FIZ353_05_MatrixDecomposition.html

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  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: #000000;
  background-color: #ffffff;
}
input,
button,
select,
textarea {
  font-family: inherit;
  font-size: inherit;
  line-height: inherit;
}
a {
  color: #296eaa;
  text-decoration: none;
}
a:hover,
a:focus {
  color: #1a466c;
  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: #ffffff;
  border: 1px solid #dddddd;
  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;
  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;
}
[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: 400;
  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 {
  padding: .2em;
  background-color: #fcf8e3;
}
.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-right: 5px;
  padding-left: 5px;
}
dl {
  margin-top: 0;
  margin-bottom: 18px;
}
dt,
dd {
  line-height: 1.42857143;
}
dt {
  font-weight: 700;
}
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;
}
.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;
  text-align: right;
  border-right: 5px solid #eeeeee;
  border-left: 0;
}
.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: #888888;
  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: 700;
  box-shadow: none;
}
pre {
  display: block;
  padding: 8.5px;
  margin: 0 0 9px;
  font-size: 12px;
  line-height: 1.42857143;
  color: #333333;
  word-break: break-all;
  word-wrap: break-word;
  background-color: #f5f5f5;
  border: 1px solid #cccccc;
  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 {
  padding-right: 0px;
  padding-left: 0px;
  margin-right: auto;
  margin-left: auto;
}
@media (min-width: 768px) {
  .container {
    width: 768px;
  }
}
@media (min-width: 992px) {
  .container {
    width: 940px;
  }
}
@media (min-width: 1200px) {
  .container {
    width: 1140px;
  }
}
.container-fluid {
  padding-right: 0px;
  padding-left: 0px;
  margin-right: auto;
  margin-left: auto;
}
.row {
  margin-right: 0px;
  margin-left: 0px;
}
.row-no-gutters {
  margin-right: 0;
  margin-left: 0;
}
.row-no-gutters [class*="col-"] {
  padding-right: 0;
  padding-left: 0;
}
.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-right: 0px;
  padding-left: 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;
}
table col[class*="col-"] {
  position: static;
  display: table-column;
  float: none;
}
table td[class*="col-"],
table th[class*="col-"] {
  position: static;
  display: table-cell;
  float: none;
}
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 #dddddd;
}
.table > thead > tr > th {
  vertical-align: bottom;
  border-bottom: 2px solid #dddddd;
}
.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 #dddddd;
}
.table .table {
  background-color: #ffffff;
}
.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 #dddddd;
}
.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 #dddddd;
}
.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 > 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 {
  min-height: .01%;
  overflow-x: auto;
}
@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 #dddddd;
  }
  .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 {
  min-width: 0;
  padding: 0;
  margin: 0;
  border: 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: 700;
}
input[type="search"] {
  -webkit-box-sizing: border-box;
  -moz-box-sizing: border-box;
  box-sizing: border-box;
  -webkit-appearance: none;
  appearance: none;
}
input[type="radio"],
input[type="checkbox"] {
  margin: 4px 0 0;
  margin-top: 1px \9;
  line-height: normal;
}
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;
}
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: #ffffff;
  background-image: none;
  border: 1px solid #cccccc;
  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: #999999;
  opacity: 1;
}
.form-control:-ms-input-placeholder {
  color: #999999;
}
.form-control::-webkit-input-placeholder {
  color: #999999;
}
.form-control::-ms-expand {
  background-color: transparent;
  border: 0;
}
.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;
}
@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.disabled label,
.checkbox.disabled label,
fieldset[disabled] .radio label,
fieldset[disabled] .checkbox label {
  cursor: not-allowed;
}
.radio label,
.checkbox label {
  min-height: 18px;
  padding-left: 20px;
  margin-bottom: 0;
  font-weight: 400;
  cursor: pointer;
}
.radio input[type="radio"],
.radio-inline input[type="radio"],
.checkbox input[type="checkbox"],
.checkbox-inline input[type="checkbox"] {
  position: absolute;
  margin-top: 4px \9;
  margin-left: -20px;
}
.radio + .radio,
.checkbox + .checkbox {
  margin-top: -5px;
}
.radio-inline,
.checkbox-inline {
  position: relative;
  display: inline-block;
  padding-left: 20px;
  margin-bottom: 0;
  font-weight: 400;
  vertical-align: middle;
  cursor: pointer;
}
.radio-inline.disabled,
.checkbox-inline.disabled,
fieldset[disabled] .radio-inline,
fieldset[disabled] .checkbox-inline {
  cursor: not-allowed;
}
.radio-inline + .radio-inline,
.checkbox-inline + .checkbox-inline {
  margin-top: 0;
  margin-left: 10px;
}
.form-control-static {
  min-height: 31px;
  padding-top: 7px;
  padding-bottom: 7px;
  margin-bottom: 0;
}
.form-control-static.input-lg,
.form-control-static.input-sm {
  padding-right: 0;
  padding-left: 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;
  background-color: #dff0d8;
  border-color: #3c763d;
}
.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;
  background-color: #fcf8e3;
  border-color: #8a6d3b;
}
.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;
  background-color: #f2dede;
  border-color: #a94442;
}
.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 {
  padding-top: 7px;
  margin-top: 0;
  margin-bottom: 0;
}
.form-horizontal .radio,
.form-horizontal .checkbox {
  min-height: 25px;
}
.form-horizontal .form-group {
  margin-right: 0px;
  margin-left: 0px;
}
@media (min-width: 768px) {
  .form-horizontal .control-label {
    padding-top: 7px;
    margin-bottom: 0;
    text-align: right;
  }
}
.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;
  white-space: nowrap;
  vertical-align: middle;
  touch-action: manipulation;
  cursor: pointer;
  background-image: none;
  border: 1px solid transparent;
  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: #333333;
  text-decoration: none;
}
.btn:active,
.btn.active {
  background-image: none;
  outline: 0;
  -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;
  filter: alpha(opacity=65);
  opacity: 0.65;
  -webkit-box-shadow: none;
  box-shadow: none;
}
a.btn.disabled,
fieldset[disabled] a.btn {
  pointer-events: none;
}
.btn-default {
  color: #333333;
  background-color: #ffffff;
  border-color: #cccccc;
}
.btn-default:focus,
.btn-default.focus {
  color: #333333;
  background-color: #e6e6e6;
  border-color: #8c8c8c;
}
.btn-default:hover {
  color: #333333;
  background-color: #e6e6e6;
  border-color: #adadad;
}
.btn-default:active,
.btn-default.active,
.open > .dropdown-toggle.btn-default {
  color: #333333;
  background-color: #e6e6e6;
  background-image: none;
  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: #333333;
  background-color: #d4d4d4;
  border-color: #8c8c8c;
}
.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: #ffffff;
  border-color: #cccccc;
}
.btn-default .badge {
  color: #ffffff;
  background-color: #333333;
}
.btn-primary {
  color: #ffffff;
  background-color: #337ab7;
  border-color: #2e6da4;
}
.btn-primary:focus,
.btn-primary.focus {
  color: #ffffff;
  background-color: #286090;
  border-color: #122b40;
}
.btn-primary:hover {
  color: #ffffff;
  background-color: #286090;
  border-color: #204d74;
}
.btn-primary:active,
.btn-primary.active,
.open > .dropdown-toggle.btn-primary {
  color: #ffffff;
  background-color: #286090;
  background-image: none;
  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: #ffffff;
  background-color: #204d74;
  border-color: #122b40;
}
.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: #ffffff;
}
.btn-success {
  color: #ffffff;
  background-color: #5cb85c;
  border-color: #4cae4c;
}
.btn-success:focus,
.btn-success.focus {
  color: #ffffff;
  background-color: #449d44;
  border-color: #255625;
}
.btn-success:hover {
  color: #ffffff;
  background-color: #449d44;
  border-color: #398439;
}
.btn-success:active,
.btn-success.active,
.open > .dropdown-toggle.btn-success {
  color: #ffffff;
  background-color: #449d44;
  background-image: none;
  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: #ffffff;
  background-color: #398439;
  border-color: #255625;
}
.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: #ffffff;
}
.btn-info {
  color: #ffffff;
  background-color: #5bc0de;
  border-color: #46b8da;
}
.btn-info:focus,
.btn-info.focus {
  color: #ffffff;
  background-color: #31b0d5;
  border-color: #1b6d85;
}
.btn-info:hover {
  color: #ffffff;
  background-color: #31b0d5;
  border-color: #269abc;
}
.btn-info:active,
.btn-info.active,
.open > .dropdown-toggle.btn-info {
  color: #ffffff;
  background-color: #31b0d5;
  background-image: none;
  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: #ffffff;
  background-color: #269abc;
  border-color: #1b6d85;
}
.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: #ffffff;
}
.btn-warning {
  color: #ffffff;
  background-color: #f0ad4e;
  border-color: #eea236;
}
.btn-warning:focus,
.btn-warning.focus {
  color: #ffffff;
  background-color: #ec971f;
  border-color: #985f0d;
}
.btn-warning:hover {
  color: #ffffff;
  background-color: #ec971f;
  border-color: #d58512;
}
.btn-warning:active,
.btn-warning.active,
.open > .dropdown-toggle.btn-warning {
  color: #ffffff;
  background-color: #ec971f;
  background-image: none;
  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: #ffffff;
  background-color: #d58512;
  border-color: #985f0d;
}
.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: #ffffff;
}
.btn-danger {
  color: #ffffff;
  background-color: #d9534f;
  border-color: #d43f3a;
}
.btn-danger:focus,
.btn-danger.focus {
  color: #ffffff;
  background-color: #c9302c;
  border-color: #761c19;
}
.btn-danger:hover {
  color: #ffffff;
  background-color: #c9302c;
  border-color: #ac2925;
}
.btn-danger:active,
.btn-danger.active,
.open > .dropdown-toggle.btn-danger {
  color: #ffffff;
  background-color: #c9302c;
  background-image: none;
  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: #ffffff;
  background-color: #ac2925;
  border-color: #761c19;
}
.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: #ffffff;
}
.btn-link {
  font-weight: 400;
  color: #296eaa;
  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: #1a466c;
  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;
  font-size: 13px;
  text-align: left;
  list-style: none;
  background-color: #ffffff;
  background-clip: padding-box;
  border: 1px solid #cccccc;
  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);
}
.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: 400;
  line-height: 1.42857143;
  color: #333333;
  white-space: nowrap;
}
.dropdown-menu > li > a:hover,
.dropdown-menu > li > a:focus {
  color: #262626;
  text-decoration: none;
  background-color: #f5f5f5;
}
.dropdown-menu > .active > a,
.dropdown-menu > .active > a:hover,
.dropdown-menu > .active > a:focus {
  color: #ffffff;
  text-decoration: none;
  background-color: #337ab7;
  outline: 0;
}
.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;
  cursor: not-allowed;
  background-color: transparent;
  background-image: none;
  filter: progid:DXImageTransform.Microsoft.gradient(enabled = false);
}
.open > .dropdown-menu {
  display: block;
}
.open > a {
  outline: 0;
}
.dropdown-menu-right {
  right: 0;
  left: auto;
}
.dropdown-menu-left {
  right: auto;
  left: 0;
}
.dropdown-header {
  display: block;
  padding: 3px 20px;
  font-size: 12px;
  line-height: 1.42857143;
  color: #777777;
  white-space: nowrap;
}
.dropdown-backdrop {
  position: fixed;
  top: 0;
  right: 0;
  bottom: 0;
  left: 0;
  z-index: 990;
}
.pull-right > .dropdown-menu {
  right: 0;
  left: auto;
}
.dropup .caret,
.navbar-fixed-bottom .dropdown .caret {
  content: "";
  border-top: 0;
  border-bottom: 4px dashed;
  border-bottom: 4px solid \9;
}
.dropup .dropdown-menu,
.navbar-fixed-bottom .dropdown .dropdown-menu {
  top: auto;
  bottom: 100%;
  margin-bottom: 2px;
}
@media (min-width: 541px) {
  .navbar-right .dropdown-menu {
    right: 0;
    left: auto;
  }
  .navbar-right .dropdown-menu-left {
    right: auto;
    left: 0;
  }
}
.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-top-right-radius: 0;
  border-bottom-right-radius: 0;
}
.btn-group > .btn:last-child:not(:first-child),
.btn-group > .dropdown-toggle:not(:first-child) {
  border-top-left-radius: 0;
  border-bottom-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-top-right-radius: 0;
  border-bottom-right-radius: 0;
}
.btn-group > .btn-group:last-child:not(:first-child) > .btn:first-child {
  border-top-left-radius: 0;
  border-bottom-left-radius: 0;
}
.btn-group .dropdown-toggle:active,
.btn-group.open .dropdown-toggle {
  outline: 0;
}
.btn-group > .btn + .dropdown-toggle {
  padding-right: 8px;
  padding-left: 8px;
}
.btn-group > .btn-lg + .dropdown-toggle {
  padding-right: 12px;
  padding-left: 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-left-radius: 2px;
  border-top-right-radius: 2px;
  border-bottom-right-radius: 0;
  border-bottom-left-radius: 0;
}
.btn-group-vertical > .btn:last-child:not(:first-child) {
  border-top-left-radius: 0;
  border-top-right-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-left-radius: 0;
  border-top-right-radius: 0;
}
.btn-group-justified {
  display: table;
  width: 100%;
  table-layout: fixed;
  border-collapse: separate;
}
.btn-group-justified > .btn,
.btn-group-justified > .btn-group {
  display: table-cell;
  float: none;
  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-right: 0;
  padding-left: 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: 400;
  line-height: 1;
  color: #555555;
  text-align: center;
  background-color: #eeeeee;
  border: 1px solid #cccccc;
  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-top-right-radius: 0;
  border-bottom-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-top-left-radius: 0;
  border-bottom-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 {
  padding-left: 0;
  margin-bottom: 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;
  cursor: not-allowed;
  background-color: transparent;
}
.nav .open > a,
.nav .open > a:hover,
.nav .open > a:focus {
  background-color: #eeeeee;
  border-color: #296eaa;
}
.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 #dddddd;
}
.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 #dddddd;
}
.nav-tabs > li.active > a,
.nav-tabs > li.active > a:hover,
.nav-tabs > li.active > a:focus {
  color: #555555;
  cursor: default;
  background-color: #ffffff;
  border: 1px solid #dddddd;
  border-bottom-color: transparent;
}
.nav-tabs.nav-justified {
  width: 100%;
  border-bottom: 0;
}
.nav-tabs.nav-justified > li {
  float: none;
}
.nav-tabs.nav-justified > li > a {
  margin-bottom: 5px;
  text-align: center;
}
.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 #dddddd;
}
@media (min-width: 768px) {
  .nav-tabs.nav-justified > li > a {
    border-bottom: 1px solid #dddddd;
    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: #ffffff;
  }
}
.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: #ffffff;
  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 {
  margin-bottom: 5px;
  text-align: center;
}
.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 #dddddd;
}
@media (min-width: 768px) {
  .nav-tabs-justified > li > a {
    border-bottom: 1px solid #dddddd;
    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: #ffffff;
  }
}
.tab-content > .tab-pane {
  display: none;
}
.tab-content > .active {
  display: block;
}
.nav-tabs .dropdown-menu {
  margin-top: -1px;
  border-top-left-radius: 0;
  border-top-right-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 {
  padding-right: 0px;
  padding-left: 0px;
  overflow-x: visible;
  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-right: 0;
    padding-left: 0;
  }
}
.navbar-fixed-top,
.navbar-fixed-bottom {
  position: fixed;
  right: 0;
  left: 0;
  z-index: 1030;
}
.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;
  }
}
@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;
}
.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-brand {
  float: left;
  height: 30px;
  padding: 6px 0px;
  font-size: 17px;
  line-height: 18px;
}
.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;
  padding: 9px 10px;
  margin-right: 0px;
  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 {
  padding: 10px 0px;
  margin-right: 0px;
  margin-left: 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;
    padding-top: 0;
    padding-bottom: 0;
    margin-right: 0;
    margin-left: 0;
    border: 0;
    -webkit-box-shadow: none;
    box-shadow: none;
  }
}
.navbar-nav > li > .dropdown-menu {
  margin-top: 0;
  border-top-left-radius: 0;
  border-top-right-radius: 0;
}
.navbar-fixed-bottom .navbar-nav > li > .dropdown-menu {
  margin-bottom: 0;
  border-top-left-radius: 2px;
  border-top-right-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-right: 0px;
    margin-left: 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: #565656;
}
.navbar-default .navbar-brand:hover,
.navbar-default .navbar-brand:focus {
  color: #3c3c3c;
  background-color: transparent;
}
.navbar-default .navbar-text {
  color: #777777;
}
.navbar-default .navbar-nav > li > a {
  color: #565656;
}
.navbar-default .navbar-nav > li > a:hover,
.navbar-default .navbar-nav > li > a:focus {
  color: #333333;
  background-color: transparent;
}
.navbar-default .navbar-nav > .active > a,
.navbar-default .navbar-nav > .active > a:hover,
.navbar-default .navbar-nav > .active > a:focus {
  color: #555555;
  background-color: #e7e7e7;
}
.navbar-default .navbar-nav > .disabled > a,
.navbar-default .navbar-nav > .disabled > a:hover,
.navbar-default .navbar-nav > .disabled > a:focus {
  color: #cccccc;
  background-color: transparent;
}
.navbar-default .navbar-nav > .open > a,
.navbar-default .navbar-nav > .open > a:hover,
.navbar-default .navbar-nav > .open > a:focus {
  color: #555555;
  background-color: #e7e7e7;
}
@media (max-width: 540px) {
  .navbar-default .navbar-nav .open .dropdown-menu > li > a {
    color: #565656;
  }
  .navbar-default .navbar-nav .open .dropdown-menu > li > a:hover,
  .navbar-default .navbar-nav .open .dropdown-menu > li > a:focus {
    color: #333333;
    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: #555555;
    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: #cccccc;
    background-color: transparent;
  }
}
.navbar-default .navbar-toggle {
  border-color: #dddddd;
}
.navbar-default .navbar-toggle:hover,
.navbar-default .navbar-toggle:focus {
  background-color: #dddddd;
}
.navbar-default .navbar-toggle .icon-bar {
  background-color: #888888;
}
.navbar-default .navbar-collapse,
.navbar-default .navbar-form {
  border-color: #e7e7e7;
}
.navbar-default .navbar-link {
  color: #565656;
}
.navbar-default .navbar-link:hover {
  color: #333333;
}
.navbar-default .btn-link {
  color: #565656;
}
.navbar-default .btn-link:hover,
.navbar-default .btn-link:focus {
  color: #333333;
}
.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: #cccccc;
}
.navbar-inverse {
  background-color: #222222;
  border-color: #080808;
}
.navbar-inverse .navbar-brand {
  color: #9d9d9d;
}
.navbar-inverse .navbar-brand:hover,
.navbar-inverse .navbar-brand:focus {
  color: #ffffff;
  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: #ffffff;
  background-color: transparent;
}
.navbar-inverse .navbar-nav > .active > a,
.navbar-inverse .navbar-nav > .active > a:hover,
.navbar-inverse .navbar-nav > .active > a:focus {
  color: #ffffff;
  background-color: #080808;
}
.navbar-inverse .navbar-nav > .disabled > a,
.navbar-inverse .navbar-nav > .disabled > a:hover,
.navbar-inverse .navbar-nav > .disabled > a:focus {
  color: #444444;
  background-color: transparent;
}
.navbar-inverse .navbar-nav > .open > a,
.navbar-inverse .navbar-nav > .open > a:hover,
.navbar-inverse .navbar-nav > .open > a:focus {
  color: #ffffff;
  background-color: #080808;
}
@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: #ffffff;
    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: #ffffff;
    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: #444444;
    background-color: transparent;
  }
}
.navbar-inverse .navbar-toggle {
  border-color: #333333;
}
.navbar-inverse .navbar-toggle:hover,
.navbar-inverse .navbar-toggle:focus {
  background-color: #333333;
}
.navbar-inverse .navbar-toggle .icon-bar {
  background-color: #ffffff;
}
.navbar-inverse .navbar-collapse,
.navbar-inverse .navbar-form {
  border-color: #101010;
}
.navbar-inverse .navbar-link {
  color: #9d9d9d;
}
.navbar-inverse .navbar-link:hover {
  color: #ffffff;
}
.navbar-inverse .btn-link {
  color: #9d9d9d;
}
.navbar-inverse .btn-link:hover,
.navbar-inverse .btn-link:focus {
  color: #ffffff;
}
.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: #444444;
}
.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 {
  padding: 0 5px;
  color: #5e5e5e;
  content: "/\00a0";
}
.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;
  margin-left: -1px;
  line-height: 1.42857143;
  color: #296eaa;
  text-decoration: none;
  background-color: #ffffff;
  border: 1px solid #dddddd;
}
.pagination > li > a:hover,
.pagination > li > span:hover,
.pagination > li > a:focus,
.pagination > li > span:focus {
  z-index: 2;
  color: #1a466c;
  background-color: #eeeeee;
  border-color: #dddddd;
}
.pagination > li:first-child > a,
.pagination > li:first-child > span {
  margin-left: 0;
  border-top-left-radius: 2px;
  border-bottom-left-radius: 2px;
}
.pagination > li:last-child > a,
.pagination > li:last-child > span {
  border-top-right-radius: 2px;
  border-bottom-right-radius: 2px;
}
.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: #ffffff;
  cursor: default;
  background-color: #337ab7;
  border-color: #337ab7;
}
.pagination > .disabled > span,
.pagination > .disabled > span:hover,
.pagination > .disabled > span:focus,
.pagination > .disabled > a,
.pagination > .disabled > a:hover,
.pagination > .disabled > a:focus {
  color: #777777;
  cursor: not-allowed;
  background-color: #ffffff;
  border-color: #dddddd;
}
.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-top-left-radius: 3px;
  border-bottom-left-radius: 3px;
}
.pagination-lg > li:last-child > a,
.pagination-lg > li:last-child > span {
  border-top-right-radius: 3px;
  border-bottom-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-top-left-radius: 1px;
  border-bottom-left-radius: 1px;
}
.pagination-sm > li:last-child > a,
.pagination-sm > li:last-child > span {
  border-top-right-radius: 1px;
  border-bottom-right-radius: 1px;
}
.pager {
  padding-left: 0;
  margin: 18px 0;
  text-align: center;
  list-style: none;
}
.pager li {
  display: inline;
}
.pager li > a,
.pager li > span {
  display: inline-block;
  padding: 5px 14px;
  background-color: #ffffff;
  border: 1px solid #dddddd;
  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;
  cursor: not-allowed;
  background-color: #ffffff;
}
.label {
  display: inline;
  padding: .2em .6em .3em;
  font-size: 75%;
  font-weight: 700;
  line-height: 1;
  color: #ffffff;
  text-align: center;
  white-space: nowrap;
  vertical-align: baseline;
  border-radius: .25em;
}
a.label:hover,
a.label:focus {
  color: #ffffff;
  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;
  line-height: 1;
  color: #ffffff;
  text-align: center;
  white-space: nowrap;
  vertical-align: middle;
  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: #ffffff;
  text-decoration: none;
  cursor: pointer;
}
.list-group-item.active > .badge,
.nav-pills > .active > a > .badge {
  color: #296eaa;
  background-color: #ffffff;
}
.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 {
  padding-right: 0px;
  padding-left: 0px;
  border-radius: 3px;
}
.jumbotron .container {
  max-width: 100%;
}
@media screen and (min-width: 768px) {
  .jumbotron {
    padding-top: 48px;
    padding-bottom: 48px;
  }
  .container .jumbotron,
  .container-fluid .jumbotron {
    padding-right: 60px;
    padding-left: 60px;
  }
  .jumbotron h1,
  .jumbotron .h1 {
    font-size: 59px;
  }
}
.thumbnail {
  display: block;
  padding: 4px;
  margin-bottom: 18px;
  line-height: 1.42857143;
  background-color: #ffffff;
  border: 1px solid #dddddd;
  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-right: auto;
  margin-left: auto;
}
a.thumbnail:hover,
a.thumbnail:focus,
a.thumbnail.active {
  border-color: #296eaa;
}
.thumbnail .caption {
  padding: 9px;
  color: #000000;
}
.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 {
  color: #3c763d;
  background-color: #dff0d8;
  border-color: #d6e9c6;
}
.alert-success hr {
  border-top-color: #c9e2b3;
}
.alert-success .alert-link {
  color: #2b542c;
}
.alert-info {
  color: #31708f;
  background-color: #d9edf7;
  border-color: #bce8f1;
}
.alert-info hr {
  border-top-color: #a6e1ec;
}
.alert-info .alert-link {
  color: #245269;
}
.alert-warning {
  color: #8a6d3b;
  background-color: #fcf8e3;
  border-color: #faebcc;
}
.alert-warning hr {
  border-top-color: #f7e1b5;
}
.alert-warning .alert-link {
  color: #66512c;
}
.alert-danger {
  color: #a94442;
  background-color: #f2dede;
  border-color: #ebccd1;
}
.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 {
  height: 18px;
  margin-bottom: 18px;
  overflow: hidden;
  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: #ffffff;
  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 {
  overflow: hidden;
  zoom: 1;
}
.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 {
  padding-left: 0;
  margin-bottom: 20px;
}
.list-group-item {
  position: relative;
  display: block;
  padding: 10px 15px;
  margin-bottom: -1px;
  background-color: #ffffff;
  border: 1px solid #dddddd;
}
.list-group-item:first-child {
  border-top-left-radius: 2px;
  border-top-right-radius: 2px;
}
.list-group-item:last-child {
  margin-bottom: 0;
  border-bottom-right-radius: 2px;
  border-bottom-left-radius: 2px;
}
.list-group-item.disabled,
.list-group-item.disabled:hover,
.list-group-item.disabled:focus {
  color: #777777;
  cursor: not-allowed;
  background-color: #eeeeee;
}
.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: #ffffff;
  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;
}
a.list-group-item,
button.list-group-item {
  color: #555555;
}
a.list-group-item .list-group-item-heading,
button.list-group-item .list-group-item-heading {
  color: #333333;
}
a.list-group-item:hover,
button.list-group-item:hover,
a.list-group-item:focus,
button.list-group-item:focus {
  color: #555555;
  text-decoration: none;
  background-color: #f5f5f5;
}
button.list-group-item {
  width: 100%;
  text-align: left;
}
.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: #ffffff;
  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-left-radius: 1px;
  border-top-right-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 #dddddd;
  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-left-radius: 1px;
  border-top-right-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-left-radius: 0;
  border-top-right-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-right: 15px;
  padding-left: 15px;
}
.panel > .table:first-child,
.panel > .table-responsive:first-child > .table:first-child {
  border-top-left-radius: 1px;
  border-top-right-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-right-radius: 1px;
  border-bottom-left-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 #dddddd;
}
.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 {
  margin-bottom: 0;
  border: 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 #dddddd;
}
.panel-group .panel-footer {
  border-top: 0;
}
.panel-group .panel-footer + .panel-collapse .panel-body {
  border-bottom: 1px solid #dddddd;
}
.panel-default {
  border-color: #dddddd;
}
.panel-default > .panel-heading {
  color: #333333;
  background-color: #f5f5f5;
  border-color: #dddddd;
}
.panel-default > .panel-heading + .panel-collapse > .panel-body {
  border-top-color: #dddddd;
}
.panel-default > .panel-heading .badge {
  color: #f5f5f5;
  background-color: #333333;
}
.panel-default > .panel-footer + .panel-collapse > .panel-body {
  border-bottom-color: #dddddd;
}
.panel-primary {
  border-color: #337ab7;
}
.panel-primary > .panel-heading {
  color: #ffffff;
  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: #ffffff;
}
.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;
  bottom: 0;
  left: 0;
  width: 100%;
  height: 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: #000000;
  text-shadow: 0 1px 0 #ffffff;
  filter: alpha(opacity=20);
  opacity: 0.2;
}
.close:hover,
.close:focus {
  color: #000000;
  text-decoration: none;
  cursor: pointer;
  filter: alpha(opacity=50);
  opacity: 0.5;
}
button.close {
  padding: 0;
  cursor: pointer;
  background: transparent;
  border: 0;
  -webkit-appearance: none;
  appearance: none;
}
.modal-open {
  overflow: hidden;
}
.modal {
  position: fixed;
  top: 0;
  right: 0;
  bottom: 0;
  left: 0;
  z-index: 1050;
  display: none;
  overflow: hidden;
  -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: #ffffff;
  background-clip: padding-box;
  border: 1px solid #999999;
  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);
  outline: 0;
}
.modal-backdrop {
  position: fixed;
  top: 0;
  right: 0;
  bottom: 0;
  left: 0;
  z-index: 1040;
  background-color: #000000;
}
.modal-backdrop.fade {
  filter: alpha(opacity=0);
  opacity: 0;
}
.modal-backdrop.in {
  filter: alpha(opacity=50);
  opacity: 0.5;
}
.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-bottom: 0;
  margin-left: 5px;
}
.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: 400;
  line-height: 1.42857143;
  line-break: auto;
  text-align: left;
  text-align: start;
  text-decoration: none;
  text-shadow: none;
  text-transform: none;
  letter-spacing: normal;
  word-break: normal;
  word-spacing: normal;
  word-wrap: normal;
  white-space: normal;
  font-size: 12px;
  filter: alpha(opacity=0);
  opacity: 0;
}
.tooltip.in {
  filter: alpha(opacity=90);
  opacity: 0.9;
}
.tooltip.top {
  padding: 5px 0;
  margin-top: -3px;
}
.tooltip.right {
  padding: 0 5px;
  margin-left: 3px;
}
.tooltip.bottom {
  padding: 5px 0;
  margin-top: 3px;
}
.tooltip.left {
  padding: 0 5px;
  margin-left: -3px;
}
.tooltip.top .tooltip-arrow {
  bottom: 0;
  left: 50%;
  margin-left: -5px;
  border-width: 5px 5px 0;
  border-top-color: #000000;
}
.tooltip.top-left .tooltip-arrow {
  right: 5px;
  bottom: 0;
  margin-bottom: -5px;
  border-width: 5px 5px 0;
  border-top-color: #000000;
}
.tooltip.top-right .tooltip-arrow {
  bottom: 0;
  left: 5px;
  margin-bottom: -5px;
  border-width: 5px 5px 0;
  border-top-color: #000000;
}
.tooltip.right .tooltip-arrow {
  top: 50%;
  left: 0;
  margin-top: -5px;
  border-width: 5px 5px 5px 0;
  border-right-color: #000000;
}
.tooltip.left .tooltip-arrow {
  top: 50%;
  right: 0;
  margin-top: -5px;
  border-width: 5px 0 5px 5px;
  border-left-color: #000000;
}
.tooltip.bottom .tooltip-arrow {
  top: 0;
  left: 50%;
  margin-left: -5px;
  border-width: 0 5px 5px;
  border-bottom-color: #000000;
}
.tooltip.bottom-left .tooltip-arrow {
  top: 0;
  right: 5px;
  margin-top: -5px;
  border-width: 0 5px 5px;
  border-bottom-color: #000000;
}
.tooltip.bottom-right .tooltip-arrow {
  top: 0;
  left: 5px;
  margin-top: -5px;
  border-width: 0 5px 5px;
  border-bottom-color: #000000;
}
.tooltip-inner {
  max-width: 200px;
  padding: 3px 8px;
  color: #ffffff;
  text-align: center;
  background-color: #000000;
  border-radius: 2px;
}
.tooltip-arrow {
  position: absolute;
  width: 0;
  height: 0;
  border-color: transparent;
  border-style: solid;
}
.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: 400;
  line-height: 1.42857143;
  line-break: auto;
  text-align: left;
  text-align: start;
  text-decoration: none;
  text-shadow: none;
  text-transform: none;
  letter-spacing: normal;
  word-break: normal;
  word-spacing: normal;
  word-wrap: normal;
  white-space: normal;
  font-size: 13px;
  background-color: #ffffff;
  background-clip: padding-box;
  border: 1px solid #cccccc;
  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 > .arrow {
  border-width: 11px;
}
.popover > .arrow,
.popover > .arrow:after {
  position: absolute;
  display: block;
  width: 0;
  height: 0;
  border-color: transparent;
  border-style: solid;
}
.popover > .arrow:after {
  content: "";
  border-width: 10px;
}
.popover.top > .arrow {
  bottom: -11px;
  left: 50%;
  margin-left: -11px;
  border-top-color: #999999;
  border-top-color: rgba(0, 0, 0, 0.25);
  border-bottom-width: 0;
}
.popover.top > .arrow:after {
  bottom: 1px;
  margin-left: -10px;
  content: " ";
  border-top-color: #ffffff;
  border-bottom-width: 0;
}
.popover.right > .arrow {
  top: 50%;
  left: -11px;
  margin-top: -11px;
  border-right-color: #999999;
  border-right-color: rgba(0, 0, 0, 0.25);
  border-left-width: 0;
}
.popover.right > .arrow:after {
  bottom: -10px;
  left: 1px;
  content: " ";
  border-right-color: #ffffff;
  border-left-width: 0;
}
.popover.bottom > .arrow {
  top: -11px;
  left: 50%;
  margin-left: -11px;
  border-top-width: 0;
  border-bottom-color: #999999;
  border-bottom-color: rgba(0, 0, 0, 0.25);
}
.popover.bottom > .arrow:after {
  top: 1px;
  margin-left: -10px;
  content: " ";
  border-top-width: 0;
  border-bottom-color: #ffffff;
}
.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 {
  right: 1px;
  bottom: -10px;
  content: " ";
  border-right-width: 0;
  border-left-color: #ffffff;
}
.popover-title {
  padding: 8px 14px;
  margin: 0;
  font-size: 13px;
  background-color: #f7f7f7;
  border-bottom: 1px solid #ebebeb;
  border-radius: 2px 2px 0 0;
}
.popover-content {
  padding: 9px 14px;
}
.carousel {
  position: relative;
}
.carousel-inner {
  position: relative;
  width: 100%;
  overflow: hidden;
}
.carousel-inner > .item {
  position: relative;
  display: none;
  -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;
  bottom: 0;
  left: 0;
  width: 15%;
  font-size: 20px;
  color: #ffffff;
  text-align: center;
  text-shadow: 0 1px 2px rgba(0, 0, 0, 0.6);
  background-color: rgba(0, 0, 0, 0);
  filter: alpha(opacity=50);
  opacity: 0.5;
}
.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%);
  filter: progid:DXImageTransform.Microsoft.gradient(startColorstr='#80000000', endColorstr='#00000000', GradientType=1);
  background-repeat: repeat-x;
}
.carousel-control.right {
  right: 0;
  left: auto;
  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%);
  filter: progid:DXImageTransform.Microsoft.gradient(startColorstr='#00000000', endColorstr='#80000000', GradientType=1);
  background-repeat: repeat-x;
}
.carousel-control:hover,
.carousel-control:focus {
  color: #ffffff;
  text-decoration: none;
  outline: 0;
  filter: alpha(opacity=90);
  opacity: 0.9;
}
.carousel-control .icon-prev,
.carousel-control .icon-next,
.carousel-control .glyphicon-chevron-left,
.carousel-control .glyphicon-chevron-right {
  position: absolute;
  top: 50%;
  z-index: 5;
  display: inline-block;
  margin-top: -10px;
}
.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;
  font-family: serif;
  line-height: 1;
}
.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%;
  padding-left: 0;
  margin-left: -30%;
  text-align: center;
  list-style: none;
}
.carousel-indicators li {
  display: inline-block;
  width: 10px;
  height: 10px;
  margin: 1px;
  text-indent: -999px;
  cursor: pointer;
  background-color: #000 \9;
  background-color: rgba(0, 0, 0, 0);
  border: 1px solid #ffffff;
  border-radius: 10px;
}
.carousel-indicators .active {
  width: 12px;
  height: 12px;
  margin: 0;
  background-color: #ffffff;
}
.carousel-caption {
  position: absolute;
  right: 15%;
  bottom: 20px;
  left: 15%;
  z-index: 10;
  padding-top: 20px;
  padding-bottom: 20px;
  color: #ffffff;
  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 {
    right: 20%;
    left: 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 {
  display: table;
  content: " ";
}
.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-right: auto;
  margin-left: 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 #eeeeee;
  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: #ffffff;
}
/* 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: #000000;
}
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 compatibility 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: #ffffff;
  /* 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: #ffffff;
  /* 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,
#shutdown {
  color: #333333;
  background-color: #ffffff;
  border-color: #cccccc;
  margin-left: 10px;
}
span#login_widget > .button:focus,
#logout:focus,
#shutdown:focus,
span#login_widget > .button.focus,
#logout.focus,
#shutdown.focus {
  color: #333333;
  background-color: #e6e6e6;
  border-color: #8c8c8c;
}
span#login_widget > .button:hover,
#logout:hover,
#shutdown:hover {
  color: #333333;
  background-color: #e6e6e6;
  border-color: #adadad;
}
span#login_widget > .button:active,
#logout:active,
#shutdown:active,
span#login_widget > .button.active,
#logout.active,
#shutdown.active,
.open > .dropdown-togglespan#login_widget > .button,
.open > .dropdown-toggle#logout,
.open > .dropdown-toggle#shutdown {
  color: #333333;
  background-color: #e6e6e6;
  background-image: none;
  border-color: #adadad;
}
span#login_widget > .button:active:hover,
#logout:active:hover,
#shutdown:active:hover,
span#login_widget > .button.active:hover,
#logout.active:hover,
#shutdown.active:hover,
.open > .dropdown-togglespan#login_widget > .button:hover,
.open > .dropdown-toggle#logout:hover,
.open > .dropdown-toggle#shutdown:hover,
span#login_widget > .button:active:focus,
#logout:active:focus,
#shutdown:active:focus,
span#login_widget > .button.active:focus,
#logout.active:focus,
#shutdown.active:focus,
.open > .dropdown-togglespan#login_widget > .button:focus,
.open > .dropdown-toggle#logout:focus,
.open > .dropdown-toggle#shutdown:focus,
span#login_widget > .button:active.focus,
#logout:active.focus,
#shutdown:active.focus,
span#login_widget > .button.active.focus,
#logout.active.focus,
#shutdown.active.focus,
.open > .dropdown-togglespan#login_widget > .button.focus,
.open > .dropdown-toggle#logout.focus,
.open > .dropdown-toggle#shutdown.focus {
  color: #333333;
  background-color: #d4d4d4;
  border-color: #8c8c8c;
}
span#login_widget > .button.disabled:hover,
#logout.disabled:hover,
#shutdown.disabled:hover,
span#login_widget > .button[disabled]:hover,
#logout[disabled]:hover,
#shutdown[disabled]:hover,
fieldset[disabled] span#login_widget > .button:hover,
fieldset[disabled] #logout:hover,
fieldset[disabled] #shutdown:hover,
span#login_widget > .button.disabled:focus,
#logout.disabled:focus,
#shutdown.disabled:focus,
span#login_widget > .button[disabled]:focus,
#logout[disabled]:focus,
#shutdown[disabled]:focus,
fieldset[disabled] span#login_widget > .button:focus,
fieldset[disabled] #logout:focus,
fieldset[disabled] #shutdown:focus,
span#login_widget > .button.disabled.focus,
#logout.disabled.focus,
#shutdown.disabled.focus,
span#login_widget > .button[disabled].focus,
#logout[disabled].focus,
#shutdown[disabled].focus,
fieldset[disabled] span#login_widget > .button.focus,
fieldset[disabled] #logout.focus,
fieldset[disabled] #shutdown.focus {
  background-color: #ffffff;
  border-color: #cccccc;
}
span#login_widget > .button .badge,
#logout .badge,
#shutdown .badge {
  color: #ffffff;
  background-color: #333333;
}
.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;
  /* Old browsers */
  -webkit-box-flex: 0;
  -moz-box-flex: 0;
  box-flex: 0;
  /* Modern browsers */
  flex: none;
  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;
  }
}
/* rtl fixes for the error, connecting, and renaming window */
[dir="rtl"] .modal-footer {
  text-align: left !important;
}
[dir="rtl"] .close {
  float: left;
}
[dir="rtl"] .fa-step-forward::before {
  content: "\f048";
}
/*!
*
* 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: #eeeeee;
}
.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 #dddddd;
  border-radius: 2px;
}
.list_container > div {
  border-bottom: 1px solid #dddddd;
}
.list_container > div:hover .list-item {
  background-color: red;
}
.list_container > div:last-child {
  border: none;
}
.list_item:hover .list_item {
  background-color: #dddddd;
}
.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;
}
.file_size {
  width: 65px;
  text-align: right;
}
[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: #357935;
}
.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: #eeeeee;
  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 #dddddd;
}
#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: #eeeeee;
  }
}
@media print {
  #texteditor-backdrop #texteditor-container .CodeMirror-gutter,
  #texteditor-backdrop #texteditor-container .CodeMirror-gutters {
    background-color: #ffffff;
  }
}
@media not print {
  #texteditor-backdrop #texteditor-container .CodeMirror-gutter,
  #texteditor-backdrop #texteditor-container .CodeMirror-gutters {
    background-color: #ffffff;
  }
}
@media not print {
  #texteditor-backdrop #texteditor-container {
    padding: 0px;
    background-color: #ffffff;
    -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: #ffffff;
}
/*!
*
* 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-#000000-fg {
  color: #3e424d;
}
.ansi-#000000-bg {
  background-color: #3e424d;
}
.ansi-#000000-intense-fg {
  color: #282c36;
}
.ansi-#000000-intense-bg {
  background-color: #282c36;
}
.ansi-#ff0000-fg {
  color: #e75c58;
}
.ansi-#ff0000-bg {
  background-color: #e75c58;
}
.ansi-#ff0000-intense-fg {
  color: #b22b31;
}
.ansi-#ff0000-intense-bg {
  background-color: #b22b31;
}
.ansi-#008000-fg {
  color: #00a250;
}
.ansi-#008000-bg {
  background-color: #00a250;
}
.ansi-#008000-intense-fg {
  color: #007427;
}
.ansi-#008000-intense-bg {
  background-color: #007427;
}
.ansi-#ffff00-fg {
  color: #ddb62b;
}
.ansi-#ffff00-bg {
  background-color: #ddb62b;
}
.ansi-#ffff00-intense-fg {
  color: #b27d12;
}
.ansi-#ffff00-intense-bg {
  background-color: #b27d12;
}
.ansi-#0000ff-fg {
  color: #208ffb;
}
.ansi-#0000ff-bg {
  background-color: #208ffb;
}
.ansi-#0000ff-intense-fg {
  color: #0065ca;
}
.ansi-#0000ff-intense-bg {
  background-color: #0065ca;
}
.ansi-#ff00ff-fg {
  color: #d160c4;
}
.ansi-#ff00ff-bg {
  background-color: #d160c4;
}
.ansi-#ff00ff-intense-fg {
  color: #a03196;
}
.ansi-#ff00ff-intense-bg {
  background-color: #a03196;
}
.ansi-#00ffff-fg {
  color: #60c6c8;
}
.ansi-#00ffff-bg {
  background-color: #60c6c8;
}
.ansi-#00ffff-intense-fg {
  color: #258f8f;
}
.ansi-#00ffff-intense-bg {
  background-color: #258f8f;
}
.ansi-#ffffff-fg {
  color: #c5c1b4;
}
.ansi-#ffffff-bg {
  background-color: #c5c1b4;
}
.ansi-#ffffff-intense-fg {
  color: #a1a6b2;
}
.ansi-#ffffff-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;
}
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;
  /* Old browsers */
  -webkit-box-flex: 0;
  -moz-box-flex: 0;
  box-flex: 0;
  /* Modern browsers */
  flex: none;
  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: 0;
  -moz-box-flex: 0;
  box-flex: 0;
  /* Modern browsers */
  flex: none;
  /* 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;
  /* Old browsers */
  -webkit-box-flex: 0;
  -moz-box-flex: 0;
  box-flex: 0;
  /* Modern browsers */
  flex: none;
}
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;
  /* Old browsers */
  -webkit-box-flex: 0;
  -moz-box-flex: 0;
  box-flex: 0;
  /* Modern browsers */
  flex: none;
}
@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;
    /* Old browsers */
    -webkit-box-flex: 0;
    -moz-box-flex: 0;
    box-flex: 0;
    /* Modern browsers */
    flex: none;
  }
}
div.prompt_container {
  display: flex;
  flex-direction: row;
  justify-content: space-between;
  align-items: flex-start;
  text-align: right;
}
/* 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.run_this_cell {
  display: none;
  cursor: pointer;
  color: #333;
  padding-top: 5px;
  padding-bottom: 5px;
  padding-left: 2ex;
  padding-right: 2ex;
  width: 1ex;
}
div.prompt {
  min-width: 15ex;
}
@media (-moz-touch-enabled: 1), (any-pointer: coarse) {
  div.run_this_cell {
    display: block;
  }
}
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: #000000;
}
.highlight-variable {
  color: #000000;
}
.highlight-variable-2 {
  color: #1a1a1a;
}
.highlight-variable-3 {
  color: #333333;
}
.highlight-string {
  color: #BA2121;
}
.highlight-comment {
  color: #007979;
  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: #000000;
}
.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: #007979;
  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;
  /* Old browsers */
  -webkit-box-flex: 0;
  -moz-box-flex: 0;
  box-flex: 0;
  /* Modern browsers */
  flex: none;
  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;
  /* Old browsers */
  -webkit-box-flex: 0;
  -moz-box-flex: 0;
  box-flex: 0;
  /* Modern browsers */
  flex: none;
}
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 #000000;
  box-shadow: inset 0 0 1px #000000;
  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;
  /* Old browsers */
  -webkit-box-flex: 0;
  -moz-box-flex: 0;
  box-flex: 0;
  /* Modern browsers */
  flex: none;
}
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;
  /* Old browsers */
  -webkit-box-flex: 0;
  -moz-box-flex: 0;
  box-flex: 0;
  /* Modern browsers */
  flex: none;
}
@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;
    /* Old browsers */
    -webkit-box-flex: 0;
    -moz-box-flex: 0;
    box-flex: 0;
    /* Modern browsers */
    flex: none;
  }
}
div.output_area pre {
  margin: 0;
  padding: 1px 0 1px 0;
  border: 0;
  vertical-align: baseline;
  color: #000000;
  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: #000000;
  /* 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: #000000;
  /* 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: #000000;
  background-color: #000000;
}
.rendered_html pre {
  margin: 1em 2em;
  padding: 0px;
  background-color: #ffffff;
}
.rendered_html code {
  background-color: #eff0f1;
}
.rendered_html p code {
  padding: 1px 5px;
}
.rendered_html pre code {
  background-color: #ffffff;
}
.rendered_html pre,
.rendered_html code {
  border: 0;
  color: #000000;
  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: #000000;
  font-size: 12px;
  table-layout: fixed;
}
.rendered_html thead {
  border-bottom: 1px solid #000000;
  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;
  /* Old browsers */
  -webkit-box-flex: 0;
  -moz-box-flex: 0;
  box-flex: 0;
  /* Modern browsers */
  flex: none;
}
@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: #000000;
  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;
  padding-bottom: 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: #ffffff;
    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: #eeeeee;
  }
}
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-flex: 0;
  -moz-box-flex: 0;
  box-flex: 0;
  /* Modern browsers */
  flex: none;
  /* 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: #ffffff;
  background-image: none;
  border: 1px solid #cccccc;
  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: #999999;
  opacity: 1;
}
.celltoolbar select:-ms-input-placeholder {
  color: #999999;
}
.celltoolbar select::-webkit-input-placeholder {
  color: #999999;
}
.celltoolbar select::-ms-expand {
  background-color: transparent;
  border: 0;
}
.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), #eeeeee);
}
.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: #ffffff;
  background-image: none;
  border: 1px solid #cccccc;
  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: #999999;
  opacity: 1;
}
.cell-tag:-ms-input-placeholder,
.tags-input input:-ms-input-placeholder,
.tags-input button:-ms-input-placeholder {
  color: #999999;
}
.cell-tag::-webkit-input-placeholder,
.tags-input input::-webkit-input-placeholder,
.tags-input button::-webkit-input-placeholder {
  color: #999999;
}
.cell-tag::-ms-expand,
.tags-input input::-ms-expand,
.tags-input button::-ms-expand {
  background-color: transparent;
  border: 0;
}
.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: #000000;
  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: #565656;
  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: #565656;
  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: #565656;
  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: #565656;
  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: #565656;
  z-index: 10;
  background: rgba(240, 240, 240, 0.5);
  margin-right: 4px;
  color: #333333;
  background-color: #ffffff;
  border-color: #cccccc;
}
.notification_widget:focus,
.notification_widget.focus {
  color: #333333;
  background-color: #e6e6e6;
  border-color: #8c8c8c;
}
.notification_widget:hover {
  color: #333333;
  background-color: #e6e6e6;
  border-color: #adadad;
}
.notification_widget:active,
.notification_widget.active,
.open > .dropdown-toggle.notification_widget {
  color: #333333;
  background-color: #e6e6e6;
  background-image: none;
  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: #333333;
  background-color: #d4d4d4;
  border-color: #8c8c8c;
}
.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: #ffffff;
  border-color: #cccccc;
}
.notification_widget .badge {
  color: #ffffff;
  background-color: #333333;
}
.notification_widget.warning {
  background-color: #f0ad4e;
  border-color: #eea236;
  color: #ffffff;
  background-color: #b46102;
  border-color: #b46102;
}
.notification_widget.warning:focus,
.notification_widget.warning.focus {
  color: #ffffff;
  background-color: #ec971f;
  border-color: #985f0d;
}
.notification_widget.warning:hover {
  color: #ffffff;
  background-color: #ec971f;
  border-color: #d58512;
}
.notification_widget.warning:active,
.notification_widget.warning.active,
.open > .dropdown-toggle.notification_widget.warning {
  color: #ffffff;
  background-color: #ec971f;
  background-image: none;
  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: #ffffff;
  background-color: #d58512;
  border-color: #985f0d;
}
.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: #ffffff;
}
.notification_widget.success {
  color: #ffffff;
  background-color: #5cb85c;
  border-color: #4cae4c;
}
.notification_widget.success:focus,
.notification_widget.success.focus {
  color: #ffffff;
  background-color: #449d44;
  border-color: #255625;
}
.notification_widget.success:hover {
  color: #ffffff;
  background-color: #449d44;
  border-color: #398439;
}
.notification_widget.success:active,
.notification_widget.success.active,
.open > .dropdown-toggle.notification_widget.success {
  color: #ffffff;
  background-color: #449d44;
  background-image: none;
  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: #ffffff;
  background-color: #398439;
  border-color: #255625;
}
.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: #ffffff;
}
.notification_widget.info {
  color: #ffffff;
  background-color: #5bc0de;
  border-color: #46b8da;
}
.notification_widget.info:focus,
.notification_widget.info.focus {
  color: #ffffff;
  background-color: #31b0d5;
  border-color: #1b6d85;
}
.notification_widget.info:hover {
  color: #ffffff;
  background-color: #31b0d5;
  border-color: #269abc;
}
.notification_widget.info:active,
.notification_widget.info.active,
.open > .dropdown-toggle.notification_widget.info {
  color: #ffffff;
  background-color: #31b0d5;
  background-image: none;
  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: #ffffff;
  background-color: #269abc;
  border-color: #1b6d85;
}
.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: #ffffff;
}
.notification_widget.danger {
  background-color: #d9534f;
  border-color: #d43f3a;
  color: #ffffff;
  background-color: #df0404;
  border-color: #df0404;
}
.notification_widget.danger:focus,
.notification_widget.danger.focus {
  color: #ffffff;
  background-color: #c9302c;
  border-color: #761c19;
}
.notification_widget.danger:hover {
  color: #ffffff;
  background-color: #c9302c;
  border-color: #ac2925;
}
.notification_widget.danger:active,
.notification_widget.danger.active,
.open > .dropdown-toggle.notification_widget.danger {
  color: #ffffff;
  background-color: #c9302c;
  background-image: none;
  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: #ffffff;
  background-color: #ac2925;
  border-color: #761c19;
}
.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: #ffffff;
}
div#pager {
  background-color: #ffffff;
  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: #000000;
  background-color: #f7f7f7;
  padding: 0.4em;
}
div#pager #pager-button-area {
  position: absolute;
  top: 8px;
  right: 20px;
}
div#pager #pager-button-area .ui-button {
  padding-top: 0px;
  padding-bottom: 0px;
  padding-right: 10px;
  padding-left: 10px;
}
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;
  /* Old browsers */
  -webkit-box-flex: 0;
  -moz-box-flex: 0;
  box-flex: 0;
  /* Modern browsers */
  flex: none;
  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: 85px;
}
.tooltipbuttons {
  position: absolute;
  padding-right: 15px;
  top: 0px;
  right: 0px;
}
.tooltipbuttons .ui-button {
  padding-top: 0px;
  padding-bottom: 0px;
  padding-right: 10px;
  padding-left: 10px;
}
.tooltiptext {
  /*avoid the button to overlap on some docstring*/
  padding-right: 30px;
  /*avoid the ui-icon(s) from overlapping the tooltip*/
  padding-top: 5px;
}
.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: #eeeeee;
}
.terminal-app #header {
  background: #ffffff;
  -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);
  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-container {
  padding-top: 20px;
  height: 100%;
}
.terminal-app #terminado-container {
  height: 100%;
}
.btn-danger {
  color: #ffffff;
  background-color: #df0404;
  border-color: #df0404;
}
.btn-warning {
  color: #ffffff;
  background-color: #b46102;
  border-color: #b46102;
}
.close {
  float: right;
  font-size: 19.5px;
  font-weight: bold;
  line-height: 1;
  color: #000000;
  text-shadow: 0 1px 0 #ffffff;
  filter: alpha(opacity=60);
  opacity: 0.6;
}
.close:hover,
.close:focus {
  color: #000000;
  text-decoration: none;
  cursor: pointer;
  filter: alpha(opacity=100);
  opacity: 1;
}
button.close {
  padding: 0;
  cursor: pointer;
  background: transparent;
  border: 0;
  -webkit-appearance: none;
  appearance: none;
}
.navbar-nav > li > a {
  color: #565656;
}
.navbar-nav > li > a:focus {
  /* -webkit-focus-ring-color = '#5B9DD9' */
  outline: -webkit-focus-ring-color auto 5px;
}
/*# 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 */
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<h1 id="Matrix-Decomposition">Matrix Decomposition<a class="anchor-link" href="#Matrix-Decomposition">&#182;</a></h1><p><strong>FIZ353 - Numerical Analysis | 06/11/2020</strong></p>
<p>Emre S. Tasci <a href="mailto:emre.tasci@hacettepe.edu.tr">emre.tasci@hacettepe.edu.tr</a></p>

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<p>Any set of linear relations involving variables can be represented in different formats and -most of the time- can be solved via a number of methods. Before we delve unto some of these methods, a little revision might be useful.</p>
<h2 id="Revision-of-systems-of-linear-equations">Revision of systems of linear equations<a class="anchor-link" href="#Revision-of-systems-of-linear-equations">&#182;</a></h2><h3 id="Classification-of-linear-systems">Classification of linear systems<a class="anchor-link" href="#Classification-of-linear-systems">&#182;</a></h3><p>Any equation that contains -at most- 1st power of its variables is called a linear equation (e.g., $3x + 5y = 1$ is a <em>linear equation</em> whereas $3x^2 + 5\sqrt y$ isn't (it is a <em>non-linear equation</em>)). If we have more than one linear equation, then we are working on a linear system. Depending on the number of <u>independent</u> equations ($n_e$) and the number of variables ($n_v$) our linear system will belong to one of these three classes:</p>
<ol>
<li><strong>Underdetermined linear system</strong><br>
When the number of the variables ($n_v$) is greater than the number of equations ($n_e$) there will be infinite solutions. Consider the equation: $x - y = 5$ in this case any one of the pairs (-3.4, -8.4), (5,0), (6.2,1.2), (7,2), ... will satisfy the equation.</li>
<li><strong>Independent linear system</strong><br>
When we have $n_v = n_e$ then there is one and only one solution set, i.e., the equation will be satisfied for exactly one value of each variable. For example: $x - 3 = 5$ is satisfied only when $x=8$, likewise $3x + 2y = 8\: \&amp;\:x - y = 1$ equations are <em>simultaneously</em> satisfied only for (x,y) = (2,1) values.</li>
<li><strong>Overdetermined linear system</strong><br>
When $n_v$ &lt; $n_e$ we have an overdetermined system where there is no solution. This kind of systems usually appear in experimental measurings. Suppose that the weight with respect to mass is measured for a specific mass. From Newton's 2nd equation: $F_g = mg$, so, we would expect to find the same reading, however, there will be a discrepancy regarding the measured weights. So, even though we have the same value for m, and fixed value for g, their product manifestation will differ a little bit for each measurement. We usually take the average of these values to transform an overdetermined linear system into an independent linear system.</li>
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<h3 id="Transformation-of-a-set-of-linear-equations-into-a-linear-system">Transformation of a set of linear equations into a linear system<a class="anchor-link" href="#Transformation-of-a-set-of-linear-equations-into-a-linear-system">&#182;</a></h3><p>Usually, the physical problem at hand will be presented to be composed of some variables collected in a number of equations. Before proceeding to solve them, one must rearrange them so that the variables are ordered in the same way in each equation and the numerical value is written to the right hand side of the equation, e.g.:</p>
\begin{align}
x - 3 &amp;= y\\
y - 2x + 2 &amp;= 11
\end{align}<p>can be rearranged into:</p>
\begin{align}
x - y &amp;= 3\\
-2x + y &amp;= 9
\end{align}
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<h3 id="Gaussian-Elimination">Gaussian Elimination<a class="anchor-link" href="#Gaussian-Elimination">&#182;</a></h3><p>The most popular method to solve a linear system is the Gaussian Elimination where one equation is picked and by being multiplied by a scalar to fit the negative of the coefficient of the variable that is wanted to be eliminated in another equation and afterwards added to that equation. Take this linear system:</p>
\begin{align}
10x_1 + 2x_2 - x_3 &amp;= 27\quad\quad[1]\\
-3x_1 - 5x_2 + 2x_3 &amp;= -61.5\quad[2]\\
x_1 + x_2 + 6x_3 &amp;= -21.5\quad[3]
\end{align}<p>To eliminate $x_1$ in the 2nd equation, we multiply the 1st equation by -3/10 and subtract it from the 2nd equation (as we are adding/subtracting <u>an equation</u> (which in essence, has the same meaning like 2=2 or 5=5, both sides of the 2nd equation will be affected the same and even though it will become a different equation, the equality will still hold, e.g., "4 = 4" + "5 = 5" =&gt; "9 = 9" (still valid)). We do a similar thing to eliminate $x_1$ in the 3rd equation as well (multiply the 1st by 1/10 and subtract it from the 3rd).</p>
<p>After this modification, the equations becomes:
\begin{align}
[1]:\quad10x_1 + 2x_2 - x_3 &amp;= 27\\
\left[[2] - \left(-{\tfrac{3} {10}}\right)\cdot[1]\right]:\quad 0 - 4.4x_2 + 1.7x_3&amp;=-53.4\\
\left[[3] - \left({\tfrac{1} {10}}\right)\cdot[1]\right]:\quad 0 + 0.8x_2 + 6.1x_3 &amp;= -24.2
\end{align}</p>
<p>Now we will use 2nd equation to eliminate $x_2$ in the 3rd equation. If we multiply the 2nd equation by $\left(\frac{0.8}{-4.4}\right)$ and subtract it from the 3rd equation:</p>
\begin{align}
[1]:\quad10x_1 + 2x_2 - x_3 &amp;= 27\\
[2]:\quad 0 - 4.4x_2 + 1.7x_3&amp;=-53.4\\
\left[[3] - \left(-{\tfrac{0.8} {4.4}}\right)\cdot[2]\right]:\quad 0 + 0 + 6.41x_3 &amp;= -33.91
\end{align}
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<p>The 3rd equation only contains $x_3$ so we can immediately calculate it:</p>
<p>$x_3 = \frac{-33.91}{6.41} = -5.29$</p>
<p>Now that we know $x_3$, substituting this value into the 2nd equation, we can find $x_2$:</p>
<p>$-4.4x_2 + 1.7\cdot(-5.29) = -53.4 \Rightarrow x_2 = \frac{-53.4 + 8.99}{(-4.4)} = 10.09$</p>
<p>and finally, substituting the newly found values of $x_2$ and $x_3$ into the 1st equation:</p>
<p>$10x_1 + 2\cdot(10.09) - (-5.29) = 27 \Rightarrow x_1 = 0.15$</p>

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<p>When we were going downward, eliminating one of the variables on each run in the equations below, this process is called <strong>forward elimination</strong>. Then, when we reached the bottom, we had a direct equality for only a single variable and we went back to the top by substituting the found values to find the other variables. This going back process to recover all the unknowns is called <strong>backward substitution</strong>.</p>

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<h3 id="Matrix-Representation-of-Linear-Systems">Matrix Representation of Linear Systems<a class="anchor-link" href="#Matrix-Representation-of-Linear-Systems">&#182;</a></h3><p>We can fasten the analyzing process by representing our linear system as a matrix multiplication. Continuing with the same case, i.e.,\begin{align}
10x_1 + 2x_2 - x_3 &amp;= 27\\
-3x_1 - 5x_2 + 2x_3 &amp;= -61.5\\
x_1 + x_2 + 6x_3 &amp;= -21.5
\end{align}</p>
<p>we can represent it, without any loss of information, as:</p>
$$\begin{bmatrix}
10 &amp; 2 &amp; -1\\
-3 &amp; -5 &amp; 2\\
1 &amp; 1 &amp; 6
\end{bmatrix}\begin{bmatrix}x_1\\x_2\\x_3\end{bmatrix}=\begin{bmatrix}27\\-61.5\\-21.5\end{bmatrix}$$<p>Therefore it is now a matrix multiplication, i.e., $A\cdot x=b$, where:</p>
$$A=\begin{bmatrix}
10 &amp; 2 &amp; -1\\
-3 &amp; -5 &amp; 2\\
1 &amp; 1 &amp; 6
\end{bmatrix} \quad x=\begin{bmatrix}x_1\\x_2\\x_3\end{bmatrix} \quad b=\begin{bmatrix}27\\-61.5\\-21.5\end{bmatrix}$$
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<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="n">A</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">10.</span><span class="p">,</span> <span class="mf">2.</span><span class="p">,</span> <span class="o">-</span><span class="mf">1.</span><span class="p">],[</span><span class="o">-</span><span class="mf">3.</span><span class="p">,</span> <span class="o">-</span><span class="mf">5.</span><span class="p">,</span> <span class="mf">2.</span><span class="p">],[</span><span class="mf">1.</span><span class="p">,</span> <span class="mf">1.</span><span class="p">,</span> <span class="mf">6.</span><span class="p">]])</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;A:</span><span class="se">\n</span><span class="s2">&quot;</span><span class="p">,</span><span class="n">A</span><span class="p">,</span><span class="s2">&quot;</span><span class="se">\n</span><span class="s2">&quot;</span><span class="p">)</span>

<span class="n">b</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">27.</span><span class="p">],[</span><span class="o">-</span><span class="mf">61.5</span><span class="p">],[</span><span class="o">-</span><span class="mf">21.5</span><span class="p">]])</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;b:</span><span class="se">\n</span><span class="s2">&quot;</span><span class="p">,</span><span class="n">b</span><span class="p">,</span><span class="s2">&quot;</span><span class="se">\n</span><span class="s2">&quot;</span><span class="p">)</span>

<span class="c1"># Define a new matrix to store the modified values:</span>
<span class="n">A2</span> <span class="o">=</span> <span class="n">A</span> 

<span class="c1"># Multiply the first row by (-3/10) and subtract it from the second:</span>
<span class="n">A2</span><span class="p">[</span><span class="mi">1</span><span class="p">,:]</span> <span class="o">=</span> <span class="n">A</span><span class="p">[</span><span class="mi">1</span><span class="p">,:]</span> <span class="o">-</span> <span class="p">(</span><span class="o">-</span><span class="mi">3</span><span class="o">/</span><span class="mi">10</span><span class="p">)</span><span class="o">*</span><span class="n">A</span><span class="p">[</span><span class="mi">0</span><span class="p">,:]</span>

<span class="c1"># Multiply the first row by (1/10) and subtract it from the second:</span>
<span class="n">A2</span><span class="p">[</span><span class="mi">2</span><span class="p">,:]</span> <span class="o">=</span> <span class="n">A</span><span class="p">[</span><span class="mi">2</span><span class="p">,:]</span> <span class="o">-</span> <span class="p">(</span><span class="mi">1</span><span class="o">/</span><span class="mi">10</span><span class="p">)</span><span class="o">*</span><span class="n">A</span><span class="p">[</span><span class="mi">0</span><span class="p">,:]</span>

<span class="c1"># Here&#39;s the current situation:</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;A2:</span><span class="se">\n</span><span class="s2">&quot;</span><span class="p">,</span><span class="n">A2</span><span class="p">,</span><span class="s2">&quot;</span><span class="se">\n</span><span class="s2">&quot;</span><span class="p">)</span>

<span class="c1"># We need to do apply the same operations to the right hand side</span>
<span class="c1"># of the equation, as well:</span>
<span class="n">b2</span> <span class="o">=</span> <span class="n">b</span>
<span class="n">b2</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">-=</span> <span class="p">(</span><span class="o">-</span><span class="mf">3.</span><span class="o">/</span><span class="mf">10.</span><span class="p">)</span><span class="o">*</span><span class="n">b2</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
<span class="n">b2</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="o">-=</span> <span class="p">(</span> <span class="mf">1.</span><span class="o">/</span><span class="mf">10.</span><span class="p">)</span><span class="o">*</span><span class="n">b2</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;b:</span><span class="se">\n</span><span class="s2">&quot;</span><span class="p">,</span><span class="n">b</span><span class="p">,</span><span class="s2">&quot;</span><span class="se">\n</span><span class="s2">&quot;</span><span class="p">)</span>

<span class="c1"># In the next iteration, we multiply the second row by -0.8/4.4</span>
<span class="c1"># and subtract it from the third to eliminate x_2</span>
<span class="n">A2</span><span class="p">[</span><span class="mi">2</span><span class="p">,:]</span> <span class="o">-=</span> <span class="p">(</span><span class="o">-</span><span class="mf">0.8</span><span class="o">/</span><span class="mf">4.4</span><span class="p">)</span><span class="o">*</span><span class="n">A2</span><span class="p">[</span><span class="mi">1</span><span class="p">,:]</span>
<span class="n">b2</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="o">-=</span> <span class="p">(</span><span class="o">-</span><span class="mf">0.8</span><span class="o">/</span><span class="mf">4.4</span><span class="p">)</span><span class="o">*</span><span class="n">b2</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;A2:</span><span class="se">\n</span><span class="s2">&quot;</span><span class="p">,</span><span class="n">A2</span><span class="p">,</span><span class="s2">&quot;</span><span class="se">\n</span><span class="s2">&quot;</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;b2:</span><span class="se">\n</span><span class="s2">&quot;</span><span class="p">,</span><span class="n">b2</span><span class="p">,</span><span class="s2">&quot;</span><span class="se">\n</span><span class="s2">&quot;</span><span class="p">)</span>

<span class="c1"># Now we can solve </span>
<span class="n">x3</span> <span class="o">=</span> <span class="n">b2</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="o">/</span> <span class="n">A</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">x2</span> <span class="o">=</span> <span class="p">(</span><span class="n">b2</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="n">A</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="o">*</span><span class="n">x3</span><span class="p">)</span> <span class="o">/</span> <span class="n">A</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="n">x1</span> <span class="o">=</span> <span class="p">(</span><span class="n">b2</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">-</span> <span class="n">A</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span><span class="mi">2</span><span class="p">]</span><span class="o">*</span><span class="n">x3</span> <span class="o">-</span> <span class="n">A</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="o">*</span><span class="n">x2</span><span class="p">)</span> <span class="o">/</span> <span class="n">A</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="nb">print</span> <span class="p">(</span><span class="s2">&quot;x1: </span><span class="si">%.5f</span><span class="se">\t</span><span class="s2">x2: </span><span class="si">%.5f</span><span class="se">\t</span><span class="s2">x3: </span><span class="si">%.5f</span><span class="se">\n</span><span class="s2">&quot;</span><span class="o">%</span><span class="p">(</span><span class="n">x1</span><span class="p">,</span><span class="n">x2</span><span class="p">,</span><span class="n">x3</span><span class="p">))</span>
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<pre>A:
 [[10.  2. -1.]
 [-3. -5.  2.]
 [ 1.  1.  6.]] 

b:
 [[ 27. ]
 [-61.5]
 [-21.5]] 

A2:
 [[10.   2.  -1. ]
 [ 0.  -4.4  1.7]
 [ 0.   0.8  6.1]] 

b:
 [[ 27. ]
 [-53.4]
 [-24.2]] 

A2:
 [[10.          2.         -1.        ]
 [ 0.         -4.4         1.7       ]
 [ 0.          0.          6.40909091]] 

b2:
 [[ 27.        ]
 [-53.4       ]
 [-33.90909091]] 

x1: 0.15248	x2: 10.09220	x3: -5.29078

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<p>In each step, modifying both the rows of A and b is a little bit tiring, therefore we can "merge" the two to have an <em>augmented matrix</em> for practical purposes:</p>
$$\left[ \begin{array}{ccc|c}
10 &amp; 2 &amp; -1 &amp; 27\\
-3 &amp; -5 &amp; 2 &amp; -61.5\\
1 &amp; 1 &amp; 6 &amp; -21.5
\end{array} \right]$$<p>and take it from there all at once:</p>

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<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="n">AA</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">10.</span><span class="p">,</span> <span class="mf">2.</span><span class="p">,</span> <span class="o">-</span><span class="mf">1.</span><span class="p">,</span> <span class="mf">27.</span><span class="p">],[</span><span class="o">-</span><span class="mf">3.</span><span class="p">,</span> <span class="o">-</span><span class="mf">5.</span><span class="p">,</span> <span class="mf">2.</span><span class="p">,</span> <span class="o">-</span><span class="mf">61.5</span><span class="p">],[</span><span class="mf">1.</span><span class="p">,</span> <span class="mf">1.</span><span class="p">,</span> <span class="mf">6.</span><span class="p">,</span><span class="o">-</span><span class="mf">21.5</span><span class="p">]])</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Initial AA:</span><span class="se">\n</span><span class="s2">&quot;</span><span class="p">,</span><span class="n">AA</span><span class="p">,</span><span class="s2">&quot;</span><span class="se">\n</span><span class="s2">&quot;</span><span class="p">)</span>

<span class="n">AA</span><span class="p">[</span><span class="mi">1</span><span class="p">,:]</span> <span class="o">-=</span> <span class="o">-</span><span class="mf">3.</span><span class="o">/</span><span class="mf">10.</span><span class="o">*</span><span class="n">AA</span><span class="p">[</span><span class="mi">0</span><span class="p">,:]</span>
<span class="n">AA</span><span class="p">[</span><span class="mi">2</span><span class="p">,:]</span> <span class="o">-=</span>  <span class="mf">1.</span><span class="o">/</span><span class="mf">10.</span><span class="o">*</span><span class="n">AA</span><span class="p">[</span><span class="mi">0</span><span class="p">,:]</span>
<span class="n">AA</span><span class="p">[</span><span class="mi">2</span><span class="p">,:]</span> <span class="o">-=</span>  <span class="o">-</span><span class="mf">0.8</span><span class="o">/</span><span class="mf">4.4</span><span class="o">*</span><span class="n">AA</span><span class="p">[</span><span class="mi">1</span><span class="p">,:]</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Eliminated AA:</span><span class="se">\n</span><span class="s2">&quot;</span><span class="p">,</span><span class="n">AA</span><span class="p">,</span><span class="s2">&quot;</span><span class="se">\n</span><span class="s2">&quot;</span><span class="p">)</span>
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<pre>Initial AA:
 [[ 10.    2.   -1.   27. ]
 [ -3.   -5.    2.  -61.5]
 [  1.    1.    6.  -21.5]] 

Eliminated AA:
 [[ 10.           2.          -1.          27.        ]
 [  0.          -4.4          1.7        -53.4       ]
 [  0.           0.           6.40909091 -33.90909091]] 

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<h3 id="Pivoting-in-Gaussian">Pivoting in Gaussian<a class="anchor-link" href="#Pivoting-in-Gaussian">&#182;</a></h3><p>It's a good strategy from precision's point of view to reorder the rows such that the diagonal elements are the ones with the greater absolute value in their column.</p>
<p>If we were to pivot our case example, but this time we'll assume that we had the rows interchanged to start with:
$$\left[ \begin{array}{ccc|c}
1 &amp; 1 &amp; 6 &amp; -21.5\\
-3 &amp; -5 &amp; 2 &amp; -61.5\\
10 &amp; 2 &amp; -1 &amp; 27
\end{array} \right]$$</p>
<ol>
<li>We start with the 1st column. Since 10 is the biggest number in that column, we bring it to the top and proceed with the elimination of $x_1$<br>
$$\left[ \begin{array}{ccc|c}
10 &amp; 2 &amp; -1 &amp; 27\\
1 &amp; 1 &amp; 6 &amp; -21.5\\
-3 &amp; -5 &amp; 2 &amp; -61.5
\end{array} \right]$$</li>
</ol>
$$\left[ \begin{array}{ccc|c}
10 &amp; 2 &amp; -1 &amp; 27\\
0 &amp; 0.8 &amp; 6.1 &amp; -24.2\\
0 &amp; -4.4 &amp; 1.7 &amp; -53.4
\end{array} \right]$$<ol>
<li>Checking the 2nd column we have |-4.4| for the biggest number, so we swap rows 3 and 2. (Even if the 1st row had the greates number, we would be ignoring it because we can only manipulate the current row and below)
$$\left[ \begin{array}{ccc|c}
10 &amp; 2 &amp; -1 &amp; 27\\
0 &amp; -4.4 &amp; 1.7 &amp; -53.4\\
0 &amp; 0.8 &amp; 6.1 &amp; -24.2
\end{array} \right]$$</li>
</ol>
<p>and do the elimination for $x_2$ in the 3rd equation:</p>
$$\left[ \begin{array}{ccc|c}
10 &amp; 2 &amp; -1 &amp; 27\\
0 &amp; -4.4 &amp; 1.7 &amp; -53.4\\
0 &amp; 0 &amp; 6.41 &amp; -33.9
\end{array} \right]$$<p>...and we have arrived at the same (and most optimal) ordering that we had taken for granted in the previous section.</p>
<p>But what can differ by simply changing the order of the equations and then proceeding elimination? To illustrate the importance of pivoting, consider the following case:</p>

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<p><strong>Example</strong> Use Gauss elimination with and without pivoting to solve the following linear system:</p>
$$\begin{align}
0.0003x_1 + 3.0000x_2 &amp;= 2.0001\\
1.0000x_1 + 1.0000x_2 &amp;= 1.0000
\end{align}$$<p><em><strong>Without pivoting:</strong></em>
To eliminate x_1 in the second equation, we need to multiply the 1st equation by 1.0000/0.0003 and then subtract it:</p>
$$1.0000/0.0003 \times \text{[1st equation]: } x_1 + 10000x_2 = 6667$$<p>subtract this from the 2nd equation:</p>
$$-9999x_2 = -6666\\
x_2 = \frac{6666}{9999} = 2/3$$<p>Substitute this value into the 1st equation:
$$\Rightarrow x_1 = \frac{2.0001 - 3x_2}{0.0003} = \frac{2.0001 - 3(2/3)}{0.0003}$$</p>
<p>The obtained values for $x_1$ will be dependent on the number of significant figures taken for $x_2 = 2/3$:</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">x1_true</span> <span class="o">=</span> <span class="mi">1</span><span class="o">/</span><span class="mi">3</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;#SF</span><span class="se">\t</span><span class="s2">x2</span><span class="se">\t\t</span><span class="s2"> x1</span><span class="se">\t\t</span><span class="s2">Err%&quot;</span><span class="p">)</span>
<span class="k">for</span> <span class="n">sigfig_no</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="mi">8</span><span class="p">):</span>
    <span class="n">formatstr</span> <span class="o">=</span> <span class="s2">&quot;%.&quot;</span><span class="o">+</span><span class="s2">&quot;</span><span class="si">%d</span><span class="s2">&quot;</span><span class="o">%</span><span class="k">sigfig_no</span>+&quot;f&quot;
    <span class="n">numstr</span> <span class="o">=</span> <span class="n">formatstr</span><span class="o">%</span><span class="p">(</span><span class="mi">2</span><span class="o">/</span><span class="mi">3</span><span class="p">)</span>
    <span class="n">x2</span> <span class="o">=</span> <span class="nb">float</span><span class="p">(</span><span class="n">numstr</span><span class="p">)</span>
    <span class="n">x1</span> <span class="o">=</span> <span class="p">(</span><span class="mf">2.0001</span> <span class="o">-</span> <span class="mi">3</span><span class="o">*</span><span class="n">x2</span><span class="p">)</span> <span class="o">/</span> <span class="mf">0.0003</span>
    <span class="n">abs_per_rel_err_x1</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">x1_true</span><span class="o">-</span><span class="n">x1</span><span class="p">)</span> <span class="o">/</span> <span class="p">(</span><span class="n">x1_true</span><span class="p">)</span> <span class="o">*</span> <span class="mi">100</span>
    <span class="nb">print</span><span class="p">(</span><span class="s2">&quot;</span><span class="si">%2d</span><span class="se">\t</span><span class="si">%.9f</span><span class="se">\t</span><span class="si">%12.9f</span><span class="se">\t</span><span class="si">%7.2f</span><span class="s2">&quot;</span><span class="o">%</span><span class="p">(</span><span class="n">sigfig_no</span><span class="p">,</span><span class="n">x2</span><span class="p">,</span><span class="n">x1</span><span class="p">,</span><span class="n">abs_per_rel_err_x1</span><span class="p">))</span>
    
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<pre>#SF	x2		 x1		Err%
 3	0.667000000	-3.000000000	1000.00
 4	0.666700000	 0.000000000	 100.00
 5	0.666670000	 0.300000000	  10.00
 6	0.666667000	 0.330000000	   1.00
 7	0.666666700	 0.333000000	   0.10
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<p><em><strong>With pivoting:</strong></em>
This time, let's first proceed with pivoting. For the first column, second row has the greatest value (1 &gt; 0.0003) so, let's rearrange:</p>
$$\begin{align}
1.0000x_1 + 1.0000x_2 &amp;= 1.0000\\
0.0003x_1 + 3.0000x_2 &amp;= 2.0001
\end{align}$$<p>Solving once again, we multiply the 1st equation with 0.0003 and subtract it from the 2nd:</p>
$$0.0003 \times \text{[1st equation]: } 0.0003x_1 + 0.0003x_2 = 0.0003$$<p>subtract this from the 2nd equation:</p>
$$2.9997x_2 = 1.9998\\
x_2 = \frac{1.9998}{2.9997} = 2/3$$<p>We still get the same value for $x_2$, howeveri this time, the equation we'll substitute this value is "a little bit" different than the previous one:</p>
<p>Substitute this value into the 1st equation:
$$\Rightarrow x_1 = 1.0000 - x_2 = 1 - (2/3)$$</p>
<p>The obtained values for $x_1$ will still be dependent on the number of significant figures taken for $x_2 = 2/3$, but let's see what happens this time:</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">x1_true</span> <span class="o">=</span> <span class="mi">1</span><span class="o">/</span><span class="mi">3</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;#SF</span><span class="se">\t</span><span class="s2">x2</span><span class="se">\t\t</span><span class="s2"> x1</span><span class="se">\t\t</span><span class="s2">   Err%&quot;</span><span class="p">)</span>
<span class="k">for</span> <span class="n">sigfig_no</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="mi">8</span><span class="p">):</span>
    <span class="n">formatstr</span> <span class="o">=</span> <span class="s2">&quot;%.&quot;</span><span class="o">+</span><span class="s2">&quot;</span><span class="si">%d</span><span class="s2">&quot;</span><span class="o">%</span><span class="k">sigfig_no</span>+&quot;f&quot;
    <span class="n">numstr</span> <span class="o">=</span> <span class="n">formatstr</span><span class="o">%</span><span class="p">(</span><span class="mi">2</span><span class="o">/</span><span class="mi">3</span><span class="p">)</span>
    <span class="n">x2</span> <span class="o">=</span> <span class="nb">float</span><span class="p">(</span><span class="n">numstr</span><span class="p">)</span>
    <span class="n">x1</span> <span class="o">=</span> <span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="n">x2</span><span class="p">)</span> 
    <span class="n">abs_per_rel_err_x1</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">x1_true</span><span class="o">-</span><span class="n">x1</span><span class="p">)</span> <span class="o">/</span> <span class="p">(</span><span class="n">x1_true</span><span class="p">)</span> <span class="o">*</span> <span class="mi">100</span>
    <span class="nb">print</span><span class="p">(</span><span class="s2">&quot;</span><span class="si">%2d</span><span class="se">\t</span><span class="si">%.9f</span><span class="se">\t</span><span class="si">%12.9f</span><span class="se">\t</span><span class="si">%7.2f</span><span class="s2">&quot;</span><span class="o">%</span><span class="p">(</span><span class="n">sigfig_no</span><span class="p">,</span><span class="n">x2</span><span class="p">,</span><span class="n">x1</span><span class="p">,</span><span class="n">abs_per_rel_err_x1</span><span class="p">))</span>
  
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<pre>#SF	x2		 x1		   Err%
 3	0.667000000	 0.333000000	   0.10
 4	0.666700000	 0.333300000	   0.01
 5	0.666670000	 0.333330000	   0.00
 6	0.666667000	 0.333333000	   0.00
 7	0.666666700	 0.333333300	   0.00
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<p>Thus, the precision has been greatly increased!</p>

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<h3 id="LU-Decomposition">LU Decomposition<a class="anchor-link" href="#LU-Decomposition">&#182;</a></h3><p>Suppose that in the $A\cdot x=b$ linear system, $A$ remains fixed but b keeps changing. This can be a situation where the medium changes but the equipment remains the same, e.g., measuring the magnetic field in different parts of a room. In order to not to do all the forward elimination &amp; backwards substition all over again when <em>b</em> changes, we apply the LU decomposition, developed by none other than Alan Turing himself! In other words, decompose our A matrix into the multiplication of two other matrices L and U, such that L is a lower trigonal matrix and U is an upper trigonal matrix:</p>
$$ A = L \cdot U\\
L = \begin{bmatrix}
1 &amp; 0 &amp; 0\\
l_{21} &amp; 1 &amp; 0\\
l_{31} &amp; l_{32} &amp; 1
\end{bmatrix},\quad
U = \begin{bmatrix}
u_{11} &amp; u_{12} &amp; u_{13}\\
0 &amp; u_{22} &amp; u_{23}\\
0 &amp; 0 &amp; u_{33}
\end{bmatrix}
$$<p>When we were applying the Gauss elimination method, we were already working on this decomposition. Remember the coefficients we multiplied the rows to subtract from the other rows to eliminate? Those were our elements of the L matrix, and the transformed part was the U matrix!</p>
<p>In our case study, we had:
\begin{align}10x_1 + 2x_2 - x_3 &amp;= 27\\
-3x_1 - 5x_2 + 2x_3 &amp;= -61.5\\
x_1 + x_2 + 6x_3 &amp;= -21.5
\end{align}</p>
$$\begin{bmatrix}
10 &amp; 2 &amp; -1\\
-3 &amp; -5 &amp; 2\\
1 &amp; 1 &amp; 6
\end{bmatrix}\begin{bmatrix}x_1\\x_2\\x_3\end{bmatrix}=\begin{bmatrix}27\\-61.5\\-21.5\end{bmatrix}$$<p>The steps we took in elimination were as follows:</p>
<ol>
<li>Multiplied the 1st eqn by -3/10 and subtracted it from the 2nd eqn.</li>
<li>Multiplied the 1st eqn by  1/10 and subtracted it from the 3rd eqn.</li>
<li>Multiplied the 2nd eqn by -0.8/4.4 and subtracted it from the 3rd eqn.</li>
</ol>
<p>These coefficients yield the L matrix:
$$l_{21} = -3/10 = -0.3\\
l_{31} = 1/10 = 0.1\quad l_{32} = -0.8 / 4.4 = -0.18\\\\
L = \begin{bmatrix}
1 &amp; 0 &amp; 0\\
-3/10 &amp; 1 &amp; 0\\
1/10 &amp; -0.8/4.4 &amp; 1
\end{bmatrix}
$$</p>
<p>After the eliminations we had <em>A</em> transformed into:
$$\begin{bmatrix}
10 &amp; 2 &amp; -1\\
0 &amp; -4.4 &amp; 1.7\\
0 &amp; 0 &amp; 6.41
\end{bmatrix}$$</p>
<p>which is actually our U matrix. Let's test if their multiplication indeed yields <em>A</em>:</p>

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<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="n">L</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">1.</span><span class="p">,</span> <span class="mf">0.</span><span class="p">,</span> <span class="mf">0.</span><span class="p">],[</span><span class="o">-</span><span class="mf">3.</span><span class="o">/</span><span class="mf">10.</span><span class="p">,</span> <span class="mf">1.</span><span class="p">,</span> <span class="mf">0.</span><span class="p">],[</span><span class="mf">1.</span><span class="o">/</span><span class="mf">10.</span><span class="p">,</span><span class="o">-</span><span class="mf">0.8</span><span class="o">/</span><span class="mf">4.4</span><span class="p">,</span><span class="mf">1.</span><span class="p">]])</span>
<span class="n">U</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">10.</span><span class="p">,</span> <span class="mf">2.</span><span class="p">,</span> <span class="o">-</span><span class="mf">1.</span><span class="p">],[</span><span class="mf">0.</span><span class="p">,</span><span class="o">-</span><span class="mf">4.4</span><span class="p">,</span> <span class="mf">1.7</span><span class="p">],[</span><span class="mf">0.</span><span class="p">,</span><span class="mf">0.</span><span class="p">,</span><span class="mf">6.41</span><span class="p">]])</span>

<span class="n">LU</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">L</span><span class="p">,</span><span class="n">U</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;LU:</span><span class="se">\n</span><span class="s2">&quot;</span><span class="p">,</span><span class="n">LU</span><span class="p">,</span><span class="s2">&quot;</span><span class="se">\n</span><span class="s2">&quot;</span><span class="p">)</span>
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<pre>LU:
 [[10.          2.         -1.        ]
 [-3.         -5.          2.        ]
 [ 1.          1.          6.00090909]] 

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<p>Thus we have verified that $A = L\cdot U$</p>
<p>To proceed we first solve $L\cdot z = b$ where $z$ is a column vector of unknowns $z$. Continuing with our case study:
$$
L = \begin{bmatrix}
1 &amp; 0 &amp; 0\\
l_{21} &amp; 1 &amp; 0\\
l_{31} &amp; l_{32} &amp; 1
\end{bmatrix}\begin{bmatrix}z_1\\z_2\\z_3\end{bmatrix}=\begin{bmatrix}27\\-61.5\\-21.5\end{bmatrix}$$</p>
<p>$z_1$ is directly available, and forward substituting, we also find $z_2$ and $z_3$:</p>
$$\begin{bmatrix}z_1\\z_2\\z_3\end{bmatrix} = \begin{bmatrix}27\\-53.4\\-33.91\end{bmatrix}$$<p>Now we solve the $U\cdot x = z$ system:
$$\begin{bmatrix}
10 &amp; 2 &amp; -1\\
0 &amp; -4.4 &amp; 1.7\\
0 &amp; 0 &amp; 6.41
\end{bmatrix}\begin{bmatrix}x_1\\x_2\\x_3\end{bmatrix}=\begin{bmatrix}z_1\\z_2\\z_3\end{bmatrix}$$</p>
<p>This time, $x_3$ is readily available, and backward substituting, we derive $x_2$ and $x_1$:</p>
$$\begin{bmatrix}x_1\\x_2\\x_3\end{bmatrix}=\begin{bmatrix}0.15\\10.09\\-5.29\end{bmatrix}$$<p>Now that we have decomposed our system, even if the results ($b$) change, all we have to do is direct backward/forward substitution!</p>

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<h3 id="Inverse-of-a-matrix">Inverse of a matrix<a class="anchor-link" href="#Inverse-of-a-matrix">&#182;</a></h3><p>Inverse of a matrix $A$ can be calculated via various ways.</p>
<p><strong>The systematical way</strong></p>
<ol>
<li>Calculate the <em>matrix of minors</em>, $M$ whose element $m_{i,j}$ is the determinant of the minor matrice constructed from $A$ with the ith row and jth column removed.</li>
<li>Construct <em>matrix of cofactors</em> $C$ from $M$ such that: $c_{i,j}=(-1)^{i+j}\cdot m_{i,j}$</li>
<li>Calculate the <em>adjoint</em> of $C$: $C^{*T}$</li>
<li>Calculate $\frac{1}{\det (A)}$ (having already calculated $C$, it will be very straightforward to calculate $\det (A)$)</li>
<li>$A^{-1} = \frac{C^{*T}}{\det(A)}$</li>
</ol>
<p><strong>Example:</strong> Calculate the inverse of $A=\begin{bmatrix}
10 &amp; 2 &amp; -1\\
-3 &amp; -5 &amp; 2\\
1 &amp; 1 &amp; 6
\end{bmatrix}$</p>

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<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="k">def</span> <span class="nf">minor</span><span class="p">(</span><span class="n">arr</span><span class="p">,</span><span class="n">i</span><span class="p">,</span><span class="n">j</span><span class="p">):</span>
    <span class="c1"># ith row, jth column removed</span>
    <span class="k">return</span> <span class="n">arr</span><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="nb">list</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="n">i</span><span class="p">))</span><span class="o">+</span><span class="nb">list</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="n">i</span><span class="o">+</span><span class="mi">1</span><span class="p">,</span><span class="n">arr</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="n">np</span><span class="o">.</span><span class="n">newaxis</span><span class="p">],</span>
               <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="nb">list</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="n">j</span><span class="p">))</span><span class="o">+</span><span class="nb">list</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="n">j</span><span class="o">+</span><span class="mi">1</span><span class="p">,</span><span class="n">arr</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"># Source: https://stackoverflow.com/a/3858333</span>

<span class="n">A</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">mat</span><span class="p">([[</span><span class="mf">10.</span><span class="p">,</span> <span class="mf">2.</span><span class="p">,</span> <span class="o">-</span><span class="mf">1.</span><span class="p">],[</span><span class="o">-</span><span class="mf">3.</span><span class="p">,</span> <span class="o">-</span><span class="mf">5.</span><span class="p">,</span> <span class="mf">2.</span><span class="p">],[</span><span class="mf">1.</span><span class="p">,</span> <span class="mf">1.</span><span class="p">,</span> <span class="mf">6.</span><span class="p">]])</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;A:</span><span class="se">\n</span><span class="s2">&quot;</span><span class="p">,</span><span class="n">A</span><span class="p">,</span><span class="s2">&quot;</span><span class="se">\n</span><span class="s2">&quot;</span><span class="p">)</span>

<span class="n">C</span> <span class="o">=</span> <span class="n">A</span><span class="o">*</span><span class="mi">2</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="mi">3</span><span class="p">):</span>
    <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="mi">3</span><span class="p">):</span>
        <span class="n">C</span><span class="p">[</span><span class="n">i</span><span class="p">,</span><span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span><span class="o">**</span><span class="p">(</span><span class="n">i</span><span class="o">+</span><span class="n">j</span><span class="p">)</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">det</span><span class="p">(</span><span class="n">minor</span><span class="p">(</span><span class="n">A</span><span class="p">,</span><span class="n">i</span><span class="p">,</span><span class="n">j</span><span class="p">))</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;C:</span><span class="se">\n</span><span class="s2">&quot;</span><span class="p">,</span><span class="n">C</span><span class="p">,</span><span class="s2">&quot;</span><span class="se">\n</span><span class="s2">&quot;</span><span class="p">)</span>
<span class="n">CT</span> <span class="o">=</span> <span class="n">C</span><span class="o">.</span><span class="n">H</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;C^*T:</span><span class="se">\n</span><span class="s2">&quot;</span><span class="p">,</span><span class="n">CT</span><span class="p">,</span><span class="s2">&quot;</span><span class="se">\n</span><span class="s2">&quot;</span><span class="p">)</span>

<span class="n">detA</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">det</span><span class="p">(</span><span class="n">A</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;detA: &quot;</span><span class="p">,</span><span class="n">detA</span><span class="p">,</span><span class="s2">&quot;</span><span class="se">\n</span><span class="s2">&quot;</span><span class="p">)</span>
<span class="c1"># or det is also:</span>
<span class="c1">#print(np.dot(A[0,:],np.squeeze(np.asarray(C[0,:]))))</span>

<span class="n">invA</span> <span class="o">=</span> <span class="n">CT</span> <span class="o">/</span> <span class="n">detA</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;invA:</span><span class="se">\n</span><span class="s2">&quot;</span><span class="p">,</span><span class="n">invA</span><span class="p">,</span><span class="s2">&quot;</span><span class="se">\n</span><span class="s2">&quot;</span><span class="p">)</span>
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<pre>A:
 [[10.  2. -1.]
 [-3. -5.  2.]
 [ 1.  1.  6.]] 

C:
 [[-32.  20.   2.]
 [-13.  61.  -8.]
 [ -1. -17. -44.]] 

C^*T:
 [[-32. -13.  -1.]
 [ 20.  61. -17.]
 [  2.  -8. -44.]] 

detA:  -282.00000000000006 

invA:
 [[ 0.11347518  0.04609929  0.0035461 ]
 [-0.07092199 -0.21631206  0.06028369]
 [-0.0070922   0.02836879  0.15602837]] 

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<p>As we now have $A^{-1}$, we can directly multiply from left of both sides of the $A\cdot x = b$ equation to get:
\begin{align}A^{-1} (A\cdot x) = (A^{-1}A)x &amp;=A^{-1}b\\
x &amp;= A^{-1}b\end{align}</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="c1"># Continuing from the previous code where invA was calculated</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;invA:</span><span class="se">\n</span><span class="s2">&quot;</span><span class="p">,</span><span class="n">invA</span><span class="p">,</span><span class="s2">&quot;</span><span class="se">\n</span><span class="s2">&quot;</span><span class="p">)</span>

<span class="n">b</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">27.</span><span class="p">],[</span><span class="o">-</span><span class="mf">61.5</span><span class="p">],[</span><span class="o">-</span><span class="mf">21.5</span><span class="p">]])</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;b</span><span class="se">\n</span><span class="s2">&quot;</span><span class="p">,</span><span class="n">b</span><span class="p">,</span><span class="s2">&quot;</span><span class="se">\n</span><span class="s2">&quot;</span><span class="p">)</span>

<span class="n">x</span> <span class="o">=</span> <span class="n">invA</span> <span class="o">*</span> <span class="n">b</span>
<span class="nb">print</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
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<pre>invA:
 [[ 0.11347518  0.04609929  0.0035461 ]
 [-0.07092199 -0.21631206  0.06028369]
 [-0.0070922   0.02836879  0.15602837]] 

b
 [[ 27. ]
 [-61.5]
 [-21.5]] 

[[ 0.15248227]
 [10.09219858]
 [-5.29078014]]
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<h3 id="Cramer's-Rule">Cramer's Rule<a class="anchor-link" href="#Cramer's-Rule">&#182;</a></h3><p>In this method, we substitute the value column vector <em>b</em> into the relevant column of the coefficients matrix <em>A</em> to form the $D_i$ matrix. The unknown value is found by calculating: $$\frac{\det (D_i)}{\det (A)}$$</p>
$$\begin{bmatrix}
a_{11} &amp; a_{12} &amp; a_{13}\\
a_{21} &amp; a_{22} &amp; a_{23}\\
a_{31} &amp; a_{32} &amp; a_{33}
\end{bmatrix}\begin{bmatrix}x_1\\x_2\\x_3\end{bmatrix}=\begin{bmatrix}y_1\\y_2\\y_3\end{bmatrix}$$$$x_1 = \frac{\det\begin{bmatrix}
y_1 &amp; a_{12} &amp; a_{13}\\
y_2 &amp; a_{22} &amp; a_{23}\\
y_3 &amp; a_{32} &amp; a_{33}
\end{bmatrix} }{\det \begin{bmatrix}
a_{11} &amp; a_{12} &amp; a_{13}\\
a_{21} &amp; a_{22} &amp; a_{23}\\
a_{31} &amp; a_{32} &amp; a_{33}
\end{bmatrix}}
,\quad
x_2 = \frac{\det\begin{bmatrix}
a_{11} &amp; y_1 &amp; a_{13}\\
a_{21} &amp; y_2 &amp; a_{23}\\
a_{31} &amp; y_3 &amp; a_{33}
\end{bmatrix} }{\det \begin{bmatrix}
a_{11} &amp; a_{12} &amp; a_{13}\\
a_{21} &amp; a_{22} &amp; a_{23}\\
a_{31} &amp; a_{32} &amp; a_{33}
\end{bmatrix}},\quad ...
$$<p>This method is used when one needs to find not all the unknowns, but some of them.</p>
<p><strong>Example</strong>
\begin{align}
10x_1 + 2x_2 - x_3 &amp;= 27\\
-3x_1 - 5x_2 + 2x_3 &amp;= -61.5\\
x_1 + x_2 + 6x_3 &amp;= -21.5
\end{align}</p>
$$A=\begin{bmatrix}
10 &amp; 2 &amp; -1\\
-3 &amp; -5 &amp; 2\\
1 &amp; 1 &amp; 6
\end{bmatrix} \quad x=\begin{bmatrix}x_1\\x_2\\x_3\end{bmatrix} \quad b=\begin{bmatrix}27\\-61.5\\-21.5\end{bmatrix}$$
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<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="n">A</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">10.</span><span class="p">,</span> <span class="mf">2.</span><span class="p">,</span> <span class="o">-</span><span class="mf">1.</span><span class="p">],[</span><span class="o">-</span><span class="mf">3.</span><span class="p">,</span> <span class="o">-</span><span class="mf">5.</span><span class="p">,</span> <span class="mf">2.</span><span class="p">],[</span><span class="mf">1.</span><span class="p">,</span> <span class="mf">1.</span><span class="p">,</span> <span class="mf">6.</span><span class="p">]])</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;A:</span><span class="se">\n</span><span class="s2">&quot;</span><span class="p">,</span><span class="n">A</span><span class="p">,</span><span class="s2">&quot;</span><span class="se">\n</span><span class="s2">&quot;</span><span class="p">)</span>

<span class="n">b</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">27.</span><span class="p">],[</span><span class="o">-</span><span class="mf">61.5</span><span class="p">],[</span><span class="o">-</span><span class="mf">21.5</span><span class="p">]])</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;b:</span><span class="se">\n</span><span class="s2">&quot;</span><span class="p">,</span><span class="n">b</span><span class="p">,</span><span class="s2">&quot;</span><span class="se">\n</span><span class="s2">&quot;</span><span class="p">)</span>

<span class="n">D1</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">copy</span><span class="p">(</span><span class="n">A</span><span class="p">)</span>
<span class="n">D2</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">copy</span><span class="p">(</span><span class="n">A</span><span class="p">)</span>
<span class="n">D3</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">copy</span><span class="p">(</span><span class="n">A</span><span class="p">)</span>

<span class="n">D1</span><span class="p">[:,</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">transpose</span><span class="p">(</span><span class="n">b</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;D1:</span><span class="se">\n</span><span class="s2">&quot;</span><span class="p">,</span><span class="n">D1</span><span class="p">,</span><span class="s2">&quot;</span><span class="se">\n</span><span class="s2">&quot;</span><span class="p">)</span>
<span class="n">det_D1</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">det</span><span class="p">(</span><span class="n">D1</span><span class="p">)</span>

<span class="n">D2</span><span class="p">[:,</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">transpose</span><span class="p">(</span><span class="n">b</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;D2:</span><span class="se">\n</span><span class="s2">&quot;</span><span class="p">,</span><span class="n">D2</span><span class="p">,</span><span class="s2">&quot;</span><span class="se">\n</span><span class="s2">&quot;</span><span class="p">)</span>
<span class="n">det_D2</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">det</span><span class="p">(</span><span class="n">D2</span><span class="p">)</span>

<span class="n">D3</span><span class="p">[:,</span><span class="mi">2</span><span class="p">]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">transpose</span><span class="p">(</span><span class="n">b</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;D3:</span><span class="se">\n</span><span class="s2">&quot;</span><span class="p">,</span><span class="n">D3</span><span class="p">,</span><span class="s2">&quot;</span><span class="se">\n</span><span class="s2">&quot;</span><span class="p">)</span>
<span class="n">det_D3</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">det</span><span class="p">(</span><span class="n">D3</span><span class="p">)</span>

<span class="n">det_A</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">det</span><span class="p">(</span><span class="n">A</span><span class="p">)</span>

<span class="n">x1</span> <span class="o">=</span> <span class="n">det_D1</span> <span class="o">/</span> <span class="n">det_A</span>
<span class="n">x2</span> <span class="o">=</span> <span class="n">det_D2</span> <span class="o">/</span> <span class="n">det_A</span>
<span class="n">x3</span> <span class="o">=</span> <span class="n">det_D3</span> <span class="o">/</span> <span class="n">det_A</span>
<span class="nb">print</span> <span class="p">(</span><span class="s2">&quot;x1: </span><span class="si">%.5f</span><span class="se">\t</span><span class="s2">x2: </span><span class="si">%.5f</span><span class="se">\t</span><span class="s2">x3: </span><span class="si">%.5f</span><span class="se">\n</span><span class="s2">&quot;</span><span class="o">%</span><span class="p">(</span><span class="n">x1</span><span class="p">,</span><span class="n">x2</span><span class="p">,</span><span class="n">x3</span><span class="p">))</span>
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<pre>A:
 [[10.  2. -1.]
 [-3. -5.  2.]
 [ 1.  1.  6.]] 

b:
 [[ 27. ]
 [-61.5]
 [-21.5]] 

D1:
 [[ 27.    2.   -1. ]
 [-61.5  -5.    2. ]
 [-21.5   1.    6. ]] 

D2:
 [[ 10.   27.   -1. ]
 [ -3.  -61.5   2. ]
 [  1.  -21.5   6. ]] 

D3:
 [[ 10.    2.   27. ]
 [ -3.   -5.  -61.5]
 [  1.    1.  -21.5]] 

x1: 0.15248	x2: 10.09220	x3: -5.29078

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<h3 id="solve()-function">solve() function<a class="anchor-link" href="#solve()-function">&#182;</a></h3><p><code>solve(A,b)</code> function from numpy.linalg package directly solves the $A\cdot b = x$ system of linear equations:</p>

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<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="n">A</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">10.</span><span class="p">,</span> <span class="mf">2.</span><span class="p">,</span> <span class="o">-</span><span class="mf">1.</span><span class="p">],[</span><span class="o">-</span><span class="mf">3.</span><span class="p">,</span> <span class="o">-</span><span class="mf">5.</span><span class="p">,</span> <span class="mf">2.</span><span class="p">],[</span><span class="mf">1.</span><span class="p">,</span> <span class="mf">1.</span><span class="p">,</span> <span class="mf">6.</span><span class="p">]])</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;A:</span><span class="se">\n</span><span class="s2">&quot;</span><span class="p">,</span><span class="n">A</span><span class="p">,</span><span class="s2">&quot;</span><span class="se">\n</span><span class="s2">&quot;</span><span class="p">)</span>

<span class="n">b</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">27.</span><span class="p">],[</span><span class="o">-</span><span class="mf">61.5</span><span class="p">],[</span><span class="o">-</span><span class="mf">21.5</span><span class="p">]])</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;b:</span><span class="se">\n</span><span class="s2">&quot;</span><span class="p">,</span><span class="n">b</span><span class="p">,</span><span class="s2">&quot;</span><span class="se">\n</span><span class="s2">&quot;</span><span class="p">)</span>

<span class="n">x</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">solve</span><span class="p">(</span><span class="n">A</span><span class="p">,</span><span class="n">b</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;x:</span><span class="se">\n</span><span class="s2">&quot;</span><span class="p">,</span><span class="n">x</span><span class="p">,</span><span class="s2">&quot;</span><span class="se">\n</span><span class="s2">&quot;</span><span class="p">)</span>
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<pre>A:
 [[10.  2. -1.]
 [-3. -5.  2.]
 [ 1.  1.  6.]] 

b:
 [[ 27. ]
 [-61.5]
 [-21.5]] 

x:
 [[ 0.15248227]
 [10.09219858]
 [-5.29078014]] 

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<h3 id="lu()-function">lu() function<a class="anchor-link" href="#lu()-function">&#182;</a></h3><p><code>LU = lu(A)</code> from scipy.linalg gives the LU decomposition of A</p>

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<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">scipy.linalg</span> <span class="k">as</span> <span class="nn">la</span>
<span class="n">A</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">mat</span><span class="p">([[</span><span class="mf">10.</span><span class="p">,</span> <span class="mf">2.</span><span class="p">,</span> <span class="o">-</span><span class="mf">1.</span><span class="p">],[</span><span class="o">-</span><span class="mf">3.</span><span class="p">,</span> <span class="o">-</span><span class="mf">5.</span><span class="p">,</span> <span class="mf">2.</span><span class="p">],[</span><span class="mf">1.</span><span class="p">,</span> <span class="mf">1.</span><span class="p">,</span> <span class="mf">6.</span><span class="p">]])</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;A:</span><span class="se">\n</span><span class="s2">&quot;</span><span class="p">,</span><span class="n">A</span><span class="p">,</span><span class="s2">&quot;</span><span class="se">\n</span><span class="s2">&quot;</span><span class="p">)</span>

<span class="n">b</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">mat</span><span class="p">([[</span><span class="mf">27.</span><span class="p">],[</span><span class="o">-</span><span class="mf">61.5</span><span class="p">],[</span><span class="o">-</span><span class="mf">21.5</span><span class="p">]])</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;b:</span><span class="se">\n</span><span class="s2">&quot;</span><span class="p">,</span><span class="n">b</span><span class="p">,</span><span class="s2">&quot;</span><span class="se">\n</span><span class="s2">&quot;</span><span class="p">)</span>

<span class="p">(</span><span class="n">P</span><span class="p">,</span><span class="n">L</span><span class="p">,</span><span class="n">U</span><span class="p">)</span><span class="o">=</span> <span class="n">la</span><span class="o">.</span><span class="n">lu</span><span class="p">(</span><span class="n">A</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;L</span><span class="se">\n</span><span class="s2">&quot;</span><span class="p">,</span><span class="n">L</span><span class="p">,</span><span class="s2">&quot;</span><span class="se">\n</span><span class="s2">&quot;</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;U</span><span class="se">\n</span><span class="s2">&quot;</span><span class="p">,</span><span class="n">U</span><span class="p">,</span><span class="s2">&quot;</span><span class="se">\n</span><span class="s2">&quot;</span><span class="p">)</span>

<span class="n">z</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">solve</span><span class="p">(</span><span class="n">L</span><span class="p">,</span><span class="n">b</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;z</span><span class="se">\n</span><span class="s2">&quot;</span><span class="p">,</span><span class="n">z</span><span class="p">,</span><span class="s2">&quot;</span><span class="se">\n</span><span class="s2">&quot;</span><span class="p">)</span>
<span class="n">x</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">solve</span><span class="p">(</span><span class="n">U</span><span class="p">,</span><span class="n">z</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;x</span><span class="se">\n</span><span class="s2">&quot;</span><span class="p">,</span><span class="n">x</span><span class="p">,</span><span class="s2">&quot;</span><span class="se">\n</span><span class="s2">&quot;</span><span class="p">)</span>
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<pre>A:
 [[10.  2. -1.]
 [-3. -5.  2.]
 [ 1.  1.  6.]] 

b:
 [[ 27. ]
 [-61.5]
 [-21.5]] 

L
 [[ 1.          0.          0.        ]
 [-0.3         1.          0.        ]
 [ 0.1        -0.18181818  1.        ]] 

U
 [[10.          2.         -1.        ]
 [ 0.         -4.4         1.7       ]
 [ 0.          0.          6.40909091]] 

z
 [[ 27.        ]
 [-53.4       ]
 [-33.90909091]] 

x
 [[ 0.15248227]
 [10.09219858]
 [-5.29078014]] 

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<h1 id="Eigenvalues-and-Eigenvectors-as-Decomposition">Eigenvalues and Eigenvectors as Decomposition<a class="anchor-link" href="#Eigenvalues-and-Eigenvectors-as-Decomposition">&#182;</a></h1>
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<p>We have already seen that for an $A$ (square) matrix, we could find such a special vector $\vec{u}$ that when multiplied it returned the vector itself, scaled by a scalar $\lambda$:</p>
$$A\cdot\vec{u} = \lambda \vec{u}$$<p>For such a case, the scalar $\lambda$ was called as the <em>eigenvalue</em> and the vector $\vec{u}$ was called as the <em>eigenvector</em>. Eigenvalues and eigenvectors play a very special part in all branches of physics, most notably in Quantum Mechanics.</p>
<p>Now, we will treat them as a way to decompose our matrix, into a multiplication of 3 matrices, one being a diagonal matrix holding the eigenvalues and the other two being the inverse of each other. So:</p>
$$ U^{-1}\cdot A \cdot U = D$$<p>and hence, equivalently:</p>
$$ U\cdot D \cdot U^{-1} = A$$<p>where $U = \begin{bmatrix}\rule[-1ex]{0.5pt}{2.5ex} &amp; \rule[-1ex]{0.5pt}{2.5ex} &amp; &amp;\rule[-1ex]{0.5pt}{2.5ex}\\ \vec{u}_1 &amp; \vec{u}_2&amp;\cdots&amp;\vec{u}_n\\\rule[-1ex]{0.5pt}{2.5ex} &amp; \rule[-1ex]{0.5pt}{2.5ex}  &amp; &amp;\rule[-1ex]{0.5pt}{2.5ex} \end{bmatrix}$ and $D=\begin{bmatrix}\lambda_1 &amp; &amp; \\ &amp; \ddots &amp; \\ &amp;  &amp; \lambda_n\end{bmatrix}$ such that:</p>
$$A\cdot \vec{u}_i = \lambda_i\, \vec{u}_i$$
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<p><strong>Example</strong><br>
Consider:
$$A=\begin{bmatrix}2&amp;3\\4&amp;5\end{bmatrix}$$</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">A</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">2</span><span class="p">,</span><span class="mi">3</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="p">[</span><span class="n">lambdas</span><span class="p">,</span> <span class="n">U</span><span class="p">]</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">eig</span><span class="p">(</span><span class="n">A</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Eigenvalues: &quot;</span><span class="p">,</span><span class="n">lambdas</span><span class="p">,</span><span class="s2">&quot;</span><span class="se">\n</span><span class="s2">-----</span><span class="se">\n</span><span class="s2">Eigenvectors Matrix:</span><span class="se">\n</span><span class="s2">&quot;</span><span class="p">,</span><span class="n">U</span><span class="p">)</span>
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<pre>Eigenvalues:  [-0.27491722  7.27491722] 
-----
Eigenvectors Matrix:
 [[-0.79681209 -0.49436913]
 [ 0.60422718 -0.86925207]]
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">D</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">diag</span><span class="p">(</span><span class="n">lambdas</span><span class="p">)</span>
<span class="n">D</span>
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<pre>array([[-0.27491722,  0.        ],
       [ 0.        ,  7.27491722]])</pre>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="c1"># U.D.(inv(U)) ==&gt; A</span>
<span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">multi_dot</span><span class="p">((</span><span class="n">U</span><span class="p">,</span><span class="n">D</span><span class="p">,</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">U</span><span class="p">)))</span>
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<pre>array([[2., 3.],
       [4., 5.]])</pre>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="c1">#(inv(U)).A.U ==&gt; D</span>
<span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">multi_dot</span><span class="p">((</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">U</span><span class="p">),</span><span class="n">A</span><span class="p">,</span><span class="n">U</span><span class="p">))</span>
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<pre>array([[-2.74917218e-01,  0.00000000e+00],
       [-2.77555756e-17,  7.27491722e+00]])</pre>
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<h2 id="Numerical-calculation-of-eigenvectors-(not-na&#239;ve,-nor-optimized)">Numerical calculation of eigenvectors (not na&#239;ve, nor optimized)<a class="anchor-link" href="#Numerical-calculation-of-eigenvectors-(not-na&#239;ve,-nor-optimized)">&#182;</a></h2><p>Consider a zombie breakout (with cure): at every hour, 20% of the humans turn to zombies while %10 of the zombies recover and once again become human. So if the current number of humans is $h_0$ and number of zombies is $z_0$, after 1 hour, this numbers will be:</p>
$$\begin{align*}
h_1 &amp;= h_0\times 80\% + z_0\times 10\%\\
z_1 &amp;= z_0\times 90\% + h_0\times 20\%
\end{align*}$$<p>or, rearranging the above equations into a matrix multiplication:</p>
$$\begin{pmatrix}h_1 \\ z_1 \end{pmatrix} = \begin{bmatrix}0.80 &amp; 0.10 \\ 0.20 &amp; 0.90\end{bmatrix}\begin{pmatrix}h_0 \\ z_0 \end{pmatrix}$$<p>Let's start with a total number of 120 humans and 60 zombies:</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">h0</span> <span class="o">=</span> <span class="mi">120</span>
<span class="n">z0</span> <span class="o">=</span> <span class="mi">60</span>
<span class="n">hz0</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">h0</span><span class="p">],[</span><span class="n">z0</span><span class="p">]])</span>

<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Hour: </span><span class="si">{:2d}</span><span class="s2"> | Humans # </span><span class="si">{:8.4f}</span><span class="s2"> | Zombies # </span><span class="si">{:8.4f}</span><span class="s2">&quot;</span>
      <span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="n">h0</span><span class="p">,</span><span class="n">z0</span><span class="p">))</span>

<span class="n">trmat</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">0.8</span><span class="p">,</span> <span class="mf">0.1</span><span class="p">],[</span><span class="mf">0.2</span><span class="p">,</span> <span class="mf">0.9</span><span class="p">]])</span>


<span class="k">for</span> <span class="n">hour</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="mi">200</span><span class="p">):</span>
    <span class="n">hz1</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">trmat</span><span class="p">,</span><span class="n">hz0</span><span class="p">)</span>
    <span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Hour: </span><span class="si">{:2d}</span><span class="s2"> | Humans # </span><span class="si">{:8.4f}</span><span class="s2"> | Zombies # </span><span class="si">{:8.4f}</span><span class="s2">&quot;</span>
      <span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">hour</span><span class="p">,</span><span class="n">hz1</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="n">hz1</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="c1"># check if hz1 &amp; hz0 are parallel</span>
    <span class="n">cross_p</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">cross</span><span class="p">(</span><span class="n">hz0</span><span class="p">[:,</span><span class="mi">0</span><span class="p">],</span><span class="n">hz1</span><span class="p">[:,</span><span class="mi">0</span><span class="p">])</span>
    <span class="k">if</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">norm</span><span class="p">(</span><span class="n">cross_p</span><span class="p">)</span> <span class="o">&lt;</span> <span class="mf">1E-2</span><span class="p">):</span>
        <span class="c1"># They are parallel</span>
        <span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Found it!</span><span class="se">\n</span><span class="s2">&quot;</span><span class="p">,</span><span class="n">hz1</span><span class="p">)</span>
        <span class="k">break</span>
    <span class="k">else</span><span class="p">:</span>
        <span class="c1"># continue the &quot;evolution&quot;</span>
        <span class="n">hz0</span> <span class="o">=</span> <span class="n">hz1</span><span class="o">.</span><span class="n">copy</span><span class="p">()</span>
    
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<pre>Hour:  0 | Humans # 120.0000 | Zombies #  60.0000
Hour:  1 | Humans # 102.0000 | Zombies #  78.0000
Hour:  2 | Humans #  89.4000 | Zombies #  90.6000
Hour:  3 | Humans #  80.5800 | Zombies #  99.4200
Hour:  4 | Humans #  74.4060 | Zombies # 105.5940
Hour:  5 | Humans #  70.0842 | Zombies # 109.9158
Hour:  6 | Humans #  67.0589 | Zombies # 112.9411
Hour:  7 | Humans #  64.9413 | Zombies # 115.0587
Hour:  8 | Humans #  63.4589 | Zombies # 116.5411
Hour:  9 | Humans #  62.4212 | Zombies # 117.5788
Hour: 10 | Humans #  61.6949 | Zombies # 118.3051
Hour: 11 | Humans #  61.1864 | Zombies # 118.8136
Hour: 12 | Humans #  60.8305 | Zombies # 119.1695
Hour: 13 | Humans #  60.5813 | Zombies # 119.4187
Hour: 14 | Humans #  60.4069 | Zombies # 119.5931
Hour: 15 | Humans #  60.2849 | Zombies # 119.7151
Hour: 16 | Humans #  60.1994 | Zombies # 119.8006
Hour: 17 | Humans #  60.1396 | Zombies # 119.8604
Hour: 18 | Humans #  60.0977 | Zombies # 119.9023
Hour: 19 | Humans #  60.0684 | Zombies # 119.9316
Hour: 20 | Humans #  60.0479 | Zombies # 119.9521
Hour: 21 | Humans #  60.0335 | Zombies # 119.9665
Hour: 22 | Humans #  60.0235 | Zombies # 119.9765
Hour: 23 | Humans #  60.0164 | Zombies # 119.9836
Hour: 24 | Humans #  60.0115 | Zombies # 119.9885
Hour: 25 | Humans #  60.0080 | Zombies # 119.9920
Hour: 26 | Humans #  60.0056 | Zombies # 119.9944
Hour: 27 | Humans #  60.0039 | Zombies # 119.9961
Hour: 28 | Humans #  60.0028 | Zombies # 119.9972
Hour: 29 | Humans #  60.0019 | Zombies # 119.9981
Hour: 30 | Humans #  60.0014 | Zombies # 119.9986
Hour: 31 | Humans #  60.0009 | Zombies # 119.9991
Hour: 32 | Humans #  60.0007 | Zombies # 119.9993
Hour: 33 | Humans #  60.0005 | Zombies # 119.9995
Hour: 34 | Humans #  60.0003 | Zombies # 119.9997
Hour: 35 | Humans #  60.0002 | Zombies # 119.9998
Hour: 36 | Humans #  60.0002 | Zombies # 119.9998
Hour: 37 | Humans #  60.0001 | Zombies # 119.9999
Found it!
 [[ 60.00011137]
 [119.99988863]]
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<p>So, it means that around the 37th hour, human and the zombie population will reach to an equilibrium.</p>
<p>What we did here was to interpret the transformation matrix as a rotation matrix and we kept on rotating an initial vector accordingly, until it did not rotate, meaning that it converged to an eigenvector.</p>
<p>As opposed to the conventional analytic solution, here we first find the eigenvector, and then we can proceed to calculate the corresponding eigenvalue:</p>

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<pre>array([[ 60.00011137],
       [119.99988863]])</pre>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">Au</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">trmat</span><span class="p">,</span><span class="n">hz1</span><span class="p">)</span>
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<p>meaning that the eigenvalue is equal to 1 (as A.u = (1).u)</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="c1"># Verification using built-in function:</span>
<span class="p">[</span><span class="n">l</span><span class="p">,</span><span class="n">u</span><span class="p">]</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">eig</span><span class="p">(</span><span class="n">trmat</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="n">l</span><span class="p">,</span><span class="s2">&quot;</span><span class="se">\n</span><span class="s2">&quot;</span><span class="p">,</span><span class="n">u</span><span class="p">)</span>
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<pre>[0.7 1. ] 
 [[-0.70710678 -0.4472136 ]
 [ 0.70710678 -0.89442719]]
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">hz1</span><span class="o">.</span><span class="n">T</span><span class="o">.</span><span class="n">shape</span>
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<pre>(1, 2)</pre>
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<h1 id="Singular-Value-Decomposition-(SVD)">Singular Value Decomposition (SVD)<a class="anchor-link" href="#Singular-Value-Decomposition-(SVD)">&#182;</a></h1><p>One of the most powerful decompositions is the SVD decomposition, where an $A$ matrix (not necessarily square) is decomposed into singular vector matrices $U$, $V$ along with a diagonal $\lambda \equiv\sigma^2$ matrix:</p>
$$A = U\cdot S\cdot V^T$$<p>There are many magical things involved. 8) $U$ and $V$ share the same eigenvalues $\sigma^2$, and they are orthogonal within each other. Furthermore, defining the symmetrical matrices $AA^T$ and $A^TA$, $\{u_i\} \in U$ are the eigenvectors of $AA^T$, while $\{v_i\} \in V$ are the eigenvectors of $A^TA$. Also:</p>
$$A\cdot v_i = \sigma_i u_i$$<p>and</p>
$$A=\sigma_1 u_1 v_1^T + \dots+ \sigma_r u_r v_r^T$$<p>where each $\sigma$ reports the "importance" of every term, so a controlled approximation is possible.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">AS</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">3</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="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="o">-</span><span class="mi">2</span><span class="p">]])</span>
<span class="n">AS</span>
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<pre>array([[ 3,  2,  2],
       [ 2,  3, -2]])</pre>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="p">[</span><span class="n">u</span><span class="p">,</span><span class="n">s</span><span class="p">,</span><span class="n">v</span><span class="p">]</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">svd</span><span class="p">(</span><span class="n">AS</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="n">u</span><span class="p">,</span><span class="s2">&quot;</span><span class="se">\n</span><span class="s2">&quot;</span><span class="p">,</span><span class="n">s</span><span class="p">,</span><span class="s2">&quot;</span><span class="se">\n</span><span class="s2">&quot;</span><span class="p">,</span><span class="n">v</span><span class="p">)</span>
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<pre>[[-0.70710678 -0.70710678]
 [-0.70710678  0.70710678]] 
 [5. 3.] 
 [[-7.07106781e-01 -7.07106781e-01 -5.55111512e-17]
 [-2.35702260e-01  2.35702260e-01 -9.42809042e-01]
 [-6.66666667e-01  6.66666667e-01  3.33333333e-01]]
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<div class=" highlight hl-ipython3"><pre><span></span><span class="c1"># 0.707106781 : 1/\sqrt(2)</span>
<span class="c1"># 0.235702260 : 1/\sqrt(18)</span>
<span class="c1"># 0.942809042 : 4/\sqrt(18)</span>
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<span class="n">AAT</span>
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<pre>array([[17,  8],
       [ 8, 17]])</pre>
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<pre>array([-0.70710678, -0.70710678])</pre>
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<pre>array([-0.70710678, -0.70710678])</pre>
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<pre>array([-0.70710678,  0.70710678])</pre>
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<span class="n">tot</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">2</span><span class="p">,</span><span class="mi">3</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">0</span><span class="p">,</span><span class="mi">1</span><span class="p">]:</span>
    <span class="n">k</span> <span class="o">=</span> <span class="n">s</span><span class="p">[</span><span class="n">i</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">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="n">u</span><span class="p">[:,</span><span class="n">i</span><span class="p">]])</span><span class="o">.</span><span class="n">T</span><span class="p">,</span><span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="n">v</span><span class="p">[</span><span class="n">i</span><span class="p">,:]]))</span>
    <span class="nb">print</span><span class="p">(</span><span class="n">k</span><span class="p">)</span>
    <span class="n">c</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">k</span><span class="p">)</span>
    <span class="n">tot</span> <span class="o">+=</span> <span class="n">k</span>
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<pre>[[2.50000000e+00 2.50000000e+00 1.96261557e-16]
 [2.50000000e+00 2.50000000e+00 1.96261557e-16]]
[[ 0.5 -0.5  2. ]
 [-0.5  0.5 -2. ]]
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<pre>[array([[2.50000000e+00, 2.50000000e+00, 1.96261557e-16],
        [2.50000000e+00, 2.50000000e+00, 1.96261557e-16]]),
 array([[ 0.5, -0.5,  2. ],
        [-0.5,  0.5, -2. ]])]</pre>
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<pre>array([[ 3.,  2.,  2.],
       [ 2.,  3., -2.]])</pre>
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<h2 id="Image-compression-using-SVD">Image compression using SVD<a class="anchor-link" href="#Image-compression-using-SVD">&#182;</a></h2>
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<span class="kn">from</span> <span class="nn">PIL</span> <span class="k">import</span> <span class="n">Image</span>
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<span class="n">data</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">asarray</span><span class="p">(</span><span class="n">image</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="n">data</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span>
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<pre>(2171, 3000)
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<pre>[[231 231 226 218 211 202 187 174 148 131]
 [227 228 225 219 212 202 186 171 145 130]
 [224 225 224 219 212 202 186 171 150 135]
 [224 224 222 216 211 203 189 176 162 148]
 [225 224 219 213 209 205 196 186 172 157]
 [223 222 216 210 208 208 201 193 176 161]
 [217 217 213 210 209 209 203 195 179 164]
 [211 212 212 210 211 210 203 194 183 167]
 [213 210 208 210 212 209 202 195 176 162]
 [205 205 205 209 212 209 201 194 174 162]]
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<span class="n">im</span> <span class="o">=</span> <span class="n">image2</span><span class="o">.</span><span class="n">save</span><span class="p">(</span><span class="s1">&#39;../Scratch_and_Demo/saved.jpg&#39;</span><span class="p">)</span>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">image</span><span class="o">.</span><span class="n">mode</span> <span class="c1"># &#39;L&#39; for greyscale</span>
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<pre>&#39;L&#39;</pre>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="p">[</span><span class="n">u</span><span class="p">,</span><span class="n">s</span><span class="p">,</span><span class="n">vh</span><span class="p">]</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">svd</span><span class="p">(</span><span class="n">data</span><span class="p">)</span>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">s</span><span class="o">.</span><span class="n">shape</span>
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<pre>(2171,)</pre>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">s</span>
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<pre>array([3.47512434e+05, 5.48806502e+04, 4.11336359e+04, ...,
       3.73601343e+00, 3.71561252e+00, 3.64186396e+00])</pre>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">s</span><span class="o">&gt;</span><span class="mi">100</span><span class="p">)</span>
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<pre>1020</pre>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">s</span><span class="p">)</span>
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<pre>1853672.188755236</pre>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">tot</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">s</span><span class="p">)</span>
<span class="n">x</span> <span class="o">=</span> <span class="mi">70</span>
<span class="n">tot_xp</span> <span class="o">=</span> <span class="n">tot</span><span class="o">*</span><span class="n">x</span><span class="o">/</span><span class="mi">100</span>
<span class="n">tot_aux</span> <span class="o">=</span> <span class="mi">0</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">s</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="n">tot_aux</span> <span class="o">+=</span> <span class="n">s</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
    <span class="k">if</span><span class="p">(</span><span class="n">tot_aux</span><span class="o">&gt;</span><span class="n">tot_xp</span><span class="p">):</span>
        <span class="nb">print</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
        <span class="k">break</span>
<span class="n">threshold</span> <span class="o">=</span> <span class="n">i</span>  
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<pre>100
</pre>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">c</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">empty</span><span class="p">(</span><span class="n">data</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">threshold</span><span class="p">):</span>
    <span class="n">c</span> <span class="o">+=</span> <span class="n">s</span><span class="p">[</span><span class="n">i</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">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="n">u</span><span class="p">[:,</span><span class="n">i</span><span class="p">]])</span><span class="o">.</span><span class="n">T</span><span class="p">,</span><span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="n">vh</span><span class="p">[</span><span class="n">i</span><span class="p">,:]]))</span>
<span class="n">c</span><span class="o">.</span><span class="n">shape</span>
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<pre>(2171, 3000)</pre>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">image2</span> <span class="o">=</span> <span class="n">Image</span><span class="o">.</span><span class="n">fromarray</span><span class="p">(</span><span class="n">c</span><span class="p">)</span>
<span class="n">image2</span> <span class="o">=</span> <span class="n">image2</span><span class="o">.</span><span class="n">convert</span><span class="p">(</span><span class="s2">&quot;L&quot;</span><span class="p">)</span>
<span class="n">im</span> <span class="o">=</span> <span class="n">image2</span><span class="o">.</span><span class="n">save</span><span class="p">(</span><span class="s1">&#39;../Scratch_and_Demo/compressed_x.jpg&#39;</span><span class="p">)</span>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="mf">597.8</span><span class="o">/</span><span class="mf">745.2</span><span class="o">*</span><span class="mi">100</span>
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<pre>80.22007514761137</pre>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="mf">533.4</span><span class="o">/</span><span class="mf">745.2</span><span class="o">*</span><span class="mi">100</span>
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<pre>71.5780998389694</pre>
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<h2 id="Pseudo-Inverse-($A^+$)">Pseudo-Inverse ($A^+$)<a class="anchor-link" href="#Pseudo-Inverse-($A^+$)">&#182;</a></h2><p>SVD can also be used to calculate the _pseudo-_inverse of a matrix which is not necessarily square. Given that $A$ is a $(m\times n)$ matrix, its pseudo-inverse counterpart $A^+$ will be an $(n\times m)$ matrix such that:</p>
$$A\cdot A^+ \approx \mathbb{1}$$<p>where $\mathbb{1}$ is the $(m\times m)$ identity matrix (<em>right inverse</em>). A similar definition is also present for a <em>left inverse</em> where $A^+_{(n\times m)} \cdot A_{(m\times n)} \approx \mathbb{1}_{(n\times n)}$.</p>
<p>Pseudo-inverse matrix can be calculated from:</p>
$$A^+ = VD^+U^T$$<p>where $D^+$ indicates $\{\tfrac{1}{\sigma_i}\}$ of the non-zero elements of $D$. This equation is guaranteed to minimize the least squares error $|AA^+ - \mathbb{1}_n|_2$.</p>

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<p><strong>Example</strong><br>
Pseudo-inverse of $A=\begin{bmatrix}1 &amp; 1\\1 &amp; 1\end{bmatrix}$</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">A</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">1</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="mi">1</span><span class="p">]])</span>
<span class="p">[</span><span class="n">u</span><span class="p">,</span><span class="n">s</span><span class="p">,</span><span class="n">vh</span><span class="p">]</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">svd</span><span class="p">(</span><span class="n">A</span><span class="p">)</span>

<span class="n">s</span><span class="p">[</span><span class="n">s</span><span class="o">!=</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="mi">1</span><span class="o">/</span><span class="n">s</span><span class="p">[</span><span class="n">s</span><span class="o">!=</span><span class="mi">0</span><span class="p">]</span>
<span class="n">D_p</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">diag</span><span class="p">(</span><span class="n">s</span><span class="p">)</span>
<span class="n">D_p</span>

<span class="n">A_pinv</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">multi_dot</span><span class="p">((</span><span class="n">vh</span><span class="o">.</span><span class="n">T</span><span class="p">,</span><span class="n">D_p</span><span class="o">.</span><span class="n">T</span><span class="p">,</span><span class="n">u</span><span class="o">.</span><span class="n">T</span><span class="p">))</span>
<span class="n">A_pinv</span>
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<pre>array([[0.25, 0.25],
       [0.25, 0.25]])</pre>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">np</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">A</span><span class="p">,</span><span class="n">A_pinv</span><span class="p">)</span>
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<pre>array([[0.5, 0.5],
       [0.5, 0.5]])</pre>
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<p><strong>Example</strong><br>
Pseudo-inverse of $B=\begin{bmatrix}1&amp;2&amp;3\\4&amp;5&amp;6\end{bmatrix}$</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">B</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="mi">7</span><span class="p">)</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">)</span>
<span class="n">B</span>
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<pre>array([[1, 2, 3],
       [4, 5, 6]])</pre>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="p">[</span><span class="n">u</span><span class="p">,</span><span class="n">s</span><span class="p">,</span><span class="n">vh</span><span class="p">]</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">svd</span><span class="p">(</span><span class="n">B</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="n">u</span><span class="p">,</span><span class="s2">&quot;</span><span class="se">\n</span><span class="s2">&quot;</span><span class="p">,</span><span class="n">s</span><span class="p">,</span><span class="s2">&quot;</span><span class="se">\n</span><span class="s2">&quot;</span><span class="p">,</span><span class="n">vh</span><span class="p">)</span>
<span class="n">s</span><span class="p">[</span><span class="n">s</span><span class="o">!=</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="mi">1</span><span class="o">/</span><span class="n">s</span><span class="p">[</span><span class="n">s</span><span class="o">!=</span><span class="mi">0</span><span class="p">]</span>
<span class="n">D_p</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">diag</span><span class="p">(</span><span class="n">s</span><span class="p">,</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span>
<span class="n">D_p</span> <span class="o">=</span> <span class="n">D_p</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="nb">print</span><span class="p">(</span><span class="n">D_p</span><span class="p">)</span>

<span class="n">B_pinv</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">multi_dot</span><span class="p">((</span><span class="n">vh</span><span class="o">.</span><span class="n">T</span><span class="p">,</span><span class="n">D_p</span><span class="o">.</span><span class="n">T</span><span class="p">,</span><span class="n">u</span><span class="o">.</span><span class="n">T</span><span class="p">))</span>
<span class="n">B_pinv</span>
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<pre>[[-0.3863177  -0.92236578]
 [-0.92236578  0.3863177 ]] 
 [9.508032   0.77286964] 
 [[-0.42866713 -0.56630692 -0.7039467 ]
 [ 0.80596391  0.11238241 -0.58119908]
 [ 0.40824829 -0.81649658  0.40824829]]
[[0.10517424 0.         0.        ]
 [0.         1.29387927 0.        ]]
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<pre>array([[-0.94444444,  0.44444444],
       [-0.11111111,  0.11111111],
       [ 0.72222222, -0.22222222]])</pre>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">np</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">B</span><span class="p">,</span><span class="n">B_pinv</span><span class="p">)</span>
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<pre>array([[ 1.00000000e+00,  2.22044605e-16],
       [-8.88178420e-16,  1.00000000e+00]])</pre>
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<h1 id="Principal-Component-Analysis-(PCA)">Principal Component Analysis (PCA)<a class="anchor-link" href="#Principal-Component-Analysis-(PCA)">&#182;</a></h1>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">data</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">1.</span>    <span class="p">,</span>  <span class="mf">4.9142</span><span class="p">],</span>
       <span class="p">[</span> <span class="mf">2.</span>    <span class="p">,</span>  <span class="mf">7.1201</span><span class="p">],</span>
       <span class="p">[</span> <span class="mf">3.</span>    <span class="p">,</span>  <span class="mf">8.8456</span><span class="p">],</span>
       <span class="p">[</span> <span class="mf">4.</span>    <span class="p">,</span> <span class="mf">10.8113</span><span class="p">],</span>
       <span class="p">[</span> <span class="mf">5.</span>    <span class="p">,</span> <span class="mf">13.2231</span><span class="p">]])</span>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">data</span><span class="p">[:,</span><span class="mi">0</span><span class="p">],</span><span class="n">data</span><span class="p">[:,</span><span class="mi">1</span><span class="p">],</span><span class="s2">&quot;ro&quot;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">m</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">data</span><span class="p">,</span><span class="mi">0</span><span class="p">)</span>
<span class="n">m</span>
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<pre>array([3.     , 8.98286])</pre>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">data_2</span> <span class="o">=</span> <span class="n">data</span> <span class="o">-</span> <span class="n">m</span>
<span class="n">S</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">data_2</span><span class="o">.</span><span class="n">T</span><span class="p">,</span><span class="n">data_2</span><span class="p">)</span><span class="o">/</span><span class="mi">4</span> <span class="c1"># 4 factor is coming from 1/(n-1)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">data_2</span><span class="p">[:,</span><span class="mi">0</span><span class="p">],</span><span class="n">data_2</span><span class="p">[:,</span><span class="mi">1</span><span class="p">],</span><span class="s2">&quot;ro&quot;</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="n">S</span><span class="p">)</span> 
<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;------------&quot;</span><span class="p">)</span>
<span class="n">Sigma</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">cov</span><span class="p">(</span><span class="n">data_2</span><span class="p">[:,</span><span class="mi">0</span><span class="p">],</span><span class="n">data_2</span><span class="p">[:,</span><span class="mi">1</span><span class="p">])</span>
<span class="nb">print</span><span class="p">(</span><span class="n">Sigma</span><span class="p">)</span>
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<pre>[[ 2.5         5.07725   ]
 [ 5.07725    10.34138435]]
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[[ 2.5         5.07725   ]
 [ 5.07725    10.34138435]]
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<div class=" highlight hl-ipython3"><pre><span></span><span class="p">[</span><span class="n">u</span><span class="p">,</span><span class="n">s</span><span class="p">,</span><span class="n">vh</span><span class="p">]</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">svd</span><span class="p">(</span><span class="n">S</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="n">u</span><span class="p">,</span><span class="s2">&quot;</span><span class="se">\n\n</span><span class="s2">&quot;</span><span class="p">,</span><span class="n">s</span><span class="p">,</span><span class="s2">&quot;</span><span class="se">\n\n</span><span class="s2">&quot;</span><span class="p">,</span><span class="n">vh</span><span class="p">)</span>
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<pre>[[-0.4409138  -0.89754945]
 [-0.89754945  0.4409138 ]] 

 [1.28355417e+01 5.84262991e-03] 

 [[-0.4409138  -0.89754945]
 [-0.89754945  0.4409138 ]]
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">s</span><span class="p">[</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">sum</span><span class="p">(</span><span class="n">s</span><span class="p">)</span><span class="o">*</span><span class="mi">100</span>
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<pre>0.04549844277505694</pre>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">norm</span><span class="p">(</span><span class="n">u</span><span class="p">[:,</span><span class="mi">1</span><span class="p">])</span>
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<pre>1.0</pre>
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$$A=U\cdot S\cdot U^T$$
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">u1</span><span class="o">=</span><span class="n">u</span><span class="p">[:,</span><span class="mi">0</span><span class="p">]</span>
<span class="n">u2</span><span class="o">=</span><span class="n">u</span><span class="p">[:,</span><span class="mi">1</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">u1</span><span class="p">,</span><span class="n">u2</span><span class="p">)</span>
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<pre>0.0</pre>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">u1</span> <span class="c1"># principal axis</span>
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<pre>array([-0.4409138 , -0.89754945])</pre>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">m1</span><span class="o">=</span><span class="n">u1</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">/</span><span class="n">u1</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
<span class="n">m2</span><span class="o">=</span><span class="n">u2</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">/</span><span class="n">u2</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
<span class="nb">print</span><span class="p">(</span><span class="n">m1</span><span class="p">,</span><span class="n">m2</span><span class="p">)</span>
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<pre>2.035657437212789 -0.4912417883871436
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<pre>array([[-2.     , -4.06866],
       [-1.     , -1.86276],
       [ 0.     , -0.13726],
       [ 1.     ,  1.82844],
       [ 2.     ,  4.24024]])</pre>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">x</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="o">-</span><span class="mi">4</span><span class="p">,</span><span class="mi">4</span><span class="p">,</span><span class="mi">30</span><span class="p">)</span>
<span class="n">y1</span> <span class="o">=</span> <span class="n">m1</span><span class="o">*</span><span class="n">x</span>
<span class="n">y2</span> <span class="o">=</span> <span class="n">m2</span><span class="o">*</span><span class="n">x</span>
<span class="n">fig</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">()</span>
<span class="n">ax</span> <span class="o">=</span> <span class="n">fig</span><span class="o">.</span><span class="n">add_subplot</span><span class="p">(</span><span class="mi">111</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_aspect</span><span class="p">(</span><span class="s1">&#39;equal&#39;</span><span class="p">,</span><span class="s1">&#39;datalim&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">data_2</span><span class="p">[:,</span><span class="mi">0</span><span class="p">],</span><span class="n">data_2</span><span class="p">[:,</span><span class="mi">1</span><span class="p">],</span><span class="s2">&quot;ro&quot;</span><span class="p">,</span><span class="n">x</span><span class="p">,</span><span class="n">y1</span><span class="p">,</span><span class="s2">&quot;b-&quot;</span><span class="p">,</span><span class="n">x</span><span class="p">,</span><span class="n">y2</span><span class="p">,</span><span class="s2">&quot;g-&quot;</span><span class="p">)</span>

<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">fig</span><span class="p">,</span><span class="n">ax1</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">1</span><span class="p">)</span>
<span class="n">ax1</span><span class="o">.</span><span class="n">set_aspect</span><span class="p">(</span><span class="s1">&#39;equal&#39;</span><span class="p">,</span><span class="s1">&#39;datalim&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">data</span><span class="p">[:,</span><span class="mi">0</span><span class="p">],</span><span class="n">data</span><span class="p">[:,</span><span class="mi">1</span><span class="p">],</span><span class="s2">&quot;ro&quot;</span><span class="p">,</span><span class="n">x</span><span class="o">+</span><span class="n">m</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span><span class="n">y1</span><span class="o">+</span><span class="n">m</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span><span class="s2">&quot;b-&quot;</span><span class="p">,</span>
         <span class="n">x</span><span class="o">+</span><span class="n">m</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span><span class="n">y2</span><span class="o">+</span><span class="n">m</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span><span class="s2">&quot;g-&quot;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
</pre></div>

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
"
>
</div>

</div>

</div>
</div>

</div>
<div class="cell border-box-sizing code_cell rendered">
<div class="input">
<div class="prompt input_prompt">In&nbsp;[66]:</div>
<div class="inner_cell">
    <div class="input_area">
<div class=" highlight hl-ipython3"><pre><span></span><span class="c1">#s1_contribution </span>
<span class="n">s</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">/</span><span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">s</span><span class="p">)</span><span class="o">*</span><span class="mi">100</span>
</pre></div>

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

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


<div class="output_area">

    <div class="prompt output_prompt">Out[66]:</div>


<div class="output_text output_subarea output_execute_result">
<pre>99.95450155722494</pre>
</div>

</div>

</div>
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<h2 id="References-&amp;-Further-reading/watching:">References &amp; Further reading/watching:<a class="anchor-link" href="#References-&amp;-Further-reading/watching:">&#182;</a></h2><ul>
<li><strong>Steven Chapra's Applied Numerical Methods with MATLAB: for Engineers &amp; Scientists</strong></li>
<li>Zach Star, <a href="https://www.youtube.com/watch?v=rowWM-MijXU">"The Applications of Matrices | What I wish my teachers told me way earlier"</a></li>
<li>Luis Serrano, <a href="https://www.youtube.com/watch?v=ZspR5PZemcs">"How does Netflix recommend movies? Matrix Factorization"</a></li>
<li><strong>Jonathan Hui, <a href="https://jonathan-hui.medium.com/machine-learning-singular-value-decomposition-svd-principal-component-analysis-pca-1d45e885e491">"Machine Learning — Singular Value Decomposition (SVD) &amp; Principal Component Analysis (PCA)"</a></strong></li>
<li><strong>Tamara Kolda, <a href="https://www.youtube.com/watch?v=L8uT6hgMt00">"Tensor Decomposition"</a></strong></li>
<li>Tamara Kolda &amp; Brett W. Bader, <a href="http://dx.doi.org/10.1137/07070111X">"Tensor Decompositions and Applications", SIAM Review 51(3) 455-500 (2009)| doi: 10.1137/07070111X</a></li>
<li><strong>Gilbert Strang, <a href="https://www.youtube.com/watch?v=mBcLRGuAFUk">"Singular Value Decomposition"</a></strong></li>
<li>Isao Tanaka, <a href="https://www.youtube.com/watch?v=XDn3al94xHk">"Data Driven Discovery of New Materials"</a></li>
<li>EST, <a href="https://emresururi.github.io/FIZ219/FIZ219_EST_UygulamaNotlari_10_Gauss_Eleme_Yontemi_ile_nxn_Dogrusal_Denklem_Cozumu.html">"FİZ219 - Bilgisayar Programlama I | Uygulama Notları #10 : Gauss eleme yöntemi ile n bilinmeyenli n -doğrusal- denklemin çözümü"</a></li>
<li>StatQuest, <a href="https://www.youtube.com/watch?v=FgakZw6K1QQ">"Principal Component Analysis (PCA)"</a></li>
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