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.glyphicon-object-align-right:before {
  content: "\e249";
}
.glyphicon-triangle-right:before {
  content: "\e250";
}
.glyphicon-triangle-left:before {
  content: "\e251";
}
.glyphicon-triangle-bottom:before {
  content: "\e252";
}
.glyphicon-triangle-top:before {
  content: "\e253";
}
.glyphicon-console:before {
  content: "\e254";
}
.glyphicon-superscript:before {
  content: "\e255";
}
.glyphicon-subscript:before {
  content: "\e256";
}
.glyphicon-menu-left:before {
  content: "\e257";
}
.glyphicon-menu-right:before {
  content: "\e258";
}
.glyphicon-menu-down:before {
  content: "\e259";
}
.glyphicon-menu-up:before {
  content: "\e260";
}
* {
  -webkit-box-sizing: border-box;
  -moz-box-sizing: border-box;
  box-sizing: border-box;
}
*:before,
*:after {
  -webkit-box-sizing: border-box;
  -moz-box-sizing: border-box;
  box-sizing: border-box;
}
html {
  font-size: 10px;
  -webkit-tap-highlight-color: rgba(0, 0, 0, 0);
}
body {
  font-family: "Helvetica Neue", Helvetica, Arial, sans-serif;
  font-size: 13px;
  line-height: 1.42857143;
  color: #000;
  background-color: #fff;
}
input,
button,
select,
textarea {
  font-family: inherit;
  font-size: inherit;
  line-height: inherit;
}
a {
  color: #337ab7;
  text-decoration: none;
}
a:hover,
a:focus {
  color: #23527c;
  text-decoration: underline;
}
a:focus {
  outline: 5px auto -webkit-focus-ring-color;
  outline-offset: -2px;
}
figure {
  margin: 0;
}
img {
  vertical-align: middle;
}
.img-responsive,
.thumbnail > img,
.thumbnail a > img,
.carousel-inner > .item > img,
.carousel-inner > .item > a > img {
  display: block;
  max-width: 100%;
  height: auto;
}
.img-rounded {
  border-radius: 3px;
}
.img-thumbnail {
  padding: 4px;
  line-height: 1.42857143;
  background-color: #fff;
  border: 1px solid #ddd;
  border-radius: 2px;
  -webkit-transition: all 0.2s ease-in-out;
  -o-transition: all 0.2s ease-in-out;
  transition: all 0.2s ease-in-out;
  display: inline-block;
  max-width: 100%;
  height: auto;
}
.img-circle {
  border-radius: 50%;
}
hr {
  margin-top: 18px;
  margin-bottom: 18px;
  border: 0;
  border-top: 1px solid #eeeeee;
}
.sr-only {
  position: absolute;
  width: 1px;
  height: 1px;
  margin: -1px;
  padding: 0;
  overflow: hidden;
  clip: rect(0, 0, 0, 0);
  border: 0;
}
.sr-only-focusable:active,
.sr-only-focusable:focus {
  position: static;
  width: auto;
  height: auto;
  margin: 0;
  overflow: visible;
  clip: auto;
}
[role="button"] {
  cursor: pointer;
}
h1,
h2,
h3,
h4,
h5,
h6,
.h1,
.h2,
.h3,
.h4,
.h5,
.h6 {
  font-family: inherit;
  font-weight: 500;
  line-height: 1.1;
  color: inherit;
}
h1 small,
h2 small,
h3 small,
h4 small,
h5 small,
h6 small,
.h1 small,
.h2 small,
.h3 small,
.h4 small,
.h5 small,
.h6 small,
h1 .small,
h2 .small,
h3 .small,
h4 .small,
h5 .small,
h6 .small,
.h1 .small,
.h2 .small,
.h3 .small,
.h4 .small,
.h5 .small,
.h6 .small {
  font-weight: normal;
  line-height: 1;
  color: #777777;
}
h1,
.h1,
h2,
.h2,
h3,
.h3 {
  margin-top: 18px;
  margin-bottom: 9px;
}
h1 small,
.h1 small,
h2 small,
.h2 small,
h3 small,
.h3 small,
h1 .small,
.h1 .small,
h2 .small,
.h2 .small,
h3 .small,
.h3 .small {
  font-size: 65%;
}
h4,
.h4,
h5,
.h5,
h6,
.h6 {
  margin-top: 9px;
  margin-bottom: 9px;
}
h4 small,
.h4 small,
h5 small,
.h5 small,
h6 small,
.h6 small,
h4 .small,
.h4 .small,
h5 .small,
.h5 .small,
h6 .small,
.h6 .small {
  font-size: 75%;
}
h1,
.h1 {
  font-size: 33px;
}
h2,
.h2 {
  font-size: 27px;
}
h3,
.h3 {
  font-size: 23px;
}
h4,
.h4 {
  font-size: 17px;
}
h5,
.h5 {
  font-size: 13px;
}
h6,
.h6 {
  font-size: 12px;
}
p {
  margin: 0 0 9px;
}
.lead {
  margin-bottom: 18px;
  font-size: 14px;
  font-weight: 300;
  line-height: 1.4;
}
@media (min-width: 768px) {
  .lead {
    font-size: 19.5px;
  }
}
small,
.small {
  font-size: 92%;
}
mark,
.mark {
  background-color: #fcf8e3;
  padding: .2em;
}
.text-left {
  text-align: left;
}
.text-right {
  text-align: right;
}
.text-center {
  text-align: center;
}
.text-justify {
  text-align: justify;
}
.text-nowrap {
  white-space: nowrap;
}
.text-lowercase {
  text-transform: lowercase;
}
.text-uppercase {
  text-transform: uppercase;
}
.text-capitalize {
  text-transform: capitalize;
}
.text-muted {
  color: #777777;
}
.text-primary {
  color: #337ab7;
}
a.text-primary:hover,
a.text-primary:focus {
  color: #286090;
}
.text-success {
  color: #3c763d;
}
a.text-success:hover,
a.text-success:focus {
  color: #2b542c;
}
.text-info {
  color: #31708f;
}
a.text-info:hover,
a.text-info:focus {
  color: #245269;
}
.text-warning {
  color: #8a6d3b;
}
a.text-warning:hover,
a.text-warning:focus {
  color: #66512c;
}
.text-danger {
  color: #a94442;
}
a.text-danger:hover,
a.text-danger:focus {
  color: #843534;
}
.bg-primary {
  color: #fff;
  background-color: #337ab7;
}
a.bg-primary:hover,
a.bg-primary:focus {
  background-color: #286090;
}
.bg-success {
  background-color: #dff0d8;
}
a.bg-success:hover,
a.bg-success:focus {
  background-color: #c1e2b3;
}
.bg-info {
  background-color: #d9edf7;
}
a.bg-info:hover,
a.bg-info:focus {
  background-color: #afd9ee;
}
.bg-warning {
  background-color: #fcf8e3;
}
a.bg-warning:hover,
a.bg-warning:focus {
  background-color: #f7ecb5;
}
.bg-danger {
  background-color: #f2dede;
}
a.bg-danger:hover,
a.bg-danger:focus {
  background-color: #e4b9b9;
}
.page-header {
  padding-bottom: 8px;
  margin: 36px 0 18px;
  border-bottom: 1px solid #eeeeee;
}
ul,
ol {
  margin-top: 0;
  margin-bottom: 9px;
}
ul ul,
ol ul,
ul ol,
ol ol {
  margin-bottom: 0;
}
.list-unstyled {
  padding-left: 0;
  list-style: none;
}
.list-inline {
  padding-left: 0;
  list-style: none;
  margin-left: -5px;
}
.list-inline > li {
  display: inline-block;
  padding-left: 5px;
  padding-right: 5px;
}
dl {
  margin-top: 0;
  margin-bottom: 18px;
}
dt,
dd {
  line-height: 1.42857143;
}
dt {
  font-weight: bold;
}
dd {
  margin-left: 0;
}
@media (min-width: 541px) {
  .dl-horizontal dt {
    float: left;
    width: 160px;
    clear: left;
    text-align: right;
    overflow: hidden;
    text-overflow: ellipsis;
    white-space: nowrap;
  }
  .dl-horizontal dd {
    margin-left: 180px;
  }
}
abbr[title],
abbr[data-original-title] {
  cursor: help;
  border-bottom: 1px dotted #777777;
}
.initialism {
  font-size: 90%;
  text-transform: uppercase;
}
blockquote {
  padding: 9px 18px;
  margin: 0 0 18px;
  font-size: inherit;
  border-left: 5px solid #eeeeee;
}
blockquote p:last-child,
blockquote ul:last-child,
blockquote ol:last-child {
  margin-bottom: 0;
}
blockquote footer,
blockquote small,
blockquote .small {
  display: block;
  font-size: 80%;
  line-height: 1.42857143;
  color: #777777;
}
blockquote footer:before,
blockquote small:before,
blockquote .small:before {
  content: '\2014 \00A0';
}
.blockquote-reverse,
blockquote.pull-right {
  padding-right: 15px;
  padding-left: 0;
  border-right: 5px solid #eeeeee;
  border-left: 0;
  text-align: right;
}
.blockquote-reverse footer:before,
blockquote.pull-right footer:before,
.blockquote-reverse small:before,
blockquote.pull-right small:before,
.blockquote-reverse .small:before,
blockquote.pull-right .small:before {
  content: '';
}
.blockquote-reverse footer:after,
blockquote.pull-right footer:after,
.blockquote-reverse small:after,
blockquote.pull-right small:after,
.blockquote-reverse .small:after,
blockquote.pull-right .small:after {
  content: '\00A0 \2014';
}
address {
  margin-bottom: 18px;
  font-style: normal;
  line-height: 1.42857143;
}
code,
kbd,
pre,
samp {
  font-family: monospace;
}
code {
  padding: 2px 4px;
  font-size: 90%;
  color: #c7254e;
  background-color: #f9f2f4;
  border-radius: 2px;
}
kbd {
  padding: 2px 4px;
  font-size: 90%;
  color: #888;
  background-color: transparent;
  border-radius: 1px;
  box-shadow: inset 0 -1px 0 rgba(0, 0, 0, 0.25);
}
kbd kbd {
  padding: 0;
  font-size: 100%;
  font-weight: bold;
  box-shadow: none;
}
pre {
  display: block;
  padding: 8.5px;
  margin: 0 0 9px;
  font-size: 12px;
  line-height: 1.42857143;
  word-break: break-all;
  word-wrap: break-word;
  color: #333333;
  background-color: #f5f5f5;
  border: 1px solid #ccc;
  border-radius: 2px;
}
pre code {
  padding: 0;
  font-size: inherit;
  color: inherit;
  white-space: pre-wrap;
  background-color: transparent;
  border-radius: 0;
}
.pre-scrollable {
  max-height: 340px;
  overflow-y: scroll;
}
.container {
  margin-right: auto;
  margin-left: auto;
  padding-left: 0px;
  padding-right: 0px;
}
@media (min-width: 768px) {
  .container {
    width: 768px;
  }
}
@media (min-width: 992px) {
  .container {
    width: 940px;
  }
}
@media (min-width: 1200px) {
  .container {
    width: 1140px;
  }
}
.container-fluid {
  margin-right: auto;
  margin-left: auto;
  padding-left: 0px;
  padding-right: 0px;
}
.row {
  margin-left: 0px;
  margin-right: 0px;
}
.col-xs-1, .col-sm-1, .col-md-1, .col-lg-1, .col-xs-2, .col-sm-2, .col-md-2, .col-lg-2, .col-xs-3, .col-sm-3, .col-md-3, .col-lg-3, .col-xs-4, .col-sm-4, .col-md-4, .col-lg-4, .col-xs-5, .col-sm-5, .col-md-5, .col-lg-5, .col-xs-6, .col-sm-6, .col-md-6, .col-lg-6, .col-xs-7, .col-sm-7, .col-md-7, .col-lg-7, .col-xs-8, .col-sm-8, .col-md-8, .col-lg-8, .col-xs-9, .col-sm-9, .col-md-9, .col-lg-9, .col-xs-10, .col-sm-10, .col-md-10, .col-lg-10, .col-xs-11, .col-sm-11, .col-md-11, .col-lg-11, .col-xs-12, .col-sm-12, .col-md-12, .col-lg-12 {
  position: relative;
  min-height: 1px;
  padding-left: 0px;
  padding-right: 0px;
}
.col-xs-1, .col-xs-2, .col-xs-3, .col-xs-4, .col-xs-5, .col-xs-6, .col-xs-7, .col-xs-8, .col-xs-9, .col-xs-10, .col-xs-11, .col-xs-12 {
  float: left;
}
.col-xs-12 {
  width: 100%;
}
.col-xs-11 {
  width: 91.66666667%;
}
.col-xs-10 {
  width: 83.33333333%;
}
.col-xs-9 {
  width: 75%;
}
.col-xs-8 {
  width: 66.66666667%;
}
.col-xs-7 {
  width: 58.33333333%;
}
.col-xs-6 {
  width: 50%;
}
.col-xs-5 {
  width: 41.66666667%;
}
.col-xs-4 {
  width: 33.33333333%;
}
.col-xs-3 {
  width: 25%;
}
.col-xs-2 {
  width: 16.66666667%;
}
.col-xs-1 {
  width: 8.33333333%;
}
.col-xs-pull-12 {
  right: 100%;
}
.col-xs-pull-11 {
  right: 91.66666667%;
}
.col-xs-pull-10 {
  right: 83.33333333%;
}
.col-xs-pull-9 {
  right: 75%;
}
.col-xs-pull-8 {
  right: 66.66666667%;
}
.col-xs-pull-7 {
  right: 58.33333333%;
}
.col-xs-pull-6 {
  right: 50%;
}
.col-xs-pull-5 {
  right: 41.66666667%;
}
.col-xs-pull-4 {
  right: 33.33333333%;
}
.col-xs-pull-3 {
  right: 25%;
}
.col-xs-pull-2 {
  right: 16.66666667%;
}
.col-xs-pull-1 {
  right: 8.33333333%;
}
.col-xs-pull-0 {
  right: auto;
}
.col-xs-push-12 {
  left: 100%;
}
.col-xs-push-11 {
  left: 91.66666667%;
}
.col-xs-push-10 {
  left: 83.33333333%;
}
.col-xs-push-9 {
  left: 75%;
}
.col-xs-push-8 {
  left: 66.66666667%;
}
.col-xs-push-7 {
  left: 58.33333333%;
}
.col-xs-push-6 {
  left: 50%;
}
.col-xs-push-5 {
  left: 41.66666667%;
}
.col-xs-push-4 {
  left: 33.33333333%;
}
.col-xs-push-3 {
  left: 25%;
}
.col-xs-push-2 {
  left: 16.66666667%;
}
.col-xs-push-1 {
  left: 8.33333333%;
}
.col-xs-push-0 {
  left: auto;
}
.col-xs-offset-12 {
  margin-left: 100%;
}
.col-xs-offset-11 {
  margin-left: 91.66666667%;
}
.col-xs-offset-10 {
  margin-left: 83.33333333%;
}
.col-xs-offset-9 {
  margin-left: 75%;
}
.col-xs-offset-8 {
  margin-left: 66.66666667%;
}
.col-xs-offset-7 {
  margin-left: 58.33333333%;
}
.col-xs-offset-6 {
  margin-left: 50%;
}
.col-xs-offset-5 {
  margin-left: 41.66666667%;
}
.col-xs-offset-4 {
  margin-left: 33.33333333%;
}
.col-xs-offset-3 {
  margin-left: 25%;
}
.col-xs-offset-2 {
  margin-left: 16.66666667%;
}
.col-xs-offset-1 {
  margin-left: 8.33333333%;
}
.col-xs-offset-0 {
  margin-left: 0%;
}
@media (min-width: 768px) {
  .col-sm-1, .col-sm-2, .col-sm-3, .col-sm-4, .col-sm-5, .col-sm-6, .col-sm-7, .col-sm-8, .col-sm-9, .col-sm-10, .col-sm-11, .col-sm-12 {
    float: left;
  }
  .col-sm-12 {
    width: 100%;
  }
  .col-sm-11 {
    width: 91.66666667%;
  }
  .col-sm-10 {
    width: 83.33333333%;
  }
  .col-sm-9 {
    width: 75%;
  }
  .col-sm-8 {
    width: 66.66666667%;
  }
  .col-sm-7 {
    width: 58.33333333%;
  }
  .col-sm-6 {
    width: 50%;
  }
  .col-sm-5 {
    width: 41.66666667%;
  }
  .col-sm-4 {
    width: 33.33333333%;
  }
  .col-sm-3 {
    width: 25%;
  }
  .col-sm-2 {
    width: 16.66666667%;
  }
  .col-sm-1 {
    width: 8.33333333%;
  }
  .col-sm-pull-12 {
    right: 100%;
  }
  .col-sm-pull-11 {
    right: 91.66666667%;
  }
  .col-sm-pull-10 {
    right: 83.33333333%;
  }
  .col-sm-pull-9 {
    right: 75%;
  }
  .col-sm-pull-8 {
    right: 66.66666667%;
  }
  .col-sm-pull-7 {
    right: 58.33333333%;
  }
  .col-sm-pull-6 {
    right: 50%;
  }
  .col-sm-pull-5 {
    right: 41.66666667%;
  }
  .col-sm-pull-4 {
    right: 33.33333333%;
  }
  .col-sm-pull-3 {
    right: 25%;
  }
  .col-sm-pull-2 {
    right: 16.66666667%;
  }
  .col-sm-pull-1 {
    right: 8.33333333%;
  }
  .col-sm-pull-0 {
    right: auto;
  }
  .col-sm-push-12 {
    left: 100%;
  }
  .col-sm-push-11 {
    left: 91.66666667%;
  }
  .col-sm-push-10 {
    left: 83.33333333%;
  }
  .col-sm-push-9 {
    left: 75%;
  }
  .col-sm-push-8 {
    left: 66.66666667%;
  }
  .col-sm-push-7 {
    left: 58.33333333%;
  }
  .col-sm-push-6 {
    left: 50%;
  }
  .col-sm-push-5 {
    left: 41.66666667%;
  }
  .col-sm-push-4 {
    left: 33.33333333%;
  }
  .col-sm-push-3 {
    left: 25%;
  }
  .col-sm-push-2 {
    left: 16.66666667%;
  }
  .col-sm-push-1 {
    left: 8.33333333%;
  }
  .col-sm-push-0 {
    left: auto;
  }
  .col-sm-offset-12 {
    margin-left: 100%;
  }
  .col-sm-offset-11 {
    margin-left: 91.66666667%;
  }
  .col-sm-offset-10 {
    margin-left: 83.33333333%;
  }
  .col-sm-offset-9 {
    margin-left: 75%;
  }
  .col-sm-offset-8 {
    margin-left: 66.66666667%;
  }
  .col-sm-offset-7 {
    margin-left: 58.33333333%;
  }
  .col-sm-offset-6 {
    margin-left: 50%;
  }
  .col-sm-offset-5 {
    margin-left: 41.66666667%;
  }
  .col-sm-offset-4 {
    margin-left: 33.33333333%;
  }
  .col-sm-offset-3 {
    margin-left: 25%;
  }
  .col-sm-offset-2 {
    margin-left: 16.66666667%;
  }
  .col-sm-offset-1 {
    margin-left: 8.33333333%;
  }
  .col-sm-offset-0 {
    margin-left: 0%;
  }
}
@media (min-width: 992px) {
  .col-md-1, .col-md-2, .col-md-3, .col-md-4, .col-md-5, .col-md-6, .col-md-7, .col-md-8, .col-md-9, .col-md-10, .col-md-11, .col-md-12 {
    float: left;
  }
  .col-md-12 {
    width: 100%;
  }
  .col-md-11 {
    width: 91.66666667%;
  }
  .col-md-10 {
    width: 83.33333333%;
  }
  .col-md-9 {
    width: 75%;
  }
  .col-md-8 {
    width: 66.66666667%;
  }
  .col-md-7 {
    width: 58.33333333%;
  }
  .col-md-6 {
    width: 50%;
  }
  .col-md-5 {
    width: 41.66666667%;
  }
  .col-md-4 {
    width: 33.33333333%;
  }
  .col-md-3 {
    width: 25%;
  }
  .col-md-2 {
    width: 16.66666667%;
  }
  .col-md-1 {
    width: 8.33333333%;
  }
  .col-md-pull-12 {
    right: 100%;
  }
  .col-md-pull-11 {
    right: 91.66666667%;
  }
  .col-md-pull-10 {
    right: 83.33333333%;
  }
  .col-md-pull-9 {
    right: 75%;
  }
  .col-md-pull-8 {
    right: 66.66666667%;
  }
  .col-md-pull-7 {
    right: 58.33333333%;
  }
  .col-md-pull-6 {
    right: 50%;
  }
  .col-md-pull-5 {
    right: 41.66666667%;
  }
  .col-md-pull-4 {
    right: 33.33333333%;
  }
  .col-md-pull-3 {
    right: 25%;
  }
  .col-md-pull-2 {
    right: 16.66666667%;
  }
  .col-md-pull-1 {
    right: 8.33333333%;
  }
  .col-md-pull-0 {
    right: auto;
  }
  .col-md-push-12 {
    left: 100%;
  }
  .col-md-push-11 {
    left: 91.66666667%;
  }
  .col-md-push-10 {
    left: 83.33333333%;
  }
  .col-md-push-9 {
    left: 75%;
  }
  .col-md-push-8 {
    left: 66.66666667%;
  }
  .col-md-push-7 {
    left: 58.33333333%;
  }
  .col-md-push-6 {
    left: 50%;
  }
  .col-md-push-5 {
    left: 41.66666667%;
  }
  .col-md-push-4 {
    left: 33.33333333%;
  }
  .col-md-push-3 {
    left: 25%;
  }
  .col-md-push-2 {
    left: 16.66666667%;
  }
  .col-md-push-1 {
    left: 8.33333333%;
  }
  .col-md-push-0 {
    left: auto;
  }
  .col-md-offset-12 {
    margin-left: 100%;
  }
  .col-md-offset-11 {
    margin-left: 91.66666667%;
  }
  .col-md-offset-10 {
    margin-left: 83.33333333%;
  }
  .col-md-offset-9 {
    margin-left: 75%;
  }
  .col-md-offset-8 {
    margin-left: 66.66666667%;
  }
  .col-md-offset-7 {
    margin-left: 58.33333333%;
  }
  .col-md-offset-6 {
    margin-left: 50%;
  }
  .col-md-offset-5 {
    margin-left: 41.66666667%;
  }
  .col-md-offset-4 {
    margin-left: 33.33333333%;
  }
  .col-md-offset-3 {
    margin-left: 25%;
  }
  .col-md-offset-2 {
    margin-left: 16.66666667%;
  }
  .col-md-offset-1 {
    margin-left: 8.33333333%;
  }
  .col-md-offset-0 {
    margin-left: 0%;
  }
}
@media (min-width: 1200px) {
  .col-lg-1, .col-lg-2, .col-lg-3, .col-lg-4, .col-lg-5, .col-lg-6, .col-lg-7, .col-lg-8, .col-lg-9, .col-lg-10, .col-lg-11, .col-lg-12 {
    float: left;
  }
  .col-lg-12 {
    width: 100%;
  }
  .col-lg-11 {
    width: 91.66666667%;
  }
  .col-lg-10 {
    width: 83.33333333%;
  }
  .col-lg-9 {
    width: 75%;
  }
  .col-lg-8 {
    width: 66.66666667%;
  }
  .col-lg-7 {
    width: 58.33333333%;
  }
  .col-lg-6 {
    width: 50%;
  }
  .col-lg-5 {
    width: 41.66666667%;
  }
  .col-lg-4 {
    width: 33.33333333%;
  }
  .col-lg-3 {
    width: 25%;
  }
  .col-lg-2 {
    width: 16.66666667%;
  }
  .col-lg-1 {
    width: 8.33333333%;
  }
  .col-lg-pull-12 {
    right: 100%;
  }
  .col-lg-pull-11 {
    right: 91.66666667%;
  }
  .col-lg-pull-10 {
    right: 83.33333333%;
  }
  .col-lg-pull-9 {
    right: 75%;
  }
  .col-lg-pull-8 {
    right: 66.66666667%;
  }
  .col-lg-pull-7 {
    right: 58.33333333%;
  }
  .col-lg-pull-6 {
    right: 50%;
  }
  .col-lg-pull-5 {
    right: 41.66666667%;
  }
  .col-lg-pull-4 {
    right: 33.33333333%;
  }
  .col-lg-pull-3 {
    right: 25%;
  }
  .col-lg-pull-2 {
    right: 16.66666667%;
  }
  .col-lg-pull-1 {
    right: 8.33333333%;
  }
  .col-lg-pull-0 {
    right: auto;
  }
  .col-lg-push-12 {
    left: 100%;
  }
  .col-lg-push-11 {
    left: 91.66666667%;
  }
  .col-lg-push-10 {
    left: 83.33333333%;
  }
  .col-lg-push-9 {
    left: 75%;
  }
  .col-lg-push-8 {
    left: 66.66666667%;
  }
  .col-lg-push-7 {
    left: 58.33333333%;
  }
  .col-lg-push-6 {
    left: 50%;
  }
  .col-lg-push-5 {
    left: 41.66666667%;
  }
  .col-lg-push-4 {
    left: 33.33333333%;
  }
  .col-lg-push-3 {
    left: 25%;
  }
  .col-lg-push-2 {
    left: 16.66666667%;
  }
  .col-lg-push-1 {
    left: 8.33333333%;
  }
  .col-lg-push-0 {
    left: auto;
  }
  .col-lg-offset-12 {
    margin-left: 100%;
  }
  .col-lg-offset-11 {
    margin-left: 91.66666667%;
  }
  .col-lg-offset-10 {
    margin-left: 83.33333333%;
  }
  .col-lg-offset-9 {
    margin-left: 75%;
  }
  .col-lg-offset-8 {
    margin-left: 66.66666667%;
  }
  .col-lg-offset-7 {
    margin-left: 58.33333333%;
  }
  .col-lg-offset-6 {
    margin-left: 50%;
  }
  .col-lg-offset-5 {
    margin-left: 41.66666667%;
  }
  .col-lg-offset-4 {
    margin-left: 33.33333333%;
  }
  .col-lg-offset-3 {
    margin-left: 25%;
  }
  .col-lg-offset-2 {
    margin-left: 16.66666667%;
  }
  .col-lg-offset-1 {
    margin-left: 8.33333333%;
  }
  .col-lg-offset-0 {
    margin-left: 0%;
  }
}
table {
  background-color: transparent;
}
caption {
  padding-top: 8px;
  padding-bottom: 8px;
  color: #777777;
  text-align: left;
}
th {
  text-align: left;
}
.table {
  width: 100%;
  max-width: 100%;
  margin-bottom: 18px;
}
.table > thead > tr > th,
.table > tbody > tr > th,
.table > tfoot > tr > th,
.table > thead > tr > td,
.table > tbody > tr > td,
.table > tfoot > tr > td {
  padding: 8px;
  line-height: 1.42857143;
  vertical-align: top;
  border-top: 1px solid #ddd;
}
.table > thead > tr > th {
  vertical-align: bottom;
  border-bottom: 2px solid #ddd;
}
.table > caption + thead > tr:first-child > th,
.table > colgroup + thead > tr:first-child > th,
.table > thead:first-child > tr:first-child > th,
.table > caption + thead > tr:first-child > td,
.table > colgroup + thead > tr:first-child > td,
.table > thead:first-child > tr:first-child > td {
  border-top: 0;
}
.table > tbody + tbody {
  border-top: 2px solid #ddd;
}
.table .table {
  background-color: #fff;
}
.table-condensed > thead > tr > th,
.table-condensed > tbody > tr > th,
.table-condensed > tfoot > tr > th,
.table-condensed > thead > tr > td,
.table-condensed > tbody > tr > td,
.table-condensed > tfoot > tr > td {
  padding: 5px;
}
.table-bordered {
  border: 1px solid #ddd;
}
.table-bordered > thead > tr > th,
.table-bordered > tbody > tr > th,
.table-bordered > tfoot > tr > th,
.table-bordered > thead > tr > td,
.table-bordered > tbody > tr > td,
.table-bordered > tfoot > tr > td {
  border: 1px solid #ddd;
}
.table-bordered > thead > tr > th,
.table-bordered > thead > tr > td {
  border-bottom-width: 2px;
}
.table-striped > tbody > tr:nth-of-type(odd) {
  background-color: #f9f9f9;
}
.table-hover > tbody > tr:hover {
  background-color: #f5f5f5;
}
table col[class*="col-"] {
  position: static;
  float: none;
  display: table-column;
}
table td[class*="col-"],
table th[class*="col-"] {
  position: static;
  float: none;
  display: table-cell;
}
.table > thead > tr > td.active,
.table > tbody > tr > td.active,
.table > tfoot > tr > td.active,
.table > thead > tr > th.active,
.table > tbody > tr > th.active,
.table > tfoot > tr > th.active,
.table > thead > tr.active > td,
.table > tbody > tr.active > td,
.table > tfoot > tr.active > td,
.table > thead > tr.active > th,
.table > tbody > tr.active > th,
.table > tfoot > tr.active > th {
  background-color: #f5f5f5;
}
.table-hover > tbody > tr > td.active:hover,
.table-hover > tbody > tr > th.active:hover,
.table-hover > tbody > tr.active:hover > td,
.table-hover > tbody > tr:hover > .active,
.table-hover > tbody > tr.active:hover > th {
  background-color: #e8e8e8;
}
.table > thead > tr > td.success,
.table > tbody > tr > td.success,
.table > tfoot > tr > td.success,
.table > thead > tr > th.success,
.table > tbody > tr > th.success,
.table > tfoot > tr > th.success,
.table > thead > tr.success > td,
.table > tbody > tr.success > td,
.table > tfoot > tr.success > td,
.table > thead > tr.success > th,
.table > tbody > tr.success > th,
.table > tfoot > tr.success > th {
  background-color: #dff0d8;
}
.table-hover > tbody > tr > td.success:hover,
.table-hover > tbody > tr > th.success:hover,
.table-hover > tbody > tr.success:hover > td,
.table-hover > tbody > tr:hover > .success,
.table-hover > tbody > tr.success:hover > th {
  background-color: #d0e9c6;
}
.table > thead > tr > td.info,
.table > tbody > tr > td.info,
.table > tfoot > tr > td.info,
.table > thead > tr > th.info,
.table > tbody > tr > th.info,
.table > tfoot > tr > th.info,
.table > thead > tr.info > td,
.table > tbody > tr.info > td,
.table > tfoot > tr.info > td,
.table > thead > tr.info > th,
.table > tbody > tr.info > th,
.table > tfoot > tr.info > th {
  background-color: #d9edf7;
}
.table-hover > tbody > tr > td.info:hover,
.table-hover > tbody > tr > th.info:hover,
.table-hover > tbody > tr.info:hover > td,
.table-hover > tbody > tr:hover > .info,
.table-hover > tbody > tr.info:hover > th {
  background-color: #c4e3f3;
}
.table > thead > tr > td.warning,
.table > tbody > tr > td.warning,
.table > tfoot > tr > td.warning,
.table > thead > tr > th.warning,
.table > tbody > tr > th.warning,
.table > tfoot > tr > th.warning,
.table > thead > tr.warning > td,
.table > tbody > tr.warning > td,
.table > tfoot > tr.warning > td,
.table > thead > tr.warning > th,
.table > tbody > tr.warning > th,
.table > tfoot > tr.warning > th {
  background-color: #fcf8e3;
}
.table-hover > tbody > tr > td.warning:hover,
.table-hover > tbody > tr > th.warning:hover,
.table-hover > tbody > tr.warning:hover > td,
.table-hover > tbody > tr:hover > .warning,
.table-hover > tbody > tr.warning:hover > th {
  background-color: #faf2cc;
}
.table > thead > tr > td.danger,
.table > tbody > tr > td.danger,
.table > tfoot > tr > td.danger,
.table > thead > tr > th.danger,
.table > tbody > tr > th.danger,
.table > tfoot > tr > th.danger,
.table > thead > tr.danger > td,
.table > tbody > tr.danger > td,
.table > tfoot > tr.danger > td,
.table > thead > tr.danger > th,
.table > tbody > tr.danger > th,
.table > tfoot > tr.danger > th {
  background-color: #f2dede;
}
.table-hover > tbody > tr > td.danger:hover,
.table-hover > tbody > tr > th.danger:hover,
.table-hover > tbody > tr.danger:hover > td,
.table-hover > tbody > tr:hover > .danger,
.table-hover > tbody > tr.danger:hover > th {
  background-color: #ebcccc;
}
.table-responsive {
  overflow-x: auto;
  min-height: 0.01%;
}
@media screen and (max-width: 767px) {
  .table-responsive {
    width: 100%;
    margin-bottom: 13.5px;
    overflow-y: hidden;
    -ms-overflow-style: -ms-autohiding-scrollbar;
    border: 1px solid #ddd;
  }
  .table-responsive > .table {
    margin-bottom: 0;
  }
  .table-responsive > .table > thead > tr > th,
  .table-responsive > .table > tbody > tr > th,
  .table-responsive > .table > tfoot > tr > th,
  .table-responsive > .table > thead > tr > td,
  .table-responsive > .table > tbody > tr > td,
  .table-responsive > .table > tfoot > tr > td {
    white-space: nowrap;
  }
  .table-responsive > .table-bordered {
    border: 0;
  }
  .table-responsive > .table-bordered > thead > tr > th:first-child,
  .table-responsive > .table-bordered > tbody > tr > th:first-child,
  .table-responsive > .table-bordered > tfoot > tr > th:first-child,
  .table-responsive > .table-bordered > thead > tr > td:first-child,
  .table-responsive > .table-bordered > tbody > tr > td:first-child,
  .table-responsive > .table-bordered > tfoot > tr > td:first-child {
    border-left: 0;
  }
  .table-responsive > .table-bordered > thead > tr > th:last-child,
  .table-responsive > .table-bordered > tbody > tr > th:last-child,
  .table-responsive > .table-bordered > tfoot > tr > th:last-child,
  .table-responsive > .table-bordered > thead > tr > td:last-child,
  .table-responsive > .table-bordered > tbody > tr > td:last-child,
  .table-responsive > .table-bordered > tfoot > tr > td:last-child {
    border-right: 0;
  }
  .table-responsive > .table-bordered > tbody > tr:last-child > th,
  .table-responsive > .table-bordered > tfoot > tr:last-child > th,
  .table-responsive > .table-bordered > tbody > tr:last-child > td,
  .table-responsive > .table-bordered > tfoot > tr:last-child > td {
    border-bottom: 0;
  }
}
fieldset {
  padding: 0;
  margin: 0;
  border: 0;
  min-width: 0;
}
legend {
  display: block;
  width: 100%;
  padding: 0;
  margin-bottom: 18px;
  font-size: 19.5px;
  line-height: inherit;
  color: #333333;
  border: 0;
  border-bottom: 1px solid #e5e5e5;
}
label {
  display: inline-block;
  max-width: 100%;
  margin-bottom: 5px;
  font-weight: bold;
}
input[type="search"] {
  -webkit-box-sizing: border-box;
  -moz-box-sizing: border-box;
  box-sizing: border-box;
}
input[type="radio"],
input[type="checkbox"] {
  margin: 4px 0 0;
  margin-top: 1px \9;
  line-height: normal;
}
input[type="file"] {
  display: block;
}
input[type="range"] {
  display: block;
  width: 100%;
}
select[multiple],
select[size] {
  height: auto;
}
input[type="file"]:focus,
input[type="radio"]:focus,
input[type="checkbox"]:focus {
  outline: 5px auto -webkit-focus-ring-color;
  outline-offset: -2px;
}
output {
  display: block;
  padding-top: 7px;
  font-size: 13px;
  line-height: 1.42857143;
  color: #555555;
}
.form-control {
  display: block;
  width: 100%;
  height: 32px;
  padding: 6px 12px;
  font-size: 13px;
  line-height: 1.42857143;
  color: #555555;
  background-color: #fff;
  background-image: none;
  border: 1px solid #ccc;
  border-radius: 2px;
  -webkit-box-shadow: inset 0 1px 1px rgba(0, 0, 0, 0.075);
  box-shadow: inset 0 1px 1px rgba(0, 0, 0, 0.075);
  -webkit-transition: border-color ease-in-out .15s, box-shadow ease-in-out .15s;
  -o-transition: border-color ease-in-out .15s, box-shadow ease-in-out .15s;
  transition: border-color ease-in-out .15s, box-shadow ease-in-out .15s;
}
.form-control:focus {
  border-color: #66afe9;
  outline: 0;
  -webkit-box-shadow: inset 0 1px 1px rgba(0,0,0,.075), 0 0 8px rgba(102, 175, 233, 0.6);
  box-shadow: inset 0 1px 1px rgba(0,0,0,.075), 0 0 8px rgba(102, 175, 233, 0.6);
}
.form-control::-moz-placeholder {
  color: #999;
  opacity: 1;
}
.form-control:-ms-input-placeholder {
  color: #999;
}
.form-control::-webkit-input-placeholder {
  color: #999;
}
.form-control::-ms-expand {
  border: 0;
  background-color: transparent;
}
.form-control[disabled],
.form-control[readonly],
fieldset[disabled] .form-control {
  background-color: #eeeeee;
  opacity: 1;
}
.form-control[disabled],
fieldset[disabled] .form-control {
  cursor: not-allowed;
}
textarea.form-control {
  height: auto;
}
input[type="search"] {
  -webkit-appearance: none;
}
@media screen and (-webkit-min-device-pixel-ratio: 0) {
  input[type="date"].form-control,
  input[type="time"].form-control,
  input[type="datetime-local"].form-control,
  input[type="month"].form-control {
    line-height: 32px;
  }
  input[type="date"].input-sm,
  input[type="time"].input-sm,
  input[type="datetime-local"].input-sm,
  input[type="month"].input-sm,
  .input-group-sm input[type="date"],
  .input-group-sm input[type="time"],
  .input-group-sm input[type="datetime-local"],
  .input-group-sm input[type="month"] {
    line-height: 30px;
  }
  input[type="date"].input-lg,
  input[type="time"].input-lg,
  input[type="datetime-local"].input-lg,
  input[type="month"].input-lg,
  .input-group-lg input[type="date"],
  .input-group-lg input[type="time"],
  .input-group-lg input[type="datetime-local"],
  .input-group-lg input[type="month"] {
    line-height: 45px;
  }
}
.form-group {
  margin-bottom: 15px;
}
.radio,
.checkbox {
  position: relative;
  display: block;
  margin-top: 10px;
  margin-bottom: 10px;
}
.radio label,
.checkbox label {
  min-height: 18px;
  padding-left: 20px;
  margin-bottom: 0;
  font-weight: normal;
  cursor: pointer;
}
.radio input[type="radio"],
.radio-inline input[type="radio"],
.checkbox input[type="checkbox"],
.checkbox-inline input[type="checkbox"] {
  position: absolute;
  margin-left: -20px;
  margin-top: 4px \9;
}
.radio + .radio,
.checkbox + .checkbox {
  margin-top: -5px;
}
.radio-inline,
.checkbox-inline {
  position: relative;
  display: inline-block;
  padding-left: 20px;
  margin-bottom: 0;
  vertical-align: middle;
  font-weight: normal;
  cursor: pointer;
}
.radio-inline + .radio-inline,
.checkbox-inline + .checkbox-inline {
  margin-top: 0;
  margin-left: 10px;
}
input[type="radio"][disabled],
input[type="checkbox"][disabled],
input[type="radio"].disabled,
input[type="checkbox"].disabled,
fieldset[disabled] input[type="radio"],
fieldset[disabled] input[type="checkbox"] {
  cursor: not-allowed;
}
.radio-inline.disabled,
.checkbox-inline.disabled,
fieldset[disabled] .radio-inline,
fieldset[disabled] .checkbox-inline {
  cursor: not-allowed;
}
.radio.disabled label,
.checkbox.disabled label,
fieldset[disabled] .radio label,
fieldset[disabled] .checkbox label {
  cursor: not-allowed;
}
.form-control-static {
  padding-top: 7px;
  padding-bottom: 7px;
  margin-bottom: 0;
  min-height: 31px;
}
.form-control-static.input-lg,
.form-control-static.input-sm {
  padding-left: 0;
  padding-right: 0;
}
.input-sm {
  height: 30px;
  padding: 5px 10px;
  font-size: 12px;
  line-height: 1.5;
  border-radius: 1px;
}
select.input-sm {
  height: 30px;
  line-height: 30px;
}
textarea.input-sm,
select[multiple].input-sm {
  height: auto;
}
.form-group-sm .form-control {
  height: 30px;
  padding: 5px 10px;
  font-size: 12px;
  line-height: 1.5;
  border-radius: 1px;
}
.form-group-sm select.form-control {
  height: 30px;
  line-height: 30px;
}
.form-group-sm textarea.form-control,
.form-group-sm select[multiple].form-control {
  height: auto;
}
.form-group-sm .form-control-static {
  height: 30px;
  min-height: 30px;
  padding: 6px 10px;
  font-size: 12px;
  line-height: 1.5;
}
.input-lg {
  height: 45px;
  padding: 10px 16px;
  font-size: 17px;
  line-height: 1.3333333;
  border-radius: 3px;
}
select.input-lg {
  height: 45px;
  line-height: 45px;
}
textarea.input-lg,
select[multiple].input-lg {
  height: auto;
}
.form-group-lg .form-control {
  height: 45px;
  padding: 10px 16px;
  font-size: 17px;
  line-height: 1.3333333;
  border-radius: 3px;
}
.form-group-lg select.form-control {
  height: 45px;
  line-height: 45px;
}
.form-group-lg textarea.form-control,
.form-group-lg select[multiple].form-control {
  height: auto;
}
.form-group-lg .form-control-static {
  height: 45px;
  min-height: 35px;
  padding: 11px 16px;
  font-size: 17px;
  line-height: 1.3333333;
}
.has-feedback {
  position: relative;
}
.has-feedback .form-control {
  padding-right: 40px;
}
.form-control-feedback {
  position: absolute;
  top: 0;
  right: 0;
  z-index: 2;
  display: block;
  width: 32px;
  height: 32px;
  line-height: 32px;
  text-align: center;
  pointer-events: none;
}
.input-lg + .form-control-feedback,
.input-group-lg + .form-control-feedback,
.form-group-lg .form-control + .form-control-feedback {
  width: 45px;
  height: 45px;
  line-height: 45px;
}
.input-sm + .form-control-feedback,
.input-group-sm + .form-control-feedback,
.form-group-sm .form-control + .form-control-feedback {
  width: 30px;
  height: 30px;
  line-height: 30px;
}
.has-success .help-block,
.has-success .control-label,
.has-success .radio,
.has-success .checkbox,
.has-success .radio-inline,
.has-success .checkbox-inline,
.has-success.radio label,
.has-success.checkbox label,
.has-success.radio-inline label,
.has-success.checkbox-inline label {
  color: #3c763d;
}
.has-success .form-control {
  border-color: #3c763d;
  -webkit-box-shadow: inset 0 1px 1px rgba(0, 0, 0, 0.075);
  box-shadow: inset 0 1px 1px rgba(0, 0, 0, 0.075);
}
.has-success .form-control:focus {
  border-color: #2b542c;
  -webkit-box-shadow: inset 0 1px 1px rgba(0, 0, 0, 0.075), 0 0 6px #67b168;
  box-shadow: inset 0 1px 1px rgba(0, 0, 0, 0.075), 0 0 6px #67b168;
}
.has-success .input-group-addon {
  color: #3c763d;
  border-color: #3c763d;
  background-color: #dff0d8;
}
.has-success .form-control-feedback {
  color: #3c763d;
}
.has-warning .help-block,
.has-warning .control-label,
.has-warning .radio,
.has-warning .checkbox,
.has-warning .radio-inline,
.has-warning .checkbox-inline,
.has-warning.radio label,
.has-warning.checkbox label,
.has-warning.radio-inline label,
.has-warning.checkbox-inline label {
  color: #8a6d3b;
}
.has-warning .form-control {
  border-color: #8a6d3b;
  -webkit-box-shadow: inset 0 1px 1px rgba(0, 0, 0, 0.075);
  box-shadow: inset 0 1px 1px rgba(0, 0, 0, 0.075);
}
.has-warning .form-control:focus {
  border-color: #66512c;
  -webkit-box-shadow: inset 0 1px 1px rgba(0, 0, 0, 0.075), 0 0 6px #c0a16b;
  box-shadow: inset 0 1px 1px rgba(0, 0, 0, 0.075), 0 0 6px #c0a16b;
}
.has-warning .input-group-addon {
  color: #8a6d3b;
  border-color: #8a6d3b;
  background-color: #fcf8e3;
}
.has-warning .form-control-feedback {
  color: #8a6d3b;
}
.has-error .help-block,
.has-error .control-label,
.has-error .radio,
.has-error .checkbox,
.has-error .radio-inline,
.has-error .checkbox-inline,
.has-error.radio label,
.has-error.checkbox label,
.has-error.radio-inline label,
.has-error.checkbox-inline label {
  color: #a94442;
}
.has-error .form-control {
  border-color: #a94442;
  -webkit-box-shadow: inset 0 1px 1px rgba(0, 0, 0, 0.075);
  box-shadow: inset 0 1px 1px rgba(0, 0, 0, 0.075);
}
.has-error .form-control:focus {
  border-color: #843534;
  -webkit-box-shadow: inset 0 1px 1px rgba(0, 0, 0, 0.075), 0 0 6px #ce8483;
  box-shadow: inset 0 1px 1px rgba(0, 0, 0, 0.075), 0 0 6px #ce8483;
}
.has-error .input-group-addon {
  color: #a94442;
  border-color: #a94442;
  background-color: #f2dede;
}
.has-error .form-control-feedback {
  color: #a94442;
}
.has-feedback label ~ .form-control-feedback {
  top: 23px;
}
.has-feedback label.sr-only ~ .form-control-feedback {
  top: 0;
}
.help-block {
  display: block;
  margin-top: 5px;
  margin-bottom: 10px;
  color: #404040;
}
@media (min-width: 768px) {
  .form-inline .form-group {
    display: inline-block;
    margin-bottom: 0;
    vertical-align: middle;
  }
  .form-inline .form-control {
    display: inline-block;
    width: auto;
    vertical-align: middle;
  }
  .form-inline .form-control-static {
    display: inline-block;
  }
  .form-inline .input-group {
    display: inline-table;
    vertical-align: middle;
  }
  .form-inline .input-group .input-group-addon,
  .form-inline .input-group .input-group-btn,
  .form-inline .input-group .form-control {
    width: auto;
  }
  .form-inline .input-group > .form-control {
    width: 100%;
  }
  .form-inline .control-label {
    margin-bottom: 0;
    vertical-align: middle;
  }
  .form-inline .radio,
  .form-inline .checkbox {
    display: inline-block;
    margin-top: 0;
    margin-bottom: 0;
    vertical-align: middle;
  }
  .form-inline .radio label,
  .form-inline .checkbox label {
    padding-left: 0;
  }
  .form-inline .radio input[type="radio"],
  .form-inline .checkbox input[type="checkbox"] {
    position: relative;
    margin-left: 0;
  }
  .form-inline .has-feedback .form-control-feedback {
    top: 0;
  }
}
.form-horizontal .radio,
.form-horizontal .checkbox,
.form-horizontal .radio-inline,
.form-horizontal .checkbox-inline {
  margin-top: 0;
  margin-bottom: 0;
  padding-top: 7px;
}
.form-horizontal .radio,
.form-horizontal .checkbox {
  min-height: 25px;
}
.form-horizontal .form-group {
  margin-left: 0px;
  margin-right: 0px;
}
@media (min-width: 768px) {
  .form-horizontal .control-label {
    text-align: right;
    margin-bottom: 0;
    padding-top: 7px;
  }
}
.form-horizontal .has-feedback .form-control-feedback {
  right: 0px;
}
@media (min-width: 768px) {
  .form-horizontal .form-group-lg .control-label {
    padding-top: 11px;
    font-size: 17px;
  }
}
@media (min-width: 768px) {
  .form-horizontal .form-group-sm .control-label {
    padding-top: 6px;
    font-size: 12px;
  }
}
.btn {
  display: inline-block;
  margin-bottom: 0;
  font-weight: normal;
  text-align: center;
  vertical-align: middle;
  touch-action: manipulation;
  cursor: pointer;
  background-image: none;
  border: 1px solid transparent;
  white-space: nowrap;
  padding: 6px 12px;
  font-size: 13px;
  line-height: 1.42857143;
  border-radius: 2px;
  -webkit-user-select: none;
  -moz-user-select: none;
  -ms-user-select: none;
  user-select: none;
}
.btn:focus,
.btn:active:focus,
.btn.active:focus,
.btn.focus,
.btn:active.focus,
.btn.active.focus {
  outline: 5px auto -webkit-focus-ring-color;
  outline-offset: -2px;
}
.btn:hover,
.btn:focus,
.btn.focus {
  color: #333;
  text-decoration: none;
}
.btn:active,
.btn.active {
  outline: 0;
  background-image: none;
  -webkit-box-shadow: inset 0 3px 5px rgba(0, 0, 0, 0.125);
  box-shadow: inset 0 3px 5px rgba(0, 0, 0, 0.125);
}
.btn.disabled,
.btn[disabled],
fieldset[disabled] .btn {
  cursor: not-allowed;
  opacity: 0.65;
  filter: alpha(opacity=65);
  -webkit-box-shadow: none;
  box-shadow: none;
}
a.btn.disabled,
fieldset[disabled] a.btn {
  pointer-events: none;
}
.btn-default {
  color: #333;
  background-color: #fff;
  border-color: #ccc;
}
.btn-default:focus,
.btn-default.focus {
  color: #333;
  background-color: #e6e6e6;
  border-color: #8c8c8c;
}
.btn-default:hover {
  color: #333;
  background-color: #e6e6e6;
  border-color: #adadad;
}
.btn-default:active,
.btn-default.active,
.open > .dropdown-toggle.btn-default {
  color: #333;
  background-color: #e6e6e6;
  border-color: #adadad;
}
.btn-default:active:hover,
.btn-default.active:hover,
.open > .dropdown-toggle.btn-default:hover,
.btn-default:active:focus,
.btn-default.active:focus,
.open > .dropdown-toggle.btn-default:focus,
.btn-default:active.focus,
.btn-default.active.focus,
.open > .dropdown-toggle.btn-default.focus {
  color: #333;
  background-color: #d4d4d4;
  border-color: #8c8c8c;
}
.btn-default:active,
.btn-default.active,
.open > .dropdown-toggle.btn-default {
  background-image: none;
}
.btn-default.disabled:hover,
.btn-default[disabled]:hover,
fieldset[disabled] .btn-default:hover,
.btn-default.disabled:focus,
.btn-default[disabled]:focus,
fieldset[disabled] .btn-default:focus,
.btn-default.disabled.focus,
.btn-default[disabled].focus,
fieldset[disabled] .btn-default.focus {
  background-color: #fff;
  border-color: #ccc;
}
.btn-default .badge {
  color: #fff;
  background-color: #333;
}
.btn-primary {
  color: #fff;
  background-color: #337ab7;
  border-color: #2e6da4;
}
.btn-primary:focus,
.btn-primary.focus {
  color: #fff;
  background-color: #286090;
  border-color: #122b40;
}
.btn-primary:hover {
  color: #fff;
  background-color: #286090;
  border-color: #204d74;
}
.btn-primary:active,
.btn-primary.active,
.open > .dropdown-toggle.btn-primary {
  color: #fff;
  background-color: #286090;
  border-color: #204d74;
}
.btn-primary:active:hover,
.btn-primary.active:hover,
.open > .dropdown-toggle.btn-primary:hover,
.btn-primary:active:focus,
.btn-primary.active:focus,
.open > .dropdown-toggle.btn-primary:focus,
.btn-primary:active.focus,
.btn-primary.active.focus,
.open > .dropdown-toggle.btn-primary.focus {
  color: #fff;
  background-color: #204d74;
  border-color: #122b40;
}
.btn-primary:active,
.btn-primary.active,
.open > .dropdown-toggle.btn-primary {
  background-image: none;
}
.btn-primary.disabled:hover,
.btn-primary[disabled]:hover,
fieldset[disabled] .btn-primary:hover,
.btn-primary.disabled:focus,
.btn-primary[disabled]:focus,
fieldset[disabled] .btn-primary:focus,
.btn-primary.disabled.focus,
.btn-primary[disabled].focus,
fieldset[disabled] .btn-primary.focus {
  background-color: #337ab7;
  border-color: #2e6da4;
}
.btn-primary .badge {
  color: #337ab7;
  background-color: #fff;
}
.btn-success {
  color: #fff;
  background-color: #5cb85c;
  border-color: #4cae4c;
}
.btn-success:focus,
.btn-success.focus {
  color: #fff;
  background-color: #449d44;
  border-color: #255625;
}
.btn-success:hover {
  color: #fff;
  background-color: #449d44;
  border-color: #398439;
}
.btn-success:active,
.btn-success.active,
.open > .dropdown-toggle.btn-success {
  color: #fff;
  background-color: #449d44;
  border-color: #398439;
}
.btn-success:active:hover,
.btn-success.active:hover,
.open > .dropdown-toggle.btn-success:hover,
.btn-success:active:focus,
.btn-success.active:focus,
.open > .dropdown-toggle.btn-success:focus,
.btn-success:active.focus,
.btn-success.active.focus,
.open > .dropdown-toggle.btn-success.focus {
  color: #fff;
  background-color: #398439;
  border-color: #255625;
}
.btn-success:active,
.btn-success.active,
.open > .dropdown-toggle.btn-success {
  background-image: none;
}
.btn-success.disabled:hover,
.btn-success[disabled]:hover,
fieldset[disabled] .btn-success:hover,
.btn-success.disabled:focus,
.btn-success[disabled]:focus,
fieldset[disabled] .btn-success:focus,
.btn-success.disabled.focus,
.btn-success[disabled].focus,
fieldset[disabled] .btn-success.focus {
  background-color: #5cb85c;
  border-color: #4cae4c;
}
.btn-success .badge {
  color: #5cb85c;
  background-color: #fff;
}
.btn-info {
  color: #fff;
  background-color: #5bc0de;
  border-color: #46b8da;
}
.btn-info:focus,
.btn-info.focus {
  color: #fff;
  background-color: #31b0d5;
  border-color: #1b6d85;
}
.btn-info:hover {
  color: #fff;
  background-color: #31b0d5;
  border-color: #269abc;
}
.btn-info:active,
.btn-info.active,
.open > .dropdown-toggle.btn-info {
  color: #fff;
  background-color: #31b0d5;
  border-color: #269abc;
}
.btn-info:active:hover,
.btn-info.active:hover,
.open > .dropdown-toggle.btn-info:hover,
.btn-info:active:focus,
.btn-info.active:focus,
.open > .dropdown-toggle.btn-info:focus,
.btn-info:active.focus,
.btn-info.active.focus,
.open > .dropdown-toggle.btn-info.focus {
  color: #fff;
  background-color: #269abc;
  border-color: #1b6d85;
}
.btn-info:active,
.btn-info.active,
.open > .dropdown-toggle.btn-info {
  background-image: none;
}
.btn-info.disabled:hover,
.btn-info[disabled]:hover,
fieldset[disabled] .btn-info:hover,
.btn-info.disabled:focus,
.btn-info[disabled]:focus,
fieldset[disabled] .btn-info:focus,
.btn-info.disabled.focus,
.btn-info[disabled].focus,
fieldset[disabled] .btn-info.focus {
  background-color: #5bc0de;
  border-color: #46b8da;
}
.btn-info .badge {
  color: #5bc0de;
  background-color: #fff;
}
.btn-warning {
  color: #fff;
  background-color: #f0ad4e;
  border-color: #eea236;
}
.btn-warning:focus,
.btn-warning.focus {
  color: #fff;
  background-color: #ec971f;
  border-color: #985f0d;
}
.btn-warning:hover {
  color: #fff;
  background-color: #ec971f;
  border-color: #d58512;
}
.btn-warning:active,
.btn-warning.active,
.open > .dropdown-toggle.btn-warning {
  color: #fff;
  background-color: #ec971f;
  border-color: #d58512;
}
.btn-warning:active:hover,
.btn-warning.active:hover,
.open > .dropdown-toggle.btn-warning:hover,
.btn-warning:active:focus,
.btn-warning.active:focus,
.open > .dropdown-toggle.btn-warning:focus,
.btn-warning:active.focus,
.btn-warning.active.focus,
.open > .dropdown-toggle.btn-warning.focus {
  color: #fff;
  background-color: #d58512;
  border-color: #985f0d;
}
.btn-warning:active,
.btn-warning.active,
.open > .dropdown-toggle.btn-warning {
  background-image: none;
}
.btn-warning.disabled:hover,
.btn-warning[disabled]:hover,
fieldset[disabled] .btn-warning:hover,
.btn-warning.disabled:focus,
.btn-warning[disabled]:focus,
fieldset[disabled] .btn-warning:focus,
.btn-warning.disabled.focus,
.btn-warning[disabled].focus,
fieldset[disabled] .btn-warning.focus {
  background-color: #f0ad4e;
  border-color: #eea236;
}
.btn-warning .badge {
  color: #f0ad4e;
  background-color: #fff;
}
.btn-danger {
  color: #fff;
  background-color: #d9534f;
  border-color: #d43f3a;
}
.btn-danger:focus,
.btn-danger.focus {
  color: #fff;
  background-color: #c9302c;
  border-color: #761c19;
}
.btn-danger:hover {
  color: #fff;
  background-color: #c9302c;
  border-color: #ac2925;
}
.btn-danger:active,
.btn-danger.active,
.open > .dropdown-toggle.btn-danger {
  color: #fff;
  background-color: #c9302c;
  border-color: #ac2925;
}
.btn-danger:active:hover,
.btn-danger.active:hover,
.open > .dropdown-toggle.btn-danger:hover,
.btn-danger:active:focus,
.btn-danger.active:focus,
.open > .dropdown-toggle.btn-danger:focus,
.btn-danger:active.focus,
.btn-danger.active.focus,
.open > .dropdown-toggle.btn-danger.focus {
  color: #fff;
  background-color: #ac2925;
  border-color: #761c19;
}
.btn-danger:active,
.btn-danger.active,
.open > .dropdown-toggle.btn-danger {
  background-image: none;
}
.btn-danger.disabled:hover,
.btn-danger[disabled]:hover,
fieldset[disabled] .btn-danger:hover,
.btn-danger.disabled:focus,
.btn-danger[disabled]:focus,
fieldset[disabled] .btn-danger:focus,
.btn-danger.disabled.focus,
.btn-danger[disabled].focus,
fieldset[disabled] .btn-danger.focus {
  background-color: #d9534f;
  border-color: #d43f3a;
}
.btn-danger .badge {
  color: #d9534f;
  background-color: #fff;
}
.btn-link {
  color: #337ab7;
  font-weight: normal;
  border-radius: 0;
}
.btn-link,
.btn-link:active,
.btn-link.active,
.btn-link[disabled],
fieldset[disabled] .btn-link {
  background-color: transparent;
  -webkit-box-shadow: none;
  box-shadow: none;
}
.btn-link,
.btn-link:hover,
.btn-link:focus,
.btn-link:active {
  border-color: transparent;
}
.btn-link:hover,
.btn-link:focus {
  color: #23527c;
  text-decoration: underline;
  background-color: transparent;
}
.btn-link[disabled]:hover,
fieldset[disabled] .btn-link:hover,
.btn-link[disabled]:focus,
fieldset[disabled] .btn-link:focus {
  color: #777777;
  text-decoration: none;
}
.btn-lg,
.btn-group-lg > .btn {
  padding: 10px 16px;
  font-size: 17px;
  line-height: 1.3333333;
  border-radius: 3px;
}
.btn-sm,
.btn-group-sm > .btn {
  padding: 5px 10px;
  font-size: 12px;
  line-height: 1.5;
  border-radius: 1px;
}
.btn-xs,
.btn-group-xs > .btn {
  padding: 1px 5px;
  font-size: 12px;
  line-height: 1.5;
  border-radius: 1px;
}
.btn-block {
  display: block;
  width: 100%;
}
.btn-block + .btn-block {
  margin-top: 5px;
}
input[type="submit"].btn-block,
input[type="reset"].btn-block,
input[type="button"].btn-block {
  width: 100%;
}
.fade {
  opacity: 0;
  -webkit-transition: opacity 0.15s linear;
  -o-transition: opacity 0.15s linear;
  transition: opacity 0.15s linear;
}
.fade.in {
  opacity: 1;
}
.collapse {
  display: none;
}
.collapse.in {
  display: block;
}
tr.collapse.in {
  display: table-row;
}
tbody.collapse.in {
  display: table-row-group;
}
.collapsing {
  position: relative;
  height: 0;
  overflow: hidden;
  -webkit-transition-property: height, visibility;
  transition-property: height, visibility;
  -webkit-transition-duration: 0.35s;
  transition-duration: 0.35s;
  -webkit-transition-timing-function: ease;
  transition-timing-function: ease;
}
.caret {
  display: inline-block;
  width: 0;
  height: 0;
  margin-left: 2px;
  vertical-align: middle;
  border-top: 4px dashed;
  border-top: 4px solid \9;
  border-right: 4px solid transparent;
  border-left: 4px solid transparent;
}
.dropup,
.dropdown {
  position: relative;
}
.dropdown-toggle:focus {
  outline: 0;
}
.dropdown-menu {
  position: absolute;
  top: 100%;
  left: 0;
  z-index: 1000;
  display: none;
  float: left;
  min-width: 160px;
  padding: 5px 0;
  margin: 2px 0 0;
  list-style: none;
  font-size: 13px;
  text-align: left;
  background-color: #fff;
  border: 1px solid #ccc;
  border: 1px solid rgba(0, 0, 0, 0.15);
  border-radius: 2px;
  -webkit-box-shadow: 0 6px 12px rgba(0, 0, 0, 0.175);
  box-shadow: 0 6px 12px rgba(0, 0, 0, 0.175);
  background-clip: padding-box;
}
.dropdown-menu.pull-right {
  right: 0;
  left: auto;
}
.dropdown-menu .divider {
  height: 1px;
  margin: 8px 0;
  overflow: hidden;
  background-color: #e5e5e5;
}
.dropdown-menu > li > a {
  display: block;
  padding: 3px 20px;
  clear: both;
  font-weight: normal;
  line-height: 1.42857143;
  color: #333333;
  white-space: nowrap;
}
.dropdown-menu > li > a:hover,
.dropdown-menu > li > a:focus {
  text-decoration: none;
  color: #262626;
  background-color: #f5f5f5;
}
.dropdown-menu > .active > a,
.dropdown-menu > .active > a:hover,
.dropdown-menu > .active > a:focus {
  color: #fff;
  text-decoration: none;
  outline: 0;
  background-color: #337ab7;
}
.dropdown-menu > .disabled > a,
.dropdown-menu > .disabled > a:hover,
.dropdown-menu > .disabled > a:focus {
  color: #777777;
}
.dropdown-menu > .disabled > a:hover,
.dropdown-menu > .disabled > a:focus {
  text-decoration: none;
  background-color: transparent;
  background-image: none;
  filter: progid:DXImageTransform.Microsoft.gradient(enabled = false);
  cursor: not-allowed;
}
.open > .dropdown-menu {
  display: block;
}
.open > a {
  outline: 0;
}
.dropdown-menu-right {
  left: auto;
  right: 0;
}
.dropdown-menu-left {
  left: 0;
  right: auto;
}
.dropdown-header {
  display: block;
  padding: 3px 20px;
  font-size: 12px;
  line-height: 1.42857143;
  color: #777777;
  white-space: nowrap;
}
.dropdown-backdrop {
  position: fixed;
  left: 0;
  right: 0;
  bottom: 0;
  top: 0;
  z-index: 990;
}
.pull-right > .dropdown-menu {
  right: 0;
  left: auto;
}
.dropup .caret,
.navbar-fixed-bottom .dropdown .caret {
  border-top: 0;
  border-bottom: 4px dashed;
  border-bottom: 4px solid \9;
  content: "";
}
.dropup .dropdown-menu,
.navbar-fixed-bottom .dropdown .dropdown-menu {
  top: auto;
  bottom: 100%;
  margin-bottom: 2px;
}
@media (min-width: 541px) {
  .navbar-right .dropdown-menu {
    left: auto;
    right: 0;
  }
  .navbar-right .dropdown-menu-left {
    left: 0;
    right: auto;
  }
}
.btn-group,
.btn-group-vertical {
  position: relative;
  display: inline-block;
  vertical-align: middle;
}
.btn-group > .btn,
.btn-group-vertical > .btn {
  position: relative;
  float: left;
}
.btn-group > .btn:hover,
.btn-group-vertical > .btn:hover,
.btn-group > .btn:focus,
.btn-group-vertical > .btn:focus,
.btn-group > .btn:active,
.btn-group-vertical > .btn:active,
.btn-group > .btn.active,
.btn-group-vertical > .btn.active {
  z-index: 2;
}
.btn-group .btn + .btn,
.btn-group .btn + .btn-group,
.btn-group .btn-group + .btn,
.btn-group .btn-group + .btn-group {
  margin-left: -1px;
}
.btn-toolbar {
  margin-left: -5px;
}
.btn-toolbar .btn,
.btn-toolbar .btn-group,
.btn-toolbar .input-group {
  float: left;
}
.btn-toolbar > .btn,
.btn-toolbar > .btn-group,
.btn-toolbar > .input-group {
  margin-left: 5px;
}
.btn-group > .btn:not(:first-child):not(:last-child):not(.dropdown-toggle) {
  border-radius: 0;
}
.btn-group > .btn:first-child {
  margin-left: 0;
}
.btn-group > .btn:first-child:not(:last-child):not(.dropdown-toggle) {
  border-bottom-right-radius: 0;
  border-top-right-radius: 0;
}
.btn-group > .btn:last-child:not(:first-child),
.btn-group > .dropdown-toggle:not(:first-child) {
  border-bottom-left-radius: 0;
  border-top-left-radius: 0;
}
.btn-group > .btn-group {
  float: left;
}
.btn-group > .btn-group:not(:first-child):not(:last-child) > .btn {
  border-radius: 0;
}
.btn-group > .btn-group:first-child:not(:last-child) > .btn:last-child,
.btn-group > .btn-group:first-child:not(:last-child) > .dropdown-toggle {
  border-bottom-right-radius: 0;
  border-top-right-radius: 0;
}
.btn-group > .btn-group:last-child:not(:first-child) > .btn:first-child {
  border-bottom-left-radius: 0;
  border-top-left-radius: 0;
}
.btn-group .dropdown-toggle:active,
.btn-group.open .dropdown-toggle {
  outline: 0;
}
.btn-group > .btn + .dropdown-toggle {
  padding-left: 8px;
  padding-right: 8px;
}
.btn-group > .btn-lg + .dropdown-toggle {
  padding-left: 12px;
  padding-right: 12px;
}
.btn-group.open .dropdown-toggle {
  -webkit-box-shadow: inset 0 3px 5px rgba(0, 0, 0, 0.125);
  box-shadow: inset 0 3px 5px rgba(0, 0, 0, 0.125);
}
.btn-group.open .dropdown-toggle.btn-link {
  -webkit-box-shadow: none;
  box-shadow: none;
}
.btn .caret {
  margin-left: 0;
}
.btn-lg .caret {
  border-width: 5px 5px 0;
  border-bottom-width: 0;
}
.dropup .btn-lg .caret {
  border-width: 0 5px 5px;
}
.btn-group-vertical > .btn,
.btn-group-vertical > .btn-group,
.btn-group-vertical > .btn-group > .btn {
  display: block;
  float: none;
  width: 100%;
  max-width: 100%;
}
.btn-group-vertical > .btn-group > .btn {
  float: none;
}
.btn-group-vertical > .btn + .btn,
.btn-group-vertical > .btn + .btn-group,
.btn-group-vertical > .btn-group + .btn,
.btn-group-vertical > .btn-group + .btn-group {
  margin-top: -1px;
  margin-left: 0;
}
.btn-group-vertical > .btn:not(:first-child):not(:last-child) {
  border-radius: 0;
}
.btn-group-vertical > .btn:first-child:not(:last-child) {
  border-top-right-radius: 2px;
  border-top-left-radius: 2px;
  border-bottom-right-radius: 0;
  border-bottom-left-radius: 0;
}
.btn-group-vertical > .btn:last-child:not(:first-child) {
  border-top-right-radius: 0;
  border-top-left-radius: 0;
  border-bottom-right-radius: 2px;
  border-bottom-left-radius: 2px;
}
.btn-group-vertical > .btn-group:not(:first-child):not(:last-child) > .btn {
  border-radius: 0;
}
.btn-group-vertical > .btn-group:first-child:not(:last-child) > .btn:last-child,
.btn-group-vertical > .btn-group:first-child:not(:last-child) > .dropdown-toggle {
  border-bottom-right-radius: 0;
  border-bottom-left-radius: 0;
}
.btn-group-vertical > .btn-group:last-child:not(:first-child) > .btn:first-child {
  border-top-right-radius: 0;
  border-top-left-radius: 0;
}
.btn-group-justified {
  display: table;
  width: 100%;
  table-layout: fixed;
  border-collapse: separate;
}
.btn-group-justified > .btn,
.btn-group-justified > .btn-group {
  float: none;
  display: table-cell;
  width: 1%;
}
.btn-group-justified > .btn-group .btn {
  width: 100%;
}
.btn-group-justified > .btn-group .dropdown-menu {
  left: auto;
}
[data-toggle="buttons"] > .btn input[type="radio"],
[data-toggle="buttons"] > .btn-group > .btn input[type="radio"],
[data-toggle="buttons"] > .btn input[type="checkbox"],
[data-toggle="buttons"] > .btn-group > .btn input[type="checkbox"] {
  position: absolute;
  clip: rect(0, 0, 0, 0);
  pointer-events: none;
}
.input-group {
  position: relative;
  display: table;
  border-collapse: separate;
}
.input-group[class*="col-"] {
  float: none;
  padding-left: 0;
  padding-right: 0;
}
.input-group .form-control {
  position: relative;
  z-index: 2;
  float: left;
  width: 100%;
  margin-bottom: 0;
}
.input-group .form-control:focus {
  z-index: 3;
}
.input-group-lg > .form-control,
.input-group-lg > .input-group-addon,
.input-group-lg > .input-group-btn > .btn {
  height: 45px;
  padding: 10px 16px;
  font-size: 17px;
  line-height: 1.3333333;
  border-radius: 3px;
}
select.input-group-lg > .form-control,
select.input-group-lg > .input-group-addon,
select.input-group-lg > .input-group-btn > .btn {
  height: 45px;
  line-height: 45px;
}
textarea.input-group-lg > .form-control,
textarea.input-group-lg > .input-group-addon,
textarea.input-group-lg > .input-group-btn > .btn,
select[multiple].input-group-lg > .form-control,
select[multiple].input-group-lg > .input-group-addon,
select[multiple].input-group-lg > .input-group-btn > .btn {
  height: auto;
}
.input-group-sm > .form-control,
.input-group-sm > .input-group-addon,
.input-group-sm > .input-group-btn > .btn {
  height: 30px;
  padding: 5px 10px;
  font-size: 12px;
  line-height: 1.5;
  border-radius: 1px;
}
select.input-group-sm > .form-control,
select.input-group-sm > .input-group-addon,
select.input-group-sm > .input-group-btn > .btn {
  height: 30px;
  line-height: 30px;
}
textarea.input-group-sm > .form-control,
textarea.input-group-sm > .input-group-addon,
textarea.input-group-sm > .input-group-btn > .btn,
select[multiple].input-group-sm > .form-control,
select[multiple].input-group-sm > .input-group-addon,
select[multiple].input-group-sm > .input-group-btn > .btn {
  height: auto;
}
.input-group-addon,
.input-group-btn,
.input-group .form-control {
  display: table-cell;
}
.input-group-addon:not(:first-child):not(:last-child),
.input-group-btn:not(:first-child):not(:last-child),
.input-group .form-control:not(:first-child):not(:last-child) {
  border-radius: 0;
}
.input-group-addon,
.input-group-btn {
  width: 1%;
  white-space: nowrap;
  vertical-align: middle;
}
.input-group-addon {
  padding: 6px 12px;
  font-size: 13px;
  font-weight: normal;
  line-height: 1;
  color: #555555;
  text-align: center;
  background-color: #eeeeee;
  border: 1px solid #ccc;
  border-radius: 2px;
}
.input-group-addon.input-sm {
  padding: 5px 10px;
  font-size: 12px;
  border-radius: 1px;
}
.input-group-addon.input-lg {
  padding: 10px 16px;
  font-size: 17px;
  border-radius: 3px;
}
.input-group-addon input[type="radio"],
.input-group-addon input[type="checkbox"] {
  margin-top: 0;
}
.input-group .form-control:first-child,
.input-group-addon:first-child,
.input-group-btn:first-child > .btn,
.input-group-btn:first-child > .btn-group > .btn,
.input-group-btn:first-child > .dropdown-toggle,
.input-group-btn:last-child > .btn:not(:last-child):not(.dropdown-toggle),
.input-group-btn:last-child > .btn-group:not(:last-child) > .btn {
  border-bottom-right-radius: 0;
  border-top-right-radius: 0;
}
.input-group-addon:first-child {
  border-right: 0;
}
.input-group .form-control:last-child,
.input-group-addon:last-child,
.input-group-btn:last-child > .btn,
.input-group-btn:last-child > .btn-group > .btn,
.input-group-btn:last-child > .dropdown-toggle,
.input-group-btn:first-child > .btn:not(:first-child),
.input-group-btn:first-child > .btn-group:not(:first-child) > .btn {
  border-bottom-left-radius: 0;
  border-top-left-radius: 0;
}
.input-group-addon:last-child {
  border-left: 0;
}
.input-group-btn {
  position: relative;
  font-size: 0;
  white-space: nowrap;
}
.input-group-btn > .btn {
  position: relative;
}
.input-group-btn > .btn + .btn {
  margin-left: -1px;
}
.input-group-btn > .btn:hover,
.input-group-btn > .btn:focus,
.input-group-btn > .btn:active {
  z-index: 2;
}
.input-group-btn:first-child > .btn,
.input-group-btn:first-child > .btn-group {
  margin-right: -1px;
}
.input-group-btn:last-child > .btn,
.input-group-btn:last-child > .btn-group {
  z-index: 2;
  margin-left: -1px;
}
.nav {
  margin-bottom: 0;
  padding-left: 0;
  list-style: none;
}
.nav > li {
  position: relative;
  display: block;
}
.nav > li > a {
  position: relative;
  display: block;
  padding: 10px 15px;
}
.nav > li > a:hover,
.nav > li > a:focus {
  text-decoration: none;
  background-color: #eeeeee;
}
.nav > li.disabled > a {
  color: #777777;
}
.nav > li.disabled > a:hover,
.nav > li.disabled > a:focus {
  color: #777777;
  text-decoration: none;
  background-color: transparent;
  cursor: not-allowed;
}
.nav .open > a,
.nav .open > a:hover,
.nav .open > a:focus {
  background-color: #eeeeee;
  border-color: #337ab7;
}
.nav .nav-divider {
  height: 1px;
  margin: 8px 0;
  overflow: hidden;
  background-color: #e5e5e5;
}
.nav > li > a > img {
  max-width: none;
}
.nav-tabs {
  border-bottom: 1px solid #ddd;
}
.nav-tabs > li {
  float: left;
  margin-bottom: -1px;
}
.nav-tabs > li > a {
  margin-right: 2px;
  line-height: 1.42857143;
  border: 1px solid transparent;
  border-radius: 2px 2px 0 0;
}
.nav-tabs > li > a:hover {
  border-color: #eeeeee #eeeeee #ddd;
}
.nav-tabs > li.active > a,
.nav-tabs > li.active > a:hover,
.nav-tabs > li.active > a:focus {
  color: #555555;
  background-color: #fff;
  border: 1px solid #ddd;
  border-bottom-color: transparent;
  cursor: default;
}
.nav-tabs.nav-justified {
  width: 100%;
  border-bottom: 0;
}
.nav-tabs.nav-justified > li {
  float: none;
}
.nav-tabs.nav-justified > li > a {
  text-align: center;
  margin-bottom: 5px;
}
.nav-tabs.nav-justified > .dropdown .dropdown-menu {
  top: auto;
  left: auto;
}
@media (min-width: 768px) {
  .nav-tabs.nav-justified > li {
    display: table-cell;
    width: 1%;
  }
  .nav-tabs.nav-justified > li > a {
    margin-bottom: 0;
  }
}
.nav-tabs.nav-justified > li > a {
  margin-right: 0;
  border-radius: 2px;
}
.nav-tabs.nav-justified > .active > a,
.nav-tabs.nav-justified > .active > a:hover,
.nav-tabs.nav-justified > .active > a:focus {
  border: 1px solid #ddd;
}
@media (min-width: 768px) {
  .nav-tabs.nav-justified > li > a {
    border-bottom: 1px solid #ddd;
    border-radius: 2px 2px 0 0;
  }
  .nav-tabs.nav-justified > .active > a,
  .nav-tabs.nav-justified > .active > a:hover,
  .nav-tabs.nav-justified > .active > a:focus {
    border-bottom-color: #fff;
  }
}
.nav-pills > li {
  float: left;
}
.nav-pills > li > a {
  border-radius: 2px;
}
.nav-pills > li + li {
  margin-left: 2px;
}
.nav-pills > li.active > a,
.nav-pills > li.active > a:hover,
.nav-pills > li.active > a:focus {
  color: #fff;
  background-color: #337ab7;
}
.nav-stacked > li {
  float: none;
}
.nav-stacked > li + li {
  margin-top: 2px;
  margin-left: 0;
}
.nav-justified {
  width: 100%;
}
.nav-justified > li {
  float: none;
}
.nav-justified > li > a {
  text-align: center;
  margin-bottom: 5px;
}
.nav-justified > .dropdown .dropdown-menu {
  top: auto;
  left: auto;
}
@media (min-width: 768px) {
  .nav-justified > li {
    display: table-cell;
    width: 1%;
  }
  .nav-justified > li > a {
    margin-bottom: 0;
  }
}
.nav-tabs-justified {
  border-bottom: 0;
}
.nav-tabs-justified > li > a {
  margin-right: 0;
  border-radius: 2px;
}
.nav-tabs-justified > .active > a,
.nav-tabs-justified > .active > a:hover,
.nav-tabs-justified > .active > a:focus {
  border: 1px solid #ddd;
}
@media (min-width: 768px) {
  .nav-tabs-justified > li > a {
    border-bottom: 1px solid #ddd;
    border-radius: 2px 2px 0 0;
  }
  .nav-tabs-justified > .active > a,
  .nav-tabs-justified > .active > a:hover,
  .nav-tabs-justified > .active > a:focus {
    border-bottom-color: #fff;
  }
}
.tab-content > .tab-pane {
  display: none;
}
.tab-content > .active {
  display: block;
}
.nav-tabs .dropdown-menu {
  margin-top: -1px;
  border-top-right-radius: 0;
  border-top-left-radius: 0;
}
.navbar {
  position: relative;
  min-height: 30px;
  margin-bottom: 18px;
  border: 1px solid transparent;
}
@media (min-width: 541px) {
  .navbar {
    border-radius: 2px;
  }
}
@media (min-width: 541px) {
  .navbar-header {
    float: left;
  }
}
.navbar-collapse {
  overflow-x: visible;
  padding-right: 0px;
  padding-left: 0px;
  border-top: 1px solid transparent;
  box-shadow: inset 0 1px 0 rgba(255, 255, 255, 0.1);
  -webkit-overflow-scrolling: touch;
}
.navbar-collapse.in {
  overflow-y: auto;
}
@media (min-width: 541px) {
  .navbar-collapse {
    width: auto;
    border-top: 0;
    box-shadow: none;
  }
  .navbar-collapse.collapse {
    display: block !important;
    height: auto !important;
    padding-bottom: 0;
    overflow: visible !important;
  }
  .navbar-collapse.in {
    overflow-y: visible;
  }
  .navbar-fixed-top .navbar-collapse,
  .navbar-static-top .navbar-collapse,
  .navbar-fixed-bottom .navbar-collapse {
    padding-left: 0;
    padding-right: 0;
  }
}
.navbar-fixed-top .navbar-collapse,
.navbar-fixed-bottom .navbar-collapse {
  max-height: 340px;
}
@media (max-device-width: 540px) and (orientation: landscape) {
  .navbar-fixed-top .navbar-collapse,
  .navbar-fixed-bottom .navbar-collapse {
    max-height: 200px;
  }
}
.container > .navbar-header,
.container-fluid > .navbar-header,
.container > .navbar-collapse,
.container-fluid > .navbar-collapse {
  margin-right: 0px;
  margin-left: 0px;
}
@media (min-width: 541px) {
  .container > .navbar-header,
  .container-fluid > .navbar-header,
  .container > .navbar-collapse,
  .container-fluid > .navbar-collapse {
    margin-right: 0;
    margin-left: 0;
  }
}
.navbar-static-top {
  z-index: 1000;
  border-width: 0 0 1px;
}
@media (min-width: 541px) {
  .navbar-static-top {
    border-radius: 0;
  }
}
.navbar-fixed-top,
.navbar-fixed-bottom {
  position: fixed;
  right: 0;
  left: 0;
  z-index: 1030;
}
@media (min-width: 541px) {
  .navbar-fixed-top,
  .navbar-fixed-bottom {
    border-radius: 0;
  }
}
.navbar-fixed-top {
  top: 0;
  border-width: 0 0 1px;
}
.navbar-fixed-bottom {
  bottom: 0;
  margin-bottom: 0;
  border-width: 1px 0 0;
}
.navbar-brand {
  float: left;
  padding: 6px 0px;
  font-size: 17px;
  line-height: 18px;
  height: 30px;
}
.navbar-brand:hover,
.navbar-brand:focus {
  text-decoration: none;
}
.navbar-brand > img {
  display: block;
}
@media (min-width: 541px) {
  .navbar > .container .navbar-brand,
  .navbar > .container-fluid .navbar-brand {
    margin-left: 0px;
  }
}
.navbar-toggle {
  position: relative;
  float: right;
  margin-right: 0px;
  padding: 9px 10px;
  margin-top: -2px;
  margin-bottom: -2px;
  background-color: transparent;
  background-image: none;
  border: 1px solid transparent;
  border-radius: 2px;
}
.navbar-toggle:focus {
  outline: 0;
}
.navbar-toggle .icon-bar {
  display: block;
  width: 22px;
  height: 2px;
  border-radius: 1px;
}
.navbar-toggle .icon-bar + .icon-bar {
  margin-top: 4px;
}
@media (min-width: 541px) {
  .navbar-toggle {
    display: none;
  }
}
.navbar-nav {
  margin: 3px 0px;
}
.navbar-nav > li > a {
  padding-top: 10px;
  padding-bottom: 10px;
  line-height: 18px;
}
@media (max-width: 540px) {
  .navbar-nav .open .dropdown-menu {
    position: static;
    float: none;
    width: auto;
    margin-top: 0;
    background-color: transparent;
    border: 0;
    box-shadow: none;
  }
  .navbar-nav .open .dropdown-menu > li > a,
  .navbar-nav .open .dropdown-menu .dropdown-header {
    padding: 5px 15px 5px 25px;
  }
  .navbar-nav .open .dropdown-menu > li > a {
    line-height: 18px;
  }
  .navbar-nav .open .dropdown-menu > li > a:hover,
  .navbar-nav .open .dropdown-menu > li > a:focus {
    background-image: none;
  }
}
@media (min-width: 541px) {
  .navbar-nav {
    float: left;
    margin: 0;
  }
  .navbar-nav > li {
    float: left;
  }
  .navbar-nav > li > a {
    padding-top: 6px;
    padding-bottom: 6px;
  }
}
.navbar-form {
  margin-left: 0px;
  margin-right: 0px;
  padding: 10px 0px;
  border-top: 1px solid transparent;
  border-bottom: 1px solid transparent;
  -webkit-box-shadow: inset 0 1px 0 rgba(255, 255, 255, 0.1), 0 1px 0 rgba(255, 255, 255, 0.1);
  box-shadow: inset 0 1px 0 rgba(255, 255, 255, 0.1), 0 1px 0 rgba(255, 255, 255, 0.1);
  margin-top: -1px;
  margin-bottom: -1px;
}
@media (min-width: 768px) {
  .navbar-form .form-group {
    display: inline-block;
    margin-bottom: 0;
    vertical-align: middle;
  }
  .navbar-form .form-control {
    display: inline-block;
    width: auto;
    vertical-align: middle;
  }
  .navbar-form .form-control-static {
    display: inline-block;
  }
  .navbar-form .input-group {
    display: inline-table;
    vertical-align: middle;
  }
  .navbar-form .input-group .input-group-addon,
  .navbar-form .input-group .input-group-btn,
  .navbar-form .input-group .form-control {
    width: auto;
  }
  .navbar-form .input-group > .form-control {
    width: 100%;
  }
  .navbar-form .control-label {
    margin-bottom: 0;
    vertical-align: middle;
  }
  .navbar-form .radio,
  .navbar-form .checkbox {
    display: inline-block;
    margin-top: 0;
    margin-bottom: 0;
    vertical-align: middle;
  }
  .navbar-form .radio label,
  .navbar-form .checkbox label {
    padding-left: 0;
  }
  .navbar-form .radio input[type="radio"],
  .navbar-form .checkbox input[type="checkbox"] {
    position: relative;
    margin-left: 0;
  }
  .navbar-form .has-feedback .form-control-feedback {
    top: 0;
  }
}
@media (max-width: 540px) {
  .navbar-form .form-group {
    margin-bottom: 5px;
  }
  .navbar-form .form-group:last-child {
    margin-bottom: 0;
  }
}
@media (min-width: 541px) {
  .navbar-form {
    width: auto;
    border: 0;
    margin-left: 0;
    margin-right: 0;
    padding-top: 0;
    padding-bottom: 0;
    -webkit-box-shadow: none;
    box-shadow: none;
  }
}
.navbar-nav > li > .dropdown-menu {
  margin-top: 0;
  border-top-right-radius: 0;
  border-top-left-radius: 0;
}
.navbar-fixed-bottom .navbar-nav > li > .dropdown-menu {
  margin-bottom: 0;
  border-top-right-radius: 2px;
  border-top-left-radius: 2px;
  border-bottom-right-radius: 0;
  border-bottom-left-radius: 0;
}
.navbar-btn {
  margin-top: -1px;
  margin-bottom: -1px;
}
.navbar-btn.btn-sm {
  margin-top: 0px;
  margin-bottom: 0px;
}
.navbar-btn.btn-xs {
  margin-top: 4px;
  margin-bottom: 4px;
}
.navbar-text {
  margin-top: 6px;
  margin-bottom: 6px;
}
@media (min-width: 541px) {
  .navbar-text {
    float: left;
    margin-left: 0px;
    margin-right: 0px;
  }
}
@media (min-width: 541px) {
  .navbar-left {
    float: left !important;
    float: left;
  }
  .navbar-right {
    float: right !important;
    float: right;
    margin-right: 0px;
  }
  .navbar-right ~ .navbar-right {
    margin-right: 0;
  }
}
.navbar-default {
  background-color: #f8f8f8;
  border-color: #e7e7e7;
}
.navbar-default .navbar-brand {
  color: #777;
}
.navbar-default .navbar-brand:hover,
.navbar-default .navbar-brand:focus {
  color: #5e5e5e;
  background-color: transparent;
}
.navbar-default .navbar-text {
  color: #777;
}
.navbar-default .navbar-nav > li > a {
  color: #777;
}
.navbar-default .navbar-nav > li > a:hover,
.navbar-default .navbar-nav > li > a:focus {
  color: #333;
  background-color: transparent;
}
.navbar-default .navbar-nav > .active > a,
.navbar-default .navbar-nav > .active > a:hover,
.navbar-default .navbar-nav > .active > a:focus {
  color: #555;
  background-color: #e7e7e7;
}
.navbar-default .navbar-nav > .disabled > a,
.navbar-default .navbar-nav > .disabled > a:hover,
.navbar-default .navbar-nav > .disabled > a:focus {
  color: #ccc;
  background-color: transparent;
}
.navbar-default .navbar-toggle {
  border-color: #ddd;
}
.navbar-default .navbar-toggle:hover,
.navbar-default .navbar-toggle:focus {
  background-color: #ddd;
}
.navbar-default .navbar-toggle .icon-bar {
  background-color: #888;
}
.navbar-default .navbar-collapse,
.navbar-default .navbar-form {
  border-color: #e7e7e7;
}
.navbar-default .navbar-nav > .open > a,
.navbar-default .navbar-nav > .open > a:hover,
.navbar-default .navbar-nav > .open > a:focus {
  background-color: #e7e7e7;
  color: #555;
}
@media (max-width: 540px) {
  .navbar-default .navbar-nav .open .dropdown-menu > li > a {
    color: #777;
  }
  .navbar-default .navbar-nav .open .dropdown-menu > li > a:hover,
  .navbar-default .navbar-nav .open .dropdown-menu > li > a:focus {
    color: #333;
    background-color: transparent;
  }
  .navbar-default .navbar-nav .open .dropdown-menu > .active > a,
  .navbar-default .navbar-nav .open .dropdown-menu > .active > a:hover,
  .navbar-default .navbar-nav .open .dropdown-menu > .active > a:focus {
    color: #555;
    background-color: #e7e7e7;
  }
  .navbar-default .navbar-nav .open .dropdown-menu > .disabled > a,
  .navbar-default .navbar-nav .open .dropdown-menu > .disabled > a:hover,
  .navbar-default .navbar-nav .open .dropdown-menu > .disabled > a:focus {
    color: #ccc;
    background-color: transparent;
  }
}
.navbar-default .navbar-link {
  color: #777;
}
.navbar-default .navbar-link:hover {
  color: #333;
}
.navbar-default .btn-link {
  color: #777;
}
.navbar-default .btn-link:hover,
.navbar-default .btn-link:focus {
  color: #333;
}
.navbar-default .btn-link[disabled]:hover,
fieldset[disabled] .navbar-default .btn-link:hover,
.navbar-default .btn-link[disabled]:focus,
fieldset[disabled] .navbar-default .btn-link:focus {
  color: #ccc;
}
.navbar-inverse {
  background-color: #222;
  border-color: #080808;
}
.navbar-inverse .navbar-brand {
  color: #9d9d9d;
}
.navbar-inverse .navbar-brand:hover,
.navbar-inverse .navbar-brand:focus {
  color: #fff;
  background-color: transparent;
}
.navbar-inverse .navbar-text {
  color: #9d9d9d;
}
.navbar-inverse .navbar-nav > li > a {
  color: #9d9d9d;
}
.navbar-inverse .navbar-nav > li > a:hover,
.navbar-inverse .navbar-nav > li > a:focus {
  color: #fff;
  background-color: transparent;
}
.navbar-inverse .navbar-nav > .active > a,
.navbar-inverse .navbar-nav > .active > a:hover,
.navbar-inverse .navbar-nav > .active > a:focus {
  color: #fff;
  background-color: #080808;
}
.navbar-inverse .navbar-nav > .disabled > a,
.navbar-inverse .navbar-nav > .disabled > a:hover,
.navbar-inverse .navbar-nav > .disabled > a:focus {
  color: #444;
  background-color: transparent;
}
.navbar-inverse .navbar-toggle {
  border-color: #333;
}
.navbar-inverse .navbar-toggle:hover,
.navbar-inverse .navbar-toggle:focus {
  background-color: #333;
}
.navbar-inverse .navbar-toggle .icon-bar {
  background-color: #fff;
}
.navbar-inverse .navbar-collapse,
.navbar-inverse .navbar-form {
  border-color: #101010;
}
.navbar-inverse .navbar-nav > .open > a,
.navbar-inverse .navbar-nav > .open > a:hover,
.navbar-inverse .navbar-nav > .open > a:focus {
  background-color: #080808;
  color: #fff;
}
@media (max-width: 540px) {
  .navbar-inverse .navbar-nav .open .dropdown-menu > .dropdown-header {
    border-color: #080808;
  }
  .navbar-inverse .navbar-nav .open .dropdown-menu .divider {
    background-color: #080808;
  }
  .navbar-inverse .navbar-nav .open .dropdown-menu > li > a {
    color: #9d9d9d;
  }
  .navbar-inverse .navbar-nav .open .dropdown-menu > li > a:hover,
  .navbar-inverse .navbar-nav .open .dropdown-menu > li > a:focus {
    color: #fff;
    background-color: transparent;
  }
  .navbar-inverse .navbar-nav .open .dropdown-menu > .active > a,
  .navbar-inverse .navbar-nav .open .dropdown-menu > .active > a:hover,
  .navbar-inverse .navbar-nav .open .dropdown-menu > .active > a:focus {
    color: #fff;
    background-color: #080808;
  }
  .navbar-inverse .navbar-nav .open .dropdown-menu > .disabled > a,
  .navbar-inverse .navbar-nav .open .dropdown-menu > .disabled > a:hover,
  .navbar-inverse .navbar-nav .open .dropdown-menu > .disabled > a:focus {
    color: #444;
    background-color: transparent;
  }
}
.navbar-inverse .navbar-link {
  color: #9d9d9d;
}
.navbar-inverse .navbar-link:hover {
  color: #fff;
}
.navbar-inverse .btn-link {
  color: #9d9d9d;
}
.navbar-inverse .btn-link:hover,
.navbar-inverse .btn-link:focus {
  color: #fff;
}
.navbar-inverse .btn-link[disabled]:hover,
fieldset[disabled] .navbar-inverse .btn-link:hover,
.navbar-inverse .btn-link[disabled]:focus,
fieldset[disabled] .navbar-inverse .btn-link:focus {
  color: #444;
}
.breadcrumb {
  padding: 8px 15px;
  margin-bottom: 18px;
  list-style: none;
  background-color: #f5f5f5;
  border-radius: 2px;
}
.breadcrumb > li {
  display: inline-block;
}
.breadcrumb > li + li:before {
  content: "/\00a0";
  padding: 0 5px;
  color: #5e5e5e;
}
.breadcrumb > .active {
  color: #777777;
}
.pagination {
  display: inline-block;
  padding-left: 0;
  margin: 18px 0;
  border-radius: 2px;
}
.pagination > li {
  display: inline;
}
.pagination > li > a,
.pagination > li > span {
  position: relative;
  float: left;
  padding: 6px 12px;
  line-height: 1.42857143;
  text-decoration: none;
  color: #337ab7;
  background-color: #fff;
  border: 1px solid #ddd;
  margin-left: -1px;
}
.pagination > li:first-child > a,
.pagination > li:first-child > span {
  margin-left: 0;
  border-bottom-left-radius: 2px;
  border-top-left-radius: 2px;
}
.pagination > li:last-child > a,
.pagination > li:last-child > span {
  border-bottom-right-radius: 2px;
  border-top-right-radius: 2px;
}
.pagination > li > a:hover,
.pagination > li > span:hover,
.pagination > li > a:focus,
.pagination > li > span:focus {
  z-index: 2;
  color: #23527c;
  background-color: #eeeeee;
  border-color: #ddd;
}
.pagination > .active > a,
.pagination > .active > span,
.pagination > .active > a:hover,
.pagination > .active > span:hover,
.pagination > .active > a:focus,
.pagination > .active > span:focus {
  z-index: 3;
  color: #fff;
  background-color: #337ab7;
  border-color: #337ab7;
  cursor: default;
}
.pagination > .disabled > span,
.pagination > .disabled > span:hover,
.pagination > .disabled > span:focus,
.pagination > .disabled > a,
.pagination > .disabled > a:hover,
.pagination > .disabled > a:focus {
  color: #777777;
  background-color: #fff;
  border-color: #ddd;
  cursor: not-allowed;
}
.pagination-lg > li > a,
.pagination-lg > li > span {
  padding: 10px 16px;
  font-size: 17px;
  line-height: 1.3333333;
}
.pagination-lg > li:first-child > a,
.pagination-lg > li:first-child > span {
  border-bottom-left-radius: 3px;
  border-top-left-radius: 3px;
}
.pagination-lg > li:last-child > a,
.pagination-lg > li:last-child > span {
  border-bottom-right-radius: 3px;
  border-top-right-radius: 3px;
}
.pagination-sm > li > a,
.pagination-sm > li > span {
  padding: 5px 10px;
  font-size: 12px;
  line-height: 1.5;
}
.pagination-sm > li:first-child > a,
.pagination-sm > li:first-child > span {
  border-bottom-left-radius: 1px;
  border-top-left-radius: 1px;
}
.pagination-sm > li:last-child > a,
.pagination-sm > li:last-child > span {
  border-bottom-right-radius: 1px;
  border-top-right-radius: 1px;
}
.pager {
  padding-left: 0;
  margin: 18px 0;
  list-style: none;
  text-align: center;
}
.pager li {
  display: inline;
}
.pager li > a,
.pager li > span {
  display: inline-block;
  padding: 5px 14px;
  background-color: #fff;
  border: 1px solid #ddd;
  border-radius: 15px;
}
.pager li > a:hover,
.pager li > a:focus {
  text-decoration: none;
  background-color: #eeeeee;
}
.pager .next > a,
.pager .next > span {
  float: right;
}
.pager .previous > a,
.pager .previous > span {
  float: left;
}
.pager .disabled > a,
.pager .disabled > a:hover,
.pager .disabled > a:focus,
.pager .disabled > span {
  color: #777777;
  background-color: #fff;
  cursor: not-allowed;
}
.label {
  display: inline;
  padding: .2em .6em .3em;
  font-size: 75%;
  font-weight: bold;
  line-height: 1;
  color: #fff;
  text-align: center;
  white-space: nowrap;
  vertical-align: baseline;
  border-radius: .25em;
}
a.label:hover,
a.label:focus {
  color: #fff;
  text-decoration: none;
  cursor: pointer;
}
.label:empty {
  display: none;
}
.btn .label {
  position: relative;
  top: -1px;
}
.label-default {
  background-color: #777777;
}
.label-default[href]:hover,
.label-default[href]:focus {
  background-color: #5e5e5e;
}
.label-primary {
  background-color: #337ab7;
}
.label-primary[href]:hover,
.label-primary[href]:focus {
  background-color: #286090;
}
.label-success {
  background-color: #5cb85c;
}
.label-success[href]:hover,
.label-success[href]:focus {
  background-color: #449d44;
}
.label-info {
  background-color: #5bc0de;
}
.label-info[href]:hover,
.label-info[href]:focus {
  background-color: #31b0d5;
}
.label-warning {
  background-color: #f0ad4e;
}
.label-warning[href]:hover,
.label-warning[href]:focus {
  background-color: #ec971f;
}
.label-danger {
  background-color: #d9534f;
}
.label-danger[href]:hover,
.label-danger[href]:focus {
  background-color: #c9302c;
}
.badge {
  display: inline-block;
  min-width: 10px;
  padding: 3px 7px;
  font-size: 12px;
  font-weight: bold;
  color: #fff;
  line-height: 1;
  vertical-align: middle;
  white-space: nowrap;
  text-align: center;
  background-color: #777777;
  border-radius: 10px;
}
.badge:empty {
  display: none;
}
.btn .badge {
  position: relative;
  top: -1px;
}
.btn-xs .badge,
.btn-group-xs > .btn .badge {
  top: 0;
  padding: 1px 5px;
}
a.badge:hover,
a.badge:focus {
  color: #fff;
  text-decoration: none;
  cursor: pointer;
}
.list-group-item.active > .badge,
.nav-pills > .active > a > .badge {
  color: #337ab7;
  background-color: #fff;
}
.list-group-item > .badge {
  float: right;
}
.list-group-item > .badge + .badge {
  margin-right: 5px;
}
.nav-pills > li > a > .badge {
  margin-left: 3px;
}
.jumbotron {
  padding-top: 30px;
  padding-bottom: 30px;
  margin-bottom: 30px;
  color: inherit;
  background-color: #eeeeee;
}
.jumbotron h1,
.jumbotron .h1 {
  color: inherit;
}
.jumbotron p {
  margin-bottom: 15px;
  font-size: 20px;
  font-weight: 200;
}
.jumbotron > hr {
  border-top-color: #d5d5d5;
}
.container .jumbotron,
.container-fluid .jumbotron {
  border-radius: 3px;
  padding-left: 0px;
  padding-right: 0px;
}
.jumbotron .container {
  max-width: 100%;
}
@media screen and (min-width: 768px) {
  .jumbotron {
    padding-top: 48px;
    padding-bottom: 48px;
  }
  .container .jumbotron,
  .container-fluid .jumbotron {
    padding-left: 60px;
    padding-right: 60px;
  }
  .jumbotron h1,
  .jumbotron .h1 {
    font-size: 59px;
  }
}
.thumbnail {
  display: block;
  padding: 4px;
  margin-bottom: 18px;
  line-height: 1.42857143;
  background-color: #fff;
  border: 1px solid #ddd;
  border-radius: 2px;
  -webkit-transition: border 0.2s ease-in-out;
  -o-transition: border 0.2s ease-in-out;
  transition: border 0.2s ease-in-out;
}
.thumbnail > img,
.thumbnail a > img {
  margin-left: auto;
  margin-right: auto;
}
a.thumbnail:hover,
a.thumbnail:focus,
a.thumbnail.active {
  border-color: #337ab7;
}
.thumbnail .caption {
  padding: 9px;
  color: #000;
}
.alert {
  padding: 15px;
  margin-bottom: 18px;
  border: 1px solid transparent;
  border-radius: 2px;
}
.alert h4 {
  margin-top: 0;
  color: inherit;
}
.alert .alert-link {
  font-weight: bold;
}
.alert > p,
.alert > ul {
  margin-bottom: 0;
}
.alert > p + p {
  margin-top: 5px;
}
.alert-dismissable,
.alert-dismissible {
  padding-right: 35px;
}
.alert-dismissable .close,
.alert-dismissible .close {
  position: relative;
  top: -2px;
  right: -21px;
  color: inherit;
}
.alert-success {
  background-color: #dff0d8;
  border-color: #d6e9c6;
  color: #3c763d;
}
.alert-success hr {
  border-top-color: #c9e2b3;
}
.alert-success .alert-link {
  color: #2b542c;
}
.alert-info {
  background-color: #d9edf7;
  border-color: #bce8f1;
  color: #31708f;
}
.alert-info hr {
  border-top-color: #a6e1ec;
}
.alert-info .alert-link {
  color: #245269;
}
.alert-warning {
  background-color: #fcf8e3;
  border-color: #faebcc;
  color: #8a6d3b;
}
.alert-warning hr {
  border-top-color: #f7e1b5;
}
.alert-warning .alert-link {
  color: #66512c;
}
.alert-danger {
  background-color: #f2dede;
  border-color: #ebccd1;
  color: #a94442;
}
.alert-danger hr {
  border-top-color: #e4b9c0;
}
.alert-danger .alert-link {
  color: #843534;
}
@-webkit-keyframes progress-bar-stripes {
  from {
    background-position: 40px 0;
  }
  to {
    background-position: 0 0;
  }
}
@keyframes progress-bar-stripes {
  from {
    background-position: 40px 0;
  }
  to {
    background-position: 0 0;
  }
}
.progress {
  overflow: hidden;
  height: 18px;
  margin-bottom: 18px;
  background-color: #f5f5f5;
  border-radius: 2px;
  -webkit-box-shadow: inset 0 1px 2px rgba(0, 0, 0, 0.1);
  box-shadow: inset 0 1px 2px rgba(0, 0, 0, 0.1);
}
.progress-bar {
  float: left;
  width: 0%;
  height: 100%;
  font-size: 12px;
  line-height: 18px;
  color: #fff;
  text-align: center;
  background-color: #337ab7;
  -webkit-box-shadow: inset 0 -1px 0 rgba(0, 0, 0, 0.15);
  box-shadow: inset 0 -1px 0 rgba(0, 0, 0, 0.15);
  -webkit-transition: width 0.6s ease;
  -o-transition: width 0.6s ease;
  transition: width 0.6s ease;
}
.progress-striped .progress-bar,
.progress-bar-striped {
  background-image: -webkit-linear-gradient(45deg, rgba(255, 255, 255, 0.15) 25%, transparent 25%, transparent 50%, rgba(255, 255, 255, 0.15) 50%, rgba(255, 255, 255, 0.15) 75%, transparent 75%, transparent);
  background-image: -o-linear-gradient(45deg, rgba(255, 255, 255, 0.15) 25%, transparent 25%, transparent 50%, rgba(255, 255, 255, 0.15) 50%, rgba(255, 255, 255, 0.15) 75%, transparent 75%, transparent);
  background-image: linear-gradient(45deg, rgba(255, 255, 255, 0.15) 25%, transparent 25%, transparent 50%, rgba(255, 255, 255, 0.15) 50%, rgba(255, 255, 255, 0.15) 75%, transparent 75%, transparent);
  background-size: 40px 40px;
}
.progress.active .progress-bar,
.progress-bar.active {
  -webkit-animation: progress-bar-stripes 2s linear infinite;
  -o-animation: progress-bar-stripes 2s linear infinite;
  animation: progress-bar-stripes 2s linear infinite;
}
.progress-bar-success {
  background-color: #5cb85c;
}
.progress-striped .progress-bar-success {
  background-image: -webkit-linear-gradient(45deg, rgba(255, 255, 255, 0.15) 25%, transparent 25%, transparent 50%, rgba(255, 255, 255, 0.15) 50%, rgba(255, 255, 255, 0.15) 75%, transparent 75%, transparent);
  background-image: -o-linear-gradient(45deg, rgba(255, 255, 255, 0.15) 25%, transparent 25%, transparent 50%, rgba(255, 255, 255, 0.15) 50%, rgba(255, 255, 255, 0.15) 75%, transparent 75%, transparent);
  background-image: linear-gradient(45deg, rgba(255, 255, 255, 0.15) 25%, transparent 25%, transparent 50%, rgba(255, 255, 255, 0.15) 50%, rgba(255, 255, 255, 0.15) 75%, transparent 75%, transparent);
}
.progress-bar-info {
  background-color: #5bc0de;
}
.progress-striped .progress-bar-info {
  background-image: -webkit-linear-gradient(45deg, rgba(255, 255, 255, 0.15) 25%, transparent 25%, transparent 50%, rgba(255, 255, 255, 0.15) 50%, rgba(255, 255, 255, 0.15) 75%, transparent 75%, transparent);
  background-image: -o-linear-gradient(45deg, rgba(255, 255, 255, 0.15) 25%, transparent 25%, transparent 50%, rgba(255, 255, 255, 0.15) 50%, rgba(255, 255, 255, 0.15) 75%, transparent 75%, transparent);
  background-image: linear-gradient(45deg, rgba(255, 255, 255, 0.15) 25%, transparent 25%, transparent 50%, rgba(255, 255, 255, 0.15) 50%, rgba(255, 255, 255, 0.15) 75%, transparent 75%, transparent);
}
.progress-bar-warning {
  background-color: #f0ad4e;
}
.progress-striped .progress-bar-warning {
  background-image: -webkit-linear-gradient(45deg, rgba(255, 255, 255, 0.15) 25%, transparent 25%, transparent 50%, rgba(255, 255, 255, 0.15) 50%, rgba(255, 255, 255, 0.15) 75%, transparent 75%, transparent);
  background-image: -o-linear-gradient(45deg, rgba(255, 255, 255, 0.15) 25%, transparent 25%, transparent 50%, rgba(255, 255, 255, 0.15) 50%, rgba(255, 255, 255, 0.15) 75%, transparent 75%, transparent);
  background-image: linear-gradient(45deg, rgba(255, 255, 255, 0.15) 25%, transparent 25%, transparent 50%, rgba(255, 255, 255, 0.15) 50%, rgba(255, 255, 255, 0.15) 75%, transparent 75%, transparent);
}
.progress-bar-danger {
  background-color: #d9534f;
}
.progress-striped .progress-bar-danger {
  background-image: -webkit-linear-gradient(45deg, rgba(255, 255, 255, 0.15) 25%, transparent 25%, transparent 50%, rgba(255, 255, 255, 0.15) 50%, rgba(255, 255, 255, 0.15) 75%, transparent 75%, transparent);
  background-image: -o-linear-gradient(45deg, rgba(255, 255, 255, 0.15) 25%, transparent 25%, transparent 50%, rgba(255, 255, 255, 0.15) 50%, rgba(255, 255, 255, 0.15) 75%, transparent 75%, transparent);
  background-image: linear-gradient(45deg, rgba(255, 255, 255, 0.15) 25%, transparent 25%, transparent 50%, rgba(255, 255, 255, 0.15) 50%, rgba(255, 255, 255, 0.15) 75%, transparent 75%, transparent);
}
.media {
  margin-top: 15px;
}
.media:first-child {
  margin-top: 0;
}
.media,
.media-body {
  zoom: 1;
  overflow: hidden;
}
.media-body {
  width: 10000px;
}
.media-object {
  display: block;
}
.media-object.img-thumbnail {
  max-width: none;
}
.media-right,
.media > .pull-right {
  padding-left: 10px;
}
.media-left,
.media > .pull-left {
  padding-right: 10px;
}
.media-left,
.media-right,
.media-body {
  display: table-cell;
  vertical-align: top;
}
.media-middle {
  vertical-align: middle;
}
.media-bottom {
  vertical-align: bottom;
}
.media-heading {
  margin-top: 0;
  margin-bottom: 5px;
}
.media-list {
  padding-left: 0;
  list-style: none;
}
.list-group {
  margin-bottom: 20px;
  padding-left: 0;
}
.list-group-item {
  position: relative;
  display: block;
  padding: 10px 15px;
  margin-bottom: -1px;
  background-color: #fff;
  border: 1px solid #ddd;
}
.list-group-item:first-child {
  border-top-right-radius: 2px;
  border-top-left-radius: 2px;
}
.list-group-item:last-child {
  margin-bottom: 0;
  border-bottom-right-radius: 2px;
  border-bottom-left-radius: 2px;
}
a.list-group-item,
button.list-group-item {
  color: #555;
}
a.list-group-item .list-group-item-heading,
button.list-group-item .list-group-item-heading {
  color: #333;
}
a.list-group-item:hover,
button.list-group-item:hover,
a.list-group-item:focus,
button.list-group-item:focus {
  text-decoration: none;
  color: #555;
  background-color: #f5f5f5;
}
button.list-group-item {
  width: 100%;
  text-align: left;
}
.list-group-item.disabled,
.list-group-item.disabled:hover,
.list-group-item.disabled:focus {
  background-color: #eeeeee;
  color: #777777;
  cursor: not-allowed;
}
.list-group-item.disabled .list-group-item-heading,
.list-group-item.disabled:hover .list-group-item-heading,
.list-group-item.disabled:focus .list-group-item-heading {
  color: inherit;
}
.list-group-item.disabled .list-group-item-text,
.list-group-item.disabled:hover .list-group-item-text,
.list-group-item.disabled:focus .list-group-item-text {
  color: #777777;
}
.list-group-item.active,
.list-group-item.active:hover,
.list-group-item.active:focus {
  z-index: 2;
  color: #fff;
  background-color: #337ab7;
  border-color: #337ab7;
}
.list-group-item.active .list-group-item-heading,
.list-group-item.active:hover .list-group-item-heading,
.list-group-item.active:focus .list-group-item-heading,
.list-group-item.active .list-group-item-heading > small,
.list-group-item.active:hover .list-group-item-heading > small,
.list-group-item.active:focus .list-group-item-heading > small,
.list-group-item.active .list-group-item-heading > .small,
.list-group-item.active:hover .list-group-item-heading > .small,
.list-group-item.active:focus .list-group-item-heading > .small {
  color: inherit;
}
.list-group-item.active .list-group-item-text,
.list-group-item.active:hover .list-group-item-text,
.list-group-item.active:focus .list-group-item-text {
  color: #c7ddef;
}
.list-group-item-success {
  color: #3c763d;
  background-color: #dff0d8;
}
a.list-group-item-success,
button.list-group-item-success {
  color: #3c763d;
}
a.list-group-item-success .list-group-item-heading,
button.list-group-item-success .list-group-item-heading {
  color: inherit;
}
a.list-group-item-success:hover,
button.list-group-item-success:hover,
a.list-group-item-success:focus,
button.list-group-item-success:focus {
  color: #3c763d;
  background-color: #d0e9c6;
}
a.list-group-item-success.active,
button.list-group-item-success.active,
a.list-group-item-success.active:hover,
button.list-group-item-success.active:hover,
a.list-group-item-success.active:focus,
button.list-group-item-success.active:focus {
  color: #fff;
  background-color: #3c763d;
  border-color: #3c763d;
}
.list-group-item-info {
  color: #31708f;
  background-color: #d9edf7;
}
a.list-group-item-info,
button.list-group-item-info {
  color: #31708f;
}
a.list-group-item-info .list-group-item-heading,
button.list-group-item-info .list-group-item-heading {
  color: inherit;
}
a.list-group-item-info:hover,
button.list-group-item-info:hover,
a.list-group-item-info:focus,
button.list-group-item-info:focus {
  color: #31708f;
  background-color: #c4e3f3;
}
a.list-group-item-info.active,
button.list-group-item-info.active,
a.list-group-item-info.active:hover,
button.list-group-item-info.active:hover,
a.list-group-item-info.active:focus,
button.list-group-item-info.active:focus {
  color: #fff;
  background-color: #31708f;
  border-color: #31708f;
}
.list-group-item-warning {
  color: #8a6d3b;
  background-color: #fcf8e3;
}
a.list-group-item-warning,
button.list-group-item-warning {
  color: #8a6d3b;
}
a.list-group-item-warning .list-group-item-heading,
button.list-group-item-warning .list-group-item-heading {
  color: inherit;
}
a.list-group-item-warning:hover,
button.list-group-item-warning:hover,
a.list-group-item-warning:focus,
button.list-group-item-warning:focus {
  color: #8a6d3b;
  background-color: #faf2cc;
}
a.list-group-item-warning.active,
button.list-group-item-warning.active,
a.list-group-item-warning.active:hover,
button.list-group-item-warning.active:hover,
a.list-group-item-warning.active:focus,
button.list-group-item-warning.active:focus {
  color: #fff;
  background-color: #8a6d3b;
  border-color: #8a6d3b;
}
.list-group-item-danger {
  color: #a94442;
  background-color: #f2dede;
}
a.list-group-item-danger,
button.list-group-item-danger {
  color: #a94442;
}
a.list-group-item-danger .list-group-item-heading,
button.list-group-item-danger .list-group-item-heading {
  color: inherit;
}
a.list-group-item-danger:hover,
button.list-group-item-danger:hover,
a.list-group-item-danger:focus,
button.list-group-item-danger:focus {
  color: #a94442;
  background-color: #ebcccc;
}
a.list-group-item-danger.active,
button.list-group-item-danger.active,
a.list-group-item-danger.active:hover,
button.list-group-item-danger.active:hover,
a.list-group-item-danger.active:focus,
button.list-group-item-danger.active:focus {
  color: #fff;
  background-color: #a94442;
  border-color: #a94442;
}
.list-group-item-heading {
  margin-top: 0;
  margin-bottom: 5px;
}
.list-group-item-text {
  margin-bottom: 0;
  line-height: 1.3;
}
.panel {
  margin-bottom: 18px;
  background-color: #fff;
  border: 1px solid transparent;
  border-radius: 2px;
  -webkit-box-shadow: 0 1px 1px rgba(0, 0, 0, 0.05);
  box-shadow: 0 1px 1px rgba(0, 0, 0, 0.05);
}
.panel-body {
  padding: 15px;
}
.panel-heading {
  padding: 10px 15px;
  border-bottom: 1px solid transparent;
  border-top-right-radius: 1px;
  border-top-left-radius: 1px;
}
.panel-heading > .dropdown .dropdown-toggle {
  color: inherit;
}
.panel-title {
  margin-top: 0;
  margin-bottom: 0;
  font-size: 15px;
  color: inherit;
}
.panel-title > a,
.panel-title > small,
.panel-title > .small,
.panel-title > small > a,
.panel-title > .small > a {
  color: inherit;
}
.panel-footer {
  padding: 10px 15px;
  background-color: #f5f5f5;
  border-top: 1px solid #ddd;
  border-bottom-right-radius: 1px;
  border-bottom-left-radius: 1px;
}
.panel > .list-group,
.panel > .panel-collapse > .list-group {
  margin-bottom: 0;
}
.panel > .list-group .list-group-item,
.panel > .panel-collapse > .list-group .list-group-item {
  border-width: 1px 0;
  border-radius: 0;
}
.panel > .list-group:first-child .list-group-item:first-child,
.panel > .panel-collapse > .list-group:first-child .list-group-item:first-child {
  border-top: 0;
  border-top-right-radius: 1px;
  border-top-left-radius: 1px;
}
.panel > .list-group:last-child .list-group-item:last-child,
.panel > .panel-collapse > .list-group:last-child .list-group-item:last-child {
  border-bottom: 0;
  border-bottom-right-radius: 1px;
  border-bottom-left-radius: 1px;
}
.panel > .panel-heading + .panel-collapse > .list-group .list-group-item:first-child {
  border-top-right-radius: 0;
  border-top-left-radius: 0;
}
.panel-heading + .list-group .list-group-item:first-child {
  border-top-width: 0;
}
.list-group + .panel-footer {
  border-top-width: 0;
}
.panel > .table,
.panel > .table-responsive > .table,
.panel > .panel-collapse > .table {
  margin-bottom: 0;
}
.panel > .table caption,
.panel > .table-responsive > .table caption,
.panel > .panel-collapse > .table caption {
  padding-left: 15px;
  padding-right: 15px;
}
.panel > .table:first-child,
.panel > .table-responsive:first-child > .table:first-child {
  border-top-right-radius: 1px;
  border-top-left-radius: 1px;
}
.panel > .table:first-child > thead:first-child > tr:first-child,
.panel > .table-responsive:first-child > .table:first-child > thead:first-child > tr:first-child,
.panel > .table:first-child > tbody:first-child > tr:first-child,
.panel > .table-responsive:first-child > .table:first-child > tbody:first-child > tr:first-child {
  border-top-left-radius: 1px;
  border-top-right-radius: 1px;
}
.panel > .table:first-child > thead:first-child > tr:first-child td:first-child,
.panel > .table-responsive:first-child > .table:first-child > thead:first-child > tr:first-child td:first-child,
.panel > .table:first-child > tbody:first-child > tr:first-child td:first-child,
.panel > .table-responsive:first-child > .table:first-child > tbody:first-child > tr:first-child td:first-child,
.panel > .table:first-child > thead:first-child > tr:first-child th:first-child,
.panel > .table-responsive:first-child > .table:first-child > thead:first-child > tr:first-child th:first-child,
.panel > .table:first-child > tbody:first-child > tr:first-child th:first-child,
.panel > .table-responsive:first-child > .table:first-child > tbody:first-child > tr:first-child th:first-child {
  border-top-left-radius: 1px;
}
.panel > .table:first-child > thead:first-child > tr:first-child td:last-child,
.panel > .table-responsive:first-child > .table:first-child > thead:first-child > tr:first-child td:last-child,
.panel > .table:first-child > tbody:first-child > tr:first-child td:last-child,
.panel > .table-responsive:first-child > .table:first-child > tbody:first-child > tr:first-child td:last-child,
.panel > .table:first-child > thead:first-child > tr:first-child th:last-child,
.panel > .table-responsive:first-child > .table:first-child > thead:first-child > tr:first-child th:last-child,
.panel > .table:first-child > tbody:first-child > tr:first-child th:last-child,
.panel > .table-responsive:first-child > .table:first-child > tbody:first-child > tr:first-child th:last-child {
  border-top-right-radius: 1px;
}
.panel > .table:last-child,
.panel > .table-responsive:last-child > .table:last-child {
  border-bottom-right-radius: 1px;
  border-bottom-left-radius: 1px;
}
.panel > .table:last-child > tbody:last-child > tr:last-child,
.panel > .table-responsive:last-child > .table:last-child > tbody:last-child > tr:last-child,
.panel > .table:last-child > tfoot:last-child > tr:last-child,
.panel > .table-responsive:last-child > .table:last-child > tfoot:last-child > tr:last-child {
  border-bottom-left-radius: 1px;
  border-bottom-right-radius: 1px;
}
.panel > .table:last-child > tbody:last-child > tr:last-child td:first-child,
.panel > .table-responsive:last-child > .table:last-child > tbody:last-child > tr:last-child td:first-child,
.panel > .table:last-child > tfoot:last-child > tr:last-child td:first-child,
.panel > .table-responsive:last-child > .table:last-child > tfoot:last-child > tr:last-child td:first-child,
.panel > .table:last-child > tbody:last-child > tr:last-child th:first-child,
.panel > .table-responsive:last-child > .table:last-child > tbody:last-child > tr:last-child th:first-child,
.panel > .table:last-child > tfoot:last-child > tr:last-child th:first-child,
.panel > .table-responsive:last-child > .table:last-child > tfoot:last-child > tr:last-child th:first-child {
  border-bottom-left-radius: 1px;
}
.panel > .table:last-child > tbody:last-child > tr:last-child td:last-child,
.panel > .table-responsive:last-child > .table:last-child > tbody:last-child > tr:last-child td:last-child,
.panel > .table:last-child > tfoot:last-child > tr:last-child td:last-child,
.panel > .table-responsive:last-child > .table:last-child > tfoot:last-child > tr:last-child td:last-child,
.panel > .table:last-child > tbody:last-child > tr:last-child th:last-child,
.panel > .table-responsive:last-child > .table:last-child > tbody:last-child > tr:last-child th:last-child,
.panel > .table:last-child > tfoot:last-child > tr:last-child th:last-child,
.panel > .table-responsive:last-child > .table:last-child > tfoot:last-child > tr:last-child th:last-child {
  border-bottom-right-radius: 1px;
}
.panel > .panel-body + .table,
.panel > .panel-body + .table-responsive,
.panel > .table + .panel-body,
.panel > .table-responsive + .panel-body {
  border-top: 1px solid #ddd;
}
.panel > .table > tbody:first-child > tr:first-child th,
.panel > .table > tbody:first-child > tr:first-child td {
  border-top: 0;
}
.panel > .table-bordered,
.panel > .table-responsive > .table-bordered {
  border: 0;
}
.panel > .table-bordered > thead > tr > th:first-child,
.panel > .table-responsive > .table-bordered > thead > tr > th:first-child,
.panel > .table-bordered > tbody > tr > th:first-child,
.panel > .table-responsive > .table-bordered > tbody > tr > th:first-child,
.panel > .table-bordered > tfoot > tr > th:first-child,
.panel > .table-responsive > .table-bordered > tfoot > tr > th:first-child,
.panel > .table-bordered > thead > tr > td:first-child,
.panel > .table-responsive > .table-bordered > thead > tr > td:first-child,
.panel > .table-bordered > tbody > tr > td:first-child,
.panel > .table-responsive > .table-bordered > tbody > tr > td:first-child,
.panel > .table-bordered > tfoot > tr > td:first-child,
.panel > .table-responsive > .table-bordered > tfoot > tr > td:first-child {
  border-left: 0;
}
.panel > .table-bordered > thead > tr > th:last-child,
.panel > .table-responsive > .table-bordered > thead > tr > th:last-child,
.panel > .table-bordered > tbody > tr > th:last-child,
.panel > .table-responsive > .table-bordered > tbody > tr > th:last-child,
.panel > .table-bordered > tfoot > tr > th:last-child,
.panel > .table-responsive > .table-bordered > tfoot > tr > th:last-child,
.panel > .table-bordered > thead > tr > td:last-child,
.panel > .table-responsive > .table-bordered > thead > tr > td:last-child,
.panel > .table-bordered > tbody > tr > td:last-child,
.panel > .table-responsive > .table-bordered > tbody > tr > td:last-child,
.panel > .table-bordered > tfoot > tr > td:last-child,
.panel > .table-responsive > .table-bordered > tfoot > tr > td:last-child {
  border-right: 0;
}
.panel > .table-bordered > thead > tr:first-child > td,
.panel > .table-responsive > .table-bordered > thead > tr:first-child > td,
.panel > .table-bordered > tbody > tr:first-child > td,
.panel > .table-responsive > .table-bordered > tbody > tr:first-child > td,
.panel > .table-bordered > thead > tr:first-child > th,
.panel > .table-responsive > .table-bordered > thead > tr:first-child > th,
.panel > .table-bordered > tbody > tr:first-child > th,
.panel > .table-responsive > .table-bordered > tbody > tr:first-child > th {
  border-bottom: 0;
}
.panel > .table-bordered > tbody > tr:last-child > td,
.panel > .table-responsive > .table-bordered > tbody > tr:last-child > td,
.panel > .table-bordered > tfoot > tr:last-child > td,
.panel > .table-responsive > .table-bordered > tfoot > tr:last-child > td,
.panel > .table-bordered > tbody > tr:last-child > th,
.panel > .table-responsive > .table-bordered > tbody > tr:last-child > th,
.panel > .table-bordered > tfoot > tr:last-child > th,
.panel > .table-responsive > .table-bordered > tfoot > tr:last-child > th {
  border-bottom: 0;
}
.panel > .table-responsive {
  border: 0;
  margin-bottom: 0;
}
.panel-group {
  margin-bottom: 18px;
}
.panel-group .panel {
  margin-bottom: 0;
  border-radius: 2px;
}
.panel-group .panel + .panel {
  margin-top: 5px;
}
.panel-group .panel-heading {
  border-bottom: 0;
}
.panel-group .panel-heading + .panel-collapse > .panel-body,
.panel-group .panel-heading + .panel-collapse > .list-group {
  border-top: 1px solid #ddd;
}
.panel-group .panel-footer {
  border-top: 0;
}
.panel-group .panel-footer + .panel-collapse .panel-body {
  border-bottom: 1px solid #ddd;
}
.panel-default {
  border-color: #ddd;
}
.panel-default > .panel-heading {
  color: #333333;
  background-color: #f5f5f5;
  border-color: #ddd;
}
.panel-default > .panel-heading + .panel-collapse > .panel-body {
  border-top-color: #ddd;
}
.panel-default > .panel-heading .badge {
  color: #f5f5f5;
  background-color: #333333;
}
.panel-default > .panel-footer + .panel-collapse > .panel-body {
  border-bottom-color: #ddd;
}
.panel-primary {
  border-color: #337ab7;
}
.panel-primary > .panel-heading {
  color: #fff;
  background-color: #337ab7;
  border-color: #337ab7;
}
.panel-primary > .panel-heading + .panel-collapse > .panel-body {
  border-top-color: #337ab7;
}
.panel-primary > .panel-heading .badge {
  color: #337ab7;
  background-color: #fff;
}
.panel-primary > .panel-footer + .panel-collapse > .panel-body {
  border-bottom-color: #337ab7;
}
.panel-success {
  border-color: #d6e9c6;
}
.panel-success > .panel-heading {
  color: #3c763d;
  background-color: #dff0d8;
  border-color: #d6e9c6;
}
.panel-success > .panel-heading + .panel-collapse > .panel-body {
  border-top-color: #d6e9c6;
}
.panel-success > .panel-heading .badge {
  color: #dff0d8;
  background-color: #3c763d;
}
.panel-success > .panel-footer + .panel-collapse > .panel-body {
  border-bottom-color: #d6e9c6;
}
.panel-info {
  border-color: #bce8f1;
}
.panel-info > .panel-heading {
  color: #31708f;
  background-color: #d9edf7;
  border-color: #bce8f1;
}
.panel-info > .panel-heading + .panel-collapse > .panel-body {
  border-top-color: #bce8f1;
}
.panel-info > .panel-heading .badge {
  color: #d9edf7;
  background-color: #31708f;
}
.panel-info > .panel-footer + .panel-collapse > .panel-body {
  border-bottom-color: #bce8f1;
}
.panel-warning {
  border-color: #faebcc;
}
.panel-warning > .panel-heading {
  color: #8a6d3b;
  background-color: #fcf8e3;
  border-color: #faebcc;
}
.panel-warning > .panel-heading + .panel-collapse > .panel-body {
  border-top-color: #faebcc;
}
.panel-warning > .panel-heading .badge {
  color: #fcf8e3;
  background-color: #8a6d3b;
}
.panel-warning > .panel-footer + .panel-collapse > .panel-body {
  border-bottom-color: #faebcc;
}
.panel-danger {
  border-color: #ebccd1;
}
.panel-danger > .panel-heading {
  color: #a94442;
  background-color: #f2dede;
  border-color: #ebccd1;
}
.panel-danger > .panel-heading + .panel-collapse > .panel-body {
  border-top-color: #ebccd1;
}
.panel-danger > .panel-heading .badge {
  color: #f2dede;
  background-color: #a94442;
}
.panel-danger > .panel-footer + .panel-collapse > .panel-body {
  border-bottom-color: #ebccd1;
}
.embed-responsive {
  position: relative;
  display: block;
  height: 0;
  padding: 0;
  overflow: hidden;
}
.embed-responsive .embed-responsive-item,
.embed-responsive iframe,
.embed-responsive embed,
.embed-responsive object,
.embed-responsive video {
  position: absolute;
  top: 0;
  left: 0;
  bottom: 0;
  height: 100%;
  width: 100%;
  border: 0;
}
.embed-responsive-16by9 {
  padding-bottom: 56.25%;
}
.embed-responsive-4by3 {
  padding-bottom: 75%;
}
.well {
  min-height: 20px;
  padding: 19px;
  margin-bottom: 20px;
  background-color: #f5f5f5;
  border: 1px solid #e3e3e3;
  border-radius: 2px;
  -webkit-box-shadow: inset 0 1px 1px rgba(0, 0, 0, 0.05);
  box-shadow: inset 0 1px 1px rgba(0, 0, 0, 0.05);
}
.well blockquote {
  border-color: #ddd;
  border-color: rgba(0, 0, 0, 0.15);
}
.well-lg {
  padding: 24px;
  border-radius: 3px;
}
.well-sm {
  padding: 9px;
  border-radius: 1px;
}
.close {
  float: right;
  font-size: 19.5px;
  font-weight: bold;
  line-height: 1;
  color: #000;
  text-shadow: 0 1px 0 #fff;
  opacity: 0.2;
  filter: alpha(opacity=20);
}
.close:hover,
.close:focus {
  color: #000;
  text-decoration: none;
  cursor: pointer;
  opacity: 0.5;
  filter: alpha(opacity=50);
}
button.close {
  padding: 0;
  cursor: pointer;
  background: transparent;
  border: 0;
  -webkit-appearance: none;
}
.modal-open {
  overflow: hidden;
}
.modal {
  display: none;
  overflow: hidden;
  position: fixed;
  top: 0;
  right: 0;
  bottom: 0;
  left: 0;
  z-index: 1050;
  -webkit-overflow-scrolling: touch;
  outline: 0;
}
.modal.fade .modal-dialog {
  -webkit-transform: translate(0, -25%);
  -ms-transform: translate(0, -25%);
  -o-transform: translate(0, -25%);
  transform: translate(0, -25%);
  -webkit-transition: -webkit-transform 0.3s ease-out;
  -moz-transition: -moz-transform 0.3s ease-out;
  -o-transition: -o-transform 0.3s ease-out;
  transition: transform 0.3s ease-out;
}
.modal.in .modal-dialog {
  -webkit-transform: translate(0, 0);
  -ms-transform: translate(0, 0);
  -o-transform: translate(0, 0);
  transform: translate(0, 0);
}
.modal-open .modal {
  overflow-x: hidden;
  overflow-y: auto;
}
.modal-dialog {
  position: relative;
  width: auto;
  margin: 10px;
}
.modal-content {
  position: relative;
  background-color: #fff;
  border: 1px solid #999;
  border: 1px solid rgba(0, 0, 0, 0.2);
  border-radius: 3px;
  -webkit-box-shadow: 0 3px 9px rgba(0, 0, 0, 0.5);
  box-shadow: 0 3px 9px rgba(0, 0, 0, 0.5);
  background-clip: padding-box;
  outline: 0;
}
.modal-backdrop {
  position: fixed;
  top: 0;
  right: 0;
  bottom: 0;
  left: 0;
  z-index: 1040;
  background-color: #000;
}
.modal-backdrop.fade {
  opacity: 0;
  filter: alpha(opacity=0);
}
.modal-backdrop.in {
  opacity: 0.5;
  filter: alpha(opacity=50);
}
.modal-header {
  padding: 15px;
  border-bottom: 1px solid #e5e5e5;
}
.modal-header .close {
  margin-top: -2px;
}
.modal-title {
  margin: 0;
  line-height: 1.42857143;
}
.modal-body {
  position: relative;
  padding: 15px;
}
.modal-footer {
  padding: 15px;
  text-align: right;
  border-top: 1px solid #e5e5e5;
}
.modal-footer .btn + .btn {
  margin-left: 5px;
  margin-bottom: 0;
}
.modal-footer .btn-group .btn + .btn {
  margin-left: -1px;
}
.modal-footer .btn-block + .btn-block {
  margin-left: 0;
}
.modal-scrollbar-measure {
  position: absolute;
  top: -9999px;
  width: 50px;
  height: 50px;
  overflow: scroll;
}
@media (min-width: 768px) {
  .modal-dialog {
    width: 600px;
    margin: 30px auto;
  }
  .modal-content {
    -webkit-box-shadow: 0 5px 15px rgba(0, 0, 0, 0.5);
    box-shadow: 0 5px 15px rgba(0, 0, 0, 0.5);
  }
  .modal-sm {
    width: 300px;
  }
}
@media (min-width: 992px) {
  .modal-lg {
    width: 900px;
  }
}
.tooltip {
  position: absolute;
  z-index: 1070;
  display: block;
  font-family: "Helvetica Neue", Helvetica, Arial, sans-serif;
  font-style: normal;
  font-weight: normal;
  letter-spacing: normal;
  line-break: auto;
  line-height: 1.42857143;
  text-align: left;
  text-align: start;
  text-decoration: none;
  text-shadow: none;
  text-transform: none;
  white-space: normal;
  word-break: normal;
  word-spacing: normal;
  word-wrap: normal;
  font-size: 12px;
  opacity: 0;
  filter: alpha(opacity=0);
}
.tooltip.in {
  opacity: 0.9;
  filter: alpha(opacity=90);
}
.tooltip.top {
  margin-top: -3px;
  padding: 5px 0;
}
.tooltip.right {
  margin-left: 3px;
  padding: 0 5px;
}
.tooltip.bottom {
  margin-top: 3px;
  padding: 5px 0;
}
.tooltip.left {
  margin-left: -3px;
  padding: 0 5px;
}
.tooltip-inner {
  max-width: 200px;
  padding: 3px 8px;
  color: #fff;
  text-align: center;
  background-color: #000;
  border-radius: 2px;
}
.tooltip-arrow {
  position: absolute;
  width: 0;
  height: 0;
  border-color: transparent;
  border-style: solid;
}
.tooltip.top .tooltip-arrow {
  bottom: 0;
  left: 50%;
  margin-left: -5px;
  border-width: 5px 5px 0;
  border-top-color: #000;
}
.tooltip.top-left .tooltip-arrow {
  bottom: 0;
  right: 5px;
  margin-bottom: -5px;
  border-width: 5px 5px 0;
  border-top-color: #000;
}
.tooltip.top-right .tooltip-arrow {
  bottom: 0;
  left: 5px;
  margin-bottom: -5px;
  border-width: 5px 5px 0;
  border-top-color: #000;
}
.tooltip.right .tooltip-arrow {
  top: 50%;
  left: 0;
  margin-top: -5px;
  border-width: 5px 5px 5px 0;
  border-right-color: #000;
}
.tooltip.left .tooltip-arrow {
  top: 50%;
  right: 0;
  margin-top: -5px;
  border-width: 5px 0 5px 5px;
  border-left-color: #000;
}
.tooltip.bottom .tooltip-arrow {
  top: 0;
  left: 50%;
  margin-left: -5px;
  border-width: 0 5px 5px;
  border-bottom-color: #000;
}
.tooltip.bottom-left .tooltip-arrow {
  top: 0;
  right: 5px;
  margin-top: -5px;
  border-width: 0 5px 5px;
  border-bottom-color: #000;
}
.tooltip.bottom-right .tooltip-arrow {
  top: 0;
  left: 5px;
  margin-top: -5px;
  border-width: 0 5px 5px;
  border-bottom-color: #000;
}
.popover {
  position: absolute;
  top: 0;
  left: 0;
  z-index: 1060;
  display: none;
  max-width: 276px;
  padding: 1px;
  font-family: "Helvetica Neue", Helvetica, Arial, sans-serif;
  font-style: normal;
  font-weight: normal;
  letter-spacing: normal;
  line-break: auto;
  line-height: 1.42857143;
  text-align: left;
  text-align: start;
  text-decoration: none;
  text-shadow: none;
  text-transform: none;
  white-space: normal;
  word-break: normal;
  word-spacing: normal;
  word-wrap: normal;
  font-size: 13px;
  background-color: #fff;
  background-clip: padding-box;
  border: 1px solid #ccc;
  border: 1px solid rgba(0, 0, 0, 0.2);
  border-radius: 3px;
  -webkit-box-shadow: 0 5px 10px rgba(0, 0, 0, 0.2);
  box-shadow: 0 5px 10px rgba(0, 0, 0, 0.2);
}
.popover.top {
  margin-top: -10px;
}
.popover.right {
  margin-left: 10px;
}
.popover.bottom {
  margin-top: 10px;
}
.popover.left {
  margin-left: -10px;
}
.popover-title {
  margin: 0;
  padding: 8px 14px;
  font-size: 13px;
  background-color: #f7f7f7;
  border-bottom: 1px solid #ebebeb;
  border-radius: 2px 2px 0 0;
}
.popover-content {
  padding: 9px 14px;
}
.popover > .arrow,
.popover > .arrow:after {
  position: absolute;
  display: block;
  width: 0;
  height: 0;
  border-color: transparent;
  border-style: solid;
}
.popover > .arrow {
  border-width: 11px;
}
.popover > .arrow:after {
  border-width: 10px;
  content: "";
}
.popover.top > .arrow {
  left: 50%;
  margin-left: -11px;
  border-bottom-width: 0;
  border-top-color: #999999;
  border-top-color: rgba(0, 0, 0, 0.25);
  bottom: -11px;
}
.popover.top > .arrow:after {
  content: " ";
  bottom: 1px;
  margin-left: -10px;
  border-bottom-width: 0;
  border-top-color: #fff;
}
.popover.right > .arrow {
  top: 50%;
  left: -11px;
  margin-top: -11px;
  border-left-width: 0;
  border-right-color: #999999;
  border-right-color: rgba(0, 0, 0, 0.25);
}
.popover.right > .arrow:after {
  content: " ";
  left: 1px;
  bottom: -10px;
  border-left-width: 0;
  border-right-color: #fff;
}
.popover.bottom > .arrow {
  left: 50%;
  margin-left: -11px;
  border-top-width: 0;
  border-bottom-color: #999999;
  border-bottom-color: rgba(0, 0, 0, 0.25);
  top: -11px;
}
.popover.bottom > .arrow:after {
  content: " ";
  top: 1px;
  margin-left: -10px;
  border-top-width: 0;
  border-bottom-color: #fff;
}
.popover.left > .arrow {
  top: 50%;
  right: -11px;
  margin-top: -11px;
  border-right-width: 0;
  border-left-color: #999999;
  border-left-color: rgba(0, 0, 0, 0.25);
}
.popover.left > .arrow:after {
  content: " ";
  right: 1px;
  border-right-width: 0;
  border-left-color: #fff;
  bottom: -10px;
}
.carousel {
  position: relative;
}
.carousel-inner {
  position: relative;
  overflow: hidden;
  width: 100%;
}
.carousel-inner > .item {
  display: none;
  position: relative;
  -webkit-transition: 0.6s ease-in-out left;
  -o-transition: 0.6s ease-in-out left;
  transition: 0.6s ease-in-out left;
}
.carousel-inner > .item > img,
.carousel-inner > .item > a > img {
  line-height: 1;
}
@media all and (transform-3d), (-webkit-transform-3d) {
  .carousel-inner > .item {
    -webkit-transition: -webkit-transform 0.6s ease-in-out;
    -moz-transition: -moz-transform 0.6s ease-in-out;
    -o-transition: -o-transform 0.6s ease-in-out;
    transition: transform 0.6s ease-in-out;
    -webkit-backface-visibility: hidden;
    -moz-backface-visibility: hidden;
    backface-visibility: hidden;
    -webkit-perspective: 1000px;
    -moz-perspective: 1000px;
    perspective: 1000px;
  }
  .carousel-inner > .item.next,
  .carousel-inner > .item.active.right {
    -webkit-transform: translate3d(100%, 0, 0);
    transform: translate3d(100%, 0, 0);
    left: 0;
  }
  .carousel-inner > .item.prev,
  .carousel-inner > .item.active.left {
    -webkit-transform: translate3d(-100%, 0, 0);
    transform: translate3d(-100%, 0, 0);
    left: 0;
  }
  .carousel-inner > .item.next.left,
  .carousel-inner > .item.prev.right,
  .carousel-inner > .item.active {
    -webkit-transform: translate3d(0, 0, 0);
    transform: translate3d(0, 0, 0);
    left: 0;
  }
}
.carousel-inner > .active,
.carousel-inner > .next,
.carousel-inner > .prev {
  display: block;
}
.carousel-inner > .active {
  left: 0;
}
.carousel-inner > .next,
.carousel-inner > .prev {
  position: absolute;
  top: 0;
  width: 100%;
}
.carousel-inner > .next {
  left: 100%;
}
.carousel-inner > .prev {
  left: -100%;
}
.carousel-inner > .next.left,
.carousel-inner > .prev.right {
  left: 0;
}
.carousel-inner > .active.left {
  left: -100%;
}
.carousel-inner > .active.right {
  left: 100%;
}
.carousel-control {
  position: absolute;
  top: 0;
  left: 0;
  bottom: 0;
  width: 15%;
  opacity: 0.5;
  filter: alpha(opacity=50);
  font-size: 20px;
  color: #fff;
  text-align: center;
  text-shadow: 0 1px 2px rgba(0, 0, 0, 0.6);
  background-color: rgba(0, 0, 0, 0);
}
.carousel-control.left {
  background-image: -webkit-linear-gradient(left, rgba(0, 0, 0, 0.5) 0%, rgba(0, 0, 0, 0.0001) 100%);
  background-image: -o-linear-gradient(left, rgba(0, 0, 0, 0.5) 0%, rgba(0, 0, 0, 0.0001) 100%);
  background-image: linear-gradient(to right, rgba(0, 0, 0, 0.5) 0%, rgba(0, 0, 0, 0.0001) 100%);
  background-repeat: repeat-x;
  filter: progid:DXImageTransform.Microsoft.gradient(startColorstr='#80000000', endColorstr='#00000000', GradientType=1);
}
.carousel-control.right {
  left: auto;
  right: 0;
  background-image: -webkit-linear-gradient(left, rgba(0, 0, 0, 0.0001) 0%, rgba(0, 0, 0, 0.5) 100%);
  background-image: -o-linear-gradient(left, rgba(0, 0, 0, 0.0001) 0%, rgba(0, 0, 0, 0.5) 100%);
  background-image: linear-gradient(to right, rgba(0, 0, 0, 0.0001) 0%, rgba(0, 0, 0, 0.5) 100%);
  background-repeat: repeat-x;
  filter: progid:DXImageTransform.Microsoft.gradient(startColorstr='#00000000', endColorstr='#80000000', GradientType=1);
}
.carousel-control:hover,
.carousel-control:focus {
  outline: 0;
  color: #fff;
  text-decoration: none;
  opacity: 0.9;
  filter: alpha(opacity=90);
}
.carousel-control .icon-prev,
.carousel-control .icon-next,
.carousel-control .glyphicon-chevron-left,
.carousel-control .glyphicon-chevron-right {
  position: absolute;
  top: 50%;
  margin-top: -10px;
  z-index: 5;
  display: inline-block;
}
.carousel-control .icon-prev,
.carousel-control .glyphicon-chevron-left {
  left: 50%;
  margin-left: -10px;
}
.carousel-control .icon-next,
.carousel-control .glyphicon-chevron-right {
  right: 50%;
  margin-right: -10px;
}
.carousel-control .icon-prev,
.carousel-control .icon-next {
  width: 20px;
  height: 20px;
  line-height: 1;
  font-family: serif;
}
.carousel-control .icon-prev:before {
  content: '\2039';
}
.carousel-control .icon-next:before {
  content: '\203a';
}
.carousel-indicators {
  position: absolute;
  bottom: 10px;
  left: 50%;
  z-index: 15;
  width: 60%;
  margin-left: -30%;
  padding-left: 0;
  list-style: none;
  text-align: center;
}
.carousel-indicators li {
  display: inline-block;
  width: 10px;
  height: 10px;
  margin: 1px;
  text-indent: -999px;
  border: 1px solid #fff;
  border-radius: 10px;
  cursor: pointer;
  background-color: #000 \9;
  background-color: rgba(0, 0, 0, 0);
}
.carousel-indicators .active {
  margin: 0;
  width: 12px;
  height: 12px;
  background-color: #fff;
}
.carousel-caption {
  position: absolute;
  left: 15%;
  right: 15%;
  bottom: 20px;
  z-index: 10;
  padding-top: 20px;
  padding-bottom: 20px;
  color: #fff;
  text-align: center;
  text-shadow: 0 1px 2px rgba(0, 0, 0, 0.6);
}
.carousel-caption .btn {
  text-shadow: none;
}
@media screen and (min-width: 768px) {
  .carousel-control .glyphicon-chevron-left,
  .carousel-control .glyphicon-chevron-right,
  .carousel-control .icon-prev,
  .carousel-control .icon-next {
    width: 30px;
    height: 30px;
    margin-top: -10px;
    font-size: 30px;
  }
  .carousel-control .glyphicon-chevron-left,
  .carousel-control .icon-prev {
    margin-left: -10px;
  }
  .carousel-control .glyphicon-chevron-right,
  .carousel-control .icon-next {
    margin-right: -10px;
  }
  .carousel-caption {
    left: 20%;
    right: 20%;
    padding-bottom: 30px;
  }
  .carousel-indicators {
    bottom: 20px;
  }
}
.clearfix:before,
.clearfix:after,
.dl-horizontal dd:before,
.dl-horizontal dd:after,
.container:before,
.container:after,
.container-fluid:before,
.container-fluid:after,
.row:before,
.row:after,
.form-horizontal .form-group:before,
.form-horizontal .form-group:after,
.btn-toolbar:before,
.btn-toolbar:after,
.btn-group-vertical > .btn-group:before,
.btn-group-vertical > .btn-group:after,
.nav:before,
.nav:after,
.navbar:before,
.navbar:after,
.navbar-header:before,
.navbar-header:after,
.navbar-collapse:before,
.navbar-collapse:after,
.pager:before,
.pager:after,
.panel-body:before,
.panel-body:after,
.modal-header:before,
.modal-header:after,
.modal-footer:before,
.modal-footer:after,
.item_buttons:before,
.item_buttons:after {
  content: " ";
  display: table;
}
.clearfix:after,
.dl-horizontal dd:after,
.container:after,
.container-fluid:after,
.row:after,
.form-horizontal .form-group:after,
.btn-toolbar:after,
.btn-group-vertical > .btn-group:after,
.nav:after,
.navbar:after,
.navbar-header:after,
.navbar-collapse:after,
.pager:after,
.panel-body:after,
.modal-header:after,
.modal-footer:after,
.item_buttons:after {
  clear: both;
}
.center-block {
  display: block;
  margin-left: auto;
  margin-right: auto;
}
.pull-right {
  float: right !important;
}
.pull-left {
  float: left !important;
}
.hide {
  display: none !important;
}
.show {
  display: block !important;
}
.invisible {
  visibility: hidden;
}
.text-hide {
  font: 0/0 a;
  color: transparent;
  text-shadow: none;
  background-color: transparent;
  border: 0;
}
.hidden {
  display: none !important;
}
.affix {
  position: fixed;
}
@-ms-viewport {
  width: device-width;
}
.visible-xs,
.visible-sm,
.visible-md,
.visible-lg {
  display: none !important;
}
.visible-xs-block,
.visible-xs-inline,
.visible-xs-inline-block,
.visible-sm-block,
.visible-sm-inline,
.visible-sm-inline-block,
.visible-md-block,
.visible-md-inline,
.visible-md-inline-block,
.visible-lg-block,
.visible-lg-inline,
.visible-lg-inline-block {
  display: none !important;
}
@media (max-width: 767px) {
  .visible-xs {
    display: block !important;
  }
  table.visible-xs {
    display: table !important;
  }
  tr.visible-xs {
    display: table-row !important;
  }
  th.visible-xs,
  td.visible-xs {
    display: table-cell !important;
  }
}
@media (max-width: 767px) {
  .visible-xs-block {
    display: block !important;
  }
}
@media (max-width: 767px) {
  .visible-xs-inline {
    display: inline !important;
  }
}
@media (max-width: 767px) {
  .visible-xs-inline-block {
    display: inline-block !important;
  }
}
@media (min-width: 768px) and (max-width: 991px) {
  .visible-sm {
    display: block !important;
  }
  table.visible-sm {
    display: table !important;
  }
  tr.visible-sm {
    display: table-row !important;
  }
  th.visible-sm,
  td.visible-sm {
    display: table-cell !important;
  }
}
@media (min-width: 768px) and (max-width: 991px) {
  .visible-sm-block {
    display: block !important;
  }
}
@media (min-width: 768px) and (max-width: 991px) {
  .visible-sm-inline {
    display: inline !important;
  }
}
@media (min-width: 768px) and (max-width: 991px) {
  .visible-sm-inline-block {
    display: inline-block !important;
  }
}
@media (min-width: 992px) and (max-width: 1199px) {
  .visible-md {
    display: block !important;
  }
  table.visible-md {
    display: table !important;
  }
  tr.visible-md {
    display: table-row !important;
  }
  th.visible-md,
  td.visible-md {
    display: table-cell !important;
  }
}
@media (min-width: 992px) and (max-width: 1199px) {
  .visible-md-block {
    display: block !important;
  }
}
@media (min-width: 992px) and (max-width: 1199px) {
  .visible-md-inline {
    display: inline !important;
  }
}
@media (min-width: 992px) and (max-width: 1199px) {
  .visible-md-inline-block {
    display: inline-block !important;
  }
}
@media (min-width: 1200px) {
  .visible-lg {
    display: block !important;
  }
  table.visible-lg {
    display: table !important;
  }
  tr.visible-lg {
    display: table-row !important;
  }
  th.visible-lg,
  td.visible-lg {
    display: table-cell !important;
  }
}
@media (min-width: 1200px) {
  .visible-lg-block {
    display: block !important;
  }
}
@media (min-width: 1200px) {
  .visible-lg-inline {
    display: inline !important;
  }
}
@media (min-width: 1200px) {
  .visible-lg-inline-block {
    display: inline-block !important;
  }
}
@media (max-width: 767px) {
  .hidden-xs {
    display: none !important;
  }
}
@media (min-width: 768px) and (max-width: 991px) {
  .hidden-sm {
    display: none !important;
  }
}
@media (min-width: 992px) and (max-width: 1199px) {
  .hidden-md {
    display: none !important;
  }
}
@media (min-width: 1200px) {
  .hidden-lg {
    display: none !important;
  }
}
.visible-print {
  display: none !important;
}
@media print {
  .visible-print {
    display: block !important;
  }
  table.visible-print {
    display: table !important;
  }
  tr.visible-print {
    display: table-row !important;
  }
  th.visible-print,
  td.visible-print {
    display: table-cell !important;
  }
}
.visible-print-block {
  display: none !important;
}
@media print {
  .visible-print-block {
    display: block !important;
  }
}
.visible-print-inline {
  display: none !important;
}
@media print {
  .visible-print-inline {
    display: inline !important;
  }
}
.visible-print-inline-block {
  display: none !important;
}
@media print {
  .visible-print-inline-block {
    display: inline-block !important;
  }
}
@media print {
  .hidden-print {
    display: none !important;
  }
}
/*!
*
* Font Awesome
*
*/
/*!
 *  Font Awesome 4.7.0 by @davegandy - http://fontawesome.io - @fontawesome
 *  License - http://fontawesome.io/license (Font: SIL OFL 1.1, CSS: MIT License)
 */
/* FONT PATH
 * -------------------------- */
@font-face {
  font-family: 'FontAwesome';
  src: url('../components/font-awesome/fonts/fontawesome-webfont.eot?v=4.7.0');
  src: url('../components/font-awesome/fonts/fontawesome-webfont.eot?#iefix&v=4.7.0') format('embedded-opentype'), url('../components/font-awesome/fonts/fontawesome-webfont.woff2?v=4.7.0') format('woff2'), url('../components/font-awesome/fonts/fontawesome-webfont.woff?v=4.7.0') format('woff'), url('../components/font-awesome/fonts/fontawesome-webfont.ttf?v=4.7.0') format('truetype'), url('../components/font-awesome/fonts/fontawesome-webfont.svg?v=4.7.0#fontawesomeregular') format('svg');
  font-weight: normal;
  font-style: normal;
}
.fa {
  display: inline-block;
  font: normal normal normal 14px/1 FontAwesome;
  font-size: inherit;
  text-rendering: auto;
  -webkit-font-smoothing: antialiased;
  -moz-osx-font-smoothing: grayscale;
}
/* makes the font 33% larger relative to the icon container */
.fa-lg {
  font-size: 1.33333333em;
  line-height: 0.75em;
  vertical-align: -15%;
}
.fa-2x {
  font-size: 2em;
}
.fa-3x {
  font-size: 3em;
}
.fa-4x {
  font-size: 4em;
}
.fa-5x {
  font-size: 5em;
}
.fa-fw {
  width: 1.28571429em;
  text-align: center;
}
.fa-ul {
  padding-left: 0;
  margin-left: 2.14285714em;
  list-style-type: none;
}
.fa-ul > li {
  position: relative;
}
.fa-li {
  position: absolute;
  left: -2.14285714em;
  width: 2.14285714em;
  top: 0.14285714em;
  text-align: center;
}
.fa-li.fa-lg {
  left: -1.85714286em;
}
.fa-border {
  padding: .2em .25em .15em;
  border: solid 0.08em #eee;
  border-radius: .1em;
}
.fa-pull-left {
  float: left;
}
.fa-pull-right {
  float: right;
}
.fa.fa-pull-left {
  margin-right: .3em;
}
.fa.fa-pull-right {
  margin-left: .3em;
}
/* Deprecated as of 4.4.0 */
.pull-right {
  float: right;
}
.pull-left {
  float: left;
}
.fa.pull-left {
  margin-right: .3em;
}
.fa.pull-right {
  margin-left: .3em;
}
.fa-spin {
  -webkit-animation: fa-spin 2s infinite linear;
  animation: fa-spin 2s infinite linear;
}
.fa-pulse {
  -webkit-animation: fa-spin 1s infinite steps(8);
  animation: fa-spin 1s infinite steps(8);
}
@-webkit-keyframes fa-spin {
  0% {
    -webkit-transform: rotate(0deg);
    transform: rotate(0deg);
  }
  100% {
    -webkit-transform: rotate(359deg);
    transform: rotate(359deg);
  }
}
@keyframes fa-spin {
  0% {
    -webkit-transform: rotate(0deg);
    transform: rotate(0deg);
  }
  100% {
    -webkit-transform: rotate(359deg);
    transform: rotate(359deg);
  }
}
.fa-rotate-90 {
  -ms-filter: "progid:DXImageTransform.Microsoft.BasicImage(rotation=1)";
  -webkit-transform: rotate(90deg);
  -ms-transform: rotate(90deg);
  transform: rotate(90deg);
}
.fa-rotate-180 {
  -ms-filter: "progid:DXImageTransform.Microsoft.BasicImage(rotation=2)";
  -webkit-transform: rotate(180deg);
  -ms-transform: rotate(180deg);
  transform: rotate(180deg);
}
.fa-rotate-270 {
  -ms-filter: "progid:DXImageTransform.Microsoft.BasicImage(rotation=3)";
  -webkit-transform: rotate(270deg);
  -ms-transform: rotate(270deg);
  transform: rotate(270deg);
}
.fa-flip-horizontal {
  -ms-filter: "progid:DXImageTransform.Microsoft.BasicImage(rotation=0, mirror=1)";
  -webkit-transform: scale(-1, 1);
  -ms-transform: scale(-1, 1);
  transform: scale(-1, 1);
}
.fa-flip-vertical {
  -ms-filter: "progid:DXImageTransform.Microsoft.BasicImage(rotation=2, mirror=1)";
  -webkit-transform: scale(1, -1);
  -ms-transform: scale(1, -1);
  transform: scale(1, -1);
}
:root .fa-rotate-90,
:root .fa-rotate-180,
:root .fa-rotate-270,
:root .fa-flip-horizontal,
:root .fa-flip-vertical {
  filter: none;
}
.fa-stack {
  position: relative;
  display: inline-block;
  width: 2em;
  height: 2em;
  line-height: 2em;
  vertical-align: middle;
}
.fa-stack-1x,
.fa-stack-2x {
  position: absolute;
  left: 0;
  width: 100%;
  text-align: center;
}
.fa-stack-1x {
  line-height: inherit;
}
.fa-stack-2x {
  font-size: 2em;
}
.fa-inverse {
  color: #fff;
}
/* Font Awesome uses the Unicode Private Use Area (PUA) to ensure screen
   readers do not read off random characters that represent icons */
.fa-glass:before {
  content: "\f000";
}
.fa-music:before {
  content: "\f001";
}
.fa-search:before {
  content: "\f002";
}
.fa-envelope-o:before {
  content: "\f003";
}
.fa-heart:before {
  content: "\f004";
}
.fa-star:before {
  content: "\f005";
}
.fa-star-o:before {
  content: "\f006";
}
.fa-user:before {
  content: "\f007";
}
.fa-film:before {
  content: "\f008";
}
.fa-th-large:before {
  content: "\f009";
}
.fa-th:before {
  content: "\f00a";
}
.fa-th-list:before {
  content: "\f00b";
}
.fa-check:before {
  content: "\f00c";
}
.fa-remove:before,
.fa-close:before,
.fa-times:before {
  content: "\f00d";
}
.fa-search-plus:before {
  content: "\f00e";
}
.fa-search-minus:before {
  content: "\f010";
}
.fa-power-off:before {
  content: "\f011";
}
.fa-signal:before {
  content: "\f012";
}
.fa-gear:before,
.fa-cog:before {
  content: "\f013";
}
.fa-trash-o:before {
  content: "\f014";
}
.fa-home:before {
  content: "\f015";
}
.fa-file-o:before {
  content: "\f016";
}
.fa-clock-o:before {
  content: "\f017";
}
.fa-road:before {
  content: "\f018";
}
.fa-download:before {
  content: "\f019";
}
.fa-arrow-circle-o-down:before {
  content: "\f01a";
}
.fa-arrow-circle-o-up:before {
  content: "\f01b";
}
.fa-inbox:before {
  content: "\f01c";
}
.fa-play-circle-o:before {
  content: "\f01d";
}
.fa-rotate-right:before,
.fa-repeat:before {
  content: "\f01e";
}
.fa-refresh:before {
  content: "\f021";
}
.fa-list-alt:before {
  content: "\f022";
}
.fa-lock:before {
  content: "\f023";
}
.fa-flag:before {
  content: "\f024";
}
.fa-headphones:before {
  content: "\f025";
}
.fa-volume-off:before {
  content: "\f026";
}
.fa-volume-down:before {
  content: "\f027";
}
.fa-volume-up:before {
  content: "\f028";
}
.fa-qrcode:before {
  content: "\f029";
}
.fa-barcode:before {
  content: "\f02a";
}
.fa-tag:before {
  content: "\f02b";
}
.fa-tags:before {
  content: "\f02c";
}
.fa-book:before {
  content: "\f02d";
}
.fa-bookmark:before {
  content: "\f02e";
}
.fa-print:before {
  content: "\f02f";
}
.fa-camera:before {
  content: "\f030";
}
.fa-font:before {
  content: "\f031";
}
.fa-bold:before {
  content: "\f032";
}
.fa-italic:before {
  content: "\f033";
}
.fa-text-height:before {
  content: "\f034";
}
.fa-text-width:before {
  content: "\f035";
}
.fa-align-left:before {
  content: "\f036";
}
.fa-align-center:before {
  content: "\f037";
}
.fa-align-right:before {
  content: "\f038";
}
.fa-align-justify:before {
  content: "\f039";
}
.fa-list:before {
  content: "\f03a";
}
.fa-dedent:before,
.fa-outdent:before {
  content: "\f03b";
}
.fa-indent:before {
  content: "\f03c";
}
.fa-video-camera:before {
  content: "\f03d";
}
.fa-photo:before,
.fa-image:before,
.fa-picture-o:before {
  content: "\f03e";
}
.fa-pencil:before {
  content: "\f040";
}
.fa-map-marker:before {
  content: "\f041";
}
.fa-adjust:before {
  content: "\f042";
}
.fa-tint:before {
  content: "\f043";
}
.fa-edit:before,
.fa-pencil-square-o:before {
  content: "\f044";
}
.fa-share-square-o:before {
  content: "\f045";
}
.fa-check-square-o:before {
  content: "\f046";
}
.fa-arrows:before {
  content: "\f047";
}
.fa-step-backward:before {
  content: "\f048";
}
.fa-fast-backward:before {
  content: "\f049";
}
.fa-backward:before {
  content: "\f04a";
}
.fa-play:before {
  content: "\f04b";
}
.fa-pause:before {
  content: "\f04c";
}
.fa-stop:before {
  content: "\f04d";
}
.fa-forward:before {
  content: "\f04e";
}
.fa-fast-forward:before {
  content: "\f050";
}
.fa-step-forward:before {
  content: "\f051";
}
.fa-eject:before {
  content: "\f052";
}
.fa-chevron-left:before {
  content: "\f053";
}
.fa-chevron-right:before {
  content: "\f054";
}
.fa-plus-circle:before {
  content: "\f055";
}
.fa-minus-circle:before {
  content: "\f056";
}
.fa-times-circle:before {
  content: "\f057";
}
.fa-check-circle:before {
  content: "\f058";
}
.fa-question-circle:before {
  content: "\f059";
}
.fa-info-circle:before {
  content: "\f05a";
}
.fa-crosshairs:before {
  content: "\f05b";
}
.fa-times-circle-o:before {
  content: "\f05c";
}
.fa-check-circle-o:before {
  content: "\f05d";
}
.fa-ban:before {
  content: "\f05e";
}
.fa-arrow-left:before {
  content: "\f060";
}
.fa-arrow-right:before {
  content: "\f061";
}
.fa-arrow-up:before {
  content: "\f062";
}
.fa-arrow-down:before {
  content: "\f063";
}
.fa-mail-forward:before,
.fa-share:before {
  content: "\f064";
}
.fa-expand:before {
  content: "\f065";
}
.fa-compress:before {
  content: "\f066";
}
.fa-plus:before {
  content: "\f067";
}
.fa-minus:before {
  content: "\f068";
}
.fa-asterisk:before {
  content: "\f069";
}
.fa-exclamation-circle:before {
  content: "\f06a";
}
.fa-gift:before {
  content: "\f06b";
}
.fa-leaf:before {
  content: "\f06c";
}
.fa-fire:before {
  content: "\f06d";
}
.fa-eye:before {
  content: "\f06e";
}
.fa-eye-slash:before {
  content: "\f070";
}
.fa-warning:before,
.fa-exclamation-triangle:before {
  content: "\f071";
}
.fa-plane:before {
  content: "\f072";
}
.fa-calendar:before {
  content: "\f073";
}
.fa-random:before {
  content: "\f074";
}
.fa-comment:before {
  content: "\f075";
}
.fa-magnet:before {
  content: "\f076";
}
.fa-chevron-up:before {
  content: "\f077";
}
.fa-chevron-down:before {
  content: "\f078";
}
.fa-retweet:before {
  content: "\f079";
}
.fa-shopping-cart:before {
  content: "\f07a";
}
.fa-folder:before {
  content: "\f07b";
}
.fa-folder-open:before {
  content: "\f07c";
}
.fa-arrows-v:before {
  content: "\f07d";
}
.fa-arrows-h:before {
  content: "\f07e";
}
.fa-bar-chart-o:before,
.fa-bar-chart:before {
  content: "\f080";
}
.fa-twitter-square:before {
  content: "\f081";
}
.fa-facebook-square:before {
  content: "\f082";
}
.fa-camera-retro:before {
  content: "\f083";
}
.fa-key:before {
  content: "\f084";
}
.fa-gears:before,
.fa-cogs:before {
  content: "\f085";
}
.fa-comments:before {
  content: "\f086";
}
.fa-thumbs-o-up:before {
  content: "\f087";
}
.fa-thumbs-o-down:before {
  content: "\f088";
}
.fa-star-half:before {
  content: "\f089";
}
.fa-heart-o:before {
  content: "\f08a";
}
.fa-sign-out:before {
  content: "\f08b";
}
.fa-linkedin-square:before {
  content: "\f08c";
}
.fa-thumb-tack:before {
  content: "\f08d";
}
.fa-external-link:before {
  content: "\f08e";
}
.fa-sign-in:before {
  content: "\f090";
}
.fa-trophy:before {
  content: "\f091";
}
.fa-github-square:before {
  content: "\f092";
}
.fa-upload:before {
  content: "\f093";
}
.fa-lemon-o:before {
  content: "\f094";
}
.fa-phone:before {
  content: "\f095";
}
.fa-square-o:before {
  content: "\f096";
}
.fa-bookmark-o:before {
  content: "\f097";
}
.fa-phone-square:before {
  content: "\f098";
}
.fa-twitter:before {
  content: "\f099";
}
.fa-facebook-f:before,
.fa-facebook:before {
  content: "\f09a";
}
.fa-github:before {
  content: "\f09b";
}
.fa-unlock:before {
  content: "\f09c";
}
.fa-credit-card:before {
  content: "\f09d";
}
.fa-feed:before,
.fa-rss:before {
  content: "\f09e";
}
.fa-hdd-o:before {
  content: "\f0a0";
}
.fa-bullhorn:before {
  content: "\f0a1";
}
.fa-bell:before {
  content: "\f0f3";
}
.fa-certificate:before {
  content: "\f0a3";
}
.fa-hand-o-right:before {
  content: "\f0a4";
}
.fa-hand-o-left:before {
  content: "\f0a5";
}
.fa-hand-o-up:before {
  content: "\f0a6";
}
.fa-hand-o-down:before {
  content: "\f0a7";
}
.fa-arrow-circle-left:before {
  content: "\f0a8";
}
.fa-arrow-circle-right:before {
  content: "\f0a9";
}
.fa-arrow-circle-up:before {
  content: "\f0aa";
}
.fa-arrow-circle-down:before {
  content: "\f0ab";
}
.fa-globe:before {
  content: "\f0ac";
}
.fa-wrench:before {
  content: "\f0ad";
}
.fa-tasks:before {
  content: "\f0ae";
}
.fa-filter:before {
  content: "\f0b0";
}
.fa-briefcase:before {
  content: "\f0b1";
}
.fa-arrows-alt:before {
  content: "\f0b2";
}
.fa-group:before,
.fa-users:before {
  content: "\f0c0";
}
.fa-chain:before,
.fa-link:before {
  content: "\f0c1";
}
.fa-cloud:before {
  content: "\f0c2";
}
.fa-flask:before {
  content: "\f0c3";
}
.fa-cut:before,
.fa-scissors:before {
  content: "\f0c4";
}
.fa-copy:before,
.fa-files-o:before {
  content: "\f0c5";
}
.fa-paperclip:before {
  content: "\f0c6";
}
.fa-save:before,
.fa-floppy-o:before {
  content: "\f0c7";
}
.fa-square:before {
  content: "\f0c8";
}
.fa-navicon:before,
.fa-reorder:before,
.fa-bars:before {
  content: "\f0c9";
}
.fa-list-ul:before {
  content: "\f0ca";
}
.fa-list-ol:before {
  content: "\f0cb";
}
.fa-strikethrough:before {
  content: "\f0cc";
}
.fa-underline:before {
  content: "\f0cd";
}
.fa-table:before {
  content: "\f0ce";
}
.fa-magic:before {
  content: "\f0d0";
}
.fa-truck:before {
  content: "\f0d1";
}
.fa-pinterest:before {
  content: "\f0d2";
}
.fa-pinterest-square:before {
  content: "\f0d3";
}
.fa-google-plus-square:before {
  content: "\f0d4";
}
.fa-google-plus:before {
  content: "\f0d5";
}
.fa-money:before {
  content: "\f0d6";
}
.fa-caret-down:before {
  content: "\f0d7";
}
.fa-caret-up:before {
  content: "\f0d8";
}
.fa-caret-left:before {
  content: "\f0d9";
}
.fa-caret-right:before {
  content: "\f0da";
}
.fa-columns:before {
  content: "\f0db";
}
.fa-unsorted:before,
.fa-sort:before {
  content: "\f0dc";
}
.fa-sort-down:before,
.fa-sort-desc:before {
  content: "\f0dd";
}
.fa-sort-up:before,
.fa-sort-asc:before {
  content: "\f0de";
}
.fa-envelope:before {
  content: "\f0e0";
}
.fa-linkedin:before {
  content: "\f0e1";
}
.fa-rotate-left:before,
.fa-undo:before {
  content: "\f0e2";
}
.fa-legal:before,
.fa-gavel:before {
  content: "\f0e3";
}
.fa-dashboard:before,
.fa-tachometer:before {
  content: "\f0e4";
}
.fa-comment-o:before {
  content: "\f0e5";
}
.fa-comments-o:before {
  content: "\f0e6";
}
.fa-flash:before,
.fa-bolt:before {
  content: "\f0e7";
}
.fa-sitemap:before {
  content: "\f0e8";
}
.fa-umbrella:before {
  content: "\f0e9";
}
.fa-paste:before,
.fa-clipboard:before {
  content: "\f0ea";
}
.fa-lightbulb-o:before {
  content: "\f0eb";
}
.fa-exchange:before {
  content: "\f0ec";
}
.fa-cloud-download:before {
  content: "\f0ed";
}
.fa-cloud-upload:before {
  content: "\f0ee";
}
.fa-user-md:before {
  content: "\f0f0";
}
.fa-stethoscope:before {
  content: "\f0f1";
}
.fa-suitcase:before {
  content: "\f0f2";
}
.fa-bell-o:before {
  content: "\f0a2";
}
.fa-coffee:before {
  content: "\f0f4";
}
.fa-cutlery:before {
  content: "\f0f5";
}
.fa-file-text-o:before {
  content: "\f0f6";
}
.fa-building-o:before {
  content: "\f0f7";
}
.fa-hospital-o:before {
  content: "\f0f8";
}
.fa-ambulance:before {
  content: "\f0f9";
}
.fa-medkit:before {
  content: "\f0fa";
}
.fa-fighter-jet:before {
  content: "\f0fb";
}
.fa-beer:before {
  content: "\f0fc";
}
.fa-h-square:before {
  content: "\f0fd";
}
.fa-plus-square:before {
  content: "\f0fe";
}
.fa-angle-double-left:before {
  content: "\f100";
}
.fa-angle-double-right:before {
  content: "\f101";
}
.fa-angle-double-up:before {
  content: "\f102";
}
.fa-angle-double-down:before {
  content: "\f103";
}
.fa-angle-left:before {
  content: "\f104";
}
.fa-angle-right:before {
  content: "\f105";
}
.fa-angle-up:before {
  content: "\f106";
}
.fa-angle-down:before {
  content: "\f107";
}
.fa-desktop:before {
  content: "\f108";
}
.fa-laptop:before {
  content: "\f109";
}
.fa-tablet:before {
  content: "\f10a";
}
.fa-mobile-phone:before,
.fa-mobile:before {
  content: "\f10b";
}
.fa-circle-o:before {
  content: "\f10c";
}
.fa-quote-left:before {
  content: "\f10d";
}
.fa-quote-right:before {
  content: "\f10e";
}
.fa-spinner:before {
  content: "\f110";
}
.fa-circle:before {
  content: "\f111";
}
.fa-mail-reply:before,
.fa-reply:before {
  content: "\f112";
}
.fa-github-alt:before {
  content: "\f113";
}
.fa-folder-o:before {
  content: "\f114";
}
.fa-folder-open-o:before {
  content: "\f115";
}
.fa-smile-o:before {
  content: "\f118";
}
.fa-frown-o:before {
  content: "\f119";
}
.fa-meh-o:before {
  content: "\f11a";
}
.fa-gamepad:before {
  content: "\f11b";
}
.fa-keyboard-o:before {
  content: "\f11c";
}
.fa-flag-o:before {
  content: "\f11d";
}
.fa-flag-checkered:before {
  content: "\f11e";
}
.fa-terminal:before {
  content: "\f120";
}
.fa-code:before {
  content: "\f121";
}
.fa-mail-reply-all:before,
.fa-reply-all:before {
  content: "\f122";
}
.fa-star-half-empty:before,
.fa-star-half-full:before,
.fa-star-half-o:before {
  content: "\f123";
}
.fa-location-arrow:before {
  content: "\f124";
}
.fa-crop:before {
  content: "\f125";
}
.fa-code-fork:before {
  content: "\f126";
}
.fa-unlink:before,
.fa-chain-broken:before {
  content: "\f127";
}
.fa-question:before {
  content: "\f128";
}
.fa-info:before {
  content: "\f129";
}
.fa-exclamation:before {
  content: "\f12a";
}
.fa-superscript:before {
  content: "\f12b";
}
.fa-subscript:before {
  content: "\f12c";
}
.fa-eraser:before {
  content: "\f12d";
}
.fa-puzzle-piece:before {
  content: "\f12e";
}
.fa-microphone:before {
  content: "\f130";
}
.fa-microphone-slash:before {
  content: "\f131";
}
.fa-shield:before {
  content: "\f132";
}
.fa-calendar-o:before {
  content: "\f133";
}
.fa-fire-extinguisher:before {
  content: "\f134";
}
.fa-rocket:before {
  content: "\f135";
}
.fa-maxcdn:before {
  content: "\f136";
}
.fa-chevron-circle-left:before {
  content: "\f137";
}
.fa-chevron-circle-right:before {
  content: "\f138";
}
.fa-chevron-circle-up:before {
  content: "\f139";
}
.fa-chevron-circle-down:before {
  content: "\f13a";
}
.fa-html5:before {
  content: "\f13b";
}
.fa-css3:before {
  content: "\f13c";
}
.fa-anchor:before {
  content: "\f13d";
}
.fa-unlock-alt:before {
  content: "\f13e";
}
.fa-bullseye:before {
  content: "\f140";
}
.fa-ellipsis-h:before {
  content: "\f141";
}
.fa-ellipsis-v:before {
  content: "\f142";
}
.fa-rss-square:before {
  content: "\f143";
}
.fa-play-circle:before {
  content: "\f144";
}
.fa-ticket:before {
  content: "\f145";
}
.fa-minus-square:before {
  content: "\f146";
}
.fa-minus-square-o:before {
  content: "\f147";
}
.fa-level-up:before {
  content: "\f148";
}
.fa-level-down:before {
  content: "\f149";
}
.fa-check-square:before {
  content: "\f14a";
}
.fa-pencil-square:before {
  content: "\f14b";
}
.fa-external-link-square:before {
  content: "\f14c";
}
.fa-share-square:before {
  content: "\f14d";
}
.fa-compass:before {
  content: "\f14e";
}
.fa-toggle-down:before,
.fa-caret-square-o-down:before {
  content: "\f150";
}
.fa-toggle-up:before,
.fa-caret-square-o-up:before {
  content: "\f151";
}
.fa-toggle-right:before,
.fa-caret-square-o-right:before {
  content: "\f152";
}
.fa-euro:before,
.fa-eur:before {
  content: "\f153";
}
.fa-gbp:before {
  content: "\f154";
}
.fa-dollar:before,
.fa-usd:before {
  content: "\f155";
}
.fa-rupee:before,
.fa-inr:before {
  content: "\f156";
}
.fa-cny:before,
.fa-rmb:before,
.fa-yen:before,
.fa-jpy:before {
  content: "\f157";
}
.fa-ruble:before,
.fa-rouble:before,
.fa-rub:before {
  content: "\f158";
}
.fa-won:before,
.fa-krw:before {
  content: "\f159";
}
.fa-bitcoin:before,
.fa-btc:before {
  content: "\f15a";
}
.fa-file:before {
  content: "\f15b";
}
.fa-file-text:before {
  content: "\f15c";
}
.fa-sort-alpha-asc:before {
  content: "\f15d";
}
.fa-sort-alpha-desc:before {
  content: "\f15e";
}
.fa-sort-amount-asc:before {
  content: "\f160";
}
.fa-sort-amount-desc:before {
  content: "\f161";
}
.fa-sort-numeric-asc:before {
  content: "\f162";
}
.fa-sort-numeric-desc:before {
  content: "\f163";
}
.fa-thumbs-up:before {
  content: "\f164";
}
.fa-thumbs-down:before {
  content: "\f165";
}
.fa-youtube-square:before {
  content: "\f166";
}
.fa-youtube:before {
  content: "\f167";
}
.fa-xing:before {
  content: "\f168";
}
.fa-xing-square:before {
  content: "\f169";
}
.fa-youtube-play:before {
  content: "\f16a";
}
.fa-dropbox:before {
  content: "\f16b";
}
.fa-stack-overflow:before {
  content: "\f16c";
}
.fa-instagram:before {
  content: "\f16d";
}
.fa-flickr:before {
  content: "\f16e";
}
.fa-adn:before {
  content: "\f170";
}
.fa-bitbucket:before {
  content: "\f171";
}
.fa-bitbucket-square:before {
  content: "\f172";
}
.fa-tumblr:before {
  content: "\f173";
}
.fa-tumblr-square:before {
  content: "\f174";
}
.fa-long-arrow-down:before {
  content: "\f175";
}
.fa-long-arrow-up:before {
  content: "\f176";
}
.fa-long-arrow-left:before {
  content: "\f177";
}
.fa-long-arrow-right:before {
  content: "\f178";
}
.fa-apple:before {
  content: "\f179";
}
.fa-windows:before {
  content: "\f17a";
}
.fa-android:before {
  content: "\f17b";
}
.fa-linux:before {
  content: "\f17c";
}
.fa-dribbble:before {
  content: "\f17d";
}
.fa-skype:before {
  content: "\f17e";
}
.fa-foursquare:before {
  content: "\f180";
}
.fa-trello:before {
  content: "\f181";
}
.fa-female:before {
  content: "\f182";
}
.fa-male:before {
  content: "\f183";
}
.fa-gittip:before,
.fa-gratipay:before {
  content: "\f184";
}
.fa-sun-o:before {
  content: "\f185";
}
.fa-moon-o:before {
  content: "\f186";
}
.fa-archive:before {
  content: "\f187";
}
.fa-bug:before {
  content: "\f188";
}
.fa-vk:before {
  content: "\f189";
}
.fa-weibo:before {
  content: "\f18a";
}
.fa-renren:before {
  content: "\f18b";
}
.fa-pagelines:before {
  content: "\f18c";
}
.fa-stack-exchange:before {
  content: "\f18d";
}
.fa-arrow-circle-o-right:before {
  content: "\f18e";
}
.fa-arrow-circle-o-left:before {
  content: "\f190";
}
.fa-toggle-left:before,
.fa-caret-square-o-left:before {
  content: "\f191";
}
.fa-dot-circle-o:before {
  content: "\f192";
}
.fa-wheelchair:before {
  content: "\f193";
}
.fa-vimeo-square:before {
  content: "\f194";
}
.fa-turkish-lira:before,
.fa-try:before {
  content: "\f195";
}
.fa-plus-square-o:before {
  content: "\f196";
}
.fa-space-shuttle:before {
  content: "\f197";
}
.fa-slack:before {
  content: "\f198";
}
.fa-envelope-square:before {
  content: "\f199";
}
.fa-wordpress:before {
  content: "\f19a";
}
.fa-openid:before {
  content: "\f19b";
}
.fa-institution:before,
.fa-bank:before,
.fa-university:before {
  content: "\f19c";
}
.fa-mortar-board:before,
.fa-graduation-cap:before {
  content: "\f19d";
}
.fa-yahoo:before {
  content: "\f19e";
}
.fa-google:before {
  content: "\f1a0";
}
.fa-reddit:before {
  content: "\f1a1";
}
.fa-reddit-square:before {
  content: "\f1a2";
}
.fa-stumbleupon-circle:before {
  content: "\f1a3";
}
.fa-stumbleupon:before {
  content: "\f1a4";
}
.fa-delicious:before {
  content: "\f1a5";
}
.fa-digg:before {
  content: "\f1a6";
}
.fa-pied-piper-pp:before {
  content: "\f1a7";
}
.fa-pied-piper-alt:before {
  content: "\f1a8";
}
.fa-drupal:before {
  content: "\f1a9";
}
.fa-joomla:before {
  content: "\f1aa";
}
.fa-language:before {
  content: "\f1ab";
}
.fa-fax:before {
  content: "\f1ac";
}
.fa-building:before {
  content: "\f1ad";
}
.fa-child:before {
  content: "\f1ae";
}
.fa-paw:before {
  content: "\f1b0";
}
.fa-spoon:before {
  content: "\f1b1";
}
.fa-cube:before {
  content: "\f1b2";
}
.fa-cubes:before {
  content: "\f1b3";
}
.fa-behance:before {
  content: "\f1b4";
}
.fa-behance-square:before {
  content: "\f1b5";
}
.fa-steam:before {
  content: "\f1b6";
}
.fa-steam-square:before {
  content: "\f1b7";
}
.fa-recycle:before {
  content: "\f1b8";
}
.fa-automobile:before,
.fa-car:before {
  content: "\f1b9";
}
.fa-cab:before,
.fa-taxi:before {
  content: "\f1ba";
}
.fa-tree:before {
  content: "\f1bb";
}
.fa-spotify:before {
  content: "\f1bc";
}
.fa-deviantart:before {
  content: "\f1bd";
}
.fa-soundcloud:before {
  content: "\f1be";
}
.fa-database:before {
  content: "\f1c0";
}
.fa-file-pdf-o:before {
  content: "\f1c1";
}
.fa-file-word-o:before {
  content: "\f1c2";
}
.fa-file-excel-o:before {
  content: "\f1c3";
}
.fa-file-powerpoint-o:before {
  content: "\f1c4";
}
.fa-file-photo-o:before,
.fa-file-picture-o:before,
.fa-file-image-o:before {
  content: "\f1c5";
}
.fa-file-zip-o:before,
.fa-file-archive-o:before {
  content: "\f1c6";
}
.fa-file-sound-o:before,
.fa-file-audio-o:before {
  content: "\f1c7";
}
.fa-file-movie-o:before,
.fa-file-video-o:before {
  content: "\f1c8";
}
.fa-file-code-o:before {
  content: "\f1c9";
}
.fa-vine:before {
  content: "\f1ca";
}
.fa-codepen:before {
  content: "\f1cb";
}
.fa-jsfiddle:before {
  content: "\f1cc";
}
.fa-life-bouy:before,
.fa-life-buoy:before,
.fa-life-saver:before,
.fa-support:before,
.fa-life-ring:before {
  content: "\f1cd";
}
.fa-circle-o-notch:before {
  content: "\f1ce";
}
.fa-ra:before,
.fa-resistance:before,
.fa-rebel:before {
  content: "\f1d0";
}
.fa-ge:before,
.fa-empire:before {
  content: "\f1d1";
}
.fa-git-square:before {
  content: "\f1d2";
}
.fa-git:before {
  content: "\f1d3";
}
.fa-y-combinator-square:before,
.fa-yc-square:before,
.fa-hacker-news:before {
  content: "\f1d4";
}
.fa-tencent-weibo:before {
  content: "\f1d5";
}
.fa-qq:before {
  content: "\f1d6";
}
.fa-wechat:before,
.fa-weixin:before {
  content: "\f1d7";
}
.fa-send:before,
.fa-paper-plane:before {
  content: "\f1d8";
}
.fa-send-o:before,
.fa-paper-plane-o:before {
  content: "\f1d9";
}
.fa-history:before {
  content: "\f1da";
}
.fa-circle-thin:before {
  content: "\f1db";
}
.fa-header:before {
  content: "\f1dc";
}
.fa-paragraph:before {
  content: "\f1dd";
}
.fa-sliders:before {
  content: "\f1de";
}
.fa-share-alt:before {
  content: "\f1e0";
}
.fa-share-alt-square:before {
  content: "\f1e1";
}
.fa-bomb:before {
  content: "\f1e2";
}
.fa-soccer-ball-o:before,
.fa-futbol-o:before {
  content: "\f1e3";
}
.fa-tty:before {
  content: "\f1e4";
}
.fa-binoculars:before {
  content: "\f1e5";
}
.fa-plug:before {
  content: "\f1e6";
}
.fa-slideshare:before {
  content: "\f1e7";
}
.fa-twitch:before {
  content: "\f1e8";
}
.fa-yelp:before {
  content: "\f1e9";
}
.fa-newspaper-o:before {
  content: "\f1ea";
}
.fa-wifi:before {
  content: "\f1eb";
}
.fa-calculator:before {
  content: "\f1ec";
}
.fa-paypal:before {
  content: "\f1ed";
}
.fa-google-wallet:before {
  content: "\f1ee";
}
.fa-cc-visa:before {
  content: "\f1f0";
}
.fa-cc-mastercard:before {
  content: "\f1f1";
}
.fa-cc-discover:before {
  content: "\f1f2";
}
.fa-cc-amex:before {
  content: "\f1f3";
}
.fa-cc-paypal:before {
  content: "\f1f4";
}
.fa-cc-stripe:before {
  content: "\f1f5";
}
.fa-bell-slash:before {
  content: "\f1f6";
}
.fa-bell-slash-o:before {
  content: "\f1f7";
}
.fa-trash:before {
  content: "\f1f8";
}
.fa-copyright:before {
  content: "\f1f9";
}
.fa-at:before {
  content: "\f1fa";
}
.fa-eyedropper:before {
  content: "\f1fb";
}
.fa-paint-brush:before {
  content: "\f1fc";
}
.fa-birthday-cake:before {
  content: "\f1fd";
}
.fa-area-chart:before {
  content: "\f1fe";
}
.fa-pie-chart:before {
  content: "\f200";
}
.fa-line-chart:before {
  content: "\f201";
}
.fa-lastfm:before {
  content: "\f202";
}
.fa-lastfm-square:before {
  content: "\f203";
}
.fa-toggle-off:before {
  content: "\f204";
}
.fa-toggle-on:before {
  content: "\f205";
}
.fa-bicycle:before {
  content: "\f206";
}
.fa-bus:before {
  content: "\f207";
}
.fa-ioxhost:before {
  content: "\f208";
}
.fa-angellist:before {
  content: "\f209";
}
.fa-cc:before {
  content: "\f20a";
}
.fa-shekel:before,
.fa-sheqel:before,
.fa-ils:before {
  content: "\f20b";
}
.fa-meanpath:before {
  content: "\f20c";
}
.fa-buysellads:before {
  content: "\f20d";
}
.fa-connectdevelop:before {
  content: "\f20e";
}
.fa-dashcube:before {
  content: "\f210";
}
.fa-forumbee:before {
  content: "\f211";
}
.fa-leanpub:before {
  content: "\f212";
}
.fa-sellsy:before {
  content: "\f213";
}
.fa-shirtsinbulk:before {
  content: "\f214";
}
.fa-simplybuilt:before {
  content: "\f215";
}
.fa-skyatlas:before {
  content: "\f216";
}
.fa-cart-plus:before {
  content: "\f217";
}
.fa-cart-arrow-down:before {
  content: "\f218";
}
.fa-diamond:before {
  content: "\f219";
}
.fa-ship:before {
  content: "\f21a";
}
.fa-user-secret:before {
  content: "\f21b";
}
.fa-motorcycle:before {
  content: "\f21c";
}
.fa-street-view:before {
  content: "\f21d";
}
.fa-heartbeat:before {
  content: "\f21e";
}
.fa-venus:before {
  content: "\f221";
}
.fa-mars:before {
  content: "\f222";
}
.fa-mercury:before {
  content: "\f223";
}
.fa-intersex:before,
.fa-transgender:before {
  content: "\f224";
}
.fa-transgender-alt:before {
  content: "\f225";
}
.fa-venus-double:before {
  content: "\f226";
}
.fa-mars-double:before {
  content: "\f227";
}
.fa-venus-mars:before {
  content: "\f228";
}
.fa-mars-stroke:before {
  content: "\f229";
}
.fa-mars-stroke-v:before {
  content: "\f22a";
}
.fa-mars-stroke-h:before {
  content: "\f22b";
}
.fa-neuter:before {
  content: "\f22c";
}
.fa-genderless:before {
  content: "\f22d";
}
.fa-facebook-official:before {
  content: "\f230";
}
.fa-pinterest-p:before {
  content: "\f231";
}
.fa-whatsapp:before {
  content: "\f232";
}
.fa-server:before {
  content: "\f233";
}
.fa-user-plus:before {
  content: "\f234";
}
.fa-user-times:before {
  content: "\f235";
}
.fa-hotel:before,
.fa-bed:before {
  content: "\f236";
}
.fa-viacoin:before {
  content: "\f237";
}
.fa-train:before {
  content: "\f238";
}
.fa-subway:before {
  content: "\f239";
}
.fa-medium:before {
  content: "\f23a";
}
.fa-yc:before,
.fa-y-combinator:before {
  content: "\f23b";
}
.fa-optin-monster:before {
  content: "\f23c";
}
.fa-opencart:before {
  content: "\f23d";
}
.fa-expeditedssl:before {
  content: "\f23e";
}
.fa-battery-4:before,
.fa-battery:before,
.fa-battery-full:before {
  content: "\f240";
}
.fa-battery-3:before,
.fa-battery-three-quarters:before {
  content: "\f241";
}
.fa-battery-2:before,
.fa-battery-half:before {
  content: "\f242";
}
.fa-battery-1:before,
.fa-battery-quarter:before {
  content: "\f243";
}
.fa-battery-0:before,
.fa-battery-empty:before {
  content: "\f244";
}
.fa-mouse-pointer:before {
  content: "\f245";
}
.fa-i-cursor:before {
  content: "\f246";
}
.fa-object-group:before {
  content: "\f247";
}
.fa-object-ungroup:before {
  content: "\f248";
}
.fa-sticky-note:before {
  content: "\f249";
}
.fa-sticky-note-o:before {
  content: "\f24a";
}
.fa-cc-jcb:before {
  content: "\f24b";
}
.fa-cc-diners-club:before {
  content: "\f24c";
}
.fa-clone:before {
  content: "\f24d";
}
.fa-balance-scale:before {
  content: "\f24e";
}
.fa-hourglass-o:before {
  content: "\f250";
}
.fa-hourglass-1:before,
.fa-hourglass-start:before {
  content: "\f251";
}
.fa-hourglass-2:before,
.fa-hourglass-half:before {
  content: "\f252";
}
.fa-hourglass-3:before,
.fa-hourglass-end:before {
  content: "\f253";
}
.fa-hourglass:before {
  content: "\f254";
}
.fa-hand-grab-o:before,
.fa-hand-rock-o:before {
  content: "\f255";
}
.fa-hand-stop-o:before,
.fa-hand-paper-o:before {
  content: "\f256";
}
.fa-hand-scissors-o:before {
  content: "\f257";
}
.fa-hand-lizard-o:before {
  content: "\f258";
}
.fa-hand-spock-o:before {
  content: "\f259";
}
.fa-hand-pointer-o:before {
  content: "\f25a";
}
.fa-hand-peace-o:before {
  content: "\f25b";
}
.fa-trademark:before {
  content: "\f25c";
}
.fa-registered:before {
  content: "\f25d";
}
.fa-creative-commons:before {
  content: "\f25e";
}
.fa-gg:before {
  content: "\f260";
}
.fa-gg-circle:before {
  content: "\f261";
}
.fa-tripadvisor:before {
  content: "\f262";
}
.fa-odnoklassniki:before {
  content: "\f263";
}
.fa-odnoklassniki-square:before {
  content: "\f264";
}
.fa-get-pocket:before {
  content: "\f265";
}
.fa-wikipedia-w:before {
  content: "\f266";
}
.fa-safari:before {
  content: "\f267";
}
.fa-chrome:before {
  content: "\f268";
}
.fa-firefox:before {
  content: "\f269";
}
.fa-opera:before {
  content: "\f26a";
}
.fa-internet-explorer:before {
  content: "\f26b";
}
.fa-tv:before,
.fa-television:before {
  content: "\f26c";
}
.fa-contao:before {
  content: "\f26d";
}
.fa-500px:before {
  content: "\f26e";
}
.fa-amazon:before {
  content: "\f270";
}
.fa-calendar-plus-o:before {
  content: "\f271";
}
.fa-calendar-minus-o:before {
  content: "\f272";
}
.fa-calendar-times-o:before {
  content: "\f273";
}
.fa-calendar-check-o:before {
  content: "\f274";
}
.fa-industry:before {
  content: "\f275";
}
.fa-map-pin:before {
  content: "\f276";
}
.fa-map-signs:before {
  content: "\f277";
}
.fa-map-o:before {
  content: "\f278";
}
.fa-map:before {
  content: "\f279";
}
.fa-commenting:before {
  content: "\f27a";
}
.fa-commenting-o:before {
  content: "\f27b";
}
.fa-houzz:before {
  content: "\f27c";
}
.fa-vimeo:before {
  content: "\f27d";
}
.fa-black-tie:before {
  content: "\f27e";
}
.fa-fonticons:before {
  content: "\f280";
}
.fa-reddit-alien:before {
  content: "\f281";
}
.fa-edge:before {
  content: "\f282";
}
.fa-credit-card-alt:before {
  content: "\f283";
}
.fa-codiepie:before {
  content: "\f284";
}
.fa-modx:before {
  content: "\f285";
}
.fa-fort-awesome:before {
  content: "\f286";
}
.fa-usb:before {
  content: "\f287";
}
.fa-product-hunt:before {
  content: "\f288";
}
.fa-mixcloud:before {
  content: "\f289";
}
.fa-scribd:before {
  content: "\f28a";
}
.fa-pause-circle:before {
  content: "\f28b";
}
.fa-pause-circle-o:before {
  content: "\f28c";
}
.fa-stop-circle:before {
  content: "\f28d";
}
.fa-stop-circle-o:before {
  content: "\f28e";
}
.fa-shopping-bag:before {
  content: "\f290";
}
.fa-shopping-basket:before {
  content: "\f291";
}
.fa-hashtag:before {
  content: "\f292";
}
.fa-bluetooth:before {
  content: "\f293";
}
.fa-bluetooth-b:before {
  content: "\f294";
}
.fa-percent:before {
  content: "\f295";
}
.fa-gitlab:before {
  content: "\f296";
}
.fa-wpbeginner:before {
  content: "\f297";
}
.fa-wpforms:before {
  content: "\f298";
}
.fa-envira:before {
  content: "\f299";
}
.fa-universal-access:before {
  content: "\f29a";
}
.fa-wheelchair-alt:before {
  content: "\f29b";
}
.fa-question-circle-o:before {
  content: "\f29c";
}
.fa-blind:before {
  content: "\f29d";
}
.fa-audio-description:before {
  content: "\f29e";
}
.fa-volume-control-phone:before {
  content: "\f2a0";
}
.fa-braille:before {
  content: "\f2a1";
}
.fa-assistive-listening-systems:before {
  content: "\f2a2";
}
.fa-asl-interpreting:before,
.fa-american-sign-language-interpreting:before {
  content: "\f2a3";
}
.fa-deafness:before,
.fa-hard-of-hearing:before,
.fa-deaf:before {
  content: "\f2a4";
}
.fa-glide:before {
  content: "\f2a5";
}
.fa-glide-g:before {
  content: "\f2a6";
}
.fa-signing:before,
.fa-sign-language:before {
  content: "\f2a7";
}
.fa-low-vision:before {
  content: "\f2a8";
}
.fa-viadeo:before {
  content: "\f2a9";
}
.fa-viadeo-square:before {
  content: "\f2aa";
}
.fa-snapchat:before {
  content: "\f2ab";
}
.fa-snapchat-ghost:before {
  content: "\f2ac";
}
.fa-snapchat-square:before {
  content: "\f2ad";
}
.fa-pied-piper:before {
  content: "\f2ae";
}
.fa-first-order:before {
  content: "\f2b0";
}
.fa-yoast:before {
  content: "\f2b1";
}
.fa-themeisle:before {
  content: "\f2b2";
}
.fa-google-plus-circle:before,
.fa-google-plus-official:before {
  content: "\f2b3";
}
.fa-fa:before,
.fa-font-awesome:before {
  content: "\f2b4";
}
.fa-handshake-o:before {
  content: "\f2b5";
}
.fa-envelope-open:before {
  content: "\f2b6";
}
.fa-envelope-open-o:before {
  content: "\f2b7";
}
.fa-linode:before {
  content: "\f2b8";
}
.fa-address-book:before {
  content: "\f2b9";
}
.fa-address-book-o:before {
  content: "\f2ba";
}
.fa-vcard:before,
.fa-address-card:before {
  content: "\f2bb";
}
.fa-vcard-o:before,
.fa-address-card-o:before {
  content: "\f2bc";
}
.fa-user-circle:before {
  content: "\f2bd";
}
.fa-user-circle-o:before {
  content: "\f2be";
}
.fa-user-o:before {
  content: "\f2c0";
}
.fa-id-badge:before {
  content: "\f2c1";
}
.fa-drivers-license:before,
.fa-id-card:before {
  content: "\f2c2";
}
.fa-drivers-license-o:before,
.fa-id-card-o:before {
  content: "\f2c3";
}
.fa-quora:before {
  content: "\f2c4";
}
.fa-free-code-camp:before {
  content: "\f2c5";
}
.fa-telegram:before {
  content: "\f2c6";
}
.fa-thermometer-4:before,
.fa-thermometer:before,
.fa-thermometer-full:before {
  content: "\f2c7";
}
.fa-thermometer-3:before,
.fa-thermometer-three-quarters:before {
  content: "\f2c8";
}
.fa-thermometer-2:before,
.fa-thermometer-half:before {
  content: "\f2c9";
}
.fa-thermometer-1:before,
.fa-thermometer-quarter:before {
  content: "\f2ca";
}
.fa-thermometer-0:before,
.fa-thermometer-empty:before {
  content: "\f2cb";
}
.fa-shower:before {
  content: "\f2cc";
}
.fa-bathtub:before,
.fa-s15:before,
.fa-bath:before {
  content: "\f2cd";
}
.fa-podcast:before {
  content: "\f2ce";
}
.fa-window-maximize:before {
  content: "\f2d0";
}
.fa-window-minimize:before {
  content: "\f2d1";
}
.fa-window-restore:before {
  content: "\f2d2";
}
.fa-times-rectangle:before,
.fa-window-close:before {
  content: "\f2d3";
}
.fa-times-rectangle-o:before,
.fa-window-close-o:before {
  content: "\f2d4";
}
.fa-bandcamp:before {
  content: "\f2d5";
}
.fa-grav:before {
  content: "\f2d6";
}
.fa-etsy:before {
  content: "\f2d7";
}
.fa-imdb:before {
  content: "\f2d8";
}
.fa-ravelry:before {
  content: "\f2d9";
}
.fa-eercast:before {
  content: "\f2da";
}
.fa-microchip:before {
  content: "\f2db";
}
.fa-snowflake-o:before {
  content: "\f2dc";
}
.fa-superpowers:before {
  content: "\f2dd";
}
.fa-wpexplorer:before {
  content: "\f2de";
}
.fa-meetup:before {
  content: "\f2e0";
}
.sr-only {
  position: absolute;
  width: 1px;
  height: 1px;
  padding: 0;
  margin: -1px;
  overflow: hidden;
  clip: rect(0, 0, 0, 0);
  border: 0;
}
.sr-only-focusable:active,
.sr-only-focusable:focus {
  position: static;
  width: auto;
  height: auto;
  margin: 0;
  overflow: visible;
  clip: auto;
}
.sr-only-focusable:active,
.sr-only-focusable:focus {
  position: static;
  width: auto;
  height: auto;
  margin: 0;
  overflow: visible;
  clip: auto;
}
/*!
*
* IPython base
*
*/
.modal.fade .modal-dialog {
  -webkit-transform: translate(0, 0);
  -ms-transform: translate(0, 0);
  -o-transform: translate(0, 0);
  transform: translate(0, 0);
}
code {
  color: #000;
}
pre {
  font-size: inherit;
  line-height: inherit;
}
label {
  font-weight: normal;
}
/* Make the page background atleast 100% the height of the view port */
/* Make the page itself atleast 70% the height of the view port */
.border-box-sizing {
  box-sizing: border-box;
  -moz-box-sizing: border-box;
  -webkit-box-sizing: border-box;
}
.corner-all {
  border-radius: 2px;
}
.no-padding {
  padding: 0px;
}
/* Flexible box model classes */
/* Taken from Alex Russell http://infrequently.org/2009/08/css-3-progress/ */
/* This file is a compatability layer.  It allows the usage of flexible box 
model layouts accross multiple browsers, including older browsers.  The newest,
universal implementation of the flexible box model is used when available (see
`Modern browsers` comments below).  Browsers that are known to implement this 
new spec completely include:

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

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

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

*/
.highlight-base {
  color: #000;
}
.highlight-variable {
  color: #000;
}
.highlight-variable-2 {
  color: #1a1a1a;
}
.highlight-variable-3 {
  color: #333333;
}
.highlight-string {
  color: #BA2121;
}
.highlight-comment {
  color: #408080;
  font-style: italic;
}
.highlight-number {
  color: #080;
}
.highlight-atom {
  color: #88F;
}
.highlight-keyword {
  color: #008000;
  font-weight: bold;
}
.highlight-builtin {
  color: #008000;
}
.highlight-error {
  color: #f00;
}
.highlight-operator {
  color: #AA22FF;
  font-weight: bold;
}
.highlight-meta {
  color: #AA22FF;
}
/* previously not defined, copying from default codemirror */
.highlight-def {
  color: #00f;
}
.highlight-string-2 {
  color: #f50;
}
.highlight-qualifier {
  color: #555;
}
.highlight-bracket {
  color: #997;
}
.highlight-tag {
  color: #170;
}
.highlight-attribute {
  color: #00c;
}
.highlight-header {
  color: blue;
}
.highlight-quote {
  color: #090;
}
.highlight-link {
  color: #00c;
}
/* apply the same style to codemirror */
.cm-s-ipython span.cm-keyword {
  color: #008000;
  font-weight: bold;
}
.cm-s-ipython span.cm-atom {
  color: #88F;
}
.cm-s-ipython span.cm-number {
  color: #080;
}
.cm-s-ipython span.cm-def {
  color: #00f;
}
.cm-s-ipython span.cm-variable {
  color: #000;
}
.cm-s-ipython span.cm-operator {
  color: #AA22FF;
  font-weight: bold;
}
.cm-s-ipython span.cm-variable-2 {
  color: #1a1a1a;
}
.cm-s-ipython span.cm-variable-3 {
  color: #333333;
}
.cm-s-ipython span.cm-comment {
  color: #408080;
  font-style: italic;
}
.cm-s-ipython span.cm-string {
  color: #BA2121;
}
.cm-s-ipython span.cm-string-2 {
  color: #f50;
}
.cm-s-ipython span.cm-meta {
  color: #AA22FF;
}
.cm-s-ipython span.cm-qualifier {
  color: #555;
}
.cm-s-ipython span.cm-builtin {
  color: #008000;
}
.cm-s-ipython span.cm-bracket {
  color: #997;
}
.cm-s-ipython span.cm-tag {
  color: #170;
}
.cm-s-ipython span.cm-attribute {
  color: #00c;
}
.cm-s-ipython span.cm-header {
  color: blue;
}
.cm-s-ipython span.cm-quote {
  color: #090;
}
.cm-s-ipython span.cm-link {
  color: #00c;
}
.cm-s-ipython span.cm-error {
  color: #f00;
}
.cm-s-ipython span.cm-tab {
  background: url(data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADAAAAAMCAYAAAAkuj5RAAAAAXNSR0IArs4c6QAAAGFJREFUSMft1LsRQFAQheHPowAKoACx3IgEKtaEHujDjORSgWTH/ZOdnZOcM/sgk/kFFWY0qV8foQwS4MKBCS3qR6ixBJvElOobYAtivseIE120FaowJPN75GMu8j/LfMwNjh4HUpwg4LUAAAAASUVORK5CYII=);
  background-position: right;
  background-repeat: no-repeat;
}
div.output_wrapper {
  /* this position must be relative to enable descendents to be absolute within it */
  position: relative;
  /* Old browsers */
  display: -webkit-box;
  -webkit-box-orient: vertical;
  -webkit-box-align: stretch;
  display: -moz-box;
  -moz-box-orient: vertical;
  -moz-box-align: stretch;
  display: box;
  box-orient: vertical;
  box-align: stretch;
  /* Modern browsers */
  display: flex;
  flex-direction: column;
  align-items: stretch;
  z-index: 1;
}
/* class for the output area when it should be height-limited */
div.output_scroll {
  /* ideally, this would be max-height, but FF barfs all over that */
  height: 24em;
  /* FF needs this *and the wrapper* to specify full width, or it will shrinkwrap */
  width: 100%;
  overflow: auto;
  border-radius: 2px;
  -webkit-box-shadow: inset 0 2px 8px rgba(0, 0, 0, 0.8);
  box-shadow: inset 0 2px 8px rgba(0, 0, 0, 0.8);
  display: block;
}
/* output div while it is collapsed */
div.output_collapsed {
  margin: 0px;
  padding: 0px;
  /* Old browsers */
  display: -webkit-box;
  -webkit-box-orient: vertical;
  -webkit-box-align: stretch;
  display: -moz-box;
  -moz-box-orient: vertical;
  -moz-box-align: stretch;
  display: box;
  box-orient: vertical;
  box-align: stretch;
  /* Modern browsers */
  display: flex;
  flex-direction: column;
  align-items: stretch;
}
div.out_prompt_overlay {
  height: 100%;
  padding: 0px 0.4em;
  position: absolute;
  border-radius: 2px;
}
div.out_prompt_overlay:hover {
  /* use inner shadow to get border that is computed the same on WebKit/FF */
  -webkit-box-shadow: inset 0 0 1px #000;
  box-shadow: inset 0 0 1px #000;
  background: rgba(240, 240, 240, 0.5);
}
div.output_prompt {
  color: #D84315;
}
/* This class is the outer container of all output sections. */
div.output_area {
  padding: 0px;
  page-break-inside: avoid;
  /* Old browsers */
  display: -webkit-box;
  -webkit-box-orient: horizontal;
  -webkit-box-align: stretch;
  display: -moz-box;
  -moz-box-orient: horizontal;
  -moz-box-align: stretch;
  display: box;
  box-orient: horizontal;
  box-align: stretch;
  /* Modern browsers */
  display: flex;
  flex-direction: row;
  align-items: stretch;
}
div.output_area .MathJax_Display {
  text-align: left !important;
}
div.output_area .rendered_html table {
  margin-left: 0;
  margin-right: 0;
}
div.output_area .rendered_html img {
  margin-left: 0;
  margin-right: 0;
}
div.output_area img,
div.output_area svg {
  max-width: 100%;
  height: auto;
}
div.output_area img.unconfined,
div.output_area svg.unconfined {
  max-width: none;
}
div.output_area .mglyph > img {
  max-width: none;
}
/* This is needed to protect the pre formating from global settings such
   as that of bootstrap */
.output {
  /* Old browsers */
  display: -webkit-box;
  -webkit-box-orient: vertical;
  -webkit-box-align: stretch;
  display: -moz-box;
  -moz-box-orient: vertical;
  -moz-box-align: stretch;
  display: box;
  box-orient: vertical;
  box-align: stretch;
  /* Modern browsers */
  display: flex;
  flex-direction: column;
  align-items: stretch;
}
@media (max-width: 540px) {
  div.output_area {
    /* Old browsers */
    display: -webkit-box;
    -webkit-box-orient: vertical;
    -webkit-box-align: stretch;
    display: -moz-box;
    -moz-box-orient: vertical;
    -moz-box-align: stretch;
    display: box;
    box-orient: vertical;
    box-align: stretch;
    /* Modern browsers */
    display: flex;
    flex-direction: column;
    align-items: stretch;
  }
}
div.output_area pre {
  margin: 0;
  padding: 1px 0 1px 0;
  border: 0;
  vertical-align: baseline;
  color: black;
  background-color: transparent;
  border-radius: 0;
}
/* This class is for the output subarea inside the output_area and after
   the prompt div. */
div.output_subarea {
  overflow-x: auto;
  padding: 0.4em;
  /* Old browsers */
  -webkit-box-flex: 1;
  -moz-box-flex: 1;
  box-flex: 1;
  /* Modern browsers */
  flex: 1;
  max-width: calc(100% - 14ex);
}
div.output_scroll div.output_subarea {
  overflow-x: visible;
}
/* The rest of the output_* classes are for special styling of the different
   output types */
/* all text output has this class: */
div.output_text {
  text-align: left;
  color: #000;
  /* This has to match that of the the CodeMirror class line-height below */
  line-height: 1.21429em;
}
/* stdout/stderr are 'text' as well as 'stream', but execute_result/error are *not* streams */
div.output_stderr {
  background: #fdd;
  /* very light red background for stderr */
}
div.output_latex {
  text-align: left;
}
/* Empty output_javascript divs should have no height */
div.output_javascript:empty {
  padding: 0;
}
.js-error {
  color: darkred;
}
/* raw_input styles */
div.raw_input_container {
  line-height: 1.21429em;
  padding-top: 5px;
}
pre.raw_input_prompt {
  /* nothing needed here. */
}
input.raw_input {
  font-family: monospace;
  font-size: inherit;
  color: inherit;
  width: auto;
  /* make sure input baseline aligns with prompt */
  vertical-align: baseline;
  /* padding + margin = 0.5em between prompt and cursor */
  padding: 0em 0.25em;
  margin: 0em 0.25em;
}
input.raw_input:focus {
  box-shadow: none;
}
p.p-space {
  margin-bottom: 10px;
}
div.output_unrecognized {
  padding: 5px;
  font-weight: bold;
  color: red;
}
div.output_unrecognized a {
  color: inherit;
  text-decoration: none;
}
div.output_unrecognized a:hover {
  color: inherit;
  text-decoration: none;
}
.rendered_html {
  color: #000;
  /* any extras will just be numbers: */
}
.rendered_html em {
  font-style: italic;
}
.rendered_html strong {
  font-weight: bold;
}
.rendered_html u {
  text-decoration: underline;
}
.rendered_html :link {
  text-decoration: underline;
}
.rendered_html :visited {
  text-decoration: underline;
}
.rendered_html h1 {
  font-size: 185.7%;
  margin: 1.08em 0 0 0;
  font-weight: bold;
  line-height: 1.0;
}
.rendered_html h2 {
  font-size: 157.1%;
  margin: 1.27em 0 0 0;
  font-weight: bold;
  line-height: 1.0;
}
.rendered_html h3 {
  font-size: 128.6%;
  margin: 1.55em 0 0 0;
  font-weight: bold;
  line-height: 1.0;
}
.rendered_html h4 {
  font-size: 100%;
  margin: 2em 0 0 0;
  font-weight: bold;
  line-height: 1.0;
}
.rendered_html h5 {
  font-size: 100%;
  margin: 2em 0 0 0;
  font-weight: bold;
  line-height: 1.0;
  font-style: italic;
}
.rendered_html h6 {
  font-size: 100%;
  margin: 2em 0 0 0;
  font-weight: bold;
  line-height: 1.0;
  font-style: italic;
}
.rendered_html h1:first-child {
  margin-top: 0.538em;
}
.rendered_html h2:first-child {
  margin-top: 0.636em;
}
.rendered_html h3:first-child {
  margin-top: 0.777em;
}
.rendered_html h4:first-child {
  margin-top: 1em;
}
.rendered_html h5:first-child {
  margin-top: 1em;
}
.rendered_html h6:first-child {
  margin-top: 1em;
}
.rendered_html ul:not(.list-inline),
.rendered_html ol:not(.list-inline) {
  padding-left: 2em;
}
.rendered_html ul {
  list-style: disc;
}
.rendered_html ul ul {
  list-style: square;
  margin-top: 0;
}
.rendered_html ul ul ul {
  list-style: circle;
}
.rendered_html ol {
  list-style: decimal;
}
.rendered_html ol ol {
  list-style: upper-alpha;
  margin-top: 0;
}
.rendered_html ol ol ol {
  list-style: lower-alpha;
}
.rendered_html ol ol ol ol {
  list-style: lower-roman;
}
.rendered_html ol ol ol ol ol {
  list-style: decimal;
}
.rendered_html * + ul {
  margin-top: 1em;
}
.rendered_html * + ol {
  margin-top: 1em;
}
.rendered_html hr {
  color: black;
  background-color: black;
}
.rendered_html pre {
  margin: 1em 2em;
  padding: 0px;
  background-color: #fff;
}
.rendered_html code {
  background-color: #eff0f1;
}
.rendered_html p code {
  padding: 1px 5px;
}
.rendered_html pre code {
  background-color: #fff;
}
.rendered_html pre,
.rendered_html code {
  border: 0;
  color: #000;
  font-size: 100%;
}
.rendered_html blockquote {
  margin: 1em 2em;
}
.rendered_html table {
  margin-left: auto;
  margin-right: auto;
  border: none;
  border-collapse: collapse;
  border-spacing: 0;
  color: black;
  font-size: 12px;
  table-layout: fixed;
}
.rendered_html thead {
  border-bottom: 1px solid black;
  vertical-align: bottom;
}
.rendered_html tr,
.rendered_html th,
.rendered_html td {
  text-align: right;
  vertical-align: middle;
  padding: 0.5em 0.5em;
  line-height: normal;
  white-space: normal;
  max-width: none;
  border: none;
}
.rendered_html th {
  font-weight: bold;
}
.rendered_html tbody tr:nth-child(odd) {
  background: #f5f5f5;
}
.rendered_html tbody tr:hover {
  background: rgba(66, 165, 245, 0.2);
}
.rendered_html * + table {
  margin-top: 1em;
}
.rendered_html p {
  text-align: left;
}
.rendered_html * + p {
  margin-top: 1em;
}
.rendered_html img {
  display: block;
  margin-left: auto;
  margin-right: auto;
}
.rendered_html * + img {
  margin-top: 1em;
}
.rendered_html img,
.rendered_html svg {
  max-width: 100%;
  height: auto;
}
.rendered_html img.unconfined,
.rendered_html svg.unconfined {
  max-width: none;
}
.rendered_html .alert {
  margin-bottom: initial;
}
.rendered_html * + .alert {
  margin-top: 1em;
}
[dir="rtl"] .rendered_html p {
  text-align: right;
}
div.text_cell {
  /* Old browsers */
  display: -webkit-box;
  -webkit-box-orient: horizontal;
  -webkit-box-align: stretch;
  display: -moz-box;
  -moz-box-orient: horizontal;
  -moz-box-align: stretch;
  display: box;
  box-orient: horizontal;
  box-align: stretch;
  /* Modern browsers */
  display: flex;
  flex-direction: row;
  align-items: stretch;
}
@media (max-width: 540px) {
  div.text_cell > div.prompt {
    display: none;
  }
}
div.text_cell_render {
  /*font-family: "Helvetica Neue", Arial, Helvetica, Geneva, sans-serif;*/
  outline: none;
  resize: none;
  width: inherit;
  border-style: none;
  padding: 0.5em 0.5em 0.5em 0.4em;
  color: #000;
  box-sizing: border-box;
  -moz-box-sizing: border-box;
  -webkit-box-sizing: border-box;
}
a.anchor-link:link {
  text-decoration: none;
  padding: 0px 20px;
  visibility: hidden;
}
h1:hover .anchor-link,
h2:hover .anchor-link,
h3:hover .anchor-link,
h4:hover .anchor-link,
h5:hover .anchor-link,
h6:hover .anchor-link {
  visibility: visible;
}
.text_cell.rendered .input_area {
  display: none;
}
.text_cell.rendered .rendered_html {
  overflow-x: auto;
  overflow-y: hidden;
}
.text_cell.rendered .rendered_html tr,
.text_cell.rendered .rendered_html th,
.text_cell.rendered .rendered_html td {
  max-width: none;
}
.text_cell.unrendered .text_cell_render {
  display: none;
}
.text_cell .dropzone .input_area {
  border: 2px dashed #bababa;
  margin: -1px;
}
.cm-header-1,
.cm-header-2,
.cm-header-3,
.cm-header-4,
.cm-header-5,
.cm-header-6 {
  font-weight: bold;
  font-family: "Helvetica Neue", Helvetica, Arial, sans-serif;
}
.cm-header-1 {
  font-size: 185.7%;
}
.cm-header-2 {
  font-size: 157.1%;
}
.cm-header-3 {
  font-size: 128.6%;
}
.cm-header-4 {
  font-size: 110%;
}
.cm-header-5 {
  font-size: 100%;
  font-style: italic;
}
.cm-header-6 {
  font-size: 100%;
  font-style: italic;
}
/*!
*
* IPython notebook webapp
*
*/
@media (max-width: 767px) {
  .notebook_app {
    padding-left: 0px;
    padding-right: 0px;
  }
}
#ipython-main-app {
  box-sizing: border-box;
  -moz-box-sizing: border-box;
  -webkit-box-sizing: border-box;
  height: 100%;
}
div#notebook_panel {
  margin: 0px;
  padding: 0px;
  box-sizing: border-box;
  -moz-box-sizing: border-box;
  -webkit-box-sizing: border-box;
  height: 100%;
}
div#notebook {
  font-size: 14px;
  line-height: 20px;
  overflow-y: hidden;
  overflow-x: auto;
  width: 100%;
  /* This spaces the page away from the edge of the notebook area */
  padding-top: 20px;
  margin: 0px;
  outline: none;
  box-sizing: border-box;
  -moz-box-sizing: border-box;
  -webkit-box-sizing: border-box;
  min-height: 100%;
}
@media not print {
  #notebook-container {
    padding: 15px;
    background-color: #fff;
    min-height: 0;
    -webkit-box-shadow: 0px 0px 12px 1px rgba(87, 87, 87, 0.2);
    box-shadow: 0px 0px 12px 1px rgba(87, 87, 87, 0.2);
  }
}
@media print {
  #notebook-container {
    width: 100%;
  }
}
div.ui-widget-content {
  border: 1px solid #ababab;
  outline: none;
}
pre.dialog {
  background-color: #f7f7f7;
  border: 1px solid #ddd;
  border-radius: 2px;
  padding: 0.4em;
  padding-left: 2em;
}
p.dialog {
  padding: 0.2em;
}
/* Word-wrap output correctly.  This is the CSS3 spelling, though Firefox seems
   to not honor it correctly.  Webkit browsers (Chrome, rekonq, Safari) do.
 */
pre,
code,
kbd,
samp {
  white-space: pre-wrap;
}
#fonttest {
  font-family: monospace;
}
p {
  margin-bottom: 0;
}
.end_space {
  min-height: 100px;
  transition: height .2s ease;
}
.notebook_app > #header {
  -webkit-box-shadow: 0px 0px 12px 1px rgba(87, 87, 87, 0.2);
  box-shadow: 0px 0px 12px 1px rgba(87, 87, 87, 0.2);
}
@media not print {
  .notebook_app {
    background-color: #EEE;
  }
}
kbd {
  border-style: solid;
  border-width: 1px;
  box-shadow: none;
  margin: 2px;
  padding-left: 2px;
  padding-right: 2px;
  padding-top: 1px;
  padding-bottom: 1px;
}
.jupyter-keybindings {
  padding: 1px;
  line-height: 24px;
  border-bottom: 1px solid gray;
}
.jupyter-keybindings input {
  margin: 0;
  padding: 0;
  border: none;
}
.jupyter-keybindings i {
  padding: 6px;
}
.well code {
  background-color: #ffffff;
  border-color: #ababab;
  border-width: 1px;
  border-style: solid;
  padding: 2px;
  padding-top: 1px;
  padding-bottom: 1px;
}
/* CSS for the cell toolbar */
.celltoolbar {
  border: thin solid #CFCFCF;
  border-bottom: none;
  background: #EEE;
  border-radius: 2px 2px 0px 0px;
  width: 100%;
  height: 29px;
  padding-right: 4px;
  /* Old browsers */
  display: -webkit-box;
  -webkit-box-orient: horizontal;
  -webkit-box-align: stretch;
  display: -moz-box;
  -moz-box-orient: horizontal;
  -moz-box-align: stretch;
  display: box;
  box-orient: horizontal;
  box-align: stretch;
  /* Modern browsers */
  display: flex;
  flex-direction: row;
  align-items: stretch;
  /* Old browsers */
  -webkit-box-pack: end;
  -moz-box-pack: end;
  box-pack: end;
  /* Modern browsers */
  justify-content: flex-end;
  display: -webkit-flex;
}
@media print {
  .celltoolbar {
    display: none;
  }
}
.ctb_hideshow {
  display: none;
  vertical-align: bottom;
}
/* ctb_show is added to the ctb_hideshow div to show the cell toolbar.
   Cell toolbars are only shown when the ctb_global_show class is also set.
*/
.ctb_global_show .ctb_show.ctb_hideshow {
  display: block;
}
.ctb_global_show .ctb_show + .input_area,
.ctb_global_show .ctb_show + div.text_cell_input,
.ctb_global_show .ctb_show ~ div.text_cell_render {
  border-top-right-radius: 0px;
  border-top-left-radius: 0px;
}
.ctb_global_show .ctb_show ~ div.text_cell_render {
  border: 1px solid #cfcfcf;
}
.celltoolbar {
  font-size: 87%;
  padding-top: 3px;
}
.celltoolbar select {
  display: block;
  width: 100%;
  height: 32px;
  padding: 6px 12px;
  font-size: 13px;
  line-height: 1.42857143;
  color: #555555;
  background-color: #fff;
  background-image: none;
  border: 1px solid #ccc;
  border-radius: 2px;
  -webkit-box-shadow: inset 0 1px 1px rgba(0, 0, 0, 0.075);
  box-shadow: inset 0 1px 1px rgba(0, 0, 0, 0.075);
  -webkit-transition: border-color ease-in-out .15s, box-shadow ease-in-out .15s;
  -o-transition: border-color ease-in-out .15s, box-shadow ease-in-out .15s;
  transition: border-color ease-in-out .15s, box-shadow ease-in-out .15s;
  height: 30px;
  padding: 5px 10px;
  font-size: 12px;
  line-height: 1.5;
  border-radius: 1px;
  width: inherit;
  font-size: inherit;
  height: 22px;
  padding: 0px;
  display: inline-block;
}
.celltoolbar select:focus {
  border-color: #66afe9;
  outline: 0;
  -webkit-box-shadow: inset 0 1px 1px rgba(0,0,0,.075), 0 0 8px rgba(102, 175, 233, 0.6);
  box-shadow: inset 0 1px 1px rgba(0,0,0,.075), 0 0 8px rgba(102, 175, 233, 0.6);
}
.celltoolbar select::-moz-placeholder {
  color: #999;
  opacity: 1;
}
.celltoolbar select:-ms-input-placeholder {
  color: #999;
}
.celltoolbar select::-webkit-input-placeholder {
  color: #999;
}
.celltoolbar select::-ms-expand {
  border: 0;
  background-color: transparent;
}
.celltoolbar select[disabled],
.celltoolbar select[readonly],
fieldset[disabled] .celltoolbar select {
  background-color: #eeeeee;
  opacity: 1;
}
.celltoolbar select[disabled],
fieldset[disabled] .celltoolbar select {
  cursor: not-allowed;
}
textarea.celltoolbar select {
  height: auto;
}
select.celltoolbar select {
  height: 30px;
  line-height: 30px;
}
textarea.celltoolbar select,
select[multiple].celltoolbar select {
  height: auto;
}
.celltoolbar label {
  margin-left: 5px;
  margin-right: 5px;
}
.tags_button_container {
  width: 100%;
  display: flex;
}
.tag-container {
  display: flex;
  flex-direction: row;
  flex-grow: 1;
  overflow: hidden;
  position: relative;
}
.tag-container > * {
  margin: 0 4px;
}
.remove-tag-btn {
  margin-left: 4px;
}
.tags-input {
  display: flex;
}
.cell-tag:last-child:after {
  content: "";
  position: absolute;
  right: 0;
  width: 40px;
  height: 100%;
  /* Fade to background color of cell toolbar */
  background: linear-gradient(to right, rgba(0, 0, 0, 0), #EEE);
}
.tags-input > * {
  margin-left: 4px;
}
.cell-tag,
.tags-input input,
.tags-input button {
  display: block;
  width: 100%;
  height: 32px;
  padding: 6px 12px;
  font-size: 13px;
  line-height: 1.42857143;
  color: #555555;
  background-color: #fff;
  background-image: none;
  border: 1px solid #ccc;
  border-radius: 2px;
  -webkit-box-shadow: inset 0 1px 1px rgba(0, 0, 0, 0.075);
  box-shadow: inset 0 1px 1px rgba(0, 0, 0, 0.075);
  -webkit-transition: border-color ease-in-out .15s, box-shadow ease-in-out .15s;
  -o-transition: border-color ease-in-out .15s, box-shadow ease-in-out .15s;
  transition: border-color ease-in-out .15s, box-shadow ease-in-out .15s;
  height: 30px;
  padding: 5px 10px;
  font-size: 12px;
  line-height: 1.5;
  border-radius: 1px;
  box-shadow: none;
  width: inherit;
  font-size: inherit;
  height: 22px;
  line-height: 22px;
  padding: 0px 4px;
  display: inline-block;
}
.cell-tag:focus,
.tags-input input:focus,
.tags-input button:focus {
  border-color: #66afe9;
  outline: 0;
  -webkit-box-shadow: inset 0 1px 1px rgba(0,0,0,.075), 0 0 8px rgba(102, 175, 233, 0.6);
  box-shadow: inset 0 1px 1px rgba(0,0,0,.075), 0 0 8px rgba(102, 175, 233, 0.6);
}
.cell-tag::-moz-placeholder,
.tags-input input::-moz-placeholder,
.tags-input button::-moz-placeholder {
  color: #999;
  opacity: 1;
}
.cell-tag:-ms-input-placeholder,
.tags-input input:-ms-input-placeholder,
.tags-input button:-ms-input-placeholder {
  color: #999;
}
.cell-tag::-webkit-input-placeholder,
.tags-input input::-webkit-input-placeholder,
.tags-input button::-webkit-input-placeholder {
  color: #999;
}
.cell-tag::-ms-expand,
.tags-input input::-ms-expand,
.tags-input button::-ms-expand {
  border: 0;
  background-color: transparent;
}
.cell-tag[disabled],
.tags-input input[disabled],
.tags-input button[disabled],
.cell-tag[readonly],
.tags-input input[readonly],
.tags-input button[readonly],
fieldset[disabled] .cell-tag,
fieldset[disabled] .tags-input input,
fieldset[disabled] .tags-input button {
  background-color: #eeeeee;
  opacity: 1;
}
.cell-tag[disabled],
.tags-input input[disabled],
.tags-input button[disabled],
fieldset[disabled] .cell-tag,
fieldset[disabled] .tags-input input,
fieldset[disabled] .tags-input button {
  cursor: not-allowed;
}
textarea.cell-tag,
textarea.tags-input input,
textarea.tags-input button {
  height: auto;
}
select.cell-tag,
select.tags-input input,
select.tags-input button {
  height: 30px;
  line-height: 30px;
}
textarea.cell-tag,
textarea.tags-input input,
textarea.tags-input button,
select[multiple].cell-tag,
select[multiple].tags-input input,
select[multiple].tags-input button {
  height: auto;
}
.cell-tag,
.tags-input button {
  padding: 0px 4px;
}
.cell-tag {
  background-color: #fff;
  white-space: nowrap;
}
.tags-input input[type=text]:focus {
  outline: none;
  box-shadow: none;
  border-color: #ccc;
}
.completions {
  position: absolute;
  z-index: 110;
  overflow: hidden;
  border: 1px solid #ababab;
  border-radius: 2px;
  -webkit-box-shadow: 0px 6px 10px -1px #adadad;
  box-shadow: 0px 6px 10px -1px #adadad;
  line-height: 1;
}
.completions select {
  background: white;
  outline: none;
  border: none;
  padding: 0px;
  margin: 0px;
  overflow: auto;
  font-family: monospace;
  font-size: 110%;
  color: #000;
  width: auto;
}
.completions select option.context {
  color: #286090;
}
#kernel_logo_widget .current_kernel_logo {
  display: none;
  margin-top: -1px;
  margin-bottom: -1px;
  width: 32px;
  height: 32px;
}
[dir="rtl"] #kernel_logo_widget {
  float: left !important;
  float: left;
}
.modal .modal-body .move-path {
  display: flex;
  flex-direction: row;
  justify-content: space;
  align-items: center;
}
.modal .modal-body .move-path .server-root {
  padding-right: 20px;
}
.modal .modal-body .move-path .path-input {
  flex: 1;
}
#menubar {
  box-sizing: border-box;
  -moz-box-sizing: border-box;
  -webkit-box-sizing: border-box;
  margin-top: 1px;
}
#menubar .navbar {
  border-top: 1px;
  border-radius: 0px 0px 2px 2px;
  margin-bottom: 0px;
}
#menubar .navbar-toggle {
  float: left;
  padding-top: 7px;
  padding-bottom: 7px;
  border: none;
}
#menubar .navbar-collapse {
  clear: left;
}
[dir="rtl"] #menubar .navbar-toggle {
  float: right;
}
[dir="rtl"] #menubar .navbar-collapse {
  clear: right;
}
[dir="rtl"] #menubar .navbar-nav {
  float: right;
}
[dir="rtl"] #menubar .nav {
  padding-right: 0px;
}
[dir="rtl"] #menubar .navbar-nav > li {
  float: right;
}
[dir="rtl"] #menubar .navbar-right {
  float: left !important;
}
[dir="rtl"] ul.dropdown-menu {
  text-align: right;
  left: auto;
}
[dir="rtl"] ul#new-menu.dropdown-menu {
  right: auto;
  left: 0;
}
.nav-wrapper {
  border-bottom: 1px solid #e7e7e7;
}
i.menu-icon {
  padding-top: 4px;
}
[dir="rtl"] i.menu-icon.pull-right {
  float: left !important;
  float: left;
}
ul#help_menu li a {
  overflow: hidden;
  padding-right: 2.2em;
}
ul#help_menu li a i {
  margin-right: -1.2em;
}
[dir="rtl"] ul#help_menu li a {
  padding-left: 2.2em;
}
[dir="rtl"] ul#help_menu li a i {
  margin-right: 0;
  margin-left: -1.2em;
}
[dir="rtl"] ul#help_menu li a i.pull-right {
  float: left !important;
  float: left;
}
.dropdown-submenu {
  position: relative;
}
.dropdown-submenu > .dropdown-menu {
  top: 0;
  left: 100%;
  margin-top: -6px;
  margin-left: -1px;
}
[dir="rtl"] .dropdown-submenu > .dropdown-menu {
  right: 100%;
  margin-right: -1px;
}
.dropdown-submenu:hover > .dropdown-menu {
  display: block;
}
.dropdown-submenu > a:after {
  display: inline-block;
  font: normal normal normal 14px/1 FontAwesome;
  font-size: inherit;
  text-rendering: auto;
  -webkit-font-smoothing: antialiased;
  -moz-osx-font-smoothing: grayscale;
  display: block;
  content: "\f0da";
  float: right;
  color: #333333;
  margin-top: 2px;
  margin-right: -10px;
}
.dropdown-submenu > a:after.fa-pull-left {
  margin-right: .3em;
}
.dropdown-submenu > a:after.fa-pull-right {
  margin-left: .3em;
}
.dropdown-submenu > a:after.pull-left {
  margin-right: .3em;
}
.dropdown-submenu > a:after.pull-right {
  margin-left: .3em;
}
[dir="rtl"] .dropdown-submenu > a:after {
  float: left;
  content: "\f0d9";
  margin-right: 0;
  margin-left: -10px;
}
.dropdown-submenu:hover > a:after {
  color: #262626;
}
.dropdown-submenu.pull-left {
  float: none;
}
.dropdown-submenu.pull-left > .dropdown-menu {
  left: -100%;
  margin-left: 10px;
}
#notification_area {
  float: right !important;
  float: right;
  z-index: 10;
}
[dir="rtl"] #notification_area {
  float: left !important;
  float: left;
}
.indicator_area {
  float: right !important;
  float: right;
  color: #777;
  margin-left: 5px;
  margin-right: 5px;
  width: 11px;
  z-index: 10;
  text-align: center;
  width: auto;
}
[dir="rtl"] .indicator_area {
  float: left !important;
  float: left;
}
#kernel_indicator {
  float: right !important;
  float: right;
  color: #777;
  margin-left: 5px;
  margin-right: 5px;
  width: 11px;
  z-index: 10;
  text-align: center;
  width: auto;
  border-left: 1px solid;
}
#kernel_indicator .kernel_indicator_name {
  padding-left: 5px;
  padding-right: 5px;
}
[dir="rtl"] #kernel_indicator {
  float: left !important;
  float: left;
  border-left: 0;
  border-right: 1px solid;
}
#modal_indicator {
  float: right !important;
  float: right;
  color: #777;
  margin-left: 5px;
  margin-right: 5px;
  width: 11px;
  z-index: 10;
  text-align: center;
  width: auto;
}
[dir="rtl"] #modal_indicator {
  float: left !important;
  float: left;
}
#readonly-indicator {
  float: right !important;
  float: right;
  color: #777;
  margin-left: 5px;
  margin-right: 5px;
  width: 11px;
  z-index: 10;
  text-align: center;
  width: auto;
  margin-top: 2px;
  margin-bottom: 0px;
  margin-left: 0px;
  margin-right: 0px;
  display: none;
}
.modal_indicator:before {
  width: 1.28571429em;
  text-align: center;
}
.edit_mode .modal_indicator:before {
  display: inline-block;
  font: normal normal normal 14px/1 FontAwesome;
  font-size: inherit;
  text-rendering: auto;
  -webkit-font-smoothing: antialiased;
  -moz-osx-font-smoothing: grayscale;
  content: "\f040";
}
.edit_mode .modal_indicator:before.fa-pull-left {
  margin-right: .3em;
}
.edit_mode .modal_indicator:before.fa-pull-right {
  margin-left: .3em;
}
.edit_mode .modal_indicator:before.pull-left {
  margin-right: .3em;
}
.edit_mode .modal_indicator:before.pull-right {
  margin-left: .3em;
}
.command_mode .modal_indicator:before {
  display: inline-block;
  font: normal normal normal 14px/1 FontAwesome;
  font-size: inherit;
  text-rendering: auto;
  -webkit-font-smoothing: antialiased;
  -moz-osx-font-smoothing: grayscale;
  content: ' ';
}
.command_mode .modal_indicator:before.fa-pull-left {
  margin-right: .3em;
}
.command_mode .modal_indicator:before.fa-pull-right {
  margin-left: .3em;
}
.command_mode .modal_indicator:before.pull-left {
  margin-right: .3em;
}
.command_mode .modal_indicator:before.pull-right {
  margin-left: .3em;
}
.kernel_idle_icon:before {
  display: inline-block;
  font: normal normal normal 14px/1 FontAwesome;
  font-size: inherit;
  text-rendering: auto;
  -webkit-font-smoothing: antialiased;
  -moz-osx-font-smoothing: grayscale;
  content: "\f10c";
}
.kernel_idle_icon:before.fa-pull-left {
  margin-right: .3em;
}
.kernel_idle_icon:before.fa-pull-right {
  margin-left: .3em;
}
.kernel_idle_icon:before.pull-left {
  margin-right: .3em;
}
.kernel_idle_icon:before.pull-right {
  margin-left: .3em;
}
.kernel_busy_icon:before {
  display: inline-block;
  font: normal normal normal 14px/1 FontAwesome;
  font-size: inherit;
  text-rendering: auto;
  -webkit-font-smoothing: antialiased;
  -moz-osx-font-smoothing: grayscale;
  content: "\f111";
}
.kernel_busy_icon:before.fa-pull-left {
  margin-right: .3em;
}
.kernel_busy_icon:before.fa-pull-right {
  margin-left: .3em;
}
.kernel_busy_icon:before.pull-left {
  margin-right: .3em;
}
.kernel_busy_icon:before.pull-right {
  margin-left: .3em;
}
.kernel_dead_icon:before {
  display: inline-block;
  font: normal normal normal 14px/1 FontAwesome;
  font-size: inherit;
  text-rendering: auto;
  -webkit-font-smoothing: antialiased;
  -moz-osx-font-smoothing: grayscale;
  content: "\f1e2";
}
.kernel_dead_icon:before.fa-pull-left {
  margin-right: .3em;
}
.kernel_dead_icon:before.fa-pull-right {
  margin-left: .3em;
}
.kernel_dead_icon:before.pull-left {
  margin-right: .3em;
}
.kernel_dead_icon:before.pull-right {
  margin-left: .3em;
}
.kernel_disconnected_icon:before {
  display: inline-block;
  font: normal normal normal 14px/1 FontAwesome;
  font-size: inherit;
  text-rendering: auto;
  -webkit-font-smoothing: antialiased;
  -moz-osx-font-smoothing: grayscale;
  content: "\f127";
}
.kernel_disconnected_icon:before.fa-pull-left {
  margin-right: .3em;
}
.kernel_disconnected_icon:before.fa-pull-right {
  margin-left: .3em;
}
.kernel_disconnected_icon:before.pull-left {
  margin-right: .3em;
}
.kernel_disconnected_icon:before.pull-right {
  margin-left: .3em;
}
.notification_widget {
  color: #777;
  z-index: 10;
  background: rgba(240, 240, 240, 0.5);
  margin-right: 4px;
  color: #333;
  background-color: #fff;
  border-color: #ccc;
}
.notification_widget:focus,
.notification_widget.focus {
  color: #333;
  background-color: #e6e6e6;
  border-color: #8c8c8c;
}
.notification_widget:hover {
  color: #333;
  background-color: #e6e6e6;
  border-color: #adadad;
}
.notification_widget:active,
.notification_widget.active,
.open > .dropdown-toggle.notification_widget {
  color: #333;
  background-color: #e6e6e6;
  border-color: #adadad;
}
.notification_widget:active:hover,
.notification_widget.active:hover,
.open > .dropdown-toggle.notification_widget:hover,
.notification_widget:active:focus,
.notification_widget.active:focus,
.open > .dropdown-toggle.notification_widget:focus,
.notification_widget:active.focus,
.notification_widget.active.focus,
.open > .dropdown-toggle.notification_widget.focus {
  color: #333;
  background-color: #d4d4d4;
  border-color: #8c8c8c;
}
.notification_widget:active,
.notification_widget.active,
.open > .dropdown-toggle.notification_widget {
  background-image: none;
}
.notification_widget.disabled:hover,
.notification_widget[disabled]:hover,
fieldset[disabled] .notification_widget:hover,
.notification_widget.disabled:focus,
.notification_widget[disabled]:focus,
fieldset[disabled] .notification_widget:focus,
.notification_widget.disabled.focus,
.notification_widget[disabled].focus,
fieldset[disabled] .notification_widget.focus {
  background-color: #fff;
  border-color: #ccc;
}
.notification_widget .badge {
  color: #fff;
  background-color: #333;
}
.notification_widget.warning {
  color: #fff;
  background-color: #f0ad4e;
  border-color: #eea236;
}
.notification_widget.warning:focus,
.notification_widget.warning.focus {
  color: #fff;
  background-color: #ec971f;
  border-color: #985f0d;
}
.notification_widget.warning:hover {
  color: #fff;
  background-color: #ec971f;
  border-color: #d58512;
}
.notification_widget.warning:active,
.notification_widget.warning.active,
.open > .dropdown-toggle.notification_widget.warning {
  color: #fff;
  background-color: #ec971f;
  border-color: #d58512;
}
.notification_widget.warning:active:hover,
.notification_widget.warning.active:hover,
.open > .dropdown-toggle.notification_widget.warning:hover,
.notification_widget.warning:active:focus,
.notification_widget.warning.active:focus,
.open > .dropdown-toggle.notification_widget.warning:focus,
.notification_widget.warning:active.focus,
.notification_widget.warning.active.focus,
.open > .dropdown-toggle.notification_widget.warning.focus {
  color: #fff;
  background-color: #d58512;
  border-color: #985f0d;
}
.notification_widget.warning:active,
.notification_widget.warning.active,
.open > .dropdown-toggle.notification_widget.warning {
  background-image: none;
}
.notification_widget.warning.disabled:hover,
.notification_widget.warning[disabled]:hover,
fieldset[disabled] .notification_widget.warning:hover,
.notification_widget.warning.disabled:focus,
.notification_widget.warning[disabled]:focus,
fieldset[disabled] .notification_widget.warning:focus,
.notification_widget.warning.disabled.focus,
.notification_widget.warning[disabled].focus,
fieldset[disabled] .notification_widget.warning.focus {
  background-color: #f0ad4e;
  border-color: #eea236;
}
.notification_widget.warning .badge {
  color: #f0ad4e;
  background-color: #fff;
}
.notification_widget.success {
  color: #fff;
  background-color: #5cb85c;
  border-color: #4cae4c;
}
.notification_widget.success:focus,
.notification_widget.success.focus {
  color: #fff;
  background-color: #449d44;
  border-color: #255625;
}
.notification_widget.success:hover {
  color: #fff;
  background-color: #449d44;
  border-color: #398439;
}
.notification_widget.success:active,
.notification_widget.success.active,
.open > .dropdown-toggle.notification_widget.success {
  color: #fff;
  background-color: #449d44;
  border-color: #398439;
}
.notification_widget.success:active:hover,
.notification_widget.success.active:hover,
.open > .dropdown-toggle.notification_widget.success:hover,
.notification_widget.success:active:focus,
.notification_widget.success.active:focus,
.open > .dropdown-toggle.notification_widget.success:focus,
.notification_widget.success:active.focus,
.notification_widget.success.active.focus,
.open > .dropdown-toggle.notification_widget.success.focus {
  color: #fff;
  background-color: #398439;
  border-color: #255625;
}
.notification_widget.success:active,
.notification_widget.success.active,
.open > .dropdown-toggle.notification_widget.success {
  background-image: none;
}
.notification_widget.success.disabled:hover,
.notification_widget.success[disabled]:hover,
fieldset[disabled] .notification_widget.success:hover,
.notification_widget.success.disabled:focus,
.notification_widget.success[disabled]:focus,
fieldset[disabled] .notification_widget.success:focus,
.notification_widget.success.disabled.focus,
.notification_widget.success[disabled].focus,
fieldset[disabled] .notification_widget.success.focus {
  background-color: #5cb85c;
  border-color: #4cae4c;
}
.notification_widget.success .badge {
  color: #5cb85c;
  background-color: #fff;
}
.notification_widget.info {
  color: #fff;
  background-color: #5bc0de;
  border-color: #46b8da;
}
.notification_widget.info:focus,
.notification_widget.info.focus {
  color: #fff;
  background-color: #31b0d5;
  border-color: #1b6d85;
}
.notification_widget.info:hover {
  color: #fff;
  background-color: #31b0d5;
  border-color: #269abc;
}
.notification_widget.info:active,
.notification_widget.info.active,
.open > .dropdown-toggle.notification_widget.info {
  color: #fff;
  background-color: #31b0d5;
  border-color: #269abc;
}
.notification_widget.info:active:hover,
.notification_widget.info.active:hover,
.open > .dropdown-toggle.notification_widget.info:hover,
.notification_widget.info:active:focus,
.notification_widget.info.active:focus,
.open > .dropdown-toggle.notification_widget.info:focus,
.notification_widget.info:active.focus,
.notification_widget.info.active.focus,
.open > .dropdown-toggle.notification_widget.info.focus {
  color: #fff;
  background-color: #269abc;
  border-color: #1b6d85;
}
.notification_widget.info:active,
.notification_widget.info.active,
.open > .dropdown-toggle.notification_widget.info {
  background-image: none;
}
.notification_widget.info.disabled:hover,
.notification_widget.info[disabled]:hover,
fieldset[disabled] .notification_widget.info:hover,
.notification_widget.info.disabled:focus,
.notification_widget.info[disabled]:focus,
fieldset[disabled] .notification_widget.info:focus,
.notification_widget.info.disabled.focus,
.notification_widget.info[disabled].focus,
fieldset[disabled] .notification_widget.info.focus {
  background-color: #5bc0de;
  border-color: #46b8da;
}
.notification_widget.info .badge {
  color: #5bc0de;
  background-color: #fff;
}
.notification_widget.danger {
  color: #fff;
  background-color: #d9534f;
  border-color: #d43f3a;
}
.notification_widget.danger:focus,
.notification_widget.danger.focus {
  color: #fff;
  background-color: #c9302c;
  border-color: #761c19;
}
.notification_widget.danger:hover {
  color: #fff;
  background-color: #c9302c;
  border-color: #ac2925;
}
.notification_widget.danger:active,
.notification_widget.danger.active,
.open > .dropdown-toggle.notification_widget.danger {
  color: #fff;
  background-color: #c9302c;
  border-color: #ac2925;
}
.notification_widget.danger:active:hover,
.notification_widget.danger.active:hover,
.open > .dropdown-toggle.notification_widget.danger:hover,
.notification_widget.danger:active:focus,
.notification_widget.danger.active:focus,
.open > .dropdown-toggle.notification_widget.danger:focus,
.notification_widget.danger:active.focus,
.notification_widget.danger.active.focus,
.open > .dropdown-toggle.notification_widget.danger.focus {
  color: #fff;
  background-color: #ac2925;
  border-color: #761c19;
}
.notification_widget.danger:active,
.notification_widget.danger.active,
.open > .dropdown-toggle.notification_widget.danger {
  background-image: none;
}
.notification_widget.danger.disabled:hover,
.notification_widget.danger[disabled]:hover,
fieldset[disabled] .notification_widget.danger:hover,
.notification_widget.danger.disabled:focus,
.notification_widget.danger[disabled]:focus,
fieldset[disabled] .notification_widget.danger:focus,
.notification_widget.danger.disabled.focus,
.notification_widget.danger[disabled].focus,
fieldset[disabled] .notification_widget.danger.focus {
  background-color: #d9534f;
  border-color: #d43f3a;
}
.notification_widget.danger .badge {
  color: #d9534f;
  background-color: #fff;
}
div#pager {
  background-color: #fff;
  font-size: 14px;
  line-height: 20px;
  overflow: hidden;
  display: none;
  position: fixed;
  bottom: 0px;
  width: 100%;
  max-height: 50%;
  padding-top: 8px;
  -webkit-box-shadow: 0px 0px 12px 1px rgba(87, 87, 87, 0.2);
  box-shadow: 0px 0px 12px 1px rgba(87, 87, 87, 0.2);
  /* Display over codemirror */
  z-index: 100;
  /* Hack which prevents jquery ui resizable from changing top. */
  top: auto !important;
}
div#pager pre {
  line-height: 1.21429em;
  color: #000;
  background-color: #f7f7f7;
  padding: 0.4em;
}
div#pager #pager-button-area {
  position: absolute;
  top: 8px;
  right: 20px;
}
div#pager #pager-contents {
  position: relative;
  overflow: auto;
  width: 100%;
  height: 100%;
}
div#pager #pager-contents #pager-container {
  position: relative;
  padding: 15px 0px;
  box-sizing: border-box;
  -moz-box-sizing: border-box;
  -webkit-box-sizing: border-box;
}
div#pager .ui-resizable-handle {
  top: 0px;
  height: 8px;
  background: #f7f7f7;
  border-top: 1px solid #cfcfcf;
  border-bottom: 1px solid #cfcfcf;
  /* This injects handle bars (a short, wide = symbol) for 
        the resize handle. */
}
div#pager .ui-resizable-handle::after {
  content: '';
  top: 2px;
  left: 50%;
  height: 3px;
  width: 30px;
  margin-left: -15px;
  position: absolute;
  border-top: 1px solid #cfcfcf;
}
.quickhelp {
  /* Old browsers */
  display: -webkit-box;
  -webkit-box-orient: horizontal;
  -webkit-box-align: stretch;
  display: -moz-box;
  -moz-box-orient: horizontal;
  -moz-box-align: stretch;
  display: box;
  box-orient: horizontal;
  box-align: stretch;
  /* Modern browsers */
  display: flex;
  flex-direction: row;
  align-items: stretch;
  line-height: 1.8em;
}
.shortcut_key {
  display: inline-block;
  width: 21ex;
  text-align: right;
  font-family: monospace;
}
.shortcut_descr {
  display: inline-block;
  /* Old browsers */
  -webkit-box-flex: 1;
  -moz-box-flex: 1;
  box-flex: 1;
  /* Modern browsers */
  flex: 1;
}
span.save_widget {
  height: 30px;
  margin-top: 4px;
  display: flex;
  justify-content: flex-start;
  align-items: baseline;
  width: 50%;
  flex: 1;
}
span.save_widget span.filename {
  height: 100%;
  line-height: 1em;
  margin-left: 16px;
  border: none;
  font-size: 146.5%;
  text-overflow: ellipsis;
  overflow: hidden;
  white-space: nowrap;
  border-radius: 2px;
}
span.save_widget span.filename:hover {
  background-color: #e6e6e6;
}
[dir="rtl"] span.save_widget.pull-left {
  float: right !important;
  float: right;
}
[dir="rtl"] span.save_widget span.filename {
  margin-left: 0;
  margin-right: 16px;
}
span.checkpoint_status,
span.autosave_status {
  font-size: small;
  white-space: nowrap;
  padding: 0 5px;
}
@media (max-width: 767px) {
  span.save_widget {
    font-size: small;
    padding: 0 0 0 5px;
  }
  span.checkpoint_status,
  span.autosave_status {
    display: none;
  }
}
@media (min-width: 768px) and (max-width: 991px) {
  span.checkpoint_status {
    display: none;
  }
  span.autosave_status {
    font-size: x-small;
  }
}
.toolbar {
  padding: 0px;
  margin-left: -5px;
  margin-top: 2px;
  margin-bottom: 5px;
  box-sizing: border-box;
  -moz-box-sizing: border-box;
  -webkit-box-sizing: border-box;
}
.toolbar select,
.toolbar label {
  width: auto;
  vertical-align: middle;
  margin-right: 2px;
  margin-bottom: 0px;
  display: inline;
  font-size: 92%;
  margin-left: 0.3em;
  margin-right: 0.3em;
  padding: 0px;
  padding-top: 3px;
}
.toolbar .btn {
  padding: 2px 8px;
}
.toolbar .btn-group {
  margin-top: 0px;
  margin-left: 5px;
}
.toolbar-btn-label {
  margin-left: 6px;
}
#maintoolbar {
  margin-bottom: -3px;
  margin-top: -8px;
  border: 0px;
  min-height: 27px;
  margin-left: 0px;
  padding-top: 11px;
  padding-bottom: 3px;
}
#maintoolbar .navbar-text {
  float: none;
  vertical-align: middle;
  text-align: right;
  margin-left: 5px;
  margin-right: 0px;
  margin-top: 0px;
}
.select-xs {
  height: 24px;
}
[dir="rtl"] .btn-group > .btn,
.btn-group-vertical > .btn {
  float: right;
}
.pulse,
.dropdown-menu > li > a.pulse,
li.pulse > a.dropdown-toggle,
li.pulse.open > a.dropdown-toggle {
  background-color: #F37626;
  color: white;
}
/**
 * Primary styles
 *
 * Author: Jupyter Development Team
 */
/** WARNING IF YOU ARE EDITTING THIS FILE, if this is a .css file, It has a lot
 * of chance of beeing generated from the ../less/[samename].less file, you can
 * try to get back the less file by reverting somme commit in history
 **/
/*
 * We'll try to get something pretty, so we
 * have some strange css to have the scroll bar on
 * the left with fix button on the top right of the tooltip
 */
@-moz-keyframes fadeOut {
  from {
    opacity: 1;
  }
  to {
    opacity: 0;
  }
}
@-webkit-keyframes fadeOut {
  from {
    opacity: 1;
  }
  to {
    opacity: 0;
  }
}
@-moz-keyframes fadeIn {
  from {
    opacity: 0;
  }
  to {
    opacity: 1;
  }
}
@-webkit-keyframes fadeIn {
  from {
    opacity: 0;
  }
  to {
    opacity: 1;
  }
}
/*properties of tooltip after "expand"*/
.bigtooltip {
  overflow: auto;
  height: 200px;
  -webkit-transition-property: height;
  -webkit-transition-duration: 500ms;
  -moz-transition-property: height;
  -moz-transition-duration: 500ms;
  transition-property: height;
  transition-duration: 500ms;
}
/*properties of tooltip before "expand"*/
.smalltooltip {
  -webkit-transition-property: height;
  -webkit-transition-duration: 500ms;
  -moz-transition-property: height;
  -moz-transition-duration: 500ms;
  transition-property: height;
  transition-duration: 500ms;
  text-overflow: ellipsis;
  overflow: hidden;
  height: 80px;
}
.tooltipbuttons {
  position: absolute;
  padding-right: 15px;
  top: 0px;
  right: 0px;
}
.tooltiptext {
  /*avoid the button to overlap on some docstring*/
  padding-right: 30px;
}
.ipython_tooltip {
  max-width: 700px;
  /*fade-in animation when inserted*/
  -webkit-animation: fadeOut 400ms;
  -moz-animation: fadeOut 400ms;
  animation: fadeOut 400ms;
  -webkit-animation: fadeIn 400ms;
  -moz-animation: fadeIn 400ms;
  animation: fadeIn 400ms;
  vertical-align: middle;
  background-color: #f7f7f7;
  overflow: visible;
  border: #ababab 1px solid;
  outline: none;
  padding: 3px;
  margin: 0px;
  padding-left: 7px;
  font-family: monospace;
  min-height: 50px;
  -moz-box-shadow: 0px 6px 10px -1px #adadad;
  -webkit-box-shadow: 0px 6px 10px -1px #adadad;
  box-shadow: 0px 6px 10px -1px #adadad;
  border-radius: 2px;
  position: absolute;
  z-index: 1000;
}
.ipython_tooltip a {
  float: right;
}
.ipython_tooltip .tooltiptext pre {
  border: 0;
  border-radius: 0;
  font-size: 100%;
  background-color: #f7f7f7;
}
.pretooltiparrow {
  left: 0px;
  margin: 0px;
  top: -16px;
  width: 40px;
  height: 16px;
  overflow: hidden;
  position: absolute;
}
.pretooltiparrow:before {
  background-color: #f7f7f7;
  border: 1px #ababab solid;
  z-index: 11;
  content: "";
  position: absolute;
  left: 15px;
  top: 10px;
  width: 25px;
  height: 25px;
  -webkit-transform: rotate(45deg);
  -moz-transform: rotate(45deg);
  -ms-transform: rotate(45deg);
  -o-transform: rotate(45deg);
}
ul.typeahead-list i {
  margin-left: -10px;
  width: 18px;
}
[dir="rtl"] ul.typeahead-list i {
  margin-left: 0;
  margin-right: -10px;
}
ul.typeahead-list {
  max-height: 80vh;
  overflow: auto;
}
ul.typeahead-list > li > a {
  /** Firefox bug **/
  /* see https://github.com/jupyter/notebook/issues/559 */
  white-space: normal;
}
ul.typeahead-list  > li > a.pull-right {
  float: left !important;
  float: left;
}
[dir="rtl"] .typeahead-list {
  text-align: right;
}
.cmd-palette .modal-body {
  padding: 7px;
}
.cmd-palette form {
  background: white;
}
.cmd-palette input {
  outline: none;
}
.no-shortcut {
  min-width: 20px;
  color: transparent;
}
[dir="rtl"] .no-shortcut.pull-right {
  float: left !important;
  float: left;
}
[dir="rtl"] .command-shortcut.pull-right {
  float: left !important;
  float: left;
}
.command-shortcut:before {
  content: "(command mode)";
  padding-right: 3px;
  color: #777777;
}
.edit-shortcut:before {
  content: "(edit)";
  padding-right: 3px;
  color: #777777;
}
[dir="rtl"] .edit-shortcut.pull-right {
  float: left !important;
  float: left;
}
#find-and-replace #replace-preview .match,
#find-and-replace #replace-preview .insert {
  background-color: #BBDEFB;
  border-color: #90CAF9;
  border-style: solid;
  border-width: 1px;
  border-radius: 0px;
}
[dir="ltr"] #find-and-replace .input-group-btn + .form-control {
  border-left: none;
}
[dir="rtl"] #find-and-replace .input-group-btn + .form-control {
  border-right: none;
}
#find-and-replace #replace-preview .replace .match {
  background-color: #FFCDD2;
  border-color: #EF9A9A;
  border-radius: 0px;
}
#find-and-replace #replace-preview .replace .insert {
  background-color: #C8E6C9;
  border-color: #A5D6A7;
  border-radius: 0px;
}
#find-and-replace #replace-preview {
  max-height: 60vh;
  overflow: auto;
}
#find-and-replace #replace-preview pre {
  padding: 5px 10px;
}
.terminal-app {
  background: #EEE;
}
.terminal-app #header {
  background: #fff;
  -webkit-box-shadow: 0px 0px 12px 1px rgba(87, 87, 87, 0.2);
  box-shadow: 0px 0px 12px 1px rgba(87, 87, 87, 0.2);
}
.terminal-app .terminal {
  width: 100%;
  float: left;
  font-family: monospace;
  color: white;
  background: black;
  padding: 0.4em;
  border-radius: 2px;
  -webkit-box-shadow: 0px 0px 12px 1px rgba(87, 87, 87, 0.4);
  box-shadow: 0px 0px 12px 1px rgba(87, 87, 87, 0.4);
}
.terminal-app .terminal,
.terminal-app .terminal dummy-screen {
  line-height: 1em;
  font-size: 14px;
}
.terminal-app .terminal .xterm-rows {
  padding: 10px;
}
.terminal-app .terminal-cursor {
  color: black;
  background: white;
}
.terminal-app #terminado-container {
  margin-top: 20px;
}
/*# sourceMappingURL=style.min.css.map */
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<style type="text/css">
    .highlight .hll { background-color: #ffffcc }
.highlight  { background: #f8f8f8; }
.highlight .c { color: #408080; font-style: italic } /* Comment */
.highlight .err { border: 1px solid #FF0000 } /* Error */
.highlight .k { color: #008000; font-weight: bold } /* Keyword */
.highlight .o { color: #666666 } /* Operator */
.highlight .ch { color: #408080; font-style: italic } /* Comment.Hashbang */
.highlight .cm { color: #408080; font-style: italic } /* Comment.Multiline */
.highlight .cp { color: #BC7A00 } /* Comment.Preproc */
.highlight .cpf { color: #408080; font-style: italic } /* Comment.PreprocFile */
.highlight .c1 { color: #408080; font-style: italic } /* Comment.Single */
.highlight .cs { color: #408080; font-style: italic } /* Comment.Special */
.highlight .gd { color: #A00000 } /* Generic.Deleted */
.highlight .ge { font-style: italic } /* Generic.Emph */
.highlight .gr { color: #FF0000 } /* Generic.Error */
.highlight .gh { color: #000080; font-weight: bold } /* Generic.Heading */
.highlight .gi { color: #00A000 } /* Generic.Inserted */
.highlight .go { color: #888888 } /* Generic.Output */
.highlight .gp { color: #000080; font-weight: bold } /* Generic.Prompt */
.highlight .gs { font-weight: bold } /* Generic.Strong */
.highlight .gu { color: #800080; font-weight: bold } /* Generic.Subheading */
.highlight .gt { color: #0044DD } /* Generic.Traceback */
.highlight .kc { color: #008000; font-weight: bold } /* Keyword.Constant */
.highlight .kd { color: #008000; font-weight: bold } /* Keyword.Declaration */
.highlight .kn { color: #008000; font-weight: bold } /* Keyword.Namespace */
.highlight .kp { color: #008000 } /* Keyword.Pseudo */
.highlight .kr { color: #008000; font-weight: bold } /* Keyword.Reserved */
.highlight .kt { color: #B00040 } /* Keyword.Type */
.highlight .m { color: #666666 } /* Literal.Number */
.highlight .s { color: #BA2121 } /* Literal.String */
.highlight .na { color: #7D9029 } /* Name.Attribute */
.highlight .nb { color: #008000 } /* Name.Builtin */
.highlight .nc { color: #0000FF; font-weight: bold } /* Name.Class */
.highlight .no { color: #880000 } /* Name.Constant */
.highlight .nd { color: #AA22FF } /* Name.Decorator */
.highlight .ni { color: #999999; font-weight: bold } /* Name.Entity */
.highlight .ne { color: #D2413A; font-weight: bold } /* Name.Exception */
.highlight .nf { color: #0000FF } /* Name.Function */
.highlight .nl { color: #A0A000 } /* Name.Label */
.highlight .nn { color: #0000FF; font-weight: bold } /* Name.Namespace */
.highlight .nt { color: #008000; font-weight: bold } /* Name.Tag */
.highlight .nv { color: #19177C } /* Name.Variable */
.highlight .ow { color: #AA22FF; font-weight: bold } /* Operator.Word */
.highlight .w { color: #bbbbbb } /* Text.Whitespace */
.highlight .mb { color: #666666 } /* Literal.Number.Bin */
.highlight .mf { color: #666666 } /* Literal.Number.Float */
.highlight .mh { color: #666666 } /* Literal.Number.Hex */
.highlight .mi { color: #666666 } /* Literal.Number.Integer */
.highlight .mo { color: #666666 } /* Literal.Number.Oct */
.highlight .sa { color: #BA2121 } /* Literal.String.Affix */
.highlight .sb { color: #BA2121 } /* Literal.String.Backtick */
.highlight .sc { color: #BA2121 } /* Literal.String.Char */
.highlight .dl { color: #BA2121 } /* Literal.String.Delimiter */
.highlight .sd { color: #BA2121; font-style: italic } /* Literal.String.Doc */
.highlight .s2 { color: #BA2121 } /* Literal.String.Double */
.highlight .se { color: #BB6622; font-weight: bold } /* Literal.String.Escape */
.highlight .sh { color: #BA2121 } /* Literal.String.Heredoc */
.highlight .si { color: #BB6688; font-weight: bold } /* Literal.String.Interpol */
.highlight .sx { color: #008000 } /* Literal.String.Other */
.highlight .sr { color: #BB6688 } /* Literal.String.Regex */
.highlight .s1 { color: #BA2121 } /* Literal.String.Single */
.highlight .ss { color: #19177C } /* Literal.String.Symbol */
.highlight .bp { color: #008000 } /* Name.Builtin.Pseudo */
.highlight .fm { color: #0000FF } /* Name.Function.Magic */
.highlight .vc { color: #19177C } /* Name.Variable.Class */
.highlight .vg { color: #19177C } /* Name.Variable.Global */
.highlight .vi { color: #19177C } /* Name.Variable.Instance */
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.highlight .il { color: #666666 } /* Literal.Number.Integer.Long */
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<style type="text/css">
    
/* Temporary definitions which will become obsolete with Notebook release 5.0 */
.ansi-black-fg { color: #3E424D; }
.ansi-black-bg { background-color: #3E424D; }
.ansi-black-intense-fg { color: #282C36; }
.ansi-black-intense-bg { background-color: #282C36; }
.ansi-red-fg { color: #E75C58; }
.ansi-red-bg { background-color: #E75C58; }
.ansi-red-intense-fg { color: #B22B31; }
.ansi-red-intense-bg { background-color: #B22B31; }
.ansi-green-fg { color: #00A250; }
.ansi-green-bg { background-color: #00A250; }
.ansi-green-intense-fg { color: #007427; }
.ansi-green-intense-bg { background-color: #007427; }
.ansi-yellow-fg { color: #DDB62B; }
.ansi-yellow-bg { background-color: #DDB62B; }
.ansi-yellow-intense-fg { color: #B27D12; }
.ansi-yellow-intense-bg { background-color: #B27D12; }
.ansi-blue-fg { color: #208FFB; }
.ansi-blue-bg { background-color: #208FFB; }
.ansi-blue-intense-fg { color: #0065CA; }
.ansi-blue-intense-bg { background-color: #0065CA; }
.ansi-magenta-fg { color: #D160C4; }
.ansi-magenta-bg { background-color: #D160C4; }
.ansi-magenta-intense-fg { color: #A03196; }
.ansi-magenta-intense-bg { background-color: #A03196; }
.ansi-cyan-fg { color: #60C6C8; }
.ansi-cyan-bg { background-color: #60C6C8; }
.ansi-cyan-intense-fg { color: #258F8F; }
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<h1 id="Reconocimiento-de-dígitos-(números)">Reconocimiento de dígitos (números)<a class="anchor-link" href="https://htmtopdf.herokuapp.com/ipynbviewer/temp/46ccb8d60bc4953329f884b04452879a/first_approach_neural_networks_p1.html?t=1670380747444#Reconocimiento-de-d%C3%ADgitos-(n%C3%BAmeros)">¶</a></h1><h2 id="Generalidades">Generalidades<a class="anchor-link" href="https://htmtopdf.herokuapp.com/ipynbviewer/temp/46ccb8d60bc4953329f884b04452879a/first_approach_neural_networks_p1.html?t=1670380747444#Generalidades">¶</a></h2><ul>
<li>Se usan imágenes de 28x28 píxeles, siendo en total 784 píxeles.</li>
<li>Cada píxel tiene un valor que se encuentra en un rango de 0 a 255, siendo <strong>0 completamente negro</strong> y <strong>255 completamente blanco</strong>.</li>
<li>Red neuronal<sup>1</sup> de dos capas<sup>2</sup>, sin contar la capa de entrada como una.</li>
<li>El conjunto de datos a utilizar es <strong><em>MNIST database</em></strong>.</li>
<li>La idea central es, que durante el proceso de entrenamiento de la red, los parámetros de esta se ajusten para aproximarse a una función deseada (reconocer dígitos).</li>
</ul>
<center><img src="./first_approach_neural_networks_p1_files/Rn65Uqq.jpg" width="" height=""></center><p><em>Elaboración propia.</em></p>
<hr>
<h1 id="La-Red-[D]">La Red <sup>[D]</sup><a class="anchor-link" href="https://htmtopdf.herokuapp.com/ipynbviewer/temp/46ccb8d60bc4953329f884b04452879a/first_approach_neural_networks_p1.html?t=1670380747444#La-Red-[D]">¶</a></h1><center><img src="./first_approach_neural_networks_p1_files/UzADRvF.jpg" width="" height=""></center><p><em>Elaboración propia.</em></p>
<h2 id="Matriz-inicial">Matriz inicial<a class="anchor-link" href="https://htmtopdf.herokuapp.com/ipynbviewer/temp/46ccb8d60bc4953329f884b04452879a/first_approach_neural_networks_p1.html?t=1670380747444#Matriz-inicial">¶</a></h2><span class="MathJax_Preview" style="color: inherit; display: none;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" id="MathJax-Element-1-Frame" tabindex="0" style="text-align: center; position: relative;" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot; display=&quot;block&quot;&gt;&lt;mtable columnalign=&quot;right left right left right left right left right left right left&quot; rowspacing=&quot;3pt&quot; columnspacing=&quot;0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em&quot; displaystyle=&quot;true&quot;&gt;&lt;mtr&gt;&lt;mtd /&gt;&lt;mtd&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mtext&gt;n&amp;#xFA;mero de im&amp;#xE1;genes&lt;/mtext&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd /&gt;&lt;mtd&gt;&lt;mi&gt;X&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;[&lt;/mo&gt;&lt;mtable rowspacing=&quot;4pt&quot; 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left: 0em;"><span style="display: inline-block; position: relative; width: 2.682em; height: 0px;"><span style="position: absolute; clip: rect(3.396em, 1001.55em, 4.348em, -999.997em); top: -6.068em; left: 50%; margin-left: -0.771em;"><span class="mtd" id="MathJax-Span-20"><span class="mrow" id="MathJax-Span-21"><span class="msubsup" id="MathJax-Span-22"><span style="display: inline-block; position: relative; width: 1.551em; height: 0px;"><span style="position: absolute; clip: rect(3.396em, 1000.54em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-23" style="font-family: MathJax_Math-italic;">x</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.807em; left: 0.598em;"><span class="texatom" id="MathJax-Span-24"><span class="mrow" id="MathJax-Span-25"><span class="mn" id="MathJax-Span-26" style="font-size: 70.7%; font-family: MathJax_Main;">1</span><span class="mspace" id="MathJax-Span-27" style="height: 0em; 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clip: rect(3.396em, 1001.55em, 4.348em, -999.997em); top: -4.64em; left: 50%; margin-left: -0.771em;"><span class="mtd" id="MathJax-Span-67"><span class="mrow" id="MathJax-Span-68"><span class="msubsup" id="MathJax-Span-69"><span style="display: inline-block; position: relative; width: 1.551em; height: 0px;"><span style="position: absolute; clip: rect(3.396em, 1000.54em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-70" style="font-family: MathJax_Math-italic;">x</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.807em; left: 0.598em;"><span class="texatom" id="MathJax-Span-71"><span class="mrow" id="MathJax-Span-72"><span class="mn" id="MathJax-Span-73" style="font-size: 70.7%; font-family: MathJax_Main;">2</span><span class="mspace" id="MathJax-Span-74" style="height: 0em; vertical-align: 0em; width: 0.182em; display: inline-block; overflow: hidden;"></span><span class="mn" id="MathJax-Span-75" style="font-size: 70.7%; font-family: MathJax_Main;">2</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.396em, 1002.68em, 4.348em, -999.997em); top: -3.211em; left: 50%; margin-left: -1.366em;"><span class="mtd" id="MathJax-Span-107"><span class="mrow" id="MathJax-Span-108"><span class="msubsup" id="MathJax-Span-109"><span style="display: inline-block; position: relative; width: 2.682em; height: 0px;"><span style="position: absolute; clip: rect(3.396em, 1000.54em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-110" style="font-family: MathJax_Math-italic;">x</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.807em; left: 0.598em;"><span class="texatom" id="MathJax-Span-111"><span class="mrow" id="MathJax-Span-112"><span class="mi" id="MathJax-Span-113" style="font-size: 70.7%; font-family: MathJax_Math-italic;">m</span><span class="mo" id="MathJax-Span-114" style="font-size: 70.7%; font-family: MathJax_Main;">−</span><span class="mn" id="MathJax-Span-115" style="font-size: 70.7%; font-family: MathJax_Main;">1</span><span class="mspace" id="MathJax-Span-116" style="height: 0em; vertical-align: 0em; width: 0.182em; display: inline-block; overflow: hidden;"></span><span class="mn" id="MathJax-Span-117" style="font-size: 70.7%; font-family: MathJax_Main;">2</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.396em, 1001.79em, 4.348em, -999.997em); top: -1.842em; left: 50%; margin-left: -0.89em;"><span class="mtd" id="MathJax-Span-151"><span class="mrow" id="MathJax-Span-152"><span class="msubsup" id="MathJax-Span-153"><span style="display: inline-block; position: relative; width: 1.789em; height: 0px;"><span style="position: absolute; clip: rect(3.396em, 1000.54em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-154" style="font-family: MathJax_Math-italic;">x</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.807em; left: 0.598em;"><span class="texatom" id="MathJax-Span-155"><span class="mrow" id="MathJax-Span-156"><span class="mi" id="MathJax-Span-157" style="font-size: 70.7%; font-family: MathJax_Math-italic;">m</span><span class="mspace" id="MathJax-Span-158" style="height: 0em; vertical-align: 0em; width: 0.182em; display: inline-block; overflow: hidden;"></span><span class="mn" id="MathJax-Span-159" style="font-size: 70.7%; font-family: MathJax_Main;">2</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 5.836em;"></span></span><span style="position: absolute; clip: rect(3.158em, 1002.92em, 8.336em, -999.997em); top: -5.83em; left: 7.384em;"><span style="display: inline-block; position: relative; width: 2.92em; height: 0px;"><span style="position: absolute; clip: rect(3.396em, 1001.79em, 4.348em, -999.997em); top: -6.068em; left: 50%; margin-left: -0.89em;"><span class="mtd" id="MathJax-Span-38"><span class="mrow" id="MathJax-Span-39"><span class="msubsup" id="MathJax-Span-40"><span style="display: inline-block; position: relative; width: 1.789em; height: 0px;"><span style="position: absolute; clip: rect(3.396em, 1000.54em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-41" style="font-family: MathJax_Math-italic;">x</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.807em; left: 0.598em;"><span class="texatom" id="MathJax-Span-42"><span class="mrow" id="MathJax-Span-43"><span class="mn" id="MathJax-Span-44" style="font-size: 70.7%; font-family: MathJax_Main;">1</span><span class="mspace" id="MathJax-Span-45" style="height: 0em; vertical-align: 0em; width: 0.182em; display: inline-block; overflow: hidden;"></span><span class="mo" id="MathJax-Span-46" style="font-size: 70.7%; font-family: MathJax_Main;">.</span><span class="mo" id="MathJax-Span-47" style="font-size: 70.7%; font-family: MathJax_Main;">.</span><span class="mo" id="MathJax-Span-48" style="font-size: 70.7%; font-family: MathJax_Main;">.</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.396em, 1001.79em, 4.348em, -999.997em); top: -4.64em; left: 50%; margin-left: -0.89em;"><span class="mtd" id="MathJax-Span-76"><span class="mrow" id="MathJax-Span-77"><span class="msubsup" id="MathJax-Span-78"><span style="display: inline-block; position: relative; width: 1.789em; height: 0px;"><span style="position: absolute; clip: rect(3.396em, 1000.54em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-79" style="font-family: MathJax_Math-italic;">x</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.807em; left: 0.598em;"><span class="texatom" id="MathJax-Span-80"><span class="mrow" id="MathJax-Span-81"><span class="mn" id="MathJax-Span-82" style="font-size: 70.7%; font-family: MathJax_Main;">2</span><span class="mspace" id="MathJax-Span-83" style="height: 0em; vertical-align: 0em; width: 0.182em; display: inline-block; overflow: hidden;"></span><span class="mo" id="MathJax-Span-84" style="font-size: 70.7%; font-family: MathJax_Main;">.</span><span class="mo" id="MathJax-Span-85" style="font-size: 70.7%; font-family: MathJax_Main;">.</span><span class="mo" id="MathJax-Span-86" style="font-size: 70.7%; font-family: MathJax_Main;">.</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.396em, 1002.92em, 4.348em, -999.997em); top: -3.211em; left: 50%; margin-left: -1.485em;"><span class="mtd" id="MathJax-Span-118"><span class="mrow" id="MathJax-Span-119"><span class="msubsup" id="MathJax-Span-120"><span style="display: inline-block; position: relative; width: 2.92em; height: 0px;"><span style="position: absolute; clip: rect(3.396em, 1000.54em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-121" style="font-family: MathJax_Math-italic;">x</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.807em; left: 0.598em;"><span class="texatom" id="MathJax-Span-122"><span class="mrow" id="MathJax-Span-123"><span class="mi" id="MathJax-Span-124" style="font-size: 70.7%; font-family: MathJax_Math-italic;">m</span><span class="mo" id="MathJax-Span-125" style="font-size: 70.7%; font-family: MathJax_Main;">−</span><span class="mn" id="MathJax-Span-126" style="font-size: 70.7%; font-family: MathJax_Main;">1</span><span class="mspace" id="MathJax-Span-127" style="height: 0em; vertical-align: 0em; width: 0.182em; display: inline-block; overflow: hidden;"></span><span class="mo" id="MathJax-Span-128" style="font-size: 70.7%; font-family: MathJax_Main;">.</span><span class="mo" id="MathJax-Span-129" style="font-size: 70.7%; font-family: MathJax_Main;">.</span><span class="mo" id="MathJax-Span-130" style="font-size: 70.7%; font-family: MathJax_Main;">.</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.396em, 1002.03em, 4.348em, -999.997em); top: -1.842em; left: 50%; margin-left: -1.009em;"><span class="mtd" id="MathJax-Span-160"><span class="mrow" id="MathJax-Span-161"><span class="msubsup" id="MathJax-Span-162"><span style="display: inline-block; position: relative; width: 2.027em; height: 0px;"><span style="position: absolute; clip: rect(3.396em, 1000.54em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-163" style="font-family: MathJax_Math-italic;">x</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.807em; left: 0.598em;"><span class="texatom" id="MathJax-Span-164"><span class="mrow" id="MathJax-Span-165"><span class="mi" id="MathJax-Span-166" style="font-size: 70.7%; font-family: MathJax_Math-italic;">m</span><span class="mspace" id="MathJax-Span-167" style="height: 0em; vertical-align: 0em; width: 0.182em; display: inline-block; overflow: hidden;"></span><span class="mo" id="MathJax-Span-168" style="font-size: 70.7%; font-family: MathJax_Main;">.</span><span class="mo" id="MathJax-Span-169" style="font-size: 70.7%; font-family: MathJax_Main;">.</span><span class="mo" id="MathJax-Span-170" style="font-size: 70.7%; font-family: MathJax_Main;">.</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 5.836em;"></span></span><span style="position: absolute; clip: rect(3.158em, 1003.4em, 8.336em, -999.997em); top: -5.83em; left: 11.313em;"><span style="display: inline-block; position: relative; width: 3.396em; height: 0px;"><span style="position: absolute; clip: rect(3.396em, 1002.21em, 4.348em, -999.997em); top: -6.068em; left: 50%; margin-left: -1.128em;"><span class="mtd" id="MathJax-Span-49"><span class="mrow" id="MathJax-Span-50"><span class="msubsup" id="MathJax-Span-51"><span style="display: inline-block; position: relative; width: 2.205em; height: 0px;"><span style="position: absolute; clip: rect(3.396em, 1000.54em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-52" style="font-family: MathJax_Math-italic;">x</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.807em; left: 0.598em;"><span class="texatom" id="MathJax-Span-53"><span class="mrow" id="MathJax-Span-54"><span class="mn" id="MathJax-Span-55" style="font-size: 70.7%; font-family: MathJax_Main;">1</span><span class="mspace" id="MathJax-Span-56" style="height: 0em; vertical-align: 0em; width: 0.182em; display: inline-block; overflow: hidden;"></span><span class="mn" id="MathJax-Span-57" style="font-size: 70.7%; font-family: MathJax_Main;">784</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.396em, 1002.21em, 4.348em, -999.997em); top: -4.64em; left: 50%; margin-left: -1.128em;"><span class="mtd" id="MathJax-Span-87"><span class="mrow" id="MathJax-Span-88"><span class="msubsup" id="MathJax-Span-89"><span style="display: inline-block; position: relative; width: 2.205em; height: 0px;"><span style="position: absolute; clip: rect(3.396em, 1000.54em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-90" style="font-family: MathJax_Math-italic;">x</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.807em; left: 0.598em;"><span class="texatom" id="MathJax-Span-91"><span class="mrow" id="MathJax-Span-92"><span class="mn" id="MathJax-Span-93" style="font-size: 70.7%; font-family: MathJax_Main;">2</span><span class="mspace" id="MathJax-Span-94" style="height: 0em; vertical-align: 0em; width: 0.182em; display: inline-block; overflow: hidden;"></span><span class="mn" id="MathJax-Span-95" style="font-size: 70.7%; font-family: MathJax_Main;">784</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.396em, 1003.4em, 4.348em, -999.997em); top: -3.211em; left: 50%; margin-left: -1.723em;"><span class="mtd" id="MathJax-Span-131"><span class="mrow" id="MathJax-Span-132"><span class="msubsup" id="MathJax-Span-133"><span style="display: inline-block; position: relative; width: 3.396em; height: 0px;"><span style="position: absolute; clip: rect(3.396em, 1000.54em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-134" style="font-family: MathJax_Math-italic;">x</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.807em; left: 0.598em;"><span class="texatom" id="MathJax-Span-135"><span class="mrow" id="MathJax-Span-136"><span class="mi" id="MathJax-Span-137" style="font-size: 70.7%; font-family: MathJax_Math-italic;">m</span><span class="mo" id="MathJax-Span-138" style="font-size: 70.7%; font-family: MathJax_Main;">−</span><span class="mn" id="MathJax-Span-139" style="font-size: 70.7%; font-family: MathJax_Main;">1</span><span class="mspace" id="MathJax-Span-140" style="height: 0em; vertical-align: 0em; width: 0.182em; display: inline-block; overflow: hidden;"></span><span class="mn" id="MathJax-Span-141" style="font-size: 70.7%; font-family: MathJax_Main;">784</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.396em, 1002.5em, 4.348em, -999.997em); top: -1.842em; left: 50%; margin-left: -1.247em;"><span class="mtd" id="MathJax-Span-171"><span class="mrow" id="MathJax-Span-172"><span class="msubsup" id="MathJax-Span-173"><span style="display: inline-block; position: relative; width: 2.503em; height: 0px;"><span style="position: absolute; clip: rect(3.396em, 1000.54em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-174" style="font-family: MathJax_Math-italic;">x</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.807em; left: 0.598em;"><span class="texatom" id="MathJax-Span-175"><span class="mrow" id="MathJax-Span-176"><span class="mi" id="MathJax-Span-177" style="font-size: 70.7%; font-family: MathJax_Math-italic;">m</span><span class="mspace" id="MathJax-Span-178" style="height: 0em; vertical-align: 0em; width: 0.182em; display: inline-block; overflow: hidden;"></span><span class="mn" id="MathJax-Span-179" style="font-size: 70.7%; font-family: MathJax_Main;">784</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 5.836em;"></span></span></span></span><span class="mo" id="MathJax-Span-180" style="vertical-align: 2.86em;"><span style="display: inline-block; position: relative; width: 0.658em; height: 0px;"><span style="position: absolute; font-family: MathJax_Size4; top: -2.854em; left: 0em;">⎤<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; font-family: MathJax_Size4; top: 0.598em; left: 0em;">⎦<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: MathJax_Size4; position: absolute; top: -1.604em; left: 0em;">⎥<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: MathJax_Size4; position: absolute; top: -1.068em; left: 0em;">⎥<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: MathJax_Size4; position: absolute; top: -0.533em; left: 0em;">⎥<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 6.193em;"></span></span></span><span style="display: inline-block; width: 0px; height: 7.503em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.205em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -3.711em; border-left: 0px solid; width: 0px; height: 7.932em;"></span></span></nobr><span class="MJX_Assistive_MathML MJX_Assistive_MathML_Block" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"><mtr><mtd></mtd><mtd><mi>m</mi><mo>=</mo><mtext>número de imágenes</mtext></mtd></mtr><mtr><mtd></mtd><mtd><mi>X</mi><mo>=</mo><mrow><mo>[</mo><mtable rowspacing="4pt" columnspacing="1em"><mtr><mtd><msub><mi>x</mi><mrow class="MJX-TeXAtom-ORD"><mn>1</mn><mspace width="thinmathspace"></mspace><mn>1</mn></mrow></msub></mtd><mtd><msub><mi>x</mi><mrow class="MJX-TeXAtom-ORD"><mn>1</mn><mspace width="thinmathspace"></mspace><mn>2</mn></mrow></msub></mtd><mtd><msub><mi>x</mi><mrow class="MJX-TeXAtom-ORD"><mn>1</mn><mspace width="thinmathspace"></mspace><mo>.</mo><mo>.</mo><mo>.</mo></mrow></msub></mtd><mtd><msub><mi>x</mi><mrow class="MJX-TeXAtom-ORD"><mn>1</mn><mspace width="thinmathspace"></mspace><mn>784</mn></mrow></msub></mtd></mtr><mtr><mtd><msub><mi>x</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn><mspace width="thinmathspace"></mspace><mn>1</mn></mrow></msub></mtd><mtd><msub><mi>x</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn><mspace width="thinmathspace"></mspace><mn>2</mn></mrow></msub></mtd><mtd><msub><mi>x</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn><mspace width="thinmathspace"></mspace><mo>.</mo><mo>.</mo><mo>.</mo></mrow></msub></mtd><mtd><msub><mi>x</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn><mspace width="thinmathspace"></mspace><mn>784</mn></mrow></msub></mtd></mtr><mtr><mtd><msub><mi>x</mi><mrow class="MJX-TeXAtom-ORD"><mi>m</mi><mo>−</mo><mn>1</mn><mspace width="thinmathspace"></mspace><mn>1</mn></mrow></msub></mtd><mtd><msub><mi>x</mi><mrow class="MJX-TeXAtom-ORD"><mi>m</mi><mo>−</mo><mn>1</mn><mspace width="thinmathspace"></mspace><mn>2</mn></mrow></msub></mtd><mtd><msub><mi>x</mi><mrow class="MJX-TeXAtom-ORD"><mi>m</mi><mo>−</mo><mn>1</mn><mspace width="thinmathspace"></mspace><mo>.</mo><mo>.</mo><mo>.</mo></mrow></msub></mtd><mtd><msub><mi>x</mi><mrow class="MJX-TeXAtom-ORD"><mi>m</mi><mo>−</mo><mn>1</mn><mspace width="thinmathspace"></mspace><mn>784</mn></mrow></msub></mtd></mtr><mtr><mtd><msub><mi>x</mi><mrow class="MJX-TeXAtom-ORD"><mi>m</mi><mspace width="thinmathspace"></mspace><mn>1</mn></mrow></msub></mtd><mtd><msub><mi>x</mi><mrow class="MJX-TeXAtom-ORD"><mi>m</mi><mspace width="thinmathspace"></mspace><mn>2</mn></mrow></msub></mtd><mtd><msub><mi>x</mi><mrow class="MJX-TeXAtom-ORD"><mi>m</mi><mspace width="thinmathspace"></mspace><mo>.</mo><mo>.</mo><mo>.</mo></mrow></msub></mtd><mtd><msub><mi>x</mi><mrow class="MJX-TeXAtom-ORD"><mi>m</mi><mspace width="thinmathspace"></mspace><mn>784</mn></mrow></msub></mtd></mtr></mtable><mo>]</mo></mrow></mtd></mtr></mtable></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-1">\begin{align}
    &m = \text{número de imágenes} \\
    &X = \begin{bmatrix}
 x_{1\,1}&  x_{1\,2}&  x_{1\,...}& x_{1\,784}\\ 
 x_{2\,1}&  x_{2\,2}&  x_{2\,...}& x_{2\,784}\\ 
 x_{m-1\,1}&  x_{m-1\,2}&  x_{m-1\,...}& x_{m-1\,784}\\ 
 x_{m\,1}&  x_{m\,2}&  x_{m\,...}& x_{m\,784}
\end{bmatrix}
\end{align}</script><p>Se trabaja con la matriz transpuesta de <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-2-Frame" tabindex="0" style="position: relative;" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;X&lt;/mi&gt;&lt;/math&gt;" role="presentation"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-181" style="width: 1.015em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.836em; height: 0px; font-size: 120%;"><span style="position: absolute; clip: rect(1.372em, 1000.84em, 2.384em, -999.997em); top: -2.199em; left: 0em;"><span class="mrow" id="MathJax-Span-182"><span class="mi" id="MathJax-Span-183" style="font-family: MathJax_Math-italic;">X<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.205em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 0.932em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi></math></span></span><script type="math/tex" id="MathJax-Element-2">X</script> (<span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-3-Frame" tabindex="0" style="position: relative;" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;msup&gt;&lt;mi&gt;X&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;" role="presentation"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-184" style="width: 1.551em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.253em; height: 0px; font-size: 120%;"><span style="position: absolute; clip: rect(1.193em, 1001.25em, 2.384em, -999.997em); top: -2.199em; left: 0em;"><span class="mrow" id="MathJax-Span-185"><span class="msubsup" id="MathJax-Span-186"><span style="display: inline-block; position: relative; width: 1.253em; height: 0px;"><span style="position: absolute; clip: rect(3.158em, 1000.84em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-187" style="font-family: MathJax_Math-italic;">X<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.342em; left: 0.896em;"><span class="texatom" id="MathJax-Span-188"><span class="mrow" id="MathJax-Span-189"><span class="mi" id="MathJax-Span-190" style="font-size: 70.7%; font-family: MathJax_Math-italic;">t</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.205em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>X</mi><mrow class="MJX-TeXAtom-ORD"><mi>t</mi></mrow></msup></math></span></span><script type="math/tex" id="MathJax-Element-3">X^{t}</script>), por lo que hay <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-4-Frame" tabindex="0" style="position: relative;" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/math&gt;" role="presentation"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-191" style="width: 1.074em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.896em; height: 0px; font-size: 120%;"><span style="position: absolute; clip: rect(1.61em, 1000.9em, 2.384em, -999.997em); top: -2.199em; left: 0em;"><span class="mrow" id="MathJax-Span-192"><span class="mi" id="MathJax-Span-193" style="font-family: MathJax_Math-italic;">m</span></span><span style="display: inline-block; width: 0px; height: 2.205em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 0.718em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math></span></span><script type="math/tex" id="MathJax-Element-4">m</script> columnas con 784 filas.</p>
<h2 id="Propagación-hacia-adelante-(forward-propagation)">Propagación hacia adelante (<em>forward propagation</em>)<a class="anchor-link" href="https://htmtopdf.herokuapp.com/ipynbviewer/temp/46ccb8d60bc4953329f884b04452879a/first_approach_neural_networks_p1.html?t=1670380747444#Propagaci%C3%B3n-hacia-adelante-(forward-propagation)">¶</a></h2><span class="MathJax_Preview" style="color: inherit; display: none;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" id="MathJax-Element-5-Frame" tabindex="0" style="text-align: center; position: relative;" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot; display=&quot;block&quot;&gt;&lt;mtable columnalign=&quot;right left right left right left right left right left right left&quot; rowspacing=&quot;3pt&quot; columnspacing=&quot;0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em&quot; displaystyle=&quot;true&quot;&gt;&lt;mtr&gt;&lt;mtd /&gt;&lt;mtd&gt;&lt;msup&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo stretchy=&quot;false&quot;&gt;[&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mtext&gt;capa de entrada (input layer)&lt;/mtext&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd /&gt;&lt;mtd&gt;&lt;msup&gt;&lt;mi&gt;Z&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo stretchy=&quot;false&quot;&gt;[&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mtext&gt;capa oculta (desactivada) (hidden layer)&lt;/mtext&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;/math&gt;" role="presentation"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-194" style="width: 24.884em; display: inline-block;"><span style="display: inline-block; position: relative; width: 20.717em; height: 0px; font-size: 120%;"><span style="position: absolute; clip: rect(0.42em, 1020.42em, 3.455em, -999.997em); top: -2.199em; left: 0em;"><span class="mrow" id="MathJax-Span-195"><span class="mtable" id="MathJax-Span-196" style="padding-right: 0.182em; padding-left: 0.182em;"><span style="display: inline-block; position: relative; width: 20.36em; height: 0px;"><span style="position: absolute; clip: rect(3.158em, 1000em, 5.003em, -999.997em); top: -3.985em; left: 0em;"><span style="display: inline-block; position: relative; width: 0em; height: 0px;"><span style="position: absolute; clip: rect(3.812em, 1000em, 4.17em, -999.997em); top: -4.64em; right: 0em;"><span class="mtd" id="MathJax-Span-197"><span class="mrow" id="MathJax-Span-198"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.812em, 1000em, 4.17em, -999.997em); top: -3.152em; right: 0em;"><span class="mtd" id="MathJax-Span-210"><span class="mrow" id="MathJax-Span-211"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(2.205em, 1020.3em, 5.241em, -999.997em); top: -3.985em; left: 0em;"><span style="display: inline-block; position: relative; width: 20.36em; height: 0px;"><span style="position: absolute; clip: rect(2.86em, 1015.48em, 4.408em, -999.997em); top: -4.64em; left: 0em;"><span class="mtd" id="MathJax-Span-199"><span class="mrow" id="MathJax-Span-200"><span class="msubsup" id="MathJax-Span-201"><span style="display: inline-block; position: relative; width: 1.551em; height: 0px;"><span style="position: absolute; clip: rect(3.098em, 1000.72em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-202" style="font-family: MathJax_Math-italic;">A</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.402em; left: 0.777em;"><span class="texatom" id="MathJax-Span-203"><span class="mrow" id="MathJax-Span-204"><span class="mo" id="MathJax-Span-205" style="font-size: 70.7%; font-family: MathJax_Main;">[</span><span class="mn" id="MathJax-Span-206" style="font-size: 70.7%; font-family: MathJax_Main;">0</span><span class="mo" id="MathJax-Span-207" style="font-size: 70.7%; font-family: MathJax_Main;">]</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mo" id="MathJax-Span-208" style="font-family: MathJax_Main; padding-left: 0.301em;">=</span><span class="mtext" id="MathJax-Span-209" style="font-family: MathJax_Main; padding-left: 0.301em;">capa de entrada (input layer)</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(2.86em, 1020.3em, 4.408em, -999.997em); top: -3.152em; left: 0em;"><span class="mtd" id="MathJax-Span-212"><span class="mrow" id="MathJax-Span-213"><span class="msubsup" id="MathJax-Span-214"><span style="display: inline-block; position: relative; width: 1.61em; height: 0px;"><span style="position: absolute; clip: rect(3.158em, 1000.72em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-215" style="font-family: MathJax_Math-italic;">Z<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.063em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.402em; left: 0.777em;"><span class="texatom" id="MathJax-Span-216"><span class="mrow" id="MathJax-Span-217"><span class="mo" id="MathJax-Span-218" style="font-size: 70.7%; font-family: MathJax_Main;">[</span><span class="mn" id="MathJax-Span-219" style="font-size: 70.7%; font-family: MathJax_Main;">1</span><span class="mo" id="MathJax-Span-220" style="font-size: 70.7%; font-family: MathJax_Main;">]</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mo" id="MathJax-Span-221" style="font-family: MathJax_Main; padding-left: 0.301em;">=</span><span class="mtext" id="MathJax-Span-222" style="font-family: MathJax_Main; padding-left: 0.301em;">capa oculta (desactivada) (hidden layer)</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.205em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -1.354em; border-left: 0px solid; width: 0px; height: 3.361em;"></span></span></nobr><span class="MJX_Assistive_MathML MJX_Assistive_MathML_Block" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"><mtr><mtd></mtd><mtd><msup><mi>A</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">[</mo><mn>0</mn><mo stretchy="false">]</mo></mrow></msup><mo>=</mo><mtext>capa de entrada (input layer)</mtext></mtd></mtr><mtr><mtd></mtd><mtd><msup><mi>Z</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">[</mo><mn>1</mn><mo stretchy="false">]</mo></mrow></msup><mo>=</mo><mtext>capa oculta (desactivada) (hidden layer)</mtext></mtd></mtr></mtable></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-5">\begin{align}
    &A^{[0]} = \text{capa de entrada (input layer)} \\
    &Z^{[1]} = \text{capa oculta (desactivada) (hidden layer)}
\end{align}</script><p>Con la finalidad de obtener <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-6-Frame" tabindex="0" style="position: relative;" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;msup&gt;&lt;mi&gt;Z&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo stretchy=&quot;false&quot;&gt;[&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;" role="presentation"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-223" style="width: 1.967em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.61em; height: 0px; font-size: 120%;"><span style="position: absolute; clip: rect(1.134em, 1001.61em, 2.384em, -999.997em); top: -2.199em; left: 0em;"><span class="mrow" id="MathJax-Span-224"><span class="msubsup" id="MathJax-Span-225"><span style="display: inline-block; position: relative; width: 1.61em; height: 0px;"><span style="position: absolute; clip: rect(3.158em, 1000.72em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-226" style="font-family: MathJax_Math-italic;">Z<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.063em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.342em; left: 0.777em;"><span class="texatom" id="MathJax-Span-227"><span class="mrow" id="MathJax-Span-228"><span class="mo" id="MathJax-Span-229" style="font-size: 70.7%; font-family: MathJax_Main;">[</span><span class="mn" id="MathJax-Span-230" style="font-size: 70.7%; font-family: MathJax_Main;">1</span><span class="mo" id="MathJax-Span-231" style="font-size: 70.7%; font-family: MathJax_Main;">]</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.205em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.218em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>Z</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">[</mo><mn>1</mn><mo stretchy="false">]</mo></mrow></msup></math></span></span><script type="math/tex" id="MathJax-Element-6">Z^{[1]}</script>, se deberá aplicar un peso (<em>weight</em>, <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-7-Frame" tabindex="0" style="position: relative;" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;msup&gt;&lt;mi&gt;W&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo stretchy=&quot;false&quot;&gt;[&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;" role="presentation"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-232" style="width: 2.384em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.967em; height: 0px; font-size: 120%;"><span style="position: absolute; clip: rect(1.134em, 1001.97em, 2.384em, -999.997em); top: -2.199em; left: 0em;"><span class="mrow" id="MathJax-Span-233"><span class="msubsup" id="MathJax-Span-234"><span style="display: inline-block; position: relative; width: 1.967em; height: 0px;"><span style="position: absolute; clip: rect(3.158em, 1001.07em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-235" style="font-family: MathJax_Math-italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.122em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.342em; left: 1.134em;"><span class="texatom" id="MathJax-Span-236"><span class="mrow" id="MathJax-Span-237"><span class="mo" id="MathJax-Span-238" style="font-size: 70.7%; font-family: MathJax_Main;">[</span><span class="mn" id="MathJax-Span-239" style="font-size: 70.7%; font-family: MathJax_Main;">1</span><span class="mo" id="MathJax-Span-240" style="font-size: 70.7%; font-family: MathJax_Main;">]</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.205em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.218em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>W</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">[</mo><mn>1</mn><mo stretchy="false">]</mo></mrow></msup></math></span></span><script type="math/tex" id="MathJax-Element-7">W^{[1]}</script>) y un sesgo (<em>bias</em>, <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-8-Frame" tabindex="0" style="position: relative;" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;msup&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo stretchy=&quot;false&quot;&gt;[&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;" role="presentation"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-241" style="width: 1.967em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.61em; height: 0px; font-size: 120%;"><span style="position: absolute; clip: rect(1.134em, 1001.61em, 2.384em, -999.997em); top: -2.199em; left: 0em;"><span class="mrow" id="MathJax-Span-242"><span class="msubsup" id="MathJax-Span-243"><span style="display: inline-block; position: relative; width: 1.61em; height: 0px;"><span style="position: absolute; clip: rect(3.158em, 1000.78em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-244" style="font-family: MathJax_Math-italic;">B</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.342em; left: 0.777em;"><span class="texatom" id="MathJax-Span-245"><span class="mrow" id="MathJax-Span-246"><span class="mo" id="MathJax-Span-247" style="font-size: 70.7%; font-family: MathJax_Main;">[</span><span class="mn" id="MathJax-Span-248" style="font-size: 70.7%; font-family: MathJax_Main;">1</span><span class="mo" id="MathJax-Span-249" style="font-size: 70.7%; font-family: MathJax_Main;">]</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.205em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.218em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>B</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">[</mo><mn>1</mn><mo stretchy="false">]</mo></mrow></msup></math></span></span><script type="math/tex" id="MathJax-Element-8">B^{[1]}</script>), de manera que:</p>
<span class="MathJax_Preview" style="color: inherit; display: none;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" id="MathJax-Element-9-Frame" tabindex="0" style="text-align: center; position: relative;" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot; display=&quot;block&quot;&gt;&lt;mtable columnalign=&quot;right left right left right left right left right left right left&quot; rowspacing=&quot;3pt&quot; columnspacing=&quot;0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em&quot; displaystyle=&quot;true&quot;&gt;&lt;mtr&gt;&lt;mtd /&gt;&lt;mtd&gt;&lt;msup&gt;&lt;mi&gt;Z&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo stretchy=&quot;false&quot;&gt;[&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;W&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo stretchy=&quot;false&quot;&gt;[&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;&amp;#x22C5;&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo stretchy=&quot;false&quot;&gt;[&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mtext&gt;&amp;#xA0;&lt;/mtext&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mtext&gt;&amp;#xA0;&lt;/mtext&gt;&lt;msup&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo stretchy=&quot;false&quot;&gt;[&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd /&gt;&lt;mtd&gt;&lt;msup&gt;&lt;mi&gt;W&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo stretchy=&quot;false&quot;&gt;[&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mtext&gt;pesos de las conexiones de la primera capa (first layer connections weight)&lt;/mtext&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;/math&gt;" role="presentation"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-250" style="width: 42.443em; display: inline-block;"><span style="display: inline-block; position: relative; width: 35.36em; height: 0px; font-size: 120%;"><span style="position: absolute; clip: rect(0.479em, 1035.06em, 3.455em, -999.997em); top: -2.199em; left: 0em;"><span class="mrow" id="MathJax-Span-251"><span class="mtable" id="MathJax-Span-252" style="padding-right: 0.182em; padding-left: 0.182em;"><span style="display: inline-block; position: relative; width: 35.003em; height: 0px;"><span style="position: absolute; clip: rect(3.217em, 1000em, 5.003em, -999.997em); top: -3.985em; left: 0em;"><span style="display: inline-block; position: relative; width: 0em; height: 0px;"><span style="position: absolute; clip: rect(3.812em, 1000em, 4.17em, -999.997em); top: -4.58em; right: 0em;"><span class="mtd" id="MathJax-Span-253"><span class="mrow" id="MathJax-Span-254"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.812em, 1000em, 4.17em, -999.997em); top: -3.152em; right: 0em;"><span class="mtd" id="MathJax-Span-290"><span class="mrow" id="MathJax-Span-291"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(2.265em, 1034.88em, 5.241em, -999.997em); top: -3.985em; left: 0em;"><span style="display: inline-block; position: relative; width: 35.003em; height: 0px;"><span style="position: absolute; clip: rect(2.86em, 1010.6em, 4.229em, -999.997em); top: -4.58em; left: 0em;"><span class="mtd" id="MathJax-Span-255"><span class="mrow" id="MathJax-Span-256"><span class="msubsup" id="MathJax-Span-257"><span style="display: inline-block; position: relative; width: 1.61em; height: 0px;"><span style="position: absolute; clip: rect(3.158em, 1000.72em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-258" style="font-family: MathJax_Math-italic;">Z<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.063em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.402em; left: 0.777em;"><span class="texatom" id="MathJax-Span-259"><span class="mrow" id="MathJax-Span-260"><span class="mo" id="MathJax-Span-261" style="font-size: 70.7%; font-family: MathJax_Main;">[</span><span class="mn" id="MathJax-Span-262" style="font-size: 70.7%; font-family: MathJax_Main;">1</span><span class="mo" id="MathJax-Span-263" style="font-size: 70.7%; font-family: MathJax_Main;">]</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mo" id="MathJax-Span-264" style="font-family: MathJax_Main; padding-left: 0.301em;">=</span><span class="msubsup" id="MathJax-Span-265" style="padding-left: 0.301em;"><span style="display: inline-block; position: relative; width: 1.967em; height: 0px;"><span style="position: absolute; clip: rect(3.158em, 1001.07em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-266" style="font-family: MathJax_Math-italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.122em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.402em; left: 1.134em;"><span class="texatom" id="MathJax-Span-267"><span class="mrow" id="MathJax-Span-268"><span class="mo" id="MathJax-Span-269" style="font-size: 70.7%; font-family: MathJax_Main;">[</span><span class="mn" id="MathJax-Span-270" style="font-size: 70.7%; font-family: MathJax_Main;">1</span><span class="mo" id="MathJax-Span-271" style="font-size: 70.7%; font-family: MathJax_Main;">]</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mo" id="MathJax-Span-272" style="font-family: MathJax_Main; padding-left: 0.241em;">⋅</span><span class="msubsup" id="MathJax-Span-273" style="padding-left: 0.241em;"><span style="display: inline-block; position: relative; width: 1.551em; height: 0px;"><span style="position: absolute; clip: rect(3.098em, 1000.72em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-274" style="font-family: MathJax_Math-italic;">A</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.402em; left: 0.777em;"><span class="texatom" id="MathJax-Span-275"><span class="mrow" id="MathJax-Span-276"><span class="mo" id="MathJax-Span-277" style="font-size: 70.7%; font-family: MathJax_Main;">[</span><span class="mn" id="MathJax-Span-278" style="font-size: 70.7%; font-family: MathJax_Main;">0</span><span class="mo" id="MathJax-Span-279" style="font-size: 70.7%; font-family: MathJax_Main;">]</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mtext" id="MathJax-Span-280" style="font-family: MathJax_Main;">&nbsp;</span><span class="mo" id="MathJax-Span-281" style="font-family: MathJax_Main; padding-left: 0.241em;">+</span><span class="mtext" id="MathJax-Span-282" style="font-family: MathJax_Main; padding-left: 0.241em;">&nbsp;</span><span class="msubsup" id="MathJax-Span-283"><span style="display: inline-block; position: relative; width: 1.61em; height: 0px;"><span style="position: absolute; clip: rect(3.158em, 1000.78em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-284" style="font-family: MathJax_Math-italic;">B</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.402em; left: 0.777em;"><span class="texatom" id="MathJax-Span-285"><span class="mrow" id="MathJax-Span-286"><span class="mo" id="MathJax-Span-287" style="font-size: 70.7%; font-family: MathJax_Main;">[</span><span class="mn" id="MathJax-Span-288" style="font-size: 70.7%; font-family: MathJax_Main;">1</span><span class="mo" id="MathJax-Span-289" style="font-size: 70.7%; font-family: MathJax_Main;">]</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(2.86em, 1034.88em, 4.408em, -999.997em); top: -3.152em; left: 0em;"><span class="mtd" id="MathJax-Span-292"><span class="mrow" id="MathJax-Span-293"><span class="msubsup" id="MathJax-Span-294"><span style="display: inline-block; position: relative; width: 1.967em; height: 0px;"><span style="position: absolute; clip: rect(3.158em, 1001.07em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-295" style="font-family: MathJax_Math-italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.122em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.402em; left: 1.134em;"><span class="texatom" id="MathJax-Span-296"><span class="mrow" id="MathJax-Span-297"><span class="mo" id="MathJax-Span-298" style="font-size: 70.7%; font-family: MathJax_Main;">[</span><span class="mn" id="MathJax-Span-299" style="font-size: 70.7%; font-family: MathJax_Main;">1</span><span class="mo" id="MathJax-Span-300" style="font-size: 70.7%; font-family: MathJax_Main;">]</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mo" id="MathJax-Span-301" style="font-family: MathJax_Main; padding-left: 0.301em;">=</span><span class="mtext" id="MathJax-Span-302" style="font-family: MathJax_Main; padding-left: 0.301em;">pesos de las conexiones de la primera capa (first layer connections weight)</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.205em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -1.354em; border-left: 0px solid; width: 0px; height: 3.289em;"></span></span></nobr><span class="MJX_Assistive_MathML MJX_Assistive_MathML_Block" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"><mtr><mtd></mtd><mtd><msup><mi>Z</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">[</mo><mn>1</mn><mo stretchy="false">]</mo></mrow></msup><mo>=</mo><msup><mi>W</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">[</mo><mn>1</mn><mo stretchy="false">]</mo></mrow></msup><mo>⋅</mo><msup><mi>A</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">[</mo><mn>0</mn><mo stretchy="false">]</mo></mrow></msup><mtext>&nbsp;</mtext><mo>+</mo><mtext>&nbsp;</mtext><msup><mi>B</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">[</mo><mn>1</mn><mo stretchy="false">]</mo></mrow></msup></mtd></mtr><mtr><mtd></mtd><mtd><msup><mi>W</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">[</mo><mn>1</mn><mo stretchy="false">]</mo></mrow></msup><mo>=</mo><mtext>pesos de las conexiones de la primera capa (first layer connections weight)</mtext></mtd></mtr></mtable></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-9">\begin{align}
    &Z^{[1]} = W^{[1]}\cdot A^{[0]} \ + \ B^{[1]} \\
    &W^{[1]} = \text{pesos de las conexiones de la primera capa (first layer connections weight)}
\end{align}</script><p>Posteriormente, se aplica una "función de activación", en este caso <strong>ReLU</strong><sup>3</sup>.</p>
<span class="MathJax_Preview" style="color: inherit; display: none;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" id="MathJax-Element-10-Frame" tabindex="0" style="text-align: center; position: relative;" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot; display=&quot;block&quot;&gt;&lt;mtable columnalign=&quot;right left right left right left right left right left right left&quot; rowspacing=&quot;3pt&quot; columnspacing=&quot;0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em&quot; displaystyle=&quot;true&quot;&gt;&lt;mtr&gt;&lt;mtd /&gt;&lt;mtd&gt;&lt;msup&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo stretchy=&quot;false&quot;&gt;[&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mtext&gt;&amp;#xA0;&lt;/mtext&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mtext&gt;&amp;#xA0;&lt;/mtext&gt;&lt;mtext&gt;ReLU&lt;/mtext&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;Z&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo stretchy=&quot;false&quot;&gt;[&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;/math&gt;" role="presentation"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-303" style="width: 10.539em; display: inline-block;"><span style="display: inline-block; position: relative; width: 8.753em; height: 0px; font-size: 120%;"><span style="position: absolute; clip: rect(1.193em, 1008.46em, 2.741em, -999.997em); top: -2.199em; left: 0em;"><span class="mrow" id="MathJax-Span-304"><span class="mtable" id="MathJax-Span-305" style="padding-right: 0.182em; padding-left: 0.182em;"><span style="display: inline-block; position: relative; width: 8.396em; height: 0px;"><span style="position: absolute; clip: rect(3.932em, 1000em, 4.289em, -999.997em); top: -3.985em; left: 0em;"><span style="display: inline-block; position: relative; width: 0em; height: 0px;"><span style="position: absolute; clip: rect(3.812em, 1000em, 4.17em, -999.997em); top: -3.866em; right: 0em;"><span class="mtd" id="MathJax-Span-306"><span class="mrow" id="MathJax-Span-307"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(2.979em, 1008.28em, 4.527em, -999.997em); top: -3.985em; left: 0em;"><span style="display: inline-block; position: relative; width: 8.396em; height: 0px;"><span style="position: absolute; clip: rect(2.86em, 1008.28em, 4.408em, -999.997em); top: -3.866em; left: 0em;"><span class="mtd" id="MathJax-Span-308"><span class="mrow" id="MathJax-Span-309"><span class="msubsup" id="MathJax-Span-310"><span style="display: inline-block; position: relative; width: 1.551em; height: 0px;"><span style="position: absolute; clip: rect(3.098em, 1000.72em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-311" style="font-family: MathJax_Math-italic;">A</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.402em; left: 0.777em;"><span class="texatom" id="MathJax-Span-312"><span class="mrow" id="MathJax-Span-313"><span class="mo" id="MathJax-Span-314" style="font-size: 70.7%; font-family: MathJax_Main;">[</span><span class="mn" id="MathJax-Span-315" style="font-size: 70.7%; font-family: MathJax_Main;">1</span><span class="mo" id="MathJax-Span-316" style="font-size: 70.7%; font-family: MathJax_Main;">]</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mtext" id="MathJax-Span-317" style="font-family: MathJax_Main;">&nbsp;</span><span class="mo" id="MathJax-Span-318" style="font-family: MathJax_Main; padding-left: 0.301em;">=</span><span class="mtext" id="MathJax-Span-319" style="font-family: MathJax_Main; padding-left: 0.301em;">&nbsp;</span><span class="mtext" id="MathJax-Span-320" style="font-family: MathJax_Main;">ReLU</span><span class="mo" id="MathJax-Span-321" style="font-family: MathJax_Main;">(</span><span class="msubsup" id="MathJax-Span-322"><span style="display: inline-block; position: relative; width: 1.61em; height: 0px;"><span style="position: absolute; clip: rect(3.158em, 1000.72em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-323" style="font-family: MathJax_Math-italic;">Z<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.063em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.402em; left: 0.777em;"><span class="texatom" id="MathJax-Span-324"><span class="mrow" id="MathJax-Span-325"><span class="mo" id="MathJax-Span-326" style="font-size: 70.7%; font-family: MathJax_Main;">[</span><span class="mn" id="MathJax-Span-327" style="font-size: 70.7%; font-family: MathJax_Main;">1</span><span class="mo" id="MathJax-Span-328" style="font-size: 70.7%; font-family: MathJax_Main;">]</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mo" id="MathJax-Span-329" style="font-family: MathJax_Main;">)</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.205em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.496em; border-left: 0px solid; width: 0px; height: 1.575em;"></span></span></nobr><span class="MJX_Assistive_MathML MJX_Assistive_MathML_Block" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"><mtr><mtd></mtd><mtd><msup><mi>A</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">[</mo><mn>1</mn><mo stretchy="false">]</mo></mrow></msup><mtext>&nbsp;</mtext><mo>=</mo><mtext>&nbsp;</mtext><mtext>ReLU</mtext><mo stretchy="false">(</mo><msup><mi>Z</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">[</mo><mn>1</mn><mo stretchy="false">]</mo></mrow></msup><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-10">\begin{align}
    &A^{[1]} \ = \ \text{ReLU}(Z^{[1]})
\end{align}</script><p>Y se pasa a la segunda capa:</p>
<span class="MathJax_Preview" style="color: inherit; display: none;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" id="MathJax-Element-11-Frame" tabindex="0" style="text-align: center; position: relative;" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot; display=&quot;block&quot;&gt;&lt;mtable columnalign=&quot;right left right left right left right left right left right left&quot; rowspacing=&quot;3pt&quot; columnspacing=&quot;0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em&quot; displaystyle=&quot;true&quot;&gt;&lt;mtr&gt;&lt;mtd /&gt;&lt;mtd&gt;&lt;msup&gt;&lt;mi&gt;Z&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo stretchy=&quot;false&quot;&gt;[&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;W&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo stretchy=&quot;false&quot;&gt;[&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;&amp;#x22C5;&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo stretchy=&quot;false&quot;&gt;[&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mtext&gt;&amp;#xA0;&lt;/mtext&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mtext&gt;&amp;#xA0;&lt;/mtext&gt;&lt;msup&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo stretchy=&quot;false&quot;&gt;[&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd /&gt;&lt;mtd&gt;&lt;msup&gt;&lt;mi&gt;W&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo stretchy=&quot;false&quot;&gt;[&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mtext&gt;pesos de las conexiones de la segunda capa&lt;/mtext&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd /&gt;&lt;mtd&gt;&lt;mtext&gt;(second layer connections weight)&lt;/mtext&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;/math&gt;" role="presentation"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-330" style="width: 26.253em; display: inline-block;"><span style="display: inline-block; position: relative; width: 21.848em; height: 0px; font-size: 120%;"><span style="position: absolute; clip: rect(-0.176em, 1021.67em, 4.11em, -999.997em); top: -2.199em; left: 0em;"><span class="mrow" id="MathJax-Span-331"><span class="mtable" id="MathJax-Span-332" style="padding-right: 0.182em; padding-left: 0.182em;"><span style="display: inline-block; position: relative; width: 21.491em; height: 0px;"><span style="position: absolute; clip: rect(2.562em, 1000em, 5.658em, -999.997em); top: -3.985em; left: 0em;"><span style="display: inline-block; position: relative; width: 0em; height: 0px;"><span style="position: absolute; clip: rect(3.812em, 1000em, 4.17em, -999.997em); top: -5.235em; right: 0em;"><span class="mtd" id="MathJax-Span-333"><span class="mrow" id="MathJax-Span-334"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.812em, 1000em, 4.17em, -999.997em); top: -3.807em; right: 0em;"><span class="mtd" id="MathJax-Span-370"><span class="mrow" id="MathJax-Span-371"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.812em, 1000em, 4.17em, -999.997em); top: -2.497em; right: 0em;"><span class="mtd" id="MathJax-Span-383"><span class="mrow" id="MathJax-Span-384"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(2.562em, 1021.49em, 6.848em, -999.997em); top: -4.938em; left: 0em;"><span style="display: inline-block; position: relative; width: 21.491em; height: 0px;"><span style="position: absolute; clip: rect(2.86em, 1010.6em, 4.229em, -999.997em); top: -5.235em; left: 0em;"><span class="mtd" id="MathJax-Span-335"><span class="mrow" id="MathJax-Span-336"><span class="msubsup" id="MathJax-Span-337"><span style="display: inline-block; position: relative; width: 1.61em; height: 0px;"><span style="position: absolute; clip: rect(3.158em, 1000.72em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-338" style="font-family: MathJax_Math-italic;">Z<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.063em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.402em; left: 0.777em;"><span class="texatom" id="MathJax-Span-339"><span class="mrow" id="MathJax-Span-340"><span class="mo" id="MathJax-Span-341" style="font-size: 70.7%; font-family: MathJax_Main;">[</span><span class="mn" id="MathJax-Span-342" style="font-size: 70.7%; font-family: MathJax_Main;">2</span><span class="mo" id="MathJax-Span-343" style="font-size: 70.7%; font-family: MathJax_Main;">]</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mo" id="MathJax-Span-344" style="font-family: MathJax_Main; padding-left: 0.301em;">=</span><span class="msubsup" id="MathJax-Span-345" style="padding-left: 0.301em;"><span style="display: inline-block; position: relative; width: 1.967em; height: 0px;"><span style="position: absolute; clip: rect(3.158em, 1001.07em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-346" style="font-family: MathJax_Math-italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.122em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.402em; left: 1.134em;"><span class="texatom" id="MathJax-Span-347"><span class="mrow" id="MathJax-Span-348"><span class="mo" id="MathJax-Span-349" style="font-size: 70.7%; font-family: MathJax_Main;">[</span><span class="mn" id="MathJax-Span-350" style="font-size: 70.7%; font-family: MathJax_Main;">2</span><span class="mo" id="MathJax-Span-351" style="font-size: 70.7%; font-family: MathJax_Main;">]</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mo" id="MathJax-Span-352" style="font-family: MathJax_Main; padding-left: 0.241em;">⋅</span><span class="msubsup" id="MathJax-Span-353" style="padding-left: 0.241em;"><span style="display: inline-block; position: relative; width: 1.551em; height: 0px;"><span style="position: absolute; clip: rect(3.098em, 1000.72em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-354" style="font-family: MathJax_Math-italic;">A</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.402em; left: 0.777em;"><span class="texatom" id="MathJax-Span-355"><span class="mrow" id="MathJax-Span-356"><span class="mo" id="MathJax-Span-357" style="font-size: 70.7%; font-family: MathJax_Main;">[</span><span class="mn" id="MathJax-Span-358" style="font-size: 70.7%; font-family: MathJax_Main;">1</span><span class="mo" id="MathJax-Span-359" style="font-size: 70.7%; font-family: MathJax_Main;">]</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mtext" id="MathJax-Span-360" style="font-family: MathJax_Main;">&nbsp;</span><span class="mo" id="MathJax-Span-361" style="font-family: MathJax_Main; padding-left: 0.241em;">+</span><span class="mtext" id="MathJax-Span-362" style="font-family: MathJax_Main; padding-left: 0.241em;">&nbsp;</span><span class="msubsup" id="MathJax-Span-363"><span style="display: inline-block; position: relative; width: 1.61em; height: 0px;"><span style="position: absolute; clip: rect(3.158em, 1000.78em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-364" style="font-family: MathJax_Math-italic;">B</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.402em; left: 0.777em;"><span class="texatom" id="MathJax-Span-365"><span class="mrow" id="MathJax-Span-366"><span class="mo" id="MathJax-Span-367" style="font-size: 70.7%; font-family: MathJax_Main;">[</span><span class="mn" id="MathJax-Span-368" style="font-size: 70.7%; font-family: MathJax_Main;">2</span><span class="mo" id="MathJax-Span-369" style="font-size: 70.7%; font-family: MathJax_Main;">]</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(2.86em, 1021.49em, 4.348em, -999.997em); top: -3.807em; left: 0em;"><span class="mtd" id="MathJax-Span-372"><span class="mrow" id="MathJax-Span-373"><span class="msubsup" id="MathJax-Span-374"><span style="display: inline-block; position: relative; width: 1.967em; height: 0px;"><span style="position: absolute; clip: rect(3.158em, 1001.07em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-375" style="font-family: MathJax_Math-italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.122em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.402em; left: 1.134em;"><span class="texatom" id="MathJax-Span-376"><span class="mrow" id="MathJax-Span-377"><span class="mo" id="MathJax-Span-378" style="font-size: 70.7%; font-family: MathJax_Main;">[</span><span class="mn" id="MathJax-Span-379" style="font-size: 70.7%; font-family: MathJax_Main;">2</span><span class="mo" id="MathJax-Span-380" style="font-size: 70.7%; font-family: MathJax_Main;">]</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mo" id="MathJax-Span-381" style="font-family: MathJax_Main; padding-left: 0.301em;">=</span><span class="mtext" id="MathJax-Span-382" style="font-family: MathJax_Main; padding-left: 0.301em;">pesos de las conexiones de la segunda capa</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.039em, 1014.41em, 4.408em, -999.997em); top: -2.497em; left: 0em;"><span class="mtd" id="MathJax-Span-385"><span class="mrow" id="MathJax-Span-386"><span class="mtext" id="MathJax-Span-387" style="font-family: MathJax_Main;">(second layer connections weight)</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.943em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.205em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -2.139em; border-left: 0px solid; width: 0px; height: 4.861em;"></span></span></nobr><span class="MJX_Assistive_MathML MJX_Assistive_MathML_Block" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"><mtr><mtd></mtd><mtd><msup><mi>Z</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">[</mo><mn>2</mn><mo stretchy="false">]</mo></mrow></msup><mo>=</mo><msup><mi>W</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">[</mo><mn>2</mn><mo stretchy="false">]</mo></mrow></msup><mo>⋅</mo><msup><mi>A</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">[</mo><mn>1</mn><mo stretchy="false">]</mo></mrow></msup><mtext>&nbsp;</mtext><mo>+</mo><mtext>&nbsp;</mtext><msup><mi>B</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">[</mo><mn>2</mn><mo stretchy="false">]</mo></mrow></msup></mtd></mtr><mtr><mtd></mtd><mtd><msup><mi>W</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">[</mo><mn>2</mn><mo stretchy="false">]</mo></mrow></msup><mo>=</mo><mtext>pesos de las conexiones de la segunda capa</mtext></mtd></mtr><mtr><mtd></mtd><mtd><mtext>(second layer connections weight)</mtext></mtd></mtr></mtable></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-11">\begin{align}
    &Z^{[2]} = W^{[2]}\cdot A^{[1]} \ + \ B^{[2]} \\
    &W^{[2]} = \text{pesos de las conexiones de la segunda capa} \\
    &\text{(second layer connections weight)}
\end{align}</script><p>Finalmente se aplicará la función de activación <strong>softmax</strong><sup>3</sup>.</p>
<span class="MathJax_Preview" style="color: inherit; display: none;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" id="MathJax-Element-12-Frame" tabindex="0" style="text-align: center; position: relative;" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot; display=&quot;block&quot;&gt;&lt;mtable columnalign=&quot;right left right left right left right left right left right left&quot; rowspacing=&quot;3pt&quot; columnspacing=&quot;0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em&quot; displaystyle=&quot;true&quot;&gt;&lt;mtr&gt;&lt;mtd /&gt;&lt;mtd&gt;&lt;mrow&gt;&lt;mo&gt;[&lt;/mo&gt;&lt;mtable rowspacing=&quot;4pt&quot; columnspacing=&quot;1em&quot;&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mn&gt;6.66&lt;/mn&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mn&gt;2.5&lt;/mn&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mn&gt;1.3&lt;/mn&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;mo&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;mspace width=&quot;thinmathspace&quot; /&gt;&lt;mfrac&gt;&lt;msup&gt;&lt;mi&gt;e&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;msub&gt;&lt;mi&gt;z&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mrow&gt;&lt;munderover&gt;&lt;mo&gt;&amp;#x2211;&lt;/mo&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi&gt;j&lt;/mi&gt;&lt;mtext&gt;&amp;#xA0;&lt;/mtext&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mtext&gt;&amp;#xA0;&lt;/mtext&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi&gt;K&lt;/mi&gt;&lt;/mrow&gt;&lt;/munderover&gt;&lt;msup&gt;&lt;mi&gt;e&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;msub&gt;&lt;mi&gt;z&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi&gt;j&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mspace width=&quot;thinmathspace&quot; /&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;mspace width=&quot;thinmathspace&quot; /&gt;&lt;mrow&gt;&lt;mo&gt;[&lt;/mo&gt;&lt;mtable rowspacing=&quot;4pt&quot; columnspacing=&quot;1em&quot;&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mn&gt;0.95&lt;/mn&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mn&gt;0.027&lt;/mn&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mn&gt;0.023&lt;/mn&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;mo&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;/math&gt;" role="presentation"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-388" style="width: 19.11em; display: inline-block;"><span style="display: inline-block; position: relative; width: 15.896em; height: 0px; font-size: 120%;"><span style="position: absolute; clip: rect(-0.116em, 1015.42em, 4.051em, -999.997em); top: -2.199em; left: 0em;"><span class="mrow" id="MathJax-Span-389"><span class="mtable" id="MathJax-Span-390" style="padding-right: 0.182em; padding-left: 0.182em;"><span style="display: inline-block; position: relative; width: 15.539em; height: 0px;"><span style="position: absolute; clip: rect(3.812em, 1000em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span style="display: inline-block; position: relative; width: 0em; height: 0px;"><span style="position: absolute; clip: rect(3.812em, 1000em, 4.17em, -999.997em); top: -3.985em; right: 0em;"><span class="mtd" id="MathJax-Span-391"><span class="mrow" id="MathJax-Span-392"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(2.503em, 1015.18em, 6.67em, -999.997em); top: -4.818em; left: 0em;"><span style="display: inline-block; position: relative; width: 15.539em; height: 0px;"><span style="position: absolute; clip: rect(2.503em, 1015.18em, 6.67em, -999.997em); top: -4.818em; left: 0em;"><span class="mtd" id="MathJax-Span-393"><span class="mrow" id="MathJax-Span-394"><span class="mrow" id="MathJax-Span-395"><span class="mo" id="MathJax-Span-396" style="vertical-align: 2.146em;"><span style="display: inline-block; position: relative; width: 0.658em; height: 0px;"><span style="position: absolute; font-family: MathJax_Size4; top: -2.854em; left: 0em;">⎡<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; font-family: MathJax_Size4; top: -0.83em; left: 0em;">⎣<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: MathJax_Size4; position: absolute; top: -1.783em; left: 0em;">⎢<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mtable" id="MathJax-Span-397" style="padding-right: 0.182em; padding-left: 0.182em;"><span style="display: inline-block; position: relative; width: 1.789em; height: 0px;"><span style="position: absolute; clip: rect(2.265em, 1001.73em, 6.134em, -999.997em); top: -4.461em; left: 0em;"><span style="display: inline-block; position: relative; width: 1.789em; height: 0px;"><span style="position: absolute; clip: rect(3.158em, 1001.73em, 4.17em, -999.997em); top: -5.354em; left: 50%; margin-left: -0.89em;"><span class="mtd" id="MathJax-Span-398"><span class="mrow" id="MathJax-Span-399"><span class="mn" id="MathJax-Span-400" style="font-family: MathJax_Main;">6.66</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.158em, 1001.25em, 4.17em, -999.997em); top: -3.926em; left: 50%; margin-left: -0.652em;"><span class="mtd" id="MathJax-Span-401"><span class="mrow" id="MathJax-Span-402"><span class="mn" id="MathJax-Span-403" style="font-family: MathJax_Main;">2.5</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.158em, 1001.25em, 4.17em, -999.997em); top: -2.557em; left: 50%; margin-left: -0.652em;"><span class="mtd" id="MathJax-Span-404"><span class="mrow" id="MathJax-Span-405"><span class="mn" id="MathJax-Span-406" style="font-family: MathJax_Main;">1.3</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.467em;"></span></span></span></span><span class="mo" id="MathJax-Span-407" style="vertical-align: 2.146em;"><span style="display: inline-block; position: relative; width: 0.658em; height: 0px;"><span style="position: absolute; font-family: MathJax_Size4; top: -2.854em; left: 0em;">⎤<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; font-family: MathJax_Size4; top: -0.83em; left: 0em;">⎦<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: MathJax_Size4; position: absolute; top: -1.783em; left: 0em;">⎥<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span class="mo" id="MathJax-Span-408" style="font-family: MathJax_Main; padding-left: 0.301em;">→</span><span class="mspace" id="MathJax-Span-409" style="height: 0em; vertical-align: 0em; width: 0.182em; display: inline-block; overflow: hidden;"></span><span class="mfrac" id="MathJax-Span-410" style="padding-left: 0.301em;"><span style="display: inline-block; position: relative; width: 4.11em; height: 0px; margin-right: 0.122em; margin-left: 0.122em;"><span style="position: absolute; clip: rect(3.158em, 1001.07em, 4.17em, -999.997em); top: -4.64em; left: 50%; margin-left: -0.533em;"><span class="msubsup" id="MathJax-Span-411"><span style="display: inline-block; position: relative; width: 1.074em; height: 0px;"><span style="position: absolute; clip: rect(3.396em, 1000.42em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-412" style="font-family: MathJax_Math-italic;">e</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.342em; left: 0.479em;"><span class="texatom" id="MathJax-Span-413"><span class="mrow" id="MathJax-Span-414"><span class="msubsup" id="MathJax-Span-415"><span style="display: inline-block; position: relative; width: 0.539em; height: 0px;"><span style="position: absolute; clip: rect(3.515em, 1000.36em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-416" style="font-size: 70.7%; font-family: MathJax_Math-italic;">z<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.866em; left: 0.36em;"><span class="texatom" id="MathJax-Span-417"><span class="mrow" id="MathJax-Span-418"><span class="mi" id="MathJax-Span-419" style="font-size: 50%; font-family: MathJax_Math-italic;">i</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(2.86em, 1003.99em, 4.586em, -999.997em); top: -3.033em; left: 50%; margin-left: -2.021em;"><span class="mrow" id="MathJax-Span-420"><span class="munderover" id="MathJax-Span-421"><span style="display: inline-block; position: relative; width: 2.682em; height: 0px;"><span style="position: absolute; clip: rect(3.039em, 1001.01em, 4.408em, -999.997em); top: -3.985em; left: 0em;"><span class="mo" id="MathJax-Span-422" style="font-family: MathJax_Size1; vertical-align: 0em;">∑</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.336em, 1000.72em, 4.17em, -999.997em); top: -4.461em; left: 1.074em;"><span class="texatom" id="MathJax-Span-423"><span class="mrow" id="MathJax-Span-424"><span class="mi" id="MathJax-Span-425" style="font-size: 70.7%; font-family: MathJax_Math-italic;">K<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.336em, 1001.61em, 4.289em, -999.997em); top: -3.688em; left: 1.074em;"><span class="texatom" id="MathJax-Span-426"><span class="mrow" id="MathJax-Span-427"><span class="mi" id="MathJax-Span-428" style="font-size: 70.7%; font-family: MathJax_Math-italic;">j</span><span class="mtext" id="MathJax-Span-429" style="font-size: 70.7%; font-family: MathJax_Main;">&nbsp;</span><span class="mo" id="MathJax-Span-430" style="font-size: 70.7%; font-family: MathJax_Main;">=</span><span class="mtext" id="MathJax-Span-431" style="font-size: 70.7%; font-family: MathJax_Main;">&nbsp;</span><span class="mn" id="MathJax-Span-432" style="font-size: 70.7%; font-family: MathJax_Main;">1</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="msubsup" id="MathJax-Span-433" style="padding-left: 0.182em;"><span style="display: inline-block; position: relative; width: 1.134em; height: 0px;"><span style="position: absolute; clip: rect(3.396em, 1000.42em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-434" style="font-family: MathJax_Math-italic;">e</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.283em; left: 0.479em;"><span class="texatom" id="MathJax-Span-435"><span class="mrow" id="MathJax-Span-436"><span class="msubsup" id="MathJax-Span-437"><span style="display: inline-block; position: relative; width: 0.598em; height: 0px;"><span style="position: absolute; clip: rect(3.515em, 1000.36em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-438" style="font-size: 70.7%; font-family: MathJax_Math-italic;">z<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.866em; left: 0.36em;"><span class="texatom" id="MathJax-Span-439"><span class="mrow" id="MathJax-Span-440"><span class="mi" id="MathJax-Span-441" style="font-size: 50%; font-family: MathJax_Math-italic;">j</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(0.836em, 1004.11em, 1.253em, -999.997em); top: -1.307em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 4.11em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.074em;"></span></span></span></span><span class="mspace" id="MathJax-Span-442" style="height: 0em; vertical-align: 0em; width: 0.182em; display: inline-block; overflow: hidden;"></span><span class="mo" id="MathJax-Span-443" style="font-family: MathJax_Main; padding-left: 0.301em;">→</span><span class="mspace" id="MathJax-Span-444" style="height: 0em; vertical-align: 0em; width: 0.182em; display: inline-block; overflow: hidden;"></span><span class="mrow" id="MathJax-Span-445" style="padding-left: 0.301em;"><span class="mo" id="MathJax-Span-446" style="vertical-align: 2.146em;"><span style="display: inline-block; position: relative; width: 0.658em; height: 0px;"><span style="position: absolute; font-family: MathJax_Size4; top: -2.854em; left: 0em;">⎡<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; font-family: MathJax_Size4; top: -0.83em; left: 0em;">⎣<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: MathJax_Size4; position: absolute; top: -1.783em; left: 0em;">⎢<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mtable" id="MathJax-Span-447" style="padding-right: 0.182em; padding-left: 0.182em;"><span style="display: inline-block; position: relative; width: 2.265em; height: 0px;"><span style="position: absolute; clip: rect(2.265em, 1002.26em, 6.134em, -999.997em); top: -4.461em; left: 0em;"><span style="display: inline-block; position: relative; width: 2.265em; height: 0px;"><span style="position: absolute; clip: rect(3.158em, 1001.73em, 4.17em, -999.997em); top: -5.354em; left: 50%; margin-left: -0.89em;"><span class="mtd" id="MathJax-Span-448"><span class="mrow" id="MathJax-Span-449"><span class="mn" id="MathJax-Span-450" style="font-family: MathJax_Main;">0.95</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.158em, 1002.26em, 4.17em, -999.997em); top: -3.926em; left: 50%; margin-left: -1.128em;"><span class="mtd" id="MathJax-Span-451"><span class="mrow" id="MathJax-Span-452"><span class="mn" id="MathJax-Span-453" style="font-family: MathJax_Main;">0.027</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.158em, 1002.26em, 4.17em, -999.997em); top: -2.557em; left: 50%; margin-left: -1.128em;"><span class="mtd" id="MathJax-Span-454"><span class="mrow" id="MathJax-Span-455"><span class="mn" id="MathJax-Span-456" style="font-family: MathJax_Main;">0.023</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.467em;"></span></span></span></span><span class="mo" id="MathJax-Span-457" style="vertical-align: 2.146em;"><span style="display: inline-block; position: relative; width: 0.658em; height: 0px;"><span style="position: absolute; font-family: MathJax_Size4; top: -2.854em; left: 0em;">⎤<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; font-family: MathJax_Size4; top: -0.83em; left: 0em;">⎦<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: MathJax_Size4; position: absolute; top: -1.783em; left: 0em;">⎥<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 4.824em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.824em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.205em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -2.068em; border-left: 0px solid; width: 0px; height: 4.718em;"></span></span></nobr><span class="MJX_Assistive_MathML MJX_Assistive_MathML_Block" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"><mtr><mtd></mtd><mtd><mrow><mo>[</mo><mtable rowspacing="4pt" columnspacing="1em"><mtr><mtd><mn>6.66</mn></mtd></mtr><mtr><mtd><mn>2.5</mn></mtd></mtr><mtr><mtd><mn>1.3</mn></mtd></mtr></mtable><mo>]</mo></mrow><mo stretchy="false">→</mo><mspace width="thinmathspace"></mspace><mfrac><msup><mi>e</mi><mrow class="MJX-TeXAtom-ORD"><msub><mi>z</mi><mrow class="MJX-TeXAtom-ORD"><mi>i</mi></mrow></msub></mrow></msup><mrow><munderover><mo>∑</mo><mrow class="MJX-TeXAtom-ORD"><mi>j</mi><mtext>&nbsp;</mtext><mo>=</mo><mtext>&nbsp;</mtext><mn>1</mn></mrow><mrow class="MJX-TeXAtom-ORD"><mi>K</mi></mrow></munderover><msup><mi>e</mi><mrow class="MJX-TeXAtom-ORD"><msub><mi>z</mi><mrow class="MJX-TeXAtom-ORD"><mi>j</mi></mrow></msub></mrow></msup></mrow></mfrac><mspace width="thinmathspace"></mspace><mo stretchy="false">→</mo><mspace width="thinmathspace"></mspace><mrow><mo>[</mo><mtable rowspacing="4pt" columnspacing="1em"><mtr><mtd><mn>0.95</mn></mtd></mtr><mtr><mtd><mn>0.027</mn></mtd></mtr><mtr><mtd><mn>0.023</mn></mtd></mtr></mtable><mo>]</mo></mrow></mtd></mtr></mtable></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-12">\begin{align}
    &\begin{bmatrix}
6.66\\ 
2.5\\ 
1.3
\end{bmatrix}\rightarrow \, \frac{e^{z_{i}}}{\sum_{j \ = \ 1}^{K}e^{z_{j}}} \,\rightarrow \, \begin{bmatrix}
0.95\\ 
0.027\\ 
0.023
\end{bmatrix}
\end{align}</script><p>En el lado izquierdo se observan los valores de una capa de entrada (<em>input layer</em>), posterior a aplicada la función <strong>softmax</strong> estos valores se transforman en probabilidades, correspondiento a la probabilidad de que una imagen sea de cierta clase.</p>
<span class="MathJax_Preview" style="color: inherit; display: none;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" id="MathJax-Element-13-Frame" tabindex="0" style="text-align: center; position: relative;" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot; display=&quot;block&quot;&gt;&lt;mtable columnalign=&quot;right left right left right left right left right left right left&quot; rowspacing=&quot;3pt&quot; columnspacing=&quot;0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em&quot; displaystyle=&quot;true&quot;&gt;&lt;mtr&gt;&lt;mtd /&gt;&lt;mtd&gt;&lt;msup&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo stretchy=&quot;false&quot;&gt;[&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mtext&gt;&amp;#xA0;&lt;/mtext&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mtext&gt;&amp;#xA0;&lt;/mtext&gt;&lt;mtext&gt;softmax&lt;/mtext&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;Z&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo stretchy=&quot;false&quot;&gt;[&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;/math&gt;" role="presentation"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-458" style="width: 11.61em; display: inline-block;"><span style="display: inline-block; position: relative; width: 9.646em; height: 0px; font-size: 120%;"><span style="position: absolute; clip: rect(1.193em, 1009.35em, 2.741em, -999.997em); top: -2.199em; left: 0em;"><span class="mrow" id="MathJax-Span-459"><span class="mtable" id="MathJax-Span-460" style="padding-right: 0.182em; padding-left: 0.182em;"><span style="display: inline-block; position: relative; width: 9.289em; height: 0px;"><span style="position: absolute; clip: rect(3.932em, 1000em, 4.289em, -999.997em); top: -3.985em; left: 0em;"><span style="display: inline-block; position: relative; width: 0em; height: 0px;"><span style="position: absolute; clip: rect(3.812em, 1000em, 4.17em, -999.997em); top: -3.866em; right: 0em;"><span class="mtd" id="MathJax-Span-461"><span class="mrow" id="MathJax-Span-462"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(2.979em, 1009.17em, 4.527em, -999.997em); top: -3.985em; left: 0em;"><span style="display: inline-block; position: relative; width: 9.289em; height: 0px;"><span style="position: absolute; clip: rect(2.86em, 1009.17em, 4.408em, -999.997em); top: -3.866em; left: 0em;"><span class="mtd" id="MathJax-Span-463"><span class="mrow" id="MathJax-Span-464"><span class="msubsup" id="MathJax-Span-465"><span style="display: inline-block; position: relative; width: 1.551em; height: 0px;"><span style="position: absolute; clip: rect(3.098em, 1000.72em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-466" style="font-family: MathJax_Math-italic;">A</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.402em; left: 0.777em;"><span class="texatom" id="MathJax-Span-467"><span class="mrow" id="MathJax-Span-468"><span class="mo" id="MathJax-Span-469" style="font-size: 70.7%; font-family: MathJax_Main;">[</span><span class="mn" id="MathJax-Span-470" style="font-size: 70.7%; font-family: MathJax_Main;">2</span><span class="mo" id="MathJax-Span-471" style="font-size: 70.7%; font-family: MathJax_Main;">]</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mtext" id="MathJax-Span-472" style="font-family: MathJax_Main;">&nbsp;</span><span class="mo" id="MathJax-Span-473" style="font-family: MathJax_Main; padding-left: 0.301em;">=</span><span class="mtext" id="MathJax-Span-474" style="font-family: MathJax_Main; padding-left: 0.301em;">&nbsp;</span><span class="mtext" id="MathJax-Span-475" style="font-family: MathJax_Main;">softmax</span><span class="mo" id="MathJax-Span-476" style="font-family: MathJax_Main;">(</span><span class="msubsup" id="MathJax-Span-477"><span style="display: inline-block; position: relative; width: 1.61em; height: 0px;"><span style="position: absolute; clip: rect(3.158em, 1000.72em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-478" style="font-family: MathJax_Math-italic;">Z<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.063em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.402em; left: 0.777em;"><span class="texatom" id="MathJax-Span-479"><span class="mrow" id="MathJax-Span-480"><span class="mo" id="MathJax-Span-481" style="font-size: 70.7%; font-family: MathJax_Main;">[</span><span class="mn" id="MathJax-Span-482" style="font-size: 70.7%; font-family: MathJax_Main;">2</span><span class="mo" id="MathJax-Span-483" style="font-size: 70.7%; font-family: MathJax_Main;">]</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mo" id="MathJax-Span-484" style="font-family: MathJax_Main;">)</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.205em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.496em; border-left: 0px solid; width: 0px; height: 1.575em;"></span></span></nobr><span class="MJX_Assistive_MathML MJX_Assistive_MathML_Block" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"><mtr><mtd></mtd><mtd><msup><mi>A</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">[</mo><mn>2</mn><mo stretchy="false">]</mo></mrow></msup><mtext>&nbsp;</mtext><mo>=</mo><mtext>&nbsp;</mtext><mtext>softmax</mtext><mo stretchy="false">(</mo><msup><mi>Z</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">[</mo><mn>2</mn><mo stretchy="false">]</mo></mrow></msup><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-13">\begin{align}
    &A^{[2]} \ = \ \text{softmax}(Z^{[2]})
\end{align}</script><h2 id="Propagación-hacia-atrás-(backwards-propagation)">Propagación hacia atrás (<em>backwards propagation</em>)<a class="anchor-link" href="https://htmtopdf.herokuapp.com/ipynbviewer/temp/46ccb8d60bc4953329f884b04452879a/first_approach_neural_networks_p1.html?t=1670380747444#Propagaci%C3%B3n-hacia-atr%C3%A1s-(backwards-propagation)">¶</a></h2><p>Se trata de ajustar los pesos según su contribución a la predicción inicial de la red.</p>
<p>En este caso, se resta el <em>label</em> que sí le correspodía a la imagen procesada, por ejemplo, si el <em>label</em> indicaba un 7, se hace esta resta a <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-14-Frame" tabindex="0" style="position: relative;" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;msup&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo stretchy=&quot;false&quot;&gt;[&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;" role="presentation"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-485" style="width: 1.908em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.551em; height: 0px; font-size: 120%;"><span style="position: absolute; clip: rect(1.134em, 1001.55em, 2.384em, -999.997em); top: -2.199em; left: 0em;"><span class="mrow" id="MathJax-Span-486"><span class="msubsup" id="MathJax-Span-487"><span style="display: inline-block; position: relative; width: 1.551em; height: 0px;"><span style="position: absolute; clip: rect(3.098em, 1000.72em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-488" style="font-family: MathJax_Math-italic;">A</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.342em; left: 0.777em;"><span class="texatom" id="MathJax-Span-489"><span class="mrow" id="MathJax-Span-490"><span class="mo" id="MathJax-Span-491" style="font-size: 70.7%; font-family: MathJax_Main;">[</span><span class="mn" id="MathJax-Span-492" style="font-size: 70.7%; font-family: MathJax_Main;">2</span><span class="mo" id="MathJax-Span-493" style="font-size: 70.7%; font-family: MathJax_Main;">]</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.205em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.218em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>A</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">[</mo><mn>2</mn><mo stretchy="false">]</mo></mrow></msup></math></span></span><script type="math/tex" id="MathJax-Element-14">A^{[2]}</script>, de la siguiente manera:</p>
<span class="MathJax_Preview" style="color: inherit; display: none;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" id="MathJax-Element-15-Frame" tabindex="0" style="text-align: center; position: relative;" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot; display=&quot;block&quot;&gt;&lt;mtable columnalign=&quot;right left right left right left right left right left right left&quot; rowspacing=&quot;3pt&quot; columnspacing=&quot;0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em&quot; displaystyle=&quot;true&quot;&gt;&lt;mtr&gt;&lt;mtd /&gt;&lt;mtd&gt;&lt;msup&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo stretchy=&quot;false&quot;&gt;[&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;&amp;#x2212;&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;[&lt;/mo&gt;&lt;mtable rowspacing=&quot;4pt&quot; columnspacing=&quot;1em&quot;&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mn&gt;0...&lt;/mn&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mn&gt;0...&lt;/mn&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mn&gt;0...&lt;/mn&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mn&gt;0...&lt;/mn&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mn&gt;0...&lt;/mn&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mn&gt;0...&lt;/mn&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mn&gt;0...&lt;/mn&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mn&gt;1...&lt;/mn&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mn&gt;0...&lt;/mn&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mn&gt;0...&lt;/mn&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;mo&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;/math&gt;" role="presentation"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-494" style="width: 7.503em; display: inline-block;"><span style="display: inline-block; position: relative; width: 6.253em; height: 0px; font-size: 120%;"><span style="position: absolute; clip: rect(-4.997em, 1005.78em, 8.932em, -999.997em); top: -2.199em; left: 0em;"><span class="mrow" id="MathJax-Span-495"><span class="mtable" id="MathJax-Span-496" style="padding-right: 0.182em; padding-left: 0.182em;"><span style="display: inline-block; position: relative; width: 5.896em; height: 0px;"><span style="position: absolute; clip: rect(3.812em, 1000em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span style="display: inline-block; position: relative; width: 0em; height: 0px;"><span style="position: absolute; clip: rect(3.812em, 1000em, 4.17em, -999.997em); top: -3.985em; right: 0em;"><span class="mtd" id="MathJax-Span-497"><span class="mrow" id="MathJax-Span-498"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(7.384em, 1005.54em, 21.313em, -999.997em); top: -14.58em; left: 0em;"><span style="display: inline-block; position: relative; width: 5.896em; height: 0px;"><span style="position: absolute; clip: rect(7.384em, 1005.54em, 21.313em, -999.997em); top: -14.58em; left: 0em;"><span class="mtd" id="MathJax-Span-499"><span class="mrow" id="MathJax-Span-500"><span class="msubsup" id="MathJax-Span-501"><span style="display: inline-block; position: relative; width: 1.551em; height: 0px;"><span style="position: absolute; clip: rect(3.098em, 1000.72em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-502" style="font-family: MathJax_Math-italic;">A</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.402em; left: 0.777em;"><span class="texatom" id="MathJax-Span-503"><span class="mrow" id="MathJax-Span-504"><span class="mo" id="MathJax-Span-505" style="font-size: 70.7%; font-family: MathJax_Main;">[</span><span class="mn" id="MathJax-Span-506" style="font-size: 70.7%; font-family: MathJax_Main;">2</span><span class="mo" id="MathJax-Span-507" style="font-size: 70.7%; font-family: MathJax_Main;">]</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mo" id="MathJax-Span-508" style="font-family: MathJax_Main; padding-left: 0.241em;">−</span><span class="mrow" id="MathJax-Span-509" style="padding-left: 0.241em;"><span class="mo" id="MathJax-Span-510" style="vertical-align: 7.027em;"><span style="display: inline-block; position: relative; width: 0.658em; height: 0px;"><span style="position: absolute; font-family: MathJax_Size4; top: -2.854em; left: 0em;">⎡<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; font-family: MathJax_Size4; top: 8.991em; left: 0em;">⎣<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: MathJax_Size4; position: absolute; top: -1.664em; left: 0em;">⎢<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: MathJax_Size4; position: absolute; top: -1.128em; left: 0em;">⎢<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: MathJax_Size4; position: absolute; top: -0.592em; left: 0em;">⎢<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: MathJax_Size4; position: absolute; top: -0.057em; left: 0em;">⎢<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: MathJax_Size4; position: absolute; top: 0.479em; left: 0em;">⎢<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: MathJax_Size4; position: absolute; top: 1.015em; left: 0em;">⎢<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: MathJax_Size4; position: absolute; top: 1.551em; left: 0em;">⎢<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: MathJax_Size4; position: absolute; top: 2.027em; left: 0em;">⎢<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: MathJax_Size4; position: absolute; top: 2.562em; left: 0em;">⎢<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: MathJax_Size4; position: absolute; top: 3.098em; left: 0em;">⎢<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: MathJax_Size4; position: absolute; top: 3.634em; left: 0em;">⎢<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: MathJax_Size4; position: absolute; top: 4.17em; left: 0em;">⎢<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: MathJax_Size4; position: absolute; top: 4.705em; left: 0em;">⎢<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: MathJax_Size4; position: absolute; top: 5.241em; left: 0em;">⎢<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: MathJax_Size4; position: absolute; top: 5.777em; left: 0em;">⎢<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: MathJax_Size4; position: absolute; top: 6.313em; left: 0em;">⎢<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: MathJax_Size4; position: absolute; top: 6.848em; left: 0em;">⎢<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: MathJax_Size4; position: absolute; top: 7.384em; left: 0em;">⎢<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: MathJax_Size4; position: absolute; top: 7.86em; left: 0em;">⎢<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mtable" id="MathJax-Span-511" style="padding-right: 0.182em; padding-left: 0.182em;"><span style="display: inline-block; position: relative; width: 1.313em; height: 0px;"><span style="position: absolute; clip: rect(7.205em, 1001.25em, 20.836em, -999.997em); top: -14.283em; left: 0em;"><span style="display: inline-block; position: relative; width: 1.313em; height: 0px;"><span style="position: absolute; clip: rect(3.158em, 1001.25em, 4.17em, -999.997em); top: -10.235em; left: 50%; margin-left: -0.652em;"><span class="mtd" id="MathJax-Span-512"><span class="mrow" id="MathJax-Span-513"><span class="mn" id="MathJax-Span-514" style="font-family: MathJax_Main;">0...</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.158em, 1001.25em, 4.17em, -999.997em); top: -8.807em; left: 50%; margin-left: -0.652em;"><span class="mtd" id="MathJax-Span-515"><span class="mrow" id="MathJax-Span-516"><span class="mn" id="MathJax-Span-517" style="font-family: MathJax_Main;">0...</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.158em, 1001.25em, 4.17em, -999.997em); top: -7.438em; left: 50%; margin-left: -0.652em;"><span class="mtd" id="MathJax-Span-518"><span class="mrow" id="MathJax-Span-519"><span class="mn" id="MathJax-Span-520" style="font-family: MathJax_Main;">0...</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.158em, 1001.25em, 4.17em, -999.997em); top: -6.009em; left: 50%; margin-left: -0.652em;"><span class="mtd" id="MathJax-Span-521"><span class="mrow" id="MathJax-Span-522"><span class="mn" id="MathJax-Span-523" style="font-family: MathJax_Main;">0...</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.158em, 1001.25em, 4.17em, -999.997em); top: -4.64em; left: 50%; margin-left: -0.652em;"><span class="mtd" id="MathJax-Span-524"><span class="mrow" id="MathJax-Span-525"><span class="mn" id="MathJax-Span-526" style="font-family: MathJax_Main;">0...</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.158em, 1001.25em, 4.17em, -999.997em); top: -3.211em; left: 50%; margin-left: -0.652em;"><span class="mtd" id="MathJax-Span-527"><span class="mrow" id="MathJax-Span-528"><span class="mn" id="MathJax-Span-529" style="font-family: MathJax_Main;">0...</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.158em, 1001.25em, 4.17em, -999.997em); top: -1.842em; left: 50%; margin-left: -0.652em;"><span class="mtd" id="MathJax-Span-530"><span class="mrow" id="MathJax-Span-531"><span class="mn" id="MathJax-Span-532" style="font-family: MathJax_Main;">0...</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.158em, 1001.25em, 4.17em, -999.997em); top: -0.414em; left: 50%; margin-left: -0.652em;"><span class="mtd" id="MathJax-Span-533"><span class="mrow" id="MathJax-Span-534"><span class="mn" id="MathJax-Span-535" style="font-family: MathJax_Main;">1...</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.158em, 1001.25em, 4.17em, -999.997em); top: 0.955em; left: 50%; margin-left: -0.652em;"><span class="mtd" id="MathJax-Span-536"><span class="mrow" id="MathJax-Span-537"><span class="mn" id="MathJax-Span-538" style="font-family: MathJax_Main;">0...</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.158em, 1001.25em, 4.17em, -999.997em); top: 2.384em; left: 50%; margin-left: -0.652em;"><span class="mtd" id="MathJax-Span-539"><span class="mrow" id="MathJax-Span-540"><span class="mn" id="MathJax-Span-541" style="font-family: MathJax_Main;">0...</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 14.289em;"></span></span></span></span><span class="mo" id="MathJax-Span-542" style="vertical-align: 7.027em;"><span style="display: inline-block; position: relative; width: 0.658em; height: 0px;"><span style="position: absolute; font-family: MathJax_Size4; top: -2.854em; left: 0em;">⎤<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; font-family: MathJax_Size4; top: 8.991em; left: 0em;">⎦<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: MathJax_Size4; position: absolute; top: -1.664em; left: 0em;">⎥<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: MathJax_Size4; position: absolute; top: -1.128em; left: 0em;">⎥<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: MathJax_Size4; position: absolute; top: -0.592em; left: 0em;">⎥<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: MathJax_Size4; position: absolute; top: -0.057em; left: 0em;">⎥<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: MathJax_Size4; position: absolute; top: 0.479em; left: 0em;">⎥<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: MathJax_Size4; position: absolute; top: 1.015em; left: 0em;">⎥<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: MathJax_Size4; position: absolute; top: 1.551em; left: 0em;">⎥<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: MathJax_Size4; position: absolute; top: 2.027em; left: 0em;">⎥<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: MathJax_Size4; position: absolute; top: 2.562em; left: 0em;">⎥<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: MathJax_Size4; position: absolute; top: 3.098em; left: 0em;">⎥<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: MathJax_Size4; position: absolute; top: 3.634em; left: 0em;">⎥<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: MathJax_Size4; position: absolute; top: 4.17em; left: 0em;">⎥<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: MathJax_Size4; position: absolute; top: 4.705em; left: 0em;">⎥<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: MathJax_Size4; position: absolute; top: 5.241em; left: 0em;">⎥<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: MathJax_Size4; position: absolute; top: 5.777em; left: 0em;">⎥<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: MathJax_Size4; position: absolute; top: 6.313em; left: 0em;">⎥<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: MathJax_Size4; position: absolute; top: 6.848em; left: 0em;">⎥<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: MathJax_Size4; position: absolute; top: 7.384em; left: 0em;">⎥<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: MathJax_Size4; position: absolute; top: 7.86em; left: 0em;">⎥<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 14.586em;"></span></span></span><span style="display: inline-block; width: 0px; height: 14.586em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.205em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -7.925em; border-left: 0px solid; width: 0px; height: 16.432em;"></span></span></nobr><span class="MJX_Assistive_MathML MJX_Assistive_MathML_Block" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"><mtr><mtd></mtd><mtd><msup><mi>A</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">[</mo><mn>2</mn><mo stretchy="false">]</mo></mrow></msup><mo>−</mo><mrow><mo>[</mo><mtable rowspacing="4pt" columnspacing="1em"><mtr><mtd><mn>0...</mn></mtd></mtr><mtr><mtd><mn>0...</mn></mtd></mtr><mtr><mtd><mn>0...</mn></mtd></mtr><mtr><mtd><mn>0...</mn></mtd></mtr><mtr><mtd><mn>0...</mn></mtd></mtr><mtr><mtd><mn>0...</mn></mtd></mtr><mtr><mtd><mn>0...</mn></mtd></mtr><mtr><mtd><mn>1...</mn></mtd></mtr><mtr><mtd><mn>0...</mn></mtd></mtr><mtr><mtd><mn>0...</mn></mtd></mtr></mtable><mo>]</mo></mrow></mtd></mtr></mtable></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-15">\begin{align}
    &A^{[2]} - \begin{bmatrix}
0...\\ 
0...\\ 
0...\\ 
0...\\ 
0...\\ 
0...\\ 
0...\\ 
1...\\ 
0...\\ 
0...
\end{bmatrix}
\end{align}</script><p>Nótese que el espacio en la matriz (ver tamaños reales abajo) que representa un 7 se le asigna un 1.</p>
<p>El proceso busca determinar el error en la predicción, además se debe encontrar la contribución de <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-16-Frame" tabindex="0" style="position: relative;" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;msup&gt;&lt;mi&gt;W&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo stretchy=&quot;false&quot;&gt;[&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;" role="presentation"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-543" style="width: 2.443em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.027em; height: 0px; font-size: 120%;"><span style="position: absolute; clip: rect(1.134em, 1002.03em, 2.384em, -999.997em); top: -2.199em; left: 0em;"><span class="mrow" id="MathJax-Span-544"><span class="msubsup" id="MathJax-Span-545"><span style="display: inline-block; position: relative; width: 2.027em; height: 0px;"><span style="position: absolute; clip: rect(3.158em, 1001.07em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-546" style="font-family: MathJax_Math-italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.122em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.342em; left: 1.134em;"><span class="texatom" id="MathJax-Span-547"><span class="mrow" id="MathJax-Span-548"><span class="mo" id="MathJax-Span-549" style="font-size: 70.7%; font-family: MathJax_Main;">[</span><span class="mi" id="MathJax-Span-550" style="font-size: 70.7%; font-family: MathJax_Math-italic;">x</span><span class="mo" id="MathJax-Span-551" style="font-size: 70.7%; font-family: MathJax_Main;">]</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.205em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.218em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>W</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">[</mo><mi>x</mi><mo stretchy="false">]</mo></mrow></msup></math></span></span><script type="math/tex" id="MathJax-Element-16">W^{[x]}</script> y <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-17-Frame" tabindex="0" style="position: relative;" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;msup&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo stretchy=&quot;false&quot;&gt;[&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;" role="presentation"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-552" style="width: 1.967em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.61em; height: 0px; font-size: 120%;"><span style="position: absolute; clip: rect(1.134em, 1001.61em, 2.384em, -999.997em); top: -2.199em; left: 0em;"><span class="mrow" id="MathJax-Span-553"><span class="msubsup" id="MathJax-Span-554"><span style="display: inline-block; position: relative; width: 1.61em; height: 0px;"><span style="position: absolute; clip: rect(3.158em, 1000.78em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-555" style="font-family: MathJax_Math-italic;">B</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.342em; left: 0.777em;"><span class="texatom" id="MathJax-Span-556"><span class="mrow" id="MathJax-Span-557"><span class="mo" id="MathJax-Span-558" style="font-size: 70.7%; font-family: MathJax_Main;">[</span><span class="mi" id="MathJax-Span-559" style="font-size: 70.7%; font-family: MathJax_Math-italic;">x</span><span class="mo" id="MathJax-Span-560" style="font-size: 70.7%; font-family: MathJax_Main;">]</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.205em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.218em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>B</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">[</mo><mi>x</mi><mo stretchy="false">]</mo></mrow></msup></math></span></span><script type="math/tex" id="MathJax-Element-17">B^{[x]}</script>, al error <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-18-Frame" tabindex="0" style="position: relative;" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;msup&gt;&lt;mi&gt;Z&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo stretchy=&quot;false&quot;&gt;[&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;" role="presentation"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-561" style="width: 2.682em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.205em; height: 0px; font-size: 120%;"><span style="position: absolute; clip: rect(1.134em, 1002.21em, 2.384em, -999.997em); top: -2.199em; left: 0em;"><span class="mrow" id="MathJax-Span-562"><span class="mi" id="MathJax-Span-563" style="font-family: MathJax_Math-italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="msubsup" id="MathJax-Span-564"><span style="display: inline-block; position: relative; width: 1.67em; height: 0px;"><span style="position: absolute; clip: rect(3.158em, 1000.72em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-565" style="font-family: MathJax_Math-italic;">Z<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.063em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.342em; left: 0.777em;"><span class="texatom" id="MathJax-Span-566"><span class="mrow" id="MathJax-Span-567"><span class="mo" id="MathJax-Span-568" style="font-size: 70.7%; font-family: MathJax_Main;">[</span><span class="mi" id="MathJax-Span-569" style="font-size: 70.7%; font-family: MathJax_Math-italic;">x</span><span class="mo" id="MathJax-Span-570" style="font-size: 70.7%; font-family: MathJax_Main;">]</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.205em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.218em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><msup><mi>Z</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">[</mo><mi>x</mi><mo stretchy="false">]</mo></mrow></msup></math></span></span><script type="math/tex" id="MathJax-Element-18">dZ^{[x]}</script>.</p>
<span class="MathJax_Preview" style="color: inherit; display: none;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" id="MathJax-Element-19-Frame" tabindex="0" style="text-align: center; position: relative;" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot; display=&quot;block&quot;&gt;&lt;mtable columnalign=&quot;right left right left right left right left right left right left&quot; rowspacing=&quot;3pt&quot; columnspacing=&quot;0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em&quot; displaystyle=&quot;true&quot;&gt;&lt;mtr&gt;&lt;mtd /&gt;&lt;mtd&gt;&lt;mi&gt;&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;mspace width=&quot;thinmathspace&quot; /&gt;&lt;mspace width=&quot;thinmathspace&quot; /&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;msup&gt;&lt;mi&gt;Z&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo stretchy=&quot;false&quot;&gt;[&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo stretchy=&quot;false&quot;&gt;[&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;&amp;#x2212;&lt;/mo&gt;&lt;mi&gt;Y&lt;/mi&gt;&lt;mtext&gt;&amp;#xA0;&lt;/mtext&gt;&lt;mtext&gt;(seg&amp;#xFA;n label)&lt;/mtext&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd /&gt;&lt;mtd&gt;&lt;mi&gt;&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;mspace width=&quot;thinmathspace&quot; /&gt;&lt;mspace width=&quot;thinmathspace&quot; /&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;msup&gt;&lt;mi&gt;W&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo stretchy=&quot;false&quot;&gt;[&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mfrac&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/mfrac&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;msup&gt;&lt;mi&gt;Z&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo stretchy=&quot;false&quot;&gt;[&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;msup&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo stretchy=&quot;false&quot;&gt;[&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;]&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd /&gt;&lt;mtd&gt;&lt;mi&gt;&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;mspace width=&quot;thinmathspace&quot; /&gt;&lt;mspace width=&quot;thinmathspace&quot; /&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;msup&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo stretchy=&quot;false&quot;&gt;[&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mfrac&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/mfrac&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;&amp;#x03A3;&lt;/mi&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;msup&gt;&lt;mi&gt;Z&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo stretchy=&quot;false&quot;&gt;[&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd /&gt;&lt;mtd&gt;&lt;mi&gt;&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;mspace width=&quot;thinmathspace&quot; /&gt;&lt;mspace width=&quot;thinmathspace&quot; /&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;msup&gt;&lt;mi&gt;Z&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo stretchy=&quot;false&quot;&gt;[&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;W&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo stretchy=&quot;false&quot;&gt;[&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;]&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;msup&gt;&lt;mi&gt;Z&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo stretchy=&quot;false&quot;&gt;[&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;&amp;#x22C5;&lt;/mo&gt;&lt;mi&gt;g&lt;/mi&gt;&lt;mi class=&quot;MJX-variant&quot; mathvariant=&quot;normal&quot;&gt;&amp;#x2032;&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;Z&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo stretchy=&quot;false&quot;&gt;[&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd /&gt;&lt;mtd&gt;&lt;mtext&gt;&amp;#xA0;siendo g la funci&amp;#xF3;n de activaci&amp;#xF3;n&lt;/mtext&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd /&gt;&lt;mtd&gt;&lt;mi&gt;&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mi&gt;e&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;mspace width=&quot;thinmathspace&quot; /&gt;&lt;mspace width=&quot;thinmathspace&quot; /&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;msup&gt;&lt;mi&gt;W&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo stretchy=&quot;false&quot;&gt;[&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mfrac&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/mfrac&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;msup&gt;&lt;mi&gt;Z&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo stretchy=&quot;false&quot;&gt;[&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;msup&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo stretchy=&quot;false&quot;&gt;[&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;]&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd /&gt;&lt;mtd&gt;&lt;mi&gt;&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;mspace width=&quot;thinmathspace&quot; /&gt;&lt;mspace width=&quot;thinmathspace&quot; /&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;msup&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo stretchy=&quot;false&quot;&gt;[&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mfrac&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/mfrac&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;&amp;#x03A3;&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;msup&gt;&lt;mi&gt;Z&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo stretchy=&quot;false&quot;&gt;[&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;/math&gt;" role="presentation"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-571" style="width: 17.801em; display: inline-block;"><span style="display: inline-block; position: relative; width: 14.824em; height: 0px; font-size: 120%;"><span style="position: absolute; clip: rect(-4.878em, 1014.53em, 8.813em, -999.997em); top: -2.199em; left: 0em;"><span class="mrow" id="MathJax-Span-572"><span class="mtable" id="MathJax-Span-573" style="padding-right: 0.182em; padding-left: 0.182em;"><span style="display: inline-block; position: relative; width: 14.467em; height: 0px;"><span style="position: absolute; clip: rect(6.61em, 1000em, 18.634em, -999.997em); top: -12.735em; left: 0em;"><span style="display: inline-block; position: relative; width: 0em; height: 0px;"><span style="position: absolute; clip: rect(3.812em, 1000em, 4.17em, -999.997em); top: -9.937em; right: 0em;"><span class="mtd" id="MathJax-Span-574"><span class="mrow" id="MathJax-Span-575"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.812em, 1000em, 4.17em, -999.997em); top: -8.092em; right: 0em;"><span class="mtd" id="MathJax-Span-604"><span class="mrow" id="MathJax-Span-605"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.812em, 1000em, 4.17em, -999.997em); top: -5.711em; right: 0em;"><span class="mtd" id="MathJax-Span-642"><span class="mrow" id="MathJax-Span-643"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.812em, 1000em, 4.17em, -999.997em); top: -3.807em; right: 0em;"><span class="mtd" id="MathJax-Span-673"><span class="mrow" id="MathJax-Span-674"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.812em, 1000em, 4.17em, -999.997em); top: -2.438em; right: 0em;"><span class="mtd" id="MathJax-Span-720"><span class="mrow" id="MathJax-Span-721"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.812em, 1000em, 4.17em, -999.997em); top: -0.592em; right: 0em;"><span class="mtd" id="MathJax-Span-725"><span class="mrow" id="MathJax-Span-726"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.812em, 1000em, 4.17em, -999.997em); top: 1.729em; right: 0em;"><span class="mtd" id="MathJax-Span-763"><span class="mrow" id="MathJax-Span-764"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 12.741em;"></span></span><span style="position: absolute; clip: rect(7.265em, 1014.41em, 20.955em, -999.997em); top: -14.342em; left: 0em;"><span style="display: inline-block; position: relative; width: 14.467em; height: 0px;"><span style="position: absolute; clip: rect(2.86em, 1014.41em, 4.408em, -999.997em); top: -9.937em; left: 0em;"><span class="mtd" id="MathJax-Span-576"><span class="mrow" id="MathJax-Span-577"><span class="mi" id="MathJax-Span-578"></span><span class="mo" id="MathJax-Span-579" style="font-family: MathJax_Main;">(</span><span class="mi" id="MathJax-Span-580" style="font-family: MathJax_Math-italic;">a</span><span class="mo" id="MathJax-Span-581" style="font-family: MathJax_Main;">)</span><span class="mspace" id="MathJax-Span-582" style="height: 0em; vertical-align: 0em; width: 0.182em; display: inline-block; overflow: hidden;"></span><span class="mspace" id="MathJax-Span-583" style="height: 0em; vertical-align: 0em; width: 0.182em; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-584" style="font-family: MathJax_Math-italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="msubsup" id="MathJax-Span-585"><span style="display: inline-block; position: relative; width: 1.61em; height: 0px;"><span style="position: absolute; clip: rect(3.158em, 1000.72em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-586" style="font-family: MathJax_Math-italic;">Z<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.063em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.402em; left: 0.777em;"><span class="texatom" id="MathJax-Span-587"><span class="mrow" id="MathJax-Span-588"><span class="mo" id="MathJax-Span-589" style="font-size: 70.7%; font-family: MathJax_Main;">[</span><span class="mn" id="MathJax-Span-590" style="font-size: 70.7%; font-family: MathJax_Main;">2</span><span class="mo" id="MathJax-Span-591" style="font-size: 70.7%; font-family: MathJax_Main;">]</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mo" id="MathJax-Span-592" style="font-family: MathJax_Main; padding-left: 0.301em;">=</span><span class="msubsup" id="MathJax-Span-593" style="padding-left: 0.301em;"><span style="display: inline-block; position: relative; width: 1.551em; height: 0px;"><span style="position: absolute; clip: rect(3.098em, 1000.72em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-594" style="font-family: MathJax_Math-italic;">A</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.402em; left: 0.777em;"><span class="texatom" id="MathJax-Span-595"><span class="mrow" id="MathJax-Span-596"><span class="mo" id="MathJax-Span-597" style="font-size: 70.7%; font-family: MathJax_Main;">[</span><span class="mn" id="MathJax-Span-598" style="font-size: 70.7%; font-family: MathJax_Main;">2</span><span class="mo" id="MathJax-Span-599" style="font-size: 70.7%; font-family: MathJax_Main;">]</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mo" id="MathJax-Span-600" style="font-family: MathJax_Main; padding-left: 0.241em;">−</span><span class="mi" id="MathJax-Span-601" style="font-family: MathJax_Math-italic; padding-left: 0.241em;">Y<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.182em;"></span></span><span class="mtext" id="MathJax-Span-602" style="font-family: MathJax_Main;">&nbsp;</span><span class="mtext" id="MathJax-Span-603" style="font-family: MathJax_Main;">(seg<span style="font-family: STIXGeneral, &quot;Arial Unicode MS&quot;, serif; font-size: 83%; font-style: normal; font-weight: normal;">ú</span>n label)</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(2.443em, 1010.6em, 4.884em, -999.997em); top: -8.092em; left: 0em;"><span class="mtd" id="MathJax-Span-606"><span class="mrow" id="MathJax-Span-607"><span class="mi" id="MathJax-Span-608"></span><span class="mo" id="MathJax-Span-609" style="font-family: MathJax_Main;">(</span><span class="mi" id="MathJax-Span-610" style="font-family: MathJax_Math-italic;">b</span><span class="mo" id="MathJax-Span-611" style="font-family: MathJax_Main;">)</span><span class="mspace" id="MathJax-Span-612" style="height: 0em; vertical-align: 0em; width: 0.182em; display: inline-block; overflow: hidden;"></span><span class="mspace" id="MathJax-Span-613" style="height: 0em; vertical-align: 0em; width: 0.182em; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-614" style="font-family: MathJax_Math-italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="msubsup" id="MathJax-Span-615"><span style="display: inline-block; position: relative; width: 1.967em; height: 0px;"><span style="position: absolute; clip: rect(3.158em, 1001.07em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-616" style="font-family: MathJax_Math-italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.122em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.402em; left: 1.134em;"><span class="texatom" id="MathJax-Span-617"><span class="mrow" id="MathJax-Span-618"><span class="mo" id="MathJax-Span-619" style="font-size: 70.7%; font-family: MathJax_Main;">[</span><span class="mn" id="MathJax-Span-620" style="font-size: 70.7%; font-family: MathJax_Main;">2</span><span class="mo" id="MathJax-Span-621" style="font-size: 70.7%; font-family: MathJax_Main;">]</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mo" id="MathJax-Span-622" style="font-family: MathJax_Main; padding-left: 0.301em;">=</span><span class="mfrac" id="MathJax-Span-623" style="padding-left: 0.301em;"><span style="display: inline-block; position: relative; width: 1.015em; height: 0px; margin-right: 0.122em; margin-left: 0.122em;"><span style="position: absolute; clip: rect(3.158em, 1000.42em, 4.17em, -999.997em); top: -4.64em; left: 50%; margin-left: -0.235em;"><span class="mn" id="MathJax-Span-624" style="font-family: MathJax_Main;">1</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.396em, 1000.84em, 4.17em, -999.997em); top: -3.271em; left: 50%; margin-left: -0.414em;"><span class="mi" id="MathJax-Span-625" style="font-family: MathJax_Math-italic;">m</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(0.836em, 1001.01em, 1.253em, -999.997em); top: -1.307em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 1.015em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.074em;"></span></span></span></span><span class="mi" id="MathJax-Span-626" style="font-family: MathJax_Math-italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="msubsup" id="MathJax-Span-627"><span style="display: inline-block; position: relative; width: 1.61em; height: 0px;"><span style="position: absolute; clip: rect(3.158em, 1000.72em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-628" style="font-family: MathJax_Math-italic;">Z<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.063em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.402em; left: 0.777em;"><span class="texatom" id="MathJax-Span-629"><span class="mrow" id="MathJax-Span-630"><span class="mo" id="MathJax-Span-631" style="font-size: 70.7%; font-family: MathJax_Main;">[</span><span class="mn" id="MathJax-Span-632" style="font-size: 70.7%; font-family: MathJax_Main;">2</span><span class="mo" id="MathJax-Span-633" style="font-size: 70.7%; font-family: MathJax_Main;">]</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="msubsup" id="MathJax-Span-634"><span style="display: inline-block; position: relative; width: 1.848em; height: 0px;"><span style="position: absolute; clip: rect(3.098em, 1000.72em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-635" style="font-family: MathJax_Math-italic;">A</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.402em; left: 0.777em;"><span class="texatom" id="MathJax-Span-636"><span class="mrow" id="MathJax-Span-637"><span class="mo" id="MathJax-Span-638" style="font-size: 70.7%; font-family: MathJax_Main;">[</span><span class="mn" id="MathJax-Span-639" style="font-size: 70.7%; font-family: MathJax_Main;">1</span><span class="mo" id="MathJax-Span-640" style="font-size: 70.7%; font-family: MathJax_Main;">]</span><span class="mi" id="MathJax-Span-641" style="font-size: 70.7%; font-family: MathJax_Math-italic;">t</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(2.443em, 1009.11em, 4.884em, -999.997em); top: -5.711em; left: 0em;"><span class="mtd" id="MathJax-Span-644"><span class="mrow" id="MathJax-Span-645"><span class="mi" id="MathJax-Span-646"></span><span class="mo" id="MathJax-Span-647" style="font-family: MathJax_Main;">(</span><span class="mi" id="MathJax-Span-648" style="font-family: MathJax_Math-italic;">c</span><span class="mo" id="MathJax-Span-649" style="font-family: MathJax_Main;">)</span><span class="mspace" id="MathJax-Span-650" style="height: 0em; vertical-align: 0em; width: 0.182em; display: inline-block; overflow: hidden;"></span><span class="mspace" id="MathJax-Span-651" style="height: 0em; vertical-align: 0em; width: 0.182em; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-652" style="font-family: MathJax_Math-italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="msubsup" id="MathJax-Span-653"><span style="display: inline-block; position: relative; width: 1.61em; height: 0px;"><span style="position: absolute; clip: rect(3.158em, 1000.78em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-654" style="font-family: MathJax_Math-italic;">B</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.402em; left: 0.777em;"><span class="texatom" id="MathJax-Span-655"><span class="mrow" id="MathJax-Span-656"><span class="mo" id="MathJax-Span-657" style="font-size: 70.7%; font-family: MathJax_Main;">[</span><span class="mn" id="MathJax-Span-658" style="font-size: 70.7%; font-family: MathJax_Main;">2</span><span class="mo" id="MathJax-Span-659" style="font-size: 70.7%; font-family: MathJax_Main;">]</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mo" id="MathJax-Span-660" style="font-family: MathJax_Main; padding-left: 0.301em;">=</span><span class="mfrac" id="MathJax-Span-661" style="padding-left: 0.301em;"><span style="display: inline-block; position: relative; width: 1.015em; height: 0px; margin-right: 0.122em; margin-left: 0.122em;"><span style="position: absolute; clip: rect(3.158em, 1000.42em, 4.17em, -999.997em); top: -4.64em; left: 50%; margin-left: -0.235em;"><span class="mn" id="MathJax-Span-662" style="font-family: MathJax_Main;">1</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.396em, 1000.84em, 4.17em, -999.997em); top: -3.271em; left: 50%; margin-left: -0.414em;"><span class="mi" id="MathJax-Span-663" style="font-family: MathJax_Math-italic;">m</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(0.836em, 1001.01em, 1.253em, -999.997em); top: -1.307em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 1.015em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.074em;"></span></span></span></span><span class="mi" id="MathJax-Span-664" style="font-family: MathJax_Main;">Σ</span><span class="mi" id="MathJax-Span-665" style="font-family: MathJax_Math-italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="msubsup" id="MathJax-Span-666"><span style="display: inline-block; position: relative; width: 1.61em; height: 0px;"><span style="position: absolute; clip: rect(3.158em, 1000.72em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-667" style="font-family: MathJax_Math-italic;">Z<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.063em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.402em; left: 0.777em;"><span class="texatom" id="MathJax-Span-668"><span class="mrow" id="MathJax-Span-669"><span class="mo" id="MathJax-Span-670" style="font-size: 70.7%; font-family: MathJax_Main;">[</span><span class="mn" id="MathJax-Span-671" style="font-size: 70.7%; font-family: MathJax_Main;">2</span><span class="mo" id="MathJax-Span-672" style="font-size: 70.7%; font-family: MathJax_Main;">]</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(2.86em, 1013.28em, 4.408em, -999.997em); top: -3.807em; left: 0em;"><span class="mtd" id="MathJax-Span-675"><span class="mrow" id="MathJax-Span-676"><span class="mi" id="MathJax-Span-677"></span><span class="mo" id="MathJax-Span-678" style="font-family: MathJax_Main;">(</span><span class="mi" id="MathJax-Span-679" style="font-family: MathJax_Math-italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" id="MathJax-Span-680" style="font-family: MathJax_Main;">)</span><span class="mspace" id="MathJax-Span-681" style="height: 0em; vertical-align: 0em; width: 0.182em; display: inline-block; overflow: hidden;"></span><span class="mspace" id="MathJax-Span-682" style="height: 0em; vertical-align: 0em; width: 0.182em; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-683" style="font-family: MathJax_Math-italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="msubsup" id="MathJax-Span-684"><span style="display: inline-block; position: relative; width: 1.61em; height: 0px;"><span style="position: absolute; clip: rect(3.158em, 1000.72em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-685" style="font-family: MathJax_Math-italic;">Z<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.063em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.402em; left: 0.777em;"><span class="texatom" id="MathJax-Span-686"><span class="mrow" id="MathJax-Span-687"><span class="mo" id="MathJax-Span-688" style="font-size: 70.7%; font-family: MathJax_Main;">[</span><span class="mn" id="MathJax-Span-689" style="font-size: 70.7%; font-family: MathJax_Main;">1</span><span class="mo" id="MathJax-Span-690" style="font-size: 70.7%; font-family: MathJax_Main;">]</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mo" id="MathJax-Span-691" style="font-family: MathJax_Main; padding-left: 0.301em;">=</span><span class="msubsup" id="MathJax-Span-692" style="padding-left: 0.301em;"><span style="display: inline-block; position: relative; width: 2.205em; height: 0px;"><span style="position: absolute; clip: rect(3.158em, 1001.07em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-693" style="font-family: MathJax_Math-italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.122em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.402em; left: 1.134em;"><span class="texatom" id="MathJax-Span-694"><span class="mrow" id="MathJax-Span-695"><span class="mo" id="MathJax-Span-696" style="font-size: 70.7%; font-family: MathJax_Main;">[</span><span class="mn" id="MathJax-Span-697" style="font-size: 70.7%; font-family: MathJax_Main;">2</span><span class="mo" id="MathJax-Span-698" style="font-size: 70.7%; font-family: MathJax_Main;">]</span><span class="mi" id="MathJax-Span-699" style="font-size: 70.7%; font-family: MathJax_Math-italic;">t</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mi" id="MathJax-Span-700" style="font-family: MathJax_Math-italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="msubsup" id="MathJax-Span-701"><span style="display: inline-block; position: relative; width: 1.61em; height: 0px;"><span style="position: absolute; clip: rect(3.158em, 1000.72em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-702" style="font-family: MathJax_Math-italic;">Z<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.063em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.402em; left: 0.777em;"><span class="texatom" id="MathJax-Span-703"><span class="mrow" id="MathJax-Span-704"><span class="mo" id="MathJax-Span-705" style="font-size: 70.7%; font-family: MathJax_Main;">[</span><span class="mn" id="MathJax-Span-706" style="font-size: 70.7%; font-family: MathJax_Main;">2</span><span class="mo" id="MathJax-Span-707" style="font-size: 70.7%; font-family: MathJax_Main;">]</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mo" id="MathJax-Span-708" style="font-family: MathJax_Main; padding-left: 0.241em;">⋅</span><span class="mi" id="MathJax-Span-709" style="font-family: MathJax_Math-italic; padding-left: 0.241em;">g<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mi" id="MathJax-Span-710" style="font-family: MathJax_Main;">′</span><span class="mo" id="MathJax-Span-711" style="font-family: MathJax_Main;">(</span><span class="msubsup" id="MathJax-Span-712"><span style="display: inline-block; position: relative; width: 1.61em; height: 0px;"><span style="position: absolute; clip: rect(3.158em, 1000.72em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-713" style="font-family: MathJax_Math-italic;">Z<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.063em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.402em; left: 0.777em;"><span class="texatom" id="MathJax-Span-714"><span class="mrow" id="MathJax-Span-715"><span class="mo" id="MathJax-Span-716" style="font-size: 70.7%; font-family: MathJax_Main;">[</span><span class="mn" id="MathJax-Span-717" style="font-size: 70.7%; font-family: MathJax_Main;">1</span><span class="mo" id="MathJax-Span-718" style="font-size: 70.7%; font-family: MathJax_Main;">]</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mo" id="MathJax-Span-719" style="font-family: MathJax_Main;">)</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(1.253em, 1013.93em, 2.562em, -999.997em); top: -0.652em; left: 0em;"><span class="mtd" id="MathJax-Span-722"><span class="mrow" id="MathJax-Span-723"><span class="mtext" id="MathJax-Span-724" style="font-family: MathJax_Main;">&nbsp;siendo g la funci<span style="font-family: STIXGeneral, &quot;Arial Unicode MS&quot;, serif; font-size: 83%; font-style: normal; font-weight: normal;">ó</span>n de activaci<span style="font-family: STIXGeneral, &quot;Arial Unicode MS&quot;, serif; font-size: 83%; font-style: normal; font-weight: normal;">ó</span>n</span></span></span><span style="display: inline-block; width: 0px; height: 2.205em;"></span></span><span style="position: absolute; clip: rect(2.443em, 1010.66em, 4.884em, -999.997em); top: -0.592em; left: 0em;"><span class="mtd" id="MathJax-Span-727"><span class="mrow" id="MathJax-Span-728"><span class="mi" id="MathJax-Span-729"></span><span class="mo" id="MathJax-Span-730" style="font-family: MathJax_Main;">(</span><span class="mi" id="MathJax-Span-731" style="font-family: MathJax_Math-italic;">e</span><span class="mo" id="MathJax-Span-732" style="font-family: MathJax_Main;">)</span><span class="mspace" id="MathJax-Span-733" style="height: 0em; vertical-align: 0em; width: 0.182em; display: inline-block; overflow: hidden;"></span><span class="mspace" id="MathJax-Span-734" style="height: 0em; vertical-align: 0em; width: 0.182em; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-735" style="font-family: MathJax_Math-italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="msubsup" id="MathJax-Span-736"><span style="display: inline-block; position: relative; width: 1.967em; height: 0px;"><span style="position: absolute; clip: rect(3.158em, 1001.07em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-737" style="font-family: MathJax_Math-italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.122em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.402em; left: 1.134em;"><span class="texatom" id="MathJax-Span-738"><span class="mrow" id="MathJax-Span-739"><span class="mo" id="MathJax-Span-740" style="font-size: 70.7%; font-family: MathJax_Main;">[</span><span class="mn" id="MathJax-Span-741" style="font-size: 70.7%; font-family: MathJax_Main;">1</span><span class="mo" id="MathJax-Span-742" style="font-size: 70.7%; font-family: MathJax_Main;">]</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mo" id="MathJax-Span-743" style="font-family: MathJax_Main; padding-left: 0.301em;">=</span><span class="mfrac" id="MathJax-Span-744" style="padding-left: 0.301em;"><span style="display: inline-block; position: relative; width: 1.015em; height: 0px; margin-right: 0.122em; margin-left: 0.122em;"><span style="position: absolute; clip: rect(3.158em, 1000.42em, 4.17em, -999.997em); top: -4.64em; left: 50%; margin-left: -0.235em;"><span class="mn" id="MathJax-Span-745" style="font-family: MathJax_Main;">1</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.396em, 1000.84em, 4.17em, -999.997em); top: -3.271em; left: 50%; margin-left: -0.414em;"><span class="mi" id="MathJax-Span-746" style="font-family: MathJax_Math-italic;">m</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(0.836em, 1001.01em, 1.253em, -999.997em); top: -1.307em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 1.015em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.074em;"></span></span></span></span><span class="mi" id="MathJax-Span-747" style="font-family: MathJax_Math-italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="msubsup" id="MathJax-Span-748"><span style="display: inline-block; position: relative; width: 1.61em; height: 0px;"><span style="position: absolute; clip: rect(3.158em, 1000.72em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-749" style="font-family: MathJax_Math-italic;">Z<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.063em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.402em; left: 0.777em;"><span class="texatom" id="MathJax-Span-750"><span class="mrow" id="MathJax-Span-751"><span class="mo" id="MathJax-Span-752" style="font-size: 70.7%; font-family: MathJax_Main;">[</span><span class="mn" id="MathJax-Span-753" style="font-size: 70.7%; font-family: MathJax_Main;">1</span><span class="mo" id="MathJax-Span-754" style="font-size: 70.7%; font-family: MathJax_Main;">]</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="msubsup" id="MathJax-Span-755"><span style="display: inline-block; position: relative; width: 1.848em; height: 0px;"><span style="position: absolute; clip: rect(3.098em, 1000.72em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-756" style="font-family: MathJax_Math-italic;">A</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.402em; left: 0.777em;"><span class="texatom" id="MathJax-Span-757"><span class="mrow" id="MathJax-Span-758"><span class="mo" id="MathJax-Span-759" style="font-size: 70.7%; font-family: MathJax_Main;">[</span><span class="mn" id="MathJax-Span-760" style="font-size: 70.7%; font-family: MathJax_Main;">0</span><span class="mo" id="MathJax-Span-761" style="font-size: 70.7%; font-family: MathJax_Main;">]</span><span class="mi" id="MathJax-Span-762" style="font-size: 70.7%; font-family: MathJax_Math-italic;">t</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(2.443em, 1009.23em, 4.884em, -999.997em); top: 1.729em; left: 0em;"><span class="mtd" id="MathJax-Span-765"><span class="mrow" id="MathJax-Span-766"><span class="mi" id="MathJax-Span-767"></span><span class="mo" id="MathJax-Span-768" style="font-family: MathJax_Main;">(</span><span class="mi" id="MathJax-Span-769" style="font-family: MathJax_Math-italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.063em;"></span></span><span class="mo" id="MathJax-Span-770" style="font-family: MathJax_Main;">)</span><span class="mspace" id="MathJax-Span-771" style="height: 0em; vertical-align: 0em; width: 0.182em; display: inline-block; overflow: hidden;"></span><span class="mspace" id="MathJax-Span-772" style="height: 0em; vertical-align: 0em; width: 0.182em; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-773" style="font-family: MathJax_Math-italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="msubsup" id="MathJax-Span-774"><span style="display: inline-block; position: relative; width: 1.61em; height: 0px;"><span style="position: absolute; clip: rect(3.158em, 1000.78em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-775" style="font-family: MathJax_Math-italic;">B</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.402em; left: 0.777em;"><span class="texatom" id="MathJax-Span-776"><span class="mrow" id="MathJax-Span-777"><span class="mo" id="MathJax-Span-778" style="font-size: 70.7%; font-family: MathJax_Main;">[</span><span class="mn" id="MathJax-Span-779" style="font-size: 70.7%; font-family: MathJax_Main;">1</span><span class="mo" id="MathJax-Span-780" style="font-size: 70.7%; font-family: MathJax_Main;">]</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mo" id="MathJax-Span-781" style="font-family: MathJax_Main; padding-left: 0.301em;">=</span><span class="mfrac" id="MathJax-Span-782" style="padding-left: 0.301em;"><span style="display: inline-block; position: relative; width: 1.015em; height: 0px; margin-right: 0.122em; margin-left: 0.122em;"><span style="position: absolute; clip: rect(3.158em, 1000.42em, 4.17em, -999.997em); top: -4.64em; left: 50%; margin-left: -0.235em;"><span class="mn" id="MathJax-Span-783" style="font-family: MathJax_Main;">1</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.396em, 1000.84em, 4.17em, -999.997em); top: -3.271em; left: 50%; margin-left: -0.414em;"><span class="mi" id="MathJax-Span-784" style="font-family: MathJax_Math-italic;">m</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(0.836em, 1001.01em, 1.253em, -999.997em); top: -1.307em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 1.015em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.074em;"></span></span></span></span><span class="mi" id="MathJax-Span-785" style="font-family: MathJax_Main;">Σ</span><span class="texatom" id="MathJax-Span-786"><span class="mrow" id="MathJax-Span-787"><span class="mi" id="MathJax-Span-788" style="font-family: MathJax_Math-italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="msubsup" id="MathJax-Span-789"><span style="display: inline-block; position: relative; width: 1.61em; height: 0px;"><span style="position: absolute; clip: rect(3.158em, 1000.72em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-790" style="font-family: MathJax_Math-italic;">Z<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.063em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.402em; left: 0.777em;"><span class="texatom" id="MathJax-Span-791"><span class="mrow" id="MathJax-Span-792"><span class="mo" id="MathJax-Span-793" style="font-size: 70.7%; font-family: MathJax_Main;">[</span><span class="mn" id="MathJax-Span-794" style="font-size: 70.7%; font-family: MathJax_Main;">1</span><span class="mo" id="MathJax-Span-795" style="font-size: 70.7%; font-family: MathJax_Main;">]</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 14.348em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.205em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -7.782em; border-left: 0px solid; width: 0px; height: 16.146em;"></span></span></nobr><span class="MJX_Assistive_MathML MJX_Assistive_MathML_Block" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"><mtr><mtd></mtd><mtd><mi></mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">)</mo><mspace width="thinmathspace"></mspace><mspace width="thinmathspace"></mspace><mi>d</mi><msup><mi>Z</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">[</mo><mn>2</mn><mo stretchy="false">]</mo></mrow></msup><mo>=</mo><msup><mi>A</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">[</mo><mn>2</mn><mo stretchy="false">]</mo></mrow></msup><mo>−</mo><mi>Y</mi><mtext>&nbsp;</mtext><mtext>(según label)</mtext></mtd></mtr><mtr><mtd></mtd><mtd><mi></mi><mo stretchy="false">(</mo><mi>b</mi><mo stretchy="false">)</mo><mspace width="thinmathspace"></mspace><mspace width="thinmathspace"></mspace><mi>d</mi><msup><mi>W</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">[</mo><mn>2</mn><mo stretchy="false">]</mo></mrow></msup><mo>=</mo><mfrac><mn>1</mn><mi>m</mi></mfrac><mi>d</mi><msup><mi>Z</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">[</mo><mn>2</mn><mo stretchy="false">]</mo></mrow></msup><msup><mi>A</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">[</mo><mn>1</mn><mo stretchy="false">]</mo><mi>t</mi></mrow></msup></mtd></mtr><mtr><mtd></mtd><mtd><mi></mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo><mspace width="thinmathspace"></mspace><mspace width="thinmathspace"></mspace><mi>d</mi><msup><mi>B</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">[</mo><mn>2</mn><mo stretchy="false">]</mo></mrow></msup><mo>=</mo><mfrac><mn>1</mn><mi>m</mi></mfrac><mi mathvariant="normal">Σ</mi><mi>d</mi><msup><mi>Z</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">[</mo><mn>2</mn><mo stretchy="false">]</mo></mrow></msup></mtd></mtr><mtr><mtd></mtd><mtd><mi></mi><mo stretchy="false">(</mo><mi>d</mi><mo stretchy="false">)</mo><mspace width="thinmathspace"></mspace><mspace width="thinmathspace"></mspace><mi>d</mi><msup><mi>Z</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">[</mo><mn>1</mn><mo stretchy="false">]</mo></mrow></msup><mo>=</mo><msup><mi>W</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">[</mo><mn>2</mn><mo stretchy="false">]</mo><mi>t</mi></mrow></msup><mi>d</mi><msup><mi>Z</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">[</mo><mn>2</mn><mo stretchy="false">]</mo></mrow></msup><mo>⋅</mo><mi>g</mi><mi class="MJX-variant" mathvariant="normal">′</mi><mo stretchy="false">(</mo><msup><mi>Z</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">[</mo><mn>1</mn><mo stretchy="false">]</mo></mrow></msup><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd></mtd><mtd><mtext>&nbsp;siendo g la función de activación</mtext></mtd></mtr><mtr><mtd></mtd><mtd><mi></mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo><mspace width="thinmathspace"></mspace><mspace width="thinmathspace"></mspace><mi>d</mi><msup><mi>W</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">[</mo><mn>1</mn><mo stretchy="false">]</mo></mrow></msup><mo>=</mo><mfrac><mn>1</mn><mi>m</mi></mfrac><mi>d</mi><msup><mi>Z</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">[</mo><mn>1</mn><mo stretchy="false">]</mo></mrow></msup><msup><mi>A</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">[</mo><mn>0</mn><mo stretchy="false">]</mo><mi>t</mi></mrow></msup></mtd></mtr><mtr><mtd></mtd><mtd><mi></mi><mo stretchy="false">(</mo><mi>f</mi><mo stretchy="false">)</mo><mspace width="thinmathspace"></mspace><mspace width="thinmathspace"></mspace><mi>d</mi><msup><mi>B</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">[</mo><mn>1</mn><mo stretchy="false">]</mo></mrow></msup><mo>=</mo><mfrac><mn>1</mn><mi>m</mi></mfrac><mi mathvariant="normal">Σ</mi><mrow class="MJX-TeXAtom-ORD"><mi>d</mi><msup><mi>Z</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">[</mo><mn>1</mn><mo stretchy="false">]</mo></mrow></msup></mrow></mtd></mtr></mtable></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-19">\begin{align}
    &(a)\,\,dZ^{[2]} = A^{[2]} - Y \ \text{(según label)} \\
    &(b)\,\,dW^{[2]} = \frac{1}{m}dZ^{[2]}A^{[1]t} \\
    &(c)\,\,dB^{[2]} = \frac{1}{m}\Sigma dZ^{[2]} \\
    &(d)\,\,dZ^{[1]} = W^{[2]t} dZ^{[2]} \cdot  g\prime (Z^{[1]}) \\
    &\text{ siendo g la función de activación} \\
    &(e)\,\,dW^{[1]} = \frac{1}{m} dZ^{[1]} A^{[0]t} \\
    &(f)\,\,dB^{[1]} = \frac{1}{m} \Sigma {dZ^{[1]}}
\end{align}</script><ol type="a">
  <li>Encuentra los errores de la segunda capa; por cuánto falló.</li>
  <li>Cuánto se deben ajustar los pesos de la segunda capa, según el error anterior.</li>
  <li>Ajuste de los sesgos.</li>
  <li>Toma los errores en la seguna capa, y se le aplican los pesos "en reversa", con la finalidad de encontrar los errores para la primera capa, y continuar con el ajuste.</li>
  <li>Ajuste de los pesos de la primera capa.</li>
  <li>Ajuste de los sesgos de la primera capa.</li>
</ol><h2 id="Actualización-de-parámetros">Actualización de parámetros<a class="anchor-link" href="https://htmtopdf.herokuapp.com/ipynbviewer/temp/46ccb8d60bc4953329f884b04452879a/first_approach_neural_networks_p1.html?t=1670380747444#Actualizaci%C3%B3n-de-par%C3%A1metros">¶</a></h2><p>Los parámetros de la red se actualizan según los valores anteriormente obtenidos, de la siguiente manera:</p>
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position: relative; width: 9.646em; height: 0px;"><span style="position: absolute; clip: rect(2.86em, 1009.65em, 4.229em, -999.997em); top: -6.009em; left: 0em;"><span class="mtd" id="MathJax-Span-801"><span class="mrow" id="MathJax-Span-802"><span class="msubsup" id="MathJax-Span-803"><span style="display: inline-block; position: relative; width: 1.967em; height: 0px;"><span style="position: absolute; clip: rect(3.158em, 1001.07em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-804" style="font-family: MathJax_Math-italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.122em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.402em; left: 1.134em;"><span class="texatom" id="MathJax-Span-805"><span class="mrow" id="MathJax-Span-806"><span class="mo" id="MathJax-Span-807" style="font-size: 70.7%; font-family: MathJax_Main;">[</span><span class="mn" id="MathJax-Span-808" style="font-size: 70.7%; font-family: MathJax_Main;">1</span><span class="mo" id="MathJax-Span-809" style="font-size: 70.7%; font-family: MathJax_Main;">]</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mo" id="MathJax-Span-810" style="font-family: MathJax_Main; padding-left: 0.301em;">=</span><span class="msubsup" id="MathJax-Span-811" style="padding-left: 0.301em;"><span style="display: inline-block; position: relative; width: 1.967em; height: 0px;"><span style="position: absolute; clip: rect(3.158em, 1001.07em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-812" style="font-family: MathJax_Math-italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.122em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.402em; left: 1.134em;"><span class="texatom" id="MathJax-Span-813"><span class="mrow" id="MathJax-Span-814"><span class="mo" id="MathJax-Span-815" style="font-size: 70.7%; font-family: MathJax_Main;">[</span><span class="mn" id="MathJax-Span-816" style="font-size: 70.7%; font-family: MathJax_Main;">1</span><span class="mo" id="MathJax-Span-817" style="font-size: 70.7%; font-family: MathJax_Main;">]</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mo" id="MathJax-Span-818" style="font-family: MathJax_Main; padding-left: 0.241em;">−</span><span class="mi" id="MathJax-Span-819" style="font-family: MathJax_Math-italic; padding-left: 0.241em;">α</span><span class="mi" id="MathJax-Span-820" style="font-family: MathJax_Math-italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="msubsup" id="MathJax-Span-821"><span style="display: inline-block; position: relative; width: 1.967em; height: 0px;"><span style="position: absolute; clip: rect(3.158em, 1001.07em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-822" style="font-family: MathJax_Math-italic;">W<span style="display: inline-block; 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position: relative; width: 1.61em; height: 0px;"><span style="position: absolute; clip: rect(3.158em, 1000.78em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-833" style="font-family: MathJax_Math-italic;">B</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.402em; left: 0.777em;"><span class="texatom" id="MathJax-Span-834"><span class="mrow" id="MathJax-Span-835"><span class="mo" id="MathJax-Span-836" style="font-size: 70.7%; font-family: MathJax_Main;">[</span><span class="mn" id="MathJax-Span-837" style="font-size: 70.7%; font-family: MathJax_Main;">1</span><span class="mo" id="MathJax-Span-838" style="font-size: 70.7%; font-family: MathJax_Main;">]</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mo" id="MathJax-Span-839" style="font-family: MathJax_Main; padding-left: 0.301em;">=</span><span class="msubsup" id="MathJax-Span-840" style="padding-left: 0.301em;"><span style="display: inline-block; 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padding-left: 0.241em;">α</span><span class="mi" id="MathJax-Span-849" style="font-family: MathJax_Math-italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="msubsup" id="MathJax-Span-850"><span style="display: inline-block; position: relative; width: 1.61em; height: 0px;"><span style="position: absolute; clip: rect(3.158em, 1000.78em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-851" style="font-family: MathJax_Math-italic;">B</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.402em; left: 0.777em;"><span class="texatom" id="MathJax-Span-852"><span class="mrow" id="MathJax-Span-853"><span class="mo" id="MathJax-Span-854" style="font-size: 70.7%; font-family: MathJax_Main;">[</span><span class="mn" id="MathJax-Span-855" style="font-size: 70.7%; font-family: MathJax_Main;">1</span><span class="mo" id="MathJax-Span-856" style="font-size: 70.7%; font-family: MathJax_Main;">]</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(2.86em, 1009.65em, 4.229em, -999.997em); top: -3.152em; left: 0em;"><span class="mtd" id="MathJax-Span-859"><span class="mrow" id="MathJax-Span-860"><span class="msubsup" id="MathJax-Span-861"><span style="display: inline-block; position: relative; width: 1.967em; height: 0px;"><span style="position: absolute; clip: rect(3.158em, 1001.07em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-862" style="font-family: MathJax_Math-italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.122em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.402em; left: 1.134em;"><span class="texatom" id="MathJax-Span-863"><span class="mrow" id="MathJax-Span-864"><span class="mo" id="MathJax-Span-865" style="font-size: 70.7%; font-family: MathJax_Main;">[</span><span class="mn" id="MathJax-Span-866" style="font-size: 70.7%; font-family: MathJax_Main;">2</span><span class="mo" id="MathJax-Span-867" style="font-size: 70.7%; font-family: MathJax_Main;">]</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mo" id="MathJax-Span-868" style="font-family: MathJax_Main; padding-left: 0.301em;">=</span><span class="msubsup" id="MathJax-Span-869" style="padding-left: 0.301em;"><span style="display: inline-block; position: relative; width: 1.967em; height: 0px;"><span style="position: absolute; clip: rect(3.158em, 1001.07em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-870" style="font-family: MathJax_Math-italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.122em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.402em; left: 1.134em;"><span class="texatom" id="MathJax-Span-871"><span class="mrow" id="MathJax-Span-872"><span class="mo" id="MathJax-Span-873" style="font-size: 70.7%; font-family: MathJax_Main;">[</span><span class="mn" id="MathJax-Span-874" style="font-size: 70.7%; font-family: MathJax_Main;">2</span><span class="mo" id="MathJax-Span-875" style="font-size: 70.7%; font-family: MathJax_Main;">]</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mo" id="MathJax-Span-876" style="font-family: MathJax_Main; padding-left: 0.241em;">−</span><span class="mi" id="MathJax-Span-877" style="font-family: MathJax_Math-italic; padding-left: 0.241em;">α</span><span class="mi" id="MathJax-Span-878" style="font-family: MathJax_Math-italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="msubsup" id="MathJax-Span-879"><span style="display: inline-block; 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width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(2.86em, 1008.57em, 4.229em, -999.997em); top: -1.723em; left: 0em;"><span class="mtd" id="MathJax-Span-888"><span class="mrow" id="MathJax-Span-889"><span class="msubsup" id="MathJax-Span-890"><span style="display: inline-block; position: relative; width: 1.61em; height: 0px;"><span style="position: absolute; clip: rect(3.158em, 1000.78em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-891" style="font-family: MathJax_Math-italic;">B</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.402em; left: 0.777em;"><span class="texatom" id="MathJax-Span-892"><span class="mrow" id="MathJax-Span-893"><span class="mo" id="MathJax-Span-894" style="font-size: 70.7%; font-family: MathJax_Main;">[</span><span class="mn" id="MathJax-Span-895" style="font-size: 70.7%; font-family: MathJax_Main;">2</span><span class="mo" id="MathJax-Span-896" style="font-size: 70.7%; font-family: MathJax_Main;">]</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mo" id="MathJax-Span-897" style="font-family: MathJax_Main; padding-left: 0.301em;">=</span><span class="msubsup" id="MathJax-Span-898" style="padding-left: 0.301em;"><span style="display: inline-block; position: relative; width: 1.61em; height: 0px;"><span style="position: absolute; clip: rect(3.158em, 1000.78em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-899" style="font-family: MathJax_Math-italic;">B</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.402em; left: 0.777em;"><span class="texatom" id="MathJax-Span-900"><span class="mrow" id="MathJax-Span-901"><span class="mo" id="MathJax-Span-902" style="font-size: 70.7%; font-family: MathJax_Main;">[</span><span class="mn" id="MathJax-Span-903" style="font-size: 70.7%; font-family: MathJax_Main;">2</span><span class="mo" id="MathJax-Span-904" style="font-size: 70.7%; font-family: MathJax_Main;">]</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mo" id="MathJax-Span-905" style="font-family: MathJax_Main; padding-left: 0.241em;">−</span><span class="mi" id="MathJax-Span-906" style="font-family: MathJax_Math-italic; padding-left: 0.241em;">α</span><span class="mi" id="MathJax-Span-907" style="font-family: MathJax_Math-italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="msubsup" id="MathJax-Span-908"><span style="display: inline-block; position: relative; width: 1.61em; height: 0px;"><span style="position: absolute; clip: rect(3.158em, 1000.78em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-909" style="font-family: MathJax_Math-italic;">B</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.402em; left: 0.777em;"><span class="texatom" id="MathJax-Span-910"><span class="mrow" id="MathJax-Span-911"><span class="mo" id="MathJax-Span-912" style="font-size: 70.7%; font-family: MathJax_Main;">[</span><span class="mn" id="MathJax-Span-913" style="font-size: 70.7%; font-family: MathJax_Main;">2</span><span class="mo" id="MathJax-Span-914" style="font-size: 70.7%; font-family: MathJax_Main;">]</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 6.372em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.205em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -3.068em; border-left: 0px solid; width: 0px; height: 6.718em;"></span></span></nobr><span class="MJX_Assistive_MathML MJX_Assistive_MathML_Block" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"><mtr><mtd></mtd><mtd><msup><mi>W</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">[</mo><mn>1</mn><mo stretchy="false">]</mo></mrow></msup><mo>=</mo><msup><mi>W</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">[</mo><mn>1</mn><mo stretchy="false">]</mo></mrow></msup><mo>−</mo><mi>α</mi><mi>d</mi><msup><mi>W</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">[</mo><mn>1</mn><mo stretchy="false">]</mo></mrow></msup></mtd></mtr><mtr><mtd></mtd><mtd><msup><mi>B</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">[</mo><mn>1</mn><mo stretchy="false">]</mo></mrow></msup><mo>=</mo><msup><mi>B</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">[</mo><mn>1</mn><mo stretchy="false">]</mo></mrow></msup><mo>−</mo><mi>α</mi><mi>d</mi><msup><mi>B</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">[</mo><mn>1</mn><mo stretchy="false">]</mo></mrow></msup></mtd></mtr><mtr><mtd></mtd><mtd><msup><mi>W</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">[</mo><mn>2</mn><mo stretchy="false">]</mo></mrow></msup><mo>=</mo><msup><mi>W</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">[</mo><mn>2</mn><mo stretchy="false">]</mo></mrow></msup><mo>−</mo><mi>α</mi><mi>d</mi><msup><mi>W</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">[</mo><mn>2</mn><mo stretchy="false">]</mo></mrow></msup></mtd></mtr><mtr><mtd></mtd><mtd><msup><mi>B</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">[</mo><mn>2</mn><mo stretchy="false">]</mo></mrow></msup><mo>=</mo><msup><mi>B</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">[</mo><mn>2</mn><mo stretchy="false">]</mo></mrow></msup><mo>−</mo><mi>α</mi><mi>d</mi><msup><mi>B</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">[</mo><mn>2</mn><mo stretchy="false">]</mo></mrow></msup></mtd></mtr></mtable></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-20">\begin{align}
        &W^{[1]} = W^{[1]} - \alpha dW^{[1]} \\
        &B^{[1]} = B^{[1]} - \alpha dB^{[1]} \\
        &W^{[2]} = W^{[2]} - \alpha dW^{[2]} \\
        &B^{[2]} = B^{[2]} - \alpha dB^{[2]} \\
\end{align}</script><p>Siendo <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-21-Frame" tabindex="0" style="position: relative;" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;&amp;#x03B1;&lt;/mi&gt;&lt;/math&gt;" role="presentation"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-915" style="width: 0.836em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.658em; height: 0px; font-size: 120%;"><span style="position: absolute; clip: rect(1.61em, 1000.6em, 2.384em, -999.997em); top: -2.199em; left: 0em;"><span class="mrow" id="MathJax-Span-916"><span class="mi" id="MathJax-Span-917" style="font-family: MathJax_Math-italic;">α</span></span><span style="display: inline-block; width: 0px; height: 2.205em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 0.718em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>α</mi></math></span></span><script type="math/tex" id="MathJax-Element-21">\alpha</script> el <em>learning rate</em><sup>[H]</sup>.</p>
<p><strong>Finalmente se repiten los tres pasos, queriendo acercar la red a la funcionalidad esperada.</strong></p>
<h2 id="Tamaños-reales-de-las-matrices-[H]">Tamaños reales de las matrices <sup>[H]</sup><a class="anchor-link" href="https://htmtopdf.herokuapp.com/ipynbviewer/temp/46ccb8d60bc4953329f884b04452879a/first_approach_neural_networks_p1.html?t=1670380747444#Tama%C3%B1os-reales-de-las-matrices-[H]">¶</a></h2><h3 id="Propagación-hacia-delante">Propagación hacia delante<a class="anchor-link" href="https://htmtopdf.herokuapp.com/ipynbviewer/temp/46ccb8d60bc4953329f884b04452879a/first_approach_neural_networks_p1.html?t=1670380747444#Propagaci%C3%B3n-hacia-delante">¶</a></h3><ul>
<li><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-22-Frame" tabindex="0" style="position: relative;" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;msup&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo stretchy=&quot;false&quot;&gt;[&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;X&lt;/mi&gt;&lt;/math&gt;" role="presentation"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-918" style="width: 4.527em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.753em; height: 0px; font-size: 120%;"><span style="position: absolute; clip: rect(1.134em, 1003.75em, 2.384em, -999.997em); top: -2.199em; left: 0em;"><span class="mrow" id="MathJax-Span-919"><span class="msubsup" id="MathJax-Span-920"><span style="display: inline-block; position: relative; width: 1.551em; height: 0px;"><span style="position: absolute; clip: rect(3.098em, 1000.72em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-921" style="font-family: MathJax_Math-italic;">A</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.342em; left: 0.777em;"><span class="texatom" id="MathJax-Span-922"><span class="mrow" id="MathJax-Span-923"><span class="mo" id="MathJax-Span-924" style="font-size: 70.7%; font-family: MathJax_Main;">[</span><span class="mn" id="MathJax-Span-925" style="font-size: 70.7%; font-family: MathJax_Main;">0</span><span class="mo" id="MathJax-Span-926" style="font-size: 70.7%; font-family: MathJax_Main;">]</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mo" id="MathJax-Span-927" style="font-family: MathJax_Main; padding-left: 0.301em;">=</span><span class="mi" id="MathJax-Span-928" style="font-family: MathJax_Math-italic; padding-left: 0.301em;">X<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.205em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.218em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>A</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">[</mo><mn>0</mn><mo stretchy="false">]</mo></mrow></msup><mo>=</mo><mi>X</mi></math></span></span><script type="math/tex" id="MathJax-Element-22">A^{[0]} = X</script>: 784 * m</li>
<li><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-23-Frame" tabindex="0" style="position: relative;" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;msup&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo stretchy=&quot;false&quot;&gt;[&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;]&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;X&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;" role="presentation"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-929" style="width: 5.36em; display: inline-block;"><span style="display: inline-block; position: relative; width: 4.467em; height: 0px; font-size: 120%;"><span style="position: absolute; clip: rect(1.134em, 1004.47em, 2.384em, -999.997em); top: -2.199em; left: 0em;"><span class="mrow" id="MathJax-Span-930"><span class="msubsup" id="MathJax-Span-931"><span style="display: inline-block; position: relative; width: 1.848em; height: 0px;"><span style="position: absolute; clip: rect(3.098em, 1000.72em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-932" style="font-family: MathJax_Math-italic;">A</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.342em; left: 0.777em;"><span class="texatom" id="MathJax-Span-933"><span class="mrow" id="MathJax-Span-934"><span class="mo" id="MathJax-Span-935" style="font-size: 70.7%; font-family: MathJax_Main;">[</span><span class="mn" id="MathJax-Span-936" style="font-size: 70.7%; font-family: MathJax_Main;">0</span><span class="mo" id="MathJax-Span-937" style="font-size: 70.7%; font-family: MathJax_Main;">]</span><span class="mi" id="MathJax-Span-938" style="font-size: 70.7%; font-family: MathJax_Math-italic;">t</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mo" id="MathJax-Span-939" style="font-family: MathJax_Main; padding-left: 0.301em;">=</span><span class="msubsup" id="MathJax-Span-940" style="padding-left: 0.301em;"><span style="display: inline-block; position: relative; width: 1.253em; height: 0px;"><span style="position: absolute; clip: rect(3.158em, 1000.84em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-941" style="font-family: MathJax_Math-italic;">X<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.342em; left: 0.896em;"><span class="texatom" id="MathJax-Span-942"><span class="mrow" id="MathJax-Span-943"><span class="mi" id="MathJax-Span-944" style="font-size: 70.7%; font-family: MathJax_Math-italic;">t</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.205em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.218em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>A</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">[</mo><mn>0</mn><mo stretchy="false">]</mo><mi>t</mi></mrow></msup><mo>=</mo><msup><mi>X</mi><mrow class="MJX-TeXAtom-ORD"><mi>t</mi></mrow></msup></math></span></span><script type="math/tex" id="MathJax-Element-23">A^{[0]t} = X^{t}</script>: m * 784</li>
<li><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-24-Frame" tabindex="0" style="position: relative;" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;msup&gt;&lt;mi&gt;Z&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo stretchy=&quot;false&quot;&gt;[&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;&amp;#x223C;&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo stretchy=&quot;false&quot;&gt;[&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;" role="presentation"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-945" style="width: 5.479em; display: inline-block;"><span style="display: inline-block; position: relative; width: 4.527em; height: 0px; font-size: 120%;"><span style="position: absolute; clip: rect(1.134em, 1004.53em, 2.384em, -999.997em); top: -2.199em; left: 0em;"><span class="mrow" id="MathJax-Span-946"><span class="msubsup" id="MathJax-Span-947"><span style="display: inline-block; position: relative; width: 1.61em; height: 0px;"><span style="position: absolute; clip: rect(3.158em, 1000.72em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-948" style="font-family: MathJax_Math-italic;">Z<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.063em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.342em; left: 0.777em;"><span class="texatom" id="MathJax-Span-949"><span class="mrow" id="MathJax-Span-950"><span class="mo" id="MathJax-Span-951" style="font-size: 70.7%; font-family: MathJax_Main;">[</span><span class="mn" id="MathJax-Span-952" style="font-size: 70.7%; font-family: MathJax_Main;">1</span><span class="mo" id="MathJax-Span-953" style="font-size: 70.7%; font-family: MathJax_Main;">]</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mo" id="MathJax-Span-954" style="font-family: MathJax_Main; padding-left: 0.301em;">∼</span><span class="msubsup" id="MathJax-Span-955" style="padding-left: 0.301em;"><span style="display: inline-block; position: relative; width: 1.551em; height: 0px;"><span style="position: absolute; clip: rect(3.098em, 1000.72em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-956" style="font-family: MathJax_Math-italic;">A</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.342em; left: 0.777em;"><span class="texatom" id="MathJax-Span-957"><span class="mrow" id="MathJax-Span-958"><span class="mo" id="MathJax-Span-959" style="font-size: 70.7%; font-family: MathJax_Main;">[</span><span class="mn" id="MathJax-Span-960" style="font-size: 70.7%; font-family: MathJax_Main;">1</span><span class="mo" id="MathJax-Span-961" style="font-size: 70.7%; font-family: MathJax_Main;">]</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.205em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.218em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>Z</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">[</mo><mn>1</mn><mo stretchy="false">]</mo></mrow></msup><mo>∼</mo><msup><mi>A</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">[</mo><mn>1</mn><mo stretchy="false">]</mo></mrow></msup></math></span></span><script type="math/tex" id="MathJax-Element-24">Z^{[1]} \sim A^{[1]}</script>: 10 * m</li>
<li><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-25-Frame" tabindex="0" style="position: relative;" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;msup&gt;&lt;mi&gt;W&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo stretchy=&quot;false&quot;&gt;[&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;" role="presentation"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-962" style="width: 2.384em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.967em; height: 0px; font-size: 120%;"><span style="position: absolute; clip: rect(1.134em, 1001.97em, 2.384em, -999.997em); top: -2.199em; left: 0em;"><span class="mrow" id="MathJax-Span-963"><span class="msubsup" id="MathJax-Span-964"><span style="display: inline-block; position: relative; width: 1.967em; height: 0px;"><span style="position: absolute; clip: rect(3.158em, 1001.07em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-965" style="font-family: MathJax_Math-italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.122em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.342em; left: 1.134em;"><span class="texatom" id="MathJax-Span-966"><span class="mrow" id="MathJax-Span-967"><span class="mo" id="MathJax-Span-968" style="font-size: 70.7%; font-family: MathJax_Main;">[</span><span class="mn" id="MathJax-Span-969" style="font-size: 70.7%; font-family: MathJax_Main;">1</span><span class="mo" id="MathJax-Span-970" style="font-size: 70.7%; font-family: MathJax_Main;">]</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.205em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.218em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>W</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">[</mo><mn>1</mn><mo stretchy="false">]</mo></mrow></msup></math></span></span><script type="math/tex" id="MathJax-Element-25">W^{[1]}</script>: 10 * 784 (según <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-26-Frame" tabindex="0" style="position: relative;" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;msup&gt;&lt;mi&gt;W&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo stretchy=&quot;false&quot;&gt;[&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;msup&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo stretchy=&quot;false&quot;&gt;[&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;&amp;#x223C;&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;Z&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo stretchy=&quot;false&quot;&gt;[&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;" role="presentation"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-971" style="width: 7.801em; display: inline-block;"><span style="display: inline-block; position: relative; width: 6.491em; height: 0px; font-size: 120%;"><span style="position: absolute; clip: rect(1.134em, 1006.49em, 2.384em, -999.997em); top: -2.199em; left: 0em;"><span class="mrow" id="MathJax-Span-972"><span class="msubsup" id="MathJax-Span-973"><span style="display: inline-block; position: relative; width: 1.967em; height: 0px;"><span style="position: absolute; clip: rect(3.158em, 1001.07em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-974" style="font-family: MathJax_Math-italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.122em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.342em; left: 1.134em;"><span class="texatom" id="MathJax-Span-975"><span class="mrow" id="MathJax-Span-976"><span class="mo" id="MathJax-Span-977" style="font-size: 70.7%; font-family: MathJax_Main;">[</span><span class="mn" id="MathJax-Span-978" style="font-size: 70.7%; font-family: MathJax_Main;">1</span><span class="mo" id="MathJax-Span-979" style="font-size: 70.7%; font-family: MathJax_Main;">]</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="msubsup" id="MathJax-Span-980"><span style="display: inline-block; position: relative; width: 1.551em; height: 0px;"><span style="position: absolute; clip: rect(3.098em, 1000.72em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-981" style="font-family: MathJax_Math-italic;">A</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.342em; left: 0.777em;"><span class="texatom" id="MathJax-Span-982"><span class="mrow" id="MathJax-Span-983"><span class="mo" id="MathJax-Span-984" style="font-size: 70.7%; font-family: MathJax_Main;">[</span><span class="mn" id="MathJax-Span-985" style="font-size: 70.7%; font-family: MathJax_Main;">0</span><span class="mo" id="MathJax-Span-986" style="font-size: 70.7%; font-family: MathJax_Main;">]</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mo" id="MathJax-Span-987" style="font-family: MathJax_Main; padding-left: 0.301em;">∼</span><span class="msubsup" id="MathJax-Span-988" style="padding-left: 0.301em;"><span style="display: inline-block; position: relative; width: 1.61em; height: 0px;"><span style="position: absolute; clip: rect(3.158em, 1000.72em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-989" style="font-family: MathJax_Math-italic;">Z<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.063em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.342em; left: 0.777em;"><span class="texatom" id="MathJax-Span-990"><span class="mrow" id="MathJax-Span-991"><span class="mo" id="MathJax-Span-992" style="font-size: 70.7%; font-family: MathJax_Main;">[</span><span class="mn" id="MathJax-Span-993" style="font-size: 70.7%; font-family: MathJax_Main;">1</span><span class="mo" id="MathJax-Span-994" style="font-size: 70.7%; font-family: MathJax_Main;">]</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.205em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.218em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>W</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">[</mo><mn>1</mn><mo stretchy="false">]</mo></mrow></msup><msup><mi>A</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">[</mo><mn>0</mn><mo stretchy="false">]</mo></mrow></msup><mo>∼</mo><msup><mi>Z</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">[</mo><mn>1</mn><mo stretchy="false">]</mo></mrow></msup></math></span></span><script type="math/tex" id="MathJax-Element-26">W^{[1]}A^{[0]} \sim Z^{[1]}</script>)</li>
<li><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-27-Frame" tabindex="0" style="position: relative;" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;msup&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo stretchy=&quot;false&quot;&gt;[&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;" role="presentation"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-995" style="width: 1.967em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.61em; height: 0px; font-size: 120%;"><span style="position: absolute; clip: rect(1.134em, 1001.61em, 2.384em, -999.997em); top: -2.199em; left: 0em;"><span class="mrow" id="MathJax-Span-996"><span class="msubsup" id="MathJax-Span-997"><span style="display: inline-block; position: relative; width: 1.61em; height: 0px;"><span style="position: absolute; clip: rect(3.158em, 1000.78em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-998" style="font-family: MathJax_Math-italic;">B</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.342em; left: 0.777em;"><span class="texatom" id="MathJax-Span-999"><span class="mrow" id="MathJax-Span-1000"><span class="mo" id="MathJax-Span-1001" style="font-size: 70.7%; font-family: MathJax_Main;">[</span><span class="mn" id="MathJax-Span-1002" style="font-size: 70.7%; font-family: MathJax_Main;">1</span><span class="mo" id="MathJax-Span-1003" style="font-size: 70.7%; font-family: MathJax_Main;">]</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.205em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.218em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>B</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">[</mo><mn>1</mn><mo stretchy="false">]</mo></mrow></msup></math></span></span><script type="math/tex" id="MathJax-Element-27">B^{[1]}</script>: 10 <em> 1 (10 </em> m)</li>
<li><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-28-Frame" tabindex="0" style="position: relative;" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;msup&gt;&lt;mi&gt;Z&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo stretchy=&quot;false&quot;&gt;[&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;&amp;#x223C;&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo stretchy=&quot;false&quot;&gt;[&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;" role="presentation"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-1004" style="width: 5.479em; display: inline-block;"><span style="display: inline-block; position: relative; width: 4.527em; height: 0px; font-size: 120%;"><span style="position: absolute; clip: rect(1.134em, 1004.53em, 2.384em, -999.997em); top: -2.199em; left: 0em;"><span class="mrow" id="MathJax-Span-1005"><span class="msubsup" id="MathJax-Span-1006"><span style="display: inline-block; position: relative; width: 1.61em; height: 0px;"><span style="position: absolute; clip: rect(3.158em, 1000.72em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-1007" style="font-family: MathJax_Math-italic;">Z<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.063em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.342em; left: 0.777em;"><span class="texatom" id="MathJax-Span-1008"><span class="mrow" id="MathJax-Span-1009"><span class="mo" id="MathJax-Span-1010" style="font-size: 70.7%; font-family: MathJax_Main;">[</span><span class="mn" id="MathJax-Span-1011" style="font-size: 70.7%; font-family: MathJax_Main;">2</span><span class="mo" id="MathJax-Span-1012" style="font-size: 70.7%; font-family: MathJax_Main;">]</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mo" id="MathJax-Span-1013" style="font-family: MathJax_Main; padding-left: 0.301em;">∼</span><span class="msubsup" id="MathJax-Span-1014" style="padding-left: 0.301em;"><span style="display: inline-block; position: relative; width: 1.551em; height: 0px;"><span style="position: absolute; clip: rect(3.098em, 1000.72em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-1015" style="font-family: MathJax_Math-italic;">A</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.342em; left: 0.777em;"><span class="texatom" id="MathJax-Span-1016"><span class="mrow" id="MathJax-Span-1017"><span class="mo" id="MathJax-Span-1018" style="font-size: 70.7%; font-family: MathJax_Main;">[</span><span class="mn" id="MathJax-Span-1019" style="font-size: 70.7%; font-family: MathJax_Main;">2</span><span class="mo" id="MathJax-Span-1020" style="font-size: 70.7%; font-family: MathJax_Main;">]</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.205em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.218em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>Z</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">[</mo><mn>2</mn><mo stretchy="false">]</mo></mrow></msup><mo>∼</mo><msup><mi>A</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">[</mo><mn>2</mn><mo stretchy="false">]</mo></mrow></msup></math></span></span><script type="math/tex" id="MathJax-Element-28">Z^{[2]} \sim A^{[2]}</script>: 10 * m</li>
<li><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-29-Frame" tabindex="0" style="position: relative;" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;msup&gt;&lt;mi&gt;W&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo stretchy=&quot;false&quot;&gt;[&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;" role="presentation"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-1021" style="width: 2.384em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.967em; height: 0px; font-size: 120%;"><span style="position: absolute; clip: rect(1.134em, 1001.97em, 2.384em, -999.997em); top: -2.199em; left: 0em;"><span class="mrow" id="MathJax-Span-1022"><span class="msubsup" id="MathJax-Span-1023"><span style="display: inline-block; position: relative; width: 1.967em; height: 0px;"><span style="position: absolute; clip: rect(3.158em, 1001.07em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-1024" style="font-family: MathJax_Math-italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.122em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.342em; left: 1.134em;"><span class="texatom" id="MathJax-Span-1025"><span class="mrow" id="MathJax-Span-1026"><span class="mo" id="MathJax-Span-1027" style="font-size: 70.7%; font-family: MathJax_Main;">[</span><span class="mn" id="MathJax-Span-1028" style="font-size: 70.7%; font-family: MathJax_Main;">2</span><span class="mo" id="MathJax-Span-1029" style="font-size: 70.7%; font-family: MathJax_Main;">]</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.205em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.218em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>W</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">[</mo><mn>2</mn><mo stretchy="false">]</mo></mrow></msup></math></span></span><script type="math/tex" id="MathJax-Element-29">W^{[2]}</script>: 10 * 10 (según <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-30-Frame" tabindex="0" style="position: relative;" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;msup&gt;&lt;mi&gt;W&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo stretchy=&quot;false&quot;&gt;[&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;msup&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo stretchy=&quot;false&quot;&gt;[&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;&amp;#x223C;&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;Z&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo stretchy=&quot;false&quot;&gt;[&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;" role="presentation"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-1030" style="width: 7.801em; display: inline-block;"><span style="display: inline-block; position: relative; width: 6.491em; height: 0px; font-size: 120%;"><span style="position: absolute; clip: rect(1.134em, 1006.49em, 2.384em, -999.997em); top: -2.199em; left: 0em;"><span class="mrow" id="MathJax-Span-1031"><span class="msubsup" id="MathJax-Span-1032"><span style="display: inline-block; position: relative; width: 1.967em; height: 0px;"><span style="position: absolute; clip: rect(3.158em, 1001.07em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-1033" style="font-family: MathJax_Math-italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.122em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.342em; left: 1.134em;"><span class="texatom" id="MathJax-Span-1034"><span class="mrow" id="MathJax-Span-1035"><span class="mo" id="MathJax-Span-1036" style="font-size: 70.7%; font-family: MathJax_Main;">[</span><span class="mn" id="MathJax-Span-1037" style="font-size: 70.7%; font-family: MathJax_Main;">2</span><span class="mo" id="MathJax-Span-1038" style="font-size: 70.7%; font-family: MathJax_Main;">]</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="msubsup" id="MathJax-Span-1039"><span style="display: inline-block; position: relative; width: 1.551em; height: 0px;"><span style="position: absolute; clip: rect(3.098em, 1000.72em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-1040" style="font-family: MathJax_Math-italic;">A</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.342em; left: 0.777em;"><span class="texatom" id="MathJax-Span-1041"><span class="mrow" id="MathJax-Span-1042"><span class="mo" id="MathJax-Span-1043" style="font-size: 70.7%; font-family: MathJax_Main;">[</span><span class="mn" id="MathJax-Span-1044" style="font-size: 70.7%; font-family: MathJax_Main;">1</span><span class="mo" id="MathJax-Span-1045" style="font-size: 70.7%; font-family: MathJax_Main;">]</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mo" id="MathJax-Span-1046" style="font-family: MathJax_Main; padding-left: 0.301em;">∼</span><span class="msubsup" id="MathJax-Span-1047" style="padding-left: 0.301em;"><span style="display: inline-block; position: relative; width: 1.61em; height: 0px;"><span style="position: absolute; clip: rect(3.158em, 1000.72em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-1048" style="font-family: MathJax_Math-italic;">Z<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.063em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.342em; left: 0.777em;"><span class="texatom" id="MathJax-Span-1049"><span class="mrow" id="MathJax-Span-1050"><span class="mo" id="MathJax-Span-1051" style="font-size: 70.7%; font-family: MathJax_Main;">[</span><span class="mn" id="MathJax-Span-1052" style="font-size: 70.7%; font-family: MathJax_Main;">2</span><span class="mo" id="MathJax-Span-1053" style="font-size: 70.7%; font-family: MathJax_Main;">]</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.205em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.218em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>W</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">[</mo><mn>2</mn><mo stretchy="false">]</mo></mrow></msup><msup><mi>A</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">[</mo><mn>1</mn><mo stretchy="false">]</mo></mrow></msup><mo>∼</mo><msup><mi>Z</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">[</mo><mn>2</mn><mo stretchy="false">]</mo></mrow></msup></math></span></span><script type="math/tex" id="MathJax-Element-30">W^{[2]}A^{[1]} \sim Z^{[2]}</script>)</li>
<li><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-31-Frame" tabindex="0" style="position: relative;" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;msup&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo stretchy=&quot;false&quot;&gt;[&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;" role="presentation"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-1054" style="width: 1.967em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.61em; height: 0px; font-size: 120%;"><span style="position: absolute; clip: rect(1.134em, 1001.61em, 2.384em, -999.997em); top: -2.199em; left: 0em;"><span class="mrow" id="MathJax-Span-1055"><span class="msubsup" id="MathJax-Span-1056"><span style="display: inline-block; position: relative; width: 1.61em; height: 0px;"><span style="position: absolute; clip: rect(3.158em, 1000.78em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-1057" style="font-family: MathJax_Math-italic;">B</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.342em; left: 0.777em;"><span class="texatom" id="MathJax-Span-1058"><span class="mrow" id="MathJax-Span-1059"><span class="mo" id="MathJax-Span-1060" style="font-size: 70.7%; font-family: MathJax_Main;">[</span><span class="mn" id="MathJax-Span-1061" style="font-size: 70.7%; font-family: MathJax_Main;">2</span><span class="mo" id="MathJax-Span-1062" style="font-size: 70.7%; font-family: MathJax_Main;">]</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.205em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.218em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>B</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">[</mo><mn>2</mn><mo stretchy="false">]</mo></mrow></msup></math></span></span><script type="math/tex" id="MathJax-Element-31">B^{[2]}</script>: 10 <em> 1 (10 </em> m)</li>
</ul>
<h3 id="Propagación-hacia-atrás">Propagación hacia atrás<a class="anchor-link" href="https://htmtopdf.herokuapp.com/ipynbviewer/temp/46ccb8d60bc4953329f884b04452879a/first_approach_neural_networks_p1.html?t=1670380747444#Propagaci%C3%B3n-hacia-atr%C3%A1s">¶</a></h3><ul>
<li><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-32-Frame" tabindex="0" style="position: relative;" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;msup&gt;&lt;mi&gt;Z&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo stretchy=&quot;false&quot;&gt;[&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;" role="presentation"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-1063" style="width: 2.622em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.146em; height: 0px; font-size: 120%;"><span style="position: absolute; clip: rect(1.134em, 1002.15em, 2.384em, -999.997em); top: -2.199em; left: 0em;"><span class="mrow" id="MathJax-Span-1064"><span class="mi" id="MathJax-Span-1065" style="font-family: MathJax_Math-italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="msubsup" id="MathJax-Span-1066"><span style="display: inline-block; position: relative; width: 1.61em; height: 0px;"><span style="position: absolute; clip: rect(3.158em, 1000.72em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-1067" style="font-family: MathJax_Math-italic;">Z<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.063em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.342em; left: 0.777em;"><span class="texatom" id="MathJax-Span-1068"><span class="mrow" id="MathJax-Span-1069"><span class="mo" id="MathJax-Span-1070" style="font-size: 70.7%; font-family: MathJax_Main;">[</span><span class="mn" id="MathJax-Span-1071" style="font-size: 70.7%; font-family: MathJax_Main;">2</span><span class="mo" id="MathJax-Span-1072" style="font-size: 70.7%; font-family: MathJax_Main;">]</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.205em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.218em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><msup><mi>Z</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">[</mo><mn>2</mn><mo stretchy="false">]</mo></mrow></msup></math></span></span><script type="math/tex" id="MathJax-Element-32">dZ^{[2]}</script>: 10 * m (<span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-33-Frame" tabindex="0" style="position: relative;" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mtext&gt;&amp;#xA0;&lt;/mtext&gt;&lt;msup&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo stretchy=&quot;false&quot;&gt;[&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;" role="presentation"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-1073" style="width: 2.146em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.789em; height: 0px; font-size: 120%;"><span style="position: absolute; clip: rect(1.134em, 1001.79em, 2.384em, -999.997em); top: -2.199em; left: 0em;"><span class="mrow" id="MathJax-Span-1074"><span class="mtext" id="MathJax-Span-1075" style="font-family: MathJax_Main;">&nbsp;</span><span class="msubsup" id="MathJax-Span-1076"><span style="display: inline-block; position: relative; width: 1.551em; height: 0px;"><span style="position: absolute; clip: rect(3.098em, 1000.72em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-1077" style="font-family: MathJax_Math-italic;">A</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.342em; left: 0.777em;"><span class="texatom" id="MathJax-Span-1078"><span class="mrow" id="MathJax-Span-1079"><span class="mo" id="MathJax-Span-1080" style="font-size: 70.7%; font-family: MathJax_Main;">[</span><span class="mn" id="MathJax-Span-1081" style="font-size: 70.7%; font-family: MathJax_Main;">2</span><span class="mo" id="MathJax-Span-1082" style="font-size: 70.7%; font-family: MathJax_Main;">]</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.205em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.218em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>&nbsp;</mtext><msup><mi>A</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">[</mo><mn>2</mn><mo stretchy="false">]</mo></mrow></msup></math></span></span><script type="math/tex" id="MathJax-Element-33">~A^{[2]}</script>)</li>
<li><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-34-Frame" tabindex="0" style="position: relative;" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;msup&gt;&lt;mi&gt;W&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo stretchy=&quot;false&quot;&gt;[&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;" role="presentation"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-1083" style="width: 3.039em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.503em; height: 0px; font-size: 120%;"><span style="position: absolute; clip: rect(1.134em, 1002.5em, 2.384em, -999.997em); top: -2.199em; left: 0em;"><span class="mrow" id="MathJax-Span-1084"><span class="mi" id="MathJax-Span-1085" style="font-family: MathJax_Math-italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="msubsup" id="MathJax-Span-1086"><span style="display: inline-block; position: relative; width: 1.967em; height: 0px;"><span style="position: absolute; clip: rect(3.158em, 1001.07em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-1087" style="font-family: MathJax_Math-italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.122em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.342em; left: 1.134em;"><span class="texatom" id="MathJax-Span-1088"><span class="mrow" id="MathJax-Span-1089"><span class="mo" id="MathJax-Span-1090" style="font-size: 70.7%; font-family: MathJax_Main;">[</span><span class="mn" id="MathJax-Span-1091" style="font-size: 70.7%; font-family: MathJax_Main;">2</span><span class="mo" id="MathJax-Span-1092" style="font-size: 70.7%; font-family: MathJax_Main;">]</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.205em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.218em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><msup><mi>W</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">[</mo><mn>2</mn><mo stretchy="false">]</mo></mrow></msup></math></span></span><script type="math/tex" id="MathJax-Element-34">dW^{[2]}</script>: 10 * 10</li>
<li><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-35-Frame" tabindex="0" style="position: relative;" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;msup&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo stretchy=&quot;false&quot;&gt;[&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;" role="presentation"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-1093" style="width: 2.622em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.146em; height: 0px; font-size: 120%;"><span style="position: absolute; clip: rect(1.134em, 1002.15em, 2.384em, -999.997em); top: -2.199em; left: 0em;"><span class="mrow" id="MathJax-Span-1094"><span class="mi" id="MathJax-Span-1095" style="font-family: MathJax_Math-italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="msubsup" id="MathJax-Span-1096"><span style="display: inline-block; position: relative; width: 1.61em; height: 0px;"><span style="position: absolute; clip: rect(3.158em, 1000.78em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-1097" style="font-family: MathJax_Math-italic;">B</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.342em; left: 0.777em;"><span class="texatom" id="MathJax-Span-1098"><span class="mrow" id="MathJax-Span-1099"><span class="mo" id="MathJax-Span-1100" style="font-size: 70.7%; font-family: MathJax_Main;">[</span><span class="mn" id="MathJax-Span-1101" style="font-size: 70.7%; font-family: MathJax_Main;">2</span><span class="mo" id="MathJax-Span-1102" style="font-size: 70.7%; font-family: MathJax_Main;">]</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.205em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.218em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><msup><mi>B</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">[</mo><mn>2</mn><mo stretchy="false">]</mo></mrow></msup></math></span></span><script type="math/tex" id="MathJax-Element-35">dB^{[2]}</script>: 10 * 1</li>
<li><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-36-Frame" tabindex="0" style="position: relative;" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;msup&gt;&lt;mi&gt;Z&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo stretchy=&quot;false&quot;&gt;[&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;" role="presentation"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-1103" style="width: 2.622em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.146em; height: 0px; font-size: 120%;"><span style="position: absolute; clip: rect(1.134em, 1002.15em, 2.384em, -999.997em); top: -2.199em; left: 0em;"><span class="mrow" id="MathJax-Span-1104"><span class="mi" id="MathJax-Span-1105" style="font-family: MathJax_Math-italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="msubsup" id="MathJax-Span-1106"><span style="display: inline-block; position: relative; width: 1.61em; height: 0px;"><span style="position: absolute; clip: rect(3.158em, 1000.72em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-1107" style="font-family: MathJax_Math-italic;">Z<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.063em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.342em; left: 0.777em;"><span class="texatom" id="MathJax-Span-1108"><span class="mrow" id="MathJax-Span-1109"><span class="mo" id="MathJax-Span-1110" style="font-size: 70.7%; font-family: MathJax_Main;">[</span><span class="mn" id="MathJax-Span-1111" style="font-size: 70.7%; font-family: MathJax_Main;">1</span><span class="mo" id="MathJax-Span-1112" style="font-size: 70.7%; font-family: MathJax_Main;">]</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.205em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.218em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><msup><mi>Z</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">[</mo><mn>1</mn><mo stretchy="false">]</mo></mrow></msup></math></span></span><script type="math/tex" id="MathJax-Element-36">dZ^{[1]}</script>: 10 * m (<span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-37-Frame" tabindex="0" style="position: relative;" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mtext&gt;&amp;#xA0;&lt;/mtext&gt;&lt;msup&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo stretchy=&quot;false&quot;&gt;[&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;" role="presentation"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-1113" style="width: 2.146em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.789em; height: 0px; font-size: 120%;"><span style="position: absolute; clip: rect(1.134em, 1001.79em, 2.384em, -999.997em); top: -2.199em; left: 0em;"><span class="mrow" id="MathJax-Span-1114"><span class="mtext" id="MathJax-Span-1115" style="font-family: MathJax_Main;">&nbsp;</span><span class="msubsup" id="MathJax-Span-1116"><span style="display: inline-block; position: relative; width: 1.551em; height: 0px;"><span style="position: absolute; clip: rect(3.098em, 1000.72em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-1117" style="font-family: MathJax_Math-italic;">A</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.342em; left: 0.777em;"><span class="texatom" id="MathJax-Span-1118"><span class="mrow" id="MathJax-Span-1119"><span class="mo" id="MathJax-Span-1120" style="font-size: 70.7%; font-family: MathJax_Main;">[</span><span class="mn" id="MathJax-Span-1121" style="font-size: 70.7%; font-family: MathJax_Main;">1</span><span class="mo" id="MathJax-Span-1122" style="font-size: 70.7%; font-family: MathJax_Main;">]</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.205em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.218em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>&nbsp;</mtext><msup><mi>A</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">[</mo><mn>1</mn><mo stretchy="false">]</mo></mrow></msup></math></span></span><script type="math/tex" id="MathJax-Element-37">~A^{[1]}</script>)</li>
<li><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-38-Frame" tabindex="0" style="position: relative;" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;msup&gt;&lt;mi&gt;W&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo stretchy=&quot;false&quot;&gt;[&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;" role="presentation"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-1123" style="width: 3.039em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.503em; height: 0px; font-size: 120%;"><span style="position: absolute; clip: rect(1.134em, 1002.5em, 2.384em, -999.997em); top: -2.199em; left: 0em;"><span class="mrow" id="MathJax-Span-1124"><span class="mi" id="MathJax-Span-1125" style="font-family: MathJax_Math-italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="msubsup" id="MathJax-Span-1126"><span style="display: inline-block; position: relative; width: 1.967em; height: 0px;"><span style="position: absolute; clip: rect(3.158em, 1001.07em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-1127" style="font-family: MathJax_Math-italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.122em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.342em; left: 1.134em;"><span class="texatom" id="MathJax-Span-1128"><span class="mrow" id="MathJax-Span-1129"><span class="mo" id="MathJax-Span-1130" style="font-size: 70.7%; font-family: MathJax_Main;">[</span><span class="mn" id="MathJax-Span-1131" style="font-size: 70.7%; font-family: MathJax_Main;">1</span><span class="mo" id="MathJax-Span-1132" style="font-size: 70.7%; font-family: MathJax_Main;">]</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.205em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.218em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><msup><mi>W</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">[</mo><mn>1</mn><mo stretchy="false">]</mo></mrow></msup></math></span></span><script type="math/tex" id="MathJax-Element-38">dW^{[1]}</script>: 10 * 10</li>
<li><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-39-Frame" tabindex="0" style="position: relative;" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;msup&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo stretchy=&quot;false&quot;&gt;[&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;" role="presentation"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-1133" style="width: 2.622em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.146em; height: 0px; font-size: 120%;"><span style="position: absolute; clip: rect(1.134em, 1002.15em, 2.384em, -999.997em); top: -2.199em; left: 0em;"><span class="mrow" id="MathJax-Span-1134"><span class="mi" id="MathJax-Span-1135" style="font-family: MathJax_Math-italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="msubsup" id="MathJax-Span-1136"><span style="display: inline-block; position: relative; width: 1.61em; height: 0px;"><span style="position: absolute; clip: rect(3.158em, 1000.78em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-1137" style="font-family: MathJax_Math-italic;">B</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.342em; left: 0.777em;"><span class="texatom" id="MathJax-Span-1138"><span class="mrow" id="MathJax-Span-1139"><span class="mo" id="MathJax-Span-1140" style="font-size: 70.7%; font-family: MathJax_Main;">[</span><span class="mn" id="MathJax-Span-1141" style="font-size: 70.7%; font-family: MathJax_Main;">1</span><span class="mo" id="MathJax-Span-1142" style="font-size: 70.7%; font-family: MathJax_Main;">]</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.205em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.218em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><msup><mi>B</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">[</mo><mn>1</mn><mo stretchy="false">]</mo></mrow></msup></math></span></span><script type="math/tex" id="MathJax-Element-39">dB^{[1]}</script>: 10 * 1</li>
</ul>
<hr>
<h2 id="Conceptos">Conceptos<a class="anchor-link" href="https://htmtopdf.herokuapp.com/ipynbviewer/temp/46ccb8d60bc4953329f884b04452879a/first_approach_neural_networks_p1.html?t=1670380747444#Conceptos">¶</a></h2><h3 id="Red-neuronal1">Red neuronal<sup>1</sup><a class="anchor-link" href="https://htmtopdf.herokuapp.com/ipynbviewer/temp/46ccb8d60bc4953329f884b04452879a/first_approach_neural_networks_p1.html?t=1670380747444#Red-neuronal1">¶</a></h3><p>Se trata de un campo de estudio de la informática, que trata de "reflejar" el comportamiento del cerebro humano en el reconocimiento de patrones.<sup>[A]</sup></p>
<p>Una red se ve compuesta por:<sup>[A]</sup></p>
<ul>
<li>Capa de entrada (<em>input layer</em>).</li>
<li>Capas ocultas (<em>deep neural network</em> ó <em>hidden layers</em>).</li>
<li>Capa de sálida (<em>output layer</em>).</li>
</ul>
<h4 id="Funcionamiento">Funcionamiento<a class="anchor-link" href="https://htmtopdf.herokuapp.com/ipynbviewer/temp/46ccb8d60bc4953329f884b04452879a/first_approach_neural_networks_p1.html?t=1670380747444#Funcionamiento">¶</a></h4><ul>
<li>Cada nodo se conecta a otro, con un peso asociado.</li>
<li>Si la salida de un nodo se encuentra por encima de un umbral (<em>threshold</em>), se activa, mandando sus datos a la siguiente capa de la red.</li>
</ul>
<center><img src="./first_approach_neural_networks_p1_files/kP4Dma1.jpg" width="" height=""></center><p><em>Elaboración propia.</em><sup>[B]</sup></p>
<h3 id="Capas2">Capas<sup>2</sup><a class="anchor-link" href="https://htmtopdf.herokuapp.com/ipynbviewer/temp/46ccb8d60bc4953329f884b04452879a/first_approach_neural_networks_p1.html?t=1670380747444#Capas2">¶</a></h3><p>Las capas son el metacomponente principal de las redes neuronales. En cuanto a la <strong>red oculta</strong>, esta realiza distintas funciones que se encargan de la transformación (análisis) de los datos.<sup>[C]</sup></p>
<h4 id="Neuronas-(nodos)">Neuronas (nodos)<a class="anchor-link" href="https://htmtopdf.herokuapp.com/ipynbviewer/temp/46ccb8d60bc4953329f884b04452879a/first_approach_neural_networks_p1.html?t=1670380747444#Neuronas-(nodos)">¶</a></h4><p>Las neuronas, son los componentes de las capas, comunicadas por conexiones, las cuales tienen un peso asignado.<sup>[D]</sup></p>
<h3 id="Funciones-de-activación3-[E]">Funciones de activación<sup>3</sup> <sup>[E]</sup><a class="anchor-link" href="https://htmtopdf.herokuapp.com/ipynbviewer/temp/46ccb8d60bc4953329f884b04452879a/first_approach_neural_networks_p1.html?t=1670380747444#Funciones-de-activaci%C3%B3n3-[E]">¶</a></h3><p>Si se mantuviese la red de una forma lineal, recordando que, las neuronas de la red reciben una suma ponderada de de sus entradas (más el sesgo), dando el resultado a la siguiente capa, por lo que el resultado (en este caso) sería el equivalente a operar en una sola capa esos valores.</p>
<p>La función de activación se colocará entre el receptor de la siguiente capa y la suma lineal de los componentes de la capa anterior.</p>
<center><img src="./first_approach_neural_networks_p1_files/niNM2kL.jpg" width="" height=""></center><p><em>Elaboración propia.</em></p>
<p>Este ajuste servirá para el posterior proceso de propagación hacia atrás (backwards propagation), en el cual con ayuda de la derivada de la función de costo, se ajustarán los pesos de las conexiones dependiendo de como se ajuste a la predicción esperada.</p>
<p>Algunas funciones son:</p>
<ul>
<li>Sigmoide (logística): tomando en cuenta el <a href="https://es.wikipedia.org/wiki/Problema_de_desvanecimiento_de_gradiente">problema del desvanecimiento de gradiente</a>, se puede usar en clasificación binaria (perro o gato)</li>
<li>Tangente hiperbólica: comprende valores de -1 a 1, dando resultados más específicos que la Sigmoide.</li>
</ul>
<h4 id="ReLU-(unidad-lineal-rectificada)-[E]">ReLU (unidad lineal rectificada) <sup>[E]</sup><a class="anchor-link" href="https://htmtopdf.herokuapp.com/ipynbviewer/temp/46ccb8d60bc4953329f884b04452879a/first_approach_neural_networks_p1.html?t=1670380747444#ReLU-(unidad-lineal-rectificada)-[E]">¶</a></h4><span class="MathJax_Preview" style="color: inherit; display: none;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" id="MathJax-Element-40-Frame" tabindex="0" style="text-align: center; position: relative;" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot; display=&quot;block&quot;&gt;&lt;mtable columnalign=&quot;right left right left right left right left right left right left&quot; rowspacing=&quot;3pt&quot; columnspacing=&quot;0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em&quot; displaystyle=&quot;true&quot;&gt;&lt;mtr&gt;&lt;mtd /&gt;&lt;mtd&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo movablelimits=&quot;true&quot; form=&quot;prefix&quot;&gt;max&lt;/mo&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;/math&gt;" role="presentation"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-1143" style="width: 9.408em; display: inline-block;"><span style="display: inline-block; position: relative; width: 7.801em; height: 0px; font-size: 120%;"><span style="position: absolute; clip: rect(1.253em, 1007.5em, 2.682em, -999.997em); top: -2.199em; left: 0em;"><span class="mrow" id="MathJax-Span-1144"><span class="mtable" id="MathJax-Span-1145" style="padding-right: 0.182em; padding-left: 0.182em;"><span style="display: inline-block; position: relative; width: 7.443em; height: 0px;"><span style="position: absolute; clip: rect(3.812em, 1000em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span style="display: inline-block; position: relative; width: 0em; height: 0px;"><span style="position: absolute; clip: rect(3.812em, 1000em, 4.17em, -999.997em); top: -3.985em; right: 0em;"><span class="mtd" id="MathJax-Span-1146"><span class="mrow" id="MathJax-Span-1147"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.098em, 1007.38em, 4.467em, -999.997em); top: -3.985em; left: 0em;"><span style="display: inline-block; position: relative; width: 7.443em; height: 0px;"><span style="position: absolute; clip: rect(3.039em, 1007.38em, 4.408em, -999.997em); top: -3.985em; left: 0em;"><span class="mtd" id="MathJax-Span-1148"><span class="mrow" id="MathJax-Span-1149"><span class="mi" id="MathJax-Span-1150" style="font-family: MathJax_Math-italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.063em;"></span></span><span class="mo" id="MathJax-Span-1151" style="font-family: MathJax_Main;">(</span><span class="mi" id="MathJax-Span-1152" style="font-family: MathJax_Math-italic;">x</span><span class="mo" id="MathJax-Span-1153" style="font-family: MathJax_Main;">)</span><span class="mo" id="MathJax-Span-1154" style="font-family: MathJax_Main; padding-left: 0.301em;">=</span><span class="mo" id="MathJax-Span-1155" style="font-family: MathJax_Main; padding-left: 0.301em;">max</span><span class="mo" id="MathJax-Span-1156" style="font-family: MathJax_Main;">(</span><span class="mn" id="MathJax-Span-1157" style="font-family: MathJax_Main;">0</span><span class="mo" id="MathJax-Span-1158" style="font-family: MathJax_Main;">,</span><span class="mi" id="MathJax-Span-1159" style="font-family: MathJax_Math-italic; padding-left: 0.182em;">x</span><span class="mo" id="MathJax-Span-1160" style="font-family: MathJax_Main;">)</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.205em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.425em; border-left: 0px solid; width: 0px; height: 1.432em;"></span></span></nobr><span class="MJX_Assistive_MathML MJX_Assistive_MathML_Block" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"><mtr><mtd></mtd><mtd><mi>f</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>=</mo><mo movablelimits="true" form="prefix">max</mo><mo stretchy="false">(</mo><mn>0</mn><mo>,</mo><mi>x</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-40">\begin{align}
    &f(x)=\max(0,x)
\end{align}</script><p>Esta función no se encuentra acotada para números positivos, permitiendo un aprendizaje más rápido de la red.</p>
<h4 id="Softmax-[F],-[G]">Softmax <sup>[F], [G]</sup><a class="anchor-link" href="https://htmtopdf.herokuapp.com/ipynbviewer/temp/46ccb8d60bc4953329f884b04452879a/first_approach_neural_networks_p1.html?t=1670380747444#Softmax-[F],-[G]">¶</a></h4><p>Es un tipo de función la cual soporta "sistemas de clasificación multinomial", siendo útil en el presente caso.</p>
<p>Esta devuelve la distribución de probabilidad de cada una de las clases (posibles categorías, en este caso los dígitos).</p>
<p>Posee la siguiente fórmula:</p>
<span class="MathJax_Preview" style="color: inherit; display: none;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" id="MathJax-Element-41-Frame" tabindex="0" style="text-align: center; position: relative;" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot; display=&quot;block&quot;&gt;&lt;mtable columnalign=&quot;right left right left right left right left right left right left&quot; rowspacing=&quot;3pt&quot; columnspacing=&quot;0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em&quot; displaystyle=&quot;true&quot;&gt;&lt;mtr&gt;&lt;mtd /&gt;&lt;mtd&gt;&lt;mi&gt;&amp;#x03C3;&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mover&gt;&lt;mi&gt;z&lt;/mi&gt;&lt;mo&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;msub&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mtext&gt;&amp;#xA0;&lt;/mtext&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mtext&gt;&amp;#xA0;&lt;/mtext&gt;&lt;mfrac&gt;&lt;msup&gt;&lt;mi&gt;e&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;msub&gt;&lt;mi&gt;z&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mrow&gt;&lt;munderover&gt;&lt;mo&gt;&amp;#x2211;&lt;/mo&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi&gt;j&lt;/mi&gt;&lt;mtext&gt;&amp;#xA0;&lt;/mtext&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mtext&gt;&amp;#xA0;&lt;/mtext&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi&gt;K&lt;/mi&gt;&lt;/mrow&gt;&lt;/munderover&gt;&lt;msup&gt;&lt;mi&gt;e&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;msub&gt;&lt;mi&gt;z&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi&gt;j&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd /&gt;&lt;mtd&gt;&lt;mover&gt;&lt;mi&gt;z&lt;/mi&gt;&lt;mo&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mtext&gt;vector de entrada (input vector).&lt;/mtext&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd /&gt;&lt;mtd&gt;&lt;msub&gt;&lt;mi&gt;z&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mtext&gt;todos los valores del vector de entrada (input vector values).&lt;/mtext&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd /&gt;&lt;mtd&gt;&lt;msup&gt;&lt;mi&gt;e&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;msub&gt;&lt;mi&gt;z&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mtext&gt;valor mayor que 0, peque&amp;#xF1;o si la entrada fue negativa, grande si la entrada lo fue.&lt;/mtext&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd /&gt;&lt;mtd&gt;&lt;mtext&gt;(value greater than 0, if the input was negative the value is small, otherwise it is large.)&lt;/mtext&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd /&gt;&lt;mtd&gt;&lt;mi&gt;&lt;/mi&gt;&lt;munderover&gt;&lt;mo&gt;&amp;#x2211;&lt;/mo&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi&gt;j&lt;/mi&gt;&lt;mtext&gt;&amp;#xA0;&lt;/mtext&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mtext&gt;&amp;#xA0;&lt;/mtext&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi&gt;K&lt;/mi&gt;&lt;/mrow&gt;&lt;/munderover&gt;&lt;msup&gt;&lt;mi&gt;e&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;msub&gt;&lt;mi&gt;z&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi&gt;j&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mtext&gt;normaliza el valor en el rango [0,1].&lt;/mtext&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd /&gt;&lt;mtd&gt;&lt;mtext&gt;(normalizes the value in the range [0,1].)&lt;/mtext&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd /&gt;&lt;mtd&gt;&lt;mi&gt;K&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mtext&gt;n&amp;#xFA;mero de clases (class number).&lt;/mtext&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;/math&gt;" role="presentation"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-1161" style="width: 45.182em; display: inline-block;"><span style="display: inline-block; position: relative; width: 37.622em; height: 0px; font-size: 120%;"><span style="position: absolute; clip: rect(-5.473em, 1037.32em, 9.348em, -999.997em); top: -2.199em; left: 0em;"><span class="mrow" id="MathJax-Span-1162"><span class="mtable" id="MathJax-Span-1163" style="padding-right: 0.182em; padding-left: 0.182em;"><span style="display: inline-block; position: relative; width: 37.265em; height: 0px;"><span style="position: absolute; clip: rect(7.562em, 1000em, 20.777em, -999.997em); top: -13.866em; left: 0em;"><span style="display: inline-block; position: relative; width: 0em; height: 0px;"><span style="position: absolute; clip: rect(3.812em, 1000em, 4.17em, -999.997em); top: -10.116em; right: 0em;"><span class="mtd" id="MathJax-Span-1164"><span class="mrow" id="MathJax-Span-1165"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.812em, 1000em, 4.17em, -999.997em); top: -7.318em; right: 0em;"><span class="mtd" id="MathJax-Span-1213"><span class="mrow" id="MathJax-Span-1214"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.812em, 1000em, 4.17em, -999.997em); top: -5.949em; right: 0em;"><span class="mtd" id="MathJax-Span-1222"><span class="mrow" id="MathJax-Span-1223"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.812em, 1000em, 4.17em, -999.997em); top: -4.64em; right: 0em;"><span class="mtd" id="MathJax-Span-1233"><span class="mrow" id="MathJax-Span-1234"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.812em, 1000em, 4.17em, -999.997em); top: -3.33em; right: 0em;"><span class="mtd" id="MathJax-Span-1248"><span class="mrow" id="MathJax-Span-1249"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.812em, 1000em, 4.17em, -999.997em); top: -1.009em; right: 0em;"><span class="mtd" id="MathJax-Span-1253"><span class="mrow" id="MathJax-Span-1254"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.812em, 1000em, 4.17em, -999.997em); top: 1.372em; right: 0em;"><span class="mtd" id="MathJax-Span-1281"><span class="mrow" id="MathJax-Span-1282"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.812em, 1000em, 4.17em, -999.997em); top: 2.741em; right: 0em;"><span class="mtd" id="MathJax-Span-1286"><span class="mrow" id="MathJax-Span-1287"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 13.872em;"></span></span><span style="position: absolute; clip: rect(7.801em, 1037.15em, 22.622em, -999.997em); top: -15.473em; left: 0em;"><span style="display: inline-block; position: relative; width: 37.265em; height: 0px;"><span style="position: absolute; clip: rect(2.443em, 1008.99em, 5.539em, -999.997em); top: -10.116em; left: 0em;"><span class="mtd" id="MathJax-Span-1166"><span class="mrow" id="MathJax-Span-1167"><span class="mi" id="MathJax-Span-1168" style="font-family: MathJax_Math-italic;">σ<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" id="MathJax-Span-1169" style="font-family: MathJax_Main;">(</span><span class="munderover" id="MathJax-Span-1170"><span style="display: inline-block; position: relative; width: 1.074em; height: 0px;"><span style="position: absolute; clip: rect(3.396em, 1000.48em, 4.17em, -999.997em); top: -3.985em; left: 0.241em;"><span class="mi" id="MathJax-Span-1171" style="font-family: MathJax_Math-italic;">z<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.277em, 1000.96em, 4.17em, -999.997em); top: -4.58em; left: 0.063em;"><span class="mo" id="MathJax-Span-1172" style=""><span style="font-family: MathJax_Main;">→</span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="msubsup" id="MathJax-Span-1173"><span style="display: inline-block; position: relative; width: 0.717em; height: 0px;"><span style="position: absolute; clip: rect(3.039em, 1000.3em, 4.408em, -999.997em); top: -3.985em; left: 0em;"><span class="mo" id="MathJax-Span-1174" style="font-family: MathJax_Main;">)</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.807em; left: 0.42em;"><span class="texatom" id="MathJax-Span-1175"><span class="mrow" id="MathJax-Span-1176"><span class="mi" id="MathJax-Span-1177" style="font-size: 70.7%; font-family: MathJax_Math-italic;">i</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mtext" id="MathJax-Span-1178" style="font-family: MathJax_Main;">&nbsp;</span><span class="mo" id="MathJax-Span-1179" style="font-family: MathJax_Main; padding-left: 0.301em;">=</span><span class="mtext" id="MathJax-Span-1180" style="font-family: MathJax_Main; padding-left: 0.301em;">&nbsp;</span><span class="mfrac" id="MathJax-Span-1181"><span style="display: inline-block; position: relative; width: 4.11em; height: 0px; margin-right: 0.122em; margin-left: 0.122em;"><span style="position: absolute; clip: rect(3.158em, 1001.07em, 4.17em, -999.997em); top: -4.64em; left: 50%; margin-left: -0.533em;"><span class="msubsup" id="MathJax-Span-1182"><span style="display: inline-block; position: relative; width: 1.074em; height: 0px;"><span style="position: absolute; clip: rect(3.396em, 1000.42em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-1183" style="font-family: MathJax_Math-italic;">e</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.342em; left: 0.479em;"><span class="texatom" id="MathJax-Span-1184"><span class="mrow" id="MathJax-Span-1185"><span class="msubsup" id="MathJax-Span-1186"><span style="display: inline-block; position: relative; width: 0.539em; height: 0px;"><span style="position: absolute; clip: rect(3.515em, 1000.36em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-1187" style="font-size: 70.7%; font-family: MathJax_Math-italic;">z<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.866em; left: 0.36em;"><span class="texatom" id="MathJax-Span-1188"><span class="mrow" id="MathJax-Span-1189"><span class="mi" id="MathJax-Span-1190" style="font-size: 50%; font-family: MathJax_Math-italic;">i</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(2.86em, 1003.99em, 4.586em, -999.997em); top: -3.033em; left: 50%; margin-left: -2.021em;"><span class="mrow" id="MathJax-Span-1191"><span class="munderover" id="MathJax-Span-1192"><span style="display: inline-block; position: relative; width: 2.682em; height: 0px;"><span style="position: absolute; clip: rect(3.039em, 1001.01em, 4.408em, -999.997em); top: -3.985em; left: 0em;"><span class="mo" id="MathJax-Span-1193" style="font-family: MathJax_Size1; vertical-align: 0em;">∑</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.336em, 1000.72em, 4.17em, -999.997em); top: -4.461em; left: 1.074em;"><span class="texatom" id="MathJax-Span-1194"><span class="mrow" id="MathJax-Span-1195"><span class="mi" id="MathJax-Span-1196" style="font-size: 70.7%; font-family: MathJax_Math-italic;">K<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.336em, 1001.61em, 4.289em, -999.997em); top: -3.688em; left: 1.074em;"><span class="texatom" id="MathJax-Span-1197"><span class="mrow" id="MathJax-Span-1198"><span class="mi" id="MathJax-Span-1199" style="font-size: 70.7%; font-family: MathJax_Math-italic;">j</span><span class="mtext" id="MathJax-Span-1200" style="font-size: 70.7%; font-family: MathJax_Main;">&nbsp;</span><span class="mo" id="MathJax-Span-1201" style="font-size: 70.7%; font-family: MathJax_Main;">=</span><span class="mtext" id="MathJax-Span-1202" style="font-size: 70.7%; font-family: MathJax_Main;">&nbsp;</span><span class="mn" id="MathJax-Span-1203" style="font-size: 70.7%; font-family: MathJax_Main;">1</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="msubsup" id="MathJax-Span-1204" style="padding-left: 0.182em;"><span style="display: inline-block; position: relative; width: 1.134em; height: 0px;"><span style="position: absolute; clip: rect(3.396em, 1000.42em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-1205" style="font-family: MathJax_Math-italic;">e</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.283em; left: 0.479em;"><span class="texatom" id="MathJax-Span-1206"><span class="mrow" id="MathJax-Span-1207"><span class="msubsup" id="MathJax-Span-1208"><span style="display: inline-block; position: relative; width: 0.598em; height: 0px;"><span style="position: absolute; clip: rect(3.515em, 1000.36em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-1209" style="font-size: 70.7%; font-family: MathJax_Math-italic;">z<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.866em; left: 0.36em;"><span class="texatom" id="MathJax-Span-1210"><span class="mrow" id="MathJax-Span-1211"><span class="mi" id="MathJax-Span-1212" style="font-size: 50%; font-family: MathJax_Math-italic;">j</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(0.836em, 1004.11em, 1.253em, -999.997em); top: -1.307em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 4.11em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.074em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(2.682em, 1016.49em, 4.408em, -999.997em); top: -7.318em; left: 0em;"><span class="mtd" id="MathJax-Span-1215"><span class="mrow" id="MathJax-Span-1216"><span class="munderover" id="MathJax-Span-1217"><span style="display: inline-block; position: relative; width: 1.074em; height: 0px;"><span style="position: absolute; clip: rect(3.396em, 1000.48em, 4.17em, -999.997em); top: -3.985em; left: 0.241em;"><span class="mi" id="MathJax-Span-1218" style="font-family: MathJax_Math-italic;">z<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.277em, 1000.96em, 4.17em, -999.997em); top: -4.58em; left: 0.063em;"><span class="mo" id="MathJax-Span-1219" style=""><span style="font-family: MathJax_Main;">→</span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mo" id="MathJax-Span-1220" style="font-family: MathJax_Main; padding-left: 0.301em;">=</span><span class="mtext" id="MathJax-Span-1221" style="font-family: MathJax_Main; padding-left: 0.301em;">vector de entrada (input vector).</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.039em, 1027.98em, 4.408em, -999.997em); top: -5.949em; left: 0em;"><span class="mtd" id="MathJax-Span-1224"><span class="mrow" id="MathJax-Span-1225"><span class="msubsup" id="MathJax-Span-1226"><span style="display: inline-block; position: relative; width: 0.777em; height: 0px;"><span style="position: absolute; clip: rect(3.396em, 1000.48em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-1227" style="font-family: MathJax_Math-italic;">z<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.807em; left: 0.479em;"><span class="texatom" id="MathJax-Span-1228"><span class="mrow" id="MathJax-Span-1229"><span class="mi" id="MathJax-Span-1230" style="font-size: 70.7%; font-family: MathJax_Math-italic;">i</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mo" id="MathJax-Span-1231" style="font-family: MathJax_Main; padding-left: 0.301em;">=</span><span class="mtext" id="MathJax-Span-1232" style="font-family: MathJax_Main; padding-left: 0.301em;">todos los valores del vector de entrada (input vector values).</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.039em, 1037.09em, 4.348em, -999.997em); top: -4.64em; left: 0em;"><span class="mtd" id="MathJax-Span-1235"><span class="mrow" id="MathJax-Span-1236"><span class="msubsup" id="MathJax-Span-1237"><span style="display: inline-block; position: relative; width: 1.074em; height: 0px;"><span style="position: absolute; clip: rect(3.396em, 1000.42em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-1238" style="font-family: MathJax_Math-italic;">e</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.402em; left: 0.479em;"><span class="texatom" id="MathJax-Span-1239"><span class="mrow" id="MathJax-Span-1240"><span class="msubsup" id="MathJax-Span-1241"><span style="display: inline-block; position: relative; width: 0.539em; height: 0px;"><span style="position: absolute; clip: rect(3.515em, 1000.36em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-1242" style="font-size: 70.7%; font-family: MathJax_Math-italic;">z<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.866em; left: 0.36em;"><span class="texatom" id="MathJax-Span-1243"><span class="mrow" id="MathJax-Span-1244"><span class="mi" id="MathJax-Span-1245" style="font-size: 50%; font-family: MathJax_Math-italic;">i</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mo" id="MathJax-Span-1246" style="font-family: MathJax_Main; padding-left: 0.301em;">=</span><span class="mtext" id="MathJax-Span-1247" style="font-family: MathJax_Main; padding-left: 0.301em;">valor mayor que 0, peque<span style="font-family: STIXGeneral, &quot;Arial Unicode MS&quot;, serif; font-size: 83%; font-style: normal; font-weight: normal;">ñ</span>o si la entrada fue negativa, grande si la entrada lo fue.</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.039em, 1037.15em, 4.408em, -999.997em); top: -3.33em; left: 0em;"><span class="mtd" id="MathJax-Span-1250"><span class="mrow" id="MathJax-Span-1251"><span class="mtext" id="MathJax-Span-1252" style="font-family: MathJax_Main;">(value greater than 0, if the input was negative the value is small, otherwise it is large.)</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(2.146em, 1019.35em, 5.539em, -999.997em); top: -1.068em; left: 0em;"><span class="mtd" id="MathJax-Span-1255"><span class="mrow" id="MathJax-Span-1256"><span class="mi" id="MathJax-Span-1257"></span><span class="munderover" id="MathJax-Span-1258" style="padding-left: 0.182em;"><span style="display: inline-block; position: relative; width: 1.551em; height: 0px;"><span style="position: absolute; clip: rect(2.86em, 1001.37em, 4.646em, -999.997em); top: -3.985em; left: 0.063em;"><span class="mo" id="MathJax-Span-1259" style="font-family: MathJax_Size2; vertical-align: 0em;">∑</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.336em, 1001.49em, 4.408em, -999.997em); top: -2.914em; left: 0em;"><span class="texatom" id="MathJax-Span-1260"><span class="mrow" id="MathJax-Span-1261"><span class="mi" id="MathJax-Span-1262" style="font-size: 70.7%; font-family: MathJax_Math-italic;">j</span><span class="mtext" id="MathJax-Span-1263" style="font-size: 70.7%; font-family: MathJax_Main;">&nbsp;</span><span class="mo" id="MathJax-Span-1264" style="font-size: 70.7%; font-family: MathJax_Main;">=</span><span class="mtext" id="MathJax-Span-1265" style="font-size: 70.7%; font-family: MathJax_Main;">&nbsp;</span><span class="mn" id="MathJax-Span-1266" style="font-size: 70.7%; font-family: MathJax_Main;">1</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.217em, 1000.66em, 4.17em, -999.997em); top: -5.116em; left: 0.479em;"><span class="texatom" id="MathJax-Span-1267"><span class="mrow" id="MathJax-Span-1268"><span class="mi" id="MathJax-Span-1269" style="font-size: 70.7%; font-family: MathJax_Math-italic;">K<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="msubsup" id="MathJax-Span-1270" style="padding-left: 0.182em;"><span style="display: inline-block; position: relative; width: 1.134em; height: 0px;"><span style="position: absolute; clip: rect(3.396em, 1000.42em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-1271" style="font-family: MathJax_Math-italic;">e</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.402em; left: 0.479em;"><span class="texatom" id="MathJax-Span-1272"><span class="mrow" id="MathJax-Span-1273"><span class="msubsup" id="MathJax-Span-1274"><span style="display: inline-block; position: relative; width: 0.598em; height: 0px;"><span style="position: absolute; clip: rect(3.515em, 1000.36em, 4.17em, -999.997em); top: -3.985em; left: 0em;"><span class="mi" id="MathJax-Span-1275" style="font-size: 70.7%; font-family: MathJax_Math-italic;">z<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.866em; left: 0.36em;"><span class="texatom" id="MathJax-Span-1276"><span class="mrow" id="MathJax-Span-1277"><span class="mi" id="MathJax-Span-1278" style="font-size: 50%; font-family: MathJax_Math-italic;">j</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mo" id="MathJax-Span-1279" style="font-family: MathJax_Main; padding-left: 0.301em;">=</span><span class="mtext" id="MathJax-Span-1280" style="font-family: MathJax_Main; padding-left: 0.301em;">normaliza el valor en el rango [0,1].</span></span></span><span style="display: inline-block; width: 0px; height: 4.051em;"></span></span><span style="position: absolute; clip: rect(3.039em, 1017.21em, 4.408em, -999.997em); top: 1.372em; left: 0em;"><span class="mtd" id="MathJax-Span-1283"><span class="mrow" id="MathJax-Span-1284"><span class="mtext" id="MathJax-Span-1285" style="font-family: MathJax_Main;">(normalizes the value in the range [0,1].)</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.039em, 1016.25em, 4.408em, -999.997em); top: 2.741em; left: 0em;"><span class="mtd" id="MathJax-Span-1288"><span class="mrow" id="MathJax-Span-1289"><span class="mi" id="MathJax-Span-1290" style="font-family: MathJax_Math-italic;">K<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.063em;"></span></span><span class="mo" id="MathJax-Span-1291" style="font-family: MathJax_Main; padding-left: 0.301em;">=</span><span class="mtext" id="MathJax-Span-1292" style="font-family: MathJax_Main; padding-left: 0.301em;">n<span style="font-family: STIXGeneral, &quot;Arial Unicode MS&quot;, serif; font-size: 83%; font-style: normal; font-weight: normal;">ú</span>mero de clases (class number).</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 15.479em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.205em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -8.425em; border-left: 0px solid; width: 0px; height: 17.504em;"></span></span></nobr><span class="MJX_Assistive_MathML MJX_Assistive_MathML_Block" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"><mtr><mtd></mtd><mtd><mi>σ</mi><mo stretchy="false">(</mo><mover><mi>z</mi><mo>→</mo></mover><msub><mo stretchy="false">)</mo><mrow class="MJX-TeXAtom-ORD"><mi>i</mi></mrow></msub><mtext>&nbsp;</mtext><mo>=</mo><mtext>&nbsp;</mtext><mfrac><msup><mi>e</mi><mrow class="MJX-TeXAtom-ORD"><msub><mi>z</mi><mrow class="MJX-TeXAtom-ORD"><mi>i</mi></mrow></msub></mrow></msup><mrow><munderover><mo>∑</mo><mrow class="MJX-TeXAtom-ORD"><mi>j</mi><mtext>&nbsp;</mtext><mo>=</mo><mtext>&nbsp;</mtext><mn>1</mn></mrow><mrow class="MJX-TeXAtom-ORD"><mi>K</mi></mrow></munderover><msup><mi>e</mi><mrow class="MJX-TeXAtom-ORD"><msub><mi>z</mi><mrow class="MJX-TeXAtom-ORD"><mi>j</mi></mrow></msub></mrow></msup></mrow></mfrac></mtd></mtr><mtr><mtd></mtd><mtd><mover><mi>z</mi><mo>→</mo></mover><mo>=</mo><mtext>vector de entrada (input vector).</mtext></mtd></mtr><mtr><mtd></mtd><mtd><msub><mi>z</mi><mrow class="MJX-TeXAtom-ORD"><mi>i</mi></mrow></msub><mo>=</mo><mtext>todos los valores del vector de entrada (input vector values).</mtext></mtd></mtr><mtr><mtd></mtd><mtd><msup><mi>e</mi><mrow class="MJX-TeXAtom-ORD"><msub><mi>z</mi><mrow class="MJX-TeXAtom-ORD"><mi>i</mi></mrow></msub></mrow></msup><mo>=</mo><mtext>valor mayor que 0, pequeño si la entrada fue negativa, grande si la entrada lo fue.</mtext></mtd></mtr><mtr><mtd></mtd><mtd><mtext>(value greater than 0, if the input was negative the value is small, otherwise it is large.)</mtext></mtd></mtr><mtr><mtd></mtd><mtd><mi></mi><munderover><mo>∑</mo><mrow class="MJX-TeXAtom-ORD"><mi>j</mi><mtext>&nbsp;</mtext><mo>=</mo><mtext>&nbsp;</mtext><mn>1</mn></mrow><mrow class="MJX-TeXAtom-ORD"><mi>K</mi></mrow></munderover><msup><mi>e</mi><mrow class="MJX-TeXAtom-ORD"><msub><mi>z</mi><mrow class="MJX-TeXAtom-ORD"><mi>j</mi></mrow></msub></mrow></msup><mo>=</mo><mtext>normaliza el valor en el rango [0,1].</mtext></mtd></mtr><mtr><mtd></mtd><mtd><mtext>(normalizes the value in the range [0,1].)</mtext></mtd></mtr><mtr><mtd></mtd><mtd><mi>K</mi><mo>=</mo><mtext>número de clases (class number).</mtext></mtd></mtr></mtable></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-41">\begin{align}
    &\sigma (\overrightarrow{z})_{i} \ = \ \frac{e^{z_{i}}}{\sum_{j \ = \ 1}^{K}e^{z_{j}}} \\
    &\overrightarrow{z} = \text{vector de entrada (input vector).} \\
    &z_{i} = \text{todos los valores del vector de entrada (input vector values).} \\
    &e^{z_{i}} = \text{valor mayor que 0, pequeño si la entrada fue negativa, grande si la entrada lo fue.} \\
    &\text{(value greater than 0, if the input was negative the value is small, otherwise it is large.)} \\
    &\sum_{j \ = \ 1}^{K}e^{z_{j}} = \text{normaliza el valor en el rango [0,1].} \\
    &\text{(normalizes the value in the range [0,1].)} \\
    &K = \text{número de clases (class number).}
\end{align}</script><h3 id="Learning-rate4-[I]"><em>Learning rate</em><sup>4</sup> <sup>[I]</sup><a class="anchor-link" href="https://htmtopdf.herokuapp.com/ipynbviewer/temp/46ccb8d60bc4953329f884b04452879a/first_approach_neural_networks_p1.html?t=1670380747444#Learning-rate4-[I]">¶</a></h3><p>Se trata de un "hiperparámetro" (denotado por <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax" id="MathJax-Element-42-Frame" tabindex="0" style="position: relative;" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;&amp;#x03B1;&lt;/mi&gt;&lt;/math&gt;" role="presentation"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-1293" style="width: 0.836em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.658em; height: 0px; font-size: 120%;"><span style="position: absolute; clip: rect(1.61em, 1000.6em, 2.384em, -999.997em); top: -2.199em; left: 0em;"><span class="mrow" id="MathJax-Span-1294"><span class="mi" id="MathJax-Span-1295" style="font-family: MathJax_Math-italic;">α</span></span><span style="display: inline-block; width: 0px; height: 2.205em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 0.718em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>α</mi></math></span></span><script type="math/tex" id="MathJax-Element-42">\alpha</script>), el cual regula los pesos de la red, respecto al gradiente de pérdida. Indica la frecuencua de actualización de la red.</p>
<h3 id="Codificación-one-hot5-[K]">Codificación <em>one-hot</em><sup>5</sup> <sup>[K]</sup><a class="anchor-link" href="https://htmtopdf.herokuapp.com/ipynbviewer/temp/46ccb8d60bc4953329f884b04452879a/first_approach_neural_networks_p1.html?t=1670380747444#Codificaci%C3%B3n-one-hot5-[K]">¶</a></h3><p>Se utiliza para codificar las etiquetas (<em>labels</em>) en números enteros o vectores de números enteros que puedan ser entendidos por la red. Tanto para las entradas como para la interpretación de las salidas.</p>
<p>Específicamente el <em>one-hot</em> transforma las etiquetas a vectores de ceros y unos.</p>
<p>El largo del vector es proporcional al número de clases (categorías), por ejemplo, se poseen tres posibles objetos:</p>
<ul>
<li>Gato.</li>
<li>Perro.</li>
<li>Pepinillo.</li>
</ul>
<p>El <em>one-hot encoding</em> para este caso sería:</p>
<ul>
<li>Gato: [1, 0, 0]</li>
<li>Perro: [0, 1, 0]</li>
<li>Pepinillo: [0, 0, 1]</li>
</ul>
<p>Donde cada espacio corresponde a cada clase, siendo donde hay un "1" la clase en específico.</p>
<h3 id="Pérdida6-[L]">Pérdida<sup>6</sup> <sup>[L]</sup><a class="anchor-link" href="https://htmtopdf.herokuapp.com/ipynbviewer/temp/46ccb8d60bc4953329f884b04452879a/first_approach_neural_networks_p1.html?t=1670380747444#P%C3%A9rdida6-[L]">¶</a></h3><p>Penalización por una mala predicción, siendo un número que indica lo mala que fue una predicción.
El objetivo del entrenamiento es conseguir un conjunto de "ponderaciones" cuyo promedio presente la menor pérdida posible.</p>
<h3 id="Gradient-descent7"><em>Gradient descent</em><sup>7</sup><a class="anchor-link" href="https://htmtopdf.herokuapp.com/ipynbviewer/temp/46ccb8d60bc4953329f884b04452879a/first_approach_neural_networks_p1.html?t=1670380747444#Gradient-descent7">¶</a></h3><p>Es usado para:</p>
<ul>
<li>Actualizar los pesos de la red.</li>
<li>Reducción de la pérdida.</li>
</ul>
<p>Las modificaciones de los pesos se harán de acuerdo al <em>learning rate</em> definido.</p>
<h2 id="Referencias">Referencias<a class="anchor-link" href="https://htmtopdf.herokuapp.com/ipynbviewer/temp/46ccb8d60bc4953329f884b04452879a/first_approach_neural_networks_p1.html?t=1670380747444#Referencias">¶</a></h2><ul>
<li><sup>[A]</sup> What are Neural Networks? (2021, August 03). Retrieved from <a href="https://www.ibm.com/cloud/learn/neural-networks">https://www.ibm.com/cloud/learn/neural-networks</a></li>
<li><sup>[B]</sup> ELEMENTOS BÁSICOS DE UNA RED NEURONAL ARTIFICIAL. (2007, October 01). Retrieved from <a href="https://advancedtech.wordpress.com/2007/08/31/elementos-basicos-de-una-red-neuronal-artificial">https://advancedtech.wordpress.com/2007/08/31/elementos-basicos-de-una-red-neuronal-artificial</a></li>
<li><sup>[C]</sup> Singh, H. (2021). Neural Network | Introduction to Neural Network | Neural Network for DL. Analytics Vidhya. Retrieved from <a href="https://www.analyticsvidhya.com/blog/2021/03/basics-of-neural-network">https://www.analyticsvidhya.com/blog/2021/03/basics-of-neural-network</a></li>
<li><sup>[D]</sup> Tech, R. (2021, July 07). Tu primera red neuronal en Python y Tensorflow. Youtube. Retrieved from <a href="https://www.youtube.com/watch?v=iX_on3VxZzk&amp;list=PLZ8REt5zt2Pn0vfJjTAPaDVSACDvnuGiG">https://www.youtube.com/watch?v=iX_on3VxZzk&amp;list=PLZ8REt5zt2Pn0vfJjTAPaDVSACDvnuGiG</a></li>
<li><sup>[E]</sup> Tech, R. (2022, May 25). Funciones de activación a detalle (Redes neuronales). Youtube. Retrieved from <a href="https://www.youtube.com/watch?v=_0wdproot34">https://www.youtube.com/watch?v=_0wdproot34</a></li>
<li><sup>[F]</sup> Las matemáticas del Machine Learning: Funciones de activación. (2021, June 25). Retrieved from <a href="https://empresas.blogthinkbig.com/las-matematicas-del-machine-learning-funciones-de-activacion">https://empresas.blogthinkbig.com/las-matematicas-del-machine-learning-funciones-de-activacion</a></li>
<li><sup>[G]</sup> Softmax Function. (2019, May 17). Retrieved from <a href="https://deepai.org/machine-learning-glossary-and-terms/softmax-layer">https://deepai.org/machine-learning-glossary-and-terms/softmax-layer</a></li>
<li><sup>[H]</sup> wwsalmon. (2020). Simple MNIST NN from scratch (numpy, no TF/Keras). Kaggle. Retrieved from <a href="https://www.kaggle.com/code/wwsalmon/simple-mnist-nn-from-scratch-numpy-no-tf-keras/notebook">https://www.kaggle.com/code/wwsalmon/simple-mnist-nn-from-scratch-numpy-no-tf-keras/notebook</a></li>
<li><sup>[I]</sup> What is Learning Rate in Machine Learning | Deepchecks. (2021, August 05). Retrieved from <a href="https://deepchecks.com/glossary/learning-rate-in-machine-learning">https://deepchecks.com/glossary/learning-rate-in-machine-learning</a></li>
<li><sup>[J]</sup> Brownlee, J. (2019). How to Avoid Overfitting in Deep Learning Neural Networks - MachineLearningMastery.com. MachineLearningMastery. Retrieved from <a href="https://machinelearningmastery.com/introduction-to-regularization-to-reduce-overfitting-and-improve-generalization-error">https://machinelearningmastery.com/introduction-to-regularization-to-reduce-overfitting-and-improve-generalization-error</a></li>
<li><sup>[K]</sup> deeplizard. (2018, January 12). One-hot Encoding explained. Youtube. Retrieved from <a href="https://www.youtube.com/watch?v=v_4KWmkwmsU">https://www.youtube.com/watch?v=v_4KWmkwmsU</a></li>
<li><sup>[L]</sup> Cómo usar el AA: entrenamiento y pérdida. (2022, September 26). Retrieved from <a href="https://developers.google.com/machine-learning/crash-course/descending-into-ml/training-and-loss">https://developers.google.com/machine-learning/crash-course/descending-into-ml/training-and-loss</a></li>
<li><sup>[M]</sup> Simplified, P. (2021, August 09). Gradient Descent - Simply Explained! ML for beginners with Code Example! Youtube. Retrieved from <a href="https://www.youtube.com/watch?v=jwStsp8JUPU">https://www.youtube.com/watch?v=jwStsp8JUPU</a></li>
<li><sup>[N]</sup> Thomas, A. (s.f.). An introduction to neural networks for beginners. Retrieved from <a href="https://adventuresinmachinelearning.com/wp-content/uploads/2017/07/An-introduction-to-neural-networks-for-beginners.pdf">https://adventuresinmachinelearning.com/wp-content/uploads/2017/07/An-introduction-to-neural-networks-for-beginners.pdf</a></li>
</ul>

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<div class=" highlight hl-python"><pre><span></span><span class="kn">import</span> <span class="nn">numpy</span> <span class="kn">as</span> <span class="nn">np</span>
<span class="kn">import</span> <span class="nn">pandas</span> <span class="kn">as</span> <span class="nn">pd</span>
<span class="kn">from</span> <span class="nn">matplotlib</span> <span class="kn">import</span> <span class="n">pyplot</span> <span class="k">as</span> <span class="n">plt</span>

<span class="c1"># LEYENDO DATOS</span>

<span class="k">try</span><span class="p">:</span>
    <span class="n">data</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">read_csv</span><span class="p">(</span><span class="s1">'/content/drive/MyDrive/Data/train.csv'</span><span class="p">)</span> 
    <span class="sd">"""</span>
<span class="sd">    1) Descargar datos desde: https://www.kaggle.com/competitions/digit-recognizer/data</span>
<span class="sd">    2) Subir datos (train.csv) a una carpeta dedicada en Google Drive.</span>
<span class="sd">    3) Conectar Google Drive a Google Colab y "copiar ruta de acceso".</span>
<span class="sd">    4) Pegar la ruta en la lectura del archivo.</span>

<span class="sd">    P. D. Si los datos ya no están disponibles, contactarme.</span>
<span class="sd">    """</span>
<span class="k">except</span><span class="p">:</span>
    <span class="k">print</span><span class="p">(</span><span class="s1">'Error: Could not find file'</span><span class="p">)</span>
    <span class="nb">exit</span><span class="p">()</span>

<span class="n">data</span><span class="o">.</span><span class="n">head</span><span class="p">()</span> <span class="c1"># Verificando integridad de los datos, resultado: 5 filas x 785 columnas.</span>
</pre></div>

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<div class=" highlight hl-python"><pre><span></span><span class="c1"># SEPARANDO DATOS</span>

<span class="sd">"""</span>
<span class="sd">    Los datos deben ser separados con la finalidad de evitar el "overfitting" de la red.</span>
<span class="sd">    El "overfitting" se trata de una red que "aprende lo suficientemente bien" el conjunto de datos,</span>
<span class="sd">    en tal magnitud, que no se comporta de la forma esperada con datos externos a ese conjunto. [J]</span>

<span class="sd">    Dev set (validation):</span>
<span class="sd">        Conjunto de verificación, utilizado para el ajuste de hiperparámetros.</span>

<span class="sd">    Training set:</span>
<span class="sd">        Conjunto de datos que se utiliza principalmente para el ajuste de parámetros.</span>

<span class="sd">    Test set:</span>
<span class="sd">        Conjunto usado para probar la funcionalidad de la red.</span>
<span class="sd">"""</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="n">data</span><span class="p">)</span> <span class="c1"># Ingresando los datos a un arreglo de numpy, para trabajar más fácilmente con ellos.</span>
<span class="n">m</span><span class="p">,</span> <span class="n">n</span> <span class="o">=</span> <span class="n">data</span><span class="o">.</span><span class="n">shape</span>
<span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">shuffle</span><span class="p">(</span><span class="n">data</span><span class="p">)</span>

<span class="n">data_dev</span> <span class="o">=</span> <span class="n">data</span><span class="p">[</span><span class="mi">0</span><span class="p">:</span><span class="mi">1000</span><span class="p">]</span><span class="o">.</span><span class="n">T</span> <span class="c1"># Cada columna representará una imagen.</span>
<span class="n">Y_dev</span> <span class="o">=</span> <span class="n">data_dev</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="c1"># Fila de labels.</span>
<span class="n">X_dev</span> <span class="o">=</span> <span class="n">data_dev</span><span class="p">[</span><span class="mi">1</span><span class="p">:</span><span class="n">n</span><span class="p">]</span> <span class="c1"># Columnas (ejemplos, imágenes).</span>
<span class="n">X_dev</span> <span class="o">=</span> <span class="n">X_dev</span> <span class="o">/</span> <span class="mf">255.</span>

<span class="n">data_train</span> <span class="o">=</span> <span class="n">data</span><span class="p">[</span><span class="mi">1000</span><span class="p">:</span><span class="n">m</span><span class="p">]</span><span class="o">.</span><span class="n">T</span>
<span class="n">Y_train</span><span class="o">=</span> <span class="n">data_train</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
<span class="n">X_train</span> <span class="o">=</span> <span class="n">data_train</span><span class="p">[</span><span class="mi">1</span><span class="p">:</span><span class="n">n</span><span class="p">]</span>
<span class="n">X_train</span> <span class="o">=</span> <span class="n">X_train</span> <span class="o">/</span> <span class="mf">255.</span>
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<div class=" highlight hl-python"><pre><span></span><span class="c1"># CREANDO LA RED</span>

<span class="k">def</span> <span class="nf">init_params</span><span class="p">():</span> <span class="c1"># Inicialización de los parámetros con los que se trabajará (ver notas arriba).</span>
    <span class="c1"># Se crean matrices con valores aleatorios en el rango [0,1), de tamaño (x, y).</span>
    <span class="n">W1</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">normal</span><span class="p">(</span><span class="n">size</span><span class="o">=</span><span class="p">(</span><span class="mi">10</span><span class="p">,</span> <span class="mi">784</span><span class="p">))</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="mf">1.</span><span class="o">/</span><span class="p">(</span><span class="mi">784</span><span class="p">))</span> <span class="c1"># "./" se asegura que el resultado sea float.</span>
    <span class="n">B1</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">normal</span><span class="p">(</span><span class="n">size</span><span class="o">=</span><span class="p">(</span><span class="mi">10</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">sqrt</span><span class="p">(</span><span class="mf">1.</span><span class="o">/</span><span class="mi">10</span><span class="p">)</span>
    <span class="n">W2</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">normal</span><span class="p">(</span><span class="n">size</span><span class="o">=</span><span class="p">(</span><span class="mi">10</span><span class="p">,</span> <span class="mi">10</span><span class="p">))</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="mf">1.</span><span class="o">/</span><span class="mi">20</span><span class="p">)</span>
    <span class="n">B2</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">normal</span><span class="p">(</span><span class="n">size</span><span class="o">=</span><span class="p">(</span><span class="mi">10</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">sqrt</span><span class="p">(</span><span class="mf">1.</span><span class="o">/</span><span class="p">(</span><span class="mi">784</span><span class="p">))</span>
    <span class="k">return</span> <span class="n">W1</span><span class="p">,</span> <span class="n">B1</span><span class="p">,</span> <span class="n">W2</span><span class="p">,</span> <span class="n">B2</span>

<span class="k">def</span> <span class="nf">relu</span><span class="p">(</span><span class="n">Z</span><span class="p">):</span>
    <span class="c1"># "np.maximun" recorre cada elemento "x_i" de "x", aplicando la función max(0, x_i).</span>
    <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">maximum</span><span class="p">(</span><span class="n">Z</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span>

<span class="k">def</span> <span class="nf">derivative_relu</span><span class="p">(</span><span class="n">Z</span><span class="p">):</span>
    <span class="k">return</span> <span class="n">Z</span> <span class="o">&gt;</span> <span class="mi">0</span>

<span class="k">def</span> <span class="nf">softmax</span><span class="p">(</span><span class="n">Z</span><span class="p">):</span>
    <span class="c1"># AL igual que anteriormente, "np.exp" y "np.sum" aplica para todos los elementos "z_i" de "z".</span>
    <span class="c1"># A = (np.exp(Z) / np.sum(np.exp(Z)))</span>
    <span class="k">return</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="n">Z</span><span class="p">)</span> <span class="o">/</span> <span class="nb">sum</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="n">Z</span><span class="p">)))</span>
    <span class="c1"># "np.sum" devolverá un vector de "m" columnas, sumando todas las filas.</span>

<span class="k">def</span> <span class="nf">forward_propagation</span><span class="p">(</span><span class="n">W1</span><span class="p">,</span> <span class="n">B1</span><span class="p">,</span> <span class="n">W2</span><span class="p">,</span> <span class="n">B2</span><span class="p">,</span> <span class="n">X</span><span class="p">):</span>
    <span class="n">Z1</span> <span class="o">=</span> <span class="n">W1</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">X</span><span class="p">)</span> <span class="o">+</span> <span class="n">B1</span>
    <span class="n">A1</span> <span class="o">=</span> <span class="n">relu</span><span class="p">(</span><span class="n">Z1</span><span class="p">)</span>
    <span class="n">Z2</span> <span class="o">=</span> <span class="n">W2</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">A1</span><span class="p">)</span> <span class="o">+</span> <span class="n">B2</span>
    <span class="n">A2</span> <span class="o">=</span> <span class="n">softmax</span><span class="p">(</span><span class="n">Z2</span><span class="p">)</span>
    <span class="k">return</span> <span class="n">Z1</span><span class="p">,</span> <span class="n">A1</span><span class="p">,</span> <span class="n">Z2</span><span class="p">,</span> <span class="n">A2</span>

<span class="k">def</span> <span class="nf">one_hot</span><span class="p">(</span><span class="n">Y</span><span class="p">):</span>
    <span class="n">one_hot_Y</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="n">Y</span><span class="o">.</span><span class="n">size</span><span class="p">,</span> <span class="n">Y</span><span class="o">.</span><span class="n">max</span><span class="p">()</span> <span class="o">+</span> <span class="mi">1</span><span class="p">))</span> <span class="c1"># Se crea una matriz de ceros, de tamaño (Y.size, Y.max()) + 1) -&gt; (~m, 10)</span>
    <span class="n">one_hot_Y</span><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="n">Y</span><span class="o">.</span><span class="n">size</span><span class="p">),</span> <span class="n">Y</span><span class="p">]</span> <span class="o">=</span> <span class="mi">1</span> <span class="c1"># Se recorre cada posición de la matriz y se le asigna un 1, donde la etiqueta lo indique.</span>
    <span class="c1"># one_hot_Y = one_hot_Y.T</span>
    <span class="k">return</span> <span class="n">one_hot_Y</span><span class="o">.</span><span class="n">T</span> <span class="c1"># Se devuelve transpuesta de manera que cada columna es un ejemplo.</span>

<span class="k">def</span> <span class="nf">backwards_propagation</span><span class="p">(</span><span class="n">Z1</span><span class="p">,</span> <span class="n">A1</span><span class="p">,</span> <span class="n">Z2</span><span class="p">,</span> <span class="n">A2</span><span class="p">,</span> <span class="n">W1</span><span class="p">,</span> <span class="n">W2</span><span class="p">,</span> <span class="n">X</span><span class="p">,</span> <span class="n">Y</span><span class="p">):</span>
    <span class="n">m</span> <span class="o">=</span> <span class="n">Y</span><span class="o">.</span><span class="n">size</span>
    <span class="n">one_hot_Y</span> <span class="o">=</span> <span class="n">one_hot</span><span class="p">(</span><span class="n">Y</span><span class="p">)</span> <span class="c1"># Concepto 5</span>
    <span class="n">dZ2</span> <span class="o">=</span> <span class="n">A2</span> <span class="o">-</span> <span class="n">one_hot_Y</span>
    <span class="n">dW2</span> <span class="o">=</span> <span class="mi">1</span> <span class="o">/</span> <span class="n">m</span>  <span class="o">*</span> <span class="n">dZ2</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">A1</span><span class="o">.</span><span class="n">T</span><span class="p">)</span>
    <span class="n">dB2</span> <span class="o">=</span> <span class="mi">1</span> <span class="o">/</span> <span class="n">m</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">dZ2</span><span class="p">)</span>
    <span class="n">dZ1</span> <span class="o">=</span> <span class="n">W2</span><span class="o">.</span><span class="n">T</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">dZ2</span><span class="p">)</span> <span class="o">*</span> <span class="n">derivative_relu</span><span class="p">(</span><span class="n">Z1</span><span class="p">)</span>
    <span class="n">dW1</span> <span class="o">=</span> <span class="mi">1</span> <span class="o">/</span> <span class="n">m</span>  <span class="o">*</span> <span class="n">dZ1</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">X</span><span class="o">.</span><span class="n">T</span><span class="p">)</span>
    <span class="n">dB1</span> <span class="o">=</span> <span class="mi">1</span> <span class="o">/</span> <span class="n">m</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">dZ1</span><span class="p">)</span>
    <span class="k">return</span> <span class="n">dW1</span><span class="p">,</span> <span class="n">dB1</span><span class="p">,</span> <span class="n">dW2</span><span class="p">,</span> <span class="n">dB2</span>

<span class="k">def</span> <span class="nf">update_params</span><span class="p">(</span><span class="n">W1</span><span class="p">,</span> <span class="n">B1</span><span class="p">,</span> <span class="n">W2</span><span class="p">,</span> <span class="n">B2</span><span class="p">,</span> <span class="n">dW1</span><span class="p">,</span> <span class="n">dB1</span><span class="p">,</span> <span class="n">dW2</span><span class="p">,</span> <span class="n">dB2</span><span class="p">,</span> <span class="n">alpha</span><span class="p">):</span>
    <span class="n">W1</span> <span class="o">=</span> <span class="n">W1</span> <span class="o">-</span> <span class="n">alpha</span> <span class="o">*</span> <span class="n">dW1</span>
    <span class="n">B1</span> <span class="o">=</span> <span class="n">B1</span> <span class="o">-</span> <span class="n">alpha</span> <span class="o">*</span> <span class="n">dB1</span>
    <span class="n">W2</span> <span class="o">=</span> <span class="n">W2</span> <span class="o">-</span> <span class="n">alpha</span> <span class="o">*</span> <span class="n">dW2</span>
    <span class="n">B2</span> <span class="o">=</span> <span class="n">B2</span> <span class="o">-</span> <span class="n">alpha</span> <span class="o">*</span> <span class="n">dB2</span>
    <span class="k">return</span> <span class="n">W1</span><span class="p">,</span> <span class="n">B1</span><span class="p">,</span> <span class="n">W2</span><span class="p">,</span> <span class="n">B2</span>
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<div class=" highlight hl-python"><pre><span></span><span class="c1"># ENTRENANDO</span>

<span class="k">def</span> <span class="nf">get_predictions</span><span class="p">(</span><span class="n">A2</span><span class="p">):</span>
    <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">argmax</span><span class="p">(</span><span class="n">A2</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span>

<span class="k">def</span> <span class="nf">get_accuracy</span><span class="p">(</span><span class="n">predictions</span><span class="p">,</span> <span class="n">Y</span><span class="p">):</span>
    <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">predictions</span> <span class="o">==</span> <span class="n">Y</span><span class="p">)</span> <span class="o">/</span> <span class="n">Y</span><span class="o">.</span><span class="n">size</span>

<span class="n">iterations_arr</span> <span class="o">=</span> <span class="p">[]</span>
<span class="n">accuracy_arr</span> <span class="o">=</span> <span class="p">[]</span>

<span class="k">def</span> <span class="nf">gradient_descent</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">Y</span><span class="p">,</span> <span class="n">alpha</span><span class="p">,</span> <span class="n">iterations</span><span class="p">):</span> <span class="c1"># Concepto 7</span>
    <span class="n">W1</span><span class="p">,</span> <span class="n">B1</span><span class="p">,</span> <span class="n">W2</span><span class="p">,</span> <span class="n">B2</span> <span class="o">=</span> <span class="n">init_params</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">iterations</span><span class="p">):</span>
        <span class="n">Z1</span><span class="p">,</span> <span class="n">A1</span><span class="p">,</span> <span class="n">Z2</span><span class="p">,</span> <span class="n">A2</span> <span class="o">=</span> <span class="n">forward_propagation</span><span class="p">(</span><span class="n">W1</span><span class="p">,</span> <span class="n">B1</span><span class="p">,</span> <span class="n">W2</span><span class="p">,</span> <span class="n">B2</span><span class="p">,</span> <span class="n">X</span><span class="p">)</span>
        <span class="n">dW1</span><span class="p">,</span> <span class="n">dB1</span><span class="p">,</span> <span class="n">dW2</span><span class="p">,</span> <span class="n">dB2</span> <span class="o">=</span> <span class="n">backwards_propagation</span><span class="p">(</span><span class="n">Z1</span><span class="p">,</span> <span class="n">A1</span><span class="p">,</span> <span class="n">Z2</span><span class="p">,</span> <span class="n">A2</span><span class="p">,</span> <span class="n">W1</span><span class="p">,</span> <span class="n">W2</span><span class="p">,</span> <span class="n">X</span><span class="p">,</span> <span class="n">Y</span><span class="p">)</span>
        <span class="n">W1</span><span class="p">,</span> <span class="n">B1</span><span class="p">,</span> <span class="n">W2</span><span class="p">,</span> <span class="n">B2</span> <span class="o">=</span> <span class="n">update_params</span><span class="p">(</span><span class="n">W1</span><span class="p">,</span> <span class="n">B1</span><span class="p">,</span> <span class="n">W2</span><span class="p">,</span> <span class="n">B2</span><span class="p">,</span> <span class="n">dW1</span><span class="p">,</span> <span class="n">dB1</span><span class="p">,</span> <span class="n">dW2</span><span class="p">,</span> <span class="n">dB2</span><span class="p">,</span> <span class="n">alpha</span><span class="p">)</span>   
        <span class="k">if</span> <span class="n">i</span> <span class="o">%</span> <span class="mi">20</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
            <span class="k">print</span><span class="p">(</span><span class="s2">"Iteration: "</span><span class="p">,</span> <span class="n">i</span><span class="p">)</span>
            <span class="k">print</span><span class="p">(</span><span class="s2">"Accuracy: "</span><span class="p">,</span> <span class="n">get_accuracy</span><span class="p">(</span><span class="n">get_predictions</span><span class="p">(</span><span class="n">A2</span><span class="p">),</span> <span class="n">Y</span><span class="p">))</span>
        <span class="n">iterations_arr</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
        <span class="n">accuracy_arr</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">get_accuracy</span><span class="p">(</span><span class="n">get_predictions</span><span class="p">(</span><span class="n">A2</span><span class="p">),</span> <span class="n">Y</span><span class="p">))</span>          
    <span class="k">return</span> <span class="n">W1</span><span class="p">,</span> <span class="n">B1</span><span class="p">,</span> <span class="n">W2</span><span class="p">,</span> <span class="n">B2</span>

<span class="n">W1</span><span class="p">,</span> <span class="n">B1</span><span class="p">,</span> <span class="n">W2</span><span class="p">,</span> <span class="n">B2</span> <span class="o">=</span> <span class="n">gradient_descent</span><span class="p">(</span><span class="n">X_train</span><span class="p">,</span> <span class="n">Y_train</span><span class="p">,</span> <span class="mf">0.10</span><span class="p">,</span> <span class="mi">500</span><span class="p">)</span>
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<pre>Iteration:  0
Accuracy:  0.08280487804878049
Iteration:  20
Accuracy:  0.4856829268292683
Iteration:  40
Accuracy:  0.676439024390244
Iteration:  60
Accuracy:  0.785829268292683
Iteration:  80
Accuracy:  0.8176585365853658
Iteration:  100
Accuracy:  0.8373414634146341
Iteration:  120
Accuracy:  0.8513414634146341
Iteration:  140
Accuracy:  0.8626585365853658
Iteration:  160
Accuracy:  0.8722926829268293
Iteration:  180
Accuracy:  0.8786829268292683
Iteration:  200
Accuracy:  0.8831707317073171
Iteration:  220
Accuracy:  0.8870975609756098
Iteration:  240
Accuracy:  0.8902682926829268
Iteration:  260
Accuracy:  0.8920487804878049
Iteration:  280
Accuracy:  0.8942682926829268
Iteration:  300
Accuracy:  0.8961219512195122
Iteration:  320
Accuracy:  0.8978048780487805
Iteration:  340
Accuracy:  0.8995365853658537
Iteration:  360
Accuracy:  0.9007317073170732
Iteration:  380
Accuracy:  0.902219512195122
Iteration:  400
Accuracy:  0.9033170731707317
Iteration:  420
Accuracy:  0.9043170731707317
Iteration:  440
Accuracy:  0.9050243902439025
Iteration:  460
Accuracy:  0.9056829268292683
Iteration:  480
Accuracy:  0.9063170731707317
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<div class=" highlight hl-python"><pre><span></span><span class="c1"># MOSTRANDO RESULTADOS</span>

<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">iterations_arr</span><span class="p">,</span> <span class="n">accuracy_arr</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="s1">'Iteraciones'</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="s1">'Precisión'</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s1">'Evolución de la precisión en el tiempo'</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">text</span><span class="p">(</span><span class="mi">375</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.1</span><span class="p">,</span> <span class="s1">'Elaboración propia'</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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">
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<div class=" highlight hl-python"><pre><span></span><span class="c1"># MOSTRANDO RESULTADOS</span>

<span class="kn">import</span> <span class="nn">random</span>

<span class="k">def</span> <span class="nf">make_predictions</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">W1</span><span class="p">,</span> <span class="n">B1</span><span class="p">,</span> <span class="n">W2</span><span class="p">,</span> <span class="n">B2</span><span class="p">):</span>
    <span class="n">_</span><span class="p">,</span> <span class="n">_</span><span class="p">,</span> <span class="n">_</span><span class="p">,</span> <span class="n">A2</span> <span class="o">=</span> <span class="n">forward_propagation</span><span class="p">(</span><span class="n">W1</span><span class="p">,</span> <span class="n">B1</span><span class="p">,</span> <span class="n">W2</span><span class="p">,</span> <span class="n">B2</span><span class="p">,</span> <span class="n">X</span><span class="p">)</span> <span class="c1"># Se envía al programa, con los datos ya entrenados.</span>
    <span class="k">return</span> <span class="n">get_predictions</span><span class="p">(</span><span class="n">A2</span><span class="p">)</span> <span class="c1"># Se extraen las predicciones de la última capa.</span>

<span class="k">def</span> <span class="nf">test_prediction</span><span class="p">(</span><span class="n">index</span><span class="p">,</span> <span class="n">W1</span><span class="p">,</span> <span class="n">B1</span><span class="p">,</span> <span class="n">W2</span><span class="p">,</span> <span class="n">B2</span><span class="p">):</span>
    <span class="n">current_image</span> <span class="o">=</span> <span class="n">X_train</span><span class="p">[:,</span> <span class="n">index</span><span class="p">,</span> <span class="bp">None</span><span class="p">]</span> <span class="c1"># Busca una imagen según el índice administrado.</span>
    <span class="n">prediction</span> <span class="o">=</span> <span class="n">make_predictions</span><span class="p">(</span><span class="n">current_image</span><span class="p">,</span> <span class="n">W1</span><span class="p">,</span> <span class="n">B1</span><span class="p">,</span> <span class="n">W2</span><span class="p">,</span> <span class="n">B2</span><span class="p">)</span> <span class="c1"># Envía los datos para ser procesados.</span>
    <span class="n">label</span> <span class="o">=</span> <span class="n">Y_train</span><span class="p">[</span><span class="n">index</span><span class="p">]</span> <span class="c1"># Extrae la label.</span>
    <span class="k">if</span> <span class="n">prediction</span> <span class="o">==</span> <span class="n">label</span><span class="p">:</span>
        <span class="k">print</span><span class="p">(</span><span class="s2">"Success!"</span><span class="p">)</span>
    <span class="k">else</span><span class="p">:</span> <span class="k">print</span><span class="p">(</span><span class="s2">"Failure!"</span><span class="p">)</span>
    <span class="k">print</span><span class="p">(</span><span class="s2">"Prediction: "</span><span class="p">,</span> <span class="n">prediction</span><span class="p">)</span>
    <span class="k">print</span><span class="p">(</span><span class="s2">"Label: "</span><span class="p">,</span> <span class="n">label</span><span class="p">)</span>
    
    <span class="n">current_image</span> <span class="o">=</span> <span class="n">current_image</span><span class="o">.</span><span class="n">reshape</span><span class="p">((</span><span class="mi">28</span><span class="p">,</span> <span class="mi">28</span><span class="p">))</span> <span class="o">*</span> <span class="mi">255</span>
    <span class="n">plt</span><span class="o">.</span><span class="n">gray</span><span class="p">()</span>
    <span class="n">plt</span><span class="o">.</span><span class="n">imshow</span><span class="p">(</span><span class="n">current_image</span><span class="p">,</span> <span class="n">interpolation</span><span class="o">=</span><span class="s1">'nearest'</span><span class="p">)</span>
    <span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span> <span class="c1"># Muestra la imagen usada.</span>
    <span class="k">print</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="mi">5</span><span class="p">):</span>
    <span class="n">test_prediction</span><span class="p">(</span><span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">99</span><span class="p">),</span> <span class="n">W1</span><span class="p">,</span> <span class="n">B1</span><span class="p">,</span> <span class="n">W2</span><span class="p">,</span> <span class="n">B2</span><span class="p">)</span>
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<pre>Success!
Prediction:  [4]
Label:  4
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<img src="data:image/png;base64,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">
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<pre>Failure!
Prediction:  [9]
Label:  7
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<img src="data:image/png;base64,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">
</div>

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


<div class="output_subarea output_stream output_stdout output_text">
<pre>Success!
Prediction:  [4]
Label:  4
</pre>
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    <div class="prompt"></div>


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

</div>

<div class="output_area">

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


<div class="output_subarea output_stream output_stdout output_text">
<pre>Success!
Prediction:  [1]
Label:  1
</pre>
</div>
</div>

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<pre>Success!
Prediction:  [9]
Label:  9
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<p></p><h2 style="text-align: center;">Licencia / License</h2><p></p>
<p></p><h3 style="text-align: center;">Isaac-PM @ <a href="https://github.com/Isaac-PM">https://github.com/Isaac-PM</a></h3><p></p>
<p style="text-align: center;">&nbsp;</p>
<p style="text-align: center;">Salvo que se indique lo contrario, esta obra tiene licencia <strong>Attribution-ShareAlike 4.0 International (CC BY-SA 4.0)</strong> @ <a href="https://creativecommons.org/licenses/by-sa/4.0/">https://creativecommons.org/licenses/by-sa/4.0/</a></p>
<p style="text-align: center;">Unless otherwise noted, this work is licensed <strong>Attribution-ShareAlike 4.0 International (CC BY-SA 4.0)</strong> @ <a href="https://creativecommons.org/licenses/by-sa/4.0/">https://creativecommons.org/licenses/by-sa/4.0/</a>.</p>
<p style="text-align: center;">&nbsp;</p>
<p style="text-align: center;"><strong>Derechos reservados a los autores indicados en el campo de referencias.</strong></p>
<p style="text-align: center;"><strong>All rights reserved to the authors indicated in the reference field.</strong></p>
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