linear/LinearRegressionBivariateQuality.html

    <!DOCTYPE html>
<html>
<head><meta charset="utf-8" />

<title>LinearRegressionBivariateQuality</title>

<script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.1.10/require.min.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/2.0.3/jquery.min.js"></script>


<style type="text/css">
    /*!
*
* Twitter Bootstrap
*
*/
/*!
 * Bootstrap v3.3.7 (http://getbootstrap.com)
 * Copyright 2011-2016 Twitter, Inc.
 * Licensed under MIT (https://github.com/twbs/bootstrap/blob/master/LICENSE)
 */
/*! normalize.css v3.0.3 | MIT License | github.com/necolas/normalize.css */
html {
  font-family: sans-serif;
  -ms-text-size-adjust: 100%;
  -webkit-text-size-adjust: 100%;
}
body {
  margin: 0;
}
article,
aside,
details,
figcaption,
figure,
footer,
header,
hgroup,
main,
menu,
nav,
section,
summary {
  display: block;
}
audio,
canvas,
progress,
video {
  display: inline-block;
  vertical-align: baseline;
}
audio:not([controls]) {
  display: none;
  height: 0;
}
[hidden],
template {
  display: none;
}
a {
  background-color: transparent;
}
a:active,
a:hover {
  outline: 0;
}
abbr[title] {
  border-bottom: 1px dotted;
}
b,
strong {
  font-weight: bold;
}
dfn {
  font-style: italic;
}
h1 {
  font-size: 2em;
  margin: 0.67em 0;
}
mark {
  background: #ff0;
  color: #000;
}
small {
  font-size: 80%;
}
sub,
sup {
  font-size: 75%;
  line-height: 0;
  position: relative;
  vertical-align: baseline;
}
sup {
  top: -0.5em;
}
sub {
  bottom: -0.25em;
}
img {
  border: 0;
}
svg:not(:root) {
  overflow: hidden;
}
figure {
  margin: 1em 40px;
}
hr {
  box-sizing: content-box;
  height: 0;
}
pre {
  overflow: auto;
}
code,
kbd,
pre,
samp {
  font-family: monospace, monospace;
  font-size: 1em;
}
button,
input,
optgroup,
select,
textarea {
  color: inherit;
  font: inherit;
  margin: 0;
}
button {
  overflow: visible;
}
button,
select {
  text-transform: none;
}
button,
html input[type="button"],
input[type="reset"],
input[type="submit"] {
  -webkit-appearance: button;
  cursor: pointer;
}
button[disabled],
html input[disabled] {
  cursor: default;
}
button::-moz-focus-inner,
input::-moz-focus-inner {
  border: 0;
  padding: 0;
}
input {
  line-height: normal;
}
input[type="checkbox"],
input[type="radio"] {
  box-sizing: border-box;
  padding: 0;
}
input[type="number"]::-webkit-inner-spin-button,
input[type="number"]::-webkit-outer-spin-button {
  height: auto;
}
input[type="search"] {
  -webkit-appearance: textfield;
  box-sizing: content-box;
}
input[type="search"]::-webkit-search-cancel-button,
input[type="search"]::-webkit-search-decoration {
  -webkit-appearance: none;
}
fieldset {
  border: 1px solid #c0c0c0;
  margin: 0 2px;
  padding: 0.35em 0.625em 0.75em;
}
legend {
  border: 0;
  padding: 0;
}
textarea {
  overflow: auto;
}
optgroup {
  font-weight: bold;
}
table {
  border-collapse: collapse;
  border-spacing: 0;
}
td,
th {
  padding: 0;
}
/*! Source: https://github.com/h5bp/html5-boilerplate/blob/master/src/css/main.css */
@media print {
  *,
  *:before,
  *:after {
    background: transparent !important;
    box-shadow: none !important;
    text-shadow: none !important;
  }
  a,
  a:visited {
    text-decoration: underline;
  }
  a[href]:after {
    content: " (" attr(href) ")";
  }
  abbr[title]:after {
    content: " (" attr(title) ")";
  }
  a[href^="#"]:after,
  a[href^="javascript:"]:after {
    content: "";
  }
  pre,
  blockquote {
    border: 1px solid #999;
    page-break-inside: avoid;
  }
  thead {
    display: table-header-group;
  }
  tr,
  img {
    page-break-inside: avoid;
  }
  img {
    max-width: 100% !important;
  }
  p,
  h2,
  h3 {
    orphans: 3;
    widows: 3;
  }
  h2,
  h3 {
    page-break-after: avoid;
  }
  .navbar {
    display: none;
  }
  .btn > .caret,
  .dropup > .btn > .caret {
    border-top-color: #000 !important;
  }
  .label {
    border: 1px solid #000;
  }
  .table {
    border-collapse: collapse !important;
  }
  .table td,
  .table th {
    background-color: #fff !important;
  }
  .table-bordered th,
  .table-bordered td {
    border: 1px solid #ddd !important;
  }
}
@font-face {
  font-family: 'Glyphicons Halflings';
  src: url('../components/bootstrap/fonts/glyphicons-halflings-regular.eot');
  src: url('../components/bootstrap/fonts/glyphicons-halflings-regular.eot?#iefix') format('embedded-opentype'), url('../components/bootstrap/fonts/glyphicons-halflings-regular.woff2') format('woff2'), url('../components/bootstrap/fonts/glyphicons-halflings-regular.woff') format('woff'), url('../components/bootstrap/fonts/glyphicons-halflings-regular.ttf') format('truetype'), url('../components/bootstrap/fonts/glyphicons-halflings-regular.svg#glyphicons_halflingsregular') format('svg');
}
.glyphicon {
  position: relative;
  top: 1px;
  display: inline-block;
  font-family: 'Glyphicons Halflings';
  font-style: normal;
  font-weight: normal;
  line-height: 1;
  -webkit-font-smoothing: antialiased;
  -moz-osx-font-smoothing: grayscale;
}
.glyphicon-asterisk:before {
  content: "\002a";
}
.glyphicon-plus:before {
  content: "\002b";
}
.glyphicon-euro:before,
.glyphicon-eur:before {
  content: "\20ac";
}
.glyphicon-minus:before {
  content: "\2212";
}
.glyphicon-cloud:before {
  content: "\2601";
}
.glyphicon-envelope:before {
  content: "\2709";
}
.glyphicon-pencil:before {
  content: "\270f";
}
.glyphicon-glass:before {
  content: "\e001";
}
.glyphicon-music:before {
  content: "\e002";
}
.glyphicon-search:before {
  content: "\e003";
}
.glyphicon-heart:before {
  content: "\e005";
}
.glyphicon-star:before {
  content: "\e006";
}
.glyphicon-star-empty:before {
  content: "\e007";
}
.glyphicon-user:before {
  content: "\e008";
}
.glyphicon-film:before {
  content: "\e009";
}
.glyphicon-th-large:before {
  content: "\e010";
}
.glyphicon-th:before {
  content: "\e011";
}
.glyphicon-th-list:before {
  content: "\e012";
}
.glyphicon-ok:before {
  content: "\e013";
}
.glyphicon-remove:before {
  content: "\e014";
}
.glyphicon-zoom-in:before {
  content: "\e015";
}
.glyphicon-zoom-out:before {
  content: "\e016";
}
.glyphicon-off:before {
  content: "\e017";
}
.glyphicon-signal:before {
  content: "\e018";
}
.glyphicon-cog:before {
  content: "\e019";
}
.glyphicon-trash:before {
  content: "\e020";
}
.glyphicon-home:before {
  content: "\e021";
}
.glyphicon-file:before {
  content: "\e022";
}
.glyphicon-time:before {
  content: "\e023";
}
.glyphicon-road:before {
  content: "\e024";
}
.glyphicon-download-alt:before {
  content: "\e025";
}
.glyphicon-download:before {
  content: "\e026";
}
.glyphicon-upload:before {
  content: "\e027";
}
.glyphicon-inbox:before {
  content: "\e028";
}
.glyphicon-play-circle:before {
  content: "\e029";
}
.glyphicon-repeat:before {
  content: "\e030";
}
.glyphicon-refresh:before {
  content: "\e031";
}
.glyphicon-list-alt:before {
  content: "\e032";
}
.glyphicon-lock:before {
  content: "\e033";
}
.glyphicon-flag:before {
  content: "\e034";
}
.glyphicon-headphones:before {
  content: "\e035";
}
.glyphicon-volume-off:before {
  content: "\e036";
}
.glyphicon-volume-down:before {
  content: "\e037";
}
.glyphicon-volume-up:before {
  content: "\e038";
}
.glyphicon-qrcode:before {
  content: "\e039";
}
.glyphicon-barcode:before {
  content: "\e040";
}
.glyphicon-tag:before {
  content: "\e041";
}
.glyphicon-tags:before {
  content: "\e042";
}
.glyphicon-book:before {
  content: "\e043";
}
.glyphicon-bookmark:before {
  content: "\e044";
}
.glyphicon-print:before {
  content: "\e045";
}
.glyphicon-camera:before {
  content: "\e046";
}
.glyphicon-font:before {
  content: "\e047";
}
.glyphicon-bold:before {
  content: "\e048";
}
.glyphicon-italic:before {
  content: "\e049";
}
.glyphicon-text-height:before {
  content: "\e050";
}
.glyphicon-text-width:before {
  content: "\e051";
}
.glyphicon-align-left:before {
  content: "\e052";
}
.glyphicon-align-center:before {
  content: "\e053";
}
.glyphicon-align-right:before {
  content: "\e054";
}
.glyphicon-align-justify:before {
  content: "\e055";
}
.glyphicon-list:before {
  content: "\e056";
}
.glyphicon-indent-left:before {
  content: "\e057";
}
.glyphicon-indent-right:before {
  content: "\e058";
}
.glyphicon-facetime-video:before {
  content: "\e059";
}
.glyphicon-picture:before {
  content: "\e060";
}
.glyphicon-map-marker:before {
  content: "\e062";
}
.glyphicon-adjust:before {
  content: "\e063";
}
.glyphicon-tint:before {
  content: "\e064";
}
.glyphicon-edit:before {
  content: "\e065";
}
.glyphicon-share:before {
  content: "\e066";
}
.glyphicon-check:before {
  content: "\e067";
}
.glyphicon-move:before {
  content: "\e068";
}
.glyphicon-step-backward:before {
  content: "\e069";
}
.glyphicon-fast-backward:before {
  content: "\e070";
}
.glyphicon-backward:before {
  content: "\e071";
}
.glyphicon-play:before {
  content: "\e072";
}
.glyphicon-pause:before {
  content: "\e073";
}
.glyphicon-stop:before {
  content: "\e074";
}
.glyphicon-forward:before {
  content: "\e075";
}
.glyphicon-fast-forward:before {
  content: "\e076";
}
.glyphicon-step-forward:before {
  content: "\e077";
}
.glyphicon-eject:before {
  content: "\e078";
}
.glyphicon-chevron-left:before {
  content: "\e079";
}
.glyphicon-chevron-right:before {
  content: "\e080";
}
.glyphicon-plus-sign:before {
  content: "\e081";
}
.glyphicon-minus-sign:before {
  content: "\e082";
}
.glyphicon-remove-sign:before {
  content: "\e083";
}
.glyphicon-ok-sign:before {
  content: "\e084";
}
.glyphicon-question-sign:before {
  content: "\e085";
}
.glyphicon-info-sign:before {
  content: "\e086";
}
.glyphicon-screenshot:before {
  content: "\e087";
}
.glyphicon-remove-circle:before {
  content: "\e088";
}
.glyphicon-ok-circle:before {
  content: "\e089";
}
.glyphicon-ban-circle:before {
  content: "\e090";
}
.glyphicon-arrow-left:before {
  content: "\e091";
}
.glyphicon-arrow-right:before {
  content: "\e092";
}
.glyphicon-arrow-up:before {
  content: "\e093";
}
.glyphicon-arrow-down:before {
  content: "\e094";
}
.glyphicon-share-alt:before {
  content: "\e095";
}
.glyphicon-resize-full:before {
  content: "\e096";
}
.glyphicon-resize-small:before {
  content: "\e097";
}
.glyphicon-exclamation-sign:before {
  content: "\e101";
}
.glyphicon-gift:before {
  content: "\e102";
}
.glyphicon-leaf:before {
  content: "\e103";
}
.glyphicon-fire:before {
  content: "\e104";
}
.glyphicon-eye-open:before {
  content: "\e105";
}
.glyphicon-eye-close:before {
  content: "\e106";
}
.glyphicon-warning-sign:before {
  content: "\e107";
}
.glyphicon-plane:before {
  content: "\e108";
}
.glyphicon-calendar:before {
  content: "\e109";
}
.glyphicon-random:before {
  content: "\e110";
}
.glyphicon-comment:before {
  content: "\e111";
}
.glyphicon-magnet:before {
  content: "\e112";
}
.glyphicon-chevron-up:before {
  content: "\e113";
}
.glyphicon-chevron-down:before {
  content: "\e114";
}
.glyphicon-retweet:before {
  content: "\e115";
}
.glyphicon-shopping-cart:before {
  content: "\e116";
}
.glyphicon-folder-close:before {
  content: "\e117";
}
.glyphicon-folder-open:before {
  content: "\e118";
}
.glyphicon-resize-vertical:before {
  content: "\e119";
}
.glyphicon-resize-horizontal:before {
  content: "\e120";
}
.glyphicon-hdd:before {
  content: "\e121";
}
.glyphicon-bullhorn:before {
  content: "\e122";
}
.glyphicon-bell:before {
  content: "\e123";
}
.glyphicon-certificate:before {
  content: "\e124";
}
.glyphicon-thumbs-up:before {
  content: "\e125";
}
.glyphicon-thumbs-down:before {
  content: "\e126";
}
.glyphicon-hand-right:before {
  content: "\e127";
}
.glyphicon-hand-left:before {
  content: "\e128";
}
.glyphicon-hand-up:before {
  content: "\e129";
}
.glyphicon-hand-down:before {
  content: "\e130";
}
.glyphicon-circle-arrow-right:before {
  content: "\e131";
}
.glyphicon-circle-arrow-left:before {
  content: "\e132";
}
.glyphicon-circle-arrow-up:before {
  content: "\e133";
}
.glyphicon-circle-arrow-down:before {
  content: "\e134";
}
.glyphicon-globe:before {
  content: "\e135";
}
.glyphicon-wrench:before {
  content: "\e136";
}
.glyphicon-tasks:before {
  content: "\e137";
}
.glyphicon-filter:before {
  content: "\e138";
}
.glyphicon-briefcase:before {
  content: "\e139";
}
.glyphicon-fullscreen:before {
  content: "\e140";
}
.glyphicon-dashboard:before {
  content: "\e141";
}
.glyphicon-paperclip:before {
  content: "\e142";
}
.glyphicon-heart-empty:before {
  content: "\e143";
}
.glyphicon-link:before {
  content: "\e144";
}
.glyphicon-phone:before {
  content: "\e145";
}
.glyphicon-pushpin:before {
  content: "\e146";
}
.glyphicon-usd:before {
  content: "\e148";
}
.glyphicon-gbp:before {
  content: "\e149";
}
.glyphicon-sort:before {
  content: "\e150";
}
.glyphicon-sort-by-alphabet:before {
  content: "\e151";
}
.glyphicon-sort-by-alphabet-alt:before {
  content: "\e152";
}
.glyphicon-sort-by-order:before {
  content: "\e153";
}
.glyphicon-sort-by-order-alt:before {
  content: "\e154";
}
.glyphicon-sort-by-attributes:before {
  content: "\e155";
}
.glyphicon-sort-by-attributes-alt:before {
  content: "\e156";
}
.glyphicon-unchecked:before {
  content: "\e157";
}
.glyphicon-expand:before {
  content: "\e158";
}
.glyphicon-collapse-down:before {
  content: "\e159";
}
.glyphicon-collapse-up:before {
  content: "\e160";
}
.glyphicon-log-in:before {
  content: "\e161";
}
.glyphicon-flash:before {
  content: "\e162";
}
.glyphicon-log-out:before {
  content: "\e163";
}
.glyphicon-new-window:before {
  content: "\e164";
}
.glyphicon-record:before {
  content: "\e165";
}
.glyphicon-save:before {
  content: "\e166";
}
.glyphicon-open:before {
  content: "\e167";
}
.glyphicon-saved:before {
  content: "\e168";
}
.glyphicon-import:before {
  content: "\e169";
}
.glyphicon-export:before {
  content: "\e170";
}
.glyphicon-send:before {
  content: "\e171";
}
.glyphicon-floppy-disk:before {
  content: "\e172";
}
.glyphicon-floppy-saved:before {
  content: "\e173";
}
.glyphicon-floppy-remove:before {
  content: "\e174";
}
.glyphicon-floppy-save:before {
  content: "\e175";
}
.glyphicon-floppy-open:before {
  content: "\e176";
}
.glyphicon-credit-card:before {
  content: "\e177";
}
.glyphicon-transfer:before {
  content: "\e178";
}
.glyphicon-cutlery:before {
  content: "\e179";
}
.glyphicon-header:before {
  content: "\e180";
}
.glyphicon-compressed:before {
  content: "\e181";
}
.glyphicon-earphone:before {
  content: "\e182";
}
.glyphicon-phone-alt:before {
  content: "\e183";
}
.glyphicon-tower:before {
  content: "\e184";
}
.glyphicon-stats:before {
  content: "\e185";
}
.glyphicon-sd-video:before {
  content: "\e186";
}
.glyphicon-hd-video:before {
  content: "\e187";
}
.glyphicon-subtitles:before {
  content: "\e188";
}
.glyphicon-sound-stereo:before {
  content: "\e189";
}
.glyphicon-sound-dolby:before {
  content: "\e190";
}
.glyphicon-sound-5-1:before {
  content: "\e191";
}
.glyphicon-sound-6-1:before {
  content: "\e192";
}
.glyphicon-sound-7-1:before {
  content: "\e193";
}
.glyphicon-copyright-mark:before {
  content: "\e194";
}
.glyphicon-registration-mark:before {
  content: "\e195";
}
.glyphicon-cloud-download:before {
  content: "\e197";
}
.glyphicon-cloud-upload:before {
  content: "\e198";
}
.glyphicon-tree-conifer:before {
  content: "\e199";
}
.glyphicon-tree-deciduous:before {
  content: "\e200";
}
.glyphicon-cd:before {
  content: "\e201";
}
.glyphicon-save-file:before {
  content: "\e202";
}
.glyphicon-open-file:before {
  content: "\e203";
}
.glyphicon-level-up:before {
  content: "\e204";
}
.glyphicon-copy:before {
  content: "\e205";
}
.glyphicon-paste:before {
  content: "\e206";
}
.glyphicon-alert:before {
  content: "\e209";
}
.glyphicon-equalizer:before {
  content: "\e210";
}
.glyphicon-king:before {
  content: "\e211";
}
.glyphicon-queen:before {
  content: "\e212";
}
.glyphicon-pawn:before {
  content: "\e213";
}
.glyphicon-bishop:before {
  content: "\e214";
}
.glyphicon-knight:before {
  content: "\e215";
}
.glyphicon-baby-formula:before {
  content: "\e216";
}
.glyphicon-tent:before {
  content: "\26fa";
}
.glyphicon-blackboard:before {
  content: "\e218";
}
.glyphicon-bed:before {
  content: "\e219";
}
.glyphicon-apple:before {
  content: "\f8ff";
}
.glyphicon-erase:before {
  content: "\e221";
}
.glyphicon-hourglass:before {
  content: "\231b";
}
.glyphicon-lamp:before {
  content: "\e223";
}
.glyphicon-duplicate:before {
  content: "\e224";
}
.glyphicon-piggy-bank:before {
  content: "\e225";
}
.glyphicon-scissors:before {
  content: "\e226";
}
.glyphicon-bitcoin:before {
  content: "\e227";
}
.glyphicon-btc:before {
  content: "\e227";
}
.glyphicon-xbt:before {
  content: "\e227";
}
.glyphicon-yen:before {
  content: "\00a5";
}
.glyphicon-jpy:before {
  content: "\00a5";
}
.glyphicon-ruble:before {
  content: "\20bd";
}
.glyphicon-rub:before {
  content: "\20bd";
}
.glyphicon-scale:before {
  content: "\e230";
}
.glyphicon-ice-lolly:before {
  content: "\e231";
}
.glyphicon-ice-lolly-tasted:before {
  content: "\e232";
}
.glyphicon-education:before {
  content: "\e233";
}
.glyphicon-option-horizontal:before {
  content: "\e234";
}
.glyphicon-option-vertical:before {
  content: "\e235";
}
.glyphicon-menu-hamburger:before {
  content: "\e236";
}
.glyphicon-modal-window:before {
  content: "\e237";
}
.glyphicon-oil:before {
  content: "\e238";
}
.glyphicon-grain:before {
  content: "\e239";
}
.glyphicon-sunglasses:before {
  content: "\e240";
}
.glyphicon-text-size:before {
  content: "\e241";
}
.glyphicon-text-color:before {
  content: "\e242";
}
.glyphicon-text-background:before {
  content: "\e243";
}
.glyphicon-object-align-top:before {
  content: "\e244";
}
.glyphicon-object-align-bottom:before {
  content: "\e245";
}
.glyphicon-object-align-horizontal:before {
  content: "\e246";
}
.glyphicon-object-align-left:before {
  content: "\e247";
}
.glyphicon-object-align-vertical:before {
  content: "\e248";
}
.glyphicon-object-align-right:before {
  content: "\e249";
}
.glyphicon-triangle-right:before {
  content: "\e250";
}
.glyphicon-triangle-left:before {
  content: "\e251";
}
.glyphicon-triangle-bottom:before {
  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 */
    </style>


<style type="text/css">
/* Overrides of notebook CSS for static HTML export */
body {
  overflow: visible;
  padding: 8px;
}

div#notebook {
  overflow: visible;
  border-top: none;
}@media print {
  div.cell {
    display: block;
    page-break-inside: avoid;
  } 
  div.output_wrapper { 
    display: block;
    page-break-inside: avoid; 
  }
  div.output { 
    display: block;
    page-break-inside: avoid; 
  }
}
</style>

<!-- Custom stylesheet, it must be in the same directory as the html file -->
<link rel="stylesheet" href="custom.css">

<!-- Loading mathjax macro -->
<!-- Load mathjax -->
    <script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/latest.js?config=TeX-AMS_HTML"></script>
    <!-- MathJax configuration -->
    <script type="text/x-mathjax-config">
    MathJax.Hub.Config({
        tex2jax: {
            inlineMath: [ ['$','$'], ["\\(","\\)"] ],
            displayMath: [ ['$$','$$'], ["\\[","\\]"] ],
            processEscapes: true,
            processEnvironments: true
        },
        // Center justify equations in code and markdown cells. Elsewhere
        // we use CSS to left justify single line equations in code cells.
        displayAlign: 'center',
        "HTML-CSS": {
            styles: {'.MathJax_Display': {"margin": 0}},
            linebreaks: { automatic: true }
        }
    });
    </script>
    <!-- End of mathjax configuration --></head>
    <script async defer src="https://buttons.github.io/buttons.js"></script>
    <link rel="stylesheet" type="text/css" media="screen" href="/data-science/assets/css/style.css?v=9033ce03a74e40fe7a9f1cd464f761ff7c5f4711">
    <style>
        #project_star {
            color: #fff;
            font-size: 16px;
            font-weight: 300;
            background: none;
         }
    </style>

    <div id="header_wrap" class="outer">
        <header class="inner">
          <a id="forkme_banner" href="https://github.com/tonio73/data-science">View on GitHub</a>

          <h1 id="project_title"><a href="/data-science">data-science</a></h1>
          <h2 id="project_tagline">Notebooks and Python about data science</h2>
          <h5 id="project_star">If you like this project please add your <a class="github-button" href="https://github.com/tonio73/data-science" data-icon="octicon-star" aria-label="Star tonio73/data-science on GitHub">Star</a>
          </h5>
        </header>
    </div>
    
    <div id="main_content_wrap" class="outer">
      <section id="main_content">
        
<body>
  <div tabindex="-1" id="notebook" class="border-box-sizing">
    <div class="container" id="notebook-container">

<div class="cell border-box-sizing text_cell rendered"><div class="prompt input_prompt">
</div><div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<h1 id="Linear-regression-estimate-quality-(bivariate-with-Gaussian-noise)">Linear regression estimate quality (bivariate with Gaussian noise)<a class="anchor-link" href="#Linear-regression-estimate-quality-(bivariate-with-Gaussian-noise)">&#182;</a></h1><p>Up to now, the regression models with <a href="LinearRegressionUnivariate.ipynb">1</a> or <a href="LinearRegressionBivariate.ipynb">2</a> features were based on a infinite length dataset. As a consequence, all estimates were (almost) perfect.</p>
<p>In a given "real life" application, the dataset might be limited for many reasons like:</p>
<ul>
<li>the data collect is slow (low frequency) and it has started recently</li>
<li>the phenomena to explain is not that stable (stationary), and quasi stationarity time interval corresponds to a small dataset</li>
</ul>
<p>Data analysis and modeling is possible still, but then we must take into account for variability</p>
<h3 id="Learning-goals">Learning goals<a class="anchor-link" href="#Learning-goals">&#182;</a></h3><ul>
<li>Learn about the Gaussian linear model</li>
<li>Show the impact of reduced length dataset on estimate quality (bias, variance)</li>
<li><strong>Theory</strong> and experiments using small length training datasets</li>
<li><strong>Confidence intervals</strong> on the estimates </li>
</ul>
<h3 id="References">References<a class="anchor-link" href="#References">&#182;</a></h3><ul>
<li>Lectures notes on ordinary least squares, Telecom Paris, François Portier and Anne Sabourin (Unpublished)</li>
<li>High-Dimensional Statistics, chapter 2 : Fixed Design linear regression, <a href="https://ocw.mit.edu/courses/mathematics/18-s997-high-dimensional-statistics-spring-2015/lecture-notes/MIT18_S997S15_Chapter2.pdf">MIT 18.S997 2015</a></li>
</ul>

</div>
</div>
</div>
<div class="cell border-box-sizing code_cell rendered">
<div class="input">
<div class="prompt input_prompt">In&nbsp;[1]:</div>
<div class="inner_cell">
    <div class="input_area">
<div class=" highlight hl-ipython3"><pre><span></span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
<span class="kn">from</span> <span class="nn">sklearn</span> <span class="k">import</span> <span class="n">metrics</span>
<span class="kn">from</span> <span class="nn">sklearn.preprocessing</span> <span class="k">import</span> <span class="n">normalize</span> <span class="k">as</span> <span class="n">skNormalize</span>
<span class="kn">import</span> <span class="nn">pandas</span> <span class="k">as</span> <span class="nn">pd</span>
<span class="kn">import</span> <span class="nn">math</span>
<span class="kn">import</span> <span class="nn">scipy.stats</span> <span class="k">as</span> <span class="nn">stats</span>
<span class="kn">import</span> <span class="nn">seaborn</span> <span class="k">as</span> <span class="nn">sns</span>
</pre></div>

    </div>
</div>
</div>

</div>
<div class="cell border-box-sizing text_cell rendered"><div class="prompt input_prompt">
</div><div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<h2 id="Helpers">Helpers<a class="anchor-link" href="#Helpers">&#182;</a></h2>
</div>
</div>
</div>
<div class="cell border-box-sizing code_cell rendered">
<div class="input">
<div class="prompt input_prompt">In&nbsp;[2]:</div>
<div class="inner_cell">
    <div class="input_area">
<div class=" highlight hl-ipython3"><pre><span></span><span class="k">def</span> <span class="nf">plotHistParams</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">label</span><span class="p">,</span> <span class="n">ax</span><span class="p">,</span> <span class="n">span</span><span class="p">,</span> <span class="n">nBins</span> <span class="o">=</span> <span class="mi">100</span><span class="p">,</span> <span class="n">pdfRefX</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">pdfRefY</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
    <span class="sd">&quot;&quot;&quot;Plot histogram x, compute &quot;&quot;&quot;</span>
    <span class="n">ax</span><span class="o">.</span><span class="n">hist</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">bins</span><span class="o">=</span><span class="n">nBins</span><span class="p">,</span> <span class="n">density</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="nb">range</span><span class="o">=</span><span class="n">span</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s1">&#39;histogram&#39;</span><span class="p">)</span>
    <span class="n">mu</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
    <span class="n">x_c</span> <span class="o">=</span> <span class="n">x</span> <span class="o">-</span> <span class="n">mu</span>
    <span class="n">ax</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s1">&#39;</span><span class="si">%s</span><span class="se">\n</span><span class="s1">$\mu$=</span><span class="si">%.3f</span><span class="s1">, $\sigma^2$=</span><span class="si">%.3f</span><span class="s1">&#39;</span> <span class="o">%</span> <span class="p">(</span><span class="n">label</span><span class="p">,</span> <span class="n">mu</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">x_c</span><span class="p">,</span><span class="n">x_c</span><span class="p">)</span> <span class="o">/</span> <span class="nb">len</span><span class="p">(</span><span class="n">x</span><span class="p">)))</span>
    <span class="k">if</span> <span class="ow">not</span> <span class="n">pdfRefX</span> <span class="ow">is</span> <span class="kc">None</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">pdfRefX</span><span class="p">,</span> <span class="n">pdfRefY</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s1">&#39;ref&#39;</span><span class="p">)</span>
        <span class="n">ax</span><span class="o">.</span><span class="n">legend</span><span class="p">()</span>
        
<span class="k">def</span> <span class="nf">plotToRef</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">ref</span><span class="p">,</span> <span class="n">ax</span><span class="p">,</span> <span class="n">title</span><span class="p">,</span> <span class="n">xLabel</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">yErr</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
    <span class="sd">&quot;&quot;&quot; Plot y and a reference (or target) value&quot;&quot;&quot;</span>
    <span class="k">if</span> <span class="n">yErr</span> <span class="ow">is</span> <span class="kc">None</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">x</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span>
    <span class="k">else</span><span class="p">:</span>
        <span class="n">ax</span><span class="o">.</span><span class="n">errorbar</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">yerr</span><span class="o">=</span><span class="n">yErr</span><span class="p">,</span> <span class="n">ecolor</span><span class="o">=</span><span class="s1">&#39;red&#39;</span><span class="p">,</span> <span class="n">capsize</span><span class="o">=</span><span class="mf">3.0</span><span class="p">)</span>
    <span class="k">if</span> <span class="n">xLabel</span><span class="p">:</span>
        <span class="n">ax</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="n">xLabel</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">x</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">((</span><span class="nb">len</span><span class="p">(</span><span class="n">x</span><span class="p">)))</span><span class="o">*</span><span class="n">ref</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.5</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s1">&#39;orange&#39;</span><span class="p">)</span>
    <span class="n">ax</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="n">title</span><span class="p">)</span>
    <span class="n">ax</span><span class="o">.</span><span class="n">grid</span><span class="p">()</span>
    
<span class="k">def</span> <span class="nf">plotHeatMap</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">classes</span><span class="p">,</span> <span class="n">title</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">fmt</span><span class="o">=</span><span class="s1">&#39;.2g&#39;</span><span class="p">,</span> <span class="n">ax</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
    <span class="sd">&quot;&quot;&quot; Fix heatmap plot from Seaborn with pyplot 3.1.0, 3.1.1</span>
<span class="sd">        https://stackoverflow.com/questions/56942670/matplotlib-seaborn-first-and-last-row-cut-in-half-of-heatmap-plot</span>
<span class="sd">    &quot;&quot;&quot;</span>
    <span class="n">ax</span> <span class="o">=</span> <span class="n">sns</span><span class="o">.</span><span class="n">heatmap</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">xticklabels</span><span class="o">=</span><span class="n">classes</span><span class="p">,</span> <span class="n">yticklabels</span><span class="o">=</span><span class="n">classes</span><span class="p">,</span> <span class="n">annot</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="n">fmt</span><span class="o">=</span><span class="n">fmt</span><span class="p">,</span> <span class="n">cmap</span><span class="o">=</span><span class="n">plt</span><span class="o">.</span><span class="n">cm</span><span class="o">.</span><span class="n">Blues</span><span class="p">,</span> <span class="n">ax</span><span class="o">=</span><span class="n">ax</span><span class="p">)</span> <span class="c1">#notation: &quot;annot&quot; not &quot;annote&quot;</span>
    <span class="n">bottom</span><span class="p">,</span> <span class="n">top</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">set_ylim</span><span class="p">(</span><span class="n">bottom</span> <span class="o">+</span> <span class="mf">0.5</span><span class="p">,</span> <span class="n">top</span> <span class="o">-</span> <span class="mf">0.5</span><span class="p">)</span>
    <span class="k">if</span> <span class="n">title</span><span class="p">:</span>
        <span class="n">ax</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="n">title</span><span class="p">)</span>
</pre></div>

    </div>
</div>
</div>

</div>
<div class="cell border-box-sizing text_cell rendered"><div class="prompt input_prompt">
</div><div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<h2 id="Model">Model<a class="anchor-link" href="#Model">&#182;</a></h2><p>We will use a linear model with Gaussian noise, also called <em>Fixed Design</em> $f_1(x) = 0.5 x_0 - 0.7 x_1 + 0.35 + \epsilon$</p>
<p>With :</p>
<ul>
<li>$x_0 \in [0, 0.5], x_1 \in [-0.5, 0.5]$ the two features (co-variables) </li>
<li>$\epsilon \sim \mathcal{N}(0, \sigma^2)$ a Gaussian distributed unknown</li>
</ul>

</div>
</div>
</div>
<div class="cell border-box-sizing code_cell rendered">
<div class="input">
<div class="prompt input_prompt">In&nbsp;[3]:</div>
<div class="inner_cell">
    <div class="input_area">
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">nFeatures</span> <span class="o">=</span> <span class="mi">2</span>
<span class="n">bLin</span> <span class="o">=</span> <span class="mf">0.35</span>
<span class="n">wLin</span> <span class="o">=</span> <span class="p">[</span><span class="mf">0.5</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.7</span><span class="p">]</span>
<span class="n">sigmaLin</span> <span class="o">=</span> <span class="mf">0.5</span>
<span class="k">def</span> <span class="nf">generateBatchLinear</span><span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="n">sigma</span><span class="o">=</span><span class="n">sigmaLin</span><span class="p">):</span>
    <span class="c1">#</span>
    <span class="n">xMin</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mi">0</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.5</span><span class="p">])</span>
    <span class="n">xMax</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mf">0.5</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">])</span>
    <span class="c1">#</span>
    <span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">uniform</span><span class="p">(</span><span class="n">xMin</span><span class="p">,</span> <span class="n">xMax</span><span class="p">,</span> <span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="mi">2</span><span class="p">))</span>
    <span class="n">yClean</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">wLin</span><span class="p">)</span> <span class="o">+</span> <span class="n">bLin</span>
    <span class="k">return</span> <span class="n">x</span><span class="p">,</span> <span class="n">yClean</span><span class="p">,</span> <span class="n">yClean</span> <span class="o">+</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">normal</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">sigma</span><span class="p">,</span> <span class="n">n</span><span class="p">)</span>
</pre></div>

    </div>
</div>
</div>

</div>
<div class="cell border-box-sizing code_cell rendered">
<div class="input">
<div class="prompt input_prompt">In&nbsp;[4]:</div>
<div class="inner_cell">
    <div class="input_area">
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">x_1000</span><span class="p">,</span> <span class="n">yClean_1000</span><span class="p">,</span> <span class="n">y_1000</span> <span class="o">=</span> <span class="n">generateBatchLinear</span><span class="p">(</span><span class="mi">1000</span><span class="p">,</span> <span class="n">sigmaLin</span><span class="p">)</span>
<span class="n">fix</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="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span> <span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">15</span><span class="p">,</span> <span class="mi">6</span><span class="p">))</span>
<span class="k">for</span> <span class="n">i</span><span class="p">,</span><span class="n">a</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">ax</span><span class="p">):</span>
    <span class="n">a</span><span class="o">.</span><span class="n">scatter</span><span class="p">(</span><span class="n">x_1000</span><span class="p">[:,</span> <span class="n">i</span><span class="p">],</span> <span class="n">y_1000</span><span class="p">)</span>
    <span class="n">a</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="s1">&#39;$x_</span><span class="si">%d</span><span class="s1">$&#39;</span> <span class="o">%</span> <span class="n">i</span><span class="p">)</span>
    <span class="n">a</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="s1">&#39;$y$&#39;</span><span class="p">);</span>
</pre></div>

    </div>
</div>
</div>

<div class="output_wrapper">
<div class="output">


<div class="output_area">

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


<div class="output_png output_subarea ">
<img src="data:image/png;base64,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
"
>
</div>

</div>

</div>
</div>

</div>
<div class="cell border-box-sizing text_cell rendered"><div class="prompt input_prompt">
</div><div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<p>With <em>a priori</em> knowledge restricted to the model to apply, i.e. Gaussian, there are five quantities to evaluate :</p>
<ul>
<li>$\hat{w}_0, \hat{w}_1$ the weights to apply to the features</li>
<li>$\hat{b}$ the intercept</li>
<li>the Gaussian noise with the mean $\hat{\mu}$, and variance (power) $\hat{\sigma}^2$  </li>
</ul>

</div>
</div>
</div>
<div class="cell border-box-sizing text_cell rendered"><div class="prompt input_prompt">
</div><div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<h2 id="Closed-form-linear-regression">Closed form linear regression<a class="anchor-link" href="#Closed-form-linear-regression">&#182;</a></h2><p>As explained in more details in previous notebook (<a href="LinearRegressionBivariate.html">HTML</a> / <a href="LinearRegressionBivariate.ipynb">Jupyter</a>, the linear regression estimates are computed in closed form by <strong>minimizing the Euclidian norm</strong> $\lVert X_m \Theta - Y \rVert_2^2$ where:</p>
<ul>
<li>$X \in \mathbb{R}^{n \times 2}$</li>
<li>$\Theta = 
\begin{bmatrix}
b \\
w_0 \\
w_1 \end{bmatrix} $</li>
<li>$X_m = 
\begin{bmatrix}
\mathbb{1}_n &amp; X \\
\end{bmatrix}$, a modified $X$ with a column of 1s to evaluate the intercept</li>
</ul>
<p>Then :  $ Y = X_m \Theta + \epsilon $</p>
<p>Leading to the closed form computation of the linear regression, assuming the matrix is invertible (or at least pseudo invertible) : 
$$\hat{\Theta} = (X_m^T X_m)^{-1} X_m^T Y$$</p>

</div>
</div>
</div>
<div class="cell border-box-sizing code_cell rendered">
<div class="input">
<div class="prompt input_prompt">In&nbsp;[5]:</div>
<div class="inner_cell">
    <div class="input_area">
<div class=" highlight hl-ipython3"><pre><span></span><span class="k">def</span> <span class="nf">xWithIntercept</span><span class="p">(</span><span class="n">x</span><span class="p">):</span>
    <span class="sd">&quot;&quot;&quot; Add a column of ones in order to compute the intercept along with coefficients related to X&quot;&quot;&quot;</span>
    <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">((</span><span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">((</span><span class="n">x</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="mi">1</span><span class="p">)),</span> <span class="n">x</span><span class="p">),</span> <span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>

<span class="n">x_m_1000</span> <span class="o">=</span> <span class="n">xWithIntercept</span><span class="p">(</span><span class="n">x_1000</span><span class="p">)</span>

<span class="k">def</span> <span class="nf">linearRegression</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">):</span>
    <span class="n">xTxInv</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">inv</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">matmul</span><span class="p">(</span><span class="n">x</span><span class="o">.</span><span class="n">T</span><span class="p">,</span> <span class="n">x</span><span class="p">))</span>
    <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">matmul</span><span class="p">(</span><span class="n">xTxInv</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">matmul</span><span class="p">(</span><span class="n">x</span><span class="o">.</span><span class="n">T</span><span class="p">,</span> <span class="n">y</span><span class="p">))</span>

<span class="n">thetaEst0</span> <span class="o">=</span> <span class="n">linearRegression</span><span class="p">(</span><span class="n">x_m_1000</span><span class="p">,</span> <span class="n">yClean_1000</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Estimation on clean y : Intercept=</span><span class="si">%.4f</span><span class="s2">, coefficients=</span><span class="si">%s</span><span class="s2">&quot;</span> <span class="o">%</span> <span class="p">(</span><span class="n">thetaEst0</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">thetaEst0</span><span class="p">[</span><span class="mi">1</span><span class="p">:]))</span>

<span class="n">thetaEst_1000</span> <span class="o">=</span> <span class="n">linearRegression</span><span class="p">(</span><span class="n">x_m_1000</span><span class="p">,</span> <span class="n">y_1000</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Estimation on noisy y : Intercept=</span><span class="si">%.4f</span><span class="s2">, coefficients=</span><span class="si">%s</span><span class="s2">&quot;</span> <span class="o">%</span> <span class="p">(</span><span class="n">thetaEst_1000</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">thetaEst_1000</span><span class="p">[</span><span class="mi">1</span><span class="p">:]))</span>
</pre></div>

    </div>
</div>
</div>

<div class="output_wrapper">
<div class="output">


<div class="output_area">

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


<div class="output_subarea output_stream output_stdout output_text">
<pre>Estimation on clean y : Intercept=0.3500, coefficients=[ 0.5 -0.7]
Estimation on noisy y : Intercept=0.3715, coefficients=[ 0.45111285 -0.67426465]
</pre>
</div>
</div>

</div>
</div>

</div>
<div class="cell border-box-sizing text_cell rendered"><div class="prompt input_prompt">
</div><div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<h2 id="Noise-estimation">Noise estimation<a class="anchor-link" href="#Noise-estimation">&#182;</a></h2><p>The noise mean is simply computed as the mean of $Y - X_m \Theta$. It is expected to be 0 in our case.</p>
<p>Given a noise mean equal to 0, the <strong>unbiased noise variance</strong> estimation is then : 
$$ \hat{\sigma}^2 = \frac{1}{n-p-1} \Vert Y - X_m \hat{\Theta} \Vert_2^2$$</p>
<p>with:</p>
<ul>
<li>$n$ the number of samples in our set</li>
<li>$p$ the rank of the matrix $X^TX$, equals to 2 in our example</li>
</ul>

</div>
</div>
</div>
<div class="cell border-box-sizing code_cell rendered">
<div class="input">
<div class="prompt input_prompt">In&nbsp;[6]:</div>
<div class="inner_cell">
    <div class="input_area">
<div class=" highlight hl-ipython3"><pre><span></span><span class="k">def</span> <span class="nf">noiseEstimation</span><span class="p">(</span><span class="n">yEst</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">p</span><span class="p">):</span>
    <span class="sd">&quot;&quot;&quot; Unbiased noise mean and variance estimation &quot;&quot;&quot;</span>
    <span class="n">epsilonEst</span> <span class="o">=</span> <span class="n">y</span> <span class="o">-</span> <span class="n">yEst</span>
    <span class="n">mu</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">epsilonEst</span><span class="p">)</span>
    <span class="n">epsilonEst_c</span> <span class="o">=</span> <span class="n">epsilonEst</span> <span class="o">-</span> <span class="n">mu</span>
    <span class="n">var</span> <span class="o">=</span> <span class="mi">1</span> <span class="o">/</span> <span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">y</span><span class="p">)</span> <span class="o">-</span> <span class="n">p</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">epsilonEst_c</span><span class="p">,</span> <span class="n">epsilonEst_c</span><span class="p">)</span>
    <span class="k">return</span> <span class="n">mu</span><span class="p">,</span> <span class="n">var</span>

<span class="n">noiseMu_1000</span><span class="p">,</span> <span class="n">noiseVar_1000</span> <span class="o">=</span> <span class="n">noiseEstimation</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">matmul</span><span class="p">(</span><span class="n">x_m_1000</span><span class="p">,</span> <span class="n">thetaEst_1000</span><span class="p">),</span> <span class="n">y_1000</span><span class="p">,</span> <span class="n">nFeatures</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="s1">&#39;Estimated noise mean=</span><span class="si">%.2e</span><span class="s1"> and std deviation=</span><span class="si">%.4f</span><span class="s1">&#39;</span> <span class="o">%</span> <span class="p">(</span><span class="n">noiseMu_1000</span><span class="p">,</span> <span class="n">math</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">noiseVar_1000</span><span class="p">)))</span>
</pre></div>

    </div>
</div>
</div>

<div class="output_wrapper">
<div class="output">


<div class="output_area">

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


<div class="output_subarea output_stream output_stdout output_text">
<pre>Estimated noise mean=-1.82e-16 and std deviation=0.5051
</pre>
</div>
</div>

</div>
</div>

</div>
<div class="cell border-box-sizing text_cell rendered"><div class="prompt input_prompt">
</div><div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<h3 id="Other-important-theorerical-results-on-the-Gaussian-linear-model">Other important theorerical results on the Gaussian linear model<a class="anchor-link" href="#Other-important-theorerical-results-on-the-Gaussian-linear-model">&#182;</a></h3><p>Given $\hat{\Theta_{n,k}}$ the component $k$ of the estimate of $\Theta$ on $n$ samples, and $\Theta_k$ actual value of this component:</p>
<ul>
<li><p>Lemma 1: variations on the estimated components of $\Theta$ are Gaussian distributed
$$\left(\hat{\Theta_n} - \Theta \right) \sim \mathcal{N}\left( 0, (X^T X)^{-1} \sigma^2 \right)$$</p>
</li>
<li><p>Lemma 2: the ratio of the estimated $\hat{\sigma}^2$ to the true (unknown) $\sigma$ is $\chi^2$ distributed
$$\frac{\hat{\sigma_n}^2(n-p-1)}{\sigma^2} \sim  \chi^2(n-p-1)$$</p>
<ul>
<li>$\chi^2(n-p-1)$ is a Chi-2 law with n-p-1 degrees of freedom</li>
</ul>
</li>
</ul>
<ul>
<li>Lemma 3: the ratio of the variation of the coefficient over the estimated $\hat{\sigma}$ follows a Student law
$$\sqrt{\frac{n}{\hat{\sigma_n}^2 S_{n,k}}} (\hat{\Theta_{n,k}} - \Theta_k) \sim \mathcal{T}_{n-p-1}$$ <ul>
<li>$\mathcal{T}_{n-p-1}$ is the Student law with (n-p-1) degrees of freedom</li>
<li>$S_{n,k} = n (X^TX)^{-1}_{k,k}$ (select element k,k of the Gram matrix)</li>
</ul>
</li>
</ul>

</div>
</div>
</div>
<div class="cell border-box-sizing code_cell rendered">
<div class="input">
<div class="prompt input_prompt">In&nbsp;[7]:</div>
<div class="inner_cell">
    <div class="input_area">
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">xx</span> <span class="o">=</span> <span class="p">[</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="mi">16</span><span class="p">),</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="o">-</span><span class="mi">5</span><span class="p">,</span> <span class="mi">5</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="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">12</span><span class="p">,</span> <span class="mi">5</span><span class="p">))</span>
<span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">a</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">ax</span><span class="p">):</span>
    <span class="n">a</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">xx</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="n">stats</span><span class="o">.</span><span class="n">norm</span><span class="o">.</span><span class="n">pdf</span><span class="p">(</span><span class="n">xx</span><span class="p">[</span><span class="n">i</span><span class="p">]),</span> <span class="n">label</span><span class="o">=</span><span class="s1">&#39;$\mathcal</span><span class="si">{N}</span><span class="s1">(0,1)$&#39;</span><span class="p">)</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</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="mi">4</span><span class="p">,</span> <span class="mi">8</span><span class="p">]:</span>
    <span class="n">label0</span> <span class="o">=</span> <span class="s1">&#39;$\chi^2(</span><span class="si">%d</span><span class="s1">)$&#39;</span> <span class="o">%</span> <span class="n">i</span>
    <span class="n">ax</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">xx</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">stats</span><span class="o">.</span><span class="n">chi2</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="o">.</span><span class="n">pdf</span><span class="p">(</span><span class="n">xx</span><span class="p">[</span><span class="mi">0</span><span class="p">]),</span> <span class="n">label</span><span class="o">=</span><span class="n">label0</span><span class="p">)</span>
    <span class="n">label1</span> <span class="o">=</span> <span class="s1">&#39;$\mathcal</span><span class="si">{T}</span><span class="s1">(</span><span class="si">%d</span><span class="s1">)$&#39;</span> <span class="o">%</span> <span class="n">i</span>
    <span class="n">ax</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">xx</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">stats</span><span class="o">.</span><span class="n">t</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="o">.</span><span class="n">pdf</span><span class="p">(</span><span class="n">xx</span><span class="p">[</span><span class="mi">1</span><span class="p">]),</span> <span class="n">label</span><span class="o">=</span><span class="n">label1</span><span class="p">)</span>
<span class="k">for</span> <span class="n">a</span> <span class="ow">in</span> <span class="n">ax</span><span class="p">:</span>
    <span class="n">a</span><span class="o">.</span><span class="n">legend</span><span class="p">()</span>
    <span class="n">a</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="s1">&#39;Density (PDF)&#39;</span><span class="p">)</span>
    <span class="n">a</span><span class="o">.</span><span class="n">grid</span><span class="p">()</span>
<span class="n">ax</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s1">&#39;$\chi^2$ distributions vs. Normal&#39;</span><span class="p">)</span>
<span class="n">ax</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s1">&#39;$\mathcal</span><span class="si">{T}</span><span class="s1">$ distributions vs. Normal&#39;</span><span class="p">);</span>
</pre></div>

    </div>
</div>
</div>

<div class="output_wrapper">
<div class="output">


<div class="output_area">

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


<div class="output_png output_subarea ">
<img src="data:image/png;base64,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
"
>
</div>

</div>

</div>
</div>

</div>
<div class="cell border-box-sizing text_cell rendered"><div class="prompt input_prompt">
</div><div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<p>As shown on right hand figure above, the Student law quickly converges to the Gaussian law when the degrees of freedom increase.</p>

</div>
</div>
</div>
<div class="cell border-box-sizing text_cell rendered"><div class="prompt input_prompt">
</div><div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<p>Application of Lemma 1:</p>

</div>
</div>
</div>
<div class="cell border-box-sizing code_cell rendered">
<div class="input">
<div class="prompt input_prompt">In&nbsp;[8]:</div>
<div class="inner_cell">
    <div class="input_area">
<div class=" highlight hl-ipython3"><pre><span></span><span class="k">def</span> <span class="nf">weightCovariance</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">sigma</span><span class="p">):</span>
    <span class="sd">&quot;&quot;&quot; Compute weight covariance as per Lemma 1&quot;&quot;&quot;</span>
    <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">inv</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">matmul</span><span class="p">(</span><span class="n">x</span><span class="o">.</span><span class="n">T</span><span class="p">,</span> <span class="n">x</span><span class="p">))</span> <span class="o">*</span> <span class="n">sigma</span><span class="o">**</span><span class="mi">2</span>

<span class="n">wCovTheo_1000</span> <span class="o">=</span> <span class="n">weightCovariance</span><span class="p">(</span><span class="n">x_m_1000</span><span class="p">,</span> <span class="n">sigmaLin</span><span class="p">)</span> 
<span class="n">plotHeatMap</span><span class="p">(</span><span class="n">wCovTheo_1000</span><span class="p">,</span> <span class="p">(</span><span class="s1">&#39;b&#39;</span><span class="p">,</span><span class="s1">&#39;$w_0$&#39;</span><span class="p">,</span> <span class="s1">&#39;$w_1$&#39;</span><span class="p">),</span> <span class="n">title</span><span class="o">=</span><span class="s1">&#39;Correlation matrix&#39;</span><span class="p">,</span> <span class="n">fmt</span><span class="o">=</span><span class="s1">&#39;.2e&#39;</span><span class="p">)</span>
</pre></div>

    </div>
</div>
</div>

<div class="output_wrapper">
<div class="output">


<div class="output_area">

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


<div class="output_png output_subarea ">
<img src="data:image/png;base64,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
"
>
</div>

</div>

</div>
</div>

</div>
<div class="cell border-box-sizing text_cell rendered"><div class="prompt input_prompt">
</div><div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<h2 id="Sweep-over-dataset-length">Sweep over dataset length<a class="anchor-link" href="#Sweep-over-dataset-length">&#182;</a></h2><p>In a first move, let's sweep over the length of the dataset from 4 to 1000 items and estimate the linear regression and the noise parameters.</p>
<p>Note: the minimum value of n is:  $\min_{n \in \mathbb{N}} (n-p-1 &gt; 0) = 4$</p>

</div>
</div>
</div>
<div class="cell border-box-sizing code_cell rendered">
<div class="input">
<div class="prompt input_prompt">In&nbsp;[9]:</div>
<div class="inner_cell">
    <div class="input_area">
<div class=" highlight hl-ipython3"><pre><span></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="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">16</span><span class="p">,</span> <span class="mi">10</span><span class="p">),</span> <span class="n">subplot_kw</span><span class="o">=</span><span class="p">{</span><span class="s1">&#39;xscale&#39;</span><span class="p">:</span><span class="s1">&#39;log&#39;</span><span class="p">})</span>

<span class="n">regressions</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">n</span> <span class="ow">in</span> <span class="p">[</span><span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">10</span><span class="p">,</span> <span class="mi">20</span><span class="p">,</span> <span class="mi">40</span><span class="p">,</span> <span class="mi">100</span><span class="p">,</span> <span class="mi">200</span><span class="p">,</span> <span class="mi">500</span><span class="p">,</span> <span class="mi">1000</span><span class="p">]:</span>
    <span class="n">x_m_n</span> <span class="o">=</span> <span class="n">x_m_1000</span><span class="p">[:</span><span class="n">n</span><span class="p">]</span>
    <span class="n">y_n</span> <span class="o">=</span> <span class="n">y_1000</span><span class="p">[:</span><span class="n">n</span><span class="p">]</span>
    <span class="n">thetaEst</span> <span class="o">=</span> <span class="n">linearRegression</span><span class="p">(</span><span class="n">x_m_n</span><span class="p">,</span> <span class="n">y_n</span><span class="p">)</span>
    <span class="n">noiseMu</span><span class="p">,</span> <span class="n">noiseVar</span> <span class="o">=</span> <span class="n">noiseEstimation</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">matmul</span><span class="p">(</span><span class="n">x_m_n</span><span class="p">,</span> <span class="n">thetaEst</span><span class="p">),</span> <span class="n">y_n</span><span class="p">,</span> <span class="n">nFeatures</span><span class="p">)</span>
    <span class="n">regressions</span><span class="o">.</span><span class="n">append</span><span class="p">([</span><span class="n">n</span><span class="p">,</span> <span class="n">thetaEst</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">thetaEst</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">thetaEst</span><span class="p">[</span><span class="mi">2</span><span class="p">],</span> <span class="n">noiseMu</span><span class="p">,</span> <span class="n">noiseVar</span><span class="p">])</span>

<span class="n">dfSweepN</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">DataFrame</span><span class="p">(</span><span class="n">regressions</span><span class="p">,</span> <span class="n">columns</span><span class="o">=</span><span class="p">(</span><span class="s1">&#39;n&#39;</span><span class="p">,</span> <span class="s1">&#39;b&#39;</span><span class="p">,</span> <span class="s1">&#39;w0&#39;</span><span class="p">,</span><span class="s1">&#39;w1&#39;</span><span class="p">,</span> <span class="s1">&#39;noise mean&#39;</span><span class="p">,</span> <span class="s1">&#39;noise var&#39;</span><span class="p">))</span>
<span class="n">plotToRef</span><span class="p">(</span><span class="n">dfSweepN</span><span class="p">[</span><span class="s1">&#39;n&#39;</span><span class="p">],</span> <span class="n">dfSweepN</span><span class="p">[</span><span class="s1">&#39;b&#39;</span><span class="p">],</span> <span class="n">bLin</span><span class="p">,</span> <span class="n">ax</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span><span class="mi">0</span><span class="p">],</span> <span class="s1">&#39;$\hat</span><span class="si">{b}</span><span class="s1">$&#39;</span><span class="p">)</span>
<span class="n">plotToRef</span><span class="p">(</span><span class="n">dfSweepN</span><span class="p">[</span><span class="s1">&#39;n&#39;</span><span class="p">],</span> <span class="n">dfSweepN</span><span class="p">[</span><span class="s1">&#39;noise var&#39;</span><span class="p">],</span> <span class="n">sigmaLin</span><span class="o">**</span><span class="mi">2</span><span class="p">,</span> <span class="n">ax</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span><span class="mi">0</span><span class="p">],</span> <span class="s1">&#39;$\hat{\sigma}^2$&#39;</span><span class="p">,</span> <span class="n">xLabel</span><span class="o">=</span><span class="s1">&#39;n&#39;</span><span class="p">)</span>
<span class="n">plotToRef</span><span class="p">(</span><span class="n">dfSweepN</span><span class="p">[</span><span class="s1">&#39;n&#39;</span><span class="p">],</span> <span class="n">dfSweepN</span><span class="p">[</span><span class="s1">&#39;w0&#39;</span><span class="p">],</span> <span class="n">wLin</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">ax</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span><span class="mi">1</span><span class="p">],</span> <span class="s1">&#39;$\hat</span><span class="si">{w_0}</span><span class="s1">$&#39;</span><span class="p">)</span>
<span class="n">plotToRef</span><span class="p">(</span><span class="n">dfSweepN</span><span class="p">[</span><span class="s1">&#39;n&#39;</span><span class="p">],</span> <span class="n">dfSweepN</span><span class="p">[</span><span class="s1">&#39;w1&#39;</span><span class="p">],</span> <span class="n">wLin</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">ax</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span><span class="mi">1</span><span class="p">],</span> <span class="s1">&#39;$\hat</span><span class="si">{w_1}</span><span class="s1">$&#39;</span><span class="p">,</span> <span class="n">xLabel</span><span class="o">=</span><span class="s1">&#39;n&#39;</span><span class="p">);</span>
</pre></div>

    </div>
</div>
</div>

<div class="output_wrapper">
<div class="output">


<div class="output_area">

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


<div class="output_png output_subarea ">
<img src="data:image/png;base64,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
"
>
</div>

</div>

</div>
</div>

</div>
<div class="cell border-box-sizing text_cell rendered"><div class="prompt input_prompt">
</div><div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<h2 id="Distributions-with-$n-=-5$,-fixed-design">Distributions with $n = 5$, fixed design<a class="anchor-link" href="#Distributions-with-$n-=-5$,-fixed-design">&#182;</a></h2><p>In this set of experiments, noise samples are drawn at each experiment. The $x_i$ are known and fixed.</p>
<p>Let's draw many experiences with n = 5 in order to plot the histograms of the estimators</p>

</div>
</div>
</div>
<div class="cell border-box-sizing code_cell rendered">
<div class="input">
<div class="prompt input_prompt">In&nbsp;[10]:</div>
<div class="inner_cell">
    <div class="input_area">
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">regressions</span> <span class="o">=</span> <span class="p">[]</span>
<span class="n">n</span> <span class="o">=</span> <span class="mi">5</span>
<span class="n">x_m_5</span> <span class="o">=</span> <span class="n">x_m_1000</span><span class="p">[:</span><span class="n">n</span><span class="p">]</span>
<span class="n">yClean_5</span> <span class="o">=</span> <span class="n">yClean_1000</span><span class="p">[:</span><span class="n">n</span><span class="p">]</span>
<span class="k">for</span> <span class="n">l</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">50000</span><span class="p">):</span>
    <span class="c1"># Draw noise</span>
    <span class="n">y_5</span> <span class="o">=</span> <span class="n">yClean_5</span> <span class="o">+</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">normal</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">sigmaLin</span><span class="p">,</span> <span class="n">n</span><span class="p">)</span>
    <span class="n">thetaEst</span> <span class="o">=</span> <span class="n">linearRegression</span><span class="p">(</span><span class="n">x_m_5</span><span class="p">,</span> <span class="n">y_5</span><span class="p">)</span>
    <span class="n">noiseMu</span><span class="p">,</span> <span class="n">noiseVar</span> <span class="o">=</span> <span class="n">noiseEstimation</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">matmul</span><span class="p">(</span><span class="n">x_m_5</span><span class="p">,</span> <span class="n">thetaEst</span><span class="p">),</span> <span class="n">y_5</span><span class="p">,</span> <span class="n">nFeatures</span><span class="p">)</span>
    <span class="n">regressions</span><span class="o">.</span><span class="n">append</span><span class="p">([</span><span class="n">thetaEst</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">thetaEst</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">thetaEst</span><span class="p">[</span><span class="mi">2</span><span class="p">],</span> <span class="n">noiseMu</span><span class="p">,</span> <span class="n">noiseVar</span><span class="p">])</span>
    
<span class="n">df_5</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">DataFrame</span><span class="p">(</span><span class="n">regressions</span><span class="p">,</span> <span class="n">columns</span><span class="o">=</span><span class="p">(</span><span class="s1">&#39;b&#39;</span><span class="p">,</span> <span class="s1">&#39;w0&#39;</span><span class="p">,</span><span class="s1">&#39;w1&#39;</span><span class="p">,</span> <span class="s1">&#39;noise mean&#39;</span><span class="p">,</span> <span class="s1">&#39;noise var&#39;</span><span class="p">))</span>
</pre></div>

    </div>
</div>
</div>

</div>
<div class="cell border-box-sizing code_cell rendered">
<div class="input">
<div class="prompt input_prompt">In&nbsp;[11]:</div>
<div class="inner_cell">
    <div class="input_area">
<div class=" highlight hl-ipython3"><pre><span></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="mi">1</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">16</span><span class="p">,</span> <span class="mi">5</span><span class="p">))</span>
<span class="n">plotHistParams</span><span class="p">(</span><span class="n">df_5</span><span class="p">[</span><span class="s1">&#39;b&#39;</span><span class="p">]</span>  <span class="o">-</span> <span class="n">bLin</span><span class="p">,</span>    <span class="s1">&#39;$\hat</span><span class="si">{b}</span><span class="s1"> - b$&#39;</span><span class="p">,</span>     <span class="n">ax</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="p">[</span><span class="o">-</span><span class="mi">3</span><span class="p">,</span> <span class="mi">3</span><span class="p">])</span>
<span class="n">plotHistParams</span><span class="p">(</span><span class="n">df_5</span><span class="p">[</span><span class="s1">&#39;w0&#39;</span><span class="p">]</span> <span class="o">-</span> <span class="n">wLin</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="s1">&#39;$\hat</span><span class="si">{w_0}</span><span class="s1"> - w_0$&#39;</span><span class="p">,</span> <span class="n">ax</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="p">[</span><span class="o">-</span><span class="mi">5</span><span class="p">,</span> <span class="mi">5</span><span class="p">])</span>
<span class="n">plotHistParams</span><span class="p">(</span><span class="n">df_5</span><span class="p">[</span><span class="s1">&#39;w1&#39;</span><span class="p">]</span> <span class="o">-</span> <span class="n">wLin</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="s1">&#39;$\hat</span><span class="si">{w_1}</span><span class="s1"> - w_1$&#39;</span><span class="p">,</span> <span class="n">ax</span><span class="p">[</span><span class="mi">2</span><span class="p">],</span> <span class="p">[</span><span class="o">-</span><span class="mi">5</span><span class="p">,</span> <span class="mi">5</span><span class="p">])</span>

<span class="n">dFree</span> <span class="o">=</span> <span class="n">n</span> <span class="o">-</span> <span class="n">nFeatures</span> <span class="o">-</span> <span class="mi">1</span>
<span class="n">xx</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="mi">15</span><span class="p">)</span>
<span class="n">plotHistParams</span><span class="p">(</span><span class="n">df_5</span><span class="p">[</span><span class="s1">&#39;noise var&#39;</span><span class="p">]</span> <span class="o">*</span> <span class="n">dFree</span> <span class="o">/</span> <span class="n">sigmaLin</span><span class="o">**</span><span class="mi">2</span><span class="p">,</span> <span class="s1">&#39;$(n-p-1)\hat{\sigma}^2 / \sigma^2$ vs. $\chi^2(2)$&#39;</span><span class="p">,</span> 
                    <span class="n">ax</span><span class="p">[</span><span class="mi">3</span><span class="p">],</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span><span class="mi">20</span><span class="p">],</span> <span class="n">pdfRefX</span><span class="o">=</span><span class="n">xx</span><span class="p">,</span> <span class="n">pdfRefY</span><span class="o">=</span><span class="n">stats</span><span class="o">.</span><span class="n">chi2</span><span class="p">(</span><span class="n">dFree</span><span class="p">)</span><span class="o">.</span><span class="n">pdf</span><span class="p">(</span><span class="n">xx</span><span class="p">))</span>
</pre></div>

    </div>
</div>
</div>

<div class="output_wrapper">
<div class="output">


<div class="output_area">

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


<div class="output_png output_subarea ">
<img src="data:image/png;base64,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
"
>
</div>

</div>

</div>
</div>

</div>
<div class="cell border-box-sizing text_cell rendered"><div class="prompt input_prompt">
</div><div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<p>On above graph, the regression intercept $b$ and weigths ($w_0, w_1$) look like gaussian distributed and the noise variance scaled by $\frac{n-p-1}{\sigma^2}$ with n=5, p=2, is matching the expected $\chi^2(2)$ (see Lemma 2)</p>

</div>
</div>
</div>
<div class="cell border-box-sizing text_cell rendered"><div class="prompt input_prompt">
</div><div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<h4 id="Verification-of-Lemma-1">Verification of Lemma 1<a class="anchor-link" href="#Verification-of-Lemma-1">&#182;</a></h4><p>As per Lemma 1, we expect the following covariance matrix for the coefficients: 
$$\left(\hat{\Theta_n} - \Theta \right) \sim \mathcal{N}\left( 0, (X^T X)^{-1} \sigma^2 \right)$$</p>

</div>
</div>
</div>
<div class="cell border-box-sizing code_cell rendered">
<div class="input">
<div class="prompt input_prompt">In&nbsp;[12]:</div>
<div class="inner_cell">
    <div class="input_area">
<div class=" highlight hl-ipython3"><pre><span></span><span class="k">def</span> <span class="nf">autoCovariance</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">):</span>
    <span class="n">x_c</span> <span class="o">=</span> <span class="n">x</span> <span class="o">-</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
    <span class="k">return</span> <span class="mi">1</span> <span class="o">/</span> <span class="n">x</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="n">axis</span><span class="p">]</span> <span class="o">*</span>  <span class="n">np</span><span class="o">.</span><span class="n">matmul</span><span class="p">(</span><span class="n">x_c</span><span class="o">.</span><span class="n">T</span><span class="p">,</span> <span class="n">x_c</span><span class="p">)</span>

<span class="c1"># Covariance of the intercept and weights</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="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">10</span><span class="p">,</span> <span class="mi">4</span><span class="p">))</span>
<span class="n">ThetaCov_5</span> <span class="o">=</span> <span class="n">autoCovariance</span><span class="p">(</span><span class="n">df_5</span><span class="p">[[</span><span class="s1">&#39;b&#39;</span><span class="p">,</span> <span class="s1">&#39;w0&#39;</span><span class="p">,</span> <span class="s1">&#39;w1&#39;</span><span class="p">]]</span><span class="o">.</span><span class="n">values</span><span class="p">)</span>
<span class="n">plotHeatMap</span><span class="p">(</span><span class="n">ThetaCov_5</span><span class="p">,</span> <span class="p">(</span><span class="s1">&#39;b&#39;</span><span class="p">,</span><span class="s1">&#39;$w_0$&#39;</span><span class="p">,</span> <span class="s1">&#39;$w_1$&#39;</span><span class="p">),</span> <span class="n">title</span><span class="o">=</span><span class="s1">&#39;Weight covariance matrix&#39;</span><span class="p">,</span> <span class="n">ax</span><span class="o">=</span><span class="n">ax</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">fmt</span><span class="o">=</span><span class="s1">&#39;.3f&#39;</span><span class="p">);</span>

<span class="c1"># Covariance matrix based on the design matrix (X^T X)</span>
<span class="n">wCovTheo_5</span> <span class="o">=</span> <span class="n">weightCovariance</span><span class="p">(</span><span class="n">x_m_5</span><span class="p">,</span> <span class="n">sigmaLin</span><span class="p">)</span>
<span class="n">plotHeatMap</span><span class="p">(</span><span class="n">wCovTheo_5</span><span class="p">,</span> <span class="p">(</span><span class="s1">&#39;b&#39;</span><span class="p">,</span><span class="s1">&#39;$w_0$&#39;</span><span class="p">,</span> <span class="s1">&#39;$w_1$&#39;</span><span class="p">),</span> <span class="n">title</span><span class="o">=</span><span class="s1">&#39;Theoretical covariance matrix&#39;</span><span class="p">,</span> <span class="n">ax</span><span class="o">=</span><span class="n">ax</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">fmt</span><span class="o">=</span><span class="s1">&#39;.3f&#39;</span><span class="p">);</span>
</pre></div>

    </div>
</div>
</div>

<div class="output_wrapper">
<div class="output">


<div class="output_area">

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


<div class="output_png output_subarea ">
<img src="data:image/png;base64,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
"
>
</div>

</div>

</div>
</div>

</div>
<div class="cell border-box-sizing text_cell rendered"><div class="prompt input_prompt">
</div><div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<p>Covariance matrices are matching !</p>

</div>
</div>
</div>
<div class="cell border-box-sizing text_cell rendered"><div class="prompt input_prompt">
</div><div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<h4 id="Verification-of-Lemma-3">Verification of Lemma 3<a class="anchor-link" href="#Verification-of-Lemma-3">&#182;</a></h4><p>Let's now verify the law involving only the $\hat{\Theta}$ and $\hat{\sigma}^2$ estimates, as per Lemma 3:</p>
<ul>
<li>$J(\hat{\Theta_{n,k}}) = \sqrt{\frac{n}{\hat{\sigma_n}^2 S_{n,k}}} (\hat{\Theta_{n,k}} - \Theta_k) \sim \mathcal{T}_{n-p-1}$ <ul>
<li>$\mathcal{T}_{n-p-1}$ is the Student law with (n-p-1) degrees of freedom</li>
<li>$S_{n,k} = n (X^TX)^{-1}_{k,k}$ (select element k,k of the inverted Gram matrix)</li>
</ul>
</li>
</ul>

</div>
</div>
</div>
<div class="cell border-box-sizing code_cell rendered">
<div class="input">
<div class="prompt input_prompt">In&nbsp;[13]:</div>
<div class="inner_cell">
    <div class="input_area">
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">n</span> <span class="o">=</span> <span class="mi">5</span>
<span class="n">Theta_5Est</span> <span class="o">=</span> <span class="n">df_5</span><span class="p">[[</span><span class="s1">&#39;b&#39;</span><span class="p">,</span> <span class="s1">&#39;w0&#39;</span><span class="p">,</span> <span class="s1">&#39;w1&#39;</span><span class="p">]]</span><span class="o">.</span><span class="n">values</span>
<span class="n">Theta_5Exp</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="n">bLin</span><span class="p">,</span> <span class="n">wLin</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">wLin</span><span class="p">[</span><span class="mi">1</span><span class="p">]])</span>
<span class="n">estim</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="mi">3</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">df_5</span><span class="p">)))</span>
<span class="n">xTXInv_5</span> <span class="o">=</span> <span class="n">n</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">inv</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">matmul</span><span class="p">(</span><span class="n">x_m_5</span><span class="o">.</span><span class="n">T</span><span class="p">,</span> <span class="n">x_m_5</span><span class="p">))</span>
<span class="n">nOverNoiseVarSqrt</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">n</span> <span class="o">/</span> <span class="n">df_5</span><span class="p">[</span><span class="s1">&#39;noise var&#39;</span><span class="p">])</span>
<span class="k">for</span> <span class="n">k</span><span class="p">,</span> <span class="n">theta</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">Theta_5Est</span><span class="o">.</span><span class="n">T</span><span class="p">):</span>
    <span class="n">Snk</span> <span class="o">=</span> <span class="n">xTXInv_5</span><span class="p">[</span><span class="n">k</span><span class="p">,</span> <span class="n">k</span><span class="p">]</span>
    <span class="n">estim</span><span class="p">[</span><span class="n">k</span><span class="p">]</span> <span class="o">=</span> <span class="n">math</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="mi">1</span><span class="o">/</span><span class="n">Snk</span><span class="p">)</span> \
        <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">multiply</span><span class="p">(</span><span class="n">nOverNoiseVarSqrt</span><span class="p">,</span> <span class="p">(</span><span class="n">theta</span> <span class="o">-</span> <span class="n">Theta_5Exp</span><span class="p">[</span><span class="n">k</span><span class="p">]))</span>
</pre></div>

    </div>
</div>
</div>

</div>
<div class="cell border-box-sizing code_cell rendered">
<div class="input">
<div class="prompt input_prompt">In&nbsp;[14]:</div>
<div class="inner_cell">
    <div class="input_area">
<div class=" highlight hl-ipython3"><pre><span></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="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">16</span><span class="p">,</span> <span class="mi">5</span><span class="p">))</span>
<span class="n">span</span><span class="p">,</span> <span class="n">xx</span> <span class="o">=</span> <span class="p">[</span><span class="o">-</span><span class="mi">10</span><span class="p">,</span> <span class="mi">10</span><span class="p">],</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="o">-</span><span class="mi">10</span><span class="p">,</span> <span class="mi">10</span><span class="p">)</span>
<span class="n">pdfXx</span> <span class="o">=</span> <span class="n">stats</span><span class="o">.</span><span class="n">t</span><span class="p">(</span><span class="n">n</span> <span class="o">-</span> <span class="n">nFeatures</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span><span class="o">.</span><span class="n">pdf</span><span class="p">(</span><span class="n">xx</span><span class="p">)</span>
<span class="n">labels</span> <span class="o">=</span> <span class="p">[</span><span class="s1">&#39;$J(\hat</span><span class="si">{b}</span><span class="s1">)$ vs. $\mathcal</span><span class="si">{T}</span><span class="s1">(2)$&#39;</span><span class="p">,</span> <span class="s1">&#39;$J(\hat</span><span class="si">{w_0}</span><span class="s1">)$ vs. $\mathcal</span><span class="si">{T}</span><span class="s1">(2)$&#39;</span><span class="p">,</span> <span class="s1">&#39;$J(\hat</span><span class="si">{w_1}</span><span class="s1">)$ vs. $\mathcal</span><span class="si">{T}</span><span class="s1">(2)$&#39;</span><span class="p">]</span>
<span class="k">for</span> <span class="n">est</span><span class="p">,</span> <span class="n">l</span><span class="p">,</span> <span class="n">a</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">estim</span><span class="p">,</span> <span class="n">labels</span><span class="p">,</span> <span class="n">ax</span><span class="p">):</span>
    <span class="n">plotHistParams</span><span class="p">(</span><span class="n">est</span><span class="p">,</span> <span class="n">l</span><span class="p">,</span> <span class="n">a</span><span class="p">,</span> <span class="n">span</span><span class="p">,</span> <span class="n">pdfRefX</span><span class="o">=</span><span class="n">xx</span><span class="p">,</span> <span class="n">pdfRefY</span><span class="o">=</span><span class="n">pdfXx</span><span class="p">)</span>
</pre></div>

    </div>
</div>
</div>

<div class="output_wrapper">
<div class="output">


<div class="output_area">

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


<div class="output_png output_subarea ">
<img src="data:image/png;base64,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
"
>
</div>

</div>

</div>
</div>

</div>
<div class="cell border-box-sizing text_cell rendered"><div class="prompt input_prompt">
</div><div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<p>Theory is verified, we now have a closed form expression to compute the confidence interval on the estimates</p>

</div>
</div>
</div>
<div class="cell border-box-sizing text_cell rendered"><div class="prompt input_prompt">
</div><div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<h2 id="Confidence-intervals">Confidence intervals<a class="anchor-link" href="#Confidence-intervals">&#182;</a></h2><p>For this Gaussian linear model, for each coefficient, the confidence interval with level $\alpha$ is:
$$IC(\theta_k) = \left[ \hat{\theta_{n,k}} + \sqrt{\frac{\hat{\sigma_n}^2 S_{n,k}}{n}} q_{\frac{\alpha}{2}}, \hat{\theta_{n,k}} + \sqrt{\frac{\hat{\sigma_n}^2 S_{n,k}}{n}} q_{1-\frac{\alpha}{2}} \right]$$</p>
<p>With $q_{\frac{\alpha}{2}}$ and $q_{1-\frac{\alpha}{2}}$ the quantiles of the Student law $\mathcal{T}(n-p-1)$</p>
<p>We may now create a specific regression procedure that is estimating the noise variance $\hat{\sigma}^2$ and provides confidence intervals for the coefficients:</p>

</div>
</div>
</div>
<div class="cell border-box-sizing code_cell rendered">
<div class="input">
<div class="prompt input_prompt">In&nbsp;[15]:</div>
<div class="inner_cell">
    <div class="input_area">
<div class=" highlight hl-ipython3"><pre><span></span><span class="k">def</span> <span class="nf">linearRegressionLinearGaussian</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">alpha</span><span class="p">):</span>
    <span class="sd">&quot;&quot;&quot; Compute linear regression coefficients and their confidence interval</span>
<span class="sd">            Assume that X is full rank</span>
<span class="sd">    &quot;&quot;&quot;</span>
    <span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">y</span><span class="p">)</span>
    <span class="n">rank</span> <span class="o">=</span> <span class="n">x</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="c1"># = p + 1</span>
    <span class="c1"># Design matrix</span>
    <span class="n">xTxInv</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">inv</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">matmul</span><span class="p">(</span><span class="n">x</span><span class="o">.</span><span class="n">T</span><span class="p">,</span> <span class="n">x</span><span class="p">))</span>
    <span class="c1"># Regression coefficients</span>
    <span class="n">thetas</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">matmul</span><span class="p">(</span><span class="n">xTxInv</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">matmul</span><span class="p">(</span><span class="n">x</span><span class="o">.</span><span class="n">T</span><span class="p">,</span> <span class="n">y</span><span class="p">))</span>
    <span class="c1"># Predictions</span>
    <span class="n">yEst</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">matmul</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">thetas</span><span class="p">)</span>
    <span class="c1"># Noise variance</span>
    <span class="n">epsilonEst</span> <span class="o">=</span> <span class="n">y</span> <span class="o">-</span> <span class="n">yEst</span>
    <span class="n">noiseMu</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">epsilonEst</span><span class="p">)</span> <span class="c1"># for verification, but assumed 0</span>
    <span class="n">epsilonEst_c</span> <span class="o">=</span> <span class="n">epsilonEst</span> <span class="o">-</span> <span class="n">noiseMu</span>
    <span class="n">noiseVar</span> <span class="o">=</span> <span class="mi">1</span> <span class="o">/</span> <span class="p">(</span><span class="n">n</span> <span class="o">-</span> <span class="n">rank</span><span class="p">)</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">epsilonEst_c</span><span class="p">,</span> <span class="n">epsilonEst_c</span><span class="p">)</span>
    <span class="c1"># Student quantile</span>
    <span class="n">qAlpha</span> <span class="o">=</span> <span class="n">stats</span><span class="o">.</span><span class="n">t</span><span class="p">(</span><span class="n">n</span> <span class="o">-</span> <span class="n">rank</span><span class="p">)</span><span class="o">.</span><span class="n">ppf</span><span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="n">alpha</span><span class="o">/</span><span class="mi">2</span><span class="p">)</span>
    <span class="c1"># Confidence interval half range</span>
    <span class="n">xTxInvDiag</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">diagonal</span><span class="p">(</span><span class="n">xTxInv</span><span class="p">)</span>
    <span class="n">confidence</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">noiseVar</span> <span class="o">*</span> <span class="n">xTxInvDiag</span><span class="p">)</span> <span class="o">*</span> <span class="n">qAlpha</span>
    <span class="k">return</span> <span class="n">thetas</span><span class="p">,</span> <span class="n">confidence</span><span class="p">,</span> <span class="n">noiseVar</span>
</pre></div>

    </div>
</div>
</div>

</div>
<div class="cell border-box-sizing text_cell rendered"><div class="prompt input_prompt">
</div><div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<h4 id="Test-with-$n=5$">Test with $n=5$<a class="anchor-link" href="#Test-with-$n=5$">&#182;</a></h4>
</div>
</div>
</div>
<div class="cell border-box-sizing code_cell rendered">
<div class="input">
<div class="prompt input_prompt">In&nbsp;[16]:</div>
<div class="inner_cell">
    <div class="input_area">
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">alpha</span> <span class="o">=</span> <span class="mf">0.1</span>
<span class="n">thetas</span><span class="p">,</span> <span class="n">confidence</span><span class="p">,</span> <span class="n">noiseVar</span> <span class="o">=</span> <span class="n">linearRegressionLinearGaussian</span><span class="p">(</span><span class="n">x_m_5</span><span class="p">,</span> <span class="n">y_5</span><span class="p">,</span> <span class="n">alpha</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="s1">&#39;Coefficients =&#39;</span><span class="p">,</span> <span class="n">thetas</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="s1">&#39;Confidence intervals @ </span><span class="si">%.0f%%</span><span class="s1"> :</span><span class="se">\n</span><span class="s1">&#39;</span> <span class="o">%</span> <span class="p">((</span><span class="mi">1</span><span class="o">-</span><span class="n">alpha</span><span class="p">)</span><span class="o">*</span><span class="mi">100</span><span class="p">),</span> 
      <span class="n">np</span><span class="o">.</span><span class="n">vstack</span><span class="p">((</span><span class="n">thetas</span> <span class="o">-</span> <span class="n">confidence</span><span class="p">,</span> <span class="n">thetas</span> <span class="o">+</span> <span class="n">confidence</span><span class="p">))</span><span class="o">.</span><span class="n">T</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="s1">&#39;Noise variance estimate = </span><span class="si">%.3f</span><span class="s1">&#39;</span> <span class="o">%</span> <span class="n">noiseVar</span><span class="p">)</span>
</pre></div>

    </div>
</div>
</div>

<div class="output_wrapper">
<div class="output">


<div class="output_area">

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


<div class="output_subarea output_stream output_stdout output_text">
<pre>Coefficients = [ 0.29391061 -1.18995093 -0.81258792]
Confidence intervals @ 90% :
 [[-0.84904567  1.43686688]
 [-6.26703783  3.88713597]
 [-3.28128106  1.65610521]]
Noise variance estimate = 0.116
</pre>
</div>
</div>

</div>
</div>

</div>
<div class="cell border-box-sizing text_cell rendered"><div class="prompt input_prompt">
</div><div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<p>With so few samples in the dataset, the confidence intervals are very wide, this is shown on the three series of graphs above.</p>
<p>Note: all confidence intervals depend on the noise variance estimate, any error on it will drive a large impact on the resulting error.</p>

</div>
</div>
</div>
<div class="cell border-box-sizing text_cell rendered"><div class="prompt input_prompt">
</div><div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<h4 id="Full-test-of-the-confidence-interval">Full test of the confidence interval<a class="anchor-link" href="#Full-test-of-the-confidence-interval">&#182;</a></h4><p>Let's redo the sweep on the dataset length computing also confidence intervals:</p>

</div>
</div>
</div>
<div class="cell border-box-sizing code_cell rendered">
<div class="input">
<div class="prompt input_prompt">In&nbsp;[17]:</div>
<div class="inner_cell">
    <div class="input_area">
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">alpha</span> <span class="o">=</span> <span class="mf">0.05</span>

<span class="n">regressions</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">n</span> <span class="ow">in</span> <span class="p">[</span><span class="mi">5</span><span class="p">,</span> <span class="mi">10</span><span class="p">,</span> <span class="mi">20</span><span class="p">,</span> <span class="mi">40</span><span class="p">,</span> <span class="mi">100</span><span class="p">,</span> <span class="mi">200</span><span class="p">,</span> <span class="mi">500</span><span class="p">,</span> <span class="mi">1000</span><span class="p">]:</span>
    <span class="n">x_m_n</span> <span class="o">=</span> <span class="n">x_m_1000</span><span class="p">[:</span><span class="n">n</span><span class="p">]</span>
    <span class="n">y_n</span> <span class="o">=</span> <span class="n">y_1000</span><span class="p">[:</span><span class="n">n</span><span class="p">]</span>
    <span class="n">thetaEst</span><span class="p">,</span> <span class="n">confidence</span><span class="p">,</span> <span class="n">noiseVar</span> <span class="o">=</span> <span class="n">linearRegressionLinearGaussian</span><span class="p">(</span><span class="n">x_m_n</span><span class="p">,</span> <span class="n">y_n</span><span class="p">,</span> <span class="n">alpha</span><span class="p">)</span>
    <span class="n">regressions</span><span class="o">.</span><span class="n">append</span><span class="p">([</span><span class="n">n</span><span class="p">,</span> 
                        <span class="n">thetaEst</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">thetaEst</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">thetaEst</span><span class="p">[</span><span class="mi">2</span><span class="p">],</span> 
                        <span class="n">confidence</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">confidence</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">confidence</span><span class="p">[</span><span class="mi">2</span><span class="p">],</span>
                        <span class="n">noiseVar</span><span class="p">])</span>

<span class="n">dfSweepN2</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">DataFrame</span><span class="p">(</span><span class="n">regressions</span><span class="p">,</span> <span class="n">columns</span><span class="o">=</span><span class="p">(</span><span class="s1">&#39;n&#39;</span><span class="p">,</span> <span class="s1">&#39;b&#39;</span><span class="p">,</span> <span class="s1">&#39;w0&#39;</span><span class="p">,</span><span class="s1">&#39;w1&#39;</span><span class="p">,</span> <span class="s1">&#39;bConf&#39;</span><span class="p">,</span> <span class="s1">&#39;w0Conf&#39;</span><span class="p">,</span> <span class="s1">&#39;w1Conf&#39;</span><span class="p">,</span> <span class="s1">&#39;noise var&#39;</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="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">16</span><span class="p">,</span> <span class="mi">8</span><span class="p">),</span> <span class="n">subplot_kw</span><span class="o">=</span><span class="p">{</span><span class="s1">&#39;xscale&#39;</span><span class="p">:</span><span class="s1">&#39;log&#39;</span><span class="p">})</span>
<span class="n">plotToRef</span><span class="p">(</span><span class="n">dfSweepN2</span><span class="p">[</span><span class="s1">&#39;n&#39;</span><span class="p">],</span> <span class="n">dfSweepN2</span><span class="p">[</span><span class="s1">&#39;b&#39;</span><span class="p">],</span> <span class="n">bLin</span><span class="p">,</span> <span class="n">ax</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span><span class="mi">0</span><span class="p">],</span> <span class="s1">&#39;$\hat</span><span class="si">{b}</span><span class="s1">$&#39;</span><span class="p">,</span> <span class="n">yErr</span><span class="o">=</span><span class="n">dfSweepN2</span><span class="p">[</span><span class="s1">&#39;bConf&#39;</span><span class="p">])</span>
<span class="n">plotToRef</span><span class="p">(</span><span class="n">dfSweepN2</span><span class="p">[</span><span class="s1">&#39;n&#39;</span><span class="p">],</span> <span class="n">dfSweepN2</span><span class="p">[</span><span class="s1">&#39;noise var&#39;</span><span class="p">],</span> <span class="n">sigmaLin</span><span class="o">**</span><span class="mi">2</span><span class="p">,</span> <span class="n">ax</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span><span class="mi">0</span><span class="p">],</span> <span class="s1">&#39;$\hat{\sigma}^2$&#39;</span><span class="p">,</span> <span class="n">xLabel</span><span class="o">=</span><span class="s1">&#39;n&#39;</span><span class="p">)</span>
<span class="n">plotToRef</span><span class="p">(</span><span class="n">dfSweepN2</span><span class="p">[</span><span class="s1">&#39;n&#39;</span><span class="p">],</span> <span class="n">dfSweepN2</span><span class="p">[</span><span class="s1">&#39;w0&#39;</span><span class="p">],</span> <span class="n">wLin</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">ax</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span><span class="mi">1</span><span class="p">],</span> <span class="s1">&#39;$\hat</span><span class="si">{w_0}</span><span class="s1">$&#39;</span><span class="p">,</span> <span class="n">yErr</span><span class="o">=</span><span class="n">dfSweepN2</span><span class="p">[</span><span class="s1">&#39;w0Conf&#39;</span><span class="p">])</span>
<span class="n">plotToRef</span><span class="p">(</span><span class="n">dfSweepN2</span><span class="p">[</span><span class="s1">&#39;n&#39;</span><span class="p">],</span> <span class="n">dfSweepN2</span><span class="p">[</span><span class="s1">&#39;w1&#39;</span><span class="p">],</span> <span class="n">wLin</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">ax</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span><span class="mi">1</span><span class="p">],</span> <span class="s1">&#39;$\hat</span><span class="si">{w_1}</span><span class="s1">$&#39;</span><span class="p">,</span> <span class="n">yErr</span><span class="o">=</span><span class="n">dfSweepN2</span><span class="p">[</span><span class="s1">&#39;w1Conf&#39;</span><span class="p">],</span> <span class="n">xLabel</span><span class="o">=</span><span class="s1">&#39;n&#39;</span><span class="p">);</span>
</pre></div>

    </div>
</div>
</div>

<div class="output_wrapper">
<div class="output">


<div class="output_area">

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


<div class="output_png output_subarea ">
<img src="data:image/png;base64,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
"
>
</div>

</div>

</div>
</div>

</div>
<div class="cell border-box-sizing text_cell rendered"><div class="prompt input_prompt">
</div><div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<p>On above graphs, the error bars, in red, correspond to the confidence interval. For short dataset lengths the confidence interval is tremendous. From 10 samples and over, the confidence interval is narrowing quickly.</p>
<p>The true value (orance line) should be within reach of the error bar, if not it means that the case is out of the 95% probability.</p>

</div>
</div>
</div>
<div class="cell border-box-sizing text_cell rendered"><div class="prompt input_prompt">
</div><div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<h2 id="Distributions-with-$n-=-5$-and-stochastic-$X$-values">Distributions with $n = 5$ and stochastic $X$ values<a class="anchor-link" href="#Distributions-with-$n-=-5$-and-stochastic-$X$-values">&#182;</a></h2><p>A different set of experiments in which noise is drawn from the gaussian distribution, and X from the uniform distributions.</p>

</div>
</div>
</div>
<div class="cell border-box-sizing code_cell rendered">
<div class="input">
<div class="prompt input_prompt">In&nbsp;[18]:</div>
<div class="inner_cell">
    <div class="input_area">
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">n</span> <span class="o">=</span> <span class="mi">5</span>

<span class="n">regressions</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">l</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">50000</span><span class="p">):</span>
    <span class="c1"># Draw a new batch</span>
    <span class="n">x</span><span class="p">,</span> <span class="n">yClean</span><span class="p">,</span> <span class="n">y</span> <span class="o">=</span> <span class="n">generateBatchLinear</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
    <span class="n">x_m</span> <span class="o">=</span> <span class="n">xWithIntercept</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
    <span class="n">thetaEst</span> <span class="o">=</span> <span class="n">linearRegression</span><span class="p">(</span><span class="n">x_m</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span>
    <span class="n">noiseMu</span><span class="p">,</span> <span class="n">noiseVar</span> <span class="o">=</span> <span class="n">noiseEstimation</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">matmul</span><span class="p">(</span><span class="n">x_m</span><span class="p">,</span> <span class="n">thetaEst</span><span class="p">),</span> <span class="n">y</span><span class="p">,</span> <span class="n">nFeatures</span><span class="p">)</span>
    <span class="n">regressions</span><span class="o">.</span><span class="n">append</span><span class="p">([</span><span class="n">thetaEst</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">thetaEst</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">thetaEst</span><span class="p">[</span><span class="mi">2</span><span class="p">],</span> <span class="n">noiseMu</span><span class="p">,</span> <span class="n">noiseVar</span><span class="p">])</span>
    
<span class="n">df_5s</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">DataFrame</span><span class="p">(</span><span class="n">regressions</span><span class="p">,</span> <span class="n">columns</span><span class="o">=</span><span class="p">(</span><span class="s1">&#39;b&#39;</span><span class="p">,</span> <span class="s1">&#39;w0&#39;</span><span class="p">,</span><span class="s1">&#39;w1&#39;</span><span class="p">,</span> <span class="s1">&#39;noise mean&#39;</span><span class="p">,</span> <span class="s1">&#39;noise var&#39;</span><span class="p">))</span>
</pre></div>

    </div>
</div>
</div>

</div>
<div class="cell border-box-sizing code_cell rendered">
<div class="input">
<div class="prompt input_prompt">In&nbsp;[19]:</div>
<div class="inner_cell">
    <div class="input_area">
<div class=" highlight hl-ipython3"><pre><span></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="mi">1</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">16</span><span class="p">,</span> <span class="mi">5</span><span class="p">))</span>
<span class="n">plotHistParams</span><span class="p">(</span><span class="n">df_5s</span><span class="p">[</span><span class="s1">&#39;b&#39;</span><span class="p">]</span>  <span class="o">-</span> <span class="n">bLin</span><span class="p">,</span>    <span class="s1">&#39;$\hat</span><span class="si">{b}</span><span class="s1"> - b$&#39;</span><span class="p">,</span>     <span class="n">ax</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="p">[</span><span class="o">-</span><span class="mi">3</span><span class="p">,</span> <span class="mi">3</span><span class="p">])</span>
<span class="n">plotHistParams</span><span class="p">(</span><span class="n">df_5s</span><span class="p">[</span><span class="s1">&#39;w0&#39;</span><span class="p">]</span> <span class="o">-</span> <span class="n">wLin</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="s1">&#39;$\hat</span><span class="si">{w_0}</span><span class="s1"> - w_0$&#39;</span><span class="p">,</span> <span class="n">ax</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="p">[</span><span class="o">-</span><span class="mi">5</span><span class="p">,</span> <span class="mi">5</span><span class="p">])</span>
<span class="n">plotHistParams</span><span class="p">(</span><span class="n">df_5s</span><span class="p">[</span><span class="s1">&#39;w1&#39;</span><span class="p">]</span> <span class="o">-</span> <span class="n">wLin</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="s1">&#39;$\hat</span><span class="si">{w_1}</span><span class="s1"> - w_1$&#39;</span><span class="p">,</span> <span class="n">ax</span><span class="p">[</span><span class="mi">2</span><span class="p">],</span> <span class="p">[</span><span class="o">-</span><span class="mi">5</span><span class="p">,</span> <span class="mi">5</span><span class="p">])</span>

<span class="n">dFree</span> <span class="o">=</span> <span class="n">n</span> <span class="o">-</span> <span class="n">nFeatures</span> <span class="o">-</span> <span class="mi">1</span>
<span class="n">ax</span><span class="p">[</span><span class="mi">3</span><span class="p">]</span><span class="o">.</span><span class="n">hist</span><span class="p">(</span><span class="n">df_5s</span><span class="p">[</span><span class="s1">&#39;noise var&#39;</span><span class="p">]</span> <span class="o">*</span> <span class="n">dFree</span> <span class="o">/</span> <span class="n">sigmaLin</span><span class="o">**</span><span class="mi">2</span><span class="p">,</span> <span class="n">bins</span><span class="o">=</span><span class="mi">100</span><span class="p">,</span> <span class="n">density</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s1">&#39;histogram&#39;</span><span class="p">)</span>
<span class="n">xx</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="mi">15</span><span class="p">)</span>
<span class="n">ax</span><span class="p">[</span><span class="mi">3</span><span class="p">]</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">xx</span><span class="p">,</span> <span class="n">stats</span><span class="o">.</span><span class="n">chi2</span><span class="p">(</span><span class="n">dFree</span><span class="p">)</span><span class="o">.</span><span class="n">pdf</span><span class="p">(</span><span class="n">xx</span><span class="p">),</span> <span class="n">label</span><span class="o">=</span><span class="s1">&#39;$\chi^2(2)$&#39;</span><span class="p">)</span>
<span class="n">ax</span><span class="p">[</span><span class="mi">3</span><span class="p">]</span><span class="o">.</span><span class="n">legend</span><span class="p">()</span>
<span class="n">ax</span><span class="p">[</span><span class="mi">3</span><span class="p">]</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s1">&#39;$(n-p-1)\hat{\sigma}^2 / \sigma^2$ vs. $\chi^2(2)$&#39;</span><span class="p">);</span>
</pre></div>

    </div>
</div>
</div>

<div class="output_wrapper">
<div class="output">


<div class="output_area">

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


<div class="output_png output_subarea ">
<img src="data:image/png;base64,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
"
>
</div>

</div>

</div>
</div>

</div>
<div class="cell border-box-sizing text_cell rendered"><div class="prompt input_prompt">
</div><div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<p>On above graphs, compared to previous graphs, we observe that the shapes are similar but the variances are higher on $b, w_0, w_1$</p>
<p>Whereas the scaled noise variance is still matching the Chi-2 distribution</p>

</div>
</div>
</div>
<div class="cell border-box-sizing code_cell rendered">
<div class="input">
<div class="prompt input_prompt">In&nbsp;[20]:</div>
<div class="inner_cell">
    <div class="input_area">
<div class=" highlight hl-ipython3"><pre><span></span><span class="c1"># Covariance of the intercept and weights</span>
<span class="n">ThetaCov_5s</span> <span class="o">=</span> <span class="n">autoCovariance</span><span class="p">(</span><span class="n">df_5s</span><span class="p">[[</span><span class="s1">&#39;b&#39;</span><span class="p">,</span> <span class="s1">&#39;w0&#39;</span><span class="p">,</span> <span class="s1">&#39;w1&#39;</span><span class="p">]]</span><span class="o">.</span><span class="n">values</span><span class="p">)</span>
<span class="n">plotHeatMap</span><span class="p">(</span><span class="n">ThetaCov_5s</span><span class="p">,</span> <span class="p">(</span><span class="s1">&#39;b&#39;</span><span class="p">,</span><span class="s1">&#39;$w_0$&#39;</span><span class="p">,</span> <span class="s1">&#39;$w_1$&#39;</span><span class="p">),</span> <span class="n">title</span><span class="o">=</span><span class="s1">&#39;Correlation matrix&#39;</span><span class="p">,</span> <span class="n">fmt</span><span class="o">=</span><span class="s1">&#39;.3f&#39;</span><span class="p">);</span>
</pre></div>

    </div>
</div>
</div>

<div class="output_wrapper">
<div class="output">


<div class="output_area">

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


<div class="output_png output_subarea ">
<img src="data:image/png;base64,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
"
>
</div>

</div>

</div>
</div>

</div>
<div class="cell border-box-sizing text_cell rendered"><div class="prompt input_prompt">
</div><div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<p>Globally the variance on the coefficients has increased, this reflects variability on fitting Y as a linear relation to X.</p>

</div>
</div>
</div>
<div class="cell border-box-sizing text_cell rendered"><div class="prompt input_prompt">
</div><div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<h1 id="Conclusion">Conclusion<a class="anchor-link" href="#Conclusion">&#182;</a></h1><p>Starting from "raw theory", we have shown first how to match it with experiment, and then an application of this theory.</p>
<p>In this notebook, the data prior (inherent) model is Gaussian, which is somehow ideal. In the next notebooks, we will investigate more complex models and situations.</p>

</div>
</div>
</div>
    </div>
  </div>
</body>
      </section>
    </div>
    
    <div id="footer_wrap" class="outer">
      <footer class="inner">
        <h5 id="project_star">If you like this project please add your <a class="github-button" href="https://github.com/tonio73/data-science" data-icon="octicon-star" aria-label="Star tonio73/data-science on GitHub">Star</a>
          </h5>
        <p class="copyright">data-science maintained by <a href="https://github.com/tonio73">tonio73</a></p>
      </footer>
    </div>


</html>