20190819-曲面上随机采样.html

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  content: "\e251";
}
.glyphicon-triangle-bottom:before {
  content: "\e252";
}
.glyphicon-triangle-top:before {
  content: "\e253";
}
.glyphicon-console:before {
  content: "\e254";
}
.glyphicon-superscript:before {
  content: "\e255";
}
.glyphicon-subscript:before {
  content: "\e256";
}
.glyphicon-menu-left:before {
  content: "\e257";
}
.glyphicon-menu-right:before {
  content: "\e258";
}
.glyphicon-menu-down:before {
  content: "\e259";
}
.glyphicon-menu-up:before {
  content: "\e260";
}
* {
  -webkit-box-sizing: border-box;
  -moz-box-sizing: border-box;
  box-sizing: border-box;
}
*:before,
*:after {
  -webkit-box-sizing: border-box;
  -moz-box-sizing: border-box;
  box-sizing: border-box;
}
html {
  font-size: 10px;
  -webkit-tap-highlight-color: rgba(0, 0, 0, 0);
}
body {
  font-family: "Helvetica Neue", Helvetica, Arial, sans-serif;
  font-size: 13px;
  line-height: 1.42857143;
  color: #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 4.2.0 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=4.2.0');
  src: url('../components/font-awesome/fonts/fontawesome-webfont.eot?#iefix&v=4.2.0') format('embedded-opentype'), url('../components/font-awesome/fonts/fontawesome-webfont.woff?v=4.2.0') format('woff'), url('../components/font-awesome/fonts/fontawesome-webfont.ttf?v=4.2.0') format('truetype'), url('../components/font-awesome/fonts/fontawesome-webfont.svg?v=4.2.0#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;
}
.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;
}
@-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 {
  filter: progid:DXImageTransform.Microsoft.BasicImage(rotation=1);
  -webkit-transform: rotate(90deg);
  -ms-transform: rotate(90deg);
  transform: rotate(90deg);
}
.fa-rotate-180 {
  filter: progid:DXImageTransform.Microsoft.BasicImage(rotation=2);
  -webkit-transform: rotate(180deg);
  -ms-transform: rotate(180deg);
  transform: rotate(180deg);
}
.fa-rotate-270 {
  filter: progid:DXImageTransform.Microsoft.BasicImage(rotation=3);
  -webkit-transform: rotate(270deg);
  -ms-transform: rotate(270deg);
  transform: rotate(270deg);
}
.fa-flip-horizontal {
  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 {
  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:before {
  content: "\f09a";
}
.fa-github:before {
  content: "\f09b";
}
.fa-unlock:before {
  content: "\f09c";
}
.fa-credit-card:before {
  content: "\f09d";
}
.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 {
  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: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-rebel:before {
  content: "\f1d0";
}
.fa-ge:before,
.fa-empire:before {
  content: "\f1d1";
}
.fa-git-square:before {
  content: "\f1d2";
}
.fa-git:before {
  content: "\f1d3";
}
.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";
}
/*!
*
* 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;
}
/**
 * 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 {
  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;
}
@media (max-width: 991px) {
  #ipython_notebook {
    margin-left: 10px;
  }
}
[dir="rtl"] #ipython_notebook {
  float: right !important;
}
#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#login_widget {
  float: right;
}
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;
}
@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;
}
/*!
*
* 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 {
  text-align: center;
  vertical-align: middle;
  display: inline;
  opacity: 0;
  z-index: 2;
  width: 12ex;
  margin-right: -12ex;
}
.alternate_upload .btn-upload {
  height: 22px;
}
/**
 * Primary styles
 *
 * Author: Jupyter Development Team
 */
[dir="rtl"] #tabs li {
  float: right;
}
ul#tabs {
  margin-bottom: 4px;
}
[dir="rtl"] ul#tabs {
  margin-right: 0px;
}
ul#tabs a {
  padding-top: 6px;
  padding-bottom: 4px;
}
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 {
  float: left !important;
}
[dir="rtl"] .list_toolbar .pull-right {
  padding-top: 1px;
  float: left !important;
}
[dir="rtl"] .list_toolbar .pull-left {
  float: right !important;
}
.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: baseline;
  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;
}
.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_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;
}
.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;
}
#tree-selector {
  padding-right: 0px;
}
[dir="rtl"] #tree-selector a {
  float: right;
}
#button-select-all {
  min-width: 50px;
}
#select-all {
  margin-left: 7px;
  margin-right: 2px;
}
.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.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.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.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.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;
}
[dir="rtl"] #new-menu {
  text-align: right;
}
.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;
}
[dir="rtl"] #running .col-sm-8 {
  float: right !important;
}
.delete-button {
  display: none;
}
.duplicate-button {
  display: none;
}
.rename-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.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.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.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.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);
  }
}
/*!
*
* IPython notebook
*
*/
/* CSS font colors for translated ANSI colors. */
.ansibold {
  font-weight: bold;
}
/* 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;
  border-left-width: 1px;
  padding-left: 5px;
  background: linear-gradient(to right, transparent -40px, transparent 1px, transparent 1px, transparent 100%);
}
div.cell.jupyter-soft-selected {
  border-left-color: #90CAF9;
  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 {
  border-color: #ababab;
  border-left-width: 0px;
  padding-left: 6px;
  background: linear-gradient(to right, #42A5F5 -40px, #42A5F5 5px, transparent 5px, transparent 100%);
}
@media print {
  div.cell.selected {
    border-color: transparent;
  }
}
div.cell.selected.jupyter-soft-selected {
  border-left-width: 0;
  padding-left: 6px;
  background: linear-gradient(to right, #42A5F5 -40px, #42A5F5 7px, #E3F2FD 7px, #E3F2FD 100%);
}
.edit_mode div.cell.selected {
  border-color: #66BB6A;
  border-left-width: 0px;
  padding-left: 6px;
  background: linear-gradient(to right, #66BB6A -40px, #66BB6A 5px, transparent 5px, transparent 100%);
}
@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. */
  padding: 0.4em;
}
.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. We need the 0 value because of how we size */
  /* .CodeMirror-lines */
  padding: 0;
  border: 0;
  border-radius: 0;
}
/*

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;
}
/* 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: 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 {
  list-style: disc;
  margin: 0em 2em;
  padding-left: 0px;
}
.rendered_html ul ul {
  list-style: square;
  margin: 0em 2em;
}
.rendered_html ul ul ul {
  list-style: circle;
  margin: 0em 2em;
}
.rendered_html ol {
  list-style: decimal;
  margin: 0em 2em;
  padding-left: 0px;
}
.rendered_html ol ol {
  list-style: upper-alpha;
  margin: 0em 2em;
}
.rendered_html ol ol ol {
  list-style: lower-alpha;
  margin: 0em 2em;
}
.rendered_html ol ol ol ol {
  list-style: lower-roman;
  margin: 0em 2em;
}
.rendered_html ol ol ol ol ol {
  list-style: decimal;
  margin: 0em 2em;
}
.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;
}
.rendered_html pre,
.rendered_html code {
  border: 0;
  background-color: #fff;
  color: #000;
  font-size: 100%;
  padding: 0px;
}
.rendered_html blockquote {
  margin: 1em 2em;
}
.rendered_html table {
  margin-left: auto;
  margin-right: auto;
  border: 1px solid black;
  border-collapse: collapse;
}
.rendered_html tr,
.rendered_html th,
.rendered_html td {
  border: 1px solid black;
  border-collapse: collapse;
  margin: 1em 2em;
}
.rendered_html td,
.rendered_html th {
  text-align: left;
  vertical-align: middle;
  padding: 4px;
}
.rendered_html th {
  font-weight: bold;
}
.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;
}
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.unrendered .text_cell_render {
  display: none;
}
.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;
}
/* 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;
}
.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 {
  float: right !important;
  float: right;
}
#kernel_logo_widget .current_kernel_logo {
  display: none;
  margin-top: -1px;
  margin-bottom: -1px;
  width: 32px;
  height: 32px;
}
#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;
}
.nav-wrapper {
  border-bottom: 1px solid #e7e7e7;
}
i.menu-icon {
  padding-top: 4px;
}
ul#help_menu li a {
  overflow: hidden;
  padding-right: 2.2em;
}
ul#help_menu li a i {
  margin-right: -1.2em;
}
.dropdown-submenu {
  position: relative;
}
.dropdown-submenu > .dropdown-menu {
  top: 0;
  left: 100%;
  margin-top: -6px;
  margin-left: -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.pull-left {
  margin-right: .3em;
}
.dropdown-submenu > a:after.pull-right {
  margin-left: .3em;
}
.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;
}
.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;
}
#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;
}
#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;
}
#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.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.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.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.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.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.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 {
  margin-top: 6px;
}
span.save_widget span.filename {
  height: 1em;
  line-height: 1em;
  padding: 3px;
  margin-left: 16px;
  border: none;
  font-size: 146.5%;
  border-radius: 2px;
}
span.save_widget span.filename:hover {
  background-color: #e6e6e6;
}
span.checkpoint_status,
span.autosave_status {
  font-size: small;
}
@media (max-width: 767px) {
  span.save_widget {
    font-size: small;
  }
  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;
}
#maintoolbar {
  margin-bottom: -3px;
  margin-top: -8px;
  border: 0px;
  min-height: 27px;
  margin-left: 0px;
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<h2 id="&#26354;&#32447;&#19978;&#30340;&#38543;&#26426;&#37319;&#26679;&#65306;&#25968;&#20540;+&#35299;&#26041;&#31243;">&#26354;&#32447;&#19978;&#30340;&#38543;&#26426;&#37319;&#26679;&#65306;&#25968;&#20540;+&#35299;&#26041;&#31243;<a class="anchor-link" href="#&#26354;&#32447;&#19978;&#30340;&#38543;&#26426;&#37319;&#26679;&#65306;&#25968;&#20540;+&#35299;&#26041;&#31243;">&#182;</a></h2><h2 id="&#25551;&#36848;">&#25551;&#36848;<a class="anchor-link" href="#&#25551;&#36848;">&#182;</a></h2><p>在随机模拟实验中，在一个给定的曲面上生成均匀随机点是一个常见的需求。<br>
但是还没发现有太好通用的算法，这里进行一些探索。</p>
<h3 id="&#23450;&#20041;">&#23450;&#20041;<a class="anchor-link" href="#&#23450;&#20041;">&#182;</a></h3><p>我们把问题分解成两个：</p>
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<li>在n维空间（n&gt;=2）上的一条曲线上生成均匀随机点</li>
<li>在n维空间（n&gt;=3）上的一条曲面上生成均匀随机点</li>
</ol>
<h4 id="&#20309;&#20026;&#38543;&#26426;&#65311;">&#20309;&#20026;&#38543;&#26426;&#65311;<a class="anchor-link" href="#&#20309;&#20026;&#38543;&#26426;&#65311;">&#182;</a></h4><p>我们已经知道 <strong>同余发生器</strong> 或者 <strong>混沌迭代式</strong> 都可以生成伪随机数，这里的随机的定义保持一致。</p>
<h4 id="&#20309;&#20026;&#22343;&#21248;&#38543;&#26426;&#65311;">&#20309;&#20026;&#22343;&#21248;&#38543;&#26426;&#65311;<a class="anchor-link" href="#&#20309;&#20026;&#22343;&#21248;&#38543;&#26426;&#65311;">&#182;</a></h4><p>我们把均匀随机定义为某种度量上的随机：</p>
<ul>
<li>把曲线上的均匀随机，定义为沿着曲线的长度均匀随机采样。</li>
<li>把曲面上的均匀随机，定义为沿着曲面上的面积均匀采样。</li>
</ul>
<h4 id="&#20026;&#20309;&#19981;&#28041;&#21450;&#20854;&#23427;&#32500;&#24230;&#65311;">&#20026;&#20309;&#19981;&#28041;&#21450;&#20854;&#23427;&#32500;&#24230;&#65311;<a class="anchor-link" href="#&#20026;&#20309;&#19981;&#28041;&#21450;&#20854;&#23427;&#32500;&#24230;&#65311;">&#182;</a></h4><p>因为都是已经解决的问题。</p>
<p>维度为1的曲线上的均匀分布，实际上就是一般说的均匀分布 <code>np.random.rand()</code> 已经有大量的讨论了。</p>
<p>维度为2的曲面上的均匀分布，实际上就是平面上某一块区域，以二维圆面为例，算法如下：</p>

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<div class=" highlight hl-ipython2"><pre><span></span><span class="c1">#```python</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">matplotlib.pyplot</span> <span class="kn">as</span> <span class="nn">plt</span>
<span class="o">%</span><span class="k">matplotlib</span> inline
<span class="k">def</span> <span class="nf">random_surface</span><span class="p">():</span>
    <span class="k">while</span> <span class="bp">True</span><span class="p">:</span>
        <span class="n">x</span><span class="p">,</span> <span class="n">y</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">rand</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span> <span class="o">*</span> <span class="mi">2</span> <span class="o">-</span> <span class="mi">1</span>
        <span class="k">if</span> <span class="n">x</span> <span class="o">**</span> <span class="mi">2</span> <span class="o">+</span> <span class="n">y</span> <span class="o">**</span> <span class="mi">2</span> <span class="o">&lt;=</span> <span class="mi">1</span><span class="p">:</span>
            <span class="k">return</span> <span class="n">x</span><span class="p">,</span> <span class="n">y</span>


<span class="n">sample</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">random_surface</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">1000</span><span class="p">)])</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">sample</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">sample</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">],</span> <span class="s1">&#39;.&#39;</span><span class="p">)</span>
<span class="c1"># ```</span>
<span class="c1"># ![random_surface2](https://user-images.githubusercontent.com/19920283/63161511-d67edb80-c052-11e9-8cdd-14128c919613.png)</span>
</pre></div>

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<pre>[&lt;matplotlib.lines.Line2D at 0x7fbb5f6cf750&gt;]</pre>
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<h2 id="&#26354;&#32447;&#19978;&#30340;&#22343;&#21248;&#38543;&#26426;">&#26354;&#32447;&#19978;&#30340;&#22343;&#21248;&#38543;&#26426;<a class="anchor-link" href="#&#26354;&#32447;&#19978;&#30340;&#22343;&#21248;&#38543;&#26426;">&#182;</a></h2><p>假设曲线的表示是:<br>
$$x=\phi(t),y=\psi(t), t\in [a,b]$$</p>
<p>第一类曲线积分 $\int_{a}^{b} ds$ 就是曲线的长度，<br>
我们找到x，使得 $\dfrac{\int_{a}^{x} ds}{\int_{a}^{b} ds}=r$，其中$r\in[0,1]$<br>
也就是$\dfrac{\int_{a}^{x} \sqrt{x'^2+y'^2} dt}{\int_{a}^{b} \sqrt{x'^2+y'^2} dt}=r, r\in[0,1]$</p>
<p>算法就是根据上面的方程，找到$x=f(r)$，然后生成随机的r，进而就找到x了。</p>
<h3 id="&#26696;&#20363;&#65306;&#22278;">&#26696;&#20363;&#65306;&#22278;<a class="anchor-link" href="#&#26696;&#20363;&#65306;&#22278;">&#182;</a></h3><p>$x=\cos t+1,y=\sin t, t\in [0,\pi]$<br>
$\int_0^t ds = \int_0^t \sqrt{x'^2+y'^2} dt= t$</p>
<p>方程是 $t/\pi =r$</p>
<p>代码就有了：</p>

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<div class=" highlight hl-ipython2"><pre><span></span><span class="k">def</span> <span class="nf">random_surface</span><span class="p">():</span>
    <span class="n">r</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">rand</span><span class="p">()</span>
    <span class="n">t</span> <span class="o">=</span> <span class="n">r</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span>
    <span class="n">x</span><span class="p">,</span> <span class="n">y</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">t</span><span class="p">)</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">t</span><span class="p">)</span>
    <span class="k">return</span> <span class="n">x</span><span class="p">,</span> <span class="n">y</span>


<span class="n">sample</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">random_surface</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">500</span><span class="p">)])</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">sample</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">sample</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">],</span> <span class="s1">&#39;.&#39;</span><span class="p">)</span>
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<pre>[&lt;matplotlib.lines.Line2D at 0x7fbb5f55e890&gt;]</pre>
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6DkngINzX5WvRm5L/vZji4ldpEL9O2bK3rVOWDlG/t6X5znlNxToLapjeg9MudOHZ2eYESy2KKZZcye1OuoCI6cPJuGaDKbknuSNTT7OfDxGQoLPBjgseC+7OpnF7k4T983s1eCH3XFYHXNRLF0bbteXV3t6uvr0/LaqdI97bG9M0CBx/ha9TjumjFW3TEiCVBT18KazS3sPHSSroCjqMCTF+NYZtbgnKse6Dq13JOkpq6F7z63jXMdAQIuOHVrzPDLcv6NJ5Iqi2aW8ZXKUroCjoCDjs4AtU1t6Q4rYyi5J0FNXQsPr21kf9tpHMH57IUFHmZVlKQ7NJGcMquihKICD14L/h87daaDb/xrnRY4of3ck2Lj9kMR5fKSIfzdPdPVahdJsKpyH8/cP4vapjZOnelgxabgrLQ39xynpe3TvF4cqJZ7gtXUtXDo4zMRdYtnT1RiF0mSqnIfD37xGnYcOhlRv3JTU14PsqrlnkAPrd4asT/7NVddzrc/P0EzY0RSYO7U0bwZdlSlA17Y0pq3DSu13BMkOrEDjB42WIldJEUWzSxjcmlxRN07H3yUt613JfcEqKlriXmikhYqiaTW9VGt9L1HP+HrT9XmZYJXck+A6AFUgPnTx6jVLpJid88YS1H43sDA2Y5AzFPPcp2S+yVqaPZzrqMrom7+9DE8seD6NEUkkr+qyn08u/gmFs0si9hB8p39fpZvyK8Er+R+CRqa/dy76u2e4/IstLWAErtI+lSV+/jJndMYPqQwor7mnfya+67kfgl+unEXnV1h2zc4KL6ssO8vEJGUmTjy8ojyybOdebW4Scn9Ii3fsKvXAdcej2kVqkiGWDa39wKmWONjuUrJ/SI0NPtZuampV/2P7piat3NqRTJNVbmPpbMj93+/rNCbNzNnlNwvwgtbWoneS/OG8T7NjhHJMMvmTeYnd07js2OH4fXAKzuPsHDV23mR4JXcL8LxU+ciykbsj4Aikn6LZpZRefUwugLBVavtXY4XtrSmO6ykU3K/QDV1Lbz6/tGessfg8TunqTtGJINZVPm1XUdyfnA1ruRuZnPMbLeZ7TWzZX1cc4+Z7TSzHWZWk9gwM0NDs58frGukKxDslDFg4Y1l6o4RyXB3zRhLUcH5dHf45DkeXtuY0wl+wORuZl7gSWAuMAVYaGZToq6ZBPw18HnnXCXwUBJiTbsVb+wjfOajx2PcNWNs+gISkbhUlft49oFZjC8ZElH/z6/vSVNEyRdPy/1GYK9zrsk51w6sBu6IuuYB4EnnnB/AOXeUHFNT18Kvdx2JqPvSZ65Sd4xIlqgq97F49sSIutaPz+bsytV4kvvVwIdh5dZQXbhrgWvN7L/NrNbM5sT6Rma22Mzqzaz+2LFjFxdxGjQ0+3n0pe2EHzfr9RhLbpnY9xeJSMZZNLOMK6NWrr6843CaokmuRA2oFgCTgFuBhcDPzGx49EXOuVXOuWrnXPXIkSMT9NLJ94N1jXQGzmd2j2lOu0i2uqd6XES5syuQk33v8RzWcQAIvxtjQ3XhWoE651wH8IGZ/Y5gst+ckCjT6KHVW9l56FRP2YAfz5+mQVSRLNV99N5z9R/y0ekOWj8+y8NrGwFy6v91PC33zcAkM5tgZkXAAmB91DXrCLbaMbMRBLtpei/hzEK/jPrINrjQk1NvAJF8tGzeZCqvHhZRt2ZzbrXeB0zuzrlO4DvAL4FdwHPOuR1m9kMzuz102S+BNjPbCbwO/JVzri1ZQadKTV0LZzoCEXXjS4amKRoRSaTow3S2HzyRUytX4zpD1Tm3AdgQVfdo2GMH/GXoT05oaPbzg5e2R9QZ8OM7p6UnIBFJqEUzy1i3tbVnA8CuALyYQ2euaoVqH17c0tqzWAmCe7VrJapIbrlmVOSZq0ejthbJZkrufYj+IVeXa2MwkVxz94yxhC1c5bX3j+bMzBkl9z5E70VxbdRveBHJflXlPu694XyjrSvgeGRdY070vSu5xxC9OViBV9sMiOSqu2aMjThvNeBg5Rv70hdQgii5R4m1Odi91ePU1y6So6rKfVSMiJwF13T80zRFkzhK7lG0OZhI/vn2zZEnNu09+knW7zmj5B6modnPa+9H7nmmzcFEct+imWV8ecqoiLoVm5qyenBVyT1M9PRHbQ4mkj+W3jIxou8dsvtAbSX3kJq6Fla/c/63tNdj2hxMJI9UlftY/IXI7pnK0VekKZpLp+TO+S19w/va771hnOa1i+SZZfMms3R2BR4LTqb4xdv7s3ZapJI7UNvUFtEdU+Ax7tYgqkheKr4suN+7Azo6A9Q2Zec2WUruwJ4jpwhrtHP/zRPUHSOSp2ZVlFBU4MFrUFjgYVZFSbpDuihxbRyWy2rqWli37WBEXfdvbhHJP1XlPp65fxa1TW3sOXKK7z63jTmVpT37wGeLvG+5R4+Ge4ys/U0tIolRVe7j1JkO1m07yP6206zY1JR1897zPrlHj4Yv/kKFumREhHXbIg+ce67hwz6uzEx5ndwbmv384u39QLDFvnR2RdZ99BKR5Ci7ckhE+aNPO7JqUVNeJ/fapjbaO4MnLRnqaxeR8743d3Kv3WEffWl71kyNzOvkniuj4iKSeFXlPh6/c1rEqtWugMuaqZF5PVsmfFR8VkWJ+tpFJMKimWW0tH3Kik1NQHDuu29IUXqDilPeJveGZn9PUn/wi9ekOxwRyVDFlxXiseA+7wbsOHgi3SHFJS+T+/INu1j5ZhPOQVGBh2cfmKVWu4jENKuihAKvh/bOAA5Y/U4LlWOGZfz2JHnX515T18KKTcHEDtDeGeDFLa3pDUpEMlZVuY8/qjq/HUmXy46B1bxL7rG28HQxrhMR6RY8SPv8yGpnwPFChjcK8y65lwyNHAzxGNokTET6VVXu4/6bJ0TUrdn8YUa33vMquTc0+/nP9yJb7gtuLFN/u4gMKHodTFfAZXSXbl4l91gnLanVLiLxmFVRgjdqVVMmd+nmVXKP/kH8vs5HFZE4VZX7eCDqpKapY4alKZqB5VVyv3vGWIq8hgFFXmOpzkcVkQvQPecdgnPet2fwnPe8mefevWjpsdun4j/drhWpInLBZlWUUOAx2rscjuCg6tQMnfOeF8m9odnPwp/V0tEZoFCLlkTkIlWV+/ha9TieCe0O2RVwPLKuketKizMup8TVLWNmc8xst5ntNbNl/Vx3t5k5M6tOXIiX7sUtrT2ry7RoSUQuxV0zxkZsJhZwsPKNfekLqA8DJncz8wJPAnOBKcBCM5sS47pi4C+AukQHeamiB1IzeYRbRDJbVbmP0cMGR9Rl4n4z8bTcbwT2OueanHPtwGrgjhjX/Qj4KXA2gfElxBWDCnr2ZS7yavqjiFyayqhZMgdPnM24BU3xJPergfDzpVpDdT3MbAYwzjn3/xIYW0L07CUTKn/78xMyrm9MRLLLklsmRnTNOEfGdfde8lRIM/MAfw98N45rF5tZvZnVHzt27FJfOi7Re8nsOHQyJa8rIrmrqtzHlyaPiqjLtO7eeJL7AWBcWHlsqK5bMTAV+I2Z7QdmAetjDao651Y556qdc9UjR468+KgvQPReMnOnjk7J64pIblt6y8SedTNey7wFTfEk983AJDObYGZFwAJgffeTzrkTzrkRzrnxzrnxQC1wu3OuPikRX4CauhbWbTvYU54/fUxGzkcVkexTVe7jsdun9hzk8dj6zNoGeMDk7pzrBL4D/BLYBTznnNthZj80s9uTHeCliO6Safu0PU2RiEgu2n7wBF0u2CXT3uVYvnFXukPqEVefu3Nug3PuWufcROfc46G6R51z62Nce2smtNqhdxeMumREJJGi9hFj834/NaEFTumW03vLLJpZxk/unMYXJo3gJ3dOU5eMiCTUXTPGYlEZPtaBQOmQs9sPhB+AraQuIslQVe7jC9eMYNOe4z110a35dMnJ5K69ZEQkVU6c6Ygob9pznIZmf9pzTk52y2gvGRFJlVFXDO5Vlwnnq+Zkcv9t2EckgC0ZND1JRHJL9GpVyIyumZxL7g3Nfpo/Oh1R5z+tKZAikhxV5T5u/+yYiLriQenv8c655B7r49D86VfHuFJEJDGi19BkwjYnOZfc9x45FVEuvWIQy+ZNTlM0IpIPotfQVI6+Ik2RnJdzyf2jqN+gl2fAxyMRyW2LZpaxdHZFT9/7U7/9IO2LmXIuuRcVRP6TKkZenqZIRCSfFF9W2PO4M+B49KX07jWTU8m9pq6FnYfOd8t4LDiSLSKSbLMqSvCELVftDDhqm9rSFk9OJfc1myM/BlWMGJr2hQQikh+qyn384e9F9r2filrglEo5ldyjFxOoS0ZEUimTZs3kVHKvGDE0onzrdVelKRIRyUfRs2aiDwtKpZxJ7g3Nfn722w96yoYWL4lIai2aWcb86ecXNK3bdjBts2ZyJrm/uKWVrsD5Uww9FhzgEBFJpeiumXRtAZwzyf3oqXMR5apynwZTRSTlMuWQoJxZ4RO9Uc+kUcVpiUNE8lv3+RFrNrcw6orBXFeanlyUEy33hmY/r75/pKdc4DXumjE2jRGJSD67rrSYXYdP8crOIyz8WW1aFjPlRHJf+cY+ugLnyzPGDVeXjIikTSacKZETyb3p+KcR5Y9Op2/hgIiIG6CcCjmR3K8cUthvWUQkle6eMZYir2GA12DqmGEpjyEnkns0DaaKSDpVlft47PapGNDl4NGXGlPe7571yb2mroV39p+/aV4PGkwVkbR7ffdRuocCOwOw4o19KX39rE/u//z6nojylUOKNJgqImn3QdRYYHQ52bI+uZ+I2nXtbEdXmiIRETlvQtReV9HlZMv65D7WNySiPDkDjrcSEVl6y0S8odWVXguWUymrk3tDs5/dRyIP5/jeXJ2XKiKZwesNptgA8MqOwyl97axO7j/duIuwvcL4TGmx+ttFJCPUNrXR3hkcUnUOVmxqSukOkVmd3Fs+Oh1Rjj4cW0QkXWZVlPTa8yr6tLhkyurkPn/61f2WRUTSparcR9mVkWOC3S35VIgruZvZHDPbbWZ7zWxZjOf/0sx2mtl7ZvaqmZUnPtTels2bzPzpYxg+pJD508ewbJ7620UkcwyPWi1fVJC69vSAr2RmXuBJYC4wBVhoZlOiLtsKVDvnfg94Hvg/iQ40lpq6Fv7rvUOcON3ByzsOp2XnNRGRvtwUdWBQdDmZ4vk1ciOw1znX5JxrB1YDd4Rf4Jx73TnX3QFeCyR9iWhDs5+H1zbSGXDBndc6AtQ2tSX7ZUVE4nbyXGe/5WSKJ7lfDXwYVm4N1fXlPmDjpQQVj0fWNkaUA+hYPRHJLNEDqsejToxLpoR2AJnZHwPVwN/28fxiM6s3s/pjx45d0mt96I+cKXNZoVfTIEUko9w1YyyF3vMp/tX3j6Ss+zie5H4AGBdWHhuqi2BmtwHfB253zsX89eScW+Wcq3bOVY8cOfJi4u1x2+RREeU/qBzVx5UiIulRVe7j+nHDe8pdgeDhQqkQT3LfDEwyswlmVgQsANaHX2Bm1wMrCSb2o4kPs7cbJ5T0WxYRyQTRhwdFHy6ULAMmd+dcJ/Ad4JfALuA559wOM/uhmd0euuxvgcuB/zCzbWa2vo9vlzAbtx/qtywikgkKPdZvOVkK4rnIObcB2BBV92jY49sSHNeA5k4dzZt7jkeURUQyTfTc9lTNdY8ruWei60qL+cqUURw5eZZ7byhj0cyydIckItLLvTeU8W7r+dl9qZrrnpXJvaHZz4JVb9PR5Sj0GteV6lg9EclMi2aW0dL2KSs3NeGAp37bxJcrS5M+uy8r95ZZ+cY+OrqC20F2dLmUjT6LiFyMfcc/pXsD21QduZeVyf3IybP9lkVEMkk6jtzLyuSezv0aREQulC9qA7HocjJkZXKPnieaqnmjIiIXI3ryYyomQ2Zlcle3jIhkk3NR+7hHl5MhK5P7vTeU9VsWEckk6chZWTkVsntO+8bth5g7dbTmuItIRuueDvnyjsPMqSxNSc7KyuTe0OzHf7qdh267VjtBikjGa2j284u399PeGeCp335AWcnQpCf4rEvuDc1+vv5ULe2dAYoKPDxz/ywleBHJaLVNbbR3Bgg4CDjHoy9t57rS4qTmrqzrcw+/SR2dOn1JRDLfrIoSPHZ+jkxXwCU9d2Vdcp9VUUJRgQeS5DW8AAAJBElEQVSvQWGBR6cviUjGqyr3cf/NE3rKDvANKUrqa2Zdcq8q9/Gtm8Yz7sohfOum8eqSEZGsEL0e5ze7k3v0Rdb1udfUtbBiUxMAKzY1pWRgQkTkUqV6fU7WtdzXbG7ptywikolSPdc965L7kRNn+y2LiGSiRTPLmD99DMOHFDJ/+pik9zhkXXL/pL2z37KISCaqqWth3baDfHy6g3XbDlJTl9xeh6xL7rdNHtVvWUQkE6X63OesS+5PLLg+4qPNEwuuT3dIIiIDij7nOdnnPmddcgcovWIwwy8rpPSKwekORUQkI2Vdcl++YRcrNjWxv+00KzY1sXzDrnSHJCIyoFTP9Mu65P7yjsP9lkVEMtFVUT0N0eVEy7rkPqeytN+yiEgmWnrLRApCGbfAEywnU9atUP1yZSkNLX4+/Og086dfzbJ5k9MdkojIgKrKfaxZ8jle3NKKS8HrZVVyb2j2c++qt+nschR4jS+r1S4iWeY/Glrp6AzwfEMrzz6QvC3Ls6pbZuUb++jsCv7O6+xyrHxjX5ojEhGJ34tbWmnvDOCA9s4AL25pTdprZVVyj95VLbosIpLJjp461285kbIquRd6rN+yiEgma/3odL/lRMqq5N4RcP2WRUQy2ZFTZ/stJ1Jcyd3M5pjZbjPba2bLYjw/yMzWhJ6vM7PxiQ4UoGLE0H7LIiKZbFTx4H7LiTRgcjczL/AkMBeYAiw0sylRl90H+J1z1wD/APw00YECLLllIgXeYFdMgddYkuR5oiIiiTQjamZMdDmR4pkKeSOw1znXBGBmq4E7gJ1h19wBPBZ6/DzwT2ZmzrmE9ptUlftYs/gmapvamFVRoiP2RCSrFA8q6LecSPF0y1wNfBhWbg3VxbzGOdcJnACScnJ1VbmPB794jRK7iGSd/3zvYL/lRErpgKqZLTazejOrP3bsWCpfWkQk7c60d/VbTqR4kvsBYFxYeWyoLuY1ZlYADAPaor+Rc26Vc67aOVc9cuTIi4tYRCRL3VM9rt9yIsXT4bMZmGRmEwgm8QXAoqhr1gN/ArwN/BHwWqL720VEsl33Xlgv7zjMnMrSpO6NZfHkYDObBzwBeIGfO+ceN7MfAvXOufVmNhj4d+B64CNgQfcAbF+qq6tdfX39Jf8DRETyiZk1OOeqB7ourqFa59wGYENU3aNhj88CX7vQIEVEJDmyaoWqiIjER8ldRCQHKbmLiOQgJXcRkRyk5C4ikoPimgqZlBc2OwY0X+SXjwCOJzCcRFFcF0ZxXbhMjU1xXZhLiavcOTfgKtC0JfdLYWb18czzTDXFdWEU14XL1NgU14VJRVzqlhERyUFK7iIiOShbk/uqdAfQB8V1YRTXhcvU2BTXhUl6XFnZ5y4iIv3L1pa7iIj0I+OS+6Ucxm1mfx2q321mf5DiuP7SzHaa2Xtm9qqZlYc912Vm20J/1qc4rm+Z2bGw178/7Lk/MbM9oT9/kuK4/iEspt+Z2cdhzyXzfv3czI6a2fY+njcz+8dQ3O+Z2Yyw55Jyv+KI6euhWBrN7C0z+2zYc/tD9dvMLOHbrMYR261mdiLs5/Vo2HP9vgeSHNdfhcW0PfSeujL0XFLumZmNM7PXQ3lgh5n9RYxrUvf+cs5lzB+CWwrvAyqAIuBdYErUNf8TWBF6vABYE3o8JXT9IGBC6Pt4UxjXF4Ehocd/1h1XqPxJGu/Xt4B/ivG1VwJNob99oce+VMUVdf2fE9xKOqn3K/S9ZwMzgO19PD8P2AgYMAuoS8H9Giimz3W/FsGD6uvCntsPjEjj/boV+K9LfQ8kOq6oa79K8IyJpN4zYDQwI/S4GPhdjP+PKXt/ZVrLvecwbudcO9B9GHe4O4B/Cz1+HviSmVmofrVz7pxz7gNgb+j7pSQu59zrzrnToWItwROrki2e+9WXPwBecc595JzzA68Ac9IU10Lg2QS9dr+cc5sInjnQlzuAp11QLTDczEaTxPs1UEzOubdCrwmpe291v/ZA96svl/LeTHRcKXl/OecOOee2hB6fAnbR+7zplL2/Mi25X8ph3PF8bTLjCncfwd/O3QZb8OzYWjObn6CYLiSuu0MfAZ83s+5zvTLifoW6ryYAr4VVJ+t+xaOv2JN5vy5E9HvLAb8yswYzW5yGeABuMrN3zWyjmVWG6jLifpnZEIJJ8oWw6qTfMwt2F18P1EU9lbL3V1yHdUj8zOyPgWrglrDqcufcATOrAF4zs0bn3L4UhfSfwLPOuXNmtoTgp57fT9Frx2MB8LxzLvyk4HTer4xlZl8kmNxvDqu+OXSvrgJeMbP3Q63aVNlC8Of1iQVPbFsHTErh6w/kq8B/O+fCW/lJvWdmdjnBXyYPOedOJur7XqhMa7lfymHc8XxtMuPCzG4Dvg/c7pw7113vnDsQ+rsJ+A3B3+gpics51xYWy1NAVbxfm8y4wiwg6iNzEu9XPPqKPZn3a0Bm9nsEf353OOd6Dp8Pu1dHgbUkrisyLs65k865T0KPNwCFZjaCNN+vMP29vxJ+z8yskGBif8Y592KMS1L3/kr0oMIlDkgUEBxImMD5QZjKqGseJHJA9bnQ40oiB1SbSNyAajxxXU9wAGlSVL0PGBR6PALYQ4IGluKMa3TY4zuBWnd+AOeDUHy+0OMrUxVX6LrPEBzcslTcr7DXGE/fA4T/g8gBr3eSfb/iiKmM4BjS56LqhwLFYY/fAuYk8l7FEVtp98+PYJJsCd27uN4DyYor9Pwwgv3yQ1Nxz0L/7qeBJ/q5JmXvr4S+CRJ0g+YRHGXeB3w/VPdDgq1hgMHAf4Te7O8AFWFf+/3Q1+0G5qY4rl8DR4BtoT/rQ/WfAxpDb+5G4L4Ux/W/gR2h138d+EzY1347dB/3An+ayrhC5ceA5VFfl+z79SxwCOgg2K95H7AUWBp63oAnQ3E3AtXJvl9xxPQU4A97b9WH6itC9+nd0M/4+4m8V3HG9p2w91ctYb+AYr0HUhVX6JpvEZxkEf51SbtnBLvLHPBe2M9qXrreX1qhKiKSgzKtz11ERBJAyV1EJAcpuYuI5CAldxGRHKTkLiKSg5TcRURykJK7iEgOUnIXEclB/x811Q03OnOH/wAAAABJRU5ErkJggg==
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<h3 id="&#32570;&#28857;&#19982;&#25913;&#36827;">&#32570;&#28857;&#19982;&#25913;&#36827;<a class="anchor-link" href="#&#32570;&#28857;&#19982;&#25913;&#36827;">&#182;</a></h3><p>以阿基米德螺旋线$x=t\cos t, y=t\sin t$为例，<br>
$\int_0^t ds = \int_0^t \sqrt{x'^2+y'^2} dt$<br>
$= \int_0^t \sqrt{1+t^2}dt$<br>
$=t/2\sqrt{1+t^2}+1/2 \ln (t+\sqrt{1+t^2})$</p>
<p>求积分那一步就已经有点计算量了，<br>
解方程 $t/2\sqrt{1+t^2}+1/2 \ln (t+\sqrt{1+t^2})=r$ 更是几乎不可能。<br>
因此必须找到一个数值方法。</p>
<ul>
<li>手算出被积函数的解析形式（相对来说，不很难）</li>
<li>使用了scipy的积分算法、解方程算法（因此效率会变低）</li>
<li>为了展示是否均匀，r用均匀值，而不是随机值。在实战中改成随机值。</li>
<li>fprime 是雅克比矩阵，用于解方程时，加快迭代速度，可以省略。根据Lebniz定理，雅克比矩阵正好等于被积函数。</li>
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<div class=" highlight hl-ipython2"><pre><span></span><span class="kn">import</span> <span class="nn">scipy.optimize</span> <span class="kn">as</span> <span class="nn">opt</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="kn">as</span> <span class="nn">np</span>


<span class="k">def</span> <span class="nf">func</span><span class="p">(</span><span class="n">t</span><span class="p">):</span>
    <span class="c1"># 被积部分</span>
    <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="mi">1</span> <span class="o">+</span> <span class="n">np</span><span class="o">.</span><span class="n">square</span><span class="p">(</span><span class="n">t</span><span class="p">))</span>


<span class="kn">from</span> <span class="nn">scipy</span> <span class="kn">import</span> <span class="n">integrate</span>

<span class="n">s</span><span class="p">,</span> <span class="n">_</span> <span class="o">=</span> <span class="n">integrate</span><span class="o">.</span><span class="n">quad</span><span class="p">(</span><span class="n">func</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">4</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span><span class="p">)</span>  <span class="c1"># 分母</span>

<span class="n">result</span> <span class="o">=</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">300</span><span class="p">):</span>
    <span class="c1"># r = np.random.rand()</span>
    <span class="n">r</span> <span class="o">=</span> <span class="n">i</span> <span class="o">/</span> <span class="mf">300.</span>
    <span class="n">t</span> <span class="o">=</span> <span class="n">opt</span><span class="o">.</span><span class="n">fsolve</span><span class="p">(</span><span class="k">lambda</span> <span class="n">t</span><span class="p">:</span> <span class="n">integrate</span><span class="o">.</span><span class="n">quad</span><span class="p">(</span><span class="n">func</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="n">t</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span> <span class="o">/</span> <span class="n">s</span> <span class="o">-</span> <span class="n">r</span><span class="p">,</span> <span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">fprime</span><span class="o">=</span><span class="n">func</span><span class="p">)</span>
    <span class="n">x</span> <span class="o">=</span> <span class="n">t</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">t</span><span class="p">)</span>
    <span class="n">y</span> <span class="o">=</span> <span class="n">t</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">t</span><span class="p">)</span>
    <span class="n">result</span><span class="o">.</span><span class="n">append</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">result</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">result</span><span class="p">)</span>

<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">result</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">result</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">],</span> <span class="s1">&#39;.&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
</pre></div>

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iVxPkHjeXbeWdVjWgajjaIT2HaNbObWDA5JjRPMyH7t7HnmqlN2DbhtKB/nnyVBxqiMK9+SLiWNAMfc/TiAme0DbgHCgeEW4K7q7UeBr5iZuSfUtVLjORHhEtL8fJmNay/M9EU1bkOg3pLR21Nifr6yj8Ot+uCwZNqopzskHRg2Aq+G7k8B7210jLvPmdkvgXXA6XafTFBKCjees3zxypM87YQX3RCo7F4JaGVn18hmNqawblNX0Yik3MtN89nM9gB7AAYGBpb1NfJ08cqTvM0mD2c3VM/Zqo3SvJS/surAxBSz89qoJ++SDgyngM2h+5uqj8UdM2VmvcA/AhaMb3P3B4AHAIaHh5f8USRvF688ydtOeMFmMsHWn9oDuj3UvE9WUP7sxPs06cBwGNhiZu+iEgB2A78dOeYJ4OPA3wK3Af8rif6CVlRNRh6HAIeX21YwaJ9g/gKoed9u4fJnJ/YLSTQwVHsGnwG+B/QAX3f3o2Z2NzDm7k8AXwP+ysyOAW9SCR5tFx6RlIeLV17kdQhwdOtPWbnw/IU+Ne/bKvzBthObHyXeY3D3p4CnIo/tDd3+f8DtSZ8HoBFJCdAQYIH6+Qs9KtW2Xac3PyrMkhhxI5KkTYJAq4BbWJq/kKxg8yPozOZHhQkMWlU1GQq4AqHNr0ybXyWhf3UfPaXK69u3KvnXtzCBAdAn2wRoNzzRMhjJSuP1LUxgGD1+praq6pzW2G8LDQEW0MKDSUujTFeYwNC/uq82pLJM8s2bItBueKK5C8lLY+OjwgSG6XMzlKoVpJIl37wpgmCiWAm0P3JBae5Ch3R4mZHCBIZw87lXzee2qO2PXKqsN6T9kYsn3HS+YJXmLiQhjY2PChMYADWfExDsj1x27Y9cNGo6d0YaI74KExg0rDIZGgZcXJq7kLy0gm9hAoMuYAlSJlZImruQvLRGfBUmMAC6gCUgnInNzpXZPzGV9ilJB6iMlLw0R3wVJjColJSMIBMDcODR8Sk1oLvc+OQ09x58WWWkhKU54qswgUGlpGQMDfZz+/Dm2jouCrrdLVj++flXTlN2VEZKUHj+Qqe3mi1MYABUSkrIzm2bWNWjoFsE4YZzCbj2ivWJ7w1QaCltk1qYwKBSUsIUdLve+OQ0p86ep7enRE91Mbc7r79SQSEhacxfCORmz+eVCmbpzsyWNUu3zeKCri4W3SW8g1hvydg9MsBO7Y+dqPDGR50u1xUmY9As3eQEQbfHKqWk186e12vbRcLN5rJXPr1euvZCBYUEpT3qK5HAYGb/1cx+amZ/Z2aPmdnaBsedMLMfm9kLZjaWxLmETZ+bYb5cmaU7M6tyUrsEeyjvGhkAMx45dJKPPjiq4NAF1GxOR9qTB5PKGJ4Frnb3fwq8DHyuybHXufs17j6c0LnUaIXV5AwN9rNx7YXMzVc+Vb41qzkNeRcdlqpmc+ekPXkwkcDg7s+4+1z17iiQiZW1tMJqsjSnoXvEZQpqNndG2mUk6EyP4RPA0w2ec+AZMxs3sz1Jn0h4meiSGtBtpzkN3UPDUtOThY2Plh0YzOygmR2J+XNL6JjPA3PAQw2+zPvdfRtwE3CHmf2LJt9vj5mNmdnYG2+8saxzVgM6eTu3beKCVWpE55mGpaYnKxsfLXu4qrtf3+x5M/tdYAfwm+7xszPc/VT171+Y2WPACPD9Bsc+ADwAMDw8vOzZHnHLROsN3z5BI3r/xBSPjk/xyKGT7J+Y0qfNnNCw1HRlZeOjpEYl3Qj8B+Bfuvu5Bse8w8zWBLeBG4AjSZxPmHYdS160ET0zW+begy8rc8g4DUtNX1Y2Pkqqx/AVYA3wbHUo6v0AZnapmT1VPeZi4Hkz+xFwCPiOu383ofOpUTmpM8IBuAz84NhpDWHNMA1LTV8Wms6BRGY+u/sVDR5/Dbi5evs48J4kvv9iVE5KXlBSuvfgy/zg2Om6zEH16uwYn5xm9PgZXjt7fkGzWT+nzkp77kJYYZbECAuGVc7OuxZ9S9DQYD93Xn8lh0+8ycxsuZY5HD7xpnoOGRDtJ/T2lJifL7OqV83mTgs3/IOfQZrXpUIGBqC62Jtr0beExWUOytLSF9dP2DWymY1rL2T75ev0s+mgLDb8CxkY4nYd0y9CcsKZw+xcuW4Yq173zgsuRMFY+aCfcKtGH6UiPG8hKw3/wiyiF6YZup2n9ZTSNz45zX3PHePAxJQmr2VEVuYtRBUyYwhm6D78w5NaKrqDhgb7a9laUFLaPzHF6PEzKl8kTP2EbMrKvIWoQgYGqMzQ3T8xpf0ZOiwYxhqUlB4dn2Juvkxfb0mfWhMQHXWkfkK2hPdc6Ovw9p3NFDYwBPMZ9j5+pDaf4aoNa/RLkrCgpBRcrB45dFJDWdssCAb9q/u4+8mjsVmC+gnpC89b6CmlO28hqrCBATSfIS1Dg/0MDfYzPjldy9rCQ1n37tjK9LkZfZpdhnDJqGRWe38rS8ieLM1biCp0YNB2n+lqNAkuyOJUXmpdXMkId0olw6pbQypLyI6szVuIKnRgUDkpfdGhrBb6lKvmdGuaNZaVfWVPFuctRBU6MEB9OSnYdSxLP6AiCPcdgrq4mtOLU2M5n7I4byGq8IEhmNMwM++1OQ1KuTsv6DsAXLVhzYLmdNADAgqdQaixnG9ZnbcQVfjAoDkN2RNtTs/OVS54/av7ail4X0HKJEEgCC4eaiznW1bnLUQVPjDA23MatFxDtoRLTNsvX1cbxRHXpO6mIBGXFQRj3NVYzq+4hnNW5i1EKTCgXceyLFxiAmqT48JN6riRTJCfklMrWcFsdVhj8P9XYzlf8tBwDlNgqIpbrkElpWxp1KSOG8kUrAeU1WxiuVnBrds25Sbgydvy0HAOU2AI0byG7ItrUoeDxKreEgYNS07RbCJ8u92/qNFMoF1ZQZYvKLJQXhrOYYkFBjO7C/g3wBvVh/7I3Z+KOe5G4EtAD/Cgu/9xUue0GM1ryJe4IBH8wgU9o2bZRG/JwKxuOCzUB4rwxT16v9mxQF3pIPx9lBUUS14azmFJZwxfdPc/a/SkmfUA9wEfBKaAw2b2hLu/mPB5NRSe16D1e/Ij2ouIKzlFs4nZeQe8bl+OaAkqXOYJ349e7KPHhi/+0e+jrKA48tRwDku7lDQCHKvu/4yZ7QNuAVILDOFykraizK9Wsome6sU9+IWtCxpzZZ4+8nrj+5GLffTY8MU/+n2UFRRD3hrOYUkHhs+Y2e8AY8Afunt0V5aNwKuh+1PAexM+p6a0FWX3aZRNxNX+w/Mmbrr6ktpSHdH70Yt99NjoxT/8fZQVdL+4rVOz3nAOW1FgMLODwIaYpz4PfBX4ApVN0r4A3AN8YgXfaw+wB2BgYGC5X6Yl0U3s1YjuLtFA0ShoDA3212Ub0ftA02OjXzsvFwVZmUZbp2a94Rxm7r74USv9JmaXAU+6+9WRx98H3OXuH6re/xyAu/+XZl9veHjYx8bGkjnZkId/eFIrfYrIktz33DHueeYlyl7dOnXL+sz0Kc1s3N2HFzsusT2fzeyS0N0PA0diDjsMbDGzd5lZH7AbeCKpc1qquEa09igWkUbCzeYeg75V+dw6Nckew5+a2TVUSkkngE8DmNmlVIal3uzuc2b2GeB7VIarft3djyZ4TkuiRrSItCrPzeaoxAKDu3+sweOvATeH7j8FLJjfkAVqRItIK/LebI5KrJTULYJGdF9vJTUML7InIhJkCs+/UvnwmMdmc5QCQwuCzGHXyACY8cihk3z0wVEFB5GCC2cKTrXZfMX63JebFRhaNDTYz8a1F9YW2Qt2exORYorLFPLabI5SYFiCYLc3oLbbm7IGkWIK9gfppkwhoMCwBMFub1a9H+z2JiLF0i3DUhtRYFiinds2ccEqNaJFiiooIe07dBLc2T0y0DWZQkCBYYnUiBYprm4bltqIAsMyRBvRmhUt0v26cVhqIwoMyxTMii5BbVa0MgeR7tStw1IbUWBYpqCkdO2W9ZQMZQ4iXaqbh6U2kvZGPbkWXZ5b6ymJdI9gq9bXzp5fkCl0c1AABYYV03pKIt0nuiBeeGvObg8KoMDQFuHMIdjBq391H/c9d0xbN4rkUDB5LRh5tGtkMxvXXliY32cFhjYJMofwBvTBxvAqK4nkR3jyWnif7iL9Dqv53EZDg/3ccd0VTJ+bqX3aUENaJD+KMHmtFQoMCdBQVpH8KcrktVYoMCRAQ1lF8qVIk9dakUiPwcy+CVxVvbsWOOvu18QcdwL4FTAPzLWySXVeaCirSPYVeUhqM4kEBnffFdw2s3uAXzY5/Dp3P53EeaQtbihrkDkU+U0nkgVFH5LaTKKjkszMgN8CfiPJ75NlyhxEsieun1C0IanNJD1c9Z8DP3f3Vxo878AzZubAX7j7AwmfTyoaTYLbPzHF6PEzeiOKdFCQKbw1Wy0dVfsJRRuS2syyA4OZHQQ2xDz1eXd/vHr7I8AjTb7M+939lJm9E3jWzH7q7t9v8P32AHsABgYGlnvaqYlOguspGY+OTzE3r7kOIp2gfkLrzN2T+cJmvcApYMjdF90c2czuAn7t7n+22LHDw8M+Nja28pNMQfjN+cihk5Qdegx2jQwojRVJSLSfgFmtn1CkD2VmNt7KIJ8kS0nXAz9tFBTM7B1Ayd1/Vb19A3B3gueTCUOD/QwN9jM+Oc3+iSllDyIJimYJ6ie0JsnAsJtIGcnMLgUedPebgYuBxyr9aXqBh939uwmeT6aEl9AIZw8atSTSHs1GHamf0FxipaQk5bmUFKf2Bq6OWioZyhxEViAYdRQM9lC5tiILpSRpkUYtibSPRh2tnAJDRmjUksjKaNRR+ygwZEijvoOyB5F4QTAIL3WvWcwrp8CQMRq1JNKacHO5ZEbZXaOO2kSBIaM0akkkXtwQVNwplQzD1U9oAwWGDItmD1prSYqu2RDUvTu2Mn1uRllCGygw5IBGLUnRaaJaZykw5IRGLUlRaaJa5ykw5IhGLUmRKEtIjwJDzrQyakm1VsmrVoafKktInpbEyLG4lVpLQKlUGbqnEpPkSaPhp1rOon20JEYBxGUPFvqFUolJ8kDDT7NHgaELhHsPQQquEpNkWSslI71f06NSUhdSiUmyTCWj9KiUVGCtlJhGj58BUJlJOkYlo/xQYOhijUpMq3pL9K/uq31qU5lJkhAEgu2XrwPQjOUcUWDockH2AHDVhjW1X9TR42dqn9pmZsvsffyIykyyYnG9g75qJqC5CPmxosBgZrcDdwH/BBhx97HQc58DPgnMA//W3b8X8+/fBewD1gHjwMfcfWYl5ySNhYMEVHaJ00gmaZdGvYPZ6t4IwftNJaPsW2nGcATYCfxF+EEzezeVPZ+3ApcCB83sSnefj/z7PwG+6O77zOx+KoHkqys8J2mBRjJJu7TaO7h12yZ94MiJFQUGd/8JgJlFn7oF2OfubwE/M7NjwAjwt8EBVvlHvwH8dvWhb1DJPhQYOiSuzBRd4jtaYgI1rItuJb0DvWfyIakew0ZgNHR/qvpY2DrgrLvPNTlGOqTVyXIHJqbUsC4g9Q6KZdHAYGYHgQ0xT33e3R9v/yk1PI89wB6AgYGBTn3bwmk2ksmgYcNaQaL7xAUD9Q6KYdHA4O7XL+PrngI2h+5vqj4WdgZYa2a91awh7pjweTwAPACVCW7LOCdpUaORTEBsNqGSU3doVCIKBwP1DoohqVLSE8DDZvbnVJrPW4BD4QPc3c3sOeA2KiOTPg50LAOR1kRHMsVlEyo55VcrJaJoMFDvoPutdLjqh4EvAxcB3zGzF9z9Q+5+1My+BbwIzAF3BCOSzOwp4FPu/hrwH4F9Zvafgf8NfG0l5yPJi8smllJyUjaRrlaygrgSkYJ7sWitJGmLuAtONJsI1sJRNtFZzbKC6Fpa7pWsQAG8O2mtJOmoVkpOyiaSEQ7KwciydmUF+hkUkwKDJGKpDey43kQ0UIRvF/2C1SgL2Ltja8u9AjWOpREFBknccrKJaKDoLRmY1WZkx2UX0U/OebbcLODpI6/XvYbKCmQ5FBik41rJJhYEinkHHKfxyKfoJ+fwBbDZhbZTF8bFzqEdWcBNV1/C4RNv1s0rUFYgS6XAIKlqlE1EA0VPNWMIlluIZhfhT8pxk++aXWiXGkSin97bcbEP319pFhAOtsoKZDnkfS7oAAADs0lEQVQUGCRTFgsUjbKL8CflaO8iemFdaRAJb0UZLm+t5GIfvr/SLCD6GooslQKDZFr0ItcoaIQ/KUd7F9EL63KDyIL7kfLWSi720fvKAiRNCgySW3FBI653EXdhXU4Qid6PlrdWerGPu/g3+r+KJEkT3KTwltJTWG6PQY1fyYJWJ7gpMIiIFESrgaHUiZMREZH8UGAQEZE6CgwiIlJHgUFEROooMIiISB0FBhERqZPL4apm9gYw2eSQ9cDpDp1OXug1WUivyUJ6TRbqptdk0N0vWuygXAaGxZjZWCtjdYtEr8lCek0W0muyUBFfE5WSRESkjgKDiIjU6dbA8EDaJ5BBek0W0muykF6ThQr3mnRlj0FERJavWzMGERFZpq4JDGZ2u5kdNbOymQ1HnvucmR0zs5fM7ENpnWPazOwuMztlZi9U/9yc9jmlwcxurL4XjpnZZ9M+n6wwsxNm9uPqe6OQyxeb2dfN7BdmdiT02D82s2fN7JXq312/fnrXBAbgCLAT+H74QTN7N7Ab2ArcCPw3M+vp/Ollxhfd/Zrqn6fSPplOq/7s7wNuAt4NfKT6HpGK66rvjUINzwz5H1SuE2GfBf7a3bcAf12939W6JjC4+0/c/aWYp24B9rn7W+7+M+AYMNLZs5MMGQGOuftxd58B9lF5j4jg7t8H3ow8fAvwjertbwD/qqMnlYKuCQxNbAReDd2fqj5WVJ8xs7+rpsxdnxLH0PuhMQeeMbNxM9uT9slkyMXu/nr19v8FLk7zZDohV3s+m9lBYEPMU59398c7fT5Z1Ow1Ar4KfIHKBeALwD3AJzp3dpJx73f3U2b2TuBZM/tp9RO0VLm7m1nXD+XMVWBw9+uX8c9OAZtD9zdVH+tKrb5GZvbfgScTPp0sKtT7YSnc/VT171+Y2WNUym4KDPBzM7vE3V83s0uAX6R9QkkrQinpCWC3mV1gZu8CtgCHUj6nVFTf1IEPU2nYF81hYIuZvcvM+qgMTHgi5XNKnZm9w8zWBLeBGyjm+yPOE8DHq7c/DnR9dSJXGUMzZvZh4MvARcB3zOwFd/+Qux81s28BLwJzwB3uPp/muaboT83sGiqlpBPAp9M9nc5z9zkz+wzwPaAH+Lq7H035tLLgYuAxM4PKdeFhd/9uuqfUeWb2CPABYL2ZTQH/Cfhj4Ftm9kkqqzr/Vnpn2Bma+SwiInWKUEoSEZElUGAQEZE6CgwiIlJHgUFEROooMIiISB0FBhERqaPAICIidRQYRESkzv8H2ITpcjEvvgsAAAAASUVORK5CYII=
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<h3 id="&#26041;&#26696;3">&#26041;&#26696;3<a class="anchor-link" href="#&#26041;&#26696;3">&#182;</a></h3><p>观察到这样的事实，如果把 $f(t)=\sqrt{x'^2+y'^2}$（还需要归一化） 看成一个概率密度函数，那么就可以用蒙特卡洛方法来做了。</p>
<p>算法步骤：</p>
<ol>
<li>计算解析形式$f(t)=\sqrt{x'^2+y'^2} dt$</li>
<li>计算$m=\max f(t)$ （或者m比最大值大一些也ok）</li>
<li>在t可能的区域内随机选取一点$t$，计算$f(t)/m$</li>
<li>生成一个随机数$r\in [0,1]$，如果$f(x)/m&gt;r$，则保留x，否则丢弃x并回到2</li>
</ol>
<p>优缺点：</p>
<ul>
<li>不用解积分，也不用解方程。大大提高效率</li>
<li>但是会有大量空运算（丢弃），所以当f不均匀，或者返回太大时，效率变低。不过貌似效率再低也比方案2强。</li>
</ul>

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<div class=" highlight hl-ipython2"><pre><span></span><span class="kn">import</span> <span class="nn">scipy.optimize</span> <span class="kn">as</span> <span class="nn">opt</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="kn">as</span> <span class="nn">np</span>


<span class="k">def</span> <span class="nf">func</span><span class="p">(</span><span class="n">t</span><span class="p">):</span>
    <span class="c1"># 被积部分</span>
    <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="mi">1</span> <span class="o">+</span> <span class="n">np</span><span class="o">.</span><span class="n">square</span><span class="p">(</span><span class="n">t</span><span class="p">))</span>


<span class="n">left</span><span class="p">,</span> <span class="n">right</span> <span class="o">=</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">4</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span>
<span class="n">m</span> <span class="o">=</span> <span class="o">-</span><span class="n">opt</span><span class="o">.</span><span class="n">minimize</span><span class="p">(</span><span class="n">fun</span><span class="o">=</span><span class="k">lambda</span> <span class="n">t</span><span class="p">:</span> <span class="o">-</span><span class="n">func</span><span class="p">(</span><span class="n">t</span><span class="p">),</span> <span class="n">x0</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mf">0.1</span><span class="p">]),</span>
                  <span class="n">method</span><span class="o">=</span><span class="bp">None</span><span class="p">,</span> <span class="n">jac</span><span class="o">=</span><span class="bp">None</span><span class="p">,</span>
                  <span class="n">bounds</span><span class="o">=</span><span class="p">((</span><span class="n">left</span><span class="p">,</span> <span class="n">right</span><span class="p">),))</span><span class="o">.</span><span class="n">fun</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>

<span class="n">t_list</span> <span class="o">=</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">1000</span><span class="p">):</span>
    <span class="n">t</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">rand</span><span class="p">()</span> <span class="o">*</span> <span class="p">(</span><span class="n">right</span> <span class="o">-</span> <span class="n">left</span><span class="p">)</span> <span class="o">+</span> <span class="n">left</span>
    <span class="k">if</span> <span class="n">func</span><span class="p">(</span><span class="n">t</span><span class="p">)</span> <span class="o">/</span> <span class="n">m</span> <span class="o">&gt;</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">rand</span><span class="p">():</span>
        <span class="n">t_list</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">t</span><span class="p">)</span>

<span class="n">x</span> <span class="o">=</span> <span class="n">t_list</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">t_list</span><span class="p">)</span>
<span class="n">y</span> <span class="o">=</span> <span class="n">t_list</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">t_list</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="s1">&#39;.&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
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<h2 id="&#26354;&#38754;&#19978;&#30340;&#22343;&#21248;&#38543;&#26426;">&#26354;&#38754;&#19978;&#30340;&#22343;&#21248;&#38543;&#26426;<a class="anchor-link" href="#&#26354;&#38754;&#19978;&#30340;&#22343;&#21248;&#38543;&#26426;">&#182;</a></h2><h3 id="&#25512;&#24191;">&#25512;&#24191;<a class="anchor-link" href="#&#25512;&#24191;">&#182;</a></h3><p>回到曲线上均匀分布的推导过程，我们找到方程 $\dfrac{\int_{a}^{x} ds}{\int_{a}^{b} ds}=r$，其中$r\in[0,1]$ 的解，作为随机生成算法。<br>
由于积分和方程难以解出，求助了数值方法去计算。</p>
<p>对于曲面上的情况，类似的，<br>
$\iint_D 1d\sigma=\iint_{\Omega_{xy}}\sqrt{1+(\dfrac{\partial z}{\partial x})^2+(\dfrac{\partial z}{\partial y})^2}dxdy=r$</p>
<h2 id="&#26696;&#20363;&#65306;&#29699;&#38754;">&#26696;&#20363;&#65306;&#29699;&#38754;<a class="anchor-link" href="#&#26696;&#20363;&#65306;&#29699;&#38754;">&#182;</a></h2><p>$z=\sqrt{1-x^2-y^2}$</p>
<p>$f(x,y)=\sqrt{1+(\dfrac{\partial z}{\partial x})^2+(\dfrac{\partial z}{\partial y})^2}=\sqrt{1/(1-x^2-y^2)}$</p>
<p>为了符号统一，我们把$f(x,y)$定义在$R^2$上，并且对于原本没有定义的点，定义$f(x,y)=0$<br>
不影响积分$\int_{-\infty}^{+\infty}\int_{-\infty}^{+\infty} f(x,y)dxdy$</p>
<p>又记 $g(x)=\int_{-\infty}^{+\infty} f(x,y)dy$<br>
得到$\int_{-\infty}^{x}g(x)/\int_{-\infty}^{+\infty}g(x)=r$，并求解$x=x'$<br>
$\int_{-\infty}^{y} f(x',y)dy/\int_{-\infty}^{+\infty} f(x',y)dy=r'$，求解$y=y'$</p>
<p>之后得到$(x',y')$就是我们要的结果</p>

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<div class=" highlight hl-ipython2"><pre><span></span><span class="kn">from</span> <span class="nn">scipy</span> <span class="kn">import</span> <span class="n">optimize</span> <span class="k">as</span> <span class="n">opt</span>
<span class="kn">from</span> <span class="nn">scipy</span> <span class="kn">import</span> <span class="n">integrate</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">matplotlib.pyplot</span> <span class="kn">as</span> <span class="nn">plt</span>
<span class="kn">from</span> <span class="nn">mpl_toolkits.mplot3d</span> <span class="kn">import</span> <span class="n">Axes3D</span>

<span class="n">fig</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">()</span>
<span class="n">ax</span> <span class="o">=</span> <span class="n">fig</span><span class="o">.</span><span class="n">gca</span><span class="p">(</span><span class="n">projection</span><span class="o">=</span><span class="s1">&#39;3d&#39;</span><span class="p">)</span>


<span class="k">def</span> <span class="nf">bound</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">):</span>
    <span class="k">return</span> <span class="n">x</span> <span class="o">**</span> <span class="mi">2</span> <span class="o">+</span> <span class="n">y</span> <span class="o">**</span> <span class="mi">2</span> <span class="o">&lt;=</span> <span class="mf">0.9</span>


<span class="k">def</span> <span class="nf">func</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">):</span>
    <span class="k">if</span> <span class="n">bound</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">):</span>
        <span class="k">return</span> <span class="mi">1</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="mi">1</span> <span class="o">-</span> <span class="n">x</span> <span class="o">**</span> <span class="mi">2</span> <span class="o">-</span> <span class="n">y</span> <span class="o">**</span> <span class="mi">2</span><span class="p">)</span>
    <span class="k">else</span><span class="p">:</span>
        <span class="k">return</span> <span class="mi">0</span>


<span class="n">x_min</span><span class="p">,</span> <span class="n">x_max</span><span class="p">,</span> <span class="n">y_min</span><span class="p">,</span> <span class="n">y_max</span> <span class="o">=</span> <span class="o">-</span><span class="mf">0.9</span><span class="p">,</span> <span class="mf">0.9</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.9</span><span class="p">,</span> <span class="mf">0.9</span>


<span class="k">def</span> <span class="nf">func_g</span><span class="p">(</span><span class="n">x</span><span class="p">):</span>
    <span class="n">g</span> <span class="o">=</span> <span class="n">integrate</span><span class="o">.</span><span class="n">quad</span><span class="p">(</span><span class="k">lambda</span> <span class="n">y</span><span class="p">:</span> <span class="n">func</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="o">-</span><span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="n">x</span> <span class="o">**</span> <span class="mi">2</span><span class="p">),</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="n">x</span> <span class="o">**</span> <span class="mi">2</span><span class="p">))</span>
    <span class="k">return</span> <span class="n">g</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>


<span class="c1"># g(x)的最大值</span>
<span class="n">m1</span> <span class="o">=</span> <span class="o">-</span><span class="n">opt</span><span class="o">.</span><span class="n">minimize</span><span class="p">(</span><span class="n">fun</span><span class="o">=</span><span class="k">lambda</span> <span class="n">x</span><span class="p">:</span> <span class="o">-</span><span class="n">func_g</span><span class="p">(</span><span class="n">x</span><span class="p">),</span> <span class="n">x0</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mf">0.1</span><span class="p">]),</span>
                   <span class="n">bounds</span><span class="o">=</span><span class="p">((</span><span class="n">x_min</span><span class="p">,</span> <span class="n">x_max</span><span class="p">),))</span><span class="o">.</span><span class="n">fun</span>
<span class="c1"># f(x,y)的最大值</span>
<span class="c1"># m2 = -opt.minimize(fun=lambda xy: -func(xy[0], xy[1]), x0=np.array([0.1, 0.1]),</span>
<span class="c1">#                    bounds=((x_min, x_max), (y_min, y_max))).fun</span>

<span class="n">m2</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="mi">10</span><span class="p">)</span>

<span class="n">result</span> <span class="o">=</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">1000</span><span class="p">):</span>
    <span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">rand</span><span class="p">()</span> <span class="o">*</span> <span class="p">(</span><span class="n">x_max</span> <span class="o">-</span> <span class="n">x_min</span><span class="p">)</span> <span class="o">+</span> <span class="n">x_min</span>
    <span class="k">if</span> <span class="n">func_g</span><span class="p">(</span><span class="n">x</span><span class="p">)</span> <span class="o">/</span> <span class="n">m1</span> <span class="o">&gt;</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">rand</span><span class="p">():</span>
        <span class="n">not_find</span> <span class="o">=</span> <span class="bp">True</span>
        <span class="k">while</span> <span class="n">not_find</span><span class="p">:</span>
            <span class="n">y</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">rand</span><span class="p">()</span> <span class="o">*</span> <span class="p">(</span><span class="n">y_max</span> <span class="o">-</span> <span class="n">y_min</span><span class="p">)</span> <span class="o">+</span> <span class="n">y_min</span>
            <span class="k">if</span> <span class="n">func</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="o">/</span> <span class="n">m2</span> <span class="o">&gt;</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">rand</span><span class="p">():</span>
                <span class="n">result</span><span class="o">.</span><span class="n">append</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">not_find</span> <span class="o">=</span> <span class="bp">False</span>

<span class="c1"># 整理并绘图</span>
<span class="n">result</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">result</span><span class="p">)</span>

<span class="n">X</span> <span class="o">=</span> <span class="n">result</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">]</span>
<span class="n">Y</span> <span class="o">=</span> <span class="n">result</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">]</span>
<span class="n">Z</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="n">X</span> <span class="o">**</span> <span class="mi">2</span> <span class="o">-</span> <span class="n">Y</span> <span class="o">**</span> <span class="mi">2</span><span class="p">)</span>
<span class="n">surf</span> <span class="o">=</span> <span class="n">ax</span><span class="o">.</span><span class="n">scatter</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">Z</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"># %%</span>
<span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="n">func_g</span><span class="p">(</span><span class="n">i</span><span class="p">)</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mf">0.1</span><span class="p">)]);</span>
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<pre>/home/shouldsee/.local/lib/python2.7/site-packages/scipy/integrate/quadpack.py:385: IntegrationWarning: The maximum number of subdivisions (50) has been achieved.
  If increasing the limit yields no improvement it is advised to analyze 
  the integrand in order to determine the difficulties.  If the position of a 
  local difficulty can be determined (singularity, discontinuity) one will 
  probably gain from splitting up the interval and calling the integrator 
  on the subranges.  Perhaps a special-purpose integrator should be used.
  warnings.warn(msg, IntegrationWarning)
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<pre>array([0.        , 1.51814042, 2.03135032, 2.22413782, 2.3288371 ,
       2.3940083 , 2.43704523, 2.46581343, 2.48432633, 2.49473205,
       2.49809155, 2.49473205, 2.48432633, 2.46581343, 2.43704523,
       2.3940083 , 2.3288371 , 2.22413782, 2.03135032, 1.51814042])</pre>
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<p>考虑把曲面方程变成参数形式（曲线线的情况就是这么干的）。</p>
<p>假设我们的曲面方程式这个形式 $\vec r=\vec r(u,v)$<br>
曲面积分为 $\iint_{D}=\mid\vec r_u\times\vec r_v\mid dudv$</p>
<p>推导过程就不写了，直接上算法流程</p>
<ol>
<li>对于通常的曲面可以（并不）轻松地找到上述参数表示形式，使得：<ul>
<li>$\vec r_u\times\vec r_v \neq 0$</li>
<li>$u,v$的边界都是常数（而不是互相有关）</li>
</ul>
</li>
<li>计算 $I(u,v)=\mid\vec r_u\times\vec r_v\mid$</li>
<li>计算 $m=\max I+\delta$（其中$\delta\geq0$可以自行制定，如果对m的计算没有信心，可以指定为一个正数，这个数如果太大，算法效率会有所降低。）</li>
<li>对$u,v$在其边界内均匀采样，并且以$I(u,v)/m$的概率丢弃这次采样结果</li>
</ol>
<p>以球面为例$\vec r=(\sin u\cos v,\sin u\sin v,\cos u)$</p>
<p>跑了一下，效果极好</p>

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<div class=" highlight hl-ipython2"><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">scipy.optimize</span> <span class="kn">as</span> <span class="nn">opt</span>
<span class="o">%</span><span class="k">matplotlib</span> inline

<span class="k">if</span> <span class="mi">1</span><span class="p">:</span>
    <span class="c1"># 参数方程$r=r(u,v$</span>
    <span class="k">def</span> <span class="nf">func</span><span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="n">v</span><span class="p">):</span>
        <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">u</span><span class="p">)</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">v</span><span class="p">),</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">u</span><span class="p">)</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">v</span><span class="p">),</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">u</span><span class="p">)</span>


    <span class="c1"># r对u的偏导数</span>
    <span class="k">def</span> <span class="nf">func_r_u</span><span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="n">v</span><span class="p">):</span>
        <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">u</span><span class="p">)</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">v</span><span class="p">),</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">u</span><span class="p">)</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">v</span><span class="p">),</span> <span class="o">-</span><span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">u</span><span class="p">)</span>


    <span class="c1"># r对v的偏导数</span>
    <span class="k">def</span> <span class="nf">func_r_v</span><span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="n">v</span><span class="p">):</span>
        <span class="k">return</span> <span class="o">-</span><span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">u</span><span class="p">)</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">v</span><span class="p">),</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">u</span><span class="p">)</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">v</span><span class="p">),</span> <span class="mi">0</span> <span class="o">*</span> <span class="n">u</span>


    <span class="k">def</span> <span class="nf">func_I</span><span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="n">v</span><span class="p">):</span>
        <span class="n">r_u</span> <span class="o">=</span> <span class="n">func_r_u</span><span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="n">v</span><span class="p">)</span>
        <span class="n">r_v</span> <span class="o">=</span> <span class="n">func_r_v</span><span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="n">v</span><span class="p">)</span>
        <span class="n">E</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">norm</span><span class="p">(</span><span class="n">r_u</span><span class="p">,</span> <span class="nb">ord</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
        <span class="n">G</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">norm</span><span class="p">(</span><span class="n">r_v</span><span class="p">,</span> <span class="nb">ord</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
        <span class="n">F</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">r_u</span><span class="p">,</span> <span class="n">r_v</span><span class="p">)</span>
        <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span> <span class="p">(</span><span class="n">E</span> <span class="o">*</span> <span class="n">G</span><span class="p">)</span> <span class="o">-</span> <span class="n">F</span> <span class="o">**</span> <span class="mi">2</span><span class="p">)</span>
    
    <span class="k">def</span> <span class="nf">func_I_new</span><span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="n">v</span><span class="p">):</span>
        <span class="n">r_u</span> <span class="o">=</span> <span class="n">func_r_u</span><span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="n">v</span><span class="p">)</span>
        <span class="n">r_v</span> <span class="o">=</span> <span class="n">func_r_v</span><span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="n">v</span><span class="p">)</span>
        <span class="n">E</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">norm</span><span class="p">(</span><span class="n">r_u</span><span class="p">,</span> <span class="nb">ord</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
        <span class="n">G</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">norm</span><span class="p">(</span><span class="n">r_v</span><span class="p">,</span> <span class="nb">ord</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
        <span class="n">F</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">r_u</span><span class="p">,</span> <span class="n">r_v</span><span class="p">)</span>
        <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span> <span class="p">(</span><span class="n">E</span> <span class="o">*</span> <span class="n">G</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span> <span class="o">-</span> <span class="n">F</span> <span class="o">**</span> <span class="mi">2</span><span class="p">)</span>
    
<span class="k">def</span> <span class="nf">sample_sphere_v0</span><span class="p">(</span><span class="n">N</span><span class="p">):</span>


    <span class="n">left</span><span class="p">,</span> <span class="n">right</span> <span class="o">=</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span>
    <span class="n">m</span> <span class="o">=</span> <span class="o">-</span><span class="n">opt</span><span class="o">.</span><span class="n">minimize</span><span class="p">(</span><span class="n">fun</span><span class="o">=</span><span class="k">lambda</span> <span class="n">t</span><span class="p">:</span> <span class="o">-</span><span class="n">func_I</span><span class="p">(</span><span class="n">t</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">t</span><span class="p">[</span><span class="mi">1</span><span class="p">]),</span> <span class="n">x0</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mf">0.1</span><span class="p">,</span> <span class="mf">0.1</span><span class="p">]),</span>
                      <span class="n">bounds</span><span class="o">=</span><span class="p">((</span><span class="n">left</span><span class="p">,</span> <span class="n">right</span><span class="p">),</span> <span class="p">(</span><span class="n">left</span><span class="p">,</span> <span class="n">right</span><span class="p">)))</span><span class="o">.</span><span class="n">fun</span>

    <span class="n">m</span> <span class="o">=</span> <span class="n">m</span> <span class="o">+</span> <span class="mf">0.1</span>
    <span class="c1"># %%</span>
    <span class="n">points</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">rand</span><span class="p">(</span><span class="n">N</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="mi">2</span>
    <span class="n">result</span> <span class="o">=</span> <span class="p">[]</span>
    <span class="k">for</span> <span class="n">point</span> <span class="ow">in</span> <span class="n">points</span><span class="p">:</span>
        <span class="k">if</span> <span class="n">func_I</span><span class="p">(</span><span class="n">point</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">point</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span> <span class="o">/</span> <span class="n">m</span> <span class="o">&gt;</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">rand</span><span class="p">():</span>
            <span class="n">result</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">point</span><span class="p">)</span>
    <span class="n">uvs</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">result</span><span class="p">)</span>

    <span class="c1"># %%画图</span>


    <span class="n">X</span><span class="p">,</span> <span class="n">Y</span><span class="p">,</span> <span class="n">Z</span> <span class="o">=</span> <span class="p">[],</span> <span class="p">[],</span> <span class="p">[]</span>
    <span class="k">for</span> <span class="n">point</span> <span class="ow">in</span> <span class="n">result</span><span class="p">:</span>
        <span class="n">u</span><span class="p">,</span> <span class="n">v</span> <span class="o">=</span> <span class="n">point</span>
        <span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">z</span> <span class="o">=</span> <span class="n">func</span><span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="n">v</span><span class="p">)</span>
        <span class="n">X</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
        <span class="n">Y</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">y</span><span class="p">)</span>
        <span class="n">Z</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">z</span><span class="p">)</span>

    <span class="n">X</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">X</span><span class="p">)</span>
    <span class="n">Y</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">Y</span><span class="p">)</span>
    <span class="n">Z</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">Z</span><span class="p">)</span>

    <span class="n">coords</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">vstack</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">Z</span><span class="p">])</span><span class="o">.</span><span class="n">T</span>
    <span class="k">return</span> <span class="n">coords</span><span class="p">,</span> <span class="n">uvs</span>


<span class="kn">from</span> <span class="nn">pymisca.vis_util</span> <span class="kn">import</span> <span class="n">pyvis</span>

<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="kn">as</span> <span class="nn">plt</span>
<span class="kn">from</span> <span class="nn">mpl_toolkits.mplot3d</span> <span class="kn">import</span> <span class="n">Axes3D</span>

<span class="k">def</span> <span class="nf">qc_plot_2d</span><span class="p">(</span><span class="n">coords</span><span class="p">):</span>
    <span class="n">xs</span><span class="p">,</span><span class="n">ys</span><span class="p">,</span><span class="n">zs</span> <span class="o">=</span> <span class="n">coords</span><span class="o">.</span><span class="n">T</span>
<span class="c1">#     N = len(xs)</span>
    <span class="n">us</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arccos</span><span class="p">(</span><span class="n">zs</span><span class="p">)</span>
    <span class="n">vs</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arctan</span><span class="p">(</span><span class="n">ys</span><span class="o">/</span><span class="n">xs</span><span class="p">)</span>
    <span class="n">uvs</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">stack</span><span class="p">([</span><span class="n">us</span><span class="p">,</span><span class="n">vs</span><span class="p">],</span><span class="n">axis</span><span class="o">=-</span><span class="mi">1</span><span class="p">)</span>
    <span class="n">uvs</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">nan_to_num</span><span class="p">(</span><span class="n">uvs</span><span class="p">)</span>


<span class="c1">#     xbin = np.linspace(0.01,6.3,50,endpoint=0)</span>
<span class="c1">#     ybin = np.linspace(0.01,6.3,50,endpoint=0)</span>

    <span class="n">xbin</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mf">0.01</span><span class="p">,</span><span class="mf">6.3</span><span class="o">/</span><span class="mf">2.</span><span class="p">,</span> <span class="mi">50</span><span class="p">,</span><span class="n">endpoint</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
    <span class="n">ybin</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mf">0.01</span><span class="p">,</span><span class="mf">6.3</span><span class="o">/</span><span class="mf">4.</span><span class="p">,</span> <span class="mi">50</span><span class="p">,</span><span class="n">endpoint</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
    <span class="n">xlim</span> <span class="o">=</span> <span class="n">xbin</span><span class="o">.</span><span class="n">min</span><span class="p">(),</span><span class="n">xbin</span><span class="o">.</span><span class="n">max</span><span class="p">()</span>
    <span class="n">ylim</span> <span class="o">=</span> <span class="n">ybin</span><span class="o">.</span><span class="n">min</span><span class="p">(),</span><span class="n">ybin</span><span class="o">.</span><span class="n">max</span><span class="p">()</span>
    <span class="n">xs</span><span class="p">,</span><span class="n">ys</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">meshgrid</span><span class="p">(</span><span class="n">xbin</span><span class="p">,</span><span class="n">ybin</span><span class="p">)</span>

    <span class="n">zs</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">vectorize</span><span class="p">(</span><span class="n">func_I</span><span class="p">)(</span><span class="n">xs</span><span class="p">,</span><span class="n">ys</span><span class="p">)</span>
    <span class="n">fig</span><span class="p">,</span><span class="n">axs</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="n">figsize</span><span class="o">=</span><span class="p">[</span><span class="mi">14</span><span class="p">,</span><span class="mi">4</span><span class="p">])</span>
    <span class="n">ax</span> <span class="o">=</span> <span class="n">axs</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
    <span class="n">ax</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s1">&#39;theoretical_func-I&#39;</span><span class="p">)</span>
    <span class="n">zs1</span> <span class="o">=</span> <span class="n">zs</span> <span class="o">=</span> <span class="n">zs</span> <span class="o">/</span> <span class="n">zs</span><span class="o">.</span><span class="n">sum</span><span class="p">()</span>
    <span class="c1"># max()</span>
    <span class="n">vlim</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span><span class="mf">8E-4</span><span class="p">]</span>
    <span class="n">pyvis</span><span class="o">.</span><span class="n">heatmap</span><span class="p">(</span><span class="n">zs</span><span class="p">,</span>
                  <span class="n">xlim</span><span class="o">=</span><span class="n">xlim</span><span class="p">,</span><span class="n">ylim</span><span class="o">=</span><span class="n">ylim</span><span class="p">,</span><span class="n">xlab</span><span class="o">=</span><span class="s1">&#39;u&#39;</span><span class="p">,</span><span class="n">ylab</span><span class="o">=</span><span class="s1">&#39;v&#39;</span><span class="p">,</span><span class="n">cname</span><span class="o">=</span><span class="s1">&#39;test&#39;</span><span class="p">,</span>
                  <span class="n">vlim</span> <span class="o">=</span> <span class="n">vlim</span><span class="p">,</span>
                  
                 <span class="n">ax</span><span class="o">=</span><span class="n">ax</span><span class="p">)</span>
    <span class="n">ax</span> <span class="o">=</span> <span class="n">axs</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span>
    <span class="n">ax</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s1">&#39;sampled&#39;</span><span class="p">)</span>
    <span class="n">zs</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">histogram2d</span><span class="p">(</span><span class="o">*</span><span class="n">uvs</span><span class="o">.</span><span class="n">T</span><span class="p">,</span><span class="n">bins</span><span class="o">=</span><span class="p">(</span><span class="n">xbin</span><span class="p">,</span><span class="n">ybin</span><span class="p">))[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">T</span>
    <span class="n">zs2</span> <span class="o">=</span> <span class="n">zs</span> <span class="o">=</span> <span class="n">zs</span> <span class="o">/</span> <span class="n">zs</span><span class="o">.</span><span class="n">sum</span><span class="p">()</span>
    <span class="n">pyvis</span><span class="o">.</span><span class="n">heatmap</span><span class="p">(</span><span class="n">zs</span><span class="p">,</span>
                  <span class="n">xlim</span><span class="o">=</span><span class="n">xlim</span><span class="p">,</span><span class="n">ylim</span><span class="o">=</span><span class="n">ylim</span><span class="p">,</span><span class="n">xlab</span><span class="o">=</span><span class="s1">&#39;u&#39;</span><span class="p">,</span><span class="n">ylab</span><span class="o">=</span><span class="s1">&#39;v&#39;</span><span class="p">,</span><span class="n">cname</span><span class="o">=</span><span class="s1">&#39;test&#39;</span><span class="p">,</span>
                  <span class="n">vlim</span> <span class="o">=</span> <span class="n">vlim</span><span class="p">,</span>
                 <span class="n">ax</span><span class="o">=</span><span class="n">ax</span><span class="p">)</span>
    <span class="n">zs</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">vectorize</span><span class="p">(</span><span class="n">func_I_new</span><span class="p">)(</span><span class="n">xs</span><span class="p">,</span><span class="n">ys</span><span class="p">)</span>
    <span class="n">zs3</span> <span class="o">=</span> <span class="n">zs</span> <span class="o">=</span> <span class="n">zs</span> <span class="o">/</span> <span class="n">zs</span><span class="o">.</span><span class="n">sum</span><span class="p">()</span>

    <span class="n">ax</span> <span class="o">=</span> <span class="n">axs</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span>
    <span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">xbin</span><span class="p">[:],</span> <span class="n">zs1</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">),</span><span class="n">label</span><span class="o">=</span><span class="s1">&#39;theoretical_func-I&#39;</span><span class="p">)</span>
    <span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">xbin</span><span class="p">[:</span><span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="n">zs2</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">),</span><span class="n">label</span><span class="o">=</span><span class="s1">&#39;sampled&#39;</span><span class="p">)</span>
    <span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">xbin</span><span class="p">[:],</span> <span class="n">zs3</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">),</span><span class="n">label</span><span class="o">=</span><span class="s1">&#39;theoretical_func-I-new&#39;</span><span class="p">)</span>
    <span class="n">ax</span><span class="o">.</span><span class="n">set_ylim</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="bp">None</span><span class="p">)</span>
    <span class="n">ax</span><span class="o">.</span><span class="n">legend</span><span class="p">()</span>
    <span class="n">fig</span><span class="o">.</span><span class="n">suptitle</span><span class="p">(</span><span class="s2">&quot;N=</span><span class="si">%d</span><span class="s2">&quot;</span><span class="o">%</span><span class="k">len</span>(coords))
    <span class="k">return</span> <span class="n">ax</span>


<span class="k">def</span> <span class="nf">qc_plot_3d</span><span class="p">(</span><span class="n">coords</span><span class="p">):</span>
    <span class="n">fig</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">()</span>
    <span class="n">ax</span> <span class="o">=</span> <span class="n">fig</span><span class="o">.</span><span class="n">gca</span><span class="p">(</span><span class="n">projection</span><span class="o">=</span><span class="s1">&#39;3d&#39;</span><span class="p">)</span>

    <span class="n">surf</span> <span class="o">=</span> <span class="n">ax</span><span class="o">.</span><span class="n">scatter</span><span class="p">(</span><span class="o">*</span><span class="n">coords</span><span class="o">.</span><span class="n">T</span><span class="p">,</span> <span class="n">marker</span><span class="o">=</span><span class="s1">&#39;.&#39;</span><span class="p">)</span>
    <span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
    <span class="k">return</span> <span class="n">ax</span>
</pre></div>

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<div class="prompt input_prompt">In&nbsp;[38]:</div>
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<div class=" highlight hl-ipython2"><pre><span></span><span class="n">coords</span><span class="p">,</span><span class="n">uvs</span> <span class="o">=</span> <span class="n">sample_sphere_v0</span><span class="p">(</span><span class="mi">250000</span><span class="p">)</span>
<span class="n">qc_plot_3d</span><span class="p">(</span><span class="n">coords</span><span class="p">[:</span><span class="mi">1000</span><span class="p">])</span>
<span class="n">qc_plot_2d</span><span class="p">(</span><span class="n">coords</span><span class="p">)</span>
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>
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<pre>&lt;matplotlib.axes._subplots.AxesSubplot at 0x7efc9e88d890&gt;</pre>
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<div class="prompt input_prompt">In&nbsp;[35]:</div>
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<div class=" highlight hl-ipython2"><pre><span></span><span class="kn">import</span> <span class="nn">IPython.display</span> <span class="kn">as</span> <span class="nn">ipd</span>
<span class="n">ipd</span><span class="o">.</span><span class="n">display</span><span class="p">(</span>
    <span class="n">ipd</span><span class="o">.</span><span class="n">Markdown</span><span class="p">(</span>
<span class="sa">u</span><span class="sd">&#39;&#39;&#39;</span>
<span class="sd">### 投影采样</span>

<span class="sd">- 相比之下, 将三维高斯$\mathcal{N}(0,I_3)$投影到球面上. 可以看到`func_I()`所的出的Jacobian是</span>
<span class="sd">有些系统性误差的. 这是因为`np.linalg.norm`已经完成了L2-norm的开方了</span>

<span class="sd">&#39;&#39;&#39;</span>
<span class="p">)</span>
<span class="p">)</span>


<span class="n">N</span> <span class="o">=</span> <span class="mi">250000</span>
<span class="n">coords</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="n">N</span><span class="p">,</span><span class="mi">3</span><span class="p">))</span>
<span class="n">coords</span> <span class="o">=</span> <span class="n">coords</span> <span class="o">/</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">norm</span><span class="p">(</span><span class="n">coords</span><span class="p">,</span><span class="nb">ord</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span><span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span><span class="n">keepdims</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>

<span class="n">qc_plot_3d</span><span class="p">(</span><span class="n">coords</span><span class="p">[:</span><span class="mi">1000</span><span class="p">])</span>
<span class="n">qc_plot_2d</span><span class="p">(</span><span class="n">coords</span><span class="p">)</span>
</pre></div>

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<h3 id="&#25237;&#24433;&#37319;&#26679;">&#25237;&#24433;&#37319;&#26679;<a class="anchor-link" href="#&#25237;&#24433;&#37319;&#26679;">&#182;</a></h3><ul>
<li>相比之下, 将三维高斯$\mathcal{N}(0,I_3)$投影到球面上. 可以看到<code>func_I()</code>所的出的Jacobian是
有些系统性误差的. 这是因为<code>np.linalg.norm</code>已经完成了L2-norm的开方了</li>
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>
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<pre>&lt;matplotlib.axes._subplots.AxesSubplot at 0x7efc9eb9a290&gt;</pre>
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odPziqIiD50jMJxj0yIBCGE8eQOkZsYQRAah9gSISQpK4RvHwEUfHIb7FkJZz4C9gjYtRxmXgeterP9rId4a8HjfLLxEypdlZzY+kQmDZ3EkMwhJEcfJrLcCR2h92VkKjuZNhsDvLtv2bOKog9vYm7ZVr5rk8b0te8yY+27XBLVihvyd5G5bztkD4WcC6HXGEhqcyyvhtAIZEIkCCGOW57qCoIQAMSWCCHHD49DdSnc8hMseRPm/Rvy18DZf4NpV1AVk8wr/c5lyhdXoVCc1+k8xvcaT7cW3erv2x556L5WOaTc9AMX/PA4F/w8mR12xavJycxMdPJBso2LW5/KHwoKSP5yEnw5yTM5OvtxyBoY+HMXAkqThdBQSk1RSuUrpVbWU2+wUsqplLq0qcYiCM2Vg09169tCHbEngtC0NNSWNAd7IjQT8tfAoikw+AZo1QvOeRIueB62/gQvnsQCXc4l2W15Zd00RncYzexLZvPIsEcaNhmqi4goOONBuOEb2p7xNx665EP+e/HnjOl2CTMrtnNxRhw/X/EqjPxfKN4BUy+EvMWBOWehyWjKN0RvAM8Db9VWQSllB54EvmrCcQhCs0WjcDXdc43jiTdoCnuiFCrSxzm+2nT219lWUILqZNNhN7LMdHYv7mRGH2qxznJ+P9DeXFO+34wTQMJqs++yDlbAAmemOSabX2AAp1+S16JKy9E+JsEMBDCi/UZDntTKDJxw5eprasqdkwsN3dBkM0FqjDKTgk5ee3pNOcJmjvG0LPO4a4tbGfJ9nb+sKR9wm9fx+91dDflffacb8pxSK0HsmlIziMQF7cz581vLhxrysC5WItpIv+y4SyPMpS7+SW1LO1ufS+wm8/OLyTf/Jytb1p5c1RFjTjCiSwyRyFIz4EZVmnV94lbtMvvl6AkjWyI0F2Y/ANGJMOJ+a9+A8ZSntOPxOffwsa2CbHskL5/5Mie3OTnwx88aWPPmpy3w4EkPcmm3S3ngxwe4ZcEjXN7tcu6e8Alxb18Cb18E18yCNv0CPw4hIDSZ9dNazwX21VPtD8AHQH499QRBqAW3VvVuoY7YE0FoehpiS4JpT5RSo5VS65RSG5VSkw6jj1ZKzfDq5yulOvjo7vfuX6eUOru+PpWHx5RS65VSa5RSdzT1+QlHwIavYdO3cNokiLMiT+aW5DJuxWRm2au4sc+NfHjBh00zGaqFnLQcZpw/gwm9JvD++ve5dM4drBrzDEQnw1tjYPeKYzYW4cgI2uMgpVRb4CLg0LiGgiA0CI2iWtvr3Zo7Yk8EoXE01JYEy5543wC/AJwD9AKuVEr18qt2A7Bfa90FeBbPG2O89cYCOcBo4N9KKXs9fV4LZAM9tNY9AfPVpBA8XA6Y/T+Q2hkG31ize/6u+Vz52ZXkl+fz0hkvceeAO4OSNyjaHs2fB/+ZKWdPwel2ct3P9/PD6P+DqHh48wLYs/qYj0mon2C+H58M3Ke1rjcXnFLqZqXUIqXUomp3xTEYmiCEBp5kirZ6tzDgqOyJQ1fWV10QwoKG2pIg2pMhwEat9WatdTWeCcoYvzpjgDe95ZnAKOVJFDMGmK61rtJabwE2evurq89bgYcP2hSttbx5Pl5Y/AYUroezH4OIKLTWvLPmHX7/9e/JiM1g+nnTOanNScEeJYMyBzHtvGl0Su7EnQsfY9qpt4A9CmZeD25X/R0Ix5RgRpkbBEz3JrVKB85VSjm11h/7V9RavwK8ApAc2bIxy6QFodkhTs7A0doTe7pW9tqfeKsdVgZN1SrO0DnizXYRlaZpqkq1IhT5P1SP22V+ZpWpZlsdYcl2v2Sq7v2mv0p8z/2G3CHZWlm4cG97Q9cq6oAh/2f/EEPeX2qdY3Wi+fPw8S5z7fs73cwH5l+3tB7Wd4k3Mo+yzxFvyJ0S9xryM1vOqin3arHb0J3c0vRdemn3CEOev65TTdkebd5k7M00j5vTzvS5SYiw/IC+/3SAoavMNn2kbDF+yXOrrYmBK8b8/KrTzXEkrTWvpc3h8/n6fW8cceZ3w5lt+p+lrCyiVlr4hQ8uPHy12jjObUlbINdHzgOG1lZHa+1UShUDad798/zatvWWa+uzM3CFUuoioAC4Q2u9wX9QSqmbgZsB2rVrd+RnJRwZLgf8+Ay0HwbdRqO15qlFTzF19VRGZo/k8eGPEx8ZX38/x4j02HSmnD2FST9O4vFVr5Kbcyp/nv8e9lUfQR+J/XM8EbRHPVrrjlrrDlrrDnie5Nx2uJsXQRBqR2uFS9vq3Zo7Yk8EoXE01JaEgz3xEg1Uaq0HAa8CUw5XSWv9itZ6kNZ6UEZGxjEdYFiy+hMo2QnD7kQDf1/4d6aunspVPa5i8sjJx9Vk6CBxkXE8O+JZxvUcx9v585iU3Qnn94+By1l/Y+GY0ZRht98FfgW6K6XylFI3KKVuUUrd0lTHFIRwxI2qd2sIx9hh+Uel1FLvtlMpVefkReyJIDQ9DbElQbQnO4B+B/sExnn31dgToB3wm1LqY6VUBJAM7PXWy/Y5fJZ3X237wfO26ENv+SOgb4NOXGg6tIZfn4e0rujOZ/Dkwid5e83bXN3zaiYNmYRNHb+TdbvNzqQhk7hr4F18GeHkQVsR7mXvBntYgg9NtmROa33lEdS9tqnGIQjNGY8jdOP/jX2ci8/EcyOwUCk1S2vt6/1Z47CslBqLx2H5Cj+H5TbAN0qpg4keDtun1nq4z7E/AD6p8zzFnghCkxIoWwJNZk8WAycAo7zlQu8xOGhPlFITgbvxTGQuBb7TWmul1CxgmlLqGW+fXYEFgAK6KqU64pkIjQWu8o7vY2AksAU4DVgfkIsjHD3b58HO39Dn/oMnFv2daWunMb7XeO4ZdA/e5dLHPdf3vp5qVzUvLH2BmIV/53/7XI6KjK6/odDkHL/TaUEQ6iWAQRWOtcMyAEqpJOB0PDcfgiAEiQAHVWgKezIQWA685v07F+itlHpYKXWBt5/38LzleRD4EzAJQGu9yqtbDXwJTNRau7TWTuB2YDawBnjPWxfgCeASpdQK4HHACmcmBId5L0BMCv9wFzBt7TQm9JoQUpOhg/y+7++5ru3pvBcDT395M1qLa/zxQDCDKgiCEABcgckLcqwdlg9yIfCt1voAQUBrjXZZDvDKzyndnWKtR48oNx3l/YO5umL8knGmWJEUDnQ06zqSzEAJLTqZKZZKl6ZZYywyIzK4/RK1HticYsjz8xNryqmZxYbu+z1mhvaSKjNAg9NhHat/Uq6h+8+OEw35ju3nG3J2rBXcoW/cdkP3zMYzDdnhMq9V8QHrOt/W4XtDN323Gfhhbb6Z1LVP5zyrbVuz7cRfrzLkwZ22GfIXS/vUlPufYfrLb9mfZsjF+03fhIgDPp+L3xwhbbH5mUUXm9+dylSrQWUr8/83MbeemyOb1dadmmiqDpTX3bYeAmRLoOnsyW9a6xsBlFLjgaFa69t96p4DzNJaH+KtrrV+DHjsMPs/Bz4/zP4i4Lw6zlE4luzbAms/490Tfsdb695lXM9x3D3o7pCbDAEopbjr9GepfPNk3ty3hLgl/+S2gXcGe1hhj7whEoQQ5mB2+fo2IP1gqGnvdnOwx+7lSkAWUgtCkGmoLRF7IjQphRvhnctgzafm/vkvMzc2lieKlzMie0RIvhnyRdlsTBrxd8aUlPLiytf4dNOn9TcSmhR5QyQIIY67YVGfCr3RkmqjLudi/zp5DXRYpq4+lVLpeJbCXNSQExAEoWlpoC0BsSdCU3BgF0y9CIq3w4avoPclcM5TYI9g3Ypp3NMqg+6p3Xly+JPYbaGfcNzW8VQeTOzDzqoNPPTzX+iQ1IE+GX3qbyg0CfKGSBBCGA0NfaJbHwvxOhcrpaLwOBfP8qszC5jgLdc4LHv3j/VGjeqI5bBcX5+XAv/VWrKjCkKwaagtEXsiNAkVRfD2JVCxD274Gkb+L6yeBS8MIf+TW5mYFk9CdDL/Ov1fxEXG1d9fiBB5/nM87Uoho7qSO7+8nvySncEeUtgib4gEIYTRKBz+WT+Pph/PGv6DzsV2YIrWepVS6mFgkdZ6FvA6MNUb8nYfnhsSvPUOOiw78TosAxyuT5/DjsXjuHzcoMoqDNkWZSVXrcyINXTuKHO5hiPevFG0uSxfkIhyUxdRbrbdl5hkyCl9LX+cji3MJKbLc7MMedAQM/jVku3WQ/QKPx+hmEgz70X7ZDOpa6/sNTXlEpfpJeWoMn8udpeZY/b1IUqymfekwzM3GfIHy80kqJvPer2mfMGG0YYuK85MRNoiy/yMou3WOb2y81RDd36vFYa8ttj0P+rffavVb5TZ7zab6eelK8z/s7b9rCSve35pY+gcpmvPIUl8bT45X5V5GKpSzO9K2krzWlanWd/DqIIyc4wlpRwtgbIlIPZEOEIcFfDuWChcD+Peh+whnq3HuVR9fAt3FC/iQFQMb531Cq3iW9XfXyiR2pEWN37HPz+7g6v3/8IfZ57Hf85/j+j0rsEeWdghEyJBCGG0JmCJEg/nXKy1/otPuRK4rJa2R+Sw7NWNaMRwBUEIIIG0JZ7+xJ4IDcDlhJnXe0JqXzoFOo+0dK1yePqEs1m1bgaTB95Lj9QewRtnUxIZS7cLX+Xxn/7GHze9y1/f/x2Pnfp3VI5/YEahKZElc4IQ0gQukaIgCOFMw2yJ2BMhoMx/CdZ9Duc+Bb0vNlRfb/uad9fNYHyv8YzqfXWQBnjsGHXK/3B793F8GhfFe1/eBp/9GRyyAvRYIRMiQQhhNJ6nuvVtgiAIddFQWyL2RAgoy6ZD1mAYcpOxO7cklwd/fpA+6X24a8BdQRrcseemofcyrPXJPJWezqal/4HXz/BE3hOaHLFsghDiBMgJWhCEMCeAQRUEoX4K1sGeFdDbTBvlcDm4d869APz91L8TaY88XOtmiU3ZeHT4Y8THpHBvt4FUFefBy6fC5jnBHlqzR3yIBCGE0SjcgUumKET7JSpNsRzY7dWm97sjwTSfkWWm3jcxa4RfvszKlmbyzaQV5nHLU1vUlH9rm1DnkBcuMJOt6haWx77L6Xfz6tdV54TCWvvd5zATkSYlmUEHLstabMizC3Jqyh1izH6fyvzNkKNtZnCHe3b3rylXOM2bnxHJawz5lxLT2fjHnZ1qypF28zMocZiBIXL3mklsO6RbCXF/W+2XPdcvP2pCphmwYOdeK4mvu6t5bRy7og05stT8HOLzrM5tZswIEreb18YZ65fkda+1hMa2r8QcssNseySILRGOOSs/ABTkXGjsfnbJs6zcu5JnRzxLVmLW4ds2Y9Jj03lk2CNM/HYik08ez32/fQaf3Q23zQO73LY3FfKoRxBCGA04dES9myAIQl001JaIPRECgtaeCVGHUyAxs2b3zzt+ZurqqVzZ40rOaH9GEAcYXE7NOpVxPcfx9uaPmTvkati7AX6bGuxhNWtkQiQIIY3C1YBNEAShbhpmS8SeCAFh93LYuxH6WMvlSqtLefCXB+mU3Im7B90dxMEdH9w18C66tujK/237hMLswfDDE1BdVn9D4aiQCZEghDAaT3b5+jZBEIS6aKgtEXsiBIQVM8EWAT0vqNn19OKnKago4JFhjxBtj66jcXgQbY/mqVOfosxRxiOZbaB0N8z7d7CH1WyRd9+CEOLIE9vAoaNM/xV7aVVNOaLIL2lrteljU55p+gFFVFp+IvYC0yGlpJMh4mhbbY7DYd10xm0w+61o6zLkwX6JWXNLLD+ZHin5hu7sVDNR6fTdQww5M9bySckrN/1tbH6JSp9bdrohn9hhS015yYH2hu6aYtM/Z3tJqiF3TrJ8jvq1yDN0W6paGvLSvaZPwYM9/ltT/u5AL0M3J6+LIWemmD4367a2rinHppuOXmd1XGvIn3072JATuluJaIvyzUyssfvNSUNCnvn5R5Zb13LXaYaKxO2mXN7S/JmO3WV9/jrG/G4Qk2bKxRwRYkuEY4LbDas+gs6nQ5zHFvy681dmrp/JdTnX0Tejb5AHePzQOaUzE/tN5JnFz/B11+Gc+dNzMPB6iE+rv7FwRMijHkEIYbRW8kRXEIRG01BbIvZEaDR5C6E4tya6XJmjjAd/eZAOSR24rd9tQR7c8cf4XuPpmdqTv9mLKXaVw4//CPaQmiVi2QQhhPE4Qtvr3QR9p2UZAAAgAElEQVRBEOqiobZE7InQaFbOhIgY6H4OAM8ufpbdZbt5ZNgjxETE1NM4/IiwRfDXk//K/uoSnu0yCBa8Cvu3BntYzQ6ZEAlCSKMkkaIgCAGgYbZE7IlwRKz6CDZ951kmB+ByevZ1PQtikliwawEz1s1gfK/x9GvZL7hjPY7pmdaTCTkT+KB6FwtiY+G7R4M9pGaH+BAJQgjjcYSWdf9Hi4qIwJ6Rbu2odhh6HWP5FFVkJxk633wwAO5I0wnY5rD8RioyzKfqiZvNcTgSzLauOKtteTszt4yKNX2Ilu5oa8hpSVYUok0H0g3dD/aehnxt658N+W8bzqU2MuLN6Eant91gyAsLLb+hXi12G7oxKcsN+YL2pr/OXwss3x//NxDfF5h5liLt5vn7jjkxusrQxUWbvlklVabPjT3a6svpMI/r73/kamn2VbTT+j5ElPjlCtpviBQOMH2I7FXWpCJtiVm3Osn8f07Z4JfEygflNK+FO7/2vFL1IbZECDjl++D9az3l1E4w8DpIzoKyAuhzKQ6Xg0fnP0pWQha39789qEMNBW494Va+2fYND9nj+XDlTGJOmght+tffUGgQ8qhHEEIcySwvCEIgaIgtEXsiNJi8hZ6/p9wFCa3g6/+DmddBVAJ0PYu317zNluIt3D/0fmIjYuvuSyAmIoYHT3qQXFcZL2a0gq/+z5PPSQgITfaGSCk1BfgdkK+17n0Y/TjgPkABJcCtWutlTTUeQWiOhEt2ebEngtC0hIstEY4hufNB2eHUeyEqDvashiVvQXoXdlcX8+KyFxmRNYJTs0495kMrq3KybW85uw9UsLu4it3FFRSUVlPldFHtdFPldON0uYmOsBMfHUFiTATx0XYyEqLJTo3zbC3iiI06tj51Q1oP4aIuF/HWxk+4MO9XOq6fDd1HH9MxNFeacsncG8DzwFu16LcAp2mt9yulzgFeAYY24XgEoVniDo8ntm8g9kQQmpQwsSXCsSJ3AWT28UyGAFr1gnOeAODpOffg1m7uG3Jfkw+jotrFwq37WJ5XxJpdJazedYCte8uMlytKQVp8FNERdqIjbERF2Ii026h0uCirclJa5aSs2oXLbb6RaZ0cQ9+sZE7ITuGErBT6ZCWTFBNJU3LngDv5etvX/L1VW178+i/Q5QywiwdMY2myK6i1nquU6lCH/hcfcR6QVVtdQRAOj9bgcDf/mxixJ4LQtISLLRGOES4n7FgM/ccfopq/az5fbv2S2064jazEwJtqrTXL8or5aUMBP20sZMm2IqpdnqAO7VLj6NU6iYv6t6VLywQyk2PITIohIzGaSHvd33+tNYWl1eTuLyd3n2fbkF/K8rxiZq/aA4BNQf92LRjZPYMR3VuS0yYJpQL75jUtNo1bT7iVpxY9xdy92zj1t7dg0PUBPUY4crxMKW8AvqhNqZS6GbgZIMaWcKzGJAjHPZ5lLnIT40fD7QlxuAosR3RbZzOhqHJaCTRj9pjO7aWdzGSckWVm4tKyTGsphdv/gaFZ9RAn/DKfrlOzigxdSam51t5RZZrx7ESr/oINZkLU4gozpO3uCvMcqhxWXx1b7DV0p6aZQRSKnXGGnBRtBZm4Js0M1vDHtVcY8rTkfYa8tdhK1Lqv2Ex426mVGSjgk+4fGPIf8qwEsZelLzR0k7efYchxkWbQjJhIK2CF73UDWPJjd0Mm1m+tfpwV0CCi1LzhqWphVo32S9Rq98nxG1ViBkaIOmDKjkTzyxNRWFpTdieZn4HN6XdgMw5GnYgtEQJK/ipwlEO2mfzZ4XLwt/l/o21CW67rfV3ADqe1Zs2uEmYt28mny3ayw5tIu1frJK4d1oFTuqTTv10KiY14e6OUIiMxmozEaAa0M//XissdLN9RxMKt+5mzLp9/fLWef3y1npaJ0ZzbpzWXDMiid9vATY6u7HklMzfM5Elt58TvHyeqz2UQnVh/Q6FWgj4hUkqNxHMDc0ptdbTWr+BZAkNyZEvxIBMEHyS7vMWR2pMkW5rYE0HwIrZECBi5Czx//SZE09ZOY3PxZp4//fmA5BwqrnDw/qJcpi/MZWN+KXabYnjXdO46sxsju2eQ5hfBs6lIjotkeNcMhnfN4E9ndqOgpIq56wv4Zs0epi3Yzhu/bKVbqwQuHpDFxQPa0jKxceceaYvkvsH3ccs3t/B2RAXX//IvGPk/ATqb8CSoj4OUUn2B14AxWuu99dUXBMHkYKjc+raGoJQarZRap5TaqJSadBh9tFJqhlc/33cJm1Lqfu/+dUqps+vrU3l4TCm1Xim1Ril1R2Oug7dPsSeCcJQ01JaEiz0RGknuAkjIhOTsml37K/fz0rKXGN52OKdln9ao7tfvKeF/PlrBiX/7lkc/W0NKbCSPXdSbhQ+cwRvXDeHSgVnHbDJ0ODISo7lkYBYvXj2Qhf9zBo9d1JvEmEie+GItpzzxPfe8v4x1u0sadYxhbYcxImsEL6emUTDveSjZE6DRhydBe0OklGoHfAiM11qvD9Y4BCG0CcwyF6WUHXgBOBPIAxYqpWZprVf7VLsB2K+17qKUGgs8CVyhlOoFjAVygDbAN0qpg8ljauvzWiAb6KG1diulWjZy/GJPBKFRBG7JXBPakylAJZ5Fp3cexp70Bd4E7vJGnrxCa73VO6b7vcd0AXdorWd7948GngPswGta6ye8+98ATgOKvce+Vmu9NCAXKBzIne95O+SzROyV5a9Q7izn7kF3H3W3S3OLePbr9cxZX0B0hI0x/dow4eQO5LRJDsSom4TkuEjGDW3PuKHt2VxQyhu/bOX9RXm8vziPU7tlcMupnTipc9pRLae7Z/A9XLjzJyYnxfDYz8/B6L81wRmEB00ZdvtdYASQrpTKAx4EIgG01i8BfwHSgH97vwROrfWgphqPIDRX3IFZ5jIE2Ki13gyglJoOjAF8b2DGAA95yzOB55Xnn3cMMF1rXQVsUUpt9PZHHX3eClyltXYDaK3z6xpcU9kTZVPYoq2niKq8sta6FdnmnC2izPT1sDnN1XeRZdbNpTKrUt6q4Z/ZvgIzIawqMc12TNtSQ1642fKDatmy2NAV+fkf7as0/XV88U/aWuI22368w8wq3y8tr6a8qspMFjsgI8+QV+/PNOSLsq0I6d9E9zB052eaSV3fLWlnyKe3WFNTfmTjeYauc7Lpf1TqMJ8Y7yu3zim3JMXQ9T55oyEvXd7JkKPyrc+hsrWZPDdml/kZxe2qfWWmtpnfBVeMOSmJ3VVhyL7JglWl6RPl6w93NATIlkDT2BMbkAL0xjPJ2gbcBNyF154A1+OZZHUMwEMbgHu01jMDdVHChpI9ULQNhtxUsyv3QC7T103noi4X0Tml8xF3uXJHMc9+vZ5v1+bTIi6Se87uzpVD2pEaH1V/4+OIThkJPDymN3ed0Y135m/jjV+2cdVr8zm5cxr3je7BCdkp9XfiQ7ukdozvdQ1TVk5h3LI36TXsDkjMrL+hcAhNGWXuynr0NwI3NtXxBSEc8ESGCkgehLZAro+cx6Fhq2vqaK2dSqliPJOQtngiu/m2PXhHXFufnfHcqFwEFOB5Ymt67fsg9kQQmpYA2hJoGnvSDdjnM8n6ETjRW6czcAVwL7BaKdWVxj+0EY6WvIP+Q9ZH/txvzxFpi2Riv4lH1FXuvnL+9vkavli5m+RYz0RowskdSIgOugt8o2gRH8Xtp3flxuGdmDZ/O89/v5ExL/zMOb0z+fPZ3emc0fAAYjf2uZEP1r3Pc8mVvPzT5JrQ5sKRISFlBCGEOZhMsQFr/tOVUot8tpuDPPRooNL7FudVPEthBEEIEg21JUG0J6mA7+vQfcDBV5zReJbS5eKxJVO01k48y90OTrL8J2ht69h/kMeUUsuVUs8qpQ7rkKKUuvngdSgoKDjqk2tW5C4AexS0PgGA5QXLmb11NhNyJpARl9GgLiodLp79ej1nPDOHOesLuHNUV368byQTR3YJ+cmQLzGRdq4/pSNz7x3JnaO6Mnd9AWc9O5dH/7uasipn/R0AiVGJ3HTC7/klNoZ5K96GAzubeNTNE5kQCUKI40bVuwGFWutBPtsrft3swLMG/yBZ3n2HraOUigCSgb11tK2rzzw8Pj8AH+FZ+y8IQhBpiC0Joj3ZB/g+Nk/FCizua0++IDD25H6gBzDYe6zDZhDVWr9y8DpkZDTsZr/Zk7sAWveDiGi01jy96GlSY1K5NufaeptqrZm9ajdnPDOH577dwFk5mXx792ncdWa3Jk94GkwSoiO468xuzLl3JJcPyua1n7ZwxjNzmL1qN1rXHwx1bI+xZMakMzklHv3jM8dgxM0PmRAJQggTwChzC4GuSqmOSqkoPOvtZ/nVmQVM8JYvBb7THks9CxjrjRrVEegKLKinz4+Bkd7yaYAEQhCEIBLgKHNNYU/mAqk+fQ7HWlp30J7sAC4A1jf2oY3Wepf2UAX8B2uJnVAXzmrY+VtNuO0fcn9gSf4SJvabSHxk7T6LAHtLq5g4bQm/n7qY+KgI3r3pRP51ZX9aJ8fW2a45kZ4QzeMX9+GDW08mOTaS309dzE1vLWJnUUWd7aLt0UwceCeroqP4as10KM6rs75wKM3nvaMghCmBiAzlXcN/OzAbT7SlKVrrVUqph4FFWutZwOvAVO/6+314bnLw1nsPz7p7JzBRa+0COFyf3kM+AbyjlLoLzzKYoPj/aLfGXVVVI9vK/BzYW6fVlONW7TJ0ZX3aGLIz1vwcKjIs2WHmz8TmtxKiuoX5BNCRZlVQ5aZfh/JL6upaZybj63Si9UO4eWe6oUtJMTN1OtzmmE/LsgIJPLlptKEr2G8e57a+cwz5Dymba8rnrTvf0FU6zSe7H/WcZsjrfIIdVKabdU+M3WTIO5ym0/G/to+iNqrd5k/csm1ZhpyZYQWd2LXODJqxMy7NkCPTzIAbjgSrb3uhOWZXnPl5+gfVqEyzJhV2vzgeEX5yVZqZrySq2PrMIsqrDJ0tyQzAQe0xQg5LoKLMNYU9UUrNw7ME7ls88zfwhNkHrz3BE3DhBOBsfCZZSqlZwDSl1DN4giocnGQpvBM3PBOhsXiCM6CUaq213uX1QboQWBmQi9Pc2b0cXFWQPQSn28mzS56lQ1IHLup6UZ3Nvly5mwc+WkFJpZN7R3fn5uGdiLCH7zP7ge1b8N8/nMIbv2zlma/Xc/bkuTx6YW/G9Gtba5vzO53Pm8tf5V8OJ6fP/QeR508+hiMOfWRCJAghjNYKZ+BuYj4HPvfb9xefciVwWS1tHwMea0if3v1FwHn++wVBCA6BtCWe/gJrT7yTrBuAyXgmWc/7TbLOU0rFAFOBD2j8Q5t3lFIZeCZNS4FbjvpihBMHE7JmDeGLLV+wpXgLz4x4hkjb4Ze7FZc7eHDWSj5eupOcNklMu6kf3TMTD1s33Iiw27hxeCfO6pXJXe8t5c7pS/lubT4Pj+lNcuyh19Nus3PHoD9zx/d38NGGD7m86G5IyT5Mz8LhkAmRIIQ4DU2UKAiCUBfHuy05xg9tTm/seMOS3PmQ3A5nQgYvfvMiPVJ7MKrd4d/irsgr5tZ3FrO7uJI7R3Xl9tO7EBnGb4Vqo11aHDNuPpEXf9jE5G83sHDLPp69oh9DO6UdUndE9gj6p/biJecKzv/5WWLPE3+ihiLfPEEIYQLoQyQIQhgTYB8iIVzJWwjZg/l006fkluRy2wm3YVPmrabWmnfmb+OSF3/B5dbM+P1J3HVmN5kM1UGE3cYfRnXlg1tPJjrSzlWvzee1HzcfEnBBKcUfh9xHQYSdGRs/hNI6U/wJPsgbIkEIceQG5ehRSqHstedecftENarMaW3oHAnmj7e92vxhSt5s+QGVZ5jH8E/MmuwXUmJfH6u+O9Z0GorJNP2A3G6zr7FtFtaUP4kwk6fml5m5LU5uucWQl+63fGxaxZUYusQo01/FPzHr3L1da8pRdtNpZmSGeYJ/3nGWIY/P+KWmvLjITLzq0Oa1ax1VZMhD07bWlH/KNxM+XtvKTC67rtD0E3L5+FB165Nr6vyWj+3Yn2zI7h2Wo7duZV6b+F9NJ/Aqv1yLcbut74rLdBHC6Z+YtdRMvmovtY7lTjGd1G3FZpLeI0VsidAoinLhwA4cWYN4efnL9ErrxYjsEUaV8monD3y0ko9+28Gp3TKYfEW/kEuuGkz6Zafw6R9O4Z73l/HoZ2tYmlvEk5f0Jd4nFPmAVgM4Mf0E/uNawhU/P0fs2Ye8GBUOg0zHBSGEOYI8RIIgCLVyhHmIBMHEUQEf/R5sEXwSqdlRuoOJ/SbiiUnhYWdRBRf/+xc+XrqDP53ZjTeuHSyToaMgITqCf48bwH2je/D5il1c/O9f2FJoPii7ddCf2Ge389666VCxP0gjDS1kQiQIIU4D84YIgiDUyRHkIRIEC5cD3psA236heswLvLLlE/qm92V42+E1VZbnFTHmhZ/Zsb+CN64bwh2jumKzyXfpaFFKceuIzrx5/RDySyq54Pmf+HXT3hr9gFYDGJqaw5SEaCrmvRTEkYYOMiEShBBGa3C6bfVugiAIddFQWyL2RDBwu+HjW2HDbPjdM3wUrdhVtst4OzR71W4uf/lXouw2PrjtZE7rJglsA8XwrhnMuv0UWiXFMGHKAj5ZauU/vnXIPeyz23l/5X+gqnHLacMBsWyCEOLIEhdBEAKBLJkTjgit4Yt7YMX7MOpBqvqP45UVr9C/ZX9OanMSAK/O3cwtby+mR2YSH08cRrdWElI70GSnxvHBLSfTr10Kd05fyktzNqG1ZmCrgQxJ6cF/4iKoXPR6sId53CNBFQQhhDm47l84OrTbjbvSclKPSDYTW9r3WU/VbIl1r3V3RZmfQ1EXKxhAzD4z4EJsoSnv72XKvsk3K5PNLK5VuWZghOyc3Ya8tsIK/uAfRGF4ppnkdF+16ZS/LT/VqtvRrJsQaQYOKKo2s80+kP1ZTfmv2y8w2/plH3X4ByxwtqgpZ0SbTzJ3VZrBDPxZtM8KwtCrhXkt3i8cbMg2mxmgolsLKwLTgtz2dR6nOt88X98z8AuiRVULU/ZPxOv2SSHin7TV7ZdepDLV/Jl2RVk3lPFr9piVI2oPEFIfYkuEI2bha55t2J0w/E98vHYG+eX5PHaKx4n/iS/W8tKcTZzXpzVPX34CMZFH//0U6iY5LpKpNwzh7veW8cQXa9mxv4KHLsjhlqH3cv3s65m59GWuHnoLRETX31mYIhMiQQhxtNzECIIQAMSWCA1Ga5j/EmQNgTP+itPt5D+r/kPf9L4MbjmE//tkJW/P2864oe14ZExv8Rc6BkRH2Pnn2P60TYnl5bmbOVDp4OnLBjIoqQuvO9dx6ZI3iRlyc7CHedwiS+YEIcQRJ2hBEAKBBFUQGsz2ebB3IwycAErxxZYv2FG6g+tybuCemct5e952fn9aJx69UCZDxxKbTXH/uT25d3R3Plm6kzum/8ZNg++jMMLOB4v/BS5n/Z2EKfKGSBBCGK0ld4ggCI1HbIlwRPw2FaISoNeFuLWbKSun0Cm5M+/NTeCr1Tu45+zu3DaisxF2Wzh23DaiC1F2G49+toYqZ0v6JbTnTecmLl8xg8h+44I9vOMSmRAJQkijjOSSwpGhbDZsMdaaanerVEOvI6xr64oyr3N1Yt2JWSPKrbLbbt4UOE13FHQr08eGUp/Eni6z7cPnvm/If1lg+uvERFiJPFNiKgzdR2vMZKpZGWZ+iugYq+3JyRsN3ZyibobcKaHQkB/YclFNuU/KTkOXYi835LfazzXkWWXWBYm2m08wc+J3GPLAmK2G/Nm2nJpyQZnpE5URb+bmSI0zr0dOwq6acmQ707/o+0U5hty5p3lOWxdbSWzd+ea6/MrWpmNQixXmdyV+t6X3yztLZYq5I6bU7Ct6r/VdcbQxnZUit/j5FB0RYkuEBlJVAqs+gj6XQnQCc7Z/z8aijXRVN/HV6gIePL8X1w3rGOxRhj03Du9EVISNv3yyiv7dzmdXxPN8Oe9pzu87Fmziz+WPWD9BCHG0VvVugiAI9dEQWyL2RGDlh+Aoh/7XoLXm1RWvEkM6S1Z3kMnQccY1J3Xg8Yv7sHRDG1q4kpliL0Ov/iTYwzoukQmRIIQwGgm7LQhC42moLRF7IvDbVEjvDlmDmL9rASsKV1C06xTuHS2ToeORK4e047ELT2D3njPZGBXF3J+f8KyRFQyabEKklJqilMpXSq2sRa+UUv9USm1USi1XSg1oqrEIQrNFe+xafVuoI/ZEEJqYBtqS5mBPhEaQvxbyFsKA8Wjgge+fw+1M4Mb+l3PbiC7BHp1QC1cNbcedJ40lxhHDFPaj138Z7CEddzTlG6I3gNF16M8Bunq3m4EXm3AsgtBsCZOoUG8g9kQQmhSJMifUy29TwRYBfcfywGefk+9cQb+kC7j3rN7BHplQDxNHdKd3ymUsiYnh2y8ekqcbfjRZUAWt9VylVIc6qowB3tJaa2CeUipFKdVaa72rjjaCIPigw8QRuqnsidYa7bKc1tX6rYbe1qZVTTnaL3Ssb/JUgL19zEgJsXstJ/2yTLOuf/LN6FiHIVe2sJz0VaTp7P/QJ5cb8uBh68xxVFqBBQpLzSADY3MWGXKpywwGsDbCOt+v9/UydNUu0wn3zsxvDPmpSmu++t2OroZuVM/Vhtxn/lWGPLr9mpryiOQ1hm5NRVtDnl4x1JBv7PpzTfnjXWbQiJaxJYY8IGm72de2QTXlIt9AFoCtRbUhb8ptacjEWZ+LSjbrxq42+9rfy/wMqxOtn97YAvOmJC7fDCqh3Ka+2ue7Ebtpr6FzFx/gaAkXWyI0Amc1LJsO3c9hxpoKPtwyjdikOF664HaJJhciPH/BREZOm8GsqEKqPnmX8y68qv5GYUIwrV9bINdHzvPuOwSl1M1KqUVKqUXV7orDVRGEsEWWuABHaU8cuvJwVQQhLJElc0KdrP8SygtZ0XIMD3w6l8jEFVzV63ISoxODPTKhgcRHxTO+zzV8Hx9H+fLn+HyFvIM4SEg8DtJav6K1HqS1HhRli62/gSCEERIV6sjwtSeRKibYwxGE4waJMifUSsV++OkZHHGtGPd9HBltF2K32RnfS3LahBpX51xDjLKzLDWfR2bMYWluUbCHdFwQzAnRDiDbR87y7hMEoYF4ntgG5gZGKTVaKbXOG5hg0mH00UqpGV79fN8lbEqp+7371ymlzq6vT6XUG0qpLUqppd7NXOt05Ig9EYRG0FBbEib2RPClcAO8Ogq9eyUPVo0jLk7jTpjP2R3OIjM+M9ijE46QFjEtuDDrdD5PiOfshPnc+OYi8vaX19+wmRPMxKyzgNuVUtOBoUCx+A8JwpETiDC4Sik78AJwJp7lZguVUrO01r7OHzcA+7XWXZRSY4EngSuUUr2AsUAO0Ab4Ril1MItnXX3eo7We2ejBezgqe6LsNmwJPn42DtN/A5v1zMgdbZrLsjam/43NdAMyZH+df2JW9zpzyYndx8fIWWH67jiTzESdG/alG3LbJMuP5Ixs079oe4WZyPPnjZ0N+Zq+833qmklqz083fXs2OTIMuX+StWLxxJTNhm5agen3M6rdekO+J+OnmvJmh/nW7sPSgYbs6yMFsLnUOv93uk03dJevMZ9eX5Ux35CrHNZnmpZkJnHdszfZkOOTzeXaZVirFdxlplOYI9lcVxafaz57TMy1fIoqMkyd3mv+P7ujTDmmoKqmrCpN3yVXZRWNIVAhtZuBPREOsvFbeP86tD2Se+IfZfaBjlxz5jbeWlfGNTnXBHt0wlFy9cA7mLH9a1JaLaZq22hueGMRM289icSYyPobN1OaMuz2u8CvQHelVJ5S6gal1C1KqVu8VT4HNgMbgVeB25pqLILQnAnQmv8hwEat9WatdTUwHU+gAl/GAG96yzOBUcrjSTsGmK61rtJab8HzPz2kgX02CLEngtD0BNCH6Li2J0IDWfAqvHMZOrktD2X+iw8Ks5l8ZV++zpvJoFaDyEnLCfYIhaOkfXIHTotpxUe6kH9f2oFNBaXcPu03XO7wdRJssgmR1vpKrXVrrXWk1jpLa/261volrfVLXr3WWk/UWnfWWvfRWi+qr09BEEw0CrfbVu8GpB8MJODdbvbrqiFBCWrqaK2dQDGQVkfb+vp8zJsz6FmllPm6xf88xZ4IQpPSUFvSHOyJ0ACKtsPnf4Yuo3ijx8u8uVpzz9ndcUQvY1fZLq7pJW+HQp2re45jn91OYcFbPDymN3PWF/DM1+vqb9hMCYmgCoIg1I5uwAYUHgwk4N1eCc5oa7gf6AEMBlKB+4I7HEEQGmJLxJ6ECWv+C8DCnvfyyNe5nNsnk1tO7cSbq96kfVJ7Tss+LcgDFBrLkN7X0M3hZmruV1w5JJuxg7N54ftNfL16T7CHFhRkQiQIoUzggio0JChBTR2lVASQDOyto22tfWqtd3nf6lQB/8GzHEYQhGAR2KAKTWVP+h0MqgCMw8+eeOtnA/c1NlCDj/6fSqnShpx0s2Ltf6lO68FN/91Pl5YJPHXpCSwrXMbKvSsZ33M8NiW3j6GOstu5OiWHDbqS+Xk/8tAFOfRpm8yf3lvK1sKy+jtoZgQzqIIgCIEgMEt+FwJdlVId8dxkjAX8M7bNAibg8eW5FPhOa62VUrOAaUqpZ/A4QXcFFgCqtj4PJk31+gxcCKwMyFkcKW6NrvDJRdStg6G2FVn3QZUZUYYufqfpwF7SvvZVOi6/6N4JeeaHtvcEU07uYIVBLdqZZI4p3ozQsG9HiiHHRFqBIZY6swzdjv1moICubfMNeU+1dayTkzcautn7TH+B1CgzKtG8PR1qyue0NROx+lPtNn96nio4paacHmnee3aJLzDkKJsZ+OLs1FU15Tu2n2/oLmy71JBv/XqCIadmWdc5LdY8n7QsU95YYAaviNxhfR8cyWbiVVdbM79Vi19NR+XiTtb5J+SZQTIiS83zq0o1265Wgc0AACAASURBVNpLre+djjG/kxFt/CJ+5XJkBM59oCnsiR04ARgFLAYK8QRZqLEneAI1pAP/ApbSyEANSqlBgBmJJBwoK0Rv/5WZ0ZfjcmteHj+I+OgI3lr1FsnRyZzf+fz6+xBCgnP7Xsfkn+7m7SXPc+KYU/n3uAGc//xP3PL2Yj66bRixUfb6O2kmyBRfEEKcQDzR9a7hvx2YDawB3tNar1JKPayUusBb7XUgzft09k/AJG/bVcB7wGrgS2Ci1tpVW5/evt5RSq0AVuC5gXk0IBdDEISjJlBviJrCngADgeXAa96/c4He3r4O2pMngZ147EmjAjV4I+U9Bdx7VBczlFn3OUq7eae4L8+N7UfH9Hh2le7iu9zvuLTrpcRFxtXfhxASRHcaxRXlDuYUrWHbgW1kp8Yx+Yp+rNtTwgMfr0CHUSZmeUMkCCGMBtzuwITK1Vp/jidam+++v/iUK4HLamn7GPBYQ/r07j+9seMVBCFwBNKWQJPYk7bAb1rrGwGUUuPxhNivsSdKqZXAjVrrUq/sG6hhnk9fvgEZ/AM1HIwRfzswy/smuwFn3HzIXzCTap3OSSeP4PQerQCYsW4GAFd0vyKYQxMCTUQUl2cO47XSRby9aioPnPS/jOjekjtHdWXyNxsY2jGVKwa3C/YojwnyhkgQQhkNaFX/JgiCUBcNtSVhYE+UUm3wTNb+1YC6Nx+MtldQUFBf9eOenfkFpOz+mcWxw7j3nJ4AVLmq+GDDB4zMHknrhNZBHqEQaNJ7Xcy5pWV8svEjDlR78tjdcXpXhnVJ46FZq9lcEB4udPKGSBBCnDB6o93kqNKKWnUJm0sMubi76dtTlWQ+X4rda/mVxO02P6TyTPOmUvnlfijam2AdN9P8MSrbYSZxVQmmz0l2ouUX45ssFeCl9SMNOa6lGU1oSYHlc7S7wjzOJa2WGPKaijaGfFH2sppypdv0e9leYiZ53VtmLrlJi7f8dQanbzN0PWLN/LpD4jcZ8ms7T60pr9pu3qxVtzfXv7dqv8+QYyKsa9cpodDQfbu9myHHRptJUMurrM8webV5nPLWptPY/q7m5+3ycTdzxJnfm8rupi9a0lbTZ0xV+shRfkkU/RK1HinHuS05kkANeQ0M1EAt+/sDXYCN3rdDcUqpjVrrLv6D8kbYewVg0KBBx/cVrAeny830d17nTzgZcs4EoiI8380vt3xJUVURV/a4MsgjFJqELqO46lMHnyRWM2vjLK7udTU2m+Lpy/ox+rm5/HHGUmbecnLN96G50rzPThDCgQbGyRUEQaiTI4i7HQRqAjUopaLwBEmY5VfnYKAG8AnU4N0/VikV7Q30cDBQw2H71Fp/prXO1Fp30Fp3AMoPNxlqbvzzu4103jeHqqgWtO4zAgCtNdPWTqNzcmeGZEow0GZJVDy92p9GX4dmxrrpuLXnYV5mcgxPXNyX5XnFTP5mfZAH2fTIhEgQQpqAhckVBCGsaZgtCZY9CULgl7Bi4dZ9vPzdGs6KXEZ0znlg87z1XF64nNV7V3NljysJN1+qsCLnIsbu38vWA9uYt8tytxvdO5Oxg7N5cc4m5m3eG8QBNj0yIRKEUOf4faIrCEIocXy/IUJr/bnWupvWurM38AJa679orWd5y5Va68u01l201kO01pt92j7mbddda/1FXX0e5rgJh9vfXCivdvLn95fxu6QNxLrLoIcVVvvdte+SEJkgobabO73GcLa9BanaxvS10w3V//2uFx3S4vnTjKUUlztq6SD0ER8iQQhlNOgARoYKN7TbjbvSyusS4TRzwjjaWClI3H75GCIqzdwz2MznS3aHdedYkm3q/NLwoMzDYt9nVSgvNn2VVLqZ/8jtMMc1f3XnmnLPIbsN3aVDFxpyboWZYqWsysprc3O3uYbup1LTp+b73V0Nedduq68Hhn5m6DLjDxhy5yTTX8c351HnKDM30pzSHoYcY6v9B/niHDPv0MLC9oY8PNP0P1pRZPlB+edGKttuXvfyVPO608L6/N3Rdf8Par9UHr6plMramG1b/2rmMCrNMnMNuSPTasrxm4sMnY7zS3h1JIgtCVv+/uU6tu0t570+G2FbAnQaAUBhRSGzt85mbPexEmq7uWOPJOrEW7l44VNMyf2BXaW7agJoxEdHMPmKflzy4i88OGslk8f2D/JgmwZ5QyQIIY9qwCYIglAfDbElYk+aE/M37+WNX7Zy7YlZtNr5LXQ5AyI9E+sP1n+A0+2UUNvhwoAJXFYFoHl//fuG6oTsFG4/vQsfL93J/7N35uFRVvfi/5xZk5A9YclCSEhYw77JqiAgqCyiKFhrtbXaXrvZXq3a21rtrfdq29vW2nq91r0/rSKKoKwiRVBBdlnCngRIgJB932bm/P6YITNnSDIDzCQZOJ/nmSfvec/3nPe87zvzzXve8102HCpqtXmooydEGk2o04VNXDQaTQjRxU3mNIGlrsnGz9/fS1p8BI8Nq4XaczDIaRrX7GhmyZElTEqeRHpMeucOVNMxhEWTPOIerq2r5/3DS2iyq1ErH5yaxYCeUfzig/1UNVx5pnN6QqTRhDr6AUaj0QQCPSG6qjhvKve7hcMIy/8XCANkTQdg06lNnKs7x+KBizt5lJoOZfy/cWd1HWVNlaw7sU6pspgMPLtwGOeqG3hm9aFOGmDw0BMijSaU0YlZNRpNINCJWa8qtuWVOU3lJqYzvm8CHN8AKaMh3OkLuOTIEnp168WUlCmdPFJNhxKdzPisufRptvNOzv+7oHpE71jum5zB21+dZMvxKyvqnA6qoNGEOF08mWLXx+GOaCBNXoETStxJUR3R4UpdfXc1KWZYmRpkoSHW/b7JpPrJU5uuRlGQVq8ADXb3Q6ewqQ+gXrEbGJCuJi4tqnYnVN1ZkabUdbeqSV53neytlAcmu23DnzyiRpV6ZsAHSvmkV0CG4QmnW7arHapzf5Ndva6PJG9QyoM8LuWyWjW5qvc5fG7LVMrZse7z9w6iEGZSzTqavaIbFFbGtGwfLeyh1FlLvRKmWr2SoEa676Hd6/y8gyhEnqRNjF7fDVu42jjqhBrMwVTpTh7cmKQmz7XuyWv7QH6gdcnVQZPNweMfOE3lfj57ANSXw+ldcO0jAJyqPsWXp7/kwREPYjQYffSmudIwTPoxi95aye/MBzhYepBBCYOU+p/NHMC6nCIe+2Ava35yLeGWK+M7oleINJpQxyF8fzQajcYX/ugSrU9Cnr9vzuV4cS1Pzc8mwmKCvE0gHdB3GgBLjyzFKIzcmnVrJ49U0yn0zGZ+4mjCpGTpoXcvqA63GHnm1mGcKK3jj58c7oQBBgc9IdJoQhwhfX80Go3GF/7oEq1PQptTZXU8v+EoNw7pxbQBrlXR4xvAEgWpY2i2N/PhsQ+5LvU6enbr2bmD1XQa0ZN/yg01tazM/Yi65roL6idkJnDnuDRe/SKfQ2erWukh9NATIo0mlNFO0BqNJhD4q0u0PglpnvooB4MQ/GrOYOcOKZ0TooxrwWjm05OfUtZQxu0Dbu/cgWo6l/Rrud0RQa2jiTX5a1oVeXT2AKLDTPx6+QHkFWBvG1QfIiHEbOA5wAi8LKV8xqs+DXgDiHXJPCalXBXMMWk0VxZXvpOzEOJTKeV0L32ClDLLS+7i9YkQCKvVXfRKzCo9NKQtUk2Qaa5R/X6aolU7aluE+77YvPJlmmrUd1GiXC3b0t2OJY4GVU0bDOpxI0xNbdbv36f61AwZekIp3zfkS6X8yv6JLdt9e6rJU188O1UpWzyziwL3JboTuX5cNUKVNarX9YH931TK1TVu/6yoyHql7ulBy5Xy/5y4QSnHmdxvLyf3UBOv1titSnlPaapSnt3nYMv2ipXjlbqGJPX8sKjXPTLOfdzaRtWXJ+q4+l2o83rRHlHkfnhojFV/v+Y67/eU6v03l7rHYa70ShZ7WVz5ugTc+sTXviuRT3KKWH+wiF/cNJDkWNdvriwXKk7CxB8D8N6R90iJTGFi8sR2etJc8RgMDO8/n6xTH7D00Dvc2u9C88nYCAsPzxrAfyzbz0d7zzBveHIrHYUOQVshEkIYgb8BNwKDgTuFEIO9xH4JLJFSjgQWAy8EazwazRXLFfpGVwgRJoSIBxKFEAnA/+LUEzcCqVqfaDQB5gpeIfLSJ3FCiHjXJx1I6dzRBZ+6JhtPrjhA/56RfHtShrviuCvASeb15FXmse3sNhb2X4hBaAOiqx2RvYCF1dXsKzvIobLWw2wvHpvGkJRonl6ZQ22jrVWZUCGY3/hxwDEpZa6Usgl4B5jvJSOBaNd2DHAajUZzcTj8+IQm3wN2AgOBvUBP4ANgKbAWrU80msDijy65MvTJTo/PcuCvnTiuDuGvG45RWFHPb28Zitno8eiXuxFi0yC+L0uPLMUkTNySdUunjVPThUgdwxxDHFYES48sbVXEaBA8NW8IRVWN/PVfxzp4gIElmBOiFOCUR7mAC9/CPAl8UwhRAKwCfhTE8Wg0Vx5XcB4iKeVzUsoM4GHgJ8DbUsoMKeVwnJMirU80mkBxhech8tQnUsq+Ll2SIaUcLqW8oidEp8rqeHlzHreOTGFcRry7wm5zRpjrO41GRxPLjy/n+rTrSQxP7LzBaroOQhAzaD6zamr5+HjrwRUARveJY+HoVF7enEtucU2rMqFAZ6+J3gm8LqVMBW4C/iHEheu0QogHhBA7hBA7mhz1F3Si0VzNBCoqlBBithDisBDimBDisVbqrUKId131X7lMTc7XPe7af1gIMesi+vyLEMKXBj0LhLnkfymE+ADo04rcReuTZtlwQScazdVKIKPMdWV9IoSIcsn/UgjxgRBilH9nFZr8fu1hDAZ4ZPYAtaJwJzRWQeb1fHLiEyobK3UwBY1K9q0srKqi1lbH2vy1bYo9OnsgYSYjT36UE7IBFoIZVKEQ8Mz6l+ra58l9wGwAKeUWIUQYkAic8xSSUr4EvAQQY+4RmldaowkWAfhFePj8zcS5mrtdCLFCSpnjIXYfUC6lzBJCLAaeBRa5fHkWA9lAMrBeCNHf1abNPoUQYwA1u2fr/AqnucuPgCzg9zj9if7XS+6i9Um0IUG5etKiJt9sSnYn7jTVqMELGuO7KWVzrWpLVJ/Q9vum8DPqW3a7V9AFaXL3Jc1qv/ExtUp594EMpTxggFvNjhijWg02S3VMy04NV8pTMtxBCY5XqW+J8xvUxLRRVtWhf1nl6JZt72AGI6NPKeVT1bFK+foBe1u2rV7BGt4rGauUb+61Tym/csTt/G0xtW/DHmVV7+HSPe4x/+TW1W32C5DQTX07eqLAfX3CStQgCgavWAfdqtUfaW2y+/7HH1QDTtSkqn31/EqdtFcPdP9kInOrlTpZf5kT/AD9d+3q+kRK+Z4QYjIwA7c+uebyzrprsudUBSu+Ps2Prs8iKUb9DXN8AwgDZFzLss2PkBqZyrhe4zpnoJquScooRoT1IhMLS48sZUG/Ba2KdY+y8tDM/vznxzlsPFLsDukeQvhcIRJC/EwIcSkOh9uBfkKIDCGEBaeCW+ElcxKY7jrOIJxvgYsv4Vgajeby8Mfnbz7OKG7gNFmbLoQQrv3vSCkbpZR5wDFXf631+XshRIrrgen3wM/9GJsdpz7pDywDPgG6o/WJRtNV6Sh9Mh9aJmAXo08AbgZeklKuBCztyIcsUkr+a+VBEiMtfO+6zAsFjm+A5JGcstWy7ew2FvRboIMpaFSEQGTPZ2FZMXtL9nK4rO1ErHeP70NafATPrj6EwxF6axf+fPOjgHVCiM1CiB8KIfzK1CWltAE/xOn8fBBn9KcDQojfCCHmucT+HbhfCPE18E/gXhmqa20aTSfhp4lL4nkzMdfnAa9u/PH5a5Fx/b4rgYR22ra2PxFYBxwByvDPRbsQ55vhBpyrRAeBCq1PNJrAchEmc11Fn5zv84fACinlGT9Os1AI8X/AImCVEMJK57sPBIV1OUVsyy/joRn9ibR6GQTVVzhN5jKvZ9mxZRiEgfmZ3nNWjQbIXsDc6moswthmcAUAi8nAw7MGcOhsNcu/9jYI6/r4NJmTUj4FPCWEGIZTgXwmhCiQUs7wo+0qnM7Nnvue8NjOASZd9Kg1Go0TCTj8cnIukVKOCfJo/GE78F/Ax8Bh4DNc/kHtcAdOU7g/SCmPCiGSgKGg9YlGEzD81yXQdfQJQohk4HZgqp9NPPVJhUufPBKk4XUazXYHz6w+RGb3biwe2/tCgfzNIO3YMq5j+fYnmZwymZ7d/HrfrbnaSB5FTHQqM4hgZd5KHh77MFajtVXROUOT+L/PjvM/645w09AkrCZjq3JdkYvxITqH07m5FAg940CN5kolMGsg/vj8nZcpEEKYcIa2LvXRtrX9I13b3wO6AUYhxDHvRKvnkVLWCSHOAZOBo4DN9TfgiGrVP8fi4YLT2Fv1e7GWNSvl5khVnZoa3DfGrHZLxSC1bKpWH0SbK9z/bIzR6nGKTsQrZXOs6rBytNCtni1pqn/KudpIpTy+Z75SPlCR1LJdUKy6Yzw+SvWxefWE6mOTaHb7s3xVmq7U3d1XTQB7JFZ98CrySGz62xQ1l+60z9RggUlDK5XyN7O2t2yvPzdQqTt2NEkpk1KhFD2TqxY2qufbzcvf6MRx9d+eCHdfW3uY+iOsSVcPay1V729MrnthtK67+sDQHKG2NTSp97DbSfeXqTlWfZdgsquyF03g1lM7Wp9kAcecFndEdBV90pn8c9tJ8kpqeeWeMZiMrSyAHf0ELJF8aWjmXP05fpH1i44fpCY0EAKyF7Bg999Z1TORDSc3cGPGja2KGgyCx24cyN2vbOOtrSf5zuSMVuW6Iv74ED0ohNgIfIpzOft+KeWwYA9Mo9H4R4CiQvnj87cCuMe1vRDY4DJJWwEsdkWNygD6Adva6DMC59vYYuB5YBRQ29bDC4AQ4tfAo8Djrl1m4P/5dVYajcZvAhhlrqP0yQop5UopZS8pZbqUMh2ou9r1SXVDM39ef5QJfRO4fmAr76/tNji0EvrP4v3jy4kPi+fa3td2/EA1ocPgWxhXV0eKOYZlR5e1KzqlX3cmZyXy/IajVDU0tyvblfDHbrY38JCUMltK+aRXlBiNRtPZBCCzvJ8+f68ACUKIY8DPgMdcbQ8AS4AcYA3wAymlvbU+ca5KX6w+WQDMA2pdxzuN07dRo9EEEn90SRfSJy7Zi+WK1ydvbjlBWW0Tj904ENeqmcrJL6GuhJJ+09lUsIl5mfMwG8wXymk050keiSEunfnNBrae2crpmvbznj86eyDldc38fVNuBw3w8vHHh+hxXzIajaYTCZCZix8+fw04bfVba/s08LQ/fbYiE9lePdAkpZRCON9NCyG6+ZDXaDSXQgBDkGh90jlUNzTz9825XD+wB8O9zHxbyFkOpnA+ogabtLUZSlmjaUEIGLKQ+Vue4397J7P82HL+bcS/tSk+NDWGOcOSeHlzHneP70OPaF+uwp3PFRlZRaO5WghkIsUuzBJXVKhYIcT9wHrg7508Jo3misJfXaL1SdfmzS0nqKhr5ifT+7Uu4HDAwY+QWTP4IPdjRvYYSd+Yvh07SE1oMuwOkm3NjI9I4cNjH+KQ7QeJffiGATTZHbz4WWisEgUzMatGo+kI/I8MFap0x5mnpAoYADyBM6Hi5SMlstmdzFM2qY70mKJbNkuGqFF1euyqV8q2cPU+ODwsUBq7q3XCrj5V1qeqCUUNDe53Vd7vu4Vd7cvWqKrxtOTSlu1Dp9XgBZ6JVwH2lKYq5czokpbtGcMOKXXLz41Qyj/p+6lS/uXOW9o8ztOnblbK1ya07cP+1OnZSnl4nwJ1HHlDlXJzszsoweBeZ5W660eoFpnxFjW6hWdi1g9q1POTdvV9YdgZ9To3R7vr7Vb1fprq1Htk9MqXWt/d3Ta8WH2oMNeqbet7qVEWws65v3fe3yND72T1QBcbKuDK1yUQTH3SydQ02nyvDp36CmqK2N1nFPlHXuM7Q77TsYPUhC7dB0CvYSyorOTn5mq2nd3G+KTxbYqnJ3bjlhEpvL3tBA9OyyQxsvXIdF0FvUKk0YQ4V8Eb3ZlSyk+klI9IKR+WUn4CtB7iRqPRXDJdfYVICDFbCHFYCHFMCPFYK/VWIcS7rvqvhBDpHnWPu/yVfgIYzusTwAj8xLtPIcQrQoivhRB7hRBLhRC+TPE6nTe+zG9/dQic5nJGK8uazxFhimBW+qyOG6Am9Bl2B9cXHiDK3M1ncAWAB6dl0mhz8MrneR0wuMtDT4g0mlAnAE7QXREhxL8JIfYBA1wPJec/ecDezh6fRnPFEaCgCsFACGHEmaD5RmAwcKcQYrCX2H1AuSvK3J+AZ11tBwM/wJnc2QGsOK9PgI9wBm/w7vOnUsrhrqi6J3EGdOiy+LU65HDAwRXUZU5j7akNzEqfRYQ5onVZjaY1htyGVQputiaz/sR6Khsr2xXP7B7JzUOT+MeWE1TWde2Ic3pCpNGEMl38je5l8jYwF2cY3rken9FSym925sA0miuOru9DNA44JqXMlVI2Ae8A871k5gNvuLaXAtOFM8zafOBlYA6wHNgK/Nr12SSlvMW7TyllFYCrfThd/NWSX6tDhTuhqpD1SVnU2+qZn+V9+TQaH0QnQ/pkbj2TR5OjidV5q302+cG0LGoabbz+ZX7wx3cZaB8ijSbU6dL/pi8dKWUlUAnc2WEHjYtRx2Bxq8i4I+rbrcZ4NUxtU5T6fsla4b4xBq8XY8YG1VfDblXbmmvcZcvJcKWuaoDqb2Q0qz4o8WFuP5nqSItSt+1MmlKekqo6u1oM7r53V6nZ7VMj1KSm48PUPJvLJrzYsv330ilKndWojjm/IVEpH6pUfZ08mdb9iFLOjCxpQxIijWqS2n8eHq2U0xPLlLIwuO+Ro0H9dxjbo1op1w5Sz0Gedd8XS7l6/xp7eCdIVesjzrjvf2OsV12R2tZSqX55hMM9ZnOp6hMlalW/touma+uSFOCUR7kAuKYtGSmlTQhRiTN/YgqwVUqZj3MV6BWcpnIAnrY8Sp9CiNeAm3CGAP/31gYlhHgAeAAgLS2tNZGg49fqEEDOh2Aws6KhkNTIVEb1GNVxg9RcOQy7g0ErfsTApMksO7aMxQMXtys+KCmamYN78uoXedw3JYNIa9eceugVIo0mxBEO3x+NRqPxhT+65GrSJ1LKbwPJOPMeLWpD5iUp5Rgp5Zju3bt36PjO8/ZXPiLLAUgJOSs43XcKX53byfys+a3nKNJofDFoHhgtzCeSnNIcjpb7jt7yw2lZVNY38/+2nuiAAV4aekKk0Wg0Go2mq1OIM1H8eVJd+1qVEUKYgBigtJ22PvuUUtpxmtLddtlnEASa7Q5e/yKfCX0T2l8dOr0bKk+yIrEXAPMy57Utq9G0R3gs9J/FTXm7MAkTHx3/yGeT4b1jmdIvkZc351Lf5L2C3jXQEyKNJtTpok7QGo0mxOjCQRWA7UA/IUSGEMICLMbpX+jJCuAe1/ZCYIOUUrr2L3ZFocsA+gHb2upTOMmCFh+iecAhuiCr95/ldGUD352S0b7gwRVIg4nlNblc0+sakiOT25fXaNpj6O3E15xjctxAPs79GJvD5rPJj67vR0lNE+9sP9kBA7x49IRIowllurYTtEajCRW6eFAFKaUNZ6S3tThN2JZIKQ8IIX4jhDi/3PEKkOAKr/0z4DFX2wPAEpy+QGuAH0gp7W31CQjgDVeUy31AEvCbDjpVv5FS8vLmXPomdmPagB5tCzocsP8DdqWPpaD2tA6moLl8+s0Cawzz620U1xez9cxWn03GZcQzNj2OV7/Iw+7oeg8mXdOzSaPR+E/X0yuhgxAIc9tq0B7hDpwgjV6BECxq2VzrlWzVI/mmudorgaaXxYDwSojZmOgWsId5vbfyut+OZrW+zuYOpNBkU8+tX0KxUj5apfo8TE50J1StNoYpdfFm1YH/urU/VcpD+7v93UfHqm8AR0bkK+ViW7RS9gyqcOyM+mA3Jl7ta2D4GaX83hl34IQIk5pY12BQL1Z1U9uJAcPj1IAE9Y1q0Iy+PdVgDofrk1q2G81Gpc7gFTQj0uuFaFOUe7vbWdUpx1KlfjmEXa23eQTKkDHq+ViL2g444RddXJdIKVcBq7z2PeGx3QDc3kbbp4Gn/ezTAUwKwJCDyo4T5ewtqOS3twzBYGjHHyhvI1ScYHnWcCIqy5meNr3Dxqi5QjGHwZAFXPv1O8T0zWTFsRVMTpnss9m3J2Xw4Fu72HDoHDMHtx1MpzPQK0QaTajTdU1cNBpNKNG1TeY0Xry8OZfYCDO3jUptX3DnG9RFxLGu8ig3pN+gcw9pAsPkn2GRDm40RLHh1Aaqm6p9NrlhcE+SYsJ4/cuul6hVT4g0mhBGoKNCaTSay8dfXaL1SdfgRGkt63KKuOuaNMItxrYFa4rh0Eo+7XcttbZa5mdqczlNgIjrA2PuY37ebhrtjazNX+uziclo4O4JffjiWClHinxPoDoSPSHSaEKZLmzzr9FoQogu7kOkUXnti3xMBsG3JqS3L/j12+BoZrnZ5sw91FPnHtIEkGsfJlta6CusrDjuHeOkdRaPTcNqMnS5RK3ah0ijCXX0A0rgsHglW41x+2t4J8hsilb9Nxq8Emx6+omY6tTD1KSpN81c6eWPVOl+42utVNtWRqqyprNq8lU8ckNGhzcoVfsL1chSfXqoiUpP1se3bCeFqQd+e884pfz98RuV8kt73Pbjk+KPK3WZ5lK1r3PjlfLdKW6H3H+g1g2LUB1wntijhgt+a+wrLds/PqwmCLQfjlLK5QOUIjFxbr+o3rFq4tnCKtXP6fDhFKVsrHXfb2Ojek+k1wv7Gi+LJqN6W1TZFPU7GHeouQ1JCMtRo07byivbkPQTrUtCgsq6ZpbsOMXc4cn0jA5rW1BK2PUmZ3uPZVvpfr4//PsYhH4Prgkg3RIRk37M7VMNkgAAIABJREFUvF1/4c+ykZNVJ0mLbj9BcXw3C7eMSGHZrkIenTWQmAhzu/Idhf5laDShjrb512g0gUD7EIUE/9x+kromO/dN9hFq+8QXUHqMlb0HIZHM7Tu3YwaouboY/yBzHOEYJH6vEt0zMZ36ZjtLdpzyLdxBBHVCJISYLYQ4LIQ4JoR4rA2ZO4QQOUKIA0KIt4M5Ho3mSuRqMXHR+kSjCS7aZK7r43BI/rntJOMy4slOjmlfeOfrSGsMH9edZHj34fSO7t2+vEZzKVgj6Tnl54yvr+ejw0twSN+OhoOTo7kmI543tuR3mRDcQZsQCSGMwN+AG4HBwJ1CiMFeMv2Ax4FJUsps4KFgjUejuWK5Ct7oan2i0XQAeoWoy7M1r5QTpXXcOc7H5KauDHJWcGjwbI5V5urVIU1wGX0v82QEpxvL2Xl2u19N7p2YTkF5PZ8eLAry4PwjmD5E44BjUspcACHEO8B8nInRznM/8DcpZTmAlPJcEMej0Vx5yMBFfRJCzAaeA4zAy1LKZ7zqrcCbwGigFFgkpcx31T0O3AfYgR9LKde216cQ4hVgDM7gVkeAe6WUNe0Mr0P0iahSc+2En3GrSGlS3x+Za738jaJUP5L4w+4bUzpIdSqxqi41NMWpT5nS41DWci//lAg1T42plzpmi9Ejh5FDHXP3ODWqT5RZdWbZdsZt+50So/qjPDNxqVL2ziV059AdLdvv5I5W6hL7q8cdGa2aSRQ0uX2XPMcP8EL+NKX8/ezNSnlzXf+W7dt771LqzGlqX729fJleOOXuu7ReDUUcZVVzGpXb1fuQONid86fxYzV3UmOcUsQe1vYswhbm5RPWoMraw9V/05ZSd74k2S1cqTNmpaudH27zsBcSQF0CXV6fhCxLtp8iKszEjUOS2hfc+y7YG/koJhZTlYlZ6bM6ZoCaqxOjmesnPELEnmdYufc1xiZd47PJzME9SY4J4/Uv87khu1cHDLJ9gmkylwJ4/tcrcO3zpD/QXwjxhRBiq0vZXYAQ4gEhxA4hxI4mR31rIhrN1UsA3uj6swKD8wGlXEqZBfwJeNbVdjCwGMgGZgMvCCGMPvr8qZRyuJRyGHASZ7b49giKPmmW7Xi3azRXGwFaIQoBfRKSVNY1s2r/WW4ZkUKYuZ1Q21LCztexpYxiVdE2rk25ltiw2I4bqOaqJHzwAmbUN7Ku6Csa7Y0+5U1GA3eN78OXx0s5WVrnUz7YdHZQBRPQD5gK3An8XQhxwa9WSvmSlHKMlHKMxRDuXa3RXNUEyOa/ZQVGStkEnF+B8WQ+8IZreykwXQghXPvfkVI2SinzgGOu/trsU0pZBeBqH05gDHEuWp+YRTsRmjSaq4wA+hBdCfqky7H860KabA4WjfVhLnd6FxQfYmu/ayltKGVupjaX03QA1khujhlEtbSx6dRnfjVZMDIFIeD9XQVBHpxvgjkhKgQ8f7Wprn2eFAArpJTNLsV3BOcDjUaj8Rf/3ugmnl8VcX0e8OrFnxWYFhkppQ2oBBLaadtun0KI14CzwEDgeR9nqfWJRhNs/F8hCnV9EpK8s+0U2cnRDEnxEUxh3/tgMPORrCLaEs21qdd2zAA1Vz3XDF5Md5uNj3Pe8ks+OTaciZkJfLC7AEcnB1cI5oRoO9BPCJEhhLDgXAL3jsf3Ic63uQghEnGavOQGcUwazZWF/w8wJedXRVyflzpnwG6klN8GkoGDwCIf4lqfaDTBxF9dcmXok5Bjf2ElOWeqWOxrdchhh/3vU5s1nQ2FnzMrfRYWo6X9NhpNgDAOvImbahvYVLybioYK3w2A20alcqqsnu35Zb6Fg0jQgipIKW1CiB8Ca3E6QL4qpTwghPgNsENKucJVd4MQIgen8+QjUsrStnvVaDSeCAIWBtefFZjzMgVCCBMQg9MZur227fYppbS7AiT8HHitrcF1mD4xqXb5do+EcQ6LWieNqjN87DHVCb9kmDtxq7VcPYzDRx46U42774qhNqXOHK4m6oyOUP2gmuzucVbVqSaBE1LzlXJxY6Tal0ci14ExauSftWVDlbJ34lazcAcweHzQaqXu49LhSjk78oxSfmn99JbtX8z+UKkLM6jn+3rBRKXc7HG+0Vb1WnS3qn7171WpwR4abO5/gUaDGlGgtFYNsiCN6g+tqNAdOUEMUNtGnPYKwFGiflcMHrEevE7vgiALDpNX2eN7aGpQv3PY1SASF0MAdQl0cX0Siryz/SRWk4F5I7wX2rw48QXUnGV9ygAa8nO0uZymYwmPY07sIN6Qp1iXv5Y7Bvp+NzF7SC9+9eF+3t9VwDV9EzpgkK0TVB8iKeUqKWV/KWWmlPJp174nXA8vSCc/k1IOllIOlVK+E8zxaDRXIgGy+fdnBWYFcI9reyGwQUopXfsXCyGsQogMnGZq29rqUzjJghab/3nAIV8D1PpEowkuAfQh6vL6JJSob7KzfM9pbhqaREy4j7cp+94DSyQf1ReQGpnKiO4jOmaQGo2LAYNuI6upiY8Pv+eXfITFxE1Dk1i17yz1TZf+Uudy6eygChqN5nIJQFQolw3/+RWYg8CS8yswQoh5LrFXgAQhxDHgZ8BjrrYHgCU4Q2CvAX4gpbS31SfOl9FvCCH2AfuAJOA3l3kVNBrN5RKgKHNanwSW1fvPUN1g444xPszlbI2Qs4Ki/jPYVrSDOZlzcM4RNZqOQwycw5yaOnZXHOZU9SnfDYDbRqdS02hj7YGzQR5d2wQzD5FGo+kIAmTmIqVcBazy2veEx3YDcHsbbZ8GnvazTwcwKQBD1mg0gSSAPs1anwSOd7efIj0hgvF949sXPPYpNFSwJjEFWbuLmzNu7pgBajSeRPXk5pgB/JkiVuWu4nvDv+ezybj0eFLjwnl/VwG3jPRhFhok9IRIowll/Ddh0bSCEAJhdPtkSItqjmI+6U6+ae+lZts0l6l5E2qyvCI/ebiVNCR6HdfLKsBc6eVj4uFXElakqukGq+qvcu6c2nnyyOMt21ndS5S6A2Vq8rspvY4r5S/rM1q2+4WrPkSxker5flSi+gU9krymZfs/8hYodd9J/VwpN0v1nMaOO9KyvfycauJzrlb1c/Iec6TRne/iw/xhSt2wPqrbysajatDBXt3dflC9o1QH4KPN6nWNT1XrHR5JbyvORSl1dqtqfOF9vz2Tr3r7k1kr1fvbkKBeq7Ai931oTlPHaD7t5ax2MWhd0iU5W9nAV3ll/HRGf9+rPfuXQng8K6uOkp2QTXpMeoeMUaPxptegBYz9+s98fPQDHhj2gM/vrsEguHVUKs9vOMqZynqSYjo+xY42mdNoQp0AmLhoNBpNoEzmNIHjvAnRzcN6tS/YWAOHVpE7YCYHyw9xc1+9OqTpRAbNZW5NLfm1p9lfst+vJreNSkFKWLbbO/5Kx6AnRBpNiCMcvj8ajUbjC390idYnHcvq/Wfo1yOSrB5R7QseXg22elbGxmEQBmanz+6YAWo0rRGbxoyoTCwSVuWt8i0P9Enoxtj0ON7fWYAzvkrHoidEGk2IE6CoUBqN5iongFHmNAGguLqRbXll3Dg0ybfwvveQ0SmsKt3LuF7j6B7RPfgD1GjaIWrQfK6rq2N17krsDv+ix902KpXjxbXsL6wK8uguRE+INJpQRpu4aDSaQHBxiVk1HcC6nLM4JNw4xIe5XF0ZHP+Uvf2nUVBToM3lNF2DQfO4qaaW0sZytp3d5leTG7J7YRDwSU7HR5vTQRU0mlBHP6AEjlLVKV3GuQMleCdmrU/rppQdarXiLB/mlYC7rqd60yxeQRVqMt3JWA2RaubOcK/ErE1latCBOps7K31KhJo89fpENT3Lh4VqAINvpG1v2S5pVk10auxqkldv3im/pmX77pStSt2ciGKl/FJlf6XsmUy2b6QaCOK7yZuU8lOH5ijlO9J3t2xnxKl5eHOq1AdJzyAKAKVV7nt4Ol8NUGCMUq+zxaqWp/Y51rL9xcZRSl1Donp/ow6rZc/vRnVv9b2kPUz9IkUUqW9WbVHuhL+m6kalTtbWc1loXdKlWL3vLBmJ3RjYy4e53I5XwGFjZUQYlnIL09Omty+v0XQEif2YYu1JJE6zuQnJE3w2ie9mYUyfeNblFPGzGwYEf4we6BUijSaEOZ9dXpu4aDSay8FfXaL1ScdQXtvEltxSbhzSq/0IXZUFsPmPNA+cw9riHVzX+zqiLD4mUBpNRyAE1v6zmV5by/oTn9Bob/TdBpg5uCeHzlZzyiuSa7DREyKNJsQRDunzo9FoNL7wR5d0pj4RQswWQhwWQhwTQjzWSr1VCPGuq/4rIUS6R93jrv2HhRCzfPUphHjLtX+/EOJVIYRXgPTg8klOEXaH5CZf/kPrfgXSwVcjb6OsoUyby2m6Fv1u4Kaqamqaa9lcsNmvJjMG9wRg/cEiH5KBRU+INJpQRtv8azSaQNDFfYiEEEbgb8CNwGDgTiHEYC+x+4ByKWUW8CfgWVfbwcBiIBuYDbwghDD66PMtYCAwFAgHvhvE07uAVfvP0Ds+nOzk6LaF8jbDgQ9g0kOsPLedKEsUU1KmdNwgNRpfpE9mnN1IgrD4HW0uI7EbWT0i+SSnYydE2odIowlxtAlL4BBRqj+O56X19iEKP9uglOt7qT420kO8WXU3wtCsmsDU9lZjGZtj3aYF9rNqgrrwrFql3JSkmiFMSMhr2f68JFOp21KQrpRvzfpaKa8tzm7Z/nXaCqVu0ZdqtvEx6Sdoi+ePT1PKH8WoTlRHy1R/ne7d3Od0oEJ9I769OE0pZyeqzrbrzw1s2W62q/fosb6rlfKnVV7Pzz08xnhsiFKVEK1e59On45Xy6p0eSWD725Q6c6U6jqYor/ud7C732KW2lV6+aHaL2lbY3d8VQ0WNUueoVcd8sXRxXTIOOCalzAUQQrwDzAdyPGTmA0+6tpcCfxVOe7P5wDtSykYgTwhxzNUfbfUppWx5ehNCbANSg3Vi3lTWNfPFsRK+PSmjbXM5uw1WPwoxadSN/x6ffjCbmzJuwmK0tC6v0XQGJiumvlOZXbWX9059RnVTtV8mnTMH9+SlTblU1jUTE9Exi7N6hUijCXW66BtdjUYTYnThFSIgBTjlUS5w7WtVRkppAyqBhHba+uzTZSp3N7Dmss/AT9YfLKLZLtuPLrfjVTh3AGY9zWdnv6LeVs9NGTd11BA1Gv/pfwM3lRXR5Gji05Of+tVk5uCe2B2SjUfOBXlwbvSESKMJcbQTtEajCQQ6qEKrvABsklK26gAhhHhACLFDCLGjuLi4NZGLZvX+syTHhDGid2zrArUl8K/fQt+pMGguq/JW0SO8B6N7jg7I8TWagJI1k6GNTaSaoliV65/Z3IjUWBIjrazrQLM5PSHSaEKdrvtGV6PRhBJde4WoEOjtUU517WtVRghhAmKA0nbattunEOLXQHfgZ20NSkr5kpRyjJRyTPful58MtabRxqajxcwektS2udymP0BTLdz4Oyqbqvi88HNmZczCaDC2Lq/RdCYxKYieQ7mpWfDV2a8oqS/x2cRgEMwY1IPPDhfTaPMvqevloidEGk0oI0E4fH80Go2mXfzUJZ2oT7YD/YQQGUIIC84gCSu8ZFYA97i2FwIbpJTStX+xKwpdBtAP2NZen0KI7wKzgDullB121l/lltJkczBjUI/WBezNsG8JDJoL3Qew4eQGbA6bNpfTdG3638DNp4/ikA7W5q/1q8nMwT2pabTxVW6Zb+EAoIMqaDQhzPncIZpLxGjAENN2FCfh8WaqMV517DTWq29j7Wb1bW7yZreDe9FYNaqC9HoVZS33Ss5ZH9Gybe6rOs7X7E1Qyo5I9Qvw5l53gtTstDNK3c19Dyhls1DfvFU1ugNDPH1KDd97/7DPlfLw8JNK+X9O3NCyvbjPDqWu0hahlL/fa6NSXlI2rmW7f4QaNOG9U2rS057WaqUcaWpq2Y43q0EFXi+apJT3FKouJ56BE5rqVGf0gWl5SvnM2TilbD3r8e/T63HZYVbviWcQBQCLR37YqnT133B0vhpkIbxYTQhrD3fLG2PVICAG7zepFxFjoavrEimlTQjxQ2AtYARelVIeEEL8BtghpVwBvAL8wxU0oQznBAeX3BKcARhswA+klHaA1vp0HfJF4ASwxbVS84GU8jfBPs8tx0uxmAyM6hPXukDuRqgrhaF3AM6El72jepOdkN26vEbTFeg3i76b/4eB4b1YlbuKuwbd5bPJpKxEws1GPskp4tr+l7/66gs9IdJoQh3ZhZ9iNBpN6NDFdYkr8tsqr31PeGw3ALe30fZp4Gl/+nTt75Tnoy+PlzI6LY4wcxvmb/veg7BYyJpBSX0J285u474h97WfvFWj6WxSx0B4HLPtFv5cspeC6gJSo9oP3BhmNnJt/0TWHyziN/Ozg/4d1yZzGk2Io52gNRpNINBBFTqXiromDp6tYkJmQusCTXVw8GMYPB9MFtblr8MhHdpcTtP1MRghawazCw8BsCbfv6CNMwb15ExlA/sLq4I5OiDIEyJfWaU95G4TQkghxJhgjkejueLo2k7QAUXrE40miHTxxKxXA1tzy5CStidER1ZDcy0MdS6Crc5bTb+4fmTFZXXgKDWaS6TfLFJqShgek8nqvNW+5YHpg3oCsPFw8MNvB21J2CMD9Eycsf23CyFWSClzvOSigJ8AXwVrLBrNlUygnJyFELOB53Da0r8spXzGq94KvAmMxhm5aZGUMt9V9zjOLPF24MdSyrXt9SmEeAsYAzTjdG7+npRSdZZQjx0UfSJtduxl5S1lQx+vJXyH++KGFTcpVWWD1USsibtVX5/SYR7+HV6vngzN7Zcb093HMh9V/UREP/U43cyq30hdjbVl+9DpnkrdEaNqhx1uVQ88tMdpt2y56tRtTVBl11QOpS0eistXypP23qqUR2aq9Z5+Q7uq1ESsmTFqRCKrQfWxOVztPsc7UrcpdatPLVTKBoP6NN8zwu2PVJav5nzZ0KAmcU1OV8dx1uP6hJ9Vb7Cwq6Yd1nKlSFSh+xzqE1TTqOZual+GZrVsbHR/J6VJrZP19VwOgQyY0JX1SVdla24p4WYjw1PbCLe9bylEJUOfiZyuOc2e4j38eOSPO3aQGs2lkjUdhIEbRQzPlO/ieMVxMmMz220S381C/56R7DxZ3q5cIAjmClFLVmkpZRNwPgO0N/8JPAs0tFKn0Wh8EIioUB4TjhuBwcCdQojBXmL3AeVSyizgTzh/t7jkFgPZwGzgBSGE0UefbwEDgaFAOPBdH0PU+kSjCTKBijIXAvqkS/Ll8RLGpMdhMbXyaFZXBkc/gSG3gsHYYnI0O2N2B49So7lEIuKh93huOH0EgzD4bTY3uk88u06U43AEd3k6mBMifzJAjwJ6SylXBnEcGs2Vi8TpCO3r4xt/JhzzgTdc20uB6cLp5TgfeEdK2SilzAOOufprs08p5SrpAucb3fa9K7U+0WiCi7+65MrQJ12OkppGjhTVtG0ud3AFOJphqHPVc3XeaoYlDqN3VO/W5TWarsiguXQvymFsfDar81Yj/dAno/vEUdVg4+i5Gp+yl0OnRZkTQhiAPwL3+iH7APAAQJgh0oe0RnN14aeTc6IQwjMW8ktSypc8yq1NOK5BpUXGFQK3Ekhw7d/q1fb8ZKXdPoUQZuBunGZul8wl6xMifEhrNFcPFxEw4YrWJ53B1txSACb0bWNCtG8pJGRB0ghyK3M5VHaIR8c+etHHaW5upqCggIYGvYiuuXTCwsJITU3FbDb7FvZk0FxY+zizDdE8VbWPg2UHGZzgvXisMsYVgn7HiTIG9Iq61CH7JJgTIl9ZpaOAIcBGVyi9XsAKIcQ8KaWSxMKlaF8CiDH30C6dGo0n/v0iSqSUXTHIwAvAJinlZh9yQdEn0YYErU80mvP4/2sIdX3S5dhyvJRIq4mhKTEXVladhvzPYepjIARr8tYgENyQfsOFsj4oKCggKiqK9PR0Hapbc0lIKSktLaWgoICMjIyLaxzbG5JHMqPwEE9bTazJW+NzQtQnIYLESAs7T5Rz1zV9LmPk7RPMCVFLBmicDy6LgW+cr5RSVgKJ58tCiI3Aw94PLxqNpm0CmEzR14TDU6ZACGECYnA6Q7fXts0+hRC/BroD3/NjfMHRJ1Iim90O7qJazWQp49xJW431qo92t7Pqm7GaPupqU9Qpt3xTtOo4XzLMy1G+QX0wiUvwcPZ3qIljjc2q2vZOKJrUy+18Wteo1vWOrVDb2tVx/aTX+pbtp5rmKXVTIo4o5U2l/ZTyvalftmz/8lzbARcA3j43Xim/2sdtS/7rRjUhZVmTmtR25Qk1AeV1qcdath/YdrdS1z1OTeI6JTlXKaeHuQMlHHSo5yMa1Xt09qAaZMLYyx3AwHxUHWPFSPW7Yq5TvyuVfd330Fqm/oAtVWqQDFs39R6FnfEwGzF4BXMID+dSCXBi1q6uT7ocW46XMjY9DpOxFU+G/R8AEoYsRErJ6rzVjOk1hh4RPS6U9UFDQ4OeDGkuCyEECQkJFBcXX1oHg+YR++lTTBh/G2vy1/DQ6IcwiLY9eIQQjO4Tx84TwQ2sEDQfIimlDTifAfogsOR8VmkhxLz2W2s0Gr+QEuHw/fGDlgmHEMKCc8KxwktmBXCPa3shsMFls78CWCyEsLomLP1w2vG32acQ4rvALOBOKaVPN22tTzSaIOOnLrkS9ElXo6iqgdySWiZmJrYusH8pJI+ExCyOlB8hvyqf2emXHkxBT4Y0l8tlfYcGOf9l3yhiOFN7hq+Lv/bZZHSfOE6U1lFc3Xjpx/VBUH2IfGWV9to/NZhj0WiuWALwVtdlw39+wmEEXj0/4QB2SClXAK8A/xBCHAPKcD6Q4JJbAuQANuAHUko7QGt9ug75InAC2OJSrB9IKX/jY4xan2g0wSRAK0ShoE+6EluOu/yHWguoUF8Bp/fA1McBZzAFozAys8/MjhyiRhM4ErOgx2CmnT6I1Wxldd5qRvYY2W6T0X3iAdh5oozZQ5KCMqxOC6qg0WgCQ6DMXHxNOKSUDcDtbbR9Gnjanz5d+7Xu0Wi6GAE0mdP65CLYcryU6DATg5KiL6w8tQ2Q0GcCUkrW5K/hmqRriAuLu1BWowkVBs0l8rPfce3kb7A2fy2Pjn0Uo8HYpviQlGgsJgM78sv1hEij0bSCBIIcm/9KRhgMGMLciUwdlVVqvYcPUWOCmojVblFNBkz16n2oyHT779QlqXVRJ9RxNHsFzqk4Ft+ybVRdSjClqSYDTSWq/4o52W0xVHFGfcCKsKrJZaf1OqqUF33pdr8wGFTLo+IUdZA2qf7zSjG57buPCTUh7NP9PlTKS8rGKeVfFE1s2c6tUc2GlmWpz7/PR/VVyiUeF+++IV8qdW8cVgObfdaYpZQ/rnH7OsWMVROvNlWo11WWWZWyrdT9ffBye8JyTv3XalO/OkQUub8PYRXqDW6MU69rbI76nTSUuf2i7L28Dmz3+rJcDFqXdBpf5pZwTd8EjIZWzJBObgGDCVJGc6D0AIU1hXxvWEi6SQFQUVHB22+/zYMPPsjGjRv5wx/+wMcff9xhx9+4cSMWi4WJE50658UXXyQiIoJvfetbF91XZGQkNTVth4J+5JFHWLVqFTfddBO///3vL3nM7XHvvfcyZ84cFi5c6Fu4KzFoHnz2LLNEDJ80lLGjaAfXJHkHonRjNRkZnhoT1AStekKk0YQ6+hlGo9EEAq1LOpyC8jpOldXz7YltROs6uRWShoOlG2vy1mAymLg+7fqAHPupjw6Qc7rKt+BFMDg5ml/PzW6zvqKighdeeIEHH3wwoMf1xGazYTK1/ni7ceNGIiMjWyZE3//+94M2jpdeeomysjKMxrZXPq5aemZDfF+uLTxIuCm8ZeWzPUb3ieeVz3NpaLYTZg78NQ1mYlaNRtMBCOn7o9FoNL7wR5dofRJYtuWVAW34D9kaoXAnpE3AIR2syV/DpORJxFhbCc0dIjz22GMcP36cESNG8Mgjj1BTU8PChQsZOHAgd911V0uizp07d3LdddcxevRoZs2axZkzZwDYs2cP48ePZ9iwYSxYsIDycueKwdSpU3nooYcYM2YMzz33HMXFxdx2222MHTuWsWPH8sUXX5Cfn8+LL77In/70J0aMGMHmzZt58skn+cMf/gDAsWPHmDFjBsOHD2fUqFEcP36cmpoapk+fzqhRoxg6dCjLly/36zznzZtHTU0No0eP5t133+Xee+9l6dKlLfWRkc6cmhs3bmTq1KmtXoPt27czceJEhg8fzrhx46iurm71WCGJEDBoLuH5m5maNJH1J9bT7Ghut8noPnE02yV7CyqDMiS9QqTRhDh+Rn3SaDSadtG6pOM5eq4Gs1HQr0crSedP7wZ7I6RN4OvirymqK+InowKXc7a9lZxg8cwzz7B//3727NnDxo0bmT9/PgcOHCA5OZlJkybxxRdfcM011/CjH/2I5cuX0717d959913+4z/+g1dffZVvfetbPP/881x33XU88cQTPPXUU/z5z38GoKmpiR07nJkWvvGNb/DTn/6UyZMnc/LkSWbNmsXBgwf5/ve/T2RkJA8//DAAn376acvY7rrrLh577DEWLFhAQ0MDDocDi8XCsmXLiI6OpqSkhPHjxzNv3jyfUdZWrFhBZGQke/bsAWD16tVtyu7evfuCazBu3DgWLVrEu+++y9ixY6mqqiL8MsLqd0kGzYcvnmOWMY7VjRVsO7ONSSmT2hQf7ZGgdVxGfJtyl4qeEGk0oYxEm7loNJrLR+uSTiGvuJa0+IjW8w+d3OL8mzaeNfv/jtVoZVrvaR07wCAzbtw4UlNTARgxYgT5+fnExsayf/9+Zs50RtKz2+0kJSVRWVlJRUUF1113HQD33HMPt9/ujsuxaNGilu3169eTk5PTUq6qqmrX36e6uprCwkIWLFgAQFiY0/GvubmZX/ziF2zAXqP8AAAgAElEQVTatAmDwUBhYSFFRUX06tUrQFeg9WsQExNDUlISY8eOBSA6upWAG6FO8kiITmFy4UEizZHOFdB2JkTx3Sz07d6NXUHKR6QnRBpNCONMpqifYi4VKSXSwxHdYFUd50W5274+zKQ+sDRFq2YrlkqvZJy1bhtnh9otVapvPyYvSwjZjjFz0zk1AaypR71SNntEYbDGq3WZMWrggChjg1LO6OWuT+um/tP5tErNJt43Uu2r0OZ28M8KK2qzDuCFlK1K+VmPJK+zU/Ypdd8+OVUpx1vqlHKTo+1/Y1nd1TFen3hIKa886w6qUFanvn2VlWpSWxGvBrNwNLiP2xyj3jBTnfr22OJl4WGudf9m6xNUW3hbmNq2to+6cmBOcI8z7PBZAoXWJZ1DXkktGYmtrA6B038ooR/28DjWnVjHlJQpRFrakA1RrB4612g0YrPZkFKSnZ3Nli1bFNnKyvZNpbp1cwdCcTgcbN26tWVic6m89dZbFBcXs3PnTsxmM+np6TQ0NPhu6IXJZMLhcLSMranJHeCmtWvQFt/+9rfZvXs3ycnJrFp1QcDF0MJggMHzsW5/mWmT7+bTk5/yxPgnMBvNbTYZ0yeOT3KKkFIGPJ+W9iHSaEIdhx8fjUaj8YU/ukTrk4DhcEjyS2vJSIxordI5IUobz86inZTUlzArY1bHDzLAREVF+fSFGTBgAMXFxS0ToubmZg4cOEBMTAxxcXFs3rwZgH/84x8tq0Xe3HDDDTz//PMt5fOma20dPyoqitTUVD780BkRs7Gxkbq6OiorK+nRowdms5l//etfnDhx4oK2/pCens7OnTsBpzldc3P7/jIDBgzgzJkzbN++HXCuYNlsNl577TX27NkT+pOh84y6B+xNzGqSVDdVs+XMlnbFR/eJo7yumePFtQEfip4QaTQhjpDS50ej0Wh84Y8u0fokcJypaqDR5mh9hajkMDRUQNoE1uSvIdwUzrUp13b8IANMQkICkyZNYsiQITzyyCOtylgsFpYuXcqjjz7K8OHDGTFiBF9+6Qyp/8Ybb/DII48wbNgw9uzZwxNPtJqbm7/85S/s2LGDYcOGMXjwYF588UUA5s6dy7Jly1qCKnjyj3/8g7/85S8MGzaMiRMncvbsWe666y527NjB0KFDefPNNxk4cOAlnff999/PZ599xvDhw9myZYuymtXWNXj33Xf50Y9+xPDhw5k5c+YlrUx1eXoMhPQpTMxZT5QlijV5a9oV90zQGmi0yZxGE8pou3+NRhMItC7pcPJcb7kzElt5OD7hnADYeo9j/fr/47rU64gwt7KSFIK8/fbbre7/61//2rI9YsQINm3adIHMiBEj2Lp16wX7N27cqJQTExN59913L5Dr378/e/fubSlPmTKlZbtfv35s2LDhgjbepnvnac8nybu+Z8+eyrifffZZwBkdb+rUqS37Pa/B2LFjWz1XT15//fV260OCcfdjXvItpg+4lU9ObaDR3ojVaG1VNLN7N+IizOw8Uc6isWkBHYaeEGk0IY3UkaEuAyEEwjNHRA819G1zD4/ErPGqgjbXqLZDzZGqOvXMWxqruq5Qk6baPjfHqPfQ4GFN4ZX/lBHDcpXy7hw1f0l1jHuc4VbVLMPb3+ZMk+oH5elHkx17Rj1ut5NK+Ylt85TyoRR3MtbqJvVafSNtOyqlSinSw5fp9SLVqbaiUfXtyYxQ/YLCPC7WiQb1/pmEmqh0V5X6D/TYEXfGc2uC6m9liFOT2HonqpV17htjt6r3zx6hyjbFeNu6u40zjE1q2+57VFMQ6eVsL+wefV9OItYL0Lqko8krbWdCdHIrRPZkW2Mx5Y3lzE6f3cGj02g6iAE3QVQSs0vP8KGjls8LP2d62vRWRYUQzBmWTHR44KcvekKk0YQ62oRFo9EEAq1LOpS84lrCzUZ6RrfyNtzlP7TuxDoiTBFMTp3c8QPU+GTfvn3cfffdyj6r1cpXX33VSSMKQYxmGP1txm38L2L7Z7M2b22bEyKA/7xlSFCGoSdEGk0oI0FoJ2eNRnO5aF3S4eSV1JCR2O3CaFmVBVB5kubx32P9iXeYljatTRMiTecydOjQloANmstg9D2YN/2OGaZ4VhZspN5WT7ipY/Mu6aAKGk2oI6Xvj0aj0fjCH12i9UnAyC+ta9tcDtjWLZrKxkpm9Qn96HIaTbtE9YJBc5ldkEO9rZ7NBZt9twkweoVIowl19PPJpWMQiHCPPBWVqpOs2eb20WiO6qHU2cPU90nS2HZOBIdXWoXIk+pNq+yv1ssUd84bs1nNSZFXrvrJGLqpfkIVNe63at45i/K9+vrqcF+lfM0At3/S2Mg8pS7FpOYlGttXDT87MvpUy3ZJsxo1a1dVH6X8rF3NDdLgcYG88wyVNqgPjDEmtd4zl5DRa4njwd7/UspPHZqjlH85dUXL9v8cmKHURUWqPkUNO9XM6FaPYTTFef0IHV4+YtFqvef3wewVPbain3rPzHXqOXUrdPtb2VMSlTpjoepfddF0cV0ihJgNPAcYgZellM941VuBN4HROB3VFkkp8111jwP3AXbgx1LKte31KYT4IfAQkAl0l1Je5sVVabY7OFlWx81Dky6sPLkFLJGsrTpCpDmSiSkTA3lojaZrMvZ+Rh9YRnzP7qzNX8sN6Td06OH1CpFGE+IIh8PnR6PRaHzhjy7pLH0ihDACfwNuBAYDdwohBnuJ3QeUSymzgD8Bz7raDgYWA9nAbOAFIYTRR59fADOAS0s844NTZXXYHbLNFaLmlDGsP7WBab21uZzmKqHPREzdBzGzwc7mwk3UNdf5bhNA9IRIowllJDqRokajuXz81SWdp0/GAceklLlSyibgHWC+l8x84A3X9lJgunA66MwH3pFSNkop84Bjrv7a7FNKufv86lIwyHdFmEv3nhDVl0PRAbb06EN1UzWz0rW53KUydepUduzY4bf8xo0bmTNnjm9BTXAQAsbex6zik9TbGthc2LFmc3pCpNGEMAKdSFGj0Vw+/uqSTtQnKcApj3KBa1+rMlJKG1AJJLTT1p8+20UI8YAQYocQYkdxcbHf7XJdOYj6ek+IclYAkrXGJqLMUUxInnAxw9FoQpuBcxjV0EiCMZy1+Ws79NDah0ijCXX0hEej0QQCrUsuGinlS8BLAGPGjPH7AuaV1BIbYSaum0Wt2PM2TYn9+VfJXq5Pux6L0dJ6B4Fg9WNwdl9g++w1FG58ps3q2tpa7rjjDgoKCrDb7fzqV7/i8OHDfPTRR9TX1zNx4kT+7//+DyEEU6dOZeTIkWzevJna2lrefPNN/vu//5t9+/axaNEifvvb35Kfn8/s2bMZPXo0u3btIjs7mzfffJOICNUXb926dfz617+msbGRzMxMXnvtNSIjI1mzZg0PPfQQERERTJ6sQ5t3OtFJGHsMZqZd8GHBZuqa6zosIbGeEGk0oU6AHmKuJIdlv5ESmt2BBkS0GuZTWtze76Y6NQlmY6zJq6w60js8gizE5KmBD0qz1SgL5kp1WA0e76ibC9U3yI0xamAEbxqb3QlDrx9zQKlLCy9Tyifj1UABhXXuRK17atUkpq+Xq47dzXY1Y+yMZPexPq4aodRZw9QxN3hFmThY06tl+2xttFJ3fx/VbKLYFqWUqxvd/hXZ8We9ZNW+qmvU+7uy2B2QYUJqvlK3eeNQpeyVH5W6FLftmLFRvffSK4iGtVxt7B1kw5PGeLWvmFw1Qayxxh1ww1BcoTY2emXxvVgCOCEKgj4pBEYIIQ67+jwGfOaS99QnQ4ACIYQJiHH1XQj09jh8qmsf7ewPKvmltaQneK0OlRyDU1vZMvG7VJ9Zd0Way61Zs4bk5GRWrlwJQGVlJTNnzuSJJ54A4O677+bjjz9m7ty5AFgsFnbs2MFzzz3H/Pnz2blzJ/Hx8WRmZvLTn/4UgMOHD/PKK68wadIkvvOd7/DCCy/w8MMPtxyzpKSE3/72t6xfv55u3brx7LPP8sc//pGf//zn3H///WzYsIGsrCwWLVrUwVdD0yp9pzFr7xu80zOeTQWbmJ3RMUmJgzoh8kMh/gz4LmADioHvSCmD4sCo0VyRnLf7v0w8nItn4jQb2S6EWCGlzPEQa3FYFkIsxumwvMjLYTkZWC+EOB83ra0+vwA+BjZexBi1PtFogkWAdAkETZ/sBIYD013bJa5jgFuf7HS1XQMsBDZIKaUQYgXwthDij64++wHbAAH0E0Jk4JwILQa+EZir0D55xbWM76tGjOTrt0EYWGt2EG2JZnzS+OAOop2VnGAxdOhQ/v3f/51HH32UOXPmMGXKFN5//31+97vfUVdXR1lZGdnZ2S0Tonnz5rW0y87OJinJGZWvb9++nDp1itjYWHr37s2kSZMA+OY3v8lf/vIXZUK0detWcnJyWmSampqYMGEChw4dIiMjg379+rW0femllzrsWmjaIHMaI7f+je7mdNbmrw39CZGfCnE3MEZKWSeE+Dfgd4Ceoms0F0GAoj61OBcDCCHOOxd7/l7nA0+6tpcCf/V2WAbyhBDnHZZpq08p5W7XPr8Gp/WJRhN8AhhBLlj6ZC/wMs6XIpuAIUKIscAOKeVuIUQNEOdqU4ZzgoOU8oAQYonr+DbgB1JKu2tsPwTWuvp8VUp5wLX/x8DPgV7AXiHEKinldwNxceqb7JyubFAjzDnssOefNGZez7/ObGVmn5mYje0sJYYo/fv3Z9euXaxatYpf/vKXTJ8+nb/97W/s2LGD3r178+STT9LQ4A4tb7U6V4ANBkPL9vmyzeZcefb+P+JdllIyc+ZM/vnPfyr7dULVLkqfiRiNFmaYE/igcDO1zbV0M7cSjTHABDOogs+IMFLKf0kpz8fV24pzuVqj0fz/9u48OuryfvT4+zOTyUZWSAIhIAFUkAjEsopsVVlcSuq5tmrd21tL+9P6q6ccrZ5jLaWn9dxz+/PCreXyq1QRe0W51eb2glApUQqogEQBWQQMO5iwZIPsz/1jhsw8Q5YJzJbM53VOzvk+83zn+33mOzOfzPN9toAFbSHFqByw7EPjiVIhFWAsiWw82W6MudYYMxRYDuQZY543xlxcUMoAPzDGXG2MGX+xQuY5x2+MMUONMcOMMat9Hl918ZjGmN/4PL7QGDPAGBNnjOkfrMoQtDPD3MESqD7OpsFjqWmsCfsaLOFy/PhxkpOTeeCBB5g3bx6ffvopAFlZWdTU1LBy5couH/Pw4cNs3rwZgL/85S+XjAWaOHEiGzduZP/+/YB7HNO+ffsYPnw4ZWVlHDhwAOCSCpOKkPheMHACs858TX1zPR8c+SAspw1ll7m2gtqEDvb/AbC6rQwReQx4DCDRkdLWLkrFJkOgP1CyRMR3/tElnsHA3UVo4gnJNNd4V8Z05thdWKTBO/anId2+W5twzh4X46q17y81pHnTJybZoTb5hF2m6iH2nfmWWu+5pLPbVvX2Dq4M7xiTRmPnbT492EqX19p33Qqzj/s81x6P0ifRXkF0Ru8vrPQrFVNbtwt62cMwEsUeQ/WfX9k/WKb0O9C6PTHjoL3voSl2GfsctdLPXrOqdfuXX8yx8j49ZdeJe6fbr6G60btA7PZd9rVJurraSrf4LbYav9M7lqlxmL2Iq+tLe6xSi8v+jib6DOXyu8ykHbLHqkmz/dloyPa+Z/EOvw/HvjIuW+CxBLp/PImosgr359BqISr9CyRlsqbpLOkJ6UzI7Si8dV87duxg3rx5OBwOXC4Xf/zjH3n33Xe5/vrr6devH+PGjevyMYcNG8Yf/vAHvv/97zNixAh+/OMfW/nZ2dm8+uqr3HfffdTXu+PjggULuPbaa1myZAl33HEHycnJTJkyherq6rZOocJtyHRu+Oevyb7uBtaUreH2IbeH/JRRMamCiDwAjAWmtZXvO4tLuitHp8FRyldgvVwqjDFjO8jvaNCx/z5RPWC5K/EkTXprPFHqosB7zMVMPAmFg/4VogvnYM/fqb/hfkqOfcis/Fm4HD2vuxzArFmzmDXLnixi7NixLFiw4JJ9S0pKWrenT5/O9OnTL8krKysjLi6O5cuXd/j8m2++mS1btlyyz+zZs9mzZ0/XXoQKvaE34/jnr5mZOpS3j/2LmoYaUuJD2yASyi5zgQRERORW4DlgjqfPsFKqC4K0bsgWPIOLRSQed9/7Yr99ioGHPdutA5Y9j98rIgmewckXBywHcsxAaTxRKsSCuA5RtMeTiPqqopac1AR6JXjuSe/6KzTVsTFvBLWNtcwc1DO7yykVsNzRkJTJrNo6GloaWH9kfchPGcoKUafBS0RuAP4X7h8vX4ewLEr1XEHo8+/pw39xcPFu4C3PQOT5InKxH9IrQB/PgOWngGc8z90FXByw/B6eAcvtHRPcA5ZF5Cjuis3nIvKnToqo8USpUAvSGKJuEE8iqqyi1u4ut/0NyClgbdV+0hPSGZ87vv0nK0t+fj47d+6MdDFUsDmcMHgaow9vIyc5h7WH1ob8lCHrMmeMaWpr9hYRmY97Rphi4L8BKcDbnllBDhtj5rR7UKWUzRhoDs7MUMaYVcAqv8ee99muA77TznN/A/ymjccvOabn8YXAwi6UTeOJUqEUxFjiPlz0xpNI+6qilpkFfd2J8r1wbCv1t/6KksNv9ujuckp1ydBv4vjiXWZmF/HWkfdD3m0upGOIAgiIt4by/ErFhBhZXT4U8UQcDhyJ3qlc+fq0ld8yxDsoP+nkeSvv3HA7MDvr7ffBdz6D3rvtvPN97QH6zb3sH6KS6B1Y7//2JqXVWWn/wf79MryDgreftCcVyEu3V4DtnWxPBlBe731NpeX9rbxtY96y0m/VpNOeNeUFVnpAsr2AaEaifd68hLOt26kO+/VVXki00lvK7QVj91T2bd0enGm/f76TJrQlKc5nsocE+z2oq0mw0g6XX2XBZyKFSyZRcPpNovC136K9PpMsXMiy85wNdto+MiQc8bmWcX4zMvTva6e/pGtiJJZEUuWFRk7XNngXZd35VxAHG3MGUXtAu8sp1WrINwGY2ZLA8pYGSo6WcOeQO0N2ulB2mVNKhUNwpslVSsW64E27rdpxyQxze1fBwImsOfmRdpdTylfmIOg9hNHHd5OTnMOasjUhPZ1WiJTqzgzQYjr/U0qpjgQaSzSeXJGvPBWiIdm9oPIonPycumtmUHKkhFuuukW7yynla+jNOA5tZObAW9h0bBM1DTUhO5VWiJTq1gyYls7/lFKqQwHGEo0nV+RgRS0OgYG9k2Gve6m0jZl9Od90nlmDZnXy7O7v3LlzvPzyy4B7Wuw77wxdF6i2lJSUsGnTptb04sWLWbZs2WUdKyWl4/Es8+bNo6CggHnz5l3W8QPxyCOPXNZitt3GkG9CYy0zk/Jo8HSbC5WoWIdIKXWZDEEdCB3rTJO92Ko0eNOVw3pbeWkH7XEwF/rZ41XO+yzM6qq176o3x9vnTTpqh+IL+e3fhW9qtMeNpKbY5Tiyq1/r9jWjj1h5zX4LtR45nWGlG857CzZ0oD1R3xvV9qK1Rxvs69E3vqp1O95hX8cUpz0D+vQBu6300qPehVpzkuyFER+/tsRK/+PMCCt9Q5r3NRYfG0lHZuba640s+zzwxS+bq+w795LkHefVmGJ/B5NO2te5zm/5vOQT3nFC2Z/Z1yrugr0wa9zXVVa6YUBm63bC/lN+hbSf2yUaS8KirKKWvMwkEuKc7u5yfa5h7ZnPSU9IZ1xu1xcl7W4uVoh+8pOfhOwcTU1NxMW1/fO2pKSElJQUJk2aBMDcuXNDVo4lS5Zw5swZnE5n5zurtg2eAuJk9LlTrd3mQjWOSCtESnV32qdfKRUMGktC7o5Rudw4tA/UVcFXG6ib8BglR9Yxe/DssHeXe/GTF9lzJriLkg7vPZynxz/dbv4zzzzDgQMHKCwsxOVy0atXL+6++2527tzJmDFjWL58OSLCtm3beOqpp6ipqSErK4tXX32V3NxcSktLmTt3LufPn2fo0KEsXbqUzMxMpk+fTmFhIf/617+47777eOihh5g7dy6HDx8G4KWXXiIvL4/FixfjdDpZvnw5ixYtYt26daSkpPDzn/+c/fv3M3fuXMrLy3E6nbz99tv07duXoqIizp49S2NjIwsWLKCoqKjT6zBnzhxqamoYM2YMv/jFL1i9ejV33nknd999N+BuXaqpqaGkpIQXXniBrKysS67Bli1bePLJJ6mtrSUhIYF169aRmpoa0PvQ0XHburZOp5PbbruNbdu28dlnn1FYWMihQ4e46qqrGDp0KDt27CA5OTmgcwdVYjr89FMcGYOYsaWFt/e+HbLZ5rRCpFR3pz9ilFLBoLEk5GYVeFpwd70DLY1s7DOA8ydjo7scwO9+9zt27txJaWkpJSUlFBUVsWvXLvr3789NN93Exo0bmTBhAk888QR/+9vfyM7OZsWKFTz33HMsXbqUhx56iEWLFjFt2jSef/55fvWrX/HSSy8B0NDQwNatWwH43ve+x89+9jMmT57M4cOHmTVrFrt372bu3LmtFSCAdevWtZbt/vvv55lnnuGuu+6irq6OlpYW4uPjeeedd0hLS6OiooKJEycyZ84cPEs7tKu4uJiUlBRKS0sBWL16dbv7bt++/ZJrMH78eO655x5WrFjBuHHjqKqqIinJf87JjrV13I6ubV1dHVVVVWzYsIGxY8eyYcMGJk+eTE5OTmQqQxdl5gMwK38Wb+x+I2SzzWmFSKluTWd9UkoFg8aSsNq7GpJ6s7a2LGLd5TpqyQmX8ePHM2CAe3mAwsJCysrKyMjIYOfOncyYMQOA5uZmcnNzqays5Ny5c0ybNg2Ahx9+mO98x7uU1T333NO6/f777/PFF1+0pquqqqipaX9AfnV1NceOHeOuu+4CIDHR3QW6sbGRZ599lg8//BCHw8GxY8c4deoU/fr1a/dYXdXWNUhPTyc3N5dx49yfi7S0tKAct71rCzBp0iQ2btzIhx9+yLPPPst7772HMYYpU6YE42VesdHZo92LtJat1QqRUsqPAVq0379S6gppLAmf5ibYt4b6a2fzwbEPY3ox1oQE73pfTqeTpqYmjDEUFBSwefNma9/Kykr/p1t69erVut3S0sJHH33UWrG5XG+88Qbl5eVs27YNl8tFfn4+dXV1nT/RT1xcHC2e71dLSwsNDQ2teW1dg/Y8+uijbN++nf79+7NqlXdZvo8//pgf/ehHAMyfP5+0tLQuXVuAqVOnsmHDBg4dOkRRUREvvvgiIsIdd9zR5dcbCg5xMGPQjJB1m9MKkVLdnd7VvXxxcThysrzpJntQekucd3B8yhF78oLGVPsHTHyl/U+saYjTZ1+7e8WFfvYPz7jzdn7/gd4FRk/tzLHyEvo1Wum8NHvQ/VmXd9D9/hP2c+8t2GqlJ9jzJLD6yHWt2yer7L7q/pMo1LXYr//RzE9at39fPt3Kq2+x/9Ucb8y00tUN3n/cyXENVt6eC7lWemDSWSt9qM7vRfg4XdXLSm+OH2ylk1O8kz3Ex9nv35ly+45sQh/7/W867HPsXHvSiKYqu2uL8RtT7XvpqvLta5Ny3P4suDLs12Cdp7/9njj3HGp334BoLAmPIx9B3Tk29h1M7f5NMbUYa2pqKtXV1R3uM2zYMMrLy9m8eTM33ngjjY2N7Nu3j4KCAjIzM9mwYQNTpkzh9ddfb20t8jdz5kwWLVrUOsNbaWkphYWFpKamUlVVdcn+qampDBgwgHfffZdvf/vb1NfX09zcTGVlJTk5ObhcLtavX8+hQ5f3HcvPz2fbtm1897vfpbi4mMbGxg73HzZsGCdOnGDLli2MGzeO6upqkpKS+POf/9zm/hMmTGjtngfuMUTtHbe9aztlyhSee+45pk6disPhoHfv3qxatYrf/va3l/WaQyGU3eZ02m2lujXjnhmqsz+llOpQgLFE48mV27sanPGsbayIucVY+/Tpw0033cT111/f7nTU8fHxrFy5kqeffprRo0dTWFjYOlX2a6+9xrx58xg1ahSlpaU8//zzbR5j4cKFbN26lVGjRjFixAgWL14MwLe+9S3eeecdCgsL2bBhg/Wc119/nYULFzJq1CgmTZrEyZMnuf/++9m6dSsjR45k2bJlDB8+/LJe9w9/+EM++OADRo8ezebNm63WrPauwYoVK3jiiScYPXo0M2bMuKyWqbaO2961zc/PxxjD1KlTAZg8eTIZGRlkZmZ2dMiw8u02F2xiutkdoXRXjrkxy9tntOnq/q3b9b3tuWzr0+z6XmMv7523piT7Llyz31g132lxWxLsa+R3Y5SWeG++cdn7mji/fx5xdr745Dv88hwO+7kOp8++Dntfp9PeV8Sb7xTTbl5b6ctljN81bfFef/8ztLQ4/NLe5zY3++X5p332NU12nmnyG+joly8++dJg7+vwT/vcwHHW23l+swjj9IlTceftVxtf45eu8rZCJJbbd53/seWFbcaYsQQoPS7b3JhxV6f7rTn9n106bqxIT+hnJuXd733Av4Wot7eVpDklwcrzbyFyNNnv89c3ePf3byHorIUoa4x3OmX/FqKkofbdzcG9z1jpnTsGecuUabe2+LcQ+fNtIWposlsuHrh6i5XuSguRS+zrmpdgt/K8feQbrdt9k+27x0NTKjosc22z9zp/drq/leffQpSfZV+rY5XprdudthCl+LUCddBC5Npr/0NpTrY/G0mnvO+3w+9Gccpx+1r1OlxrnzfF+8/Jed5+sn8L0ZrKpQF/7wONJaDxpD1jx441Fwf1t8sYWHgD9b2HMM15nJmDZjL/pvnhKSCwe/durrvuus53VKoTkfosrTq4ioyEDCblTep0XxEJOFZplzmlujtdOV4pFQwaS0KvYh+c/YpNI2+n9siXzMyPne5ySgXD7UNuD8lxtUKkVHfXzVp5o4lpbKT5hLc1xjHQbmFoSfS2gvgvkFmd37fDYyee8b4vF2SkMLkAAAuhSURBVLL9xghtsN+zkxPt/BMnvV0UxK916XyZ3XKx+8t0K51zfXnrdqNf6+rWM1dZ6bxke5ByYfbx1u3DtXY3ibvSSq30yxV23/1En2loH+y9ycp7pWKqlf60yi5Hssvb0nFH9g4rryDhmJVedvomK+3bKjQ8w15MtjHdfv0usVvmztV5W3JOHbNf78hr7UVtD7w3xEo3DPO2CsX5tebX5dqtTfFn7DexwectS7SLjPOCfazGdLtl0tHgzXfW2C1Tkua3RknHY9AvpbEk9Pa6B8KvNbWkxacxITfwxYFV9NmxYwcPPvig9VhCQgIff/xxhEqkLpdWiJTqzozRmaGUUldOY0l4HPmEhtzRlJz6hFsH3Rqzs8v1FCNHjrQmM1Ddl06qoFR3Z0znf0op1ZlAYonGkytzzxts+uZT1DTWRGx2ue42dlxFn574GdIWIqW6NYNpbu58N6WU6pDGkrBwOFh76hPS4tOYmDsx7KdPTEzk9OnT9OnTBxHp/AlK+THGcPr06Ste4ynaaIVIqe7MoAOhlVJXTmNJWDQ0N7D+yHp3dzln+LvLDRgwgKNHj1JeXt75zkq1IzExkQEDBkS6GEGlFSKlujsTnH7/IjIb+B+AE/iTMeZ3fvkJwDJgDHAauMcYU+bJ+wXwA6AZ+KkxZk1HxxSRwcCbQB9gG/CgMcaeIzoMxOnAkeKdPllq7WnQHcneAe3Vo+zpr5td9t3VuDr7x2RTsjc/qdzOOzPMHmTvaLTz4w56z1vX3x6g70q3B9Jfn3fcSp867x1Yf+pkhpV39rQ96H5vXZ6VnjByf+v2Vb3sqbEPNtqLgG44bk8yMNdnEoYRaSetvKPn7XLcnLXHSr9d6Z12+83j46y86vrJVvreQfa0xvXN3n9jG74aauU11dv/4iYP+9JKO30mQ7it0J7M4b1dBVY6bpQ9/bX4TOmfsM2e3lsy/SoW/qsv1Hi3k8vtVpnGFLsnu/OM3xTtld7PaGMf+7yupits4QlSLIGQxZPngF96DrHOGHOb53HfeBIPNHThmGGNUZuPb45odzmXy8XgwYM731GpGKNjiJTqxgxgWkynf50RESfwB+A2YARwn4iM8NvtB8BZY8zVwH8AL3qeOwK4FygAZgMvi4izk2O+CPyH51hnPcdWSkVIoLEkgvHEBbwAzAAygeki8i3PsV70HOP3QDXw3wM8Zthj1NpDa0mNT41IdzmlVPu0QqRUd2aM+65uZ3+dGw/sN8Yc9NwFfRMo8tunCHjNs70SuEXcndCLgDeNMfXGmK+A/Z7jtXlMz3Nu9hwDzzG/fdnXQCl15QKNJZGLJ48AlcaYD4wxtcAHwL/5xZMi4CXc8SQqY9TNA2/m8cLHI9JdTinVPu0yp1Q3F6SB0HmA78IrRwH/BTJa9zHGNIlIJe7uJHnAR37PvdgXq61j9gHOGWOa2thfKRUhQZxUIRTxZBhQ4fN4GTAJn3giInlAKfBktMaoWwbdEozDKKWCrNtViKqayivWnHz5UOsDJzvYufvLwv4H0NPp64VBXTlANWfXvG9WZgWwa6KI+A6+WGKMWdKVc/VEVU0VFWsqlhxqdwff4Tmfhb48l+NA4Lt2+v063EHeq5c8sstK+a7E8bdOCvL/Lnnk/U6e4bUl4D0vfb3tv9H2r+Vu6oriSRdiCWg8aSUijwGPeZI1IrK3k6dEy/85LYdNy2HrKeUIOAZ2uwqRMSY70mUIFxHZaowZG+lyhIu+3q4zxswOUnGOAQN90gM8j7W1z1ERiQPScQ9c7ui5bT1+GsgQkTjPHdi2zhUWGk96Ln29XRPEWAKhiSd7cXebuygf9y2L1nji2a8QOBauGOWpCAZcGYyWz6WWQ8uh5bDpGCKlFLhvvF8jIoNFJB73AORiv32KgYc923cD/zTu1dmKgXtFJMEzM9M1wCftHdPznPWeY+A5ZmeNCkqp7iMU8WQZkC4iU0SkFzANeNkvnhQD/447nmiMUkoFrNu1ECmlgs/T3/5xYA3u6WeXGmN2ich8YKsxphh4BXhdRPYDZ3D/eMCz31vAF0AT8G/GmGaAto7pOeXTwJsisgDY7jm2UqoHCFE8aRaRXwPrAAHWG2OKPcdcCzyFd9rtpwI8psYopRQA4r4RoqKRiDwWS/2y9fUqFTqx9nnT16uiUbS8T1oOLYeWw+9cWiFSSimllFJKxSodQ6SUUkoppZSKWVohikIislREvhaRnZEuSziIyEARWS8iX4jILhF5MtJlChURSRSRT0TkM89r/VWky6R6tliKJ7EUS0DjSTQTkdkisldE9ovIM23kJ4jICk/+xyKSH6FyPCIi5SJS6vn7ryEoQ4cxSNwWesr4uYh8I9hlCLAc00Wk0udaPB+icnQap8JxTQIsR8ivSSBxLCzfF2OM/kXZHzAV+AawM9JlCdPrzQW+4dlOBfYBIyJdrhC9VgFSPNsu4GNgYqTLpX899y+W4kksxRLPa9R4EoV/uCdoOAAMwT3Jw2f+n0PgJ8Biz/a9wIoIleMR4H+G+Hp0GIOA24HVns/zRODjCJVjOvD3MHw+Oo1T4bgmAZYj5NckkDgWju+LthBFIWPMh7hnyIkJxpgTxphPPdvVwG6CtCp4tDFuNZ6ky/OnA/lUyMRSPImlWAIaT6LYeGC/MeagMaYBeBMo8tunCHjNs70SuEVEJALlCLkAYlARsMzzef4I9xpQuREoR1gEGKdCfk2iJV4GGMdC/n3RCpGKKp5m0Btw3yHokUTEKSKlwNfAP4wxPfa1KhUpsRBLQONJlMoDjvikj3LpD83WfYx78ddK3NOGh7scAP/F0y1rpYgMbCM/1AItZzjc6Om6tVpECkJ9sg7iVFivSSfxMuTXJIA4FvLvi1aIVNQQkRTg/wD/boypinR5QsUY02yMKcS9+vl4Ebk+0mVSqieJlVgCGk/UFfu/QL4xZhTwD7x34WPRp8AgY8xoYBHwbihPFi1xqpNyhOWaREMc0wqRigoi4sL9hXzDGPPXSJcnHIwx53Cvhj470mVRqqeIxVgCGk+izDHAt6VlgOexNvcRkTggHTgd7nIYY04bY+o9yT8BY4JchkAEcr1CzhhTdbHrljFmFeASkaxQnCuAOBWWa9JZOcJ5TTznaC+Ohfz7ohUiFXGefqCvALuNMb+PdHlCSUSyRSTDs50EzAD2RLZUSvUMsRRLQONJFNsCXCMig0UkHvcg8GK/fYqBhz3bdwP/NJ4R4+Esh9+4lDm4x5GEWzHwkGdmtYlApTHmRLgLISL9Lo5LEZHxuH8jB7uSGmicCvk1CaQc4bgmAcaxkH9f4oJ5MBUcIvK/cc/skSUiR4FfGmNeiWypQuom4EFgh6cPKcCznrsRPU0u8JqIOHEHlreMMX+PcJlUDxZj8SSWYgloPIlKxpgmEXkcWIN7prelxphdIjIf2GqMKcb9Q/R1EdmPe6D/vREqx09FZA7Q5CnHI8EuR1sxCPfAeYwxi4FVuGdV2w+cBx4NdhkCLMfdwI9FpAm4ANwbgkoqtBOngKt8yhKOaxJIOcJxTdqMY+H+vkho3mullFJKKaWUin7aZU4ppZRSSikVs7RCpJRSSimllIpZWiFSSimllFJKxSytECmllFJKKaVillaIlFJKKaWUUjFLK0RKKaWUUkqpmKUVIqWUUkoppVTM0gqRapOI5IvITp/0z0XkhQgWSSnVTWk8UUopFc20QqSUUkoppZSKWVohUkoppZRSSsUsrRCp9jRhfz4SI1UQpVS3p/FEKaVU1NIKkWrPKSBHRPqISAJwZ6QLpJTqtjSeKKWUilpxkS6Aik7GmEYRmQ98AhwD9kS4SEqpbkrjiVJKqWgmxphIl0EppZRSSimlIkK7zCmllFJKKaVillaIlFJKKaWUUjFLK0RKKaWUUkqpmKUVIqWUUkoppVTM0gqRUkoppZRSKmZphUgppZRSSikVs7RCpJRSSimllIpZWiFSSimllFJKxaz/D2ITYpjBRJkcAAAAAElFTkSuQmCC
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<div class=" highlight hl-ipython2"><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">scipy.optimize</span> <span class="kn">as</span> <span class="nn">opt</span>
<span class="kn">from</span> <span class="nn">scipy.misc</span> <span class="kn">import</span> <span class="n">derivative</span>


<span class="c1"># 参数方程$r=r(u,v)$</span>
<span class="k">def</span> <span class="nf">func</span><span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="n">v</span><span class="p">):</span>
    <span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">u</span><span class="p">)</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">v</span><span class="p">)</span>
    <span class="n">y</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">u</span><span class="p">)</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">v</span><span class="p">)</span>
    <span class="n">z</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">u</span><span class="p">)</span>
    <span class="k">return</span> <span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">z</span>


<span class="c1"># r对u的偏导数，可以手算，这里用数值方法</span>
<span class="k">def</span> <span class="nf">func_r_u</span><span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="n">v</span><span class="p">):</span>
    <span class="k">return</span> <span class="n">derivative</span><span class="p">(</span><span class="k">lambda</span> <span class="n">u</span><span class="p">:</span> <span class="n">func</span><span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="n">v</span><span class="p">)[</span><span class="mi">0</span><span class="p">],</span> <span class="n">u</span><span class="p">),</span> \
           <span class="n">derivative</span><span class="p">(</span><span class="k">lambda</span> <span class="n">u</span><span class="p">:</span> <span class="n">func</span><span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="n">v</span><span class="p">)[</span><span class="mi">1</span><span class="p">],</span> <span class="n">u</span><span class="p">),</span> \
           <span class="n">derivative</span><span class="p">(</span><span class="k">lambda</span> <span class="n">u</span><span class="p">:</span> <span class="n">func</span><span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="n">v</span><span class="p">)[</span><span class="mi">2</span><span class="p">],</span> <span class="n">u</span><span class="p">)</span>


<span class="c1"># r对v的偏导数</span>
<span class="k">def</span> <span class="nf">func_r_v</span><span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="n">v</span><span class="p">):</span>
    <span class="k">return</span> <span class="n">derivative</span><span class="p">(</span><span class="k">lambda</span> <span class="n">v</span><span class="p">:</span> <span class="n">func</span><span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="n">v</span><span class="p">)[</span><span class="mi">0</span><span class="p">],</span> <span class="n">v</span><span class="p">),</span> \
           <span class="n">derivative</span><span class="p">(</span><span class="k">lambda</span> <span class="n">v</span><span class="p">:</span> <span class="n">func</span><span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="n">v</span><span class="p">)[</span><span class="mi">1</span><span class="p">],</span> <span class="n">v</span><span class="p">),</span> \
           <span class="n">derivative</span><span class="p">(</span><span class="k">lambda</span> <span class="n">v</span><span class="p">:</span> <span class="n">func</span><span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="n">v</span><span class="p">)[</span><span class="mi">2</span><span class="p">],</span> <span class="n">v</span><span class="p">)</span>

<span class="c1"># surf = ax.scatter(X, Y, Z, &#39;.&#39;)</span>
<span class="c1"># coords3 = coords = np.vstack([X,Y,Z]).T</span>

<span class="c1"># qc_plot_3d(coords[:1000])</span>
<span class="c1"># qc_plot_2d(coords)</span>

<span class="c1"># plt.show()</span>
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<div class=" highlight hl-ipython2"><pre><span></span><span class="o">!</span>jupyter nbconvert --to html <span class="m">20190819</span>-曲面上随机采样.ipynb
<span class="c1"># !jupyter nbconvert --to markdown 20190819-曲面上随机采样.ipynb </span>
<span class="c1"># !jupyter nbconvert --to pdf 20190819-曲面上随机采样.ipynb </span>
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<pre>[NbConvertApp] Converting notebook 20190819-曲面上随机采样.ipynb to html
[NbConvertApp] Writing 623354 bytes to 20190819-曲面上随机采样.html
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