Class_07_OLG.html

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  content: "\e252";
}
.glyphicon-triangle-top:before {
  content: "\e253";
}
.glyphicon-console:before {
  content: "\e254";
}
.glyphicon-superscript:before {
  content: "\e255";
}
.glyphicon-subscript:before {
  content: "\e256";
}
.glyphicon-menu-left:before {
  content: "\e257";
}
.glyphicon-menu-right:before {
  content: "\e258";
}
.glyphicon-menu-down:before {
  content: "\e259";
}
.glyphicon-menu-up:before {
  content: "\e260";
}
* {
  -webkit-box-sizing: border-box;
  -moz-box-sizing: border-box;
  box-sizing: border-box;
}
*:before,
*:after {
  -webkit-box-sizing: border-box;
  -moz-box-sizing: border-box;
  box-sizing: border-box;
}
html {
  font-size: 10px;
  -webkit-tap-highlight-color: rgba(0, 0, 0, 0);
}
body {
  font-family: "Helvetica Neue", Helvetica, Arial, sans-serif;
  font-size: 13px;
  line-height: 1.42857143;
  color: #000;
  background-color: #fff;
}
input,
button,
select,
textarea {
  font-family: inherit;
  font-size: inherit;
  line-height: inherit;
}
a {
  color: #337ab7;
  text-decoration: none;
}
a:hover,
a:focus {
  color: #23527c;
  text-decoration: underline;
}
a:focus {
  outline: 5px auto -webkit-focus-ring-color;
  outline-offset: -2px;
}
figure {
  margin: 0;
}
img {
  vertical-align: middle;
}
.img-responsive,
.thumbnail > img,
.thumbnail a > img,
.carousel-inner > .item > img,
.carousel-inner > .item > a > img {
  display: block;
  max-width: 100%;
  height: auto;
}
.img-rounded {
  border-radius: 3px;
}
.img-thumbnail {
  padding: 4px;
  line-height: 1.42857143;
  background-color: #fff;
  border: 1px solid #ddd;
  border-radius: 2px;
  -webkit-transition: all 0.2s ease-in-out;
  -o-transition: all 0.2s ease-in-out;
  transition: all 0.2s ease-in-out;
  display: inline-block;
  max-width: 100%;
  height: auto;
}
.img-circle {
  border-radius: 50%;
}
hr {
  margin-top: 18px;
  margin-bottom: 18px;
  border: 0;
  border-top: 1px solid #eeeeee;
}
.sr-only {
  position: absolute;
  width: 1px;
  height: 1px;
  margin: -1px;
  padding: 0;
  overflow: hidden;
  clip: rect(0, 0, 0, 0);
  border: 0;
}
.sr-only-focusable:active,
.sr-only-focusable:focus {
  position: static;
  width: auto;
  height: auto;
  margin: 0;
  overflow: visible;
  clip: auto;
}
[role="button"] {
  cursor: pointer;
}
h1,
h2,
h3,
h4,
h5,
h6,
.h1,
.h2,
.h3,
.h4,
.h5,
.h6 {
  font-family: inherit;
  font-weight: 500;
  line-height: 1.1;
  color: inherit;
}
h1 small,
h2 small,
h3 small,
h4 small,
h5 small,
h6 small,
.h1 small,
.h2 small,
.h3 small,
.h4 small,
.h5 small,
.h6 small,
h1 .small,
h2 .small,
h3 .small,
h4 .small,
h5 .small,
h6 .small,
.h1 .small,
.h2 .small,
.h3 .small,
.h4 .small,
.h5 .small,
.h6 .small {
  font-weight: normal;
  line-height: 1;
  color: #777777;
}
h1,
.h1,
h2,
.h2,
h3,
.h3 {
  margin-top: 18px;
  margin-bottom: 9px;
}
h1 small,
.h1 small,
h2 small,
.h2 small,
h3 small,
.h3 small,
h1 .small,
.h1 .small,
h2 .small,
.h2 .small,
h3 .small,
.h3 .small {
  font-size: 65%;
}
h4,
.h4,
h5,
.h5,
h6,
.h6 {
  margin-top: 9px;
  margin-bottom: 9px;
}
h4 small,
.h4 small,
h5 small,
.h5 small,
h6 small,
.h6 small,
h4 .small,
.h4 .small,
h5 .small,
.h5 .small,
h6 .small,
.h6 .small {
  font-size: 75%;
}
h1,
.h1 {
  font-size: 33px;
}
h2,
.h2 {
  font-size: 27px;
}
h3,
.h3 {
  font-size: 23px;
}
h4,
.h4 {
  font-size: 17px;
}
h5,
.h5 {
  font-size: 13px;
}
h6,
.h6 {
  font-size: 12px;
}
p {
  margin: 0 0 9px;
}
.lead {
  margin-bottom: 18px;
  font-size: 14px;
  font-weight: 300;
  line-height: 1.4;
}
@media (min-width: 768px) {
  .lead {
    font-size: 19.5px;
  }
}
small,
.small {
  font-size: 92%;
}
mark,
.mark {
  background-color: #fcf8e3;
  padding: .2em;
}
.text-left {
  text-align: left;
}
.text-right {
  text-align: right;
}
.text-center {
  text-align: center;
}
.text-justify {
  text-align: justify;
}
.text-nowrap {
  white-space: nowrap;
}
.text-lowercase {
  text-transform: lowercase;
}
.text-uppercase {
  text-transform: uppercase;
}
.text-capitalize {
  text-transform: capitalize;
}
.text-muted {
  color: #777777;
}
.text-primary {
  color: #337ab7;
}
a.text-primary:hover,
a.text-primary:focus {
  color: #286090;
}
.text-success {
  color: #3c763d;
}
a.text-success:hover,
a.text-success:focus {
  color: #2b542c;
}
.text-info {
  color: #31708f;
}
a.text-info:hover,
a.text-info:focus {
  color: #245269;
}
.text-warning {
  color: #8a6d3b;
}
a.text-warning:hover,
a.text-warning:focus {
  color: #66512c;
}
.text-danger {
  color: #a94442;
}
a.text-danger:hover,
a.text-danger:focus {
  color: #843534;
}
.bg-primary {
  color: #fff;
  background-color: #337ab7;
}
a.bg-primary:hover,
a.bg-primary:focus {
  background-color: #286090;
}
.bg-success {
  background-color: #dff0d8;
}
a.bg-success:hover,
a.bg-success:focus {
  background-color: #c1e2b3;
}
.bg-info {
  background-color: #d9edf7;
}
a.bg-info:hover,
a.bg-info:focus {
  background-color: #afd9ee;
}
.bg-warning {
  background-color: #fcf8e3;
}
a.bg-warning:hover,
a.bg-warning:focus {
  background-color: #f7ecb5;
}
.bg-danger {
  background-color: #f2dede;
}
a.bg-danger:hover,
a.bg-danger:focus {
  background-color: #e4b9b9;
}
.page-header {
  padding-bottom: 8px;
  margin: 36px 0 18px;
  border-bottom: 1px solid #eeeeee;
}
ul,
ol {
  margin-top: 0;
  margin-bottom: 9px;
}
ul ul,
ol ul,
ul ol,
ol ol {
  margin-bottom: 0;
}
.list-unstyled {
  padding-left: 0;
  list-style: none;
}
.list-inline {
  padding-left: 0;
  list-style: none;
  margin-left: -5px;
}
.list-inline > li {
  display: inline-block;
  padding-left: 5px;
  padding-right: 5px;
}
dl {
  margin-top: 0;
  margin-bottom: 18px;
}
dt,
dd {
  line-height: 1.42857143;
}
dt {
  font-weight: bold;
}
dd {
  margin-left: 0;
}
@media (min-width: 541px) {
  .dl-horizontal dt {
    float: left;
    width: 160px;
    clear: left;
    text-align: right;
    overflow: hidden;
    text-overflow: ellipsis;
    white-space: nowrap;
  }
  .dl-horizontal dd {
    margin-left: 180px;
  }
}
abbr[title],
abbr[data-original-title] {
  cursor: help;
  border-bottom: 1px dotted #777777;
}
.initialism {
  font-size: 90%;
  text-transform: uppercase;
}
blockquote {
  padding: 9px 18px;
  margin: 0 0 18px;
  font-size: inherit;
  border-left: 5px solid #eeeeee;
}
blockquote p:last-child,
blockquote ul:last-child,
blockquote ol:last-child {
  margin-bottom: 0;
}
blockquote footer,
blockquote small,
blockquote .small {
  display: block;
  font-size: 80%;
  line-height: 1.42857143;
  color: #777777;
}
blockquote footer:before,
blockquote small:before,
blockquote .small:before {
  content: '\2014 \00A0';
}
.blockquote-reverse,
blockquote.pull-right {
  padding-right: 15px;
  padding-left: 0;
  border-right: 5px solid #eeeeee;
  border-left: 0;
  text-align: right;
}
.blockquote-reverse footer:before,
blockquote.pull-right footer:before,
.blockquote-reverse small:before,
blockquote.pull-right small:before,
.blockquote-reverse .small:before,
blockquote.pull-right .small:before {
  content: '';
}
.blockquote-reverse footer:after,
blockquote.pull-right footer:after,
.blockquote-reverse small:after,
blockquote.pull-right small:after,
.blockquote-reverse .small:after,
blockquote.pull-right .small:after {
  content: '\00A0 \2014';
}
address {
  margin-bottom: 18px;
  font-style: normal;
  line-height: 1.42857143;
}
code,
kbd,
pre,
samp {
  font-family: monospace;
}
code {
  padding: 2px 4px;
  font-size: 90%;
  color: #c7254e;
  background-color: #f9f2f4;
  border-radius: 2px;
}
kbd {
  padding: 2px 4px;
  font-size: 90%;
  color: #888;
  background-color: transparent;
  border-radius: 1px;
  box-shadow: inset 0 -1px 0 rgba(0, 0, 0, 0.25);
}
kbd kbd {
  padding: 0;
  font-size: 100%;
  font-weight: bold;
  box-shadow: none;
}
pre {
  display: block;
  padding: 8.5px;
  margin: 0 0 9px;
  font-size: 12px;
  line-height: 1.42857143;
  word-break: break-all;
  word-wrap: break-word;
  color: #333333;
  background-color: #f5f5f5;
  border: 1px solid #ccc;
  border-radius: 2px;
}
pre code {
  padding: 0;
  font-size: inherit;
  color: inherit;
  white-space: pre-wrap;
  background-color: transparent;
  border-radius: 0;
}
.pre-scrollable {
  max-height: 340px;
  overflow-y: scroll;
}
.container {
  margin-right: auto;
  margin-left: auto;
  padding-left: 0px;
  padding-right: 0px;
}
@media (min-width: 768px) {
  .container {
    width: 768px;
  }
}
@media (min-width: 992px) {
  .container {
    width: 940px;
  }
}
@media (min-width: 1200px) {
  .container {
    width: 1140px;
  }
}
.container-fluid {
  margin-right: auto;
  margin-left: auto;
  padding-left: 0px;
  padding-right: 0px;
}
.row {
  margin-left: 0px;
  margin-right: 0px;
}
.col-xs-1, .col-sm-1, .col-md-1, .col-lg-1, .col-xs-2, .col-sm-2, .col-md-2, .col-lg-2, .col-xs-3, .col-sm-3, .col-md-3, .col-lg-3, .col-xs-4, .col-sm-4, .col-md-4, .col-lg-4, .col-xs-5, .col-sm-5, .col-md-5, .col-lg-5, .col-xs-6, .col-sm-6, .col-md-6, .col-lg-6, .col-xs-7, .col-sm-7, .col-md-7, .col-lg-7, .col-xs-8, .col-sm-8, .col-md-8, .col-lg-8, .col-xs-9, .col-sm-9, .col-md-9, .col-lg-9, .col-xs-10, .col-sm-10, .col-md-10, .col-lg-10, .col-xs-11, .col-sm-11, .col-md-11, .col-lg-11, .col-xs-12, .col-sm-12, .col-md-12, .col-lg-12 {
  position: relative;
  min-height: 1px;
  padding-left: 0px;
  padding-right: 0px;
}
.col-xs-1, .col-xs-2, .col-xs-3, .col-xs-4, .col-xs-5, .col-xs-6, .col-xs-7, .col-xs-8, .col-xs-9, .col-xs-10, .col-xs-11, .col-xs-12 {
  float: left;
}
.col-xs-12 {
  width: 100%;
}
.col-xs-11 {
  width: 91.66666667%;
}
.col-xs-10 {
  width: 83.33333333%;
}
.col-xs-9 {
  width: 75%;
}
.col-xs-8 {
  width: 66.66666667%;
}
.col-xs-7 {
  width: 58.33333333%;
}
.col-xs-6 {
  width: 50%;
}
.col-xs-5 {
  width: 41.66666667%;
}
.col-xs-4 {
  width: 33.33333333%;
}
.col-xs-3 {
  width: 25%;
}
.col-xs-2 {
  width: 16.66666667%;
}
.col-xs-1 {
  width: 8.33333333%;
}
.col-xs-pull-12 {
  right: 100%;
}
.col-xs-pull-11 {
  right: 91.66666667%;
}
.col-xs-pull-10 {
  right: 83.33333333%;
}
.col-xs-pull-9 {
  right: 75%;
}
.col-xs-pull-8 {
  right: 66.66666667%;
}
.col-xs-pull-7 {
  right: 58.33333333%;
}
.col-xs-pull-6 {
  right: 50%;
}
.col-xs-pull-5 {
  right: 41.66666667%;
}
.col-xs-pull-4 {
  right: 33.33333333%;
}
.col-xs-pull-3 {
  right: 25%;
}
.col-xs-pull-2 {
  right: 16.66666667%;
}
.col-xs-pull-1 {
  right: 8.33333333%;
}
.col-xs-pull-0 {
  right: auto;
}
.col-xs-push-12 {
  left: 100%;
}
.col-xs-push-11 {
  left: 91.66666667%;
}
.col-xs-push-10 {
  left: 83.33333333%;
}
.col-xs-push-9 {
  left: 75%;
}
.col-xs-push-8 {
  left: 66.66666667%;
}
.col-xs-push-7 {
  left: 58.33333333%;
}
.col-xs-push-6 {
  left: 50%;
}
.col-xs-push-5 {
  left: 41.66666667%;
}
.col-xs-push-4 {
  left: 33.33333333%;
}
.col-xs-push-3 {
  left: 25%;
}
.col-xs-push-2 {
  left: 16.66666667%;
}
.col-xs-push-1 {
  left: 8.33333333%;
}
.col-xs-push-0 {
  left: auto;
}
.col-xs-offset-12 {
  margin-left: 100%;
}
.col-xs-offset-11 {
  margin-left: 91.66666667%;
}
.col-xs-offset-10 {
  margin-left: 83.33333333%;
}
.col-xs-offset-9 {
  margin-left: 75%;
}
.col-xs-offset-8 {
  margin-left: 66.66666667%;
}
.col-xs-offset-7 {
  margin-left: 58.33333333%;
}
.col-xs-offset-6 {
  margin-left: 50%;
}
.col-xs-offset-5 {
  margin-left: 41.66666667%;
}
.col-xs-offset-4 {
  margin-left: 33.33333333%;
}
.col-xs-offset-3 {
  margin-left: 25%;
}
.col-xs-offset-2 {
  margin-left: 16.66666667%;
}
.col-xs-offset-1 {
  margin-left: 8.33333333%;
}
.col-xs-offset-0 {
  margin-left: 0%;
}
@media (min-width: 768px) {
  .col-sm-1, .col-sm-2, .col-sm-3, .col-sm-4, .col-sm-5, .col-sm-6, .col-sm-7, .col-sm-8, .col-sm-9, .col-sm-10, .col-sm-11, .col-sm-12 {
    float: left;
  }
  .col-sm-12 {
    width: 100%;
  }
  .col-sm-11 {
    width: 91.66666667%;
  }
  .col-sm-10 {
    width: 83.33333333%;
  }
  .col-sm-9 {
    width: 75%;
  }
  .col-sm-8 {
    width: 66.66666667%;
  }
  .col-sm-7 {
    width: 58.33333333%;
  }
  .col-sm-6 {
    width: 50%;
  }
  .col-sm-5 {
    width: 41.66666667%;
  }
  .col-sm-4 {
    width: 33.33333333%;
  }
  .col-sm-3 {
    width: 25%;
  }
  .col-sm-2 {
    width: 16.66666667%;
  }
  .col-sm-1 {
    width: 8.33333333%;
  }
  .col-sm-pull-12 {
    right: 100%;
  }
  .col-sm-pull-11 {
    right: 91.66666667%;
  }
  .col-sm-pull-10 {
    right: 83.33333333%;
  }
  .col-sm-pull-9 {
    right: 75%;
  }
  .col-sm-pull-8 {
    right: 66.66666667%;
  }
  .col-sm-pull-7 {
    right: 58.33333333%;
  }
  .col-sm-pull-6 {
    right: 50%;
  }
  .col-sm-pull-5 {
    right: 41.66666667%;
  }
  .col-sm-pull-4 {
    right: 33.33333333%;
  }
  .col-sm-pull-3 {
    right: 25%;
  }
  .col-sm-pull-2 {
    right: 16.66666667%;
  }
  .col-sm-pull-1 {
    right: 8.33333333%;
  }
  .col-sm-pull-0 {
    right: auto;
  }
  .col-sm-push-12 {
    left: 100%;
  }
  .col-sm-push-11 {
    left: 91.66666667%;
  }
  .col-sm-push-10 {
    left: 83.33333333%;
  }
  .col-sm-push-9 {
    left: 75%;
  }
  .col-sm-push-8 {
    left: 66.66666667%;
  }
  .col-sm-push-7 {
    left: 58.33333333%;
  }
  .col-sm-push-6 {
    left: 50%;
  }
  .col-sm-push-5 {
    left: 41.66666667%;
  }
  .col-sm-push-4 {
    left: 33.33333333%;
  }
  .col-sm-push-3 {
    left: 25%;
  }
  .col-sm-push-2 {
    left: 16.66666667%;
  }
  .col-sm-push-1 {
    left: 8.33333333%;
  }
  .col-sm-push-0 {
    left: auto;
  }
  .col-sm-offset-12 {
    margin-left: 100%;
  }
  .col-sm-offset-11 {
    margin-left: 91.66666667%;
  }
  .col-sm-offset-10 {
    margin-left: 83.33333333%;
  }
  .col-sm-offset-9 {
    margin-left: 75%;
  }
  .col-sm-offset-8 {
    margin-left: 66.66666667%;
  }
  .col-sm-offset-7 {
    margin-left: 58.33333333%;
  }
  .col-sm-offset-6 {
    margin-left: 50%;
  }
  .col-sm-offset-5 {
    margin-left: 41.66666667%;
  }
  .col-sm-offset-4 {
    margin-left: 33.33333333%;
  }
  .col-sm-offset-3 {
    margin-left: 25%;
  }
  .col-sm-offset-2 {
    margin-left: 16.66666667%;
  }
  .col-sm-offset-1 {
    margin-left: 8.33333333%;
  }
  .col-sm-offset-0 {
    margin-left: 0%;
  }
}
@media (min-width: 992px) {
  .col-md-1, .col-md-2, .col-md-3, .col-md-4, .col-md-5, .col-md-6, .col-md-7, .col-md-8, .col-md-9, .col-md-10, .col-md-11, .col-md-12 {
    float: left;
  }
  .col-md-12 {
    width: 100%;
  }
  .col-md-11 {
    width: 91.66666667%;
  }
  .col-md-10 {
    width: 83.33333333%;
  }
  .col-md-9 {
    width: 75%;
  }
  .col-md-8 {
    width: 66.66666667%;
  }
  .col-md-7 {
    width: 58.33333333%;
  }
  .col-md-6 {
    width: 50%;
  }
  .col-md-5 {
    width: 41.66666667%;
  }
  .col-md-4 {
    width: 33.33333333%;
  }
  .col-md-3 {
    width: 25%;
  }
  .col-md-2 {
    width: 16.66666667%;
  }
  .col-md-1 {
    width: 8.33333333%;
  }
  .col-md-pull-12 {
    right: 100%;
  }
  .col-md-pull-11 {
    right: 91.66666667%;
  }
  .col-md-pull-10 {
    right: 83.33333333%;
  }
  .col-md-pull-9 {
    right: 75%;
  }
  .col-md-pull-8 {
    right: 66.66666667%;
  }
  .col-md-pull-7 {
    right: 58.33333333%;
  }
  .col-md-pull-6 {
    right: 50%;
  }
  .col-md-pull-5 {
    right: 41.66666667%;
  }
  .col-md-pull-4 {
    right: 33.33333333%;
  }
  .col-md-pull-3 {
    right: 25%;
  }
  .col-md-pull-2 {
    right: 16.66666667%;
  }
  .col-md-pull-1 {
    right: 8.33333333%;
  }
  .col-md-pull-0 {
    right: auto;
  }
  .col-md-push-12 {
    left: 100%;
  }
  .col-md-push-11 {
    left: 91.66666667%;
  }
  .col-md-push-10 {
    left: 83.33333333%;
  }
  .col-md-push-9 {
    left: 75%;
  }
  .col-md-push-8 {
    left: 66.66666667%;
  }
  .col-md-push-7 {
    left: 58.33333333%;
  }
  .col-md-push-6 {
    left: 50%;
  }
  .col-md-push-5 {
    left: 41.66666667%;
  }
  .col-md-push-4 {
    left: 33.33333333%;
  }
  .col-md-push-3 {
    left: 25%;
  }
  .col-md-push-2 {
    left: 16.66666667%;
  }
  .col-md-push-1 {
    left: 8.33333333%;
  }
  .col-md-push-0 {
    left: auto;
  }
  .col-md-offset-12 {
    margin-left: 100%;
  }
  .col-md-offset-11 {
    margin-left: 91.66666667%;
  }
  .col-md-offset-10 {
    margin-left: 83.33333333%;
  }
  .col-md-offset-9 {
    margin-left: 75%;
  }
  .col-md-offset-8 {
    margin-left: 66.66666667%;
  }
  .col-md-offset-7 {
    margin-left: 58.33333333%;
  }
  .col-md-offset-6 {
    margin-left: 50%;
  }
  .col-md-offset-5 {
    margin-left: 41.66666667%;
  }
  .col-md-offset-4 {
    margin-left: 33.33333333%;
  }
  .col-md-offset-3 {
    margin-left: 25%;
  }
  .col-md-offset-2 {
    margin-left: 16.66666667%;
  }
  .col-md-offset-1 {
    margin-left: 8.33333333%;
  }
  .col-md-offset-0 {
    margin-left: 0%;
  }
}
@media (min-width: 1200px) {
  .col-lg-1, .col-lg-2, .col-lg-3, .col-lg-4, .col-lg-5, .col-lg-6, .col-lg-7, .col-lg-8, .col-lg-9, .col-lg-10, .col-lg-11, .col-lg-12 {
    float: left;
  }
  .col-lg-12 {
    width: 100%;
  }
  .col-lg-11 {
    width: 91.66666667%;
  }
  .col-lg-10 {
    width: 83.33333333%;
  }
  .col-lg-9 {
    width: 75%;
  }
  .col-lg-8 {
    width: 66.66666667%;
  }
  .col-lg-7 {
    width: 58.33333333%;
  }
  .col-lg-6 {
    width: 50%;
  }
  .col-lg-5 {
    width: 41.66666667%;
  }
  .col-lg-4 {
    width: 33.33333333%;
  }
  .col-lg-3 {
    width: 25%;
  }
  .col-lg-2 {
    width: 16.66666667%;
  }
  .col-lg-1 {
    width: 8.33333333%;
  }
  .col-lg-pull-12 {
    right: 100%;
  }
  .col-lg-pull-11 {
    right: 91.66666667%;
  }
  .col-lg-pull-10 {
    right: 83.33333333%;
  }
  .col-lg-pull-9 {
    right: 75%;
  }
  .col-lg-pull-8 {
    right: 66.66666667%;
  }
  .col-lg-pull-7 {
    right: 58.33333333%;
  }
  .col-lg-pull-6 {
    right: 50%;
  }
  .col-lg-pull-5 {
    right: 41.66666667%;
  }
  .col-lg-pull-4 {
    right: 33.33333333%;
  }
  .col-lg-pull-3 {
    right: 25%;
  }
  .col-lg-pull-2 {
    right: 16.66666667%;
  }
  .col-lg-pull-1 {
    right: 8.33333333%;
  }
  .col-lg-pull-0 {
    right: auto;
  }
  .col-lg-push-12 {
    left: 100%;
  }
  .col-lg-push-11 {
    left: 91.66666667%;
  }
  .col-lg-push-10 {
    left: 83.33333333%;
  }
  .col-lg-push-9 {
    left: 75%;
  }
  .col-lg-push-8 {
    left: 66.66666667%;
  }
  .col-lg-push-7 {
    left: 58.33333333%;
  }
  .col-lg-push-6 {
    left: 50%;
  }
  .col-lg-push-5 {
    left: 41.66666667%;
  }
  .col-lg-push-4 {
    left: 33.33333333%;
  }
  .col-lg-push-3 {
    left: 25%;
  }
  .col-lg-push-2 {
    left: 16.66666667%;
  }
  .col-lg-push-1 {
    left: 8.33333333%;
  }
  .col-lg-push-0 {
    left: auto;
  }
  .col-lg-offset-12 {
    margin-left: 100%;
  }
  .col-lg-offset-11 {
    margin-left: 91.66666667%;
  }
  .col-lg-offset-10 {
    margin-left: 83.33333333%;
  }
  .col-lg-offset-9 {
    margin-left: 75%;
  }
  .col-lg-offset-8 {
    margin-left: 66.66666667%;
  }
  .col-lg-offset-7 {
    margin-left: 58.33333333%;
  }
  .col-lg-offset-6 {
    margin-left: 50%;
  }
  .col-lg-offset-5 {
    margin-left: 41.66666667%;
  }
  .col-lg-offset-4 {
    margin-left: 33.33333333%;
  }
  .col-lg-offset-3 {
    margin-left: 25%;
  }
  .col-lg-offset-2 {
    margin-left: 16.66666667%;
  }
  .col-lg-offset-1 {
    margin-left: 8.33333333%;
  }
  .col-lg-offset-0 {
    margin-left: 0%;
  }
}
table {
  background-color: transparent;
}
caption {
  padding-top: 8px;
  padding-bottom: 8px;
  color: #777777;
  text-align: left;
}
th {
  text-align: left;
}
.table {
  width: 100%;
  max-width: 100%;
  margin-bottom: 18px;
}
.table > thead > tr > th,
.table > tbody > tr > th,
.table > tfoot > tr > th,
.table > thead > tr > td,
.table > tbody > tr > td,
.table > tfoot > tr > td {
  padding: 8px;
  line-height: 1.42857143;
  vertical-align: top;
  border-top: 1px solid #ddd;
}
.table > thead > tr > th {
  vertical-align: bottom;
  border-bottom: 2px solid #ddd;
}
.table > caption + thead > tr:first-child > th,
.table > colgroup + thead > tr:first-child > th,
.table > thead:first-child > tr:first-child > th,
.table > caption + thead > tr:first-child > td,
.table > colgroup + thead > tr:first-child > td,
.table > thead:first-child > tr:first-child > td {
  border-top: 0;
}
.table > tbody + tbody {
  border-top: 2px solid #ddd;
}
.table .table {
  background-color: #fff;
}
.table-condensed > thead > tr > th,
.table-condensed > tbody > tr > th,
.table-condensed > tfoot > tr > th,
.table-condensed > thead > tr > td,
.table-condensed > tbody > tr > td,
.table-condensed > tfoot > tr > td {
  padding: 5px;
}
.table-bordered {
  border: 1px solid #ddd;
}
.table-bordered > thead > tr > th,
.table-bordered > tbody > tr > th,
.table-bordered > tfoot > tr > th,
.table-bordered > thead > tr > td,
.table-bordered > tbody > tr > td,
.table-bordered > tfoot > tr > td {
  border: 1px solid #ddd;
}
.table-bordered > thead > tr > th,
.table-bordered > thead > tr > td {
  border-bottom-width: 2px;
}
.table-striped > tbody > tr:nth-of-type(odd) {
  background-color: #f9f9f9;
}
.table-hover > tbody > tr:hover {
  background-color: #f5f5f5;
}
table col[class*="col-"] {
  position: static;
  float: none;
  display: table-column;
}
table td[class*="col-"],
table th[class*="col-"] {
  position: static;
  float: none;
  display: table-cell;
}
.table > thead > tr > td.active,
.table > tbody > tr > td.active,
.table > tfoot > tr > td.active,
.table > thead > tr > th.active,
.table > tbody > tr > th.active,
.table > tfoot > tr > th.active,
.table > thead > tr.active > td,
.table > tbody > tr.active > td,
.table > tfoot > tr.active > td,
.table > thead > tr.active > th,
.table > tbody > tr.active > th,
.table > tfoot > tr.active > th {
  background-color: #f5f5f5;
}
.table-hover > tbody > tr > td.active:hover,
.table-hover > tbody > tr > th.active:hover,
.table-hover > tbody > tr.active:hover > td,
.table-hover > tbody > tr:hover > .active,
.table-hover > tbody > tr.active:hover > th {
  background-color: #e8e8e8;
}
.table > thead > tr > td.success,
.table > tbody > tr > td.success,
.table > tfoot > tr > td.success,
.table > thead > tr > th.success,
.table > tbody > tr > th.success,
.table > tfoot > tr > th.success,
.table > thead > tr.success > td,
.table > tbody > tr.success > td,
.table > tfoot > tr.success > td,
.table > thead > tr.success > th,
.table > tbody > tr.success > th,
.table > tfoot > tr.success > th {
  background-color: #dff0d8;
}
.table-hover > tbody > tr > td.success:hover,
.table-hover > tbody > tr > th.success:hover,
.table-hover > tbody > tr.success:hover > td,
.table-hover > tbody > tr:hover > .success,
.table-hover > tbody > tr.success:hover > th {
  background-color: #d0e9c6;
}
.table > thead > tr > td.info,
.table > tbody > tr > td.info,
.table > tfoot > tr > td.info,
.table > thead > tr > th.info,
.table > tbody > tr > th.info,
.table > tfoot > tr > th.info,
.table > thead > tr.info > td,
.table > tbody > tr.info > td,
.table > tfoot > tr.info > td,
.table > thead > tr.info > th,
.table > tbody > tr.info > th,
.table > tfoot > tr.info > th {
  background-color: #d9edf7;
}
.table-hover > tbody > tr > td.info:hover,
.table-hover > tbody > tr > th.info:hover,
.table-hover > tbody > tr.info:hover > td,
.table-hover > tbody > tr:hover > .info,
.table-hover > tbody > tr.info:hover > th {
  background-color: #c4e3f3;
}
.table > thead > tr > td.warning,
.table > tbody > tr > td.warning,
.table > tfoot > tr > td.warning,
.table > thead > tr > th.warning,
.table > tbody > tr > th.warning,
.table > tfoot > tr > th.warning,
.table > thead > tr.warning > td,
.table > tbody > tr.warning > td,
.table > tfoot > tr.warning > td,
.table > thead > tr.warning > th,
.table > tbody > tr.warning > th,
.table > tfoot > tr.warning > th {
  background-color: #fcf8e3;
}
.table-hover > tbody > tr > td.warning:hover,
.table-hover > tbody > tr > th.warning:hover,
.table-hover > tbody > tr.warning:hover > td,
.table-hover > tbody > tr:hover > .warning,
.table-hover > tbody > tr.warning:hover > th {
  background-color: #faf2cc;
}
.table > thead > tr > td.danger,
.table > tbody > tr > td.danger,
.table > tfoot > tr > td.danger,
.table > thead > tr > th.danger,
.table > tbody > tr > th.danger,
.table > tfoot > tr > th.danger,
.table > thead > tr.danger > td,
.table > tbody > tr.danger > td,
.table > tfoot > tr.danger > td,
.table > thead > tr.danger > th,
.table > tbody > tr.danger > th,
.table > tfoot > tr.danger > th {
  background-color: #f2dede;
}
.table-hover > tbody > tr > td.danger:hover,
.table-hover > tbody > tr > th.danger:hover,
.table-hover > tbody > tr.danger:hover > td,
.table-hover > tbody > tr:hover > .danger,
.table-hover > tbody > tr.danger:hover > th {
  background-color: #ebcccc;
}
.table-responsive {
  overflow-x: auto;
  min-height: 0.01%;
}
@media screen and (max-width: 767px) {
  .table-responsive {
    width: 100%;
    margin-bottom: 13.5px;
    overflow-y: hidden;
    -ms-overflow-style: -ms-autohiding-scrollbar;
    border: 1px solid #ddd;
  }
  .table-responsive > .table {
    margin-bottom: 0;
  }
  .table-responsive > .table > thead > tr > th,
  .table-responsive > .table > tbody > tr > th,
  .table-responsive > .table > tfoot > tr > th,
  .table-responsive > .table > thead > tr > td,
  .table-responsive > .table > tbody > tr > td,
  .table-responsive > .table > tfoot > tr > td {
    white-space: nowrap;
  }
  .table-responsive > .table-bordered {
    border: 0;
  }
  .table-responsive > .table-bordered > thead > tr > th:first-child,
  .table-responsive > .table-bordered > tbody > tr > th:first-child,
  .table-responsive > .table-bordered > tfoot > tr > th:first-child,
  .table-responsive > .table-bordered > thead > tr > td:first-child,
  .table-responsive > .table-bordered > tbody > tr > td:first-child,
  .table-responsive > .table-bordered > tfoot > tr > td:first-child {
    border-left: 0;
  }
  .table-responsive > .table-bordered > thead > tr > th:last-child,
  .table-responsive > .table-bordered > tbody > tr > th:last-child,
  .table-responsive > .table-bordered > tfoot > tr > th:last-child,
  .table-responsive > .table-bordered > thead > tr > td:last-child,
  .table-responsive > .table-bordered > tbody > tr > td:last-child,
  .table-responsive > .table-bordered > tfoot > tr > td:last-child {
    border-right: 0;
  }
  .table-responsive > .table-bordered > tbody > tr:last-child > th,
  .table-responsive > .table-bordered > tfoot > tr:last-child > th,
  .table-responsive > .table-bordered > tbody > tr:last-child > td,
  .table-responsive > .table-bordered > tfoot > tr:last-child > td {
    border-bottom: 0;
  }
}
fieldset {
  padding: 0;
  margin: 0;
  border: 0;
  min-width: 0;
}
legend {
  display: block;
  width: 100%;
  padding: 0;
  margin-bottom: 18px;
  font-size: 19.5px;
  line-height: inherit;
  color: #333333;
  border: 0;
  border-bottom: 1px solid #e5e5e5;
}
label {
  display: inline-block;
  max-width: 100%;
  margin-bottom: 5px;
  font-weight: bold;
}
input[type="search"] {
  -webkit-box-sizing: border-box;
  -moz-box-sizing: border-box;
  box-sizing: border-box;
}
input[type="radio"],
input[type="checkbox"] {
  margin: 4px 0 0;
  margin-top: 1px \9;
  line-height: normal;
}
input[type="file"] {
  display: block;
}
input[type="range"] {
  display: block;
  width: 100%;
}
select[multiple],
select[size] {
  height: auto;
}
input[type="file"]:focus,
input[type="radio"]:focus,
input[type="checkbox"]:focus {
  outline: 5px auto -webkit-focus-ring-color;
  outline-offset: -2px;
}
output {
  display: block;
  padding-top: 7px;
  font-size: 13px;
  line-height: 1.42857143;
  color: #555555;
}
.form-control {
  display: block;
  width: 100%;
  height: 32px;
  padding: 6px 12px;
  font-size: 13px;
  line-height: 1.42857143;
  color: #555555;
  background-color: #fff;
  background-image: none;
  border: 1px solid #ccc;
  border-radius: 2px;
  -webkit-box-shadow: inset 0 1px 1px rgba(0, 0, 0, 0.075);
  box-shadow: inset 0 1px 1px rgba(0, 0, 0, 0.075);
  -webkit-transition: border-color ease-in-out .15s, box-shadow ease-in-out .15s;
  -o-transition: border-color ease-in-out .15s, box-shadow ease-in-out .15s;
  transition: border-color ease-in-out .15s, box-shadow ease-in-out .15s;
}
.form-control:focus {
  border-color: #66afe9;
  outline: 0;
  -webkit-box-shadow: inset 0 1px 1px rgba(0,0,0,.075), 0 0 8px rgba(102, 175, 233, 0.6);
  box-shadow: inset 0 1px 1px rgba(0,0,0,.075), 0 0 8px rgba(102, 175, 233, 0.6);
}
.form-control::-moz-placeholder {
  color: #999;
  opacity: 1;
}
.form-control:-ms-input-placeholder {
  color: #999;
}
.form-control::-webkit-input-placeholder {
  color: #999;
}
.form-control::-ms-expand {
  border: 0;
  background-color: transparent;
}
.form-control[disabled],
.form-control[readonly],
fieldset[disabled] .form-control {
  background-color: #eeeeee;
  opacity: 1;
}
.form-control[disabled],
fieldset[disabled] .form-control {
  cursor: not-allowed;
}
textarea.form-control {
  height: auto;
}
input[type="search"] {
  -webkit-appearance: none;
}
@media screen and (-webkit-min-device-pixel-ratio: 0) {
  input[type="date"].form-control,
  input[type="time"].form-control,
  input[type="datetime-local"].form-control,
  input[type="month"].form-control {
    line-height: 32px;
  }
  input[type="date"].input-sm,
  input[type="time"].input-sm,
  input[type="datetime-local"].input-sm,
  input[type="month"].input-sm,
  .input-group-sm input[type="date"],
  .input-group-sm input[type="time"],
  .input-group-sm input[type="datetime-local"],
  .input-group-sm input[type="month"] {
    line-height: 30px;
  }
  input[type="date"].input-lg,
  input[type="time"].input-lg,
  input[type="datetime-local"].input-lg,
  input[type="month"].input-lg,
  .input-group-lg input[type="date"],
  .input-group-lg input[type="time"],
  .input-group-lg input[type="datetime-local"],
  .input-group-lg input[type="month"] {
    line-height: 45px;
  }
}
.form-group {
  margin-bottom: 15px;
}
.radio,
.checkbox {
  position: relative;
  display: block;
  margin-top: 10px;
  margin-bottom: 10px;
}
.radio label,
.checkbox label {
  min-height: 18px;
  padding-left: 20px;
  margin-bottom: 0;
  font-weight: normal;
  cursor: pointer;
}
.radio input[type="radio"],
.radio-inline input[type="radio"],
.checkbox input[type="checkbox"],
.checkbox-inline input[type="checkbox"] {
  position: absolute;
  margin-left: -20px;
  margin-top: 4px \9;
}
.radio + .radio,
.checkbox + .checkbox {
  margin-top: -5px;
}
.radio-inline,
.checkbox-inline {
  position: relative;
  display: inline-block;
  padding-left: 20px;
  margin-bottom: 0;
  vertical-align: middle;
  font-weight: normal;
  cursor: pointer;
}
.radio-inline + .radio-inline,
.checkbox-inline + .checkbox-inline {
  margin-top: 0;
  margin-left: 10px;
}
input[type="radio"][disabled],
input[type="checkbox"][disabled],
input[type="radio"].disabled,
input[type="checkbox"].disabled,
fieldset[disabled] input[type="radio"],
fieldset[disabled] input[type="checkbox"] {
  cursor: not-allowed;
}
.radio-inline.disabled,
.checkbox-inline.disabled,
fieldset[disabled] .radio-inline,
fieldset[disabled] .checkbox-inline {
  cursor: not-allowed;
}
.radio.disabled label,
.checkbox.disabled label,
fieldset[disabled] .radio label,
fieldset[disabled] .checkbox label {
  cursor: not-allowed;
}
.form-control-static {
  padding-top: 7px;
  padding-bottom: 7px;
  margin-bottom: 0;
  min-height: 31px;
}
.form-control-static.input-lg,
.form-control-static.input-sm {
  padding-left: 0;
  padding-right: 0;
}
.input-sm {
  height: 30px;
  padding: 5px 10px;
  font-size: 12px;
  line-height: 1.5;
  border-radius: 1px;
}
select.input-sm {
  height: 30px;
  line-height: 30px;
}
textarea.input-sm,
select[multiple].input-sm {
  height: auto;
}
.form-group-sm .form-control {
  height: 30px;
  padding: 5px 10px;
  font-size: 12px;
  line-height: 1.5;
  border-radius: 1px;
}
.form-group-sm select.form-control {
  height: 30px;
  line-height: 30px;
}
.form-group-sm textarea.form-control,
.form-group-sm select[multiple].form-control {
  height: auto;
}
.form-group-sm .form-control-static {
  height: 30px;
  min-height: 30px;
  padding: 6px 10px;
  font-size: 12px;
  line-height: 1.5;
}
.input-lg {
  height: 45px;
  padding: 10px 16px;
  font-size: 17px;
  line-height: 1.3333333;
  border-radius: 3px;
}
select.input-lg {
  height: 45px;
  line-height: 45px;
}
textarea.input-lg,
select[multiple].input-lg {
  height: auto;
}
.form-group-lg .form-control {
  height: 45px;
  padding: 10px 16px;
  font-size: 17px;
  line-height: 1.3333333;
  border-radius: 3px;
}
.form-group-lg select.form-control {
  height: 45px;
  line-height: 45px;
}
.form-group-lg textarea.form-control,
.form-group-lg select[multiple].form-control {
  height: auto;
}
.form-group-lg .form-control-static {
  height: 45px;
  min-height: 35px;
  padding: 11px 16px;
  font-size: 17px;
  line-height: 1.3333333;
}
.has-feedback {
  position: relative;
}
.has-feedback .form-control {
  padding-right: 40px;
}
.form-control-feedback {
  position: absolute;
  top: 0;
  right: 0;
  z-index: 2;
  display: block;
  width: 32px;
  height: 32px;
  line-height: 32px;
  text-align: center;
  pointer-events: none;
}
.input-lg + .form-control-feedback,
.input-group-lg + .form-control-feedback,
.form-group-lg .form-control + .form-control-feedback {
  width: 45px;
  height: 45px;
  line-height: 45px;
}
.input-sm + .form-control-feedback,
.input-group-sm + .form-control-feedback,
.form-group-sm .form-control + .form-control-feedback {
  width: 30px;
  height: 30px;
  line-height: 30px;
}
.has-success .help-block,
.has-success .control-label,
.has-success .radio,
.has-success .checkbox,
.has-success .radio-inline,
.has-success .checkbox-inline,
.has-success.radio label,
.has-success.checkbox label,
.has-success.radio-inline label,
.has-success.checkbox-inline label {
  color: #3c763d;
}
.has-success .form-control {
  border-color: #3c763d;
  -webkit-box-shadow: inset 0 1px 1px rgba(0, 0, 0, 0.075);
  box-shadow: inset 0 1px 1px rgba(0, 0, 0, 0.075);
}
.has-success .form-control:focus {
  border-color: #2b542c;
  -webkit-box-shadow: inset 0 1px 1px rgba(0, 0, 0, 0.075), 0 0 6px #67b168;
  box-shadow: inset 0 1px 1px rgba(0, 0, 0, 0.075), 0 0 6px #67b168;
}
.has-success .input-group-addon {
  color: #3c763d;
  border-color: #3c763d;
  background-color: #dff0d8;
}
.has-success .form-control-feedback {
  color: #3c763d;
}
.has-warning .help-block,
.has-warning .control-label,
.has-warning .radio,
.has-warning .checkbox,
.has-warning .radio-inline,
.has-warning .checkbox-inline,
.has-warning.radio label,
.has-warning.checkbox label,
.has-warning.radio-inline label,
.has-warning.checkbox-inline label {
  color: #8a6d3b;
}
.has-warning .form-control {
  border-color: #8a6d3b;
  -webkit-box-shadow: inset 0 1px 1px rgba(0, 0, 0, 0.075);
  box-shadow: inset 0 1px 1px rgba(0, 0, 0, 0.075);
}
.has-warning .form-control:focus {
  border-color: #66512c;
  -webkit-box-shadow: inset 0 1px 1px rgba(0, 0, 0, 0.075), 0 0 6px #c0a16b;
  box-shadow: inset 0 1px 1px rgba(0, 0, 0, 0.075), 0 0 6px #c0a16b;
}
.has-warning .input-group-addon {
  color: #8a6d3b;
  border-color: #8a6d3b;
  background-color: #fcf8e3;
}
.has-warning .form-control-feedback {
  color: #8a6d3b;
}
.has-error .help-block,
.has-error .control-label,
.has-error .radio,
.has-error .checkbox,
.has-error .radio-inline,
.has-error .checkbox-inline,
.has-error.radio label,
.has-error.checkbox label,
.has-error.radio-inline label,
.has-error.checkbox-inline label {
  color: #a94442;
}
.has-error .form-control {
  border-color: #a94442;
  -webkit-box-shadow: inset 0 1px 1px rgba(0, 0, 0, 0.075);
  box-shadow: inset 0 1px 1px rgba(0, 0, 0, 0.075);
}
.has-error .form-control:focus {
  border-color: #843534;
  -webkit-box-shadow: inset 0 1px 1px rgba(0, 0, 0, 0.075), 0 0 6px #ce8483;
  box-shadow: inset 0 1px 1px rgba(0, 0, 0, 0.075), 0 0 6px #ce8483;
}
.has-error .input-group-addon {
  color: #a94442;
  border-color: #a94442;
  background-color: #f2dede;
}
.has-error .form-control-feedback {
  color: #a94442;
}
.has-feedback label ~ .form-control-feedback {
  top: 23px;
}
.has-feedback label.sr-only ~ .form-control-feedback {
  top: 0;
}
.help-block {
  display: block;
  margin-top: 5px;
  margin-bottom: 10px;
  color: #404040;
}
@media (min-width: 768px) {
  .form-inline .form-group {
    display: inline-block;
    margin-bottom: 0;
    vertical-align: middle;
  }
  .form-inline .form-control {
    display: inline-block;
    width: auto;
    vertical-align: middle;
  }
  .form-inline .form-control-static {
    display: inline-block;
  }
  .form-inline .input-group {
    display: inline-table;
    vertical-align: middle;
  }
  .form-inline .input-group .input-group-addon,
  .form-inline .input-group .input-group-btn,
  .form-inline .input-group .form-control {
    width: auto;
  }
  .form-inline .input-group > .form-control {
    width: 100%;
  }
  .form-inline .control-label {
    margin-bottom: 0;
    vertical-align: middle;
  }
  .form-inline .radio,
  .form-inline .checkbox {
    display: inline-block;
    margin-top: 0;
    margin-bottom: 0;
    vertical-align: middle;
  }
  .form-inline .radio label,
  .form-inline .checkbox label {
    padding-left: 0;
  }
  .form-inline .radio input[type="radio"],
  .form-inline .checkbox input[type="checkbox"] {
    position: relative;
    margin-left: 0;
  }
  .form-inline .has-feedback .form-control-feedback {
    top: 0;
  }
}
.form-horizontal .radio,
.form-horizontal .checkbox,
.form-horizontal .radio-inline,
.form-horizontal .checkbox-inline {
  margin-top: 0;
  margin-bottom: 0;
  padding-top: 7px;
}
.form-horizontal .radio,
.form-horizontal .checkbox {
  min-height: 25px;
}
.form-horizontal .form-group {
  margin-left: 0px;
  margin-right: 0px;
}
@media (min-width: 768px) {
  .form-horizontal .control-label {
    text-align: right;
    margin-bottom: 0;
    padding-top: 7px;
  }
}
.form-horizontal .has-feedback .form-control-feedback {
  right: 0px;
}
@media (min-width: 768px) {
  .form-horizontal .form-group-lg .control-label {
    padding-top: 11px;
    font-size: 17px;
  }
}
@media (min-width: 768px) {
  .form-horizontal .form-group-sm .control-label {
    padding-top: 6px;
    font-size: 12px;
  }
}
.btn {
  display: inline-block;
  margin-bottom: 0;
  font-weight: normal;
  text-align: center;
  vertical-align: middle;
  touch-action: manipulation;
  cursor: pointer;
  background-image: none;
  border: 1px solid transparent;
  white-space: nowrap;
  padding: 6px 12px;
  font-size: 13px;
  line-height: 1.42857143;
  border-radius: 2px;
  -webkit-user-select: none;
  -moz-user-select: none;
  -ms-user-select: none;
  user-select: none;
}
.btn:focus,
.btn:active:focus,
.btn.active:focus,
.btn.focus,
.btn:active.focus,
.btn.active.focus {
  outline: 5px auto -webkit-focus-ring-color;
  outline-offset: -2px;
}
.btn:hover,
.btn:focus,
.btn.focus {
  color: #333;
  text-decoration: none;
}
.btn:active,
.btn.active {
  outline: 0;
  background-image: none;
  -webkit-box-shadow: inset 0 3px 5px rgba(0, 0, 0, 0.125);
  box-shadow: inset 0 3px 5px rgba(0, 0, 0, 0.125);
}
.btn.disabled,
.btn[disabled],
fieldset[disabled] .btn {
  cursor: not-allowed;
  opacity: 0.65;
  filter: alpha(opacity=65);
  -webkit-box-shadow: none;
  box-shadow: none;
}
a.btn.disabled,
fieldset[disabled] a.btn {
  pointer-events: none;
}
.btn-default {
  color: #333;
  background-color: #fff;
  border-color: #ccc;
}
.btn-default:focus,
.btn-default.focus {
  color: #333;
  background-color: #e6e6e6;
  border-color: #8c8c8c;
}
.btn-default:hover {
  color: #333;
  background-color: #e6e6e6;
  border-color: #adadad;
}
.btn-default:active,
.btn-default.active,
.open > .dropdown-toggle.btn-default {
  color: #333;
  background-color: #e6e6e6;
  border-color: #adadad;
}
.btn-default:active:hover,
.btn-default.active:hover,
.open > .dropdown-toggle.btn-default:hover,
.btn-default:active:focus,
.btn-default.active:focus,
.open > .dropdown-toggle.btn-default:focus,
.btn-default:active.focus,
.btn-default.active.focus,
.open > .dropdown-toggle.btn-default.focus {
  color: #333;
  background-color: #d4d4d4;
  border-color: #8c8c8c;
}
.btn-default:active,
.btn-default.active,
.open > .dropdown-toggle.btn-default {
  background-image: none;
}
.btn-default.disabled:hover,
.btn-default[disabled]:hover,
fieldset[disabled] .btn-default:hover,
.btn-default.disabled:focus,
.btn-default[disabled]:focus,
fieldset[disabled] .btn-default:focus,
.btn-default.disabled.focus,
.btn-default[disabled].focus,
fieldset[disabled] .btn-default.focus {
  background-color: #fff;
  border-color: #ccc;
}
.btn-default .badge {
  color: #fff;
  background-color: #333;
}
.btn-primary {
  color: #fff;
  background-color: #337ab7;
  border-color: #2e6da4;
}
.btn-primary:focus,
.btn-primary.focus {
  color: #fff;
  background-color: #286090;
  border-color: #122b40;
}
.btn-primary:hover {
  color: #fff;
  background-color: #286090;
  border-color: #204d74;
}
.btn-primary:active,
.btn-primary.active,
.open > .dropdown-toggle.btn-primary {
  color: #fff;
  background-color: #286090;
  border-color: #204d74;
}
.btn-primary:active:hover,
.btn-primary.active:hover,
.open > .dropdown-toggle.btn-primary:hover,
.btn-primary:active:focus,
.btn-primary.active:focus,
.open > .dropdown-toggle.btn-primary:focus,
.btn-primary:active.focus,
.btn-primary.active.focus,
.open > .dropdown-toggle.btn-primary.focus {
  color: #fff;
  background-color: #204d74;
  border-color: #122b40;
}
.btn-primary:active,
.btn-primary.active,
.open > .dropdown-toggle.btn-primary {
  background-image: none;
}
.btn-primary.disabled:hover,
.btn-primary[disabled]:hover,
fieldset[disabled] .btn-primary:hover,
.btn-primary.disabled:focus,
.btn-primary[disabled]:focus,
fieldset[disabled] .btn-primary:focus,
.btn-primary.disabled.focus,
.btn-primary[disabled].focus,
fieldset[disabled] .btn-primary.focus {
  background-color: #337ab7;
  border-color: #2e6da4;
}
.btn-primary .badge {
  color: #337ab7;
  background-color: #fff;
}
.btn-success {
  color: #fff;
  background-color: #5cb85c;
  border-color: #4cae4c;
}
.btn-success:focus,
.btn-success.focus {
  color: #fff;
  background-color: #449d44;
  border-color: #255625;
}
.btn-success:hover {
  color: #fff;
  background-color: #449d44;
  border-color: #398439;
}
.btn-success:active,
.btn-success.active,
.open > .dropdown-toggle.btn-success {
  color: #fff;
  background-color: #449d44;
  border-color: #398439;
}
.btn-success:active:hover,
.btn-success.active:hover,
.open > .dropdown-toggle.btn-success:hover,
.btn-success:active:focus,
.btn-success.active:focus,
.open > .dropdown-toggle.btn-success:focus,
.btn-success:active.focus,
.btn-success.active.focus,
.open > .dropdown-toggle.btn-success.focus {
  color: #fff;
  background-color: #398439;
  border-color: #255625;
}
.btn-success:active,
.btn-success.active,
.open > .dropdown-toggle.btn-success {
  background-image: none;
}
.btn-success.disabled:hover,
.btn-success[disabled]:hover,
fieldset[disabled] .btn-success:hover,
.btn-success.disabled:focus,
.btn-success[disabled]:focus,
fieldset[disabled] .btn-success:focus,
.btn-success.disabled.focus,
.btn-success[disabled].focus,
fieldset[disabled] .btn-success.focus {
  background-color: #5cb85c;
  border-color: #4cae4c;
}
.btn-success .badge {
  color: #5cb85c;
  background-color: #fff;
}
.btn-info {
  color: #fff;
  background-color: #5bc0de;
  border-color: #46b8da;
}
.btn-info:focus,
.btn-info.focus {
  color: #fff;
  background-color: #31b0d5;
  border-color: #1b6d85;
}
.btn-info:hover {
  color: #fff;
  background-color: #31b0d5;
  border-color: #269abc;
}
.btn-info:active,
.btn-info.active,
.open > .dropdown-toggle.btn-info {
  color: #fff;
  background-color: #31b0d5;
  border-color: #269abc;
}
.btn-info:active:hover,
.btn-info.active:hover,
.open > .dropdown-toggle.btn-info:hover,
.btn-info:active:focus,
.btn-info.active:focus,
.open > .dropdown-toggle.btn-info:focus,
.btn-info:active.focus,
.btn-info.active.focus,
.open > .dropdown-toggle.btn-info.focus {
  color: #fff;
  background-color: #269abc;
  border-color: #1b6d85;
}
.btn-info:active,
.btn-info.active,
.open > .dropdown-toggle.btn-info {
  background-image: none;
}
.btn-info.disabled:hover,
.btn-info[disabled]:hover,
fieldset[disabled] .btn-info:hover,
.btn-info.disabled:focus,
.btn-info[disabled]:focus,
fieldset[disabled] .btn-info:focus,
.btn-info.disabled.focus,
.btn-info[disabled].focus,
fieldset[disabled] .btn-info.focus {
  background-color: #5bc0de;
  border-color: #46b8da;
}
.btn-info .badge {
  color: #5bc0de;
  background-color: #fff;
}
.btn-warning {
  color: #fff;
  background-color: #f0ad4e;
  border-color: #eea236;
}
.btn-warning:focus,
.btn-warning.focus {
  color: #fff;
  background-color: #ec971f;
  border-color: #985f0d;
}
.btn-warning:hover {
  color: #fff;
  background-color: #ec971f;
  border-color: #d58512;
}
.btn-warning:active,
.btn-warning.active,
.open > .dropdown-toggle.btn-warning {
  color: #fff;
  background-color: #ec971f;
  border-color: #d58512;
}
.btn-warning:active:hover,
.btn-warning.active:hover,
.open > .dropdown-toggle.btn-warning:hover,
.btn-warning:active:focus,
.btn-warning.active:focus,
.open > .dropdown-toggle.btn-warning:focus,
.btn-warning:active.focus,
.btn-warning.active.focus,
.open > .dropdown-toggle.btn-warning.focus {
  color: #fff;
  background-color: #d58512;
  border-color: #985f0d;
}
.btn-warning:active,
.btn-warning.active,
.open > .dropdown-toggle.btn-warning {
  background-image: none;
}
.btn-warning.disabled:hover,
.btn-warning[disabled]:hover,
fieldset[disabled] .btn-warning:hover,
.btn-warning.disabled:focus,
.btn-warning[disabled]:focus,
fieldset[disabled] .btn-warning:focus,
.btn-warning.disabled.focus,
.btn-warning[disabled].focus,
fieldset[disabled] .btn-warning.focus {
  background-color: #f0ad4e;
  border-color: #eea236;
}
.btn-warning .badge {
  color: #f0ad4e;
  background-color: #fff;
}
.btn-danger {
  color: #fff;
  background-color: #d9534f;
  border-color: #d43f3a;
}
.btn-danger:focus,
.btn-danger.focus {
  color: #fff;
  background-color: #c9302c;
  border-color: #761c19;
}
.btn-danger:hover {
  color: #fff;
  background-color: #c9302c;
  border-color: #ac2925;
}
.btn-danger:active,
.btn-danger.active,
.open > .dropdown-toggle.btn-danger {
  color: #fff;
  background-color: #c9302c;
  border-color: #ac2925;
}
.btn-danger:active:hover,
.btn-danger.active:hover,
.open > .dropdown-toggle.btn-danger:hover,
.btn-danger:active:focus,
.btn-danger.active:focus,
.open > .dropdown-toggle.btn-danger:focus,
.btn-danger:active.focus,
.btn-danger.active.focus,
.open > .dropdown-toggle.btn-danger.focus {
  color: #fff;
  background-color: #ac2925;
  border-color: #761c19;
}
.btn-danger:active,
.btn-danger.active,
.open > .dropdown-toggle.btn-danger {
  background-image: none;
}
.btn-danger.disabled:hover,
.btn-danger[disabled]:hover,
fieldset[disabled] .btn-danger:hover,
.btn-danger.disabled:focus,
.btn-danger[disabled]:focus,
fieldset[disabled] .btn-danger:focus,
.btn-danger.disabled.focus,
.btn-danger[disabled].focus,
fieldset[disabled] .btn-danger.focus {
  background-color: #d9534f;
  border-color: #d43f3a;
}
.btn-danger .badge {
  color: #d9534f;
  background-color: #fff;
}
.btn-link {
  color: #337ab7;
  font-weight: normal;
  border-radius: 0;
}
.btn-link,
.btn-link:active,
.btn-link.active,
.btn-link[disabled],
fieldset[disabled] .btn-link {
  background-color: transparent;
  -webkit-box-shadow: none;
  box-shadow: none;
}
.btn-link,
.btn-link:hover,
.btn-link:focus,
.btn-link:active {
  border-color: transparent;
}
.btn-link:hover,
.btn-link:focus {
  color: #23527c;
  text-decoration: underline;
  background-color: transparent;
}
.btn-link[disabled]:hover,
fieldset[disabled] .btn-link:hover,
.btn-link[disabled]:focus,
fieldset[disabled] .btn-link:focus {
  color: #777777;
  text-decoration: none;
}
.btn-lg,
.btn-group-lg > .btn {
  padding: 10px 16px;
  font-size: 17px;
  line-height: 1.3333333;
  border-radius: 3px;
}
.btn-sm,
.btn-group-sm > .btn {
  padding: 5px 10px;
  font-size: 12px;
  line-height: 1.5;
  border-radius: 1px;
}
.btn-xs,
.btn-group-xs > .btn {
  padding: 1px 5px;
  font-size: 12px;
  line-height: 1.5;
  border-radius: 1px;
}
.btn-block {
  display: block;
  width: 100%;
}
.btn-block + .btn-block {
  margin-top: 5px;
}
input[type="submit"].btn-block,
input[type="reset"].btn-block,
input[type="button"].btn-block {
  width: 100%;
}
.fade {
  opacity: 0;
  -webkit-transition: opacity 0.15s linear;
  -o-transition: opacity 0.15s linear;
  transition: opacity 0.15s linear;
}
.fade.in {
  opacity: 1;
}
.collapse {
  display: none;
}
.collapse.in {
  display: block;
}
tr.collapse.in {
  display: table-row;
}
tbody.collapse.in {
  display: table-row-group;
}
.collapsing {
  position: relative;
  height: 0;
  overflow: hidden;
  -webkit-transition-property: height, visibility;
  transition-property: height, visibility;
  -webkit-transition-duration: 0.35s;
  transition-duration: 0.35s;
  -webkit-transition-timing-function: ease;
  transition-timing-function: ease;
}
.caret {
  display: inline-block;
  width: 0;
  height: 0;
  margin-left: 2px;
  vertical-align: middle;
  border-top: 4px dashed;
  border-top: 4px solid \9;
  border-right: 4px solid transparent;
  border-left: 4px solid transparent;
}
.dropup,
.dropdown {
  position: relative;
}
.dropdown-toggle:focus {
  outline: 0;
}
.dropdown-menu {
  position: absolute;
  top: 100%;
  left: 0;
  z-index: 1000;
  display: none;
  float: left;
  min-width: 160px;
  padding: 5px 0;
  margin: 2px 0 0;
  list-style: none;
  font-size: 13px;
  text-align: left;
  background-color: #fff;
  border: 1px solid #ccc;
  border: 1px solid rgba(0, 0, 0, 0.15);
  border-radius: 2px;
  -webkit-box-shadow: 0 6px 12px rgba(0, 0, 0, 0.175);
  box-shadow: 0 6px 12px rgba(0, 0, 0, 0.175);
  background-clip: padding-box;
}
.dropdown-menu.pull-right {
  right: 0;
  left: auto;
}
.dropdown-menu .divider {
  height: 1px;
  margin: 8px 0;
  overflow: hidden;
  background-color: #e5e5e5;
}
.dropdown-menu > li > a {
  display: block;
  padding: 3px 20px;
  clear: both;
  font-weight: normal;
  line-height: 1.42857143;
  color: #333333;
  white-space: nowrap;
}
.dropdown-menu > li > a:hover,
.dropdown-menu > li > a:focus {
  text-decoration: none;
  color: #262626;
  background-color: #f5f5f5;
}
.dropdown-menu > .active > a,
.dropdown-menu > .active > a:hover,
.dropdown-menu > .active > a:focus {
  color: #fff;
  text-decoration: none;
  outline: 0;
  background-color: #337ab7;
}
.dropdown-menu > .disabled > a,
.dropdown-menu > .disabled > a:hover,
.dropdown-menu > .disabled > a:focus {
  color: #777777;
}
.dropdown-menu > .disabled > a:hover,
.dropdown-menu > .disabled > a:focus {
  text-decoration: none;
  background-color: transparent;
  background-image: none;
  filter: progid:DXImageTransform.Microsoft.gradient(enabled = false);
  cursor: not-allowed;
}
.open > .dropdown-menu {
  display: block;
}
.open > a {
  outline: 0;
}
.dropdown-menu-right {
  left: auto;
  right: 0;
}
.dropdown-menu-left {
  left: 0;
  right: auto;
}
.dropdown-header {
  display: block;
  padding: 3px 20px;
  font-size: 12px;
  line-height: 1.42857143;
  color: #777777;
  white-space: nowrap;
}
.dropdown-backdrop {
  position: fixed;
  left: 0;
  right: 0;
  bottom: 0;
  top: 0;
  z-index: 990;
}
.pull-right > .dropdown-menu {
  right: 0;
  left: auto;
}
.dropup .caret,
.navbar-fixed-bottom .dropdown .caret {
  border-top: 0;
  border-bottom: 4px dashed;
  border-bottom: 4px solid \9;
  content: "";
}
.dropup .dropdown-menu,
.navbar-fixed-bottom .dropdown .dropdown-menu {
  top: auto;
  bottom: 100%;
  margin-bottom: 2px;
}
@media (min-width: 541px) {
  .navbar-right .dropdown-menu {
    left: auto;
    right: 0;
  }
  .navbar-right .dropdown-menu-left {
    left: 0;
    right: auto;
  }
}
.btn-group,
.btn-group-vertical {
  position: relative;
  display: inline-block;
  vertical-align: middle;
}
.btn-group > .btn,
.btn-group-vertical > .btn {
  position: relative;
  float: left;
}
.btn-group > .btn:hover,
.btn-group-vertical > .btn:hover,
.btn-group > .btn:focus,
.btn-group-vertical > .btn:focus,
.btn-group > .btn:active,
.btn-group-vertical > .btn:active,
.btn-group > .btn.active,
.btn-group-vertical > .btn.active {
  z-index: 2;
}
.btn-group .btn + .btn,
.btn-group .btn + .btn-group,
.btn-group .btn-group + .btn,
.btn-group .btn-group + .btn-group {
  margin-left: -1px;
}
.btn-toolbar {
  margin-left: -5px;
}
.btn-toolbar .btn,
.btn-toolbar .btn-group,
.btn-toolbar .input-group {
  float: left;
}
.btn-toolbar > .btn,
.btn-toolbar > .btn-group,
.btn-toolbar > .input-group {
  margin-left: 5px;
}
.btn-group > .btn:not(:first-child):not(:last-child):not(.dropdown-toggle) {
  border-radius: 0;
}
.btn-group > .btn:first-child {
  margin-left: 0;
}
.btn-group > .btn:first-child:not(:last-child):not(.dropdown-toggle) {
  border-bottom-right-radius: 0;
  border-top-right-radius: 0;
}
.btn-group > .btn:last-child:not(:first-child),
.btn-group > .dropdown-toggle:not(:first-child) {
  border-bottom-left-radius: 0;
  border-top-left-radius: 0;
}
.btn-group > .btn-group {
  float: left;
}
.btn-group > .btn-group:not(:first-child):not(:last-child) > .btn {
  border-radius: 0;
}
.btn-group > .btn-group:first-child:not(:last-child) > .btn:last-child,
.btn-group > .btn-group:first-child:not(:last-child) > .dropdown-toggle {
  border-bottom-right-radius: 0;
  border-top-right-radius: 0;
}
.btn-group > .btn-group:last-child:not(:first-child) > .btn:first-child {
  border-bottom-left-radius: 0;
  border-top-left-radius: 0;
}
.btn-group .dropdown-toggle:active,
.btn-group.open .dropdown-toggle {
  outline: 0;
}
.btn-group > .btn + .dropdown-toggle {
  padding-left: 8px;
  padding-right: 8px;
}
.btn-group > .btn-lg + .dropdown-toggle {
  padding-left: 12px;
  padding-right: 12px;
}
.btn-group.open .dropdown-toggle {
  -webkit-box-shadow: inset 0 3px 5px rgba(0, 0, 0, 0.125);
  box-shadow: inset 0 3px 5px rgba(0, 0, 0, 0.125);
}
.btn-group.open .dropdown-toggle.btn-link {
  -webkit-box-shadow: none;
  box-shadow: none;
}
.btn .caret {
  margin-left: 0;
}
.btn-lg .caret {
  border-width: 5px 5px 0;
  border-bottom-width: 0;
}
.dropup .btn-lg .caret {
  border-width: 0 5px 5px;
}
.btn-group-vertical > .btn,
.btn-group-vertical > .btn-group,
.btn-group-vertical > .btn-group > .btn {
  display: block;
  float: none;
  width: 100%;
  max-width: 100%;
}
.btn-group-vertical > .btn-group > .btn {
  float: none;
}
.btn-group-vertical > .btn + .btn,
.btn-group-vertical > .btn + .btn-group,
.btn-group-vertical > .btn-group + .btn,
.btn-group-vertical > .btn-group + .btn-group {
  margin-top: -1px;
  margin-left: 0;
}
.btn-group-vertical > .btn:not(:first-child):not(:last-child) {
  border-radius: 0;
}
.btn-group-vertical > .btn:first-child:not(:last-child) {
  border-top-right-radius: 2px;
  border-top-left-radius: 2px;
  border-bottom-right-radius: 0;
  border-bottom-left-radius: 0;
}
.btn-group-vertical > .btn:last-child:not(:first-child) {
  border-top-right-radius: 0;
  border-top-left-radius: 0;
  border-bottom-right-radius: 2px;
  border-bottom-left-radius: 2px;
}
.btn-group-vertical > .btn-group:not(:first-child):not(:last-child) > .btn {
  border-radius: 0;
}
.btn-group-vertical > .btn-group:first-child:not(:last-child) > .btn:last-child,
.btn-group-vertical > .btn-group:first-child:not(:last-child) > .dropdown-toggle {
  border-bottom-right-radius: 0;
  border-bottom-left-radius: 0;
}
.btn-group-vertical > .btn-group:last-child:not(:first-child) > .btn:first-child {
  border-top-right-radius: 0;
  border-top-left-radius: 0;
}
.btn-group-justified {
  display: table;
  width: 100%;
  table-layout: fixed;
  border-collapse: separate;
}
.btn-group-justified > .btn,
.btn-group-justified > .btn-group {
  float: none;
  display: table-cell;
  width: 1%;
}
.btn-group-justified > .btn-group .btn {
  width: 100%;
}
.btn-group-justified > .btn-group .dropdown-menu {
  left: auto;
}
[data-toggle="buttons"] > .btn input[type="radio"],
[data-toggle="buttons"] > .btn-group > .btn input[type="radio"],
[data-toggle="buttons"] > .btn input[type="checkbox"],
[data-toggle="buttons"] > .btn-group > .btn input[type="checkbox"] {
  position: absolute;
  clip: rect(0, 0, 0, 0);
  pointer-events: none;
}
.input-group {
  position: relative;
  display: table;
  border-collapse: separate;
}
.input-group[class*="col-"] {
  float: none;
  padding-left: 0;
  padding-right: 0;
}
.input-group .form-control {
  position: relative;
  z-index: 2;
  float: left;
  width: 100%;
  margin-bottom: 0;
}
.input-group .form-control:focus {
  z-index: 3;
}
.input-group-lg > .form-control,
.input-group-lg > .input-group-addon,
.input-group-lg > .input-group-btn > .btn {
  height: 45px;
  padding: 10px 16px;
  font-size: 17px;
  line-height: 1.3333333;
  border-radius: 3px;
}
select.input-group-lg > .form-control,
select.input-group-lg > .input-group-addon,
select.input-group-lg > .input-group-btn > .btn {
  height: 45px;
  line-height: 45px;
}
textarea.input-group-lg > .form-control,
textarea.input-group-lg > .input-group-addon,
textarea.input-group-lg > .input-group-btn > .btn,
select[multiple].input-group-lg > .form-control,
select[multiple].input-group-lg > .input-group-addon,
select[multiple].input-group-lg > .input-group-btn > .btn {
  height: auto;
}
.input-group-sm > .form-control,
.input-group-sm > .input-group-addon,
.input-group-sm > .input-group-btn > .btn {
  height: 30px;
  padding: 5px 10px;
  font-size: 12px;
  line-height: 1.5;
  border-radius: 1px;
}
select.input-group-sm > .form-control,
select.input-group-sm > .input-group-addon,
select.input-group-sm > .input-group-btn > .btn {
  height: 30px;
  line-height: 30px;
}
textarea.input-group-sm > .form-control,
textarea.input-group-sm > .input-group-addon,
textarea.input-group-sm > .input-group-btn > .btn,
select[multiple].input-group-sm > .form-control,
select[multiple].input-group-sm > .input-group-addon,
select[multiple].input-group-sm > .input-group-btn > .btn {
  height: auto;
}
.input-group-addon,
.input-group-btn,
.input-group .form-control {
  display: table-cell;
}
.input-group-addon:not(:first-child):not(:last-child),
.input-group-btn:not(:first-child):not(:last-child),
.input-group .form-control:not(:first-child):not(:last-child) {
  border-radius: 0;
}
.input-group-addon,
.input-group-btn {
  width: 1%;
  white-space: nowrap;
  vertical-align: middle;
}
.input-group-addon {
  padding: 6px 12px;
  font-size: 13px;
  font-weight: normal;
  line-height: 1;
  color: #555555;
  text-align: center;
  background-color: #eeeeee;
  border: 1px solid #ccc;
  border-radius: 2px;
}
.input-group-addon.input-sm {
  padding: 5px 10px;
  font-size: 12px;
  border-radius: 1px;
}
.input-group-addon.input-lg {
  padding: 10px 16px;
  font-size: 17px;
  border-radius: 3px;
}
.input-group-addon input[type="radio"],
.input-group-addon input[type="checkbox"] {
  margin-top: 0;
}
.input-group .form-control:first-child,
.input-group-addon:first-child,
.input-group-btn:first-child > .btn,
.input-group-btn:first-child > .btn-group > .btn,
.input-group-btn:first-child > .dropdown-toggle,
.input-group-btn:last-child > .btn:not(:last-child):not(.dropdown-toggle),
.input-group-btn:last-child > .btn-group:not(:last-child) > .btn {
  border-bottom-right-radius: 0;
  border-top-right-radius: 0;
}
.input-group-addon:first-child {
  border-right: 0;
}
.input-group .form-control:last-child,
.input-group-addon:last-child,
.input-group-btn:last-child > .btn,
.input-group-btn:last-child > .btn-group > .btn,
.input-group-btn:last-child > .dropdown-toggle,
.input-group-btn:first-child > .btn:not(:first-child),
.input-group-btn:first-child > .btn-group:not(:first-child) > .btn {
  border-bottom-left-radius: 0;
  border-top-left-radius: 0;
}
.input-group-addon:last-child {
  border-left: 0;
}
.input-group-btn {
  position: relative;
  font-size: 0;
  white-space: nowrap;
}
.input-group-btn > .btn {
  position: relative;
}
.input-group-btn > .btn + .btn {
  margin-left: -1px;
}
.input-group-btn > .btn:hover,
.input-group-btn > .btn:focus,
.input-group-btn > .btn:active {
  z-index: 2;
}
.input-group-btn:first-child > .btn,
.input-group-btn:first-child > .btn-group {
  margin-right: -1px;
}
.input-group-btn:last-child > .btn,
.input-group-btn:last-child > .btn-group {
  z-index: 2;
  margin-left: -1px;
}
.nav {
  margin-bottom: 0;
  padding-left: 0;
  list-style: none;
}
.nav > li {
  position: relative;
  display: block;
}
.nav > li > a {
  position: relative;
  display: block;
  padding: 10px 15px;
}
.nav > li > a:hover,
.nav > li > a:focus {
  text-decoration: none;
  background-color: #eeeeee;
}
.nav > li.disabled > a {
  color: #777777;
}
.nav > li.disabled > a:hover,
.nav > li.disabled > a:focus {
  color: #777777;
  text-decoration: none;
  background-color: transparent;
  cursor: not-allowed;
}
.nav .open > a,
.nav .open > a:hover,
.nav .open > a:focus {
  background-color: #eeeeee;
  border-color: #337ab7;
}
.nav .nav-divider {
  height: 1px;
  margin: 8px 0;
  overflow: hidden;
  background-color: #e5e5e5;
}
.nav > li > a > img {
  max-width: none;
}
.nav-tabs {
  border-bottom: 1px solid #ddd;
}
.nav-tabs > li {
  float: left;
  margin-bottom: -1px;
}
.nav-tabs > li > a {
  margin-right: 2px;
  line-height: 1.42857143;
  border: 1px solid transparent;
  border-radius: 2px 2px 0 0;
}
.nav-tabs > li > a:hover {
  border-color: #eeeeee #eeeeee #ddd;
}
.nav-tabs > li.active > a,
.nav-tabs > li.active > a:hover,
.nav-tabs > li.active > a:focus {
  color: #555555;
  background-color: #fff;
  border: 1px solid #ddd;
  border-bottom-color: transparent;
  cursor: default;
}
.nav-tabs.nav-justified {
  width: 100%;
  border-bottom: 0;
}
.nav-tabs.nav-justified > li {
  float: none;
}
.nav-tabs.nav-justified > li > a {
  text-align: center;
  margin-bottom: 5px;
}
.nav-tabs.nav-justified > .dropdown .dropdown-menu {
  top: auto;
  left: auto;
}
@media (min-width: 768px) {
  .nav-tabs.nav-justified > li {
    display: table-cell;
    width: 1%;
  }
  .nav-tabs.nav-justified > li > a {
    margin-bottom: 0;
  }
}
.nav-tabs.nav-justified > li > a {
  margin-right: 0;
  border-radius: 2px;
}
.nav-tabs.nav-justified > .active > a,
.nav-tabs.nav-justified > .active > a:hover,
.nav-tabs.nav-justified > .active > a:focus {
  border: 1px solid #ddd;
}
@media (min-width: 768px) {
  .nav-tabs.nav-justified > li > a {
    border-bottom: 1px solid #ddd;
    border-radius: 2px 2px 0 0;
  }
  .nav-tabs.nav-justified > .active > a,
  .nav-tabs.nav-justified > .active > a:hover,
  .nav-tabs.nav-justified > .active > a:focus {
    border-bottom-color: #fff;
  }
}
.nav-pills > li {
  float: left;
}
.nav-pills > li > a {
  border-radius: 2px;
}
.nav-pills > li + li {
  margin-left: 2px;
}
.nav-pills > li.active > a,
.nav-pills > li.active > a:hover,
.nav-pills > li.active > a:focus {
  color: #fff;
  background-color: #337ab7;
}
.nav-stacked > li {
  float: none;
}
.nav-stacked > li + li {
  margin-top: 2px;
  margin-left: 0;
}
.nav-justified {
  width: 100%;
}
.nav-justified > li {
  float: none;
}
.nav-justified > li > a {
  text-align: center;
  margin-bottom: 5px;
}
.nav-justified > .dropdown .dropdown-menu {
  top: auto;
  left: auto;
}
@media (min-width: 768px) {
  .nav-justified > li {
    display: table-cell;
    width: 1%;
  }
  .nav-justified > li > a {
    margin-bottom: 0;
  }
}
.nav-tabs-justified {
  border-bottom: 0;
}
.nav-tabs-justified > li > a {
  margin-right: 0;
  border-radius: 2px;
}
.nav-tabs-justified > .active > a,
.nav-tabs-justified > .active > a:hover,
.nav-tabs-justified > .active > a:focus {
  border: 1px solid #ddd;
}
@media (min-width: 768px) {
  .nav-tabs-justified > li > a {
    border-bottom: 1px solid #ddd;
    border-radius: 2px 2px 0 0;
  }
  .nav-tabs-justified > .active > a,
  .nav-tabs-justified > .active > a:hover,
  .nav-tabs-justified > .active > a:focus {
    border-bottom-color: #fff;
  }
}
.tab-content > .tab-pane {
  display: none;
}
.tab-content > .active {
  display: block;
}
.nav-tabs .dropdown-menu {
  margin-top: -1px;
  border-top-right-radius: 0;
  border-top-left-radius: 0;
}
.navbar {
  position: relative;
  min-height: 30px;
  margin-bottom: 18px;
  border: 1px solid transparent;
}
@media (min-width: 541px) {
  .navbar {
    border-radius: 2px;
  }
}
@media (min-width: 541px) {
  .navbar-header {
    float: left;
  }
}
.navbar-collapse {
  overflow-x: visible;
  padding-right: 0px;
  padding-left: 0px;
  border-top: 1px solid transparent;
  box-shadow: inset 0 1px 0 rgba(255, 255, 255, 0.1);
  -webkit-overflow-scrolling: touch;
}
.navbar-collapse.in {
  overflow-y: auto;
}
@media (min-width: 541px) {
  .navbar-collapse {
    width: auto;
    border-top: 0;
    box-shadow: none;
  }
  .navbar-collapse.collapse {
    display: block !important;
    height: auto !important;
    padding-bottom: 0;
    overflow: visible !important;
  }
  .navbar-collapse.in {
    overflow-y: visible;
  }
  .navbar-fixed-top .navbar-collapse,
  .navbar-static-top .navbar-collapse,
  .navbar-fixed-bottom .navbar-collapse {
    padding-left: 0;
    padding-right: 0;
  }
}
.navbar-fixed-top .navbar-collapse,
.navbar-fixed-bottom .navbar-collapse {
  max-height: 340px;
}
@media (max-device-width: 540px) and (orientation: landscape) {
  .navbar-fixed-top .navbar-collapse,
  .navbar-fixed-bottom .navbar-collapse {
    max-height: 200px;
  }
}
.container > .navbar-header,
.container-fluid > .navbar-header,
.container > .navbar-collapse,
.container-fluid > .navbar-collapse {
  margin-right: 0px;
  margin-left: 0px;
}
@media (min-width: 541px) {
  .container > .navbar-header,
  .container-fluid > .navbar-header,
  .container > .navbar-collapse,
  .container-fluid > .navbar-collapse {
    margin-right: 0;
    margin-left: 0;
  }
}
.navbar-static-top {
  z-index: 1000;
  border-width: 0 0 1px;
}
@media (min-width: 541px) {
  .navbar-static-top {
    border-radius: 0;
  }
}
.navbar-fixed-top,
.navbar-fixed-bottom {
  position: fixed;
  right: 0;
  left: 0;
  z-index: 1030;
}
@media (min-width: 541px) {
  .navbar-fixed-top,
  .navbar-fixed-bottom {
    border-radius: 0;
  }
}
.navbar-fixed-top {
  top: 0;
  border-width: 0 0 1px;
}
.navbar-fixed-bottom {
  bottom: 0;
  margin-bottom: 0;
  border-width: 1px 0 0;
}
.navbar-brand {
  float: left;
  padding: 6px 0px;
  font-size: 17px;
  line-height: 18px;
  height: 30px;
}
.navbar-brand:hover,
.navbar-brand:focus {
  text-decoration: none;
}
.navbar-brand > img {
  display: block;
}
@media (min-width: 541px) {
  .navbar > .container .navbar-brand,
  .navbar > .container-fluid .navbar-brand {
    margin-left: 0px;
  }
}
.navbar-toggle {
  position: relative;
  float: right;
  margin-right: 0px;
  padding: 9px 10px;
  margin-top: -2px;
  margin-bottom: -2px;
  background-color: transparent;
  background-image: none;
  border: 1px solid transparent;
  border-radius: 2px;
}
.navbar-toggle:focus {
  outline: 0;
}
.navbar-toggle .icon-bar {
  display: block;
  width: 22px;
  height: 2px;
  border-radius: 1px;
}
.navbar-toggle .icon-bar + .icon-bar {
  margin-top: 4px;
}
@media (min-width: 541px) {
  .navbar-toggle {
    display: none;
  }
}
.navbar-nav {
  margin: 3px 0px;
}
.navbar-nav > li > a {
  padding-top: 10px;
  padding-bottom: 10px;
  line-height: 18px;
}
@media (max-width: 540px) {
  .navbar-nav .open .dropdown-menu {
    position: static;
    float: none;
    width: auto;
    margin-top: 0;
    background-color: transparent;
    border: 0;
    box-shadow: none;
  }
  .navbar-nav .open .dropdown-menu > li > a,
  .navbar-nav .open .dropdown-menu .dropdown-header {
    padding: 5px 15px 5px 25px;
  }
  .navbar-nav .open .dropdown-menu > li > a {
    line-height: 18px;
  }
  .navbar-nav .open .dropdown-menu > li > a:hover,
  .navbar-nav .open .dropdown-menu > li > a:focus {
    background-image: none;
  }
}
@media (min-width: 541px) {
  .navbar-nav {
    float: left;
    margin: 0;
  }
  .navbar-nav > li {
    float: left;
  }
  .navbar-nav > li > a {
    padding-top: 6px;
    padding-bottom: 6px;
  }
}
.navbar-form {
  margin-left: 0px;
  margin-right: 0px;
  padding: 10px 0px;
  border-top: 1px solid transparent;
  border-bottom: 1px solid transparent;
  -webkit-box-shadow: inset 0 1px 0 rgba(255, 255, 255, 0.1), 0 1px 0 rgba(255, 255, 255, 0.1);
  box-shadow: inset 0 1px 0 rgba(255, 255, 255, 0.1), 0 1px 0 rgba(255, 255, 255, 0.1);
  margin-top: -1px;
  margin-bottom: -1px;
}
@media (min-width: 768px) {
  .navbar-form .form-group {
    display: inline-block;
    margin-bottom: 0;
    vertical-align: middle;
  }
  .navbar-form .form-control {
    display: inline-block;
    width: auto;
    vertical-align: middle;
  }
  .navbar-form .form-control-static {
    display: inline-block;
  }
  .navbar-form .input-group {
    display: inline-table;
    vertical-align: middle;
  }
  .navbar-form .input-group .input-group-addon,
  .navbar-form .input-group .input-group-btn,
  .navbar-form .input-group .form-control {
    width: auto;
  }
  .navbar-form .input-group > .form-control {
    width: 100%;
  }
  .navbar-form .control-label {
    margin-bottom: 0;
    vertical-align: middle;
  }
  .navbar-form .radio,
  .navbar-form .checkbox {
    display: inline-block;
    margin-top: 0;
    margin-bottom: 0;
    vertical-align: middle;
  }
  .navbar-form .radio label,
  .navbar-form .checkbox label {
    padding-left: 0;
  }
  .navbar-form .radio input[type="radio"],
  .navbar-form .checkbox input[type="checkbox"] {
    position: relative;
    margin-left: 0;
  }
  .navbar-form .has-feedback .form-control-feedback {
    top: 0;
  }
}
@media (max-width: 540px) {
  .navbar-form .form-group {
    margin-bottom: 5px;
  }
  .navbar-form .form-group:last-child {
    margin-bottom: 0;
  }
}
@media (min-width: 541px) {
  .navbar-form {
    width: auto;
    border: 0;
    margin-left: 0;
    margin-right: 0;
    padding-top: 0;
    padding-bottom: 0;
    -webkit-box-shadow: none;
    box-shadow: none;
  }
}
.navbar-nav > li > .dropdown-menu {
  margin-top: 0;
  border-top-right-radius: 0;
  border-top-left-radius: 0;
}
.navbar-fixed-bottom .navbar-nav > li > .dropdown-menu {
  margin-bottom: 0;
  border-top-right-radius: 2px;
  border-top-left-radius: 2px;
  border-bottom-right-radius: 0;
  border-bottom-left-radius: 0;
}
.navbar-btn {
  margin-top: -1px;
  margin-bottom: -1px;
}
.navbar-btn.btn-sm {
  margin-top: 0px;
  margin-bottom: 0px;
}
.navbar-btn.btn-xs {
  margin-top: 4px;
  margin-bottom: 4px;
}
.navbar-text {
  margin-top: 6px;
  margin-bottom: 6px;
}
@media (min-width: 541px) {
  .navbar-text {
    float: left;
    margin-left: 0px;
    margin-right: 0px;
  }
}
@media (min-width: 541px) {
  .navbar-left {
    float: left !important;
    float: left;
  }
  .navbar-right {
    float: right !important;
    float: right;
    margin-right: 0px;
  }
  .navbar-right ~ .navbar-right {
    margin-right: 0;
  }
}
.navbar-default {
  background-color: #f8f8f8;
  border-color: #e7e7e7;
}
.navbar-default .navbar-brand {
  color: #777;
}
.navbar-default .navbar-brand:hover,
.navbar-default .navbar-brand:focus {
  color: #5e5e5e;
  background-color: transparent;
}
.navbar-default .navbar-text {
  color: #777;
}
.navbar-default .navbar-nav > li > a {
  color: #777;
}
.navbar-default .navbar-nav > li > a:hover,
.navbar-default .navbar-nav > li > a:focus {
  color: #333;
  background-color: transparent;
}
.navbar-default .navbar-nav > .active > a,
.navbar-default .navbar-nav > .active > a:hover,
.navbar-default .navbar-nav > .active > a:focus {
  color: #555;
  background-color: #e7e7e7;
}
.navbar-default .navbar-nav > .disabled > a,
.navbar-default .navbar-nav > .disabled > a:hover,
.navbar-default .navbar-nav > .disabled > a:focus {
  color: #ccc;
  background-color: transparent;
}
.navbar-default .navbar-toggle {
  border-color: #ddd;
}
.navbar-default .navbar-toggle:hover,
.navbar-default .navbar-toggle:focus {
  background-color: #ddd;
}
.navbar-default .navbar-toggle .icon-bar {
  background-color: #888;
}
.navbar-default .navbar-collapse,
.navbar-default .navbar-form {
  border-color: #e7e7e7;
}
.navbar-default .navbar-nav > .open > a,
.navbar-default .navbar-nav > .open > a:hover,
.navbar-default .navbar-nav > .open > a:focus {
  background-color: #e7e7e7;
  color: #555;
}
@media (max-width: 540px) {
  .navbar-default .navbar-nav .open .dropdown-menu > li > a {
    color: #777;
  }
  .navbar-default .navbar-nav .open .dropdown-menu > li > a:hover,
  .navbar-default .navbar-nav .open .dropdown-menu > li > a:focus {
    color: #333;
    background-color: transparent;
  }
  .navbar-default .navbar-nav .open .dropdown-menu > .active > a,
  .navbar-default .navbar-nav .open .dropdown-menu > .active > a:hover,
  .navbar-default .navbar-nav .open .dropdown-menu > .active > a:focus {
    color: #555;
    background-color: #e7e7e7;
  }
  .navbar-default .navbar-nav .open .dropdown-menu > .disabled > a,
  .navbar-default .navbar-nav .open .dropdown-menu > .disabled > a:hover,
  .navbar-default .navbar-nav .open .dropdown-menu > .disabled > a:focus {
    color: #ccc;
    background-color: transparent;
  }
}
.navbar-default .navbar-link {
  color: #777;
}
.navbar-default .navbar-link:hover {
  color: #333;
}
.navbar-default .btn-link {
  color: #777;
}
.navbar-default .btn-link:hover,
.navbar-default .btn-link:focus {
  color: #333;
}
.navbar-default .btn-link[disabled]:hover,
fieldset[disabled] .navbar-default .btn-link:hover,
.navbar-default .btn-link[disabled]:focus,
fieldset[disabled] .navbar-default .btn-link:focus {
  color: #ccc;
}
.navbar-inverse {
  background-color: #222;
  border-color: #080808;
}
.navbar-inverse .navbar-brand {
  color: #9d9d9d;
}
.navbar-inverse .navbar-brand:hover,
.navbar-inverse .navbar-brand:focus {
  color: #fff;
  background-color: transparent;
}
.navbar-inverse .navbar-text {
  color: #9d9d9d;
}
.navbar-inverse .navbar-nav > li > a {
  color: #9d9d9d;
}
.navbar-inverse .navbar-nav > li > a:hover,
.navbar-inverse .navbar-nav > li > a:focus {
  color: #fff;
  background-color: transparent;
}
.navbar-inverse .navbar-nav > .active > a,
.navbar-inverse .navbar-nav > .active > a:hover,
.navbar-inverse .navbar-nav > .active > a:focus {
  color: #fff;
  background-color: #080808;
}
.navbar-inverse .navbar-nav > .disabled > a,
.navbar-inverse .navbar-nav > .disabled > a:hover,
.navbar-inverse .navbar-nav > .disabled > a:focus {
  color: #444;
  background-color: transparent;
}
.navbar-inverse .navbar-toggle {
  border-color: #333;
}
.navbar-inverse .navbar-toggle:hover,
.navbar-inverse .navbar-toggle:focus {
  background-color: #333;
}
.navbar-inverse .navbar-toggle .icon-bar {
  background-color: #fff;
}
.navbar-inverse .navbar-collapse,
.navbar-inverse .navbar-form {
  border-color: #101010;
}
.navbar-inverse .navbar-nav > .open > a,
.navbar-inverse .navbar-nav > .open > a:hover,
.navbar-inverse .navbar-nav > .open > a:focus {
  background-color: #080808;
  color: #fff;
}
@media (max-width: 540px) {
  .navbar-inverse .navbar-nav .open .dropdown-menu > .dropdown-header {
    border-color: #080808;
  }
  .navbar-inverse .navbar-nav .open .dropdown-menu .divider {
    background-color: #080808;
  }
  .navbar-inverse .navbar-nav .open .dropdown-menu > li > a {
    color: #9d9d9d;
  }
  .navbar-inverse .navbar-nav .open .dropdown-menu > li > a:hover,
  .navbar-inverse .navbar-nav .open .dropdown-menu > li > a:focus {
    color: #fff;
    background-color: transparent;
  }
  .navbar-inverse .navbar-nav .open .dropdown-menu > .active > a,
  .navbar-inverse .navbar-nav .open .dropdown-menu > .active > a:hover,
  .navbar-inverse .navbar-nav .open .dropdown-menu > .active > a:focus {
    color: #fff;
    background-color: #080808;
  }
  .navbar-inverse .navbar-nav .open .dropdown-menu > .disabled > a,
  .navbar-inverse .navbar-nav .open .dropdown-menu > .disabled > a:hover,
  .navbar-inverse .navbar-nav .open .dropdown-menu > .disabled > a:focus {
    color: #444;
    background-color: transparent;
  }
}
.navbar-inverse .navbar-link {
  color: #9d9d9d;
}
.navbar-inverse .navbar-link:hover {
  color: #fff;
}
.navbar-inverse .btn-link {
  color: #9d9d9d;
}
.navbar-inverse .btn-link:hover,
.navbar-inverse .btn-link:focus {
  color: #fff;
}
.navbar-inverse .btn-link[disabled]:hover,
fieldset[disabled] .navbar-inverse .btn-link:hover,
.navbar-inverse .btn-link[disabled]:focus,
fieldset[disabled] .navbar-inverse .btn-link:focus {
  color: #444;
}
.breadcrumb {
  padding: 8px 15px;
  margin-bottom: 18px;
  list-style: none;
  background-color: #f5f5f5;
  border-radius: 2px;
}
.breadcrumb > li {
  display: inline-block;
}
.breadcrumb > li + li:before {
  content: "/\00a0";
  padding: 0 5px;
  color: #5e5e5e;
}
.breadcrumb > .active {
  color: #777777;
}
.pagination {
  display: inline-block;
  padding-left: 0;
  margin: 18px 0;
  border-radius: 2px;
}
.pagination > li {
  display: inline;
}
.pagination > li > a,
.pagination > li > span {
  position: relative;
  float: left;
  padding: 6px 12px;
  line-height: 1.42857143;
  text-decoration: none;
  color: #337ab7;
  background-color: #fff;
  border: 1px solid #ddd;
  margin-left: -1px;
}
.pagination > li:first-child > a,
.pagination > li:first-child > span {
  margin-left: 0;
  border-bottom-left-radius: 2px;
  border-top-left-radius: 2px;
}
.pagination > li:last-child > a,
.pagination > li:last-child > span {
  border-bottom-right-radius: 2px;
  border-top-right-radius: 2px;
}
.pagination > li > a:hover,
.pagination > li > span:hover,
.pagination > li > a:focus,
.pagination > li > span:focus {
  z-index: 2;
  color: #23527c;
  background-color: #eeeeee;
  border-color: #ddd;
}
.pagination > .active > a,
.pagination > .active > span,
.pagination > .active > a:hover,
.pagination > .active > span:hover,
.pagination > .active > a:focus,
.pagination > .active > span:focus {
  z-index: 3;
  color: #fff;
  background-color: #337ab7;
  border-color: #337ab7;
  cursor: default;
}
.pagination > .disabled > span,
.pagination > .disabled > span:hover,
.pagination > .disabled > span:focus,
.pagination > .disabled > a,
.pagination > .disabled > a:hover,
.pagination > .disabled > a:focus {
  color: #777777;
  background-color: #fff;
  border-color: #ddd;
  cursor: not-allowed;
}
.pagination-lg > li > a,
.pagination-lg > li > span {
  padding: 10px 16px;
  font-size: 17px;
  line-height: 1.3333333;
}
.pagination-lg > li:first-child > a,
.pagination-lg > li:first-child > span {
  border-bottom-left-radius: 3px;
  border-top-left-radius: 3px;
}
.pagination-lg > li:last-child > a,
.pagination-lg > li:last-child > span {
  border-bottom-right-radius: 3px;
  border-top-right-radius: 3px;
}
.pagination-sm > li > a,
.pagination-sm > li > span {
  padding: 5px 10px;
  font-size: 12px;
  line-height: 1.5;
}
.pagination-sm > li:first-child > a,
.pagination-sm > li:first-child > span {
  border-bottom-left-radius: 1px;
  border-top-left-radius: 1px;
}
.pagination-sm > li:last-child > a,
.pagination-sm > li:last-child > span {
  border-bottom-right-radius: 1px;
  border-top-right-radius: 1px;
}
.pager {
  padding-left: 0;
  margin: 18px 0;
  list-style: none;
  text-align: center;
}
.pager li {
  display: inline;
}
.pager li > a,
.pager li > span {
  display: inline-block;
  padding: 5px 14px;
  background-color: #fff;
  border: 1px solid #ddd;
  border-radius: 15px;
}
.pager li > a:hover,
.pager li > a:focus {
  text-decoration: none;
  background-color: #eeeeee;
}
.pager .next > a,
.pager .next > span {
  float: right;
}
.pager .previous > a,
.pager .previous > span {
  float: left;
}
.pager .disabled > a,
.pager .disabled > a:hover,
.pager .disabled > a:focus,
.pager .disabled > span {
  color: #777777;
  background-color: #fff;
  cursor: not-allowed;
}
.label {
  display: inline;
  padding: .2em .6em .3em;
  font-size: 75%;
  font-weight: bold;
  line-height: 1;
  color: #fff;
  text-align: center;
  white-space: nowrap;
  vertical-align: baseline;
  border-radius: .25em;
}
a.label:hover,
a.label:focus {
  color: #fff;
  text-decoration: none;
  cursor: pointer;
}
.label:empty {
  display: none;
}
.btn .label {
  position: relative;
  top: -1px;
}
.label-default {
  background-color: #777777;
}
.label-default[href]:hover,
.label-default[href]:focus {
  background-color: #5e5e5e;
}
.label-primary {
  background-color: #337ab7;
}
.label-primary[href]:hover,
.label-primary[href]:focus {
  background-color: #286090;
}
.label-success {
  background-color: #5cb85c;
}
.label-success[href]:hover,
.label-success[href]:focus {
  background-color: #449d44;
}
.label-info {
  background-color: #5bc0de;
}
.label-info[href]:hover,
.label-info[href]:focus {
  background-color: #31b0d5;
}
.label-warning {
  background-color: #f0ad4e;
}
.label-warning[href]:hover,
.label-warning[href]:focus {
  background-color: #ec971f;
}
.label-danger {
  background-color: #d9534f;
}
.label-danger[href]:hover,
.label-danger[href]:focus {
  background-color: #c9302c;
}
.badge {
  display: inline-block;
  min-width: 10px;
  padding: 3px 7px;
  font-size: 12px;
  font-weight: bold;
  color: #fff;
  line-height: 1;
  vertical-align: middle;
  white-space: nowrap;
  text-align: center;
  background-color: #777777;
  border-radius: 10px;
}
.badge:empty {
  display: none;
}
.btn .badge {
  position: relative;
  top: -1px;
}
.btn-xs .badge,
.btn-group-xs > .btn .badge {
  top: 0;
  padding: 1px 5px;
}
a.badge:hover,
a.badge:focus {
  color: #fff;
  text-decoration: none;
  cursor: pointer;
}
.list-group-item.active > .badge,
.nav-pills > .active > a > .badge {
  color: #337ab7;
  background-color: #fff;
}
.list-group-item > .badge {
  float: right;
}
.list-group-item > .badge + .badge {
  margin-right: 5px;
}
.nav-pills > li > a > .badge {
  margin-left: 3px;
}
.jumbotron {
  padding-top: 30px;
  padding-bottom: 30px;
  margin-bottom: 30px;
  color: inherit;
  background-color: #eeeeee;
}
.jumbotron h1,
.jumbotron .h1 {
  color: inherit;
}
.jumbotron p {
  margin-bottom: 15px;
  font-size: 20px;
  font-weight: 200;
}
.jumbotron > hr {
  border-top-color: #d5d5d5;
}
.container .jumbotron,
.container-fluid .jumbotron {
  border-radius: 3px;
  padding-left: 0px;
  padding-right: 0px;
}
.jumbotron .container {
  max-width: 100%;
}
@media screen and (min-width: 768px) {
  .jumbotron {
    padding-top: 48px;
    padding-bottom: 48px;
  }
  .container .jumbotron,
  .container-fluid .jumbotron {
    padding-left: 60px;
    padding-right: 60px;
  }
  .jumbotron h1,
  .jumbotron .h1 {
    font-size: 59px;
  }
}
.thumbnail {
  display: block;
  padding: 4px;
  margin-bottom: 18px;
  line-height: 1.42857143;
  background-color: #fff;
  border: 1px solid #ddd;
  border-radius: 2px;
  -webkit-transition: border 0.2s ease-in-out;
  -o-transition: border 0.2s ease-in-out;
  transition: border 0.2s ease-in-out;
}
.thumbnail > img,
.thumbnail a > img {
  margin-left: auto;
  margin-right: auto;
}
a.thumbnail:hover,
a.thumbnail:focus,
a.thumbnail.active {
  border-color: #337ab7;
}
.thumbnail .caption {
  padding: 9px;
  color: #000;
}
.alert {
  padding: 15px;
  margin-bottom: 18px;
  border: 1px solid transparent;
  border-radius: 2px;
}
.alert h4 {
  margin-top: 0;
  color: inherit;
}
.alert .alert-link {
  font-weight: bold;
}
.alert > p,
.alert > ul {
  margin-bottom: 0;
}
.alert > p + p {
  margin-top: 5px;
}
.alert-dismissable,
.alert-dismissible {
  padding-right: 35px;
}
.alert-dismissable .close,
.alert-dismissible .close {
  position: relative;
  top: -2px;
  right: -21px;
  color: inherit;
}
.alert-success {
  background-color: #dff0d8;
  border-color: #d6e9c6;
  color: #3c763d;
}
.alert-success hr {
  border-top-color: #c9e2b3;
}
.alert-success .alert-link {
  color: #2b542c;
}
.alert-info {
  background-color: #d9edf7;
  border-color: #bce8f1;
  color: #31708f;
}
.alert-info hr {
  border-top-color: #a6e1ec;
}
.alert-info .alert-link {
  color: #245269;
}
.alert-warning {
  background-color: #fcf8e3;
  border-color: #faebcc;
  color: #8a6d3b;
}
.alert-warning hr {
  border-top-color: #f7e1b5;
}
.alert-warning .alert-link {
  color: #66512c;
}
.alert-danger {
  background-color: #f2dede;
  border-color: #ebccd1;
  color: #a94442;
}
.alert-danger hr {
  border-top-color: #e4b9c0;
}
.alert-danger .alert-link {
  color: #843534;
}
@-webkit-keyframes progress-bar-stripes {
  from {
    background-position: 40px 0;
  }
  to {
    background-position: 0 0;
  }
}
@keyframes progress-bar-stripes {
  from {
    background-position: 40px 0;
  }
  to {
    background-position: 0 0;
  }
}
.progress {
  overflow: hidden;
  height: 18px;
  margin-bottom: 18px;
  background-color: #f5f5f5;
  border-radius: 2px;
  -webkit-box-shadow: inset 0 1px 2px rgba(0, 0, 0, 0.1);
  box-shadow: inset 0 1px 2px rgba(0, 0, 0, 0.1);
}
.progress-bar {
  float: left;
  width: 0%;
  height: 100%;
  font-size: 12px;
  line-height: 18px;
  color: #fff;
  text-align: center;
  background-color: #337ab7;
  -webkit-box-shadow: inset 0 -1px 0 rgba(0, 0, 0, 0.15);
  box-shadow: inset 0 -1px 0 rgba(0, 0, 0, 0.15);
  -webkit-transition: width 0.6s ease;
  -o-transition: width 0.6s ease;
  transition: width 0.6s ease;
}
.progress-striped .progress-bar,
.progress-bar-striped {
  background-image: -webkit-linear-gradient(45deg, rgba(255, 255, 255, 0.15) 25%, transparent 25%, transparent 50%, rgba(255, 255, 255, 0.15) 50%, rgba(255, 255, 255, 0.15) 75%, transparent 75%, transparent);
  background-image: -o-linear-gradient(45deg, rgba(255, 255, 255, 0.15) 25%, transparent 25%, transparent 50%, rgba(255, 255, 255, 0.15) 50%, rgba(255, 255, 255, 0.15) 75%, transparent 75%, transparent);
  background-image: linear-gradient(45deg, rgba(255, 255, 255, 0.15) 25%, transparent 25%, transparent 50%, rgba(255, 255, 255, 0.15) 50%, rgba(255, 255, 255, 0.15) 75%, transparent 75%, transparent);
  background-size: 40px 40px;
}
.progress.active .progress-bar,
.progress-bar.active {
  -webkit-animation: progress-bar-stripes 2s linear infinite;
  -o-animation: progress-bar-stripes 2s linear infinite;
  animation: progress-bar-stripes 2s linear infinite;
}
.progress-bar-success {
  background-color: #5cb85c;
}
.progress-striped .progress-bar-success {
  background-image: -webkit-linear-gradient(45deg, rgba(255, 255, 255, 0.15) 25%, transparent 25%, transparent 50%, rgba(255, 255, 255, 0.15) 50%, rgba(255, 255, 255, 0.15) 75%, transparent 75%, transparent);
  background-image: -o-linear-gradient(45deg, rgba(255, 255, 255, 0.15) 25%, transparent 25%, transparent 50%, rgba(255, 255, 255, 0.15) 50%, rgba(255, 255, 255, 0.15) 75%, transparent 75%, transparent);
  background-image: linear-gradient(45deg, rgba(255, 255, 255, 0.15) 25%, transparent 25%, transparent 50%, rgba(255, 255, 255, 0.15) 50%, rgba(255, 255, 255, 0.15) 75%, transparent 75%, transparent);
}
.progress-bar-info {
  background-color: #5bc0de;
}
.progress-striped .progress-bar-info {
  background-image: -webkit-linear-gradient(45deg, rgba(255, 255, 255, 0.15) 25%, transparent 25%, transparent 50%, rgba(255, 255, 255, 0.15) 50%, rgba(255, 255, 255, 0.15) 75%, transparent 75%, transparent);
  background-image: -o-linear-gradient(45deg, rgba(255, 255, 255, 0.15) 25%, transparent 25%, transparent 50%, rgba(255, 255, 255, 0.15) 50%, rgba(255, 255, 255, 0.15) 75%, transparent 75%, transparent);
  background-image: linear-gradient(45deg, rgba(255, 255, 255, 0.15) 25%, transparent 25%, transparent 50%, rgba(255, 255, 255, 0.15) 50%, rgba(255, 255, 255, 0.15) 75%, transparent 75%, transparent);
}
.progress-bar-warning {
  background-color: #f0ad4e;
}
.progress-striped .progress-bar-warning {
  background-image: -webkit-linear-gradient(45deg, rgba(255, 255, 255, 0.15) 25%, transparent 25%, transparent 50%, rgba(255, 255, 255, 0.15) 50%, rgba(255, 255, 255, 0.15) 75%, transparent 75%, transparent);
  background-image: -o-linear-gradient(45deg, rgba(255, 255, 255, 0.15) 25%, transparent 25%, transparent 50%, rgba(255, 255, 255, 0.15) 50%, rgba(255, 255, 255, 0.15) 75%, transparent 75%, transparent);
  background-image: linear-gradient(45deg, rgba(255, 255, 255, 0.15) 25%, transparent 25%, transparent 50%, rgba(255, 255, 255, 0.15) 50%, rgba(255, 255, 255, 0.15) 75%, transparent 75%, transparent);
}
.progress-bar-danger {
  background-color: #d9534f;
}
.progress-striped .progress-bar-danger {
  background-image: -webkit-linear-gradient(45deg, rgba(255, 255, 255, 0.15) 25%, transparent 25%, transparent 50%, rgba(255, 255, 255, 0.15) 50%, rgba(255, 255, 255, 0.15) 75%, transparent 75%, transparent);
  background-image: -o-linear-gradient(45deg, rgba(255, 255, 255, 0.15) 25%, transparent 25%, transparent 50%, rgba(255, 255, 255, 0.15) 50%, rgba(255, 255, 255, 0.15) 75%, transparent 75%, transparent);
  background-image: linear-gradient(45deg, rgba(255, 255, 255, 0.15) 25%, transparent 25%, transparent 50%, rgba(255, 255, 255, 0.15) 50%, rgba(255, 255, 255, 0.15) 75%, transparent 75%, transparent);
}
.media {
  margin-top: 15px;
}
.media:first-child {
  margin-top: 0;
}
.media,
.media-body {
  zoom: 1;
  overflow: hidden;
}
.media-body {
  width: 10000px;
}
.media-object {
  display: block;
}
.media-object.img-thumbnail {
  max-width: none;
}
.media-right,
.media > .pull-right {
  padding-left: 10px;
}
.media-left,
.media > .pull-left {
  padding-right: 10px;
}
.media-left,
.media-right,
.media-body {
  display: table-cell;
  vertical-align: top;
}
.media-middle {
  vertical-align: middle;
}
.media-bottom {
  vertical-align: bottom;
}
.media-heading {
  margin-top: 0;
  margin-bottom: 5px;
}
.media-list {
  padding-left: 0;
  list-style: none;
}
.list-group {
  margin-bottom: 20px;
  padding-left: 0;
}
.list-group-item {
  position: relative;
  display: block;
  padding: 10px 15px;
  margin-bottom: -1px;
  background-color: #fff;
  border: 1px solid #ddd;
}
.list-group-item:first-child {
  border-top-right-radius: 2px;
  border-top-left-radius: 2px;
}
.list-group-item:last-child {
  margin-bottom: 0;
  border-bottom-right-radius: 2px;
  border-bottom-left-radius: 2px;
}
a.list-group-item,
button.list-group-item {
  color: #555;
}
a.list-group-item .list-group-item-heading,
button.list-group-item .list-group-item-heading {
  color: #333;
}
a.list-group-item:hover,
button.list-group-item:hover,
a.list-group-item:focus,
button.list-group-item:focus {
  text-decoration: none;
  color: #555;
  background-color: #f5f5f5;
}
button.list-group-item {
  width: 100%;
  text-align: left;
}
.list-group-item.disabled,
.list-group-item.disabled:hover,
.list-group-item.disabled:focus {
  background-color: #eeeeee;
  color: #777777;
  cursor: not-allowed;
}
.list-group-item.disabled .list-group-item-heading,
.list-group-item.disabled:hover .list-group-item-heading,
.list-group-item.disabled:focus .list-group-item-heading {
  color: inherit;
}
.list-group-item.disabled .list-group-item-text,
.list-group-item.disabled:hover .list-group-item-text,
.list-group-item.disabled:focus .list-group-item-text {
  color: #777777;
}
.list-group-item.active,
.list-group-item.active:hover,
.list-group-item.active:focus {
  z-index: 2;
  color: #fff;
  background-color: #337ab7;
  border-color: #337ab7;
}
.list-group-item.active .list-group-item-heading,
.list-group-item.active:hover .list-group-item-heading,
.list-group-item.active:focus .list-group-item-heading,
.list-group-item.active .list-group-item-heading > small,
.list-group-item.active:hover .list-group-item-heading > small,
.list-group-item.active:focus .list-group-item-heading > small,
.list-group-item.active .list-group-item-heading > .small,
.list-group-item.active:hover .list-group-item-heading > .small,
.list-group-item.active:focus .list-group-item-heading > .small {
  color: inherit;
}
.list-group-item.active .list-group-item-text,
.list-group-item.active:hover .list-group-item-text,
.list-group-item.active:focus .list-group-item-text {
  color: #c7ddef;
}
.list-group-item-success {
  color: #3c763d;
  background-color: #dff0d8;
}
a.list-group-item-success,
button.list-group-item-success {
  color: #3c763d;
}
a.list-group-item-success .list-group-item-heading,
button.list-group-item-success .list-group-item-heading {
  color: inherit;
}
a.list-group-item-success:hover,
button.list-group-item-success:hover,
a.list-group-item-success:focus,
button.list-group-item-success:focus {
  color: #3c763d;
  background-color: #d0e9c6;
}
a.list-group-item-success.active,
button.list-group-item-success.active,
a.list-group-item-success.active:hover,
button.list-group-item-success.active:hover,
a.list-group-item-success.active:focus,
button.list-group-item-success.active:focus {
  color: #fff;
  background-color: #3c763d;
  border-color: #3c763d;
}
.list-group-item-info {
  color: #31708f;
  background-color: #d9edf7;
}
a.list-group-item-info,
button.list-group-item-info {
  color: #31708f;
}
a.list-group-item-info .list-group-item-heading,
button.list-group-item-info .list-group-item-heading {
  color: inherit;
}
a.list-group-item-info:hover,
button.list-group-item-info:hover,
a.list-group-item-info:focus,
button.list-group-item-info:focus {
  color: #31708f;
  background-color: #c4e3f3;
}
a.list-group-item-info.active,
button.list-group-item-info.active,
a.list-group-item-info.active:hover,
button.list-group-item-info.active:hover,
a.list-group-item-info.active:focus,
button.list-group-item-info.active:focus {
  color: #fff;
  background-color: #31708f;
  border-color: #31708f;
}
.list-group-item-warning {
  color: #8a6d3b;
  background-color: #fcf8e3;
}
a.list-group-item-warning,
button.list-group-item-warning {
  color: #8a6d3b;
}
a.list-group-item-warning .list-group-item-heading,
button.list-group-item-warning .list-group-item-heading {
  color: inherit;
}
a.list-group-item-warning:hover,
button.list-group-item-warning:hover,
a.list-group-item-warning:focus,
button.list-group-item-warning:focus {
  color: #8a6d3b;
  background-color: #faf2cc;
}
a.list-group-item-warning.active,
button.list-group-item-warning.active,
a.list-group-item-warning.active:hover,
button.list-group-item-warning.active:hover,
a.list-group-item-warning.active:focus,
button.list-group-item-warning.active:focus {
  color: #fff;
  background-color: #8a6d3b;
  border-color: #8a6d3b;
}
.list-group-item-danger {
  color: #a94442;
  background-color: #f2dede;
}
a.list-group-item-danger,
button.list-group-item-danger {
  color: #a94442;
}
a.list-group-item-danger .list-group-item-heading,
button.list-group-item-danger .list-group-item-heading {
  color: inherit;
}
a.list-group-item-danger:hover,
button.list-group-item-danger:hover,
a.list-group-item-danger:focus,
button.list-group-item-danger:focus {
  color: #a94442;
  background-color: #ebcccc;
}
a.list-group-item-danger.active,
button.list-group-item-danger.active,
a.list-group-item-danger.active:hover,
button.list-group-item-danger.active:hover,
a.list-group-item-danger.active:focus,
button.list-group-item-danger.active:focus {
  color: #fff;
  background-color: #a94442;
  border-color: #a94442;
}
.list-group-item-heading {
  margin-top: 0;
  margin-bottom: 5px;
}
.list-group-item-text {
  margin-bottom: 0;
  line-height: 1.3;
}
.panel {
  margin-bottom: 18px;
  background-color: #fff;
  border: 1px solid transparent;
  border-radius: 2px;
  -webkit-box-shadow: 0 1px 1px rgba(0, 0, 0, 0.05);
  box-shadow: 0 1px 1px rgba(0, 0, 0, 0.05);
}
.panel-body {
  padding: 15px;
}
.panel-heading {
  padding: 10px 15px;
  border-bottom: 1px solid transparent;
  border-top-right-radius: 1px;
  border-top-left-radius: 1px;
}
.panel-heading > .dropdown .dropdown-toggle {
  color: inherit;
}
.panel-title {
  margin-top: 0;
  margin-bottom: 0;
  font-size: 15px;
  color: inherit;
}
.panel-title > a,
.panel-title > small,
.panel-title > .small,
.panel-title > small > a,
.panel-title > .small > a {
  color: inherit;
}
.panel-footer {
  padding: 10px 15px;
  background-color: #f5f5f5;
  border-top: 1px solid #ddd;
  border-bottom-right-radius: 1px;
  border-bottom-left-radius: 1px;
}
.panel > .list-group,
.panel > .panel-collapse > .list-group {
  margin-bottom: 0;
}
.panel > .list-group .list-group-item,
.panel > .panel-collapse > .list-group .list-group-item {
  border-width: 1px 0;
  border-radius: 0;
}
.panel > .list-group:first-child .list-group-item:first-child,
.panel > .panel-collapse > .list-group:first-child .list-group-item:first-child {
  border-top: 0;
  border-top-right-radius: 1px;
  border-top-left-radius: 1px;
}
.panel > .list-group:last-child .list-group-item:last-child,
.panel > .panel-collapse > .list-group:last-child .list-group-item:last-child {
  border-bottom: 0;
  border-bottom-right-radius: 1px;
  border-bottom-left-radius: 1px;
}
.panel > .panel-heading + .panel-collapse > .list-group .list-group-item:first-child {
  border-top-right-radius: 0;
  border-top-left-radius: 0;
}
.panel-heading + .list-group .list-group-item:first-child {
  border-top-width: 0;
}
.list-group + .panel-footer {
  border-top-width: 0;
}
.panel > .table,
.panel > .table-responsive > .table,
.panel > .panel-collapse > .table {
  margin-bottom: 0;
}
.panel > .table caption,
.panel > .table-responsive > .table caption,
.panel > .panel-collapse > .table caption {
  padding-left: 15px;
  padding-right: 15px;
}
.panel > .table:first-child,
.panel > .table-responsive:first-child > .table:first-child {
  border-top-right-radius: 1px;
  border-top-left-radius: 1px;
}
.panel > .table:first-child > thead:first-child > tr:first-child,
.panel > .table-responsive:first-child > .table:first-child > thead:first-child > tr:first-child,
.panel > .table:first-child > tbody:first-child > tr:first-child,
.panel > .table-responsive:first-child > .table:first-child > tbody:first-child > tr:first-child {
  border-top-left-radius: 1px;
  border-top-right-radius: 1px;
}
.panel > .table:first-child > thead:first-child > tr:first-child td:first-child,
.panel > .table-responsive:first-child > .table:first-child > thead:first-child > tr:first-child td:first-child,
.panel > .table:first-child > tbody:first-child > tr:first-child td:first-child,
.panel > .table-responsive:first-child > .table:first-child > tbody:first-child > tr:first-child td:first-child,
.panel > .table:first-child > thead:first-child > tr:first-child th:first-child,
.panel > .table-responsive:first-child > .table:first-child > thead:first-child > tr:first-child th:first-child,
.panel > .table:first-child > tbody:first-child > tr:first-child th:first-child,
.panel > .table-responsive:first-child > .table:first-child > tbody:first-child > tr:first-child th:first-child {
  border-top-left-radius: 1px;
}
.panel > .table:first-child > thead:first-child > tr:first-child td:last-child,
.panel > .table-responsive:first-child > .table:first-child > thead:first-child > tr:first-child td:last-child,
.panel > .table:first-child > tbody:first-child > tr:first-child td:last-child,
.panel > .table-responsive:first-child > .table:first-child > tbody:first-child > tr:first-child td:last-child,
.panel > .table:first-child > thead:first-child > tr:first-child th:last-child,
.panel > .table-responsive:first-child > .table:first-child > thead:first-child > tr:first-child th:last-child,
.panel > .table:first-child > tbody:first-child > tr:first-child th:last-child,
.panel > .table-responsive:first-child > .table:first-child > tbody:first-child > tr:first-child th:last-child {
  border-top-right-radius: 1px;
}
.panel > .table:last-child,
.panel > .table-responsive:last-child > .table:last-child {
  border-bottom-right-radius: 1px;
  border-bottom-left-radius: 1px;
}
.panel > .table:last-child > tbody:last-child > tr:last-child,
.panel > .table-responsive:last-child > .table:last-child > tbody:last-child > tr:last-child,
.panel > .table:last-child > tfoot:last-child > tr:last-child,
.panel > .table-responsive:last-child > .table:last-child > tfoot:last-child > tr:last-child {
  border-bottom-left-radius: 1px;
  border-bottom-right-radius: 1px;
}
.panel > .table:last-child > tbody:last-child > tr:last-child td:first-child,
.panel > .table-responsive:last-child > .table:last-child > tbody:last-child > tr:last-child td:first-child,
.panel > .table:last-child > tfoot:last-child > tr:last-child td:first-child,
.panel > .table-responsive:last-child > .table:last-child > tfoot:last-child > tr:last-child td:first-child,
.panel > .table:last-child > tbody:last-child > tr:last-child th:first-child,
.panel > .table-responsive:last-child > .table:last-child > tbody:last-child > tr:last-child th:first-child,
.panel > .table:last-child > tfoot:last-child > tr:last-child th:first-child,
.panel > .table-responsive:last-child > .table:last-child > tfoot:last-child > tr:last-child th:first-child {
  border-bottom-left-radius: 1px;
}
.panel > .table:last-child > tbody:last-child > tr:last-child td:last-child,
.panel > .table-responsive:last-child > .table:last-child > tbody:last-child > tr:last-child td:last-child,
.panel > .table:last-child > tfoot:last-child > tr:last-child td:last-child,
.panel > .table-responsive:last-child > .table:last-child > tfoot:last-child > tr:last-child td:last-child,
.panel > .table:last-child > tbody:last-child > tr:last-child th:last-child,
.panel > .table-responsive:last-child > .table:last-child > tbody:last-child > tr:last-child th:last-child,
.panel > .table:last-child > tfoot:last-child > tr:last-child th:last-child,
.panel > .table-responsive:last-child > .table:last-child > tfoot:last-child > tr:last-child th:last-child {
  border-bottom-right-radius: 1px;
}
.panel > .panel-body + .table,
.panel > .panel-body + .table-responsive,
.panel > .table + .panel-body,
.panel > .table-responsive + .panel-body {
  border-top: 1px solid #ddd;
}
.panel > .table > tbody:first-child > tr:first-child th,
.panel > .table > tbody:first-child > tr:first-child td {
  border-top: 0;
}
.panel > .table-bordered,
.panel > .table-responsive > .table-bordered {
  border: 0;
}
.panel > .table-bordered > thead > tr > th:first-child,
.panel > .table-responsive > .table-bordered > thead > tr > th:first-child,
.panel > .table-bordered > tbody > tr > th:first-child,
.panel > .table-responsive > .table-bordered > tbody > tr > th:first-child,
.panel > .table-bordered > tfoot > tr > th:first-child,
.panel > .table-responsive > .table-bordered > tfoot > tr > th:first-child,
.panel > .table-bordered > thead > tr > td:first-child,
.panel > .table-responsive > .table-bordered > thead > tr > td:first-child,
.panel > .table-bordered > tbody > tr > td:first-child,
.panel > .table-responsive > .table-bordered > tbody > tr > td:first-child,
.panel > .table-bordered > tfoot > tr > td:first-child,
.panel > .table-responsive > .table-bordered > tfoot > tr > td:first-child {
  border-left: 0;
}
.panel > .table-bordered > thead > tr > th:last-child,
.panel > .table-responsive > .table-bordered > thead > tr > th:last-child,
.panel > .table-bordered > tbody > tr > th:last-child,
.panel > .table-responsive > .table-bordered > tbody > tr > th:last-child,
.panel > .table-bordered > tfoot > tr > th:last-child,
.panel > .table-responsive > .table-bordered > tfoot > tr > th:last-child,
.panel > .table-bordered > thead > tr > td:last-child,
.panel > .table-responsive > .table-bordered > thead > tr > td:last-child,
.panel > .table-bordered > tbody > tr > td:last-child,
.panel > .table-responsive > .table-bordered > tbody > tr > td:last-child,
.panel > .table-bordered > tfoot > tr > td:last-child,
.panel > .table-responsive > .table-bordered > tfoot > tr > td:last-child {
  border-right: 0;
}
.panel > .table-bordered > thead > tr:first-child > td,
.panel > .table-responsive > .table-bordered > thead > tr:first-child > td,
.panel > .table-bordered > tbody > tr:first-child > td,
.panel > .table-responsive > .table-bordered > tbody > tr:first-child > td,
.panel > .table-bordered > thead > tr:first-child > th,
.panel > .table-responsive > .table-bordered > thead > tr:first-child > th,
.panel > .table-bordered > tbody > tr:first-child > th,
.panel > .table-responsive > .table-bordered > tbody > tr:first-child > th {
  border-bottom: 0;
}
.panel > .table-bordered > tbody > tr:last-child > td,
.panel > .table-responsive > .table-bordered > tbody > tr:last-child > td,
.panel > .table-bordered > tfoot > tr:last-child > td,
.panel > .table-responsive > .table-bordered > tfoot > tr:last-child > td,
.panel > .table-bordered > tbody > tr:last-child > th,
.panel > .table-responsive > .table-bordered > tbody > tr:last-child > th,
.panel > .table-bordered > tfoot > tr:last-child > th,
.panel > .table-responsive > .table-bordered > tfoot > tr:last-child > th {
  border-bottom: 0;
}
.panel > .table-responsive {
  border: 0;
  margin-bottom: 0;
}
.panel-group {
  margin-bottom: 18px;
}
.panel-group .panel {
  margin-bottom: 0;
  border-radius: 2px;
}
.panel-group .panel + .panel {
  margin-top: 5px;
}
.panel-group .panel-heading {
  border-bottom: 0;
}
.panel-group .panel-heading + .panel-collapse > .panel-body,
.panel-group .panel-heading + .panel-collapse > .list-group {
  border-top: 1px solid #ddd;
}
.panel-group .panel-footer {
  border-top: 0;
}
.panel-group .panel-footer + .panel-collapse .panel-body {
  border-bottom: 1px solid #ddd;
}
.panel-default {
  border-color: #ddd;
}
.panel-default > .panel-heading {
  color: #333333;
  background-color: #f5f5f5;
  border-color: #ddd;
}
.panel-default > .panel-heading + .panel-collapse > .panel-body {
  border-top-color: #ddd;
}
.panel-default > .panel-heading .badge {
  color: #f5f5f5;
  background-color: #333333;
}
.panel-default > .panel-footer + .panel-collapse > .panel-body {
  border-bottom-color: #ddd;
}
.panel-primary {
  border-color: #337ab7;
}
.panel-primary > .panel-heading {
  color: #fff;
  background-color: #337ab7;
  border-color: #337ab7;
}
.panel-primary > .panel-heading + .panel-collapse > .panel-body {
  border-top-color: #337ab7;
}
.panel-primary > .panel-heading .badge {
  color: #337ab7;
  background-color: #fff;
}
.panel-primary > .panel-footer + .panel-collapse > .panel-body {
  border-bottom-color: #337ab7;
}
.panel-success {
  border-color: #d6e9c6;
}
.panel-success > .panel-heading {
  color: #3c763d;
  background-color: #dff0d8;
  border-color: #d6e9c6;
}
.panel-success > .panel-heading + .panel-collapse > .panel-body {
  border-top-color: #d6e9c6;
}
.panel-success > .panel-heading .badge {
  color: #dff0d8;
  background-color: #3c763d;
}
.panel-success > .panel-footer + .panel-collapse > .panel-body {
  border-bottom-color: #d6e9c6;
}
.panel-info {
  border-color: #bce8f1;
}
.panel-info > .panel-heading {
  color: #31708f;
  background-color: #d9edf7;
  border-color: #bce8f1;
}
.panel-info > .panel-heading + .panel-collapse > .panel-body {
  border-top-color: #bce8f1;
}
.panel-info > .panel-heading .badge {
  color: #d9edf7;
  background-color: #31708f;
}
.panel-info > .panel-footer + .panel-collapse > .panel-body {
  border-bottom-color: #bce8f1;
}
.panel-warning {
  border-color: #faebcc;
}
.panel-warning > .panel-heading {
  color: #8a6d3b;
  background-color: #fcf8e3;
  border-color: #faebcc;
}
.panel-warning > .panel-heading + .panel-collapse > .panel-body {
  border-top-color: #faebcc;
}
.panel-warning > .panel-heading .badge {
  color: #fcf8e3;
  background-color: #8a6d3b;
}
.panel-warning > .panel-footer + .panel-collapse > .panel-body {
  border-bottom-color: #faebcc;
}
.panel-danger {
  border-color: #ebccd1;
}
.panel-danger > .panel-heading {
  color: #a94442;
  background-color: #f2dede;
  border-color: #ebccd1;
}
.panel-danger > .panel-heading + .panel-collapse > .panel-body {
  border-top-color: #ebccd1;
}
.panel-danger > .panel-heading .badge {
  color: #f2dede;
  background-color: #a94442;
}
.panel-danger > .panel-footer + .panel-collapse > .panel-body {
  border-bottom-color: #ebccd1;
}
.embed-responsive {
  position: relative;
  display: block;
  height: 0;
  padding: 0;
  overflow: hidden;
}
.embed-responsive .embed-responsive-item,
.embed-responsive iframe,
.embed-responsive embed,
.embed-responsive object,
.embed-responsive video {
  position: absolute;
  top: 0;
  left: 0;
  bottom: 0;
  height: 100%;
  width: 100%;
  border: 0;
}
.embed-responsive-16by9 {
  padding-bottom: 56.25%;
}
.embed-responsive-4by3 {
  padding-bottom: 75%;
}
.well {
  min-height: 20px;
  padding: 19px;
  margin-bottom: 20px;
  background-color: #f5f5f5;
  border: 1px solid #e3e3e3;
  border-radius: 2px;
  -webkit-box-shadow: inset 0 1px 1px rgba(0, 0, 0, 0.05);
  box-shadow: inset 0 1px 1px rgba(0, 0, 0, 0.05);
}
.well blockquote {
  border-color: #ddd;
  border-color: rgba(0, 0, 0, 0.15);
}
.well-lg {
  padding: 24px;
  border-radius: 3px;
}
.well-sm {
  padding: 9px;
  border-radius: 1px;
}
.close {
  float: right;
  font-size: 19.5px;
  font-weight: bold;
  line-height: 1;
  color: #000;
  text-shadow: 0 1px 0 #fff;
  opacity: 0.2;
  filter: alpha(opacity=20);
}
.close:hover,
.close:focus {
  color: #000;
  text-decoration: none;
  cursor: pointer;
  opacity: 0.5;
  filter: alpha(opacity=50);
}
button.close {
  padding: 0;
  cursor: pointer;
  background: transparent;
  border: 0;
  -webkit-appearance: none;
}
.modal-open {
  overflow: hidden;
}
.modal {
  display: none;
  overflow: hidden;
  position: fixed;
  top: 0;
  right: 0;
  bottom: 0;
  left: 0;
  z-index: 1050;
  -webkit-overflow-scrolling: touch;
  outline: 0;
}
.modal.fade .modal-dialog {
  -webkit-transform: translate(0, -25%);
  -ms-transform: translate(0, -25%);
  -o-transform: translate(0, -25%);
  transform: translate(0, -25%);
  -webkit-transition: -webkit-transform 0.3s ease-out;
  -moz-transition: -moz-transform 0.3s ease-out;
  -o-transition: -o-transform 0.3s ease-out;
  transition: transform 0.3s ease-out;
}
.modal.in .modal-dialog {
  -webkit-transform: translate(0, 0);
  -ms-transform: translate(0, 0);
  -o-transform: translate(0, 0);
  transform: translate(0, 0);
}
.modal-open .modal {
  overflow-x: hidden;
  overflow-y: auto;
}
.modal-dialog {
  position: relative;
  width: auto;
  margin: 10px;
}
.modal-content {
  position: relative;
  background-color: #fff;
  border: 1px solid #999;
  border: 1px solid rgba(0, 0, 0, 0.2);
  border-radius: 3px;
  -webkit-box-shadow: 0 3px 9px rgba(0, 0, 0, 0.5);
  box-shadow: 0 3px 9px rgba(0, 0, 0, 0.5);
  background-clip: padding-box;
  outline: 0;
}
.modal-backdrop {
  position: fixed;
  top: 0;
  right: 0;
  bottom: 0;
  left: 0;
  z-index: 1040;
  background-color: #000;
}
.modal-backdrop.fade {
  opacity: 0;
  filter: alpha(opacity=0);
}
.modal-backdrop.in {
  opacity: 0.5;
  filter: alpha(opacity=50);
}
.modal-header {
  padding: 15px;
  border-bottom: 1px solid #e5e5e5;
}
.modal-header .close {
  margin-top: -2px;
}
.modal-title {
  margin: 0;
  line-height: 1.42857143;
}
.modal-body {
  position: relative;
  padding: 15px;
}
.modal-footer {
  padding: 15px;
  text-align: right;
  border-top: 1px solid #e5e5e5;
}
.modal-footer .btn + .btn {
  margin-left: 5px;
  margin-bottom: 0;
}
.modal-footer .btn-group .btn + .btn {
  margin-left: -1px;
}
.modal-footer .btn-block + .btn-block {
  margin-left: 0;
}
.modal-scrollbar-measure {
  position: absolute;
  top: -9999px;
  width: 50px;
  height: 50px;
  overflow: scroll;
}
@media (min-width: 768px) {
  .modal-dialog {
    width: 600px;
    margin: 30px auto;
  }
  .modal-content {
    -webkit-box-shadow: 0 5px 15px rgba(0, 0, 0, 0.5);
    box-shadow: 0 5px 15px rgba(0, 0, 0, 0.5);
  }
  .modal-sm {
    width: 300px;
  }
}
@media (min-width: 992px) {
  .modal-lg {
    width: 900px;
  }
}
.tooltip {
  position: absolute;
  z-index: 1070;
  display: block;
  font-family: "Helvetica Neue", Helvetica, Arial, sans-serif;
  font-style: normal;
  font-weight: normal;
  letter-spacing: normal;
  line-break: auto;
  line-height: 1.42857143;
  text-align: left;
  text-align: start;
  text-decoration: none;
  text-shadow: none;
  text-transform: none;
  white-space: normal;
  word-break: normal;
  word-spacing: normal;
  word-wrap: normal;
  font-size: 12px;
  opacity: 0;
  filter: alpha(opacity=0);
}
.tooltip.in {
  opacity: 0.9;
  filter: alpha(opacity=90);
}
.tooltip.top {
  margin-top: -3px;
  padding: 5px 0;
}
.tooltip.right {
  margin-left: 3px;
  padding: 0 5px;
}
.tooltip.bottom {
  margin-top: 3px;
  padding: 5px 0;
}
.tooltip.left {
  margin-left: -3px;
  padding: 0 5px;
}
.tooltip-inner {
  max-width: 200px;
  padding: 3px 8px;
  color: #fff;
  text-align: center;
  background-color: #000;
  border-radius: 2px;
}
.tooltip-arrow {
  position: absolute;
  width: 0;
  height: 0;
  border-color: transparent;
  border-style: solid;
}
.tooltip.top .tooltip-arrow {
  bottom: 0;
  left: 50%;
  margin-left: -5px;
  border-width: 5px 5px 0;
  border-top-color: #000;
}
.tooltip.top-left .tooltip-arrow {
  bottom: 0;
  right: 5px;
  margin-bottom: -5px;
  border-width: 5px 5px 0;
  border-top-color: #000;
}
.tooltip.top-right .tooltip-arrow {
  bottom: 0;
  left: 5px;
  margin-bottom: -5px;
  border-width: 5px 5px 0;
  border-top-color: #000;
}
.tooltip.right .tooltip-arrow {
  top: 50%;
  left: 0;
  margin-top: -5px;
  border-width: 5px 5px 5px 0;
  border-right-color: #000;
}
.tooltip.left .tooltip-arrow {
  top: 50%;
  right: 0;
  margin-top: -5px;
  border-width: 5px 0 5px 5px;
  border-left-color: #000;
}
.tooltip.bottom .tooltip-arrow {
  top: 0;
  left: 50%;
  margin-left: -5px;
  border-width: 0 5px 5px;
  border-bottom-color: #000;
}
.tooltip.bottom-left .tooltip-arrow {
  top: 0;
  right: 5px;
  margin-top: -5px;
  border-width: 0 5px 5px;
  border-bottom-color: #000;
}
.tooltip.bottom-right .tooltip-arrow {
  top: 0;
  left: 5px;
  margin-top: -5px;
  border-width: 0 5px 5px;
  border-bottom-color: #000;
}
.popover {
  position: absolute;
  top: 0;
  left: 0;
  z-index: 1060;
  display: none;
  max-width: 276px;
  padding: 1px;
  font-family: "Helvetica Neue", Helvetica, Arial, sans-serif;
  font-style: normal;
  font-weight: normal;
  letter-spacing: normal;
  line-break: auto;
  line-height: 1.42857143;
  text-align: left;
  text-align: start;
  text-decoration: none;
  text-shadow: none;
  text-transform: none;
  white-space: normal;
  word-break: normal;
  word-spacing: normal;
  word-wrap: normal;
  font-size: 13px;
  background-color: #fff;
  background-clip: padding-box;
  border: 1px solid #ccc;
  border: 1px solid rgba(0, 0, 0, 0.2);
  border-radius: 3px;
  -webkit-box-shadow: 0 5px 10px rgba(0, 0, 0, 0.2);
  box-shadow: 0 5px 10px rgba(0, 0, 0, 0.2);
}
.popover.top {
  margin-top: -10px;
}
.popover.right {
  margin-left: 10px;
}
.popover.bottom {
  margin-top: 10px;
}
.popover.left {
  margin-left: -10px;
}
.popover-title {
  margin: 0;
  padding: 8px 14px;
  font-size: 13px;
  background-color: #f7f7f7;
  border-bottom: 1px solid #ebebeb;
  border-radius: 2px 2px 0 0;
}
.popover-content {
  padding: 9px 14px;
}
.popover > .arrow,
.popover > .arrow:after {
  position: absolute;
  display: block;
  width: 0;
  height: 0;
  border-color: transparent;
  border-style: solid;
}
.popover > .arrow {
  border-width: 11px;
}
.popover > .arrow:after {
  border-width: 10px;
  content: "";
}
.popover.top > .arrow {
  left: 50%;
  margin-left: -11px;
  border-bottom-width: 0;
  border-top-color: #999999;
  border-top-color: rgba(0, 0, 0, 0.25);
  bottom: -11px;
}
.popover.top > .arrow:after {
  content: " ";
  bottom: 1px;
  margin-left: -10px;
  border-bottom-width: 0;
  border-top-color: #fff;
}
.popover.right > .arrow {
  top: 50%;
  left: -11px;
  margin-top: -11px;
  border-left-width: 0;
  border-right-color: #999999;
  border-right-color: rgba(0, 0, 0, 0.25);
}
.popover.right > .arrow:after {
  content: " ";
  left: 1px;
  bottom: -10px;
  border-left-width: 0;
  border-right-color: #fff;
}
.popover.bottom > .arrow {
  left: 50%;
  margin-left: -11px;
  border-top-width: 0;
  border-bottom-color: #999999;
  border-bottom-color: rgba(0, 0, 0, 0.25);
  top: -11px;
}
.popover.bottom > .arrow:after {
  content: " ";
  top: 1px;
  margin-left: -10px;
  border-top-width: 0;
  border-bottom-color: #fff;
}
.popover.left > .arrow {
  top: 50%;
  right: -11px;
  margin-top: -11px;
  border-right-width: 0;
  border-left-color: #999999;
  border-left-color: rgba(0, 0, 0, 0.25);
}
.popover.left > .arrow:after {
  content: " ";
  right: 1px;
  border-right-width: 0;
  border-left-color: #fff;
  bottom: -10px;
}
.carousel {
  position: relative;
}
.carousel-inner {
  position: relative;
  overflow: hidden;
  width: 100%;
}
.carousel-inner > .item {
  display: none;
  position: relative;
  -webkit-transition: 0.6s ease-in-out left;
  -o-transition: 0.6s ease-in-out left;
  transition: 0.6s ease-in-out left;
}
.carousel-inner > .item > img,
.carousel-inner > .item > a > img {
  line-height: 1;
}
@media all and (transform-3d), (-webkit-transform-3d) {
  .carousel-inner > .item {
    -webkit-transition: -webkit-transform 0.6s ease-in-out;
    -moz-transition: -moz-transform 0.6s ease-in-out;
    -o-transition: -o-transform 0.6s ease-in-out;
    transition: transform 0.6s ease-in-out;
    -webkit-backface-visibility: hidden;
    -moz-backface-visibility: hidden;
    backface-visibility: hidden;
    -webkit-perspective: 1000px;
    -moz-perspective: 1000px;
    perspective: 1000px;
  }
  .carousel-inner > .item.next,
  .carousel-inner > .item.active.right {
    -webkit-transform: translate3d(100%, 0, 0);
    transform: translate3d(100%, 0, 0);
    left: 0;
  }
  .carousel-inner > .item.prev,
  .carousel-inner > .item.active.left {
    -webkit-transform: translate3d(-100%, 0, 0);
    transform: translate3d(-100%, 0, 0);
    left: 0;
  }
  .carousel-inner > .item.next.left,
  .carousel-inner > .item.prev.right,
  .carousel-inner > .item.active {
    -webkit-transform: translate3d(0, 0, 0);
    transform: translate3d(0, 0, 0);
    left: 0;
  }
}
.carousel-inner > .active,
.carousel-inner > .next,
.carousel-inner > .prev {
  display: block;
}
.carousel-inner > .active {
  left: 0;
}
.carousel-inner > .next,
.carousel-inner > .prev {
  position: absolute;
  top: 0;
  width: 100%;
}
.carousel-inner > .next {
  left: 100%;
}
.carousel-inner > .prev {
  left: -100%;
}
.carousel-inner > .next.left,
.carousel-inner > .prev.right {
  left: 0;
}
.carousel-inner > .active.left {
  left: -100%;
}
.carousel-inner > .active.right {
  left: 100%;
}
.carousel-control {
  position: absolute;
  top: 0;
  left: 0;
  bottom: 0;
  width: 15%;
  opacity: 0.5;
  filter: alpha(opacity=50);
  font-size: 20px;
  color: #fff;
  text-align: center;
  text-shadow: 0 1px 2px rgba(0, 0, 0, 0.6);
  background-color: rgba(0, 0, 0, 0);
}
.carousel-control.left {
  background-image: -webkit-linear-gradient(left, rgba(0, 0, 0, 0.5) 0%, rgba(0, 0, 0, 0.0001) 100%);
  background-image: -o-linear-gradient(left, rgba(0, 0, 0, 0.5) 0%, rgba(0, 0, 0, 0.0001) 100%);
  background-image: linear-gradient(to right, rgba(0, 0, 0, 0.5) 0%, rgba(0, 0, 0, 0.0001) 100%);
  background-repeat: repeat-x;
  filter: progid:DXImageTransform.Microsoft.gradient(startColorstr='#80000000', endColorstr='#00000000', GradientType=1);
}
.carousel-control.right {
  left: auto;
  right: 0;
  background-image: -webkit-linear-gradient(left, rgba(0, 0, 0, 0.0001) 0%, rgba(0, 0, 0, 0.5) 100%);
  background-image: -o-linear-gradient(left, rgba(0, 0, 0, 0.0001) 0%, rgba(0, 0, 0, 0.5) 100%);
  background-image: linear-gradient(to right, rgba(0, 0, 0, 0.0001) 0%, rgba(0, 0, 0, 0.5) 100%);
  background-repeat: repeat-x;
  filter: progid:DXImageTransform.Microsoft.gradient(startColorstr='#00000000', endColorstr='#80000000', GradientType=1);
}
.carousel-control:hover,
.carousel-control:focus {
  outline: 0;
  color: #fff;
  text-decoration: none;
  opacity: 0.9;
  filter: alpha(opacity=90);
}
.carousel-control .icon-prev,
.carousel-control .icon-next,
.carousel-control .glyphicon-chevron-left,
.carousel-control .glyphicon-chevron-right {
  position: absolute;
  top: 50%;
  margin-top: -10px;
  z-index: 5;
  display: inline-block;
}
.carousel-control .icon-prev,
.carousel-control .glyphicon-chevron-left {
  left: 50%;
  margin-left: -10px;
}
.carousel-control .icon-next,
.carousel-control .glyphicon-chevron-right {
  right: 50%;
  margin-right: -10px;
}
.carousel-control .icon-prev,
.carousel-control .icon-next {
  width: 20px;
  height: 20px;
  line-height: 1;
  font-family: serif;
}
.carousel-control .icon-prev:before {
  content: '\2039';
}
.carousel-control .icon-next:before {
  content: '\203a';
}
.carousel-indicators {
  position: absolute;
  bottom: 10px;
  left: 50%;
  z-index: 15;
  width: 60%;
  margin-left: -30%;
  padding-left: 0;
  list-style: none;
  text-align: center;
}
.carousel-indicators li {
  display: inline-block;
  width: 10px;
  height: 10px;
  margin: 1px;
  text-indent: -999px;
  border: 1px solid #fff;
  border-radius: 10px;
  cursor: pointer;
  background-color: #000 \9;
  background-color: rgba(0, 0, 0, 0);
}
.carousel-indicators .active {
  margin: 0;
  width: 12px;
  height: 12px;
  background-color: #fff;
}
.carousel-caption {
  position: absolute;
  left: 15%;
  right: 15%;
  bottom: 20px;
  z-index: 10;
  padding-top: 20px;
  padding-bottom: 20px;
  color: #fff;
  text-align: center;
  text-shadow: 0 1px 2px rgba(0, 0, 0, 0.6);
}
.carousel-caption .btn {
  text-shadow: none;
}
@media screen and (min-width: 768px) {
  .carousel-control .glyphicon-chevron-left,
  .carousel-control .glyphicon-chevron-right,
  .carousel-control .icon-prev,
  .carousel-control .icon-next {
    width: 30px;
    height: 30px;
    margin-top: -10px;
    font-size: 30px;
  }
  .carousel-control .glyphicon-chevron-left,
  .carousel-control .icon-prev {
    margin-left: -10px;
  }
  .carousel-control .glyphicon-chevron-right,
  .carousel-control .icon-next {
    margin-right: -10px;
  }
  .carousel-caption {
    left: 20%;
    right: 20%;
    padding-bottom: 30px;
  }
  .carousel-indicators {
    bottom: 20px;
  }
}
.clearfix:before,
.clearfix:after,
.dl-horizontal dd:before,
.dl-horizontal dd:after,
.container:before,
.container:after,
.container-fluid:before,
.container-fluid:after,
.row:before,
.row:after,
.form-horizontal .form-group:before,
.form-horizontal .form-group:after,
.btn-toolbar:before,
.btn-toolbar:after,
.btn-group-vertical > .btn-group:before,
.btn-group-vertical > .btn-group:after,
.nav:before,
.nav:after,
.navbar:before,
.navbar:after,
.navbar-header:before,
.navbar-header:after,
.navbar-collapse:before,
.navbar-collapse:after,
.pager:before,
.pager:after,
.panel-body:before,
.panel-body:after,
.modal-header:before,
.modal-header:after,
.modal-footer:before,
.modal-footer:after,
.item_buttons:before,
.item_buttons:after {
  content: " ";
  display: table;
}
.clearfix:after,
.dl-horizontal dd:after,
.container:after,
.container-fluid:after,
.row:after,
.form-horizontal .form-group:after,
.btn-toolbar:after,
.btn-group-vertical > .btn-group:after,
.nav:after,
.navbar:after,
.navbar-header:after,
.navbar-collapse:after,
.pager:after,
.panel-body:after,
.modal-header:after,
.modal-footer:after,
.item_buttons:after {
  clear: both;
}
.center-block {
  display: block;
  margin-left: auto;
  margin-right: auto;
}
.pull-right {
  float: right !important;
}
.pull-left {
  float: left !important;
}
.hide {
  display: none !important;
}
.show {
  display: block !important;
}
.invisible {
  visibility: hidden;
}
.text-hide {
  font: 0/0 a;
  color: transparent;
  text-shadow: none;
  background-color: transparent;
  border: 0;
}
.hidden {
  display: none !important;
}
.affix {
  position: fixed;
}
@-ms-viewport {
  width: device-width;
}
.visible-xs,
.visible-sm,
.visible-md,
.visible-lg {
  display: none !important;
}
.visible-xs-block,
.visible-xs-inline,
.visible-xs-inline-block,
.visible-sm-block,
.visible-sm-inline,
.visible-sm-inline-block,
.visible-md-block,
.visible-md-inline,
.visible-md-inline-block,
.visible-lg-block,
.visible-lg-inline,
.visible-lg-inline-block {
  display: none !important;
}
@media (max-width: 767px) {
  .visible-xs {
    display: block !important;
  }
  table.visible-xs {
    display: table !important;
  }
  tr.visible-xs {
    display: table-row !important;
  }
  th.visible-xs,
  td.visible-xs {
    display: table-cell !important;
  }
}
@media (max-width: 767px) {
  .visible-xs-block {
    display: block !important;
  }
}
@media (max-width: 767px) {
  .visible-xs-inline {
    display: inline !important;
  }
}
@media (max-width: 767px) {
  .visible-xs-inline-block {
    display: inline-block !important;
  }
}
@media (min-width: 768px) and (max-width: 991px) {
  .visible-sm {
    display: block !important;
  }
  table.visible-sm {
    display: table !important;
  }
  tr.visible-sm {
    display: table-row !important;
  }
  th.visible-sm,
  td.visible-sm {
    display: table-cell !important;
  }
}
@media (min-width: 768px) and (max-width: 991px) {
  .visible-sm-block {
    display: block !important;
  }
}
@media (min-width: 768px) and (max-width: 991px) {
  .visible-sm-inline {
    display: inline !important;
  }
}
@media (min-width: 768px) and (max-width: 991px) {
  .visible-sm-inline-block {
    display: inline-block !important;
  }
}
@media (min-width: 992px) and (max-width: 1199px) {
  .visible-md {
    display: block !important;
  }
  table.visible-md {
    display: table !important;
  }
  tr.visible-md {
    display: table-row !important;
  }
  th.visible-md,
  td.visible-md {
    display: table-cell !important;
  }
}
@media (min-width: 992px) and (max-width: 1199px) {
  .visible-md-block {
    display: block !important;
  }
}
@media (min-width: 992px) and (max-width: 1199px) {
  .visible-md-inline {
    display: inline !important;
  }
}
@media (min-width: 992px) and (max-width: 1199px) {
  .visible-md-inline-block {
    display: inline-block !important;
  }
}
@media (min-width: 1200px) {
  .visible-lg {
    display: block !important;
  }
  table.visible-lg {
    display: table !important;
  }
  tr.visible-lg {
    display: table-row !important;
  }
  th.visible-lg,
  td.visible-lg {
    display: table-cell !important;
  }
}
@media (min-width: 1200px) {
  .visible-lg-block {
    display: block !important;
  }
}
@media (min-width: 1200px) {
  .visible-lg-inline {
    display: inline !important;
  }
}
@media (min-width: 1200px) {
  .visible-lg-inline-block {
    display: inline-block !important;
  }
}
@media (max-width: 767px) {
  .hidden-xs {
    display: none !important;
  }
}
@media (min-width: 768px) and (max-width: 991px) {
  .hidden-sm {
    display: none !important;
  }
}
@media (min-width: 992px) and (max-width: 1199px) {
  .hidden-md {
    display: none !important;
  }
}
@media (min-width: 1200px) {
  .hidden-lg {
    display: none !important;
  }
}
.visible-print {
  display: none !important;
}
@media print {
  .visible-print {
    display: block !important;
  }
  table.visible-print {
    display: table !important;
  }
  tr.visible-print {
    display: table-row !important;
  }
  th.visible-print,
  td.visible-print {
    display: table-cell !important;
  }
}
.visible-print-block {
  display: none !important;
}
@media print {
  .visible-print-block {
    display: block !important;
  }
}
.visible-print-inline {
  display: none !important;
}
@media print {
  .visible-print-inline {
    display: inline !important;
  }
}
.visible-print-inline-block {
  display: none !important;
}
@media print {
  .visible-print-inline-block {
    display: inline-block !important;
  }
}
@media print {
  .hidden-print {
    display: none !important;
  }
}
/*!
*
* Font Awesome
*
*/
/*!
 *  Font Awesome 4.7.0 by @davegandy - http://fontawesome.io - @fontawesome
 *  License - http://fontawesome.io/license (Font: SIL OFL 1.1, CSS: MIT License)
 */
/* FONT PATH
 * -------------------------- */
@font-face {
  font-family: 'FontAwesome';
  src: url('../components/font-awesome/fonts/fontawesome-webfont.eot?v=4.7.0');
  src: url('../components/font-awesome/fonts/fontawesome-webfont.eot?#iefix&v=4.7.0') format('embedded-opentype'), url('../components/font-awesome/fonts/fontawesome-webfont.woff2?v=4.7.0') format('woff2'), url('../components/font-awesome/fonts/fontawesome-webfont.woff?v=4.7.0') format('woff'), url('../components/font-awesome/fonts/fontawesome-webfont.ttf?v=4.7.0') format('truetype'), url('../components/font-awesome/fonts/fontawesome-webfont.svg?v=4.7.0#fontawesomeregular') format('svg');
  font-weight: normal;
  font-style: normal;
}
.fa {
  display: inline-block;
  font: normal normal normal 14px/1 FontAwesome;
  font-size: inherit;
  text-rendering: auto;
  -webkit-font-smoothing: antialiased;
  -moz-osx-font-smoothing: grayscale;
}
/* makes the font 33% larger relative to the icon container */
.fa-lg {
  font-size: 1.33333333em;
  line-height: 0.75em;
  vertical-align: -15%;
}
.fa-2x {
  font-size: 2em;
}
.fa-3x {
  font-size: 3em;
}
.fa-4x {
  font-size: 4em;
}
.fa-5x {
  font-size: 5em;
}
.fa-fw {
  width: 1.28571429em;
  text-align: center;
}
.fa-ul {
  padding-left: 0;
  margin-left: 2.14285714em;
  list-style-type: none;
}
.fa-ul > li {
  position: relative;
}
.fa-li {
  position: absolute;
  left: -2.14285714em;
  width: 2.14285714em;
  top: 0.14285714em;
  text-align: center;
}
.fa-li.fa-lg {
  left: -1.85714286em;
}
.fa-border {
  padding: .2em .25em .15em;
  border: solid 0.08em #eee;
  border-radius: .1em;
}
.fa-pull-left {
  float: left;
}
.fa-pull-right {
  float: right;
}
.fa.fa-pull-left {
  margin-right: .3em;
}
.fa.fa-pull-right {
  margin-left: .3em;
}
/* Deprecated as of 4.4.0 */
.pull-right {
  float: right;
}
.pull-left {
  float: left;
}
.fa.pull-left {
  margin-right: .3em;
}
.fa.pull-right {
  margin-left: .3em;
}
.fa-spin {
  -webkit-animation: fa-spin 2s infinite linear;
  animation: fa-spin 2s infinite linear;
}
.fa-pulse {
  -webkit-animation: fa-spin 1s infinite steps(8);
  animation: fa-spin 1s infinite steps(8);
}
@-webkit-keyframes fa-spin {
  0% {
    -webkit-transform: rotate(0deg);
    transform: rotate(0deg);
  }
  100% {
    -webkit-transform: rotate(359deg);
    transform: rotate(359deg);
  }
}
@keyframes fa-spin {
  0% {
    -webkit-transform: rotate(0deg);
    transform: rotate(0deg);
  }
  100% {
    -webkit-transform: rotate(359deg);
    transform: rotate(359deg);
  }
}
.fa-rotate-90 {
  -ms-filter: "progid:DXImageTransform.Microsoft.BasicImage(rotation=1)";
  -webkit-transform: rotate(90deg);
  -ms-transform: rotate(90deg);
  transform: rotate(90deg);
}
.fa-rotate-180 {
  -ms-filter: "progid:DXImageTransform.Microsoft.BasicImage(rotation=2)";
  -webkit-transform: rotate(180deg);
  -ms-transform: rotate(180deg);
  transform: rotate(180deg);
}
.fa-rotate-270 {
  -ms-filter: "progid:DXImageTransform.Microsoft.BasicImage(rotation=3)";
  -webkit-transform: rotate(270deg);
  -ms-transform: rotate(270deg);
  transform: rotate(270deg);
}
.fa-flip-horizontal {
  -ms-filter: "progid:DXImageTransform.Microsoft.BasicImage(rotation=0, mirror=1)";
  -webkit-transform: scale(-1, 1);
  -ms-transform: scale(-1, 1);
  transform: scale(-1, 1);
}
.fa-flip-vertical {
  -ms-filter: "progid:DXImageTransform.Microsoft.BasicImage(rotation=2, mirror=1)";
  -webkit-transform: scale(1, -1);
  -ms-transform: scale(1, -1);
  transform: scale(1, -1);
}
:root .fa-rotate-90,
:root .fa-rotate-180,
:root .fa-rotate-270,
:root .fa-flip-horizontal,
:root .fa-flip-vertical {
  filter: none;
}
.fa-stack {
  position: relative;
  display: inline-block;
  width: 2em;
  height: 2em;
  line-height: 2em;
  vertical-align: middle;
}
.fa-stack-1x,
.fa-stack-2x {
  position: absolute;
  left: 0;
  width: 100%;
  text-align: center;
}
.fa-stack-1x {
  line-height: inherit;
}
.fa-stack-2x {
  font-size: 2em;
}
.fa-inverse {
  color: #fff;
}
/* Font Awesome uses the Unicode Private Use Area (PUA) to ensure screen
   readers do not read off random characters that represent icons */
.fa-glass:before {
  content: "\f000";
}
.fa-music:before {
  content: "\f001";
}
.fa-search:before {
  content: "\f002";
}
.fa-envelope-o:before {
  content: "\f003";
}
.fa-heart:before {
  content: "\f004";
}
.fa-star:before {
  content: "\f005";
}
.fa-star-o:before {
  content: "\f006";
}
.fa-user:before {
  content: "\f007";
}
.fa-film:before {
  content: "\f008";
}
.fa-th-large:before {
  content: "\f009";
}
.fa-th:before {
  content: "\f00a";
}
.fa-th-list:before {
  content: "\f00b";
}
.fa-check:before {
  content: "\f00c";
}
.fa-remove:before,
.fa-close:before,
.fa-times:before {
  content: "\f00d";
}
.fa-search-plus:before {
  content: "\f00e";
}
.fa-search-minus:before {
  content: "\f010";
}
.fa-power-off:before {
  content: "\f011";
}
.fa-signal:before {
  content: "\f012";
}
.fa-gear:before,
.fa-cog:before {
  content: "\f013";
}
.fa-trash-o:before {
  content: "\f014";
}
.fa-home:before {
  content: "\f015";
}
.fa-file-o:before {
  content: "\f016";
}
.fa-clock-o:before {
  content: "\f017";
}
.fa-road:before {
  content: "\f018";
}
.fa-download:before {
  content: "\f019";
}
.fa-arrow-circle-o-down:before {
  content: "\f01a";
}
.fa-arrow-circle-o-up:before {
  content: "\f01b";
}
.fa-inbox:before {
  content: "\f01c";
}
.fa-play-circle-o:before {
  content: "\f01d";
}
.fa-rotate-right:before,
.fa-repeat:before {
  content: "\f01e";
}
.fa-refresh:before {
  content: "\f021";
}
.fa-list-alt:before {
  content: "\f022";
}
.fa-lock:before {
  content: "\f023";
}
.fa-flag:before {
  content: "\f024";
}
.fa-headphones:before {
  content: "\f025";
}
.fa-volume-off:before {
  content: "\f026";
}
.fa-volume-down:before {
  content: "\f027";
}
.fa-volume-up:before {
  content: "\f028";
}
.fa-qrcode:before {
  content: "\f029";
}
.fa-barcode:before {
  content: "\f02a";
}
.fa-tag:before {
  content: "\f02b";
}
.fa-tags:before {
  content: "\f02c";
}
.fa-book:before {
  content: "\f02d";
}
.fa-bookmark:before {
  content: "\f02e";
}
.fa-print:before {
  content: "\f02f";
}
.fa-camera:before {
  content: "\f030";
}
.fa-font:before {
  content: "\f031";
}
.fa-bold:before {
  content: "\f032";
}
.fa-italic:before {
  content: "\f033";
}
.fa-text-height:before {
  content: "\f034";
}
.fa-text-width:before {
  content: "\f035";
}
.fa-align-left:before {
  content: "\f036";
}
.fa-align-center:before {
  content: "\f037";
}
.fa-align-right:before {
  content: "\f038";
}
.fa-align-justify:before {
  content: "\f039";
}
.fa-list:before {
  content: "\f03a";
}
.fa-dedent:before,
.fa-outdent:before {
  content: "\f03b";
}
.fa-indent:before {
  content: "\f03c";
}
.fa-video-camera:before {
  content: "\f03d";
}
.fa-photo:before,
.fa-image:before,
.fa-picture-o:before {
  content: "\f03e";
}
.fa-pencil:before {
  content: "\f040";
}
.fa-map-marker:before {
  content: "\f041";
}
.fa-adjust:before {
  content: "\f042";
}
.fa-tint:before {
  content: "\f043";
}
.fa-edit:before,
.fa-pencil-square-o:before {
  content: "\f044";
}
.fa-share-square-o:before {
  content: "\f045";
}
.fa-check-square-o:before {
  content: "\f046";
}
.fa-arrows:before {
  content: "\f047";
}
.fa-step-backward:before {
  content: "\f048";
}
.fa-fast-backward:before {
  content: "\f049";
}
.fa-backward:before {
  content: "\f04a";
}
.fa-play:before {
  content: "\f04b";
}
.fa-pause:before {
  content: "\f04c";
}
.fa-stop:before {
  content: "\f04d";
}
.fa-forward:before {
  content: "\f04e";
}
.fa-fast-forward:before {
  content: "\f050";
}
.fa-step-forward:before {
  content: "\f051";
}
.fa-eject:before {
  content: "\f052";
}
.fa-chevron-left:before {
  content: "\f053";
}
.fa-chevron-right:before {
  content: "\f054";
}
.fa-plus-circle:before {
  content: "\f055";
}
.fa-minus-circle:before {
  content: "\f056";
}
.fa-times-circle:before {
  content: "\f057";
}
.fa-check-circle:before {
  content: "\f058";
}
.fa-question-circle:before {
  content: "\f059";
}
.fa-info-circle:before {
  content: "\f05a";
}
.fa-crosshairs:before {
  content: "\f05b";
}
.fa-times-circle-o:before {
  content: "\f05c";
}
.fa-check-circle-o:before {
  content: "\f05d";
}
.fa-ban:before {
  content: "\f05e";
}
.fa-arrow-left:before {
  content: "\f060";
}
.fa-arrow-right:before {
  content: "\f061";
}
.fa-arrow-up:before {
  content: "\f062";
}
.fa-arrow-down:before {
  content: "\f063";
}
.fa-mail-forward:before,
.fa-share:before {
  content: "\f064";
}
.fa-expand:before {
  content: "\f065";
}
.fa-compress:before {
  content: "\f066";
}
.fa-plus:before {
  content: "\f067";
}
.fa-minus:before {
  content: "\f068";
}
.fa-asterisk:before {
  content: "\f069";
}
.fa-exclamation-circle:before {
  content: "\f06a";
}
.fa-gift:before {
  content: "\f06b";
}
.fa-leaf:before {
  content: "\f06c";
}
.fa-fire:before {
  content: "\f06d";
}
.fa-eye:before {
  content: "\f06e";
}
.fa-eye-slash:before {
  content: "\f070";
}
.fa-warning:before,
.fa-exclamation-triangle:before {
  content: "\f071";
}
.fa-plane:before {
  content: "\f072";
}
.fa-calendar:before {
  content: "\f073";
}
.fa-random:before {
  content: "\f074";
}
.fa-comment:before {
  content: "\f075";
}
.fa-magnet:before {
  content: "\f076";
}
.fa-chevron-up:before {
  content: "\f077";
}
.fa-chevron-down:before {
  content: "\f078";
}
.fa-retweet:before {
  content: "\f079";
}
.fa-shopping-cart:before {
  content: "\f07a";
}
.fa-folder:before {
  content: "\f07b";
}
.fa-folder-open:before {
  content: "\f07c";
}
.fa-arrows-v:before {
  content: "\f07d";
}
.fa-arrows-h:before {
  content: "\f07e";
}
.fa-bar-chart-o:before,
.fa-bar-chart:before {
  content: "\f080";
}
.fa-twitter-square:before {
  content: "\f081";
}
.fa-facebook-square:before {
  content: "\f082";
}
.fa-camera-retro:before {
  content: "\f083";
}
.fa-key:before {
  content: "\f084";
}
.fa-gears:before,
.fa-cogs:before {
  content: "\f085";
}
.fa-comments:before {
  content: "\f086";
}
.fa-thumbs-o-up:before {
  content: "\f087";
}
.fa-thumbs-o-down:before {
  content: "\f088";
}
.fa-star-half:before {
  content: "\f089";
}
.fa-heart-o:before {
  content: "\f08a";
}
.fa-sign-out:before {
  content: "\f08b";
}
.fa-linkedin-square:before {
  content: "\f08c";
}
.fa-thumb-tack:before {
  content: "\f08d";
}
.fa-external-link:before {
  content: "\f08e";
}
.fa-sign-in:before {
  content: "\f090";
}
.fa-trophy:before {
  content: "\f091";
}
.fa-github-square:before {
  content: "\f092";
}
.fa-upload:before {
  content: "\f093";
}
.fa-lemon-o:before {
  content: "\f094";
}
.fa-phone:before {
  content: "\f095";
}
.fa-square-o:before {
  content: "\f096";
}
.fa-bookmark-o:before {
  content: "\f097";
}
.fa-phone-square:before {
  content: "\f098";
}
.fa-twitter:before {
  content: "\f099";
}
.fa-facebook-f:before,
.fa-facebook:before {
  content: "\f09a";
}
.fa-github:before {
  content: "\f09b";
}
.fa-unlock:before {
  content: "\f09c";
}
.fa-credit-card:before {
  content: "\f09d";
}
.fa-feed:before,
.fa-rss:before {
  content: "\f09e";
}
.fa-hdd-o:before {
  content: "\f0a0";
}
.fa-bullhorn:before {
  content: "\f0a1";
}
.fa-bell:before {
  content: "\f0f3";
}
.fa-certificate:before {
  content: "\f0a3";
}
.fa-hand-o-right:before {
  content: "\f0a4";
}
.fa-hand-o-left:before {
  content: "\f0a5";
}
.fa-hand-o-up:before {
  content: "\f0a6";
}
.fa-hand-o-down:before {
  content: "\f0a7";
}
.fa-arrow-circle-left:before {
  content: "\f0a8";
}
.fa-arrow-circle-right:before {
  content: "\f0a9";
}
.fa-arrow-circle-up:before {
  content: "\f0aa";
}
.fa-arrow-circle-down:before {
  content: "\f0ab";
}
.fa-globe:before {
  content: "\f0ac";
}
.fa-wrench:before {
  content: "\f0ad";
}
.fa-tasks:before {
  content: "\f0ae";
}
.fa-filter:before {
  content: "\f0b0";
}
.fa-briefcase:before {
  content: "\f0b1";
}
.fa-arrows-alt:before {
  content: "\f0b2";
}
.fa-group:before,
.fa-users:before {
  content: "\f0c0";
}
.fa-chain:before,
.fa-link:before {
  content: "\f0c1";
}
.fa-cloud:before {
  content: "\f0c2";
}
.fa-flask:before {
  content: "\f0c3";
}
.fa-cut:before,
.fa-scissors:before {
  content: "\f0c4";
}
.fa-copy:before,
.fa-files-o:before {
  content: "\f0c5";
}
.fa-paperclip:before {
  content: "\f0c6";
}
.fa-save:before,
.fa-floppy-o:before {
  content: "\f0c7";
}
.fa-square:before {
  content: "\f0c8";
}
.fa-navicon:before,
.fa-reorder:before,
.fa-bars:before {
  content: "\f0c9";
}
.fa-list-ul:before {
  content: "\f0ca";
}
.fa-list-ol:before {
  content: "\f0cb";
}
.fa-strikethrough:before {
  content: "\f0cc";
}
.fa-underline:before {
  content: "\f0cd";
}
.fa-table:before {
  content: "\f0ce";
}
.fa-magic:before {
  content: "\f0d0";
}
.fa-truck:before {
  content: "\f0d1";
}
.fa-pinterest:before {
  content: "\f0d2";
}
.fa-pinterest-square:before {
  content: "\f0d3";
}
.fa-google-plus-square:before {
  content: "\f0d4";
}
.fa-google-plus:before {
  content: "\f0d5";
}
.fa-money:before {
  content: "\f0d6";
}
.fa-caret-down:before {
  content: "\f0d7";
}
.fa-caret-up:before {
  content: "\f0d8";
}
.fa-caret-left:before {
  content: "\f0d9";
}
.fa-caret-right:before {
  content: "\f0da";
}
.fa-columns:before {
  content: "\f0db";
}
.fa-unsorted:before,
.fa-sort:before {
  content: "\f0dc";
}
.fa-sort-down:before,
.fa-sort-desc:before {
  content: "\f0dd";
}
.fa-sort-up:before,
.fa-sort-asc:before {
  content: "\f0de";
}
.fa-envelope:before {
  content: "\f0e0";
}
.fa-linkedin:before {
  content: "\f0e1";
}
.fa-rotate-left:before,
.fa-undo:before {
  content: "\f0e2";
}
.fa-legal:before,
.fa-gavel:before {
  content: "\f0e3";
}
.fa-dashboard:before,
.fa-tachometer:before {
  content: "\f0e4";
}
.fa-comment-o:before {
  content: "\f0e5";
}
.fa-comments-o:before {
  content: "\f0e6";
}
.fa-flash:before,
.fa-bolt:before {
  content: "\f0e7";
}
.fa-sitemap:before {
  content: "\f0e8";
}
.fa-umbrella:before {
  content: "\f0e9";
}
.fa-paste:before,
.fa-clipboard:before {
  content: "\f0ea";
}
.fa-lightbulb-o:before {
  content: "\f0eb";
}
.fa-exchange:before {
  content: "\f0ec";
}
.fa-cloud-download:before {
  content: "\f0ed";
}
.fa-cloud-upload:before {
  content: "\f0ee";
}
.fa-user-md:before {
  content: "\f0f0";
}
.fa-stethoscope:before {
  content: "\f0f1";
}
.fa-suitcase:before {
  content: "\f0f2";
}
.fa-bell-o:before {
  content: "\f0a2";
}
.fa-coffee:before {
  content: "\f0f4";
}
.fa-cutlery:before {
  content: "\f0f5";
}
.fa-file-text-o:before {
  content: "\f0f6";
}
.fa-building-o:before {
  content: "\f0f7";
}
.fa-hospital-o:before {
  content: "\f0f8";
}
.fa-ambulance:before {
  content: "\f0f9";
}
.fa-medkit:before {
  content: "\f0fa";
}
.fa-fighter-jet:before {
  content: "\f0fb";
}
.fa-beer:before {
  content: "\f0fc";
}
.fa-h-square:before {
  content: "\f0fd";
}
.fa-plus-square:before {
  content: "\f0fe";
}
.fa-angle-double-left:before {
  content: "\f100";
}
.fa-angle-double-right:before {
  content: "\f101";
}
.fa-angle-double-up:before {
  content: "\f102";
}
.fa-angle-double-down:before {
  content: "\f103";
}
.fa-angle-left:before {
  content: "\f104";
}
.fa-angle-right:before {
  content: "\f105";
}
.fa-angle-up:before {
  content: "\f106";
}
.fa-angle-down:before {
  content: "\f107";
}
.fa-desktop:before {
  content: "\f108";
}
.fa-laptop:before {
  content: "\f109";
}
.fa-tablet:before {
  content: "\f10a";
}
.fa-mobile-phone:before,
.fa-mobile:before {
  content: "\f10b";
}
.fa-circle-o:before {
  content: "\f10c";
}
.fa-quote-left:before {
  content: "\f10d";
}
.fa-quote-right:before {
  content: "\f10e";
}
.fa-spinner:before {
  content: "\f110";
}
.fa-circle:before {
  content: "\f111";
}
.fa-mail-reply:before,
.fa-reply:before {
  content: "\f112";
}
.fa-github-alt:before {
  content: "\f113";
}
.fa-folder-o:before {
  content: "\f114";
}
.fa-folder-open-o:before {
  content: "\f115";
}
.fa-smile-o:before {
  content: "\f118";
}
.fa-frown-o:before {
  content: "\f119";
}
.fa-meh-o:before {
  content: "\f11a";
}
.fa-gamepad:before {
  content: "\f11b";
}
.fa-keyboard-o:before {
  content: "\f11c";
}
.fa-flag-o:before {
  content: "\f11d";
}
.fa-flag-checkered:before {
  content: "\f11e";
}
.fa-terminal:before {
  content: "\f120";
}
.fa-code:before {
  content: "\f121";
}
.fa-mail-reply-all:before,
.fa-reply-all:before {
  content: "\f122";
}
.fa-star-half-empty:before,
.fa-star-half-full:before,
.fa-star-half-o:before {
  content: "\f123";
}
.fa-location-arrow:before {
  content: "\f124";
}
.fa-crop:before {
  content: "\f125";
}
.fa-code-fork:before {
  content: "\f126";
}
.fa-unlink:before,
.fa-chain-broken:before {
  content: "\f127";
}
.fa-question:before {
  content: "\f128";
}
.fa-info:before {
  content: "\f129";
}
.fa-exclamation:before {
  content: "\f12a";
}
.fa-superscript:before {
  content: "\f12b";
}
.fa-subscript:before {
  content: "\f12c";
}
.fa-eraser:before {
  content: "\f12d";
}
.fa-puzzle-piece:before {
  content: "\f12e";
}
.fa-microphone:before {
  content: "\f130";
}
.fa-microphone-slash:before {
  content: "\f131";
}
.fa-shield:before {
  content: "\f132";
}
.fa-calendar-o:before {
  content: "\f133";
}
.fa-fire-extinguisher:before {
  content: "\f134";
}
.fa-rocket:before {
  content: "\f135";
}
.fa-maxcdn:before {
  content: "\f136";
}
.fa-chevron-circle-left:before {
  content: "\f137";
}
.fa-chevron-circle-right:before {
  content: "\f138";
}
.fa-chevron-circle-up:before {
  content: "\f139";
}
.fa-chevron-circle-down:before {
  content: "\f13a";
}
.fa-html5:before {
  content: "\f13b";
}
.fa-css3:before {
  content: "\f13c";
}
.fa-anchor:before {
  content: "\f13d";
}
.fa-unlock-alt:before {
  content: "\f13e";
}
.fa-bullseye:before {
  content: "\f140";
}
.fa-ellipsis-h:before {
  content: "\f141";
}
.fa-ellipsis-v:before {
  content: "\f142";
}
.fa-rss-square:before {
  content: "\f143";
}
.fa-play-circle:before {
  content: "\f144";
}
.fa-ticket:before {
  content: "\f145";
}
.fa-minus-square:before {
  content: "\f146";
}
.fa-minus-square-o:before {
  content: "\f147";
}
.fa-level-up:before {
  content: "\f148";
}
.fa-level-down:before {
  content: "\f149";
}
.fa-check-square:before {
  content: "\f14a";
}
.fa-pencil-square:before {
  content: "\f14b";
}
.fa-external-link-square:before {
  content: "\f14c";
}
.fa-share-square:before {
  content: "\f14d";
}
.fa-compass:before {
  content: "\f14e";
}
.fa-toggle-down:before,
.fa-caret-square-o-down:before {
  content: "\f150";
}
.fa-toggle-up:before,
.fa-caret-square-o-up:before {
  content: "\f151";
}
.fa-toggle-right:before,
.fa-caret-square-o-right:before {
  content: "\f152";
}
.fa-euro:before,
.fa-eur:before {
  content: "\f153";
}
.fa-gbp:before {
  content: "\f154";
}
.fa-dollar:before,
.fa-usd:before {
  content: "\f155";
}
.fa-rupee:before,
.fa-inr:before {
  content: "\f156";
}
.fa-cny:before,
.fa-rmb:before,
.fa-yen:before,
.fa-jpy:before {
  content: "\f157";
}
.fa-ruble:before,
.fa-rouble:before,
.fa-rub:before {
  content: "\f158";
}
.fa-won:before,
.fa-krw:before {
  content: "\f159";
}
.fa-bitcoin:before,
.fa-btc:before {
  content: "\f15a";
}
.fa-file:before {
  content: "\f15b";
}
.fa-file-text:before {
  content: "\f15c";
}
.fa-sort-alpha-asc:before {
  content: "\f15d";
}
.fa-sort-alpha-desc:before {
  content: "\f15e";
}
.fa-sort-amount-asc:before {
  content: "\f160";
}
.fa-sort-amount-desc:before {
  content: "\f161";
}
.fa-sort-numeric-asc:before {
  content: "\f162";
}
.fa-sort-numeric-desc:before {
  content: "\f163";
}
.fa-thumbs-up:before {
  content: "\f164";
}
.fa-thumbs-down:before {
  content: "\f165";
}
.fa-youtube-square:before {
  content: "\f166";
}
.fa-youtube:before {
  content: "\f167";
}
.fa-xing:before {
  content: "\f168";
}
.fa-xing-square:before {
  content: "\f169";
}
.fa-youtube-play:before {
  content: "\f16a";
}
.fa-dropbox:before {
  content: "\f16b";
}
.fa-stack-overflow:before {
  content: "\f16c";
}
.fa-instagram:before {
  content: "\f16d";
}
.fa-flickr:before {
  content: "\f16e";
}
.fa-adn:before {
  content: "\f170";
}
.fa-bitbucket:before {
  content: "\f171";
}
.fa-bitbucket-square:before {
  content: "\f172";
}
.fa-tumblr:before {
  content: "\f173";
}
.fa-tumblr-square:before {
  content: "\f174";
}
.fa-long-arrow-down:before {
  content: "\f175";
}
.fa-long-arrow-up:before {
  content: "\f176";
}
.fa-long-arrow-left:before {
  content: "\f177";
}
.fa-long-arrow-right:before {
  content: "\f178";
}
.fa-apple:before {
  content: "\f179";
}
.fa-windows:before {
  content: "\f17a";
}
.fa-android:before {
  content: "\f17b";
}
.fa-linux:before {
  content: "\f17c";
}
.fa-dribbble:before {
  content: "\f17d";
}
.fa-skype:before {
  content: "\f17e";
}
.fa-foursquare:before {
  content: "\f180";
}
.fa-trello:before {
  content: "\f181";
}
.fa-female:before {
  content: "\f182";
}
.fa-male:before {
  content: "\f183";
}
.fa-gittip:before,
.fa-gratipay:before {
  content: "\f184";
}
.fa-sun-o:before {
  content: "\f185";
}
.fa-moon-o:before {
  content: "\f186";
}
.fa-archive:before {
  content: "\f187";
}
.fa-bug:before {
  content: "\f188";
}
.fa-vk:before {
  content: "\f189";
}
.fa-weibo:before {
  content: "\f18a";
}
.fa-renren:before {
  content: "\f18b";
}
.fa-pagelines:before {
  content: "\f18c";
}
.fa-stack-exchange:before {
  content: "\f18d";
}
.fa-arrow-circle-o-right:before {
  content: "\f18e";
}
.fa-arrow-circle-o-left:before {
  content: "\f190";
}
.fa-toggle-left:before,
.fa-caret-square-o-left:before {
  content: "\f191";
}
.fa-dot-circle-o:before {
  content: "\f192";
}
.fa-wheelchair:before {
  content: "\f193";
}
.fa-vimeo-square:before {
  content: "\f194";
}
.fa-turkish-lira:before,
.fa-try:before {
  content: "\f195";
}
.fa-plus-square-o:before {
  content: "\f196";
}
.fa-space-shuttle:before {
  content: "\f197";
}
.fa-slack:before {
  content: "\f198";
}
.fa-envelope-square:before {
  content: "\f199";
}
.fa-wordpress:before {
  content: "\f19a";
}
.fa-openid:before {
  content: "\f19b";
}
.fa-institution:before,
.fa-bank:before,
.fa-university:before {
  content: "\f19c";
}
.fa-mortar-board:before,
.fa-graduation-cap:before {
  content: "\f19d";
}
.fa-yahoo:before {
  content: "\f19e";
}
.fa-google:before {
  content: "\f1a0";
}
.fa-reddit:before {
  content: "\f1a1";
}
.fa-reddit-square:before {
  content: "\f1a2";
}
.fa-stumbleupon-circle:before {
  content: "\f1a3";
}
.fa-stumbleupon:before {
  content: "\f1a4";
}
.fa-delicious:before {
  content: "\f1a5";
}
.fa-digg:before {
  content: "\f1a6";
}
.fa-pied-piper-pp:before {
  content: "\f1a7";
}
.fa-pied-piper-alt:before {
  content: "\f1a8";
}
.fa-drupal:before {
  content: "\f1a9";
}
.fa-joomla:before {
  content: "\f1aa";
}
.fa-language:before {
  content: "\f1ab";
}
.fa-fax:before {
  content: "\f1ac";
}
.fa-building:before {
  content: "\f1ad";
}
.fa-child:before {
  content: "\f1ae";
}
.fa-paw:before {
  content: "\f1b0";
}
.fa-spoon:before {
  content: "\f1b1";
}
.fa-cube:before {
  content: "\f1b2";
}
.fa-cubes:before {
  content: "\f1b3";
}
.fa-behance:before {
  content: "\f1b4";
}
.fa-behance-square:before {
  content: "\f1b5";
}
.fa-steam:before {
  content: "\f1b6";
}
.fa-steam-square:before {
  content: "\f1b7";
}
.fa-recycle:before {
  content: "\f1b8";
}
.fa-automobile:before,
.fa-car:before {
  content: "\f1b9";
}
.fa-cab:before,
.fa-taxi:before {
  content: "\f1ba";
}
.fa-tree:before {
  content: "\f1bb";
}
.fa-spotify:before {
  content: "\f1bc";
}
.fa-deviantart:before {
  content: "\f1bd";
}
.fa-soundcloud:before {
  content: "\f1be";
}
.fa-database:before {
  content: "\f1c0";
}
.fa-file-pdf-o:before {
  content: "\f1c1";
}
.fa-file-word-o:before {
  content: "\f1c2";
}
.fa-file-excel-o:before {
  content: "\f1c3";
}
.fa-file-powerpoint-o:before {
  content: "\f1c4";
}
.fa-file-photo-o:before,
.fa-file-picture-o:before,
.fa-file-image-o:before {
  content: "\f1c5";
}
.fa-file-zip-o:before,
.fa-file-archive-o:before {
  content: "\f1c6";
}
.fa-file-sound-o:before,
.fa-file-audio-o:before {
  content: "\f1c7";
}
.fa-file-movie-o:before,
.fa-file-video-o:before {
  content: "\f1c8";
}
.fa-file-code-o:before {
  content: "\f1c9";
}
.fa-vine:before {
  content: "\f1ca";
}
.fa-codepen:before {
  content: "\f1cb";
}
.fa-jsfiddle:before {
  content: "\f1cc";
}
.fa-life-bouy:before,
.fa-life-buoy:before,
.fa-life-saver:before,
.fa-support:before,
.fa-life-ring:before {
  content: "\f1cd";
}
.fa-circle-o-notch:before {
  content: "\f1ce";
}
.fa-ra:before,
.fa-resistance:before,
.fa-rebel:before {
  content: "\f1d0";
}
.fa-ge:before,
.fa-empire:before {
  content: "\f1d1";
}
.fa-git-square:before {
  content: "\f1d2";
}
.fa-git:before {
  content: "\f1d3";
}
.fa-y-combinator-square:before,
.fa-yc-square:before,
.fa-hacker-news:before {
  content: "\f1d4";
}
.fa-tencent-weibo:before {
  content: "\f1d5";
}
.fa-qq:before {
  content: "\f1d6";
}
.fa-wechat:before,
.fa-weixin:before {
  content: "\f1d7";
}
.fa-send:before,
.fa-paper-plane:before {
  content: "\f1d8";
}
.fa-send-o:before,
.fa-paper-plane-o:before {
  content: "\f1d9";
}
.fa-history:before {
  content: "\f1da";
}
.fa-circle-thin:before {
  content: "\f1db";
}
.fa-header:before {
  content: "\f1dc";
}
.fa-paragraph:before {
  content: "\f1dd";
}
.fa-sliders:before {
  content: "\f1de";
}
.fa-share-alt:before {
  content: "\f1e0";
}
.fa-share-alt-square:before {
  content: "\f1e1";
}
.fa-bomb:before {
  content: "\f1e2";
}
.fa-soccer-ball-o:before,
.fa-futbol-o:before {
  content: "\f1e3";
}
.fa-tty:before {
  content: "\f1e4";
}
.fa-binoculars:before {
  content: "\f1e5";
}
.fa-plug:before {
  content: "\f1e6";
}
.fa-slideshare:before {
  content: "\f1e7";
}
.fa-twitch:before {
  content: "\f1e8";
}
.fa-yelp:before {
  content: "\f1e9";
}
.fa-newspaper-o:before {
  content: "\f1ea";
}
.fa-wifi:before {
  content: "\f1eb";
}
.fa-calculator:before {
  content: "\f1ec";
}
.fa-paypal:before {
  content: "\f1ed";
}
.fa-google-wallet:before {
  content: "\f1ee";
}
.fa-cc-visa:before {
  content: "\f1f0";
}
.fa-cc-mastercard:before {
  content: "\f1f1";
}
.fa-cc-discover:before {
  content: "\f1f2";
}
.fa-cc-amex:before {
  content: "\f1f3";
}
.fa-cc-paypal:before {
  content: "\f1f4";
}
.fa-cc-stripe:before {
  content: "\f1f5";
}
.fa-bell-slash:before {
  content: "\f1f6";
}
.fa-bell-slash-o:before {
  content: "\f1f7";
}
.fa-trash:before {
  content: "\f1f8";
}
.fa-copyright:before {
  content: "\f1f9";
}
.fa-at:before {
  content: "\f1fa";
}
.fa-eyedropper:before {
  content: "\f1fb";
}
.fa-paint-brush:before {
  content: "\f1fc";
}
.fa-birthday-cake:before {
  content: "\f1fd";
}
.fa-area-chart:before {
  content: "\f1fe";
}
.fa-pie-chart:before {
  content: "\f200";
}
.fa-line-chart:before {
  content: "\f201";
}
.fa-lastfm:before {
  content: "\f202";
}
.fa-lastfm-square:before {
  content: "\f203";
}
.fa-toggle-off:before {
  content: "\f204";
}
.fa-toggle-on:before {
  content: "\f205";
}
.fa-bicycle:before {
  content: "\f206";
}
.fa-bus:before {
  content: "\f207";
}
.fa-ioxhost:before {
  content: "\f208";
}
.fa-angellist:before {
  content: "\f209";
}
.fa-cc:before {
  content: "\f20a";
}
.fa-shekel:before,
.fa-sheqel:before,
.fa-ils:before {
  content: "\f20b";
}
.fa-meanpath:before {
  content: "\f20c";
}
.fa-buysellads:before {
  content: "\f20d";
}
.fa-connectdevelop:before {
  content: "\f20e";
}
.fa-dashcube:before {
  content: "\f210";
}
.fa-forumbee:before {
  content: "\f211";
}
.fa-leanpub:before {
  content: "\f212";
}
.fa-sellsy:before {
  content: "\f213";
}
.fa-shirtsinbulk:before {
  content: "\f214";
}
.fa-simplybuilt:before {
  content: "\f215";
}
.fa-skyatlas:before {
  content: "\f216";
}
.fa-cart-plus:before {
  content: "\f217";
}
.fa-cart-arrow-down:before {
  content: "\f218";
}
.fa-diamond:before {
  content: "\f219";
}
.fa-ship:before {
  content: "\f21a";
}
.fa-user-secret:before {
  content: "\f21b";
}
.fa-motorcycle:before {
  content: "\f21c";
}
.fa-street-view:before {
  content: "\f21d";
}
.fa-heartbeat:before {
  content: "\f21e";
}
.fa-venus:before {
  content: "\f221";
}
.fa-mars:before {
  content: "\f222";
}
.fa-mercury:before {
  content: "\f223";
}
.fa-intersex:before,
.fa-transgender:before {
  content: "\f224";
}
.fa-transgender-alt:before {
  content: "\f225";
}
.fa-venus-double:before {
  content: "\f226";
}
.fa-mars-double:before {
  content: "\f227";
}
.fa-venus-mars:before {
  content: "\f228";
}
.fa-mars-stroke:before {
  content: "\f229";
}
.fa-mars-stroke-v:before {
  content: "\f22a";
}
.fa-mars-stroke-h:before {
  content: "\f22b";
}
.fa-neuter:before {
  content: "\f22c";
}
.fa-genderless:before {
  content: "\f22d";
}
.fa-facebook-official:before {
  content: "\f230";
}
.fa-pinterest-p:before {
  content: "\f231";
}
.fa-whatsapp:before {
  content: "\f232";
}
.fa-server:before {
  content: "\f233";
}
.fa-user-plus:before {
  content: "\f234";
}
.fa-user-times:before {
  content: "\f235";
}
.fa-hotel:before,
.fa-bed:before {
  content: "\f236";
}
.fa-viacoin:before {
  content: "\f237";
}
.fa-train:before {
  content: "\f238";
}
.fa-subway:before {
  content: "\f239";
}
.fa-medium:before {
  content: "\f23a";
}
.fa-yc:before,
.fa-y-combinator:before {
  content: "\f23b";
}
.fa-optin-monster:before {
  content: "\f23c";
}
.fa-opencart:before {
  content: "\f23d";
}
.fa-expeditedssl:before {
  content: "\f23e";
}
.fa-battery-4:before,
.fa-battery:before,
.fa-battery-full:before {
  content: "\f240";
}
.fa-battery-3:before,
.fa-battery-three-quarters:before {
  content: "\f241";
}
.fa-battery-2:before,
.fa-battery-half:before {
  content: "\f242";
}
.fa-battery-1:before,
.fa-battery-quarter:before {
  content: "\f243";
}
.fa-battery-0:before,
.fa-battery-empty:before {
  content: "\f244";
}
.fa-mouse-pointer:before {
  content: "\f245";
}
.fa-i-cursor:before {
  content: "\f246";
}
.fa-object-group:before {
  content: "\f247";
}
.fa-object-ungroup:before {
  content: "\f248";
}
.fa-sticky-note:before {
  content: "\f249";
}
.fa-sticky-note-o:before {
  content: "\f24a";
}
.fa-cc-jcb:before {
  content: "\f24b";
}
.fa-cc-diners-club:before {
  content: "\f24c";
}
.fa-clone:before {
  content: "\f24d";
}
.fa-balance-scale:before {
  content: "\f24e";
}
.fa-hourglass-o:before {
  content: "\f250";
}
.fa-hourglass-1:before,
.fa-hourglass-start:before {
  content: "\f251";
}
.fa-hourglass-2:before,
.fa-hourglass-half:before {
  content: "\f252";
}
.fa-hourglass-3:before,
.fa-hourglass-end:before {
  content: "\f253";
}
.fa-hourglass:before {
  content: "\f254";
}
.fa-hand-grab-o:before,
.fa-hand-rock-o:before {
  content: "\f255";
}
.fa-hand-stop-o:before,
.fa-hand-paper-o:before {
  content: "\f256";
}
.fa-hand-scissors-o:before {
  content: "\f257";
}
.fa-hand-lizard-o:before {
  content: "\f258";
}
.fa-hand-spock-o:before {
  content: "\f259";
}
.fa-hand-pointer-o:before {
  content: "\f25a";
}
.fa-hand-peace-o:before {
  content: "\f25b";
}
.fa-trademark:before {
  content: "\f25c";
}
.fa-registered:before {
  content: "\f25d";
}
.fa-creative-commons:before {
  content: "\f25e";
}
.fa-gg:before {
  content: "\f260";
}
.fa-gg-circle:before {
  content: "\f261";
}
.fa-tripadvisor:before {
  content: "\f262";
}
.fa-odnoklassniki:before {
  content: "\f263";
}
.fa-odnoklassniki-square:before {
  content: "\f264";
}
.fa-get-pocket:before {
  content: "\f265";
}
.fa-wikipedia-w:before {
  content: "\f266";
}
.fa-safari:before {
  content: "\f267";
}
.fa-chrome:before {
  content: "\f268";
}
.fa-firefox:before {
  content: "\f269";
}
.fa-opera:before {
  content: "\f26a";
}
.fa-internet-explorer:before {
  content: "\f26b";
}
.fa-tv:before,
.fa-television:before {
  content: "\f26c";
}
.fa-contao:before {
  content: "\f26d";
}
.fa-500px:before {
  content: "\f26e";
}
.fa-amazon:before {
  content: "\f270";
}
.fa-calendar-plus-o:before {
  content: "\f271";
}
.fa-calendar-minus-o:before {
  content: "\f272";
}
.fa-calendar-times-o:before {
  content: "\f273";
}
.fa-calendar-check-o:before {
  content: "\f274";
}
.fa-industry:before {
  content: "\f275";
}
.fa-map-pin:before {
  content: "\f276";
}
.fa-map-signs:before {
  content: "\f277";
}
.fa-map-o:before {
  content: "\f278";
}
.fa-map:before {
  content: "\f279";
}
.fa-commenting:before {
  content: "\f27a";
}
.fa-commenting-o:before {
  content: "\f27b";
}
.fa-houzz:before {
  content: "\f27c";
}
.fa-vimeo:before {
  content: "\f27d";
}
.fa-black-tie:before {
  content: "\f27e";
}
.fa-fonticons:before {
  content: "\f280";
}
.fa-reddit-alien:before {
  content: "\f281";
}
.fa-edge:before {
  content: "\f282";
}
.fa-credit-card-alt:before {
  content: "\f283";
}
.fa-codiepie:before {
  content: "\f284";
}
.fa-modx:before {
  content: "\f285";
}
.fa-fort-awesome:before {
  content: "\f286";
}
.fa-usb:before {
  content: "\f287";
}
.fa-product-hunt:before {
  content: "\f288";
}
.fa-mixcloud:before {
  content: "\f289";
}
.fa-scribd:before {
  content: "\f28a";
}
.fa-pause-circle:before {
  content: "\f28b";
}
.fa-pause-circle-o:before {
  content: "\f28c";
}
.fa-stop-circle:before {
  content: "\f28d";
}
.fa-stop-circle-o:before {
  content: "\f28e";
}
.fa-shopping-bag:before {
  content: "\f290";
}
.fa-shopping-basket:before {
  content: "\f291";
}
.fa-hashtag:before {
  content: "\f292";
}
.fa-bluetooth:before {
  content: "\f293";
}
.fa-bluetooth-b:before {
  content: "\f294";
}
.fa-percent:before {
  content: "\f295";
}
.fa-gitlab:before {
  content: "\f296";
}
.fa-wpbeginner:before {
  content: "\f297";
}
.fa-wpforms:before {
  content: "\f298";
}
.fa-envira:before {
  content: "\f299";
}
.fa-universal-access:before {
  content: "\f29a";
}
.fa-wheelchair-alt:before {
  content: "\f29b";
}
.fa-question-circle-o:before {
  content: "\f29c";
}
.fa-blind:before {
  content: "\f29d";
}
.fa-audio-description:before {
  content: "\f29e";
}
.fa-volume-control-phone:before {
  content: "\f2a0";
}
.fa-braille:before {
  content: "\f2a1";
}
.fa-assistive-listening-systems:before {
  content: "\f2a2";
}
.fa-asl-interpreting:before,
.fa-american-sign-language-interpreting:before {
  content: "\f2a3";
}
.fa-deafness:before,
.fa-hard-of-hearing:before,
.fa-deaf:before {
  content: "\f2a4";
}
.fa-glide:before {
  content: "\f2a5";
}
.fa-glide-g:before {
  content: "\f2a6";
}
.fa-signing:before,
.fa-sign-language:before {
  content: "\f2a7";
}
.fa-low-vision:before {
  content: "\f2a8";
}
.fa-viadeo:before {
  content: "\f2a9";
}
.fa-viadeo-square:before {
  content: "\f2aa";
}
.fa-snapchat:before {
  content: "\f2ab";
}
.fa-snapchat-ghost:before {
  content: "\f2ac";
}
.fa-snapchat-square:before {
  content: "\f2ad";
}
.fa-pied-piper:before {
  content: "\f2ae";
}
.fa-first-order:before {
  content: "\f2b0";
}
.fa-yoast:before {
  content: "\f2b1";
}
.fa-themeisle:before {
  content: "\f2b2";
}
.fa-google-plus-circle:before,
.fa-google-plus-official:before {
  content: "\f2b3";
}
.fa-fa:before,
.fa-font-awesome:before {
  content: "\f2b4";
}
.fa-handshake-o:before {
  content: "\f2b5";
}
.fa-envelope-open:before {
  content: "\f2b6";
}
.fa-envelope-open-o:before {
  content: "\f2b7";
}
.fa-linode:before {
  content: "\f2b8";
}
.fa-address-book:before {
  content: "\f2b9";
}
.fa-address-book-o:before {
  content: "\f2ba";
}
.fa-vcard:before,
.fa-address-card:before {
  content: "\f2bb";
}
.fa-vcard-o:before,
.fa-address-card-o:before {
  content: "\f2bc";
}
.fa-user-circle:before {
  content: "\f2bd";
}
.fa-user-circle-o:before {
  content: "\f2be";
}
.fa-user-o:before {
  content: "\f2c0";
}
.fa-id-badge:before {
  content: "\f2c1";
}
.fa-drivers-license:before,
.fa-id-card:before {
  content: "\f2c2";
}
.fa-drivers-license-o:before,
.fa-id-card-o:before {
  content: "\f2c3";
}
.fa-quora:before {
  content: "\f2c4";
}
.fa-free-code-camp:before {
  content: "\f2c5";
}
.fa-telegram:before {
  content: "\f2c6";
}
.fa-thermometer-4:before,
.fa-thermometer:before,
.fa-thermometer-full:before {
  content: "\f2c7";
}
.fa-thermometer-3:before,
.fa-thermometer-three-quarters:before {
  content: "\f2c8";
}
.fa-thermometer-2:before,
.fa-thermometer-half:before {
  content: "\f2c9";
}
.fa-thermometer-1:before,
.fa-thermometer-quarter:before {
  content: "\f2ca";
}
.fa-thermometer-0:before,
.fa-thermometer-empty:before {
  content: "\f2cb";
}
.fa-shower:before {
  content: "\f2cc";
}
.fa-bathtub:before,
.fa-s15:before,
.fa-bath:before {
  content: "\f2cd";
}
.fa-podcast:before {
  content: "\f2ce";
}
.fa-window-maximize:before {
  content: "\f2d0";
}
.fa-window-minimize:before {
  content: "\f2d1";
}
.fa-window-restore:before {
  content: "\f2d2";
}
.fa-times-rectangle:before,
.fa-window-close:before {
  content: "\f2d3";
}
.fa-times-rectangle-o:before,
.fa-window-close-o:before {
  content: "\f2d4";
}
.fa-bandcamp:before {
  content: "\f2d5";
}
.fa-grav:before {
  content: "\f2d6";
}
.fa-etsy:before {
  content: "\f2d7";
}
.fa-imdb:before {
  content: "\f2d8";
}
.fa-ravelry:before {
  content: "\f2d9";
}
.fa-eercast:before {
  content: "\f2da";
}
.fa-microchip:before {
  content: "\f2db";
}
.fa-snowflake-o:before {
  content: "\f2dc";
}
.fa-superpowers:before {
  content: "\f2dd";
}
.fa-wpexplorer:before {
  content: "\f2de";
}
.fa-meetup:before {
  content: "\f2e0";
}
.sr-only {
  position: absolute;
  width: 1px;
  height: 1px;
  padding: 0;
  margin: -1px;
  overflow: hidden;
  clip: rect(0, 0, 0, 0);
  border: 0;
}
.sr-only-focusable:active,
.sr-only-focusable:focus {
  position: static;
  width: auto;
  height: auto;
  margin: 0;
  overflow: visible;
  clip: auto;
}
.sr-only-focusable:active,
.sr-only-focusable:focus {
  position: static;
  width: auto;
  height: auto;
  margin: 0;
  overflow: visible;
  clip: auto;
}
/*!
*
* IPython base
*
*/
.modal.fade .modal-dialog {
  -webkit-transform: translate(0, 0);
  -ms-transform: translate(0, 0);
  -o-transform: translate(0, 0);
  transform: translate(0, 0);
}
code {
  color: #000;
}
pre {
  font-size: inherit;
  line-height: inherit;
}
label {
  font-weight: normal;
}
/* Make the page background atleast 100% the height of the view port */
/* Make the page itself atleast 70% the height of the view port */
.border-box-sizing {
  box-sizing: border-box;
  -moz-box-sizing: border-box;
  -webkit-box-sizing: border-box;
}
.corner-all {
  border-radius: 2px;
}
.no-padding {
  padding: 0px;
}
/* Flexible box model classes */
/* Taken from Alex Russell http://infrequently.org/2009/08/css-3-progress/ */
/* This file is a compatability layer.  It allows the usage of flexible box 
model layouts accross multiple browsers, including older browsers.  The newest,
universal implementation of the flexible box model is used when available (see
`Modern browsers` comments below).  Browsers that are known to implement this 
new spec completely include:

    Firefox 28.0+
    Chrome 29.0+
    Internet Explorer 11+ 
    Opera 17.0+

Browsers not listed, including Safari, are supported via the styling under the
`Old browsers` comments below.
*/
.hbox {
  /* Old browsers */
  display: -webkit-box;
  -webkit-box-orient: horizontal;
  -webkit-box-align: stretch;
  display: -moz-box;
  -moz-box-orient: horizontal;
  -moz-box-align: stretch;
  display: box;
  box-orient: horizontal;
  box-align: stretch;
  /* Modern browsers */
  display: flex;
  flex-direction: row;
  align-items: stretch;
}
.hbox > * {
  /* Old browsers */
  -webkit-box-flex: 0;
  -moz-box-flex: 0;
  box-flex: 0;
  /* Modern browsers */
  flex: none;
}
.vbox {
  /* Old browsers */
  display: -webkit-box;
  -webkit-box-orient: vertical;
  -webkit-box-align: stretch;
  display: -moz-box;
  -moz-box-orient: vertical;
  -moz-box-align: stretch;
  display: box;
  box-orient: vertical;
  box-align: stretch;
  /* Modern browsers */
  display: flex;
  flex-direction: column;
  align-items: stretch;
}
.vbox > * {
  /* Old browsers */
  -webkit-box-flex: 0;
  -moz-box-flex: 0;
  box-flex: 0;
  /* Modern browsers */
  flex: none;
}
.hbox.reverse,
.vbox.reverse,
.reverse {
  /* Old browsers */
  -webkit-box-direction: reverse;
  -moz-box-direction: reverse;
  box-direction: reverse;
  /* Modern browsers */
  flex-direction: row-reverse;
}
.hbox.box-flex0,
.vbox.box-flex0,
.box-flex0 {
  /* Old browsers */
  -webkit-box-flex: 0;
  -moz-box-flex: 0;
  box-flex: 0;
  /* Modern browsers */
  flex: none;
  width: auto;
}
.hbox.box-flex1,
.vbox.box-flex1,
.box-flex1 {
  /* Old browsers */
  -webkit-box-flex: 1;
  -moz-box-flex: 1;
  box-flex: 1;
  /* Modern browsers */
  flex: 1;
}
.hbox.box-flex,
.vbox.box-flex,
.box-flex {
  /* Old browsers */
  /* Old browsers */
  -webkit-box-flex: 1;
  -moz-box-flex: 1;
  box-flex: 1;
  /* Modern browsers */
  flex: 1;
}
.hbox.box-flex2,
.vbox.box-flex2,
.box-flex2 {
  /* Old browsers */
  -webkit-box-flex: 2;
  -moz-box-flex: 2;
  box-flex: 2;
  /* Modern browsers */
  flex: 2;
}
.box-group1 {
  /*  Deprecated */
  -webkit-box-flex-group: 1;
  -moz-box-flex-group: 1;
  box-flex-group: 1;
}
.box-group2 {
  /* Deprecated */
  -webkit-box-flex-group: 2;
  -moz-box-flex-group: 2;
  box-flex-group: 2;
}
.hbox.start,
.vbox.start,
.start {
  /* Old browsers */
  -webkit-box-pack: start;
  -moz-box-pack: start;
  box-pack: start;
  /* Modern browsers */
  justify-content: flex-start;
}
.hbox.end,
.vbox.end,
.end {
  /* Old browsers */
  -webkit-box-pack: end;
  -moz-box-pack: end;
  box-pack: end;
  /* Modern browsers */
  justify-content: flex-end;
}
.hbox.center,
.vbox.center,
.center {
  /* Old browsers */
  -webkit-box-pack: center;
  -moz-box-pack: center;
  box-pack: center;
  /* Modern browsers */
  justify-content: center;
}
.hbox.baseline,
.vbox.baseline,
.baseline {
  /* Old browsers */
  -webkit-box-pack: baseline;
  -moz-box-pack: baseline;
  box-pack: baseline;
  /* Modern browsers */
  justify-content: baseline;
}
.hbox.stretch,
.vbox.stretch,
.stretch {
  /* Old browsers */
  -webkit-box-pack: stretch;
  -moz-box-pack: stretch;
  box-pack: stretch;
  /* Modern browsers */
  justify-content: stretch;
}
.hbox.align-start,
.vbox.align-start,
.align-start {
  /* Old browsers */
  -webkit-box-align: start;
  -moz-box-align: start;
  box-align: start;
  /* Modern browsers */
  align-items: flex-start;
}
.hbox.align-end,
.vbox.align-end,
.align-end {
  /* Old browsers */
  -webkit-box-align: end;
  -moz-box-align: end;
  box-align: end;
  /* Modern browsers */
  align-items: flex-end;
}
.hbox.align-center,
.vbox.align-center,
.align-center {
  /* Old browsers */
  -webkit-box-align: center;
  -moz-box-align: center;
  box-align: center;
  /* Modern browsers */
  align-items: center;
}
.hbox.align-baseline,
.vbox.align-baseline,
.align-baseline {
  /* Old browsers */
  -webkit-box-align: baseline;
  -moz-box-align: baseline;
  box-align: baseline;
  /* Modern browsers */
  align-items: baseline;
}
.hbox.align-stretch,
.vbox.align-stretch,
.align-stretch {
  /* Old browsers */
  -webkit-box-align: stretch;
  -moz-box-align: stretch;
  box-align: stretch;
  /* Modern browsers */
  align-items: stretch;
}
div.error {
  margin: 2em;
  text-align: center;
}
div.error > h1 {
  font-size: 500%;
  line-height: normal;
}
div.error > p {
  font-size: 200%;
  line-height: normal;
}
div.traceback-wrapper {
  text-align: left;
  max-width: 800px;
  margin: auto;
}
div.traceback-wrapper pre.traceback {
  max-height: 600px;
  overflow: auto;
}
/**
 * Primary styles
 *
 * Author: Jupyter Development Team
 */
body {
  background-color: #fff;
  /* This makes sure that the body covers the entire window and needs to
       be in a different element than the display: box in wrapper below */
  position: absolute;
  left: 0px;
  right: 0px;
  top: 0px;
  bottom: 0px;
  overflow: visible;
}
body > #header {
  /* Initially hidden to prevent FLOUC */
  display: none;
  background-color: #fff;
  /* Display over codemirror */
  position: relative;
  z-index: 100;
}
body > #header #header-container {
  display: flex;
  flex-direction: row;
  justify-content: space-between;
  padding: 5px;
  padding-bottom: 5px;
  padding-top: 5px;
  box-sizing: border-box;
  -moz-box-sizing: border-box;
  -webkit-box-sizing: border-box;
}
body > #header .header-bar {
  width: 100%;
  height: 1px;
  background: #e7e7e7;
  margin-bottom: -1px;
}
@media print {
  body > #header {
    display: none !important;
  }
}
#header-spacer {
  width: 100%;
  visibility: hidden;
}
@media print {
  #header-spacer {
    display: none;
  }
}
#ipython_notebook {
  padding-left: 0px;
  padding-top: 1px;
  padding-bottom: 1px;
}
[dir="rtl"] #ipython_notebook {
  margin-right: 10px;
  margin-left: 0;
}
[dir="rtl"] #ipython_notebook.pull-left {
  float: right !important;
  float: right;
}
.flex-spacer {
  flex: 1;
}
#noscript {
  width: auto;
  padding-top: 16px;
  padding-bottom: 16px;
  text-align: center;
  font-size: 22px;
  color: red;
  font-weight: bold;
}
#ipython_notebook img {
  height: 28px;
}
#site {
  width: 100%;
  display: none;
  box-sizing: border-box;
  -moz-box-sizing: border-box;
  -webkit-box-sizing: border-box;
  overflow: auto;
}
@media print {
  #site {
    height: auto !important;
  }
}
/* Smaller buttons */
.ui-button .ui-button-text {
  padding: 0.2em 0.8em;
  font-size: 77%;
}
input.ui-button {
  padding: 0.3em 0.9em;
}
span#kernel_logo_widget {
  margin: 0 10px;
}
span#login_widget {
  float: right;
}
[dir="rtl"] span#login_widget {
  float: left;
}
span#login_widget > .button,
#logout {
  color: #333;
  background-color: #fff;
  border-color: #ccc;
}
span#login_widget > .button:focus,
#logout:focus,
span#login_widget > .button.focus,
#logout.focus {
  color: #333;
  background-color: #e6e6e6;
  border-color: #8c8c8c;
}
span#login_widget > .button:hover,
#logout:hover {
  color: #333;
  background-color: #e6e6e6;
  border-color: #adadad;
}
span#login_widget > .button:active,
#logout:active,
span#login_widget > .button.active,
#logout.active,
.open > .dropdown-togglespan#login_widget > .button,
.open > .dropdown-toggle#logout {
  color: #333;
  background-color: #e6e6e6;
  border-color: #adadad;
}
span#login_widget > .button:active:hover,
#logout:active:hover,
span#login_widget > .button.active:hover,
#logout.active:hover,
.open > .dropdown-togglespan#login_widget > .button:hover,
.open > .dropdown-toggle#logout:hover,
span#login_widget > .button:active:focus,
#logout:active:focus,
span#login_widget > .button.active:focus,
#logout.active:focus,
.open > .dropdown-togglespan#login_widget > .button:focus,
.open > .dropdown-toggle#logout:focus,
span#login_widget > .button:active.focus,
#logout:active.focus,
span#login_widget > .button.active.focus,
#logout.active.focus,
.open > .dropdown-togglespan#login_widget > .button.focus,
.open > .dropdown-toggle#logout.focus {
  color: #333;
  background-color: #d4d4d4;
  border-color: #8c8c8c;
}
span#login_widget > .button:active,
#logout:active,
span#login_widget > .button.active,
#logout.active,
.open > .dropdown-togglespan#login_widget > .button,
.open > .dropdown-toggle#logout {
  background-image: none;
}
span#login_widget > .button.disabled:hover,
#logout.disabled:hover,
span#login_widget > .button[disabled]:hover,
#logout[disabled]:hover,
fieldset[disabled] span#login_widget > .button:hover,
fieldset[disabled] #logout:hover,
span#login_widget > .button.disabled:focus,
#logout.disabled:focus,
span#login_widget > .button[disabled]:focus,
#logout[disabled]:focus,
fieldset[disabled] span#login_widget > .button:focus,
fieldset[disabled] #logout:focus,
span#login_widget > .button.disabled.focus,
#logout.disabled.focus,
span#login_widget > .button[disabled].focus,
#logout[disabled].focus,
fieldset[disabled] span#login_widget > .button.focus,
fieldset[disabled] #logout.focus {
  background-color: #fff;
  border-color: #ccc;
}
span#login_widget > .button .badge,
#logout .badge {
  color: #fff;
  background-color: #333;
}
.nav-header {
  text-transform: none;
}
#header > span {
  margin-top: 10px;
}
.modal_stretch .modal-dialog {
  /* Old browsers */
  display: -webkit-box;
  -webkit-box-orient: vertical;
  -webkit-box-align: stretch;
  display: -moz-box;
  -moz-box-orient: vertical;
  -moz-box-align: stretch;
  display: box;
  box-orient: vertical;
  box-align: stretch;
  /* Modern browsers */
  display: flex;
  flex-direction: column;
  align-items: stretch;
  min-height: 80vh;
}
.modal_stretch .modal-dialog .modal-body {
  max-height: calc(100vh - 200px);
  overflow: auto;
  flex: 1;
}
.modal-header {
  cursor: move;
}
@media (min-width: 768px) {
  .modal .modal-dialog {
    width: 700px;
  }
}
@media (min-width: 768px) {
  select.form-control {
    margin-left: 12px;
    margin-right: 12px;
  }
}
/*!
*
* IPython auth
*
*/
.center-nav {
  display: inline-block;
  margin-bottom: -4px;
}
[dir="rtl"] .center-nav form.pull-left {
  float: right !important;
  float: right;
}
[dir="rtl"] .center-nav .navbar-text {
  float: right;
}
[dir="rtl"] .navbar-inner {
  text-align: right;
}
[dir="rtl"] div.text-left {
  text-align: right;
}
/*!
*
* IPython tree view
*
*/
/* We need an invisible input field on top of the sentense*/
/* "Drag file onto the list ..." */
.alternate_upload {
  background-color: none;
  display: inline;
}
.alternate_upload.form {
  padding: 0;
  margin: 0;
}
.alternate_upload input.fileinput {
  position: absolute;
  display: block;
  width: 100%;
  height: 100%;
  overflow: hidden;
  cursor: pointer;
  opacity: 0;
  z-index: 2;
}
.alternate_upload .btn-xs > input.fileinput {
  margin: -1px -5px;
}
.alternate_upload .btn-upload {
  position: relative;
  height: 22px;
}
::-webkit-file-upload-button {
  cursor: pointer;
}
/**
 * Primary styles
 *
 * Author: Jupyter Development Team
 */
ul#tabs {
  margin-bottom: 4px;
}
ul#tabs a {
  padding-top: 6px;
  padding-bottom: 4px;
}
[dir="rtl"] ul#tabs.nav-tabs > li {
  float: right;
}
[dir="rtl"] ul#tabs.nav.nav-tabs {
  padding-right: 0;
}
ul.breadcrumb a:focus,
ul.breadcrumb a:hover {
  text-decoration: none;
}
ul.breadcrumb i.icon-home {
  font-size: 16px;
  margin-right: 4px;
}
ul.breadcrumb span {
  color: #5e5e5e;
}
.list_toolbar {
  padding: 4px 0 4px 0;
  vertical-align: middle;
}
.list_toolbar .tree-buttons {
  padding-top: 1px;
}
[dir="rtl"] .list_toolbar .tree-buttons .pull-right {
  float: left !important;
  float: left;
}
[dir="rtl"] .list_toolbar .col-sm-4,
[dir="rtl"] .list_toolbar .col-sm-8 {
  float: right;
}
.dynamic-buttons {
  padding-top: 3px;
  display: inline-block;
}
.list_toolbar [class*="span"] {
  min-height: 24px;
}
.list_header {
  font-weight: bold;
  background-color: #EEE;
}
.list_placeholder {
  font-weight: bold;
  padding-top: 4px;
  padding-bottom: 4px;
  padding-left: 7px;
  padding-right: 7px;
}
.list_container {
  margin-top: 4px;
  margin-bottom: 20px;
  border: 1px solid #ddd;
  border-radius: 2px;
}
.list_container > div {
  border-bottom: 1px solid #ddd;
}
.list_container > div:hover .list-item {
  background-color: red;
}
.list_container > div:last-child {
  border: none;
}
.list_item:hover .list_item {
  background-color: #ddd;
}
.list_item a {
  text-decoration: none;
}
.list_item:hover {
  background-color: #fafafa;
}
.list_header > div,
.list_item > div {
  padding-top: 4px;
  padding-bottom: 4px;
  padding-left: 7px;
  padding-right: 7px;
  line-height: 22px;
}
.list_header > div input,
.list_item > div input {
  margin-right: 7px;
  margin-left: 14px;
  vertical-align: text-bottom;
  line-height: 22px;
  position: relative;
  top: -1px;
}
.list_header > div .item_link,
.list_item > div .item_link {
  margin-left: -1px;
  vertical-align: baseline;
  line-height: 22px;
}
[dir="rtl"] .list_item > div input {
  margin-right: 0;
}
.new-file input[type=checkbox] {
  visibility: hidden;
}
.item_name {
  line-height: 22px;
  height: 24px;
}
.item_icon {
  font-size: 14px;
  color: #5e5e5e;
  margin-right: 7px;
  margin-left: 7px;
  line-height: 22px;
  vertical-align: baseline;
}
.item_modified {
  margin-right: 7px;
  margin-left: 7px;
}
[dir="rtl"] .item_modified.pull-right {
  float: left !important;
  float: left;
}
.item_buttons {
  line-height: 1em;
  margin-left: -5px;
}
.item_buttons .btn,
.item_buttons .btn-group,
.item_buttons .input-group {
  float: left;
}
.item_buttons > .btn,
.item_buttons > .btn-group,
.item_buttons > .input-group {
  margin-left: 5px;
}
.item_buttons .btn {
  min-width: 13ex;
}
.item_buttons .running-indicator {
  padding-top: 4px;
  color: #5cb85c;
}
.item_buttons .kernel-name {
  padding-top: 4px;
  color: #5bc0de;
  margin-right: 7px;
  float: left;
}
[dir="rtl"] .item_buttons.pull-right {
  float: left !important;
  float: left;
}
[dir="rtl"] .item_buttons .kernel-name {
  margin-left: 7px;
  float: right;
}
.toolbar_info {
  height: 24px;
  line-height: 24px;
}
.list_item input:not([type=checkbox]) {
  padding-top: 3px;
  padding-bottom: 3px;
  height: 22px;
  line-height: 14px;
  margin: 0px;
}
.highlight_text {
  color: blue;
}
#project_name {
  display: inline-block;
  padding-left: 7px;
  margin-left: -2px;
}
#project_name > .breadcrumb {
  padding: 0px;
  margin-bottom: 0px;
  background-color: transparent;
  font-weight: bold;
}
.sort_button {
  display: inline-block;
  padding-left: 7px;
}
[dir="rtl"] .sort_button.pull-right {
  float: left !important;
  float: left;
}
#tree-selector {
  padding-right: 0px;
}
#button-select-all {
  min-width: 50px;
}
[dir="rtl"] #button-select-all.btn {
  float: right ;
}
#select-all {
  margin-left: 7px;
  margin-right: 2px;
  margin-top: 2px;
  height: 16px;
}
[dir="rtl"] #select-all.pull-left {
  float: right !important;
  float: right;
}
.menu_icon {
  margin-right: 2px;
}
.tab-content .row {
  margin-left: 0px;
  margin-right: 0px;
}
.folder_icon:before {
  display: inline-block;
  font: normal normal normal 14px/1 FontAwesome;
  font-size: inherit;
  text-rendering: auto;
  -webkit-font-smoothing: antialiased;
  -moz-osx-font-smoothing: grayscale;
  content: "\f114";
}
.folder_icon:before.fa-pull-left {
  margin-right: .3em;
}
.folder_icon:before.fa-pull-right {
  margin-left: .3em;
}
.folder_icon:before.pull-left {
  margin-right: .3em;
}
.folder_icon:before.pull-right {
  margin-left: .3em;
}
.notebook_icon:before {
  display: inline-block;
  font: normal normal normal 14px/1 FontAwesome;
  font-size: inherit;
  text-rendering: auto;
  -webkit-font-smoothing: antialiased;
  -moz-osx-font-smoothing: grayscale;
  content: "\f02d";
  position: relative;
  top: -1px;
}
.notebook_icon:before.fa-pull-left {
  margin-right: .3em;
}
.notebook_icon:before.fa-pull-right {
  margin-left: .3em;
}
.notebook_icon:before.pull-left {
  margin-right: .3em;
}
.notebook_icon:before.pull-right {
  margin-left: .3em;
}
.running_notebook_icon:before {
  display: inline-block;
  font: normal normal normal 14px/1 FontAwesome;
  font-size: inherit;
  text-rendering: auto;
  -webkit-font-smoothing: antialiased;
  -moz-osx-font-smoothing: grayscale;
  content: "\f02d";
  position: relative;
  top: -1px;
  color: #5cb85c;
}
.running_notebook_icon:before.fa-pull-left {
  margin-right: .3em;
}
.running_notebook_icon:before.fa-pull-right {
  margin-left: .3em;
}
.running_notebook_icon:before.pull-left {
  margin-right: .3em;
}
.running_notebook_icon:before.pull-right {
  margin-left: .3em;
}
.file_icon:before {
  display: inline-block;
  font: normal normal normal 14px/1 FontAwesome;
  font-size: inherit;
  text-rendering: auto;
  -webkit-font-smoothing: antialiased;
  -moz-osx-font-smoothing: grayscale;
  content: "\f016";
  position: relative;
  top: -2px;
}
.file_icon:before.fa-pull-left {
  margin-right: .3em;
}
.file_icon:before.fa-pull-right {
  margin-left: .3em;
}
.file_icon:before.pull-left {
  margin-right: .3em;
}
.file_icon:before.pull-right {
  margin-left: .3em;
}
#notebook_toolbar .pull-right {
  padding-top: 0px;
  margin-right: -1px;
}
ul#new-menu {
  left: auto;
  right: 0;
}
#new-menu .dropdown-header {
  font-size: 10px;
  border-bottom: 1px solid #e5e5e5;
  padding: 0 0 3px;
  margin: -3px 20px 0;
}
.kernel-menu-icon {
  padding-right: 12px;
  width: 24px;
  content: "\f096";
}
.kernel-menu-icon:before {
  content: "\f096";
}
.kernel-menu-icon-current:before {
  content: "\f00c";
}
#tab_content {
  padding-top: 20px;
}
#running .panel-group .panel {
  margin-top: 3px;
  margin-bottom: 1em;
}
#running .panel-group .panel .panel-heading {
  background-color: #EEE;
  padding-top: 4px;
  padding-bottom: 4px;
  padding-left: 7px;
  padding-right: 7px;
  line-height: 22px;
}
#running .panel-group .panel .panel-heading a:focus,
#running .panel-group .panel .panel-heading a:hover {
  text-decoration: none;
}
#running .panel-group .panel .panel-body {
  padding: 0px;
}
#running .panel-group .panel .panel-body .list_container {
  margin-top: 0px;
  margin-bottom: 0px;
  border: 0px;
  border-radius: 0px;
}
#running .panel-group .panel .panel-body .list_container .list_item {
  border-bottom: 1px solid #ddd;
}
#running .panel-group .panel .panel-body .list_container .list_item:last-child {
  border-bottom: 0px;
}
.delete-button {
  display: none;
}
.duplicate-button {
  display: none;
}
.rename-button {
  display: none;
}
.move-button {
  display: none;
}
.download-button {
  display: none;
}
.shutdown-button {
  display: none;
}
.dynamic-instructions {
  display: inline-block;
  padding-top: 4px;
}
/*!
*
* IPython text editor webapp
*
*/
.selected-keymap i.fa {
  padding: 0px 5px;
}
.selected-keymap i.fa:before {
  content: "\f00c";
}
#mode-menu {
  overflow: auto;
  max-height: 20em;
}
.edit_app #header {
  -webkit-box-shadow: 0px 0px 12px 1px rgba(87, 87, 87, 0.2);
  box-shadow: 0px 0px 12px 1px rgba(87, 87, 87, 0.2);
}
.edit_app #menubar .navbar {
  /* Use a negative 1 bottom margin, so the border overlaps the border of the
    header */
  margin-bottom: -1px;
}
.dirty-indicator {
  display: inline-block;
  font: normal normal normal 14px/1 FontAwesome;
  font-size: inherit;
  text-rendering: auto;
  -webkit-font-smoothing: antialiased;
  -moz-osx-font-smoothing: grayscale;
  width: 20px;
}
.dirty-indicator.fa-pull-left {
  margin-right: .3em;
}
.dirty-indicator.fa-pull-right {
  margin-left: .3em;
}
.dirty-indicator.pull-left {
  margin-right: .3em;
}
.dirty-indicator.pull-right {
  margin-left: .3em;
}
.dirty-indicator-dirty {
  display: inline-block;
  font: normal normal normal 14px/1 FontAwesome;
  font-size: inherit;
  text-rendering: auto;
  -webkit-font-smoothing: antialiased;
  -moz-osx-font-smoothing: grayscale;
  width: 20px;
}
.dirty-indicator-dirty.fa-pull-left {
  margin-right: .3em;
}
.dirty-indicator-dirty.fa-pull-right {
  margin-left: .3em;
}
.dirty-indicator-dirty.pull-left {
  margin-right: .3em;
}
.dirty-indicator-dirty.pull-right {
  margin-left: .3em;
}
.dirty-indicator-clean {
  display: inline-block;
  font: normal normal normal 14px/1 FontAwesome;
  font-size: inherit;
  text-rendering: auto;
  -webkit-font-smoothing: antialiased;
  -moz-osx-font-smoothing: grayscale;
  width: 20px;
}
.dirty-indicator-clean.fa-pull-left {
  margin-right: .3em;
}
.dirty-indicator-clean.fa-pull-right {
  margin-left: .3em;
}
.dirty-indicator-clean.pull-left {
  margin-right: .3em;
}
.dirty-indicator-clean.pull-right {
  margin-left: .3em;
}
.dirty-indicator-clean:before {
  display: inline-block;
  font: normal normal normal 14px/1 FontAwesome;
  font-size: inherit;
  text-rendering: auto;
  -webkit-font-smoothing: antialiased;
  -moz-osx-font-smoothing: grayscale;
  content: "\f00c";
}
.dirty-indicator-clean:before.fa-pull-left {
  margin-right: .3em;
}
.dirty-indicator-clean:before.fa-pull-right {
  margin-left: .3em;
}
.dirty-indicator-clean:before.pull-left {
  margin-right: .3em;
}
.dirty-indicator-clean:before.pull-right {
  margin-left: .3em;
}
#filename {
  font-size: 16pt;
  display: table;
  padding: 0px 5px;
}
#current-mode {
  padding-left: 5px;
  padding-right: 5px;
}
#texteditor-backdrop {
  padding-top: 20px;
  padding-bottom: 20px;
}
@media not print {
  #texteditor-backdrop {
    background-color: #EEE;
  }
}
@media print {
  #texteditor-backdrop #texteditor-container .CodeMirror-gutter,
  #texteditor-backdrop #texteditor-container .CodeMirror-gutters {
    background-color: #fff;
  }
}
@media not print {
  #texteditor-backdrop #texteditor-container .CodeMirror-gutter,
  #texteditor-backdrop #texteditor-container .CodeMirror-gutters {
    background-color: #fff;
  }
}
@media not print {
  #texteditor-backdrop #texteditor-container {
    padding: 0px;
    background-color: #fff;
    -webkit-box-shadow: 0px 0px 12px 1px rgba(87, 87, 87, 0.2);
    box-shadow: 0px 0px 12px 1px rgba(87, 87, 87, 0.2);
  }
}
.CodeMirror-dialog {
  background-color: #fff;
}
/*!
*
* IPython notebook
*
*/
/* CSS font colors for translated ANSI escape sequences */
/* The color values are a mix of
   http://www.xcolors.net/dl/baskerville-ivorylight and
   http://www.xcolors.net/dl/euphrasia */
.ansi-black-fg {
  color: #3E424D;
}
.ansi-black-bg {
  background-color: #3E424D;
}
.ansi-black-intense-fg {
  color: #282C36;
}
.ansi-black-intense-bg {
  background-color: #282C36;
}
.ansi-red-fg {
  color: #E75C58;
}
.ansi-red-bg {
  background-color: #E75C58;
}
.ansi-red-intense-fg {
  color: #B22B31;
}
.ansi-red-intense-bg {
  background-color: #B22B31;
}
.ansi-green-fg {
  color: #00A250;
}
.ansi-green-bg {
  background-color: #00A250;
}
.ansi-green-intense-fg {
  color: #007427;
}
.ansi-green-intense-bg {
  background-color: #007427;
}
.ansi-yellow-fg {
  color: #DDB62B;
}
.ansi-yellow-bg {
  background-color: #DDB62B;
}
.ansi-yellow-intense-fg {
  color: #B27D12;
}
.ansi-yellow-intense-bg {
  background-color: #B27D12;
}
.ansi-blue-fg {
  color: #208FFB;
}
.ansi-blue-bg {
  background-color: #208FFB;
}
.ansi-blue-intense-fg {
  color: #0065CA;
}
.ansi-blue-intense-bg {
  background-color: #0065CA;
}
.ansi-magenta-fg {
  color: #D160C4;
}
.ansi-magenta-bg {
  background-color: #D160C4;
}
.ansi-magenta-intense-fg {
  color: #A03196;
}
.ansi-magenta-intense-bg {
  background-color: #A03196;
}
.ansi-cyan-fg {
  color: #60C6C8;
}
.ansi-cyan-bg {
  background-color: #60C6C8;
}
.ansi-cyan-intense-fg {
  color: #258F8F;
}
.ansi-cyan-intense-bg {
  background-color: #258F8F;
}
.ansi-white-fg {
  color: #C5C1B4;
}
.ansi-white-bg {
  background-color: #C5C1B4;
}
.ansi-white-intense-fg {
  color: #A1A6B2;
}
.ansi-white-intense-bg {
  background-color: #A1A6B2;
}
.ansi-default-inverse-fg {
  color: #FFFFFF;
}
.ansi-default-inverse-bg {
  background-color: #000000;
}
.ansi-bold {
  font-weight: bold;
}
.ansi-underline {
  text-decoration: underline;
}
/* The following styles are deprecated an will be removed in a future version */
.ansibold {
  font-weight: bold;
}
.ansi-inverse {
  outline: 0.5px dotted;
}
/* use dark versions for foreground, to improve visibility */
.ansiblack {
  color: black;
}
.ansired {
  color: darkred;
}
.ansigreen {
  color: darkgreen;
}
.ansiyellow {
  color: #c4a000;
}
.ansiblue {
  color: darkblue;
}
.ansipurple {
  color: darkviolet;
}
.ansicyan {
  color: steelblue;
}
.ansigray {
  color: gray;
}
/* and light for background, for the same reason */
.ansibgblack {
  background-color: black;
}
.ansibgred {
  background-color: red;
}
.ansibggreen {
  background-color: green;
}
.ansibgyellow {
  background-color: yellow;
}
.ansibgblue {
  background-color: blue;
}
.ansibgpurple {
  background-color: magenta;
}
.ansibgcyan {
  background-color: cyan;
}
.ansibggray {
  background-color: gray;
}
div.cell {
  /* Old browsers */
  display: -webkit-box;
  -webkit-box-orient: vertical;
  -webkit-box-align: stretch;
  display: -moz-box;
  -moz-box-orient: vertical;
  -moz-box-align: stretch;
  display: box;
  box-orient: vertical;
  box-align: stretch;
  /* Modern browsers */
  display: flex;
  flex-direction: column;
  align-items: stretch;
  border-radius: 2px;
  box-sizing: border-box;
  -moz-box-sizing: border-box;
  -webkit-box-sizing: border-box;
  border-width: 1px;
  border-style: solid;
  border-color: transparent;
  width: 100%;
  padding: 5px;
  /* This acts as a spacer between cells, that is outside the border */
  margin: 0px;
  outline: none;
  position: relative;
  overflow: visible;
}
div.cell:before {
  position: absolute;
  display: block;
  top: -1px;
  left: -1px;
  width: 5px;
  height: calc(100% +  2px);
  content: '';
  background: transparent;
}
div.cell.jupyter-soft-selected {
  border-left-color: #E3F2FD;
  border-left-width: 1px;
  padding-left: 5px;
  border-right-color: #E3F2FD;
  border-right-width: 1px;
  background: #E3F2FD;
}
@media print {
  div.cell.jupyter-soft-selected {
    border-color: transparent;
  }
}
div.cell.selected,
div.cell.selected.jupyter-soft-selected {
  border-color: #ababab;
}
div.cell.selected:before,
div.cell.selected.jupyter-soft-selected:before {
  position: absolute;
  display: block;
  top: -1px;
  left: -1px;
  width: 5px;
  height: calc(100% +  2px);
  content: '';
  background: #42A5F5;
}
@media print {
  div.cell.selected,
  div.cell.selected.jupyter-soft-selected {
    border-color: transparent;
  }
}
.edit_mode div.cell.selected {
  border-color: #66BB6A;
}
.edit_mode div.cell.selected:before {
  position: absolute;
  display: block;
  top: -1px;
  left: -1px;
  width: 5px;
  height: calc(100% +  2px);
  content: '';
  background: #66BB6A;
}
@media print {
  .edit_mode div.cell.selected {
    border-color: transparent;
  }
}
.prompt {
  /* This needs to be wide enough for 3 digit prompt numbers: In[100]: */
  min-width: 14ex;
  /* This padding is tuned to match the padding on the CodeMirror editor. */
  padding: 0.4em;
  margin: 0px;
  font-family: monospace;
  text-align: right;
  /* This has to match that of the the CodeMirror class line-height below */
  line-height: 1.21429em;
  /* Don't highlight prompt number selection */
  -webkit-touch-callout: none;
  -webkit-user-select: none;
  -khtml-user-select: none;
  -moz-user-select: none;
  -ms-user-select: none;
  user-select: none;
  /* Use default cursor */
  cursor: default;
}
@media (max-width: 540px) {
  .prompt {
    text-align: left;
  }
}
div.inner_cell {
  min-width: 0;
  /* Old browsers */
  display: -webkit-box;
  -webkit-box-orient: vertical;
  -webkit-box-align: stretch;
  display: -moz-box;
  -moz-box-orient: vertical;
  -moz-box-align: stretch;
  display: box;
  box-orient: vertical;
  box-align: stretch;
  /* Modern browsers */
  display: flex;
  flex-direction: column;
  align-items: stretch;
  /* Old browsers */
  -webkit-box-flex: 1;
  -moz-box-flex: 1;
  box-flex: 1;
  /* Modern browsers */
  flex: 1;
}
/* input_area and input_prompt must match in top border and margin for alignment */
div.input_area {
  border: 1px solid #cfcfcf;
  border-radius: 2px;
  background: #f7f7f7;
  line-height: 1.21429em;
}
/* This is needed so that empty prompt areas can collapse to zero height when there
   is no content in the output_subarea and the prompt. The main purpose of this is
   to make sure that empty JavaScript output_subareas have no height. */
div.prompt:empty {
  padding-top: 0;
  padding-bottom: 0;
}
div.unrecognized_cell {
  padding: 5px 5px 5px 0px;
  /* Old browsers */
  display: -webkit-box;
  -webkit-box-orient: horizontal;
  -webkit-box-align: stretch;
  display: -moz-box;
  -moz-box-orient: horizontal;
  -moz-box-align: stretch;
  display: box;
  box-orient: horizontal;
  box-align: stretch;
  /* Modern browsers */
  display: flex;
  flex-direction: row;
  align-items: stretch;
}
div.unrecognized_cell .inner_cell {
  border-radius: 2px;
  padding: 5px;
  font-weight: bold;
  color: red;
  border: 1px solid #cfcfcf;
  background: #eaeaea;
}
div.unrecognized_cell .inner_cell a {
  color: inherit;
  text-decoration: none;
}
div.unrecognized_cell .inner_cell a:hover {
  color: inherit;
  text-decoration: none;
}
@media (max-width: 540px) {
  div.unrecognized_cell > div.prompt {
    display: none;
  }
}
div.code_cell {
  /* avoid page breaking on code cells when printing */
}
@media print {
  div.code_cell {
    page-break-inside: avoid;
  }
}
/* any special styling for code cells that are currently running goes here */
div.input {
  page-break-inside: avoid;
  /* Old browsers */
  display: -webkit-box;
  -webkit-box-orient: horizontal;
  -webkit-box-align: stretch;
  display: -moz-box;
  -moz-box-orient: horizontal;
  -moz-box-align: stretch;
  display: box;
  box-orient: horizontal;
  box-align: stretch;
  /* Modern browsers */
  display: flex;
  flex-direction: row;
  align-items: stretch;
}
@media (max-width: 540px) {
  div.input {
    /* Old browsers */
    display: -webkit-box;
    -webkit-box-orient: vertical;
    -webkit-box-align: stretch;
    display: -moz-box;
    -moz-box-orient: vertical;
    -moz-box-align: stretch;
    display: box;
    box-orient: vertical;
    box-align: stretch;
    /* Modern browsers */
    display: flex;
    flex-direction: column;
    align-items: stretch;
  }
}
/* input_area and input_prompt must match in top border and margin for alignment */
div.input_prompt {
  color: #303F9F;
  border-top: 1px solid transparent;
}
div.input_area > div.highlight {
  margin: 0.4em;
  border: none;
  padding: 0px;
  background-color: transparent;
}
div.input_area > div.highlight > pre {
  margin: 0px;
  border: none;
  padding: 0px;
  background-color: transparent;
}
/* The following gets added to the <head> if it is detected that the user has a
 * monospace font with inconsistent normal/bold/italic height.  See
 * notebookmain.js.  Such fonts will have keywords vertically offset with
 * respect to the rest of the text.  The user should select a better font.
 * See: https://github.com/ipython/ipython/issues/1503
 *
 * .CodeMirror span {
 *      vertical-align: bottom;
 * }
 */
.CodeMirror {
  line-height: 1.21429em;
  /* Changed from 1em to our global default */
  font-size: 14px;
  height: auto;
  /* Changed to auto to autogrow */
  background: none;
  /* Changed from white to allow our bg to show through */
}
.CodeMirror-scroll {
  /*  The CodeMirror docs are a bit fuzzy on if overflow-y should be hidden or visible.*/
  /*  We have found that if it is visible, vertical scrollbars appear with font size changes.*/
  overflow-y: hidden;
  overflow-x: auto;
}
.CodeMirror-lines {
  /* In CM2, this used to be 0.4em, but in CM3 it went to 4px. We need the em value because */
  /* we have set a different line-height and want this to scale with that. */
  /* Note that this should set vertical padding only, since CodeMirror assumes
       that horizontal padding will be set on CodeMirror pre */
  padding: 0.4em 0;
}
.CodeMirror-linenumber {
  padding: 0 8px 0 4px;
}
.CodeMirror-gutters {
  border-bottom-left-radius: 2px;
  border-top-left-radius: 2px;
}
.CodeMirror pre {
  /* In CM3 this went to 4px from 0 in CM2. This sets horizontal padding only,
    use .CodeMirror-lines for vertical */
  padding: 0 0.4em;
  border: 0;
  border-radius: 0;
}
.CodeMirror-cursor {
  border-left: 1.4px solid black;
}
@media screen and (min-width: 2138px) and (max-width: 4319px) {
  .CodeMirror-cursor {
    border-left: 2px solid black;
  }
}
@media screen and (min-width: 4320px) {
  .CodeMirror-cursor {
    border-left: 4px solid black;
  }
}
/*

Original style from softwaremaniacs.org (c) Ivan Sagalaev <Maniac@SoftwareManiacs.Org>
Adapted from GitHub theme

*/
.highlight-base {
  color: #000;
}
.highlight-variable {
  color: #000;
}
.highlight-variable-2 {
  color: #1a1a1a;
}
.highlight-variable-3 {
  color: #333333;
}
.highlight-string {
  color: #BA2121;
}
.highlight-comment {
  color: #408080;
  font-style: italic;
}
.highlight-number {
  color: #080;
}
.highlight-atom {
  color: #88F;
}
.highlight-keyword {
  color: #008000;
  font-weight: bold;
}
.highlight-builtin {
  color: #008000;
}
.highlight-error {
  color: #f00;
}
.highlight-operator {
  color: #AA22FF;
  font-weight: bold;
}
.highlight-meta {
  color: #AA22FF;
}
/* previously not defined, copying from default codemirror */
.highlight-def {
  color: #00f;
}
.highlight-string-2 {
  color: #f50;
}
.highlight-qualifier {
  color: #555;
}
.highlight-bracket {
  color: #997;
}
.highlight-tag {
  color: #170;
}
.highlight-attribute {
  color: #00c;
}
.highlight-header {
  color: blue;
}
.highlight-quote {
  color: #090;
}
.highlight-link {
  color: #00c;
}
/* apply the same style to codemirror */
.cm-s-ipython span.cm-keyword {
  color: #008000;
  font-weight: bold;
}
.cm-s-ipython span.cm-atom {
  color: #88F;
}
.cm-s-ipython span.cm-number {
  color: #080;
}
.cm-s-ipython span.cm-def {
  color: #00f;
}
.cm-s-ipython span.cm-variable {
  color: #000;
}
.cm-s-ipython span.cm-operator {
  color: #AA22FF;
  font-weight: bold;
}
.cm-s-ipython span.cm-variable-2 {
  color: #1a1a1a;
}
.cm-s-ipython span.cm-variable-3 {
  color: #333333;
}
.cm-s-ipython span.cm-comment {
  color: #408080;
  font-style: italic;
}
.cm-s-ipython span.cm-string {
  color: #BA2121;
}
.cm-s-ipython span.cm-string-2 {
  color: #f50;
}
.cm-s-ipython span.cm-meta {
  color: #AA22FF;
}
.cm-s-ipython span.cm-qualifier {
  color: #555;
}
.cm-s-ipython span.cm-builtin {
  color: #008000;
}
.cm-s-ipython span.cm-bracket {
  color: #997;
}
.cm-s-ipython span.cm-tag {
  color: #170;
}
.cm-s-ipython span.cm-attribute {
  color: #00c;
}
.cm-s-ipython span.cm-header {
  color: blue;
}
.cm-s-ipython span.cm-quote {
  color: #090;
}
.cm-s-ipython span.cm-link {
  color: #00c;
}
.cm-s-ipython span.cm-error {
  color: #f00;
}
.cm-s-ipython span.cm-tab {
  background: url(data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADAAAAAMCAYAAAAkuj5RAAAAAXNSR0IArs4c6QAAAGFJREFUSMft1LsRQFAQheHPowAKoACx3IgEKtaEHujDjORSgWTH/ZOdnZOcM/sgk/kFFWY0qV8foQwS4MKBCS3qR6ixBJvElOobYAtivseIE120FaowJPN75GMu8j/LfMwNjh4HUpwg4LUAAAAASUVORK5CYII=);
  background-position: right;
  background-repeat: no-repeat;
}
div.output_wrapper {
  /* this position must be relative to enable descendents to be absolute within it */
  position: relative;
  /* Old browsers */
  display: -webkit-box;
  -webkit-box-orient: vertical;
  -webkit-box-align: stretch;
  display: -moz-box;
  -moz-box-orient: vertical;
  -moz-box-align: stretch;
  display: box;
  box-orient: vertical;
  box-align: stretch;
  /* Modern browsers */
  display: flex;
  flex-direction: column;
  align-items: stretch;
  z-index: 1;
}
/* class for the output area when it should be height-limited */
div.output_scroll {
  /* ideally, this would be max-height, but FF barfs all over that */
  height: 24em;
  /* FF needs this *and the wrapper* to specify full width, or it will shrinkwrap */
  width: 100%;
  overflow: auto;
  border-radius: 2px;
  -webkit-box-shadow: inset 0 2px 8px rgba(0, 0, 0, 0.8);
  box-shadow: inset 0 2px 8px rgba(0, 0, 0, 0.8);
  display: block;
}
/* output div while it is collapsed */
div.output_collapsed {
  margin: 0px;
  padding: 0px;
  /* Old browsers */
  display: -webkit-box;
  -webkit-box-orient: vertical;
  -webkit-box-align: stretch;
  display: -moz-box;
  -moz-box-orient: vertical;
  -moz-box-align: stretch;
  display: box;
  box-orient: vertical;
  box-align: stretch;
  /* Modern browsers */
  display: flex;
  flex-direction: column;
  align-items: stretch;
}
div.out_prompt_overlay {
  height: 100%;
  padding: 0px 0.4em;
  position: absolute;
  border-radius: 2px;
}
div.out_prompt_overlay:hover {
  /* use inner shadow to get border that is computed the same on WebKit/FF */
  -webkit-box-shadow: inset 0 0 1px #000;
  box-shadow: inset 0 0 1px #000;
  background: rgba(240, 240, 240, 0.5);
}
div.output_prompt {
  color: #D84315;
}
/* This class is the outer container of all output sections. */
div.output_area {
  padding: 0px;
  page-break-inside: avoid;
  /* Old browsers */
  display: -webkit-box;
  -webkit-box-orient: horizontal;
  -webkit-box-align: stretch;
  display: -moz-box;
  -moz-box-orient: horizontal;
  -moz-box-align: stretch;
  display: box;
  box-orient: horizontal;
  box-align: stretch;
  /* Modern browsers */
  display: flex;
  flex-direction: row;
  align-items: stretch;
}
div.output_area .MathJax_Display {
  text-align: left !important;
}
div.output_area .rendered_html table {
  margin-left: 0;
  margin-right: 0;
}
div.output_area .rendered_html img {
  margin-left: 0;
  margin-right: 0;
}
div.output_area img,
div.output_area svg {
  max-width: 100%;
  height: auto;
}
div.output_area img.unconfined,
div.output_area svg.unconfined {
  max-width: none;
}
div.output_area .mglyph > img {
  max-width: none;
}
/* This is needed to protect the pre formating from global settings such
   as that of bootstrap */
.output {
  /* Old browsers */
  display: -webkit-box;
  -webkit-box-orient: vertical;
  -webkit-box-align: stretch;
  display: -moz-box;
  -moz-box-orient: vertical;
  -moz-box-align: stretch;
  display: box;
  box-orient: vertical;
  box-align: stretch;
  /* Modern browsers */
  display: flex;
  flex-direction: column;
  align-items: stretch;
}
@media (max-width: 540px) {
  div.output_area {
    /* Old browsers */
    display: -webkit-box;
    -webkit-box-orient: vertical;
    -webkit-box-align: stretch;
    display: -moz-box;
    -moz-box-orient: vertical;
    -moz-box-align: stretch;
    display: box;
    box-orient: vertical;
    box-align: stretch;
    /* Modern browsers */
    display: flex;
    flex-direction: column;
    align-items: stretch;
  }
}
div.output_area pre {
  margin: 0;
  padding: 1px 0 1px 0;
  border: 0;
  vertical-align: baseline;
  color: black;
  background-color: transparent;
  border-radius: 0;
}
/* This class is for the output subarea inside the output_area and after
   the prompt div. */
div.output_subarea {
  overflow-x: auto;
  padding: 0.4em;
  /* Old browsers */
  -webkit-box-flex: 1;
  -moz-box-flex: 1;
  box-flex: 1;
  /* Modern browsers */
  flex: 1;
  max-width: calc(100% - 14ex);
}
div.output_scroll div.output_subarea {
  overflow-x: visible;
}
/* The rest of the output_* classes are for special styling of the different
   output types */
/* all text output has this class: */
div.output_text {
  text-align: left;
  color: #000;
  /* This has to match that of the the CodeMirror class line-height below */
  line-height: 1.21429em;
}
/* stdout/stderr are 'text' as well as 'stream', but execute_result/error are *not* streams */
div.output_stderr {
  background: #fdd;
  /* very light red background for stderr */
}
div.output_latex {
  text-align: left;
}
/* Empty output_javascript divs should have no height */
div.output_javascript:empty {
  padding: 0;
}
.js-error {
  color: darkred;
}
/* raw_input styles */
div.raw_input_container {
  line-height: 1.21429em;
  padding-top: 5px;
}
pre.raw_input_prompt {
  /* nothing needed here. */
}
input.raw_input {
  font-family: monospace;
  font-size: inherit;
  color: inherit;
  width: auto;
  /* make sure input baseline aligns with prompt */
  vertical-align: baseline;
  /* padding + margin = 0.5em between prompt and cursor */
  padding: 0em 0.25em;
  margin: 0em 0.25em;
}
input.raw_input:focus {
  box-shadow: none;
}
p.p-space {
  margin-bottom: 10px;
}
div.output_unrecognized {
  padding: 5px;
  font-weight: bold;
  color: red;
}
div.output_unrecognized a {
  color: inherit;
  text-decoration: none;
}
div.output_unrecognized a:hover {
  color: inherit;
  text-decoration: none;
}
.rendered_html {
  color: #000;
  /* any extras will just be numbers: */
}
.rendered_html em {
  font-style: italic;
}
.rendered_html strong {
  font-weight: bold;
}
.rendered_html u {
  text-decoration: underline;
}
.rendered_html :link {
  text-decoration: underline;
}
.rendered_html :visited {
  text-decoration: underline;
}
.rendered_html h1 {
  font-size: 185.7%;
  margin: 1.08em 0 0 0;
  font-weight: bold;
  line-height: 1.0;
}
.rendered_html h2 {
  font-size: 157.1%;
  margin: 1.27em 0 0 0;
  font-weight: bold;
  line-height: 1.0;
}
.rendered_html h3 {
  font-size: 128.6%;
  margin: 1.55em 0 0 0;
  font-weight: bold;
  line-height: 1.0;
}
.rendered_html h4 {
  font-size: 100%;
  margin: 2em 0 0 0;
  font-weight: bold;
  line-height: 1.0;
}
.rendered_html h5 {
  font-size: 100%;
  margin: 2em 0 0 0;
  font-weight: bold;
  line-height: 1.0;
  font-style: italic;
}
.rendered_html h6 {
  font-size: 100%;
  margin: 2em 0 0 0;
  font-weight: bold;
  line-height: 1.0;
  font-style: italic;
}
.rendered_html h1:first-child {
  margin-top: 0.538em;
}
.rendered_html h2:first-child {
  margin-top: 0.636em;
}
.rendered_html h3:first-child {
  margin-top: 0.777em;
}
.rendered_html h4:first-child {
  margin-top: 1em;
}
.rendered_html h5:first-child {
  margin-top: 1em;
}
.rendered_html h6:first-child {
  margin-top: 1em;
}
.rendered_html ul:not(.list-inline),
.rendered_html ol:not(.list-inline) {
  padding-left: 2em;
}
.rendered_html ul {
  list-style: disc;
}
.rendered_html ul ul {
  list-style: square;
  margin-top: 0;
}
.rendered_html ul ul ul {
  list-style: circle;
}
.rendered_html ol {
  list-style: decimal;
}
.rendered_html ol ol {
  list-style: upper-alpha;
  margin-top: 0;
}
.rendered_html ol ol ol {
  list-style: lower-alpha;
}
.rendered_html ol ol ol ol {
  list-style: lower-roman;
}
.rendered_html ol ol ol ol ol {
  list-style: decimal;
}
.rendered_html * + ul {
  margin-top: 1em;
}
.rendered_html * + ol {
  margin-top: 1em;
}
.rendered_html hr {
  color: black;
  background-color: black;
}
.rendered_html pre {
  margin: 1em 2em;
  padding: 0px;
  background-color: #fff;
}
.rendered_html code {
  background-color: #eff0f1;
}
.rendered_html p code {
  padding: 1px 5px;
}
.rendered_html pre code {
  background-color: #fff;
}
.rendered_html pre,
.rendered_html code {
  border: 0;
  color: #000;
  font-size: 100%;
}
.rendered_html blockquote {
  margin: 1em 2em;
}
.rendered_html table {
  margin-left: auto;
  margin-right: auto;
  border: none;
  border-collapse: collapse;
  border-spacing: 0;
  color: black;
  font-size: 12px;
  table-layout: fixed;
}
.rendered_html thead {
  border-bottom: 1px solid black;
  vertical-align: bottom;
}
.rendered_html tr,
.rendered_html th,
.rendered_html td {
  text-align: right;
  vertical-align: middle;
  padding: 0.5em 0.5em;
  line-height: normal;
  white-space: normal;
  max-width: none;
  border: none;
}
.rendered_html th {
  font-weight: bold;
}
.rendered_html tbody tr:nth-child(odd) {
  background: #f5f5f5;
}
.rendered_html tbody tr:hover {
  background: rgba(66, 165, 245, 0.2);
}
.rendered_html * + table {
  margin-top: 1em;
}
.rendered_html p {
  text-align: left;
}
.rendered_html * + p {
  margin-top: 1em;
}
.rendered_html img {
  display: block;
  margin-left: auto;
  margin-right: auto;
}
.rendered_html * + img {
  margin-top: 1em;
}
.rendered_html img,
.rendered_html svg {
  max-width: 100%;
  height: auto;
}
.rendered_html img.unconfined,
.rendered_html svg.unconfined {
  max-width: none;
}
.rendered_html .alert {
  margin-bottom: initial;
}
.rendered_html * + .alert {
  margin-top: 1em;
}
[dir="rtl"] .rendered_html p {
  text-align: right;
}
div.text_cell {
  /* Old browsers */
  display: -webkit-box;
  -webkit-box-orient: horizontal;
  -webkit-box-align: stretch;
  display: -moz-box;
  -moz-box-orient: horizontal;
  -moz-box-align: stretch;
  display: box;
  box-orient: horizontal;
  box-align: stretch;
  /* Modern browsers */
  display: flex;
  flex-direction: row;
  align-items: stretch;
}
@media (max-width: 540px) {
  div.text_cell > div.prompt {
    display: none;
  }
}
div.text_cell_render {
  /*font-family: "Helvetica Neue", Arial, Helvetica, Geneva, sans-serif;*/
  outline: none;
  resize: none;
  width: inherit;
  border-style: none;
  padding: 0.5em 0.5em 0.5em 0.4em;
  color: #000;
  box-sizing: border-box;
  -moz-box-sizing: border-box;
  -webkit-box-sizing: border-box;
}
a.anchor-link:link {
  text-decoration: none;
  padding: 0px 20px;
  visibility: hidden;
}
h1:hover .anchor-link,
h2:hover .anchor-link,
h3:hover .anchor-link,
h4:hover .anchor-link,
h5:hover .anchor-link,
h6:hover .anchor-link {
  visibility: visible;
}
.text_cell.rendered .input_area {
  display: none;
}
.text_cell.rendered .rendered_html {
  overflow-x: auto;
  overflow-y: hidden;
}
.text_cell.rendered .rendered_html tr,
.text_cell.rendered .rendered_html th,
.text_cell.rendered .rendered_html td {
  max-width: none;
}
.text_cell.unrendered .text_cell_render {
  display: none;
}
.text_cell .dropzone .input_area {
  border: 2px dashed #bababa;
  margin: -1px;
}
.cm-header-1,
.cm-header-2,
.cm-header-3,
.cm-header-4,
.cm-header-5,
.cm-header-6 {
  font-weight: bold;
  font-family: "Helvetica Neue", Helvetica, Arial, sans-serif;
}
.cm-header-1 {
  font-size: 185.7%;
}
.cm-header-2 {
  font-size: 157.1%;
}
.cm-header-3 {
  font-size: 128.6%;
}
.cm-header-4 {
  font-size: 110%;
}
.cm-header-5 {
  font-size: 100%;
  font-style: italic;
}
.cm-header-6 {
  font-size: 100%;
  font-style: italic;
}
/*!
*
* IPython notebook webapp
*
*/
@media (max-width: 767px) {
  .notebook_app {
    padding-left: 0px;
    padding-right: 0px;
  }
}
#ipython-main-app {
  box-sizing: border-box;
  -moz-box-sizing: border-box;
  -webkit-box-sizing: border-box;
  height: 100%;
}
div#notebook_panel {
  margin: 0px;
  padding: 0px;
  box-sizing: border-box;
  -moz-box-sizing: border-box;
  -webkit-box-sizing: border-box;
  height: 100%;
}
div#notebook {
  font-size: 14px;
  line-height: 20px;
  overflow-y: hidden;
  overflow-x: auto;
  width: 100%;
  /* This spaces the page away from the edge of the notebook area */
  padding-top: 20px;
  margin: 0px;
  outline: none;
  box-sizing: border-box;
  -moz-box-sizing: border-box;
  -webkit-box-sizing: border-box;
  min-height: 100%;
}
@media not print {
  #notebook-container {
    padding: 15px;
    background-color: #fff;
    min-height: 0;
    -webkit-box-shadow: 0px 0px 12px 1px rgba(87, 87, 87, 0.2);
    box-shadow: 0px 0px 12px 1px rgba(87, 87, 87, 0.2);
  }
}
@media print {
  #notebook-container {
    width: 100%;
  }
}
div.ui-widget-content {
  border: 1px solid #ababab;
  outline: none;
}
pre.dialog {
  background-color: #f7f7f7;
  border: 1px solid #ddd;
  border-radius: 2px;
  padding: 0.4em;
  padding-left: 2em;
}
p.dialog {
  padding: 0.2em;
}
/* Word-wrap output correctly.  This is the CSS3 spelling, though Firefox seems
   to not honor it correctly.  Webkit browsers (Chrome, rekonq, Safari) do.
 */
pre,
code,
kbd,
samp {
  white-space: pre-wrap;
}
#fonttest {
  font-family: monospace;
}
p {
  margin-bottom: 0;
}
.end_space {
  min-height: 100px;
  transition: height .2s ease;
}
.notebook_app > #header {
  -webkit-box-shadow: 0px 0px 12px 1px rgba(87, 87, 87, 0.2);
  box-shadow: 0px 0px 12px 1px rgba(87, 87, 87, 0.2);
}
@media not print {
  .notebook_app {
    background-color: #EEE;
  }
}
kbd {
  border-style: solid;
  border-width: 1px;
  box-shadow: none;
  margin: 2px;
  padding-left: 2px;
  padding-right: 2px;
  padding-top: 1px;
  padding-bottom: 1px;
}
.jupyter-keybindings {
  padding: 1px;
  line-height: 24px;
  border-bottom: 1px solid gray;
}
.jupyter-keybindings input {
  margin: 0;
  padding: 0;
  border: none;
}
.jupyter-keybindings i {
  padding: 6px;
}
.well code {
  background-color: #ffffff;
  border-color: #ababab;
  border-width: 1px;
  border-style: solid;
  padding: 2px;
  padding-top: 1px;
  padding-bottom: 1px;
}
/* CSS for the cell toolbar */
.celltoolbar {
  border: thin solid #CFCFCF;
  border-bottom: none;
  background: #EEE;
  border-radius: 2px 2px 0px 0px;
  width: 100%;
  height: 29px;
  padding-right: 4px;
  /* Old browsers */
  display: -webkit-box;
  -webkit-box-orient: horizontal;
  -webkit-box-align: stretch;
  display: -moz-box;
  -moz-box-orient: horizontal;
  -moz-box-align: stretch;
  display: box;
  box-orient: horizontal;
  box-align: stretch;
  /* Modern browsers */
  display: flex;
  flex-direction: row;
  align-items: stretch;
  /* Old browsers */
  -webkit-box-pack: end;
  -moz-box-pack: end;
  box-pack: end;
  /* Modern browsers */
  justify-content: flex-end;
  display: -webkit-flex;
}
@media print {
  .celltoolbar {
    display: none;
  }
}
.ctb_hideshow {
  display: none;
  vertical-align: bottom;
}
/* ctb_show is added to the ctb_hideshow div to show the cell toolbar.
   Cell toolbars are only shown when the ctb_global_show class is also set.
*/
.ctb_global_show .ctb_show.ctb_hideshow {
  display: block;
}
.ctb_global_show .ctb_show + .input_area,
.ctb_global_show .ctb_show + div.text_cell_input,
.ctb_global_show .ctb_show ~ div.text_cell_render {
  border-top-right-radius: 0px;
  border-top-left-radius: 0px;
}
.ctb_global_show .ctb_show ~ div.text_cell_render {
  border: 1px solid #cfcfcf;
}
.celltoolbar {
  font-size: 87%;
  padding-top: 3px;
}
.celltoolbar select {
  display: block;
  width: 100%;
  height: 32px;
  padding: 6px 12px;
  font-size: 13px;
  line-height: 1.42857143;
  color: #555555;
  background-color: #fff;
  background-image: none;
  border: 1px solid #ccc;
  border-radius: 2px;
  -webkit-box-shadow: inset 0 1px 1px rgba(0, 0, 0, 0.075);
  box-shadow: inset 0 1px 1px rgba(0, 0, 0, 0.075);
  -webkit-transition: border-color ease-in-out .15s, box-shadow ease-in-out .15s;
  -o-transition: border-color ease-in-out .15s, box-shadow ease-in-out .15s;
  transition: border-color ease-in-out .15s, box-shadow ease-in-out .15s;
  height: 30px;
  padding: 5px 10px;
  font-size: 12px;
  line-height: 1.5;
  border-radius: 1px;
  width: inherit;
  font-size: inherit;
  height: 22px;
  padding: 0px;
  display: inline-block;
}
.celltoolbar select:focus {
  border-color: #66afe9;
  outline: 0;
  -webkit-box-shadow: inset 0 1px 1px rgba(0,0,0,.075), 0 0 8px rgba(102, 175, 233, 0.6);
  box-shadow: inset 0 1px 1px rgba(0,0,0,.075), 0 0 8px rgba(102, 175, 233, 0.6);
}
.celltoolbar select::-moz-placeholder {
  color: #999;
  opacity: 1;
}
.celltoolbar select:-ms-input-placeholder {
  color: #999;
}
.celltoolbar select::-webkit-input-placeholder {
  color: #999;
}
.celltoolbar select::-ms-expand {
  border: 0;
  background-color: transparent;
}
.celltoolbar select[disabled],
.celltoolbar select[readonly],
fieldset[disabled] .celltoolbar select {
  background-color: #eeeeee;
  opacity: 1;
}
.celltoolbar select[disabled],
fieldset[disabled] .celltoolbar select {
  cursor: not-allowed;
}
textarea.celltoolbar select {
  height: auto;
}
select.celltoolbar select {
  height: 30px;
  line-height: 30px;
}
textarea.celltoolbar select,
select[multiple].celltoolbar select {
  height: auto;
}
.celltoolbar label {
  margin-left: 5px;
  margin-right: 5px;
}
.tags_button_container {
  width: 100%;
  display: flex;
}
.tag-container {
  display: flex;
  flex-direction: row;
  flex-grow: 1;
  overflow: hidden;
  position: relative;
}
.tag-container > * {
  margin: 0 4px;
}
.remove-tag-btn {
  margin-left: 4px;
}
.tags-input {
  display: flex;
}
.cell-tag:last-child:after {
  content: "";
  position: absolute;
  right: 0;
  width: 40px;
  height: 100%;
  /* Fade to background color of cell toolbar */
  background: linear-gradient(to right, rgba(0, 0, 0, 0), #EEE);
}
.tags-input > * {
  margin-left: 4px;
}
.cell-tag,
.tags-input input,
.tags-input button {
  display: block;
  width: 100%;
  height: 32px;
  padding: 6px 12px;
  font-size: 13px;
  line-height: 1.42857143;
  color: #555555;
  background-color: #fff;
  background-image: none;
  border: 1px solid #ccc;
  border-radius: 2px;
  -webkit-box-shadow: inset 0 1px 1px rgba(0, 0, 0, 0.075);
  box-shadow: inset 0 1px 1px rgba(0, 0, 0, 0.075);
  -webkit-transition: border-color ease-in-out .15s, box-shadow ease-in-out .15s;
  -o-transition: border-color ease-in-out .15s, box-shadow ease-in-out .15s;
  transition: border-color ease-in-out .15s, box-shadow ease-in-out .15s;
  height: 30px;
  padding: 5px 10px;
  font-size: 12px;
  line-height: 1.5;
  border-radius: 1px;
  box-shadow: none;
  width: inherit;
  font-size: inherit;
  height: 22px;
  line-height: 22px;
  padding: 0px 4px;
  display: inline-block;
}
.cell-tag:focus,
.tags-input input:focus,
.tags-input button:focus {
  border-color: #66afe9;
  outline: 0;
  -webkit-box-shadow: inset 0 1px 1px rgba(0,0,0,.075), 0 0 8px rgba(102, 175, 233, 0.6);
  box-shadow: inset 0 1px 1px rgba(0,0,0,.075), 0 0 8px rgba(102, 175, 233, 0.6);
}
.cell-tag::-moz-placeholder,
.tags-input input::-moz-placeholder,
.tags-input button::-moz-placeholder {
  color: #999;
  opacity: 1;
}
.cell-tag:-ms-input-placeholder,
.tags-input input:-ms-input-placeholder,
.tags-input button:-ms-input-placeholder {
  color: #999;
}
.cell-tag::-webkit-input-placeholder,
.tags-input input::-webkit-input-placeholder,
.tags-input button::-webkit-input-placeholder {
  color: #999;
}
.cell-tag::-ms-expand,
.tags-input input::-ms-expand,
.tags-input button::-ms-expand {
  border: 0;
  background-color: transparent;
}
.cell-tag[disabled],
.tags-input input[disabled],
.tags-input button[disabled],
.cell-tag[readonly],
.tags-input input[readonly],
.tags-input button[readonly],
fieldset[disabled] .cell-tag,
fieldset[disabled] .tags-input input,
fieldset[disabled] .tags-input button {
  background-color: #eeeeee;
  opacity: 1;
}
.cell-tag[disabled],
.tags-input input[disabled],
.tags-input button[disabled],
fieldset[disabled] .cell-tag,
fieldset[disabled] .tags-input input,
fieldset[disabled] .tags-input button {
  cursor: not-allowed;
}
textarea.cell-tag,
textarea.tags-input input,
textarea.tags-input button {
  height: auto;
}
select.cell-tag,
select.tags-input input,
select.tags-input button {
  height: 30px;
  line-height: 30px;
}
textarea.cell-tag,
textarea.tags-input input,
textarea.tags-input button,
select[multiple].cell-tag,
select[multiple].tags-input input,
select[multiple].tags-input button {
  height: auto;
}
.cell-tag,
.tags-input button {
  padding: 0px 4px;
}
.cell-tag {
  background-color: #fff;
  white-space: nowrap;
}
.tags-input input[type=text]:focus {
  outline: none;
  box-shadow: none;
  border-color: #ccc;
}
.completions {
  position: absolute;
  z-index: 110;
  overflow: hidden;
  border: 1px solid #ababab;
  border-radius: 2px;
  -webkit-box-shadow: 0px 6px 10px -1px #adadad;
  box-shadow: 0px 6px 10px -1px #adadad;
  line-height: 1;
}
.completions select {
  background: white;
  outline: none;
  border: none;
  padding: 0px;
  margin: 0px;
  overflow: auto;
  font-family: monospace;
  font-size: 110%;
  color: #000;
  width: auto;
}
.completions select option.context {
  color: #286090;
}
#kernel_logo_widget .current_kernel_logo {
  display: none;
  margin-top: -1px;
  margin-bottom: -1px;
  width: 32px;
  height: 32px;
}
[dir="rtl"] #kernel_logo_widget {
  float: left !important;
  float: left;
}
.modal .modal-body .move-path {
  display: flex;
  flex-direction: row;
  justify-content: space;
  align-items: center;
}
.modal .modal-body .move-path .server-root {
  padding-right: 20px;
}
.modal .modal-body .move-path .path-input {
  flex: 1;
}
#menubar {
  box-sizing: border-box;
  -moz-box-sizing: border-box;
  -webkit-box-sizing: border-box;
  margin-top: 1px;
}
#menubar .navbar {
  border-top: 1px;
  border-radius: 0px 0px 2px 2px;
  margin-bottom: 0px;
}
#menubar .navbar-toggle {
  float: left;
  padding-top: 7px;
  padding-bottom: 7px;
  border: none;
}
#menubar .navbar-collapse {
  clear: left;
}
[dir="rtl"] #menubar .navbar-toggle {
  float: right;
}
[dir="rtl"] #menubar .navbar-collapse {
  clear: right;
}
[dir="rtl"] #menubar .navbar-nav {
  float: right;
}
[dir="rtl"] #menubar .nav {
  padding-right: 0px;
}
[dir="rtl"] #menubar .navbar-nav > li {
  float: right;
}
[dir="rtl"] #menubar .navbar-right {
  float: left !important;
}
[dir="rtl"] ul.dropdown-menu {
  text-align: right;
  left: auto;
}
[dir="rtl"] ul#new-menu.dropdown-menu {
  right: auto;
  left: 0;
}
.nav-wrapper {
  border-bottom: 1px solid #e7e7e7;
}
i.menu-icon {
  padding-top: 4px;
}
[dir="rtl"] i.menu-icon.pull-right {
  float: left !important;
  float: left;
}
ul#help_menu li a {
  overflow: hidden;
  padding-right: 2.2em;
}
ul#help_menu li a i {
  margin-right: -1.2em;
}
[dir="rtl"] ul#help_menu li a {
  padding-left: 2.2em;
}
[dir="rtl"] ul#help_menu li a i {
  margin-right: 0;
  margin-left: -1.2em;
}
[dir="rtl"] ul#help_menu li a i.pull-right {
  float: left !important;
  float: left;
}
.dropdown-submenu {
  position: relative;
}
.dropdown-submenu > .dropdown-menu {
  top: 0;
  left: 100%;
  margin-top: -6px;
  margin-left: -1px;
}
[dir="rtl"] .dropdown-submenu > .dropdown-menu {
  right: 100%;
  margin-right: -1px;
}
.dropdown-submenu:hover > .dropdown-menu {
  display: block;
}
.dropdown-submenu > a:after {
  display: inline-block;
  font: normal normal normal 14px/1 FontAwesome;
  font-size: inherit;
  text-rendering: auto;
  -webkit-font-smoothing: antialiased;
  -moz-osx-font-smoothing: grayscale;
  display: block;
  content: "\f0da";
  float: right;
  color: #333333;
  margin-top: 2px;
  margin-right: -10px;
}
.dropdown-submenu > a:after.fa-pull-left {
  margin-right: .3em;
}
.dropdown-submenu > a:after.fa-pull-right {
  margin-left: .3em;
}
.dropdown-submenu > a:after.pull-left {
  margin-right: .3em;
}
.dropdown-submenu > a:after.pull-right {
  margin-left: .3em;
}
[dir="rtl"] .dropdown-submenu > a:after {
  float: left;
  content: "\f0d9";
  margin-right: 0;
  margin-left: -10px;
}
.dropdown-submenu:hover > a:after {
  color: #262626;
}
.dropdown-submenu.pull-left {
  float: none;
}
.dropdown-submenu.pull-left > .dropdown-menu {
  left: -100%;
  margin-left: 10px;
}
#notification_area {
  float: right !important;
  float: right;
  z-index: 10;
}
[dir="rtl"] #notification_area {
  float: left !important;
  float: left;
}
.indicator_area {
  float: right !important;
  float: right;
  color: #777;
  margin-left: 5px;
  margin-right: 5px;
  width: 11px;
  z-index: 10;
  text-align: center;
  width: auto;
}
[dir="rtl"] .indicator_area {
  float: left !important;
  float: left;
}
#kernel_indicator {
  float: right !important;
  float: right;
  color: #777;
  margin-left: 5px;
  margin-right: 5px;
  width: 11px;
  z-index: 10;
  text-align: center;
  width: auto;
  border-left: 1px solid;
}
#kernel_indicator .kernel_indicator_name {
  padding-left: 5px;
  padding-right: 5px;
}
[dir="rtl"] #kernel_indicator {
  float: left !important;
  float: left;
  border-left: 0;
  border-right: 1px solid;
}
#modal_indicator {
  float: right !important;
  float: right;
  color: #777;
  margin-left: 5px;
  margin-right: 5px;
  width: 11px;
  z-index: 10;
  text-align: center;
  width: auto;
}
[dir="rtl"] #modal_indicator {
  float: left !important;
  float: left;
}
#readonly-indicator {
  float: right !important;
  float: right;
  color: #777;
  margin-left: 5px;
  margin-right: 5px;
  width: 11px;
  z-index: 10;
  text-align: center;
  width: auto;
  margin-top: 2px;
  margin-bottom: 0px;
  margin-left: 0px;
  margin-right: 0px;
  display: none;
}
.modal_indicator:before {
  width: 1.28571429em;
  text-align: center;
}
.edit_mode .modal_indicator:before {
  display: inline-block;
  font: normal normal normal 14px/1 FontAwesome;
  font-size: inherit;
  text-rendering: auto;
  -webkit-font-smoothing: antialiased;
  -moz-osx-font-smoothing: grayscale;
  content: "\f040";
}
.edit_mode .modal_indicator:before.fa-pull-left {
  margin-right: .3em;
}
.edit_mode .modal_indicator:before.fa-pull-right {
  margin-left: .3em;
}
.edit_mode .modal_indicator:before.pull-left {
  margin-right: .3em;
}
.edit_mode .modal_indicator:before.pull-right {
  margin-left: .3em;
}
.command_mode .modal_indicator:before {
  display: inline-block;
  font: normal normal normal 14px/1 FontAwesome;
  font-size: inherit;
  text-rendering: auto;
  -webkit-font-smoothing: antialiased;
  -moz-osx-font-smoothing: grayscale;
  content: ' ';
}
.command_mode .modal_indicator:before.fa-pull-left {
  margin-right: .3em;
}
.command_mode .modal_indicator:before.fa-pull-right {
  margin-left: .3em;
}
.command_mode .modal_indicator:before.pull-left {
  margin-right: .3em;
}
.command_mode .modal_indicator:before.pull-right {
  margin-left: .3em;
}
.kernel_idle_icon:before {
  display: inline-block;
  font: normal normal normal 14px/1 FontAwesome;
  font-size: inherit;
  text-rendering: auto;
  -webkit-font-smoothing: antialiased;
  -moz-osx-font-smoothing: grayscale;
  content: "\f10c";
}
.kernel_idle_icon:before.fa-pull-left {
  margin-right: .3em;
}
.kernel_idle_icon:before.fa-pull-right {
  margin-left: .3em;
}
.kernel_idle_icon:before.pull-left {
  margin-right: .3em;
}
.kernel_idle_icon:before.pull-right {
  margin-left: .3em;
}
.kernel_busy_icon:before {
  display: inline-block;
  font: normal normal normal 14px/1 FontAwesome;
  font-size: inherit;
  text-rendering: auto;
  -webkit-font-smoothing: antialiased;
  -moz-osx-font-smoothing: grayscale;
  content: "\f111";
}
.kernel_busy_icon:before.fa-pull-left {
  margin-right: .3em;
}
.kernel_busy_icon:before.fa-pull-right {
  margin-left: .3em;
}
.kernel_busy_icon:before.pull-left {
  margin-right: .3em;
}
.kernel_busy_icon:before.pull-right {
  margin-left: .3em;
}
.kernel_dead_icon:before {
  display: inline-block;
  font: normal normal normal 14px/1 FontAwesome;
  font-size: inherit;
  text-rendering: auto;
  -webkit-font-smoothing: antialiased;
  -moz-osx-font-smoothing: grayscale;
  content: "\f1e2";
}
.kernel_dead_icon:before.fa-pull-left {
  margin-right: .3em;
}
.kernel_dead_icon:before.fa-pull-right {
  margin-left: .3em;
}
.kernel_dead_icon:before.pull-left {
  margin-right: .3em;
}
.kernel_dead_icon:before.pull-right {
  margin-left: .3em;
}
.kernel_disconnected_icon:before {
  display: inline-block;
  font: normal normal normal 14px/1 FontAwesome;
  font-size: inherit;
  text-rendering: auto;
  -webkit-font-smoothing: antialiased;
  -moz-osx-font-smoothing: grayscale;
  content: "\f127";
}
.kernel_disconnected_icon:before.fa-pull-left {
  margin-right: .3em;
}
.kernel_disconnected_icon:before.fa-pull-right {
  margin-left: .3em;
}
.kernel_disconnected_icon:before.pull-left {
  margin-right: .3em;
}
.kernel_disconnected_icon:before.pull-right {
  margin-left: .3em;
}
.notification_widget {
  color: #777;
  z-index: 10;
  background: rgba(240, 240, 240, 0.5);
  margin-right: 4px;
  color: #333;
  background-color: #fff;
  border-color: #ccc;
}
.notification_widget:focus,
.notification_widget.focus {
  color: #333;
  background-color: #e6e6e6;
  border-color: #8c8c8c;
}
.notification_widget:hover {
  color: #333;
  background-color: #e6e6e6;
  border-color: #adadad;
}
.notification_widget:active,
.notification_widget.active,
.open > .dropdown-toggle.notification_widget {
  color: #333;
  background-color: #e6e6e6;
  border-color: #adadad;
}
.notification_widget:active:hover,
.notification_widget.active:hover,
.open > .dropdown-toggle.notification_widget:hover,
.notification_widget:active:focus,
.notification_widget.active:focus,
.open > .dropdown-toggle.notification_widget:focus,
.notification_widget:active.focus,
.notification_widget.active.focus,
.open > .dropdown-toggle.notification_widget.focus {
  color: #333;
  background-color: #d4d4d4;
  border-color: #8c8c8c;
}
.notification_widget:active,
.notification_widget.active,
.open > .dropdown-toggle.notification_widget {
  background-image: none;
}
.notification_widget.disabled:hover,
.notification_widget[disabled]:hover,
fieldset[disabled] .notification_widget:hover,
.notification_widget.disabled:focus,
.notification_widget[disabled]:focus,
fieldset[disabled] .notification_widget:focus,
.notification_widget.disabled.focus,
.notification_widget[disabled].focus,
fieldset[disabled] .notification_widget.focus {
  background-color: #fff;
  border-color: #ccc;
}
.notification_widget .badge {
  color: #fff;
  background-color: #333;
}
.notification_widget.warning {
  color: #fff;
  background-color: #f0ad4e;
  border-color: #eea236;
}
.notification_widget.warning:focus,
.notification_widget.warning.focus {
  color: #fff;
  background-color: #ec971f;
  border-color: #985f0d;
}
.notification_widget.warning:hover {
  color: #fff;
  background-color: #ec971f;
  border-color: #d58512;
}
.notification_widget.warning:active,
.notification_widget.warning.active,
.open > .dropdown-toggle.notification_widget.warning {
  color: #fff;
  background-color: #ec971f;
  border-color: #d58512;
}
.notification_widget.warning:active:hover,
.notification_widget.warning.active:hover,
.open > .dropdown-toggle.notification_widget.warning:hover,
.notification_widget.warning:active:focus,
.notification_widget.warning.active:focus,
.open > .dropdown-toggle.notification_widget.warning:focus,
.notification_widget.warning:active.focus,
.notification_widget.warning.active.focus,
.open > .dropdown-toggle.notification_widget.warning.focus {
  color: #fff;
  background-color: #d58512;
  border-color: #985f0d;
}
.notification_widget.warning:active,
.notification_widget.warning.active,
.open > .dropdown-toggle.notification_widget.warning {
  background-image: none;
}
.notification_widget.warning.disabled:hover,
.notification_widget.warning[disabled]:hover,
fieldset[disabled] .notification_widget.warning:hover,
.notification_widget.warning.disabled:focus,
.notification_widget.warning[disabled]:focus,
fieldset[disabled] .notification_widget.warning:focus,
.notification_widget.warning.disabled.focus,
.notification_widget.warning[disabled].focus,
fieldset[disabled] .notification_widget.warning.focus {
  background-color: #f0ad4e;
  border-color: #eea236;
}
.notification_widget.warning .badge {
  color: #f0ad4e;
  background-color: #fff;
}
.notification_widget.success {
  color: #fff;
  background-color: #5cb85c;
  border-color: #4cae4c;
}
.notification_widget.success:focus,
.notification_widget.success.focus {
  color: #fff;
  background-color: #449d44;
  border-color: #255625;
}
.notification_widget.success:hover {
  color: #fff;
  background-color: #449d44;
  border-color: #398439;
}
.notification_widget.success:active,
.notification_widget.success.active,
.open > .dropdown-toggle.notification_widget.success {
  color: #fff;
  background-color: #449d44;
  border-color: #398439;
}
.notification_widget.success:active:hover,
.notification_widget.success.active:hover,
.open > .dropdown-toggle.notification_widget.success:hover,
.notification_widget.success:active:focus,
.notification_widget.success.active:focus,
.open > .dropdown-toggle.notification_widget.success:focus,
.notification_widget.success:active.focus,
.notification_widget.success.active.focus,
.open > .dropdown-toggle.notification_widget.success.focus {
  color: #fff;
  background-color: #398439;
  border-color: #255625;
}
.notification_widget.success:active,
.notification_widget.success.active,
.open > .dropdown-toggle.notification_widget.success {
  background-image: none;
}
.notification_widget.success.disabled:hover,
.notification_widget.success[disabled]:hover,
fieldset[disabled] .notification_widget.success:hover,
.notification_widget.success.disabled:focus,
.notification_widget.success[disabled]:focus,
fieldset[disabled] .notification_widget.success:focus,
.notification_widget.success.disabled.focus,
.notification_widget.success[disabled].focus,
fieldset[disabled] .notification_widget.success.focus {
  background-color: #5cb85c;
  border-color: #4cae4c;
}
.notification_widget.success .badge {
  color: #5cb85c;
  background-color: #fff;
}
.notification_widget.info {
  color: #fff;
  background-color: #5bc0de;
  border-color: #46b8da;
}
.notification_widget.info:focus,
.notification_widget.info.focus {
  color: #fff;
  background-color: #31b0d5;
  border-color: #1b6d85;
}
.notification_widget.info:hover {
  color: #fff;
  background-color: #31b0d5;
  border-color: #269abc;
}
.notification_widget.info:active,
.notification_widget.info.active,
.open > .dropdown-toggle.notification_widget.info {
  color: #fff;
  background-color: #31b0d5;
  border-color: #269abc;
}
.notification_widget.info:active:hover,
.notification_widget.info.active:hover,
.open > .dropdown-toggle.notification_widget.info:hover,
.notification_widget.info:active:focus,
.notification_widget.info.active:focus,
.open > .dropdown-toggle.notification_widget.info:focus,
.notification_widget.info:active.focus,
.notification_widget.info.active.focus,
.open > .dropdown-toggle.notification_widget.info.focus {
  color: #fff;
  background-color: #269abc;
  border-color: #1b6d85;
}
.notification_widget.info:active,
.notification_widget.info.active,
.open > .dropdown-toggle.notification_widget.info {
  background-image: none;
}
.notification_widget.info.disabled:hover,
.notification_widget.info[disabled]:hover,
fieldset[disabled] .notification_widget.info:hover,
.notification_widget.info.disabled:focus,
.notification_widget.info[disabled]:focus,
fieldset[disabled] .notification_widget.info:focus,
.notification_widget.info.disabled.focus,
.notification_widget.info[disabled].focus,
fieldset[disabled] .notification_widget.info.focus {
  background-color: #5bc0de;
  border-color: #46b8da;
}
.notification_widget.info .badge {
  color: #5bc0de;
  background-color: #fff;
}
.notification_widget.danger {
  color: #fff;
  background-color: #d9534f;
  border-color: #d43f3a;
}
.notification_widget.danger:focus,
.notification_widget.danger.focus {
  color: #fff;
  background-color: #c9302c;
  border-color: #761c19;
}
.notification_widget.danger:hover {
  color: #fff;
  background-color: #c9302c;
  border-color: #ac2925;
}
.notification_widget.danger:active,
.notification_widget.danger.active,
.open > .dropdown-toggle.notification_widget.danger {
  color: #fff;
  background-color: #c9302c;
  border-color: #ac2925;
}
.notification_widget.danger:active:hover,
.notification_widget.danger.active:hover,
.open > .dropdown-toggle.notification_widget.danger:hover,
.notification_widget.danger:active:focus,
.notification_widget.danger.active:focus,
.open > .dropdown-toggle.notification_widget.danger:focus,
.notification_widget.danger:active.focus,
.notification_widget.danger.active.focus,
.open > .dropdown-toggle.notification_widget.danger.focus {
  color: #fff;
  background-color: #ac2925;
  border-color: #761c19;
}
.notification_widget.danger:active,
.notification_widget.danger.active,
.open > .dropdown-toggle.notification_widget.danger {
  background-image: none;
}
.notification_widget.danger.disabled:hover,
.notification_widget.danger[disabled]:hover,
fieldset[disabled] .notification_widget.danger:hover,
.notification_widget.danger.disabled:focus,
.notification_widget.danger[disabled]:focus,
fieldset[disabled] .notification_widget.danger:focus,
.notification_widget.danger.disabled.focus,
.notification_widget.danger[disabled].focus,
fieldset[disabled] .notification_widget.danger.focus {
  background-color: #d9534f;
  border-color: #d43f3a;
}
.notification_widget.danger .badge {
  color: #d9534f;
  background-color: #fff;
}
div#pager {
  background-color: #fff;
  font-size: 14px;
  line-height: 20px;
  overflow: hidden;
  display: none;
  position: fixed;
  bottom: 0px;
  width: 100%;
  max-height: 50%;
  padding-top: 8px;
  -webkit-box-shadow: 0px 0px 12px 1px rgba(87, 87, 87, 0.2);
  box-shadow: 0px 0px 12px 1px rgba(87, 87, 87, 0.2);
  /* Display over codemirror */
  z-index: 100;
  /* Hack which prevents jquery ui resizable from changing top. */
  top: auto !important;
}
div#pager pre {
  line-height: 1.21429em;
  color: #000;
  background-color: #f7f7f7;
  padding: 0.4em;
}
div#pager #pager-button-area {
  position: absolute;
  top: 8px;
  right: 20px;
}
div#pager #pager-contents {
  position: relative;
  overflow: auto;
  width: 100%;
  height: 100%;
}
div#pager #pager-contents #pager-container {
  position: relative;
  padding: 15px 0px;
  box-sizing: border-box;
  -moz-box-sizing: border-box;
  -webkit-box-sizing: border-box;
}
div#pager .ui-resizable-handle {
  top: 0px;
  height: 8px;
  background: #f7f7f7;
  border-top: 1px solid #cfcfcf;
  border-bottom: 1px solid #cfcfcf;
  /* This injects handle bars (a short, wide = symbol) for 
        the resize handle. */
}
div#pager .ui-resizable-handle::after {
  content: '';
  top: 2px;
  left: 50%;
  height: 3px;
  width: 30px;
  margin-left: -15px;
  position: absolute;
  border-top: 1px solid #cfcfcf;
}
.quickhelp {
  /* Old browsers */
  display: -webkit-box;
  -webkit-box-orient: horizontal;
  -webkit-box-align: stretch;
  display: -moz-box;
  -moz-box-orient: horizontal;
  -moz-box-align: stretch;
  display: box;
  box-orient: horizontal;
  box-align: stretch;
  /* Modern browsers */
  display: flex;
  flex-direction: row;
  align-items: stretch;
  line-height: 1.8em;
}
.shortcut_key {
  display: inline-block;
  width: 21ex;
  text-align: right;
  font-family: monospace;
}
.shortcut_descr {
  display: inline-block;
  /* Old browsers */
  -webkit-box-flex: 1;
  -moz-box-flex: 1;
  box-flex: 1;
  /* Modern browsers */
  flex: 1;
}
span.save_widget {
  height: 30px;
  margin-top: 4px;
  display: flex;
  justify-content: flex-start;
  align-items: baseline;
  width: 50%;
  flex: 1;
}
span.save_widget span.filename {
  height: 100%;
  line-height: 1em;
  margin-left: 16px;
  border: none;
  font-size: 146.5%;
  text-overflow: ellipsis;
  overflow: hidden;
  white-space: nowrap;
  border-radius: 2px;
}
span.save_widget span.filename:hover {
  background-color: #e6e6e6;
}
[dir="rtl"] span.save_widget.pull-left {
  float: right !important;
  float: right;
}
[dir="rtl"] span.save_widget span.filename {
  margin-left: 0;
  margin-right: 16px;
}
span.checkpoint_status,
span.autosave_status {
  font-size: small;
  white-space: nowrap;
  padding: 0 5px;
}
@media (max-width: 767px) {
  span.save_widget {
    font-size: small;
    padding: 0 0 0 5px;
  }
  span.checkpoint_status,
  span.autosave_status {
    display: none;
  }
}
@media (min-width: 768px) and (max-width: 991px) {
  span.checkpoint_status {
    display: none;
  }
  span.autosave_status {
    font-size: x-small;
  }
}
.toolbar {
  padding: 0px;
  margin-left: -5px;
  margin-top: 2px;
  margin-bottom: 5px;
  box-sizing: border-box;
  -moz-box-sizing: border-box;
  -webkit-box-sizing: border-box;
}
.toolbar select,
.toolbar label {
  width: auto;
  vertical-align: middle;
  margin-right: 2px;
  margin-bottom: 0px;
  display: inline;
  font-size: 92%;
  margin-left: 0.3em;
  margin-right: 0.3em;
  padding: 0px;
  padding-top: 3px;
}
.toolbar .btn {
  padding: 2px 8px;
}
.toolbar .btn-group {
  margin-top: 0px;
  margin-left: 5px;
}
.toolbar-btn-label {
  margin-left: 6px;
}
#maintoolbar {
  margin-bottom: -3px;
  margin-top: -8px;
  border: 0px;
  min-height: 27px;
  margin-left: 0px;
  padding-top: 11px;
  padding-bottom: 3px;
}
#maintoolbar .navbar-text {
  float: none;
  vertical-align: middle;
  text-align: right;
  margin-left: 5px;
  margin-right: 0px;
  margin-top: 0px;
}
.select-xs {
  height: 24px;
}
[dir="rtl"] .btn-group > .btn,
.btn-group-vertical > .btn {
  float: right;
}
.pulse,
.dropdown-menu > li > a.pulse,
li.pulse > a.dropdown-toggle,
li.pulse.open > a.dropdown-toggle {
  background-color: #F37626;
  color: white;
}
/**
 * Primary styles
 *
 * Author: Jupyter Development Team
 */
/** WARNING IF YOU ARE EDITTING THIS FILE, if this is a .css file, It has a lot
 * of chance of beeing generated from the ../less/[samename].less file, you can
 * try to get back the less file by reverting somme commit in history
 **/
/*
 * We'll try to get something pretty, so we
 * have some strange css to have the scroll bar on
 * the left with fix button on the top right of the tooltip
 */
@-moz-keyframes fadeOut {
  from {
    opacity: 1;
  }
  to {
    opacity: 0;
  }
}
@-webkit-keyframes fadeOut {
  from {
    opacity: 1;
  }
  to {
    opacity: 0;
  }
}
@-moz-keyframes fadeIn {
  from {
    opacity: 0;
  }
  to {
    opacity: 1;
  }
}
@-webkit-keyframes fadeIn {
  from {
    opacity: 0;
  }
  to {
    opacity: 1;
  }
}
/*properties of tooltip after "expand"*/
.bigtooltip {
  overflow: auto;
  height: 200px;
  -webkit-transition-property: height;
  -webkit-transition-duration: 500ms;
  -moz-transition-property: height;
  -moz-transition-duration: 500ms;
  transition-property: height;
  transition-duration: 500ms;
}
/*properties of tooltip before "expand"*/
.smalltooltip {
  -webkit-transition-property: height;
  -webkit-transition-duration: 500ms;
  -moz-transition-property: height;
  -moz-transition-duration: 500ms;
  transition-property: height;
  transition-duration: 500ms;
  text-overflow: ellipsis;
  overflow: hidden;
  height: 80px;
}
.tooltipbuttons {
  position: absolute;
  padding-right: 15px;
  top: 0px;
  right: 0px;
}
.tooltiptext {
  /*avoid the button to overlap on some docstring*/
  padding-right: 30px;
}
.ipython_tooltip {
  max-width: 700px;
  /*fade-in animation when inserted*/
  -webkit-animation: fadeOut 400ms;
  -moz-animation: fadeOut 400ms;
  animation: fadeOut 400ms;
  -webkit-animation: fadeIn 400ms;
  -moz-animation: fadeIn 400ms;
  animation: fadeIn 400ms;
  vertical-align: middle;
  background-color: #f7f7f7;
  overflow: visible;
  border: #ababab 1px solid;
  outline: none;
  padding: 3px;
  margin: 0px;
  padding-left: 7px;
  font-family: monospace;
  min-height: 50px;
  -moz-box-shadow: 0px 6px 10px -1px #adadad;
  -webkit-box-shadow: 0px 6px 10px -1px #adadad;
  box-shadow: 0px 6px 10px -1px #adadad;
  border-radius: 2px;
  position: absolute;
  z-index: 1000;
}
.ipython_tooltip a {
  float: right;
}
.ipython_tooltip .tooltiptext pre {
  border: 0;
  border-radius: 0;
  font-size: 100%;
  background-color: #f7f7f7;
}
.pretooltiparrow {
  left: 0px;
  margin: 0px;
  top: -16px;
  width: 40px;
  height: 16px;
  overflow: hidden;
  position: absolute;
}
.pretooltiparrow:before {
  background-color: #f7f7f7;
  border: 1px #ababab solid;
  z-index: 11;
  content: "";
  position: absolute;
  left: 15px;
  top: 10px;
  width: 25px;
  height: 25px;
  -webkit-transform: rotate(45deg);
  -moz-transform: rotate(45deg);
  -ms-transform: rotate(45deg);
  -o-transform: rotate(45deg);
}
ul.typeahead-list i {
  margin-left: -10px;
  width: 18px;
}
[dir="rtl"] ul.typeahead-list i {
  margin-left: 0;
  margin-right: -10px;
}
ul.typeahead-list {
  max-height: 80vh;
  overflow: auto;
}
ul.typeahead-list > li > a {
  /** Firefox bug **/
  /* see https://github.com/jupyter/notebook/issues/559 */
  white-space: normal;
}
ul.typeahead-list  > li > a.pull-right {
  float: left !important;
  float: left;
}
[dir="rtl"] .typeahead-list {
  text-align: right;
}
.cmd-palette .modal-body {
  padding: 7px;
}
.cmd-palette form {
  background: white;
}
.cmd-palette input {
  outline: none;
}
.no-shortcut {
  min-width: 20px;
  color: transparent;
}
[dir="rtl"] .no-shortcut.pull-right {
  float: left !important;
  float: left;
}
[dir="rtl"] .command-shortcut.pull-right {
  float: left !important;
  float: left;
}
.command-shortcut:before {
  content: "(command mode)";
  padding-right: 3px;
  color: #777777;
}
.edit-shortcut:before {
  content: "(edit)";
  padding-right: 3px;
  color: #777777;
}
[dir="rtl"] .edit-shortcut.pull-right {
  float: left !important;
  float: left;
}
#find-and-replace #replace-preview .match,
#find-and-replace #replace-preview .insert {
  background-color: #BBDEFB;
  border-color: #90CAF9;
  border-style: solid;
  border-width: 1px;
  border-radius: 0px;
}
[dir="ltr"] #find-and-replace .input-group-btn + .form-control {
  border-left: none;
}
[dir="rtl"] #find-and-replace .input-group-btn + .form-control {
  border-right: none;
}
#find-and-replace #replace-preview .replace .match {
  background-color: #FFCDD2;
  border-color: #EF9A9A;
  border-radius: 0px;
}
#find-and-replace #replace-preview .replace .insert {
  background-color: #C8E6C9;
  border-color: #A5D6A7;
  border-radius: 0px;
}
#find-and-replace #replace-preview {
  max-height: 60vh;
  overflow: auto;
}
#find-and-replace #replace-preview pre {
  padding: 5px 10px;
}
.terminal-app {
  background: #EEE;
}
.terminal-app #header {
  background: #fff;
  -webkit-box-shadow: 0px 0px 12px 1px rgba(87, 87, 87, 0.2);
  box-shadow: 0px 0px 12px 1px rgba(87, 87, 87, 0.2);
}
.terminal-app .terminal {
  width: 100%;
  float: left;
  font-family: monospace;
  color: white;
  background: black;
  padding: 0.4em;
  border-radius: 2px;
  -webkit-box-shadow: 0px 0px 12px 1px rgba(87, 87, 87, 0.4);
  box-shadow: 0px 0px 12px 1px rgba(87, 87, 87, 0.4);
}
.terminal-app .terminal,
.terminal-app .terminal dummy-screen {
  line-height: 1em;
  font-size: 14px;
}
.terminal-app .terminal .xterm-rows {
  padding: 10px;
}
.terminal-app .terminal-cursor {
  color: black;
  background: white;
}
.terminal-app #terminado-container {
  margin-top: 20px;
}
/*# sourceMappingURL=style.min.css.map */
    </style>
<style type="text/css">
    .highlight .hll { background-color: #ffffcc }
.highlight  { background: #f8f8f8; }
.highlight .c { color: #408080; font-style: italic } /* Comment */
.highlight .err { border: 1px solid #FF0000 } /* Error */
.highlight .k { color: #008000; font-weight: bold } /* Keyword */
.highlight .o { color: #666666 } /* Operator */
.highlight .ch { color: #408080; font-style: italic } /* Comment.Hashbang */
.highlight .cm { color: #408080; font-style: italic } /* Comment.Multiline */
.highlight .cp { color: #BC7A00 } /* Comment.Preproc */
.highlight .cpf { color: #408080; font-style: italic } /* Comment.PreprocFile */
.highlight .c1 { color: #408080; font-style: italic } /* Comment.Single */
.highlight .cs { color: #408080; font-style: italic } /* Comment.Special */
.highlight .gd { color: #A00000 } /* Generic.Deleted */
.highlight .ge { font-style: italic } /* Generic.Emph */
.highlight .gr { color: #FF0000 } /* Generic.Error */
.highlight .gh { color: #000080; font-weight: bold } /* Generic.Heading */
.highlight .gi { color: #00A000 } /* Generic.Inserted */
.highlight .go { color: #888888 } /* Generic.Output */
.highlight .gp { color: #000080; font-weight: bold } /* Generic.Prompt */
.highlight .gs { font-weight: bold } /* Generic.Strong */
.highlight .gu { color: #800080; font-weight: bold } /* Generic.Subheading */
.highlight .gt { color: #0044DD } /* Generic.Traceback */
.highlight .kc { color: #008000; font-weight: bold } /* Keyword.Constant */
.highlight .kd { color: #008000; font-weight: bold } /* Keyword.Declaration */
.highlight .kn { color: #008000; font-weight: bold } /* Keyword.Namespace */
.highlight .kp { color: #008000 } /* Keyword.Pseudo */
.highlight .kr { color: #008000; font-weight: bold } /* Keyword.Reserved */
.highlight .kt { color: #B00040 } /* Keyword.Type */
.highlight .m { color: #666666 } /* Literal.Number */
.highlight .s { color: #BA2121 } /* Literal.String */
.highlight .na { color: #7D9029 } /* Name.Attribute */
.highlight .nb { color: #008000 } /* Name.Builtin */
.highlight .nc { color: #0000FF; font-weight: bold } /* Name.Class */
.highlight .no { color: #880000 } /* Name.Constant */
.highlight .nd { color: #AA22FF } /* Name.Decorator */
.highlight .ni { color: #999999; font-weight: bold } /* Name.Entity */
.highlight .ne { color: #D2413A; font-weight: bold } /* Name.Exception */
.highlight .nf { color: #0000FF } /* Name.Function */
.highlight .nl { color: #A0A000 } /* Name.Label */
.highlight .nn { color: #0000FF; font-weight: bold } /* Name.Namespace */
.highlight .nt { color: #008000; font-weight: bold } /* Name.Tag */
.highlight .nv { color: #19177C } /* Name.Variable */
.highlight .ow { color: #AA22FF; font-weight: bold } /* Operator.Word */
.highlight .w { color: #bbbbbb } /* Text.Whitespace */
.highlight .mb { color: #666666 } /* Literal.Number.Bin */
.highlight .mf { color: #666666 } /* Literal.Number.Float */
.highlight .mh { color: #666666 } /* Literal.Number.Hex */
.highlight .mi { color: #666666 } /* Literal.Number.Integer */
.highlight .mo { color: #666666 } /* Literal.Number.Oct */
.highlight .sa { color: #BA2121 } /* Literal.String.Affix */
.highlight .sb { color: #BA2121 } /* Literal.String.Backtick */
.highlight .sc { color: #BA2121 } /* Literal.String.Char */
.highlight .dl { color: #BA2121 } /* Literal.String.Delimiter */
.highlight .sd { color: #BA2121; font-style: italic } /* Literal.String.Doc */
.highlight .s2 { color: #BA2121 } /* Literal.String.Double */
.highlight .se { color: #BB6622; font-weight: bold } /* Literal.String.Escape */
.highlight .sh { color: #BA2121 } /* Literal.String.Heredoc */
.highlight .si { color: #BB6688; font-weight: bold } /* Literal.String.Interpol */
.highlight .sx { color: #008000 } /* Literal.String.Other */
.highlight .sr { color: #BB6688 } /* Literal.String.Regex */
.highlight .s1 { color: #BA2121 } /* Literal.String.Single */
.highlight .ss { color: #19177C } /* Literal.String.Symbol */
.highlight .bp { color: #008000 } /* Name.Builtin.Pseudo */
.highlight .fm { color: #0000FF } /* Name.Function.Magic */
.highlight .vc { color: #19177C } /* Name.Variable.Class */
.highlight .vg { color: #19177C } /* Name.Variable.Global */
.highlight .vi { color: #19177C } /* Name.Variable.Instance */
.highlight .vm { color: #19177C } /* Name.Variable.Magic */
.highlight .il { color: #666666 } /* Literal.Number.Integer.Long */
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<style type="text/css">
    
/* Temporary definitions which will become obsolete with Notebook release 5.0 */
.ansi-black-fg { color: #3E424D; }
.ansi-black-bg { background-color: #3E424D; }
.ansi-black-intense-fg { color: #282C36; }
.ansi-black-intense-bg { background-color: #282C36; }
.ansi-red-fg { color: #E75C58; }
.ansi-red-bg { background-color: #E75C58; }
.ansi-red-intense-fg { color: #B22B31; }
.ansi-red-intense-bg { background-color: #B22B31; }
.ansi-green-fg { color: #00A250; }
.ansi-green-bg { background-color: #00A250; }
.ansi-green-intense-fg { color: #007427; }
.ansi-green-intense-bg { background-color: #007427; }
.ansi-yellow-fg { color: #DDB62B; }
.ansi-yellow-bg { background-color: #DDB62B; }
.ansi-yellow-intense-fg { color: #B27D12; }
.ansi-yellow-intense-bg { background-color: #B27D12; }
.ansi-blue-fg { color: #208FFB; }
.ansi-blue-bg { background-color: #208FFB; }
.ansi-blue-intense-fg { color: #0065CA; }
.ansi-blue-intense-bg { background-color: #0065CA; }
.ansi-magenta-fg { color: #D160C4; }
.ansi-magenta-bg { background-color: #D160C4; }
.ansi-magenta-intense-fg { color: #A03196; }
.ansi-magenta-intense-bg { background-color: #A03196; }
.ansi-cyan-fg { color: #60C6C8; }
.ansi-cyan-bg { background-color: #60C6C8; }
.ansi-cyan-intense-fg { color: #258F8F; }
.ansi-cyan-intense-bg { background-color: #258F8F; }
.ansi-white-fg { color: #C5C1B4; }
.ansi-white-bg { background-color: #C5C1B4; }
.ansi-white-intense-fg { color: #A1A6B2; }
.ansi-white-intense-bg { background-color: #A1A6B2; }

.ansi-bold { font-weight: bold; }

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<h1 id="Overlapping-Generations-(OLG)-model">Overlapping Generations (OLG) model<a class="anchor-link" href="#Overlapping-Generations-(OLG)-model">&#182;</a></h1>
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<p>In the OLG model, the economy is populated by people who differ by age: 
some are young and working, while some are old and retired.</p>
<p>The fact that incomes of the old tend to be lower than incomes of the young,
creates a natural desire for saving. Therefore, the OLG model will serve us to investigate
the reasons for different saving rates across countries.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="c1"># Make graphs appear within the notebook</span>
<span class="o">%</span><span class="k">matplotlib</span> inline

<span class="c1"># Import numerical computations library</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>

<span class="c1"># Import plotting library</span>
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>

<span class="c1"># Import functions from AppliedMacroPlots.py</span>
<span class="kn">from</span> <span class="nn">AppliedMacroPlots</span> <span class="k">import</span> <span class="o">*</span>
</pre></div>

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<h2 id="Intertemporal-choice-of-a-consumer">Intertemporal choice of a consumer<a class="anchor-link" href="#Intertemporal-choice-of-a-consumer">&#182;</a></h2>
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<p>Before we encounter the OLG model, let us talk first on how to model the choice of a consumer,
whose life is divided in two time periods: $t$ and $t+1$.</p>
<p>If it helps you in building your intuition, imagine that the first time period ($t$) represents the period when the agent is young and working, while the second time period ($t+1$) represents the period when the agent is old and retired.</p>
<p>I have also picked a specific functional form for the utility function: the logarithmic function. The reason for this choice is that the logarithmic function has a super easy derivative:</p>
\begin{align}
\frac{\partial log x}{\partial x} = \frac{1}{x}
\end{align}<p>and this will simplify our calculations quite a lot.</p>

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<h3 id="Utility-maximization-problem">Utility maximization problem<a class="anchor-link" href="#Utility-maximization-problem">&#182;</a></h3><p>Our aim is to construct an optimization problem, the solution to which will closely approximate the choices of actual people.</p>
<p>Imagine that our consumer earns income $y_{t}$ in the first period, and income $y_{t+1}$ in the second period.</p>
<p>Moreover the consumer can either save a part of the first period income, or borrow against second period income. For simplicity, the real interest rate for saving and borrowing is the same and is denoted with $r$.</p>
<p>The consumer is also impatient, in the sense that she prefers to consume today rather than in the future (although she does not want to starve in the future!). We capture this feature of human behavior by assuming that future outcomes are discounted with the discount factor $0&lt;\beta&lt;1$.</p>
<p>Formally, we set up a maximization problem, constrained by the consumer's budget constraint:</p>
\begin{align}
\max_{c_{t}, c_{t+1}} \quad &amp; U=\log c_{t}+\beta\log c_{t+1}\\
\text{subject to} \quad &amp; c_{t}+\frac{c_{t+1}}{1+r}\leq y_{t}+\frac{y_{t+1}}{1+r}
\end{align}<p>where the constraint implies that the present dicounted value (PDV) of lifetime consumption cannot exceed the PDV of lifetime income.</p>
<p>Let us first plot the budget set: the set of all attainable consumption bundles given our endowments: incomes in period $t$ and $t+1$, which we will denote in <code>python codes</code> as period 0 and 1.</p>

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<p>In the graph below, the point $(y_{t}, y_{t+1})$ denotes the initial endowment of consumer's incomes.</p>
<p>Thanks to the ability to save or borrow, the consumer can choose at maximum the amount $y_{t}+y_{t+1}/(1+r)$ in the first period (and consume 0 in the second period) or save the entire first period income and consume $(1+r)\cdot y_{t}+y_{t+1}$ in the second period (and consume 0 in the first period).</p>
<p>All three mentioned points lie on the same budget line. The budget set contains also some points where the PDV of consumption is smaller than the PDV of income, but in this context choosing any point that does not lie on the budget line would not be optimal.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">y_0</span> <span class="o">=</span> <span class="mi">2</span>
<span class="n">y_1</span> <span class="o">=</span> <span class="mi">1</span>
<span class="n">r</span> <span class="o">=</span> <span class="mf">0.05</span>
<span class="n">β</span> <span class="o">=</span> <span class="mf">0.95</span>

<span class="n">PlotBudgetSet</span><span class="p">(</span><span class="n">y_0</span><span class="p">,</span> <span class="n">y_1</span><span class="p">,</span> <span class="n">r</span><span class="p">,</span> <span class="n">full_labels</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
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<p>The graph below depicts a so-called indifference map, that is, a set of indifference curves, corresponding to allocations between which the consumer is indifferent. Indifference curves that lie to the northeast represent higher levels of utility.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">PlotIndifferenceCurves</span><span class="p">(</span><span class="n">y_0</span><span class="p">,</span> <span class="n">y_1</span><span class="p">,</span> <span class="n">β</span><span class="p">,</span> <span class="n">r</span><span class="p">,</span> <span class="n">levels</span><span class="o">=</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mf">1.5</span><span class="p">],</span> <span class="n">full_labels</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
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<p>The graph below shows the budget set and two indifference curves. The green indifference curve is infeasible -- there are no points in the budget set that lie on this curve. The yellow indifference curve is feasible -- there are points in the budget set that lie on this curve -- but is clearly not optimal, as we could find some points in the budget set that lie to the northeast of the yellow indifference curve.</p>
<p>Graphically, optimal choice involves choosing such a point from the budget set that lies on the highest possible indifference curve, such that this surve is tangent to the budget line.</p>
<p>You can attempt to find an (approximate) graphical solution by appending a number to the <code>levels=[0.5, 1]</code> list in the code below.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="c1"># This will make both plots appear in the same figure</span>
<span class="n">fig</span><span class="p">,</span> <span class="n">ax</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">5</span><span class="p">,</span> <span class="mi">5</span><span class="p">))</span>

<span class="n">PlotBudgetSet</span><span class="p">(</span><span class="n">y_0</span><span class="p">,</span> <span class="n">y_1</span><span class="p">,</span> <span class="n">r</span><span class="p">,</span> <span class="n">fig_ax</span><span class="o">=</span><span class="p">(</span><span class="n">fig</span><span class="p">,</span> <span class="n">ax</span><span class="p">))</span>
<span class="n">PlotIndifferenceCurves</span><span class="p">(</span><span class="n">y_0</span><span class="p">,</span> <span class="n">y_1</span><span class="p">,</span> <span class="n">β</span><span class="p">,</span> <span class="n">levels</span><span class="o">=</span><span class="p">[</span><span class="mf">0.5</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="n">fig_ax</span><span class="o">=</span><span class="p">(</span><span class="n">fig</span><span class="p">,</span> <span class="n">ax</span><span class="p">))</span>

<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
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<p>The code below solves the Utility Maximization Problem of the consumer and displays the results.</p>
<p>If you want, you can change the parameters of the problem, for example to see when the consumer is a saver, and when a borrower (although be aware that for crazy parameters you can get crazy outcomes).</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">y_0</span> <span class="o">=</span> <span class="mi">2</span>
<span class="n">y_1</span> <span class="o">=</span> <span class="mi">1</span>
<span class="n">r</span> <span class="o">=</span> <span class="mf">0.05</span>
<span class="n">β</span> <span class="o">=</span> <span class="mf">0.95</span>

<span class="n">SolveUtilityMaximizationProblem</span><span class="p">(</span><span class="n">y_0</span><span class="p">,</span> <span class="n">y_1</span><span class="p">,</span> <span class="n">β</span><span class="p">,</span> <span class="n">r</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
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<pre>Consumer&#39;s income:
  y_0: 2.0000
  y_1: 1.0000

Optimal consumption:
  c_0: 1.5140
  c_1: 1.5103

c_0 &lt; y_0: Consumer is a saver

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<p>Note that in the above graph there appears an <strong>Euler equation</strong> curve. You will find an explanation below.</p>
<h3 id="Solving-UMP-with-the-Lagrange-method">Solving UMP with the Lagrange method<a class="anchor-link" href="#Solving-UMP-with-the-Lagrange-method">&#182;</a></h3><p>Although in principle the UMP could be solved with a variety of methods, we will solve it with the Lagrange method. The advantage of this method is that it scales well to problems with a large (or even infinite) number of variables involved.</p>
<p>Recall our problem:</p>
\begin{align}
\max\quad &amp; U=\log c_{t}+\beta\log c_{t+1}\\
\text{subject to}\quad &amp; c_{t}+\frac{c_{t+1}}{1+r}\leq y_{t}+\frac{y_{t+1}}{1+r}
\end{align}<p>Rewrite the budget constraint in the form of $0\leq\ldots$:</p>
\begin{align}
0\leq y_{t}+\frac{y_{t+1}}{1+r}-c_{t}-\frac{c_{t+1}}{1+r}
\end{align}<p>And set up a Lagrange function:</p>
\begin{align}
\mathcal{L}=\log c_{t}+\beta\log c_{t+1}+\lambda\left[y_{t}+\frac{y_{t+1}}{1+r}-c_{t}-\frac{c_{t+1}}{1+r}\right]
\end{align}<p>where $\lambda$ is called the Lagrange multiplier. Next we derive the First Order Conditions (FOCs), that is, calculate the derivatives of the Lagrangian with respect to the choice variables. In this problem there are two choice variables -- $c_{t}$ and $c_{t+1}$:</p>
\begin{align}
\frac{\partial\mathcal{L}}{\partial c_{t}} &amp; =\frac{1}{c_{t}}+\lambda\left[-1\right]=0\\
\frac{\partial\mathcal{L}}{\partial c_{t+1}} &amp; =\beta\cdot\frac{1}{c_{t+1}}+\lambda\left[-\frac{1}{1+r}\right]=0
\end{align}<p>Let us simplify the above equations:</p>
\begin{align}
\lambda &amp; =\frac{1}{c_{t}}\\
\lambda &amp; =\beta\left(1+r\right)\frac{1}{c_{t+1}}
\end{align}<p>And combine them:</p>
\begin{align}
\frac{1}{c_{t}} &amp; =\beta\left(1+r\right)\frac{1}{c_{t+1}}\\
c_{t+1} &amp; =\beta\left(1+r\right)c_{t}
\end{align}<p>The resulting equation is called the intertemporal condition (from Latin: across time) or the <a href="https://www.econjobrumors.com/topic/why-is-it-called-euler-equation">Euler equation</a>.</p>
<p>At this stage, the Lagrangian procedure has allowed us to restate our problem, involving finding a point on a curve tangent to a line, to the problem of finding an intersection of two curves: the budget constraint and the Euler equation, which is much simpler to solve:</p>
\begin{align}
\begin{cases}
c_{t}+\dfrac{c_{t+1}}{1+r}=y_{t}+\dfrac{y_{t+1}}{1+r}\\
c_{t+1}=\beta\left(1+r\right)c_{t}
\end{cases}
\end{align}<p>Plug the Euler equation into the budget constraint:</p>
\begin{align}
c_{t}+\frac{\beta\left(1+r\right)c_{t}}{1+r} &amp; =y_{t}+\frac{y_{t+1}}{1+r}\\
c_{t}+\beta c_{t} &amp; =y_{t}+\frac{y_{t+1}}{1+r}\\
\left(1+\beta\right)c_{t} &amp; =y_{t}+\frac{y_{t+1}}{1+r}\\
c_{t} &amp; =\frac{1}{1+\beta}\left[y_{t}+\frac{y_{t+1}}{1+r}\right]
\end{align}<p>We can use the Euler equation again to find the level of consumption in the second period:</p>
\begin{align}
c_{t+1} &amp; =\frac{\beta}{1+\beta}\left[\left(1+r\right)y_{t}+y_{t+1}\right]
\end{align}<p>Finally, we can define the stock of assets (which can be negative) that agent has at the end of period $t$. In this problem, the stock of assets will be given as the difference between first period income and consumption:</p>
\begin{align}
a\equiv y_{t}-c_{t}=y_{t}-\frac{1}{1+\beta}\left[y_{t}+\frac{y_{t+1}}{1+r}\right]=\frac{\beta}{1+\beta}y_{t}-\frac{1}{1+\beta}\frac{y_{t+1}}{1+r}
\end{align}<p>If $a&gt;0$, the agent is a saver ($c_{t}&lt;y_{t}$), and if $a&lt;0$, the agent is a borrower ($c_{t}&gt;y_{t}$). If $a=0$, the agent is neither a saver nor a borrower and simply consumes the initial endowments ($c_{t}=y_{t}$ and $c_{t+1}=y_{t+1}$). You can see an example for the $a=0$ case below.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">y_0</span> <span class="o">=</span> <span class="mi">1</span>
<span class="n">y_1</span> <span class="o">=</span> <span class="mi">1</span>
<span class="n">r</span> <span class="o">=</span> <span class="mf">0.05</span>
<span class="n">β</span> <span class="o">=</span> <span class="mi">1</span><span class="o">/</span><span class="p">(</span><span class="mi">1</span><span class="o">+</span><span class="n">r</span><span class="p">)</span>

<span class="n">SolveUtilityMaximizationProblem</span><span class="p">(</span><span class="n">y_0</span><span class="p">,</span> <span class="n">y_1</span><span class="p">,</span> <span class="n">β</span><span class="p">,</span> <span class="n">r</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
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<pre>Consumer&#39;s income:
  y_0: 1.0000
  y_1: 1.0000

Optimal consumption:
  c_0: 1.0000
  c_1: 1.0000

c_0 = y_0: Consumer is neither a borrower nor a saver

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<h3 id="Comparative-statics">Comparative statics<a class="anchor-link" href="#Comparative-statics">&#182;</a></h3><p>Let us now perform a few comparative statics exercises, so that we may gain intuition on the factors affecting the choice of consumption and savings.</p>
\begin{align}
a &amp; =\frac{\beta}{1+\beta}y_{t}-\frac{1}{1+\beta}\frac{y_{t+1}}{1+r}\\
c_{t} &amp; =\frac{1}{1+\beta}\left[y_{t}+\frac{y_{t+1}}{1+r}\right]\\
c_{t+1} &amp; =\frac{\beta}{1+\beta}\left[\left(1+r\right)y_{t}+y_{t+1}\right]
\end{align}<h4 id="Changes-in-$\beta$">Changes in $\beta$<a class="anchor-link" href="#Changes-in-$\beta$">&#182;</a></h4><p>The higher $\beta$ is, the more patient is our agent. Intuitively, since the agent with higher $\beta$ cares more about the future, she would save more in the first period (and thus consume less in the first period) in order to consume more in the second period:</p>
\begin{align}
\frac{\partial a}{\partial\beta} &amp; =\frac{1+\beta-\beta}{\left(1+\beta\right)^{2}}y_{t}-\left[-\frac{1}{\left(1+\beta\right)^{2}}\right]\frac{y_{t+1}}{1+r}=\frac{1}{\left(1+\beta\right)^{2}}\left[y_{t}+\frac{y_{t+1}}{1+r}\right]&gt;0\\
\frac{\partial c_{t}}{\partial\beta} &amp; =-\frac{1}{\left(1+\beta\right)^{2}}\left[y_{t}+\frac{y_{t+1}}{1+r}\right]&lt;0\\
\frac{\partial c_{t+1}}{\partial\beta} &amp; =\frac{1+\beta-\beta}{\left(1+\beta\right)^{2}}\left[\left(1+r\right)y_{t}+y_{t+1}\right]&gt;0
\end{align}<h4 id="Changes-in-$y_{t}$">Changes in $y_{t}$<a class="anchor-link" href="#Changes-in-$y_{t}$">&#182;</a></h4><p>An increase in the first period income increases consumption in both time periods. Since the agent will want to transfer a part of the additional first period income to the second period, savings will also increase:</p>
\begin{align}
\frac{\partial a}{\partial y_{t}} &amp; =\frac{\beta}{1+\beta}&gt;0\\
\frac{\partial c_{t}}{\partial y_{t}} &amp; =\frac{1}{1+\beta}&gt;0\\
\frac{\partial c_{t+1}}{\partial y_{t}} &amp; =\frac{\beta}{1+\beta}\left(1+r\right)&gt;0
\end{align}<h4 id="Changes-in-$y_{t+1}$">Changes in $y_{t+1}$<a class="anchor-link" href="#Changes-in-$y_{t+1}$">&#182;</a></h4><p>An increase in the second period income increases consumption in both time periods. Since the agent will want to transfer a part of the additional second period income to the first period, savings will decrease:</p>
\begin{align}
\frac{\partial a}{\partial y_{t+1}} &amp; =-\frac{1}{1+\beta}\frac{1}{1+r}&lt;0\\
\frac{\partial c_{t}}{\partial y_{t+1}} &amp; =\frac{1}{1+\beta}\frac{1}{1+r}&gt;0\\
\frac{\partial c_{t+1}}{\partial y_{t+1}} &amp; =\frac{\beta}{1+\beta}&gt;0
\end{align}<h4 id="Changes-in-$r$">Changes in $r$<a class="anchor-link" href="#Changes-in-$r$">&#182;</a></h4><p>An increase in the interest rate generates two effects: substitution effect and income effect. Substitution effect is generated by the change in relative prices of consumption in the first period versus consumption in the second period. It induces the agent to consume more in the second period and consume less in the first period. Income effect is generated by the fact that the PDV of income changes due to the changes in the discounting rate. The sign of the effect depends on whether an agent is a saver or a borrower. An increase in interest rates creates a positive income effect for the saver, increasing her consumption in both periods. Conversely, an increase in interest rates creates a negative income effect for the borrower, decreasing her consumption in both periods.</p>
<p>These effects can be summarized by the following table, where pluses and minuses describe the direction of change in a variable for which we can be certain of the direction, regardless of the assumed utility function:</p>
<table>
<thead><tr>
<th>Effects of an increase in $r$</th>
<th>Saver</th>
<th>&nbsp;</th>
<th>&nbsp;</th>
<th>&nbsp;</th>
<th>Borrower</th>
<th>&nbsp;</th>
<th>&nbsp;</th>
<th>&nbsp;</th>
</tr>
</thead>
<tbody>
<tr>
<td>&nbsp;</td>
<td>&nbsp;</td>
<td>$c_{t}$</td>
<td>$c_{t+1}$</td>
<td>$a$</td>
<td>&nbsp;</td>
<td>$c_{t}$</td>
<td>$c_{t+1}$</td>
<td>$a$</td>
</tr>
<tr>
<td>Income</td>
<td>&nbsp;</td>
<td><code>+</code></td>
<td><code>+</code></td>
<td><code>-</code></td>
<td>&nbsp;</td>
<td><code>-</code></td>
<td><code>-</code></td>
<td><code>+</code></td>
</tr>
<tr>
<td>Substitution</td>
<td>&nbsp;</td>
<td><code>-</code></td>
<td><code>+</code></td>
<td><code>+</code></td>
<td>&nbsp;</td>
<td><code>-</code></td>
<td><code>+</code></td>
<td><code>+</code></td>
</tr>
<tr>
<td>Net</td>
<td>&nbsp;</td>
<td><code>?</code></td>
<td><code>+</code></td>
<td><code>?</code></td>
<td>&nbsp;</td>
<td><code>-</code></td>
<td><code>?</code></td>
<td><code>+</code></td>
</tr>
</tbody>
</table>
<p>There are however also changes in variables marked with question marks, where the direction of change in a variable depends on the relative strength of substitution and income effects. In the case of a saver, if the income effect is stronger (weaker) than the substitution effect, consumption in the first period increases (decreases) and savings decrease (increase). In the case of a borrower, if the income effect is stronger (weaker) than the substitution effect, consumption in the second period decreases (increases).</p>
<p>In figures below, the initial endowment point is labeled as $E$, the optimal choice for old $r$ as $O$ and the optimal choice for new $r$ as $O^{\prime}$. Point $S$ represents the pure substitution effect, that is what would be the optimal choice of a consumer given new prices, if we changed the budget constraint such that the consumer's utility would be unchanged. Therefore, vector $O\to S$ represents the substitution effect, while vector $S\to O^{\prime}$ represents the income effect.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Saver&#39;s case&quot;</span><span class="p">)</span>

<span class="n">y_0</span> <span class="o">=</span> <span class="mf">2.5</span>
<span class="n">y_1</span> <span class="o">=</span> <span class="mi">1</span>
<span class="n">β</span> <span class="o">=</span> <span class="mf">0.95</span>
<span class="n">r</span> <span class="o">=</span> <span class="mf">0.05</span>
<span class="n">r_new</span> <span class="o">=</span> <span class="mi">1</span>

<span class="n">ShowIncomeAndSubstitutionEffects</span><span class="p">(</span><span class="n">y_0</span><span class="p">,</span> <span class="n">y_1</span><span class="p">,</span> <span class="n">β</span><span class="p">,</span> <span class="n">r</span><span class="p">,</span> <span class="n">r_new</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
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<pre>Saver&#39;s case
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<div class="prompt input_prompt">In&nbsp;[8]:</div>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Borrower&#39;s case&quot;</span><span class="p">)</span>

<span class="n">y_0</span> <span class="o">=</span> <span class="mf">0.5</span>
<span class="n">y_1</span> <span class="o">=</span> <span class="mf">3.1</span>
<span class="n">β</span> <span class="o">=</span> <span class="mf">0.95</span>
<span class="n">r</span> <span class="o">=</span> <span class="mf">0.05</span>
<span class="n">r_new</span> <span class="o">=</span> <span class="mi">1</span>

<span class="n">ShowIncomeAndSubstitutionEffects</span><span class="p">(</span><span class="n">y_0</span><span class="p">,</span> <span class="n">y_1</span><span class="p">,</span> <span class="n">β</span><span class="p">,</span> <span class="n">r</span><span class="p">,</span> <span class="n">r_new</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
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<pre>Borrower&#39;s case
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<p>The relative strength of the two effects depends on the shape of the indifference curves. In the case of the logarithmic utility function the reactions to the changes in the interest rate are the same, regardless of whether the agent is a borrower or a saver:</p>
\begin{align}
\frac{\partial a}{\partial r} &amp; =-\frac{1}{1+\beta}\left[-\frac{y_{t+1}}{\left(1+r\right)^{2}}\right]=\frac{1}{1+\beta}\frac{y_{t+1}}{\left(1+r\right)^{2}}&gt;0\\
\frac{\partial c_{t}}{\partial r} &amp; =\frac{1}{1+\beta}\left[-\frac{y_{t+1}}{\left(1+r\right)^{2}}\right]=-\frac{1}{1+\beta}\frac{y_{t+1}}{\left(1+r\right)^{2}}&lt;0\\
\frac{\partial c_{t+1}}{\partial r} &amp; =\frac{\beta}{1+\beta}y_{t}&gt;0
\end{align}<p>In response to the increase in the interest rate, second period consumption increases (as long as $y_{t}&gt;0$) and savings increase, while first period consumption decreases (as long as $y_{t+1}&gt;0$). The negative relationship between the level of interest rates and consumption is a usual assumption in macroeconomics, and is present in the undergraduate macroeconomic models such as IS-LM and AS-AD.</p>
<p>The case of logarithmic utility and $y_{t+1}=0$ is a very special case where both first period consumption and savings stay constant while second period consumption increases in response to an increase in the interest rate. The income and substitution effects have exactly equal strength and cancel each other out. We will use this set of assumptions when we will encounter the basic OLG model.</p>

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<p>Figures below illustrate the dependence of the relative strength of the substitution and income effects on the specific utility function.</p>
<p>The consumer's utility function is assumed to be the Constant Relative Risk Aversion (CRRA) function, which is commonly used in economic growth and financial literature. Parameter $\sigma&gt;0$ regulates the risk aversion of the consumer (the higher $\sigma$ is, the more risk averse is the consumer):</p>
\begin{align}
U=\frac{c_{t}^{1-\sigma}-1}{1-\sigma}+\beta\frac{c_{t+1}^{1-\sigma}-1}{1-\sigma}
\end{align}<p>For $\sigma=1$, the CRRA utility function reduces to the logarithmic function.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="nb">print</span><span class="p">(</span><span class="s1">&#39;Assuming second period income = 0&#39;</span><span class="p">)</span>

<span class="n">y_0</span> <span class="o">=</span> <span class="mi">1</span>
<span class="n">y_1</span> <span class="o">=</span> <span class="mi">0</span>
<span class="n">β</span> <span class="o">=</span> <span class="mf">0.95</span>

<span class="n">σ_vec</span> <span class="o">=</span> <span class="p">[</span><span class="mf">0.5</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">]</span>
<span class="n">r_vec</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">,</span> <span class="mi">6</span><span class="p">)</span>

<span class="k">for</span> <span class="n">σ</span> <span class="ow">in</span> <span class="n">σ_vec</span><span class="p">:</span>
    <span class="n">fig</span><span class="p">,</span> <span class="n">ax</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">()</span>
    <span class="k">for</span> <span class="n">r</span> <span class="ow">in</span> <span class="n">r_vec</span><span class="p">:</span>
        <span class="n">SolveUtilityMaximizationProblemCRRA</span><span class="p">(</span><span class="n">y_0</span><span class="p">,</span> <span class="n">y_1</span><span class="p">,</span> <span class="n">β</span><span class="p">,</span> <span class="n">σ</span><span class="p">,</span> <span class="n">r</span><span class="p">,</span> <span class="p">(</span><span class="n">fig</span><span class="p">,</span> <span class="n">ax</span><span class="p">))</span>
    <span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s1">&#39;Optimal choice for different $r$ with σ =  </span><span class="si">{:.1f}</span><span class="s1">&#39;</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">σ</span><span class="p">))</span>
    <span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="s1">&#39;Consumption in period $t$&#39;</span><span class="p">)</span>
    <span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="s1">&#39;Consumption in period $t+1$&#39;</span><span class="p">)</span>
    <span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
    <span class="nb">print</span><span class="p">(</span><span class="s1">&#39;&#39;</span><span class="p">)</span>
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<pre>Assuming second period income = 0
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<div class="prompt input_prompt">In&nbsp;[10]:</div>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="nb">print</span><span class="p">(</span><span class="s1">&#39;Assuming second period income smaller then first period income&#39;</span><span class="p">)</span>

<span class="n">y_0</span> <span class="o">=</span> <span class="mi">2</span>
<span class="n">y_1</span> <span class="o">=</span> <span class="mi">1</span>
<span class="n">β</span> <span class="o">=</span> <span class="mf">0.95</span>

<span class="n">σ_vec</span> <span class="o">=</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mf">2.5</span><span class="p">,</span> <span class="mi">3</span><span class="p">]</span>
<span class="n">r_vec</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">,</span> <span class="mi">6</span><span class="p">)</span>

<span class="k">for</span> <span class="n">σ</span> <span class="ow">in</span> <span class="n">σ_vec</span><span class="p">:</span>
    <span class="n">fig</span><span class="p">,</span> <span class="n">ax</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">()</span>
    <span class="k">for</span> <span class="n">r</span> <span class="ow">in</span> <span class="n">r_vec</span><span class="p">:</span>
        <span class="n">SolveUtilityMaximizationProblemCRRA</span><span class="p">(</span><span class="n">y_0</span><span class="p">,</span> <span class="n">y_1</span><span class="p">,</span> <span class="n">β</span><span class="p">,</span> <span class="n">σ</span><span class="p">,</span> <span class="n">r</span><span class="p">,</span> <span class="p">(</span><span class="n">fig</span><span class="p">,</span> <span class="n">ax</span><span class="p">))</span>
    <span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s1">&#39;Optimal choice for different $r$ with σ =  </span><span class="si">{:.1f}</span><span class="s1">&#39;</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">σ</span><span class="p">))</span>
    <span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="s1">&#39;Consumption in period $t$&#39;</span><span class="p">)</span>
    <span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="s1">&#39;Consumption in period $t+1$&#39;</span><span class="p">)</span>
    <span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
    <span class="nb">print</span><span class="p">(</span><span class="s1">&#39;&#39;</span><span class="p">)</span>
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<pre>Assuming second period income smaller then first period income
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+qBVx7ghmduYNnaZezSYxfGDB/DibufWJJ1l7oU/IgRIxqUgp89e/YWpeCnTp3KscceS5cuXfj2t78NwDXXXJOpj5q4TkTSOa0NwMysEh545QHGPzWeurV1BEHd2jrGPzWeB155oOh1VrsU/HHHHUeXLsmh7cMOO4zFi1tXTLIYrU2Zl5ckCjOzMrvhmRtYv3F9g7b1G9dzwzOtu6554cKFjB49mjlz5jBo0KAG04otwFhMKfhJkyZxwgknFP9GitTi2VmS5jU1CfDFgGbWJixbu6yg9qxqoRT8lVdeSZcuXTjrrLOK6q81spziuzNwPPBWo3YBT5U8IjOzMtilxy7Ura3L294aLZWCL+amVAMGDOCxxx7b/Hrx4sUcffTReeedPHky999/P48++mhV7jmSJYncD2wbEXMbT5D0WMkjMjMrgzHDxzD+qfENhrS6de7GmOHlOxG03KXgH3roIa655hr+9Kc/sc0227Qq1mK1eEwkIr4cEU80Me0LpQ/JzKz0Ttz9RMZ/fDz9evRDiH49+jH+4+NLdnZWKWUtBf+Nb3yD1atXM2rUKA444ADOO++85lZbFj7F18ysA6qJU3zNzKxjKziJSBpVjkDMzKztKaYA4zXAI6UOxJr34sxlzLj3ZdasfI9t+2zN4afuwZ6Htu6sEjOz1qqZKr7WtBdnLmPa7S+w4f1NAKxZ+R7Tbn8BwInEzKoqUxKRdAsQJNeGDEzvlw5ARHypTLFZasa9L29OIPU2vL+JGfe+7CRiZlWVdU/k1pznRwL5S0paWaxZ+V5B7WZmlZLpwHpE/Kn+Aaxu9NrKbNs+WxfUbmZtX5ZS8OPGjWPYsGEccMABHHfccSxdurTCURZ3iu/7JY/CmnX4qXvQZauGv6ouW3Xi8FP3qFJEZm3TqilTeOnYkSzY+2O8dOxIVk2ZUrJ1RwSbNm1qecYMVq5cyeWXX87MmTN5+umnufzyyzdfvZ7rkksuYd68ecydO5eTTjqJK664oiT9F6LgJBIR+SuNWdnseeguHHPWXpv3PLbtszXHnLWXj4eYFWDVlCnUjbuMDUuXQgQbli6lbtxlrUok1S4Fv912221+vnbt2pqtnWU1YM9Dd3HSMGuF5dddT6xvWAo+1q9n+XXXs/3JJxe93oULF3LLLbdw0003bTGt2AKMhZSC/+53v8ttt93G9ttvn7evcsucRCQNiojXyxmMmVm5bKjbsoJvc+1ZVbsU/JVXXsmVV17JVVddxYQJE7j88sre5qmQ4ay7GzdI8tCWmbUJXfr1K6g9q5ZKwRdzU6oBAwY0GBpbvHgxu+66a7PLfOELX+D3v/99YcGXQJabUn0OGA70lLQ38GJEbEwnTwSGlTE+M7OS2OmiC6kbd1mDIS1168ZOF11Ytj7LXQr+pZdeYsiQIQDcd9997LXXXsUHW6Qsw1lPAt2ArwA/BoZKehtYCqwrY2xmZiVTf9xj+XXXs6Guji79+rHTRRe26nhIueSWgge2KAV/3nnnMWLECMaOHcvChQvp1KkTgwYN4uabb654rJlLwUs6IiKeTJ/3AT4CvBARa8sYX4tcCt7MrHClKgWf+cB6fQJJn68EVra2czMza9t8PxEzMyuak4iZmRUty9lZ/97c9Ij4cenCMTOztiTLMZGe6c+hwMHAfenrk4HHyxGUmZm1DS0mkYi4HEDSVGB4RKxOX48HflvW6MzMrKYVckxkIA0r+L4PDM66sKRJkpZLeq6J6dtLmiLpWUnPSzqngNjMzNqVLKXg6/3oRz9CEitWrKhQdB8qpADjL4GnJdWXPzmNwm5OdSswAbitielfB/4SESdL2hFYKOn2iHDpeTMriRdnLmPGvS+zZuV7bNtnaw4/dY+SFTaNCCKCTp1af75SfSn4WbNmIYmDDjqIU045hd69e28x76JFi3jkkUcYOHBgq/stRuZ3GxFXAucAb5FcI3JORGx5HX7Tyz9O89eWBElpFQHbpvNuyLp+M7PmvDhzGdNuf2HzHUHXrHyPabe/wIszlxW9zmqXgoekPtcPf/jDqpSBh8JLwW8ENpF84Zfm7isfmkBy0H4pycH8MyIibx+SzgXOBaqWfc2sbZlx78tseL/hV8qG9zcx496XW7U3Us1S8Pfddx/9+/dn//33LzL61iukFPwY4KvA7wEBv5I0MSJ+UqJYjgfmAscCewCPSJoeEe80njEiJpIUf2TEiBHZ6raYWYdWvweStT2rapWCf/fdd7nyyiuZOnVqUX2USiGDd18GDo2I70fEZcBhJEmlVM4B7orEX4FXgcqXpDSzdqn+zqBZ27OqVin4l19+mVdffZX999+fwYMHs3jxYoYPH86yZcUPzxWjkOEskQxn1duYtpXK34CRwHRJO5Ncl/JKCddvZh3Y4afuwbTbX2gwpNVlq04cfuoeZeuznKXg99tvP5YvX7759eDBg5k1axZ9+/YtPuAiFJJEbgFmNjo76xdZF5Z0B3A00FfSYuD7QFeAiLgZ+A/gVknzSZLTtyOi8uermVm7VH/co1xnZ5VS1lLwtSBzKXgASQcBR5B8yT8eEXPKFVhWLgVvZla4ipeCB4iI2cDs1nZqZmbtQ5YCjE9ExJGSVpOc2rt5EhARsV3ZojMzs5qWpXbWkekFgPtExN8qEJOZmbURmU7xjeTAyd0tzmhmZh1KIdeJ/FnSwWWLxMzM2pxCDqwfA5wn6TVgLR8eExlWjsDMzKz2FbIncgKwO0lZkpOBk9KfZmZWYllKwY8fP57+/ftvvhL+wQcfrHCUhe2J/A04C9g9Iq6QNBDYBXi9LJGZmZXYgunTmP7r21j99xX03KEvR505mr2POqYk665WKfiLLrqIiy++uNV9FquQd3sTcDjw+fT1auC/Sh6RdQirpkzhpWNHsmDvj/HSsSNZNWVKtUOydm7B9GlMnTiB1SvehAhWr3iTqRMnsGD6llV2s6qFUvDVVkgSOTQivg6sB4iIt4CtyhKVtWurpkyhbtxlbFi6FCLYsHQpdeMucyKxspr+69vY8H7Dir0b3n+P6b9u6j552SxcuJDRo0czZ84cBg0a1GBasQUYs5aCB5gwYQLDhg3jS1/60uZaW5VUyHDWB5I6k15wmN59sNT3FLEOYPl11xPr1zdoi/XrWX7d9Wx/sg+zWXms/nv+UnxNtWdVrVLwAOeffz7jxo1DEuPGjeOb3/wmkyZNKqrPYhWyJ3IjybUiO0m6EngC+H9licratQ11dQW1m5VCzx3yV7dtqj2rapWCB9h5553p3LkznTp14qtf/SpPP/108W+kSJn3RCLidkmzScq1CzgtIhaULTJrt7r065cMZeVpNyuXo84czdSJExoMaXXZamuOOnN02fosZyl4gLq6Ovqlfzd33303++67b/HBFqnQAowvAC+UKRbrIHa66ELqxl3WYEhL3bqx00UXVjEqa+/qz8Iq19lZpZS1FPy3vvUt5s6diyQGDx7Mz372s4rHmrkUvKRuwNeAI0mOizwB/DQi1je7YJm5FHzbtGrKFJZfdz0b6uro0q8fO110oY+HmFVQqUrBF5JE7iQ5rfdXadPngd4R8U+tDaI1nETMzApXjfuJDI2I/XNeT5P0bGsDMDOztquQs7PmSNp8HpukQ4EnSx+SmZm1FYXsiRwKjJZUf0+RgcCC9J7oLsRoZtYBFZJEPlW2KMzMrE0q5DoRF1o0M7MGWl9u0szMOiwnETMzK1rm4SxJWwP/CAzOXS4irih9WGZm1hYUcmD9XmAVMBt4r4V5zcysAygkiQyICJ+hZWZmmxVyTOQpSfuVLRIzM2tzCkkiRwKzJS2UNE/SfEnzsi4saZKk5ZKea2L6JZLmpo/nJG2U1KeA+MzMrMIKGc46oZV93QpMAPLeizIirgWuBZB0MnBRRKxsZZ9mZlZGFbvYMCIelzQ44+yfB+5oTX9mZlZ+LQ5nSXoi/bla0js5j9WS3il1QJK2ISmx8vtm5jlX0ixJs958881Sh2BmZhm1mEQi4sj0Z8+I2C7n0TMititDTCcDTzY3lBUREyNiRESM2HHHHcsQgpmZZVGLV6yfiYeyzMzahJpKIpK2Bz5BcmGjmZnVuELOzmoVSXcARwN9JS0Gvg90BYiIm9PZTgemRsTaSsVlZmbFq1gSiYjPZ5jnVpJTgc3MrA1wAUYzMyuaCzCamVnRXIDRzMyK5gKMZmZWtEL2RI4EvijpVZLhLAEREcPKEpmZmdW8ShZgNDOzdibzcFZagLEXSVmSk4FerS3KaGZmbVvmJCJpDHA7sFP6+JWkfytXYGbtzQOvPMBxvzuOYZOHcdzvjuOBVx6odkhmrVbIcNaXgUPrryaXdA0wA/hJOQIza08eeOUBxj81nvUb1wNQt7aO8U+NB+DE3U+sYmRmrVPI2VkCNua83pi2mVkLbnjmhs0JpN76jeu54ZkbqhSRWWkUsidyCzBT0t3p69OAX5Q+JLP2Z9naZQW1m7UVhdzZ8MeS/gQcQbIHck5EzClbZGbtyC49dqFubV3edrO2rKBS8BExOyJujIgbnEDMshszfAzdOndr0NatczfGDB9TpYjMSqPFPRFJT0TEkZJWA5E7ieRiw3Lc3dCsXak/eH7DMzewbO0ydumxC2OGj/FBdWvzWkwi9bfHBX4aEd/KnSbph2WJyqwdOnH3E500rN0pZDjrk3naXJDRzKwDyzKcdT7wNWAPSfNyJvUEnipXYGZmVvuynJ31P8AfgKuAsTntqyNiZVmiMjOzNiHLMZFVJDejavH2tmZm1rEUcnvcbiTDWkeSnKX1BMnB9vXNLmhmZu1WIVes3was5sNaWZ8Hfgn8U6mDMjOztqGQJDI0IvbPeT1N0rOlDsjMzNqOQk7xnSPpsPoXkg4Fnix9SGZm1lYUsidyKDBa0t/S1wOBBZLm49vkmpl1SIUkEV9YaGZmDRRSxde3wjUzswYKOcV3BPBdYFC6XH0BRg9jmZl1UIUMZ90OXALMBzYV2pGkScBJwPKI2LeJeY4Grge6Aisi4hOF9mNmZpVTSBJ5MyLua0VftwITSK432YKkXsBNwKci4m+SdmpFX2ZmVgGFJJHvS/o58CjwXn1jRNyVZeGIeFzS4GZm+QJwV0T8LZ1/eQGxmZlZFRSSRM4B9iIZaqofzgogUxLJYE+gq6THSCoE3xARTe21nAucCzBw4MASdW9mZoUqJInsHxH7lS2SJJaDgJFAd2CGpD9HxIuNZ4yIicBEgBEjRkTj6WZmVhmFXLH+Z0kfK1sksBh4KCLWRsQK4HFg/xaWMTOzKiokiRwJPCtpoaR5kuY3uklVa90LHCWpi6RtSK6QX1DC9ZuZWYlV7Ip1SXcARwN9JS0Gvk9yfIWIuDkiFkh6CJhHcszl5xHxXGv6NDOz8iokiZzdRPsVWRaOiBZvahUR1wLXFhCTmZlVUSFJZG3O824kFw56uMnMrAMrpHbWf+a+lvQjoDUXH5qZWRtXyIH1xrYBdi9VIGZm1vYUUoBxPsnFhQCdgR3JeDzEzMzap0KOiZyU83wD8EZEbChxPGZm1oYUMpx1CLAyva/IOcCdkoaXJywzM2sLCkki4yJitaQjgeOBycBPyxOWmXU48+6E6/aF8b2Sn/PurHZElkEhSWRj+vNE4KcRcS+wVelDMrMOZ96dMOUCWLUIiOTnlAucSNqAQpLIEkk/A84AHpS0dYHLm5nl9+gV8MG6hm0frEvaraYVkgQ+BzwMHB8RbwO9Se50aGbWOqsWF9ZuNaOQs7M2klyp/k+ScpebWtqQzKzD2X5AOpSVp91qWiF7IvcCp5Cc3rs252Fm1jojL4Ou3Ru2de2etFtNK2RPZEBEtKqSr5lZXsM+l/x89IpkCGv7AUkCqW+3mlVIEnlK0n4RMb9s0ZhZxzXsc04abVAhSeRI4IuSXgXeAwRERAwrS2RmZlbzCkkiJ5QtCjMza5MKKQX/ejkDMTOztqeQPREk7Q8clb6cHhHPlj4kMzNrKzKf4itpDHA7sFP6+JWkfytXYGZmVvsK2RP5MnBoRKwFkHQNMAP4STkCMzOz2lfIxYbiwyKMpM9V2nDMzKwtKWRP5BZgpqS709enAb8ofUhmZtZWtJhEJH0U2DkifizpMZLrRQRcACwpb3hmZlbLsgxnXQ+sBoiIZyLixoi4AXg3nWbuIgruAAAME0lEQVRmZh1UliQyOCLmNW6MiFnA4JJHZGZmbUaWJNKtmWndm5lmZmbtXJYk8n+Svtq4UdKXgdmlD8nMzNqKLGdnXQjcLeksPkwaI0jur3561o4kTQJOApZHxL55ph9Ncs+SV9OmuyLC98Y0M6thLSaRiHgD+LikY4D6L/8HIuKPBfZ1KzABuK2ZeaZHxEkFrtfMzKqkkAKM04BpxXYUEY9LGlzs8mZmVnsKuWK9Eg6X9KykP0jap9rBmJlZ8wqq4ltmzwCDImKNpE8D9wBD8s0o6VzgXICBAwdWLkIzM2ugZvZEIuKdiFiTPn8Q6CqpbxPzToyIERExYscdd6xonGZm9qGaSSKSdpGk9PkhJLH9vbpRmZlZcyo2nCXpDuBooK+kxcD3ga4AEXEz8FngfEkbgHXAmRERlYrPzMwKV7EkEhGfb2H6BJJTgM3MrI2omeEsMzNre5xEzMysaE4iZmZWNCcRMzMrmpOImZkVrZauWDczszK4Z84Srn14IUvfXseuvbpzyfFDS7ZuJxEzs3bsnjlL+M5d81n3wUYAlry9ju/cNZ9O3bfrU4r1ezjLzKwdu/bhhZsTSL11H2yk87Z9+pdi/U4iZmbt2NK31+VtV+cuW5Vi/U4iZmbt2K69uudtj40b3i/F+p1EzMzasUuOH0r3rp0btHXv2pmNa1YuKcX6nUTMzNqx0w7sz1Wf2Y/+vbojoH+v7lz1mf3YtO6dlaVYv8/OMjNr5047sD+nHViS4+hb8J6ImZkVzUnEzMyK5iRiZmZFcxIxM7OiOYmYmVnRnETMzKxoTiJmZlY0JxEzMyuak4iZmRXNScTMzIrmJGJmZkVzEjEzs6I5iZiZWdGcRMzMrGhOImZmVrSKJRFJkyQtl/RcC/MdLGmjpM9WKjYzMytOJfdEbgU+1dwMkjoD1wAPVyIgMzNrnYolkYh4HGjpdoz/BvweWF7+iMzMrLVq5va4kvoDpwPHAge3MO+5wLnpy/daGiKrgr7AimoHkUctxuWYsnFM2dViXLUY09BSrKRmkghwPfDtiNgoqdkZI2IiMBFA0qyIGFGB+DKrxZigNuNyTNk4puxqMa5ajakU66mlJDIC+HWaQPoCn5a0ISLuqW5YZmbWlJpJIhHxkfrnkm4F7ncCMTOrbRVLIpLuAI4G+kpaDHwf6AoQETe3YtUTWx9dydViTFCbcTmmbBxTdrUYV7uNSRFRivWYmVkH5CvWzcysaE4iZmZWtJpNIi2VSZF0qqR5kuZKmiXpyJxpAyVNlbRA0l8kDa6BmH4o6fk0phvV0nnMJYwrZ74tSspIOlvSS+nj7GrHJOkASTPSz2qepDOqHVNO+3aSlkiaUAsxVWs7byGmqm3nko6WtCr9+5sr6bKcaZ+StFDSXyWNrXZMknaTNC39nJ6XNKbaMeVM7yxpjqT7M3UYETX5AP4BGA4818T0bfnwmM4w4IWcaY8Bo3Lm26aaMQEfB54EOqePGcDRlfqs0nk6A38EHgQ+m7b1AV5Jf/ZOn/euckx7AkPS57sCdUCvasaUM+0G4H+ACdX+3VVzO2/md1fV7ZzkxJ37m4j1ZWB3YCvgWeBjVY6pHzA8fd4TeLHaMeVM//d0O29yntxHze6JRAtlUiJiTaTvGOgBBICkjwFdIuKRnPnerWZM6c9uJBvw1iRnpb1RipiyxJXKV1LmeOCRiFgZEW8Bj9BCfbNyxxQRL0bES+nzpem0HasZE4Ckg4CdgamliKW1MVVzO28qJmpjO8/nEOCvEfFKRLwP/Bo4tZoxRURdRDyTPl8NLAD6VzMmAEkDgBOBn2ddpmaTSBaSTpf0AvAA8KW0eU/gbUl3pbtk1yop7Fi1mCJiBjCN5L/qOuDhiFhQwZjqS8o0PpW6P7Ao5/ViSrQhtyKm3HkOIflCermaMUnqBPwncEkl4sgSE1XczpuKqdrbeepwSc9K+oOkfdK2qm3nzcS0WToMeSAwswZiuh74FrAp64radBKJiLsjYi/gNOA/0uYuwFHAxSQ1uHYHvljNmCR9FNgbGECy8R4r6R8qFRM5JWUatecbr67UOd9NxQSApH7AL4FzIiLzBl2mmL4GPBgRi/IsU62Yqrmd542pBrbzZ4BBEbE/8BOg/mLlam7nTcUEgKRtSfboLoyId6oZk6STgOURMbuQldXMFeutERGPS9pDUl+S/zLmRMQrAJLuAQ4DflHFmE4H/hwRa9KY/pDG9HiFwslbUobkszo6Z74BJOPsVYspIu6RtB3Jntz3IuLPFYqnyZiAw4GjJH2N5NjDVpLWRETJDtAWEVM1t/OmYhpCFbfz3C/hiHhQ0k053wm75cw6AFhazZgiYoWkriQJ5PaIuKsS8TQXE3AEcIqkT5MMS24n6VcR8c8trbBmH8Bgmj449FE+PIg9HFhC8h9HZ5IDZzum024Bvl7lmM4A/pckaXcFHgVOrtRn1Wi+W2l4YP1VkoPqvdPnfaoc01bp53NhpbeppmJq1P5FSnhgvRWfU9W282Ziqup2DuyS8/d3CPC39O+vC8lJIx/hwwPr+1Q5JgG3AdeX8vNpTUyN5jmajAfWa3ZPRC2XSflHYLSkD4B1wBmRvPuNki4GHk1PL5wN/Hc1Y5L0O5IS9/NJdqMfiogppYgpY1x5RcRKSf8B/F/adEVEFHVArlQxAZ8jObtkB0lfTNu+GBFzqxhT2bTid1fN7bwp1d7OPwucn+4VrQPOTL8TNkj6BsnN7joDkyLi+WrGpOT0/38B5kuq37YvjYgHqxVT0f21YlkzM+vg2vSBdTMzqy4nETMzK5qTiJmZFc1JxMzMiuYkYmZmRXMSMTOzojmJmJlZ0ZxErKIk7SLp15JeVnIPjAcl7VntuFoiqVda9qT+9VMlXHfJ1lWuPiWNTy9ubNw+QCW854u1PU4iVjHpldV3A49FxB4R8THgUpIS67WuF0khRgAi4uOlWnEp19USJTqVsM+RJCV+rINyErFKOgb4ILd0RkTMjYjpkv5d0nPp48L66ZIGK7n7238ruQPcVEndJfWQ9EBazvo5SWek8z6Xs+zF6X/QgyW9IOnn6by3S/qkpCeV3NHxkJy+XpA0WcldFX8naZt0dVcDeyi5E9y1ktbk9LNF7E3Fne9DqV9XlmVaiBFJ/yzp6TTOnym5S139em8iqeC6W0vxp+3fVXI3wP8FhuaJ+0jgx8Bn0/4+0twv39qpchT/8sOPfA/gAuC6PO0HkdRb6kFSJfd54MB02mBgA3BA+vpO4J9J6pT9d846tqdR0TmSMunjc9axH8k/TrOBSSRF8E4F7snpK4Aj0teTgItzpuWue01zsTcVdxOfy5rm3mujeZuLcW9gCtA1fX0TMDpdZhNwWAHx17dvA2wH/LW+n0bxPATsW+1ty4/qPbwnYrXgSODuiFgbSRnxu0julVHv1fiwAONski/F+cAnJV0j6aiIWNVCH69GxPxI7k3yPPBoRES6nsE58y2KiCfT579KYys29nxxtyTLMk3FOJLky///0qJ+I0nuMwLweuQvq99U/Eel7e9GUjr8vibiHQoszPC+rJ1yErFKep7kS66xfDcNyvVezvONJLeFfZEP/1u+StJlJP/F527T3ZpYx6ac15toeF+dxhVJW6pQ2lzsW8TdwrqyLtNUjAImR8QB6WNoRIxPp61tor/m4m/2vUvaAVgVER80N5+1b04iVkl/BLaW9NX6BkkHA3OA0yRtI6kHyU28pje3Ikm7Au9GxK+AH5Ec3H0D2EnSDpK2Bk4qIsaBkg5Pn38eeCJ9vhromWf+xwuNvQSaivFRkuMTOwFI6iNpUAvrair+x4HT0+NPPYGT8yz7ESp0cyerXTV7PxFrfyIiJJ0OXC9pLLAeeA24kOTmRk+ns/48Iua0sLr9gGslbQI+AM6PiA8kXUFyr+pXgReKCHMBcLaknwEvAT9NY/97eiD+OeAPOe/pGUlbxK7kvtnl0lSMf5H0PWCqkvvCfwB8HVjW1Iqaih9A0m+AucDr5E+ML5Dcs+I54NyIqPipylZ9vp+IWSr94r8/IvatcihNagsxWsfi4SwzMyua90TMzKxo3hMxM7OiOYmYmVnRnETMzKxoTiJmZlY0JxEzMyuak4iZmRXNScTMzIr2/wHYiAI7EX/XsQAAAABJRU5ErkJggg==
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>
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
"
>
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<div class="output_area">

    <div class="prompt"></div>


<div class="output_subarea output_stream output_stdout output_text">
<pre>
</pre>
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</div>
<div class="cell border-box-sizing code_cell rendered">
<div class="input">
<div class="prompt input_prompt">In&nbsp;[11]:</div>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="nb">print</span><span class="p">(</span><span class="s1">&#39;Assuming second period income bigger then first period income&#39;</span><span class="p">)</span>

<span class="n">y_0</span> <span class="o">=</span> <span class="mi">1</span>
<span class="n">y_1</span> <span class="o">=</span> <span class="mi">2</span>
<span class="n">β</span> <span class="o">=</span> <span class="mf">0.95</span>

<span class="n">σ_vec</span> <span class="o">=</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mf">3.5</span><span class="p">,</span> <span class="mi">4</span><span class="p">]</span>
<span class="n">r_vec</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">,</span> <span class="mi">6</span><span class="p">)</span>

<span class="k">for</span> <span class="n">σ</span> <span class="ow">in</span> <span class="n">σ_vec</span><span class="p">:</span>
    <span class="n">fig</span><span class="p">,</span> <span class="n">ax</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">()</span>
    <span class="k">for</span> <span class="n">r</span> <span class="ow">in</span> <span class="n">r_vec</span><span class="p">:</span>
        <span class="n">SolveUtilityMaximizationProblemCRRA</span><span class="p">(</span><span class="n">y_0</span><span class="p">,</span> <span class="n">y_1</span><span class="p">,</span> <span class="n">β</span><span class="p">,</span> <span class="n">σ</span><span class="p">,</span> <span class="n">r</span><span class="p">,</span> <span class="p">(</span><span class="n">fig</span><span class="p">,</span> <span class="n">ax</span><span class="p">))</span>
    <span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s1">&#39;Optimal choice for different $r$ with σ =  </span><span class="si">{:.1f}</span><span class="s1">&#39;</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">σ</span><span class="p">))</span>
    <span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="s1">&#39;Consumption in period $t$&#39;</span><span class="p">)</span>
    <span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="s1">&#39;Consumption in period $t+1$&#39;</span><span class="p">)</span>
    <span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
    <span class="nb">print</span><span class="p">(</span><span class="s1">&#39;&#39;</span><span class="p">)</span>
</pre></div>

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<pre>Assuming second period income bigger then first period income
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<h2 id="Overlapping-Generations-model">Overlapping Generations model<a class="anchor-link" href="#Overlapping-Generations-model">&#182;</a></h2><p>We are now ready to tackle the OLG model. This particular version follows <a href="http://www.jstor.org/stable/1809231">Diamond (1965)</a> and is the simplest setup of a general equilibrium OLG model.</p>
<p>The model is populated by firms and households. Each household belongs to a certain generation and within each time period there are two generations alive at the same time, which we will label as young (<code>y</code>) and old (<code>o</code>). Time is divided into discrete periods, each representing around 30 years. Therefore, period $t$ young will become period $t$ old:</p>
<p><img src="img/OLG/OLG_generations.png" alt="OLG Generations Structure"></p>
<p>Author: <a href="http://www.econ.ku.dk/okocg/">Christian Groth</a></p>
<p>The number of young agents in period $t$ is denoted with $N_{t}^{y}$, and the number of old agents in period $t$ is denoted with $N_{t}^{o}$. We assume that all young survive into the old age, but all old die with certainty. Therefore, the number of old agents in period $t$ is equal to the number of young agents in period $t-1$:</p>
\begin{align}
N_{t}^{o} = N_{t-1}^{y}
\end{align}<p>and the total population $N_{t}$ is equal to the sum of young and old:</p>
\begin{align}
N_{t} = N_{t}^{y} + N_{t}^{o}
\end{align}<p>We will also assume that the ratio of number of children to number of their parents is equal to $1+n$ (each couple has $2\cdot (1+n)$ children). This implies that the rate of growth of the entire population is also equal to $n$:</p>
\begin{align}
\frac{N_{t+1}}{N_{t}} &amp; =\frac{N_{t+1}^{y}+N_{t+1}^{o}}{N_{t}^{y}+N_{t}^{o}}=\frac{\left(1+n\right)N_{t}^{y}+N_{t}^{y}}{\left(1+n\right)N_{t}^{o}+N_{t}^{o}}\\
 &amp; =\frac{\left(1+n\right)^{2}N_{t}^{o}+\left(1+n\right)N_{t}^{o}}{\left(1+n\right)N_{t}^{o}+N_{t}^{o}}=\frac{\left(1+n\right)\left[\left(1+n\right)+1\right]}{\left(1+n\right)+1}\\
 &amp; =1+n
\end{align}
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<h3 id="Households'-problem">Households' problem<a class="anchor-link" href="#Households'-problem">&#182;</a></h3><p>The households solve a familiar two-period Utility Maximization Problem:</p>
\begin{align}
\max\quad &amp; U=\log c_{t}^{y}+\beta\log c_{t+1}^{o}\\
\text{subject to}\quad &amp; c_{t}^{y}+a_{t+1}=w_{t}\\
 &amp; c_{t+1}^{o}\quad\,\,\,\,\,=\left(1+r_{t+1}\right)a_{t+1}
\end{align}<p>where $c_{t}^{y}$ denotes consumption in period $t$ when young <code>y</code> and $c_{t+1}^{o}$ denotes consumption in period $t+1$ when old <code>o</code>.</p>
<p>For simplicity, we assume that the household receives labor income in the first period in the form of wages, and no labor income in the second period. The only way the old can finance their consumption is through their assets. We denote the stock of assets of young <code>y</code> at the end of period $t$ as $a_{t+1}$, and the reason for choosing this "shifted" time subscript will become clear later on.</p>
<p>Note that both the wage $w$ and the real interest rate $r$ have time subscripts. This is because the rewards to factors of production will depend on the level of capital stock in the economy.</p>
<p>As before, let us solve the problem by using the Lagrange method. First, construct the lifetime budget constraint:</p>
\begin{align}
c_{t+1}^{o} &amp; =\left(1+r_{t+1}\right)a_{t+1}\\
a_{t+1} &amp; =\frac{c_{t+1}^{o}}{1+r_{t+1}}
\end{align}\begin{align}
c_{t}^{y}+a_{t+1} &amp; =w_{t}\\
c_{t}^{y}+\frac{c_{t+1}^{o}}{1+r_{t+1}} &amp; =w_{t}
\end{align}<p>Again, the present discounted value (PDV) of lifetime consumption expenditures cannot exceed the PDV of lifetime income, and in this case the latter is simply first period labor income.</p>
<p>Note that although we are using equality signs for convenience, we should keep in the back of our heads that we can always consume less than what we earn, but not the other way around. Therefore, we rewrite the budget constraint for the purpose of plugging into the Lagrangian as:</p>
\begin{align}
0=w_{t}-c_{t}^{y}-\frac{c_{t+1}^{o}}{1+r_{t+1}}
\end{align}<p>Now we construct the Lagrangian:</p>
\begin{align}
\mathcal{L}=\log c_{t}^{y}+\beta\log c_{t+1}^{o}+\lambda_{t}\left[w_{t}-c_{t}^{y}-\frac{c_{t+1}^{o}}{1+r_{t+1}}\right]
\end{align}<p>And derive the First Order Conditions (FOCs):</p>
\begin{align}
\frac{\partial\mathcal{L}}{\partial c_{t}^{y}} &amp; =\frac{1}{c_{t}^{y}}+\lambda_{t}\left[-1\right]=0\\
\frac{\partial\mathcal{L}}{\partial c_{t+1}^{o}} &amp; =\beta\frac{1}{c_{t+1}^{o}}+\lambda_{t}\left[-\frac{1}{1+r_{t+1}}\right]=0
\end{align}<p>Let us simplify the above equations:</p>
\begin{align}
\lambda_{t}&amp;=\frac{1}{c_{t}^{y}}\\
\lambda_{t}&amp;=\beta\left(1+r_{t+1}\right)\frac{1}{c_{t+1}^{o}}
\end{align}<p>And combine them:</p>
\begin{align}
\frac{1}{c_{t}^{y}}&amp;=\beta\left(1+r_{t+1}\right)\frac{1}{c_{t+1}^{o}}\\
c_{t+1}^{o}&amp;=\beta\left(1+r_{t+1}\right)c_{t}^{y}
\end{align}<p>Plug in the obtained Euler equation into the lifetime budget constraint:</p>
\begin{align}
c_{t}^{y}+\frac{c_{t+1}^{o}}{1+r_{t+1}} &amp; =w_{t}\\
c_{t}^{y}+\frac{\beta\left(1+r_{t+1}\right)c_{t}^{y}}{1+r_{t+1}} &amp; =w_{t}\\
c_{t}^{y}+\beta c_{t}^{y} &amp; =w_{t}
\end{align}<p>The resulting optimal levels of consumption are:</p>
\begin{align}
c_{t}^{y} &amp; =\frac{1}{1+\beta}w_{t}\\
c_{t+1}^{o} &amp; =\frac{\beta}{1+\beta}\left(1+r_{t+1}\right)w_{t}
\end{align}<p>And the end of period $t$ stock of assets of the young is equal to:</p>
\begin{align}
a_{t+1}=w_{t}-c_{t}=\frac{\beta}{1+\beta}w_{t}
\end{align}<p>Thanks to our simplifying assumptions (logarithmic utility and no pension income), the expressions for consumption of young and their stock of assets depend only on $t$ period variables.</p>

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<h3 id="Firms'-problem">Firms' problem<a class="anchor-link" href="#Firms'-problem">&#182;</a></h3><p>The firms want to hire optimal quantities of labor and capital to maximize their profits:</p>
\begin{align}
\max\quad\Pi_{t}=K_{t}^{\alpha}\left(A_{t}L_{t}\right)^{1-\alpha}-w_{t}L_{t}-r_{t}^{k}K_{t}
\end{align}<p>First order conditions (FOCs):</p>
\begin{align}
\frac{\partial\Pi_{t}}{\partial L_{t}} &amp; =\left(1-\alpha\right)K_{t}^{\alpha}A_{t}^{1-\alpha}L_{t}^{-\alpha}-w_{t}=0\\
\frac{\partial\Pi_{t}}{\partial K_{t}} &amp; =\alpha K_{t}^{\alpha-1}\left(A_{t}L_{t}\right)^{1-\alpha}-r_{t}^{k}=0
\end{align}<p>Simplify the above expressions:</p>
\begin{align}
w_{t} &amp; =\left(1-\alpha\right)A_{t}\left(\frac{K_{t}}{A_{t}L_{t}}\right)^{\alpha}=\left(1-\alpha\right)\frac{Y_{t}}{L_{t}}\\
r_{t}^{k} &amp; =\alpha\left(\frac{K_{t}}{A_{t}L_{t}}\right)^{\alpha-1}=\alpha\frac{Y_{t}}{K_{t}}
\end{align}<p>The above equations determine both the wage $w$ and the capital rental rate $r^{k}$ as functions of capital (per effective labor). The real interest rate is equal to the capital rental rate, less the capital depreciation rate:</p>
\begin{align}
r_{t} &amp; =r_{t}^{k}-\delta
\end{align}<p>In the simplest OLG model we assume that capital depreciates fully between time periods ($\delta=1$). This is justified by the fact that each period of time represents decades in real world. Just think about how few machines and equipments that were used in 1990 are still in use today.</p>

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<h3 id="General-Equilibrium">General Equilibrium<a class="anchor-link" href="#General-Equilibrium">&#182;</a></h3><p>The General Equilibrium assumption allows us to integrate the decisions of hosueholds and firms in a consistent manner. Behind the scenes, the GE concept involves assuming that all markets are simultaneously in equilibrium. In this model there are three markets: one for goods, one for labor and one for capital.</p>
<h4 id="Labor-market">Labor market<a class="anchor-link" href="#Labor-market">&#182;</a></h4><p>We have assumed that all young work, and that the old do not work. Accordingly, the number of employees $L_{t}$ in equilibrium is equal to the number of the young $N_{t}^{y}$:</p>
\begin{align}
L_{t} = N_{t}^{y}
\end{align}<h4 id="Capital-market">Capital market<a class="anchor-link" href="#Capital-market">&#182;</a></h4><p>In equilibrium, the net assets of the households are equal to the productive capital employed by firms. In time period $t$ the only agents with positive assets are the old <code>o</code> and thus:</p>
\begin{align}
K_{t} = N_{t}^{o}a_{t} = N_{t-1}^{y}a_{t}
\end{align}<p>where $a_{t}$ is the end of period $t-1$ stock of assets of then-young agents, who in period $t$ are old.</p>
<p>Accordingly, the capital stock in period $t+1$ is equal to the end of period $t$ stock of assets of agents who are young in period $t$:</p>
\begin{align}
K_{t+1} = N_{t}^{y}a_{t+1}
\end{align}<p>Let us compare the above expression with the already familiar capital accumulation equation:</p>
\begin{align}
K_{t+1} = I_{t} + \left(1-\delta\right)K_{t} = I_{t}
\end{align}<p>where in the second equality the assumption of $\delta=1$ was used. This also implies that:</p>
\begin{align}
I_{t} = N_{t}^{y}a_{t+1}
\end{align}
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<h4 id="Goods-market">Goods market<a class="anchor-link" href="#Goods-market">&#182;</a></h4><p>The equilibrium in the goods market requires that supply of goods equals demand for goods, which in this model is equivalent to the national accounting identity:</p>
\begin{align}
Y_{t} = C_{t} + I_{t} + G_{t} + NX_{t} = C_{t} + I_{t}
\end{align}<p>where, as in the previous lecture, we have assumed that there is no government ($G=0$) and that the economy is closed ($NX=0$).</p>
<p>The aggregate consumption is equal to the sum of consumption of young and old, and so:</p>
\begin{align}
Y_{t} = N_{t}^{y}c_{t}^{y} + N_{t}^{o}c_{t}^{o} + I_{t}
\end{align}<p>We can show that equilibrium in the goods market is equivalent to equilibrium in both labor and capital markets (this was already guaranteed by <a href="https://en.wikipedia.org/wiki/Walras%27s_law">Walras' law</a>):</p>
\begin{align}
Y_{t} &amp; =N_{t}^{y}c_{t}^{y}+N_{t}^{o}c_{t}^{o}+I_{t}\\
Y_{t} &amp; =N_{t}^{y}c_{t}^{y}+N_{t}^{o}c_{t}^{o}+N_{t}^{y}a_{t+1}\\
Y_{t} &amp; =N_{t}^{y}\left(c_{t}^{y}+a_{t+1}\right)+N_{t}^{o}\left(1+r_{t}\right)a_{t}\\
Y_{t} &amp; =L_{t}w_{t}+\left(1+r_{t}\right)K_{t}\\
Y_{t} &amp; =L_{t}\left(1-\alpha\right)\frac{Y_{t}}{L_{t}}+\left(1+r_{t}^{k}-\delta\right)K_{t}\\
Y_{t} &amp; =\left(1-\alpha\right)Y_{t}+\alpha\frac{Y_{t}}{K_{t}}K_{t}\\
Y_{t} &amp; =\left(1-\alpha\right)Y_{t}+\alpha Y_{t}\\
Y_{t} &amp; =Y_{t}
\end{align}<p>where the following expressions for the factor prices were used:</p>
\begin{align}
w_{t} &amp; =\left(1-\alpha\right)\frac{Y_{t}}{L_{t}}\\
r_{t}^{k} &amp; =\alpha\frac{Y_{t}}{K_{t}}
\end{align}
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<h3 id="Saving-rate-of-the-OLG-economy">Saving rate of the OLG economy<a class="anchor-link" href="#Saving-rate-of-the-OLG-economy">&#182;</a></h3><p>We can also derive the saving rate of this economy, and show that it is constant, just like in the Solow-Swan case. This model however will give us the link between the saving rate and households' preferences.</p>
<p>We already know that investment (equal to aggregate savings) is equal to:</p>
\begin{align}
I_{t} = N_{t}^{y}a_{t+1}
\end{align}<p>And that the young households choose the end of period $t$ level of assets to be equal to:</p>
\begin{align}
a_{t+1}=\frac{\beta}{1+\beta}w_{t}
\end{align}<p>Investment can be then expressed as:</p>
\begin{align}
I_{t} = L_{t}\cdot\frac{\beta}{1+\beta}w_{t}=L_{t}\cdot\frac{\beta}{1+\beta}\left(1-\alpha\right)\frac{Y_{t}}{L_{t}} = \left(1-\alpha\right)\frac{\beta}{1+\beta}\cdot Y_{t}
\end{align}<p>So the ratio of investment to GDP (equivalent to the saving rate) is equal to:</p>
\begin{align}
s\equiv\frac{I_{t}}{Y_{t}}=\frac{\left(1-\alpha\right)\frac{\beta}{1+\beta}\cdot Y_{t}}{Y_{t}}=\left(1-\alpha\right)\frac{\beta}{1+\beta}
\end{align}<p>As expected, the saving rate $s$ depends positively on households' discount factor $\beta$:</p>
\begin{align}
\frac{\partial s}{\partial\beta}=\left(1-\alpha\right)\frac{\left(1+\beta\right)-\beta}{\left(1+\beta\right)^{2}}=\frac{1-\alpha}{\left(1+\beta\right)^{2}}&gt;0
\end{align}<p>The more patient the households are (the higher $\beta$ is), the higher the aggregate saving rate in an economy.</p>

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<h3 id="Capital-accumulation-over-time">Capital accumulation over time<a class="anchor-link" href="#Capital-accumulation-over-time">&#182;</a></h3><p>Just as in the Solow-Swan model, we will assume that technology $A$ grows at a rate $g$:</p>
\begin{align}
\frac{A_{t+1}}{A_{t}} = 1+g \quad \longrightarrow \quad g_{A} = \frac{\Delta A_{t+1}}{A_{t}} = g
\end{align}<p>We can now describe the dynamic behavior of capital over time:</p>
\begin{align}
K_{t+1} = I_{t} + \left(1-\delta\right)K_{t} = I_{t} = sY_{t}
\end{align}<p>where again the assumption of $\delta=1$ was used.</p>
\begin{align}
K_{t+1} &amp; =sY_{t}\\
K_{t+1} &amp; =sK_{t}^{\alpha}\left(A_{t}L_{t}\right)^{1-\alpha}\quad|\quad:A_{t}L_{t}\\
\frac{K_{t+1}}{A_{t}L_{t}} &amp; =s\frac{K_{t}^{\alpha}}{\left(A_{t}L_{t}\right)^{\alpha}}\frac{\left(A_{t}L_{t}\right)^{1-\alpha}}{\left(A_{t}L_{t}\right)^{1-\alpha}}\\
\frac{L_{t+1}}{L_{t}}\frac{A_{t+1}}{A_{t}}\frac{K_{t+1}}{A_{t+1}L_{t+1}} &amp; =s\hat{k}_{t}^{\alpha}\\
\left(1+n\right)\left(1+g\right)\hat{k}_{t+1} &amp; =s\hat{k}_{t}^{\alpha}
\end{align}\begin{align}
\hat{k}_{t+1}=\frac{s}{\left(1+n\right)\left(1+g\right)}\hat{k}_{t}^{\alpha}
\end{align}<p>This forward equation in capital per effective labor $\hat{k}$ is identical to the Solow-Swan case, once we assume that $\delta=1$. We can also find the steady state level of capital per effective labor:</p>
\begin{align}
\hat{k}^{*} &amp; =\frac{s}{\left(1+n\right)\left(1+g\right)}\left(\hat{k}^{*}\right)^{\alpha}\\
\left(\hat{k}^{*}\right)^{1-\alpha} &amp; =\frac{s}{\left(1+n\right)\left(1+g\right)}\\
\hat{k}^{*} &amp; =\left(\frac{s}{1+n+g+ng}\right)^{1/\left(1-\alpha\right)}
\end{align}<p>This time I will not approximate $ng\approx 0$, since over the timespan of decades the product of population and technological growth is not trivial.</p>
<p>Let us plot the forward equation for capital per effective labor in the OLG model.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="c1"># Population and technology growth rates, note that the time period corresponds to 30 years</span>
<span class="n">n</span> <span class="o">=</span> <span class="p">(</span><span class="mi">1</span><span class="o">+</span><span class="mf">0.01</span><span class="p">)</span><span class="o">**</span><span class="mi">30</span> <span class="o">-</span> <span class="mi">1</span>
<span class="n">g</span> <span class="o">=</span> <span class="p">(</span><span class="mi">1</span><span class="o">+</span><span class="mf">0.02</span><span class="p">)</span><span class="o">**</span><span class="mi">30</span> <span class="o">-</span> <span class="mi">1</span>

<span class="nb">print</span><span class="p">(</span><span class="s1">&#39;n*g =&#39;</span><span class="p">,</span> <span class="n">n</span><span class="o">*</span><span class="n">g</span><span class="p">)</span>

<span class="c1"># Similarly, raise the annual discount factor to the power of 30</span>
<span class="n">β</span> <span class="o">=</span> <span class="mf">0.95</span><span class="o">**</span><span class="mi">30</span>

<span class="c1"># Share of capital in income</span>
<span class="n">α</span> <span class="o">=</span> <span class="mf">0.33</span>

<span class="c1"># Resulting saving rate</span>
<span class="n">s</span> <span class="o">=</span> <span class="p">(</span><span class="mi">1</span><span class="o">-</span><span class="n">α</span><span class="p">)</span> <span class="o">*</span> <span class="n">β</span><span class="o">/</span><span class="p">(</span><span class="mi">1</span><span class="o">+</span><span class="n">β</span><span class="p">)</span>

<span class="c1"># Capital per effective labor in the next period</span>
<span class="k">def</span> <span class="nf">k_hat_next</span><span class="p">(</span><span class="n">k_hat</span><span class="p">):</span>
    <span class="k">return</span> <span class="n">s</span><span class="o">/</span><span class="p">(</span><span class="mi">1</span><span class="o">+</span><span class="n">n</span><span class="o">+</span><span class="n">g</span><span class="o">+</span><span class="n">n</span><span class="o">*</span><span class="n">g</span><span class="p">)</span> <span class="o">*</span> <span class="n">k_hat</span><span class="o">**</span><span class="n">α</span>

<span class="c1"># Steady state level of capital per effective labor</span>
<span class="n">k_hat_star</span> <span class="o">=</span> <span class="p">(</span><span class="n">s</span><span class="o">/</span><span class="p">(</span><span class="mi">1</span><span class="o">+</span><span class="n">n</span><span class="o">+</span><span class="n">g</span><span class="o">+</span><span class="n">n</span><span class="o">*</span><span class="n">g</span><span class="p">))</span><span class="o">**</span><span class="p">(</span><span class="mi">1</span><span class="o">/</span><span class="p">(</span><span class="mi">1</span><span class="o">-</span><span class="n">α</span><span class="p">))</span>

<span class="c1"># Range of values for k_hat</span>
<span class="n">kk</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mf">1e-6</span><span class="p">,</span> <span class="mf">1.5</span><span class="o">*</span><span class="n">k_hat_star</span><span class="p">,</span> <span class="mi">1000</span><span class="p">)</span>
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<pre>n*g = 0.2822312469731404
</pre>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="c1"># Plot dynamics of capital per effective labor in the OLG model</span>

<span class="n">fig</span><span class="p">,</span> <span class="n">ax</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">5</span><span class="p">,</span> <span class="mi">5</span><span class="p">))</span>

<span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">kk</span><span class="p">,</span> <span class="n">k_hat_next</span><span class="p">(</span><span class="n">kk</span><span class="p">),</span> <span class="n">lw</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">kk</span><span class="p">,</span> <span class="n">kk</span><span class="p">,</span> <span class="n">lw</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>

<span class="n">ax</span><span class="o">.</span><span class="n">hlines</span><span class="p">(</span><span class="n">k_hat_star</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="n">k_hat_star</span><span class="p">,</span> <span class="n">lw</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">linestyle</span><span class="o">=</span><span class="s1">&#39;dashed&#39;</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">vlines</span><span class="p">(</span><span class="n">k_hat_star</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="n">k_hat_star</span><span class="p">,</span> <span class="n">lw</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">linestyle</span><span class="o">=</span><span class="s1">&#39;dashed&#39;</span><span class="p">)</span>

<span class="n">NiceFigs</span><span class="p">(</span><span class="n">fig</span><span class="p">,</span> <span class="n">ax</span><span class="p">)</span>

<span class="n">xmin</span><span class="p">,</span> <span class="n">xmax</span> <span class="o">=</span> <span class="n">ax</span><span class="o">.</span><span class="n">get_xlim</span><span class="p">()</span>
<span class="n">ymin</span><span class="p">,</span> <span class="n">ymax</span> <span class="o">=</span> <span class="n">ax</span><span class="o">.</span><span class="n">get_ylim</span><span class="p">()</span>

<span class="n">plt</span><span class="o">.</span><span class="n">xticks</span><span class="p">((</span><span class="mi">0</span><span class="p">,</span> <span class="n">k_hat_star</span><span class="p">,</span> <span class="n">xmax</span><span class="p">),</span> <span class="p">(</span><span class="s1">&#39;0&#39;</span><span class="p">,</span> <span class="s1">&#39;$\hat</span><span class="si">{k}</span><span class="s1">^{*}$&#39;</span><span class="p">,</span> <span class="s1">&#39;$\hat</span><span class="si">{k}</span><span class="s1">_</span><span class="si">{t}</span><span class="s1">$&#39;</span><span class="p">),</span> <span class="n">fontsize</span><span class="o">=</span><span class="mi">12</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">yticks</span><span class="p">((</span><span class="mi">0</span><span class="p">,</span> <span class="n">k_hat_star</span><span class="p">,</span> <span class="n">ymax</span><span class="p">),</span> <span class="p">(</span><span class="s1">&#39;&#39;</span><span class="p">,</span> <span class="s1">&#39;$\hat</span><span class="si">{k}</span><span class="s1">^{*}$&#39;</span><span class="p">,</span> <span class="s1">&#39;$\hat</span><span class="si">{k}</span><span class="s1">_{t+1}$&#39;</span><span class="p">),</span> <span class="n">fontsize</span><span class="o">=</span><span class="mi">12</span><span class="p">)</span>

<span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s1">&#39;Dynamics of capital per effective labor&#39;</span><span class="p">)</span>

<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
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<div class="prompt input_prompt">In&nbsp;[14]:</div>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="c1"># Plot dynamics of capital per effective labor in the OLG model</span>

<span class="n">fig</span><span class="p">,</span> <span class="n">ax</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">5</span><span class="p">,</span> <span class="mi">5</span><span class="p">))</span>

<span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">kk</span><span class="p">,</span> <span class="p">(</span><span class="n">k_hat_next</span><span class="p">(</span><span class="n">kk</span><span class="p">)</span><span class="o">-</span><span class="n">kk</span><span class="p">)</span><span class="o">/</span><span class="n">kk</span><span class="p">,</span> <span class="n">lw</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>

<span class="n">ax</span><span class="o">.</span><span class="n">set_ylim</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">5</span><span class="p">)</span>

<span class="n">NiceFigs</span><span class="p">(</span><span class="n">fig</span><span class="p">,</span> <span class="n">ax</span><span class="p">,</span> <span class="n">northeast</span><span class="o">=</span><span class="kc">False</span><span class="p">)</span>

<span class="n">xmin</span><span class="p">,</span> <span class="n">xmax</span> <span class="o">=</span> <span class="n">ax</span><span class="o">.</span><span class="n">get_xlim</span><span class="p">()</span>
<span class="n">ymin</span><span class="p">,</span> <span class="n">ymax</span> <span class="o">=</span> <span class="n">ax</span><span class="o">.</span><span class="n">get_ylim</span><span class="p">()</span>

<span class="n">ax</span><span class="o">.</span><span class="n">text</span><span class="p">(</span><span class="n">k_hat_star</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.2</span><span class="p">,</span> <span class="s1">&#39;$\hat</span><span class="si">{k}</span><span class="s1">^{*}$&#39;</span><span class="p">,</span> <span class="n">verticalalignment</span><span class="o">=</span><span class="s1">&#39;top&#39;</span><span class="p">,</span> <span class="n">fontsize</span><span class="o">=</span><span class="mi">12</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">text</span><span class="p">(</span><span class="n">xmax</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.2</span><span class="p">,</span> <span class="s1">&#39;$\hat</span><span class="si">{k}</span><span class="s1">_</span><span class="si">{t}</span><span class="s1">$&#39;</span><span class="p">,</span> <span class="n">va</span><span class="o">=</span><span class="s1">&#39;top&#39;</span><span class="p">,</span> <span class="n">ha</span><span class="o">=</span><span class="s1">&#39;center&#39;</span><span class="p">,</span> <span class="n">fontsize</span><span class="o">=</span><span class="mi">12</span><span class="p">)</span>

<span class="n">plt</span><span class="o">.</span><span class="n">xticks</span><span class="p">((</span><span class="mi">0</span><span class="p">,</span> <span class="n">xmax</span><span class="p">),</span> <span class="p">(</span><span class="s1">&#39;&#39;</span><span class="p">,</span> <span class="s1">&#39;&#39;</span><span class="p">),</span> <span class="n">fontsize</span><span class="o">=</span><span class="mi">12</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">yticks</span><span class="p">((</span><span class="mi">0</span><span class="p">,</span> <span class="n">ymax</span><span class="p">),</span> <span class="p">(</span><span class="s1">&#39;0&#39;</span><span class="p">,</span> <span class="s1">&#39;$g_</span><span class="si">{k}</span><span class="s1">$&#39;</span><span class="p">),</span> <span class="n">fontsize</span><span class="o">=</span><span class="mi">12</span><span class="p">)</span>

<span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s1">&#39;Growth rates of capital per effective labor&#39;</span><span class="p">)</span>

<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
</pre></div>

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<h3 id="Dynamic-inefficiency-and-pension-systems">Dynamic inefficiency and pension systems<a class="anchor-link" href="#Dynamic-inefficiency-and-pension-systems">&#182;</a></h3><p>As in the Solow-Swan model, also in the OLG model there is a possibility that households save inefficiently too much. Recall that for the Cobb-Douglas production function the golden rule saving rate is equal to $\alpha$:</p>
\begin{align}
s_{GR} = \alpha
\end{align}<p>and if the economy's saving rate is higher than $s_{GR}$, the economy is dynamically inefficeint.</p>
<p>In our OLG model, the saving rate is given by:</p>
\begin{align}
s = \left(1-\alpha\right)\frac{\beta}{1+\beta}
\end{align}<p>Therefore, for the OLG economy to be dynamically inefficient, the following has to hold:</p>
\begin{align}
\left(1-\alpha\right)\frac{\beta}{1+\beta} &gt; \alpha
\end{align}<p>After a bit of tedious algebra, we can rewrite the above condition as:</p>
\begin{align}
\beta &gt;\frac{\alpha}{1-2\alpha}
\end{align}<p>If we assume that $\alpha=0.3$, then the condition is equivalent to $\beta&gt;0.75$, which is quite possible for "patient" societies.</p>
<p>One of the possible ways to escape the dynamic inefficiency is to introduce a pay-as-you-go retirement system. On one hand, the retirement system gives the old some additional income, which decreases asset accumulation. On the other, the retirement system requires funding through taxes, which lower the disposable income of the young and decreases asset accumulation.</p>
<p>There is an equivalent condition for dynamic inefficiency, which sometimes is easier to use. Whenever we observe that:</p>
\begin{align}
(1+r) &lt; (1+n)(1+g)
\end{align}<p>then we know that the economy is dynamically inefficient. In such situation, the rent from a PAYGO pension system exceeds the real interest rate, and from the point of view of the households it is optimal to introduce such a system.</p>
<p>On the other hand, if we observe that:</p>
\begin{align}
(1+r) \geq (1+n)(1+g)
\end{align}<p>then the economy is dynamically efficient, and the PAYGO system actually lowers the welfare of the households. It would be better to switch from a PAYGO to a fully funded (FF) scheme, where the pension contributions are not paid to the old, but invested in assets. However, once a PAYGO system exists, changing it to a FF scheme is costly, and we might be "stuck" in a less efficient equilibrium. If you want to read more on these topics, check out <a href="http://coin.wne.uw.edu.pl/mbielecki/index.php?show=ContactGeneral">my papers</a>.</p>

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<h3 id="Lifecycle-models">Lifecycle models<a class="anchor-link" href="#Lifecycle-models">&#182;</a></h3><p>The two period OLG model has the advantage of being relatively simple, but it is also highly stylized and some questions are hard to answer within that framework.</p>
<p>We will now turn to solving models where people live for many periods. A common assumption in the economic literature is that people enter activity at age of 20 (<code>0</code> in our <code>python codes</code>) and live at most 99 years (die for sure on their 100th birthday, <code>J=80</code> in our <code>codes</code>). They will also face age-dependent mortality risk. We will also assume that they become retired at age 65 (<code>JR=45</code> in our <code>codes</code>).</p>
<p>For simplicity, all working-age individuals supply 1 unit of labor, and retirees do not receive any pensions. Also, we will assume that the economy has converged to a steady state with no technology and population growth, so that both wage and the interest rate are time-independent and constant.</p>
<p>The problem of the youngest household can then be stated as follows:</p>
\begin{align}
\max\quad &amp; U=\sum_{j=0}^{J-1}\beta^{j}\frac{N_{j}}{N_{0}}\cdot\log c_{j}\\
\text{subject to}\quad &amp; c_{j}+a_{j+1}=w+\left(1+r\right)a_{j} &amp;\text{for all }j&lt;JR\\
 &amp; c_{j}+a_{j+1}=\left(1+r\right)a_{j} &amp;\text{for all }j\geq JR\\
 &amp; a_{0} = a_{J} = 0
\end{align}<p>where $N_{j}/N_{0}$ represents the probability of surviving for at least $j$ years since "birth".</p>
<p>The problem can be solved using the Lagrangian. I present here the final solution:</p>
\begin{align}
lti &amp; =\sum_{j=0}^{JR-1}\frac{w}{\left(1+r\right)^{j}}\\
disc &amp; =\sum_{j=0}^{J-1}\left(\beta^{j}\frac{N_{j}}{N_{0}}\right)\\
c_{0} &amp; =\frac{lti}{disc}\\
c_{j+1} &amp; =\beta\frac{N_{j+1}}{N_{j}}\left(1+r\right)c_{j}
\end{align}<p>where $lti$ is the PDV of lifetime income and $disc$ is the sum of effective discount factors from the perspective of age $j=0$. As you can see, the last equation is an Euler equation, modified to account for mortality risk.</p>
<p>Let us plot the resulting lifecycle profiles for consumption, labor income and the stock of assets below.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">J</span>  <span class="o">=</span> <span class="mi">80</span>
<span class="n">JR</span> <span class="o">=</span> <span class="mi">45</span>

<span class="n">β</span> <span class="o">=</span> <span class="mf">0.96</span>

<span class="n">w</span> <span class="o">=</span> <span class="mi">1</span>
<span class="n">r</span> <span class="o">=</span> <span class="mf">0.05</span>

<span class="n">mort</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">J</span><span class="p">)</span>
<span class="n">surv</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">J</span><span class="p">)</span>

<span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">J</span><span class="p">):</span>
    <span class="n">mort</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="nb">min</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="o">-</span><span class="mf">6.7374</span> <span class="o">+</span> <span class="mf">0.0345</span><span class="o">*</span><span class="n">j</span> <span class="o">+</span> <span class="mf">0.0011</span><span class="o">*</span><span class="n">j</span><span class="o">**</span><span class="mi">2</span> <span class="o">-</span> <span class="mf">8e-06</span><span class="o">*</span><span class="n">j</span><span class="o">**</span><span class="mi">3</span><span class="p">),</span> <span class="mi">1</span><span class="o">-</span><span class="mf">1e-2</span><span class="p">)</span>

<span class="n">surv</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="mi">1</span>
<span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">J</span><span class="o">-</span><span class="mi">1</span><span class="p">):</span>
    <span class="n">surv</span><span class="p">[</span><span class="n">j</span><span class="o">+</span><span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="p">(</span><span class="mi">1</span><span class="o">-</span><span class="n">mort</span><span class="p">[</span><span class="n">j</span><span class="p">])</span><span class="o">*</span><span class="n">surv</span><span class="p">[</span><span class="n">j</span><span class="p">]</span>
    
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">20</span><span class="p">,</span> <span class="mi">100</span><span class="p">),</span> <span class="n">surv</span><span class="p">,</span> <span class="n">lw</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s1">&#39;Probability of survival from age 20&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="s1">&#39;Age&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>

<span class="n">lti</span> <span class="o">=</span> <span class="mi">0</span>
<span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">JR</span><span class="o">-</span><span class="mi">1</span><span class="p">):</span>
    <span class="n">lti</span> <span class="o">+=</span> <span class="n">w</span><span class="o">/</span><span class="p">(</span><span class="mi">1</span><span class="o">+</span><span class="n">r</span><span class="p">)</span><span class="o">**</span><span class="n">j</span>

<span class="n">disc</span> <span class="o">=</span> <span class="mi">0</span>
<span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">J</span><span class="o">-</span><span class="mi">1</span><span class="p">):</span>
    <span class="n">disc</span> <span class="o">+=</span> <span class="n">surv</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="o">*</span><span class="n">β</span><span class="o">**</span><span class="n">j</span>
</pre></div>

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<div class="prompt input_prompt">In&nbsp;[16]:</div>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">c</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">J</span><span class="p">)</span>
<span class="n">h</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">J</span><span class="p">)</span>
<span class="n">a</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">J</span><span class="p">)</span>

<span class="n">h</span><span class="p">[:</span><span class="n">JR</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="mi">1</span>

<span class="n">c</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">lti</span><span class="o">/</span><span class="n">disc</span>
<span class="n">a</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="mi">0</span>

<span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">J</span><span class="o">-</span><span class="mi">1</span><span class="p">):</span>
    <span class="n">c</span><span class="p">[</span><span class="n">j</span><span class="o">+</span><span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="n">β</span><span class="o">*</span><span class="p">(</span><span class="mi">1</span><span class="o">-</span><span class="n">mort</span><span class="p">[</span><span class="n">j</span><span class="p">])</span><span class="o">*</span><span class="p">(</span><span class="mi">1</span><span class="o">+</span><span class="n">r</span><span class="p">)</span><span class="o">*</span><span class="n">c</span><span class="p">[</span><span class="n">j</span><span class="p">]</span>
    <span class="n">a</span><span class="p">[</span><span class="n">j</span><span class="o">+</span><span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="n">w</span><span class="o">*</span><span class="n">h</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">+</span> <span class="p">(</span><span class="mi">1</span><span class="o">+</span><span class="n">r</span><span class="p">)</span><span class="o">*</span><span class="n">a</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">-</span> <span class="n">c</span><span class="p">[</span><span class="n">j</span><span class="p">]</span>

<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">20</span><span class="p">,</span> <span class="mi">100</span><span class="p">),</span> <span class="n">c</span><span class="p">,</span> <span class="n">lw</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s1">&#39;Consumption over the lifecycle&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="s1">&#39;Age&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>

<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">20</span><span class="p">,</span> <span class="mi">100</span><span class="p">),</span> <span class="n">w</span><span class="o">*</span><span class="n">h</span><span class="p">,</span> <span class="n">lw</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">ylim</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mf">1.2</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s1">&#39;Labor income over the lifecycle&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="s1">&#39;Age&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>

<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">20</span><span class="p">,</span> <span class="mi">100</span><span class="p">),</span> <span class="n">a</span><span class="p">,</span> <span class="n">lw</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s1">&#39;Assets over the lifecycle&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="s1">&#39;Age&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
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WnJUa5S4pFCvxur2lPHwg0VvL2hMgj6DZXs3Ft/wDRJCca4/EyOLMjhyPCww9F5vXVSUhcq2bmXh+Zv4P55G9hSVQNAZmoSF80cxqUnjCC3t5p+pOso9LsJd2d9WTVF68t5e0MFC96vYNX2XTRd/YNzejF1SA7ThuYwdUgOkwZnk5asJppYUN/QyEvLt3H3m+uZu7YcCJrVLpwxlMtPHEl+dq8oVyjxQKEfo2rrG1m6uYqi9eUUra/g7Q0VlO6qPWCalMQEJhdkc9SwPkwfmsO0oX0YkJUWpYrlULy9oYLb/7Wal9/bDkBKUgJfOm44XztpNNnpavaRzqPQjxG799bz9oYK5q8r56315byzsZKaugPPYO3XO4WjhvUJb32ZNDirxxwiGa+Wba7i9ldW8+ySrQBk90rmmx8bzUUzh+m1lU6h0I+S8t21zF9fzlvrypm/vpxlm3d86Jj4UXkZHD28L4XD+1I4rA/DctPVF0wPtbi4kh89u3x/s09Bn15cf85ETpswIMqVSU+j0O8i23fUMG9dOfPWlfHWunJWbtt1wPjEBGPSoCyOHt6Xo0cEIa8dfPHF3Xl1RQk/fm75/vfHaRMGcMOsiQzOUXu/dAyFfifZXLmHeevKmLe2nHnryllXuvuA8alJCUwbmsOM4X2ZMSKXaUNzyOhG3RRI56lvaOTeue/zy3+uZNfeenolJ3LlqWP48gkjSNZRV3KYFPodpLiimrlry5m3toy568rYWH7gCVAZKYkcNbwvx4wIbpMLstVmKwe1taqGm55+l2eWBL2SHFmQzS8/M5XR/XtHuTLpzhT67bQv5OeuLWPu2rIPneWamZrE0WHAHzMyl0mDsnRsvLTLqyu28/3Hl7Kpcg+pSQl874xxXDxzuM7slXZR6LfRpso9zFlT1mLIZ6UlMWNELseO7MuxI3MZn5+lM1ylw+yoqePGf7zLowuKATh+dC6/uOBIHdsvh0yh34ItVR+E/Jy1H26uUchLNDy/dCvXPL6E8t219ElP5tbZ0/joEXnRLku6EYV+aPuOGuaEW/Fz1pSxvqz6gPGZaUnMGN6XmaNyFfISVSU79/LtRxbx75UlmME3PzaGb50yRu9HaZO4Df2yXXuZu7acOWtLmbOmjDUlBx5d0zs1iaOH92HmqFxmjuzHhEEKeYkdjY3O7a+s5lcvrcQdThjdj1tnT6WfDvOVVsRN6FdW1+7f8TpnTRkrtu08YHx6SiKFw/syc2QuM0dpx6t0D6+vKuVbDy6kbHctg7LTuOvio5kwKCvaZUkM67Ghv7OmjrfWlTNnTdAm/+6WHQd0TpaalEDh8D77Q35KQY6OgZZuaWtVDV+7fwFvb6gkPSWR386exqk6k1da0GNCv7q2nvnrK/aH/NJNVQd0a5CSGJwMFTTX5DJ1aI6Ok5ceo6auge/9fTFPvLMZM/j+meO59IQR6rZDPiQWrpHbLu7w5upS5oTNNe9srNx/oQoI+pE/atgHW/JHDeujLoalx0pLTuTXn53KyLze/OrFldz8zHLWlOzmpnMnqplSOlTUtvTT8sf4wItv3X8/wWDy4GyODbfkjx7eV90aSFx6evFmrnp4EXvrG/n4hAH89sJp2uCR/brvlj4wIT9rf3PNjJF9dfk5EeDsKYPIz07jS3+Zzz/f3caX757PnV8spLc2gqQDRG1Lf9r0o3zh2wuismyR7mD5lh188c9vUbJzL1MKsvnLJUer51Y57C39qDUW6ph5kYMbn5/F3796HEP7prO4uIrP/GEOW8Nr9Iq0l/YQicSwobnpPPrVmYwbmMmakt187o9z2bZDwS/tp9AXiXH9s9J44LJjGZ+fxdrS3Vz4x7lsV/BLOyn0RbqBPhkp3P+VYxg3MJO1JWHw71Twy6FT6It0E30zUvjbZcdGNPXMo2Tn3miXJd2MQl+kG+kbbvGPHZDJ6u27uOQvb7Gzpi7aZUk3otAX6WZye6dy31eOYXhuOss27+Cye4qoqWuIdlnSTbQp9M3sdDNbYWarzex7zYwfamavmNlCM1tsZmd2fKkisk9eZir3XnoM/TNTmbu2nG89uPCAvqpEWtJq6JtZInA7cAYwAbjQzCY0mexa4GF3nwbMBu7o6EJF5EBD+qZzz6UzyEpL4oVl27j2iSVE62RL6T7asqU/A1jt7mvdvRZ4EDi3yTQO7OsEPBvY3HElikhLxg3M4k+XHE1qUgIPvLWRX7+4MtolSYxrS+gPBjZG3C8Oh0W6AfiCmRUDzwLfbG5GZna5mRWZWVFJSUk7yhWRpo4e3pc7Pj+dBIPf/ms1j71dHO2SJIa1JfSb6y+h6W/IC4G73b0AOBO418w+NG93v9PdC929MC9PF4MW6SinjB/ADbMmAvC9vy/hrXXlUa5IYlVbQr8YGBJxv4APN99cCjwM4O5zgDSgX0cUKCJt88WZw7nkuOHUNjRyxb1FrC/d3fqDJO60JfTnA2PMbISZpRDsqH2qyTQbgFMAzGw8Qeir/Uaki/3g7AmcPDaPiuo6vnz3fKqqdQy/HKjV0Hf3euAbwAvAcoKjdJaZ2Y1mNiuc7CrgMjNbBDwAXOI6jECkyyUmGP/3uelBdw2lu/na3xZQ39AY7bIkhsTMNXJFpONsqtzDube9TumuWi4/cSTXnDk+2iVJB+m2/emLSOcZnNOL2z83naQE487X1vKPRTqKWgIKfZEe6piRuXz/rGAL/7uPLua9rTuiXJHEAoW+SA92yXHD+eS0weypa+CKexdox64o9EV6MjPjR5+czMRBWbxfVs2VDy2kUX30xDWFvkgPl5acyO+/cBQ56cm8sqKE37+2JtolSRQp9EXiwJC+6fz6M1MB+OU/VzJ/vc7YjVcKfZE4cfK4/lxx4kgaGp3/emAhFbtro12SRIFCXySOfPsTY5k+NIctVTVc9cgite/HIYW+SBxJTkzg/z43nexeyfzrve3c9fraaJckXUyhLxJnBuf04hcXHAnAz55fwaKNlVGuSLqSQl8kDp02YQBfOn449Y3OlQ+9Q3VtfbRLki6i0BeJU/97+jjGDshkXelubnp6ebTLkS6i0BeJU2nJidw6eyopiQk88NYGXnx3W7RLki6g0BeJY+Pzs/ju6WMB+N+/L2b7zpooVySdTaEvEue+fPwIThjdj/LdtXznkcXoUhg9m0JfJM4lJBi/uOBIctKT+ffKEu6btyHaJUknUuiLCAOz07jlvMkA/PjZ5Wwsr45yRdJZFPoiAsBZU/I5a0o+1bUNfOdRna3bUyn0RWS/G2dNJDcjhblry7lv3vvRLkc6gUJfRPbL7Z3KzedNAuDHz77H+2W7o1yRdDSFvogc4IzJ+cw6chB76hr4zqOL1czTwyj0ReRDfjhrIv16p/LWunL+Omd9tMuRDqTQF5EP6ZORwi3nB808P39hBcUVOpqnp1Doi0izPjFxIGdNDo7m+f7jS3XSVg+h0BeRFl0/awLZvYKTtp58Z3O0y5EOoNAXkRb1z0zj+2eNB+CH/1hG2a69Ua5IDpdCX0QO6oKjCjh+dC4V1XXc9PS70S5HDlObQt/MTjezFWa22sy+18I0nzGzd81smZn9rWPLFJFoMTN+fP4U0pITeOKdzbzy3vZolySHodXQN7NE4HbgDGACcKGZTWgyzRjgauB4d58IXNkJtYpIlAzNTeeq04IumK99YqmutNWNtWVLfwaw2t3Xunst8CBwbpNpLgNud/cKAHfXpoBID/Ol44czcVAWmyr38JuXVkW7HGmntoT+YGBjxP3icFikI4AjzOwNM5trZqc3NyMzu9zMisysqKSkpH0Vi0hUJCUmcMv5kzGDu15fx3tbd0S7JGmHtoS+NTOs6QG7ScAY4CTgQuAuM8v50IPc73T3QncvzMvLO9RaRSTKpg7J4aJjh9HQ6Fzz2BJ10dANtSX0i4EhEfcLgKYH7BYDT7p7nbuvA1YQfAmISA/z7U+MJS8zlbc3VPLg/I2tP0BiSltCfz4wxsxGmFkKMBt4qsk0TwAnA5hZP4LmnrUdWaiIxIastGSuOzs4luMnzy2nZKeO3e9OWg19d68HvgG8ACwHHnb3ZWZ2o5nNCid7ASgzs3eBV4DvuHtZZxUtItF19pR8Tjwijx019dzyjI7d704sWv1pFBYWelFRUVSWLSKHb0NZNaf9+t/srW/kgcuOZeao3GiXFBfMbIG7F7b38TojV0TaZWhuOl8/eTQA1z25lLqGxihXJG2h0BeRdrv8xJEMy01n1fZd3P3G+miXI22g0BeRdktLTuSGWRMBuPWllWytqolyRdIahb6IHJaTx/bnExMHsLu2gVueXR7tcqQVCn0ROWw/OHsCackJ/GPRZt5cXRrtcuQgFPoictgK+qTzzY8F52P+4Mml1NZrp26sUuiLSIf4ykdGMLJfBmtKdvPXN9dHuxxpgUJfRDpEalIi150TnKn7m5dXsX2HdurGIoW+iHSYk8b259Tx/dm1t56fPP9etMuRZij0RaRD/eDsCaQkJfDY25tY8H55tMuRJhT6ItKhhuVmcPlHRgJw3ZPLaFD3yzFFoS8iHe5rJ49iUHYayzbv4MH5G6JdjkRQ6ItIh0tPSeKas8YD8PMXVlBZXRvlimQfhb6IdIqzJuczc2QuldV1/PrFldEuR0IKfRHpFGbG9bMmkGBw37wNrNi6M9olCQp9EelE4wZm8YXwmro//McyonX9DvmAQl9EOtX/nHYEOenJvLmmjBeWbY12OXFPoS8inSonPYWrTjsCgJufWU5NXUOUK4pvCn0R6XQXzhjKuIGZFFfs4Y+vrY12OXFNoS8inS4pMYHrzwkutnLHq2vYXLknyhXFL4W+iHSJmaNyOWtyPnvqGvjJc+qXJ1oU+iLSZa4+cxypSQk8tWgz89erX55oUOiLSJcp6JPOFR8dBcANT6lfnmhQ6ItIl/p/Hx1FftgvzyNFG6NdTtxR6ItIl+qVksjVZ37QL0/VnrooVxRfFPoi0uXOmZLP0cP7ULa7lt++vCra5cQVhb6IdDkz4/pzJmIGf31zPau3q1+ertKm0Dez081shZmtNrPvHWS6T5uZm1lhx5UoIj3RpMHZzD56CPWNzo1PL1e/PF2k1dA3s0TgduAMYAJwoZlNaGa6TOC/gHkdXaSI9Ezf/vhYMtOSeG1lCS8v3x7tcuJCW7b0ZwCr3X2tu9cCDwLnNjPdTcDPgJoOrE9EerDc3qlceWrQL89Nz7zL3nr1y9PZ2hL6g4HI46qKw2H7mdk0YIi7P32wGZnZ5WZWZGZFJSUlh1ysiPQ8X5w5jNH9e/N+WTV/en1dtMvp8doS+tbMsP2Nb2aWAPwauKq1Gbn7ne5e6O6FeXl5ba9SRHqs5MQErj8naDG+7V+r2bZDjQWdqS2hXwwMibhfAGyOuJ8JTAJeNbP1wLHAU9qZKyJt9ZExeXx8wgCqa9UvT2drS+jPB8aY2QgzSwFmA0/tG+nuVe7ez92Hu/twYC4wy92LOqViEemRrj1rAilJCTy+cBML3q+Idjk9Vquh7+71wDeAF4DlwMPuvszMbjSzWZ1doIjEh6G56Vz+kZGA+uXpTG06Tt/dn3X3I9x9lLvfEg67zt2fambak7SVLyLt8bWTg355lmyq4mH1y9MpdEauiMSM9JQkrgn75fnZ8+9RWV0b5Yp6HoW+iMSUs6fkc+zIvlRU1/HLf66Mdjk9jkJfRGKKmfHDWZNITDDun/c+SzdVRbukHkWhLyIxZ+zATC6eOZxGh+ufWqZ+eTqQQl9EYtKVp42hX+8UFrxfweMLN0W7nB5DoS8iMSkrLZnvnRHs1P3xc++xo0YXW+kICn0RiVmfnDaY6UNzKNm5l19pp26HUOiLSMxKSDBuPm8yCQb3zFnPss3aqXu4FPoiEtMmDMrikuNG0Ohw7RNLadSZuodFoS8iMe+/TxtD/8xUFm6o1Jm6h0mhLyIxLzMtmWvPDrpf/snz71G+W2fqtpdCX0S6hXOm5HP86Fwqq+v4qbpfbjeFvoh0C2bGjedOIjnReKhoI/PXl0e7pG5JoS8i3caovN589aOjALj6sSW6pm47KPRFpFv5+smjGdEvg9Xbd/GHf6+NdjndjkJfRLqVtOREfnT+ZCC4pu6akl1Rrqh7UeiLSLczc1QunyksoLahkasfW6Jj9w/CTikHAAAOAElEQVSBQl9EuqVrzhxPbkYKb60r55EFOna/rRT6ItIt5aSncN05wbH7tzyznO07a6JcUfeg0BeRbmvWkYP46BF57Kip57on1O9+Wyj0RaTbMjNuOX8SGSmJPL9sK88s2RLtkmKeQl9EurWCPulcc1bQ7/51Ty6jdNfeKFcU2xT6ItLtfW7GUE4Y3Y/y3bVc9+TSaJcT0xT6ItLtmRk//uRkMlISeXbJVp5ZrGaelij0RaRHGNI3navPDJp5fvDkUsrUzNMshb6I9BifmzGU40blUr67lmseX6KjeZqh0BeRHiMhwfjpp6aQmZrEC8u26YIrzWhT6JvZ6Wa2wsxWm9n3mhn/P2b2rpktNrOXzWxYx5cqItK6IX3Tuem8SQDc8NS7rCvdHeWKYkuroW9micDtwBnABOBCM5vQZLKFQKG7TwEeBX7W0YWKiLTVedMGM+vIQeypa+DKBxdS19AY7ZJiRlu29GcAq919rbvXAg8C50ZO4O6vuHt1eHcuUNCxZYqIHJqbzpvE4JxeLCqu4jcvrYp2OTGjLaE/GIhsGCsOh7XkUuC5wylKRORwZfdK5lefORIzuOPV1by1TlfagraFvjUzrNld4mb2BaAQ+HkL4y83syIzKyopKWl7lSIi7XDMyFy+dtIoGh2+9eBCXVCdtoV+MTAk4n4BsLnpRGZ2KvB9YJa7N3uArLvf6e6F7l6Yl5fXnnpFRA7JlacewfShOWypquFbDy6kIc773m9L6M8HxpjZCDNLAWYDT0VOYGbTgD8QBP72ji9TRKR9khMTuO1z0+mbkcJ/VpVy279WR7ukqGo19N29HvgG8AKwHHjY3ZeZ2Y1mNiuc7OdAb+ARM3vHzJ5qYXYiIl1uUE4vbv3sVMzg1pdX8p9V8du8bNE6Y62wsNCLioqismwRiU+3vrSSW19aRd+MFJ75rxPIz+4V7ZIOmZktcPfC9j5eZ+SKSNz45sfG8JExQW+cX7v/bWrqGqJdUpdT6ItI3EhMMH4zexqDstNYuKGSqx+Lv/55FPoiElf6ZqTwx4sLSU9J5PGFm7jj1TXRLqlLKfRFJO5MHJS9f8fuz19YwXNxdJlFhb6IxKWPTxzI/54+DoD/fvgdlhRXRbmirqHQF5G4dcWJI7ngqAJq6hr5yj3zKa6obv1B3ZxCX0Tilplxy/mTOWZEX7bt2MsX7ppHyc6efcUthb6IxLWUpAT+eHEhEwdlsb6smov+NI+q6rpol9VpFPoiEvey0pL565dnMDIvg/e27uRLd7/F7r310S6rUyj0RUSAfr1Tue/SYxic04u3N1Ryxb0LeuTJWwp9EZHQoJxe3PeVY+jXO4XXV5dy6V/n97gtfoW+iEiEEf0ywuBP5Y3VZT2ujV+hLyLSxLiBWTzy1Zn7m3pm/3FujzmqR6EvItKMEf0yeOSrMxnZL4PlW3bwmT/MYWN59z+OX6EvItKCQTm9eOiKmYzPz2Jd6W7Ovf0N5q0ti3ZZh0WhLyJyEHmZqTx4+bH7u2T+/F3zuG/u+9Euq90U+iIircjulcxfLjmayz4ygvpG59onlnLtE0uoa2iMdmmHTKEvItIGSYkJfP+sCfzygiNJSUrgvrkbuOD3c1hbsivapR0Shb6IyCH41FEFPHzFTAZlp/HOxkrO/O1/uHfO+m5zMRaFvojIIZo6JIfnrjyR86cNpqaukR88uYyL/zKfrVU10S6tVQp9EZF2yO6VzK8/O5U7Pj+dnPRkXltZwim/fJXfvbqGvfWx232DQl9E5DCcOTmff155IqdNGMDu2gZ++vx7nPar13hh2daYbPJR6IuIHKb+WWn88YuF3HvpDMb0782G8mquuHcBs++cy+urSmMq/C1axRQWFnpRUVFUli0i0lnqGxq5f94GfvXiSqr2BH32TB6czVc/OorTJw0kMcEOa/5mtsDdC9v9eIW+iEjHq9pTx31z3+fPr6+jbHctAMNy07ngqALOn17A4Jxe7ZqvQl9EJIbV1DXwyIJi7nxtDRvL9wBgBjNH5vKp6QWcMr4/OekpbZ6fQl9EpBuob2jkP6tL+fuCYv757jZq64OzeRMMpg/tw0lj8zhpbH8m5GeRcJAmIIW+iEg3U7WnjmcWb+HpxZuZv76cuoYPcjgzNYkpQ7KZNqQPU4fkMHVoDv16p+4f3yWhb2anA78BEoG73P0nTcanAvcARwFlwGfdff3B5qnQFxGBXXvreWN1Ka+uKOG1lSVsqtxzwPi8zFTeuuYUzIKt/8MN/aTWJjCzROB24DSgGJhvZk+5+7sRk10KVLj7aDObDfwU+Gx7ixIRiRe9U5P4xMSBfGLiQAC276hh4cZK3tlYycINFeRn99of+B2h1dAHZgCr3X0tgJk9CJwLRIb+ucAN4f+PAreZmXksHZwqItIN9M9KO+BLoKO1JfQHAxsj7hcDx7Q0jbvXm1kVkAuURk5kZpcDl4d395rZ0vYU3cX60eR5xCjV2bG6Q53doUZQnR1t7OE8uC2h39zviqZb8G2ZBne/E7gTwMyKDqddqquozo6lOjtOd6gRVGdHM7PD2hnalm4YioEhEfcLgM0tTWNmSUA2UH44hYmISMdrS+jPB8aY2QgzSwFmA081meYp4OLw/08D/1J7vohI7Gm1eSdso/8G8ALBIZt/dvdlZnYjUOTuTwF/Au41s9UEW/iz27DsOw+j7q6kOjuW6uw43aFGUJ0d7bDqjNrJWSIi0vXUtbKISBxR6IuIxJEuCX0zG2Jmr5jZcjNbZmbfCof3NbMXzWxV+LdPV9RzkDrTzOwtM1sU1vnDcPgIM5sX1vlQuEM7qsws0cwWmtnTMVzjejNbYmbv7DvMLNZe87CmHDN71MzeC9+jM2OtTjMbG67HfbcdZnZlrNUZ1vrf4ednqZk9EH6uYur9aWbfCutbZmZXhsNiYl2a2Z/NbHvkeUwt1WaB35rZajNbbGbTW5t/V23p1wNXuft44Fjg62Y2Afge8LK7jwFeDu9H017gY+5+JDAVON3MjiXoVuLXYZ0VBN1ORNu3gOUR92OxRoCT3X1qxPHPsfaaQ9Cv1PPuPg44kmC9xlSd7r4iXI9TCfq4qgYeJ8bqNLPBwH8Bhe4+ieDgj31ds8TE+9PMJgGXEfQ2cCRwtpmNIXbW5d3A6U2GtVTbGcCY8HY58LtW5+7uXX4DniToy2cFkB8OywdWRKOeFmpMB94mOPu4FEgKh88EXohybQXhC/8x4GmCk+NiqsawjvVAvybDYuo1B7KAdYQHNcRqnU1q+zjwRizWyQdn5/clODrwaeATsfT+BC4g6Dhy3/0fAN+NpXUJDAeWRtxvtjbgD8CFzU3X0q3L2/TNbDgwDZgHDHD3LQDh3/5dXU9TYbPJO8B24EVgDVDp7vXhJMUEb+xoupXgTdoY3s8l9mqE4Kzsf5rZgrALDoi913wkUAL8JWwuu8vMMoi9OiPNBh4I/4+pOt19E/ALYAOwBagCFhBb78+lwIlmlmtm6cCZBCeXxtS6bKKl2prrJueg67ZLQ9/MegN/B6509x1duey2cvcGD35CFxD8/Bvf3GRdW9UHzOxsYLu7L4gc3MyksXAs7vHuPp3gJ+jXzezEaBfUjCRgOvA7d58G7CY2mpyaFbaFzwIeiXYtzQnbms8FRgCDgAyC17+pqL0/3X05QXPTi8DzwCKCJuju6JA/+10W+maWTBD497v7Y+HgbWaWH47PJ9i6jgnuXgm8SrAPIifsXgKa74aiKx0PzDKz9cCDBE08txJbNQLg7pvDv9sJ2p9nEHuveTFQ7O7zwvuPEnwJxFqd+5wBvO3u28L7sVbnqcA6dy9x9zrgMeA4Yuz96e5/cvfp7n4iwQmlq4i9dRmppdra0k3OAbrq6B0jOGt3ubv/KmJUZPcNFxO09UeNmeWZWU74fy+CN/By4BWC7iUgynW6+9XuXuDuwwl+5v/L3T9PDNUIYGYZZpa573+CduilxNhr7u5bgY1mtq/nwlMIug2PqTojXMgHTTsQe3VuAI41s/Twc79vfcba+7N/+Hco8EmCdRpr6zJSS7U9BXwxPIrnWKBqXzNQi7pop8QJBD85FgPvhLczCdqiXyb4ln0Z6ButHSdhnVOAhWGdS4HrwuEjgbeA1QQ/q1OjWWdEvScBT8dijWE9i8LbMuD74fCYes3DmqYCReHr/gTQJ0brTCe4Ml12xLBYrPOHwHvhZ+heIDUG35//IfgyWgScEkvrkuALaAtQR7Alf2lLtRE079xOsO9xCcFRUwedv7phEBGJIzojV0Qkjij0RUTiiEJfRCSOKPRFROKIQl9EJI4o9CUumdn5ZuZmNi7atYh0JYW+xKsLgddp26U9RXoMhb7EnbAPqOMJTnqZHQ5LMLM7wv7VnzazZ83s0+G4o8zs32HHcS/sOx1epDtS6Es8Oo+g//yVQHl44YlPEnRnOxn4CkH3v/v6jPo/4NPufhTwZ+CWaBQt0hGSWp9EpMe5kKCTOgg6rbsQSAYecfdGYKuZvRKOHwtMAl4MupIhkeAUeZFuSaEvccXMcgl6Jp1kZk4Q4k7QC2izDwGWufvMLipRpFOpeUfizaeBe9x9mLsPd/chBFfOKgU+FbbtDyDozA6CKxHlmdn+5h4zmxiNwkU6gkJf4s2FfHir/u8EF/woJugZ8g8EV3arcvdagi+Kn5rZIoIeYo/runJFOpZ62RQJmVlvd98VNgG9RXDlr63RrkukI6lNX+QDT4cX0UkBblLgS0+kLX0RkTiiNn0RkTii0BcRiSMKfRGROKLQFxGJIwp9EZE48v8BO3dhqB1DrVEAAAAASUVORK5CYII=
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2eMmW6MGWyMGZyQ4N12r0o1xI68Ej5etZsQl3DTaZ2djkNkmJsJ9j6CWYvSnQ2jAkpDhm7OAnYYY3KNMZXAe8BI78RSqvE9+/1WPAYuHZhMUnyk03GAn/rffLhyN/tLKxxOowJFQwr9LmC4iESJdXTJaGCDd2Ip1bgy95Xy3vIsXAK/Ot35rfkaHVtFc0rXVpRXebT/jfKahozRLwbeAZYDa+znmu6lXEo1qufnbafKYxjXr53XzgfrLTU7ZbX/jfKWBs26McY8YIzpbozpbYy5yhhT7q1gSjWW7KIy3kyzTsx96xldHE7zS6N7JJIUH0l6fqn2v1FeoUfGqqAz/X/bqajycG7vNnRNbNxWxPXhdglXDksBtP+N8g4t9Cqo5BSXMdtuM3Dbmb63NV/jiiHtCXUL327MIXOf9r9RDaOFXgWVZ77bRlmlh7N7JtKrXZzTcY6qVUw45/Vpi8fA64t3OR1H+Tkt9Cpo7N5/kNcX70IE7j7nJKfjHFfNTtk3l2ZQXqX9b1T9aaFXQePpb7dSUe3hgr7t6N4m1uk4xzWoQ3N6tI0lv6SCz9fudTqO8mNa6FVQ2JlfwttpGbgE7jqrq9NxTsjP+t8s1P43qv600Kug8OTXW6jyGMYPTKZzQozTcU7YRf3b0Sw8hLSd+1i/u8jpOMpPaaFXAW9LdjHvr8wi1C3cOdo/tuZrRIeHcOmgZEBPSqLqTwu9CnhPfL0FY6wpi+1bRDkdp86mDLfm1H+wIouiskqH0yh/pIVeBbQ1mYV8smYPYSEubjvDv7bma3Rp3YwRnVpSWlHNe9r/RtWDFnoVsIwx/PVTq8/etJGptInz3zNd1pxqcNainRij/W9U3WihVwHru005LNyeT1xkKLee7rtHwZ6Is3smkhgbzrbcEhZuz3c6jvIzWuhVQKqq9vC3TzcCcPuZXYiLCnU4UcOEul1MGmqN1b+mpxpUdaSFXgWkd5ZlsiXnAO1bRB4a9vB3k4am4HYJX6zLJruozOk4yo9ooVcBp7Siin9/tRmAe8Z0JzzE7XAi70iMjWBMr0SqPYY5S7T/jTpxWuhVwJkxfwc5xeX0S47jwr5tnY7jVTWnGpyzZBeV1R6H0yh/oYVeBZTc4nKen7cNgN+d1wPrLJeBY0SnlnROiCa7qJyv1mc7HUf5CS30KqD884uNlFRUc1aPRIZ1aul0HK/T/jeqPrTQq4CxKmM/by/LJNQt/P78Hk7HaTTjByUTFeZm4fZ8tuYUOx1H+QEt9CogeDyGBz9ehzFw7aiOdPSxE357U2xEKBcPSALgtUW6U1YdnxZ6FRA+WJnFil37SWgWzu1n+merg7qYMswavnl3WSYl5VUOp1G+Tgu98nsHyqt49DPr4Kh7x3YnJjzE4USNr2e7WAZ3aE5xeRUfrMxyOo7ycVrold/7z7dbremU7eMZbw9pBIND/W8Wav8bdWxa6JVfS88r4aUfdgDw53G9cLkCazrlsYzt3YZWMWFs3FtM2s59TsdRPkwLvfJbxhge+GgdFdUeLhuUTP/28U5HalLhIW6uGNIe0KmW6ti00Cu/9cmaPczbnEtsRAj3ju3udBxHXDmsAy6Bz9buIbe43Ok4ykdpoVd+qaiskr98vB6A+87tQUKzcIcTOSMpPpLRPRKprDa8uVSnWqoj00Kv/NK/v9xMTnE5A1LimWgPXwSrq+2dsrMX76JK+9+oI9BCr/zO6sz9vLowHbdL+OslfYJqB+yRnNy5FZ1aRbOnsIxvNuY4HUf5IC30yq9Uewy/e38NxsB1ozrSo22s05Ec53IJk7X/jToGLfTKr8xcmM7arCLaxUVw5+jAPwL2RF02KJnIUDc/bM1jW+4Bp+MoH6OFXvmNjIJS/vnFJgAeHNeL6CA4AvZExUWGcvGAdoBu1atf0kKv/IIx1pBNaUU15/dpyzm92jgdyefUnJRE+9+ow2mhV37h7bRM5m/JIz4qlAfH9XI6jk/q1S7uUP+b91do/xv1kwYVehGJF5F3RGSjiGwQkRHeCqZUjeyiMh76xJoz/+CFvYJ2zvyJuHpkKqD9b9TPNXSL/kngc2NMd6AfsKHhkZT6iTGGP3ywluKyKs7s3pqL+rdzOpJPG9urDa1iwtmUXcziHQVOx1E+ot6FXkRigVOBFwGMMRXGmP3eCqYUwNzVe/hqfTbNwkN45JLeAXcOWG8LC3Fx5bAUQHfKqp80ZIu+E5ALvCwiK0Rkhoj84rQ+InKjiKSJSFpubm4DVqeCTU5xGQ98tA6A+8/rQdu4SIcT+Ycrh6bgdgmfr9vL3sIyp+MoH9CQQh8CDASeNcYMAEqA+w6/kzFmujFmsDFmcEJCQgNWp4KJMYb7311DQUkFo7q0YtLQ4G5zUBdt4iIY0yuRao/h9SXa/0Y1rNBnApnGmMX29XewCr9SDfZWWgbfbMwhNiKEf07oq0M2dXT1iFQAXl+8i4oq7X8T7Opd6I0xe4EMEelmLxoNrPdKKhXUduWXHupM+dDFvXXIph6GdWzBSYkx5B0o57O1e5yOoxzW0Fk3twOzRWQ10B/4a8MjqWBW7TH839urKLEPjBrXT2fZ1IeIHNqqn6k7ZYNegwq9MWalPf7e1xhzsTFGz2emGmTG/O0sSS8goVk4D1+ss2wa4pIBSTSLCGHZzn2szSp0Oo5ykB4Zq3zGut2F/OvLzQD849K+NI8OcziRf4sOD2HCIGsn9is/pjsbRjlKC73yCaUVVdw+ZwUV1R4mD0vhjO6tnY4UEK4e0QER+GjVbvIP6KkGg5UWeuUT/vzRerbnlnBSYgx/vKCn03ECRmqraE4/KYGKKg9vLM1wOo5yiBZ65bi5q3fzZloG4SEunp40kIhQt9ORAspUu//N7EU79VSDQUoLvXJURkEp97+3BoA/nN+Dbm2aOZwo8JzaNYGOraLZXVjGV+uznY6jHKCFXjmmqtrDXW+upLisirN7Jh7qp668y+WSQycQ152ywUkLvXLMY19uZtnOfbSJjeAfl+rRr43pskHJRIe5WbyjgA17ipyOo5qYFnrliG82ZPPcvG24XcJTkwboVMpG1iwilEsHJQPWeXdVcNFCr5pcRkEpv3lrFQD3jOnG0I4tHE4UHGqOlH1/RRb7SyucDaOalBZ61aTKq6q59fXlFB6s5KwerbnxlE5ORwoaXVrHcOpJCZRVepizRKdaBhMt9KpJPfLJBlZnFpLcPJJ/TeiPy6Xj8k3pmpNTAZi1MF2nWgYRLfSqyXy4MouZC3cS5nbxzOSBxEWFOh0p6JzWNYFO9lTLL9bpVMtgoYVeNYn1u4u4993VAPzxgh70TY53OFFwcrmEafZW/csLdjgbRjUZLfSq0e0vreCm19Ioq/Rw2aBknS/vsEsHJtMsIoS0nftYk6ldLYOBFnrVqKo9htvnrCCj4CB9k+O09bAPiA4PYeIQq6ulbtUHBy30qlH984tNzN+SR8voMJ6bMkj72PiIq0ek4hL4ePVucor1BOKBTgu9ajRzV+8+dFDUf64cSLt4PSWgr2jfIoqzeyZSWW2YvUhPIB7otNCrRrEms5D/e9s6KOr+c7szonNLhxOpw11zckcAZi/eSVlltcNpVGPSQq+8LqeojBtmWjtfJwxK5rpRHZ2OpI5gWMcW9GwbS96BCj5atdvpOKoRaaFXXlVWWc0NM9PYW1TGkNTmPHyJ7nz1VSLC9adYH8Iv/bADY4zDiVRj0UKvvMYYwz3vrGaVfeTrc1MGER6iO1992QV929G6WTgb9xazYGu+03FUI9FCr7zmP99u5eNVu4kOc/Pi1CG0jAl3OpI6jrAQ16EzUM34YbuzYVSj0UKvvOLDlVn866vNiMBTkwbomaL8yJVDU4gIdfH9ply2ZBc7HUc1Ai30qsEWb8/nnrft9gbn92R0j0SHE6m6aB4dxmV2r/qX9ACqgKSFXjXI1pwD3DhrGRXVHqaNTOVanWHjl2qmWr67PIv8A+UOp1HepoVe1VvegXKueWWJ3Vs+kT9e0NPpSKqeOifEMLp7ayqqPLymB1AFHC30ql5KK6q4/tW0Qz1snprUH7f2lvdr19lTLWctStcDqAKMFnpVZ5XVHm6dvZyVGftJio9kxtTBRIWFOB1LNdCITi0PHUD1wYosp+MoL9JCr+rEGMN9767hu025NI8KZeZ1Q2ndLMLpWMoLRIQbT7VO7Th9/nY8Hj2AKlBooVd18o8vNvHu8kwiQ928NG0InRNinI6kvOj8vm1pFxfB9twSvtmY43Qc5SVa6NUJe3nBDp793upG+cyUgQxIae50JOVloW7XoZlTz8/b5nAa5S1a6NUJ+WBFFn+Zux6Av1/alzO6tXY4kWosE4emEGufgWrZzn1Ox1FeoIVeHdfX67O5++1VGGO1HK45uEYFppjwkEOne5z+P92qDwRa6NUxLdyWzy2vL6faY7jl9M7cdFpnpyOpJjBtZCphbhdfrs9me+4Bp+OoBtJCr45qVcZ+rn91KRVVHqYMT+GeMd2cjqSaSOvYCC4ZkIQxMOMHbYvg7xpc6EXELSIrRGSuNwIp37A5u5hpLy+hpKKacf3a8Zdx2lc+2NxwqrVT9p1lmeQWa1sEf+aNLfo7gQ1eeB7lI7bnHuDKFxazr7SSM7u35l+X98OlR70GnS6tm3FWj0Qqqjy88qNu1fuzBhV6EUkGzgdmeCeOctqu/FKufGExeQfKOblLS56ZPJBQt47wBatfnW7tk5m5cCdFZZUOp1H11dC/4CeA3wKeo91BRG4UkTQRScvNzW3g6lRjytp/kEkvLGJvURlDU1vwwtWDiQjVM0QFs0EdmjO8UwuKy6p4bdFOp+Ooeqp3oReRC4AcY8yyY93PGDPdGDPYGDM4ISGhvqtTjSy7qIzJLywia/9BBqTE89I1Q7R/jQLgltO7ANZ5ZbXZmX9qyBb9ycA4EUkH3gDOFJHXvJJKNamcojImTV9Een4pvZNieeWaocSEa5FXllO6tqJPUhx5Byp4Ky3D6TiqHupd6I0x9xtjko0xqcBE4FtjzBSvJVNNIqeojInTF7E9r4QebWOZde0w4iJDnY6lfIiIcIs9Vv/8vO1UVh91pFb5KN3LFsQOL/Kzrx9G8+gwp2MpHzSmVxs6J0STtf8gH6/a7XQcVUdeKfTGmO+NMRd447lU0zhSkW+hRV4dhcsl3GwfFf3M99u0hbGf0S36ILSn8CBXaJFXdXTxgCSS4iPZmnOAL9dnOx1H1YEW+iCTUVDK5c8vZIcWeVVHoW7XoROTPP3tFozRrXp/oYU+iKTnlXDF8wvJKDhIv+Q45tygRV7VzRVD2pPQLJx1u4v4ZoOemMRfaKEPEltzDnDF9IXsLixjUIfmzLp+GPFRWuRV3USEug+N1T/5jW7V+wst9EFg/e4iJk5fSHZROcM6tuDVa4cSG6FTKFX9XDk0hVYx4azJKuS7TbpV7w+00Ae45bv2MXH6QvIOVHBK11Z6MJRqsMgwNzfZY/VPfrNVt+r9gBb6APbj1jymzFhMUVkV5/RMZMbUwUSGae8a1XCTh6fQMjqMVRn7mbdZe1j5Oi30AeqbDdlMe2UppRXVXDIgiWcmDyQ8RIu88o6osJBDM3B0rN73aaEPQO+vyOTGWcsOnRnqXxP6EaKthpWXTRnegRbRYazYtZ/5W/KcjqOOQf/6A8zLC3bw6zdXUe0x/Or0zjx0UW89aYhqFNHhIVx/inUWqse/3qxb9T5MC32AMMbwry838eeP1wPw+/N6cO/Y7nr6P9Wopo5IpaW9Vf/tRp2B46u00AeAao/hDx+s5elvt+J2CY9N6McN9vipUo0pOjzk0FmoHvtys/bA8VFa6P1cWWU1t85ezuzFuwgLcfHclEFcNijZ6VgqiEwZ3oE2sRFs2FPEJ2v2OB1HHYEWej9WeLCSq19awufr9tIsIoRZ1w7l7J6JTsdSQSYi1M0do7sC8PhXm6nSfvU+Rwu9n9pTeJDLn1vIkh0FtImN4O2bRzCsU0unY6kgNWFwMh1aRrE9r4T3VmQ5HUcdRgu9H9qSXcylz/zIpuxiurSO4d1bRtK9TazTsVQQC3W7uOssa6v+ya+3UF6l55b1JVro/czCbfmMf/bHQ83J3rl5BEnxkU7HUopx/ZI4KTGGrP0HeWOJnlvWl2ih9yMfrsxi6ktLKC6J02HvAAAU4UlEQVSrYkyvRF67TjtQKt/hdgm/ObsbAE9/u5WS8iqHE6kaWuj9gDGGZ7/fxp1vrKSi2sO0kak8M3mQ9q1RPmdMr0T6t48n70A50/+33ek4yqaF3sdVVXv444dr+fvnGwH4w/k9eHBcL9x6tKvyQSLC78/vAcD0/20nu6jM4UQKtND7tOKySq57NY3XFllz5P975UCuP0UPhFK+bUhqC87pmcjBymoe/2qz03EUWuh91u79B5nw3ELmbc6lRXQYc24Yxvl92zodS6kTct+53QlxCW+lZbBpb7HTcYKeFnoftDarkEueWcDGvcV0Sojm/VtGMqhDC6djKXXCOiXEcOWwFDwG/vbZBqfjBD0t9D7mi3V7mfDcT6f9e+9XI+nQMtrpWErV2Z2juxITHsL3m3JZsFXbGDtJC72PMMbw3Lxt3PzaMg5WVjN+QBIzrxuq0yeV32oZE36o4dkjn2ygWhueOUYLvQ+oqPLw23dW8+hnGzEG7hnTjX9d3k/PCKX83rUnd6RtXATr9xTxdpoeROUULfQOKyip4KoXF/P2skwiQl08O3kgt57RRfvIq4AQGebm/vOs6Zb/+GIThaWVDicKTlroHbQ5u5iL/vsDi3cU0LpZOG/dNIJz++jMGhVYLuzblqEdW1BQUsHjX+t0SydooXfINxuyGf/Mj2QUHKRPUhwf3TaKvsnxTsdSyutEhAcv7IVLYNainWzcW+R0pKCjhb6JGWOY/r9tXD8zjQPlVVzQty1v3TSCNnERTkdTqtH0bBfLlOEdqPYYHvhwnZ5ftolpoW9CZZXV/OatVfz1U2un62/OPomnJw3QnjUqKPzm7JNoHhXK4h0FzF2tZ6JqSlrom8jewjKueH4h76/IIjLUzTOTB3LH6K6601UFjfioMO4Z0x2Av366gdIK7W7ZVLTQN4Hlu/Yx7j8/sCqzkOTmkbz7q5GcpztdVRC6Ykh7eifFsqewjCe+3uJ0nKChhb6RvZWWwcTnF5FTXM7wTi346LZR9GynZ4NSwcntEh65uA8ugRnzt7M2q9DpSEGh3oVeRNqLyHciskFE1onInd4M5u8qqz386cO1/Pad1VRUe7hqeAdmXTeMFtF6pKsKbv3axzNtZEc8Bu57b7WeTLwJNGSLvgq42xjTAxgO3CoiPb0Ty7/lHShn8ozFzFy4kzC3i79f2oeHLu5NqFu/QCkFcPc5J5EUH8narCJeXpDudJyAV+/KY4zZY4xZbl8uBjYASd4K5q9WZ+7nwqd/YIl9ENQbNw3niiEpTsdSyqdEh4fw8MW9Afj3V5vJKCh1OFFg88ompoikAgOAxUe47UYRSRORtNzcXG+szme9lZbBZc8tZE9hGQNT4pl7+ygGpjR3OpZSPumM7q25oG9bDlZW84cP1urc+kbU4EIvIjHAu8BdxphfHPJmjJlujBlsjBmckJDQ0NX5pIoqD79/f401Hl/lYfKwFObcOJzWsXoQlFLH8sCFvYiNCGHe5lzeX5HldJyA1aBCLyKhWEV+tjHmPe9E8i/ZRWVMnL6Q2Yt3EeZ28Y9L+/LIJX2086RSJyChWTh/uMDatffAR+vYvf+gw4kCU0Nm3QjwIrDBGPNv70XyH4u353P+Uz+wfNd+2sZF8PbNI7h8SHunYynlVyYMSuasHq0pLqvinndW4dG+9V7XkC36k4GrgDNFZKX9c56Xcvk0Ywwz5m/nyhmLyTtQzohOLfn49lH0a69NyZSqKxHhb+P70iI6jAVb85m5MN3pSAEnpL4PNMb8AATd8fsl5VX89t3VfGL36rjptE7cc043QnTqpFL1ltAsnL9e0oebX1vG3z7byKiuCXRpHeN0rICh1akOtuYUc9F/F/DJ6j1Eh7l5dvJA7j+3hxZ5pbxgbO82XDowmfIqD795ayWVeiCV12iFOkEfr9rNuP8sYGvOAbq0juHD20bpSUKU8rIHxvUkKT6S1ZmFPP2N9sLxFi30x1FR5eHBj9Zx+5wVlFZUM65fOz689WT9WqlUI4iNCOWxCf0Qgae/28r8LYF97E1T0UJ/DLv3H2Ti9IW88mM6oW7hz+N68eTE/kSH13vXhlLqOEZ0bsmdo7tiDNz1xkr2FpY5HcnvaaE/inmbczn/qfmHpk6+edMIpo5M1f7xSjWB28/syildW5FfUsHtc5Zr47MG0kJ/mGqP4fGvNjPt5SXsK63k1JMS+OSOU7SVgVJNyO0SHr+iP4mx4SxN38djX+pJxRtCC30teQfKmfbyEp60dwL95uyTeGXaEG0trJQDWsWE8/SkgbhdwnPztvHNhmynI/ktLfQ26yjX+czfkkfL6DBmXTuMO0Z3xeXSoRqlnDK0YwvuGdMNgLveXMnWnGKHE/mnoC/0Ho/hme+3cuWMxWQXlTMktTmf3HEKo7q2cjqaUgq48ZROnNu7DcVlVVz7ShoFJRVOR/I7QV3o95VUcN2rS/nH55uo9hh+dXpn5twwnDZx2nVSKV/hcgn/vrw/fZLi2FVQys2zllFeVe10LL8StIV+aXoB5z01n+825RIfFcrL04Zw79juepSrUj4oMszNjKmDaRMbwZL0An73nvavr4ugq2o1QzUTpy86dIKQT+44hTO6t3Y6mlLqGBJjI5gxdTCRoW7eXZ7Js/O2OR3JbwRVoc8/UM41r/w0VHPTaZ1486YRJMVHOh1NKXUCeifF8fgV/QH4x+ebeCstw+FE/iFoCv3Cbfmc99R85m3Opbk9VHP/uT30hN1K+ZmxvdvwJ/tkJffV6iSrji7gj+Wv9hie/nYLT32zBY+BIanNeWrSANrG6Va8Uv7q2lEdKS6r4vGvN3PnGyuICnPr8OsxBPTmbHZRGVNmLOaJr7dggNvO6MKcG4ZrkVcqANwxugs3ntqJKo/h5teWsXBbvtORfFbAFvrvNuVw7pPzWbg9n1Yx4cy6dhj/N0ZPEKJUoBAR7j+3O5OGplBe5eH6V5dqsT+KgKt6FVUeHvlkPde8vJSCkgpO7tKST+8cpQdAKRWARISHL+7NJQOSKKmoZurLS/h6vbZKOFxAFfqd+SVc9tyPvDB/B26XcM+Ybsy6dhitm+kBUEoFKrdLeGxCPyYPS6GiysNNry3j/RWZTsfyKQGzM/bDlVn8/v21HCivIik+kqcm9WdQhxZOx1JKNQG3y9qyj4sM5Znvt/HrN1dRdLCKqSNTnY7mE/y+0JeUV/HAR+t4Z5n1CX5u7zY8Or4vcVGhDidTSjUlEeG3Y7sTHxXKXz/dyAMfrSNzX6ke8Y6fF/q1WYXcMWcF2/NKCA9x8cCFvZg0tL2eHESpIHbjqZ2Jjwzjd++v4YX5O9i4t5inJw0gPip424375cecx2N48YcdjH/mR7bnldAtsRkf3z6KK4elaJFXSnH5kPbMvn4YLaPDmL8lj3H/WcCmvcHb4tjvCn1usdXG4KG566mo9jBleAof3nYyJyU2czqaUsqHDOvUko9vH0XvpFh2FZRyyTML+GBFVlA2Q/OrQj9vcy7nPmm1MYiPCmX6VYN4+OI+RIS6nY6mlPJB7eIjeefmkVzcvx2lFdXc9eZKbnt9BfuCrKe9XxT68qpqHpq7nqkvLSHvQDkjOrXk8ztP5ZxebZyOppTycRGhbh6/oj9/v7QP0WFuPlmzh3Oe+B/fbcxxOlqTkab8GjN48GCTlpZWp8dszSnm9jkr2bCnCLdL+M3ZJ3HzaZ1x6yn+lFJ1tCu/lLvfXsnS9H0AXDYomXvHdiehWbjDyY5NRJYZYwbX+/G+WuiNMby+ZBcPzV1PWaWHlBZRPDmxPwNSmjdySqVUIKv2GGbM386/vtxMRbWHmPAQ7hjdhWkjOxIW4puDHAFZ6AtKKrjv3dV8aR/KPH5gEn+5qDcx4X49G1Qp5UO25x7g4U828K09hNOpVTT3n9eDs3q09rnZewFX6OdvyeXut1aRU1xOs/AQHr6kNxf1T2qihEqpYPPdphwe+ng92/NKAOjVLpbbzujCmF5tcPnIEHHAFPryqmr++fkmZvywA7D6xv/78v60bxHVZPmUUsGposrDrEU7eW7eNnKLywHo0jqGm0/rzAV92zo+sy8gCv3m7GLufOOnHa53je7KLWd00R2uSqkmVVZZzdtpGTw3bztZ+w8CEBcZyiUDkpg0NIVubZw5XsevC70xhld/TOdvn22kvMpDh5ZRPHGF7nBVSjmrosrDByuymLkonbVZRYeW928fz/l92jKmVxtSWjbdaIPfFvqc4jJ++85qvt+UC8Dlg5P504W9dIerUsqnrM0q5I2lu/hwxW6Ky6sOLe/ephljerXhlK6t6Jsc36gzdvyy0H+5bi/3vbeGgpIK4qNCeXR8H8b2bttkOZRSqq5KK6r4dmMOX6zL5ruNORyoVfQjQl0M6tCc4R1b0j8lnl7t4mgR7b0mao4WehEZCzwJuIEZxphHj3X/gYMGmXN+9zJvLM0AYFSXVjw2oR9t4vTEIEop/1FeVc2P2/L5dkMOi7bnsyXnwC/u0zYugl7tYjkpsRmpraLp1Cqa1FbRtIwOq/P0TccKvYi4gc3A2UAmsBSYZIxZf7THNEvuZlpO+TdhIS7uG9udaSNTfWb6klJK1VfegXKW7ChgyY4C1mQVsmFPEaUV1Ue8b3SYmzZxEbSNi6RNXASJseG0iA6nRXQozaPCaBkdTnLzSJrX+kbQ0ELfkAHxocBWY8x2O8gbwEXAUQt9RbWH7m2a8cTE/nRvE9uAVSullO9oFRPOeX3acl4fawi62mNIzy9h3e4ituUcID2/hB15JezILaG4vIptuSVsyy056vPdO7Y7vzq9s9fyNWSL/jJgrDHmevv6VcAwY8xth93vRuBG+2pvYG394zaZVkCe0yFOgD/k9IeMoDm9TXN6VzdjTL3ndjZki/5IYy6/+NQwxkwHpgOISFpDvn40Fc3pPf6QETSnt2lO7xKRunWDPExD5gNlAu1rXU8GdjckjFJKKe9rSKFfCnQVkY4iEgZMBD7yTiyllFLeUu+hG2NMlYjcBnyBNb3yJWPMuuM8bHp919fENKf3+ENG0Jzepjm9q0E5m/SAKaWUUk3PN7vsK6WU8hot9EopFeAapdCLSHsR+U5ENojIOhG5017eQkS+EpEt9r+OtqkUkQgRWSIiq+ycf7aXdxSRxXbON+2dzY4TEbeIrBCRufZ1n8spIukiskZEVtZMCfO137udKV5E3hGRjfb7dISv5RSRbvbrWPNTJCJ3+WDOX9t/P2tFZI79d+WL78077YzrROQue5njr6WIvCQiOSKyttayI+YSy1MislVEVovIwBNZR2Nt0VcBdxtjegDDgVtFpCdwH/CNMaYr8I193UnlwJnGmH5Af2CsiAwH/g48bufcB1znYMba7gQ21LruqznPMMb0rzU/2dd+72D1aPrcGNMd6If1uvpUTmPMJvt17A8MAkqB9/GhnCKSBNwBDDbG9MaamDERH3tvikhv4AasI/r7AReISFd847V8BRh72LKj5ToX6Gr/3Ag8e0JrMMY0+g/wIVZPnE1AW3tZW2BTU6z/BDNGAcuBYVhHyoXYy0cAX/hAvmT7F34mMBfrgDVfzJkOtDpsmU/93oFYYAf2ZARfzXlYtnOABb6WE0gCMoAWWLP45gJjfO29CUzAarxYc/2PwG995bUEUoG1ta4fMRfwPFZPsV/c71g/jT5GLyKpwABgMZBojNkDYP/burHXfzz2cMhKIAf4CtgG7DfG1PQgzcR6MzvtCaw3pse+3hLfzGmAL0Vkmd3+Anzv994JyAVetofCZohINL6Xs7aJwBz7ss/kNMZkAY8Bu4A9QCGwDN97b64FThWRliISBZyHdcCnz7yWhzlarpoP1hon9No2aqEXkRjgXeAuY0zR8e7vBGNMtbG+Gidjfa3rcaS7NW2qnxORC4AcY8yy2ouPcFdfmCt7sjFmINZXzFtF5FSnAx1BCDAQeNYYMwAowTeGk47IHt8eB7ztdJbD2WPHFwEdgXZANNbv/nCOvjeNMRuwhpO+Aj4HVmENMfubev3dN1qhF5FQrCI/2xjznr04W0Ta2re3xdqK9gnGmP3A91j7FOJFpOZgMl9o7XAyME5E0oE3sIZvnsD3cmKM2W3/m4M1njwU3/u9ZwKZxpjF9vV3sAq/r+WscS6w3BiTbV/3pZxnATuMMbnGmErgPWAkvvnefNEYM9AYcypQAGzBt17L2o6Wq16tZxpr1o0ALwIbjDH/rnXTR8BU+/JUrLF7x4hIgojE25cjsd60G4DvgMvsuzme0xhzvzEm2RiTivUV/ltjzGR8LKeIRItIs5rLWOPKa/Gx37sxZi+QISLd7EWjsdpr+1TOWibx07AN+FbOXcBwEYmy/+5rXkufem8CiEhr+98UYDzWa+pLr2VtR8v1EXC1PftmOFBYM8RzTI20Y2EU1teJ1cBK++c8rHHlb7A+Sb8BWjix46NWzr7ACjvnWuBP9vJOwBJgK9bX5XAncx6W+XRgri/mtPOssn/WAb+3l/vU793O1B9Is3/3HwDNfTRnFJAPxNVa5lM5gT8DG+2/oVlAuK+9N+2c87E+hFYBo33ltcT6wNkDVGJtsV93tFxYQzf/xdqXuAZrttNx16EtEJRSKsDpkbFKKRXgtNArpVSA00KvlFIBTgu9UkoFOC30SikV4LTQq6AhIpeIiBGR7k5nUaopaaFXwWQS8APWQWdKBQ0t9Coo2H2XTsY6GGWivcwlIs/Y/cnnisinInKZfdsgEZlnN2f7ouZwdKX8kRZ6FSwuxuo/vxkosE/YMB6rPWwf4Hqsdro1fZqeBi4zxgwCXgIecSK0Ut4Qcvy7KBUQJmE1ggOrMdwkIBR42xjjAfaKyHf27d2A3sBXVvsW3FiHqCvll7TQq4AnIi2xOn72FhGDVbgNVnfNIz4EWGeMGdFEEZVqVDp0o4LBZcBMY0wHY0yqMaY91hmm8oBL7bH6RKyGcWCdtSdBRA4N5YhILyeCK+UNWuhVMJjEL7fe38U6UUYmVtfF57HOglZojKnA+nD4u4iswuq+OrLp4irlXdq9UgU1EYkxxhywh3eWYJ0ha6/TuZTyJh2jV8Furn3ymTDgIS3yKhDpFr1SSgU4HaNXSqkAp4VeKaUCnBZ6pZQKcFrolVIqwGmhV0qpAPf/SlytcszSNvEAAAAASUVORK5CYII=
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<p>In the above model, consumption of the elderly falls rapidly, as it is quite unlikely to live for so long. This illustrates another role of pension systems as insurance against long life.</p>
<p>At this stage however the model is only in Partial Equilibrium, as the households solve only their own problem given factor prices. But we know that the prices depend on capital, which in turn depends on the stock of assets of households! Therefore, we will set up a General Equilibrium environment and solve jointly for prices and households' choices.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="c1"># Additional parameters</span>
<span class="n">α</span> <span class="o">=</span> <span class="mf">0.33</span>
<span class="n">δ</span> <span class="o">=</span> <span class="mf">0.1</span>

<span class="c1"># Capital per worker demanded by firms for a given real interest rate</span>
<span class="k">def</span> <span class="nf">CapitalDemand</span><span class="p">(</span><span class="n">r</span><span class="p">):</span>
    <span class="k">return</span> <span class="p">(</span><span class="n">α</span><span class="o">/</span><span class="p">(</span><span class="n">r</span><span class="o">+</span><span class="n">δ</span><span class="p">))</span><span class="o">**</span><span class="p">(</span><span class="mi">1</span><span class="o">/</span><span class="p">(</span><span class="mi">1</span><span class="o">-</span><span class="n">α</span><span class="p">))</span>

<span class="c1"># Wage in General Equilibrium</span>
<span class="k">def</span> <span class="nf">Wage</span><span class="p">(</span><span class="n">r</span><span class="p">):</span>
    <span class="k">return</span> <span class="p">(</span><span class="mi">1</span><span class="o">-</span><span class="n">α</span><span class="p">)</span> <span class="o">*</span> <span class="n">CapitalDemand</span><span class="p">(</span><span class="n">r</span><span class="p">)</span><span class="o">**</span><span class="n">α</span>

<span class="c1"># Household&#39;s proble solution</span>
<span class="k">def</span> <span class="nf">HouseholdProblem</span><span class="p">(</span><span class="n">r</span><span class="p">):</span>
    <span class="n">w</span> <span class="o">=</span> <span class="n">Wage</span><span class="p">(</span><span class="n">r</span><span class="p">)</span>
    
    <span class="n">c</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">J</span><span class="p">)</span>
    <span class="n">h</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">J</span><span class="p">)</span>
    <span class="n">a</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">J</span><span class="p">)</span>

    <span class="n">h</span><span class="p">[:</span><span class="n">JR</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="mi">1</span>
    
    <span class="n">lti</span> <span class="o">=</span> <span class="mi">0</span>
    <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">JR</span><span class="o">-</span><span class="mi">1</span><span class="p">):</span>
        <span class="n">lti</span> <span class="o">+=</span> <span class="n">w</span><span class="o">/</span><span class="p">(</span><span class="mi">1</span><span class="o">+</span><span class="n">r</span><span class="p">)</span><span class="o">**</span><span class="n">j</span>

    <span class="n">disc</span> <span class="o">=</span> <span class="mi">0</span>
    <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">J</span><span class="o">-</span><span class="mi">1</span><span class="p">):</span>
        <span class="n">disc</span> <span class="o">+=</span> <span class="n">surv</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="o">*</span><span class="n">β</span><span class="o">**</span><span class="n">j</span>
        
    <span class="n">c</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">lti</span><span class="o">/</span><span class="n">disc</span>
    <span class="n">a</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="mi">0</span>

    <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">J</span><span class="o">-</span><span class="mi">1</span><span class="p">):</span>
        <span class="n">c</span><span class="p">[</span><span class="n">j</span><span class="o">+</span><span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="n">β</span><span class="o">*</span><span class="p">(</span><span class="mi">1</span><span class="o">-</span><span class="n">mort</span><span class="p">[</span><span class="n">j</span><span class="p">])</span><span class="o">*</span><span class="p">(</span><span class="mi">1</span><span class="o">+</span><span class="n">r</span><span class="p">)</span><span class="o">*</span><span class="n">c</span><span class="p">[</span><span class="n">j</span><span class="p">]</span>
        <span class="n">a</span><span class="p">[</span><span class="n">j</span><span class="o">+</span><span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="n">w</span><span class="o">*</span><span class="n">h</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">+</span> <span class="p">(</span><span class="mi">1</span><span class="o">+</span><span class="n">r</span><span class="p">)</span><span class="o">*</span><span class="n">a</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">-</span> <span class="n">c</span><span class="p">[</span><span class="n">j</span><span class="p">]</span>
        
    <span class="k">return</span> <span class="n">c</span><span class="p">,</span> <span class="n">h</span><span class="p">,</span> <span class="n">a</span>

<span class="c1"># Vectorization allows to pass an array of values for arguments</span>
<span class="n">HouseholdProblem</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">vectorize</span><span class="p">(</span><span class="n">HouseholdProblem</span><span class="p">)</span>

<span class="c1"># Households&#39; decisions determine the aggregate capital supply</span>
<span class="k">def</span> <span class="nf">CapitalSupply</span><span class="p">(</span><span class="n">r</span><span class="p">):</span>
    <span class="n">c</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">J</span><span class="p">)</span>
    <span class="n">h</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">J</span><span class="p">)</span>
    <span class="n">a</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">J</span><span class="p">)</span>
    
    <span class="n">c</span><span class="p">,</span> <span class="n">h</span><span class="p">,</span> <span class="n">a</span> <span class="o">=</span> <span class="n">HouseholdProblem</span><span class="p">(</span><span class="n">r</span><span class="p">)</span>

    <span class="n">K</span> <span class="o">=</span> <span class="nb">sum</span><span class="p">(</span><span class="n">a</span><span class="o">*</span><span class="n">surv</span><span class="p">)</span>
    <span class="n">H</span> <span class="o">=</span> <span class="nb">sum</span><span class="p">(</span><span class="n">h</span><span class="o">*</span><span class="n">surv</span><span class="p">)</span>
    <span class="k">return</span> <span class="n">K</span><span class="o">/</span><span class="n">H</span>

<span class="n">CapitalSupply</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">vectorize</span><span class="p">(</span><span class="n">CapitalSupply</span><span class="p">)</span>

<span class="c1"># Excess demand (squared) function, we will minimize this function</span>
<span class="k">def</span> <span class="nf">CapitalExcessDemand</span><span class="p">(</span><span class="n">r</span><span class="p">):</span>
    <span class="k">return</span> <span class="p">(</span><span class="n">CapitalDemand</span><span class="p">(</span><span class="n">r</span><span class="p">)</span> <span class="o">-</span> <span class="n">CapitalSupply</span><span class="p">(</span><span class="n">r</span><span class="p">))</span><span class="o">**</span><span class="mi">2</span>
</pre></div>

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<div class="prompt input_prompt">In&nbsp;[18]:</div>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="c1"># Range of plausible annual real interest rates</span>
<span class="n">rr</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mf">0.1</span><span class="p">)</span>

<span class="c1"># Plot capital supply and demand curves</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">CapitalSupply</span><span class="p">(</span><span class="n">rr</span><span class="p">),</span> <span class="n">rr</span><span class="p">,</span> <span class="n">lw</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">CapitalDemand</span><span class="p">(</span><span class="n">rr</span><span class="p">),</span> <span class="n">rr</span><span class="p">,</span> <span class="n">lw</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>

<span class="c1"># Plot excess demand (squared) function to see where it has a root</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">rr</span><span class="p">,</span> <span class="n">CapitalExcessDemand</span><span class="p">(</span><span class="n">rr</span><span class="p">),</span> <span class="n">lw</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="c1"># Import bounded minimization function</span>
<span class="kn">from</span> <span class="nn">scipy.optimize</span> <span class="k">import</span> <span class="n">fminbound</span>

<span class="c1"># Find the minimum of excess demand (squared) function</span>
<span class="n">result</span> <span class="o">=</span> <span class="n">fminbound</span><span class="p">(</span><span class="n">CapitalExcessDemand</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mf">0.1</span><span class="p">,</span> <span class="n">full_output</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="n">result</span><span class="p">)</span>
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<pre>(0.04240795915224549, 1.914004308774482e-10, 0, 8)
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<div class="prompt input_prompt">In&nbsp;[20]:</div>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">r_GE</span> <span class="o">=</span> <span class="n">result</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
<span class="n">w_GE</span> <span class="o">=</span> <span class="n">Wage</span><span class="p">(</span><span class="n">r_GE</span><span class="p">)</span>

<span class="n">c</span><span class="p">,</span> <span class="n">h</span><span class="p">,</span> <span class="n">a</span> <span class="o">=</span> <span class="n">HouseholdProblem</span><span class="p">(</span><span class="n">r_GE</span><span class="p">)</span>

<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">20</span><span class="p">,</span> <span class="mi">100</span><span class="p">),</span> <span class="n">c</span><span class="p">,</span> <span class="n">lw</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s1">&#39;Consumption over the lifecycle&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="s1">&#39;Age&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>

<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">20</span><span class="p">,</span> <span class="mi">100</span><span class="p">),</span> <span class="n">w</span><span class="o">*</span><span class="n">h</span><span class="p">,</span> <span class="n">lw</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">ylim</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mf">1.2</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s1">&#39;Labor income over the lifecycle&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="s1">&#39;Age&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>

<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">20</span><span class="p">,</span> <span class="mi">100</span><span class="p">),</span> <span class="n">a</span><span class="p">,</span> <span class="n">lw</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s1">&#39;Assets over the lifecycle&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="s1">&#39;Age&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">k</span> <span class="o">=</span> <span class="n">CapitalSupply</span><span class="p">(</span><span class="n">r_GE</span><span class="p">)</span>
<span class="n">y</span> <span class="o">=</span> <span class="n">k</span><span class="o">**</span><span class="n">α</span>
<span class="n">i</span> <span class="o">=</span> <span class="n">δ</span><span class="o">*</span><span class="n">k</span>

<span class="nb">print</span><span class="p">(</span><span class="s1">&#39;Real interest rate = </span><span class="si">{:.2f}</span><span class="s1"> %&#39;</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="mi">100</span><span class="o">*</span><span class="n">r_GE</span><span class="p">))</span>
<span class="nb">print</span><span class="p">(</span><span class="s1">&#39;Investment rate    = </span><span class="si">{:.2f}</span><span class="s1"> %&#39;</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="mi">100</span><span class="o">*</span><span class="n">i</span><span class="o">/</span><span class="n">y</span><span class="p">))</span>
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<pre>Real interest rate = 4.24 %
Investment rate    = 23.17 %
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<h3 id="Life-expectancy-vs-saving-rates">Life expectancy vs saving rates<a class="anchor-link" href="#Life-expectancy-vs-saving-rates">&#182;</a></h3><p>Both theoretical and empirical evidence suggest that when life expectancy increases (survival probability increases), households will save a bigger portion of their income.</p>
<p>Below you can see graphs of the relationship between the survival probability and national saving rate for several countries:</p>
<p><img src="img/OLG/OLG_survival_savings.png" alt="OLG Saving vs Survival"></p>
<p>Source: <a href="https://www.sciencedirect.com/science/article/pii/S0305750X06001781">Kinugasa and Mason (2007) Why Countries Become Wealthy: The Effects of Adult Longevity on Saving</a></p>
<p>We can also see a similar pattern in a cross-section of countries, where in countries with higher life expectancy people seem to be more "patient". Below you can see the results of field experiments, where actual people were asked to choose between getting an amount of money now vs a bigger amount in a month time. The graph shows the proportion of people who chose to wait, binned by country groups:</p>
<p><img src="img/OLG/OLG_wait.png" alt="OLG Proportion of people waiting"></p>
<p>Source: <a href="https://www.sciencedirect.com/science/article/pii/S0167487015001439">Wang et al. (2016) How time preferences differ: Evidence from 53 countries</a></p>

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<h2 id="Homework:-impact-of-ageing">Homework: impact of ageing<a class="anchor-link" href="#Homework:-impact-of-ageing">&#182;</a></h2><p>Investigate how an increase in survival probabilities will impact the real interest rate and saving/investment rate in General Equilibrium.</p>
<p>In the previous codes I have used the mortality pattern from the 1950s in the US. The new mortality pattern is from the 2015 in the US.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">mort_2015</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">J</span><span class="p">)</span>
<span class="n">surv_2015</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">J</span><span class="p">)</span>

<span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">J</span><span class="p">):</span>
    <span class="n">mort_2015</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="nb">min</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="o">-</span><span class="mf">7.3432</span> <span class="o">+</span> <span class="mf">0.023</span><span class="o">*</span><span class="n">j</span> <span class="o">+</span> <span class="mf">0.0013</span><span class="o">*</span><span class="n">j</span><span class="o">**</span><span class="mi">2</span> <span class="o">-</span> <span class="mf">7e-06</span><span class="o">*</span><span class="n">j</span><span class="o">**</span><span class="mi">3</span><span class="p">),</span> <span class="mi">1</span><span class="o">-</span><span class="mf">1e-2</span><span class="p">)</span>

<span class="n">surv_2015</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="mi">1</span>
<span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">J</span><span class="o">-</span><span class="mi">1</span><span class="p">):</span>
    <span class="n">surv_2015</span><span class="p">[</span><span class="n">j</span><span class="o">+</span><span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="p">(</span><span class="mi">1</span><span class="o">-</span><span class="n">mort_2015</span><span class="p">[</span><span class="n">j</span><span class="p">])</span><span class="o">*</span><span class="n">surv_2015</span><span class="p">[</span><span class="n">j</span><span class="p">]</span>
    
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">20</span><span class="p">,</span> <span class="mi">100</span><span class="p">),</span> <span class="n">surv_2015</span><span class="p">,</span> <span class="n">lw</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s1">&#39;Probability of survival from age 20&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="s1">&#39;Age&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
</pre></div>

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<p><strong>Task 1</strong>: Find the new level of real interest rate in General Equilibrium. Remember to update the relevant functions, as now the mortality pattern is different. Comment on whether the new level of interest rates is higher or lower than for the previous mortality profile.</p>
<p><strong>Task 2</strong>: Plot the resulting lifecycle patterns of the consumer.</p>
<p><strong>Task 3</strong>: Find the new investment/saving rate. Is it higher or lower than for the previous mortality profile?</p>

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<div class="prompt input_prompt">In&nbsp;[23]:</div>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="c1"># Your codes</span>
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