Inference of Polygenic Risk Scores from Biobank Data.ipynb

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    "<h1 align=\"center\">Tokyo Symposium on Genomic Medicine (2024)</h1>\n",
    "<h2 align=\"center\">Workshop: Inference of Polygenic Risk Scores from Biobank Data</h2>\n",
    "<h2 align=\"center\">April 13th, 2024</h2>\n",
    "<br>\n",
    "<h2 align=\"center\">Shadi Zabad</h2>\n",
    "<h3 align=\"center\">McGill University, Montreal, Canada</h3>\n",
    "\n",
    "Quick links:\n",
    "\n",
    "* [Shadi Zabad GitHub Page](https://github.com/shz9/viprs)\n",
    "* [Yue Li Lab website](https://www.cs.mcgill.ca/~yueli/) | [Simon Gravel Lab website](https://gravellab.github.io/)\n",
    "\n",
    "* [`viprs` package](https://shz9.github.io/viprs/) | [`magenpy` package](https://shz9.github.io/magenpy/)\n",
    "* [VIPRS AJHG Manuscript](https://doi.org/10.1016/j.ajhg.2023.03.009)"
   ]
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   "source": [
    "### Environment setup / Required packages"
   ]
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   "source": [
    "This tutorial requires:\n",
    "    \n",
    "* `python>=3.8`\n",
    "* Jupyter notebook.\n",
    "\n",
    "#### Install required packages"
   ]
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   "source": [
    "!pip install --user viprs magenpy>=0.1.1 matplotlib scikit-learn"
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    "**Note**: If you encounter issues installing `viprs` or `magenpy` in your environment, please follow the installation guide on the [documentation website](https://shz9.github.io/viprs/installation/#installation). In particular, it may be helpful to setup the environment with `conda` before proceeding with the installation.\n",
    "\n",
    "#### Import main packages"
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   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import magenpy as mgp\n",
    "import viprs as vp\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Silence warnings:\n",
    "import warnings\n",
    "warnings.filterwarnings(\"ignore\")"
   ]
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   "source": [
    "# Introduction"
   ]
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    "In Statistical Genetics, Polygenic Risk Scores (PRS) are a **predictive tool**: \n",
    "They allow us to assess someone's **lifetime risk of disease based on their DNA sequence alone**. This, of course, \n",
    "hinges on us knowing which genetic variants are associated with a given disease, and which alleles are *risk-increasing* in the population. This is why discussions of PRS and PRS methods are often tied to the main powerhouse of modern medical genetics: **Genome-wide Association Studies (GWASs)**. GWASs are a powerful methodology for detecting statistical associations between genetic variants and disease in a given study cohort. With increasing sample sizes and improved statistical methodologies in recent GWAS analyses, interest in using their insights for developing more accurate polygenic scores has become an important priority.\n",
    "\n",
    "<img src=\"./figures/prs_intro.png\" alt=\"drawing\" width=\"500\"/>"
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   "source": [
    "### What are Polygenic Scores useful for?\n",
    "\n",
    "Among the many promising applications of polygenic risk scores in genomic medicine, the following areas have received the most attention:\n",
    "\n",
    "<img src=\"./figures/prs_applications.png\" alt=\"drawing\" width=\"1000\"/>"
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   "source": [
    "## Outline / Table of Contents\n",
    "\n",
    "This hands-on tutorial will explain how we can go about inferring polygenic scores from biobank data. \n",
    "Specifically, we will discuss the following important concepts and considerations that are important to understand \n",
    "polygenic score and the methods used to infer them:\n",
    "\n",
    "- [(0) The Data: The data needed for Inference of Polygenic Scores.](#(0)-The-Data:-The-data-needed-for-Inference-of-Polygenic-Scores.)\n",
    "    - [(0.1) Genotype data]((0.1)-Genotype-data)\n",
    "    - [(0.2) Phenotype data](#(0.2)-Phenotype-data)\n",
    "- [(1) Modeling the relationship between Genotypes and Complex Traits](#(1)-Modeling-the-Relationship-between-Genotypes-and-Complex-Traits)\n",
    "    - [(1.1) The Linear Model](#(1.1)-The-Linear-Model)\n",
    "    - [(1.2) The effect sizes $\\beta$](#(1.2)-The-effect-sizes-$\\beta$)\n",
    "    - [(1.3) Assumptions about the distribution of effect sizes](#(1.3)-Assumptions-about-the-distribution-of-effect-sizes)\n",
    "    - [(1.4) Heritability](#(1.4)-Heritability)\n",
    "- [(2) Simulating Complex Traits using `magenpy`](#(2)-Simulating-Complex-Traits-using-magenpy)\n",
    "- [(3) Inference of Polygenic Risk Scores (PRS) from Individual-level Data](#(3)-Inference-of-Polygenic-Risk-Scores-(PRS)-from-Individual-level-Data)\n",
    "    - [(3.1) Multiple Linear Regression](#(3.1)-Multiple-Linear-Regression)\n",
    "    - [(3.2) Regularized Linear Regression](#(3.2)-Regularized-Linear-Regression)\n",
    "- [(4) Inference of Polygenic Risk Scores (PRS) from GWAS Summary Statistics](#(4)-Inference-of-Polygenic-Risk-Scores-(PRS)-from-GWAS-Summary-Statistics)\n",
    "    - [(4.1) Naive PRS](#(4.1)-Naive-PRS)\n",
    "    - [(4.2) Clumping + Thresholding (C+T)](#(4.2)-Clumping-+-Thresholding-(C+T))\n",
    "    - [(4.3) Bayesian PRS (`VIPRS`)](#(4.3)-Bayesian-PRS-(VIPRS))\n",
    "- [(5) PRS Evaluation Strategies / Metrics](#(5)-PRS-Evaluation-Strategies-/-Metrics)\n",
    "- [(6) Inference of Polygenic Risk Scores (PRS) from Publicly Available GWAS Summary Statistics](#(6)-Inference-of-Polygenic-Risk-Scores-(PRS)-from-Publicly-Available-GWAS-Summary-Statistics)\n"
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   "source": [
    "## (0) The Data: The data needed for Inference of Polygenic Scores."
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    "Recall that polygenic scores are a predictive tool: They map from the space of DNA (i.e. genetic variants) to \n",
    "to the space of phenotypes (e.g. disease status or continuous phenotype, such as height). \n",
    "\n",
    "Therefore, in order for us to infer polygenic scores and learn this mapping, we need access to **matched genotype \n",
    "and phenotype data** from the same set of individuals.\n",
    "\n",
    "<img src=\"./figures/genetic_data.png\" alt=\"drawing\" width=\"600\"/>\n",
    "\n",
    "\n",
    "### (0.1) Genotype data\n",
    "\n",
    "Learning polygenic scores requires precisely defining the input data used to generate the prediction. Similar to \n",
    "GWAS settings, **the input for each individual is the number of non-reference alleles (i.e. mutations) at a particular position in the genome**. Which allele is considered reference here is arbitrary, though typically in many applications the more common allele in the population is taken as reference.\n",
    "\n",
    "For our purposes here, we will mainly focus on **Single Nucleotide Polymorphisms (SNPs)**, that, as the name suggests, record differences in a single DNA nucleotide between individuals in the population. Furthermore, we will consider only **bi-allelic variants**: i.e. only 2 alleles, such as A and G, are present in the population. \n",
    "\n",
    "#### Example Genotype Data from 1000G Project\n",
    "\n",
    "To make things concrete, let's look at some real genotype data from the 1000G Project. The package `magenpy`, which we installed / imported at the beginning of this tutorial, is shipped with genotype data for about ~15,000 SNPs and 378 individuals of European ancestry.\n",
    "\n",
    "We will load the genotype data from disk using the `xarray` backend and inspect its characteristics:"
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       ".xr-var-attrs,\n",
       ".xr-var-data,\n",
       ".xr-index-data {\n",
       "  grid-column: 1 / -1;\n",
       "}\n",
       "\n",
       "dl.xr-attrs {\n",
       "  padding: 0;\n",
       "  margin: 0;\n",
       "  display: grid;\n",
       "  grid-template-columns: 125px auto;\n",
       "}\n",
       "\n",
       ".xr-attrs dt,\n",
       ".xr-attrs dd {\n",
       "  padding: 0;\n",
       "  margin: 0;\n",
       "  float: left;\n",
       "  padding-right: 10px;\n",
       "  width: auto;\n",
       "}\n",
       "\n",
       ".xr-attrs dt {\n",
       "  font-weight: normal;\n",
       "  grid-column: 1;\n",
       "}\n",
       "\n",
       ".xr-attrs dt:hover span {\n",
       "  display: inline-block;\n",
       "  background: var(--xr-background-color);\n",
       "  padding-right: 10px;\n",
       "}\n",
       "\n",
       ".xr-attrs dd {\n",
       "  grid-column: 2;\n",
       "  white-space: pre-wrap;\n",
       "  word-break: break-all;\n",
       "}\n",
       "\n",
       ".xr-icon-database,\n",
       ".xr-icon-file-text2,\n",
       ".xr-no-icon {\n",
       "  display: inline-block;\n",
       "  vertical-align: middle;\n",
       "  width: 1em;\n",
       "  height: 1.5em !important;\n",
       "  stroke-width: 0;\n",
       "  stroke: currentColor;\n",
       "  fill: currentColor;\n",
       "}\n",
       "</style><pre class='xr-text-repr-fallback'>&lt;xarray.DataArray &#x27;genotype&#x27; (sample: 378, variant: 15938)&gt;\n",
       "dask.array&lt;transpose, shape=(378, 15938), dtype=float32, chunksize=(378, 1024), chunktype=numpy.ndarray&gt;\n",
       "Coordinates: (12/14)\n",
       "  * sample   (sample) object &#x27;HG00096&#x27; &#x27;HG00097&#x27; ... &#x27;NA20826&#x27; &#x27;NA20828&#x27;\n",
       "  * variant  (variant) &lt;U12 &#x27;variant0&#x27; &#x27;variant1&#x27; ... &#x27;variant15937&#x27;\n",
       "    fid      (sample) object &#x27;HG00096&#x27; &#x27;HG00097&#x27; ... &#x27;NA20826&#x27; &#x27;NA20828&#x27;\n",
       "    iid      (sample) object &#x27;HG00096&#x27; &#x27;HG00097&#x27; ... &#x27;NA20826&#x27; &#x27;NA20828&#x27;\n",
       "    father   (sample) object &#x27;0&#x27; &#x27;0&#x27; &#x27;0&#x27; &#x27;0&#x27; &#x27;0&#x27; &#x27;0&#x27; ... &#x27;0&#x27; &#x27;0&#x27; &#x27;0&#x27; &#x27;0&#x27; &#x27;0&#x27; &#x27;0&#x27;\n",
       "    mother   (sample) object &#x27;0&#x27; &#x27;0&#x27; &#x27;0&#x27; &#x27;0&#x27; &#x27;0&#x27; &#x27;0&#x27; ... &#x27;0&#x27; &#x27;0&#x27; &#x27;0&#x27; &#x27;0&#x27; &#x27;0&#x27; &#x27;0&#x27;\n",
       "    ...       ...\n",
       "    chrom    (variant) object &#x27;22&#x27; &#x27;22&#x27; &#x27;22&#x27; &#x27;22&#x27; &#x27;22&#x27; ... &#x27;22&#x27; &#x27;22&#x27; &#x27;22&#x27; &#x27;22&#x27;\n",
       "    snp      (variant) object &#x27;rs131538&#x27; &#x27;rs9605903&#x27; ... &#x27;rs28729663&#x27;\n",
       "    cm       (variant) float64 2.236 2.336 2.34 2.344 ... 75.08 75.09 75.12\n",
       "    pos      (variant) int32 16871137 17054720 17057138 ... 51178090 51219006\n",
       "    a0       (variant) object &#x27;A&#x27; &#x27;C&#x27; &#x27;G&#x27; &#x27;T&#x27; &#x27;A&#x27; &#x27;C&#x27; ... &#x27;A&#x27; &#x27;A&#x27; &#x27;G&#x27; &#x27;A&#x27; &#x27;A&#x27;\n",
       "    a1       (variant) object &#x27;G&#x27; &#x27;T&#x27; &#x27;T&#x27; &#x27;C&#x27; &#x27;T&#x27; &#x27;T&#x27; ... &#x27;G&#x27; &#x27;G&#x27; &#x27;A&#x27; &#x27;G&#x27; &#x27;G&#x27;</pre><div class='xr-wrap' style='display:none'><div class='xr-header'><div class='xr-obj-type'>xarray.DataArray</div><div class='xr-array-name'>'genotype'</div><ul class='xr-dim-list'><li><span class='xr-has-index'>sample</span>: 378</li><li><span class='xr-has-index'>variant</span>: 15938</li></ul></div><ul class='xr-sections'><li class='xr-section-item'><div class='xr-array-wrap'><input id='section-3a7952a9-6bbe-4c21-9aa6-dcd50179af9d' class='xr-array-in' type='checkbox' checked><label for='section-3a7952a9-6bbe-4c21-9aa6-dcd50179af9d' title='Show/hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-array-preview xr-preview'><span>dask.array&lt;chunksize=(378, 1024), meta=np.ndarray&gt;</span></div><div class='xr-array-data'><table>\n",
       "    <tr>\n",
       "        <td>\n",
       "            <table style=\"border-collapse: collapse;\">\n",
       "                <thead>\n",
       "                    <tr>\n",
       "                        <td> </td>\n",
       "                        <th> Array </th>\n",
       "                        <th> Chunk </th>\n",
       "                    </tr>\n",
       "                </thead>\n",
       "                <tbody>\n",
       "                    \n",
       "                    <tr>\n",
       "                        <th> Bytes </th>\n",
       "                        <td> 22.98 MiB </td>\n",
       "                        <td> 1.48 MiB </td>\n",
       "                    </tr>\n",
       "                    \n",
       "                    <tr>\n",
       "                        <th> Shape </th>\n",
       "                        <td> (378, 15938) </td>\n",
       "                        <td> (378, 1024) </td>\n",
       "                    </tr>\n",
       "                    <tr>\n",
       "                        <th> Dask graph </th>\n",
       "                        <td colspan=\"2\"> 16 chunks in 34 graph layers </td>\n",
       "                    </tr>\n",
       "                    <tr>\n",
       "                        <th> Data type </th>\n",
       "                        <td colspan=\"2\"> float32 numpy.ndarray </td>\n",
       "                    </tr>\n",
       "                </tbody>\n",
       "            </table>\n",
       "        </td>\n",
       "        <td>\n",
       "        <svg width=\"170\" height=\"80\" style=\"stroke:rgb(0,0,0);stroke-width:1\" >\n",
       "\n",
       "  <!-- Horizontal lines -->\n",
       "  <line x1=\"0\" y1=\"0\" x2=\"120\" y2=\"0\" style=\"stroke-width:2\" />\n",
       "  <line x1=\"0\" y1=\"30\" x2=\"120\" y2=\"30\" style=\"stroke-width:2\" />\n",
       "\n",
       "  <!-- Vertical lines -->\n",
       "  <line x1=\"0\" y1=\"0\" x2=\"0\" y2=\"30\" style=\"stroke-width:2\" />\n",
       "  <line x1=\"7\" y1=\"0\" x2=\"7\" y2=\"30\" />\n",
       "  <line x1=\"15\" y1=\"0\" x2=\"15\" y2=\"30\" />\n",
       "  <line x1=\"23\" y1=\"0\" x2=\"23\" y2=\"30\" />\n",
       "  <line x1=\"30\" y1=\"0\" x2=\"30\" y2=\"30\" />\n",
       "  <line x1=\"38\" y1=\"0\" x2=\"38\" y2=\"30\" />\n",
       "  <line x1=\"46\" y1=\"0\" x2=\"46\" y2=\"30\" />\n",
       "  <line x1=\"53\" y1=\"0\" x2=\"53\" y2=\"30\" />\n",
       "  <line x1=\"61\" y1=\"0\" x2=\"61\" y2=\"30\" />\n",
       "  <line x1=\"69\" y1=\"0\" x2=\"69\" y2=\"30\" />\n",
       "  <line x1=\"77\" y1=\"0\" x2=\"77\" y2=\"30\" />\n",
       "  <line x1=\"84\" y1=\"0\" x2=\"84\" y2=\"30\" />\n",
       "  <line x1=\"92\" y1=\"0\" x2=\"92\" y2=\"30\" />\n",
       "  <line x1=\"100\" y1=\"0\" x2=\"100\" y2=\"30\" />\n",
       "  <line x1=\"107\" y1=\"0\" x2=\"107\" y2=\"30\" />\n",
       "  <line x1=\"115\" y1=\"0\" x2=\"115\" y2=\"30\" />\n",
       "  <line x1=\"120\" y1=\"0\" x2=\"120\" y2=\"30\" style=\"stroke-width:2\" />\n",
       "\n",
       "  <!-- Colored Rectangle -->\n",
       "  <polygon points=\"0.0,0.0 120.0,0.0 120.0,30.004690389415643 0.0,30.004690389415643\" style=\"fill:#ECB172A0;stroke-width:0\"/>\n",
       "\n",
       "  <!-- Text -->\n",
       "  <text x=\"60.000000\" y=\"50.004690\" font-size=\"1.0rem\" font-weight=\"100\" text-anchor=\"middle\" >15938</text>\n",
       "  <text x=\"140.000000\" y=\"15.002345\" font-size=\"1.0rem\" font-weight=\"100\" text-anchor=\"middle\" transform=\"rotate(-90,140.000000,15.002345)\">378</text>\n",
       "</svg>\n",
       "        </td>\n",
       "    </tr>\n",
       "</table></div></div></li><li class='xr-section-item'><input id='section-c26b1ee9-6e4f-4af8-853d-dc18b56a1674' class='xr-section-summary-in' type='checkbox'  checked><label for='section-c26b1ee9-6e4f-4af8-853d-dc18b56a1674' class='xr-section-summary' >Coordinates: <span>(14)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>sample</span></div><div class='xr-var-dims'>(sample)</div><div class='xr-var-dtype'>object</div><div class='xr-var-preview xr-preview'>&#x27;HG00096&#x27; &#x27;HG00097&#x27; ... &#x27;NA20828&#x27;</div><input id='attrs-f86cf2c9-0091-45e5-a0fb-5a4f7650f541' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-f86cf2c9-0091-45e5-a0fb-5a4f7650f541' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-2d593c5b-8498-4d2c-9301-7e5da5bfc36c' class='xr-var-data-in' type='checkbox'><label for='data-2d593c5b-8498-4d2c-9301-7e5da5bfc36c' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([&#x27;HG00096&#x27;, &#x27;HG00097&#x27;, &#x27;HG00099&#x27;, ..., &#x27;NA20819&#x27;, &#x27;NA20826&#x27;, &#x27;NA20828&#x27;],\n",
       "      dtype=object)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>variant</span></div><div class='xr-var-dims'>(variant)</div><div class='xr-var-dtype'>&lt;U12</div><div class='xr-var-preview xr-preview'>&#x27;variant0&#x27; ... &#x27;variant15937&#x27;</div><input id='attrs-f15e35d2-61c0-4101-b816-f5ba7faa6a11' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-f15e35d2-61c0-4101-b816-f5ba7faa6a11' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-b9c7abe1-3582-4440-9181-dd2fb95e621e' class='xr-var-data-in' type='checkbox'><label for='data-b9c7abe1-3582-4440-9181-dd2fb95e621e' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([&#x27;variant0&#x27;, &#x27;variant1&#x27;, &#x27;variant2&#x27;, ..., &#x27;variant15935&#x27;, &#x27;variant15936&#x27;,\n",
       "       &#x27;variant15937&#x27;], dtype=&#x27;&lt;U12&#x27;)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>fid</span></div><div class='xr-var-dims'>(sample)</div><div class='xr-var-dtype'>object</div><div class='xr-var-preview xr-preview'>&#x27;HG00096&#x27; &#x27;HG00097&#x27; ... &#x27;NA20828&#x27;</div><input id='attrs-0a53ce2f-035a-4f66-93c0-177cedc21acc' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-0a53ce2f-035a-4f66-93c0-177cedc21acc' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-ef3a045a-ed61-44c9-895d-5454033aa6ff' class='xr-var-data-in' type='checkbox'><label for='data-ef3a045a-ed61-44c9-895d-5454033aa6ff' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([&#x27;HG00096&#x27;, &#x27;HG00097&#x27;, &#x27;HG00099&#x27;, &#x27;HG00100&#x27;, &#x27;HG00101&#x27;, &#x27;HG00102&#x27;,\n",
       "       &#x27;HG00103&#x27;, &#x27;HG00105&#x27;, &#x27;HG00106&#x27;, &#x27;HG00107&#x27;, &#x27;HG00108&#x27;, &#x27;HG00109&#x27;,\n",
       "       &#x27;HG00110&#x27;, &#x27;HG00111&#x27;, &#x27;HG00112&#x27;, &#x27;HG00113&#x27;, &#x27;HG00114&#x27;, &#x27;HG00115&#x27;,\n",
       "       &#x27;HG00116&#x27;, &#x27;HG00117&#x27;, &#x27;HG00118&#x27;, &#x27;HG00119&#x27;, &#x27;HG00120&#x27;, &#x27;HG00121&#x27;,\n",
       "       &#x27;HG00122&#x27;, &#x27;HG00123&#x27;, &#x27;HG00125&#x27;, &#x27;HG00126&#x27;, &#x27;HG00127&#x27;, &#x27;HG00128&#x27;,\n",
       "       &#x27;HG00129&#x27;, &#x27;HG00130&#x27;, &#x27;HG00131&#x27;, &#x27;HG00132&#x27;, &#x27;HG00133&#x27;, &#x27;HG00136&#x27;,\n",
       "       &#x27;HG00137&#x27;, &#x27;HG00138&#x27;, &#x27;HG00139&#x27;, &#x27;HG00140&#x27;, &#x27;HG00141&#x27;, &#x27;HG00142&#x27;,\n",
       "       &#x27;HG00143&#x27;, &#x27;HG00145&#x27;, &#x27;HG00146&#x27;, &#x27;HG00148&#x27;, &#x27;HG00149&#x27;, &#x27;HG00150&#x27;,\n",
       "       &#x27;HG00151&#x27;, &#x27;HG00154&#x27;, &#x27;HG00155&#x27;, &#x27;HG00157&#x27;, &#x27;HG00158&#x27;, &#x27;HG00159&#x27;,\n",
       "       &#x27;HG00160&#x27;, &#x27;HG00171&#x27;, &#x27;HG00173&#x27;, &#x27;HG00174&#x27;, &#x27;HG00176&#x27;, &#x27;HG00177&#x27;,\n",
       "       &#x27;HG00178&#x27;, &#x27;HG00179&#x27;, &#x27;HG00180&#x27;, &#x27;HG00181&#x27;, &#x27;HG00182&#x27;, &#x27;HG00183&#x27;,\n",
       "       &#x27;HG00185&#x27;, &#x27;HG00186&#x27;, &#x27;HG00187&#x27;, &#x27;HG00188&#x27;, &#x27;HG00189&#x27;, &#x27;HG00190&#x27;,\n",
       "       &#x27;HG00231&#x27;, &#x27;HG00232&#x27;, &#x27;HG00233&#x27;, &#x27;HG00234&#x27;, &#x27;HG00235&#x27;, &#x27;HG00236&#x27;,\n",
       "       &#x27;HG00237&#x27;, &#x27;HG00238&#x27;, &#x27;HG00239&#x27;, &#x27;HG00240&#x27;, &#x27;HG00242&#x27;, &#x27;HG00243&#x27;,\n",
       "       &#x27;HG00244&#x27;, &#x27;HG00245&#x27;, &#x27;HG00246&#x27;, &#x27;HG00250&#x27;, &#x27;HG00251&#x27;, &#x27;HG00252&#x27;,\n",
       "       &#x27;HG00253&#x27;, &#x27;HG00254&#x27;, &#x27;HG00255&#x27;, &#x27;HG00256&#x27;, &#x27;HG00257&#x27;, &#x27;HG00258&#x27;,\n",
       "       &#x27;HG00259&#x27;, &#x27;HG00260&#x27;, &#x27;HG00261&#x27;, &#x27;HG00262&#x27;, &#x27;HG00263&#x27;, &#x27;HG00264&#x27;,\n",
       "       &#x27;HG00265&#x27;, &#x27;HG00266&#x27;, &#x27;HG00267&#x27;, &#x27;HG00268&#x27;, &#x27;HG00269&#x27;, &#x27;HG00271&#x27;,\n",
       "       &#x27;HG00272&#x27;, &#x27;HG00273&#x27;, &#x27;HG00274&#x27;, &#x27;HG00275&#x27;, &#x27;HG00276&#x27;, &#x27;HG00277&#x27;,\n",
       "       &#x27;HG00278&#x27;, &#x27;HG00280&#x27;, &#x27;HG00281&#x27;, &#x27;HG00282&#x27;, &#x27;HG00284&#x27;, &#x27;HG00285&#x27;,\n",
       "...\n",
       "       &#x27;NA12778&#x27;, &#x27;NA12812&#x27;, &#x27;NA12813&#x27;, &#x27;NA12814&#x27;, &#x27;NA12815&#x27;, &#x27;NA12827&#x27;,\n",
       "       &#x27;NA12828&#x27;, &#x27;NA12829&#x27;, &#x27;NA12830&#x27;, &#x27;NA12842&#x27;, &#x27;NA12843&#x27;, &#x27;NA12872&#x27;,\n",
       "       &#x27;NA12873&#x27;, &#x27;NA12874&#x27;, &#x27;NA12878&#x27;, &#x27;NA12889&#x27;, &#x27;NA12890&#x27;, &#x27;NA20502&#x27;,\n",
       "       &#x27;NA20503&#x27;, &#x27;NA20504&#x27;, &#x27;NA20505&#x27;, &#x27;NA20506&#x27;, &#x27;NA20507&#x27;, &#x27;NA20508&#x27;,\n",
       "       &#x27;NA20509&#x27;, &#x27;NA20510&#x27;, &#x27;NA20512&#x27;, &#x27;NA20513&#x27;, &#x27;NA20514&#x27;, &#x27;NA20515&#x27;,\n",
       "       &#x27;NA20516&#x27;, &#x27;NA20517&#x27;, &#x27;NA20518&#x27;, &#x27;NA20519&#x27;, &#x27;NA20520&#x27;, &#x27;NA20521&#x27;,\n",
       "       &#x27;NA20522&#x27;, &#x27;NA20524&#x27;, &#x27;NA20525&#x27;, &#x27;NA20527&#x27;, &#x27;NA20528&#x27;, &#x27;NA20529&#x27;,\n",
       "       &#x27;NA20530&#x27;, &#x27;NA20531&#x27;, &#x27;NA20532&#x27;, &#x27;NA20533&#x27;, &#x27;NA20534&#x27;, &#x27;NA20535&#x27;,\n",
       "       &#x27;NA20536&#x27;, &#x27;NA20538&#x27;, &#x27;NA20539&#x27;, &#x27;NA20540&#x27;, &#x27;NA20541&#x27;, &#x27;NA20542&#x27;,\n",
       "       &#x27;NA20543&#x27;, &#x27;NA20544&#x27;, &#x27;NA20581&#x27;, &#x27;NA20582&#x27;, &#x27;NA20585&#x27;, &#x27;NA20586&#x27;,\n",
       "       &#x27;NA20588&#x27;, &#x27;NA20589&#x27;, &#x27;NA20752&#x27;, &#x27;NA20753&#x27;, &#x27;NA20754&#x27;, &#x27;NA20755&#x27;,\n",
       "       &#x27;NA20756&#x27;, &#x27;NA20757&#x27;, &#x27;NA20758&#x27;, &#x27;NA20759&#x27;, &#x27;NA20760&#x27;, &#x27;NA20761&#x27;,\n",
       "       &#x27;NA20765&#x27;, &#x27;NA20766&#x27;, &#x27;NA20768&#x27;, &#x27;NA20769&#x27;, &#x27;NA20770&#x27;, &#x27;NA20771&#x27;,\n",
       "       &#x27;NA20772&#x27;, &#x27;NA20773&#x27;, &#x27;NA20774&#x27;, &#x27;NA20775&#x27;, &#x27;NA20778&#x27;, &#x27;NA20783&#x27;,\n",
       "       &#x27;NA20785&#x27;, &#x27;NA20786&#x27;, &#x27;NA20787&#x27;, &#x27;NA20790&#x27;, &#x27;NA20792&#x27;, &#x27;NA20795&#x27;,\n",
       "       &#x27;NA20796&#x27;, &#x27;NA20797&#x27;, &#x27;NA20798&#x27;, &#x27;NA20799&#x27;, &#x27;NA20800&#x27;, &#x27;NA20801&#x27;,\n",
       "       &#x27;NA20802&#x27;, &#x27;NA20803&#x27;, &#x27;NA20804&#x27;, &#x27;NA20805&#x27;, &#x27;NA20806&#x27;, &#x27;NA20807&#x27;,\n",
       "       &#x27;NA20808&#x27;, &#x27;NA20809&#x27;, &#x27;NA20810&#x27;, &#x27;NA20811&#x27;, &#x27;NA20812&#x27;, &#x27;NA20813&#x27;,\n",
       "       &#x27;NA20814&#x27;, &#x27;NA20815&#x27;, &#x27;NA20818&#x27;, &#x27;NA20819&#x27;, &#x27;NA20826&#x27;, &#x27;NA20828&#x27;],\n",
       "      dtype=object)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>iid</span></div><div class='xr-var-dims'>(sample)</div><div class='xr-var-dtype'>object</div><div class='xr-var-preview xr-preview'>&#x27;HG00096&#x27; &#x27;HG00097&#x27; ... &#x27;NA20828&#x27;</div><input id='attrs-7c890344-8008-4de0-97b3-b9ebeb8bea29' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-7c890344-8008-4de0-97b3-b9ebeb8bea29' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-dd767a16-f3c4-4fff-8d0c-1b2fe75a3431' class='xr-var-data-in' type='checkbox'><label for='data-dd767a16-f3c4-4fff-8d0c-1b2fe75a3431' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([&#x27;HG00096&#x27;, &#x27;HG00097&#x27;, &#x27;HG00099&#x27;, &#x27;HG00100&#x27;, &#x27;HG00101&#x27;, &#x27;HG00102&#x27;,\n",
       "       &#x27;HG00103&#x27;, &#x27;HG00105&#x27;, &#x27;HG00106&#x27;, &#x27;HG00107&#x27;, &#x27;HG00108&#x27;, &#x27;HG00109&#x27;,\n",
       "       &#x27;HG00110&#x27;, &#x27;HG00111&#x27;, &#x27;HG00112&#x27;, &#x27;HG00113&#x27;, &#x27;HG00114&#x27;, &#x27;HG00115&#x27;,\n",
       "       &#x27;HG00116&#x27;, &#x27;HG00117&#x27;, &#x27;HG00118&#x27;, &#x27;HG00119&#x27;, &#x27;HG00120&#x27;, &#x27;HG00121&#x27;,\n",
       "       &#x27;HG00122&#x27;, &#x27;HG00123&#x27;, &#x27;HG00125&#x27;, &#x27;HG00126&#x27;, &#x27;HG00127&#x27;, &#x27;HG00128&#x27;,\n",
       "       &#x27;HG00129&#x27;, &#x27;HG00130&#x27;, &#x27;HG00131&#x27;, &#x27;HG00132&#x27;, &#x27;HG00133&#x27;, &#x27;HG00136&#x27;,\n",
       "       &#x27;HG00137&#x27;, &#x27;HG00138&#x27;, &#x27;HG00139&#x27;, &#x27;HG00140&#x27;, &#x27;HG00141&#x27;, &#x27;HG00142&#x27;,\n",
       "       &#x27;HG00143&#x27;, &#x27;HG00145&#x27;, &#x27;HG00146&#x27;, &#x27;HG00148&#x27;, &#x27;HG00149&#x27;, &#x27;HG00150&#x27;,\n",
       "       &#x27;HG00151&#x27;, &#x27;HG00154&#x27;, &#x27;HG00155&#x27;, &#x27;HG00157&#x27;, &#x27;HG00158&#x27;, &#x27;HG00159&#x27;,\n",
       "       &#x27;HG00160&#x27;, &#x27;HG00171&#x27;, &#x27;HG00173&#x27;, &#x27;HG00174&#x27;, &#x27;HG00176&#x27;, &#x27;HG00177&#x27;,\n",
       "       &#x27;HG00178&#x27;, &#x27;HG00179&#x27;, &#x27;HG00180&#x27;, &#x27;HG00181&#x27;, &#x27;HG00182&#x27;, &#x27;HG00183&#x27;,\n",
       "       &#x27;HG00185&#x27;, &#x27;HG00186&#x27;, &#x27;HG00187&#x27;, &#x27;HG00188&#x27;, &#x27;HG00189&#x27;, &#x27;HG00190&#x27;,\n",
       "       &#x27;HG00231&#x27;, &#x27;HG00232&#x27;, &#x27;HG00233&#x27;, &#x27;HG00234&#x27;, &#x27;HG00235&#x27;, &#x27;HG00236&#x27;,\n",
       "       &#x27;HG00237&#x27;, &#x27;HG00238&#x27;, &#x27;HG00239&#x27;, &#x27;HG00240&#x27;, &#x27;HG00242&#x27;, &#x27;HG00243&#x27;,\n",
       "       &#x27;HG00244&#x27;, &#x27;HG00245&#x27;, &#x27;HG00246&#x27;, &#x27;HG00250&#x27;, &#x27;HG00251&#x27;, &#x27;HG00252&#x27;,\n",
       "       &#x27;HG00253&#x27;, &#x27;HG00254&#x27;, &#x27;HG00255&#x27;, &#x27;HG00256&#x27;, &#x27;HG00257&#x27;, &#x27;HG00258&#x27;,\n",
       "       &#x27;HG00259&#x27;, &#x27;HG00260&#x27;, &#x27;HG00261&#x27;, &#x27;HG00262&#x27;, &#x27;HG00263&#x27;, &#x27;HG00264&#x27;,\n",
       "       &#x27;HG00265&#x27;, &#x27;HG00266&#x27;, &#x27;HG00267&#x27;, &#x27;HG00268&#x27;, &#x27;HG00269&#x27;, &#x27;HG00271&#x27;,\n",
       "       &#x27;HG00272&#x27;, &#x27;HG00273&#x27;, &#x27;HG00274&#x27;, &#x27;HG00275&#x27;, &#x27;HG00276&#x27;, &#x27;HG00277&#x27;,\n",
       "       &#x27;HG00278&#x27;, &#x27;HG00280&#x27;, &#x27;HG00281&#x27;, &#x27;HG00282&#x27;, &#x27;HG00284&#x27;, &#x27;HG00285&#x27;,\n",
       "...\n",
       "       &#x27;NA12778&#x27;, &#x27;NA12812&#x27;, &#x27;NA12813&#x27;, &#x27;NA12814&#x27;, &#x27;NA12815&#x27;, &#x27;NA12827&#x27;,\n",
       "       &#x27;NA12828&#x27;, &#x27;NA12829&#x27;, &#x27;NA12830&#x27;, &#x27;NA12842&#x27;, &#x27;NA12843&#x27;, &#x27;NA12872&#x27;,\n",
       "       &#x27;NA12873&#x27;, &#x27;NA12874&#x27;, &#x27;NA12878&#x27;, &#x27;NA12889&#x27;, &#x27;NA12890&#x27;, &#x27;NA20502&#x27;,\n",
       "       &#x27;NA20503&#x27;, &#x27;NA20504&#x27;, &#x27;NA20505&#x27;, &#x27;NA20506&#x27;, &#x27;NA20507&#x27;, &#x27;NA20508&#x27;,\n",
       "       &#x27;NA20509&#x27;, &#x27;NA20510&#x27;, &#x27;NA20512&#x27;, &#x27;NA20513&#x27;, &#x27;NA20514&#x27;, &#x27;NA20515&#x27;,\n",
       "       &#x27;NA20516&#x27;, &#x27;NA20517&#x27;, &#x27;NA20518&#x27;, &#x27;NA20519&#x27;, &#x27;NA20520&#x27;, &#x27;NA20521&#x27;,\n",
       "       &#x27;NA20522&#x27;, &#x27;NA20524&#x27;, &#x27;NA20525&#x27;, &#x27;NA20527&#x27;, &#x27;NA20528&#x27;, &#x27;NA20529&#x27;,\n",
       "       &#x27;NA20530&#x27;, &#x27;NA20531&#x27;, &#x27;NA20532&#x27;, &#x27;NA20533&#x27;, &#x27;NA20534&#x27;, &#x27;NA20535&#x27;,\n",
       "       &#x27;NA20536&#x27;, &#x27;NA20538&#x27;, &#x27;NA20539&#x27;, &#x27;NA20540&#x27;, &#x27;NA20541&#x27;, &#x27;NA20542&#x27;,\n",
       "       &#x27;NA20543&#x27;, &#x27;NA20544&#x27;, &#x27;NA20581&#x27;, &#x27;NA20582&#x27;, &#x27;NA20585&#x27;, &#x27;NA20586&#x27;,\n",
       "       &#x27;NA20588&#x27;, &#x27;NA20589&#x27;, &#x27;NA20752&#x27;, &#x27;NA20753&#x27;, &#x27;NA20754&#x27;, &#x27;NA20755&#x27;,\n",
       "       &#x27;NA20756&#x27;, &#x27;NA20757&#x27;, &#x27;NA20758&#x27;, &#x27;NA20759&#x27;, &#x27;NA20760&#x27;, &#x27;NA20761&#x27;,\n",
       "       &#x27;NA20765&#x27;, &#x27;NA20766&#x27;, &#x27;NA20768&#x27;, &#x27;NA20769&#x27;, &#x27;NA20770&#x27;, &#x27;NA20771&#x27;,\n",
       "       &#x27;NA20772&#x27;, &#x27;NA20773&#x27;, &#x27;NA20774&#x27;, &#x27;NA20775&#x27;, &#x27;NA20778&#x27;, &#x27;NA20783&#x27;,\n",
       "       &#x27;NA20785&#x27;, &#x27;NA20786&#x27;, &#x27;NA20787&#x27;, &#x27;NA20790&#x27;, &#x27;NA20792&#x27;, &#x27;NA20795&#x27;,\n",
       "       &#x27;NA20796&#x27;, &#x27;NA20797&#x27;, &#x27;NA20798&#x27;, &#x27;NA20799&#x27;, &#x27;NA20800&#x27;, &#x27;NA20801&#x27;,\n",
       "       &#x27;NA20802&#x27;, &#x27;NA20803&#x27;, &#x27;NA20804&#x27;, &#x27;NA20805&#x27;, &#x27;NA20806&#x27;, &#x27;NA20807&#x27;,\n",
       "       &#x27;NA20808&#x27;, &#x27;NA20809&#x27;, &#x27;NA20810&#x27;, &#x27;NA20811&#x27;, &#x27;NA20812&#x27;, &#x27;NA20813&#x27;,\n",
       "       &#x27;NA20814&#x27;, &#x27;NA20815&#x27;, &#x27;NA20818&#x27;, &#x27;NA20819&#x27;, &#x27;NA20826&#x27;, &#x27;NA20828&#x27;],\n",
       "      dtype=object)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>father</span></div><div class='xr-var-dims'>(sample)</div><div class='xr-var-dtype'>object</div><div class='xr-var-preview xr-preview'>&#x27;0&#x27; &#x27;0&#x27; &#x27;0&#x27; &#x27;0&#x27; ... &#x27;0&#x27; &#x27;0&#x27; &#x27;0&#x27; &#x27;0&#x27;</div><input id='attrs-b1ae76d5-5e71-4c8b-9fbd-0e9072d034b9' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-b1ae76d5-5e71-4c8b-9fbd-0e9072d034b9' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-913b773b-e29a-4502-93c9-98696f725bba' class='xr-var-data-in' type='checkbox'><label for='data-913b773b-e29a-4502-93c9-98696f725bba' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([&#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;,\n",
       "       &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;,\n",
       "       &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;,\n",
       "       &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;,\n",
       "       &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;,\n",
       "       &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;,\n",
       "       &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;,\n",
       "       &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;,\n",
       "       &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;,\n",
       "       &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;,\n",
       "       &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;,\n",
       "       &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;,\n",
       "       &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;,\n",
       "       &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;,\n",
       "       &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;,\n",
       "       &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;,\n",
       "       &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;,\n",
       "       &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;,\n",
       "       &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;,\n",
       "       &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;,\n",
       "       &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;,\n",
       "       &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;,\n",
       "       &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;,\n",
       "       &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;,\n",
       "       &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;,\n",
       "       &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;,\n",
       "       &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;,\n",
       "       &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;,\n",
       "       &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;,\n",
       "       &#x27;0&#x27;], dtype=object)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>mother</span></div><div class='xr-var-dims'>(sample)</div><div class='xr-var-dtype'>object</div><div class='xr-var-preview xr-preview'>&#x27;0&#x27; &#x27;0&#x27; &#x27;0&#x27; &#x27;0&#x27; ... &#x27;0&#x27; &#x27;0&#x27; &#x27;0&#x27; &#x27;0&#x27;</div><input id='attrs-d74c4eb4-2428-4b99-97da-bf86791b367a' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-d74c4eb4-2428-4b99-97da-bf86791b367a' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-61684e8e-26b4-4de0-9e64-46c1e4d35d2c' class='xr-var-data-in' type='checkbox'><label for='data-61684e8e-26b4-4de0-9e64-46c1e4d35d2c' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([&#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;,\n",
       "       &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;,\n",
       "       &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;,\n",
       "       &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;,\n",
       "       &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;,\n",
       "       &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;,\n",
       "       &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;,\n",
       "       &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;,\n",
       "       &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;,\n",
       "       &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;,\n",
       "       &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;,\n",
       "       &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;,\n",
       "       &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;,\n",
       "       &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;,\n",
       "       &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;,\n",
       "       &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;,\n",
       "       &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;,\n",
       "       &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;,\n",
       "       &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;,\n",
       "       &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;,\n",
       "       &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;,\n",
       "       &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;,\n",
       "       &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;,\n",
       "       &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;,\n",
       "       &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;,\n",
       "       &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;,\n",
       "       &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;,\n",
       "       &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;,\n",
       "       &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;,\n",
       "       &#x27;0&#x27;], dtype=object)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>gender</span></div><div class='xr-var-dims'>(sample)</div><div class='xr-var-dtype'>object</div><div class='xr-var-preview xr-preview'>&#x27;0&#x27; &#x27;0&#x27; &#x27;0&#x27; &#x27;0&#x27; ... &#x27;0&#x27; &#x27;0&#x27; &#x27;0&#x27; &#x27;0&#x27;</div><input id='attrs-1701fa70-d4f7-4fe7-aece-bc2db8a6df43' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-1701fa70-d4f7-4fe7-aece-bc2db8a6df43' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-a7b207b5-c315-4622-ac18-6292fd9f8377' class='xr-var-data-in' type='checkbox'><label for='data-a7b207b5-c315-4622-ac18-6292fd9f8377' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([&#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;,\n",
       "       &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;,\n",
       "       &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;,\n",
       "       &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;,\n",
       "       &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;,\n",
       "       &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;,\n",
       "       &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;,\n",
       "       &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;,\n",
       "       &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;,\n",
       "       &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;,\n",
       "       &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;,\n",
       "       &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;,\n",
       "       &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;,\n",
       "       &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;,\n",
       "       &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;,\n",
       "       &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;,\n",
       "       &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;,\n",
       "       &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;,\n",
       "       &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;,\n",
       "       &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;,\n",
       "       &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;,\n",
       "       &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;,\n",
       "       &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;,\n",
       "       &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;,\n",
       "       &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;,\n",
       "       &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;,\n",
       "       &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;,\n",
       "       &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;,\n",
       "       &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;, &#x27;0&#x27;,\n",
       "       &#x27;0&#x27;], dtype=object)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>trait</span></div><div class='xr-var-dims'>(sample)</div><div class='xr-var-dtype'>object</div><div class='xr-var-preview xr-preview'>&#x27;-9&#x27; &#x27;-9&#x27; &#x27;-9&#x27; ... &#x27;-9&#x27; &#x27;-9&#x27; &#x27;-9&#x27;</div><input id='attrs-ba87bb2d-f144-4beb-aa22-b7b60cfe18de' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-ba87bb2d-f144-4beb-aa22-b7b60cfe18de' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-88ba99ee-4015-4737-9d01-f4e9eb3b70f2' class='xr-var-data-in' type='checkbox'><label for='data-88ba99ee-4015-4737-9d01-f4e9eb3b70f2' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([&#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;,\n",
       "       &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;,\n",
       "       &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;,\n",
       "       &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;,\n",
       "       &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;,\n",
       "       &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;,\n",
       "       &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;,\n",
       "       &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;,\n",
       "       &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;,\n",
       "       &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;,\n",
       "       &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;,\n",
       "       &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;,\n",
       "       &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;,\n",
       "       &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;,\n",
       "       &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;,\n",
       "       &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;,\n",
       "       &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;,\n",
       "       &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;,\n",
       "       &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;,\n",
       "       &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;,\n",
       "       &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;,\n",
       "       &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;,\n",
       "       &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;,\n",
       "       &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;,\n",
       "       &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;,\n",
       "       &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;,\n",
       "       &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;,\n",
       "       &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;,\n",
       "       &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;,\n",
       "       &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;,\n",
       "       &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;,\n",
       "       &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;,\n",
       "       &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;,\n",
       "       &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;,\n",
       "       &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;, &#x27;-9&#x27;], dtype=object)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>chrom</span></div><div class='xr-var-dims'>(variant)</div><div class='xr-var-dtype'>object</div><div class='xr-var-preview xr-preview'>&#x27;22&#x27; &#x27;22&#x27; &#x27;22&#x27; ... &#x27;22&#x27; &#x27;22&#x27; &#x27;22&#x27;</div><input id='attrs-a7e0e745-021f-4f76-ab6f-75dbaec2f562' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-a7e0e745-021f-4f76-ab6f-75dbaec2f562' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-b6571030-fb44-4c48-b12a-b102669ff588' class='xr-var-data-in' type='checkbox'><label for='data-b6571030-fb44-4c48-b12a-b102669ff588' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([&#x27;22&#x27;, &#x27;22&#x27;, &#x27;22&#x27;, ..., &#x27;22&#x27;, &#x27;22&#x27;, &#x27;22&#x27;], dtype=object)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>snp</span></div><div class='xr-var-dims'>(variant)</div><div class='xr-var-dtype'>object</div><div class='xr-var-preview xr-preview'>&#x27;rs131538&#x27; ... &#x27;rs28729663&#x27;</div><input id='attrs-10eadb5d-14ab-4d12-927a-a755ab29dc93' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-10eadb5d-14ab-4d12-927a-a755ab29dc93' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-6592bc2a-4ce3-4c8d-bba3-634157a3d2c4' class='xr-var-data-in' type='checkbox'><label for='data-6592bc2a-4ce3-4c8d-bba3-634157a3d2c4' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([&#x27;rs131538&#x27;, &#x27;rs9605903&#x27;, &#x27;rs5746647&#x27;, ..., &#x27;rs3810648&#x27;,\n",
       "       &#x27;rs2285395&#x27;, &#x27;rs28729663&#x27;], dtype=object)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>cm</span></div><div class='xr-var-dims'>(variant)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>2.236 2.336 2.34 ... 75.09 75.12</div><input id='attrs-b21d66e2-f793-4823-9867-0f6719764880' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-b21d66e2-f793-4823-9867-0f6719764880' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-8082edb8-9acb-4eca-ba07-c0b75de7d974' class='xr-var-data-in' type='checkbox'><label for='data-8082edb8-9acb-4eca-ba07-c0b75de7d974' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([ 2.2360313,  2.3360723,  2.3404978, ..., 75.083207 , 75.085202 ,\n",
       "       75.116298 ])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>pos</span></div><div class='xr-var-dims'>(variant)</div><div class='xr-var-dtype'>int32</div><div class='xr-var-preview xr-preview'>16871137 17054720 ... 51219006</div><input id='attrs-600ea49c-b938-44b0-8e01-2541aadadf67' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-600ea49c-b938-44b0-8e01-2541aadadf67' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-95a86245-ab73-4405-abff-ee0f7d5ed3a4' class='xr-var-data-in' type='checkbox'><label for='data-95a86245-ab73-4405-abff-ee0f7d5ed3a4' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([16871137, 17054720, 17057138, ..., 51175626, 51178090, 51219006],\n",
       "      dtype=int32)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>a0</span></div><div class='xr-var-dims'>(variant)</div><div class='xr-var-dtype'>object</div><div class='xr-var-preview xr-preview'>&#x27;A&#x27; &#x27;C&#x27; &#x27;G&#x27; &#x27;T&#x27; ... &#x27;A&#x27; &#x27;G&#x27; &#x27;A&#x27; &#x27;A&#x27;</div><input id='attrs-8128ced3-7c3d-414f-9e85-a8013350bd39' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-8128ced3-7c3d-414f-9e85-a8013350bd39' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-316e0474-7287-47fa-93b7-9fd28334020d' class='xr-var-data-in' type='checkbox'><label for='data-316e0474-7287-47fa-93b7-9fd28334020d' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([&#x27;A&#x27;, &#x27;C&#x27;, &#x27;G&#x27;, ..., &#x27;G&#x27;, &#x27;A&#x27;, &#x27;A&#x27;], dtype=object)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>a1</span></div><div class='xr-var-dims'>(variant)</div><div class='xr-var-dtype'>object</div><div class='xr-var-preview xr-preview'>&#x27;G&#x27; &#x27;T&#x27; &#x27;T&#x27; &#x27;C&#x27; ... &#x27;G&#x27; &#x27;A&#x27; &#x27;G&#x27; &#x27;G&#x27;</div><input id='attrs-729dc512-7071-4288-8987-e1a02da371cd' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-729dc512-7071-4288-8987-e1a02da371cd' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-9d1b43a6-ebc8-4be6-9369-9ceb7dd359c7' class='xr-var-data-in' type='checkbox'><label for='data-9d1b43a6-ebc8-4be6-9369-9ceb7dd359c7' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([&#x27;G&#x27;, &#x27;T&#x27;, &#x27;T&#x27;, ..., &#x27;A&#x27;, &#x27;G&#x27;, &#x27;G&#x27;], dtype=object)</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-8ab1d8ee-1a26-4de7-b914-9fca8d564ddc' class='xr-section-summary-in' type='checkbox'  ><label for='section-8ab1d8ee-1a26-4de7-b914-9fca8d564ddc' class='xr-section-summary' >Indexes: <span>(2)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-index-name'><div>sample</div></div><div class='xr-index-preview'>PandasIndex</div><div></div><input id='index-3876e6d3-2df9-4b16-8a72-2fbd1ebe39fe' class='xr-index-data-in' type='checkbox'/><label for='index-3876e6d3-2df9-4b16-8a72-2fbd1ebe39fe' title='Show/Hide index repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-index-data'><pre>PandasIndex(Index([&#x27;HG00096&#x27;, &#x27;HG00097&#x27;, &#x27;HG00099&#x27;, &#x27;HG00100&#x27;, &#x27;HG00101&#x27;, &#x27;HG00102&#x27;,\n",
       "       &#x27;HG00103&#x27;, &#x27;HG00105&#x27;, &#x27;HG00106&#x27;, &#x27;HG00107&#x27;,\n",
       "       ...\n",
       "       &#x27;NA20810&#x27;, &#x27;NA20811&#x27;, &#x27;NA20812&#x27;, &#x27;NA20813&#x27;, &#x27;NA20814&#x27;, &#x27;NA20815&#x27;,\n",
       "       &#x27;NA20818&#x27;, &#x27;NA20819&#x27;, &#x27;NA20826&#x27;, &#x27;NA20828&#x27;],\n",
       "      dtype=&#x27;object&#x27;, name=&#x27;sample&#x27;, length=378))</pre></div></li><li class='xr-var-item'><div class='xr-index-name'><div>variant</div></div><div class='xr-index-preview'>PandasIndex</div><div></div><input id='index-c1f60c3d-982e-4d12-bce9-2348097b75ed' class='xr-index-data-in' type='checkbox'/><label for='index-c1f60c3d-982e-4d12-bce9-2348097b75ed' title='Show/Hide index repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-index-data'><pre>PandasIndex(Index([&#x27;variant0&#x27;, &#x27;variant1&#x27;, &#x27;variant2&#x27;, &#x27;variant3&#x27;, &#x27;variant4&#x27;, &#x27;variant5&#x27;,\n",
       "       &#x27;variant6&#x27;, &#x27;variant7&#x27;, &#x27;variant8&#x27;, &#x27;variant9&#x27;,\n",
       "       ...\n",
       "       &#x27;variant15928&#x27;, &#x27;variant15929&#x27;, &#x27;variant15930&#x27;, &#x27;variant15931&#x27;,\n",
       "       &#x27;variant15932&#x27;, &#x27;variant15933&#x27;, &#x27;variant15934&#x27;, &#x27;variant15935&#x27;,\n",
       "       &#x27;variant15936&#x27;, &#x27;variant15937&#x27;],\n",
       "      dtype=&#x27;object&#x27;, name=&#x27;variant&#x27;, length=15938))</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-112d1c1f-f433-4cbf-a851-66b1007dffff' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-112d1c1f-f433-4cbf-a851-66b1007dffff' class='xr-section-summary'  title='Expand/collapse section'>Attributes: <span>(0)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'></dl></div></li></ul></div></div>"
      ],
      "text/plain": [
       "<xarray.DataArray 'genotype' (sample: 378, variant: 15938)>\n",
       "dask.array<transpose, shape=(378, 15938), dtype=float32, chunksize=(378, 1024), chunktype=numpy.ndarray>\n",
       "Coordinates: (12/14)\n",
       "  * sample   (sample) object 'HG00096' 'HG00097' ... 'NA20826' 'NA20828'\n",
       "  * variant  (variant) <U12 'variant0' 'variant1' ... 'variant15937'\n",
       "    fid      (sample) object 'HG00096' 'HG00097' ... 'NA20826' 'NA20828'\n",
       "    iid      (sample) object 'HG00096' 'HG00097' ... 'NA20826' 'NA20828'\n",
       "    father   (sample) object '0' '0' '0' '0' '0' '0' ... '0' '0' '0' '0' '0' '0'\n",
       "    mother   (sample) object '0' '0' '0' '0' '0' '0' ... '0' '0' '0' '0' '0' '0'\n",
       "    ...       ...\n",
       "    chrom    (variant) object '22' '22' '22' '22' '22' ... '22' '22' '22' '22'\n",
       "    snp      (variant) object 'rs131538' 'rs9605903' ... 'rs28729663'\n",
       "    cm       (variant) float64 2.236 2.336 2.34 2.344 ... 75.08 75.09 75.12\n",
       "    pos      (variant) int32 16871137 17054720 17057138 ... 51178090 51219006\n",
       "    a0       (variant) object 'A' 'C' 'G' 'T' 'A' 'C' ... 'A' 'A' 'G' 'A' 'A'\n",
       "    a1       (variant) object 'G' 'T' 'T' 'C' 'T' 'T' ... 'G' 'G' 'A' 'G' 'G'"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from magenpy.GenotypeMatrix import xarrayGenotypeMatrix\n",
    "\n",
    "# Load the genotype matrix by providing path to BED file:\n",
    "g_matrix = xarrayGenotypeMatrix.from_file(mgp.tgp_eur_data_path())\n",
    "# Inspect the xarray object:\n",
    "g_matrix.xr_mat"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "caecfecb",
   "metadata": {},
   "source": [
    "This representation is known as a `DataArray` and it summarizes the matrix itself (its shape, size, etc.) \n",
    "but also the characteristics of the the two main dimensions:\n",
    "    \n",
    "* The `sample` dimension contains information about the individuals, such as their IDs, gender, etc.\n",
    "* The `variant` dimension contains information about the SNPs, such as their IDs, genomic position, reference and alternative alleles, etc.\n",
    "\n",
    "To examine the contents of the genotype matrix itself (i.e. the mutation counts), we can load the data into \n",
    "memory and represent using `numpy` arrays:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "ec373bbc",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-04-12T16:10:06.973989Z",
     "start_time": "2024-04-12T16:10:06.655158Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 0, 0, ..., 0, 0, 0],\n",
       "       [0, 0, 0, ..., 0, 0, 0],\n",
       "       [0, 1, 0, ..., 0, 0, 1],\n",
       "       ...,\n",
       "       [0, 0, 0, ..., 0, 0, 0],\n",
       "       [0, 1, 0, ..., 0, 0, 0],\n",
       "       [0, 0, 0, ..., 0, 0, 0]], dtype=int8)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np_matrix = g_matrix.to_numpy()\n",
    "np_matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9997a20f",
   "metadata": {},
   "source": [
    "### Quick Exercise (1): For each variant, count how many mutations are present in the entire sample"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "02b19b7c",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-04-12T16:10:07.532495Z",
     "start_time": "2024-04-12T16:10:07.529660Z"
    }
   },
   "outputs": [],
   "source": [
    "# YOUR SOLUTION GOES FOR EXERCISE (1) GOES HERE"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "738f9536",
   "metadata": {},
   "source": [
    "### (0.2) Phenotype data\n",
    "\n",
    "In the context of PRS, phenotype data encomposses **measurements, diagnoses, health records, or self-reports** that are specific to each individual. Historically, the most well-studied phenotypes have been relatively easy to measure and define, primarily anthropomorphic traits such as height, weight, and Body Mass Index (BMI). These phenotypes display continuous variation in the population, which is why they are often referred to as **quantitative traits**. Another class of phenotypes that have also been well studied are **case-control or binary** phenotypes, primarily disease diagnoses, such as whether the subject has been diagonsed with Type 2 Diabetes, Heart Disease, and Alzheimer. \n",
    "\n",
    "More recently, with the emergence of large-scale genetic biobanks that are paired with **Electronic Health Records (EHR)**, everything from **medication use** to **self-reports of insomnia** have been defined as phenotypes and studied in the context of GWAS and PRS. More interestingly, computational post-processing of these raw EHR records could also result in **\"computationally-defined\" phenotypes** that are useful for some downstream applications.\n",
    "\n",
    "Unfortunately, the 1000G project does not come with phenotype data for us to inspect, but we can easily simulate \n",
    "complex traits, as we will discuss in the next section."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6e7c20f8",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-04-06T21:39:26.899290Z",
     "start_time": "2024-04-06T21:39:26.893639Z"
    }
   },
   "source": [
    "## (1) Modeling the Relationship between Genotypes and Complex Traits"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ae2cb230",
   "metadata": {},
   "source": [
    "Learning a predictor between any two modalities always proceeds by first defining a model. A model is not \n",
    "a mechanism, it doesn't define precisely how the input `X` influences the output `y` in every detail. It's a way for researchers to encode our assumptions about the dependence between input and output. In the context of statistical genetics and complex traits, the dependence between genotype and phenotype was understood, analyzed, and interrogated using the linear model."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "81b8b483",
   "metadata": {},
   "source": [
    "### (1.1) The Linear Model\n",
    "\n",
    "The linear model is the simplest possible way to parametrize the dependence between the phenotype and genotype. It assumes that each genetic variant influences the phenotype **additively** (i.e. without interaction or dependence on other variants), and the **magnitude/direction of influence** is parametrized by a quantitative parameter typically denoted by $\\beta$:\n",
    "\n",
    "$$\n",
    "y_i = \\textbf{X}_i\\beta + \\epsilon_i = \\sum_{j=1}^M X_{ij}\\beta_j + \\epsilon_i\n",
    "$$\n",
    "\n",
    "This equation tells us that the phenotype of individual $i$ is the sum of their genotype (i.e. number of mutations they carry) at each position, weighted by the **effect size** $\\beta$. Here, $M$ denotes that total number of genetic variants in our study. The variable $\\epsilon$ is known as the **residual**, capturing all non-additive and non-genetic effects on the phenotype. \n",
    "\n",
    "To make things more concrete, let's focus on a simple case where there are only 2 genetic variants $X_1$ and $X_2$. We will assume that:\n",
    "\n",
    "* Variant 1 has an effect of $\\beta_1 = 10$ on the phenotype.\n",
    "* Variant 2 has an effect of $\\beta_2 = -3$ on the phenotype.\n",
    "\n",
    "Furthermore, let's assume that individual $i$ carries:\n",
    "\n",
    "* 1 mutation on the first variant $X_1$\n",
    "* 2 mutations on the second variant $X_2$\n",
    "    \n",
    "Assuming this phenotype does not have any non-genetic / non-additive influences ($\\epsilon = 0$), we get that the phenotype for individual $i$ is:\n",
    "\n",
    "$$\n",
    "y_i = X_1*\\beta_1 + X_2*\\beta_2 = 1*10 + 2*(-3) = 4\n",
    "$$\n",
    "\n",
    "\n",
    "This simple model is the basis for most statistical genetics analyses and tools, from GWAS to PRS. In the context of the linear model, the **prediction (or polygenic score) for individual $i$ is simply defined as**:\n",
    "\n",
    "$$\n",
    "PRS_i = \\hat{y}_i = \\sum_{j=1}^M X_{ij}*\\hat{\\beta}_j\n",
    "$$\n",
    "\n",
    "Note that the hat $\\hat{\\beta}_j$ is used here to indicate that the effects are **estimated** from data.\n",
    "\n",
    "\n",
    "### (1.2) The effect sizes $\\beta$\n",
    "\n",
    "As mentioned above, the $\\beta$ parameter is a simple weight that captures the magnitude and direction of the effect on phenotype. The magnitude (absolute value) of the effect ($|\\beta|$) tells us about the strength of this effect. In the example above, variant 1 had a much larger effect, in absolute terms, on the phenotype than variant 2. The direction (i.e. sign) also conveys important information:\n",
    "\n",
    "* Variants / alleles with **positive $\\beta$ will increase** the phenotype.\n",
    "* Variants / alleles with **negative $\\beta$ will decrease** the phenotype.\n",
    "\n",
    "**Note**: We say \"variants / alleles\" here because this depends on how we choose our \"reference allele\" when we construct the genotype matrix. If the reference allele is changed, the effect direction will flip.\n",
    "\n",
    "A natural consequence of the above definitions is that **variants whose weight is set to zero (i.e. $\\beta = 0$) will have no effect on the phenotype**.\n",
    "\n",
    "A **central question in statistical genetics concerns the genetic architecture of complex traits: The distribution of effect sizes for a particular trait or disease**. Some of the questions that are asked in this context:\n",
    "\n",
    "* How many variants have **non-zero weights** (i.e. $\\beta \\neq 0$)? This quantity is known as **polygenicity**.\n",
    "* How does the **distribution of variant effect sizes vary by genomic contexts**?\n",
    "    * E.g. Do variants in coding or regulatory regions have larger effect magnitudes than the rest of the genome?\n",
    "    * These questions are studied in the context of **stratified SNP-heritability**.\n",
    "\n",
    "### (1.3) Assumptions about the distribution of effect sizes\n",
    "\n",
    "\n",
    "#### (1.3.1) The infinitesimal model\n",
    "\n",
    "In the early days of statistical genetics, the most commonly used models assumed that most or all variants had an effect on the phenotype. This is sometimes known as the **infinitesimal model**. A common way to parametrize this belief is to assume that the effect sizes for all variants are drawn from a Gaussian distribution with mean zero and variance set to the per-SNP heritability (to be discussed in the next section):\n",
    "\n",
    "$$\n",
    "\\beta_j \\sim \\mathcal{N}(0, \\frac{h^2}{M})\n",
    "$$\n",
    "\n",
    "**NOTE**: This formulation assumes total phenotypic variance $\\sigma^2_y$ is set to 1. More on this later.\n",
    "\n",
    "To illustrate what this model implies in practice, let's try and simulate it:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "0178aa04",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-04-12T16:10:11.055296Z",
     "start_time": "2024-04-12T16:10:10.638258Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def sample_beta_infinitesimal(n_snps, h2, random_seed=7209):\n",
    "    \"\"\"\n",
    "    Sample variant effect sizes (BETA) according to the \n",
    "    infinitesimal model.\n",
    "    \n",
    "    :param n_snps: The number of genetic variants.\n",
    "    :param h2: The heritability for the phenotype of interest (float from 0 to 1).\n",
    "    :param random_seed: The seed for the random number generator.\n",
    "    \"\"\"\n",
    "    \n",
    "    # Sanity checks\n",
    "    assert 0. <= h2 <= 1.\n",
    "    \n",
    "    per_snp_h2 = h2 / n_snps\n",
    "    \n",
    "    return np.random.normal(\n",
    "        loc=0.,  # The mean\n",
    "        scale=np.sqrt(per_snp_h2),  # sqrt(variance)\n",
    "        size=n_snps  # The number of variants\n",
    "    )\n",
    "\n",
    "# Sample effect sizes according to the infinitesimal model\n",
    "# where the heritability is set to 0.5 and the number of variants \n",
    "# is set to 10k:\n",
    "beta = sample_beta_infinitesimal(n_snps=10_000, h2=0.5)\n",
    "\n",
    "\n",
    "# Plot a histogram of the effect sizes:\n",
    "plt.hist(beta, bins=50)\n",
    "plt.xlabel(\"BETA\")\n",
    "plt.title(\"Infinitesimal model\\nDistribution of variant effect sizes ($h^2=0.5$; $M=10000$)\");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "97aa13dc",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-04-06T23:37:45.897675Z",
     "start_time": "2024-04-06T23:37:45.890790Z"
    }
   },
   "source": [
    "#### (1.3.1) Encoding sparsity with the spike-and-slab prior\n",
    "\n",
    "From an an evolutionary perspective, as well as given our current understanding of genetics from \n",
    "molecular and genetic epidemiology studies, we know that most variants have no or negligible effect \n",
    "on most phenotypes. This evidence and observations motivated an alternative model that gives \n",
    "parametric form to this \"**sparsity**\": The **spike-and-slab prior**. \n",
    "    \n",
    "The spike-and-slab is a mixture distribution: Instead of having a single Gaussian distribution from which \n",
    "we draw the effect size, we are going to have two distributions:\n",
    "    \n",
    "* **The spike distribution** $\\delta_0$: The spike distribution is a degenerate density where all of its \n",
    "    weight is centered at zero. Visually, this distribution looks like a \"spike\" at the value zero, \n",
    "    hence the name. As we'd expect, the spike distribution is used to model variants \n",
    "    with no or negligible effect on the phenotype.\n",
    "\n",
    "* **The slab distribution** $\\mathcal{N}(0, \\frac{h^2}{\\pi M})$: The slab distribution is a Gaussian distribution similar to \n",
    "    one we encountered before with the infinitesimal model. It's called a \"slab\" because, visually, \n",
    "    it looks flatter compared to the spike. The slab distribution is used to model variants with \n",
    "    an effect on the phenotype.\n",
    "    \n",
    "The other component that goes into defining the spike-and-slab is a **mixing weight**, denoted by $\\pi$, \n",
    "that tells us **what proportion of variants come from the slab distribution** (i.e. what proportion of variants \n",
    "have an effect on the phenotype). Mathematically, this is distribution is often written as:\n",
    "\n",
    "$$\n",
    "\\beta_j \\sim \\pi\\mathcal{N}(0, \\frac{h^2}{\\pi M}) + (1 - \\pi)\\delta_0\n",
    "$$\n",
    "\n",
    "**NOTE**: Unlike in the infinitesimal model, the variance of the slab distribution is proportion to per-SNP heritability of causal variants (i.e. we scale $M$ by $\\pi$).\n",
    "\n",
    "#### Data generative process\n",
    "\n",
    "In terms of the data generative process, mixture models are usually thought of as hierarchical models:\n",
    "\n",
    "1) Determine which mixture component the variant effect comes from: \n",
    "    * This is done by sampling from a **Bernoulli with success probability** $p = \\pi$.\n",
    "    * If the Bernoulli draw is a success, then the variant is assigned to the slab. Otherwise it's assigned to the spike.\n",
    "2) Draw the effect according to the mixture component that the variant was assigned in Step 1.\n",
    "\n",
    "\n",
    "\n",
    "To illustrate what the spike-and-slab model implies in practice, let's try and simulate it:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "ca240aaf",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-04-12T16:10:12.492306Z",
     "start_time": "2024-04-12T16:10:12.204206Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def sample_beta_spike_and_slab(n_snps, h2, pi, random_seed=7209):\n",
    "    \"\"\"\n",
    "    Sample variant effect sizes (BETA) according to the \n",
    "    infinitesimal model.\n",
    "    \n",
    "    :param n_snps: The number of genetic variants.\n",
    "    :param h2: The heritability for the phenotype of interest (float ranging from 0 to 1).\n",
    "    :param pi: The proportion of causal variants (float ranging from 0 to 1)\n",
    "    :param random_seed: The seed for the random number generator.\n",
    "    \"\"\"\n",
    "    \n",
    "    # Sanity checks\n",
    "    assert 0. <= h2 <= 1.\n",
    "    assert 0. <= pi <= 1.\n",
    "    \n",
    "    per_snp_h2 = h2 / (pi*n_snps)\n",
    "    \n",
    "    # Draw mixture assignment from Bernoulli:\n",
    "    # NOTE: In numpy Bernoulli sampling is done via binomial with number of trials set to 1.\n",
    "    mixture_assignment = np.random.binomial(1, pi, size=n_snps)\n",
    "\n",
    "    # NOTE: For ease of implementation, we draw effect for all variants from \n",
    "    # slab, but then we zero the effect of non-slab variants\n",
    "\n",
    "    # Draw from Gaussian:\n",
    "    beta = np.random.normal(loc=0., # mean\n",
    "                            scale=np.sqrt(per_snp_h2), # sqrt(var)\n",
    "                            size=n_snps) # number of variants\n",
    "    \n",
    "    # Final beta:\n",
    "    beta *=mixture_assignment\n",
    "    \n",
    "    return beta\n",
    "\n",
    "\n",
    "# Sample betas from the spike-and-slab model:\n",
    "beta = sample_beta_spike_and_slab(n_snps=10_000,\n",
    "                                  h2=0.5,\n",
    "                                  pi=0.5)\n",
    "\n",
    "\n",
    "# Plot a histogram of the effect sizes:\n",
    "\n",
    "plt.hist(beta, bins=50)\n",
    "plt.xlabel(\"BETA\")\n",
    "plt.title(f\"Spike-and-Slab model\\nDistribution of variant effect sizes ($h^2={0.5}$; $M={10000}$; $\\pi={0.5}$)\");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b078abab",
   "metadata": {},
   "source": [
    "### (1.4) Heritability\n",
    "\n",
    "The concept of heritability is defined as **the proportion of phenotypic variance attributable to genetics**:\n",
    "\n",
    "$$\n",
    "h^2 = \\frac{\\sigma^2_g}{\\sigma^2_y} \n",
    "$$\n",
    "\n",
    "Hence, its value ranges between 0 and 1. When genetic factors explain very little of phenotypic variation in a given sample, heritability will tend towards 0. If, on the other hand, genetic factors explain most observed variation in the phenotype, its value will tend towards 1.\n",
    "\n",
    "Another important concept to understand in this context is **narrow-sense heritability** ($h^2_A$): which is defined as the proportion of phenotypic variance explained by **additive genetic effects**. And here is where the linear model comes back again: When we talk about narrow-sense heritability, we're mainly concerned about the variance of $X\\beta$ as a proportion of phenotypic variance $\\sigma^2_y$:\n",
    "\n",
    "$$\n",
    "h^2_A = \\frac{Var(X\\beta)}{\\sigma^2_y} \n",
    "$$\n",
    "\n",
    "In other words, with narrow-sense heritability, we're not concerned about variation arising due to dominance, epistasis, or other non-linear genetic effects.\n",
    "\n",
    "For the purposes of our discussions in this tutorial, heritability factors in in **two important ways**:\n",
    "\n",
    "1) Heritability is important to define the **residual component** ($\\epsilon$) in the linear model above. In most statistical genetics models, the residual effect is modelled with a Gaussian density with mean zero and variance \n",
    "set to the total phenotypic variance not captured by genetics:\n",
    "\n",
    "$$\n",
    "\\epsilon_i \\sim \\mathcal{N}(0, \\sigma^2_y*(1 - h^2))\n",
    "$$\n",
    "\n",
    "For example, if the total phenotypic variance $\\sigma^2_y$ is 1 and the heritability of the phenotype is 0.5, then the variance of $\\epsilon$ will simply be set to 0.5.\n",
    "\n",
    "2) Narrow-sense heritability provides us with an **upper bound for how well we can predict the phenotype using linear models**. In statistical genetics, we often use the coefficient of determination (R-Squared or $R^2$) to evaluate model performance. R-squared is the proportion of phenotypic variance explained by the predictor. Thus, for these predictors, the $R^2$ performance is upper-bounded by narrow-sense heritability. Intuitively, if the phenotype is strongly heritable, genetic predictors can in principle perform well. On the other hand, if the phenotype is mildly heritable, prediction accuracy will be poor."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1bbe5dd1",
   "metadata": {},
   "source": [
    "## Exercise (2): Simulating data according to the linear model\n",
    "\n",
    "Now that we learned all about linear models, heritability, mixture distributions, and spike-and-slab priors, let's take some time to practice simulating complex traits / phenotypes. In this exercise, you'll be given genotype data for a subset of 378 European individuals from the 1000G project. For each individual, we have mutation counts at ~15,000 variants on Chromosome 22. \n",
    "\n",
    "Your task is to simulate a phenotype for these individuals according to the following criteria:\n",
    "\n",
    "1) The **heritability** for the phenotype should be set to $h^2 = 0.5$\n",
    "2) Use the **spike-and-slab** model to simulate the effect sizes.\n",
    "    * Mixing proportion $\\pi$ should be set to $\\pi = 0.1$ (i.e. only 10% of the variants influence the trait).\n",
    "3) Total phenotypic variance $\\sigma_y^2$ should be set to 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "3e9b3aad",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-04-12T16:10:14.455504Z",
     "start_time": "2024-04-12T16:10:14.342633Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "''"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Let's define the parameters of the model:\n",
    "\n",
    "h2 = 0.01  # Heritability\n",
    "pi = 0.1  # Mixing proportion\n",
    "sigma2_y = 1.  # Phenotypic variance\n",
    "\n",
    "# Extract and standardize the genotype matrix:\n",
    "X = g_matrix.to_numpy().astype(np.float32)\n",
    "# Standardize the genotype matrix:\n",
    "X -= X.mean(axis=0)\n",
    "X /= X.std(axis=0)\n",
    "\n",
    "# Get the sample size and number of variants in\n",
    "# in the genotype matrix:\n",
    "\n",
    "n = X.shape[0] # Number of samples\n",
    "n_snps = X.shape[1] # Number of variants\n",
    "\n",
    "################ STEP 1 ################\n",
    "# Sample the effect sizes from spike-and-slab:\n",
    "\n",
    "# FILL IN HERE\n",
    "\n",
    "################ STEP 2 ################\n",
    "# Compute the polygenic score (X\\beta)\n",
    "\n",
    "# FILL IN HERE\n",
    "\n",
    "\n",
    "################ STEP 3 ################\n",
    "# Sample the residual component (epsilon)\n",
    "\n",
    "# FILL IN HERE\n",
    "\n",
    "################ STEP 4 ################\n",
    "# Compute the final phenotype according to the linear model:\n",
    "\n",
    "# FILL IN HERE\n",
    "\n",
    "################ STEP 5 ################\n",
    "# Plot the distribution of the phenotype:\n",
    "\n",
    "# FILL IN HERE\n",
    "\n",
    ";"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b0474c4d",
   "metadata": {},
   "source": [
    "## (2) Simulating Complex Traits using `magenpy`\n",
    "\n",
    "Now that we understand the data generative process better, we can avoid having to do this low-level work \n",
    "ourselves and instead delegate it to `magenpy`. `magenpy` is a `python` package for statistical genetics applications and it supports various phenotype simulation tools.\n",
    "\n",
    "For example, to simulate a phenotype with the same parameters as the exercise above, we can simply invoke:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "299d39ba",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-04-12T16:10:21.064012Z",
     "start_time": "2024-04-12T16:10:15.528294Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "> Reading BED file...\n",
      "> Generating polygenic scores...\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>FID</th>\n",
       "      <th>IID</th>\n",
       "      <th>phenotype</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>HG00096</td>\n",
       "      <td>HG00096</td>\n",
       "      <td>1.412844</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>HG00097</td>\n",
       "      <td>HG00097</td>\n",
       "      <td>0.178778</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>HG00099</td>\n",
       "      <td>HG00099</td>\n",
       "      <td>-0.346534</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>HG00100</td>\n",
       "      <td>HG00100</td>\n",
       "      <td>-0.531910</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>HG00101</td>\n",
       "      <td>HG00101</td>\n",
       "      <td>-1.722824</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>373</th>\n",
       "      <td>NA20815</td>\n",
       "      <td>NA20815</td>\n",
       "      <td>0.736829</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>374</th>\n",
       "      <td>NA20818</td>\n",
       "      <td>NA20818</td>\n",
       "      <td>-0.876931</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>375</th>\n",
       "      <td>NA20819</td>\n",
       "      <td>NA20819</td>\n",
       "      <td>0.208573</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>376</th>\n",
       "      <td>NA20826</td>\n",
       "      <td>NA20826</td>\n",
       "      <td>-0.758937</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>377</th>\n",
       "      <td>NA20828</td>\n",
       "      <td>NA20828</td>\n",
       "      <td>-0.505278</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>378 rows × 3 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "         FID      IID  phenotype\n",
       "0    HG00096  HG00096   1.412844\n",
       "1    HG00097  HG00097   0.178778\n",
       "2    HG00099  HG00099  -0.346534\n",
       "3    HG00100  HG00100  -0.531910\n",
       "4    HG00101  HG00101  -1.722824\n",
       "..       ...      ...        ...\n",
       "373  NA20815  NA20815   0.736829\n",
       "374  NA20818  NA20818  -0.876931\n",
       "375  NA20819  NA20819   0.208573\n",
       "376  NA20826  NA20826  -0.758937\n",
       "377  NA20828  NA20828  -0.505278\n",
       "\n",
       "[378 rows x 3 columns]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Sed random seed:\n",
    "np.random.seed(7209)\n",
    "\n",
    "# Initialize the simulator object:\n",
    "sim = mgp.PhenotypeSimulator(mgp.tgp_eur_data_path(),\n",
    "                             min_mac=10,\n",
    "                             h2=0.8,\n",
    "                             pi=0.1)\n",
    "# Filter to a smaller subset of variants:\n",
    "sim.filter_snps(sim.snps[22][:300])\n",
    "\n",
    "# Simulate a phenotype:\n",
    "sim.simulate()\n",
    "\n",
    "# Get a table with the simulated phenotype:\n",
    "pheno_table = sim.to_phenotype_table()\n",
    "\n",
    "# Display the phenotype table:\n",
    "display(pheno_table)\n",
    "\n",
    "# Plot a histogram of the simulated phenotype:\n",
    "\n",
    "plt.hist(pheno_table.phenotype, bins=20)\n",
    "plt.xlabel(\"Simulated Quantitative Trait\")\n",
    "plt.title(f\"Distribution of {sim.phenotype_likelihood} trait\\n Spike-and-slab model ($h^2={sim.h2}$; $M={sim.n_snps}$; $\\pi={sim.pi}$)\");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9b007389",
   "metadata": {},
   "source": [
    "In addition to saving the simulated phenotype for us, we can also examine the simulated effect sizes and the \n",
    "results of the simulation from the spike-and-slab prior. To be specific, the package records which mixture \n",
    "component each variant was assigned to, its per-SNP heritability, its sampled effect size ($\\beta$), and whether it comes from the a non-spike mixture component (`Causal` column):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "d3cca6ad",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-04-12T16:10:22.561921Z",
     "start_time": "2024-04-12T16:10:22.275956Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>CHR</th>\n",
       "      <th>SNP</th>\n",
       "      <th>A1</th>\n",
       "      <th>A2</th>\n",
       "      <th>MixtureComponent</th>\n",
       "      <th>Heritability</th>\n",
       "      <th>BETA</th>\n",
       "      <th>Causal</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>22</td>\n",
       "      <td>rs131538</td>\n",
       "      <td>A</td>\n",
       "      <td>G</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>22</td>\n",
       "      <td>rs9605903</td>\n",
       "      <td>C</td>\n",
       "      <td>T</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>22</td>\n",
       "      <td>rs5746647</td>\n",
       "      <td>G</td>\n",
       "      <td>T</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>22</td>\n",
       "      <td>rs16980739</td>\n",
       "      <td>T</td>\n",
       "      <td>C</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>22</td>\n",
       "      <td>rs9605923</td>\n",
       "      <td>A</td>\n",
       "      <td>T</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>295</th>\n",
       "      <td>22</td>\n",
       "      <td>rs12160031</td>\n",
       "      <td>A</td>\n",
       "      <td>G</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>296</th>\n",
       "      <td>22</td>\n",
       "      <td>rs5749022</td>\n",
       "      <td>C</td>\n",
       "      <td>G</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>297</th>\n",
       "      <td>22</td>\n",
       "      <td>rs5749028</td>\n",
       "      <td>G</td>\n",
       "      <td>A</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>298</th>\n",
       "      <td>22</td>\n",
       "      <td>rs4819996</td>\n",
       "      <td>A</td>\n",
       "      <td>G</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>299</th>\n",
       "      <td>22</td>\n",
       "      <td>rs9606682</td>\n",
       "      <td>T</td>\n",
       "      <td>C</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>300 rows × 8 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     CHR         SNP A1 A2  MixtureComponent  Heritability  BETA  Causal\n",
       "0     22    rs131538  A  G                 0           0.0   0.0   False\n",
       "1     22   rs9605903  C  T                 0           0.0   0.0   False\n",
       "2     22   rs5746647  G  T                 0           0.0   0.0   False\n",
       "3     22  rs16980739  T  C                 0           0.0   0.0   False\n",
       "4     22   rs9605923  A  T                 0           0.0   0.0   False\n",
       "..   ...         ... .. ..               ...           ...   ...     ...\n",
       "295   22  rs12160031  A  G                 0           0.0   0.0   False\n",
       "296   22   rs5749022  C  G                 0           0.0   0.0   False\n",
       "297   22   rs5749028  G  A                 0           0.0   0.0   False\n",
       "298   22   rs4819996  A  G                 0           0.0   0.0   False\n",
       "299   22   rs9606682  T  C                 0           0.0   0.0   False\n",
       "\n",
       "[300 rows x 8 columns]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Get the simulated BETAs:\n",
    "effect_table = sim.to_true_beta_table()\n",
    "\n",
    "# Display the table of effect sizes:\n",
    "display(effect_table)\n",
    "\n",
    "# Plot the distribution of simulated BETAs:\n",
    "plt.hist(effect_table.BETA, bins=30)\n",
    "plt.xlabel(\"Simulated BETA\")\n",
    "plt.title(f\"Distribution of variant effect sizes\\n Spike-and-slab model ($h^2={sim.h2}$; $M={sim.n_snps}$; $\\pi={sim.pi}$)\");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f163d0b4",
   "metadata": {},
   "source": [
    "### Train / test split\n",
    "\n",
    "One useful feature that `magenpy` provides is to allow us to split the simulated data into independent training \n",
    "and test sets, which we can use for robustly evaluating the predictive performance of PRS models. This can be done \n",
    "by simply invoking the `.split_by_samples()` method on the simulated data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "8eb4e95b",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-04-12T16:10:23.348470Z",
     "start_time": "2024-04-12T16:10:23.309070Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of samples in training set: 272\n",
      "Number of samples in the test set: 106\n"
     ]
    }
   ],
   "source": [
    "# Set random seed:\n",
    "np.random.seed(7209)\n",
    "\n",
    "# Split the simulated data into 75% training and 25% testing:\n",
    "train, test = sim.split_by_samples([0.75, 0.25])\n",
    "\n",
    "# Print the number of samples in the training and test sets:\n",
    "print(\"Number of samples in training set:\", train.n)\n",
    "print(\"Number of samples in the test set:\", test.n)\n",
    "\n",
    "# To streamline following steps, extract input / output data:\n",
    "\n",
    "# Training data:\n",
    "X_train = train.genotype[22].to_numpy()\n",
    "y_train = train.sample_table.phenotype\n",
    "\n",
    "# Test data:\n",
    "X_test = test.genotype[22].to_numpy()\n",
    "y_test = test.sample_table.phenotype"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4ae06346",
   "metadata": {},
   "source": [
    "## (3) Inference of Polygenic Risk Scores (PRS) from Individual-level Data\n",
    "\n",
    "Now that we understand better the concepts underlying polygenic risk scores, let us turn to how we might go \n",
    "about estimating them from biobank data. **In practical terms, inferring polygenic scores means obtaining an estimate for the weights of the linear model $\\beta$**. \n",
    "\n",
    "### (3.1) Multiple Linear Regression\n",
    "\n",
    "The straightforward approach for performing inference in this context is to simply **fit a linear model to paired genotype and phenotype data**. The optimal $\\beta$s are those the minimize the **mean squared error** across across individuals in the training set:\n",
    "\n",
    "$$\n",
    "MSE = \\frac{1}{N} \\sum_{i=1}^N (y_i - X_i\\beta)^2\n",
    "$$\n",
    "\n",
    "How is this achieved in practice? Solving the above objective function for the $\\beta$s gives a closed-form solution:\n",
    "\n",
    "$$\n",
    "\\hat{\\beta} = (X^\\top X)^{-1}(X^\\top y)\n",
    "$$\n",
    "\n",
    "In `python`, this can be done in a variety of ways, but here we will show you how to do it using the popular `scikit-learn` package. `scikit-learn` provides a variety of interfaces for fitting \n",
    "linear models to data, all of them under than `sklearn.linear_model` module. \n",
    "\n",
    "Let's start by first fitting a simple linear model to our data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "85ba85f3",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-04-12T16:10:25.008026Z",
     "start_time": "2024-04-12T16:10:24.487063Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Import the LinearRegression module:\n",
    "from sklearn.linear_model import LinearRegression\n",
    "\n",
    "# ------------ Model fitting ------------\n",
    "# Initialize the LinearRegression object:\n",
    "prs_lm = LinearRegression()\n",
    "# Fit the model to the training data:\n",
    "prs_lm.fit(X_train, y_train)\n",
    "\n",
    "# ------------ Evaluation ------------\n",
    "\n",
    "def plot_scatter(true, pred, title=None):\n",
    "    \"\"\"\n",
    "    Helper function to plot the PRS vs. phenotype \n",
    "    and display the R-Squared metric.\n",
    "    \"\"\"\n",
    "    \n",
    "    from scipy.stats import linregress\n",
    "    b, a, r_val, _, _ = linregress(true, pred)\n",
    "    \n",
    "    x = np.linspace(true.min(), true.max(), 100)\n",
    "    \n",
    "    # Add zero lines:\n",
    "    plt.axvline(0., ls='--', color='gray')\n",
    "    plt.axhline(0., ls='--', color='gray')\n",
    "    # Plot true vs. predicted:\n",
    "    plt.scatter(true, pred)\n",
    "    \n",
    "    # Plot the fitted line:\n",
    "    plt.plot(x, x*b + a, label=f\"$R^2 = {round(r_val**2, 2)}$\", c='red')\n",
    "    \n",
    "    # Add labels / title:\n",
    "    plt.xlabel(\"True Phenotype\")\n",
    "    plt.ylabel(\"PRS (Predicted Phenotype)\")\n",
    "    plt.legend()\n",
    "    if title is not None:\n",
    "        plt.title(title)\n",
    "\n",
    "# Predict on the test set:\n",
    "prs_lm_pred = prs_lm.predict(X_test)\n",
    "\n",
    "# Let's compare the model prediction to the simulated phenotypes:\n",
    "plot_scatter(y_test, prs_lm_pred, title=\"LinearRegression Model\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "50f79915",
   "metadata": {},
   "source": [
    "As we see in the example above, a major limitation of the using the vanilla linear model outlined above is that, given the high-dimensionality of genetic data and the strong correlations (Linkage-Disequilibrium - LD) between genetic variants, the solution often becomes becomes ill-defined. This usually happens in general regression contexts where the number of features is much larger than the number of samples and where the features can be highly correlation with each other (**multicollinearity**).\n",
    "\n",
    "**Intuition**: Why the solution fails? Recall the solution to the system of linear equations is:\n",
    "\n",
    "\n",
    "$$\n",
    "\\hat{\\beta} = (X^\\top X)^{-1}(X^\\top y)\n",
    "$$\n",
    "\n",
    "This solution assumes that the $X^\\top X$ matrix (e.g. LD matrix) is invertible. However, when the number of features is much larger than the number of samples or there are highly correlated features, this matrix is no longer invertible, as we can verify with `numpy`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "691397d6",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Attempt to invert the X'X matrix:\n",
    "np.linalg.inv(X_train.T.dot(X_train))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f7821383",
   "metadata": {},
   "source": [
    "### (3.2) Regularized Linear Regression\n",
    "\n",
    "A standard way to resolve these issues with the linear model in practice is to use **regularization techniques**, such as **Ridge regression** or the **Lasso**. Regularization provides a way to incorporate preference for sparse or small effect sizes when solving for the optimal $\\beta$S. This is typically done by adding a \"penalty\" on the values of the effect sizes to the optimization objective:  \n",
    "\n",
    "$$\n",
    "\\text{Ridge objective:} \\frac{1}{N} \\sum_{i=1}^N (y_i - X_i\\beta)^2 + \\alpha \\underbrace{\\sum_{j=1}^M \\beta^2_j}_{Penalty}\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\text{Lasso objective:} \\frac{1}{N} \\sum_{i=1}^N (y_i - X_i\\beta)^2 + \\alpha \\underbrace{\\sum_{j=1}^M |\\beta_j|}_{Penalty}\n",
    "$$\n",
    "\n",
    "Here, the parameter $\\alpha$ determines the strength of the penalty. Larger $\\alpha$ will tend to impose stronger shrinkage on the effect sizes. In `scikit-learn`, fitting regularized models can be done in very similar ways to what we have seen before:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "b1425b97",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-04-12T16:10:26.973476Z",
     "start_time": "2024-04-12T16:10:26.374533Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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IiYnRtunevTtUKlWF91WrVq1SIyWmeHiLAiGEUdsWTJw4ESdPnsS+ffv0rh80aJD297Zt2yIiIgJNmjTBqlWrMGXKFLP7SbYX2SYQA0IDWFGYHJ5mdHHC98cgA/QCG2uPLlLlcPpJAo4fP45u3bqhadOmCAsLw8KFC/HZZ5+VShI2hrnTT3Xq1IG7u3upUZmcnJxSozcPe/3117Fp0yYkJibikUceKbdt1apV0bZtW1y4cMHk50b25+4mQ0ST2ojq0AARTWrzS4EclmZ0MUCuP8UUIPfBolGdOLrooDhSY4ivr3rExF6PbaS0tDTcvn1bb8omNDQUTZs2xerVq/Hee++Z9NDmTj95eXmhc+fO2LFjB4YNG6a9fseOHYiKiirzfoQQeP3117Fhwwbs3r0bISEhFfavsLAQZ86cQY8ePSpsS0RUGRxddD4MagyRyUyaArKX5ORkeHh4oHnz5nrXDxgwABs2bDA5qKnM9NOUKVMwevRohIWFISIiAkuXLkVGRgbGjx+vbfO///0PGzZswM6dO/Haa6/hxx9/RHx8PPz8/LSjPHK5HFWqVAEATJ06FUOGDEHDhg2Rk5ODjz/+GPn5+RgzZoxZfSQiMoVmdJGcA4MaJ3fs2DE0b94cXl5eetcPGDAACxcuxLVr1yqc0rGUZ599Fjdv3sSHH36IrKwstGnTBtu2bUNwcLC2zY0bN3Dp0iUA0C717t27t979xMXFafOBrl27hueeew43btxA3bp1ER4ejoMHD+rdJxEREQDIhBAuUxIxPz8fcrkceXl5qF69ut6xgoICpKena6vhkvPi35I0iouL8fPPPwMAhg8fzqrCRE6qvO/vkvgfTkSS5eHhgeeff97e3SAiG+HqJyIiIpIEBjVEREQkCZx+IiLJKioqwrx58wCoV9I9nFBPRNLCoIaIJE2hUNi7C0RkI5x+IiIiIklgUPMQF1rhLln8GxIRuSYGNf/w9PQEANy3187cZDGav6Hmb0pERK6BOTX/cHd3R40aNZCTkwMA8PX1NWp3aXIcQgjcv38fOTk5qFGjBtzd3e3dJSIisiGnCWoWLVqERYsW4fLlywCA1q1bY8aMGRg0aJDFHiMgIAAAtIENOacaNWpo/5ZEROQ6nCaoeeSRR/DJJ5+gadOmAIBVq1YhKioKx48fR+vWrS3yGDKZDIGBgfD39+eKCSfl6enJERrSkslk2n3COPJKJH1OvfdTrVq18Pnnn+PFF180qr2xe0cQERGR45D03k9KpRJr167FvXv3EBERYbBdYWEhCgsLtZfz8/Nt0T0iIiKyA6da/fTnn3+iWrVq8Pb2xvjx47FhwwaEhoYabD937lzI5XLtT1BQkA17S0RERLbkVNNPRUVFyMjIwO3bt7Fu3TosW7YMe/bsMRjYlDVSExQUxOknIhdRVFSEBQsWAAAmT57MbRKInJQkp5+8vLy0icJhYWE4cuQIFixYgCVLlpTZ3tvbG97e3rbsIhE5GNaeInIdTjX99DAhhN5IDBEREbkupxmpee+99zBo0CAEBQXhzp07+Omnn7B7924kJCTYu2tERETkAJwmqPnrr78wevRoZGVlQS6Xo127dkhISMCAAQPs3TUiIiJyAE4T1CxfvtzeXSAiIrIrpUrgcPot5NwpgL+fD7qE1IK7GwtLajhNUENEROTKEk5lIXZzKrLyCrTXBcp9MHNIKCLbBNqxZ44TbDGoISLJkslkqF+/vvZ3cm2O8sVrjoRTWZjw/TE8XIMlO68AE74/hkWjOtktsHGkYMup6tRUFrdJICJyTY70xWsqpUqg+6e79PpekgxAgNwH+97ta/MgzVCwpemFpYItY7+/nXpJNxG5HqVKIOnSTcSnXEfSpZtQqlzmvIzMpPnifTgo0IxyJJzKslPPjHM4/ZbBgAYABICsvAIcTr9lu05B/b8Yuzm1VECj6RMAxG5Oten/KKefiMhpOPPZNtlHRV+8Mqi/eAeEBjjsVFTOHcMBjTntLMWUYCuiSW2b9IkjNUTkFMw521YoFPjqq6/w1VdfQaFQ2Kqr5EAcdZTDFP5+PhZtZymOGGwxqCEih2fuMLcQAnl5ecjLy4MLpQ9SCY74xWuqLiG1ECj3gaFxJBnUI5ZdQmrZslsOGWwxqCEihyeFs22yD0f84jWVu5sMM4eoN25+OLDRXJ45JNTm02eOGGwxqCEihyeFs22yD0f84jVHZJtALBrVCQFy/eArQO5jt+XcjhhsMVGYiByeFM62yT40X7wTvj8GGaA3hWnPUQ5zRLYJxIDQAIeqtaMJth5O4A+wUwI/gxoicnias+3svIIy82o0dToc/Wyb7MPRvngrw91NZrOVRMZypGCLQQ0ROTwpnW2TfTjSF68UOUqwxaCGiJyCOWfbMpkMdevW1f5Ors1RvnjJerhNAhE5FWfev4eIzGPs9zdHaojIqfBsm4gM4ZJuIiIikgSO1BCRZCkUCnzzzTcAgJdffhmenp527hERWRODGiKSLCEEcnNztb8TkbRx+omIiIgkgUENERERSQKDGiIiIpIE5tQQEdkB6+0QWR6DGiIiG0s4lVWqMnKgE+5DRORoOP1ERJIlk8kgl8shl8sdZpuEhFNZmPD9Mb2ABgCy8wow4ftjSDiVZaeeETk/bpNARGQjSpVA9093lQpoNDS7je97ty+noohKMPb7myM1REQ2cjj9lsGABlDvPp6VV4DD6bds1ykiCWFQQ0RkIzl3DAc05rQjIn1MFCYiyVIoFFi5ciUAICYmxu7bJPj7+Vi0HRHpY1BDRJIlhEBmZqb2d3vrElILgXIfZOcVoKzeaHJquoTUsnXX6CFccu+cGNQQEdmIu5sMM4eEYsL3xyAD9AIbzdflzCGh/PK0My65d17MqSEisqHINoFYNKoTAuT6U0wBch8sGtWJX5p2xiX3zo0jNURENhbZJhADQgM4vWEFlZk2UqoEYjenljk1KKAeTYvdnIoBoQH8WzkoBjVERHbg7iZDRJPa9u6GpFR22siUJff82zkmTj8REZHTs8S0EZfcOz8GNUQkab6+vvD19bV3N8iKKpo2AtTTRkpV+SvguOTe+XH6iYgky8vLC2+//ba9u0FWZqlpIy65d34cqSEiIqdmqWkjzZJ7QLfEXoNL7p2D0wQ1c+fOxaOPPgo/Pz/4+/sjOjoa586ds3e3iIjIziw5bcQl987Naaaf9uzZg9deew2PPvooiouL8f7772PgwIFITU1F1apV7d09InJACoUCP/zwAwBg5MiRdt8mgazD0tNGXHLvvJwmqElISNC7HBcXB39/fyQnJ6Nnz5526hUROTIhBK5cuaL9naTJGpWaueTeOTnN9NPD8vLyAAC1ajFhi4gck1IlkHTpJuJTriPp0s0KV9+Q+ThtRIATjdSUJITAlClT0L17d7Rp08Zgu8LCQhQWFmov5+fn26J7RETcP8gOOG1EThnUTJw4ESdPnsS+ffvKbTd37lzExsbaqFdEJAWW2J1ZUwju4XEZTSE4jhxYj62mjbiLt2NyuqDm9ddfx6ZNm/DHH3/gkUceKbft9OnTMWXKFO3l/Px8BAUFWbuLROSkLDG6wv2DpI+jcI7LaXJqhBCYOHEi1q9fj127diEkJKTC23h7e6N69ep6P0REZbHU7symFIIj58NdvB1bpYKakvkq1vbaa6/h+++/x48//gg/Pz9kZ2cjOzsbDx48sFkfiMj5eHp6VriU25wy+4aSgLl/kHRZajsGsh6Tpp+2b9+O1atXY+/evcjIyIBKpYKvry86deqEgQMHYuzYsahfv75VOrpo0SIAQO/evfWuj4uLQ0xMjFUek4icm5eXF957770K25laZr+86QfuHyRd3MXb8Rk1UrNx40a0aNECY8aMgZubG95++22sX78e27dvx/Lly9GrVy/8/vvvaNy4McaPH4/c3FyLd1QIUeYPAxoiqixTRlcqmn74+14hAuU+pcrsa8igDoC4f5Dz4Sic4zNqpGbOnDmYN28ennjiCbi5lY6Dhg8fDgC4fv06FixYgG+//RZvvfWWZXtKRGQEc1alGDtqUqeaN6auPVFuEvBHW8/ggydC8dqPlisER46Bo3COz6ig5vDhw0bdWYMGDfDZZ59VqkNEROZ6eFrIHSpE+qajeb1qeO3FF+DhUfZHnrFl9iFg1PRDzapeWDSqU6kpqgCukHFq3MXb8Zm9pLuoqAjp6elo0qSJwQ8KIiJbKas2jAwC/uJv3M7+G9tPZeKJDg3LvK2xZfZv3DNucUTOnQJEdWjAQnASY43tGMiyTF79dP/+fbz44ovw9fVF69atkZGRAQCYNGkSPvnkE4t3kIioIuWtStGYu+1suatSjCmzb+r0g6YQXFSHBohoUptfdhLA7Rgcm8lDLNOnT8eJEyewe/duREZGaq/v378/Zs6ciWnTplm0g0REFaloVQoAZOdXvCqlojL7nH4ggNsxODKTg5qNGzdizZo1CA8Ph0ym+wOGhobi0qVLFu0cEZExLLkqpbwy+448/cCy/bbFXbwdk8lBTW5uLvz9/Utdf+/ePb0gh4jIVmy5KkUz/eBIScAs20+kZnJQ8+ijj2Lr1q14/fXXAUAbyHzzzTeIiIiwbO+IiIxQ0bQQAARUt9y0kCNNP3DzTCIdk4OauXPnIjIyEqmpqSguLsaCBQtw+vRpJCUlYc+ePdboIxFRucqbFtKYPrilRYMOR5h+4OaZRPpMXv3UrVs37N+/H/fv30eTJk3w22+/oV69ekhKSkLnzp2t0UciogqVtSqlGO5I8OqOrk//2+BybmfGzTOJ9JlVYKZt27ZYtWqVpftCRFQpjjQtZAss20+kz6ygRqlUYsOGDThz5gxkMhlatWqFqKgoFuEjIrtzhGkhW2HZfiJ9Jkchp06dQlRUFLKzs9GiRQsAwPnz51G3bl1s2rQJbdu2tXgniYjMUVxcjA0bNgAAhg0b5tAnXuYsyWbdHCJ9Jv+Hv/TSS2jdujWOHj2KmjVrAgD+/vtvxMTE4N///jeSkpIs3kkiInOoVCqkpqYCAKKiouzcG8PMXZLtyHVziOzB5EThEydOYO7cudqABgBq1qyJ2bNnIyUlxZJ9IyKSPM2S7IcTfjVLshNOZZV7e5btJ2MoVQJJl24iPuU6ki7dLHfLEGdm8khNixYt8Ndff6F169Z61+fk5KBp06YW6xgRkdRZakm2qyVIk2lcqTijySM1c+bMwaRJk/DLL7/g2rVruHbtGn755Re88cYb+PTTT5Gfn6/9ISIiwyy5JJubZ1JZKjsS6GxMHql58sknAQDDhw/XVhMWQn2eMWTIEO1lmUwGpVJpqX4SEUkOl2STNdm8OKNKBRw9Cjz6KGCnbZNMDmp27drFPZ7IpXHjQLIULskmazJlJNDsMgiFhcCuXcDGjUB8PPDXX8CJE0C7dubdXyWZHNT07t3bCt0gcg6uNDdN1scl2WRNVhsJvH0b2LZNHcRs2wbcvas7JpcDFy44T1ATEhKCsWPHIiYmBg0bSq/sOJEh3DjQ+Xh6emL69Ona3x0Nl2STNVl0JPDaNWDTJvWITGIiUFysO1a/PhAdrf7p1Qvw8jKnuxZhcqLwlClTEB8fj8aNG2PAgAH46aefUFhYaI2+ETmMiuamAfXctFSXSTormUwGLy8veHl5Oey0udSXZLvKUmJHpBkJNPTOl0E90lzmSKAQwOnTwOzZ6hyZoCDgtdeAHTvUAU1oKDB9OnDoEHD1KvD118CAAXYNaABAJjRZviY6ceIEVqxYgdWrV6O4uBjPP/88xo0bh06dOlm6jxaTn58PuVyOvLw8VK9e3d7dISeSdOkmnvvmYIXtVr8c7jIl+smypJirxela+9OMMANljwTqBc5KJXDwoHo0ZuNG4OLFEjeQARERwLBhQFQU0KyZDXqvY+z3t9lBjYZCocDChQvx7rvvQqFQoE2bNpg8eTLGjh3rcGdGDGrIXPEp1zH5p5QK2y0Y0QFRHRpYv0MuztgAoLi4GFu2bAGgXrnpyNskSI2h6doyv0zJqsoNLpvWBHbuVAcxmzYBOTm6G3p7A/37q6eVhgwB6tWzed81jP3+Nvs/XKFQYMOGDYiLi8OOHTsQHh6OF198EZmZmXj//ffx+++/48cffzT37okcClepOA5Tzv5VKhVOnDgBABg8eLBN++nKbL6UmMr1cHHGQFUBwk4dgNusRUBCAnDvnq5xjRrAE0+oR2MiIwE/P3t12ywmBzXHjh1DXFwcVq9eDXd3d4wePRpffvklWrZsqW0zcOBA9OzZ06IdJbInrlJxDEzWdg42WUpMJnG/fg0Rv8arR2T27NFP9H3kEXUQM2wY0LMn4IBJ9cYyOah59NFHMWDAACxatAjR0dFlrigIDQ3FiBEjLNJBIkfAVSr2x7N/58Gigg5Ak+iryY9JTtY/3qaNbsVSp052K5ZnaSYHNWlpaQgODi63TdWqVREXF2d2p4gckWaVysNTHwFMfLQJnv07D2tP10oxqdoilEogKUkXyFy6pDsmkwGPPaYOYqKioGzcRPcapt2SzGtoclDTp08fHDlyBLVr639o3L59G506dUJaWprFOkfkaLhxoP3w7N95WHO6liuqHvLggXqZdXw8sHkzkJurO+btrV5mHRUFDB0K+PsD+Oc1/HSXJF9Dk4Oay5cvl7mnU2FhIa5fv26RThE5Ms3GgWRbTNZ2HtaarmVO1T9u3gS2blWPxmzfDty/rztWo4Z6pVJ0NDBwIFCtmt5Npf4aGh3UbNq0Sfv79u3bIZfLtZeVSiV27tyJRo0aWbRzREQaTNZ2LpaernX5nKorV9SjMRs3An/8oZ5q0ggK0uXH9OhhMNHXFV5Do4Oa6OhoAOoKnWPGjNE75unpiUaNGuGLL76waOeIiEoa8WgQvvz9QqnrDZ39e3p6YurUqdrfybYsOV3rcjlVQgAnT+ryY1JS9I+3bavNjzE20dcVXkOjgxqVSgVAvffTkSNHUKdOHat1ioiopLLyKEoydPYvk8lQtWpVW3SRDLDUdK1L5FQVFwP79+sCmcuXdcfc3IDu3XWBTOPGJt+9K7yGJufUpKenW6MfRERlMpQDoPFm/+aY2Lep0w6Xk3Ekm1N1/7460XfjRnWi782bumM+PsDjj6sDmSefBCo5mCDZ17AEsyoK79mzB/PmzcOZM2cgk8nQqlUrvP322+jRo4el+0dELqy8HABAPe3005EMTOzbtMzjxcXF2L59OwDg8ccf5zYJTszaOVU2XSZ+8yawZYsu0ffBA92xWrXUib5RUepEXwuONLpCXprJ/+Hff/89xo4di6eeegqTJk2CEAIHDhxAv379sHLlSjz//PPW6CcRuaDK5gCoVCocPXoUADBgwABrdZMqyZiAwpoFMG2yTDw9XZ3oGx+vTvT9J6UDABAcrKvo2707YKXg2xWKiJr8ys2ePRufffYZ3nzzTe11kydPxvz58/HRRx8xqCEiizE1B+DhL8cODapVcEuyN1MCCmsUwLTaEmchgBMndPkx/+xBptWhgzqQiY4G2re3WUVfqRcRNXmXbm9vb5w+fRpNm+oP9168eBFt2rRBQYHjJhhxl24i55J06Sae++Zghe1WvxyOvAdFpT6oH6nuiQGKJADA9OnT4eXlZbW+kunM3cnbUlNFSpVA94eK0D3cjwC5D/a929e4+y8uBvbuVQcx8fHqZdgabm7qfZU0ib52LoHibFWZrbZLd1BQEHbu3FkqqNm5cyeCgoJM76kJ/vjjD3z++edITk5GVlYWNmzYoF1qTkTSY2wOwN/3CvHaj8dLtfkrvwCoYoOOkskqUzPFUiuqLLLE+d494Lff1IHMli3ArVu6Y1WqqBN9o6IskuhrSVItImpyUPPWW29h0qRJSElJQbdu3SCTybBv3z6sXLkSCxYssEYfte7du4f27dtj7NixePrpp636WERkf8bkAHzwRCg+2mr4y1FDqTJpUJqszBFqppi9xDk3V71SKT5eHdCUnKGoXRsYMgTKoVE42qwzsovd1CMhtWrB3YJ9p7KZHNRMmDABAQEB+OKLL/Dzzz8DAFq1aoU1a9YgKirK4h0sadCgQRg0aJBVH4OIHEtFOQDyKl7lfjlqHL3yN3q0CLBmV8kEjlAzxaQlzmlpuvyY/fv1E31DQnQVfbt1Q8LZXPX79dBJbROp7K3k6MxKsR42bBiGDRtm6b5YXGFhIQoLC7WX8/Pz7dgbIjJXeZVp41OM23Mu906B0+URSJkj1Ewpd3pTCLT56xKeyjiK8G3TgT//1D/eqZMuP6ZtW22ir9T3VnJ0Zq8bKyoqQk5OjrbSsEbDhg0r3SlLmTt3LmJjY+3dDSKyAEM5AOV96RXDDWsL2gIA5H8XlkoK5dmz/ThCzZSHpzfdlcV49NppDLxwEAPPH0SDOyV2vHZ3Vyf6DhumDmTK+K5zhb2VHJ3JQc2FCxcwbtw4HDhwQO96IQRkMlmZO3jby/Tp0zFlyhTt5fz8fKsnMxORbf19rwhuMqDslBkZ7glv1PD1xFc7L5Y6yrNn+3GUmimRjfywPiAb2d/+hIgzB1Gj4K72WHGVKvAYPFgdxDzxhLowXjkcIU/I1Zkc1MTExMDDwwNbtmxBYGAgZDZaW28Ob29veHt727sb5MI43WFdCaey8NqPhrdQ0DB0nGfP9mW3mik5OepE340bgR070LFEmkJhzdrI6xeJ2qOGw2PgAPUKJmPv1gHyhFydyUFNSkoKkpOT0bJlS2v0h0gybFKl1IVVtIUCAHjIVHix8X0kX/kbx9AAKriVasOzZ/uy5E7e5bp4Ub1aSZPoW7JEW+PG2mkl727d4O9u3jolR8gTcnUmBzWhoaG4ceOGNfpSobt37+LiRd0Qcnp6OlJSUlCrVi2HyuUhYrKg9VU01A8AEAJFmWfR1hNIKa4PVTlNefZsP1apmSIEcPSoLpA5fVr/eOfOuq0JWre2SEVfR8gTcnUmBzWffvop3nnnHcyZMwdt27aFp6en3nFrVuo9evQo+vTpo72syZcZM2YMVq5cabXHJTIFkwVtw9JBCM+eJaCoCNizR1fR93qJlXEeHkDv3upAJioKsEJ+paPkCbkyk4Oa/v37AwD69eund70tEoV79+4NE3d1ILI5JgvahqlBiKGvEZ49O7k7d4CEBHUgs3UrkJenO1a1KjBokC7Rt2ZNq3dH6nsrOTqTg5rExERr9INIMpgsaBtGDfVX9wEU+tfx7Nl5aRLv89Iz0OzQbjTe/ztkO39Xj9Bo+PvrRmP69QN8bD8CZ7M8ISrF5KCmV69e1ugHkWQwWdA2jBnqnz64JY7Gqze0/GpEB3z86wWePTupP7bsw8mvv0X4n/sw8PpZuJX8izdtqs6NiY4GunZV15SxM6nureTozCq+t3fvXixZsgRpaWlYu3YtGjRogO+++w4hISHo3r27pftI5FSYLGg7FQ31921eG0fj1dcNCA1AZLsgnj07C5VKnei7cSPurvkFPdMuoGeJwymBzbCjWQR2NO2KKW9EI7Jtfbt1lRyHyUHNunXrMHr0aIwcORLHjh3TbkNw584dzJkzB9u2bbN4J4mcCZMFbau8of6iktMS4NmzwysqAnbv1iX6ZmYCAKoBULi5I6lhO/zWPAI7mnbBX37qHa9lAGK3nMGA1oH8nyLIhImZtx07dsSbb76JF154AX5+fjhx4gQaN26MlJQUREZGIjs721p9rbT8/HzI5XLk5eVZdZUWEcA6NY5ACIHcXHWp+7p16zp0sVCXlZ8P/PqrOojZulV9WaNaNdzo2Q8fujfH7sadke9TzeDdrH45nAGrhBn7/W3ySM25c+fQs2fPUtdXr14dt2/fNvXuiCTL1ZMFHaGaskwmg7+/v00fk4yQlQVs2qQekdm5E1CUyOauV0+d5BsdDfTti/1nbmDTTykV3iUT7wkwI6gJDAzExYsX0ahRI73r9+3bh8aNG1uqX0SS4KrTHRylolLOnlUHMRs3AocO6R9r3lwdxGgSfd10lZ+ZeE+mMDmoeeWVVzB58mSsWLECMpkMmZmZSEpKwtSpUzFjxgxr9JGInIgjVVNWKpXYu3cvAKBHjx5wd4BVMS5DpQIOH9YFMufO6R/v0kW3YqmcbXeYeE+mMDmoeeedd5CXl4c+ffqgoKAAPXv2hLe3N6ZOnYqJEydao49E5CQcrZqyUqnEnj17AADdunVz2aDGZlOBhYVAYqIu0bdkjqWnp7puTFQUMHQoUN+41UqOlnjvCNOqZJhZS7pnz56N999/H6mpqVCpVAgNDUW1aoYTuIjINbCasuOx+lRgXh6wbZs6iNm2TV3hV6N6dWDwYHUgM3iw+rIZHKVKL6dVHZ9ZQQ0A+Pr6IiwszJJ9IXI5UjvrYzVlx1LeVOD4749h3GONMCA0wPT33fXrukTfxET9RN/AQN1Gkb17A15eFngm9k+8d6RpVTLM5KDm3r17+OSTT7Bz507k5ORApdLf9zYtLc1inSOSMime9TGp03FUNBUIACv2X8aK/Zcrft8JoZ/oe/iw/vFWrXSBTFiYXqKvJdkr8d7RplXJMJODmpdeegl79uzB6NGjERgYyLoPRGaQ6lkfkzodR0VTgSWV+b5TqdSrlDSBzPnzuhvIZEB4OBAdDeWQoTjsVVc3egIZpJa5xGlV52FyUPPrr79i69ateOyxx6zRHyLJk/JZn6MldboyU6b4NO+7uetTMODyMbhvildPL/31l66Rl5c60Tc6GhgyBAgMVI82bkxFVt4lbTNnH20sC6dVnYfJQU3NmjVRqxbPsojMJfWzPkdJ6nR1xk7xVS+4i95pRzHw/EH0Tk+Ge9ED3UG5HHjiCXUgExkJ+PlpD1lqtNEZ8srqVPU2qh2nVe3P5KDmo48+wowZM7Bq1Sr4+vpao09Ekmbs2dyO1GynDGoA+yd1anh4eOCll17S/u5KypsKDMi/gQEXD2Lg+YMIv/onPFVK7bEHdeuhyjNPqwOZXr3KTPS11GijM+SVJZzKwqxNqeW24bSq4zDqv7xjx456uTMXL15EvXr10KhRI3h6euq1PXbsmGV7SCQxxp7Nrdh/GV1CajnMh7upKkrqtMUZupubGxo0aGDR+3QWelOBQqDZjSsYeOEgBlw4hPbZF/Tanq/dEDuadcX25hGY/p9RiGhWt9z7tsRoozPklRnqY0mcVnUsRgU10dHRVu4GkevQnEFXlMTpzLk1FSnrDL1WVS9Ed6hv3hJjKk2pROTtS9iVvRmemzfjkVuZ2kMqyHCsQUtsbxaBHc264nKtBrrRhiZ1KrzryuaYOENeWXl9LKledW/MGtra7gEYqRkV1MycOdPa/SByGZoz6PHflz+q6ey5NYYYOvu9da/I+CXGRlIqlTh48CAAIDw8XPoVhR88UG8QuXGjOtE3Nxch/xxSeXnjYvtwLKvdHruaPoobVWtqb2bqaENll+47Q16ZsavHvhjeAY81rTgQJNswaZJ57dq12LhxIxQKBfr3749///vf1uoXkaRFtgnEi481wvL9lytsK6UVFcae/WZZaApCqVTi999/BwA8+uij0gxq/v4b2LpVHcgkJAD37umO1agBPPkkEBUFt8hINK9WDX1PZWHv5lSgEknclV267wyriYx97Bt3C63cEzKF0UHN0qVLMX78eDRr1gw+Pj5Yt24d0tPTMXfuXGv2j0iy+ocGGBXUSGlFhSm1UwD7T0FUltXyhq5eVW9LsHEjsHs3oNQl+uKRR3SF8Hr2VO+5VIIlkrgru3TfGYo0OkMfqTSjg5r//ve/eP/99/HRRx8BAFauXInXX3+dQQ2RmVyxUJ2ptVPsPQVRGRZd2SMEcOqULpBJTtY/3raterVSdDTQsaO6OF45LFGZtzJL953hve8MfaTSjA5q0tLSMHbsWO3l0aNH49///jeys7MREBBglc4RSZkrFqoz56zWGaffLLKyR6kEDhzQVfQtuQWNTAZ0764OYqKigCZNLPsEjGTuqI8zvPedoY9UmtFBzYMHD/R24nZ3d4e3tzfu379vlY6RdDlDsS1bcbVCdRWd/ZbF2Yb3K7Wy58EDYMcO9YjM5s1Abq7umLc3MHCgOogZMgTw97fiszCeuaM+zvDed4Y+kj6TEoWXLVumF9gUFxdj5cqVqFNHl/k9adIky/WOJMcZim3ZmqMUqrOF8s5+H+asw/smr+y5eVOX6Lt9O1DyRLFmTXWib3S0OqAp8fkrBY703jd0suVIfaSKyYQQRp0wNWrUqMLNK2UymUPv0p2fnw+5XI68vDxUr17d3t1xOYaG5DXvKkcotkW2UVZwW5Kl3hNFRUXavL/p06fDq4zquJYWn3Idk39KKbdNg7wcLPa7irZHdwN//KGf6NuwoS4/pnv3Uom+ZHk82XJ8xn5/Gx3USAGDGvtRqgS6f7qr3C+xALkP9r3bl2dALkJzZvx7ajY2pFzHrXsK7TFLfaGoVCpkZGQAABo2bAg3Nzez+mjKGfr+Czcwcvkh/SuFQKvcdAw8fxADLxxE65yHTv7atdOtWOrQocJEX7Icnmw5B2O/v11rMxSyG2cotkW2pcnFiGhSG+89EWqV4X03Nzc0atTIrNuac/Zecp8gd5USYddSMfCCOpAJytPteK2UucGtR3fIhg1TBzMhIWXeH1mXM1Q2JtMwqCGbcIZiW6Rmj0RuSywxtiRzVi8lnMrCm3EH0P1yCt46fxD9Lh1GrQf52uMPPLyxN6QjfmsWjkHTXkS/Hm1s8EyoPDzZkh4GNWQTLGTlHKSWW6BUKpH8T02Xzp07G1VR2OSz9xs3oNq0GVXmLcOxC8moUqyrMHurSnXsbNIFO5p1xR8hHVGjthyzhrZGPyd8LaWIJ1vSw6CGbIKFrByfM+yabCqlUolff/0VANChQwejghpjzt7dr1xGxow5CNm3A9i7F24qFXr9c/yqvB52NFXveH30kVAo3XSPyX2CLMcSI4o82ZIeBjVkEyxk5diYW6CTnfeg9JVCoHVOGgb8kx8TmpOud/h2i9aIq9MevzUPx5m6IQYTfblPkGVYakSRJ1vSY1RQk5+fX3Gjf3BVERnCQlaOi7kFagmnsvDR1jMA1Im+Xa6exsALSRhw4SAeydcVwlPK3HC3SwTkzz0DREXhjNIPC745WOH984y/8iw5osiTLekxKqipUaNGhTVqNJQl6y0QPYSFrBwTcwvUX5ZTVhxAj/RjGHghCf0uHUGNgrva4w88vLGncSfsaBqOU526Y1vsMOCf920XleAZvw1YY0SRJ1vSYlRQk5iYqP398uXLmDZtGmJiYhAREQEASEpKwqpVq7i5JRnF0Va6kIvnFuTmQhW/CVW/WI5jF5PhU1ykPXSrSnX83rQLfmsWgX2N2qPA0wcyAIue7aT3pckzftuw1ogiT7akw6igplevXtrfP/zwQ8yfPx/PPfec9rqhQ4eibdu2WLp0KcaMGWP5XhKRVblcbkFamm6jyP374aZSocc/hzLk9bC9eQR2NAtHcoNWeom+tap6Ys6wtmWevfOM3/qsOaLIky1pMDlROCkpCYsXLy51fVhYGF566SWLdIqIbEvyIw1CQHb8uG6PpT//1Dt8u1VbLK/dDjuaheNs3UYGE30/eLJ1ucGJPc74XWmDWJceUSSjmBzUBAUFYfHixfjiiy/0rl+yZAmCgoIs1jEisi3JjTQoFPDYsweTLl5EtZ074Rkbqzvm7g706qXeXykqCmcUVfFfIxJ9A6pX/GVpyzN+qdUVqojLjSiSyUwOar788ks8/fTT2L59O8LDwwEABw8exKVLl7Bu3TqLd/BhCxcuxOeff46srCy0bt0aX331FXr06FHxDYmciL3Ovp0+t+DuXfVO1xs3Alu2wO32bdTUHPP1BQYNUgcygwcDtXRffM6Y6CvFukIVkfyIIlWaWRtaXr16FYsWLcLZs2chhEBoaCjGjx9v9ZGaNWvWYPTo0Vi4cCEee+wxLFmyBMuWLUNqaioaNmxY4e25oSU5A1c7+660nBxg82Z1ILNjB1BYohZM3brA0KHq/ZX69weqVDF4N5ogASj7y9KRggRX3yDWFv8jrjSt5wwkuUt3165d0alTJyxatEh7XatWrRAdHW3UyivNi5Kbm1vmi+Lm5gYPD93gVVFRUak2GjKZDJ6enma1VSgUMPSyW6stAHh5eZnVtri4GCqVyiJtPT09teUBrNVWqVSWW1rAlLYeHh7anZ1t0XZHajbe+ClF70tVCTdovloXPt8B/VrWNXi/7u7u2qq5KpUKxcXFdm0rhIBCobBI25L/n+L8eSjXr4fb5s2QJSVBVuK9LBo3hhg6FG5PPw1lly44efo0lEolWrdurX0spUrg6JW/kXunAP7VqyCiqT/c3WRIOJWFjzf9iez8EtNv1X0wfXBLDAgNcJjPiKMZ+Xjun+kydyhh6Kt25dgu6N4iwKj7BZzrM0KpEjh+7Q5y7xbC388HnYKqQ1bmOFvp+63o/3PnuRv4cMsZZOUVwA0quEHovQ9KsvVnREVtHeH/3hqfEVbdpXvv3r1YsmQJ0tLSsHbtWjRo0ADfffcdQkJC0L17d3PuskJFRUVITk7GtGnT9K4fOHAgDhw4UOZtCgsLUVjirE1TRPCLL76Aj0/pufFmzZrh+eef116eN2+ewRc7ODgYMTEx2ssLFizA/fv3y2xbv359vPzyy9rLX3/9NfLy8spsW7duXbz66qvay9988w1yc3PLbCuXy/HGG29oL69cuRKZmZlltvX19cXbb7+tvfzDDz/gypUrZbb19PTEe++9p738888/48KFC2W2BYCZM2dqf9+wYQNSU1MNtp0+fbr2A27Lli04ceKEwbZTp05F1apVAQDbt2/H0aNHDbadPHkyatSoAQDYuXMnkpKSDLadMGEC/P39Aajfy3v27DHY9qWXXkKDBg0AqKdZf//9d4Ntx4wZo90ROjk5WVuevyzPPfccmjdvDgD4888/ER8frz026qHBhMTCxrisqgUZgCWb9+HwhrMG7zcqKgodOnQAAFy8eBGrV6822HbQoEHo0qULACAjIwOrVq0y2LZ///547LHHAABZWVlYtmyZwba9evVC7969AQC5ubl6JyEPi4iIwMCBAwEAeXl5WLBgQdkNVSr0q1ED3W/cADZuhCw1Ve/D63r9+jjXsiXOtmiBXH9/tO/QAdHdu0NZVIRNmzYBALZu3VrmXacra+LtKq21Z/mH1i0FSv4NFMDR+CQcjXecz4gG3aK0l4d4n0FNt7JHbP6Iv4Du77ylvWypzwg3dw+899572pEL+35GqLed2Lp1q8U+IzYWtMbfQv0maOeRhY6eWXrvg5Ls8RnxsH/9619o3bo1AODMmTP45ZdfDLZ15s8IY5gc1Kxbtw6jR4/GyJEjcezYMW3QcOfOHcyZMwfbtm0z9S6NcuPGDSiVStSrV0/v+nr16iE7O7vM28ydOxexJZMDiZyYAHD7XhHgbe+e2IZbcTEaXbmClmfPosXZs6h+5472mPDwQFrDhjjXsiXOtWiBfLm8Uo9VMg/FGRi7usda0yWFxSp0/3SXZKdEnWb6gkoxefqpY8eOePPNN/HCCy/Az88PJ06cQOPGjZGSkoLIyEiDAUZlZWZmokGDBjhw4IC26B8AzJ49G9999x3Oni199lrWSE1QUBCnn0xsy+kn2wwtbzmZiXd+OVmqrRJuEP9MMMgg8MW/2uDJdvXLvF9nHVrWtN1+4Ay2fr4K/S8cRJ9LyaheeE/b9p6nD+707o+AF56FGDwYimrVDN6v5n+5qKhIOzX9xptT0PfLfch7oN8fARmUcNPmoex6s7vBYMBRPiPc3D3Q/dNdyM4rgFsZ008yAPWq++D3t3rDx9u8/3tN27KmRAFACfXfbdGoTujfsq4kPiMOpd/C2LjDKC4x5auZfiopbmwXdP0naZzTT5Vra/fpp3PnzqFnz56lrq9evTpu375t6t0ZrU6dOnB3dy8VNOXk5JQavdHw9vaGt3fp01ovLy+9fzJDjGljTtuSH17O0Lbkh7gztC35D+NMbQNr+qEY5d9GQIbAmn5Gvd/c3NyMfl9aq61MJqu4bXY2sGkTsDEefX/bgUil7gMu17cGdjTrit+ahSMpuD1q1a6Ofc+rk1+N/49Ti0u6ipsPVICB11hTjTbl+l2jl2Tb8zNCswpIBfcyE5v/M7StXkBT0f0qVQJJl27qJcYCwMe/XoDCwGum25agL7yM/B915M+IWw+Upf4HVXDDw6HSrQfKMv+ejvB54gj/9xb/jDCByUFNYGAgLl68qJ0X1Ni3bx8aN25sqX6V4uXlhc6dO2PHjh0YNmyY9vodO3YgKiqqnFsSOQeXqsFx/ryuou/Bg+rieAC8AKTVrI/fmoXjt2YRSKnfHKoSFX0rs6nmdwfLzg95mLPsb2XJukKGVhONeLShS210yuJ+zs/koOaVV17B5MmTsWLFCshkMmRmZiIpKQlTp07FjBkzrNFHrSlTpmD06NEICwtDREQEli5dioyMDIwfP96qj0tkC5KuwaFSAUeP6gKZM2f0j3fpgtQufTHpQUNcrB1ksKIvYH7QoZ52qvhs15m+sCxRV6i8ejdf/n7eqPtwlkCwIi51YiFRJgc177zzDvLy8tCnTx8UFBSgZ8+e8Pb2xtSpUzFx4kRr9FHr2Wefxc2bN/Hhhx8iKysLbdq0wbZt2xAcHGzVxyWyFUet6mtWzY6iImD3bnUQEx8PlFx14+EB9OkDDBumriPToAHyLt3ERSOq+loz6Kjh6+l0X1iVqWBc0a7XxnKmQLA8kj6xcBFm16m5f/8+UlNToVKpEBoaimrlJO05Chbfkz6pFMxypOdhUqGz/Hzg11/VQczWrerLGtWqqSv5RkerK/v+s7xWQ1NQrqKzZFMKyqlUKpw5cwbn/7qLKb/lahOuDXmzf3NM7t/MqPuWgqRLN7X1bswh1SJ/LIDpeKxWfG/cuHFYsGAB/Pz89K6/d+8eXn/9daxYscK8HtsAgxpp4weR5RmamtCrsltLqBN94+OBnTuBkisZAgLUIzHR0UDfvkAZiftlPR5g2aq+FQVMgHqUJvk/AyT15VyR+JTrmPxTilFtDY1cOFKlZUuy1ImFI52gODOrBTXu7u7IysrSFi/TuHHjBgICAspdxmVvDGqky6gvXwMfvOZ86LjCB1V5pfib3LyKgRcO4om0Q2hz9aFyCs2bq4OYYcOALl2Af5aaGstawamhgEljsUS/nMtj7EjNm/2b4acjV3nCYCKeaFmOxZd05+fnQwgBIQTu3LmjV5FXqVRi27ZtpQIdIluoKC9At+w0oFTgYc6Hjqt8UB1Ov6V9jjKhQofM8xh44SAGXjiIJreu6Tfu2lUdyERHAy1bVupxLbmppmb6CQAGhrYqM19Jin87YxmbGDuxbzNM7NtM8oG8JbnihqOOwOigpkaNGpDJZJDJZNrSzSXJZDJW7yW7KPnlWxZDy07N+dBxpQ+qGzfz0PvSUQy8cBD9Lx6C/72/tceK3DxwILg9fmsejl5TxuLxgZ0t+tiVSX4tqbi4WFsyfvr06c6/C7mFmZoYK4Vl27ZQmRMtqhyjg5rExEQIIdC3b1+sW7cOtWrpVgh4eXkhODgY9euXXeWUyJqMXU5asp05Hzou8UGVlwds2wZs3IhBW7dhyL272kP5Xr5IbPIodjTrit2Nw3DX2xcAMKRJIzt11jyWCpikwlFX3Dkzc0+0qPKMDmp69eoFAEhPT0fDhg215aaJ7M2cglnmfOhI9oPq+vV/KvpuBBITtYm+HgBy/Wojoam6ou/Bhm2hcNdVpGXNDungCJZlmXOiRZZhcp2aXbt2oVq1anjmmWf0rl+7di3u37+PMWPGWKxzRMYwp2CWOR86kvmgEgI4e1ZXCO/wYf3jrVpp82OSfRpgxo8p6puVaMKaHdLDESzLYWVi+zFtWQKATz75BHXq1Cl1vb+/P+bMmWORThGZQpMXAKBUFRJDX77mfOg49QeVSgUcOAC88w7QogUQGgq89546oJHJgIgI4NNP1cFOaiowZw7QpQsi2zXAolGdECDXf04Bch+80b85CotVSLp0E0oV9zUm0tCcaBkK92VQJ6hzlNPyTB6puXLlCkJCQkpdHxwcjIyMDIt0ishUpuYFmDO643Ql1AsKgF271KMxmzYBf/2lO+blBfTrp152PWSIup6MAQ9PTVy+cQ+rD2foldB35RVERA9jZWL7MTmo8ff3x8mTJ0ttaHnixAnUrs2hS7IfU/ICzPnQcYoPqr//Vif6xserK/ve1SX6Qi4HnnhCPbUUGQk8VECzPJqpiYRTWfjq9wsusfqLqDKYgG0fJgc1I0aMwKRJk+Dn54eePXsCAPbs2YPJkydjxIgRFu8gkSlMyQsw50PHIT+orl7VJfru3g2ULIDZoAEQFaUOZHr1Uo/QmMkZV3+5u7sjKipK+zuRLTEB2/ZMrihcVFSE0aNHY+3atfDwUMdEKpUKL7zwAhYvXgyvSnxoWhsrClNZnK6isBDA6dO6RN/kZP3jrVvrApnOnU2u6GuIsdVnV78cLsmEU1eoIk3kqCxeUVjDy8sLa9aswUcffYQTJ06gSpUqaNu2LXfKJqdlzqqP8m5jlS8/pRJIStIFMpcu6Y7JZEC3buogJioKaGadDRkls/rLREqVwP92XUTc/nTcfqDb18rZ84gYpJEUmRzUaDRv3rzMysLk2PhBZl0W3ULhwQP1BpGaRN/cXN0xb29gwAB1IPPkk0C9ehbpf3mccfWXSqXCxYsXAQBNmzaFmxn7UE1b/ydu31eUOubMeUSustUHuR6jgpopU6bgo48+QtWqVTFlypRy286fP98iHZMqewYV/CCzLotsoXDrFrB1qzqQ2b4duHdPd6xGDXUAExWlTvStVs3Cz6B8Trf6C+ptElavXg1AvU2CKdPjCaeyMP6fDTDL4qh5RBVxpa0+yPUYFdQcP34cin+qjB4/ftxgO1YZLp89gwp+kFlXpZJoMzLUq5U2bgT27FFPNWk88ohuo8iePQFPT9iLtVZ/OeLooebvWRFnqyLtjMneRKYwKqhJTEws83cynj2DCn6QWZ9JWyg0rgWcOqXLjzn20GhA27a6QKZjR3XOjIOw9Oqvygb6pgZExrav6O/5MGfJI5LsVh8OwBGDc1dkdk4NGc/eQQU/yKyvoi81N5USna+fQd1Zm4ADvwNpaSUOugGPPaZL9G3SxLqdrSRLLVOtbKBvakC0IzUbH/96waj2pgYpjpRHVB5XTfa2Nk7tOw6jgpqnnnrK6Dtcv3692Z2RKmsGFcacHfCDzPrK+lLzVhSix+UUDLyQhH4XD6P2g3zdQR8foH9/dUXfJ58E/P11f8uU6w5/plfZfYIqG+ibExC98VMKFHA3qr0pQYozlbt3xmRvR8epfcdiVFAjl8u1vwshsGHDBsjlcoSFhQEAkpOTcfv2bZOCH1diraDC2LMDfpBZnyaJtiA7B30vHsHAC0nocfk4fBWF2jb5VfxQ7V/D4DYsGhg4EKhaVXvMkmd6zjAMXplA35SA6OFjFbXXvE4VJUVryOAAVaRN4IzJ3o7M3qPwVJpRQU1cXJz293fffRfDhw/H4sWLtRU6lUolXn31VRa0M8AaQYUpZwf8ILOyy5fhHh+PLRt+hvzoQXgIlfbQtep1saNZOH5rFoGYd0bi8Y4NS93ckmd6zjIMXplA35SAqHNQxVtBlBVAlZcUrVHT1xNzn2rrUK9rRZxiqw8nwql9x2NyqdEVK1Zg6tSpeiXH3d3dMWXKFKxYscKinZMKS+/YWtHZAaA+O9DsnGzOLtZUDiGAEyeA2Fh1Im9ICPDGG6h95AA8hAoXAhpjQbcReCJmAbqPX4GlT0/GmPdjygxoTP1blkcTHD38IasJjhJOZZnxZK2jTjVvs9uZEhC5u7ujQdtuSCpqCKXB/8Cy71eTFP3wDuU1qnjizf7NcPQ/A5wqoNEw9LwC5D6cKjERp/Ydj8mJwsXFxThz5gxatGihd/2ZM2egUqkM3Mq1WfrsyJyzA4fcs8iZFBcD+/apVyvFxwOXL+uOubkB3bur82OiotA4uBG6pN9CIyOmfyx1pud0w+DGbs5SRjtTRj7d3d3Run0nfHy4yKj2D5Pq3j1SfV62xql9x2NyUDN27FiMGzcOFy9eRHh4OADg4MGD+OSTTzB27FiLd1AqLBlUmHt24MofZGblmdy/D2XCdtz84WfU2JkAr7zbumNVqgCPP65esfTEE0CdOtpD7oDRQ82WOtOz5TC4JXJ2btwrrLiRgXamTqdWdvq1sknRjkqqz8uWOLXveEwOaubNm4eAgAB8+eWXyMpSD2cHBgbinXfewVtvvWXxDkqJpYKKypwduLvJ0CWklrYPh9NvST6wMSnP5MYNYMsWYONGKLdvh3tBAfz/OXSrSnUcaBWB+i8MR6eXRwC+vpXum6XO9Gw1DG6pnJ3KvoeNHflUqVS4mpGBN8NrYNr2LACyCkdKnSHRmhwDc5Qcj8m7dJeUn69eouosCcJS2aVbqRLo/umuCs8O9r3bt9Q/k7MkklqKoSRczauyaFQnRFYt0E0r7d0LlJhGvSqvhx1Nu2J78wgcfSQUKjd33e0s8HpV5m9Zki120DbqtTTyNbHE8zbmvVxUVIS5c+cCAMKixlZYp8bV/j/sRWqBI9831mfs97dZQU1xcTF2796NS5cu4fnnn4efnx8yMzNRvXp1VLPxfjSmkEpQA+i+YICyzw7K+oKx5JeSM9B8cZaalhECrXPSMPD8QQxOO4Rm2Wn6hzt0wLLa7bC+YRjO1A0pVdHX2EDDWOb8LR9mqeCoovs3NMVlzv1b6nmX9+VYMqiZPn063D08DbZ3tf8Pe5FqACC1QM3RGPv9bfL005UrVxAZGYmMjAwUFhZiwIAB8PPzw2effYaCggIsXry4Uh0n45iao+N0iaQWUDLPxENZjEevncbACwcx4MJBPJKv2/FauLtD1rOnOj9m6FAcVPphdjmjHpZepmmJfCtrD4NbI2envOf9wROtIK/ihfgKChGamhdiqL0r/n/Yg5QL1TFHyTGYHNRMnjwZYWFhOHHiBGrX1v0Bhw0bhpdeesminaPymZKj44r1FG7m3MLj5w6oK/peOoIaBXe1xx54eOOPkI7Y3jwC/aeOw+DebbTHclKuG3X/llymaYl8K2uucLNWzk5Zz/vve0X4aKttz+Rd8f/D1hg4ki2YHNTs27cP+/fvh5eXl971wcHBuH7duC8Dshxjzw5cpp5CTg6weTMQH4/Bv+3Ak4W653OrSnX83rQLfmsWgX2N2qPAU52E+kyQ/helvZZpWuJMz1or3Kz5mpR83gmnsvDaj7Y/k3eZ/w87YuBItmByUKNSqaBUKktdf+3aNfj5VVy9k+xD0vUULl3S7Xi9f7+6OB7UlSWv1QpEQpOu+K1ZOJIbtILSTVc00tByS2dfpmmNYXBbvCb2PJOX9P+Hg2DgSLZgckXhAQMG4KuvvtJelslkuHv3LmbOnInBgwdbsm9kQZauamxXQgDJycAHHwBt2wJNmwJTp6qL4wkBdO4MfPgh8OefOLX7KGb3fQlHgtqUCmiAsvNMTK3ArFQJJF26ifiU60i6dNOo6r/OxhZVqU05k7c0Sf1/OCgGjmQLJo/UzJ8/H3379kVoaCgKCgrw/PPP48KFC6hTpw5Wr15tjT6SBTh9PQWFAtizR73sOj4euHpVd8zdHejVS13Rd+hQoKFuO4JIAItGyUzOMzE2P0WqKznKYu2q1NY4k3d3d0f//v21vxts5+z/H07A2UdAyTmYtaT7wYMH+Omnn5CcnAyVSoVOnTph5MiRqFKlijX6aDFSWtJtLlO/hO26TPHuXSAhQT2ttHUrcPu27ljVqkBkpK6ib82a5d6Vuc+jvNu56hJga70nbFFrpyKuFKTagyWW8ZNrskqdGoVCgRYtWmDLli0IDQ21SEdtiUGNmrFfSnb5gP/rL3Wi78aNwO+/A4UlyuTXrQtERal/+vVTb1VgJ9ao2+LqrF1rx5R+sN6I9TBwJHNYpU6Np6cnCgsLIZPxH9yZGZNIatN6EhcuqKeUNm4EDhzQJvoCUOfLREWpp5bCw9VTTQ6AKzmsY8SjDfHl7+dLXW/uFJBKpdLbzsXNreI0QtYbsS5X3oOOrM/knJrXX38dn376KZYtWwYPD5NvTk7A6qtQVCrg6FFdIJOaqn88LEwdxERHA61alaro6wi4ksOyyjp7L8ncvJ3i4mIsW7YMgLqi8MOlKMg+GDiStZgclRw6dAg7d+7Eb7/9hrZt26Jq1ap6x9evX2+xzpU0e/ZsbN26FSkpKfDy8sLtkvkVZFFWGYUoKgJ279btsZSZqTvm4QH06aOt6ItHHqlE722DKzksx9CooMab/ZthYt9mPJMnogqZHNTUqFEDTz/9tDX6Uq6ioiI888wziIiIwPLly23++K7EYqMQ+fn6ib7/bIAKAKhWDRg0SD219MQTQI0aZvfXHriSwzLKGxUE1K/jT0euYmLfZrbsFhE5KZODmri4OGv0o0KxsbEAgJUrV9rl8V1JpUYhsrOBTZvUgczOneoRGo169dQjMdHRQN++gI/zjmJwCbBlMDeJiCzJ6KBGpVLhiy++wMaNG6FQKNC/f3/MmDEDPk78xURlM3kU4vx5XUXfgwf1E32bNdPlx3TtChiRqOksrF23xRUwN4mILMnooObTTz/Ff/7zH/Tr1w9VqlTB/PnzcePGDSxdutSa/auUwsJCFJZYEpxfcvqDDKpoFEImVJgfXAD3999TBzJnz+rfQZcuuhVLLVs6ZKKvpXAlR+UwN4mILMnooGblypX473//i1dffRUAkJCQgOjoaCxZssTsJd6zZs3STisZcuTIEYSFhZl1/3Pnzq3w/qlsD49CeCoViLhyEtFXjmBw+hH45P6la+zpqU701VT0rV/ffh23EdYysQzmJhGRJRldfM/Hxwfnz59Hw39K0Ash4OPjg7S0NDRo0MCsB79x4wZu3LhRbptGjRrpTXGtXLkSb7zxhlGrn8oaqQkKCnL54ntGy8+Haus23PrxZ8h3/w7Pu3d0x/z8gMGD1dNKgwYBcrndumlrLB5mWdasMqtUKrF3714AQI8ePcrdKoGIHJfFi+8VFRXpbYMgk8ng5eWlFzSYqk6dOqhTp47Zt6+It7c3vL29rXb/kpSZqUv03bULbgoFtH+hgABdRd++fQEXfG1tWpTQRVgzN8nd3R29e/e2QC+JyBmYtPrpgw8+gK+vr/ZyUVERZs+eDXmJs/T58+dbrnclZGRk4NatW8jIyIBSqURKSgoAoGnTpqhWrZpVHtMlCKHOidEk+h4+rH+8RQtdfkyXLpJK9DWV1YsSujDmJhGRJRgd1PTs2RPnzp3Tu65bt25IS0vTXrbm9gkzZszAqlWrtJc7duwIAEhMTOSZmKlUKuDQIV0gc/6hsvTh4epppagodaIvAeDyY2uzRpVZIQRyc3MBAHXr1uUWL0QSZ3RQs3v3bit2o2IrV65kjZrKKCwEdu3SVfT9q0Sir5eXejopOhoYMsQlEn3NweXHzkehUGDRokUAuE0CkSvg5k1SlpcHbNumDmS2bQPu3tUdq15dXck3Kkqd6MvE6Qpx+TERkWMzKqj55JNP8Prrr5fa56kshw4dwo0bN/DEE09UunNkhuvX1SMx8fFAYiKgUOiO1a+vDmKio4HevdUjNGQ0Lj8mInJsRgU1qampCA4OxjPPPIOhQ4ciLCwMdevWBaDeBTc1NRX79u3D999/j6ysLHz77bdW7TSVIARw5owuP+bIEf3joaHqICY6Gujc2aUTfSuLWyMQETk2o4Kab7/9FidPnsTXX3+NkSNHIi8vD+7u7vD29sb9+/cBqBN3//3vf2PMmDFcRm1tSqV+ou+FC7pjMhkQEaFL9G3e3E6dlCZujUBE5LiMzqlp164dlixZgsWLF+PkyZO4fPkyHjx4gDp16qBDhw5WrTdDAAoK1BtExser68g8nOjbr5962fWQIep6MmQ1XH5MROSYTE4UlslkaN++Pdq3b2+N/lBJf/+tS/T99Vfg3j3dMbkcePJJ9YjM44+rK/ySzVhj+TEREVUOVz85mqtX1aMxGzcCe/YAxcW6Yw0a6KaVevVymkRf7pNE9uLu7o6IiAjt70QkbQxq7E0I4PRpXX5McrL+8datdRV9O3d2uh2vuU8S2ZO7uzsGDhxo724QkY0wqLEHpRJIStIFMpcu6Y7JZEC3buogJioKaNrUXr2sNO6TREREtsSgxlYePAB+/10dxGzeDPxTuh2AemPIAQN0FX39/e3VS4vhPknkCIQQyMvLAwDI5XJuk0AkcZUOaq5cuYJ79+6hZcuWcGMNFH23bgFbt6oDmYQE4J/l7wCAGjXUib5RUUBkJCCxTTm5TxI5AoVCgQULFgCw/jYJlsgdY/4ZUeUYHdSsWrUKf//9N9544w3tdf/+97+xfPlyAECLFi2wfft2BAUFWbyTTiUjQz/RV6nUHQsK0hXC69ED8PS0Uyetj/skkSuxRO4Y88+IKs/ooZXFixdDLpdrLyckJCAuLg7ffvstjhw5gho1aiA2NtYqnXR4J08CH34IdOoEBAcDkyapN49UKoF27YAZM4Bjx4ArV4D/+z/15pESDmgA7pNErkOTO/bwyKQmdyzhVJZN7oOITBipOX/+PMLCwrSX4+PjMXToUIwcORIAMGfOHIwdO9byPXQGo0erAxtAvQ1B9+66pdeNG9u1a/bCfZLIFVgid4z5Z0SWY/RIzYMHD1C9xE7OBw4cQM+ePbWXGzdujOzsbMv2zlmMGAEMHQqsWAFkZ6unnd5802UDGkC3TxKg2xdJg/skkVSYkjtmzfsgIjWjR2qCg4ORnJyM4OBg3LhxA6dPn0b37t21x7Ozs/Wmp1zK9On27oFVVDZpkfskkdRZIneM+WdElmN0UPPCCy/gtddew+nTp7Fr1y60bNkSnTt31h4/cOAA2rRpY5VOku1ZKmmR+ySRlFkid4z5Z0SWY3RQ8+677+L+/ftYv349AgICsHbtWr3j+/fvx4gRIyzeQbI9SxfN4z5JZC9ubm7aXEBrlJywRO4Y88+ILEcmhCjr/0iS8vPzIZfLkZeXp5cfRDpKlUD3T3cZnOPXfMDue7cvR1sewhojrklzEgBALyjR/OWNOQmwxH0QSZmx398WO3XJysrCxIkTLXV3TkOpEki6dBPxKdeRdOkmlCrnjhGZtGiehFNZ6P7pLjz3zUFM/ikFz31zEN0/3cWluC5AkzsWINefHgqQ+xgdjBi6j5pVPfH18x0Z0BAZyaSKwqmpqUhMTISnpyeGDx+OGjVq4MaNG5g9ezYWL16MkJAQa/XTIUmxWBaTFk3HPa4clxAC9/+p5O3r62u1bRIskTsW2SYQKhXwn/hTuHWvCABw654CH209Azc3Gd9DREYweqRmy5Yt6NixI15//XWMHz8eYWFhSExMRKtWrZCSkoK1a9ciNTXVmn11KFItlsWkRdNUVGMEUNcYcfYRPGelUCgwb948zJs3DwqFwqqPpckdi+rQABFNaps89ZhwKguv/XhMG9BoOPtnCpEtGR3UzJ49G+PHj0d+fj7mzZuHtLQ0jB8/HuvWrUNiYiKefPJJa/bToUj5i0yTtGjo41gG9WgUkxbVOF1HliDlzxQiWzI6qDlz5gxee+01VKtWDZMmTYKbmxu++uorvQJ8rkLKX2QsmmcaTteRJUj5M4XIlowOavLz81GjRg0AgIeHB6pUqYLmzZtbq18OTepfZJZIfHQVnK6rPKkl25tD6p8pRLZicqKwZisEIQTOnTuHe/fu6bVp166d5XrnoFzhi4xF84zDGiOVYyjZ/oMnWkHu64WkSzcBCEQ0roNwM/JUnIUrfKYQ2YJJQU2/fv1QsqyNJo9GJpNBCAGZTAalUmnZHjogV/kiY9G8immm6yZ8fwwylF1jhNN1ZTO0aiwrrwCv/nhc77r/JV5CDV9PfPJUW0mOFLrKZwqRtRk9/ZSeno60tDSkp6eX+tFcn5aWZs2+OgzmnVBJnK4zXXmJsYbcvq/AeImuAuJnCpFlsKJwJUixTg2ZjxWFjZd06Sae++agWbcNqO6N/dP6GfXaFhcXY8uWLQDUI8seHiYNTtscP1OIymbs97fRQc39+/fx9ttvY+PGjVAoFOjfvz/+7//+D3Xq1LFYp63NGtskVPaLjF+E5IriU65j8k8pZt9+9cvhkp0a5WcCUWnGfn8bfdoyc+ZMrFy5EiNHjoSPjw9Wr16NCRMmlNrY0tVUJu+EZ2Xkqiqb8CrlVUDMZSMyn9FBzfr167F8+XLtTtyjRo3CY489BqVSCXd3d6t1UKpYWp9cWUWJsRUxNigSQmgrCXt6elptmwQicgxGJwpfvXoVPXr00F7u0qULPDw8kJmZaZWOSRmrh5KrKy8xtiIB1b2NXgWkUCgwd+5czJ071+rbJBCR/Rkd1CiVSnh5eeld5+HhgeLiYot3SupYPZTI8Kqxiswa2po5JhLAootkDUZPPwkhEBMTA29vb+11BQUFGD9+PKpWraq9bv369ZbtoQSxeiiRWllFHv++V4T3Nv6J2/f1R1akXKfG1TCfkKzF6KBmzJgxpa4bNWqURTvjKlg9lEinrMTYx9sE4GDaTZepKOxKmE9I1mR0UBMXF2fNfrgUVg8lKp+7mwyPNa2Dx5o6T8kIqlhF+YQyqPMJB4QGMIAlsxidU0OWw+qhROSKmE9I1uYUQc3ly5fx4osvIiQkBFWqVEGTJk0wc+ZMFBUV2btrZmNpfSJyNcwnJGtz7Jrh/zh79ixUKhWWLFmCpk2b4tSpU3j55Zdx7949zJs3z97dMxt3wiayLjc3N4SGhmp/J/tiPiFZm9Pu/fT5559j0aJFJm2iaY1tEoiIyDhKlUD3T3dVmE+4792+PLkjPcZ+fzvtqUteXh5q1So/kbawsBD5+fl6P0REZB/MJyRrc8qg5tKlS/jvf/+L8ePHl9tu7ty5kMvl2p+goCAb9ZCIiMrCfEKyJrtOP82aNQuxsbHltjly5AjCwsK0lzMzM9GrVy/06tULy5YtK/e2hYWFKCws1F7Oz89HUFAQp5+IXERRURHmzp0LAJg+fXqpquhkP9yNnExh8V26rWHixInaDTINadSokfb3zMxM9OnTBxEREVi6dGmF9+/t7a1XAZmIiBwDdyMna7BrUFOnTh3UqWNcca3r16+jT58+6Ny5M+Li4riSgYiIiPQ4xZLuzMxM9O7dGw0bNsS8efOQm5urPRYQEGDHnhEREZGjcIqg5rfffsPFixdx8eJFPPLII3rHnHRFOhEREVmYU8zhxMTEQAhR5g8RERER4CQjNURE1sAVOETSwqCGiCTLzc0NzZo10/5eUsKpLMRuTtXbYDFQ7oOZQ0JZK4XISTntNgnm4DYJRASoA5oJ3x8rVapfM0bDInBEjkXy2yQQEZlDqRKI3Zxa5t5DmutiN6dCqXKZ8z0iyWBQQ0Qu5XD6Lb0pp4cJAFl5BTicfst2nSIii2BODRFJVlFREebNmwcAmDp1Kry8vJBzx3BAU5Kx7YjIcTCoISJJUygUepf9/XwMtNRnbDsichycfiIil9IlpBYC5T4wtHBbBvUqqC4htWzZLSKyAAY1RORS3N1kmDkkFABKBTaayzOHhLJeDZETYlBDRJWiVAkkXbqJ+JTrSLp00ylWDUW2CcSiUZ0QINefYgqQ+3A5N5ETY04NEZnNmQvYRbYJxIDQAFYUJpIQBjVEZBZDBeyy8wow4ftjTjHi4e4mQ0ST2vbuBhFZCKefiMhkzlLATiaTITg4GMHBwZDJOAJDJHUcqSEik5lSwM6eIyGenp6IiYmx2+MTkW1xpIaITMYCdkTkiBjUEJHJWMCOiBwRgxoiMpmzFLArKirC559/js8//xxFRUV27QsRWR+DGiIymTMVsLt//z7u379v724QkQ0wqCEis7CAHRE5Gq5+IiKzsYAdETkSBjVEVCksYEdEjoJBDRlFqRI8GyciIofGoIYq5Mz7+xARketgojCVS7O/z8PVYzX7+yScyrJTz4gqJpPJUL9+fdSvX5/bJBC5AJkQwr6bs9hQfn4+5HI58vLyUL16dXt3x+EpVQLdP91lsBy+DOqVLvve7cupKCIishpjv785UkMGmbK/DxERkb0xqCGDuL8PERE5EyYKk0Hc34ecnUKhwNdffw0AeO211+Dp6WnnHhGRNXGkhgxylv19iAwRQiAvLw95eXlwofRBIpfFoIYMcqb9fYiIiBjUULm4vw8RETkL5tRQhbi/DwGsKk1Ejo9BDRmF+/u4NlaVJiJnwOknIioXq0oTkbNgUENEBilVArGbU1HWuiHNdbGbU6FUOebKIplMhrp166Ju3brcJoHIBXD6iYgMMqWqtCNOT3p6euLVV1+1dzeIyEY4UkNEBrGqNBE5EwY1RGQQq0oTkTNxmqBm6NChaNiwIXx8fBAYGIjRo0cjMzPT3t0ikjRnryqtUCiwcOFCLFy4EAqFwt7dISIrc5qgpk+fPvj5559x7tw5rFu3DpcuXcK//vUve3eLSNKcvaq0EAK5ubnIzc3lNglELsBpEoXffPNN7e/BwcGYNm0aoqOjoVAouEkdkRVpqko/XKcmgHVqiMjBOE1QU9KtW7fwww8/oFu3buUGNIWFhSgsLNRezs/Pt0X3iCSHVaWJyBk4zfQTALz77ruoWrUqateujYyMDMTHx5fbfu7cuZDL5dqfoKAgG/WUSHo0VaWjOjRARJPaDGiIyOHYNaiZNWsWZDJZuT9Hjx7Vtn/77bdx/Phx/Pbbb3B3d8cLL7xQ7jz59OnTkZeXp/25evWqLZ4WERER2YFdp58mTpyIESNGlNumUaNG2t/r1KmDOnXqoHnz5mjVqhWCgoJw8OBBRERElHlbb29veHt7W7LLRERE5KDsGtRoghRzaEZoSubMEBGVJJPJIJfLtb8TkbTJhBOsczx8+DAOHz6M7t27o2bNmkhLS8OMGTOQlZWF06dPGz0ak5+fD7lcjry8PFSvXt3KvSYiIiJLMPb72ykShatUqYL169ejX79+aNGiBcaNG4c2bdpgz549nF4iIiIiAE6ypLtt27bYtWuXvbtBREREDswpghoiInMoFAqsXLkSABATE8NCnUQSx6CGiCRLCKHdI84J0geJqJKcIqeGiIiIqCIMaoiIiEgSGNQQERGRJDCoISIiIklgUENERESSwNVPRCRpvr6+9u4CEdmIU2yTYCncJoHsTakSOJx+Czl3CuDv54MuIbXg7sY9iYiIymPs9zdHaohsJOFUFmI3pyIrr0B7XaDcBzOHhCKyTaAde0ZEJA3MqSGygYRTWZjw/TG9gAYAsvMKMOH7Y0g4lWWnnhERSQeDGiIrU6oEYjenoqx5Xs11sZtToVS5zEywzWi2SVi5ciUUCoW9u0NEVsaghsjKDqffKjVCU5IAkJVXgMPpt2zXKRchhMCVK1dw5coVbpNA5AIY1BBZWc4dwwGNOe2IiKhsDGqIrMzfz8ei7YiIqGwMaoisrEtILQTKfWBo4bYM6lVQXUJq2bJbRESSw6CGyMrc3WSYOSQUAEoFNprLM4eEsl4NEVElMaghsoHINoFYNKoTAuT6U0wBch8sGtWJdWqIiCyAxfeIbCSyTSAGhAaworCNeXp62rsLRGQj3CaBiIiIHJqx39+cfiIiIiJJYFBDREREksCcGiKSrOLiYvz8888AgOHDh8PDgx95RFLG/3AikiyVSoULFy5ofyciaeP0ExEREUkCgxoiIiKSBAY1REREJAkMaoiIiEgSGNQQERGRJLjU6idN8eT8/Hw794SIbKGoqAgFBQUA1P/3Xl5edu4REZlD871d0SYILrVNwrVr1xAUFGTvbhAREZEZrl69ikceecTgcZcKalQqFTIzM+Hn5weZzPk2EczPz0dQUBCuXr3Kvav+wdekNL4m+vh6lMbXpDS+JqU50msihMCdO3dQv359uLkZzpxxqeknNze3ciM8Z1G9enW7v8EcDV+T0via6OPrURpfk9L4mpTmKK+JXC6vsA0ThYmIiEgSGNQQERGRJDCocSLe3t6YOXMmvL297d0Vh8HXpDS+Jvr4epTG16Q0vialOeNr4lKJwkRERCRdHKkhIiIiSWBQQ0RERJLAoIaIiIgkgUENERERSQKDGgc2e/ZsdOvWDb6+vqhRo4ZRt4mJiYFMJtP7CQ8Pt25Hbcic10QIgVmzZqF+/fqoUqUKevfujdOnT1u3ozb0999/Y/To0ZDL5ZDL5Rg9ejRu375d7m2k9j5ZuHAhQkJC4OPjg86dO2Pv3r3ltt+zZw86d+4MHx8fNG7cGIsXL7ZRT23HlNdk9+7dpd4PMpkMZ8+etWGPreuPP/7AkCFDUL9+fchkMmzcuLHC20j9fWLqa+IM7xMGNQ6sqKgIzzzzDCZMmGDS7SIjI5GVlaX92bZtm5V6aHvmvCafffYZ5s+fj//97384cuQIAgICMGDAANy5c8eKPbWd559/HikpKUhISEBCQgJSUlIwevToCm8nlffJmjVr8MYbb+D999/H8ePH0aNHDwwaNAgZGRlltk9PT8fgwYPRo0cPHD9+HO+99x4mTZqEdevW2bjn1mPqa6Jx7tw5vfdEs2bNbNRj67t37x7at2+P//3vf0a1d4X3iamviYZDv08EOby4uDghl8uNajtmzBgRFRVl1f44AmNfE5VKJQICAsQnn3yiva6goEDI5XKxePFiK/bQNlJTUwUAcfDgQe11SUlJAoA4e/aswdtJ6X3SpUsXMX78eL3rWrZsKaZNm1Zm+3feeUe0bNlS77pXXnlFhIeHW62Ptmbqa5KYmCgAiL///tsGvbM/AGLDhg3ltnGF90lJxrwmzvA+4UiNBO3evRv+/v5o3rw5Xn75ZeTk5Ni7S3aTnp6O7OxsDBw4UHudt7c3evXqhQMHDtixZ5aRlJQEuVyOrl27aq8LDw+HXC6v8PlJ4X1SVFSE5ORkvb8vAAwcONDg809KSirV/vHHH8fRo0ehUCis1ldbMec10ejYsSMCAwPRr18/JCYmWrObDk/q75PKcOT3CYMaiRk0aBB++OEH7Nq1C1988QWOHDmCvn37orCw0N5ds4vs7GwAQL169fSur1evnvaYM8vOzoa/v3+p6/39/ct9flJ5n9y4cQNKpdKkv292dnaZ7YuLi3Hjxg2r9dVWzHlNAgMDsXTpUqxbtw7r169HixYt0K9fP/zxxx+26LJDkvr7xBzO8D5xqV26HcGsWbMQGxtbbpsjR44gLCzMrPt/9tlntb+3adMGYWFhCA4OxtatW/HUU0+ZdZ/WZu3XBABkMpneZSFEqescibGvCVD6uQEVPz9nfJ+Ux9S/b1nty7remZnymrRo0QItWrTQXo6IiMDVq1cxb9489OzZ06r9dGSu8D4xhTO8TxjU2NjEiRMxYsSIcts0atTIYo8XGBiI4OBgXLhwwWL3aWnWfE0CAgIAqM+6AgMDtdfn5OSUOgtzJMa+JidPnsRff/1V6lhubq5Jz88Z3idlqVOnDtzd3UuNQJT39w0ICCizvYeHB2rXrm21vtqKOa9JWcLDw/H9999buntOQ+rvE0txtPcJgxobq1OnDurUqWOzx7t58yauXr2q94XuaKz5moSEhCAgIAA7duxAx44dAahzDvbs2YNPP/3UKo9pCca+JhEREcjLy8Phw4fRpUsXAMChQ4eQl5eHbt26Gf14zvA+KYuXlxc6d+6MHTt2YNiwYdrrd+zYgaioqDJvExERgc2bN+td99tvvyEsLAyenp5W7a8tmPOalOX48eNO936wJKm/TyzF4d4n9sxSpvJduXJFHD9+XMTGxopq1aqJ48ePi+PHj4s7d+5o27Ro0UKsX79eCCHEnTt3xFtvvSUOHDgg0tPTRWJiooiIiBANGjQQ+fn59noaFmXqayKEEJ988omQy+Vi/fr14s8//xTPPfecCAwMlMxrEhkZKdq1ayeSkpJEUlKSaNu2rXjyySf12kj5ffLTTz8JT09PsXz5cpGamireeOMNUbVqVXH58mUhhBDTpk0To0eP1rZPS0sTvr6+4s033xSpqali+fLlwtPTU/zyyy/2egoWZ+pr8uWXX4oNGzaI8+fPi1OnTolp06YJAGLdunX2egoWd+fOHe3nBQAxf/58cfz4cXHlyhUhhGu+T0x9TZzhfcKgxoGNGTNGACj1k5iYqG0DQMTFxQkhhLh//74YOHCgqFu3rvD09BQNGzYUY8aMERkZGfZ5AlZg6msihHpZ98yZM0VAQIDw9vYWPXv2FH/++aftO28lN2/eFCNHjhR+fn7Cz89PjBw5stSSS6m/T77++msRHBwsvLy8RKdOncSePXu0x8aMGSN69eql13737t2iY8eOwsvLSzRq1EgsWrTIxj22PlNek08//VQ0adJE+Pj4iJo1a4ru3buLrVu32qHX1qNZjvzwz5gxY4QQrvk+MfU1cYb3iUyIfzKfiIiIiJwYl3QTERGRJDCoISIiIklgUENERESSwKCGiIiIJIFBDREREUkCgxoiIiKSBAY1REREJAkMaojIoe3evRsymQy3b9+2d1eIyMExqCFyQTKZrNyfmJgYm/UlJiZG+7ienp5o3Lgxpk6dinv37tmsD8bq3bs33njjDXt3g4gM4IaWRC4oKytL+/uaNWswY8YMnDt3TntdlSpV9NorFAqrbuIXGRmJuLg4KBQK7N27Fy+99BLu3buHRYsWWe0xiUh6OFJD5IICAgK0P3K5HDKZTHu5oKAANWrUwM8//4zevXvDx8cH33//PWbNmoUOHTro3c9XX32FRo0a6V0XFxeHVq1awcfHBy1btsTChQsr7I+3tzcCAgIQFBSE559/HiNHjsTGjRv12iQnJyMsLAy+vr7o1q2bXhAGAJs3b0bnzp3h4+ODxo0bIzY2FsXFxdrjMpkMy5Ytw7Bhw+Dr64tmzZph06ZNevexZ88edOnSBd7e3ggMDMS0adO09xETE4M9e/ZgwYIF2pGl9PR0NG3aFPPmzdO7n1OnTsHNzQ2XLl3SPvaiRYswaNAgVKlSBSEhIVi7dq3eba5fv45nn30WNWvWRO3atREVFYXLly9X+NoRkQ6DGiIq07vvvotJkybhzJkzePzxx426zTfffIP3338fs2fPxpkzZzBnzhx88MEHWLVqlUmPXaVKFSgUCr3r3n//fXzxxRc4evQoPDw8MG7cOO2x7du3Y9SoUZg0aRJSU1OxZMkSrFy5ErNnz9a7j9jYWAwfPhwnT57E4MGDMXLkSNy6dQuAOqgYPHgwHn30UZw4cQKLFi3C8uXL8fHHHwMAFixYgIiICLz88svIyspCVlYWGjZsiHHjxiEuLk7vcVasWIEePXqgSZMm2us++OADPP300zhx4gRGjRqF5557DmfOnAEA3L9/H3369EG1atXwxx9/YN++fahWrRoiIyNRVFRk0mtH5NLsvaMmEdlXXFyckMvl2svp6ekCgPjqq6/02s2cOVO0b99e77ovv/xSBAcHay8HBQWJH3/8Ua/NRx99JCIiIgw+/pgxY0RUVJT28qFDh0Tt2rXF8OHDhRC6nYR///13bZutW7cKAOLBgwdCCCF69Ogh5syZo3e/3333nQgMDNReBiD+85//aC/fvXtXyGQy8euvvwohhHjvvfdEixYthEql0rb5+uuvRbVq1YRSqRRCCNGrVy8xefJkvcfJzMwU7u7u4tChQ0IIIYqKikTdunXFypUr9R57/Pjxerfr2rWrmDBhghBCiOXLl5d67MLCQlGlShWxfft2g68dEeljTg0RlSksLMyk9rm5ubh69SpefPFFvPzyy9rri4uLIZfLy73tli1bUK1aNRQXF0OhUCAqKgr//e9/9dq0a9dO+3tgYCAAICcnBw0bNkRycjKOHDmiNzKjVCpRUFCA+/fvw9fXt9R9VK1aFX5+fsjJyQEAnDlzBhEREZDJZNo2jz32GO7evYtr166hYcOGZfY9MDAQTzzxBFasWIEuXbpgy5YtKCgowDPPPKPXLiIiotTllJQUAOqptYsXL8LPz0+vTUFBgXYKi4gqxqCGiMpUtWpVvctubm4QQuhdV3KKSKVSAVBPQXXt2lWvnbu7e7mP1adPHyxatAienp6oX79+mUnJJa/TBB6ax1SpVIiNjcVTTz1V6nY+Pj5l3ofmfjT3IYTQC2g015V8PENeeukljB49Gl9++SXi4uLw7LPPagOp8pR8Hp07d8YPP/xQqk3dunUrvB8iUmNQQ0RGqVu3LrKzs/W+/DUjDQBQr149NGjQAGlpaRg5cqRJ9121alU0bdrU7L516tQJ586dq9R9hIaGYt26dXrP78CBA/Dz80ODBg0AAF5eXlAqlaVuO3jwYFStWhWLFi3Cr7/+ij/++KNUm4MHD+KFF17Qu9yxY0dt/9esWQN/f39Ur17d7OdA5OqYKExERunduzdyc3Px2Wef4dKlS/j666/x66+/6rWZNWsW5s6diwULFuD8+fP4888/ERcXh/nz51u1bzNmzMC3336LWbNm4fTp0zhz5gzWrFmD//znP0bfx6uvvoqrV6/i9ddfx9mzZxEfH4+ZM2diypQpcHNTf1Q2atQIhw4dwuXLl3Hjxg3tKI+7uztiYmIwffp0NG3atNRUEwCsXbsWK1aswPnz5zFz5kwcPnwYEydOBACMHDkSderUQVRUFPbu3Yv09HTs2bMHkydPxrVr1yzwChG5BgY1RGSUVq1aYeHChfj666/Rvn17HD58GFOnTtVr89JLL2HZsmVYuXIl2rZti169emHlypUICQmxat8ef/xxbNmyBTt27MCjjz6K8PBwzJ8/H8HBwUbfR4MGDbBt2zYcPnwY7du3x/jx4/Hiiy/qBUZTp06Fu7s7QkNDUbduXWRkZGiPvfjiiygqKtJblVVSbGwsfvrpJ7Rr1w6rVq3CDz/8gNDQUACAr68v/vjjDzRs2BBPPfUUWrVqhXHjxuHBgwccuSEygUw8PElOREQm279/P3r37o1r166hXr16esdkMhk2bNiA6Oho+3SOyEUwp4aIqBIKCwtx9epVfPDBBxg+fHipgIaIbIfTT0RElbB69Wq0aNECeXl5+Oyzz+zdHSKXxuknIiIikgSO1BAREZEkMKghIiIiSWBQQ0RERJLAoIaIiIgkgUENERERSQKDGiIiIpIEBjVEREQkCQxqiIiISBIY1BAREZEk/D929+b3BcpNQQAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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WIjIbRwcJQqqVRWjDigipVpaBkBVhz5ChubuLvTTmeF4d/f3330hJSUHdunVVZYGBgahevToiIiLw5Zdf6vXUhR0mc3FxQVBQEA4dOoRevXqpyg8dOoTQ0FCNx2nfvj2uXbumVjZs2DDUqlULn3/+ORwdHfVqOxEREYMhQ5NI9BquMoeoqCg4OTmhZs2aauUdOnTAjh079A6GijJMNmXKFAwePBhNmjRBSEgIVqxYgbi4OIwZM0ZVZ/HixdixYweOHDkCDw8PtSAOAIoXL46yZcvmKSciItKFVQ2TnTx5Ej169ECFChUgkUhUSb3aHD9+XLWoYM6fW7dumabBFurSpUuoWbMmXFxc1Mo7dOiAqKgoPHz40GRt6devHxYsWID//Oc/aNiwIU6ePIl9+/bBz89PVefp06e4d++eydpEZG5yhYDIe8nYFf0IkfeSuZUDkZFJBEGwmr+y/fv3488//0Tjxo3x3nvvYceOHejZs6fW+sePH0fbtm1x+/ZtlCxZUlVerlw5nYdT0tLSIJVKkZqaqnYMAEhPT0dsbKxq9WSyXPxdkT6ysrLw22+/AQD69u1r0lWoufs5kWHkd/3OzaqGybp06YIuXbro/TgvLy+UKlXK8A0iIpvk5OSEgQMHmvx5lbuf5/6Gqtz9fNkHjRkQERmBVQ2TFVajRo3g4+OD9u3b49ixY+ZuDhFRHtz9nMh8bDoY8vHxwYoVK7Bt2zZs374dAQEBaN++PU6ePKn1MRkZGUhLS1P7ISIyNn12Pyciw7KqYTJ9BQQEICAgQHU/JCQE8fHxmDdvHlq1aqXxMbNnz8bMmTNN1UQiskAymQzz5s0DAEydOjXPZANj4O7nROZj0z1DmgQHB+POnTta/3/atGlITU1V/cTHx5uwdURkKTIzM5GZmWmy5+Pu50TmY9M9Q5pcvnwZPj7aExBdXV3h6upqwhYRkbWTK4Qib8Og3P08KTVdY96QBOJeV9z9nMjwrCoYevnyJe7evau6Hxsbi+joaJQpUwaVK1fGtGnT8OjRI6xfvx4AsGDBAlSpUgV16tSBTCbDxo0bsW3bNmzbts2g7bKi1QnsFn9HZCyGmgqv3P187MZLkABqARF3PycyLqsaJrt48SIaNWqERo0aARBXL27UqBG+/fZbAEBiYiLi4uJU9WUyGaZOnYr69evj7bffxunTp7F371707t3bIO1xdnYGALw2xy71pBeZTAYA3K6DDEo5FT534rNyKvyB64l6HU+5+7m3VH0ozFvqxmn1REZkVYsumkNBizYlJiYiJSUFXl5ecHd317rbOpmPQqFAQkICnJ2dUblyZf6OqEAymQyzZ88GIOYRakqglisEtJxzVOsMMOWw1unP2+ndm2OIYTcie2eziy5aIm9vbwDiTutkuRwcHBgIkUHpMxU+pFpZvY6t3P2ciEyDwVARSSQS+Pj4wMvLy6QzT0g/Li4ucHCwqlFhMiOJRKLaH09bAM2p8ES2g8GQgTg6OjIfhchGODs7IywsLN86nApPZDv4VZmIqBCUU+G1DbxKIM4q41R4IsvHYIiIqBCUU+EB5AmIOBW+aOQKAZH3krEr+hEi7yUbfT82Uz8fWR4OkxER5SKTybBw4UIAwKRJk7Rux6GcCp97nSHvQqwzRCJDrdtkqc9HlonBEBGRBrquH9a5rg86BHpzKrwBKNdtyt0vo1y3ydBrLZn6+chycZiMiKiIlFPhQxtWREi1sgyECkGuEDBzd4zGrUiUZTN3xxhsCMvUz0eWjcEQEZEds5R8GX3WbbLG5yPLxmEyIiI7ZUn5MqZet4nrRFFO7BkiIrJDht5XrahMvW4T14minBgMERHZGUvMlzH1uk1cJ4pyYjBERJSLRCJBhQoVUKFCBZvcz84S82VMvW4T14minBgMERHl4uzsjFGjRmHUqFFwdnY2d3MMzlLzZZTrNnlL1YemvKVuRpnmburnI8vFBGoiIjtjyfkypl63ietEEcBgiIjI7ijzZZJS0zXmDUkg9o6YK19GuW6TrT4fWR4OkxER5ZKZmYkFCxZgwYIFyMzMNHdzDI75MkTqGAwREeUiCAJSU1ORmpoKQbDNFYiZL0OUjcNkRER2ivkyRCIGQ0REdoz5MkQcJiMiIiI7x2CIiIiI7BqDISIiIrJrzBkiIspFIpGgXLlyqttEZNsYDBER5eLs7Ixx48aZuxlEZCIcJiMiIiK7xmCIiIiI7BqHyYiIcsnMzMTKlSsBwGZ3ricyN7lCsJgFPxkMERHlIggCnjx5orpNRIZ14HoiZu6OQWJquqrMR+qG6T0CzbIVDIfJiIiIyGQOXE/E2I2X1AIhAEhKTcfYjZdw4HqiydvEYIiIiIhMQq4QMHN3DDT1tyrLZu6OgVxh2h5ZBkNERERkEudjn+XpEcpJAJCYmo7zsc9M1ygwGCIiIiITefxCeyBUmHqGwmCIiIiITMLLw82g9QyFs8mIiHKRSCSQSqWq20SGYknTyc2hqX8Z+EjdkJSarjFvSALAWyqeF1NiMERENsNQFxpnZ2dMnjzZ8A0ku2Zp08nNwdFBguk9AjF24yVIALWASPmXOr1HoMkDRInARTTylZaWBqlUitTUVJQsWdLczSEiLezhQmPvvQrWTDmdPPcFV/nbW/ZBY5t5n+rCFH+v+ly/GQwVgMEQkeWzhwuNPQR71k5bsCpXCGg556jWWVTKoaHTn7ezq+DW2MG9PtdvDpMRkVUraN0SCcR1SzoEeuv8QZuZmYnw8HAAQFhYmNm349AW7CkXqbOFYM/a5ResSou56DydPKRaWRO01jI4Okgs5vVyNhkRWTVjrFsiCAISEhKQkJBg9u04LHWROspW0IrKq07d0+k4pp5OTtkYDBGRVbPUdUsMxVIXqSNRQcGqAODIrSc6HcvU08kpG4fJiMiqWeq6JYZi68GetSsoWNWFuaaTUzb2DBGRVVOuW6ItG0gCMXfDWi80th7sWTtDBKECzDOdnLJZVTB08uRJ9OjRAxUqVIBEIsHOnTsLfMyJEycQFBQENzc3VK1aFcuXLzd+Q4nIZJTrlgDIExCZc90SQ7H1YM/aGSIIHd6iisUmwMsVAiLvJWNX9CNE3ku22dw0qwqGXr16hQYNGmDx4sU61Y+NjUXXrl3x9ttv4/Lly/jyyy8xceJEbNu2zcgtJSJT6lzXB8s+aAxvqfqFyVvqZvUzrWw92LN2BQWruugQ6G2w9hjSgeuJaDnnKAasPItJm6MxYOVZtJxzFAeuJ5q7aQZnVTlDXbp0QZcuXXSuv3z5clSuXBkLFiwAANSuXRsXL17EvHnz8N577xmplURkDp3r+qBDoLfB1i1xd3c3cAsLTxns5Z667c11hswuvxWVC2LJuUL2tpyDVQVD+oqMjETHjh3Vyjp16oTVq1cjMzNT49ohGRkZyMjIUN1PS0szejuJyDAMtW6Ji4sLPv30UwO0yHAMHeyR4WgLVnVhib16xli7y9JZ1TCZvpKSklC+fHm1svLlyyMrKwtPnz7V+JjZs2dDKpWqfnx9fU3RVCKiAimDvdCGFRFSrazNXIhsQee6Pjj9eTt80622TvXLFHe22N4Ve1zOwaaDISDvjtPKBdS07UQ9bdo0pKamqn7i4+ON3kYiIrJ+jg4ShLXwLzCHqGxxF5yd9o5FBkKAfS7nYNPBkLe3N5KSktTKHj9+DCcnJ5Qtq7kr3dXVFSVLllT7ISL7otyOIzw8HJmZmeZuDlmRghLeJQBm9aoLFyfLvfza43IOlvvbMICQkBAcOnRIreyPP/5AkyZNzL7XEBFZLkEQ8ODBAzx48MDs23GQ9bH22Y32uJyDVSVQv3z5Enfv3lXdj42NRXR0NMqUKYPKlStj2rRpePToEdavXw8AGDNmDBYvXowpU6Zg1KhRiIyMxOrVqxEREWGul0BERHbAmhPe85shZ6vLOVhVMHTx4kW0bdtWdX/KlCkAgKFDhyI8PByJiYmIi4tT/b+/vz/27duHjz/+GEuWLEGFChXwyy+/cFo9EREZnSXtyq4ve1vOwaqCoTZt2uTbZR0eHp6nrHXr1rh06ZIRW0VERGR7TNK7dfUqsGgRMGkSULeu4Y6rJ6sKhoiIiGyVXCFY3LCaUXq3srKAnTvFIOjkSbHMwQH49VfDPo8eGAwRERGZ2YHriXmGpHxsbUjqyRNg5Upg2TLg4UOxzNER6N0bGDLErE0rUjCUkZEBV1dXQ7WFiMhicMYpmYrNb30RFSX2Am3eDCh3eChXDvjwQ2DMGKBSJfO2D4BE0GPe6MGDBxEREYFTp04hLi4OCoUC7u7uaNy4MTp27Ihhw4ahQoUKxmyvyaWlpUEqlSI1NZVrDhERkUHJFQJazjmqdcVn5f5lpz9vZ/YhM71kZgLbtolB0Jkz2eVNmgAffQT07Qu4GXedIn2u3zqtM7Rz504EBARg6NChcHBwwKeffort27fj4MGDWL16NVq3bo3Dhw+jatWqGDNmDJ48eWKQF0JERGTLbG7ri3/+Af7zH8DPDxgwQAyEnJ2BgQOByEjg/HlxSMzIgZC+dBom++GHHzBv3jx069YNDg5546e+ffsCAB49eoSFCxdi/fr1+OSTTwzbUiIiIhtjM1tfnDsn9gL99pvYKwQA3t7iMNjo0eJtC6ZTMHT+/HmdDlaxYkXMnTu3SA0iIjK3rKws/PbbbwDEL3tOTpxrQsZh1VtfZGQAW7cCv/wCXLiQXR4SIg6Fvfce4OJivvbpodB/4TKZDLGxsahWrRo/KIjIpigUCty5c0d1m8hYlFtfJKWm50mgBrJzhixq64tHj4Dly4EVK4DHj8UyFxdxWOyjj4CgIPO2rxD03pvs9evXGDFiBNzd3VGnTh3Vis8TJ07Ejz/+aPAGEhER5SZXCIi8l4xd0Y8QeS8ZcoV17iFX0MaugIVsfSEIwOnTQL9+QJUqwPffi4FQxYrArFniVPnwcKsMhIBCBEPTpk3DlStXcPz4cbjlSIB65513sGXLFoM2joiIKLcD1xPRcs5RDFh5FpM2R2PAyrNoOecoDlxPNHfTCsWiN3Z98wZYswZo3Bh4+20xJygrK/t2bCzw5ZfiVHkrpvf41s6dO7FlyxYEBwdDIsmOVAMDA3Hv3j2DNo6IiCgnW12Tx+I2do2LExdHXLkSSE4Wy9zcgEGDxKGwBg3M0y4j0TsYevLkCby8vPKUv3r1Si04IiIiMiS5QsDM3TEac2sEiMNKM3fHoEOgt/mHlQrB7Bu7CgJw4oQ4K2znTkCZL+fnB4wbB4wYAZS1zo1nC6L3MNlbb72FvXv3qu4rA6CVK1ciJCTEcC0jIiLKwebW5LEUr16JydD16wNt2wLbt4uBUPv2YlB07x7w2Wc2GwgBhegZmj17Njp37oyYmBhkZWVh4cKFuHHjBiIjI3HixAljtJGIiMh21uSxFH//DSxdCqxeDaSkiGXu7uKiiBMmAHXqmLV5pqR3MNS8eXP8+eefmDdvHqpVq4Y//vgDjRs3RmRkJOrVq2eMNhIRmZSLiwumT59u7mZYFEvYUd2q1+SxFIIAHD4sDoXt2SPeB4Bq1YDx44Fhw4BSpczaRHMo1AJB9erVw7p16wzdFiIiskCWsqO6Va7JYylevADWrwcWLwZu3cou79RJTIju0gXQsMOEvShUMCSXy7Fjxw7cvHkTEokEtWvXRmhoKBdfJCKyMZY0e0u5Js/YjZcgAdTaZFFr8liSO3fEACg8HEhLE8tKlADCwsShsIAAc7bOYugdvVy/fh2hoaFISkpCwL8n8a+//kK5cuXw+++/c6iMiKxeVlYWduzYAQDo1auX3X7Rs8TZW8o1eXL3VHmboafKYikUwIED4lDYgQPZ5QEBYgA0ZAhQwC7u9kbvv/CRI0eiTp06uHjxIkqXLg0AeP78OcLCwvDhhx8iMjLS4I0kItLEWHksCoUCMTExAIDQ0NAiH89a6TN7y5RTwi1lTR5LyKNSk5oKrF0LLFkC3L0rlkkkQLdu4lDYO+/Y9VBYfvQOhq5cuaIWCAFA6dKlMWvWLLz11lsGbRwRkTaWksdiyyx59pa51+SxqPdfTIw4FLZ+vThNHgCkUnFdoHHjxORoypfeIWJAQAD++eefPOWPHz9G9erVDdIoIqL8KPNYcvdaKPNYrHVbBkvD2VuaWcT7Ty4Hfv9d7O2pU0dcLfrVKyAwULz98CHw008MhHSkdzD0ww8/YOLEifjf//6Hhw8f4uHDh/jf//6HyZMnY86cOUhLS1P9EBEZWkF5LICYx2KtG3daEuXsLW0DPxKIvSH2NHvL7O+/Z8+AefOA6tWB0FDgyBFx6KtnT/H29evAmDFikjTpTO9hsu7duwMA+vbtq1p9Wvh3nYIePXqo7kskEsjlckO1k4gIgOXmsdgizt7Ky2zvv2vXxITojRvFzVMBoHRpYNQoYOxYcSd5KjS9g6GjR49yDzIiMhtLzmOxRZy9pc6k77+sLGDXLjEIyrnDQ4MGYkL0gAHiitFUZHoHQ23atDFCM4iIdMM8FtOzlNlblsAk77+nT8Xd4pcuFXN/AMDREejdWwyCWrYUZ4mRwegdDPn7+2PYsGEICwtD5cqVjdEmIiKtTLEKsbOzM6ZNm6a6TeafvWUpjPr+u3RJ7AWKiAAyMsSycuWADz8U84AqVSpK0ykfeidQT5kyBbt27ULVqlXRoUMHbN68GRnKXxoRkZEp81gA5EnsNVQei0QigYuLC1xcXJgWQGoM/v7LzAQ2bwZatACCgsSVojMyxNvr1gFxccD33xcpEJIrBETeS8au6EeIvJfMyQUaSARl9rOerly5gjVr1iAiIgJZWVkYOHAghg8fjsaNGxu6jWaVlpYGqVSK1NRUlOSKnUQWw6LWeSG7U+T33z//AL/+CixfDiT+OxXfyQno00ccCgsONshQmD3/nehz/S50MKSUmZmJpUuX4vPPP0dmZibq1q2LSZMmYdiwYTbxjYrBEJHlMtYKwFlZWdizZw8AcQatvW7HYUuM8V6RZSmwIfI+Hjx7Db8y7hgcUgUuTgUMuJw/Lw6Fbdki9goBgLc3MHq0+ONjuABF275yyldtyn3lzEGf63eh/8IzMzOxY8cOrF27FocOHUJwcDBGjBiBhIQEfPXVVzh8+DD++9//FvbwREQFMlYei0KhwJUrVwAAXbt2NfjxybSM0Tui6ZirTsdqPmZGBrB1qxgEnT+fXR4cLPYCvf8+4OJSqHZoY4n7ylkyvYOhS5cuYe3atYiIiICjoyMGDx6Mn3/+GbVq1VLV6dixI1q1amXQhhIRkf0qbM+Ott4R5WrRhekd0fmYCQniMNivvwKPH4uVXFyAfv3EIMiIW1hxPS796B0MvfXWW+jQoQOWLVuGnj17apxpERgYiP79+xukgUS2wuI2dSSyEoXt2TFG70iBxxQE7Fj8Gzo+j4TD9m3iWkEAULGiuDjiqFGAl5dOz1UUXI9LP3oHQ3///Tf8/PzyrVO8eHGsXbu20I0isjX2nMRIVBRF6dkxRu+ItmO6Zmbg3ZsnMfTSHtT95172f7z9ttgL1LMnYMJlGrgel370nlrftm1bJCcn5ylPSUlB1apVDdIoIltiEZs6Elmhou4DZozekdx1K6Q9xmcnwhG5bBj+b/9C1P3nHtKdXPCgZ3/g8mXg5ElxhpiJ16vivnL60btn6P79+xr3HMvIyMCjR48M0igiW8EkRqLCK2rPjjF6R7w83ABBQHD8NQyN2oOOd87CUVAAAB6WLIeNjbphc4OOWDaxI/zMmIvDfeX0o3Mw9Pvvv6tuHzx4EFKpVHVfLpfjyJEjqMKN4ojUMImRqPCK2rNj8NWiX79Gs0P/w+H1c1A9KVZVfKZyfawL6o7D1ZtB4eBY5BXQAcPkGHJfOd3pHAz17NkTgLgy69ChQ9X+z9nZGVWqVMFPP/1k0MYRWTsmMVonZ2dnTJ06VXWbzKOoPTsG6x2JjRX3CVu9Gg7Pn6M6gNfOrthRpy3WNe6Ov8pV0f+Y+TBkjiH3ldONzsGQQiF2A/r7++PChQvw9PQ0WqOIbAWTGK2TRCJB8eLFzd0MndjyLEVD9OwUundEEIDDh4HFi4Hdu8X7AFC1KjB+PM4064LFJxMM3uNijKUAuK9cwYq8ArWt4wrUVBRyhYCWc44W+GF++vN2NnMBI9Oxh1mKyuAA0Nyzo2twoHPQ+OIFsH69GATdupVd3rGjOCusSxdxB3l9jqkj5eeFtqF1fl7oR5/rt96zyQDgxIkT6NGjB6pXr44aNWrg3XffxalTpwrVWCJbZopNRcnwsrKysHfvXuzduxdZynViLIy9zFJU9ux4S9V7T72lbnr1kih7R0IbVkRItbJ5/+bu3AEmTRI3RJ0wQQyESpTIvn3wINC9uyoQ0umYetInx5AMS+/ZZBs3bsSwYcPQu3dvTJw4EYIg4MyZM2jfvj3Cw8MxcOBAY7STyGoxidH6KBQKXLx4EQDQoUMHM7cmL3ubpWi0vBeFQgxyFi0C9u/PLq9ZUwyChg4FTDgiwBxD89E7GJo1axbmzp2Ljz/+WFU2adIkzJ8/H9999x2DISINmMRIhmSPsxQNmveSmgqEhwNLlog9QoC4Q3yXLuJQWMeOgEOhBk6KhDmG5lOoFah79OiRp/zdd9/Fl19+aZBGEdkiJjGSobAHoZBu3hRzgdavB16+FMukUmD4cGDcOKB6dbM2z+BLAZDO9A59fX19ceTIkTzlR44cga+vr0EalZ+lS5fC398fbm5uCAoKyjdX6fjx45BIJHl+buVMiiMisjLsQdCdPDMLt37diMfBrYDAQHGK/MuX4u1ly4CHD4H5880eCAHMMTQnvXuGPvnkE0ycOBHR0dFo3rw5JBIJTp8+jfDwcCxcuNAYbVTZsmULJk+ejKVLl6JFixb49ddf0aVLF8TExKBy5cpaH3f79m21TPJy5coZtZ1ERMbEHgQdPH+OW7N+hsealaj1PAkAIJc44HTtEBSbMglNh78vDo0ZQVFmmTHH0Dz0DobGjh0Lb29v/PTTT/jtt98AALVr18aWLVsQGhpq8AbmNH/+fIwYMQIjR44EACxYsAAHDx7EsmXLMHv2bK2P8/LyQqlSpYzaNiIiU+FWC/m4dg1YtAjyDRtQK10MJlLcSmBz/Y7Y2LgbHknLA3eAZTeSjBJYGGK5A+YYmp7ewRAA9OrVC7169TJ0W/Ilk8kQFRWFL774Qq28Y8eOOHPmTL6PbdSoEdLT0xEYGIivv/4abdu21Vo3IyMDGRkZqvtpaWlFazgRkRGwByGHrCzg99/FWWHHjwMAHAHcLFcF4UE9sCuwNdKds4cMjTXbzpALJjLH0LQKFQwBYnDy+PFj1crUSvkNVxXF06dPIZfLUb58ebXy8uXLIykpSeNjfHx8sGLFCgQFBSEjIwMbNmxA+/btcfz4cbRq1UrjY2bPno2ZM2cavP1EZD2cnZ0xadIk1W1LZfc9CE+fAqtWiXlA8fFimaMjkjt0w9gyzXG+Uh2NQ2HGmG1nb8sd2Bq9g6E7d+5g+PDheXpjBEGARCLRuKO9IUlyvbGVz6tJQEAAAgICVPdDQkIQHx+PefPmaQ2Gpk2bhilTpqjup6WlmSQxnIgsh0QisZqhdUvuQTDaViGXL4u9QBERwL9DYfD0BD78EBgzBqeTHXB+c3SBhzHkbDt7XO7AlugdDIWFhcHJyQl79uyBj4+P1kDE0Dw9PeHo6JinF+jx48d5eovyExwcjI0bN2r9f1dXV7i6uha6nUREZIStQjIzge3bxSDozz+zy4OCxLWB+vUD3MShMC9Zsk6HNORsOy53YN30Doaio6MRFRWFWrVqGaM9Wrm4uCAoKAiHDh1Sy1c6dOiQXonbly9fho+PHY2lE5He5HK5agmR9u3bwzHHFgz2TNeeHoNuNvrPP8CKFcDy5UBCgljm5AT06SMGQcHBeYbCzDHbjssdWDe9g6HAwEA8ffrUGG0p0JQpUzB48GA0adIEISEhWLFiBeLi4jBmzBgA4hDXo0ePsH79egDibLMqVaqgTp06kMlk2LhxI7Zt24Zt27aZpf1EZB3kcjkiIyMBAG3atGEwBN17egyWO3P+vNgL9NtvgEwmlpUvD4wZA4weDeTzpdYcs+243IF103vRxTlz5uCzzz7D8ePHkZycjLS0NLUfY+rXrx8WLFiA//znP2jYsCFOnjyJffv2wc/PDwCQmJiIuLg4VX2ZTIapU6eifv36ePvtt3H69Gns3bsXvXv3Nmo7iYhsiT6bwhZps9GMDGDjRqBZM/Fn40YxEGrWDNi0CYiLA2bMyDcQUjLUBq+64oKJ1k0iCIKmIFYrh3/3a9GWyGzsBGpTS0tLg1QqRWpqqtrCjURku2QymWrtsmnTpsHFxcXMLTIfuUJAyzlHtQY4yh6P05+3g6ODBLuiH2GSDsnLC/s3RGjDiuKdhATg11/Fn3/+EctcXMQ8oI8+At56q0jtL2oStz7HMHiuFBWaPtdvvYfJjh07VuiGERGRddF3lpTOuTMlXMVE6EWLgG3bxLWCAKBCBWDsWHFmmJdXkdtf1Nl2+gY3dr/cgZXSOxhq3bq1MdpBREQWSN9ZUgXlzrhmyTD4/hkE9/1GnCKv1LKl2AvUqxdgIWs7FTYR3JKXOyDN9M4ZAoBTp07hgw8+QPPmzfHo0SMAwIYNG3D69GmDNo6IiMxL31lS2nJnKqQ9xmcnwhG5NAxfb5sHyeXL4lT44cPFoOjUKaBvX4sJhApKBAfERHC5Qq9ME6snVwiIvJeMXdGPEHkv2WZev949Q9u2bcPgwYMxaNAgXLp0SbV1xYsXL/DDDz9g3759Bm8kERGZR2FmSam2Cvn9Bipfv4ihUbvR6c5ZOAr/7lhQuTIwbhwwciRQ1jJ7ULiIYl62nA+ld8/Q999/j+XLl2PlypVqy9Q3b94cly5dMmjjiIjMwdnZGWPHjsXYsWMtejsOUyjULKnXr9E5cg/ObJ6CLRHT0PWvM3AUFBDathUXTrx3D/JPP0NkCkzaw6BPrwYXUVSnz4xCa6R3z9Dt27c1bmVRsmRJpKSkGKJNRERGl98MIYlEAi8DJO/aCp03hb1/H1iyBFi9Gnj+XAyW3N2BDz4AJkyApF49AObpYdD3ObmIYjZ72HdN72DIx8cHd+/eRZUqVdTKT58+japVqxqqXURERmPL3f3GonWWlATA4cPirLDduwHlai1VqwLjxwPDhgGlS6uOY9DVqXVUmOfkIorZ7GHIUO9hstGjR2PSpEk4d+4cJBIJEhISsGnTJkydOhXjxo0zRhuJiAxGl+5+uVyO48eP4/jx4za3dlpRKGdJhTasiJDyrnBcvgyoUwfo0AH4/XcxEOrYUQyK/voLmDJFLRAyR1JyYZ+Tiyhms4chQ717hj777DOkpqaibdu2SE9PR6tWreDq6oqpU6diwoQJxmgjEZFB6Nrd37p6GZw4cQKAmA/p6OhovB3Yrc2dO+JQ2Nq1gHLXgRIlgLAwsScon30rzdHDUJTn1Hl40MbZw5Ch3sEQAMyaNQtfffUVYmJioFAoEBgYiBIlShi6bUREBqXrhfHig+dq5XY/rKZQAAcPikNh+/dnl9eoAUyYIAZCOqzQb44ehqI+JxdRtI8hw0IFQwDg7u6OJk2aGLItRERGpeuF8UmOeodikjBh8zWT5rhYjLQ0IDwcWLxY7BFS6tpVXCCxY0fAQfdsC3P0MBjiOe19EUVzbHxranoHQ69evcKPP/6II0eO4PHjx1AoFGr///fffxuscUREhqTrhbFcjnqz992y6Vk0Gt26JQZA69YBL1+KZSVLigskjh8PVK9eqMOao4fBHno1TMHWhwz1DoZGjhyJEydOYPDgwfDx8cmzYSsRkaXS9cLYxK80jv5blpSWDsBR4/FsYRaNilwO7NsnDoUdOpRdHhgoDoUNHizmBhWBOXoY7KFXw1RsechQ72Bo//792Lt3L1q0aGGM9hARGY2xLoyGyHExW4L28+fiukBLlwKxsWKZgwPQo4c4FNauHWDAL73m6GGw9V4NU7LVIUO9g6HSpUujTBl2JxKRddLlwiiTyfQ6ZlFzXMySoH3tmjgUtmED8OaNWFa6tLhFxrhxQK615AzJHD0MttyrQUUnEQRBrwUdNm7ciF27dmHdunVwd3c3VrssRlpaGqRSKVJTU1FSh9kSRGQd8uuJUSgUSExMhEIQ0Hf9LSSlZeQ7rHb683aFvqhqWxBQeTSDJmhnZYnrAS1aBBw/nl1ev77YCzRwoLhiNJEN0Of6rVPPUKNGjdRyg+7evYvy5cujSpUqefbt4f5kRGRptAU+2rr7HRwcULFiRQDA9HcdjZZvYrJtDp4+BVatApYtA+LixDJHR6BnTzEIatXKoENhRNZGp2CoZ8+eRm4GEZFxFHUIypj5JkZfhPDyZXEo7L//BdL/fR5PT2DUKGDsWMDXt3ANJ7IxOgVD06dPN3Y7iGwaVy82j8LugyWXy3H27FkAQHBwsNHyTYyyCGFmJrBjhzgUdvp0dnnjxmIvUP/+gJv1rhRMZAx6JVBv3boVO3fuRGZmJt555x18+OGHxmoXkc3Q1DPhXdINA5pWRhVPdwZHRlKUISi5XI7Dhw8DAN566y04OjoaZRaNQRchfPwYWLECWL4cePRILHNyAt5/X5wa37w5h8IsEL8oWQadg6EVK1ZgzJgxqFGjBtzc3LBt2zbExsZi9uzZxmwfkVXT2jORlo6fD/+lum9XWzuYiDXstG2QBQEvXBB7gbZsAZSz4MqXB0aPFn8qVDBG08kA7H6bFwui8zrqixYtwldffYXbt2/jypUrWL16NRYvXmzMthFZtfx6JnLLuWN6UZ8z8l4ydkU/QuS9ZIPu/m1trGGn7ULvjC6TAZs2AcHBQNOm4vR4mQxo1gzYuFFMkp45k4GQBVN+UcodsBvqs4D0o3PP0N9//41hw4ap7g8ePBgffvghkpKS4O3tbZTGEVmzgnomcjLEzCF+y1RnLTtt65WgnZAA/Pqr+PPPP2KZiwvQr5+YD/TWWyZuPRWGyWYRks50DobevHmjtjO9o6MjXF1d8fr1a6M0jMja6dvjUJRhm8ImCtsyS9yTSlt+SL4J2oIAREaKQ2H/+5+4VhAg9vqMHSvODCtf3mSvgYrOGoZw7Y1eCdSrVq1SC4iysrIQHh4OT09PVdnEiRMN1zoiK1bYHgd9gyh+y9TM0vakKqjnLk+Cdno6sHmzGATlXL+tRQuxF6h3byDXOm9kHaxhCNfe6BwMVa5cGStXrlQr8/b2xoYNG1T3JRIJgyGifxXUM6GNvkEUv2VqZyl7UunVc/fwobg44ooV4mKJAODqKq4OPWGCOEWerJq1DOHaE52Dofv37xuxGUS2J7+eCU0KO2zDb5n5K8waQU5OThg6dKjqdlHo1HP3+w10eHIbjkuXiGsEyeViBV9fcZ+wkSPFxRJNiFO+jccSh3DtXdH+yokoX9p6JjQRAHzTrbbeFxx+yyyYvmsEOTg4oIqBNirNr+fOLTMdoTEnEBa1G45f3c/+jzZtxKGwd98V1woyMSbjG5elDeESgyEio8vdM3H/6StEnI9DUlpGnrrf7b0Jh38TanXFb5mWTVOPXKXUf/DBpb3of/UPlEp/CQDIcnOD05AhwIQJkNepK75frv+Tb6+MMXpvmIxvGpYyhEsivXettzfctZ6MYd/VRIz7b95NjQu7U7nyAgZo/pbJC5h+5HI5oqKiAABBQUFwdHQs9LEi7yVjwMqzgCCg+YMrCLu0B+3vnoejoAAAxEvLY32jbug4bxreCqquc6+MMXpv5AoBLecc1dqTpQysT3/ejr0WBsLhSOMx+K71RGQ4coWA7/bGaPy/ws7+spdvmaa6cMjlcuzfvx8A0LBhwyIFQ029XDHu1iGE/rkDAU/jVOWn/BpiXVAPHKvWBF6li+OLRtV07pUxVu8Nk/FNzxjbvJD+GAwRmZixLjjG2kzU3JQB0KGYJOyMTsCzVzLV/1l0Hsvdu8CSJXBcuxafpaYCAF45u2Fb3fZY17g77nn6quWHANBpiYR2tcobbSkFJuOTvdIpGEpLS9P5gBxKIsqfMS84tvYtU9NQUE4Wl8eiUAB//CGuDbR/v7hgIgBUr46b7w3BR671cTcj+2M3Z89d5L1knYLkDZH3jdZ7w2R8slc6BUOlSpWCRMfdjuXKKaFEpBEvOLrRNhSUk/L/vth+DR6uzgiuVtbgPWFyhYA/7zxF5N9PAYjBZnDVXM+TlgaEhwOLFwN37mSXd+kCTJwIdOyI2g4OOJjPMJ+uwe+DZ7qt+l+YYJrJ+GSvdAqGjh07prp9//59fPHFFwgLC0NISAgAIDIyEuvWreMO9kQ6sNcLjj75PvpscgsAKa8zMWj1OaMMm7WccxTJbxSq+4uP3UUpd2f82LseOjuniQFQeDjwUpwVhpIlgWHDgPHjgRo11I6VX8+drsGvXxl3neoVJpjmlG+yVzoFQ61bt1bd/s9//oP58+djwIABqrJ3330X9erVw4oVK1QLlRGRZvZ4wdF35pM+m9zmZIxhs9Q3mQCyE6glggKNr/4J97VfAPcvZ1esVUtcG2jwYMDDQ+/n0TVIHhxSBatOxxotmLaXZHyinPROoI6MjMTy5cvzlDdp0gQjR440SKOIbJ09XXAKM/OpsAm6htqLTa7IG2aUTH+JPlcPYcjlvfBLSQIAKCQSSLp1h2TiR8A77wA6phNoomuQ7OLkYPRg2laT8Ym00TsY8vX1xfLly/HTTz+plf/666/w9fU1WMOIbJ09XHAKu4lsUfKlDDH9+1J8Gg5lVAcAVHsSjyGX9qDXjWNwzxQXykx1LY7NDTphY6OumPtpT4MlresaJJsimLa1ZHyi/OgdDP3888947733cPDgQQQHBwMAzp49i3v37mHbtm0GbyCRLbP1C05hlxEo7Ca3ORVl+ndy6mvUuRWDoVF70Dzuqqr8ZrkqWNe4O3bWaYN0Z7ciP48mugbJ9hBME5mK3sFQ165d8ddff2HZsmW4desWBEFAaGgoxowZw54hIlJT2GUE9N3kVpNC9S4lJwOrVqHTL4vxbsJDAIBc4oCDNYKxLqgHzvnWzTMUZoxZf7oGybYeTBOZSqEWXfT19cUPP/xg6LYQkY0pyjIC2oaCyhR3RnqmAq9lmpfxKFQCcXS0uDbQf/8LpKfDFUCaewnsbdAaixv2xqOS5TU+zMcGZ/0R2aNCBUOnTp3Cr7/+ir///htbt25FxYoVsWHDBvj7+6Nly5aGbiORxeF+Qrop6jIC2oaCDsUk5bsXmzKBON/fU2YmsHMn8MsvwOnT2Qdp1AhZY8di0YMHyHJ2xj9vPLW+Plub9Udkrxz0fcC2bdvQqVMnFCtWDJcuXUJGhphQ+OLFC5P0Fi1duhT+/v5wc3NDUFAQTp06lW/9EydOICgoCG5ubqhatarGmXBE+jhwPREt5xzFgJVnMWlzNAasPIuWc47iwPVEczfN4iiHu4DsQEVJ15lPyqGg0IYVEfLvoorKXiNvqXqPkrfUTW3/Lk2/p6MnrgGzZgH+/kDfvmIg5OQE9Osn3o6KgmLoUGQ5OwMApMWc87SptLszllvKqtdEVGR671rfqFEjfPzxxxgyZAg8PDxw5coVVK1aFdHR0ejcuTOSkpKM1VZs2bIFgwcPxtKlS9GiRQv8+uuvWLVqFWJiYlC5cuU89WNjY1G3bl2MGjUKo0ePxp9//olx48YhIiIC7733nk7PyV3rKSdt08S5O3z+DL3DurLHJyktHc9eZqBMcRd4S4upen40/Z7qJd5B2KXd6H7zJFzlWWKhlxcwerT4U7Giqq5MJlMtIvvZ51/gUvyL/FegtlPsISVLZtRd62/fvo1WrVrlKS9ZsiRSUlL0PZxe5s+fjxEjRqjWM1qwYAEOHjyIZcuWaVz9evny5ahcuTIWLFgAAKhduzYuXryIefPm6RwMKclkMshksjzlDg4OcHJyUqunjUQigbOzc6HqZmZmQlvcaqy6AODi4lKoullZWVAoFAap6+zsrNoOxlh15XJ5vlvJODs7QyGI08AlUMBRw6CPBMD3v19D+1pecHZy1Om4Tk5OcHBwMGpdhUKBrKwsrXUdHR1Vu7Ibq27HwPJoXb0MLj54jicv0lHOww1N/ErD0UECmUymVlcQBGRmZmo97uFbj/Hd3tv/BlYCnKCAd0k3TOtaC/IsD8gUAr7//RocIYejPAudbkciLGo3GifcVh0jplIAqv/nc+D99wFXVwCAQ1aW6m855/tcnpWJt/xK4i2/7A9TQSEHHHT7u7fVz4hDMUmYve8WHqZl/64qlnTGl11roUOgt8Zj2/pnhK51TfF3b22fEfrULegzImddXekdDPn4+ODu3buoUqWKWvnp06dRtWpVfQ+nM5lMhqioKHzxxRdq5R07dsSZM2c0PiYyMhIdO3ZUK+vUqRNWr16NzMxMtT94pYyMDNXQH5C9Se1PP/0EN7e8SZ41atTAwIEDVffnzZun9Zfk5+eHsLAw1f2FCxfi9WvN+wxVqFABo0aNUt1fsmQJUv/d+Tq3cuXKYdy4car7K1euxJMnTzTWlUqlmDx5sup+eHg4EhISNNZ1d3fHp59+qrq/adMmPHjwQGNdZ2dnfPnll6r7v/32G+7k3KMpl+nTp6tu79ixAzExMVrrTps2TfXBuGfPHly5ckVr3alTp6J48eIAgIMHD+LixYta606aNAmlSpUCABw5cgSRkZFa644dOxb3XjgiMTUdDZ0S0chZy5BYJnAkqhI6NxOHhs6ePYvDhw9rPe7QoUNVf0tRUVHYv3+/1roDBgxAzZo1AQDXrl3Drl27tNZ9//33UadOHQDAzZs38b///U9r3dDQUDRs2BAAcPfuXURERGit26VLFzRt2hQAEBcXh3Xr1mmt+84776BFixYAgMTERKxatUrt/4/muN26dWu0adMGAPDkyRMsW7ZM63GvZ5ZHYpY4c7WERIY+bteATODirkhc/PeU9HrxAkEXL6JB1GWUfin+DcscnHCzbiDON22KhEqVgLg4YP581XEbNGiAnj17AoDa33DuNdUAIDAwEH369FHdz28rIlv+jHhbcEIEGqru10+/pvZ7yMkePiO8vLwAiHm1J06c0Fp35MiRqPhvTyQ/I7R/RuSkz2dESEhInmt/QfQOhkaPHo1JkyZhzZo1kEgkSEhIQGRkJKZOnYpvv/1W38Pp7OnTp5DL5ShfXn1WR/ny5bUOzSUlJWmsn5WVhadPn8LHJ2/3/OzZszFz5kzDNZxshq7TxJ+/1v5tnopOa9+kIKDSw4doeu4cAmNi4PjvN/5/SpTBxoZdsK3hO+jkqTmYJ8Mo7JpQROamd84QAHz11Vf4+eefkZ4uXhxcXV0xdepUfPfddwZvoFJCQgIqVqyIM2fOqDaIBYBZs2Zhw4YNuHXrVp7H1KxZE8OGDcO0adNUZX/++SdatmyJxMREeHvn7crV1DPk6+uLJ0+eaBxztNUucCUOk2XXPfv3MwxYeRYOUMAhn4/99SNC0LxGOZ2Oyy7wvHW1dYGfi32GYWvPQwEJFKq5HwLcs9LR7eZpDLm0B/WS7qnqR1WshfCgHthfswWyHJ2gHFJTWjusKZrlmMWW8285IyMDP/74IwDgk08+UXu/5q4L2NcwmfL3oJSVY982Rygg+fdvI/f5BWz/M4LDZJY1TGbUnCFADEC++uorxMTEQKFQIDAwECVKlCjMoXTm6ekJR0fHPL1Ajx8/ztP7o+Tt7a2xvpOTE8qW1bxQmaurK1z/zSHIycXFJc8Hoia61NG3rlwh4GJcms5JipqG/0xdN+eHvyHqFiZRU5826DLGnHOauKY/WeU08WbVsqdi6zN2bay6Dg4OOr/XLKGuRCLRWPfZG7nahdc77SkGRe/HgCsH4PlaHB7KcHRGUteemF65LU6UqJwrZJUgC46q31PzGuW1voecnZ3x/vvvAxCHi5UXDW2M8Xevb11T/d3n/j3kJM8xQfnZG3m+7Tf0Z4Sx61rC3zI/I0TaPiOKQu9gaPjw4Vi4cCE8PDzQpEkTVfmrV6/w0UcfYc2aNQZtoJKLiwuCgoJw6NAh9OrVS1V+6NAhhIaGanxMSEgIdu/erVb2xx9/oEmTJnp9GJiToWfhFJY5Z41Yyjmwx93mLYmXhxsgCGj68AaGRu1Gp78i4SSI3+ofeZTDpkZdENGgE5ZO6oT+b2Q4UYTfk4ODgyqfgtQVZSFNIkul9zCZo6MjEhMTVYliSk+fPoW3t3e+3VxFpZxav3z5coSEhGDFihVYuXIlbty4AT8/P0ybNg2PHj3C+vXrAWRPrR89ejRGjRqFyMhIjBkzxmqm1lvKNG5zBiOWcg5yt8kSgjO78vo1FBs34e6MOaiZmD0Udta3LsKDeuBQjWAoHBzhLXXD6c/bqabX8/dkeHKFgJZzjha4kKby90BkLkYZJktLS4MgCBAEAS9evFCbWSWXy7Fv3748AZKh9evXD8nJyfjPf/6DxMRE1K1bF/v27YOfnx8AMRs9Li5OVd/f3x/79u3Dxx9/jCVLlqBChQr45Zdf9J5Wbw6F3e3b0LQFI0mp6Ri78ZJRgxFLOQe5WdoGmTa91sv9+8DSpcDq1XB49gw1AbxxcsXOOm2wrnF33PLyB6C5x6covyeFQoGbN28CEJfkKGiYrLCs8XfHHlKyRTr3DDk4OKiSwzQeSCLBzJkz8dVXXxmscZbAXD1DkfeSMWDl2QLrRYwKNtpGjcpvgNp2HTf2N0BLOAeWziZ7PwQBOHZM3Cvs998BZYJrlSrA+PE4EtIVX59MNOprzrnoYs5p24Zk7b87a28/2T6j9AwdO3YMgiCgXbt22LZtG8qUyZ4l4OLiAj8/P1SoUKHwrSY1hd3t25DOxz7TGggB4jfCxNR0nI99ZpRgxBLOgSXbdzUB4/57OU+5KXrtjOLVK2DDBmDxYuDGjezyd94BPvoI6NYNcHREewBtQmpbXY9KTubscTUUS+shJSoKnYOh1q1bAxDzcCpXrpxvLxEVnSUkKZo7GLGEc2Cp9l1NxISIvIEQYJ4hxCIN99y7ByxZAqxZAygXDSxeHBg6FBg/HggMzPMQ5X5l1shSh38Lw5p/D0Q56T2b7OjRoyhRooTa6qsAsHXrVrx+/RpDhw41WOPsWVF3+zYEcwcjlnAOLNGB64kY999L+dYxdq9d7vboPVyiUACHDolDYfv2iUNjAFC9OjBhAhAWBkilRm23uZi7x5WI8tI7K/DHH3+Ep6dnnnIvLy+T7FpvLwyx23dRKYMRbc8ggXjRM1YwYgnnwNIoexV0ZewhROVwT+6Lu3K4Z9/VBETeS8au6EeIvJcMeUqqGADVrg107gzs3SsGQl26iEHR7dvApEk2GwgB5u9xJaK89O4ZevDgAfz9/fOU+/n5qc3koqLrXNcHyz5onOdbt7eJkhQtYdaIuc+BpSmoVyE3Yw4hFjTcAwATIi5DIQBVkx9iyKU9qH/9CIrL3oj/WbIkMGyYOBRWo4bR2mlqBQ0ZmrvH1ZpZ4+w7sg56B0NeXl64evVqno1ar1y5onVVZyo8cycpWkIwYu5zYEn06S0wZq8dUHBgJhEUaHP3IsKidqPV/ez8prtlKkE2ZiwCv/gI8PAwWvvMQZchQw7/Fg5nr5Ex6R0M9e/fHxMnToSHhwdatWoFADhx4gQmTZqE/v37G7yBZP4kRUsIRsx9DiyFPr0Fxu610xaYlUx/iT7XDmPwpb2okpIIAFBAgiPV38K6xj3wZ5WG8C5RDKeLl9CyqYP5OTo6qla213VLA11niFlCj6u1sYXZd2TZ9A6Gvv/+ezx48ADt27dX7euiUCgwZMgQ5gzZMAYjlqGgXgUAcJAAiwc0MvrFIXdgVuPJAwy9tAe9bhxD8UwxUEp1LY4t9TtiQ+NuiC+VvTGypScIOzo6omHDhjrX13eGmCX0uFoLW5p9R5ZL72DIxcUFW7ZswXfffYcrV66gWLFiqFevnmoVaCIynvx6FZQWD2iMrvWNfzFt6l8GFT2cUTfqBIZG7UHzuKuq/7vl6Yd1QT2wM7AN3rho7s2ypQThwswQM2ePqzXl3nD2HZlCoXatB4CaNWuiZs2ahmwLEelAW6+CSfMnkpPhuGoVDi9ZhGKJjwAAcokD/qgRjPCgHjjnWxcoYC2yoiQIG/tirlAocPfuXQBA9erVC9yOo7AzxMzR42ptuTecfUemoFMwNGXKFHz33XcoXrw4pkyZkm/d+fPnG6RhRKSd2XoVrlwRp8Zv2gSkp6MYAFmp0tjcoBOWB3ZEQklxf0IHCaDQMo5X1ARhU1zMs7KyEBERAUC37TisZYaYNebe6HrO7j99beSWkC3TKRi6fPkyMjMzVbe14arURKZjsl6FzExg504xCDp1Kru8USPgo4/g0r8/Brm6oUaOwOz5KxnG/7swpCEThC31Ym4NM8SsNfdGlzw5AFhw+C8EeJewuGCOrINOwdCxY8c03iYiG/bkCbBiBbBsGfBIHAqDoyPw3nviXmEtWqiGwhyBPIHZMgfDJghb8sXcGmaIWWvujfLcjtmY/6rrgGUGc2QdCp0zREQ26uJFsRdo82ZAJhPLvLyADz8ExowBKlbU6TCGHsqz9Iu5pc8Qs+bcm851ffDxOzXw8+E7WuuY+/dP1k2nYKh37946H3D79u2FbgwRmYlMBmzbJgZBkZHZ5U2aABMnAn37Aq6ueh/WkEN51nAxt4Q1ubSxlrwmbap4FtepniUGc2T5dAqGpDn2CRIEATt27IBUKkWTJk0AAFFRUUhJSdEraCIiC5CUBPz6K7B8uXgbAJydxeDno4+AZs3M274crOVibqlrcllDXlN+rOX3T9ZJp2Bo7dq1qtuff/45+vbti+XLl6tWZpXL5Rg3bhxKlixpnFYSkeEIAnDunNgLtHWrmCANAD4+4jDYhx8C3t75H8MMgvxK5ztLDRBnsSU8f43Ie7CYHhlLYQ15Tfmx9mCOLJtEEIT8EvTzKFeuHE6fPo2AgAC18tu3b6N58+ZITk42aAPNLS0tDVKpFKmpqQz2yLplZABbtgC//AJERWWXN28u9gL17g0UMIXcnCLvJWPAyrM61y/KdHu5XI6of89RUFCQzltyWANrW2coJ+VsQkBzMGeJSwOQ+ehz/dY7gTorKws3b97MEwzdvHkTCoVC38MRkbE9fCgOg61YIc4QA8T8n/79xXygxo3N2z4d6ZsLUpTp9o6OjmjatKlej7EWlpzXVBBLT1In66V3MDRs2DAMHz4cd+/eRXBwMADg7Nmz+PHHHzFs2DCDN5DI3hhkdWVBAE6fFofCtm8H5HKxvFIlYNw4YORIoFw5wzfeiPTNBTHldHtr2t4CsNy8Jl1YczBHlkvvYGjevHnw9vbGzz//jMREcUdqHx8ffPbZZ/jkk08M3kAie1LkIYw3b4CICDEIio7OLm/VShwK69kTcLLOFTV0XXwvp8JOt1YoFIiLiwMAVK5cOd/tOKx52MlaWXMwR5ZJ75yhnNLS0gDApnNpmDNEpqJtdWWd8iEePACWLgVWrQKePRPLihUDBg0Sg6D69Y3VbJPSljNSkIX9GyK0oW7rIwGATCbD7NmzAeS/HUeRfmdEZFT6XL/z331Qi6ysLBw+fBgRERGqLTgSEhLw8uXLwhyOyO4VtLoyIA73yHNOpRIE4OhRoFcvoGpVYO5cMRCqUkW8/fAhsHKlzQRCQHbOiLdUvyGzgobY5AoBkfeSsSv6ESLvJauf53weo/fvjIgskt795Q8ePEDnzp0RFxeHjIwMdOjQAR4eHpg7dy7S09OxfPlyY7STyKbptbqytxuwYQOweDFw40Z2pfbtxYTobt3EbTNsVM6ckaS0dHy35waevcrUWFeX6daahrkqlXRGhwLaYekrYhOR7vQOhiZNmoQmTZrgypUrKFs2+w+8V69eGDlypEEbR2QvdJkp5ZuShHIzvgT2/AakpIiFxYsDQ4YAEyYAgYHGbaQFyZkzUszZId/p1vmtnaNtmOuftHSgWP5tsKQVsa0tgZvI0ugdDJ0+fRp//vlnnjF0Pz8/PFJu5kgF4ocX5aR1GEcQ8Pb9yxgatRvt7l2Eg/KyXa2aGACFhQGlSpmqmRapsNOtdRnmUtbT9NinLzJ0ap+xV0RmAjdR0ekdDCkUCsiV03RzePjwITw8PAzSKFvHDy/KLfdMqeIZr/He9SMYemkvqj17qKondOoMyUcTgC5dgHxmONkb5dDZ2XvJiPz7KQCx5yi4qvbhqYKGuZQuPniOtwOyV+TW9PeriSlWRNbWs1WUNZaI7JHewVCHDh2wYMECrFixAgAgkUjw8uVLTJ8+HV27djV4A20NP7xIE+VWCXN/2Y0hl/bgvWuH4SF7AwB44VIM/6v3DqrN+Ayturc0c0st16GYJLUgZfGxu/l+ydB1+OpJjnra/n5zM8X2FgX1bJlqjSUiW6B3MDR//ny0a9cOgYGBSE9Px8CBA3Hnzh14enoiIiLCGG20GfzwIo0UCmD/fnRetAidDx5UFd8tUwnrgrrjTPOu+PT9JmjFIFmrwnzJyG/4SgEJLmRWAgC8U9IdQP5/v7mZYkVkJnATGY7ewVDFihURHR2NzZs3IyoqCgqFAiNGjMCgQYNQrFgBGYd2jh9epCYlBVi7FliyBLh3TyyTSCB0646b7w/FnfrN0LVkMcxgPlm+CvslI79FHBVwwI0sb3hL3RBcXVypW9dhtW+61UZYC3+j/84sKYGbyNrpFQxlZmYiICAAe/bswbBhw7j9hp4s5cOLydtmFhMjrhC9YQPw6pVYVqoUMHw4MG4cJNWqIRCA/cwNK5rCfsnQdxd3Xf8uPT1cTfL3pGtitrETuIlsgV7BkLOzMzIyMlQLLZJ+LOHDy1qSt20uYJPLgT17xB3jjx7NLq9TR1wh+oMPxGnypLeifMnQOhOtpCs+aVkO9UoroFAo4ODgYBF/vzkVtD2JKRK4iWyF3sNkH330EebMmYNVq1bByUr3ODIXc394WUvytrUEbDp59gxYvVrcKuP+fbHMwQEIDRWDoDZtAH65KJKiBimaNv5sWLEE5s75ETeOZW/HYe6/39z07dkiIu30jmbOnTuHI0eO4I8//kC9evVQPNe32e3btxuscbbGnB9e1pK8bS0BW4GuXBGHwjZtAtL/DerKlAFGjQLGjgX8/MzbPhtiiCAl98afMplMYx1LCz4Ku8YSEanTOxgqVaoU3nvvPWO0xS6Y68PLGpK3rSVg0yorC9i5UxwKO3Uqu7xhQ7EXaMAAcfNUMihTBimWGHxo6tmy+mFlIhPTOxhau3atMdphV8zx4WUpydv5sYaATaMnT8QNUZctEzdHBcS9wd57TwyCWrQw6FCYzeVTGYApgxRLDD5y92wRkX50DoYUCgV++ukn7Ny5E5mZmXjnnXfw7bffws2NMxUKw9QfXpaW/KmJNQRsaqKixKGwzZuBjH+3ZihXDhg9GhgzBqhY0eBPaVP5VAZmyiCFwQeRbdE5GJozZw6+/vprtG/fHsWKFcP8+fPx9OlT1UrUZNksLflTE2sI2CCTAdu2iUFQZGR2eZMm4o7xffsCrq5GeWprzKcydS+WsYIU9sYR2Tadg6Hw8HAsWrQI48aNAwAcOHAAPXv2xK+//sqp9lbAEpM/c7PogC0pCfj1V/EnMVEsc3YG+vQRh8KaNTPqrDBrzKeylV6sQzFJ+H7/Hat/HUSknc47PT548ADdu3dX3e/UqRMEQUBCQoJRGkbayRUCIu8lY1f0I0TeS9a4q7YmyrwKb6l6z4q31M0iehWUARuQHaApmSVgEwTg7Flg0CCgcmVgxgwxEPLxAWbOBOLixNliwcFGnx6vTz6VJVD2YuVus7IX68D1RDO1TDeOjo5o3bo1KtZujImbr1jt6yAi3ejcMySTydS225BIJHBxcUGGMleCTKKo37YtMfkzJ4uYrZORAWzZIg6FXbyYXR4SIg6F9e4NuLgYvx05WFM+lTX2YuXm6OiIt1u1xrQ5RyFH3nNqLa+DiHSj12yyb775Bu7u7qr7MpkMs2bNglQqVZXNnz/fcK0jNYbKGbH05E+zBWyPHokzwlasEGeIAWLQM2CAOBQWFGTc58+HVeRT/ctqZwXmYiuvg4gKpnMw1KpVK9y+fVutrHnz5vj7779V95k7ZDy28G1bHyYL2AQBOH1a7AXavl3cNgMAKlUSF0ccNUqcIWZmFp1PlYs19WJpIwgCHjxKRCnJG6QIbsg7cJvNkl8HEelG52Do+PHjRmxGwZ4/f46JEyfi999/BwC8++67WLRoEUqVKqX1MWFhYVi3bp1aWbNmzXD27FljNtUo+C3VwN68ASIixCAoOjq7/O23xaGwnj0BC9puxhoS4JWsqRdLm8zMTNw+tg293IANbxohC45a61ry6yAi3eicQG1uAwcORHR0NA4cOIADBw4gOjoagwcPLvBxnTt3RmJioupn3759Jmit4dnCt22L8OAB8MUXgK8vMGKEGAgVKwaMHCnePnkSeP99iwqElCw9AV5J2YulLSyTQMxzs4ReLF3YyusgIu10+sT/8ccf8dFHH+XZh0yTc+fO4enTp+jWrVuRG6d08+ZNHDhwAGfPnkWzZs0AACtXrkRISAhu376NgIAArY91dXWFt7e3wdpiLrbwbdtsBAE4flzsBdq1C1AoxHI/P2D8eDEoKmMdFzRLT4AHrKsXS1e28jqISDOdeoZiYmLg5+eHsWPHYv/+/XiiTC4FkJWVhatXr2Lp0qVo3rw5+vfvj5IlSxq0kZGRkZBKpapACACCg4MhlUpx5syZfB97/PhxeHl5oWbNmhg1ahQeP36cb/2MjAykpaWp/VgCc3/bLux0frN69UpcF6hePaBdO2DHDjEQat9e3EPs3j3g00+tJhBSUuZThTasiJBqZS3yYmwtvVi6WNC/oU28DiLSTqeeofXr1+Pq1atYsmQJBg0ahNTUVDg6OsLV1RWvX78GADRq1Agffvghhg4dClcDr8CblJQELy+vPOVeXl5ISkrS+rguXbqgT58+8PPzQ2xsLL755hu0a9cOUVFRWts4e/ZszJw502BtNxRzftu2usXz/v4bWLIEWLMGSEkRy9zdgSFDxFlhgYFmbZ69sIZeLF10CPRG5/q+Vv86iEg7iSAIen3FFwQBV69exf379/HmzRt4enqiYcOG8PT01PvJZ8yYUWDgceHCBfzxxx9Yt25dntlsNWrUwIgRI/DFF1/o9HyJiYnw8/PD5s2b0bt3b411MjIy1NZOSktLg6+vL1JTUw3e41UYpg5MtE3nV14GLObbsSAAhw6JQ2F794r3AaBaNWDCBCAsDMgn2Z4oJ5lMhtmzZwMApk2bBhcTrytFREWXlpYGqVSq0/Vb7yxRiUSCBg0aoEGDBoVuoNKECRPQv3//fOtUqVIFV69exT///JPn/548eYLy5cvr/Hw+Pj7w8/PDnTt3tNZxdXU1eM+WIZny27ZVTOd/8QJYvx5YvBi4dSu7vFMnsReoSxfAwWrmCdgsTXt7AWBvCxFZBLNOmfH09NSpRykkJASpqak4f/48mjZtCkBM1E5NTUXz5s11fr7k5GTEx8fDx8cCejKKwFRr8Fj0dP6//hIDoPBwMSACAA8PsQdo/Hggn6R6Mi1NvZml3J0BACmvM1VlljT06ujoiJCQENVtIrJtVvGVuXbt2ujcuTNGjRqFs2fP4uzZsxg1ahS6d++uNpOsVq1a2LFjBwDg5cuXmDp1KiIjI3H//n0cP34cPXr0gKenJ3r16mWul2JVLG46v0IhDoF17iwGO4sWiYGQ8vajR8AvvzAQsiDa9ihLeZ2pFggBlrXfl6OjIzp27IiOHTsyGCKyA5a3mIoWmzZtwsSJE9GxY0cA4qKLixcvVqtz+/ZtpKamAhA/zK5du4b169cjJSUFPj4+aNu2LbZs2QIPDw+Tt98aWcx0/pQUYO1aMSn63j2xTCIBunUTF0h85x2jb5RK+stvmFUTixl6JSK7YzXBUJkyZbBx48Z86+TMBS9WrBgOHjxo7GbZNLNvARETIw6FrV8vTpMHAKlUXBdo3DgxOZosVkHDrJpYykrqgiCovlhJpVJuNURk44o8TPbgwQPExMRAoVzIjmyGcjo/kHcVXqNN55fLxYUR33kHqFNH3Dj11Svx9vLl4lDYTz8xELICRRk+NfdK6pmZmVi4cCEWLlyIzMzMgh9ARFZN52Bo3bp1WLBggVrZhx9+iKpVq6JevXqoW7cu4uPjDd0+MjOTLZ737Bnwf/8HVK8u7gt25Ig4C0x5+9o1YPRoQIdV0MkyFGX4lCupE5Ep6TxMtnz5cnz44Yeq+wcOHMDatWuxfv161K5dGxMmTMDMmTOxatUqozSUzMeo0/mvXhWTnzdtEjdPBcQVoUeOFIfC/PyK/hxkFgUNs2pi9KFXIiINdA6G/vrrLzRp0kR1f9euXXj33XcxaNAgAMAPP/yAYcOGGb6FZBEMOp0/K0scClu0CDhxIru8QQNxbaCBA8XNU8mq5bdquibc74uIzEXnYbI3b96oreB45swZtGrVSnW/atWq+W6NQYQnT4AffgD8/cWd4U+cABwdgT59xN3iL18Wk6MZCNkMbcOspd2dVWsNKXG/LyIyF517hvz8/BAVFQU/Pz88ffoUN27cQMuWLVX/n5SUBKlUapRGkpWLihJ7gTZvBpRbnZQrB3z4ITBmDFCpknnbR0albZgVsKwVqHOukl2mGNcWIrInOgdDQ4YMwfjx43Hjxg0cPXoUtWrVQlBQkOr/z5w5g7p16xqlkWSFMjOBbdvERRAjI7PLmzQRh8L69gXcmCRrL7QNs2oq07R1h7GDpNyrZDtBjsHsoCSyGzoHQ59//jlev36N7du3w9vbG1u3blX7/z///LPAfcbI9skTEpEwdyHKbQqH29N/95NzdhaHwj76CGjWjAskklam3ohY+Zy5NyNWQIKbWeUAAIdvPkbXBvn3XuYO4IL8SiPqwXOL6fUiovzpvWu9vdFn11u7du4cEr6bi3IHfoezPAsA8Lh4aewK7oHqX32Mtm0bmrd9ZPE0BSVAdmK1MfKJ5AoBLecc1bo4pHJ22+nP22kNZjQFcA4SQJHjhVjSvmtE9kKf67fB9iZLTEzEhAkTDHU4sgYZGcCGDUDTpkBwMCrs3Q5neRYuVQjAxB5T0WLsGvzQpC+GH3xkEftNkeXKb+sOZdnM3TGQKwz73U2fzYg10bb3Wu5mWtK+a0SUl17bccTExODYsWNwdnZG3759UapUKTx9+hSzZs3C8uXL4e/vb6x2kiV59EhcDXrFCuDxYwCAzNEZv9duhXWNu+OaTw216txvigqiT1BS1CUecg5p3fnnhdZndIXYw5kBJ40rYuuz9xr3XSOybDoHQ3v27MF7772nWpp+7ty5WLlyJfr27Yu6deti69at6N69u9EaSmYmCMCff4qzwrZvF9cKAoBKlRDXdyh6yWojuXgpzQ+FZew3lR9zJO1SNl233yjqNh2ahrQ0cYICA4tdAQBseNNI44rY+u69Zg1/B0T2SudgaNasWRgzZgxmzZqFFStWYOrUqRgzZgy2bdumtt4Q2Zg3b4CICDEIio7OLn/7bXHH+J49cfn6P0jeHK3tCCrm3m9KG3Mk7ZI6XbffKMo2HdpykgriXVLzitiFfT9b6t8BkT3TOWfo5s2bGD9+PEqUKIGJEyfCwcEBCxYsYCBkq+LigGnTAF9fcSHE6GhxKvyIEeLiiCdPigsnOjmZ5EJmLNpyPoyR4yFXCIi8l4xd0Y8QeS/Z4Pkv1ky5dYe2vjgJxAC1sNt06DOkldu0rrU09hIW9v1siX8HRPZO556htLQ0lCpVSnyQkxOKFSuGmjVrGqtdZA6CIK4KvWgRsHMnoFCI5ZUrA+PHi4FQ2bzd+wXtQWWp+00VlLRryBwP9j7lL7+tOwyxTYe+Q1o5dQj01liu795rlvp3QER6ziaLiYnB1atXcfXqVQiCgNu3b6vuK3/ICr16JSZDN2gAtG0r5gQpFEC7duLte/eAzz7TGAgB2RcyAHm+2VvyflNFnUmkK1P2PlkzbVt3GGKbDl2Hpia0rY6F/Rti7bCmBdbN732fmyX/HRCRnrPJ2rdvj5zLEikTpiUSCQRBgEQigVwuN2wLyXj+/htYuhRYvRpISRHL3N2BIUOACROAOnV0PpTyQpa798Pbgns/TJG0a8reJ1ugbeuOop4bXYemWlT3REi1spDJZDiqY3s1ve9zrzNkyX8HRKRHMBQbG2vMdpCpCAJw+LA4FLZnj3gfAKpVE4fChg0D/h0O1ZexLmTGYopcJ1NOGbcV2rbuKApjDuVqet9zBWoi66LXRq1kxV68ANavF4Og27ezyzt1ErfJ6NIFcCj6GpzGuJAZiylynUw1ZZzyp29OkoODAxo0aKC6rcvxc7/vreXvgIj0yBl6/fo1xo8fj4oVK8LLywsDBw7E06dPjdk2MoS//gImTQIqVhSHvm7fBjw8xADo1i3gwAGgWzeDBELWxhS5TtY8087W6JOT5OTkhJ49e6Jnz55wctIrm4CIrJDOe5N9+umnWLp0KQYNGgQ3NzdERESgTZs2eTZstTVWuTeZQiEGOYsWif8qBQSIAdGQIYC1vBYTMOZML+XeVwX1PuW39xUZFhfYJLIP+ly/dQ6GqlWrhlmzZql2pj9//jxatGiB9PR0ODo6Fr3VFsqqgqHUVGDtWmDJEuDuXbFMIhF7fj76CHjnHbvsAdKFMS+QytlkgObhGWNsQEpFIwiCarV9Z2dnSCQMloisjVGCIRcXF8TGxqJixYqqsmLFiuGvv/6Cr69v0VpswawiGIqJARYvFnOCXr0Sy6RSYPhwMSm6WjXzto+4zpCVkclkmD17NgBg2rRpcHFxMXOLiEhf+ly/dR4Ml8vleT4QnJyckKXco4pMSy4XZ4MtWgQcOZJdHhgo9gJ98AFQooT52kdqrG2mHRGRPdE5GBIEAWFhYXB1dVWVpaenY8yYMShevLiqbPv27YZtIal7/lxcF2jJEuD+fbHMwQF4910xCGrbVhwaI4tjTTPtiIjsic7B0NChQ/OUffDBBwZtDOXj2jWxF2jjRnHzVAAoUwYYORIYOxaoUsWszSMiIrJWOgdDa9euNWY7SJOsLGDXLjEIOnEiu7x+fXHH+AEDxBWjiYiIqNC4gIYlevoUWLkSWLYMiI8Xyxwdgd69xaGwli05FGZHOBWciMi4GAxZkkuXxF6giAggI0MsK1cO+PBDYMwYoFIl87aPTI6z0IiIjI/BkLllZgLbtolB0Jkz2eVBQeJQWN++gBtXJ7Z1mnp/DsUkYezGS3kWa1Tuds/1iYzHwcEBgYGBqttEZNsYDJnLP/8AK1aIQ2GJiWKZkxPQp484FBYczKEwO6Gp98e7pBvSs+Tc7d6A9BludHJyQp8+fUzcQiIyFwZD5vL118CqVeJtb29g9Gjxx4ff9O2JcnXqPL0/aflv3Mrd7vXD4UYiyg/7f81l/Hix92fTJuDBA2DGDAZCdkauEDBzd4zG3h9dcbf7gikDzpyBEJA93HjgeqKZWkZEloI9Q+bSsCEQGWnuVpAZnY99lucCrS/udp+//ALO/IYbuR0HkX1hMERkJkXp1VHudt/Uv4zB2mOLU/gLCjiNPdxoi+eUyBYxGCKD4wVAN4Xt1VGeyek9Ag12Xm01p0bXgNMYw422ek6JbBGDITIoXgB019S/DHykbkhKTdc4jCMBUMrdGa5ODkhKy1CVexv4fGpN4raBKfy6BpyGHm605XNKZIsYDJHB8AKgH0cHCab3CMTYjZcgAdTOm7K/Z3bvekbd7b6wOTXWQpeA0xjDjbZ8TolsEWeTkUEUdAEAxAuAXFGUuVO2p3NdHyz7oDG8peo9E95SN1XwqNztPrRhRYRUK2vQC6g+OTXWSBlwAtkBppIxhhsB2z+nRLaIPUNkEOZOVLVmnev6GLX3Jz/mzKkxFWXAmWdhSyMN39rDOSWyNQyGyCB4ASgaZe+PqZkrp8bU9A04HRwcUKNGDdVtfdjLOSWyJQyGyCB4AbBO5sipMRd9Ak4nJycMHDiwUM9jT+eUyFZYTc7QrFmz0Lx5c7i7u6NUqVI6PUYQBMyYMQMVKlRAsWLF0KZNG9y4ccO4DbVTyguAtoEdCcRZZbwAWBZz5NTYOp5TIutjNcGQTCZDnz59MHbsWJ0fM3fuXMyfPx+LFy/GhQsX4O3tjQ4dOuDFixdGbKl94gXAeumSxE364Tklsi4SQRCsanpPeHg4Jk+ejJSUlHzrCYKAChUqYPLkyfj8888BABkZGShfvjzmzJmD0aNH6/R8aWlpkEqlSE1NRcmSJYvafJvHdYasFxfLzCaTyTBv3jwAwNSpUwu9HQfPKZH56HP9ttmcodjYWCQlJaFjx46qMldXV7Ru3RpnzpzRORgi/ZhzZhQVjbmSuC1VZmZmkY/Bc0pkHWw2GEpKSgIAlC9fXq28fPnyePDggdbHZWRkICMje7XftLQ04zTQhvECQERE1sSsOUMzZsyARCLJ9+fixYtFeg6JRL1HQhCEPGU5zZ49G1KpVPXj6+tbpOcnIiIiy2bWnqEJEyagf//++dapUqVKoY7t7e0NQOwh8vHJzlV5/Phxnt6inKZNm4YpU6ao7qelpTEgIiIismFmDYY8PT3h6elplGP7+/vD29sbhw4dQqNGjQCISZEnTpzAnDlztD7O1dUVrq6uRmkTERERWR6rmVofFxeH6OhoxMXFQS6XIzo6GtHR0Xj58qWqTq1atbBjxw4A4vDY5MmT8cMPP2DHjh24fv06wsLC4O7uXujF1IiIiMj2WE0C9bfffot169ap7it7e44dO4Y2bdoAAG7fvo3U1FRVnc8++wxv3rzBuHHj8Pz5czRr1gx//PEHPDw8TNp2IrIuEokEfn5+qttEZNusbp0hU+M6Q0RERNZHn+u31QyTERERERkDgyEiIiKya1aTM0REVBBDbX8hk8mwcOFCAMCkSZMKvR0HEVkHBkNEZBMMvS/e69evDdk8IrJgHCYjIqt34Hoixm68pBYIAUBSajrGbryEA9cTzdQyIrIGDIaIyKrJFQJm7o6BpmmxyrKZu2MgV3DiLBFpxmCIiKza+dhneXqEchIAJKam43zsM9M1ioisCoMhIrJqj19oD4QKU4+I7A8TqIkMzFAzmkg3Xh5uBq1HRPaHwRAZjT0GBYae0UQFa+pfBj5SNySlpmvMG5IA8JaK7z9dSSQSVKhQQXWbiGwbt+MoALfjKBx7DAqUM5py/0EpL6XLPmhss6/d3JTnHoDa+ee5J7Jf3I6DzMoepzlzRpN5da7rg2UfNIa3VH0ozFvqxkCIiArEYTIyqIKCAgnEoKBDoLdNDZnpM6MppFpZ0zXMjnSu64MOgd52NzRLREXHYIgMyl6DAs5osgyODhKDvK8yMzOxZMkSAMD48ePh7Oxc5GMSkeViMEQGZa9BAWc02RZBEJCamqq6TUS2jTlDZFD2GhQoZzRpG5CRQEwg12dGExERmQaDITIoew0KHB0kmN4jEADyvHbl/ek9Apm/QkRkgRgMkUHZc1DAGU1ERNaJOUNkcMqgIPc6Q942vs4QwBlNRETWiMEQGYU9BwWGmtFERESmwWCIjIZBAVkriUSCcuXKqW4TkW1jMERElIuzszPGjRtn7mYQkYkwgZqIiIjsGoMhIiIismscJiMiyiUzMxMrV64EAIwaNYrbcRDZOAZDRES5CIKAJ0+eqG4TkW3jMBkRERHZNQZDREREZNcYDBEREZFdYzBEREREdo3BEBEREdk1ziYjIspFIpFAKpWqbhORbWMwRESUi7OzMyZPnmzuZhCRiXCYjIiIiOwagyEiIiKyaxwmIyLKJTMzE+Hh4QCAsLAwbsdBZOMYDBER5SIIAhISElS3ici2cZiMiIiI7BqDISIiIrJrDIaIiIjIrjEYIiIiIrvGYIiIiIjsGmeTERFp4O7ubu4mEJGJWE3P0KxZs9C8eXO4u7ujVKlSOj0mLCwMEolE7Sc4ONi4DSWbIVcIiLyXjF3RjxB5LxlyBadY2wsXFxd8+umn+PTTT+Hi4mLu5hCRkVlNz5BMJkOfPn0QEhKC1atX6/y4zp07Y+3atar7/GAjXRy4noiZu2OQmJquKvORumF6j0B0rutjxpYREZGhWU0wNHPmTABQrQqrK1dXV3h7exuhRWSrDlxPxNiNl5C7HygpNR1jN17Csg8aMyAiIrIhVjNMVljHjx+Hl5cXatasiVGjRuHx48f51s/IyEBaWpraD9kPuULAzN0xeQIhAKqymbtjOGRm45TbcYSHhyMzM9PczSEiI7PpYKhLly7YtGkTjh49ip9++gkXLlxAu3btkJGRofUxs2fPhlQqVf34+vqasMVkbudjn6kNjeUmAEhMTcf52GemaxSZnCAIePDgAR48eMDtOIjsgFmDoRkzZuRJcM79c/HixUIfv1+/fujWrRvq1q2LHj16YP/+/fjrr7+wd+9erY+ZNm0aUlNTVT/x8fGFfn6yPo9faA+EClOPiIgsn1lzhiZMmID+/fvnW6dKlSoGez4fHx/4+fnhzp07Wuu4urrC1dXVYM9J1sXLw82g9YiIyPKZNRjy9PSEp6enyZ4vOTkZ8fHx8PFh8itp1tS/DHykbkhKTdeYNyQB4C11Q1P/MqZuGhERGYnV5AzFxcUhOjoacXFxkMvliI6ORnR0NF6+fKmqU6tWLezYsQMA8PLlS0ydOhWRkZG4f/8+jh8/jh49esDT0xO9evUy18sgC+foIMH0HoEAxMAnJ+X96T0C4eiQ+3+JiMhaWc3U+m+//Rbr1q1T3W/UqBEA4NixY2jTpg0A4Pbt20hNTQUAODo64tq1a1i/fj1SUlLg4+ODtm3bYsuWLfDw8DB5+8l6dK7rg2UfNM6zzpA31xkiIrJJEoFTJfKVlpYGqVSK1NRUlCxZ0tzNIROSKwScj32Gxy/S4eUhDo2xR8g+yGQyzJs3DwAwdepULtZKZIX0uX4zGCoAgyEiIiLro8/122pyhoiIiIiMgcEQERER2TWrSaAmIjKVrKws/PbbbwCAvn37wsmJH5VEtox/4UREuSgUCtXirAqFwsytISJj4zAZERER2TUGQ0RERGTXGAwRERGRXWMwRERERHaNwRARERHZNc4mK4Byge60tDQzt4SITEUmkyE9XdyXLi0tjdtxEFkh5XVbl402uB1HAR4+fAhfX19zN4OIiIgKIT4+HpUqVcq3DoOhAigUCiQkJMDDwwMSifVt0pmWlgZfX1/Ex8dzb7V/8ZzkxXOSF89JXjwnefGc5GUp50QQBLx48QIVKlSAg0P+WUEcJiuAg4NDgRGlNShZsiT/UHPhOcmL5yQvnpO8eE7y4jnJyxLOiVQq1akeE6iJiIjIrjEYIiIiIrvGYMjGubq6Yvr06XB1dTV3UywGz0lePCd58ZzkxXOSF89JXtZ4TphATURERHaNPUNERERk1xgMERERkV1jMERERER2jcEQERER2TUGQzZm1qxZaN68Odzd3VGqVCmdHhMWFgaJRKL2ExwcbNyGmlBhzokgCJgxYwYqVKiAYsWKoU2bNrhx44ZxG2pCz58/x+DBgyGVSiGVSjF48GCkpKTk+xhbfJ8sXboU/v7+cHNzQ1BQEE6dOpVv/RMnTiAoKAhubm6oWrUqli9fbqKWmo4+5+T48eN53hMSiQS3bt0yYYuN5+TJk+jRowcqVKgAiUSCnTt3FvgYW3+P6HtOrOU9wmDIxshkMvTp0wdjx47V63GdO3dGYmKi6mffvn1GaqHpFeaczJ07F/Pnz8fixYtx4cIFeHt7o0OHDnjx4oURW2o6AwcORHR0NA4cOIADBw4gOjoagwcPLvBxtvQ+2bJlCyZPnoyvvvoKly9fxttvv40uXbogLi5OY/3Y2Fh07doVb7/9Ni5fvowvv/wSEydOxLZt20zccuPR95wo3b59W+19UaNGDRO12LhevXqFBg0aYPHixTrVt4f3iL7nRMni3yMC2aS1a9cKUqlUp7pDhw4VQkNDjdoeS6DrOVEoFIK3t7fw448/qsrS09MFqVQqLF++3IgtNI2YmBgBgHD27FlVWWRkpABAuHXrltbH2dr7pGnTpsKYMWPUymrVqiV88cUXGut/9tlnQq1atdTKRo8eLQQHBxutjaam7zk5duyYAEB4/vy5CVpnXgCEHTt25FvHHt4jOelyTqzlPcKeIQIgdmV6eXmhZs2aGDVqFB4/fmzuJplNbGwskpKS0LFjR1WZq6srWrdujTNnzpixZYYRGRkJqVSKZs2aqcqCg4MhlUoLfH228j6RyWSIiopS+x0DQMeOHbWeg8jIyDz1O3XqhIsXLyIzM9NobTWVwpwTpUaNGsHHxwft27fHsWPHjNlMi2br75GisPT3CIMhQpcuXbBp0yYcPXoUP/30Ey5cuIB27dohIyPD3E0zi6SkJABA+fLl1crLly+v+j9rlpSUBC8vrzzlXl5e+b4+W3qfPH36FHK5XK/fcVJSksb6WVlZePr0qdHaaiqFOSc+Pj5YsWIFtm3bhu3btyMgIADt27fHyZMnTdFki2Pr75HCsJb3CHettwIzZszAzJkz861z4cIFNGnSpFDH79evn+p23bp10aRJE/j5+WHv3r3o3bt3oY5pbMY+JwAgkUjU7guCkKfMkuh6ToC8rw0o+PVZ4/ukIPr+jjXV11RuzfQ5JwEBAQgICFDdDwkJQXx8PObNm4dWrVoZtZ2Wyh7eI/qwlvcIgyErMGHCBPTv3z/fOlWqVDHY8/n4+MDPzw937twx2DENzZjnxNvbG4D4Lc/Hx0dV/vjx4zzf+iyJrufk6tWr+Oeff/L835MnT/R6fdbwPtHG09MTjo6OeXo88vsde3t7a6zv5OSEsmXLGq2tplKYc6JJcHAwNm7caOjmWQVbf48YiiW+RxgMWQFPT094enqa7PmSk5MRHx+vFghYGmOeE39/f3h7e+PQoUNo1KgRADGf4sSJE5gzZ45RntMQdD0nISEhSE1Nxfnz59G0aVMAwLlz55CamormzZvr/HzW8D7RxsXFBUFBQTh06BB69eqlKj906BBCQ0M1PiYkJAS7d+9WK/vjjz/QpEkTODs7G7W9plCYc6LJ5cuXrfI9YQi2/h4xFIt8j5gze5sM78GDB8Lly5eFmTNnCiVKlBAuX74sXL58WXjx4oWqTkBAgLB9+3ZBEAThxYsXwieffCKcOXNGiI2NFY4dOyaEhIQIFStWFNLS0sz1MgxK33MiCILw448/ClKpVNi+fbtw7do1YcCAAYKPj4/NnJPOnTsL9evXFyIjI4XIyEihXr16Qvfu3dXq2Pr7ZPPmzYKzs7OwevVqISYmRpg8ebJQvHhx4f79+4IgCMIXX3whDB48WFX/77//Ftzd3YWPP/5YiImJEVavXi04OzsL//vf/8z1EgxO33Py888/Czt27BD++usv4fr168IXX3whABC2bdtmrpdgUC9evFB9XgAQ5s+fL1y+fFl48OCBIAj2+R7R95xYy3uEwZCNGTp0qAAgz8+xY8dUdQAIa9euFQRBEF6/fi107NhRKFeunODs7CxUrlxZGDp0qBAXF2eeF2AE+p4TQRCn10+fPl3w9vYWXF1dhVatWgnXrl0zfeONJDk5WRg0aJDg4eEheHh4CIMGDcoz9dUe3idLliwR/Pz8BBcXF6Fx48bCiRMnVP83dOhQoXXr1mr1jx8/LjRq1EhwcXERqlSpIixbtszELTY+fc7JnDlzhGrVqglubm5C6dKlhZYtWwp79+41Q6uNQzktPPfP0KFDBUGwz/eIvufEWt4jEkH4N7uLiIiIyA5xaj0RERHZNQZDREREZNcYDBEREZFdYzBEREREdo3BEBEREdk1BkNERERk1xgMERERkV1jMERENuf48eOQSCRISUkxd1OIyAowGCIinUgkknx/wsLCTNaWsLAw1fM6OzujatWqmDp1Kl69emWyNuiqTZs2mDx5srmbQUT54EatRKSTxMRE1e0tW7bg22+/xe3bt1VlxYoVU6ufmZlp1M0pO3fujLVr1yIzMxOnTp3CyJEj8erVKyxbtsxoz0lEtok9Q0SkE29vb9WPVCqFRCJR3U9PT0epUqXw22+/oU2bNnBzc8PGjRsxY8YMNGzYUO04CxYsQJUqVdTK1q5di9q1a8PNzQ21atXC0qVLC2yPq6srvL294evri4EDB2LQoEHYuXOnWp2oqCg0adIE7u7uaN68uVrwBgC7d+9GUFAQ3NzcULVqVcycORNZWVmq/5dIJFi1ahV69eoFd3d31KhRA7///rvaMU6cOIGmTZvC1dUVPj4++OKLL1THCAsLw4kTJ7Bw4UJVT1ZsbCyqV6+OefPmqR3n+vXrcHBwwL1791TPvWzZMnTp0gXFihWDv78/tm7dqvaYR48eoV+/fihdujTKli2L0NBQ3L9/v8BzR0TqGAwRkcF8/vnnmDhxIm7evIlOnTrp9JiVK1fiq6++wqxZs3Dz5k388MMP+Oabb7Bu3Tq9nrtYsWLIzMxUK/vqq6/w008/4eLFi3BycsLw4cNV/3fw4EF88MEHmDhxImJiYvDrr78iPDwcs2bNUjvGzJkz0bdvX1y9ehVdu3bFoEGD8OzZMwBiMNK1a1e89dZbuHLlCpYtW4bVq1fj+++/BwAsXLgQISEhGDVqFBITE5GYmIjKlStj+PDhWLt2rdrzrFmzBm+//TaqVaumKvvmm2/w3nvv4cqVK/jggw8wYMAA3Lx5EwDw+vVrtG3bFiVKlMDJkydx+vRplChRAp07d4ZMJtPr3BHZPXPvFEtE1mft2rWCVCpV3Y+NjRUACAsWLFCrN336dKFBgwZqZT///LPg5+enuu/r6yv897//Vavz3XffCSEhIVqff+jQoUJoaKjq/rlz54SyZcsKffv2FQQhe2ftw4cPq+rs3btXACC8efNGEARBePvtt4UffvhB7bgbNmwQfHx8VPcBCF9//bXq/suXLwWJRCLs379fEARB+PLLL4WAgABBoVCo6ixZskQoUaKEIJfLBUEQhNatWwuTJk1Se56EhATB0dFROHfunCAIgiCTyYRy5coJ4eHhas89ZswYtcc1a9ZMGDt2rCAIgrB69eo8z52RkSEUK1ZMOHjwoNZzR0R5MWeIiAymSZMmetV/8uQJ4uPjMWLECIwaNUpVnpWVBalUmu9j9+zZgxIlSiArKwuZmZkIDQ3FokWL1OrUr19fddvHxwcA8PjxY1SuXBlRUVG4cOGCWk+QXC5Heno6Xr9+DXd39zzHKF68ODw8PPD48WMAwM2bNxESEgKJRKKq06JFC7x8+RIPHz5E5cqVNbbdx8cH3bp1w5o1a9C0aVPs2bMH6enp6NOnj1q9kJCQPPejo6MBiEOAd+/ehYeHh1qd9PR01VAbEemGwRARGUzx4sXV7js4OEAQBLWynENZCoUCgDhU1qxZM7V6jo6O+T5X27ZtsWzZMjg7O6NChQoak7VzlikDFuVzKhQKzJw5E717987zODc3N43HUB5HeQxBENQCIWVZzufTZuTIkRg8eDB+/vlnrF27Fv369VMFYPnJ+TqCgoKwadOmPHXKlStX4HGIKBuDISIymnLlyiEpKUktaFD2bABA+fLlUbFiRfz9998YNGiQXscuXrw4qlevXui2NW7cGLdv3y7SMQIDA7Ft2za113fmzBl4eHigYsWKAAAXFxfI5fI8j+3atSuKFy+OZcuWYf/+/Th58mSeOmfPnsWQIUPU7jdq1EjV/i1btsDLywslS5Ys9GsgIiZQE5ERtWnTBk+ePMHcuXNx7949LFmyBPv371erM2PGDMyePRsLFy7EX3/9hWvXrmHt2rWYP3++Udv27bffYv369ZgxYwZu3LiBmzdvYsuWLfj66691Psa4ceMQHx+Pjz76CLdu3cKuXbswffp0TJkyBQ4O4sdrlSpVcO7cOdy/fx9Pnz5V9So5OjoiLCwM06ZNQ/Xq1fMMiQHA1q1bsWbNGvz111+YPn06zp8/jwkTJgAABg0aBE9PT4SGhuLUqVOIjY3FiRMnMGnSJDx8+NAAZ4jIfjAYIiKjqV27NpYuXYolS5agQYMGOH/+PKZOnapWZ+TIkVi1ahXCw8NRr149tG7dGuHh4fD39zdq2zp16oQ9e/bg0KFDeOuttxAcHIz58+fDz89P52NUrFgR+/btw/nz59GgQQOMGTMGI0aMUAuopk6dCkdHRwQGBqJcuXKIi4tT/d+IESMgk8nUZrnlNHPmTGzevBn169fHunXrsGnTJgQGBgIA3N3dcfLkSVSuXBm9e/dG7dq1MXz4cLx584Y9RUR6kgi5B/SJiMgk/vzzT7Rp0wYPHz5E+fLl1f5PIpFgx44d6Nmzp3kaR2RHmDNERGRiGRkZiI+PxzfffIO+ffvmCYSIyLQ4TEZEZGIREREICAhAamoq5s6da+7mENk9DpMRERGRXWPPEBEREdk1BkNERERk1xgMERERkV1jMERERER2jcEQERER2TUGQ0RERGTXGAwRERGRXWMwRERERHaNwRARERHZtf8H06q3t0b1VFkAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.linear_model import Ridge, Lasso\n",
    "\n",
    "# ------------ Model fitting ------------\n",
    "# Initialize the Ridge object:\n",
    "prs_ridge = Ridge(alpha=1e-3)\n",
    "# Fit the model to the training data:\n",
    "prs_ridge.fit(X_train, y_train)\n",
    "\n",
    "# Initialize the Lasso object:\n",
    "prs_lasso = Lasso(alpha=1e-3)\n",
    "# Fit the model to the training data:\n",
    "prs_lasso.fit(X_train, y_train)\n",
    "\n",
    "# ------------ Evaluation ------------\n",
    "\n",
    "# Predict on the test set:\n",
    "prs_ridge_pred = prs_ridge.predict(X_test)\n",
    "prs_lasso_pred = prs_lasso.predict(X_test)\n",
    "\n",
    "# Let's compare the model prediction to the simulated phenotypes:\n",
    "plot_scatter(y_test, prs_ridge_pred, title=\"Ridge Model\")\n",
    "plt.show()\n",
    "plot_scatter(y_test, prs_lasso_pred, title=\"Lasso Model\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "11c0df0e",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-04-12T03:02:04.111258Z",
     "start_time": "2024-04-12T03:02:04.000811Z"
    }
   },
   "source": [
    "### Established PRS Methods that operate on individual-level data\n",
    "\n",
    "* [bayesR](https://github.com/syntheke/bayesR)\n",
    "* [snpnet](https://github.com/junyangq/snpnet)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "624ddf29",
   "metadata": {},
   "source": [
    "## (4) Inference of Polygenic Risk Scores (PRS) from GWAS Summary Statistics\n",
    "\n",
    "While individual-level data is valuable and offers the best and most straightforward way to infer accurate polygenic scores, in many cases, access to this data is restricted due to privacy or other concerns. Even when large-scale individual-level data is available, as in the case of the UK Biobank, we'd usually be restricted to using one biobank or one data source at a time for performing inference, which can severely limit the sample sizes that can be obtained. These concerns, among others, motivated researchers to develop ways to infer polygenic scores from GWAS summary statistics alone. The benefits of this are:\n",
    "\n",
    "1) **Protect individual privacy**: No need to access individual-level data. These analyses can be done via publicly available data only.\n",
    "2) **Larger sample sizes**: Can Leverage much larger sample sizes via meta-analysis of many smaller GWAS studies.\n",
    "3) **Computational efficiency**: It can be much faster and computationally efficient to infer polygenic scores in this way.\n",
    "\n",
    "\n",
    "### Intuition\n",
    "\n",
    "To see how polygenic scores can be inferred from GWAS summary statistics, let us turn back to the solution of the linear model we discussed previously:\n",
    "\n",
    "$$\n",
    "\\hat{\\beta} = (X^\\top X)^{-1}(X^\\top y)\n",
    "$$\n",
    "\n",
    "Here, we see that the solution depends on two quantities: \n",
    "\n",
    "* **The Linkage-Disequilibrium (LD) matrix** $X^\\top X$: This quantity is roughly similar across individuals of same ancestry, which means we can use publicly available data (e.g. 1000G Project) to estimate it.\n",
    "* **GWAS Summary Statistics** ($X^\\top y$): A measure that tells us about the correlation of the phenotype with each position in the genome. This can be approximated via Z-scores or p-values from GWAS studies.\n",
    "\n",
    "\n",
    "<img src=\"./figures/sumstats.png\" alt=\"drawing\" width=\"750\"/>\n",
    "\n",
    "In order for us to perform PRS inference from GWAS summary statistics, let's first go ahead and compute the LD matrix and perform GWAS on the training data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "62be21c7",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-04-12T16:13:59.597108Z",
     "start_time": "2024-04-12T16:13:59.270970Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "> Performing GWAS...\n",
      "> Computing LD matrix...\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, '-log10(P-Value)')"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Perform GWAS on the training data only:\n",
    "train.perform_gwas()\n",
    "\n",
    "# Compute LD matrix from training samples:\n",
    "train.compute_ld('sample', \n",
    "                 output_dir='./', \n",
    "                 dtype='float32')\n",
    "\n",
    "# -------- Visualize GWAS results: --------\n",
    "\n",
    "# Get GWAS summary statistics table:\n",
    "sumstats_table = train.to_summary_statistics_table()\n",
    "plt.scatter(sumstats_table.POS, -np.log10(sumstats_table.PVAL), marker='.')\n",
    "plt.xlabel(\"Genomic Position (Chromosome 22)\")\n",
    "plt.ylabel(\"-log10(P-Value)\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "387e76dc",
   "metadata": {},
   "source": [
    "### (4.1) Naive PRS\n",
    "\n",
    "In the initial work on PRS leveraging GWAS summary statistics, the first approach simply used the marginal $\\beta$s inferred by the GWAS as the PRS weights. To be concrete, if the marginal betas from the GWAS are denoted as $\\beta^{(GWAS)}$s, then the PRS prediction under this model is simply:\n",
    "\n",
    "$$\n",
    "\\hat{PRS}_i = \\sum_{j=1}^M X_{ij}\\beta^{(GWAS)}_j\n",
    "$$\n",
    "\n",
    "Since we just performed a GWAS, we can use the marginal BETAs to perform the prediction and see how well this approach fares in practice:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "e203b1bc",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-04-12T16:14:15.027425Z",
     "start_time": "2024-04-12T16:14:14.801944Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "> Generating polygenic scores...\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Score using the marginal BETAs:\n",
    "\n",
    "naive_prs_pred = test.predict({22: train.sumstats_table[22].marginal_beta})\n",
    "\n",
    "# Let's compare the model prediction to the simulated phenotypes:\n",
    "plot_scatter(y_test, naive_prs_pred, title=\"NaivePRS\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5f692356",
   "metadata": {},
   "source": [
    "As we can see, the `NaivePRS` approach is not as accurate as the models we derived from individual-level data. This is because this model assumes an infinitesimal architecture where all variants are causal and does not account for the fact that genetic variants tend to be highly correlated with each other. The latter fact implies that some non-causal variants may have large marginal effects by virtue of being correlated with a causal variant nearby in the genome.\n",
    "\n",
    "### (4.2) Clumping + Thresholding (C+T)\n",
    "\n",
    "An alternative approach to using all the marginal BETAs from GWAS is to restrict to **genome-wide significant variants**, e.g. those that pass the Bonferroni-correct P-Value threshold of $\\sim 5^{-8}$ (or some other user-provided threshold). This procedure is known as \"**Thresholding**\", because for variants that are above the p-value threshold, their effects will be set to zero. \n",
    "\n",
    "Thresholding on its own, however, will not tackle the issue of variants in a locus being highly correlated. So, the other procedure that we need to perform here is \"**Clumping**\", where, in each locus, we remove variants that are highly correlated (e.g. $r^2 > 0.9$) with the lead variant in that locus.\n",
    "\n",
    "In summary, for this method to work, the user has to specify **two parameters**:\n",
    "\n",
    "1) The P-value threshold for selecting \"significant\" variants.\n",
    "2) The $r^2$ threshold for clumping variants in LD with the lead variant.\n",
    "\n",
    "The following example shows how to perform this using the GWAS data we derived earlier:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "d432974d",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-04-12T16:14:20.694945Z",
     "start_time": "2024-04-12T16:14:20.270690Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Variants remaining after Clumping + Thresholding:\n"
     ]
    },
    {
     "data": {
      "text/html": [
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       "\n",
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       "        vertical-align: top;\n",
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       "\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>CHR</th>\n",
       "      <th>SNP</th>\n",
       "      <th>POS</th>\n",
       "      <th>A1</th>\n",
       "      <th>A2</th>\n",
       "      <th>MAF</th>\n",
       "      <th>N</th>\n",
       "      <th>BETA</th>\n",
       "      <th>Z</th>\n",
       "      <th>SE</th>\n",
       "      <th>PVAL</th>\n",
       "      <th>Keep_T</th>\n",
       "      <th>Keep_C</th>\n",
       "      <th>Keep_Final</th>\n",
       "      <th>CT_BETA</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>22</td>\n",
       "      <td>rs4819849</td>\n",
       "      <td>17152611</td>\n",
       "      <td>G</td>\n",
       "      <td>A</td>\n",
       "      <td>0.362132</td>\n",
       "      <td>272</td>\n",
       "      <td>0.271026</td>\n",
       "      <td>4.581396</td>\n",
       "      <td>0.059158</td>\n",
       "      <td>4.618815e-06</td>\n",
       "      <td>True</td>\n",
       "      <td>True</td>\n",
       "      <td>True</td>\n",
       "      <td>0.271026</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>22</td>\n",
       "      <td>rs738045</td>\n",
       "      <td>17281931</td>\n",
       "      <td>A</td>\n",
       "      <td>G</td>\n",
       "      <td>0.281250</td>\n",
       "      <td>272</td>\n",
       "      <td>0.284128</td>\n",
       "      <td>4.420265</td>\n",
       "      <td>0.064278</td>\n",
       "      <td>9.857992e-06</td>\n",
       "      <td>True</td>\n",
       "      <td>True</td>\n",
       "      <td>True</td>\n",
       "      <td>0.284128</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>91</th>\n",
       "      <td>22</td>\n",
       "      <td>rs7292561</td>\n",
       "      <td>17398508</td>\n",
       "      <td>C</td>\n",
       "      <td>T</td>\n",
       "      <td>0.351103</td>\n",
       "      <td>272</td>\n",
       "      <td>0.260404</td>\n",
       "      <td>4.470429</td>\n",
       "      <td>0.058250</td>\n",
       "      <td>7.806295e-06</td>\n",
       "      <td>True</td>\n",
       "      <td>True</td>\n",
       "      <td>True</td>\n",
       "      <td>0.260404</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>96</th>\n",
       "      <td>22</td>\n",
       "      <td>rs887755</td>\n",
       "      <td>17404605</td>\n",
       "      <td>G</td>\n",
       "      <td>A</td>\n",
       "      <td>0.384191</td>\n",
       "      <td>272</td>\n",
       "      <td>-0.263676</td>\n",
       "      <td>-4.449519</td>\n",
       "      <td>0.059259</td>\n",
       "      <td>8.606278e-06</td>\n",
       "      <td>True</td>\n",
       "      <td>True</td>\n",
       "      <td>True</td>\n",
       "      <td>-0.263676</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>98</th>\n",
       "      <td>22</td>\n",
       "      <td>rs5992587</td>\n",
       "      <td>17407349</td>\n",
       "      <td>T</td>\n",
       "      <td>C</td>\n",
       "      <td>0.415441</td>\n",
       "      <td>272</td>\n",
       "      <td>-0.282112</td>\n",
       "      <td>-4.861582</td>\n",
       "      <td>0.058029</td>\n",
       "      <td>1.164513e-06</td>\n",
       "      <td>True</td>\n",
       "      <td>True</td>\n",
       "      <td>True</td>\n",
       "      <td>-0.282112</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>104</th>\n",
       "      <td>22</td>\n",
       "      <td>rs5992589</td>\n",
       "      <td>17410790</td>\n",
       "      <td>A</td>\n",
       "      <td>G</td>\n",
       "      <td>0.334559</td>\n",
       "      <td>272</td>\n",
       "      <td>-0.325247</td>\n",
       "      <td>-5.447235</td>\n",
       "      <td>0.059709</td>\n",
       "      <td>5.115872e-08</td>\n",
       "      <td>True</td>\n",
       "      <td>True</td>\n",
       "      <td>True</td>\n",
       "      <td>-0.325247</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>106</th>\n",
       "      <td>22</td>\n",
       "      <td>rs9605179</td>\n",
       "      <td>17412216</td>\n",
       "      <td>G</td>\n",
       "      <td>A</td>\n",
       "      <td>0.373162</td>\n",
       "      <td>272</td>\n",
       "      <td>0.265622</td>\n",
       "      <td>4.541590</td>\n",
       "      <td>0.058487</td>\n",
       "      <td>5.583161e-06</td>\n",
       "      <td>True</td>\n",
       "      <td>True</td>\n",
       "      <td>True</td>\n",
       "      <td>0.265622</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>249</th>\n",
       "      <td>22</td>\n",
       "      <td>rs5992637</td>\n",
       "      <td>17675900</td>\n",
       "      <td>A</td>\n",
       "      <td>C</td>\n",
       "      <td>0.395221</td>\n",
       "      <td>272</td>\n",
       "      <td>-0.317252</td>\n",
       "      <td>-5.318850</td>\n",
       "      <td>0.059647</td>\n",
       "      <td>1.044252e-07</td>\n",
       "      <td>True</td>\n",
       "      <td>True</td>\n",
       "      <td>True</td>\n",
       "      <td>-0.317252</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>274</th>\n",
       "      <td>22</td>\n",
       "      <td>rs5747035</td>\n",
       "      <td>17718606</td>\n",
       "      <td>C</td>\n",
       "      <td>T</td>\n",
       "      <td>0.068015</td>\n",
       "      <td>272</td>\n",
       "      <td>0.607540</td>\n",
       "      <td>5.478188</td>\n",
       "      <td>0.110902</td>\n",
       "      <td>4.297024e-08</td>\n",
       "      <td>True</td>\n",
       "      <td>True</td>\n",
       "      <td>True</td>\n",
       "      <td>0.607540</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>275</th>\n",
       "      <td>22</td>\n",
       "      <td>rs5748976</td>\n",
       "      <td>17718911</td>\n",
       "      <td>C</td>\n",
       "      <td>G</td>\n",
       "      <td>0.066176</td>\n",
       "      <td>272</td>\n",
       "      <td>0.609581</td>\n",
       "      <td>5.263391</td>\n",
       "      <td>0.115815</td>\n",
       "      <td>1.414221e-07</td>\n",
       "      <td>True</td>\n",
       "      <td>True</td>\n",
       "      <td>True</td>\n",
       "      <td>0.609581</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>280</th>\n",
       "      <td>22</td>\n",
       "      <td>rs5748979</td>\n",
       "      <td>17722885</td>\n",
       "      <td>G</td>\n",
       "      <td>A</td>\n",
       "      <td>0.062500</td>\n",
       "      <td>272</td>\n",
       "      <td>0.714398</td>\n",
       "      <td>5.905964</td>\n",
       "      <td>0.120962</td>\n",
       "      <td>3.505901e-09</td>\n",
       "      <td>True</td>\n",
       "      <td>True</td>\n",
       "      <td>True</td>\n",
       "      <td>0.714398</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     CHR        SNP       POS A1 A2       MAF    N      BETA         Z  \\\n",
       "16    22  rs4819849  17152611  G  A  0.362132  272  0.271026  4.581396   \n",
       "30    22   rs738045  17281931  A  G  0.281250  272  0.284128  4.420265   \n",
       "91    22  rs7292561  17398508  C  T  0.351103  272  0.260404  4.470429   \n",
       "96    22   rs887755  17404605  G  A  0.384191  272 -0.263676 -4.449519   \n",
       "98    22  rs5992587  17407349  T  C  0.415441  272 -0.282112 -4.861582   \n",
       "104   22  rs5992589  17410790  A  G  0.334559  272 -0.325247 -5.447235   \n",
       "106   22  rs9605179  17412216  G  A  0.373162  272  0.265622  4.541590   \n",
       "249   22  rs5992637  17675900  A  C  0.395221  272 -0.317252 -5.318850   \n",
       "274   22  rs5747035  17718606  C  T  0.068015  272  0.607540  5.478188   \n",
       "275   22  rs5748976  17718911  C  G  0.066176  272  0.609581  5.263391   \n",
       "280   22  rs5748979  17722885  G  A  0.062500  272  0.714398  5.905964   \n",
       "\n",
       "           SE          PVAL  Keep_T  Keep_C  Keep_Final   CT_BETA  \n",
       "16   0.059158  4.618815e-06    True    True        True  0.271026  \n",
       "30   0.064278  9.857992e-06    True    True        True  0.284128  \n",
       "91   0.058250  7.806295e-06    True    True        True  0.260404  \n",
       "96   0.059259  8.606278e-06    True    True        True -0.263676  \n",
       "98   0.058029  1.164513e-06    True    True        True -0.282112  \n",
       "104  0.059709  5.115872e-08    True    True        True -0.325247  \n",
       "106  0.058487  5.583161e-06    True    True        True  0.265622  \n",
       "249  0.059647  1.044252e-07    True    True        True -0.317252  \n",
       "274  0.110902  4.297024e-08    True    True        True  0.607540  \n",
       "275  0.115815  1.414221e-07    True    True        True  0.609581  \n",
       "280  0.120962  3.505901e-09    True    True        True  0.714398  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "> Generating polygenic scores...\n"
     ]
    },
    {
     "data": {
      "image/png": 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ExETUrVsXv//+OypXrmxY5s6dO7h48aLhsTldQvS3iLdp08bo82JiYoz6DclJUePUFJW597kTkTpkZWVhxYoVAIA+ffpwVGGVKWhcE1IeOcap4S+ciFTLw8MDr776qqPDICI7UdTge0RERESmMKkhIiIiVWDzExGpVkZGBmbMmAEAeOedd/J0yiQidWFSQ0SqlpmZ6egQiMhO2PxEREREqsCkhoiIFM2FRiZRNTm+RyY1RESkSJ6engCAVEfMyk2y03+P+u/VGuxTQ0REiuTu7o6SJUvi1q1bAAA/P79CZ5Ym5yOKIlJTU3Hr1i2ULFkS7u7uVr8XkxoiIlKsoKAgADAkNqRcJUuWNHyf1mJSQ0SqJQiCYf4aXsGrkyAICA4ORmBgIO90UzBPT88i1dDoMakhItXy9PS02cR55Fzc3d1lOSmSsrGjMBEREakCkxoiIiJSBTY/EZFqZWRkYNasWQCAcePGcZoEIpVjUkNEqsYxTIhcB5ufiIiISBWY1BAREZEqMKkhIiIiVWBSQ0RERKrApIaIiIhUgXc/EZFqCYKA8uXLG/4msjetTsTBhHu49SANgf4+aBZaGu5u6tsXnWU9mdQQkWp5enpi+PDhjg6DXNTmU4mI2hCPxOQ0Q1mwxgcTu4Uhsm6wXWOxZdLhTOspiKIo2vUTHSglJQUajQbJyckoUaKEo8MhIiKV2nwqEaOWHEHuE6w+jZjTv7HdTvi2TDrstZ7mnr/Zp4aIiEhGWp2IqA3xeU70AAxlURviodXZvk5Bn3TkTGgAICk5DaOWHMHmU4lWv7czracekxoiUq3MzEx8++23+Pbbb5GZmenocMhFHEy4lyeJyEkEkJichoMJ92wah62TDmdZz5yY1BCRaomiiOTkZCQnJ8OFWtrJwW49MH2it2Y5a9k66XCW9cyJSQ0REZGMAv19ZF3OWrZOOpxlPXNiUkNERCSjZqGlEazxgal7iwRIHXWbhZa2aRy2TjqcZT1zYlJDREQkI3c3ARO7hQFAnhO+/vHEbmE2H8fF1kmHs6xnTkxqiIiIZBZZNxhz+jdGkMa4FiRI42O327ntkXQ4w3rmxMH3iIiIbCCybjA6hgU5dKRdfdKRe5yaIBkHx3OG9dRjUkNEqiUIAsqWLWv4m8je3N0ERFQr49AY7JF0OMN6AhxRmIiIiJwcRxQmIiIil8KkhoiIiFSBfWqISLUyMzMxf/58AMDw4cPh6enp4IiIyJaY1BCRaomiiNu3bxv+JiJ1Y/MTERERqQKTGiIiIlIFJjVERESkCuxTQ0REZCatTnSKkXMpf0xqiIhIURyVWGw+lZhnuoGSvp4Y/EwVjG73FJMbJ8CkhohUSxAEaDQaw9+kfPklFsEyzmNU0OeOWnIEue+hu/84E9/8eR4x+y5j2gv17D6BIxnjNAlERKQIphILfbpqq1mhtToRz07fbpRI5UewYQyujtMkEBGRamh1IqI2xOdJaAAYyqI2xEOrk/86/WDCvUITGn0ctoqBzMOkhoiInF5hiYUIIDE5DQcT7sn+2bceFJ7Q6NkqBjIP+9QQkWplZmYiNjYWADBo0CBOk6Bg5iYWliQg5gr097FoeVvEQOZhUkNEqiWKIm7evGn4m5TL3MTC0gTEHM1CSyNY42NWE5StYiDzsPmJiIicnj6xMHUPmwDpLqhmoaVl/2x3NwETu4UVupwtYyDzMKkhIiKnlzOxyJ3Y6B9P7BZms7FiIusGI7p/Y5T0y78J0x4xUOGY1BARkSJE1g3GnP6NEaQxbt4J0vjY5VbqyLrBiPu4I/7XoQZK+honN/aKgQqmmD41U6dOxerVq/HPP//A19cXLVq0wPTp01GzZk1Hh0ZERHYSWTcYHcOCHDZVgbubgHEdnsLodtU5XYITUkxSs2vXLrz55pto2rQpsrKy8NFHH6FTp06Ij49HsWLFHB0eERHZibubgIhqZVw+BspLMUnN5s2bjR7HxMQgMDAQcXFxaNWqlYOiIiJn5+fn5+gQiMhOFJPU5JacnAwAKF2avcyJKH9eXl549913HR0GEdmJIpMaURTx1ltv4dlnn0XdunVNLpeeno709HTD45SUFHuER0RERA6gyLufRo8ejRMnTmDZsmUFLjd16lRoNBrDv5CQEDtFSERERPamuFm6x4wZg7Vr12L37t0IDQ0tcNn8ampCQkI4SzeRi8jMzMTSpUsBAP369eM0CUQKZe4s3YppfhJFEWPGjMGaNWuwc+fOQhMaAPD29oa3t7cdoiMiZySKIq5cuWL4m4jUTTFJzZtvvomff/4Z69atg7+/P5KSkgAAGo0Gvr6+Do6OiFydVidy3BIiB1NMUjNnzhwAQJs2bYzKY2JiMGjQIPsHRET0xOZTiYjaEG804WGwxgcTu4VxhFkiO1JMUsOqYyJ1UnoNx+ZTiRi15AhyH6GSktMwaskRDp1PZEeKSWqISH2UXsOh1YmI2hCfJ6EBABHSJIdRG+LRMSxIUYkakVIp8pZuIlI+fQ1HzoQGyK7h2Hwq0UGRme9gwr088eckAkhMTsPBhHv2C4rIhRUpqcl5uzQRkbkKq+EApBoOra7ozc6enp42u5X71gPTCY01yxFR0VjU/LRlyxYsW7YMe/bswdWrV6HT6eDn54fGjRujU6dOGDx4MMqXL2+rWIlIJSyp4SjKpIFeXl748MMPrX59YQL9fWRdjoiKxqyamrVr16JmzZoYOHAg3Nzc8O6772L16tXYsmULFi5ciNatW+PPP/9E1apVMXLkSNy+fdvWcRORgqmlhqNZaGkEa3xgqreMAKmPULNQzlFHZA9m1dRMmTIFM2bMwHPPPQc3t7x5UJ8+fQAAN27cwKxZs/DTTz/h7bffljdSIlINtdRwuLsJmNgtDKOWHIEAGDWn6ROdid3C2EmYyE4UN01CUZg7zDIR2ZZWJ+LZ6duRlJyWb78aAUCQxgd7329XpIQgKysLK1asACBdfHl42OaGT6XfxUXk7Gw+TUJGRgYSEhJQrVo1mx0oiEid7FXDodPpcP78ecPfthJZNxgdw4IUPd4OkRpYfPdTamoqhg4dCj8/P9SpUwdXr14FAIwdOxbTpk2TPUAiUqfIusGY078xgjTGTUxBGh9FDljn7iYgoloZ9GhYARHVyjChIXIAi6tYJkyYgOPHj2Pnzp2IjIw0lHfo0AETJ07EBx98IGuARKRerOEgtVL6SNlKZXFSs3btWixfvhzNmzeHIGR/QWFhYbh48aKswRGR+ulrOIjUgn2sHMfi5qfbt28jMDAwT/mjR4+MkhwiIiJXo4aRspXM4qSmadOm+O233wyP9YnM/PnzERERIV9kRERECmLPkbIpfxY3P02dOhWRkZGIj49HVlYWZs2ahdOnT2P//v3YtWuXLWJ0amw3JSK58HiibPYaKZtMszipadGiBf766y/MmDED1apVwx9//IHGjRtj//79qFevni1idFpsNyVybl5eXpg4caKjwzALjyfKp5aRspWMg+9ZSd9umnvj6a+plHhLKhE5Bo8n6rD/4l28Mv9AocstG97c6poaV63Ns+nge1qtFmvWrMGZM2cgCAJq166NHj16uMwgfIW1mwqQ2k07hgW5xM5GRNZT+/HElU7C+rnAChsp29q5wFibVziLs5BTp06hR48eSEpKQs2aNQEA586dQ9myZbF+/XqXaIJiuymRMmRlZWHNmjUAgF69ejnlhZeajyeudhK25UjZpmrz9HdVsTZPYvHdT8OGDUOdOnVw/fp1HDlyBEeOHMG1a9dQv359jBgxwhYxOh22mxIpg06nQ3x8POLj4206TUJRqPV44qq3NttipGzeVWU+iy9bjh8/jsOHD6NUqVKGslKlSmHy5Mlo2rSprME5K7XMMExEjqfG44nam9QKI/dI2WquzZObxUlNzZo18e+//6JOnTpG5bdu3UL16tVlC8yZ2brdlIjMo4b+Gmo8nvAkLO9I2WqtzbMFi5OaKVOmYOzYsZg0aRKaN28OADhw4AA+++wzTJ8+HSkpKYZli3qHkbOy1wzDRGSaWvpr6I8nI5ccyfOcUo8nPAnLS421ebZicVLz/PPPAwD69OljGE1Yf1d4t27dDI8FQYBWq5UrTqejbzfNfVANUuBBlUhp1NhpsqSfJ+6nZhqVafw8Me2FeopbF56E5aXG2jxbsTip2b59O+d4eoIzDBPZnyX9NZTAVIIGAMm5khyl4ElYXmwdMJ/FSU2bNm1sEIZycYZhIvuypL9GkxB/+wVmhYISND0ldqjlSVh+bB0wj8VJTWhoKAYPHoxBgwahUqVKtoiJiMgkS/preHqWxoQJEwAAnp6etgzLKmruUMuTsPzYOlA4i5Oat956C7Gxsfjss8/Qtm1bDB06FL169YK3t7ct4iMiMmJJfw1BEODl5WXjiKyn9g61PAnLj60DBbN48L0xY8YgLi4OcXFxCAsLw9ixYxEcHIzRo0fjyJG8vfeJiOSk769h6rQoQLoLSgn9NVyhQ63+JNyjYQVEVCvDhEbNrl8HZs4EHDilpMVJjV6DBg0wa9Ys3LhxAxMnTsSCBQvQtGlTNGjQAD/++CNcaJ5MIrIjfX8NAHkSm9z9NbKysrB27VqsXbsWWVlZdo3THGpK0MhF6XTA5s1Az55A5crA228DO3Y4LByrk5rMzEysWLEC3bt3x9tvv43w8HAsWLAAffr0wUcffYR+/frJGScRkYG5Q9HrdDocP34cx48fd8ppEixJ0Iicyr//AtOmAdWrA126AOvWSQlO69aAA5t8Le5Tc+TIEcTExGDZsmVwd3fHgAED8M0336BWrVqGZTp16oRWrVrJGigRUU5q6a/BDrWkGKII7NwJREcDa9YAmU+GHChZEhg4EHj9daB2bUdGaHlS07RpU3Ts2BFz5sxBz549872jICwsDH379pUlQCIiU9TSaVItCRqp1L17wKJFwNy5wNmz2eVPPy0lMi+/DPj5OS6+HCxOai5duoTKlSsXuEyxYsUQExNjdVBERK5GLQkaqYQoAgcOSLUyy5cD6elSefHiQP/+UjLTsKFDQ8yPxUlN27ZtcejQIZQpY/zju3//Pho3boxLly7JFhwREZE9qGFyVFmkpABLlki1MidOZJc3aACMHAn06wf4O++glhYnNZcvX853Tqf09HTcuHFDlqCIiIjsRS2ToxbJkSNSrczPPwOPHkllPj5A375SMtOsGaCAKZLMTmrWr19v+HvLli3QaDSGx1qtFtu2bUOVKlVkDY6IiMiW1Dg5qtkePZKalqKjgUOHsstr15aal157DShVynHxWUEQzRxQxs1NuvtbEIQ8Y9B4enqiSpUq+Prrrw2zeDujlJQUaDQaJCcno0SJEo4Oh4hsTBRFpKamAgD8/Pw4GS8Z0epEPDt9u8mpKvQTb+59v526mqJOnZKalxYvBpKTpTJPT+Cll6RamZYtna5Wxtzzt9k1NfoxHkJDQ3Ho0CEEBAQUPUoiIhsSBAHFihVzdBjkpNQ891YeaWnAqlVSrczevdnlVatKtTKDBgGBgQ4LTy4W96lJSEiwRRxERER2pfa5twAAFy5ItTIxMcDdu1KZuzvQvbtUK9OhA+Bm9Ti8TsfipAYAdu3ahRkzZuDMmTMQBAG1a9fGu+++i5YtW8odHxG5CFvcfZKVlYUtW7YAADp37gwPD6sOeaRSqp17KzMTWL9eqpX588/s8ooVgeHDgaFDgQoVHBefDVn8C1+yZAkGDx6MF154AWPHjoUoiti3bx/at2+P2NhYvPrqq7aIk4hUzFZ3n+h0Ohw+fBgA0LFjxyLHSeqin3srKTktT0dhILtPjTlzbznFLeFXrwLz5wMLFgBJSVKZIACRkcCoUdJ0BipP7M3uKKxXu3ZtjBgxAv/73/+MymfOnIn58+fjzJkzsgYoJ3YUJnI+pu4+0Z8OinL3SUZGBqZOnQoAmDBhArwcOCcNOSf9/gfAaB+0ZP9z6C3hWi2waZPUxPT779L8SwBQrpxUIzN8OKCCO5PNPX9b3JB26dIldOvWLU959+7d2d+GiCyi1YmI2hCf71WyvixqQzy0OouuvYjMZu7kqKbok6LcHY71t4RvPpUoe8wAgMRE4IsvpI6+3boBGzdKCU3btsCKFVKtzeTJqkhoLGFxPVRISAi2bduG6tWrG5Vv27YNISEhsgVGROrnUnefkNOydu6twpJyAVJS3jEsSJ6mKJ0O2L5d6iuzbh2QlSWVly4NDB4MjBgB1KhR9M9RMIuTmrfffhtjx47FsWPH0KJFCwiCgL179yI2NhazZs2yRYxEpFIucfcJKYI1c2/ZLSm/cweIjZWamC5cyC5/5hnpduzevaXRf8nypGbUqFEICgrC119/jRUrVgCQ+tksX74cPXr0kD1AIlIv1d59Qi7Bpkm5KAJ//SXVyqxcCWRkSOX+/tJIv6+/DtSrZ/n7qpxV3aB79eqFXr16yR0LEbkYOe8+IbI3myTl9+9LE0pGRwOnT2eXN24sjSvzyivSTNmUL6vv7crIyMCtW7cMIw3rVapUqchBEZFrcHcTMLFbGEYtOQIB+d99MrFbmNX9ETw9PTFu3DjD30Ryki0pF0Xg8GEpkVm2DHj8WCr385OSmJEjgfBwucNXJYuTmvPnz2PIkCHYt2+fUbkoihAEId8ZvImITNHffZL7ltggGW6JFQQBJUuWlCFKoryKnJQ/fCglMdHR0izZenXqSIlM//4A91+LWDxOzTPPPAMPDw988MEHCA4OzjNBXIMGDWQNUE4cp4bIeTnF4GUyU+M6UV4Wj1Nz4kT2hJIPHkhl3t5Sh9+RI4EWLZxuQklHM/f8bXFSU6xYMcTFxaFWrVpFDtLemNQQuRatVott27YBANq3bw93d3e7fbZDB2Qjuys0gX38WOrwGx0N7N+fXf7UU1Kn34EDAU4UbZLss3TrhYWF4c6dO0UKjkjpeAWuDFqtFvufnEDatGljt6TG1CjJ+gHZijJKMkmc7Tdo8pbws2elWpnYWOC//6QyDw+gVy8pmWnb1iETSjrb9pOLxUnN9OnT8d5772HKlCmoV69ens53rAEhteMVOBXE7gOyuSCn/w1mZABr1kjJzI4d2eWVK0sD5A0ZAgQFOSw8p99+RWBxUtOhQwcAUlVuTuwoTK6AV+BUGI6SbFu2+g3KUnORkADMmwf8+CNw65ZU5uYGdO0qTSjZuTNgxybQ/Kj9GGZxUrMjZ9ZJ5EJ4BZ5NrVXXcjB3oLWklDTsv3iX29ACtvoNFqnmIisL+O03qa/Mli3S7dkAEBwMDBsm/XOSoU5c4RhmcVLTunVrW8Rhlt27d+Orr75CXFwcEhMTsWbNGvTs2dNh8ZBr4RW4RM1V13Iwd6C1zzeexr1HmYbH3IaFs8Vv0Oqaixs3gAULgPnzpb/1OnSQamW6dQOcbGwkVziGWdU7ac+ePejfvz9atGiBG0++zMWLF2Pv3r2yBpfbo0eP0KBBA3z//fc2/Ryi/HCeIgfOSKwg+gHZCrvOzZnQANyG5pD7N2jxLPE6nVQb06uX1D9m0iQpoQkIAN59Fzh/Hti6FXjhBadLaADXOIZZnNSsWrUKnTt3hq+vL44cOYL09HQAwIMHDzBlyhTZA8ypS5cu+OKLL/DCCy/Y9HOI8uPq8xRZfAJwUfoB2QDkSWwKSnS4DQsn92/Q3JqLI4fPAtOnA9WrA5GRwNq1gFYLtGoFLF0KXL8OfPml9LwTc4VjmMVJzRdffIHo6GjMnz/f6M6nFi1a4EjOERGJVKawK3ABUhOCWucpsqTq2ll4enpi1KhRGDVqlF2nSdCPkhykMT45lC7mVeDrnHEbOhO5f4MF1kiIIppfPYHv1k1Hk2fqAx98IHUE1miAsWOleZl27QJefVUaOE8BXOEYZnGfmrNnz6JVq1Z5ykuUKIH79+/LEZNs0tPTDTVJgDR4D5G1bD1PkbNTYtW1IAgIDAx0yGdH1g1Gx7Agow7VScmP8b8Vxwt9rTNtQ2ci928wvxoJzeMHePHUdrx6bBOq37ue/cTTT0vjyrz8sjQnkwK5wjHM4pqa4OBgXLhwIU/53r17UbVqVVmCksvUqVOh0WgM/0JCQhwdEimcqSvwII2P4m+FLIwrVF3LTT8gW4+GFRBRrQyCNL5mvY7b0DQ5f4OGmgtRROMbZzDjt2/w9+yB+HT7fFS/dx0PvXyxptnz0B6OAw4cAAYPVmxCo6f2Y5jFNTWvv/46xo0bhx9//BGCIODmzZvYv38/3nnnHXz66ae2iNFqEyZMwFtvvWV4nJKSwsSGiiy/K3BXuB1XthmJ7Uir1WLPnj0AgJYtW9p1moT8KHEbOiO5foPuDx9gQeohuMXMRe3blw3l8YGhWNqwC9aHtcFXQ5+Fu8JP9Lmp+RhmcVLz3nvvITk5GW3btkVaWhpatWoFb29vvPPOOxg9erQtYrSat7c3vBXS1knKYnJIdBVTYtW1VqvFrl27AEj9/hyd1ChxGzqrIv0Gjx6VxpVZuhR1Hj0CAKR7eGF9rVZY2qgLjgXXQHBJX3yl4lvs1XoMszipAYDJkyfjo48+Qnx8PHQ6HcLCwlC8eHG5Y8vj4cOHRk1fCQkJOHbsGEqXLo1KTjK4EZGa6auuc49TE8QxVszGbeggqanA8uVSMnPwYHZ5rVrAyJHw6D8AFe+LGKyymgtXY1VSAwB+fn4IDw+XM5ZCHT58GG3btjU81jctDRw4ELGxsXaNhchVqbnq2l64De0oPl6ag2nRIiA5WSrz9JTGkhk1SrotWxDgDiBCfRUXLsfipObRo0eYNm0atm3bhlu3bkGn0xk9f+nSJdmCy61NmzYQRY7fQORoaq26tiduQxtKTwdWr5ZqZXbvzi4PDZXuYBo8GHDQXXFkWxYnNcOGDcOuXbswYMAABAcHQxB4ZUFERE7gwgVpQsmYGODOHanM3V2asmDkSKBjR2mCSVIti5OaTZs24bfffsMzzzxji3iIiIjMl5kJbNgg1cps3ZpdXrEiMHw4MHQoUKGC4+Iju7I4qSlVqhRKl+bthkRE5EBXr0oTSi5YACQ+mS9LEIDOnaW+Ml27Ah5WdxslhRJECzupLFmyBOvWrcOiRYvgp7BBiFJSUqDRaJCcnIwSJUo4OhwisjGdTofEJye84OBguJnR9KDViezA66y0WmDzZqlW5vffpQkmAal/zLBhUs1MlSoODZFsw9zzt1lpbKNGjYz6zly4cAHlypVDlSpV8synwvmfiEgOliQXppZ1c3NDBQuaHjafSsxzq3Uwb7V2vKQkYOFCqb/M1avZ5e3aSR1/e/YEvAqeV4tcg1lJTc+ePW0cBhFRNkuSC7kSkc2nEjFqyZE8I/0mJadh1JIjqhhCXlFEEdi+XaqVWbsWyMqSykuVku5eGjECqFnToSGS87G4+UnJ2PxE5PxMJRf6OpqcyUVhy/7wagNoHlwBADRv3tzkiMJanYhnp283OQu5fvqCve+3Y1OUTEzWxN29C8TGSrUy585lv6BFC6lWpndvwNe8ObRIPWRtftJbuXIl1q5di8zMTHTo0AEjRowocqBERHpanYgPVp/Md14kEVJyEbUhHh3DgoAnfxe07JSN8eiYuR8A0LRpU5NJzcGEeyYTGv37JSan4WDCPY4tI4M8tWuiiLZ3z+N/F7ej7r6tcMtIl8r9/YEBA6Rkpn59xwVMimF2UjNv3jyMHDkSTz31FHx8fLBq1SokJCRg6tSptoyPiFzI99vP435qpsnncyYXePJ3QcsmpaQBZlzU33pg+n2sWY5My1m75p/+CD1P70C/o5tQ684VwzL/lH8KWcNHoO47IwE7TMFD6mF2UvPdd9/ho48+wueffw4AiI2NxZgxY5jUEJEstDoRMX9dNmtZuZOLQH8fWZej/Gl1IqI2xKNu4nn0O7YJ3c/sgl+mVCvz2MMb68JaY2nDLjgV/BSQBsy5/ACRdZnUkPnMTmouXbqEwYMHGx4PGDAAI0aMQFJSEoKCgmwSHBG5joMJ93D/selampzkTi6ahZZGsManwJqfYI3U74Os9PAhLv/fAsz97gfUT8qemPhsQCUsbdgFa+u0RYpPdgKTs6mR/ZjIXGYnNY8fPzaaidvd3R3e3t5ITU21SWCkXhwHhPJjbu1LST9PQ3IRrPFBUnJavv1qBABBJXwAM/IkdzcB3RsEY+7uBJPLdG8QzP3UGidPShNKLl6MaikpAIB0dw9sqvkMljTqisMVwqRB83JhPyayhkUdhRcsWGCU2GRlZSE2NhYBAQGGsrFjx8oXHakOxwEhU8ytfRncItSQXEzsFoZRS45AAIwSG/0pckLXWji8bn+h76nViVh/PLHAZdYfT8R7kbWZ2Jjj8WPg11+l27H37csurhyKr6u2xaq67fGfn8ast2I/JrKE2UlNpUqVMH/+fKOyoKAgLF682PBYEAQmNWQSxwGhguibgEzVvABSLc3odtUNjyPrBmNO/8Z5EuWgJ4lyuxplcHhd4Z9d2N1PAGsNzHLunFQrExsL3JM6c8PDA+jRAxg1Cl6t2+C3r3bifiHbOif2YyJLmJ3UXL582YZhkNrpOwiac6sur4Rdk7ubYLLmRW/aC/Xy7B+RdYPRMSwo3yZNnU6HgQMHAgA8CpgHiHc/FUFGBrBunVQrs317dnmlStIAeUOGAMHSxYo7smvXCqMfG4j9mMgSnO2L7ILjgJA5TNW8FNZE6e4m5LvfuLm5oYoZcwG54t1PRe7bdvkyMH++NH3Bv/9KZYIAPPecNK5Mly5APuMCmfqOc9JHMbFbGC9yyCJMasgueCVM5iqo5sVWCmv6UlutgdV927KypIkk584FNm2SpjIApJqYoUOlSSUrVy7083N+x1vjk7D22E3ce5RheD6I/ezISkxqyC5c8UqYrGeq5sVSWq0WcXFxAIAmTZqYHFG4oKYvtdUaWNW37cYNqUZmwQLg2rXs8o4dpVqZ7t2BXJMbF0b/HUdUK4OPngvjHZEkCyY1ZBeudiVMzkGr1WLTpk0AgIYNG5pMaoDCOx2rodbAor5tEIE//5T6yqxfD2i10oJlykj9ZEaMAKpXz+edLCdXEkvEpIbswpWuhEm5HNH0ZU/m9G3LuJmE6x9MQuVVS4BLl7KfbNlSqpV56SXA29v2wRJZwaykJuXJgEnm4OzXZIorXAmT8plba6DEQSRN9lkTRTx97RT6HduEyLP74KXLkso1GmDgQCmZCQuzX6BEVjIrqSlZsiSEfEZ8zI9WX0VJlA+1XwmTa1DqIJK5+6yVSHuIF09tQ7+jm1D93nVD+YMGjeE/bjTw8suAn5+9wySymllJzY4dOwx/X758GR988AEGDRqEiIgIAMD+/fuxaNEiTm5JZmH7OSmZkgeRbBZaGsElvBF05jhePbYZ3f7ZDZ8s6a6jR54+WBfWBlue7YEf/+91wMUvNPQ1cUnJj3HvUQZKF/dGUAlehDk7s5Ka1q1bG/7+7LPPMHPmTLzyyiuGsu7du6NevXqYN2+eYaArIiK1UfQgkg8ewH3pUmz56TuUOBtvKD5TtgqWNOqK9WFt8NDbD3P6N3a+2GVibpNhfjVxekqokXNlFncU3r9/P6Kjo/OUh4eHY9iwYbIEReTMTB0YldjHgiyjyEEkjx+X7mBasgR4+BAlAGi9vPFHnZaYX6czjpSvBQgCgjU++ErFJ2tzmwxN1cTpJSqgRs6VWZzUhISEIDo6Gl9//bVR+dy5cxESEiJbYETOyNSBsXuDYKw/nqi4Phb2Zm7iJ1eC6OHhYahVLmiaBHMpZhDJ1FRgxQopmfn77+zymjWBkSPh/tpr6FSyFEq6SBJubpNhQTVxuTltjZyLs/hX/s033+DFF1/Eli1b0Lx5cwDAgQMHcPHiRaxatUr2AImchakDY2JyGubuTsizvBL6WNiTJVfKcnXCdXNzQ40aNYoe/BNOP4jkmTPSaL+LFgH370tlnp5Ar17AqFFA69bSVAaQ5mFymtokG7KkydCciU31r3O6GjkCALhZ+oKuXbvi3Llz6N69O+7du4e7d++iR48eOHfuHLp27WqLGIkczpIrOD39slEb4qHVWfJK9dEnhLlPGPrEb/OpRIuWcxT9IJKmrs0FSAmYXQeRTE8Hli0D2rSRbrueNUtKaKpUAaZOlUYAXr5cet7Mu1jVxJImQ0tr2BxeI0d5WFUfGxISgilTpsgdC5HTMvcKLjde0Zl/pdyuVjnZO+FqtVqcPHkSAFCvXr0CRxQ2h1MNInnxIjBvHvDjj8CdO1KZm5s0ZcHrrwOdOkmPXZwlTYaW1rBxWhfnY9Uev2fPHvTv3x8tWrTAjRs3AACLFy/G3r17ZQ2OyFkU9YrMla/ozL1SXrz/stlX1ObSarVYt24d1q1bJ9sYWvpBJIM0xie0II2P7ZsaMzOBNWuAzp2lKQq+/FJKaCpUACZNAq5ckZ6PjGRC84QlTYb6mrjCOKRGjsxicU3NqlWrMGDAAPTr1w9HjhxBeno6AODBgweYMmUKfv/9d9mDJHK0ol6RufIVnbkJ3ZV7qbK+ny3ZfRDJa9ekySQXLABu3pTKBEFKbl5/HXj+eUCGjtBqZMm8czlr4gprMOa0Ls7J4lT+iy++QHR0NObPnw/PHLOytmjRAkeOHJE1OCJnUVhfClN4RWd+Qle5tHkj1zpLgqgfRLJHwwqIqFZG/hOcVgts2gT06CH1j/nsMymhCQwEJkyQmp82bQJ69mRCUwB9ogIgz+83vyZDfU2cqRqbYHvUyJHVLP4lnD17Fq1atcpTXqJECdzX97YnUpmC+lKYwok6JeZeKQ+IqIIFexM4k/u//0r9ZObNAy5fzi5v2xYYOVJKYry8HBWdIlk671zOmjiOKKwsFic1wcHBuHDhAqpUqWJUvnfvXlStWlWuuIicjqkDo6lxajhRp8TczrVeHm7O0wnX3kQR2LFDGldmzRog68mEkqVKAYMGASNGALVqOTREpbO0yZDTuSiTxUnN66+/jnHjxuHHH3+EIAi4efMm9u/fj3feeQeffvqpLWIkchoFHRjfi6zNEYVNMPdK2eVmcr97VxpTZu5c4Ny57PKICKlWpndvwNfXcfGpDBMV9bM4qXnvvfeQnJyMtm3bIi0tDa1atYK3tzfeeecdjB492hYxEjkVUwdGHjALZu6VsupnchdFYN8+KZFZsUIaZwYAihcHBgyQOv42aODYGIkUShBF0apRwVJTUxEfHw+dToewsDAUL15c7thkl5KSAo1Gg+TkZJQoUcLR4RCRjel0Opw5cwYAULt2bbg58jbn5GRp/qXoaODUqezyRo2k0X5feUVKbIgoD3PP3xbX1AwZMgSzZs2Cv78/wsPDDeWPHj3CmDFj8OOPP1oXMRGRzNzc3FCnTh3HBhEXJyUyP/8szckESE1KfftKyUx4uMuN9MvJX8lWLK6pcXd3R2JiIgIDA43K79y5g6CgIGTpO7g5IdbUEJFdPHokTV0wdy5w+HB2eViY1FdmwACgZEmHhedIcs7tRa5D9pqalJQUiKIIURTx4MED+Phk38Ov1Wrx+++/50l0iIgcye7NT6dOSbUyixcDKSlSmZcX8NJLUq3MM8+4XK1MTubOlk1kLbOTmpIlS0IQBAiCkO+st4IgICoqStbgiIiKIisrC7/++isAYMKECfCyxfguaWnAr79Kycxff2WXV6sm1coMGgQEBMj/ubk4qknH3M+1ZLbsosTNpi3XZnZSs2PHDoiiiHbt2mHVqlUoXTp7ACwvLy9UrlwZ5cuXt0mQRGqnpAOxM8RqbQz618kyoNr581LzUmysdGs2ALi7SyMAv/460KGD3eZfclSTjiWfa8ls2dbeRWir7eAM+zyZx+ykpnXr1gCAhIQEVKpUCYILV6ESyUlJfQycIVZrY9gan4QvNp3P98Rq9jpkZgLr1km1Mtu2ZZeHhEgD5A0ZAtj54s5RTTqWfq4ls2XbIx5L3tfR+zyZz+LLiO3btxuqc3NauXIlFi1aJEtQRK5CfyDOfaLVH4g3n0p0UGR5OUOsRYlh/C/HTNYUJBb2+itXgI8/BipVkgbE27ZN6hvz3HPA+vVAQoL0vJ0TmsKadACpSUers2rkDlk/15LZsu0RjzmcYZ8ny1ic1EybNg0B+bQPBwYGYsqUKbIEpWZanYj9F+9i3bEb2H/xruwHG1IOR52QrGHLWM39TRQ1BnMii9oQj4wsnRRP3FX8M28pxK7PAaGhwOTJQFISEBQkJTAJCcDGjUC3blKzkwNY0qTj6M8tbFLYokz+aovtoKTfJ2WzeJyaK1euIDQ0NE955cqVcfXqVVmCUitnqcZk+7BzsEcfA7nYKlZn6pOhf/3zE1ag84GN6Hv8D1R4cDt7gQ4dpI6/3bsDnp4Wv78t2LpJR87PNXcOMGuORbbYDkr6fVI2i5OawMBAnDhxIs+ElsePH0eZMvxiTXGWWxmdJbEix52QrGGLWJ2pT4Yg6vDM5ePod2wTOp4/AA9RBwC451sCv9brgGUNOuP9sd2c7jdiyyad3HJeDN15kG7V59pqbi9bbAcl/T4pm8VJTd++fTF27Fj4+/ujVatWAIBdu3Zh3Lhx6Nu3r+wBqoG9bmUsjLMkViSx5wmpqOSO1ZrfhDUxuLu7o05Ee0TvughtPg0fpVOT0fvkVrx6bDMq308ylP9dsQ6WNuqCLTVaIN3Dy26/UUvpm3SSktPy3ZYCpITBmiadnPK7GHITAFMtLwV9ri3m9rLFdlDS75OyWZzUfPHFF7hy5Qrat28PDw/p5TqdDq+99hr71JjgDNWYzpJYUTZ7nZDkIHes1vwmrInB3d0dvTo8g6/j0iHqP08U0ez6afQ7ugmR5/6Ct1YaBT3FuxhW12mLpQ274HzZyoXG4wxs2aSjZ+piqKCEprDPlXvyV1tsByX9PimbxR2Fvby8sHz5cvzzzz9YunQpVq9ejYsXL+LHH3+0zcBWKuAM1ZiO6lBIpukPxADy1CHIdUKSi9yxFqVPhqUx6F+nSXuIQYfXY+vCN7Di5w/Q48wueGuzcCz4KbzbZSyefmMRJnUcmSehsSZue9I36QRpjGsMgjQ+Ra59LehiSC/3Vy7H51pD7u2gpN8nZbO4pkavRo0a+Y4sTHk5QzWmMyRWlJet+hjYgpyxWvubsDQGnVaL62vWIGLZMhz5/Xe4p0mvSfX0xrrarbG0UVecCqqO0sU88fhRpmxx25stmnSAwi+GAKnG5pPnaiPA39vhNx7IvR2U9PskiVlJzVtvvYXPP/8cxYoVw1tvvVXgsjNnzpQlMDVxhmpMZ0isKH+2OiHZglyxFuU3YVYMDx5IE0rOmYNKx44ZisV69ZDw4gCcbvMcUt18MPTJiMJNKpdC6692KLqpQe4mHcD8i5wAf2/0aFhB1s+2ltzbQUm/TzIzqTl69CgyMzMNf5vCUYbzZ49278I4Q2JFptnihGQrcsRa1N+EyRiOH5dG+126FHjwAG4AstzdcbpOHYT93//Bs1UrVBUEVM3nPR39G3VGvBiSKOn36eoEURRdZuQgc6cutxVH306t7/AH5H/Q5t1PZG+y/CYePwZWrJCSmQMHsstr1EDWsGGYeecOHvv5mTWhpaN/o85GqxPx7PTthV4M7X2/ncslfGRf5p6/mdTYmaMHvuNBm5yN1b+Jf/6RJpRctAj47z+pzNMT6NVLmlCybVtkZGZi6tSpAMyfpdvRv1Fn46oXQ9wPnIu552+zmp9eeOEFsz949erVZi/rihxdjcn2YXI2Fv0m0tOBNWukWpldu7LLq1SREpnBg4Fy5ewXjwtwxc6yvPhTLrOSGo1GY/hbFEWsWbMGGo0G4eHhAIC4uDjcv3/fouTHWrNnz8ZXX32FxMRE1KlTB99++y1atmxp889VEx60SXEuXQLmzQN+/BG4/WTqAjc3ad6l118HOneWHjsBpV7hFxS3K10McZBSZTMrqYmJiTH8/f7776NPnz6Ijo6G+5NJ3LRaLd544w2bN+ksX74c48ePx+zZs/HMM89g7ty56NKlC+Lj41GpUiWbfjYR2VlWljRhZHQ0sGVLdnmFCsDw4cDQoUDFio6LLx9KvcI3J25XuBjiIKXKZ3GfmrJly2Lv3r2oWbOmUfnZs2fRokUL3L17V9YAc3r66afRuHFjzJkzx1BWu3Zt9OzZ09BuXhB9m9zt27fzTcDc3NwMoyQDQEZGhsn3EgQBnjkmtbNk2czMTJja7LZaFoBRfwJLls3KyoJOp5NlWU9PT8NdcrZaVqvVQqvVyrKsh4cH3J7UADjDsjqdDllZWSaXdXd3N1xsOMOyoiga7pwsaFmtTsTfl+4i6f5DVHh0D423roZHbCyEGzcMy+o6dYLbG28Azz0H0d29wPfV/5a1Wi0OHz4MrVaLRo0aGeLKb1m9gn7LBS27NT4J4385ZjghihCghZuh78n3feuhY1hQvu9blN99WnoGDl2+h9sP0lDW3wfhlUsZTrjmvG/OuLOQvX08oIMAEd/2bZhv3Go8RvydcA+DYw4iC27Q9xpygw5uudKcmMHN8PSTO0V5jCjasuYeI2TtU5NTVlYWzpw5kyepOXPmTIE7VFFlZGQgLi4OH3zwgVF5p06dsG/fvnxfk56ejvT07InXUlJSAABff/01fHzy3oL41FNP4dVXXzU8njFjhsmNXblyZQwaNMjweNasWUhNTc132fLly2P48OGGxz/88AOSk5PzXbZs2bJ44403DI/nz5+P27dv57usRqPB+PHjDY9jY2Nx8+bNfJf18/PDu+++a3i8dOlSXLlyJd9lPT098eGHHxoer1ixAufPn893WQCYOHGi4e81a9YgPj7e5LI5O2tu3LgRx48fN7nsO++8g2LFigEAtmzZgsOHD5tcdty4cShZsiS0OhGLV/2GK2dMDz0watQoBAYGAgD27NmDXTn7ZuQybNgwVKggjb9x4MAB/PnnnyaXHThwoGGi17i4OGzatMnksq+88oph8MqTJ09i3bp1Jpd96aWXUKdOHQDS7+zXX381uWyPHj3QsGFDAMCFCxewbNkyk8t26dIFzZo1AwBcvXoVixYtMrlshw4d8MwzzwAAEhMTsWDBApPLtm7dGm3atAEA3L592+giJLeIiAjoytfDZ+tOod6J3fjf8ZWoce4c3J6ceB/5+eFoo0aIa9IE1Tt1wnPPPQcASH30CDNmzDD5vg0aNEDPnj3h7u6ORo0aYerUqdi6dWu+y4aFhaF3796GxwVdIBV2jOjvm71sorY4NmfUMlzh71u3GIfX5X+gz3mM0OpEzJz1HdIePch32ZzHiM2nEvHn6iXwF7OPPdtzLGvuMaK/L5AmemBZWkNDWQevcwh2f4jD647icK7dU8nHCADYtm0b9u/fn+9yA3yBNWl1cF+Uvsz6Holo5JlotMz2X44atjOPERJbHiM6depk8vncLE5qBg8ejCFDhuDChQto3rw5AOmLnDZtGgYPHmzp25ntzp070Gq1KJerE2C5cuWQlJSU72umTp2KqKgom8VEzkVfhV7h0U3U8yx8eQC4cCv/EwfZx78XbyBx8lIsP74FIcn/GsoTqlRBXJMm+Kd2bWg9rB743GmIeDJXUiEtFvp9+Jm0dPgX0kVI3/ejh7fOiglviNTJ4uYnnU6HGTNmYNasWUhMlLLX4OBgjBs3Dm+//Xa+1btyuHnzJipUqIB9+/YhIiLCUD558mQsXrwY//zzT57X5FdTExISwuYnC5dVQtXytrN38MbSoxBhXF2sP4fkrELXv+/mU4l4c8lhCLmqlnO+pkv9iqxaLsKy+VYtiyKEXbsgzJsPce1aeD6ZUDLZuxhW122HXxp2xsWAEAgAypXwwda3WsPdTTD6fRZWZa1fVqfT4cqVK8jKykJISIhhO+a3rJ41zU8bT9zEe7+eMF7NJ81Peh7Q4suX6uP5+uXzvK8gCNh29o6hg6p7jjnFc+/DgiDAzd0Dz07fjsTkNKNlkeM15Ur44M+328DH2/TvPnfcOZuf3J80PwHIN26lHSPMaX7S6kR0nLkLN1IyIObT/JR7nwTY/FTUZR3e/OTm5ob33nsP7733nqE5xx5jvgQEBMDd3T1PrcytW7fy1N7oeXt7w9vbO0+5l5eXWeNVWDJBpyXL5kxElLCshwVXyo5YVqsT8dnGM4bURAc35Dy0CQC+2HQekfVDDAcifYdArYlL3Jyv0cv5QyyMrZZ1c3Mze19zhmUFQche9t49aUyZ6Gjg3DnDMnHla+Hnhl2wsdazSPc0/r1eT8nEsRsP83RQNXrfAmRlZeGnn34CYP44Ndb87oNL+RslBPnGAncEl/LP9/1zd1DV5nqv3Pvw/ot3DZ16cy+rdz0lE0evPzDadrl/9wXFnfO3YSpuPWc/RuRW0G/u4+71jEaW1h9PhBzP+/rkPa8U9r72WtYZfvdWHyNkYFWlZVZWFv78808sW7bMkPnevHkTDx8+lC2w3Ly8vNCkSZM87eJbt25FixYtbPa55PysmYGcs5bbiSgC+/YBr70GlC8PvPWWlNAUL46Elwagy+D/w4sDZmBVvfZ5Eho9JUyyqp+GxFTrkgDpbiJT05BYuj/KNUFtUeNWI1vOek62Z3FNzZUrVxAZGYmrV68iPT0dHTt2hL+/P7788kukpaUhOjraFnECkCbWHDBgAMLDwxEREYF58+bh6tWrGDlypM0+k5yfNQd4zlpuY8nJ0vxL0dHAyZPZ5Y0aASNHAq+8gqRbGTgz/4Dp93hCCfMKFXUuK0v3R7nmZHKGeemckSuNy6M2Fic148aNQ3h4OI4fP44yZbKrNXv16oVhw4bJGlxuL7/8Mu7evYvPPvsMiYmJqFu3Ln7//XdUrlzZpp9Lzs2aAzwn6rORuDhp6oKffwYePZLKfH2Bvn2lQfKaNQOe1O42KyaqapLVooy8a+n+KOcEta44YrA5XGFcHjWyOKnZu3cv/vrrrzxtYJUrV8aNHGNK2Mobb7xhdMszkTUHeM5aLqNHj4Dly6VamUOHsstr15ZqZQYMAEqVyvMyNdYSWHuFb+n+KPe2Y80EqYXFfWp0Ol2+vbCvX78Of39/WYIisoT+AA/kvWPW1AHemtdQLqdPA2PHSiP8Dh0qJTReXsArrwA7d2Y/n09Co6fG/gv6K/weDSsgoloZs/Yha/ZHubedNXETORuLb+l++eWXodFoMG/ePPj7++PEiRMoW7YsevTogUqVKhlNqeBsnGGWbrIda4aoV+qw9g6TlgasWiU1Me3Zk11erZrUvDRoEFC2rMVva6v5kjIyMiyepduRrNkflTrXFJElzD1/W5zU3LhxA+3atYO7uzvOnz+P8PBwnD9/HgEBAdi9e7dhpFZnxKRG/aw5wPOkYIbz56UJJWNiAP1UKO7uQI8eUhNT+/ZOM6FkTlqtFgcOSJ2RmzdvbrNxtOTE/ZEoL5slNQDw+PFj/PLLL4iLi4NOp0Pjxo3Rr18/+Pr6Fv5iB2JSQ2SBzExg/Xqpr0zOod8rVgRGjJCanMrnHUiOiEhuNklqMjMzUbNmTWzcuBFhYWGyBGpPTGqIzHDlCjB/PrBwIaAf7FIQgC5dpFqZLl0AFUxdQETKYZMRhT09PZGenm4YcI+IVEKrBTZtkmplfv9dGjQPAMqVA4YNk/49mYhPSXQ6ndF0LvlNk0BE6mHxL3zMmDGYPn16gfM6EJFC3LwJfP45EBoKdOsG/PablNC0bw+sXAlcuwZ88YUiExpAGv18wYIFWLBgAY9ZRC7A4jrkv//+G9u2bcMff/yBevXqGaZ911u9erVswRGRDeh0wLZtUq3MunVSLQ0AlC4t3b30+utAjRoODZGIyBoWJzUlS5bEiy++aItYiMiWbt8GYmOl27EvXswuf+YZqa/MSy8BPhxBmYiUy+KkxpnHoSGiXEQR2LtXqpX59VcgI0MqL1EC6N9fSmbq1XNsjBbiLc9EZIrZSY1Op8PXX3+NtWvXIjMzEx06dMCnn34KH17ZETmf+/eBxYulZCY+Prs8PFxKZPr2BXI1HSsBB0skooKYndRMnz4dH3/8Mdq3bw9fX1/MnDkTd+7cwbx582wZHzkQr4gVRhSlqQrmzgWWLQMeP5bK/fyAV1+V+sqEhzs2xiLYfCoRo5YcyTM3UlJyGkYtOWKYGiDnflva1/kH2yMi+Zid1MTGxuK7774zTCa5efNm9OzZE3PnzuUt3irEK2IFefhQmhU7Oho4ejS7vG5dqVamf39Ao3FcfDLQ6kREbYjPd7JHEdL8SFEb4qHTifj8tzOG/dYDWgxw7jFBiUhGZg++5+Pjg3PnzqFSpUoAAFEU4ePjg0uXLqFChQo2DVIuHHzPPKauiPWpq1InGnQEm9Z2HT8u1cosWQI8eCCVeXsDffpItTItWkiD5jlTzFbaf/EuXpl/wOLXuUGHBh7SODXD+3RF1/oVLXp9UbeFM25LIiWSffC9jIwMo2kQBEGAl5cX0tPTixYpORVzr4g7hgXx4FwIm9R2PX4sjR8THQ3s359d/tRTUq3MwIFAmTLOFbMMbj1IK3yhfOjghqNZFSAA+Py3s+hct4LZ+21Rt4WzbkuAyRapl0V3P33yySfw8/MzPM7IyMDkyZOhyVG1PXPmTPmiI7s7mHDP6CCcmwggMTkNBxPuIaKa9SdPtTO3/4fZ/vlHqpVZtAj47z+pzMMD6NVLSmbatrWqVsamMcso0L9oNyRYut8WdVs487Z05mSLqKjMTmpatWqFs2fPGpW1aNECly5dMjxm3xrlM/eK2NorZ1cgW21XRgawZo1UK7NzZ3Z55cpS89LgwUBQkHPFbCPNQksjWOODpOS0fGM0TURJQdpX74s+Zu23Rd0WzrwtnTnZIpKD2UnNzpwHVVItc6+Ii3rlrGZFru1KSADmzZMmlLx9WypzcwOef16qlenUCXCX964eZ6+hc3cTMLFbGEYtOQLhSTx6uR/n5AEdevmcBgAsftzIrP22qNvCWbelMydbRHLh7G5kRH9FbOqQJkCqqm4WWtqeYSmKVbVdWVnSlAVdugDVqgHTpkkJTXAw8MknwOXL2c/LnNBYHbOdRdYNxpz+jRGkMU5MgjQ+mP1q4wL3WwAIKmHeflvUbeGs29KSZItIqcyqqZk2bRrGjBmTZ56n/Pz999+4c+cOnnvuuSIHR/ZX2BUxAEzsFsYruQJYVNt1/TqwYIH078aN7Cc7dZJqZZ5/HvD0tFGkuWKRcTlbiawbjI5hQfl2cnVzQ777rd6ErrXM2m+Lui2cdVs6a7JFJCezamri4+NRuXJljBo1Cps2bcJtfZU4pFlwT5w4gdmzZ6NFixbo27cvb5dWuIKuiNnmXrjCarvcRB16/XsCzd8aKvWPiYqSEpqAAODdd4ELF4AtW6ROwHZIaMyJ2Zlq6NzdBERUK4MeDSsgoloZQ6Jiar/V6xhmXv+jom4LZ92WzppsEcnJrJqan376CSdOnMAPP/yAfv36ITk5Ge7u7vD29kZqaioAoFGjRhgxYgQGDhwIb29vmwZNtlfQFTEVzFRtV8Cj/9D75J945dhmVEr+N/sFrVtLtTK9eknjzDiAWmrocu+3pX3dsf2Xo4W/MIeibgtn3ZaFdbYWIF24OEPiSmQtswff0xNFESdOnMDly5fx+PFjBAQEoGHDhggICLBVjLLh4HtkT5tPJSJq/WlUOXkIrx7bhM7n9sNLlyU9WbIk8NprUjJTu7ZD48xJbbf7ZmRkYOrUqQCACRMmwMvLy+zXqnGcGv3dT0D+yRZrYslZmXv+tjipUTImNWQ39+4BixZBnDsXQo6hEMSnn4YwcqQ06m+OMZ+ciZoGZitKUgOoc0RhZ0y2iArDpCYfTGrIpkQROHBAGldmxQog7clJo3hxaf6l118HGjZ0aIiuRqvVYtu2bQCA9u3bw90Gd44pkTMmW0QFkX2aBCIyISUFWLpUSmZOnMgub9BAal7q1w/w93dcfC7M3d0dnTp1cnQYTkff2ZpIbZjUEFnr6FEpkVm6FHj0SCrz8QFeflmqlWnevMhTF5BtscaCSF2Y1BBZIjUVWL5cSmYOHswur1VLqpV57TWgVCnHxeficicpTauUwsMHKQAAjUZjNJUL+5YQqU+Rk5orV67g0aNHqFWrFtzcOEAxqdTp09KEkj/9BCQnS2WensCLL0rJTKtWrJWxkNy1JPklKRVLeKJjpjSbec6OwpwDyXmwtozkZHZSs2jRIvz3338YP368oWzEiBFYuHAhAKBmzZrYsmULQkJCZA+S5MMDiAXS04FVq6RamT17ssurVpWalwYNAgIDHRaeksldS2IqSfk3JQ3wNS7jHEjOg7VlJDezq1aio6Oh0WgMjzdv3oyYmBj89NNPOHToEEqWLImoqCibBEny2HwqEc9O345X5h/AuF+O4ZX5B/Ds9O3YfCrR0aE5l/PnpZF9K1aUOvnu2SPNt9SrlzTS7/nzwHvvMaGxkj4ByT0Pkb6WxNL9sbAkJedyAOdAchZy7wdEgAVJzblz5xAeHm54vG7dOnTv3h39+vVD48aNMWXKFMOtk+R8eAApRGamVCvTsSNQowYwYwZw546U2EyaBFy5AqxeLc3JxGZWq5mTgERtiDckIOYoLEnRO3zlPwCcA8kZ2GI/IAIsaH56/Pix0b3h+/btw5AhQwyPq1atiqSkJHmjI1mwur0AV68C8+dLE0rq919BkGbDHjlS+t/Ddv3pczYHBhTzBgTgzsN0VTQN5tfUaUktSe5bjk01nZqbfNx+shznQHK8ouwHRAUx+2hduXJlxMXFoXLlyrhz5w5Onz6NZ5991vB8UlKSUfMUOQ8eQHLRaoHNm6W+Mr//Duh0Unm5csCQIcCIEUCVKjYPI7/+BDkpuW+Bqb4SXeuaN6nkn/FJRvtiQX0vzE0+yj5ZjnMgOR5ry8hWzK5Hf+211/Dmm2/i888/R+/evVGrVi00adLE8Py+fftQt25dmwRJRcMDyBOJicDkyVJH3+efBzZulBKadu2kEYCvXgWmTLFbQpNfc2BOSm0aLKipc+Ffl816j4V/XTasd2FNp/89yihwVmy98MrSrfb6CScB5HmNkibvVDLWlpGtmJ3UvP/++xg2bBhWr14NHx8frFy50uj5v/76C3379pU9QCo6lz6A6HTAtm1A795ApUrAxx9LyUupUsBbbwH//JP9vIXzAlmroObAnJTYt8CcvhJuQt5kIj9RG+KRkaUr9P0+/y0enzwnTQqa+31FCDiTVRaBVcPg6ZE9RUJk3WDM6d8YQRrjfT5I48Pbue1AX1tmaj8QINXEsbaMLMW5n1yAVifi2enbC61u3/t+O/Vcnd65A8TGSmPLXLiQXd6ihdRX5qWXAF9fky+3pf0X7+KV+Qcses2y4c0V0TRozboV5JPnauPz384Uutyy4c2R/DjD4tuDOcSB43DGcLKE3ed+SkxMxOTJk/H999/L9ZYkE311+6glRyAg/wOIKqrbRRH46y+pr8zKlUBGhlTu7w8MGCCNLVO/vmNjhHXNfEppGjQ3ztY1ymLXuduFLnflXqrZn9ujYQV0DAuyKEnhHEiOo68ty52IBim4Lxk5nkVJTXx8PHbs2AFPT0/06dMHJUuWxJ07dzB58mRER0cjNDTUVnFSEan6AHL/PrBkiZTMnD6dXd64MTBqFNC3rzRTtpOwpplPKU2D5sbZ6qkAs5KayqX9LPrc3EmKKIp49GReLj8/P6NpEsjxIusGW5yIEhXE7KRm48aNePHFF5GZmQkA+PLLLzF//nz06dMHdevWxcqVK/H888/bLFAqOlUdQEQROHxYSmSWLQMeP5bK/fyAV16RamWaNnVsjCYUdvdNTkq7E8fcO4sGRFTBgr0Jsi1navtkZmZixowZAIynSSDnwdoykpPZHYUnT56MkSNHIiUlBTNmzMClS5cwcuRIrFq1Cjt27GBCoxD6A0iPhhUQUa2M8hKahw+lcWXCw4FmzYAff5QSmjp1gO+/B27elMaccdKEBij47puclNg0aO6dRV4ebrIup5TtQ0S2ZXZSc+bMGbz55psoXrw4xo4dCzc3N3z77bdo1aqVLeMjkpw4Abz5JlC+vDSOzJEjgLc30L8/sHcvcPKk9LxCxkoydfdNTkq9E8fcO4vkXo6IyOzmp5SUFJQsWVJ6kYcHfH19UaNGDVvFRSTVwKxcKTUx7d+fXf7UU1Lz0sCBQECA4+IrotzNgWoaUdjcpk65lyMi12ZxR2H9VAiiKOLs2bOGTnh69Z3g7hJSuLNnpVuxY2OB/6T5euDhAfTsKd2O3batauZfUnN/AnPXTe7liMh1WZTUtG/fHjmHtdH3oxEEAaIoQhAEaLVaeSMk15CRAaxdK9XK7NiRXV6pEjB8ODB0KBDMZgYiIjLN7KQmISHBlnGQq0pIkDr+LlwI3Lollbm5Ac89JzUxRUYC7u4Fv4eDcQA3cnbcR8lVWDShJZEssrKkiSSjo6WJJfW1f8HBUo3M8OFSDY0CFDTRIjuwOp6bmxsaNGhg+NsVcR8lV2L2NAmpqal49913sXbtWmRmZqJDhw74v//7PwQoqKOmq06T4DRu3JBut54/X/pbr2NHqa9Mt26Ap6fj4rOQfpj33D8gDvNOzoL7KKmF7NMkTJw4EbGxsejXrx98fHywbNkyjBo1Ks/ElkRGdDpg61apVmbDBkDf5yogABgyRKqVqV7dsTFaobCJGwVIEzJ2DAtiNb+TcZWmGO6j5IrMTmpWr16NhQsXGmbi7t+/P5555hlotVq4O3mfB3KAW7eAmBjpLqac/bFatZJqZV54QRpnxk7kPpEdTLhnVJ2fmwggMTkNBxPu8Y4dBxJF0TAKuqenJ7acTnKZphjuo+SKzE5qrl27hpYtWxoeN2vWDB4eHrh58yZCQkJsEhwpjCgCu3dLtTKrVgFPTibQaKQxZV5/HQgLs3tYtuhTYO7EjUqZiFKtMjMzMXXqVABAeI/BGP3LyTw1F0nJaRi15IjqmmK4j5IrMrvnnFarzTNvioeHB7KysmQPihTmv/+AWbOkhKVNG+CXX6SEpmlTaRqDmzezn7czfZ+C3Fes+hPZ5lOJVr2vuRM3KmUiSlcw9fd/TDbFAFJTjFZnVhdDReA+Sq7I7JoaURQxaNAgeOdoMkhLS8PIkSNRrFgxQ9nq1avljZCckygCf/8t1cosXw6kPUkaihUD+vWTamUaN3ZoiLbsU2DuxI1KmYjSFSSlpAHIv6lcjU0x3EfJFZmd1AwcODBPWf/+/WUNhhTgwQNg6VIpmTl+PLu8fn2pr0y/foCT3Flm6z4FfZuG4Js/z+cpV+NEi67SuVZNTTH6yUVHLTkCATBKbNS4jxIBFiQ1MTExtoyDnN3Ro1Kn36VLpZmyAcDHB3j5ZSmZefppQHCug6Ot+hTk10cnpyCVdTx1pXFO1NYUo58MNPf3p7Z9lEjPomkSHGny5Mn47bffcOzYMXh5eeH+/fuODkn9UlOlpqXoaODgwezymjWlROa114DSzlt1bYs+BabG/dD7X4caGN2uumqufk2trxI71waV8MGNlEyXa4rhZKDkShQzxGZGRgZ69+6NUaNGOToU9YuPB8aNA8qXl8aSOXhQGhSvb19g507gzBlg/HinTmiA7D4Fpg7dAqQaB3NPZAX10dG/3y+HrloRqXMqrE8SoKzOtRO61gKAPPuDKzTF6CcD7dGwAiKqlVHtehIpJqmJiorC//73P9SrV8/RoahTejqwbBnQujVQpw7wf/8HJCcDoaHA1KnA9evZzztZM5Mp+j4FgDwnMkv66KiBGtbXzc0NYWFhCAsLQ+e65TGnf2MEaYxr5oI0PoqqcSIi0xTT/GSN9PR0pKenGx6npKQ4MBondfEiMG+edOv1nTtSmbs70L27dAdTx47SBJMKJWefAlcb90MN6+vh4YHevXsbHrMphkjdVJ3UTJ06FVFRUY4Ow/lkZkpTFsydC/zxR3Z5hQrStAXDhkl/q4RcJzJXG/dDreurb4ohIvVx6CX4pEmTIAhCgf8OHz5s9ftPmDABycnJhn/Xrl2TMXoFunoV+PRToHJl4MUXpYRGEIAuXYB164DLl4GJE1WV0OjJ0adA7j46zs7V1peIlM+hNTWjR482zCVlSpUqVax+f29vb6PBAl2SVgts3izVyvz2mzTBJAAEBmZPKFm1qmNjVAhXG/dDDeubkZFhmCZhwoQJeUZFJyJ1cWhSExAQgICAAEeGoF6JiVI/mXnzpBoavbZtpduxe/YEeIC3mKuN++Fq60tEyqaYPjVXr17FvXv3cPXqVWi1Whw7dgwAUL16dRQvXtyxwTkLnQ7YsUMaV2btWkA/L1epUsDgwcCIEdIYM1QkrtbZ1NXWl4iUSzFJzaeffopFixYZHjdq1AgAsGPHDrRp08ZBUTmJu3eB2Fipiel8jmH7IyKAUaOAl14CfH0dFp4auVpnU1dbXyJSJsUkNbGxsYiNjXV0GM5DFIF9+6RamZUrpXFmAMDfHxgwQLodu359x8ZIRERkR4pJauiJ5GRg8WIpmTl9Oru8USOpVuaVVwAna45zlckQ1U4N36Ma1oGITGNSoxSHD0uJzLJl0pxMgNSk9OqrUq1MeLhTjvTrSpMhqpkavset8Un4YtN5Ra8DERVMEEVRGRO3yCAlJQUajQbJyckoUaKEo8Mp3MOHwC+/SMlMXFx2eZ06UiIzYABQsqTDwiuMqckQ9akXh6ZXBiV/j1lZWVixYgVuP0jDdwllkZVraC4lrAMRmX/+Vu7492p28iQwenT2CL9xcdLt1/36AXv2SM+PGePUCY3aJkNUEq1OxP6Ld7Hu2A3sv3i3SNtY6d+jh4cHXu77Cn65VzlPQgMoYx2IyHxsfnIWaWnAr79KtTJ//ZVdXr26dCv24MGAgsb0sWQyRN5VIx+5m4nU8D2qYR2IyDxMahzt3DnpVuzYWODek9mOPTyAHj2kQfLatVPkhJJqmAxRaUw1EyUlp2HUkiNWNbGo4XtUwzoQkXmY1DhCRoY011J0NLB9e3Z5pUpSc9PQoUCwstv31ToZorMqrJlIgNTE0jEsyKK7fZT+PWZkZODExlj099Hhl7QGyIK7yWWddR2IyHxMauzp8mVg/nxg4ULg33+lMkEAnntOqpWJjATcTR90lUQ/GWJSclq+J1oB0lD7nAxRHrZqYlHD96jTZsFTQIETczr7OhCReZTXrqE0WVnA+vVS4lK1KjBlipTQBAUBH38MJCQAGzZIz6skoQGyJ0ME8p5MlDIZopLYqolFbd+jGtaBiExjUmMrN24An30GhIZK/WN+/10aBbh9e6lD8NWrwOefA5UrOzpSm9FPhhikMa7WD9L48BZamdmymUgt3+O3fRsqfh2IqGBsfpKTTgf8+afUV2b9ekCrlcrLlMmeUPKppxwbo51xMkT7sHUzkRq+x45hQYisH6LodSCigjGpkcPt20BMjHQX06VL2eXPPiv1lXnxRcDHdTshcjJE29M3E41acgQCYJTYyNXEoobvUQ3rQESmMakpKlGUZsO+eFF6rNEAr70mjfhbp45jYyOXom8myj1OTRCnAiAiF8GkpqgEQUpiNm6UamVefhkoVszRUZGLUkMzkZwEQUDlJ/3WBCecG42I5MW5n+SQlSUNmEdERESy49xP9sSEhoiIyOGY1BAREZEqsIqBiFQrIyMDs2bNAgCMGzcOXl5eDo6IiGyJSQ0RqVpqaqqjQyAiO2HzExEREakCkxoiIiJSBSY1REREpArsU0NETkerEzmAIBFZjEkNETmVzacS80z1EMypHojIDGx+IiKnsflUIkYtOWKU0ABAUnIaRi05gs2nEi16P0EQUL58eZQvX57TJBC5AE6TQEROQasT8ez07XkSGj0B0uSce99vx6YoIhfDaRKISFEOJtwzmdAAgAggMTkNBxPu2S8oIlIUJjVE5BRuPTCd0FizHBG5HnYUJiKnEOjvI+tyAJCZmYkffvgBAPDmm2/C09PTqtiISBlYU0NETqFZaGkEa3xgqreMAOkuqGahpc1+T1EUkZycjOTkZLhQ90Eil8WkhoicgrubgIndwgAgT2KjfzyxWxg7CRORSUxqiMhpRNYNxpz+jRGkMW5iCtL4YE7/xhynhogKxD41RORUIusGo2NYEEcUJiKLMakhIqfj7iYgoloZR4dBRArD5iciIiJSBdbUEJFqCYKAsmXLGv4mInVjUuNgnI2YyHY8PT3xxhtvODoMIrITJjUOxNmISQ3Unpirff2I1IRJjYPoZyPOPRyYfjZi3r5KSqD2xFzt60ekNuwo7ABanYioDfF5EhoAhrKoDfHQ6jgCqhJpdSL2X7yLdcduYP/Fu6r9HvWJee5JKPWJ+eZTiQ6KLFtmZiZmz56N2bNnIzMz06LXKmH9iMgYa2ocwJLZiB19Wyur3i0j15W9s2/3whJzAVJi3jEsyKFxi6KI27dvG/42lzkXHpPWn3b4+hGRMSY1DqCU2YhZ9W4ZuZoUlbDdlZSYW6Ow9QOApJR0fL/9AsZ1eMpOURFRYdj85AC2mI1Ybqx6t4xcTYpK2e5KScytZW7c3/x5zmm+EyJiUuMQtpiNWE7s82M5S2ouTFHSdldCYl4UlsTtLN8JETGpcQhnn41YjhO0q5Gj5kJJ293ZE/Oi0q+fOZzlOyEiJjUO48yzEau9acEW5Ki5UNJ2d/bEvKhyrp85nOE7ISJ2FHYoZ52NWO1NC7agv7JPSk7Lt/lIgJSwFlRzobTtrk/Mc3dqDnKiTs2CIECj0Rj+tkRk3WD8r8NT+ObP84Uu6yzfCZGrY1LjYM44G7EcJ2hXo7+yH7XkCATAaLuZW3OhxO3urIm5nqenJ8aPH2/160e3ewrLDl5DUkr+NTHO+J0QuTI2P1Eeam9asJWiNikqdbvrE/MeDSsgoloZp4uvKNzdBEzqHgYByvpOiFyVIFoyIpXCpaSkQKPRIDk5GSVKlHB0OE5PCeOlOKOiDpzH7e58+J0QOZa5528mNVQgZx/ZVq243eWRmZmJ2NhYAMCgQYPg6elp9XvxOyFyHHPP3+xTQwVyxj4/roDbXR6iKOLmzZuGv4uC3wmR82OfGiIiIlIFJjVERESkCkxqiIiISBUUkdRcvnwZQ4cORWhoKHx9fVGtWjVMnDgRGRkZjg6NiIiInIQiOgr/888/0Ol0mDt3LqpXr45Tp05h+PDhePToEWbMmOHo8IiIiMgJKCKpiYyMRGRkpOFx1apVcfbsWcyZM8flkxreZqos/L7sz8/Pz9EhEJGdKCKpyU9ycjJKly54aPL09HSkp6cbHqekpNg6LLuy54BgrnoylnO9OYCb/Xl5eeHdd991dBhEZCeKHHzv4sWLaNy4Mb7++msMGzbM5HKTJk1CVFRUnnI1DL63+VQiRi05kmeOIP3pVs6Zvl31ZCznetvz+yIiUhtzB99zaEfhSZMmQRCEAv8dPnzY6DU3b95EZGQkevfuXWBCAwATJkxAcnKy4d+1a9dsuTp2o9WJiNoQn++kh/qyqA3x0OqKnq/qT8Y5T+wAkJSchlFLjmDzqcQif4YzknO97fl9ERG5Moc2P40ePRp9+/YtcJkqVaoY/r558ybatm2LiIgIzJs3r9D39/b2hre3d1HDdDoHE+7lOdnmJAJITE7DwYR7RRoBtbCTsQDpZNwxLEhVTVFyr7e9vi/KKzMzE0uXLgUA9OvXr0jTJBCR83NoUhMQEICAgACzlr1x4wbatm2LJk2aICYmBm5uirgb3SZuPTB9grRmOVNc9WQs93rb6/uivERRxJUrVwx/E5G6KaKj8M2bN9GmTRtUqlQJM2bMwO3btw3PBQUFOTAyxwj095F1OVNc9WQs93rb6/siInJ1ikhq/vjjD1y4cAEXLlxAxYoVjZ5zxauvZqGlEazxQVJyWr5NJAKAII10p05RuOrJWO71ttf3RUTk6hTRhjNo0CCIopjvP1fk7iZgYrcwANl3z+jpH0/sFlbkfi76k7GpdxEg3Q2ktpOx3Ottr++LiMjVKSKpobwi6wZjTv/GCNIY1xYEaXxkuz3YVU/Gtlhve3xfRESuThHNT5S/yLrB6BgWZNNB8fQn49zjtQSpfJwaW6y3Pb4vIiJXxqRG4dzdBJvfeeSqJ2NbrLc9vi8yxtu4iVyHIkcUtpa5IxISERGR81DEiMJEREREcmFSQ0RERKrAPjVEpFpZWVlYsWIFAKBPnz7w8OAhj0jN+AsnItXS6XQ4f/684W8iUjc2PxEREZEqMKkhIiIiVWBSQ0RERKrApIaIiIhUgUkNERERqYJL3f2kHzw5JSXFwZEQkT1kZGQgLU2auyslJQVeXl4OjoiIrKE/bxc2CYJLTZNw/fp1hISEODoMIiIissK1a9dQsWJFk8+7VFKj0+lw8+ZN+Pv7QxCUNxljSkoKQkJCcO3aNc5d9QS3SV7cJsa4PfLiNsmL2yQvZ9omoijiwYMHKF++PNzcTPeccanmJzc3twIzPKUoUaKEw3cwZ8Ntkhe3iTFuj7y4TfLiNsnLWbaJRqMpdBl2FCYiIiJVYFJDREREqsCkRkG8vb0xceJEeHt7OzoUp8Ftkhe3iTFuj7y4TfLiNslLidvEpToKExERkXqxpoaIiIhUgUkNERERqQKTGiIiIlIFJjVERESkCkxqnNjkyZPRokUL+Pn5oWTJkma9ZtCgQRAEwehf8+bNbRuoHVmzTURRxKRJk1C+fHn4+vqiTZs2OH36tG0DtaP//vsPAwYMgEajgUajwYABA3D//v0CX6O2/WT27NkIDQ2Fj48PmjRpgj179hS4/K5du9CkSRP4+PigatWqiI6OtlOk9mPJNtm5c2ee/UEQBPzzzz92jNi2du/ejW7duqF8+fIQBAFr164t9DVq308s3SZK2E+Y1DixjIwM9O7dG6NGjbLodZGRkUhMTDT8+/33320Uof1Zs02+/PJLzJw5E99//z0OHTqEoKAgdOzYEQ8ePLBhpPbz6quv4tixY9i8eTM2b96MY8eOYcCAAYW+Ti37yfLlyzF+/Hh89NFHOHr0KFq2bIkuXbrg6tWr+S6fkJCArl27omXLljh69Cg+/PBDjB07FqtWrbJz5LZj6TbRO3v2rNE+8dRTT9kpYtt79OgRGjRogO+//96s5V1hP7F0m+g59X4iktOLiYkRNRqNWcsOHDhQ7NGjh03jcQbmbhOdTicGBQWJ06ZNM5SlpaWJGo1GjI6OtmGE9hEfHy8CEA8cOGAo279/vwhA/Oeff0y+Tk37SbNmzcSRI0caldWqVUv84IMP8l3+vffeE2vVqmVU9vrrr4vNmze3WYz2Zuk22bFjhwhA/O+//+wQneMBENesWVPgMq6wn+RkzjZRwn7CmhoV2rlzJwIDA1GjRg0MHz4ct27dcnRIDpOQkICkpCR06tTJUObt7Y3WrVtj3759DoxMHvv374dGo8HTTz9tKGvevDk0Gk2h66eG/SQjIwNxcXFG3y8AdOrUyeT679+/P8/ynTt3xuHDh5GZmWmzWO3Fmm2i16hRIwQHB6N9+/bYsWOHLcN0emrfT4rCmfcTJjUq06VLFyxduhTbt2/H119/jUOHDqFdu3ZIT093dGgOkZSUBAAoV66cUXm5cuUMzylZUlISAgMD85QHBgYWuH5q2U/u3LkDrVZr0feblJSU7/JZWVm4c+eOzWK1F2u2SXBwMObNm4dVq1Zh9erVqFmzJtq3b4/du3fbI2SnpPb9xBpK2E9capZuZzBp0iRERUUVuMyhQ4cQHh5u1fu//PLLhr/r1q2L8PBwVK5cGb/99hteeOEFq97T1my9TQBAEASjx6Io5ilzJuZuEyDvugGFr58S95OCWPr95rd8fuVKZsk2qVmzJmrWrGl4HBERgWvXrmHGjBlo1aqVTeN0Zq6wn1hCCfsJkxo7Gz16NPr27VvgMlWqVJHt84KDg1G5cmWcP39etveUmy23SVBQEADpqis4ONhQfuvWrTxXYc7E3G1y4sQJ/Pvvv3meu337tkXrp4T9JD8BAQFwd3fPUwNR0PcbFBSU7/IeHh4oU6aMzWK1F2u2SX6aN2+OJUuWyB2eYqh9P5GLs+0nTGrsLCAgAAEBAXb7vLt37+LatWtGJ3RnY8ttEhoaiqCgIGzduhWNGjUCIPU52LVrF6ZPn26Tz5SDudskIiICycnJOHjwIJo1awYA+Pvvv5GcnIwWLVqY/XlK2E/y4+XlhSZNmmDr1q3o1auXoXzr1q3o0aNHvq+JiIjAhg0bjMr++OMPhIeHw9PT06bx2oM12yQ/R48eVdz+ICe17ydycbr9xJG9lKlgV65cEY8ePSpGRUWJxYsXF48ePSoePXpUfPDggWGZmjVriqtXrxZFURQfPHggvv322+K+ffvEhIQEcceOHWJERIRYoUIFMSUlxVGrIStLt4koiuK0adNEjUYjrl69Wjx58qT4yiuviMHBwarZJpGRkWL9+vXF/fv3i/v37xfr1asnPv/880bLqHk/+eWXX0RPT09x4cKFYnx8vDh+/HixWLFi4uXLl0VRFMUPPvhAHDBggGH5S5cuiX5+fuL//vc/MT4+Xly4cKHo6ekp/vrrr45aBdlZuk2++eYbcc2aNeK5c+fEU6dOiR988IEIQFy1apWjVkF2Dx48MBwvAIgzZ84Ujx49Kl65ckUURdfcTyzdJkrYT5jUOLGBAweKAPL827Fjh2EZAGJMTIwoiqKYmpoqdurUSSxbtqzo6ekpVqpUSRw4cKB49epVx6yADVi6TURRuq174sSJYlBQkOjt7S22atVKPHnypP2Dt5G7d++K/fr1E/39/UV/f3+xX79+eW65VPt+8sMPP4iVK1cWvby8xMaNG4u7du0yPDdw4ECxdevWRsvv3LlTbNSokejl5SVWqVJFnDNnjp0jtj1Ltsn06dPFatWqiT4+PmKpUqXEZ599Vvztt98cELXt6G9Hzv1v4MCBoii65n5i6TZRwn4iiOKTnk9ERERECsZbuomIiEgVmNQQERGRKjCpISIiIlVgUkNERESqwKSGiIiIVIFJDREREakCkxoiIiJSBSY1ROTUdu7cCUEQcP/+fUeHQkROjkkNkQsSBKHAf4MGDbJbLIMGDTJ8rqenJ6pWrYp33nkHjx49slsM5mrTpg3Gjx/v6DCIyAROaEnkghITEw1/L1++HJ9++inOnj1rKPP19TVaPjMz06aT+EVGRiImJgaZmZnYs2cPhg0bhkePHmHOnDk2+0wiUh/W1BC5oKCgIMM/jUYDQRAMj9PS0lCyZEmsWLECbdq0gY+PD5YsWYJJkyahYcOGRu/z7bffokqVKkZlMTExqF27Nnx8fFCrVi3Mnj270Hi8vb0RFBSEkJAQvPrqq+jXrx/Wrl1rtExcXBzCw8Ph5+eHFi1aGCVhALBhwwY0adIEPj4+qFq1KqKiopCVlWV4XhAELFiwAL169YKfnx+eeuoprF+/3ug9du3ahWbNmsHb2xvBwcH44IMPDO8xaNAg7Nq1C7NmzTLULCUkJKB69eqYMWOG0fucOnUKbm5uuHjxouGz58yZgy5dusDX1xehoaFYuXKl0Wtu3LiBl19+GaVKlUKZMmXQo0cPXL58udBtR0TZmNQQUb7ef/99jB07FmfOnEHnzp3Nes38+fPx0UcfYfLkyThz5gymTJmCTz75BIsWLbLos319fZGZmWlU9tFHH+Hrr7/G4cOH4eHhgSFDhhie27JlC/r374+xY8ciPj4ec+fORWxsLCZPnmz0HlFRUejTpw9OnDiBrl27ol+/frh37x4AKano2rUrmjZtiuPHj2POnDlYuHAhvvjiCwDArFmzEBERgeHDhyMxMRGJiYmoVKkShgwZgpiYGKPP+fHHH9GyZUtUq1bNUPbJJ5/gxRdfxPHjx9G/f3+88sorOHPmDAAgNTUVbdu2RfHixbF7927s3bsXxYsXR2RkJDIyMizadkQuzdEzahKRY8XExIgajcbwOCEhQQQgfvvtt0bLTZw4UWzQoIFR2TfffCNWrlzZ8DgkJET8+eefjZb5/PPPxYiICJOfP3DgQLFHjx6Gx3///bdYpkwZsU+fPqIoZs8k/OeffxqW+e2330QA4uPHj0VRFMWWLVuKU6ZMMXrfxYsXi8HBwYbHAMSPP/7Y8Pjhw4eiIAjipk2bRFEUxQ8//FCsWbOmqNPpDMv88MMPYvHixUWtViuKoii2bt1aHDdunNHn3Lx5U3R3dxf//vtvURRFMSMjQyxbtqwYGxtr9NkjR440et3TTz8tjho1ShRFUVy4cGGez05PTxd9fX3FLVu2mNx2RGSMfWqIKF/h4eEWLX/79m1cu3YNQ4cOxfDhww3lWVlZ0Gg0Bb5248aNKF68OLKyspCZmYkePXrgu+++M1qmfv36hr+Dg4MBALdu3UKlSpUQFxeHQ4cOGdXMaLVapKWlITU1FX5+fnneo1ixYvD398etW7cAAGfOnEFERAQEQTAs88wzz+Dhw4e4fv06KlWqlG/swcHBeO655/Djjz+iWbNm2LhxI9LS0tC7d2+j5SIiIvI8PnbsGACpae3ChQvw9/c3WiYtLc3QhEVEhWNSQ0T5KlasmNFjNzc3iKJoVJaziUin0wGQmqCefvppo+Xc3d0L/Ky2bdtizpw58PT0RPny5fPtlJyzTJ946D9Tp9MhKioKL7zwQp7X+fj45Pse+vfRv4coikYJjb4s5+eZMmzYMAwYMADffPMNYmJi8PLLLxsSqYLkXI8mTZpg6dKleZYpW7Zsoe9DRBImNURklrJlyyIpKcno5K+vaQCAcuXKoUKFCrh06RL69etn0XsXK1YM1atXtzq2xo0b4+zZs0V6j7CwMKxatcpo/fbt2wd/f39UqFABAODl5QWtVpvntV27dkWxYsUwZ84cbNq0Cbt3786zzIEDB/Daa68ZPW7UqJEh/uXLlyMwMBAlSpSweh2IXB07ChORWdq0aYPbt2/jyy+/xMWLF/HDDz9g06ZNRstMmjQJU6dOxaxZs3Du3DmcPHkSMTExmDlzpk1j+/TTT/HTTz9h0qRJOH36NM6cOYPly5fj448/Nvs93njjDVy7dg1jxozBP//8g3Xr1mHixIl466234OYmHSqrVKmCv//+G5cvX8adO3cMtTzu7u4YNGgQJkyYgOrVq+dpagKAlStX4scff8S5c+cwceJEHDx4EKNHjwYA9OvXDwEBAejRowf27NmDhIQE7Nq1C+PGjcP169dl2EJEroFJDRGZpXbt2pg9ezZ++OEHNGjQAAcPHsQ777xjtMywYcOwYMECxMbGol69emjdujViY2MRGhpq09g6d+6MjRs3YuvWrWjatCmaN2+OmTNnonLlyma/R4UKFfD777/j4MGDaNCgAUaOHImhQ4caJUbvvPMO3N3dERYWhrJly+Lq1auG54YOHYqMjAyju7JyioqKwi+//IL69etj0aJFWLp0KcLCwgAAfn5+2L17NypVqoQXXngBtWvXxpAhQ/D48WPW3BBZQBBzN5ITEZHF/vrrL7Rp0wbXr19HuXLljJ4TBAFr1qxBz549HRMckYtgnxoioiJIT0/HtWvX8Mknn6BPnz55Ehoish82PxERFcGyZctQs2ZNJCcn48svv3R0OEQujc1PREREpAqsqSEiIiJVYFJDREREqsCkhoiIiFSBSQ0RERGpApMaIiIiUgUmNURERKQKTGqIiIhIFZjUEBERkSowqSEiIiJV+H8WF+h8kcK1ZQAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Import helper function to performing clumping:\n",
    "from magenpy.stats.ld.utils import clump_snps\n",
    "\n",
    "# Set the thresholds:\n",
    "pval_threshold = 1e-5\n",
    "rsq_threshold = 0.9\n",
    "\n",
    "# Step 1: Find which variants to keep by thresholding based on P-values:\n",
    "sumstats_table = train.to_summary_statistics_table()\n",
    "sumstats_table['Keep_T'] = sumstats_table.PVAL < pval_threshold\n",
    "\n",
    "# Step 2: Find which variants to keep after clumping variants that are highly correlated: \n",
    "clumped_snps = clump_snps(train.ld[22], \n",
    "                          statistic=sumstats_table.PVAL, \n",
    "                          rsq_threshold=rsq_threshold)\n",
    "# Create a dataframe with the clumped SNPs:\n",
    "clumped_snps = pd.DataFrame({'SNP': clumped_snps, 'Keep_C': True})\n",
    "# Merge with the original sumstats table:\n",
    "sumstats_table = sumstats_table.merge(clumped_snps, how='left').fillna(False)\n",
    "\n",
    "# Step 3: Combine both conditions:\n",
    "sumstats_table['Keep_Final'] = sumstats_table['Keep_T'] & sumstats_table['Keep_C']\n",
    "\n",
    "# Step 4: Compute the final BETA by taking into account both Clumping + Thresholding\n",
    "sumstats_table['CT_BETA'] = sumstats_table.BETA * sumstats_table.Keep_Final\n",
    "\n",
    "# Display the variants remaining after Clumping + Thresholding:\n",
    "\n",
    "print(\"Variants remaining after Clumping + Thresholding:\")\n",
    "display(sumstats_table.loc[sumstats_table.Keep_Final])\n",
    "\n",
    "# Score using the C+T betas:\n",
    "\n",
    "ct_prs_pred = test.predict({22: sumstats_table.CT_BETA})\n",
    "\n",
    "# Let's compare the model prediction to the simulated phenotypes:\n",
    "plot_scatter(y_test, ct_prs_pred, title=\"C+T PRS\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9cee3a51",
   "metadata": {},
   "source": [
    "### (4.3) Bayesian PRS (`VIPRS`)\n",
    "\n",
    "The final major category of approaches that we will discuss in this context are those that use Bayesian inference techniques to infer polygenic risk score weights from GWAS summary statistics. Bayesian PRS methods operate by specifying priors distributions on the effect size, specifying the data likelihood, and then performing approximate Bayesian inference using Markov Chain Monte Carlo (MCMC) or Variational Inference (VI). \n",
    "\n",
    "In this presentation, we will discuss our recently proposed method for Bayesian PRS inference: **VIPRS**. `VIPRS` assigns a spike-and-slab prior on the effect size, as discussed in the previous section. Then, in order to approximate the Bayesian posterior, the method employs variational inference techniques to achieve fast and accurate posterior approximation. This is in contrast to many popular Bayesian PRS methods, which use Markov Chain Monte Carlo (MCMC) for posterior approximation.\n",
    "\n",
    "<img src=\"./figures/mcmc.png\" alt=\"drawing\" width=\"700\"/>\n",
    "\n",
    "<img src=\"./figures/vi.png\" alt=\"drawing\" width=\"700\"/>\n",
    "\n",
    "\n",
    "`VIPRS` was developed in conjunction with `magenpy`, so the interfaces should work together quite nicely. To perform inference on the summary statistics that we derived previously, you only need to pass the `train` object to `VIPRS` and then call `.fit` method:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "ab4810e9",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-04-12T16:14:27.704231Z",
     "start_time": "2024-04-12T16:14:27.224186Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Chromosome 22: 100%|███████████████| 77/77 [00:00<00:00, 443.43it/s, Final ELBO=-322.6504]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "> Generating polygenic scores...\n"
     ]
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Initialize the VIPRS object:\n",
    "v = vp.VIPRS(train, low_memory=True)\n",
    "# Fit the model to data:\n",
    "v.fit()\n",
    "\n",
    "# Predict on the test samples:\n",
    "viprs_pred = v.predict(test)\n",
    "\n",
    "# Let's compare the model prediction to the simulated phenotypes:\n",
    "plot_scatter(y_test, viprs_pred, title=\"VIPRS\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b8704fcd",
   "metadata": {},
   "source": [
    "In addition to the prediction accuracy on the held-out test set, we can also interrogate and inspect the behavior of the `VIPRS` model by examining the **Evidence Lower BOund (ELBO)**, the metric that the model is aiming to maximize:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "56eb542b",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-04-12T16:14:33.370994Z",
     "start_time": "2024-04-12T16:14:32.936880Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<seaborn.axisgrid.FacetGrid at 0x129ddbc50>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from viprs.plot.diagnostics import plot_history\n",
    "\n",
    "plot_history(v)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "da8e7e2f",
   "metadata": {},
   "source": [
    "One advantage of Bayesian methods like `VIPRS` is that we can also obtain interpretable outputs, such as \n",
    "the probability for given variant being causal for the phenotype of interest. This quantity is known in the \n",
    "literature as **Posterior Inclusion Probability (PIP)**. Since our phenotype here is simulated and we \n",
    "have a record of the true causal variants, we can compare the estimated **PIPs** to the causal status of the variants in the simulation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "218807c8",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-04-12T16:14:38.282351Z",
     "start_time": "2024-04-12T16:14:38.044098Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>CHR</th>\n",
       "      <th>SNP</th>\n",
       "      <th>POS</th>\n",
       "      <th>A1</th>\n",
       "      <th>A2</th>\n",
       "      <th>BETA</th>\n",
       "      <th>PIP</th>\n",
       "      <th>VAR_BETA</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>22</td>\n",
       "      <td>rs131538</td>\n",
       "      <td>16871137</td>\n",
       "      <td>A</td>\n",
       "      <td>G</td>\n",
       "      <td>0.002283</td>\n",
       "      <td>0.038480</td>\n",
       "      <td>0.000183</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>22</td>\n",
       "      <td>rs9605903</td>\n",
       "      <td>17054720</td>\n",
       "      <td>C</td>\n",
       "      <td>T</td>\n",
       "      <td>-0.000257</td>\n",
       "      <td>0.012718</td>\n",
       "      <td>0.000023</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>22</td>\n",
       "      <td>rs5746647</td>\n",
       "      <td>17057138</td>\n",
       "      <td>G</td>\n",
       "      <td>T</td>\n",
       "      <td>-0.000538</td>\n",
       "      <td>0.016258</td>\n",
       "      <td>0.000040</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>22</td>\n",
       "      <td>rs16980739</td>\n",
       "      <td>17058616</td>\n",
       "      <td>T</td>\n",
       "      <td>C</td>\n",
       "      <td>0.000198</td>\n",
       "      <td>0.012088</td>\n",
       "      <td>0.000020</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>22</td>\n",
       "      <td>rs9605923</td>\n",
       "      <td>17065079</td>\n",
       "      <td>A</td>\n",
       "      <td>T</td>\n",
       "      <td>-0.000267</td>\n",
       "      <td>0.012826</td>\n",
       "      <td>0.000023</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>295</th>\n",
       "      <td>22</td>\n",
       "      <td>rs12160031</td>\n",
       "      <td>17784602</td>\n",
       "      <td>A</td>\n",
       "      <td>G</td>\n",
       "      <td>-0.000989</td>\n",
       "      <td>0.022260</td>\n",
       "      <td>0.000073</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>296</th>\n",
       "      <td>22</td>\n",
       "      <td>rs5749022</td>\n",
       "      <td>17787836</td>\n",
       "      <td>C</td>\n",
       "      <td>G</td>\n",
       "      <td>0.001333</td>\n",
       "      <td>0.026737</td>\n",
       "      <td>0.000101</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>297</th>\n",
       "      <td>22</td>\n",
       "      <td>rs5749028</td>\n",
       "      <td>17789010</td>\n",
       "      <td>G</td>\n",
       "      <td>A</td>\n",
       "      <td>-0.000237</td>\n",
       "      <td>0.012490</td>\n",
       "      <td>0.000022</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>298</th>\n",
       "      <td>22</td>\n",
       "      <td>rs4819996</td>\n",
       "      <td>17790731</td>\n",
       "      <td>A</td>\n",
       "      <td>G</td>\n",
       "      <td>-0.000270</td>\n",
       "      <td>0.012860</td>\n",
       "      <td>0.000023</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>299</th>\n",
       "      <td>22</td>\n",
       "      <td>rs9606682</td>\n",
       "      <td>17791564</td>\n",
       "      <td>T</td>\n",
       "      <td>C</td>\n",
       "      <td>-0.000205</td>\n",
       "      <td>0.012152</td>\n",
       "      <td>0.000020</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>300 rows × 8 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     CHR         SNP       POS A1 A2      BETA       PIP  VAR_BETA\n",
       "0     22    rs131538  16871137  A  G  0.002283  0.038480  0.000183\n",
       "1     22   rs9605903  17054720  C  T -0.000257  0.012718  0.000023\n",
       "2     22   rs5746647  17057138  G  T -0.000538  0.016258  0.000040\n",
       "3     22  rs16980739  17058616  T  C  0.000198  0.012088  0.000020\n",
       "4     22   rs9605923  17065079  A  T -0.000267  0.012826  0.000023\n",
       "..   ...         ...       ... .. ..       ...       ...       ...\n",
       "295   22  rs12160031  17784602  A  G -0.000989  0.022260  0.000073\n",
       "296   22   rs5749022  17787836  C  G  0.001333  0.026737  0.000101\n",
       "297   22   rs5749028  17789010  G  A -0.000237  0.012490  0.000022\n",
       "298   22   rs4819996  17790731  A  G -0.000270  0.012860  0.000023\n",
       "299   22   rs9606682  17791564  T  C -0.000205  0.012152  0.000020\n",
       "\n",
       "[300 rows x 8 columns]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Export the inferred variant effect sizes:\n",
    "post_effect_table = v.to_table(col_subset=('CHR', 'SNP', 'POS', 'A1', 'A2'))\n",
    "\n",
    "display(post_effect_table)\n",
    "\n",
    "# Plot the Posterior Inclusion Probability (PIP):\n",
    "plt.scatter(post_effect_table.POS, post_effect_table.PIP, \n",
    "            marker='.', label='Non-causal variants')\n",
    "mask = train.get_causal_status()[22]\n",
    "plt.scatter(post_effect_table.POS[mask], post_effect_table.PIP[mask], color='red',\n",
    "            label='Causal variants')\n",
    "plt.xlabel(\"Genomic Position (Chromosome 22)\")\n",
    "plt.ylabel(\"Posterior Inclusion Probability (PIP)\")\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b0a2cd09",
   "metadata": {},
   "source": [
    "### Other established PRS Methods that operate on GWAS Summary Statistics\n",
    "\n",
    "\n",
    "#### Bayesian:\n",
    "* [LDPred2](https://privefl.github.io/bigsnpr/articles/LDpred2.html)\n",
    "* [SBayesR](https://cnsgenomics.com/software/gctb/#Overview)\n",
    "* [PRScs](https://github.com/getian107/PRScs)\n",
    "\n",
    "#### Regularized Linear Models\n",
    "* [Lassosum](https://github.com/tshmak/lassosum)\n",
    "\n",
    "#### C+T\n",
    "* [plink2](https://www.cog-genomics.org/plink/2.0/)\n",
    "* [PRSice2](https://choishingwan.github.io/PRSice/)\n",
    "\n",
    "\n",
    "## (5) PRS Evaluation Strategies / Metrics\n",
    "\n",
    "Once a PRS model is fit to data, the next step is to evaluate its prediction accuracy on a held-out test set. Accuracy is measured differently depending on the type of phenotype considered (continuous vs. binary) as well as the data available about the validation / test cohort. \n",
    "\n",
    "\n",
    "For **continuous phenotypes**, common evaluation metrics include:\n",
    "\n",
    "* **Pearson Correlation Coefficient**: Measure the correlation between the PRS and the phenotype.\n",
    "* **R-Squared (Coefficient of Determination)**: The proportion of phenotypic variance expalined by the PRS.\n",
    "   * **Incremental R-Squared**: In research papers on PRS, the most common metric is incremental R-Squared, which takes the difference between the $R^2$ of a null model (with no PRS) and a full model with the PRS included. The null model is typically a linear model with only covariates (sex, age, Pricipal Components - PCs), whereas the full model is a linear model with these covariates plus the PRS:\n",
    "   \n",
    "   **Null model**: $y \\sim \\alpha_0 + \\sum_{c=1}^C C_k*\\beta_c$\n",
    "   \n",
    "   **Full model**: $y \\sim \\alpha_0 + PRS*\\beta_{prs} + \\sum_{c=1}^C C_k*\\beta_c$ \n",
    "\n",
    "\n",
    "<img src=\"figures/r2.png\" alt=\"drawing\" width=\"500\"/>\n",
    "\n",
    "\n",
    "For **binary, case-control phenotypes**, common evaluation metrics include:\n",
    "\n",
    "* **Area Under the ROC Curve (AUROC)**: A measure of separability between cases and controls that ranges between 0.5 (random predictor) and 1 (perfect separability).\n",
    "* **Nagelkerke R-Squared**: A pseudo R-squared metric that works for binary traits.\n",
    "* **Liability R-Squared**: A pseudo R-squared metric that is less biased than Nagelkerke.\n",
    "\n",
    "\n",
    "<img src=\"https://upload.wikimedia.org/wikipedia/commons/thumb/1/13/Roc_curve.svg/1920px-Roc_curve.svg.png\" alt=\"drawing\" width=\"400\"/>\n",
    "\n",
    "Source: [Wikipedia](https://en.wikipedia.org/wiki/Receiver_operating_characteristic)\n",
    "\n",
    "These metrics provide global summaries about the predictive performance of the PRS and its potential usefulness in aggregate. Many of these metrics are available with the `viprs` package and can be accessed as follows:\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "e9f527c5",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-04-12T16:15:43.430864Z",
     "start_time": "2024-04-12T16:15:42.666387Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Pearson Correlation (VIPRS): 0.7125266707429876\n",
      "Incremental R-Squared (VIPRS): 0.5076942565200865\n"
     ]
    }
   ],
   "source": [
    "# import continuous metrics:\n",
    "\n",
    "from viprs.eval.continuous_metrics import incremental_r2, pearson_r\n",
    "\n",
    "print(\"Pearson Correlation (VIPRS):\", pearson_r(y_test, viprs_pred))\n",
    "\n",
    "# NOTE: In this case, because we don't have covariates, the null model\n",
    "# is a model with only intercept:\n",
    "print(\"Incremental R-Squared (VIPRS):\", incremental_r2(y_test, viprs_pred))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5e0203be",
   "metadata": {},
   "source": [
    "A full listing of PRS evaluation metrics and their implementation in `python` is available [here](https://shz9.github.io/viprs/api/overview/#model-evaluation)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a23887c2",
   "metadata": {},
   "source": [
    "## (6) Inference of Polygenic Risk Scores (PRS) from Publicly Available GWAS Summary Statistics\n",
    "\n",
    "Refer to [notebook](https://github.com/shz9/viprs/blob/master/notebooks/height_example.ipynb) attached with the `viprs` package.\n",
    "\n",
    "For commandline tools, refer to tutorials / references on the `viprs` [documentation](https://shz9.github.io/viprs/) page."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1cc0394f",
   "metadata": {},
   "source": [
    "## References / Further reading\n",
    "\n",
    "* [Common polygenic variation contributes to risk of schizophrenia and bipolar disorder](https://doi.org/10.1038/nature08185)\n",
    "* [PRSice-2: Polygenic Risk Score software for biobank-scale data](https://doi.org/10.1093/gigascience/giz082)\n",
    "* [A guide to performing Polygenic Risk Score analyses](https://doi.org/10.1101/416545)\n",
    "* [Polygenic risk scores: from research tools to clinical instruments](https://doi.org/10.1186/s13073-020-00742-5)\n",
    "* [Modeling Linkage Disequilibrium Increases Accuracy of Polygenic Risk Scores](https://doi.org/10.1016%2Fj.ajhg.2015.09.001)\n",
    "* [LDpred2: better, faster, stronger](https://doi.org/10.1093/bioinformatics/btaa1029)\n",
    "* [Polygenic prediction via Bayesian regression and continuous shrinkage priors](https://doi.org/10.1038/s41467-019-09718-5)\n",
    "* [Improved polygenic prediction by Bayesian multiple regression on summary statistics](https://doi.org/10.1038/s41467-019-12653-0)\n",
    "* [Fast and accurate Bayesian polygenic risk modeling with variational inference](https://doi.org/10.1016/j.ajhg.2023.03.009)\n",
    "* [A fast and scalable framework for large-scale and ultrahigh-dimensional sparse regression with application to the UK Biobank](https://doi.org/10.1371/journal.pgen.1009141)\n",
    "* [Scalable Variational Inference for Bayesian Variable Selection in Regression, and Its Accuracy in Genetic Association Studies](https://doi.org/10.1214/12-BA703)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d4bfb1aa",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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