100L ## [1] FALSE suppressWarnings(st_crs(sids2_sf) <- st_crs(nc_sf)) xx <- st_equals(sids2_sf, nc_sf, sparse=FALSE) all(diag(xx)) && sum(xx) == 100L ## [1] FALSE all.equal(as.data.frame(nc_sf)[,1:14], as.data.frame(sids_sf)[,1:14]) ##  [1] \"Names: 12 string mismatches\"                                   ##  [2] \"Component 4: Modes: numeric, character\"                        ##  [3] \"Component 4: target is numeric, current is character\"          ##  [4] \"Component 5: 100 string mismatches\"                            ##  [5] \"Component 6: Modes: character, numeric\"                        ##  [6] \"Component 6: target is character, current is numeric\"          ##  [7] \"Component 7: Mean relative difference: 0.9986388\"              ##  [8] \"Component 8: Mean relative difference: 64.33901\"               ##  [9] \"Component 9: Mean relative difference: 0.9979786\"              ## [10] \"Component 10: Mean relative difference: 156.5427\"              ## [11] \"Component 11: Mean relative difference: 3.01968\"               ## [12] \"Component 12: Mean relative difference: 0.9980208\"             ## [13] \"Component 13: Mean relative difference: 160.8194\"              ## [14] \"Component 14: Modes: numeric, list\"                            ## [15] \"Component 14: Attributes: < target is NULL, current is list >\" ## [16] \"Component 14: target is numeric, current is sfc_MULTIPOLYGON\" all.equal(as.data.frame(nc_sf)[,1:14], as.data.frame(sids2_sf)[,1:14]) ##  [1] \"Names: 12 string mismatches\"                          ##  [2] \"Component 4: Modes: numeric, character\"               ##  [3] \"Component 4: target is numeric, current is character\" ##  [4] \"Component 5: 100 string mismatches\"                   ##  [5] \"Component 6: Modes: character, numeric\"               ##  [6] \"Component 6: target is character, current is numeric\" ##  [7] \"Component 7: Mean relative difference: 0.9986388\"     ##  [8] \"Component 8: Mean relative difference: 64.33901\"      ##  [9] \"Component 9: Mean relative difference: 0.9979786\"     ## [10] \"Component 10: Mean relative difference: 156.5427\"     ## [11] \"Component 11: Mean relative difference: 3.01968\"      ## [12] \"Component 12: Mean relative difference: 0.9980208\"    ## [13] \"Component 13: Mean relative difference: 160.8194\"     ## [14] \"Component 14: Mean relative difference: 0.9984879\" all.equal(as.data.frame(nc_sf)[,1:14], as.data.frame(nc)[,c(2,3,4,1,5:14)]) ## [1] \"Component \\\"NWBIR74\\\": Mean relative difference: 0.04891304\" which(!(nc_sf$NWBIR74 == nc$NWBIR74)) ## [1] 21 c(nc$NWBIR74[21], nc_sf$NWBIR74[21]) ## [1] 386 368 gal_file <- system.file(\"weights/ncCR85.gal\", package=\"spData\")[1] ncCR85 <- read.gal(gal_file, region.id=nc$FIPSNO) ncCR85 ## Neighbour list object: ## Number of regions: 100  ## Number of nonzero links: 492  ## Percentage nonzero weights: 4.92  ## Average number of links: 4.92 gal_file <- system.file(\"weights/ncCC89.gal\", package=\"spData\")[1] ncCC89 <- read.gal(gal_file, region.id=nc$FIPSNO) ncCC89 ## Neighbour list object: ## Number of regions: 100  ## Number of nonzero links: 394  ## Percentage nonzero weights: 3.94  ## Average number of links: 3.94  ## 2 regions with no links: ## 37055, 37095 ## 3 disjoint connected subgraphs plot(st_geometry(nc), border=\"grey\") plot(ncCC89, st_centroid(st_geometry(nc), of_largest_polygon), add=TRUE, col=\"blue\") r.id <- attr(ncCC89, \"region.id\") ncCC89[[match(\"37001\", r.id)]] ## [1] 11 26 29 30 48 r.id[ncCC89[[match(\"37001\", r.id)]]] ## [1] 37033 37081 37135 37063 37037 as.character(nc$NAME)[card(ncCC89) == 0] ## [1] \"Dare\" \"Hyde\""},{"path":"https://r-spatial.github.io/spdep/articles/sids.html","id":"probability-mapping","dir":"Articles","previous_headings":"Getting the data into R","what":"Probability mapping","title":"Introduction to the North Carolina SIDS data set (re-revised)","text":"Rather review functions measuring modelling spatial dependence spdep package, focus probability mapping disease rates data. Typically, counts incidence disease spatial unit, associated counts populations risk. task try establish whether spatial units seem characterised higher lower counts cases might expected general terms (Bailey Gatrell 1995). early approach Choynowski (1959), described Cressie Read (1985) Bailey Gatrell (1995), assumes, given true rate spatial units small, population risk increases infinity, spatial unit case counts Poisson mean value equal population risk times rate study area whole. Choynowski’s approach folds two tails measured probabilities together, small values, chosen α\\alpha, occur spatial units either unusually high low rates. reason, high low counties plotted separately . Note cut returns factor labeled cut intervals.  complicated thematic maps, may helpful use ColorBrewer (https://colorbrewer2.org) colour palettes. use palettes accessed tmap, available R RColorBrewer package. choynowski() function provides probability map values required, probmap() function returns raw (crude) rates, expected counts (assuming constant rate across study area), relative risks, Poisson probability map values calculated using standard cumulative distribution function ppois(). fold tails together, counties lower observed counts expected, based population size, values lower tail, higher observed counts expected values upper tail, can see.  Marilia Carvalho (personal communication) Virgilio Gómez Rubio (Gómez-Rubio, Ferrándiz-Ferragud, López-Quílez 2005) pointed unusual shape distribution Poisson probability values (histogram ), repeating doubts probability mapping voiced Cressie (1991, 392): “extreme value …\\ldots may due lack fit Poisson model deviation constant rate assumption”. many high values one expected, suggesting perhaps overdispersion, ratio variance mean larger unity.  One ad-hoc way assess impact possible failure assumption counts follow Poisson distribution estimate dispersion fitting generalized linear model observed counts including intercept (null model) offset observed population risk (suggested Marilia Carvalho associates):  dispersion equal 2.2786188, much greater unity; calculate corrected probability map values taking standardised residuals model, taking size dispersion account; results shown . Many fewer counties appear now unexpectedly large small numbers cases. ad-hoc adjustment made R provides access wide range model-fitting functions can used help check assumptions. Gómez-Rubio, Ferrándiz-Ferragud, López-Quílez (2005) chose rather construct probability map hypothesis data drawn Negative Binomial distribution. far, none maps presented made use spatial dependence possibly present data. elementary step can taken map Empirical Bayes estimates rates, smoothed relation raw rates. underlying question linked larger variance associated rate estimates counties small populations risk compared counties large populations risk. Empirical Bayes estimates place credence raw rates counties large populations risk, modify much less modify rates small counties. case small populations risk, confidence placed either global rate study area whole, local Empirical Bayes estimates, rates larger moving window including neighbours county estimated. function used spdep EBlocal(), initially contributed Marilia Carvalho. parallels similar function GeoDa, uses Bailey Gatrell (1995) interpretation Marshall (1991), rather GeoDa (Anselin, Syabri, Smirnov 2002).  results shown Figure . Like relevant functions spdep,EBlocal() takes zero.policy argument allow missing values passed . case, local estimate available two counties neighbours, marked stars. addition Empirical Bayes smoothing globally, used disease mapping Assuncão Reis correction Moran’s II rates data (shrink towards global rate population risk small, Monte Carlo test), lists local neighbours can used shrink towards local rate.","code":"ch <- choynowski(nc$SID74, nc$BIR74) nc$ch_pmap_low <- ifelse(ch$type, ch$pmap, NA) nc$ch_pmap_high <- ifelse(!ch$type, ch$pmap, NA) prbs <- c(0,.001,.01,.05,.1,1) nc$high = cut(nc$ch_pmap_high, prbs) nc$low = cut(nc$ch_pmap_low,prbs ) is_tmap <- FALSE if (require(tmap, quietly=TRUE)) is_tmap <- TRUE is_tmap ## [1] TRUE library(tmap) tmap4 <- packageVersion(\"tmap\") >= \"3.99\" if (tmap4) {   tm_shape(nc) + tm_polygons(fill=c(\"low\", \"high\"), fill.scale = tm_scale(values=\"brewer.set1\"), fill.legend = tm_legend(\"p-values\", frame=FALSE, item.r = 0), fill.free=FALSE, lwd=0.01) + tm_layout(panel.labels=c(\"low\", \"high\")) } else { tm_shape(nc) + tm_fill(c(\"low\", \"high\"), palette=\"Set1\", title=\"p-values\") +   tm_facets(free.scales=FALSE) + tm_layout(panel.labels=c(\"low\", \"high\")) } pmap <- probmap(nc$SID74, nc$BIR74) nc$pmap <- pmap$pmap brks <- c(0,0.001,0.01,0.025,0.05,0.95,0.975,0.99,0.999,1) if (tmap4) {   tm_shape(nc) + tm_polygons(fill=\"pmap\", fill.scale = tm_scale(values=\"brewer.rd_bu\", midpoint=0.5, breaks=brks), fill.legend = tm_legend(frame=FALSE, item.r = 0, position = tm_pos_out(\"right\", \"center\")), lwd=0.01) + tm_layout(component.autoscale=FALSE) } else { tm_shape(nc) + tm_fill(\"pmap\", breaks=brks, midpoint=0.5, palette=\"RdBu\") + tm_layout(legend.outside=TRUE) } hist(nc$pmap, main=\"\") res <- glm(SID74 ~ offset(log(BIR74)), data=nc, family=\"quasipoisson\") nc$stdres <- rstandard(res) brks <- c(-4, -3, -2, -1.5, -1, -0.5, 0.5, 1, 1.5, 2, 3, 4) if (tmap4) {   tm_shape(nc) + tm_polygons(fill=\"stdres\", fill.scale = tm_scale(values=\"brewer.rd_bu\", midpoint=0.5, breaks=brks), fill.legend = tm_legend(frame=FALSE, item.r = 0, position = tm_pos_out(\"right\", \"center\")), lwd=0.01) + tm_layout(component.autoscale=FALSE) } else {   tm_shape(nc) + tm_fill(\"stdres\", breaks=brks, midpoint=0, palette=\"RdBu\") + tm_layout(legend.outside=TRUE) } global_rate <- sum(nc$SID74)/sum(nc$BIR74) nc$Expected <- global_rate * nc$BIR74 res <- EBlocal(nc$SID74, nc$Expected, ncCC89, zero.policy=TRUE) nc$EB_loc <- res$est brks <- c(0, 0.25, 0.5, 0.75, 1, 2, 3, 4, 5) nc_miss <- st_centroid(st_geometry(nc[card(ncCC89) == 0,]), of_largest_polygon) if (tmap4) {   tm_shape(nc) + tm_polygons(fill=\"stdres\", fill.scale = tm_scale(values=\"brewer.rd_bu\", midpoint=0.5, breaks=brks), fill.legend = tm_legend(frame=FALSE, item.r = 0, position = tm_pos_out(\"right\", \"center\")), lwd=0.01) + tm_layout(component.autoscale=FALSE) + tm_shape(nc_miss) + tm_symbols(shape=8, size=0.5) } else { tm_shape(nc) + tm_fill(\"EB_loc\", breaks=brks, midpoint=1, palette=\"RdBu\") + tm_layout(legend.outside=TRUE) + tm_shape(nc_miss) + tm_symbols(shape=8, size=0.5) } set.seed(1) EBImoran.mc(nc$SID74, nc$BIR74, nb2listw(ncCC89, style=\"B\", zero.policy=TRUE), nsim=999, zero.policy=TRUE) ##  ##  Monte-Carlo simulation of Empirical Bayes Index (mean subtracted) ##  ## data:  cases: nc$SID74, risk population: nc$BIR74 ## weights: nb2listw(ncCC89, style = \"B\", zero.policy = TRUE) ## number of simulations + 1: 1000 ##  ## statistic = 0.25789, observed rank = 998, p-value = 0.002 ## alternative hypothesis: greater"},{"path":"https://r-spatial.github.io/spdep/articles/sids.html","id":"exploration-and-modelling-of-the-data","dir":"Articles","previous_headings":"","what":"Exploration and modelling of the data","title":"Introduction to the North Carolina SIDS data set (re-revised)","text":"One first steps taken Cressie Read (1985) try bring spatial trends dividing North Carolina 4×44\\times4 rough rectangles. Just see works, let us map rough rectangles proceeding .  Cressie constructs transformed SIDS rates variable, 1974–78, analyses (co-workers). can replicate stem--leaf figure p. 396 book, taken Cressie Read (1989):","code":"nc$both <- factor(paste(nc$L_id, nc$M_id, sep=\":\")) nboth <- length(table(unclass(nc$both))) if (tmap4) {   tm_shape(nc) + tm_polygons(fill=\"both\", fill.scale=tm_scale(values=\"brewer.set1\"), fill.legend = tm_legend(\"rough\\nrectangles\", frame=FALSE, item.r = 0, position = tm_pos_out(\"right\", \"center\")), lwd=0.01) + tm_layout(component.autoscale=FALSE) } else { tm_shape(nc) + tm_fill(\"both\", palette=\"Set1\", title=\"rough\\nrectangles\") + tm_layout(legend.outside=TRUE) } nc$ft.SID74 <- sqrt(1000)*(sqrt(nc$SID74/nc$BIR74) + sqrt((nc$SID74+1)/nc$BIR74)) stem(round(nc$ft.SID74, 1), scale=2) ##  ##   The decimal point is at the | ##  ##   0 | 9 ##   1 | 111244 ##   1 | 567789999 ##   2 | 0011111222334444 ##   2 | 55555666677778999999999 ##   3 | 000111122333333344444444 ##   3 | 5568999 ##   4 | 013344 ##   4 | 555557 ##   5 | 2 ##   5 |  ##   6 | 3"},{"path":"https://r-spatial.github.io/spdep/articles/sids.html","id":"medpol","dir":"Articles","previous_headings":"Exploration and modelling of the data","what":"Median polish smoothing","title":"Introduction to the North Carolina SIDS data set (re-revised)","text":"Cressie (1991, 46–48, 393–400) discusses detail smoothing may used partition variation data smooth rough. order try North Carolina SIDS data set, use coarse gridding four columns four rows given Cressie (1991, 553–54), four grid cells empty; given variables L_id M_id object nc. Next aggregate number live births number SIDS cases 1974–1978 grid cells: Using Freeman-Tukey transformation used county data, coerce data correctly configured matrix, cells empty. medpolish function applied matrix, told remove empty cells; function iterates rows columns matrix using median extract overall effect, row column effects, residuals: Returning factors linking rows columns counties, generating matrices dummy variables using model.matrix, can calculate fitted values Freeman-Tukey adjusted rate county, residuals subtracting fitted value observed rate. Naturally, fitted value counties grid cell:  figure shows median polish smoothing results three maps, observed Freeman-Tukey transformed SIDS rates, fitted smoothed values, residuals. addition, plot median polish object also shown, plotting smooth residuals outer product row column effects divided overall effect, indicate lack additivity row column case — relevant analysis tables covariates rather geographical grids.","code":"mBIR74 <- tapply(nc$BIR74, nc$both, sum) mSID74 <- tapply(nc$SID74, nc$both, sum) mFT <- sqrt(1000)*(sqrt(mSID74/mBIR74) + sqrt((mSID74+1)/mBIR74)) # mFT1 <- t(matrix(mFT, 4, 4, byrow=TRUE)) # wrong assignment of 12 elements to a 4x4 matrix detected by CRAN test 2021-05-22 rc <- do.call(\"rbind\", lapply(strsplit(names(mFT), \":\"), as.integer)) mFT1 <- matrix(as.numeric(NA), 4, 4) for (i in 1:nrow(rc)) mFT1[rc[i,1], rc[i,2]] <- mFT[i] med <- medpolish(mFT1, na.rm=TRUE, trace.iter=FALSE) med ##  ## Median Polish Results (Dataset: \"mFT1\") ##  ## Overall: 2.90965 ##  ## Row Effects: ## [1] -0.05686791 -0.37236370  0.05686791  0.79541774 ##  ## Column Effects: ## [1] -0.005484562 -0.446250551  0.003656375  0.726443256 ##  ## Residuals: ##           [,1]     [,2]      [,3]     [,4] ## [1,]        NA -0.45800  0.000000  0.37556 ## [2,] -0.092554  0.00000  0.101695  0.00000 ## [3,]  0.092554  0.30464 -0.090726 -0.55364 ## [4,]        NA       NA  0.000000       NA mL_id <- model.matrix(~ as.factor(nc$L_id) -1) mM_id <- model.matrix(~ as.factor(nc$M_id) -1) nc$pred <- c(med$overall + mL_id %*% med$row + mM_id %*% med$col) nc$mp_resid <- nc$ft.SID74 - nc$pred if (tmap4) {   out1 <- tm_shape(nc) + tm_polygons(fill=c(\"ft.SID74\", \"pred\"), fill.scale=tm_scale(values=\"brewer.yl_or_br\"), fill.legend=tm_legend(position=tm_pos_out(\"right\", \"center\"), frame=FALSE, item.r = 0), fill.free=FALSE, lwd=0.01) + tm_layout(panel.labels=c(\"Observed\", \"Median polish prediction\"))   out2 <- tm_shape(nc) + tm_polygons(fill=\"mp_resid\", fill.scale=tm_scale(values=\"brewer.rd_yl_gn\", midpoint=0), fill.legend=tm_legend(position=tm_pos_out(\"right\", \"center\"), frame=FALSE, item.r = 0), lwd=0.01) } else { out1 <- tm_shape(nc) + tm_fill(c(\"ft.SID74\", \"pred\")) + tm_facets(free.scales=FALSE) + tm_layout(panel.labels=c(\"Observed\", \"Median polish prediction\")) out2 <- tm_shape(nc) + tm_fill(\"mp_resid\", midpoint=0) + tm_layout(legend.outside=TRUE) } tmap_arrange(out1, out2, ncol=1)"},{"path":[]},{"path":"https://r-spatial.github.io/spdep/articles/subgraphs.html","id":"introduction","dir":"Articles","previous_headings":"","what":"Introduction","title":"No-neighbour observation and subgraph handling","text":"spdep package always careful disconnected graphs, especially disconnected observations graph nodes neighbours, incoming outgoing edges. nb neighbour objects, encoded integer vectors length 1 containing integer 0, invalid index [1,N][1, N], NN observation count. Functions taking neighbour objects arguments use zero.policy argument guide handle -neighbour observations. spdep also n.comp.nb find number disjoint connected subgraphs nb object, contributed Nicholas Lewin-Koh 2001 using depth-first search symmetric neighbours, showing addition observations belong subgraph. Obviously, -neighbour observations singleton graph nodes, subgraphs also troubling spatial analysis, connection spatial processes subgraphs. ripples one pond cross separate pond connected. spdep 1.3-1, steps began raise awareness possibility neighbour objects might created disconnected way, mostly warnings, computation subgraph measures default. vignette intended provide background steps.","code":""},{"path":"https://r-spatial.github.io/spdep/articles/subgraphs.html","id":"no-neighbour-observations","dir":"Articles","previous_headings":"","what":"No-neighbour observations","title":"No-neighbour observation and subgraph handling","text":"start, nb objects recorded -neighbour observations integer vector unit length value 0, neighbours recorded ID values 1 N, N observation count. print summary methods always reported presence -neighbour observations, listed IDs (region.id values). nb object contains -neighbour observations, user decide whether drop observations, retained, value give weights. zero.policy argument uses zero value TRUE, FALSE causes nb2listw fail. value zero.policy call functions like nb2listw, subset.listw mat2listw creating listw objects representing sparse spatial weights matrices added created object attribute, used subsequently pass choice functions. example, moran.test takes value attribute default zero.policy argument: observation ii neighbours, weights sum ∑j=1Nwij=0\\sum_{j=1}^N w_{ij} = 0, wij=0,∀jw_{ij} = 0, \\forall j (see discussion Bivand Portnov (2004)). eigenvalue also zero, consequences analytical inference: adjust.n argument measures spatial autocorrelation default TRUE, subtracts count singleton nodes NN attempt acknowledge reduction information available. discussion address problems arising analysing areal/lattice data, neighbours defined polygon features contiguous boundaries. One way -neighbour observations may occur islands. clearly case Freni-Sterrantino, Ventrucci, Rue (2018), Capraia Giglio Isles singleton nodes. take Westminster constituencies Wales used July 2024 UK general election. GDAL least version 3.7.0, driver supports compressed GeoPackage files, must decompressed first. boundaries taken Ordnance Survey Boundary-Line site, https://osdatahub.os.uk/downloads/open/BoundaryLine, choosing 2024 Westminster constituencies (https://www.os.uk/opendata/licence), simplified using tolerance 50m reduce object size, merged selected voting outcomes constituencies Great Britain https://electionresults.parliament.uk/countries/1, (https://www.nationalarchives.gov.uk/doc/open-government-licence/version/3/). , subset Wales useful see: two subgraphs singleton Ynys Môn 31 constituencies: left map shows Ynys Môn can shown selecting name, black border, zero cardinality neighbour set, using card, filling polygon. right map shows location island, known English Anglesey, north-west Welsh mainland, neighbour links:  maps, can see island close two constituencies across Afon Menai (Menai Strait English), three simplified polygons less 280m apart, measured polygon boundaries: Using snap distance 280m, can join island two obvious proximate neighbours:  case, increasing snap default 10mm (close equivalents geometries known metrics; previously sqrt(.Machine$double.eps) 1.4901161^{-8} cases) helps. symmetric links added : always going case, strait narrow. islands much offshore, steps may required, large snap distance draw extra neighbours already connected observations. also possible increasing snap distance may fail link islands considered candidate neighbours, extents (bounding boxes), buffered snap value, intersect. can also use distances pick neighbour candidates meet criterion 280m, taking care lose ordering needed identify correct observations: candidates island , two neighbours across Menai Strait: addlinks1 function can used add links Ynys Môn neighbours, symmetry Ynys Môn. approach means island treated separately (scripted sequence), risk adding spurious neighbours denser parts study area. Since constituency observations areal support, surprising changing support points using kk-nearest neighbours work adequately, distance measurements points representing polygons rather areal unit boundaries: , Clwyd North, east Bangor Aberconwy, given neighbour Ynys Môn Dwyfor Meirionnydd, west Bangor Aberconwy, . addition, two subgraphs, still remain k=6k=6.","code":"library(spdep) ## Loading required package: spData ## Loading required package: sf ## Linking to GEOS 3.13.0, GDAL 3.10.0, PROJ 9.5.0; sf_use_s2() is TRUE args(moran.test) ## function (x, listw, randomisation = TRUE, zero.policy = attr(listw,  ##     \"zero.policy\"), alternative = \"greater\", rank = FALSE, na.action = na.fail,  ##     spChk = NULL, adjust.n = TRUE, drop.EI2 = FALSE)  ## NULL eigen(0)$values ## [1] 0 (GDAL37 <- as.numeric_version(unname(sf_extSoftVersion()[\"GDAL\"])) >= \"3.7.0\") ## [1] TRUE file <- \"etc/shapes/GB_2024_Wales_50m.gpkg.zip\" zipfile <- system.file(file, package=\"spdep\") if (GDAL37) {     w50m <- st_read(zipfile) } else {     td <- tempdir()     bn <- sub(\".zip\", \"\", basename(file), fixed=TRUE)     target <- unzip(zipfile, files=bn, exdir=td)     w50m <- st_read(target) } ## Reading layer `GB_2024_Wales_50m' from data source  ##   `/tmp/RtmpzEChJG/temp_libpath8ee3b7c361c1e/spdep/etc/shapes/GB_2024_Wales_50m.gpkg.zip'  ##   using driver `GPKG' ## Simple feature collection with 32 features and 19 fields ## Geometry type: MULTIPOLYGON ## Dimension:     XY ## Bounding box:  xmin: 146597.1 ymin: 164536.5 xmax: 355287 ymax: 395993.5 ## Projected CRS: OSGB36 / British National Grid (w50m |> poly2nb(row.names=as.character(w50m$Constituency)) -> nb_W_50m) ## Warning in poly2nb(w50m, row.names = as.character(w50m$Constituency)): some observations have no neighbours; ## if this seems unexpected, try increasing the snap argument. ## Warning in poly2nb(w50m, row.names = as.character(w50m$Constituency)): neighbour object has 2 sub-graphs; ## if this sub-graph count seems unexpected, try increasing the snap argument. ## Neighbour list object: ## Number of regions: 32  ## Number of nonzero links: 136  ## Percentage nonzero weights: 13.28125  ## Average number of links: 4.25  ## 1 region with no links: ## Ynys Môn ## 2 disjoint connected subgraphs attr(nb_W_50m, \"ncomp\")$comp.id |>table() |> table() ##  ##  1 31  ##  1  1 ynys_mon <- w50m$Constituency == \"Ynys Môn\" pts <- st_point_on_surface(st_geometry(w50m)) opar <- par(mfrow=c(1, 2)) plot(st_geometry(w50m), border=\"grey75\") plot(st_geometry(w50m)[ynys_mon], add=TRUE) plot(st_geometry(w50m)[card(nb_W_50m) == 0L], add=TRUE, border=\"transparent\", col=\"wheat1\") plot(st_geometry(w50m), border=\"grey75\") plot(nb_W_50m, pts, add=TRUE) par(opar) dym <- c(st_distance(w50m[ynys_mon,], w50m)) sort(dym)[1:12] ## Units: [m] ##  [1]      0.0000    123.4132    277.5414  16658.7265  37985.7086  54096.7729 ##  [7]  58146.4320  65550.2491  67696.3323  93741.9873 113007.3659 137858.1826 (nb_W_50m_snap <- poly2nb(w50m, row.names=as.character(w50m$Constituency), snap=280)) ## Neighbour list object: ## Number of regions: 32  ## Number of nonzero links: 140  ## Percentage nonzero weights: 13.67188  ## Average number of links: 4.375 plot(st_geometry(w50m), border=\"grey75\") plot(nb_W_50m_snap, pts, add=TRUE) attr(nb_W_50m_snap, \"region.id\")[nb_W_50m_snap[[which(ynys_mon)]]] ## [1] \"Bangor Aberconwy\"   \"Dwyfor Meirionnydd\" (meet_criterion <- sum(dym <= units::set_units(280, \"m\"))) ## [1] 3 (cands <- attr(nb_W_50m, \"region.id\")[order(dym)[1:meet_criterion]]) ## [1] \"Ynys Môn\"           \"Bangor Aberconwy\"   \"Dwyfor Meirionnydd\" (nb_W_50m_add <- addlinks1(nb_W_50m, from = cands[1], to = cands[2:meet_criterion])) ## Neighbour list object: ## Number of regions: 32  ## Number of nonzero links: 140  ## Percentage nonzero weights: 13.67188  ## Average number of links: 4.375 all.equal(nb_W_50m_add, nb_W_50m_snap, check.attributes=FALSE) ## [1] TRUE k2 <- knn2nb(knearneigh(pts, k=2), row.names=as.character(w50m$Constituency), sym=TRUE) ## Warning in knn2nb(knearneigh(pts, k = 2), row.names = ## as.character(w50m$Constituency), : neighbour object has 2 sub-graphs attr(k2, \"region.id\")[k2[[which(ynys_mon)]]] ## [1] \"Bangor Aberconwy\" \"Clwyd North\""},{"path":"https://r-spatial.github.io/spdep/articles/subgraphs.html","id":"subgraphs","dir":"Articles","previous_headings":"","what":"Subgraphs","title":"No-neighbour observation and subgraph handling","text":"Subgraphs may found -neighbour observations present, also graph split two blocks observations path observation block another block, across low population density constituencies mid-Wales: can show block structure displaying binary spatial weights matrix:  occurs frequently point support, may also occur areal support, Freni-Sterrantino, Ventrucci, Rue (2018) find eight municipalities island Elba. spdep 1.3-6, igraph spatialreg packages available, n.comp.nb uses igraph::components compute graph components, also using depth-first search. original implementation fast, directed (asymmetric) graphs converts first symmetry, igraph::components can handle directed graphs without conversion (see https://github.com/r-spatial/spdep/issues/160 details). Another case demonstrates cyclical subgraphs may appear; taken constituencies 2024 UK general election, subsetted England south London. second subgraph two members, others’ neighbours, known cyclical component. constituencies Isle Wight:  consequences eigenvalues spatial weights matrix, pointed Smirnov Anselin (2009) Bivand, Hauke, Kossowski (2013). row-standardised weights, eigenvalues component : “takes ” lower domain boundary, whole data set now : compared lower domain boundary remainder study area: subgraph may added remainder shown : Using 5km cutoff seems prudent, work snap value. Taking Isle Wight East first, four constituencies boundaries within 5km: Obviously contiguous neighbour among zero distance, needs dropped, although addlinks1 drop duplicate: Although constituencies now linked, see whether using 5km criterion brings extra neighbours Isle Wight West: , , need beware sorting order zero self-distance contiguous neighbour distance, now second position: yields links north-west:  remains add suitable generalisation addlinks1 handle vector argument argument taking list vectors.","code":"(k6 <- knn2nb(knearneigh(pts, k=6), row.names=as.character(w50m$Constituency), sym=TRUE)) ## Warning in knn2nb(knearneigh(pts, k = 6), row.names = ## as.character(w50m$Constituency), : neighbour object has 2 sub-graphs ## Neighbour list object: ## Number of regions: 32  ## Number of nonzero links: 238  ## Percentage nonzero weights: 23.24219  ## Average number of links: 7.4375  ## 2 disjoint connected subgraphs plot(st_geometry(w50m), border=\"grey75\") plot(k6, pts, add=TRUE) o <- order(attr(k6, \"ncomp\")$comp.id) image(t(nb2mat(k6, style=\"B\")[o, rev(o)]), axes=FALSE, asp=1) (k6a <- knn2nb(knearneigh(pts, k=6), row.names=as.character(w50m$Constituency))) ## Warning in knn2nb(knearneigh(pts, k = 6), row.names = ## as.character(w50m$Constituency)): neighbour object has 2 sub-graphs ## Neighbour list object: ## Number of regions: 32  ## Number of nonzero links: 192  ## Percentage nonzero weights: 18.75  ## Average number of links: 6  ## 2 disjoint connected subgraphs ## Non-symmetric neighbours list file <- \"etc/shapes/GB_2024_southcoast_50m.gpkg.zip\" zipfile <- system.file(file, package=\"spdep\") if (GDAL37) {     sc50m <- st_read(zipfile) } else {     td <- tempdir()     bn <- sub(\".zip\", \"\", basename(file), fixed=TRUE)     target <- unzip(zipfile, files=bn, exdir=td)     sc50m <- st_read(target) } ## Reading layer `GB_2024_southcoast_50m' from data source  ##   `/tmp/RtmpzEChJG/temp_libpath8ee3b7c361c1e/spdep/etc/shapes/GB_2024_southcoast_50m.gpkg.zip'  ##   using driver `GPKG' ## Simple feature collection with 119 features and 19 fields ## Geometry type: MULTIPOLYGON ## Dimension:     XY ## Bounding box:  xmin: 82643.12 ymin: 5342.9 xmax: 640301.6 ymax: 187226.2 ## Projected CRS: OSGB36 / British National Grid (nb_sc_50m <- poly2nb(sc50m, row.names=as.character(sc50m$Constituency))) ## Warning in poly2nb(sc50m, row.names = as.character(sc50m$Constituency)): neighbour object has 2 sub-graphs; ## if this sub-graph count seems unexpected, try increasing the snap argument. ## Neighbour list object: ## Number of regions: 119  ## Number of nonzero links: 530  ## Percentage nonzero weights: 3.742674  ## Average number of links: 4.453782  ## 2 disjoint connected subgraphs nc <- attr(nb_sc_50m, \"ncomp\")$comp.id table(nc) ## nc ##   1   2  ## 117   2 (sub2 <- attr(nb_sc_50m, \"region.id\")[nc == 2L]) ## [1] \"Isle of Wight East\" \"Isle of Wight West\" pts <- st_point_on_surface(st_geometry(sc50m)) plot(st_geometry(sc50m), border=\"grey75\") plot(st_geometry(sc50m)[nc == 2L], border=\"orange\", lwd=2, add=TRUE) plot(nb_sc_50m, pts, add=TRUE) 1/range(eigen(cbind(c(0, 1), c(1, 0)))$values) ## [1] -1  1 1/range(eigen(nb2mat(subset(nb_sc_50m, nc == 2L), style=\"W\"))$values) ## [1] -1  1 1/range(eigen(nb2mat(nb_sc_50m, style=\"W\"))$values) ## [1] -1  1 1/range(eigen(nb2mat(subset(nb_sc_50m, nc == 1L), style=\"W\"))$values) ## [1] -1.094637  1.000000 iowe <- match(sub2[1], attr(nb_sc_50m, \"region.id\")) diowe <- c(st_distance(sc50m[iowe,], sc50m)) sort(diowe)[1:12] ## Units: [m] ##  [1]     0.000     0.000  1886.833  3509.366  6693.575  6943.672  7678.999 ##  [8]  8576.454 10579.530 12163.332 16875.920 17161.786 ioww <- match(sub2[2], attr(nb_sc_50m, \"region.id\")) dioww <- c(st_distance(sc50m[ioww,], sc50m)) sort(dioww)[1:12] ## Units: [m] ##  [1]     0.000     0.000  1232.724  2541.318  5746.764  5770.602  8902.579 ##  [8]  9747.265 10529.540 10909.845 12250.564 12379.871 (meet_criterion <- sum(diowe <= units::set_units(5000, \"m\"))) ## [1] 4 (cands <- attr(nb_sc_50m, \"region.id\")[order(diowe)[1:meet_criterion]]) ## [1] \"Isle of Wight East\" \"Isle of Wight West\" \"Portsmouth South\"   ## [4] \"Gosport\" (nb_sc_50m_iowe <- addlinks1(nb_sc_50m, from = cands[1], to = cands[3:meet_criterion])) ## Neighbour list object: ## Number of regions: 119  ## Number of nonzero links: 534  ## Percentage nonzero weights: 3.77092  ## Average number of links: 4.487395 (meet_criterion <- sum(dioww <= units::set_units(5000, \"m\"))) ## [1] 4 (cands <- attr(nb_sc_50m, \"region.id\")[order(dioww)[1:meet_criterion]]) ## [1] \"Isle of Wight East\" \"Isle of Wight West\" \"New Forest West\"    ## [4] \"New Forest East\" (nb_sc_50m_iow <- addlinks1(nb_sc_50m_iowe, from = cands[2], to = cands[3:meet_criterion])) ## Neighbour list object: ## Number of regions: 119  ## Number of nonzero links: 538  ## Percentage nonzero weights: 3.799167  ## Average number of links: 4.521008 pts <- st_point_on_surface(st_geometry(sc50m)) plot(st_geometry(sc50m), border=\"grey75\") plot(st_geometry(sc50m)[nc == 2L], border=\"orange\", lwd=2, add=TRUE) plot(nb_sc_50m_iow, pts, add=TRUE)"},{"path":"https://r-spatial.github.io/spdep/articles/subgraphs.html","id":"per-session-control-of-function-behaviour","dir":"Articles","previous_headings":"","what":"Per-session control of function behaviour","title":"No-neighbour observation and subgraph handling","text":"early , default value zero.policy argument many methods functions NULL. value NULL, zero.policy set get.ZeroPolicyOption: loading spdep, internal option set FALSE, functions methods using zero.policy need choose handle islands: case, shown island may reasonably associated proximate constituencies mainland. , however, user wishes override default, set.ZeroPolicyOption may used set different per-session default: listw object created zero.policy set TRUE, choice added output object attribute applied object used (unless specifically overridden). Note also 32 constituencies, observation count reported spweights.constants called print method listw object argument adjust.n TRUE, dropping -neighbour observations observation count. internal options introduced suppress -neighbour subgraph warnings creating nb objects. default values follows: get.NoNeighbourOption controls issuing warnings nb objects created -neighbour observations; get.SubgraphOption works similarly warnings issued one graph component; TRUE default. get.SubgraphCeiling sets integer value graph nodes plus graph edges calculating graph considered costly compute time, default 100,000. corresponds dense neighbour set just 300 nodes (almost 100000 edges) needed use inverse distance weights, just 14,000 nodes average neighbour count 6. print method nb objects reports -neighbour subgraph status anyway, careful users always examine generated objects may prefer supress warnings, warnings seem prudent users may examine objects, generation subsetting larger objects, example creation training test data sets. Welsh constituency boundaries used show behaviour internal options: Turning removes warnings: get.SubgraphOption FALSE, attribute containing output n.comp.nb added: reduction ceiling node count 32 plus edge count 136 also supresses calculation graph components: Restoring remaining default values:","code":"get.ZeroPolicyOption() ## [1] FALSE try(nb2listw(nb_W_50m)) ## Error in nb2listw(nb_W_50m) :  ##   Empty neighbour sets found (zero.policy: FALSE) set.ZeroPolicyOption(TRUE) get.ZeroPolicyOption() ## [1] TRUE (lw <- nb2listw(nb_W_50m)) ## Characteristics of weights list object: ## Neighbour list object: ## Number of regions: 32  ## Number of nonzero links: 136  ## Percentage nonzero weights: 13.28125  ## Average number of links: 4.25  ## 1 region with no links: ## Ynys Môn ## 2 disjoint connected subgraphs ##  ## Weights style: W  ## Weights constants summary: ##    n  nn S0       S1      S2 ## W 31 961 31 15.36355 129.051 attr(lw, \"zero.policy\") ## [1] TRUE set.ZeroPolicyOption(FALSE) get.NoNeighbourOption() ## [1] TRUE get.SubgraphOption() ## [1] TRUE get.SubgraphCeiling() ## [1] 100000 set.NoNeighbourOption(FALSE) (w50m |> poly2nb(row.names=as.character(w50m$Constituency)) -> nb_W_50mz) ## Warning in poly2nb(w50m, row.names = as.character(w50m$Constituency)): neighbour object has 2 sub-graphs; ## if this sub-graph count seems unexpected, try increasing the snap argument. ## Neighbour list object: ## Number of regions: 32  ## Number of nonzero links: 136  ## Percentage nonzero weights: 13.28125  ## Average number of links: 4.25  ## 1 region with no links: ## Ynys Môn ## 2 disjoint connected subgraphs set.SubgraphOption(FALSE) (w50m |> poly2nb(row.names=as.character(w50m$Constituency)) -> nb_W_50my) ## Neighbour list object: ## Number of regions: 32  ## Number of nonzero links: 136  ## Percentage nonzero weights: 13.28125  ## Average number of links: 4.25  ## 1 region with no links: ## Ynys Môn str(attr(nb_W_50my, \"ncomp\")) ##  NULL set.SubgraphOption(TRUE) set.SubgraphCeiling(100L) (w50m |> poly2nb(row.names=as.character(w50m$Constituency)) -> nb_W_50mx) ## Neighbour list object: ## Number of regions: 32  ## Number of nonzero links: 136  ## Percentage nonzero weights: 13.28125  ## Average number of links: 4.25  ## 1 region with no links: ## Ynys Môn str(attr(nb_W_50mx, \"ncomp\")) ##  NULL set.SubgraphCeiling(100000L) set.NoNeighbourOption(TRUE)"},{"path":"https://r-spatial.github.io/spdep/articles/subgraphs.html","id":"unintentional-disconnected-graphs","dir":"Articles","previous_headings":"","what":"Unintentional disconnected graphs","title":"No-neighbour observation and subgraph handling","text":"Sometimes apparently sensible polygons turn represented way disconnected graphs generated extracting contiguities. One case raised https://github.com/r-spatial/spdep/issues/162, subdivisions Tokyo. original data file tokyomet262.* https://sgsup.asu.edu/sites/default/files/SparcFiles/tokyo_0.zip created twenty years ago Tomoki Nakaya Martin Charlton, geometry issues known time. possibility may affect legacy files projection geometries 32-bit platforms, known whether affected file. re-packaged compressed GeoPackage: correcting invalid polygons: applying poly2nb legacy default snap value produced numerous singleton observations well many multiple-observation subgraphs: legacy default snap value coordinates measured metres 15 nanometres, effectively assumed coordinates making polygon boundaries identical: Stepping little 2mm, lack contact ceased problem. basis, default changed spdep 1.3-6 10mm projected polygons, snap value used returned attribute neighbour object: polygons represented geographical (spherical) coordinates, new default spdep 1.3-6 set value mimicking 10mm: default snap value used poly2nb polygons expressed decimal degrees : set based apparent “size” 10mm decimal degrees:","code":"file <- \"etc/shapes/tokyo.gpkg.zip\" zipfile <- system.file(file, package=\"spdep\") if (GDAL37) {     tokyo <- st_read(zipfile) } else {     td <- tempdir()     bn <- sub(\".zip\", \"\", basename(file), fixed=TRUE)     target <- unzip(zipfile, files=bn, exdir=td)     tokyo <- st_read(target) } ## Reading layer `tokyo' from data source  ##   `/tmp/RtmpzEChJG/temp_libpath8ee3b7c361c1e/spdep/etc/shapes/tokyo.gpkg.zip'  ##   using driver `GPKG' ## Simple feature collection with 262 features and 3 fields ## Geometry type: MULTIPOLYGON ## Dimension:     XY ## Bounding box:  xmin: 266206.6 ymin: -90932.11 xmax: 411400.3 ymax: 37142.75 ## Projected CRS: Tokyo / Japan Plane Rectangular CS VI all(st_is_valid(tokyo)) ## [1] TRUE tokyo <- st_make_valid(tokyo) (nb_t0 <- poly2nb(tokyo, snap=sqrt(.Machine$double.eps))) ## Warning in poly2nb(tokyo, snap = sqrt(.Machine$double.eps)): some observations have no neighbours; ## if this seems unexpected, try increasing the snap argument. ## Warning in poly2nb(tokyo, snap = sqrt(.Machine$double.eps)): neighbour object has 23 sub-graphs; ## if this sub-graph count seems unexpected, try increasing the snap argument. ## Neighbour list object: ## Number of regions: 262  ## Number of nonzero links: 946  ## Percentage nonzero weights: 1.378125  ## Average number of links: 3.610687  ## 10 regions with no links: ## 101, 127, 134, 135, 152, 154, 167, 237, 242, 243 ## 23 disjoint connected subgraphs units::set_units(units::set_units(attr(nb_t0, \"snap\"), \"m\"), \"nm\") ## 14.90116 [nm] (nb_t1 <- poly2nb(tokyo, snap=0.002)) ## Neighbour list object: ## Number of regions: 262  ## Number of nonzero links: 1390  ## Percentage nonzero weights: 2.02494  ## Average number of links: 5.305344 units::set_units(units::set_units(attr(nb_t1, \"snap\"), \"m\"), \"mm\") ## 2 [mm] (nb_t2 <- poly2nb(tokyo)) ## Neighbour list object: ## Number of regions: 262  ## Number of nonzero links: 1390  ## Percentage nonzero weights: 2.02494  ## Average number of links: 5.305344 units::set_units(units::set_units(attr(nb_t2, \"snap\"), \"m\"), \"mm\") ## 10 [mm] (nb_t3 <- poly2nb(st_transform(tokyo, \"OGC:CRS84\"))) ## Neighbour list object: ## Number of regions: 262  ## Number of nonzero links: 1336  ## Percentage nonzero weights: 1.946274  ## Average number of links: 5.099237 attr(nb_t3, \"snap\") ## [1] 9e-08 (180 * 0.01) / (pi * 6378137) ## [1] 8.983153e-08"},{"path":[]},{"path":"https://r-spatial.github.io/spdep/authors.html","id":null,"dir":"","previous_headings":"","what":"Authors","title":"Authors and Citation","text":"Roger Bivand. Maintainer, author. Micah Altman. Contributor. Luc Anselin. Contributor. Renato Assunção. Contributor. Anil Bera. Contributor. Olaf Berke. Contributor. F. Guillaume Blanchet. Contributor. Marilia Carvalho. Contributor. Bjarke Christensen. Contributor. Yongwan Chun. Contributor. Carsten Dormann. Contributor. Stéphane Dray. Contributor. Dewey Dunnington. Contributor. Virgilio Gómez-Rubio. Contributor. Malabika Koley. Contributor. Tomasz Kossowski. Contributor. Elias Krainski. Contributor. Pierre Legendre. Contributor. Nicholas Lewin-Koh. Contributor. Angela Li. Contributor. Giovanni Millo. Contributor. Werner Mueller. Contributor. Hisaji Ono. Contributor. Josiah Parry. Contributor. Pedro Peres-Neto. Contributor. Michał Pietrzak. Contributor. Gianfranco Piras. Contributor. Markus Reder. Contributor. Jeff Sauer. Contributor. Michael Tiefelsdorf. Contributor. René Westerholt. Contributor. Justyna Wilk. Contributor. Levi Wolf. Contributor. Danlin Yu. Contributor.","code":""},{"path":"https://r-spatial.github.io/spdep/authors.html","id":"citation","dir":"","previous_headings":"","what":"Citation","title":"Authors and Citation","text":"Bivand R, Wong D (2018). “Comparing implementations global local indicators spatial association.” TEST, 27(3), 716–748. doi:10.1007/s11749-018-0599-x. Roger Bivand (2022). “R Packages Analyzing Spatial Data: Comparative Case Study Areal Data.” Geographical Analysis, 54(3), 488-518. doi:10.1111/gean.12319. Bivand R, Pebesma E, Gómez-Rubio V (2013). Applied spatial data analysis R, Second edition. Springer, NY. https://asdar-book.org/. Pebesma E, Bivand R (2023). Spatial Data Science Applications R. Chapman & Hall. https://r-spatial.org/book/.","code":"@Article{,   author = {Roger Bivand and David W. S. Wong},   title = {Comparing implementations of global and local indicators of spatial association},   journal = {TEST},   year = {2018},   volume = {27},   number = {3},   pages = {716--748},   doi = {10.1007/s11749-018-0599-x}, } @Article{,   author = {{Roger Bivand}},   title = {R Packages for Analyzing Spatial Data: A Comparative Case Study with Areal Data},   journal = {Geographical Analysis},   year = {2022},   volume = {54},   number = {3},   pages = {488-518},   doi = {10.1111/gean.12319}, } @Book{,   author = {Roger S. Bivand and Edzer Pebesma and Virgilio Gómez-Rubio},   title = {Applied spatial data analysis with {R}, Second edition},   year = {2013},   publisher = {Springer, NY},   url = {https://asdar-book.org/}, } @Book{,   author = {Edzer Pebesma and Roger S. Bivand},   title = {Spatial Data Science With Applications in {R}},   year = {2023},   publisher = {Chapman & Hall},   url = {https://r-spatial.org/book/}, }"},{"path":[]},{"path":"https://r-spatial.github.io/spdep/index.html","id":"spatial-dependence-weighting-schemes-and-statistics","dir":"","previous_headings":"","what":"Spatial Dependence: Weighting Schemes and Statistics","title":"Spatial Dependence: Weighting Schemes, Statistics","text":"collection functions create spatial weights matrix objects polygon contiguities, point patterns distance tessellations, summarizing objects, permitting use spatial data analysis, including regional aggregation minimum spanning tree; collection tests spatial autocorrelation, including global Morans Gearys C proposed Cliff Ord (1973, ISBN: 0850860369) (1981, ISBN: 0850860814), Hubert/Mantel general cross product statistic, Empirical Bayes estimates Assunção/Reis (1999) (https://doi.org/10.1002/(SICI)1097-0258(19990830)18:16%3C2147%3A%3AAID-SIM179%3E3.0.CO%3B2-) Index, Getis/Ord G (Getis Ord 1992) (https://doi.org/10.1111/j.1538-4632.1992.tb00261.x) multicoloured join count statistics, APLE (Li et al. ) (https://doi.org/10.1111/j.1538-4632.2007.00708.x), local Morans (Anselin 1995) (https://doi.org/10.1111/j.1538-4632.1995.tb00338.x) Getis/Ord G (Ord Getis 1995) (https://doi.org/10.1111/j.1538-4632.1995.tb00912.x), saddlepoint approximations (Tiefelsdorf 2002) (https://doi.org/10.1111/j.1538-4632.2002.tb01084.x) exact tests global local Morans (Bivand et al. 2009) (https://doi.org/10.1016/j.csda.2008.07.021) LOSH local indicators spatial heteroscedasticity (Ord Getis) (https://doi.org/10.1007/s00168-011-0492-y), extensions ‘Bivand’ (2022) doi:10.1111/gean.12319. implementation measures described Bivand Wong (2018) (https://doi.org/10.1007/s11749-018-0599-x). Extra measures contributed Josiah Parry. Lagrange multiplier tests spatial dependence linear models provided (Anselin et al. 1996) (https://doi.org/10.1016/0166-0462(95)02111-6), Rao’s score tests hypothesised spatial Durbin models based fitted linear models (Koley Bera 2024) (https://doi.org/10.1080/17421772.2023.2256810). local indicators categorical data (LICD) implementation based Carrer et al. (2021) (https://doi.org/10.1016/j.jas.2020.105306) ‘Bivand et al.’ (2017) (https://doi.org/10.1016/j.spasta.2017.03.003) added 1.3-7. sfdep (https://cran.r-project.org/package=sfdep) provides piped interface spdep. spdep spatialreg versions >= 1.2-1, model fitting functions previously present package defunct spdep may found spatialreg. Default branch now main Moved R-Forge","code":""},{"path":"https://r-spatial.github.io/spdep/reference/COL.OLD.html","id":null,"dir":"Reference","previous_headings":"","what":"Columbus OH spatial analysis data set - old numbering — oldcol","title":"Columbus OH spatial analysis data set - old numbering — oldcol","text":"COL.OLD data frame 49 rows 22 columns. observations ordered numbered original analyses data set SpaceStat documentation Anselin, L. 1988 Spatial econometrics: methods models, Dordrecht: Kluwer. Unit analysis: 49 neighbourhoods Columbus, OH, 1980 data. addition data set includes COL.nb, neighbours list used Anselin (1988).","code":""},{"path":"https://r-spatial.github.io/spdep/reference/COL.OLD.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Columbus OH spatial analysis data set - old numbering — oldcol","text":"","code":"data(oldcol)"},{"path":"https://r-spatial.github.io/spdep/reference/COL.OLD.html","id":"format","dir":"Reference","previous_headings":"","what":"Format","title":"Columbus OH spatial analysis data set - old numbering — oldcol","text":"data frame contains following columns: AREA_PL computed ArcView (agrees areas polygons “columbus” data set PERIMETER computed ArcView COLUMBUS. internal polygon ID (ignore) COLUMBUS.another internal polygon ID (ignore) POLYID yet another polygon ID NEIG neighborhood id value (1-49);              conforms id value used Spatial Econometrics book. HOVAL housing value ($1,000) INC household income ($1,000) CRIME residential burglaries vehicle thefts per thousand         households neighborhood OPEN open space neighborhood PLUMB percentage housing units without plumbin DISCBD distance CBD X x coordinate (arbitrary digitizing units, polygon coordinates) Y y coordinate (arbitrary digitizing units, polygon coordinates) AREA_SS neighborhood area (computed SpaceStat) NSA north-south dummy (North=1) NSB north-south dummy (North=1) EW east-west dummy (East=1) CP core-periphery dummy (Core=1) THOUS constant=1,000 NEIGNO NEIG+1,000, alternative neighborhood id value PERIM polygon perimeter (computed SpaceStat)","code":""},{"path":"https://r-spatial.github.io/spdep/reference/COL.OLD.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Columbus OH spatial analysis data set - old numbering — oldcol","text":"row names COL.OLD region.id attribute COL.nb set columbus$NEIGNO.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/COL.OLD.html","id":"source","dir":"Reference","previous_headings":"","what":"Source","title":"Columbus OH spatial analysis data set - old numbering — oldcol","text":"Anselin, Luc.  1988.  Spatial econometrics: methods models.  Dordrecht: Kluwer Academic, Table 12.1 p. 189.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/COL.OLD.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Columbus OH spatial analysis data set - old numbering — oldcol","text":"source data files prepared Luc Anselin, Spatial Analysis Laboratory, Department Agricultural Consumer Economics, University Illinois, Urbana-Champaign.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/EBImoran.mc.html","id":null,"dir":"Reference","previous_headings":"","what":"Permutation test for empirical Bayes index — EBImoran.mc","title":"Permutation test for empirical Bayes index — EBImoran.mc","text":"empirical Bayes index modification Moran's testing spatial autocorrelation rate, typically number observed cases population risk. index value tested using nsim random permutations index given spatial weighting scheme, establish rank observed statistic relation nsim simulated values.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/EBImoran.mc.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Permutation test for empirical Bayes index — EBImoran.mc","text":"","code":"EBImoran.mc(n, x, listw, nsim, zero.policy = attr(listw, \"zero.policy\"),   alternative = \"greater\", spChk=NULL, return_boot=FALSE,  subtract_mean_in_numerator=TRUE)"},{"path":"https://r-spatial.github.io/spdep/reference/EBImoran.mc.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Permutation test for empirical Bayes index — EBImoran.mc","text":"n numeric vector counts cases length neighbours list listw x numeric vector populations risk length neighbours list listw listw listw object created example nb2listw nsim number permutations zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA alternative character string specifying alternative hypothesis, must one \"greater\" (default), \"two.sided\", \"less\" spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption() return_boot return object class boot equivalent permutation bootstrap rather object class htest subtract_mean_in_numerator default TRUE, TRUE subtract mean z numerator EBI equation p. 2157 reference (consulted Renato Assunção 2016-02-19); February 2016 default FALSE agreeing printed paper.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/EBImoran.mc.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Permutation test for empirical Bayes index — EBImoran.mc","text":"statistic used (m number observations): $$EBI = \\frac{m}{\\sum_{=1}^{m}\\sum_{j=1}^{m}w_{ij}} \\frac{\\sum_{=1}^{m}\\sum_{j=1}^{m}w_{ij}z_i z_j}{\\sum_{=1}^{m}(z_i - \\bar{z})^2} $$ : $$z_i = \\frac{p_i - b}{\\sqrt{v_i}}$$ : $$p_i = n_i / x_i$$ $$v_i = + (b / x_i)$$ $$b = \\sum_{=1}^{m} n_i / \\sum_{=1}^{m} x_i $$ $$= s^2 - b / (\\sum_{=1}^{m} x_i / m)$$ $$s^2 = \\sum_{=1}^{m} x_i (p_i - b)^2 / \\sum_{=1}^{m} x_i $$","code":""},{"path":"https://r-spatial.github.io/spdep/reference/EBImoran.mc.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Permutation test for empirical Bayes index — EBImoran.mc","text":"list class htest mc.sim containing following components: statistic value observed Moran's . parameter rank observed Moran's . p.value pseudo p-value test. alternative character string describing alternative hypothesis. method character string giving method used. data.name character string giving name(s) data, number simulations. res nsim simulated values statistic, final value observed statistic z numerical vector Empirical Bayes indices z ","code":""},{"path":"https://r-spatial.github.io/spdep/reference/EBImoran.mc.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Permutation test for empirical Bayes index — EBImoran.mc","text":"Assunção RM, Reis EA 1999 new proposal adjust Moran's population density. Statistics Medicine 18, pp. 2147–2162; Bivand RS, Wong DWS 2018 Comparing implementations global local indicators spatial association. TEST, 27(3), 716–748 doi:10.1007/s11749-018-0599-x","code":""},{"path":"https://r-spatial.github.io/spdep/reference/EBImoran.mc.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Permutation test for empirical Bayes index — EBImoran.mc","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/EBImoran.mc.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Permutation test for empirical Bayes index — EBImoran.mc","text":"","code":"nc.sids <- st_read(system.file(\"shapes/sids.gpkg\", package=\"spData\")[1], quiet=TRUE) rn <- as.character(nc.sids$FIPS) ncCC89_nb <- read.gal(system.file(\"weights/ncCC89.gal\", package=\"spData\")[1],  region.id=rn) #> Warning: neighbour object has 3 sub-graphs EBImoran.mc(nc.sids$SID74, nc.sids$BIR74,  nb2listw(ncCC89_nb, style=\"B\", zero.policy=TRUE), nsim=999,  alternative=\"two.sided\", zero.policy=TRUE) #> The default for subtract_mean_in_numerator set TRUE from February 2016 #>  #> \tMonte-Carlo simulation of Empirical Bayes Index (mean subtracted) #>  #> data:  cases: nc.sids$SID74, risk population: nc.sids$BIR74 #> weights: nb2listw(ncCC89_nb, style = \"B\", zero.policy = TRUE) #> number of simulations + 1: 1000 #>  #> statistic = 0.25789, observed rank = 999, p-value = 0.002 #> alternative hypothesis: two.sided #>  sids.p <- nc.sids$SID74 / nc.sids$BIR74 moran.mc(sids.p, nb2listw(ncCC89_nb, style=\"B\", zero.policy=TRUE),  nsim=999, alternative=\"two.sided\", zero.policy=TRUE) #>  #> \tMonte-Carlo simulation of Moran I #>  #> data:  sids.p  #> weights: nb2listw(ncCC89_nb, style = \"B\", zero.policy = TRUE)   #> number of simulations + 1: 1000  #>  #> statistic = 0.20904, observed rank = 997, p-value = 0.006 #> alternative hypothesis: two.sided #>"},{"path":"https://r-spatial.github.io/spdep/reference/EBest.html","id":null,"dir":"Reference","previous_headings":"","what":"Global Empirical Bayes estimator — EBest","title":"Global Empirical Bayes estimator — EBest","text":"function computes global empirical Bayes estimates rates \"shrunk\" overall mean.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/EBest.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Global Empirical Bayes estimator — EBest","text":"","code":"EBest(n, x, family=\"poisson\")"},{"path":"https://r-spatial.github.io/spdep/reference/EBest.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Global Empirical Bayes estimator — EBest","text":"n numeric vector counts cases x numeric vector populations risk family either \"poisson\" rare conditions \"binomial\" non-rare conditions","code":""},{"path":"https://r-spatial.github.io/spdep/reference/EBest.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Global Empirical Bayes estimator — EBest","text":"Details implementation \"poisson\" family found Marshall, p. 284–5, Bailey Gatrell p. 303–306 exercise 8.2, pp. 328–330. \"binomial\" family, see Martuzzi Elliott (implementation Olaf Berke).","code":""},{"path":"https://r-spatial.github.io/spdep/reference/EBest.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Global Empirical Bayes estimator — EBest","text":"data frame two columns: raw numerical vector raw (crude) rates estmm numerical vector empirical Bayes estimates parameters attribute list components:  global method moments phi value m global method moments gamma value","code":""},{"path":"https://r-spatial.github.io/spdep/reference/EBest.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Global Empirical Bayes estimator — EBest","text":"Marshall R M (1991) Mapping disease mortality rates using Empirical Bayes Estimators, Applied Statistics, 40, 283–294; Bailey T, Gatrell (1995) Interactive Spatial Data Analysis, Harlow: Longman, pp. 303–306, Martuzzi M, Elliott P (1996) Empirical Bayes estimation small area prevalence non-rare conditions, Statistics Medicine 15, 1867–1873.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/EBest.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Global Empirical Bayes estimator — EBest","text":"Roger Bivand Roger.Bivand@nhh.Olaf Berke, Population Medicine, OVC, University Guelph, CANADA","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/EBest.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Global Empirical Bayes estimator — EBest","text":"","code":"auckland <- st_read(system.file(\"shapes/auckland.gpkg\", package=\"spData\")[1], quiet=TRUE) res <- EBest(auckland$M77_85, 9*auckland$Und5_81) attr(res, \"parameters\") #> $a #> [1] 7.284173e-07 #>  #> $b #> [1] 0.002633436 #>  auckland$estmm000 <- res$estmm*1000 plot(auckland[,\"estmm000\"], breaks=c(0,2,2.5,3,3.5,5),  main=\"Infant mortality per 1000 per year\")  data(huddersfield, package=\"spData\") res <- EBest(huddersfield$cases, huddersfield$total, family=\"binomial\") round(res[,1:2],4)*100 #>      raw estmm #> 1  42.86 34.44 #> 2  28.95 29.56 #> 3  28.31 28.94 #> 4  21.43 28.93 #> 5  33.33 30.72 #> 6  30.86 30.43 #> 7  33.70 31.85 #> 8  45.61 35.93 #> 9  26.67 28.95 #> 10 29.41 29.95 #> 11 27.76 28.36 #> 12 33.75 31.75 #> 13 32.67 31.84 #> 14 22.91 25.36 #> 15 34.21 32.33 #> 16 33.77 31.72 #> 17 29.09 29.69 #> 18 15.87 24.36 #> 19 40.91 32.11 #> 20 40.00 31.01 #> 21 28.79 29.53 #> 22 38.89 31.47 #> 23 28.32 29.10 #> 24 33.33 31.44 #> 25 13.95 22.36 #> 26 33.77 31.72 #> 27 31.58 30.31 #> 28 33.33 30.42 #> 29 26.67 28.26 #> 30 63.64 33.57 #> 31 34.38 32.24 #> 32 20.00 27.62 #> 33 19.15 24.60 #> 34 25.53 28.54 #> 35 24.14 27.79 #> 36 44.00 32.98 #> 37 25.33 27.95 #> 38 18.18 26.96 #> 39 31.78 30.97 #> 40 32.20 30.88 #> 41 26.19 28.23 #> 42 19.05 26.65 #> 43 16.67 26.81 #> 44 20.00 28.66 #> 45 32.99 31.54 #> 46 50.00 31.97 #> 47 37.21 32.30 #> 48 32.79 31.13 #> 49 38.89 31.47 #> 50 25.00 27.26 #> 51 26.03 28.29 #> 52 30.43 30.18 #> 53 19.75 25.28 #> 54 50.00 31.61 #> 55 21.62 27.67 #> 56 22.22 27.88 #> 57 36.36 30.71 #> 58 31.25 30.22 #> 59  0.00 29.73 #> 60 29.41 29.95 #> 61 31.16 30.71 #> 62 33.33 30.58 #> 63 33.87 32.22 #> 64 30.00 30.04 #> 65 30.34 30.19 #> 66 40.74 35.00 #> 67 46.43 38.96 #> 68 34.21 31.91 #> 69 24.26 26.10 #> 70 29.41 29.75 #> 71 47.17 39.13"},{"path":"https://r-spatial.github.io/spdep/reference/EBlocal.html","id":null,"dir":"Reference","previous_headings":"","what":"Local Empirical Bayes estimator — EBlocal","title":"Local Empirical Bayes estimator — EBlocal","text":"function computes local empirical Bayes estimates rates \"shrunk\" neighbourhood mean neighbourhoods given nb neighbourhood list.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/EBlocal.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Local Empirical Bayes estimator — EBlocal","text":"","code":"EBlocal(ri, ni, nb, zero.policy = NULL, spChk = NULL, geoda=FALSE)"},{"path":"https://r-spatial.github.io/spdep/reference/EBlocal.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Local Empirical Bayes estimator — EBlocal","text":"ri numeric vector counts cases length neighbours list nb; many zero counts, estimates may affected division zero, see https://stat.ethz.ch/pipermail/r-sig-geo/2022-January/028882.html ni numeric vector populations risk length neighbours list nb nb nb object neighbour relationships zero.policy default NULL, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption() geoda default=FALSE, following Marshall's algorithm interpreted Bailey Gatrell, pp. 305-307, exercise 8.2, pp. 328-330 definition phi; TRUE definition phi used GeoDa (see discussion OpenSpace mailing list June 2003: http://agec221.agecon.uiuc.edu/pipermail/openspace/2003-June/thread.html)","code":""},{"path":"https://r-spatial.github.io/spdep/reference/EBlocal.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Local Empirical Bayes estimator — EBlocal","text":"Details implementation found Marshall, p. 286, Bailey Gatrell p. 307 exercise 8.2, pp. 328–330. example results fully correspond sources slightly differing neighbourhoods, generally close. many zero counts, estimates may affected division zero, see https://stat.ethz.ch/pipermail/r-sig-geo/2022-January/028882.html.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/EBlocal.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Local Empirical Bayes estimator — EBlocal","text":"data frame two columns: raw numerical vector raw (crude) rates est numerical vector local empirical Bayes estimates parameters attribute list components (zero, estimate NaN, https://stat.ethz.ch/pipermail/r-sig-geo/2022-January/028882.html):  numerical vector local phi values m numerical vector local gamma values","code":""},{"path":"https://r-spatial.github.io/spdep/reference/EBlocal.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Local Empirical Bayes estimator — EBlocal","text":"Marshall R M (1991) Mapping disease mortality rates using Empirical Bayes Estimators, Applied Statistics, 40, 283–294; Bailey T, Gatrell (1995) Interactive Spatial Data Analysis, Harlow: Longman, pp. 303–306.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/EBlocal.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Local Empirical Bayes estimator — EBlocal","text":"Roger Bivand Roger.Bivand@nhh., based contributions Marilia Carvalho","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/EBlocal.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Local Empirical Bayes estimator — EBlocal","text":"","code":"auckland <- st_read(system.file(\"shapes/auckland.gpkg\", package=\"spData\")[1], quiet=TRUE) auckland.nb <- poly2nb(auckland) res <- EBlocal(auckland$M77_85,  9*auckland$Und5_81, auckland.nb) auckland$est000 <- res$est*1000 plot(auckland[,\"est000\"], breaks=c(0,2,2.5,3,3.5,8),  main=\"Infant mortality per 1000 per year\")"},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.cs.html","id":null,"dir":"Reference","previous_headings":"","what":"Chi-square based test for local spatial heteroscedasticity — LOSH.cs","title":"Chi-square based test for local spatial heteroscedasticity — LOSH.cs","text":"function implements chi-square based test statistic local spatial heteroscedasticity (LOSH) proposed Ord & Getis (2012).","code":""},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.cs.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Chi-square based test for local spatial heteroscedasticity — LOSH.cs","text":"","code":"LOSH.cs(x, listw, zero.policy = attr(listw, \"zero.policy\"), na.action = na.fail,                   p.adjust.method = \"none\", spChk = NULL)"},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.cs.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Chi-square based test for local spatial heteroscedasticity — LOSH.cs","text":"x numeric vector length neighbours list listw listw listw object created example nb2listw zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA na.action function (default na.fail), can also na.omit na.exclude - cases weights list subsetted remove NAs data. may necessary set zero.policy TRUE subsetting may create -neighbour observations. Note weights lists created without using glist argument nb2listw may subsetted. na.pass used, zero substituted NA values calculating spatial lag. (Note na.exclude work properly starting R 1.9.0, na.omit na.exclude assign wrong classes 1.8.*) p.adjust.method character string specifying probability value adjustment multiple tests, default \"none\"; see p.adjustSP. Note number multiple tests region taken number neighbours + 1 region, rather total number regions. spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption()","code":""},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.cs.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Chi-square based test for local spatial heteroscedasticity — LOSH.cs","text":"test uses = 2 (see LOSH) chi-square based inference applicable exponents. function makes use LOSH calculations.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.cs.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Chi-square based test for local spatial heteroscedasticity — LOSH.cs","text":"Hi LOSH statistic E.Hi expectation LOSH Var.Hi variance LOSH Z.Hi approximately chi-square distributed test statistics x_bar_i local spatially weighted mean values ei residuals local spatially weighted mean values Pr() p-values Hi obtained non-central Chi-square distribution \\(2/Var.Hi\\) degrees freedom","code":""},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.cs.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Chi-square based test for local spatial heteroscedasticity — LOSH.cs","text":"Ord, J. K., & Getis, . 2012. Local spatial heteroscedasticity (LOSH), Annals Regional Science, 48 (2), 529–539.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.cs.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Chi-square based test for local spatial heteroscedasticity — LOSH.cs","text":"René Westerholt rene.westerholt@tu-dortmund.de","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.cs.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Chi-square based test for local spatial heteroscedasticity — LOSH.cs","text":"","code":"data(boston, package=\"spData\")     resLOSH <- LOSH.cs(boston.c$NOX, nb2listw(boston.soi))     hist(resLOSH[,\"Hi\"])      mean(resLOSH[,\"Hi\"]) #> [1] 0.9919329"},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.html","id":null,"dir":"Reference","previous_headings":"","what":"Local spatial heteroscedasticity — LOSH","title":"Local spatial heteroscedasticity — LOSH","text":"Local spatial heteroscedasticity calculated location based spatial weights object used. statistic :     $$H_i = \\frac{\\sum_j^n w_{ij} \\cdot |e_j|^}{h_1 \\cdot \\sum_j^n w_{ij}}$$ $$e_j = x_j - \\bar{x}_j$$ $$\\bar{x}_j = \\frac{\\sum_k^n w_{jk} \\cdot x_k}{\\sum_k^n w_{jk}}$$     expectation variance given Ord & Getis (2012). exponent allows investigating different types mean dispersal.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Local spatial heteroscedasticity — LOSH","text":"","code":"LOSH(x, listw, a=2, var_hi=TRUE, zero.policy=attr(listw, \"zero.policy\"),  na.action=na.fail, spChk=NULL)"},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Local spatial heteroscedasticity — LOSH","text":"x numeric vector length neighbours list listw listw listw object created example nb2listw exponent applied local residuals; default value 2 leads measure heterogeneity spatial variance var_hi default TRUE, moments test statistics calculated location; FALSE, plain LOSH measures, \\(\\bar{x}_i\\) \\(e_i\\) calculated zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA na.action function (default na.fail), can also na.omit na.exclude - cases weights list subsetted remove NAs data. may necessary set zero.policy TRUE subsetting may create -neighbour observations. Note weights lists created without using glist argument nb2listw may subsetted. na.pass used, zero substituted NA values calculating spatial lag. (Note na.exclude work properly starting R 1.9.0, na.omit na.exclude assign wrong classes 1.8.*) spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption()","code":""},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Local spatial heteroscedasticity — LOSH","text":"addition LOSH measure, values returned include local spatially weighted mean values \\(\\bar{x}_i\\) local residuals \\(e_i\\) estimated means. values facilitate interpretation LOSH values. , specified var_hi, statistical moments test statistics proposed Ord & Getis (2012) also calculated returned.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Local spatial heteroscedasticity — LOSH","text":"Hi LOSH statistic E.Hi (optional) expectation LOSH Var.Hi (optional) variance LOSH Z.Hi (optional) approximately Chi-square distributed test statistics x_bar_i local spatially weighted mean values ei residuals local spatially weighted mean values","code":""},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Local spatial heteroscedasticity — LOSH","text":"Ord, J. K., & Getis, . 2012. Local spatial heteroscedasticity (LOSH),     Annals Regional Science, 48 (2), 529–539.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Local spatial heteroscedasticity — LOSH","text":"René Westerholt rene.westerholt@tu-dortmund.de","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Local spatial heteroscedasticity — LOSH","text":"","code":"data(boston, package=\"spData\")     resLOSH <- LOSH(boston.c$NOX, nb2listw(boston.soi))     hist(resLOSH[,\"Hi\"])      mean(resLOSH[,\"Hi\"]) #> [1] 0.9919329"},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.mc.html","id":null,"dir":"Reference","previous_headings":"","what":"Bootstrapping-based test for local spatial heteroscedasticity — LOSH.mc","title":"Bootstrapping-based test for local spatial heteroscedasticity — LOSH.mc","text":"function draws inferences local spatial heteroscedasticity (LOSH) means randomisation-based Monte-Carlo bootstrap proposed Xu et al. (2014).","code":""},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.mc.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Bootstrapping-based test for local spatial heteroscedasticity — LOSH.mc","text":"","code":"LOSH.mc(x, listw, a = 2, nsim = 99, zero.policy = attr(listw, \"zero.policy\"),  na.action = na.fail, spChk = NULL, adjust.n = TRUE, p.adjust.method = \"none\")"},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.mc.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Bootstrapping-based test for local spatial heteroscedasticity — LOSH.mc","text":"x numeric vector length neighbours list listw listw listw object created example nb2listw exponent applied local residuals; default value 2 leads measure heterogeneity spatial variance nsim number randomisations used bootstrap zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA na.action function (default na.fail), can also na.omit na.exclude - cases weights list subsetted remove NAs data. may necessary set zero.policy TRUE subsetting may create -neighbour observations. Note weights lists created without using glist argument nb2listw may subsetted. na.pass used, zero substituted NA values calculating spatial lag. (Note na.exclude work properly starting R 1.9.0, na.omit na.exclude assign wrong classes 1.8.*) spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption() adjust.n default TRUE, FALSE number observations adjusted -neighbour observations, TRUE, number observations adjusted p.adjust.method character string specifying probability value adjustment multiple tests, default \"none\"; see p.adjustSP. Note number multiple tests region taken number neighbours + 1 region, rather total number regions.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.mc.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Bootstrapping-based test for local spatial heteroscedasticity — LOSH.mc","text":"test calculates LOSH (see LOSH) estimates pseudo p-values conditional bootstrap. Thereby, -th value location held fixed, whereas values permuted nsim times spatial units.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.mc.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Bootstrapping-based test for local spatial heteroscedasticity — LOSH.mc","text":"Hi LOSH statistic E.Hi expectation LOSH Var.Hi variance LOSH Z.Hi approximately chi-square distributed test statistics x_bar_i local spatially weighted mean values ei residuals local spatially weighted mean values Pr() p-values Hi obtained conditional bootstrap distribution","code":""},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.mc.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Bootstrapping-based test for local spatial heteroscedasticity — LOSH.mc","text":"Ord, J. K., & Getis, . 2012. Local spatial heteroscedasticity (LOSH), Annals Regional Science, 48 (2), 529–539; Xu, M., Mei, C. L., & Yan, N. 2014. note null distribution local spatial heteroscedasticity (LOSH) statistic. Annals Regional Science, 52 (3), 697–710.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.mc.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Bootstrapping-based test for local spatial heteroscedasticity — LOSH.mc","text":"René Westerholt rene.westerholt@tu-dortmund.de","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.mc.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Bootstrapping-based test for local spatial heteroscedasticity — LOSH.mc","text":"","code":"data(columbus, package=\"spData\")     resLOSH_mc <- LOSH.mc(columbus$CRIME, nb2listw(col.gal.nb), 2, 100)     summary(resLOSH_mc) #>        Hi             x_bar_i            ei                 Pr()          #>  Min.   :0.03438   Min.   :13.85   Min.   :   0.0298   Min.   :0.009901   #>  1st Qu.:0.23838   1st Qu.:24.71   1st Qu.:   7.0114   1st Qu.:0.079208   #>  Median :0.66689   Median :35.90   Median :  52.1094   Median :0.653465   #>  Mean   :1.06592   Mean   :34.88   Mean   : 151.9232   Mean   :0.552233   #>  3rd Qu.:1.59680   3rd Qu.:45.39   3rd Qu.: 105.0551   3rd Qu.:0.900990   #>  Max.   :4.68765   Max.   :54.91   Max.   :2455.2201   Max.   :0.990099       resLOSH_cs <- LOSH.cs(columbus$CRIME, nb2listw(col.gal.nb))     summary(resLOSH_cs) #>        Hi               E.Hi       Var.Hi            Z.Hi         #>  Min.   :0.03438   Min.   :1   Min.   :0.4972   Min.   :0.04356   #>  1st Qu.:0.23838   1st Qu.:1   1st Qu.:0.9136   1st Qu.:0.35069   #>  Median :0.66689   Median :1   Median :1.4342   Median :1.19175   #>  Mean   :1.06592   Mean   :1   Mean   :1.4758   Mean   :1.89447   #>  3rd Qu.:1.59680   3rd Qu.:1   3rd Qu.:1.9547   3rd Qu.:2.65120   #>  Max.   :4.68765   Max.   :1   Max.   :2.9958   Max.   :7.25681   #>     x_bar_i            ei                 Pr()        #>  Min.   :13.85   Min.   :   0.0298   Min.   :0.0190   #>  1st Qu.:24.71   1st Qu.:   7.0114   1st Qu.:0.2050   #>  Median :35.90   Median :  52.1094   Median :0.5264   #>  Mean   :34.88   Mean   : 151.9232   Mean   :0.4507   #>  3rd Qu.:45.39   3rd Qu.: 105.0551   3rd Qu.:0.6529   #>  Max.   :54.91   Max.   :2455.2201   Max.   :0.9540       plot(resLOSH_mc[,\"Pr()\"], resLOSH_cs[,\"Pr()\"])"},{"path":"https://r-spatial.github.io/spdep/reference/SD.RStests.html","id":null,"dir":"Reference","previous_headings":"","what":"Rao's score and adjusted Rao's score tests of linear hypotheses for spatial Durbin and spatial Durbin error models — SD.RStests","title":"Rao's score and adjusted Rao's score tests of linear hypotheses for spatial Durbin and spatial Durbin error models — SD.RStests","text":"Rao's score adjusted Rao's score tests linear hypotheses applied fitted linear model examine whether either spatially lagged dependent variable lag spatially lagged independent variable(s) WX included model, (SDM). Adjusted tests provided lag WX adapting presence , joint test . joint test equal unadjusted one plus adjusted . addition, draft tests added Koley (2024, section 6) spatial Durbin error models examine whether either spatially lagged error err spatially lagged independent variable(s) WX included model, (SDEM); orthogonality, adjusted tests required.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/SD.RStests.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Rao's score and adjusted Rao's score tests of linear hypotheses for spatial Durbin and spatial Durbin error models — SD.RStests","text":"","code":"SD.RStests(model, listw, zero.policy = attr(listw, \"zero.policy\"), test = \"SDM\",  Durbin = TRUE)"},{"path":"https://r-spatial.github.io/spdep/reference/SD.RStests.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Rao's score and adjusted Rao's score tests of linear hypotheses for spatial Durbin and spatial Durbin error models — SD.RStests","text":"model object class lm returned lm listw listw object created example nb2listw, expected row-standardised (W-style) zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA test test=“SDM” computes SDM tests, character vector tests requested chosen SDM_RSlag, SDM_adjRSlag, SDM_RSWX, SDM_adjRSWX, SDM_Joint, test=“SDEM” computes SDEM tests, character vector tests requested chosen SDEM_RSerr, SDEM_RSWX, SDEM_Joint; test=“” computes tests Durbin default TRUE Durbin models including WX; TRUE, full spatial Durbin model; formula object, subset explanatory variables lag","code":""},{"path":"https://r-spatial.github.io/spdep/reference/SD.RStests.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Rao's score and adjusted Rao's score tests of linear hypotheses for spatial Durbin and spatial Durbin error models — SD.RStests","text":"list class LMtestlist htest objects, : statistic value Lagrange Multiplier test. parameter number degrees freedom p.value p-value test. method character string giving method used. data.name character string giving name(s) data.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/SD.RStests.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Rao's score and adjusted Rao's score tests of linear hypotheses for spatial Durbin and spatial Durbin error models — SD.RStests","text":"Malabika Koley Anil K. Bera (2024) use, use spatial Durbin model? – question, Spatial Economic Analysis, 19:1, 30-56, doi:10.1080/17421772.2023.2256810 ; Malabika Koley (2024) Specification Testing General Nesting Spatial Model (Appendix C), https://sites.google.com/view/malabikakoley/research.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/SD.RStests.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Rao's score and adjusted Rao's score tests of linear hypotheses for spatial Durbin and spatial Durbin error models — SD.RStests","text":"Roger Bivand Roger.Bivand@nhh., Malabika Koley Anil K. Bera","code":""},{"path":"https://r-spatial.github.io/spdep/reference/SD.RStests.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Rao's score and adjusted Rao's score tests of linear hypotheses for spatial Durbin and spatial Durbin error models — SD.RStests","text":"results example agree Table 3, p. 22 Koley Bera (2024).","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/SD.RStests.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Rao's score and adjusted Rao's score tests of linear hypotheses for spatial Durbin and spatial Durbin error models — SD.RStests","text":"","code":"columbus <- sf::st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1]) #> Reading layer `columbus' from data source  #>   `/home/rsb/lib/r_libs/spData/shapes/columbus.gpkg' using driver `GPKG' #> Simple feature collection with 49 features and 20 fields #> Geometry type: POLYGON #> Dimension:     XY #> Bounding box:  xmin: 5.874907 ymin: 10.78863 xmax: 11.28742 ymax: 14.74245 #> Projected CRS: Undefined Cartesian SRS with unknown unit col.gal.nb <- read.gal(system.file(\"weights/columbus.gal\", package=\"spData\")[1]) col.listw <- nb2listw(col.gal.nb, style=\"W\") lm_obj <- lm(CRIME ~ INC + HOVAL, data=columbus) summary(lm.RStests(lm_obj, col.listw, test=\"all\")) #> \tRao's score (a.k.a Lagrange multiplier) diagnostics for spatial #> \tdependence #> data:   #> model: lm(formula = CRIME ~ INC + HOVAL, data = columbus) #> test weights: col.listw #>   #>          statistic parameter  p.value    #> RSerr     4.611126         1 0.031765 *  #> RSlag     7.855675         1 0.005066 ** #> adjRSerr  0.033514         1 0.854744    #> adjRSlag  3.278064         1 0.070212 .  #> SARMA     7.889190         2 0.019359 *  #> --- #> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 res <- SD.RStests(lm_obj, col.listw, test=\"SDM\") summary(res) #> \tRao's score test spatial Durbin diagnostics #> data:   #> model: lm(formula = CRIME ~ INC + HOVAL, data = columbus) #> weights: col.listw #>   #>              statistic parameter  p.value    #> SDM_RSlag       7.8557         1 0.005066 ** #> SDM_adjRSlag    4.6111         1 0.031765 *  #> SDM_RSWX        6.1376         2 0.046477 *  #> SDM_adjRSWX     2.8931         2 0.235386    #> SDM_Joint      10.7487         3 0.013165 *  #> --- #> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 all.equal(unname(res$SDM_Joint$statistic),  unname(res$SDM_RSlag$statistic + res$SDM_adjRSWX$statistic)) #> [1] TRUE all.equal(unname(res$SDM_Joint$statistic),  unname(res$SDM_adjRSlag$statistic + res$SDM_RSWX$statistic)) #> [1] TRUE res <- SD.RStests(lm_obj, col.listw, test=\"SDEM\") summary(res) #> \tRao's score test spatial Durbin diagnostics #> data:   #> model: lm(formula = CRIME ~ INC + HOVAL, data = columbus) #> weights: col.listw #>   #>            statistic parameter p.value   #> SDEM_RSerr    4.6111         1 0.03177 * #> SDEM_RSWX     6.1376         2 0.04648 * #> SDEM_Joint   10.7487         3 0.01317 * #> --- #> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 all.equal(unname(res$SDEM_Joint$statistic),  unname(res$SDEM_RSerr$statistic + res$SDEM_RSWX$statistic)) #> [1] TRUE summary(SD.RStests(lm_obj, nb2listw(col.gal.nb, style=\"C\"), test=\"all\")) #> Warning: Spatial weights matrix not row standardized #> \tRao's score test spatial Durbin diagnostics #> data:   #> model: lm(formula = CRIME ~ INC + HOVAL, data = columbus) #> weights: nb2listw(col.gal.nb, style = \"C\") #>   #>              statistic parameter  p.value    #> SDM_RSlag      10.6095         1 0.001125 ** #> SDM_adjRSlag    4.8428         1 0.027762 *  #> SDM_RSWX        9.2305         3 0.026378 *  #> SDM_adjRSWX     3.4637         3 0.325498    #> SDM_Joint      14.0733         4 0.007065 ** #> SDEM_RSerr      4.8428         1 0.027762 *  #> SDEM_RSWX       9.2305         3 0.026378 *  #> SDEM_Joint     14.0733         4 0.007065 ** #> --- #> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 summary(SD.RStests(lm_obj, col.listw, test=\"all\", Durbin= ~ INC)) #> \tRao's score test spatial Durbin diagnostics #> data:   #> model: lm(formula = CRIME ~ INC + HOVAL, data = columbus) #> weights: col.listw #> Durbin: ~ INC #>   #>              statistic parameter  p.value    #> SDM_RSlag      7.85568         1 0.005066 ** #> SDM_adjRSlag   3.16076         1 0.075428 .  #> SDM_RSWX       4.92399         1 0.026486 *  #> SDM_adjRSWX    0.22908         1 0.632210    #> SDM_Joint      8.08475         2 0.017556 *  #> SDEM_RSerr     4.61113         1 0.031765 *  #> SDEM_RSWX      4.92399         1 0.026486 *  #> SDEM_Joint     9.53512         2 0.008501 ** #> --- #> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 lm_obj0 <- lm(I(scale(CRIME)) ~ 0 + I(scale(INC)) + I(scale(HOVAL)),  data=columbus) summary(SD.RStests(lm_obj0, col.listw, test=\"all\")) #> \tRao's score test spatial Durbin diagnostics #> data:   #> model: lm(formula = I(scale(CRIME)) ~ 0 + I(scale(INC)) + #> I(scale(HOVAL)), data = columbus) #> weights: col.listw #>   #>              statistic parameter  p.value    #> SDM_RSlag       7.8250         1 0.005153 ** #> SDM_adjRSlag    4.6111         1 0.031765 *  #> SDM_RSWX        6.0609         2 0.048295 *  #> SDM_adjRSWX     2.8470         2 0.240873    #> SDM_Joint      10.6720         3 0.013638 *  #> SDEM_RSerr      4.6111         1 0.031765 *  #> SDEM_RSWX       6.0609         2 0.048295 *  #> SDEM_Joint     10.6720         3 0.013638 *  #> --- #> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 columbusNA <- columbus columbusNA$HOVAL[15] <- NA lm_objNA <- lm(CRIME ~ INC + HOVAL, data=columbusNA) summary(SD.RStests(lm_objNA, col.listw, test=\"all\")) #> \tRao's score test spatial Durbin diagnostics #> data:   #> model: lm(formula = CRIME ~ INC + HOVAL, data = columbusNA) #> weights: col.listw #>   #>              statistic parameter  p.value    #> SDM_RSlag       7.6010         1 0.005834 ** #> SDM_adjRSlag    4.4716         1 0.034463 *  #> SDM_RSWX        6.0812         2 0.047807 *  #> SDM_adjRSWX     2.9518         2 0.228576    #> SDM_Joint      10.5527         3 0.014407 *  #> SDEM_RSerr      4.4716         1 0.034463 *  #> SDEM_RSWX       6.0812         2 0.047807 *  #> SDEM_Joint     10.5527         3 0.014407 *  #> --- #> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1"},{"path":"https://r-spatial.github.io/spdep/reference/aggregate.nb.html","id":null,"dir":"Reference","previous_headings":"","what":"Aggregate a spatial neighbours object — aggregate.nb","title":"Aggregate a spatial neighbours object — aggregate.nb","text":"method aggregates spatial neighbours object, creating new object listing neighbours aggregates.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/aggregate.nb.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Aggregate a spatial neighbours object — aggregate.nb","text":"","code":"# S3 method for class 'nb' aggregate(x, IDs, remove.self = TRUE, ...)"},{"path":"https://r-spatial.github.io/spdep/reference/aggregate.nb.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Aggregate a spatial neighbours object — aggregate.nb","text":"x nb neighbour object IDs character vector IDs grouping members neighbour object remove.self default TRUE: remove self-neighbours resulting aggregation ... unused - arguments passed ","code":""},{"path":"https://r-spatial.github.io/spdep/reference/aggregate.nb.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Aggregate a spatial neighbours object — aggregate.nb","text":"nb neighbour object, empty aggregates dropped.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/aggregate.nb.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Aggregate a spatial neighbours object — aggregate.nb","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/aggregate.nb.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Aggregate a spatial neighbours object — aggregate.nb","text":"Method suggested Roberto Patuelli","code":""},{"path":"https://r-spatial.github.io/spdep/reference/aggregate.nb.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Aggregate a spatial neighbours object — aggregate.nb","text":"","code":"data(used.cars, package=\"spData\") data(state) cont_st <- match(attr(usa48.nb, \"region.id\"), state.abb) cents <- as.matrix(as.data.frame(state.center))[cont_st,] opar <- par(mfrow=c(2,1)) plot(usa48.nb, cents, xlim=c(-125, -65), ylim=c(25, 50)) IDs <- as.character(state.division[cont_st]) agg_cents <- aggregate(cents, list(IDs), mean) agg_nb <- aggregate(usa48.nb, IDs) plot(agg_nb, agg_cents[, 2:3], xlim=c(-125, -65), ylim=c(25, 50)) text(agg_cents[, 2:3], agg_cents[, 1], cex=0.6)  par(opar)"},{"path":"https://r-spatial.github.io/spdep/reference/airdist.html","id":null,"dir":"Reference","previous_headings":"","what":"Measure distance from plot — airdist","title":"Measure distance from plot — airdist","text":"Measure distance two points plot using locator; function checks par(\"plt\") par(\"usr\") try ensure aspect ratio y/x 1, units measurement x y equivalent.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/airdist.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Measure distance from plot — airdist","text":"","code":"airdist(ann=FALSE)"},{"path":"https://r-spatial.github.io/spdep/reference/airdist.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Measure distance from plot — airdist","text":"ann annotate plot line measured distance","code":""},{"path":"https://r-spatial.github.io/spdep/reference/airdist.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Measure distance from plot — airdist","text":"list members: dist distance measured coords coordinates distance measured","code":""},{"path":"https://r-spatial.github.io/spdep/reference/airdist.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Measure distance from plot — airdist","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/autocov_dist.html","id":null,"dir":"Reference","previous_headings":"","what":"Distance-weighted autocovariate — autocov_dist","title":"Distance-weighted autocovariate — autocov_dist","text":"Calculates autocovariate used autonormal, autopoisson autologistic regression. Three distance-weighting schemes available.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/autocov_dist.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Distance-weighted autocovariate — autocov_dist","text":"","code":"autocov_dist(z, xy, nbs = 1, type = \"inverse\", zero.policy = NULL,  style = \"B\", longlat=NULL)"},{"path":"https://r-spatial.github.io/spdep/reference/autocov_dist.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Distance-weighted autocovariate — autocov_dist","text":"z response variable xy matrix coordinates SpatialPoints, sf sfc points object nbs neighbourhood radius; default 1 type weighting scheme: \"one\" gives equal weight data points neighbourhood; \"inverse\" (default) weights inverse distance; \"inverse.squared\" weights square \"inverse\" zero.policy default NULL, use global option value; FALSE stop error empty neighbour sets, TRUE permit weights list formed zero-length weights vectors style default “B” (changed “W” 2015-01-27); style can take values “W”, “B”, “C”, “U”, “S” longlat TRUE point coordinates longitude-latitude decimal, case distances measured kilometers; xy SpatialPoints object, value taken object ","code":""},{"path":"https://r-spatial.github.io/spdep/reference/autocov_dist.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Distance-weighted autocovariate — autocov_dist","text":"numeric vector autocovariate values","code":""},{"path":"https://r-spatial.github.io/spdep/reference/autocov_dist.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Distance-weighted autocovariate — autocov_dist","text":"validity approach strongly hinges correct choice neighbourhood scheme! Using style=\"B\" ensures symmetry neighbourhood matrix (.e. \\(w_{nm} = w_{mn}\\)). Please see Bardos et al. (2015) details.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/autocov_dist.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Distance-weighted autocovariate — autocov_dist","text":"Augustin N.H., Mugglestone M.. Buckland S.T. (1996) autologistic model spatial distribution wildlife. Journal Applied Ecology, 33, 339-347; Gumpertz M.L., Graham J.M. Ristaino J.B. (1997) Autologistic model spatial pattern Phytophthora epidemic bell pepper: effects soil variables disease presence. Journal Agricultural, Biological Environmental Statistics, 2, 131-156; Bardos, D.C., Guillera-Arroita, G. Wintle, B.. (2015) Valid auto-models spatially autocorrelated occupancy abundance data. arXiv, 1501.06529.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/autocov_dist.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Distance-weighted autocovariate — autocov_dist","text":"Carsten F. Dormann Roger Bivand","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/autocov_dist.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Distance-weighted autocovariate — autocov_dist","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) #xy <- cbind(columbus$X, columbus$Y) xy <- st_coordinates(st_centroid(st_geometry(columbus),  of_largest_polygon=TRUE)) ac1a <- autocov_dist(columbus$CRIME, xy, nbs=10, style=\"B\",  type=\"one\") acinva <- autocov_dist(columbus$CRIME, xy, nbs=10, style=\"B\",  type=\"inverse\") acinv2a <- autocov_dist(columbus$CRIME, xy, nbs=10, style=\"B\",  type=\"inverse.squared\") plot(ac1a ~ columbus$CRIME, pch=16, ylim=c(0,9000)) points(acinva ~ columbus$CRIME, pch=16, col=\"red\") points(acinv2a ~ columbus$CRIME, pch=16, col=\"blue\") legend(\"topleft\", legend=c(\"one\", \"inverse\", \"inverse.squared\"),  col=c(\"black\", \"red\", \"blue\"), bty=\"n\", pch=16)  nb <- dnearneigh(xy, 0, 10) lw <- nb2listw(nb, style=\"B\") ac1b <- lag(lw, columbus$CRIME) all.equal(ac1b, ac1a) #> [1] TRUE nbd <- nbdists(nb, xy) gl <- lapply(nbd, function(x) 1/x) lw <- nb2listw(nb, glist=gl, style=\"B\") acinvb <- lag(lw, columbus$CRIME) all.equal(acinvb, acinva) #> [1] TRUE gl2 <- lapply(nbd, function(x) 1/(x^2)) lw <- nb2listw(nb, glist=gl2, style=\"B\") acinv2b <- lag(lw, columbus$CRIME) all.equal(acinv2b, acinv2a) #> [1] TRUE #xy <- SpatialPoints(xy) #acinva <- autocov_dist(columbus$CRIME, xy, nbs=10, style=\"W\", # type=\"inverse\") #nb <- dnearneigh(xy, 0, 10) #nbd <- nbdists(nb, xy) #gl <- lapply(nbd, function(x) 1/x) #lw <- nb2listw(nb, glist=gl) #acinvb <- lag(lw, columbus$CRIME) #all.equal(acinvb, acinva) acinvc <- autocov_dist(columbus$CRIME, st_centroid(st_geometry(columbus),  of_largest_polygon=TRUE), nbs=10, style=\"W\", type=\"inverse\") all.equal(acinvc, acinva) #> [1] \"Mean relative difference: 40.63575\""},{"path":"https://r-spatial.github.io/spdep/reference/bhicv.html","id":null,"dir":"Reference","previous_headings":"","what":"Data set with 4 life condition indices of Belo Horizonte region — bhicv","title":"Data set with 4 life condition indices of Belo Horizonte region — bhicv","text":"data collected inthe  Atlas condition indices published   Joao Pinheiro Foundation UNDP.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/bhicv.html","id":"format","dir":"Reference","previous_headings":"","what":"Format","title":"Data set with 4 life condition indices of Belo Horizonte region — bhicv","text":"shape polygon object seven variables: id identificator Name Name city Population population city HLCI Health Life Condition Index ELCI Education Life Condition Index CLCI Children Life Condition Index ELCI Economic Life Condition Index","code":""},{"path":"https://r-spatial.github.io/spdep/reference/bhicv.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Data set with 4 life condition indices of Belo Horizonte region — bhicv","text":"","code":"(GDAL37 <- as.numeric_version(unname(sf_extSoftVersion()[\"GDAL\"])) >= \"3.7.0\") #> [1] TRUE file <- \"etc/shapes/bhicv.gpkg.zip\" zipfile <- system.file(file, package=\"spdep\") if (GDAL37) {     bh <- st_read(zipfile) } else {     td <- tempdir()     bn <- sub(\".zip\", \"\", basename(file), fixed=TRUE)     target <- unzip(zipfile, files=bn, exdir=td)     bh <- st_read(target) } #> Reading layer `bhicv' from data source  #>   `/tmp/RtmpzEChJG/temp_libpath8ee3b7c361c1e/spdep/etc/shapes/bhicv.gpkg.zip'  #>   using driver `GPKG' #> Simple feature collection with 98 features and 8 fields #> Geometry type: POLYGON #> Dimension:     XY #> Bounding box:  xmin: -45.02175 ymin: -20.93007 xmax: -42.50321 ymax: -18.08342 #> Geodetic CRS:  Corrego Alegre 1970-72"},{"path":"https://r-spatial.github.io/spdep/reference/card.html","id":null,"dir":"Reference","previous_headings":"","what":"Cardinalities for neighbours lists — card","title":"Cardinalities for neighbours lists — card","text":"function tallies numbers neighbours regions neighbours list.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/card.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Cardinalities for neighbours lists — card","text":"","code":"card(nb)"},{"path":"https://r-spatial.github.io/spdep/reference/card.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Cardinalities for neighbours lists — card","text":"nb neighbours list object class nb","code":""},{"path":"https://r-spatial.github.io/spdep/reference/card.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Cardinalities for neighbours lists — card","text":"integer vector numbers neighbours regions neighbours list.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/card.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Cardinalities for neighbours lists — card","text":"“nb” objects stored lists integer vectors, vectors contain either indices range 1:n n length(nb) neighbours region , .integer(0) signal neighbours. function card(nb) used extract numbers neighbours “nb” object.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/card.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Cardinalities for neighbours lists — card","text":"Bivand R, Pebesma EJ, Gomez-Rubio V, (2008) Applied Spatial Data Analysis R, Springer, New York, pp. 239-251; Bivand R, Portnov B, (2004) Exploring spatial data analysis techniques using R: case observations neighbours. : Anselin L, Florax R, Rey S, (eds.), Advances Spatial Econometrics, Methodology, Tools Applications. Berlin: Springer-Verlag, pp. 121-142, doi:10.1007/978-3-662-05617-2_6 .","code":""},{"path":"https://r-spatial.github.io/spdep/reference/card.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Cardinalities for neighbours lists — card","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/card.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Cardinalities for neighbours lists — card","text":"","code":"col.gal.nb <- read.gal(system.file(\"weights/columbus.gal\", package=\"spData\")[1]) table(card(col.gal.nb)) #>  #>  2  3  4  5  6  7  8  9 10  #>  7  7 13  4  9  6  1  1  1"},{"path":"https://r-spatial.github.io/spdep/reference/cell2nb.html","id":null,"dir":"Reference","previous_headings":"","what":"Generate neighbours list for grid cells — cell2nb","title":"Generate neighbours list for grid cells — cell2nb","text":"function generates list neighbours grid cells. Helper functions used convert vector indices row column grid positions, rook (shared edge) queen (shared edge vertex) neighbour definitions applied type. torus TRUE, grid mapped onto torus, removing edge effects.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/cell2nb.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Generate neighbours list for grid cells — cell2nb","text":"","code":"cell2nb(nrow, ncol, type=\"rook\", torus=FALSE, legacy=FALSE, x=NULL) vi2mrc(i, nrow, ncol)"},{"path":"https://r-spatial.github.io/spdep/reference/cell2nb.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Generate neighbours list for grid cells — cell2nb","text":"nrow number rows grid, may also object inheriting class \"SpatialGrid\" \"GridTopology\" cell2nb ncol number columns grid; nrow x object inheriting class \"SpatialGrid\" \"GridTopology\", may omitted type default rook, may also queen torus default FALSE, TRUE map grid onto torus legacy default FALSE, nrow/ncol reversed, TRUE wrong col/row directions (see https://github.com/r-spatial/spdep/issues/20) x given, object inheriting class \"SpatialGrid\" \"GridTopology\", replaces nrow ncol vector vector indices corresponding rowcol, matrix two columns row, column indices","code":""},{"path":"https://r-spatial.github.io/spdep/reference/cell2nb.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Generate neighbours list for grid cells — cell2nb","text":"function returns object class nb list integer vectors containing neighbour region number ids. See card details “nb” objects.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/cell2nb.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Generate neighbours list for grid cells — cell2nb","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/cell2nb.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Generate neighbours list for grid cells — cell2nb","text":"","code":"nb7rt <- cell2nb(7, 7) summary(nb7rt) #> Neighbour list object: #> Number of regions: 49  #> Number of nonzero links: 168  #> Percentage nonzero weights: 6.997085  #> Average number of links: 3.428571  #> Link number distribution: #>  #>  2  3  4  #>  4 20 25  #> 4 least connected regions: #> 1:1 7:1 1:7 7:7 with 2 links #> 25 most connected regions: #> 2:2 3:2 4:2 5:2 6:2 2:3 3:3 4:3 5:3 6:3 2:4 3:4 4:4 5:4 6:4 2:5 3:5 4:5 5:5 6:5 2:6 3:6 4:6 5:6 6:6 with 4 links xyc <- attr(nb7rt, \"region.id\") xy <- matrix(as.integer(unlist(strsplit(xyc, \":\"))), ncol=2, byrow=TRUE) plot(nb7rt, xy)  nb7rt <- cell2nb(7, 7, torus=TRUE) summary(nb7rt) #> Neighbour list object: #> Number of regions: 49  #> Number of nonzero links: 196  #> Percentage nonzero weights: 8.163265  #> Average number of links: 4  #> Link number distribution: #>  #>  4  #> 49  #> 49 least connected regions: #> 1:1 2:1 3:1 4:1 5:1 6:1 7:1 1:2 2:2 3:2 4:2 5:2 6:2 7:2 1:3 2:3 3:3 4:3 5:3 6:3 7:3 1:4 2:4 3:4 4:4 5:4 6:4 7:4 1:5 2:5 3:5 4:5 5:5 6:5 7:5 1:6 2:6 3:6 4:6 5:6 6:6 7:6 1:7 2:7 3:7 4:7 5:7 6:7 7:7 with 4 links #> 49 most connected regions: #> 1:1 2:1 3:1 4:1 5:1 6:1 7:1 1:2 2:2 3:2 4:2 5:2 6:2 7:2 1:3 2:3 3:3 4:3 5:3 6:3 7:3 1:4 2:4 3:4 4:4 5:4 6:4 7:4 1:5 2:5 3:5 4:5 5:5 6:5 7:5 1:6 2:6 3:6 4:6 5:6 6:6 7:6 1:7 2:7 3:7 4:7 5:7 6:7 7:7 with 4 links run <- FALSE if (require(\"sp\", quietly=TRUE)) run <- TRUE if (run) { # https://github.com/r-spatial/spdep/issues/20 GT <- GridTopology(c(1, 1), c(1, 1), c(10, 50)) SPix <- as(SpatialGrid(GT), \"SpatialPixels\") nb_rook_cont <- poly2nb(as(SPix, \"SpatialPolygons\"), queen=FALSE) nb_rook_dist <- dnearneigh(coordinates(SPix), 0, 1.01) all.equal(nb_rook_cont, nb_rook_dist, check.attributes=FALSE) ## [1] TRUE } #> [1] TRUE if (run) { t.nb <- cell2nb(GT, type='rook', legacy=TRUE) isTRUE(all.equal(nb_rook_cont, t.nb, check.attributes=FALSE)) ## [1] FALSE } #> [1] FALSE if (run) { t.nb <- cell2nb(GT, type='rook') isTRUE(all.equal(nb_rook_cont, t.nb, check.attributes=FALSE)) ## [1] TRUE } #> [1] TRUE if (run) { # https://github.com/r-spatial/spdep/issues/55 # problem reported in issue caused by rep() cycling in unexpected order GT <- GridTopology(c(1, 1), c(1, 1), c(22, 11)) SPix <- as(SpatialGrid(GT), \"SpatialPixels\") nb_rook_cont <- poly2nb(as(SPix, \"SpatialPolygons\"), queen=FALSE) nb_rook_dist <- dnearneigh(coordinates(SPix), 0, 1.01) all.equal(nb_rook_cont, nb_rook_dist, check.attributes=FALSE) } #> [1] TRUE if (run) { t.nb <- cell2nb(GT, type='rook', legacy=TRUE) isTRUE(all.equal(nb_rook_cont, t.nb, check.attributes=FALSE)) ## [1] FALSE } #> [1] FALSE if (run) { t.nb <- cell2nb(GT, type='rook', legacy=FALSE) isTRUE(all.equal(nb_rook_cont, t.nb, check.attributes=FALSE)) ## [1] TRUE } #> [1] TRUE"},{"path":"https://r-spatial.github.io/spdep/reference/choynowski.html","id":null,"dir":"Reference","previous_headings":"","what":"Choynowski probability map values — choynowski","title":"Choynowski probability map values — choynowski","text":"Calculates Choynowski probability map values.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/choynowski.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Choynowski probability map values — choynowski","text":"","code":"choynowski(n, x, row.names=NULL, tol = .Machine$double.eps^0.5, legacy=FALSE)"},{"path":"https://r-spatial.github.io/spdep/reference/choynowski.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Choynowski probability map values — choynowski","text":"n numeric vector counts cases x numeric vector populations risk row.names row names passed output data frame tol accumulate values observed counts >= expected value less tol legacy default FALSE using vectorised alternating side ppois version, true use original version written sources iterating tol","code":""},{"path":"https://r-spatial.github.io/spdep/reference/choynowski.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Choynowski probability map values — choynowski","text":"data frame columns: pmap Poisson probability map values: probablility getting “extreme” count actually observed, one-tailed less expected expected folded together type logical: TRUE observed count less expected","code":""},{"path":"https://r-spatial.github.io/spdep/reference/choynowski.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Choynowski probability map values — choynowski","text":"Choynowski, M (1959) Maps based probabilities, Journal American Statistical Association, 54, 385–388; Cressie, N, Read, TRC (1985), sudden infant deaths come clusters? Statistics Decisions, Supplement Issue 2, 333–349; Bailey T, Gatrell (1995) Interactive Spatial Data Analysis, Harlow: Longman, pp. 300–303.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/choynowski.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Choynowski probability map values — choynowski","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/choynowski.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Choynowski probability map values — choynowski","text":"","code":"auckland <- st_read(system.file(\"shapes/auckland.gpkg\", package=\"spData\")[1], quiet=TRUE) auckland.nb <- poly2nb(auckland) res <- choynowski(auckland$M77_85, 9*auckland$Und5_81) resl <- choynowski(auckland$M77_85, 9*auckland$Und5_81, legacy=TRUE) all.equal(res, resl) #> [1] TRUE rt <- sum(auckland$M77_85)/sum(9*auckland$Und5_81) ch_ppois_pmap <- numeric(length(auckland$Und5_81)) side <- c(\"greater\", \"less\") for (i in seq(along=ch_ppois_pmap)) {   ch_ppois_pmap[i] <- poisson.test(auckland$M77_85[i], r=rt,     T=(9*auckland$Und5_81[i]), alternative=side[(res$type[i]+1)])$p.value } all.equal(ch_ppois_pmap, res$pmap) #> [1] TRUE res1 <- probmap(auckland$M77_85, 9*auckland$Und5_81) table(abs(res$pmap - res1$pmap) < 0.00001, res$type) #>         #>         FALSE TRUE #>   FALSE    74    0 #>   TRUE      0   93 lt005 <- (res$pmap < 0.05) & (res$type) ge005 <- (res$pmap < 0.05) & (!res$type) cols <- rep(\"nonsig\", length(lt005)) cols[lt005] <- \"low\" cols[ge005] <- \"high\" auckland$cols <- factor(cols) plot(auckland[,\"cols\"], main=\"Probability map\")"},{"path":"https://r-spatial.github.io/spdep/reference/columbus.html","id":null,"dir":"Reference","previous_headings":"","what":"Columbus OH spatial analysis data set — columbus","title":"Columbus OH spatial analysis data set — columbus","text":"data set now part spData package","code":""},{"path":"https://r-spatial.github.io/spdep/reference/columbus.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Columbus OH spatial analysis data set — columbus","text":"","code":"data(columbus)"},{"path":"https://r-spatial.github.io/spdep/reference/columbus.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Columbus OH spatial analysis data set — columbus","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) col.gal.nb <- read.gal(system.file(\"weights/columbus.gal\", package=\"spData\")[1])"},{"path":"https://r-spatial.github.io/spdep/reference/compon.html","id":null,"dir":"Reference","previous_headings":"","what":"Depth First Search on Neighbor Lists — Graph Components","title":"Depth First Search on Neighbor Lists — Graph Components","text":"n.comp.nb() finds number disjoint connected subgraphs graph depicted nb.obj - spatial neighbours list object.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/compon.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Depth First Search on Neighbor Lists — Graph Components","text":"","code":"n.comp.nb(nb.obj)"},{"path":"https://r-spatial.github.io/spdep/reference/compon.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Depth First Search on Neighbor Lists — Graph Components","text":"nb.obj neighbours list object class nb","code":""},{"path":"https://r-spatial.github.io/spdep/reference/compon.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Depth First Search on Neighbor Lists — Graph Components","text":"attr(nb.obj, \"sym\") FALSE igraph::components available, components directed graph found simple breadth-first search; igraph::components available, object made symmetric (may time-consuming large numbers neighbours) components found depth-first search. attr(nb.obj, \"sym\") TRUE, components directed graph found depth-first search. time complexity algorithms used native code igraph::components linear sum number nodes number edges graph, see https://github.com/r-spatial/spdep/issues/160 details; dense neighbour objects large numbers edges.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/compon.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Depth First Search on Neighbor Lists — Graph Components","text":"list : nc number disjoint connected subgraphs comp.id vector indices disjoint connected subgraphs  nodes nb.obj belong ","code":""},{"path":"https://r-spatial.github.io/spdep/reference/compon.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Depth First Search on Neighbor Lists — Graph Components","text":"Nicholas Lewin-Koh nikko@hailmail.net","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/compon.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Depth First Search on Neighbor Lists — Graph Components","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) col.gal.nb <- read.gal(system.file(\"weights/columbus.gal\", package=\"spData\")[1]) coords <- st_coordinates(st_centroid(st_geometry(columbus))) plot(col.gal.nb, coords, col=\"grey\") col2 <- droplinks(col.gal.nb, 21) #> Warning: some observations have no neighbours #> Warning: neighbour object has 3 sub-graphs res <- n.comp.nb(col2) table(res$comp.id) #>  #>  1  2  3  #> 42  1  6  plot(col2, coords, add=TRUE) points(coords, col=res$comp.id, pch=16)  run <- FALSE if (require(\"igraph\", quietly=TRUE) && require(\"spatialreg\", quietly=TRUE)) run <- TRUE #>  #> Attaching package: ‘igraph’ #> The following objects are masked from ‘package:stats’: #>  #>     decompose, spectrum #> The following object is masked from ‘package:base’: #>  #>     union #>  #> Attaching package: ‘spatialreg’ #> The following objects are masked from ‘package:spdep’: #>  #>     get.ClusterOption, get.VerboseOption, get.ZeroPolicyOption, #>     get.coresOption, get.mcOption, set.ClusterOption, #>     set.VerboseOption, set.ZeroPolicyOption, set.coresOption, #>     set.mcOption if (run) { B <- as(nb2listw(col2, style=\"B\", zero.policy=TRUE), \"CsparseMatrix\") g1 <- graph_from_adjacency_matrix(B, mode=\"undirected\") c1 <- components(g1) print(c1$no == res$nc) } #> [1] TRUE if (run) { print(all.equal(c1$membership, res$comp.id)) } #> [1] \"names for target but not for current\" if (run) { print(all.equal(c1$csize, c(table(res$comp.id)), check.attributes=FALSE)) } #> [1] TRUE if (run) { W <- as(nb2listw(col2, style=\"W\", zero.policy=TRUE), \"CsparseMatrix\") g1W <- graph_from_adjacency_matrix(W, mode=\"directed\", weighted=\"W\") c1W <- components(g1W, mode=\"weak\") print(all.equal(c1W$membership, res$comp.id, check.attributes=FALSE)) } #> [1] TRUE # \\donttest{ if (run) { data(house, package=\"spData\") house <- sf::st_as_sf(house) k6 <- knn2nb(knearneigh(house, k=6)) is.symmetric.nb(k6) } #> [1] FALSE if (run) { print(k6) } #> Neighbour list object: #> Number of regions: 25357  #> Number of nonzero links: 152142  #> Percentage nonzero weights: 0.02366211  #> Average number of links: 6  #> Non-symmetric neighbours list if (run) { length(k6) + sum(card(k6)) } #> [1] 177499 if (run) { # no pre-computed graph components str(attr(k6, \"ncomp\")) } #>  NULL if (run) { # raising the subgraph compute ceiling to above |N|+|E| computes and stores the # object in the neighbour object set.SubgraphCeiling(180000L) k6 <- knn2nb(knearneigh(house, k=6)) str(attr(k6, \"ncomp\")) } #> Warning: neighbour object has 47 sub-graphs #> List of 2 #>  $ nc     : num 47 #>  $ comp.id: num [1:25357] 1 1 1 1 1 1 1 1 1 1 ... if (run) { print(k6) } #> Neighbour list object: #> Number of regions: 25357  #> Number of nonzero links: 152142  #> Percentage nonzero weights: 0.02366211  #> Average number of links: 6  #> 47 disjoint connected subgraphs #> Non-symmetric neighbours list if (run) { system.time(udir <- n.comp.nb(make.sym.nb(k6))) } #>    user  system elapsed  #>   2.461   0.000   2.470  if (run) { system.time(dir <- n.comp.nb(k6)) } #>    user  system elapsed  #>   0.786   0.002   0.792  if (run) { udir$nc } #> [1] 47 if (run) { dir$nc } #> [1] 47 if (run) { all.equal(dir, udir) } #> [1] TRUE # }"},{"path":"https://r-spatial.github.io/spdep/reference/diffnb.html","id":null,"dir":"Reference","previous_headings":"","what":"Differences between neighbours lists — diffnb","title":"Differences between neighbours lists — diffnb","text":"function finds differences lists neighbours, returning nb neighbour list found","code":""},{"path":"https://r-spatial.github.io/spdep/reference/diffnb.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Differences between neighbours lists — diffnb","text":"","code":"diffnb(x, y, verbose=NULL)"},{"path":"https://r-spatial.github.io/spdep/reference/diffnb.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Differences between neighbours lists — diffnb","text":"x object class nb y object class nb verbose default NULL, use global option value; report regions ids taken object attribute \"region.id\" differences","code":""},{"path":"https://r-spatial.github.io/spdep/reference/diffnb.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Differences between neighbours lists — diffnb","text":"neighbours list class nb","code":""},{"path":"https://r-spatial.github.io/spdep/reference/diffnb.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Differences between neighbours lists — diffnb","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/diffnb.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Differences between neighbours lists — diffnb","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) coords <- st_centroid(st_geometry(columbus), of_largest_polygon=TRUE) rn <- row.names(columbus) knn1 <- knearneigh(coords, 1) knn2 <- knearneigh(coords, 2) nb1 <- knn2nb(knn1, row.names=rn) #> Warning: neighbour object has 13 sub-graphs nb2 <- knn2nb(knn2, row.names=rn) diffs <- diffnb(nb2, nb1) #> Warning: neighbour object has 10 sub-graphs opar <- par(no.readonly=TRUE) plot(st_geometry(columbus), border=\"grey\", reset=FALSE,  main=\"Plot of first (black) and second (red)\\nnearest neighbours\") plot(nb1, coords, add=TRUE) plot(diffs, coords, add=TRUE, col=\"red\", lty=2)  par(opar)"},{"path":"https://r-spatial.github.io/spdep/reference/dnearneigh.html","id":null,"dir":"Reference","previous_headings":"","what":"Neighbourhood contiguity by distance — dnearneigh","title":"Neighbourhood contiguity by distance — dnearneigh","text":"function identifies neighbours region points Euclidean distance metric points lower (greater equal (changed version 1.1-7)) upper (less equal ) bounds, longlat = TRUE, Great Circle distance kilometers. x \"sf\" object use_s2= TRUE, spherical distances km used.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/dnearneigh.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Neighbourhood contiguity by distance — dnearneigh","text":"","code":"dnearneigh(x, d1, d2, row.names = NULL, longlat = NULL, bounds=c(\"GE\", \"LE\"),  use_kd_tree=TRUE, symtest=FALSE, use_s2=packageVersion(\"s2\") > \"1.0.7\", k=200,  dwithin=TRUE)"},{"path":"https://r-spatial.github.io/spdep/reference/dnearneigh.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Neighbourhood contiguity by distance — dnearneigh","text":"x matrix point coordinates, object inheriting SpatialPoints \"sf\" \"sfc\" object; \"sf\" \"sfc\" object geometries geographical coordinates (use_s2=FALSE, sf::st_is_longlat(x) == TRUE sf::sf_use_s2() == TRUE), s2 used find neighbours (hope) use spatial indexing https://github.com/r-spatial/s2/issues/125 opposed legacy method uses brute-force (present s2 also uses brute-force) d1 lower distance bound metric points planar coordinates, km geographical coordinates d2 upper distance boundd metric points planar coordinates, km geographical coordinates row.names character vector region ids added neighbours list attribute region.id, default seq(1, nrow(x)) longlat TRUE point coordinates geographical longitude-latitude decimal degrees, case distances measured kilometers; x SpatialPoints object, value taken object , overrides argument NULL bounds character vector length 2, default c(\"GE\", \"LE\"), (GE: greater equal , LE: less equal ) finite closed interval [d1, d2], d1 <= x <= d2. first element may also \"GT\" (GT: greater ), second \"LT\" (LT: less ) finite, open intervals excluding bounds; first bound default changed \"GT\" \"GE\" release 1.1-7. creating multiple distance bands, finite, half-open right-closed intervals may used final interval avoid overlapping bounds: \"GE\", \"LT\", [d1, d2), d1 <= x < d2 use_kd_tree default TRUE, TRUE, use dbscan frNN available (permitting 3D distances). symtest Default FALSE; release 1.1-7, TRUE - run symmetry check output object, costly large numbers points. use_s2 default=packageVersion(\"s2\") > \"1.0.7\", s2 > 1.0-7, distance bound computations use spatial indexing sf::sf_use_s2() TRUE, s2::s2_dwithin_matrix() used distances sphere \"sf\" \"sfc\" objects s2 > 1.0-7. k default 200, number closest points consider searching using  s2::s2_closest_edges() dwithin default TRUE, FALSE, use s2::s2_closest_edges(), use_s2=TRUE, sf::st_is_longlat(x) == TRUE sf::sf_use_s2() == TRUE; s2::s2_dwithin_matrix() yields lists neighbours s2::s2_closest_edges() k= set correctly.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/dnearneigh.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Neighbourhood contiguity by distance — dnearneigh","text":"function returns list integer vectors giving region id numbers neighbours satisfying distance criteria. See card details “nb” objects.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/dnearneigh.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Neighbourhood contiguity by distance — dnearneigh","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/dnearneigh.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Neighbourhood contiguity by distance — dnearneigh","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) coords <- st_centroid(st_geometry(columbus), of_largest_polygon=TRUE) rn <- row.names(columbus) k1 <- knn2nb(knearneigh(coords)) #> Warning: neighbour object has 13 sub-graphs all.linked <- max(unlist(nbdists(k1, coords))) col.nb.0.all <- dnearneigh(coords, 0, all.linked, row.names=rn) #> Warning: neighbour object has 2 sub-graphs summary(col.nb.0.all, coords) #> Neighbour list object: #> Number of regions: 49  #> Number of nonzero links: 252  #> Percentage nonzero weights: 10.49563  #> Average number of links: 5.142857  #> 2 disjoint connected subgraphs #> Link number distribution: #>  #>  1  2  3  4  5  6  7  8  9 10 11  #>  4  8  6  2  5  8  6  2  6  1  1  #> 4 least connected regions: #> 6 10 21 47 with 1 link #> 1 most connected region: #> 28 with 11 links opar <- par(no.readonly=TRUE) plot(st_geometry(columbus), border=\"grey\", reset=FALSE,  main=paste(\"Distance based neighbours 0-\",  format(all.linked), sep=\"\")) plot(col.nb.0.all, coords, add=TRUE)  par(opar) (sfc_obj <- st_centroid(st_geometry(columbus))) #> Geometry set for 49 features  #> Geometry type: POINT #> Dimension:     XY #> Bounding box:  xmin: 6.221943 ymin: 11.01003 xmax: 10.95359 ymax: 14.36908 #> Projected CRS: Undefined Cartesian SRS with unknown unit #> First 5 geometries: #> POINT (8.827218 14.36908) #> POINT (8.332658 14.03162) #> POINT (9.012265 13.81972) #> POINT (8.460801 13.71696) #> POINT (9.007982 13.29637) col.nb.0.all_sf <- dnearneigh(sfc_obj, 0, all.linked, row.names=rn) #> Warning: neighbour object has 2 sub-graphs all.equal(col.nb.0.all, col.nb.0.all_sf, check.attributes=FALSE) #> [1] TRUE data(state) us48.fipsno <- read.geoda(system.file(\"etc/weights/us48.txt\",  package=\"spdep\")[1]) if (as.numeric(paste(version$major, version$minor, sep=\"\")) < 19) {  m50.48 <- match(us48.fipsno$\"State.name\", state.name) } else {  m50.48 <- match(us48.fipsno$\"State_name\", state.name) } xy <- as.matrix(as.data.frame(state.center))[m50.48,] llk1 <- knn2nb(knearneigh(xy, k=1, longlat=FALSE)) #> Warning: neighbour object has 12 sub-graphs (all.linked <- max(unlist(nbdists(llk1, xy, longlat=FALSE)))) #> [1] 5.161223 ll.nb <- dnearneigh(xy, 0, all.linked, longlat=FALSE) #> Warning: neighbour object has 5 sub-graphs summary(ll.nb, xy, longlat=TRUE, scale=0.5) #> Neighbour list object: #> Number of regions: 48  #> Number of nonzero links: 190  #> Percentage nonzero weights: 8.246528  #> Average number of links: 3.958333  #> 5 disjoint connected subgraphs #> Link number distribution: #>  #>  1  2  3  4  5  7  8  9 10  #> 11  9  4  8  4  4  4  3  1  #> 11 least connected regions: #> 2 4 8 10 24 26 29 32 35 41 45 with 1 link #> 1 most connected region: #> 28 with 10 links gck1 <- knn2nb(knearneigh(xy, k=1, longlat=TRUE)) #> Warning: neighbour object has 11 sub-graphs (all.linked <- max(unlist(nbdists(gck1, xy, longlat=TRUE)))) #> [1] 523.5819 gc.nb <- dnearneigh(xy, 0, all.linked, longlat=TRUE) #> Warning: neighbour object has 2 sub-graphs summary(gc.nb, xy, longlat=TRUE, scale=0.5) #> Neighbour list object: #> Number of regions: 48  #> Number of nonzero links: 220  #> Percentage nonzero weights: 9.548611  #> Average number of links: 4.583333  #> 2 disjoint connected subgraphs #> Link number distribution: #>  #>  1  2  3  4  5  6  7  8  9 10  #>  5  9  6  8  5  2  3  3  5  2  #> 5 least connected regions: #> 2 4 8 41 45 with 1 link #> 2 most connected regions: #> 7 28 with 10 links plot(ll.nb, xy) plot(diffnb(ll.nb, gc.nb), xy, add=TRUE, col=\"red\", lty=2) #> Warning: neighbour object has 27 sub-graphs title(main=\"Differences Euclidean/Great Circle\")   #xy1 <- SpatialPoints((as.data.frame(state.center))[m50.48,], #  proj4string=CRS(\"+proj=longlat +ellps=GRS80\")) #gck1a <- knn2nb(knearneigh(xy1, k=1)) #(all.linked <- max(unlist(nbdists(gck1a, xy1)))) #gc.nb <- dnearneigh(xy1, 0, all.linked) #summary(gc.nb, xy1, scale=0.5)  xy1 <- st_as_sf((as.data.frame(state.center))[m50.48,], coords=1:2,   crs=st_crs(\"OGC:CRS84\")) old_use_s2 <- sf_use_s2() sf_use_s2(TRUE) gck1b <- knn2nb(knearneigh(xy1, k=1)) #> Warning: neighbour object has 11 sub-graphs system.time(o <- nbdists(gck1b, xy1)) #>    user  system elapsed  #>   0.007   0.000   0.007  (all.linked <- max(unlist(o))) #> [1] 522.4464 # use s2 brute-force dwithin_matrix approach for s2 <= 1.0.7 system.time(gc.nb.dwithin <- dnearneigh(xy1, 0, all.linked, use_s2=TRUE, dwithin=TRUE)) #> Warning: neighbour object has 3 sub-graphs #>    user  system elapsed  #>   0.012   0.000   0.012  summary(gc.nb, xy1, scale=0.5) #> Neighbour list object: #> Number of regions: 48  #> Number of nonzero links: 220  #> Percentage nonzero weights: 9.548611  #> Average number of links: 4.583333  #> 2 disjoint connected subgraphs #> Link number distribution: #>  #>  1  2  3  4  5  6  7  8  9 10  #>  5  9  6  8  5  2  3  3  5  2  #> 5 least connected regions: #> 2 4 8 41 45 with 1 link #> 2 most connected regions: #> 7 28 with 10 links # use s2 closest_edges approach s2 > 1.0.7 if (packageVersion(\"s2\") > \"1.0.7\") { (system.time(gc.nb.closest <- dnearneigh(xy1, 0, all.linked, dwithin=FALSE))) } #> Warning: neighbour object has 3 sub-graphs #>    user  system elapsed  #>   0.012   0.000   0.013  if (packageVersion(\"s2\") > \"1.0.7\") { system.time(gc.nb.dwithin <- dnearneigh(xy1, 0, all.linked, use_s2=TRUE, dwithin=TRUE)) } #> Warning: neighbour object has 3 sub-graphs #>    user  system elapsed  #>   0.013   0.000   0.013  if (packageVersion(\"s2\") > \"1.0.7\") { summary(gc.nb.dwithin, xy1, scale=0.5) } #> Neighbour list object: #> Number of regions: 48  #> Number of nonzero links: 218  #> Percentage nonzero weights: 9.461806  #> Average number of links: 4.541667  #> 1 region with no links: #> 2 #> 3 disjoint connected subgraphs #> Link number distribution: #>  #>  0  1  2  3  4  5  6  7  8  9 10  #>  1  5  8  6  8  5  2  3  3  5  2  #> 5 least connected regions: #> 4 8 29 41 45 with 1 link #> 2 most connected regions: #> 7 28 with 10 links if (packageVersion(\"s2\") > \"1.0.7\") { summary(gc.nb.closest, xy1, scale=0.5) } #> Neighbour list object: #> Number of regions: 48  #> Number of nonzero links: 218  #> Percentage nonzero weights: 9.461806  #> Average number of links: 4.541667  #> 1 region with no links: #> 2 #> 3 disjoint connected subgraphs #> Link number distribution: #>  #>  0  1  2  3  4  5  6  7  8  9 10  #>  1  5  8  6  8  5  2  3  3  5  2  #> 5 least connected regions: #> 4 8 29 41 45 with 1 link #> 2 most connected regions: #> 7 28 with 10 links # use legacy symmetric brute-force approach system.time(gc.nb.legacy <- dnearneigh(xy1, 0, all.linked, use_s2=FALSE)) #> Warning: neighbour object has 3 sub-graphs #>    user  system elapsed  #>   0.006   0.000   0.006  summary(gc.nb, xy1, scale=0.5) #> Neighbour list object: #> Number of regions: 48  #> Number of nonzero links: 220  #> Percentage nonzero weights: 9.548611  #> Average number of links: 4.583333  #> 2 disjoint connected subgraphs #> Link number distribution: #>  #>  1  2  3  4  5  6  7  8  9 10  #>  5  9  6  8  5  2  3  3  5  2  #> 5 least connected regions: #> 2 4 8 41 45 with 1 link #> 2 most connected regions: #> 7 28 with 10 links if (packageVersion(\"s2\") > \"1.0.7\") all.equal(gc.nb.closest, gc.nb.dwithin, check.attributes=FALSE) #> [1] TRUE # legacy is ellipsoidal, s2 spherical, so minor differences expected if (packageVersion(\"s2\") > \"1.0.7\") all.equal(gc.nb, gc.nb.closest, check.attributes=FALSE) #> [1] \"Component 2: Mean relative difference: 1\"     #> [2] \"Component 29: Numeric: lengths (2, 1) differ\" all.equal(gc.nb, gc.nb.dwithin, check.attributes=FALSE) #> [1] \"Component 2: Mean relative difference: 1\"     #> [2] \"Component 29: Numeric: lengths (2, 1) differ\" sf_use_s2(old_use_s2) # example of reading points with readr::read_csv() yielding a tibble load(system.file(\"etc/misc/coords.rda\", package=\"spdep\")) class(coords) #> [1] \"spec_tbl_df\" \"tbl_df\"      \"tbl\"         \"data.frame\"  k1 <- knn2nb(knearneigh(coords, k=1)) #> Warning: neighbour object has 29 sub-graphs all.linked <- max(unlist(nbdists(k1, coords))) dnearneigh(coords, 0, all.linked) #> Neighbour list object: #> Number of regions: 100  #> Number of nonzero links: 676  #> Percentage nonzero weights: 6.76  #> Average number of links: 6.76"},{"path":"https://r-spatial.github.io/spdep/reference/droplinks.html","id":null,"dir":"Reference","previous_headings":"","what":"Drop and add links in a neighbours list — droplinks","title":"Drop and add links in a neighbours list — droplinks","text":"droplinks drops links just region neighbours list. example corresponds Fingleton's Table 1, (1999) p. 6, lattices 5 19. addlinks1 adds links single region specified regions.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/droplinks.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Drop and add links in a neighbours list — droplinks","text":"","code":"droplinks(nb, drop, sym=TRUE) addlinks1(nb, from, to, sym=TRUE)"},{"path":"https://r-spatial.github.io/spdep/reference/droplinks.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Drop and add links in a neighbours list — droplinks","text":"nb neighbours list object class nb drop either logical vector length nb, character vector named regions corresponding nb's region.id attribute, integer vector region numbers sym TRUE removal \"row\" \"column\" links, FALSE \"row\" links; adding links, inserts links region regions single region adding links, either character vector length 1 named region corresponding nb's region.id attribute, integer vector length 1 holding region number regions, either character vector named regions corresponding nb's region.id attribute, integer vector region numbers","code":""},{"path":"https://r-spatial.github.io/spdep/reference/droplinks.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Drop and add links in a neighbours list — droplinks","text":"function returns object class nb list integer vectors containing neighbour region number ids.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/droplinks.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Drop and add links in a neighbours list — droplinks","text":"B. Fingleton (1999) Spurious spatial regression: Monte Carlo results spatial unit root spatial cointegration, Journal Regional Science 39, pp. 1–19.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/droplinks.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Drop and add links in a neighbours list — droplinks","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/droplinks.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Drop and add links in a neighbours list — droplinks","text":"","code":"# \\donttest{ rho <- c(0.2, 0.5, 0.95, 0.999, 1.0) ns <- c(5, 7, 9, 11, 13, 15, 17, 19) mns <- matrix(0, nrow=length(ns), ncol=length(rho)) rownames(mns) <- ns colnames(mns) <- rho mxs <- matrix(0, nrow=length(ns), ncol=length(rho)) rownames(mxs) <- ns colnames(mxs) <- rho for (i in 1:length(ns)) {   nblist <- cell2nb(ns[i], ns[i])   nbdropped <- droplinks(nblist, ((ns[i]*ns[i])+1)/2, sym=FALSE)   listw <- nb2listw(nbdropped, style=\"W\", zero.policy=TRUE)   wmat <- listw2mat(listw)   for (j in 1:length(rho)) {     mat <- diag(ns[i]*ns[i]) - rho[j] * wmat     res <- diag(solve(t(mat) %*% mat))     mns[i,j] <- mean(res)     mxs[i,j] <- max(res)   } } #> Warning: some observations have no neighbours #> Warning: some observations have no neighbours #> Warning: some observations have no neighbours #> Warning: some observations have no neighbours #> Warning: some observations have no neighbours #> Warning: some observations have no neighbours #> Warning: some observations have no neighbours #> Warning: some observations have no neighbours print(mns) #>         0.2      0.5      0.95     0.999          1 #> 5  1.038271 1.312627  9.486051  30.81487   32.04915 #> 7  1.036443 1.295621 10.899580  83.25437   92.09812 #> 9  1.035356 1.285145 10.798611 160.90951  195.02166 #> 11 1.034639 1.278279 10.383083 254.83998  347.71145 #> 13 1.034132 1.273442  9.968389 353.66366  555.88699 #> 15 1.033753 1.269852  9.619387 447.19245  824.46560 #> 17 1.033460 1.267082  9.337167 528.49015 1157.77630 #> 19 1.033227 1.264879  9.109487 594.23907 1559.69614 print(mxs) #>         0.2      0.5     0.95     0.999          1 #> 5  1.048834 1.401934 12.00215  39.22742   40.79967 #> 7  1.048834 1.402174 14.66823 106.90031  118.01556 #> 9  1.048834 1.402176 15.49606 207.28928  249.74893 #> 11 1.048834 1.402176 15.75744 329.22973  443.97194 #> 13 1.048834 1.402176 15.83957 458.75739  707.14827 #> 15 1.048834 1.402176 15.86474 583.50722 1044.75562 #> 17 1.048834 1.402176 15.87225 695.10288 1461.57017 #> 19 1.048834 1.402176 15.87445 789.50575 1961.84025  # }"},{"path":"https://r-spatial.github.io/spdep/reference/edit.nb.html","id":null,"dir":"Reference","previous_headings":"","what":"Interactive editing of neighbours lists — edit.nb","title":"Interactive editing of neighbours lists — edit.nb","text":"function provides simple interactive editing neighbours lists allow unneeded links deleted, missing links inserted. uses identify pick endpoints link deleted added, asks confirmation committing. result assigned new object, editing lost - edit. method relies direct contact graphics device. use RStudio.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/edit.nb.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Interactive editing of neighbours lists — edit.nb","text":"","code":"# S3 method for class 'nb' edit(name, coords, polys=NULL, ..., use_region.id=FALSE)"},{"path":"https://r-spatial.github.io/spdep/reference/edit.nb.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Interactive editing of neighbours lists — edit.nb","text":"name object class nb coords matrix region point coordinates; missing polys= inherits SpatialPolygons, label points object used polys polygon boundaries supplied, used background; must inherit SpatialPolygons ... arguments passed methods use_region.id default FALSE, identify use 1-based observation numbers, otherwise use nb region.id attribute values","code":""},{"path":"https://r-spatial.github.io/spdep/reference/edit.nb.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Interactive editing of neighbours lists — edit.nb","text":"function returns object class nb edited list integer vectors containing neighbour region number ids, added attributes tallying added deleted links.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/edit.nb.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Interactive editing of neighbours lists — edit.nb","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/edit.nb.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Interactive editing of neighbours lists — edit.nb","text":"","code":"# \\dontrun{ columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) class(columbus) #> [1] \"sf\"         \"data.frame\" if (FALSE) nnb1 <- edit.nb(col.gal.nb, polys=as(columbus, \"Spatial\")) # }"},{"path":"https://r-spatial.github.io/spdep/reference/eire.html","id":null,"dir":"Reference","previous_headings":"","what":"Eire data sets — eire","title":"Eire data sets — eire","text":"data set now part spData package","code":""},{"path":"https://r-spatial.github.io/spdep/reference/eire.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Eire data sets — eire","text":"","code":"data(eire)"},{"path":"https://r-spatial.github.io/spdep/reference/geary.html","id":null,"dir":"Reference","previous_headings":"","what":"Compute Geary's C — geary","title":"Compute Geary's C — geary","text":"simple function compute Geary's C, called geary.test geary.mc; $$C = \\frac{(n-1)}{2\\sum_{=1}^{n}\\sum_{j=1}^{n}w_{ij}} \\frac{\\sum_{=1}^{n}\\sum_{j=1}^{n}w_{ij}(x_i-x_j)^2}{\\sum_{=1}^{n}(x_i - \\bar{x})^2} $$ geary.intern internal function used vary similarity criterion.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/geary.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Compute Geary's C — geary","text":"","code":"geary(x, listw, n, n1, S0, zero.policy=attr(listw, \"zero.policy\"), scale=TRUE) <!-- %geary.intern(x, listw, n, zero.policy, type=\"geary\") -->"},{"path":"https://r-spatial.github.io/spdep/reference/geary.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Compute Geary's C — geary","text":"x numeric vector length neighbours list listw listw listw object created example nb2listw n number zones n1 n - 1 S0 global sum weights zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA  scale default TRUE, may FALSE revert changes made accommodate localC November 2021 (see #151)","code":""},{"path":"https://r-spatial.github.io/spdep/reference/geary.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Compute Geary's C — geary","text":"list C Geary's C K sample kurtosis x","code":""},{"path":"https://r-spatial.github.io/spdep/reference/geary.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Compute Geary's C — geary","text":"Cliff, . D., Ord, J. K. 1981 Spatial processes, Pion, p. 17.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/geary.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Compute Geary's C — geary","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/geary.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Compute Geary's C — geary","text":"","code":"data(oldcol) col.W <- nb2listw(COL.nb, style=\"W\") str(geary(COL.OLD$CRIME, col.W, length(COL.nb), length(COL.nb)-1,  Szero(col.W))) #> List of 2 #>  $ C: num 0.53 #>  $ K: num 2.23"},{"path":"https://r-spatial.github.io/spdep/reference/geary.mc.html","id":null,"dir":"Reference","previous_headings":"","what":"Permutation test for Geary's C statistic — geary.mc","title":"Permutation test for Geary's C statistic — geary.mc","text":"permutation test Geary's C statistic calculated using nsim random permutations x given spatial weighting scheme, establish rank observed statistic relation nsim simulated values.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/geary.mc.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Permutation test for Geary's C statistic — geary.mc","text":"","code":"geary.mc(x, listw, nsim, zero.policy=attr(listw, \"zero.policy\"), alternative=\"greater\",  spChk=NULL, adjust.n=TRUE, return_boot=FALSE, na.action=na.fail, scale=TRUE)"},{"path":"https://r-spatial.github.io/spdep/reference/geary.mc.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Permutation test for Geary's C statistic — geary.mc","text":"x numeric vector length neighbours list listw listw listw object created example nb2listw nsim number permutations zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA alternative character string specifying alternative hypothesis, must one \"greater\" (default), \"less\"; reversal corresponds geary.test described section output statistic value, based Cliff Ord 1973, p. 21 (changed 2011-04-11, thanks Daniel Garavito). spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption() adjust.n default TRUE, FALSE number observations adjusted -neighbour observations, TRUE, number observations adjusted return_boot return object class boot equivalent permutation bootstrap rather object class htest na.action function (default na.fail), can also na.omit na.exclude - cases weights list subsetted remove NAs data. may necessary set zero.policy TRUE subsetting may create -neighbour observations. Note weights lists created without using glist argument nb2listw may subsetted. na.pass permitted meaningless permutation test. scale default TRUE, may FALSE revert changes made accommodate localC November 2021 (see #151)","code":""},{"path":"https://r-spatial.github.io/spdep/reference/geary.mc.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Permutation test for Geary's C statistic — geary.mc","text":"list class htest mc.sim containing following components: statistic value observed Geary's C. parameter rank observed Geary's C. p.value pseudo p-value test. alternative character string describing alternative hypothesis. method character string giving method used. data.name character string giving name(s) data, number simulations. res nsim simulated values statistic, final value observed statistic","code":""},{"path":"https://r-spatial.github.io/spdep/reference/geary.mc.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Permutation test for Geary's C statistic — geary.mc","text":"Cliff, . D., Ord, J. K. 1981 Spatial processes, Pion, p. 63-5.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/geary.mc.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Permutation test for Geary's C statistic — geary.mc","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/geary.mc.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Permutation test for Geary's C statistic — geary.mc","text":"","code":"data(oldcol) set.seed(1) sim1 <- geary.mc(COL.OLD$CRIME, nb2listw(COL.nb, style=\"W\"),  nsim=99, alternative=\"less\") sim1 #>  #> \tMonte-Carlo simulation of Geary C #>  #> data:  COL.OLD$CRIME  #> weights: nb2listw(COL.nb, style = \"W\")   #> number of simulations + 1: 100  #>  #> statistic = 0.52987, observed rank = 1, p-value = 0.99 #> alternative hypothesis: less #>  mean(sim1$res) #> [1] 1.002705 var(sim1$res) #> [1] 0.01043616 summary(sim1$res) #>    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.  #>  0.5299  0.9362  1.0141  1.0027  1.0673  1.2459  colold.lags <- nblag(COL.nb, 3) sim2 <- geary.mc(COL.OLD$CRIME, nb2listw(colold.lags[[2]],  style=\"W\"), nsim=99) sim2 #>  #> \tMonte-Carlo simulation of Geary C #>  #> data:  COL.OLD$CRIME  #> weights: nb2listw(colold.lags[[2]], style = \"W\")   #> number of simulations + 1: 100  #>  #> statistic = 0.81129, observed rank = 1, p-value = 0.01 #> alternative hypothesis: greater #>  summary(sim2$res) #>    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.  #>  0.8113  0.9500  1.0173  1.0147  1.0731  1.1962  sim3 <- geary.mc(COL.OLD$CRIME, nb2listw(colold.lags[[3]],  style=\"W\"), nsim=99) sim3 #>  #> \tMonte-Carlo simulation of Geary C #>  #> data:  COL.OLD$CRIME  #> weights: nb2listw(colold.lags[[3]], style = \"W\")   #> number of simulations + 1: 100  #>  #> statistic = 1.1303, observed rank = 89, p-value = 0.89 #> alternative hypothesis: greater #>  summary(sim3$res) #>    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.  #>  0.7903  0.9609  0.9989  1.0148  1.0656  1.2726  crime <- COL.OLD$CRIME is.na(crime) <- sample(1:length(crime), 10) try(geary.mc(crime, nb2listw(COL.nb, style=\"W\"), nsim=99,  na.action=na.fail)) #> Error in na.fail.default(x) : missing values in object geary.mc(crime, nb2listw(COL.nb, style=\"W\"), nsim=99, zero.policy=TRUE,  na.action=na.omit) #> Warning: subsetting caused increase in subgraph count #>  #> \tMonte-Carlo simulation of Geary C #>  #> data:  crime  #> weights: nb2listw(COL.nb, style = \"W\")  #> omitted: 14, 16, 17, 21, 24, 31, 32, 42, 44, 47  #> number of simulations + 1: 100  #>  #> statistic = 0.49368, observed rank = 1, p-value = 0.01 #> alternative hypothesis: greater #>  geary.mc(crime, nb2listw(COL.nb, style=\"W\"), nsim=99, zero.policy=TRUE,  return_boot=TRUE, na.action=na.omit) #> Warning: subsetting caused increase in subgraph count #> NA observations omitted: 14, 16, 17, 21, 24, 31, 32, 42, 44, 47 #>  #> DATA PERMUTATION #>  #>  #> Call: #> boot(data = x, statistic = geary_boot, R = nsim, sim = \"permutation\",  #>     listw = listw, n = n, n1 = wc$n1, S0 = wc$S0, zero.policy = zero.policy,  #>     scale = scale, parallel = parallel, ncpus = ncpus, cl = cl) #>  #>  #> Bootstrap Statistics : #>      original    bias    std. error #> t1* 0.4936767 0.4891213   0.1517218 geary.mc(crime, nb2listw(COL.nb, style=\"W\"), nsim=99, zero.policy=TRUE,  na.action=na.exclude) #> Warning: subsetting caused increase in subgraph count #>  #> \tMonte-Carlo simulation of Geary C #>  #> data:  crime  #> weights: nb2listw(COL.nb, style = \"W\")  #> omitted: 14, 16, 17, 21, 24, 31, 32, 42, 44, 47  #> number of simulations + 1: 100  #>  #> statistic = 0.49368, observed rank = 1, p-value = 0.01 #> alternative hypothesis: greater #>  geary.mc(crime, nb2listw(COL.nb, style=\"W\"), nsim=99, zero.policy=TRUE,  return_boot=TRUE, na.action=na.exclude) #> Warning: subsetting caused increase in subgraph count #> NA observations omitted: 14, 16, 17, 21, 24, 31, 32, 42, 44, 47 #>  #> DATA PERMUTATION #>  #>  #> Call: #> boot(data = x, statistic = geary_boot, R = nsim, sim = \"permutation\",  #>     listw = listw, n = n, n1 = wc$n1, S0 = wc$S0, zero.policy = zero.policy,  #>     scale = scale, parallel = parallel, ncpus = ncpus, cl = cl) #>  #>  #> Bootstrap Statistics : #>      original    bias    std. error #> t1* 0.4936767 0.4570379   0.1307276 try(geary.mc(crime, nb2listw(COL.nb, style=\"W\"), nsim=99, na.action=na.pass)) #> Error in geary.mc(crime, nb2listw(COL.nb, style = \"W\"), nsim = 99, na.action = na.pass) :  #>   na.pass not permitted"},{"path":"https://r-spatial.github.io/spdep/reference/geary.test.html","id":null,"dir":"Reference","previous_headings":"","what":"Geary's C test for spatial autocorrelation — geary.test","title":"Geary's C test for spatial autocorrelation — geary.test","text":"Geary's test spatial autocorrelation using spatial weights matrix weights list form. assumptions underlying test sensitive form graph neighbour relationships factors, results may checked geary.mc permutations.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/geary.test.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Geary's C test for spatial autocorrelation — geary.test","text":"","code":"geary.test(x, listw, randomisation=TRUE, zero.policy=attr(listw, \"zero.policy\"),     alternative=\"greater\", spChk=NULL, adjust.n=TRUE, na.action=na.fail,     scale=TRUE)"},{"path":"https://r-spatial.github.io/spdep/reference/geary.test.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Geary's C test for spatial autocorrelation — geary.test","text":"x numeric vector length neighbours list listw listw listw object created example nb2listw randomisation variance calculated assumption randomisation, FALSE normality zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA alternative character string specifying alternative hypothesis, must one \"greater\" (default), \"less\" \"two.sided\". spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption() adjust.n default TRUE, FALSE number observations adjusted -neighbour observations, TRUE, number observations adjusted na.action function (default na.fail), can also na.omit na.exclude - cases weights list subsetted remove NAs data. may necessary set zero.policy TRUE subsetting may create -neighbour observations. Note weights lists created without using glist argument nb2listw may subsetted. na.pass permitted. scale default TRUE, may FALSE revert changes made accommodate localC November 2021 (see #151)","code":""},{"path":"https://r-spatial.github.io/spdep/reference/geary.test.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Geary's C test for spatial autocorrelation — geary.test","text":"list class htest containing following components: statistic value standard deviate Geary's C, order given Cliff Ord 1973, p. 21, (EC - C) / sqrt(VC), sign reversed respect usual (C - EC) / sqrt(VC); means “greater” alternative Geary C test corresponds “greater” alternative Moran's test. p.value p-value test. estimate value observed Geary's C, expectation  variance method assumption. alternative character string describing alternative hypothesis. method character string giving assumption used calculating  standard deviate. data.name character string giving name(s) data.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/geary.test.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Geary's C test for spatial autocorrelation — geary.test","text":"Cliff, . D., Ord, J. K. 1981 Spatial processes, Pion, p. 21, Cliff, . D., Ord, J. K. 1973 Spatial Autocorrelation, Pion, pp. 15-16, 21; Bivand RS, Wong DWS 2018 Comparing implementations global local indicators spatial association. TEST, 27(3), 716–748 doi:10.1007/s11749-018-0599-x","code":""},{"path":"https://r-spatial.github.io/spdep/reference/geary.test.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Geary's C test for spatial autocorrelation — geary.test","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/geary.test.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Geary's C test for spatial autocorrelation — geary.test","text":"derivation test (Cliff Ord, 1981, p. 18) assumes weights matrix symmetric. inherently non-symmetric matrices, k-nearest neighbour matrices, listw2U() can used make matrix symmetric. non-symmetric weights matrix cases, variance test statistic may negative (thanks Franz Munoz well documented bug report). Geary's C affected non-symmetric weights normality much Moran's . 0.4-35, sign standard deviate C changed match Cliff Ord (1973, p. 21).","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/geary.test.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Geary's C test for spatial autocorrelation — geary.test","text":"","code":"data(oldcol) geary.test(COL.OLD$CRIME, nb2listw(COL.nb, style=\"W\")) #>  #> \tGeary C test under randomisation #>  #> data:  COL.OLD$CRIME  #> weights: nb2listw(COL.nb, style = \"W\")    #>  #> Geary C statistic standard deviate = 4.7605, p-value = 9.655e-07 #> alternative hypothesis: Expectation greater than statistic #> sample estimates: #> Geary C statistic       Expectation          Variance  #>        0.52986993        1.00000000        0.00975278  #>  geary.test(COL.OLD$CRIME, nb2listw(COL.nb, style=\"W\"),  randomisation=FALSE) #>  #> \tGeary C test under normality #>  #> data:  COL.OLD$CRIME  #> weights: nb2listw(COL.nb, style = \"W\")    #>  #> Geary C statistic standard deviate = 4.6388, p-value = 1.752e-06 #> alternative hypothesis: Expectation greater than statistic #> sample estimates: #> Geary C statistic       Expectation          Variance  #>        0.52986993        1.00000000        0.01027137  #>  colold.lags <- nblag(COL.nb, 3) geary.test(COL.OLD$CRIME, nb2listw(colold.lags[[2]],  style=\"W\")) #>  #> \tGeary C test under randomisation #>  #> data:  COL.OLD$CRIME  #> weights: nb2listw(colold.lags[[2]], style = \"W\")    #>  #> Geary C statistic standard deviate = 2.2896, p-value = 0.01102 #> alternative hypothesis: Expectation greater than statistic #> sample estimates: #> Geary C statistic       Expectation          Variance  #>       0.811285136       1.000000000       0.006793327  #>  geary.test(COL.OLD$CRIME, nb2listw(colold.lags[[3]],  style=\"W\"), alternative=\"greater\") #>  #> \tGeary C test under randomisation #>  #> data:  COL.OLD$CRIME  #> weights: nb2listw(colold.lags[[3]], style = \"W\")    #>  #> Geary C statistic standard deviate = -1.5667, p-value = 0.9414 #> alternative hypothesis: Expectation greater than statistic #> sample estimates: #> Geary C statistic       Expectation          Variance  #>       1.130277918       1.000000000       0.006914551  #>  print(is.symmetric.nb(COL.nb)) #> [1] TRUE coords.OLD <- cbind(COL.OLD$X, COL.OLD$Y) COL.k4.nb <- knn2nb(knearneigh(coords.OLD, 4)) print(is.symmetric.nb(COL.k4.nb)) #> [1] FALSE geary.test(COL.OLD$CRIME, nb2listw(COL.k4.nb, style=\"W\")) #>  #> \tGeary C test under randomisation #>  #> data:  COL.OLD$CRIME  #> weights: nb2listw(COL.k4.nb, style = \"W\")    #>  #> Geary C statistic standard deviate = 6.4415, p-value = 5.916e-11 #> alternative hypothesis: Expectation greater than statistic #> sample estimates: #> Geary C statistic       Expectation          Variance  #>       0.399254423       1.000000000       0.008697812  #>  geary.test(COL.OLD$CRIME, nb2listw(COL.k4.nb, style=\"W\"),  randomisation=FALSE) #>  #> \tGeary C test under normality #>  #> data:  COL.OLD$CRIME  #> weights: nb2listw(COL.k4.nb, style = \"W\")    #>  #> Geary C statistic standard deviate = 6.2873, p-value = 1.615e-10 #> alternative hypothesis: Expectation greater than statistic #> sample estimates: #> Geary C statistic       Expectation          Variance  #>       0.399254423       1.000000000       0.009129529  #>  cat(\"Note non-symmetric weights matrix - use listw2U()\\n\") #> Note non-symmetric weights matrix - use listw2U() geary.test(COL.OLD$CRIME, listw2U(nb2listw(COL.k4.nb,  style=\"W\"))) #>  #> \tGeary C test under randomisation #>  #> data:  COL.OLD$CRIME  #> weights: listw2U(nb2listw(COL.k4.nb, style = \"W\"))    #>  #> Geary C statistic standard deviate = 6.4415, p-value = 5.916e-11 #> alternative hypothesis: Expectation greater than statistic #> sample estimates: #> Geary C statistic       Expectation          Variance  #>       0.399254423       1.000000000       0.008697812  #>  geary.test(COL.OLD$CRIME, listw2U(nb2listw(COL.k4.nb,  style=\"W\")), randomisation=FALSE) #>  #> \tGeary C test under normality #>  #> data:  COL.OLD$CRIME  #> weights: listw2U(nb2listw(COL.k4.nb, style = \"W\"))    #>  #> Geary C statistic standard deviate = 6.2873, p-value = 1.615e-10 #> alternative hypothesis: Expectation greater than statistic #> sample estimates: #> Geary C statistic       Expectation          Variance  #>       0.399254423       1.000000000       0.009129529  #>  crime <- COL.OLD$CRIME is.na(crime) <- sample(1:length(crime), 10) try(geary.test(crime, nb2listw(COL.nb, style=\"W\"), na.action=na.fail)) #> Error in na.fail.default(x) : missing values in object geary.test(crime, nb2listw(COL.nb, style=\"W\"), zero.policy=TRUE,  na.action=na.omit) #>  #> \tGeary C test under randomisation #>  #> data:  crime  #> weights: nb2listw(COL.nb, style = \"W\")  #> omitted: 3, 4, 10, 20, 21, 23, 27, 29, 31, 38   #>  #> Geary C statistic standard deviate = 4.2726, p-value = 9.661e-06 #> alternative hypothesis: Expectation greater than statistic #> sample estimates: #> Geary C statistic       Expectation          Variance  #>        0.45199742        1.00000000        0.01645071  #>  geary.test(crime, nb2listw(COL.nb, style=\"W\"), zero.policy=TRUE,  na.action=na.exclude) #>  #> \tGeary C test under randomisation #>  #> data:  crime  #> weights: nb2listw(COL.nb, style = \"W\")  #> omitted: 3, 4, 10, 20, 21, 23, 27, 29, 31, 38   #>  #> Geary C statistic standard deviate = 4.2726, p-value = 9.661e-06 #> alternative hypothesis: Expectation greater than statistic #> sample estimates: #> Geary C statistic       Expectation          Variance  #>        0.45199742        1.00000000        0.01645071  #>  try(geary.test(crime, nb2listw(COL.nb, style=\"W\"), na.action=na.pass)) #> Error in geary.test(crime, nb2listw(COL.nb, style = \"W\"), na.action = na.pass) :  #>   na.pass not permitted"},{"path":"https://r-spatial.github.io/spdep/reference/globalG.test.html","id":null,"dir":"Reference","previous_headings":"","what":"Global G test for spatial autocorrelation — globalG.test","title":"Global G test for spatial autocorrelation — globalG.test","text":"global G statistic spatial autocorrelation, complementing local Gi LISA measures: localG.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/globalG.test.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Global G test for spatial autocorrelation — globalG.test","text":"","code":"globalG.test(x, listw, zero.policy=attr(listw, \"zero.policy\"), alternative=\"greater\",  spChk=NULL, adjust.n=TRUE, B1correct=TRUE, adjust.x=TRUE, Arc_all_x=FALSE,  na.action=na.fail)"},{"path":"https://r-spatial.github.io/spdep/reference/globalG.test.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Global G test for spatial autocorrelation — globalG.test","text":"x numeric vector length neighbours list listw listw listw object created example nb2listw; sequence distance bands used, recommended weights style binary (one c(\"B\", \"C\", \"U\")). zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA alternative character string specifying alternative hypothesis, must one \"greater\" (default), \"less\" \"two.sided\". spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption() adjust.n default TRUE, FALSE number observations adjusted -neighbour observations, TRUE, number observations adjusted B1correct default TRUE, TRUE, erratum referenced : \"page 195, coefficient W2 B1, (just center page) 6,  3.\" applied; FALSE, 3 used (CrimeStat IV) adjust.x default TRUE, TRUE, x values observations neighbours omitted denominator G Arc_all_x default FALSE, Arc_all_x=TRUE adjust.x=TRUE, use full x vector part denominator term G na.action function (default na.fail), can also na.omit na.exclude - cases weights list subsetted remove NAs data. may necessary set zero.policy TRUE subsetting may create -neighbour observations. Note weights lists created without using glist argument nb2listw may subsetted. na.pass permitted.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/globalG.test.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Global G test for spatial autocorrelation — globalG.test","text":"list class htest containing following components: statistic value standard deviate Getis-Ord G. p.value p-value test. estimate value observed statistic, expectation variance. alternative character string describing alternative hypothesis. data.name character string giving name(s) data.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/globalG.test.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Global G test for spatial autocorrelation — globalG.test","text":"Getis. , Ord, J. K. 1992 analysis spatial association use distance statistics, Geographical Analysis, 24, p. 195; see also Getis. , Ord, J. K. 1993 Erratum, Geographical Analysis, 25, p. 276; Bivand RS, Wong DWS 2018 Comparing implementations global local indicators spatial association. TEST, 27(3), 716–748 doi:10.1007/s11749-018-0599-x","code":""},{"path":"https://r-spatial.github.io/spdep/reference/globalG.test.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Global G test for spatial autocorrelation — globalG.test","text":"Hisaji ONO hi-ono@mn.xdsl.ne.jp Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/globalG.test.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Global G test for spatial autocorrelation — globalG.test","text":"","code":"nc.sids <- st_read(system.file(\"shapes/sids.gpkg\", package=\"spData\")[1], quiet=TRUE) sidsrate79 <- (1000*nc.sids$SID79)/nc.sids$BIR79 dists <- c(10, 20, 30, 33, 40, 50, 60, 70, 80, 90, 100) ndists <- length(dists) ZG <- vector(mode=\"list\", length=ndists) names(ZG) <- as.character(dists) milesxy <- cbind(nc.sids$east, nc.sids$north) for (i in 1:ndists) {   thisnb <- dnearneigh(milesxy, 0, dists[i])   thislw <- nb2listw(thisnb, style=\"B\", zero.policy=TRUE)   ZG[[i]] <- globalG.test(sidsrate79, thislw, zero.policy=TRUE) } #> Warning: neighbour object has 98 sub-graphs #> Warning: neighbour object has 37 sub-graphs #> Warning: neighbour object has 3 sub-graphs t(sapply(ZG, function(x) c(x$estimate[1], x$statistic, p.value=unname(x$p.value)))) #>     Global G statistic standard deviate   p.value #> 10          0.33548581       0.04859237 0.4806221 #> 20          0.02024945      -0.73262399 0.7681061 #> 30          0.04032434      -0.75011405 0.7734070 #> 33          0.05312271       0.40157023 0.3440002 #> 40          0.07400279      -0.04345713 0.5173314 #> 50          0.11471743       0.58686472 0.2786473 #> 60          0.15457553      -0.35823892 0.6399177 #> 70          0.19839023      -0.27864299 0.6097406 #> 80          0.24606972      -0.18791364 0.5745278 #> 90          0.30073463       0.11457610 0.4543906 #> 100         0.34879996       0.31591356 0.3760341 for (i in 1:ndists) {   thisnb <- dnearneigh(milesxy, 0, dists[i])   thislw <- nb2listw(thisnb, style=\"B\", zero.policy=TRUE)   ZG[[i]] <- globalG.test(sidsrate79, thislw, zero.policy=TRUE, alternative=\"two.sided\") } #> Warning: neighbour object has 98 sub-graphs #> Warning: neighbour object has 37 sub-graphs #> Warning: neighbour object has 3 sub-graphs t(sapply(ZG, function(x) c(x$estimate[1], x$statistic, p.value=unname(x$p.value)))) #>     Global G statistic standard deviate   p.value #> 10          0.33548581       0.04859237 0.9612441 #> 20          0.02024945      -0.73262399 0.4637878 #> 30          0.04032434      -0.75011405 0.4531860 #> 33          0.05312271       0.40157023 0.6880003 #> 40          0.07400279      -0.04345713 0.9653371 #> 50          0.11471743       0.58686472 0.5572946 #> 60          0.15457553      -0.35823892 0.7201645 #> 70          0.19839023      -0.27864299 0.7805188 #> 80          0.24606972      -0.18791364 0.8509443 #> 90          0.30073463       0.11457610 0.9087811 #> 100         0.34879996       0.31591356 0.7520681 data(oldcol) crime <- COL.OLD$CRIME is.na(crime) <- sample(1:length(crime), 10) res <- try(globalG.test(crime, nb2listw(COL.nb, style=\"B\"),  na.action=na.fail)) #> Error in na.fail.default(x) : missing values in object res #> [1] \"Error in na.fail.default(x) : missing values in object\\n\" #> attr(,\"class\") #> [1] \"try-error\" #> attr(,\"condition\") #> <simpleError in na.fail.default(x): missing values in object> globalG.test(crime, nb2listw(COL.nb, style=\"B\"), zero.policy=TRUE,  na.action=na.omit) #> Warning: subsetting caused increase in subgraph count #>  #> \tGetis-Ord global G statistic #>  #> data:  crime  #> weights: nb2listw(COL.nb, style = \"B\")  #> omitted: 2, 3, 5, 6, 7, 10, 13, 30, 39, 49  #> n reduced by no-neighbour observations  #>  #> standard deviate = 3.8084, p-value = 6.993e-05 #> alternative hypothesis: greater #> sample estimates: #> Global G statistic        Expectation           Variance  #>       1.441233e-01       1.123755e-01       6.949287e-05  #>  globalG.test(crime, nb2listw(COL.nb, style=\"B\"), zero.policy=TRUE,  na.action=na.exclude) #> Warning: subsetting caused increase in subgraph count #>  #> \tGetis-Ord global G statistic #>  #> data:  crime  #> weights: nb2listw(COL.nb, style = \"B\")  #> omitted: 2, 3, 5, 6, 7, 10, 13, 30, 39, 49  #> n reduced by no-neighbour observations  #>  #> standard deviate = 3.8084, p-value = 6.993e-05 #> alternative hypothesis: greater #> sample estimates: #> Global G statistic        Expectation           Variance  #>       1.441233e-01       1.123755e-01       6.949287e-05  #>  try(globalG.test(crime, nb2listw(COL.nb, style=\"B\"), na.action=na.pass)) #> Error in globalG.test(crime, nb2listw(COL.nb, style = \"B\"), na.action = na.pass) :  #>   na.pass not permitted"},{"path":"https://r-spatial.github.io/spdep/reference/graphneigh.html","id":null,"dir":"Reference","previous_headings":"","what":"Graph based spatial weights — graphneigh","title":"Graph based spatial weights — graphneigh","text":"Functions return graph object containing list vertex coordinates indices defining edges. /functions assume coordinates exactly regularly spaced. helper function graph2nb converts graph object neighbour list. plot functions plot graph objects.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/graphneigh.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Graph based spatial weights — graphneigh","text":"","code":"gabrielneigh(coords, nnmult=3) relativeneigh(coords, nnmult=3) <!-- %beta.skel(coords,beta) --> soi.graph(tri.nb, coords, quadsegs=10) graph2nb(gob, row.names=NULL,sym=FALSE) # S3 method for class 'Gabriel' plot(x, show.points=FALSE, add=FALSE, linecol=par(col), ...) # S3 method for class 'relative' plot(x, show.points=FALSE, add=FALSE, linecol=par(col),...)"},{"path":"https://r-spatial.github.io/spdep/reference/graphneigh.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Graph based spatial weights — graphneigh","text":"coords matrix region point coordinates SpatialPoints object sfc points object nnmult scaling factor memory allocation, default 3; higher values required, function exit error; example thanks Dan Putler tri.nb neighbor list created tri2nb quadsegs number line segments making quarter circle buffer, see nQuadSegs argument geos_unary  gob graph object created graph funtions row.names character vector region ids added     neighbours list attribute region.id, default seq(1,       nrow(x)) sym logical argument indicating whether neighbors     symetric (->j j->) x object plotted show.points (logical) add points plot add (logical) add existing plot linecol edge plotting colour ... graphical parameters par(..)","code":""},{"path":"https://r-spatial.github.io/spdep/reference/graphneigh.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Graph based spatial weights — graphneigh","text":"graph functions produce graphs 2d point set    subgraphs Delaunay triangulation. relative neighbor graph defined relation, x y neighbors $$d(x,y) \\le min(max(d(x,z),d(y,z))| z \\S)$$ d() distance, S set points z arbitrary point S. Gabriel graph subgraph delaunay triangulation relative neighbor graph sub-graph. relative neighbor graph defined relation x y Gabriel neighbors $$d(x,y) \\le min((d(x,z)^2 + d(y,z)^2)^{1/2} |z \\S)$$ x,y,z S . sphere influence graph defined finite point set S, let \\(r_x\\) distance point x nearest neighbor S, \\(C_x\\) circle centered x. x y SOI neigbors iff \\(C_x\\) \\(C_y\\) intersect least 2 places. 2016-05-31, Computational Geometry C code replaced calls functions dbscan sf; large quadsegs= argument, behaviour function , otherwise buffer intersections closely approximate original function. See card details “nb” objects.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/graphneigh.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Graph based spatial weights — graphneigh","text":"list class Graph following elements np number input points array origin ids array destination ids nedges number edges graph x input x coordinates y input y coordinates helper functions return nb object list integer  vectors containing neighbour region number ids.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/graphneigh.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Graph based spatial weights — graphneigh","text":"Matula, D. W. Sokal R. R. 1980, Properties Gabriel   graphs relevant geographic variation research clustering   points plane, Geographic Analysis, 12(3), pp. 205-222. Toussaint, G. T. 1980, relative neighborhood graph finite   planar set, Pattern Recognition, 12(4), pp. 261-268. Kirkpatrick, D. G. Radke, J. D. 1985, framework   computational morphology. Computational Geometry,   Ed. G. T. Toussaint, North Holland.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/graphneigh.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Graph based spatial weights — graphneigh","text":"Nicholas Lewin-Koh nikko@hailmail.net","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/graphneigh.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Graph based spatial weights — graphneigh","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) sf_obj <- st_centroid(st_geometry(columbus), of_largest_polygon) sp_obj <- as(sf_obj, \"Spatial\") coords <- st_coordinates(sf_obj) suppressMessages(col.tri.nb <- tri2nb(coords)) col.gab.nb <- graph2nb(gabrielneigh(coords), sym=TRUE) col.rel.nb <- graph2nb(relativeneigh(coords), sym=TRUE) par(mfrow=c(2,2)) plot(st_geometry(columbus), border=\"grey\") plot(col.tri.nb,coords,add=TRUE) title(main=\"Delaunay Triangulation\", cex.main=0.6) plot(st_geometry(columbus), border=\"grey\") plot(col.gab.nb, coords, add=TRUE) title(main=\"Gabriel Graph\", cex.main=0.6) plot(st_geometry(columbus), border=\"grey\") plot(col.rel.nb, coords, add=TRUE) title(main=\"Relative Neighbor Graph\", cex.main=0.6) plot(st_geometry(columbus), border=\"grey\") if (require(\"dbscan\", quietly=TRUE)) {   col.soi.nb <- graph2nb(soi.graph(col.tri.nb,coords), sym=TRUE)   plot(col.soi.nb, coords, add=TRUE)   title(main=\"Sphere of Influence Graph\", cex.main=0.6) } #>  #> Attaching package: ‘dbscan’ #> The following object is masked from ‘package:stats’: #>  #>     as.dendrogram  par(mfrow=c(1,1)) col.tri.nb_sf <- tri2nb(sf_obj) all.equal(col.tri.nb, col.tri.nb_sf, check.attributes=FALSE) #> [1] TRUE col.tri.nb_sp <- tri2nb(sp_obj) all.equal(col.tri.nb, col.tri.nb_sp, check.attributes=FALSE) #> [1] TRUE if (require(\"dbscan\", quietly=TRUE)) {   col.soi.nb_sf <- graph2nb(soi.graph(col.tri.nb, sf_obj), sym=TRUE)   all.equal(col.soi.nb, col.soi.nb_sf, check.attributes=FALSE)   col.soi.nb_sp <- graph2nb(soi.graph(col.tri.nb, sp_obj), sym=TRUE)   all.equal(col.soi.nb, col.soi.nb_sp, check.attributes=FALSE) } #> [1] TRUE col.gab.nb_sp <- graph2nb(gabrielneigh(sp_obj), sym=TRUE) all.equal(col.gab.nb, col.gab.nb_sp, check.attributes=FALSE) #> [1] TRUE col.gab.nb_sf <- graph2nb(gabrielneigh(sf_obj), sym=TRUE) all.equal(col.gab.nb, col.gab.nb_sf, check.attributes=FALSE) #> [1] TRUE col.rel.nb_sp <- graph2nb(relativeneigh(sp_obj), sym=TRUE) all.equal(col.rel.nb, col.rel.nb_sp, check.attributes=FALSE) #> [1] TRUE col.rel.nb_sf <- graph2nb(relativeneigh(sf_obj), sym=TRUE) all.equal(col.rel.nb, col.rel.nb_sf, check.attributes=FALSE) #> [1] TRUE dx <- rep(0.25*0:4,5) dy <- c(rep(0,5),rep(0.25,5),rep(0.5,5), rep(0.75,5),rep(1,5)) m <- cbind(c(dx, dx, 3+dx, 3+dx), c(dy, 3+dy, dy, 3+dy)) cat(try(res <- gabrielneigh(m), silent=TRUE), \"\\n\") #> Error in gabrielneigh(m) : number of neighbours overrun - increase nnmult #>   res <- gabrielneigh(m, nnmult=4) summary(graph2nb(res)) #> Neighbour list object: #> Number of regions: 100  #> Number of nonzero links: 342  #> Percentage nonzero weights: 3.42  #> Average number of links: 3.42  #> 1 region with no links: #> 100 #> Non-symmetric neighbours list #> Link number distribution: #>  #>  0  1  2  3  4  5  #>  1  8 10 18 55  8  #> 8 least connected regions: #> 46 47 48 49 96 97 98 99 with 1 link #> 8 most connected regions: #> 10 15 20 25 30 35 40 45 with 5 links grd <- as.matrix(expand.grid(x=1:5, y=1:5)) #gridded data r2 <- gabrielneigh(grd) set.seed(1) grd1 <- as.matrix(expand.grid(x=1:5, y=1:5)) + matrix(runif(50, .0001, .0006), nrow=25) r3 <- gabrielneigh(grd1) opar <- par(mfrow=c(1,2)) plot(r2, show=TRUE, linecol=2) plot(r3, show=TRUE, linecol=2)  par(opar) # example of reading points with readr::read_csv() yielding a tibble load(system.file(\"etc/misc/coords.rda\", package=\"spdep\")) class(coords) #> [1] \"spec_tbl_df\" \"tbl_df\"      \"tbl\"         \"data.frame\"  graph2nb(gabrielneigh(coords)) #> Neighbour list object: #> Number of regions: 100  #> Number of nonzero links: 179  #> Percentage nonzero weights: 1.79  #> Average number of links: 1.79  #> 23 regions with no links: #> 22, 39, 43, 53, 58, 61, 66, 70, 71, 73, 76, 78, 81, 88, 90, 93, 94, 95, #> 96, 97, 98, 99, 100 #> Non-symmetric neighbours list graph2nb(relativeneigh(coords)) #> Neighbour list object: #> Number of regions: 100  #> Number of nonzero links: 117  #> Percentage nonzero weights: 1.17  #> Average number of links: 1.17  #> 31 regions with no links: #> 22, 29, 33, 39, 41, 42, 43, 44, 53, 58, 61, 64, 65, 66, 70, 71, 73, 75, #> 76, 78, 81, 88, 90, 93, 94, 95, 96, 97, 98, 99, 100 #> Non-symmetric neighbours list"},{"path":"https://r-spatial.github.io/spdep/reference/grid2nb.html","id":null,"dir":"Reference","previous_headings":"","what":"Construct neighbours for a GridTopology — grid2nb","title":"Construct neighbours for a GridTopology — grid2nb","text":"function builds neighbours list grid topology.   works k-dimentional grid topology, k>=1.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/grid2nb.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Construct neighbours for a GridTopology — grid2nb","text":"","code":"grid2nb(grid, d = grid@cells.dim,         queen = TRUE, nb = TRUE, self = FALSE)"},{"path":"https://r-spatial.github.io/spdep/reference/grid2nb.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Construct neighbours for a GridTopology — grid2nb","text":"grid object class GridTopology. One can avoid   supply just suplying dimentions d argument. d scalar (one dimentional grid) length k vector   specyfying number grid cells direction k   dimentions. queen Logical. Default TRUE. inform queen   neighbourhood structure considered. FALSE,   hyper-cube common face considered neighbour.   TRUE, single shared coordinate meets contiguity condition. nb Default TRUE. TRUE, return result neighbours   list class nb. FALSE, result matrix   3^k columns self = TRUE 3^k-1   self = FALSE. Zeros used hyper-cubes boundaries. self Default FALSE, indicate hyper-cube neighbour   considered neighbour.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/grid2nb.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Construct neighbours for a GridTopology — grid2nb","text":"Either matrix, “nb” FALSE neighbours list   class nb. See card details “nb”   objects.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/grid2nb.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Construct neighbours for a GridTopology — grid2nb","text":"applies k-dimentional grid topology.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/grid2nb.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Construct neighbours for a GridTopology — grid2nb","text":"Elias T Krainski eliaskrainski@gmail.com","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/grid2nb.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Construct neighbours for a GridTopology — grid2nb","text":"","code":"nb <- grid2nb(d = c(5L, 5L, 5L)) nb #> Neighbour list object: #> Number of regions: 125  #> Number of nonzero links: 2072  #> Percentage nonzero weights: 13.2608  #> Average number of links: 16.576  summary(nb) #> Neighbour list object: #> Number of regions: 125  #> Number of nonzero links: 2072  #> Percentage nonzero weights: 13.2608  #> Average number of links: 16.576  #> Link number distribution: #>  #>  7 11 17 26  #>  8 36 54 27  #> 8 least connected regions: #> 1 5 21 25 101 105 121 125 with 7 links #> 27 most connected regions: #> 32 33 34 37 38 39 42 43 44 57 58 59 62 63 64 67 68 69 82 83 84 87 88 89 92 93 94 with 26 links if (require(\"sp\", quietly=TRUE)) { gt <- GridTopology(c(.125,.1), c(.25,.2), c(4L, 5L)) nb1 <- grid2nb(gt, queen = FALSE) nb2 <- grid2nb(gt)  sg <- SpatialGrid(gt) plot(sg, lwd=3) plot(nb1, coordinates(sg), add=TRUE, lty=2, col=2, lwd=2) plot(nb2, coordinates(sg), add=TRUE, lty=3, col=4)  str(grid2nb(d=5)) }  #> List of 5 #>  $ : int 2 #>  $ : int [1:2] 1 3 #>  $ : int [1:2] 2 4 #>  $ : int [1:2] 3 5 #>  $ : int 4 #>  - attr(*, \"class\")= chr \"nb\""},{"path":"https://r-spatial.github.io/spdep/reference/hotspotmap.html","id":null,"dir":"Reference","previous_headings":"","what":"Cluster Classifications for Local Indicators of Spatial Association and Local Indicators for Categorical Data — hotspot","title":"Cluster Classifications for Local Indicators of Spatial Association and Local Indicators for Categorical Data — hotspot","text":"Used return factor showing -called cluster classification local indicators spatial association local Moran's , local Geary's C (multivariate variant) local Getis-Ord G. factor vector can added spatial object mapping. obj class licd, list six factors measures local composition (analytical permutation), local configuration (analytical permutation), combined measures, interaction composition configuration, simplified recoding .","code":""},{"path":"https://r-spatial.github.io/spdep/reference/hotspotmap.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Cluster Classifications for Local Indicators of Spatial Association and Local Indicators for Categorical Data — hotspot","text":"","code":"hotspot(obj, ...)  # Default S3 method hotspot(obj, ...)  # S3 method for class 'localmoran' hotspot(obj, Prname, cutoff=0.005, quadrant.type=\"mean\",  p.adjust=\"fdr\", droplevels=TRUE, ...) # S3 method for class 'summary.localmoransad' hotspot(obj, Prname, cutoff=0.005,  quadrant.type=\"mean\", p.adjust=\"fdr\", droplevels=TRUE, ...) # S3 method for class 'data.frame.localmoranex' hotspot(obj, Prname, cutoff=0.005,  quadrant.type=\"mean\", p.adjust=\"fdr\", droplevels=TRUE, ...)  # S3 method for class 'localG' hotspot(obj, Prname, cutoff=0.005, p.adjust=\"fdr\", droplevels=TRUE, ...)  # S3 method for class 'localC' hotspot(obj, Prname, cutoff=0.005, p.adjust=\"fdr\", droplevels=TRUE, ...) # S3 method for class 'licd' hotspot(obj, type = \"both\", cutoff = 0.05, p.adjust = \"none\",   droplevels = TRUE, control = list(), ...)"},{"path":"https://r-spatial.github.io/spdep/reference/hotspotmap.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Cluster Classifications for Local Indicators of Spatial Association and Local Indicators for Categorical Data — hotspot","text":"obj object class localmoran, localC localG Prname character string, name column containing probability values classified cluster type found “interesting” cutoff Default 0.005, probability value cutoff larger observation found “interesting” p.adjust Default \"fdr\", p.adjust() method used, one c(\"holm\", \"hochberg\", \"hommel\", \"bonferroni\", \"BH\", \"\", \"fdr\", \"none\") droplevels Default TRUE, empty levels input cluster factor dropped quadrant.type Default \"mean\", \"localmoran\" objects , can c(\"mean\", \"median\", \"pysal\") partition Moran scatterplot; \"mean\" partitions means variable spatial lag, \"median\" medians variable spatial lag, \"pysal\" zero centred variable spatial lag type obj class licd, default , may also comp local composition config local configuration control obj class licd, default binomial_sidak 2, binomial_overlap TRUE, jcm_sidak 3. binomial_overlap  may set FALSE avoid Binomial probability values summing unity - tests Boots (2003, p. 141) overlap (>= <=), Šidák exponents may set 1 prevent -observation correction 2 Binomial 3 Normal probability values per observation ... arguments passed methods.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/hotspotmap.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Cluster Classifications for Local Indicators of Spatial Association and Local Indicators for Categorical Data — hotspot","text":"factor showing -called cluster classification local indicators spatial association. obj class licd, list six factors measures local composition (analytical permutation), local configuration (analytical permutation), combined measures, interaction composition configuration, simplified recoding .","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/hotspotmap.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Cluster Classifications for Local Indicators of Spatial Association and Local Indicators for Categorical Data — hotspot","text":"Roger Bivand","code":""},{"path":"https://r-spatial.github.io/spdep/reference/hotspotmap.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Cluster Classifications for Local Indicators of Spatial Association and Local Indicators for Categorical Data — hotspot","text":"","code":"orig <- spData::africa.rook.nb listw <- nb2listw(orig) x <- spData::afcon$totcon  set.seed(1) C <- localC_perm(x, listw) Ch <- hotspot(C, Prname=\"Pr(z != E(Ci)) Sim\", cutoff=0.05, p.adjust=\"none\") table(addNA(Ch)) #>  #> High-High   Low-Low      <NA>  #>         4         1        37  set.seed(1) I <- localmoran_perm(x, listw) Ih <- hotspot(I, Prname=\"Pr(z != E(Ii)) Sim\", cutoff=0.05, p.adjust=\"none\") table(addNA(Ih)) #>  #> High-High      <NA>  #>         6        36  Is <- summary(localmoran.sad(lm(x ~ 1), nb=orig)) Ish <- hotspot(Is, Prname=\"Pr. (Sad)\", cutoff=0.05, p.adjust=\"none\") table(addNA(Ish)) #>  #> High-High      <NA>  #>         5        37  Ie <- as.data.frame(localmoran.exact(lm(x ~ 1), nb=orig)) Ieh <- hotspot(Ie, Prname=\"Pr. (exact)\", cutoff=0.05, p.adjust=\"none\") table(addNA(Ieh)) #>  #> High-High      <NA>  #>         5        37  set.seed(1) G <- localG_perm(x, listw) Gh <- hotspot(G, Prname=\"Pr(z != E(Gi)) Sim\", cutoff=0.05, p.adjust=\"none\") table(addNA(Gh)) #>  #> High <NA>  #>    6   36"},{"path":"https://r-spatial.github.io/spdep/reference/include.self.html","id":null,"dir":"Reference","previous_headings":"","what":"Include self in neighbours list — include.self","title":"Include self in neighbours list — include.self","text":"function includes region list neighbours, sets attribute \"self.included\" TRUE; remove.self reverts effects include.self.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/include.self.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Include self in neighbours list — include.self","text":"","code":"include.self(nb) remove.self(nb)"},{"path":"https://r-spatial.github.io/spdep/reference/include.self.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Include self in neighbours list — include.self","text":"nb input neighbours list class nb","code":""},{"path":"https://r-spatial.github.io/spdep/reference/include.self.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Include self in neighbours list — include.self","text":"function returns object class nb list integer vectors containing neighbour region number ids; attribute \"self.included\" set TRUE.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/include.self.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Include self in neighbours list — include.self","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/include.self.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Include self in neighbours list — include.self","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) col.gal.nb <- read.gal(system.file(\"weights/columbus.gal\", package=\"spData\")[1]) coords <- st_coordinates(st_centroid(columbus)) #> Warning: st_centroid assumes attributes are constant over geometries summary(col.gal.nb, coords) #> Neighbour list object: #> Number of regions: 49  #> Number of nonzero links: 230  #> Percentage nonzero weights: 9.579342  #> Average number of links: 4.693878  #> Link number distribution: #>  #>  2  3  4  5  6  7  8  9 10  #>  7  7 13  4  9  6  1  1  1  #> 7 least connected regions: #> 1 6 31 39 42 46 47 with 2 links #> 1 most connected region: #> 20 with 10 links summary(include.self(col.gal.nb), coords) #> Neighbour list object: #> Number of regions: 49  #> Number of nonzero links: 279  #> Percentage nonzero weights: 11.62016  #> Average number of links: 5.693878  #> Link number distribution: #>  #>  3  4  5  6  7  8  9 10 11  #>  7  7 13  4  9  6  1  1  1  #> 7 least connected regions: #> 1 6 31 39 42 46 47 with 3 links #> 1 most connected region: #> 20 with 11 links summary(remove.self(include.self(col.gal.nb)), coords) #> Neighbour list object: #> Number of regions: 49  #> Number of nonzero links: 230  #> Percentage nonzero weights: 9.579342  #> Average number of links: 4.693878  #> Link number distribution: #>  #>  2  3  4  5  6  7  8  9 10  #>  7  7 13  4  9  6  1  1  1  #> 7 least connected regions: #> 1 6 31 39 42 46 47 with 2 links #> 1 most connected region: #> 20 with 10 links"},{"path":"https://r-spatial.github.io/spdep/reference/joincount.mc.html","id":null,"dir":"Reference","previous_headings":"","what":"Permutation test for same colour join count statistics — joincount.mc","title":"Permutation test for same colour join count statistics — joincount.mc","text":"permutation test colour join count statistics calculated using nsim random permutations fx given spatial weighting scheme, establish ranks observed statistics (colour) relation nsim simulated values.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/joincount.mc.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Permutation test for same colour join count statistics — joincount.mc","text":"","code":"joincount.mc(fx, listw, nsim, zero.policy=attr(listw, \"zero.policy\"),  alternative=\"greater\", spChk=NULL)"},{"path":"https://r-spatial.github.io/spdep/reference/joincount.mc.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Permutation test for same colour join count statistics — joincount.mc","text":"fx factor length neighbours weights objects listw listw listw object created example nb2listw nsim number permutations zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA alternative character string specifying alternative hypothesis, must one \"greater\" (default), \"two.sided\", \"less\". spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption()","code":""},{"path":"https://r-spatial.github.io/spdep/reference/joincount.mc.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Permutation test for same colour join count statistics — joincount.mc","text":"list class jclist lists class htest mc.sim k colours containing following components: statistic value observed statistic. parameter rank observed statistic. method character string giving method used. data.name character string giving name(s) data. p.value pseudo p-value test. alternative character string describing alternative hypothesis. estimate mean variance simulated distribution. res nsim simulated values statistic, final element observed statistic","code":""},{"path":"https://r-spatial.github.io/spdep/reference/joincount.mc.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Permutation test for same colour join count statistics — joincount.mc","text":"Cliff, . D., Ord, J. K. 1981 Spatial processes, Pion, p. 63-5.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/joincount.mc.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Permutation test for same colour join count statistics — joincount.mc","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/joincount.mc.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Permutation test for same colour join count statistics — joincount.mc","text":"","code":"data(oldcol) HICRIME <- cut(COL.OLD$CRIME, breaks=c(0,35,80), labels=c(\"low\",\"high\")) names(HICRIME) <- rownames(COL.OLD) joincount.mc(HICRIME, nb2listw(COL.nb, style=\"B\"), nsim=99, alternative=\"two.sided\") #>  #> \tMonte-Carlo simulation of join-count statistic #>  #> data:  HICRIME  #> weights: nb2listw(COL.nb, style = \"B\")  #> number of simulations + 1: 100  #>  #> Join-count statistic for low = 34, rank of observed statistic = 88.5, #> p-value = 0.23 #> alternative hypothesis: two.sided #> sample estimates: #>     mean of simulation variance of simulation  #>               28.96970               18.19295  #>  #>  #> \tMonte-Carlo simulation of join-count statistic #>  #> data:  HICRIME  #> weights: nb2listw(COL.nb, style = \"B\")  #> number of simulations + 1: 100  #>  #> Join-count statistic for high = 54, rank of observed statistic = 100, #> p-value < 2.2e-16 #> alternative hypothesis: two.sided #> sample estimates: #>     mean of simulation variance of simulation  #>               26.83838               20.13688  #>  joincount.test(HICRIME, nb2listw(COL.nb, style=\"B\"), alternative=\"two.sided\") #>  #> \tJoin count test under nonfree sampling #>  #> data:  HICRIME  #> weights: nb2listw(COL.nb, style = \"B\")  #>  #> Std. deviate for low = 1.0141, p-value = 0.3105 #> alternative hypothesis: two.sided #> sample estimates: #> Same colour statistic           Expectation              Variance  #>              34.00000              29.59184              18.89550  #>  #>  #> \tJoin count test under nonfree sampling #>  #> data:  HICRIME  #> weights: nb2listw(COL.nb, style = \"B\")  #>  #> Std. deviate for high = 6.3307, p-value = 2.44e-10 #> alternative hypothesis: two.sided #> sample estimates: #> Same colour statistic           Expectation              Variance  #>              54.00000              27.22449              17.88838  #>"},{"path":"https://r-spatial.github.io/spdep/reference/joincount.multi.html","id":null,"dir":"Reference","previous_headings":"","what":"BB, BW and Jtot join count statistic for k-coloured factors — joincount.multi","title":"BB, BW and Jtot join count statistic for k-coloured factors — joincount.multi","text":"function tallying join counts -colour different colour spatial objects, neighbour relations defined weights list. Given global counts colour, expected counts variances calculated non-free sampling, z-value reported. Since multiple tests reported, p-values given, allowing user adjust significance level applied. Jtot count different-colour joins.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/joincount.multi.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"BB, BW and Jtot join count statistic for k-coloured factors — joincount.multi","text":"","code":"joincount.multi(fx, listw, zero.policy = attr(listw, \"zero.policy\"),  spChk = NULL, adjust.n=TRUE) # S3 method for class 'jcmulti' print(x, ...)"},{"path":"https://r-spatial.github.io/spdep/reference/joincount.multi.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"BB, BW and Jtot join count statistic for k-coloured factors — joincount.multi","text":"fx factor length neighbours weights objects listw listw listw object created example nb2listw zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA adjust.n default TRUE, FALSE number observations adjusted -neighbour observations, TRUE, number observations adjusted consistently (including spdep 0.3-28 adjustment inconsistent - thanks Tomoki NAKAYA careful bug report) spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption() x object printed ... arguments passed printing","code":""},{"path":"https://r-spatial.github.io/spdep/reference/joincount.multi.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"BB, BW and Jtot join count statistic for k-coloured factors — joincount.multi","text":"matrix class jcmulti row column names observed expected counts, variance, z-value.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/joincount.multi.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"BB, BW and Jtot join count statistic for k-coloured factors — joincount.multi","text":"Cliff, . D., Ord, J. K. 1981 Spatial processes, Pion, p. 20; Upton, G., Fingleton, B. 1985 Spatial data analysis example: point pattern qualitative data, Wiley, pp. 158–170.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/joincount.multi.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"BB, BW and Jtot join count statistic for k-coloured factors — joincount.multi","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/joincount.multi.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"BB, BW and Jtot join count statistic for k-coloured factors — joincount.multi","text":"derivation test (Cliff Ord, 1981, p. 18) assumes weights matrix symmetric. inherently non-symmetric matrices, k-nearest neighbour matrices, listw2U() can used make matrix symmetric. non-symmetric weights matrix cases, variance test statistic may negative.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/joincount.multi.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"BB, BW and Jtot join count statistic for k-coloured factors — joincount.multi","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) HICRIME <- cut(columbus$CRIME, breaks=c(0,35,80), labels=c(\"low\",\"high\")) (nb <- poly2nb(columbus)) #> Neighbour list object: #> Number of regions: 49  #> Number of nonzero links: 236  #> Percentage nonzero weights: 9.829238  #> Average number of links: 4.816327  lw <- nb2listw(nb, style=\"B\") joincount.multi(HICRIME, lw) #>           Joincount Expected Variance z-value #> low:low      35.000   30.102   19.247  1.1164 #> high:high    54.000   27.694   18.219  6.1630 #> high:low     29.000   60.204   26.630 -6.0468 #> Jtot         29.000   60.204   26.630 -6.0468 col_geoms <- st_geometry(columbus) col_geoms[21] <- st_buffer(col_geoms[21], dist=-0.05) st_geometry(columbus) <- col_geoms (nb <- poly2nb(columbus)) #> Warning: some observations have no neighbours; #> if this seems unexpected, try increasing the snap argument. #> Warning: neighbour object has 3 sub-graphs; #> if this sub-graph count seems unexpected, try increasing the snap argument. #> Neighbour list object: #> Number of regions: 49  #> Number of nonzero links: 230  #> Percentage nonzero weights: 9.579342  #> Average number of links: 4.693878  #> 1 region with no links: #> 21 #> 3 disjoint connected subgraphs lw <- nb2listw(nb, style=\"B\", zero.policy=TRUE) joincount.multi(HICRIME, lw) #>           Joincount Expected Variance z-value #> low:low      35.000   30.585   19.350  1.0036 #> high:high    52.000   28.138   18.342  5.5716 #> high:low     28.000   61.170   25.882 -6.5200 #> Jtot         28.000   61.170   33.190 -5.7577 # \\dontrun{ data(oldcol) HICRIME <- cut(COL.OLD$CRIME, breaks=c(0,35,80), labels=c(\"low\",\"high\")) names(HICRIME) <- rownames(COL.OLD) joincount.multi(HICRIME, nb2listw(COL.nb, style=\"B\")) #>           Joincount Expected Variance z-value #> low:low      34.000   29.592   18.895  1.0141 #> high:high    54.000   27.224   17.888  6.3307 #> high:low     28.000   59.184   26.233 -6.0884 #> Jtot         28.000   59.184   26.233 -6.0884 data(hopkins, package=\"spData\") image(1:32, 1:32, hopkins[5:36,36:5], breaks=c(-0.5, 3.5, 20),  col=c(\"white\", \"black\")) box()  hopkins.rook.nb <- cell2nb(32, 32, type=\"rook\") unlist(spweights.constants(nb2listw(hopkins.rook.nb, style=\"B\"))) #>       n      n1      n2      n3      nn      S0      S1      S2  #>    1024    1023    1022    1021 1048576    3968    7936   61984  hopkins.queen.nb <- cell2nb(32, 32, type=\"queen\") hopkins.bishop.nb <- diffnb(hopkins.rook.nb, hopkins.queen.nb, verbose=FALSE) #> Warning: neighbour object has 2 sub-graphs hopkins4 <- hopkins[5:36,36:5] hopkins4[which(hopkins4 > 3, arr.ind=TRUE)] <- 4 hopkins4.f <- factor(hopkins4) table(hopkins4.f) #> hopkins4.f #>   0   1   2   3   4  #> 657 215  98  30  24  joincount.multi(hopkins4.f, nb2listw(hopkins.rook.nb, style=\"B\")) #>       Joincount   Expected   Variance z-value #> 0:0   864.00000  816.27273  116.05233  4.4304 #> 1:1    94.00000   87.14015   55.25216  0.9229 #> 2:2    18.00000   18.00379   14.81562 -0.0010 #> 3:3     2.00000    1.64773    1.55539  0.2825 #> 4:4     5.00000    1.04545    0.99845  3.9576 #> 1:0   503.00000  535.05682  227.76750 -2.1241 #> 2:0   213.00000  243.88636   97.21769 -3.1325 #> 2:1    99.00000   79.81061   59.01930  2.4978 #> 3:0    61.00000   74.65909   28.58592 -2.5547 #> 3:1    28.00000   24.43182   18.99976  0.8186 #> 3:2    15.00000   11.13636    9.82411  1.2327 #> 4:0    40.00000   59.72727   22.78583 -4.1327 #> 4:1    23.00000   19.54545   15.26564  0.8842 #> 4:2    14.00000    8.90909    7.90051  1.8112 #> 4:3     5.00000    2.72727    2.58616  1.4133 #> Jtot 1001.00000 1059.89015  273.78610 -3.5591 cat(\"replicates Upton & Fingleton table 3.4 (p. 166)\\n\") #> replicates Upton & Fingleton table 3.4 (p. 166) joincount.multi(hopkins4.f, nb2listw(hopkins.bishop.nb, style=\"B\")) #>       Joincount   Expected   Variance z-value #> 0:0   823.00000  790.76420  144.44877  2.6821 #> 1:1   101.00000   84.41702   55.98143  2.2164 #> 2:2    19.00000   17.44117   14.61542  0.4077 #> 3:3     3.00000    1.59624    1.51444  1.1407 #> 4:4     3.00000    1.01278    0.97111  2.0166 #> 1:0   497.00000  518.33629  234.93545 -1.3920 #> 2:0   216.00000  236.26491  104.42142 -1.9831 #> 2:1    81.00000   77.31652   58.70829  0.4807 #> 3:0    58.00000   72.32599   31.49151 -2.5529 #> 3:1    21.00000   23.66832   18.85316 -0.6145 #> 3:2    17.00000   10.78835    9.62487  2.0022 #> 4:0    48.00000   57.86080   25.15973 -1.9659 #> 4:1    21.00000   18.93466   15.14473  0.5307 #> 4:2    10.00000    8.63068    7.73708  0.4923 #> 4:3     4.00000    2.64205    2.51686  0.8560 #> Jtot  973.00000 1026.76858  284.51030 -3.1877 cat(\"replicates Upton & Fingleton table 3.6 (p. 168)\\n\") #> replicates Upton & Fingleton table 3.6 (p. 168) joincount.multi(hopkins4.f, nb2listw(hopkins.queen.nb, style=\"B\")) #>      Joincount  Expected  Variance z-value #> 0:0  1687.0000 1607.0369  303.8034  4.5877 #> 1:1   195.0000  171.5572  114.2057  2.1936 #> 2:2    37.0000   35.4450   29.6821  0.2854 #> 3:3     5.0000    3.2440    3.0687  1.0024 #> 4:4     8.0000    2.0582    1.9674  4.2361 #> 1:0  1000.0000 1053.3931  480.6959 -2.4353 #> 2:0   429.0000  480.1513  215.0360 -3.4882 #> 2:1   180.0000  157.1271  119.3987  2.0932 #> 3:0   119.0000  146.9851   65.1029 -3.4684 #> 3:1    49.0000   48.1001   38.3268  0.1454 #> 3:2    32.0000   21.9247   19.5237  2.2802 #> 4:0    88.0000  117.5881   52.0312 -4.1019 #> 4:1    44.0000   38.4801   30.7868  0.9948 #> 4:2    24.0000   17.5398   15.6933  1.6308 #> 4:3     9.0000    5.3693    5.0994  1.6078 #> Jtot 1974.0000 2086.6587  582.8326 -4.6665 cat(\"replicates Upton & Fingleton table 3.7 (p. 169)\\n\") #> replicates Upton & Fingleton table 3.7 (p. 169) # } GDAL37 <- as.numeric_version(unname(sf_extSoftVersion()[\"GDAL\"])) >= \"3.7.0\" file <- \"etc/shapes/GB_2024_southcoast_50m.gpkg.zip\" zipfile <- system.file(file, package=\"spdep\") if (GDAL37) {     sc50m <- st_read(zipfile) } else {     td <- tempdir()     bn <- sub(\".zip\", \"\", basename(file), fixed=TRUE)     target <- unzip(zipfile, files=bn, exdir=td)     sc50m <- st_read(target) } #> Reading layer `GB_2024_southcoast_50m' from data source  #>   `/tmp/RtmpzEChJG/temp_libpath8ee3b7c361c1e/spdep/etc/shapes/GB_2024_southcoast_50m.gpkg.zip'  #>   using driver `GPKG' #> Simple feature collection with 119 features and 19 fields #> Geometry type: MULTIPOLYGON #> Dimension:     XY #> Bounding box:  xmin: 82643.12 ymin: 5342.9 xmax: 640301.6 ymax: 187226.2 #> Projected CRS: OSGB36 / British National Grid sc50m$Winner <- factor(sc50m$Winner, levels=c(\"Con\", \"Green\", \"Lab\", \"LD\")) plot(sc50m[,\"Winner\"], pal=c(\"#2297E6\", \"#61D04F\", \"#DF536B\", \"#F5C710\"))  nb_sc_50m <- poly2nb(sc50m, row.names=as.character(sc50m$Constituency)) #> Warning: neighbour object has 2 sub-graphs; #> if this sub-graph count seems unexpected, try increasing the snap argument. sub2 <- attr(nb_sc_50m, \"region.id\")[attr(nb_sc_50m, \"ncomp\")$comp.id == 2L] iowe <- match(sub2[1], attr(nb_sc_50m, \"region.id\")) diowe <- c(st_distance(sc50m[iowe,], sc50m)) meet_criterion <- sum(diowe <= units::set_units(5000, \"m\")) cands <- attr(nb_sc_50m, \"region.id\")[order(diowe)[1:meet_criterion]] nb_sc_50m_iowe <- addlinks1(nb_sc_50m, from = cands[1],  to = cands[3:meet_criterion]) ioww <- match(sub2[2], attr(nb_sc_50m, \"region.id\")) dioww <- c(st_distance(sc50m[ioww,], sc50m)) meet_criterion <- sum(dioww <= units::set_units(5000, \"m\")) cands <- attr(nb_sc_50m, \"region.id\")[order(dioww)[1:meet_criterion]] nb_sc_50m_iow <- addlinks1(nb_sc_50m_iowe, from = cands[2], to = cands[3:meet_criterion]) nb_sc_1_2 <- nblag_cumul(nblag(nb_sc_50m_iow, 2)) joincount.multi(sc50m$Winner, nb2listw(nb_sc_1_2, style=\"B\")) #>             Joincount Expected Variance z-value #> Con:Con      146.0000  84.4324 116.3530  5.7077 #> Green:Green    0.0000   0.0000   0.0000     NaN #> Lab:Lab       63.0000  98.1057 136.0379 -3.0099 #> LD:LD        100.0000  75.8866 103.9440  2.3651 #> Green:Con      4.0000   4.4438   5.8532 -0.1834 #> Lab:Con      184.0000 186.6401 180.9233 -0.1963 #> Lab:Green      3.0000   4.7856   6.4663 -0.7022 #> LD:Con       198.0000 164.4210 166.3583  2.6034 #> LD:Green       4.0000   4.2159   5.4573 -0.0924 #> LD:Lab        98.0000 177.0688 175.2035 -5.9736 #> Jtot         491.0000 541.5753 153.6123 -4.0806"},{"path":"https://r-spatial.github.io/spdep/reference/joincount.test.html","id":null,"dir":"Reference","previous_headings":"","what":"BB join count statistic for k-coloured factors — joincount.test","title":"BB join count statistic for k-coloured factors — joincount.test","text":"BB join count test spatial autocorrelation using spatial weights matrix weights list form testing whether -colour joins occur frequently expected zones labelled spatially random way. assumptions underlying test sensitive form graph neighbour relationships factors, results may checked joincount.mc permutations.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/joincount.test.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"BB join count statistic for k-coloured factors — joincount.test","text":"","code":"joincount.test(fx, listw, zero.policy=attr(listw, \"zero.policy\"), alternative=\"greater\",  sampling=\"nonfree\", spChk=NULL, adjust.n=TRUE) # S3 method for class 'jclist' print(x, ...)"},{"path":"https://r-spatial.github.io/spdep/reference/joincount.test.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"BB join count statistic for k-coloured factors — joincount.test","text":"fx factor length neighbours weights objects listw listw listw object created example nb2listw zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA alternative character string specifying alternative hypothesis, must one \"greater\" (default), \"less\" \"two.sided\". sampling default “nonfree”, may “free” adjust.n default TRUE, FALSE number observations adjusted -neighbour observations, TRUE, number observations adjusted consistently (including spdep 0.3-28 adjustment inconsistent - thanks Tomoki NAKAYA careful bug report) spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption() x object printed ... arguments passed printing","code":""},{"path":"https://r-spatial.github.io/spdep/reference/joincount.test.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"BB join count statistic for k-coloured factors — joincount.test","text":"list class jclist lists class htest k colours containing following components: statistic value standard deviate join count statistic. p.value p-value test. estimate value observed statistic, expectation variance non-free sampling. alternative character string describing alternative hypothesis. method character string giving method used. data.name character string giving name(s) data.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/joincount.test.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"BB join count statistic for k-coloured factors — joincount.test","text":"Cliff, . D., Ord, J. K. 1981 Spatial processes, Pion, pp. 19-20.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/joincount.test.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"BB join count statistic for k-coloured factors — joincount.test","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/joincount.test.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"BB join count statistic for k-coloured factors — joincount.test","text":"derivation test (Cliff Ord, 1981, p. 18) assumes weights matrix symmetric. inherently non-symmetric matrices, k-nearest neighbour matrices, listw2U() can used make matrix symmetric. non-symmetric weights matrix cases, variance test statistic may negative.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/joincount.test.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"BB join count statistic for k-coloured factors — joincount.test","text":"","code":"data(oldcol) HICRIME <- cut(COL.OLD$CRIME, breaks=c(0,35,80), labels=c(\"low\",\"high\")) names(HICRIME) <- rownames(COL.OLD) joincount.test(HICRIME, nb2listw(COL.nb, style=\"B\")) #>  #> \tJoin count test under nonfree sampling #>  #> data:  HICRIME  #> weights: nb2listw(COL.nb, style = \"B\")  #>  #> Std. deviate for low = 1.0141, p-value = 0.1553 #> alternative hypothesis: greater #> sample estimates: #> Same colour statistic           Expectation              Variance  #>              34.00000              29.59184              18.89550  #>  #>  #> \tJoin count test under nonfree sampling #>  #> data:  HICRIME  #> weights: nb2listw(COL.nb, style = \"B\")  #>  #> Std. deviate for high = 6.3307, p-value = 1.22e-10 #> alternative hypothesis: greater #> sample estimates: #> Same colour statistic           Expectation              Variance  #>              54.00000              27.22449              17.88838  #>  joincount.test(HICRIME, nb2listw(COL.nb, style=\"B\"), sampling=\"free\") #>  #> \tJoin count test under free sampling #>  #> data:  HICRIME  #> weights: nb2listw(COL.nb, style = \"B\")  #>  #> Std. deviate for low = 0.3993, p-value = 0.3448 #> alternative hypothesis: greater #> sample estimates: #> Same colour statistic           Expectation              Variance  #>              34.00000              30.19575              90.76809  #>  #>  #> \tJoin count test under free sampling #>  #> data:  HICRIME  #> weights: nb2listw(COL.nb, style = \"B\")  #>  #> Std. deviate for high = 2.8518, p-value = 0.002173 #> alternative hypothesis: greater #> sample estimates: #> Same colour statistic           Expectation              Variance  #>               54.0000               27.8284               84.2198  #>  joincount.test(HICRIME, nb2listw(COL.nb, style=\"C\")) #>  #> \tJoin count test under nonfree sampling #>  #> data:  HICRIME  #> weights: nb2listw(COL.nb, style = \"C\")  #>  #> Std. deviate for low = 1.0141, p-value = 0.1553 #> alternative hypothesis: greater #> sample estimates: #> Same colour statistic           Expectation              Variance  #>             7.1810345             6.2500000             0.8428969  #>  #>  #> \tJoin count test under nonfree sampling #>  #> data:  HICRIME  #> weights: nb2listw(COL.nb, style = \"C\")  #>  #> Std. deviate for high = 6.3307, p-value = 1.22e-10 #> alternative hypothesis: greater #> sample estimates: #> Same colour statistic           Expectation              Variance  #>            11.4051724             5.7500000             0.7979712  #>  joincount.test(HICRIME, nb2listw(COL.nb, style=\"S\")) #>  #> \tJoin count test under nonfree sampling #>  #> data:  HICRIME  #> weights: nb2listw(COL.nb, style = \"S\")  #>  #> Std. deviate for low = 2.5786, p-value = 0.00496 #> alternative hypothesis: greater #> sample estimates: #> Same colour statistic           Expectation              Variance  #>             8.2425673             6.2500000             0.5971141  #>  #>  #> \tJoin count test under nonfree sampling #>  #> data:  HICRIME  #> weights: nb2listw(COL.nb, style = \"S\")  #>  #> Std. deviate for high = 6.1736, p-value = 3.337e-10 #> alternative hypothesis: greater #> sample estimates: #> Same colour statistic           Expectation              Variance  #>            10.4249914             5.7500000             0.5734265  #>  joincount.test(HICRIME, nb2listw(COL.nb, style=\"W\")) #>  #> \tJoin count test under nonfree sampling #>  #> data:  HICRIME  #> weights: nb2listw(COL.nb, style = \"W\")  #>  #> Std. deviate for low = 4.6675, p-value = 1.524e-06 #> alternative hypothesis: greater #> sample estimates: #> Same colour statistic           Expectation              Variance  #>             9.5190476             6.2500000             0.4905378  #>  #>  #> \tJoin count test under nonfree sampling #>  #> data:  HICRIME  #> weights: nb2listw(COL.nb, style = \"W\")  #>  #> Std. deviate for high = 5.1205, p-value = 1.523e-07 #> alternative hypothesis: greater #> sample estimates: #> Same colour statistic           Expectation              Variance  #>             9.2920635             5.7500000             0.4784979  #>  by(card(COL.nb), HICRIME, summary) #> HICRIME: low #>    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.  #>    2.00    2.00    4.00    3.84    4.00   10.00  #> ------------------------------------------------------------  #> HICRIME: high #>    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.  #>   3.000   4.750   6.000   5.667   7.000   9.000  print(is.symmetric.nb(COL.nb)) #> [1] TRUE coords.OLD <- cbind(COL.OLD$X, COL.OLD$Y) COL.k4.nb <- knn2nb(knearneigh(coords.OLD, 4)) print(is.symmetric.nb(COL.k4.nb)) #> [1] FALSE joincount.test(HICRIME, nb2listw(COL.k4.nb, style=\"B\")) #>  #> \tJoin count test under nonfree sampling #>  #> data:  HICRIME  #> weights: nb2listw(COL.k4.nb, style = \"B\")  #>  #> Std. deviate for low = 4.3698, p-value = 6.217e-06 #> alternative hypothesis: greater #> sample estimates: #> Same colour statistic           Expectation              Variance  #>             36.500000             25.000000              6.925749  #>  #>  #> \tJoin count test under nonfree sampling #>  #> data:  HICRIME  #> weights: nb2listw(COL.k4.nb, style = \"B\")  #>  #> Std. deviate for high = 6.7293, p-value = 8.523e-12 #> alternative hypothesis: greater #> sample estimates: #> Same colour statistic           Expectation              Variance  #>             40.500000             23.000000              6.762918  #>  cat(\"Note non-symmetric weights matrix - use listw2U()\\n\") #> Note non-symmetric weights matrix - use listw2U() joincount.test(HICRIME, listw2U(nb2listw(COL.k4.nb, style=\"B\"))) #>  #> \tJoin count test under nonfree sampling #>  #> data:  HICRIME  #> weights: listw2U(nb2listw(COL.k4.nb, style = \"B\"))  #>  #> Std. deviate for low = 4.3698, p-value = 6.217e-06 #> alternative hypothesis: greater #> sample estimates: #> Same colour statistic           Expectation              Variance  #>             36.500000             25.000000              6.925749  #>  #>  #> \tJoin count test under nonfree sampling #>  #> data:  HICRIME  #> weights: listw2U(nb2listw(COL.k4.nb, style = \"B\"))  #>  #> Std. deviate for high = 6.7293, p-value = 8.523e-12 #> alternative hypothesis: greater #> sample estimates: #> Same colour statistic           Expectation              Variance  #>             40.500000             23.000000              6.762918  #>  columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) HICRIME <- cut(columbus$CRIME, breaks=c(0,35,80), labels=c(\"low\",\"high\")) (nb <- poly2nb(columbus)) #> Neighbour list object: #> Number of regions: 49  #> Number of nonzero links: 236  #> Percentage nonzero weights: 9.829238  #> Average number of links: 4.816327  lw <- nb2listw(nb, style=\"B\") joincount.test(HICRIME, lw) #>  #> \tJoin count test under nonfree sampling #>  #> data:  HICRIME  #> weights: lw  #>  #> Std. deviate for low = 1.1164, p-value = 0.1321 #> alternative hypothesis: greater #> sample estimates: #> Same colour statistic           Expectation              Variance  #>              35.00000              30.10204              19.24708  #>  #>  #> \tJoin count test under nonfree sampling #>  #> data:  HICRIME  #> weights: lw  #>  #> Std. deviate for high = 6.163, p-value = 3.57e-10 #> alternative hypothesis: greater #> sample estimates: #> Same colour statistic           Expectation              Variance  #>              54.00000              27.69388              18.21936  #>  col_geoms <- st_geometry(columbus) col_geoms[21] <- st_buffer(col_geoms[21], dist=-0.05) st_geometry(columbus) <- col_geoms (nb <- poly2nb(columbus)) #> Warning: some observations have no neighbours; #> if this seems unexpected, try increasing the snap argument. #> Warning: neighbour object has 3 sub-graphs; #> if this sub-graph count seems unexpected, try increasing the snap argument. #> Neighbour list object: #> Number of regions: 49  #> Number of nonzero links: 230  #> Percentage nonzero weights: 9.579342  #> Average number of links: 4.693878  #> 1 region with no links: #> 21 #> 3 disjoint connected subgraphs lw <- nb2listw(nb, style=\"B\", zero.policy=TRUE) joincount.test(HICRIME, lw) #>  #> \tJoin count test under nonfree sampling #>  #> data:  HICRIME  #> weights: lw  #>  #> Std. deviate for low = 1.0036, p-value = 0.1578 #> alternative hypothesis: greater #> sample estimates: #> Same colour statistic           Expectation              Variance  #>              35.00000              30.58511              19.35032  #>  #>  #> \tJoin count test under nonfree sampling #>  #> data:  HICRIME  #> weights: lw  #>  #> Std. deviate for high = 5.5716, p-value = 1.262e-08 #> alternative hypothesis: greater #> sample estimates: #> Same colour statistic           Expectation              Variance  #>              52.00000              28.13830              18.34187  #>"},{"path":"https://r-spatial.github.io/spdep/reference/knearneigh.html","id":null,"dir":"Reference","previous_headings":"","what":"K nearest neighbours for spatial weights — knearneigh","title":"K nearest neighbours for spatial weights — knearneigh","text":"function returns matrix indices points belonging set k nearest neighbours . longlat = TRUE, Great Circle distances used. warning given identical points found.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/knearneigh.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"K nearest neighbours for spatial weights — knearneigh","text":"","code":"knearneigh(x, k=1, longlat = NULL, use_kd_tree=TRUE)"},{"path":"https://r-spatial.github.io/spdep/reference/knearneigh.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"K nearest neighbours for spatial weights — knearneigh","text":"x matrix point coordinates, object inheriting SpatialPoints \"sf\" \"sfc\" object; \"sf\" \"sfc\" object geometries geographical coordinates (sf::st_is_longlat(x) == TRUE sf::sf_use_s2() == TRUE), s2 used find neighbours uses spatial indexing https://github.com/r-spatial/s2/issues/125 opposed legacy method uses brute-force k number nearest neighbours returned; identical points present, k least large largest count identical points (k smaller, error occur s2 used) longlat TRUE point coordinates longitude-latitude decimal degrees, case distances measured kilometers; x SpatialPoints object, value taken object ; longlat override kd_tree use_kd_tree logical value, dbscan package available, use finding k nearest neighbours longlat FALSE, identical points; https://github.com/r-spatial/spdep/issues/38, input data may two columns dbscan used","code":""},{"path":"https://r-spatial.github.io/spdep/reference/knearneigh.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"K nearest neighbours for spatial weights — knearneigh","text":"underlying legacy C code based knn function class package.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/knearneigh.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"K nearest neighbours for spatial weights — knearneigh","text":"list class knn nn integer matrix region number ids np number input points k input required k dimension number columns x x input coordinates","code":""},{"path":"https://r-spatial.github.io/spdep/reference/knearneigh.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"K nearest neighbours for spatial weights — knearneigh","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/knearneigh.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"K nearest neighbours for spatial weights — knearneigh","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) coords <- st_centroid(st_geometry(columbus), of_largest_polygon=TRUE) col.knn <- knearneigh(coords, k=4) plot(st_geometry(columbus), border=\"grey\") plot(knn2nb(col.knn), coords, add=TRUE) title(main=\"K nearest neighbours, k = 4\")  data(state) us48.fipsno <- read.geoda(system.file(\"etc/weights/us48.txt\",  package=\"spdep\")[1]) if (as.numeric(paste(version$major, version$minor, sep=\"\")) < 19) {  m50.48 <- match(us48.fipsno$\"State.name\", state.name) } else {  m50.48 <- match(us48.fipsno$\"State_name\", state.name) } xy <- as.matrix(as.data.frame(state.center))[m50.48,] llk4.nb <- knn2nb(knearneigh(xy, k=4, longlat=FALSE)) gck4.nb <- knn2nb(knearneigh(xy, k=4, longlat=TRUE)) plot(llk4.nb, xy) plot(diffnb(llk4.nb, gck4.nb), xy, add=TRUE, col=\"red\", lty=2) #> Warning: neighbour object has 22 sub-graphs title(main=\"Differences between Euclidean and Great Circle k=4 neighbours\")  summary(llk4.nb, xy, longlat=TRUE, scale=0.5) #> Neighbour list object: #> Number of regions: 48  #> Number of nonzero links: 192  #> Percentage nonzero weights: 8.333333  #> Average number of links: 4  #> Non-symmetric neighbours list #> Link number distribution: #>  #>  4  #> 48  #> 48 least connected regions: #> 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 with 4 links #> 48 most connected regions: #> 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 with 4 links summary(gck4.nb, xy, longlat=TRUE, scale=0.5) #> Neighbour list object: #> Number of regions: 48  #> Number of nonzero links: 192  #> Percentage nonzero weights: 8.333333  #> Average number of links: 4  #> Non-symmetric neighbours list #> Link number distribution: #>  #>  4  #> 48  #> 48 least connected regions: #> 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 with 4 links #> 48 most connected regions: #> 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 with 4 links  #xy1 <- SpatialPoints((as.data.frame(state.center))[m50.48,], #  proj4string=CRS(\"+proj=longlat +ellps=GRS80\")) #gck4a.nb <- knn2nb(knearneigh(xy1, k=4)) #summary(gck4a.nb, xy1, scale=0.5)  xy1 <- st_as_sf((as.data.frame(state.center))[m50.48,], coords=1:2,   crs=st_crs(\"OGC:CRS84\")) old_use_s2 <- sf_use_s2() sf_use_s2(TRUE) system.time(gck4a.nb <- knn2nb(knearneigh(xy1, k=4))) #>    user  system elapsed  #>   0.014   0.000   0.014  summary(gck4a.nb, xy1, scale=0.5) #> Neighbour list object: #> Number of regions: 48  #> Number of nonzero links: 192  #> Percentage nonzero weights: 8.333333  #> Average number of links: 4  #> Non-symmetric neighbours list #> Link number distribution: #>  #>  4  #> 48  #> 48 least connected regions: #> 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 with 4 links #> 48 most connected regions: #> 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 with 4 links sf_use_s2(FALSE) #> Spherical geometry (s2) switched off system.time(gck4a.nb <- knn2nb(knearneigh(xy1, k=4))) #>    user  system elapsed  #>   0.008   0.000   0.009  summary(gck4a.nb, xy1, scale=0.5) #> Neighbour list object: #> Number of regions: 48  #> Number of nonzero links: 192  #> Percentage nonzero weights: 8.333333  #> Average number of links: 4  #> Non-symmetric neighbours list #> Link number distribution: #>  #>  4  #> 48  #> 48 least connected regions: #> 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 with 4 links #> 48 most connected regions: #> 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 with 4 links sf_use_s2(old_use_s2) #> Spherical geometry (s2) switched on  # https://github.com/r-spatial/spdep/issues/38 if (require(\"dbscan\", quietly=TRUE)) {   set.seed(1)   x <- cbind(runif(50), runif(50), runif(50))   out <- knearneigh(x, k=5)   knn2nb(out)   try(out <- knearneigh(rbind(x, x[1:10,]), k=5)) } #> Warning: knearneigh: identical points found #> Warning: knearneigh: kd_tree not available for identical points #> Error in knearneigh(rbind(x, x[1:10, ]), k = 5) :  #>   kd_tree required for more than 2 dimensions"},{"path":"https://r-spatial.github.io/spdep/reference/knn2nb.html","id":null,"dir":"Reference","previous_headings":"","what":"Neighbours list from knn object — knn2nb","title":"Neighbours list from knn object — knn2nb","text":"function converts knn object returned knearneigh neighbours list class nb list integer vectors containing neighbour region number ids.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/knn2nb.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Neighbours list from knn object — knn2nb","text":"","code":"knn2nb(knn, row.names = NULL, sym = FALSE)"},{"path":"https://r-spatial.github.io/spdep/reference/knn2nb.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Neighbours list from knn object — knn2nb","text":"knn knn object returned knearneigh row.names character vector region ids added neighbours list attribute region.id, default seq(1, nrow(x)) sym force output neighbours list symmetry","code":""},{"path":"https://r-spatial.github.io/spdep/reference/knn2nb.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Neighbours list from knn object — knn2nb","text":"function returns object class nb list integer vectors containing neighbour region number ids. See card details “nb” objects.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/knn2nb.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Neighbours list from knn object — knn2nb","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/knn2nb.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Neighbours list from knn object — knn2nb","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) coords <- st_coordinates(st_centroid(columbus)) #> Warning: st_centroid assumes attributes are constant over geometries col.knn <- knearneigh(coords, k=4) plot(st_geometry(columbus), border=\"grey\") plot(knn2nb(col.knn), coords, add=TRUE) title(main=\"K nearest neighbours, k = 4\")  # example of reading points with readr::read_csv() yielding a tibble load(system.file(\"etc/misc/coords.rda\", package=\"spdep\")) class(coords) #> [1] \"spec_tbl_df\" \"tbl_df\"      \"tbl\"         \"data.frame\"  knn2nb(knearneigh(coords, k=4)) #> Neighbour list object: #> Number of regions: 100  #> Number of nonzero links: 400  #> Percentage nonzero weights: 4  #> Average number of links: 4  #> Non-symmetric neighbours list"},{"path":"https://r-spatial.github.io/spdep/reference/lag.listw.html","id":null,"dir":"Reference","previous_headings":"","what":"Spatial lag of a numeric vector — lag.listw","title":"Spatial lag of a numeric vector — lag.listw","text":"Using listw sparse representation spatial weights matrix, compute lag vector \\(V x\\)","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lag.listw.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Spatial lag of a numeric vector — lag.listw","text":"","code":"# S3 method for class 'listw' lag(x, var, zero.policy=attr(listw, \"zero.policy\"), NAOK=FALSE, ...)"},{"path":"https://r-spatial.github.io/spdep/reference/lag.listw.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Spatial lag of a numeric vector — lag.listw","text":"x listw object created example nb2listw var numeric vector length neighbours list listw zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA NAOK 'FALSE', presence 'NA' values regarded error; 'TRUE' 'NA' 'NaN' 'Inf' values var represented NA lagged value. ... additional arguments","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lag.listw.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Spatial lag of a numeric vector — lag.listw","text":"numeric vector length var","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lag.listw.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Spatial lag of a numeric vector — lag.listw","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/lag.listw.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Spatial lag of a numeric vector — lag.listw","text":"","code":"data(oldcol) Vx <- lag.listw(nb2listw(COL.nb, style=\"W\"), COL.OLD$CRIME) plot(Vx, COL.OLD$CRIME)  plot(ecdf(COL.OLD$CRIME)) plot(ecdf(Vx), add=TRUE, col.points=\"red\", col.hor=\"red\")  is.na(COL.OLD$CRIME[5]) <- TRUE VxNA <- lag.listw(nb2listw(COL.nb, style=\"W\"), COL.OLD$CRIME, NAOK=TRUE) #> Warning: NAs in lagged values"},{"path":"https://r-spatial.github.io/spdep/reference/lee.html","id":null,"dir":"Reference","previous_headings":"","what":"Compute Lee's statistic — lee","title":"Compute Lee's statistic — lee","text":"simple function compute Lee's L statistic bivariate spatial data;  $$L(x,y) = \\frac{n}{\\sum_{=1}^{n}(\\sum_{j=1}^{n}w_{ij})^2} \\frac{\\sum_{=1}^{n}(\\sum_{j=1}^{n}w_{ij}(x_i-\\bar{x})) ((\\sum_{j=1}^{n}w_{ij}(y_j-\\bar{y}))}{\\sqrt{\\sum_{=1}^{n}(x_i - \\bar{x})^2} \\sqrt{\\sum_{=1}^{n}(y_i - \\bar{y})^2}} $$","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lee.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Compute Lee's statistic — lee","text":"","code":"lee(x, y, listw, n, S2, zero.policy=attr(listw, \"zero.policy\"), NAOK=FALSE)"},{"path":"https://r-spatial.github.io/spdep/reference/lee.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Compute Lee's statistic — lee","text":"x numeric vector length neighbours list listw y numeric vector length neighbours list listw listw listw object created example nb2listw n number zones S2 Sum squared sum weights rows. zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA NAOK 'TRUE' 'NA' 'NaN' 'Inf' values x passed foreign function.  'FALSE', presence 'NA' 'NaN' 'Inf' values regarded error.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lee.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Compute Lee's statistic — lee","text":"list L Lee's L statistic local L Lee's local L statistic","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lee.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Compute Lee's statistic — lee","text":"Lee (2001). Developing bivariate spatial association measure: integration Pearson's r Moran's . J Geograph Syst  3: 369-385","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lee.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Compute Lee's statistic — lee","text":"Roger Bivand Virgiio Gómez-Rubio Virgilio.Gomez@uclm.es","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/lee.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Compute Lee's statistic — lee","text":"","code":"data(boston, package=\"spData\") lw<-nb2listw(boston.soi)  x<-boston.c$CMEDV y<-boston.c$CRIM z<-boston.c$RAD  Lxy<-lee(x, y, lw, length(x), zero.policy=TRUE) Lxz<-lee(x, z, lw, length(x), zero.policy=TRUE)"},{"path":"https://r-spatial.github.io/spdep/reference/lee.mc.html","id":null,"dir":"Reference","previous_headings":"","what":"Permutation test for Lee's L statistic — lee.mc","title":"Permutation test for Lee's L statistic — lee.mc","text":"permutation test Lee's L  statistic calculated using nsim random permutations x y given spatial weighting scheme, establish rank observed statistic relation nsim simulated values.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lee.mc.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Permutation test for Lee's L statistic — lee.mc","text":"","code":"lee.mc(x, y, listw, nsim, zero.policy=attr(listw, \"zero.policy\"), alternative=\"greater\",  na.action=na.fail, spChk=NULL, return_boot=FALSE)"},{"path":"https://r-spatial.github.io/spdep/reference/lee.mc.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Permutation test for Lee's L statistic — lee.mc","text":"x numeric vector length neighbours list listw y numeric vector length neighbours list listw listw listw object created example nb2listw nsim number permutations zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA alternative character string specifying alternative hypothesis, must one \"greater\" (default), \"two.sided\", \"less\". na.action function (default na.fail), can also na.omit na.exclude - cases weights list subsetted remove NAs data. may necessary set zero.policy TRUE subsetting may create -neighbour observations. Note weights lists created without using glist argument nb2listw may subsetted. na.pass permitted meaningless permutation test. spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption() return_boot return object class boot equivalent permutation bootstrap rather object class htest","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lee.mc.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Permutation test for Lee's L statistic — lee.mc","text":"list class htest mc.sim containing following components: statistic value observed Lee's L. parameter rank observed Lee's L. p.value pseudo p-value test. alternative character string describing alternative hypothesis. method character string giving method used. data.name character string giving name(s) data, number simulations. res nsim simulated values statistic, final value observed statistic","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lee.mc.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Permutation test for Lee's L statistic — lee.mc","text":"Lee (2001). Developing bivariate spatial association measure: integration Pearson's r Moran's . J Geograph Syst  3: 369-385","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lee.mc.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Permutation test for Lee's L statistic — lee.mc","text":"Roger Bivand, Virgilio Gómez-Rubio Virgilio.Gomez@uclm.es","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/lee.mc.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Permutation test for Lee's L statistic — lee.mc","text":"","code":"data(boston, package=\"spData\") lw<-nb2listw(boston.soi)  x<-boston.c$CMEDV y<-boston.c$CRIM  lee.mc(x, y, nsim=99, lw, zero.policy=TRUE, alternative=\"two.sided\") #>  #> \tMonte-Carlo simulation of Lee's L #>  #> data:  x ,  y  #> weights: lw   #> number of simulations + 1: 100  #>  #> statistic = -0.3263, observed rank = 1, p-value = 0.02 #> alternative hypothesis: two.sided #>   #Test with missing values x[1:5]<-NA y[3:7]<-NA  lee.mc(x, y, nsim=99, lw, zero.policy=TRUE, alternative=\"two.sided\",     na.action=na.omit) #>  #> \tMonte-Carlo simulation of Lee's L #>  #> data:  x ,  y  #> weights: lw  #> omitted: 1, 2, 3, 4, 5, 6, 7  #> number of simulations + 1: 100  #>  #> statistic = -0.32447, observed rank = 1, p-value = 0.02 #> alternative hypothesis: two.sided #>"},{"path":"https://r-spatial.github.io/spdep/reference/lee.test.html","id":null,"dir":"Reference","previous_headings":"","what":"Lee's L test for spatial autocorrelation — lee.test","title":"Lee's L test for spatial autocorrelation — lee.test","text":"Lee's L test spatial autocorrelation using spatial weights matrix weights list form. assumptions underlying test sensitive form graph neighbour relationships factors, results may checked lee.mc permutations.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lee.test.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Lee's L test for spatial autocorrelation — lee.test","text":"","code":"lee.test(x, y, listw, zero.policy=attr(listw, \"zero.policy\"),  alternative=\"greater\", na.action=na.fail, spChk=NULL)"},{"path":"https://r-spatial.github.io/spdep/reference/lee.test.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Lee's L test for spatial autocorrelation — lee.test","text":"x numeric vector length neighbours list listw y numeric vector length neighbours list listw listw listw object created example nb2listw  zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA alternative character string specifying alternative hypothesis, must one greater (default), less two.sided.  na.action function (default na.fail), can also na.omit na.exclude - cases weights list subsetted remove NAs data. may necessary set zero.policy TRUE subsetting may create -neighbour observations. Note weights lists created without using glist argument nb2listw may subsetted. na.pass used, zero substituted NA values calculating spatial lag spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption()","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lee.test.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Lee's L test for spatial autocorrelation — lee.test","text":"list class htest containing following components: statistic value standard deviate Lee's L. p.value p-value test. estimate value observed Lee's L, expectation variance method assumption. alternative character string describing alternative hypothesis. method character string giving assumption used calculating standard deviate. data.name character string giving name(s) data.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lee.test.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Lee's L test for spatial autocorrelation — lee.test","text":"See Lee (2004) details asymptotic expectation variance Lee's L computed. particular, check Lee (2004), table 1, page 1690. test may fail large datasets computation asymptotic expectation variance requires use dense matrices.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lee.test.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Lee's L test for spatial autocorrelation — lee.test","text":"Lee (2004). generalized significance testing method global measures spatial association: extension Mantel test.  Environment Planning 2004, volume 36, pages 1687 - 1703","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lee.test.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Lee's L test for spatial autocorrelation — lee.test","text":"Roger Bivand Virgilio Gómez-Rubio Virgilio.Gomez@uclm.es","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/lee.test.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Lee's L test for spatial autocorrelation — lee.test","text":"","code":"data(oldcol) col.W <- nb2listw(COL.nb, style=\"W\") crime <- COL.OLD$CRIME  lee.test(crime, crime, col.W, zero.policy=TRUE) #>  #> \tLee's L statistic randomisation #>  #> data:  crime ,  crime  #> weights: col.W   #>  #> Lee's L statistic standard deviate = 5.2343, p-value = 8.279e-08 #> alternative hypothesis: greater #> sample estimates: #> Lee's L statistic       Expectation          Variance  #>       0.547064219       0.239417989       0.003454459  #>   #Test with missing values x<-crime y<-crime x[1:5]<-NA y[3:7]<-NA  lee.test(x, y, col.W, zero.policy=TRUE, na.action=na.omit) #>  #> \tLee's L statistic randomisation #>  #> data:  x ,  y  #> weights: col.W  #> omitted: 1, 2, 3, 4, 5, 6, 7  #>  #> Lee's L statistic standard deviate = 6.6873, p-value = 1.137e-11 #> alternative hypothesis: greater #> sample estimates: #> Lee's L statistic       Expectation          Variance  #>       0.706469726       0.260143244       0.004454563  #>  #  lee.test(x, y, col.W, zero.policy=TRUE)#Stops with an error    data(boston, package=\"spData\") lw<-nb2listw(boston.soi)  x<-boston.c$CMEDV y<-boston.c$CRIM  lee.test(x, y, lw, zero.policy=TRUE, alternative=\"less\") #>  #> \tLee's L statistic randomisation #>  #> data:  x ,  y  #> weights: lw   #>  #> Lee's L statistic standard deviate = -11.54, p-value < 2.2e-16 #> alternative hypothesis: less #> sample estimates: #> Lee's L statistic       Expectation          Variance  #>      -0.326297206      -0.105040316       0.000367637  #>   #Test with missing values x[1:5]<-NA y[3:7]<-NA  lee.test(x, y, lw, zero.policy=TRUE, alternative=\"less\", na.action=na.omit) #>  #> \tLee's L statistic randomisation #>  #> data:  x ,  y  #> weights: lw  #> omitted: 1, 2, 3, 4, 5, 6, 7  #>  #> Lee's L statistic standard deviate = -11.284, p-value < 2.2e-16 #> alternative hypothesis: less #> sample estimates: #> Lee's L statistic       Expectation          Variance  #>     -0.3244748280     -0.1053154332      0.0003772109  #>"},{"path":"https://r-spatial.github.io/spdep/reference/licd_multi.html","id":null,"dir":"Reference","previous_headings":"","what":"Local Indicators for Categorical Data — licd_multi","title":"Local Indicators for Categorical Data — licd_multi","text":"Local indicators categorical data combine measure local composition window given per-observation set neighbouring observations, local multi-category joincount test simplified neighbours different categories compared focal observation","code":""},{"path":"https://r-spatial.github.io/spdep/reference/licd_multi.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Local Indicators for Categorical Data — licd_multi","text":"","code":"licd_multi(fx, listw, zero.policy = attr(listw, \"zero.policy\"), adjust.n = TRUE,  nsim = 0L, iseed = NULL, no_repeat_in_row = FALSE, control = list())"},{"path":"https://r-spatial.github.io/spdep/reference/licd_multi.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Local Indicators for Categorical Data — licd_multi","text":"fx factor two categories, length neighbours weights objects listw listw listw object created example nb2listw zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA adjust.n default TRUE, FALSE number observations adjusted -neighbour observations, TRUE, number observations adjusted nsim default 0, number conditonal permutation simulations iseed default NULL, used set seed; output reproducible count CPU cores across computation distributed no_repeat_in_row default FALSE, TRUE, sample conditionally row without replacements avoid duplicate values, https://github.com/r-spatial/spdep/issues/124 control comp_binary=TRUE default TRUE, ignoring weights styles binary composition measures, binomial_punif_alternative=\"greater\", jcm_same_punif_alternative=\"less\", jcm_diff_punif_alternative=\"greater\", rank_ties.method=\"min\" default \"min\", na.last=\"keep\" leading rank NA returned observed joincount variance non-positive; TRUE joincount NAs ranked highest using rank, others see ?rank, check_reps=FALSE, unique_ceiling=1/3 used check_reps TRUE, check_reps=FALSE TRUE, check report many unique draws made among nsim draws, number unique draws less unique_ceiling, compute measures unique draws copy replicated draws, pysal_rank=FALSE use rank rank_ties.method na.last; TRUE, use pysal-style ranking find rank sum(sims <= obs, na.rm=TRUE)+1 pysal_sim_obs \"GE\", sum(sims < obs, na.rm=TRUE)+1 count observed greater \"GT\" simulated values, pysal_sim_obs=\"GT\" may also \"GE\", xtras=FALSE TRUE return calculated compostion values BW chi-squared, k-colour chi-squared, BW Anscombe","code":""},{"path":"https://r-spatial.github.io/spdep/reference/licd_multi.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Local Indicators for Categorical Data — licd_multi","text":"original code may found doi:10.5281/zenodo.4283766","code":""},{"path":"https://r-spatial.github.io/spdep/reference/licd_multi.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Local Indicators for Categorical Data — licd_multi","text":"local_comp data.frame object LICD local composition columns: ID,     category_i, count_like_i, prop_i, count_nbs_i, pbinom_like_BW,     pbinom_unlike_BW, pbinom_unlike_BW_alt, chi_BW_i, chi_K_i, anscombe_BW local_config data.frame object LICD local configuration columns: ID, jcm_chi_obs, jcm_count_BB_obs, jcm_count_BW_obs, jcm_count_WW_obs, pval_jcm_obs_BB, pval_jcm_obs_WW, pval_jcm_obs_BW local_comp_sim data.frame object permutation-based LICD local composition columns: ID, pbinom_like_BW, pbinom_unlike_BW, pbinom_unlike_BW_alt, rank_sim_chi_BW, rank_sim_chi_K, rank_sim_anscombe local_config_sim data.frame object permutation-based LICD local configuration columns: ID, jcm_chi_sim_rank, pval_jcm_obs_BB, pval_jcm_obs_BW, pval_jcm_obs_WW","code":""},{"path":"https://r-spatial.github.io/spdep/reference/licd_multi.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Local Indicators for Categorical Data — licd_multi","text":"Cliff, . D., Ord, J. K. 1981 Spatial processes, Pion, p. 20; Upton, G., Fingleton, B. 1985 Spatial data analysis example: point pattern qualitative data, Wiley, pp. 158–170; Boots, B., 2003. Developing local measures spatial association categorical data. Journal Geographical Systems 5, 139–160; Boots, B., 2006. Local configuration measures categorical spatial data: binary regular lattices. Journal Geographical Systems 8 (1), 1–24; Pietrzak, M.B., Wilk, J., Kossowski, T., Bivand, R.S., 2014. application local indicators categorical data (LICD) spatial analysis economic development. Comparative Economic Research 17 (4), 203–220 doi:10.2478/cer-2014-0041 ; Bivand, R.S., Wilk, J., Kossowski, T., 2017. Spatial association population pyramids across Europe: application symbolic data, cluster analysis join-count tests. Spatial Statistics 21 (B), 339–361 doi:10.1016/j.spasta.2017.03.003 ; Francesco Carrer, Tomasz M. Kossowski, Justyna Wilk, Michał B. Pietrzak, Roger S. Bivand, application Local Indicators Categorical Data (LICD) explore spatial dependence archaeological spaces, Journal Archaeological Science, 126, 2021, doi:10.1016/j.jas.2020.105306","code":""},{"path":"https://r-spatial.github.io/spdep/reference/licd_multi.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Local Indicators for Categorical Data — licd_multi","text":"Roger Bivand Roger.Bivand@nhh.based earlier code Tomasz M. Kossowski, Justyna Wilk Michał B. Pietrzak","code":""},{"path":"https://r-spatial.github.io/spdep/reference/licd_multi.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Local Indicators for Categorical Data — licd_multi","text":"order increase numbers neighbours using nblag nblag_cumul advisable; use binary weights advised case used composition measure","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/licd_multi.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Local Indicators for Categorical Data — licd_multi","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) HICRIME <- cut(columbus$CRIME, breaks=c(0,35,80), labels=c(\"low\",\"high\")) (nb <- poly2nb(columbus)) #> Neighbour list object: #> Number of regions: 49  #> Number of nonzero links: 236  #> Percentage nonzero weights: 9.829238  #> Average number of links: 4.816327  lw <- nb2listw(nblag_cumul(nblag(nb, 2)), style=\"B\") obj <- licd_multi(HICRIME, lw) str(obj) #> List of 4 #>  $ local_comp      :'data.frame':\t49 obs. of  11 variables: #>   ..$ ID                  : int [1:49] 1 2 3 4 5 6 7 8 9 10 ... #>   ..$ category_i          : num [1:49] 1 1 1 1 2 1 1 2 1 1 ... #>   ..$ count_like_i        : num [1:49] 4 4 6 7 12 7 2 8 10 8 ... #>   ..$ prop_i              : num [1:49] 0.51 0.51 0.51 0.51 0.49 ... #>   ..$ count_nbs_i         : num [1:49] 5 6 11 14 22 14 11 14 25 17 ... #>   ..$ pbinom_like_BW      : num [1:49] 0.965 0.881 0.702 0.575 0.769 ... #>   ..$ pbinom_unlike_BW    : num [1:49] 0.0346 0.1192 0.2979 0.4255 0.2313 ... #>   ..$ pbinom_unlike_BW_alt: num [1:49] 0.201 0.363 0.528 0.634 0.379 ... #>   ..$ chi_BW_i            : num [1:49] NA NA NA NA NA NA NA NA NA NA ... #>   ..$ chi_K_i             : num [1:49] NA NA NA NA NA NA NA NA NA NA ... #>   ..$ anscombe_BW         : num [1:49] NA NA NA NA NA NA NA NA NA NA ... #>  $ local_config    :'data.frame':\t49 obs. of  8 variables: #>   ..$ ID              : int [1:49] 1 2 3 4 5 6 7 8 9 10 ... #>   ..$ jcm_chi_obs     : num [1:49] 0 0.0625 0.625 2.7468 14.1889 ... #>   ..$ jcm_count_BB_obs: num [1:49] 6 6 11 12 55 15 1 27 30 25 ... #>   ..$ jcm_count_BW_obs: num [1:49] 4 7 23 31 50 36 15 31 73 53 ... #>   ..$ jcm_count_WW_obs: num [1:49] 0 1 10 20 21 19 32 9 61 24 ... #>   ..$ pval_jcm_obs_BB : num [1:49] 1 0.207108 0.70232 0.820405 0.000214 ... #>   ..$ pval_jcm_obs_WW : num [1:49] 1 0.3946 0.0981 0.0243 0.7839 ... #>   ..$ pval_jcm_obs_BW : num [1:49] 1.00 1.75e-01 2.08e-01 5.10e-02 3.52e-06 ... #>  $ local_comp_sim  : NULL #>  $ local_config_sim: NULL #>  - attr(*, \"timings\")=List of 3 #>   ..$ set_up        : 'proc_time' Named num [1:5] 0 0 0 0 0 #>   .. ..- attr(*, \"names\")= chr [1:5] \"user.self\" \"sys.self\" \"elapsed\" \"user.child\" ... #>   ..$ processing    : 'proc_time' Named num [1:5] 0.106 0 0.107 0 0 #>   .. ..- attr(*, \"names\")= chr [1:5] \"user.self\" \"sys.self\" \"elapsed\" \"user.child\" ... #>   ..$ postprocessing: 'proc_time' Named num [1:5] 0.001 0 0.001 0 0 #>   .. ..- attr(*, \"names\")= chr [1:5] \"user.self\" \"sys.self\" \"elapsed\" \"user.child\" ... #>  - attr(*, \"out\")= num [1:49, 1:35] 1 1 1 1 2 1 1 2 1 1 ... #>   ..- attr(*, \"ncpus\")= int 1 #>   ..- attr(*, \"dimnames\")=List of 2 #>   .. ..$ : NULL #>   .. ..$ : chr [1:35] \"category_i\" \"count_like_i\" \"prop_i\" \"count_nbs_i\" ... #>  - attr(*, \"ncpus\")= int 1 #>  - attr(*, \"nsim\")= int 0 #>  - attr(*, \"con\")=List of 11 #>   ..$ comp_binary               : logi TRUE #>   ..$ binomial_punif_alternative: chr \"greater\" #>   ..$ jcm_same_punif_alternative: chr \"less\" #>   ..$ jcm_diff_punif_alternative: chr \"greater\" #>   ..$ rank_ties.method          : chr \"min\" #>   ..$ unique_ceiling            : num 0.333 #>   ..$ check_reps                : logi FALSE #>   ..$ pysal_rank                : logi FALSE #>   ..$ pysal_sim_obs             : chr \"GT\" #>   ..$ na.last                   : chr \"keep\" #>   ..$ xtras                     : logi FALSE #>  - attr(*, \"class\")= chr [1:2] \"licd\" \"list\" h_obj <- hotspot(obj) str(h_obj) #> List of 9 #>  $ ID              : int [1:49] 1 2 3 4 5 6 7 8 9 10 ... #>  $ local_comp      : Factor w/ 2 levels \"Cluster\",\"Dispersed\": 2 2 2 2 2 2 2 2 2 2 ... #>  $ local_comp_sim  : NULL #>  $ local_config    : Factor w/ 3 levels \"Cluster\",\"Dispersed\",..: 3 3 3 3 2 3 3 2 3 3 ... #>  $ local_config_sim: NULL #>  $ both            : Factor w/ 6 levels \"Cluster.Cluster\",..: 6 6 6 6 4 6 6 4 6 6 ... #>  $ both_sim        : NULL #>  $ both_recode     : Factor w/ 4 levels \"Clump\",\"Cluster\",..: 4 4 4 4 3 4 4 3 4 4 ... #>  $ both_recode_sim : NULL table(h_obj$both_recode) #>  #>      Clump    Cluster  Dispersed No cluster  #>          8          3         11         27  columbus$both <- h_obj$both_recode plot(columbus[, \"both\"])  GDAL37 <- as.numeric_version(unname(sf_extSoftVersion()[\"GDAL\"])) >= \"3.7.0\" file <- \"etc/shapes/GB_2024_southcoast_50m.gpkg.zip\" zipfile <- system.file(file, package=\"spdep\") if (GDAL37) {     sc50m <- st_read(zipfile) } else {     td <- tempdir()     bn <- sub(\".zip\", \"\", basename(file), fixed=TRUE)     target <- unzip(zipfile, files=bn, exdir=td)     sc50m <- st_read(target) } #> Reading layer `GB_2024_southcoast_50m' from data source  #>   `/tmp/RtmpzEChJG/temp_libpath8ee3b7c361c1e/spdep/etc/shapes/GB_2024_southcoast_50m.gpkg.zip'  #>   using driver `GPKG' #> Simple feature collection with 119 features and 19 fields #> Geometry type: MULTIPOLYGON #> Dimension:     XY #> Bounding box:  xmin: 82643.12 ymin: 5342.9 xmax: 640301.6 ymax: 187226.2 #> Projected CRS: OSGB36 / British National Grid sc50m$Winner <- factor(sc50m$Winner, levels=c(\"Con\", \"Green\", \"Lab\", \"LD\")) plot(sc50m[,\"Winner\"], pal=c(\"#2297E6\", \"#61D04F\", \"#DF536B\", \"#F5C710\"))  nb_sc_50m <- poly2nb(sc50m, row.names=as.character(sc50m$Constituency)) #> Warning: neighbour object has 2 sub-graphs; #> if this sub-graph count seems unexpected, try increasing the snap argument. sub2 <- attr(nb_sc_50m, \"region.id\")[attr(nb_sc_50m, \"ncomp\")$comp.id == 2L] iowe <- match(sub2[1], attr(nb_sc_50m, \"region.id\")) diowe <- c(st_distance(sc50m[iowe,], sc50m)) meet_criterion <- sum(diowe <= units::set_units(5000, \"m\")) cands <- attr(nb_sc_50m, \"region.id\")[order(diowe)[1:meet_criterion]] nb_sc_50m_iowe <- addlinks1(nb_sc_50m, from = cands[1],  to = cands[3:meet_criterion]) ioww <- match(sub2[2], attr(nb_sc_50m, \"region.id\")) dioww <- c(st_distance(sc50m[ioww,], sc50m)) meet_criterion <- sum(dioww <= units::set_units(5000, \"m\")) cands <- attr(nb_sc_50m, \"region.id\")[order(dioww)[1:meet_criterion]] nb_sc_50m_iow <- addlinks1(nb_sc_50m_iowe, from = cands[2], to = cands[3:meet_criterion]) nb_sc_1_2 <- nblag_cumul(nblag(nb_sc_50m_iow, 2)) lw <- nb2listw(nb_sc_1_2, style=\"B\") licd_obj <- licd_multi(sc50m$Winner, lw) h_obj <- hotspot(licd_obj) sc50m$both <- h_obj$both_recode plot(sc50m[, \"both\"])  ljc <- local_joincount_uni(factor(sc50m$Winner == \"LD\"), chosen=\"TRUE\", lw) sc50m$LD_pv <- ljc[, 2] plot(sc50m[, \"LD_pv\"], breaks=c(0, 0.025, 0.05, 0.1, 0.5, 1))"},{"path":"https://r-spatial.github.io/spdep/reference/listw2sn.html","id":null,"dir":"Reference","previous_headings":"","what":"Spatial neighbour sparse representation — listw2sn","title":"Spatial neighbour sparse representation — listw2sn","text":"function makes \"spatial neighbour\" object representation (similar S-PLUS spatial statististics module representation \"listw\" spatial weights object. sn2listw() inverse function listw2sn(), creating \"listw\" object \"spatial neighbour\" object.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/listw2sn.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Spatial neighbour sparse representation — listw2sn","text":"","code":"listw2sn(listw) sn2listw(sn, style = NULL, zero.policy = NULL, from_mat2listw=FALSE)"},{"path":"https://r-spatial.github.io/spdep/reference/listw2sn.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Spatial neighbour sparse representation — listw2sn","text":"listw listw object example nb2listw sn spatial.neighbour object style default NULL, missing, set \"M\" warning given; \"M\", passed nb2listw re-build object zero.policy default NULL, use global option value; FALSE stop error empty neighbour sets, TRUE permit weights list formed zero-length weights vectors from_mat2listw default FALSE, set TRUE called mat2listw","code":""},{"path":"https://r-spatial.github.io/spdep/reference/listw2sn.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Spatial neighbour sparse representation — listw2sn","text":"listw2sn()returns data frame three columns, class spatial.neighbour: region number id start link (S-PLUS row.id) region number id end link (S-PLUS col.id) weights weight link","code":""},{"path":"https://r-spatial.github.io/spdep/reference/listw2sn.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Spatial neighbour sparse representation — listw2sn","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/listw2sn.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Spatial neighbour sparse representation — listw2sn","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) col.gal.nb <- read.gal(system.file(\"weights/columbus.gal\", package=\"spData\")[1]) col.listw <- nb2listw(col.gal.nb) col.listw$neighbours[[1]] #> [1] 2 3 col.listw$weights[[1]] #> [1] 0.5 0.5 col.sn <- listw2sn(col.listw) str(col.sn) #> Classes ‘spatial.neighbour’ and 'data.frame':\t230 obs. of  3 variables: #>  $ from   : int  1 1 2 2 2 3 3 3 3 4 ... #>  $ to     : int  2 3 1 3 4 1 2 4 5 2 ... #>  $ weights: num  0.5 0.5 0.333 0.333 0.333 ... #>  - attr(*, \"n\")= int 49 #>  - attr(*, \"region.id\")= chr [1:49] \"1\" \"2\" \"3\" \"4\" ... #>  - attr(*, \"neighbours.attrs\")= chr [1:7] \"class\" \"region.id\" \"GeoDa\" \"gal\" ... #>  - attr(*, \"weights.attrs\")= chr [1:3] \"mode\" \"W\" \"comp\" #>  - attr(*, \"GeoDa\")=List of 2 #>   ..$ shpfile: chr NA #>   ..$ ind    : chr NA #>  - attr(*, \"listw.call\")= language nb2listw(neighbours = col.gal.nb)"},{"path":"https://r-spatial.github.io/spdep/reference/lm.RStests.html","id":null,"dir":"Reference","previous_headings":"","what":"Rao's score (a.k.a Lagrange Multiplier) diagnostics for spatial dependence in linear models — lm.LMtests","title":"Rao's score (a.k.a Lagrange Multiplier) diagnostics for spatial dependence in linear models — lm.LMtests","text":"function reports estimates tests chosen among five statistics testing spatial dependence linear models. statistics simple RS test error dependence (“RSerr”), simple RS test missing spatially lagged dependent variable (“RSlag”), variants adjusted presence (“adjRSerr” tests error dependence possible presence missing lagged dependent variable, “adjRSlag” way round), portmanteau test (“SARMA”, fact “RSerr” + “adjRSlag”). Note: spdep 1.3-2, tests re-named “RS” - Rao's score tests, rather “LM” - Lagrange multiplier tests match naming tests family SDM.RStests.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lm.RStests.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Rao's score (a.k.a Lagrange Multiplier) diagnostics for spatial dependence in linear models — lm.LMtests","text":"","code":"lm.RStests(model, listw, zero.policy=attr(listw, \"zero.policy\"), test=\"RSerr\",  spChk=NULL, naSubset=TRUE) lm.LMtests(model, listw, zero.policy=attr(listw, \"zero.policy\"), test=\"LMerr\",  spChk=NULL, naSubset=TRUE) # S3 method for class 'RStestlist' print(x, ...) # S3 method for class 'RStestlist' summary(object, p.adjust.method=\"none\", ...) # S3 method for class 'RStestlist.summary' print(x, digits=max(3, getOption(\"digits\") - 2), ...) <!-- %tracew(listw) -->"},{"path":"https://r-spatial.github.io/spdep/reference/lm.RStests.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Rao's score (a.k.a Lagrange Multiplier) diagnostics for spatial dependence in linear models — lm.LMtests","text":"model object class lm returned lm, optionally vector externally calculated residuals (run though na.omit NAs present) use \"RSerr\" chosen; weights offsets used lm object listw listw object created example nb2listw, expected row-standardised (W-style) zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA test character vector tests requested chosen RSerr, RSlag, adjRSerr, adjRSlag, SARMA; test=\"\" computes tests. spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption() naSubset default TRUE subset listw object omitted observations model object (change earlier behaviour, model$na.action component ignored, listw object subsetted hand) x, object object printed p.adjust.method character string specifying probability value adjustment (see p.adjust) multiple tests, default \"none\" digits minimum number significant digits used numbers ... printing arguments passed ","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lm.RStests.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Rao's score (a.k.a Lagrange Multiplier) diagnostics for spatial dependence in linear models — lm.LMtests","text":"two types dependence spatial lag \\(\\rho\\) spatial error \\(\\lambda\\): $$ \\mathbf{y} = \\mathbf{X \\beta} + \\rho \\mathbf{W_{(1)} y} + \\mathbf{u}, $$ $$ \\mathbf{u} = \\lambda \\mathbf{W_{(2)} u} + \\mathbf{e} $$ \\(\\mathbf{e}\\) well-behaved, uncorrelated error term. Tests missing spatially lagged dependent variable test \\(\\rho = 0\\), tests spatial autocorrelation error \\(\\mathbf{u}\\) test whether \\(\\lambda = 0\\). \\(\\mathbf{W}\\) spatial weights matrix; tests used identical.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lm.RStests.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Rao's score (a.k.a Lagrange Multiplier) diagnostics for spatial dependence in linear models — lm.LMtests","text":"list class RStestlist htest objects, : statistic value Rao's score (.k.Lagrange multiplier) test. parameter number degrees freedom p.value p-value test. method character string giving method used. data.name character string giving name(s) data.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lm.RStests.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Rao's score (a.k.a Lagrange Multiplier) diagnostics for spatial dependence in linear models — lm.LMtests","text":"Anselin, L. 1988 Spatial econometrics: methods models. (Dordrecht: Kluwer); Anselin, L., Bera, . K., Florax, R. Yoon, M. J. 1996 Simple diagnostic tests spatial dependence. Regional Science Urban Economics, 26, 77–104 doi:10.1016/0166-0462(95)02111-6 ; Malabika Koley (2024) Specification Testing General Nesting Spatial Model, https://sites.google.com/view/malabikakoley/research.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lm.RStests.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Rao's score (a.k.a Lagrange Multiplier) diagnostics for spatial dependence in linear models — lm.LMtests","text":"Roger Bivand Roger.Bivand@nhh.Andrew Bernat","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/lm.RStests.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Rao's score (a.k.a Lagrange Multiplier) diagnostics for spatial dependence in linear models — lm.LMtests","text":"","code":"data(oldcol) oldcrime.lm <- lm(CRIME ~ HOVAL + INC, data = COL.OLD) summary(oldcrime.lm) #>  #> Call: #> lm(formula = CRIME ~ HOVAL + INC, data = COL.OLD) #>  #> Residuals: #>     Min      1Q  Median      3Q     Max  #> -34.418  -6.388  -1.580   9.052  28.649  #>  #> Coefficients: #>             Estimate Std. Error t value Pr(>|t|)     #> (Intercept)  68.6190     4.7355  14.490  < 2e-16 *** #> HOVAL        -0.2739     0.1032  -2.654   0.0109 *   #> INC          -1.5973     0.3341  -4.780 1.83e-05 *** #> --- #> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 #>  #> Residual standard error: 11.43 on 46 degrees of freedom #> Multiple R-squared:  0.5524,\tAdjusted R-squared:  0.5329  #> F-statistic: 28.39 on 2 and 46 DF,  p-value: 9.341e-09 #>  lw <- nb2listw(COL.nb) res <- lm.RStests(oldcrime.lm, listw=lw, test=\"all\") summary(res) #> \tRao's score (a.k.a Lagrange multiplier) diagnostics for spatial #> \tdependence #> data:   #> model: lm(formula = CRIME ~ HOVAL + INC, data = COL.OLD) #> test weights: lw #>   #>          statistic parameter  p.value    #> RSerr     5.723131         1 0.016743 *  #> RSlag     9.363684         1 0.002213 ** #> adjRSerr  0.079495         1 0.777983    #> adjRSlag  3.720048         1 0.053763 .  #> SARMA     9.443178         2 0.008901 ** #> --- #> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 if (require(\"spatialreg\", quietly=TRUE)) {   oldcrime.slx <- lmSLX(CRIME ~ HOVAL + INC, data = COL.OLD, listw=lw)   summary(lm.RStests(oldcrime.slx, listw=lw, test=c(\"adjRSerr\", \"adjRSlag\"))) } #> \tRao's score (a.k.a Lagrange multiplier) diagnostics for spatial #> \tdependence #> data:   #> model: lm(CRIME ~ HOVAL + INC + lag.HOVAL + lag.INC, data = COL.OLD, #> listw = lw) #> test weights: lw #>   #>              statistic parameter p.value #> GNM_adjRSerr   0.10933         1  0.7409 #> GNM_adjRSlag   0.61580         1  0.4326"},{"path":"https://r-spatial.github.io/spdep/reference/lm.morantest.exact.html","id":null,"dir":"Reference","previous_headings":"","what":"Exact global Moran's I test — lm.morantest.exact","title":"Exact global Moran's I test — lm.morantest.exact","text":"function implements Tiefelsdorf's exact global Moran's test.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lm.morantest.exact.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Exact global Moran's I test — lm.morantest.exact","text":"","code":"lm.morantest.exact(model, listw, zero.policy = attr(listw, \"zero.policy\"),  alternative = \"greater\", spChk = NULL, resfun = weighted.residuals,  zero.tol = 1e-07, Omega=NULL, save.M=NULL, save.U=NULL, useTP=FALSE,  truncErr=1e-6, zeroTreat=0.1) # S3 method for class 'moranex' print(x, ...)"},{"path":"https://r-spatial.github.io/spdep/reference/lm.morantest.exact.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Exact global Moran's I test — lm.morantest.exact","text":"model object class lm returned lm; weights may specified lm fit, offsets used listw listw object created example nb2listw zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA alternative character string specifying alternative hypothesis, must one greater (default), less two.sided. spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption() resfun default: weighted.residuals; function used extract residuals lm object, may residuals, weighted.residuals, rstandard, rstudent zero.tol tolerance used find eigenvalues close absolute zero Omega SAR process matrix may passed test alternative hypothesis, example Omega <- invIrW(listw, rho=0.1); Omega <- tcrossprod(Omega), chol() taken internally save.M return full M matrix use spdep:::exactMoranAlt save.U return full U matrix use spdep:::exactMoranAlt useTP default FALSE, TRUE, use truncation point integration rather upper=Inf, see Tiefelsdorf (2000), eq. 6.7, p.69 truncErr useTP=TRUE, pass truncation error truncation point function zeroTreat useTP=TRUE, pass zero adjustment truncation point function x moranex object ... arguments passed ","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lm.morantest.exact.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Exact global Moran's I test — lm.morantest.exact","text":"list class moranex following components: statistic value exact standard deviate global Moran's . p.value p-value test. estimate value observed global Moran's . method character string giving method used. alternative character string describing alternative hypothesis. gamma eigenvalues (excluding zero values) oType usually set \"E\" data.name character string giving name(s) data. df degrees freedom","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lm.morantest.exact.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Exact global Moran's I test — lm.morantest.exact","text":"Markus Reder Roger Bivand","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lm.morantest.exact.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Exact global Moran's I test — lm.morantest.exact","text":"Roger Bivand, Werner G. Müller Markus Reder (2009) \"Power calculations global local Moran's .\" Computational Statistics & Data Analysis 53, 2859-2872.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/lm.morantest.exact.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Exact global Moran's I test — lm.morantest.exact","text":"","code":"eire <- st_read(system.file(\"shapes/eire.gpkg\", package=\"spData\")[1]) #> Reading layer `eire' from data source  #>   `/home/rsb/lib/r_libs/spData/shapes/eire.gpkg' using driver `GPKG' #> Simple feature collection with 26 features and 10 fields #> Geometry type: MULTIPOLYGON #> Dimension:     XY #> Bounding box:  xmin: -4.12 ymin: 5768 xmax: 300.82 ymax: 6119.25 #> Projected CRS: Undefined Cartesian SRS with unknown unit row.names(eire) <- as.character(eire$names) eire.nb <- poly2nb(eire) e.lm <- lm(OWNCONS ~ ROADACC, data=eire) lm.morantest(e.lm, nb2listw(eire.nb)) #>  #> \tGlobal Moran I for regression residuals #>  #> data:   #> model: lm(formula = OWNCONS ~ ROADACC, data = eire) #> weights: nb2listw(eire.nb) #>  #> Moran I statistic standard deviate = 3.2575, p-value = 0.0005619 #> alternative hypothesis: greater #> sample estimates: #> Observed Moran I      Expectation         Variance  #>       0.33660565      -0.05877741       0.01473183  #>  lm.morantest.sad(e.lm, nb2listw(eire.nb)) #>  #> \tSaddlepoint approximation for global Moran's I (Barndorff-Nielsen #> \tformula) #>  #> data:   #> model:lm(formula = OWNCONS ~ ROADACC, data = eire) #> weights: nb2listw(eire.nb) #>  #> Saddlepoint approximation = 2.9395, p-value = 0.001644 #> alternative hypothesis: greater #> sample estimates: #> Observed Moran I  #>        0.3366057  #>  lm.morantest.exact(e.lm, nb2listw(eire.nb)) #>  #> \tGlobal Moran I statistic with exact p-value #>  #> data:   #> model:lm(formula = OWNCONS ~ ROADACC, data = eire) #> weights: nb2listw(eire.nb) #>  #> Exact standard deviate = 2.9316, p-value = 0.001686 #> alternative hypothesis: greater #> sample estimates: #> [1] 0.3366057 #>  lm.morantest.exact(e.lm, nb2listw(eire.nb), useTP=TRUE) #>  #> \tGlobal Moran I statistic with exact p-value #>  #> data:   #> model:lm(formula = OWNCONS ~ ROADACC, data = eire) #> weights: nb2listw(eire.nb) #>  #> Exact standard deviate = 2.9315, p-value = 0.001686 #> alternative hypothesis: greater #> sample estimates: #> [1] 0.3366057 #>"},{"path":"https://r-spatial.github.io/spdep/reference/lm.morantest.html","id":null,"dir":"Reference","previous_headings":"","what":"Moran's I test for residual spatial autocorrelation — lm.morantest","title":"Moran's I test for residual spatial autocorrelation — lm.morantest","text":"Moran's test spatial autocorrelation residuals estimated linear model (lm()).","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lm.morantest.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Moran's I test for residual spatial autocorrelation — lm.morantest","text":"","code":"lm.morantest(model, listw, zero.policy=attr(listw, \"zero.policy\"),  alternative = \"greater\", spChk=NULL, resfun=weighted.residuals, naSubset=TRUE)"},{"path":"https://r-spatial.github.io/spdep/reference/lm.morantest.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Moran's I test for residual spatial autocorrelation — lm.morantest","text":"model object class lm returned lm; weights may specified lm fit, offsets used listw listw object created example nb2listw zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA alternative character string specifying alternative hypothesis, must one \"greater\" (default), \"less\" \"two.sided\". spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption() resfun default: weighted.residuals; function used extract residuals lm object, may residuals, weighted.residuals, rstandard, rstudent naSubset default TRUE subset listw object omitted observations model object (change earlier behaviour, model$na.action component ignored, listw object subsetted hand)","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lm.morantest.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Moran's I test for residual spatial autocorrelation — lm.morantest","text":"list class htest containing following components: statistic value standard deviate Moran's . p.value p-value test. estimate value observed Moran's , expectation variance method assumption. alternative character string describing alternative hypothesis. method character string giving method used. data.name character string giving name(s) data.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lm.morantest.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Moran's I test for residual spatial autocorrelation — lm.morantest","text":"Cliff, . D., Ord, J. K. 1981 Spatial processes, Pion, p. 203,","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lm.morantest.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Moran's I test for residual spatial autocorrelation — lm.morantest","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/lm.morantest.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Moran's I test for residual spatial autocorrelation — lm.morantest","text":"","code":"data(oldcol) oldcrime1.lm <- lm(CRIME ~ 1, data = COL.OLD) oldcrime.lm <- lm(CRIME ~ HOVAL + INC, data = COL.OLD) lm.morantest(oldcrime.lm, nb2listw(COL.nb, style=\"W\")) #>  #> \tGlobal Moran I for regression residuals #>  #> data:   #> model: lm(formula = CRIME ~ HOVAL + INC, data = COL.OLD) #> weights: nb2listw(COL.nb, style = \"W\") #>  #> Moran I statistic standard deviate = 2.9539, p-value = 0.001569 #> alternative hypothesis: greater #> sample estimates: #> Observed Moran I      Expectation         Variance  #>      0.235638354     -0.033302866      0.008289408  #>  lm.LMtests(oldcrime.lm, nb2listw(COL.nb, style=\"W\")) #> Please update scripts to use lm.RStests in place of lm.LMtests #>  #> \tRao's score (a.k.a Lagrange multiplier) diagnostics for spatial #> \tdependence #>  #> data:   #> model: lm(formula = CRIME ~ HOVAL + INC, data = COL.OLD) #> test weights: listw #>  #> RSerr = 5.7231, df = 1, p-value = 0.01674 #>  lm.morantest(oldcrime.lm, nb2listw(COL.nb, style=\"S\")) #>  #> \tGlobal Moran I for regression residuals #>  #> data:   #> model: lm(formula = CRIME ~ HOVAL + INC, data = COL.OLD) #> weights: nb2listw(COL.nb, style = \"S\") #>  #> Moran I statistic standard deviate = 3.1745, p-value = 0.0007504 #> alternative hypothesis: greater #> sample estimates: #> Observed Moran I      Expectation         Variance  #>      0.239317561     -0.033431740      0.007381982  #>  lm.morantest(oldcrime1.lm, nb2listw(COL.nb, style=\"W\")) #>  #> \tGlobal Moran I for regression residuals #>  #> data:   #> model: lm(formula = CRIME ~ 1, data = COL.OLD) #> weights: nb2listw(COL.nb, style = \"W\") #>  #> Moran I statistic standard deviate = 5.6754, p-value = 6.92e-09 #> alternative hypothesis: greater #> sample estimates: #> Observed Moran I      Expectation         Variance  #>      0.510951264     -0.020833333      0.008779831  #>  moran.test(COL.OLD$CRIME, nb2listw(COL.nb, style=\"W\"),  randomisation=FALSE) #>  #> \tMoran I test under normality #>  #> data:  COL.OLD$CRIME   #> weights: nb2listw(COL.nb, style = \"W\")     #>  #> Moran I statistic standard deviate = 5.6754, p-value = 6.92e-09 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic       Expectation          Variance  #>       0.510951264      -0.020833333       0.008779831  #>  oldcrime.wlm <- lm(CRIME ~ HOVAL + INC, data = COL.OLD,  weights = I(1/AREA_PL)) lm.morantest(oldcrime.wlm, nb2listw(COL.nb, style=\"W\"),  resfun=weighted.residuals) #>  #> \tGlobal Moran I for regression residuals #>  #> data:   #> model: lm(formula = CRIME ~ HOVAL + INC, data = COL.OLD, weights = #> I(1/AREA_PL)) #> weights: nb2listw(COL.nb, style = \"W\") #>  #> Moran I statistic standard deviate = 3.0141, p-value = 0.001289 #> alternative hypothesis: greater #> sample estimates: #> Observed Moran I      Expectation         Variance  #>      0.241298974     -0.032224366      0.008235091  #>  lm.morantest(oldcrime.wlm, nb2listw(COL.nb, style=\"W\"),  resfun=rstudent) #>  #> \tGlobal Moran I for regression residuals #>  #> data:   #> model: lm(formula = CRIME ~ HOVAL + INC, data = COL.OLD, weights = #> I(1/AREA_PL)) #> weights: nb2listw(COL.nb, style = \"W\") #>  #> Moran I statistic standard deviate = 2.822, p-value = 0.002387 #> alternative hypothesis: greater #> sample estimates: #> Observed Moran I      Expectation         Variance  #>      0.223860298     -0.032224366      0.008235091  #>"},{"path":"https://r-spatial.github.io/spdep/reference/lm.morantest.sad.html","id":null,"dir":"Reference","previous_headings":"","what":"Saddlepoint approximation of global Moran's I test — lm.morantest.sad","title":"Saddlepoint approximation of global Moran's I test — lm.morantest.sad","text":"function implements Tiefelsdorf's application Saddlepoint approximation global Moran's 's reference distribution.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lm.morantest.sad.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Saddlepoint approximation of global Moran's I test — lm.morantest.sad","text":"","code":"lm.morantest.sad(model, listw, zero.policy=attr(listw, \"zero.policy\"),   alternative=\"greater\", spChk=NULL, resfun=weighted.residuals,   tol=.Machine$double.eps^0.5, maxiter=1000, tol.bounds=0.0001,   zero.tol = 1e-07, Omega=NULL, save.M=NULL, save.U=NULL) # S3 method for class 'moransad' print(x, ...) # S3 method for class 'moransad' summary(object, ...) # S3 method for class 'summary.moransad' print(x, ...)"},{"path":"https://r-spatial.github.io/spdep/reference/lm.morantest.sad.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Saddlepoint approximation of global Moran's I test — lm.morantest.sad","text":"model object class lm returned lm; weights may specified lm fit, offsets used listw listw object created example nb2listw zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA alternative character string specifying alternative hypothesis, must one greater (default), less two.sided. spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption() resfun default: weighted.residuals; function used extract residuals lm object, may residuals, weighted.residuals, rstandard, rstudent tol desired accuracy (convergence tolerance) uniroot maxiter maximum number iterations uniroot tol.bounds offset bounds uniroot zero.tol tolerance used find eigenvalues close absolute zero Omega SAR process matrix may passed test alternative hypothesis, example Omega <- invIrW(listw, rho=0.1); Omega <- tcrossprod(Omega), chol() taken internally save.M return full M matrix use spdep:::exactMoranAlt save.U return full U matrix use spdep:::exactMoranAlt x object printed object object summarised ... arguments passed ","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lm.morantest.sad.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Saddlepoint approximation of global Moran's I test — lm.morantest.sad","text":"function involves finding eigenvalues n n matrix, numerically finding root Saddlepoint approximation, therefore used care n large.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lm.morantest.sad.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Saddlepoint approximation of global Moran's I test — lm.morantest.sad","text":"list class moransad following components: statistic value saddlepoint approximation  standard deviate global Moran's . p.value p-value test. estimate value observed global Moran's . alternative character string describing alternative hypothesis. method character string giving method used. data.name character string giving name(s) data. internal1 Saddlepoint omega, r u internal2 f.root, iter estim.prec uniroot df degrees freedom tau eigenvalues (excluding zero values)","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lm.morantest.sad.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Saddlepoint approximation of global Moran's I test — lm.morantest.sad","text":"Tiefelsdorf, M. 2002 Saddlepoint approximation Moran's local Moran's Ii reference distributions numerical evaluation. Geographical Analysis, 34, pp. 187–206; Bivand RS, Wong DWS 2018 Comparing implementations global local indicators spatial association. TEST, 27(3), 716–748 doi:10.1007/s11749-018-0599-x","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lm.morantest.sad.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Saddlepoint approximation of global Moran's I test — lm.morantest.sad","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/lm.morantest.sad.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Saddlepoint approximation of global Moran's I test — lm.morantest.sad","text":"","code":"eire <- st_read(system.file(\"shapes/eire.gpkg\", package=\"spData\")[1]) #> Reading layer `eire' from data source  #>   `/home/rsb/lib/r_libs/spData/shapes/eire.gpkg' using driver `GPKG' #> Simple feature collection with 26 features and 10 fields #> Geometry type: MULTIPOLYGON #> Dimension:     XY #> Bounding box:  xmin: -4.12 ymin: 5768 xmax: 300.82 ymax: 6119.25 #> Projected CRS: Undefined Cartesian SRS with unknown unit row.names(eire) <- as.character(eire$names) eire.nb <- poly2nb(eire) e.lm <- lm(OWNCONS ~ ROADACC, data=eire) lm.morantest(e.lm, nb2listw(eire.nb)) #>  #> \tGlobal Moran I for regression residuals #>  #> data:   #> model: lm(formula = OWNCONS ~ ROADACC, data = eire) #> weights: nb2listw(eire.nb) #>  #> Moran I statistic standard deviate = 3.2575, p-value = 0.0005619 #> alternative hypothesis: greater #> sample estimates: #> Observed Moran I      Expectation         Variance  #>       0.33660565      -0.05877741       0.01473183  #>  lm.morantest.sad(e.lm, nb2listw(eire.nb)) #>  #> \tSaddlepoint approximation for global Moran's I (Barndorff-Nielsen #> \tformula) #>  #> data:   #> model:lm(formula = OWNCONS ~ ROADACC, data = eire) #> weights: nb2listw(eire.nb) #>  #> Saddlepoint approximation = 2.9395, p-value = 0.001644 #> alternative hypothesis: greater #> sample estimates: #> Observed Moran I  #>        0.3366057  #>  summary(lm.morantest.sad(e.lm, nb2listw(eire.nb))) #>  #> \tSaddlepoint approximation for global Moran's I (Barndorff-Nielsen #> \tformula) #>  #> data:   #> model:lm(formula = OWNCONS ~ ROADACC, data = eire) #> weights: nb2listw(eire.nb) #>  #> Saddlepoint approximation = 2.9395, p-value = 0.001644 #> alternative hypothesis: greater #> sample estimates: #> Observed Moran I  #>        0.3366057  #>  #>  Expectation     Variance Std. deviate     Skewness     Kurtosis      Minimum  #>  -0.05877741   0.01473183   3.25753938   0.31336881   3.05047361  -0.67545810  #>      Maximum        omega        sad.r        sad.u  #>   0.89091555   0.76549075   2.77616585   4.36854629  #>      f.root        iter  estim.prec  #> 7.01314e-14 1.10000e+01          NA  e.wlm <- lm(OWNCONS ~ ROADACC, data=eire, weights=RETSALE) lm.morantest(e.wlm, nb2listw(eire.nb), resfun=rstudent) #>  #> \tGlobal Moran I for regression residuals #>  #> data:   #> model: lm(formula = OWNCONS ~ ROADACC, data = eire, weights = RETSALE) #> weights: nb2listw(eire.nb) #>  #> Moran I statistic standard deviate = 3.1385, p-value = 0.0008491 #> alternative hypothesis: greater #> sample estimates: #> Observed Moran I      Expectation         Variance  #>       0.34500329      -0.04049313       0.01508687  #>  lm.morantest.sad(e.wlm, nb2listw(eire.nb), resfun=rstudent) #>  #> \tSaddlepoint approximation for global Moran's I (Barndorff-Nielsen #> \tformula) #>  #> data:   #> model:lm(formula = OWNCONS ~ ROADACC, data = eire, weights = RETSALE) #> weights: nb2listw(eire.nb) #>  #> Saddlepoint approximation = 2.8708, p-value = 0.002047 #> alternative hypothesis: greater #> sample estimates: #> Observed Moran I  #>        0.3450033  #>"},{"path":"https://r-spatial.github.io/spdep/reference/localC.html","id":null,"dir":"Reference","previous_headings":"","what":"Compute Local Geary statistic — localC","title":"Compute Local Geary statistic — localC","text":"Local Geary local adaptation Geary's C statistic spatial autocorrelation. Local Geary uses squared differences measure dissimilarity unlike Local Moran. Low values Local Geary indicate positive spatial autocorrelation large refers negative spatial autocorrelation. Inference Local Geary based permutation approach compares observed value reference distribution spatial randomness. localC_perm() returns pseudo p-value. analytical p-value based number permutations used care.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localC.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Compute Local Geary statistic — localC","text":"","code":"localC(x, ..., zero.policy=NULL)  # Default S3 method localC(x, listw, ..., zero.policy=attr(listw, \"zero.policy\"))  # S3 method for class 'formula' localC(formula, data, listw, ..., zero.policy=attr(listw, \"zero.policy\"))  # S3 method for class 'list' localC(x, listw, ..., zero.policy=attr(listw, \"zero.policy\"))  # S3 method for class 'matrix' localC(x, listw, ..., zero.policy=attr(listw, \"zero.policy\"))  # S3 method for class 'data.frame' localC(x, listw, ..., zero.policy=attr(listw, \"zero.policy\"))  localC_perm(x, ..., zero.policy=NULL, iseed=NULL, no_repeat_in_row=FALSE)  # Default S3 method localC_perm(x, listw, nsim = 499, alternative = \"two.sided\", ...,  zero.policy=attr(listw, \"zero.policy\"), iseed=NULL, no_repeat_in_row=FALSE)  # S3 method for class 'formula' localC_perm(formula, data, listw, nsim = 499,  alternative = \"two.sided\", ..., zero.policy=attr(listw, \"zero.policy\"), iseed=NULL,  no_repeat_in_row=FALSE)"},{"path":"https://r-spatial.github.io/spdep/reference/localC.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Compute Local Geary statistic — localC","text":"x numeric vector, numeric matrix, list. See details . formula one-sided formula determining variables used. listw listw object created example nb2listw. data Used formula provided. matrix data frame containing variables formula formula. nsim number simulations used permutation test. alternative character defining alternative hypothesis. Must one \"two.sided\", \"less\" \"greater\". ... arguments passed methods. zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA. iseed default NULL, used set seed;output reproducible count CPU cores across computation distributed no_repeat_in_row default FALSE, TRUE, sample conditionally row without replacements avoid duplicate values, https://github.com/r-spatial/spdep/issues/124","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localC.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Compute Local Geary statistic — localC","text":"Local Geary can extended multivariate context. x numeric vector, univariate Local Geary calculated. calculate multivariate Local Moran provide either list matrix. x list, element must numeric vector length length neighbours listw. case x matrix number rows must length neighbours listw. required univariate context, standardized Local Geary calculated. multivariate Local Geary always standardized. univariate Local Geary calculated \\(c_i = \\sum_j w_{ij}(x_i - x_j)^2\\) multivariate Local Geary calculated \\(c_{k,} = \\sum_{v=1}^{k} c_{v,}\\) described Anselin (2019).","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localC.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Compute Local Geary statistic — localC","text":"numeric vector containing Local Geary statistic attribute pseudo-p localC_perm() used. pseudo-p 8 column matrix containing  E.Ci expectation Local Geary statistic based permutation sample Var.Ci variance Local Geary based permutation sample Z.Ci standard deviate Local Geary based permutation sample Pr() p-value Local Geary statistic using pnorm() using standard deviates based permutation sample means standard deviations Pr() Sim rank() punif() observed statistic rank [0, 1] p-values using alternative= Pr(folded) Sim simulation folded [0, 0.5] range ranked p-value (based https://github.com/pysal/esda/blob/4a63e0b5df1e754b17b5f1205b8cadcbecc5e061/esda/crand.py#L211-L213) Skewness output e1071::skewness() permutation samples underlying standard deviates Kurtosis output e1071::kurtosis() permutation samples underlying standard deviates","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localC.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Compute Local Geary statistic — localC","text":"Anselin, L. (1995), Local Indicators Spatial Association—LISA. Geographical Analysis, 27: 93-115. doi:10.1111/j.1538-4632.1995.tb00338.x Anselin, L. (2019), Local Indicator Multivariate Spatial Association: Extending Gearys c. Geogr Anal, 51: 133-150. doi:10.1111/gean.12164","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localC.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Compute Local Geary statistic — localC","text":"Josiah Parry josiah.parry@gmail.com Roger Bivand","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localC.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Compute Local Geary statistic — localC","text":"","code":"orig <- spData::africa.rook.nb listw <- nb2listw(orig) x <- spData::afcon$totcon  (A <- localC(x, listw)) #>  [1] 0.39025457 0.50460439 0.15303047 2.90814878 3.40006901 0.17103368 #>  [7] 0.29947832 0.72444806 2.30617282 5.70252541 2.23161263 0.17833029 #> [13] 0.18420002 0.18680408 0.37851643 0.11056720 0.14814835 0.17257920 #> [19] 0.03254150 0.18992772 0.08749322 3.71970760 0.09566918 0.26112918 #> [25] 0.09505331 2.99934478 1.17465032 1.64868780 0.87901004 0.05909537 #> [31] 2.54591475 3.85570655 2.99413462 0.96084992 0.80678832 1.56869350 #> [37] 0.86422915 0.38817470 0.23425755 1.26191610 1.34455327 1.80707481 listw1 <- nb2listw(droplinks(sym.attr.nb(orig), 3, sym=TRUE), zero.policy=TRUE) #> Warning: some observations have no neighbours #> Warning: neighbour object has 2 sub-graphs (A1 <- localC(x, listw1, zero.policy=FALSE)) #>  [1] 0.39025457 0.57491918         NA 2.90814878 3.40006901 0.17103368 #>  [7] 0.29947832 0.72444806 2.30617282 5.70252541 2.23161263 0.17833029 #> [13] 0.18420002 0.18680408 0.37851643 0.11056720 0.14814835 0.17257920 #> [19] 0.03254150 0.18992772 0.08749322 3.71970760 0.09566918 0.26112918 #> [25] 0.09505331 2.99934478 1.17465032 1.64868780 0.87901004 0.05909537 #> [31] 2.54591475 3.85570655 2.99413462 0.96084992 0.80678832 1.56869350 #> [37] 0.86422915 0.38817470 0.23425755 1.26191610 1.34455327 1.80707481 (A2 <- localC(x, listw1, zero.policy=TRUE)) #>  [1] 0.39025457 0.57491918 0.00000000 2.90814878 3.40006901 0.17103368 #>  [7] 0.29947832 0.72444806 2.30617282 5.70252541 2.23161263 0.17833029 #> [13] 0.18420002 0.18680408 0.37851643 0.11056720 0.14814835 0.17257920 #> [19] 0.03254150 0.18992772 0.08749322 3.71970760 0.09566918 0.26112918 #> [25] 0.09505331 2.99934478 1.17465032 1.64868780 0.87901004 0.05909537 #> [31] 2.54591475 3.85570655 2.99413462 0.96084992 0.80678832 1.56869350 #> [37] 0.86422915 0.38817470 0.23425755 1.26191610 1.34455327 1.80707481   # \\dontrun{ library(reticulate) use_python(\"/usr/bin/python\", required = TRUE) gp <- import(\"geopandas\") ps <- import(\"libpysal\") W <- listw2mat(listw) w <- ps$weights$full2W(W, rownames(W)) w$transform <- \"R\" esda <- import(\"esda\") lM <- esda$Moran_Local(x, w) all.equal(unname(localmoran(x, listw, mlvar=FALSE)[,1]), c(lM$Is)) #> [1] TRUE # confirm x and w the same lC <- esda$Geary_Local(connectivity=w)$fit(scale(x)) # np$std missing ddof=1 n <- length(x) D0 <- spdep:::geary.intern((x - mean(x)) / sqrt(var(x)*(n-1)/n), listw, n=n) # lC components probably wrongly ordered https://github.com/pysal/esda/issues/192 o <- match(round(D0, 6), round(lC$localG, 6)) all.equal(c(lC$localG)[o], D0) #> [1] TRUE # simulation order not retained lC$p_sim[o] #>  [1] 0.258 0.448 0.123 0.019 0.123 0.021 0.294 0.439 0.155 0.001 0.127 0.131 #> [13] 0.149 0.256 0.456 0.191 0.111 0.293 0.001 0.037 0.027 0.098 0.059 0.279 #> [25] 0.150 0.028 0.114 0.277 0.484 0.001 0.067 0.099 0.091 0.243 0.299 0.001 #> [37] 0.301 0.488 0.307 0.209 0.248 0.269 attr(C, \"pseudo-p\")[,6] #> NULL # }"},{"path":"https://r-spatial.github.io/spdep/reference/localG.html","id":null,"dir":"Reference","previous_headings":"","what":"G and Gstar local spatial statistics — localG","title":"G and Gstar local spatial statistics — localG","text":"local spatial statistic G calculated zone based spatial weights object used. value returned Z-value, may used diagnostic tool. High positive values indicate posibility local cluster high values variable analysed, low relative values similar cluster low values. inference, Bonferroni-type test suggested references, tables critical values may found (see also details ).","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localG.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"G and Gstar local spatial statistics — localG","text":"","code":"localG(x, listw, zero.policy=attr(listw, \"zero.policy\"), spChk=NULL, GeoDa=FALSE,  alternative = \"two.sided\", return_internals=TRUE) localG_perm(x, listw, nsim=499, zero.policy=attr(listw, \"zero.policy\"), spChk=NULL,  alternative = \"two.sided\", iseed=NULL, fix_i_in_Gstar_permutations=TRUE,  no_repeat_in_row=FALSE)"},{"path":"https://r-spatial.github.io/spdep/reference/localG.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"G and Gstar local spatial statistics — localG","text":"x numeric vector length neighbours list listw listw listw object created example nb2listw zero.policy default NULL, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption() GeoDa default FALSE, TRUE, drop x values -neighbour self-neighbour observations summations nsim default 499, number conditonal permutation simulations alternative character string specifying alternative hypothesis, must one \"two.sided\" (default), \"greater\" \"less\". return_internals default TRUE, unused iseed default NULL, used set seed; output reproducible count CPU cores across computation distributed fix_i_in_Gstar_permutations default TRUE (fix x self permutations local G-star), set FALSE use pre-1.2-8 behaviour no_repeat_in_row default FALSE, TRUE, sample conditionally row without replacements avoid duplicate values, https://github.com/r-spatial/spdep/issues/124","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localG.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"G and Gstar local spatial statistics — localG","text":"neighbours member listw \"self.included\" attribute set TRUE, Gstar variant, including self-weight \\(w_{ii} > 0\\), calculated returned.  returned vector \"gstari\" attribute set TRUE.  Self-weights must included using include.self function converting neighbour list spatial weights list nb2listw shown example. critical values statistic assumptions given references 95th percentile n=1: 1.645, n=50: 3.083, n=100: 3.289, n=1000: 3.886.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localG.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"G and Gstar local spatial statistics — localG","text":"vector G Gstar standard deviate values, attributes \"gstari\" set TRUE FALSE, \"call\" set function call, class \"localG\". conditional permutation, returned value localG(), simulated standard deviate returned column \"StdDev.Gi\" attr(., \"internals\").","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localG.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"G and Gstar local spatial statistics — localG","text":"Conditional permutations added comparative purposes; permutations whole data vector omitting observation , 1.2-8 fixing observation neighbour local G-star.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localG.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"G and Gstar local spatial statistics — localG","text":"Ord, J. K. Getis, . 1995 Local spatial autocorrelation statistics: distributional issues application. Geographical Analysis, 27, 286–306; Getis, . Ord, J. K. 1996 Local spatial statistics: overview. P. Longley M. Batty (eds) Spatial analysis: modelling GIS environment (Cambridge: Geoinformation International), 261–277; Bivand RS, Wong DWS 2018 Comparing implementations global local indicators spatial association. TEST, 27(3), 716–748 doi:10.1007/s11749-018-0599-x","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localG.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"G and Gstar local spatial statistics — localG","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localG.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"G and Gstar local spatial statistics — localG","text":"","code":"data(getisord, package=\"spData\") # spData 0.3.2 changes x, y, xyz object names to go_x, go_y, go_xyz to # avoid putting these objects into the global environment via lazy loading if (exists(\"go_xyz\") && packageVersion(\"spData\") >= \"0.3.2\") {   xyz <- go_xyz   x <- go_x   y <- go_y } xycoords <- cbind(xyz$x, xyz$y) nb30 <- dnearneigh(xycoords, 0, 30) G30 <- localG(xyz$val, nb2listw(nb30, style=\"B\")) G30[length(xyz$val)-136] #> [1] 1.221979 set.seed(1) G30_sim <- localG_perm(xyz$val, nb2listw(nb30, style=\"B\")) G30_sim[length(xyz$val)-136] #> [1] 1.221979 nb60 <- dnearneigh(xycoords, 0, 60) G60 <- localG(xyz$val, nb2listw(nb60, style=\"B\")) G60[length(xyz$val)-136] #> [1] 1.748098 nb90 <- dnearneigh(xycoords, 0, 90) G90 <- localG(xyz$val, nb2listw(nb90, style=\"B\")) G90[length(xyz$val)-136] #> [1] 1.986135 nb120 <- dnearneigh(xycoords, 0, 120) G120 <- localG(xyz$val, nb2listw(nb120, style=\"B\")) G120[length(xyz$val)-136] #> [1] 1.893374 nb150 <- dnearneigh(xycoords, 0, 150) G150 <- localG(xyz$val, nb2listw(nb150, style=\"B\")) G150[length(xyz$val)-136] #> [1] 1.237454 brks <- seq(-5,5,1) cm.col <- cm.colors(length(brks)-1) image(x, y, t(matrix(G30, nrow=16, ncol=16, byrow=TRUE)),   breaks=brks, col=cm.col, asp=1) text(xyz$x, xyz$y, round(G30, digits=1), cex=0.7) polygon(c(195,225,225,195), c(195,195,225,225), lwd=2) title(main=expression(paste(\"Values of the \", G[i], \" statistic\")))  G30s <- localG(xyz$val, nb2listw(include.self(nb30),  style=\"B\")) cat(\"value according to Getis and Ord's eq. 14.2, p. 263 (1996)\\n\") #> value according to Getis and Ord's eq. 14.2, p. 263 (1996) G30s[length(xyz$val)-136] #> [1] 1.45078 cat(paste(\"value given by Getis and Ord (1996), p. 267\",   \"(division by n-1 rather than n \\n in variance)\\n\")) #> value given by Getis and Ord (1996), p. 267 (division by n-1 rather than n  #>  in variance) G30s[length(xyz$val)-136] *   (sqrt(sum(scale(xyz$val, scale=FALSE)^2)/length(xyz$val)) /   sqrt(var(xyz$val))) #> [1] 1.447943 image(x, y, t(matrix(G30s, nrow=16, ncol=16, byrow=TRUE)),   breaks=brks, col=cm.col, asp=1) text(xyz$x, xyz$y, round(G30s, digits=1), cex=0.7) polygon(c(195,225,225,195), c(195,195,225,225), lwd=2) title(main=expression(paste(\"Values of the \", G[i]^\"*\", \" statistic\")))"},{"path":"https://r-spatial.github.io/spdep/reference/localGS.html","id":null,"dir":"Reference","previous_headings":"","what":"A local hotspot statistic for analysing multiscale datasets — localGS","title":"A local hotspot statistic for analysing multiscale datasets — localGS","text":"function implements \\(GS_i\\) test statistic local hotspots specific pairwise evaluated distance bands, proposed Westerholt et al. (2015).  Like hotspot estimator \\(G_i^*\\), \\(GS_i\\) statistic given z-scores can evaluated accordingly. idea method identify hotspots datasets comprise several, difficult--separate processes operating different scales. often case complex user-generated datasets Twitter feeds. example, football match reflected tweets pubs, homes, stadium vicinity. exemplified phenomena represent different processes may detected different geometric scales. \\(GS_i\\) method enables identification specifying geometric scale band strictly calculating statistical quantities mean variance solely respective relevant observations interact range adjusted scale band. addition, neighbourhood relationships respective central unit, scale-relevant relationships considered. way, hotspots can detected specific scale ranges independently scales. statistic given : $$GS_i = \\frac{\\displaystyle\\sum_{j; k < j}{w_{ij}w_{ik}\\phi_{jk}a_{jk}} - \\frac{W_i}{\\Phi} \\displaystyle\\sum_{j; k < j}{\\phi_{jk}a_{jk}}}{\\sqrt{\\frac{W_i}{\\Phi}\\displaystyle\\sum_{j; k < j}{\\phi_{jk}a_{jk}^2} + \\frac{W_i\\left(W_i-1\\right)}{\\Phi\\left(\\Phi-1\\right)}\\left(\\Gamma^2 -\\!\\! \\displaystyle\\sum_{j; k < j}{\\left(\\phi_{jk}a_{jk}\\right)^2}\\right) - \\left(\\frac{W_i}{\\Phi}\\displaystyle\\sum_{j; k < j}{\\phi_{jk}a_{jk}}\\right)^2}}$$ $$a_{jk} = x_j + x_k,\\;\\;\\; W_i = \\displaystyle\\sum_{j; k < j}{w_{ij}w_{ik}\\phi_{jk}},\\;\\;\\; \\Phi = \\displaystyle\\sum_{j; k < j}{\\phi_{jk}},\\;\\;\\; \\textrm{} \\;\\;\\; \\Gamma = \\displaystyle\\sum_{j; k < j}{\\phi_{jk}a_{jk}}.$$","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localGS.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"A local hotspot statistic for analysing multiscale datasets — localGS","text":"","code":"localGS(x, listw, dmin, dmax, attr, longlat = NULL)"},{"path":"https://r-spatial.github.io/spdep/reference/localGS.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"A local hotspot statistic for analysing multiscale datasets — localGS","text":"x sf sp object listw listw object dmin lower distance bound (greater equal) dmax upper distance bound (less equal) attr name attribute interest longlat default NULL; TRUE point coordinates longitude-latitude decimal degrees, case distances measured kilometres; x SpatialPoints object, value taken object , overrides argument NULL; distances measured map units FALSE NULL","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localGS.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"A local hotspot statistic for analysing multiscale datasets — localGS","text":"pairs observations shared distance (map units) interval [dmin, dmax] within maximum radius dmax around corresponding output observation considered. Thereby, also mean values variance terms estimated within measure adjusted scale range consideration. application examples method see Westerholt et al. (2015) (applied tweets) Sonea & Westerholt (2021) (applied access banking scenario).","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localGS.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"A local hotspot statistic for analysing multiscale datasets — localGS","text":"vector \\(GS_i\\) values given z-scores.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localGS.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"A local hotspot statistic for analysing multiscale datasets — localGS","text":"Westerholt, R., Resch, B. & Zipf, . 2015. local scale-sensitive indicator spatial autocorrelation assessing high-low-value clusters multiscale datasets. International Journal Geographical Information Science, 29(5), 868–887, doi:10.1080/13658816.2014.1002499 . Sonea, . Westerholt, R. (2021): Geographic temporal access basic banking services Wales. Applied Spatial Analysis Policy, 14 (4), 879–905, doi:10.1007/s12061-021-09386-3 .","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localGS.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"A local hotspot statistic for analysing multiscale datasets — localGS","text":"René Westerholt rene.westerholt@tu-dortmund.de","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/localGS.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"A local hotspot statistic for analysing multiscale datasets — localGS","text":"","code":"# \\donttest{ boston.tr <- sf::st_read(system.file(\"shapes/boston_tracts.gpkg\", package=\"spData\")[1]) #> Reading layer `boston_tracts' from data source  #>   `/home/rsb/lib/r_libs/spData/shapes/boston_tracts.gpkg' using driver `GPKG' #> Simple feature collection with 506 features and 36 fields #> Geometry type: POLYGON #> Dimension:     XY #> Bounding box:  xmin: -71.52311 ymin: 42.00305 xmax: -70.63823 ymax: 42.67307 #> Geodetic CRS:  NAD27 boston.tr_utm <- st_transform(boston.tr, 32619) #26786  boston_listw1 <- nb2listwdist(dnearneigh(st_centroid(boston.tr_utm), 1, 2000),     boston.tr_utm, type = \"dpd\", alpha = 2, zero.policy = TRUE, dmax = 9500) #> Warning: st_centroid assumes attributes are constant over geometries #> Warning: neighbour object has 120 sub-graphs  boston_listw2 <- nb2listwdist(dnearneigh(st_centroid(boston.tr_utm), 5000, 9500),      boston.tr_utm, type = \"dpd\", alpha = 2, zero.policy = TRUE, dmax = 9500) #> Warning: st_centroid assumes attributes are constant over geometries  boston_RM_gsi_1 <- localGS(boston.tr_utm, boston_listw1, 1, 2000, \"RM\", FALSE) boston_RM_gsi_2 <- localGS(boston.tr_utm, boston_listw2, 2000, 9500, \"RM\", FALSE) # }"},{"path":"https://r-spatial.github.io/spdep/reference/local_joincount_bv.html","id":null,"dir":"Reference","previous_headings":"","what":"Calculate the local bivariate join count — local_joincount_bv","title":"Calculate the local bivariate join count — local_joincount_bv","text":"bivariate join count (BJC) evaluates event occurrences predefined regions tests co-occurrence events deviates complete spatial randomness.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/local_joincount_bv.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Calculate the local bivariate join count — local_joincount_bv","text":"","code":"local_joincount_bv(   x,   z,   listw,   nsim = 199,   alternative = \"two.sided\" )"},{"path":"https://r-spatial.github.io/spdep/reference/local_joincount_bv.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Calculate the local bivariate join count — local_joincount_bv","text":"x binary variable either numeric logical z binary variable either numeric logical length x listw listw object containing binary weights created, example, nb2listw(nb, style = \"B\") nsim number conditional permutation simulations alternative default \"greater\". One \"less\" \"greater\".","code":""},{"path":"https://r-spatial.github.io/spdep/reference/local_joincount_bv.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Calculate the local bivariate join count — local_joincount_bv","text":"two cases evaluated bivariate join count. first -situ colocation (CLC) xi = 1 zi = 1. second general form bivariate join count (BJC) used -situ colocation. BJC case \"useful x z occur location, x z correspond two different values single categorical variable\" \"x z can co-locate, \" (Anselin Li, 2019). Whereas CLC case useful evaluating simultaneous occurrences events. local bivariate join count statistic requires binary weights list can generated nb2listw(nb, style = \"B\"). P-values reported regions match CLC BJC criteria. Others associated p-value. P-values estimated using conditional permutation approach. creates reference distribution observed statistic compared.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/local_joincount_bv.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Calculate the local bivariate join count — local_joincount_bv","text":"data.frame two columns join_count p_sim number rows equal length arguments x.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/local_joincount_bv.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Calculate the local bivariate join count — local_joincount_bv","text":"Anselin, L., & Li, X. (2019). Operational Local Join Count Statistics Cluster Detection. Journal geographical systems, 21(2), 189–210. doi:10.1007/s10109-019-00299-x","code":""},{"path":"https://r-spatial.github.io/spdep/reference/local_joincount_bv.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Calculate the local bivariate join count — local_joincount_bv","text":"Josiah Parry josiah.parry@gmail.com","code":""},{"path":"https://r-spatial.github.io/spdep/reference/local_joincount_bv.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Calculate the local bivariate join count — local_joincount_bv","text":"","code":"data(\"oldcol\") listw <- nb2listw(COL.nb, style = \"B\") # Colocation case x <- COL.OLD[[\"CP\"]] z <- COL.OLD[[\"EW\"]] set.seed(1) res <- local_joincount_bv(x, z, listw) na.omit(res) #>    join_count p_sim #> 9           2 0.480 #> 19          3 0.180 #> 20          4 0.020 #> 21          3 0.040 #> 22          3 0.060 #> 23          4 0.070 #> 24          5 0.005 #> 27          2 0.300 #> 28          3 0.050 #> 29          5 0.010 #> 30          5 0.010 #> 31          9 0.005 #> 32          4 0.090 #> 33          4 0.055 # no colocation case z <- 1 - x set.seed(1) res <- local_joincount_bv(x, z, listw) na.omit(res) #>    join_count p_sim #> 9           2 0.065 #> 19          3 0.300 #> 20          1 0.015 #> 21          1 0.040 #> 22          1 0.045 #> 23          3 0.165 #> 24          1 0.000 #> 27          2 0.230 #> 28          1 0.050 #> 29          1 0.000 #> 36          1 0.000 #> 37          2 0.005 #> 38          2 0.185 #> 39          2 0.265 #> 40          1 0.005 #> 43          1 0.070"},{"path":"https://r-spatial.github.io/spdep/reference/local_joincount_uni.html","id":null,"dir":"Reference","previous_headings":"","what":"Calculate the local univariate join count — local_joincount_uni","title":"Calculate the local univariate join count — local_joincount_uni","text":"univariate local join count statistic used identify clusters rarely occurring binary variables. binary variable interest occur less half time.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/local_joincount_uni.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Calculate the local univariate join count — local_joincount_uni","text":"","code":"local_joincount_uni(   fx,   chosen,   listw,   alternative = \"two.sided\",   nsim = 199,   iseed = NULL,   no_repeat_in_row=FALSE )"},{"path":"https://r-spatial.github.io/spdep/reference/local_joincount_uni.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Calculate the local univariate join count — local_joincount_uni","text":"fx binary variable either numeric logical chosen scalar character containing level fx considered observed value (1). listw listw object containing binary weights created, example, nbwlistw(nb, style = \"B\") alternative default \"greater\". One \"less\" \"greater\". nsim number conditional permutation simulations iseed default NULL, used set seed; output reproducible count CPU cores across computation distributed no_repeat_in_row default FALSE, TRUE, sample conditionally row without replacements avoid duplicate values, https://github.com/r-spatial/spdep/issues/124","code":""},{"path":"https://r-spatial.github.io/spdep/reference/local_joincount_uni.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Calculate the local univariate join count — local_joincount_uni","text":"data.frame two columns BB Pr() number rows equal length x.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/local_joincount_uni.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Calculate the local univariate join count — local_joincount_uni","text":"local join count statistic requires binary weights list can generated nb2listw(nb, style = \"B\"). Additionally, ensure binary variable interest rarely occurring half observations. P-values estimated using conditional permutation approach. creates reference distribution observed statistic compared. see Geoda Glossary.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/local_joincount_uni.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Calculate the local univariate join count — local_joincount_uni","text":"Anselin, L., & Li, X. (2019). Operational Local Join Count Statistics Cluster Detection. Journal geographical systems, 21(2), 189–210. doi:10.1007/s10109-019-00299-x","code":""},{"path":"https://r-spatial.github.io/spdep/reference/local_joincount_uni.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Calculate the local univariate join count — local_joincount_uni","text":"Josiah Parry josiah.parry@gmail.com","code":""},{"path":"https://r-spatial.github.io/spdep/reference/local_joincount_uni.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Calculate the local univariate join count — local_joincount_uni","text":"","code":"data(oldcol) fx <- as.factor(ifelse(COL.OLD$CRIME < 35, \"low-crime\", \"high-crime\")) listw <- nb2listw(COL.nb, style = \"B\") set.seed(1) (res <- local_joincount_uni(fx, chosen = \"high-crime\", listw)) #>    BB Pr(z != E(BBi)) #> 1   0              NA #> 2   0              NA #> 3   4            0.50 #> 4   0              NA #> 5   0              NA #> 6   0              NA #> 7   4            0.89 #> 8   0              NA #> 9   5            0.11 #> 10  0              NA #> 11  0              NA #> 12  0              NA #> 13  0              NA #> 14  0              NA #> 15  0              NA #> 16  0              NA #> 17  0              NA #> 18  0              NA #> 19  0              NA #> 20  3            0.55 #> 21  2            0.84 #> 22  3            0.30 #> 23  4            0.61 #> 24  5            0.12 #> 25  0              NA #> 26  0              NA #> 27  0              NA #> 28  0              NA #> 29  3            0.98 #> 30  5            0.09 #> 31  8            0.01 #> 32  7            0.02 #> 33  6            0.02 #> 34  5            0.04 #> 35  7            0.03 #> 36  8            0.02 #> 37  6            0.05 #> 38  5            0.04 #> 39  3            0.44 #> 40  5            0.14 #> 41  3            0.13 #> 42  5            0.05 #> 43  2            0.63 #> 44  0              NA #> 45  0              NA #> 46  0              NA #> 47  0              NA #> 48  0              NA #> 49  0              NA"},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.exact.html","id":null,"dir":"Reference","previous_headings":"","what":"Exact local Moran's Ii tests — localmoran.exact","title":"Exact local Moran's Ii tests — localmoran.exact","text":"localmoran.exact provides exact local Moran's Ii tests null hypothesis, localmoran.exact.alt provides exact local Moran's Ii tests alternative hypothesis. case, model may fitted model derived model fitted spatialreg::errorsarlm, covariance matrix can passed Omega= argument.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.exact.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Exact local Moran's Ii tests — localmoran.exact","text":"","code":"localmoran.exact(model, select, nb, glist = NULL, style = \"W\",   zero.policy = NULL, alternative = \"two.sided\", spChk = NULL,   resfun = weighted.residuals, save.Vi = FALSE, useTP=FALSE, truncErr=1e-6,   zeroTreat=0.1) localmoran.exact.alt(model, select, nb, glist = NULL, style = \"W\",  zero.policy = NULL, alternative = \"two.sided\", spChk = NULL,  resfun = weighted.residuals, Omega = NULL, save.Vi = FALSE,  save.M = FALSE, useTP=FALSE, truncErr=1e-6, zeroTreat=0.1) # S3 method for class 'localmoranex' print(x, ...) # S3 method for class 'localmoranex' as.data.frame(x, row.names=NULL, optional=FALSE, ...)"},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.exact.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Exact local Moran's Ii tests — localmoran.exact","text":"model object class lm returned lm (assuming global spatial autocorrelation), object class sarlm returned spatial simultaneous autoregressive model fit (assuming global spatial autocorrelation represented model spatial coefficient); weights may specified lm fit, offsets used select integer vector id. numbers zones tested; missing, zones nb list neighbours class nb glist list general weights corresponding neighbours style can take values W, B, C, S zero.policy default NULL, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA alternative character string specifying alternative hypothesis, must one greater (default), less two.sided. spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption() resfun default: weighted.residuals; function used extract residuals lm object, may residuals, weighted.residuals, rstandard, rstudent Omega SAR process matrix may passed test alternative hypothesis, example Omega <- invIrW(listw, rho=0.1); Omega <- tcrossprod(Omega), chol() taken internally save.Vi TRUE, return star-shaped weights lists zone tested save.M TRUE, save list left right M products useTP default FALSE, TRUE, use truncation point integration rather upper=Inf, see Tiefelsdorf (2000), eq. 6.7, p.69 truncErr useTP=TRUE, pass truncation error truncation point function zeroTreat useTP=TRUE, pass zero adjustment truncation point function x object printed row.names ignored argument .data.frame.localmoranex; row names assigned localmoranex object optional ignored argument .data.frame.localmoranex; row names assigned localmoranex object ... arguments passed ","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.exact.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Exact local Moran's Ii tests — localmoran.exact","text":"list class localmoranex containing \"select\" lists,  class moranex following components: statistic value exact standard deviate global Moran's . p.value p-value test. estimate value observed local Moran's Ii. method character string giving method used. alternative character string describing alternative hypothesis. gamma eigenvalues (two extreme values null, vector alternative) oType usually set \"E\", set \"N\" integration leads domain value qnorm, Normal assumption substituted. occurs output p-value close zero data.name character string giving name(s) data. df degrees freedom zone tested Vi zone tested alternative tested, list left right M products attribute M.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.exact.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Exact local Moran's Ii tests — localmoran.exact","text":"Bivand RS, Müller W, Reder M (2009) Power calculations global local Moran’s . Comput Stat Data Anal 53:2859–2872; Bivand RS, Wong DWS 2018 Comparing implementations global local indicators spatial association. TEST, 27(3), 716–748 doi:10.1007/s11749-018-0599-x","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.exact.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Exact local Moran's Ii tests — localmoran.exact","text":"Markus Reder Roger Bivand","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.exact.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Exact local Moran's Ii tests — localmoran.exact","text":"","code":"eire <- st_read(system.file(\"shapes/eire.gpkg\", package=\"spData\")[1]) #> Reading layer `eire' from data source  #>   `/home/rsb/lib/r_libs/spData/shapes/eire.gpkg' using driver `GPKG' #> Simple feature collection with 26 features and 10 fields #> Geometry type: MULTIPOLYGON #> Dimension:     XY #> Bounding box:  xmin: -4.12 ymin: 5768 xmax: 300.82 ymax: 6119.25 #> Projected CRS: Undefined Cartesian SRS with unknown unit row.names(eire) <- as.character(eire$names) eire.nb <- poly2nb(eire) e.lm <- lm(OWNCONS ~ ROADACC, data=eire) localmoran.sad(e.lm, nb=eire.nb) #>              Local Morans I Saddlepoint    Pr. (Sad) #> 1 Carlow         0.21699668  0.95074844 3.417321e-01 #> 2 Cavan         -0.37257361 -1.00603119 3.144006e-01 #> 3 Clare          0.23197510  0.67166518 5.017969e-01 #> 4 Cork           0.78193548  1.74761575 8.053059e-02 #> 5 Donegal       -1.69064059 -1.72031078 8.537596e-02 #> 6 Dublin        -0.16069692 -0.35212627 7.247436e-01 #> 7 Galway         1.31371473  2.66849536 7.619183e-03 #> 8 Kerry          0.36534866  0.78073279 4.349597e-01 #> 9 Kildare       -0.02557544  0.04167665 9.667565e-01 #> 10 Kilkenny      0.57684331  1.70897697 8.745521e-02 #> 11 Laoghis      -0.05951798 -0.12155465 9.032517e-01 #> 12 Leitrim       0.38484587  1.47227033 1.409479e-01 #> 13 Limerick      0.11817987  0.45727712 6.474719e-01 #> 14 Longford      1.41643200  2.51113769 1.203427e-02 #> 15 Louth         0.56242920  1.07441571 2.826364e-01 #> 16 Mayo          0.87572704  2.05251226 4.011990e-02 #> 17 Meath         0.00367856  0.12813539 8.980418e-01 #> 18 Monaghan      0.55098311  1.23999193 2.149784e-01 #> 19 Offaly        0.15155556  0.80786519 4.191682e-01 #> 20 Roscommon     2.04368839  4.53187292 5.846302e-06 #> 21 Sligo        -0.47579871 -0.94578114 3.442602e-01 #> 22 Tipperary    -0.03454106 -0.06919691 9.448329e-01 #> 23 Waterford     0.85723423  1.91385108 5.563919e-02 #> 24 Westmeath     0.45138572  1.36017204 1.737755e-01 #> 25 Wexford       0.64371834  1.63188492 1.027037e-01 #> 26 Wicklow       0.02441950  0.21197000 8.321304e-01 localmoran.exact(e.lm, nb=eire.nb) #>              Local Morans I    Exact SD  Pr. (exact) #> 1 Carlow         0.21699668  1.02706083 3.043918e-01 #> 2 Cavan         -0.37257361 -1.04864802 2.943401e-01 #> 3 Clare          0.23197510  0.76362894 4.450884e-01 #> 4 Cork           0.78193548  1.77727656 7.552275e-02 #> 5 Donegal       -1.69064059 -1.74428756 8.110896e-02 #> 6 Dublin        -0.16069692 -0.44236119 6.582279e-01 #> 7 Galway         1.31371473  2.69199974 7.102500e-03 #> 8 Kerry          0.36534866  0.85742696 3.912090e-01 #> 9 Kildare       -0.02557544 -0.03475476 9.722753e-01 #> 10 Kilkenny      0.57684331  1.74146177 8.160267e-02 #> 11 Laoghis      -0.05951798 -0.21824035 8.272419e-01 #> 12 Leitrim       0.38484587  1.51434641 1.299380e-01 #> 13 Limerick      0.11817987  0.56922630 5.692026e-01 #> 14 Longford      1.41643200  2.53491837 1.124735e-02 #> 15 Louth         0.56242920  1.12775107 2.594251e-01 #> 16 Mayo          0.87572704  2.08125803 3.741029e-02 #> 17 Meath         0.00367856  0.16372685 8.699462e-01 #> 18 Monaghan      0.55098311  1.28435459 1.990179e-01 #> 19 Offaly        0.15155556  0.89537870 3.705847e-01 #> 20 Roscommon     2.04368839  4.55244870 5.302509e-06 #> 21 Sligo        -0.47579871 -0.98101752 3.265841e-01 #> 22 Tipperary    -0.03454106 -0.16132608 8.718366e-01 #> 23 Waterford     0.85723423  1.94188723 5.215075e-02 #> 24 Westmeath     0.45138572  1.40091422 1.612397e-01 #> 25 Wexford       0.64371834  1.66488051 9.593660e-02 #> 26 Wicklow       0.02441950  0.29717701 7.663314e-01 localmoran.exact(e.lm, nb=eire.nb, useTP=TRUE) #>              Local Morans I    Exact SD  Pr. (exact) #> 1 Carlow         0.21699668  1.02706127 3.043916e-01 #> 2 Cavan         -0.37257361 -1.04864834 2.943400e-01 #> 3 Clare          0.23197510  0.76362936 4.450881e-01 #> 4 Cork           0.78193548  1.77727666 7.552273e-02 #> 5 Donegal       -1.69064059 -1.74428741 8.110899e-02 #> 6 Dublin        -0.16069692 -0.44236158 6.582276e-01 #> 7 Galway         1.31371473  2.69199162 7.102673e-03 #> 8 Kerry          0.36534866  0.85742736 3.912087e-01 #> 9 Kildare       -0.02557544 -0.03540278 9.717586e-01 #> 10 Kilkenny      0.57684331  1.74146192 8.160264e-02 #> 11 Laoghis      -0.05951798 -0.21823772 8.272439e-01 #> 12 Leitrim       0.38484587  1.51434680 1.299379e-01 #> 13 Limerick      0.11817987  0.56922674 5.692023e-01 #> 14 Longford      1.41643200  2.53491383 1.124750e-02 #> 15 Louth         0.56242920  1.12775145 2.594249e-01 #> 16 Mayo          0.87572704  2.08125778 3.741032e-02 #> 17 Meath         0.00367856  0.15714487 8.751307e-01 #> 18 Monaghan      0.55098311  1.28435495 1.990178e-01 #> 19 Offaly        0.15155556  0.89537914 3.705844e-01 #> 20 Roscommon     2.04368839  4.53362873 5.797890e-06 #> 21 Sligo        -0.47579871 -0.98101780 3.265840e-01 #> 22 Tipperary    -0.03454106 -0.16116590 8.719627e-01 #> 23 Waterford     0.85723423  1.94188711 5.215077e-02 #> 24 Westmeath     0.45138572  1.40091457 1.612396e-01 #> 25 Wexford       0.64371834  1.66488069 9.593656e-02 #> 26 Wicklow       0.02441950  0.29790569 7.657751e-01 run <- FALSE if (requireNamespace(\"spatialreg\", quietly=TRUE)) run <- TRUE if (run) { e.errorsar <- spatialreg::errorsarlm(OWNCONS ~ ROADACC, data=eire,  listw=nb2listw(eire.nb)) lm.target <- lm(e.errorsar$tary ~ e.errorsar$tarX - 1) localmoran.exact.alt(lm.target, nb=eire.nb) } #>              Local Morans I    Exact SD Pr. (exact) #> 1 Carlow         0.17958462  0.83313548 0.404768327 #> 2 Cavan         -0.24752628 -0.82861508 0.407322251 #> 3 Clare         -0.27901334 -0.72313220 0.469598670 #> 4 Cork           0.37808655  1.15083938 0.249798320 #> 5 Donegal       -1.01894688 -1.50937607 0.131202704 #> 6 Dublin        -0.18171297 -0.50995181 0.610085224 #> 7 Galway         1.02193390  2.27605549 0.022842689 #> 8 Kerry         -0.94967914 -1.46954733 0.141684395 #> 9 Kildare        0.07005053  0.56174770 0.574287931 #> 10 Kilkenny      0.43022231  1.39078833 0.164289622 #> 11 Laoghis      -0.12239133 -0.45750046 0.647311369 #> 12 Leitrim      -0.24203970 -0.84925558 0.395739092 #> 13 Limerick     -0.03214546 -0.13098232 0.895789292 #> 14 Longford      0.38307454  1.17909760 0.238359315 #> 15 Louth         0.21301552  0.62068302 0.534808204 #> 16 Mayo          0.93971200  1.94079901 0.052282661 #> 17 Meath         0.12484415  0.78747315 0.431004937 #> 18 Monaghan     -0.16109919 -0.48277561 0.629255068 #> 19 Offaly       -0.00632492  0.03008421 0.975999892 #> 20 Roscommon     1.02089429  2.64333471 0.008209384 #> 21 Sligo        -2.01629233 -2.54211789 0.011018300 #> 22 Tipperary    -0.10810709 -0.51063241 0.609608478 #> 23 Waterford     0.44099279  1.28152280 0.200010096 #> 24 Westmeath    -0.06329661 -0.26575204 0.790430182 #> 25 Wexford       0.30764883  1.02115599 0.307180540 #> 26 Wicklow      -0.01696406 -0.04109885 0.967217095 if (run) { Omega <- spatialreg::invIrW(nb2listw(eire.nb), rho=e.errorsar$lambda) Omega1 <- tcrossprod(Omega) localmoran.exact.alt(lm.target, nb=eire.nb, Omega=Omega1) } #>              Local Morans I     Exact SD  Pr. (exact) #> 1 Carlow         0.17958462  0.009413917 0.9924888919 #> 2 Cavan         -0.24752628 -1.416786314 0.1565454123 #> 3 Clare         -0.27901334 -1.512813055 0.1303271517 #> 4 Cork           0.37808655  0.078686494 0.9372819884 #> 5 Donegal       -1.01894688 -1.935314161 0.0529517556 #> 6 Dublin        -0.18171297 -1.226543250 0.2199943101 #> 7 Galway         1.02193390  1.477322295 0.1395892645 #> 8 Kerry         -0.94967914 -2.427948363 0.0151845050 #> 9 Kildare        0.07005053 -0.042522018 0.9660825597 #> 10 Kilkenny      0.43022231  0.488471215 0.6252161096 #> 11 Laoghis      -0.12239133 -1.091910863 0.2748722827 #> 12 Leitrim      -0.24203970 -1.631825829 0.1027161824 #> 13 Limerick     -0.03214546 -0.921751557 0.3566581813 #> 14 Longford      0.38307454  0.183273193 0.8545836671 #> 15 Louth         0.21301552 -0.184065307 0.8539622227 #> 16 Mayo          0.93971200  1.182398031 0.2370478040 #> 17 Meath         0.12484415 -0.060499926 0.9517574750 #> 18 Monaghan     -0.16109919 -1.342787509 0.1793407892 #> 19 Offaly       -0.00632492 -0.409598788 0.6821002863 #> 20 Roscommon     1.02089429  1.238387417 0.2155724441 #> 21 Sligo        -2.01629233 -3.623597237 0.0002905339 #> 22 Tipperary    -0.10810709 -1.227333133 0.2196974073 #> 23 Waterford     0.44099279  0.433358039 0.6647546796 #> 24 Westmeath    -0.06329661 -0.956519228 0.3388099748 #> 25 Wexford       0.30764883  0.141381248 0.8875687671 #> 26 Wicklow      -0.01696406 -0.783977878 0.4330530911 if (run) { localmoran.exact.alt(lm.target, nb=eire.nb, Omega=Omega1, useTP=TRUE) } #>              Local Morans I     Exact SD  Pr. (exact) #> 1 Carlow         0.17958462  0.009414171 0.9924886892 #> 2 Cavan         -0.24752628 -1.416786809 0.1565452674 #> 3 Clare         -0.27901334 -1.512813519 0.1303270338 #> 4 Cork           0.37808655  0.078686628 0.9372818822 #> 5 Donegal       -1.01894688 -1.935314436 0.0529517219 #> 6 Dublin        -0.18171297 -1.226543734 0.2199941280 #> 7 Galway         1.02193390  1.477322399 0.1395892367 #> 8 Kerry         -0.94967914 -2.427949220 0.0151844691 #> 9 Kildare        0.07005053 -0.042526751 0.9660787872 #> 10 Kilkenny      0.43022231  0.488471349 0.6252160152 #> 11 Laoghis      -0.12239133 -1.091912026 0.2748717711 #> 12 Leitrim      -0.24203970 -1.631826543 0.1027160320 #> 13 Limerick     -0.03214546 -0.921785589 0.3566404259 #> 14 Longford      0.38307454  0.183273325 0.8545835636 #> 15 Louth         0.21301552 -0.184065128 0.8539623631 #> 16 Mayo          0.93971200  1.182398127 0.2370477661 #> 17 Meath         0.12484415 -0.060499243 0.9517580190 #> 18 Monaghan     -0.16109919 -1.342788191 0.1793405681 #> 19 Offaly       -0.00632492 -0.407816672 0.6834082724 #> 20 Roscommon     1.02089429  1.238387488 0.2155724178 #> 21 Sligo        -2.01629233 -3.623590126 0.0002905419 #> 22 Tipperary    -0.10810709 -1.227335007 0.2196967033 #> 23 Waterford     0.44099279  0.433358168 0.6647545858 #> 24 Westmeath    -0.06329661 -0.956505669 0.3388168214 #> 25 Wexford       0.30764883  0.141381402 0.8875686460 #> 26 Wicklow      -0.01696406 -0.784451761 0.4327750768"},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.html","id":null,"dir":"Reference","previous_headings":"","what":"Local Moran's I statistic — localmoran","title":"Local Moran's I statistic — localmoran","text":"local spatial statistic Moran's calculated zone based spatial weights object used. values returned include Z-value, may used diagnostic tool. statistic : $$I_i = \\frac{(x_i-\\bar{x})}{{\\sum_{k=1}^{n}(x_k-\\bar{x})^2}/(n-1)}{\\sum_{j=1}^{n}w_{ij}(x_j-\\bar{x})}$$, expectation variance given Anselin (1995), Sokal et al. (1998) implemented .","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Local Moran's I statistic — localmoran","text":"","code":"localmoran(x, listw, zero.policy=attr(listw, \"zero.policy\"), na.action=na.fail,         conditional=TRUE, alternative = \"two.sided\", mlvar=TRUE,         spChk=NULL, adjust.x=FALSE) localmoran_perm(x, listw, nsim=499, zero.policy=attr(listw, \"zero.policy\"),          na.action=na.fail, alternative = \"two.sided\", mlvar=TRUE,         spChk=NULL, adjust.x=FALSE, sample_Ei=TRUE, iseed=NULL,         no_repeat_in_row=FALSE)"},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Local Moran's I statistic — localmoran","text":"x numeric vector length neighbours list listw listw listw object created example nb2listw zero.policy default default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA na.action function (default na.fail), can also na.omit na.exclude - cases weights list subsetted remove NAs data. may necessary set zero.policy TRUE subsetting may create -neighbour observations. Note weights lists created without using glist argument nb2listw may subsetted. na.pass used, zero substituted NA values calculating spatial lag. (Note na.exclude work properly starting R 1.9.0, na.omit na.exclude assign wrong classes 1.8.*) conditional default TRUE: expectation variance calculated using conditional randomization null (Sokal 1998 Eqs. A7 & A8). Elaboration changes available Sauer et al. (2021). FALSE: expectation variance calculated using total randomization null (Sokal 1998 Eqs. A3 & A4). alternative character string specifying alternative hypothesis, must one greater, less two.sided (default). mlvar default TRUE: values local Moran's reported using variance variable interest (sum squared deviances n), can reported sample variance, dividing (n-1) instead; used implementations. spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption() adjust.x default FALSE, TRUE, x values observations neighbours omitted mean x nsim default 499, number conditonal permutation simulations sample_Ei default TRUE; conditional permutation, use sample $E_i$ values, analytical values, leaving variances calculated simulation. iseed default NULL, used set seed; output reproducible count CPU cores across computation distributed no_repeat_in_row default FALSE, TRUE, sample conditionally row without replacements avoid duplicate values, https://github.com/r-spatial/spdep/issues/124","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Local Moran's I statistic — localmoran","text":"values local Moran's divided variance (sample variance) variable interest accord Table 1, p. 103, formula (12), p. 99, Anselin (1995), rather formula (7), p. 98. variance local Moran statistic taken Sokal et al. (1998) p. 334, equations 4 & 5 equations 7 & 8 located depending user specification. default, implementation divides n, (n-1) calculating variance higher moments. Conditional code contributed Jeff Sauer Levi Wolf.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Local Moran's I statistic — localmoran","text":"Ii local moran statistic E.Ii expectation local moran statistic; localmoran_permthe permutation sample means Var.Ii variance local moran statistic; localmoran_permthe permutation sample standard deviations Z.Ii standard deviate local moran statistic; localmoran_perm based permutation sample means standard deviations Pr() p-value local moran statistic using pnorm(); localmoran_perm using standard deviatse based permutation sample means standard deviations Pr() Sim localmoran_perm, rank() punif() observed statistic rank [0, 1] p-values using alternative= Pr(folded) Sim simulation folded [0, 0.5] range ranked p-value (based https://github.com/pysal/esda/blob/4a63e0b5df1e754b17b5f1205b8cadcbecc5e061/esda/crand.py#L211-L213) Skewness localmoran_perm, output e1071::skewness() permutation samples underlying standard deviates Kurtosis localmoran_perm, output e1071::kurtosis() permutation samples underlying standard deviates addition, attribute data frame \"quadr\" mean median quadrant columns, column splitting demeaned variable lagged demeaned variable zero.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Local Moran's I statistic — localmoran","text":"Conditional permutations added comparative purposes; permutations whole data vector omitting observation . p-value adjustment, use p.adjust() p.adjustSP() output vector.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Local Moran's I statistic — localmoran","text":"Anselin, L. 1995. Local indicators spatial association, Geographical Analysis, 27, 93–115; Getis, . Ord, J. K. 1996 Local spatial statistics: overview. P. Longley M. Batty (eds) Spatial analysis: modelling GIS environment (Cambridge: Geoinformation International), 261–277; Sokal, R. R, Oden, N. L. Thomson, B. . 1998. Local Spatial Autocorrelation Biological Model. Geographical Analysis, 30. 331–354; Bivand RS, Wong DWS 2018 Comparing implementations global local indicators spatial association. TEST, 27(3), 716–748 doi:10.1007/s11749-018-0599-x ; Sauer, J., Oshan, T. M., Rey, S., & Wolf, L. J. 2021. Importance Null Hypotheses: Understanding Differences Local Moran’s Heteroskedasticity. Geographical Analysis. doi:10.1111/gean.12304 Bivand, R. (2022), R Packages Analyzing Spatial Data: Comparative Case Study Areal Data. Geographical Analysis, 54(3), 488-518. doi:10.1111/gean.12319","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Local Moran's I statistic — localmoran","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Local Moran's I statistic — localmoran","text":"","code":"data(afcon, package=\"spData\") oid <- order(afcon$id) resI <- localmoran(afcon$totcon, nb2listw(paper.nb)) printCoefmat(data.frame(resI[oid,], row.names=afcon$name[oid]),  check.names=FALSE) #>                                   Ii        E.Ii      Var.Ii        Z.Ii #> THE GAMBIA                3.7523e-01 -2.4317e-02  9.9646e-01  4.0025e-01 #> MALI                      4.6363e-01 -2.1841e-02  1.0896e-01  1.4708e+00 #> SENEGAL                   2.5670e-01 -3.4444e-03  3.3339e-02  1.4248e+00 #> BENIN                     1.9412e-01 -2.4556e-03  2.3792e-02  1.2744e+00 #> MAURITANIA                9.7053e-02 -5.7508e-03  5.5533e-02  4.3625e-01 #> NIGER                     2.3071e-01 -1.9459e-02  9.7310e-02  8.0198e-01 #> IVORY COAST               2.9004e-01 -6.9359e-03  5.2072e-02  1.3014e+00 #> GUINEA                    1.8263e-01 -2.2246e-03  1.6780e-02  1.4270e+00 #> BURKINA FASO              5.0828e-01 -1.9893e-02  1.1942e-01  1.5284e+00 #> LIBERIA                   1.8565e-01 -2.7127e-03  3.5982e-02  9.9300e-01 #> SIERRA LEONE              2.6523e-01 -1.6994e-02  3.4204e-01  4.8257e-01 #> GHANA                     1.4764e-01 -1.3414e-03  1.7817e-02  1.1161e+00 #> TOGO                      2.1934e-01 -4.9892e-03  6.6025e-02  8.7305e-01 #> CAMEROON                  2.5925e-01 -1.1009e-02  8.2313e-02  9.4198e-01 #> NIGERIA                   1.1377e-01 -9.6126e-04  9.3272e-03  1.1880e+00 #> GABON                     2.0366e-01 -5.4771e-03  1.1153e-01  6.2625e-01 #> CENTRAL AFRICAN REPUBLIC -4.4206e-01 -1.0600e-02  7.9287e-02 -1.5323e+00 #> CHAD                     -1.0528e-01 -4.0998e-03  2.5008e-02 -6.3985e-01 #> CONGO                     1.1380e-02 -8.5953e-04  8.3410e-03  1.3402e-01 #> ZAIRE                     7.0978e-01 -5.9545e-02  2.0906e-01  1.6826e+00 #> ANGOLA                    1.1797e-01 -6.2140e-04  8.2594e-03  1.3050e+00 #> UGANDA                    1.9425e+00 -6.2812e-02  4.4503e-01  3.0060e+00 #> KENYA                     1.1969e+00 -1.6803e-02  1.2489e-01  3.4344e+00 #> TANZANIA                  2.7185e-01 -4.6254e-02  1.9107e-01  7.2774e-01 #> BURUNDI                  -4.8428e-01 -1.1009e-02  1.4481e-01 -1.2437e+00 #> RWANDA                   -7.5236e-01 -1.4730e-02  1.4096e-01 -1.9647e+00 #> SOMALIA                   4.5277e-01 -1.1751e-02  2.3778e-01  9.5260e-01 #> ETHIOPIA                  7.2512e-01 -5.4929e-03  7.2655e-02  2.7106e+00 #> ZAMBIA                    4.2160e-02 -8.1691e-04  3.5354e-03  7.2280e-01 #> ZIMBABWE                 -9.5068e-03 -6.0969e-03  5.8855e-02 -1.4056e-02 #> MALAWI                   -2.2888e-01 -1.0284e-02  1.3537e-01 -5.9413e-01 #> MOZAMBIQUE                1.6790e-02 -6.1629e-03  3.7515e-02  1.1850e-01 #> SOUTH AFRICA             -1.8254e-01 -5.4306e-03  2.7546e-02 -1.0671e+00 #> LESOTHO                  -4.1935e-01 -1.9263e-02  7.9348e-01 -4.4914e-01 #> BOTSWANA                 -3.9316e-03 -1.4141e-04  1.8805e-03 -8.7403e-02 #> SWAZILAND                 1.6684e-02 -2.8611e-02  5.6905e-01  6.0045e-02 #> MOROCCO                  -9.6961e-02 -5.1445e-03  1.0479e-01 -2.8363e-01 #> ALGERIA                  -1.0037e-02 -9.7828e-05  5.9914e-04 -4.0605e-01 #> TUNISIA                   5.3873e-03 -3.0273e-06  6.1985e-05  6.8466e-01 #> LIBYA                     8.0382e-01 -1.9923e-02  1.1960e-01  2.3820e+00 #> SUDAN                     2.9878e+00 -2.2835e-01  7.6320e-01  3.6814e+00 #> EGYPT                     6.9467e+00 -2.9968e-01  4.2971e+00  3.4957e+00 #>                          Pr.z....E.Ii.. #> THE GAMBIA                       0.6890 #> MALI                             0.1414 #> SENEGAL                          0.1542 #> BENIN                            0.2025 #> MAURITANIA                       0.6627 #> NIGER                            0.4226 #> IVORY COAST                      0.1931 #> GUINEA                           0.1536 #> BURKINA FASO                     0.1264 #> LIBERIA                          0.3207 #> SIERRA LEONE                     0.6294 #> GHANA                            0.2644 #> TOGO                             0.3826 #> CAMEROON                         0.3462 #> NIGERIA                          0.2348 #> GABON                            0.5312 #> CENTRAL AFRICAN REPUBLIC         0.1255 #> CHAD                             0.5223 #> CONGO                            0.8934 #> ZAIRE                            0.0925 #> ANGOLA                           0.1919 #> UGANDA                           0.0026 #> KENYA                            0.0006 #> TANZANIA                         0.4668 #> BURUNDI                          0.2136 #> RWANDA                           0.0494 #> SOMALIA                          0.3408 #> ETHIOPIA                         0.0067 #> ZAMBIA                           0.4698 #> ZIMBABWE                         0.9888 #> MALAWI                           0.5524 #> MOZAMBIQUE                       0.9057 #> SOUTH AFRICA                     0.2859 #> LESOTHO                          0.6533 #> BOTSWANA                         0.9304 #> SWAZILAND                        0.9521 #> MOROCCO                          0.7767 #> ALGERIA                          0.6847 #> TUNISIA                          0.4936 #> LIBYA                            0.0172 #> SUDAN                            0.0002 #> EGYPT                            0.0005 hist(resI[,5])  mean(resI[,1]) #> [1] 0.4167956 sum(resI[,1])/Szero(nb2listw(paper.nb)) #> [1] 0.4167956 moran.test(afcon$totcon, nb2listw(paper.nb)) #>  #> \tMoran I test under randomisation #>  #> data:  afcon$totcon   #> weights: nb2listw(paper.nb)     #>  #> Moran I statistic standard deviate = 4.3485, p-value = 6.854e-06 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic       Expectation          Variance  #>        0.41679563       -0.02439024        0.01029358  #>  # note equality for mean() only when the sum of weights equals # the number of observations (thanks to Juergen Symanzik) resI <- localmoran(afcon$totcon, nb2listw(paper.nb)) printCoefmat(data.frame(resI[oid,], row.names=afcon$name[oid]),  check.names=FALSE) #>                                   Ii        E.Ii      Var.Ii        Z.Ii #> THE GAMBIA                3.7523e-01 -2.4317e-02  9.9646e-01  4.0025e-01 #> MALI                      4.6363e-01 -2.1841e-02  1.0896e-01  1.4708e+00 #> SENEGAL                   2.5670e-01 -3.4444e-03  3.3339e-02  1.4248e+00 #> BENIN                     1.9412e-01 -2.4556e-03  2.3792e-02  1.2744e+00 #> MAURITANIA                9.7053e-02 -5.7508e-03  5.5533e-02  4.3625e-01 #> NIGER                     2.3071e-01 -1.9459e-02  9.7310e-02  8.0198e-01 #> IVORY COAST               2.9004e-01 -6.9359e-03  5.2072e-02  1.3014e+00 #> GUINEA                    1.8263e-01 -2.2246e-03  1.6780e-02  1.4270e+00 #> BURKINA FASO              5.0828e-01 -1.9893e-02  1.1942e-01  1.5284e+00 #> LIBERIA                   1.8565e-01 -2.7127e-03  3.5982e-02  9.9300e-01 #> SIERRA LEONE              2.6523e-01 -1.6994e-02  3.4204e-01  4.8257e-01 #> GHANA                     1.4764e-01 -1.3414e-03  1.7817e-02  1.1161e+00 #> TOGO                      2.1934e-01 -4.9892e-03  6.6025e-02  8.7305e-01 #> CAMEROON                  2.5925e-01 -1.1009e-02  8.2313e-02  9.4198e-01 #> NIGERIA                   1.1377e-01 -9.6126e-04  9.3272e-03  1.1880e+00 #> GABON                     2.0366e-01 -5.4771e-03  1.1153e-01  6.2625e-01 #> CENTRAL AFRICAN REPUBLIC -4.4206e-01 -1.0600e-02  7.9287e-02 -1.5323e+00 #> CHAD                     -1.0528e-01 -4.0998e-03  2.5008e-02 -6.3985e-01 #> CONGO                     1.1380e-02 -8.5953e-04  8.3410e-03  1.3402e-01 #> ZAIRE                     7.0978e-01 -5.9545e-02  2.0906e-01  1.6826e+00 #> ANGOLA                    1.1797e-01 -6.2140e-04  8.2594e-03  1.3050e+00 #> UGANDA                    1.9425e+00 -6.2812e-02  4.4503e-01  3.0060e+00 #> KENYA                     1.1969e+00 -1.6803e-02  1.2489e-01  3.4344e+00 #> TANZANIA                  2.7185e-01 -4.6254e-02  1.9107e-01  7.2774e-01 #> BURUNDI                  -4.8428e-01 -1.1009e-02  1.4481e-01 -1.2437e+00 #> RWANDA                   -7.5236e-01 -1.4730e-02  1.4096e-01 -1.9647e+00 #> SOMALIA                   4.5277e-01 -1.1751e-02  2.3778e-01  9.5260e-01 #> ETHIOPIA                  7.2512e-01 -5.4929e-03  7.2655e-02  2.7106e+00 #> ZAMBIA                    4.2160e-02 -8.1691e-04  3.5354e-03  7.2280e-01 #> ZIMBABWE                 -9.5068e-03 -6.0969e-03  5.8855e-02 -1.4056e-02 #> MALAWI                   -2.2888e-01 -1.0284e-02  1.3537e-01 -5.9413e-01 #> MOZAMBIQUE                1.6790e-02 -6.1629e-03  3.7515e-02  1.1850e-01 #> SOUTH AFRICA             -1.8254e-01 -5.4306e-03  2.7546e-02 -1.0671e+00 #> LESOTHO                  -4.1935e-01 -1.9263e-02  7.9348e-01 -4.4914e-01 #> BOTSWANA                 -3.9316e-03 -1.4141e-04  1.8805e-03 -8.7403e-02 #> SWAZILAND                 1.6684e-02 -2.8611e-02  5.6905e-01  6.0045e-02 #> MOROCCO                  -9.6961e-02 -5.1445e-03  1.0479e-01 -2.8363e-01 #> ALGERIA                  -1.0037e-02 -9.7828e-05  5.9914e-04 -4.0605e-01 #> TUNISIA                   5.3873e-03 -3.0273e-06  6.1985e-05  6.8466e-01 #> LIBYA                     8.0382e-01 -1.9923e-02  1.1960e-01  2.3820e+00 #> SUDAN                     2.9878e+00 -2.2835e-01  7.6320e-01  3.6814e+00 #> EGYPT                     6.9467e+00 -2.9968e-01  4.2971e+00  3.4957e+00 #>                          Pr.z....E.Ii.. #> THE GAMBIA                       0.6890 #> MALI                             0.1414 #> SENEGAL                          0.1542 #> BENIN                            0.2025 #> MAURITANIA                       0.6627 #> NIGER                            0.4226 #> IVORY COAST                      0.1931 #> GUINEA                           0.1536 #> BURKINA FASO                     0.1264 #> LIBERIA                          0.3207 #> SIERRA LEONE                     0.6294 #> GHANA                            0.2644 #> TOGO                             0.3826 #> CAMEROON                         0.3462 #> NIGERIA                          0.2348 #> GABON                            0.5312 #> CENTRAL AFRICAN REPUBLIC         0.1255 #> CHAD                             0.5223 #> CONGO                            0.8934 #> ZAIRE                            0.0925 #> ANGOLA                           0.1919 #> UGANDA                           0.0026 #> KENYA                            0.0006 #> TANZANIA                         0.4668 #> BURUNDI                          0.2136 #> RWANDA                           0.0494 #> SOMALIA                          0.3408 #> ETHIOPIA                         0.0067 #> ZAMBIA                           0.4698 #> ZIMBABWE                         0.9888 #> MALAWI                           0.5524 #> MOZAMBIQUE                       0.9057 #> SOUTH AFRICA                     0.2859 #> LESOTHO                          0.6533 #> BOTSWANA                         0.9304 #> SWAZILAND                        0.9521 #> MOROCCO                          0.7767 #> ALGERIA                          0.6847 #> TUNISIA                          0.4936 #> LIBYA                            0.0172 #> SUDAN                            0.0002 #> EGYPT                            0.0005 hist(p.adjust(resI[,5], method=\"bonferroni\"))  totcon <-afcon$totcon is.na(totcon) <- sample(1:length(totcon), 5) totcon #>  [1] 1363 1421 1861 2355 5246  811  299  358  895   NA   NA  933  347 1130  241 #> [16]  604 1015  998 2122 1090   NA   NA  758  423   NA 3087 2273 3134 1142  824 #> [31] 2881  487  604 1528 1554  629  792  795 1266 1875  147  363 resI.na <- localmoran(totcon, nb2listw(paper.nb), na.action=na.exclude,  zero.policy=TRUE) if (class(attr(resI.na, \"na.action\")) == \"exclude\") {  print(data.frame(resI.na[oid,], row.names=afcon$name[oid]), digits=2) } else print(resI.na, digits=2) #>                               Ii     E.Ii  Var.Ii  Z.Ii Pr.z....E.Ii.. #> THE GAMBIA                0.3528 -2.9e-02 1.03887  0.37          0.708 #> MALI                      0.4524 -2.6e-02 0.11007  1.44          0.149 #> SENEGAL                   0.2347 -3.3e-03 0.02800  1.42          0.155 #> BENIN                     0.1862 -2.2e-03 0.02572  1.17          0.240 #> MAURITANIA                0.0722 -6.0e-03 0.05043  0.35          0.728 #> NIGER                     0.1981 -2.3e-02 0.09763  0.71          0.480 #> IVORY COAST               0.3020 -7.4e-03 0.06218  1.24          0.215 #> GUINEA                    0.1774 -2.0e-03 0.01658  1.39          0.164 #> BURKINA FASO              0.5248 -2.3e-02 0.14950  1.42          0.156 #> LIBERIA                       NA       NA      NA    NA             NA #> SIERRA LEONE              0.2241 -2.0e-02 0.71575  0.29          0.773 #> GHANA                     0.1382 -1.0e-03 0.01854  1.02          0.307 #> TOGO                          NA       NA      NA    NA             NA #> CAMEROON                  0.1884 -1.2e-02 0.10306  0.63          0.532 #> NIGERIA                   0.0861 -6.6e-04 0.00556  1.16          0.245 #> GABON                     0.1828 -5.7e-03 0.10144  0.59          0.554 #> CENTRAL AFRICAN REPUBLIC      NA       NA      NA    NA             NA #> CHAD                      0.0657 -4.1e-03 0.03430  0.38          0.706 #> CONGO                    -0.0301 -5.6e-04 0.00652 -0.37          0.715 #> ZAIRE                     0.5651 -8.5e-02 0.34207  1.11          0.266 #> ANGOLA                    0.2017 -1.5e-03 0.01766  1.53          0.126 #> UGANDA                    1.5678 -9.0e-02 0.69207  1.99          0.046 #> KENYA                     1.3328 -2.6e-02 0.29012  2.52          0.012 #> TANZANIA                  0.4269 -6.7e-02 0.23117  1.03          0.304 #> BURUNDI                  -0.5611 -1.2e-02 0.14171 -1.46          0.145 #> RWANDA                   -0.8661 -1.7e-02 0.14069 -2.26          0.024 #> SOMALIA                   0.7805 -1.8e-02 0.66673  0.98          0.328 #> ETHIOPIA                      NA       NA      NA    NA             NA #> ZAMBIA                    0.0806 -1.9e-03 0.00690  0.99          0.321 #> ZIMBABWE                 -0.0393 -6.4e-03 0.05385 -0.14          0.887 #> MALAWI                   -0.2844 -1.1e-02 0.13166 -0.75          0.452 #> MOZAMBIQUE               -0.0121 -6.5e-03 0.03407 -0.03          0.976 #> SOUTH AFRICA             -0.2047 -9.1e-03 0.03947 -0.98          0.325 #> LESOTHO                  -0.5158 -2.3e-02 0.81614 -0.55          0.585 #> BOTSWANA                 -0.0025 -1.3e-05 0.00015 -0.20          0.838 #> SWAZILAND                -0.0494 -3.4e-02 0.59593 -0.02          0.984 #> MOROCCO                  -0.0936 -8.7e-03 0.15440 -0.22          0.829 #> ALGERIA                  -0.0143 -4.7e-04 0.00247 -0.28          0.780 #> TUNISIA                   0.0428 -1.5e-04 0.00268  0.83          0.406 #> LIBYA                     0.5764 -3.0e-02 0.19100  1.39          0.165 #> SUDAN                         NA       NA      NA    NA             NA #> EGYPT                     4.0118 -4.1e-01 8.97211  1.48          0.140 resG <- localG(afcon$totcon, nb2listw(include.self(paper.nb))) print(data.frame(resG[oid], row.names=afcon$name[oid]), digits=2) #>                          resG.oid. #> THE GAMBIA                  -0.984 #> MALI                        -1.699 #> SENEGAL                     -1.463 #> BENIN                       -1.301 #> MAURITANIA                  -0.605 #> NIGER                       -1.049 #> IVORY COAST                 -1.417 #> GUINEA                      -1.449 #> BURKINA FASO                -1.751 #> LIBERIA                     -1.041 #> SIERRA LEONE                -0.870 #> GHANA                       -1.103 #> TOGO                        -0.991 #> CAMEROON                    -1.133 #> NIGERIA                     -1.173 #> GABON                       -0.789 #> CENTRAL AFRICAN REPUBLIC     1.173 #> CHAD                         0.463 #> CONGO                       -0.203 #> ZAIRE                        2.023 #> ANGOLA                       1.235 #> UGANDA                       3.336 #> KENYA                        3.503 #> TANZANIA                     1.098 #> BURUNDI                      0.774 #> RWANDA                       1.457 #> SOMALIA                      1.183 #> ETHIOPIA                     2.627 #> ZAMBIA                       0.753 #> ZIMBABWE                    -0.200 #> MALAWI                       0.212 #> MOZAMBIQUE                  -0.288 #> SOUTH AFRICA                -0.868 #> LESOTHO                     -0.298 #> BOTSWANA                     0.041 #> SWAZILAND                   -0.659 #> MOROCCO                      0.022 #> ALGERIA                     -0.363 #> TUNISIA                      0.579 #> LIBYA                        2.553 #> SUDAN                        4.039 #> EGYPT                        4.421 set.seed(1) resI_p <- localmoran_perm(afcon$totcon, nb2listw(paper.nb)) printCoefmat(data.frame(resI_p[oid,], row.names=afcon$name[oid]),  check.names=FALSE) #>                                   Ii        E.Ii      Var.Ii        Z.Ii #> THE GAMBIA                3.7523e-01 -3.0853e-02  9.0476e-01  4.2692e-01 #> MALI                      4.6363e-01 -2.1690e-02  1.2192e-01  1.3899e+00 #> SENEGAL                   2.5670e-01 -1.1288e-02  3.2719e-02  1.4816e+00 #> BENIN                     1.9412e-01 -6.5012e-03  2.6046e-02  1.2431e+00 #> MAURITANIA                9.7053e-02 -2.0574e-03  5.7209e-02  4.1437e-01 #> NIGER                     2.3071e-01 -2.8428e-02  1.1981e-01  7.4867e-01 #> IVORY COAST               2.9004e-01 -8.1011e-03  5.5564e-02  1.2648e+00 #> GUINEA                    1.8263e-01  5.3454e-04  1.8397e-02  1.3425e+00 #> BURKINA FASO              5.0828e-01 -2.9727e-02  1.4019e-01  1.4369e+00 #> LIBERIA                   1.8565e-01 -1.9247e-03  3.6524e-02  9.8147e-01 #> SIERRA LEONE              2.6523e-01  1.0225e-02  3.1505e-01  4.5432e-01 #> GHANA                     1.4764e-01 -6.7639e-03  1.8646e-02  1.1307e+00 #> TOGO                      2.1934e-01 -1.8012e-03  6.5187e-02  8.6616e-01 #> CAMEROON                  2.5925e-01 -1.0726e-02  9.4789e-02  8.7688e-01 #> NIGERIA                   1.1377e-01 -2.5672e-03  8.7720e-03  1.2421e+00 #> GABON                     2.0366e-01 -3.5024e-03  1.0958e-01  6.2584e-01 #> CENTRAL AFRICAN REPUBLIC -4.4206e-01  2.3901e-02  8.1700e-02 -1.6302e+00 #> CHAD                     -1.0528e-01  5.9042e-03  3.0168e-02 -6.4016e-01 #> CONGO                     1.1380e-02  7.0349e-03  8.9435e-03  4.5949e-02 #> ZAIRE                     7.0978e-01 -2.9589e-02  2.9068e-01  1.3714e+00 #> ANGOLA                    1.1797e-01 -3.0421e-04  8.6526e-03  1.2716e+00 #> UGANDA                    1.9425e+00 -7.0491e-02  5.2046e-01  2.7903e+00 #> KENYA                     1.1969e+00 -1.6362e-02  1.3644e-01  3.2847e+00 #> TANZANIA                  2.7185e-01 -7.3309e-02  2.3454e-01  7.1272e-01 #> BURUNDI                  -4.8428e-01  9.5351e-03  1.4866e-01 -1.2807e+00 #> RWANDA                   -7.5236e-01 -4.0426e-02  1.7628e-01 -1.6956e+00 #> SOMALIA                   4.5277e-01 -1.1165e-02  2.6266e-01  9.0523e-01 #> ETHIOPIA                  7.2512e-01  8.3618e-04  7.8477e-02  2.5855e+00 #> ZAMBIA                    4.2160e-02 -5.1840e-03  3.6852e-03  7.7989e-01 #> ZIMBABWE                 -9.5068e-03 -6.5338e-03  6.5357e-02 -1.1629e-02 #> MALAWI                   -2.2888e-01  3.6276e-03  1.3417e-01 -6.3477e-01 #> MOZAMBIQUE                1.6790e-02 -2.0694e-03  4.5436e-02  8.8476e-02 #> SOUTH AFRICA             -1.8254e-01 -1.1611e-02  3.0240e-02 -9.8293e-01 #> LESOTHO                  -4.1935e-01 -6.6258e-02  8.7314e-01 -3.7787e-01 #> BOTSWANA                 -3.9316e-03 -4.7713e-03  2.2167e-03  1.7833e-02 #> SWAZILAND                 1.6684e-02 -8.4486e-02  6.4807e-01  1.2567e-01 #> MOROCCO                  -9.6961e-02 -2.1623e-03  1.1253e-01 -2.8260e-01 #> ALGERIA                  -1.0037e-02 -3.4326e-04  6.3541e-04 -3.8456e-01 #> TUNISIA                   5.3873e-03 -1.6456e-04  6.4187e-05  6.9298e-01 #> LIBYA                     8.0382e-01 -2.9038e-02  1.3319e-01  2.2821e+00 #> SUDAN                     2.9878e+00 -2.5952e-01  8.2522e-01  3.5747e+00 #> EGYPT                     6.9467e+00 -3.7869e-01  4.1318e+00  3.6038e+00 #>                          Pr.z....E.Ii.. Pr.z....E.Ii...Sim Pr.folded..Sim #> THE GAMBIA                   6.6944e-01         8.3200e-01     4.2800e-01 #> MALI                         1.6455e-01         8.8000e-02     4.4000e-02 #> SENEGAL                      1.3846e-01         6.4000e-02     3.2000e-02 #> BENIN                        2.1384e-01         1.3200e-01     6.6000e-02 #> MAURITANIA                   6.7860e-01         7.5600e-01     3.7800e-01 #> NIGER                        4.5406e-01         5.0000e-01     2.5000e-01 #> IVORY COAST                  2.0595e-01         1.1600e-01     5.8000e-02 #> GUINEA                       1.7943e-01         7.2000e-02     3.6000e-02 #> BURKINA FASO                 1.5075e-01         9.2000e-02     4.6000e-02 #> LIBERIA                      3.2636e-01         3.0400e-01     1.5200e-01 #> SIERRA LEONE                 6.4960e-01         8.2400e-01     4.1200e-01 #> GHANA                        2.5816e-01         1.8400e-01     9.2000e-02 #> TOGO                         3.8640e-01         3.6800e-01     1.8400e-01 #> CAMEROON                     3.8055e-01         4.3200e-01     2.1600e-01 #> NIGERIA                      2.1418e-01         1.4400e-01     7.2000e-02 #> GABON                        5.3142e-01         5.8400e-01     2.9600e-01 #> CENTRAL AFRICAN REPUBLIC     1.0306e-01         1.8400e-01     9.2000e-02 #> CHAD                         5.2207e-01         4.5200e-01     2.2600e-01 #> CONGO                        9.6335e-01         8.5600e-01     4.2800e-01 #> ZAIRE                        1.7026e-01         2.0000e-01     1.0000e-01 #> ANGOLA                       2.0353e-01         2.3600e-01     1.1800e-01 #> UGANDA                       5.2662e-03         4.0000e-02     2.0000e-02 #> KENYA                        1.0210e-03         8.0000e-03     4.0000e-03 #> TANZANIA                     4.7602e-01         4.2400e-01     2.1200e-01 #> BURUNDI                      2.0029e-01         2.6800e-01     1.3400e-01 #> RWANDA                       8.9953e-02         1.4000e-01     7.0000e-02 #> SOMALIA                      3.6535e-01         2.8800e-01     1.4600e-01 #> ETHIOPIA                     9.7244e-03         3.6000e-02     1.8000e-02 #> ZAMBIA                       4.3546e-01         4.1200e-01     2.0600e-01 #> ZIMBABWE                     9.9072e-01         8.6800e-01     4.3400e-01 #> MALAWI                       5.2558e-01         4.5600e-01     2.2800e-01 #> MOZAMBIQUE                   9.2950e-01         9.4400e-01     4.7200e-01 #> SOUTH AFRICA                 3.2564e-01         3.5200e-01     1.7600e-01 #> LESOTHO                      7.0553e-01         4.6800e-01     2.2400e-01 #> BOTSWANA                     9.8577e-01         8.4400e-01     4.2200e-01 #> SWAZILAND                    8.9999e-01         8.8400e-01     4.4200e-01 #> MOROCCO                      7.7749e-01         9.7600e-01     4.8800e-01 #> ALGERIA                      7.0057e-01         8.0400e-01     4.0200e-01 #> TUNISIA                      4.8832e-01         4.2800e-01     2.1600e-01 #> LIBYA                        2.2482e-02         4.8000e-02     2.4000e-02 #> SUDAN                        3.5067e-04         8.0000e-03     4.0000e-03 #> EGYPT                        3.1358e-04         1.6000e-02     8.0000e-03 #>                             Skewness Kurtosis #> THE GAMBIA               -1.7643e+00   3.3422 #> MALI                     -8.2875e-01   0.8397 #> SENEGAL                  -7.1779e-01   0.3689 #> BENIN                    -8.5318e-01   0.5520 #> MAURITANIA               -9.6301e-01   1.3949 #> NIGER                    -6.3767e-01   0.2577 #> IVORY COAST              -8.3750e-01   0.6786 #> GUINEA                   -8.8298e-01   0.7691 #> BURKINA FASO             -7.7665e-01   0.5911 #> LIBERIA                  -9.7191e-01   1.2327 #> SIERRA LEONE             -1.0737e+00   0.6367 #> GHANA                    -9.6554e-01   0.8587 #> TOGO                     -1.0772e+00   1.2283 #> CAMEROON                 -8.1844e-01   1.1746 #> NIGERIA                  -6.3061e-01   0.1168 #> GABON                    -1.1947e+00   1.1977 #> CENTRAL AFRICAN REPUBLIC -6.7964e-01  -0.1428 #> CHAD                     -9.5123e-01   0.8025 #> CONGO                    -9.5359e-01   0.9288 #> ZAIRE                     6.6929e-01   0.5829 #> ANGOLA                    1.0230e+00   1.0841 #> UGANDA                    9.6607e-01   1.3331 #> KENYA                     8.5205e-01   0.5240 #> TANZANIA                  8.5767e-01   1.2127 #> BURUNDI                  -1.0634e+00   0.9779 #> RWANDA                   -9.5905e-01   0.8365 #> SOMALIA                   1.5185e+00   2.7876 #> ETHIOPIA                  9.9587e-01   0.7374 #> ZAMBIA                    4.9495e-01   0.1900 #> ZIMBABWE                 -8.0240e-01   0.4192 #> MALAWI                   -1.1246e+00   1.7228 #> MOZAMBIQUE               -7.6989e-01   0.5793 #> SOUTH AFRICA              5.6394e-01   0.1988 #> LESOTHO                  -1.7905e+00   2.9865 #> BOTSWANA                 -9.4637e-01   0.5722 #> SWAZILAND                -1.3081e+00   1.7612 #> MOROCCO                   1.2705e+00   1.5574 #> ALGERIA                   6.3958e-01   0.2677 #> TUNISIA                   1.2498e+00   1.2249 #> LIBYA                     7.3453e-01   0.5219 #> SUDAN                     4.3993e-01  -0.1019 #> EGYPT                     1.1875e+00   1.6480"},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.sad.html","id":null,"dir":"Reference","previous_headings":"","what":"Saddlepoint approximation of local Moran's Ii tests — localmoran.sad","title":"Saddlepoint approximation of local Moran's Ii tests — localmoran.sad","text":"function implements Tiefelsdorf's application Saddlepoint approximation local Moran's Ii's reference distribution. model object class \"lm\", global independence assumed; class \"sarlm\", global dependence assumed represented spatial parameter model. Tests reported separately zone selected, may summarised using summary.localmoransad. Values local Moran's Ii agree localmoran(), function, standard deviate - Saddlepoint approximation - based randomisation assumption.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.sad.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Saddlepoint approximation of local Moran's Ii tests — localmoran.sad","text":"","code":"localmoran.sad(model, select, nb, glist=NULL, style=\"W\",  zero.policy=NULL, alternative=\"two.sided\", spChk=NULL,  resfun=weighted.residuals, save.Vi=FALSE,  tol = .Machine$double.eps^0.5, maxiter = 1000, tol.bounds=0.0001,  save.M=FALSE, Omega = NULL) <!-- %as.data.frame.localmoransad(x, row.names=NULL, optional=FALSE)  --> # S3 method for class 'localmoransad' print(x, ...) # S3 method for class 'localmoransad' summary(object, ...) # S3 method for class 'summary.localmoransad' print(x, ...) listw2star(listw, ireg, style, n, D, a, zero.policy=attr(listw, \"zero.policy\"))"},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.sad.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Saddlepoint approximation of local Moran's Ii tests — localmoran.sad","text":"model object class lm returned lm (assuming global spatial autocorrelation), object class sarlm returned spatial simultaneous autoregressive model fit (assuming global spatial autocorrelation represented model spatial coefficient); weights may specified lm fit, offsets used select integer vector id. numbers zones tested; missing, zones nb list neighbours class nb glist list general weights corresponding neighbours style can take values W, B, C, S zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA alternative character string specifying alternative hypothesis, must one greater (default), less two.sided. spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption() resfun default: weighted.residuals; function used extract residuals lm object, may residuals, weighted.residuals, rstandard, rstudent save.Vi TRUE, return star-shaped weights lists zone tested tol desired accuracy (convergence tolerance) uniroot maxiter maximum number iterations uniroot tol.bounds offset bounds uniroot save.M TRUE, save list left right M products list conditional tests, list regression model matrix components Omega SAR process matrix may passed test alternative hypothesis, example Omega <- invIrW(listw, rho=0.1); Omega <- tcrossprod(Omega), chol() taken internally x object printed  object object summarised ... arguments passed listw listw object created example nb2listw ireg zone number n internal value depending listw style D internal value depending listw style internal value depending listw style","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.sad.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Saddlepoint approximation of local Moran's Ii tests — localmoran.sad","text":"function implements analytical eigenvalue calculation together trace shortcuts given suggested Tiefelsdorf (2002), partly following remarks J. Keith Ord, uses Saddlepoint analytical solution Tiefelsdorf's SPSS code. histogram probability values saddlepoint estimate assumption global independence approximately flat, assumption probably unjustified, re-estimation global dependence recommended. n n matrices needed point test assuming global dependence, star-shaped weights matrices handled listw lists. test made residuals spatial regression, taking global process account. n n matrices necessary, memory constraints may reached large lattices.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.sad.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Saddlepoint approximation of local Moran's Ii tests — localmoran.sad","text":"list class localmoransad containing \"select\" lists,  class moransad following components: statistic value saddlepoint approximation  standard deviate local Moran's Ii. p.value p-value test. estimate value observed local Moran's Ii. alternative character string describing alternative hypothesis. method character string giving method used. data.name character string giving name(s) data. internal1 Saddlepoint omega, r u df degrees freedom tau maximum minimum analytical eigenvalues zone tested","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.sad.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Saddlepoint approximation of local Moran's Ii tests — localmoran.sad","text":"Tiefelsdorf, M. 2002 Saddlepoint approximation Moran's local Moran's Ii reference distributions numerical evaluation. Geographical Analysis, 34, pp. 187–206.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.sad.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Saddlepoint approximation of local Moran's Ii tests — localmoran.sad","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.sad.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Saddlepoint approximation of local Moran's Ii tests — localmoran.sad","text":"","code":"eire <- st_read(system.file(\"shapes/eire.gpkg\", package=\"spData\")[1]) #> Reading layer `eire' from data source  #>   `/home/rsb/lib/r_libs/spData/shapes/eire.gpkg' using driver `GPKG' #> Simple feature collection with 26 features and 10 fields #> Geometry type: MULTIPOLYGON #> Dimension:     XY #> Bounding box:  xmin: -4.12 ymin: 5768 xmax: 300.82 ymax: 6119.25 #> Projected CRS: Undefined Cartesian SRS with unknown unit row.names(eire) <- as.character(eire$names) eire.nb <- poly2nb(eire) lw <- nb2listw(eire.nb) e.lm <- lm(OWNCONS ~ ROADACC, data=eire) e.locmor <- summary(localmoran.sad(e.lm, nb=eire.nb)) e.locmor #>              Local Morans I Stand. dev. (N)      Pr. (N) Saddlepoint #> 1 Carlow         0.21699668      0.74177148 4.582258e-01  0.95074844 #> 2 Cavan         -0.37257361     -0.81297374 1.583767e+00 -1.00603119 #> 3 Clare          0.23197510      0.49502499 6.205825e-01  0.67166518 #> 4 Cork           0.78193548      1.75999915 7.840795e-02  1.74761575 #> 5 Donegal       -1.69064059     -1.98244914 1.952571e+00 -1.72031078 #> 6 Dublin        -0.16069692     -0.15041940 1.119566e+00 -0.35212627 #> 7 Galway         1.31371473      3.34305297 8.286208e-04  2.66849536 #> 8 Kerry          0.36534866      0.58147812 5.609183e-01  0.78073279 #> 9 Kildare       -0.02557544      0.15146558 8.796085e-01  0.04167665 #> 10 Kilkenny      0.57684331      1.62868431 1.033799e-01  1.70897697 #> 11 Laoghis      -0.05951798      0.01724651 9.862400e-01 -0.12155465 #> 12 Leitrim       0.38484587      1.27548777 2.021367e-01  1.47227033 #> 13 Limerick      0.11817987      0.34038037 7.335701e-01  0.45727712 #> 14 Longford      1.41643200      3.10732224 1.887905e-03  2.51113769 #> 15 Louth         0.56242920      0.87665682 3.806731e-01  1.07441571 #> 16 Mayo          0.87572704      2.02375701 4.299516e-02  2.05251226 #> 17 Meath         0.00367856      0.16081712 8.722374e-01  0.12813539 #> 18 Monaghan      0.55098311      1.06684464 2.860420e-01  1.23999193 #> 19 Offaly        0.15155556      0.61933942 5.356928e-01  0.80786519 #> 20 Roscommon     2.04368839      6.66107106 2.718381e-11  4.53187292 #> 21 Sligo        -0.47579871     -0.73430274 1.537236e+00 -0.94578114 #> 22 Tipperary    -0.03454106      0.04843351 9.613708e-01 -0.06919691 #> 23 Waterford     0.85723423      1.98516133 4.712653e-02  1.91385108 #> 24 Westmeath     0.45138572      1.20305006 2.289569e-01  1.36017204 #> 25 Wexford       0.64371834      1.55468550 1.200210e-01  1.63188492 #> 26 Wicklow       0.02441950      0.21823347 8.272472e-01  0.21197000 #>                 Pr. (Sad) Expectation   Variance   Skewness Kurtosis    Minimum #> 1 Carlow     3.417321e-01 -0.06471134 0.14423085 -0.7895263 7.059116  -5.461326 #> 2 Cavan      3.144006e-01 -0.04030838 0.16703857 -0.4622793 6.813004  -5.567356 #> 3 Clare      5.017969e-01 -0.04219377 0.30674823 -0.3579185 6.761932  -7.406885 #> 4 Cork       8.053059e-02 -0.04363826 0.22003250 -0.4363325 6.799081  -6.360927 #> 5 Donegal    8.537596e-02 -0.11935726 0.62821008 -0.7004303 6.979051 -11.236382 #> 6 Dublin     7.247436e-01 -0.08240217 0.27093033 -0.7352902 7.009201  -7.420687 #> 7 Galway     7.619183e-03 -0.04389010 0.16491503 -0.5059997 6.838308  -5.573707 #> 8 Kerry      4.349597e-01 -0.03212369 0.46724761 -0.2212594 6.714810  -8.915104 #> 9 Kildare    9.667565e-01 -0.07623733 0.11187546 -1.0416026 7.339962  -4.999621 #> 10 Kilkenny  8.745521e-02 -0.05911601 0.15247016 -0.7040737 6.982131  -5.538889 #> 11 Laoghis   9.032517e-01 -0.06620117 0.15016408 -0.7915137 7.061015  -5.574277 #> 12 Leitrim   1.409479e-01 -0.06828680 0.12621127 -0.8864130 7.157471  -5.186756 #> 13 Limerick  6.474719e-01 -0.04172917 0.22070746 -0.4167943 6.789132  -6.348870 #> 14 Longford  1.203427e-02 -0.04055162 0.21985521 -0.4059156 6.783792  -6.324457 #> 15 Louth     2.826364e-01 -0.04386717 0.47831137 -0.2983105 6.738631  -9.149779 #> 16 Mayo      4.011990e-02 -0.10340651 0.23408152 -0.9804377 7.264328  -7.165847 #> 17 Meath     8.980418e-01 -0.04799533 0.10324707 -0.6949022 6.974408  -4.551176 #> 18 Monaghan  2.149784e-01 -0.04136950 0.30828917 -0.3501006 6.758633  -7.415047 #> 19 Offaly    4.191682e-01 -0.04662212 0.10238870 -0.6782821 6.960676  -4.519986 #> 20 Roscommon 5.846302e-06 -0.04435301 0.09826301 -0.6591526 6.945294  -4.414164 #> 21 Sligo     3.442602e-01 -0.11041170 0.24760301 -1.0156782 7.307311  -7.409091 #> 22 Tipperary 9.448329e-01 -0.04872132 0.08571886 -0.7716947 7.042300  -4.198353 #> 23 Waterford 5.563919e-02 -0.05435079 0.21086415 -0.5533724 6.868342  -6.353514 #> 24 Westmeath 1.737755e-01 -0.04181671 0.16806722 -0.4779156 6.821788  -5.599610 #> 25 Wexford   1.027037e-01 -0.05432673 0.20159596 -0.5654870 6.876461  -6.225016 #> 26 Wicklow   8.321304e-01 -0.07022471 0.18808122 -0.7515626 7.023792  -6.198974 #>               Maximum        omega       sad.r       sad.u #> 1 Carlow     3.908254  0.071122863  0.71853146  0.84900467 #> 2 Cavan      4.599954 -0.051532330 -0.69003582 -0.85816092 #> 3 Clare      6.394234  0.031939551  0.46982957  0.51656357 #> 4 Cork       5.313609  0.083281515  1.43928884  2.24323856 #> 5 Donegal    8.371808 -0.039371561 -1.39288713 -2.19776923 #> 6 Dublin     5.443035 -0.010354512 -0.14127218 -0.14554367 #> 7 Galway     4.520344  0.134873939  2.39189491  4.63522665 #> 8 Kerry      8.144135  0.028431952  0.54051534  0.61545648 #> 9 Kildare    3.169925  0.018723213  0.14926096  0.14688325 #> 10 Kilkenny  4.120105  0.105365819  1.40668493  2.15214600 #> 11 Laoghis   3.985449  0.001724096  0.01660985  0.01657177 #> 12 Leitrim   3.547872  0.109608339  1.18229964  1.66578026 #> 13 Limerick  5.347370  0.027585567  0.32820959  0.34241163 #> 14 Longford  5.351218  0.108368224  2.22687206  4.19385821 #> 15 Louth     8.096967  0.037745731  0.78968254  0.98878788 #> 16 Mayo      4.684091  0.105317102  1.75922892  2.94711915 #> 17 Meath     3.399289  0.020074178  0.15693992  0.15623206 #> 18 Monaghan  6.422179  0.053418031  0.94193428  1.24723730 #> 19 Offaly    3.401055  0.071432961  0.59871278  0.67858124 #> 20 Roscommon 3.349691  0.357114199  4.33885200 10.02517077 #> 21 Sligo     4.759210 -0.036185300 -0.60775394 -0.74635955 #> 22 Tipperary 3.029041  0.006482570  0.04683010  0.04657633 #> 23 Waterford 5.049095  0.093409563  1.61022194  2.62552879 #> 24 Westmeath 4.596009  0.080097979  1.05978192  1.45704611 #> 25 Wexford   4.921174  0.085478829  1.32647942  1.98902088 #> 26 Wicklow   4.513581  0.020437514  0.21417067  0.21406975 mean(e.locmor[,1]) #> [1] 0.3366057 sum(e.locmor[,1])/Szero(lw) #> [1] 0.3366057 lm.morantest(e.lm, lw) #>  #> \tGlobal Moran I for regression residuals #>  #> data:   #> model: lm(formula = OWNCONS ~ ROADACC, data = eire) #> weights: lw #>  #> Moran I statistic standard deviate = 3.2575, p-value = 0.0005619 #> alternative hypothesis: greater #> sample estimates: #> Observed Moran I      Expectation         Variance  #>       0.33660565      -0.05877741       0.01473183  #>  # note equality for mean() only when the sum of weights equals # the number of observations (thanks to Juergen Symanzik) hist(e.locmor[,\"Pr. (Sad)\"])  e.wlm <- lm(OWNCONS ~ ROADACC, data=eire, weights=RETSALE) e.locmorw1 <- summary(localmoran.sad(e.wlm, nb=eire.nb, resfun=weighted.residuals)) e.locmorw1 #>              Local Morans I Stand. dev. (N)      Pr. (N) Saddlepoint #> 1 Carlow        0.160490657      0.41009538 6.817360e-01  0.57729730 #> 2 Cavan        -0.144663771     -0.27825575 1.219184e+00 -0.45305168 #> 3 Clare         0.301676582      0.59021701 5.550452e-01  0.78987327 #> 4 Cork          1.520488153      3.49016956 4.827142e-04  2.83665634 #> 5 Donegal      -0.435899664     -0.44665946 1.344879e+00 -0.67136090 #> 6 Dublin       -0.340222996     -0.60886675 1.457387e+00 -0.85658016 #> 7 Galway        1.469009037      3.64546192 2.669119e-04  2.82274510 #> 8 Kerry         0.268957279      0.49517211 6.204786e-01  0.66861012 #> 9 Kildare       0.002996577      0.12659200 8.992633e-01  0.09978249 #> 10 Kilkenny     0.497968801      1.20610829 2.277757e-01  1.34091379 #> 11 Laoghis     -0.026328708     -0.01713904 1.013674e+00 -0.06511750 #> 12 Leitrim      0.277306386      0.80644537 4.199861e-01  1.01176491 #> 13 Limerick     0.263122939      0.67591893 4.990921e-01  0.87759628 #> 14 Longford     0.605211711      1.23874274 2.154408e-01  1.35375850 #> 15 Louth        0.359469683      0.53572990 5.921452e-01  0.73280188 #> 16 Mayo         1.742480472      3.68118786 2.321499e-04  3.01500163 #> 17 Meath       -0.112171618     -0.26680698 1.210382e+00 -0.45470531 #> 18 Monaghan     0.241044892      0.46013751 6.454175e-01  0.64094159 #> 19 Offaly       0.129191178      0.40988983 6.818868e-01  0.57205532 #> 20 Roscommon    1.469671750      4.39927211 1.086146e-05  3.13215267 #> 21 Sligo        0.095559559      0.31036587 7.562827e-01  0.38503064 #> 22 Tipperary    0.088352646      0.39958273 6.894639e-01  0.52592105 #> 23 Waterford    1.212658861      2.69846035 6.966104e-03  2.29292584 #> 24 Westmeath    0.256165310      0.61222265 5.403905e-01  0.81620859 #> 25 Wexford      0.619197906      1.31967483 1.869436e-01  1.42553832 #> 26 Wicklow      0.006531073      0.13142161 8.954418e-01  0.10986725 #>                Pr. (Sad) Expectation   Variance   Skewness Kurtosis    Minimum #> 1 Carlow     0.563738639 -0.01840558 0.19029731 -0.1986977 6.709176  -5.665283 #> 2 Cavan      0.650511526 -0.02184465 0.19482455 -0.2329761 6.717975  -5.769371 #> 3 Clare      0.429601786 -0.02782578 0.31166901 -0.2346279 6.718435  -7.299407 #> 4 Cork       0.004558865 -0.07147410 0.20805228 -0.7280203 7.002789  -6.495227 #> 5 Donegal    0.501990650 -0.07638800 0.64784767 -0.4450323 6.803659 -10.931345 #> 6 Dublin     0.391676955 -0.11187469 0.14065367 -1.3324828 7.767845  -5.846924 #> 7 Galway     0.004761441 -0.04407925 0.17227545 -0.4973247 6.833103  -5.688263 #> 8 Kerry      0.503744214 -0.05644300 0.43184063 -0.4031537 6.782459  -8.859407 #> 9 Kildare    0.920517009 -0.04145378 0.12329287 -0.5519841 6.867423  -4.857131 #> 10 Kilkenny  0.179948446 -0.02321457 0.18672759 -0.2528322 6.723714  -5.669156 #> 11 Laoghis   0.948080445 -0.01882531 0.19166504 -0.2024943 6.710081  -5.689691 #> 12 Leitrim   0.311650473 -0.03314655 0.14819776 -0.4041387 6.782933  -5.190860 #> 13 Limerick  0.380162847 -0.04800976 0.21188592 -0.4885390 6.827925  -6.298874 #> 14 Longford  0.175813436 -0.01321709 0.24923967 -0.1247567 6.694960  -6.392250 #> 15 Louth     0.463679274 -0.02272663 0.50895713 -0.1500895 6.699098  -9.179410 #> 16 Mayo      0.002569779 -0.09458039 0.24904116 -0.8745463 7.144787  -7.272523 #> 17 Meath     0.649321260 -0.02548973 0.10555100 -0.3685280 6.766525  -4.353122 #> 18 Monaghan  0.521560632 -0.02333303 0.33012248 -0.1912612 6.707452  -7.451275 #> 19 Offaly    0.567284497 -0.01927989 0.13120470 -0.2505068 6.723017  -4.750083 #> 20 Roscommon 0.001735296 -0.02385522 0.11525625 -0.3302939 6.750604  -4.517676 #> 21 Sligo     0.700214717 -0.06927688 0.28207107 -0.6087587 6.906925  -7.416881 #> 22 Tipperary 0.598943063 -0.03719246 0.09871568 -0.5534442 6.868390  -4.347214 #> 23 Waterford 0.021852275 -0.04027429 0.21558757 -0.4070996 6.784366  -6.264083 #> 24 Westmeath 0.414380842 -0.01522814 0.19650786 -0.1618342 6.701275  -5.716689 #> 25 Wexford   0.154001651 -0.02786850 0.24041626 -0.2674357 6.728234  -6.450174 #> 26 Wicklow   0.912514660 -0.04751424 0.16911517 -0.5404006 6.859847  -5.677417 #>               Maximum        omega       sad.r       sad.u #> 1 Carlow     5.223549  0.033637462  0.38794383  0.41751442 #> 2 Cavan      5.245099 -0.022294725 -0.26091513 -0.27432856 #> 3 Clare      6.631589  0.035302524  0.54866959  0.62630505 #> 4 Cork       4.779848  0.134384022  2.56890121  5.11058941 #> 5 Donegal    9.098033 -0.017507303 -0.40402088 -0.45010348 #> 6 Dublin     3.161931 -0.040828131 -0.50710580 -0.60543071 #> 7 Galway     4.630361  0.138454493  2.55314856  5.08170760 #> 8 Kerry      7.504775  0.027195108  0.47167584  0.51758880 #> 9 Kildare    3.862240  0.014230854  0.12280697  0.12246022 #> 10 Kilkenny  5.112007  0.071351828  1.03314661  1.41988761 #> 11 Laoghis   5.237883 -0.001502568 -0.01645549 -0.01646868 #> 12 Leitrim   4.395343  0.066207108  0.74158109  0.90609823 #> 13 Limerick  5.146640  0.050265468  0.63703133  0.74253221 #> 14 Longford  6.075040  0.060534639  1.04112815  1.44165700 #> 15 Louth     8.633971  0.025231866  0.49793592  0.55971045 #> 16 Mayo      5.002594  0.135902733  2.75603129  5.62669411 #> 17 Meath     3.741368 -0.028724497 -0.24912602 -0.26221742 #> 18 Monaghan  6.891283  0.028042744  0.43280552  0.47360371 #> 19 Offaly    4.287365  0.040883462  0.38909358  0.41780262 #> 20 Roscommon 3.945151  0.180270100  2.87643937  6.00202551 #> 21 Sligo     5.754236  0.023145822  0.30299868  0.31062426 #> 22 Tipperary 3.454595  0.048932861  0.38768333  0.40902706 #> 23 Waterford 5.297500  0.101874758  1.99944904  3.59542986 #> 24 Westmeath 5.351214  0.044919886  0.56403221  0.65024353 #> 25 Wexford   5.781330  0.066083430  1.11524637  1.57637406 #> 26 Wicklow   4.537075  0.012609906  0.12748740  0.12720134 e.locmorw2 <- summary(localmoran.sad(e.wlm, nb=eire.nb, resfun=rstudent)) e.locmorw2 #>              Local Morans I Stand. dev. (N)      Pr. (N) Saddlepoint #> 1 Carlow        0.121997164      0.32185426 0.7475631028  0.45871930 #> 2 Cavan        -0.110588620     -0.20105599 1.1593452023 -0.34808741 #> 3 Clare         0.308759283      0.60290381 0.5465726820  0.80379674 #> 4 Cork          1.404203115      3.23522979 0.0012154487  2.69598105 #> 5 Donegal      -0.421182109     -0.42837428 1.3316213558 -0.65187732 #> 6 Dublin       -0.443534307     -0.88433550 1.6234848706 -1.05167518 #> 7 Galway        1.376190254      3.42183495 0.0006220006  2.70663064 #> 8 Kerry         0.241623387      0.45357724 0.6501331373  0.61515126 #> 9 Kildare       0.008842913      0.14324202 0.8860990418  0.12690939 #> 10 Kilkenny     0.382893124      0.93980330 0.3473184643  1.12810394 #> 11 Laoghis     -0.019904450     -0.00246494 1.0019667357 -0.04176107 #> 12 Leitrim      0.200483743      0.60688769 0.5439254449  0.80241456 #> 13 Limerick     0.238810092      0.62310059 0.5332184222  0.81824678 #> 14 Longford     0.466942853      0.96178354 0.3361583457  1.14088225 #> 15 Louth        0.271710988      0.41271732 0.6798137369  0.58520655 #> 16 Mayo         1.705850161      3.60778634 0.0003088206  2.97346461 #> 17 Meath       -0.160603054     -0.41587901 1.3225014587 -0.63254531 #> 18 Monaghan     0.181378604      0.35629110 0.7216225742  0.50697175 #> 19 Offaly       0.107919508      0.35116431 0.7254650854  0.49312417 #> 20 Roscommon    1.249826037      3.75170355 0.0001756371  2.81402777 #> 21 Sligo        0.079431883      0.27999953 0.7794778655  0.33741411 #> 22 Tipperary    0.085153638      0.38940098 0.6969795442  0.51126046 #> 23 Waterford    1.022922345      2.28982205 0.0220316342  2.06385578 #> 24 Westmeath    0.201539331      0.48899468 0.6248454598  0.67791734 #> 25 Wexford      0.481114325      1.03805702 0.2992435100  1.21094348 #> 26 Wicklow     -0.011694661      0.08710223 0.9305902563  0.03786608 #>                Pr. (Sad) Expectation   Variance   Skewness Kurtosis    Minimum #> 1 Carlow     0.646435751 -0.01840558 0.19029731 -0.1986977 6.709176  -5.665283 #> 2 Cavan      0.727774542 -0.02184465 0.19482455 -0.2329761 6.717975  -5.769371 #> 3 Clare      0.421514374 -0.02782578 0.31166901 -0.2346279 6.718435  -7.299407 #> 4 Cork       0.007018166 -0.07147410 0.20805228 -0.7280203 7.002789  -6.495227 #> 5 Donegal    0.514480318 -0.07638800 0.64784767 -0.4450323 6.803659 -10.931345 #> 6 Dublin     0.292948602 -0.11187469 0.14065367 -1.3324828 7.767845  -5.846924 #> 7 Galway     0.006796983 -0.04407925 0.17227545 -0.4973247 6.833103  -5.688263 #> 8 Kerry      0.538454834 -0.05644300 0.43184063 -0.4031537 6.782459  -8.859407 #> 9 Kildare    0.899012117 -0.04145378 0.12329287 -0.5519841 6.867423  -4.857131 #> 10 Kilkenny  0.259276027 -0.02321457 0.18672759 -0.2528322 6.723714  -5.669156 #> 11 Laoghis   0.966689166 -0.01882531 0.19166504 -0.2024943 6.710081  -5.689691 #> 12 Leitrim   0.422313193 -0.03314655 0.14819776 -0.4041387 6.782933  -5.190860 #> 13 Limerick  0.413216288 -0.04800976 0.21188592 -0.4885390 6.827925  -6.298874 #> 14 Longford  0.253918927 -0.01321709 0.24923967 -0.1247567 6.694960  -6.392250 #> 15 Louth     0.558408841 -0.02272663 0.50895713 -0.1500895 6.699098  -9.179410 #> 16 Mayo      0.002944584 -0.09458039 0.24904116 -0.8745463 7.144787  -7.272523 #> 17 Meath     0.527030613 -0.02548973 0.10555100 -0.3685280 6.766525  -4.353122 #> 18 Monaghan  0.612174643 -0.02333303 0.33012248 -0.1912612 6.707452  -7.451275 #> 19 Offaly    0.621924855 -0.01927989 0.13120470 -0.2505068 6.723017  -4.750083 #> 20 Roscommon 0.004892500 -0.02385522 0.11525625 -0.3302939 6.750604  -4.517676 #> 21 Sligo     0.735804747 -0.06927688 0.28207107 -0.6087587 6.906925  -7.416881 #> 22 Tipperary 0.609168686 -0.03719246 0.09871568 -0.5534442 6.868390  -4.347214 #> 23 Waterford 0.039031392 -0.04027429 0.21558757 -0.4070996 6.784366  -6.264083 #> 24 Westmeath 0.497824103 -0.01522814 0.19650786 -0.1618342 6.701275  -5.716689 #> 25 Wexford   0.225917068 -0.02786850 0.24041626 -0.2674357 6.728234  -6.450174 #> 26 Wicklow   0.969794461 -0.04751424 0.16911517 -0.5404006 6.859847  -5.677417 #>               Maximum         omega        sad.r        sad.u #> 1 Carlow     5.223549  0.0272472954  0.306852385  0.321490350 #> 2 Cavan      5.245099 -0.0166242430 -0.190223798 -0.196022741 #> 3 Clare      6.631589  0.0358559846  0.559584155  0.641527095 #> 4 Cork       4.779848  0.1283688794  2.421993662  4.702934834 #> 5 Donegal    9.098033 -0.0169574018 -0.388662370 -0.430528174 #> 6 Dublin     3.161931 -0.0507848831 -0.696824139 -0.892299501 #> 7 Galway     4.630361  0.1333224875  2.431707338  4.745166958 #> 8 Kerry      7.504775  0.0252982005  0.433626352  0.469138111 #> 9 Kildare    3.862240  0.0161278548  0.139072871  0.138837812 #> 10 Kilkenny  5.112007  0.0622219791  0.835166590  1.066654825 #> 11 Laoghis   5.237883 -0.0002164925 -0.002368023 -0.002368244 #> 12 Leitrim   4.395343  0.0543844388  0.571625643  0.652237768 #> 13 Limerick  5.146640  0.0473787285  0.590605630  0.675595582 #> 14 Longford  6.075040  0.0528365356  0.840671447  1.082014178 #> 15 Louth     8.633971  0.0204960239  0.389078238  0.419930705 #> 16 Mayo      5.002594  0.1340509166  2.712635049  5.503894365 #> 17 Meath     3.741368 -0.0415411327 -0.379736494 -0.417998694 #> 18 Monaghan  6.891283  0.0226076552  0.338579266  0.358443998 #> 19 Offaly    4.287365  0.0357600182  0.335019324  0.353243066 #> 20 Roscommon 3.945151  0.1623235556  2.543240406  5.063795948 #> 21 Sligo     5.754236  0.0209568244  0.273376649  0.278204612 #> 22 Tipperary 3.454595  0.0478130890  0.377982061  0.397511387 #> 23 Waterford 5.297500  0.0941811771  1.762051071  2.998984773 #> 24 Westmeath 5.351214  0.0379323563  0.457473561  0.506014991 #> 25 Wexford   5.781330  0.0582538352  0.911459483  1.197527949 #> 26 Wicklow   4.537075  0.0083101099  0.084281843  0.083952776 run <- FALSE if (requireNamespace(\"spatialreg\", quietly=TRUE)) run <- TRUE if (run) { e.errorsar <- spatialreg::errorsarlm(OWNCONS ~ ROADACC, data=eire,   listw=lw) if (packageVersion(\"spatialreg\") < \"1.1.7\")   spatialreg::print.sarlm(e.errorsar) else   print(e.errorsar) } #>  #> Call: #> spatialreg::errorsarlm(formula = OWNCONS ~ ROADACC, data = eire,  #>     listw = lw) #> Type: error  #>  #> Coefficients: #>      lambda (Intercept)     ROADACC  #> 0.783970989 2.892719569 0.002800913  #>  #> Log likelihood: -64.12465  if (run) { lm.target <- lm(e.errorsar$tary ~ e.errorsar$tarX - 1) Omega <- tcrossprod(spatialreg::invIrW(lw, rho=e.errorsar$lambda)) e.clocmor <- summary(localmoran.sad(lm.target, nb=eire.nb, Omega=Omega)) e.clocmor } #>              Local Morans I Stand. dev. (N)   Pr. (N) Saddlepoint    Pr. (Sad) #> 1 Carlow         0.17958462      -0.5947094 1.4479623 -0.01890335 0.9849182097 #> 2 Cavan         -0.24752628      -0.9775195 1.6716880 -1.30903979 0.1905208730 #> 3 Clare         -0.27901334      -0.9987481 1.6820833 -1.41535136 0.1569655035 #> 4 Cork           0.37808655      -0.5304596 1.4042067  0.06399747 0.9489722431 #> 5 Donegal       -1.01894688      -1.4634181 1.8566470 -1.88871177 0.0589304608 #> 6 Dublin        -0.18171297      -0.9790853 1.6724621 -1.11436913 0.2651208631 #> 7 Galway         1.02193390       0.9527103 0.3407369  1.44844014 0.1474939944 #> 8 Kerry         -0.94967914      -1.1410950 1.7461696 -2.37909992 0.0173549707 #> 9 Kildare        0.07005053      -0.6531380 1.4863327 -0.10338270 0.9176592421 #> 10 Kilkenny      0.43022231      -0.3097714 1.2432652  0.46873471 0.6392592765 #> 11 Laoghis      -0.12239133      -0.9818401 1.6738214 -0.97718184 0.3284791346 #> 12 Leitrim      -0.24203970      -0.9591963 1.6625401 -1.53246533 0.1254076470 #> 13 Limerick     -0.03214546      -0.7729433 1.5604441 -0.80301568 0.4219656705 #> 14 Longford      0.38307454      -0.4899146 1.3758057  0.16621954 0.8679841832 #> 15 Louth         0.21301552      -0.6509309 1.4849089 -0.21224290 0.8319175422 #> 16 Mayo          0.93971200       0.3895188 0.6968924  1.15011408 0.2500968882 #> 17 Meath         0.12484415      -0.6182203 1.4635699 -0.09720926 0.9225602152 #> 18 Monaghan     -0.16109919      -0.8608004 1.6106520 -1.20575831 0.2279106933 #> 19 Offaly       -0.00632492      -0.7740865 1.5611204 -0.33915072 0.7344961920 #> 20 Roscommon     1.02089429       0.6454801 0.5186161  1.21215474 0.2254531515 #> 21 Sligo        -2.01629233      -1.8957526 1.9420072 -3.59571732 0.0003234989 #> 22 Tipperary    -0.10810709      -0.9082666 1.6362626 -1.09721448 0.2725476427 #> 23 Waterford     0.44099279      -0.3488980 1.2728341  0.41219202 0.6801986841 #> 24 Westmeath    -0.06329661      -0.8267635 1.5916289 -0.81444158 0.4153920274 #> 25 Wexford       0.30764883      -0.5219835 1.3983182  0.12395154 0.9013536461 #> 26 Wicklow      -0.01696406      -0.7708237 1.5591886 -0.68244661 0.4949565907 #>              Expectation   Variance Skewness  Kurtosis       Minimum   Maximum #> 1 Carlow       0.8594106  1.3067303 2.362830 10.416149  6.743373e-17 20.625856 #> 2 Cavan        1.1247112  1.9706416 2.347202 10.347468  1.645654e+00 25.347414 #> 3 Clare        1.2679076  2.3989670 2.334022 10.287656  2.485514e+00 27.944268 #> 4 Cork         1.2841620  2.9175890 2.362830 10.416149 -2.406699e-16 30.819888 #> 5 Donegal      1.7253177  3.5165365 2.172101  9.492322  8.227735e+00 33.179890 #> 6 Dublin       0.9462667  1.3272768 2.331563 10.276363  1.928660e+00 20.781740 #> 7 Galway       0.4507425  0.3594525 2.362830 10.416149  1.587770e-16 10.817821 #> 8 Kerry        2.6933183 10.1923447 2.307813 10.165571  7.170614e+00 57.469026 #> 9 Kildare      0.5337376  0.5040110 2.362830 10.416149 -6.444628e-18 12.809701 #> 10 Kilkenny    0.7317135  0.9472545 2.362830 10.416149  5.035617e-16 17.561125 #> 11 Laoghis     0.6035313  0.5466372 2.336004 10.296727  1.143655e+00 13.341096 #> 12 Leitrim     1.2258675  2.3419747 2.347302 10.347916  1.788145e+00 27.632674 #> 13 Limerick    1.5147254  4.0050955 2.362668 10.415466  2.341575e-01 36.119253 #> 14 Longford    1.0996747  2.1395031 2.362830 10.416149  5.674463e-16 26.392192 #> 15 Louth       1.5875248  4.4588771 2.362830 10.416149  4.309554e-16 38.100594 #> 16 Mayo        0.6190019  0.6779043 2.362830 10.416149 -2.035156e-16 14.856045 #> 17 Meath       0.7025948  0.8733620 2.362830 10.416149 -7.624840e-18 16.862274 #> 18 Monaghan    1.5519577  3.9603958 2.357838 10.394611  1.306155e+00 35.940829 #> 19 Offaly      0.3048481  0.1615939 2.362560 10.415009  6.073803e-02  7.255616 #> 20 Roscommon   0.5492905  0.5338125 2.362830 10.416149  9.144870e-16 13.182973 #> 21 Sligo       2.3130311  5.2152695 1.886102  7.938452  1.739456e+01 38.118185 #> 22 Tipperary   0.7147979  0.8208668 2.354040 10.377921  7.922254e-01 16.362924 #> 23 Waterford   0.8228671  1.1979644 2.362830 10.416149  1.408133e-15 19.748811 #> 24 Westmeath   0.8426747  1.2007879 2.360962 10.408167  4.379239e-01 19.786270 #> 25 Wexford     1.0063848  1.7918953 2.362830 10.416149  1.028640e-17 24.153236 #> 26 Wicklow     0.9927147  1.7157589 2.362598 10.415171  1.833509e-01 23.641801 #>                     omega       sad.r       sad.u #> 1 Carlow     -0.017838447 -0.38297869 -0.33313448 #> 2 Cavan      -0.066132684 -1.21593175 -1.36168605 #> 3 Clare      -0.066612498 -1.30513958 -1.50704646 #> 4 Cork       -0.010368850 -0.33915229 -0.29581081 #> 5 Donegal    -0.045800559 -1.66568212 -2.41507712 #> 6 Dublin     -0.056683668 -1.03296356 -1.12358099 #> 7 Galway      0.031762997  1.14153962  1.62047125 #> 8 Kerry      -0.079689480 -2.19374456 -3.29442701 #> 9 Kildare    -0.025051491 -0.36678693 -0.33300845 #> 10 Kilkenny   0.003214928  0.09217307  0.09542846 #> 11 Laoghis   -0.065438986 -0.89335507 -0.96282454 #> 12 Leitrim   -0.092395573 -1.43474097 -1.65069014 #> 13 Limerick  -0.047140362 -0.97737323 -0.82423542 #> 14 Longford  -0.007176482 -0.22762630 -0.20810767 #> 15 Louth     -0.018552546 -0.58005974 -0.46861210 #> 16 Mayo       0.019992304  0.84088281  1.09059594 #> 17 Meath     -0.026958325 -0.44558661 -0.38151850 #> 18 Monaghan  -0.062388996 -1.21509194 -1.20138917 #> 19 Offaly    -0.044380046 -0.41568118 -0.40266554 #> 20 Roscommon  0.023338184  0.88169755  1.17993235 #> 21 Sligo     -0.131646728 -3.40243100 -6.56750200 #> 22 Tipperary -0.089378129 -1.06748205 -1.10190609 #> 23 Waterford  0.001151041  0.03534520  0.03581914 #> 24 Westmeath -0.058470593 -0.88397327 -0.83127666 #> 25 Wexford   -0.009550496 -0.26689930 -0.24045996 #> 26 Wicklow   -0.050401553 -0.84395069 -0.73641410 if (run) { hist(e.clocmor[,\"Pr. (Sad)\"]) }"},{"path":"https://r-spatial.github.io/spdep/reference/localmoran_bv.html","id":null,"dir":"Reference","previous_headings":"","what":"Compute the Local Bivariate Moran's I Statistic — localmoran_bv","title":"Compute the Local Bivariate Moran's I Statistic — localmoran_bv","text":"Given two continuous numeric variables, calculate bivariate Local Moran's .","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localmoran_bv.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Compute the Local Bivariate Moran's I Statistic — localmoran_bv","text":"","code":"localmoran_bv(x, y, listw, nsim = 199, scale = TRUE, alternative=\"two.sided\",  iseed=1L, no_repeat_in_row=FALSE, zero.policy=attr(listw, \"zero.policy\"))"},{"path":"https://r-spatial.github.io/spdep/reference/localmoran_bv.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Compute the Local Bivariate Moran's I Statistic — localmoran_bv","text":"x numeric vector length y. y numeric vector length x. listw listw object example created nb2listw(). nsim number simulations run. scale default TRUE. alternative character string specifying alternative hypothesis, must one \"greater\" (default), \"two.sided\", \"less\". iseed default NULL, used set seed; output reproducible count CPU cores across computation distributed . no_repeat_in_row default FALSE, TRUE, sample conditionally row without replacements avoid duplicate values, https://github.com/r-spatial/spdep/issues/124 zero.policy default default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localmoran_bv.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Compute the Local Bivariate Moran's I Statistic — localmoran_bv","text":"data.frame containing two columns Ib p_sim containing local bivariate Moran's simulated p-values respectively.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localmoran_bv.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Compute the Local Bivariate Moran's I Statistic — localmoran_bv","text":"Bivariate Local Moran, like global counterpart, evaluates value x observation spatial neighbors' value y. value \\(I_i^B\\) xi * Wyi. , simpler words, local bivariate Moran result multiplying x spatial lag y. Formally defined \\( I_i^B= cx_i\\Sigma_j{w_{ij}y_j} \\)","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localmoran_bv.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Compute the Local Bivariate Moran's I Statistic — localmoran_bv","text":"Anselin, Luc, Ibnu Syabri, Oleg Smirnov. 2002. “Visualizing Multivariate Spatial Correlation Dynamically Linked Windows.” New Tools Spatial Data Analysis: Proceedings Specialist Meeting, edited Luc Anselin Sergio Rey. University California, Santa Barbara: Center Spatially Integrated Social Science (CSISS).","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localmoran_bv.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Compute the Local Bivariate Moran's I Statistic — localmoran_bv","text":"Josiah Parry josiah.parry@gmail.com","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localmoran_bv.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Compute the Local Bivariate Moran's I Statistic — localmoran_bv","text":"","code":"# load columbus datay columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")) #> Reading layer `columbus' from data source  #>   `/home/rsb/lib/r_libs/spData/shapes/columbus.gpkg' using driver `GPKG' #> Simple feature collection with 49 features and 20 fields #> Geometry type: POLYGON #> Dimension:     XY #> Bounding box:  xmin: 5.874907 ymin: 10.78863 xmax: 11.28742 ymax: 14.74245 #> Projected CRS: Undefined Cartesian SRS with unknown unit nb <- poly2nb(columbus) listw <- nb2listw(nb) set.seed(1) (res <- localmoran_bv(columbus$CRIME, columbus$INC, listw, nsim = 499)) #>                Ibvi        E.Ibvi    Var.Ibvi      Z.Ibvi Pr(z != E(Ibvi)) #>  [1,] -0.8578252210 -1.826370e-02 0.731541578 -0.98159654     3.262987e-01 #>  [2,]  0.1802618568  2.554658e-02 0.334247968  0.26760782     7.890012e-01 #>  [3,]  0.0118856298  7.791116e-03 0.017162929  0.03125407     9.750669e-01 #>  [4,] -0.0163525887 -3.452848e-03 0.005852145 -0.16862558     8.660912e-01 #>  [5,] -0.5037734606  1.811633e-02 0.101966376 -1.63436973     1.021812e-01 #>  [6,] -0.0041841415  1.293651e-02 0.139142736 -0.04589760     9.633919e-01 #>  [7,]  1.5201688711 -1.466392e-04 1.099034279  1.45020069     1.470026e-01 #>  [8,] -0.2016456990  7.471406e-03 0.007231278 -2.45913301     1.392730e-02 #>  [9,]  0.0297432891  1.600490e-03 0.009219518  0.29309821     7.694471e-01 #> [10,] -0.0374203146  1.218906e-03 0.001100110 -1.16495823     2.440359e-01 #> [11,] -1.2368494456  7.720869e-02 0.498286158 -1.86155199     6.266627e-02 #> [12,] -1.2010054212  4.055009e-02 0.266658169 -2.40430022     1.620346e-02 #> [13,] -0.5377131737  1.218864e-02 0.122363375 -1.57202494     1.159448e-01 #> [14,] -0.9879712511  3.048475e-02 0.320475271 -1.79905736     7.200961e-02 #> [15,] -0.6057303757  2.137030e-02 0.102916086 -1.95476986     5.061024e-02 #> [16,] -0.7878039284  1.378587e-02 0.161039891 -1.99749384     4.577156e-02 #> [17,]  0.1379508106  9.352179e-04 0.003351141  2.36686570     1.793944e-02 #> [18,] -0.3253226893  1.066349e-02 0.078469609 -1.19941831     2.303653e-01 #> [19,] -0.3888822685 -7.104732e-06 0.432305953 -0.59144532     5.542221e-01 #> [20,] -0.4544889957  1.367811e-01 0.355060554 -0.99228105     3.210604e-01 #> [21,] -0.0006014046  3.919068e-03 0.031597455 -0.02543067     9.797114e-01 #> [22,] -0.0068813684 -3.664201e-03 0.001242910 -0.09125440     9.272904e-01 #> [23,] -0.8788967496  1.189579e-02 0.289002627 -1.65701209     9.751703e-02 #> [24,] -0.1256865340 -3.048451e-03 0.004692164 -1.79035349     7.339710e-02 #> [25,] -0.9307459211  4.509269e-02 0.303474056 -1.77140234     7.649382e-02 #> [26,] -0.2252775788  1.039843e-02 0.019527743 -1.68651169     9.169728e-02 #> [27,]  0.1413018326 -1.409345e-02 0.236810168  0.31932848     7.494774e-01 #> [28,] -0.7804482928  3.200178e-02 0.184987862 -1.88897002     5.889585e-02 #> [29,] -0.7654416689  5.928648e-02 0.364667175 -1.36572255     1.720261e-01 #> [30,] -0.9074829015  7.597435e-03 0.737090639 -1.06585659     2.864885e-01 #> [31,] -0.5510119267 -1.377557e-03 0.388899970 -0.88136323     3.781213e-01 #> [32,] -1.9581476375  2.561515e-02 0.239115219 -4.05682367     4.974461e-05 #> [33,]  0.0907015890  3.048227e-02 0.043681309  0.28812970     7.732475e-01 #> [34,] -0.4297843082  2.130996e-02 0.104683121 -1.39421250     1.632534e-01 #> [35,]  0.1181174820  6.746380e-04 0.008393054  1.28193663     1.998649e-01 #> [36,] -0.9901007017  2.760845e-02 0.278368628 -1.92891697     5.374117e-02 #> [37,] -0.2195812498 -7.723065e-03 0.032151838 -1.18152344     2.373948e-01 #> [38,] -0.3096268627  3.401135e-02 0.205499338 -0.75804717     4.484227e-01 #> [39,] -0.6090192229  1.689079e-02 0.308320019 -1.12722610     2.596469e-01 #> [40,] -1.2709838927  6.528265e-02 0.216905961 -2.86917707     4.115413e-03 #> [41,] -1.3940681427  9.430182e-02 0.304439982 -2.69749131     6.986411e-03 #> [42,] -0.4820987026  3.961324e-02 0.632999863 -0.65573592     5.119941e-01 #> [43,] -0.0064402410  2.939096e-03 0.001385154 -0.25201308     8.010310e-01 #> [44,]  0.0761664412  2.162964e-02 0.054095662  0.23448142     8.146113e-01 #> [45,] -0.0560342555  7.788766e-03 0.029796273 -0.36973996     7.115763e-01 #> [46,] -0.8249832451 -2.301643e-02 0.673531467 -0.97718648     3.284768e-01 #> [47,] -0.8915318222  2.294960e-02 0.095247718 -2.96310881     3.045489e-03 #> [48,] -0.1282863305 -9.674295e-03 0.061579149 -0.47798241     6.326627e-01 #> [49,]  0.0094888641 -4.828535e-03 0.222107368  0.03037964     9.757643e-01 #>       Pr(z != E(Ibvi)) Sim Pr(folded) Sim #>  [1,]                0.324          0.162 #>  [2,]                0.880          0.440 #>  [3,]                0.976          0.488 #>  [4,]                0.800          0.400 #>  [5,]                0.112          0.056 #>  [6,]                0.864          0.430 #>  [7,]                0.096          0.048 #>  [8,]                0.004          0.002 #>  [9,]                0.852          0.426 #> [10,]                0.260          0.130 #> [11,]                0.056          0.028 #> [12,]                0.008          0.004 #> [13,]                0.084          0.042 #> [14,]                0.064          0.032 #> [15,]                0.052          0.026 #> [16,]                0.028          0.014 #> [17,]                0.028          0.014 #> [18,]                0.192          0.096 #> [19,]                0.608          0.304 #> [20,]                0.368          0.184 #> [21,]                0.936          0.468 #> [22,]                0.928          0.464 #> [23,]                0.120          0.060 #> [24,]                0.040          0.020 #> [25,]                0.044          0.022 #> [26,]                0.076          0.038 #> [27,]                0.736          0.368 #> [28,]                0.032          0.016 #> [29,]                0.140          0.070 #> [30,]                0.284          0.142 #> [31,]                0.408          0.204 #> [32,]                0.004          0.002 #> [33,]                0.724          0.362 #> [34,]                0.188          0.094 #> [35,]                0.216          0.108 #> [36,]                0.084          0.042 #> [37,]                0.232          0.116 #> [38,]                0.464          0.232 #> [39,]                0.268          0.134 #> [40,]                0.004          0.002 #> [41,]                0.020          0.010 #> [42,]                0.468          0.234 #> [43,]                0.884          0.442 #> [44,]                0.904          0.452 #> [45,]                0.672          0.336 #> [46,]                0.344          0.172 #> [47,]                0.012          0.006 #> [48,]                0.544          0.272 #> [49,]                0.896          0.448 #> attr(,\"quadr\") #>         mean    median     pysal #> 1   Low-High  Low-High  Low-High #> 2    Low-Low   Low-Low   Low-Low #> 3    Low-Low   Low-Low   Low-Low #> 4   Low-High  Low-High  Low-High #> 5   High-Low  High-Low  High-Low #> 6    Low-Low  Low-High  Low-High #> 7    Low-Low   Low-Low   Low-Low #> 8   High-Low  High-Low  High-Low #> 9    Low-Low   Low-Low   Low-Low #> 10  Low-High  Low-High  Low-High #> 11  High-Low  High-Low  High-Low #> 12  High-Low  High-Low  High-Low #> 13  High-Low  High-Low  High-Low #> 14  High-Low  High-Low  High-Low #> 15  High-Low  High-Low  High-Low #> 16  High-Low  High-Low  High-Low #> 17 High-High High-High High-High #> 18  High-Low  High-Low  High-Low #> 19  High-Low  High-Low  High-Low #> 20  Low-High  Low-High  Low-High #> 21  High-Low High-High  High-Low #> 22  Low-High  Low-High  Low-High #> 23  Low-High  Low-High  Low-High #> 24  High-Low  High-Low  High-Low #> 25  High-Low  High-Low  High-Low #> 26  High-Low  High-Low  High-Low #> 27 High-High High-High High-High #> 28  High-Low  High-Low  High-Low #> 29  High-Low  High-Low  High-Low #> 30  High-Low  High-Low  High-Low #> 31  Low-High  Low-High  Low-High #> 32  Low-High  Low-High  Low-High #> 33 High-High High-High High-High #> 34  Low-High  Low-High  Low-High #> 35 High-High High-High High-High #> 36  Low-High  Low-High  Low-High #> 37  High-Low  High-Low  High-Low #> 38  High-Low  High-Low  High-Low #> 39  Low-High  Low-High  Low-High #> 40  Low-High  Low-High  Low-High #> 41  Low-High  Low-High  Low-High #> 42  Low-High  Low-High  Low-High #> 43  High-Low  High-Low  High-Low #> 44   Low-Low   Low-Low   Low-Low #> 45  Low-High  Low-High  Low-High #> 46  Low-High  Low-High  Low-High #> 47  Low-High  Low-High  Low-High #> 48  Low-High  Low-High  Low-High #> 49   Low-Low   Low-Low   Low-Low #> attr(,\"class\") #> [1] \"localmoran\" \"matrix\"     \"array\"      #> attr(,\"ncpus\") #> [1] 1 columbus$hs <- hotspot(res, Prname=\"Pr(folded) Sim\", cutoff=0.05,  quadrant.type=\"pysal\", p.adjust=\"none\") # \\donttest{ if (require(\"tmap\", quietly=TRUE)) { tmap4 <- packageVersion(\"tmap\") >= \"3.99\" if (tmap4) {   tm_shape(columbus) + tm_polygons(fill=\"hs\",     fill.scale=tm_scale(values=\"brewer.set3\"),     fill.legend=tm_legend(position=tm_pos_in(\"left\", \"top\"),       frame=FALSE, item.r=0), lwd=0.01) } else {   tm_shape(columbus) + tm_fill(\"hs\") } } #> Breaking News: tmap 3.x is retiring. Please test v4, e.g. with #> remotes::install_github('r-tmap/tmap')  # } moran.plot(x=columbus$CRIME, y=columbus$INC, listw=listw)"},{"path":"https://r-spatial.github.io/spdep/reference/mat2listw.html","id":null,"dir":"Reference","previous_headings":"","what":"Convert a square spatial weights matrix to a weights list object — mat2listw","title":"Convert a square spatial weights matrix to a weights list object — mat2listw","text":"function converts square spatial weights matrix, optionally sparse matrix weights list object, optionally adding region IDs row names matrix, sequence numbers 1:nrow(x), given argument. style can imposed rebuilting weights list object internally.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/mat2listw.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Convert a square spatial weights matrix to a weights list object — mat2listw","text":"","code":"mat2listw(x, row.names = NULL, style=NULL, zero.policy = NULL)"},{"path":"https://r-spatial.github.io/spdep/reference/mat2listw.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Convert a square spatial weights matrix to a weights list object — mat2listw","text":"x square non-negative matrix NAs representing spatial weights; may matrix class “sparseMatrix” row.names row names use region IDs style default NULL, missing, set \"M\" warning given; \"M\", passed nb2listw re-build object zero.policy default NULL, use global option value; FALSE stop error empty neighbour sets, TRUE permit weights list formed zero-length weights vectors","code":""},{"path":"https://r-spatial.github.io/spdep/reference/mat2listw.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Convert a square spatial weights matrix to a weights list object — mat2listw","text":"listw object following members: style \"M\", meaning matrix style, underlying style unknown, assigned style argument rebuilt object neighbours derived neighbours list weights weights neighbours derived matrix","code":""},{"path":"https://r-spatial.github.io/spdep/reference/mat2listw.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Convert a square spatial weights matrix to a weights list object — mat2listw","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/mat2listw.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Convert a square spatial weights matrix to a weights list object — mat2listw","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) col005 <- dnearneigh(st_coordinates(st_centroid(st_geometry(columbus),  of_largest_polygon=TRUE)), 0, 0.5, as.character(columbus$NEIGNO)) #> Warning: neighbour object has 8 sub-graphs summary(col005) #> Neighbour list object: #> Number of regions: 49  #> Number of nonzero links: 170  #> Percentage nonzero weights: 7.080383  #> Average number of links: 3.469388  #> 4 regions with no links: #> 1005, 1006, 1008, 1043 #> 8 disjoint connected subgraphs #> Link number distribution: #>  #>  0  1  2  3  4  5  6  7  8  9  #>  4 11  5  8  3  9  2  2  3  2  #> 11 least connected regions: #> 1001 1007 1018 1010 1045 1044 1046 1047 1049 1048 1015 with 1 link #> 2 most connected regions: #> 1038 1036 with 9 links col005.w.mat <- nb2mat(col005, style=\"W\", zero.policy=TRUE) try(col005.w.b <- mat2listw(col005.w.mat, style=\"W\")) #> Warning: no-neighbour observations found, set zero.policy to TRUE; #> this warning will soon become an error #> Warning: neighbour object has 8 sub-graphs #> Error in nb2listw(res$neighbours, glist = res$weights, style = style,  :  #>   Empty neighbour sets found (zero.policy: FALSE) col005.w.b <- mat2listw(col005.w.mat, style=\"W\", zero.policy=TRUE) #> Warning: neighbour object has 8 sub-graphs summary(col005.w.b$neighbours) #> Neighbour list object: #> Number of regions: 49  #> Number of nonzero links: 170  #> Percentage nonzero weights: 7.080383  #> Average number of links: 3.469388  #> 4 regions with no links: #> 1005, 1006, 1008, 1043 #> 8 disjoint connected subgraphs #> Link number distribution: #>  #>  0  1  2  3  4  5  6  7  8  9  #>  4 11  5  8  3  9  2  2  3  2  #> 11 least connected regions: #> 1001 1007 1018 1010 1045 1044 1046 1047 1049 1048 1015 with 1 link #> 2 most connected regions: #> 1038 1036 with 9 links diffnb(col005, col005.w.b$neighbours) #> Warning: neighbour object has 49 sub-graphs #> Neighbour list object: #> Number of regions: 49  #> Number of nonzero links: 0  #> Percentage nonzero weights: 0  #> Average number of links: 0  #> 49 regions with no links: #> 1005, 1001, 1006, 1002, 1007, 1008, 1004, 1003, 1018, 1010, 1038, 1037, #> 1039, 1040, 1009, 1036, 1011, 1042, 1041, 1017, 1043, 1019, 1012, 1035, #> 1032, 1020, 1021, 1031, 1033, 1034, 1045, 1013, 1022, 1044, 1023, 1046, #> 1030, 1024, 1047, 1016, 1014, 1049, 1029, 1025, 1028, 1048, 1015, 1027, #> 1026 #> 49 disjoint connected subgraphs col005.w.mat.3T <- kronecker(diag(3), col005.w.mat) col005.w.b.3T <- mat2listw(col005.w.mat.3T, style=\"W\", zero.policy=TRUE) #> Warning: neighbour object has 24 sub-graphs summary(col005.w.b.3T$neighbours) #> Neighbour list object: #> Number of regions: 147  #> Number of nonzero links: 510  #> Percentage nonzero weights: 2.360128  #> Average number of links: 3.469388  #> 12 regions with no links: #> 1, 3, 6, 21, 50, 52, 55, 70, 99, 101, 104, 119 #> 24 disjoint connected subgraphs #> Link number distribution: #>  #>  0  1  2  3  4  5  6  7  8  9  #> 12 33 15 24  9 27  6  6  9  6  #> 33 least connected regions: #> 2 5 9 10 31 34 36 39 42 46 47 51 54 58 59 80 83 85 88 91 95 96 100 103 107 108 129 132 134 137 140 144 145 with 1 link #> 6 most connected regions: #> 11 16 60 65 109 114 with 9 links run <- FALSE if (require(\"spatialreg\", quiet=TRUE)) run <- TRUE if (run) { W <- as(nb2listw(col005, style=\"W\", zero.policy=TRUE), \"CsparseMatrix\") try(col005.spM <- mat2listw(W)) col005.spM <- mat2listw(W, style=\"W\", zero.policy=TRUE) summary(col005.spM$neighbours) } #> Warning: style is M (missing); style should be set to a valid value #> Warning: style is M (missing); style should be set to a valid value #> Warning: 1005, 1006, 1008, 1043 are not origins #> Warning: no-neighbour observations found, set zero.policy to TRUE; #> this warning will soon become an error #> Warning: neighbour object has 8 sub-graphs #> Warning: no-neighbour observations found, set zero.policy to TRUE; #> this warning will soon become an error #> Warning: neighbour object has 8 sub-graphs #> Warning: no-neighbour observations found, set zero.policy to TRUE; #> this warning will soon become an error #> Warning: neighbour object has 8 sub-graphs #> Warning: neighbour object has 8 sub-graphs #> Neighbour list object: #> Number of regions: 49  #> Number of nonzero links: 170  #> Percentage nonzero weights: 7.080383  #> Average number of links: 3.469388  #> 4 regions with no links: #> 1005, 1006, 1008, 1043 #> 8 disjoint connected subgraphs #> Link number distribution: #>  #>  0  1  2  3  4  5  6  7  8  9  #>  4 11  5  8  3  9  2  2  3  2  #> 11 least connected regions: #> 1001 1007 1018 1010 1045 1044 1046 1047 1049 1048 1015 with 1 link #> 2 most connected regions: #> 1038 1036 with 9 links if (run) { diffnb(col005, col005.spM$neighbours) } #> Warning: neighbour object has 49 sub-graphs #> Neighbour list object: #> Number of regions: 49  #> Number of nonzero links: 0  #> Percentage nonzero weights: 0  #> Average number of links: 0  #> 49 regions with no links: #> 1005, 1001, 1006, 1002, 1007, 1008, 1004, 1003, 1018, 1010, 1038, 1037, #> 1039, 1040, 1009, 1036, 1011, 1042, 1041, 1017, 1043, 1019, 1012, 1035, #> 1032, 1020, 1021, 1031, 1033, 1034, 1045, 1013, 1022, 1044, 1023, 1046, #> 1030, 1024, 1047, 1016, 1014, 1049, 1029, 1025, 1028, 1048, 1015, 1027, #> 1026 #> 49 disjoint connected subgraphs if (run && require(\"Matrix\", quiet=TRUE)) { IW <- kronecker(Diagonal(3), W) col005.spM.3T <- mat2listw(as(IW, \"CsparseMatrix\"), style=\"W\", zero.policy=TRUE) summary(col005.spM.3T$neighbours) } #> Warning: no-neighbour observations found, set zero.policy to TRUE; #> this warning will soon become an error #> Warning: neighbour object has 24 sub-graphs #> Warning: neighbour object has 24 sub-graphs #> Neighbour list object: #> Number of regions: 147  #> Number of nonzero links: 510  #> Percentage nonzero weights: 2.360128  #> Average number of links: 3.469388  #> 12 regions with no links: #> 1, 3, 6, 21, 50, 52, 55, 70, 99, 101, 104, 119 #> 24 disjoint connected subgraphs #> Link number distribution: #>  #>  0  1  2  3  4  5  6  7  8  9  #> 12 33 15 24  9 27  6  6  9  6  #> 33 least connected regions: #> 2 5 9 10 31 34 36 39 42 46 47 51 54 58 59 80 83 85 88 91 95 96 100 103 107 108 129 132 134 137 140 144 145 with 1 link #> 6 most connected regions: #> 11 16 60 65 109 114 with 9 links"},{"path":"https://r-spatial.github.io/spdep/reference/moran.html","id":null,"dir":"Reference","previous_headings":"","what":"Compute Moran's I — moran","title":"Compute Moran's I — moran","text":"simple function compute Moran's , called moran.test moran.mc; $$= \\frac{n}{\\sum_{=1}^{n}\\sum_{j=1}^{n}w_{ij}} \\frac{\\sum_{=1}^{n}\\sum_{j=1}^{n}w_{ij}(x_i-\\bar{x})(x_j-\\bar{x})}{\\sum_{=1}^{n}(x_i - \\bar{x})^2} $$","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Compute Moran's I — moran","text":"","code":"moran(x, listw, n, S0, zero.policy=attr(listw, \"zero.policy\"), NAOK=FALSE)"},{"path":"https://r-spatial.github.io/spdep/reference/moran.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Compute Moran's I — moran","text":"x numeric vector length neighbours list listw listw listw object created example nb2listw n number zones S0 global sum weights zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA NAOK 'TRUE' 'NA' 'NaN' 'Inf' values x passed foreign function.  'FALSE', presence 'NA' 'NaN' 'Inf' values regarded error.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Compute Moran's I — moran","text":"list Moran's K sample kurtosis x","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Compute Moran's I — moran","text":"Cliff, . D., Ord, J. K. 1981 Spatial processes, Pion, p. 17.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Compute Moran's I — moran","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/moran.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Compute Moran's I — moran","text":"","code":"data(oldcol) col.W <- nb2listw(COL.nb, style=\"W\") crime <- COL.OLD$CRIME str(moran(crime, col.W, length(COL.nb), Szero(col.W))) #> List of 2 #>  $ I: num 0.511 #>  $ K: num 2.23 is.na(crime) <- sample(1:length(crime), 10) str(moran(crime, col.W, length(COL.nb), Szero(col.W), NAOK=TRUE)) #> Warning: NAs in lagged values #> List of 2 #>  $ I: num 0.166 #>  $ K: num 2.87"},{"path":"https://r-spatial.github.io/spdep/reference/moran.mc.html","id":null,"dir":"Reference","previous_headings":"","what":"Permutation test for Moran's I statistic — moran.mc","title":"Permutation test for Moran's I statistic — moran.mc","text":"permutation test Moran's statistic calculated using nsim random permutations x given spatial weighting scheme, establish rank observed statistic relation nsim simulated values.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran.mc.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Permutation test for Moran's I statistic — moran.mc","text":"","code":"moran.mc(x, listw, nsim, zero.policy=attr(listw, \"zero.policy\"),  alternative=\"greater\", na.action=na.fail, spChk=NULL, return_boot=FALSE,  adjust.n=TRUE)"},{"path":"https://r-spatial.github.io/spdep/reference/moran.mc.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Permutation test for Moran's I statistic — moran.mc","text":"x numeric vector length neighbours list listw listw listw object created example nb2listw nsim number permutations zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA alternative character string specifying alternative hypothesis, must one \"greater\" (default), \"two.sided\", \"less\". na.action function (default na.fail), can also na.omit na.exclude - cases weights list subsetted remove NAs data. may necessary set zero.policy TRUE subsetting may create -neighbour observations. Note weights lists created without using glist argument nb2listw may subsetted. na.pass permitted meaningless permutation test. spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption() return_boot return object class boot equivalent permutation bootstrap rather object class htest adjust.n default TRUE, FALSE number observations adjusted -neighbour observations, TRUE, number observations adjusted","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran.mc.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Permutation test for Moran's I statistic — moran.mc","text":"list class htest mc.sim containing following components: statistic value observed Moran's . parameter rank observed Moran's . p.value pseudo p-value test. alternative character string describing alternative hypothesis. method character string giving method used. data.name character string giving name(s) data, number simulations. res nsim simulated values statistic, final value observed statistic","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran.mc.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Permutation test for Moran's I statistic — moran.mc","text":"Cliff, . D., Ord, J. K. 1981 Spatial processes, Pion, p. 63-5.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran.mc.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Permutation test for Moran's I statistic — moran.mc","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/moran.mc.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Permutation test for Moran's I statistic — moran.mc","text":"","code":"data(oldcol) colw <- nb2listw(COL.nb, style=\"W\") nsim <- 99 set.seed(1234) sim1 <- moran.mc(COL.OLD$CRIME, listw=colw, nsim=nsim) sim1 #>  #> \tMonte-Carlo simulation of Moran I #>  #> data:  COL.OLD$CRIME  #> weights: colw   #> number of simulations + 1: 100  #>  #> statistic = 0.51095, observed rank = 100, p-value = 0.01 #> alternative hypothesis: greater #>  mean(sim1$res[1:nsim]) #> [1] -0.003196117 var(sim1$res[1:nsim]) #> [1] 0.008543554 summary(sim1$res[1:nsim]) #>      Min.   1st Qu.    Median      Mean   3rd Qu.      Max.  #> -0.180085 -0.073721 -0.009528 -0.003196  0.063865  0.206779  colold.lags <- nblag(COL.nb, 3) set.seed(1234) sim2 <- moran.mc(COL.OLD$CRIME, nb2listw(colold.lags[[2]],  style=\"W\"), nsim=nsim) summary(sim2$res[1:nsim]) #>     Min.  1st Qu.   Median     Mean  3rd Qu.     Max.  #> -0.15905 -0.07503 -0.01535 -0.02060  0.03305  0.13023  sim3 <- moran.mc(COL.OLD$CRIME, nb2listw(colold.lags[[3]],  style=\"W\"), nsim=nsim) summary(sim3$res[1:nsim]) #>      Min.   1st Qu.    Median      Mean   3rd Qu.      Max.  #> -0.192986 -0.055468 -0.024154 -0.026327  0.004769  0.129996  crime <- COL.OLD$CRIME is.na(crime) <- sample(1:length(crime), 10) try(moran.mc(crime, nb2listw(COL.nb, style=\"W\"), nsim=99,  na.action=na.fail)) #> Error in na.fail.default(x) : missing values in object moran.mc(crime, nb2listw(COL.nb, style=\"W\"), nsim=99, zero.policy=TRUE,  na.action=na.omit) #>  #> \tMonte-Carlo simulation of Moran I #>  #> data:  crime  #> weights: nb2listw(COL.nb, style = \"W\")  #> omitted: 5, 7, 9, 15, 19, 33, 40, 45, 47, 48  #> number of simulations + 1: 100  #>  #> statistic = 0.42342, observed rank = 100, p-value = 0.01 #> alternative hypothesis: greater #>  moran.mc(crime, nb2listw(COL.nb, style=\"W\"), nsim=99, zero.policy=TRUE,  return_boot=TRUE, na.action=na.omit) #> NA observations omitted: 5, 7, 9, 15, 19, 33, 40, 45, 47, 48 #>  #> DATA PERMUTATION #>  #>  #> Call: #> boot(data = x, statistic = moran_boot, R = nsim, sim = \"permutation\",  #>     listw = listw, n = n, S0 = S0, zero.policy = zero.policy,  #>     parallel = parallel, ncpus = ncpus, cl = cl) #>  #>  #> Bootstrap Statistics : #>      original     bias    std. error #> t1* 0.4234221 -0.4429891   0.1293935 moran.mc(crime, nb2listw(COL.nb, style=\"W\"), nsim=99, zero.policy=TRUE,  na.action=na.exclude) #>  #> \tMonte-Carlo simulation of Moran I #>  #> data:  crime  #> weights: nb2listw(COL.nb, style = \"W\")  #> omitted: 5, 7, 9, 15, 19, 33, 40, 45, 47, 48  #> number of simulations + 1: 100  #>  #> statistic = 0.42342, observed rank = 100, p-value = 0.01 #> alternative hypothesis: greater #>  moran.mc(crime, nb2listw(COL.nb, style=\"W\"), nsim=99, zero.policy=TRUE,  return_boot=TRUE, na.action=na.exclude) #> NA observations omitted: 5, 7, 9, 15, 19, 33, 40, 45, 47, 48 #>  #> DATA PERMUTATION #>  #>  #> Call: #> boot(data = x, statistic = moran_boot, R = nsim, sim = \"permutation\",  #>     listw = listw, n = n, S0 = S0, zero.policy = zero.policy,  #>     parallel = parallel, ncpus = ncpus, cl = cl) #>  #>  #> Bootstrap Statistics : #>      original     bias    std. error #> t1* 0.4234221 -0.4384413   0.1243937 try(moran.mc(crime, nb2listw(COL.nb, style=\"W\"), nsim=99, na.action=na.pass)) #> Error in moran.mc(crime, nb2listw(COL.nb, style = \"W\"), nsim = 99, na.action = na.pass) :  #>   na.pass not permitted"},{"path":"https://r-spatial.github.io/spdep/reference/moran.plot.html","id":null,"dir":"Reference","previous_headings":"","what":"Moran scatterplot — moran.plot","title":"Moran scatterplot — moran.plot","text":"plot spatial data spatially lagged values, augmented reporting summary influence measures linear relationship data lag. zero policy TRUE, observations also marked occur.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran.plot.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Moran scatterplot — moran.plot","text":"","code":"moran.plot(x, listw, y=NULL, zero.policy=attr(listw, \"zero.policy\"), spChk=NULL,  labels=NULL, xlab=NULL, ylab=NULL, quiet=NULL, plot=TRUE, return_df=TRUE, ...)"},{"path":"https://r-spatial.github.io/spdep/reference/moran.plot.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Moran scatterplot — moran.plot","text":"x numeric vector length neighbours list listw listw listw object created example nb2listw y optional numeric vector length neighbours list listw bi-variate plot zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption() labels character labels points high influence measures, set FALSE, labels plotted points large influence xlab label x axis ylab label x axis quiet default NULL, use !verbose global option value; TRUE, output summary influence object suppressed plot default TRUE, false, plotting suppressed return_df default TRUE, invisibly return data.frame object; FALSE invisibly return influence measures object ... graphical parameters par(..)","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran.plot.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Moran scatterplot — moran.plot","text":"function returns data.frame object coordinates influence measures return_df TRUE, influence object influence.measures.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran.plot.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Moran scatterplot — moran.plot","text":"Anselin, L. 1996. Moran scatterplot ESDA tool assess local instability spatial association. pp. 111–125 M. M. Fischer, H. J. Scholten D. Unwin (eds) Spatial analytical perspectives GIS, London, Taylor Francis; Anselin, L. 1995. Local indicators spatial association, Geographical Analysis, 27, 93–115","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran.plot.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Moran scatterplot — moran.plot","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/moran.plot.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Moran scatterplot — moran.plot","text":"","code":"data(afcon, package=\"spData\") mp <- moran.plot(afcon$totcon, nb2listw(paper.nb),  labels=as.character(afcon$name), pch=19)  moran.plot(as.vector(scale(afcon$totcon)), nb2listw(paper.nb),  labels=as.character(afcon$name), xlim=c(-2, 4), ylim=c(-2,4), pch=19)  if (require(ggplot2, quietly=TRUE)) {   xname <- attr(mp, \"xname\")   ggplot(mp, aes(x=x, y=wx)) + geom_point(shape=1) +      geom_smooth(formula=y ~ x, method=\"lm\") +      geom_hline(yintercept=mean(mp$wx), lty=2) +      geom_vline(xintercept=mean(mp$x), lty=2) + theme_minimal() +      geom_point(data=mp[mp$is_inf,], aes(x=x, y=wx), shape=9) +     geom_text(data=mp[mp$is_inf,], aes(x=x, y=wx, label=labels, vjust=1.5)) +     xlab(xname) + ylab(paste0(\"Spatially lagged \", xname)) }  columbus <- st_read(system.file(\"shapes/columbus.shp\", package=\"spData\")) #> Reading layer `columbus' from data source  #>   `/home/rsb/lib/r_libs/spData/shapes/columbus.shp' using driver `ESRI Shapefile' #> Simple feature collection with 49 features and 20 fields #> Geometry type: POLYGON #> Dimension:     XY #> Bounding box:  xmin: 5.874907 ymin: 10.78863 xmax: 11.28742 ymax: 14.74245 #> CRS:           NA nb <- poly2nb(columbus) listw <- nb2listw(nb) moran.plot(x=columbus$CRIME, y=columbus$INC, listw=listw)  moran.plot(x=columbus$INC, y=columbus$CRIME, listw=listw)"},{"path":"https://r-spatial.github.io/spdep/reference/moran.test.html","id":null,"dir":"Reference","previous_headings":"","what":"Moran's I test for spatial autocorrelation — moran.test","title":"Moran's I test for spatial autocorrelation — moran.test","text":"Moran's test spatial autocorrelation using spatial weights matrix weights list form. assumptions underlying test sensitive form graph neighbour relationships factors, results may checked moran.mc permutations.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran.test.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Moran's I test for spatial autocorrelation — moran.test","text":"","code":"moran.test(x, listw, randomisation=TRUE, zero.policy=attr(listw, \"zero.policy\"),  alternative=\"greater\", rank = FALSE, na.action=na.fail, spChk=NULL,  adjust.n=TRUE, drop.EI2=FALSE)"},{"path":"https://r-spatial.github.io/spdep/reference/moran.test.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Moran's I test for spatial autocorrelation — moran.test","text":"x numeric vector length neighbours list listw listw listw object created example nb2listw randomisation variance calculated assumption randomisation, FALSE normality zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA alternative character string specifying alternative hypothesis, must one greater (default), less two.sided. rank logical value - default FALSE continuous variables, TRUE, uses adaptation Moran's ranks suggested Cliff Ord (1981, p. 46) na.action function (default na.fail), can also na.omit na.exclude - cases weights list subsetted remove NAs data. may necessary set zero.policy TRUE subsetting may create -neighbour observations. Note weights lists created without using glist argument nb2listw may subsetted. na.pass used, zero substituted NA values calculating spatial lag spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption() adjust.n default TRUE, FALSE number observations adjusted -neighbour observations, TRUE, number observations adjusted drop.EI2 default FALSE, TRUE, emulate CrimeStat <= 4.02","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran.test.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Moran's I test for spatial autocorrelation — moran.test","text":"list class htest containing following components: statistic value standard deviate Moran's . p.value p-value test. estimate value observed Moran's , expectation variance method assumption. alternative character string describing alternative hypothesis. method character string giving assumption used calculating standard deviate. data.name character string giving name(s) data.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran.test.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Moran's I test for spatial autocorrelation — moran.test","text":"Var() taken Cliff Ord (1969, p. 28), Goodchild's CATMOG 47 (1986), see also Upton & Fingleton (1985) p. 171; agrees SpaceStat, see Tutorial workbook Chapter 22; VI second crude moment minus square first crude moment. derivation test (Cliff Ord, 1981, p. 18) assumes weights matrix symmetric. inherently non-symmetric matrices, k-nearest neighbour matrices, listw2U() can used make matrix symmetric.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran.test.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Moran's I test for spatial autocorrelation — moran.test","text":"Cliff, . D., Ord, J. K. 1981 Spatial processes, Pion, p. 21; Bivand RS, Wong DWS 2018 Comparing implementations global local indicators spatial association. TEST, 27(3), 716–748 doi:10.1007/s11749-018-0599-x","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran.test.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Moran's I test for spatial autocorrelation — moran.test","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/moran.test.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Moran's I test for spatial autocorrelation — moran.test","text":"","code":"data(oldcol) coords.OLD <- cbind(COL.OLD$X, COL.OLD$Y) moran.test(COL.OLD$CRIME, nb2listw(COL.nb, style=\"W\")) #>  #> \tMoran I test under randomisation #>  #> data:  COL.OLD$CRIME   #> weights: nb2listw(COL.nb, style = \"W\")     #>  #> Moran I statistic standard deviate = 5.6341, p-value = 8.797e-09 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic       Expectation          Variance  #>       0.510951264      -0.020833333       0.008908762  #>  moran.test(COL.OLD$CRIME, nb2listw(COL.nb, style=\"B\")) #>  #> \tMoran I test under randomisation #>  #> data:  COL.OLD$CRIME   #> weights: nb2listw(COL.nb, style = \"B\")     #>  #> Moran I statistic standard deviate = 6.2116, p-value = 2.622e-10 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic       Expectation          Variance  #>        0.52063815       -0.02083333        0.00759872  #>  moran.test(COL.OLD$CRIME, nb2listw(COL.nb, style=\"C\")) #>  #> \tMoran I test under randomisation #>  #> data:  COL.OLD$CRIME   #> weights: nb2listw(COL.nb, style = \"C\")     #>  #> Moran I statistic standard deviate = 6.2116, p-value = 2.622e-10 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic       Expectation          Variance  #>        0.52063815       -0.02083333        0.00759872  #>  moran.test(COL.OLD$CRIME, nb2listw(COL.nb, style=\"S\")) #>  #> \tMoran I test under randomisation #>  #> data:  COL.OLD$CRIME   #> weights: nb2listw(COL.nb, style = \"S\")     #>  #> Moran I statistic standard deviate = 5.9786, p-value = 1.125e-09 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic       Expectation          Variance  #>       0.512957470      -0.020833333       0.007971504  #>  moran.test(COL.OLD$CRIME, nb2listw(COL.nb, style=\"W\"),  randomisation=FALSE) #>  #> \tMoran I test under normality #>  #> data:  COL.OLD$CRIME   #> weights: nb2listw(COL.nb, style = \"W\")     #>  #> Moran I statistic standard deviate = 5.6754, p-value = 6.92e-09 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic       Expectation          Variance  #>       0.510951264      -0.020833333       0.008779831  #>  colold.lags <- nblag(COL.nb, 3) moran.test(COL.OLD$CRIME, nb2listw(colold.lags[[2]],  style=\"W\")) #>  #> \tMoran I test under randomisation #>  #> data:  COL.OLD$CRIME   #> weights: nb2listw(colold.lags[[2]], style = \"W\")     #>  #> Moran I statistic standard deviate = 2.6076, p-value = 0.004559 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic       Expectation          Variance  #>       0.168485742      -0.020833333       0.005271314  #>  moran.test(COL.OLD$CRIME, nb2listw(colold.lags[[3]],  style=\"W\")) #>  #> \tMoran I test under randomisation #>  #> data:  COL.OLD$CRIME   #> weights: nb2listw(colold.lags[[3]], style = \"W\")     #>  #> Moran I statistic standard deviate = -1.7896, p-value = 0.9632 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic       Expectation          Variance  #>      -0.138930745      -0.020833333       0.004354683  #>  print(is.symmetric.nb(COL.nb)) #> [1] TRUE COL.k4.nb <- knn2nb(knearneigh(coords.OLD, 4)) print(is.symmetric.nb(COL.k4.nb)) #> [1] FALSE moran.test(COL.OLD$CRIME, nb2listw(COL.k4.nb, style=\"W\")) #>  #> \tMoran I test under randomisation #>  #> data:  COL.OLD$CRIME   #> weights: nb2listw(COL.k4.nb, style = \"W\")     #>  #> Moran I statistic standard deviate = 7.2183, p-value = 2.632e-13 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic       Expectation          Variance  #>       0.624933667      -0.020833333       0.008003503  #>  moran.test(COL.OLD$CRIME, nb2listw(COL.k4.nb, style=\"W\"),  randomisation=FALSE) #>  #> \tMoran I test under normality #>  #> data:  COL.OLD$CRIME   #> weights: nb2listw(COL.k4.nb, style = \"W\")     #>  #> Moran I statistic standard deviate = 7.2711, p-value = 1.782e-13 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic       Expectation          Variance  #>       0.624933667      -0.020833333       0.007887613  #>  cat(\"Note: non-symmetric weights matrix, use listw2U()\") #> Note: non-symmetric weights matrix, use listw2U() moran.test(COL.OLD$CRIME, listw2U(nb2listw(COL.k4.nb,  style=\"W\"))) #>  #> \tMoran I test under randomisation #>  #> data:  COL.OLD$CRIME   #> weights: listw2U(nb2listw(COL.k4.nb, style = \"W\"))     #>  #> Moran I statistic standard deviate = 7.2183, p-value = 2.632e-13 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic       Expectation          Variance  #>       0.624933667      -0.020833333       0.008003503  #>  moran.test(COL.OLD$CRIME, listw2U(nb2listw(COL.k4.nb,  style=\"W\")), randomisation=FALSE) #>  #> \tMoran I test under normality #>  #> data:  COL.OLD$CRIME   #> weights: listw2U(nb2listw(COL.k4.nb, style = \"W\"))     #>  #> Moran I statistic standard deviate = 7.2711, p-value = 1.782e-13 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic       Expectation          Variance  #>       0.624933667      -0.020833333       0.007887613  #>  ranks <- rank(COL.OLD$CRIME) names(ranks) <- rownames(COL.OLD) moran.test(ranks, nb2listw(COL.nb, style=\"W\"), rank=TRUE) #>  #> \tMoran I test under randomisation #>  #> data:  ranks using rank correction  #> weights: nb2listw(COL.nb, style = \"W\")     #>  #> Moran I statistic standard deviate = 6.3815, p-value = 8.766e-11 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic       Expectation          Variance  #>       0.584333495      -0.020833333       0.008992923  #>  crime <- COL.OLD$CRIME is.na(crime) <- sample(1:length(crime), 10) res <- try(moran.test(crime, nb2listw(COL.nb, style=\"W\"),  na.action=na.fail)) #> Error in na.fail.default(x) : missing values in object res #> [1] \"Error in na.fail.default(x) : missing values in object\\n\" #> attr(,\"class\") #> [1] \"try-error\" #> attr(,\"condition\") #> <simpleError in na.fail.default(x): missing values in object> moran.test(crime, nb2listw(COL.nb, style=\"W\"), zero.policy=TRUE,  na.action=na.omit) #> Warning: subsetting caused increase in subgraph count #>  #> \tMoran I test under randomisation #>  #> data:  crime   #> weights: nb2listw(COL.nb, style = \"W\")  #> omitted: 7, 10, 12, 13, 14, 18, 26, 41, 42, 47  #> n reduced by no-neighbour observations   #>  #> Moran I statistic standard deviate = 3.9826, p-value = 3.408e-05 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic       Expectation          Variance  #>        0.43709247       -0.02702703        0.01358066  #>  moran.test(crime, nb2listw(COL.nb, style=\"W\"), zero.policy=TRUE,  na.action=na.exclude) #> Warning: subsetting caused increase in subgraph count #>  #> \tMoran I test under randomisation #>  #> data:  crime   #> weights: nb2listw(COL.nb, style = \"W\")  #> omitted: 7, 10, 12, 13, 14, 18, 26, 41, 42, 47  #> n reduced by no-neighbour observations   #>  #> Moran I statistic standard deviate = 3.9826, p-value = 3.408e-05 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic       Expectation          Variance  #>        0.43709247       -0.02702703        0.01358066  #>  moran.test(crime, nb2listw(COL.nb, style=\"W\"), na.action=na.pass) #> Warning: NAs in lagged values #>  #> \tMoran I test under randomisation #>  #> data:  crime   #> weights: nb2listw(COL.nb, style = \"W\")     #>  #> Moran I statistic standard deviate = 2.4925, p-value = 0.006342 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic       Expectation          Variance  #>       0.212782897      -0.020833333       0.008784908  #>  columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) col_geoms <- st_geometry(columbus) col_geoms[1] <- st_buffer(col_geoms[1], dist=-0.05) st_geometry(columbus) <- col_geoms (nb1 <- poly2nb(columbus)) #> Warning: some observations have no neighbours; #> if this seems unexpected, try increasing the snap argument. #> Warning: neighbour object has 2 sub-graphs; #> if this sub-graph count seems unexpected, try increasing the snap argument. #> Neighbour list object: #> Number of regions: 49  #> Number of nonzero links: 232  #> Percentage nonzero weights: 9.662641  #> Average number of links: 4.734694  #> 1 region with no links: #> 1 #> 2 disjoint connected subgraphs try(lw <- nb2listw(nb1, style=\"W\")) #> Error in nb2listw(nb1, style = \"W\") :  #>   Empty neighbour sets found (zero.policy: FALSE) (lw <- nb2listw(nb1, style=\"W\", zero.policy=TRUE)) #> Characteristics of weights list object: #> Neighbour list object: #> Number of regions: 49  #> Number of nonzero links: 232  #> Percentage nonzero weights: 9.662641  #> Average number of links: 4.734694  #> 1 region with no links: #> 1 #> 2 disjoint connected subgraphs #>  #> Weights style: W  #> Weights constants summary: #>    n   nn S0       S1       S2 #> W 48 2304 48 22.23035 199.8188 moran.test(COL.OLD$CRIME, lw) #>  #> \tMoran I test under randomisation #>  #> data:  COL.OLD$CRIME   #> weights: lw   #> n reduced by no-neighbour observations   #>  #> Moran I statistic standard deviate = 2.7707, p-value = 0.002797 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic       Expectation          Variance  #>        0.23901261       -0.02127660        0.00882535  #>"},{"path":"https://r-spatial.github.io/spdep/reference/moran_bv.html","id":null,"dir":"Reference","previous_headings":"","what":"Compute the Global Bivariate Moran's I — moran_bv","title":"Compute the Global Bivariate Moran's I — moran_bv","text":"Given two continuous numeric variables, calculate bivariate Moran's . See details .","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran_bv.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Compute the Global Bivariate Moran's I — moran_bv","text":"","code":"moran_bv(x, y, listw, nsim = 499, scale = TRUE)"},{"path":"https://r-spatial.github.io/spdep/reference/moran_bv.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Compute the Global Bivariate Moran's I — moran_bv","text":"x numeric vector length y. y numeric vector length x. listw listw object example created nb2listw(). nsim number simulations run. scale default TRUE.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran_bv.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Compute the Global Bivariate Moran's I — moran_bv","text":"object class \"boot\", observed statistic component t0.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran_bv.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Compute the Global Bivariate Moran's I — moran_bv","text":"Global Bivariate Moran defined \\( I_B = \\frac{\\Sigma_i(\\Sigma_j{w_{ij}y_j\\times x_i})}{\\Sigma_i{x_i^2}} \\) important note measure autocorrelation X spatial lag Y. , resultant measure may overestimate amount spatial autocorrelation may product inherent correlation X Y. output object class \"boot\", plots confidence intervals available using appropriate methods.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran_bv.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Compute the Global Bivariate Moran's I — moran_bv","text":"Wartenberg, D. (1985), Multivariate Spatial Correlation: Method Exploratory Geographical Analysis. Geographical Analysis, 17: 263-283. doi:10.1111/j.1538-4632.1985.tb00849.x","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran_bv.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Compute the Global Bivariate Moran's I — moran_bv","text":"Josiah Parry josiah.parry@gmail.com","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran_bv.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Compute the Global Bivariate Moran's I — moran_bv","text":"","code":"data(boston, package = \"spData\") x <- boston.c$CRIM y <- boston.c$NOX listw <- nb2listw(boston.soi) set.seed(1) res_xy <- moran_bv(x, y, listw, nsim=499) res_xy$t0 #> [1] 0.4082073 boot::boot.ci(res_xy, conf=c(0.99, 0.95, 0.9), type=\"basic\") #> BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS #> Based on 499 bootstrap replicates #>  #> CALL :  #> boot::boot.ci(boot.out = res_xy, conf = c(0.99, 0.95, 0.9), type = \"basic\") #>  #> Intervals :  #> Level      Basic          #> 99%   ( 0.7443,  0.8789 )    #> 95%   ( 0.7639,  0.8673 )    #> 90%   ( 0.7739,  0.8615 )   #> Calculations and Intervals on Original Scale #> Some basic intervals may be unstable plot(res_xy)  set.seed(1) lee_xy <- lee.mc(x, y, listw, nsim=499, return_boot=TRUE) lee_xy$t0 #> [1] 0.3993476 boot::boot.ci(lee_xy, conf=c(0.99, 0.95, 0.9), type=\"basic\") #> BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS #> Based on 499 bootstrap replicates #>  #> CALL :  #> boot::boot.ci(boot.out = lee_xy, conf = c(0.99, 0.95, 0.9), type = \"basic\") #>  #> Intervals :  #> Level      Basic          #> 99%   ( 0.6363,  0.7236 )    #> 95%   ( 0.6538,  0.7131 )    #> 90%   ( 0.6584,  0.7098 )   #> Calculations and Intervals on Original Scale #> Some basic intervals may be unstable plot(lee_xy)  set.seed(1) res_yx <- moran_bv(y, x, listw, nsim=499) res_yx$t0 #> [1] 0.4029821 boot::boot.ci(res_yx, conf=c(0.99, 0.95, 0.9), type=\"basic\") #> BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS #> Based on 499 bootstrap replicates #>  #> CALL :  #> boot::boot.ci(boot.out = res_yx, conf = c(0.99, 0.95, 0.9), type = \"basic\") #>  #> Intervals :  #> Level      Basic          #> 99%   ( 0.7301,  0.8729 )    #> 95%   ( 0.7574,  0.8584 )    #> 90%   ( 0.7664,  0.8541 )   #> Calculations and Intervals on Original Scale #> Some basic intervals may be unstable plot(res_yx)  set.seed(1) lee_yx <- lee.mc(y, x, listw, nsim=499, return_boot=TRUE) lee_yx$t0 #> [1] 0.3993476 boot::boot.ci(lee_yx, conf=c(0.99, 0.95, 0.9), type=\"basic\") #> BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS #> Based on 499 bootstrap replicates #>  #> CALL :  #> boot::boot.ci(boot.out = lee_yx, conf = c(0.99, 0.95, 0.9), type = \"basic\") #>  #> Intervals :  #> Level      Basic          #> 99%   ( 0.6363,  0.7236 )    #> 95%   ( 0.6538,  0.7131 )    #> 90%   ( 0.6584,  0.7098 )   #> Calculations and Intervals on Original Scale #> Some basic intervals may be unstable plot(lee_yx)"},{"path":"https://r-spatial.github.io/spdep/reference/mstree.html","id":null,"dir":"Reference","previous_headings":"","what":"Find the minimal spanning tree — mstree","title":"Find the minimal spanning tree — mstree","text":"minimal spanning tree connected graph n nodes n-1   edges. smaller class possible partitions graph   pruning edges high dissimilarity. one edge removed,   graph partioned two unconnected subgraphs. function   implements algorithm due Prim (1987).","code":""},{"path":"https://r-spatial.github.io/spdep/reference/mstree.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Find the minimal spanning tree — mstree","text":"","code":"mstree(nbw, ini = NULL)"},{"path":"https://r-spatial.github.io/spdep/reference/mstree.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Find the minimal spanning tree — mstree","text":"nbw object listw class returned     nb2listw function. See help details. ini initial node minimal spanning tree.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/mstree.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Find the minimal spanning tree — mstree","text":"minimum spanning tree algorithm. Input connected graph. Begin empty set nodes. Add arbitrary note set. nodes set, find minimum cost edge connecting   node set node set add node   set. set edges minimum spanning tree.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/mstree.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Find the minimal spanning tree — mstree","text":"matrix n-1 rows tree columns. row two nodes   cost, . e. edge cost.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/mstree.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Find the minimal spanning tree — mstree","text":"R. C. Prim (1957) Shortest connection networks   generalisations. : Bell System Technical Journal, 36, pp. 1389-1401","code":""},{"path":"https://r-spatial.github.io/spdep/reference/mstree.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Find the minimal spanning tree — mstree","text":"Renato M. Assuncao Elias T. Krainski","code":""},{"path":"https://r-spatial.github.io/spdep/reference/mstree.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Find the minimal spanning tree — mstree","text":"","code":"### loading data (GDAL37 <- as.numeric_version(unname(sf_extSoftVersion()[\"GDAL\"])) >= \"3.7.0\") #> [1] TRUE file <- \"etc/shapes/bhicv.gpkg.zip\" zipfile <- system.file(file, package=\"spdep\") if (GDAL37) {     bh <- st_read(zipfile) } else {     td <- tempdir()     bn <- sub(\".zip\", \"\", basename(file), fixed=TRUE)     target <- unzip(zipfile, files=bn, exdir=td)     bh <- st_read(target) } #> Reading layer `bhicv' from data source  #>   `/tmp/RtmpzEChJG/temp_libpath8ee3b7c361c1e/spdep/etc/shapes/bhicv.gpkg.zip'  #>   using driver `GPKG' #> Simple feature collection with 98 features and 8 fields #> Geometry type: POLYGON #> Dimension:     XY #> Bounding box:  xmin: -45.02175 ymin: -20.93007 xmax: -42.50321 ymax: -18.08342 #> Geodetic CRS:  Corrego Alegre 1970-72 ### data padronized dpad <- data.frame(scale(as.data.frame(bh)[,5:8]))  ### neighboorhod list  bh.nb <- poly2nb(bh)  ### calculing costs lcosts <- nbcosts(bh.nb, dpad)  ### making listw nb.w <- nb2listw(bh.nb, lcosts, style=\"B\")  ### find a minimum spanning tree system.time(mst.bh <- mstree(nb.w,5)) #>    user  system elapsed  #>   0.003   0.000   0.004  dim(mst.bh) #> [1] 97  3 head(mst.bh) #>      [,1] [,2]      [,3] #> [1,]    5   12 1.2951120 #> [2,]   12   13 0.6141101 #> [3,]   13   11 0.7913745 #> [4,]   13    6 0.9775650 #> [5,]   11   31 0.9965625 #> [6,]   31   39 0.6915158 tail(mst.bh) #>       [,1] [,2]      [,3] #> [92,]   89   90 2.5743702 #> [93,]   26   56 2.6235317 #> [94,]   86   87 2.6471303 #> [95,]   87   72 0.7874461 #> [96,]   49   36 2.8743677 #> [97,]   24   25 3.4675168 ### the mstree plot par(mar=c(0,0,0,0)) plot(st_geometry(bh), border=gray(.5)) plot(mst.bh, st_coordinates(st_centroid(bh)), col=2,       cex.lab=.6, cex.circles=0.035, fg=\"blue\", add=TRUE) #> Warning: st_centroid assumes attributes are constant over geometries"},{"path":"https://r-spatial.github.io/spdep/reference/nb2INLA.html","id":null,"dir":"Reference","previous_headings":"","what":"Output spatial neighbours for INLA — nb2INLA","title":"Output spatial neighbours for INLA — nb2INLA","text":"Output spatial neighbours INLA","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2INLA.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Output spatial neighbours for INLA — nb2INLA","text":"","code":"nb2INLA(file, nb)"},{"path":"https://r-spatial.github.io/spdep/reference/nb2INLA.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Output spatial neighbours for INLA — nb2INLA","text":"file file adjacency matrix stored nb object class nb","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2INLA.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Output spatial neighbours for INLA — nb2INLA","text":"Nothing returned file created representation adjacency matrix required INLA spatial models.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2INLA.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Output spatial neighbours for INLA — nb2INLA","text":"http://www.r-inla.org","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2INLA.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Output spatial neighbours for INLA — nb2INLA","text":"Virgilio Gomez-Rubio","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2INLA.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Output spatial neighbours for INLA — nb2INLA","text":"","code":"col.gal.nb <- read.gal(system.file(\"weights/columbus.gal\", package=\"spData\")[1]) td <- tempdir() x <- nb2INLA(paste(td, \"columbus-INLA.adj\", sep=\"/\"), col.gal.nb) readLines(paste(td, \"columbus-INLA.adj\", sep=\"/\"), n=10) #>  [1] \"49\"                        \"1 2 2 3\"                   #>  [3] \"2 3 1 3 4\"                 \"3 4 1 2 4 5\"               #>  [5] \"4 4 2 3 5 8\"               \"5 7 3 4 6 8 9 11 15\"       #>  [7] \"6 2 5 9\"                   \"7 4 8 12 13 14\"            #>  [9] \"8 6 4 5 7 11 12 13\"        \"9 8 5 6 10 15 20 22 25 26\""},{"path":"https://r-spatial.github.io/spdep/reference/nb2WB.html","id":null,"dir":"Reference","previous_headings":"","what":"Output spatial weights for WinBUGS — nb2WB","title":"Output spatial weights for WinBUGS — nb2WB","text":"Output spatial weights WinBUGS","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2WB.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Output spatial weights for WinBUGS — nb2WB","text":"","code":"nb2WB(nb) listw2WB(listw)"},{"path":"https://r-spatial.github.io/spdep/reference/nb2WB.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Output spatial weights for WinBUGS — nb2WB","text":"nb object class nb listw listw object example nb2listw","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2WB.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Output spatial weights for WinBUGS — nb2WB","text":"list suitable convering using dput WinBUGS","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2WB.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Output spatial weights for WinBUGS — nb2WB","text":"http://www.mrc-bsu.cam.ac.uk/bugs/winbugs/geobugs12manual.pdf","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2WB.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Output spatial weights for WinBUGS — nb2WB","text":"Virgilio Gomez-Rubio","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/nb2WB.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Output spatial weights for WinBUGS — nb2WB","text":"","code":"col.gal.nb <- read.gal(system.file(\"weights/columbus.gal\", package=\"spData\")[1]) x <- nb2WB(col.gal.nb) dput(x, control=NULL) #> list(c(2, 3, 1, 3, 4, 1, 2, 4, 5, 2, 3, 5, 8, 3, 4, 6, 8, 9,  #> 11, 15, 5, 9, 8, 12, 13, 14, 4, 5, 7, 11, 12, 13, 5, 6, 10, 15,  #> 20, 22, 25, 26, 9, 17, 20, 22, 5, 8, 12, 15, 16, 7, 8, 11, 13,  #> 14, 16, 7, 8, 12, 14, 7, 12, 13, 16, 18, 19, 5, 9, 11, 16, 25,  #> 26, 11, 12, 14, 15, 18, 24, 25, 10, 20, 23, 14, 16, 19, 24, 14,  #> 18, 24, 9, 10, 17, 22, 23, 27, 32, 33, 35, 40, 24, 30, 34, 9,  #> 10, 20, 26, 27, 28, 17, 20, 32, 16, 18, 19, 21, 25, 29, 30, 9,  #> 15, 16, 24, 26, 28, 29, 9, 15, 22, 25, 28, 29, 20, 22, 28, 33,  #> 22, 25, 26, 27, 29, 33, 35, 37, 38, 24, 25, 26, 28, 30, 37, 38,  #> 21, 24, 29, 37, 34, 36, 20, 23, 40, 41, 20, 27, 28, 35, 21, 31,  #> 36, 42, 20, 28, 33, 38, 40, 43, 44, 31, 34, 39, 42, 46, 28, 29,  #> 30, 38, 43, 45, 28, 29, 35, 37, 43, 44, 36, 46, 20, 32, 35, 41,  #> 47, 32, 40, 47, 34, 36, 35, 37, 38, 44, 45, 48, 35, 38, 43, 48,  #> 49, 37, 43, 48, 49, 36, 39, 40, 41, 43, 44, 45, 49, 44, 45, 48 #> ), c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,  #> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,  #> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,  #> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,  #> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,  #> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,  #> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,  #> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,  #> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,  #> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,  #> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,  #> 1), c(2, 3, 4, 4, 7, 2, 4, 6, 8, 4, 5, 6, 4, 6, 6, 7, 3, 4, 3,  #> 10, 3, 6, 3, 7, 7, 6, 4, 9, 7, 4, 2, 4, 4, 4, 7, 5, 6, 6, 2,  #> 5, 3, 2, 6, 5, 4, 2, 2, 4, 3)) x <- listw2WB(nb2listw(col.gal.nb)) dput(x, control=NULL) #> list(c(2, 3, 1, 3, 4, 1, 2, 4, 5, 2, 3, 5, 8, 3, 4, 6, 8, 9,  #> 11, 15, 5, 9, 8, 12, 13, 14, 4, 5, 7, 11, 12, 13, 5, 6, 10, 15,  #> 20, 22, 25, 26, 9, 17, 20, 22, 5, 8, 12, 15, 16, 7, 8, 11, 13,  #> 14, 16, 7, 8, 12, 14, 7, 12, 13, 16, 18, 19, 5, 9, 11, 16, 25,  #> 26, 11, 12, 14, 15, 18, 24, 25, 10, 20, 23, 14, 16, 19, 24, 14,  #> 18, 24, 9, 10, 17, 22, 23, 27, 32, 33, 35, 40, 24, 30, 34, 9,  #> 10, 20, 26, 27, 28, 17, 20, 32, 16, 18, 19, 21, 25, 29, 30, 9,  #> 15, 16, 24, 26, 28, 29, 9, 15, 22, 25, 28, 29, 20, 22, 28, 33,  #> 22, 25, 26, 27, 29, 33, 35, 37, 38, 24, 25, 26, 28, 30, 37, 38,  #> 21, 24, 29, 37, 34, 36, 20, 23, 40, 41, 20, 27, 28, 35, 21, 31,  #> 36, 42, 20, 28, 33, 38, 40, 43, 44, 31, 34, 39, 42, 46, 28, 29,  #> 30, 38, 43, 45, 28, 29, 35, 37, 43, 44, 36, 46, 20, 32, 35, 41,  #> 47, 32, 40, 47, 34, 36, 35, 37, 38, 44, 45, 48, 35, 38, 43, 48,  #> 49, 37, 43, 48, 49, 36, 39, 40, 41, 43, 44, 45, 49, 44, 45, 48 #> ), c(0.5, 0.5, 0.333333333333333, 0.333333333333333, 0.333333333333333,  #> 0.25, 0.25, 0.25, 0.25, 0.25, 0.25, 0.25, 0.25, 0.142857142857143,  #> 0.142857142857143, 0.142857142857143, 0.142857142857143, 0.142857142857143,  #> 0.142857142857143, 0.142857142857143, 0.5, 0.5, 0.25, 0.25, 0.25,  #> 0.25, 0.166666666666667, 0.166666666666667, 0.166666666666667,  #> 0.166666666666667, 0.166666666666667, 0.166666666666667, 0.125,  #> 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.25, 0.25,  #> 0.25, 0.25, 0.2, 0.2, 0.2, 0.2, 0.2, 0.166666666666667, 0.166666666666667,  #> 0.166666666666667, 0.166666666666667, 0.166666666666667, 0.166666666666667,  #> 0.25, 0.25, 0.25, 0.25, 0.166666666666667, 0.166666666666667,  #> 0.166666666666667, 0.166666666666667, 0.166666666666667, 0.166666666666667,  #> 0.166666666666667, 0.166666666666667, 0.166666666666667, 0.166666666666667,  #> 0.166666666666667, 0.166666666666667, 0.142857142857143, 0.142857142857143,  #> 0.142857142857143, 0.142857142857143, 0.142857142857143, 0.142857142857143,  #> 0.142857142857143, 0.333333333333333, 0.333333333333333, 0.333333333333333,  #> 0.25, 0.25, 0.25, 0.25, 0.333333333333333, 0.333333333333333,  #> 0.333333333333333, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1,  #> 0.1, 0.333333333333333, 0.333333333333333, 0.333333333333333,  #> 0.166666666666667, 0.166666666666667, 0.166666666666667, 0.166666666666667,  #> 0.166666666666667, 0.166666666666667, 0.333333333333333, 0.333333333333333,  #> 0.333333333333333, 0.142857142857143, 0.142857142857143, 0.142857142857143,  #> 0.142857142857143, 0.142857142857143, 0.142857142857143, 0.142857142857143,  #> 0.142857142857143, 0.142857142857143, 0.142857142857143, 0.142857142857143,  #> 0.142857142857143, 0.142857142857143, 0.142857142857143, 0.166666666666667,  #> 0.166666666666667, 0.166666666666667, 0.166666666666667, 0.166666666666667,  #> 0.166666666666667, 0.25, 0.25, 0.25, 0.25, 0.111111111111111,  #> 0.111111111111111, 0.111111111111111, 0.111111111111111, 0.111111111111111,  #> 0.111111111111111, 0.111111111111111, 0.111111111111111, 0.111111111111111,  #> 0.142857142857143, 0.142857142857143, 0.142857142857143, 0.142857142857143,  #> 0.142857142857143, 0.142857142857143, 0.142857142857143, 0.25,  #> 0.25, 0.25, 0.25, 0.5, 0.5, 0.25, 0.25, 0.25, 0.25, 0.25, 0.25,  #> 0.25, 0.25, 0.25, 0.25, 0.25, 0.25, 0.142857142857143, 0.142857142857143,  #> 0.142857142857143, 0.142857142857143, 0.142857142857143, 0.142857142857143,  #> 0.142857142857143, 0.2, 0.2, 0.2, 0.2, 0.2, 0.166666666666667,  #> 0.166666666666667, 0.166666666666667, 0.166666666666667, 0.166666666666667,  #> 0.166666666666667, 0.166666666666667, 0.166666666666667, 0.166666666666667,  #> 0.166666666666667, 0.166666666666667, 0.166666666666667, 0.5,  #> 0.5, 0.2, 0.2, 0.2, 0.2, 0.2, 0.333333333333333, 0.333333333333333,  #> 0.333333333333333, 0.5, 0.5, 0.166666666666667, 0.166666666666667,  #> 0.166666666666667, 0.166666666666667, 0.166666666666667, 0.166666666666667,  #> 0.2, 0.2, 0.2, 0.2, 0.2, 0.25, 0.25, 0.25, 0.25, 0.5, 0.5, 0.5,  #> 0.5, 0.25, 0.25, 0.25, 0.25, 0.333333333333333, 0.333333333333333,  #> 0.333333333333333), c(2, 3, 4, 4, 7, 2, 4, 6, 8, 4, 5, 6, 4,  #> 6, 6, 7, 3, 4, 3, 10, 3, 6, 3, 7, 7, 6, 4, 9, 7, 4, 2, 4, 4,  #> 4, 7, 5, 6, 6, 2, 5, 3, 2, 6, 5, 4, 2, 2, 4, 3))"},{"path":"https://r-spatial.github.io/spdep/reference/nb2blocknb.html","id":null,"dir":"Reference","previous_headings":"","what":"Block up neighbour list for location-less observations — nb2blocknb","title":"Block up neighbour list for location-less observations — nb2blocknb","text":"function blocks neighbour list known spatial locations create new neighbour list multiple location-less observations know belong spatial locations, using identification tags locations key.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2blocknb.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Block up neighbour list for location-less observations — nb2blocknb","text":"","code":"nb2blocknb(nb=NULL, ID, row.names = NULL)"},{"path":"https://r-spatial.github.io/spdep/reference/nb2blocknb.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Block up neighbour list for location-less observations — nb2blocknb","text":"nb object class nb list integer vectors containing neighbour region number ids; null, nb object neighbours created length unique(.character(ID)) ID identification tags locations location-less observations; sort(unique(.character(ID))) must identical sort(.character(attr(nb, \"region.id\"))); length row.names provided. row.names character vector observation ids added neighbours list attribute region.id, default seq(1, nrow(x)); length ID provided.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2blocknb.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Block up neighbour list for location-less observations — nb2blocknb","text":"Assume list unique locations, neighbour list can build , create input neighbour list. needs \"unfolded\", observations belonging unique location observation neighbours, observations belonging location neighbours unique location question also observation neighbours, finally removing observation (neighbour). scenario also arises say post codes available, post codes contain multiple observations, known belong specific post code, located within (given post code locations known).","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2blocknb.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Block up neighbour list for location-less observations — nb2blocknb","text":"function returns object class nb list integer vectors containing neighbour observation number ids.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2blocknb.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Block up neighbour list for location-less observations — nb2blocknb","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/nb2blocknb.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Block up neighbour list for location-less observations — nb2blocknb","text":"","code":"# \\dontrun{ data(boston, package=\"spData\") summary(as.vector(table(boston.c$TOWN))) #>    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.  #>     1.0     2.0     4.0     5.5     7.0    30.0  townaggr <- aggregate(boston.utm, list(town=boston.c$TOWN), mean) block.rel <- graph2nb(relativeneigh(as.matrix(townaggr[,2:3])),  as.character(townaggr[,1]), sym=TRUE) block.rel #> Neighbour list object: #> Number of regions: 92  #> Number of nonzero links: 240  #> Percentage nonzero weights: 2.835539  #> Average number of links: 2.608696  print(is.symmetric.nb(block.rel)) #> [1] TRUE plot(block.rel, as.matrix(townaggr[,2:3])) points(boston.utm, pch=18, col=\"lightgreen\")  block.nb <- nb2blocknb(block.rel, as.character(boston.c$TOWN)) block.nb #> Neighbour list object: #> Number of regions: 506  #> Number of nonzero links: 15234  #> Percentage nonzero weights: 5.949945  #> Average number of links: 30.10672  print(is.symmetric.nb(block.nb)) #> [1] TRUE plot(block.nb, boston.utm) points(boston.utm, pch=18, col=\"lightgreen\")  n.comp.nb(block.nb)$nc #> [1] 1 moran.test(boston.c$CMEDV, nb2listw(boston.soi)) #>  #> \tMoran I test under randomisation #>  #> data:  boston.c$CMEDV   #> weights: nb2listw(boston.soi)     #>  #> Moran I statistic standard deviate = 21.786, p-value < 2.2e-16 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic       Expectation          Variance  #>       0.690285059      -0.001980198       0.001009685  #>  moran.test(boston.c$CMEDV, nb2listw(block.nb)) #>  #> \tMoran I test under randomisation #>  #> data:  boston.c$CMEDV   #> weights: nb2listw(block.nb)     #>  #> Moran I statistic standard deviate = 22.455, p-value < 2.2e-16 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic       Expectation          Variance  #>      0.3122905961     -0.0019801980      0.0001958827  #>  block.nb <- nb2blocknb(NULL, as.character(boston.c$TOWN)) #> Warning: neighbour object has 92 sub-graphs block.nb #> Neighbour list object: #> Number of regions: 506  #> Number of nonzero links: 4868  #> Percentage nonzero weights: 1.901295  #> Average number of links: 9.620553  #> 17 regions with no links: #> 1, 55, 56, 57, 58, 65, 196, 257, 284, 285, 286, 287, 342, 343, 348, #> 349, 354 #> 92 disjoint connected subgraphs print(is.symmetric.nb(block.nb)) #> [1] TRUE plot(block.nb, boston.utm)  n.comp.nb(block.nb)$nc #> [1] 92 moran.test(boston.c$CMEDV, nb2listw(block.nb, zero.policy=TRUE), zero.policy=TRUE) #>  #> \tMoran I test under randomisation #>  #> data:  boston.c$CMEDV   #> weights: nb2listw(block.nb, zero.policy = TRUE)   #> n reduced by no-neighbour observations   #>  #> Moran I statistic standard deviate = 21.145, p-value < 2.2e-16 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic       Expectation          Variance  #>      0.6188830566     -0.0020491803      0.0008623116  #>  # }"},{"path":"https://r-spatial.github.io/spdep/reference/nb2lines.html","id":null,"dir":"Reference","previous_headings":"","what":"Use vector files for import and export of weights — nb2lines","title":"Use vector files for import and export of weights — nb2lines","text":"Use vector files import export weights, storing spatial entity coordinates arcs, entity indices data frame.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2lines.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Use vector files for import and export of weights — nb2lines","text":"","code":"nb2lines(nb, wts, coords, proj4string=NULL, as_sf=FALSE) listw2lines(listw, coords, proj4string=NULL, as_sf=FALSE) df2sn(df, i=\"i\", i_ID=\"i_ID\", j=\"j\", wt=\"wt\")"},{"path":"https://r-spatial.github.io/spdep/reference/nb2lines.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Use vector files for import and export of weights — nb2lines","text":"nb neighbour object class nb wts list general weights corresponding neighbours coords matrix region point coordinates, Spatial object (points polygons), sfc object (points polygons) proj4string default NULL; coords Spatial sf object, value used, otherwise value converted appropriately as_sf output object Spatial sf format, default FALSE, set TRUE coords sfc object FALSE Spatial object listw listw object spatial weights df data frame read shapefile, derived output nb2lines character name column df entity index i_ID character name column df entity region ID j character name column df entity index wt character name column df weights","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2lines.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Use vector files for import and export of weights — nb2lines","text":"neighbour weights objects may retrieved converting specified columns data slot SpatialLinesDataFrame object spatial.neighbour object, converted weights list object.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2lines.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Use vector files for import and export of weights — nb2lines","text":"nb2lines listw2lines return SpatialLinesDataFrame object sf object; data frame contains indices neighbour links weights. df2sn converts data retrieved reading data df back spatial.neighbour object.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2lines.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Use vector files for import and export of weights — nb2lines","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2lines.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Use vector files for import and export of weights — nb2lines","text":"Original idea due Gidske Leknes Andersen, Department Biology, University Bergen, Norway","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/nb2lines.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Use vector files for import and export of weights — nb2lines","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) col.gal.nb <- read.gal(system.file(\"weights/columbus.gal\", package=\"spData\")[1]) res <- listw2lines(nb2listw(col.gal.nb), st_geometry(columbus)) summary(res) #>        i               j             i_ID               j_ID           #>  Min.   : 1.00   Min.   : 1.00   Length:230         Length:230         #>  1st Qu.:13.00   1st Qu.:13.00   Class :character   Class :character   #>  Median :24.00   Median :24.00   Mode  :character   Mode  :character   #>  Mean   :24.19   Mean   :24.19                                         #>  3rd Qu.:35.00   3rd Qu.:35.00                                         #>  Max.   :49.00   Max.   :49.00                                         #>        wt               geometry   #>  Min.   :0.1000   LINESTRING:230   #>  1st Qu.:0.1429   epsg:NA   :  0   #>  Median :0.1667                    #>  Mean   :0.2130                    #>  3rd Qu.:0.2500                    #>  Max.   :0.5000                    tf <- paste0(tempfile(), \".gpkg\") st_write(res, dsn=tf, driver=\"GPKG\") #> Writing layer `file8efec6591ae67' to data source  #>   `/tmp/RtmpGWmmWp/file8efec6591ae67.gpkg' using driver `GPKG' #> Writing 230 features with 5 fields and geometry type Line String. inMap <- st_read(tf) #> Reading layer `file8efec6591ae67' from data source  #>   `/tmp/RtmpGWmmWp/file8efec6591ae67.gpkg' using driver `GPKG' #> Simple feature collection with 230 features and 5 fields #> Geometry type: LINESTRING #> Dimension:     XY #> Bounding box:  xmin: 6.165913 ymin: 11.04088 xmax: 10.96206 ymax: 14.43766 #> Projected CRS: Undefined Cartesian SRS with unknown unit summary(inMap) #>        i               j             i_ID               j_ID           #>  Min.   : 1.00   Min.   : 1.00   Length:230         Length:230         #>  1st Qu.:13.00   1st Qu.:13.00   Class :character   Class :character   #>  Median :24.00   Median :24.00   Mode  :character   Mode  :character   #>  Mean   :24.19   Mean   :24.19                                         #>  3rd Qu.:35.00   3rd Qu.:35.00                                         #>  Max.   :49.00   Max.   :49.00                                         #>        wt                 geom     #>  Min.   :0.1000   LINESTRING:230   #>  1st Qu.:0.1429   epsg:NA   :  0   #>  Median :0.1667                    #>  Mean   :0.2130                    #>  3rd Qu.:0.2500                    #>  Max.   :0.5000                    diffnb(sn2listw(df2sn(as.data.frame(inMap)))$neighbours, col.gal.nb) #> Warning: style is M (missing); style should be set to a valid value #> Warning: neighbour object has 49 sub-graphs #> Neighbour list object: #> Number of regions: 49  #> Number of nonzero links: 0  #> Percentage nonzero weights: 0  #> Average number of links: 0  #> 49 regions with no links: #> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, #> 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, #> 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49 #> 49 disjoint connected subgraphs res1 <- listw2lines(nb2listw(col.gal.nb), as(columbus, \"Spatial\")) summary(res1) #> Object of class SpatialLinesDataFrame #> Coordinates: #>         min      max #> x  6.221943 10.95359 #> y 11.010031 14.36908 #> Is projected: TRUE  #> proj4string : [NA] #> Data attributes: #>        i               j             i_ID               j_ID           #>  Min.   : 1.00   Min.   : 1.00   Length:230         Length:230         #>  1st Qu.:13.00   1st Qu.:13.00   Class :character   Class :character   #>  Median :24.00   Median :24.00   Mode  :character   Mode  :character   #>  Mean   :24.19   Mean   :24.19                                         #>  3rd Qu.:35.00   3rd Qu.:35.00                                         #>  Max.   :49.00   Max.   :49.00                                         #>        wt         #>  Min.   :0.1000   #>  1st Qu.:0.1429   #>  Median :0.1667   #>  Mean   :0.2130   #>  3rd Qu.:0.2500   #>  Max.   :0.5000"},{"path":"https://r-spatial.github.io/spdep/reference/nb2listw.html","id":null,"dir":"Reference","previous_headings":"","what":"Spatial weights for neighbours lists — nb2listw","title":"Spatial weights for neighbours lists — nb2listw","text":"nb2listw function supplements neighbours list spatial weights chosen coding scheme. can..simmed helper function checks whether spatial weights object similar symmetric can transformed yield real eigenvalues Cholesky decomposition. helper function listw2U() constructs weights list object corresponding sparse matrix \\(\\frac{1}{2} ( \\mathbf{W} + \\mathbf{W}'\\).","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2listw.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Spatial weights for neighbours lists — nb2listw","text":"","code":"nb2listw(neighbours, glist=NULL, style=\"W\", zero.policy=NULL) listw2U(listw)"},{"path":"https://r-spatial.github.io/spdep/reference/nb2listw.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Spatial weights for neighbours lists — nb2listw","text":"neighbours object class nb glist list general weights corresponding neighbours style style can take values “W”, “B”, “C”, “U”, “minmax” “S” zero.policy default NULL, use global option value; FALSE stop error empty neighbour sets, TRUE permit weights list formed zero-length weights vectors listw listw object created example nb2listw","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2listw.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Spatial weights for neighbours lists — nb2listw","text":"Starting binary neighbours list, regions either listed neighbours absent (thus set neighbours definition), function adds weights list values given coding scheme style chosen. B basic binary coding, W row standardised (sums links n), C globally standardised (sums links n), U equal C divided number neighbours (sums links unity), S variance-stabilizing coding scheme proposed Tiefelsdorf et al. 1999, p. 167-168 (sums links n). zero policy set TRUE, weights vectors zero length inserted regions without neighbour neighbours list. turn generate lag values zero, equivalent sum products zero row t(rep(0, length=length(neighbours))) %*% x, arbitraty numerical vector x length length(neighbours). spatially lagged value x zero-neighbour region zero, may (may ) sensible choice. sum glist vector one observations zero, warning message issued. consequence later operations -neighbour observations present zero.policy argument set true. “minmax” style based Kelejian Prucha (2010), divides weights minimum maximum row sums maximum column sums input weights. similar C U styles; also available Stata.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2listw.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Spatial weights for neighbours lists — nb2listw","text":"listw object following members: style one W, B, C, U, S, minmax neighbours input neighbours list weights weights neighbours chosen style, attributes set report type relationships (binary general, general form glist argument), style attributes: region.id character, neighbour object call function call zero.policy logical; value zero.policy object created","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2listw.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Spatial weights for neighbours lists — nb2listw","text":"Tiefelsdorf, M., Griffith, D. ., Boots, B. 1999 variance-stabilizing coding scheme spatial link matrices, Environment Planning , 31, pp. 165–180; Kelejian, H. H., . R. Prucha. 2010. Specification estimation spatial autoregressive models autoregressive heteroskedastic disturbances. Journal Econometrics, 157: pp. 53–67.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2listw.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Spatial weights for neighbours lists — nb2listw","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/nb2listw.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Spatial weights for neighbours lists — nb2listw","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) col.gal.nb <- read.gal(system.file(\"weights/columbus.gal\", package=\"spData\")[1]) coords <- st_coordinates(st_centroid(columbus)) #> Warning: st_centroid assumes attributes are constant over geometries cards <- card(col.gal.nb) col.w <- nb2listw(col.gal.nb) plot(cards, unlist(lapply(col.w$weights, sum)),xlim=c(0,10), ylim=c(0,10), xlab=\"number of links\", ylab=\"row sums of weights\") col.b <- nb2listw(col.gal.nb, style=\"B\") points(cards, unlist(lapply(col.b$weights, sum)), col=\"red\") col.c <- nb2listw(col.gal.nb, style=\"C\") points(cards, unlist(lapply(col.c$weights, sum)), col=\"green\") col.u <- nb2listw(col.gal.nb, style=\"U\") points(cards, unlist(lapply(col.u$weights, sum)), col=\"orange\") col.s <- nb2listw(col.gal.nb, style=\"S\") points(cards, unlist(lapply(col.s$weights, sum)), col=\"blue\") legend(x=c(0, 1), y=c(7, 9), legend=c(\"W\", \"B\", \"C\", \"U\", \"S\"), bty=\"n\", col=c(\"black\", \"red\", \"green\", \"orange\", \"blue\"), pch=rep(1,5), cex=0.8, y.intersp=2.5)  summary(nb2listw(col.gal.nb, style=\"minmax\")) #> Characteristics of weights list object: #> Neighbour list object: #> Number of regions: 49  #> Number of nonzero links: 230  #> Percentage nonzero weights: 9.579342  #> Average number of links: 4.693878  #> Link number distribution: #>  #>  2  3  4  5  6  7  8  9 10  #>  7  7 13  4  9  6  1  1  1  #> 7 least connected regions: #> 1 6 31 39 42 46 47 with 2 links #> 1 most connected region: #> 20 with 10 links #>  #> Weights style: minmax  #> Weights constants summary: #>         n   nn S0  S1    S2 #> minmax 49 2401 23 4.6 50.48 dlist <- nbdists(col.gal.nb, coords) dlist <- lapply(dlist, function(x) 1/x) col.w.d <- nb2listw(col.gal.nb, glist=dlist) summary(unlist(col.w$weights)) #>    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.  #>  0.1000  0.1429  0.1667  0.2130  0.2500  0.5000  summary(unlist(col.w.d$weights)) #>    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.  #> 0.06977 0.13114 0.17710 0.21304 0.27124 0.67178  # introducing other conditions into weights - only earlier sales count # see http://sal.uiuc.edu/pipermail/openspace/2005-October/000610.html data(baltimore, package=\"spData\") set.seed(211) dates <- sample(1:500, nrow(baltimore), replace=TRUE) nb_15nn <- knn2nb(knearneigh(cbind(baltimore$X, baltimore$Y), k=15)) glist <- vector(mode=\"list\", length=length(nb_15nn)) for (i in seq(along=nb_15nn))   glist[[i]] <- ifelse(dates[i] > dates[nb_15nn[[i]]], 1, 0) listw_15nn_dates <- nb2listw(nb_15nn, glist=glist, style=\"B\") #> Warning: zero sum general weights which(lag(listw_15nn_dates, baltimore$PRICE) == 0.0) #>  [1]   1  22  29  35  66  74  80  99 117 147 155 169 195 197 200 which(sapply(glist, sum) == 0) #>  [1]   1  22  29  35  66  74  80  99 117 147 155 169 195 197 200 ex <- which(sapply(glist, sum) == 0)[1] dates[ex] #> [1] 28 dates[nb_15nn[[ex]]] #>  [1] 395 247 275 179 142 484 111 239 369 199 294 251 448 390 229"},{"path":"https://r-spatial.github.io/spdep/reference/nb2listwdist.html","id":null,"dir":"Reference","previous_headings":"","what":"Distance-based spatial weights for neighbours lists — nb2listwdist","title":"Distance-based spatial weights for neighbours lists — nb2listwdist","text":"nb2listwdist function supplements neighbours list spatial weights chosen types distance modelling coding scheme. offered coding schemes parallel nb2listw function, three distance-based types weights available: inverse distance weighting (IDW), double-power distance weights, exponential distance decay. can..simmed helper function checks whether spatial weights object similar symmetric can transformed yield real eigenvalues Cholesky decomposition.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2listwdist.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Distance-based spatial weights for neighbours lists — nb2listwdist","text":"","code":"nb2listwdist(neighbours, x, type=\"idw\", style=\"raw\",    alpha = 1, dmax = NULL, longlat = NULL, zero.policy=NULL)"},{"path":"https://r-spatial.github.io/spdep/reference/nb2listwdist.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Distance-based spatial weights for neighbours lists — nb2listwdist","text":"neighbours object class nb x sp sf, sfc object type default “idw”; intended type distance modelling, can take values “idw”, “exp”, “dpd” style default “raw”; style can take values “raw”, “W”, “B”, “C”, “U”, “minmax”, “S” alpha default 0; parameter controlling distance modelling, see “Details” dmax default NULL, maximum distance threshold required type “dpd” optional types longlat default NULL; TRUE point coordinates longitude-latitude decimal degrees, case distances measured metres; x SpatialPoints object, value taken object , overrides argument NULL; distances measured map units FALSE NULL zero.policy default NULL; use global option value; FALSE stop error empty neighbour sets, TRUE permit weights list formed zero-length weights vectors","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2listwdist.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Distance-based spatial weights for neighbours lists — nb2listwdist","text":"Starting binary neighbours list, regions either listed neighbours absent (thus set neighbours definition), function adds distance-based weights list. Three types distance weight calculations based pairwise distances \\(d_{ij}\\) possible, controlled parameter “alpha” (\\(\\alpha\\) ): $$\\textrm{idw: } w_{ij} = d_{ij}^{-\\alpha},$$ $$\\textrm{exp: } w_{ij} = \\exp(-\\alpha \\cdot d_{ij}),$$ $$\\textrm{dpd: } w_{ij} = \\left[1 - \\left(d_{ij}/d_{\\textrm{max}}\\right)^{\\alpha}\\right]^{\\alpha},$$ latter leads \\(w_{ij} = 0\\) \\(d_{ij} > d_{\\textrm{max}}\\). Note IDW weights show extreme behaviour close 0 can take value infinity. cases, infinite values replaced largest finite weight present weights list. default coding scheme “raw”, outputs raw distance-based weights without applying kind normalisation. addition, coding scheme styles also available nb2listw function can chosen. B basic binary coding, W row standardised (sums links n), C globally standardised (sums links n), U equal C divided number neighbours (sums links unity), S variance-stabilising coding scheme proposed Tiefelsdorf et al. 1999, p. 167-168 (sums links n). “minmax” style based Kelejian Prucha (2010), divides weights minimum maximum row sums maximum column sums input weights. similar C U styles; also available Stata. zero.policy set TRUE, weights vectors zero length inserted regions without neighbour neighbours list. turn generate lag values zero, equivalent sum products zero row t(rep(0, length=length(neighbours))) %*% x, arbitraty numerical vector x length length(neighbours). spatially lagged value x zero-neighbour region zero, may (may ) sensible choice.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2listwdist.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Distance-based spatial weights for neighbours lists — nb2listwdist","text":"listw object following members: style one W, B, C, U, S, minmax type one idw, exp, dpd neighbours input neighbours list weights weights neighbours chosen style, attributes set report type relationships (binary general, general form glist argument), style ","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2listwdist.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Distance-based spatial weights for neighbours lists — nb2listwdist","text":"Tiefelsdorf, M., Griffith, D. ., Boots, B. 1999 variance-stabilizing coding scheme spatial link matrices, Environment Planning , 31, pp. 165–180; Kelejian, H. H., . R. Prucha. 2010. Specification estimation spatial autoregressive models autoregressive heteroskedastic disturbances. Journal Econometrics, 157: pp. 53–67.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2listwdist.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Distance-based spatial weights for neighbours lists — nb2listwdist","text":"Rene Westerholt rene.westerholt@tu-dortmund.de","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/nb2listwdist.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Distance-based spatial weights for neighbours lists — nb2listwdist","text":"","code":"# World examples data(world, package=\"spData\") # neighbours on distance interval [0, 1000] kilometres # suppressWarnings(st_crs(world) <- \"+proj=longlat\") # for older PROJ pts <- st_centroid(st_transform(world, 3857)) #> Warning: st_centroid assumes attributes are constant over geometries nb_world <- dnearneigh(pts, 0, 1000000) #> Warning: neighbour object has 46 sub-graphs # Moran's I (life expectancy) with IDW with alpha = 2, no coding scheme world_weights <- nb2listwdist(nb_world, as(pts, \"Spatial\"), type = \"idw\",   alpha = 2, zero.policy = TRUE) moran.test(world$lifeExp, world_weights, zero.policy = TRUE, na.action = na.pass) #> Warning: NAs in lagged values #>  #> \tMoran I test under randomisation #>  #> data:  world$lifeExp   #> weights: world_weights   #> n reduced by no-neighbour observations   #>  #> Moran I statistic standard deviate = 2.7769, p-value = 0.002744 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic       Expectation          Variance  #>       0.473883371      -0.007042254       0.029994057  #>  # \\dontrun{ # Moran's I (life expectancy) with IDW with alpha = 2, no coding scheme world_weights <- nb2listwdist(nb_world, pts, type = \"idw\",   alpha = 2, zero.policy = TRUE) moran.test(world$lifeExp, world_weights, zero.policy = TRUE, na.action = na.pass) #> Warning: NAs in lagged values #>  #> \tMoran I test under randomisation #>  #> data:  world$lifeExp   #> weights: world_weights   #> n reduced by no-neighbour observations   #>  #> Moran I statistic standard deviate = 2.7769, p-value = 0.002744 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic       Expectation          Variance  #>       0.473883371      -0.007042254       0.029994057  #>  # Moran's I (life expectancy), DPD, alpha = 2, dmax = 1000 km, no coding scheme world_weights <- nb2listwdist(nb_world, pts, type = \"dpd\",   dmax = 1000000, alpha = 2, zero.policy = TRUE) moran.test(world$lifeExp, world_weights, zero.policy = TRUE, na.action = na.pass) #> Warning: NAs in lagged values #>  #> \tMoran I test under randomisation #>  #> data:  world$lifeExp   #> weights: world_weights   #> n reduced by no-neighbour observations   #>  #> Moran I statistic standard deviate = 8.8557, p-value < 2.2e-16 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic       Expectation          Variance  #>       0.601498970      -0.007042254       0.004722063  #>  # Boston examples data(boston, package=\"spData\") boston_coords <- data.frame(x = boston.utm[,1], y = boston.utm[,2]) boston.geoms <- st_as_sf(boston_coords, coords = c(\"x\", \"y\"), remove = FALSE) nb_boston <- dnearneigh(boston.geoms, 0, 3) #> Warning: neighbour object has 9 sub-graphs # Moran's I (crime) with exp weights with alpha = 2, no coding scheme boston_weights <- nb2listwdist(nb_boston, boston.geoms, type = \"exp\", alpha = 2,   style=\"raw\", zero.policy = TRUE) moran.test(boston.c$CRIM, boston_weights, zero.policy = TRUE, na.action = na.pass) #>  #> \tMoran I test under randomisation #>  #> data:  boston.c$CRIM   #> weights: boston_weights   #> n reduced by no-neighbour observations   #>  #> Moran I statistic standard deviate = 51.34, p-value < 2.2e-16 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic       Expectation          Variance  #>      0.8845114518     -0.0019960080      0.0002981586  #>  # Moran's I (crime) with idw weights with alpha = 2, coding scheme = W boston_weights <- nb2listwdist(nb_boston, boston.geoms, type = \"idw\", alpha = 2,   style=\"W\", zero.policy = TRUE) moran.test(boston.c$CRIM, boston_weights, zero.policy = TRUE, na.action = na.pass) #>  #> \tMoran I test under randomisation #>  #> data:  boston.c$CRIM   #> weights: boston_weights   #> n reduced by no-neighbour observations   #>  #> Moran I statistic standard deviate = 18.976, p-value < 2.2e-16 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic       Expectation          Variance  #>      0.4392852330     -0.0019960080      0.0005408065  #>  # }"},{"path":"https://r-spatial.github.io/spdep/reference/nb2mat.html","id":null,"dir":"Reference","previous_headings":"","what":"Spatial weights matrices for neighbours lists — nb2mat","title":"Spatial weights matrices for neighbours lists — nb2mat","text":"function generates weights matrix neighbours list spatial weights chosen coding scheme.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2mat.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Spatial weights matrices for neighbours lists — nb2mat","text":"","code":"nb2mat(neighbours, glist=NULL, style=\"W\", zero.policy=NULL) listw2mat(listw)"},{"path":"https://r-spatial.github.io/spdep/reference/nb2mat.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Spatial weights matrices for neighbours lists — nb2mat","text":"neighbours object class nb glist list general weights corresponding neighbours style style can take values W, B, C, S zero.policy default NULL, use global option value; FALSE stop error empty neighbour sets, TRUE permit weights list formed zero-length weights vectors listw listw object example nb2listw","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2mat.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Spatial weights matrices for neighbours lists — nb2mat","text":"Starting binary neighbours list, regions either listed neighbours absent (thus set neighbours definition), function creates n n weights matrix values given coding scheme style chosen. B basic binary coding, W row standardised, C globally standardised, S variance-stabilizing coding scheme proposed Tiefelsdorf et al. 1999, p. 167-168. function leaves matrix rows zero regions zero neighbours fore zero.policy TRUE. turn generate lag values zero, equivalent sum products zero row t(rep(0, length=length(neighbours))) %*% x, arbitraty numerical vector x length length(neighbours). spatially lagged value x zero-neighbour region zero, may (may ) sensible choice.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2mat.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Spatial weights matrices for neighbours lists — nb2mat","text":"n n matrix, n=length(neighbours)","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2mat.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Spatial weights matrices for neighbours lists — nb2mat","text":"Tiefelsdorf, M., Griffith, D. ., Boots, B. 1999 variance-stabilizing coding scheme spatial link matrices, Environment Planning , 31, pp. 165-180.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2mat.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Spatial weights matrices for neighbours lists — nb2mat","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/nb2mat.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Spatial weights matrices for neighbours lists — nb2mat","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) col005 <- dnearneigh(st_coordinates(st_centroid(st_geometry(columbus),  of_largest_polygon=TRUE)), 0, 0.5, as.character(columbus$NEIGNO)) #> Warning: neighbour object has 8 sub-graphs summary(col005) #> Neighbour list object: #> Number of regions: 49  #> Number of nonzero links: 170  #> Percentage nonzero weights: 7.080383  #> Average number of links: 3.469388  #> 4 regions with no links: #> 1005, 1006, 1008, 1043 #> 8 disjoint connected subgraphs #> Link number distribution: #>  #>  0  1  2  3  4  5  6  7  8  9  #>  4 11  5  8  3  9  2  2  3  2  #> 11 least connected regions: #> 1001 1007 1018 1010 1045 1044 1046 1047 1049 1048 1015 with 1 link #> 2 most connected regions: #> 1038 1036 with 9 links col005.w.mat <- nb2mat(col005, style=\"B\", zero.policy=TRUE) table(round(rowSums(col005.w.mat))) #>  #>  0  1  2  3  4  5  6  7  8  9  #>  4 11  5  8  3  9  2  2  3  2"},{"path":"https://r-spatial.github.io/spdep/reference/nbcosts.html","id":null,"dir":"Reference","previous_headings":"","what":"Compute cost of edges — nbcosts","title":"Compute cost of edges — nbcosts","text":"cost edge distance nodes. function   compute distance using data.frame observations vector   node.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nbcosts.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Compute cost of edges — nbcosts","text":"","code":"nbcost(data, id, id.neigh,  method = c(\"euclidean\", \"maximum\",      \"manhattan\", \"canberra\", \"binary\", \"minkowski\", \"mahalanobis\"),     p = 2, cov, inverted = FALSE) nbcosts(nb, data,  method = c(\"euclidean\", \"maximum\",      \"manhattan\", \"canberra\", \"binary\", \"minkowski\", \"mahalanobis\"),     p = 2, cov, inverted = FALSE)"},{"path":"https://r-spatial.github.io/spdep/reference/nbcosts.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Compute cost of edges — nbcosts","text":"nb object nb class. See poly2nb     details. data matrix observations nodes. id Node index compute cost id.neigh Idex neighbours nodes node id method Character function declare distance method.     method character, method must \"mahalanobis\"     \"euclidean\", \"maximum\", \"manhattan\", \"canberra\", \"binary\"     \"minkowisk\".     method one \"euclidean\", \"maximum\",     \"manhattan\", \"canberra\", \"binary\" \"minkowisk\", see     dist details,      function used compute distance.      method=\"mahalanobis\", mahalanobis distance      computed neighbour areas.      method function, function      used compute distance. p power Minkowski distance. cov covariance matrix used compute mahalanobis    distance. inverted logical.  'TRUE', 'cov' supposed contain           inverse covariance matrix.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nbcosts.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Compute cost of edges — nbcosts","text":"object nbdist class. See nbdists   details.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nbcosts.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Compute cost of edges — nbcosts","text":"neighbours must connected graph.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nbcosts.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Compute cost of edges — nbcosts","text":"Elias T. Krainski Renato M. Assuncao","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/nbdists.html","id":null,"dir":"Reference","previous_headings":"","what":"Spatial link distance measures — nbdists","title":"Spatial link distance measures — nbdists","text":"Given list spatial neighbour links (neighbours list object type   nb), function returns Euclidean distances along links   list form neighbours list. longlat = TRUE, Great   Circle distances used.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nbdists.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Spatial link distance measures — nbdists","text":"","code":"nbdists(nb, coords, longlat = NULL)"},{"path":"https://r-spatial.github.io/spdep/reference/nbdists.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Spatial link distance measures — nbdists","text":"nb object class nb coords matrix point coordinates, object inheriting SpatialPoints \"sf\" \"sfc\" object; \"sf\" \"sfc\" object geometries geographical coordinates (sf::st_is_longlat(x) == TRUE sf::sf_use_s2() == TRUE), s2 used find distances https://github.com/r-spatial/s2/issues/125 longlat TRUE point coordinates longitude-latitude decimal degrees, case distances measured kilometers; coords SpatialPoints object, value taken object ","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nbdists.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Spatial link distance measures — nbdists","text":"list class nbdist","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nbdists.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Spatial link distance measures — nbdists","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/nbdists.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Spatial link distance measures — nbdists","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) col.gal.nb <- read.gal(system.file(\"weights/columbus.gal\", package=\"spData\")[1]) coords <- st_coordinates(st_centroid(columbus)) #> Warning: st_centroid assumes attributes are constant over geometries dlist <- nbdists(col.gal.nb, coords) dlist <- lapply(dlist, function(x) 1/x) stem(unlist(dlist)) #>  #>   The decimal point is at the | #>  #>   1 | 1111112222223333334444444444 #>   1 | 555555556666667777777777888888888899999999999999999999 #>   2 | 00000000111111111111111122222222222222333333333333334444 #>   2 | 55555555556666666666666677777777888888999999 #>   3 | 0000111111222233334444 #>   3 | 77779999 #>   4 | 223344 #>   4 | 77 #>   5 | 001144 #>   5 |  #>   6 |  #>   6 | 99 #>   7 |  #>   7 | 88 #>"},{"path":"https://r-spatial.github.io/spdep/reference/nblag.html","id":null,"dir":"Reference","previous_headings":"","what":"Higher order neighbours lists — nblag","title":"Higher order neighbours lists — nblag","text":"function creates higher order neighbour lists, higher order neighbours lags links graph described input neighbours list. refuse lag neighbours lists attribute self.included set TRUE. nblag_cumul cumulates neighbour lists single neighbour list (“nb” object).","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nblag.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Higher order neighbours lists — nblag","text":"","code":"nblag(neighbours, maxlag) nblag_cumul(nblags)"},{"path":"https://r-spatial.github.io/spdep/reference/nblag.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Higher order neighbours lists — nblag","text":"neighbours input neighbours list class nb maxlag maximum lag constructed nblags list neighbour lists output nblag","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nblag.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Higher order neighbours lists — nblag","text":"returns list lagged neighbours lists class nb","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nblag.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Higher order neighbours lists — nblag","text":"Roger Bivand Roger.Bivand@nhh.Giovanni Millo","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/nblag.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Higher order neighbours lists — nblag","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) col.gal.nb <- read.gal(system.file(\"weights/columbus.gal\", package=\"spData\")[1]) coords <- st_coordinates(st_centroid(columbus)) #> Warning: st_centroid assumes attributes are constant over geometries summary(col.gal.nb, coords) #> Neighbour list object: #> Number of regions: 49  #> Number of nonzero links: 230  #> Percentage nonzero weights: 9.579342  #> Average number of links: 4.693878  #> Link number distribution: #>  #>  2  3  4  5  6  7  8  9 10  #>  7  7 13  4  9  6  1  1  1  #> 7 least connected regions: #> 1 6 31 39 42 46 47 with 2 links #> 1 most connected region: #> 20 with 10 links col.lags <- nblag(col.gal.nb, 2) print(col.lags) #> [[1]] #> Neighbour list object: #> Number of regions: 49  #> Number of nonzero links: 230  #> Percentage nonzero weights: 9.579342  #> Average number of links: 4.693878  #>  #> [[2]] #> Neighbour list object: #> Number of regions: 49  #> Number of nonzero links: 406  #> Percentage nonzero weights: 16.90962  #> Average number of links: 8.285714  #>  #> attr(,\"call\") #> nblag(neighbours = col.gal.nb, maxlag = 2) summary(col.lags[[2]], coords) #> Neighbour list object: #> Number of regions: 49  #> Number of nonzero links: 406  #> Percentage nonzero weights: 16.90962  #> Average number of links: 8.285714  #> Link number distribution: #>  #>  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17  #>  1  2  5  4  2  3  5  4  2  3  7  3  4  1  1  1  1  #> 1 least connected region: #> 36 with 1 link #> 1 most connected region: #> 25 with 17 links plot(st_geometry(columbus), border=\"grey\") plot(col.gal.nb, coords, add=TRUE) title(main=\"GAL order 1 (black) and 2 (red) links\") plot(col.lags[[2]], coords, add=TRUE, col=\"red\", lty=2)  cuml <- nblag_cumul(col.lags) cuml #> Neighbour list object: #> Number of regions: 49  #> Number of nonzero links: 636  #> Percentage nonzero weights: 26.48896  #> Average number of links: 12.97959  run <- FALSE if (require(igraph, quietly=TRUE) && require(spatialreg, quietly=TRUE)) run <- TRUE if (run) { W <- as(nb2listw(col.gal.nb), \"CsparseMatrix\") G <- graph_from_adjacency_matrix(W, mode=\"directed\", weight=\"W\") D <- diameter(G) nbs <- nblag(col.gal.nb, maxlag=D) n <- length(col.gal.nb) lmat <- lapply(nbs, nb2mat, style=\"B\", zero.policy=TRUE) mat <- matrix(0, n, n) for (i in seq(along=lmat)) mat = mat + i*lmat[[i]] G2 <- distances(G) print(all.equal(G2, mat, check.attributes=FALSE)) } #> Warning: lag 6 neighbour object has 5 sub-graphs #> Warning: lag 7 neighbour object has 20 sub-graphs #> Warning: lag 8 neighbour object has 36 sub-graphs #> Warning: lag 9 neighbour object has 44 sub-graphs #> [1] TRUE"},{"path":"https://r-spatial.github.io/spdep/reference/nboperations.html","id":null,"dir":"Reference","previous_headings":"","what":"Set operations on neighborhood objects — nb.set.operations","title":"Set operations on neighborhood objects — nb.set.operations","text":"Set operations neighbors list objects","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nboperations.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Set operations on neighborhood objects — nb.set.operations","text":"","code":"intersect.nb(nb.obj1,nb.obj2) union.nb(nb.obj1,nb.obj2) setdiff.nb(nb.obj1,nb.obj2) complement.nb(nb.obj)"},{"path":"https://r-spatial.github.io/spdep/reference/nboperations.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Set operations on neighborhood objects — nb.set.operations","text":"nb.obj neighbor list created neighborhood     list funtions nb.obj1 neighbor list created neighborhood     list funtions nb.obj2 neighbor list created neighborhood     list funtions","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nboperations.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Set operations on neighborhood objects — nb.set.operations","text":"functions perform set operations element   neighborlist. arguments must neighbor lists created   coordinates, region.id attributes must identical.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nboperations.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Set operations on neighborhood objects — nb.set.operations","text":"nb.obj new neighborlist created set operations                input neighbor list(s)","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nboperations.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Set operations on neighborhood objects — nb.set.operations","text":"Nicholas Lewin-Koh nikko@hailmail.net","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/nboperations.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Set operations on neighborhood objects — nb.set.operations","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) col.gal.nb <- read.gal(system.file(\"weights/columbus.gal\", package=\"spData\")[1]) coords <- st_coordinates(st_centroid(columbus)) #> Warning: st_centroid assumes attributes are constant over geometries col.tri.nb <- tri2nb(coords) oldpar <- par(mfrow=c(1,2)) if (require(\"dbscan\", quietly=TRUE)) {   col.soi.nb <- graph2nb(soi.graph(col.tri.nb, coords))   plot(st_geometry(columbus), border=\"grey\")   plot(col.soi.nb, coords, add=TRUE)   title(main=\"Sphere of Influence Graph\", cex.main=0.7)   plot(st_geometry(columbus), border=\"grey\")   plot(complement.nb(col.soi.nb), coords, add=TRUE)   title(main=\"Complement of Sphere of Influence Graph\", cex.main=0.7) }  par(mfrow=c(2,2)) col2 <- droplinks(col.gal.nb, 21) #> Warning: some observations have no neighbours #> Warning: neighbour object has 3 sub-graphs plot(intersect.nb(col.gal.nb, col2), coords) #> Warning: neighbour object has 3 sub-graphs title(main=\"Intersect\", cex.main=0.7) plot(union.nb(col.gal.nb, col2), coords) title(main=\"Union\", cex.main=0.7) plot(setdiff.nb(col.gal.nb, col2), coords) #> Warning: neighbour object has 46 sub-graphs title(main=\"Set diff\", cex.main=0.7) par(oldpar)"},{"path":"https://r-spatial.github.io/spdep/reference/p.adjustSP.html","id":null,"dir":"Reference","previous_headings":"","what":"Adjust local association measures' p-values — p.adjustSP","title":"Adjust local association measures' p-values — p.adjustSP","text":"Make adjustment local association measures' p-values based number neighbours (+1) region, rather total number regions.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/p.adjustSP.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Adjust local association measures' p-values — p.adjustSP","text":"","code":"p.adjustSP(p, nb, method = \"none\")"},{"path":"https://r-spatial.github.io/spdep/reference/p.adjustSP.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Adjust local association measures' p-values — p.adjustSP","text":"p vector p-values nb list neighbours class nb method correction method defined p.adjust: \"adjustment methods include Bonferroni correction ('\"bonferroni\"') p-values multiplied number comparisons.  Four less conservative corrections also included Holm (1979) ('holm'), Hochberg (1988) ('hochberg'), Hommel (1988) ('hommel') Benjamini & Hochberg (1995) ('fdr'), respectively. pass-option ('none') also included.\"","code":""},{"path":"https://r-spatial.github.io/spdep/reference/p.adjustSP.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Adjust local association measures' p-values — p.adjustSP","text":"vector corrected p-values using number neighbours + 1.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/p.adjustSP.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Adjust local association measures' p-values — p.adjustSP","text":"Danlin Yu Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/p.adjustSP.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Adjust local association measures' p-values — p.adjustSP","text":"","code":"data(afcon, package=\"spData\") oid <- order(afcon$id) resG <- as.vector(localG(afcon$totcon, nb2listw(include.self(paper.nb)))) non <- format.pval(pnorm(2*(abs(resG)), lower.tail=FALSE), 2) bon <- format.pval(p.adjustSP(pnorm(2*(abs(resG)), lower.tail=FALSE),  paper.nb, \"bonferroni\"), 2) tot <- format.pval(p.adjust(pnorm(2*(abs(resG)), lower.tail=FALSE),  \"bonferroni\", n=length(resG)), 2) data.frame(resG, non, bon, tot, row.names=afcon$name)[oid,] #>                                 resG     non     bon     tot #> THE GAMBIA               -0.98383592 0.02455 0.04911  1.0000 #> MALI                     -1.69893391 0.00034 0.00272  0.0143 #> SENEGAL                  -1.46321911 0.00171 0.00857  0.0720 #> BENIN                    -1.30139679 0.00462 0.02312  0.1942 #> MAURITANIA               -0.60496775 0.11315 0.56576  1.0000 #> NIGER                    -1.04877003 0.01797 0.14378  0.7549 #> IVORY COAST              -1.41712454 0.00230 0.01378  0.0965 #> GUINEA                   -1.44888005 0.00188 0.01128  0.0789 #> BURKINA FASO             -1.75085492 0.00023 0.00162  0.0097 #> LIBERIA                  -1.04053617 0.01871 0.07485  0.7860 #> SIERRA LEONE             -0.87032623 0.04087 0.12262  1.0000 #> GHANA                    -1.10269327 0.01371 0.05485  0.5760 #> TOGO                     -0.99053008 0.02379 0.09517  0.9993 #> CAMEROON                 -1.13328519 0.01171 0.07025  0.4917 #> NIGERIA                  -1.17261672 0.00951 0.04754  0.3993 #> GABON                    -0.78935857 0.05720 0.17160  1.0000 #> CENTRAL AFRICAN REPUBLIC  1.17349763 0.00946 0.05678  0.3974 #> CHAD                      0.46259185 0.17744 1.00000  1.0000 #> CONGO                    -0.20253005 0.34272 1.00000  1.0000 #> ZAIRE                     2.02270432 2.6e-05 0.00026  0.0011 #> ANGOLA                    1.23450728 0.00677 0.02710  0.2845 #> UGANDA                    3.33600851 1.3e-11 7.6e-11 5.3e-10 #> KENYA                     3.50301896 1.2e-12 7.4e-12 5.1e-11 #> TANZANIA                  1.09843592 0.01401 0.12613  0.5886 #> BURUNDI                   0.77417084 0.06077 0.24308  1.0000 #> RWANDA                    1.45720776 0.00178 0.00891  0.0748 #> SOMALIA                   1.18316273 0.00898 0.02695  0.3773 #> ETHIOPIA                  2.62720027 7.4e-08 3.0e-07 3.1e-06 #> ZAMBIA                    0.75273285 0.06610 0.59492  1.0000 #> ZIMBABWE                 -0.19956472 0.34490 1.00000  1.0000 #> MALAWI                    0.21195283 0.33582 1.00000  1.0000 #> MOZAMBIQUE               -0.28761679 0.28257 1.00000  1.0000 #> SOUTH AFRICA             -0.86814954 0.04126 0.33004  1.0000 #> LESOTHO                  -0.29841469 0.27531 0.55062  1.0000 #> BOTSWANA                  0.04090396 0.46740 1.00000  1.0000 #> SWAZILAND                -0.65938417 0.09362 0.28087  1.0000 #> MOROCCO                   0.02191606 0.48252 1.00000  1.0000 #> ALGERIA                  -0.36307938 0.23387 1.00000  1.0000 #> TUNISIA                   0.57910139 0.12339 0.37017  1.0000 #> LIBYA                     2.55272169 1.7e-07 1.2e-06 6.9e-06 #> SUDAN                     4.03925235 3.3e-16 3.0e-15 1.4e-14 #> EGYPT                     4.42133637 < 2e-16 < 2e-16 < 2e-16"},{"path":"https://r-spatial.github.io/spdep/reference/plot.mst.html","id":null,"dir":"Reference","previous_headings":"","what":"Plot the Minimum Spanning Tree — plot.mst","title":"Plot the Minimum Spanning Tree — plot.mst","text":"function plots MST, nodes circles edges   segments.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/plot.mst.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Plot the Minimum Spanning Tree — plot.mst","text":"","code":"# S3 method for class 'mst' plot(x, coords, label.areas = NULL,     cex.circles = 1, cex.labels = 1, add=FALSE, ...)"},{"path":"https://r-spatial.github.io/spdep/reference/plot.mst.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Plot the Minimum Spanning Tree — plot.mst","text":"x Object mst class. coords two column matrix coordinates nodes. label.areas vector labels nodes cex.circles length circles plot. cex.labels length nodes labels ploted. add default FALSE, create new plot ... arguments passed plotting functions.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/plot.mst.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Plot the Minimum Spanning Tree — plot.mst","text":"Elias T. Krainski Renato M. Assuncao","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/plot.mst.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Plot the Minimum Spanning Tree — plot.mst","text":"","code":"### see example in mstree function documentation"},{"path":"https://r-spatial.github.io/spdep/reference/plot.nb.html","id":null,"dir":"Reference","previous_headings":"","what":"Plot a neighbours list — plot.nb","title":"Plot a neighbours list — plot.nb","text":"function plot neighbours list given point coordinates represent region two dimensions; plot.listw wrapper passes neighbours component plot.nb.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/plot.nb.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Plot a neighbours list — plot.nb","text":"","code":"# S3 method for class 'nb' plot(x, coords, col=\"black\", points=TRUE, add=FALSE, arrows=FALSE,  length=0.1, xlim=NULL, ylim=NULL, ...) # S3 method for class 'listw' plot(x, coords, col=\"black\", points=TRUE, add=FALSE, arrows=FALSE,  length=0.1, xlim=NULL, ylim=NULL, ...)"},{"path":"https://r-spatial.github.io/spdep/reference/plot.nb.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Plot a neighbours list — plot.nb","text":"x object class nb (plot.listw) class listw coords matrix region point coordinates, Spatial object (points polygons), sfc object (points polygons) col plotting colour points (logical) add points plot add (logical) add existing plot arrows (logical) draw arrowheads asymmetric neighbours length length plot inches arrow heads drawn asymmetric neighbours lists xlim, ylim plot window bounds ... graphical parameters par(..)","code":""},{"path":"https://r-spatial.github.io/spdep/reference/plot.nb.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Plot a neighbours list — plot.nb","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/plot.nb.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Plot a neighbours list — plot.nb","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) col.gal.nb <- read.gal(system.file(\"weights/columbus.gal\", package=\"spData\")[1]) plot(col.gal.nb, st_geometry(columbus)) title(main=\"GAL order 1 links with first nearest neighbours in red\", cex.main=0.6)  plot(col.gal.nb, as(columbus, \"Spatial\")) title(main=\"GAL order 1 links with first nearest neighbours in red\", cex.main=0.6) coords <- st_centroid(st_geometry(columbus), of_largest_polygon=TRUE) col.knn <- knearneigh(coords, k=1) plot(knn2nb(col.knn), coords, add=TRUE, col=\"red\", length=0.08) #> Warning: neighbour object has 13 sub-graphs"},{"path":"https://r-spatial.github.io/spdep/reference/plot.skater.html","id":null,"dir":"Reference","previous_headings":"","what":"Plot the object of skater class — plot.skater","title":"Plot the object of skater class — plot.skater","text":"function displays results skater function. subgraphs   plotted different colours.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/plot.skater.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Plot the object of skater class — plot.skater","text":"","code":"# S3 method for class 'skater' plot(x, coords, label.areas = NULL,     groups.colors, cex.circles = 1, cex.labels = 1, ...)"},{"path":"https://r-spatial.github.io/spdep/reference/plot.skater.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Plot the object of skater class — plot.skater","text":"x object skater class. coords matrix two colums coordinates nodes. label.areas vector labels nodes. groups.colors vector colors groups ou sub-graphs. cex.circles length circles represent nodes. cex.labels length labels nodes. ... arguments passed plotting funcitons.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/plot.skater.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Plot the object of skater class — plot.skater","text":"Elias T. Krainski Renato M. Assuncao","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/plot.skater.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Plot the object of skater class — plot.skater","text":"","code":"### see example in the skater function documentation"},{"path":"https://r-spatial.github.io/spdep/reference/poly2nb.html","id":null,"dir":"Reference","previous_headings":"","what":"Construct neighbours list from polygon list — poly2nb","title":"Construct neighbours list from polygon list — poly2nb","text":"function builds neighbours list based regions contiguous boundaries, sharing one boundary point. current function part interpreted may run slowly many regions detailed boundaries, 0.2-16 fail lack memory single polygons built many border coordinates.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/poly2nb.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Construct neighbours list from polygon list — poly2nb","text":"","code":"poly2nb(pl, row.names = NULL, snap=NULL, queen=TRUE, useC=TRUE, foundInBox=NULL)"},{"path":"https://r-spatial.github.io/spdep/reference/poly2nb.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Construct neighbours list from polygon list — poly2nb","text":"pl list polygons class extending SpatialPolygons, sf sfc object containing non-empty (multi-)polygon objects row.names character vector region ids added neighbours list attribute region.id, default seq(1, nrow(x)); pl row.names, used instead default sequence. snap boundary points less snap distance apart considered indicate contiguity; used find candidate actual neighbours planar geometries, actual neighbours spherical geometries, spherical spatial indexing injects fuzzyness. set, SpatialPolygons objects, default sqrt(.Machine$double.eps), value also used sf objects coordinate reference system. sf objects defined coordinate reference system, default value 1e-7 geographical coordinates (approximately 10mm), 10mm projected coordinates metre units, converted 10mm distance units coordinates. conversion fail, snap reverts sqrt(.Machine$double.eps). queen TRUE, single shared boundary point meets contiguity condition, FALSE, one shared point required; note one shared boundary point necessarily mean shared boundary line useC default TRUE, work loop C, may set false revert R code calling two C functions n*k work loop, k average number candidate neighbours foundInBox default NULL using R code st_intersects() generate candidate neighbours (using snap= geometries spherical); NULL (legacy purposes) list length (n-1) integer vectors candidate neighbours (j > ) (created poly_findInBoxGEOS function rgeos clean polygons)","code":""},{"path":"https://r-spatial.github.io/spdep/reference/poly2nb.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Construct neighbours list from polygon list — poly2nb","text":"neighbours list class nb. See card details “nb” objects.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/poly2nb.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Construct neighbours list from polygon list — poly2nb","text":"0.5-8, function includes faster bounding box indexing improvements contributed Micah Altman. cluster provided using set.ClusterOption, used finding candidate bounding box overlaps exact testing contiguity. 1.1-7, sf polygons included start end points, erroneously report queen neighbourhood rook present, see https://github.com/r-spatial/spdep/issues/50. 1.1-9 sf 1.0-0, s2 used bounding box indexing internally pl geographical coordinates. topology engine s2 differs use GEOS planar coordinates sf, output differences may expected. Since treating spherical geometries planar also questionable, clear whether spherical contiguous polygon neighbours simply follow neighbours found treating geometries planar https://github.com/r-spatial/s2/issues/125#issuecomment-864403372. However, current advice necessarily use s2 finding contiguity neighbours, least check output.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/poly2nb.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Construct neighbours list from polygon list — poly2nb","text":"Roger Bivand Roger.Bivand@nhh.contributions Micah Altman","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/poly2nb.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Construct neighbours list from polygon list — poly2nb","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) col.gal.nb <- read.gal(system.file(\"weights/columbus.gal\", package=\"spData\")[1]) coords <- st_coordinates(st_centroid(st_geometry(columbus))) xx <- poly2nb(as(columbus, \"Spatial\")) dxx <- diffnb(xx, col.gal.nb) #> Warning: neighbour object has 46 sub-graphs plot(st_geometry(columbus), border=\"grey\") plot(col.gal.nb, coords, add=TRUE) plot(dxx, coords, add=TRUE, col=\"red\") title(main=paste(\"Differences (red) in Columbus GAL weights (black)\",  \"and polygon generated queen weights\", sep=\"\\n\"), cex.main=0.6)  # poly2nb with sf sfc_MULTIPOLYGON objects sf_xx <- poly2nb(columbus) diffnb(sf_xx, xx) #> Warning: neighbour object has 49 sub-graphs #> Neighbour list object: #> Number of regions: 49  #> Number of nonzero links: 0  #> Percentage nonzero weights: 0  #> Average number of links: 0  #> 49 regions with no links: #> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, #> 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, #> 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49 #> 49 disjoint connected subgraphs sfc_xx <- poly2nb(st_geometry(columbus)) diffnb(sfc_xx, xx) #> Warning: neighbour object has 49 sub-graphs #> Neighbour list object: #> Number of regions: 49  #> Number of nonzero links: 0  #> Percentage nonzero weights: 0  #> Average number of links: 0  #> 49 regions with no links: #> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, #> 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, #> 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49 #> 49 disjoint connected subgraphs xxx <- poly2nb(as(columbus, \"Spatial\"), queen=FALSE) dxxx <- diffnb(xxx, col.gal.nb) #> Warning: neighbour object has 34 sub-graphs plot(st_geometry(columbus), border = \"grey\") plot(col.gal.nb, coords, add = TRUE) plot(dxxx, coords, add = TRUE, col = \"red\") title(main=paste(\"Differences (red) in Columbus GAL weights (black)\",  \"and polygon generated rook weights\", sep=\"\\n\"), cex.main=0.6)  cards <- card(xx) maxconts <- which(cards == max(cards)) if(length(maxconts) > 1) maxconts <- maxconts[1] fg <- rep(\"grey\", length(cards)) fg[maxconts] <- \"red\" fg[xx[[maxconts]]] <- \"green\" plot(st_geometry(columbus), col=fg) title(main=\"Region with largest number of contiguities\", cex.main=0.6)  nc.sids <- st_read(system.file(\"shapes/sids.gpkg\", package=\"spData\")[1], quiet=TRUE) system.time(xxnb <- poly2nb(nc.sids)) #>    user  system elapsed  #>   0.041   0.000   0.041  system.time(xxnb <- poly2nb(as(nc.sids, \"Spatial\"))) #>    user  system elapsed  #>   0.059   0.000   0.059  plot(st_geometry(nc.sids)) plot(xxnb, st_coordinates(st_centroid(nc.sids)), add=TRUE, col=\"blue\") #> Warning: st_centroid assumes attributes are constant over geometries  sq <- st_polygon(list(rbind(c(0,0), c(1,0), c(1,1), c(0,1), c(0,0)))) sq2 <- sq + c(0,1) sq3 <- sq + c(1,0) sq4 <- sq + c(1,1) gm <- st_sfc(list(sq, sq2, sq3, sq4)) df <- st_as_sf(data.frame(gm, id=1:4)) plot(st_geometry(df)) text(st_coordinates(st_centroid(gm)), as.character(df$id))  unclass(poly2nb(df, queen = FALSE)) #> [[1]] #> [1] 2 3 #>  #> [[2]] #> [1] 1 4 #>  #> [[3]] #> [1] 1 4 #>  #> [[4]] #> [1] 2 3 #>  #> attr(,\"region.id\") #> [1] \"1\" \"2\" \"3\" \"4\" #> attr(,\"call\") #> poly2nb(pl = df, queen = FALSE) #> attr(,\"type\") #> [1] \"rook\" #> attr(,\"snap\") #> [1] 1.490116e-08 #> attr(,\"sym\") #> [1] TRUE #> attr(,\"ncomp\") #> attr(,\"ncomp\")$nc #> [1] 1 #>  #> attr(,\"ncomp\")$comp.id #> [1] 1 1 1 1 #>  col_geoms <- st_geometry(columbus) col_geoms[1] <- st_buffer(col_geoms[1], dist=-0.05) st_geometry(columbus) <- col_geoms poly2nb(columbus) #> Warning: some observations have no neighbours; #> if this seems unexpected, try increasing the snap argument. #> Warning: neighbour object has 2 sub-graphs; #> if this sub-graph count seems unexpected, try increasing the snap argument. #> Neighbour list object: #> Number of regions: 49  #> Number of nonzero links: 232  #> Percentage nonzero weights: 9.662641  #> Average number of links: 4.734694  #> 1 region with no links: #> 1 #> 2 disjoint connected subgraphs"},{"path":"https://r-spatial.github.io/spdep/reference/probmap.html","id":null,"dir":"Reference","previous_headings":"","what":"Probability mapping for rates — probmap","title":"Probability mapping for rates — probmap","text":"function returns data frame rates counts populations risk crude rates, expected counts cases, relative risks, Poisson probabilities.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/probmap.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Probability mapping for rates — probmap","text":"","code":"probmap(n, x, row.names=NULL, alternative=\"less\")"},{"path":"https://r-spatial.github.io/spdep/reference/probmap.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Probability mapping for rates — probmap","text":"n numeric vector counts cases x numeric vector populations risk row.names row names passed output data frame alternative default “less”, may set “greater”","code":""},{"path":"https://r-spatial.github.io/spdep/reference/probmap.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Probability mapping for rates — probmap","text":"function returns data frame, rates may mapped class intervals chosen. class intervals used examples mostly taken referenced source.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/probmap.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Probability mapping for rates — probmap","text":"raw raw (crude) rates expCount expected counts cases assuming global rate relRisk relative risks: ratio observed expected counts cases multiplied 100 pmap Poisson probability map values: probablility getting “extreme” count actually observed - one-tailed, default alternative observed “less” expected","code":""},{"path":"https://r-spatial.github.io/spdep/reference/probmap.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Probability mapping for rates — probmap","text":"Bailey T, Gatrell (1995) Interactive Spatial Data Analysis, Harlow: Longman, pp. 300–303.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/probmap.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Probability mapping for rates — probmap","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/probmap.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Probability mapping for rates — probmap","text":"","code":"auckland <- st_read(system.file(\"shapes/auckland.gpkg\", package=\"spData\")[1], quiet=TRUE) res <- probmap(auckland$M77_85, 9*auckland$Und5_81) rt <- sum(auckland$M77_85)/sum(9*auckland$Und5_81) ppois_pmap <- numeric(length(auckland$Und5_81)) for (i in seq(along=ppois_pmap)) { ppois_pmap[i] <- poisson.test(auckland$M77_85[i], r=rt,   T=(9*auckland$Und5_81[i]), alternative=\"less\")$p.value all.equal(ppois_pmap, res$pmap) } res$id <- 1:nrow(res) auckland$id <- res$id <- 1:nrow(res) auckland_res <- merge(auckland, res, by=\"id\") plot(auckland_res[, \"raw\"], main=\"Crude (raw) estimates\")  plot(auckland_res[, \"relRisk\"], main=\"Standardised mortality ratios\")  plot(auckland_res[, \"pmap\"], main=\"Poisson probabilities\",  breaks=c(0, 0.05, 0.1, 0.5, 0.9, 0.95, 1))"},{"path":"https://r-spatial.github.io/spdep/reference/prunecost.html","id":null,"dir":"Reference","previous_headings":"","what":"Compute cost of prune each edge — prunecost","title":"Compute cost of prune each edge — prunecost","text":"edge dropped, MST pruned. generate two   subgraphs. , makes tree graphs tree dissimilarity values   computed, one graph. dissimilarity sum   sqared differences observactions nodes mean   vector observations graph. dissimilarity original   graph sum dissimilarity subgraphs returned.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/prunecost.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Compute cost of prune each edge — prunecost","text":"","code":"prunecost(edges, data, method = c(\"euclidean\", \"maximum\", \"manhattan\",      \"canberra\", \"binary\", \"minkowski\", \"mahalanobis\"),      p = 2, cov, inverted = FALSE)"},{"path":"https://r-spatial.github.io/spdep/reference/prunecost.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Compute cost of prune each edge — prunecost","text":"edges matrix 2 colums row one edge data data.frame observations nodes. method Character function declare distance method.     method character, method must \"mahalanobis\"     \"euclidean\", \"maximum\", \"manhattan\", \"canberra\", \"binary\"     \"minkowisk\".     method one \"euclidean\", \"maximum\",     \"manhattan\", \"canberra\", \"binary\" \"minkowisk\", see     dist details,      function used compute distance.      method=\"mahalanobis\", mahalanobis distance      computed neighbour areas.      method function, function      used compute distance. p power Minkowski distance. cov covariance matrix used compute mahalanobis    distance. inverted logical.  'TRUE', 'cov' supposed contain           inverse covariance matrix.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/prunecost.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Compute cost of prune each edge — prunecost","text":"vector differences dissimilarity nodes   dissimilarity sum subgraphs obtained pruning one   edge time.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/prunecost.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Compute cost of prune each edge — prunecost","text":"Elias T. Krainski Renato M. Assuncao","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/prunecost.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Compute cost of prune each edge — prunecost","text":"","code":"d <- data.frame(a=-2:2, b=runif(5)) e <- matrix(c(1,2, 2,3, 3,4, 4,5), ncol=2, byrow=TRUE)  sum(sweep(d, 2, colMeans(d))^2) #> [1] 10.35574  prunecost(e, d) #> [1] 2.138259 2.875555 2.820048 2.169740"},{"path":"https://r-spatial.github.io/spdep/reference/prunemst.html","id":null,"dir":"Reference","previous_headings":"","what":"Prune a Minimun Spanning Tree — prunemst","title":"Prune a Minimun Spanning Tree — prunemst","text":"function deletes first edge makes two subsets edges.   subset Minimun Spanning Treee.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/prunemst.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Prune a Minimun Spanning Tree — prunemst","text":"","code":"prunemst(edges, only.nodes = TRUE)"},{"path":"https://r-spatial.github.io/spdep/reference/prunemst.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Prune a Minimun Spanning Tree — prunemst","text":"edges matrix two colums row one edge .nodes .nodes=FALSE, return edges nodes   MST resulted. .nodes=TRUE, return two sets   nodes. Defalt TRUE","code":""},{"path":"https://r-spatial.github.io/spdep/reference/prunemst.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Prune a Minimun Spanning Tree — prunemst","text":"list length two. .nodes=TRUE element   vector nodes. .nodes=FALSE element list   nodes edges.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/prunemst.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Prune a Minimun Spanning Tree — prunemst","text":"Elias T. Krainski Renato M. Assuncao","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/prunemst.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Prune a Minimun Spanning Tree — prunemst","text":"","code":"e <- matrix(c(2,3, 1,2, 3,4, 4,5), ncol=2, byrow=TRUE) e #>      [,1] [,2] #> [1,]    2    3 #> [2,]    1    2 #> [3,]    3    4 #> [4,]    4    5 prunemst(e) #> $node1 #> [1] 2 1 #>  #> $node2 #> [1] 3 4 5 #>  prunemst(e, only.nodes=FALSE) #> [[1]] #> [[1]]$node #> [1] 2 1 #>  #> [[1]]$edge #>      [,1] [,2] #> [1,]    1    2 #>  #>  #> [[2]] #> [[2]]$node #> [1] 3 4 5 #>  #> [[2]]$edge #>      [,1] [,2] #> [1,]    3    4 #> [2,]    4    5 #>  #>"},{"path":"https://r-spatial.github.io/spdep/reference/read.gal.html","id":null,"dir":"Reference","previous_headings":"","what":"Read a GAL lattice file into a neighbours list — read.gal","title":"Read a GAL lattice file into a neighbours list — read.gal","text":"function read.gal() reads GAL lattice file neighbours list spatial analysis. read old new style (GeoDa) GAL files. function read.geoda helper file reading comma separated value data files, calling read.csv().","code":""},{"path":"https://r-spatial.github.io/spdep/reference/read.gal.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Read a GAL lattice file into a neighbours list — read.gal","text":"","code":"read.gal(file, region.id=NULL, override.id=FALSE) read.geoda(file, row.names=NULL, skip=0)"},{"path":"https://r-spatial.github.io/spdep/reference/read.gal.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Read a GAL lattice file into a neighbours list — read.gal","text":"file name file GAL lattice data region.id region IDs specified order coerse neighbours list order numbering region.id override.id override given (NULL) region.id, collecting region.id numbering order GAL file. row.names row.names read.csv(), typically character string naming column file used skip skip number lines, read.csv()","code":""},{"path":"https://r-spatial.github.io/spdep/reference/read.gal.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Read a GAL lattice file into a neighbours list — read.gal","text":"Luc Anselin (2003): Spatial Analysis Laboratory, Department Agricultural Consumer Economics, University Illinois, Urbana-Champaign, now dead link: http://www.csiss.org/gispopsci/workshops/2011/PSU/readings/W15_Anselin2007.pdf; Luc Anselin (2003) GeoDa 0.9 User's Guide, pp. 80–81, Spatial Analysis Laboratory, Department Agricultural Consumer Economics, University Illinois, Urbana-Champaign, http://geodacenter.github.io/docs/geoda093.pdf; GAL - Geographical Algorithms Library, University Newcastle","code":""},{"path":"https://r-spatial.github.io/spdep/reference/read.gal.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Read a GAL lattice file into a neighbours list — read.gal","text":"function read.gal() returns object class nb list integer vectors containing neighbour region number ids. function read.geoda returns data frame, issues warning returned object one column.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/read.gal.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Read a GAL lattice file into a neighbours list — read.gal","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/read.gal.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Read a GAL lattice file into a neighbours list — read.gal","text":"Example data originally downloaded now dead link: http://sal.agecon.uiuc.edu/weights/zips/us48.zip","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/read.gal.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Read a GAL lattice file into a neighbours list — read.gal","text":"","code":"us48.fipsno <- read.geoda(system.file(\"etc/weights/us48.txt\",  package=\"spdep\")[1]) us48.q <- read.gal(system.file(\"etc/weights/us48_q.GAL\", package=\"spdep\")[1],  us48.fipsno$Fipsno) us48.r <- read.gal(system.file(\"etc/weights/us48_rk.GAL\", package=\"spdep\")[1],  us48.fipsno$Fipsno) data(state) if (as.numeric(paste(version$major, version$minor, sep=\"\")) < 19) {  m50.48 <- match(us48.fipsno$\"State.name\", state.name) } else {  m50.48 <- match(us48.fipsno$\"State_name\", state.name) } plot(us48.q, as.matrix(as.data.frame(state.center))[m50.48,]) plot(diffnb(us48.r, us48.q),  as.matrix(as.data.frame(state.center))[m50.48,], add=TRUE, col=\"red\") #> Warning: neighbour object has 46 sub-graphs title(main=\"Differences between rook and queen criteria imported neighbours lists\")"},{"path":"https://r-spatial.github.io/spdep/reference/read.gwt2nb.html","id":null,"dir":"Reference","previous_headings":"","what":"Read and write spatial neighbour files — read.gwt2nb","title":"Read and write spatial neighbour files — read.gwt2nb","text":"\"gwt\" functions read write GeoDa GWT files (example file baltk4.GWT downloaded site given reference), \"dat\" functions read write Matlab sparse matrix files used James LeSage's Spatial Econometrics Toolbox (example file wmat.dat downloaded site given reference). body files headers three columns separated white space, third column must numeric locale reading platform (correct decimal separator).","code":""},{"path":"https://r-spatial.github.io/spdep/reference/read.gwt2nb.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Read and write spatial neighbour files — read.gwt2nb","text":"","code":"read.gwt2nb(file, region.id=NULL) write.sn2gwt(sn, file, shpfile=NULL, ind=NULL, useInd=FALSE, legacy=FALSE) read.dat2listw(file) write.sn2dat(sn, file) read.swmdbf2listw(fn, region.id=NULL, style=NULL, zero.policy=NULL) read_swm_dbf(fn) write.swmdbf(listw, file, ind, region.id = attr(listw, \"region.id\")) write_swm_dbf(listw, file, ind, region.id = attr(listw, \"region.id\")) write.sn2DBF(sn, file)"},{"path":"https://r-spatial.github.io/spdep/reference/read.gwt2nb.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Read and write spatial neighbour files — read.gwt2nb","text":"file, fn name file weights data region.id character vector region IDs - ArcGIS SWM DBFs, values must character integers (numbers starting zero) listw listw object sn spatial.neighbour object shpfile character string: given Shapefile name taken GWT file dataset ind character string: region id indicator field name useInd default FALSE, TRUE, write region.id attribute ID key tags output file (use OpenGeoDa depend shapefile field named ind argument matching exported tags) legacy default FALSE; TRUE, header single field number observations style default NULL, missing, set \"M\" warning given; \"M\", passed nb2listw re-build object zero.policy default NULL, use global option value; FALSE stop error empty neighbour sets, TRUE permit weights list formed zero-length weights vectors","code":""},{"path":"https://r-spatial.github.io/spdep/reference/read.gwt2nb.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Read and write spatial neighbour files — read.gwt2nb","text":"Attempts honour region.id argument given reading GWT SWM/DBF files. region IDs given region.id= match origins destinations GWT file, error warning thrown, considered carefully. read_swm_dbf simplified interface read.swmdbf2listw -neighbour observations present, advised region.id= given read.swmdbf2listw; function read correctly minimum maximum IDs present observations neighbours without region.id= set, reading using read.swmdbf2listw fail minimum maximum ID observations neighbours region.id= given.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/read.gwt2nb.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Read and write spatial neighbour files — read.gwt2nb","text":"read.gwt2nb returns neighbour \"nb\" object generalised weights stored list element called \"dlist\" \"GeoDa\" attribute; read.swmdbf2listw returns \"listw\" object read DBF file exported ArcGIS SWM object.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/read.gwt2nb.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Read and write spatial neighbour files — read.gwt2nb","text":"Luc Anselin (2003) GeoDa 0.9 User's Guide, pp. 80–81, Spatial Analysis Laboratory, Department Agricultural Consumer Economics, University Illinois, Urbana-Champaign, http://geodacenter.github.io/docs/geoda093.pdf; also material formerly spatial-econometrics.com/data/contents.html","code":""},{"path":"https://r-spatial.github.io/spdep/reference/read.gwt2nb.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Read and write spatial neighbour files — read.gwt2nb","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/read.gwt2nb.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Read and write spatial neighbour files — read.gwt2nb","text":"","code":"data(baltimore, package=\"spData\") STATION <- baltimore$STATION gwt1 <- read.gwt2nb(system.file(\"weights/baltk4.GWT\", package=\"spData\")[1],  STATION) #> Warning: 102, 115, 208 are not destinations cat(paste(\"Neighbours list symmetry;\", is.symmetric.nb(gwt1, FALSE, TRUE),  \"\\n\")) #> Neighbours list symmetry; FALSE  listw1 <- nb2listw(gwt1, style=\"B\", glist=attr(gwt1, \"GeoDa\")$dist) tmpGWT <- tempfile() write.sn2gwt(listw2sn(listw1), tmpGWT) gwt2 <- read.gwt2nb(tmpGWT, STATION) #> Warning: 102, 115, 208 are not destinations cat(paste(\"Neighbours list symmetry;\", is.symmetric.nb(gwt2, FALSE, TRUE),  \"\\n\")) #> Neighbours list symmetry; FALSE  diffnb(gwt1, gwt2) #> Warning: neighbour object has 211 sub-graphs #> Neighbour list object: #> Number of regions: 211  #> Number of nonzero links: 0  #> Percentage nonzero weights: 0  #> Average number of links: 0  #> 211 regions with no links: #> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, #> 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, #> 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, #> 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, #> 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, #> 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, #> 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, #> 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, #> 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, #> 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, #> 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, #> 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, #> 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, #> 206, 207, 208, 209, 210, 211 #> 211 disjoint connected subgraphs data(oldcol) tmpMAT <- tempfile() COL.W <- nb2listw(COL.nb) write.sn2dat(listw2sn(COL.W), tmpMAT) listwmat1 <- read.dat2listw(tmpMAT) #> Warning: style is M (missing); style should be set to a valid value diffnb(listwmat1$neighbours, COL.nb, verbose=TRUE) #> Warning: region.id differ; using ids of first list #> Warning: neighbour object has 49 sub-graphs #> Neighbour list object: #> Number of regions: 49  #> Number of nonzero links: 0  #> Percentage nonzero weights: 0  #> Average number of links: 0  #> 49 regions with no links: #> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, #> 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, #> 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49 #> 49 disjoint connected subgraphs listwmat2 <- read.dat2listw(system.file(\"etc/weights/wmat.dat\",   package=\"spdep\")[1]) #> Warning: style is M (missing); style should be set to a valid value diffnb(listwmat1$neighbours, listwmat2$neighbours, verbose=TRUE) #> Warning: neighbour object has 49 sub-graphs #> Neighbour list object: #> Number of regions: 49  #> Number of nonzero links: 0  #> Percentage nonzero weights: 0  #> Average number of links: 0  #> 49 regions with no links: #> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, #> 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, #> 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49 #> 49 disjoint connected subgraphs if (require(\"foreign\", quietly=TRUE)) { nc_sf <- sf::st_read(system.file(\"gpkg/nc.gpkg\", package=\"sf\")[1]) nc_sf$UniqueID <- 1:nrow(nc_sf) fn <- system.file(\"etc/misc/nc_contiguity_unique_id.dbf\", package=\"spdep\")[1] nc1 <- read.swmdbf2listw(fn, style=\"B\") nc1 nc1a <- read.swmdbf2listw(fn, region.id=as.character(nc_sf$UniqueID),  style=\"B\") all.equal(nc1, nc1a) fn <- system.file(\"etc/misc/nc_contiguity_unique_id_islands.dbf\",  package=\"spdep\")[1] try(nc1i <- read.swmdbf2listw(fn, style=\"B\")) nc1i <- read.swmdbf2listw(fn, style=\"B\", zero.policy=TRUE) nc1ia <- read.swmdbf2listw(fn, region.id=as.character(nc_sf$UniqueID),  style=\"B\", zero.policy=TRUE) nc1ia all.equal(nc1i, nc1ia) (GDAL37 <- as.numeric_version(unname(sf_extSoftVersion()[\"GDAL\"])) >= \"3.7.0\") file <- \"etc/shapes/california.gpkg.zip\" zipfile <- system.file(file, package=\"spdep\") if (GDAL37) {     cal <- st_read(zipfile) } else {     td <- tempdir()     bn <- sub(\".zip\", \"\", basename(file), fixed=TRUE)     target <- unzip(zipfile, files=bn, exdir=td)     cal <- st_read(target) } fn <- system.file(\"etc/misc/contiguity_myid.dbf\", package=\"spdep\")[1] cal1 <- read.swmdbf2listw(fn, style=\"B\") cal1a <- read.swmdbf2listw(fn, region.id=as.character(cal$MYID), style=\"B\") all.equal(cal1, cal1a) fn <- system.file(\"etc/misc/contiguity_unique_id.dbf\", package=\"spdep\")[1] cal2 <- read.swmdbf2listw(fn, style=\"B\") cal2a <- read.swmdbf2listw(fn, region.id=as.character(cal$UniqueID), style=\"B\") all.equal(cal2, cal2a) fn <- system.file(\"etc/misc/contiguity_unique_id_islands.dbf\", package=\"spdep\")[1] try(cal3i <- read.swmdbf2listw(fn, style=\"B\")) cal3i <- read.swmdbf2listw(fn, style=\"B\", zero.policy=TRUE) cal3ia <- read.swmdbf2listw(fn, region.id=as.character(cal$UniqueID), style=\"B\", zero.policy=TRUE) all.equal(cal3i, cal3ia) cal1a_1n_nb <- cal1a$neighbours cal1a_1n_nb <- droplinks(cal1a_1n_nb, drop=c(\"158\", \"180\", \"215\"), sym=TRUE) cal1a_1n <- nb2listw(cal1a_1n_nb, style=\"B\", zero.policy=TRUE) cal1a_1n_sn <- listw2sn(cal1a_1n) file <- tempfile(fileext=\".dbf\") write.sn2DBF(cal1a_1n_sn, file) cal1a_1n_rt <- read.swmdbf2listw(file, region.id=as.character(cal$MYID),  style=\"B\", zero.policy=TRUE) all.equal(cal1a_1n$neighbours, cal1a_1n_rt$neighbours) all.equal(cal1a_1n$weights, cal1a_1n_rt$weights, check.attributes=FALSE) cal1_1n_rt <- read.swmdbf2listw(file, style=\"B\", zero.policy=TRUE) all(isTRUE(all.equal(cal1a_1n$neighbours, cal1_1n_rt$neighbours))) all(isTRUE(all.equal(cal1a_1n$weights, cal1_1n_rt$weights)))  } #> Reading layer `nc.gpkg' from data source `/home/rsb/lib/r_libs/sf/gpkg/nc.gpkg' using driver `GPKG' #> Simple feature collection with 100 features and 14 fields #> Geometry type: MULTIPOLYGON #> Dimension:     XY #> Bounding box:  xmin: -84.32385 ymin: 33.88199 xmax: -75.45698 ymax: 36.58965 #> Geodetic CRS:  NAD27 #> Warning: region.id not given, c(MYID, NID) range is 1:100 #> Warning: region.id not given, c(MYID, NID) range is 1:100 #> Warning: 81 is not an origin #> Error in read.swmdbf2listw(fn, style = \"B\") :  #>   Error in sn2listw(df1, style = style, zero.policy = zero.policy) :  #>   no-neighbour observations found, set zero.policy to TRUE #>  #> Warning: region.id not given, c(MYID, NID) range is 1:100 #> Reading layer `california' from data source  #>   `/tmp/RtmpzEChJG/temp_libpath8ee3b7c361c1e/spdep/etc/shapes/california.gpkg.zip'  #>   using driver `GPKG' #> Simple feature collection with 58 features and 2 fields #> Geometry type: MULTIPOLYGON #> Dimension:     XY #> Bounding box:  xmin: -13847330 ymin: 3810869 xmax: -12704360 ymax: 5132708 #> Projected CRS: World_Mercator #> Warning: region.id not given, c(MYID, NID) range is 158:215 #> Warning: region.id not given, c(MYID, NID) range is 1:58 #> Warning: region.id not given, c(MYID, NID) range is 1:58 #> Warning: 21, 38 are not origins #> Error in read.swmdbf2listw(fn, style = \"B\") :  #>   Error in sn2listw(df1, style = style, zero.policy = zero.policy) :  #>   no-neighbour observations found, set zero.policy to TRUE #>  #> Warning: region.id not given, c(MYID, NID) range is 1:58 #> Warning: some observations have no neighbours #> Warning: neighbour object has 4 sub-graphs #> Warning: neighbour object has 4 sub-graphs #> Warning: region.id not given, c(MYID, NID) range is 159:214 #> Warning: neighbour object has 2 sub-graphs #> [1] FALSE"},{"path":"https://r-spatial.github.io/spdep/reference/rotation.html","id":null,"dir":"Reference","previous_headings":"","what":"Rotate a set of point by a certain angle — Rotation","title":"Rotate a set of point by a certain angle — Rotation","text":"Rotate set XY coordinates angle (radians)","code":""},{"path":"https://r-spatial.github.io/spdep/reference/rotation.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Rotate a set of point by a certain angle — Rotation","text":"","code":"Rotation(xy, angle)"},{"path":"https://r-spatial.github.io/spdep/reference/rotation.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Rotate a set of point by a certain angle — Rotation","text":"xy 2-columns matrix data frame containing set X Y coordinates. angle Numeric. scalar giving angle points rotated. angle radians.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/rotation.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Rotate a set of point by a certain angle — Rotation","text":"2-columns matrix size xy giving rotated coordinates.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/rotation.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Rotate a set of point by a certain angle — Rotation","text":"F. Guillaume Blanchet","code":""},{"path":"https://r-spatial.github.io/spdep/reference/rotation.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Rotate a set of point by a certain angle — Rotation","text":"","code":"set.seed(1) ### Create a set of coordinates coords <- cbind(runif(20), runif(20))  ### Create a series of angles rad <- seq(0, pi, l=20)  opar <- par(mfrow=c(5,4), mar=c(3,3,1,1)) for(i in rad){   coords.rot <- Rotation(coords, i)   plot(coords.rot, xlab=\"\", ylab=\"\") }  par(opar)  ### Rotate the coordinates by an angle of 90 degrees coords.90 <- Rotation(coords, 90*pi/180) coords.90 #>              [,1]       [,2] #>  [1,] -0.93470523 0.26550866 #>  [2,] -0.21214252 0.37212390 #>  [3,] -0.65167377 0.57285336 #>  [4,] -0.12555510 0.90820779 #>  [5,] -0.26722067 0.20168193 #>  [6,] -0.38611409 0.89838968 #>  [7,] -0.01339033 0.94467527 #>  [8,] -0.38238796 0.66079779 #>  [9,] -0.86969085 0.62911404 #> [10,] -0.34034900 0.06178627 #> [11,] -0.48208012 0.20597457 #> [12,] -0.59956583 0.17655675 #> [13,] -0.49354131 0.68702285 #> [14,] -0.18621760 0.38410372 #> [15,] -0.82737332 0.76984142 #> [16,] -0.66846674 0.49769924 #> [17,] -0.79423986 0.71761851 #> [18,] -0.10794363 0.99190609 #> [19,] -0.72371095 0.38003518 #> [20,] -0.41127443 0.77744522  plot(coords, xlim=range(rbind(coords.90,coords)[,1]),  ylim=range(rbind(coords.90,coords)[,2]), asp=1) points(coords.90, pch=19)"},{"path":"https://r-spatial.github.io/spdep/reference/set.mcOption.html","id":null,"dir":"Reference","previous_headings":"","what":"Options for parallel support — set.mcOption","title":"Options for parallel support — set.mcOption","text":"Provides support use parallel computation parallel package.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/set.mcOption.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Options for parallel support — set.mcOption","text":"","code":"set.mcOption(value) get.mcOption() set.coresOption(value) get.coresOption() set.ClusterOption(cl) get.ClusterOption()"},{"path":"https://r-spatial.github.io/spdep/reference/set.mcOption.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Options for parallel support — set.mcOption","text":"value valid replacement value cl cluster object created makeCluster parallel","code":""},{"path":"https://r-spatial.github.io/spdep/reference/set.mcOption.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Options for parallel support — set.mcOption","text":"Options spdep package held environment local package namespace exported. Option values set retrieved pairs access functions, get set. mc option set default FALSE Windows systems, fork R session; default TRUE systems, may set FALSE. mc FALSE, Cluster option used: mc FALSE Cluster option NULL parallel computing done, Cluster option passed “cluster” object created parallel snow package access without passed argument. cores option set NULL default, can used store number cores use integer. cores NULL, facilities parallel package used.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/set.mcOption.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Options for parallel support — set.mcOption","text":"option access functions return current settings, assignment functions usually return previous value option.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/set.mcOption.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Options for parallel support — set.mcOption","text":"extended example shown documentation aple.mc, including treatment seeding RNG multicore/cluster.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/set.mcOption.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Options for parallel support — set.mcOption","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/set.mcOption.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Options for parallel support — set.mcOption","text":"","code":"ls(envir=spdep:::.spdepOptions) #>  [1] \"cluster\"                \"cores\"                  \"listw_is_CsparseMatrix\" #>  [4] \"mc\"                     \"nb_subgraphs_N+E\"       \"report_nb_noneighs\"     #>  [7] \"report_nb_subgraphs\"    \"rlecuyerSeed\"           \"spChkID\"                #> [10] \"verbose\"                \"zeroPolicy\"             if (require(parallel, quietly=TRUE)) {  nc <- max(2L, detectCores(logical=FALSE), na.rm = TRUE)-1L  nc # set nc to 1L here  if (nc > 1L) nc <- 1L #nc <- ifelse(nc > 2L, 2L, nc)  coresOpt <- get.coresOption()  coresOpt  if (!is.na(nc)) {   invisible(set.coresOption(nc))   print(exists(\"moran.mc\"))   if(.Platform$OS.type == \"windows\") { # forking not permitted on Windows - start cluster    print(get.mcOption())    cl <- makeCluster(get.coresOption())    print(clusterEvalQ(cl, exists(\"moran.mc\")))    set.ClusterOption(cl)    clusterEvalQ(get.ClusterOption(), library(spdep))    print(clusterEvalQ(cl, exists(\"moran.mc\")))    clusterEvalQ(get.ClusterOption(), detach(package:spdep))    set.ClusterOption(NULL)    print(clusterEvalQ(cl, exists(\"moran.mc\")))    stopCluster(cl)   } else {    mcOpt <- get.mcOption()    print(mcOpt)    print(mclapply(1:get.coresOption(), function(i) exists(\"moran.mc\"),     mc.cores=get.coresOption()))    invisible(set.mcOption(FALSE))    cl <- makeCluster(nc)    print(clusterEvalQ(cl, exists(\"moran.mc\")))    set.ClusterOption(cl)    clusterEvalQ(get.ClusterOption(), library(spdep))    print(clusterEvalQ(cl, exists(\"moran.mc\")))    clusterEvalQ(get.ClusterOption(), detach(package:spdep))    set.ClusterOption(NULL)    print(clusterEvalQ(cl, exists(\"moran.mc\")))    stopCluster(cl)    invisible(set.mcOption(mcOpt))   }   invisible(set.coresOption(coresOpt))  } } #> [1] TRUE #> [1] TRUE #> [[1]] #> [1] TRUE #>  #> [[1]] #> [1] FALSE #>  #> [[1]] #> [1] TRUE #>  #> [[1]] #> [1] FALSE #>"},{"path":"https://r-spatial.github.io/spdep/reference/set.spChkOption.html","id":null,"dir":"Reference","previous_headings":"","what":"Control checking of spatial object IDs — set.spChkOption","title":"Control checking of spatial object IDs — set.spChkOption","text":"Provides support checking mutual integrity spatial neighbour weights spatial data; similar mechanisms used passing global verbose zero.policy options, causing functions creating neighbour objects warn multiple subgraphs.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/set.spChkOption.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Control checking of spatial object IDs — set.spChkOption","text":"","code":"set.spChkOption(check) get.spChkOption() chkIDs(x, listw) spNamedVec(var, data) set.VerboseOption(check) get.VerboseOption() set.ZeroPolicyOption(check) get.ZeroPolicyOption() set.SubgraphOption(check) get.SubgraphOption() set.SubgraphCeiling(value) get.SubgraphCeiling() set.NoNeighbourOption(check) get.NoNeighbourOption() set.listw_is_CsparseMatrix_Option(check) get.listw_is_CsparseMatrix_Option()"},{"path":"https://r-spatial.github.io/spdep/reference/set.spChkOption.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Control checking of spatial object IDs — set.spChkOption","text":"check logical value, TRUE FALSE value integer value, initialised 100000L, sum numbers nodes edges neighbour graph x vector length, two-dimensional array, data frame number rows neighbours list listw listw listw object nb object inheriting \"nb\" var character string integer value column selected data two-dimensional array data frame containing var","code":""},{"path":"https://r-spatial.github.io/spdep/reference/set.spChkOption.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Control checking of spatial object IDs — set.spChkOption","text":"Analysis functions spChk argument default set NULL, call get.spChkOption() get global spatial option whether check — initialised FALSE, consequently break anything. can changed TRUE using set.spChkOption(TRUE), spChk argument can assigned analysis functions. spNamedVec() provided ensure rownames passed single columns taken two-dimensional arrays data frames.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/set.spChkOption.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Control checking of spatial object IDs — set.spChkOption","text":"set.spChkOption() returns old logical value, get.spChkOption() returns current logical value, chkIDs() returns logical value test lack difference. spNamedVec() returns selected column names set row names object extracted.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/set.spChkOption.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Control checking of spatial object IDs — set.spChkOption","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/set.spChkOption.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Control checking of spatial object IDs — set.spChkOption","text":"motivation mechanism provided observation spatial objects map attribute data values need linked uniquely, avoid spurious results. reordering legacy Columbus data set used earlier publications available download Spacestat website just one example common problem.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/set.spChkOption.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Control checking of spatial object IDs — set.spChkOption","text":"","code":"data(oldcol) rownames(COL.OLD) #>  [1] \"1001\" \"1002\" \"1003\" \"1004\" \"1005\" \"1006\" \"1007\" \"1008\" \"1009\" \"1010\" #> [11] \"1011\" \"1012\" \"1013\" \"1014\" \"1015\" \"1016\" \"1017\" \"1018\" \"1019\" \"1020\" #> [21] \"1021\" \"1022\" \"1023\" \"1024\" \"1025\" \"1026\" \"1027\" \"1028\" \"1029\" \"1030\" #> [31] \"1031\" \"1032\" \"1033\" \"1034\" \"1035\" \"1036\" \"1037\" \"1038\" \"1039\" \"1040\" #> [41] \"1041\" \"1042\" \"1043\" \"1044\" \"1045\" \"1046\" \"1047\" \"1048\" \"1049\" data(columbus, package=\"spData\") rownames(columbus) #>  [1] \"1005\" \"1001\" \"1006\" \"1002\" \"1007\" \"1008\" \"1004\" \"1003\" \"1018\" \"1010\" #> [11] \"1038\" \"1037\" \"1039\" \"1040\" \"1009\" \"1036\" \"1011\" \"1042\" \"1041\" \"1017\" #> [21] \"1043\" \"1019\" \"1012\" \"1035\" \"1032\" \"1020\" \"1021\" \"1031\" \"1033\" \"1034\" #> [31] \"1045\" \"1013\" \"1022\" \"1044\" \"1023\" \"1046\" \"1030\" \"1024\" \"1047\" \"1016\" #> [41] \"1014\" \"1049\" \"1029\" \"1025\" \"1028\" \"1048\" \"1015\" \"1027\" \"1026\" get.spChkOption() #> [1] FALSE oldChk <- set.spChkOption(TRUE) get.spChkOption() #> [1] TRUE chkIDs(COL.OLD, nb2listw(COL.nb)) #> [1] TRUE chkIDs(columbus, nb2listw(col.gal.nb)) #> [1] TRUE chkIDs(columbus, nb2listw(COL.nb)) #> [1] FALSE tmp <- try(moran.test(spNamedVec(\"CRIME\", COL.OLD), nb2listw(COL.nb))) print(tmp) #>  #> \tMoran I test under randomisation #>  #> data:  spNamedVec(\"CRIME\", COL.OLD)   #> weights: nb2listw(COL.nb)     #>  #> Moran I statistic standard deviate = 5.6341, p-value = 8.797e-09 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic       Expectation          Variance  #>       0.510951264      -0.020833333       0.008908762  #>  tmp <- try(moran.test(spNamedVec(\"CRIME\", columbus), nb2listw(col.gal.nb))) print(tmp) #>  #> \tMoran I test under randomisation #>  #> data:  spNamedVec(\"CRIME\", columbus)   #> weights: nb2listw(col.gal.nb)     #>  #> Moran I statistic standard deviate = 5.3427, p-value = 4.578e-08 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic       Expectation          Variance  #>       0.485770914      -0.020833333       0.008991121  #>  tmp <- try(moran.test(spNamedVec(\"CRIME\", columbus), nb2listw(COL.nb))) #> Error in moran.test(spNamedVec(\"CRIME\", columbus), nb2listw(COL.nb)) :  #>   Check of data and weights ID integrity failed print(tmp) #> [1] \"Error in moran.test(spNamedVec(\\\"CRIME\\\", columbus), nb2listw(COL.nb)) : \\n  Check of data and weights ID integrity failed\\n\" #> attr(,\"class\") #> [1] \"try-error\" #> attr(,\"condition\") #> <simpleError in moran.test(spNamedVec(\"CRIME\", columbus), nb2listw(COL.nb)): Check of data and weights ID integrity failed> set.spChkOption(FALSE) get.spChkOption() #> [1] FALSE moran.test(spNamedVec(\"CRIME\", columbus), nb2listw(COL.nb)) #>  #> \tMoran I test under randomisation #>  #> data:  spNamedVec(\"CRIME\", columbus)   #> weights: nb2listw(COL.nb)     #>  #> Moran I statistic standard deviate = 3.8402, p-value = 6.147e-05 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic       Expectation          Variance  #>       0.341628707      -0.020833333       0.008908762  #>  tmp <- try(moran.test(spNamedVec(\"CRIME\", columbus), nb2listw(COL.nb),  spChk=TRUE), silent=TRUE) print(tmp) #> [1] \"Error in moran.test(spNamedVec(\\\"CRIME\\\", columbus), nb2listw(COL.nb), spChk = TRUE) : \\n  Check of data and weights ID integrity failed\\n\" #> attr(,\"class\") #> [1] \"try-error\" #> attr(,\"condition\") #> <simpleError in moran.test(spNamedVec(\"CRIME\", columbus), nb2listw(COL.nb), spChk = TRUE): Check of data and weights ID integrity failed> set.spChkOption(oldChk) get.spChkOption() #> [1] FALSE"},{"path":"https://r-spatial.github.io/spdep/reference/skater.html","id":null,"dir":"Reference","previous_headings":"","what":"Spatial 'K'luster Analysis by Tree Edge Removal — skater","title":"Spatial 'K'luster Analysis by Tree Edge Removal — skater","text":"function implements SKATER procedure spatial clustering   analysis. procedure essentialy begins edges set, data set   number cuts. output object 'skater' class   valid input .","code":""},{"path":"https://r-spatial.github.io/spdep/reference/skater.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Spatial 'K'luster Analysis by Tree Edge Removal — skater","text":"","code":"skater(edges, data, ncuts, crit, vec.crit, method = c(\"euclidean\",      \"maximum\", \"manhattan\", \"canberra\", \"binary\", \"minkowski\",      \"mahalanobis\"), p = 2, cov, inverted = FALSE)"},{"path":"https://r-spatial.github.io/spdep/reference/skater.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Spatial 'K'luster Analysis by Tree Edge Removal — skater","text":"edges matrix 2 colums row edge data data.frame data observed nodes. ncuts number cuts crit scalar two dimensional vector     criteria groups. Examples: limits group size     limits population size. scalar, minimum     criteria groups. vec.crit vector evaluating criteria. method Character function declare distance method.     method character, method must \"mahalanobis\"     \"euclidean\", \"maximum\", \"manhattan\", \"canberra\", \"binary\"     \"minkowisk\".     method one \"euclidean\", \"maximum\",     \"manhattan\", \"canberra\", \"binary\" \"minkowski\", see     dist details,      function used compute distance.      method=\"mahalanobis\", mahalanobis distance      computed neighbour areas.      method function, function      used compute distance. p power Minkowski distance. cov covariance matrix used compute mahalanobis    distance. inverted logical.  'TRUE', 'cov' supposed contain           inverse covariance matrix.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/skater.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Spatial 'K'luster Analysis by Tree Edge Removal — skater","text":"object skater class :  groups vector length equal number nodes.     position identifies group node edges.groups list length equal number groups     element set edges .prune vector identifying groups     candidates partition. candidates vector identifying groups candidates     partition. ssto total dissimilarity step edge removal.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/skater.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Spatial 'K'luster Analysis by Tree Edge Removal — skater","text":"Assuncao, R.M., Lage J.P., Reis, E.. (2002). Analise de   conglomerados espaciais via arvore geradora minima. Revista Brasileira   de Estatistica, 62, 1-23. Assuncao, R. M, Neves, M. C., Camara, G. Freitas, C. da   C. (2006). Efficient regionalization techniques socio-economic   geographical units using minimum spanning trees. International Journal   Geographical Information Science Vol. 20, . 7, August 2006,   797-811","code":""},{"path":"https://r-spatial.github.io/spdep/reference/skater.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Spatial 'K'luster Analysis by Tree Edge Removal — skater","text":"Renato M. Assuncao Elias T. Krainski","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/skater.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Spatial 'K'luster Analysis by Tree Edge Removal — skater","text":"","code":"### loading data (GDAL37 <- as.numeric_version(unname(sf_extSoftVersion()[\"GDAL\"])) >= \"3.7.0\") #> [1] TRUE file <- \"etc/shapes/bhicv.gpkg.zip\" zipfile <- system.file(file, package=\"spdep\") if (GDAL37) {     bh <- st_read(zipfile) } else {     td <- tempdir()     bn <- sub(\".zip\", \"\", basename(file), fixed=TRUE)     target <- unzip(zipfile, files=bn, exdir=td)     bh <- st_read(target) } #> Reading layer `bhicv' from data source  #>   `/tmp/RtmpzEChJG/temp_libpath8ee3b7c361c1e/spdep/etc/shapes/bhicv.gpkg.zip'  #>   using driver `GPKG' #> Simple feature collection with 98 features and 8 fields #> Geometry type: POLYGON #> Dimension:     XY #> Bounding box:  xmin: -45.02175 ymin: -20.93007 xmax: -42.50321 ymax: -18.08342 #> Geodetic CRS:  Corrego Alegre 1970-72 ### data standardized  dim(bh) #> [1] 98  9 dpad <- data.frame(scale(as.data.frame(bh)[,5:8]))  ### neighboorhod list bh.nb <- poly2nb(bh) bh.nb #> Neighbour list object: #> Number of regions: 98  #> Number of nonzero links: 508  #> Percentage nonzero weights: 5.289463  #> Average number of links: 5.183673   ### calculating costs lcosts <- nbcosts(bh.nb, dpad) head(lcosts) #> [[1]] #>  [1] 1.5418355 2.5253558 1.4738620 1.8462822 1.7089412 1.5613667 1.0279919 #>  [8] 0.6334314 1.9029531 2.5816759 #>  #> [[2]] #> [1] 1.0847913 1.7723275 0.7940341 #>  #> [[3]] #> [1] 1.257984 2.634043 0.847224 1.807124 #>  #> [[4]] #> [1] 1.2579836 1.0548805 0.7862035 #>  #> [[5]] #> [1] 1.541835 1.295112 2.206320 #>  #> [[6]] #> [1] 0.9981915 1.3801441 1.5225548 1.3606678 0.9775650 #>   ### making listw nb.w <- nb2listw(bh.nb, lcosts, style=\"B\") nb.w #> Characteristics of weights list object: #> Neighbour list object: #> Number of regions: 98  #> Number of nonzero links: 508  #> Percentage nonzero weights: 5.289463  #> Average number of links: 5.183673  #>  #> Weights style: B  #> Weights constants summary: #>    n   nn       S0       S1       S2 #> B 98 9604 1027.424 5192.868 55983.97  ### find a minimum spanning tree mst.bh <- mstree(nb.w,5) str(mst.bh) #>  'mst' num [1:97, 1:3] 5 12 13 13 11 31 39 40 31 40 ...  ### the mstree plot par(mar=c(0,0,0,0)) plot(st_geometry(bh), border=gray(.5)) pts <- st_coordinates(st_centroid(bh)) #> Warning: st_centroid assumes attributes are constant over geometries plot(mst.bh, pts, col=2,       cex.lab=.6, cex.circles=0.035, fg=\"blue\", add=TRUE)  ### three groups with no restriction res1 <- skater(mst.bh[,1:2], dpad, 2)  ### groups size table(res1$groups) #>  #>  1  2  3  #> 18 23 57   ### the skater plot opar <- par(mar=c(0,0,0,0)) plot(res1, pts, cex.circles=0.035, cex.lab=.7)   ### the skater plot, using other colors plot(res1, pts, cex.circles=0.035, cex.lab=.7,      groups.colors=heat.colors(length(res1$ed)))   ### the Spatial Polygons plot plot(st_geometry(bh), col=heat.colors(length(res1$edg))[res1$groups])   #par(opar) ### EXPERT OPTIONS  ### more one partition res1b <- skater(res1, dpad, 1)  ### length groups frequency table(res1$groups) #>  #>  1  2  3  #> 18 23 57   table(res1b$groups) #>  #>  1  2  3  4  #> 18 23 55  2   ### thee groups with minimum population  res2 <- skater(mst.bh[,1:2], dpad, 2, 200000, bh$Pop) table(res2$groups) #>  #>  1  2  3  #> 22 37 39   ### thee groups with minimun number of areas res3 <- skater(mst.bh[,1:2], dpad, 2, 3, rep(1,nrow(bh))) table(res3$groups) #>  #>  1  2  3  #> 18 23 57   ### thee groups with minimun and maximun number of areas res4 <- skater(mst.bh[,1:2], dpad, 2, c(20,50), rep(1,nrow(bh))) table(res4$groups) #>  #>  1  2  3  #> 50 24 24   ### if I want to get groups with 20 to 40 elements res5 <- skater(mst.bh[,1:2], dpad, 2,    c(20,40), rep(1,nrow(bh))) ## DON'T MAKE DIVISIONS  table(res5$groups) #>  #>  1  #> 98   ### In this MST don't have groups with this restrictions ### In this case, first I do one division ### with the minimun criteria res5a <- skater(mst.bh[,1:2], dpad, 1, 20, rep(1,nrow(bh)))  table(res5a$groups) #>  #>  1  2  #> 75 23   ### and do more one division with the full criteria res5b <- skater(res5a, dpad, 1, c(20, 40), rep(1,nrow(bh))) table(res5b$groups) #>  #>  1  2  3  #> 22 23 53   ### and do more one division with the full criteria res5c <- skater(res5b, dpad, 1, c(20, 40), rep(1,nrow(bh))) table(res5c$groups) #>  #>  1  2  3  4  #> 22 23 33 20   ### It don't have another divison with this criteria res5d <- skater(res5c, dpad, 1, c(20, 40), rep(1,nrow(bh))) table(res5d$groups) #>  #>  1  2  3  4  #> 22 23 33 20   # \\dontrun{ data(boston, package=\"spData\") bh.nb <- boston.soi dpad <- data.frame(scale(boston.c[,c(7:10)])) ### calculating costs system.time(lcosts <- nbcosts(bh.nb, dpad)) #>    user  system elapsed  #>   0.047   0.000   0.047  ### making listw nb.w <- nb2listw(bh.nb, lcosts, style=\"B\") ### find a minimum spanning tree mst.bh <- mstree(nb.w,5) ### three groups with no restriction system.time(res1 <- skater(mst.bh[,1:2], dpad, 2)) #>    user  system elapsed  #>   1.743   0.177   1.929  library(parallel) nc <- max(2L, detectCores(logical=FALSE), na.rm = TRUE)-1L # set nc to 1L here if (nc > 1L) nc <- 1L coresOpt <- get.coresOption() invisible(set.coresOption(nc)) if(!get.mcOption()) { # no-op, \"snow\" parallel calculation not available   cl <- makeCluster(get.coresOption())   set.ClusterOption(cl) } ### calculating costs system.time(plcosts <- nbcosts(bh.nb, dpad)) #>    user  system elapsed  #>   0.047   0.000   0.048  all.equal(lcosts, plcosts, check.attributes=FALSE) #> [1] TRUE ### making listw pnb.w <- nb2listw(bh.nb, plcosts, style=\"B\") ### find a minimum spanning tree pmst.bh <- mstree(pnb.w,5) ### three groups with no restriction system.time(pres1 <- skater(pmst.bh[,1:2], dpad, 2)) #>    user  system elapsed  #>   1.764   0.192   1.964  if(!get.mcOption()) {   set.ClusterOption(NULL)   stopCluster(cl) } all.equal(res1, pres1, check.attributes=FALSE) #> [1] TRUE invisible(set.coresOption(coresOpt)) # }"},{"path":"https://r-spatial.github.io/spdep/reference/sp.correlogram.html","id":null,"dir":"Reference","previous_headings":"","what":"Spatial correlogram — sp.correlogram","title":"Spatial correlogram — sp.correlogram","text":"Spatial correlograms Moran's autocorrelation coefficient, print plot helper functions.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/sp.correlogram.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Spatial correlogram — sp.correlogram","text":"","code":"sp.correlogram(neighbours, var, order = 1, method = \"corr\",  style = \"W\", randomisation = TRUE, zero.policy = NULL, spChk=NULL) # S3 method for class 'spcor' plot(x, main, ylab, ylim, ...) # S3 method for class 'spcor' print(x, p.adj.method=\"none\", ...)"},{"path":"https://r-spatial.github.io/spdep/reference/sp.correlogram.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Spatial correlogram — sp.correlogram","text":"neighbours object class nb var numeric vector order maximum lag order method \"corr\" correlation, \"\" Moran's , \"C\" Geary's C style style can take values W, B, C, S randomisation variance C calculated assumption randomisation, FALSE normality zero.policy default NULL, use global option value; FALSE stop error empty neighbour sets, TRUE permit weights list formed zero-length weights vectors spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption() x object sp.correlogram() class spcor p.adj.method correction method p.adjust main overall title plot ylab title y axis ylim y limits plot ... arguments passed ","code":""},{"path":"https://r-spatial.github.io/spdep/reference/sp.correlogram.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Spatial correlogram — sp.correlogram","text":"print function also calculates standard deviates Moran's Geary's C two-sided probability value, optionally using p.adjust correct nymber lags. plot function plots bar estimated Moran's , Geary's C value +/- twice square root variance (previous releases , twice). table includes count included observations brackets lag order. Care needs shown interpreting results remaining included observations lag order increases.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/sp.correlogram.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Spatial correlogram — sp.correlogram","text":"returns list class spcor: res \"corr\" vector values; \"\", matrix estimates \"\", expectations, variances method \"\" \"corr\" cardnos list tables neighbour cardinalities lag orders used var variable name","code":""},{"path":"https://r-spatial.github.io/spdep/reference/sp.correlogram.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Spatial correlogram — sp.correlogram","text":"Cliff, . D., Ord, J. K. 1981 Spatial processes, Pion, pp. 118–122, Martin, R. L., Oeppen, J. E. 1975 identification regional forecasting models using space-time correlation functions, Transactions Institute British Geographers, 66, 95–118.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/sp.correlogram.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Spatial correlogram — sp.correlogram","text":"Roger Bivand, Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/sp.correlogram.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Spatial correlogram — sp.correlogram","text":"","code":"nc.sids <- st_read(system.file(\"shapes/sids.gpkg\", package=\"spData\")[1], quiet=TRUE) rn <- as.character(nc.sids$FIPS) ncCC89_nb <- read.gal(system.file(\"weights/ncCC89.gal\", package=\"spData\")[1],  region.id=rn) #> Warning: neighbour object has 3 sub-graphs ft.SID74 <- sqrt(1000)*(sqrt(nc.sids$SID74/nc.sids$BIR74) +   sqrt((nc.sids$SID74+1)/nc.sids$BIR74)) tr.SIDS74 <- ft.SID74*sqrt(nc.sids$BIR74) cspc <- sp.correlogram(ncCC89_nb, tr.SIDS74, order=8, method=\"corr\",  zero.policy=TRUE) #> Warning: lag 1 neighbour object has 3 sub-graphs #> Warning: lag 2 neighbour object has 3 sub-graphs #> Warning: lag 3 neighbour object has 3 sub-graphs #> Warning: lag 4 neighbour object has 3 sub-graphs #> Warning: lag 5 neighbour object has 3 sub-graphs #> Warning: lag 6 neighbour object has 3 sub-graphs #> Warning: lag 7 neighbour object has 3 sub-graphs #> Warning: lag 8 neighbour object has 3 sub-graphs print(cspc) #> Spatial correlogram for tr.SIDS74  #> method: Spatial autocorrelation #>           1           2           3           4           5           6  #>  0.38193491  0.47679881  0.11740653  0.09935901  0.27819159  0.30153012  #>           7           8  #> -0.05150923  0.05283813  plot(cspc)  Ispc <- sp.correlogram(ncCC89_nb, tr.SIDS74, order=8, method=\"I\",  zero.policy=TRUE) #> Warning: lag 1 neighbour object has 3 sub-graphs #> Warning: lag 2 neighbour object has 3 sub-graphs #> Warning: lag 3 neighbour object has 3 sub-graphs #> Warning: lag 4 neighbour object has 3 sub-graphs #> Warning: lag 5 neighbour object has 3 sub-graphs #> Warning: lag 6 neighbour object has 3 sub-graphs #> Warning: lag 7 neighbour object has 3 sub-graphs #> Warning: lag 8 neighbour object has 3 sub-graphs print(Ispc) #> Spatial correlogram for tr.SIDS74  #> method: Moran's I #>          estimate expectation   variance standard deviate Pr(I) two sided     #> 1 (98)  0.2311685  -0.0103093  0.0055378           3.2450       0.0011747 **  #> 2 (98)  0.2246930  -0.0103093  0.0037817           3.8214       0.0001327 *** #> 3 (98)  0.0193576  -0.0103093  0.0029386           0.5473       0.5841914     #> 4 (98)  0.0042255  -0.0103093  0.0024974           0.2908       0.7711687     #> 5 (98)  0.0875548  -0.0103093  0.0022875           2.0462       0.0407386 *   #> 6 (98)  0.0758362  -0.0103093  0.0021583           1.8543       0.0637011 .   #> 7 (98) -0.0752243  -0.0103093  0.0022282          -1.3752       0.1690654     #> 8 (98) -0.0261063  -0.0103093  0.0025211          -0.3146       0.7530514     #> --- #> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 print(Ispc, \"bonferroni\") #> Spatial correlogram for tr.SIDS74  #> method: Moran's I #>          estimate expectation   variance standard deviate Pr(I) two sided    #> 1 (98)  0.2311685  -0.0103093  0.0055378           3.2450        0.009397 ** #> 2 (98)  0.2246930  -0.0103093  0.0037817           3.8214        0.001061 ** #> 3 (98)  0.0193576  -0.0103093  0.0029386           0.5473        1.000000    #> 4 (98)  0.0042255  -0.0103093  0.0024974           0.2908        1.000000    #> 5 (98)  0.0875548  -0.0103093  0.0022875           2.0462        0.325909    #> 6 (98)  0.0758362  -0.0103093  0.0021583           1.8543        0.509609    #> 7 (98) -0.0752243  -0.0103093  0.0022282          -1.3752        1.000000    #> 8 (98) -0.0261063  -0.0103093  0.0025211          -0.3146        1.000000    #> --- #> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 plot(Ispc)  Cspc <- sp.correlogram(ncCC89_nb, tr.SIDS74, order=8, method=\"C\",  zero.policy=TRUE) #> Warning: lag 1 neighbour object has 3 sub-graphs #> Warning: lag 2 neighbour object has 3 sub-graphs #> Warning: lag 3 neighbour object has 3 sub-graphs #> Warning: lag 4 neighbour object has 3 sub-graphs #> Warning: lag 5 neighbour object has 3 sub-graphs #> Warning: lag 6 neighbour object has 3 sub-graphs #> Warning: lag 7 neighbour object has 3 sub-graphs #> Warning: lag 8 neighbour object has 3 sub-graphs print(Cspc) #> Spatial correlogram for tr.SIDS74  #> method: Geary's C #>         estimate expectation  variance standard deviate Pr(I) two sided     #> 1 (98) 0.7172624   1.0000000 0.0059986          -3.6506       0.0002617 *** #> 2 (98) 0.6817819   1.0000000 0.0046785          -4.6523       3.282e-06 *** #> 3 (98) 0.9470179   1.0000000 0.0044311          -0.7959       0.4260762     #> 4 (98) 1.0016202   1.0000000 0.0041985           0.0250       0.9800516     #> 5 (98) 0.8977501   1.0000000 0.0038054          -1.6575       0.0974119 .   #> 6 (98) 0.9173310   1.0000000 0.0036428          -1.3697       0.1707819     #> 7 (98) 1.0527148   1.0000000 0.0037227           0.8640       0.3875979     #> 8 (98) 1.0067939   1.0000000 0.0036482           0.1125       0.9104415     #> --- #> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 print(Cspc, \"bonferroni\") #> Spatial correlogram for tr.SIDS74  #> method: Geary's C #>         estimate expectation  variance standard deviate Pr(I) two sided     #> 1 (98) 0.7172624   1.0000000 0.0059986          -3.6506        0.002093 **  #> 2 (98) 0.6817819   1.0000000 0.0046785          -4.6523       2.626e-05 *** #> 3 (98) 0.9470179   1.0000000 0.0044311          -0.7959        1.000000     #> 4 (98) 1.0016202   1.0000000 0.0041985           0.0250        1.000000     #> 5 (98) 0.8977501   1.0000000 0.0038054          -1.6575        0.779295     #> 6 (98) 0.9173310   1.0000000 0.0036428          -1.3697        1.000000     #> 7 (98) 1.0527148   1.0000000 0.0037227           0.8640        1.000000     #> 8 (98) 1.0067939   1.0000000 0.0036482           0.1125        1.000000     #> --- #> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 plot(Cspc)  drop.no.neighs <- !(1:length(ncCC89_nb) %in% which(card(ncCC89_nb) == 0)) sub.ncCC89.nb <- subset(ncCC89_nb, drop.no.neighs) plot(sp.correlogram(sub.ncCC89.nb, subset(tr.SIDS74,  drop.no.neighs),  order=8, method=\"corr\"))"},{"path":"https://r-spatial.github.io/spdep/reference/sp.mantel.mc.html","id":null,"dir":"Reference","previous_headings":"","what":"Mantel-Hubert spatial general cross product statistic — sp.mantel.mc","title":"Mantel-Hubert spatial general cross product statistic — sp.mantel.mc","text":"permutation test spatial general cross product statistic Moran (\\(C_{ij} = z_i z_j\\)), Geary (\\(C_{ij} = (z_i - z_j)^2\\)), Sokal (\\(C_{ij} = |z_i - z_j|\\)) criteria, \\(z_i = (x_i - \\bar{x}) / \\sigma_{x}\\). plot.mc.sim helper function plot outcomes permutation test.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/sp.mantel.mc.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Mantel-Hubert spatial general cross product statistic — sp.mantel.mc","text":"","code":"sp.mantel.mc(var, listw, nsim, type = \"moran\", zero.policy = attr(listw, \"zero.policy\"),  alternative = \"greater\", spChk=NULL, return_boot=FALSE) # S3 method for class 'mc.sim' plot(x, xlim, xlab, main, sub, ..., ptype=\"density\")"},{"path":"https://r-spatial.github.io/spdep/reference/sp.mantel.mc.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Mantel-Hubert spatial general cross product statistic — sp.mantel.mc","text":"var numeric vector length neighbours list listw listw listw object created example nb2listw nsim number permutations type \"moran\", \"geary\" \"sokal\" criteria similarity zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without   neighbours, FALSE assign NA alternative character string specifying alternative hypothesis,   must one \"greater\" (default), \"two.sided\", \"less\". spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption() return_boot return object class boot equivalent permutation bootstrap rather object class htest x object plotted xlim range x axis xlab title x axis main overall title plot sub sub title plot ptype either \"density\" \"hist\" ... arguments passed ","code":""},{"path":"https://r-spatial.github.io/spdep/reference/sp.mantel.mc.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Mantel-Hubert spatial general cross product statistic — sp.mantel.mc","text":"list class htest mc.sim containing following components: statistic value observed Geary's C. parameter rank observed Geary's C. alternative character string describing alternative hypothesis. method character string giving method used. data.name character string giving name(s) data,   number simulations. p.value pseudo p-value test. res nsim simulated values statistic, final value observed   statistic estimate mean variance simulated distribution.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/sp.mantel.mc.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Mantel-Hubert spatial general cross product statistic — sp.mantel.mc","text":"Cliff, . D., Ord, J. K. 1981 Spatial processes, Pion, p. 22-24, Haining, R. 1990 Spatial data analysis social environmental sciences, Cambridge: Cambridge University Press, p. 230–1. function checked general matrix code posted r-help list Ben Bolker 1 May 2001; another mantel() function vegan package.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/sp.mantel.mc.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Mantel-Hubert spatial general cross product statistic — sp.mantel.mc","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/sp.mantel.mc.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Mantel-Hubert spatial general cross product statistic — sp.mantel.mc","text":"","code":"data(oldcol) sim1 <- sp.mantel.mc(COL.OLD$CRIME, nb2listw(COL.nb),  nsim=99, type=\"geary\", alternative=\"two.sided\") sim1 #>  #> \tMantel permutation test for geary measure #>  #> data:  COL.OLD$CRIME  #> weights: nb2listw(COL.nb)  #> number of simulations + 1: 100  #>  #> statistic = 51.927, observed rank = 1, p-value = 0.02 #> alternative hypothesis: two.sided #> sample estimates: #> mean of permutations   sd of permutations  #>            98.852997             8.934135  #>  plot(sim1)  sp.mantel.mc(COL.OLD$CRIME, nb2listw(COL.nb), nsim=99,  type=\"sokal\", alternative=\"two.sided\") #>  #> \tMantel permutation test for sokal measure #>  #> data:  COL.OLD$CRIME  #> weights: nb2listw(COL.nb)  #> number of simulations + 1: 100  #>  #> statistic = 36.695, observed rank = 1, p-value = 0.02 #> alternative hypothesis: two.sided #> sample estimates: #> mean of permutations   sd of permutations  #>            56.418584             3.227064  #>  sp.mantel.mc(COL.OLD$CRIME, nb2listw(COL.nb), nsim=99,  type=\"moran\") #>  #> \tMantel permutation test for moran measure #>  #> data:  COL.OLD$CRIME  #> weights: nb2listw(COL.nb)  #> number of simulations + 1: 100  #>  #> statistic = 24.526, observed rank = 100, p-value = 0.01 #> alternative hypothesis: greater #> sample estimates: #> mean of permutations   sd of permutations  #>           -0.3401381            4.5579226  #>"},{"path":"https://r-spatial.github.io/spdep/reference/spdep-defunct.html","id":null,"dir":"Reference","previous_headings":"","what":"Defunct Functions in Package spdep — spdep-defunct","title":"Defunct Functions in Package spdep — spdep-defunct","text":"functions defunct release 1.2-1.   functions moved spatialreg package.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/spdep-defunct.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Defunct Functions in Package spdep — spdep-defunct","text":"","code":"aple.plot() localAple() aple.mc() aple() lextrB() lextrW() lextrS() griffith_sone() subgraph_eigenw() mom_calc() mom_calc_int2() stsls() # S3 method for class 'stsls' impacts() GMerrorsar() # S3 method for class 'gmsar' summary() gstsls()  # S3 method for class 'gmsar' impacts() # S3 method for class 'gmsar' Hausman.test() lagmess() ME() SpatialFiltering() LR.sarlm() # S3 method for class 'sarlm' logLik() LR1.sarlm() Wald1.sarlm() # S3 method for class 'sarlm' Hausman.test() as.spam.listw() as_dgRMatrix_listw() as_dsTMatrix_listw() as_dsCMatrix_I() as_dsCMatrix_IrW() Jacobian_W() powerWeights() # S3 method for class 'lagImpact' plot() # S3 method for class 'lagImpact' print() # S3 method for class 'lagImpact' summary() # S3 method for class 'lagImpact' HPDinterval() intImpacts() can.be.simmed() eigenw() similar.listw() do_ldet() jacobianSetup() cheb_setup() mcdet_setup() eigen_setup() eigen_pre_setup() spam_setup() spam_update_setup() Matrix_setup() Matrix_J_setup() LU_setup() LU_prepermutate_setup() moments_setup() SE_classic_setup() SE_whichMin_setup() SE_interp_setup() MCMCsamp() # S3 method for class 'spautolm' MCMCsamp() # S3 method for class 'sarlm' MCMCsamp() spautolm() # S3 method for class 'spautolm' summary() spBreg_sac() # S3 method for class 'MCMC_sar_g' impacts() # S3 method for class 'MCMC_sem_g' impacts() # S3 method for class 'MCMC_sac_g' impacts() spBreg_err() spBreg_lag() # S3 method for class 'SLX' predict() lmSLX() # S3 method for class 'SLX' impacts() create_WX() # S3 method for class 'sarlm' anova() bptest.sarlm() errorsarlm() # S3 method for class 'sarlm' impacts() lagsarlm() # S3 method for class 'sarlm' predict() # S3 method for class 'sarlm.pred' print() # S3 method for class 'sarlm.pred' as.data.frame() # S3 method for class 'sarlm' residuals() # S3 method for class 'sarlm' deviance() # S3 method for class 'sarlm' coef() # S3 method for class 'sarlm' vcov() # S3 method for class 'sarlm' fitted() sacsarlm() # S3 method for class 'sarlm' summary() # S3 method for class 'sarlm' print() # S3 method for class 'summary.sarlm' print() trW()"},{"path":"https://r-spatial.github.io/spdep/reference/spdep-defunct.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Defunct Functions in Package spdep — spdep-defunct","text":"Model-fitting functions functions supporting model fitting moved spatialreg package.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/spdep.html","id":null,"dir":"Reference","previous_headings":"","what":"Return package version number — spdep","title":"Return package version number — spdep","text":"function retreives package version build information","code":""},{"path":"https://r-spatial.github.io/spdep/reference/spdep.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Return package version number — spdep","text":"","code":"spdep(build = FALSE)"},{"path":"https://r-spatial.github.io/spdep/reference/spdep.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Return package version number — spdep","text":"build TRUE, also returns build information","code":""},{"path":"https://r-spatial.github.io/spdep/reference/spdep.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Return package version number — spdep","text":"character vector one two elements","code":""},{"path":"https://r-spatial.github.io/spdep/reference/spdep.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Return package version number — spdep","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/spweights.constants.html","id":null,"dir":"Reference","previous_headings":"","what":"Provides constants for spatial weights matrices — spweights.constants","title":"Provides constants for spatial weights matrices — spweights.constants","text":"function calculates constants needed tests spatial autocorrelation general weights matrices represented listw objects. Note: spdep 0.3-32, values S1 S2 returned correctly underlying symmetric asymmetric neighbour lists, 0.3-32, S1 S2 wrong listw objects based asymmetric neighbour lists, k-nearest neighbours (thanks Luc Anselin finding bug).","code":""},{"path":"https://r-spatial.github.io/spdep/reference/spweights.constants.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Provides constants for spatial weights matrices — spweights.constants","text":"","code":"spweights.constants(listw, zero.policy=attr(listw, \"zero.policy\"), adjust.n=TRUE) Szero(listw)"},{"path":"https://r-spatial.github.io/spdep/reference/spweights.constants.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Provides constants for spatial weights matrices — spweights.constants","text":"listw listw object example nb2listw zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE ignore zones without neighbours, FALSE fail encountered adjust.n default TRUE, FALSE number observations adjusted -neighbour observations, TRUE, number observations adjusted","code":""},{"path":"https://r-spatial.github.io/spdep/reference/spweights.constants.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Provides constants for spatial weights matrices — spweights.constants","text":"n number zones n1 n - 1 n2 n - 2 n3 n - 3 nn n * n S0 global sum weights S1 S1 sum weights S2 S2 sum weights","code":""},{"path":"https://r-spatial.github.io/spdep/reference/spweights.constants.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Provides constants for spatial weights matrices — spweights.constants","text":"Haining, R. 1990 Spatial data analysis social environmental sciences, Cambridge University Press, p. 233; Cliff, . D., Ord, J. K. 1981 Spatial processes, Pion, p. 19, 21.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/spweights.constants.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Provides constants for spatial weights matrices — spweights.constants","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/spweights.constants.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Provides constants for spatial weights matrices — spweights.constants","text":"","code":"data(oldcol) B <- spweights.constants(nb2listw(COL.nb, style=\"B\")) W <- spweights.constants(nb2listw(COL.nb, style=\"W\")) C <- spweights.constants(nb2listw(COL.nb, style=\"C\")) S <- spweights.constants(nb2listw(COL.nb, style=\"S\")) U <- spweights.constants(nb2listw(COL.nb, style=\"U\")) print(data.frame(rbind(unlist(B), unlist(W), unlist(C), unlist(S), unlist(U)),   row.names=c(\"B\", \"W\", \"C\", \"S\", \"U\"))) #>    n n1 n2 n3   nn  S0           S1           S2 #> B 49 48 47 46 2401 232 464.00000000 5.136000e+03 #> W 49 48 47 46 2401  49  23.29434146 2.048729e+02 #> C 49 48 47 46 2401  49  20.69827586 2.291085e+02 #> S 49 48 47 46 2401  49  21.25561347 2.134568e+02 #> U 49 48 47 46 2401   1   0.00862069 9.542212e-02"},{"path":"https://r-spatial.github.io/spdep/reference/ssw.html","id":null,"dir":"Reference","previous_headings":"","what":"Compute the sum of dissimilarity — ssw","title":"Compute the sum of dissimilarity — ssw","text":"function computes sum dissimilarity   observation mean (scalar vector) observations.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/ssw.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Compute the sum of dissimilarity — ssw","text":"","code":"ssw(data, id, method = c(\"euclidean\", \"maximum\",      \"manhattan\", \"canberra\", \"binary\", \"minkowski\",     \"mahalanobis\"), p = 2, cov, inverted = FALSE)"},{"path":"https://r-spatial.github.io/spdep/reference/ssw.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Compute the sum of dissimilarity — ssw","text":"data matrix observations nodes. id Node index compute cost method Character function declare distance method.     method character, method must \"mahalanobis\"     \"euclidean\", \"maximum\", \"manhattan\", \"canberra\", \"binary\"     \"minkowisk\".     method one \"euclidean\", \"maximum\",     \"manhattan\", \"canberra\", \"binary\" \"minkowisk\", see     dist details,      function used compute distance.      method=\"mahalanobis\", mahalanobis distance      computed neighbour areas.      method function, function      used compute distance. p power Minkowski distance. cov covariance matrix used compute mahalanobis    distance. inverted logical.  'TRUE', 'cov' supposed contain           inverse covariance matrix.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/ssw.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Compute the sum of dissimilarity — ssw","text":"numeric, sum dissimilarity observations   id data mean (scalar vector)   observations.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/ssw.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Compute the sum of dissimilarity — ssw","text":"Elias T. Krainski Renato M. Assuncao","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/ssw.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Compute the sum of dissimilarity — ssw","text":"","code":"data(USArrests) n <- nrow(USArrests) ssw(USArrests, 1:n) #> [1] 3701.394 ssw(USArrests, 1:(n/2)) #> [1] 1910.214 ssw(USArrests, (n/2+1):n) #> [1] 1625.882 ssw(USArrests, 1:(n/2)) + ssw(USArrests, (n/2+1):n) #> [1] 3536.096"},{"path":"https://r-spatial.github.io/spdep/reference/subset.listw.html","id":null,"dir":"Reference","previous_headings":"","what":"Subset a spatial weights list — subset.listw","title":"Subset a spatial weights list — subset.listw","text":"function subsets spatial weights list, retaining objects subset argument vector TRUE. present subset non-general weights lists (created nb2listw glist=NULL).","code":""},{"path":"https://r-spatial.github.io/spdep/reference/subset.listw.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Subset a spatial weights list — subset.listw","text":"","code":"# S3 method for class 'listw' subset(x, subset, zero.policy = attr(x, \"zero.policy\"), ...)"},{"path":"https://r-spatial.github.io/spdep/reference/subset.listw.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Subset a spatial weights list — subset.listw","text":"x object class listw subset logical expression zero.policy default attr(x, \"zero.policy\") set x created, attribute set, use global option value; FALSE stop error empty neighbour sets, TRUE permit weights list formed zero-length weights vectors - passed nb2listw ... generic function pass-","code":""},{"path":"https://r-spatial.github.io/spdep/reference/subset.listw.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Subset a spatial weights list — subset.listw","text":"function returns object class listw component style input object, component neighbours list integer vectors containing neighbour region number ids (compacted run 1:number regions subset), component weights weights computed neighbours using style. -neighbour observations created subsetting zero.policy input weights object FALSE, set TRUE warning issued.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/subset.listw.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Subset a spatial weights list — subset.listw","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/subset.listw.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Subset a spatial weights list — subset.listw","text":"","code":"col.gal.nb <- read.gal(system.file(\"weights/columbus.gal\", package=\"spData\")[1]) to.be.dropped <- c(31, 34, 36, 39, 42, 46) pre <- nb2listw(col.gal.nb) print(pre) #> Characteristics of weights list object: #> Neighbour list object: #> Number of regions: 49  #> Number of nonzero links: 230  #> Percentage nonzero weights: 9.579342  #> Average number of links: 4.693878  #>  #> Weights style: W  #> Weights constants summary: #>    n   nn S0       S1       S2 #> W 49 2401 49 23.48489 204.6687 post <- subset(pre, !(1:length(col.gal.nb) %in% to.be.dropped)) print(post) #> Characteristics of weights list object: #> Neighbour list object: #> Number of regions: 43  #> Number of nonzero links: 212  #> Percentage nonzero weights: 11.46566  #> Average number of links: 4.930233  #>  #> Weights style: W  #> Weights constants summary: #>    n   nn S0       S1       S2 #> W 43 1849 43 19.26584 178.4604 columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) nb <- poly2nb(columbus) lw <- nb2listw(nb, style=\"W\") attr(lw, \"zero.policy\") #> [1] FALSE (lwa <- subset(lw, 1:nrow(columbus) != c(21))) #> Warning: subsetting caused increase in subgraph count #> Characteristics of weights list object: #> Neighbour list object: #> Number of regions: 48  #> Number of nonzero links: 230  #> Percentage nonzero weights: 9.982639  #> Average number of links: 4.791667  #> 2 disjoint connected subgraphs #>  #> Weights style: W  #> Weights constants summary: #>    n   nn S0       S1       S2 #> W 48 2304 48 22.46811 199.4398 attr(lwa, \"zero.policy\") #> [1] FALSE (lwb <- subset(lw, !(1:nrow(columbus) %in% c(21, 36, 39)))) #> Warning: subsetting caused increase in subgraph count #> Warning: subsetting created no-neighbour observations, zero.policy set TRUE #> Characteristics of weights list object: #> Neighbour list object: #> Number of regions: 46  #> Number of nonzero links: 216  #> Percentage nonzero weights: 10.20794  #> Average number of links: 4.695652  #> 1 region with no links: #> 46 #> 3 disjoint connected subgraphs #>  #> Weights style: W  #> Weights constants summary: #>    n   nn S0     S1       S2 #> W 45 2025 45 22.857 187.4843 attr(lwb, \"zero.policy\") #> [1] TRUE"},{"path":"https://r-spatial.github.io/spdep/reference/subset.nb.html","id":null,"dir":"Reference","previous_headings":"","what":"Subset a neighbours list — subset.nb","title":"Subset a neighbours list — subset.nb","text":"function subsets neighbors list, retaining objects subset argument vector TRUE.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/subset.nb.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Subset a neighbours list — subset.nb","text":"","code":"# S3 method for class 'nb' subset(x, subset, ...)"},{"path":"https://r-spatial.github.io/spdep/reference/subset.nb.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Subset a neighbours list — subset.nb","text":"x object class nb subset logical expression ... generic function pass-","code":""},{"path":"https://r-spatial.github.io/spdep/reference/subset.nb.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Subset a neighbours list — subset.nb","text":"function returns object class nb list    integer vectors containing neighbour region number ids (compacted    run 1:number regions subset).","code":""},{"path":"https://r-spatial.github.io/spdep/reference/subset.nb.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Subset a neighbours list — subset.nb","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/subset.nb.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Subset a neighbours list — subset.nb","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) col.gal.nb <- read.gal(system.file(\"weights/columbus.gal\", package=\"spData\")[1]) coords <- st_coordinates(st_centroid(columbus)) #> Warning: st_centroid assumes attributes are constant over geometries plot(col.gal.nb, coords) to.be.dropped <- c(31, 34, 36, 39, 42, 46) text(coords[to.be.dropped,1], coords[to.be.dropped,2], labels=to.be.dropped,   pos=2, offset=0.3) sub.col.gal.nb <- subset(col.gal.nb,   !(1:length(col.gal.nb) %in% to.be.dropped)) plot(sub.col.gal.nb, coords[-to.be.dropped,], col=\"red\", add=TRUE)  which(!(attr(col.gal.nb, \"region.id\") %in%   attr(sub.col.gal.nb, \"region.id\"))) #> [1] 31 34 36 39 42 46"},{"path":"https://r-spatial.github.io/spdep/reference/summary.nb.html","id":null,"dir":"Reference","previous_headings":"","what":"Print and summary function for neighbours and weights lists — summary.nb","title":"Print and summary function for neighbours and weights lists — summary.nb","text":"function prints summary measures links neighbours list. matrix coordinates given well, summary descriptive measures link lengths also printed. Print summary functions also available \"listw\" weights list objects, also reporting constants (S0, S1, S2) used inference global spatial autocorrelation statistics Moran's , Geary's C, join-count tests Getis-Ord G.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/summary.nb.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Print and summary function for neighbours and weights lists — summary.nb","text":"","code":"# S3 method for class 'nb' summary(object, coords=NULL, longlat = NULL, scale = 1, ...) # S3 method for class 'nb' print(x, ...) # S3 method for class 'listw' summary(object, coords, longlat, zero.policy = attr(object, \"zero.policy\"),   scale = 1, adjust.n=TRUE, ...) # S3 method for class 'listw' print(x, zero.policy = attr(x, \"zero.policy\"), ...)"},{"path":"https://r-spatial.github.io/spdep/reference/summary.nb.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Print and summary function for neighbours and weights lists — summary.nb","text":"object object class nb coords matrix region point coordinates SpatialPoints object sfc points object longlat TRUE point coordinates longitude-latitude decimal degrees, case distances measured kilometers; coords SpatialPoints object, value taken object ... additional arguments affecting output produced x object class nb zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; FALSE stop error empty neighbour sets scale passed stem() control plot length adjust.n default TRUE, FALSE number observations adjusted -neighbour observations, TRUE, number observations spweights.constants adjusted","code":""},{"path":"https://r-spatial.github.io/spdep/reference/summary.nb.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Print and summary function for neighbours and weights lists — summary.nb","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/summary.nb.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Print and summary function for neighbours and weights lists — summary.nb","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) col.gal.nb <- read.gal(system.file(\"weights/columbus.gal\", package=\"spData\")[1]) coords <- st_centroid(st_geometry(columbus), of_largest_polygon=TRUE) col.gal.nb #> Neighbour list object: #> Number of regions: 49  #> Number of nonzero links: 230  #> Percentage nonzero weights: 9.579342  #> Average number of links: 4.693878  summary(col.gal.nb, coords) #> Neighbour list object: #> Number of regions: 49  #> Number of nonzero links: 230  #> Percentage nonzero weights: 9.579342  #> Average number of links: 4.693878  #> Link number distribution: #>  #>  2  3  4  5  6  7  8  9 10  #>  7  7 13  4  9  6  1  1  1  #> 7 least connected regions: #> 1 6 31 39 42 46 47 with 2 links #> 1 most connected region: #> 20 with 10 links col.listw <- nb2listw(col.gal.nb, style=\"W\") col.listw #> Characteristics of weights list object: #> Neighbour list object: #> Number of regions: 49  #> Number of nonzero links: 230  #> Percentage nonzero weights: 9.579342  #> Average number of links: 4.693878  #>  #> Weights style: W  #> Weights constants summary: #>    n   nn S0       S1       S2 #> W 49 2401 49 23.48489 204.6687 summary(col.listw) #> Characteristics of weights list object: #> Neighbour list object: #> Number of regions: 49  #> Number of nonzero links: 230  #> Percentage nonzero weights: 9.579342  #> Average number of links: 4.693878  #> Link number distribution: #>  #>  2  3  4  5  6  7  8  9 10  #>  7  7 13  4  9  6  1  1  1  #> 7 least connected regions: #> 1 6 31 39 42 46 47 with 2 links #> 1 most connected region: #> 20 with 10 links #>  #> Weights style: W  #> Weights constants summary: #>    n   nn S0       S1       S2 #> W 49 2401 49 23.48489 204.6687 col_geoms <- st_geometry(columbus) col_geoms[21] <- st_buffer(col_geoms[21], dist=-0.05) st_geometry(columbus) <- col_geoms nb <- poly2nb(columbus) #> Warning: some observations have no neighbours; #> if this seems unexpected, try increasing the snap argument. #> Warning: neighbour object has 3 sub-graphs; #> if this sub-graph count seems unexpected, try increasing the snap argument. summary(nb) #> Neighbour list object: #> Number of regions: 49  #> Number of nonzero links: 230  #> Percentage nonzero weights: 9.579342  #> Average number of links: 4.693878  #> 1 region with no links: #> 21 #> 3 disjoint connected subgraphs #> Link number distribution: #>  #>  0  2  3  4  5  6  7  8  9 10  #>  1  5  9 12  4 10  2  4  1  1  #> 5 least connected regions: #> 1 6 42 46 47 with 2 links #> 1 most connected region: #> 20 with 10 links try(nb2listw(nb, style=\"W\")) #> Error in nb2listw(nb, style = \"W\") :  #>   Empty neighbour sets found (zero.policy: FALSE) summary(nb2listw(nb, style=\"W\", zero.policy=TRUE)) #> Characteristics of weights list object: #> Neighbour list object: #> Number of regions: 49  #> Number of nonzero links: 230  #> Percentage nonzero weights: 9.579342  #> Average number of links: 4.693878  #> 1 region with no links: #> 21 #> 3 disjoint connected subgraphs #> Link number distribution: #>  #>  0  2  3  4  5  6  7  8  9 10  #>  1  5  9 12  4 10  2  4  1  1  #> 5 least connected regions: #> 1 6 42 46 47 with 2 links #> 1 most connected region: #> 20 with 10 links #>  #> Weights style: W  #> Weights constants summary: #>    n   nn S0       S1       S2 #> W 48 2304 48 22.46811 199.4398 summary(nb2listw(nb, style=\"W\", zero.policy=TRUE), adjust.n=FALSE) #> Characteristics of weights list object: #> Neighbour list object: #> Number of regions: 49  #> Number of nonzero links: 230  #> Percentage nonzero weights: 9.579342  #> Average number of links: 4.693878  #> 1 region with no links: #> 21 #> 3 disjoint connected subgraphs #> Link number distribution: #>  #>  0  2  3  4  5  6  7  8  9 10  #>  1  5  9 12  4 10  2  4  1  1  #> 5 least connected regions: #> 1 6 42 46 47 with 2 links #> 1 most connected region: #> 20 with 10 links #>  #> Weights style: W  #> Weights constants summary: #>    n   nn S0       S1       S2 #> W 49 2401 48 22.46811 199.4398"},{"path":"https://r-spatial.github.io/spdep/reference/testnb.html","id":null,"dir":"Reference","previous_headings":"","what":"Test a neighbours list for symmetry — is.symmetric.nb","title":"Test a neighbours list for symmetry — is.symmetric.nb","text":"Checks neighbours list symmetry/transitivity (neighbour j, j neighbour ). holds distance contiguity based neighbours, k-nearest neighbours. helper function sym.attr.nb() calls .symmetric.nb() set sym attribute needed, make.sym.nb makes non-symmetric list symmetric adding neighbors. .symmetric.glist checks list general weights corresponding neighbours symmetry symmetric neighbours.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/testnb.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Test a neighbours list for symmetry — is.symmetric.nb","text":"","code":"is.symmetric.nb(nb, verbose = NULL, force = FALSE) sym.attr.nb(nb) make.sym.nb(nb) old.make.sym.nb(nb) is.symmetric.glist(nb, glist)"},{"path":"https://r-spatial.github.io/spdep/reference/testnb.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Test a neighbours list for symmetry — is.symmetric.nb","text":"nb object class nb list integer vectors containing neighbour region number ids. verbose default NULL, use global option value; TRUE prints non-matching pairs force respect neighbours list sym attribute test anyway glist list general weights corresponding neighbours","code":""},{"path":"https://r-spatial.github.io/spdep/reference/testnb.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Test a neighbours list for symmetry — is.symmetric.nb","text":"TRUE symmetric, FALSE ; .symmetric.glist returns value attribute, \"d\", indicating failed symmetry largest failing value.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/testnb.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Test a neighbours list for symmetry — is.symmetric.nb","text":"new version make.sym.nb Bjarke Christensen now included. older version renamed old.make.sym.nb, comparison constitutes nice demonstration vectorising speedup using sapply lapply rather loops. -neighbour observations present, old.make.sym.nb used.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/testnb.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Test a neighbours list for symmetry — is.symmetric.nb","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/testnb.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Test a neighbours list for symmetry — is.symmetric.nb","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) col.gal.nb <- read.gal(system.file(\"weights/columbus.gal\", package=\"spData\")[1]) coords <- st_coordinates(st_centroid(columbus)) #> Warning: st_centroid assumes attributes are constant over geometries ind <- row.names(as(columbus, \"Spatial\")) print(is.symmetric.nb(col.gal.nb, verbose=TRUE, force=TRUE)) #> [1] TRUE k4 <- knn2nb(knearneigh(coords, k=4), row.names=ind) k4 <- sym.attr.nb(k4) print(is.symmetric.nb(k4)) #> [1] FALSE k4.sym <- make.sym.nb(k4) print(is.symmetric.nb(k4.sym)) #> [1] TRUE"},{"path":"https://r-spatial.github.io/spdep/reference/tolerance.nb.html","id":null,"dir":"Reference","previous_headings":"","what":"Function to construct edges based on a tolerance angle and a maximum distance — tolerance.nb","title":"Function to construct edges based on a tolerance angle and a maximum distance — tolerance.nb","text":"function creates object class nb (defined library spdep) containing connexion diagram. edges sites based tolerance angle maximum distance. angle directional; direction always bottow top screen.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/tolerance.nb.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Function to construct edges based on a tolerance angle and a maximum distance — tolerance.nb","text":"","code":"tolerance.nb(coords, unit.angle = \"degrees\", max.dist, tolerance, rot.angle,  plot.sites=FALSE)"},{"path":"https://r-spatial.github.io/spdep/reference/tolerance.nb.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Function to construct edges based on a tolerance angle and a maximum distance — tolerance.nb","text":"coords matrix data frame containing X Y coordinates study sites. unit.angle Character. measurement units angles defined: either \"degrees\" (default) \"radians\". max.dist Numeric. maximum distance edge linking two sites together. tolerance Numeric. tolerance angle site can influence another site. angle measured vertically bottom top pictures rotation points. rot.angle Numeric, optional. angle set coordinates rotated creating connexion diagram. set coordinates rotated counterclockwise. Negative values produce clockwise rotation. plot.sites Logical (TRUE, FALSE) determining site plotted graphic window. graph allows one make sure points rotated correct direction.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/tolerance.nb.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Function to construct edges based on a tolerance angle and a maximum distance — tolerance.nb","text":"Even though function creates connexion diagram based tolerance angle going bottom top screen, resulting object symmetric, meaning site influences another vice versa. final object represent directional connexion network.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/tolerance.nb.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Function to construct edges based on a tolerance angle and a maximum distance — tolerance.nb","text":"function returns object class nb list integer vectors  corresponding neighbour region numbers.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/tolerance.nb.html","id":"warning","dir":"Reference","previous_headings":"","what":"Warning","title":"Function to construct edges based on a tolerance angle and a maximum distance — tolerance.nb","text":"function design handle large number rows coords. use function set coordinates 1500 entries memory intensive.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/tolerance.nb.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Function to construct edges based on a tolerance angle and a maximum distance — tolerance.nb","text":"F. Guillaume Blanchet","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/tolerance.nb.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Function to construct edges based on a tolerance angle and a maximum distance — tolerance.nb","text":"","code":"set.seed(1) ex.data<-cbind(runif(50),rexp(50))  ### Construct object of class nb with a tolerance angle of 30 degrees ### and a maximum distance of 2 m. nb.ex<-tolerance.nb(ex.data, unit.angle = \"degrees\", max.dist=1,  tolerance = 30) #> Warning: neighbour object has 3 sub-graphs  ### Construct object of class nb with a tolerance angle of 30 degrees ### and a maximum distance of 2 m. The coordinates are rotated at an angle ### of 45 degrees counterclockwise. nb.ex2<-tolerance.nb(ex.data, unit.angle = \"degrees\", max.dist=1,  tolerance = 30, rot.angle = 45) #> Warning: neighbour object has 4 sub-graphs  ### Construct object of class nb with a tolerance angle of pi/8 radians ### and a maximum distance of 1.5 m. The coordinates are rotated at ### an angle of pi/4 radians clockwise. nb.ex3<-tolerance.nb(ex.data, unit.angle = \"radians\", max.dist=1.5,  tolerance = pi/8, rot.angle = -pi*2/3) #> Warning: neighbour object has 5 sub-graphs  par(mfrow=c(1,3)) plot(nb.ex,ex.data,asp=1) plot(nb.ex2,ex.data,asp=1) plot(nb.ex3,ex.data,asp=1)"},{"path":"https://r-spatial.github.io/spdep/reference/tri2nb.html","id":null,"dir":"Reference","previous_headings":"","what":"Neighbours list from tri object — tri2nb","title":"Neighbours list from tri object — tri2nb","text":"function uses deldir package convert matrix two-dimensional coordinates neighbours list class nb list integer vectors containing neighbour region number ids.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/tri2nb.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Neighbours list from tri object — tri2nb","text":"","code":"tri2nb(coords, row.names = NULL)"},{"path":"https://r-spatial.github.io/spdep/reference/tri2nb.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Neighbours list from tri object — tri2nb","text":"coords matrix, data.frame tibble point coordinates two columns, SpatialPoints object sfc points object row.names character vector region ids added neighbours list attribute region.id, default seq(1, nrow(x))","code":""},{"path":"https://r-spatial.github.io/spdep/reference/tri2nb.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Neighbours list from tri object — tri2nb","text":"coordinates duplicated, function used. coordinates grid, need ordered first three collinear, first triangle can constructed. can achieved randomising order coordinates (possibly several times), re-ordering order data match new order neighbour list - fix used, remember re-order row.names argument well coordinates! Please also note triangulation grid points give arbitrary diagonal neighbours, may sensible outcome, dnearneigh() may serve better tri2nb() used.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/tri2nb.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Neighbours list from tri object — tri2nb","text":"function returns object class nb list integer vectors containing neighbour region number ids.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/tri2nb.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Neighbours list from tri object — tri2nb","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/tri2nb.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Neighbours list from tri object — tri2nb","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) coords <- st_centroid(st_geometry(columbus), of_largest_polygon=TRUE) ind <- row.names(columbus) suppressPackageStartupMessages(require(deldir)) col.tri.nb <- tri2nb(coords, row.names=ind) plot(st_geometry(columbus), border=\"grey\") plot(col.tri.nb, coords, add=TRUE) title(main=\"Raw triangulation links\", cex.main=0.6)  x <- seq(0,1,0.1) y <- seq(0,2,0.2) xy <- expand.grid(x, y) try(xy.nb <- tri2nb(xy)) seed <- 1234 xid <- sample(1:nrow(xy)) xy.nb <- tri2nb(xy[xid,]) plot(xy.nb, xy[xid,])  # example of reading points with readr::read_csv() yielding a tibble load(system.file(\"etc/misc/coords.rda\", package=\"spdep\")) class(coords) #> [1] \"spec_tbl_df\" \"tbl_df\"      \"tbl\"         \"data.frame\"  nb <- tri2nb(coords) plot(nb, coords)"},{"path":"https://r-spatial.github.io/spdep/reference/write.nb.gal.html","id":null,"dir":"Reference","previous_headings":"","what":"Write a neighbours list as a GAL lattice file — write.nb.gal","title":"Write a neighbours list as a GAL lattice file — write.nb.gal","text":"Write neighbours list GAL lattice file, may also use newer GeoDa header format","code":""},{"path":"https://r-spatial.github.io/spdep/reference/write.nb.gal.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Write a neighbours list as a GAL lattice file — write.nb.gal","text":"","code":"write.nb.gal(nb, file, oldstyle=TRUE, shpfile=NULL, ind=NULL)"},{"path":"https://r-spatial.github.io/spdep/reference/write.nb.gal.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Write a neighbours list as a GAL lattice file — write.nb.gal","text":"nb object class nb list integer vectors containing neighbour region number ids. file name file GAL lattice data oldstyle TRUE, first line file contains number spatial units, FALSE, uses newer GeoDa style shpfile Shapefile name taken GAL file dataset ind region id indicator variable name","code":""},{"path":"https://r-spatial.github.io/spdep/reference/write.nb.gal.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Write a neighbours list as a GAL lattice file — write.nb.gal","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/write.nb.gal.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Write a neighbours list as a GAL lattice file — write.nb.gal","text":"","code":"col.gal.nb <- read.gal(system.file(\"weights/columbus.gal\", package=\"spData\")[1]) GALfile <- tempfile(\"GAL\") write.nb.gal(col.gal.nb, GALfile) col.queen <- read.gal(GALfile) summary(diffnb(col.queen, col.gal.nb)) #> Warning: neighbour object has 49 sub-graphs #> Neighbour list object: #> Number of regions: 49  #> Number of nonzero links: 0  #> Percentage nonzero weights: 0  #> Average number of links: 0  #> 49 regions with no links: #> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, #> 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, #> 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49 #> 49 disjoint connected subgraphs #> Link number distribution: #>  #>  0  #> 49"},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-13-7-development","dir":"Changelog","previous_headings":"","what":"Version 1.3-7 (development)","title":"Version 1.3-7 (development)","text":"(temporarily) remove rgeoda references successfully re-submitted CRAN add write.swmdbf #171 complement #163 modify defaults licd_multi","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-13-6-2024-09-13","dir":"Changelog","previous_headings":"","what":"Version 1.3-6 (2024-09-13)","title":"Version 1.3-6 (2024-09-13)","text":"CRAN release: 2024-09-13 adding vignette describing recent changes poly2nb #162, subgraph -neighbour (island) handling adding prototype LICD ESDA function licd_multi hotspot method add read.swmdbf2listw #163 reading DBF files exported ArcGIS representing SWM objects; note problems observation IDs known, see help file #162 add option -neighbour checking poly2nb - default report whether -neighbour observations present #162 change default snap= argument poly2nb 10mm Condition forthcoming tmap 4 #160 handle n.comp.nb delay print.nb elsewhere total number neighbours large","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-13-5-2024-06-10","dir":"Changelog","previous_headings":"","what":"Version 1.3-5 (2024-06-10)","title":"Version 1.3-5 (2024-06-10)","text":"CRAN release: 2024-06-10 #157 migrate ESRI Shapefile GPKG files; convert bhicv.shp GPKG #155 Throw error hotspot despatched object without \"quadr\" attribute #154 turn s2 vignette","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-13-4-2024-05-31","dir":"Changelog","previous_headings":"","what":"Version 1.3-4 (2024-05-31)","title":"Version 1.3-4 (2024-05-31)","text":"CRAN release: 2024-05-31 add scale argument geary.test, geary.mc geary #151, appropriate tests Introduce error knearneigh k less largest count identical points; encountered, increase k remove spurious warning knearneigh longlat geometries fix https://github.com/edzer/sdsr/issues/121, wrong assignment old test names lmRStests fix #144 plot.nb nb2lines","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-13-3-2024-02-07","dir":"Changelog","previous_headings":"","what":"Version 1.3-3 (2024-02-07)","title":"Version 1.3-3 (2024-02-07)","text":"CRAN release: 2024-02-07 change lm.LMtests lm.RStests re-name Lagrange multiplier Rao’s score; add GNM_ prefix test names input object inherits SlX created spatialreg::lmSLX (Koley, forthcoming) add SD.RStests implementation Rao’s score tests spatial Durbin models (Koley Bera, 2024) SDEM models (Koley, forthcoming) #143 row.names pass-poly2nb corrected, harmonised row.names pass-also nbdists dnearneigh #139 add na.action argument geary.test, geary.mc globalG.test add style sn2listw use tri2nb","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-13-1-2023-11-23","dir":"Changelog","previous_headings":"","what":"Version 1.3-1 (2023-11-23)","title":"Version 1.3-1 (2023-11-23)","text":"CRAN release: 2023-11-23 functions creating nb objects now warn object sub-graph count > 1 get.SubgraphOption TRUE (default FALSE): complement.nb, diffnb, dnearneigh, droplinks, edit.nb, graph2nb, knn2nb, nb2blocknb, nblag, nblag_cumul, poly2nb, read.gal, read.gwt2nb, setdiff.nb, tolerance.nb, tri2nb, union.nb summary.nb, print.nb, summary.listw print.listw now report subgraph count n.comp.nb one subset.nb now reports subgraph count neighbour object increases subsetting adding zero.policy attribute functions creating listw objects: nb2listw, sn2listw, mat2listw, nb2listwdist. Default zero.policy= argument updated use attr(., \"zero.policy\") summary.listw, print.listw, moran, moran.test, moran.mc, moran.plot, geary.mc, geary, geary.test, globalG.test, joincount.test, joincount.mc, joincount.multi, localC, localC_perm, localmoran, localmoran_perm, localG, localG_perm, lee, lee.test, lee.mc, lm.morantest, lm.LMtests, sp.mantel.mc, listw2star, lag.listw, lm.morantest, lm.LMtests, subset.listw, EBImoran.mc, LOSH, LOSH.mc, LOSH.cs, lm.morantest.exactand lm.morantest.sad confusing error message moran.plot() -neighbour cases, zero.policy=FALSE replace rgrass7 rgrass vignette fix #133 (edit.nb affected attaching sp)","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-12-8-2023-02-28","dir":"Changelog","previous_headings":"","what":"Version 1.2-8 (2023-02-28)","title":"Version 1.2-8 (2023-02-28)","text":"CRAN release: 2023-02-28 mat2listw() warning style= argument given, M\" given https://github.com/r-spatial/spatialreg/issues/24, https://github.com/r-spatial/spatialreg/issues/23. remaining users run_perm() - localC(), localmoran_bv() local_joincount_uni() get no_repeat_in_row= arguments. Address 2) #124; localG_perm() localmoran_perm() get no_repeat_in_row= arguments use conditional permutation without replacement sample vectors; default implementation uses sampling replacement, acceptable across simulation draws, arguably less acceptable within draws. Feedback valued. Address 1) #124; localG_perm() localG() now return analytical standard deviates. standard deviates simulated distributions now returned attr(., \"internals\")[,\"StdDev.Gi\"] localG_perm(), p-values, etc. move sp Depends Imports, reduce visual impression sp objects required spdep; sf objects now preferred, sp objects can used , although users may need attach sp expliciitly. fix #121 #123; correcting returned values localG_perm() estimating G-star measure (fix self x values weights) address #120, moving documentation listw2U() ?lm.morantest ?nb2listw addressing #119 interpretation moran_bv() results adding #116, René Westerholt fix #113, low R version grDevices::hcl.colors() addressing #111 Josiah Parry PRs René Westerholt, ending #109, local GS measure","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-12-7-2022-10-01","dir":"Changelog","previous_headings":"","what":"Version 1.2-7 (2022-10-01)","title":"Version 1.2-7 (2022-10-01)","text":"CRAN release: 2022-10-01 #103 refactoring local joincount test Josiah Parry add hotspot methods localmoran (analytical, permutation, Saddlepoint exact), localC (univariate multivariate) localG (analytical permutation) #95 add \"two.sided\" lee.mc(), sp.mantel.mc(), EBImoran.mc(), joincount.mc(), geary.mc() #92, #93, #94, #96, #97 contributions prototype bivariate Moran, local bivariate Moran local joincount bivariate joincount tests Josiah Parry #91 tolerance.nb() update F. Guillaume Blanchet updating coercion Matrix 1.4-2 fix ncpus issue dontrun examples remove suggested packages rgdal, rgeos, maptools","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-12-5-2022-08-11","dir":"Changelog","previous_headings":"","what":"Version 1.2-5 (2022-08-11)","title":"Version 1.2-5 (2022-08-11)","text":"CRAN release: 2022-08-11 permit use data.frame tibble matrix functions creating neighbour objects 2D points (preferred use object inheriting `\"SpatialPoints\" \"sfc\") fix #87 wrong logic infinite weights nb2listwdist() https://github.com/r-spatial/s2/pull/174 speeds dnearneigh() geographical coordinates without using s2::s2_closest_edges(). Adapting vignettes absence rgdal maptools","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-12-4-2022-04-18","dir":"Changelog","previous_headings":"","what":"Version 1.2-4 (2022-04-18)","title":"Version 1.2-4 (2022-04-18)","text":"CRAN release: 2022-04-18 added remove.self(), thanks Josiah Parry #83. unescape underscores help pages.","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-12-3-2022-03-29","dir":"Changelog","previous_headings":"","what":"Version 1.2-3 (2022-03-29)","title":"Version 1.2-3 (2022-03-29)","text":"CRAN release: 2022-03-29 replace deprecated S-compatibility macros DOUBLE_ #81 improved dnearneigh() help page. #79 remove \"htest\" class LOSH.mc() output object. Added GA SI article citations.","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-12-2-2022-01-28","dir":"Changelog","previous_headings":"","what":"Version 1.2-2 (2022-01-28)","title":"Version 1.2-2 (2022-01-28)","text":"CRAN release: 2022-01-28 Replace rainbow() hcl.colors(..., \"Set 2\") plot.skater(). Add link R-sig-geo thread EBlocal() NaN estimates many counts zero help page. Revise add documentation object returned localC_perm() #68 #72 #73 #74 #75 #76 localmoran.sad(), localmoran.exact() localmoran.exact.alt() now use multiple compute nodes needed; Omega used, multiple cores may need memory #77 s2 > 1.0.7, use indexed distances dnearneigh() https://github.com/r-spatial/s2/pull/162.","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-12-1-2022-01-05","dir":"Changelog","previous_headings":"","what":"Version 1.2-1 (2022-01-05)","title":"Version 1.2-1 (2022-01-05)","text":"CRAN release: 2022-01-04 Switching deprecated functions moved spatialreg defunct.","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-11-13-2021-12-14","dir":"Changelog","previous_headings":"","what":"Version 1.1-13 (2021-12-14)","title":"Version 1.1-13 (2021-12-14)","text":"CRAN release: 2021-12-14 Recent changes poly2nb() reduced recently (1.1-8) removed use snap= finding candidate neighbours; many thanks Matilda Brown clear well-documented issue #65 Add local Geary’s C #66 thanks Josiah Parry, discussion work #68 localmoran_perm() returns look-folded rank p-values","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-11-12-2021-11-09","dir":"Changelog","previous_headings":"","what":"Version 1.1-12 (2021-11-09)","title":"Version 1.1-12 (2021-11-09)","text":"CRAN release: 2021-11-09 poly2nb(), reverted removal legacy interpreted overlapping envelope code sp objects coerced sf without rgeos. Add Fortran character handling USE_FC_LEN_T WRE §6.6.1. Checks OK forthcoming deldir 1.0-0. Fixes #62 clarifying dnearneigh() help page","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-11-11-2021-09-07","dir":"Changelog","previous_headings":"","what":"Version 1.1-11 (2021-09-07)","title":"Version 1.1-11 (2021-09-07)","text":"CRAN release: 2021-09-07 knearneigh() nbdists(); added prototype adaptation s2 unprojected coordinates, used sf_use_s2() TRUE became default sf 1.0.0 https://github.com/r-spatial/s2/issues/125. activated default. dnearneigh() can choose prototype s2 approach sf_use_s2() TRUE use_s2=TRUE unprojected coordinates; https://github.com/r-spatial/s2/issues/125 seems distance thresholds present use brute-force rather spatial indexing. Use activated default. poly2nb() now uses sf::st_intersects() find candidate neighbours unless findInBounds= NULL. spatial indexing, fast scales well large data sets. sf_use_s2() TRUE, sf::st_intersects() passes geometries s2::s2_intersects_matrix(), also uses spatial indexing fast, scaling well large data sets. localmoran() localmoran_perm() return cluster quadrants attribute three splits, zeros, means medians variable interest spatial lag. localmoran_perm() returns skewness kurtosis permutation samples.","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-11-8-2021-05-23","dir":"Changelog","previous_headings":"","what":"Version 1.1-8 (2021-05-23)","title":"Version 1.1-8 (2021-05-23)","text":"CRAN release: 2021-05-23 #55 related #20 cycling order setting grids provoked re-design interface cell2nb(), passing \"GridTopology\" \"SpatialGrid\" objects unnamed first x= argument. Coerce \"RasterLayer\" similar raster, terra stars objects sp class objects first need . working renewing arguments cell2nb(), useful add tinytest support, now present function may extended functions creating \"nb\" objects. #58 contributed Jeff Sauer Levi Wolf (https://doi.org/10.31219/osf.io/ugkhp) providing conditional standard deviates local Moran’s Error assignment matrix detected CRAN check SIDS vignette, section median polish","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-11-7-2021-04-03","dir":"Changelog","previous_headings":"","what":"Version 1.1-7 (2021-04-03)","title":"Version 1.1-7 (2021-04-03)","text":"CRAN release: 2021-04-03 Changes continuous integration vignettes. Error poly2nb(, queen=FALSE) sf grids (double counting closed polygon start/end points), https://github.com/r-spatial/spdep/issues/50, thanks Christopher Kenny. Adding local Moran local G conditional permutation: localmoran_perm() localG_perm(). Adding nb2listwdist() contributed René Westerholt. Adding use sf GEOS find polygon contiguity candidates poly2nb() geometry count >= 500 - uses intersections polygon envelopes. #38, #53 removing RANN, adding dbscan suggestions fast dnearneigh() knearneigh() via use_kd_tree= argument fast planar neighbour set finding 2D 3D. Affects soi.graph() , used RANN. #54 avoid partial matching glist= handling. Disambiguating spdep spatialreg model output object class names prior making spdep model fitting functions defunct.","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-11-5-2020-06-29","dir":"Changelog","previous_headings":"","what":"Version 1.1-5 (2020-06-29)","title":"Version 1.1-5 (2020-06-29)","text":"CRAN release: 2020-06-29 Replacing broken geoda URLs, moving knitr rmarkdown, work-around missing weights files spData.","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-11-3-2019-09-18","dir":"Changelog","previous_headings":"","what":"Version 1.1-3 (2019-09-18)","title":"Version 1.1-3 (2019-09-18)","text":"CRAN release: 2019-09-18 small maintenance update accommodate forthcoming change spData (dataset used example spdep spData changing name; name involved putting “x”, “y” “xyz” global environment lazy loading dataset).","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-11-2-2019-04-05","dir":"Changelog","previous_headings":"","what":"Version 1.1-2 (2019-04-05)","title":"Version 1.1-2 (2019-04-05)","text":"CRAN release: 2019-04-05 Follow-version spdep functions methods transferred spatialreg package marked deprecated, still exported spdep. Reverse dependencies passing released version still pass version.","code":""}]
+[{"path":"https://r-spatial.github.io/spdep/articles/CO69.html","id":"introduction","dir":"Articles","previous_headings":"","what":"Introduction","title":"“The Problem of Spatial Autocorrelation:” forty years on","text":"Cliff Ord (1969), published forty years ago, marked turning point treatment spatial autocorrelation quantitative geography. provided framework needed applied researcher attempt implementation different system, possibly using different programming language. spirit, examine spatial weights represented implementations may reproduced, tabulated results paper may reproduced, may extended cover simulation. One major assertions Cliff Ord (1969) statistic advances measurement spatial autocorrelation respect Moran (1950) Geary (1954) general specification spatial weights used. general form implications preparation weights , calculation measures. look spatial weights first, moving consider measures presented paper subsequent developments. , put together data set matching used Cliff Ord (1969). provide tabulated data counties Irish Republic, omit Dublin analyses. shapefile included package, kindly made available Michael Tiefelsdorf, used starting point: read SpatialPolygonsDataFrame — classes used handling spatial data fully described Roger S. Bivand, Pebesma, Gómez-Rubio (2008). need add data tabulated paper Table 2,1 p. 40, form text file added rainfall values Table 9, p. 49: Since assigned county names feature identifiers reading shapefiles, extra data, combine objects: Finally, need drop Dublin county omitted analyses conducted Cliff Ord (1969): double-check data, let us calculate sample Beta coefficients, using formulae given paper sample moments: differ somewhat ways skewness kurtosis computed modern statistical software, see example Joanes Gill (1998). However, purposes, let us reproduce Table 3, p. 42: Using tabulated value 23.623.6 percentage agricultural holdings 50 1950 Waterford, skewness kurtosis reproduced, comparison irishdata dataset , turns value rather 26.626.6, yields tabulated skewness kurtosis values. going , variables considered presented Table varsvars. Description variables Geary data set.","code":"library(spdep) eire <- as(sf::st_read(system.file(\"shapes/eire.gpkg\", package=\"spData\")[1]), \"Spatial\") row.names(eire) <- as.character(eire$names) #proj4string(eire) <- CRS(\"+proj=utm +zone=30 +ellps=airy +units=km\") class(eire) ## [1] \"SpatialPolygonsDataFrame\" ## attr(,\"package\") ## [1] \"sp\" names(eire) ##  [1] \"A\"       \"towns\"   \"pale\"    \"size\"    \"ROADACC\" \"OWNCONS\" \"POPCHG\"  ##  [8] \"RETSALE\" \"INCOME\"  \"names\" fn <- system.file(\"etc/misc/geary_eire.txt\", package=\"spdep\")[1] ge <- read.table(fn, header=TRUE) names(ge) ##  [1] \"serlet\"        \"county\"        \"pagval2_10\"    \"pagval10_50\"   ##  [5] \"pagval50p\"     \"cowspacre\"     \"ocattlepacre\"  \"pigspacre\"     ##  [9] \"sheeppacre\"    \"townvillp\"     \"carspcap\"      \"radiopcap\"     ## [13] \"retailpcap\"    \"psinglem30_34\" \"rainfall\" row.names(ge) <- as.character(ge$county) all.equal(row.names(ge), row.names(eire)) ## [1] TRUE eire_ge <- cbind(eire, ge) eire_ge1 <- eire_ge[!(row.names(eire_ge) %in% \"Dublin\"),] length(row.names(eire_ge1)) ## [1] 25 skewness <- function(z) {z <- scale(z, scale=FALSE); ((sum(z^3)/length(z))^2)/((sum(z^2)/length(z))^3)} kurtosis <- function(z) {z <- scale(z, scale=FALSE); (sum(z^4)/length(z))/((sum(z^2)/length(z))^2)} print(sapply(as(eire_ge1, \"data.frame\")[13:24], skewness), digits=3) ##    pagval2_10   pagval10_50     pagval50p     cowspacre  ocattlepacre  ##      1.675429      1.294978      0.000382      1.682094      0.086267  ##     pigspacre    sheeppacre     townvillp      carspcap     radiopcap  ##      1.138387      1.842362      0.472748      0.011111      0.342805  ##    retailpcap psinglem30_34  ##      0.002765      0.068169 print(sapply(as(eire_ge1, \"data.frame\")[13:24], kurtosis), digits=4) ##    pagval2_10   pagval10_50     pagval50p     cowspacre  ocattlepacre  ##         3.790         4.331         1.508         4.294         2.985  ##     pigspacre    sheeppacre     townvillp      carspcap     radiopcap  ##         3.754         4.527         2.619         1.865         2.730  ##    retailpcap psinglem30_34  ##         2.188         2.034 print(sapply(as(eire_ge1, \"data.frame\")[c(13,16,18,19)], function(x) skewness(log(x))), digits=3) ## pagval2_10  cowspacre  pigspacre sheeppacre  ##    0.68801    0.17875    0.00767    0.04184 print(sapply(as(eire_ge1, \"data.frame\")[c(13,16,18,19)], function(x) kurtosis(log(x))), digits=4) ## pagval2_10  cowspacre  pigspacre sheeppacre  ##      2.883      2.799      2.212      2.421"},{"path":"https://r-spatial.github.io/spdep/articles/CO69.html","id":"spatial-weights","dir":"Articles","previous_headings":"","what":"Spatial weights","title":"“The Problem of Spatial Autocorrelation:” forty years on","text":"basis comparison, first read unstandardised weighting matrix given Table A1, p. 54, paper, reading file corrected misprint giving O rather D neighbour V: file, counties represented serial letters, ordering conversion integer index representation required reach representation similar SpatialStats module spatial neighbours: done , can change representation listw object, assigning appropriate style (generalised binary) unstandardised values: Note values S0, S1, S2 correspond closely given page 42 paper, 0.846886720.84688672, 0.018699860.01869986 0.122673190.12267319. discrepancies appear due rounding printed table weights. contiguous neighbours represented object match found using poly2nb. However, see reproduced contiguities smaller link count: missing link Clare Kerry, perhaps Tarbert–Killimer ferry, counties contiguous, Figure plot_nbplot\\_nb shows: County boundaries contiguities attempt also made reproduce generalised weights 25 Irish counties reported Cliff Ord (1969), Dublin omitted. Reproducing inverse distance component dij−1d_{ij}^{-1} generalised weights dij−1βi(j)d_{ij}^{-1} \\beta_{(j)} eased statement Cliff Ord (1973, 55) points chosen represent counties “geographic centres,” different centroids yielded applying chosen computational geometry function. distance metric given, may kilometers miles — tried, results sensitive difference applies equally across weights; miles used . Computing proportion shared distance measure βi(j)\\beta_{(j)} harder, requires availability full topology input polygons. Roger S. Bivand, Pebesma, Gómez-Rubio (2008, 244) show employ vect2neigh function (written Markus Neteler) package using GRASS GIS vector handling create full topology spaghetti vector data extract border segment lengths; similar approach also mentioned using ArcGIS coverages purpose. GRASS used create topology, next proportion shared distance measure calculated. compare, need remove Tarbert–Killimer ferry link manually, view summary original weights, well correlation coefficient reconstructed weights. Naturally, unless boundary coordinates used identical original analysis, presumably measured hand, small differences occur. Even though differences general weights, identical contiguities, small, consequences measure spatial autocorrelation substantial, use fifth variable, cattle per 1000 acres crops pasture (1952), see reconstructed weights seem “reveal” autocorrelation original weights.","code":"fn <- system.file(\"etc/misc/unstand_sn.txt\", package=\"spdep\")[1] unstand <- read.table(fn, header=TRUE) summary(unstand) ##      from                to                weight         ##  Length:110         Length:110         Min.   :0.000600   ##  Class :character   Class :character   1st Qu.:0.003225   ##  Mode  :character   Mode  :character   Median :0.007550   ##                                        Mean   :0.007705   ##                                        3rd Qu.:0.010225   ##                                        Max.   :0.032400 class(unstand) <- c(\"spatial.neighbour\", class(unstand)) of <- ordered(unstand$from) attr(unstand, \"region.id\") <- levels(of) unstand$from <- as.integer(of) unstand$to <- as.integer(ordered(unstand$to)) attr(unstand, \"n\") <- length(unique(unstand$from)) lw_unstand <- sn2listw(unstand) lw_unstand$style <- \"B\" lw_unstand ## Characteristics of weights list object: ## Neighbour list object: ## Number of regions: 25  ## Number of nonzero links: 110  ## Percentage nonzero weights: 17.6  ## Average number of links: 4.4  ##  ## Weights style: B  ## Weights constants summary: ##    n  nn     S0         S1        S2 ## B 25 625 0.8476 0.01871808 0.1229232 nb <- poly2nb(eire_ge1) nb ## Neighbour list object: ## Number of regions: 25  ## Number of nonzero links: 108  ## Percentage nonzero weights: 17.28  ## Average number of links: 4.32 xx <- diffnb(nb, lw_unstand$neighbours, verbose=TRUE) ## Neighbour difference for region id: Clare in relation to id: Kerry  ## Neighbour difference for region id: Kerry in relation to id: Clare plot(eire_ge1, border=\"grey60\") plot(nb, coordinates(eire_ge1), add=TRUE, pch=\".\", lwd=2) plot(xx, coordinates(eire_ge1), add=TRUE, pch=\".\", lwd=2, col=3) library(terra) v_eire_ge1 <-vect(eire_ge1) SG <- rasterize(v_eire_ge1, rast(nrows=70, ncols=50, extent=ext(v_eire_ge1)), field=\"county\") library(rgrass) grass_home <- \"/home/rsb/topics/grass/g820/grass82\" initGRASS(grass_home, home=tempdir(), SG=SG, override=TRUE) write_VECT(v_eire_ge1, \"eire\", flags=c(\"o\", \"overwrite\")) res <- vect2neigh(\"eire\", ID=\"serlet\") res$length <- res$length*1000 attr(res, \"external\") <- attr(res, \"external\")*1000 attr(res, \"total\") <- attr(res, \"total\")*1000 grass_borders <- sn2listw(res) raw_borders <- grass_borders$weights int_tot <- attr(res, \"total\") - attr(res, \"external\") prop_borders <- lapply(1:length(int_tot), function(i) raw_borders[[i]]/int_tot[i]) dlist <- nbdists(grass_borders$neighbours, coordinates(eire_ge1)) inv_dlist <- lapply(dlist, function(x) 1/(x/1.609344)) combo_km <- lapply(1:length(inv_dlist), function(i) inv_dlist[[i]]*prop_borders[[i]]) combo_km_lw <- nb2listw(grass_borders$neighbours, glist=combo_km, style=\"B\") summary(combo_km_lw) ## Characteristics of weights list object: ## Neighbour list object: ## Number of regions: 25  ## Number of nonzero links: 108  ## Percentage nonzero weights: 17.28  ## Average number of links: 4.32  ## Link number distribution: ##  ## 1 2 3 4 5 6 7 8  ## 1 2 5 5 8 1 2 1  ## 1 least connected region: ## E with 1 link ## 1 most connected region: ## V with 8 links ##  ## Weights style: B  ## Weights constants summary: ##    n  nn        S0       S1.5        S2 ## B 25 625 0.9083144 0.02191845 0.1427746 red_lw_unstand <- lw_unstand Clare <- which(attr(lw_unstand, \"region.id\") == \"C\") Kerry <- which(attr(lw_unstand, \"region.id\") == \"H\") Kerry_in_Clare <- which(lw_unstand$neighbours[[Clare]] == Kerry) Clare_in_Kerry <- which(lw_unstand$neighbours[[Kerry]] == Clare) red_lw_unstand$neighbours[[Clare]] <- red_lw_unstand$neighbours[[Clare]][-Kerry_in_Clare] red_lw_unstand$neighbours[[Kerry]] <- red_lw_unstand$neighbours[[Kerry]][-Clare_in_Kerry] red_lw_unstand$weights[[Clare]] <- red_lw_unstand$weights[[Clare]][-Kerry_in_Clare] red_lw_unstand$weights[[Kerry]] <- red_lw_unstand$weights[[Kerry]][-Clare_in_Kerry] summary(red_lw_unstand) ## Characteristics of weights list object: ## Neighbour list object: ## Number of regions: 25  ## Number of nonzero links: 108  ## Percentage nonzero weights: 17.28  ## Average number of links: 4.32  ## Link number distribution: ##  ## 1 2 3 4 5 6 7 8  ## 1 2 5 5 8 1 2 1  ## 1 least connected region: ## E with 1 link ## 1 most connected region: ## V with 8 links ##  ## Weights style: B  ## Weights constants summary: ##    n  nn     S0         S1        S2 ## B 25 625 0.8437 0.01870287 0.1222501 cor(unlist(red_lw_unstand$weights), unlist(combo_km_lw$weights)) ## [1] 0.969543 flatten <- function(x, digits=3, statistic=\"I\") {   res <- c(format(x$estimate, digits=digits),     format(x$statistic, digits=digits),     format.pval(x$p.value, digits=digits))   res <- matrix(res, ncol=length(res))   colnames(res) <- paste(c(\"\", \"E\", \"V\", \"SD_\", \"P_\"), \"I\", sep=\"\")   rownames(res) <- deparse(substitute(x))   res } `reconstructed weights` <- moran.test(eire_ge1$ocattlepacre, combo_km_lw) `original weights` <- moran.test(eire_ge1$ocattlepacre, red_lw_unstand) print(rbind(flatten(`reconstructed weights`), flatten(`original weights`)), quote=FALSE) ##                       I       EI      VI      SD_I P_I     ## reconstructed weights  0.3203 -0.0417  0.0225 2.41 0.00792 ## original weights       0.2779 -0.0417  0.0223 2.14 0.0161"},{"path":"https://r-spatial.github.io/spdep/articles/CO69.html","id":"measures-of-spatial-autocorrelation","dir":"Articles","previous_headings":"","what":"Measures of spatial autocorrelation","title":"“The Problem of Spatial Autocorrelation:” forty years on","text":"targets reproduction Tables 4 5 Cliff Ord (1969, 43–44), first containing standard deviates normality randomisation original Moran measure binary weights, original Geary measure binary weights, proposed measure unstandardised general weights, proposed measure row-standardised general weights. addition, four variables log-transformed basis skewness kurtosis results presented . carry transformation variables, generate additional binary row-standardised general spatial weights objects — note weights constants row-standardised general weights agree given p. 42 paper, allowing small differences due rounding weights values displayed paper (p. 54): standard representation measures : =n∑=1n∑j=1nwij∑=1n∑j=1nwij(xi−x‾)(xj−x‾)∑=1n(xi−x‾)2I = \\frac{n}{\\sum_{=1}^{n}\\sum_{j=1}^{n}w_{ij}} \\frac{\\sum_{=1}^{n}\\sum_{j=1}^{n}w_{ij}(x_i-\\bar{x})(x_j-\\bar{x})}{\\sum_{=1}^{n}(x_i - \\bar{x})^2} Moran’s II — paper termed proposed statistic, Geary’s CC: C=(n−1)2∑=1n∑j=1nwij∑=1n∑j=1nwij(xi−xj)2∑=1n(xi−x‾)2C = \\frac{(n-1)}{2\\sum_{=1}^{n}\\sum_{j=1}^{n}w_{ij}} \\frac{\\sum_{=1}^{n}\\sum_{j=1}^{n}w_{ij}(x_i-x_j)^2}{\\sum_{=1}^{n}(x_i - \\bar{x})^2} xi,=1,…,nx_i, =1, \\ldots, n nn observations numeric variable interest, wijw_{ij} spatial weights. order reproduce standard deviates given paper, sufficient apply moran.test variables three different spatial weights objects, two different values randomisation= argument. addition, geary.test applied single spatial weights objects, two different values randomisation= argument. order conduct 8 different tests 16 variables, use lapply list variables specified order, sapply list output objects name generate table row column order original (save copy six columns comparison bootstrap results ): values standard deviates agree Table 4 original paper, exception proposed statistic standardised weights normality untransformed variables. can see happened substituting weights constants standardised weights unstandardised weights: Next, let us look Table 5 original paper. tabulate values measures , , since expectation constant measure, square root variance measure randomisation — extracting values calculated : values follows, match original exception initial version Moran’s II first two columns. write function implementing equations 3 4: =∑=1n∑j=+1nwij(xi−x‾)(xj−x‾)∑=1n(xi−x‾)2I = \\frac{\\sum_{=1}^{n}\\sum_{j=+1}^{n}w_{ij}(x_i-\\bar{x})(x_j-\\bar{x})}{\\sum_{=1}^{n}(x_i - \\bar{x})^2} crucially inner summation +1…ni+1 \\ldots n, 1…n1 \\ldots n, can reproduce values measure shown original Table 5: variance term given equation 7 original paper case normality, randomisation; reference p. 28 equation 38 p. 26 permit reproduction values second column Table 5. variance equation given equation 1.35 Cliff Ord (1973, 9) either, time possible say tabulated values computed. Note since standard deviances reproduced correctly, can reproduced second column values using measure expectance, just matter establishing formula used, far proved possible.","code":"eire_ge1$ln_pagval2_10 <- log(eire_ge1$pagval2_10) eire_ge1$ln_cowspacre <- log(eire_ge1$cowspacre) eire_ge1$ln_pigspacre <- log(eire_ge1$pigspacre) eire_ge1$ln_sheeppacre <- log(eire_ge1$sheeppacre) vars <- c(\"pagval2_10\", \"ln_pagval2_10\", \"pagval10_50\", \"pagval50p\",  \"cowspacre\", \"ln_cowspacre\", \"ocattlepacre\", \"pigspacre\",  \"ln_pigspacre\", \"sheeppacre\", \"ln_sheeppacre\", \"townvillp\",  \"carspcap\", \"radiopcap\", \"retailpcap\", \"psinglem30_34\") nb_B <- nb2listw(lw_unstand$neighbours, style=\"B\") nb_B ## Characteristics of weights list object: ## Neighbour list object: ## Number of regions: 25  ## Number of nonzero links: 110  ## Percentage nonzero weights: 17.6  ## Average number of links: 4.4  ##  ## Weights style: B  ## Weights constants summary: ##    n  nn  S0  S1   S2 ## B 25 625 110 220 2176 lw_std <- nb2listw(lw_unstand$neighbours, glist=lw_unstand$weights, style=\"W\") lw_std ## Characteristics of weights list object: ## Neighbour list object: ## Number of regions: 25  ## Number of nonzero links: 110  ## Percentage nonzero weights: 17.6  ## Average number of links: 4.4  ##  ## Weights style: W  ## Weights constants summary: ##    n  nn S0       S1       S2 ## W 25 625 25 15.84089 103.6197 system.time({ MoranN <- lapply(vars, function(x) moran.test(eire_ge1[[x]], listw=nb_B, randomisation=FALSE)) MoranR <- lapply(vars, function(x) moran.test(eire_ge1[[x]], listw=nb_B, randomisation=TRUE)) GearyN <- lapply(vars, function(x) geary.test(eire_ge1[[x]], listw=nb_B, randomisation=FALSE)) GearyR <- lapply(vars, function(x) geary.test(eire_ge1[[x]], listw=nb_B, randomisation=TRUE)) Prop_unstdN  <- lapply(vars, function(x) moran.test(eire_ge1[[x]], listw=lw_unstand, randomisation=FALSE)) Prop_unstdR  <- lapply(vars, function(x) moran.test(eire_ge1[[x]], listw=lw_unstand, randomisation=TRUE)) Prop_stdN  <- lapply(vars, function(x) moran.test(eire_ge1[[x]], listw=lw_std, randomisation=FALSE)) Prop_stdR  <- lapply(vars, function(x) moran.test(eire_ge1[[x]], listw=lw_std, randomisation=TRUE)) }) ##    user  system elapsed  ##   0.117   0.000   0.118 res <- sapply(c(\"MoranN\", \"MoranR\", \"GearyN\", \"GearyR\", \"Prop_unstdN\", \"Prop_unstdR\", \"Prop_stdN\", \"Prop_stdR\"), function(x) sapply(get(x), \"[[\", \"statistic\")) rownames(res) <- vars ores <- res[,c(1,2,5:8)] print(formatC(res, format=\"f\", digits=4), quote=FALSE) ##               MoranN MoranR GearyN  GearyR  Prop_unstdN Prop_unstdR Prop_stdN Prop_stdR ## pagval2_10    3.7851 3.8779 4.3142  3.9016  3.3307      3.4159      3.9276    4.0292    ## ln_pagval2_10 4.0965 4.1074 4.0841  4.0343  3.5795      3.5894      4.1278    4.1393    ## pagval10_50   1.0899 1.1316 2.7511  2.3760  1.3348      1.3882      1.5127    1.5738    ## pagval50p     5.2011 5.0555 4.0178  4.7194  4.6604      4.5247      4.8823    4.7387    ## cowspacre     5.1969 5.3907 4.3531  3.7709  4.1379      4.2991      4.7274    4.9135    ## ln_cowspacre  5.2420 5.2455 3.9211  3.9085  4.2007      4.2037      4.6532    4.6566    ## ocattlepacre  0.5565 0.5593 -0.1707 -0.1668 2.1366      2.1478      1.9219    1.9320    ## pigspacre     2.4807 2.5393 2.2928  2.0802  2.8312      2.9010      3.1908    3.2703    ## ln_pigspacre  2.3015 2.2724 2.0520  2.1893  2.5171      2.4839      2.8460    2.8081    ## sheeppacre    1.0188 1.0630 0.8689  0.7387  1.7398      1.8187      1.4792    1.5470    ## ln_sheeppacre 1.2930 1.2827 1.5156  1.5767  2.3708      2.3511      2.0374    2.0203    ## townvillp     2.2759 2.2681 2.5475  2.5902  1.2148      1.2104      1.6275    1.6216    ## carspcap      4.4927 4.4015 3.2247  3.5992  3.8897      3.8075      4.1826    4.0934    ## radiopcap     0.3156 0.3153 1.2294  1.2348  0.5915      0.5909      0.7857    0.7849    ## retailpcap    3.4985 3.4524 3.1303  3.3497  2.9291      2.8888      3.0346    2.9926    ## psinglem30_34 2.7349 2.6895 2.3382  2.5519  2.7541      2.7065      2.7078    2.6605 wc_unstd <- spweights.constants(lw_unstand) wrong_N_sqVI <- sqrt((wc_unstd$nn*wc_unstd$S1 - wc_unstd$n*wc_unstd$S2 + 3*wc_unstd$S0*wc_unstd$S0)/((wc_unstd$nn-1)*wc_unstd$S0*wc_unstd$S0)-((-1/(wc_unstd$n-1))^2)) raw_data <- grep(\"^ln_\", vars, invert=TRUE) I <- sapply(Prop_stdN, function(x) x$estimate[1])[raw_data] EI <- sapply(Prop_stdN, function(x) x$estimate[2])[raw_data] res <- (I - EI)/wrong_N_sqVI names(res) <- vars[raw_data] print(formatC(res, format=\"f\", digits=4), quote=FALSE) ##    pagval2_10   pagval10_50     pagval50p     cowspacre  ocattlepacre     pigspacre  ##        3.8836        1.4957        4.8276        4.6744        1.9003        3.1550  ##    sheeppacre     townvillp      carspcap     radiopcap    retailpcap psinglem30_34  ##        1.4627        1.6093        4.1357        0.7769        3.0006        2.6774 res <- lapply(c(\"MoranR\", \"GearyR\", \"Prop_unstdR\", \"Prop_stdR\"), function(x) sapply(get(x), function(y) c(y$estimate[1], sqrt(y$estimate[3])))) res <- t(do.call(\"rbind\", res)) colnames(res) <- c(\"I\", \"sigma_I\", \"C\", \"sigma_C\", \"unstd_r\", \"sigma_r\", \"std_r\", \"sigma_r\") rownames(res) <- vars print(formatC(res, format=\"f\", digits=4), quote=FALSE) ##               I       sigma_I C      sigma_C unstd_r sigma_r std_r  sigma_r ## pagval2_10    0.4074  0.1158  0.3477 0.1672  0.4559  0.1456  0.5384 0.1440  ## ln_pagval2_10 0.4444  0.1183  0.3825 0.1531  0.4930  0.1490  0.5680 0.1473  ## pagval10_50   0.0877  0.1143  0.5840 0.1751  0.1577  0.1436  0.1818 0.1420  ## pagval50p     0.5754  0.1221  0.3925 0.1287  0.6545  0.1539  0.6795 0.1522  ## cowspacre     0.5749  0.1144  0.3418 0.1745  0.5764  0.1438  0.6566 0.1421  ## ln_cowspacre  0.5803  0.1186  0.4071 0.1517  0.5858  0.1493  0.6456 0.1476  ## ocattlepacre  0.0244  0.1181  1.0258 0.1547  0.2775  0.1486  0.2422 0.1469  ## pigspacre     0.2527  0.1159  0.6533 0.1667  0.3812  0.1458  0.4296 0.1441  ## ln_pigspacre  0.2314  0.1202  0.6897 0.1417  0.3343  0.1514  0.3787 0.1497  ## sheeppacre    0.0792  0.1137  0.8686 0.1778  0.2182  0.1429  0.1768 0.1412  ## ln_sheeppacre 0.1117  0.1196  0.7708 0.1453  0.3125  0.1506  0.2593 0.1489  ## townvillp     0.2284  0.1191  0.6148 0.1487  0.1398  0.1499  0.1987 0.1482  ## carspcap      0.4914  0.1211  0.5124 0.1355  0.5394  0.1526  0.5761 0.1509  ## radiopcap     -0.0042 0.1188  0.8141 0.1505  0.0467  0.1495  0.0744 0.1478  ## retailpcap    0.3734  0.1202  0.5267 0.1413  0.3959  0.1515  0.4066 0.1498  ## psinglem30_34 0.2828  0.1207  0.6465 0.1385  0.3697  0.1520  0.3583 0.1503 oMoranf <- function(x, nb) {   z <- scale(x, scale=FALSE)   n <- length(z)   glist <- lapply(1:n, function(i) {ii <- nb[[i]]; ifelse(ii > i, 1, 0)})   lw <- nb2listw(nb, glist=glist, style=\"B\")   wz <- lag(lw, z)   I <- (sum(z*wz)/sum(z*z))   I } res <- sapply(vars, function(x) oMoranf(eire_ge1[[x]], nb=lw_unstand$neighbours)) print(formatC(res, format=\"f\", digits=4), quote=FALSE) ##    pagval2_10 ln_pagval2_10   pagval10_50     pagval50p     cowspacre  ln_cowspacre  ##        0.8964        0.9776        0.1928        1.2660        1.2649        1.2766  ##  ocattlepacre     pigspacre  ln_pigspacre    sheeppacre ln_sheeppacre     townvillp  ##        0.0536        0.5559        0.5091        0.1743        0.2458        0.5024  ##      carspcap     radiopcap    retailpcap psinglem30_34  ##        1.0811       -0.0093        0.8215        0.6222"},{"path":"https://r-spatial.github.io/spdep/articles/CO69.html","id":"simulating-measures-of-spatial-autocorrelation","dir":"Articles","previous_headings":"","what":"Simulating measures of spatial autocorrelation","title":"“The Problem of Spatial Autocorrelation:” forty years on","text":"Cliff Ord (1969) conduct simulation experiments, although sequels , notably Cliff Ord (1973), among many others. Simulation studies necessarily demanding computationally, especially spatially autocorrelated variables created, Cliff Ord (1973, 146–53). book, also report use permutation tests, also known Monte Carlo Hope hypothesis testing procedures (Cliff Ord 1973, 50–52). procedures provided way examine distribution statistic interest exchanging random observed values observations, comparing simulated distribution null hypothesis spatial patterning observed value statistic question. First let us define function MoranI.boot just return value Moran’s II variable var permutation index , function Nsim generate random samples variable interest assuming Normality. make easier process variables turn, encapsulate calls boot wrapper functions f_bperm f_bpara. Running 4999 simulations 16 three different weights specifications parametric permutation bootstrap takes quite lot time. collate results compare analytical standard deviates Normality randomisation, see fact differences large, expressed median absolute difference tables. can also see inferences based one-sided α=0.05\\alpha=0.05 cut-analytical bootstrap approaches. indicates can, general, rely analytical standard deviates, bootstrap methods help assumptions underlying measures met. assumptions affect shape distribution measure tails; one possibility use Saddlepoint approximation find equivalent analytical bootstrap-based standard deviate inference (Tiefelsdorf 2002). Saddlepoint approximation requires eigenvalues weights matrix iterative root-finding global Moran’s II, local Moran’s IiI_i, analytical forms known. Even computational burden, Saddlepoint approximation global Moran’s II runs quite quickly. First need fit null linear models (including intercept) variables, apply lm.morantest.sad fitted model objects: Although analytical standard deviates (Normality) larger reached using Saddlepoint approximation measured median absolute deviation, differences lead different inferences chosen cut-. reflects fact shape distribution sensitive small nn, moderate nn global Moran’s II, effects seen tails. consequences local Moran’s IiI_i much stronger, clique neighbours observation typically small. perhaps interest differences much smaller case general weights unstandardised binary weights. addition choose use exact distribution Moran’s II, described Tiefelsdorf (2000); implementation covered R. S. Bivand, Müller, Reder (2009). global case also needs eigenvalues weights matrix, solution numerical integration function, cases, timings quite acceptable. output comparable Saddlepoint approximation, inferences drawn chosen cut-analytical standard deviates calculated Normality. Li, Calder, Cressie (2007) take challenge Cliff Ord (1969, 31), try give statistic bounded fixed range. APLE measure intended approximate spatial dependence parameter simultaneous autoregressive model better Moran’s II, re-scales measure function eigenvalues spatial weights matrix. APLE requires use row standardised weights. order save time, use two internal functions spatialreg:::preAple spatialreg:::inAple, since definition spatial weights, eigenvalue calculations need made. notation using ::: operator says function named operator found namespace package named operator. APLE values repeat pattern already seen — variables, measured autocorrelation similar irrespective spatial weights definition, others, change definition binary general make difference.","code":"MoranI.boot <- function(var, i, ...) {   var <- var[i]   return(moran(x=var, ...)$I) } Nsim <- function(d, mle) {   n <- length(d)   rnorm(n, mle$mean, mle$sd) } f_bperm <- function(x, nsim, listw) {   boot(x, statistic=MoranI.boot, R=nsim, sim=\"permutation\", listw=listw,     n=length(x), S0=Szero(listw)) } f_bpara <- function(x, nsim, listw) {   boot(x, statistic=MoranI.boot, R=nsim, sim=\"parametric\", ran.gen=Nsim,     mle=list(mean=mean(x), sd=sd(x)), listw=listw, n=length(x),     S0=Szero(listw)) } nsim <- 4999 set.seed(1234) system.time({ MoranNb <- lapply(vars, function(x) f_bpara(x=eire_ge1[[x]], nsim=nsim, listw=nb_B)) MoranRb <- lapply(vars, function(x) f_bperm(x=eire_ge1[[x]], nsim=nsim, listw=nb_B)) Prop_unstdNb  <- lapply(vars, function(x) f_bpara(x=eire_ge1[[x]], nsim=nsim, listw=lw_unstand)) Prop_unstdRb  <- lapply(vars, function(x) f_bperm(x=eire_ge1[[x]], nsim=nsim, listw=lw_unstand)) Prop_stdNb  <- lapply(vars, function(x) f_bpara(x=eire_ge1[[x]], nsim=nsim, listw=lw_std)) Prop_stdRb  <- lapply(vars, function(x) f_bperm(x=eire_ge1[[x]], nsim=nsim, listw=lw_std)) }) res <- lapply(c(\"MoranNb\", \"MoranRb\", \"Prop_unstdNb\", \"Prop_unstdRb\", \"Prop_stdNb\", \"Prop_stdRb\"), function(x) sapply(get(x), function(y) (y$t0 - mean(y$t))/sd(y$t))) res <- t(do.call(\"rbind\", res)) colnames(res) <- c(\"MoranNb\", \"MoranRb\", \"Prop_unstdNb\", \"Prop_unstdRb\", \"Prop_stdNb\", \"Prop_stdRb\") rownames(res) <- vars print(formatC(res, format=\"f\", digits=4), quote=FALSE) ##    pagval2_10 ln_pagval2_10   pagval10_50     pagval50p     cowspacre  ln_cowspacre  ##        0.8964        0.9776        0.1928        1.2660        1.2649        1.2766  ##  ocattlepacre     pigspacre  ln_pigspacre    sheeppacre ln_sheeppacre     townvillp  ##        0.0536        0.5559        0.5091        0.1743        0.2458        0.5024  ##      carspcap     radiopcap    retailpcap psinglem30_34  ##        1.0811       -0.0093        0.8215        0.6222 oores <- ores - res apply(oores, 2, mad) ##      MoranN      MoranR Prop_unstdN Prop_unstdR   Prop_stdN   Prop_stdR  ##   1.6470091   1.6241614   0.7681895   0.7170636   1.2615083   1.2723149 alpha_0.05 <- qnorm(0.05, lower.tail=FALSE) all((res >= alpha_0.05) == (ores >= alpha_0.05)) ## [1] FALSE lm_objs <- lapply(vars, function(x) lm(formula(paste(x, \"~1\")), data=eire_ge1)) system.time({ MoranSad <- lapply(lm_objs, function(x) lm.morantest.sad(x, listw=nb_B)) Prop_unstdSad  <- lapply(lm_objs, function(x) lm.morantest.sad(x, listw=lw_unstand)) Prop_stdSad  <- lapply(lm_objs, function(x) lm.morantest.sad(x, listw=lw_std)) }) ##    user  system elapsed  ##   0.066   0.000   0.066 res <- sapply(c(\"MoranSad\", \"Prop_unstdSad\", \"Prop_stdSad\"), function(x) sapply(get(x), \"[[\", \"statistic\")) rownames(res) <- vars print(formatC(res, format=\"f\", digits=4), quote=FALSE) ##               MoranSad Prop_unstdSad Prop_stdSad ## pagval2_10    3.2903   3.1711        3.8283      ## ln_pagval2_10 3.5346   3.3982        4.0441      ## pagval10_50   1.0883   1.3219        1.4791      ## pagval50p     4.4402   4.4258        4.9377      ## cowspacre     4.4366   3.9164        4.7406      ## ln_cowspacre  4.4758   3.9760        4.6493      ## ocattlepacre  0.6030   2.0748        1.8642      ## pigspacre     2.2611   2.7154        3.0775      ## ln_pigspacre  2.1158   2.4271        2.7417      ## sheeppacre    1.0250   1.7040        1.4476      ## ln_sheeppacre 1.2669   2.2921        1.9731      ## townvillp     2.0949   1.2079        1.5872      ## carspcap      3.8500   3.6840        4.1044      ## radiopcap     0.3750   0.6094        0.7906      ## retailpcap    3.0663   2.8049        2.9245      ## psinglem30_34 2.4649   2.6449        2.6089 oores <- res - ores[,c(1,3,5)] apply(oores, 2, mad) ##      MoranSad Prop_unstdSad   Prop_stdSad  ##    0.37142684    0.10779060    0.05650183 all((res >= alpha_0.05) == (ores[,c(1,3,5)] >= alpha_0.05)) ## [1] TRUE system.time({  MoranEx <- lapply(lm_objs, function(x) lm.morantest.exact(x, listw=nb_B)) Prop_unstdEx  <- lapply(lm_objs, function(x) lm.morantest.exact(x, listw=lw_unstand)) Prop_stdEx  <- lapply(lm_objs, function(x) lm.morantest.exact(x, listw=lw_std)) }) ##    user  system elapsed  ##   0.083   0.000   0.083 res <- sapply(c(\"MoranEx\", \"Prop_unstdEx\", \"Prop_stdEx\"), function(x) sapply(get(x), \"[[\", \"statistic\")) rownames(res) <- vars print(formatC(res, format=\"f\", digits=4), quote=FALSE) ##               MoranEx Prop_unstdEx Prop_stdEx ## pagval2_10    3.2895  3.1660       3.8261     ## ln_pagval2_10 3.5384  3.3979       4.0430     ## pagval10_50   1.0798  1.3131       1.4745     ## pagval50p     4.4568  4.4430       4.9446     ## cowspacre     4.4532  3.9268       4.7453     ## ln_cowspacre  4.4928  3.9875       4.6531     ## ocattlepacre  0.5967  2.0611       1.8596     ## pigspacre     2.2486  2.7033       3.0740     ## ln_pigspacre  2.1031  2.4131       2.7380     ## sheeppacre    1.0168  1.6924       1.4430     ## ln_sheeppacre 1.2575  2.2779       1.9685     ## townvillp     2.0822  1.1999       1.5826     ## carspcap      3.8593  3.6899       4.1037     ## radiopcap     0.3696  0.6054       0.7873     ## retailpcap    3.0616  2.7938       2.9210     ## psinglem30_34 2.4533  2.6321       2.6050 oores <- res - ores[,c(1,3,5)] apply(oores, 2, mad) ##      MoranEx Prop_unstdEx   Prop_stdEx  ##   0.37187539   0.09751723   0.05419300 all((res >= alpha_0.05) == (ores[,c(1,3,5)] >= alpha_0.05)) ## [1] TRUE vars_scaled <- lapply(vars, function(x) scale(eire_ge1[[x]], scale=FALSE)) nb_W <- nb2listw(lw_unstand$neighbours, style=\"W\") pre <- spatialreg:::preAple(0, listw=nb_W) MoranAPLE <- sapply(vars_scaled, function(x) spatialreg:::inAple(x, pre)) pre <- spatialreg:::preAple(0, listw=lw_std, override_similarity_check=TRUE) Prop_stdAPLE <- sapply(vars_scaled, function(x) spatialreg:::inAple(x, pre)) res <- cbind(MoranAPLE, Prop_stdAPLE) colnames(res) <- c(\"APLE W\", \"APLE Gstd\") rownames(res) <- vars print(formatC(res, format=\"f\", digits=4), quote=FALSE) ##               APLE W APLE Gstd ## pagval2_10    0.7702 0.6628    ## ln_pagval2_10 0.7615 0.6655    ## pagval10_50   0.3954 0.3446    ## pagval50p     0.7519 0.7313    ## cowspacre     0.8329 0.7408    ## ln_cowspacre  0.8148 0.7487    ## ocattlepacre  0.1468 0.4092    ## pigspacre     0.6227 0.6205    ## ln_pigspacre  0.5582 0.5887    ## sheeppacre    0.1594 0.2841    ## ln_sheeppacre 0.2046 0.4550    ## townvillp     0.3442 0.2644    ## carspcap      0.7140 0.6166    ## radiopcap     0.0083 0.1376    ## retailpcap    0.6376 0.5307    ## psinglem30_34 0.4094 0.4889"},{"path":"https://r-spatial.github.io/spdep/articles/CO69.html","id":"odds-and-ends-ldots","dir":"Articles","previous_headings":"","what":"Odds and ends …\\ldots","title":"“The Problem of Spatial Autocorrelation:” forty years on","text":"differences found case variables inference using original binary weights, general weights proposed Cliff Ord (1969) necessarily related weights thenselves. Figures plot_wtsplot\\_wts plot_mapplot\\_map show values weights sparse matrix form, sums weights county sums identical design. case binary weights, matrix entries equal, sums -weight counties many neighbours. General weights -weight counties close , neighbours, share larger boundary proportions (asymmetric relationship). impact using boundary proportions, boundary county exterior subtracted, thus boosting weights edge counties neighbours, even . Standardised general weights -weight -weight counties neighbours, chiefly edges study area. small data set, n=25n=25, possible edge configuration effects relatively strong, may impact inference different ways. issue egde effects really satisfactorily resolved, kept mind analyses data sets size shape.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/articles/nb.html","id":"creating-neighbours","dir":"Articles","previous_headings":"","what":"Creating Neighbours","title":"Creating Neighbours","text":"vignette formed pp. 239–251 first edition Bivand, R. S., Pebesma, E. Gómez-Rubio V. (2008) Applied Spatial Data Analysis R, Springer-Verlag, New York. retired second edition (2013) accommodate material topics, made available form understanding publishers.","code":""},{"path":"https://r-spatial.github.io/spdep/articles/nb.html","id":"introduction","dir":"Articles","previous_headings":"Creating Neighbours","what":"Introduction","title":"Creating Neighbours","text":"Creating spatial weights necessary step using areal data, perhaps just check remaining spatial patterning residuals. first step define relationships observations given non-zero weight, choose neighbour criterion used; second assign weights identified neighbour links. 281 census tract data set eight central New York State counties featured prominently (Waller Gotway 2004) used many examples, supplemented tract boundaries derived TIGER 1992 distributed SEDAC/CIESIN. boundaries projected geographical coordinates UTM zone~18. file identical boundaries used original source, close may re-distributed, unlike version used book. Starting census tract queen contiguities, touching polygons neighbours, used (Waller Gotway 2004) provided DBF file website, GAL format file created read R. sake simplicity showing create neighbour objects, work subset map consisting census tracts within Syracuse, although principles apply full data set. retrieve part neighbour list Syracuse using subset method.","code":"library(spdep) ## Loading required package: spData ## Loading required package: sf ## Linking to GEOS 3.13.0, GDAL 3.10.0, PROJ 9.5.1; sf_use_s2() is TRUE if (packageVersion(\"spData\") >= \"2.3.2\") {     NY8a <- sf::st_read(system.file(\"shapes/NY8_utm18.gpkg\", package=\"spData\")) } else {     NY8a <- sf::st_read(system.file(\"shapes/NY8_bna_utm18.gpkg\", package=\"spData\"))     sf::st_crs(NY8a) <- \"EPSG:32618\"     NY8a$Cases <- NY8a$TRACTCAS } ## Reading layer `NY8_utm18' from data source  ##   `/home/rsb/lib/r_libs/spData/shapes/NY8_utm18.gpkg' using driver `GPKG' ## Simple feature collection with 281 features and 17 fields ## Geometry type: POLYGON ## Dimension:     XY ## Bounding box:  xmin: 358241.9 ymin: 4649755 xmax: 480393.1 ymax: 4808545 ## Projected CRS: WGS 84 / UTM zone 18N NY8 <- as(NY8a, \"Spatial\") NY_nb <- read.gal(system.file(\"weights/NY_nb.gal\", package=\"spData\"), region.id=as.character(as.integer(row.names(NY8))-1L)) Syracuse <- NY8[!is.na(NY8$AREANAME) & NY8$AREANAME == \"Syracuse city\",] Sy0_nb <- subset(NY_nb, !is.na(NY8$AREANAME) & NY8$AREANAME == \"Syracuse city\") summary(Sy0_nb) ## Neighbour list object: ## Number of regions: 63  ## Number of nonzero links: 346  ## Percentage nonzero weights: 8.717561  ## Average number of links: 5.492063  ## Link number distribution: ##  ##  1  2  3  4  5  6  7  8  9  ##  1  1  5  9 14 17  9  6  1  ## 1 least connected region: ## 164 with 1 link ## 1 most connected region: ## 136 with 9 links"},{"path":"https://r-spatial.github.io/spdep/articles/nb.html","id":"creating-contiguity-neighbours","dir":"Articles","previous_headings":"Creating Neighbours","what":"Creating Contiguity Neighbours","title":"Creating Neighbours","text":"can create copy neighbours object polygon contiguities using poly2nb() function spdep. takes object extending SpatialPolygons class first argument, using heuristics identifies polygons sharing boundary points neighbours. also snap= argument, allow shared boundary points short distance one another. can see, creating contiguity neighbours Syracuse object reproduces neighbours (Waller Gotway 2004). Careful examination next figure shows, however, graph neighbours planar, since neighbour links cross . default, contiguity condition met least one point boundary one polygon within snap distance least one point neighbour. relationship given argument queen=TRUE analogy movements chessboard. three polygons meet single point, meet contiguity condition, giving rise crossed links. queen=FALSE, least two boundary points must within snap distance , conventional name `rook’ relationship. figure shows crossed line differences arise polygons touch single point, compared stricter rook criterion. : Queen-style census tract contiguities, Syracuse; b: Rook-style contiguity differences shown thicker orange lines access GIS GRASS ArcGIS, can export SpatialPolygonsDataFrame object use topology engine GIS find contiguities graph polygon edges - shared edge yield output rook relationship. procedure , however, depend topology set polygons clean, holds subset, full eight-county data set. infrequently, small artefacts, slivers boundary lines intersect diverge distances seen plots, require intervention keep geometries data correctly associated. geometrical artefacts present, topology clean, unambiguous shared polygon boundaries found cases; artefacts typically arise data collected one purpose combined data used another purpose. Topologies usually cleaned GIS snapping' vertices closer threshold distance together, removing artefacts -- example, snapping across river channel correct boundary median line input polygons stop channel banks side. Thepoly2nb()function asnap` argument, may also used input data possess geometrical artefacts. Similar approaches may also used read ArcGIS coverage data tallying left neighbour right neighbour arc indices polygons data set, using either RArcInfo rgdal. Syracuse case, exclaves islands' belonging data set, sharing boundary points within snap distance. number polygons moderate, missing neighbour links may added interactively using theedit()method fornb` objects, displaying polygon background. method may used removing links , although contiguity exists, may considered void, across mountain range.","code":"class(Syracuse) ## [1] \"SpatialPolygonsDataFrame\" ## attr(,\"package\") ## [1] \"sp\" Sy1_nb <- poly2nb(Syracuse) isTRUE(all.equal(Sy0_nb, Sy1_nb, check.attributes=FALSE)) ## [1] TRUE Sy2_nb <- poly2nb(Syracuse, queen=FALSE) isTRUE(all.equal(Sy0_nb, Sy2_nb, check.attributes=FALSE)) ## [1] FALSE oopar <- par(mfrow=c(1,2), mar=c(3,3,1,1)+0.1) plot(Syracuse, border=\"grey60\") plot(Sy0_nb, coordinates(Syracuse), add=TRUE, pch=19, cex=0.6) text(bbox(Syracuse)[1,1], bbox(Syracuse)[2,2], labels=\"a)\", cex=0.8) plot(Syracuse, border=\"grey60\") plot(Sy0_nb, coordinates(Syracuse), add=TRUE, pch=19, cex=0.6) plot(diffnb(Sy0_nb, Sy2_nb, verbose=FALSE), coordinates(Syracuse),   add=TRUE, pch=\".\", cex=0.6, lwd=2, col=\"orange\") text(bbox(Syracuse)[1,1], bbox(Syracuse)[2,2], labels=\"b)\", cex=0.8) par(oopar) library(rgrass) v <- terra::vect(sf::st_as_sf(Syracuse)) SG <- terra::rast(terra::ext(v), crs=terra::crs(v)) pr <- initGRASS(\"/home/rsb/topics/grass/g840/grass84\", tempdir(), SG=SG, override=TRUE) write_VECT(v, \"SY0\", flags=c(\"o\", \"overwrite\")) contig <- vect2neigh(\"SY0\") Sy3_nb <- sn2listw(contig, style=\"B\")$neighbours isTRUE(all.equal(Sy3_nb, Sy2_nb, check.attributes=FALSE)) ## [1] TRUE"},{"path":"https://r-spatial.github.io/spdep/articles/nb.html","id":"creating-graph-based-neighbours","dir":"Articles","previous_headings":"Creating Neighbours","what":"Creating Graph-Based Neighbours","title":"Creating Neighbours","text":"Continuing irregularly located areal entities, possible choose point represent polygon-support entities. often polygon centroid, average coordinates dimension, takes proper care weight component triangles polygon area. also possible use points, data available, construct, example population-weighted centroids. representative points available, criteria neighbourhood can extended just contiguity include graph measures, distance thresholds, kk-nearest neighbours. direct graph representation neighbours make Delaunay triangulation points, shown first panel figure. neighbour relationships defined triangulation, extends outwards convex hull points planar. Note graph-based representations construct interpoint relationships based Euclidean distance, option use Great Circle distances geographical coordinates. joins distant points around convex hull, may worthwhile thin triangulation Sphere Influence (SOI) graph, removing links relatively long. Points SOI neighbours circles centred points, radius equal points’ nearest neighbour distances, intersect two places (Avis Horton 1985). Functions graph-based neighbours kindly contributed Nicholas Lewin-Koh. : Delauney triangulation neighbours; b: Sphere influence neighbours (available); c: Gabriel graph neighbours; d: Relative graph neighbours Delaunay triangulation neighbours SOI neighbours symmetric design – ii neighbour jj, jj neighbour ii. Gabriel graph also subgraph Delaunay triangulation, retaining different set neighbours (Matula Sokal 1980). , however, guarantee symmetry; applies Relative graph neighbours (Toussaint 1980). graph2nb() function takes sym argument insert links restore symmetry, graphs longer exactly fulfil neighbour criteria. graph-based neighbour schemes always ensure points least one neighbour. Subgraphs full triangulation may also one graph trimming. functions .symmetric.nb() can used check symmetry, argument force=TRUE symmetry attribute overridden, n.comp.nb() reports number graph components ~components points belong (enforcing symmetry, algorithm assumes graph directed). one graph component, matrix representation spatial weights can become block-diagonal observations appropriately sorted.","code":"coords <- coordinates(Syracuse) IDs <- row.names(as(Syracuse, \"data.frame\")) #FIXME library(tripack) Sy4_nb <- tri2nb(coords, row.names=IDs) if (require(dbscan, quietly=TRUE)) {   Sy5_nb <- graph2nb(soi.graph(Sy4_nb, coords), row.names=IDs) } else Sy5_nb <- NULL ##  ## Attaching package: 'dbscan' ## The following object is masked from 'package:stats': ##  ##     as.dendrogram Sy6_nb <- graph2nb(gabrielneigh(coords), row.names=IDs) Sy7_nb <- graph2nb(relativeneigh(coords), row.names=IDs) oopar <- par(mfrow=c(2,2), mar=c(1,1,1,1)+0.1) plot(Syracuse, border=\"grey60\") plot(Sy4_nb, coords, add=TRUE, pch=\".\") text(bbox(Syracuse)[1,1], bbox(Syracuse)[2,2], labels=\"a)\", cex=0.8) plot(Syracuse, border=\"grey60\") if (!is.null(Sy5_nb)) {   plot(Sy5_nb, coords, add=TRUE, pch=\".\")   text(bbox(Syracuse)[1,1], bbox(Syracuse)[2,2], labels=\"b)\", cex=0.8) } plot(Syracuse, border=\"grey60\") plot(Sy6_nb, coords, add=TRUE, pch=\".\") text(bbox(Syracuse)[1,1], bbox(Syracuse)[2,2], labels=\"c)\", cex=0.8) plot(Syracuse, border=\"grey60\") plot(Sy7_nb, coords, add=TRUE, pch=\".\") text(bbox(Syracuse)[1,1], bbox(Syracuse)[2,2], labels=\"d)\", cex=0.8) par(oopar) nb_l <- list(Triangulation=Sy4_nb, Gabriel=Sy6_nb,   Relative=Sy7_nb) if (!is.null(Sy5_nb)) nb_l <- c(nb_l, list(SOI=Sy5_nb)) sapply(nb_l, function(x) is.symmetric.nb(x, verbose=FALSE, force=TRUE)) ## Triangulation       Gabriel      Relative           SOI  ##          TRUE         FALSE         FALSE          TRUE sapply(nb_l, function(x) n.comp.nb(x)$nc) ## Triangulation       Gabriel      Relative           SOI  ##             1             1             1             1"},{"path":"https://r-spatial.github.io/spdep/articles/nb.html","id":"distance-based-neighbours","dir":"Articles","previous_headings":"Creating Neighbours","what":"Distance-Based Neighbours","title":"Creating Neighbours","text":"alternative method choose kk nearest points neighbours – adapts across study area, taking account differences densities areal entities. Naturally, overwhelming majority cases, leads asymmetric neighbours, ensure areas kk neighbours. knearneigh() function returns intermediate form converted nb object knn2nb(); knearneigh() can also take longlat= argument handle geographical coordinates. : k=1k=1 neighbours; b: k=2k=2 neighbours; c: k=4k=4 neighbours figure shows neighbour relationships k=1,2,4k= 1, 2, 4, many components k=1k=1. need , kk-nearest neighbour objects can made symmetrical using make.sym.nb() function. k=1k=1 object also useful finding minimum distance areas distance-based neighbour. Using nbdists() function, can calculate list vectors distances corresponding neighbour object, first nearest neighbours. greatest value minimum distance needed make sure areas linked least one neighbour. dnearneigh() function used find neighbours interpoint distance, arguments d1 d2 setting lower upper distance bounds; can also take longlat argument handle geographical coordinates. : Neighbours within 1,158m; b: neighbours within 1,545m; c: neighbours within 2,317m figure shows numbers distance-based neighbours increase moderate increases distance. Moving 0.750.75 times minimum -included distance, -included distance, 1.51.5 times minimum -included distance, numbers links grow rapidly. major problem first nearest neighbour distances study area much larger others, since avoid -neighbour areal entities, distance criterion need set many areas many neighbours. Distance-based neighbours: frequencies numbers neighbours census tract figure shows counts sizes sets neighbours three different distance limits. Syracuse, census tracts similar areas, try use distance-based neighbour criterion eight-county study area, smallest distance securing least one neighbour every areal entity 38km. areal entities approximately regularly spaced, using distance-based neighbours necessarily problem. Provided care taken handle side effects “weighting” areas analysis, using lists neighbours -neighbour areas necessarily problem either, certainly raise questions. Different disciplines handle definition neighbours ways convention; particular, seems ecologists frequently use distance bands. many distance bands used, approach variogram, although underlying understanding spatial autocorrelation seems contagion rather continuous.","code":"Sy8_nb <- knn2nb(knearneigh(coords, k=1), row.names=IDs) ## Warning in knn2nb(knearneigh(coords, k = 1), row.names = IDs): neighbour object ## has 15 sub-graphs Sy9_nb <- knn2nb(knearneigh(coords, k=2), row.names=IDs) Sy10_nb <- knn2nb(knearneigh(coords, k=4), row.names=IDs) nb_l <- list(k1=Sy8_nb, k2=Sy9_nb, k4=Sy10_nb) sapply(nb_l, function(x) is.symmetric.nb(x, verbose=FALSE, force=TRUE)) ##    k1    k2    k4  ## FALSE FALSE FALSE sapply(nb_l, function(x) n.comp.nb(x)$nc) ## k1 k2 k4  ## 15  1  1 oopar <- par(mfrow=c(1,3), mar=c(1,1,1,1)+0.1) plot(Syracuse, border=\"grey60\") plot(Sy8_nb, coords, add=TRUE, pch=\".\") text(bbox(Syracuse)[1,1], bbox(Syracuse)[2,2], labels=\"a)\", cex=0.8) plot(Syracuse, border=\"grey60\") plot(Sy9_nb, coords, add=TRUE, pch=\".\") text(bbox(Syracuse)[1,1], bbox(Syracuse)[2,2], labels=\"b)\", cex=0.8) plot(Syracuse, border=\"grey60\") plot(Sy10_nb, coords, add=TRUE, pch=\".\") text(bbox(Syracuse)[1,1], bbox(Syracuse)[2,2], labels=\"c)\", cex=0.8) par(oopar) dsts <- unlist(nbdists(Sy8_nb, coords)) summary(dsts) ##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.  ##   395.7   587.3   700.1   760.4   906.1  1544.6 max_1nn <- max(dsts) max_1nn ## [1] 1544.615 Sy11_nb <- dnearneigh(coords, d1=0, d2=0.75*max_1nn, row.names=IDs) ## Warning in dnearneigh(coords, d1 = 0, d2 = 0.75 * max_1nn, row.names = IDs): ## neighbour object has 4 sub-graphs Sy12_nb <- dnearneigh(coords, d1=0, d2=1*max_1nn, row.names=IDs) Sy13_nb <- dnearneigh(coords, d1=0, d2=1.5*max_1nn, row.names=IDs) nb_l <- list(d1=Sy11_nb, d2=Sy12_nb, d3=Sy13_nb) sapply(nb_l, function(x) is.symmetric.nb(x, verbose=FALSE, force=TRUE)) ##   d1   d2   d3  ## TRUE TRUE TRUE sapply(nb_l, function(x) n.comp.nb(x)$nc) ## d1 d2 d3  ##  4  1  1 oopar <- par(mfrow=c(1,3), mar=c(1,1,1,1)+0.1) plot(Syracuse, border=\"grey60\") plot(Sy11_nb, coords, add=TRUE, pch=\".\") text(bbox(Syracuse)[1,1], bbox(Syracuse)[2,2], labels=\"a)\", cex=0.8) plot(Syracuse, border=\"grey60\") plot(Sy12_nb, coords, add=TRUE, pch=\".\") text(bbox(Syracuse)[1,1], bbox(Syracuse)[2,2], labels=\"b)\", cex=0.8) plot(Syracuse, border=\"grey60\") plot(Sy13_nb, coords, add=TRUE, pch=\".\") text(bbox(Syracuse)[1,1], bbox(Syracuse)[2,2], labels=\"c)\", cex=0.8) par(oopar) dS <- c(0.75, 1, 1.5)*max_1nn res <- sapply(nb_l, function(x) table(card(x))) mx <- max(card(Sy13_nb)) res1 <- matrix(0, ncol=(mx+1), nrow=3) rownames(res1) <- names(res) colnames(res1) <- as.character(0:mx) res1[1, names(res$d1)] <- res$d1 res1[2, names(res$d2)] <- res$d2 res1[3, names(res$d3)] <- res$d3 library(RColorBrewer) pal <- grey.colors(3, 0.95, 0.55, 2.2) # RSB quietening greys barplot(res1, col=pal, beside=TRUE, legend.text=FALSE, xlab=\"numbers of neighbours\", ylab=\"tracts\") legend(\"topright\", legend=format(dS, digits=1), fill=pal, bty=\"n\", cex=0.8, title=\"max. distance\") dsts0 <- unlist(nbdists(NY_nb, coordinates(NY8))) summary(dsts0) ##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.  ##    82.7  1505.0  3378.7  5865.8  8954.3 38438.1"},{"path":"https://r-spatial.github.io/spdep/articles/nb.html","id":"higher-order-neighbours","dir":"Articles","previous_headings":"Creating Neighbours","what":"Higher-Order Neighbours","title":"Creating Neighbours","text":"Distance bands can generated using sequence d1 d2 argument values dnearneigh() function needed construct spatial autocorrelogram understood ecology. conventions, correlograms constructed taking input list neighbours first-order sets, stepping across graph second-, third-, higher-order neighbours based number links traversed, permitting cycles, risk making ii neighbour ii (O’Sullivan Unwin 2003). nblag() function takes existing neighbour list returns list lists, first maxlag= order neighbours. shows wave connectedness graph spreads third order, receding eighth order, dying away ninth order - tracts nine steps graph. distance bands graph step order approaches spreading neighbourhoods can used examine shape relationship intensities space, like variogram, can used attempting look effects scale.","code":"Sy0_nb_lags <- nblag(Sy0_nb, maxlag=9) ## Warning in nblag(Sy0_nb, maxlag = 9): lag 6 neighbour object has 7 sub-graphs ## Warning in nblag(Sy0_nb, maxlag = 9): lag 7 neighbour object has 22 sub-graphs ## Warning in nblag(Sy0_nb, maxlag = 9): lag 8 neighbour object has 52 sub-graphs ## Warning in nblag(Sy0_nb, maxlag = 9): lag 9 neighbour object has 63 sub-graphs names(Sy0_nb_lags) <- c(\"first\", \"second\", \"third\", \"fourth\", \"fifth\", \"sixth\", \"seventh\", \"eighth\", \"ninth\") res <- sapply(Sy0_nb_lags, function(x) table(card(x))) mx <- max(unlist(sapply(Sy0_nb_lags, function(x) card(x)))) nn <- length(Sy0_nb_lags) res1 <- matrix(0, ncol=(mx+1), nrow=nn) rownames(res1) <- names(res) colnames(res1) <- as.character(0:mx) for (i in 1:nn) res1[i, names(res[[i]])] <- res[[i]] res1 ##          0 1 2 3 4  5  6 7 8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 ## first    0 1 1 5 9 14 17 9 6  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 ## second   0 0 0 0 2  2  0 6 6 11 11  4  3  7  4  6  1  0  0  0  0  0  0  0  0 ## third    0 0 0 0 0  0  0 1 3  5  5  7 14  6  8  3  3  0  1  1  1  3  1  0  1 ## fourth   0 0 0 0 0  0  0 0 1  3  5  7 16 16  5  3  3  2  0  1  1  0  0  0  0 ## fifth    0 0 0 1 1  3  1 1 3  7 13 12  8  9  3  1  0  0  0  0  0  0  0  0  0 ## sixth    6 3 0 2 8  2  5 5 4  8  9  5  5  1  0  0  0  0  0  0  0  0  0  0  0 ## seventh 21 7 4 5 9  7  3 5 1  0  0  0  1  0  0  0  0  0  0  0  0  0  0  0  0 ## eighth  49 6 5 2 1  0  0 0 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 ## ninth   63 0 0 0 0  0  0 0 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0"},{"path":"https://r-spatial.github.io/spdep/articles/nb.html","id":"grid-neighbours","dir":"Articles","previous_headings":"Creating Neighbours","what":"Grid Neighbours","title":"Creating Neighbours","text":"data known arranged regular, rectangular grid, cell2nb() function can used construct neighbour lists, including torus. useful simulations, , since areal entities equal numbers neighbours, edges, structure graph neutral can achieved. Neighbours can either type rook queen. regular, rectangular grid complete, can use knowledge cell size stored grid topology create appropriate list neighbours, using tightly bounded distance criterion. Neighbour lists kind commonly found ecological assays, studies species richness national continental scale. also settings, moderately large nn, n=3n=3,103, use sparse, list based representation shows strength. Handling 281×281281 \\times 281 matrix eight-county census tracts feasible, easy 63×6363 \\times 63 matrix Syracuse census tracts, demanding 3,103×3103 \\times 3,103 matrix.","code":"cell2nb(7, 7, type=\"rook\", torus=TRUE) ## Neighbour list object: ## Number of regions: 49  ## Number of nonzero links: 196  ## Percentage nonzero weights: 8.163265  ## Average number of links: 4 cell2nb(7, 7, type=\"rook\", torus=FALSE) ## Neighbour list object: ## Number of regions: 49  ## Number of nonzero links: 168  ## Percentage nonzero weights: 6.997085  ## Average number of links: 3.428571 data(meuse.grid) coordinates(meuse.grid) <- c(\"x\", \"y\") gridded(meuse.grid) <- TRUE dst <- max(slot(slot(meuse.grid, \"grid\"), \"cellsize\")) mg_nb <- dnearneigh(coordinates(meuse.grid), 0, dst) mg_nb ## Neighbour list object: ## Number of regions: 3103  ## Number of nonzero links: 12022  ## Percentage nonzero weights: 0.1248571  ## Average number of links: 3.874315 table(card(mg_nb)) ##  ##    1    2    3    4  ##    1  133  121 2848"},{"path":[]},{"path":[]},{"path":"https://r-spatial.github.io/spdep/articles/nb_sf.html","id":"introduction","dir":"Articles","previous_headings":"Creating Neighbours using sf objects","what":"Introduction","title":"Creating Neighbours using sf objects","text":"vignette tracks legacy nb vignette, based part first (2008) edition ASDAR. adds hints code nb vignette use sf vector representation instead sp vector representation create neighbour objects. .","code":""},{"path":"https://r-spatial.github.io/spdep/articles/nb_sf.html","id":"summary","dir":"Articles","previous_headings":"Creating Neighbours using sf objects","what":"Summary","title":"Creating Neighbours using sf objects","text":"summary results : general, need reproduce results using \"Spatial\" objects spdep, coerce sf objects sp objects constructing neighbour objects (particularly polygon centroids used point representation). However, new work, use \"sf\" objects read using sf. spdep 1.1-7, number steps taken choose efficient approaches especially larger data sets, using functions sf approximate nearest neighbour (ANN) implementation dbscan rather RANN.","code":""},{"path":"https://r-spatial.github.io/spdep/articles/nb_sf.html","id":"data-set","dir":"Articles","previous_headings":"Creating Neighbours using sf objects","what":"Data set","title":"Creating Neighbours using sf objects","text":"’ll use whole NY 8 county set boundaries, challenge implementations just Syracuse subset. description input geometries ADSAR : New York leukemia: used documented extensively Waller Gotway (2004) data formerly made available Chap. 9 http://web1.sph.emory.edu/users/lwaller/ch9index.htm; data import process described help file NY_data spData; geometries downloaded CIESIN server formerly sedac.ciesin.columbia.edu/data/set/acrp-boundary-1992/data-download, now possibly https://earthdata.nasa.gov/data/catalog/sedac-ciesin-sedac-acrp-1992-bf-1.00, file /pub/census/usa/tiger/ny/bna_st/t8_36.zip, extensively edited; zip archive NY_data.zip shapefiles GAL format neighbours list book website. , zipfile now new location requiring login. object listw_NY directly imported nyadjwts.dbf Waller & Gotway (2004) chapter 9 website. version New York 8 counties geometries used ASDAR included shapefile spdep converted original BNA file using external utility program convert MapInfo format converted using GDAL 1.4.1 (OGR BNA driver available; entered OGR 1.5.0, release end 2007), contains invalid geometries. found mid-2007 included villages /excluded -umbilical cords boundary enclosing tract, underlying BNA file first converted MapInfo (holes exist ). use GPKG file created follows (rgdal also used output; GDAL prior GDAL 3.3 built GEOS, BNA vector driver use geometry tests: BNA driver supports reading polygons holes lakes. determines hole lake geometrical analysis (inclusion, non-intersection tests) ignores completely notion polygon winding (whether polygon edges described clockwise counter-clockwise). GDAL must built GEOS enabled make geometry test work.):","code":"library(sf) sf_bna <- st_read(\"t8_36.bna\", stringsAsFactors=FALSE) table(st_is_valid(sf_bna)) sf_bna$AREAKEY <- gsub(\"\\\\.\", \"\", sf_bna$Primary.ID) data(NY_data, package=\"spData\") key <- as.character(nydata$AREAKEY) sf_bna1 <- sf_bna[match(key, sf_bna$AREAKEY), c(\"AREAKEY\")] sf_bna2 <- merge(sf_bna1, nydata, by=\"AREAKEY\") sf_bna2_utm18 <- st_transform(sf_bna2, \"+proj=utm +zone=18 +datum=NAD27\") st_write(sf_bna2_utm18, \"NY8_bna_utm18.gpkg\")"},{"path":"https://r-spatial.github.io/spdep/articles/nb_sf.html","id":"nb-and-listw-objects-copied-from-the-nb_igraph-vignette","dir":"Articles","previous_headings":"Creating Neighbours using sf objects","what":"nb and listw objects (copied from the nb_igraph vignette)","title":"Creating Neighbours using sf objects","text":"Since spdep package created, spatial weights objects constructed lists three components attributes, old-style class listw objects. first component listw object nb object, list n integer vectors, least character vector region.id attribute n unique values (like row.names data.frame object); n number spatial entities. Component list contains integer identifiers neighbours sorted vector duplication values 1:n; neighbours, component vector length 1 value 0L. nb object may contain attribute indicating whether symmetric , whether neighbour j implies j neighbour . neighbour definitions symmetric construction, contiguities distance thresholds, others asymmetric, k-nearest neighbours. nb object redundantly stores -j j-links. second component listw object list n numeric vectors, length corresponding non-zero vectors nbobject. give values spatial weights -j neighbour pair. often case neighbours symmetric construction, weights , example weights row-standardised dividing row input weights count neighbours cardinality neighbour set . nb2listwfunction, also possible pass general weights, inverse distances, shares boundary lengths . third component listw object records style weights character code, \"B\" binary weights taking values zero one (one recorded), \"W\" row-standardised weights, . order subset listw objects, knowledge style may necessary.","code":""},{"path":"https://r-spatial.github.io/spdep/articles/nb_sf.html","id":"comparison-of-sp-and-sf-approaches","dir":"Articles","previous_headings":"Creating Neighbours using sf objects","what":"Comparison of sp and sf approaches","title":"Creating Neighbours using sf objects","text":"First housekeeping setup permit vignette built packages missing --date: Let us read GPKG file valid geometries ‘sf’ ‘sp’ objects:","code":"if (!suppressPackageStartupMessages(require(sf, quietly=TRUE))) {   message(\"install the sf package\")   dothis <- FALSE } if (dothis) sf_extSoftVersion() ##           GEOS           GDAL         proj.4 GDAL_with_GEOS     USE_PROJ_H  ##       \"3.13.0\"       \"3.10.0\"        \"9.5.1\"         \"true\"         \"true\"  ##           PROJ  ##        \"9.5.1\" NY8_sf <- st_read(system.file(\"shapes/NY8_bna_utm18.gpkg\", package=\"spData\"), quiet=TRUE) table(st_is_valid(NY8_sf)) ##  ## TRUE  ##  281"},{"path":"https://r-spatial.github.io/spdep/articles/nb_sf.html","id":"contiguity-neighbours-for-polygon-support","dir":"Articles","previous_headings":"Creating Neighbours using sf objects > Comparison of sp and sf approaches","what":"Contiguity neighbours for polygon support","title":"Creating Neighbours using sf objects","text":"first generate queen contiguity nb object using legacy spdep approach. first either uses pre-computed list vectors probable neighbours finds intersecting bounding boxes internally. points boundaries set polygons making observation checked distance less snap points set polygons making observation included set candidate neighbours. contiguity symmetric, j contiguities tested. queen contiguity found soon one point matches, rook contiguity soon two points match: Using spatial indices check intersection polygons much faster legacy method poly2nb. spdep 1.1-7, use made GEOS sf find candidate neighbours foundInBox=NULL, default value. contiguity symmetric definition, foundInBox= requires intersections higher indices, leading slight overhead remove duplicates, st_intersects() reports j ans j relationships. st_intersects() report whether neighbours queen rook, step needed distinguish two cases. spdep::poly2nb uses two heuristics, first find candidate neighbours intersecting polygons (st_intersects()), second use symmetry relationship halve number remaining tests. means performance linear n, overhead identifying candidates, back-filling symmetric neighbours. , spdep::poly2nb() stops searching queen contiguity soon first neighbour point found within snap distance (identical, tested first); second neighbour point indicates rook contiguities. details alternatives spherical geometries, see section @ref(spher-poly2nb) .","code":"suppressPackageStartupMessages(library(spdep)) reps <- 10 eps <- sqrt(.Machine$double.eps) system.time(for(i in 1:reps) NY8_sf_1_nb <- poly2nb(NY8_sf, queen=TRUE, snap=eps))/reps ##    user  system elapsed  ##  0.1810  0.0094  0.1912 NY8_sf_1_nb ## Neighbour list object: ## Number of regions: 281  ## Number of nonzero links: 1632  ## Percentage nonzero weights: 2.066843  ## Average number of links: 5.807829"},{"path":"https://r-spatial.github.io/spdep/articles/nb_sf.html","id":"contiguity-neighbours-from-invalid-polygons","dir":"Articles","previous_headings":"Creating Neighbours using sf objects > Comparison of sp and sf approaches","what":"Contiguity neighbours from invalid polygons","title":"Creating Neighbours using sf objects","text":"Next, explore possible source differences neighbour object reproduction, using original version tract boundaries used ASDAR, invalid geometries mentioned earlier (NY8_utm18.gpkg created original ESRI Shapefile used ASDAR): can see number differences neighbour sets derived fully valid geometries older partly invalid set: Using st_make_valid() make geometries valid: also see geometry type geometry column changes: checking \"sfg\" objects, two now objects different topological dimensions. can remedied using st_collection_extract() get polygon objects: However, making geometries valid, change geometries, new sets neighbours still differ made valid geometries ways imposing validity: neighbour sets old boundaries without imposing validity:","code":"if (packageVersion(\"spData\") >= \"2.3.2\") {     NY8_sf_old <- sf::st_read(system.file(\"shapes/NY8_utm18.gpkg\", package=\"spData\")) } else {     NY8_sf_old <- sf::st_read(system.file(\"shapes/NY8_utm18.shp\", package=\"spData\")) } ## Reading layer `NY8_utm18' from data source  ##   `/home/rsb/lib/r_libs/spData/shapes/NY8_utm18.gpkg' using driver `GPKG' ## Simple feature collection with 281 features and 17 fields ## Geometry type: POLYGON ## Dimension:     XY ## Bounding box:  xmin: 358241.9 ymin: 4649755 xmax: 480393.1 ymax: 4808545 ## Projected CRS: WGS 84 / UTM zone 18N table(st_is_valid(NY8_sf_old)) ##  ## FALSE  TRUE  ##     5   276 try(NY8_sf_old_1_nb <- poly2nb(NY8_sf_old), silent = TRUE) all.equal(NY8_sf_old_1_nb, NY8_sf_1_nb, check.attributes=FALSE) ## [1] \"Component 57: Numeric: lengths (4, 5) differ\"  ## [2] \"Component 58: Numeric: lengths (5, 6) differ\"  ## [3] \"Component 66: Numeric: lengths (7, 11) differ\" ## [4] \"Component 73: Numeric: lengths (4, 5) differ\"  ## [5] \"Component 260: Numeric: lengths (8, 9) differ\" NY8_sf_old_val <- st_make_valid(NY8_sf_old, dist=0) table(st_is_valid(NY8_sf_old_val)) ##  ## TRUE  ##  281 class(st_geometry(NY8_sf_old)) ## [1] \"sfc_POLYGON\" \"sfc\" class(st_geometry(NY8_sf_old_val)) ## [1] \"sfc_GEOMETRY\" \"sfc\" table(sapply(st_geometry(NY8_sf_old_val), function(x) class(x)[[2]])) ##  ## MULTIPOLYGON      POLYGON  ##            3          278 NY8_sf_old_val <- st_collection_extract(NY8_sf_old_val, \"POLYGON\") table(sapply(st_geometry(NY8_sf_old_val), function(x) class(x)[[2]])) ##  ## MULTIPOLYGON  ##          281 try(NY8_sf_old_1_nb_val <- poly2nb(NY8_sf_old_val), silent = TRUE) all.equal(NY8_sf_old_1_nb_val, NY8_sf_1_nb, check.attributes=FALSE) ## [1] \"Component 57: Numeric: lengths (4, 5) differ\"  ## [2] \"Component 58: Numeric: lengths (5, 6) differ\"  ## [3] \"Component 66: Numeric: lengths (7, 11) differ\" ## [4] \"Component 73: Numeric: lengths (4, 5) differ\"  ## [5] \"Component 260: Numeric: lengths (8, 9) differ\" all.equal(NY8_sf_old_1_nb_val, NY8_sf_old_1_nb, check.attributes=FALSE) ## [1] TRUE"},{"path":[]},{"path":"https://r-spatial.github.io/spdep/articles/nb_sf.html","id":"finding-points-for-polygon-objects","dir":"Articles","previous_headings":"Creating Neighbours using sf objects > Planar point-based neighbours","what":"Finding points for polygon objects","title":"Creating Neighbours using sf objects","text":"knearneigh() dnearneigh() require point support, decisions must taken place point areal object. can use st_centroid() get centroids, using of_largest_polygon=TRUE argument make sure centroid largest polygon id observation made one external ring: st_point_on_surface() guarantees point fall surface member polygon: indeed taking centre largest inscribed circle (function returns radius line segment, choose central point, point circle): need check whether coordinates planar :","code":"NY8_ct_sf <- st_centroid(st_geometry(NY8_sf), of_largest_polygon=TRUE) NY8_pos_sf <- st_point_on_surface(st_geometry(NY8_sf)) if (unname(sf_extSoftVersion()[\"GEOS\"] >= \"3.9.0\"))      NY8_cic_sf <- st_cast(st_inscribed_circle(st_geometry(NY8_sf), nQuadSegs=0), \"POINT\")[(1:(2*nrow(NY8_sf)) %% 2) != 0] st_is_longlat(NY8_ct_sf) ## [1] FALSE"},{"path":"https://r-spatial.github.io/spdep/articles/nb_sf.html","id":"graph-based-neighbours","dir":"Articles","previous_headings":"Creating Neighbours using sf objects > Planar point-based neighbours","what":"Graph-based neighbours","title":"Creating Neighbours using sf objects","text":", can check graph-based neighbours (planar coordinates ):","code":"suppressPackageStartupMessages(require(deldir)) NY84_nb <- tri2nb(NY8_ct_sf) if (require(dbscan, quietly=TRUE)) {   NY85_nb <- graph2nb(soi.graph(NY84_nb, NY8_ct_sf)) } else NY85_nb <- NULL ##  ## Attaching package: 'dbscan' ## The following object is masked from 'package:stats': ##  ##     as.dendrogram ## Warning in graph2nb(soi.graph(NY84_nb, NY8_ct_sf)): neighbour object has 2 ## sub-graphs NY86_nb <- graph2nb(gabrielneigh(NY8_ct_sf)) NY87_nb <- graph2nb(relativeneigh(NY8_ct_sf))"},{"path":"https://r-spatial.github.io/spdep/articles/nb_sf.html","id":"k-nearest-neighbours","dir":"Articles","previous_headings":"Creating Neighbours using sf objects > Planar point-based neighbours","what":"K-nearest neighbours","title":"Creating Neighbours using sf objects","text":"K-nearest neighbours use coordinate matrices, can handle Great Circle distances, demonstrated , data set used planar, case dbscan::kNN() 2D 3D building kd-tree used: Legacy code may used omitting kd-tree:","code":"system.time(for (i in 1:reps) suppressWarnings(NY88_nb_sf <- knn2nb(knearneigh(NY8_ct_sf, k=1))))/reps ##    user  system elapsed  ##  0.0238  0.0013  0.0253 system.time(for (i in 1:reps) suppressWarnings(NY89_nb_sf <- knn2nb(knearneigh(NY8_ct_sf, k=1, use_kd_tree=FALSE))))/reps ##    user  system elapsed  ##  0.0242  0.0011  0.0253"},{"path":"https://r-spatial.github.io/spdep/articles/nb_sf.html","id":"distance-neighbours","dir":"Articles","previous_headings":"Creating Neighbours using sf objects > Planar point-based neighbours","what":"Distance neighbours","title":"Creating Neighbours using sf objects","text":"Distance neighbours need threshold - nbdists shows maximum distance first nearest neighbour: dnearneigh can also handle Great Circle distances, demonstrated , data set used planar: default, function uses dbscan::frNN() build kd-tree 2D 3D used find distance neighbours. small n, argument use_kd_tree=FALSE may speed computation little reverting legacy code building kd-tree first, general differences small user notice:","code":"dsts <- unlist(nbdists(NY88_nb_sf, NY8_ct_sf)) summary(dsts) ##     Min.  1st Qu.   Median     Mean  3rd Qu.     Max.  ##    82.85   912.85  1801.11  3441.04  4461.26 17033.11 max_1nn <- max(dsts) system.time(for (i in 1:reps) suppressWarnings(NY810_nb <- dnearneigh(NY8_ct_sf, d1=0, d2=0.75*max_1nn)))/reps ##    user  system elapsed  ##  0.0618  0.0018  0.0638 system.time(for (i in 1:reps) suppressWarnings(NY811_nb <- dnearneigh(NY8_ct_sf, d1=0, d2=0.75*max_1nn, use_kd_tree=FALSE)))/reps ##    user  system elapsed  ##  0.0472  0.0006  0.0480"},{"path":"https://r-spatial.github.io/spdep/articles/nb_sf.html","id":"spherical-point-based-neighbours","dir":"Articles","previous_headings":"Creating Neighbours using sf objects","what":"Spherical point-based neighbours","title":"Creating Neighbours using sf objects","text":"Spherical point-based neighbours may found using Great Circle distances. used many years, switch sf 1.0-0 use s2 default opened new opportunities spatial indexing sphere may help.","code":"pts_ll <- st_transform(NY8_ct_sf, \"OGC:CRS84\") st_is_longlat(pts_ll) ## [1] TRUE"},{"path":"https://r-spatial.github.io/spdep/articles/nb_sf.html","id":"k-nearest-neighbours-1","dir":"Articles","previous_headings":"Creating Neighbours using sf objects > Spherical point-based neighbours","what":"K-nearest neighbours","title":"Creating Neighbours using sf objects","text":"input geometries geographical coordinates, sf_use_s2() TRUE, knearneigh() use spatially indexed points s2::s2_closest_edges() (see https://github.com/r-spatial/s2/issues/125#issuecomment-860107442) performs well also larger data sets: smaller data set, legacy approach without spatial indexing adequate, slows number observations increases: WGS84 ellipsoid Great Circle distances differ little s2 spherical distances, yielding output diverges two tract centroids:","code":"(old_use_s2 <- sf_use_s2()) ## [1] TRUE sf_use_s2(TRUE) system.time(for (i in 1:reps) pts_ll1_nb <- knn2nb(knearneigh(pts_ll, k=6)))/reps ##    user  system elapsed  ##  0.0340  0.0000  0.0341 sf_use_s2(FALSE) ## Spherical geometry (s2) switched off system.time(for (i in 1:reps) pts_ll2_nb <- knn2nb(knearneigh(pts_ll, k=6)))/reps ##    user  system elapsed  ##  0.0283  0.0000  0.0284 all.equal(pts_ll1_nb, pts_ll2_nb, check.attributes=FALSE) ## [1] \"Component 52: Mean relative difference: 1.466667\"   ## [2] \"Component 124: Mean relative difference: 0.0251046\" pts_ll1_nb[[52]] ## [1] 15 38 48 49 50 53 pts_ll2_nb[[52]] ## [1] 37 38 48 49 50 53 pts_ll1_nb[[124]] ## [1] 117 122 123 125 133 134 pts_ll2_nb[[124]] ## [1] 116 117 123 125 133 134 sf_use_s2(old_use_s2) ## Spherical geometry (s2) switched on"},{"path":"https://r-spatial.github.io/spdep/articles/nb_sf.html","id":"distance-neighbours-1","dir":"Articles","previous_headings":"Creating Neighbours using sf objects > Spherical point-based neighbours","what":"Distance neighbours","title":"Creating Neighbours using sf objects","text":"Distance neighbours problematic. nbdists() works well s2 spherical coordinates, none tried adaptations dnearneigh() work adequately yet. argument use_s2= set TRUE s2 > 1.0-7, using s2::s2_closest_edges() legacy brute-force approach, calculating distances j copying j symmetry. distance metric alway \"km\". permit s2 methods run, without arguments set, s2 > 1.0-7, s2::s2_dwithin_matrix() run: Alternatively, spherical distances can used dwithin=FALSE s2::s2_closest_edges(); although running similar time, s2::s2_closest_edges() depends additional k= argument, , mis-set, may miss valid neighbours: Using s2::s2_closest_edges() respects d1 > 0 without requiring second pass R, faster s2::s2_dwithin_matrix(): Using s2::s2_dwithin_matrix() requires second pass, one lower bound, another upper bound, set difference operation find neighbours distance band: Setting use_s2=FALSE falls back legacy version, uses symmetry reduce time: Minor differences may occur legacy ellipsoid s2 spherical approaches:","code":"max_1nn_ll <- max(unlist(nbdists(knn2nb(knearneigh(pts_ll, k=1)), pts_ll))) ## Warning in knn2nb(knearneigh(pts_ll, k = 1)): neighbour object has 62 ## sub-graphs args(dnearneigh) ## function (x, d1, d2, row.names = NULL, longlat = NULL, bounds = c(\"GE\",  ##     \"LE\"), use_kd_tree = TRUE, symtest = FALSE, use_s2 = packageVersion(\"s2\") >  ##     \"1.0.7\", k = 200, dwithin = TRUE)  ## NULL if (packageVersion(\"s2\") > \"1.0.7\") {   system.time(for (i in 1:(reps/5)) suppressWarnings(pts_ll3_nb <- dnearneigh(pts_ll, d1=0,       d2=0.75*max_1nn_ll)))/(reps/5) } ##    user  system elapsed  ##  0.0685  0.0000  0.0685 system.time(for (i in 1:(reps/5)) suppressWarnings(pts_ll5_nb <- dnearneigh(pts_ll, d1=0, d2=0.75*max_1nn_ll, dwithin=FALSE)))/(reps/5) ##    user  system elapsed  ##  0.0590  0.0000  0.0595 if (packageVersion(\"s2\") > \"1.0.7\") all.equal(pts_ll3_nb, pts_ll5_nb, check.attributes=FALSE) ## [1] TRUE if (packageVersion(\"s2\") > \"1.0.7\") {   system.time(for (i in 1:(reps/5)) suppressWarnings(pts_ll3a_nb <- dnearneigh(pts_ll, d1=5,       d2=0.75*max_1nn_ll, dwithin=FALSE)))/(reps/5) } ##    user  system elapsed  ##  0.0475  0.0005  0.0480 if (packageVersion(\"s2\") > \"1.0.7\") {     system.time(for (i in 1:(reps/5)) suppressWarnings(pts_ll5a_nb <- dnearneigh(pts_ll, d1=5,         d2=0.75*max_1nn_ll)))/(reps/5) } ##    user  system elapsed  ##  0.0890  0.0000  0.0895 if (packageVersion(\"s2\") > \"1.0.7\") all.equal(pts_ll3a_nb, pts_ll5a_nb, check.attributes=FALSE) ## [1] TRUE system.time(for (i in 1:reps) suppressWarnings(pts_ll6_nb <- dnearneigh(pts_ll, d1=0, d2=0.75*max_1nn_ll, use_s2=FALSE)))/reps ##    user  system elapsed  ##  0.0397  0.0000  0.0400 all.equal(pts_ll5_nb, pts_ll6_nb, check.attributes=FALSE) ##  [1] \"Component 20: Numeric: lengths (6, 5) differ\"      ##  [2] \"Component 28: Numeric: lengths (7, 6) differ\"      ##  [3] \"Component 112: Numeric: lengths (109, 108) differ\" ##  [4] \"Component 116: Numeric: lengths (109, 108) differ\" ##  [5] \"Component 122: Numeric: lengths (105, 106) differ\" ##  [6] \"Component 123: Numeric: lengths (108, 107) differ\" ##  [7] \"Component 130: Numeric: lengths (108, 109) differ\" ##  [8] \"Component 134: Numeric: lengths (106, 105) differ\" ##  [9] \"Component 158: Numeric: lengths (101, 102) differ\" ## [10] \"Component 165: Numeric: lengths (101, 102) differ\" ## [11] \"Component 168: Numeric: lengths (101, 102) differ\" ## [12] \"Component 179: Numeric: lengths (89, 90) differ\"   ## [13] \"Component 180: Numeric: lengths (96, 97) differ\"   ## [14] \"Component 188: Numeric: lengths (46, 47) differ\"   ## [15] \"Component 189: Numeric: lengths (55, 56) differ\"   ## [16] \"Component 196: Numeric: lengths (47, 46) differ\"   ## [17] \"Component 210: Numeric: lengths (106, 104) differ\" ## [18] \"Component 226: Numeric: lengths (88, 87) differ\"   ## [19] \"Component 229: Numeric: lengths (55, 53) differ\"   ## [20] \"Component 235: Numeric: lengths (40, 39) differ\"   ## [21] \"Component 237: Numeric: lengths (14, 15) differ\"   ## [22] \"Component 245: Numeric: lengths (16, 15) differ\" system.time(for (i in 1:reps) suppressWarnings(pts_ll6a_nb <- dnearneigh(pts_ll, d1=5, d2=0.75*max_1nn_ll, use_s2=FALSE)))/reps ##    user  system elapsed  ##  0.0295  0.0002  0.0298 if (packageVersion(\"s2\") > \"1.0.7\") all.equal(pts_ll5a_nb, pts_ll6a_nb, check.attributes=FALSE) ##  [1] \"Component 20: Numeric: lengths (6, 5) differ\"        ##  [2] \"Component 28: Numeric: lengths (7, 6) differ\"        ##  [3] \"Component 112: Numeric: lengths (62, 61) differ\"     ##  [4] \"Component 113: Numeric: lengths (62, 63) differ\"     ##  [5] \"Component 116: Numeric: lengths (56, 55) differ\"     ##  [6] \"Component 119: Numeric: lengths (68, 69) differ\"     ##  [7] \"Component 122: Numeric: lengths (43, 44) differ\"     ##  [8] \"Component 123: Numeric: lengths (50, 49) differ\"     ##  [9] \"Component 128: Numeric: lengths (65, 64) differ\"     ## [10] \"Component 130: Numeric: lengths (61, 63) differ\"     ## [11] \"Component 132: Numeric: lengths (45, 46) differ\"     ## [12] \"Component 134: Numeric: lengths (46, 45) differ\"     ## [13] \"Component 136: Numeric: lengths (61, 62) differ\"     ## [14] \"Component 147: Numeric: lengths (50, 51) differ\"     ## [15] \"Component 154: Numeric: lengths (56, 57) differ\"     ## [16] \"Component 158: Numeric: lengths (49, 50) differ\"     ## [17] \"Component 165: Mean relative difference: 0.02823018\" ## [18] \"Component 168: Numeric: lengths (54, 56) differ\"     ## [19] \"Component 179: Numeric: lengths (77, 78) differ\"     ## [20] \"Component 180: Numeric: lengths (85, 86) differ\"     ## [21] \"Component 188: Numeric: lengths (39, 40) differ\"     ## [22] \"Component 189: Numeric: lengths (48, 49) differ\"     ## [23] \"Component 196: Numeric: lengths (45, 44) differ\"     ## [24] \"Component 210: Numeric: lengths (68, 66) differ\"     ## [25] \"Component 226: Numeric: lengths (82, 81) differ\"     ## [26] \"Component 229: Numeric: lengths (48, 46) differ\"     ## [27] \"Component 235: Numeric: lengths (38, 37) differ\"     ## [28] \"Component 237: Numeric: lengths (14, 15) differ\"     ## [29] \"Component 245: Numeric: lengths (15, 14) differ\""},{"path":"https://r-spatial.github.io/spdep/articles/nb_sf.html","id":"spher-poly2nb","dir":"Articles","previous_headings":"Creating Neighbours using sf objects > Spherical point-based neighbours","what":"Contiguity neighbours for spherical polygon support","title":"Creating Neighbours using sf objects","text":"also turns sf functions used find contiguity neighbours, s2 spatial indexing functionality accessed finding candidate neighbours intersecting geometries. timings little slower st_intersects() hands geometry predicates s2_intersects_matrix(), results , spatial indexing used, scales well larger data sets:","code":"NY8_sf_ll <- st_transform(NY8_sf, \"OGC:CRS84\") st_is_longlat(NY8_sf_ll) ## [1] TRUE sf_use_s2(TRUE) system.time(for (i in 1:reps) NY8_sf_1_nb_ll <- poly2nb(NY8_sf_ll, queen=TRUE, snap=eps))/reps ##    user  system elapsed  ##  0.1675  0.0024  0.1708 all.equal(NY8_sf_1_nb, NY8_sf_1_nb_ll, check.attributes=FALSE) ## [1] TRUE"},{"path":"https://r-spatial.github.io/spdep/articles/sids.html","id":"introduction","dir":"Articles","previous_headings":"","what":"Introduction","title":"Introduction to the North Carolina SIDS data set (re-revised)","text":"data set presented first Symons, Grimson, Yuan (1983), analysed reference spatial nature data Cressie Read (1985), expanded Cressie Chan (1989), used detail Cressie (1991). 100 counties North Carolina, includes counts numbers live births (also non-white live births) numbers sudden infant deaths, July 1, 1974 June 30, 1978 July 1, 1979 June 30, 1984 periods. Cressie Read (1985), listing county neighbours based shared boundaries (contiguity) given, Cressie Chan (1989), Cressie (1991, 386–89), different listing based criterion distance county seats, cutoff 30 miles. county seat location coordinates given miles local (unknown) coordinate reference system. data also used exemplify range functions spatial statistics module user’s manual (Kaluzny et al. 1996).","code":""},{"path":"https://r-spatial.github.io/spdep/articles/sids.html","id":"getting-the-data-into-r","dir":"Articles","previous_headings":"","what":"Getting the data into R","title":"Introduction to the North Carolina SIDS data set (re-revised)","text":"using spdep spreg packages, version: spdep, version 1.3-8, 2024-11-25, sf package tmap package. data sources referred documented help page nc.sids data set spData. actual data, included shapefile county boundaries North Carolina made available maptools package 1. data known geographical coordinates (longitude-latitude decimal degrees) assumed use NAD27 datum. ESRI Shapefile deprecated, replaced GeoPackage, written reading original files spData 2.3.1: shapefile format presupposed three files extensions .shp, .shx, .dbf, first contains geometry data, second spatial index, third attribute data. required name apart extension, read using sf::st_read() sf object nc; class defined sf. centroids largest polygon county available using st_centroid method sf sfc POINT object, can used place labels extraction coordinate matrix: can examine names columns data frame see contains — fact columns examining , others useful cleaning data set. Let’s check different versions data - sf spData NC SIDS files, GeoDa Center two forms: actual CRS unknown, GeoPackage spData version updated \"EPSG:4267\". Next, geometries ? sf::st_equals returns logical matrix, ’ll check diagonal values TRUE, values TRUE summing recalling n 100: Next, let’s download GeoDa files repeat comparisons: looks though external files assuming WGS84/NAD83 datum, also contain geometries. Now contents files - sids2 also contains rates, file spData contains coordinates given Cressie (1991), parcels contiguous counties p. 554, aggregations used median polishing. spData data set columns reordered surprise: difference NWBIR74: spData follows Cressie (1991) sf Geoda follow Cressie Chan (1989) NWBIR74 Chowan county. now examine data set reproduced Cressie collaborators, included spData (formerly spdep), add neighbour relationships used Cressie Chan (1989) background map graph shown Figure : Printing neighbour object shows neighbour list object, sparse structure — displayed matrix, 3.94% cells filled. Objects class nb contain list long number counties; component list vector index numbers neighbours county question, neighbours county region.id 37001 can retreived matching indices. information can obtained using summary() nb object. Finally, associate vector names neighbour list, row.names argument. names unique, data frame row names. neighbour list object records neighbours order relation list , neighbours list county region.id “37001” seventeenth, nineteenth, thirty-second, forty-first sixty-eighth list. can retreive codes looking region.id attribute. also note neighbour criterion generates two counties neighbours, Dare Hyde, whose county seats 30 miles nearest neighbours. card() function returns cardinality neighbour set. need return methods handling -neighbour objects later . also show new neighbours lists may constructed , compare literature.","code":"library(spdep) nc <- st_read(system.file(\"shapes/sids.gpkg\", package=\"spData\")[1], quiet=TRUE) #st_crs(nc) <- \"EPSG:4267\" row.names(nc) <- as.character(nc$FIPSNO) sf_use_s2(TRUE) plot(st_geometry(nc), axes=TRUE) text(st_coordinates(st_centroid(st_geometry(nc), of_largest_polygon=TRUE)), label=nc$FIPSNO, cex=0.5) names(nc) ##  [1] \"CNTY_ID\"   \"AREA\"      \"PERIMETER\" \"CNTY_\"     \"NAME\"      \"FIPS\"      ##  [7] \"FIPSNO\"    \"CRESS_ID\"  \"BIR74\"     \"SID74\"     \"NWBIR74\"   \"BIR79\"     ## [13] \"SID79\"     \"NWBIR79\"   \"east\"      \"north\"     \"x\"         \"y\"         ## [19] \"lon\"       \"lat\"       \"L_id\"      \"M_id\"      \"geom\" summary(nc) ##     CNTY_ID          AREA          PERIMETER         CNTY_      ##  Min.   :1825   Min.   :0.0420   Min.   :0.999   Min.   :1825   ##  1st Qu.:1902   1st Qu.:0.0910   1st Qu.:1.324   1st Qu.:1902   ##  Median :1982   Median :0.1205   Median :1.609   Median :1982   ##  Mean   :1986   Mean   :0.1263   Mean   :1.673   Mean   :1986   ##  3rd Qu.:2067   3rd Qu.:0.1542   3rd Qu.:1.859   3rd Qu.:2067   ##  Max.   :2241   Max.   :0.2410   Max.   :3.640   Max.   :2241   ##      NAME               FIPS               FIPSNO         CRESS_ID      ##  Length:100         Length:100         Min.   :37001   Min.   :  1.00   ##  Class :character   Class :character   1st Qu.:37050   1st Qu.: 25.75   ##  Mode  :character   Mode  :character   Median :37100   Median : 50.50   ##                                        Mean   :37100   Mean   : 50.50   ##                                        3rd Qu.:37150   3rd Qu.: 75.25   ##                                        Max.   :37199   Max.   :100.00   ##      BIR74           SID74          NWBIR74           BIR79       ##  Min.   :  248   Min.   : 0.00   Min.   :   1.0   Min.   :  319   ##  1st Qu.: 1077   1st Qu.: 2.00   1st Qu.: 190.0   1st Qu.: 1336   ##  Median : 2180   Median : 4.00   Median : 697.5   Median : 2636   ##  Mean   : 3300   Mean   : 6.67   Mean   :1051.0   Mean   : 4224   ##  3rd Qu.: 3936   3rd Qu.: 8.25   3rd Qu.:1168.5   3rd Qu.: 4889   ##  Max.   :21588   Max.   :44.00   Max.   :8027.0   Max.   :30757   ##      SID79          NWBIR79             east           north       ##  Min.   : 0.00   Min.   :    3.0   Min.   : 19.0   Min.   :  6.0   ##  1st Qu.: 2.00   1st Qu.:  250.5   1st Qu.:178.8   1st Qu.: 97.0   ##  Median : 5.00   Median :  874.5   Median :285.0   Median :125.5   ##  Mean   : 8.36   Mean   : 1352.8   Mean   :271.3   Mean   :122.1   ##  3rd Qu.:10.25   3rd Qu.: 1406.8   3rd Qu.:361.2   3rd Qu.:151.5   ##  Max.   :57.00   Max.   :11631.0   Max.   :482.0   Max.   :182.0   ##        x                 y             lon              lat        ##  Min.   :-328.04   Min.   :3757   Min.   :-84.08   Min.   :33.92   ##  1st Qu.: -60.55   1st Qu.:3920   1st Qu.:-81.20   1st Qu.:35.26   ##  Median : 114.38   Median :3963   Median :-79.26   Median :35.68   ##  Mean   :  91.46   Mean   :3953   Mean   :-79.51   Mean   :35.62   ##  3rd Qu.: 240.03   3rd Qu.:4000   3rd Qu.:-77.87   3rd Qu.:36.05   ##  Max.   : 439.65   Max.   :4060   Max.   :-75.67   Max.   :36.52   ##       L_id           M_id                 geom     ##  Min.   :1.00   Min.   :1.00   MULTIPOLYGON :100   ##  1st Qu.:1.00   1st Qu.:2.00   epsg:4267    :  0   ##  Median :2.00   Median :3.00   +proj=long...:  0   ##  Mean   :2.12   Mean   :2.67                       ##  3rd Qu.:3.00   3rd Qu.:3.25                       ##  Max.   :4.00   Max.   :4.00 library(sf) nc_sf <- st_read(system.file(\"shape/nc.shp\", package=\"sf\"),                  quiet=TRUE) st_crs(nc_sf) ## Coordinate Reference System: ##   User input: NAD27  ##   wkt: ## GEOGCRS[\"NAD27\", ##     DATUM[\"North American Datum 1927\", ##         ELLIPSOID[\"Clarke 1866\",6378206.4,294.978698213898, ##             LENGTHUNIT[\"metre\",1]]], ##     PRIMEM[\"Greenwich\",0, ##         ANGLEUNIT[\"degree\",0.0174532925199433]], ##     CS[ellipsoidal,2], ##         AXIS[\"latitude\",north, ##             ORDER[1], ##             ANGLEUNIT[\"degree\",0.0174532925199433]], ##         AXIS[\"longitude\",east, ##             ORDER[2], ##             ANGLEUNIT[\"degree\",0.0174532925199433]], ##     ID[\"EPSG\",4267]] nc <- st_read(system.file(\"shapes/sids.gpkg\",                  package=\"spData\"), quiet=TRUE) st_crs(nc) ## Coordinate Reference System: ##   User input: NAD27  ##   wkt: ## GEOGCRS[\"NAD27\", ##     DATUM[\"North American Datum 1927\", ##         ELLIPSOID[\"Clarke 1866\",6378206.4,294.978698213898, ##             LENGTHUNIT[\"metre\",1]]], ##     PRIMEM[\"Greenwich\",0, ##         ANGLEUNIT[\"degree\",0.0174532925199433]], ##     CS[ellipsoidal,2], ##         AXIS[\"geodetic latitude (Lat)\",north, ##             ORDER[1], ##             ANGLEUNIT[\"degree\",0.0174532925199433]], ##         AXIS[\"geodetic longitude (Lon)\",east, ##             ORDER[2], ##             ANGLEUNIT[\"degree\",0.0174532925199433]], ##     USAGE[ ##         SCOPE[\"Geodesy.\"], ##         AREA[\"North and central America: Antigua and Barbuda - onshore. Bahamas - onshore plus offshore over internal continental shelf only. Belize - onshore. British Virgin Islands - onshore. Canada onshore - Alberta, British Columbia, Manitoba, New Brunswick, Newfoundland and Labrador, Northwest Territories, Nova Scotia, Nunavut, Ontario, Prince Edward Island, Quebec, Saskatchewan and Yukon - plus offshore east coast. Cuba - onshore and offshore. El Salvador - onshore. Guatemala - onshore. Honduras - onshore. Panama - onshore. Puerto Rico - onshore. Mexico - onshore plus offshore east coast. Nicaragua - onshore. United States (USA) onshore and offshore - Alabama, Alaska, Arizona, Arkansas, California, Colorado, Connecticut, Delaware, Florida, Georgia, Idaho, Illinois, Indiana, Iowa, Kansas, Kentucky, Louisiana, Maine, Maryland, Massachusetts, Michigan, Minnesota, Mississippi, Missouri, Montana, Nebraska, Nevada, New Hampshire, New Jersey, New Mexico, New York, North Carolina, North Dakota, Ohio, Oklahoma, Oregon, Pennsylvania, Rhode Island, South Carolina, South Dakota, Tennessee, Texas, Utah, Vermont, Virginia, Washington, West Virginia, Wisconsin and Wyoming - plus offshore . US Virgin Islands - onshore.\"], ##         BBOX[7.15,167.65,83.17,-47.74]], ##     ID[\"EPSG\",4267]] suppressWarnings(st_crs(nc_sf) <- st_crs(nc)) xx <- st_equals(nc, nc_sf, sparse=FALSE) all(diag(xx)) && sum(xx) == 100L ## [1] TRUE td <- tempdir() #download.file(\"https://geodacenter.github.io/data-and-lab//data/sids.zip\", file.path(td, \"sids.zip\"), quiet=TRUE)  # local copy (2020-10-22) as repository sometimes offline file.copy(system.file(\"etc/misc/sids.zip\", package=\"spdep\"), td) ## [1] TRUE unzip(file.path(td, \"sids.zip\"), c(\"sids/sids.dbf\", \"sids/sids.prj\", \"sids/sids.shp\", \"sids/sids.shx\"), exdir=td) sids_sf <- st_read(file.path(td, \"sids/sids.shp\"), quiet=TRUE) #download.file(\"https://geodacenter.github.io/data-and-lab//data/sids2.zip\", file.path(td, \"sids2.zip\"), quiet=TRUE) file.copy(system.file(\"etc/misc/sids2.zip\", package=\"spdep\"), td) ## [1] TRUE unzip(file.path(td, \"sids2.zip\"), c(\"sids2/sids2.dbf\", \"sids2/sids2.prj\", \"sids2/sids2.shp\", \"sids2/sids2.shx\"), exdir=td) sids2_sf <- st_read(file.path(td, \"sids2/sids2.shp\"), quiet=TRUE) st_crs(sids_sf) ## Coordinate Reference System: ##   User input: WGS 84  ##   wkt: ## GEOGCRS[\"WGS 84\", ##     DATUM[\"World Geodetic System 1984\", ##         ELLIPSOID[\"WGS 84\",6378137,298.257223563, ##             LENGTHUNIT[\"metre\",1]]], ##     PRIMEM[\"Greenwich\",0, ##         ANGLEUNIT[\"degree\",0.0174532925199433]], ##     CS[ellipsoidal,2], ##         AXIS[\"latitude\",north, ##             ORDER[1], ##             ANGLEUNIT[\"degree\",0.0174532925199433]], ##         AXIS[\"longitude\",east, ##             ORDER[2], ##             ANGLEUNIT[\"degree\",0.0174532925199433]], ##     ID[\"EPSG\",4326]] st_crs(sids2_sf) ## Coordinate Reference System: ##   User input: WGS 84  ##   wkt: ## GEOGCRS[\"WGS 84\", ##     DATUM[\"World Geodetic System 1984\", ##         ELLIPSOID[\"WGS 84\",6378137,298.257223563, ##             LENGTHUNIT[\"metre\",1]]], ##     PRIMEM[\"Greenwich\",0, ##         ANGLEUNIT[\"degree\",0.0174532925199433]], ##     CS[ellipsoidal,2], ##         AXIS[\"latitude\",north, ##             ORDER[1], ##             ANGLEUNIT[\"degree\",0.0174532925199433]], ##         AXIS[\"longitude\",east, ##             ORDER[2], ##             ANGLEUNIT[\"degree\",0.0174532925199433]], ##     ID[\"EPSG\",4326]] suppressWarnings(st_crs(sids_sf) <- st_crs(nc_sf)) xx <- st_equals(sids_sf, nc_sf, sparse=FALSE) all(diag(xx)) && sum(xx) == 100L ## [1] FALSE suppressWarnings(st_crs(sids2_sf) <- st_crs(nc_sf)) xx <- st_equals(sids2_sf, nc_sf, sparse=FALSE) all(diag(xx)) && sum(xx) == 100L ## [1] FALSE all.equal(as.data.frame(nc_sf)[,1:14], as.data.frame(sids_sf)[,1:14]) ##  [1] \"Names: 12 string mismatches\"                                   ##  [2] \"Component 4: Modes: numeric, character\"                        ##  [3] \"Component 4: target is numeric, current is character\"          ##  [4] \"Component 5: 100 string mismatches\"                            ##  [5] \"Component 6: Modes: character, numeric\"                        ##  [6] \"Component 6: target is character, current is numeric\"          ##  [7] \"Component 7: Mean relative difference: 0.9986388\"              ##  [8] \"Component 8: Mean relative difference: 64.33901\"               ##  [9] \"Component 9: Mean relative difference: 0.9979786\"              ## [10] \"Component 10: Mean relative difference: 156.5427\"              ## [11] \"Component 11: Mean relative difference: 3.01968\"               ## [12] \"Component 12: Mean relative difference: 0.9980208\"             ## [13] \"Component 13: Mean relative difference: 160.8194\"              ## [14] \"Component 14: Modes: numeric, list\"                            ## [15] \"Component 14: Attributes: < target is NULL, current is list >\" ## [16] \"Component 14: target is numeric, current is sfc_MULTIPOLYGON\" all.equal(as.data.frame(nc_sf)[,1:14], as.data.frame(sids2_sf)[,1:14]) ##  [1] \"Names: 12 string mismatches\"                          ##  [2] \"Component 4: Modes: numeric, character\"               ##  [3] \"Component 4: target is numeric, current is character\" ##  [4] \"Component 5: 100 string mismatches\"                   ##  [5] \"Component 6: Modes: character, numeric\"               ##  [6] \"Component 6: target is character, current is numeric\" ##  [7] \"Component 7: Mean relative difference: 0.9986388\"     ##  [8] \"Component 8: Mean relative difference: 64.33901\"      ##  [9] \"Component 9: Mean relative difference: 0.9979786\"     ## [10] \"Component 10: Mean relative difference: 156.5427\"     ## [11] \"Component 11: Mean relative difference: 3.01968\"      ## [12] \"Component 12: Mean relative difference: 0.9980208\"    ## [13] \"Component 13: Mean relative difference: 160.8194\"     ## [14] \"Component 14: Mean relative difference: 0.9984879\" all.equal(as.data.frame(nc_sf)[,1:14], as.data.frame(nc)[,c(2,3,4,1,5:14)]) ## [1] \"Component \\\"NWBIR74\\\": Mean relative difference: 0.04891304\" which(!(nc_sf$NWBIR74 == nc$NWBIR74)) ## [1] 21 c(nc$NWBIR74[21], nc_sf$NWBIR74[21]) ## [1] 386 368 gal_file <- system.file(\"weights/ncCR85.gal\", package=\"spData\")[1] ncCR85 <- read.gal(gal_file, region.id=nc$FIPSNO) ncCR85 ## Neighbour list object: ## Number of regions: 100  ## Number of nonzero links: 492  ## Percentage nonzero weights: 4.92  ## Average number of links: 4.92 gal_file <- system.file(\"weights/ncCC89.gal\", package=\"spData\")[1] ncCC89 <- read.gal(gal_file, region.id=nc$FIPSNO) ncCC89 ## Neighbour list object: ## Number of regions: 100  ## Number of nonzero links: 394  ## Percentage nonzero weights: 3.94  ## Average number of links: 3.94  ## 2 regions with no links: ## 37055, 37095 ## 3 disjoint connected subgraphs plot(st_geometry(nc), border=\"grey\") plot(ncCC89, st_centroid(st_geometry(nc), of_largest_polygon), add=TRUE, col=\"blue\") r.id <- attr(ncCC89, \"region.id\") ncCC89[[match(\"37001\", r.id)]] ## [1] 11 26 29 30 48 r.id[ncCC89[[match(\"37001\", r.id)]]] ## [1] 37033 37081 37135 37063 37037 as.character(nc$NAME)[card(ncCC89) == 0] ## [1] \"Dare\" \"Hyde\""},{"path":"https://r-spatial.github.io/spdep/articles/sids.html","id":"probability-mapping","dir":"Articles","previous_headings":"Getting the data into R","what":"Probability mapping","title":"Introduction to the North Carolina SIDS data set (re-revised)","text":"Rather review functions measuring modelling spatial dependence spdep package, focus probability mapping disease rates data. Typically, counts incidence disease spatial unit, associated counts populations risk. task try establish whether spatial units seem characterised higher lower counts cases might expected general terms (Bailey Gatrell 1995). early approach Choynowski (1959), described Cressie Read (1985) Bailey Gatrell (1995), assumes, given true rate spatial units small, population risk increases infinity, spatial unit case counts Poisson mean value equal population risk times rate study area whole. Choynowski’s approach folds two tails measured probabilities together, small values, chosen α\\alpha, occur spatial units either unusually high low rates. reason, high low counties plotted separately . Note cut returns factor labeled cut intervals.  complicated thematic maps, may helpful use ColorBrewer (https://colorbrewer2.org) colour palettes. use palettes accessed tmap, available R RColorBrewer package. choynowski() function provides probability map values required, probmap() function returns raw (crude) rates, expected counts (assuming constant rate across study area), relative risks, Poisson probability map values calculated using standard cumulative distribution function ppois(). fold tails together, counties lower observed counts expected, based population size, values lower tail, higher observed counts expected values upper tail, can see.  Marilia Carvalho (personal communication) Virgilio Gómez Rubio (Gómez-Rubio, Ferrándiz-Ferragud, López-Quílez 2005) pointed unusual shape distribution Poisson probability values (histogram ), repeating doubts probability mapping voiced Cressie (1991, 392): “extreme value …\\ldots may due lack fit Poisson model deviation constant rate assumption”. many high values one expected, suggesting perhaps overdispersion, ratio variance mean larger unity.  One ad-hoc way assess impact possible failure assumption counts follow Poisson distribution estimate dispersion fitting generalized linear model observed counts including intercept (null model) offset observed population risk (suggested Marilia Carvalho associates):  dispersion equal 2.2786188, much greater unity; calculate corrected probability map values taking standardised residuals model, taking size dispersion account; results shown . Many fewer counties appear now unexpectedly large small numbers cases. ad-hoc adjustment made R provides access wide range model-fitting functions can used help check assumptions. Gómez-Rubio, Ferrándiz-Ferragud, López-Quílez (2005) chose rather construct probability map hypothesis data drawn Negative Binomial distribution. far, none maps presented made use spatial dependence possibly present data. elementary step can taken map Empirical Bayes estimates rates, smoothed relation raw rates. underlying question linked larger variance associated rate estimates counties small populations risk compared counties large populations risk. Empirical Bayes estimates place credence raw rates counties large populations risk, modify much less modify rates small counties. case small populations risk, confidence placed either global rate study area whole, local Empirical Bayes estimates, rates larger moving window including neighbours county estimated. function used spdep EBlocal(), initially contributed Marilia Carvalho. parallels similar function GeoDa, uses Bailey Gatrell (1995) interpretation Marshall (1991), rather GeoDa (Anselin, Syabri, Smirnov 2002).  results shown Figure . Like relevant functions spdep,EBlocal() takes zero.policy argument allow missing values passed . case, local estimate available two counties neighbours, marked stars. addition Empirical Bayes smoothing globally, used disease mapping Assuncão Reis correction Moran’s II rates data (shrink towards global rate population risk small, Monte Carlo test), lists local neighbours can used shrink towards local rate.","code":"ch <- choynowski(nc$SID74, nc$BIR74) nc$ch_pmap_low <- ifelse(ch$type, ch$pmap, NA) nc$ch_pmap_high <- ifelse(!ch$type, ch$pmap, NA) prbs <- c(0,.001,.01,.05,.1,1) nc$high = cut(nc$ch_pmap_high, prbs) nc$low = cut(nc$ch_pmap_low,prbs ) is_tmap <- FALSE if (require(tmap, quietly=TRUE)) is_tmap <- TRUE is_tmap ## [1] TRUE library(tmap) tmap4 <- packageVersion(\"tmap\") >= \"3.99\" if (tmap4) {   tm_shape(nc) + tm_polygons(fill=c(\"low\", \"high\"), fill.scale = tm_scale(values=\"brewer.set1\"), fill.legend = tm_legend(\"p-values\", frame=FALSE, item.r = 0), fill.free=FALSE, lwd=0.01) + tm_layout(panel.labels=c(\"low\", \"high\")) } else { tm_shape(nc) + tm_fill(c(\"low\", \"high\"), palette=\"Set1\", title=\"p-values\") +   tm_facets(free.scales=FALSE) + tm_layout(panel.labels=c(\"low\", \"high\")) } pmap <- probmap(nc$SID74, nc$BIR74) nc$pmap <- pmap$pmap brks <- c(0,0.001,0.01,0.025,0.05,0.95,0.975,0.99,0.999,1) if (tmap4) {   tm_shape(nc) + tm_polygons(fill=\"pmap\", fill.scale = tm_scale(values=\"brewer.rd_bu\", midpoint=0.5, breaks=brks), fill.legend = tm_legend(frame=FALSE, item.r = 0, position = tm_pos_out(\"right\", \"center\")), lwd=0.01) + tm_layout(component.autoscale=FALSE) } else { tm_shape(nc) + tm_fill(\"pmap\", breaks=brks, midpoint=0.5, palette=\"RdBu\") + tm_layout(legend.outside=TRUE) } hist(nc$pmap, main=\"\") res <- glm(SID74 ~ offset(log(BIR74)), data=nc, family=\"quasipoisson\") nc$stdres <- rstandard(res) brks <- c(-4, -3, -2, -1.5, -1, -0.5, 0.5, 1, 1.5, 2, 3, 4) if (tmap4) {   tm_shape(nc) + tm_polygons(fill=\"stdres\", fill.scale = tm_scale(values=\"brewer.rd_bu\", midpoint=0.5, breaks=brks), fill.legend = tm_legend(frame=FALSE, item.r = 0, position = tm_pos_out(\"right\", \"center\")), lwd=0.01) + tm_layout(component.autoscale=FALSE) } else {   tm_shape(nc) + tm_fill(\"stdres\", breaks=brks, midpoint=0, palette=\"RdBu\") + tm_layout(legend.outside=TRUE) } global_rate <- sum(nc$SID74)/sum(nc$BIR74) nc$Expected <- global_rate * nc$BIR74 res <- EBlocal(nc$SID74, nc$Expected, ncCC89, zero.policy=TRUE) nc$EB_loc <- res$est brks <- c(0, 0.25, 0.5, 0.75, 1, 2, 3, 4, 5) nc_miss <- st_centroid(st_geometry(nc[card(ncCC89) == 0,]), of_largest_polygon) if (tmap4) {   tm_shape(nc) + tm_polygons(fill=\"stdres\", fill.scale = tm_scale(values=\"brewer.rd_bu\", midpoint=0.5, breaks=brks), fill.legend = tm_legend(frame=FALSE, item.r = 0, position = tm_pos_out(\"right\", \"center\")), lwd=0.01) + tm_layout(component.autoscale=FALSE) + tm_shape(nc_miss) + tm_symbols(shape=8, size=0.5) } else { tm_shape(nc) + tm_fill(\"EB_loc\", breaks=brks, midpoint=1, palette=\"RdBu\") + tm_layout(legend.outside=TRUE) + tm_shape(nc_miss) + tm_symbols(shape=8, size=0.5) } set.seed(1) EBImoran.mc(nc$SID74, nc$BIR74, nb2listw(ncCC89, style=\"B\", zero.policy=TRUE), nsim=999, zero.policy=TRUE) ##  ##  Monte-Carlo simulation of Empirical Bayes Index (mean subtracted) ##  ## data:  cases: nc$SID74, risk population: nc$BIR74 ## weights: nb2listw(ncCC89, style = \"B\", zero.policy = TRUE) ## number of simulations + 1: 1000 ##  ## statistic = 0.25789, observed rank = 998, p-value = 0.002 ## alternative hypothesis: greater"},{"path":"https://r-spatial.github.io/spdep/articles/sids.html","id":"exploration-and-modelling-of-the-data","dir":"Articles","previous_headings":"","what":"Exploration and modelling of the data","title":"Introduction to the North Carolina SIDS data set (re-revised)","text":"One first steps taken Cressie Read (1985) try bring spatial trends dividing North Carolina 4×44\\times4 rough rectangles. Just see works, let us map rough rectangles proceeding .  Cressie constructs transformed SIDS rates variable, 1974–78, analyses (co-workers). can replicate stem--leaf figure p. 396 book, taken Cressie Read (1989):","code":"nc$both <- factor(paste(nc$L_id, nc$M_id, sep=\":\")) nboth <- length(table(unclass(nc$both))) if (tmap4) {   tm_shape(nc) + tm_polygons(fill=\"both\", fill.scale=tm_scale(values=\"brewer.set1\"), fill.legend = tm_legend(\"rough\\nrectangles\", frame=FALSE, item.r = 0, position = tm_pos_out(\"right\", \"center\")), lwd=0.01) + tm_layout(component.autoscale=FALSE) } else { tm_shape(nc) + tm_fill(\"both\", palette=\"Set1\", title=\"rough\\nrectangles\") + tm_layout(legend.outside=TRUE) } nc$ft.SID74 <- sqrt(1000)*(sqrt(nc$SID74/nc$BIR74) + sqrt((nc$SID74+1)/nc$BIR74)) stem(round(nc$ft.SID74, 1), scale=2) ##  ##   The decimal point is at the | ##  ##   0 | 9 ##   1 | 111244 ##   1 | 567789999 ##   2 | 0011111222334444 ##   2 | 55555666677778999999999 ##   3 | 000111122333333344444444 ##   3 | 5568999 ##   4 | 013344 ##   4 | 555557 ##   5 | 2 ##   5 |  ##   6 | 3"},{"path":"https://r-spatial.github.io/spdep/articles/sids.html","id":"medpol","dir":"Articles","previous_headings":"Exploration and modelling of the data","what":"Median polish smoothing","title":"Introduction to the North Carolina SIDS data set (re-revised)","text":"Cressie (1991, 46–48, 393–400) discusses detail smoothing may used partition variation data smooth rough. order try North Carolina SIDS data set, use coarse gridding four columns four rows given Cressie (1991, 553–54), four grid cells empty; given variables L_id M_id object nc. Next aggregate number live births number SIDS cases 1974–1978 grid cells: Using Freeman-Tukey transformation used county data, coerce data correctly configured matrix, cells empty. medpolish function applied matrix, told remove empty cells; function iterates rows columns matrix using median extract overall effect, row column effects, residuals: Returning factors linking rows columns counties, generating matrices dummy variables using model.matrix, can calculate fitted values Freeman-Tukey adjusted rate county, residuals subtracting fitted value observed rate. Naturally, fitted value counties grid cell:  figure shows median polish smoothing results three maps, observed Freeman-Tukey transformed SIDS rates, fitted smoothed values, residuals. addition, plot median polish object also shown, plotting smooth residuals outer product row column effects divided overall effect, indicate lack additivity row column case — relevant analysis tables covariates rather geographical grids.","code":"mBIR74 <- tapply(nc$BIR74, nc$both, sum) mSID74 <- tapply(nc$SID74, nc$both, sum) mFT <- sqrt(1000)*(sqrt(mSID74/mBIR74) + sqrt((mSID74+1)/mBIR74)) # mFT1 <- t(matrix(mFT, 4, 4, byrow=TRUE)) # wrong assignment of 12 elements to a 4x4 matrix detected by CRAN test 2021-05-22 rc <- do.call(\"rbind\", lapply(strsplit(names(mFT), \":\"), as.integer)) mFT1 <- matrix(as.numeric(NA), 4, 4) for (i in 1:nrow(rc)) mFT1[rc[i,1], rc[i,2]] <- mFT[i] med <- medpolish(mFT1, na.rm=TRUE, trace.iter=FALSE) med ##  ## Median Polish Results (Dataset: \"mFT1\") ##  ## Overall: 2.90965 ##  ## Row Effects: ## [1] -0.05686791 -0.37236370  0.05686791  0.79541774 ##  ## Column Effects: ## [1] -0.005484562 -0.446250551  0.003656375  0.726443256 ##  ## Residuals: ##           [,1]     [,2]      [,3]     [,4] ## [1,]        NA -0.45800  0.000000  0.37556 ## [2,] -0.092554  0.00000  0.101695  0.00000 ## [3,]  0.092554  0.30464 -0.090726 -0.55364 ## [4,]        NA       NA  0.000000       NA mL_id <- model.matrix(~ as.factor(nc$L_id) -1) mM_id <- model.matrix(~ as.factor(nc$M_id) -1) nc$pred <- c(med$overall + mL_id %*% med$row + mM_id %*% med$col) nc$mp_resid <- nc$ft.SID74 - nc$pred if (tmap4) {   out1 <- tm_shape(nc) + tm_polygons(fill=c(\"ft.SID74\", \"pred\"), fill.scale=tm_scale(values=\"brewer.yl_or_br\"), fill.legend=tm_legend(position=tm_pos_out(\"right\", \"center\"), frame=FALSE, item.r = 0), fill.free=FALSE, lwd=0.01) + tm_layout(panel.labels=c(\"Observed\", \"Median polish prediction\"))   out2 <- tm_shape(nc) + tm_polygons(fill=\"mp_resid\", fill.scale=tm_scale(values=\"brewer.rd_yl_gn\", midpoint=0), fill.legend=tm_legend(position=tm_pos_out(\"right\", \"center\"), frame=FALSE, item.r = 0), lwd=0.01) } else { out1 <- tm_shape(nc) + tm_fill(c(\"ft.SID74\", \"pred\")) + tm_facets(free.scales=FALSE) + tm_layout(panel.labels=c(\"Observed\", \"Median polish prediction\")) out2 <- tm_shape(nc) + tm_fill(\"mp_resid\", midpoint=0) + tm_layout(legend.outside=TRUE) } tmap_arrange(out1, out2, ncol=1)"},{"path":[]},{"path":"https://r-spatial.github.io/spdep/articles/subgraphs.html","id":"introduction","dir":"Articles","previous_headings":"","what":"Introduction","title":"No-neighbour observation and subgraph handling","text":"spdep package always careful disconnected graphs, especially disconnected observations graph nodes neighbours, incoming outgoing edges. nb neighbour objects, encoded integer vectors length 1 containing integer 0, invalid index [1,N][1, N], NN observation count. Functions taking neighbour objects arguments use zero.policy argument guide handle -neighbour observations. spdep also n.comp.nb find number disjoint connected subgraphs nb object, contributed Nicholas Lewin-Koh 2001 using depth-first search symmetric neighbours, showing addition observations belong subgraph. Obviously, -neighbour observations singleton graph nodes, subgraphs also troubling spatial analysis, connection spatial processes subgraphs. ripples one pond cross separate pond connected. spdep 1.3-1, steps began raise awareness possibility neighbour objects might created disconnected way, mostly warnings, computation subgraph measures default. vignette intended provide background steps.","code":""},{"path":"https://r-spatial.github.io/spdep/articles/subgraphs.html","id":"no-neighbour-observations","dir":"Articles","previous_headings":"","what":"No-neighbour observations","title":"No-neighbour observation and subgraph handling","text":"start, nb objects recorded -neighbour observations integer vector unit length value 0, neighbours recorded ID values 1 N, N observation count. print summary methods always reported presence -neighbour observations, listed IDs (region.id values). nb object contains -neighbour observations, user decide whether drop observations, retained, value give weights. zero.policy argument uses zero value TRUE, FALSE causes nb2listw fail. value zero.policy call functions like nb2listw, subset.listw mat2listw creating listw objects representing sparse spatial weights matrices added created object attribute, used subsequently pass choice functions. example, moran.test takes value attribute default zero.policy argument: observation ii neighbours, weights sum ∑j=1Nwij=0\\sum_{j=1}^N w_{ij} = 0, wij=0,∀jw_{ij} = 0, \\forall j (see discussion Bivand Portnov (2004)). eigenvalue also zero, consequences analytical inference: adjust.n argument measures spatial autocorrelation default TRUE, subtracts count singleton nodes NN attempt acknowledge reduction information available. discussion address problems arising analysing areal/lattice data, neighbours defined polygon features contiguous boundaries. One way -neighbour observations may occur islands. clearly case Freni-Sterrantino, Ventrucci, Rue (2018), Capraia Giglio Isles singleton nodes. take Westminster constituencies Wales used July 2024 UK general election. GDAL least version 3.7.0, driver supports compressed GeoPackage files, must decompressed first. boundaries taken Ordnance Survey Boundary-Line site, https://osdatahub.os.uk/downloads/open/BoundaryLine, choosing 2024 Westminster constituencies (https://www.os.uk/opendata/licence), simplified using tolerance 50m reduce object size, merged selected voting outcomes constituencies Great Britain https://electionresults.parliament.uk/countries/1, (https://www.nationalarchives.gov.uk/doc/open-government-licence/version/3/). , subset Wales useful see: two subgraphs singleton Ynys Môn 31 constituencies: left map shows Ynys Môn can shown selecting name, black border, zero cardinality neighbour set, using card, filling polygon. right map shows location island, known English Anglesey, north-west Welsh mainland, neighbour links:  maps, can see island close two constituencies across Afon Menai (Menai Strait English), three simplified polygons less 280m apart, measured polygon boundaries: Using snap distance 280m, can join island two obvious proximate neighbours:  case, increasing snap default 10mm (close equivalents geometries known metrics; previously sqrt(.Machine$double.eps) 1.4901161^{-8} cases) helps. symmetric links added : always going case, strait narrow. islands much offshore, steps may required, large snap distance draw extra neighbours already connected observations. also possible increasing snap distance may fail link islands considered candidate neighbours, extents (bounding boxes), buffered snap value, intersect. can also use distances pick neighbour candidates meet criterion 280m, taking care lose ordering needed identify correct observations: candidates island , two neighbours across Menai Strait: addlinks1 function can used add links Ynys Môn neighbours, symmetry Ynys Môn. approach means island treated separately (scripted sequence), risk adding spurious neighbours denser parts study area. Since constituency observations areal support, surprising changing support points using kk-nearest neighbours work adequately, distance measurements points representing polygons rather areal unit boundaries: , Clwyd North, east Bangor Aberconwy, given neighbour Ynys Môn Dwyfor Meirionnydd, west Bangor Aberconwy, . addition, two subgraphs, still remain k=6k=6.","code":"library(spdep) ## Loading required package: spData ## Loading required package: sf ## Linking to GEOS 3.13.0, GDAL 3.10.0, PROJ 9.5.1; sf_use_s2() is TRUE args(moran.test) ## function (x, listw, randomisation = TRUE, zero.policy = attr(listw,  ##     \"zero.policy\"), alternative = \"greater\", rank = FALSE, na.action = na.fail,  ##     spChk = NULL, adjust.n = TRUE, drop.EI2 = FALSE)  ## NULL eigen(0)$values ## [1] 0 (GDAL37 <- as.numeric_version(unname(sf_extSoftVersion()[\"GDAL\"])) >= \"3.7.0\") ## [1] TRUE file <- \"etc/shapes/GB_2024_Wales_50m.gpkg.zip\" zipfile <- system.file(file, package=\"spdep\") if (GDAL37) {     w50m <- st_read(zipfile) } else {     td <- tempdir()     bn <- sub(\".zip\", \"\", basename(file), fixed=TRUE)     target <- unzip(zipfile, files=bn, exdir=td)     w50m <- st_read(target) } ## Reading layer `GB_2024_Wales_50m' from data source  ##   `/tmp/RtmpXVTJuL/temp_libpath3b356d487bad39/spdep/etc/shapes/GB_2024_Wales_50m.gpkg.zip'  ##   using driver `GPKG' ## Simple feature collection with 32 features and 19 fields ## Geometry type: MULTIPOLYGON ## Dimension:     XY ## Bounding box:  xmin: 146597.1 ymin: 164536.5 xmax: 355287 ymax: 395993.5 ## Projected CRS: OSGB36 / British National Grid (w50m |> poly2nb(row.names=as.character(w50m$Constituency)) -> nb_W_50m) ## Warning in poly2nb(w50m, row.names = as.character(w50m$Constituency)): some observations have no neighbours; ## if this seems unexpected, try increasing the snap argument. ## Warning in poly2nb(w50m, row.names = as.character(w50m$Constituency)): neighbour object has 2 sub-graphs; ## if this sub-graph count seems unexpected, try increasing the snap argument. ## Neighbour list object: ## Number of regions: 32  ## Number of nonzero links: 136  ## Percentage nonzero weights: 13.28125  ## Average number of links: 4.25  ## 1 region with no links: ## Ynys Môn ## 2 disjoint connected subgraphs attr(nb_W_50m, \"ncomp\")$comp.id |>table() |> table() ##  ##  1 31  ##  1  1 ynys_mon <- w50m$Constituency == \"Ynys Môn\" pts <- st_point_on_surface(st_geometry(w50m)) opar <- par(mfrow=c(1, 2)) plot(st_geometry(w50m), border=\"grey75\") plot(st_geometry(w50m)[ynys_mon], add=TRUE) plot(st_geometry(w50m)[card(nb_W_50m) == 0L], add=TRUE, border=\"transparent\", col=\"wheat1\") plot(st_geometry(w50m), border=\"grey75\") plot(nb_W_50m, pts, add=TRUE) par(opar) dym <- c(st_distance(w50m[ynys_mon,], w50m)) sort(dym)[1:12] ## Units: [m] ##  [1]      0.0000    123.4132    277.5414  16658.7265  37985.7086  54096.7729 ##  [7]  58146.4320  65550.2491  67696.3323  93741.9873 113007.3659 137858.1826 (nb_W_50m_snap <- poly2nb(w50m, row.names=as.character(w50m$Constituency), snap=280)) ## Neighbour list object: ## Number of regions: 32  ## Number of nonzero links: 140  ## Percentage nonzero weights: 13.67188  ## Average number of links: 4.375 plot(st_geometry(w50m), border=\"grey75\") plot(nb_W_50m_snap, pts, add=TRUE) attr(nb_W_50m_snap, \"region.id\")[nb_W_50m_snap[[which(ynys_mon)]]] ## [1] \"Bangor Aberconwy\"   \"Dwyfor Meirionnydd\" (meet_criterion <- sum(dym <= units::set_units(280, \"m\"))) ## [1] 3 (cands <- attr(nb_W_50m, \"region.id\")[order(dym)[1:meet_criterion]]) ## [1] \"Ynys Môn\"           \"Bangor Aberconwy\"   \"Dwyfor Meirionnydd\" (nb_W_50m_add <- addlinks1(nb_W_50m, from = cands[1], to = cands[2:meet_criterion])) ## Neighbour list object: ## Number of regions: 32  ## Number of nonzero links: 140  ## Percentage nonzero weights: 13.67188  ## Average number of links: 4.375 all.equal(nb_W_50m_add, nb_W_50m_snap, check.attributes=FALSE) ## [1] TRUE k2 <- knn2nb(knearneigh(pts, k=2), row.names=as.character(w50m$Constituency), sym=TRUE) ## Warning in knn2nb(knearneigh(pts, k = 2), row.names = ## as.character(w50m$Constituency), : neighbour object has 2 sub-graphs attr(k2, \"region.id\")[k2[[which(ynys_mon)]]] ## [1] \"Bangor Aberconwy\" \"Clwyd North\""},{"path":"https://r-spatial.github.io/spdep/articles/subgraphs.html","id":"subgraphs","dir":"Articles","previous_headings":"","what":"Subgraphs","title":"No-neighbour observation and subgraph handling","text":"Subgraphs may found -neighbour observations present, also graph split two blocks observations path observation block another block, across low population density constituencies mid-Wales: can show block structure displaying binary spatial weights matrix:  occurs frequently point support, may also occur areal support, Freni-Sterrantino, Ventrucci, Rue (2018) find eight municipalities island Elba. spdep 1.3-6, igraph spatialreg packages available, n.comp.nb uses igraph::components compute graph components, also using depth-first search. original implementation fast, directed (asymmetric) graphs converts first symmetry, igraph::components can handle directed graphs without conversion (see https://github.com/r-spatial/spdep/issues/160 details). Another case demonstrates cyclical subgraphs may appear; taken constituencies 2024 UK general election, subsetted England south London. second subgraph two members, others’ neighbours, known cyclical component. constituencies Isle Wight:  consequences eigenvalues spatial weights matrix, pointed Smirnov Anselin (2009) Bivand, Hauke, Kossowski (2013). row-standardised weights, eigenvalues component : “takes ” lower domain boundary, whole data set now : compared lower domain boundary remainder study area: subgraph may added remainder shown : Using 5km cutoff seems prudent, work snap value. Taking Isle Wight East first, four constituencies boundaries within 5km: Obviously contiguous neighbour among zero distance, needs dropped, although addlinks1 drop duplicate: Although constituencies now linked, see whether using 5km criterion brings extra neighbours Isle Wight West: , , need beware sorting order zero self-distance contiguous neighbour distance, now second position: yields links north-west:  remains add suitable generalisation addlinks1 handle vector argument argument taking list vectors.","code":"(k6 <- knn2nb(knearneigh(pts, k=6), row.names=as.character(w50m$Constituency), sym=TRUE)) ## Warning in knn2nb(knearneigh(pts, k = 6), row.names = ## as.character(w50m$Constituency), : neighbour object has 2 sub-graphs ## Neighbour list object: ## Number of regions: 32  ## Number of nonzero links: 238  ## Percentage nonzero weights: 23.24219  ## Average number of links: 7.4375  ## 2 disjoint connected subgraphs plot(st_geometry(w50m), border=\"grey75\") plot(k6, pts, add=TRUE) o <- order(attr(k6, \"ncomp\")$comp.id) image(t(nb2mat(k6, style=\"B\")[o, rev(o)]), axes=FALSE, asp=1) (k6a <- knn2nb(knearneigh(pts, k=6), row.names=as.character(w50m$Constituency))) ## Warning in knn2nb(knearneigh(pts, k = 6), row.names = ## as.character(w50m$Constituency)): neighbour object has 2 sub-graphs ## Neighbour list object: ## Number of regions: 32  ## Number of nonzero links: 192  ## Percentage nonzero weights: 18.75  ## Average number of links: 6  ## 2 disjoint connected subgraphs ## Non-symmetric neighbours list file <- \"etc/shapes/GB_2024_southcoast_50m.gpkg.zip\" zipfile <- system.file(file, package=\"spdep\") if (GDAL37) {     sc50m <- st_read(zipfile) } else {     td <- tempdir()     bn <- sub(\".zip\", \"\", basename(file), fixed=TRUE)     target <- unzip(zipfile, files=bn, exdir=td)     sc50m <- st_read(target) } ## Reading layer `GB_2024_southcoast_50m' from data source  ##   `/tmp/RtmpXVTJuL/temp_libpath3b356d487bad39/spdep/etc/shapes/GB_2024_southcoast_50m.gpkg.zip'  ##   using driver `GPKG' ## Simple feature collection with 119 features and 19 fields ## Geometry type: MULTIPOLYGON ## Dimension:     XY ## Bounding box:  xmin: 82643.12 ymin: 5342.9 xmax: 640301.6 ymax: 187226.2 ## Projected CRS: OSGB36 / British National Grid (nb_sc_50m <- poly2nb(sc50m, row.names=as.character(sc50m$Constituency))) ## Warning in poly2nb(sc50m, row.names = as.character(sc50m$Constituency)): neighbour object has 2 sub-graphs; ## if this sub-graph count seems unexpected, try increasing the snap argument. ## Neighbour list object: ## Number of regions: 119  ## Number of nonzero links: 530  ## Percentage nonzero weights: 3.742674  ## Average number of links: 4.453782  ## 2 disjoint connected subgraphs nc <- attr(nb_sc_50m, \"ncomp\")$comp.id table(nc) ## nc ##   1   2  ## 117   2 (sub2 <- attr(nb_sc_50m, \"region.id\")[nc == 2L]) ## [1] \"Isle of Wight East\" \"Isle of Wight West\" pts <- st_point_on_surface(st_geometry(sc50m)) plot(st_geometry(sc50m), border=\"grey75\") plot(st_geometry(sc50m)[nc == 2L], border=\"orange\", lwd=2, add=TRUE) plot(nb_sc_50m, pts, add=TRUE) 1/range(eigen(cbind(c(0, 1), c(1, 0)))$values) ## [1] -1  1 1/range(eigen(nb2mat(subset(nb_sc_50m, nc == 2L), style=\"W\"))$values) ## [1] -1  1 1/range(eigen(nb2mat(nb_sc_50m, style=\"W\"))$values) ## [1] -1  1 1/range(eigen(nb2mat(subset(nb_sc_50m, nc == 1L), style=\"W\"))$values) ## [1] -1.094637  1.000000 iowe <- match(sub2[1], attr(nb_sc_50m, \"region.id\")) diowe <- c(st_distance(sc50m[iowe,], sc50m)) sort(diowe)[1:12] ## Units: [m] ##  [1]     0.000     0.000  1886.833  3509.366  6693.575  6943.672  7678.999 ##  [8]  8576.454 10579.530 12163.332 16875.920 17161.786 ioww <- match(sub2[2], attr(nb_sc_50m, \"region.id\")) dioww <- c(st_distance(sc50m[ioww,], sc50m)) sort(dioww)[1:12] ## Units: [m] ##  [1]     0.000     0.000  1232.724  2541.318  5746.764  5770.602  8902.579 ##  [8]  9747.265 10529.540 10909.845 12250.564 12379.871 (meet_criterion <- sum(diowe <= units::set_units(5000, \"m\"))) ## [1] 4 (cands <- attr(nb_sc_50m, \"region.id\")[order(diowe)[1:meet_criterion]]) ## [1] \"Isle of Wight East\" \"Isle of Wight West\" \"Portsmouth South\"   ## [4] \"Gosport\" (nb_sc_50m_iowe <- addlinks1(nb_sc_50m, from = cands[1], to = cands[3:meet_criterion])) ## Neighbour list object: ## Number of regions: 119  ## Number of nonzero links: 534  ## Percentage nonzero weights: 3.77092  ## Average number of links: 4.487395 (meet_criterion <- sum(dioww <= units::set_units(5000, \"m\"))) ## [1] 4 (cands <- attr(nb_sc_50m, \"region.id\")[order(dioww)[1:meet_criterion]]) ## [1] \"Isle of Wight East\" \"Isle of Wight West\" \"New Forest West\"    ## [4] \"New Forest East\" (nb_sc_50m_iow <- addlinks1(nb_sc_50m_iowe, from = cands[2], to = cands[3:meet_criterion])) ## Neighbour list object: ## Number of regions: 119  ## Number of nonzero links: 538  ## Percentage nonzero weights: 3.799167  ## Average number of links: 4.521008 pts <- st_point_on_surface(st_geometry(sc50m)) plot(st_geometry(sc50m), border=\"grey75\") plot(st_geometry(sc50m)[nc == 2L], border=\"orange\", lwd=2, add=TRUE) plot(nb_sc_50m_iow, pts, add=TRUE)"},{"path":"https://r-spatial.github.io/spdep/articles/subgraphs.html","id":"per-session-control-of-function-behaviour","dir":"Articles","previous_headings":"","what":"Per-session control of function behaviour","title":"No-neighbour observation and subgraph handling","text":"early , default value zero.policy argument many methods functions NULL. value NULL, zero.policy set get.ZeroPolicyOption: loading spdep, internal option set FALSE, functions methods using zero.policy need choose handle islands: case, shown island may reasonably associated proximate constituencies mainland. , however, user wishes override default, set.ZeroPolicyOption may used set different per-session default: listw object created zero.policy set TRUE, choice added output object attribute applied object used (unless specifically overridden). Note also 32 constituencies, observation count reported spweights.constants called print method listw object argument adjust.n TRUE, dropping -neighbour observations observation count. internal options introduced suppress -neighbour subgraph warnings creating nb objects. default values follows: get.NoNeighbourOption controls issuing warnings nb objects created -neighbour observations; get.SubgraphOption works similarly warnings issued one graph component; TRUE default. get.SubgraphCeiling sets integer value graph nodes plus graph edges calculating graph considered costly compute time, default 100,000. corresponds dense neighbour set just 300 nodes (almost 100000 edges) needed use inverse distance weights, just 14,000 nodes average neighbour count 6. print method nb objects reports -neighbour subgraph status anyway, careful users always examine generated objects may prefer supress warnings, warnings seem prudent users may examine objects, generation subsetting larger objects, example creation training test data sets. Welsh constituency boundaries used show behaviour internal options: Turning removes warnings: get.SubgraphOption FALSE, attribute containing output n.comp.nb added: reduction ceiling node count 32 plus edge count 136 also supresses calculation graph components: Restoring remaining default values:","code":"get.ZeroPolicyOption() ## [1] FALSE try(nb2listw(nb_W_50m)) ## Error in nb2listw(nb_W_50m) :  ##   Empty neighbour sets found (zero.policy: FALSE) set.ZeroPolicyOption(TRUE) get.ZeroPolicyOption() ## [1] TRUE (lw <- nb2listw(nb_W_50m)) ## Characteristics of weights list object: ## Neighbour list object: ## Number of regions: 32  ## Number of nonzero links: 136  ## Percentage nonzero weights: 13.28125  ## Average number of links: 4.25  ## 1 region with no links: ## Ynys Môn ## 2 disjoint connected subgraphs ##  ## Weights style: W  ## Weights constants summary: ##    n  nn S0       S1      S2 ## W 31 961 31 15.36355 129.051 attr(lw, \"zero.policy\") ## [1] TRUE set.ZeroPolicyOption(FALSE) get.NoNeighbourOption() ## [1] TRUE get.SubgraphOption() ## [1] TRUE get.SubgraphCeiling() ## [1] 100000 set.NoNeighbourOption(FALSE) (w50m |> poly2nb(row.names=as.character(w50m$Constituency)) -> nb_W_50mz) ## Warning in poly2nb(w50m, row.names = as.character(w50m$Constituency)): neighbour object has 2 sub-graphs; ## if this sub-graph count seems unexpected, try increasing the snap argument. ## Neighbour list object: ## Number of regions: 32  ## Number of nonzero links: 136  ## Percentage nonzero weights: 13.28125  ## Average number of links: 4.25  ## 1 region with no links: ## Ynys Môn ## 2 disjoint connected subgraphs set.SubgraphOption(FALSE) (w50m |> poly2nb(row.names=as.character(w50m$Constituency)) -> nb_W_50my) ## Neighbour list object: ## Number of regions: 32  ## Number of nonzero links: 136  ## Percentage nonzero weights: 13.28125  ## Average number of links: 4.25  ## 1 region with no links: ## Ynys Môn str(attr(nb_W_50my, \"ncomp\")) ##  NULL set.SubgraphOption(TRUE) set.SubgraphCeiling(100L) (w50m |> poly2nb(row.names=as.character(w50m$Constituency)) -> nb_W_50mx) ## Neighbour list object: ## Number of regions: 32  ## Number of nonzero links: 136  ## Percentage nonzero weights: 13.28125  ## Average number of links: 4.25  ## 1 region with no links: ## Ynys Môn str(attr(nb_W_50mx, \"ncomp\")) ##  NULL set.SubgraphCeiling(100000L) set.NoNeighbourOption(TRUE)"},{"path":"https://r-spatial.github.io/spdep/articles/subgraphs.html","id":"unintentional-disconnected-graphs","dir":"Articles","previous_headings":"","what":"Unintentional disconnected graphs","title":"No-neighbour observation and subgraph handling","text":"Sometimes apparently sensible polygons turn represented way disconnected graphs generated extracting contiguities. One case raised https://github.com/r-spatial/spdep/issues/162, subdivisions Tokyo. original data file tokyomet262.* https://sgsup.asu.edu/sites/default/files/SparcFiles/tokyo_0.zip created twenty years ago Tomoki Nakaya Martin Charlton, geometry issues known time. possibility may affect legacy files projection geometries 32-bit platforms, known whether affected file. re-packaged compressed GeoPackage: correcting invalid polygons: applying poly2nb legacy default snap value produced numerous singleton observations well many multiple-observation subgraphs: legacy default snap value coordinates measured metres 15 nanometres, effectively assumed coordinates making polygon boundaries identical: Stepping little 2mm, lack contact ceased problem. basis, default changed spdep 1.3-6 10mm projected polygons, snap value used returned attribute neighbour object: polygons represented geographical (spherical) coordinates, new default spdep 1.3-6 set value mimicking 10mm: default snap value used poly2nb polygons expressed decimal degrees : set based apparent “size” 10mm decimal degrees:","code":"file <- \"etc/shapes/tokyo.gpkg.zip\" zipfile <- system.file(file, package=\"spdep\") if (GDAL37) {     tokyo <- st_read(zipfile) } else {     td <- tempdir()     bn <- sub(\".zip\", \"\", basename(file), fixed=TRUE)     target <- unzip(zipfile, files=bn, exdir=td)     tokyo <- st_read(target) } ## Reading layer `tokyo' from data source  ##   `/tmp/RtmpXVTJuL/temp_libpath3b356d487bad39/spdep/etc/shapes/tokyo.gpkg.zip'  ##   using driver `GPKG' ## Simple feature collection with 262 features and 3 fields ## Geometry type: MULTIPOLYGON ## Dimension:     XY ## Bounding box:  xmin: 266206.6 ymin: -90932.11 xmax: 411400.3 ymax: 37142.75 ## Projected CRS: Tokyo / Japan Plane Rectangular CS VI all(st_is_valid(tokyo)) ## [1] TRUE tokyo <- st_make_valid(tokyo) (nb_t0 <- poly2nb(tokyo, snap=sqrt(.Machine$double.eps))) ## Warning in poly2nb(tokyo, snap = sqrt(.Machine$double.eps)): some observations have no neighbours; ## if this seems unexpected, try increasing the snap argument. ## Warning in poly2nb(tokyo, snap = sqrt(.Machine$double.eps)): neighbour object has 23 sub-graphs; ## if this sub-graph count seems unexpected, try increasing the snap argument. ## Neighbour list object: ## Number of regions: 262  ## Number of nonzero links: 946  ## Percentage nonzero weights: 1.378125  ## Average number of links: 3.610687  ## 10 regions with no links: ## 101, 127, 134, 135, 152, 154, 167, 237, 242, 243 ## 23 disjoint connected subgraphs units::set_units(units::set_units(attr(nb_t0, \"snap\"), \"m\"), \"nm\") ## 14.90116 [nm] (nb_t1 <- poly2nb(tokyo, snap=0.002)) ## Neighbour list object: ## Number of regions: 262  ## Number of nonzero links: 1390  ## Percentage nonzero weights: 2.02494  ## Average number of links: 5.305344 units::set_units(units::set_units(attr(nb_t1, \"snap\"), \"m\"), \"mm\") ## 2 [mm] (nb_t2 <- poly2nb(tokyo)) ## Neighbour list object: ## Number of regions: 262  ## Number of nonzero links: 1390  ## Percentage nonzero weights: 2.02494  ## Average number of links: 5.305344 units::set_units(units::set_units(attr(nb_t2, \"snap\"), \"m\"), \"mm\") ## 10 [mm] (nb_t3 <- poly2nb(st_transform(tokyo, \"OGC:CRS84\"))) ## Neighbour list object: ## Number of regions: 262  ## Number of nonzero links: 1336  ## Percentage nonzero weights: 1.946274  ## Average number of links: 5.099237 attr(nb_t3, \"snap\") ## [1] 9e-08 (180 * 0.01) / (pi * 6378137) ## [1] 8.983153e-08"},{"path":[]},{"path":"https://r-spatial.github.io/spdep/authors.html","id":null,"dir":"","previous_headings":"","what":"Authors","title":"Authors and Citation","text":"Roger Bivand. Maintainer, author. Micah Altman. Contributor. Luc Anselin. Contributor. Renato Assunção. Contributor. Anil Bera. Contributor. Olaf Berke. Contributor. F. Guillaume Blanchet. Contributor. Marilia Carvalho. Contributor. Bjarke Christensen. Contributor. Yongwan Chun. Contributor. Carsten Dormann. Contributor. Stéphane Dray. Contributor. Dewey Dunnington. Contributor. Virgilio Gómez-Rubio. Contributor. Malabika Koley. Contributor. Tomasz Kossowski. Contributor. Elias Krainski. Contributor. Pierre Legendre. Contributor. Nicholas Lewin-Koh. Contributor. Angela Li. Contributor. Giovanni Millo. Contributor. Werner Mueller. Contributor. Hisaji Ono. Contributor. Josiah Parry. Contributor. Pedro Peres-Neto. Contributor. Michał Pietrzak. Contributor. Gianfranco Piras. Contributor. Markus Reder. Contributor. Jeff Sauer. Contributor. Michael Tiefelsdorf. Contributor. René Westerholt. Contributor. Justyna Wilk. Contributor. Levi Wolf. Contributor. Danlin Yu. Contributor.","code":""},{"path":"https://r-spatial.github.io/spdep/authors.html","id":"citation","dir":"","previous_headings":"","what":"Citation","title":"Authors and Citation","text":"Bivand R, Wong D (2018). “Comparing implementations global local indicators spatial association.” TEST, 27(3), 716–748. doi:10.1007/s11749-018-0599-x. Roger Bivand (2022). “R Packages Analyzing Spatial Data: Comparative Case Study Areal Data.” Geographical Analysis, 54(3), 488-518. doi:10.1111/gean.12319. Bivand R, Pebesma E, Gómez-Rubio V (2013). Applied spatial data analysis R, Second edition. Springer, NY. https://asdar-book.org/. Pebesma E, Bivand R (2023). Spatial Data Science Applications R. Chapman & Hall. https://r-spatial.org/book/.","code":"@Article{,   author = {Roger Bivand and David W. S. Wong},   title = {Comparing implementations of global and local indicators of spatial association},   journal = {TEST},   year = {2018},   volume = {27},   number = {3},   pages = {716--748},   doi = {10.1007/s11749-018-0599-x}, } @Article{,   author = {{Roger Bivand}},   title = {R Packages for Analyzing Spatial Data: A Comparative Case Study with Areal Data},   journal = {Geographical Analysis},   year = {2022},   volume = {54},   number = {3},   pages = {488-518},   doi = {10.1111/gean.12319}, } @Book{,   author = {Roger S. Bivand and Edzer Pebesma and Virgilio Gómez-Rubio},   title = {Applied spatial data analysis with {R}, Second edition},   year = {2013},   publisher = {Springer, NY},   url = {https://asdar-book.org/}, } @Book{,   author = {Edzer Pebesma and Roger S. Bivand},   title = {Spatial Data Science With Applications in {R}},   year = {2023},   publisher = {Chapman & Hall},   url = {https://r-spatial.org/book/}, }"},{"path":[]},{"path":"https://r-spatial.github.io/spdep/index.html","id":"spatial-dependence-weighting-schemes-and-statistics","dir":"","previous_headings":"","what":"Spatial Dependence: Weighting Schemes and Statistics","title":"Spatial Dependence: Weighting Schemes, Statistics","text":"collection functions create spatial weights matrix objects polygon contiguities, point patterns distance tessellations, summarizing objects, permitting use spatial data analysis, including regional aggregation minimum spanning tree; collection tests spatial autocorrelation, including global Morans Gearys C proposed Cliff Ord (1973, ISBN: 0850860369) (1981, ISBN: 0850860814), Hubert/Mantel general cross product statistic, Empirical Bayes estimates Assunção/Reis (1999) (https://doi.org/10.1002/(SICI)1097-0258(19990830)18:16%3C2147%3A%3AAID-SIM179%3E3.0.CO%3B2-) Index, Getis/Ord G (Getis Ord 1992) (https://doi.org/10.1111/j.1538-4632.1992.tb00261.x) multicoloured join count statistics, APLE (Li et al. ) (https://doi.org/10.1111/j.1538-4632.2007.00708.x), local Morans (Anselin 1995) (https://doi.org/10.1111/j.1538-4632.1995.tb00338.x) Getis/Ord G (Ord Getis 1995) (https://doi.org/10.1111/j.1538-4632.1995.tb00912.x), saddlepoint approximations (Tiefelsdorf 2002) (https://doi.org/10.1111/j.1538-4632.2002.tb01084.x) exact tests global local Morans (Bivand et al. 2009) (https://doi.org/10.1016/j.csda.2008.07.021) LOSH local indicators spatial heteroscedasticity (Ord Getis) (https://doi.org/10.1007/s00168-011-0492-y), extensions Bivand (2022) doi:10.1111/gean.12319. implementation measures described Bivand Wong (2018) (https://doi.org/10.1007/s11749-018-0599-x). Extra measures contributed Josiah Parry. Lagrange multiplier tests spatial dependence linear models provided (Anselin et al. 1996) (https://doi.org/10.1016/0166-0462(95)02111-6), Rao’s score tests hypothesised spatial Durbin models based fitted linear models (Koley Bera 2024) (https://doi.org/10.1080/17421772.2023.2256810). local indicators categorical data (LICD) implementation based Carrer et al. (2021) (https://doi.org/10.1016/j.jas.2020.105306) Bivand et al. (2017) (https://doi.org/10.1016/j.spasta.2017.03.003) added 1.3-7. sfdep (https://cran.r-project.org/package=sfdep) provides piped interface spdep. spdep spatialreg versions >= 1.2-1, model fitting functions previously present package defunct spdep may found spatialreg. Default branch now main Moved R-Forge","code":""},{"path":"https://r-spatial.github.io/spdep/reference/COL.OLD.html","id":null,"dir":"Reference","previous_headings":"","what":"Columbus OH spatial analysis data set - old numbering — oldcol","title":"Columbus OH spatial analysis data set - old numbering — oldcol","text":"COL.OLD data frame 49 rows 22 columns. observations ordered numbered original analyses data set SpaceStat documentation Anselin, L. 1988 Spatial econometrics: methods models, Dordrecht: Kluwer. Unit analysis: 49 neighbourhoods Columbus, OH, 1980 data. addition data set includes COL.nb, neighbours list used Anselin (1988).","code":""},{"path":"https://r-spatial.github.io/spdep/reference/COL.OLD.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Columbus OH spatial analysis data set - old numbering — oldcol","text":"","code":"data(oldcol)"},{"path":"https://r-spatial.github.io/spdep/reference/COL.OLD.html","id":"format","dir":"Reference","previous_headings":"","what":"Format","title":"Columbus OH spatial analysis data set - old numbering — oldcol","text":"data frame contains following columns: AREA_PL computed ArcView (agrees areas polygons “columbus” data set PERIMETER computed ArcView COLUMBUS. internal polygon ID (ignore) COLUMBUS.another internal polygon ID (ignore) POLYID yet another polygon ID NEIG neighborhood id value (1-49);              conforms id value used Spatial Econometrics book. HOVAL housing value ($1,000) INC household income ($1,000) CRIME residential burglaries vehicle thefts per thousand         households neighborhood OPEN open space neighborhood PLUMB percentage housing units without plumbin DISCBD distance CBD X x coordinate (arbitrary digitizing units, polygon coordinates) Y y coordinate (arbitrary digitizing units, polygon coordinates) AREA_SS neighborhood area (computed SpaceStat) NSA north-south dummy (North=1) NSB north-south dummy (North=1) EW east-west dummy (East=1) CP core-periphery dummy (Core=1) THOUS constant=1,000 NEIGNO NEIG+1,000, alternative neighborhood id value PERIM polygon perimeter (computed SpaceStat)","code":""},{"path":"https://r-spatial.github.io/spdep/reference/COL.OLD.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Columbus OH spatial analysis data set - old numbering — oldcol","text":"row names COL.OLD region.id attribute COL.nb set columbus$NEIGNO.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/COL.OLD.html","id":"source","dir":"Reference","previous_headings":"","what":"Source","title":"Columbus OH spatial analysis data set - old numbering — oldcol","text":"Anselin, Luc.  1988.  Spatial econometrics: methods models.  Dordrecht: Kluwer Academic, Table 12.1 p. 189.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/COL.OLD.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Columbus OH spatial analysis data set - old numbering — oldcol","text":"source data files prepared Luc Anselin, Spatial Analysis Laboratory, Department Agricultural Consumer Economics, University Illinois, Urbana-Champaign.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/EBImoran.mc.html","id":null,"dir":"Reference","previous_headings":"","what":"Permutation test for empirical Bayes index — EBImoran.mc","title":"Permutation test for empirical Bayes index — EBImoran.mc","text":"empirical Bayes index modification Moran's testing spatial autocorrelation rate, typically number observed cases population risk. index value tested using nsim random permutations index given spatial weighting scheme, establish rank observed statistic relation nsim simulated values.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/EBImoran.mc.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Permutation test for empirical Bayes index — EBImoran.mc","text":"","code":"EBImoran.mc(n, x, listw, nsim, zero.policy = attr(listw, \"zero.policy\"),   alternative = \"greater\", spChk=NULL, return_boot=FALSE,  subtract_mean_in_numerator=TRUE)"},{"path":"https://r-spatial.github.io/spdep/reference/EBImoran.mc.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Permutation test for empirical Bayes index — EBImoran.mc","text":"n numeric vector counts cases length neighbours list listw x numeric vector populations risk length neighbours list listw listw listw object created example nb2listw nsim number permutations zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA alternative character string specifying alternative hypothesis, must one \"greater\" (default), \"two.sided\", \"less\" spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption() return_boot return object class boot equivalent permutation bootstrap rather object class htest subtract_mean_in_numerator default TRUE, TRUE subtract mean z numerator EBI equation p. 2157 reference (consulted Renato Assunção 2016-02-19); February 2016 default FALSE agreeing printed paper.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/EBImoran.mc.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Permutation test for empirical Bayes index — EBImoran.mc","text":"statistic used (m number observations): $$EBI = \\frac{m}{\\sum_{=1}^{m}\\sum_{j=1}^{m}w_{ij}} \\frac{\\sum_{=1}^{m}\\sum_{j=1}^{m}w_{ij}z_i z_j}{\\sum_{=1}^{m}(z_i - \\bar{z})^2} $$ : $$z_i = \\frac{p_i - b}{\\sqrt{v_i}}$$ : $$p_i = n_i / x_i$$ $$v_i = + (b / x_i)$$ $$b = \\sum_{=1}^{m} n_i / \\sum_{=1}^{m} x_i $$ $$= s^2 - b / (\\sum_{=1}^{m} x_i / m)$$ $$s^2 = \\sum_{=1}^{m} x_i (p_i - b)^2 / \\sum_{=1}^{m} x_i $$","code":""},{"path":"https://r-spatial.github.io/spdep/reference/EBImoran.mc.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Permutation test for empirical Bayes index — EBImoran.mc","text":"list class htest mc.sim containing following components: statistic value observed Moran's . parameter rank observed Moran's . p.value pseudo p-value test. alternative character string describing alternative hypothesis. method character string giving method used. data.name character string giving name(s) data, number simulations. res nsim simulated values statistic, final value observed statistic z numerical vector Empirical Bayes indices z ","code":""},{"path":"https://r-spatial.github.io/spdep/reference/EBImoran.mc.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Permutation test for empirical Bayes index — EBImoran.mc","text":"Assunção RM, Reis EA 1999 new proposal adjust Moran's population density. Statistics Medicine 18, pp. 2147–2162; Bivand RS, Wong DWS 2018 Comparing implementations global local indicators spatial association. TEST, 27(3), 716–748 doi:10.1007/s11749-018-0599-x","code":""},{"path":"https://r-spatial.github.io/spdep/reference/EBImoran.mc.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Permutation test for empirical Bayes index — EBImoran.mc","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/EBImoran.mc.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Permutation test for empirical Bayes index — EBImoran.mc","text":"","code":"nc.sids <- st_read(system.file(\"shapes/sids.gpkg\", package=\"spData\")[1], quiet=TRUE) rn <- as.character(nc.sids$FIPS) ncCC89_nb <- read.gal(system.file(\"weights/ncCC89.gal\", package=\"spData\")[1],  region.id=rn) #> Warning: neighbour object has 3 sub-graphs EBImoran.mc(nc.sids$SID74, nc.sids$BIR74,  nb2listw(ncCC89_nb, style=\"B\", zero.policy=TRUE), nsim=999,  alternative=\"two.sided\", zero.policy=TRUE) #> The default for subtract_mean_in_numerator set TRUE from February 2016 #>  #> \tMonte-Carlo simulation of Empirical Bayes Index (mean subtracted) #>  #> data:  cases: nc.sids$SID74, risk population: nc.sids$BIR74 #> weights: nb2listw(ncCC89_nb, style = \"B\", zero.policy = TRUE) #> number of simulations + 1: 1000 #>  #> statistic = 0.25789, observed rank = 999, p-value = 0.002 #> alternative hypothesis: two.sided #>  sids.p <- nc.sids$SID74 / nc.sids$BIR74 moran.mc(sids.p, nb2listw(ncCC89_nb, style=\"B\", zero.policy=TRUE),  nsim=999, alternative=\"two.sided\", zero.policy=TRUE) #>  #> \tMonte-Carlo simulation of Moran I #>  #> data:  sids.p  #> weights: nb2listw(ncCC89_nb, style = \"B\", zero.policy = TRUE)   #> number of simulations + 1: 1000  #>  #> statistic = 0.20904, observed rank = 997, p-value = 0.006 #> alternative hypothesis: two.sided #>"},{"path":"https://r-spatial.github.io/spdep/reference/EBest.html","id":null,"dir":"Reference","previous_headings":"","what":"Global Empirical Bayes estimator — EBest","title":"Global Empirical Bayes estimator — EBest","text":"function computes global empirical Bayes estimates rates \"shrunk\" overall mean.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/EBest.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Global Empirical Bayes estimator — EBest","text":"","code":"EBest(n, x, family=\"poisson\")"},{"path":"https://r-spatial.github.io/spdep/reference/EBest.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Global Empirical Bayes estimator — EBest","text":"n numeric vector counts cases x numeric vector populations risk family either \"poisson\" rare conditions \"binomial\" non-rare conditions","code":""},{"path":"https://r-spatial.github.io/spdep/reference/EBest.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Global Empirical Bayes estimator — EBest","text":"Details implementation \"poisson\" family found Marshall, p. 284–5, Bailey Gatrell p. 303–306 exercise 8.2, pp. 328–330. \"binomial\" family, see Martuzzi Elliott (implementation Olaf Berke).","code":""},{"path":"https://r-spatial.github.io/spdep/reference/EBest.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Global Empirical Bayes estimator — EBest","text":"data frame two columns: raw numerical vector raw (crude) rates estmm numerical vector empirical Bayes estimates parameters attribute list components:  global method moments phi value m global method moments gamma value","code":""},{"path":"https://r-spatial.github.io/spdep/reference/EBest.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Global Empirical Bayes estimator — EBest","text":"Marshall R M (1991) Mapping disease mortality rates using Empirical Bayes Estimators, Applied Statistics, 40, 283–294; Bailey T, Gatrell (1995) Interactive Spatial Data Analysis, Harlow: Longman, pp. 303–306, Martuzzi M, Elliott P (1996) Empirical Bayes estimation small area prevalence non-rare conditions, Statistics Medicine 15, 1867–1873.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/EBest.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Global Empirical Bayes estimator — EBest","text":"Roger Bivand Roger.Bivand@nhh.Olaf Berke, Population Medicine, OVC, University Guelph, CANADA","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/EBest.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Global Empirical Bayes estimator — EBest","text":"","code":"auckland <- st_read(system.file(\"shapes/auckland.gpkg\", package=\"spData\")[1], quiet=TRUE) res <- EBest(auckland$M77_85, 9*auckland$Und5_81) attr(res, \"parameters\") #> $a #> [1] 7.284173e-07 #>  #> $b #> [1] 0.002633436 #>  auckland$estmm000 <- res$estmm*1000 plot(auckland[,\"estmm000\"], breaks=c(0,2,2.5,3,3.5,5),  main=\"Infant mortality per 1000 per year\")  data(huddersfield, package=\"spData\") res <- EBest(huddersfield$cases, huddersfield$total, family=\"binomial\") round(res[,1:2],4)*100 #>      raw estmm #> 1  42.86 34.44 #> 2  28.95 29.56 #> 3  28.31 28.94 #> 4  21.43 28.93 #> 5  33.33 30.72 #> 6  30.86 30.43 #> 7  33.70 31.85 #> 8  45.61 35.93 #> 9  26.67 28.95 #> 10 29.41 29.95 #> 11 27.76 28.36 #> 12 33.75 31.75 #> 13 32.67 31.84 #> 14 22.91 25.36 #> 15 34.21 32.33 #> 16 33.77 31.72 #> 17 29.09 29.69 #> 18 15.87 24.36 #> 19 40.91 32.11 #> 20 40.00 31.01 #> 21 28.79 29.53 #> 22 38.89 31.47 #> 23 28.32 29.10 #> 24 33.33 31.44 #> 25 13.95 22.36 #> 26 33.77 31.72 #> 27 31.58 30.31 #> 28 33.33 30.42 #> 29 26.67 28.26 #> 30 63.64 33.57 #> 31 34.38 32.24 #> 32 20.00 27.62 #> 33 19.15 24.60 #> 34 25.53 28.54 #> 35 24.14 27.79 #> 36 44.00 32.98 #> 37 25.33 27.95 #> 38 18.18 26.96 #> 39 31.78 30.97 #> 40 32.20 30.88 #> 41 26.19 28.23 #> 42 19.05 26.65 #> 43 16.67 26.81 #> 44 20.00 28.66 #> 45 32.99 31.54 #> 46 50.00 31.97 #> 47 37.21 32.30 #> 48 32.79 31.13 #> 49 38.89 31.47 #> 50 25.00 27.26 #> 51 26.03 28.29 #> 52 30.43 30.18 #> 53 19.75 25.28 #> 54 50.00 31.61 #> 55 21.62 27.67 #> 56 22.22 27.88 #> 57 36.36 30.71 #> 58 31.25 30.22 #> 59  0.00 29.73 #> 60 29.41 29.95 #> 61 31.16 30.71 #> 62 33.33 30.58 #> 63 33.87 32.22 #> 64 30.00 30.04 #> 65 30.34 30.19 #> 66 40.74 35.00 #> 67 46.43 38.96 #> 68 34.21 31.91 #> 69 24.26 26.10 #> 70 29.41 29.75 #> 71 47.17 39.13"},{"path":"https://r-spatial.github.io/spdep/reference/EBlocal.html","id":null,"dir":"Reference","previous_headings":"","what":"Local Empirical Bayes estimator — EBlocal","title":"Local Empirical Bayes estimator — EBlocal","text":"function computes local empirical Bayes estimates rates \"shrunk\" neighbourhood mean neighbourhoods given nb neighbourhood list.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/EBlocal.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Local Empirical Bayes estimator — EBlocal","text":"","code":"EBlocal(ri, ni, nb, zero.policy = NULL, spChk = NULL, geoda=FALSE)"},{"path":"https://r-spatial.github.io/spdep/reference/EBlocal.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Local Empirical Bayes estimator — EBlocal","text":"ri numeric vector counts cases length neighbours list nb; many zero counts, estimates may affected division zero, see https://stat.ethz.ch/pipermail/r-sig-geo/2022-January/028882.html ni numeric vector populations risk length neighbours list nb nb nb object neighbour relationships zero.policy default NULL, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption() geoda default=FALSE, following Marshall's algorithm interpreted Bailey Gatrell, pp. 305-307, exercise 8.2, pp. 328-330 definition phi; TRUE definition phi used GeoDa (see discussion OpenSpace mailing list June 2003: http://agec221.agecon.uiuc.edu/pipermail/openspace/2003-June/thread.html)","code":""},{"path":"https://r-spatial.github.io/spdep/reference/EBlocal.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Local Empirical Bayes estimator — EBlocal","text":"Details implementation found Marshall, p. 286, Bailey Gatrell p. 307 exercise 8.2, pp. 328–330. example results fully correspond sources slightly differing neighbourhoods, generally close. many zero counts, estimates may affected division zero, see https://stat.ethz.ch/pipermail/r-sig-geo/2022-January/028882.html.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/EBlocal.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Local Empirical Bayes estimator — EBlocal","text":"data frame two columns: raw numerical vector raw (crude) rates est numerical vector local empirical Bayes estimates parameters attribute list components (zero, estimate NaN, https://stat.ethz.ch/pipermail/r-sig-geo/2022-January/028882.html):  numerical vector local phi values m numerical vector local gamma values","code":""},{"path":"https://r-spatial.github.io/spdep/reference/EBlocal.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Local Empirical Bayes estimator — EBlocal","text":"Marshall R M (1991) Mapping disease mortality rates using Empirical Bayes Estimators, Applied Statistics, 40, 283–294; Bailey T, Gatrell (1995) Interactive Spatial Data Analysis, Harlow: Longman, pp. 303–306.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/EBlocal.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Local Empirical Bayes estimator — EBlocal","text":"Roger Bivand Roger.Bivand@nhh., based contributions Marilia Carvalho","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/EBlocal.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Local Empirical Bayes estimator — EBlocal","text":"","code":"auckland <- st_read(system.file(\"shapes/auckland.gpkg\", package=\"spData\")[1], quiet=TRUE) auckland.nb <- poly2nb(auckland) res <- EBlocal(auckland$M77_85,  9*auckland$Und5_81, auckland.nb) auckland$est000 <- res$est*1000 plot(auckland[,\"est000\"], breaks=c(0,2,2.5,3,3.5,8),  main=\"Infant mortality per 1000 per year\")"},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.cs.html","id":null,"dir":"Reference","previous_headings":"","what":"Chi-square based test for local spatial heteroscedasticity — LOSH.cs","title":"Chi-square based test for local spatial heteroscedasticity — LOSH.cs","text":"function implements chi-square based test statistic local spatial heteroscedasticity (LOSH) proposed Ord & Getis (2012).","code":""},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.cs.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Chi-square based test for local spatial heteroscedasticity — LOSH.cs","text":"","code":"LOSH.cs(x, listw, zero.policy = attr(listw, \"zero.policy\"), na.action = na.fail,                   p.adjust.method = \"none\", spChk = NULL)"},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.cs.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Chi-square based test for local spatial heteroscedasticity — LOSH.cs","text":"x numeric vector length neighbours list listw listw listw object created example nb2listw zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA na.action function (default na.fail), can also na.omit na.exclude - cases weights list subsetted remove NAs data. may necessary set zero.policy TRUE subsetting may create -neighbour observations. Note weights lists created without using glist argument nb2listw may subsetted. na.pass used, zero substituted NA values calculating spatial lag. (Note na.exclude work properly starting R 1.9.0, na.omit na.exclude assign wrong classes 1.8.*) p.adjust.method character string specifying probability value adjustment multiple tests, default \"none\"; see p.adjustSP. Note number multiple tests region taken number neighbours + 1 region, rather total number regions. spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption()","code":""},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.cs.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Chi-square based test for local spatial heteroscedasticity — LOSH.cs","text":"test uses = 2 (see LOSH) chi-square based inference applicable exponents. function makes use LOSH calculations.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.cs.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Chi-square based test for local spatial heteroscedasticity — LOSH.cs","text":"Hi LOSH statistic E.Hi expectation LOSH Var.Hi variance LOSH Z.Hi approximately chi-square distributed test statistics x_bar_i local spatially weighted mean values ei residuals local spatially weighted mean values Pr() p-values Hi obtained non-central Chi-square distribution \\(2/Var.Hi\\) degrees freedom","code":""},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.cs.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Chi-square based test for local spatial heteroscedasticity — LOSH.cs","text":"Ord, J. K., & Getis, . 2012. Local spatial heteroscedasticity (LOSH), Annals Regional Science, 48 (2), 529–539.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.cs.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Chi-square based test for local spatial heteroscedasticity — LOSH.cs","text":"René Westerholt rene.westerholt@tu-dortmund.de","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.cs.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Chi-square based test for local spatial heteroscedasticity — LOSH.cs","text":"","code":"data(boston, package=\"spData\")     resLOSH <- LOSH.cs(boston.c$NOX, nb2listw(boston.soi))     hist(resLOSH[,\"Hi\"])      mean(resLOSH[,\"Hi\"]) #> [1] 0.9919329"},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.html","id":null,"dir":"Reference","previous_headings":"","what":"Local spatial heteroscedasticity — LOSH","title":"Local spatial heteroscedasticity — LOSH","text":"Local spatial heteroscedasticity calculated location based spatial weights object used. statistic :     $$H_i = \\frac{\\sum_j^n w_{ij} \\cdot |e_j|^}{h_1 \\cdot \\sum_j^n w_{ij}}$$ $$e_j = x_j - \\bar{x}_j$$ $$\\bar{x}_j = \\frac{\\sum_k^n w_{jk} \\cdot x_k}{\\sum_k^n w_{jk}}$$     expectation variance given Ord & Getis (2012). exponent allows investigating different types mean dispersal.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Local spatial heteroscedasticity — LOSH","text":"","code":"LOSH(x, listw, a=2, var_hi=TRUE, zero.policy=attr(listw, \"zero.policy\"),  na.action=na.fail, spChk=NULL)"},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Local spatial heteroscedasticity — LOSH","text":"x numeric vector length neighbours list listw listw listw object created example nb2listw exponent applied local residuals; default value 2 leads measure heterogeneity spatial variance var_hi default TRUE, moments test statistics calculated location; FALSE, plain LOSH measures, \\(\\bar{x}_i\\) \\(e_i\\) calculated zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA na.action function (default na.fail), can also na.omit na.exclude - cases weights list subsetted remove NAs data. may necessary set zero.policy TRUE subsetting may create -neighbour observations. Note weights lists created without using glist argument nb2listw may subsetted. na.pass used, zero substituted NA values calculating spatial lag. (Note na.exclude work properly starting R 1.9.0, na.omit na.exclude assign wrong classes 1.8.*) spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption()","code":""},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Local spatial heteroscedasticity — LOSH","text":"addition LOSH measure, values returned include local spatially weighted mean values \\(\\bar{x}_i\\) local residuals \\(e_i\\) estimated means. values facilitate interpretation LOSH values. , specified var_hi, statistical moments test statistics proposed Ord & Getis (2012) also calculated returned.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Local spatial heteroscedasticity — LOSH","text":"Hi LOSH statistic E.Hi (optional) expectation LOSH Var.Hi (optional) variance LOSH Z.Hi (optional) approximately Chi-square distributed test statistics x_bar_i local spatially weighted mean values ei residuals local spatially weighted mean values","code":""},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Local spatial heteroscedasticity — LOSH","text":"Ord, J. K., & Getis, . 2012. Local spatial heteroscedasticity (LOSH),     Annals Regional Science, 48 (2), 529–539.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Local spatial heteroscedasticity — LOSH","text":"René Westerholt rene.westerholt@tu-dortmund.de","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Local spatial heteroscedasticity — LOSH","text":"","code":"data(boston, package=\"spData\")     resLOSH <- LOSH(boston.c$NOX, nb2listw(boston.soi))     hist(resLOSH[,\"Hi\"])      mean(resLOSH[,\"Hi\"]) #> [1] 0.9919329"},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.mc.html","id":null,"dir":"Reference","previous_headings":"","what":"Bootstrapping-based test for local spatial heteroscedasticity — LOSH.mc","title":"Bootstrapping-based test for local spatial heteroscedasticity — LOSH.mc","text":"function draws inferences local spatial heteroscedasticity (LOSH) means randomisation-based Monte-Carlo bootstrap proposed Xu et al. (2014).","code":""},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.mc.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Bootstrapping-based test for local spatial heteroscedasticity — LOSH.mc","text":"","code":"LOSH.mc(x, listw, a = 2, nsim = 99, zero.policy = attr(listw, \"zero.policy\"),  na.action = na.fail, spChk = NULL, adjust.n = TRUE, p.adjust.method = \"none\")"},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.mc.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Bootstrapping-based test for local spatial heteroscedasticity — LOSH.mc","text":"x numeric vector length neighbours list listw listw listw object created example nb2listw exponent applied local residuals; default value 2 leads measure heterogeneity spatial variance nsim number randomisations used bootstrap zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA na.action function (default na.fail), can also na.omit na.exclude - cases weights list subsetted remove NAs data. may necessary set zero.policy TRUE subsetting may create -neighbour observations. Note weights lists created without using glist argument nb2listw may subsetted. na.pass used, zero substituted NA values calculating spatial lag. (Note na.exclude work properly starting R 1.9.0, na.omit na.exclude assign wrong classes 1.8.*) spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption() adjust.n default TRUE, FALSE number observations adjusted -neighbour observations, TRUE, number observations adjusted p.adjust.method character string specifying probability value adjustment multiple tests, default \"none\"; see p.adjustSP. Note number multiple tests region taken number neighbours + 1 region, rather total number regions.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.mc.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Bootstrapping-based test for local spatial heteroscedasticity — LOSH.mc","text":"test calculates LOSH (see LOSH) estimates pseudo p-values conditional bootstrap. Thereby, -th value location held fixed, whereas values permuted nsim times spatial units.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.mc.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Bootstrapping-based test for local spatial heteroscedasticity — LOSH.mc","text":"Hi LOSH statistic E.Hi expectation LOSH Var.Hi variance LOSH Z.Hi approximately chi-square distributed test statistics x_bar_i local spatially weighted mean values ei residuals local spatially weighted mean values Pr() p-values Hi obtained conditional bootstrap distribution","code":""},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.mc.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Bootstrapping-based test for local spatial heteroscedasticity — LOSH.mc","text":"Ord, J. K., & Getis, . 2012. Local spatial heteroscedasticity (LOSH), Annals Regional Science, 48 (2), 529–539; Xu, M., Mei, C. L., & Yan, N. 2014. note null distribution local spatial heteroscedasticity (LOSH) statistic. Annals Regional Science, 52 (3), 697–710.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.mc.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Bootstrapping-based test for local spatial heteroscedasticity — LOSH.mc","text":"René Westerholt rene.westerholt@tu-dortmund.de","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.mc.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Bootstrapping-based test for local spatial heteroscedasticity — LOSH.mc","text":"","code":"data(columbus, package=\"spData\")     resLOSH_mc <- LOSH.mc(columbus$CRIME, nb2listw(col.gal.nb), 2, 100)     summary(resLOSH_mc) #>        Hi             x_bar_i            ei                 Pr()          #>  Min.   :0.03438   Min.   :13.85   Min.   :   0.0298   Min.   :0.009901   #>  1st Qu.:0.23838   1st Qu.:24.71   1st Qu.:   7.0114   1st Qu.:0.079208   #>  Median :0.66689   Median :35.90   Median :  52.1094   Median :0.653465   #>  Mean   :1.06592   Mean   :34.88   Mean   : 151.9232   Mean   :0.552233   #>  3rd Qu.:1.59680   3rd Qu.:45.39   3rd Qu.: 105.0551   3rd Qu.:0.900990   #>  Max.   :4.68765   Max.   :54.91   Max.   :2455.2201   Max.   :0.990099       resLOSH_cs <- LOSH.cs(columbus$CRIME, nb2listw(col.gal.nb))     summary(resLOSH_cs) #>        Hi               E.Hi       Var.Hi            Z.Hi         #>  Min.   :0.03438   Min.   :1   Min.   :0.4972   Min.   :0.04356   #>  1st Qu.:0.23838   1st Qu.:1   1st Qu.:0.9136   1st Qu.:0.35069   #>  Median :0.66689   Median :1   Median :1.4342   Median :1.19175   #>  Mean   :1.06592   Mean   :1   Mean   :1.4758   Mean   :1.89447   #>  3rd Qu.:1.59680   3rd Qu.:1   3rd Qu.:1.9547   3rd Qu.:2.65120   #>  Max.   :4.68765   Max.   :1   Max.   :2.9958   Max.   :7.25681   #>     x_bar_i            ei                 Pr()        #>  Min.   :13.85   Min.   :   0.0298   Min.   :0.0190   #>  1st Qu.:24.71   1st Qu.:   7.0114   1st Qu.:0.2050   #>  Median :35.90   Median :  52.1094   Median :0.5264   #>  Mean   :34.88   Mean   : 151.9232   Mean   :0.4507   #>  3rd Qu.:45.39   3rd Qu.: 105.0551   3rd Qu.:0.6529   #>  Max.   :54.91   Max.   :2455.2201   Max.   :0.9540       plot(resLOSH_mc[,\"Pr()\"], resLOSH_cs[,\"Pr()\"])"},{"path":"https://r-spatial.github.io/spdep/reference/SD.RStests.html","id":null,"dir":"Reference","previous_headings":"","what":"Rao's score and adjusted Rao's score tests of linear hypotheses for spatial Durbin and spatial Durbin error models — SD.RStests","title":"Rao's score and adjusted Rao's score tests of linear hypotheses for spatial Durbin and spatial Durbin error models — SD.RStests","text":"Rao's score adjusted Rao's score tests linear hypotheses applied fitted linear model examine whether either spatially lagged dependent variable lag spatially lagged independent variable(s) WX included model, (SDM). Adjusted tests provided lag WX adapting presence , joint test . joint test equal unadjusted one plus adjusted . addition, draft tests added Koley (2024, section 6) spatial Durbin error models examine whether either spatially lagged error err spatially lagged independent variable(s) WX included model, (SDEM); orthogonality, adjusted tests required.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/SD.RStests.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Rao's score and adjusted Rao's score tests of linear hypotheses for spatial Durbin and spatial Durbin error models — SD.RStests","text":"","code":"SD.RStests(model, listw, zero.policy = attr(listw, \"zero.policy\"), test = \"SDM\",  Durbin = TRUE)"},{"path":"https://r-spatial.github.io/spdep/reference/SD.RStests.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Rao's score and adjusted Rao's score tests of linear hypotheses for spatial Durbin and spatial Durbin error models — SD.RStests","text":"model object class lm returned lm listw listw object created example nb2listw, expected row-standardised (W-style) zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA test test=“SDM” computes SDM tests, character vector tests requested chosen SDM_RSlag, SDM_adjRSlag, SDM_RSWX, SDM_adjRSWX, SDM_Joint, test=“SDEM” computes SDEM tests, character vector tests requested chosen SDEM_RSerr, SDEM_RSWX, SDEM_Joint; test=“” computes tests Durbin default TRUE Durbin models including WX; TRUE, full spatial Durbin model; formula object, subset explanatory variables lag","code":""},{"path":"https://r-spatial.github.io/spdep/reference/SD.RStests.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Rao's score and adjusted Rao's score tests of linear hypotheses for spatial Durbin and spatial Durbin error models — SD.RStests","text":"list class LMtestlist htest objects, : statistic value Lagrange Multiplier test. parameter number degrees freedom p.value p-value test. method character string giving method used. data.name character string giving name(s) data.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/SD.RStests.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Rao's score and adjusted Rao's score tests of linear hypotheses for spatial Durbin and spatial Durbin error models — SD.RStests","text":"Malabika Koley Anil K. Bera (2024) use, use spatial Durbin model? – question, Spatial Economic Analysis, 19:1, 30-56, doi:10.1080/17421772.2023.2256810 ; Malabika Koley (2024) Specification Testing General Nesting Spatial Model (Appendix C), https://sites.google.com/view/malabikakoley/research.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/SD.RStests.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Rao's score and adjusted Rao's score tests of linear hypotheses for spatial Durbin and spatial Durbin error models — SD.RStests","text":"Roger Bivand Roger.Bivand@nhh., Malabika Koley Anil K. Bera","code":""},{"path":"https://r-spatial.github.io/spdep/reference/SD.RStests.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Rao's score and adjusted Rao's score tests of linear hypotheses for spatial Durbin and spatial Durbin error models — SD.RStests","text":"results example agree Table 3, p. 22 Koley Bera (2024).","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/SD.RStests.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Rao's score and adjusted Rao's score tests of linear hypotheses for spatial Durbin and spatial Durbin error models — SD.RStests","text":"","code":"columbus <- sf::st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1]) #> Reading layer `columbus' from data source  #>   `/home/rsb/lib/r_libs/spData/shapes/columbus.gpkg' using driver `GPKG' #> Simple feature collection with 49 features and 20 fields #> Geometry type: POLYGON #> Dimension:     XY #> Bounding box:  xmin: 5.874907 ymin: 10.78863 xmax: 11.28742 ymax: 14.74245 #> Projected CRS: Undefined Cartesian SRS with unknown unit col.gal.nb <- read.gal(system.file(\"weights/columbus.gal\", package=\"spData\")[1]) col.listw <- nb2listw(col.gal.nb, style=\"W\") lm_obj <- lm(CRIME ~ INC + HOVAL, data=columbus) summary(lm.RStests(lm_obj, col.listw, test=\"all\")) #> \tRao's score (a.k.a Lagrange multiplier) diagnostics for spatial #> \tdependence #> data:   #> model: lm(formula = CRIME ~ INC + HOVAL, data = columbus) #> test weights: col.listw #>   #>          statistic parameter  p.value    #> RSerr     4.611126         1 0.031765 *  #> RSlag     7.855675         1 0.005066 ** #> adjRSerr  0.033514         1 0.854744    #> adjRSlag  3.278064         1 0.070212 .  #> SARMA     7.889190         2 0.019359 *  #> --- #> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 res <- SD.RStests(lm_obj, col.listw, test=\"SDM\") summary(res) #> \tRao's score test spatial Durbin diagnostics #> data:   #> model: lm(formula = CRIME ~ INC + HOVAL, data = columbus) #> weights: col.listw #>   #>              statistic parameter  p.value    #> SDM_RSlag       7.8557         1 0.005066 ** #> SDM_adjRSlag    4.6111         1 0.031765 *  #> SDM_RSWX        6.1376         2 0.046477 *  #> SDM_adjRSWX     2.8931         2 0.235386    #> SDM_Joint      10.7487         3 0.013165 *  #> --- #> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 all.equal(unname(res$SDM_Joint$statistic),  unname(res$SDM_RSlag$statistic + res$SDM_adjRSWX$statistic)) #> [1] TRUE all.equal(unname(res$SDM_Joint$statistic),  unname(res$SDM_adjRSlag$statistic + res$SDM_RSWX$statistic)) #> [1] TRUE res <- SD.RStests(lm_obj, col.listw, test=\"SDEM\") summary(res) #> \tRao's score test spatial Durbin diagnostics #> data:   #> model: lm(formula = CRIME ~ INC + HOVAL, data = columbus) #> weights: col.listw #>   #>            statistic parameter p.value   #> SDEM_RSerr    4.6111         1 0.03177 * #> SDEM_RSWX     6.1376         2 0.04648 * #> SDEM_Joint   10.7487         3 0.01317 * #> --- #> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 all.equal(unname(res$SDEM_Joint$statistic),  unname(res$SDEM_RSerr$statistic + res$SDEM_RSWX$statistic)) #> [1] TRUE summary(SD.RStests(lm_obj, nb2listw(col.gal.nb, style=\"C\"), test=\"all\")) #> Warning: Spatial weights matrix not row standardized #> \tRao's score test spatial Durbin diagnostics #> data:   #> model: lm(formula = CRIME ~ INC + HOVAL, data = columbus) #> weights: nb2listw(col.gal.nb, style = \"C\") #>   #>              statistic parameter  p.value    #> SDM_RSlag      10.6095         1 0.001125 ** #> SDM_adjRSlag    4.8428         1 0.027762 *  #> SDM_RSWX        9.2305         3 0.026378 *  #> SDM_adjRSWX     3.4637         3 0.325498    #> SDM_Joint      14.0733         4 0.007065 ** #> SDEM_RSerr      4.8428         1 0.027762 *  #> SDEM_RSWX       9.2305         3 0.026378 *  #> SDEM_Joint     14.0733         4 0.007065 ** #> --- #> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 summary(SD.RStests(lm_obj, col.listw, test=\"all\", Durbin= ~ INC)) #> \tRao's score test spatial Durbin diagnostics #> data:   #> model: lm(formula = CRIME ~ INC + HOVAL, data = columbus) #> weights: col.listw #> Durbin: ~ INC #>   #>              statistic parameter  p.value    #> SDM_RSlag      7.85568         1 0.005066 ** #> SDM_adjRSlag   3.16076         1 0.075428 .  #> SDM_RSWX       4.92399         1 0.026486 *  #> SDM_adjRSWX    0.22908         1 0.632210    #> SDM_Joint      8.08475         2 0.017556 *  #> SDEM_RSerr     4.61113         1 0.031765 *  #> SDEM_RSWX      4.92399         1 0.026486 *  #> SDEM_Joint     9.53512         2 0.008501 ** #> --- #> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 lm_obj0 <- lm(I(scale(CRIME)) ~ 0 + I(scale(INC)) + I(scale(HOVAL)),  data=columbus) summary(SD.RStests(lm_obj0, col.listw, test=\"all\")) #> \tRao's score test spatial Durbin diagnostics #> data:   #> model: lm(formula = I(scale(CRIME)) ~ 0 + I(scale(INC)) + #> I(scale(HOVAL)), data = columbus) #> weights: col.listw #>   #>              statistic parameter  p.value    #> SDM_RSlag       7.8250         1 0.005153 ** #> SDM_adjRSlag    4.6111         1 0.031765 *  #> SDM_RSWX        6.0609         2 0.048295 *  #> SDM_adjRSWX     2.8470         2 0.240873    #> SDM_Joint      10.6720         3 0.013638 *  #> SDEM_RSerr      4.6111         1 0.031765 *  #> SDEM_RSWX       6.0609         2 0.048295 *  #> SDEM_Joint     10.6720         3 0.013638 *  #> --- #> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 columbusNA <- columbus columbusNA$HOVAL[15] <- NA lm_objNA <- lm(CRIME ~ INC + HOVAL, data=columbusNA) summary(SD.RStests(lm_objNA, col.listw, test=\"all\")) #> \tRao's score test spatial Durbin diagnostics #> data:   #> model: lm(formula = CRIME ~ INC + HOVAL, data = columbusNA) #> weights: col.listw #>   #>              statistic parameter  p.value    #> SDM_RSlag       7.6010         1 0.005834 ** #> SDM_adjRSlag    4.4716         1 0.034463 *  #> SDM_RSWX        6.0812         2 0.047807 *  #> SDM_adjRSWX     2.9518         2 0.228576    #> SDM_Joint      10.5527         3 0.014407 *  #> SDEM_RSerr      4.4716         1 0.034463 *  #> SDEM_RSWX       6.0812         2 0.047807 *  #> SDEM_Joint     10.5527         3 0.014407 *  #> --- #> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1"},{"path":"https://r-spatial.github.io/spdep/reference/aggregate.nb.html","id":null,"dir":"Reference","previous_headings":"","what":"Aggregate a spatial neighbours object — aggregate.nb","title":"Aggregate a spatial neighbours object — aggregate.nb","text":"method aggregates spatial neighbours object, creating new object listing neighbours aggregates.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/aggregate.nb.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Aggregate a spatial neighbours object — aggregate.nb","text":"","code":"# S3 method for class 'nb' aggregate(x, IDs, remove.self = TRUE, ...)"},{"path":"https://r-spatial.github.io/spdep/reference/aggregate.nb.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Aggregate a spatial neighbours object — aggregate.nb","text":"x nb neighbour object IDs character vector IDs grouping members neighbour object remove.self default TRUE: remove self-neighbours resulting aggregation ... unused - arguments passed ","code":""},{"path":"https://r-spatial.github.io/spdep/reference/aggregate.nb.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Aggregate a spatial neighbours object — aggregate.nb","text":"nb neighbour object, empty aggregates dropped.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/aggregate.nb.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Aggregate a spatial neighbours object — aggregate.nb","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/aggregate.nb.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Aggregate a spatial neighbours object — aggregate.nb","text":"Method suggested Roberto Patuelli","code":""},{"path":"https://r-spatial.github.io/spdep/reference/aggregate.nb.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Aggregate a spatial neighbours object — aggregate.nb","text":"","code":"data(used.cars, package=\"spData\") data(state) cont_st <- match(attr(usa48.nb, \"region.id\"), state.abb) cents <- as.matrix(as.data.frame(state.center))[cont_st,] opar <- par(mfrow=c(2,1)) plot(usa48.nb, cents, xlim=c(-125, -65), ylim=c(25, 50)) IDs <- as.character(state.division[cont_st]) agg_cents <- aggregate(cents, list(IDs), mean) agg_nb <- aggregate(usa48.nb, IDs) plot(agg_nb, agg_cents[, 2:3], xlim=c(-125, -65), ylim=c(25, 50)) text(agg_cents[, 2:3], agg_cents[, 1], cex=0.6)  par(opar)"},{"path":"https://r-spatial.github.io/spdep/reference/airdist.html","id":null,"dir":"Reference","previous_headings":"","what":"Measure distance from plot — airdist","title":"Measure distance from plot — airdist","text":"Measure distance two points plot using locator; function checks par(\"plt\") par(\"usr\") try ensure aspect ratio y/x 1, units measurement x y equivalent.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/airdist.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Measure distance from plot — airdist","text":"","code":"airdist(ann=FALSE)"},{"path":"https://r-spatial.github.io/spdep/reference/airdist.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Measure distance from plot — airdist","text":"ann annotate plot line measured distance","code":""},{"path":"https://r-spatial.github.io/spdep/reference/airdist.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Measure distance from plot — airdist","text":"list members: dist distance measured coords coordinates distance measured","code":""},{"path":"https://r-spatial.github.io/spdep/reference/airdist.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Measure distance from plot — airdist","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/autocov_dist.html","id":null,"dir":"Reference","previous_headings":"","what":"Distance-weighted autocovariate — autocov_dist","title":"Distance-weighted autocovariate — autocov_dist","text":"Calculates autocovariate used autonormal, autopoisson autologistic regression. Three distance-weighting schemes available.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/autocov_dist.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Distance-weighted autocovariate — autocov_dist","text":"","code":"autocov_dist(z, xy, nbs = 1, type = \"inverse\", zero.policy = NULL,  style = \"B\", longlat=NULL)"},{"path":"https://r-spatial.github.io/spdep/reference/autocov_dist.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Distance-weighted autocovariate — autocov_dist","text":"z response variable xy matrix coordinates SpatialPoints, sf sfc points object nbs neighbourhood radius; default 1 type weighting scheme: \"one\" gives equal weight data points neighbourhood; \"inverse\" (default) weights inverse distance; \"inverse.squared\" weights square \"inverse\" zero.policy default NULL, use global option value; FALSE stop error empty neighbour sets, TRUE permit weights list formed zero-length weights vectors style default “B” (changed “W” 2015-01-27); style can take values “W”, “B”, “C”, “U”, “S” longlat TRUE point coordinates longitude-latitude decimal, case distances measured kilometers; xy SpatialPoints object, value taken object ","code":""},{"path":"https://r-spatial.github.io/spdep/reference/autocov_dist.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Distance-weighted autocovariate — autocov_dist","text":"numeric vector autocovariate values","code":""},{"path":"https://r-spatial.github.io/spdep/reference/autocov_dist.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Distance-weighted autocovariate — autocov_dist","text":"validity approach strongly hinges correct choice neighbourhood scheme! Using style=\"B\" ensures symmetry neighbourhood matrix (.e. \\(w_{nm} = w_{mn}\\)). Please see Bardos et al. (2015) details.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/autocov_dist.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Distance-weighted autocovariate — autocov_dist","text":"Augustin N.H., Mugglestone M.. Buckland S.T. (1996) autologistic model spatial distribution wildlife. Journal Applied Ecology, 33, 339-347; Gumpertz M.L., Graham J.M. Ristaino J.B. (1997) Autologistic model spatial pattern Phytophthora epidemic bell pepper: effects soil variables disease presence. Journal Agricultural, Biological Environmental Statistics, 2, 131-156; Bardos, D.C., Guillera-Arroita, G. Wintle, B.. (2015) Valid auto-models spatially autocorrelated occupancy abundance data. arXiv, 1501.06529.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/autocov_dist.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Distance-weighted autocovariate — autocov_dist","text":"Carsten F. Dormann Roger Bivand","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/autocov_dist.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Distance-weighted autocovariate — autocov_dist","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) #xy <- cbind(columbus$X, columbus$Y) xy <- st_coordinates(st_centroid(st_geometry(columbus),  of_largest_polygon=TRUE)) ac1a <- autocov_dist(columbus$CRIME, xy, nbs=10, style=\"B\",  type=\"one\") acinva <- autocov_dist(columbus$CRIME, xy, nbs=10, style=\"B\",  type=\"inverse\") acinv2a <- autocov_dist(columbus$CRIME, xy, nbs=10, style=\"B\",  type=\"inverse.squared\") plot(ac1a ~ columbus$CRIME, pch=16, ylim=c(0,9000)) points(acinva ~ columbus$CRIME, pch=16, col=\"red\") points(acinv2a ~ columbus$CRIME, pch=16, col=\"blue\") legend(\"topleft\", legend=c(\"one\", \"inverse\", \"inverse.squared\"),  col=c(\"black\", \"red\", \"blue\"), bty=\"n\", pch=16)  nb <- dnearneigh(xy, 0, 10) lw <- nb2listw(nb, style=\"B\") ac1b <- lag(lw, columbus$CRIME) all.equal(ac1b, ac1a) #> [1] TRUE nbd <- nbdists(nb, xy) gl <- lapply(nbd, function(x) 1/x) lw <- nb2listw(nb, glist=gl, style=\"B\") acinvb <- lag(lw, columbus$CRIME) all.equal(acinvb, acinva) #> [1] TRUE gl2 <- lapply(nbd, function(x) 1/(x^2)) lw <- nb2listw(nb, glist=gl2, style=\"B\") acinv2b <- lag(lw, columbus$CRIME) all.equal(acinv2b, acinv2a) #> [1] TRUE #xy <- SpatialPoints(xy) #acinva <- autocov_dist(columbus$CRIME, xy, nbs=10, style=\"W\", # type=\"inverse\") #nb <- dnearneigh(xy, 0, 10) #nbd <- nbdists(nb, xy) #gl <- lapply(nbd, function(x) 1/x) #lw <- nb2listw(nb, glist=gl) #acinvb <- lag(lw, columbus$CRIME) #all.equal(acinvb, acinva) acinvc <- autocov_dist(columbus$CRIME, st_centroid(st_geometry(columbus),  of_largest_polygon=TRUE), nbs=10, style=\"W\", type=\"inverse\") all.equal(acinvc, acinva) #> [1] \"Mean relative difference: 40.63575\""},{"path":"https://r-spatial.github.io/spdep/reference/bhicv.html","id":null,"dir":"Reference","previous_headings":"","what":"Data set with 4 life condition indices of Belo Horizonte region — bhicv","title":"Data set with 4 life condition indices of Belo Horizonte region — bhicv","text":"data collected inthe  Atlas condition indices published   Joao Pinheiro Foundation UNDP.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/bhicv.html","id":"format","dir":"Reference","previous_headings":"","what":"Format","title":"Data set with 4 life condition indices of Belo Horizonte region — bhicv","text":"shape polygon object seven variables: id identificator Name Name city Population population city HLCI Health Life Condition Index ELCI Education Life Condition Index CLCI Children Life Condition Index ELCI Economic Life Condition Index","code":""},{"path":"https://r-spatial.github.io/spdep/reference/bhicv.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Data set with 4 life condition indices of Belo Horizonte region — bhicv","text":"","code":"(GDAL37 <- as.numeric_version(unname(sf_extSoftVersion()[\"GDAL\"])) >= \"3.7.0\") #> [1] TRUE file <- \"etc/shapes/bhicv.gpkg.zip\" zipfile <- system.file(file, package=\"spdep\") if (GDAL37) {     bh <- st_read(zipfile) } else {     td <- tempdir()     bn <- sub(\".zip\", \"\", basename(file), fixed=TRUE)     target <- unzip(zipfile, files=bn, exdir=td)     bh <- st_read(target) } #> Reading layer `bhicv' from data source  #>   `/tmp/RtmpXVTJuL/temp_libpath3b356d487bad39/spdep/etc/shapes/bhicv.gpkg.zip'  #>   using driver `GPKG' #> Simple feature collection with 98 features and 8 fields #> Geometry type: POLYGON #> Dimension:     XY #> Bounding box:  xmin: -45.02175 ymin: -20.93007 xmax: -42.50321 ymax: -18.08342 #> Geodetic CRS:  Corrego Alegre 1970-72"},{"path":"https://r-spatial.github.io/spdep/reference/card.html","id":null,"dir":"Reference","previous_headings":"","what":"Cardinalities for neighbours lists — card","title":"Cardinalities for neighbours lists — card","text":"function tallies numbers neighbours regions neighbours list.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/card.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Cardinalities for neighbours lists — card","text":"","code":"card(nb)"},{"path":"https://r-spatial.github.io/spdep/reference/card.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Cardinalities for neighbours lists — card","text":"nb neighbours list object class nb","code":""},{"path":"https://r-spatial.github.io/spdep/reference/card.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Cardinalities for neighbours lists — card","text":"integer vector numbers neighbours regions neighbours list.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/card.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Cardinalities for neighbours lists — card","text":"“nb” objects stored lists integer vectors, vectors contain either indices range 1:n n length(nb) neighbours region , .integer(0) signal neighbours. function card(nb) used extract numbers neighbours “nb” object.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/card.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Cardinalities for neighbours lists — card","text":"Bivand R, Pebesma EJ, Gomez-Rubio V, (2008) Applied Spatial Data Analysis R, Springer, New York, pp. 239-251; Bivand R, Portnov B, (2004) Exploring spatial data analysis techniques using R: case observations neighbours. : Anselin L, Florax R, Rey S, (eds.), Advances Spatial Econometrics, Methodology, Tools Applications. Berlin: Springer-Verlag, pp. 121-142, doi:10.1007/978-3-662-05617-2_6 .","code":""},{"path":"https://r-spatial.github.io/spdep/reference/card.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Cardinalities for neighbours lists — card","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/card.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Cardinalities for neighbours lists — card","text":"","code":"col.gal.nb <- read.gal(system.file(\"weights/columbus.gal\", package=\"spData\")[1]) table(card(col.gal.nb)) #>  #>  2  3  4  5  6  7  8  9 10  #>  7  7 13  4  9  6  1  1  1"},{"path":"https://r-spatial.github.io/spdep/reference/cell2nb.html","id":null,"dir":"Reference","previous_headings":"","what":"Generate neighbours list for grid cells — cell2nb","title":"Generate neighbours list for grid cells — cell2nb","text":"function generates list neighbours grid cells. Helper functions used convert vector indices row column grid positions, rook (shared edge) queen (shared edge vertex) neighbour definitions applied type. torus TRUE, grid mapped onto torus, removing edge effects.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/cell2nb.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Generate neighbours list for grid cells — cell2nb","text":"","code":"cell2nb(nrow, ncol, type=\"rook\", torus=FALSE, legacy=FALSE, x=NULL) vi2mrc(i, nrow, ncol)"},{"path":"https://r-spatial.github.io/spdep/reference/cell2nb.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Generate neighbours list for grid cells — cell2nb","text":"nrow number rows grid, may also object inheriting class \"SpatialGrid\" \"GridTopology\" cell2nb ncol number columns grid; nrow x object inheriting class \"SpatialGrid\" \"GridTopology\", may omitted type default rook, may also queen torus default FALSE, TRUE map grid onto torus legacy default FALSE, nrow/ncol reversed, TRUE wrong col/row directions (see https://github.com/r-spatial/spdep/issues/20) x given, object inheriting class \"SpatialGrid\" \"GridTopology\", replaces nrow ncol vector vector indices corresponding rowcol, matrix two columns row, column indices","code":""},{"path":"https://r-spatial.github.io/spdep/reference/cell2nb.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Generate neighbours list for grid cells — cell2nb","text":"function returns object class nb list integer vectors containing neighbour region number ids. See card details “nb” objects.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/cell2nb.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Generate neighbours list for grid cells — cell2nb","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/cell2nb.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Generate neighbours list for grid cells — cell2nb","text":"","code":"nb7rt <- cell2nb(7, 7) summary(nb7rt) #> Neighbour list object: #> Number of regions: 49  #> Number of nonzero links: 168  #> Percentage nonzero weights: 6.997085  #> Average number of links: 3.428571  #> Link number distribution: #>  #>  2  3  4  #>  4 20 25  #> 4 least connected regions: #> 1:1 7:1 1:7 7:7 with 2 links #> 25 most connected regions: #> 2:2 3:2 4:2 5:2 6:2 2:3 3:3 4:3 5:3 6:3 2:4 3:4 4:4 5:4 6:4 2:5 3:5 4:5 5:5 6:5 2:6 3:6 4:6 5:6 6:6 with 4 links xyc <- attr(nb7rt, \"region.id\") xy <- matrix(as.integer(unlist(strsplit(xyc, \":\"))), ncol=2, byrow=TRUE) plot(nb7rt, xy)  nb7rt <- cell2nb(7, 7, torus=TRUE) summary(nb7rt) #> Neighbour list object: #> Number of regions: 49  #> Number of nonzero links: 196  #> Percentage nonzero weights: 8.163265  #> Average number of links: 4  #> Link number distribution: #>  #>  4  #> 49  #> 49 least connected regions: #> 1:1 2:1 3:1 4:1 5:1 6:1 7:1 1:2 2:2 3:2 4:2 5:2 6:2 7:2 1:3 2:3 3:3 4:3 5:3 6:3 7:3 1:4 2:4 3:4 4:4 5:4 6:4 7:4 1:5 2:5 3:5 4:5 5:5 6:5 7:5 1:6 2:6 3:6 4:6 5:6 6:6 7:6 1:7 2:7 3:7 4:7 5:7 6:7 7:7 with 4 links #> 49 most connected regions: #> 1:1 2:1 3:1 4:1 5:1 6:1 7:1 1:2 2:2 3:2 4:2 5:2 6:2 7:2 1:3 2:3 3:3 4:3 5:3 6:3 7:3 1:4 2:4 3:4 4:4 5:4 6:4 7:4 1:5 2:5 3:5 4:5 5:5 6:5 7:5 1:6 2:6 3:6 4:6 5:6 6:6 7:6 1:7 2:7 3:7 4:7 5:7 6:7 7:7 with 4 links run <- FALSE if (require(\"sp\", quietly=TRUE)) run <- TRUE if (run) { # https://github.com/r-spatial/spdep/issues/20 GT <- GridTopology(c(1, 1), c(1, 1), c(10, 50)) SPix <- as(SpatialGrid(GT), \"SpatialPixels\") nb_rook_cont <- poly2nb(as(SPix, \"SpatialPolygons\"), queen=FALSE) nb_rook_dist <- dnearneigh(coordinates(SPix), 0, 1.01) all.equal(nb_rook_cont, nb_rook_dist, check.attributes=FALSE) ## [1] TRUE } #> [1] TRUE if (run) { t.nb <- cell2nb(GT, type='rook', legacy=TRUE) isTRUE(all.equal(nb_rook_cont, t.nb, check.attributes=FALSE)) ## [1] FALSE } #> [1] FALSE if (run) { t.nb <- cell2nb(GT, type='rook') isTRUE(all.equal(nb_rook_cont, t.nb, check.attributes=FALSE)) ## [1] TRUE } #> [1] TRUE if (run) { # https://github.com/r-spatial/spdep/issues/55 # problem reported in issue caused by rep() cycling in unexpected order GT <- GridTopology(c(1, 1), c(1, 1), c(22, 11)) SPix <- as(SpatialGrid(GT), \"SpatialPixels\") nb_rook_cont <- poly2nb(as(SPix, \"SpatialPolygons\"), queen=FALSE) nb_rook_dist <- dnearneigh(coordinates(SPix), 0, 1.01) all.equal(nb_rook_cont, nb_rook_dist, check.attributes=FALSE) } #> [1] TRUE if (run) { t.nb <- cell2nb(GT, type='rook', legacy=TRUE) isTRUE(all.equal(nb_rook_cont, t.nb, check.attributes=FALSE)) ## [1] FALSE } #> [1] FALSE if (run) { t.nb <- cell2nb(GT, type='rook', legacy=FALSE) isTRUE(all.equal(nb_rook_cont, t.nb, check.attributes=FALSE)) ## [1] TRUE } #> [1] TRUE"},{"path":"https://r-spatial.github.io/spdep/reference/choynowski.html","id":null,"dir":"Reference","previous_headings":"","what":"Choynowski probability map values — choynowski","title":"Choynowski probability map values — choynowski","text":"Calculates Choynowski probability map values.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/choynowski.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Choynowski probability map values — choynowski","text":"","code":"choynowski(n, x, row.names=NULL, tol = .Machine$double.eps^0.5, legacy=FALSE)"},{"path":"https://r-spatial.github.io/spdep/reference/choynowski.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Choynowski probability map values — choynowski","text":"n numeric vector counts cases x numeric vector populations risk row.names row names passed output data frame tol accumulate values observed counts >= expected value less tol legacy default FALSE using vectorised alternating side ppois version, true use original version written sources iterating tol","code":""},{"path":"https://r-spatial.github.io/spdep/reference/choynowski.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Choynowski probability map values — choynowski","text":"data frame columns: pmap Poisson probability map values: probablility getting “extreme” count actually observed, one-tailed less expected expected folded together type logical: TRUE observed count less expected","code":""},{"path":"https://r-spatial.github.io/spdep/reference/choynowski.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Choynowski probability map values — choynowski","text":"Choynowski, M (1959) Maps based probabilities, Journal American Statistical Association, 54, 385–388; Cressie, N, Read, TRC (1985), sudden infant deaths come clusters? Statistics Decisions, Supplement Issue 2, 333–349; Bailey T, Gatrell (1995) Interactive Spatial Data Analysis, Harlow: Longman, pp. 300–303.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/choynowski.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Choynowski probability map values — choynowski","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/choynowski.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Choynowski probability map values — choynowski","text":"","code":"auckland <- st_read(system.file(\"shapes/auckland.gpkg\", package=\"spData\")[1], quiet=TRUE) auckland.nb <- poly2nb(auckland) res <- choynowski(auckland$M77_85, 9*auckland$Und5_81) resl <- choynowski(auckland$M77_85, 9*auckland$Und5_81, legacy=TRUE) all.equal(res, resl) #> [1] TRUE rt <- sum(auckland$M77_85)/sum(9*auckland$Und5_81) ch_ppois_pmap <- numeric(length(auckland$Und5_81)) side <- c(\"greater\", \"less\") for (i in seq(along=ch_ppois_pmap)) {   ch_ppois_pmap[i] <- poisson.test(auckland$M77_85[i], r=rt,     T=(9*auckland$Und5_81[i]), alternative=side[(res$type[i]+1)])$p.value } all.equal(ch_ppois_pmap, res$pmap) #> [1] TRUE res1 <- probmap(auckland$M77_85, 9*auckland$Und5_81) table(abs(res$pmap - res1$pmap) < 0.00001, res$type) #>         #>         FALSE TRUE #>   FALSE    74    0 #>   TRUE      0   93 lt005 <- (res$pmap < 0.05) & (res$type) ge005 <- (res$pmap < 0.05) & (!res$type) cols <- rep(\"nonsig\", length(lt005)) cols[lt005] <- \"low\" cols[ge005] <- \"high\" auckland$cols <- factor(cols) plot(auckland[,\"cols\"], main=\"Probability map\")"},{"path":"https://r-spatial.github.io/spdep/reference/columbus.html","id":null,"dir":"Reference","previous_headings":"","what":"Columbus OH spatial analysis data set — columbus","title":"Columbus OH spatial analysis data set — columbus","text":"data set now part spData package","code":""},{"path":"https://r-spatial.github.io/spdep/reference/columbus.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Columbus OH spatial analysis data set — columbus","text":"","code":"data(columbus)"},{"path":"https://r-spatial.github.io/spdep/reference/columbus.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Columbus OH spatial analysis data set — columbus","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) col.gal.nb <- read.gal(system.file(\"weights/columbus.gal\", package=\"spData\")[1])"},{"path":"https://r-spatial.github.io/spdep/reference/compon.html","id":null,"dir":"Reference","previous_headings":"","what":"Depth First Search on Neighbor Lists — Graph Components","title":"Depth First Search on Neighbor Lists — Graph Components","text":"n.comp.nb() finds number disjoint connected subgraphs graph depicted nb.obj - spatial neighbours list object.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/compon.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Depth First Search on Neighbor Lists — Graph Components","text":"","code":"n.comp.nb(nb.obj)"},{"path":"https://r-spatial.github.io/spdep/reference/compon.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Depth First Search on Neighbor Lists — Graph Components","text":"nb.obj neighbours list object class nb","code":""},{"path":"https://r-spatial.github.io/spdep/reference/compon.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Depth First Search on Neighbor Lists — Graph Components","text":"attr(nb.obj, \"sym\") FALSE igraph::components available, components directed graph found simple breadth-first search; igraph::components available, object made symmetric (may time-consuming large numbers neighbours) components found depth-first search. attr(nb.obj, \"sym\") TRUE, components directed graph found depth-first search. time complexity algorithms used native code igraph::components linear sum number nodes number edges graph, see https://github.com/r-spatial/spdep/issues/160 details; dense neighbour objects large numbers edges.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/compon.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Depth First Search on Neighbor Lists — Graph Components","text":"list : nc number disjoint connected subgraphs comp.id vector indices disjoint connected subgraphs  nodes nb.obj belong ","code":""},{"path":"https://r-spatial.github.io/spdep/reference/compon.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Depth First Search on Neighbor Lists — Graph Components","text":"Nicholas Lewin-Koh nikko@hailmail.net","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/compon.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Depth First Search on Neighbor Lists — Graph Components","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) col.gal.nb <- read.gal(system.file(\"weights/columbus.gal\", package=\"spData\")[1]) coords <- st_coordinates(st_centroid(st_geometry(columbus))) plot(col.gal.nb, coords, col=\"grey\") col2 <- droplinks(col.gal.nb, 21) #> Warning: some observations have no neighbours #> Warning: neighbour object has 3 sub-graphs res <- n.comp.nb(col2) table(res$comp.id) #>  #>  1  2  3  #> 42  1  6  plot(col2, coords, add=TRUE) points(coords, col=res$comp.id, pch=16)  run <- FALSE if (require(\"igraph\", quietly=TRUE) && require(\"spatialreg\", quietly=TRUE)) run <- TRUE #>  #> Attaching package: ‘igraph’ #> The following objects are masked from ‘package:stats’: #>  #>     decompose, spectrum #> The following object is masked from ‘package:base’: #>  #>     union #>  #> Attaching package: ‘spatialreg’ #> The following objects are masked from ‘package:spdep’: #>  #>     get.ClusterOption, get.VerboseOption, get.ZeroPolicyOption, #>     get.coresOption, get.mcOption, set.ClusterOption, #>     set.VerboseOption, set.ZeroPolicyOption, set.coresOption, #>     set.mcOption if (run) { B <- as(nb2listw(col2, style=\"B\", zero.policy=TRUE), \"CsparseMatrix\") g1 <- graph_from_adjacency_matrix(B, mode=\"undirected\") c1 <- components(g1) print(c1$no == res$nc) } #> [1] TRUE if (run) { print(all.equal(c1$membership, res$comp.id)) } #> [1] \"names for target but not for current\" if (run) { print(all.equal(c1$csize, c(table(res$comp.id)), check.attributes=FALSE)) } #> [1] TRUE if (run) { W <- as(nb2listw(col2, style=\"W\", zero.policy=TRUE), \"CsparseMatrix\") g1W <- graph_from_adjacency_matrix(W, mode=\"directed\", weighted=\"W\") c1W <- components(g1W, mode=\"weak\") print(all.equal(c1W$membership, res$comp.id, check.attributes=FALSE)) } #> [1] TRUE # \\donttest{ if (run) { data(house, package=\"spData\") house <- sf::st_as_sf(house) k6 <- knn2nb(knearneigh(house, k=6)) is.symmetric.nb(k6) } #> [1] FALSE if (run) { print(k6) } #> Neighbour list object: #> Number of regions: 25357  #> Number of nonzero links: 152142  #> Percentage nonzero weights: 0.02366211  #> Average number of links: 6  #> Non-symmetric neighbours list if (run) { length(k6) + sum(card(k6)) } #> [1] 177499 if (run) { # no pre-computed graph components str(attr(k6, \"ncomp\")) } #>  NULL if (run) { # raising the subgraph compute ceiling to above |N|+|E| computes and stores the # object in the neighbour object set.SubgraphCeiling(180000L) k6 <- knn2nb(knearneigh(house, k=6)) str(attr(k6, \"ncomp\")) } #> Warning: neighbour object has 47 sub-graphs #> List of 2 #>  $ nc     : num 47 #>  $ comp.id: num [1:25357] 1 1 1 1 1 1 1 1 1 1 ... if (run) { print(k6) } #> Neighbour list object: #> Number of regions: 25357  #> Number of nonzero links: 152142  #> Percentage nonzero weights: 0.02366211  #> Average number of links: 6  #> 47 disjoint connected subgraphs #> Non-symmetric neighbours list if (run) { system.time(udir <- n.comp.nb(make.sym.nb(k6))) } #>    user  system elapsed  #>   2.112   0.000   2.121  if (run) { system.time(dir <- n.comp.nb(k6)) } #>    user  system elapsed  #>   0.729   0.002   0.735  if (run) { udir$nc } #> [1] 47 if (run) { dir$nc } #> [1] 47 if (run) { all.equal(dir, udir) } #> [1] TRUE # }"},{"path":"https://r-spatial.github.io/spdep/reference/diffnb.html","id":null,"dir":"Reference","previous_headings":"","what":"Differences between neighbours lists — diffnb","title":"Differences between neighbours lists — diffnb","text":"function finds differences lists neighbours, returning nb neighbour list found","code":""},{"path":"https://r-spatial.github.io/spdep/reference/diffnb.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Differences between neighbours lists — diffnb","text":"","code":"diffnb(x, y, verbose=NULL)"},{"path":"https://r-spatial.github.io/spdep/reference/diffnb.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Differences between neighbours lists — diffnb","text":"x object class nb y object class nb verbose default NULL, use global option value; report regions ids taken object attribute \"region.id\" differences","code":""},{"path":"https://r-spatial.github.io/spdep/reference/diffnb.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Differences between neighbours lists — diffnb","text":"neighbours list class nb","code":""},{"path":"https://r-spatial.github.io/spdep/reference/diffnb.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Differences between neighbours lists — diffnb","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/diffnb.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Differences between neighbours lists — diffnb","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) coords <- st_centroid(st_geometry(columbus), of_largest_polygon=TRUE) rn <- row.names(columbus) knn1 <- knearneigh(coords, 1) knn2 <- knearneigh(coords, 2) nb1 <- knn2nb(knn1, row.names=rn) #> Warning: neighbour object has 13 sub-graphs nb2 <- knn2nb(knn2, row.names=rn) diffs <- diffnb(nb2, nb1) #> Warning: neighbour object has 10 sub-graphs opar <- par(no.readonly=TRUE) plot(st_geometry(columbus), border=\"grey\", reset=FALSE,  main=\"Plot of first (black) and second (red)\\nnearest neighbours\") plot(nb1, coords, add=TRUE) plot(diffs, coords, add=TRUE, col=\"red\", lty=2)  par(opar)"},{"path":"https://r-spatial.github.io/spdep/reference/dnearneigh.html","id":null,"dir":"Reference","previous_headings":"","what":"Neighbourhood contiguity by distance — dnearneigh","title":"Neighbourhood contiguity by distance — dnearneigh","text":"function identifies neighbours region points Euclidean distance metric points lower (greater equal (changed version 1.1-7)) upper (less equal ) bounds, longlat = TRUE, Great Circle distance kilometers. x \"sf\" object use_s2= TRUE, spherical distances km used.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/dnearneigh.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Neighbourhood contiguity by distance — dnearneigh","text":"","code":"dnearneigh(x, d1, d2, row.names = NULL, longlat = NULL, bounds=c(\"GE\", \"LE\"),  use_kd_tree=TRUE, symtest=FALSE, use_s2=packageVersion(\"s2\") > \"1.0.7\", k=200,  dwithin=TRUE)"},{"path":"https://r-spatial.github.io/spdep/reference/dnearneigh.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Neighbourhood contiguity by distance — dnearneigh","text":"x matrix point coordinates, object inheriting SpatialPoints \"sf\" \"sfc\" object; \"sf\" \"sfc\" object geometries geographical coordinates (use_s2=FALSE, sf::st_is_longlat(x) == TRUE sf::sf_use_s2() == TRUE), s2 used find neighbours (hope) use spatial indexing https://github.com/r-spatial/s2/issues/125 opposed legacy method uses brute-force (present s2 also uses brute-force) d1 lower distance bound metric points planar coordinates, km geographical coordinates d2 upper distance boundd metric points planar coordinates, km geographical coordinates row.names character vector region ids added neighbours list attribute region.id, default seq(1, nrow(x)) longlat TRUE point coordinates geographical longitude-latitude decimal degrees, case distances measured kilometers; x SpatialPoints object, value taken object , overrides argument NULL bounds character vector length 2, default c(\"GE\", \"LE\"), (GE: greater equal , LE: less equal ) finite closed interval [d1, d2], d1 <= x <= d2. first element may also \"GT\" (GT: greater ), second \"LT\" (LT: less ) finite, open intervals excluding bounds; first bound default changed \"GT\" \"GE\" release 1.1-7. creating multiple distance bands, finite, half-open right-closed intervals may used final interval avoid overlapping bounds: \"GE\", \"LT\", [d1, d2), d1 <= x < d2 use_kd_tree default TRUE, TRUE, use dbscan frNN available (permitting 3D distances). symtest Default FALSE; release 1.1-7, TRUE - run symmetry check output object, costly large numbers points. use_s2 default=packageVersion(\"s2\") > \"1.0.7\", s2 > 1.0-7, distance bound computations use spatial indexing sf::sf_use_s2() TRUE, s2::s2_dwithin_matrix() used distances sphere \"sf\" \"sfc\" objects s2 > 1.0-7. k default 200, number closest points consider searching using  s2::s2_closest_edges() dwithin default TRUE, FALSE, use s2::s2_closest_edges(), use_s2=TRUE, sf::st_is_longlat(x) == TRUE sf::sf_use_s2() == TRUE; s2::s2_dwithin_matrix() yields lists neighbours s2::s2_closest_edges() k= set correctly.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/dnearneigh.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Neighbourhood contiguity by distance — dnearneigh","text":"function returns list integer vectors giving region id numbers neighbours satisfying distance criteria. See card details “nb” objects.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/dnearneigh.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Neighbourhood contiguity by distance — dnearneigh","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/dnearneigh.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Neighbourhood contiguity by distance — dnearneigh","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) coords <- st_centroid(st_geometry(columbus), of_largest_polygon=TRUE) rn <- row.names(columbus) k1 <- knn2nb(knearneigh(coords)) #> Warning: neighbour object has 13 sub-graphs all.linked <- max(unlist(nbdists(k1, coords))) col.nb.0.all <- dnearneigh(coords, 0, all.linked, row.names=rn) #> Warning: neighbour object has 2 sub-graphs summary(col.nb.0.all, coords) #> Neighbour list object: #> Number of regions: 49  #> Number of nonzero links: 252  #> Percentage nonzero weights: 10.49563  #> Average number of links: 5.142857  #> 2 disjoint connected subgraphs #> Link number distribution: #>  #>  1  2  3  4  5  6  7  8  9 10 11  #>  4  8  6  2  5  8  6  2  6  1  1  #> 4 least connected regions: #> 6 10 21 47 with 1 link #> 1 most connected region: #> 28 with 11 links opar <- par(no.readonly=TRUE) plot(st_geometry(columbus), border=\"grey\", reset=FALSE,  main=paste(\"Distance based neighbours 0-\",  format(all.linked), sep=\"\")) plot(col.nb.0.all, coords, add=TRUE)  par(opar) (sfc_obj <- st_centroid(st_geometry(columbus))) #> Geometry set for 49 features  #> Geometry type: POINT #> Dimension:     XY #> Bounding box:  xmin: 6.221943 ymin: 11.01003 xmax: 10.95359 ymax: 14.36908 #> Projected CRS: Undefined Cartesian SRS with unknown unit #> First 5 geometries: #> POINT (8.827218 14.36908) #> POINT (8.332658 14.03162) #> POINT (9.012265 13.81972) #> POINT (8.460801 13.71696) #> POINT (9.007982 13.29637) col.nb.0.all_sf <- dnearneigh(sfc_obj, 0, all.linked, row.names=rn) #> Warning: neighbour object has 2 sub-graphs all.equal(col.nb.0.all, col.nb.0.all_sf, check.attributes=FALSE) #> [1] TRUE data(state) us48.fipsno <- read.geoda(system.file(\"etc/weights/us48.txt\",  package=\"spdep\")[1]) if (as.numeric(paste(version$major, version$minor, sep=\"\")) < 19) {  m50.48 <- match(us48.fipsno$\"State.name\", state.name) } else {  m50.48 <- match(us48.fipsno$\"State_name\", state.name) } xy <- as.matrix(as.data.frame(state.center))[m50.48,] llk1 <- knn2nb(knearneigh(xy, k=1, longlat=FALSE)) #> Warning: neighbour object has 12 sub-graphs (all.linked <- max(unlist(nbdists(llk1, xy, longlat=FALSE)))) #> [1] 5.161223 ll.nb <- dnearneigh(xy, 0, all.linked, longlat=FALSE) #> Warning: neighbour object has 5 sub-graphs summary(ll.nb, xy, longlat=TRUE, scale=0.5) #> Neighbour list object: #> Number of regions: 48  #> Number of nonzero links: 190  #> Percentage nonzero weights: 8.246528  #> Average number of links: 3.958333  #> 5 disjoint connected subgraphs #> Link number distribution: #>  #>  1  2  3  4  5  7  8  9 10  #> 11  9  4  8  4  4  4  3  1  #> 11 least connected regions: #> 2 4 8 10 24 26 29 32 35 41 45 with 1 link #> 1 most connected region: #> 28 with 10 links gck1 <- knn2nb(knearneigh(xy, k=1, longlat=TRUE)) #> Warning: neighbour object has 11 sub-graphs (all.linked <- max(unlist(nbdists(gck1, xy, longlat=TRUE)))) #> [1] 523.5819 gc.nb <- dnearneigh(xy, 0, all.linked, longlat=TRUE) #> Warning: neighbour object has 2 sub-graphs summary(gc.nb, xy, longlat=TRUE, scale=0.5) #> Neighbour list object: #> Number of regions: 48  #> Number of nonzero links: 220  #> Percentage nonzero weights: 9.548611  #> Average number of links: 4.583333  #> 2 disjoint connected subgraphs #> Link number distribution: #>  #>  1  2  3  4  5  6  7  8  9 10  #>  5  9  6  8  5  2  3  3  5  2  #> 5 least connected regions: #> 2 4 8 41 45 with 1 link #> 2 most connected regions: #> 7 28 with 10 links plot(ll.nb, xy) plot(diffnb(ll.nb, gc.nb), xy, add=TRUE, col=\"red\", lty=2) #> Warning: neighbour object has 27 sub-graphs title(main=\"Differences Euclidean/Great Circle\")   #xy1 <- SpatialPoints((as.data.frame(state.center))[m50.48,], #  proj4string=CRS(\"+proj=longlat +ellps=GRS80\")) #gck1a <- knn2nb(knearneigh(xy1, k=1)) #(all.linked <- max(unlist(nbdists(gck1a, xy1)))) #gc.nb <- dnearneigh(xy1, 0, all.linked) #summary(gc.nb, xy1, scale=0.5)  xy1 <- st_as_sf((as.data.frame(state.center))[m50.48,], coords=1:2,   crs=st_crs(\"OGC:CRS84\")) old_use_s2 <- sf_use_s2() sf_use_s2(TRUE) gck1b <- knn2nb(knearneigh(xy1, k=1)) #> Warning: neighbour object has 11 sub-graphs system.time(o <- nbdists(gck1b, xy1)) #>    user  system elapsed  #>   0.006   0.000   0.006  (all.linked <- max(unlist(o))) #> [1] 522.4464 # use s2 brute-force dwithin_matrix approach for s2 <= 1.0.7 system.time(gc.nb.dwithin <- dnearneigh(xy1, 0, all.linked, use_s2=TRUE, dwithin=TRUE)) #> Warning: neighbour object has 3 sub-graphs #>    user  system elapsed  #>   0.014   0.000   0.013  summary(gc.nb, xy1, scale=0.5) #> Neighbour list object: #> Number of regions: 48  #> Number of nonzero links: 220  #> Percentage nonzero weights: 9.548611  #> Average number of links: 4.583333  #> 2 disjoint connected subgraphs #> Link number distribution: #>  #>  1  2  3  4  5  6  7  8  9 10  #>  5  9  6  8  5  2  3  3  5  2  #> 5 least connected regions: #> 2 4 8 41 45 with 1 link #> 2 most connected regions: #> 7 28 with 10 links # use s2 closest_edges approach s2 > 1.0.7 if (packageVersion(\"s2\") > \"1.0.7\") { (system.time(gc.nb.closest <- dnearneigh(xy1, 0, all.linked, dwithin=FALSE))) } #> Warning: neighbour object has 3 sub-graphs #>    user  system elapsed  #>   0.011   0.000   0.011  if (packageVersion(\"s2\") > \"1.0.7\") { system.time(gc.nb.dwithin <- dnearneigh(xy1, 0, all.linked, use_s2=TRUE, dwithin=TRUE)) } #> Warning: neighbour object has 3 sub-graphs #>    user  system elapsed  #>   0.012   0.000   0.012  if (packageVersion(\"s2\") > \"1.0.7\") { summary(gc.nb.dwithin, xy1, scale=0.5) } #> Neighbour list object: #> Number of regions: 48  #> Number of nonzero links: 218  #> Percentage nonzero weights: 9.461806  #> Average number of links: 4.541667  #> 1 region with no links: #> 2 #> 3 disjoint connected subgraphs #> Link number distribution: #>  #>  0  1  2  3  4  5  6  7  8  9 10  #>  1  5  8  6  8  5  2  3  3  5  2  #> 5 least connected regions: #> 4 8 29 41 45 with 1 link #> 2 most connected regions: #> 7 28 with 10 links if (packageVersion(\"s2\") > \"1.0.7\") { summary(gc.nb.closest, xy1, scale=0.5) } #> Neighbour list object: #> Number of regions: 48  #> Number of nonzero links: 218  #> Percentage nonzero weights: 9.461806  #> Average number of links: 4.541667  #> 1 region with no links: #> 2 #> 3 disjoint connected subgraphs #> Link number distribution: #>  #>  0  1  2  3  4  5  6  7  8  9 10  #>  1  5  8  6  8  5  2  3  3  5  2  #> 5 least connected regions: #> 4 8 29 41 45 with 1 link #> 2 most connected regions: #> 7 28 with 10 links # use legacy symmetric brute-force approach system.time(gc.nb.legacy <- dnearneigh(xy1, 0, all.linked, use_s2=FALSE)) #> Warning: neighbour object has 3 sub-graphs #>    user  system elapsed  #>   0.007   0.000   0.006  summary(gc.nb, xy1, scale=0.5) #> Neighbour list object: #> Number of regions: 48  #> Number of nonzero links: 220  #> Percentage nonzero weights: 9.548611  #> Average number of links: 4.583333  #> 2 disjoint connected subgraphs #> Link number distribution: #>  #>  1  2  3  4  5  6  7  8  9 10  #>  5  9  6  8  5  2  3  3  5  2  #> 5 least connected regions: #> 2 4 8 41 45 with 1 link #> 2 most connected regions: #> 7 28 with 10 links if (packageVersion(\"s2\") > \"1.0.7\") all.equal(gc.nb.closest, gc.nb.dwithin, check.attributes=FALSE) #> [1] TRUE # legacy is ellipsoidal, s2 spherical, so minor differences expected if (packageVersion(\"s2\") > \"1.0.7\") all.equal(gc.nb, gc.nb.closest, check.attributes=FALSE) #> [1] \"Component 2: Mean relative difference: 1\"     #> [2] \"Component 29: Numeric: lengths (2, 1) differ\" all.equal(gc.nb, gc.nb.dwithin, check.attributes=FALSE) #> [1] \"Component 2: Mean relative difference: 1\"     #> [2] \"Component 29: Numeric: lengths (2, 1) differ\" sf_use_s2(old_use_s2) # example of reading points with readr::read_csv() yielding a tibble load(system.file(\"etc/misc/coords.rda\", package=\"spdep\")) class(coords) #> [1] \"spec_tbl_df\" \"tbl_df\"      \"tbl\"         \"data.frame\"  k1 <- knn2nb(knearneigh(coords, k=1)) #> Warning: neighbour object has 29 sub-graphs all.linked <- max(unlist(nbdists(k1, coords))) dnearneigh(coords, 0, all.linked) #> Neighbour list object: #> Number of regions: 100  #> Number of nonzero links: 676  #> Percentage nonzero weights: 6.76  #> Average number of links: 6.76"},{"path":"https://r-spatial.github.io/spdep/reference/droplinks.html","id":null,"dir":"Reference","previous_headings":"","what":"Drop and add links in a neighbours list — droplinks","title":"Drop and add links in a neighbours list — droplinks","text":"droplinks drops links just region neighbours list. example corresponds Fingleton's Table 1, (1999) p. 6, lattices 5 19. addlinks1 adds links single region specified regions.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/droplinks.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Drop and add links in a neighbours list — droplinks","text":"","code":"droplinks(nb, drop, sym=TRUE) addlinks1(nb, from, to, sym=TRUE)"},{"path":"https://r-spatial.github.io/spdep/reference/droplinks.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Drop and add links in a neighbours list — droplinks","text":"nb neighbours list object class nb drop either logical vector length nb, character vector named regions corresponding nb's region.id attribute, integer vector region numbers sym TRUE removal \"row\" \"column\" links, FALSE \"row\" links; adding links, inserts links region regions single region adding links, either character vector length 1 named region corresponding nb's region.id attribute, integer vector length 1 holding region number regions, either character vector named regions corresponding nb's region.id attribute, integer vector region numbers","code":""},{"path":"https://r-spatial.github.io/spdep/reference/droplinks.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Drop and add links in a neighbours list — droplinks","text":"function returns object class nb list integer vectors containing neighbour region number ids.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/droplinks.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Drop and add links in a neighbours list — droplinks","text":"B. Fingleton (1999) Spurious spatial regression: Monte Carlo results spatial unit root spatial cointegration, Journal Regional Science 39, pp. 1–19.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/droplinks.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Drop and add links in a neighbours list — droplinks","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/droplinks.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Drop and add links in a neighbours list — droplinks","text":"","code":"# \\donttest{ rho <- c(0.2, 0.5, 0.95, 0.999, 1.0) ns <- c(5, 7, 9, 11, 13, 15, 17, 19) mns <- matrix(0, nrow=length(ns), ncol=length(rho)) rownames(mns) <- ns colnames(mns) <- rho mxs <- matrix(0, nrow=length(ns), ncol=length(rho)) rownames(mxs) <- ns colnames(mxs) <- rho for (i in 1:length(ns)) {   nblist <- cell2nb(ns[i], ns[i])   nbdropped <- droplinks(nblist, ((ns[i]*ns[i])+1)/2, sym=FALSE)   listw <- nb2listw(nbdropped, style=\"W\", zero.policy=TRUE)   wmat <- listw2mat(listw)   for (j in 1:length(rho)) {     mat <- diag(ns[i]*ns[i]) - rho[j] * wmat     res <- diag(solve(t(mat) %*% mat))     mns[i,j] <- mean(res)     mxs[i,j] <- max(res)   } } #> Warning: some observations have no neighbours #> Warning: some observations have no neighbours #> Warning: some observations have no neighbours #> Warning: some observations have no neighbours #> Warning: some observations have no neighbours #> Warning: some observations have no neighbours #> Warning: some observations have no neighbours #> Warning: some observations have no neighbours print(mns) #>         0.2      0.5      0.95     0.999          1 #> 5  1.038271 1.312627  9.486051  30.81487   32.04915 #> 7  1.036443 1.295621 10.899580  83.25437   92.09812 #> 9  1.035356 1.285145 10.798611 160.90951  195.02166 #> 11 1.034639 1.278279 10.383083 254.83998  347.71145 #> 13 1.034132 1.273442  9.968389 353.66366  555.88699 #> 15 1.033753 1.269852  9.619387 447.19245  824.46560 #> 17 1.033460 1.267082  9.337167 528.49015 1157.77630 #> 19 1.033227 1.264879  9.109487 594.23907 1559.69614 print(mxs) #>         0.2      0.5     0.95     0.999          1 #> 5  1.048834 1.401934 12.00215  39.22742   40.79967 #> 7  1.048834 1.402174 14.66823 106.90031  118.01556 #> 9  1.048834 1.402176 15.49606 207.28928  249.74893 #> 11 1.048834 1.402176 15.75744 329.22973  443.97194 #> 13 1.048834 1.402176 15.83957 458.75739  707.14827 #> 15 1.048834 1.402176 15.86474 583.50722 1044.75562 #> 17 1.048834 1.402176 15.87225 695.10288 1461.57017 #> 19 1.048834 1.402176 15.87445 789.50575 1961.84025  # }"},{"path":"https://r-spatial.github.io/spdep/reference/edit.nb.html","id":null,"dir":"Reference","previous_headings":"","what":"Interactive editing of neighbours lists — edit.nb","title":"Interactive editing of neighbours lists — edit.nb","text":"function provides simple interactive editing neighbours lists allow unneeded links deleted, missing links inserted. uses identify pick endpoints link deleted added, asks confirmation committing. result assigned new object, editing lost - edit. method relies direct contact graphics device. use RStudio.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/edit.nb.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Interactive editing of neighbours lists — edit.nb","text":"","code":"# S3 method for class 'nb' edit(name, coords, polys=NULL, ..., use_region.id=FALSE)"},{"path":"https://r-spatial.github.io/spdep/reference/edit.nb.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Interactive editing of neighbours lists — edit.nb","text":"name object class nb coords matrix region point coordinates; missing polys= inherits SpatialPolygons, label points object used polys polygon boundaries supplied, used background; must inherit SpatialPolygons ... arguments passed methods use_region.id default FALSE, identify use 1-based observation numbers, otherwise use nb region.id attribute values","code":""},{"path":"https://r-spatial.github.io/spdep/reference/edit.nb.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Interactive editing of neighbours lists — edit.nb","text":"function returns object class nb edited list integer vectors containing neighbour region number ids, added attributes tallying added deleted links.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/edit.nb.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Interactive editing of neighbours lists — edit.nb","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/edit.nb.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Interactive editing of neighbours lists — edit.nb","text":"","code":"if (FALSE) { # \\dontrun{ columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) class(columbus) if (FALSE) nnb1 <- edit.nb(col.gal.nb, polys=as(columbus, \"Spatial\")) } # }"},{"path":"https://r-spatial.github.io/spdep/reference/eire.html","id":null,"dir":"Reference","previous_headings":"","what":"Eire data sets — eire","title":"Eire data sets — eire","text":"data set now part spData package","code":""},{"path":"https://r-spatial.github.io/spdep/reference/eire.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Eire data sets — eire","text":"","code":"data(eire)"},{"path":"https://r-spatial.github.io/spdep/reference/geary.html","id":null,"dir":"Reference","previous_headings":"","what":"Compute Geary's C — geary","title":"Compute Geary's C — geary","text":"simple function compute Geary's C, called geary.test geary.mc; $$C = \\frac{(n-1)}{2\\sum_{=1}^{n}\\sum_{j=1}^{n}w_{ij}} \\frac{\\sum_{=1}^{n}\\sum_{j=1}^{n}w_{ij}(x_i-x_j)^2}{\\sum_{=1}^{n}(x_i - \\bar{x})^2} $$ geary.intern internal function used vary similarity criterion.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/geary.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Compute Geary's C — geary","text":"","code":"geary(x, listw, n, n1, S0, zero.policy=attr(listw, \"zero.policy\"), scale=TRUE) <!-- %geary.intern(x, listw, n, zero.policy, type=\"geary\") -->"},{"path":"https://r-spatial.github.io/spdep/reference/geary.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Compute Geary's C — geary","text":"x numeric vector length neighbours list listw listw listw object created example nb2listw n number zones n1 n - 1 S0 global sum weights zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA  scale default TRUE, may FALSE revert changes made accommodate localC November 2021 (see #151)","code":""},{"path":"https://r-spatial.github.io/spdep/reference/geary.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Compute Geary's C — geary","text":"list C Geary's C K sample kurtosis x","code":""},{"path":"https://r-spatial.github.io/spdep/reference/geary.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Compute Geary's C — geary","text":"Cliff, . D., Ord, J. K. 1981 Spatial processes, Pion, p. 17.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/geary.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Compute Geary's C — geary","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/geary.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Compute Geary's C — geary","text":"","code":"data(oldcol) col.W <- nb2listw(COL.nb, style=\"W\") str(geary(COL.OLD$CRIME, col.W, length(COL.nb), length(COL.nb)-1,  Szero(col.W))) #> List of 2 #>  $ C: num 0.53 #>  $ K: num 2.23"},{"path":"https://r-spatial.github.io/spdep/reference/geary.mc.html","id":null,"dir":"Reference","previous_headings":"","what":"Permutation test for Geary's C statistic — geary.mc","title":"Permutation test for Geary's C statistic — geary.mc","text":"permutation test Geary's C statistic calculated using nsim random permutations x given spatial weighting scheme, establish rank observed statistic relation nsim simulated values.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/geary.mc.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Permutation test for Geary's C statistic — geary.mc","text":"","code":"geary.mc(x, listw, nsim, zero.policy=attr(listw, \"zero.policy\"), alternative=\"greater\",  spChk=NULL, adjust.n=TRUE, return_boot=FALSE, na.action=na.fail, scale=TRUE)"},{"path":"https://r-spatial.github.io/spdep/reference/geary.mc.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Permutation test for Geary's C statistic — geary.mc","text":"x numeric vector length neighbours list listw listw listw object created example nb2listw nsim number permutations zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA alternative character string specifying alternative hypothesis, must one \"greater\" (default), \"less\"; reversal corresponds geary.test described section output statistic value, based Cliff Ord 1973, p. 21 (changed 2011-04-11, thanks Daniel Garavito). spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption() adjust.n default TRUE, FALSE number observations adjusted -neighbour observations, TRUE, number observations adjusted return_boot return object class boot equivalent permutation bootstrap rather object class htest na.action function (default na.fail), can also na.omit na.exclude - cases weights list subsetted remove NAs data. may necessary set zero.policy TRUE subsetting may create -neighbour observations. Note weights lists created without using glist argument nb2listw may subsetted. na.pass permitted meaningless permutation test. scale default TRUE, may FALSE revert changes made accommodate localC November 2021 (see #151)","code":""},{"path":"https://r-spatial.github.io/spdep/reference/geary.mc.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Permutation test for Geary's C statistic — geary.mc","text":"list class htest mc.sim containing following components: statistic value observed Geary's C. parameter rank observed Geary's C. p.value pseudo p-value test. alternative character string describing alternative hypothesis. method character string giving method used. data.name character string giving name(s) data, number simulations. res nsim simulated values statistic, final value observed statistic","code":""},{"path":"https://r-spatial.github.io/spdep/reference/geary.mc.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Permutation test for Geary's C statistic — geary.mc","text":"Cliff, . D., Ord, J. K. 1981 Spatial processes, Pion, p. 63-5.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/geary.mc.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Permutation test for Geary's C statistic — geary.mc","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/geary.mc.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Permutation test for Geary's C statistic — geary.mc","text":"","code":"data(oldcol) set.seed(1) sim1 <- geary.mc(COL.OLD$CRIME, nb2listw(COL.nb, style=\"W\"),  nsim=99, alternative=\"less\") sim1 #>  #> \tMonte-Carlo simulation of Geary C #>  #> data:  COL.OLD$CRIME  #> weights: nb2listw(COL.nb, style = \"W\")   #> number of simulations + 1: 100  #>  #> statistic = 0.52987, observed rank = 1, p-value = 0.99 #> alternative hypothesis: less #>  mean(sim1$res) #> [1] 1.002705 var(sim1$res) #> [1] 0.01043616 summary(sim1$res) #>    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.  #>  0.5299  0.9362  1.0141  1.0027  1.0673  1.2459  colold.lags <- nblag(COL.nb, 3) sim2 <- geary.mc(COL.OLD$CRIME, nb2listw(colold.lags[[2]],  style=\"W\"), nsim=99) sim2 #>  #> \tMonte-Carlo simulation of Geary C #>  #> data:  COL.OLD$CRIME  #> weights: nb2listw(colold.lags[[2]], style = \"W\")   #> number of simulations + 1: 100  #>  #> statistic = 0.81129, observed rank = 1, p-value = 0.01 #> alternative hypothesis: greater #>  summary(sim2$res) #>    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.  #>  0.8113  0.9500  1.0173  1.0147  1.0731  1.1962  sim3 <- geary.mc(COL.OLD$CRIME, nb2listw(colold.lags[[3]],  style=\"W\"), nsim=99) sim3 #>  #> \tMonte-Carlo simulation of Geary C #>  #> data:  COL.OLD$CRIME  #> weights: nb2listw(colold.lags[[3]], style = \"W\")   #> number of simulations + 1: 100  #>  #> statistic = 1.1303, observed rank = 89, p-value = 0.89 #> alternative hypothesis: greater #>  summary(sim3$res) #>    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.  #>  0.7903  0.9609  0.9989  1.0148  1.0656  1.2726  crime <- COL.OLD$CRIME is.na(crime) <- sample(1:length(crime), 10) try(geary.mc(crime, nb2listw(COL.nb, style=\"W\"), nsim=99,  na.action=na.fail)) #> Error in na.fail.default(x) : missing values in object geary.mc(crime, nb2listw(COL.nb, style=\"W\"), nsim=99, zero.policy=TRUE,  na.action=na.omit) #> Warning: subsetting caused increase in subgraph count #>  #> \tMonte-Carlo simulation of Geary C #>  #> data:  crime  #> weights: nb2listw(COL.nb, style = \"W\")  #> omitted: 14, 16, 17, 21, 24, 31, 32, 42, 44, 47  #> number of simulations + 1: 100  #>  #> statistic = 0.49368, observed rank = 1, p-value = 0.01 #> alternative hypothesis: greater #>  geary.mc(crime, nb2listw(COL.nb, style=\"W\"), nsim=99, zero.policy=TRUE,  return_boot=TRUE, na.action=na.omit) #> Warning: subsetting caused increase in subgraph count #> NA observations omitted: 14, 16, 17, 21, 24, 31, 32, 42, 44, 47 #>  #> DATA PERMUTATION #>  #>  #> Call: #> boot(data = x, statistic = geary_boot, R = nsim, sim = \"permutation\",  #>     listw = listw, n = n, n1 = wc$n1, S0 = wc$S0, zero.policy = zero.policy,  #>     scale = scale, parallel = parallel, ncpus = ncpus, cl = cl) #>  #>  #> Bootstrap Statistics : #>      original    bias    std. error #> t1* 0.4936767 0.4891213   0.1517218 geary.mc(crime, nb2listw(COL.nb, style=\"W\"), nsim=99, zero.policy=TRUE,  na.action=na.exclude) #> Warning: subsetting caused increase in subgraph count #>  #> \tMonte-Carlo simulation of Geary C #>  #> data:  crime  #> weights: nb2listw(COL.nb, style = \"W\")  #> omitted: 14, 16, 17, 21, 24, 31, 32, 42, 44, 47  #> number of simulations + 1: 100  #>  #> statistic = 0.49368, observed rank = 1, p-value = 0.01 #> alternative hypothesis: greater #>  geary.mc(crime, nb2listw(COL.nb, style=\"W\"), nsim=99, zero.policy=TRUE,  return_boot=TRUE, na.action=na.exclude) #> Warning: subsetting caused increase in subgraph count #> NA observations omitted: 14, 16, 17, 21, 24, 31, 32, 42, 44, 47 #>  #> DATA PERMUTATION #>  #>  #> Call: #> boot(data = x, statistic = geary_boot, R = nsim, sim = \"permutation\",  #>     listw = listw, n = n, n1 = wc$n1, S0 = wc$S0, zero.policy = zero.policy,  #>     scale = scale, parallel = parallel, ncpus = ncpus, cl = cl) #>  #>  #> Bootstrap Statistics : #>      original    bias    std. error #> t1* 0.4936767 0.4570379   0.1307276 try(geary.mc(crime, nb2listw(COL.nb, style=\"W\"), nsim=99, na.action=na.pass)) #> Error in geary.mc(crime, nb2listw(COL.nb, style = \"W\"), nsim = 99, na.action = na.pass) :  #>   na.pass not permitted"},{"path":"https://r-spatial.github.io/spdep/reference/geary.test.html","id":null,"dir":"Reference","previous_headings":"","what":"Geary's C test for spatial autocorrelation — geary.test","title":"Geary's C test for spatial autocorrelation — geary.test","text":"Geary's test spatial autocorrelation using spatial weights matrix weights list form. assumptions underlying test sensitive form graph neighbour relationships factors, results may checked geary.mc permutations.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/geary.test.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Geary's C test for spatial autocorrelation — geary.test","text":"","code":"geary.test(x, listw, randomisation=TRUE, zero.policy=attr(listw, \"zero.policy\"),     alternative=\"greater\", spChk=NULL, adjust.n=TRUE, na.action=na.fail,     scale=TRUE)"},{"path":"https://r-spatial.github.io/spdep/reference/geary.test.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Geary's C test for spatial autocorrelation — geary.test","text":"x numeric vector length neighbours list listw listw listw object created example nb2listw randomisation variance calculated assumption randomisation, FALSE normality zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA alternative character string specifying alternative hypothesis, must one \"greater\" (default), \"less\" \"two.sided\". spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption() adjust.n default TRUE, FALSE number observations adjusted -neighbour observations, TRUE, number observations adjusted na.action function (default na.fail), can also na.omit na.exclude - cases weights list subsetted remove NAs data. may necessary set zero.policy TRUE subsetting may create -neighbour observations. Note weights lists created without using glist argument nb2listw may subsetted. na.pass permitted. scale default TRUE, may FALSE revert changes made accommodate localC November 2021 (see #151)","code":""},{"path":"https://r-spatial.github.io/spdep/reference/geary.test.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Geary's C test for spatial autocorrelation — geary.test","text":"list class htest containing following components: statistic value standard deviate Geary's C, order given Cliff Ord 1973, p. 21, (EC - C) / sqrt(VC), sign reversed respect usual (C - EC) / sqrt(VC); means “greater” alternative Geary C test corresponds “greater” alternative Moran's test. p.value p-value test. estimate value observed Geary's C, expectation  variance method assumption. alternative character string describing alternative hypothesis. method character string giving assumption used calculating  standard deviate. data.name character string giving name(s) data.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/geary.test.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Geary's C test for spatial autocorrelation — geary.test","text":"Cliff, . D., Ord, J. K. 1981 Spatial processes, Pion, p. 21, Cliff, . D., Ord, J. K. 1973 Spatial Autocorrelation, Pion, pp. 15-16, 21; Bivand RS, Wong DWS 2018 Comparing implementations global local indicators spatial association. TEST, 27(3), 716–748 doi:10.1007/s11749-018-0599-x","code":""},{"path":"https://r-spatial.github.io/spdep/reference/geary.test.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Geary's C test for spatial autocorrelation — geary.test","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/geary.test.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Geary's C test for spatial autocorrelation — geary.test","text":"derivation test (Cliff Ord, 1981, p. 18) assumes weights matrix symmetric. inherently non-symmetric matrices, k-nearest neighbour matrices, listw2U() can used make matrix symmetric. non-symmetric weights matrix cases, variance test statistic may negative (thanks Franz Munoz well documented bug report). Geary's C affected non-symmetric weights normality much Moran's . 0.4-35, sign standard deviate C changed match Cliff Ord (1973, p. 21).","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/geary.test.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Geary's C test for spatial autocorrelation — geary.test","text":"","code":"data(oldcol) geary.test(COL.OLD$CRIME, nb2listw(COL.nb, style=\"W\")) #>  #> \tGeary C test under randomisation #>  #> data:  COL.OLD$CRIME  #> weights: nb2listw(COL.nb, style = \"W\")    #>  #> Geary C statistic standard deviate = 4.7605, p-value = 9.655e-07 #> alternative hypothesis: Expectation greater than statistic #> sample estimates: #> Geary C statistic       Expectation          Variance  #>        0.52986993        1.00000000        0.00975278  #>  geary.test(COL.OLD$CRIME, nb2listw(COL.nb, style=\"W\"),  randomisation=FALSE) #>  #> \tGeary C test under normality #>  #> data:  COL.OLD$CRIME  #> weights: nb2listw(COL.nb, style = \"W\")    #>  #> Geary C statistic standard deviate = 4.6388, p-value = 1.752e-06 #> alternative hypothesis: Expectation greater than statistic #> sample estimates: #> Geary C statistic       Expectation          Variance  #>        0.52986993        1.00000000        0.01027137  #>  colold.lags <- nblag(COL.nb, 3) geary.test(COL.OLD$CRIME, nb2listw(colold.lags[[2]],  style=\"W\")) #>  #> \tGeary C test under randomisation #>  #> data:  COL.OLD$CRIME  #> weights: nb2listw(colold.lags[[2]], style = \"W\")    #>  #> Geary C statistic standard deviate = 2.2896, p-value = 0.01102 #> alternative hypothesis: Expectation greater than statistic #> sample estimates: #> Geary C statistic       Expectation          Variance  #>       0.811285136       1.000000000       0.006793327  #>  geary.test(COL.OLD$CRIME, nb2listw(colold.lags[[3]],  style=\"W\"), alternative=\"greater\") #>  #> \tGeary C test under randomisation #>  #> data:  COL.OLD$CRIME  #> weights: nb2listw(colold.lags[[3]], style = \"W\")    #>  #> Geary C statistic standard deviate = -1.5667, p-value = 0.9414 #> alternative hypothesis: Expectation greater than statistic #> sample estimates: #> Geary C statistic       Expectation          Variance  #>       1.130277918       1.000000000       0.006914551  #>  print(is.symmetric.nb(COL.nb)) #> [1] TRUE coords.OLD <- cbind(COL.OLD$X, COL.OLD$Y) COL.k4.nb <- knn2nb(knearneigh(coords.OLD, 4)) print(is.symmetric.nb(COL.k4.nb)) #> [1] FALSE geary.test(COL.OLD$CRIME, nb2listw(COL.k4.nb, style=\"W\")) #>  #> \tGeary C test under randomisation #>  #> data:  COL.OLD$CRIME  #> weights: nb2listw(COL.k4.nb, style = \"W\")    #>  #> Geary C statistic standard deviate = 6.4415, p-value = 5.916e-11 #> alternative hypothesis: Expectation greater than statistic #> sample estimates: #> Geary C statistic       Expectation          Variance  #>       0.399254423       1.000000000       0.008697812  #>  geary.test(COL.OLD$CRIME, nb2listw(COL.k4.nb, style=\"W\"),  randomisation=FALSE) #>  #> \tGeary C test under normality #>  #> data:  COL.OLD$CRIME  #> weights: nb2listw(COL.k4.nb, style = \"W\")    #>  #> Geary C statistic standard deviate = 6.2873, p-value = 1.615e-10 #> alternative hypothesis: Expectation greater than statistic #> sample estimates: #> Geary C statistic       Expectation          Variance  #>       0.399254423       1.000000000       0.009129529  #>  cat(\"Note non-symmetric weights matrix - use listw2U()\\n\") #> Note non-symmetric weights matrix - use listw2U() geary.test(COL.OLD$CRIME, listw2U(nb2listw(COL.k4.nb,  style=\"W\"))) #>  #> \tGeary C test under randomisation #>  #> data:  COL.OLD$CRIME  #> weights: listw2U(nb2listw(COL.k4.nb, style = \"W\"))    #>  #> Geary C statistic standard deviate = 6.4415, p-value = 5.916e-11 #> alternative hypothesis: Expectation greater than statistic #> sample estimates: #> Geary C statistic       Expectation          Variance  #>       0.399254423       1.000000000       0.008697812  #>  geary.test(COL.OLD$CRIME, listw2U(nb2listw(COL.k4.nb,  style=\"W\")), randomisation=FALSE) #>  #> \tGeary C test under normality #>  #> data:  COL.OLD$CRIME  #> weights: listw2U(nb2listw(COL.k4.nb, style = \"W\"))    #>  #> Geary C statistic standard deviate = 6.2873, p-value = 1.615e-10 #> alternative hypothesis: Expectation greater than statistic #> sample estimates: #> Geary C statistic       Expectation          Variance  #>       0.399254423       1.000000000       0.009129529  #>  crime <- COL.OLD$CRIME is.na(crime) <- sample(1:length(crime), 10) try(geary.test(crime, nb2listw(COL.nb, style=\"W\"), na.action=na.fail)) #> Error in na.fail.default(x) : missing values in object geary.test(crime, nb2listw(COL.nb, style=\"W\"), zero.policy=TRUE,  na.action=na.omit) #>  #> \tGeary C test under randomisation #>  #> data:  crime  #> weights: nb2listw(COL.nb, style = \"W\")  #> omitted: 3, 4, 10, 20, 21, 23, 27, 29, 31, 38   #>  #> Geary C statistic standard deviate = 4.2726, p-value = 9.661e-06 #> alternative hypothesis: Expectation greater than statistic #> sample estimates: #> Geary C statistic       Expectation          Variance  #>        0.45199742        1.00000000        0.01645071  #>  geary.test(crime, nb2listw(COL.nb, style=\"W\"), zero.policy=TRUE,  na.action=na.exclude) #>  #> \tGeary C test under randomisation #>  #> data:  crime  #> weights: nb2listw(COL.nb, style = \"W\")  #> omitted: 3, 4, 10, 20, 21, 23, 27, 29, 31, 38   #>  #> Geary C statistic standard deviate = 4.2726, p-value = 9.661e-06 #> alternative hypothesis: Expectation greater than statistic #> sample estimates: #> Geary C statistic       Expectation          Variance  #>        0.45199742        1.00000000        0.01645071  #>  try(geary.test(crime, nb2listw(COL.nb, style=\"W\"), na.action=na.pass)) #> Error in geary.test(crime, nb2listw(COL.nb, style = \"W\"), na.action = na.pass) :  #>   na.pass not permitted"},{"path":"https://r-spatial.github.io/spdep/reference/globalG.test.html","id":null,"dir":"Reference","previous_headings":"","what":"Global G test for spatial autocorrelation — globalG.test","title":"Global G test for spatial autocorrelation — globalG.test","text":"global G statistic spatial autocorrelation, complementing local Gi LISA measures: localG.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/globalG.test.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Global G test for spatial autocorrelation — globalG.test","text":"","code":"globalG.test(x, listw, zero.policy=attr(listw, \"zero.policy\"), alternative=\"greater\",  spChk=NULL, adjust.n=TRUE, B1correct=TRUE, adjust.x=TRUE, Arc_all_x=FALSE,  na.action=na.fail)"},{"path":"https://r-spatial.github.io/spdep/reference/globalG.test.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Global G test for spatial autocorrelation — globalG.test","text":"x numeric vector length neighbours list listw listw listw object created example nb2listw; sequence distance bands used, recommended weights style binary (one c(\"B\", \"C\", \"U\")). zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA alternative character string specifying alternative hypothesis, must one \"greater\" (default), \"less\" \"two.sided\". spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption() adjust.n default TRUE, FALSE number observations adjusted -neighbour observations, TRUE, number observations adjusted B1correct default TRUE, TRUE, erratum referenced : \"page 195, coefficient W2 B1, (just center page) 6,  3.\" applied; FALSE, 3 used (CrimeStat IV) adjust.x default TRUE, TRUE, x values observations neighbours omitted denominator G Arc_all_x default FALSE, Arc_all_x=TRUE adjust.x=TRUE, use full x vector part denominator term G na.action function (default na.fail), can also na.omit na.exclude - cases weights list subsetted remove NAs data. may necessary set zero.policy TRUE subsetting may create -neighbour observations. Note weights lists created without using glist argument nb2listw may subsetted. na.pass permitted.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/globalG.test.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Global G test for spatial autocorrelation — globalG.test","text":"list class htest containing following components: statistic value standard deviate Getis-Ord G. p.value p-value test. estimate value observed statistic, expectation variance. alternative character string describing alternative hypothesis. data.name character string giving name(s) data.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/globalG.test.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Global G test for spatial autocorrelation — globalG.test","text":"Getis. , Ord, J. K. 1992 analysis spatial association use distance statistics, Geographical Analysis, 24, p. 195; see also Getis. , Ord, J. K. 1993 Erratum, Geographical Analysis, 25, p. 276; Bivand RS, Wong DWS 2018 Comparing implementations global local indicators spatial association. TEST, 27(3), 716–748 doi:10.1007/s11749-018-0599-x","code":""},{"path":"https://r-spatial.github.io/spdep/reference/globalG.test.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Global G test for spatial autocorrelation — globalG.test","text":"Hisaji ONO hi-ono@mn.xdsl.ne.jp Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/globalG.test.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Global G test for spatial autocorrelation — globalG.test","text":"","code":"nc.sids <- st_read(system.file(\"shapes/sids.gpkg\", package=\"spData\")[1], quiet=TRUE) sidsrate79 <- (1000*nc.sids$SID79)/nc.sids$BIR79 dists <- c(10, 20, 30, 33, 40, 50, 60, 70, 80, 90, 100) ndists <- length(dists) ZG <- vector(mode=\"list\", length=ndists) names(ZG) <- as.character(dists) milesxy <- cbind(nc.sids$east, nc.sids$north) for (i in 1:ndists) {   thisnb <- dnearneigh(milesxy, 0, dists[i])   thislw <- nb2listw(thisnb, style=\"B\", zero.policy=TRUE)   ZG[[i]] <- globalG.test(sidsrate79, thislw, zero.policy=TRUE) } #> Warning: neighbour object has 98 sub-graphs #> Warning: neighbour object has 37 sub-graphs #> Warning: neighbour object has 3 sub-graphs t(sapply(ZG, function(x) c(x$estimate[1], x$statistic, p.value=unname(x$p.value)))) #>     Global G statistic standard deviate   p.value #> 10          0.33548581       0.04859237 0.4806221 #> 20          0.02024945      -0.73262399 0.7681061 #> 30          0.04032434      -0.75011405 0.7734070 #> 33          0.05312271       0.40157023 0.3440002 #> 40          0.07400279      -0.04345713 0.5173314 #> 50          0.11471743       0.58686472 0.2786473 #> 60          0.15457553      -0.35823892 0.6399177 #> 70          0.19839023      -0.27864299 0.6097406 #> 80          0.24606972      -0.18791364 0.5745278 #> 90          0.30073463       0.11457610 0.4543906 #> 100         0.34879996       0.31591356 0.3760341 for (i in 1:ndists) {   thisnb <- dnearneigh(milesxy, 0, dists[i])   thislw <- nb2listw(thisnb, style=\"B\", zero.policy=TRUE)   ZG[[i]] <- globalG.test(sidsrate79, thislw, zero.policy=TRUE, alternative=\"two.sided\") } #> Warning: neighbour object has 98 sub-graphs #> Warning: neighbour object has 37 sub-graphs #> Warning: neighbour object has 3 sub-graphs t(sapply(ZG, function(x) c(x$estimate[1], x$statistic, p.value=unname(x$p.value)))) #>     Global G statistic standard deviate   p.value #> 10          0.33548581       0.04859237 0.9612441 #> 20          0.02024945      -0.73262399 0.4637878 #> 30          0.04032434      -0.75011405 0.4531860 #> 33          0.05312271       0.40157023 0.6880003 #> 40          0.07400279      -0.04345713 0.9653371 #> 50          0.11471743       0.58686472 0.5572946 #> 60          0.15457553      -0.35823892 0.7201645 #> 70          0.19839023      -0.27864299 0.7805188 #> 80          0.24606972      -0.18791364 0.8509443 #> 90          0.30073463       0.11457610 0.9087811 #> 100         0.34879996       0.31591356 0.7520681 data(oldcol) crime <- COL.OLD$CRIME is.na(crime) <- sample(1:length(crime), 10) res <- try(globalG.test(crime, nb2listw(COL.nb, style=\"B\"),  na.action=na.fail)) #> Error in na.fail.default(x) : missing values in object res #> [1] \"Error in na.fail.default(x) : missing values in object\\n\" #> attr(,\"class\") #> [1] \"try-error\" #> attr(,\"condition\") #> <simpleError in na.fail.default(x): missing values in object> globalG.test(crime, nb2listw(COL.nb, style=\"B\"), zero.policy=TRUE,  na.action=na.omit) #> Warning: subsetting caused increase in subgraph count #>  #> \tGetis-Ord global G statistic #>  #> data:  crime  #> weights: nb2listw(COL.nb, style = \"B\")  #> omitted: 2, 3, 5, 6, 7, 10, 13, 30, 39, 49  #> n reduced by no-neighbour observations  #>  #> standard deviate = 3.8084, p-value = 6.993e-05 #> alternative hypothesis: greater #> sample estimates: #> Global G statistic        Expectation           Variance  #>       1.441233e-01       1.123755e-01       6.949287e-05  #>  globalG.test(crime, nb2listw(COL.nb, style=\"B\"), zero.policy=TRUE,  na.action=na.exclude) #> Warning: subsetting caused increase in subgraph count #>  #> \tGetis-Ord global G statistic #>  #> data:  crime  #> weights: nb2listw(COL.nb, style = \"B\")  #> omitted: 2, 3, 5, 6, 7, 10, 13, 30, 39, 49  #> n reduced by no-neighbour observations  #>  #> standard deviate = 3.8084, p-value = 6.993e-05 #> alternative hypothesis: greater #> sample estimates: #> Global G statistic        Expectation           Variance  #>       1.441233e-01       1.123755e-01       6.949287e-05  #>  try(globalG.test(crime, nb2listw(COL.nb, style=\"B\"), na.action=na.pass)) #> Error in globalG.test(crime, nb2listw(COL.nb, style = \"B\"), na.action = na.pass) :  #>   na.pass not permitted"},{"path":"https://r-spatial.github.io/spdep/reference/graphneigh.html","id":null,"dir":"Reference","previous_headings":"","what":"Graph based spatial weights — graphneigh","title":"Graph based spatial weights — graphneigh","text":"Functions return graph object containing list vertex coordinates indices defining edges. /functions assume coordinates exactly regularly spaced. helper function graph2nb converts graph object neighbour list. plot functions plot graph objects.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/graphneigh.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Graph based spatial weights — graphneigh","text":"","code":"gabrielneigh(coords, nnmult=3) relativeneigh(coords, nnmult=3) <!-- %beta.skel(coords,beta) --> soi.graph(tri.nb, coords, quadsegs=10) graph2nb(gob, row.names=NULL,sym=FALSE) # S3 method for class 'Gabriel' plot(x, show.points=FALSE, add=FALSE, linecol=par(col), ...) # S3 method for class 'relative' plot(x, show.points=FALSE, add=FALSE, linecol=par(col),...)"},{"path":"https://r-spatial.github.io/spdep/reference/graphneigh.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Graph based spatial weights — graphneigh","text":"coords matrix region point coordinates SpatialPoints object sfc points object nnmult scaling factor memory allocation, default 3; higher values required, function exit error; example thanks Dan Putler tri.nb neighbor list created tri2nb quadsegs number line segments making quarter circle buffer, see nQuadSegs argument geos_unary  gob graph object created graph funtions row.names character vector region ids added     neighbours list attribute region.id, default seq(1,       nrow(x)) sym logical argument indicating whether neighbors     symetric (->j j->) x object plotted show.points (logical) add points plot add (logical) add existing plot linecol edge plotting colour ... graphical parameters par(..)","code":""},{"path":"https://r-spatial.github.io/spdep/reference/graphneigh.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Graph based spatial weights — graphneigh","text":"graph functions produce graphs 2d point set    subgraphs Delaunay triangulation. relative neighbor graph defined relation, x y neighbors $$d(x,y) \\le min(max(d(x,z),d(y,z))| z \\S)$$ d() distance, S set points z arbitrary point S. Gabriel graph subgraph delaunay triangulation relative neighbor graph sub-graph. relative neighbor graph defined relation x y Gabriel neighbors $$d(x,y) \\le min((d(x,z)^2 + d(y,z)^2)^{1/2} |z \\S)$$ x,y,z S . sphere influence graph defined finite point set S, let \\(r_x\\) distance point x nearest neighbor S, \\(C_x\\) circle centered x. x y SOI neigbors iff \\(C_x\\) \\(C_y\\) intersect least 2 places. 2016-05-31, Computational Geometry C code replaced calls functions dbscan sf; large quadsegs= argument, behaviour function , otherwise buffer intersections closely approximate original function. See card details “nb” objects.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/graphneigh.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Graph based spatial weights — graphneigh","text":"list class Graph following elements np number input points array origin ids array destination ids nedges number edges graph x input x coordinates y input y coordinates helper functions return nb object list integer  vectors containing neighbour region number ids.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/graphneigh.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Graph based spatial weights — graphneigh","text":"Matula, D. W. Sokal R. R. 1980, Properties Gabriel   graphs relevant geographic variation research clustering   points plane, Geographic Analysis, 12(3), pp. 205-222. Toussaint, G. T. 1980, relative neighborhood graph finite   planar set, Pattern Recognition, 12(4), pp. 261-268. Kirkpatrick, D. G. Radke, J. D. 1985, framework   computational morphology. Computational Geometry,   Ed. G. T. Toussaint, North Holland.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/graphneigh.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Graph based spatial weights — graphneigh","text":"Nicholas Lewin-Koh nikko@hailmail.net","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/graphneigh.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Graph based spatial weights — graphneigh","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) sf_obj <- st_centroid(st_geometry(columbus), of_largest_polygon) sp_obj <- as(sf_obj, \"Spatial\") coords <- st_coordinates(sf_obj) suppressMessages(col.tri.nb <- tri2nb(coords)) col.gab.nb <- graph2nb(gabrielneigh(coords), sym=TRUE) col.rel.nb <- graph2nb(relativeneigh(coords), sym=TRUE) par(mfrow=c(2,2)) plot(st_geometry(columbus), border=\"grey\") plot(col.tri.nb,coords,add=TRUE) title(main=\"Delaunay Triangulation\", cex.main=0.6) plot(st_geometry(columbus), border=\"grey\") plot(col.gab.nb, coords, add=TRUE) title(main=\"Gabriel Graph\", cex.main=0.6) plot(st_geometry(columbus), border=\"grey\") plot(col.rel.nb, coords, add=TRUE) title(main=\"Relative Neighbor Graph\", cex.main=0.6) plot(st_geometry(columbus), border=\"grey\") if (require(\"dbscan\", quietly=TRUE)) {   col.soi.nb <- graph2nb(soi.graph(col.tri.nb,coords), sym=TRUE)   plot(col.soi.nb, coords, add=TRUE)   title(main=\"Sphere of Influence Graph\", cex.main=0.6) } #>  #> Attaching package: ‘dbscan’ #> The following object is masked from ‘package:stats’: #>  #>     as.dendrogram  par(mfrow=c(1,1)) col.tri.nb_sf <- tri2nb(sf_obj) all.equal(col.tri.nb, col.tri.nb_sf, check.attributes=FALSE) #> [1] TRUE col.tri.nb_sp <- tri2nb(sp_obj) all.equal(col.tri.nb, col.tri.nb_sp, check.attributes=FALSE) #> [1] TRUE if (require(\"dbscan\", quietly=TRUE)) {   col.soi.nb_sf <- graph2nb(soi.graph(col.tri.nb, sf_obj), sym=TRUE)   all.equal(col.soi.nb, col.soi.nb_sf, check.attributes=FALSE)   col.soi.nb_sp <- graph2nb(soi.graph(col.tri.nb, sp_obj), sym=TRUE)   all.equal(col.soi.nb, col.soi.nb_sp, check.attributes=FALSE) } #> [1] TRUE col.gab.nb_sp <- graph2nb(gabrielneigh(sp_obj), sym=TRUE) all.equal(col.gab.nb, col.gab.nb_sp, check.attributes=FALSE) #> [1] TRUE col.gab.nb_sf <- graph2nb(gabrielneigh(sf_obj), sym=TRUE) all.equal(col.gab.nb, col.gab.nb_sf, check.attributes=FALSE) #> [1] TRUE col.rel.nb_sp <- graph2nb(relativeneigh(sp_obj), sym=TRUE) all.equal(col.rel.nb, col.rel.nb_sp, check.attributes=FALSE) #> [1] TRUE col.rel.nb_sf <- graph2nb(relativeneigh(sf_obj), sym=TRUE) all.equal(col.rel.nb, col.rel.nb_sf, check.attributes=FALSE) #> [1] TRUE dx <- rep(0.25*0:4,5) dy <- c(rep(0,5),rep(0.25,5),rep(0.5,5), rep(0.75,5),rep(1,5)) m <- cbind(c(dx, dx, 3+dx, 3+dx), c(dy, 3+dy, dy, 3+dy)) cat(try(res <- gabrielneigh(m), silent=TRUE), \"\\n\") #> Error in gabrielneigh(m) : number of neighbours overrun - increase nnmult #>   res <- gabrielneigh(m, nnmult=4) summary(graph2nb(res)) #> Neighbour list object: #> Number of regions: 100  #> Number of nonzero links: 342  #> Percentage nonzero weights: 3.42  #> Average number of links: 3.42  #> 1 region with no links: #> 100 #> Non-symmetric neighbours list #> Link number distribution: #>  #>  0  1  2  3  4  5  #>  1  8 10 18 55  8  #> 8 least connected regions: #> 46 47 48 49 96 97 98 99 with 1 link #> 8 most connected regions: #> 10 15 20 25 30 35 40 45 with 5 links grd <- as.matrix(expand.grid(x=1:5, y=1:5)) #gridded data r2 <- gabrielneigh(grd) set.seed(1) grd1 <- as.matrix(expand.grid(x=1:5, y=1:5)) + matrix(runif(50, .0001, .0006), nrow=25) r3 <- gabrielneigh(grd1) opar <- par(mfrow=c(1,2)) plot(r2, show=TRUE, linecol=2) plot(r3, show=TRUE, linecol=2)  par(opar) # example of reading points with readr::read_csv() yielding a tibble load(system.file(\"etc/misc/coords.rda\", package=\"spdep\")) class(coords) #> [1] \"spec_tbl_df\" \"tbl_df\"      \"tbl\"         \"data.frame\"  graph2nb(gabrielneigh(coords)) #> Neighbour list object: #> Number of regions: 100  #> Number of nonzero links: 179  #> Percentage nonzero weights: 1.79  #> Average number of links: 1.79  #> 23 regions with no links: #> 22, 39, 43, 53, 58, 61, 66, 70, 71, 73, 76, 78, 81, 88, 90, 93, 94, 95, #> 96, 97, 98, 99, 100 #> Non-symmetric neighbours list graph2nb(relativeneigh(coords)) #> Neighbour list object: #> Number of regions: 100  #> Number of nonzero links: 117  #> Percentage nonzero weights: 1.17  #> Average number of links: 1.17  #> 31 regions with no links: #> 22, 29, 33, 39, 41, 42, 43, 44, 53, 58, 61, 64, 65, 66, 70, 71, 73, 75, #> 76, 78, 81, 88, 90, 93, 94, 95, 96, 97, 98, 99, 100 #> Non-symmetric neighbours list"},{"path":"https://r-spatial.github.io/spdep/reference/grid2nb.html","id":null,"dir":"Reference","previous_headings":"","what":"Construct neighbours for a GridTopology — grid2nb","title":"Construct neighbours for a GridTopology — grid2nb","text":"function builds neighbours list grid topology.   works k-dimentional grid topology, k>=1.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/grid2nb.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Construct neighbours for a GridTopology — grid2nb","text":"","code":"grid2nb(grid, d = grid@cells.dim,         queen = TRUE, nb = TRUE, self = FALSE)"},{"path":"https://r-spatial.github.io/spdep/reference/grid2nb.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Construct neighbours for a GridTopology — grid2nb","text":"grid object class GridTopology. One can avoid   supply just suplying dimentions d argument. d scalar (one dimentional grid) length k vector   specyfying number grid cells direction k   dimentions. queen Logical. Default TRUE. inform queen   neighbourhood structure considered. FALSE,   hyper-cube common face considered neighbour.   TRUE, single shared coordinate meets contiguity condition. nb Default TRUE. TRUE, return result neighbours   list class nb. FALSE, result matrix   3^k columns self = TRUE 3^k-1   self = FALSE. Zeros used hyper-cubes boundaries. self Default FALSE, indicate hyper-cube neighbour   considered neighbour.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/grid2nb.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Construct neighbours for a GridTopology — grid2nb","text":"Either matrix, “nb” FALSE neighbours list   class nb. See card details “nb”   objects.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/grid2nb.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Construct neighbours for a GridTopology — grid2nb","text":"applies k-dimentional grid topology.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/grid2nb.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Construct neighbours for a GridTopology — grid2nb","text":"Elias T Krainski eliaskrainski@gmail.com","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/grid2nb.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Construct neighbours for a GridTopology — grid2nb","text":"","code":"nb <- grid2nb(d = c(5L, 5L, 5L)) nb #> Neighbour list object: #> Number of regions: 125  #> Number of nonzero links: 2072  #> Percentage nonzero weights: 13.2608  #> Average number of links: 16.576  summary(nb) #> Neighbour list object: #> Number of regions: 125  #> Number of nonzero links: 2072  #> Percentage nonzero weights: 13.2608  #> Average number of links: 16.576  #> Link number distribution: #>  #>  7 11 17 26  #>  8 36 54 27  #> 8 least connected regions: #> 1 5 21 25 101 105 121 125 with 7 links #> 27 most connected regions: #> 32 33 34 37 38 39 42 43 44 57 58 59 62 63 64 67 68 69 82 83 84 87 88 89 92 93 94 with 26 links if (require(\"sp\", quietly=TRUE)) { gt <- GridTopology(c(.125,.1), c(.25,.2), c(4L, 5L)) nb1 <- grid2nb(gt, queen = FALSE) nb2 <- grid2nb(gt)  sg <- SpatialGrid(gt) plot(sg, lwd=3) plot(nb1, coordinates(sg), add=TRUE, lty=2, col=2, lwd=2) plot(nb2, coordinates(sg), add=TRUE, lty=3, col=4)  str(grid2nb(d=5)) }  #> List of 5 #>  $ : int 2 #>  $ : int [1:2] 1 3 #>  $ : int [1:2] 2 4 #>  $ : int [1:2] 3 5 #>  $ : int 4 #>  - attr(*, \"class\")= chr \"nb\""},{"path":"https://r-spatial.github.io/spdep/reference/hotspotmap.html","id":null,"dir":"Reference","previous_headings":"","what":"Cluster Classifications for Local Indicators of Spatial Association and Local Indicators for Categorical Data — hotspot","title":"Cluster Classifications for Local Indicators of Spatial Association and Local Indicators for Categorical Data — hotspot","text":"Used return factor showing -called cluster classification local indicators spatial association local Moran's , local Geary's C (multivariate variant) local Getis-Ord G. factor vector can added spatial object mapping. obj class licd, list six factors measures local composition (analytical permutation), local configuration (analytical permutation), combined measures, interaction composition configuration, simplified recoding .","code":""},{"path":"https://r-spatial.github.io/spdep/reference/hotspotmap.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Cluster Classifications for Local Indicators of Spatial Association and Local Indicators for Categorical Data — hotspot","text":"","code":"hotspot(obj, ...)  # Default S3 method hotspot(obj, ...)  # S3 method for class 'localmoran' hotspot(obj, Prname, cutoff=0.005, quadrant.type=\"mean\",  p.adjust=\"fdr\", droplevels=TRUE, ...) # S3 method for class 'summary.localmoransad' hotspot(obj, Prname, cutoff=0.005,  quadrant.type=\"mean\", p.adjust=\"fdr\", droplevels=TRUE, ...) # S3 method for class 'data.frame.localmoranex' hotspot(obj, Prname, cutoff=0.005,  quadrant.type=\"mean\", p.adjust=\"fdr\", droplevels=TRUE, ...)  # S3 method for class 'localG' hotspot(obj, Prname, cutoff=0.005, p.adjust=\"fdr\", droplevels=TRUE, ...)  # S3 method for class 'localC' hotspot(obj, Prname, cutoff=0.005, p.adjust=\"fdr\", droplevels=TRUE, ...) # S3 method for class 'licd' hotspot(obj, type = \"both\", cutoff = 0.05, p.adjust = \"none\",   droplevels = TRUE, control = list(), ...)"},{"path":"https://r-spatial.github.io/spdep/reference/hotspotmap.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Cluster Classifications for Local Indicators of Spatial Association and Local Indicators for Categorical Data — hotspot","text":"obj object class localmoran, localC localG Prname character string, name column containing probability values classified cluster type found “interesting” cutoff Default 0.005, probability value cutoff larger observation found “interesting” p.adjust Default \"fdr\", p.adjust() method used, one c(\"holm\", \"hochberg\", \"hommel\", \"bonferroni\", \"BH\", \"\", \"fdr\", \"none\") droplevels Default TRUE, empty levels input cluster factor dropped quadrant.type Default \"mean\", \"localmoran\" objects , can c(\"mean\", \"median\", \"pysal\") partition Moran scatterplot; \"mean\" partitions means variable spatial lag, \"median\" medians variable spatial lag, \"pysal\" zero centred variable spatial lag type obj class licd, default , may also comp local composition config local configuration control obj class licd, default binomial_sidak 2, binomial_overlap TRUE, jcm_sidak 3. binomial_overlap  may set FALSE avoid Binomial probability values summing unity - tests Boots (2003, p. 141) overlap (>= <=), Šidák exponents may set 1 prevent -observation correction 2 Binomial 3 Normal probability values per observation ... arguments passed methods.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/hotspotmap.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Cluster Classifications for Local Indicators of Spatial Association and Local Indicators for Categorical Data — hotspot","text":"factor showing -called cluster classification local indicators spatial association. obj class licd, list six factors measures local composition (analytical permutation), local configuration (analytical permutation), combined measures, interaction composition configuration, simplified recoding .","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/hotspotmap.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Cluster Classifications for Local Indicators of Spatial Association and Local Indicators for Categorical Data — hotspot","text":"Roger Bivand","code":""},{"path":"https://r-spatial.github.io/spdep/reference/hotspotmap.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Cluster Classifications for Local Indicators of Spatial Association and Local Indicators for Categorical Data — hotspot","text":"","code":"orig <- spData::africa.rook.nb listw <- nb2listw(orig) x <- spData::afcon$totcon  set.seed(1) C <- localC_perm(x, listw) Ch <- hotspot(C, Prname=\"Pr(z != E(Ci)) Sim\", cutoff=0.05, p.adjust=\"none\") table(addNA(Ch)) #>  #> High-High   Low-Low      <NA>  #>         4         1        37  set.seed(1) I <- localmoran_perm(x, listw) Ih <- hotspot(I, Prname=\"Pr(z != E(Ii)) Sim\", cutoff=0.05, p.adjust=\"none\") table(addNA(Ih)) #>  #> High-High      <NA>  #>         6        36  Is <- summary(localmoran.sad(lm(x ~ 1), nb=orig)) Ish <- hotspot(Is, Prname=\"Pr. (Sad)\", cutoff=0.05, p.adjust=\"none\") table(addNA(Ish)) #>  #> High-High      <NA>  #>         5        37  Ie <- as.data.frame(localmoran.exact(lm(x ~ 1), nb=orig)) Ieh <- hotspot(Ie, Prname=\"Pr. (exact)\", cutoff=0.05, p.adjust=\"none\") table(addNA(Ieh)) #>  #> High-High      <NA>  #>         5        37  set.seed(1) G <- localG_perm(x, listw) Gh <- hotspot(G, Prname=\"Pr(z != E(Gi)) Sim\", cutoff=0.05, p.adjust=\"none\") table(addNA(Gh)) #>  #> High <NA>  #>    6   36"},{"path":"https://r-spatial.github.io/spdep/reference/include.self.html","id":null,"dir":"Reference","previous_headings":"","what":"Include self in neighbours list — include.self","title":"Include self in neighbours list — include.self","text":"function includes region list neighbours, sets attribute \"self.included\" TRUE; remove.self reverts effects include.self.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/include.self.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Include self in neighbours list — include.self","text":"","code":"include.self(nb) remove.self(nb)"},{"path":"https://r-spatial.github.io/spdep/reference/include.self.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Include self in neighbours list — include.self","text":"nb input neighbours list class nb","code":""},{"path":"https://r-spatial.github.io/spdep/reference/include.self.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Include self in neighbours list — include.self","text":"function returns object class nb list integer vectors containing neighbour region number ids; attribute \"self.included\" set TRUE.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/include.self.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Include self in neighbours list — include.self","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/include.self.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Include self in neighbours list — include.self","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) col.gal.nb <- read.gal(system.file(\"weights/columbus.gal\", package=\"spData\")[1]) coords <- st_coordinates(st_centroid(columbus)) #> Warning: st_centroid assumes attributes are constant over geometries summary(col.gal.nb, coords) #> Neighbour list object: #> Number of regions: 49  #> Number of nonzero links: 230  #> Percentage nonzero weights: 9.579342  #> Average number of links: 4.693878  #> Link number distribution: #>  #>  2  3  4  5  6  7  8  9 10  #>  7  7 13  4  9  6  1  1  1  #> 7 least connected regions: #> 1 6 31 39 42 46 47 with 2 links #> 1 most connected region: #> 20 with 10 links summary(include.self(col.gal.nb), coords) #> Neighbour list object: #> Number of regions: 49  #> Number of nonzero links: 279  #> Percentage nonzero weights: 11.62016  #> Average number of links: 5.693878  #> Link number distribution: #>  #>  3  4  5  6  7  8  9 10 11  #>  7  7 13  4  9  6  1  1  1  #> 7 least connected regions: #> 1 6 31 39 42 46 47 with 3 links #> 1 most connected region: #> 20 with 11 links summary(remove.self(include.self(col.gal.nb)), coords) #> Neighbour list object: #> Number of regions: 49  #> Number of nonzero links: 230  #> Percentage nonzero weights: 9.579342  #> Average number of links: 4.693878  #> Link number distribution: #>  #>  2  3  4  5  6  7  8  9 10  #>  7  7 13  4  9  6  1  1  1  #> 7 least connected regions: #> 1 6 31 39 42 46 47 with 2 links #> 1 most connected region: #> 20 with 10 links"},{"path":"https://r-spatial.github.io/spdep/reference/joincount.mc.html","id":null,"dir":"Reference","previous_headings":"","what":"Permutation test for same colour join count statistics — joincount.mc","title":"Permutation test for same colour join count statistics — joincount.mc","text":"permutation test colour join count statistics calculated using nsim random permutations fx given spatial weighting scheme, establish ranks observed statistics (colour) relation nsim simulated values.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/joincount.mc.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Permutation test for same colour join count statistics — joincount.mc","text":"","code":"joincount.mc(fx, listw, nsim, zero.policy=attr(listw, \"zero.policy\"),  alternative=\"greater\", spChk=NULL)"},{"path":"https://r-spatial.github.io/spdep/reference/joincount.mc.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Permutation test for same colour join count statistics — joincount.mc","text":"fx factor length neighbours weights objects listw listw listw object created example nb2listw nsim number permutations zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA alternative character string specifying alternative hypothesis, must one \"greater\" (default), \"two.sided\", \"less\". spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption()","code":""},{"path":"https://r-spatial.github.io/spdep/reference/joincount.mc.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Permutation test for same colour join count statistics — joincount.mc","text":"list class jclist lists class htest mc.sim k colours containing following components: statistic value observed statistic. parameter rank observed statistic. method character string giving method used. data.name character string giving name(s) data. p.value pseudo p-value test. alternative character string describing alternative hypothesis. estimate mean variance simulated distribution. res nsim simulated values statistic, final element observed statistic","code":""},{"path":"https://r-spatial.github.io/spdep/reference/joincount.mc.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Permutation test for same colour join count statistics — joincount.mc","text":"Cliff, . D., Ord, J. K. 1981 Spatial processes, Pion, p. 63-5.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/joincount.mc.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Permutation test for same colour join count statistics — joincount.mc","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/joincount.mc.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Permutation test for same colour join count statistics — joincount.mc","text":"","code":"data(oldcol) HICRIME <- cut(COL.OLD$CRIME, breaks=c(0,35,80), labels=c(\"low\",\"high\")) names(HICRIME) <- rownames(COL.OLD) joincount.mc(HICRIME, nb2listw(COL.nb, style=\"B\"), nsim=99, alternative=\"two.sided\") #>  #> \tMonte-Carlo simulation of join-count statistic #>  #> data:  HICRIME  #> weights: nb2listw(COL.nb, style = \"B\")  #> number of simulations + 1: 100  #>  #> Join-count statistic for low = 34, rank of observed statistic = 88.5, #> p-value = 0.23 #> alternative hypothesis: two.sided #> sample estimates: #>     mean of simulation variance of simulation  #>               28.96970               18.19295  #>  #>  #> \tMonte-Carlo simulation of join-count statistic #>  #> data:  HICRIME  #> weights: nb2listw(COL.nb, style = \"B\")  #> number of simulations + 1: 100  #>  #> Join-count statistic for high = 54, rank of observed statistic = 100, #> p-value < 2.2e-16 #> alternative hypothesis: two.sided #> sample estimates: #>     mean of simulation variance of simulation  #>               26.83838               20.13688  #>  joincount.test(HICRIME, nb2listw(COL.nb, style=\"B\"), alternative=\"two.sided\") #>  #> \tJoin count test under nonfree sampling #>  #> data:  HICRIME  #> weights: nb2listw(COL.nb, style = \"B\")  #>  #> Std. deviate for low = 1.0141, p-value = 0.3105 #> alternative hypothesis: two.sided #> sample estimates: #> Same colour statistic           Expectation              Variance  #>              34.00000              29.59184              18.89550  #>  #>  #> \tJoin count test under nonfree sampling #>  #> data:  HICRIME  #> weights: nb2listw(COL.nb, style = \"B\")  #>  #> Std. deviate for high = 6.3307, p-value = 2.44e-10 #> alternative hypothesis: two.sided #> sample estimates: #> Same colour statistic           Expectation              Variance  #>              54.00000              27.22449              17.88838  #>"},{"path":"https://r-spatial.github.io/spdep/reference/joincount.multi.html","id":null,"dir":"Reference","previous_headings":"","what":"BB, BW and Jtot join count statistic for k-coloured factors — joincount.multi","title":"BB, BW and Jtot join count statistic for k-coloured factors — joincount.multi","text":"function tallying join counts -colour different colour spatial objects, neighbour relations defined weights list. Given global counts colour, expected counts variances calculated non-free sampling, z-value reported. Since multiple tests reported, p-values given, allowing user adjust significance level applied. Jtot count different-colour joins.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/joincount.multi.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"BB, BW and Jtot join count statistic for k-coloured factors — joincount.multi","text":"","code":"joincount.multi(fx, listw, zero.policy = attr(listw, \"zero.policy\"),  spChk = NULL, adjust.n=TRUE) # S3 method for class 'jcmulti' print(x, ...)"},{"path":"https://r-spatial.github.io/spdep/reference/joincount.multi.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"BB, BW and Jtot join count statistic for k-coloured factors — joincount.multi","text":"fx factor length neighbours weights objects listw listw listw object created example nb2listw zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA adjust.n default TRUE, FALSE number observations adjusted -neighbour observations, TRUE, number observations adjusted consistently (including spdep 0.3-28 adjustment inconsistent - thanks Tomoki NAKAYA careful bug report) spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption() x object printed ... arguments passed printing","code":""},{"path":"https://r-spatial.github.io/spdep/reference/joincount.multi.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"BB, BW and Jtot join count statistic for k-coloured factors — joincount.multi","text":"matrix class jcmulti row column names observed expected counts, variance, z-value.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/joincount.multi.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"BB, BW and Jtot join count statistic for k-coloured factors — joincount.multi","text":"Cliff, . D., Ord, J. K. 1981 Spatial processes, Pion, p. 20; Upton, G., Fingleton, B. 1985 Spatial data analysis example: point pattern qualitative data, Wiley, pp. 158–170.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/joincount.multi.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"BB, BW and Jtot join count statistic for k-coloured factors — joincount.multi","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/joincount.multi.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"BB, BW and Jtot join count statistic for k-coloured factors — joincount.multi","text":"derivation test (Cliff Ord, 1981, p. 18) assumes weights matrix symmetric. inherently non-symmetric matrices, k-nearest neighbour matrices, listw2U() can used make matrix symmetric. non-symmetric weights matrix cases, variance test statistic may negative.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/joincount.multi.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"BB, BW and Jtot join count statistic for k-coloured factors — joincount.multi","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) HICRIME <- cut(columbus$CRIME, breaks=c(0,35,80), labels=c(\"low\",\"high\")) (nb <- poly2nb(columbus)) #> Neighbour list object: #> Number of regions: 49  #> Number of nonzero links: 236  #> Percentage nonzero weights: 9.829238  #> Average number of links: 4.816327  lw <- nb2listw(nb, style=\"B\") joincount.multi(HICRIME, lw) #>           Joincount Expected Variance z-value #> low:low      35.000   30.102   19.247  1.1164 #> high:high    54.000   27.694   18.219  6.1630 #> high:low     29.000   60.204   26.630 -6.0468 #> Jtot         29.000   60.204   26.630 -6.0468 col_geoms <- st_geometry(columbus) col_geoms[21] <- st_buffer(col_geoms[21], dist=-0.05) st_geometry(columbus) <- col_geoms (nb <- poly2nb(columbus)) #> Warning: some observations have no neighbours; #> if this seems unexpected, try increasing the snap argument. #> Warning: neighbour object has 3 sub-graphs; #> if this sub-graph count seems unexpected, try increasing the snap argument. #> Neighbour list object: #> Number of regions: 49  #> Number of nonzero links: 230  #> Percentage nonzero weights: 9.579342  #> Average number of links: 4.693878  #> 1 region with no links: #> 21 #> 3 disjoint connected subgraphs lw <- nb2listw(nb, style=\"B\", zero.policy=TRUE) joincount.multi(HICRIME, lw) #>           Joincount Expected Variance z-value #> low:low      35.000   30.585   19.350  1.0036 #> high:high    52.000   28.138   18.342  5.5716 #> high:low     28.000   61.170   25.882 -6.5200 #> Jtot         28.000   61.170   33.190 -5.7577 if (FALSE) { # \\dontrun{ data(oldcol) HICRIME <- cut(COL.OLD$CRIME, breaks=c(0,35,80), labels=c(\"low\",\"high\")) names(HICRIME) <- rownames(COL.OLD) joincount.multi(HICRIME, nb2listw(COL.nb, style=\"B\")) data(hopkins, package=\"spData\") image(1:32, 1:32, hopkins[5:36,36:5], breaks=c(-0.5, 3.5, 20),  col=c(\"white\", \"black\")) box() hopkins.rook.nb <- cell2nb(32, 32, type=\"rook\") unlist(spweights.constants(nb2listw(hopkins.rook.nb, style=\"B\"))) hopkins.queen.nb <- cell2nb(32, 32, type=\"queen\") hopkins.bishop.nb <- diffnb(hopkins.rook.nb, hopkins.queen.nb, verbose=FALSE) hopkins4 <- hopkins[5:36,36:5] hopkins4[which(hopkins4 > 3, arr.ind=TRUE)] <- 4 hopkins4.f <- factor(hopkins4) table(hopkins4.f) joincount.multi(hopkins4.f, nb2listw(hopkins.rook.nb, style=\"B\")) cat(\"replicates Upton & Fingleton table 3.4 (p. 166)\\n\") joincount.multi(hopkins4.f, nb2listw(hopkins.bishop.nb, style=\"B\")) cat(\"replicates Upton & Fingleton table 3.6 (p. 168)\\n\") joincount.multi(hopkins4.f, nb2listw(hopkins.queen.nb, style=\"B\")) cat(\"replicates Upton & Fingleton table 3.7 (p. 169)\\n\") } # } GDAL37 <- as.numeric_version(unname(sf_extSoftVersion()[\"GDAL\"])) >= \"3.7.0\" file <- \"etc/shapes/GB_2024_southcoast_50m.gpkg.zip\" zipfile <- system.file(file, package=\"spdep\") if (GDAL37) {     sc50m <- st_read(zipfile) } else {     td <- tempdir()     bn <- sub(\".zip\", \"\", basename(file), fixed=TRUE)     target <- unzip(zipfile, files=bn, exdir=td)     sc50m <- st_read(target) } #> Reading layer `GB_2024_southcoast_50m' from data source  #>   `/tmp/RtmpXVTJuL/temp_libpath3b356d487bad39/spdep/etc/shapes/GB_2024_southcoast_50m.gpkg.zip'  #>   using driver `GPKG' #> Simple feature collection with 119 features and 19 fields #> Geometry type: MULTIPOLYGON #> Dimension:     XY #> Bounding box:  xmin: 82643.12 ymin: 5342.9 xmax: 640301.6 ymax: 187226.2 #> Projected CRS: OSGB36 / British National Grid sc50m$Winner <- factor(sc50m$Winner, levels=c(\"Con\", \"Green\", \"Lab\", \"LD\")) plot(sc50m[,\"Winner\"], pal=c(\"#2297E6\", \"#61D04F\", \"#DF536B\", \"#F5C710\"))  nb_sc_50m <- poly2nb(sc50m, row.names=as.character(sc50m$Constituency)) #> Warning: neighbour object has 2 sub-graphs; #> if this sub-graph count seems unexpected, try increasing the snap argument. sub2 <- attr(nb_sc_50m, \"region.id\")[attr(nb_sc_50m, \"ncomp\")$comp.id == 2L] iowe <- match(sub2[1], attr(nb_sc_50m, \"region.id\")) diowe <- c(st_distance(sc50m[iowe,], sc50m)) meet_criterion <- sum(diowe <= units::set_units(5000, \"m\")) cands <- attr(nb_sc_50m, \"region.id\")[order(diowe)[1:meet_criterion]] nb_sc_50m_iowe <- addlinks1(nb_sc_50m, from = cands[1],  to = cands[3:meet_criterion]) ioww <- match(sub2[2], attr(nb_sc_50m, \"region.id\")) dioww <- c(st_distance(sc50m[ioww,], sc50m)) meet_criterion <- sum(dioww <= units::set_units(5000, \"m\")) cands <- attr(nb_sc_50m, \"region.id\")[order(dioww)[1:meet_criterion]] nb_sc_50m_iow <- addlinks1(nb_sc_50m_iowe, from = cands[2], to = cands[3:meet_criterion]) nb_sc_1_2 <- nblag_cumul(nblag(nb_sc_50m_iow, 2)) joincount.multi(sc50m$Winner, nb2listw(nb_sc_1_2, style=\"B\")) #>             Joincount Expected Variance z-value #> Con:Con      146.0000  84.4324 116.3530  5.7077 #> Green:Green    0.0000   0.0000   0.0000     NaN #> Lab:Lab       63.0000  98.1057 136.0379 -3.0099 #> LD:LD        100.0000  75.8866 103.9440  2.3651 #> Green:Con      4.0000   4.4438   5.8532 -0.1834 #> Lab:Con      184.0000 186.6401 180.9233 -0.1963 #> Lab:Green      3.0000   4.7856   6.4663 -0.7022 #> LD:Con       198.0000 164.4210 166.3583  2.6034 #> LD:Green       4.0000   4.2159   5.4573 -0.0924 #> LD:Lab        98.0000 177.0688 175.2035 -5.9736 #> Jtot         491.0000 541.5753 153.6123 -4.0806"},{"path":"https://r-spatial.github.io/spdep/reference/joincount.test.html","id":null,"dir":"Reference","previous_headings":"","what":"BB join count statistic for k-coloured factors — joincount.test","title":"BB join count statistic for k-coloured factors — joincount.test","text":"BB join count test spatial autocorrelation using spatial weights matrix weights list form testing whether -colour joins occur frequently expected zones labelled spatially random way. assumptions underlying test sensitive form graph neighbour relationships factors, results may checked joincount.mc permutations.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/joincount.test.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"BB join count statistic for k-coloured factors — joincount.test","text":"","code":"joincount.test(fx, listw, zero.policy=attr(listw, \"zero.policy\"), alternative=\"greater\",  sampling=\"nonfree\", spChk=NULL, adjust.n=TRUE) # S3 method for class 'jclist' print(x, ...)"},{"path":"https://r-spatial.github.io/spdep/reference/joincount.test.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"BB join count statistic for k-coloured factors — joincount.test","text":"fx factor length neighbours weights objects listw listw listw object created example nb2listw zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA alternative character string specifying alternative hypothesis, must one \"greater\" (default), \"less\" \"two.sided\". sampling default “nonfree”, may “free” adjust.n default TRUE, FALSE number observations adjusted -neighbour observations, TRUE, number observations adjusted consistently (including spdep 0.3-28 adjustment inconsistent - thanks Tomoki NAKAYA careful bug report) spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption() x object printed ... arguments passed printing","code":""},{"path":"https://r-spatial.github.io/spdep/reference/joincount.test.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"BB join count statistic for k-coloured factors — joincount.test","text":"list class jclist lists class htest k colours containing following components: statistic value standard deviate join count statistic. p.value p-value test. estimate value observed statistic, expectation variance non-free sampling. alternative character string describing alternative hypothesis. method character string giving method used. data.name character string giving name(s) data.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/joincount.test.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"BB join count statistic for k-coloured factors — joincount.test","text":"Cliff, . D., Ord, J. K. 1981 Spatial processes, Pion, pp. 19-20.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/joincount.test.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"BB join count statistic for k-coloured factors — joincount.test","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/joincount.test.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"BB join count statistic for k-coloured factors — joincount.test","text":"derivation test (Cliff Ord, 1981, p. 18) assumes weights matrix symmetric. inherently non-symmetric matrices, k-nearest neighbour matrices, listw2U() can used make matrix symmetric. non-symmetric weights matrix cases, variance test statistic may negative.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/joincount.test.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"BB join count statistic for k-coloured factors — joincount.test","text":"","code":"data(oldcol) HICRIME <- cut(COL.OLD$CRIME, breaks=c(0,35,80), labels=c(\"low\",\"high\")) names(HICRIME) <- rownames(COL.OLD) joincount.test(HICRIME, nb2listw(COL.nb, style=\"B\")) #>  #> \tJoin count test under nonfree sampling #>  #> data:  HICRIME  #> weights: nb2listw(COL.nb, style = \"B\")  #>  #> Std. deviate for low = 1.0141, p-value = 0.1553 #> alternative hypothesis: greater #> sample estimates: #> Same colour statistic           Expectation              Variance  #>              34.00000              29.59184              18.89550  #>  #>  #> \tJoin count test under nonfree sampling #>  #> data:  HICRIME  #> weights: nb2listw(COL.nb, style = \"B\")  #>  #> Std. deviate for high = 6.3307, p-value = 1.22e-10 #> alternative hypothesis: greater #> sample estimates: #> Same colour statistic           Expectation              Variance  #>              54.00000              27.22449              17.88838  #>  joincount.test(HICRIME, nb2listw(COL.nb, style=\"B\"), sampling=\"free\") #>  #> \tJoin count test under free sampling #>  #> data:  HICRIME  #> weights: nb2listw(COL.nb, style = \"B\")  #>  #> Std. deviate for low = 0.3993, p-value = 0.3448 #> alternative hypothesis: greater #> sample estimates: #> Same colour statistic           Expectation              Variance  #>              34.00000              30.19575              90.76809  #>  #>  #> \tJoin count test under free sampling #>  #> data:  HICRIME  #> weights: nb2listw(COL.nb, style = \"B\")  #>  #> Std. deviate for high = 2.8518, p-value = 0.002173 #> alternative hypothesis: greater #> sample estimates: #> Same colour statistic           Expectation              Variance  #>               54.0000               27.8284               84.2198  #>  joincount.test(HICRIME, nb2listw(COL.nb, style=\"C\")) #>  #> \tJoin count test under nonfree sampling #>  #> data:  HICRIME  #> weights: nb2listw(COL.nb, style = \"C\")  #>  #> Std. deviate for low = 1.0141, p-value = 0.1553 #> alternative hypothesis: greater #> sample estimates: #> Same colour statistic           Expectation              Variance  #>             7.1810345             6.2500000             0.8428969  #>  #>  #> \tJoin count test under nonfree sampling #>  #> data:  HICRIME  #> weights: nb2listw(COL.nb, style = \"C\")  #>  #> Std. deviate for high = 6.3307, p-value = 1.22e-10 #> alternative hypothesis: greater #> sample estimates: #> Same colour statistic           Expectation              Variance  #>            11.4051724             5.7500000             0.7979712  #>  joincount.test(HICRIME, nb2listw(COL.nb, style=\"S\")) #>  #> \tJoin count test under nonfree sampling #>  #> data:  HICRIME  #> weights: nb2listw(COL.nb, style = \"S\")  #>  #> Std. deviate for low = 2.5786, p-value = 0.00496 #> alternative hypothesis: greater #> sample estimates: #> Same colour statistic           Expectation              Variance  #>             8.2425673             6.2500000             0.5971141  #>  #>  #> \tJoin count test under nonfree sampling #>  #> data:  HICRIME  #> weights: nb2listw(COL.nb, style = \"S\")  #>  #> Std. deviate for high = 6.1736, p-value = 3.337e-10 #> alternative hypothesis: greater #> sample estimates: #> Same colour statistic           Expectation              Variance  #>            10.4249914             5.7500000             0.5734265  #>  joincount.test(HICRIME, nb2listw(COL.nb, style=\"W\")) #>  #> \tJoin count test under nonfree sampling #>  #> data:  HICRIME  #> weights: nb2listw(COL.nb, style = \"W\")  #>  #> Std. deviate for low = 4.6675, p-value = 1.524e-06 #> alternative hypothesis: greater #> sample estimates: #> Same colour statistic           Expectation              Variance  #>             9.5190476             6.2500000             0.4905378  #>  #>  #> \tJoin count test under nonfree sampling #>  #> data:  HICRIME  #> weights: nb2listw(COL.nb, style = \"W\")  #>  #> Std. deviate for high = 5.1205, p-value = 1.523e-07 #> alternative hypothesis: greater #> sample estimates: #> Same colour statistic           Expectation              Variance  #>             9.2920635             5.7500000             0.4784979  #>  by(card(COL.nb), HICRIME, summary) #> HICRIME: low #>    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.  #>    2.00    2.00    4.00    3.84    4.00   10.00  #> ------------------------------------------------------------  #> HICRIME: high #>    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.  #>   3.000   4.750   6.000   5.667   7.000   9.000  print(is.symmetric.nb(COL.nb)) #> [1] TRUE coords.OLD <- cbind(COL.OLD$X, COL.OLD$Y) COL.k4.nb <- knn2nb(knearneigh(coords.OLD, 4)) print(is.symmetric.nb(COL.k4.nb)) #> [1] FALSE joincount.test(HICRIME, nb2listw(COL.k4.nb, style=\"B\")) #>  #> \tJoin count test under nonfree sampling #>  #> data:  HICRIME  #> weights: nb2listw(COL.k4.nb, style = \"B\")  #>  #> Std. deviate for low = 4.3698, p-value = 6.217e-06 #> alternative hypothesis: greater #> sample estimates: #> Same colour statistic           Expectation              Variance  #>             36.500000             25.000000              6.925749  #>  #>  #> \tJoin count test under nonfree sampling #>  #> data:  HICRIME  #> weights: nb2listw(COL.k4.nb, style = \"B\")  #>  #> Std. deviate for high = 6.7293, p-value = 8.523e-12 #> alternative hypothesis: greater #> sample estimates: #> Same colour statistic           Expectation              Variance  #>             40.500000             23.000000              6.762918  #>  cat(\"Note non-symmetric weights matrix - use listw2U()\\n\") #> Note non-symmetric weights matrix - use listw2U() joincount.test(HICRIME, listw2U(nb2listw(COL.k4.nb, style=\"B\"))) #>  #> \tJoin count test under nonfree sampling #>  #> data:  HICRIME  #> weights: listw2U(nb2listw(COL.k4.nb, style = \"B\"))  #>  #> Std. deviate for low = 4.3698, p-value = 6.217e-06 #> alternative hypothesis: greater #> sample estimates: #> Same colour statistic           Expectation              Variance  #>             36.500000             25.000000              6.925749  #>  #>  #> \tJoin count test under nonfree sampling #>  #> data:  HICRIME  #> weights: listw2U(nb2listw(COL.k4.nb, style = \"B\"))  #>  #> Std. deviate for high = 6.7293, p-value = 8.523e-12 #> alternative hypothesis: greater #> sample estimates: #> Same colour statistic           Expectation              Variance  #>             40.500000             23.000000              6.762918  #>  columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) HICRIME <- cut(columbus$CRIME, breaks=c(0,35,80), labels=c(\"low\",\"high\")) (nb <- poly2nb(columbus)) #> Neighbour list object: #> Number of regions: 49  #> Number of nonzero links: 236  #> Percentage nonzero weights: 9.829238  #> Average number of links: 4.816327  lw <- nb2listw(nb, style=\"B\") joincount.test(HICRIME, lw) #>  #> \tJoin count test under nonfree sampling #>  #> data:  HICRIME  #> weights: lw  #>  #> Std. deviate for low = 1.1164, p-value = 0.1321 #> alternative hypothesis: greater #> sample estimates: #> Same colour statistic           Expectation              Variance  #>              35.00000              30.10204              19.24708  #>  #>  #> \tJoin count test under nonfree sampling #>  #> data:  HICRIME  #> weights: lw  #>  #> Std. deviate for high = 6.163, p-value = 3.57e-10 #> alternative hypothesis: greater #> sample estimates: #> Same colour statistic           Expectation              Variance  #>              54.00000              27.69388              18.21936  #>  col_geoms <- st_geometry(columbus) col_geoms[21] <- st_buffer(col_geoms[21], dist=-0.05) st_geometry(columbus) <- col_geoms (nb <- poly2nb(columbus)) #> Warning: some observations have no neighbours; #> if this seems unexpected, try increasing the snap argument. #> Warning: neighbour object has 3 sub-graphs; #> if this sub-graph count seems unexpected, try increasing the snap argument. #> Neighbour list object: #> Number of regions: 49  #> Number of nonzero links: 230  #> Percentage nonzero weights: 9.579342  #> Average number of links: 4.693878  #> 1 region with no links: #> 21 #> 3 disjoint connected subgraphs lw <- nb2listw(nb, style=\"B\", zero.policy=TRUE) joincount.test(HICRIME, lw) #>  #> \tJoin count test under nonfree sampling #>  #> data:  HICRIME  #> weights: lw  #>  #> Std. deviate for low = 1.0036, p-value = 0.1578 #> alternative hypothesis: greater #> sample estimates: #> Same colour statistic           Expectation              Variance  #>              35.00000              30.58511              19.35032  #>  #>  #> \tJoin count test under nonfree sampling #>  #> data:  HICRIME  #> weights: lw  #>  #> Std. deviate for high = 5.5716, p-value = 1.262e-08 #> alternative hypothesis: greater #> sample estimates: #> Same colour statistic           Expectation              Variance  #>              52.00000              28.13830              18.34187  #>"},{"path":"https://r-spatial.github.io/spdep/reference/knearneigh.html","id":null,"dir":"Reference","previous_headings":"","what":"K nearest neighbours for spatial weights — knearneigh","title":"K nearest neighbours for spatial weights — knearneigh","text":"function returns matrix indices points belonging set k nearest neighbours . longlat = TRUE, Great Circle distances used. warning given identical points found.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/knearneigh.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"K nearest neighbours for spatial weights — knearneigh","text":"","code":"knearneigh(x, k=1, longlat = NULL, use_kd_tree=TRUE)"},{"path":"https://r-spatial.github.io/spdep/reference/knearneigh.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"K nearest neighbours for spatial weights — knearneigh","text":"x matrix point coordinates, object inheriting SpatialPoints \"sf\" \"sfc\" object; \"sf\" \"sfc\" object geometries geographical coordinates (sf::st_is_longlat(x) == TRUE sf::sf_use_s2() == TRUE), s2 used find neighbours uses spatial indexing https://github.com/r-spatial/s2/issues/125 opposed legacy method uses brute-force k number nearest neighbours returned; identical points present, k least large largest count identical points (k smaller, error occur s2 used) longlat TRUE point coordinates longitude-latitude decimal degrees, case distances measured kilometers; x SpatialPoints object, value taken object ; longlat override kd_tree use_kd_tree logical value, dbscan package available, use finding k nearest neighbours longlat FALSE, identical points; https://github.com/r-spatial/spdep/issues/38, input data may two columns dbscan used","code":""},{"path":"https://r-spatial.github.io/spdep/reference/knearneigh.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"K nearest neighbours for spatial weights — knearneigh","text":"underlying legacy C code based knn function class package.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/knearneigh.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"K nearest neighbours for spatial weights — knearneigh","text":"list class knn nn integer matrix region number ids np number input points k input required k dimension number columns x x input coordinates","code":""},{"path":"https://r-spatial.github.io/spdep/reference/knearneigh.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"K nearest neighbours for spatial weights — knearneigh","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/knearneigh.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"K nearest neighbours for spatial weights — knearneigh","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) coords <- st_centroid(st_geometry(columbus), of_largest_polygon=TRUE) col.knn <- knearneigh(coords, k=4) plot(st_geometry(columbus), border=\"grey\") plot(knn2nb(col.knn), coords, add=TRUE) title(main=\"K nearest neighbours, k = 4\")  data(state) us48.fipsno <- read.geoda(system.file(\"etc/weights/us48.txt\",  package=\"spdep\")[1]) if (as.numeric(paste(version$major, version$minor, sep=\"\")) < 19) {  m50.48 <- match(us48.fipsno$\"State.name\", state.name) } else {  m50.48 <- match(us48.fipsno$\"State_name\", state.name) } xy <- as.matrix(as.data.frame(state.center))[m50.48,] llk4.nb <- knn2nb(knearneigh(xy, k=4, longlat=FALSE)) gck4.nb <- knn2nb(knearneigh(xy, k=4, longlat=TRUE)) plot(llk4.nb, xy) plot(diffnb(llk4.nb, gck4.nb), xy, add=TRUE, col=\"red\", lty=2) #> Warning: neighbour object has 22 sub-graphs title(main=\"Differences between Euclidean and Great Circle k=4 neighbours\")  summary(llk4.nb, xy, longlat=TRUE, scale=0.5) #> Neighbour list object: #> Number of regions: 48  #> Number of nonzero links: 192  #> Percentage nonzero weights: 8.333333  #> Average number of links: 4  #> Non-symmetric neighbours list #> Link number distribution: #>  #>  4  #> 48  #> 48 least connected regions: #> 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 with 4 links #> 48 most connected regions: #> 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 with 4 links summary(gck4.nb, xy, longlat=TRUE, scale=0.5) #> Neighbour list object: #> Number of regions: 48  #> Number of nonzero links: 192  #> Percentage nonzero weights: 8.333333  #> Average number of links: 4  #> Non-symmetric neighbours list #> Link number distribution: #>  #>  4  #> 48  #> 48 least connected regions: #> 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 with 4 links #> 48 most connected regions: #> 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 with 4 links  #xy1 <- SpatialPoints((as.data.frame(state.center))[m50.48,], #  proj4string=CRS(\"+proj=longlat +ellps=GRS80\")) #gck4a.nb <- knn2nb(knearneigh(xy1, k=4)) #summary(gck4a.nb, xy1, scale=0.5)  xy1 <- st_as_sf((as.data.frame(state.center))[m50.48,], coords=1:2,   crs=st_crs(\"OGC:CRS84\")) old_use_s2 <- sf_use_s2() sf_use_s2(TRUE) system.time(gck4a.nb <- knn2nb(knearneigh(xy1, k=4))) #>    user  system elapsed  #>   0.011   0.000   0.012  summary(gck4a.nb, xy1, scale=0.5) #> Neighbour list object: #> Number of regions: 48  #> Number of nonzero links: 192  #> Percentage nonzero weights: 8.333333  #> Average number of links: 4  #> Non-symmetric neighbours list #> Link number distribution: #>  #>  4  #> 48  #> 48 least connected regions: #> 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 with 4 links #> 48 most connected regions: #> 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 with 4 links sf_use_s2(FALSE) #> Spherical geometry (s2) switched off system.time(gck4a.nb <- knn2nb(knearneigh(xy1, k=4))) #>    user  system elapsed  #>   0.008   0.000   0.008  summary(gck4a.nb, xy1, scale=0.5) #> Neighbour list object: #> Number of regions: 48  #> Number of nonzero links: 192  #> Percentage nonzero weights: 8.333333  #> Average number of links: 4  #> Non-symmetric neighbours list #> Link number distribution: #>  #>  4  #> 48  #> 48 least connected regions: #> 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 with 4 links #> 48 most connected regions: #> 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 with 4 links sf_use_s2(old_use_s2) #> Spherical geometry (s2) switched on  # https://github.com/r-spatial/spdep/issues/38 if (require(\"dbscan\", quietly=TRUE)) {   set.seed(1)   x <- cbind(runif(50), runif(50), runif(50))   out <- knearneigh(x, k=5)   knn2nb(out)   try(out <- knearneigh(rbind(x, x[1:10,]), k=5)) } #> Warning: knearneigh: identical points found #> Warning: knearneigh: kd_tree not available for identical points #> Error in knearneigh(rbind(x, x[1:10, ]), k = 5) :  #>   kd_tree required for more than 2 dimensions"},{"path":"https://r-spatial.github.io/spdep/reference/knn2nb.html","id":null,"dir":"Reference","previous_headings":"","what":"Neighbours list from knn object — knn2nb","title":"Neighbours list from knn object — knn2nb","text":"function converts knn object returned knearneigh neighbours list class nb list integer vectors containing neighbour region number ids.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/knn2nb.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Neighbours list from knn object — knn2nb","text":"","code":"knn2nb(knn, row.names = NULL, sym = FALSE)"},{"path":"https://r-spatial.github.io/spdep/reference/knn2nb.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Neighbours list from knn object — knn2nb","text":"knn knn object returned knearneigh row.names character vector region ids added neighbours list attribute region.id, default seq(1, nrow(x)) sym force output neighbours list symmetry","code":""},{"path":"https://r-spatial.github.io/spdep/reference/knn2nb.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Neighbours list from knn object — knn2nb","text":"function returns object class nb list integer vectors containing neighbour region number ids. See card details “nb” objects.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/knn2nb.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Neighbours list from knn object — knn2nb","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/knn2nb.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Neighbours list from knn object — knn2nb","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) coords <- st_coordinates(st_centroid(columbus)) #> Warning: st_centroid assumes attributes are constant over geometries col.knn <- knearneigh(coords, k=4) plot(st_geometry(columbus), border=\"grey\") plot(knn2nb(col.knn), coords, add=TRUE) title(main=\"K nearest neighbours, k = 4\")  # example of reading points with readr::read_csv() yielding a tibble load(system.file(\"etc/misc/coords.rda\", package=\"spdep\")) class(coords) #> [1] \"spec_tbl_df\" \"tbl_df\"      \"tbl\"         \"data.frame\"  knn2nb(knearneigh(coords, k=4)) #> Neighbour list object: #> Number of regions: 100  #> Number of nonzero links: 400  #> Percentage nonzero weights: 4  #> Average number of links: 4  #> Non-symmetric neighbours list"},{"path":"https://r-spatial.github.io/spdep/reference/lag.listw.html","id":null,"dir":"Reference","previous_headings":"","what":"Spatial lag of a numeric vector — lag.listw","title":"Spatial lag of a numeric vector — lag.listw","text":"Using listw sparse representation spatial weights matrix, compute lag vector \\(V x\\)","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lag.listw.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Spatial lag of a numeric vector — lag.listw","text":"","code":"# S3 method for class 'listw' lag(x, var, zero.policy=attr(listw, \"zero.policy\"), NAOK=FALSE, ...)"},{"path":"https://r-spatial.github.io/spdep/reference/lag.listw.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Spatial lag of a numeric vector — lag.listw","text":"x listw object created example nb2listw var numeric vector length neighbours list listw zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA NAOK 'FALSE', presence 'NA' values regarded error; 'TRUE' 'NA' 'NaN' 'Inf' values var represented NA lagged value. ... additional arguments","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lag.listw.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Spatial lag of a numeric vector — lag.listw","text":"numeric vector length var","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lag.listw.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Spatial lag of a numeric vector — lag.listw","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/lag.listw.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Spatial lag of a numeric vector — lag.listw","text":"","code":"data(oldcol) Vx <- lag.listw(nb2listw(COL.nb, style=\"W\"), COL.OLD$CRIME) plot(Vx, COL.OLD$CRIME)  plot(ecdf(COL.OLD$CRIME)) plot(ecdf(Vx), add=TRUE, col.points=\"red\", col.hor=\"red\")  is.na(COL.OLD$CRIME[5]) <- TRUE VxNA <- lag.listw(nb2listw(COL.nb, style=\"W\"), COL.OLD$CRIME, NAOK=TRUE) #> Warning: NAs in lagged values"},{"path":"https://r-spatial.github.io/spdep/reference/lee.html","id":null,"dir":"Reference","previous_headings":"","what":"Compute Lee's statistic — lee","title":"Compute Lee's statistic — lee","text":"simple function compute Lee's L statistic bivariate spatial data;  $$L(x,y) = \\frac{n}{\\sum_{=1}^{n}(\\sum_{j=1}^{n}w_{ij})^2} \\frac{\\sum_{=1}^{n}(\\sum_{j=1}^{n}w_{ij}(x_i-\\bar{x})) ((\\sum_{j=1}^{n}w_{ij}(y_j-\\bar{y}))}{\\sqrt{\\sum_{=1}^{n}(x_i - \\bar{x})^2} \\sqrt{\\sum_{=1}^{n}(y_i - \\bar{y})^2}} $$","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lee.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Compute Lee's statistic — lee","text":"","code":"lee(x, y, listw, n, S2, zero.policy=attr(listw, \"zero.policy\"), NAOK=FALSE)"},{"path":"https://r-spatial.github.io/spdep/reference/lee.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Compute Lee's statistic — lee","text":"x numeric vector length neighbours list listw y numeric vector length neighbours list listw listw listw object created example nb2listw n number zones S2 Sum squared sum weights rows. zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA NAOK 'TRUE' 'NA' 'NaN' 'Inf' values x passed foreign function.  'FALSE', presence 'NA' 'NaN' 'Inf' values regarded error.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lee.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Compute Lee's statistic — lee","text":"list L Lee's L statistic local L Lee's local L statistic","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lee.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Compute Lee's statistic — lee","text":"Lee (2001). Developing bivariate spatial association measure: integration Pearson's r Moran's . J Geograph Syst  3: 369-385","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lee.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Compute Lee's statistic — lee","text":"Roger Bivand Virgiio Gómez-Rubio Virgilio.Gomez@uclm.es","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/lee.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Compute Lee's statistic — lee","text":"","code":"data(boston, package=\"spData\") lw<-nb2listw(boston.soi)  x<-boston.c$CMEDV y<-boston.c$CRIM z<-boston.c$RAD  Lxy<-lee(x, y, lw, length(x), zero.policy=TRUE) Lxz<-lee(x, z, lw, length(x), zero.policy=TRUE)"},{"path":"https://r-spatial.github.io/spdep/reference/lee.mc.html","id":null,"dir":"Reference","previous_headings":"","what":"Permutation test for Lee's L statistic — lee.mc","title":"Permutation test for Lee's L statistic — lee.mc","text":"permutation test Lee's L  statistic calculated using nsim random permutations x y given spatial weighting scheme, establish rank observed statistic relation nsim simulated values.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lee.mc.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Permutation test for Lee's L statistic — lee.mc","text":"","code":"lee.mc(x, y, listw, nsim, zero.policy=attr(listw, \"zero.policy\"), alternative=\"greater\",  na.action=na.fail, spChk=NULL, return_boot=FALSE)"},{"path":"https://r-spatial.github.io/spdep/reference/lee.mc.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Permutation test for Lee's L statistic — lee.mc","text":"x numeric vector length neighbours list listw y numeric vector length neighbours list listw listw listw object created example nb2listw nsim number permutations zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA alternative character string specifying alternative hypothesis, must one \"greater\" (default), \"two.sided\", \"less\". na.action function (default na.fail), can also na.omit na.exclude - cases weights list subsetted remove NAs data. may necessary set zero.policy TRUE subsetting may create -neighbour observations. Note weights lists created without using glist argument nb2listw may subsetted. na.pass permitted meaningless permutation test. spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption() return_boot return object class boot equivalent permutation bootstrap rather object class htest","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lee.mc.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Permutation test for Lee's L statistic — lee.mc","text":"list class htest mc.sim containing following components: statistic value observed Lee's L. parameter rank observed Lee's L. p.value pseudo p-value test. alternative character string describing alternative hypothesis. method character string giving method used. data.name character string giving name(s) data, number simulations. res nsim simulated values statistic, final value observed statistic","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lee.mc.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Permutation test for Lee's L statistic — lee.mc","text":"Lee (2001). Developing bivariate spatial association measure: integration Pearson's r Moran's . J Geograph Syst  3: 369-385","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lee.mc.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Permutation test for Lee's L statistic — lee.mc","text":"Roger Bivand, Virgilio Gómez-Rubio Virgilio.Gomez@uclm.es","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/lee.mc.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Permutation test for Lee's L statistic — lee.mc","text":"","code":"data(boston, package=\"spData\") lw<-nb2listw(boston.soi)  x<-boston.c$CMEDV y<-boston.c$CRIM  lee.mc(x, y, nsim=99, lw, zero.policy=TRUE, alternative=\"two.sided\") #>  #> \tMonte-Carlo simulation of Lee's L #>  #> data:  x ,  y  #> weights: lw   #> number of simulations + 1: 100  #>  #> statistic = -0.3263, observed rank = 1, p-value = 0.02 #> alternative hypothesis: two.sided #>   #Test with missing values x[1:5]<-NA y[3:7]<-NA  lee.mc(x, y, nsim=99, lw, zero.policy=TRUE, alternative=\"two.sided\",     na.action=na.omit) #>  #> \tMonte-Carlo simulation of Lee's L #>  #> data:  x ,  y  #> weights: lw  #> omitted: 1, 2, 3, 4, 5, 6, 7  #> number of simulations + 1: 100  #>  #> statistic = -0.32447, observed rank = 1, p-value = 0.02 #> alternative hypothesis: two.sided #>"},{"path":"https://r-spatial.github.io/spdep/reference/lee.test.html","id":null,"dir":"Reference","previous_headings":"","what":"Lee's L test for spatial autocorrelation — lee.test","title":"Lee's L test for spatial autocorrelation — lee.test","text":"Lee's L test spatial autocorrelation using spatial weights matrix weights list form. assumptions underlying test sensitive form graph neighbour relationships factors, results may checked lee.mc permutations.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lee.test.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Lee's L test for spatial autocorrelation — lee.test","text":"","code":"lee.test(x, y, listw, zero.policy=attr(listw, \"zero.policy\"),  alternative=\"greater\", na.action=na.fail, spChk=NULL)"},{"path":"https://r-spatial.github.io/spdep/reference/lee.test.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Lee's L test for spatial autocorrelation — lee.test","text":"x numeric vector length neighbours list listw y numeric vector length neighbours list listw listw listw object created example nb2listw  zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA alternative character string specifying alternative hypothesis, must one greater (default), less two.sided.  na.action function (default na.fail), can also na.omit na.exclude - cases weights list subsetted remove NAs data. may necessary set zero.policy TRUE subsetting may create -neighbour observations. Note weights lists created without using glist argument nb2listw may subsetted. na.pass used, zero substituted NA values calculating spatial lag spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption()","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lee.test.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Lee's L test for spatial autocorrelation — lee.test","text":"list class htest containing following components: statistic value standard deviate Lee's L. p.value p-value test. estimate value observed Lee's L, expectation variance method assumption. alternative character string describing alternative hypothesis. method character string giving assumption used calculating standard deviate. data.name character string giving name(s) data.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lee.test.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Lee's L test for spatial autocorrelation — lee.test","text":"See Lee (2004) details asymptotic expectation variance Lee's L computed. particular, check Lee (2004), table 1, page 1690. test may fail large datasets computation asymptotic expectation variance requires use dense matrices.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lee.test.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Lee's L test for spatial autocorrelation — lee.test","text":"Lee (2004). generalized significance testing method global measures spatial association: extension Mantel test.  Environment Planning 2004, volume 36, pages 1687 - 1703","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lee.test.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Lee's L test for spatial autocorrelation — lee.test","text":"Roger Bivand Virgilio Gómez-Rubio Virgilio.Gomez@uclm.es","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/lee.test.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Lee's L test for spatial autocorrelation — lee.test","text":"","code":"data(oldcol) col.W <- nb2listw(COL.nb, style=\"W\") crime <- COL.OLD$CRIME  lee.test(crime, crime, col.W, zero.policy=TRUE) #>  #> \tLee's L statistic randomisation #>  #> data:  crime ,  crime  #> weights: col.W   #>  #> Lee's L statistic standard deviate = 5.2343, p-value = 8.279e-08 #> alternative hypothesis: greater #> sample estimates: #> Lee's L statistic       Expectation          Variance  #>       0.547064219       0.239417989       0.003454459  #>   #Test with missing values x<-crime y<-crime x[1:5]<-NA y[3:7]<-NA  lee.test(x, y, col.W, zero.policy=TRUE, na.action=na.omit) #>  #> \tLee's L statistic randomisation #>  #> data:  x ,  y  #> weights: col.W  #> omitted: 1, 2, 3, 4, 5, 6, 7  #>  #> Lee's L statistic standard deviate = 6.6873, p-value = 1.137e-11 #> alternative hypothesis: greater #> sample estimates: #> Lee's L statistic       Expectation          Variance  #>       0.706469726       0.260143244       0.004454563  #>  #  lee.test(x, y, col.W, zero.policy=TRUE)#Stops with an error    data(boston, package=\"spData\") lw<-nb2listw(boston.soi)  x<-boston.c$CMEDV y<-boston.c$CRIM  lee.test(x, y, lw, zero.policy=TRUE, alternative=\"less\") #>  #> \tLee's L statistic randomisation #>  #> data:  x ,  y  #> weights: lw   #>  #> Lee's L statistic standard deviate = -11.54, p-value < 2.2e-16 #> alternative hypothesis: less #> sample estimates: #> Lee's L statistic       Expectation          Variance  #>      -0.326297206      -0.105040316       0.000367637  #>   #Test with missing values x[1:5]<-NA y[3:7]<-NA  lee.test(x, y, lw, zero.policy=TRUE, alternative=\"less\", na.action=na.omit) #>  #> \tLee's L statistic randomisation #>  #> data:  x ,  y  #> weights: lw  #> omitted: 1, 2, 3, 4, 5, 6, 7  #>  #> Lee's L statistic standard deviate = -11.284, p-value < 2.2e-16 #> alternative hypothesis: less #> sample estimates: #> Lee's L statistic       Expectation          Variance  #>     -0.3244748280     -0.1053154332      0.0003772109  #>"},{"path":"https://r-spatial.github.io/spdep/reference/licd_multi.html","id":null,"dir":"Reference","previous_headings":"","what":"Local Indicators for Categorical Data — licd_multi","title":"Local Indicators for Categorical Data — licd_multi","text":"Local indicators categorical data combine measure local composition window given per-observation set neighbouring observations, local multi-category joincount test simplified neighbours different categories compared focal observation","code":""},{"path":"https://r-spatial.github.io/spdep/reference/licd_multi.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Local Indicators for Categorical Data — licd_multi","text":"","code":"licd_multi(fx, listw, zero.policy = attr(listw, \"zero.policy\"), adjust.n = TRUE,  nsim = 0L, iseed = NULL, no_repeat_in_row = FALSE, control = list())"},{"path":"https://r-spatial.github.io/spdep/reference/licd_multi.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Local Indicators for Categorical Data — licd_multi","text":"fx factor two categories, length neighbours weights objects listw listw listw object created example nb2listw zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA adjust.n default TRUE, FALSE number observations adjusted -neighbour observations, TRUE, number observations adjusted nsim default 0, number conditonal permutation simulations iseed default NULL, used set seed; output reproducible count CPU cores across computation distributed no_repeat_in_row default FALSE, TRUE, sample conditionally row without replacements avoid duplicate values, https://github.com/r-spatial/spdep/issues/124 control comp_binary=TRUE default TRUE, ignoring weights styles binary composition measures, binomial_punif_alternative=\"greater\", jcm_same_punif_alternative=\"less\", jcm_diff_punif_alternative=\"greater\", rank_ties.method=\"min\" default \"min\", na.last=\"keep\" leading rank NA returned observed joincount variance non-positive; TRUE joincount NAs ranked highest using rank, others see ?rank, check_reps=FALSE, unique_ceiling=1/3 used check_reps TRUE, check_reps=FALSE TRUE, check report many unique draws made among nsim draws, number unique draws less unique_ceiling, compute measures unique draws copy replicated draws, pysal_rank=FALSE use rank rank_ties.method na.last; TRUE, use pysal-style ranking find rank sum(sims <= obs, na.rm=TRUE)+1 pysal_sim_obs \"GE\", sum(sims < obs, na.rm=TRUE)+1 count observed greater \"GT\" simulated values, pysal_sim_obs=\"GT\" may also \"GE\", xtras=FALSE TRUE return calculated compostion values BW chi-squared, k-colour chi-squared, BW Anscombe","code":""},{"path":"https://r-spatial.github.io/spdep/reference/licd_multi.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Local Indicators for Categorical Data — licd_multi","text":"original code may found doi:10.5281/zenodo.4283766","code":""},{"path":"https://r-spatial.github.io/spdep/reference/licd_multi.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Local Indicators for Categorical Data — licd_multi","text":"local_comp data.frame object LICD local composition columns: ID,     category_i, count_like_i, prop_i, count_nbs_i, pbinom_like_BW,     pbinom_unlike_BW, pbinom_unlike_BW_alt, chi_BW_i, chi_K_i, anscombe_BW local_config data.frame object LICD local configuration columns: ID, jcm_chi_obs, jcm_count_BB_obs, jcm_count_BW_obs, jcm_count_WW_obs, pval_jcm_obs_BB, pval_jcm_obs_WW, pval_jcm_obs_BW local_comp_sim data.frame object permutation-based LICD local composition columns: ID, pbinom_like_BW, pbinom_unlike_BW, pbinom_unlike_BW_alt, rank_sim_chi_BW, rank_sim_chi_K, rank_sim_anscombe local_config_sim data.frame object permutation-based LICD local configuration columns: ID, jcm_chi_sim_rank, pval_jcm_obs_BB, pval_jcm_obs_BW, pval_jcm_obs_WW","code":""},{"path":"https://r-spatial.github.io/spdep/reference/licd_multi.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Local Indicators for Categorical Data — licd_multi","text":"Cliff, . D., Ord, J. K. 1981 Spatial processes, Pion, p. 20; Upton, G., Fingleton, B. 1985 Spatial data analysis example: point pattern qualitative data, Wiley, pp. 158–170; Boots, B., 2003. Developing local measures spatial association categorical data. Journal Geographical Systems 5, 139–160; Boots, B., 2006. Local configuration measures categorical spatial data: binary regular lattices. Journal Geographical Systems 8 (1), 1–24; Pietrzak, M.B., Wilk, J., Kossowski, T., Bivand, R.S., 2014. application local indicators categorical data (LICD) spatial analysis economic development. Comparative Economic Research 17 (4), 203–220 doi:10.2478/cer-2014-0041 ; Bivand, R.S., Wilk, J., Kossowski, T., 2017. Spatial association population pyramids across Europe: application symbolic data, cluster analysis join-count tests. Spatial Statistics 21 (B), 339–361 doi:10.1016/j.spasta.2017.03.003 ; Francesco Carrer, Tomasz M. Kossowski, Justyna Wilk, Michał B. Pietrzak, Roger S. Bivand, application Local Indicators Categorical Data (LICD) explore spatial dependence archaeological spaces, Journal Archaeological Science, 126, 2021, doi:10.1016/j.jas.2020.105306","code":""},{"path":"https://r-spatial.github.io/spdep/reference/licd_multi.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Local Indicators for Categorical Data — licd_multi","text":"Roger Bivand Roger.Bivand@nhh.based earlier code Tomasz M. Kossowski, Justyna Wilk Michał B. Pietrzak","code":""},{"path":"https://r-spatial.github.io/spdep/reference/licd_multi.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Local Indicators for Categorical Data — licd_multi","text":"order increase numbers neighbours using nblag nblag_cumul advisable; use binary weights advised case used composition measure","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/licd_multi.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Local Indicators for Categorical Data — licd_multi","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) HICRIME <- cut(columbus$CRIME, breaks=c(0,35,80), labels=c(\"low\",\"high\")) (nb <- poly2nb(columbus)) #> Neighbour list object: #> Number of regions: 49  #> Number of nonzero links: 236  #> Percentage nonzero weights: 9.829238  #> Average number of links: 4.816327  lw <- nb2listw(nblag_cumul(nblag(nb, 2)), style=\"B\") obj <- licd_multi(HICRIME, lw) str(obj) #> List of 4 #>  $ local_comp      :'data.frame':\t49 obs. of  11 variables: #>   ..$ ID                  : int [1:49] 1 2 3 4 5 6 7 8 9 10 ... #>   ..$ category_i          : num [1:49] 1 1 1 1 2 1 1 2 1 1 ... #>   ..$ count_like_i        : num [1:49] 4 4 6 7 12 7 2 8 10 8 ... #>   ..$ prop_i              : num [1:49] 0.51 0.51 0.51 0.51 0.49 ... #>   ..$ count_nbs_i         : num [1:49] 5 6 11 14 22 14 11 14 25 17 ... #>   ..$ pbinom_like_BW      : num [1:49] 0.965 0.881 0.702 0.575 0.769 ... #>   ..$ pbinom_unlike_BW    : num [1:49] 0.0346 0.1192 0.2979 0.4255 0.2313 ... #>   ..$ pbinom_unlike_BW_alt: num [1:49] 0.201 0.363 0.528 0.634 0.379 ... #>   ..$ chi_BW_i            : num [1:49] NA NA NA NA NA NA NA NA NA NA ... #>   ..$ chi_K_i             : num [1:49] NA NA NA NA NA NA NA NA NA NA ... #>   ..$ anscombe_BW         : num [1:49] NA NA NA NA NA NA NA NA NA NA ... #>  $ local_config    :'data.frame':\t49 obs. of  8 variables: #>   ..$ ID              : int [1:49] 1 2 3 4 5 6 7 8 9 10 ... #>   ..$ jcm_chi_obs     : num [1:49] 0 0.0625 0.625 2.7468 14.1889 ... #>   ..$ jcm_count_BB_obs: num [1:49] 6 6 11 12 55 15 1 27 30 25 ... #>   ..$ jcm_count_BW_obs: num [1:49] 4 7 23 31 50 36 15 31 73 53 ... #>   ..$ jcm_count_WW_obs: num [1:49] 0 1 10 20 21 19 32 9 61 24 ... #>   ..$ pval_jcm_obs_BB : num [1:49] 1 0.207108 0.70232 0.820405 0.000214 ... #>   ..$ pval_jcm_obs_WW : num [1:49] 1 0.3946 0.0981 0.0243 0.7839 ... #>   ..$ pval_jcm_obs_BW : num [1:49] 1.00 1.75e-01 2.08e-01 5.10e-02 3.52e-06 ... #>  $ local_comp_sim  : NULL #>  $ local_config_sim: NULL #>  - attr(*, \"timings\")=List of 3 #>   ..$ set_up        : 'proc_time' Named num [1:5] 0.001 0 0 0 0 #>   .. ..- attr(*, \"names\")= chr [1:5] \"user.self\" \"sys.self\" \"elapsed\" \"user.child\" ... #>   ..$ processing    : 'proc_time' Named num [1:5] 0.109 0 0.11 0 0 #>   .. ..- attr(*, \"names\")= chr [1:5] \"user.self\" \"sys.self\" \"elapsed\" \"user.child\" ... #>   ..$ postprocessing: 'proc_time' Named num [1:5] 0.001 0 0.001 0 0 #>   .. ..- attr(*, \"names\")= chr [1:5] \"user.self\" \"sys.self\" \"elapsed\" \"user.child\" ... #>  - attr(*, \"out\")= num [1:49, 1:35] 1 1 1 1 2 1 1 2 1 1 ... #>   ..- attr(*, \"ncpus\")= int 1 #>   ..- attr(*, \"dimnames\")=List of 2 #>   .. ..$ : NULL #>   .. ..$ : chr [1:35] \"category_i\" \"count_like_i\" \"prop_i\" \"count_nbs_i\" ... #>  - attr(*, \"ncpus\")= int 1 #>  - attr(*, \"nsim\")= int 0 #>  - attr(*, \"con\")=List of 11 #>   ..$ comp_binary               : logi TRUE #>   ..$ binomial_punif_alternative: chr \"greater\" #>   ..$ jcm_same_punif_alternative: chr \"less\" #>   ..$ jcm_diff_punif_alternative: chr \"greater\" #>   ..$ rank_ties.method          : chr \"min\" #>   ..$ unique_ceiling            : num 0.333 #>   ..$ check_reps                : logi FALSE #>   ..$ pysal_rank                : logi FALSE #>   ..$ pysal_sim_obs             : chr \"GT\" #>   ..$ na.last                   : chr \"keep\" #>   ..$ xtras                     : logi FALSE #>  - attr(*, \"class\")= chr [1:2] \"licd\" \"list\" h_obj <- hotspot(obj) str(h_obj) #> List of 9 #>  $ ID              : int [1:49] 1 2 3 4 5 6 7 8 9 10 ... #>  $ local_comp      : Factor w/ 2 levels \"Cluster\",\"Dispersed\": 2 2 2 2 2 2 2 2 2 2 ... #>  $ local_comp_sim  : NULL #>  $ local_config    : Factor w/ 3 levels \"Cluster\",\"Dispersed\",..: 3 3 3 3 2 3 3 2 3 3 ... #>  $ local_config_sim: NULL #>  $ both            : Factor w/ 6 levels \"Cluster.Cluster\",..: 6 6 6 6 4 6 6 4 6 6 ... #>  $ both_sim        : NULL #>  $ both_recode     : Factor w/ 4 levels \"Clump\",\"Cluster\",..: 4 4 4 4 3 4 4 3 4 4 ... #>  $ both_recode_sim : NULL table(h_obj$both_recode) #>  #>      Clump    Cluster  Dispersed No cluster  #>          8          3         11         27  columbus$both <- h_obj$both_recode plot(columbus[, \"both\"])  GDAL37 <- as.numeric_version(unname(sf_extSoftVersion()[\"GDAL\"])) >= \"3.7.0\" file <- \"etc/shapes/GB_2024_southcoast_50m.gpkg.zip\" zipfile <- system.file(file, package=\"spdep\") if (GDAL37) {     sc50m <- st_read(zipfile) } else {     td <- tempdir()     bn <- sub(\".zip\", \"\", basename(file), fixed=TRUE)     target <- unzip(zipfile, files=bn, exdir=td)     sc50m <- st_read(target) } #> Reading layer `GB_2024_southcoast_50m' from data source  #>   `/tmp/RtmpXVTJuL/temp_libpath3b356d487bad39/spdep/etc/shapes/GB_2024_southcoast_50m.gpkg.zip'  #>   using driver `GPKG' #> Simple feature collection with 119 features and 19 fields #> Geometry type: MULTIPOLYGON #> Dimension:     XY #> Bounding box:  xmin: 82643.12 ymin: 5342.9 xmax: 640301.6 ymax: 187226.2 #> Projected CRS: OSGB36 / British National Grid sc50m$Winner <- factor(sc50m$Winner, levels=c(\"Con\", \"Green\", \"Lab\", \"LD\")) plot(sc50m[,\"Winner\"], pal=c(\"#2297E6\", \"#61D04F\", \"#DF536B\", \"#F5C710\"))  nb_sc_50m <- poly2nb(sc50m, row.names=as.character(sc50m$Constituency)) #> Warning: neighbour object has 2 sub-graphs; #> if this sub-graph count seems unexpected, try increasing the snap argument. sub2 <- attr(nb_sc_50m, \"region.id\")[attr(nb_sc_50m, \"ncomp\")$comp.id == 2L] iowe <- match(sub2[1], attr(nb_sc_50m, \"region.id\")) diowe <- c(st_distance(sc50m[iowe,], sc50m)) meet_criterion <- sum(diowe <= units::set_units(5000, \"m\")) cands <- attr(nb_sc_50m, \"region.id\")[order(diowe)[1:meet_criterion]] nb_sc_50m_iowe <- addlinks1(nb_sc_50m, from = cands[1],  to = cands[3:meet_criterion]) ioww <- match(sub2[2], attr(nb_sc_50m, \"region.id\")) dioww <- c(st_distance(sc50m[ioww,], sc50m)) meet_criterion <- sum(dioww <= units::set_units(5000, \"m\")) cands <- attr(nb_sc_50m, \"region.id\")[order(dioww)[1:meet_criterion]] nb_sc_50m_iow <- addlinks1(nb_sc_50m_iowe, from = cands[2], to = cands[3:meet_criterion]) nb_sc_1_2 <- nblag_cumul(nblag(nb_sc_50m_iow, 2)) lw <- nb2listw(nb_sc_1_2, style=\"B\") licd_obj <- licd_multi(sc50m$Winner, lw) h_obj <- hotspot(licd_obj) sc50m$both <- h_obj$both_recode plot(sc50m[, \"both\"])  ljc <- local_joincount_uni(factor(sc50m$Winner == \"LD\"), chosen=\"TRUE\", lw) sc50m$LD_pv <- ljc[, 2] plot(sc50m[, \"LD_pv\"], breaks=c(0, 0.025, 0.05, 0.1, 0.5, 1))"},{"path":"https://r-spatial.github.io/spdep/reference/listw2sn.html","id":null,"dir":"Reference","previous_headings":"","what":"Spatial neighbour sparse representation — listw2sn","title":"Spatial neighbour sparse representation — listw2sn","text":"function makes \"spatial neighbour\" object representation (similar S-PLUS spatial statististics module representation \"listw\" spatial weights object. sn2listw() inverse function listw2sn(), creating \"listw\" object \"spatial neighbour\" object.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/listw2sn.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Spatial neighbour sparse representation — listw2sn","text":"","code":"listw2sn(listw) sn2listw(sn, style = NULL, zero.policy = NULL, from_mat2listw=FALSE)"},{"path":"https://r-spatial.github.io/spdep/reference/listw2sn.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Spatial neighbour sparse representation — listw2sn","text":"listw listw object example nb2listw sn spatial.neighbour object style default NULL, missing, set \"M\" warning given; \"M\", passed nb2listw re-build object zero.policy default NULL, use global option value; FALSE stop error empty neighbour sets, TRUE permit weights list formed zero-length weights vectors from_mat2listw default FALSE, set TRUE called mat2listw","code":""},{"path":"https://r-spatial.github.io/spdep/reference/listw2sn.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Spatial neighbour sparse representation — listw2sn","text":"listw2sn()returns data frame three columns, class spatial.neighbour: region number id start link (S-PLUS row.id) region number id end link (S-PLUS col.id) weights weight link","code":""},{"path":"https://r-spatial.github.io/spdep/reference/listw2sn.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Spatial neighbour sparse representation — listw2sn","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/listw2sn.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Spatial neighbour sparse representation — listw2sn","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) col.gal.nb <- read.gal(system.file(\"weights/columbus.gal\", package=\"spData\")[1]) col.listw <- nb2listw(col.gal.nb) col.listw$neighbours[[1]] #> [1] 2 3 col.listw$weights[[1]] #> [1] 0.5 0.5 col.sn <- listw2sn(col.listw) str(col.sn) #> Classes ‘spatial.neighbour’ and 'data.frame':\t230 obs. of  3 variables: #>  $ from   : int  1 1 2 2 2 3 3 3 3 4 ... #>  $ to     : int  2 3 1 3 4 1 2 4 5 2 ... #>  $ weights: num  0.5 0.5 0.333 0.333 0.333 ... #>  - attr(*, \"n\")= int 49 #>  - attr(*, \"region.id\")= chr [1:49] \"1\" \"2\" \"3\" \"4\" ... #>  - attr(*, \"neighbours.attrs\")= chr [1:7] \"class\" \"region.id\" \"GeoDa\" \"gal\" ... #>  - attr(*, \"weights.attrs\")= chr [1:3] \"mode\" \"W\" \"comp\" #>  - attr(*, \"GeoDa\")=List of 2 #>   ..$ shpfile: chr NA #>   ..$ ind    : chr NA #>  - attr(*, \"listw.call\")= language nb2listw(neighbours = col.gal.nb)"},{"path":"https://r-spatial.github.io/spdep/reference/lm.RStests.html","id":null,"dir":"Reference","previous_headings":"","what":"Rao's score (a.k.a Lagrange Multiplier) diagnostics for spatial dependence in linear models — lm.LMtests","title":"Rao's score (a.k.a Lagrange Multiplier) diagnostics for spatial dependence in linear models — lm.LMtests","text":"function reports estimates tests chosen among five statistics testing spatial dependence linear models. statistics simple RS test error dependence (“RSerr”), simple RS test missing spatially lagged dependent variable (“RSlag”), variants adjusted presence (“adjRSerr” tests error dependence possible presence missing lagged dependent variable, “adjRSlag” way round), portmanteau test (“SARMA”, fact “RSerr” + “adjRSlag”). Note: spdep 1.3-2, tests re-named “RS” - Rao's score tests, rather “LM” - Lagrange multiplier tests match naming tests family SDM.RStests.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lm.RStests.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Rao's score (a.k.a Lagrange Multiplier) diagnostics for spatial dependence in linear models — lm.LMtests","text":"","code":"lm.RStests(model, listw, zero.policy=attr(listw, \"zero.policy\"), test=\"RSerr\",  spChk=NULL, naSubset=TRUE) lm.LMtests(model, listw, zero.policy=attr(listw, \"zero.policy\"), test=\"LMerr\",  spChk=NULL, naSubset=TRUE) # S3 method for class 'RStestlist' print(x, ...) # S3 method for class 'RStestlist' summary(object, p.adjust.method=\"none\", ...) # S3 method for class 'RStestlist.summary' print(x, digits=max(3, getOption(\"digits\") - 2), ...) <!-- %tracew(listw) -->"},{"path":"https://r-spatial.github.io/spdep/reference/lm.RStests.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Rao's score (a.k.a Lagrange Multiplier) diagnostics for spatial dependence in linear models — lm.LMtests","text":"model object class lm returned lm, optionally vector externally calculated residuals (run though na.omit NAs present) use \"RSerr\" chosen; weights offsets used lm object listw listw object created example nb2listw, expected row-standardised (W-style) zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA test character vector tests requested chosen RSerr, RSlag, adjRSerr, adjRSlag, SARMA; test=\"\" computes tests. spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption() naSubset default TRUE subset listw object omitted observations model object (change earlier behaviour, model$na.action component ignored, listw object subsetted hand) x, object object printed p.adjust.method character string specifying probability value adjustment (see p.adjust) multiple tests, default \"none\" digits minimum number significant digits used numbers ... printing arguments passed ","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lm.RStests.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Rao's score (a.k.a Lagrange Multiplier) diagnostics for spatial dependence in linear models — lm.LMtests","text":"two types dependence spatial lag \\(\\rho\\) spatial error \\(\\lambda\\): $$ \\mathbf{y} = \\mathbf{X \\beta} + \\rho \\mathbf{W_{(1)} y} + \\mathbf{u}, $$ $$ \\mathbf{u} = \\lambda \\mathbf{W_{(2)} u} + \\mathbf{e} $$ \\(\\mathbf{e}\\) well-behaved, uncorrelated error term. Tests missing spatially lagged dependent variable test \\(\\rho = 0\\), tests spatial autocorrelation error \\(\\mathbf{u}\\) test whether \\(\\lambda = 0\\). \\(\\mathbf{W}\\) spatial weights matrix; tests used identical.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lm.RStests.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Rao's score (a.k.a Lagrange Multiplier) diagnostics for spatial dependence in linear models — lm.LMtests","text":"list class RStestlist htest objects, : statistic value Rao's score (.k.Lagrange multiplier) test. parameter number degrees freedom p.value p-value test. method character string giving method used. data.name character string giving name(s) data.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lm.RStests.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Rao's score (a.k.a Lagrange Multiplier) diagnostics for spatial dependence in linear models — lm.LMtests","text":"Anselin, L. 1988 Spatial econometrics: methods models. (Dordrecht: Kluwer); Anselin, L., Bera, . K., Florax, R. Yoon, M. J. 1996 Simple diagnostic tests spatial dependence. Regional Science Urban Economics, 26, 77–104 doi:10.1016/0166-0462(95)02111-6 ; Malabika Koley (2024) Specification Testing General Nesting Spatial Model, https://sites.google.com/view/malabikakoley/research.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lm.RStests.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Rao's score (a.k.a Lagrange Multiplier) diagnostics for spatial dependence in linear models — lm.LMtests","text":"Roger Bivand Roger.Bivand@nhh.Andrew Bernat","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/lm.RStests.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Rao's score (a.k.a Lagrange Multiplier) diagnostics for spatial dependence in linear models — lm.LMtests","text":"","code":"data(oldcol) oldcrime.lm <- lm(CRIME ~ HOVAL + INC, data = COL.OLD) summary(oldcrime.lm) #>  #> Call: #> lm(formula = CRIME ~ HOVAL + INC, data = COL.OLD) #>  #> Residuals: #>     Min      1Q  Median      3Q     Max  #> -34.418  -6.388  -1.580   9.052  28.649  #>  #> Coefficients: #>             Estimate Std. Error t value Pr(>|t|)     #> (Intercept)  68.6190     4.7355  14.490  < 2e-16 *** #> HOVAL        -0.2739     0.1032  -2.654   0.0109 *   #> INC          -1.5973     0.3341  -4.780 1.83e-05 *** #> --- #> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 #>  #> Residual standard error: 11.43 on 46 degrees of freedom #> Multiple R-squared:  0.5524,\tAdjusted R-squared:  0.5329  #> F-statistic: 28.39 on 2 and 46 DF,  p-value: 9.341e-09 #>  lw <- nb2listw(COL.nb) res <- lm.RStests(oldcrime.lm, listw=lw, test=\"all\") summary(res) #> \tRao's score (a.k.a Lagrange multiplier) diagnostics for spatial #> \tdependence #> data:   #> model: lm(formula = CRIME ~ HOVAL + INC, data = COL.OLD) #> test weights: lw #>   #>          statistic parameter  p.value    #> RSerr     5.723131         1 0.016743 *  #> RSlag     9.363684         1 0.002213 ** #> adjRSerr  0.079495         1 0.777983    #> adjRSlag  3.720048         1 0.053763 .  #> SARMA     9.443178         2 0.008901 ** #> --- #> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 if (require(\"spatialreg\", quietly=TRUE)) {   oldcrime.slx <- lmSLX(CRIME ~ HOVAL + INC, data = COL.OLD, listw=lw)   summary(lm.RStests(oldcrime.slx, listw=lw, test=c(\"adjRSerr\", \"adjRSlag\"))) } #> \tRao's score (a.k.a Lagrange multiplier) diagnostics for spatial #> \tdependence #> data:   #> model: lm(CRIME ~ HOVAL + INC + lag.HOVAL + lag.INC, data = COL.OLD, #> listw = lw) #> test weights: lw #>   #>              statistic parameter p.value #> GNM_adjRSerr   0.10933         1  0.7409 #> GNM_adjRSlag   0.61580         1  0.4326"},{"path":"https://r-spatial.github.io/spdep/reference/lm.morantest.exact.html","id":null,"dir":"Reference","previous_headings":"","what":"Exact global Moran's I test — lm.morantest.exact","title":"Exact global Moran's I test — lm.morantest.exact","text":"function implements Tiefelsdorf's exact global Moran's test.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lm.morantest.exact.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Exact global Moran's I test — lm.morantest.exact","text":"","code":"lm.morantest.exact(model, listw, zero.policy = attr(listw, \"zero.policy\"),  alternative = \"greater\", spChk = NULL, resfun = weighted.residuals,  zero.tol = 1e-07, Omega=NULL, save.M=NULL, save.U=NULL, useTP=FALSE,  truncErr=1e-6, zeroTreat=0.1) # S3 method for class 'moranex' print(x, ...)"},{"path":"https://r-spatial.github.io/spdep/reference/lm.morantest.exact.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Exact global Moran's I test — lm.morantest.exact","text":"model object class lm returned lm; weights may specified lm fit, offsets used listw listw object created example nb2listw zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA alternative character string specifying alternative hypothesis, must one greater (default), less two.sided. spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption() resfun default: weighted.residuals; function used extract residuals lm object, may residuals, weighted.residuals, rstandard, rstudent zero.tol tolerance used find eigenvalues close absolute zero Omega SAR process matrix may passed test alternative hypothesis, example Omega <- invIrW(listw, rho=0.1); Omega <- tcrossprod(Omega), chol() taken internally save.M return full M matrix use spdep:::exactMoranAlt save.U return full U matrix use spdep:::exactMoranAlt useTP default FALSE, TRUE, use truncation point integration rather upper=Inf, see Tiefelsdorf (2000), eq. 6.7, p.69 truncErr useTP=TRUE, pass truncation error truncation point function zeroTreat useTP=TRUE, pass zero adjustment truncation point function x moranex object ... arguments passed ","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lm.morantest.exact.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Exact global Moran's I test — lm.morantest.exact","text":"list class moranex following components: statistic value exact standard deviate global Moran's . p.value p-value test. estimate value observed global Moran's . method character string giving method used. alternative character string describing alternative hypothesis. gamma eigenvalues (excluding zero values) oType usually set \"E\" data.name character string giving name(s) data. df degrees freedom","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lm.morantest.exact.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Exact global Moran's I test — lm.morantest.exact","text":"Markus Reder Roger Bivand","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lm.morantest.exact.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Exact global Moran's I test — lm.morantest.exact","text":"Roger Bivand, Werner G. Müller Markus Reder (2009) \"Power calculations global local Moran's .\" Computational Statistics & Data Analysis 53, 2859-2872.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/lm.morantest.exact.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Exact global Moran's I test — lm.morantest.exact","text":"","code":"eire <- st_read(system.file(\"shapes/eire.gpkg\", package=\"spData\")[1]) #> Reading layer `eire' from data source  #>   `/home/rsb/lib/r_libs/spData/shapes/eire.gpkg' using driver `GPKG' #> Simple feature collection with 26 features and 10 fields #> Geometry type: MULTIPOLYGON #> Dimension:     XY #> Bounding box:  xmin: -4.12 ymin: 5768 xmax: 300.82 ymax: 6119.25 #> Projected CRS: Undefined Cartesian SRS with unknown unit row.names(eire) <- as.character(eire$names) eire.nb <- poly2nb(eire) e.lm <- lm(OWNCONS ~ ROADACC, data=eire) lm.morantest(e.lm, nb2listw(eire.nb)) #>  #> \tGlobal Moran I for regression residuals #>  #> data:   #> model: lm(formula = OWNCONS ~ ROADACC, data = eire) #> weights: nb2listw(eire.nb) #>  #> Moran I statistic standard deviate = 3.2575, p-value = 0.0005619 #> alternative hypothesis: greater #> sample estimates: #> Observed Moran I      Expectation         Variance  #>       0.33660565      -0.05877741       0.01473183  #>  lm.morantest.sad(e.lm, nb2listw(eire.nb)) #>  #> \tSaddlepoint approximation for global Moran's I (Barndorff-Nielsen #> \tformula) #>  #> data:   #> model:lm(formula = OWNCONS ~ ROADACC, data = eire) #> weights: nb2listw(eire.nb) #>  #> Saddlepoint approximation = 2.9395, p-value = 0.001644 #> alternative hypothesis: greater #> sample estimates: #> Observed Moran I  #>        0.3366057  #>  lm.morantest.exact(e.lm, nb2listw(eire.nb)) #>  #> \tGlobal Moran I statistic with exact p-value #>  #> data:   #> model:lm(formula = OWNCONS ~ ROADACC, data = eire) #> weights: nb2listw(eire.nb) #>  #> Exact standard deviate = 2.9316, p-value = 0.001686 #> alternative hypothesis: greater #> sample estimates: #> [1] 0.3366057 #>  lm.morantest.exact(e.lm, nb2listw(eire.nb), useTP=TRUE) #>  #> \tGlobal Moran I statistic with exact p-value #>  #> data:   #> model:lm(formula = OWNCONS ~ ROADACC, data = eire) #> weights: nb2listw(eire.nb) #>  #> Exact standard deviate = 2.9315, p-value = 0.001686 #> alternative hypothesis: greater #> sample estimates: #> [1] 0.3366057 #>"},{"path":"https://r-spatial.github.io/spdep/reference/lm.morantest.html","id":null,"dir":"Reference","previous_headings":"","what":"Moran's I test for residual spatial autocorrelation — lm.morantest","title":"Moran's I test for residual spatial autocorrelation — lm.morantest","text":"Moran's test spatial autocorrelation residuals estimated linear model (lm()).","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lm.morantest.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Moran's I test for residual spatial autocorrelation — lm.morantest","text":"","code":"lm.morantest(model, listw, zero.policy=attr(listw, \"zero.policy\"),  alternative = \"greater\", spChk=NULL, resfun=weighted.residuals, naSubset=TRUE)"},{"path":"https://r-spatial.github.io/spdep/reference/lm.morantest.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Moran's I test for residual spatial autocorrelation — lm.morantest","text":"model object class lm returned lm; weights may specified lm fit, offsets used listw listw object created example nb2listw zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA alternative character string specifying alternative hypothesis, must one \"greater\" (default), \"less\" \"two.sided\". spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption() resfun default: weighted.residuals; function used extract residuals lm object, may residuals, weighted.residuals, rstandard, rstudent naSubset default TRUE subset listw object omitted observations model object (change earlier behaviour, model$na.action component ignored, listw object subsetted hand)","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lm.morantest.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Moran's I test for residual spatial autocorrelation — lm.morantest","text":"list class htest containing following components: statistic value standard deviate Moran's . p.value p-value test. estimate value observed Moran's , expectation variance method assumption. alternative character string describing alternative hypothesis. method character string giving method used. data.name character string giving name(s) data.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lm.morantest.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Moran's I test for residual spatial autocorrelation — lm.morantest","text":"Cliff, . D., Ord, J. K. 1981 Spatial processes, Pion, p. 203,","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lm.morantest.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Moran's I test for residual spatial autocorrelation — lm.morantest","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/lm.morantest.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Moran's I test for residual spatial autocorrelation — lm.morantest","text":"","code":"data(oldcol) oldcrime1.lm <- lm(CRIME ~ 1, data = COL.OLD) oldcrime.lm <- lm(CRIME ~ HOVAL + INC, data = COL.OLD) lm.morantest(oldcrime.lm, nb2listw(COL.nb, style=\"W\")) #>  #> \tGlobal Moran I for regression residuals #>  #> data:   #> model: lm(formula = CRIME ~ HOVAL + INC, data = COL.OLD) #> weights: nb2listw(COL.nb, style = \"W\") #>  #> Moran I statistic standard deviate = 2.9539, p-value = 0.001569 #> alternative hypothesis: greater #> sample estimates: #> Observed Moran I      Expectation         Variance  #>      0.235638354     -0.033302866      0.008289408  #>  lm.LMtests(oldcrime.lm, nb2listw(COL.nb, style=\"W\")) #> Please update scripts to use lm.RStests in place of lm.LMtests #>  #> \tRao's score (a.k.a Lagrange multiplier) diagnostics for spatial #> \tdependence #>  #> data:   #> model: lm(formula = CRIME ~ HOVAL + INC, data = COL.OLD) #> test weights: listw #>  #> RSerr = 5.7231, df = 1, p-value = 0.01674 #>  lm.morantest(oldcrime.lm, nb2listw(COL.nb, style=\"S\")) #>  #> \tGlobal Moran I for regression residuals #>  #> data:   #> model: lm(formula = CRIME ~ HOVAL + INC, data = COL.OLD) #> weights: nb2listw(COL.nb, style = \"S\") #>  #> Moran I statistic standard deviate = 3.1745, p-value = 0.0007504 #> alternative hypothesis: greater #> sample estimates: #> Observed Moran I      Expectation         Variance  #>      0.239317561     -0.033431740      0.007381982  #>  lm.morantest(oldcrime1.lm, nb2listw(COL.nb, style=\"W\")) #>  #> \tGlobal Moran I for regression residuals #>  #> data:   #> model: lm(formula = CRIME ~ 1, data = COL.OLD) #> weights: nb2listw(COL.nb, style = \"W\") #>  #> Moran I statistic standard deviate = 5.6754, p-value = 6.92e-09 #> alternative hypothesis: greater #> sample estimates: #> Observed Moran I      Expectation         Variance  #>      0.510951264     -0.020833333      0.008779831  #>  moran.test(COL.OLD$CRIME, nb2listw(COL.nb, style=\"W\"),  randomisation=FALSE) #>  #> \tMoran I test under normality #>  #> data:  COL.OLD$CRIME   #> weights: nb2listw(COL.nb, style = \"W\")     #>  #> Moran I statistic standard deviate = 5.6754, p-value = 6.92e-09 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic       Expectation          Variance  #>       0.510951264      -0.020833333       0.008779831  #>  oldcrime.wlm <- lm(CRIME ~ HOVAL + INC, data = COL.OLD,  weights = I(1/AREA_PL)) lm.morantest(oldcrime.wlm, nb2listw(COL.nb, style=\"W\"),  resfun=weighted.residuals) #>  #> \tGlobal Moran I for regression residuals #>  #> data:   #> model: lm(formula = CRIME ~ HOVAL + INC, data = COL.OLD, weights = #> I(1/AREA_PL)) #> weights: nb2listw(COL.nb, style = \"W\") #>  #> Moran I statistic standard deviate = 3.0141, p-value = 0.001289 #> alternative hypothesis: greater #> sample estimates: #> Observed Moran I      Expectation         Variance  #>      0.241298974     -0.032224366      0.008235091  #>  lm.morantest(oldcrime.wlm, nb2listw(COL.nb, style=\"W\"),  resfun=rstudent) #>  #> \tGlobal Moran I for regression residuals #>  #> data:   #> model: lm(formula = CRIME ~ HOVAL + INC, data = COL.OLD, weights = #> I(1/AREA_PL)) #> weights: nb2listw(COL.nb, style = \"W\") #>  #> Moran I statistic standard deviate = 2.822, p-value = 0.002387 #> alternative hypothesis: greater #> sample estimates: #> Observed Moran I      Expectation         Variance  #>      0.223860298     -0.032224366      0.008235091  #>"},{"path":"https://r-spatial.github.io/spdep/reference/lm.morantest.sad.html","id":null,"dir":"Reference","previous_headings":"","what":"Saddlepoint approximation of global Moran's I test — lm.morantest.sad","title":"Saddlepoint approximation of global Moran's I test — lm.morantest.sad","text":"function implements Tiefelsdorf's application Saddlepoint approximation global Moran's 's reference distribution.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lm.morantest.sad.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Saddlepoint approximation of global Moran's I test — lm.morantest.sad","text":"","code":"lm.morantest.sad(model, listw, zero.policy=attr(listw, \"zero.policy\"),   alternative=\"greater\", spChk=NULL, resfun=weighted.residuals,   tol=.Machine$double.eps^0.5, maxiter=1000, tol.bounds=0.0001,   zero.tol = 1e-07, Omega=NULL, save.M=NULL, save.U=NULL) # S3 method for class 'moransad' print(x, ...) # S3 method for class 'moransad' summary(object, ...) # S3 method for class 'summary.moransad' print(x, ...)"},{"path":"https://r-spatial.github.io/spdep/reference/lm.morantest.sad.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Saddlepoint approximation of global Moran's I test — lm.morantest.sad","text":"model object class lm returned lm; weights may specified lm fit, offsets used listw listw object created example nb2listw zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA alternative character string specifying alternative hypothesis, must one greater (default), less two.sided. spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption() resfun default: weighted.residuals; function used extract residuals lm object, may residuals, weighted.residuals, rstandard, rstudent tol desired accuracy (convergence tolerance) uniroot maxiter maximum number iterations uniroot tol.bounds offset bounds uniroot zero.tol tolerance used find eigenvalues close absolute zero Omega SAR process matrix may passed test alternative hypothesis, example Omega <- invIrW(listw, rho=0.1); Omega <- tcrossprod(Omega), chol() taken internally save.M return full M matrix use spdep:::exactMoranAlt save.U return full U matrix use spdep:::exactMoranAlt x object printed object object summarised ... arguments passed ","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lm.morantest.sad.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Saddlepoint approximation of global Moran's I test — lm.morantest.sad","text":"function involves finding eigenvalues n n matrix, numerically finding root Saddlepoint approximation, therefore used care n large.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lm.morantest.sad.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Saddlepoint approximation of global Moran's I test — lm.morantest.sad","text":"list class moransad following components: statistic value saddlepoint approximation  standard deviate global Moran's . p.value p-value test. estimate value observed global Moran's . alternative character string describing alternative hypothesis. method character string giving method used. data.name character string giving name(s) data. internal1 Saddlepoint omega, r u internal2 f.root, iter estim.prec uniroot df degrees freedom tau eigenvalues (excluding zero values)","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lm.morantest.sad.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Saddlepoint approximation of global Moran's I test — lm.morantest.sad","text":"Tiefelsdorf, M. 2002 Saddlepoint approximation Moran's local Moran's Ii reference distributions numerical evaluation. Geographical Analysis, 34, pp. 187–206; Bivand RS, Wong DWS 2018 Comparing implementations global local indicators spatial association. TEST, 27(3), 716–748 doi:10.1007/s11749-018-0599-x","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lm.morantest.sad.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Saddlepoint approximation of global Moran's I test — lm.morantest.sad","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/lm.morantest.sad.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Saddlepoint approximation of global Moran's I test — lm.morantest.sad","text":"","code":"eire <- st_read(system.file(\"shapes/eire.gpkg\", package=\"spData\")[1]) #> Reading layer `eire' from data source  #>   `/home/rsb/lib/r_libs/spData/shapes/eire.gpkg' using driver `GPKG' #> Simple feature collection with 26 features and 10 fields #> Geometry type: MULTIPOLYGON #> Dimension:     XY #> Bounding box:  xmin: -4.12 ymin: 5768 xmax: 300.82 ymax: 6119.25 #> Projected CRS: Undefined Cartesian SRS with unknown unit row.names(eire) <- as.character(eire$names) eire.nb <- poly2nb(eire) e.lm <- lm(OWNCONS ~ ROADACC, data=eire) lm.morantest(e.lm, nb2listw(eire.nb)) #>  #> \tGlobal Moran I for regression residuals #>  #> data:   #> model: lm(formula = OWNCONS ~ ROADACC, data = eire) #> weights: nb2listw(eire.nb) #>  #> Moran I statistic standard deviate = 3.2575, p-value = 0.0005619 #> alternative hypothesis: greater #> sample estimates: #> Observed Moran I      Expectation         Variance  #>       0.33660565      -0.05877741       0.01473183  #>  lm.morantest.sad(e.lm, nb2listw(eire.nb)) #>  #> \tSaddlepoint approximation for global Moran's I (Barndorff-Nielsen #> \tformula) #>  #> data:   #> model:lm(formula = OWNCONS ~ ROADACC, data = eire) #> weights: nb2listw(eire.nb) #>  #> Saddlepoint approximation = 2.9395, p-value = 0.001644 #> alternative hypothesis: greater #> sample estimates: #> Observed Moran I  #>        0.3366057  #>  summary(lm.morantest.sad(e.lm, nb2listw(eire.nb))) #>  #> \tSaddlepoint approximation for global Moran's I (Barndorff-Nielsen #> \tformula) #>  #> data:   #> model:lm(formula = OWNCONS ~ ROADACC, data = eire) #> weights: nb2listw(eire.nb) #>  #> Saddlepoint approximation = 2.9395, p-value = 0.001644 #> alternative hypothesis: greater #> sample estimates: #> Observed Moran I  #>        0.3366057  #>  #>  Expectation     Variance Std. deviate     Skewness     Kurtosis      Minimum  #>  -0.05877741   0.01473183   3.25753938   0.31336881   3.05047361  -0.67545810  #>      Maximum        omega        sad.r        sad.u  #>   0.89091555   0.76549075   2.77616585   4.36854629  #>      f.root        iter  estim.prec  #> 7.01314e-14 1.10000e+01          NA  e.wlm <- lm(OWNCONS ~ ROADACC, data=eire, weights=RETSALE) lm.morantest(e.wlm, nb2listw(eire.nb), resfun=rstudent) #>  #> \tGlobal Moran I for regression residuals #>  #> data:   #> model: lm(formula = OWNCONS ~ ROADACC, data = eire, weights = RETSALE) #> weights: nb2listw(eire.nb) #>  #> Moran I statistic standard deviate = 3.1385, p-value = 0.0008491 #> alternative hypothesis: greater #> sample estimates: #> Observed Moran I      Expectation         Variance  #>       0.34500329      -0.04049313       0.01508687  #>  lm.morantest.sad(e.wlm, nb2listw(eire.nb), resfun=rstudent) #>  #> \tSaddlepoint approximation for global Moran's I (Barndorff-Nielsen #> \tformula) #>  #> data:   #> model:lm(formula = OWNCONS ~ ROADACC, data = eire, weights = RETSALE) #> weights: nb2listw(eire.nb) #>  #> Saddlepoint approximation = 2.8708, p-value = 0.002047 #> alternative hypothesis: greater #> sample estimates: #> Observed Moran I  #>        0.3450033  #>"},{"path":"https://r-spatial.github.io/spdep/reference/localC.html","id":null,"dir":"Reference","previous_headings":"","what":"Compute Local Geary statistic — localC","title":"Compute Local Geary statistic — localC","text":"Local Geary local adaptation Geary's C statistic spatial autocorrelation. Local Geary uses squared differences measure dissimilarity unlike Local Moran. Low values Local Geary indicate positive spatial autocorrelation large refers negative spatial autocorrelation. Inference Local Geary based permutation approach compares observed value reference distribution spatial randomness. localC_perm() returns pseudo p-value. analytical p-value based number permutations used care.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localC.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Compute Local Geary statistic — localC","text":"","code":"localC(x, ..., zero.policy=NULL)  # Default S3 method localC(x, listw, ..., zero.policy=attr(listw, \"zero.policy\"))  # S3 method for class 'formula' localC(formula, data, listw, ..., zero.policy=attr(listw, \"zero.policy\"))  # S3 method for class 'list' localC(x, listw, ..., zero.policy=attr(listw, \"zero.policy\"))  # S3 method for class 'matrix' localC(x, listw, ..., zero.policy=attr(listw, \"zero.policy\"))  # S3 method for class 'data.frame' localC(x, listw, ..., zero.policy=attr(listw, \"zero.policy\"))  localC_perm(x, ..., zero.policy=NULL, iseed=NULL, no_repeat_in_row=FALSE)  # Default S3 method localC_perm(x, listw, nsim = 499, alternative = \"two.sided\", ...,  zero.policy=attr(listw, \"zero.policy\"), iseed=NULL, no_repeat_in_row=FALSE)  # S3 method for class 'formula' localC_perm(formula, data, listw, nsim = 499,  alternative = \"two.sided\", ..., zero.policy=attr(listw, \"zero.policy\"), iseed=NULL,  no_repeat_in_row=FALSE)"},{"path":"https://r-spatial.github.io/spdep/reference/localC.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Compute Local Geary statistic — localC","text":"x numeric vector, numeric matrix, list. See details . formula one-sided formula determining variables used. listw listw object created example nb2listw. data Used formula provided. matrix data frame containing variables formula formula. nsim number simulations used permutation test. alternative character defining alternative hypothesis. Must one \"two.sided\", \"less\" \"greater\". ... arguments passed methods. zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA. iseed default NULL, used set seed;output reproducible count CPU cores across computation distributed no_repeat_in_row default FALSE, TRUE, sample conditionally row without replacements avoid duplicate values, https://github.com/r-spatial/spdep/issues/124","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localC.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Compute Local Geary statistic — localC","text":"Local Geary can extended multivariate context. x numeric vector, univariate Local Geary calculated. calculate multivariate Local Moran provide either list matrix. x list, element must numeric vector length length neighbours listw. case x matrix number rows must length neighbours listw. required univariate context, standardized Local Geary calculated. multivariate Local Geary always standardized. univariate Local Geary calculated \\(c_i = \\sum_j w_{ij}(x_i - x_j)^2\\) multivariate Local Geary calculated \\(c_{k,} = \\sum_{v=1}^{k} c_{v,}\\) described Anselin (2019).","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localC.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Compute Local Geary statistic — localC","text":"numeric vector containing Local Geary statistic attribute pseudo-p localC_perm() used. pseudo-p 8 column matrix containing  E.Ci expectation Local Geary statistic based permutation sample Var.Ci variance Local Geary based permutation sample Z.Ci standard deviate Local Geary based permutation sample Pr() p-value Local Geary statistic using pnorm() using standard deviates based permutation sample means standard deviations Pr() Sim rank() punif() observed statistic rank [0, 1] p-values using alternative= Pr(folded) Sim simulation folded [0, 0.5] range ranked p-value (based https://github.com/pysal/esda/blob/4a63e0b5df1e754b17b5f1205b8cadcbecc5e061/esda/crand.py#L211-L213) Skewness output e1071::skewness() permutation samples underlying standard deviates Kurtosis output e1071::kurtosis() permutation samples underlying standard deviates","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localC.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Compute Local Geary statistic — localC","text":"Anselin, L. (1995), Local Indicators Spatial Association—LISA. Geographical Analysis, 27: 93-115. doi:10.1111/j.1538-4632.1995.tb00338.x Anselin, L. (2019), Local Indicator Multivariate Spatial Association: Extending Gearys c. Geogr Anal, 51: 133-150. doi:10.1111/gean.12164","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localC.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Compute Local Geary statistic — localC","text":"Josiah Parry josiah.parry@gmail.com Roger Bivand","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localC.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Compute Local Geary statistic — localC","text":"","code":"orig <- spData::africa.rook.nb listw <- nb2listw(orig) x <- spData::afcon$totcon  (A <- localC(x, listw)) #>  [1] 0.39025457 0.50460439 0.15303047 2.90814878 3.40006901 0.17103368 #>  [7] 0.29947832 0.72444806 2.30617282 5.70252541 2.23161263 0.17833029 #> [13] 0.18420002 0.18680408 0.37851643 0.11056720 0.14814835 0.17257920 #> [19] 0.03254150 0.18992772 0.08749322 3.71970760 0.09566918 0.26112918 #> [25] 0.09505331 2.99934478 1.17465032 1.64868780 0.87901004 0.05909537 #> [31] 2.54591475 3.85570655 2.99413462 0.96084992 0.80678832 1.56869350 #> [37] 0.86422915 0.38817470 0.23425755 1.26191610 1.34455327 1.80707481 listw1 <- nb2listw(droplinks(sym.attr.nb(orig), 3, sym=TRUE), zero.policy=TRUE) #> Warning: some observations have no neighbours #> Warning: neighbour object has 2 sub-graphs (A1 <- localC(x, listw1, zero.policy=FALSE)) #>  [1] 0.39025457 0.57491918         NA 2.90814878 3.40006901 0.17103368 #>  [7] 0.29947832 0.72444806 2.30617282 5.70252541 2.23161263 0.17833029 #> [13] 0.18420002 0.18680408 0.37851643 0.11056720 0.14814835 0.17257920 #> [19] 0.03254150 0.18992772 0.08749322 3.71970760 0.09566918 0.26112918 #> [25] 0.09505331 2.99934478 1.17465032 1.64868780 0.87901004 0.05909537 #> [31] 2.54591475 3.85570655 2.99413462 0.96084992 0.80678832 1.56869350 #> [37] 0.86422915 0.38817470 0.23425755 1.26191610 1.34455327 1.80707481 (A2 <- localC(x, listw1, zero.policy=TRUE)) #>  [1] 0.39025457 0.57491918 0.00000000 2.90814878 3.40006901 0.17103368 #>  [7] 0.29947832 0.72444806 2.30617282 5.70252541 2.23161263 0.17833029 #> [13] 0.18420002 0.18680408 0.37851643 0.11056720 0.14814835 0.17257920 #> [19] 0.03254150 0.18992772 0.08749322 3.71970760 0.09566918 0.26112918 #> [25] 0.09505331 2.99934478 1.17465032 1.64868780 0.87901004 0.05909537 #> [31] 2.54591475 3.85570655 2.99413462 0.96084992 0.80678832 1.56869350 #> [37] 0.86422915 0.38817470 0.23425755 1.26191610 1.34455327 1.80707481   if (FALSE) { # \\dontrun{ library(reticulate) use_python(\"/usr/bin/python\", required = TRUE) gp <- import(\"geopandas\") ps <- import(\"libpysal\") W <- listw2mat(listw) w <- ps$weights$full2W(W, rownames(W)) w$transform <- \"R\" esda <- import(\"esda\") lM <- esda$Moran_Local(x, w) all.equal(unname(localmoran(x, listw, mlvar=FALSE)[,1]), c(lM$Is)) # confirm x and w the same lC <- esda$Geary_Local(connectivity=w)$fit(scale(x)) # np$std missing ddof=1 n <- length(x) D0 <- spdep:::geary.intern((x - mean(x)) / sqrt(var(x)*(n-1)/n), listw, n=n) # lC components probably wrongly ordered https://github.com/pysal/esda/issues/192 o <- match(round(D0, 6), round(lC$localG, 6)) all.equal(c(lC$localG)[o], D0) # simulation order not retained lC$p_sim[o] attr(C, \"pseudo-p\")[,6] } # }"},{"path":"https://r-spatial.github.io/spdep/reference/localG.html","id":null,"dir":"Reference","previous_headings":"","what":"G and Gstar local spatial statistics — localG","title":"G and Gstar local spatial statistics — localG","text":"local spatial statistic G calculated zone based spatial weights object used. value returned Z-value, may used diagnostic tool. High positive values indicate posibility local cluster high values variable analysed, low relative values similar cluster low values. inference, Bonferroni-type test suggested references, tables critical values may found (see also details ).","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localG.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"G and Gstar local spatial statistics — localG","text":"","code":"localG(x, listw, zero.policy=attr(listw, \"zero.policy\"), spChk=NULL, GeoDa=FALSE,  alternative = \"two.sided\", return_internals=TRUE) localG_perm(x, listw, nsim=499, zero.policy=attr(listw, \"zero.policy\"), spChk=NULL,  alternative = \"two.sided\", iseed=NULL, fix_i_in_Gstar_permutations=TRUE,  no_repeat_in_row=FALSE)"},{"path":"https://r-spatial.github.io/spdep/reference/localG.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"G and Gstar local spatial statistics — localG","text":"x numeric vector length neighbours list listw listw listw object created example nb2listw zero.policy default NULL, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption() GeoDa default FALSE, TRUE, drop x values -neighbour self-neighbour observations summations nsim default 499, number conditonal permutation simulations alternative character string specifying alternative hypothesis, must one \"two.sided\" (default), \"greater\" \"less\". return_internals default TRUE, unused iseed default NULL, used set seed; output reproducible count CPU cores across computation distributed fix_i_in_Gstar_permutations default TRUE (fix x self permutations local G-star), set FALSE use pre-1.2-8 behaviour no_repeat_in_row default FALSE, TRUE, sample conditionally row without replacements avoid duplicate values, https://github.com/r-spatial/spdep/issues/124","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localG.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"G and Gstar local spatial statistics — localG","text":"neighbours member listw \"self.included\" attribute set TRUE, Gstar variant, including self-weight \\(w_{ii} > 0\\), calculated returned.  returned vector \"gstari\" attribute set TRUE.  Self-weights must included using include.self function converting neighbour list spatial weights list nb2listw shown example. critical values statistic assumptions given references 95th percentile n=1: 1.645, n=50: 3.083, n=100: 3.289, n=1000: 3.886.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localG.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"G and Gstar local spatial statistics — localG","text":"vector G Gstar standard deviate values, attributes \"gstari\" set TRUE FALSE, \"call\" set function call, class \"localG\". conditional permutation, returned value localG(), simulated standard deviate returned column \"StdDev.Gi\" attr(., \"internals\").","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localG.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"G and Gstar local spatial statistics — localG","text":"Conditional permutations added comparative purposes; permutations whole data vector omitting observation , 1.2-8 fixing observation neighbour local G-star.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localG.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"G and Gstar local spatial statistics — localG","text":"Ord, J. K. Getis, . 1995 Local spatial autocorrelation statistics: distributional issues application. Geographical Analysis, 27, 286–306; Getis, . Ord, J. K. 1996 Local spatial statistics: overview. P. Longley M. Batty (eds) Spatial analysis: modelling GIS environment (Cambridge: Geoinformation International), 261–277; Bivand RS, Wong DWS 2018 Comparing implementations global local indicators spatial association. TEST, 27(3), 716–748 doi:10.1007/s11749-018-0599-x","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localG.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"G and Gstar local spatial statistics — localG","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localG.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"G and Gstar local spatial statistics — localG","text":"","code":"data(getisord, package=\"spData\") # spData 0.3.2 changes x, y, xyz object names to go_x, go_y, go_xyz to # avoid putting these objects into the global environment via lazy loading if (exists(\"go_xyz\") && packageVersion(\"spData\") >= \"0.3.2\") {   xyz <- go_xyz   x <- go_x   y <- go_y } xycoords <- cbind(xyz$x, xyz$y) nb30 <- dnearneigh(xycoords, 0, 30) G30 <- localG(xyz$val, nb2listw(nb30, style=\"B\")) G30[length(xyz$val)-136] #> [1] 1.221979 set.seed(1) G30_sim <- localG_perm(xyz$val, nb2listw(nb30, style=\"B\")) G30_sim[length(xyz$val)-136] #> [1] 1.221979 nb60 <- dnearneigh(xycoords, 0, 60) G60 <- localG(xyz$val, nb2listw(nb60, style=\"B\")) G60[length(xyz$val)-136] #> [1] 1.748098 nb90 <- dnearneigh(xycoords, 0, 90) G90 <- localG(xyz$val, nb2listw(nb90, style=\"B\")) G90[length(xyz$val)-136] #> [1] 1.986135 nb120 <- dnearneigh(xycoords, 0, 120) G120 <- localG(xyz$val, nb2listw(nb120, style=\"B\")) G120[length(xyz$val)-136] #> [1] 1.893374 nb150 <- dnearneigh(xycoords, 0, 150) G150 <- localG(xyz$val, nb2listw(nb150, style=\"B\")) G150[length(xyz$val)-136] #> [1] 1.237454 brks <- seq(-5,5,1) cm.col <- cm.colors(length(brks)-1) image(x, y, t(matrix(G30, nrow=16, ncol=16, byrow=TRUE)),   breaks=brks, col=cm.col, asp=1) text(xyz$x, xyz$y, round(G30, digits=1), cex=0.7) polygon(c(195,225,225,195), c(195,195,225,225), lwd=2) title(main=expression(paste(\"Values of the \", G[i], \" statistic\")))  G30s <- localG(xyz$val, nb2listw(include.self(nb30),  style=\"B\")) cat(\"value according to Getis and Ord's eq. 14.2, p. 263 (1996)\\n\") #> value according to Getis and Ord's eq. 14.2, p. 263 (1996) G30s[length(xyz$val)-136] #> [1] 1.45078 cat(paste(\"value given by Getis and Ord (1996), p. 267\",   \"(division by n-1 rather than n \\n in variance)\\n\")) #> value given by Getis and Ord (1996), p. 267 (division by n-1 rather than n  #>  in variance) G30s[length(xyz$val)-136] *   (sqrt(sum(scale(xyz$val, scale=FALSE)^2)/length(xyz$val)) /   sqrt(var(xyz$val))) #> [1] 1.447943 image(x, y, t(matrix(G30s, nrow=16, ncol=16, byrow=TRUE)),   breaks=brks, col=cm.col, asp=1) text(xyz$x, xyz$y, round(G30s, digits=1), cex=0.7) polygon(c(195,225,225,195), c(195,195,225,225), lwd=2) title(main=expression(paste(\"Values of the \", G[i]^\"*\", \" statistic\")))"},{"path":"https://r-spatial.github.io/spdep/reference/localGS.html","id":null,"dir":"Reference","previous_headings":"","what":"A local hotspot statistic for analysing multiscale datasets — localGS","title":"A local hotspot statistic for analysing multiscale datasets — localGS","text":"function implements \\(GS_i\\) test statistic local hotspots specific pairwise evaluated distance bands, proposed Westerholt et al. (2015).  Like hotspot estimator \\(G_i^*\\), \\(GS_i\\) statistic given z-scores can evaluated accordingly. idea method identify hotspots datasets comprise several, difficult--separate processes operating different scales. often case complex user-generated datasets Twitter feeds. example, football match reflected tweets pubs, homes, stadium vicinity. exemplified phenomena represent different processes may detected different geometric scales. \\(GS_i\\) method enables identification specifying geometric scale band strictly calculating statistical quantities mean variance solely respective relevant observations interact range adjusted scale band. addition, neighbourhood relationships respective central unit, scale-relevant relationships considered. way, hotspots can detected specific scale ranges independently scales. statistic given : $$GS_i = \\frac{\\displaystyle\\sum_{j; k < j}{w_{ij}w_{ik}\\phi_{jk}a_{jk}} - \\frac{W_i}{\\Phi} \\displaystyle\\sum_{j; k < j}{\\phi_{jk}a_{jk}}}{\\sqrt{\\frac{W_i}{\\Phi}\\displaystyle\\sum_{j; k < j}{\\phi_{jk}a_{jk}^2} + \\frac{W_i\\left(W_i-1\\right)}{\\Phi\\left(\\Phi-1\\right)}\\left(\\Gamma^2 -\\!\\! \\displaystyle\\sum_{j; k < j}{\\left(\\phi_{jk}a_{jk}\\right)^2}\\right) - \\left(\\frac{W_i}{\\Phi}\\displaystyle\\sum_{j; k < j}{\\phi_{jk}a_{jk}}\\right)^2}}$$ $$a_{jk} = x_j + x_k,\\;\\;\\; W_i = \\displaystyle\\sum_{j; k < j}{w_{ij}w_{ik}\\phi_{jk}},\\;\\;\\; \\Phi = \\displaystyle\\sum_{j; k < j}{\\phi_{jk}},\\;\\;\\; \\textrm{} \\;\\;\\; \\Gamma = \\displaystyle\\sum_{j; k < j}{\\phi_{jk}a_{jk}}.$$","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localGS.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"A local hotspot statistic for analysing multiscale datasets — localGS","text":"","code":"localGS(x, listw, dmin, dmax, attr, longlat = NULL)"},{"path":"https://r-spatial.github.io/spdep/reference/localGS.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"A local hotspot statistic for analysing multiscale datasets — localGS","text":"x sf sp object listw listw object dmin lower distance bound (greater equal) dmax upper distance bound (less equal) attr name attribute interest longlat default NULL; TRUE point coordinates longitude-latitude decimal degrees, case distances measured kilometres; x SpatialPoints object, value taken object , overrides argument NULL; distances measured map units FALSE NULL","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localGS.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"A local hotspot statistic for analysing multiscale datasets — localGS","text":"pairs observations shared distance (map units) interval [dmin, dmax] within maximum radius dmax around corresponding output observation considered. Thereby, also mean values variance terms estimated within measure adjusted scale range consideration. application examples method see Westerholt et al. (2015) (applied tweets) Sonea & Westerholt (2021) (applied access banking scenario).","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localGS.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"A local hotspot statistic for analysing multiscale datasets — localGS","text":"vector \\(GS_i\\) values given z-scores.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localGS.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"A local hotspot statistic for analysing multiscale datasets — localGS","text":"Westerholt, R., Resch, B. & Zipf, . 2015. local scale-sensitive indicator spatial autocorrelation assessing high-low-value clusters multiscale datasets. International Journal Geographical Information Science, 29(5), 868–887, doi:10.1080/13658816.2014.1002499 . Sonea, . Westerholt, R. (2021): Geographic temporal access basic banking services Wales. Applied Spatial Analysis Policy, 14 (4), 879–905, doi:10.1007/s12061-021-09386-3 .","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localGS.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"A local hotspot statistic for analysing multiscale datasets — localGS","text":"René Westerholt rene.westerholt@tu-dortmund.de","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/localGS.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"A local hotspot statistic for analysing multiscale datasets — localGS","text":"","code":"# \\donttest{ boston.tr <- sf::st_read(system.file(\"shapes/boston_tracts.gpkg\", package=\"spData\")[1]) #> Reading layer `boston_tracts' from data source  #>   `/home/rsb/lib/r_libs/spData/shapes/boston_tracts.gpkg' using driver `GPKG' #> Simple feature collection with 506 features and 36 fields #> Geometry type: POLYGON #> Dimension:     XY #> Bounding box:  xmin: -71.52311 ymin: 42.00305 xmax: -70.63823 ymax: 42.67307 #> Geodetic CRS:  NAD27 boston.tr_utm <- st_transform(boston.tr, 32619) #26786  boston_listw1 <- nb2listwdist(dnearneigh(st_centroid(boston.tr_utm), 1, 2000),     boston.tr_utm, type = \"dpd\", alpha = 2, zero.policy = TRUE, dmax = 9500) #> Warning: st_centroid assumes attributes are constant over geometries #> Warning: neighbour object has 120 sub-graphs  boston_listw2 <- nb2listwdist(dnearneigh(st_centroid(boston.tr_utm), 5000, 9500),      boston.tr_utm, type = \"dpd\", alpha = 2, zero.policy = TRUE, dmax = 9500) #> Warning: st_centroid assumes attributes are constant over geometries  boston_RM_gsi_1 <- localGS(boston.tr_utm, boston_listw1, 1, 2000, \"RM\", FALSE) boston_RM_gsi_2 <- localGS(boston.tr_utm, boston_listw2, 2000, 9500, \"RM\", FALSE) # }"},{"path":"https://r-spatial.github.io/spdep/reference/local_joincount_bv.html","id":null,"dir":"Reference","previous_headings":"","what":"Calculate the local bivariate join count — local_joincount_bv","title":"Calculate the local bivariate join count — local_joincount_bv","text":"bivariate join count (BJC) evaluates event occurrences predefined regions tests co-occurrence events deviates complete spatial randomness.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/local_joincount_bv.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Calculate the local bivariate join count — local_joincount_bv","text":"","code":"local_joincount_bv(   x,   z,   listw,   nsim = 199,   alternative = \"two.sided\" )"},{"path":"https://r-spatial.github.io/spdep/reference/local_joincount_bv.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Calculate the local bivariate join count — local_joincount_bv","text":"x binary variable either numeric logical z binary variable either numeric logical length x listw listw object containing binary weights created, example, nb2listw(nb, style = \"B\") nsim number conditional permutation simulations alternative default \"greater\". One \"less\" \"greater\".","code":""},{"path":"https://r-spatial.github.io/spdep/reference/local_joincount_bv.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Calculate the local bivariate join count — local_joincount_bv","text":"two cases evaluated bivariate join count. first -situ colocation (CLC) xi = 1 zi = 1. second general form bivariate join count (BJC) used -situ colocation. BJC case \"useful x z occur location, x z correspond two different values single categorical variable\" \"x z can co-locate, \" (Anselin Li, 2019). Whereas CLC case useful evaluating simultaneous occurrences events. local bivariate join count statistic requires binary weights list can generated nb2listw(nb, style = \"B\"). P-values reported regions match CLC BJC criteria. Others associated p-value. P-values estimated using conditional permutation approach. creates reference distribution observed statistic compared.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/local_joincount_bv.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Calculate the local bivariate join count — local_joincount_bv","text":"data.frame two columns join_count p_sim number rows equal length arguments x.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/local_joincount_bv.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Calculate the local bivariate join count — local_joincount_bv","text":"Anselin, L., & Li, X. (2019). Operational Local Join Count Statistics Cluster Detection. Journal geographical systems, 21(2), 189–210. doi:10.1007/s10109-019-00299-x","code":""},{"path":"https://r-spatial.github.io/spdep/reference/local_joincount_bv.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Calculate the local bivariate join count — local_joincount_bv","text":"Josiah Parry josiah.parry@gmail.com","code":""},{"path":"https://r-spatial.github.io/spdep/reference/local_joincount_bv.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Calculate the local bivariate join count — local_joincount_bv","text":"","code":"data(\"oldcol\") listw <- nb2listw(COL.nb, style = \"B\") # Colocation case x <- COL.OLD[[\"CP\"]] z <- COL.OLD[[\"EW\"]] set.seed(1) res <- local_joincount_bv(x, z, listw) na.omit(res) #>    join_count p_sim #> 9           2 0.480 #> 19          3 0.180 #> 20          4 0.020 #> 21          3 0.040 #> 22          3 0.060 #> 23          4 0.070 #> 24          5 0.005 #> 27          2 0.300 #> 28          3 0.050 #> 29          5 0.010 #> 30          5 0.010 #> 31          9 0.005 #> 32          4 0.090 #> 33          4 0.055 # no colocation case z <- 1 - x set.seed(1) res <- local_joincount_bv(x, z, listw) na.omit(res) #>    join_count p_sim #> 9           2 0.065 #> 19          3 0.300 #> 20          1 0.015 #> 21          1 0.040 #> 22          1 0.045 #> 23          3 0.165 #> 24          1 0.000 #> 27          2 0.230 #> 28          1 0.050 #> 29          1 0.000 #> 36          1 0.000 #> 37          2 0.005 #> 38          2 0.185 #> 39          2 0.265 #> 40          1 0.005 #> 43          1 0.070"},{"path":"https://r-spatial.github.io/spdep/reference/local_joincount_uni.html","id":null,"dir":"Reference","previous_headings":"","what":"Calculate the local univariate join count — local_joincount_uni","title":"Calculate the local univariate join count — local_joincount_uni","text":"univariate local join count statistic used identify clusters rarely occurring binary variables. binary variable interest occur less half time.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/local_joincount_uni.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Calculate the local univariate join count — local_joincount_uni","text":"","code":"local_joincount_uni(   fx,   chosen,   listw,   alternative = \"two.sided\",   nsim = 199,   iseed = NULL,   no_repeat_in_row=FALSE )"},{"path":"https://r-spatial.github.io/spdep/reference/local_joincount_uni.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Calculate the local univariate join count — local_joincount_uni","text":"fx binary variable either numeric logical chosen scalar character containing level fx considered observed value (1). listw listw object containing binary weights created, example, nbwlistw(nb, style = \"B\") alternative default \"greater\". One \"less\" \"greater\". nsim number conditional permutation simulations iseed default NULL, used set seed; output reproducible count CPU cores across computation distributed no_repeat_in_row default FALSE, TRUE, sample conditionally row without replacements avoid duplicate values, https://github.com/r-spatial/spdep/issues/124","code":""},{"path":"https://r-spatial.github.io/spdep/reference/local_joincount_uni.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Calculate the local univariate join count — local_joincount_uni","text":"data.frame two columns BB Pr() number rows equal length x.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/local_joincount_uni.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Calculate the local univariate join count — local_joincount_uni","text":"local join count statistic requires binary weights list can generated nb2listw(nb, style = \"B\"). Additionally, ensure binary variable interest rarely occurring half observations. P-values estimated using conditional permutation approach. creates reference distribution observed statistic compared. see Geoda Glossary.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/local_joincount_uni.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Calculate the local univariate join count — local_joincount_uni","text":"Anselin, L., & Li, X. (2019). Operational Local Join Count Statistics Cluster Detection. Journal geographical systems, 21(2), 189–210. doi:10.1007/s10109-019-00299-x","code":""},{"path":"https://r-spatial.github.io/spdep/reference/local_joincount_uni.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Calculate the local univariate join count — local_joincount_uni","text":"Josiah Parry josiah.parry@gmail.com","code":""},{"path":"https://r-spatial.github.io/spdep/reference/local_joincount_uni.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Calculate the local univariate join count — local_joincount_uni","text":"","code":"data(oldcol) fx <- as.factor(ifelse(COL.OLD$CRIME < 35, \"low-crime\", \"high-crime\")) listw <- nb2listw(COL.nb, style = \"B\") set.seed(1) (res <- local_joincount_uni(fx, chosen = \"high-crime\", listw)) #>    BB Pr(z != E(BBi)) #> 1   0              NA #> 2   0              NA #> 3   4            0.50 #> 4   0              NA #> 5   0              NA #> 6   0              NA #> 7   4            0.89 #> 8   0              NA #> 9   5            0.11 #> 10  0              NA #> 11  0              NA #> 12  0              NA #> 13  0              NA #> 14  0              NA #> 15  0              NA #> 16  0              NA #> 17  0              NA #> 18  0              NA #> 19  0              NA #> 20  3            0.55 #> 21  2            0.84 #> 22  3            0.30 #> 23  4            0.61 #> 24  5            0.12 #> 25  0              NA #> 26  0              NA #> 27  0              NA #> 28  0              NA #> 29  3            0.98 #> 30  5            0.09 #> 31  8            0.01 #> 32  7            0.02 #> 33  6            0.02 #> 34  5            0.04 #> 35  7            0.03 #> 36  8            0.02 #> 37  6            0.05 #> 38  5            0.04 #> 39  3            0.44 #> 40  5            0.14 #> 41  3            0.13 #> 42  5            0.05 #> 43  2            0.63 #> 44  0              NA #> 45  0              NA #> 46  0              NA #> 47  0              NA #> 48  0              NA #> 49  0              NA"},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.exact.html","id":null,"dir":"Reference","previous_headings":"","what":"Exact local Moran's Ii tests — localmoran.exact","title":"Exact local Moran's Ii tests — localmoran.exact","text":"localmoran.exact provides exact local Moran's Ii tests null hypothesis, localmoran.exact.alt provides exact local Moran's Ii tests alternative hypothesis. case, model may fitted model derived model fitted spatialreg::errorsarlm, covariance matrix can passed Omega= argument.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.exact.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Exact local Moran's Ii tests — localmoran.exact","text":"","code":"localmoran.exact(model, select, nb, glist = NULL, style = \"W\",   zero.policy = NULL, alternative = \"two.sided\", spChk = NULL,   resfun = weighted.residuals, save.Vi = FALSE, useTP=FALSE, truncErr=1e-6,   zeroTreat=0.1) localmoran.exact.alt(model, select, nb, glist = NULL, style = \"W\",  zero.policy = NULL, alternative = \"two.sided\", spChk = NULL,  resfun = weighted.residuals, Omega = NULL, save.Vi = FALSE,  save.M = FALSE, useTP=FALSE, truncErr=1e-6, zeroTreat=0.1) # S3 method for class 'localmoranex' print(x, ...) # S3 method for class 'localmoranex' as.data.frame(x, row.names=NULL, optional=FALSE, ...)"},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.exact.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Exact local Moran's Ii tests — localmoran.exact","text":"model object class lm returned lm (assuming global spatial autocorrelation), object class sarlm returned spatial simultaneous autoregressive model fit (assuming global spatial autocorrelation represented model spatial coefficient); weights may specified lm fit, offsets used select integer vector id. numbers zones tested; missing, zones nb list neighbours class nb glist list general weights corresponding neighbours style can take values W, B, C, S zero.policy default NULL, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA alternative character string specifying alternative hypothesis, must one greater (default), less two.sided. spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption() resfun default: weighted.residuals; function used extract residuals lm object, may residuals, weighted.residuals, rstandard, rstudent Omega SAR process matrix may passed test alternative hypothesis, example Omega <- invIrW(listw, rho=0.1); Omega <- tcrossprod(Omega), chol() taken internally save.Vi TRUE, return star-shaped weights lists zone tested save.M TRUE, save list left right M products useTP default FALSE, TRUE, use truncation point integration rather upper=Inf, see Tiefelsdorf (2000), eq. 6.7, p.69 truncErr useTP=TRUE, pass truncation error truncation point function zeroTreat useTP=TRUE, pass zero adjustment truncation point function x object printed row.names ignored argument .data.frame.localmoranex; row names assigned localmoranex object optional ignored argument .data.frame.localmoranex; row names assigned localmoranex object ... arguments passed ","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.exact.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Exact local Moran's Ii tests — localmoran.exact","text":"list class localmoranex containing \"select\" lists,  class moranex following components: statistic value exact standard deviate global Moran's . p.value p-value test. estimate value observed local Moran's Ii. method character string giving method used. alternative character string describing alternative hypothesis. gamma eigenvalues (two extreme values null, vector alternative) oType usually set \"E\", set \"N\" integration leads domain value qnorm, Normal assumption substituted. occurs output p-value close zero data.name character string giving name(s) data. df degrees freedom zone tested Vi zone tested alternative tested, list left right M products attribute M.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.exact.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Exact local Moran's Ii tests — localmoran.exact","text":"Bivand RS, Müller W, Reder M (2009) Power calculations global local Moran’s . Comput Stat Data Anal 53:2859–2872; Bivand RS, Wong DWS 2018 Comparing implementations global local indicators spatial association. TEST, 27(3), 716–748 doi:10.1007/s11749-018-0599-x","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.exact.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Exact local Moran's Ii tests — localmoran.exact","text":"Markus Reder Roger Bivand","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.exact.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Exact local Moran's Ii tests — localmoran.exact","text":"","code":"eire <- st_read(system.file(\"shapes/eire.gpkg\", package=\"spData\")[1]) #> Reading layer `eire' from data source  #>   `/home/rsb/lib/r_libs/spData/shapes/eire.gpkg' using driver `GPKG' #> Simple feature collection with 26 features and 10 fields #> Geometry type: MULTIPOLYGON #> Dimension:     XY #> Bounding box:  xmin: -4.12 ymin: 5768 xmax: 300.82 ymax: 6119.25 #> Projected CRS: Undefined Cartesian SRS with unknown unit row.names(eire) <- as.character(eire$names) eire.nb <- poly2nb(eire) e.lm <- lm(OWNCONS ~ ROADACC, data=eire) localmoran.sad(e.lm, nb=eire.nb) #>              Local Morans I Saddlepoint    Pr. (Sad) #> 1 Carlow         0.21699668  0.95074844 3.417321e-01 #> 2 Cavan         -0.37257361 -1.00603119 3.144006e-01 #> 3 Clare          0.23197510  0.67166518 5.017969e-01 #> 4 Cork           0.78193548  1.74761575 8.053059e-02 #> 5 Donegal       -1.69064059 -1.72031078 8.537596e-02 #> 6 Dublin        -0.16069692 -0.35212627 7.247436e-01 #> 7 Galway         1.31371473  2.66849536 7.619183e-03 #> 8 Kerry          0.36534866  0.78073279 4.349597e-01 #> 9 Kildare       -0.02557544  0.04167665 9.667565e-01 #> 10 Kilkenny      0.57684331  1.70897697 8.745521e-02 #> 11 Laoghis      -0.05951798 -0.12155465 9.032517e-01 #> 12 Leitrim       0.38484587  1.47227033 1.409479e-01 #> 13 Limerick      0.11817987  0.45727712 6.474719e-01 #> 14 Longford      1.41643200  2.51113769 1.203427e-02 #> 15 Louth         0.56242920  1.07441571 2.826364e-01 #> 16 Mayo          0.87572704  2.05251226 4.011990e-02 #> 17 Meath         0.00367856  0.12813539 8.980418e-01 #> 18 Monaghan      0.55098311  1.23999193 2.149784e-01 #> 19 Offaly        0.15155556  0.80786519 4.191682e-01 #> 20 Roscommon     2.04368839  4.53187292 5.846302e-06 #> 21 Sligo        -0.47579871 -0.94578114 3.442602e-01 #> 22 Tipperary    -0.03454106 -0.06919691 9.448329e-01 #> 23 Waterford     0.85723423  1.91385108 5.563919e-02 #> 24 Westmeath     0.45138572  1.36017204 1.737755e-01 #> 25 Wexford       0.64371834  1.63188492 1.027037e-01 #> 26 Wicklow       0.02441950  0.21197000 8.321304e-01 localmoran.exact(e.lm, nb=eire.nb) #>              Local Morans I    Exact SD  Pr. (exact) #> 1 Carlow         0.21699668  1.02706083 3.043918e-01 #> 2 Cavan         -0.37257361 -1.04864802 2.943401e-01 #> 3 Clare          0.23197510  0.76362894 4.450884e-01 #> 4 Cork           0.78193548  1.77727656 7.552275e-02 #> 5 Donegal       -1.69064059 -1.74428756 8.110896e-02 #> 6 Dublin        -0.16069692 -0.44236119 6.582279e-01 #> 7 Galway         1.31371473  2.69199974 7.102500e-03 #> 8 Kerry          0.36534866  0.85742696 3.912090e-01 #> 9 Kildare       -0.02557544 -0.03475476 9.722753e-01 #> 10 Kilkenny      0.57684331  1.74146177 8.160267e-02 #> 11 Laoghis      -0.05951798 -0.21824035 8.272419e-01 #> 12 Leitrim       0.38484587  1.51434641 1.299380e-01 #> 13 Limerick      0.11817987  0.56922630 5.692026e-01 #> 14 Longford      1.41643200  2.53491837 1.124735e-02 #> 15 Louth         0.56242920  1.12775107 2.594251e-01 #> 16 Mayo          0.87572704  2.08125803 3.741029e-02 #> 17 Meath         0.00367856  0.16372685 8.699462e-01 #> 18 Monaghan      0.55098311  1.28435459 1.990179e-01 #> 19 Offaly        0.15155556  0.89537870 3.705847e-01 #> 20 Roscommon     2.04368839  4.55244870 5.302509e-06 #> 21 Sligo        -0.47579871 -0.98101752 3.265841e-01 #> 22 Tipperary    -0.03454106 -0.16132608 8.718366e-01 #> 23 Waterford     0.85723423  1.94188723 5.215075e-02 #> 24 Westmeath     0.45138572  1.40091422 1.612397e-01 #> 25 Wexford       0.64371834  1.66488051 9.593660e-02 #> 26 Wicklow       0.02441950  0.29717701 7.663314e-01 localmoran.exact(e.lm, nb=eire.nb, useTP=TRUE) #>              Local Morans I    Exact SD  Pr. (exact) #> 1 Carlow         0.21699668  1.02706127 3.043916e-01 #> 2 Cavan         -0.37257361 -1.04864834 2.943400e-01 #> 3 Clare          0.23197510  0.76362936 4.450881e-01 #> 4 Cork           0.78193548  1.77727666 7.552273e-02 #> 5 Donegal       -1.69064059 -1.74428741 8.110899e-02 #> 6 Dublin        -0.16069692 -0.44236158 6.582276e-01 #> 7 Galway         1.31371473  2.69199162 7.102673e-03 #> 8 Kerry          0.36534866  0.85742736 3.912087e-01 #> 9 Kildare       -0.02557544 -0.03540278 9.717586e-01 #> 10 Kilkenny      0.57684331  1.74146192 8.160264e-02 #> 11 Laoghis      -0.05951798 -0.21823772 8.272439e-01 #> 12 Leitrim       0.38484587  1.51434680 1.299379e-01 #> 13 Limerick      0.11817987  0.56922674 5.692023e-01 #> 14 Longford      1.41643200  2.53491383 1.124750e-02 #> 15 Louth         0.56242920  1.12775145 2.594249e-01 #> 16 Mayo          0.87572704  2.08125778 3.741032e-02 #> 17 Meath         0.00367856  0.15714487 8.751307e-01 #> 18 Monaghan      0.55098311  1.28435495 1.990178e-01 #> 19 Offaly        0.15155556  0.89537914 3.705844e-01 #> 20 Roscommon     2.04368839  4.53362873 5.797890e-06 #> 21 Sligo        -0.47579871 -0.98101780 3.265840e-01 #> 22 Tipperary    -0.03454106 -0.16116590 8.719627e-01 #> 23 Waterford     0.85723423  1.94188711 5.215077e-02 #> 24 Westmeath     0.45138572  1.40091457 1.612396e-01 #> 25 Wexford       0.64371834  1.66488069 9.593656e-02 #> 26 Wicklow       0.02441950  0.29790569 7.657751e-01 run <- FALSE if (requireNamespace(\"spatialreg\", quietly=TRUE)) run <- TRUE if (run) { e.errorsar <- spatialreg::errorsarlm(OWNCONS ~ ROADACC, data=eire,  listw=nb2listw(eire.nb)) lm.target <- lm(e.errorsar$tary ~ e.errorsar$tarX - 1) localmoran.exact.alt(lm.target, nb=eire.nb) } #>              Local Morans I    Exact SD Pr. (exact) #> 1 Carlow         0.17958462  0.83313548 0.404768327 #> 2 Cavan         -0.24752628 -0.82861508 0.407322251 #> 3 Clare         -0.27901334 -0.72313220 0.469598670 #> 4 Cork           0.37808655  1.15083938 0.249798320 #> 5 Donegal       -1.01894688 -1.50937607 0.131202704 #> 6 Dublin        -0.18171297 -0.50995181 0.610085224 #> 7 Galway         1.02193390  2.27605549 0.022842689 #> 8 Kerry         -0.94967914 -1.46954733 0.141684395 #> 9 Kildare        0.07005053  0.56174770 0.574287931 #> 10 Kilkenny      0.43022231  1.39078833 0.164289622 #> 11 Laoghis      -0.12239133 -0.45750046 0.647311369 #> 12 Leitrim      -0.24203970 -0.84925558 0.395739092 #> 13 Limerick     -0.03214546 -0.13098232 0.895789292 #> 14 Longford      0.38307454  1.17909760 0.238359315 #> 15 Louth         0.21301552  0.62068302 0.534808204 #> 16 Mayo          0.93971200  1.94079901 0.052282661 #> 17 Meath         0.12484415  0.78747315 0.431004937 #> 18 Monaghan     -0.16109919 -0.48277561 0.629255068 #> 19 Offaly       -0.00632492  0.03008421 0.975999892 #> 20 Roscommon     1.02089429  2.64333471 0.008209384 #> 21 Sligo        -2.01629233 -2.54211789 0.011018300 #> 22 Tipperary    -0.10810709 -0.51063241 0.609608478 #> 23 Waterford     0.44099279  1.28152280 0.200010096 #> 24 Westmeath    -0.06329661 -0.26575204 0.790430182 #> 25 Wexford       0.30764883  1.02115599 0.307180540 #> 26 Wicklow      -0.01696406 -0.04109885 0.967217095 if (run) { Omega <- spatialreg::invIrW(nb2listw(eire.nb), rho=e.errorsar$lambda) Omega1 <- tcrossprod(Omega) localmoran.exact.alt(lm.target, nb=eire.nb, Omega=Omega1) } #>              Local Morans I     Exact SD  Pr. (exact) #> 1 Carlow         0.17958462  0.009413917 0.9924888919 #> 2 Cavan         -0.24752628 -1.416786314 0.1565454123 #> 3 Clare         -0.27901334 -1.512813055 0.1303271517 #> 4 Cork           0.37808655  0.078686494 0.9372819884 #> 5 Donegal       -1.01894688 -1.935314161 0.0529517556 #> 6 Dublin        -0.18171297 -1.226543250 0.2199943101 #> 7 Galway         1.02193390  1.477322295 0.1395892645 #> 8 Kerry         -0.94967914 -2.427948363 0.0151845050 #> 9 Kildare        0.07005053 -0.042522018 0.9660825597 #> 10 Kilkenny      0.43022231  0.488471215 0.6252161096 #> 11 Laoghis      -0.12239133 -1.091910863 0.2748722827 #> 12 Leitrim      -0.24203970 -1.631825829 0.1027161824 #> 13 Limerick     -0.03214546 -0.921751557 0.3566581813 #> 14 Longford      0.38307454  0.183273193 0.8545836671 #> 15 Louth         0.21301552 -0.184065307 0.8539622227 #> 16 Mayo          0.93971200  1.182398031 0.2370478040 #> 17 Meath         0.12484415 -0.060499926 0.9517574750 #> 18 Monaghan     -0.16109919 -1.342787509 0.1793407892 #> 19 Offaly       -0.00632492 -0.409598788 0.6821002863 #> 20 Roscommon     1.02089429  1.238387417 0.2155724441 #> 21 Sligo        -2.01629233 -3.623597237 0.0002905339 #> 22 Tipperary    -0.10810709 -1.227333133 0.2196974073 #> 23 Waterford     0.44099279  0.433358039 0.6647546796 #> 24 Westmeath    -0.06329661 -0.956519228 0.3388099748 #> 25 Wexford       0.30764883  0.141381248 0.8875687671 #> 26 Wicklow      -0.01696406 -0.783977878 0.4330530911 if (run) { localmoran.exact.alt(lm.target, nb=eire.nb, Omega=Omega1, useTP=TRUE) } #>              Local Morans I     Exact SD  Pr. (exact) #> 1 Carlow         0.17958462  0.009414171 0.9924886892 #> 2 Cavan         -0.24752628 -1.416786809 0.1565452674 #> 3 Clare         -0.27901334 -1.512813519 0.1303270338 #> 4 Cork           0.37808655  0.078686628 0.9372818822 #> 5 Donegal       -1.01894688 -1.935314436 0.0529517219 #> 6 Dublin        -0.18171297 -1.226543734 0.2199941280 #> 7 Galway         1.02193390  1.477322399 0.1395892367 #> 8 Kerry         -0.94967914 -2.427949220 0.0151844691 #> 9 Kildare        0.07005053 -0.042526751 0.9660787872 #> 10 Kilkenny      0.43022231  0.488471349 0.6252160152 #> 11 Laoghis      -0.12239133 -1.091912026 0.2748717711 #> 12 Leitrim      -0.24203970 -1.631826543 0.1027160320 #> 13 Limerick     -0.03214546 -0.921785589 0.3566404259 #> 14 Longford      0.38307454  0.183273325 0.8545835636 #> 15 Louth         0.21301552 -0.184065128 0.8539623631 #> 16 Mayo          0.93971200  1.182398127 0.2370477661 #> 17 Meath         0.12484415 -0.060499243 0.9517580190 #> 18 Monaghan     -0.16109919 -1.342788191 0.1793405681 #> 19 Offaly       -0.00632492 -0.407816672 0.6834082724 #> 20 Roscommon     1.02089429  1.238387488 0.2155724178 #> 21 Sligo        -2.01629233 -3.623590126 0.0002905419 #> 22 Tipperary    -0.10810709 -1.227335007 0.2196967033 #> 23 Waterford     0.44099279  0.433358168 0.6647545858 #> 24 Westmeath    -0.06329661 -0.956505669 0.3388168214 #> 25 Wexford       0.30764883  0.141381402 0.8875686460 #> 26 Wicklow      -0.01696406 -0.784451761 0.4327750768"},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.html","id":null,"dir":"Reference","previous_headings":"","what":"Local Moran's I statistic — localmoran","title":"Local Moran's I statistic — localmoran","text":"local spatial statistic Moran's calculated zone based spatial weights object used. values returned include Z-value, may used diagnostic tool. statistic : $$I_i = \\frac{(x_i-\\bar{x})}{{\\sum_{k=1}^{n}(x_k-\\bar{x})^2}/(n-1)}{\\sum_{j=1}^{n}w_{ij}(x_j-\\bar{x})}$$, expectation variance given Anselin (1995), Sokal et al. (1998) implemented .","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Local Moran's I statistic — localmoran","text":"","code":"localmoran(x, listw, zero.policy=attr(listw, \"zero.policy\"), na.action=na.fail,         conditional=TRUE, alternative = \"two.sided\", mlvar=TRUE,         spChk=NULL, adjust.x=FALSE) localmoran_perm(x, listw, nsim=499, zero.policy=attr(listw, \"zero.policy\"),          na.action=na.fail, alternative = \"two.sided\", mlvar=TRUE,         spChk=NULL, adjust.x=FALSE, sample_Ei=TRUE, iseed=NULL,         no_repeat_in_row=FALSE)"},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Local Moran's I statistic — localmoran","text":"x numeric vector length neighbours list listw listw listw object created example nb2listw zero.policy default default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA na.action function (default na.fail), can also na.omit na.exclude - cases weights list subsetted remove NAs data. may necessary set zero.policy TRUE subsetting may create -neighbour observations. Note weights lists created without using glist argument nb2listw may subsetted. na.pass used, zero substituted NA values calculating spatial lag. (Note na.exclude work properly starting R 1.9.0, na.omit na.exclude assign wrong classes 1.8.*) conditional default TRUE: expectation variance calculated using conditional randomization null (Sokal 1998 Eqs. A7 & A8). Elaboration changes available Sauer et al. (2021). FALSE: expectation variance calculated using total randomization null (Sokal 1998 Eqs. A3 & A4). alternative character string specifying alternative hypothesis, must one greater, less two.sided (default). mlvar default TRUE: values local Moran's reported using variance variable interest (sum squared deviances n), can reported sample variance, dividing (n-1) instead; used implementations. spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption() adjust.x default FALSE, TRUE, x values observations neighbours omitted mean x nsim default 499, number conditonal permutation simulations sample_Ei default TRUE; conditional permutation, use sample $E_i$ values, analytical values, leaving variances calculated simulation. iseed default NULL, used set seed; output reproducible count CPU cores across computation distributed no_repeat_in_row default FALSE, TRUE, sample conditionally row without replacements avoid duplicate values, https://github.com/r-spatial/spdep/issues/124","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Local Moran's I statistic — localmoran","text":"values local Moran's divided variance (sample variance) variable interest accord Table 1, p. 103, formula (12), p. 99, Anselin (1995), rather formula (7), p. 98. variance local Moran statistic taken Sokal et al. (1998) p. 334, equations 4 & 5 equations 7 & 8 located depending user specification. default, implementation divides n, (n-1) calculating variance higher moments. Conditional code contributed Jeff Sauer Levi Wolf.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Local Moran's I statistic — localmoran","text":"Ii local moran statistic E.Ii expectation local moran statistic; localmoran_permthe permutation sample means Var.Ii variance local moran statistic; localmoran_permthe permutation sample standard deviations Z.Ii standard deviate local moran statistic; localmoran_perm based permutation sample means standard deviations Pr() p-value local moran statistic using pnorm(); localmoran_perm using standard deviatse based permutation sample means standard deviations Pr() Sim localmoran_perm, rank() punif() observed statistic rank [0, 1] p-values using alternative= Pr(folded) Sim simulation folded [0, 0.5] range ranked p-value (based https://github.com/pysal/esda/blob/4a63e0b5df1e754b17b5f1205b8cadcbecc5e061/esda/crand.py#L211-L213) Skewness localmoran_perm, output e1071::skewness() permutation samples underlying standard deviates Kurtosis localmoran_perm, output e1071::kurtosis() permutation samples underlying standard deviates addition, attribute data frame \"quadr\" mean median quadrant columns, column splitting demeaned variable lagged demeaned variable zero.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Local Moran's I statistic — localmoran","text":"Conditional permutations added comparative purposes; permutations whole data vector omitting observation . p-value adjustment, use p.adjust() p.adjustSP() output vector.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Local Moran's I statistic — localmoran","text":"Anselin, L. 1995. Local indicators spatial association, Geographical Analysis, 27, 93–115; Getis, . Ord, J. K. 1996 Local spatial statistics: overview. P. Longley M. Batty (eds) Spatial analysis: modelling GIS environment (Cambridge: Geoinformation International), 261–277; Sokal, R. R, Oden, N. L. Thomson, B. . 1998. Local Spatial Autocorrelation Biological Model. Geographical Analysis, 30. 331–354; Bivand RS, Wong DWS 2018 Comparing implementations global local indicators spatial association. TEST, 27(3), 716–748 doi:10.1007/s11749-018-0599-x ; Sauer, J., Oshan, T. M., Rey, S., & Wolf, L. J. 2021. Importance Null Hypotheses: Understanding Differences Local Moran’s Heteroskedasticity. Geographical Analysis. doi:10.1111/gean.12304 Bivand, R. (2022), R Packages Analyzing Spatial Data: Comparative Case Study Areal Data. Geographical Analysis, 54(3), 488-518. doi:10.1111/gean.12319","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Local Moran's I statistic — localmoran","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Local Moran's I statistic — localmoran","text":"","code":"data(afcon, package=\"spData\") oid <- order(afcon$id) resI <- localmoran(afcon$totcon, nb2listw(paper.nb)) printCoefmat(data.frame(resI[oid,], row.names=afcon$name[oid]),  check.names=FALSE) #>                                   Ii        E.Ii      Var.Ii        Z.Ii #> THE GAMBIA                3.7523e-01 -2.4317e-02  9.9646e-01  4.0025e-01 #> MALI                      4.6363e-01 -2.1841e-02  1.0896e-01  1.4708e+00 #> SENEGAL                   2.5670e-01 -3.4444e-03  3.3339e-02  1.4248e+00 #> BENIN                     1.9412e-01 -2.4556e-03  2.3792e-02  1.2744e+00 #> MAURITANIA                9.7053e-02 -5.7508e-03  5.5533e-02  4.3625e-01 #> NIGER                     2.3071e-01 -1.9459e-02  9.7310e-02  8.0198e-01 #> IVORY COAST               2.9004e-01 -6.9359e-03  5.2072e-02  1.3014e+00 #> GUINEA                    1.8263e-01 -2.2246e-03  1.6780e-02  1.4270e+00 #> BURKINA FASO              5.0828e-01 -1.9893e-02  1.1942e-01  1.5284e+00 #> LIBERIA                   1.8565e-01 -2.7127e-03  3.5982e-02  9.9300e-01 #> SIERRA LEONE              2.6523e-01 -1.6994e-02  3.4204e-01  4.8257e-01 #> GHANA                     1.4764e-01 -1.3414e-03  1.7817e-02  1.1161e+00 #> TOGO                      2.1934e-01 -4.9892e-03  6.6025e-02  8.7305e-01 #> CAMEROON                  2.5925e-01 -1.1009e-02  8.2313e-02  9.4198e-01 #> NIGERIA                   1.1377e-01 -9.6126e-04  9.3272e-03  1.1880e+00 #> GABON                     2.0366e-01 -5.4771e-03  1.1153e-01  6.2625e-01 #> CENTRAL AFRICAN REPUBLIC -4.4206e-01 -1.0600e-02  7.9287e-02 -1.5323e+00 #> CHAD                     -1.0528e-01 -4.0998e-03  2.5008e-02 -6.3985e-01 #> CONGO                     1.1380e-02 -8.5953e-04  8.3410e-03  1.3402e-01 #> ZAIRE                     7.0978e-01 -5.9545e-02  2.0906e-01  1.6826e+00 #> ANGOLA                    1.1797e-01 -6.2140e-04  8.2594e-03  1.3050e+00 #> UGANDA                    1.9425e+00 -6.2812e-02  4.4503e-01  3.0060e+00 #> KENYA                     1.1969e+00 -1.6803e-02  1.2489e-01  3.4344e+00 #> TANZANIA                  2.7185e-01 -4.6254e-02  1.9107e-01  7.2774e-01 #> BURUNDI                  -4.8428e-01 -1.1009e-02  1.4481e-01 -1.2437e+00 #> RWANDA                   -7.5236e-01 -1.4730e-02  1.4096e-01 -1.9647e+00 #> SOMALIA                   4.5277e-01 -1.1751e-02  2.3778e-01  9.5260e-01 #> ETHIOPIA                  7.2512e-01 -5.4929e-03  7.2655e-02  2.7106e+00 #> ZAMBIA                    4.2160e-02 -8.1691e-04  3.5354e-03  7.2280e-01 #> ZIMBABWE                 -9.5068e-03 -6.0969e-03  5.8855e-02 -1.4056e-02 #> MALAWI                   -2.2888e-01 -1.0284e-02  1.3537e-01 -5.9413e-01 #> MOZAMBIQUE                1.6790e-02 -6.1629e-03  3.7515e-02  1.1850e-01 #> SOUTH AFRICA             -1.8254e-01 -5.4306e-03  2.7546e-02 -1.0671e+00 #> LESOTHO                  -4.1935e-01 -1.9263e-02  7.9348e-01 -4.4914e-01 #> BOTSWANA                 -3.9316e-03 -1.4141e-04  1.8805e-03 -8.7403e-02 #> SWAZILAND                 1.6684e-02 -2.8611e-02  5.6905e-01  6.0045e-02 #> MOROCCO                  -9.6961e-02 -5.1445e-03  1.0479e-01 -2.8363e-01 #> ALGERIA                  -1.0037e-02 -9.7828e-05  5.9914e-04 -4.0605e-01 #> TUNISIA                   5.3873e-03 -3.0273e-06  6.1985e-05  6.8466e-01 #> LIBYA                     8.0382e-01 -1.9923e-02  1.1960e-01  2.3820e+00 #> SUDAN                     2.9878e+00 -2.2835e-01  7.6320e-01  3.6814e+00 #> EGYPT                     6.9467e+00 -2.9968e-01  4.2971e+00  3.4957e+00 #>                          Pr.z....E.Ii.. #> THE GAMBIA                       0.6890 #> MALI                             0.1414 #> SENEGAL                          0.1542 #> BENIN                            0.2025 #> MAURITANIA                       0.6627 #> NIGER                            0.4226 #> IVORY COAST                      0.1931 #> GUINEA                           0.1536 #> BURKINA FASO                     0.1264 #> LIBERIA                          0.3207 #> SIERRA LEONE                     0.6294 #> GHANA                            0.2644 #> TOGO                             0.3826 #> CAMEROON                         0.3462 #> NIGERIA                          0.2348 #> GABON                            0.5312 #> CENTRAL AFRICAN REPUBLIC         0.1255 #> CHAD                             0.5223 #> CONGO                            0.8934 #> ZAIRE                            0.0925 #> ANGOLA                           0.1919 #> UGANDA                           0.0026 #> KENYA                            0.0006 #> TANZANIA                         0.4668 #> BURUNDI                          0.2136 #> RWANDA                           0.0494 #> SOMALIA                          0.3408 #> ETHIOPIA                         0.0067 #> ZAMBIA                           0.4698 #> ZIMBABWE                         0.9888 #> MALAWI                           0.5524 #> MOZAMBIQUE                       0.9057 #> SOUTH AFRICA                     0.2859 #> LESOTHO                          0.6533 #> BOTSWANA                         0.9304 #> SWAZILAND                        0.9521 #> MOROCCO                          0.7767 #> ALGERIA                          0.6847 #> TUNISIA                          0.4936 #> LIBYA                            0.0172 #> SUDAN                            0.0002 #> EGYPT                            0.0005 hist(resI[,5])  mean(resI[,1]) #> [1] 0.4167956 sum(resI[,1])/Szero(nb2listw(paper.nb)) #> [1] 0.4167956 moran.test(afcon$totcon, nb2listw(paper.nb)) #>  #> \tMoran I test under randomisation #>  #> data:  afcon$totcon   #> weights: nb2listw(paper.nb)     #>  #> Moran I statistic standard deviate = 4.3485, p-value = 6.854e-06 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic       Expectation          Variance  #>        0.41679563       -0.02439024        0.01029358  #>  # note equality for mean() only when the sum of weights equals # the number of observations (thanks to Juergen Symanzik) resI <- localmoran(afcon$totcon, nb2listw(paper.nb)) printCoefmat(data.frame(resI[oid,], row.names=afcon$name[oid]),  check.names=FALSE) #>                                   Ii        E.Ii      Var.Ii        Z.Ii #> THE GAMBIA                3.7523e-01 -2.4317e-02  9.9646e-01  4.0025e-01 #> MALI                      4.6363e-01 -2.1841e-02  1.0896e-01  1.4708e+00 #> SENEGAL                   2.5670e-01 -3.4444e-03  3.3339e-02  1.4248e+00 #> BENIN                     1.9412e-01 -2.4556e-03  2.3792e-02  1.2744e+00 #> MAURITANIA                9.7053e-02 -5.7508e-03  5.5533e-02  4.3625e-01 #> NIGER                     2.3071e-01 -1.9459e-02  9.7310e-02  8.0198e-01 #> IVORY COAST               2.9004e-01 -6.9359e-03  5.2072e-02  1.3014e+00 #> GUINEA                    1.8263e-01 -2.2246e-03  1.6780e-02  1.4270e+00 #> BURKINA FASO              5.0828e-01 -1.9893e-02  1.1942e-01  1.5284e+00 #> LIBERIA                   1.8565e-01 -2.7127e-03  3.5982e-02  9.9300e-01 #> SIERRA LEONE              2.6523e-01 -1.6994e-02  3.4204e-01  4.8257e-01 #> GHANA                     1.4764e-01 -1.3414e-03  1.7817e-02  1.1161e+00 #> TOGO                      2.1934e-01 -4.9892e-03  6.6025e-02  8.7305e-01 #> CAMEROON                  2.5925e-01 -1.1009e-02  8.2313e-02  9.4198e-01 #> NIGERIA                   1.1377e-01 -9.6126e-04  9.3272e-03  1.1880e+00 #> GABON                     2.0366e-01 -5.4771e-03  1.1153e-01  6.2625e-01 #> CENTRAL AFRICAN REPUBLIC -4.4206e-01 -1.0600e-02  7.9287e-02 -1.5323e+00 #> CHAD                     -1.0528e-01 -4.0998e-03  2.5008e-02 -6.3985e-01 #> CONGO                     1.1380e-02 -8.5953e-04  8.3410e-03  1.3402e-01 #> ZAIRE                     7.0978e-01 -5.9545e-02  2.0906e-01  1.6826e+00 #> ANGOLA                    1.1797e-01 -6.2140e-04  8.2594e-03  1.3050e+00 #> UGANDA                    1.9425e+00 -6.2812e-02  4.4503e-01  3.0060e+00 #> KENYA                     1.1969e+00 -1.6803e-02  1.2489e-01  3.4344e+00 #> TANZANIA                  2.7185e-01 -4.6254e-02  1.9107e-01  7.2774e-01 #> BURUNDI                  -4.8428e-01 -1.1009e-02  1.4481e-01 -1.2437e+00 #> RWANDA                   -7.5236e-01 -1.4730e-02  1.4096e-01 -1.9647e+00 #> SOMALIA                   4.5277e-01 -1.1751e-02  2.3778e-01  9.5260e-01 #> ETHIOPIA                  7.2512e-01 -5.4929e-03  7.2655e-02  2.7106e+00 #> ZAMBIA                    4.2160e-02 -8.1691e-04  3.5354e-03  7.2280e-01 #> ZIMBABWE                 -9.5068e-03 -6.0969e-03  5.8855e-02 -1.4056e-02 #> MALAWI                   -2.2888e-01 -1.0284e-02  1.3537e-01 -5.9413e-01 #> MOZAMBIQUE                1.6790e-02 -6.1629e-03  3.7515e-02  1.1850e-01 #> SOUTH AFRICA             -1.8254e-01 -5.4306e-03  2.7546e-02 -1.0671e+00 #> LESOTHO                  -4.1935e-01 -1.9263e-02  7.9348e-01 -4.4914e-01 #> BOTSWANA                 -3.9316e-03 -1.4141e-04  1.8805e-03 -8.7403e-02 #> SWAZILAND                 1.6684e-02 -2.8611e-02  5.6905e-01  6.0045e-02 #> MOROCCO                  -9.6961e-02 -5.1445e-03  1.0479e-01 -2.8363e-01 #> ALGERIA                  -1.0037e-02 -9.7828e-05  5.9914e-04 -4.0605e-01 #> TUNISIA                   5.3873e-03 -3.0273e-06  6.1985e-05  6.8466e-01 #> LIBYA                     8.0382e-01 -1.9923e-02  1.1960e-01  2.3820e+00 #> SUDAN                     2.9878e+00 -2.2835e-01  7.6320e-01  3.6814e+00 #> EGYPT                     6.9467e+00 -2.9968e-01  4.2971e+00  3.4957e+00 #>                          Pr.z....E.Ii.. #> THE GAMBIA                       0.6890 #> MALI                             0.1414 #> SENEGAL                          0.1542 #> BENIN                            0.2025 #> MAURITANIA                       0.6627 #> NIGER                            0.4226 #> IVORY COAST                      0.1931 #> GUINEA                           0.1536 #> BURKINA FASO                     0.1264 #> LIBERIA                          0.3207 #> SIERRA LEONE                     0.6294 #> GHANA                            0.2644 #> TOGO                             0.3826 #> CAMEROON                         0.3462 #> NIGERIA                          0.2348 #> GABON                            0.5312 #> CENTRAL AFRICAN REPUBLIC         0.1255 #> CHAD                             0.5223 #> CONGO                            0.8934 #> ZAIRE                            0.0925 #> ANGOLA                           0.1919 #> UGANDA                           0.0026 #> KENYA                            0.0006 #> TANZANIA                         0.4668 #> BURUNDI                          0.2136 #> RWANDA                           0.0494 #> SOMALIA                          0.3408 #> ETHIOPIA                         0.0067 #> ZAMBIA                           0.4698 #> ZIMBABWE                         0.9888 #> MALAWI                           0.5524 #> MOZAMBIQUE                       0.9057 #> SOUTH AFRICA                     0.2859 #> LESOTHO                          0.6533 #> BOTSWANA                         0.9304 #> SWAZILAND                        0.9521 #> MOROCCO                          0.7767 #> ALGERIA                          0.6847 #> TUNISIA                          0.4936 #> LIBYA                            0.0172 #> SUDAN                            0.0002 #> EGYPT                            0.0005 hist(p.adjust(resI[,5], method=\"bonferroni\"))  totcon <-afcon$totcon is.na(totcon) <- sample(1:length(totcon), 5) totcon #>  [1] 1363 1421 1861 2355 5246  811  299  358  895   NA   NA  933  347 1130  241 #> [16]  604 1015  998 2122 1090   NA   NA  758  423   NA 3087 2273 3134 1142  824 #> [31] 2881  487  604 1528 1554  629  792  795 1266 1875  147  363 resI.na <- localmoran(totcon, nb2listw(paper.nb), na.action=na.exclude,  zero.policy=TRUE) if (class(attr(resI.na, \"na.action\")) == \"exclude\") {  print(data.frame(resI.na[oid,], row.names=afcon$name[oid]), digits=2) } else print(resI.na, digits=2) #>                               Ii     E.Ii  Var.Ii  Z.Ii Pr.z....E.Ii.. #> THE GAMBIA                0.3528 -2.9e-02 1.03887  0.37          0.708 #> MALI                      0.4524 -2.6e-02 0.11007  1.44          0.149 #> SENEGAL                   0.2347 -3.3e-03 0.02800  1.42          0.155 #> BENIN                     0.1862 -2.2e-03 0.02572  1.17          0.240 #> MAURITANIA                0.0722 -6.0e-03 0.05043  0.35          0.728 #> NIGER                     0.1981 -2.3e-02 0.09763  0.71          0.480 #> IVORY COAST               0.3020 -7.4e-03 0.06218  1.24          0.215 #> GUINEA                    0.1774 -2.0e-03 0.01658  1.39          0.164 #> BURKINA FASO              0.5248 -2.3e-02 0.14950  1.42          0.156 #> LIBERIA                       NA       NA      NA    NA             NA #> SIERRA LEONE              0.2241 -2.0e-02 0.71575  0.29          0.773 #> GHANA                     0.1382 -1.0e-03 0.01854  1.02          0.307 #> TOGO                          NA       NA      NA    NA             NA #> CAMEROON                  0.1884 -1.2e-02 0.10306  0.63          0.532 #> NIGERIA                   0.0861 -6.6e-04 0.00556  1.16          0.245 #> GABON                     0.1828 -5.7e-03 0.10144  0.59          0.554 #> CENTRAL AFRICAN REPUBLIC      NA       NA      NA    NA             NA #> CHAD                      0.0657 -4.1e-03 0.03430  0.38          0.706 #> CONGO                    -0.0301 -5.6e-04 0.00652 -0.37          0.715 #> ZAIRE                     0.5651 -8.5e-02 0.34207  1.11          0.266 #> ANGOLA                    0.2017 -1.5e-03 0.01766  1.53          0.126 #> UGANDA                    1.5678 -9.0e-02 0.69207  1.99          0.046 #> KENYA                     1.3328 -2.6e-02 0.29012  2.52          0.012 #> TANZANIA                  0.4269 -6.7e-02 0.23117  1.03          0.304 #> BURUNDI                  -0.5611 -1.2e-02 0.14171 -1.46          0.145 #> RWANDA                   -0.8661 -1.7e-02 0.14069 -2.26          0.024 #> SOMALIA                   0.7805 -1.8e-02 0.66673  0.98          0.328 #> ETHIOPIA                      NA       NA      NA    NA             NA #> ZAMBIA                    0.0806 -1.9e-03 0.00690  0.99          0.321 #> ZIMBABWE                 -0.0393 -6.4e-03 0.05385 -0.14          0.887 #> MALAWI                   -0.2844 -1.1e-02 0.13166 -0.75          0.452 #> MOZAMBIQUE               -0.0121 -6.5e-03 0.03407 -0.03          0.976 #> SOUTH AFRICA             -0.2047 -9.1e-03 0.03947 -0.98          0.325 #> LESOTHO                  -0.5158 -2.3e-02 0.81614 -0.55          0.585 #> BOTSWANA                 -0.0025 -1.3e-05 0.00015 -0.20          0.838 #> SWAZILAND                -0.0494 -3.4e-02 0.59593 -0.02          0.984 #> MOROCCO                  -0.0936 -8.7e-03 0.15440 -0.22          0.829 #> ALGERIA                  -0.0143 -4.7e-04 0.00247 -0.28          0.780 #> TUNISIA                   0.0428 -1.5e-04 0.00268  0.83          0.406 #> LIBYA                     0.5764 -3.0e-02 0.19100  1.39          0.165 #> SUDAN                         NA       NA      NA    NA             NA #> EGYPT                     4.0118 -4.1e-01 8.97211  1.48          0.140 resG <- localG(afcon$totcon, nb2listw(include.self(paper.nb))) print(data.frame(resG[oid], row.names=afcon$name[oid]), digits=2) #>                          resG.oid. #> THE GAMBIA                  -0.984 #> MALI                        -1.699 #> SENEGAL                     -1.463 #> BENIN                       -1.301 #> MAURITANIA                  -0.605 #> NIGER                       -1.049 #> IVORY COAST                 -1.417 #> GUINEA                      -1.449 #> BURKINA FASO                -1.751 #> LIBERIA                     -1.041 #> SIERRA LEONE                -0.870 #> GHANA                       -1.103 #> TOGO                        -0.991 #> CAMEROON                    -1.133 #> NIGERIA                     -1.173 #> GABON                       -0.789 #> CENTRAL AFRICAN REPUBLIC     1.173 #> CHAD                         0.463 #> CONGO                       -0.203 #> ZAIRE                        2.023 #> ANGOLA                       1.235 #> UGANDA                       3.336 #> KENYA                        3.503 #> TANZANIA                     1.098 #> BURUNDI                      0.774 #> RWANDA                       1.457 #> SOMALIA                      1.183 #> ETHIOPIA                     2.627 #> ZAMBIA                       0.753 #> ZIMBABWE                    -0.200 #> MALAWI                       0.212 #> MOZAMBIQUE                  -0.288 #> SOUTH AFRICA                -0.868 #> LESOTHO                     -0.298 #> BOTSWANA                     0.041 #> SWAZILAND                   -0.659 #> MOROCCO                      0.022 #> ALGERIA                     -0.363 #> TUNISIA                      0.579 #> LIBYA                        2.553 #> SUDAN                        4.039 #> EGYPT                        4.421 set.seed(1) resI_p <- localmoran_perm(afcon$totcon, nb2listw(paper.nb)) printCoefmat(data.frame(resI_p[oid,], row.names=afcon$name[oid]),  check.names=FALSE) #>                                   Ii        E.Ii      Var.Ii        Z.Ii #> THE GAMBIA                3.7523e-01 -3.0853e-02  9.0476e-01  4.2692e-01 #> MALI                      4.6363e-01 -2.1690e-02  1.2192e-01  1.3899e+00 #> SENEGAL                   2.5670e-01 -1.1288e-02  3.2719e-02  1.4816e+00 #> BENIN                     1.9412e-01 -6.5012e-03  2.6046e-02  1.2431e+00 #> MAURITANIA                9.7053e-02 -2.0574e-03  5.7209e-02  4.1437e-01 #> NIGER                     2.3071e-01 -2.8428e-02  1.1981e-01  7.4867e-01 #> IVORY COAST               2.9004e-01 -8.1011e-03  5.5564e-02  1.2648e+00 #> GUINEA                    1.8263e-01  5.3454e-04  1.8397e-02  1.3425e+00 #> BURKINA FASO              5.0828e-01 -2.9727e-02  1.4019e-01  1.4369e+00 #> LIBERIA                   1.8565e-01 -1.9247e-03  3.6524e-02  9.8147e-01 #> SIERRA LEONE              2.6523e-01  1.0225e-02  3.1505e-01  4.5432e-01 #> GHANA                     1.4764e-01 -6.7639e-03  1.8646e-02  1.1307e+00 #> TOGO                      2.1934e-01 -1.8012e-03  6.5187e-02  8.6616e-01 #> CAMEROON                  2.5925e-01 -1.0726e-02  9.4789e-02  8.7688e-01 #> NIGERIA                   1.1377e-01 -2.5672e-03  8.7720e-03  1.2421e+00 #> GABON                     2.0366e-01 -3.5024e-03  1.0958e-01  6.2584e-01 #> CENTRAL AFRICAN REPUBLIC -4.4206e-01  2.3901e-02  8.1700e-02 -1.6302e+00 #> CHAD                     -1.0528e-01  5.9042e-03  3.0168e-02 -6.4016e-01 #> CONGO                     1.1380e-02  7.0349e-03  8.9435e-03  4.5949e-02 #> ZAIRE                     7.0978e-01 -2.9589e-02  2.9068e-01  1.3714e+00 #> ANGOLA                    1.1797e-01 -3.0421e-04  8.6526e-03  1.2716e+00 #> UGANDA                    1.9425e+00 -7.0491e-02  5.2046e-01  2.7903e+00 #> KENYA                     1.1969e+00 -1.6362e-02  1.3644e-01  3.2847e+00 #> TANZANIA                  2.7185e-01 -7.3309e-02  2.3454e-01  7.1272e-01 #> BURUNDI                  -4.8428e-01  9.5351e-03  1.4866e-01 -1.2807e+00 #> RWANDA                   -7.5236e-01 -4.0426e-02  1.7628e-01 -1.6956e+00 #> SOMALIA                   4.5277e-01 -1.1165e-02  2.6266e-01  9.0523e-01 #> ETHIOPIA                  7.2512e-01  8.3618e-04  7.8477e-02  2.5855e+00 #> ZAMBIA                    4.2160e-02 -5.1840e-03  3.6852e-03  7.7989e-01 #> ZIMBABWE                 -9.5068e-03 -6.5338e-03  6.5357e-02 -1.1629e-02 #> MALAWI                   -2.2888e-01  3.6276e-03  1.3417e-01 -6.3477e-01 #> MOZAMBIQUE                1.6790e-02 -2.0694e-03  4.5436e-02  8.8476e-02 #> SOUTH AFRICA             -1.8254e-01 -1.1611e-02  3.0240e-02 -9.8293e-01 #> LESOTHO                  -4.1935e-01 -6.6258e-02  8.7314e-01 -3.7787e-01 #> BOTSWANA                 -3.9316e-03 -4.7713e-03  2.2167e-03  1.7833e-02 #> SWAZILAND                 1.6684e-02 -8.4486e-02  6.4807e-01  1.2567e-01 #> MOROCCO                  -9.6961e-02 -2.1623e-03  1.1253e-01 -2.8260e-01 #> ALGERIA                  -1.0037e-02 -3.4326e-04  6.3541e-04 -3.8456e-01 #> TUNISIA                   5.3873e-03 -1.6456e-04  6.4187e-05  6.9298e-01 #> LIBYA                     8.0382e-01 -2.9038e-02  1.3319e-01  2.2821e+00 #> SUDAN                     2.9878e+00 -2.5952e-01  8.2522e-01  3.5747e+00 #> EGYPT                     6.9467e+00 -3.7869e-01  4.1318e+00  3.6038e+00 #>                          Pr.z....E.Ii.. Pr.z....E.Ii...Sim Pr.folded..Sim #> THE GAMBIA                   6.6944e-01         8.3200e-01     4.2800e-01 #> MALI                         1.6455e-01         8.8000e-02     4.4000e-02 #> SENEGAL                      1.3846e-01         6.4000e-02     3.2000e-02 #> BENIN                        2.1384e-01         1.3200e-01     6.6000e-02 #> MAURITANIA                   6.7860e-01         7.5600e-01     3.7800e-01 #> NIGER                        4.5406e-01         5.0000e-01     2.5000e-01 #> IVORY COAST                  2.0595e-01         1.1600e-01     5.8000e-02 #> GUINEA                       1.7943e-01         7.2000e-02     3.6000e-02 #> BURKINA FASO                 1.5075e-01         9.2000e-02     4.6000e-02 #> LIBERIA                      3.2636e-01         3.0400e-01     1.5200e-01 #> SIERRA LEONE                 6.4960e-01         8.2400e-01     4.1200e-01 #> GHANA                        2.5816e-01         1.8400e-01     9.2000e-02 #> TOGO                         3.8640e-01         3.6800e-01     1.8400e-01 #> CAMEROON                     3.8055e-01         4.3200e-01     2.1600e-01 #> NIGERIA                      2.1418e-01         1.4400e-01     7.2000e-02 #> GABON                        5.3142e-01         5.8400e-01     2.9600e-01 #> CENTRAL AFRICAN REPUBLIC     1.0306e-01         1.8400e-01     9.2000e-02 #> CHAD                         5.2207e-01         4.5200e-01     2.2600e-01 #> CONGO                        9.6335e-01         8.5600e-01     4.2800e-01 #> ZAIRE                        1.7026e-01         2.0000e-01     1.0000e-01 #> ANGOLA                       2.0353e-01         2.3600e-01     1.1800e-01 #> UGANDA                       5.2662e-03         4.0000e-02     2.0000e-02 #> KENYA                        1.0210e-03         8.0000e-03     4.0000e-03 #> TANZANIA                     4.7602e-01         4.2400e-01     2.1200e-01 #> BURUNDI                      2.0029e-01         2.6800e-01     1.3400e-01 #> RWANDA                       8.9953e-02         1.4000e-01     7.0000e-02 #> SOMALIA                      3.6535e-01         2.8800e-01     1.4600e-01 #> ETHIOPIA                     9.7244e-03         3.6000e-02     1.8000e-02 #> ZAMBIA                       4.3546e-01         4.1200e-01     2.0600e-01 #> ZIMBABWE                     9.9072e-01         8.6800e-01     4.3400e-01 #> MALAWI                       5.2558e-01         4.5600e-01     2.2800e-01 #> MOZAMBIQUE                   9.2950e-01         9.4400e-01     4.7200e-01 #> SOUTH AFRICA                 3.2564e-01         3.5200e-01     1.7600e-01 #> LESOTHO                      7.0553e-01         4.6800e-01     2.2400e-01 #> BOTSWANA                     9.8577e-01         8.4400e-01     4.2200e-01 #> SWAZILAND                    8.9999e-01         8.8400e-01     4.4200e-01 #> MOROCCO                      7.7749e-01         9.7600e-01     4.8800e-01 #> ALGERIA                      7.0057e-01         8.0400e-01     4.0200e-01 #> TUNISIA                      4.8832e-01         4.2800e-01     2.1600e-01 #> LIBYA                        2.2482e-02         4.8000e-02     2.4000e-02 #> SUDAN                        3.5067e-04         8.0000e-03     4.0000e-03 #> EGYPT                        3.1358e-04         1.6000e-02     8.0000e-03 #>                             Skewness Kurtosis #> THE GAMBIA               -1.7643e+00   3.3422 #> MALI                     -8.2875e-01   0.8397 #> SENEGAL                  -7.1779e-01   0.3689 #> BENIN                    -8.5318e-01   0.5520 #> MAURITANIA               -9.6301e-01   1.3949 #> NIGER                    -6.3767e-01   0.2577 #> IVORY COAST              -8.3750e-01   0.6786 #> GUINEA                   -8.8298e-01   0.7691 #> BURKINA FASO             -7.7665e-01   0.5911 #> LIBERIA                  -9.7191e-01   1.2327 #> SIERRA LEONE             -1.0737e+00   0.6367 #> GHANA                    -9.6554e-01   0.8587 #> TOGO                     -1.0772e+00   1.2283 #> CAMEROON                 -8.1844e-01   1.1746 #> NIGERIA                  -6.3061e-01   0.1168 #> GABON                    -1.1947e+00   1.1977 #> CENTRAL AFRICAN REPUBLIC -6.7964e-01  -0.1428 #> CHAD                     -9.5123e-01   0.8025 #> CONGO                    -9.5359e-01   0.9288 #> ZAIRE                     6.6929e-01   0.5829 #> ANGOLA                    1.0230e+00   1.0841 #> UGANDA                    9.6607e-01   1.3331 #> KENYA                     8.5205e-01   0.5240 #> TANZANIA                  8.5767e-01   1.2127 #> BURUNDI                  -1.0634e+00   0.9779 #> RWANDA                   -9.5905e-01   0.8365 #> SOMALIA                   1.5185e+00   2.7876 #> ETHIOPIA                  9.9587e-01   0.7374 #> ZAMBIA                    4.9495e-01   0.1900 #> ZIMBABWE                 -8.0240e-01   0.4192 #> MALAWI                   -1.1246e+00   1.7228 #> MOZAMBIQUE               -7.6989e-01   0.5793 #> SOUTH AFRICA              5.6394e-01   0.1988 #> LESOTHO                  -1.7905e+00   2.9865 #> BOTSWANA                 -9.4637e-01   0.5722 #> SWAZILAND                -1.3081e+00   1.7612 #> MOROCCO                   1.2705e+00   1.5574 #> ALGERIA                   6.3958e-01   0.2677 #> TUNISIA                   1.2498e+00   1.2249 #> LIBYA                     7.3453e-01   0.5219 #> SUDAN                     4.3993e-01  -0.1019 #> EGYPT                     1.1875e+00   1.6480"},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.sad.html","id":null,"dir":"Reference","previous_headings":"","what":"Saddlepoint approximation of local Moran's Ii tests — localmoran.sad","title":"Saddlepoint approximation of local Moran's Ii tests — localmoran.sad","text":"function implements Tiefelsdorf's application Saddlepoint approximation local Moran's Ii's reference distribution. model object class \"lm\", global independence assumed; class \"sarlm\", global dependence assumed represented spatial parameter model. Tests reported separately zone selected, may summarised using summary.localmoransad. Values local Moran's Ii agree localmoran(), function, standard deviate - Saddlepoint approximation - based randomisation assumption.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.sad.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Saddlepoint approximation of local Moran's Ii tests — localmoran.sad","text":"","code":"localmoran.sad(model, select, nb, glist=NULL, style=\"W\",  zero.policy=NULL, alternative=\"two.sided\", spChk=NULL,  resfun=weighted.residuals, save.Vi=FALSE,  tol = .Machine$double.eps^0.5, maxiter = 1000, tol.bounds=0.0001,  save.M=FALSE, Omega = NULL) <!-- %as.data.frame.localmoransad(x, row.names=NULL, optional=FALSE)  --> # S3 method for class 'localmoransad' print(x, ...) # S3 method for class 'localmoransad' summary(object, ...) # S3 method for class 'summary.localmoransad' print(x, ...) listw2star(listw, ireg, style, n, D, a, zero.policy=attr(listw, \"zero.policy\"))"},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.sad.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Saddlepoint approximation of local Moran's Ii tests — localmoran.sad","text":"model object class lm returned lm (assuming global spatial autocorrelation), object class sarlm returned spatial simultaneous autoregressive model fit (assuming global spatial autocorrelation represented model spatial coefficient); weights may specified lm fit, offsets used select integer vector id. numbers zones tested; missing, zones nb list neighbours class nb glist list general weights corresponding neighbours style can take values W, B, C, S zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA alternative character string specifying alternative hypothesis, must one greater (default), less two.sided. spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption() resfun default: weighted.residuals; function used extract residuals lm object, may residuals, weighted.residuals, rstandard, rstudent save.Vi TRUE, return star-shaped weights lists zone tested tol desired accuracy (convergence tolerance) uniroot maxiter maximum number iterations uniroot tol.bounds offset bounds uniroot save.M TRUE, save list left right M products list conditional tests, list regression model matrix components Omega SAR process matrix may passed test alternative hypothesis, example Omega <- invIrW(listw, rho=0.1); Omega <- tcrossprod(Omega), chol() taken internally x object printed  object object summarised ... arguments passed listw listw object created example nb2listw ireg zone number n internal value depending listw style D internal value depending listw style internal value depending listw style","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.sad.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Saddlepoint approximation of local Moran's Ii tests — localmoran.sad","text":"function implements analytical eigenvalue calculation together trace shortcuts given suggested Tiefelsdorf (2002), partly following remarks J. Keith Ord, uses Saddlepoint analytical solution Tiefelsdorf's SPSS code. histogram probability values saddlepoint estimate assumption global independence approximately flat, assumption probably unjustified, re-estimation global dependence recommended. n n matrices needed point test assuming global dependence, star-shaped weights matrices handled listw lists. test made residuals spatial regression, taking global process account. n n matrices necessary, memory constraints may reached large lattices.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.sad.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Saddlepoint approximation of local Moran's Ii tests — localmoran.sad","text":"list class localmoransad containing \"select\" lists,  class moransad following components: statistic value saddlepoint approximation  standard deviate local Moran's Ii. p.value p-value test. estimate value observed local Moran's Ii. alternative character string describing alternative hypothesis. method character string giving method used. data.name character string giving name(s) data. internal1 Saddlepoint omega, r u df degrees freedom tau maximum minimum analytical eigenvalues zone tested","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.sad.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Saddlepoint approximation of local Moran's Ii tests — localmoran.sad","text":"Tiefelsdorf, M. 2002 Saddlepoint approximation Moran's local Moran's Ii reference distributions numerical evaluation. Geographical Analysis, 34, pp. 187–206.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.sad.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Saddlepoint approximation of local Moran's Ii tests — localmoran.sad","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.sad.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Saddlepoint approximation of local Moran's Ii tests — localmoran.sad","text":"","code":"eire <- st_read(system.file(\"shapes/eire.gpkg\", package=\"spData\")[1]) #> Reading layer `eire' from data source  #>   `/home/rsb/lib/r_libs/spData/shapes/eire.gpkg' using driver `GPKG' #> Simple feature collection with 26 features and 10 fields #> Geometry type: MULTIPOLYGON #> Dimension:     XY #> Bounding box:  xmin: -4.12 ymin: 5768 xmax: 300.82 ymax: 6119.25 #> Projected CRS: Undefined Cartesian SRS with unknown unit row.names(eire) <- as.character(eire$names) eire.nb <- poly2nb(eire) lw <- nb2listw(eire.nb) e.lm <- lm(OWNCONS ~ ROADACC, data=eire) e.locmor <- summary(localmoran.sad(e.lm, nb=eire.nb)) e.locmor #>              Local Morans I Stand. dev. (N)      Pr. (N) Saddlepoint #> 1 Carlow         0.21699668      0.74177148 4.582258e-01  0.95074844 #> 2 Cavan         -0.37257361     -0.81297374 1.583767e+00 -1.00603119 #> 3 Clare          0.23197510      0.49502499 6.205825e-01  0.67166518 #> 4 Cork           0.78193548      1.75999915 7.840795e-02  1.74761575 #> 5 Donegal       -1.69064059     -1.98244914 1.952571e+00 -1.72031078 #> 6 Dublin        -0.16069692     -0.15041940 1.119566e+00 -0.35212627 #> 7 Galway         1.31371473      3.34305297 8.286208e-04  2.66849536 #> 8 Kerry          0.36534866      0.58147812 5.609183e-01  0.78073279 #> 9 Kildare       -0.02557544      0.15146558 8.796085e-01  0.04167665 #> 10 Kilkenny      0.57684331      1.62868431 1.033799e-01  1.70897697 #> 11 Laoghis      -0.05951798      0.01724651 9.862400e-01 -0.12155465 #> 12 Leitrim       0.38484587      1.27548777 2.021367e-01  1.47227033 #> 13 Limerick      0.11817987      0.34038037 7.335701e-01  0.45727712 #> 14 Longford      1.41643200      3.10732224 1.887905e-03  2.51113769 #> 15 Louth         0.56242920      0.87665682 3.806731e-01  1.07441571 #> 16 Mayo          0.87572704      2.02375701 4.299516e-02  2.05251226 #> 17 Meath         0.00367856      0.16081712 8.722374e-01  0.12813539 #> 18 Monaghan      0.55098311      1.06684464 2.860420e-01  1.23999193 #> 19 Offaly        0.15155556      0.61933942 5.356928e-01  0.80786519 #> 20 Roscommon     2.04368839      6.66107106 2.718381e-11  4.53187292 #> 21 Sligo        -0.47579871     -0.73430274 1.537236e+00 -0.94578114 #> 22 Tipperary    -0.03454106      0.04843351 9.613708e-01 -0.06919691 #> 23 Waterford     0.85723423      1.98516133 4.712653e-02  1.91385108 #> 24 Westmeath     0.45138572      1.20305006 2.289569e-01  1.36017204 #> 25 Wexford       0.64371834      1.55468550 1.200210e-01  1.63188492 #> 26 Wicklow       0.02441950      0.21823347 8.272472e-01  0.21197000 #>                 Pr. (Sad) Expectation   Variance   Skewness Kurtosis    Minimum #> 1 Carlow     3.417321e-01 -0.06471134 0.14423085 -0.7895263 7.059116  -5.461326 #> 2 Cavan      3.144006e-01 -0.04030838 0.16703857 -0.4622793 6.813004  -5.567356 #> 3 Clare      5.017969e-01 -0.04219377 0.30674823 -0.3579185 6.761932  -7.406885 #> 4 Cork       8.053059e-02 -0.04363826 0.22003250 -0.4363325 6.799081  -6.360927 #> 5 Donegal    8.537596e-02 -0.11935726 0.62821008 -0.7004303 6.979051 -11.236382 #> 6 Dublin     7.247436e-01 -0.08240217 0.27093033 -0.7352902 7.009201  -7.420687 #> 7 Galway     7.619183e-03 -0.04389010 0.16491503 -0.5059997 6.838308  -5.573707 #> 8 Kerry      4.349597e-01 -0.03212369 0.46724761 -0.2212594 6.714810  -8.915104 #> 9 Kildare    9.667565e-01 -0.07623733 0.11187546 -1.0416026 7.339962  -4.999621 #> 10 Kilkenny  8.745521e-02 -0.05911601 0.15247016 -0.7040737 6.982131  -5.538889 #> 11 Laoghis   9.032517e-01 -0.06620117 0.15016408 -0.7915137 7.061015  -5.574277 #> 12 Leitrim   1.409479e-01 -0.06828680 0.12621127 -0.8864130 7.157471  -5.186756 #> 13 Limerick  6.474719e-01 -0.04172917 0.22070746 -0.4167943 6.789132  -6.348870 #> 14 Longford  1.203427e-02 -0.04055162 0.21985521 -0.4059156 6.783792  -6.324457 #> 15 Louth     2.826364e-01 -0.04386717 0.47831137 -0.2983105 6.738631  -9.149779 #> 16 Mayo      4.011990e-02 -0.10340651 0.23408152 -0.9804377 7.264328  -7.165847 #> 17 Meath     8.980418e-01 -0.04799533 0.10324707 -0.6949022 6.974408  -4.551176 #> 18 Monaghan  2.149784e-01 -0.04136950 0.30828917 -0.3501006 6.758633  -7.415047 #> 19 Offaly    4.191682e-01 -0.04662212 0.10238870 -0.6782821 6.960676  -4.519986 #> 20 Roscommon 5.846302e-06 -0.04435301 0.09826301 -0.6591526 6.945294  -4.414164 #> 21 Sligo     3.442602e-01 -0.11041170 0.24760301 -1.0156782 7.307311  -7.409091 #> 22 Tipperary 9.448329e-01 -0.04872132 0.08571886 -0.7716947 7.042300  -4.198353 #> 23 Waterford 5.563919e-02 -0.05435079 0.21086415 -0.5533724 6.868342  -6.353514 #> 24 Westmeath 1.737755e-01 -0.04181671 0.16806722 -0.4779156 6.821788  -5.599610 #> 25 Wexford   1.027037e-01 -0.05432673 0.20159596 -0.5654870 6.876461  -6.225016 #> 26 Wicklow   8.321304e-01 -0.07022471 0.18808122 -0.7515626 7.023792  -6.198974 #>               Maximum        omega       sad.r       sad.u #> 1 Carlow     3.908254  0.071122863  0.71853146  0.84900467 #> 2 Cavan      4.599954 -0.051532330 -0.69003582 -0.85816092 #> 3 Clare      6.394234  0.031939551  0.46982957  0.51656357 #> 4 Cork       5.313609  0.083281515  1.43928884  2.24323856 #> 5 Donegal    8.371808 -0.039371561 -1.39288713 -2.19776923 #> 6 Dublin     5.443035 -0.010354512 -0.14127218 -0.14554367 #> 7 Galway     4.520344  0.134873939  2.39189491  4.63522665 #> 8 Kerry      8.144135  0.028431952  0.54051534  0.61545648 #> 9 Kildare    3.169925  0.018723213  0.14926096  0.14688325 #> 10 Kilkenny  4.120105  0.105365819  1.40668493  2.15214600 #> 11 Laoghis   3.985449  0.001724096  0.01660985  0.01657177 #> 12 Leitrim   3.547872  0.109608339  1.18229964  1.66578026 #> 13 Limerick  5.347370  0.027585567  0.32820959  0.34241163 #> 14 Longford  5.351218  0.108368224  2.22687206  4.19385821 #> 15 Louth     8.096967  0.037745731  0.78968254  0.98878788 #> 16 Mayo      4.684091  0.105317102  1.75922892  2.94711915 #> 17 Meath     3.399289  0.020074178  0.15693992  0.15623206 #> 18 Monaghan  6.422179  0.053418031  0.94193428  1.24723730 #> 19 Offaly    3.401055  0.071432961  0.59871278  0.67858124 #> 20 Roscommon 3.349691  0.357114199  4.33885200 10.02517077 #> 21 Sligo     4.759210 -0.036185300 -0.60775394 -0.74635955 #> 22 Tipperary 3.029041  0.006482570  0.04683010  0.04657633 #> 23 Waterford 5.049095  0.093409563  1.61022194  2.62552879 #> 24 Westmeath 4.596009  0.080097979  1.05978192  1.45704611 #> 25 Wexford   4.921174  0.085478829  1.32647942  1.98902088 #> 26 Wicklow   4.513581  0.020437514  0.21417067  0.21406975 mean(e.locmor[,1]) #> [1] 0.3366057 sum(e.locmor[,1])/Szero(lw) #> [1] 0.3366057 lm.morantest(e.lm, lw) #>  #> \tGlobal Moran I for regression residuals #>  #> data:   #> model: lm(formula = OWNCONS ~ ROADACC, data = eire) #> weights: lw #>  #> Moran I statistic standard deviate = 3.2575, p-value = 0.0005619 #> alternative hypothesis: greater #> sample estimates: #> Observed Moran I      Expectation         Variance  #>       0.33660565      -0.05877741       0.01473183  #>  # note equality for mean() only when the sum of weights equals # the number of observations (thanks to Juergen Symanzik) hist(e.locmor[,\"Pr. (Sad)\"])  e.wlm <- lm(OWNCONS ~ ROADACC, data=eire, weights=RETSALE) e.locmorw1 <- summary(localmoran.sad(e.wlm, nb=eire.nb, resfun=weighted.residuals)) e.locmorw1 #>              Local Morans I Stand. dev. (N)      Pr. (N) Saddlepoint #> 1 Carlow        0.160490657      0.41009538 6.817360e-01  0.57729730 #> 2 Cavan        -0.144663771     -0.27825575 1.219184e+00 -0.45305168 #> 3 Clare         0.301676582      0.59021701 5.550452e-01  0.78987327 #> 4 Cork          1.520488153      3.49016956 4.827142e-04  2.83665634 #> 5 Donegal      -0.435899664     -0.44665946 1.344879e+00 -0.67136090 #> 6 Dublin       -0.340222996     -0.60886675 1.457387e+00 -0.85658016 #> 7 Galway        1.469009037      3.64546192 2.669119e-04  2.82274510 #> 8 Kerry         0.268957279      0.49517211 6.204786e-01  0.66861012 #> 9 Kildare       0.002996577      0.12659200 8.992633e-01  0.09978249 #> 10 Kilkenny     0.497968801      1.20610829 2.277757e-01  1.34091379 #> 11 Laoghis     -0.026328708     -0.01713904 1.013674e+00 -0.06511750 #> 12 Leitrim      0.277306386      0.80644537 4.199861e-01  1.01176491 #> 13 Limerick     0.263122939      0.67591893 4.990921e-01  0.87759628 #> 14 Longford     0.605211711      1.23874274 2.154408e-01  1.35375850 #> 15 Louth        0.359469683      0.53572990 5.921452e-01  0.73280188 #> 16 Mayo         1.742480472      3.68118786 2.321499e-04  3.01500163 #> 17 Meath       -0.112171618     -0.26680698 1.210382e+00 -0.45470531 #> 18 Monaghan     0.241044892      0.46013751 6.454175e-01  0.64094159 #> 19 Offaly       0.129191178      0.40988983 6.818868e-01  0.57205532 #> 20 Roscommon    1.469671750      4.39927211 1.086146e-05  3.13215267 #> 21 Sligo        0.095559559      0.31036587 7.562827e-01  0.38503064 #> 22 Tipperary    0.088352646      0.39958273 6.894639e-01  0.52592105 #> 23 Waterford    1.212658861      2.69846035 6.966104e-03  2.29292584 #> 24 Westmeath    0.256165310      0.61222265 5.403905e-01  0.81620859 #> 25 Wexford      0.619197906      1.31967483 1.869436e-01  1.42553832 #> 26 Wicklow      0.006531073      0.13142161 8.954418e-01  0.10986725 #>                Pr. (Sad) Expectation   Variance   Skewness Kurtosis    Minimum #> 1 Carlow     0.563738639 -0.01840558 0.19029731 -0.1986977 6.709176  -5.665283 #> 2 Cavan      0.650511526 -0.02184465 0.19482455 -0.2329761 6.717975  -5.769371 #> 3 Clare      0.429601786 -0.02782578 0.31166901 -0.2346279 6.718435  -7.299407 #> 4 Cork       0.004558865 -0.07147410 0.20805228 -0.7280203 7.002789  -6.495227 #> 5 Donegal    0.501990650 -0.07638800 0.64784767 -0.4450323 6.803659 -10.931345 #> 6 Dublin     0.391676955 -0.11187469 0.14065367 -1.3324828 7.767845  -5.846924 #> 7 Galway     0.004761441 -0.04407925 0.17227545 -0.4973247 6.833103  -5.688263 #> 8 Kerry      0.503744214 -0.05644300 0.43184063 -0.4031537 6.782459  -8.859407 #> 9 Kildare    0.920517009 -0.04145378 0.12329287 -0.5519841 6.867423  -4.857131 #> 10 Kilkenny  0.179948446 -0.02321457 0.18672759 -0.2528322 6.723714  -5.669156 #> 11 Laoghis   0.948080445 -0.01882531 0.19166504 -0.2024943 6.710081  -5.689691 #> 12 Leitrim   0.311650473 -0.03314655 0.14819776 -0.4041387 6.782933  -5.190860 #> 13 Limerick  0.380162847 -0.04800976 0.21188592 -0.4885390 6.827925  -6.298874 #> 14 Longford  0.175813436 -0.01321709 0.24923967 -0.1247567 6.694960  -6.392250 #> 15 Louth     0.463679274 -0.02272663 0.50895713 -0.1500895 6.699098  -9.179410 #> 16 Mayo      0.002569779 -0.09458039 0.24904116 -0.8745463 7.144787  -7.272523 #> 17 Meath     0.649321260 -0.02548973 0.10555100 -0.3685280 6.766525  -4.353122 #> 18 Monaghan  0.521560632 -0.02333303 0.33012248 -0.1912612 6.707452  -7.451275 #> 19 Offaly    0.567284497 -0.01927989 0.13120470 -0.2505068 6.723017  -4.750083 #> 20 Roscommon 0.001735296 -0.02385522 0.11525625 -0.3302939 6.750604  -4.517676 #> 21 Sligo     0.700214717 -0.06927688 0.28207107 -0.6087587 6.906925  -7.416881 #> 22 Tipperary 0.598943063 -0.03719246 0.09871568 -0.5534442 6.868390  -4.347214 #> 23 Waterford 0.021852275 -0.04027429 0.21558757 -0.4070996 6.784366  -6.264083 #> 24 Westmeath 0.414380842 -0.01522814 0.19650786 -0.1618342 6.701275  -5.716689 #> 25 Wexford   0.154001651 -0.02786850 0.24041626 -0.2674357 6.728234  -6.450174 #> 26 Wicklow   0.912514660 -0.04751424 0.16911517 -0.5404006 6.859847  -5.677417 #>               Maximum        omega       sad.r       sad.u #> 1 Carlow     5.223549  0.033637462  0.38794383  0.41751442 #> 2 Cavan      5.245099 -0.022294725 -0.26091513 -0.27432856 #> 3 Clare      6.631589  0.035302524  0.54866959  0.62630505 #> 4 Cork       4.779848  0.134384022  2.56890121  5.11058941 #> 5 Donegal    9.098033 -0.017507303 -0.40402088 -0.45010348 #> 6 Dublin     3.161931 -0.040828131 -0.50710580 -0.60543071 #> 7 Galway     4.630361  0.138454493  2.55314856  5.08170760 #> 8 Kerry      7.504775  0.027195108  0.47167584  0.51758880 #> 9 Kildare    3.862240  0.014230854  0.12280697  0.12246022 #> 10 Kilkenny  5.112007  0.071351828  1.03314661  1.41988761 #> 11 Laoghis   5.237883 -0.001502568 -0.01645549 -0.01646868 #> 12 Leitrim   4.395343  0.066207108  0.74158109  0.90609823 #> 13 Limerick  5.146640  0.050265468  0.63703133  0.74253221 #> 14 Longford  6.075040  0.060534639  1.04112815  1.44165700 #> 15 Louth     8.633971  0.025231866  0.49793592  0.55971045 #> 16 Mayo      5.002594  0.135902733  2.75603129  5.62669411 #> 17 Meath     3.741368 -0.028724497 -0.24912602 -0.26221742 #> 18 Monaghan  6.891283  0.028042744  0.43280552  0.47360371 #> 19 Offaly    4.287365  0.040883462  0.38909358  0.41780262 #> 20 Roscommon 3.945151  0.180270100  2.87643937  6.00202551 #> 21 Sligo     5.754236  0.023145822  0.30299868  0.31062426 #> 22 Tipperary 3.454595  0.048932861  0.38768333  0.40902706 #> 23 Waterford 5.297500  0.101874758  1.99944904  3.59542986 #> 24 Westmeath 5.351214  0.044919886  0.56403221  0.65024353 #> 25 Wexford   5.781330  0.066083430  1.11524637  1.57637406 #> 26 Wicklow   4.537075  0.012609906  0.12748740  0.12720134 e.locmorw2 <- summary(localmoran.sad(e.wlm, nb=eire.nb, resfun=rstudent)) e.locmorw2 #>              Local Morans I Stand. dev. (N)      Pr. (N) Saddlepoint #> 1 Carlow        0.121997164      0.32185426 0.7475631028  0.45871930 #> 2 Cavan        -0.110588620     -0.20105599 1.1593452023 -0.34808741 #> 3 Clare         0.308759283      0.60290381 0.5465726820  0.80379674 #> 4 Cork          1.404203115      3.23522979 0.0012154487  2.69598105 #> 5 Donegal      -0.421182109     -0.42837428 1.3316213558 -0.65187732 #> 6 Dublin       -0.443534307     -0.88433550 1.6234848706 -1.05167518 #> 7 Galway        1.376190254      3.42183495 0.0006220006  2.70663064 #> 8 Kerry         0.241623387      0.45357724 0.6501331373  0.61515126 #> 9 Kildare       0.008842913      0.14324202 0.8860990418  0.12690939 #> 10 Kilkenny     0.382893124      0.93980330 0.3473184643  1.12810394 #> 11 Laoghis     -0.019904450     -0.00246494 1.0019667357 -0.04176107 #> 12 Leitrim      0.200483743      0.60688769 0.5439254449  0.80241456 #> 13 Limerick     0.238810092      0.62310059 0.5332184222  0.81824678 #> 14 Longford     0.466942853      0.96178354 0.3361583457  1.14088225 #> 15 Louth        0.271710988      0.41271732 0.6798137369  0.58520655 #> 16 Mayo         1.705850161      3.60778634 0.0003088206  2.97346461 #> 17 Meath       -0.160603054     -0.41587901 1.3225014587 -0.63254531 #> 18 Monaghan     0.181378604      0.35629110 0.7216225742  0.50697175 #> 19 Offaly       0.107919508      0.35116431 0.7254650854  0.49312417 #> 20 Roscommon    1.249826037      3.75170355 0.0001756371  2.81402777 #> 21 Sligo        0.079431883      0.27999953 0.7794778655  0.33741411 #> 22 Tipperary    0.085153638      0.38940098 0.6969795442  0.51126046 #> 23 Waterford    1.022922345      2.28982205 0.0220316342  2.06385578 #> 24 Westmeath    0.201539331      0.48899468 0.6248454598  0.67791734 #> 25 Wexford      0.481114325      1.03805702 0.2992435100  1.21094348 #> 26 Wicklow     -0.011694661      0.08710223 0.9305902563  0.03786608 #>                Pr. (Sad) Expectation   Variance   Skewness Kurtosis    Minimum #> 1 Carlow     0.646435751 -0.01840558 0.19029731 -0.1986977 6.709176  -5.665283 #> 2 Cavan      0.727774542 -0.02184465 0.19482455 -0.2329761 6.717975  -5.769371 #> 3 Clare      0.421514374 -0.02782578 0.31166901 -0.2346279 6.718435  -7.299407 #> 4 Cork       0.007018166 -0.07147410 0.20805228 -0.7280203 7.002789  -6.495227 #> 5 Donegal    0.514480318 -0.07638800 0.64784767 -0.4450323 6.803659 -10.931345 #> 6 Dublin     0.292948602 -0.11187469 0.14065367 -1.3324828 7.767845  -5.846924 #> 7 Galway     0.006796983 -0.04407925 0.17227545 -0.4973247 6.833103  -5.688263 #> 8 Kerry      0.538454834 -0.05644300 0.43184063 -0.4031537 6.782459  -8.859407 #> 9 Kildare    0.899012117 -0.04145378 0.12329287 -0.5519841 6.867423  -4.857131 #> 10 Kilkenny  0.259276027 -0.02321457 0.18672759 -0.2528322 6.723714  -5.669156 #> 11 Laoghis   0.966689166 -0.01882531 0.19166504 -0.2024943 6.710081  -5.689691 #> 12 Leitrim   0.422313193 -0.03314655 0.14819776 -0.4041387 6.782933  -5.190860 #> 13 Limerick  0.413216288 -0.04800976 0.21188592 -0.4885390 6.827925  -6.298874 #> 14 Longford  0.253918927 -0.01321709 0.24923967 -0.1247567 6.694960  -6.392250 #> 15 Louth     0.558408841 -0.02272663 0.50895713 -0.1500895 6.699098  -9.179410 #> 16 Mayo      0.002944584 -0.09458039 0.24904116 -0.8745463 7.144787  -7.272523 #> 17 Meath     0.527030613 -0.02548973 0.10555100 -0.3685280 6.766525  -4.353122 #> 18 Monaghan  0.612174643 -0.02333303 0.33012248 -0.1912612 6.707452  -7.451275 #> 19 Offaly    0.621924855 -0.01927989 0.13120470 -0.2505068 6.723017  -4.750083 #> 20 Roscommon 0.004892500 -0.02385522 0.11525625 -0.3302939 6.750604  -4.517676 #> 21 Sligo     0.735804747 -0.06927688 0.28207107 -0.6087587 6.906925  -7.416881 #> 22 Tipperary 0.609168686 -0.03719246 0.09871568 -0.5534442 6.868390  -4.347214 #> 23 Waterford 0.039031392 -0.04027429 0.21558757 -0.4070996 6.784366  -6.264083 #> 24 Westmeath 0.497824103 -0.01522814 0.19650786 -0.1618342 6.701275  -5.716689 #> 25 Wexford   0.225917068 -0.02786850 0.24041626 -0.2674357 6.728234  -6.450174 #> 26 Wicklow   0.969794461 -0.04751424 0.16911517 -0.5404006 6.859847  -5.677417 #>               Maximum         omega        sad.r        sad.u #> 1 Carlow     5.223549  0.0272472954  0.306852385  0.321490350 #> 2 Cavan      5.245099 -0.0166242430 -0.190223798 -0.196022741 #> 3 Clare      6.631589  0.0358559846  0.559584155  0.641527095 #> 4 Cork       4.779848  0.1283688794  2.421993662  4.702934834 #> 5 Donegal    9.098033 -0.0169574018 -0.388662370 -0.430528174 #> 6 Dublin     3.161931 -0.0507848831 -0.696824139 -0.892299501 #> 7 Galway     4.630361  0.1333224875  2.431707338  4.745166958 #> 8 Kerry      7.504775  0.0252982005  0.433626352  0.469138111 #> 9 Kildare    3.862240  0.0161278548  0.139072871  0.138837812 #> 10 Kilkenny  5.112007  0.0622219791  0.835166590  1.066654825 #> 11 Laoghis   5.237883 -0.0002164925 -0.002368023 -0.002368244 #> 12 Leitrim   4.395343  0.0543844388  0.571625643  0.652237768 #> 13 Limerick  5.146640  0.0473787285  0.590605630  0.675595582 #> 14 Longford  6.075040  0.0528365356  0.840671447  1.082014178 #> 15 Louth     8.633971  0.0204960239  0.389078238  0.419930705 #> 16 Mayo      5.002594  0.1340509166  2.712635049  5.503894365 #> 17 Meath     3.741368 -0.0415411327 -0.379736494 -0.417998694 #> 18 Monaghan  6.891283  0.0226076552  0.338579266  0.358443998 #> 19 Offaly    4.287365  0.0357600182  0.335019324  0.353243066 #> 20 Roscommon 3.945151  0.1623235556  2.543240406  5.063795948 #> 21 Sligo     5.754236  0.0209568244  0.273376649  0.278204612 #> 22 Tipperary 3.454595  0.0478130890  0.377982061  0.397511387 #> 23 Waterford 5.297500  0.0941811771  1.762051071  2.998984773 #> 24 Westmeath 5.351214  0.0379323563  0.457473561  0.506014991 #> 25 Wexford   5.781330  0.0582538352  0.911459483  1.197527949 #> 26 Wicklow   4.537075  0.0083101099  0.084281843  0.083952776 run <- FALSE if (requireNamespace(\"spatialreg\", quietly=TRUE)) run <- TRUE if (run) { e.errorsar <- spatialreg::errorsarlm(OWNCONS ~ ROADACC, data=eire,   listw=lw) if (packageVersion(\"spatialreg\") < \"1.1.7\")   spatialreg::print.sarlm(e.errorsar) else   print(e.errorsar) } #>  #> Call: #> spatialreg::errorsarlm(formula = OWNCONS ~ ROADACC, data = eire,  #>     listw = lw) #> Type: error  #>  #> Coefficients: #>      lambda (Intercept)     ROADACC  #> 0.783970989 2.892719569 0.002800913  #>  #> Log likelihood: -64.12465  if (run) { lm.target <- lm(e.errorsar$tary ~ e.errorsar$tarX - 1) Omega <- tcrossprod(spatialreg::invIrW(lw, rho=e.errorsar$lambda)) e.clocmor <- summary(localmoran.sad(lm.target, nb=eire.nb, Omega=Omega)) e.clocmor } #>              Local Morans I Stand. dev. (N)   Pr. (N) Saddlepoint    Pr. (Sad) #> 1 Carlow         0.17958462      -0.5947094 1.4479623 -0.01890335 0.9849182097 #> 2 Cavan         -0.24752628      -0.9775195 1.6716880 -1.30903979 0.1905208730 #> 3 Clare         -0.27901334      -0.9987481 1.6820833 -1.41535136 0.1569655035 #> 4 Cork           0.37808655      -0.5304596 1.4042067  0.06399747 0.9489722431 #> 5 Donegal       -1.01894688      -1.4634181 1.8566470 -1.88871177 0.0589304608 #> 6 Dublin        -0.18171297      -0.9790853 1.6724621 -1.11436913 0.2651208631 #> 7 Galway         1.02193390       0.9527103 0.3407369  1.44844014 0.1474939944 #> 8 Kerry         -0.94967914      -1.1410950 1.7461696 -2.37909992 0.0173549707 #> 9 Kildare        0.07005053      -0.6531380 1.4863327 -0.10338270 0.9176592421 #> 10 Kilkenny      0.43022231      -0.3097714 1.2432652  0.46873471 0.6392592765 #> 11 Laoghis      -0.12239133      -0.9818401 1.6738214 -0.97718184 0.3284791346 #> 12 Leitrim      -0.24203970      -0.9591963 1.6625401 -1.53246533 0.1254076470 #> 13 Limerick     -0.03214546      -0.7729433 1.5604441 -0.80301568 0.4219656705 #> 14 Longford      0.38307454      -0.4899146 1.3758057  0.16621954 0.8679841832 #> 15 Louth         0.21301552      -0.6509309 1.4849089 -0.21224290 0.8319175422 #> 16 Mayo          0.93971200       0.3895188 0.6968924  1.15011408 0.2500968882 #> 17 Meath         0.12484415      -0.6182203 1.4635699 -0.09720926 0.9225602152 #> 18 Monaghan     -0.16109919      -0.8608004 1.6106520 -1.20575831 0.2279106933 #> 19 Offaly       -0.00632492      -0.7740865 1.5611204 -0.33915072 0.7344961920 #> 20 Roscommon     1.02089429       0.6454801 0.5186161  1.21215474 0.2254531515 #> 21 Sligo        -2.01629233      -1.8957526 1.9420072 -3.59571732 0.0003234989 #> 22 Tipperary    -0.10810709      -0.9082666 1.6362626 -1.09721448 0.2725476427 #> 23 Waterford     0.44099279      -0.3488980 1.2728341  0.41219202 0.6801986841 #> 24 Westmeath    -0.06329661      -0.8267635 1.5916289 -0.81444158 0.4153920274 #> 25 Wexford       0.30764883      -0.5219835 1.3983182  0.12395154 0.9013536461 #> 26 Wicklow      -0.01696406      -0.7708237 1.5591886 -0.68244661 0.4949565907 #>              Expectation   Variance Skewness  Kurtosis       Minimum   Maximum #> 1 Carlow       0.8594106  1.3067303 2.362830 10.416149  6.743373e-17 20.625856 #> 2 Cavan        1.1247112  1.9706416 2.347202 10.347468  1.645654e+00 25.347414 #> 3 Clare        1.2679076  2.3989670 2.334022 10.287656  2.485514e+00 27.944268 #> 4 Cork         1.2841620  2.9175890 2.362830 10.416149 -2.406699e-16 30.819888 #> 5 Donegal      1.7253177  3.5165365 2.172101  9.492322  8.227735e+00 33.179890 #> 6 Dublin       0.9462667  1.3272768 2.331563 10.276363  1.928660e+00 20.781740 #> 7 Galway       0.4507425  0.3594525 2.362830 10.416149  1.587770e-16 10.817821 #> 8 Kerry        2.6933183 10.1923447 2.307813 10.165571  7.170614e+00 57.469026 #> 9 Kildare      0.5337376  0.5040110 2.362830 10.416149 -6.444628e-18 12.809701 #> 10 Kilkenny    0.7317135  0.9472545 2.362830 10.416149  5.035617e-16 17.561125 #> 11 Laoghis     0.6035313  0.5466372 2.336004 10.296727  1.143655e+00 13.341096 #> 12 Leitrim     1.2258675  2.3419747 2.347302 10.347916  1.788145e+00 27.632674 #> 13 Limerick    1.5147254  4.0050955 2.362668 10.415466  2.341575e-01 36.119253 #> 14 Longford    1.0996747  2.1395031 2.362830 10.416149  5.674463e-16 26.392192 #> 15 Louth       1.5875248  4.4588771 2.362830 10.416149  4.309554e-16 38.100594 #> 16 Mayo        0.6190019  0.6779043 2.362830 10.416149 -2.035156e-16 14.856045 #> 17 Meath       0.7025948  0.8733620 2.362830 10.416149 -7.624840e-18 16.862274 #> 18 Monaghan    1.5519577  3.9603958 2.357838 10.394611  1.306155e+00 35.940829 #> 19 Offaly      0.3048481  0.1615939 2.362560 10.415009  6.073803e-02  7.255616 #> 20 Roscommon   0.5492905  0.5338125 2.362830 10.416149  9.144870e-16 13.182973 #> 21 Sligo       2.3130311  5.2152695 1.886102  7.938452  1.739456e+01 38.118185 #> 22 Tipperary   0.7147979  0.8208668 2.354040 10.377921  7.922254e-01 16.362924 #> 23 Waterford   0.8228671  1.1979644 2.362830 10.416149  1.408133e-15 19.748811 #> 24 Westmeath   0.8426747  1.2007879 2.360962 10.408167  4.379239e-01 19.786270 #> 25 Wexford     1.0063848  1.7918953 2.362830 10.416149  1.028640e-17 24.153236 #> 26 Wicklow     0.9927147  1.7157589 2.362598 10.415171  1.833509e-01 23.641801 #>                     omega       sad.r       sad.u #> 1 Carlow     -0.017838447 -0.38297869 -0.33313448 #> 2 Cavan      -0.066132684 -1.21593175 -1.36168605 #> 3 Clare      -0.066612498 -1.30513958 -1.50704646 #> 4 Cork       -0.010368850 -0.33915229 -0.29581081 #> 5 Donegal    -0.045800559 -1.66568212 -2.41507712 #> 6 Dublin     -0.056683668 -1.03296356 -1.12358099 #> 7 Galway      0.031762997  1.14153962  1.62047125 #> 8 Kerry      -0.079689480 -2.19374456 -3.29442701 #> 9 Kildare    -0.025051491 -0.36678693 -0.33300845 #> 10 Kilkenny   0.003214928  0.09217307  0.09542846 #> 11 Laoghis   -0.065438986 -0.89335507 -0.96282454 #> 12 Leitrim   -0.092395573 -1.43474097 -1.65069014 #> 13 Limerick  -0.047140362 -0.97737323 -0.82423542 #> 14 Longford  -0.007176482 -0.22762630 -0.20810767 #> 15 Louth     -0.018552546 -0.58005974 -0.46861210 #> 16 Mayo       0.019992304  0.84088281  1.09059594 #> 17 Meath     -0.026958325 -0.44558661 -0.38151850 #> 18 Monaghan  -0.062388996 -1.21509194 -1.20138917 #> 19 Offaly    -0.044380046 -0.41568118 -0.40266554 #> 20 Roscommon  0.023338184  0.88169755  1.17993235 #> 21 Sligo     -0.131646728 -3.40243100 -6.56750200 #> 22 Tipperary -0.089378129 -1.06748205 -1.10190609 #> 23 Waterford  0.001151041  0.03534520  0.03581914 #> 24 Westmeath -0.058470593 -0.88397327 -0.83127666 #> 25 Wexford   -0.009550496 -0.26689930 -0.24045996 #> 26 Wicklow   -0.050401553 -0.84395069 -0.73641410 if (run) { hist(e.clocmor[,\"Pr. (Sad)\"]) }"},{"path":"https://r-spatial.github.io/spdep/reference/localmoran_bv.html","id":null,"dir":"Reference","previous_headings":"","what":"Compute the Local Bivariate Moran's I Statistic — localmoran_bv","title":"Compute the Local Bivariate Moran's I Statistic — localmoran_bv","text":"Given two continuous numeric variables, calculate bivariate Local Moran's .","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localmoran_bv.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Compute the Local Bivariate Moran's I Statistic — localmoran_bv","text":"","code":"localmoran_bv(x, y, listw, nsim = 199, scale = TRUE, alternative=\"two.sided\",  iseed=1L, no_repeat_in_row=FALSE, zero.policy=attr(listw, \"zero.policy\"))"},{"path":"https://r-spatial.github.io/spdep/reference/localmoran_bv.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Compute the Local Bivariate Moran's I Statistic — localmoran_bv","text":"x numeric vector length y. y numeric vector length x. listw listw object example created nb2listw(). nsim number simulations run. scale default TRUE. alternative character string specifying alternative hypothesis, must one \"greater\" (default), \"two.sided\", \"less\". iseed default NULL, used set seed; output reproducible count CPU cores across computation distributed . no_repeat_in_row default FALSE, TRUE, sample conditionally row without replacements avoid duplicate values, https://github.com/r-spatial/spdep/issues/124 zero.policy default default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localmoran_bv.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Compute the Local Bivariate Moran's I Statistic — localmoran_bv","text":"data.frame containing two columns Ib p_sim containing local bivariate Moran's simulated p-values respectively.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localmoran_bv.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Compute the Local Bivariate Moran's I Statistic — localmoran_bv","text":"Bivariate Local Moran, like global counterpart, evaluates value x observation spatial neighbors' value y. value \\(I_i^B\\) xi * Wyi. , simpler words, local bivariate Moran result multiplying x spatial lag y. Formally defined \\( I_i^B= cx_i\\Sigma_j{w_{ij}y_j} \\)","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localmoran_bv.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Compute the Local Bivariate Moran's I Statistic — localmoran_bv","text":"Anselin, Luc, Ibnu Syabri, Oleg Smirnov. 2002. “Visualizing Multivariate Spatial Correlation Dynamically Linked Windows.” New Tools Spatial Data Analysis: Proceedings Specialist Meeting, edited Luc Anselin Sergio Rey. University California, Santa Barbara: Center Spatially Integrated Social Science (CSISS).","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localmoran_bv.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Compute the Local Bivariate Moran's I Statistic — localmoran_bv","text":"Josiah Parry josiah.parry@gmail.com","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localmoran_bv.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Compute the Local Bivariate Moran's I Statistic — localmoran_bv","text":"","code":"# load columbus datay columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")) #> Reading layer `columbus' from data source  #>   `/home/rsb/lib/r_libs/spData/shapes/columbus.gpkg' using driver `GPKG' #> Simple feature collection with 49 features and 20 fields #> Geometry type: POLYGON #> Dimension:     XY #> Bounding box:  xmin: 5.874907 ymin: 10.78863 xmax: 11.28742 ymax: 14.74245 #> Projected CRS: Undefined Cartesian SRS with unknown unit nb <- poly2nb(columbus) listw <- nb2listw(nb) set.seed(1) (res <- localmoran_bv(columbus$CRIME, columbus$INC, listw, nsim = 499)) #>                Ibvi        E.Ibvi    Var.Ibvi      Z.Ibvi Pr(z != E(Ibvi)) #>  [1,] -0.8578252210 -1.826370e-02 0.731541578 -0.98159654     3.262987e-01 #>  [2,]  0.1802618568  2.554658e-02 0.334247968  0.26760782     7.890012e-01 #>  [3,]  0.0118856298  7.791116e-03 0.017162929  0.03125407     9.750669e-01 #>  [4,] -0.0163525887 -3.452848e-03 0.005852145 -0.16862558     8.660912e-01 #>  [5,] -0.5037734606  1.811633e-02 0.101966376 -1.63436973     1.021812e-01 #>  [6,] -0.0041841415  1.293651e-02 0.139142736 -0.04589760     9.633919e-01 #>  [7,]  1.5201688711 -1.466392e-04 1.099034279  1.45020069     1.470026e-01 #>  [8,] -0.2016456990  7.471406e-03 0.007231278 -2.45913301     1.392730e-02 #>  [9,]  0.0297432891  1.600490e-03 0.009219518  0.29309821     7.694471e-01 #> [10,] -0.0374203146  1.218906e-03 0.001100110 -1.16495823     2.440359e-01 #> [11,] -1.2368494456  7.720869e-02 0.498286158 -1.86155199     6.266627e-02 #> [12,] -1.2010054212  4.055009e-02 0.266658169 -2.40430022     1.620346e-02 #> [13,] -0.5377131737  1.218864e-02 0.122363375 -1.57202494     1.159448e-01 #> [14,] -0.9879712511  3.048475e-02 0.320475271 -1.79905736     7.200961e-02 #> [15,] -0.6057303757  2.137030e-02 0.102916086 -1.95476986     5.061024e-02 #> [16,] -0.7878039284  1.378587e-02 0.161039891 -1.99749384     4.577156e-02 #> [17,]  0.1379508106  9.352179e-04 0.003351141  2.36686570     1.793944e-02 #> [18,] -0.3253226893  1.066349e-02 0.078469609 -1.19941831     2.303653e-01 #> [19,] -0.3888822685 -7.104732e-06 0.432305953 -0.59144532     5.542221e-01 #> [20,] -0.4544889957  1.367811e-01 0.355060554 -0.99228105     3.210604e-01 #> [21,] -0.0006014046  3.919068e-03 0.031597455 -0.02543067     9.797114e-01 #> [22,] -0.0068813684 -3.664201e-03 0.001242910 -0.09125440     9.272904e-01 #> [23,] -0.8788967496  1.189579e-02 0.289002627 -1.65701209     9.751703e-02 #> [24,] -0.1256865340 -3.048451e-03 0.004692164 -1.79035349     7.339710e-02 #> [25,] -0.9307459211  4.509269e-02 0.303474056 -1.77140234     7.649382e-02 #> [26,] -0.2252775788  1.039843e-02 0.019527743 -1.68651169     9.169728e-02 #> [27,]  0.1413018326 -1.409345e-02 0.236810168  0.31932848     7.494774e-01 #> [28,] -0.7804482928  3.200178e-02 0.184987862 -1.88897002     5.889585e-02 #> [29,] -0.7654416689  5.928648e-02 0.364667175 -1.36572255     1.720261e-01 #> [30,] -0.9074829015  7.597435e-03 0.737090639 -1.06585659     2.864885e-01 #> [31,] -0.5510119267 -1.377557e-03 0.388899970 -0.88136323     3.781213e-01 #> [32,] -1.9581476375  2.561515e-02 0.239115219 -4.05682367     4.974461e-05 #> [33,]  0.0907015890  3.048227e-02 0.043681309  0.28812970     7.732475e-01 #> [34,] -0.4297843082  2.130996e-02 0.104683121 -1.39421250     1.632534e-01 #> [35,]  0.1181174820  6.746380e-04 0.008393054  1.28193663     1.998649e-01 #> [36,] -0.9901007017  2.760845e-02 0.278368628 -1.92891697     5.374117e-02 #> [37,] -0.2195812498 -7.723065e-03 0.032151838 -1.18152344     2.373948e-01 #> [38,] -0.3096268627  3.401135e-02 0.205499338 -0.75804717     4.484227e-01 #> [39,] -0.6090192229  1.689079e-02 0.308320019 -1.12722610     2.596469e-01 #> [40,] -1.2709838927  6.528265e-02 0.216905961 -2.86917707     4.115413e-03 #> [41,] -1.3940681427  9.430182e-02 0.304439982 -2.69749131     6.986411e-03 #> [42,] -0.4820987026  3.961324e-02 0.632999863 -0.65573592     5.119941e-01 #> [43,] -0.0064402410  2.939096e-03 0.001385154 -0.25201308     8.010310e-01 #> [44,]  0.0761664412  2.162964e-02 0.054095662  0.23448142     8.146113e-01 #> [45,] -0.0560342555  7.788766e-03 0.029796273 -0.36973996     7.115763e-01 #> [46,] -0.8249832451 -2.301643e-02 0.673531467 -0.97718648     3.284768e-01 #> [47,] -0.8915318222  2.294960e-02 0.095247718 -2.96310881     3.045489e-03 #> [48,] -0.1282863305 -9.674295e-03 0.061579149 -0.47798241     6.326627e-01 #> [49,]  0.0094888641 -4.828535e-03 0.222107368  0.03037964     9.757643e-01 #>       Pr(z != E(Ibvi)) Sim Pr(folded) Sim #>  [1,]                0.324          0.162 #>  [2,]                0.880          0.440 #>  [3,]                0.976          0.488 #>  [4,]                0.800          0.400 #>  [5,]                0.112          0.056 #>  [6,]                0.864          0.430 #>  [7,]                0.096          0.048 #>  [8,]                0.004          0.002 #>  [9,]                0.852          0.426 #> [10,]                0.260          0.130 #> [11,]                0.056          0.028 #> [12,]                0.008          0.004 #> [13,]                0.084          0.042 #> [14,]                0.064          0.032 #> [15,]                0.052          0.026 #> [16,]                0.028          0.014 #> [17,]                0.028          0.014 #> [18,]                0.192          0.096 #> [19,]                0.608          0.304 #> [20,]                0.368          0.184 #> [21,]                0.936          0.468 #> [22,]                0.928          0.464 #> [23,]                0.120          0.060 #> [24,]                0.040          0.020 #> [25,]                0.044          0.022 #> [26,]                0.076          0.038 #> [27,]                0.736          0.368 #> [28,]                0.032          0.016 #> [29,]                0.140          0.070 #> [30,]                0.284          0.142 #> [31,]                0.408          0.204 #> [32,]                0.004          0.002 #> [33,]                0.724          0.362 #> [34,]                0.188          0.094 #> [35,]                0.216          0.108 #> [36,]                0.084          0.042 #> [37,]                0.232          0.116 #> [38,]                0.464          0.232 #> [39,]                0.268          0.134 #> [40,]                0.004          0.002 #> [41,]                0.020          0.010 #> [42,]                0.468          0.234 #> [43,]                0.884          0.442 #> [44,]                0.904          0.452 #> [45,]                0.672          0.336 #> [46,]                0.344          0.172 #> [47,]                0.012          0.006 #> [48,]                0.544          0.272 #> [49,]                0.896          0.448 #> attr(,\"quadr\") #>         mean    median     pysal #> 1   Low-High  Low-High  Low-High #> 2    Low-Low   Low-Low   Low-Low #> 3    Low-Low   Low-Low   Low-Low #> 4   Low-High  Low-High  Low-High #> 5   High-Low  High-Low  High-Low #> 6    Low-Low  Low-High  Low-High #> 7    Low-Low   Low-Low   Low-Low #> 8   High-Low  High-Low  High-Low #> 9    Low-Low   Low-Low   Low-Low #> 10  Low-High  Low-High  Low-High #> 11  High-Low  High-Low  High-Low #> 12  High-Low  High-Low  High-Low #> 13  High-Low  High-Low  High-Low #> 14  High-Low  High-Low  High-Low #> 15  High-Low  High-Low  High-Low #> 16  High-Low  High-Low  High-Low #> 17 High-High High-High High-High #> 18  High-Low  High-Low  High-Low #> 19  High-Low  High-Low  High-Low #> 20  Low-High  Low-High  Low-High #> 21  High-Low High-High  High-Low #> 22  Low-High  Low-High  Low-High #> 23  Low-High  Low-High  Low-High #> 24  High-Low  High-Low  High-Low #> 25  High-Low  High-Low  High-Low #> 26  High-Low  High-Low  High-Low #> 27 High-High High-High High-High #> 28  High-Low  High-Low  High-Low #> 29  High-Low  High-Low  High-Low #> 30  High-Low  High-Low  High-Low #> 31  Low-High  Low-High  Low-High #> 32  Low-High  Low-High  Low-High #> 33 High-High High-High High-High #> 34  Low-High  Low-High  Low-High #> 35 High-High High-High High-High #> 36  Low-High  Low-High  Low-High #> 37  High-Low  High-Low  High-Low #> 38  High-Low  High-Low  High-Low #> 39  Low-High  Low-High  Low-High #> 40  Low-High  Low-High  Low-High #> 41  Low-High  Low-High  Low-High #> 42  Low-High  Low-High  Low-High #> 43  High-Low  High-Low  High-Low #> 44   Low-Low   Low-Low   Low-Low #> 45  Low-High  Low-High  Low-High #> 46  Low-High  Low-High  Low-High #> 47  Low-High  Low-High  Low-High #> 48  Low-High  Low-High  Low-High #> 49   Low-Low   Low-Low   Low-Low #> attr(,\"class\") #> [1] \"localmoran\" \"matrix\"     \"array\"      #> attr(,\"ncpus\") #> [1] 1 columbus$hs <- hotspot(res, Prname=\"Pr(folded) Sim\", cutoff=0.05,  quadrant.type=\"pysal\", p.adjust=\"none\") # \\donttest{ if (require(\"tmap\", quietly=TRUE)) { tmap4 <- packageVersion(\"tmap\") >= \"3.99\" if (tmap4) {   tm_shape(columbus) + tm_polygons(fill=\"hs\",     fill.scale=tm_scale(values=\"brewer.set3\"),     fill.legend=tm_legend(position=tm_pos_in(\"left\", \"top\"),       frame=FALSE, item.r=0), lwd=0.01) } else {   tm_shape(columbus) + tm_fill(\"hs\") } } #> Breaking News: tmap 3.x is retiring. Please test v4, e.g. with #> remotes::install_github('r-tmap/tmap')  # } moran.plot(x=columbus$CRIME, y=columbus$INC, listw=listw)"},{"path":"https://r-spatial.github.io/spdep/reference/mat2listw.html","id":null,"dir":"Reference","previous_headings":"","what":"Convert a square spatial weights matrix to a weights list object — mat2listw","title":"Convert a square spatial weights matrix to a weights list object — mat2listw","text":"function converts square spatial weights matrix, optionally sparse matrix weights list object, optionally adding region IDs row names matrix, sequence numbers 1:nrow(x), given argument. style can imposed rebuilting weights list object internally.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/mat2listw.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Convert a square spatial weights matrix to a weights list object — mat2listw","text":"","code":"mat2listw(x, row.names = NULL, style=NULL, zero.policy = NULL)"},{"path":"https://r-spatial.github.io/spdep/reference/mat2listw.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Convert a square spatial weights matrix to a weights list object — mat2listw","text":"x square non-negative matrix NAs representing spatial weights; may matrix class “sparseMatrix” row.names row names use region IDs style default NULL, missing, set \"M\" warning given; \"M\", passed nb2listw re-build object zero.policy default NULL, use global option value; FALSE stop error empty neighbour sets, TRUE permit weights list formed zero-length weights vectors","code":""},{"path":"https://r-spatial.github.io/spdep/reference/mat2listw.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Convert a square spatial weights matrix to a weights list object — mat2listw","text":"listw object following members: style \"M\", meaning matrix style, underlying style unknown, assigned style argument rebuilt object neighbours derived neighbours list weights weights neighbours derived matrix","code":""},{"path":"https://r-spatial.github.io/spdep/reference/mat2listw.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Convert a square spatial weights matrix to a weights list object — mat2listw","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/mat2listw.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Convert a square spatial weights matrix to a weights list object — mat2listw","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) col005 <- dnearneigh(st_coordinates(st_centroid(st_geometry(columbus),  of_largest_polygon=TRUE)), 0, 0.5, as.character(columbus$NEIGNO)) #> Warning: neighbour object has 8 sub-graphs summary(col005) #> Neighbour list object: #> Number of regions: 49  #> Number of nonzero links: 170  #> Percentage nonzero weights: 7.080383  #> Average number of links: 3.469388  #> 4 regions with no links: #> 1005, 1006, 1008, 1043 #> 8 disjoint connected subgraphs #> Link number distribution: #>  #>  0  1  2  3  4  5  6  7  8  9  #>  4 11  5  8  3  9  2  2  3  2  #> 11 least connected regions: #> 1001 1007 1018 1010 1045 1044 1046 1047 1049 1048 1015 with 1 link #> 2 most connected regions: #> 1038 1036 with 9 links col005.w.mat <- nb2mat(col005, style=\"W\", zero.policy=TRUE) try(col005.w.b <- mat2listw(col005.w.mat, style=\"W\")) #> Warning: no-neighbour observations found, set zero.policy to TRUE; #> this warning will soon become an error #> Warning: neighbour object has 8 sub-graphs #> Error in nb2listw(res$neighbours, glist = res$weights, style = style,  :  #>   Empty neighbour sets found (zero.policy: FALSE) col005.w.b <- mat2listw(col005.w.mat, style=\"W\", zero.policy=TRUE) #> Warning: neighbour object has 8 sub-graphs summary(col005.w.b$neighbours) #> Neighbour list object: #> Number of regions: 49  #> Number of nonzero links: 170  #> Percentage nonzero weights: 7.080383  #> Average number of links: 3.469388  #> 4 regions with no links: #> 1005, 1006, 1008, 1043 #> 8 disjoint connected subgraphs #> Link number distribution: #>  #>  0  1  2  3  4  5  6  7  8  9  #>  4 11  5  8  3  9  2  2  3  2  #> 11 least connected regions: #> 1001 1007 1018 1010 1045 1044 1046 1047 1049 1048 1015 with 1 link #> 2 most connected regions: #> 1038 1036 with 9 links diffnb(col005, col005.w.b$neighbours) #> Warning: neighbour object has 49 sub-graphs #> Neighbour list object: #> Number of regions: 49  #> Number of nonzero links: 0  #> Percentage nonzero weights: 0  #> Average number of links: 0  #> 49 regions with no links: #> 1005, 1001, 1006, 1002, 1007, 1008, 1004, 1003, 1018, 1010, 1038, 1037, #> 1039, 1040, 1009, 1036, 1011, 1042, 1041, 1017, 1043, 1019, 1012, 1035, #> 1032, 1020, 1021, 1031, 1033, 1034, 1045, 1013, 1022, 1044, 1023, 1046, #> 1030, 1024, 1047, 1016, 1014, 1049, 1029, 1025, 1028, 1048, 1015, 1027, #> 1026 #> 49 disjoint connected subgraphs col005.w.mat.3T <- kronecker(diag(3), col005.w.mat) col005.w.b.3T <- mat2listw(col005.w.mat.3T, style=\"W\", zero.policy=TRUE) #> Warning: neighbour object has 24 sub-graphs summary(col005.w.b.3T$neighbours) #> Neighbour list object: #> Number of regions: 147  #> Number of nonzero links: 510  #> Percentage nonzero weights: 2.360128  #> Average number of links: 3.469388  #> 12 regions with no links: #> 1, 3, 6, 21, 50, 52, 55, 70, 99, 101, 104, 119 #> 24 disjoint connected subgraphs #> Link number distribution: #>  #>  0  1  2  3  4  5  6  7  8  9  #> 12 33 15 24  9 27  6  6  9  6  #> 33 least connected regions: #> 2 5 9 10 31 34 36 39 42 46 47 51 54 58 59 80 83 85 88 91 95 96 100 103 107 108 129 132 134 137 140 144 145 with 1 link #> 6 most connected regions: #> 11 16 60 65 109 114 with 9 links run <- FALSE if (require(\"spatialreg\", quiet=TRUE)) run <- TRUE if (run) { W <- as(nb2listw(col005, style=\"W\", zero.policy=TRUE), \"CsparseMatrix\") try(col005.spM <- mat2listw(W)) col005.spM <- mat2listw(W, style=\"W\", zero.policy=TRUE) summary(col005.spM$neighbours) } #> Warning: style is M (missing); style should be set to a valid value #> Warning: style is M (missing); style should be set to a valid value #> Warning: 1005, 1006, 1008, 1043 are not origins #> Warning: no-neighbour observations found, set zero.policy to TRUE; #> this warning will soon become an error #> Warning: neighbour object has 8 sub-graphs #> Warning: no-neighbour observations found, set zero.policy to TRUE; #> this warning will soon become an error #> Warning: neighbour object has 8 sub-graphs #> Warning: no-neighbour observations found, set zero.policy to TRUE; #> this warning will soon become an error #> Warning: neighbour object has 8 sub-graphs #> Warning: neighbour object has 8 sub-graphs #> Neighbour list object: #> Number of regions: 49  #> Number of nonzero links: 170  #> Percentage nonzero weights: 7.080383  #> Average number of links: 3.469388  #> 4 regions with no links: #> 1005, 1006, 1008, 1043 #> 8 disjoint connected subgraphs #> Link number distribution: #>  #>  0  1  2  3  4  5  6  7  8  9  #>  4 11  5  8  3  9  2  2  3  2  #> 11 least connected regions: #> 1001 1007 1018 1010 1045 1044 1046 1047 1049 1048 1015 with 1 link #> 2 most connected regions: #> 1038 1036 with 9 links if (run) { diffnb(col005, col005.spM$neighbours) } #> Warning: neighbour object has 49 sub-graphs #> Neighbour list object: #> Number of regions: 49  #> Number of nonzero links: 0  #> Percentage nonzero weights: 0  #> Average number of links: 0  #> 49 regions with no links: #> 1005, 1001, 1006, 1002, 1007, 1008, 1004, 1003, 1018, 1010, 1038, 1037, #> 1039, 1040, 1009, 1036, 1011, 1042, 1041, 1017, 1043, 1019, 1012, 1035, #> 1032, 1020, 1021, 1031, 1033, 1034, 1045, 1013, 1022, 1044, 1023, 1046, #> 1030, 1024, 1047, 1016, 1014, 1049, 1029, 1025, 1028, 1048, 1015, 1027, #> 1026 #> 49 disjoint connected subgraphs if (run && require(\"Matrix\", quiet=TRUE)) { IW <- kronecker(Diagonal(3), W) col005.spM.3T <- mat2listw(as(IW, \"CsparseMatrix\"), style=\"W\", zero.policy=TRUE) summary(col005.spM.3T$neighbours) } #> Warning: no-neighbour observations found, set zero.policy to TRUE; #> this warning will soon become an error #> Warning: neighbour object has 24 sub-graphs #> Warning: neighbour object has 24 sub-graphs #> Neighbour list object: #> Number of regions: 147  #> Number of nonzero links: 510  #> Percentage nonzero weights: 2.360128  #> Average number of links: 3.469388  #> 12 regions with no links: #> 1, 3, 6, 21, 50, 52, 55, 70, 99, 101, 104, 119 #> 24 disjoint connected subgraphs #> Link number distribution: #>  #>  0  1  2  3  4  5  6  7  8  9  #> 12 33 15 24  9 27  6  6  9  6  #> 33 least connected regions: #> 2 5 9 10 31 34 36 39 42 46 47 51 54 58 59 80 83 85 88 91 95 96 100 103 107 108 129 132 134 137 140 144 145 with 1 link #> 6 most connected regions: #> 11 16 60 65 109 114 with 9 links"},{"path":"https://r-spatial.github.io/spdep/reference/moran.html","id":null,"dir":"Reference","previous_headings":"","what":"Compute Moran's I — moran","title":"Compute Moran's I — moran","text":"simple function compute Moran's , called moran.test moran.mc; $$= \\frac{n}{\\sum_{=1}^{n}\\sum_{j=1}^{n}w_{ij}} \\frac{\\sum_{=1}^{n}\\sum_{j=1}^{n}w_{ij}(x_i-\\bar{x})(x_j-\\bar{x})}{\\sum_{=1}^{n}(x_i - \\bar{x})^2} $$","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Compute Moran's I — moran","text":"","code":"moran(x, listw, n, S0, zero.policy=attr(listw, \"zero.policy\"), NAOK=FALSE)"},{"path":"https://r-spatial.github.io/spdep/reference/moran.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Compute Moran's I — moran","text":"x numeric vector length neighbours list listw listw listw object created example nb2listw n number zones S0 global sum weights zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA NAOK 'TRUE' 'NA' 'NaN' 'Inf' values x passed foreign function.  'FALSE', presence 'NA' 'NaN' 'Inf' values regarded error.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Compute Moran's I — moran","text":"list Moran's K sample kurtosis x","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Compute Moran's I — moran","text":"Cliff, . D., Ord, J. K. 1981 Spatial processes, Pion, p. 17.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Compute Moran's I — moran","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/moran.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Compute Moran's I — moran","text":"","code":"data(oldcol) col.W <- nb2listw(COL.nb, style=\"W\") crime <- COL.OLD$CRIME str(moran(crime, col.W, length(COL.nb), Szero(col.W))) #> List of 2 #>  $ I: num 0.511 #>  $ K: num 2.23 is.na(crime) <- sample(1:length(crime), 10) str(moran(crime, col.W, length(COL.nb), Szero(col.W), NAOK=TRUE)) #> Warning: NAs in lagged values #> List of 2 #>  $ I: num 0.166 #>  $ K: num 2.87"},{"path":"https://r-spatial.github.io/spdep/reference/moran.mc.html","id":null,"dir":"Reference","previous_headings":"","what":"Permutation test for Moran's I statistic — moran.mc","title":"Permutation test for Moran's I statistic — moran.mc","text":"permutation test Moran's statistic calculated using nsim random permutations x given spatial weighting scheme, establish rank observed statistic relation nsim simulated values.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran.mc.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Permutation test for Moran's I statistic — moran.mc","text":"","code":"moran.mc(x, listw, nsim, zero.policy=attr(listw, \"zero.policy\"),  alternative=\"greater\", na.action=na.fail, spChk=NULL, return_boot=FALSE,  adjust.n=TRUE)"},{"path":"https://r-spatial.github.io/spdep/reference/moran.mc.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Permutation test for Moran's I statistic — moran.mc","text":"x numeric vector length neighbours list listw listw listw object created example nb2listw nsim number permutations zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA alternative character string specifying alternative hypothesis, must one \"greater\" (default), \"two.sided\", \"less\". na.action function (default na.fail), can also na.omit na.exclude - cases weights list subsetted remove NAs data. may necessary set zero.policy TRUE subsetting may create -neighbour observations. Note weights lists created without using glist argument nb2listw may subsetted. na.pass permitted meaningless permutation test. spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption() return_boot return object class boot equivalent permutation bootstrap rather object class htest adjust.n default TRUE, FALSE number observations adjusted -neighbour observations, TRUE, number observations adjusted","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran.mc.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Permutation test for Moran's I statistic — moran.mc","text":"list class htest mc.sim containing following components: statistic value observed Moran's . parameter rank observed Moran's . p.value pseudo p-value test. alternative character string describing alternative hypothesis. method character string giving method used. data.name character string giving name(s) data, number simulations. res nsim simulated values statistic, final value observed statistic","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran.mc.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Permutation test for Moran's I statistic — moran.mc","text":"Cliff, . D., Ord, J. K. 1981 Spatial processes, Pion, p. 63-5.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran.mc.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Permutation test for Moran's I statistic — moran.mc","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/moran.mc.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Permutation test for Moran's I statistic — moran.mc","text":"","code":"data(oldcol) colw <- nb2listw(COL.nb, style=\"W\") nsim <- 99 set.seed(1234) sim1 <- moran.mc(COL.OLD$CRIME, listw=colw, nsim=nsim) sim1 #>  #> \tMonte-Carlo simulation of Moran I #>  #> data:  COL.OLD$CRIME  #> weights: colw   #> number of simulations + 1: 100  #>  #> statistic = 0.51095, observed rank = 100, p-value = 0.01 #> alternative hypothesis: greater #>  mean(sim1$res[1:nsim]) #> [1] -0.003196117 var(sim1$res[1:nsim]) #> [1] 0.008543554 summary(sim1$res[1:nsim]) #>      Min.   1st Qu.    Median      Mean   3rd Qu.      Max.  #> -0.180085 -0.073721 -0.009528 -0.003196  0.063865  0.206779  colold.lags <- nblag(COL.nb, 3) set.seed(1234) sim2 <- moran.mc(COL.OLD$CRIME, nb2listw(colold.lags[[2]],  style=\"W\"), nsim=nsim) summary(sim2$res[1:nsim]) #>     Min.  1st Qu.   Median     Mean  3rd Qu.     Max.  #> -0.15905 -0.07503 -0.01535 -0.02060  0.03305  0.13023  sim3 <- moran.mc(COL.OLD$CRIME, nb2listw(colold.lags[[3]],  style=\"W\"), nsim=nsim) summary(sim3$res[1:nsim]) #>      Min.   1st Qu.    Median      Mean   3rd Qu.      Max.  #> -0.192986 -0.055468 -0.024154 -0.026327  0.004769  0.129996  crime <- COL.OLD$CRIME is.na(crime) <- sample(1:length(crime), 10) try(moran.mc(crime, nb2listw(COL.nb, style=\"W\"), nsim=99,  na.action=na.fail)) #> Error in na.fail.default(x) : missing values in object moran.mc(crime, nb2listw(COL.nb, style=\"W\"), nsim=99, zero.policy=TRUE,  na.action=na.omit) #>  #> \tMonte-Carlo simulation of Moran I #>  #> data:  crime  #> weights: nb2listw(COL.nb, style = \"W\")  #> omitted: 5, 7, 9, 15, 19, 33, 40, 45, 47, 48  #> number of simulations + 1: 100  #>  #> statistic = 0.42342, observed rank = 100, p-value = 0.01 #> alternative hypothesis: greater #>  moran.mc(crime, nb2listw(COL.nb, style=\"W\"), nsim=99, zero.policy=TRUE,  return_boot=TRUE, na.action=na.omit) #> NA observations omitted: 5, 7, 9, 15, 19, 33, 40, 45, 47, 48 #>  #> DATA PERMUTATION #>  #>  #> Call: #> boot(data = x, statistic = moran_boot, R = nsim, sim = \"permutation\",  #>     listw = listw, n = n, S0 = S0, zero.policy = zero.policy,  #>     parallel = parallel, ncpus = ncpus, cl = cl) #>  #>  #> Bootstrap Statistics : #>      original     bias    std. error #> t1* 0.4234221 -0.4429891   0.1293935 moran.mc(crime, nb2listw(COL.nb, style=\"W\"), nsim=99, zero.policy=TRUE,  na.action=na.exclude) #>  #> \tMonte-Carlo simulation of Moran I #>  #> data:  crime  #> weights: nb2listw(COL.nb, style = \"W\")  #> omitted: 5, 7, 9, 15, 19, 33, 40, 45, 47, 48  #> number of simulations + 1: 100  #>  #> statistic = 0.42342, observed rank = 100, p-value = 0.01 #> alternative hypothesis: greater #>  moran.mc(crime, nb2listw(COL.nb, style=\"W\"), nsim=99, zero.policy=TRUE,  return_boot=TRUE, na.action=na.exclude) #> NA observations omitted: 5, 7, 9, 15, 19, 33, 40, 45, 47, 48 #>  #> DATA PERMUTATION #>  #>  #> Call: #> boot(data = x, statistic = moran_boot, R = nsim, sim = \"permutation\",  #>     listw = listw, n = n, S0 = S0, zero.policy = zero.policy,  #>     parallel = parallel, ncpus = ncpus, cl = cl) #>  #>  #> Bootstrap Statistics : #>      original     bias    std. error #> t1* 0.4234221 -0.4384413   0.1243937 try(moran.mc(crime, nb2listw(COL.nb, style=\"W\"), nsim=99, na.action=na.pass)) #> Error in moran.mc(crime, nb2listw(COL.nb, style = \"W\"), nsim = 99, na.action = na.pass) :  #>   na.pass not permitted"},{"path":"https://r-spatial.github.io/spdep/reference/moran.plot.html","id":null,"dir":"Reference","previous_headings":"","what":"Moran scatterplot — moran.plot","title":"Moran scatterplot — moran.plot","text":"plot spatial data spatially lagged values, augmented reporting summary influence measures linear relationship data lag. zero policy TRUE, observations also marked occur.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran.plot.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Moran scatterplot — moran.plot","text":"","code":"moran.plot(x, listw, y=NULL, zero.policy=attr(listw, \"zero.policy\"), spChk=NULL,  labels=NULL, xlab=NULL, ylab=NULL, quiet=NULL, plot=TRUE, return_df=TRUE, ...)"},{"path":"https://r-spatial.github.io/spdep/reference/moran.plot.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Moran scatterplot — moran.plot","text":"x numeric vector length neighbours list listw listw listw object created example nb2listw y optional numeric vector length neighbours list listw bi-variate plot zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption() labels character labels points high influence measures, set FALSE, labels plotted points large influence xlab label x axis ylab label x axis quiet default NULL, use !verbose global option value; TRUE, output summary influence object suppressed plot default TRUE, false, plotting suppressed return_df default TRUE, invisibly return data.frame object; FALSE invisibly return influence measures object ... graphical parameters par(..)","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran.plot.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Moran scatterplot — moran.plot","text":"function returns data.frame object coordinates influence measures return_df TRUE, influence object influence.measures.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran.plot.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Moran scatterplot — moran.plot","text":"Anselin, L. 1996. Moran scatterplot ESDA tool assess local instability spatial association. pp. 111–125 M. M. Fischer, H. J. Scholten D. Unwin (eds) Spatial analytical perspectives GIS, London, Taylor Francis; Anselin, L. 1995. Local indicators spatial association, Geographical Analysis, 27, 93–115","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran.plot.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Moran scatterplot — moran.plot","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/moran.plot.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Moran scatterplot — moran.plot","text":"","code":"data(afcon, package=\"spData\") mp <- moran.plot(afcon$totcon, nb2listw(paper.nb),  labels=as.character(afcon$name), pch=19)  moran.plot(as.vector(scale(afcon$totcon)), nb2listw(paper.nb),  labels=as.character(afcon$name), xlim=c(-2, 4), ylim=c(-2,4), pch=19)  if (require(ggplot2, quietly=TRUE)) {   xname <- attr(mp, \"xname\")   ggplot(mp, aes(x=x, y=wx)) + geom_point(shape=1) +      geom_smooth(formula=y ~ x, method=\"lm\") +      geom_hline(yintercept=mean(mp$wx), lty=2) +      geom_vline(xintercept=mean(mp$x), lty=2) + theme_minimal() +      geom_point(data=mp[mp$is_inf,], aes(x=x, y=wx), shape=9) +     geom_text(data=mp[mp$is_inf,], aes(x=x, y=wx, label=labels, vjust=1.5)) +     xlab(xname) + ylab(paste0(\"Spatially lagged \", xname)) }  columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")) #> Reading layer `columbus' from data source  #>   `/home/rsb/lib/r_libs/spData/shapes/columbus.gpkg' using driver `GPKG' #> Simple feature collection with 49 features and 20 fields #> Geometry type: POLYGON #> Dimension:     XY #> Bounding box:  xmin: 5.874907 ymin: 10.78863 xmax: 11.28742 ymax: 14.74245 #> Projected CRS: Undefined Cartesian SRS with unknown unit nb <- poly2nb(columbus) listw <- nb2listw(nb) moran.plot(x=columbus$CRIME, y=columbus$INC, listw=listw)  moran.plot(x=columbus$INC, y=columbus$CRIME, listw=listw)"},{"path":"https://r-spatial.github.io/spdep/reference/moran.test.html","id":null,"dir":"Reference","previous_headings":"","what":"Moran's I test for spatial autocorrelation — moran.test","title":"Moran's I test for spatial autocorrelation — moran.test","text":"Moran's test spatial autocorrelation using spatial weights matrix weights list form. assumptions underlying test sensitive form graph neighbour relationships factors, results may checked moran.mc permutations.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran.test.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Moran's I test for spatial autocorrelation — moran.test","text":"","code":"moran.test(x, listw, randomisation=TRUE, zero.policy=attr(listw, \"zero.policy\"),  alternative=\"greater\", rank = FALSE, na.action=na.fail, spChk=NULL,  adjust.n=TRUE, drop.EI2=FALSE)"},{"path":"https://r-spatial.github.io/spdep/reference/moran.test.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Moran's I test for spatial autocorrelation — moran.test","text":"x numeric vector length neighbours list listw listw listw object created example nb2listw randomisation variance calculated assumption randomisation, FALSE normality zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA alternative character string specifying alternative hypothesis, must one greater (default), less two.sided. rank logical value - default FALSE continuous variables, TRUE, uses adaptation Moran's ranks suggested Cliff Ord (1981, p. 46) na.action function (default na.fail), can also na.omit na.exclude - cases weights list subsetted remove NAs data. may necessary set zero.policy TRUE subsetting may create -neighbour observations. Note weights lists created without using glist argument nb2listw may subsetted. na.pass used, zero substituted NA values calculating spatial lag spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption() adjust.n default TRUE, FALSE number observations adjusted -neighbour observations, TRUE, number observations adjusted drop.EI2 default FALSE, TRUE, emulate CrimeStat <= 4.02","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran.test.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Moran's I test for spatial autocorrelation — moran.test","text":"list class htest containing following components: statistic value standard deviate Moran's . p.value p-value test. estimate value observed Moran's , expectation variance method assumption. alternative character string describing alternative hypothesis. method character string giving assumption used calculating standard deviate. data.name character string giving name(s) data.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran.test.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Moran's I test for spatial autocorrelation — moran.test","text":"Var() taken Cliff Ord (1969, p. 28), Goodchild's CATMOG 47 (1986), see also Upton & Fingleton (1985) p. 171; agrees SpaceStat, see Tutorial workbook Chapter 22; VI second crude moment minus square first crude moment. derivation test (Cliff Ord, 1981, p. 18) assumes weights matrix symmetric. inherently non-symmetric matrices, k-nearest neighbour matrices, listw2U() can used make matrix symmetric.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran.test.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Moran's I test for spatial autocorrelation — moran.test","text":"Cliff, . D., Ord, J. K. 1981 Spatial processes, Pion, p. 21; Bivand RS, Wong DWS 2018 Comparing implementations global local indicators spatial association. TEST, 27(3), 716–748 doi:10.1007/s11749-018-0599-x","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran.test.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Moran's I test for spatial autocorrelation — moran.test","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/moran.test.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Moran's I test for spatial autocorrelation — moran.test","text":"","code":"data(oldcol) coords.OLD <- cbind(COL.OLD$X, COL.OLD$Y) moran.test(COL.OLD$CRIME, nb2listw(COL.nb, style=\"W\")) #>  #> \tMoran I test under randomisation #>  #> data:  COL.OLD$CRIME   #> weights: nb2listw(COL.nb, style = \"W\")     #>  #> Moran I statistic standard deviate = 5.6341, p-value = 8.797e-09 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic       Expectation          Variance  #>       0.510951264      -0.020833333       0.008908762  #>  moran.test(COL.OLD$CRIME, nb2listw(COL.nb, style=\"B\")) #>  #> \tMoran I test under randomisation #>  #> data:  COL.OLD$CRIME   #> weights: nb2listw(COL.nb, style = \"B\")     #>  #> Moran I statistic standard deviate = 6.2116, p-value = 2.622e-10 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic       Expectation          Variance  #>        0.52063815       -0.02083333        0.00759872  #>  moran.test(COL.OLD$CRIME, nb2listw(COL.nb, style=\"C\")) #>  #> \tMoran I test under randomisation #>  #> data:  COL.OLD$CRIME   #> weights: nb2listw(COL.nb, style = \"C\")     #>  #> Moran I statistic standard deviate = 6.2116, p-value = 2.622e-10 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic       Expectation          Variance  #>        0.52063815       -0.02083333        0.00759872  #>  moran.test(COL.OLD$CRIME, nb2listw(COL.nb, style=\"S\")) #>  #> \tMoran I test under randomisation #>  #> data:  COL.OLD$CRIME   #> weights: nb2listw(COL.nb, style = \"S\")     #>  #> Moran I statistic standard deviate = 5.9786, p-value = 1.125e-09 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic       Expectation          Variance  #>       0.512957470      -0.020833333       0.007971504  #>  moran.test(COL.OLD$CRIME, nb2listw(COL.nb, style=\"W\"),  randomisation=FALSE) #>  #> \tMoran I test under normality #>  #> data:  COL.OLD$CRIME   #> weights: nb2listw(COL.nb, style = \"W\")     #>  #> Moran I statistic standard deviate = 5.6754, p-value = 6.92e-09 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic       Expectation          Variance  #>       0.510951264      -0.020833333       0.008779831  #>  colold.lags <- nblag(COL.nb, 3) moran.test(COL.OLD$CRIME, nb2listw(colold.lags[[2]],  style=\"W\")) #>  #> \tMoran I test under randomisation #>  #> data:  COL.OLD$CRIME   #> weights: nb2listw(colold.lags[[2]], style = \"W\")     #>  #> Moran I statistic standard deviate = 2.6076, p-value = 0.004559 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic       Expectation          Variance  #>       0.168485742      -0.020833333       0.005271314  #>  moran.test(COL.OLD$CRIME, nb2listw(colold.lags[[3]],  style=\"W\")) #>  #> \tMoran I test under randomisation #>  #> data:  COL.OLD$CRIME   #> weights: nb2listw(colold.lags[[3]], style = \"W\")     #>  #> Moran I statistic standard deviate = -1.7896, p-value = 0.9632 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic       Expectation          Variance  #>      -0.138930745      -0.020833333       0.004354683  #>  print(is.symmetric.nb(COL.nb)) #> [1] TRUE COL.k4.nb <- knn2nb(knearneigh(coords.OLD, 4)) print(is.symmetric.nb(COL.k4.nb)) #> [1] FALSE moran.test(COL.OLD$CRIME, nb2listw(COL.k4.nb, style=\"W\")) #>  #> \tMoran I test under randomisation #>  #> data:  COL.OLD$CRIME   #> weights: nb2listw(COL.k4.nb, style = \"W\")     #>  #> Moran I statistic standard deviate = 7.2183, p-value = 2.632e-13 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic       Expectation          Variance  #>       0.624933667      -0.020833333       0.008003503  #>  moran.test(COL.OLD$CRIME, nb2listw(COL.k4.nb, style=\"W\"),  randomisation=FALSE) #>  #> \tMoran I test under normality #>  #> data:  COL.OLD$CRIME   #> weights: nb2listw(COL.k4.nb, style = \"W\")     #>  #> Moran I statistic standard deviate = 7.2711, p-value = 1.782e-13 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic       Expectation          Variance  #>       0.624933667      -0.020833333       0.007887613  #>  cat(\"Note: non-symmetric weights matrix, use listw2U()\") #> Note: non-symmetric weights matrix, use listw2U() moran.test(COL.OLD$CRIME, listw2U(nb2listw(COL.k4.nb,  style=\"W\"))) #>  #> \tMoran I test under randomisation #>  #> data:  COL.OLD$CRIME   #> weights: listw2U(nb2listw(COL.k4.nb, style = \"W\"))     #>  #> Moran I statistic standard deviate = 7.2183, p-value = 2.632e-13 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic       Expectation          Variance  #>       0.624933667      -0.020833333       0.008003503  #>  moran.test(COL.OLD$CRIME, listw2U(nb2listw(COL.k4.nb,  style=\"W\")), randomisation=FALSE) #>  #> \tMoran I test under normality #>  #> data:  COL.OLD$CRIME   #> weights: listw2U(nb2listw(COL.k4.nb, style = \"W\"))     #>  #> Moran I statistic standard deviate = 7.2711, p-value = 1.782e-13 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic       Expectation          Variance  #>       0.624933667      -0.020833333       0.007887613  #>  ranks <- rank(COL.OLD$CRIME) names(ranks) <- rownames(COL.OLD) moran.test(ranks, nb2listw(COL.nb, style=\"W\"), rank=TRUE) #>  #> \tMoran I test under randomisation #>  #> data:  ranks using rank correction  #> weights: nb2listw(COL.nb, style = \"W\")     #>  #> Moran I statistic standard deviate = 6.3815, p-value = 8.766e-11 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic       Expectation          Variance  #>       0.584333495      -0.020833333       0.008992923  #>  crime <- COL.OLD$CRIME is.na(crime) <- sample(1:length(crime), 10) res <- try(moran.test(crime, nb2listw(COL.nb, style=\"W\"),  na.action=na.fail)) #> Error in na.fail.default(x) : missing values in object res #> [1] \"Error in na.fail.default(x) : missing values in object\\n\" #> attr(,\"class\") #> [1] \"try-error\" #> attr(,\"condition\") #> <simpleError in na.fail.default(x): missing values in object> moran.test(crime, nb2listw(COL.nb, style=\"W\"), zero.policy=TRUE,  na.action=na.omit) #> Warning: subsetting caused increase in subgraph count #>  #> \tMoran I test under randomisation #>  #> data:  crime   #> weights: nb2listw(COL.nb, style = \"W\")  #> omitted: 7, 10, 12, 13, 14, 18, 26, 41, 42, 47  #> n reduced by no-neighbour observations   #>  #> Moran I statistic standard deviate = 3.9826, p-value = 3.408e-05 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic       Expectation          Variance  #>        0.43709247       -0.02702703        0.01358066  #>  moran.test(crime, nb2listw(COL.nb, style=\"W\"), zero.policy=TRUE,  na.action=na.exclude) #> Warning: subsetting caused increase in subgraph count #>  #> \tMoran I test under randomisation #>  #> data:  crime   #> weights: nb2listw(COL.nb, style = \"W\")  #> omitted: 7, 10, 12, 13, 14, 18, 26, 41, 42, 47  #> n reduced by no-neighbour observations   #>  #> Moran I statistic standard deviate = 3.9826, p-value = 3.408e-05 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic       Expectation          Variance  #>        0.43709247       -0.02702703        0.01358066  #>  moran.test(crime, nb2listw(COL.nb, style=\"W\"), na.action=na.pass) #> Warning: NAs in lagged values #>  #> \tMoran I test under randomisation #>  #> data:  crime   #> weights: nb2listw(COL.nb, style = \"W\")     #>  #> Moran I statistic standard deviate = 2.4925, p-value = 0.006342 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic       Expectation          Variance  #>       0.212782897      -0.020833333       0.008784908  #>  columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) col_geoms <- st_geometry(columbus) col_geoms[1] <- st_buffer(col_geoms[1], dist=-0.05) st_geometry(columbus) <- col_geoms (nb1 <- poly2nb(columbus)) #> Warning: some observations have no neighbours; #> if this seems unexpected, try increasing the snap argument. #> Warning: neighbour object has 2 sub-graphs; #> if this sub-graph count seems unexpected, try increasing the snap argument. #> Neighbour list object: #> Number of regions: 49  #> Number of nonzero links: 232  #> Percentage nonzero weights: 9.662641  #> Average number of links: 4.734694  #> 1 region with no links: #> 1 #> 2 disjoint connected subgraphs try(lw <- nb2listw(nb1, style=\"W\")) #> Error in nb2listw(nb1, style = \"W\") :  #>   Empty neighbour sets found (zero.policy: FALSE) (lw <- nb2listw(nb1, style=\"W\", zero.policy=TRUE)) #> Characteristics of weights list object: #> Neighbour list object: #> Number of regions: 49  #> Number of nonzero links: 232  #> Percentage nonzero weights: 9.662641  #> Average number of links: 4.734694  #> 1 region with no links: #> 1 #> 2 disjoint connected subgraphs #>  #> Weights style: W  #> Weights constants summary: #>    n   nn S0       S1       S2 #> W 48 2304 48 22.23035 199.8188 moran.test(COL.OLD$CRIME, lw) #>  #> \tMoran I test under randomisation #>  #> data:  COL.OLD$CRIME   #> weights: lw   #> n reduced by no-neighbour observations   #>  #> Moran I statistic standard deviate = 2.7707, p-value = 0.002797 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic       Expectation          Variance  #>        0.23901261       -0.02127660        0.00882535  #>"},{"path":"https://r-spatial.github.io/spdep/reference/moran_bv.html","id":null,"dir":"Reference","previous_headings":"","what":"Compute the Global Bivariate Moran's I — moran_bv","title":"Compute the Global Bivariate Moran's I — moran_bv","text":"Given two continuous numeric variables, calculate bivariate Moran's . See details .","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran_bv.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Compute the Global Bivariate Moran's I — moran_bv","text":"","code":"moran_bv(x, y, listw, nsim = 499, scale = TRUE)"},{"path":"https://r-spatial.github.io/spdep/reference/moran_bv.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Compute the Global Bivariate Moran's I — moran_bv","text":"x numeric vector length y. y numeric vector length x. listw listw object example created nb2listw(). nsim number simulations run. scale default TRUE.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran_bv.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Compute the Global Bivariate Moran's I — moran_bv","text":"object class \"boot\", observed statistic component t0.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran_bv.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Compute the Global Bivariate Moran's I — moran_bv","text":"Global Bivariate Moran defined \\( I_B = \\frac{\\Sigma_i(\\Sigma_j{w_{ij}y_j\\times x_i})}{\\Sigma_i{x_i^2}} \\) important note measure autocorrelation X spatial lag Y. , resultant measure may overestimate amount spatial autocorrelation may product inherent correlation X Y. output object class \"boot\", plots confidence intervals available using appropriate methods.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran_bv.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Compute the Global Bivariate Moran's I — moran_bv","text":"Wartenberg, D. (1985), Multivariate Spatial Correlation: Method Exploratory Geographical Analysis. Geographical Analysis, 17: 263-283. doi:10.1111/j.1538-4632.1985.tb00849.x","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran_bv.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Compute the Global Bivariate Moran's I — moran_bv","text":"Josiah Parry josiah.parry@gmail.com","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran_bv.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Compute the Global Bivariate Moran's I — moran_bv","text":"","code":"data(boston, package = \"spData\") x <- boston.c$CRIM y <- boston.c$NOX listw <- nb2listw(boston.soi) set.seed(1) res_xy <- moran_bv(x, y, listw, nsim=499) res_xy$t0 #> [1] 0.4082073 boot::boot.ci(res_xy, conf=c(0.99, 0.95, 0.9), type=\"basic\") #> BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS #> Based on 499 bootstrap replicates #>  #> CALL :  #> boot::boot.ci(boot.out = res_xy, conf = c(0.99, 0.95, 0.9), type = \"basic\") #>  #> Intervals :  #> Level      Basic          #> 99%   ( 0.7443,  0.8789 )    #> 95%   ( 0.7639,  0.8673 )    #> 90%   ( 0.7739,  0.8615 )   #> Calculations and Intervals on Original Scale #> Some basic intervals may be unstable plot(res_xy)  set.seed(1) lee_xy <- lee.mc(x, y, listw, nsim=499, return_boot=TRUE) lee_xy$t0 #> [1] 0.3993476 boot::boot.ci(lee_xy, conf=c(0.99, 0.95, 0.9), type=\"basic\") #> BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS #> Based on 499 bootstrap replicates #>  #> CALL :  #> boot::boot.ci(boot.out = lee_xy, conf = c(0.99, 0.95, 0.9), type = \"basic\") #>  #> Intervals :  #> Level      Basic          #> 99%   ( 0.6363,  0.7236 )    #> 95%   ( 0.6538,  0.7131 )    #> 90%   ( 0.6584,  0.7098 )   #> Calculations and Intervals on Original Scale #> Some basic intervals may be unstable plot(lee_xy)  set.seed(1) res_yx <- moran_bv(y, x, listw, nsim=499) res_yx$t0 #> [1] 0.4029821 boot::boot.ci(res_yx, conf=c(0.99, 0.95, 0.9), type=\"basic\") #> BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS #> Based on 499 bootstrap replicates #>  #> CALL :  #> boot::boot.ci(boot.out = res_yx, conf = c(0.99, 0.95, 0.9), type = \"basic\") #>  #> Intervals :  #> Level      Basic          #> 99%   ( 0.7301,  0.8729 )    #> 95%   ( 0.7574,  0.8584 )    #> 90%   ( 0.7664,  0.8541 )   #> Calculations and Intervals on Original Scale #> Some basic intervals may be unstable plot(res_yx)  set.seed(1) lee_yx <- lee.mc(y, x, listw, nsim=499, return_boot=TRUE) lee_yx$t0 #> [1] 0.3993476 boot::boot.ci(lee_yx, conf=c(0.99, 0.95, 0.9), type=\"basic\") #> BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS #> Based on 499 bootstrap replicates #>  #> CALL :  #> boot::boot.ci(boot.out = lee_yx, conf = c(0.99, 0.95, 0.9), type = \"basic\") #>  #> Intervals :  #> Level      Basic          #> 99%   ( 0.6363,  0.7236 )    #> 95%   ( 0.6538,  0.7131 )    #> 90%   ( 0.6584,  0.7098 )   #> Calculations and Intervals on Original Scale #> Some basic intervals may be unstable plot(lee_yx)"},{"path":"https://r-spatial.github.io/spdep/reference/mstree.html","id":null,"dir":"Reference","previous_headings":"","what":"Find the minimal spanning tree — mstree","title":"Find the minimal spanning tree — mstree","text":"minimal spanning tree connected graph n nodes n-1   edges. smaller class possible partitions graph   pruning edges high dissimilarity. one edge removed,   graph partioned two unconnected subgraphs. function   implements algorithm due Prim (1987).","code":""},{"path":"https://r-spatial.github.io/spdep/reference/mstree.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Find the minimal spanning tree — mstree","text":"","code":"mstree(nbw, ini = NULL)"},{"path":"https://r-spatial.github.io/spdep/reference/mstree.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Find the minimal spanning tree — mstree","text":"nbw object listw class returned     nb2listw function. See help details. ini initial node minimal spanning tree.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/mstree.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Find the minimal spanning tree — mstree","text":"minimum spanning tree algorithm. Input connected graph. Begin empty set nodes. Add arbitrary note set. nodes set, find minimum cost edge connecting   node set node set add node   set. set edges minimum spanning tree.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/mstree.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Find the minimal spanning tree — mstree","text":"matrix n-1 rows tree columns. row two nodes   cost, . e. edge cost.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/mstree.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Find the minimal spanning tree — mstree","text":"R. C. Prim (1957) Shortest connection networks   generalisations. : Bell System Technical Journal, 36, pp. 1389-1401","code":""},{"path":"https://r-spatial.github.io/spdep/reference/mstree.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Find the minimal spanning tree — mstree","text":"Renato M. Assuncao Elias T. Krainski","code":""},{"path":"https://r-spatial.github.io/spdep/reference/mstree.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Find the minimal spanning tree — mstree","text":"","code":"### loading data (GDAL37 <- as.numeric_version(unname(sf_extSoftVersion()[\"GDAL\"])) >= \"3.7.0\") #> [1] TRUE file <- \"etc/shapes/bhicv.gpkg.zip\" zipfile <- system.file(file, package=\"spdep\") if (GDAL37) {     bh <- st_read(zipfile) } else {     td <- tempdir()     bn <- sub(\".zip\", \"\", basename(file), fixed=TRUE)     target <- unzip(zipfile, files=bn, exdir=td)     bh <- st_read(target) } #> Reading layer `bhicv' from data source  #>   `/tmp/RtmpXVTJuL/temp_libpath3b356d487bad39/spdep/etc/shapes/bhicv.gpkg.zip'  #>   using driver `GPKG' #> Simple feature collection with 98 features and 8 fields #> Geometry type: POLYGON #> Dimension:     XY #> Bounding box:  xmin: -45.02175 ymin: -20.93007 xmax: -42.50321 ymax: -18.08342 #> Geodetic CRS:  Corrego Alegre 1970-72 ### data padronized dpad <- data.frame(scale(as.data.frame(bh)[,5:8]))  ### neighboorhod list  bh.nb <- poly2nb(bh)  ### calculing costs lcosts <- nbcosts(bh.nb, dpad)  ### making listw nb.w <- nb2listw(bh.nb, lcosts, style=\"B\")  ### find a minimum spanning tree system.time(mst.bh <- mstree(nb.w,5)) #>    user  system elapsed  #>   0.002   0.000   0.002  dim(mst.bh) #> [1] 97  3 head(mst.bh) #>      [,1] [,2]      [,3] #> [1,]    5   12 1.2951120 #> [2,]   12   13 0.6141101 #> [3,]   13   11 0.7913745 #> [4,]   13    6 0.9775650 #> [5,]   11   31 0.9965625 #> [6,]   31   39 0.6915158 tail(mst.bh) #>       [,1] [,2]      [,3] #> [92,]   89   90 2.5743702 #> [93,]   26   56 2.6235317 #> [94,]   86   87 2.6471303 #> [95,]   87   72 0.7874461 #> [96,]   49   36 2.8743677 #> [97,]   24   25 3.4675168 ### the mstree plot par(mar=c(0,0,0,0)) plot(st_geometry(bh), border=gray(.5)) plot(mst.bh, st_coordinates(st_centroid(bh)), col=2,       cex.lab=.6, cex.circles=0.035, fg=\"blue\", add=TRUE) #> Warning: st_centroid assumes attributes are constant over geometries"},{"path":"https://r-spatial.github.io/spdep/reference/nb2INLA.html","id":null,"dir":"Reference","previous_headings":"","what":"Output spatial neighbours for INLA — nb2INLA","title":"Output spatial neighbours for INLA — nb2INLA","text":"Output spatial neighbours INLA","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2INLA.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Output spatial neighbours for INLA — nb2INLA","text":"","code":"nb2INLA(file, nb)"},{"path":"https://r-spatial.github.io/spdep/reference/nb2INLA.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Output spatial neighbours for INLA — nb2INLA","text":"file file adjacency matrix stored nb object class nb","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2INLA.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Output spatial neighbours for INLA — nb2INLA","text":"Nothing returned file created representation adjacency matrix required INLA spatial models.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2INLA.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Output spatial neighbours for INLA — nb2INLA","text":"http://www.r-inla.org","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2INLA.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Output spatial neighbours for INLA — nb2INLA","text":"Virgilio Gomez-Rubio","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2INLA.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Output spatial neighbours for INLA — nb2INLA","text":"","code":"col.gal.nb <- read.gal(system.file(\"weights/columbus.gal\", package=\"spData\")[1]) td <- tempdir() x <- nb2INLA(paste(td, \"columbus-INLA.adj\", sep=\"/\"), col.gal.nb) readLines(paste(td, \"columbus-INLA.adj\", sep=\"/\"), n=10) #>  [1] \"49\"                        \"1 2 2 3\"                   #>  [3] \"2 3 1 3 4\"                 \"3 4 1 2 4 5\"               #>  [5] \"4 4 2 3 5 8\"               \"5 7 3 4 6 8 9 11 15\"       #>  [7] \"6 2 5 9\"                   \"7 4 8 12 13 14\"            #>  [9] \"8 6 4 5 7 11 12 13\"        \"9 8 5 6 10 15 20 22 25 26\""},{"path":"https://r-spatial.github.io/spdep/reference/nb2WB.html","id":null,"dir":"Reference","previous_headings":"","what":"Output spatial weights for WinBUGS — nb2WB","title":"Output spatial weights for WinBUGS — nb2WB","text":"Output spatial weights WinBUGS","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2WB.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Output spatial weights for WinBUGS — nb2WB","text":"","code":"nb2WB(nb) listw2WB(listw)"},{"path":"https://r-spatial.github.io/spdep/reference/nb2WB.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Output spatial weights for WinBUGS — nb2WB","text":"nb object class nb listw listw object example nb2listw","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2WB.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Output spatial weights for WinBUGS — nb2WB","text":"list suitable convering using dput WinBUGS","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2WB.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Output spatial weights for WinBUGS — nb2WB","text":"http://www.mrc-bsu.cam.ac.uk/bugs/winbugs/geobugs12manual.pdf","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2WB.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Output spatial weights for WinBUGS — nb2WB","text":"Virgilio Gomez-Rubio","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/nb2WB.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Output spatial weights for WinBUGS — nb2WB","text":"","code":"col.gal.nb <- read.gal(system.file(\"weights/columbus.gal\", package=\"spData\")[1]) x <- nb2WB(col.gal.nb) dput(x, control=NULL) #> list(c(2, 3, 1, 3, 4, 1, 2, 4, 5, 2, 3, 5, 8, 3, 4, 6, 8, 9,  #> 11, 15, 5, 9, 8, 12, 13, 14, 4, 5, 7, 11, 12, 13, 5, 6, 10, 15,  #> 20, 22, 25, 26, 9, 17, 20, 22, 5, 8, 12, 15, 16, 7, 8, 11, 13,  #> 14, 16, 7, 8, 12, 14, 7, 12, 13, 16, 18, 19, 5, 9, 11, 16, 25,  #> 26, 11, 12, 14, 15, 18, 24, 25, 10, 20, 23, 14, 16, 19, 24, 14,  #> 18, 24, 9, 10, 17, 22, 23, 27, 32, 33, 35, 40, 24, 30, 34, 9,  #> 10, 20, 26, 27, 28, 17, 20, 32, 16, 18, 19, 21, 25, 29, 30, 9,  #> 15, 16, 24, 26, 28, 29, 9, 15, 22, 25, 28, 29, 20, 22, 28, 33,  #> 22, 25, 26, 27, 29, 33, 35, 37, 38, 24, 25, 26, 28, 30, 37, 38,  #> 21, 24, 29, 37, 34, 36, 20, 23, 40, 41, 20, 27, 28, 35, 21, 31,  #> 36, 42, 20, 28, 33, 38, 40, 43, 44, 31, 34, 39, 42, 46, 28, 29,  #> 30, 38, 43, 45, 28, 29, 35, 37, 43, 44, 36, 46, 20, 32, 35, 41,  #> 47, 32, 40, 47, 34, 36, 35, 37, 38, 44, 45, 48, 35, 38, 43, 48,  #> 49, 37, 43, 48, 49, 36, 39, 40, 41, 43, 44, 45, 49, 44, 45, 48 #> ), c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,  #> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,  #> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,  #> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,  #> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,  #> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,  #> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,  #> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,  #> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,  #> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,  #> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,  #> 1), c(2, 3, 4, 4, 7, 2, 4, 6, 8, 4, 5, 6, 4, 6, 6, 7, 3, 4, 3,  #> 10, 3, 6, 3, 7, 7, 6, 4, 9, 7, 4, 2, 4, 4, 4, 7, 5, 6, 6, 2,  #> 5, 3, 2, 6, 5, 4, 2, 2, 4, 3)) x <- listw2WB(nb2listw(col.gal.nb)) dput(x, control=NULL) #> list(c(2, 3, 1, 3, 4, 1, 2, 4, 5, 2, 3, 5, 8, 3, 4, 6, 8, 9,  #> 11, 15, 5, 9, 8, 12, 13, 14, 4, 5, 7, 11, 12, 13, 5, 6, 10, 15,  #> 20, 22, 25, 26, 9, 17, 20, 22, 5, 8, 12, 15, 16, 7, 8, 11, 13,  #> 14, 16, 7, 8, 12, 14, 7, 12, 13, 16, 18, 19, 5, 9, 11, 16, 25,  #> 26, 11, 12, 14, 15, 18, 24, 25, 10, 20, 23, 14, 16, 19, 24, 14,  #> 18, 24, 9, 10, 17, 22, 23, 27, 32, 33, 35, 40, 24, 30, 34, 9,  #> 10, 20, 26, 27, 28, 17, 20, 32, 16, 18, 19, 21, 25, 29, 30, 9,  #> 15, 16, 24, 26, 28, 29, 9, 15, 22, 25, 28, 29, 20, 22, 28, 33,  #> 22, 25, 26, 27, 29, 33, 35, 37, 38, 24, 25, 26, 28, 30, 37, 38,  #> 21, 24, 29, 37, 34, 36, 20, 23, 40, 41, 20, 27, 28, 35, 21, 31,  #> 36, 42, 20, 28, 33, 38, 40, 43, 44, 31, 34, 39, 42, 46, 28, 29,  #> 30, 38, 43, 45, 28, 29, 35, 37, 43, 44, 36, 46, 20, 32, 35, 41,  #> 47, 32, 40, 47, 34, 36, 35, 37, 38, 44, 45, 48, 35, 38, 43, 48,  #> 49, 37, 43, 48, 49, 36, 39, 40, 41, 43, 44, 45, 49, 44, 45, 48 #> ), c(0.5, 0.5, 0.333333333333333, 0.333333333333333, 0.333333333333333,  #> 0.25, 0.25, 0.25, 0.25, 0.25, 0.25, 0.25, 0.25, 0.142857142857143,  #> 0.142857142857143, 0.142857142857143, 0.142857142857143, 0.142857142857143,  #> 0.142857142857143, 0.142857142857143, 0.5, 0.5, 0.25, 0.25, 0.25,  #> 0.25, 0.166666666666667, 0.166666666666667, 0.166666666666667,  #> 0.166666666666667, 0.166666666666667, 0.166666666666667, 0.125,  #> 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.25, 0.25,  #> 0.25, 0.25, 0.2, 0.2, 0.2, 0.2, 0.2, 0.166666666666667, 0.166666666666667,  #> 0.166666666666667, 0.166666666666667, 0.166666666666667, 0.166666666666667,  #> 0.25, 0.25, 0.25, 0.25, 0.166666666666667, 0.166666666666667,  #> 0.166666666666667, 0.166666666666667, 0.166666666666667, 0.166666666666667,  #> 0.166666666666667, 0.166666666666667, 0.166666666666667, 0.166666666666667,  #> 0.166666666666667, 0.166666666666667, 0.142857142857143, 0.142857142857143,  #> 0.142857142857143, 0.142857142857143, 0.142857142857143, 0.142857142857143,  #> 0.142857142857143, 0.333333333333333, 0.333333333333333, 0.333333333333333,  #> 0.25, 0.25, 0.25, 0.25, 0.333333333333333, 0.333333333333333,  #> 0.333333333333333, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1,  #> 0.1, 0.333333333333333, 0.333333333333333, 0.333333333333333,  #> 0.166666666666667, 0.166666666666667, 0.166666666666667, 0.166666666666667,  #> 0.166666666666667, 0.166666666666667, 0.333333333333333, 0.333333333333333,  #> 0.333333333333333, 0.142857142857143, 0.142857142857143, 0.142857142857143,  #> 0.142857142857143, 0.142857142857143, 0.142857142857143, 0.142857142857143,  #> 0.142857142857143, 0.142857142857143, 0.142857142857143, 0.142857142857143,  #> 0.142857142857143, 0.142857142857143, 0.142857142857143, 0.166666666666667,  #> 0.166666666666667, 0.166666666666667, 0.166666666666667, 0.166666666666667,  #> 0.166666666666667, 0.25, 0.25, 0.25, 0.25, 0.111111111111111,  #> 0.111111111111111, 0.111111111111111, 0.111111111111111, 0.111111111111111,  #> 0.111111111111111, 0.111111111111111, 0.111111111111111, 0.111111111111111,  #> 0.142857142857143, 0.142857142857143, 0.142857142857143, 0.142857142857143,  #> 0.142857142857143, 0.142857142857143, 0.142857142857143, 0.25,  #> 0.25, 0.25, 0.25, 0.5, 0.5, 0.25, 0.25, 0.25, 0.25, 0.25, 0.25,  #> 0.25, 0.25, 0.25, 0.25, 0.25, 0.25, 0.142857142857143, 0.142857142857143,  #> 0.142857142857143, 0.142857142857143, 0.142857142857143, 0.142857142857143,  #> 0.142857142857143, 0.2, 0.2, 0.2, 0.2, 0.2, 0.166666666666667,  #> 0.166666666666667, 0.166666666666667, 0.166666666666667, 0.166666666666667,  #> 0.166666666666667, 0.166666666666667, 0.166666666666667, 0.166666666666667,  #> 0.166666666666667, 0.166666666666667, 0.166666666666667, 0.5,  #> 0.5, 0.2, 0.2, 0.2, 0.2, 0.2, 0.333333333333333, 0.333333333333333,  #> 0.333333333333333, 0.5, 0.5, 0.166666666666667, 0.166666666666667,  #> 0.166666666666667, 0.166666666666667, 0.166666666666667, 0.166666666666667,  #> 0.2, 0.2, 0.2, 0.2, 0.2, 0.25, 0.25, 0.25, 0.25, 0.5, 0.5, 0.5,  #> 0.5, 0.25, 0.25, 0.25, 0.25, 0.333333333333333, 0.333333333333333,  #> 0.333333333333333), c(2, 3, 4, 4, 7, 2, 4, 6, 8, 4, 5, 6, 4,  #> 6, 6, 7, 3, 4, 3, 10, 3, 6, 3, 7, 7, 6, 4, 9, 7, 4, 2, 4, 4,  #> 4, 7, 5, 6, 6, 2, 5, 3, 2, 6, 5, 4, 2, 2, 4, 3))"},{"path":"https://r-spatial.github.io/spdep/reference/nb2blocknb.html","id":null,"dir":"Reference","previous_headings":"","what":"Block up neighbour list for location-less observations — nb2blocknb","title":"Block up neighbour list for location-less observations — nb2blocknb","text":"function blocks neighbour list known spatial locations create new neighbour list multiple location-less observations know belong spatial locations, using identification tags locations key.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2blocknb.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Block up neighbour list for location-less observations — nb2blocknb","text":"","code":"nb2blocknb(nb=NULL, ID, row.names = NULL)"},{"path":"https://r-spatial.github.io/spdep/reference/nb2blocknb.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Block up neighbour list for location-less observations — nb2blocknb","text":"nb object class nb list integer vectors containing neighbour region number ids; null, nb object neighbours created length unique(.character(ID)) ID identification tags locations location-less observations; sort(unique(.character(ID))) must identical sort(.character(attr(nb, \"region.id\"))); length row.names provided. row.names character vector observation ids added neighbours list attribute region.id, default seq(1, nrow(x)); length ID provided.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2blocknb.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Block up neighbour list for location-less observations — nb2blocknb","text":"Assume list unique locations, neighbour list can build , create input neighbour list. needs \"unfolded\", observations belonging unique location observation neighbours, observations belonging location neighbours unique location question also observation neighbours, finally removing observation (neighbour). scenario also arises say post codes available, post codes contain multiple observations, known belong specific post code, located within (given post code locations known).","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2blocknb.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Block up neighbour list for location-less observations — nb2blocknb","text":"function returns object class nb list integer vectors containing neighbour observation number ids.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2blocknb.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Block up neighbour list for location-less observations — nb2blocknb","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/nb2blocknb.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Block up neighbour list for location-less observations — nb2blocknb","text":"","code":"if (FALSE) { # \\dontrun{ data(boston, package=\"spData\") summary(as.vector(table(boston.c$TOWN))) townaggr <- aggregate(boston.utm, list(town=boston.c$TOWN), mean) block.rel <- graph2nb(relativeneigh(as.matrix(townaggr[,2:3])),  as.character(townaggr[,1]), sym=TRUE) block.rel print(is.symmetric.nb(block.rel)) plot(block.rel, as.matrix(townaggr[,2:3])) points(boston.utm, pch=18, col=\"lightgreen\") block.nb <- nb2blocknb(block.rel, as.character(boston.c$TOWN)) block.nb print(is.symmetric.nb(block.nb)) plot(block.nb, boston.utm) points(boston.utm, pch=18, col=\"lightgreen\") n.comp.nb(block.nb)$nc moran.test(boston.c$CMEDV, nb2listw(boston.soi)) moran.test(boston.c$CMEDV, nb2listw(block.nb)) block.nb <- nb2blocknb(NULL, as.character(boston.c$TOWN)) block.nb print(is.symmetric.nb(block.nb)) plot(block.nb, boston.utm) n.comp.nb(block.nb)$nc moran.test(boston.c$CMEDV, nb2listw(block.nb, zero.policy=TRUE), zero.policy=TRUE) } # }"},{"path":"https://r-spatial.github.io/spdep/reference/nb2lines.html","id":null,"dir":"Reference","previous_headings":"","what":"Use vector files for import and export of weights — nb2lines","title":"Use vector files for import and export of weights — nb2lines","text":"Use vector files import export weights, storing spatial entity coordinates arcs, entity indices data frame.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2lines.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Use vector files for import and export of weights — nb2lines","text":"","code":"nb2lines(nb, wts, coords, proj4string=NULL, as_sf=FALSE) listw2lines(listw, coords, proj4string=NULL, as_sf=FALSE) df2sn(df, i=\"i\", i_ID=\"i_ID\", j=\"j\", wt=\"wt\")"},{"path":"https://r-spatial.github.io/spdep/reference/nb2lines.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Use vector files for import and export of weights — nb2lines","text":"nb neighbour object class nb wts list general weights corresponding neighbours coords matrix region point coordinates, Spatial object (points polygons), sfc object (points polygons) proj4string default NULL; coords Spatial sf object, value used, otherwise value converted appropriately as_sf output object Spatial sf format, default FALSE, set TRUE coords sfc object FALSE Spatial object listw listw object spatial weights df data frame read shapefile, derived output nb2lines character name column df entity index i_ID character name column df entity region ID j character name column df entity index wt character name column df weights","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2lines.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Use vector files for import and export of weights — nb2lines","text":"neighbour weights objects may retrieved converting specified columns data slot SpatialLinesDataFrame object spatial.neighbour object, converted weights list object.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2lines.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Use vector files for import and export of weights — nb2lines","text":"nb2lines listw2lines return SpatialLinesDataFrame object sf object; data frame contains indices neighbour links weights. df2sn converts data retrieved reading data df back spatial.neighbour object.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2lines.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Use vector files for import and export of weights — nb2lines","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2lines.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Use vector files for import and export of weights — nb2lines","text":"Original idea due Gidske Leknes Andersen, Department Biology, University Bergen, Norway","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/nb2lines.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Use vector files for import and export of weights — nb2lines","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) col.gal.nb <- read.gal(system.file(\"weights/columbus.gal\", package=\"spData\")[1]) res <- listw2lines(nb2listw(col.gal.nb), st_geometry(columbus)) summary(res) #>        i               j             i_ID               j_ID           #>  Min.   : 1.00   Min.   : 1.00   Length:230         Length:230         #>  1st Qu.:13.00   1st Qu.:13.00   Class :character   Class :character   #>  Median :24.00   Median :24.00   Mode  :character   Mode  :character   #>  Mean   :24.19   Mean   :24.19                                         #>  3rd Qu.:35.00   3rd Qu.:35.00                                         #>  Max.   :49.00   Max.   :49.00                                         #>        wt               geometry   #>  Min.   :0.1000   LINESTRING:230   #>  1st Qu.:0.1429   epsg:NA   :  0   #>  Median :0.1667                    #>  Mean   :0.2130                    #>  3rd Qu.:0.2500                    #>  Max.   :0.5000                    tf <- paste0(tempfile(), \".gpkg\") st_write(res, dsn=tf, driver=\"GPKG\") #> Writing layer `file3b434754c9c27d' to data source  #>   `/tmp/Rtmp2GWLZN/file3b434754c9c27d.gpkg' using driver `GPKG' #> Writing 230 features with 5 fields and geometry type Line String. inMap <- st_read(tf) #> Reading layer `file3b434754c9c27d' from data source  #>   `/tmp/Rtmp2GWLZN/file3b434754c9c27d.gpkg' using driver `GPKG' #> Simple feature collection with 230 features and 5 fields #> Geometry type: LINESTRING #> Dimension:     XY #> Bounding box:  xmin: 6.165913 ymin: 11.04088 xmax: 10.96206 ymax: 14.43766 #> Projected CRS: Undefined Cartesian SRS with unknown unit summary(inMap) #>        i               j             i_ID               j_ID           #>  Min.   : 1.00   Min.   : 1.00   Length:230         Length:230         #>  1st Qu.:13.00   1st Qu.:13.00   Class :character   Class :character   #>  Median :24.00   Median :24.00   Mode  :character   Mode  :character   #>  Mean   :24.19   Mean   :24.19                                         #>  3rd Qu.:35.00   3rd Qu.:35.00                                         #>  Max.   :49.00   Max.   :49.00                                         #>        wt                 geom     #>  Min.   :0.1000   LINESTRING:230   #>  1st Qu.:0.1429   epsg:NA   :  0   #>  Median :0.1667                    #>  Mean   :0.2130                    #>  3rd Qu.:0.2500                    #>  Max.   :0.5000                    diffnb(sn2listw(df2sn(as.data.frame(inMap)))$neighbours, col.gal.nb) #> Warning: style is M (missing); style should be set to a valid value #> Warning: neighbour object has 49 sub-graphs #> Neighbour list object: #> Number of regions: 49  #> Number of nonzero links: 0  #> Percentage nonzero weights: 0  #> Average number of links: 0  #> 49 regions with no links: #> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, #> 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, #> 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49 #> 49 disjoint connected subgraphs res1 <- listw2lines(nb2listw(col.gal.nb), as(columbus, \"Spatial\")) summary(res1) #> Object of class SpatialLinesDataFrame #> Coordinates: #>         min      max #> x  6.221943 10.95359 #> y 11.010031 14.36908 #> Is projected: TRUE  #> proj4string : [NA] #> Data attributes: #>        i               j             i_ID               j_ID           #>  Min.   : 1.00   Min.   : 1.00   Length:230         Length:230         #>  1st Qu.:13.00   1st Qu.:13.00   Class :character   Class :character   #>  Median :24.00   Median :24.00   Mode  :character   Mode  :character   #>  Mean   :24.19   Mean   :24.19                                         #>  3rd Qu.:35.00   3rd Qu.:35.00                                         #>  Max.   :49.00   Max.   :49.00                                         #>        wt         #>  Min.   :0.1000   #>  1st Qu.:0.1429   #>  Median :0.1667   #>  Mean   :0.2130   #>  3rd Qu.:0.2500   #>  Max.   :0.5000"},{"path":"https://r-spatial.github.io/spdep/reference/nb2listw.html","id":null,"dir":"Reference","previous_headings":"","what":"Spatial weights for neighbours lists — nb2listw","title":"Spatial weights for neighbours lists — nb2listw","text":"nb2listw function supplements neighbours list spatial weights chosen coding scheme. can..simmed helper function checks whether spatial weights object similar symmetric can transformed yield real eigenvalues Cholesky decomposition. helper function listw2U() constructs weights list object corresponding sparse matrix \\(\\frac{1}{2} ( \\mathbf{W} + \\mathbf{W}'\\).","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2listw.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Spatial weights for neighbours lists — nb2listw","text":"","code":"nb2listw(neighbours, glist=NULL, style=\"W\", zero.policy=NULL) listw2U(listw)"},{"path":"https://r-spatial.github.io/spdep/reference/nb2listw.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Spatial weights for neighbours lists — nb2listw","text":"neighbours object class nb glist list general weights corresponding neighbours style style can take values “W”, “B”, “C”, “U”, “minmax” “S” zero.policy default NULL, use global option value; FALSE stop error empty neighbour sets, TRUE permit weights list formed zero-length weights vectors listw listw object created example nb2listw","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2listw.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Spatial weights for neighbours lists — nb2listw","text":"Starting binary neighbours list, regions either listed neighbours absent (thus set neighbours definition), function adds weights list values given coding scheme style chosen. B basic binary coding, W row standardised (sums links n), C globally standardised (sums links n), U equal C divided number neighbours (sums links unity), S variance-stabilizing coding scheme proposed Tiefelsdorf et al. 1999, p. 167-168 (sums links n). zero policy set TRUE, weights vectors zero length inserted regions without neighbour neighbours list. turn generate lag values zero, equivalent sum products zero row t(rep(0, length=length(neighbours))) %*% x, arbitraty numerical vector x length length(neighbours). spatially lagged value x zero-neighbour region zero, may (may ) sensible choice. sum glist vector one observations zero, warning message issued. consequence later operations -neighbour observations present zero.policy argument set true. “minmax” style based Kelejian Prucha (2010), divides weights minimum maximum row sums maximum column sums input weights. similar C U styles; also available Stata.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2listw.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Spatial weights for neighbours lists — nb2listw","text":"listw object following members: style one W, B, C, U, S, minmax neighbours input neighbours list weights weights neighbours chosen style, attributes set report type relationships (binary general, general form glist argument), style attributes: region.id character, neighbour object call function call zero.policy logical; value zero.policy object created","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2listw.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Spatial weights for neighbours lists — nb2listw","text":"Tiefelsdorf, M., Griffith, D. ., Boots, B. 1999 variance-stabilizing coding scheme spatial link matrices, Environment Planning , 31, pp. 165–180; Kelejian, H. H., . R. Prucha. 2010. Specification estimation spatial autoregressive models autoregressive heteroskedastic disturbances. Journal Econometrics, 157: pp. 53–67.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2listw.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Spatial weights for neighbours lists — nb2listw","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/nb2listw.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Spatial weights for neighbours lists — nb2listw","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) col.gal.nb <- read.gal(system.file(\"weights/columbus.gal\", package=\"spData\")[1]) coords <- st_coordinates(st_centroid(columbus)) #> Warning: st_centroid assumes attributes are constant over geometries cards <- card(col.gal.nb) col.w <- nb2listw(col.gal.nb) plot(cards, unlist(lapply(col.w$weights, sum)),xlim=c(0,10), ylim=c(0,10), xlab=\"number of links\", ylab=\"row sums of weights\") col.b <- nb2listw(col.gal.nb, style=\"B\") points(cards, unlist(lapply(col.b$weights, sum)), col=\"red\") col.c <- nb2listw(col.gal.nb, style=\"C\") points(cards, unlist(lapply(col.c$weights, sum)), col=\"green\") col.u <- nb2listw(col.gal.nb, style=\"U\") points(cards, unlist(lapply(col.u$weights, sum)), col=\"orange\") col.s <- nb2listw(col.gal.nb, style=\"S\") points(cards, unlist(lapply(col.s$weights, sum)), col=\"blue\") legend(x=c(0, 1), y=c(7, 9), legend=c(\"W\", \"B\", \"C\", \"U\", \"S\"), bty=\"n\", col=c(\"black\", \"red\", \"green\", \"orange\", \"blue\"), pch=rep(1,5), cex=0.8, y.intersp=2.5)  summary(nb2listw(col.gal.nb, style=\"minmax\")) #> Characteristics of weights list object: #> Neighbour list object: #> Number of regions: 49  #> Number of nonzero links: 230  #> Percentage nonzero weights: 9.579342  #> Average number of links: 4.693878  #> Link number distribution: #>  #>  2  3  4  5  6  7  8  9 10  #>  7  7 13  4  9  6  1  1  1  #> 7 least connected regions: #> 1 6 31 39 42 46 47 with 2 links #> 1 most connected region: #> 20 with 10 links #>  #> Weights style: minmax  #> Weights constants summary: #>         n   nn S0  S1    S2 #> minmax 49 2401 23 4.6 50.48 dlist <- nbdists(col.gal.nb, coords) dlist <- lapply(dlist, function(x) 1/x) col.w.d <- nb2listw(col.gal.nb, glist=dlist) summary(unlist(col.w$weights)) #>    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.  #>  0.1000  0.1429  0.1667  0.2130  0.2500  0.5000  summary(unlist(col.w.d$weights)) #>    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.  #> 0.06977 0.13114 0.17710 0.21304 0.27124 0.67178  # introducing other conditions into weights - only earlier sales count # see http://sal.uiuc.edu/pipermail/openspace/2005-October/000610.html data(baltimore, package=\"spData\") set.seed(211) dates <- sample(1:500, nrow(baltimore), replace=TRUE) nb_15nn <- knn2nb(knearneigh(cbind(baltimore$X, baltimore$Y), k=15)) glist <- vector(mode=\"list\", length=length(nb_15nn)) for (i in seq(along=nb_15nn))   glist[[i]] <- ifelse(dates[i] > dates[nb_15nn[[i]]], 1, 0) listw_15nn_dates <- nb2listw(nb_15nn, glist=glist, style=\"B\") #> Warning: zero sum general weights which(lag(listw_15nn_dates, baltimore$PRICE) == 0.0) #>  [1]   1  22  29  35  66  74  80  99 117 147 155 169 195 197 200 which(sapply(glist, sum) == 0) #>  [1]   1  22  29  35  66  74  80  99 117 147 155 169 195 197 200 ex <- which(sapply(glist, sum) == 0)[1] dates[ex] #> [1] 28 dates[nb_15nn[[ex]]] #>  [1] 395 247 275 179 142 484 111 239 369 199 294 251 448 390 229"},{"path":"https://r-spatial.github.io/spdep/reference/nb2listwdist.html","id":null,"dir":"Reference","previous_headings":"","what":"Distance-based spatial weights for neighbours lists — nb2listwdist","title":"Distance-based spatial weights for neighbours lists — nb2listwdist","text":"nb2listwdist function supplements neighbours list spatial weights chosen types distance modelling coding scheme. offered coding schemes parallel nb2listw function, three distance-based types weights available: inverse distance weighting (IDW), double-power distance weights, exponential distance decay. can..simmed helper function checks whether spatial weights object similar symmetric can transformed yield real eigenvalues Cholesky decomposition.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2listwdist.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Distance-based spatial weights for neighbours lists — nb2listwdist","text":"","code":"nb2listwdist(neighbours, x, type=\"idw\", style=\"raw\",    alpha = 1, dmax = NULL, longlat = NULL, zero.policy=NULL)"},{"path":"https://r-spatial.github.io/spdep/reference/nb2listwdist.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Distance-based spatial weights for neighbours lists — nb2listwdist","text":"neighbours object class nb x sp sf, sfc object type default “idw”; intended type distance modelling, can take values “idw”, “exp”, “dpd” style default “raw”; style can take values “raw”, “W”, “B”, “C”, “U”, “minmax”, “S” alpha default 0; parameter controlling distance modelling, see “Details” dmax default NULL, maximum distance threshold required type “dpd” optional types longlat default NULL; TRUE point coordinates longitude-latitude decimal degrees, case distances measured metres; x SpatialPoints object, value taken object , overrides argument NULL; distances measured map units FALSE NULL zero.policy default NULL; use global option value; FALSE stop error empty neighbour sets, TRUE permit weights list formed zero-length weights vectors","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2listwdist.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Distance-based spatial weights for neighbours lists — nb2listwdist","text":"Starting binary neighbours list, regions either listed neighbours absent (thus set neighbours definition), function adds distance-based weights list. Three types distance weight calculations based pairwise distances \\(d_{ij}\\) possible, controlled parameter “alpha” (\\(\\alpha\\) ): $$\\textrm{idw: } w_{ij} = d_{ij}^{-\\alpha},$$ $$\\textrm{exp: } w_{ij} = \\exp(-\\alpha \\cdot d_{ij}),$$ $$\\textrm{dpd: } w_{ij} = \\left[1 - \\left(d_{ij}/d_{\\textrm{max}}\\right)^{\\alpha}\\right]^{\\alpha},$$ latter leads \\(w_{ij} = 0\\) \\(d_{ij} > d_{\\textrm{max}}\\). Note IDW weights show extreme behaviour close 0 can take value infinity. cases, infinite values replaced largest finite weight present weights list. default coding scheme “raw”, outputs raw distance-based weights without applying kind normalisation. addition, coding scheme styles also available nb2listw function can chosen. B basic binary coding, W row standardised (sums links n), C globally standardised (sums links n), U equal C divided number neighbours (sums links unity), S variance-stabilising coding scheme proposed Tiefelsdorf et al. 1999, p. 167-168 (sums links n). “minmax” style based Kelejian Prucha (2010), divides weights minimum maximum row sums maximum column sums input weights. similar C U styles; also available Stata. zero.policy set TRUE, weights vectors zero length inserted regions without neighbour neighbours list. turn generate lag values zero, equivalent sum products zero row t(rep(0, length=length(neighbours))) %*% x, arbitraty numerical vector x length length(neighbours). spatially lagged value x zero-neighbour region zero, may (may ) sensible choice.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2listwdist.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Distance-based spatial weights for neighbours lists — nb2listwdist","text":"listw object following members: style one W, B, C, U, S, minmax type one idw, exp, dpd neighbours input neighbours list weights weights neighbours chosen style, attributes set report type relationships (binary general, general form glist argument), style ","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2listwdist.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Distance-based spatial weights for neighbours lists — nb2listwdist","text":"Tiefelsdorf, M., Griffith, D. ., Boots, B. 1999 variance-stabilizing coding scheme spatial link matrices, Environment Planning , 31, pp. 165–180; Kelejian, H. H., . R. Prucha. 2010. Specification estimation spatial autoregressive models autoregressive heteroskedastic disturbances. Journal Econometrics, 157: pp. 53–67.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2listwdist.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Distance-based spatial weights for neighbours lists — nb2listwdist","text":"Rene Westerholt rene.westerholt@tu-dortmund.de","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/nb2listwdist.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Distance-based spatial weights for neighbours lists — nb2listwdist","text":"","code":"# World examples data(world, package=\"spData\") # neighbours on distance interval [0, 1000] kilometres # suppressWarnings(st_crs(world) <- \"+proj=longlat\") # for older PROJ pts <- st_centroid(st_transform(world, 3857)) #> Warning: st_centroid assumes attributes are constant over geometries nb_world <- dnearneigh(pts, 0, 1000000) #> Warning: neighbour object has 46 sub-graphs # Moran's I (life expectancy) with IDW with alpha = 2, no coding scheme world_weights <- nb2listwdist(nb_world, as(pts, \"Spatial\"), type = \"idw\",   alpha = 2, zero.policy = TRUE) moran.test(world$lifeExp, world_weights, zero.policy = TRUE, na.action = na.pass) #> Warning: NAs in lagged values #>  #> \tMoran I test under randomisation #>  #> data:  world$lifeExp   #> weights: world_weights   #> n reduced by no-neighbour observations   #>  #> Moran I statistic standard deviate = 2.7769, p-value = 0.002744 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic       Expectation          Variance  #>       0.473883371      -0.007042254       0.029994057  #>  if (FALSE) { # \\dontrun{ # Moran's I (life expectancy) with IDW with alpha = 2, no coding scheme world_weights <- nb2listwdist(nb_world, pts, type = \"idw\",   alpha = 2, zero.policy = TRUE) moran.test(world$lifeExp, world_weights, zero.policy = TRUE, na.action = na.pass) # Moran's I (life expectancy), DPD, alpha = 2, dmax = 1000 km, no coding scheme world_weights <- nb2listwdist(nb_world, pts, type = \"dpd\",   dmax = 1000000, alpha = 2, zero.policy = TRUE) moran.test(world$lifeExp, world_weights, zero.policy = TRUE, na.action = na.pass) # Boston examples data(boston, package=\"spData\") boston_coords <- data.frame(x = boston.utm[,1], y = boston.utm[,2]) boston.geoms <- st_as_sf(boston_coords, coords = c(\"x\", \"y\"), remove = FALSE) nb_boston <- dnearneigh(boston.geoms, 0, 3) # Moran's I (crime) with exp weights with alpha = 2, no coding scheme boston_weights <- nb2listwdist(nb_boston, boston.geoms, type = \"exp\", alpha = 2,   style=\"raw\", zero.policy = TRUE) moran.test(boston.c$CRIM, boston_weights, zero.policy = TRUE, na.action = na.pass) # Moran's I (crime) with idw weights with alpha = 2, coding scheme = W boston_weights <- nb2listwdist(nb_boston, boston.geoms, type = \"idw\", alpha = 2,   style=\"W\", zero.policy = TRUE) moran.test(boston.c$CRIM, boston_weights, zero.policy = TRUE, na.action = na.pass) } # }"},{"path":"https://r-spatial.github.io/spdep/reference/nb2mat.html","id":null,"dir":"Reference","previous_headings":"","what":"Spatial weights matrices for neighbours lists — nb2mat","title":"Spatial weights matrices for neighbours lists — nb2mat","text":"function generates weights matrix neighbours list spatial weights chosen coding scheme.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2mat.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Spatial weights matrices for neighbours lists — nb2mat","text":"","code":"nb2mat(neighbours, glist=NULL, style=\"W\", zero.policy=NULL) listw2mat(listw)"},{"path":"https://r-spatial.github.io/spdep/reference/nb2mat.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Spatial weights matrices for neighbours lists — nb2mat","text":"neighbours object class nb glist list general weights corresponding neighbours style style can take values W, B, C, S zero.policy default NULL, use global option value; FALSE stop error empty neighbour sets, TRUE permit weights list formed zero-length weights vectors listw listw object example nb2listw","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2mat.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Spatial weights matrices for neighbours lists — nb2mat","text":"Starting binary neighbours list, regions either listed neighbours absent (thus set neighbours definition), function creates n n weights matrix values given coding scheme style chosen. B basic binary coding, W row standardised, C globally standardised, S variance-stabilizing coding scheme proposed Tiefelsdorf et al. 1999, p. 167-168. function leaves matrix rows zero regions zero neighbours fore zero.policy TRUE. turn generate lag values zero, equivalent sum products zero row t(rep(0, length=length(neighbours))) %*% x, arbitraty numerical vector x length length(neighbours). spatially lagged value x zero-neighbour region zero, may (may ) sensible choice.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2mat.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Spatial weights matrices for neighbours lists — nb2mat","text":"n n matrix, n=length(neighbours)","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2mat.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Spatial weights matrices for neighbours lists — nb2mat","text":"Tiefelsdorf, M., Griffith, D. ., Boots, B. 1999 variance-stabilizing coding scheme spatial link matrices, Environment Planning , 31, pp. 165-180.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2mat.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Spatial weights matrices for neighbours lists — nb2mat","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/nb2mat.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Spatial weights matrices for neighbours lists — nb2mat","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) col005 <- dnearneigh(st_coordinates(st_centroid(st_geometry(columbus),  of_largest_polygon=TRUE)), 0, 0.5, as.character(columbus$NEIGNO)) #> Warning: neighbour object has 8 sub-graphs summary(col005) #> Neighbour list object: #> Number of regions: 49  #> Number of nonzero links: 170  #> Percentage nonzero weights: 7.080383  #> Average number of links: 3.469388  #> 4 regions with no links: #> 1005, 1006, 1008, 1043 #> 8 disjoint connected subgraphs #> Link number distribution: #>  #>  0  1  2  3  4  5  6  7  8  9  #>  4 11  5  8  3  9  2  2  3  2  #> 11 least connected regions: #> 1001 1007 1018 1010 1045 1044 1046 1047 1049 1048 1015 with 1 link #> 2 most connected regions: #> 1038 1036 with 9 links col005.w.mat <- nb2mat(col005, style=\"B\", zero.policy=TRUE) table(round(rowSums(col005.w.mat))) #>  #>  0  1  2  3  4  5  6  7  8  9  #>  4 11  5  8  3  9  2  2  3  2"},{"path":"https://r-spatial.github.io/spdep/reference/nbcosts.html","id":null,"dir":"Reference","previous_headings":"","what":"Compute cost of edges — nbcosts","title":"Compute cost of edges — nbcosts","text":"cost edge distance nodes. function   compute distance using data.frame observations vector   node.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nbcosts.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Compute cost of edges — nbcosts","text":"","code":"nbcost(data, id, id.neigh,  method = c(\"euclidean\", \"maximum\",      \"manhattan\", \"canberra\", \"binary\", \"minkowski\", \"mahalanobis\"),     p = 2, cov, inverted = FALSE) nbcosts(nb, data,  method = c(\"euclidean\", \"maximum\",      \"manhattan\", \"canberra\", \"binary\", \"minkowski\", \"mahalanobis\"),     p = 2, cov, inverted = FALSE)"},{"path":"https://r-spatial.github.io/spdep/reference/nbcosts.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Compute cost of edges — nbcosts","text":"nb object nb class. See poly2nb     details. data matrix observations nodes. id Node index compute cost id.neigh Idex neighbours nodes node id method Character function declare distance method.     method character, method must \"mahalanobis\"     \"euclidean\", \"maximum\", \"manhattan\", \"canberra\", \"binary\"     \"minkowisk\".     method one \"euclidean\", \"maximum\",     \"manhattan\", \"canberra\", \"binary\" \"minkowisk\", see     dist details,      function used compute distance.      method=\"mahalanobis\", mahalanobis distance      computed neighbour areas.      method function, function      used compute distance. p power Minkowski distance. cov covariance matrix used compute mahalanobis    distance. inverted logical.  'TRUE', 'cov' supposed contain           inverse covariance matrix.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nbcosts.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Compute cost of edges — nbcosts","text":"object nbdist class. See nbdists   details.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nbcosts.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Compute cost of edges — nbcosts","text":"neighbours must connected graph.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nbcosts.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Compute cost of edges — nbcosts","text":"Elias T. Krainski Renato M. Assuncao","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/nbdists.html","id":null,"dir":"Reference","previous_headings":"","what":"Spatial link distance measures — nbdists","title":"Spatial link distance measures — nbdists","text":"Given list spatial neighbour links (neighbours list object type   nb), function returns Euclidean distances along links   list form neighbours list. longlat = TRUE, Great   Circle distances used.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nbdists.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Spatial link distance measures — nbdists","text":"","code":"nbdists(nb, coords, longlat = NULL)"},{"path":"https://r-spatial.github.io/spdep/reference/nbdists.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Spatial link distance measures — nbdists","text":"nb object class nb coords matrix point coordinates, object inheriting SpatialPoints \"sf\" \"sfc\" object; \"sf\" \"sfc\" object geometries geographical coordinates (sf::st_is_longlat(x) == TRUE sf::sf_use_s2() == TRUE), s2 used find distances https://github.com/r-spatial/s2/issues/125 longlat TRUE point coordinates longitude-latitude decimal degrees, case distances measured kilometers; coords SpatialPoints object, value taken object ","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nbdists.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Spatial link distance measures — nbdists","text":"list class nbdist","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nbdists.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Spatial link distance measures — nbdists","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/nbdists.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Spatial link distance measures — nbdists","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) col.gal.nb <- read.gal(system.file(\"weights/columbus.gal\", package=\"spData\")[1]) coords <- st_coordinates(st_centroid(columbus)) #> Warning: st_centroid assumes attributes are constant over geometries dlist <- nbdists(col.gal.nb, coords) dlist <- lapply(dlist, function(x) 1/x) stem(unlist(dlist)) #>  #>   The decimal point is at the | #>  #>   1 | 1111112222223333334444444444 #>   1 | 555555556666667777777777888888888899999999999999999999 #>   2 | 00000000111111111111111122222222222222333333333333334444 #>   2 | 55555555556666666666666677777777888888999999 #>   3 | 0000111111222233334444 #>   3 | 77779999 #>   4 | 223344 #>   4 | 77 #>   5 | 001144 #>   5 |  #>   6 |  #>   6 | 99 #>   7 |  #>   7 | 88 #>"},{"path":"https://r-spatial.github.io/spdep/reference/nblag.html","id":null,"dir":"Reference","previous_headings":"","what":"Higher order neighbours lists — nblag","title":"Higher order neighbours lists — nblag","text":"function creates higher order neighbour lists, higher order neighbours lags links graph described input neighbours list. refuse lag neighbours lists attribute self.included set TRUE. nblag_cumul cumulates neighbour lists single neighbour list (“nb” object).","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nblag.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Higher order neighbours lists — nblag","text":"","code":"nblag(neighbours, maxlag) nblag_cumul(nblags)"},{"path":"https://r-spatial.github.io/spdep/reference/nblag.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Higher order neighbours lists — nblag","text":"neighbours input neighbours list class nb maxlag maximum lag constructed nblags list neighbour lists output nblag","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nblag.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Higher order neighbours lists — nblag","text":"returns list lagged neighbours lists class nb","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nblag.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Higher order neighbours lists — nblag","text":"Roger Bivand Roger.Bivand@nhh.Giovanni Millo","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/nblag.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Higher order neighbours lists — nblag","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) col.gal.nb <- read.gal(system.file(\"weights/columbus.gal\", package=\"spData\")[1]) coords <- st_coordinates(st_centroid(columbus)) #> Warning: st_centroid assumes attributes are constant over geometries summary(col.gal.nb, coords) #> Neighbour list object: #> Number of regions: 49  #> Number of nonzero links: 230  #> Percentage nonzero weights: 9.579342  #> Average number of links: 4.693878  #> Link number distribution: #>  #>  2  3  4  5  6  7  8  9 10  #>  7  7 13  4  9  6  1  1  1  #> 7 least connected regions: #> 1 6 31 39 42 46 47 with 2 links #> 1 most connected region: #> 20 with 10 links col.lags <- nblag(col.gal.nb, 2) print(col.lags) #> [[1]] #> Neighbour list object: #> Number of regions: 49  #> Number of nonzero links: 230  #> Percentage nonzero weights: 9.579342  #> Average number of links: 4.693878  #>  #> [[2]] #> Neighbour list object: #> Number of regions: 49  #> Number of nonzero links: 406  #> Percentage nonzero weights: 16.90962  #> Average number of links: 8.285714  #>  #> attr(,\"call\") #> nblag(neighbours = col.gal.nb, maxlag = 2) summary(col.lags[[2]], coords) #> Neighbour list object: #> Number of regions: 49  #> Number of nonzero links: 406  #> Percentage nonzero weights: 16.90962  #> Average number of links: 8.285714  #> Link number distribution: #>  #>  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17  #>  1  2  5  4  2  3  5  4  2  3  7  3  4  1  1  1  1  #> 1 least connected region: #> 36 with 1 link #> 1 most connected region: #> 25 with 17 links plot(st_geometry(columbus), border=\"grey\") plot(col.gal.nb, coords, add=TRUE) title(main=\"GAL order 1 (black) and 2 (red) links\") plot(col.lags[[2]], coords, add=TRUE, col=\"red\", lty=2)  cuml <- nblag_cumul(col.lags) cuml #> Neighbour list object: #> Number of regions: 49  #> Number of nonzero links: 636  #> Percentage nonzero weights: 26.48896  #> Average number of links: 12.97959  run <- FALSE if (require(igraph, quietly=TRUE) && require(spatialreg, quietly=TRUE)) run <- TRUE if (run) { W <- as(nb2listw(col.gal.nb), \"CsparseMatrix\") G <- graph_from_adjacency_matrix(W, mode=\"directed\", weight=\"W\") D <- diameter(G) nbs <- nblag(col.gal.nb, maxlag=D) n <- length(col.gal.nb) lmat <- lapply(nbs, nb2mat, style=\"B\", zero.policy=TRUE) mat <- matrix(0, n, n) for (i in seq(along=lmat)) mat = mat + i*lmat[[i]] G2 <- distances(G) print(all.equal(G2, mat, check.attributes=FALSE)) } #> Warning: lag 6 neighbour object has 5 sub-graphs #> Warning: lag 7 neighbour object has 20 sub-graphs #> Warning: lag 8 neighbour object has 36 sub-graphs #> Warning: lag 9 neighbour object has 44 sub-graphs #> [1] TRUE"},{"path":"https://r-spatial.github.io/spdep/reference/nboperations.html","id":null,"dir":"Reference","previous_headings":"","what":"Set operations on neighborhood objects — nb.set.operations","title":"Set operations on neighborhood objects — nb.set.operations","text":"Set operations neighbors list objects","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nboperations.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Set operations on neighborhood objects — nb.set.operations","text":"","code":"intersect.nb(nb.obj1,nb.obj2) union.nb(nb.obj1,nb.obj2) setdiff.nb(nb.obj1,nb.obj2) complement.nb(nb.obj)"},{"path":"https://r-spatial.github.io/spdep/reference/nboperations.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Set operations on neighborhood objects — nb.set.operations","text":"nb.obj neighbor list created neighborhood     list funtions nb.obj1 neighbor list created neighborhood     list funtions nb.obj2 neighbor list created neighborhood     list funtions","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nboperations.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Set operations on neighborhood objects — nb.set.operations","text":"functions perform set operations element   neighborlist. arguments must neighbor lists created   coordinates, region.id attributes must identical.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nboperations.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Set operations on neighborhood objects — nb.set.operations","text":"nb.obj new neighborlist created set operations                input neighbor list(s)","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nboperations.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Set operations on neighborhood objects — nb.set.operations","text":"Nicholas Lewin-Koh nikko@hailmail.net","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/nboperations.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Set operations on neighborhood objects — nb.set.operations","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) col.gal.nb <- read.gal(system.file(\"weights/columbus.gal\", package=\"spData\")[1]) coords <- st_coordinates(st_centroid(columbus)) #> Warning: st_centroid assumes attributes are constant over geometries col.tri.nb <- tri2nb(coords) oldpar <- par(mfrow=c(1,2)) if (require(\"dbscan\", quietly=TRUE)) {   col.soi.nb <- graph2nb(soi.graph(col.tri.nb, coords))   plot(st_geometry(columbus), border=\"grey\")   plot(col.soi.nb, coords, add=TRUE)   title(main=\"Sphere of Influence Graph\", cex.main=0.7)   plot(st_geometry(columbus), border=\"grey\")   plot(complement.nb(col.soi.nb), coords, add=TRUE)   title(main=\"Complement of Sphere of Influence Graph\", cex.main=0.7) }  par(mfrow=c(2,2)) col2 <- droplinks(col.gal.nb, 21) #> Warning: some observations have no neighbours #> Warning: neighbour object has 3 sub-graphs plot(intersect.nb(col.gal.nb, col2), coords) #> Warning: neighbour object has 3 sub-graphs title(main=\"Intersect\", cex.main=0.7) plot(union.nb(col.gal.nb, col2), coords) title(main=\"Union\", cex.main=0.7) plot(setdiff.nb(col.gal.nb, col2), coords) #> Warning: neighbour object has 46 sub-graphs title(main=\"Set diff\", cex.main=0.7) par(oldpar)"},{"path":"https://r-spatial.github.io/spdep/reference/p.adjustSP.html","id":null,"dir":"Reference","previous_headings":"","what":"Adjust local association measures' p-values — p.adjustSP","title":"Adjust local association measures' p-values — p.adjustSP","text":"Make adjustment local association measures' p-values based number neighbours (+1) region, rather total number regions.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/p.adjustSP.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Adjust local association measures' p-values — p.adjustSP","text":"","code":"p.adjustSP(p, nb, method = \"none\")"},{"path":"https://r-spatial.github.io/spdep/reference/p.adjustSP.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Adjust local association measures' p-values — p.adjustSP","text":"p vector p-values nb list neighbours class nb method correction method defined p.adjust: \"adjustment methods include Bonferroni correction ('\"bonferroni\"') p-values multiplied number comparisons.  Four less conservative corrections also included Holm (1979) ('holm'), Hochberg (1988) ('hochberg'), Hommel (1988) ('hommel') Benjamini & Hochberg (1995) ('fdr'), respectively. pass-option ('none') also included.\"","code":""},{"path":"https://r-spatial.github.io/spdep/reference/p.adjustSP.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Adjust local association measures' p-values — p.adjustSP","text":"vector corrected p-values using number neighbours + 1.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/p.adjustSP.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Adjust local association measures' p-values — p.adjustSP","text":"Danlin Yu Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/p.adjustSP.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Adjust local association measures' p-values — p.adjustSP","text":"","code":"data(afcon, package=\"spData\") oid <- order(afcon$id) resG <- as.vector(localG(afcon$totcon, nb2listw(include.self(paper.nb)))) non <- format.pval(pnorm(2*(abs(resG)), lower.tail=FALSE), 2) bon <- format.pval(p.adjustSP(pnorm(2*(abs(resG)), lower.tail=FALSE),  paper.nb, \"bonferroni\"), 2) tot <- format.pval(p.adjust(pnorm(2*(abs(resG)), lower.tail=FALSE),  \"bonferroni\", n=length(resG)), 2) data.frame(resG, non, bon, tot, row.names=afcon$name)[oid,] #>                                 resG     non     bon     tot #> THE GAMBIA               -0.98383592 0.02455 0.04911  1.0000 #> MALI                     -1.69893391 0.00034 0.00272  0.0143 #> SENEGAL                  -1.46321911 0.00171 0.00857  0.0720 #> BENIN                    -1.30139679 0.00462 0.02312  0.1942 #> MAURITANIA               -0.60496775 0.11315 0.56576  1.0000 #> NIGER                    -1.04877003 0.01797 0.14378  0.7549 #> IVORY COAST              -1.41712454 0.00230 0.01378  0.0965 #> GUINEA                   -1.44888005 0.00188 0.01128  0.0789 #> BURKINA FASO             -1.75085492 0.00023 0.00162  0.0097 #> LIBERIA                  -1.04053617 0.01871 0.07485  0.7860 #> SIERRA LEONE             -0.87032623 0.04087 0.12262  1.0000 #> GHANA                    -1.10269327 0.01371 0.05485  0.5760 #> TOGO                     -0.99053008 0.02379 0.09517  0.9993 #> CAMEROON                 -1.13328519 0.01171 0.07025  0.4917 #> NIGERIA                  -1.17261672 0.00951 0.04754  0.3993 #> GABON                    -0.78935857 0.05720 0.17160  1.0000 #> CENTRAL AFRICAN REPUBLIC  1.17349763 0.00946 0.05678  0.3974 #> CHAD                      0.46259185 0.17744 1.00000  1.0000 #> CONGO                    -0.20253005 0.34272 1.00000  1.0000 #> ZAIRE                     2.02270432 2.6e-05 0.00026  0.0011 #> ANGOLA                    1.23450728 0.00677 0.02710  0.2845 #> UGANDA                    3.33600851 1.3e-11 7.6e-11 5.3e-10 #> KENYA                     3.50301896 1.2e-12 7.4e-12 5.1e-11 #> TANZANIA                  1.09843592 0.01401 0.12613  0.5886 #> BURUNDI                   0.77417084 0.06077 0.24308  1.0000 #> RWANDA                    1.45720776 0.00178 0.00891  0.0748 #> SOMALIA                   1.18316273 0.00898 0.02695  0.3773 #> ETHIOPIA                  2.62720027 7.4e-08 3.0e-07 3.1e-06 #> ZAMBIA                    0.75273285 0.06610 0.59492  1.0000 #> ZIMBABWE                 -0.19956472 0.34490 1.00000  1.0000 #> MALAWI                    0.21195283 0.33582 1.00000  1.0000 #> MOZAMBIQUE               -0.28761679 0.28257 1.00000  1.0000 #> SOUTH AFRICA             -0.86814954 0.04126 0.33004  1.0000 #> LESOTHO                  -0.29841469 0.27531 0.55062  1.0000 #> BOTSWANA                  0.04090396 0.46740 1.00000  1.0000 #> SWAZILAND                -0.65938417 0.09362 0.28087  1.0000 #> MOROCCO                   0.02191606 0.48252 1.00000  1.0000 #> ALGERIA                  -0.36307938 0.23387 1.00000  1.0000 #> TUNISIA                   0.57910139 0.12339 0.37017  1.0000 #> LIBYA                     2.55272169 1.7e-07 1.2e-06 6.9e-06 #> SUDAN                     4.03925235 3.3e-16 3.0e-15 1.4e-14 #> EGYPT                     4.42133637 < 2e-16 < 2e-16 < 2e-16"},{"path":"https://r-spatial.github.io/spdep/reference/plot.mst.html","id":null,"dir":"Reference","previous_headings":"","what":"Plot the Minimum Spanning Tree — plot.mst","title":"Plot the Minimum Spanning Tree — plot.mst","text":"function plots MST, nodes circles edges   segments.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/plot.mst.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Plot the Minimum Spanning Tree — plot.mst","text":"","code":"# S3 method for class 'mst' plot(x, coords, label.areas = NULL,     cex.circles = 1, cex.labels = 1, add=FALSE, ...)"},{"path":"https://r-spatial.github.io/spdep/reference/plot.mst.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Plot the Minimum Spanning Tree — plot.mst","text":"x Object mst class. coords two column matrix coordinates nodes. label.areas vector labels nodes cex.circles length circles plot. cex.labels length nodes labels ploted. add default FALSE, create new plot ... arguments passed plotting functions.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/plot.mst.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Plot the Minimum Spanning Tree — plot.mst","text":"Elias T. Krainski Renato M. Assuncao","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/plot.mst.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Plot the Minimum Spanning Tree — plot.mst","text":"","code":"### see example in mstree function documentation"},{"path":"https://r-spatial.github.io/spdep/reference/plot.nb.html","id":null,"dir":"Reference","previous_headings":"","what":"Plot a neighbours list — plot.nb","title":"Plot a neighbours list — plot.nb","text":"function plot neighbours list given point coordinates represent region two dimensions; plot.listw wrapper passes neighbours component plot.nb.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/plot.nb.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Plot a neighbours list — plot.nb","text":"","code":"# S3 method for class 'nb' plot(x, coords, col=\"black\", points=TRUE, add=FALSE, arrows=FALSE,  length=0.1, xlim=NULL, ylim=NULL, ...) # S3 method for class 'listw' plot(x, coords, col=\"black\", points=TRUE, add=FALSE, arrows=FALSE,  length=0.1, xlim=NULL, ylim=NULL, ...)"},{"path":"https://r-spatial.github.io/spdep/reference/plot.nb.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Plot a neighbours list — plot.nb","text":"x object class nb (plot.listw) class listw coords matrix region point coordinates, Spatial object (points polygons), sfc object (points polygons) col plotting colour points (logical) add points plot add (logical) add existing plot arrows (logical) draw arrowheads asymmetric neighbours length length plot inches arrow heads drawn asymmetric neighbours lists xlim, ylim plot window bounds ... graphical parameters par(..)","code":""},{"path":"https://r-spatial.github.io/spdep/reference/plot.nb.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Plot a neighbours list — plot.nb","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/plot.nb.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Plot a neighbours list — plot.nb","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) col.gal.nb <- read.gal(system.file(\"weights/columbus.gal\", package=\"spData\")[1]) plot(col.gal.nb, st_geometry(columbus)) title(main=\"GAL order 1 links with first nearest neighbours in red\", cex.main=0.6)  plot(col.gal.nb, as(columbus, \"Spatial\")) title(main=\"GAL order 1 links with first nearest neighbours in red\", cex.main=0.6) coords <- st_centroid(st_geometry(columbus), of_largest_polygon=TRUE) col.knn <- knearneigh(coords, k=1) plot(knn2nb(col.knn), coords, add=TRUE, col=\"red\", length=0.08) #> Warning: neighbour object has 13 sub-graphs"},{"path":"https://r-spatial.github.io/spdep/reference/plot.skater.html","id":null,"dir":"Reference","previous_headings":"","what":"Plot the object of skater class — plot.skater","title":"Plot the object of skater class — plot.skater","text":"function displays results skater function. subgraphs   plotted different colours.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/plot.skater.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Plot the object of skater class — plot.skater","text":"","code":"# S3 method for class 'skater' plot(x, coords, label.areas = NULL,     groups.colors, cex.circles = 1, cex.labels = 1, ...)"},{"path":"https://r-spatial.github.io/spdep/reference/plot.skater.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Plot the object of skater class — plot.skater","text":"x object skater class. coords matrix two colums coordinates nodes. label.areas vector labels nodes. groups.colors vector colors groups ou sub-graphs. cex.circles length circles represent nodes. cex.labels length labels nodes. ... arguments passed plotting funcitons.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/plot.skater.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Plot the object of skater class — plot.skater","text":"Elias T. Krainski Renato M. Assuncao","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/plot.skater.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Plot the object of skater class — plot.skater","text":"","code":"### see example in the skater function documentation"},{"path":"https://r-spatial.github.io/spdep/reference/poly2nb.html","id":null,"dir":"Reference","previous_headings":"","what":"Construct neighbours list from polygon list — poly2nb","title":"Construct neighbours list from polygon list — poly2nb","text":"function builds neighbours list based regions contiguous boundaries, sharing one boundary point. current function part interpreted may run slowly many regions detailed boundaries, 0.2-16 fail lack memory single polygons built many border coordinates.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/poly2nb.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Construct neighbours list from polygon list — poly2nb","text":"","code":"poly2nb(pl, row.names = NULL, snap=NULL, queen=TRUE, useC=TRUE, foundInBox=NULL)"},{"path":"https://r-spatial.github.io/spdep/reference/poly2nb.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Construct neighbours list from polygon list — poly2nb","text":"pl list polygons class extending SpatialPolygons, sf sfc object containing non-empty (multi-)polygon objects row.names character vector region ids added neighbours list attribute region.id, default seq(1, nrow(x)); pl row.names, used instead default sequence. snap boundary points less snap distance apart considered indicate contiguity; used find candidate actual neighbours planar geometries, actual neighbours spherical geometries, spherical spatial indexing injects fuzzyness. set, SpatialPolygons objects, default sqrt(.Machine$double.eps), value also used sf objects coordinate reference system. sf objects defined coordinate reference system, default value 1e-7 geographical coordinates (approximately 10mm), 10mm projected coordinates metre units, converted 10mm distance units coordinates. conversion fail, snap reverts sqrt(.Machine$double.eps). queen TRUE, single shared boundary point meets contiguity condition, FALSE, one shared point required; note one shared boundary point necessarily mean shared boundary line useC default TRUE, work loop C, may set false revert R code calling two C functions n*k work loop, k average number candidate neighbours foundInBox default NULL using R code st_intersects() generate candidate neighbours (using snap= geometries spherical); NULL (legacy purposes) list length (n-1) integer vectors candidate neighbours (j > ) (created poly_findInBoxGEOS function rgeos clean polygons)","code":""},{"path":"https://r-spatial.github.io/spdep/reference/poly2nb.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Construct neighbours list from polygon list — poly2nb","text":"neighbours list class nb. See card details “nb” objects.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/poly2nb.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Construct neighbours list from polygon list — poly2nb","text":"0.5-8, function includes faster bounding box indexing improvements contributed Micah Altman. cluster provided using set.ClusterOption, used finding candidate bounding box overlaps exact testing contiguity. 1.1-7, sf polygons included start end points, erroneously report queen neighbourhood rook present, see https://github.com/r-spatial/spdep/issues/50. 1.1-9 sf 1.0-0, s2 used bounding box indexing internally pl geographical coordinates. topology engine s2 differs use GEOS planar coordinates sf, output differences may expected. Since treating spherical geometries planar also questionable, clear whether spherical contiguous polygon neighbours simply follow neighbours found treating geometries planar https://github.com/r-spatial/s2/issues/125#issuecomment-864403372. However, current advice necessarily use s2 finding contiguity neighbours, least check output.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/poly2nb.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Construct neighbours list from polygon list — poly2nb","text":"Roger Bivand Roger.Bivand@nhh.contributions Micah Altman","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/poly2nb.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Construct neighbours list from polygon list — poly2nb","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) col.gal.nb <- read.gal(system.file(\"weights/columbus.gal\", package=\"spData\")[1]) coords <- st_coordinates(st_centroid(st_geometry(columbus))) xx <- poly2nb(as(columbus, \"Spatial\")) dxx <- diffnb(xx, col.gal.nb) #> Warning: neighbour object has 46 sub-graphs plot(st_geometry(columbus), border=\"grey\") plot(col.gal.nb, coords, add=TRUE) plot(dxx, coords, add=TRUE, col=\"red\") title(main=paste(\"Differences (red) in Columbus GAL weights (black)\",  \"and polygon generated queen weights\", sep=\"\\n\"), cex.main=0.6)  # poly2nb with sf sfc_MULTIPOLYGON objects sf_xx <- poly2nb(columbus) diffnb(sf_xx, xx) #> Warning: neighbour object has 49 sub-graphs #> Neighbour list object: #> Number of regions: 49  #> Number of nonzero links: 0  #> Percentage nonzero weights: 0  #> Average number of links: 0  #> 49 regions with no links: #> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, #> 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, #> 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49 #> 49 disjoint connected subgraphs sfc_xx <- poly2nb(st_geometry(columbus)) diffnb(sfc_xx, xx) #> Warning: neighbour object has 49 sub-graphs #> Neighbour list object: #> Number of regions: 49  #> Number of nonzero links: 0  #> Percentage nonzero weights: 0  #> Average number of links: 0  #> 49 regions with no links: #> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, #> 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, #> 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49 #> 49 disjoint connected subgraphs xxx <- poly2nb(as(columbus, \"Spatial\"), queen=FALSE) dxxx <- diffnb(xxx, col.gal.nb) #> Warning: neighbour object has 34 sub-graphs plot(st_geometry(columbus), border = \"grey\") plot(col.gal.nb, coords, add = TRUE) plot(dxxx, coords, add = TRUE, col = \"red\") title(main=paste(\"Differences (red) in Columbus GAL weights (black)\",  \"and polygon generated rook weights\", sep=\"\\n\"), cex.main=0.6)  cards <- card(xx) maxconts <- which(cards == max(cards)) if(length(maxconts) > 1) maxconts <- maxconts[1] fg <- rep(\"grey\", length(cards)) fg[maxconts] <- \"red\" fg[xx[[maxconts]]] <- \"green\" plot(st_geometry(columbus), col=fg) title(main=\"Region with largest number of contiguities\", cex.main=0.6)  nc.sids <- st_read(system.file(\"shapes/sids.gpkg\", package=\"spData\")[1], quiet=TRUE) system.time(xxnb <- poly2nb(nc.sids)) #>    user  system elapsed  #>   0.041   0.000   0.041  system.time(xxnb <- poly2nb(as(nc.sids, \"Spatial\"))) #>    user  system elapsed  #>   0.055   0.000   0.055  plot(st_geometry(nc.sids)) plot(xxnb, st_coordinates(st_centroid(nc.sids)), add=TRUE, col=\"blue\") #> Warning: st_centroid assumes attributes are constant over geometries  sq <- st_polygon(list(rbind(c(0,0), c(1,0), c(1,1), c(0,1), c(0,0)))) sq2 <- sq + c(0,1) sq3 <- sq + c(1,0) sq4 <- sq + c(1,1) gm <- st_sfc(list(sq, sq2, sq3, sq4)) df <- st_as_sf(data.frame(gm, id=1:4)) plot(st_geometry(df)) text(st_coordinates(st_centroid(gm)), as.character(df$id))  unclass(poly2nb(df, queen = FALSE)) #> [[1]] #> [1] 2 3 #>  #> [[2]] #> [1] 1 4 #>  #> [[3]] #> [1] 1 4 #>  #> [[4]] #> [1] 2 3 #>  #> attr(,\"region.id\") #> [1] \"1\" \"2\" \"3\" \"4\" #> attr(,\"call\") #> poly2nb(pl = df, queen = FALSE) #> attr(,\"type\") #> [1] \"rook\" #> attr(,\"snap\") #> [1] 1.490116e-08 #> attr(,\"sym\") #> [1] TRUE #> attr(,\"ncomp\") #> attr(,\"ncomp\")$nc #> [1] 1 #>  #> attr(,\"ncomp\")$comp.id #> [1] 1 1 1 1 #>  col_geoms <- st_geometry(columbus) col_geoms[1] <- st_buffer(col_geoms[1], dist=-0.05) st_geometry(columbus) <- col_geoms poly2nb(columbus) #> Warning: some observations have no neighbours; #> if this seems unexpected, try increasing the snap argument. #> Warning: neighbour object has 2 sub-graphs; #> if this sub-graph count seems unexpected, try increasing the snap argument. #> Neighbour list object: #> Number of regions: 49  #> Number of nonzero links: 232  #> Percentage nonzero weights: 9.662641  #> Average number of links: 4.734694  #> 1 region with no links: #> 1 #> 2 disjoint connected subgraphs"},{"path":"https://r-spatial.github.io/spdep/reference/probmap.html","id":null,"dir":"Reference","previous_headings":"","what":"Probability mapping for rates — probmap","title":"Probability mapping for rates — probmap","text":"function returns data frame rates counts populations risk crude rates, expected counts cases, relative risks, Poisson probabilities.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/probmap.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Probability mapping for rates — probmap","text":"","code":"probmap(n, x, row.names=NULL, alternative=\"less\")"},{"path":"https://r-spatial.github.io/spdep/reference/probmap.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Probability mapping for rates — probmap","text":"n numeric vector counts cases x numeric vector populations risk row.names row names passed output data frame alternative default “less”, may set “greater”","code":""},{"path":"https://r-spatial.github.io/spdep/reference/probmap.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Probability mapping for rates — probmap","text":"function returns data frame, rates may mapped class intervals chosen. class intervals used examples mostly taken referenced source.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/probmap.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Probability mapping for rates — probmap","text":"raw raw (crude) rates expCount expected counts cases assuming global rate relRisk relative risks: ratio observed expected counts cases multiplied 100 pmap Poisson probability map values: probablility getting “extreme” count actually observed - one-tailed, default alternative observed “less” expected","code":""},{"path":"https://r-spatial.github.io/spdep/reference/probmap.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Probability mapping for rates — probmap","text":"Bailey T, Gatrell (1995) Interactive Spatial Data Analysis, Harlow: Longman, pp. 300–303.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/probmap.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Probability mapping for rates — probmap","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/probmap.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Probability mapping for rates — probmap","text":"","code":"auckland <- st_read(system.file(\"shapes/auckland.gpkg\", package=\"spData\")[1], quiet=TRUE) res <- probmap(auckland$M77_85, 9*auckland$Und5_81) rt <- sum(auckland$M77_85)/sum(9*auckland$Und5_81) ppois_pmap <- numeric(length(auckland$Und5_81)) for (i in seq(along=ppois_pmap)) { ppois_pmap[i] <- poisson.test(auckland$M77_85[i], r=rt,   T=(9*auckland$Und5_81[i]), alternative=\"less\")$p.value all.equal(ppois_pmap, res$pmap) } res$id <- 1:nrow(res) auckland$id <- res$id <- 1:nrow(res) auckland_res <- merge(auckland, res, by=\"id\") plot(auckland_res[, \"raw\"], main=\"Crude (raw) estimates\")  plot(auckland_res[, \"relRisk\"], main=\"Standardised mortality ratios\")  plot(auckland_res[, \"pmap\"], main=\"Poisson probabilities\",  breaks=c(0, 0.05, 0.1, 0.5, 0.9, 0.95, 1))"},{"path":"https://r-spatial.github.io/spdep/reference/prunecost.html","id":null,"dir":"Reference","previous_headings":"","what":"Compute cost of prune each edge — prunecost","title":"Compute cost of prune each edge — prunecost","text":"edge dropped, MST pruned. generate two   subgraphs. , makes tree graphs tree dissimilarity values   computed, one graph. dissimilarity sum   sqared differences observactions nodes mean   vector observations graph. dissimilarity original   graph sum dissimilarity subgraphs returned.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/prunecost.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Compute cost of prune each edge — prunecost","text":"","code":"prunecost(edges, data, method = c(\"euclidean\", \"maximum\", \"manhattan\",      \"canberra\", \"binary\", \"minkowski\", \"mahalanobis\"),      p = 2, cov, inverted = FALSE)"},{"path":"https://r-spatial.github.io/spdep/reference/prunecost.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Compute cost of prune each edge — prunecost","text":"edges matrix 2 colums row one edge data data.frame observations nodes. method Character function declare distance method.     method character, method must \"mahalanobis\"     \"euclidean\", \"maximum\", \"manhattan\", \"canberra\", \"binary\"     \"minkowisk\".     method one \"euclidean\", \"maximum\",     \"manhattan\", \"canberra\", \"binary\" \"minkowisk\", see     dist details,      function used compute distance.      method=\"mahalanobis\", mahalanobis distance      computed neighbour areas.      method function, function      used compute distance. p power Minkowski distance. cov covariance matrix used compute mahalanobis    distance. inverted logical.  'TRUE', 'cov' supposed contain           inverse covariance matrix.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/prunecost.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Compute cost of prune each edge — prunecost","text":"vector differences dissimilarity nodes   dissimilarity sum subgraphs obtained pruning one   edge time.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/prunecost.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Compute cost of prune each edge — prunecost","text":"Elias T. Krainski Renato M. Assuncao","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/prunecost.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Compute cost of prune each edge — prunecost","text":"","code":"d <- data.frame(a=-2:2, b=runif(5)) e <- matrix(c(1,2, 2,3, 3,4, 4,5), ncol=2, byrow=TRUE)  sum(sweep(d, 2, colMeans(d))^2) #> [1] 10.35574  prunecost(e, d) #> [1] 2.138259 2.875555 2.820048 2.169740"},{"path":"https://r-spatial.github.io/spdep/reference/prunemst.html","id":null,"dir":"Reference","previous_headings":"","what":"Prune a Minimun Spanning Tree — prunemst","title":"Prune a Minimun Spanning Tree — prunemst","text":"function deletes first edge makes two subsets edges.   subset Minimun Spanning Treee.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/prunemst.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Prune a Minimun Spanning Tree — prunemst","text":"","code":"prunemst(edges, only.nodes = TRUE)"},{"path":"https://r-spatial.github.io/spdep/reference/prunemst.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Prune a Minimun Spanning Tree — prunemst","text":"edges matrix two colums row one edge .nodes .nodes=FALSE, return edges nodes   MST resulted. .nodes=TRUE, return two sets   nodes. Defalt TRUE","code":""},{"path":"https://r-spatial.github.io/spdep/reference/prunemst.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Prune a Minimun Spanning Tree — prunemst","text":"list length two. .nodes=TRUE element   vector nodes. .nodes=FALSE element list   nodes edges.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/prunemst.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Prune a Minimun Spanning Tree — prunemst","text":"Elias T. Krainski Renato M. Assuncao","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/prunemst.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Prune a Minimun Spanning Tree — prunemst","text":"","code":"e <- matrix(c(2,3, 1,2, 3,4, 4,5), ncol=2, byrow=TRUE) e #>      [,1] [,2] #> [1,]    2    3 #> [2,]    1    2 #> [3,]    3    4 #> [4,]    4    5 prunemst(e) #> $node1 #> [1] 2 1 #>  #> $node2 #> [1] 3 4 5 #>  prunemst(e, only.nodes=FALSE) #> [[1]] #> [[1]]$node #> [1] 2 1 #>  #> [[1]]$edge #>      [,1] [,2] #> [1,]    1    2 #>  #>  #> [[2]] #> [[2]]$node #> [1] 3 4 5 #>  #> [[2]]$edge #>      [,1] [,2] #> [1,]    3    4 #> [2,]    4    5 #>  #>"},{"path":"https://r-spatial.github.io/spdep/reference/read.gal.html","id":null,"dir":"Reference","previous_headings":"","what":"Read a GAL lattice file into a neighbours list — read.gal","title":"Read a GAL lattice file into a neighbours list — read.gal","text":"function read.gal() reads GAL lattice file neighbours list spatial analysis. read old new style (GeoDa) GAL files. function read.geoda helper file reading comma separated value data files, calling read.csv().","code":""},{"path":"https://r-spatial.github.io/spdep/reference/read.gal.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Read a GAL lattice file into a neighbours list — read.gal","text":"","code":"read.gal(file, region.id=NULL, override.id=FALSE) read.geoda(file, row.names=NULL, skip=0)"},{"path":"https://r-spatial.github.io/spdep/reference/read.gal.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Read a GAL lattice file into a neighbours list — read.gal","text":"file name file GAL lattice data region.id region IDs specified order coerse neighbours list order numbering region.id override.id override given (NULL) region.id, collecting region.id numbering order GAL file. row.names row.names read.csv(), typically character string naming column file used skip skip number lines, read.csv()","code":""},{"path":"https://r-spatial.github.io/spdep/reference/read.gal.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Read a GAL lattice file into a neighbours list — read.gal","text":"Luc Anselin (2003): Spatial Analysis Laboratory, Department Agricultural Consumer Economics, University Illinois, Urbana-Champaign, now dead link: http://www.csiss.org/gispopsci/workshops/2011/PSU/readings/W15_Anselin2007.pdf; Luc Anselin (2003) GeoDa 0.9 User's Guide, pp. 80–81, Spatial Analysis Laboratory, Department Agricultural Consumer Economics, University Illinois, Urbana-Champaign, http://geodacenter.github.io/docs/geoda093.pdf; GAL - Geographical Algorithms Library, University Newcastle","code":""},{"path":"https://r-spatial.github.io/spdep/reference/read.gal.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Read a GAL lattice file into a neighbours list — read.gal","text":"function read.gal() returns object class nb list integer vectors containing neighbour region number ids. function read.geoda returns data frame, issues warning returned object one column.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/read.gal.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Read a GAL lattice file into a neighbours list — read.gal","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/read.gal.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Read a GAL lattice file into a neighbours list — read.gal","text":"Example data originally downloaded now dead link: http://sal.agecon.uiuc.edu/weights/zips/us48.zip","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/read.gal.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Read a GAL lattice file into a neighbours list — read.gal","text":"","code":"us48.fipsno <- read.geoda(system.file(\"etc/weights/us48.txt\",  package=\"spdep\")[1]) us48.q <- read.gal(system.file(\"etc/weights/us48_q.GAL\", package=\"spdep\")[1],  us48.fipsno$Fipsno) us48.r <- read.gal(system.file(\"etc/weights/us48_rk.GAL\", package=\"spdep\")[1],  us48.fipsno$Fipsno) data(state) if (as.numeric(paste(version$major, version$minor, sep=\"\")) < 19) {  m50.48 <- match(us48.fipsno$\"State.name\", state.name) } else {  m50.48 <- match(us48.fipsno$\"State_name\", state.name) } plot(us48.q, as.matrix(as.data.frame(state.center))[m50.48,]) plot(diffnb(us48.r, us48.q),  as.matrix(as.data.frame(state.center))[m50.48,], add=TRUE, col=\"red\") #> Warning: neighbour object has 46 sub-graphs title(main=\"Differences between rook and queen criteria imported neighbours lists\")"},{"path":"https://r-spatial.github.io/spdep/reference/read.gwt2nb.html","id":null,"dir":"Reference","previous_headings":"","what":"Read and write spatial neighbour files — read.gwt2nb","title":"Read and write spatial neighbour files — read.gwt2nb","text":"\"gwt\" functions read write GeoDa GWT files (example file baltk4.GWT downloaded site given reference), \"dat\" functions read write Matlab sparse matrix files used James LeSage's Spatial Econometrics Toolbox (example file wmat.dat downloaded site given reference). body files headers three columns separated white space, third column must numeric locale reading platform (correct decimal separator).","code":""},{"path":"https://r-spatial.github.io/spdep/reference/read.gwt2nb.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Read and write spatial neighbour files — read.gwt2nb","text":"","code":"read.gwt2nb(file, region.id=NULL) write.sn2gwt(sn, file, shpfile=NULL, ind=NULL, useInd=FALSE, legacy=FALSE) read.dat2listw(file) write.sn2dat(sn, file) read.swmdbf2listw(fn, region.id=NULL, style=NULL, zero.policy=NULL) read_swm_dbf(fn) write.swmdbf(listw, file, ind, region.id = attr(listw, \"region.id\")) write_swm_dbf(listw, file, ind, region.id = attr(listw, \"region.id\")) write.sn2DBF(sn, file)"},{"path":"https://r-spatial.github.io/spdep/reference/read.gwt2nb.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Read and write spatial neighbour files — read.gwt2nb","text":"file, fn name file weights data region.id character vector region IDs - ArcGIS SWM DBFs, values must character integers (numbers starting zero) listw listw object sn spatial.neighbour object shpfile character string: given Shapefile name taken GWT file dataset ind character string: region id indicator field name useInd default FALSE, TRUE, write region.id attribute ID key tags output file (use OpenGeoDa depend shapefile field named ind argument matching exported tags) legacy default FALSE; TRUE, header single field number observations style default NULL, missing, set \"M\" warning given; \"M\", passed nb2listw re-build object zero.policy default NULL, use global option value; FALSE stop error empty neighbour sets, TRUE permit weights list formed zero-length weights vectors","code":""},{"path":"https://r-spatial.github.io/spdep/reference/read.gwt2nb.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Read and write spatial neighbour files — read.gwt2nb","text":"Attempts honour region.id argument given reading GWT SWM/DBF files. region IDs given region.id= match origins destinations GWT file, error warning thrown, considered carefully. read_swm_dbf simplified interface read.swmdbf2listw -neighbour observations present, advised region.id= given read.swmdbf2listw; function read correctly minimum maximum IDs present observations neighbours without region.id= set, reading using read.swmdbf2listw fail minimum maximum ID observations neighbours region.id= given.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/read.gwt2nb.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Read and write spatial neighbour files — read.gwt2nb","text":"read.gwt2nb returns neighbour \"nb\" object generalised weights stored list element called \"dlist\" \"GeoDa\" attribute; read.swmdbf2listw returns \"listw\" object read DBF file exported ArcGIS SWM object.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/read.gwt2nb.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Read and write spatial neighbour files — read.gwt2nb","text":"Luc Anselin (2003) GeoDa 0.9 User's Guide, pp. 80–81, Spatial Analysis Laboratory, Department Agricultural Consumer Economics, University Illinois, Urbana-Champaign, http://geodacenter.github.io/docs/geoda093.pdf; also material formerly spatial-econometrics.com/data/contents.html","code":""},{"path":"https://r-spatial.github.io/spdep/reference/read.gwt2nb.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Read and write spatial neighbour files — read.gwt2nb","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/read.gwt2nb.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Read and write spatial neighbour files — read.gwt2nb","text":"","code":"data(baltimore, package=\"spData\") STATION <- baltimore$STATION gwt1 <- read.gwt2nb(system.file(\"weights/baltk4.GWT\", package=\"spData\")[1],  STATION) #> Warning: 102, 115, 208 are not destinations cat(paste(\"Neighbours list symmetry;\", is.symmetric.nb(gwt1, FALSE, TRUE),  \"\\n\")) #> Neighbours list symmetry; FALSE  listw1 <- nb2listw(gwt1, style=\"B\", glist=attr(gwt1, \"GeoDa\")$dist) tmpGWT <- tempfile() write.sn2gwt(listw2sn(listw1), tmpGWT) gwt2 <- read.gwt2nb(tmpGWT, STATION) #> Warning: 102, 115, 208 are not destinations cat(paste(\"Neighbours list symmetry;\", is.symmetric.nb(gwt2, FALSE, TRUE),  \"\\n\")) #> Neighbours list symmetry; FALSE  diffnb(gwt1, gwt2) #> Warning: neighbour object has 211 sub-graphs #> Neighbour list object: #> Number of regions: 211  #> Number of nonzero links: 0  #> Percentage nonzero weights: 0  #> Average number of links: 0  #> 211 regions with no links: #> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, #> 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, #> 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, #> 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, #> 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, #> 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, #> 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, #> 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, #> 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, #> 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, #> 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, #> 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, #> 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, #> 206, 207, 208, 209, 210, 211 #> 211 disjoint connected subgraphs data(oldcol) tmpMAT <- tempfile() COL.W <- nb2listw(COL.nb) write.sn2dat(listw2sn(COL.W), tmpMAT) listwmat1 <- read.dat2listw(tmpMAT) #> Warning: style is M (missing); style should be set to a valid value diffnb(listwmat1$neighbours, COL.nb, verbose=TRUE) #> Warning: region.id differ; using ids of first list #> Warning: neighbour object has 49 sub-graphs #> Neighbour list object: #> Number of regions: 49  #> Number of nonzero links: 0  #> Percentage nonzero weights: 0  #> Average number of links: 0  #> 49 regions with no links: #> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, #> 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, #> 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49 #> 49 disjoint connected subgraphs listwmat2 <- read.dat2listw(system.file(\"etc/weights/wmat.dat\",   package=\"spdep\")[1]) #> Warning: style is M (missing); style should be set to a valid value diffnb(listwmat1$neighbours, listwmat2$neighbours, verbose=TRUE) #> Warning: neighbour object has 49 sub-graphs #> Neighbour list object: #> Number of regions: 49  #> Number of nonzero links: 0  #> Percentage nonzero weights: 0  #> Average number of links: 0  #> 49 regions with no links: #> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, #> 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, #> 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49 #> 49 disjoint connected subgraphs if (require(\"foreign\", quietly=TRUE)) { nc_sf <- sf::st_read(system.file(\"gpkg/nc.gpkg\", package=\"sf\")[1]) nc_sf$UniqueID <- 1:nrow(nc_sf) fn <- system.file(\"etc/misc/nc_contiguity_unique_id.dbf\", package=\"spdep\")[1] nc1 <- read.swmdbf2listw(fn, style=\"B\") nc1 nc1a <- read.swmdbf2listw(fn, region.id=as.character(nc_sf$UniqueID),  style=\"B\") all.equal(nc1, nc1a) fn <- system.file(\"etc/misc/nc_contiguity_unique_id_islands.dbf\",  package=\"spdep\")[1] try(nc1i <- read.swmdbf2listw(fn, style=\"B\")) nc1i <- read.swmdbf2listw(fn, style=\"B\", zero.policy=TRUE) nc1ia <- read.swmdbf2listw(fn, region.id=as.character(nc_sf$UniqueID),  style=\"B\", zero.policy=TRUE) nc1ia all.equal(nc1i, nc1ia) (GDAL37 <- as.numeric_version(unname(sf_extSoftVersion()[\"GDAL\"])) >= \"3.7.0\") file <- \"etc/shapes/california.gpkg.zip\" zipfile <- system.file(file, package=\"spdep\") if (GDAL37) {     cal <- st_read(zipfile) } else {     td <- tempdir()     bn <- sub(\".zip\", \"\", basename(file), fixed=TRUE)     target <- unzip(zipfile, files=bn, exdir=td)     cal <- st_read(target) } fn <- system.file(\"etc/misc/contiguity_myid.dbf\", package=\"spdep\")[1] cal1 <- read.swmdbf2listw(fn, style=\"B\") cal1a <- read.swmdbf2listw(fn, region.id=as.character(cal$MYID), style=\"B\") all.equal(cal1, cal1a) fn <- system.file(\"etc/misc/contiguity_unique_id.dbf\", package=\"spdep\")[1] cal2 <- read.swmdbf2listw(fn, style=\"B\") cal2a <- read.swmdbf2listw(fn, region.id=as.character(cal$UniqueID), style=\"B\") all.equal(cal2, cal2a) fn <- system.file(\"etc/misc/contiguity_unique_id_islands.dbf\", package=\"spdep\")[1] try(cal3i <- read.swmdbf2listw(fn, style=\"B\")) cal3i <- read.swmdbf2listw(fn, style=\"B\", zero.policy=TRUE) cal3ia <- read.swmdbf2listw(fn, region.id=as.character(cal$UniqueID), style=\"B\", zero.policy=TRUE) all.equal(cal3i, cal3ia) cal1a_1n_nb <- cal1a$neighbours cal1a_1n_nb <- droplinks(cal1a_1n_nb, drop=c(\"158\", \"180\", \"215\"), sym=TRUE) cal1a_1n <- nb2listw(cal1a_1n_nb, style=\"B\", zero.policy=TRUE) cal1a_1n_sn <- listw2sn(cal1a_1n) file <- tempfile(fileext=\".dbf\") write.sn2DBF(cal1a_1n_sn, file) cal1a_1n_rt <- read.swmdbf2listw(file, region.id=as.character(cal$MYID),  style=\"B\", zero.policy=TRUE) all.equal(cal1a_1n$neighbours, cal1a_1n_rt$neighbours) all.equal(cal1a_1n$weights, cal1a_1n_rt$weights, check.attributes=FALSE) cal1_1n_rt <- read.swmdbf2listw(file, style=\"B\", zero.policy=TRUE) all(isTRUE(all.equal(cal1a_1n$neighbours, cal1_1n_rt$neighbours))) all(isTRUE(all.equal(cal1a_1n$weights, cal1_1n_rt$weights)))  } #> Reading layer `nc.gpkg' from data source `/home/rsb/lib/r_libs/sf/gpkg/nc.gpkg' using driver `GPKG' #> Simple feature collection with 100 features and 14 fields #> Geometry type: MULTIPOLYGON #> Dimension:     XY #> Bounding box:  xmin: -84.32385 ymin: 33.88199 xmax: -75.45698 ymax: 36.58965 #> Geodetic CRS:  NAD27 #> Warning: region.id not given, c(MYID, NID) range is 1:100 #> Warning: region.id not given, c(MYID, NID) range is 1:100 #> Warning: 81 is not an origin #> Error in read.swmdbf2listw(fn, style = \"B\") :  #>   Error in sn2listw(df1, style = style, zero.policy = zero.policy) :  #>   no-neighbour observations found, set zero.policy to TRUE #>  #> Warning: region.id not given, c(MYID, NID) range is 1:100 #> Reading layer `california' from data source  #>   `/tmp/RtmpXVTJuL/temp_libpath3b356d487bad39/spdep/etc/shapes/california.gpkg.zip'  #>   using driver `GPKG' #> Simple feature collection with 58 features and 2 fields #> Geometry type: MULTIPOLYGON #> Dimension:     XY #> Bounding box:  xmin: -13847330 ymin: 3810869 xmax: -12704360 ymax: 5132708 #> Projected CRS: World_Mercator #> Warning: region.id not given, c(MYID, NID) range is 158:215 #> Warning: region.id not given, c(MYID, NID) range is 1:58 #> Warning: region.id not given, c(MYID, NID) range is 1:58 #> Warning: 21, 38 are not origins #> Error in read.swmdbf2listw(fn, style = \"B\") :  #>   Error in sn2listw(df1, style = style, zero.policy = zero.policy) :  #>   no-neighbour observations found, set zero.policy to TRUE #>  #> Warning: region.id not given, c(MYID, NID) range is 1:58 #> Warning: some observations have no neighbours #> Warning: neighbour object has 4 sub-graphs #> Warning: neighbour object has 4 sub-graphs #> Warning: region.id not given, c(MYID, NID) range is 159:214 #> Warning: neighbour object has 2 sub-graphs #> [1] FALSE"},{"path":"https://r-spatial.github.io/spdep/reference/rotation.html","id":null,"dir":"Reference","previous_headings":"","what":"Rotate a set of point by a certain angle — Rotation","title":"Rotate a set of point by a certain angle — Rotation","text":"Rotate set XY coordinates angle (radians)","code":""},{"path":"https://r-spatial.github.io/spdep/reference/rotation.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Rotate a set of point by a certain angle — Rotation","text":"","code":"Rotation(xy, angle)"},{"path":"https://r-spatial.github.io/spdep/reference/rotation.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Rotate a set of point by a certain angle — Rotation","text":"xy 2-columns matrix data frame containing set X Y coordinates. angle Numeric. scalar giving angle points rotated. angle radians.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/rotation.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Rotate a set of point by a certain angle — Rotation","text":"2-columns matrix size xy giving rotated coordinates.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/rotation.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Rotate a set of point by a certain angle — Rotation","text":"F. Guillaume Blanchet","code":""},{"path":"https://r-spatial.github.io/spdep/reference/rotation.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Rotate a set of point by a certain angle — Rotation","text":"","code":"set.seed(1) ### Create a set of coordinates coords <- cbind(runif(20), runif(20))  ### Create a series of angles rad <- seq(0, pi, l=20)  opar <- par(mfrow=c(5,4), mar=c(3,3,1,1)) for(i in rad){   coords.rot <- Rotation(coords, i)   plot(coords.rot, xlab=\"\", ylab=\"\") }  par(opar)  ### Rotate the coordinates by an angle of 90 degrees coords.90 <- Rotation(coords, 90*pi/180) coords.90 #>              [,1]       [,2] #>  [1,] -0.93470523 0.26550866 #>  [2,] -0.21214252 0.37212390 #>  [3,] -0.65167377 0.57285336 #>  [4,] -0.12555510 0.90820779 #>  [5,] -0.26722067 0.20168193 #>  [6,] -0.38611409 0.89838968 #>  [7,] -0.01339033 0.94467527 #>  [8,] -0.38238796 0.66079779 #>  [9,] -0.86969085 0.62911404 #> [10,] -0.34034900 0.06178627 #> [11,] -0.48208012 0.20597457 #> [12,] -0.59956583 0.17655675 #> [13,] -0.49354131 0.68702285 #> [14,] -0.18621760 0.38410372 #> [15,] -0.82737332 0.76984142 #> [16,] -0.66846674 0.49769924 #> [17,] -0.79423986 0.71761851 #> [18,] -0.10794363 0.99190609 #> [19,] -0.72371095 0.38003518 #> [20,] -0.41127443 0.77744522  plot(coords, xlim=range(rbind(coords.90,coords)[,1]),  ylim=range(rbind(coords.90,coords)[,2]), asp=1) points(coords.90, pch=19)"},{"path":"https://r-spatial.github.io/spdep/reference/set.mcOption.html","id":null,"dir":"Reference","previous_headings":"","what":"Options for parallel support — set.mcOption","title":"Options for parallel support — set.mcOption","text":"Provides support use parallel computation parallel package.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/set.mcOption.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Options for parallel support — set.mcOption","text":"","code":"set.mcOption(value) get.mcOption() set.coresOption(value) get.coresOption() set.ClusterOption(cl) get.ClusterOption()"},{"path":"https://r-spatial.github.io/spdep/reference/set.mcOption.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Options for parallel support — set.mcOption","text":"value valid replacement value cl cluster object created makeCluster parallel","code":""},{"path":"https://r-spatial.github.io/spdep/reference/set.mcOption.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Options for parallel support — set.mcOption","text":"Options spdep package held environment local package namespace exported. Option values set retrieved pairs access functions, get set. mc option set default FALSE Windows systems, fork R session; default TRUE systems, may set FALSE. mc FALSE, Cluster option used: mc FALSE Cluster option NULL parallel computing done, Cluster option passed “cluster” object created parallel snow package access without passed argument. cores option set NULL default, can used store number cores use integer. cores NULL, facilities parallel package used.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/set.mcOption.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Options for parallel support — set.mcOption","text":"option access functions return current settings, assignment functions usually return previous value option.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/set.mcOption.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Options for parallel support — set.mcOption","text":"extended example shown documentation aple.mc, including treatment seeding RNG multicore/cluster.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/set.mcOption.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Options for parallel support — set.mcOption","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/set.mcOption.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Options for parallel support — set.mcOption","text":"","code":"ls(envir=spdep:::.spdepOptions) #>  [1] \"cluster\"                \"cores\"                  \"listw_is_CsparseMatrix\" #>  [4] \"mc\"                     \"nb_subgraphs_N+E\"       \"report_nb_noneighs\"     #>  [7] \"report_nb_subgraphs\"    \"rlecuyerSeed\"           \"spChkID\"                #> [10] \"verbose\"                \"zeroPolicy\"             if (require(parallel, quietly=TRUE)) {  nc <- max(2L, detectCores(logical=FALSE), na.rm = TRUE)-1L  nc # set nc to 1L here  if (nc > 1L) nc <- 1L #nc <- ifelse(nc > 2L, 2L, nc)  coresOpt <- get.coresOption()  coresOpt  if (!is.na(nc)) {   invisible(set.coresOption(nc))   print(exists(\"moran.mc\"))   if(.Platform$OS.type == \"windows\") { # forking not permitted on Windows - start cluster    print(get.mcOption())    cl <- makeCluster(get.coresOption())    print(clusterEvalQ(cl, exists(\"moran.mc\")))    set.ClusterOption(cl)    clusterEvalQ(get.ClusterOption(), library(spdep))    print(clusterEvalQ(cl, exists(\"moran.mc\")))    clusterEvalQ(get.ClusterOption(), detach(package:spdep))    set.ClusterOption(NULL)    print(clusterEvalQ(cl, exists(\"moran.mc\")))    stopCluster(cl)   } else {    mcOpt <- get.mcOption()    print(mcOpt)    print(mclapply(1:get.coresOption(), function(i) exists(\"moran.mc\"),     mc.cores=get.coresOption()))    invisible(set.mcOption(FALSE))    cl <- makeCluster(nc)    print(clusterEvalQ(cl, exists(\"moran.mc\")))    set.ClusterOption(cl)    clusterEvalQ(get.ClusterOption(), library(spdep))    print(clusterEvalQ(cl, exists(\"moran.mc\")))    clusterEvalQ(get.ClusterOption(), detach(package:spdep))    set.ClusterOption(NULL)    print(clusterEvalQ(cl, exists(\"moran.mc\")))    stopCluster(cl)    invisible(set.mcOption(mcOpt))   }   invisible(set.coresOption(coresOpt))  } } #> [1] TRUE #> [1] TRUE #> [[1]] #> [1] TRUE #>  #> [[1]] #> [1] FALSE #>  #> [[1]] #> [1] TRUE #>  #> [[1]] #> [1] FALSE #>"},{"path":"https://r-spatial.github.io/spdep/reference/set.spChkOption.html","id":null,"dir":"Reference","previous_headings":"","what":"Control checking of spatial object IDs — set.spChkOption","title":"Control checking of spatial object IDs — set.spChkOption","text":"Provides support checking mutual integrity spatial neighbour weights spatial data; similar mechanisms used passing global verbose zero.policy options, causing functions creating neighbour objects warn multiple subgraphs.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/set.spChkOption.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Control checking of spatial object IDs — set.spChkOption","text":"","code":"set.spChkOption(check) get.spChkOption() chkIDs(x, listw) spNamedVec(var, data) set.VerboseOption(check) get.VerboseOption() set.ZeroPolicyOption(check) get.ZeroPolicyOption() set.SubgraphOption(check) get.SubgraphOption() set.SubgraphCeiling(value) get.SubgraphCeiling() set.NoNeighbourOption(check) get.NoNeighbourOption() set.listw_is_CsparseMatrix_Option(check) get.listw_is_CsparseMatrix_Option()"},{"path":"https://r-spatial.github.io/spdep/reference/set.spChkOption.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Control checking of spatial object IDs — set.spChkOption","text":"check logical value, TRUE FALSE value integer value, initialised 100000L, sum numbers nodes edges neighbour graph x vector length, two-dimensional array, data frame number rows neighbours list listw listw listw object nb object inheriting \"nb\" var character string integer value column selected data two-dimensional array data frame containing var","code":""},{"path":"https://r-spatial.github.io/spdep/reference/set.spChkOption.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Control checking of spatial object IDs — set.spChkOption","text":"Analysis functions spChk argument default set NULL, call get.spChkOption() get global spatial option whether check — initialised FALSE, consequently break anything. can changed TRUE using set.spChkOption(TRUE), spChk argument can assigned analysis functions. spNamedVec() provided ensure rownames passed single columns taken two-dimensional arrays data frames.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/set.spChkOption.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Control checking of spatial object IDs — set.spChkOption","text":"set.spChkOption() returns old logical value, get.spChkOption() returns current logical value, chkIDs() returns logical value test lack difference. spNamedVec() returns selected column names set row names object extracted.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/set.spChkOption.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Control checking of spatial object IDs — set.spChkOption","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/set.spChkOption.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Control checking of spatial object IDs — set.spChkOption","text":"motivation mechanism provided observation spatial objects map attribute data values need linked uniquely, avoid spurious results. reordering legacy Columbus data set used earlier publications available download Spacestat website just one example common problem.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/set.spChkOption.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Control checking of spatial object IDs — set.spChkOption","text":"","code":"data(oldcol) rownames(COL.OLD) #>  [1] \"1001\" \"1002\" \"1003\" \"1004\" \"1005\" \"1006\" \"1007\" \"1008\" \"1009\" \"1010\" #> [11] \"1011\" \"1012\" \"1013\" \"1014\" \"1015\" \"1016\" \"1017\" \"1018\" \"1019\" \"1020\" #> [21] \"1021\" \"1022\" \"1023\" \"1024\" \"1025\" \"1026\" \"1027\" \"1028\" \"1029\" \"1030\" #> [31] \"1031\" \"1032\" \"1033\" \"1034\" \"1035\" \"1036\" \"1037\" \"1038\" \"1039\" \"1040\" #> [41] \"1041\" \"1042\" \"1043\" \"1044\" \"1045\" \"1046\" \"1047\" \"1048\" \"1049\" data(columbus, package=\"spData\") rownames(columbus) #>  [1] \"1005\" \"1001\" \"1006\" \"1002\" \"1007\" \"1008\" \"1004\" \"1003\" \"1018\" \"1010\" #> [11] \"1038\" \"1037\" \"1039\" \"1040\" \"1009\" \"1036\" \"1011\" \"1042\" \"1041\" \"1017\" #> [21] \"1043\" \"1019\" \"1012\" \"1035\" \"1032\" \"1020\" \"1021\" \"1031\" \"1033\" \"1034\" #> [31] \"1045\" \"1013\" \"1022\" \"1044\" \"1023\" \"1046\" \"1030\" \"1024\" \"1047\" \"1016\" #> [41] \"1014\" \"1049\" \"1029\" \"1025\" \"1028\" \"1048\" \"1015\" \"1027\" \"1026\" get.spChkOption() #> [1] FALSE oldChk <- set.spChkOption(TRUE) get.spChkOption() #> [1] TRUE chkIDs(COL.OLD, nb2listw(COL.nb)) #> [1] TRUE chkIDs(columbus, nb2listw(col.gal.nb)) #> [1] TRUE chkIDs(columbus, nb2listw(COL.nb)) #> [1] FALSE tmp <- try(moran.test(spNamedVec(\"CRIME\", COL.OLD), nb2listw(COL.nb))) print(tmp) #>  #> \tMoran I test under randomisation #>  #> data:  spNamedVec(\"CRIME\", COL.OLD)   #> weights: nb2listw(COL.nb)     #>  #> Moran I statistic standard deviate = 5.6341, p-value = 8.797e-09 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic       Expectation          Variance  #>       0.510951264      -0.020833333       0.008908762  #>  tmp <- try(moran.test(spNamedVec(\"CRIME\", columbus), nb2listw(col.gal.nb))) print(tmp) #>  #> \tMoran I test under randomisation #>  #> data:  spNamedVec(\"CRIME\", columbus)   #> weights: nb2listw(col.gal.nb)     #>  #> Moran I statistic standard deviate = 5.3427, p-value = 4.578e-08 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic       Expectation          Variance  #>       0.485770914      -0.020833333       0.008991121  #>  tmp <- try(moran.test(spNamedVec(\"CRIME\", columbus), nb2listw(COL.nb))) #> Error in moran.test(spNamedVec(\"CRIME\", columbus), nb2listw(COL.nb)) :  #>   Check of data and weights ID integrity failed print(tmp) #> [1] \"Error in moran.test(spNamedVec(\\\"CRIME\\\", columbus), nb2listw(COL.nb)) : \\n  Check of data and weights ID integrity failed\\n\" #> attr(,\"class\") #> [1] \"try-error\" #> attr(,\"condition\") #> <simpleError in moran.test(spNamedVec(\"CRIME\", columbus), nb2listw(COL.nb)): Check of data and weights ID integrity failed> set.spChkOption(FALSE) get.spChkOption() #> [1] FALSE moran.test(spNamedVec(\"CRIME\", columbus), nb2listw(COL.nb)) #>  #> \tMoran I test under randomisation #>  #> data:  spNamedVec(\"CRIME\", columbus)   #> weights: nb2listw(COL.nb)     #>  #> Moran I statistic standard deviate = 3.8402, p-value = 6.147e-05 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic       Expectation          Variance  #>       0.341628707      -0.020833333       0.008908762  #>  tmp <- try(moran.test(spNamedVec(\"CRIME\", columbus), nb2listw(COL.nb),  spChk=TRUE), silent=TRUE) print(tmp) #> [1] \"Error in moran.test(spNamedVec(\\\"CRIME\\\", columbus), nb2listw(COL.nb), spChk = TRUE) : \\n  Check of data and weights ID integrity failed\\n\" #> attr(,\"class\") #> [1] \"try-error\" #> attr(,\"condition\") #> <simpleError in moran.test(spNamedVec(\"CRIME\", columbus), nb2listw(COL.nb), spChk = TRUE): Check of data and weights ID integrity failed> set.spChkOption(oldChk) get.spChkOption() #> [1] FALSE"},{"path":"https://r-spatial.github.io/spdep/reference/skater.html","id":null,"dir":"Reference","previous_headings":"","what":"Spatial 'K'luster Analysis by Tree Edge Removal — skater","title":"Spatial 'K'luster Analysis by Tree Edge Removal — skater","text":"function implements SKATER procedure spatial clustering   analysis. procedure essentialy begins edges set, data set   number cuts. output object 'skater' class   valid input .","code":""},{"path":"https://r-spatial.github.io/spdep/reference/skater.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Spatial 'K'luster Analysis by Tree Edge Removal — skater","text":"","code":"skater(edges, data, ncuts, crit, vec.crit, method = c(\"euclidean\",      \"maximum\", \"manhattan\", \"canberra\", \"binary\", \"minkowski\",      \"mahalanobis\"), p = 2, cov, inverted = FALSE)"},{"path":"https://r-spatial.github.io/spdep/reference/skater.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Spatial 'K'luster Analysis by Tree Edge Removal — skater","text":"edges matrix 2 colums row edge data data.frame data observed nodes. ncuts number cuts crit scalar two dimensional vector     criteria groups. Examples: limits group size     limits population size. scalar, minimum     criteria groups. vec.crit vector evaluating criteria. method Character function declare distance method.     method character, method must \"mahalanobis\"     \"euclidean\", \"maximum\", \"manhattan\", \"canberra\", \"binary\"     \"minkowisk\".     method one \"euclidean\", \"maximum\",     \"manhattan\", \"canberra\", \"binary\" \"minkowski\", see     dist details,      function used compute distance.      method=\"mahalanobis\", mahalanobis distance      computed neighbour areas.      method function, function      used compute distance. p power Minkowski distance. cov covariance matrix used compute mahalanobis    distance. inverted logical.  'TRUE', 'cov' supposed contain           inverse covariance matrix.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/skater.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Spatial 'K'luster Analysis by Tree Edge Removal — skater","text":"object skater class :  groups vector length equal number nodes.     position identifies group node edges.groups list length equal number groups     element set edges .prune vector identifying groups     candidates partition. candidates vector identifying groups candidates     partition. ssto total dissimilarity step edge removal.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/skater.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Spatial 'K'luster Analysis by Tree Edge Removal — skater","text":"Assuncao, R.M., Lage J.P., Reis, E.. (2002). Analise de   conglomerados espaciais via arvore geradora minima. Revista Brasileira   de Estatistica, 62, 1-23. Assuncao, R. M, Neves, M. C., Camara, G. Freitas, C. da   C. (2006). Efficient regionalization techniques socio-economic   geographical units using minimum spanning trees. International Journal   Geographical Information Science Vol. 20, . 7, August 2006,   797-811","code":""},{"path":"https://r-spatial.github.io/spdep/reference/skater.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Spatial 'K'luster Analysis by Tree Edge Removal — skater","text":"Renato M. Assuncao Elias T. Krainski","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/skater.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Spatial 'K'luster Analysis by Tree Edge Removal — skater","text":"","code":"### loading data (GDAL37 <- as.numeric_version(unname(sf_extSoftVersion()[\"GDAL\"])) >= \"3.7.0\") #> [1] TRUE file <- \"etc/shapes/bhicv.gpkg.zip\" zipfile <- system.file(file, package=\"spdep\") if (GDAL37) {     bh <- st_read(zipfile) } else {     td <- tempdir()     bn <- sub(\".zip\", \"\", basename(file), fixed=TRUE)     target <- unzip(zipfile, files=bn, exdir=td)     bh <- st_read(target) } #> Reading layer `bhicv' from data source  #>   `/tmp/RtmpXVTJuL/temp_libpath3b356d487bad39/spdep/etc/shapes/bhicv.gpkg.zip'  #>   using driver `GPKG' #> Simple feature collection with 98 features and 8 fields #> Geometry type: POLYGON #> Dimension:     XY #> Bounding box:  xmin: -45.02175 ymin: -20.93007 xmax: -42.50321 ymax: -18.08342 #> Geodetic CRS:  Corrego Alegre 1970-72 ### data standardized  dim(bh) #> [1] 98  9 dpad <- data.frame(scale(as.data.frame(bh)[,5:8]))  ### neighboorhod list bh.nb <- poly2nb(bh) bh.nb #> Neighbour list object: #> Number of regions: 98  #> Number of nonzero links: 508  #> Percentage nonzero weights: 5.289463  #> Average number of links: 5.183673   ### calculating costs lcosts <- nbcosts(bh.nb, dpad) head(lcosts) #> [[1]] #>  [1] 1.5418355 2.5253558 1.4738620 1.8462822 1.7089412 1.5613667 1.0279919 #>  [8] 0.6334314 1.9029531 2.5816759 #>  #> [[2]] #> [1] 1.0847913 1.7723275 0.7940341 #>  #> [[3]] #> [1] 1.257984 2.634043 0.847224 1.807124 #>  #> [[4]] #> [1] 1.2579836 1.0548805 0.7862035 #>  #> [[5]] #> [1] 1.541835 1.295112 2.206320 #>  #> [[6]] #> [1] 0.9981915 1.3801441 1.5225548 1.3606678 0.9775650 #>   ### making listw nb.w <- nb2listw(bh.nb, lcosts, style=\"B\") nb.w #> Characteristics of weights list object: #> Neighbour list object: #> Number of regions: 98  #> Number of nonzero links: 508  #> Percentage nonzero weights: 5.289463  #> Average number of links: 5.183673  #>  #> Weights style: B  #> Weights constants summary: #>    n   nn       S0       S1       S2 #> B 98 9604 1027.424 5192.868 55983.97  ### find a minimum spanning tree mst.bh <- mstree(nb.w,5) str(mst.bh) #>  'mst' num [1:97, 1:3] 5 12 13 13 11 31 39 40 31 40 ...  ### the mstree plot par(mar=c(0,0,0,0)) plot(st_geometry(bh), border=gray(.5)) pts <- st_coordinates(st_centroid(bh)) #> Warning: st_centroid assumes attributes are constant over geometries plot(mst.bh, pts, col=2,       cex.lab=.6, cex.circles=0.035, fg=\"blue\", add=TRUE)  ### three groups with no restriction res1 <- skater(mst.bh[,1:2], dpad, 2)  ### groups size table(res1$groups) #>  #>  1  2  3  #> 18 23 57   ### the skater plot opar <- par(mar=c(0,0,0,0)) plot(res1, pts, cex.circles=0.035, cex.lab=.7)   ### the skater plot, using other colors plot(res1, pts, cex.circles=0.035, cex.lab=.7,      groups.colors=heat.colors(length(res1$ed)))   ### the Spatial Polygons plot plot(st_geometry(bh), col=heat.colors(length(res1$edg))[res1$groups])   #par(opar) ### EXPERT OPTIONS  ### more one partition res1b <- skater(res1, dpad, 1)  ### length groups frequency table(res1$groups) #>  #>  1  2  3  #> 18 23 57   table(res1b$groups) #>  #>  1  2  3  4  #> 18 23 55  2   ### thee groups with minimum population  res2 <- skater(mst.bh[,1:2], dpad, 2, 200000, bh$Pop) table(res2$groups) #>  #>  1  2  3  #> 22 37 39   ### thee groups with minimun number of areas res3 <- skater(mst.bh[,1:2], dpad, 2, 3, rep(1,nrow(bh))) table(res3$groups) #>  #>  1  2  3  #> 18 23 57   ### thee groups with minimun and maximun number of areas res4 <- skater(mst.bh[,1:2], dpad, 2, c(20,50), rep(1,nrow(bh))) table(res4$groups) #>  #>  1  2  3  #> 50 24 24   ### if I want to get groups with 20 to 40 elements res5 <- skater(mst.bh[,1:2], dpad, 2,    c(20,40), rep(1,nrow(bh))) ## DON'T MAKE DIVISIONS  table(res5$groups) #>  #>  1  #> 98   ### In this MST don't have groups with this restrictions ### In this case, first I do one division ### with the minimun criteria res5a <- skater(mst.bh[,1:2], dpad, 1, 20, rep(1,nrow(bh)))  table(res5a$groups) #>  #>  1  2  #> 75 23   ### and do more one division with the full criteria res5b <- skater(res5a, dpad, 1, c(20, 40), rep(1,nrow(bh))) table(res5b$groups) #>  #>  1  2  3  #> 22 23 53   ### and do more one division with the full criteria res5c <- skater(res5b, dpad, 1, c(20, 40), rep(1,nrow(bh))) table(res5c$groups) #>  #>  1  2  3  4  #> 22 23 33 20   ### It don't have another divison with this criteria res5d <- skater(res5c, dpad, 1, c(20, 40), rep(1,nrow(bh))) table(res5d$groups) #>  #>  1  2  3  4  #> 22 23 33 20   if (FALSE) { # \\dontrun{ data(boston, package=\"spData\") bh.nb <- boston.soi dpad <- data.frame(scale(boston.c[,c(7:10)])) ### calculating costs system.time(lcosts <- nbcosts(bh.nb, dpad)) ### making listw nb.w <- nb2listw(bh.nb, lcosts, style=\"B\") ### find a minimum spanning tree mst.bh <- mstree(nb.w,5) ### three groups with no restriction system.time(res1 <- skater(mst.bh[,1:2], dpad, 2)) library(parallel) nc <- max(2L, detectCores(logical=FALSE), na.rm = TRUE)-1L # set nc to 1L here if (nc > 1L) nc <- 1L coresOpt <- get.coresOption() invisible(set.coresOption(nc)) if(!get.mcOption()) { # no-op, \"snow\" parallel calculation not available   cl <- makeCluster(get.coresOption())   set.ClusterOption(cl) } ### calculating costs system.time(plcosts <- nbcosts(bh.nb, dpad)) all.equal(lcosts, plcosts, check.attributes=FALSE) ### making listw pnb.w <- nb2listw(bh.nb, plcosts, style=\"B\") ### find a minimum spanning tree pmst.bh <- mstree(pnb.w,5) ### three groups with no restriction system.time(pres1 <- skater(pmst.bh[,1:2], dpad, 2)) if(!get.mcOption()) {   set.ClusterOption(NULL)   stopCluster(cl) } all.equal(res1, pres1, check.attributes=FALSE) invisible(set.coresOption(coresOpt)) } # }"},{"path":"https://r-spatial.github.io/spdep/reference/sp.correlogram.html","id":null,"dir":"Reference","previous_headings":"","what":"Spatial correlogram — sp.correlogram","title":"Spatial correlogram — sp.correlogram","text":"Spatial correlograms Moran's autocorrelation coefficient, print plot helper functions.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/sp.correlogram.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Spatial correlogram — sp.correlogram","text":"","code":"sp.correlogram(neighbours, var, order = 1, method = \"corr\",  style = \"W\", randomisation = TRUE, zero.policy = NULL, spChk=NULL) # S3 method for class 'spcor' plot(x, main, ylab, ylim, ...) # S3 method for class 'spcor' print(x, p.adj.method=\"none\", ...)"},{"path":"https://r-spatial.github.io/spdep/reference/sp.correlogram.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Spatial correlogram — sp.correlogram","text":"neighbours object class nb var numeric vector order maximum lag order method \"corr\" correlation, \"\" Moran's , \"C\" Geary's C style style can take values W, B, C, S randomisation variance C calculated assumption randomisation, FALSE normality zero.policy default NULL, use global option value; FALSE stop error empty neighbour sets, TRUE permit weights list formed zero-length weights vectors spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption() x object sp.correlogram() class spcor p.adj.method correction method p.adjust main overall title plot ylab title y axis ylim y limits plot ... arguments passed ","code":""},{"path":"https://r-spatial.github.io/spdep/reference/sp.correlogram.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Spatial correlogram — sp.correlogram","text":"print function also calculates standard deviates Moran's Geary's C two-sided probability value, optionally using p.adjust correct nymber lags. plot function plots bar estimated Moran's , Geary's C value +/- twice square root variance (previous releases , twice). table includes count included observations brackets lag order. Care needs shown interpreting results remaining included observations lag order increases.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/sp.correlogram.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Spatial correlogram — sp.correlogram","text":"returns list class spcor: res \"corr\" vector values; \"\", matrix estimates \"\", expectations, variances method \"\" \"corr\" cardnos list tables neighbour cardinalities lag orders used var variable name","code":""},{"path":"https://r-spatial.github.io/spdep/reference/sp.correlogram.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Spatial correlogram — sp.correlogram","text":"Cliff, . D., Ord, J. K. 1981 Spatial processes, Pion, pp. 118–122, Martin, R. L., Oeppen, J. E. 1975 identification regional forecasting models using space-time correlation functions, Transactions Institute British Geographers, 66, 95–118.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/sp.correlogram.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Spatial correlogram — sp.correlogram","text":"Roger Bivand, Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/sp.correlogram.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Spatial correlogram — sp.correlogram","text":"","code":"nc.sids <- st_read(system.file(\"shapes/sids.gpkg\", package=\"spData\")[1], quiet=TRUE) rn <- as.character(nc.sids$FIPS) ncCC89_nb <- read.gal(system.file(\"weights/ncCC89.gal\", package=\"spData\")[1],  region.id=rn) #> Warning: neighbour object has 3 sub-graphs ft.SID74 <- sqrt(1000)*(sqrt(nc.sids$SID74/nc.sids$BIR74) +   sqrt((nc.sids$SID74+1)/nc.sids$BIR74)) tr.SIDS74 <- ft.SID74*sqrt(nc.sids$BIR74) cspc <- sp.correlogram(ncCC89_nb, tr.SIDS74, order=8, method=\"corr\",  zero.policy=TRUE) #> Warning: lag 1 neighbour object has 3 sub-graphs #> Warning: lag 2 neighbour object has 3 sub-graphs #> Warning: lag 3 neighbour object has 3 sub-graphs #> Warning: lag 4 neighbour object has 3 sub-graphs #> Warning: lag 5 neighbour object has 3 sub-graphs #> Warning: lag 6 neighbour object has 3 sub-graphs #> Warning: lag 7 neighbour object has 3 sub-graphs #> Warning: lag 8 neighbour object has 3 sub-graphs print(cspc) #> Spatial correlogram for tr.SIDS74  #> method: Spatial autocorrelation #>           1           2           3           4           5           6  #>  0.38193491  0.47679881  0.11740653  0.09935901  0.27819159  0.30153012  #>           7           8  #> -0.05150923  0.05283813  plot(cspc)  Ispc <- sp.correlogram(ncCC89_nb, tr.SIDS74, order=8, method=\"I\",  zero.policy=TRUE) #> Warning: lag 1 neighbour object has 3 sub-graphs #> Warning: lag 2 neighbour object has 3 sub-graphs #> Warning: lag 3 neighbour object has 3 sub-graphs #> Warning: lag 4 neighbour object has 3 sub-graphs #> Warning: lag 5 neighbour object has 3 sub-graphs #> Warning: lag 6 neighbour object has 3 sub-graphs #> Warning: lag 7 neighbour object has 3 sub-graphs #> Warning: lag 8 neighbour object has 3 sub-graphs print(Ispc) #> Spatial correlogram for tr.SIDS74  #> method: Moran's I #>          estimate expectation   variance standard deviate Pr(I) two sided     #> 1 (98)  0.2311685  -0.0103093  0.0055378           3.2450       0.0011747 **  #> 2 (98)  0.2246930  -0.0103093  0.0037817           3.8214       0.0001327 *** #> 3 (98)  0.0193576  -0.0103093  0.0029386           0.5473       0.5841914     #> 4 (98)  0.0042255  -0.0103093  0.0024974           0.2908       0.7711687     #> 5 (98)  0.0875548  -0.0103093  0.0022875           2.0462       0.0407386 *   #> 6 (98)  0.0758362  -0.0103093  0.0021583           1.8543       0.0637011 .   #> 7 (98) -0.0752243  -0.0103093  0.0022282          -1.3752       0.1690654     #> 8 (98) -0.0261063  -0.0103093  0.0025211          -0.3146       0.7530514     #> --- #> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 print(Ispc, \"bonferroni\") #> Spatial correlogram for tr.SIDS74  #> method: Moran's I #>          estimate expectation   variance standard deviate Pr(I) two sided    #> 1 (98)  0.2311685  -0.0103093  0.0055378           3.2450        0.009397 ** #> 2 (98)  0.2246930  -0.0103093  0.0037817           3.8214        0.001061 ** #> 3 (98)  0.0193576  -0.0103093  0.0029386           0.5473        1.000000    #> 4 (98)  0.0042255  -0.0103093  0.0024974           0.2908        1.000000    #> 5 (98)  0.0875548  -0.0103093  0.0022875           2.0462        0.325909    #> 6 (98)  0.0758362  -0.0103093  0.0021583           1.8543        0.509609    #> 7 (98) -0.0752243  -0.0103093  0.0022282          -1.3752        1.000000    #> 8 (98) -0.0261063  -0.0103093  0.0025211          -0.3146        1.000000    #> --- #> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 plot(Ispc)  Cspc <- sp.correlogram(ncCC89_nb, tr.SIDS74, order=8, method=\"C\",  zero.policy=TRUE) #> Warning: lag 1 neighbour object has 3 sub-graphs #> Warning: lag 2 neighbour object has 3 sub-graphs #> Warning: lag 3 neighbour object has 3 sub-graphs #> Warning: lag 4 neighbour object has 3 sub-graphs #> Warning: lag 5 neighbour object has 3 sub-graphs #> Warning: lag 6 neighbour object has 3 sub-graphs #> Warning: lag 7 neighbour object has 3 sub-graphs #> Warning: lag 8 neighbour object has 3 sub-graphs print(Cspc) #> Spatial correlogram for tr.SIDS74  #> method: Geary's C #>         estimate expectation  variance standard deviate Pr(I) two sided     #> 1 (98) 0.7172624   1.0000000 0.0059986          -3.6506       0.0002617 *** #> 2 (98) 0.6817819   1.0000000 0.0046785          -4.6523       3.282e-06 *** #> 3 (98) 0.9470179   1.0000000 0.0044311          -0.7959       0.4260762     #> 4 (98) 1.0016202   1.0000000 0.0041985           0.0250       0.9800516     #> 5 (98) 0.8977501   1.0000000 0.0038054          -1.6575       0.0974119 .   #> 6 (98) 0.9173310   1.0000000 0.0036428          -1.3697       0.1707819     #> 7 (98) 1.0527148   1.0000000 0.0037227           0.8640       0.3875979     #> 8 (98) 1.0067939   1.0000000 0.0036482           0.1125       0.9104415     #> --- #> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 print(Cspc, \"bonferroni\") #> Spatial correlogram for tr.SIDS74  #> method: Geary's C #>         estimate expectation  variance standard deviate Pr(I) two sided     #> 1 (98) 0.7172624   1.0000000 0.0059986          -3.6506        0.002093 **  #> 2 (98) 0.6817819   1.0000000 0.0046785          -4.6523       2.626e-05 *** #> 3 (98) 0.9470179   1.0000000 0.0044311          -0.7959        1.000000     #> 4 (98) 1.0016202   1.0000000 0.0041985           0.0250        1.000000     #> 5 (98) 0.8977501   1.0000000 0.0038054          -1.6575        0.779295     #> 6 (98) 0.9173310   1.0000000 0.0036428          -1.3697        1.000000     #> 7 (98) 1.0527148   1.0000000 0.0037227           0.8640        1.000000     #> 8 (98) 1.0067939   1.0000000 0.0036482           0.1125        1.000000     #> --- #> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 plot(Cspc)  drop.no.neighs <- !(1:length(ncCC89_nb) %in% which(card(ncCC89_nb) == 0)) sub.ncCC89.nb <- subset(ncCC89_nb, drop.no.neighs) plot(sp.correlogram(sub.ncCC89.nb, subset(tr.SIDS74,  drop.no.neighs),  order=8, method=\"corr\"))"},{"path":"https://r-spatial.github.io/spdep/reference/sp.mantel.mc.html","id":null,"dir":"Reference","previous_headings":"","what":"Mantel-Hubert spatial general cross product statistic — sp.mantel.mc","title":"Mantel-Hubert spatial general cross product statistic — sp.mantel.mc","text":"permutation test spatial general cross product statistic Moran (\\(C_{ij} = z_i z_j\\)), Geary (\\(C_{ij} = (z_i - z_j)^2\\)), Sokal (\\(C_{ij} = |z_i - z_j|\\)) criteria, \\(z_i = (x_i - \\bar{x}) / \\sigma_{x}\\). plot.mc.sim helper function plot outcomes permutation test.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/sp.mantel.mc.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Mantel-Hubert spatial general cross product statistic — sp.mantel.mc","text":"","code":"sp.mantel.mc(var, listw, nsim, type = \"moran\", zero.policy = attr(listw, \"zero.policy\"),  alternative = \"greater\", spChk=NULL, return_boot=FALSE) # S3 method for class 'mc.sim' plot(x, xlim, xlab, main, sub, ..., ptype=\"density\")"},{"path":"https://r-spatial.github.io/spdep/reference/sp.mantel.mc.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Mantel-Hubert spatial general cross product statistic — sp.mantel.mc","text":"var numeric vector length neighbours list listw listw listw object created example nb2listw nsim number permutations type \"moran\", \"geary\" \"sokal\" criteria similarity zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without   neighbours, FALSE assign NA alternative character string specifying alternative hypothesis,   must one \"greater\" (default), \"two.sided\", \"less\". spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption() return_boot return object class boot equivalent permutation bootstrap rather object class htest x object plotted xlim range x axis xlab title x axis main overall title plot sub sub title plot ptype either \"density\" \"hist\" ... arguments passed ","code":""},{"path":"https://r-spatial.github.io/spdep/reference/sp.mantel.mc.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Mantel-Hubert spatial general cross product statistic — sp.mantel.mc","text":"list class htest mc.sim containing following components: statistic value observed Geary's C. parameter rank observed Geary's C. alternative character string describing alternative hypothesis. method character string giving method used. data.name character string giving name(s) data,   number simulations. p.value pseudo p-value test. res nsim simulated values statistic, final value observed   statistic estimate mean variance simulated distribution.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/sp.mantel.mc.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Mantel-Hubert spatial general cross product statistic — sp.mantel.mc","text":"Cliff, . D., Ord, J. K. 1981 Spatial processes, Pion, p. 22-24, Haining, R. 1990 Spatial data analysis social environmental sciences, Cambridge: Cambridge University Press, p. 230–1. function checked general matrix code posted r-help list Ben Bolker 1 May 2001; another mantel() function vegan package.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/sp.mantel.mc.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Mantel-Hubert spatial general cross product statistic — sp.mantel.mc","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/sp.mantel.mc.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Mantel-Hubert spatial general cross product statistic — sp.mantel.mc","text":"","code":"data(oldcol) sim1 <- sp.mantel.mc(COL.OLD$CRIME, nb2listw(COL.nb),  nsim=99, type=\"geary\", alternative=\"two.sided\") sim1 #>  #> \tMantel permutation test for geary measure #>  #> data:  COL.OLD$CRIME  #> weights: nb2listw(COL.nb)  #> number of simulations + 1: 100  #>  #> statistic = 51.927, observed rank = 1, p-value = 0.02 #> alternative hypothesis: two.sided #> sample estimates: #> mean of permutations   sd of permutations  #>            98.852997             8.934135  #>  plot(sim1)  sp.mantel.mc(COL.OLD$CRIME, nb2listw(COL.nb), nsim=99,  type=\"sokal\", alternative=\"two.sided\") #>  #> \tMantel permutation test for sokal measure #>  #> data:  COL.OLD$CRIME  #> weights: nb2listw(COL.nb)  #> number of simulations + 1: 100  #>  #> statistic = 36.695, observed rank = 1, p-value = 0.02 #> alternative hypothesis: two.sided #> sample estimates: #> mean of permutations   sd of permutations  #>            56.418584             3.227064  #>  sp.mantel.mc(COL.OLD$CRIME, nb2listw(COL.nb), nsim=99,  type=\"moran\") #>  #> \tMantel permutation test for moran measure #>  #> data:  COL.OLD$CRIME  #> weights: nb2listw(COL.nb)  #> number of simulations + 1: 100  #>  #> statistic = 24.526, observed rank = 100, p-value = 0.01 #> alternative hypothesis: greater #> sample estimates: #> mean of permutations   sd of permutations  #>           -0.3401381            4.5579226  #>"},{"path":"https://r-spatial.github.io/spdep/reference/spdep-defunct.html","id":null,"dir":"Reference","previous_headings":"","what":"Defunct Functions in Package spdep — spdep-defunct","title":"Defunct Functions in Package spdep — spdep-defunct","text":"functions defunct release 1.2-1.   functions moved spatialreg package.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/spdep-defunct.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Defunct Functions in Package spdep — spdep-defunct","text":"","code":"aple.plot() localAple() aple.mc() aple() lextrB() lextrW() lextrS() griffith_sone() subgraph_eigenw() mom_calc() mom_calc_int2() stsls() # S3 method for class 'stsls' impacts() GMerrorsar() # S3 method for class 'gmsar' summary() gstsls()  # S3 method for class 'gmsar' impacts() # S3 method for class 'gmsar' Hausman.test() lagmess() ME() SpatialFiltering() LR.sarlm() # S3 method for class 'sarlm' logLik() LR1.sarlm() Wald1.sarlm() # S3 method for class 'sarlm' Hausman.test() as.spam.listw() as_dgRMatrix_listw() as_dsTMatrix_listw() as_dsCMatrix_I() as_dsCMatrix_IrW() Jacobian_W() powerWeights() # S3 method for class 'lagImpact' plot() # S3 method for class 'lagImpact' print() # S3 method for class 'lagImpact' summary() # S3 method for class 'lagImpact' HPDinterval() intImpacts() can.be.simmed() eigenw() similar.listw() do_ldet() jacobianSetup() cheb_setup() mcdet_setup() eigen_setup() eigen_pre_setup() spam_setup() spam_update_setup() Matrix_setup() Matrix_J_setup() LU_setup() LU_prepermutate_setup() moments_setup() SE_classic_setup() SE_whichMin_setup() SE_interp_setup() MCMCsamp() # S3 method for class 'spautolm' MCMCsamp() # S3 method for class 'sarlm' MCMCsamp() spautolm() # S3 method for class 'spautolm' summary() spBreg_sac() # S3 method for class 'MCMC_sar_g' impacts() # S3 method for class 'MCMC_sem_g' impacts() # S3 method for class 'MCMC_sac_g' impacts() spBreg_err() spBreg_lag() # S3 method for class 'SLX' predict() lmSLX() # S3 method for class 'SLX' impacts() create_WX() # S3 method for class 'sarlm' anova() bptest.sarlm() errorsarlm() # S3 method for class 'sarlm' impacts() lagsarlm() # S3 method for class 'sarlm' predict() # S3 method for class 'sarlm.pred' print() # S3 method for class 'sarlm.pred' as.data.frame() # S3 method for class 'sarlm' residuals() # S3 method for class 'sarlm' deviance() # S3 method for class 'sarlm' coef() # S3 method for class 'sarlm' vcov() # S3 method for class 'sarlm' fitted() sacsarlm() # S3 method for class 'sarlm' summary() # S3 method for class 'sarlm' print() # S3 method for class 'summary.sarlm' print() trW()"},{"path":"https://r-spatial.github.io/spdep/reference/spdep-defunct.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Defunct Functions in Package spdep — spdep-defunct","text":"Model-fitting functions functions supporting model fitting moved spatialreg package.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/spdep.html","id":null,"dir":"Reference","previous_headings":"","what":"Return package version number — spdep","title":"Return package version number — spdep","text":"function retreives package version build information","code":""},{"path":"https://r-spatial.github.io/spdep/reference/spdep.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Return package version number — spdep","text":"","code":"spdep(build = FALSE)"},{"path":"https://r-spatial.github.io/spdep/reference/spdep.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Return package version number — spdep","text":"build TRUE, also returns build information","code":""},{"path":"https://r-spatial.github.io/spdep/reference/spdep.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Return package version number — spdep","text":"character vector one two elements","code":""},{"path":"https://r-spatial.github.io/spdep/reference/spdep.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Return package version number — spdep","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/spweights.constants.html","id":null,"dir":"Reference","previous_headings":"","what":"Provides constants for spatial weights matrices — spweights.constants","title":"Provides constants for spatial weights matrices — spweights.constants","text":"function calculates constants needed tests spatial autocorrelation general weights matrices represented listw objects. Note: spdep 0.3-32, values S1 S2 returned correctly underlying symmetric asymmetric neighbour lists, 0.3-32, S1 S2 wrong listw objects based asymmetric neighbour lists, k-nearest neighbours (thanks Luc Anselin finding bug).","code":""},{"path":"https://r-spatial.github.io/spdep/reference/spweights.constants.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Provides constants for spatial weights matrices — spweights.constants","text":"","code":"spweights.constants(listw, zero.policy=attr(listw, \"zero.policy\"), adjust.n=TRUE) Szero(listw)"},{"path":"https://r-spatial.github.io/spdep/reference/spweights.constants.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Provides constants for spatial weights matrices — spweights.constants","text":"listw listw object example nb2listw zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE ignore zones without neighbours, FALSE fail encountered adjust.n default TRUE, FALSE number observations adjusted -neighbour observations, TRUE, number observations adjusted","code":""},{"path":"https://r-spatial.github.io/spdep/reference/spweights.constants.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Provides constants for spatial weights matrices — spweights.constants","text":"n number zones n1 n - 1 n2 n - 2 n3 n - 3 nn n * n S0 global sum weights S1 S1 sum weights S2 S2 sum weights","code":""},{"path":"https://r-spatial.github.io/spdep/reference/spweights.constants.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Provides constants for spatial weights matrices — spweights.constants","text":"Haining, R. 1990 Spatial data analysis social environmental sciences, Cambridge University Press, p. 233; Cliff, . D., Ord, J. K. 1981 Spatial processes, Pion, p. 19, 21.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/spweights.constants.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Provides constants for spatial weights matrices — spweights.constants","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/spweights.constants.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Provides constants for spatial weights matrices — spweights.constants","text":"","code":"data(oldcol) B <- spweights.constants(nb2listw(COL.nb, style=\"B\")) W <- spweights.constants(nb2listw(COL.nb, style=\"W\")) C <- spweights.constants(nb2listw(COL.nb, style=\"C\")) S <- spweights.constants(nb2listw(COL.nb, style=\"S\")) U <- spweights.constants(nb2listw(COL.nb, style=\"U\")) print(data.frame(rbind(unlist(B), unlist(W), unlist(C), unlist(S), unlist(U)),   row.names=c(\"B\", \"W\", \"C\", \"S\", \"U\"))) #>    n n1 n2 n3   nn  S0           S1           S2 #> B 49 48 47 46 2401 232 464.00000000 5.136000e+03 #> W 49 48 47 46 2401  49  23.29434146 2.048729e+02 #> C 49 48 47 46 2401  49  20.69827586 2.291085e+02 #> S 49 48 47 46 2401  49  21.25561347 2.134568e+02 #> U 49 48 47 46 2401   1   0.00862069 9.542212e-02"},{"path":"https://r-spatial.github.io/spdep/reference/ssw.html","id":null,"dir":"Reference","previous_headings":"","what":"Compute the sum of dissimilarity — ssw","title":"Compute the sum of dissimilarity — ssw","text":"function computes sum dissimilarity   observation mean (scalar vector) observations.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/ssw.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Compute the sum of dissimilarity — ssw","text":"","code":"ssw(data, id, method = c(\"euclidean\", \"maximum\",      \"manhattan\", \"canberra\", \"binary\", \"minkowski\",     \"mahalanobis\"), p = 2, cov, inverted = FALSE)"},{"path":"https://r-spatial.github.io/spdep/reference/ssw.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Compute the sum of dissimilarity — ssw","text":"data matrix observations nodes. id Node index compute cost method Character function declare distance method.     method character, method must \"mahalanobis\"     \"euclidean\", \"maximum\", \"manhattan\", \"canberra\", \"binary\"     \"minkowisk\".     method one \"euclidean\", \"maximum\",     \"manhattan\", \"canberra\", \"binary\" \"minkowisk\", see     dist details,      function used compute distance.      method=\"mahalanobis\", mahalanobis distance      computed neighbour areas.      method function, function      used compute distance. p power Minkowski distance. cov covariance matrix used compute mahalanobis    distance. inverted logical.  'TRUE', 'cov' supposed contain           inverse covariance matrix.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/ssw.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Compute the sum of dissimilarity — ssw","text":"numeric, sum dissimilarity observations   id data mean (scalar vector)   observations.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/ssw.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Compute the sum of dissimilarity — ssw","text":"Elias T. Krainski Renato M. Assuncao","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/ssw.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Compute the sum of dissimilarity — ssw","text":"","code":"data(USArrests) n <- nrow(USArrests) ssw(USArrests, 1:n) #> [1] 3701.394 ssw(USArrests, 1:(n/2)) #> [1] 1910.214 ssw(USArrests, (n/2+1):n) #> [1] 1625.882 ssw(USArrests, 1:(n/2)) + ssw(USArrests, (n/2+1):n) #> [1] 3536.096"},{"path":"https://r-spatial.github.io/spdep/reference/subset.listw.html","id":null,"dir":"Reference","previous_headings":"","what":"Subset a spatial weights list — subset.listw","title":"Subset a spatial weights list — subset.listw","text":"function subsets spatial weights list, retaining objects subset argument vector TRUE. present subset non-general weights lists (created nb2listw glist=NULL).","code":""},{"path":"https://r-spatial.github.io/spdep/reference/subset.listw.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Subset a spatial weights list — subset.listw","text":"","code":"# S3 method for class 'listw' subset(x, subset, zero.policy = attr(x, \"zero.policy\"), ...)"},{"path":"https://r-spatial.github.io/spdep/reference/subset.listw.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Subset a spatial weights list — subset.listw","text":"x object class listw subset logical expression zero.policy default attr(x, \"zero.policy\") set x created, attribute set, use global option value; FALSE stop error empty neighbour sets, TRUE permit weights list formed zero-length weights vectors - passed nb2listw ... generic function pass-","code":""},{"path":"https://r-spatial.github.io/spdep/reference/subset.listw.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Subset a spatial weights list — subset.listw","text":"function returns object class listw component style input object, component neighbours list integer vectors containing neighbour region number ids (compacted run 1:number regions subset), component weights weights computed neighbours using style. -neighbour observations created subsetting zero.policy input weights object FALSE, set TRUE warning issued.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/subset.listw.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Subset a spatial weights list — subset.listw","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/subset.listw.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Subset a spatial weights list — subset.listw","text":"","code":"col.gal.nb <- read.gal(system.file(\"weights/columbus.gal\", package=\"spData\")[1]) to.be.dropped <- c(31, 34, 36, 39, 42, 46) pre <- nb2listw(col.gal.nb) print(pre) #> Characteristics of weights list object: #> Neighbour list object: #> Number of regions: 49  #> Number of nonzero links: 230  #> Percentage nonzero weights: 9.579342  #> Average number of links: 4.693878  #>  #> Weights style: W  #> Weights constants summary: #>    n   nn S0       S1       S2 #> W 49 2401 49 23.48489 204.6687 post <- subset(pre, !(1:length(col.gal.nb) %in% to.be.dropped)) print(post) #> Characteristics of weights list object: #> Neighbour list object: #> Number of regions: 43  #> Number of nonzero links: 212  #> Percentage nonzero weights: 11.46566  #> Average number of links: 4.930233  #>  #> Weights style: W  #> Weights constants summary: #>    n   nn S0       S1       S2 #> W 43 1849 43 19.26584 178.4604 columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) nb <- poly2nb(columbus) lw <- nb2listw(nb, style=\"W\") attr(lw, \"zero.policy\") #> [1] FALSE (lwa <- subset(lw, 1:nrow(columbus) != c(21))) #> Warning: subsetting caused increase in subgraph count #> Characteristics of weights list object: #> Neighbour list object: #> Number of regions: 48  #> Number of nonzero links: 230  #> Percentage nonzero weights: 9.982639  #> Average number of links: 4.791667  #> 2 disjoint connected subgraphs #>  #> Weights style: W  #> Weights constants summary: #>    n   nn S0       S1       S2 #> W 48 2304 48 22.46811 199.4398 attr(lwa, \"zero.policy\") #> [1] FALSE (lwb <- subset(lw, !(1:nrow(columbus) %in% c(21, 36, 39)))) #> Warning: subsetting caused increase in subgraph count #> Warning: subsetting created no-neighbour observations, zero.policy set TRUE #> Characteristics of weights list object: #> Neighbour list object: #> Number of regions: 46  #> Number of nonzero links: 216  #> Percentage nonzero weights: 10.20794  #> Average number of links: 4.695652  #> 1 region with no links: #> 46 #> 3 disjoint connected subgraphs #>  #> Weights style: W  #> Weights constants summary: #>    n   nn S0     S1       S2 #> W 45 2025 45 22.857 187.4843 attr(lwb, \"zero.policy\") #> [1] TRUE"},{"path":"https://r-spatial.github.io/spdep/reference/subset.nb.html","id":null,"dir":"Reference","previous_headings":"","what":"Subset a neighbours list — subset.nb","title":"Subset a neighbours list — subset.nb","text":"function subsets neighbors list, retaining objects subset argument vector TRUE.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/subset.nb.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Subset a neighbours list — subset.nb","text":"","code":"# S3 method for class 'nb' subset(x, subset, ...)"},{"path":"https://r-spatial.github.io/spdep/reference/subset.nb.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Subset a neighbours list — subset.nb","text":"x object class nb subset logical expression ... generic function pass-","code":""},{"path":"https://r-spatial.github.io/spdep/reference/subset.nb.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Subset a neighbours list — subset.nb","text":"function returns object class nb list    integer vectors containing neighbour region number ids (compacted    run 1:number regions subset).","code":""},{"path":"https://r-spatial.github.io/spdep/reference/subset.nb.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Subset a neighbours list — subset.nb","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/subset.nb.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Subset a neighbours list — subset.nb","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) col.gal.nb <- read.gal(system.file(\"weights/columbus.gal\", package=\"spData\")[1]) coords <- st_coordinates(st_centroid(columbus)) #> Warning: st_centroid assumes attributes are constant over geometries plot(col.gal.nb, coords) to.be.dropped <- c(31, 34, 36, 39, 42, 46) text(coords[to.be.dropped,1], coords[to.be.dropped,2], labels=to.be.dropped,   pos=2, offset=0.3) sub.col.gal.nb <- subset(col.gal.nb,   !(1:length(col.gal.nb) %in% to.be.dropped)) plot(sub.col.gal.nb, coords[-to.be.dropped,], col=\"red\", add=TRUE)  which(!(attr(col.gal.nb, \"region.id\") %in%   attr(sub.col.gal.nb, \"region.id\"))) #> [1] 31 34 36 39 42 46"},{"path":"https://r-spatial.github.io/spdep/reference/summary.nb.html","id":null,"dir":"Reference","previous_headings":"","what":"Print and summary function for neighbours and weights lists — summary.nb","title":"Print and summary function for neighbours and weights lists — summary.nb","text":"function prints summary measures links neighbours list. matrix coordinates given well, summary descriptive measures link lengths also printed. Print summary functions also available \"listw\" weights list objects, also reporting constants (S0, S1, S2) used inference global spatial autocorrelation statistics Moran's , Geary's C, join-count tests Getis-Ord G.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/summary.nb.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Print and summary function for neighbours and weights lists — summary.nb","text":"","code":"# S3 method for class 'nb' summary(object, coords=NULL, longlat = NULL, scale = 1, ...) # S3 method for class 'nb' print(x, ...) # S3 method for class 'listw' summary(object, coords, longlat, zero.policy = attr(object, \"zero.policy\"),   scale = 1, adjust.n=TRUE, ...) # S3 method for class 'listw' print(x, zero.policy = attr(x, \"zero.policy\"), ...)"},{"path":"https://r-spatial.github.io/spdep/reference/summary.nb.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Print and summary function for neighbours and weights lists — summary.nb","text":"object object class nb coords matrix region point coordinates SpatialPoints object sfc points object longlat TRUE point coordinates longitude-latitude decimal degrees, case distances measured kilometers; coords SpatialPoints object, value taken object ... additional arguments affecting output produced x object class nb zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; FALSE stop error empty neighbour sets scale passed stem() control plot length adjust.n default TRUE, FALSE number observations adjusted -neighbour observations, TRUE, number observations spweights.constants adjusted","code":""},{"path":"https://r-spatial.github.io/spdep/reference/summary.nb.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Print and summary function for neighbours and weights lists — summary.nb","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/summary.nb.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Print and summary function for neighbours and weights lists — summary.nb","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) col.gal.nb <- read.gal(system.file(\"weights/columbus.gal\", package=\"spData\")[1]) coords <- st_centroid(st_geometry(columbus), of_largest_polygon=TRUE) col.gal.nb #> Neighbour list object: #> Number of regions: 49  #> Number of nonzero links: 230  #> Percentage nonzero weights: 9.579342  #> Average number of links: 4.693878  summary(col.gal.nb, coords) #> Neighbour list object: #> Number of regions: 49  #> Number of nonzero links: 230  #> Percentage nonzero weights: 9.579342  #> Average number of links: 4.693878  #> Link number distribution: #>  #>  2  3  4  5  6  7  8  9 10  #>  7  7 13  4  9  6  1  1  1  #> 7 least connected regions: #> 1 6 31 39 42 46 47 with 2 links #> 1 most connected region: #> 20 with 10 links col.listw <- nb2listw(col.gal.nb, style=\"W\") col.listw #> Characteristics of weights list object: #> Neighbour list object: #> Number of regions: 49  #> Number of nonzero links: 230  #> Percentage nonzero weights: 9.579342  #> Average number of links: 4.693878  #>  #> Weights style: W  #> Weights constants summary: #>    n   nn S0       S1       S2 #> W 49 2401 49 23.48489 204.6687 summary(col.listw) #> Characteristics of weights list object: #> Neighbour list object: #> Number of regions: 49  #> Number of nonzero links: 230  #> Percentage nonzero weights: 9.579342  #> Average number of links: 4.693878  #> Link number distribution: #>  #>  2  3  4  5  6  7  8  9 10  #>  7  7 13  4  9  6  1  1  1  #> 7 least connected regions: #> 1 6 31 39 42 46 47 with 2 links #> 1 most connected region: #> 20 with 10 links #>  #> Weights style: W  #> Weights constants summary: #>    n   nn S0       S1       S2 #> W 49 2401 49 23.48489 204.6687 col_geoms <- st_geometry(columbus) col_geoms[21] <- st_buffer(col_geoms[21], dist=-0.05) st_geometry(columbus) <- col_geoms nb <- poly2nb(columbus) #> Warning: some observations have no neighbours; #> if this seems unexpected, try increasing the snap argument. #> Warning: neighbour object has 3 sub-graphs; #> if this sub-graph count seems unexpected, try increasing the snap argument. summary(nb) #> Neighbour list object: #> Number of regions: 49  #> Number of nonzero links: 230  #> Percentage nonzero weights: 9.579342  #> Average number of links: 4.693878  #> 1 region with no links: #> 21 #> 3 disjoint connected subgraphs #> Link number distribution: #>  #>  0  2  3  4  5  6  7  8  9 10  #>  1  5  9 12  4 10  2  4  1  1  #> 5 least connected regions: #> 1 6 42 46 47 with 2 links #> 1 most connected region: #> 20 with 10 links try(nb2listw(nb, style=\"W\")) #> Error in nb2listw(nb, style = \"W\") :  #>   Empty neighbour sets found (zero.policy: FALSE) summary(nb2listw(nb, style=\"W\", zero.policy=TRUE)) #> Characteristics of weights list object: #> Neighbour list object: #> Number of regions: 49  #> Number of nonzero links: 230  #> Percentage nonzero weights: 9.579342  #> Average number of links: 4.693878  #> 1 region with no links: #> 21 #> 3 disjoint connected subgraphs #> Link number distribution: #>  #>  0  2  3  4  5  6  7  8  9 10  #>  1  5  9 12  4 10  2  4  1  1  #> 5 least connected regions: #> 1 6 42 46 47 with 2 links #> 1 most connected region: #> 20 with 10 links #>  #> Weights style: W  #> Weights constants summary: #>    n   nn S0       S1       S2 #> W 48 2304 48 22.46811 199.4398 summary(nb2listw(nb, style=\"W\", zero.policy=TRUE), adjust.n=FALSE) #> Characteristics of weights list object: #> Neighbour list object: #> Number of regions: 49  #> Number of nonzero links: 230  #> Percentage nonzero weights: 9.579342  #> Average number of links: 4.693878  #> 1 region with no links: #> 21 #> 3 disjoint connected subgraphs #> Link number distribution: #>  #>  0  2  3  4  5  6  7  8  9 10  #>  1  5  9 12  4 10  2  4  1  1  #> 5 least connected regions: #> 1 6 42 46 47 with 2 links #> 1 most connected region: #> 20 with 10 links #>  #> Weights style: W  #> Weights constants summary: #>    n   nn S0       S1       S2 #> W 49 2401 48 22.46811 199.4398"},{"path":"https://r-spatial.github.io/spdep/reference/testnb.html","id":null,"dir":"Reference","previous_headings":"","what":"Test a neighbours list for symmetry — is.symmetric.nb","title":"Test a neighbours list for symmetry — is.symmetric.nb","text":"Checks neighbours list symmetry/transitivity (neighbour j, j neighbour ). holds distance contiguity based neighbours, k-nearest neighbours. helper function sym.attr.nb() calls .symmetric.nb() set sym attribute needed, make.sym.nb makes non-symmetric list symmetric adding neighbors. .symmetric.glist checks list general weights corresponding neighbours symmetry symmetric neighbours.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/testnb.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Test a neighbours list for symmetry — is.symmetric.nb","text":"","code":"is.symmetric.nb(nb, verbose = NULL, force = FALSE) sym.attr.nb(nb) make.sym.nb(nb) old.make.sym.nb(nb) is.symmetric.glist(nb, glist)"},{"path":"https://r-spatial.github.io/spdep/reference/testnb.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Test a neighbours list for symmetry — is.symmetric.nb","text":"nb object class nb list integer vectors containing neighbour region number ids. verbose default NULL, use global option value; TRUE prints non-matching pairs force respect neighbours list sym attribute test anyway glist list general weights corresponding neighbours","code":""},{"path":"https://r-spatial.github.io/spdep/reference/testnb.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Test a neighbours list for symmetry — is.symmetric.nb","text":"TRUE symmetric, FALSE ; .symmetric.glist returns value attribute, \"d\", indicating failed symmetry largest failing value.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/testnb.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Test a neighbours list for symmetry — is.symmetric.nb","text":"new version make.sym.nb Bjarke Christensen now included. older version renamed old.make.sym.nb, comparison constitutes nice demonstration vectorising speedup using sapply lapply rather loops. -neighbour observations present, old.make.sym.nb used.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/testnb.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Test a neighbours list for symmetry — is.symmetric.nb","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/testnb.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Test a neighbours list for symmetry — is.symmetric.nb","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) col.gal.nb <- read.gal(system.file(\"weights/columbus.gal\", package=\"spData\")[1]) coords <- st_coordinates(st_centroid(columbus)) #> Warning: st_centroid assumes attributes are constant over geometries ind <- row.names(as(columbus, \"Spatial\")) print(is.symmetric.nb(col.gal.nb, verbose=TRUE, force=TRUE)) #> [1] TRUE k4 <- knn2nb(knearneigh(coords, k=4), row.names=ind) k4 <- sym.attr.nb(k4) print(is.symmetric.nb(k4)) #> [1] FALSE k4.sym <- make.sym.nb(k4) print(is.symmetric.nb(k4.sym)) #> [1] TRUE"},{"path":"https://r-spatial.github.io/spdep/reference/tolerance.nb.html","id":null,"dir":"Reference","previous_headings":"","what":"Function to construct edges based on a tolerance angle and a maximum distance — tolerance.nb","title":"Function to construct edges based on a tolerance angle and a maximum distance — tolerance.nb","text":"function creates object class nb (defined library spdep) containing connexion diagram. edges sites based tolerance angle maximum distance. angle directional; direction always bottow top screen.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/tolerance.nb.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Function to construct edges based on a tolerance angle and a maximum distance — tolerance.nb","text":"","code":"tolerance.nb(coords, unit.angle = \"degrees\", max.dist, tolerance, rot.angle,  plot.sites=FALSE)"},{"path":"https://r-spatial.github.io/spdep/reference/tolerance.nb.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Function to construct edges based on a tolerance angle and a maximum distance — tolerance.nb","text":"coords matrix data frame containing X Y coordinates study sites. unit.angle Character. measurement units angles defined: either \"degrees\" (default) \"radians\". max.dist Numeric. maximum distance edge linking two sites together. tolerance Numeric. tolerance angle site can influence another site. angle measured vertically bottom top pictures rotation points. rot.angle Numeric, optional. angle set coordinates rotated creating connexion diagram. set coordinates rotated counterclockwise. Negative values produce clockwise rotation. plot.sites Logical (TRUE, FALSE) determining site plotted graphic window. graph allows one make sure points rotated correct direction.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/tolerance.nb.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Function to construct edges based on a tolerance angle and a maximum distance — tolerance.nb","text":"Even though function creates connexion diagram based tolerance angle going bottom top screen, resulting object symmetric, meaning site influences another vice versa. final object represent directional connexion network.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/tolerance.nb.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Function to construct edges based on a tolerance angle and a maximum distance — tolerance.nb","text":"function returns object class nb list integer vectors  corresponding neighbour region numbers.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/tolerance.nb.html","id":"warning","dir":"Reference","previous_headings":"","what":"Warning","title":"Function to construct edges based on a tolerance angle and a maximum distance — tolerance.nb","text":"function design handle large number rows coords. use function set coordinates 1500 entries memory intensive.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/tolerance.nb.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Function to construct edges based on a tolerance angle and a maximum distance — tolerance.nb","text":"F. Guillaume Blanchet","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/tolerance.nb.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Function to construct edges based on a tolerance angle and a maximum distance — tolerance.nb","text":"","code":"set.seed(1) ex.data<-cbind(runif(50),rexp(50))  ### Construct object of class nb with a tolerance angle of 30 degrees ### and a maximum distance of 2 m. nb.ex<-tolerance.nb(ex.data, unit.angle = \"degrees\", max.dist=1,  tolerance = 30) #> Warning: neighbour object has 3 sub-graphs  ### Construct object of class nb with a tolerance angle of 30 degrees ### and a maximum distance of 2 m. The coordinates are rotated at an angle ### of 45 degrees counterclockwise. nb.ex2<-tolerance.nb(ex.data, unit.angle = \"degrees\", max.dist=1,  tolerance = 30, rot.angle = 45) #> Warning: neighbour object has 4 sub-graphs  ### Construct object of class nb with a tolerance angle of pi/8 radians ### and a maximum distance of 1.5 m. The coordinates are rotated at ### an angle of pi/4 radians clockwise. nb.ex3<-tolerance.nb(ex.data, unit.angle = \"radians\", max.dist=1.5,  tolerance = pi/8, rot.angle = -pi*2/3) #> Warning: neighbour object has 5 sub-graphs  par(mfrow=c(1,3)) plot(nb.ex,ex.data,asp=1) plot(nb.ex2,ex.data,asp=1) plot(nb.ex3,ex.data,asp=1)"},{"path":"https://r-spatial.github.io/spdep/reference/tri2nb.html","id":null,"dir":"Reference","previous_headings":"","what":"Neighbours list from tri object — tri2nb","title":"Neighbours list from tri object — tri2nb","text":"function uses deldir package convert matrix two-dimensional coordinates neighbours list class nb list integer vectors containing neighbour region number ids.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/tri2nb.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Neighbours list from tri object — tri2nb","text":"","code":"tri2nb(coords, row.names = NULL)"},{"path":"https://r-spatial.github.io/spdep/reference/tri2nb.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Neighbours list from tri object — tri2nb","text":"coords matrix, data.frame tibble point coordinates two columns, SpatialPoints object sfc points object row.names character vector region ids added neighbours list attribute region.id, default seq(1, nrow(x))","code":""},{"path":"https://r-spatial.github.io/spdep/reference/tri2nb.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Neighbours list from tri object — tri2nb","text":"coordinates duplicated, function used. coordinates grid, need ordered first three collinear, first triangle can constructed. can achieved randomising order coordinates (possibly several times), re-ordering order data match new order neighbour list - fix used, remember re-order row.names argument well coordinates! Please also note triangulation grid points give arbitrary diagonal neighbours, may sensible outcome, dnearneigh() may serve better tri2nb() used.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/tri2nb.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Neighbours list from tri object — tri2nb","text":"function returns object class nb list integer vectors containing neighbour region number ids.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/tri2nb.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Neighbours list from tri object — tri2nb","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/tri2nb.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Neighbours list from tri object — tri2nb","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) coords <- st_centroid(st_geometry(columbus), of_largest_polygon=TRUE) ind <- row.names(columbus) suppressPackageStartupMessages(require(deldir)) col.tri.nb <- tri2nb(coords, row.names=ind) plot(st_geometry(columbus), border=\"grey\") plot(col.tri.nb, coords, add=TRUE) title(main=\"Raw triangulation links\", cex.main=0.6)  x <- seq(0,1,0.1) y <- seq(0,2,0.2) xy <- expand.grid(x, y) try(xy.nb <- tri2nb(xy)) seed <- 1234 xid <- sample(1:nrow(xy)) xy.nb <- tri2nb(xy[xid,]) plot(xy.nb, xy[xid,])  # example of reading points with readr::read_csv() yielding a tibble load(system.file(\"etc/misc/coords.rda\", package=\"spdep\")) class(coords) #> [1] \"spec_tbl_df\" \"tbl_df\"      \"tbl\"         \"data.frame\"  nb <- tri2nb(coords) plot(nb, coords)"},{"path":"https://r-spatial.github.io/spdep/reference/write.nb.gal.html","id":null,"dir":"Reference","previous_headings":"","what":"Write a neighbours list as a GAL lattice file — write.nb.gal","title":"Write a neighbours list as a GAL lattice file — write.nb.gal","text":"Write neighbours list GAL lattice file, may also use newer GeoDa header format","code":""},{"path":"https://r-spatial.github.io/spdep/reference/write.nb.gal.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Write a neighbours list as a GAL lattice file — write.nb.gal","text":"","code":"write.nb.gal(nb, file, oldstyle=TRUE, shpfile=NULL, ind=NULL)"},{"path":"https://r-spatial.github.io/spdep/reference/write.nb.gal.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Write a neighbours list as a GAL lattice file — write.nb.gal","text":"nb object class nb list integer vectors containing neighbour region number ids. file name file GAL lattice data oldstyle TRUE, first line file contains number spatial units, FALSE, uses newer GeoDa style shpfile Shapefile name taken GAL file dataset ind region id indicator variable name","code":""},{"path":"https://r-spatial.github.io/spdep/reference/write.nb.gal.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Write a neighbours list as a GAL lattice file — write.nb.gal","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/write.nb.gal.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Write a neighbours list as a GAL lattice file — write.nb.gal","text":"","code":"col.gal.nb <- read.gal(system.file(\"weights/columbus.gal\", package=\"spData\")[1]) GALfile <- tempfile(\"GAL\") write.nb.gal(col.gal.nb, GALfile) col.queen <- read.gal(GALfile) summary(diffnb(col.queen, col.gal.nb)) #> Warning: neighbour object has 49 sub-graphs #> Neighbour list object: #> Number of regions: 49  #> Number of nonzero links: 0  #> Percentage nonzero weights: 0  #> Average number of links: 0  #> 49 regions with no links: #> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, #> 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, #> 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49 #> 49 disjoint connected subgraphs #> Link number distribution: #>  #>  0  #> 49"},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-13-8-development","dir":"Changelog","previous_headings":"","what":"Version 1.3-8 (development)","title":"Version 1.3-8 (development)","text":"Remove remaining spData ESRI shapefile use","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-13-7-2024-11-25","dir":"Changelog","previous_headings":"","what":"Version 1.3-7 (2024-11-25)","title":"Version 1.3-7 (2024-11-25)","text":"CRAN release: 2024-11-25 (temporarily) remove rgeoda references successfully re-submitted CRAN add write.swmdbf #171 complement #163 modify defaults licd_multi","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-13-6-2024-09-13","dir":"Changelog","previous_headings":"","what":"Version 1.3-6 (2024-09-13)","title":"Version 1.3-6 (2024-09-13)","text":"CRAN release: 2024-09-13 adding vignette describing recent changes poly2nb #162, subgraph -neighbour (island) handling adding prototype LICD ESDA function licd_multi hotspot method add read.swmdbf2listw #163 reading DBF files exported ArcGIS representing SWM objects; note problems observation IDs known, see help file #162 add option -neighbour checking poly2nb - default report whether -neighbour observations present #162 change default snap= argument poly2nb 10mm Condition forthcoming tmap 4 #160 handle n.comp.nb delay print.nb elsewhere total number neighbours large","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-13-5-2024-06-10","dir":"Changelog","previous_headings":"","what":"Version 1.3-5 (2024-06-10)","title":"Version 1.3-5 (2024-06-10)","text":"CRAN release: 2024-06-10 #157 migrate ESRI Shapefile GPKG files; convert bhicv.shp GPKG #155 Throw error hotspot despatched object without \"quadr\" attribute #154 turn s2 vignette","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-13-4-2024-05-31","dir":"Changelog","previous_headings":"","what":"Version 1.3-4 (2024-05-31)","title":"Version 1.3-4 (2024-05-31)","text":"CRAN release: 2024-05-31 add scale argument geary.test, geary.mc geary #151, appropriate tests Introduce error knearneigh k less largest count identical points; encountered, increase k remove spurious warning knearneigh longlat geometries fix https://github.com/edzer/sdsr/issues/121, wrong assignment old test names lmRStests fix #144 plot.nb nb2lines","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-13-3-2024-02-07","dir":"Changelog","previous_headings":"","what":"Version 1.3-3 (2024-02-07)","title":"Version 1.3-3 (2024-02-07)","text":"CRAN release: 2024-02-07 change lm.LMtests lm.RStests re-name Lagrange multiplier Rao’s score; add GNM_ prefix test names input object inherits SlX created spatialreg::lmSLX (Koley, forthcoming) add SD.RStests implementation Rao’s score tests spatial Durbin models (Koley Bera, 2024) SDEM models (Koley, forthcoming) #143 row.names pass-poly2nb corrected, harmonised row.names pass-also nbdists dnearneigh #139 add na.action argument geary.test, geary.mc globalG.test add style sn2listw use tri2nb","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-13-1-2023-11-23","dir":"Changelog","previous_headings":"","what":"Version 1.3-1 (2023-11-23)","title":"Version 1.3-1 (2023-11-23)","text":"CRAN release: 2023-11-23 functions creating nb objects now warn object sub-graph count > 1 get.SubgraphOption TRUE (default FALSE): complement.nb, diffnb, dnearneigh, droplinks, edit.nb, graph2nb, knn2nb, nb2blocknb, nblag, nblag_cumul, poly2nb, read.gal, read.gwt2nb, setdiff.nb, tolerance.nb, tri2nb, union.nb summary.nb, print.nb, summary.listw print.listw now report subgraph count n.comp.nb one subset.nb now reports subgraph count neighbour object increases subsetting adding zero.policy attribute functions creating listw objects: nb2listw, sn2listw, mat2listw, nb2listwdist. Default zero.policy= argument updated use attr(., \"zero.policy\") summary.listw, print.listw, moran, moran.test, moran.mc, moran.plot, geary.mc, geary, geary.test, globalG.test, joincount.test, joincount.mc, joincount.multi, localC, localC_perm, localmoran, localmoran_perm, localG, localG_perm, lee, lee.test, lee.mc, lm.morantest, lm.LMtests, sp.mantel.mc, listw2star, lag.listw, lm.morantest, lm.LMtests, subset.listw, EBImoran.mc, LOSH, LOSH.mc, LOSH.cs, lm.morantest.exactand lm.morantest.sad confusing error message moran.plot() -neighbour cases, zero.policy=FALSE replace rgrass7 rgrass vignette fix #133 (edit.nb affected attaching sp)","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-12-8-2023-02-28","dir":"Changelog","previous_headings":"","what":"Version 1.2-8 (2023-02-28)","title":"Version 1.2-8 (2023-02-28)","text":"CRAN release: 2023-02-28 mat2listw() warning style= argument given, M\" given https://github.com/r-spatial/spatialreg/issues/24, https://github.com/r-spatial/spatialreg/issues/23. remaining users run_perm() - localC(), localmoran_bv() local_joincount_uni() get no_repeat_in_row= arguments. Address 2) #124; localG_perm() localmoran_perm() get no_repeat_in_row= arguments use conditional permutation without replacement sample vectors; default implementation uses sampling replacement, acceptable across simulation draws, arguably less acceptable within draws. Feedback valued. Address 1) #124; localG_perm() localG() now return analytical standard deviates. standard deviates simulated distributions now returned attr(., \"internals\")[,\"StdDev.Gi\"] localG_perm(), p-values, etc. move sp Depends Imports, reduce visual impression sp objects required spdep; sf objects now preferred, sp objects can used , although users may need attach sp expliciitly. fix #121 #123; correcting returned values localG_perm() estimating G-star measure (fix self x values weights) address #120, moving documentation listw2U() ?lm.morantest ?nb2listw addressing #119 interpretation moran_bv() results adding #116, René Westerholt fix #113, low R version grDevices::hcl.colors() addressing #111 Josiah Parry PRs René Westerholt, ending #109, local GS measure","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-12-7-2022-10-01","dir":"Changelog","previous_headings":"","what":"Version 1.2-7 (2022-10-01)","title":"Version 1.2-7 (2022-10-01)","text":"CRAN release: 2022-10-01 #103 refactoring local joincount test Josiah Parry add hotspot methods localmoran (analytical, permutation, Saddlepoint exact), localC (univariate multivariate) localG (analytical permutation) #95 add \"two.sided\" lee.mc(), sp.mantel.mc(), EBImoran.mc(), joincount.mc(), geary.mc() #92, #93, #94, #96, #97 contributions prototype bivariate Moran, local bivariate Moran local joincount bivariate joincount tests Josiah Parry #91 tolerance.nb() update F. Guillaume Blanchet updating coercion Matrix 1.4-2 fix ncpus issue dontrun examples remove suggested packages rgdal, rgeos, maptools","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-12-5-2022-08-11","dir":"Changelog","previous_headings":"","what":"Version 1.2-5 (2022-08-11)","title":"Version 1.2-5 (2022-08-11)","text":"CRAN release: 2022-08-11 permit use data.frame tibble matrix functions creating neighbour objects 2D points (preferred use object inheriting `\"SpatialPoints\" \"sfc\") fix #87 wrong logic infinite weights nb2listwdist() https://github.com/r-spatial/s2/pull/174 speeds dnearneigh() geographical coordinates without using s2::s2_closest_edges(). Adapting vignettes absence rgdal maptools","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-12-4-2022-04-18","dir":"Changelog","previous_headings":"","what":"Version 1.2-4 (2022-04-18)","title":"Version 1.2-4 (2022-04-18)","text":"CRAN release: 2022-04-18 added remove.self(), thanks Josiah Parry #83. unescape underscores help pages.","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-12-3-2022-03-29","dir":"Changelog","previous_headings":"","what":"Version 1.2-3 (2022-03-29)","title":"Version 1.2-3 (2022-03-29)","text":"CRAN release: 2022-03-29 replace deprecated S-compatibility macros DOUBLE_ #81 improved dnearneigh() help page. #79 remove \"htest\" class LOSH.mc() output object. Added GA SI article citations.","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-12-2-2022-01-28","dir":"Changelog","previous_headings":"","what":"Version 1.2-2 (2022-01-28)","title":"Version 1.2-2 (2022-01-28)","text":"CRAN release: 2022-01-28 Replace rainbow() hcl.colors(..., \"Set 2\") plot.skater(). Add link R-sig-geo thread EBlocal() NaN estimates many counts zero help page. Revise add documentation object returned localC_perm() #68 #72 #73 #74 #75 #76 localmoran.sad(), localmoran.exact() localmoran.exact.alt() now use multiple compute nodes needed; Omega used, multiple cores may need memory #77 s2 > 1.0.7, use indexed distances dnearneigh() https://github.com/r-spatial/s2/pull/162.","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-12-1-2022-01-05","dir":"Changelog","previous_headings":"","what":"Version 1.2-1 (2022-01-05)","title":"Version 1.2-1 (2022-01-05)","text":"CRAN release: 2022-01-04 Switching deprecated functions moved spatialreg defunct.","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-11-13-2021-12-14","dir":"Changelog","previous_headings":"","what":"Version 1.1-13 (2021-12-14)","title":"Version 1.1-13 (2021-12-14)","text":"CRAN release: 2021-12-14 Recent changes poly2nb() reduced recently (1.1-8) removed use snap= finding candidate neighbours; many thanks Matilda Brown clear well-documented issue #65 Add local Geary’s C #66 thanks Josiah Parry, discussion work #68 localmoran_perm() returns look-folded rank p-values","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-11-12-2021-11-09","dir":"Changelog","previous_headings":"","what":"Version 1.1-12 (2021-11-09)","title":"Version 1.1-12 (2021-11-09)","text":"CRAN release: 2021-11-09 poly2nb(), reverted removal legacy interpreted overlapping envelope code sp objects coerced sf without rgeos. Add Fortran character handling USE_FC_LEN_T WRE §6.6.1. Checks OK forthcoming deldir 1.0-0. Fixes #62 clarifying dnearneigh() help page","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-11-11-2021-09-07","dir":"Changelog","previous_headings":"","what":"Version 1.1-11 (2021-09-07)","title":"Version 1.1-11 (2021-09-07)","text":"CRAN release: 2021-09-07 knearneigh() nbdists(); added prototype adaptation s2 unprojected coordinates, used sf_use_s2() TRUE became default sf 1.0.0 https://github.com/r-spatial/s2/issues/125. activated default. dnearneigh() can choose prototype s2 approach sf_use_s2() TRUE use_s2=TRUE unprojected coordinates; https://github.com/r-spatial/s2/issues/125 seems distance thresholds present use brute-force rather spatial indexing. Use activated default. poly2nb() now uses sf::st_intersects() find candidate neighbours unless findInBounds= NULL. spatial indexing, fast scales well large data sets. sf_use_s2() TRUE, sf::st_intersects() passes geometries s2::s2_intersects_matrix(), also uses spatial indexing fast, scaling well large data sets. localmoran() localmoran_perm() return cluster quadrants attribute three splits, zeros, means medians variable interest spatial lag. localmoran_perm() returns skewness kurtosis permutation samples.","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-11-8-2021-05-23","dir":"Changelog","previous_headings":"","what":"Version 1.1-8 (2021-05-23)","title":"Version 1.1-8 (2021-05-23)","text":"CRAN release: 2021-05-23 #55 related #20 cycling order setting grids provoked re-design interface cell2nb(), passing \"GridTopology\" \"SpatialGrid\" objects unnamed first x= argument. Coerce \"RasterLayer\" similar raster, terra stars objects sp class objects first need . working renewing arguments cell2nb(), useful add tinytest support, now present function may extended functions creating \"nb\" objects. #58 contributed Jeff Sauer Levi Wolf (https://doi.org/10.31219/osf.io/ugkhp) providing conditional standard deviates local Moran’s Error assignment matrix detected CRAN check SIDS vignette, section median polish","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-11-7-2021-04-03","dir":"Changelog","previous_headings":"","what":"Version 1.1-7 (2021-04-03)","title":"Version 1.1-7 (2021-04-03)","text":"CRAN release: 2021-04-03 Changes continuous integration vignettes. Error poly2nb(, queen=FALSE) sf grids (double counting closed polygon start/end points), https://github.com/r-spatial/spdep/issues/50, thanks Christopher Kenny. Adding local Moran local G conditional permutation: localmoran_perm() localG_perm(). Adding nb2listwdist() contributed René Westerholt. Adding use sf GEOS find polygon contiguity candidates poly2nb() geometry count >= 500 - uses intersections polygon envelopes. #38, #53 removing RANN, adding dbscan suggestions fast dnearneigh() knearneigh() via use_kd_tree= argument fast planar neighbour set finding 2D 3D. Affects soi.graph() , used RANN. #54 avoid partial matching glist= handling. Disambiguating spdep spatialreg model output object class names prior making spdep model fitting functions defunct.","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-11-5-2020-06-29","dir":"Changelog","previous_headings":"","what":"Version 1.1-5 (2020-06-29)","title":"Version 1.1-5 (2020-06-29)","text":"CRAN release: 2020-06-29 Replacing broken geoda URLs, moving knitr rmarkdown, work-around missing weights files spData.","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-11-3-2019-09-18","dir":"Changelog","previous_headings":"","what":"Version 1.1-3 (2019-09-18)","title":"Version 1.1-3 (2019-09-18)","text":"CRAN release: 2019-09-18 small maintenance update accommodate forthcoming change spData (dataset used example spdep spData changing name; name involved putting “x”, “y” “xyz” global environment lazy loading dataset).","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-11-2-2019-04-05","dir":"Changelog","previous_headings":"","what":"Version 1.1-2 (2019-04-05)","title":"Version 1.1-2 (2019-04-05)","text":"CRAN release: 2019-04-05 Follow-version spdep functions methods transferred spatialreg package marked deprecated, still exported spdep. Reverse dependencies passing released version still pass version.","code":""}]