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.glyphicon-bitcoin:before {
  content: "\e227";
}
.glyphicon-btc:before {
  content: "\e227";
}
.glyphicon-xbt:before {
  content: "\e227";
}
.glyphicon-yen:before {
  content: "\00a5";
}
.glyphicon-jpy:before {
  content: "\00a5";
}
.glyphicon-ruble:before {
  content: "\20bd";
}
.glyphicon-rub:before {
  content: "\20bd";
}
.glyphicon-scale:before {
  content: "\e230";
}
.glyphicon-ice-lolly:before {
  content: "\e231";
}
.glyphicon-ice-lolly-tasted:before {
  content: "\e232";
}
.glyphicon-education:before {
  content: "\e233";
}
.glyphicon-option-horizontal:before {
  content: "\e234";
}
.glyphicon-option-vertical:before {
  content: "\e235";
}
.glyphicon-menu-hamburger:before {
  content: "\e236";
}
.glyphicon-modal-window:before {
  content: "\e237";
}
.glyphicon-oil:before {
  content: "\e238";
}
.glyphicon-grain:before {
  content: "\e239";
}
.glyphicon-sunglasses:before {
  content: "\e240";
}
.glyphicon-text-size:before {
  content: "\e241";
}
.glyphicon-text-color:before {
  content: "\e242";
}
.glyphicon-text-background:before {
  content: "\e243";
}
.glyphicon-object-align-top:before {
  content: "\e244";
}
.glyphicon-object-align-bottom:before {
  content: "\e245";
}
.glyphicon-object-align-horizontal:before {
  content: "\e246";
}
.glyphicon-object-align-left:before {
  content: "\e247";
}
.glyphicon-object-align-vertical:before {
  content: "\e248";
}
.glyphicon-object-align-right:before {
  content: "\e249";
}
.glyphicon-triangle-right:before {
  content: "\e250";
}
.glyphicon-triangle-left:before {
  content: "\e251";
}
.glyphicon-triangle-bottom:before {
  content: "\e252";
}
.glyphicon-triangle-top:before {
  content: "\e253";
}
.glyphicon-console:before {
  content: "\e254";
}
.glyphicon-superscript:before {
  content: "\e255";
}
.glyphicon-subscript:before {
  content: "\e256";
}
.glyphicon-menu-left:before {
  content: "\e257";
}
.glyphicon-menu-right:before {
  content: "\e258";
}
.glyphicon-menu-down:before {
  content: "\e259";
}
.glyphicon-menu-up:before {
  content: "\e260";
}
* {
  -webkit-box-sizing: border-box;
  -moz-box-sizing: border-box;
  box-sizing: border-box;
}
*:before,
*:after {
  -webkit-box-sizing: border-box;
  -moz-box-sizing: border-box;
  box-sizing: border-box;
}
html {
  font-size: 10px;
  -webkit-tap-highlight-color: rgba(0, 0, 0, 0);
}
body {
  font-family: "Helvetica Neue", Helvetica, Arial, sans-serif;
  font-size: 13px;
  line-height: 1.42857143;
  color: #000;
  background-color: #fff;
}
input,
button,
select,
textarea {
  font-family: inherit;
  font-size: inherit;
  line-height: inherit;
}
a {
  color: #337ab7;
  text-decoration: none;
}
a:hover,
a:focus {
  color: #23527c;
  text-decoration: underline;
}
a:focus {
  outline: 5px auto -webkit-focus-ring-color;
  outline-offset: -2px;
}
figure {
  margin: 0;
}
img {
  vertical-align: middle;
}
.img-responsive,
.thumbnail > img,
.thumbnail a > img,
.carousel-inner > .item > img,
.carousel-inner > .item > a > img {
  display: block;
  max-width: 100%;
  height: auto;
}
.img-rounded {
  border-radius: 3px;
}
.img-thumbnail {
  padding: 4px;
  line-height: 1.42857143;
  background-color: #fff;
  border: 1px solid #ddd;
  border-radius: 2px;
  -webkit-transition: all 0.2s ease-in-out;
  -o-transition: all 0.2s ease-in-out;
  transition: all 0.2s ease-in-out;
  display: inline-block;
  max-width: 100%;
  height: auto;
}
.img-circle {
  border-radius: 50%;
}
hr {
  margin-top: 18px;
  margin-bottom: 18px;
  border: 0;
  border-top: 1px solid #eeeeee;
}
.sr-only {
  position: absolute;
  width: 1px;
  height: 1px;
  margin: -1px;
  padding: 0;
  overflow: hidden;
  clip: rect(0, 0, 0, 0);
  border: 0;
}
.sr-only-focusable:active,
.sr-only-focusable:focus {
  position: static;
  width: auto;
  height: auto;
  margin: 0;
  overflow: visible;
  clip: auto;
}
[role="button"] {
  cursor: pointer;
}
h1,
h2,
h3,
h4,
h5,
h6,
.h1,
.h2,
.h3,
.h4,
.h5,
.h6 {
  font-family: inherit;
  font-weight: 500;
  line-height: 1.1;
  color: inherit;
}
h1 small,
h2 small,
h3 small,
h4 small,
h5 small,
h6 small,
.h1 small,
.h2 small,
.h3 small,
.h4 small,
.h5 small,
.h6 small,
h1 .small,
h2 .small,
h3 .small,
h4 .small,
h5 .small,
h6 .small,
.h1 .small,
.h2 .small,
.h3 .small,
.h4 .small,
.h5 .small,
.h6 .small {
  font-weight: normal;
  line-height: 1;
  color: #777777;
}
h1,
.h1,
h2,
.h2,
h3,
.h3 {
  margin-top: 18px;
  margin-bottom: 9px;
}
h1 small,
.h1 small,
h2 small,
.h2 small,
h3 small,
.h3 small,
h1 .small,
.h1 .small,
h2 .small,
.h2 .small,
h3 .small,
.h3 .small {
  font-size: 65%;
}
h4,
.h4,
h5,
.h5,
h6,
.h6 {
  margin-top: 9px;
  margin-bottom: 9px;
}
h4 small,
.h4 small,
h5 small,
.h5 small,
h6 small,
.h6 small,
h4 .small,
.h4 .small,
h5 .small,
.h5 .small,
h6 .small,
.h6 .small {
  font-size: 75%;
}
h1,
.h1 {
  font-size: 33px;
}
h2,
.h2 {
  font-size: 27px;
}
h3,
.h3 {
  font-size: 23px;
}
h4,
.h4 {
  font-size: 17px;
}
h5,
.h5 {
  font-size: 13px;
}
h6,
.h6 {
  font-size: 12px;
}
p {
  margin: 0 0 9px;
}
.lead {
  margin-bottom: 18px;
  font-size: 14px;
  font-weight: 300;
  line-height: 1.4;
}
@media (min-width: 768px) {
  .lead {
    font-size: 19.5px;
  }
}
small,
.small {
  font-size: 92%;
}
mark,
.mark {
  background-color: #fcf8e3;
  padding: .2em;
}
.text-left {
  text-align: left;
}
.text-right {
  text-align: right;
}
.text-center {
  text-align: center;
}
.text-justify {
  text-align: justify;
}
.text-nowrap {
  white-space: nowrap;
}
.text-lowercase {
  text-transform: lowercase;
}
.text-uppercase {
  text-transform: uppercase;
}
.text-capitalize {
  text-transform: capitalize;
}
.text-muted {
  color: #777777;
}
.text-primary {
  color: #337ab7;
}
a.text-primary:hover,
a.text-primary:focus {
  color: #286090;
}
.text-success {
  color: #3c763d;
}
a.text-success:hover,
a.text-success:focus {
  color: #2b542c;
}
.text-info {
  color: #31708f;
}
a.text-info:hover,
a.text-info:focus {
  color: #245269;
}
.text-warning {
  color: #8a6d3b;
}
a.text-warning:hover,
a.text-warning:focus {
  color: #66512c;
}
.text-danger {
  color: #a94442;
}
a.text-danger:hover,
a.text-danger:focus {
  color: #843534;
}
.bg-primary {
  color: #fff;
  background-color: #337ab7;
}
a.bg-primary:hover,
a.bg-primary:focus {
  background-color: #286090;
}
.bg-success {
  background-color: #dff0d8;
}
a.bg-success:hover,
a.bg-success:focus {
  background-color: #c1e2b3;
}
.bg-info {
  background-color: #d9edf7;
}
a.bg-info:hover,
a.bg-info:focus {
  background-color: #afd9ee;
}
.bg-warning {
  background-color: #fcf8e3;
}
a.bg-warning:hover,
a.bg-warning:focus {
  background-color: #f7ecb5;
}
.bg-danger {
  background-color: #f2dede;
}
a.bg-danger:hover,
a.bg-danger:focus {
  background-color: #e4b9b9;
}
.page-header {
  padding-bottom: 8px;
  margin: 36px 0 18px;
  border-bottom: 1px solid #eeeeee;
}
ul,
ol {
  margin-top: 0;
  margin-bottom: 9px;
}
ul ul,
ol ul,
ul ol,
ol ol {
  margin-bottom: 0;
}
.list-unstyled {
  padding-left: 0;
  list-style: none;
}
.list-inline {
  padding-left: 0;
  list-style: none;
  margin-left: -5px;
}
.list-inline > li {
  display: inline-block;
  padding-left: 5px;
  padding-right: 5px;
}
dl {
  margin-top: 0;
  margin-bottom: 18px;
}
dt,
dd {
  line-height: 1.42857143;
}
dt {
  font-weight: bold;
}
dd {
  margin-left: 0;
}
@media (min-width: 541px) {
  .dl-horizontal dt {
    float: left;
    width: 160px;
    clear: left;
    text-align: right;
    overflow: hidden;
    text-overflow: ellipsis;
    white-space: nowrap;
  }
  .dl-horizontal dd {
    margin-left: 180px;
  }
}
abbr[title],
abbr[data-original-title] {
  cursor: help;
  border-bottom: 1px dotted #777777;
}
.initialism {
  font-size: 90%;
  text-transform: uppercase;
}
blockquote {
  padding: 9px 18px;
  margin: 0 0 18px;
  font-size: inherit;
  border-left: 5px solid #eeeeee;
}
blockquote p:last-child,
blockquote ul:last-child,
blockquote ol:last-child {
  margin-bottom: 0;
}
blockquote footer,
blockquote small,
blockquote .small {
  display: block;
  font-size: 80%;
  line-height: 1.42857143;
  color: #777777;
}
blockquote footer:before,
blockquote small:before,
blockquote .small:before {
  content: '\2014 \00A0';
}
.blockquote-reverse,
blockquote.pull-right {
  padding-right: 15px;
  padding-left: 0;
  border-right: 5px solid #eeeeee;
  border-left: 0;
  text-align: right;
}
.blockquote-reverse footer:before,
blockquote.pull-right footer:before,
.blockquote-reverse small:before,
blockquote.pull-right small:before,
.blockquote-reverse .small:before,
blockquote.pull-right .small:before {
  content: '';
}
.blockquote-reverse footer:after,
blockquote.pull-right footer:after,
.blockquote-reverse small:after,
blockquote.pull-right small:after,
.blockquote-reverse .small:after,
blockquote.pull-right .small:after {
  content: '\00A0 \2014';
}
address {
  margin-bottom: 18px;
  font-style: normal;
  line-height: 1.42857143;
}
code,
kbd,
pre,
samp {
  font-family: monospace;
}
code {
  padding: 2px 4px;
  font-size: 90%;
  color: #c7254e;
  background-color: #f9f2f4;
  border-radius: 2px;
}
kbd {
  padding: 2px 4px;
  font-size: 90%;
  color: #888;
  background-color: transparent;
  border-radius: 1px;
  box-shadow: inset 0 -1px 0 rgba(0, 0, 0, 0.25);
}
kbd kbd {
  padding: 0;
  font-size: 100%;
  font-weight: bold;
  box-shadow: none;
}
pre {
  display: block;
  padding: 8.5px;
  margin: 0 0 9px;
  font-size: 12px;
  line-height: 1.42857143;
  word-break: break-all;
  word-wrap: break-word;
  color: #333333;
  background-color: #f5f5f5;
  border: 1px solid #ccc;
  border-radius: 2px;
}
pre code {
  padding: 0;
  font-size: inherit;
  color: inherit;
  white-space: pre-wrap;
  background-color: transparent;
  border-radius: 0;
}
.pre-scrollable {
  max-height: 340px;
  overflow-y: scroll;
}
.container {
  margin-right: auto;
  margin-left: auto;
  padding-left: 0px;
  padding-right: 0px;
}
@media (min-width: 768px) {
  .container {
    width: 768px;
  }
}
@media (min-width: 992px) {
  .container {
    width: 940px;
  }
}
@media (min-width: 1200px) {
  .container {
    width: 1140px;
  }
}
.container-fluid {
  margin-right: auto;
  margin-left: auto;
  padding-left: 0px;
  padding-right: 0px;
}
.row {
  margin-left: 0px;
  margin-right: 0px;
}
.col-xs-1, .col-sm-1, .col-md-1, .col-lg-1, .col-xs-2, .col-sm-2, .col-md-2, .col-lg-2, .col-xs-3, .col-sm-3, .col-md-3, .col-lg-3, .col-xs-4, .col-sm-4, .col-md-4, .col-lg-4, .col-xs-5, .col-sm-5, .col-md-5, .col-lg-5, .col-xs-6, .col-sm-6, .col-md-6, .col-lg-6, .col-xs-7, .col-sm-7, .col-md-7, .col-lg-7, .col-xs-8, .col-sm-8, .col-md-8, .col-lg-8, .col-xs-9, .col-sm-9, .col-md-9, .col-lg-9, .col-xs-10, .col-sm-10, .col-md-10, .col-lg-10, .col-xs-11, .col-sm-11, .col-md-11, .col-lg-11, .col-xs-12, .col-sm-12, .col-md-12, .col-lg-12 {
  position: relative;
  min-height: 1px;
  padding-left: 0px;
  padding-right: 0px;
}
.col-xs-1, .col-xs-2, .col-xs-3, .col-xs-4, .col-xs-5, .col-xs-6, .col-xs-7, .col-xs-8, .col-xs-9, .col-xs-10, .col-xs-11, .col-xs-12 {
  float: left;
}
.col-xs-12 {
  width: 100%;
}
.col-xs-11 {
  width: 91.66666667%;
}
.col-xs-10 {
  width: 83.33333333%;
}
.col-xs-9 {
  width: 75%;
}
.col-xs-8 {
  width: 66.66666667%;
}
.col-xs-7 {
  width: 58.33333333%;
}
.col-xs-6 {
  width: 50%;
}
.col-xs-5 {
  width: 41.66666667%;
}
.col-xs-4 {
  width: 33.33333333%;
}
.col-xs-3 {
  width: 25%;
}
.col-xs-2 {
  width: 16.66666667%;
}
.col-xs-1 {
  width: 8.33333333%;
}
.col-xs-pull-12 {
  right: 100%;
}
.col-xs-pull-11 {
  right: 91.66666667%;
}
.col-xs-pull-10 {
  right: 83.33333333%;
}
.col-xs-pull-9 {
  right: 75%;
}
.col-xs-pull-8 {
  right: 66.66666667%;
}
.col-xs-pull-7 {
  right: 58.33333333%;
}
.col-xs-pull-6 {
  right: 50%;
}
.col-xs-pull-5 {
  right: 41.66666667%;
}
.col-xs-pull-4 {
  right: 33.33333333%;
}
.col-xs-pull-3 {
  right: 25%;
}
.col-xs-pull-2 {
  right: 16.66666667%;
}
.col-xs-pull-1 {
  right: 8.33333333%;
}
.col-xs-pull-0 {
  right: auto;
}
.col-xs-push-12 {
  left: 100%;
}
.col-xs-push-11 {
  left: 91.66666667%;
}
.col-xs-push-10 {
  left: 83.33333333%;
}
.col-xs-push-9 {
  left: 75%;
}
.col-xs-push-8 {
  left: 66.66666667%;
}
.col-xs-push-7 {
  left: 58.33333333%;
}
.col-xs-push-6 {
  left: 50%;
}
.col-xs-push-5 {
  left: 41.66666667%;
}
.col-xs-push-4 {
  left: 33.33333333%;
}
.col-xs-push-3 {
  left: 25%;
}
.col-xs-push-2 {
  left: 16.66666667%;
}
.col-xs-push-1 {
  left: 8.33333333%;
}
.col-xs-push-0 {
  left: auto;
}
.col-xs-offset-12 {
  margin-left: 100%;
}
.col-xs-offset-11 {
  margin-left: 91.66666667%;
}
.col-xs-offset-10 {
  margin-left: 83.33333333%;
}
.col-xs-offset-9 {
  margin-left: 75%;
}
.col-xs-offset-8 {
  margin-left: 66.66666667%;
}
.col-xs-offset-7 {
  margin-left: 58.33333333%;
}
.col-xs-offset-6 {
  margin-left: 50%;
}
.col-xs-offset-5 {
  margin-left: 41.66666667%;
}
.col-xs-offset-4 {
  margin-left: 33.33333333%;
}
.col-xs-offset-3 {
  margin-left: 25%;
}
.col-xs-offset-2 {
  margin-left: 16.66666667%;
}
.col-xs-offset-1 {
  margin-left: 8.33333333%;
}
.col-xs-offset-0 {
  margin-left: 0%;
}
@media (min-width: 768px) {
  .col-sm-1, .col-sm-2, .col-sm-3, .col-sm-4, .col-sm-5, .col-sm-6, .col-sm-7, .col-sm-8, .col-sm-9, .col-sm-10, .col-sm-11, .col-sm-12 {
    float: left;
  }
  .col-sm-12 {
    width: 100%;
  }
  .col-sm-11 {
    width: 91.66666667%;
  }
  .col-sm-10 {
    width: 83.33333333%;
  }
  .col-sm-9 {
    width: 75%;
  }
  .col-sm-8 {
    width: 66.66666667%;
  }
  .col-sm-7 {
    width: 58.33333333%;
  }
  .col-sm-6 {
    width: 50%;
  }
  .col-sm-5 {
    width: 41.66666667%;
  }
  .col-sm-4 {
    width: 33.33333333%;
  }
  .col-sm-3 {
    width: 25%;
  }
  .col-sm-2 {
    width: 16.66666667%;
  }
  .col-sm-1 {
    width: 8.33333333%;
  }
  .col-sm-pull-12 {
    right: 100%;
  }
  .col-sm-pull-11 {
    right: 91.66666667%;
  }
  .col-sm-pull-10 {
    right: 83.33333333%;
  }
  .col-sm-pull-9 {
    right: 75%;
  }
  .col-sm-pull-8 {
    right: 66.66666667%;
  }
  .col-sm-pull-7 {
    right: 58.33333333%;
  }
  .col-sm-pull-6 {
    right: 50%;
  }
  .col-sm-pull-5 {
    right: 41.66666667%;
  }
  .col-sm-pull-4 {
    right: 33.33333333%;
  }
  .col-sm-pull-3 {
    right: 25%;
  }
  .col-sm-pull-2 {
    right: 16.66666667%;
  }
  .col-sm-pull-1 {
    right: 8.33333333%;
  }
  .col-sm-pull-0 {
    right: auto;
  }
  .col-sm-push-12 {
    left: 100%;
  }
  .col-sm-push-11 {
    left: 91.66666667%;
  }
  .col-sm-push-10 {
    left: 83.33333333%;
  }
  .col-sm-push-9 {
    left: 75%;
  }
  .col-sm-push-8 {
    left: 66.66666667%;
  }
  .col-sm-push-7 {
    left: 58.33333333%;
  }
  .col-sm-push-6 {
    left: 50%;
  }
  .col-sm-push-5 {
    left: 41.66666667%;
  }
  .col-sm-push-4 {
    left: 33.33333333%;
  }
  .col-sm-push-3 {
    left: 25%;
  }
  .col-sm-push-2 {
    left: 16.66666667%;
  }
  .col-sm-push-1 {
    left: 8.33333333%;
  }
  .col-sm-push-0 {
    left: auto;
  }
  .col-sm-offset-12 {
    margin-left: 100%;
  }
  .col-sm-offset-11 {
    margin-left: 91.66666667%;
  }
  .col-sm-offset-10 {
    margin-left: 83.33333333%;
  }
  .col-sm-offset-9 {
    margin-left: 75%;
  }
  .col-sm-offset-8 {
    margin-left: 66.66666667%;
  }
  .col-sm-offset-7 {
    margin-left: 58.33333333%;
  }
  .col-sm-offset-6 {
    margin-left: 50%;
  }
  .col-sm-offset-5 {
    margin-left: 41.66666667%;
  }
  .col-sm-offset-4 {
    margin-left: 33.33333333%;
  }
  .col-sm-offset-3 {
    margin-left: 25%;
  }
  .col-sm-offset-2 {
    margin-left: 16.66666667%;
  }
  .col-sm-offset-1 {
    margin-left: 8.33333333%;
  }
  .col-sm-offset-0 {
    margin-left: 0%;
  }
}
@media (min-width: 992px) {
  .col-md-1, .col-md-2, .col-md-3, .col-md-4, .col-md-5, .col-md-6, .col-md-7, .col-md-8, .col-md-9, .col-md-10, .col-md-11, .col-md-12 {
    float: left;
  }
  .col-md-12 {
    width: 100%;
  }
  .col-md-11 {
    width: 91.66666667%;
  }
  .col-md-10 {
    width: 83.33333333%;
  }
  .col-md-9 {
    width: 75%;
  }
  .col-md-8 {
    width: 66.66666667%;
  }
  .col-md-7 {
    width: 58.33333333%;
  }
  .col-md-6 {
    width: 50%;
  }
  .col-md-5 {
    width: 41.66666667%;
  }
  .col-md-4 {
    width: 33.33333333%;
  }
  .col-md-3 {
    width: 25%;
  }
  .col-md-2 {
    width: 16.66666667%;
  }
  .col-md-1 {
    width: 8.33333333%;
  }
  .col-md-pull-12 {
    right: 100%;
  }
  .col-md-pull-11 {
    right: 91.66666667%;
  }
  .col-md-pull-10 {
    right: 83.33333333%;
  }
  .col-md-pull-9 {
    right: 75%;
  }
  .col-md-pull-8 {
    right: 66.66666667%;
  }
  .col-md-pull-7 {
    right: 58.33333333%;
  }
  .col-md-pull-6 {
    right: 50%;
  }
  .col-md-pull-5 {
    right: 41.66666667%;
  }
  .col-md-pull-4 {
    right: 33.33333333%;
  }
  .col-md-pull-3 {
    right: 25%;
  }
  .col-md-pull-2 {
    right: 16.66666667%;
  }
  .col-md-pull-1 {
    right: 8.33333333%;
  }
  .col-md-pull-0 {
    right: auto;
  }
  .col-md-push-12 {
    left: 100%;
  }
  .col-md-push-11 {
    left: 91.66666667%;
  }
  .col-md-push-10 {
    left: 83.33333333%;
  }
  .col-md-push-9 {
    left: 75%;
  }
  .col-md-push-8 {
    left: 66.66666667%;
  }
  .col-md-push-7 {
    left: 58.33333333%;
  }
  .col-md-push-6 {
    left: 50%;
  }
  .col-md-push-5 {
    left: 41.66666667%;
  }
  .col-md-push-4 {
    left: 33.33333333%;
  }
  .col-md-push-3 {
    left: 25%;
  }
  .col-md-push-2 {
    left: 16.66666667%;
  }
  .col-md-push-1 {
    left: 8.33333333%;
  }
  .col-md-push-0 {
    left: auto;
  }
  .col-md-offset-12 {
    margin-left: 100%;
  }
  .col-md-offset-11 {
    margin-left: 91.66666667%;
  }
  .col-md-offset-10 {
    margin-left: 83.33333333%;
  }
  .col-md-offset-9 {
    margin-left: 75%;
  }
  .col-md-offset-8 {
    margin-left: 66.66666667%;
  }
  .col-md-offset-7 {
    margin-left: 58.33333333%;
  }
  .col-md-offset-6 {
    margin-left: 50%;
  }
  .col-md-offset-5 {
    margin-left: 41.66666667%;
  }
  .col-md-offset-4 {
    margin-left: 33.33333333%;
  }
  .col-md-offset-3 {
    margin-left: 25%;
  }
  .col-md-offset-2 {
    margin-left: 16.66666667%;
  }
  .col-md-offset-1 {
    margin-left: 8.33333333%;
  }
  .col-md-offset-0 {
    margin-left: 0%;
  }
}
@media (min-width: 1200px) {
  .col-lg-1, .col-lg-2, .col-lg-3, .col-lg-4, .col-lg-5, .col-lg-6, .col-lg-7, .col-lg-8, .col-lg-9, .col-lg-10, .col-lg-11, .col-lg-12 {
    float: left;
  }
  .col-lg-12 {
    width: 100%;
  }
  .col-lg-11 {
    width: 91.66666667%;
  }
  .col-lg-10 {
    width: 83.33333333%;
  }
  .col-lg-9 {
    width: 75%;
  }
  .col-lg-8 {
    width: 66.66666667%;
  }
  .col-lg-7 {
    width: 58.33333333%;
  }
  .col-lg-6 {
    width: 50%;
  }
  .col-lg-5 {
    width: 41.66666667%;
  }
  .col-lg-4 {
    width: 33.33333333%;
  }
  .col-lg-3 {
    width: 25%;
  }
  .col-lg-2 {
    width: 16.66666667%;
  }
  .col-lg-1 {
    width: 8.33333333%;
  }
  .col-lg-pull-12 {
    right: 100%;
  }
  .col-lg-pull-11 {
    right: 91.66666667%;
  }
  .col-lg-pull-10 {
    right: 83.33333333%;
  }
  .col-lg-pull-9 {
    right: 75%;
  }
  .col-lg-pull-8 {
    right: 66.66666667%;
  }
  .col-lg-pull-7 {
    right: 58.33333333%;
  }
  .col-lg-pull-6 {
    right: 50%;
  }
  .col-lg-pull-5 {
    right: 41.66666667%;
  }
  .col-lg-pull-4 {
    right: 33.33333333%;
  }
  .col-lg-pull-3 {
    right: 25%;
  }
  .col-lg-pull-2 {
    right: 16.66666667%;
  }
  .col-lg-pull-1 {
    right: 8.33333333%;
  }
  .col-lg-pull-0 {
    right: auto;
  }
  .col-lg-push-12 {
    left: 100%;
  }
  .col-lg-push-11 {
    left: 91.66666667%;
  }
  .col-lg-push-10 {
    left: 83.33333333%;
  }
  .col-lg-push-9 {
    left: 75%;
  }
  .col-lg-push-8 {
    left: 66.66666667%;
  }
  .col-lg-push-7 {
    left: 58.33333333%;
  }
  .col-lg-push-6 {
    left: 50%;
  }
  .col-lg-push-5 {
    left: 41.66666667%;
  }
  .col-lg-push-4 {
    left: 33.33333333%;
  }
  .col-lg-push-3 {
    left: 25%;
  }
  .col-lg-push-2 {
    left: 16.66666667%;
  }
  .col-lg-push-1 {
    left: 8.33333333%;
  }
  .col-lg-push-0 {
    left: auto;
  }
  .col-lg-offset-12 {
    margin-left: 100%;
  }
  .col-lg-offset-11 {
    margin-left: 91.66666667%;
  }
  .col-lg-offset-10 {
    margin-left: 83.33333333%;
  }
  .col-lg-offset-9 {
    margin-left: 75%;
  }
  .col-lg-offset-8 {
    margin-left: 66.66666667%;
  }
  .col-lg-offset-7 {
    margin-left: 58.33333333%;
  }
  .col-lg-offset-6 {
    margin-left: 50%;
  }
  .col-lg-offset-5 {
    margin-left: 41.66666667%;
  }
  .col-lg-offset-4 {
    margin-left: 33.33333333%;
  }
  .col-lg-offset-3 {
    margin-left: 25%;
  }
  .col-lg-offset-2 {
    margin-left: 16.66666667%;
  }
  .col-lg-offset-1 {
    margin-left: 8.33333333%;
  }
  .col-lg-offset-0 {
    margin-left: 0%;
  }
}
table {
  background-color: transparent;
}
caption {
  padding-top: 8px;
  padding-bottom: 8px;
  color: #777777;
  text-align: left;
}
th {
  text-align: left;
}
.table {
  width: 100%;
  max-width: 100%;
  margin-bottom: 18px;
}
.table > thead > tr > th,
.table > tbody > tr > th,
.table > tfoot > tr > th,
.table > thead > tr > td,
.table > tbody > tr > td,
.table > tfoot > tr > td {
  padding: 8px;
  line-height: 1.42857143;
  vertical-align: top;
  border-top: 1px solid #ddd;
}
.table > thead > tr > th {
  vertical-align: bottom;
  border-bottom: 2px solid #ddd;
}
.table > caption + thead > tr:first-child > th,
.table > colgroup + thead > tr:first-child > th,
.table > thead:first-child > tr:first-child > th,
.table > caption + thead > tr:first-child > td,
.table > colgroup + thead > tr:first-child > td,
.table > thead:first-child > tr:first-child > td {
  border-top: 0;
}
.table > tbody + tbody {
  border-top: 2px solid #ddd;
}
.table .table {
  background-color: #fff;
}
.table-condensed > thead > tr > th,
.table-condensed > tbody > tr > th,
.table-condensed > tfoot > tr > th,
.table-condensed > thead > tr > td,
.table-condensed > tbody > tr > td,
.table-condensed > tfoot > tr > td {
  padding: 5px;
}
.table-bordered {
  border: 1px solid #ddd;
}
.table-bordered > thead > tr > th,
.table-bordered > tbody > tr > th,
.table-bordered > tfoot > tr > th,
.table-bordered > thead > tr > td,
.table-bordered > tbody > tr > td,
.table-bordered > tfoot > tr > td {
  border: 1px solid #ddd;
}
.table-bordered > thead > tr > th,
.table-bordered > thead > tr > td {
  border-bottom-width: 2px;
}
.table-striped > tbody > tr:nth-of-type(odd) {
  background-color: #f9f9f9;
}
.table-hover > tbody > tr:hover {
  background-color: #f5f5f5;
}
table col[class*="col-"] {
  position: static;
  float: none;
  display: table-column;
}
table td[class*="col-"],
table th[class*="col-"] {
  position: static;
  float: none;
  display: table-cell;
}
.table > thead > tr > td.active,
.table > tbody > tr > td.active,
.table > tfoot > tr > td.active,
.table > thead > tr > th.active,
.table > tbody > tr > th.active,
.table > tfoot > tr > th.active,
.table > thead > tr.active > td,
.table > tbody > tr.active > td,
.table > tfoot > tr.active > td,
.table > thead > tr.active > th,
.table > tbody > tr.active > th,
.table > tfoot > tr.active > th {
  background-color: #f5f5f5;
}
.table-hover > tbody > tr > td.active:hover,
.table-hover > tbody > tr > th.active:hover,
.table-hover > tbody > tr.active:hover > td,
.table-hover > tbody > tr:hover > .active,
.table-hover > tbody > tr.active:hover > th {
  background-color: #e8e8e8;
}
.table > thead > tr > td.success,
.table > tbody > tr > td.success,
.table > tfoot > tr > td.success,
.table > thead > tr > th.success,
.table > tbody > tr > th.success,
.table > tfoot > tr > th.success,
.table > thead > tr.success > td,
.table > tbody > tr.success > td,
.table > tfoot > tr.success > td,
.table > thead > tr.success > th,
.table > tbody > tr.success > th,
.table > tfoot > tr.success > th {
  background-color: #dff0d8;
}
.table-hover > tbody > tr > td.success:hover,
.table-hover > tbody > tr > th.success:hover,
.table-hover > tbody > tr.success:hover > td,
.table-hover > tbody > tr:hover > .success,
.table-hover > tbody > tr.success:hover > th {
  background-color: #d0e9c6;
}
.table > thead > tr > td.info,
.table > tbody > tr > td.info,
.table > tfoot > tr > td.info,
.table > thead > tr > th.info,
.table > tbody > tr > th.info,
.table > tfoot > tr > th.info,
.table > thead > tr.info > td,
.table > tbody > tr.info > td,
.table > tfoot > tr.info > td,
.table > thead > tr.info > th,
.table > tbody > tr.info > th,
.table > tfoot > tr.info > th {
  background-color: #d9edf7;
}
.table-hover > tbody > tr > td.info:hover,
.table-hover > tbody > tr > th.info:hover,
.table-hover > tbody > tr.info:hover > td,
.table-hover > tbody > tr:hover > .info,
.table-hover > tbody > tr.info:hover > th {
  background-color: #c4e3f3;
}
.table > thead > tr > td.warning,
.table > tbody > tr > td.warning,
.table > tfoot > tr > td.warning,
.table > thead > tr > th.warning,
.table > tbody > tr > th.warning,
.table > tfoot > tr > th.warning,
.table > thead > tr.warning > td,
.table > tbody > tr.warning > td,
.table > tfoot > tr.warning > td,
.table > thead > tr.warning > th,
.table > tbody > tr.warning > th,
.table > tfoot > tr.warning > th {
  background-color: #fcf8e3;
}
.table-hover > tbody > tr > td.warning:hover,
.table-hover > tbody > tr > th.warning:hover,
.table-hover > tbody > tr.warning:hover > td,
.table-hover > tbody > tr:hover > .warning,
.table-hover > tbody > tr.warning:hover > th {
  background-color: #faf2cc;
}
.table > thead > tr > td.danger,
.table > tbody > tr > td.danger,
.table > tfoot > tr > td.danger,
.table > thead > tr > th.danger,
.table > tbody > tr > th.danger,
.table > tfoot > tr > th.danger,
.table > thead > tr.danger > td,
.table > tbody > tr.danger > td,
.table > tfoot > tr.danger > td,
.table > thead > tr.danger > th,
.table > tbody > tr.danger > th,
.table > tfoot > tr.danger > th {
  background-color: #f2dede;
}
.table-hover > tbody > tr > td.danger:hover,
.table-hover > tbody > tr > th.danger:hover,
.table-hover > tbody > tr.danger:hover > td,
.table-hover > tbody > tr:hover > .danger,
.table-hover > tbody > tr.danger:hover > th {
  background-color: #ebcccc;
}
.table-responsive {
  overflow-x: auto;
  min-height: 0.01%;
}
@media screen and (max-width: 767px) {
  .table-responsive {
    width: 100%;
    margin-bottom: 13.5px;
    overflow-y: hidden;
    -ms-overflow-style: -ms-autohiding-scrollbar;
    border: 1px solid #ddd;
  }
  .table-responsive > .table {
    margin-bottom: 0;
  }
  .table-responsive > .table > thead > tr > th,
  .table-responsive > .table > tbody > tr > th,
  .table-responsive > .table > tfoot > tr > th,
  .table-responsive > .table > thead > tr > td,
  .table-responsive > .table > tbody > tr > td,
  .table-responsive > .table > tfoot > tr > td {
    white-space: nowrap;
  }
  .table-responsive > .table-bordered {
    border: 0;
  }
  .table-responsive > .table-bordered > thead > tr > th:first-child,
  .table-responsive > .table-bordered > tbody > tr > th:first-child,
  .table-responsive > .table-bordered > tfoot > tr > th:first-child,
  .table-responsive > .table-bordered > thead > tr > td:first-child,
  .table-responsive > .table-bordered > tbody > tr > td:first-child,
  .table-responsive > .table-bordered > tfoot > tr > td:first-child {
    border-left: 0;
  }
  .table-responsive > .table-bordered > thead > tr > th:last-child,
  .table-responsive > .table-bordered > tbody > tr > th:last-child,
  .table-responsive > .table-bordered > tfoot > tr > th:last-child,
  .table-responsive > .table-bordered > thead > tr > td:last-child,
  .table-responsive > .table-bordered > tbody > tr > td:last-child,
  .table-responsive > .table-bordered > tfoot > tr > td:last-child {
    border-right: 0;
  }
  .table-responsive > .table-bordered > tbody > tr:last-child > th,
  .table-responsive > .table-bordered > tfoot > tr:last-child > th,
  .table-responsive > .table-bordered > tbody > tr:last-child > td,
  .table-responsive > .table-bordered > tfoot > tr:last-child > td {
    border-bottom: 0;
  }
}
fieldset {
  padding: 0;
  margin: 0;
  border: 0;
  min-width: 0;
}
legend {
  display: block;
  width: 100%;
  padding: 0;
  margin-bottom: 18px;
  font-size: 19.5px;
  line-height: inherit;
  color: #333333;
  border: 0;
  border-bottom: 1px solid #e5e5e5;
}
label {
  display: inline-block;
  max-width: 100%;
  margin-bottom: 5px;
  font-weight: bold;
}
input[type="search"] {
  -webkit-box-sizing: border-box;
  -moz-box-sizing: border-box;
  box-sizing: border-box;
}
input[type="radio"],
input[type="checkbox"] {
  margin: 4px 0 0;
  margin-top: 1px \9;
  line-height: normal;
}
input[type="file"] {
  display: block;
}
input[type="range"] {
  display: block;
  width: 100%;
}
select[multiple],
select[size] {
  height: auto;
}
input[type="file"]:focus,
input[type="radio"]:focus,
input[type="checkbox"]:focus {
  outline: 5px auto -webkit-focus-ring-color;
  outline-offset: -2px;
}
output {
  display: block;
  padding-top: 7px;
  font-size: 13px;
  line-height: 1.42857143;
  color: #555555;
}
.form-control {
  display: block;
  width: 100%;
  height: 32px;
  padding: 6px 12px;
  font-size: 13px;
  line-height: 1.42857143;
  color: #555555;
  background-color: #fff;
  background-image: none;
  border: 1px solid #ccc;
  border-radius: 2px;
  -webkit-box-shadow: inset 0 1px 1px rgba(0, 0, 0, 0.075);
  box-shadow: inset 0 1px 1px rgba(0, 0, 0, 0.075);
  -webkit-transition: border-color ease-in-out .15s, box-shadow ease-in-out .15s;
  -o-transition: border-color ease-in-out .15s, box-shadow ease-in-out .15s;
  transition: border-color ease-in-out .15s, box-shadow ease-in-out .15s;
}
.form-control:focus {
  border-color: #66afe9;
  outline: 0;
  -webkit-box-shadow: inset 0 1px 1px rgba(0,0,0,.075), 0 0 8px rgba(102, 175, 233, 0.6);
  box-shadow: inset 0 1px 1px rgba(0,0,0,.075), 0 0 8px rgba(102, 175, 233, 0.6);
}
.form-control::-moz-placeholder {
  color: #999;
  opacity: 1;
}
.form-control:-ms-input-placeholder {
  color: #999;
}
.form-control::-webkit-input-placeholder {
  color: #999;
}
.form-control::-ms-expand {
  border: 0;
  background-color: transparent;
}
.form-control[disabled],
.form-control[readonly],
fieldset[disabled] .form-control {
  background-color: #eeeeee;
  opacity: 1;
}
.form-control[disabled],
fieldset[disabled] .form-control {
  cursor: not-allowed;
}
textarea.form-control {
  height: auto;
}
input[type="search"] {
  -webkit-appearance: none;
}
@media screen and (-webkit-min-device-pixel-ratio: 0) {
  input[type="date"].form-control,
  input[type="time"].form-control,
  input[type="datetime-local"].form-control,
  input[type="month"].form-control {
    line-height: 32px;
  }
  input[type="date"].input-sm,
  input[type="time"].input-sm,
  input[type="datetime-local"].input-sm,
  input[type="month"].input-sm,
  .input-group-sm input[type="date"],
  .input-group-sm input[type="time"],
  .input-group-sm input[type="datetime-local"],
  .input-group-sm input[type="month"] {
    line-height: 30px;
  }
  input[type="date"].input-lg,
  input[type="time"].input-lg,
  input[type="datetime-local"].input-lg,
  input[type="month"].input-lg,
  .input-group-lg input[type="date"],
  .input-group-lg input[type="time"],
  .input-group-lg input[type="datetime-local"],
  .input-group-lg input[type="month"] {
    line-height: 45px;
  }
}
.form-group {
  margin-bottom: 15px;
}
.radio,
.checkbox {
  position: relative;
  display: block;
  margin-top: 10px;
  margin-bottom: 10px;
}
.radio label,
.checkbox label {
  min-height: 18px;
  padding-left: 20px;
  margin-bottom: 0;
  font-weight: normal;
  cursor: pointer;
}
.radio input[type="radio"],
.radio-inline input[type="radio"],
.checkbox input[type="checkbox"],
.checkbox-inline input[type="checkbox"] {
  position: absolute;
  margin-left: -20px;
  margin-top: 4px \9;
}
.radio + .radio,
.checkbox + .checkbox {
  margin-top: -5px;
}
.radio-inline,
.checkbox-inline {
  position: relative;
  display: inline-block;
  padding-left: 20px;
  margin-bottom: 0;
  vertical-align: middle;
  font-weight: normal;
  cursor: pointer;
}
.radio-inline + .radio-inline,
.checkbox-inline + .checkbox-inline {
  margin-top: 0;
  margin-left: 10px;
}
input[type="radio"][disabled],
input[type="checkbox"][disabled],
input[type="radio"].disabled,
input[type="checkbox"].disabled,
fieldset[disabled] input[type="radio"],
fieldset[disabled] input[type="checkbox"] {
  cursor: not-allowed;
}
.radio-inline.disabled,
.checkbox-inline.disabled,
fieldset[disabled] .radio-inline,
fieldset[disabled] .checkbox-inline {
  cursor: not-allowed;
}
.radio.disabled label,
.checkbox.disabled label,
fieldset[disabled] .radio label,
fieldset[disabled] .checkbox label {
  cursor: not-allowed;
}
.form-control-static {
  padding-top: 7px;
  padding-bottom: 7px;
  margin-bottom: 0;
  min-height: 31px;
}
.form-control-static.input-lg,
.form-control-static.input-sm {
  padding-left: 0;
  padding-right: 0;
}
.input-sm {
  height: 30px;
  padding: 5px 10px;
  font-size: 12px;
  line-height: 1.5;
  border-radius: 1px;
}
select.input-sm {
  height: 30px;
  line-height: 30px;
}
textarea.input-sm,
select[multiple].input-sm {
  height: auto;
}
.form-group-sm .form-control {
  height: 30px;
  padding: 5px 10px;
  font-size: 12px;
  line-height: 1.5;
  border-radius: 1px;
}
.form-group-sm select.form-control {
  height: 30px;
  line-height: 30px;
}
.form-group-sm textarea.form-control,
.form-group-sm select[multiple].form-control {
  height: auto;
}
.form-group-sm .form-control-static {
  height: 30px;
  min-height: 30px;
  padding: 6px 10px;
  font-size: 12px;
  line-height: 1.5;
}
.input-lg {
  height: 45px;
  padding: 10px 16px;
  font-size: 17px;
  line-height: 1.3333333;
  border-radius: 3px;
}
select.input-lg {
  height: 45px;
  line-height: 45px;
}
textarea.input-lg,
select[multiple].input-lg {
  height: auto;
}
.form-group-lg .form-control {
  height: 45px;
  padding: 10px 16px;
  font-size: 17px;
  line-height: 1.3333333;
  border-radius: 3px;
}
.form-group-lg select.form-control {
  height: 45px;
  line-height: 45px;
}
.form-group-lg textarea.form-control,
.form-group-lg select[multiple].form-control {
  height: auto;
}
.form-group-lg .form-control-static {
  height: 45px;
  min-height: 35px;
  padding: 11px 16px;
  font-size: 17px;
  line-height: 1.3333333;
}
.has-feedback {
  position: relative;
}
.has-feedback .form-control {
  padding-right: 40px;
}
.form-control-feedback {
  position: absolute;
  top: 0;
  right: 0;
  z-index: 2;
  display: block;
  width: 32px;
  height: 32px;
  line-height: 32px;
  text-align: center;
  pointer-events: none;
}
.input-lg + .form-control-feedback,
.input-group-lg + .form-control-feedback,
.form-group-lg .form-control + .form-control-feedback {
  width: 45px;
  height: 45px;
  line-height: 45px;
}
.input-sm + .form-control-feedback,
.input-group-sm + .form-control-feedback,
.form-group-sm .form-control + .form-control-feedback {
  width: 30px;
  height: 30px;
  line-height: 30px;
}
.has-success .help-block,
.has-success .control-label,
.has-success .radio,
.has-success .checkbox,
.has-success .radio-inline,
.has-success .checkbox-inline,
.has-success.radio label,
.has-success.checkbox label,
.has-success.radio-inline label,
.has-success.checkbox-inline label {
  color: #3c763d;
}
.has-success .form-control {
  border-color: #3c763d;
  -webkit-box-shadow: inset 0 1px 1px rgba(0, 0, 0, 0.075);
  box-shadow: inset 0 1px 1px rgba(0, 0, 0, 0.075);
}
.has-success .form-control:focus {
  border-color: #2b542c;
  -webkit-box-shadow: inset 0 1px 1px rgba(0, 0, 0, 0.075), 0 0 6px #67b168;
  box-shadow: inset 0 1px 1px rgba(0, 0, 0, 0.075), 0 0 6px #67b168;
}
.has-success .input-group-addon {
  color: #3c763d;
  border-color: #3c763d;
  background-color: #dff0d8;
}
.has-success .form-control-feedback {
  color: #3c763d;
}
.has-warning .help-block,
.has-warning .control-label,
.has-warning .radio,
.has-warning .checkbox,
.has-warning .radio-inline,
.has-warning .checkbox-inline,
.has-warning.radio label,
.has-warning.checkbox label,
.has-warning.radio-inline label,
.has-warning.checkbox-inline label {
  color: #8a6d3b;
}
.has-warning .form-control {
  border-color: #8a6d3b;
  -webkit-box-shadow: inset 0 1px 1px rgba(0, 0, 0, 0.075);
  box-shadow: inset 0 1px 1px rgba(0, 0, 0, 0.075);
}
.has-warning .form-control:focus {
  border-color: #66512c;
  -webkit-box-shadow: inset 0 1px 1px rgba(0, 0, 0, 0.075), 0 0 6px #c0a16b;
  box-shadow: inset 0 1px 1px rgba(0, 0, 0, 0.075), 0 0 6px #c0a16b;
}
.has-warning .input-group-addon {
  color: #8a6d3b;
  border-color: #8a6d3b;
  background-color: #fcf8e3;
}
.has-warning .form-control-feedback {
  color: #8a6d3b;
}
.has-error .help-block,
.has-error .control-label,
.has-error .radio,
.has-error .checkbox,
.has-error .radio-inline,
.has-error .checkbox-inline,
.has-error.radio label,
.has-error.checkbox label,
.has-error.radio-inline label,
.has-error.checkbox-inline label {
  color: #a94442;
}
.has-error .form-control {
  border-color: #a94442;
  -webkit-box-shadow: inset 0 1px 1px rgba(0, 0, 0, 0.075);
  box-shadow: inset 0 1px 1px rgba(0, 0, 0, 0.075);
}
.has-error .form-control:focus {
  border-color: #843534;
  -webkit-box-shadow: inset 0 1px 1px rgba(0, 0, 0, 0.075), 0 0 6px #ce8483;
  box-shadow: inset 0 1px 1px rgba(0, 0, 0, 0.075), 0 0 6px #ce8483;
}
.has-error .input-group-addon {
  color: #a94442;
  border-color: #a94442;
  background-color: #f2dede;
}
.has-error .form-control-feedback {
  color: #a94442;
}
.has-feedback label ~ .form-control-feedback {
  top: 23px;
}
.has-feedback label.sr-only ~ .form-control-feedback {
  top: 0;
}
.help-block {
  display: block;
  margin-top: 5px;
  margin-bottom: 10px;
  color: #404040;
}
@media (min-width: 768px) {
  .form-inline .form-group {
    display: inline-block;
    margin-bottom: 0;
    vertical-align: middle;
  }
  .form-inline .form-control {
    display: inline-block;
    width: auto;
    vertical-align: middle;
  }
  .form-inline .form-control-static {
    display: inline-block;
  }
  .form-inline .input-group {
    display: inline-table;
    vertical-align: middle;
  }
  .form-inline .input-group .input-group-addon,
  .form-inline .input-group .input-group-btn,
  .form-inline .input-group .form-control {
    width: auto;
  }
  .form-inline .input-group > .form-control {
    width: 100%;
  }
  .form-inline .control-label {
    margin-bottom: 0;
    vertical-align: middle;
  }
  .form-inline .radio,
  .form-inline .checkbox {
    display: inline-block;
    margin-top: 0;
    margin-bottom: 0;
    vertical-align: middle;
  }
  .form-inline .radio label,
  .form-inline .checkbox label {
    padding-left: 0;
  }
  .form-inline .radio input[type="radio"],
  .form-inline .checkbox input[type="checkbox"] {
    position: relative;
    margin-left: 0;
  }
  .form-inline .has-feedback .form-control-feedback {
    top: 0;
  }
}
.form-horizontal .radio,
.form-horizontal .checkbox,
.form-horizontal .radio-inline,
.form-horizontal .checkbox-inline {
  margin-top: 0;
  margin-bottom: 0;
  padding-top: 7px;
}
.form-horizontal .radio,
.form-horizontal .checkbox {
  min-height: 25px;
}
.form-horizontal .form-group {
  margin-left: 0px;
  margin-right: 0px;
}
@media (min-width: 768px) {
  .form-horizontal .control-label {
    text-align: right;
    margin-bottom: 0;
    padding-top: 7px;
  }
}
.form-horizontal .has-feedback .form-control-feedback {
  right: 0px;
}
@media (min-width: 768px) {
  .form-horizontal .form-group-lg .control-label {
    padding-top: 11px;
    font-size: 17px;
  }
}
@media (min-width: 768px) {
  .form-horizontal .form-group-sm .control-label {
    padding-top: 6px;
    font-size: 12px;
  }
}
.btn {
  display: inline-block;
  margin-bottom: 0;
  font-weight: normal;
  text-align: center;
  vertical-align: middle;
  touch-action: manipulation;
  cursor: pointer;
  background-image: none;
  border: 1px solid transparent;
  white-space: nowrap;
  padding: 6px 12px;
  font-size: 13px;
  line-height: 1.42857143;
  border-radius: 2px;
  -webkit-user-select: none;
  -moz-user-select: none;
  -ms-user-select: none;
  user-select: none;
}
.btn:focus,
.btn:active:focus,
.btn.active:focus,
.btn.focus,
.btn:active.focus,
.btn.active.focus {
  outline: 5px auto -webkit-focus-ring-color;
  outline-offset: -2px;
}
.btn:hover,
.btn:focus,
.btn.focus {
  color: #333;
  text-decoration: none;
}
.btn:active,
.btn.active {
  outline: 0;
  background-image: none;
  -webkit-box-shadow: inset 0 3px 5px rgba(0, 0, 0, 0.125);
  box-shadow: inset 0 3px 5px rgba(0, 0, 0, 0.125);
}
.btn.disabled,
.btn[disabled],
fieldset[disabled] .btn {
  cursor: not-allowed;
  opacity: 0.65;
  filter: alpha(opacity=65);
  -webkit-box-shadow: none;
  box-shadow: none;
}
a.btn.disabled,
fieldset[disabled] a.btn {
  pointer-events: none;
}
.btn-default {
  color: #333;
  background-color: #fff;
  border-color: #ccc;
}
.btn-default:focus,
.btn-default.focus {
  color: #333;
  background-color: #e6e6e6;
  border-color: #8c8c8c;
}
.btn-default:hover {
  color: #333;
  background-color: #e6e6e6;
  border-color: #adadad;
}
.btn-default:active,
.btn-default.active,
.open > .dropdown-toggle.btn-default {
  color: #333;
  background-color: #e6e6e6;
  border-color: #adadad;
}
.btn-default:active:hover,
.btn-default.active:hover,
.open > .dropdown-toggle.btn-default:hover,
.btn-default:active:focus,
.btn-default.active:focus,
.open > .dropdown-toggle.btn-default:focus,
.btn-default:active.focus,
.btn-default.active.focus,
.open > .dropdown-toggle.btn-default.focus {
  color: #333;
  background-color: #d4d4d4;
  border-color: #8c8c8c;
}
.btn-default:active,
.btn-default.active,
.open > .dropdown-toggle.btn-default {
  background-image: none;
}
.btn-default.disabled:hover,
.btn-default[disabled]:hover,
fieldset[disabled] .btn-default:hover,
.btn-default.disabled:focus,
.btn-default[disabled]:focus,
fieldset[disabled] .btn-default:focus,
.btn-default.disabled.focus,
.btn-default[disabled].focus,
fieldset[disabled] .btn-default.focus {
  background-color: #fff;
  border-color: #ccc;
}
.btn-default .badge {
  color: #fff;
  background-color: #333;
}
.btn-primary {
  color: #fff;
  background-color: #337ab7;
  border-color: #2e6da4;
}
.btn-primary:focus,
.btn-primary.focus {
  color: #fff;
  background-color: #286090;
  border-color: #122b40;
}
.btn-primary:hover {
  color: #fff;
  background-color: #286090;
  border-color: #204d74;
}
.btn-primary:active,
.btn-primary.active,
.open > .dropdown-toggle.btn-primary {
  color: #fff;
  background-color: #286090;
  border-color: #204d74;
}
.btn-primary:active:hover,
.btn-primary.active:hover,
.open > .dropdown-toggle.btn-primary:hover,
.btn-primary:active:focus,
.btn-primary.active:focus,
.open > .dropdown-toggle.btn-primary:focus,
.btn-primary:active.focus,
.btn-primary.active.focus,
.open > .dropdown-toggle.btn-primary.focus {
  color: #fff;
  background-color: #204d74;
  border-color: #122b40;
}
.btn-primary:active,
.btn-primary.active,
.open > .dropdown-toggle.btn-primary {
  background-image: none;
}
.btn-primary.disabled:hover,
.btn-primary[disabled]:hover,
fieldset[disabled] .btn-primary:hover,
.btn-primary.disabled:focus,
.btn-primary[disabled]:focus,
fieldset[disabled] .btn-primary:focus,
.btn-primary.disabled.focus,
.btn-primary[disabled].focus,
fieldset[disabled] .btn-primary.focus {
  background-color: #337ab7;
  border-color: #2e6da4;
}
.btn-primary .badge {
  color: #337ab7;
  background-color: #fff;
}
.btn-success {
  color: #fff;
  background-color: #5cb85c;
  border-color: #4cae4c;
}
.btn-success:focus,
.btn-success.focus {
  color: #fff;
  background-color: #449d44;
  border-color: #255625;
}
.btn-success:hover {
  color: #fff;
  background-color: #449d44;
  border-color: #398439;
}
.btn-success:active,
.btn-success.active,
.open > .dropdown-toggle.btn-success {
  color: #fff;
  background-color: #449d44;
  border-color: #398439;
}
.btn-success:active:hover,
.btn-success.active:hover,
.open > .dropdown-toggle.btn-success:hover,
.btn-success:active:focus,
.btn-success.active:focus,
.open > .dropdown-toggle.btn-success:focus,
.btn-success:active.focus,
.btn-success.active.focus,
.open > .dropdown-toggle.btn-success.focus {
  color: #fff;
  background-color: #398439;
  border-color: #255625;
}
.btn-success:active,
.btn-success.active,
.open > .dropdown-toggle.btn-success {
  background-image: none;
}
.btn-success.disabled:hover,
.btn-success[disabled]:hover,
fieldset[disabled] .btn-success:hover,
.btn-success.disabled:focus,
.btn-success[disabled]:focus,
fieldset[disabled] .btn-success:focus,
.btn-success.disabled.focus,
.btn-success[disabled].focus,
fieldset[disabled] .btn-success.focus {
  background-color: #5cb85c;
  border-color: #4cae4c;
}
.btn-success .badge {
  color: #5cb85c;
  background-color: #fff;
}
.btn-info {
  color: #fff;
  background-color: #5bc0de;
  border-color: #46b8da;
}
.btn-info:focus,
.btn-info.focus {
  color: #fff;
  background-color: #31b0d5;
  border-color: #1b6d85;
}
.btn-info:hover {
  color: #fff;
  background-color: #31b0d5;
  border-color: #269abc;
}
.btn-info:active,
.btn-info.active,
.open > .dropdown-toggle.btn-info {
  color: #fff;
  background-color: #31b0d5;
  border-color: #269abc;
}
.btn-info:active:hover,
.btn-info.active:hover,
.open > .dropdown-toggle.btn-info:hover,
.btn-info:active:focus,
.btn-info.active:focus,
.open > .dropdown-toggle.btn-info:focus,
.btn-info:active.focus,
.btn-info.active.focus,
.open > .dropdown-toggle.btn-info.focus {
  color: #fff;
  background-color: #269abc;
  border-color: #1b6d85;
}
.btn-info:active,
.btn-info.active,
.open > .dropdown-toggle.btn-info {
  background-image: none;
}
.btn-info.disabled:hover,
.btn-info[disabled]:hover,
fieldset[disabled] .btn-info:hover,
.btn-info.disabled:focus,
.btn-info[disabled]:focus,
fieldset[disabled] .btn-info:focus,
.btn-info.disabled.focus,
.btn-info[disabled].focus,
fieldset[disabled] .btn-info.focus {
  background-color: #5bc0de;
  border-color: #46b8da;
}
.btn-info .badge {
  color: #5bc0de;
  background-color: #fff;
}
.btn-warning {
  color: #fff;
  background-color: #f0ad4e;
  border-color: #eea236;
}
.btn-warning:focus,
.btn-warning.focus {
  color: #fff;
  background-color: #ec971f;
  border-color: #985f0d;
}
.btn-warning:hover {
  color: #fff;
  background-color: #ec971f;
  border-color: #d58512;
}
.btn-warning:active,
.btn-warning.active,
.open > .dropdown-toggle.btn-warning {
  color: #fff;
  background-color: #ec971f;
  border-color: #d58512;
}
.btn-warning:active:hover,
.btn-warning.active:hover,
.open > .dropdown-toggle.btn-warning:hover,
.btn-warning:active:focus,
.btn-warning.active:focus,
.open > .dropdown-toggle.btn-warning:focus,
.btn-warning:active.focus,
.btn-warning.active.focus,
.open > .dropdown-toggle.btn-warning.focus {
  color: #fff;
  background-color: #d58512;
  border-color: #985f0d;
}
.btn-warning:active,
.btn-warning.active,
.open > .dropdown-toggle.btn-warning {
  background-image: none;
}
.btn-warning.disabled:hover,
.btn-warning[disabled]:hover,
fieldset[disabled] .btn-warning:hover,
.btn-warning.disabled:focus,
.btn-warning[disabled]:focus,
fieldset[disabled] .btn-warning:focus,
.btn-warning.disabled.focus,
.btn-warning[disabled].focus,
fieldset[disabled] .btn-warning.focus {
  background-color: #f0ad4e;
  border-color: #eea236;
}
.btn-warning .badge {
  color: #f0ad4e;
  background-color: #fff;
}
.btn-danger {
  color: #fff;
  background-color: #d9534f;
  border-color: #d43f3a;
}
.btn-danger:focus,
.btn-danger.focus {
  color: #fff;
  background-color: #c9302c;
  border-color: #761c19;
}
.btn-danger:hover {
  color: #fff;
  background-color: #c9302c;
  border-color: #ac2925;
}
.btn-danger:active,
.btn-danger.active,
.open > .dropdown-toggle.btn-danger {
  color: #fff;
  background-color: #c9302c;
  border-color: #ac2925;
}
.btn-danger:active:hover,
.btn-danger.active:hover,
.open > .dropdown-toggle.btn-danger:hover,
.btn-danger:active:focus,
.btn-danger.active:focus,
.open > .dropdown-toggle.btn-danger:focus,
.btn-danger:active.focus,
.btn-danger.active.focus,
.open > .dropdown-toggle.btn-danger.focus {
  color: #fff;
  background-color: #ac2925;
  border-color: #761c19;
}
.btn-danger:active,
.btn-danger.active,
.open > .dropdown-toggle.btn-danger {
  background-image: none;
}
.btn-danger.disabled:hover,
.btn-danger[disabled]:hover,
fieldset[disabled] .btn-danger:hover,
.btn-danger.disabled:focus,
.btn-danger[disabled]:focus,
fieldset[disabled] .btn-danger:focus,
.btn-danger.disabled.focus,
.btn-danger[disabled].focus,
fieldset[disabled] .btn-danger.focus {
  background-color: #d9534f;
  border-color: #d43f3a;
}
.btn-danger .badge {
  color: #d9534f;
  background-color: #fff;
}
.btn-link {
  color: #337ab7;
  font-weight: normal;
  border-radius: 0;
}
.btn-link,
.btn-link:active,
.btn-link.active,
.btn-link[disabled],
fieldset[disabled] .btn-link {
  background-color: transparent;
  -webkit-box-shadow: none;
  box-shadow: none;
}
.btn-link,
.btn-link:hover,
.btn-link:focus,
.btn-link:active {
  border-color: transparent;
}
.btn-link:hover,
.btn-link:focus {
  color: #23527c;
  text-decoration: underline;
  background-color: transparent;
}
.btn-link[disabled]:hover,
fieldset[disabled] .btn-link:hover,
.btn-link[disabled]:focus,
fieldset[disabled] .btn-link:focus {
  color: #777777;
  text-decoration: none;
}
.btn-lg,
.btn-group-lg > .btn {
  padding: 10px 16px;
  font-size: 17px;
  line-height: 1.3333333;
  border-radius: 3px;
}
.btn-sm,
.btn-group-sm > .btn {
  padding: 5px 10px;
  font-size: 12px;
  line-height: 1.5;
  border-radius: 1px;
}
.btn-xs,
.btn-group-xs > .btn {
  padding: 1px 5px;
  font-size: 12px;
  line-height: 1.5;
  border-radius: 1px;
}
.btn-block {
  display: block;
  width: 100%;
}
.btn-block + .btn-block {
  margin-top: 5px;
}
input[type="submit"].btn-block,
input[type="reset"].btn-block,
input[type="button"].btn-block {
  width: 100%;
}
.fade {
  opacity: 0;
  -webkit-transition: opacity 0.15s linear;
  -o-transition: opacity 0.15s linear;
  transition: opacity 0.15s linear;
}
.fade.in {
  opacity: 1;
}
.collapse {
  display: none;
}
.collapse.in {
  display: block;
}
tr.collapse.in {
  display: table-row;
}
tbody.collapse.in {
  display: table-row-group;
}
.collapsing {
  position: relative;
  height: 0;
  overflow: hidden;
  -webkit-transition-property: height, visibility;
  transition-property: height, visibility;
  -webkit-transition-duration: 0.35s;
  transition-duration: 0.35s;
  -webkit-transition-timing-function: ease;
  transition-timing-function: ease;
}
.caret {
  display: inline-block;
  width: 0;
  height: 0;
  margin-left: 2px;
  vertical-align: middle;
  border-top: 4px dashed;
  border-top: 4px solid \9;
  border-right: 4px solid transparent;
  border-left: 4px solid transparent;
}
.dropup,
.dropdown {
  position: relative;
}
.dropdown-toggle:focus {
  outline: 0;
}
.dropdown-menu {
  position: absolute;
  top: 100%;
  left: 0;
  z-index: 1000;
  display: none;
  float: left;
  min-width: 160px;
  padding: 5px 0;
  margin: 2px 0 0;
  list-style: none;
  font-size: 13px;
  text-align: left;
  background-color: #fff;
  border: 1px solid #ccc;
  border: 1px solid rgba(0, 0, 0, 0.15);
  border-radius: 2px;
  -webkit-box-shadow: 0 6px 12px rgba(0, 0, 0, 0.175);
  box-shadow: 0 6px 12px rgba(0, 0, 0, 0.175);
  background-clip: padding-box;
}
.dropdown-menu.pull-right {
  right: 0;
  left: auto;
}
.dropdown-menu .divider {
  height: 1px;
  margin: 8px 0;
  overflow: hidden;
  background-color: #e5e5e5;
}
.dropdown-menu > li > a {
  display: block;
  padding: 3px 20px;
  clear: both;
  font-weight: normal;
  line-height: 1.42857143;
  color: #333333;
  white-space: nowrap;
}
.dropdown-menu > li > a:hover,
.dropdown-menu > li > a:focus {
  text-decoration: none;
  color: #262626;
  background-color: #f5f5f5;
}
.dropdown-menu > .active > a,
.dropdown-menu > .active > a:hover,
.dropdown-menu > .active > a:focus {
  color: #fff;
  text-decoration: none;
  outline: 0;
  background-color: #337ab7;
}
.dropdown-menu > .disabled > a,
.dropdown-menu > .disabled > a:hover,
.dropdown-menu > .disabled > a:focus {
  color: #777777;
}
.dropdown-menu > .disabled > a:hover,
.dropdown-menu > .disabled > a:focus {
  text-decoration: none;
  background-color: transparent;
  background-image: none;
  filter: progid:DXImageTransform.Microsoft.gradient(enabled = false);
  cursor: not-allowed;
}
.open > .dropdown-menu {
  display: block;
}
.open > a {
  outline: 0;
}
.dropdown-menu-right {
  left: auto;
  right: 0;
}
.dropdown-menu-left {
  left: 0;
  right: auto;
}
.dropdown-header {
  display: block;
  padding: 3px 20px;
  font-size: 12px;
  line-height: 1.42857143;
  color: #777777;
  white-space: nowrap;
}
.dropdown-backdrop {
  position: fixed;
  left: 0;
  right: 0;
  bottom: 0;
  top: 0;
  z-index: 990;
}
.pull-right > .dropdown-menu {
  right: 0;
  left: auto;
}
.dropup .caret,
.navbar-fixed-bottom .dropdown .caret {
  border-top: 0;
  border-bottom: 4px dashed;
  border-bottom: 4px solid \9;
  content: "";
}
.dropup .dropdown-menu,
.navbar-fixed-bottom .dropdown .dropdown-menu {
  top: auto;
  bottom: 100%;
  margin-bottom: 2px;
}
@media (min-width: 541px) {
  .navbar-right .dropdown-menu {
    left: auto;
    right: 0;
  }
  .navbar-right .dropdown-menu-left {
    left: 0;
    right: auto;
  }
}
.btn-group,
.btn-group-vertical {
  position: relative;
  display: inline-block;
  vertical-align: middle;
}
.btn-group > .btn,
.btn-group-vertical > .btn {
  position: relative;
  float: left;
}
.btn-group > .btn:hover,
.btn-group-vertical > .btn:hover,
.btn-group > .btn:focus,
.btn-group-vertical > .btn:focus,
.btn-group > .btn:active,
.btn-group-vertical > .btn:active,
.btn-group > .btn.active,
.btn-group-vertical > .btn.active {
  z-index: 2;
}
.btn-group .btn + .btn,
.btn-group .btn + .btn-group,
.btn-group .btn-group + .btn,
.btn-group .btn-group + .btn-group {
  margin-left: -1px;
}
.btn-toolbar {
  margin-left: -5px;
}
.btn-toolbar .btn,
.btn-toolbar .btn-group,
.btn-toolbar .input-group {
  float: left;
}
.btn-toolbar > .btn,
.btn-toolbar > .btn-group,
.btn-toolbar > .input-group {
  margin-left: 5px;
}
.btn-group > .btn:not(:first-child):not(:last-child):not(.dropdown-toggle) {
  border-radius: 0;
}
.btn-group > .btn:first-child {
  margin-left: 0;
}
.btn-group > .btn:first-child:not(:last-child):not(.dropdown-toggle) {
  border-bottom-right-radius: 0;
  border-top-right-radius: 0;
}
.btn-group > .btn:last-child:not(:first-child),
.btn-group > .dropdown-toggle:not(:first-child) {
  border-bottom-left-radius: 0;
  border-top-left-radius: 0;
}
.btn-group > .btn-group {
  float: left;
}
.btn-group > .btn-group:not(:first-child):not(:last-child) > .btn {
  border-radius: 0;
}
.btn-group > .btn-group:first-child:not(:last-child) > .btn:last-child,
.btn-group > .btn-group:first-child:not(:last-child) > .dropdown-toggle {
  border-bottom-right-radius: 0;
  border-top-right-radius: 0;
}
.btn-group > .btn-group:last-child:not(:first-child) > .btn:first-child {
  border-bottom-left-radius: 0;
  border-top-left-radius: 0;
}
.btn-group .dropdown-toggle:active,
.btn-group.open .dropdown-toggle {
  outline: 0;
}
.btn-group > .btn + .dropdown-toggle {
  padding-left: 8px;
  padding-right: 8px;
}
.btn-group > .btn-lg + .dropdown-toggle {
  padding-left: 12px;
  padding-right: 12px;
}
.btn-group.open .dropdown-toggle {
  -webkit-box-shadow: inset 0 3px 5px rgba(0, 0, 0, 0.125);
  box-shadow: inset 0 3px 5px rgba(0, 0, 0, 0.125);
}
.btn-group.open .dropdown-toggle.btn-link {
  -webkit-box-shadow: none;
  box-shadow: none;
}
.btn .caret {
  margin-left: 0;
}
.btn-lg .caret {
  border-width: 5px 5px 0;
  border-bottom-width: 0;
}
.dropup .btn-lg .caret {
  border-width: 0 5px 5px;
}
.btn-group-vertical > .btn,
.btn-group-vertical > .btn-group,
.btn-group-vertical > .btn-group > .btn {
  display: block;
  float: none;
  width: 100%;
  max-width: 100%;
}
.btn-group-vertical > .btn-group > .btn {
  float: none;
}
.btn-group-vertical > .btn + .btn,
.btn-group-vertical > .btn + .btn-group,
.btn-group-vertical > .btn-group + .btn,
.btn-group-vertical > .btn-group + .btn-group {
  margin-top: -1px;
  margin-left: 0;
}
.btn-group-vertical > .btn:not(:first-child):not(:last-child) {
  border-radius: 0;
}
.btn-group-vertical > .btn:first-child:not(:last-child) {
  border-top-right-radius: 2px;
  border-top-left-radius: 2px;
  border-bottom-right-radius: 0;
  border-bottom-left-radius: 0;
}
.btn-group-vertical > .btn:last-child:not(:first-child) {
  border-top-right-radius: 0;
  border-top-left-radius: 0;
  border-bottom-right-radius: 2px;
  border-bottom-left-radius: 2px;
}
.btn-group-vertical > .btn-group:not(:first-child):not(:last-child) > .btn {
  border-radius: 0;
}
.btn-group-vertical > .btn-group:first-child:not(:last-child) > .btn:last-child,
.btn-group-vertical > .btn-group:first-child:not(:last-child) > .dropdown-toggle {
  border-bottom-right-radius: 0;
  border-bottom-left-radius: 0;
}
.btn-group-vertical > .btn-group:last-child:not(:first-child) > .btn:first-child {
  border-top-right-radius: 0;
  border-top-left-radius: 0;
}
.btn-group-justified {
  display: table;
  width: 100%;
  table-layout: fixed;
  border-collapse: separate;
}
.btn-group-justified > .btn,
.btn-group-justified > .btn-group {
  float: none;
  display: table-cell;
  width: 1%;
}
.btn-group-justified > .btn-group .btn {
  width: 100%;
}
.btn-group-justified > .btn-group .dropdown-menu {
  left: auto;
}
[data-toggle="buttons"] > .btn input[type="radio"],
[data-toggle="buttons"] > .btn-group > .btn input[type="radio"],
[data-toggle="buttons"] > .btn input[type="checkbox"],
[data-toggle="buttons"] > .btn-group > .btn input[type="checkbox"] {
  position: absolute;
  clip: rect(0, 0, 0, 0);
  pointer-events: none;
}
.input-group {
  position: relative;
  display: table;
  border-collapse: separate;
}
.input-group[class*="col-"] {
  float: none;
  padding-left: 0;
  padding-right: 0;
}
.input-group .form-control {
  position: relative;
  z-index: 2;
  float: left;
  width: 100%;
  margin-bottom: 0;
}
.input-group .form-control:focus {
  z-index: 3;
}
.input-group-lg > .form-control,
.input-group-lg > .input-group-addon,
.input-group-lg > .input-group-btn > .btn {
  height: 45px;
  padding: 10px 16px;
  font-size: 17px;
  line-height: 1.3333333;
  border-radius: 3px;
}
select.input-group-lg > .form-control,
select.input-group-lg > .input-group-addon,
select.input-group-lg > .input-group-btn > .btn {
  height: 45px;
  line-height: 45px;
}
textarea.input-group-lg > .form-control,
textarea.input-group-lg > .input-group-addon,
textarea.input-group-lg > .input-group-btn > .btn,
select[multiple].input-group-lg > .form-control,
select[multiple].input-group-lg > .input-group-addon,
select[multiple].input-group-lg > .input-group-btn > .btn {
  height: auto;
}
.input-group-sm > .form-control,
.input-group-sm > .input-group-addon,
.input-group-sm > .input-group-btn > .btn {
  height: 30px;
  padding: 5px 10px;
  font-size: 12px;
  line-height: 1.5;
  border-radius: 1px;
}
select.input-group-sm > .form-control,
select.input-group-sm > .input-group-addon,
select.input-group-sm > .input-group-btn > .btn {
  height: 30px;
  line-height: 30px;
}
textarea.input-group-sm > .form-control,
textarea.input-group-sm > .input-group-addon,
textarea.input-group-sm > .input-group-btn > .btn,
select[multiple].input-group-sm > .form-control,
select[multiple].input-group-sm > .input-group-addon,
select[multiple].input-group-sm > .input-group-btn > .btn {
  height: auto;
}
.input-group-addon,
.input-group-btn,
.input-group .form-control {
  display: table-cell;
}
.input-group-addon:not(:first-child):not(:last-child),
.input-group-btn:not(:first-child):not(:last-child),
.input-group .form-control:not(:first-child):not(:last-child) {
  border-radius: 0;
}
.input-group-addon,
.input-group-btn {
  width: 1%;
  white-space: nowrap;
  vertical-align: middle;
}
.input-group-addon {
  padding: 6px 12px;
  font-size: 13px;
  font-weight: normal;
  line-height: 1;
  color: #555555;
  text-align: center;
  background-color: #eeeeee;
  border: 1px solid #ccc;
  border-radius: 2px;
}
.input-group-addon.input-sm {
  padding: 5px 10px;
  font-size: 12px;
  border-radius: 1px;
}
.input-group-addon.input-lg {
  padding: 10px 16px;
  font-size: 17px;
  border-radius: 3px;
}
.input-group-addon input[type="radio"],
.input-group-addon input[type="checkbox"] {
  margin-top: 0;
}
.input-group .form-control:first-child,
.input-group-addon:first-child,
.input-group-btn:first-child > .btn,
.input-group-btn:first-child > .btn-group > .btn,
.input-group-btn:first-child > .dropdown-toggle,
.input-group-btn:last-child > .btn:not(:last-child):not(.dropdown-toggle),
.input-group-btn:last-child > .btn-group:not(:last-child) > .btn {
  border-bottom-right-radius: 0;
  border-top-right-radius: 0;
}
.input-group-addon:first-child {
  border-right: 0;
}
.input-group .form-control:last-child,
.input-group-addon:last-child,
.input-group-btn:last-child > .btn,
.input-group-btn:last-child > .btn-group > .btn,
.input-group-btn:last-child > .dropdown-toggle,
.input-group-btn:first-child > .btn:not(:first-child),
.input-group-btn:first-child > .btn-group:not(:first-child) > .btn {
  border-bottom-left-radius: 0;
  border-top-left-radius: 0;
}
.input-group-addon:last-child {
  border-left: 0;
}
.input-group-btn {
  position: relative;
  font-size: 0;
  white-space: nowrap;
}
.input-group-btn > .btn {
  position: relative;
}
.input-group-btn > .btn + .btn {
  margin-left: -1px;
}
.input-group-btn > .btn:hover,
.input-group-btn > .btn:focus,
.input-group-btn > .btn:active {
  z-index: 2;
}
.input-group-btn:first-child > .btn,
.input-group-btn:first-child > .btn-group {
  margin-right: -1px;
}
.input-group-btn:last-child > .btn,
.input-group-btn:last-child > .btn-group {
  z-index: 2;
  margin-left: -1px;
}
.nav {
  margin-bottom: 0;
  padding-left: 0;
  list-style: none;
}
.nav > li {
  position: relative;
  display: block;
}
.nav > li > a {
  position: relative;
  display: block;
  padding: 10px 15px;
}
.nav > li > a:hover,
.nav > li > a:focus {
  text-decoration: none;
  background-color: #eeeeee;
}
.nav > li.disabled > a {
  color: #777777;
}
.nav > li.disabled > a:hover,
.nav > li.disabled > a:focus {
  color: #777777;
  text-decoration: none;
  background-color: transparent;
  cursor: not-allowed;
}
.nav .open > a,
.nav .open > a:hover,
.nav .open > a:focus {
  background-color: #eeeeee;
  border-color: #337ab7;
}
.nav .nav-divider {
  height: 1px;
  margin: 8px 0;
  overflow: hidden;
  background-color: #e5e5e5;
}
.nav > li > a > img {
  max-width: none;
}
.nav-tabs {
  border-bottom: 1px solid #ddd;
}
.nav-tabs > li {
  float: left;
  margin-bottom: -1px;
}
.nav-tabs > li > a {
  margin-right: 2px;
  line-height: 1.42857143;
  border: 1px solid transparent;
  border-radius: 2px 2px 0 0;
}
.nav-tabs > li > a:hover {
  border-color: #eeeeee #eeeeee #ddd;
}
.nav-tabs > li.active > a,
.nav-tabs > li.active > a:hover,
.nav-tabs > li.active > a:focus {
  color: #555555;
  background-color: #fff;
  border: 1px solid #ddd;
  border-bottom-color: transparent;
  cursor: default;
}
.nav-tabs.nav-justified {
  width: 100%;
  border-bottom: 0;
}
.nav-tabs.nav-justified > li {
  float: none;
}
.nav-tabs.nav-justified > li > a {
  text-align: center;
  margin-bottom: 5px;
}
.nav-tabs.nav-justified > .dropdown .dropdown-menu {
  top: auto;
  left: auto;
}
@media (min-width: 768px) {
  .nav-tabs.nav-justified > li {
    display: table-cell;
    width: 1%;
  }
  .nav-tabs.nav-justified > li > a {
    margin-bottom: 0;
  }
}
.nav-tabs.nav-justified > li > a {
  margin-right: 0;
  border-radius: 2px;
}
.nav-tabs.nav-justified > .active > a,
.nav-tabs.nav-justified > .active > a:hover,
.nav-tabs.nav-justified > .active > a:focus {
  border: 1px solid #ddd;
}
@media (min-width: 768px) {
  .nav-tabs.nav-justified > li > a {
    border-bottom: 1px solid #ddd;
    border-radius: 2px 2px 0 0;
  }
  .nav-tabs.nav-justified > .active > a,
  .nav-tabs.nav-justified > .active > a:hover,
  .nav-tabs.nav-justified > .active > a:focus {
    border-bottom-color: #fff;
  }
}
.nav-pills > li {
  float: left;
}
.nav-pills > li > a {
  border-radius: 2px;
}
.nav-pills > li + li {
  margin-left: 2px;
}
.nav-pills > li.active > a,
.nav-pills > li.active > a:hover,
.nav-pills > li.active > a:focus {
  color: #fff;
  background-color: #337ab7;
}
.nav-stacked > li {
  float: none;
}
.nav-stacked > li + li {
  margin-top: 2px;
  margin-left: 0;
}
.nav-justified {
  width: 100%;
}
.nav-justified > li {
  float: none;
}
.nav-justified > li > a {
  text-align: center;
  margin-bottom: 5px;
}
.nav-justified > .dropdown .dropdown-menu {
  top: auto;
  left: auto;
}
@media (min-width: 768px) {
  .nav-justified > li {
    display: table-cell;
    width: 1%;
  }
  .nav-justified > li > a {
    margin-bottom: 0;
  }
}
.nav-tabs-justified {
  border-bottom: 0;
}
.nav-tabs-justified > li > a {
  margin-right: 0;
  border-radius: 2px;
}
.nav-tabs-justified > .active > a,
.nav-tabs-justified > .active > a:hover,
.nav-tabs-justified > .active > a:focus {
  border: 1px solid #ddd;
}
@media (min-width: 768px) {
  .nav-tabs-justified > li > a {
    border-bottom: 1px solid #ddd;
    border-radius: 2px 2px 0 0;
  }
  .nav-tabs-justified > .active > a,
  .nav-tabs-justified > .active > a:hover,
  .nav-tabs-justified > .active > a:focus {
    border-bottom-color: #fff;
  }
}
.tab-content > .tab-pane {
  display: none;
}
.tab-content > .active {
  display: block;
}
.nav-tabs .dropdown-menu {
  margin-top: -1px;
  border-top-right-radius: 0;
  border-top-left-radius: 0;
}
.navbar {
  position: relative;
  min-height: 30px;
  margin-bottom: 18px;
  border: 1px solid transparent;
}
@media (min-width: 541px) {
  .navbar {
    border-radius: 2px;
  }
}
@media (min-width: 541px) {
  .navbar-header {
    float: left;
  }
}
.navbar-collapse {
  overflow-x: visible;
  padding-right: 0px;
  padding-left: 0px;
  border-top: 1px solid transparent;
  box-shadow: inset 0 1px 0 rgba(255, 255, 255, 0.1);
  -webkit-overflow-scrolling: touch;
}
.navbar-collapse.in {
  overflow-y: auto;
}
@media (min-width: 541px) {
  .navbar-collapse {
    width: auto;
    border-top: 0;
    box-shadow: none;
  }
  .navbar-collapse.collapse {
    display: block !important;
    height: auto !important;
    padding-bottom: 0;
    overflow: visible !important;
  }
  .navbar-collapse.in {
    overflow-y: visible;
  }
  .navbar-fixed-top .navbar-collapse,
  .navbar-static-top .navbar-collapse,
  .navbar-fixed-bottom .navbar-collapse {
    padding-left: 0;
    padding-right: 0;
  }
}
.navbar-fixed-top .navbar-collapse,
.navbar-fixed-bottom .navbar-collapse {
  max-height: 340px;
}
@media (max-device-width: 540px) and (orientation: landscape) {
  .navbar-fixed-top .navbar-collapse,
  .navbar-fixed-bottom .navbar-collapse {
    max-height: 200px;
  }
}
.container > .navbar-header,
.container-fluid > .navbar-header,
.container > .navbar-collapse,
.container-fluid > .navbar-collapse {
  margin-right: 0px;
  margin-left: 0px;
}
@media (min-width: 541px) {
  .container > .navbar-header,
  .container-fluid > .navbar-header,
  .container > .navbar-collapse,
  .container-fluid > .navbar-collapse {
    margin-right: 0;
    margin-left: 0;
  }
}
.navbar-static-top {
  z-index: 1000;
  border-width: 0 0 1px;
}
@media (min-width: 541px) {
  .navbar-static-top {
    border-radius: 0;
  }
}
.navbar-fixed-top,
.navbar-fixed-bottom {
  position: fixed;
  right: 0;
  left: 0;
  z-index: 1030;
}
@media (min-width: 541px) {
  .navbar-fixed-top,
  .navbar-fixed-bottom {
    border-radius: 0;
  }
}
.navbar-fixed-top {
  top: 0;
  border-width: 0 0 1px;
}
.navbar-fixed-bottom {
  bottom: 0;
  margin-bottom: 0;
  border-width: 1px 0 0;
}
.navbar-brand {
  float: left;
  padding: 6px 0px;
  font-size: 17px;
  line-height: 18px;
  height: 30px;
}
.navbar-brand:hover,
.navbar-brand:focus {
  text-decoration: none;
}
.navbar-brand > img {
  display: block;
}
@media (min-width: 541px) {
  .navbar > .container .navbar-brand,
  .navbar > .container-fluid .navbar-brand {
    margin-left: 0px;
  }
}
.navbar-toggle {
  position: relative;
  float: right;
  margin-right: 0px;
  padding: 9px 10px;
  margin-top: -2px;
  margin-bottom: -2px;
  background-color: transparent;
  background-image: none;
  border: 1px solid transparent;
  border-radius: 2px;
}
.navbar-toggle:focus {
  outline: 0;
}
.navbar-toggle .icon-bar {
  display: block;
  width: 22px;
  height: 2px;
  border-radius: 1px;
}
.navbar-toggle .icon-bar + .icon-bar {
  margin-top: 4px;
}
@media (min-width: 541px) {
  .navbar-toggle {
    display: none;
  }
}
.navbar-nav {
  margin: 3px 0px;
}
.navbar-nav > li > a {
  padding-top: 10px;
  padding-bottom: 10px;
  line-height: 18px;
}
@media (max-width: 540px) {
  .navbar-nav .open .dropdown-menu {
    position: static;
    float: none;
    width: auto;
    margin-top: 0;
    background-color: transparent;
    border: 0;
    box-shadow: none;
  }
  .navbar-nav .open .dropdown-menu > li > a,
  .navbar-nav .open .dropdown-menu .dropdown-header {
    padding: 5px 15px 5px 25px;
  }
  .navbar-nav .open .dropdown-menu > li > a {
    line-height: 18px;
  }
  .navbar-nav .open .dropdown-menu > li > a:hover,
  .navbar-nav .open .dropdown-menu > li > a:focus {
    background-image: none;
  }
}
@media (min-width: 541px) {
  .navbar-nav {
    float: left;
    margin: 0;
  }
  .navbar-nav > li {
    float: left;
  }
  .navbar-nav > li > a {
    padding-top: 6px;
    padding-bottom: 6px;
  }
}
.navbar-form {
  margin-left: 0px;
  margin-right: 0px;
  padding: 10px 0px;
  border-top: 1px solid transparent;
  border-bottom: 1px solid transparent;
  -webkit-box-shadow: inset 0 1px 0 rgba(255, 255, 255, 0.1), 0 1px 0 rgba(255, 255, 255, 0.1);
  box-shadow: inset 0 1px 0 rgba(255, 255, 255, 0.1), 0 1px 0 rgba(255, 255, 255, 0.1);
  margin-top: -1px;
  margin-bottom: -1px;
}
@media (min-width: 768px) {
  .navbar-form .form-group {
    display: inline-block;
    margin-bottom: 0;
    vertical-align: middle;
  }
  .navbar-form .form-control {
    display: inline-block;
    width: auto;
    vertical-align: middle;
  }
  .navbar-form .form-control-static {
    display: inline-block;
  }
  .navbar-form .input-group {
    display: inline-table;
    vertical-align: middle;
  }
  .navbar-form .input-group .input-group-addon,
  .navbar-form .input-group .input-group-btn,
  .navbar-form .input-group .form-control {
    width: auto;
  }
  .navbar-form .input-group > .form-control {
    width: 100%;
  }
  .navbar-form .control-label {
    margin-bottom: 0;
    vertical-align: middle;
  }
  .navbar-form .radio,
  .navbar-form .checkbox {
    display: inline-block;
    margin-top: 0;
    margin-bottom: 0;
    vertical-align: middle;
  }
  .navbar-form .radio label,
  .navbar-form .checkbox label {
    padding-left: 0;
  }
  .navbar-form .radio input[type="radio"],
  .navbar-form .checkbox input[type="checkbox"] {
    position: relative;
    margin-left: 0;
  }
  .navbar-form .has-feedback .form-control-feedback {
    top: 0;
  }
}
@media (max-width: 540px) {
  .navbar-form .form-group {
    margin-bottom: 5px;
  }
  .navbar-form .form-group:last-child {
    margin-bottom: 0;
  }
}
@media (min-width: 541px) {
  .navbar-form {
    width: auto;
    border: 0;
    margin-left: 0;
    margin-right: 0;
    padding-top: 0;
    padding-bottom: 0;
    -webkit-box-shadow: none;
    box-shadow: none;
  }
}
.navbar-nav > li > .dropdown-menu {
  margin-top: 0;
  border-top-right-radius: 0;
  border-top-left-radius: 0;
}
.navbar-fixed-bottom .navbar-nav > li > .dropdown-menu {
  margin-bottom: 0;
  border-top-right-radius: 2px;
  border-top-left-radius: 2px;
  border-bottom-right-radius: 0;
  border-bottom-left-radius: 0;
}
.navbar-btn {
  margin-top: -1px;
  margin-bottom: -1px;
}
.navbar-btn.btn-sm {
  margin-top: 0px;
  margin-bottom: 0px;
}
.navbar-btn.btn-xs {
  margin-top: 4px;
  margin-bottom: 4px;
}
.navbar-text {
  margin-top: 6px;
  margin-bottom: 6px;
}
@media (min-width: 541px) {
  .navbar-text {
    float: left;
    margin-left: 0px;
    margin-right: 0px;
  }
}
@media (min-width: 541px) {
  .navbar-left {
    float: left !important;
    float: left;
  }
  .navbar-right {
    float: right !important;
    float: right;
    margin-right: 0px;
  }
  .navbar-right ~ .navbar-right {
    margin-right: 0;
  }
}
.navbar-default {
  background-color: #f8f8f8;
  border-color: #e7e7e7;
}
.navbar-default .navbar-brand {
  color: #777;
}
.navbar-default .navbar-brand:hover,
.navbar-default .navbar-brand:focus {
  color: #5e5e5e;
  background-color: transparent;
}
.navbar-default .navbar-text {
  color: #777;
}
.navbar-default .navbar-nav > li > a {
  color: #777;
}
.navbar-default .navbar-nav > li > a:hover,
.navbar-default .navbar-nav > li > a:focus {
  color: #333;
  background-color: transparent;
}
.navbar-default .navbar-nav > .active > a,
.navbar-default .navbar-nav > .active > a:hover,
.navbar-default .navbar-nav > .active > a:focus {
  color: #555;
  background-color: #e7e7e7;
}
.navbar-default .navbar-nav > .disabled > a,
.navbar-default .navbar-nav > .disabled > a:hover,
.navbar-default .navbar-nav > .disabled > a:focus {
  color: #ccc;
  background-color: transparent;
}
.navbar-default .navbar-toggle {
  border-color: #ddd;
}
.navbar-default .navbar-toggle:hover,
.navbar-default .navbar-toggle:focus {
  background-color: #ddd;
}
.navbar-default .navbar-toggle .icon-bar {
  background-color: #888;
}
.navbar-default .navbar-collapse,
.navbar-default .navbar-form {
  border-color: #e7e7e7;
}
.navbar-default .navbar-nav > .open > a,
.navbar-default .navbar-nav > .open > a:hover,
.navbar-default .navbar-nav > .open > a:focus {
  background-color: #e7e7e7;
  color: #555;
}
@media (max-width: 540px) {
  .navbar-default .navbar-nav .open .dropdown-menu > li > a {
    color: #777;
  }
  .navbar-default .navbar-nav .open .dropdown-menu > li > a:hover,
  .navbar-default .navbar-nav .open .dropdown-menu > li > a:focus {
    color: #333;
    background-color: transparent;
  }
  .navbar-default .navbar-nav .open .dropdown-menu > .active > a,
  .navbar-default .navbar-nav .open .dropdown-menu > .active > a:hover,
  .navbar-default .navbar-nav .open .dropdown-menu > .active > a:focus {
    color: #555;
    background-color: #e7e7e7;
  }
  .navbar-default .navbar-nav .open .dropdown-menu > .disabled > a,
  .navbar-default .navbar-nav .open .dropdown-menu > .disabled > a:hover,
  .navbar-default .navbar-nav .open .dropdown-menu > .disabled > a:focus {
    color: #ccc;
    background-color: transparent;
  }
}
.navbar-default .navbar-link {
  color: #777;
}
.navbar-default .navbar-link:hover {
  color: #333;
}
.navbar-default .btn-link {
  color: #777;
}
.navbar-default .btn-link:hover,
.navbar-default .btn-link:focus {
  color: #333;
}
.navbar-default .btn-link[disabled]:hover,
fieldset[disabled] .navbar-default .btn-link:hover,
.navbar-default .btn-link[disabled]:focus,
fieldset[disabled] .navbar-default .btn-link:focus {
  color: #ccc;
}
.navbar-inverse {
  background-color: #222;
  border-color: #080808;
}
.navbar-inverse .navbar-brand {
  color: #9d9d9d;
}
.navbar-inverse .navbar-brand:hover,
.navbar-inverse .navbar-brand:focus {
  color: #fff;
  background-color: transparent;
}
.navbar-inverse .navbar-text {
  color: #9d9d9d;
}
.navbar-inverse .navbar-nav > li > a {
  color: #9d9d9d;
}
.navbar-inverse .navbar-nav > li > a:hover,
.navbar-inverse .navbar-nav > li > a:focus {
  color: #fff;
  background-color: transparent;
}
.navbar-inverse .navbar-nav > .active > a,
.navbar-inverse .navbar-nav > .active > a:hover,
.navbar-inverse .navbar-nav > .active > a:focus {
  color: #fff;
  background-color: #080808;
}
.navbar-inverse .navbar-nav > .disabled > a,
.navbar-inverse .navbar-nav > .disabled > a:hover,
.navbar-inverse .navbar-nav > .disabled > a:focus {
  color: #444;
  background-color: transparent;
}
.navbar-inverse .navbar-toggle {
  border-color: #333;
}
.navbar-inverse .navbar-toggle:hover,
.navbar-inverse .navbar-toggle:focus {
  background-color: #333;
}
.navbar-inverse .navbar-toggle .icon-bar {
  background-color: #fff;
}
.navbar-inverse .navbar-collapse,
.navbar-inverse .navbar-form {
  border-color: #101010;
}
.navbar-inverse .navbar-nav > .open > a,
.navbar-inverse .navbar-nav > .open > a:hover,
.navbar-inverse .navbar-nav > .open > a:focus {
  background-color: #080808;
  color: #fff;
}
@media (max-width: 540px) {
  .navbar-inverse .navbar-nav .open .dropdown-menu > .dropdown-header {
    border-color: #080808;
  }
  .navbar-inverse .navbar-nav .open .dropdown-menu .divider {
    background-color: #080808;
  }
  .navbar-inverse .navbar-nav .open .dropdown-menu > li > a {
    color: #9d9d9d;
  }
  .navbar-inverse .navbar-nav .open .dropdown-menu > li > a:hover,
  .navbar-inverse .navbar-nav .open .dropdown-menu > li > a:focus {
    color: #fff;
    background-color: transparent;
  }
  .navbar-inverse .navbar-nav .open .dropdown-menu > .active > a,
  .navbar-inverse .navbar-nav .open .dropdown-menu > .active > a:hover,
  .navbar-inverse .navbar-nav .open .dropdown-menu > .active > a:focus {
    color: #fff;
    background-color: #080808;
  }
  .navbar-inverse .navbar-nav .open .dropdown-menu > .disabled > a,
  .navbar-inverse .navbar-nav .open .dropdown-menu > .disabled > a:hover,
  .navbar-inverse .navbar-nav .open .dropdown-menu > .disabled > a:focus {
    color: #444;
    background-color: transparent;
  }
}
.navbar-inverse .navbar-link {
  color: #9d9d9d;
}
.navbar-inverse .navbar-link:hover {
  color: #fff;
}
.navbar-inverse .btn-link {
  color: #9d9d9d;
}
.navbar-inverse .btn-link:hover,
.navbar-inverse .btn-link:focus {
  color: #fff;
}
.navbar-inverse .btn-link[disabled]:hover,
fieldset[disabled] .navbar-inverse .btn-link:hover,
.navbar-inverse .btn-link[disabled]:focus,
fieldset[disabled] .navbar-inverse .btn-link:focus {
  color: #444;
}
.breadcrumb {
  padding: 8px 15px;
  margin-bottom: 18px;
  list-style: none;
  background-color: #f5f5f5;
  border-radius: 2px;
}
.breadcrumb > li {
  display: inline-block;
}
.breadcrumb > li + li:before {
  content: "/\00a0";
  padding: 0 5px;
  color: #5e5e5e;
}
.breadcrumb > .active {
  color: #777777;
}
.pagination {
  display: inline-block;
  padding-left: 0;
  margin: 18px 0;
  border-radius: 2px;
}
.pagination > li {
  display: inline;
}
.pagination > li > a,
.pagination > li > span {
  position: relative;
  float: left;
  padding: 6px 12px;
  line-height: 1.42857143;
  text-decoration: none;
  color: #337ab7;
  background-color: #fff;
  border: 1px solid #ddd;
  margin-left: -1px;
}
.pagination > li:first-child > a,
.pagination > li:first-child > span {
  margin-left: 0;
  border-bottom-left-radius: 2px;
  border-top-left-radius: 2px;
}
.pagination > li:last-child > a,
.pagination > li:last-child > span {
  border-bottom-right-radius: 2px;
  border-top-right-radius: 2px;
}
.pagination > li > a:hover,
.pagination > li > span:hover,
.pagination > li > a:focus,
.pagination > li > span:focus {
  z-index: 2;
  color: #23527c;
  background-color: #eeeeee;
  border-color: #ddd;
}
.pagination > .active > a,
.pagination > .active > span,
.pagination > .active > a:hover,
.pagination > .active > span:hover,
.pagination > .active > a:focus,
.pagination > .active > span:focus {
  z-index: 3;
  color: #fff;
  background-color: #337ab7;
  border-color: #337ab7;
  cursor: default;
}
.pagination > .disabled > span,
.pagination > .disabled > span:hover,
.pagination > .disabled > span:focus,
.pagination > .disabled > a,
.pagination > .disabled > a:hover,
.pagination > .disabled > a:focus {
  color: #777777;
  background-color: #fff;
  border-color: #ddd;
  cursor: not-allowed;
}
.pagination-lg > li > a,
.pagination-lg > li > span {
  padding: 10px 16px;
  font-size: 17px;
  line-height: 1.3333333;
}
.pagination-lg > li:first-child > a,
.pagination-lg > li:first-child > span {
  border-bottom-left-radius: 3px;
  border-top-left-radius: 3px;
}
.pagination-lg > li:last-child > a,
.pagination-lg > li:last-child > span {
  border-bottom-right-radius: 3px;
  border-top-right-radius: 3px;
}
.pagination-sm > li > a,
.pagination-sm > li > span {
  padding: 5px 10px;
  font-size: 12px;
  line-height: 1.5;
}
.pagination-sm > li:first-child > a,
.pagination-sm > li:first-child > span {
  border-bottom-left-radius: 1px;
  border-top-left-radius: 1px;
}
.pagination-sm > li:last-child > a,
.pagination-sm > li:last-child > span {
  border-bottom-right-radius: 1px;
  border-top-right-radius: 1px;
}
.pager {
  padding-left: 0;
  margin: 18px 0;
  list-style: none;
  text-align: center;
}
.pager li {
  display: inline;
}
.pager li > a,
.pager li > span {
  display: inline-block;
  padding: 5px 14px;
  background-color: #fff;
  border: 1px solid #ddd;
  border-radius: 15px;
}
.pager li > a:hover,
.pager li > a:focus {
  text-decoration: none;
  background-color: #eeeeee;
}
.pager .next > a,
.pager .next > span {
  float: right;
}
.pager .previous > a,
.pager .previous > span {
  float: left;
}
.pager .disabled > a,
.pager .disabled > a:hover,
.pager .disabled > a:focus,
.pager .disabled > span {
  color: #777777;
  background-color: #fff;
  cursor: not-allowed;
}
.label {
  display: inline;
  padding: .2em .6em .3em;
  font-size: 75%;
  font-weight: bold;
  line-height: 1;
  color: #fff;
  text-align: center;
  white-space: nowrap;
  vertical-align: baseline;
  border-radius: .25em;
}
a.label:hover,
a.label:focus {
  color: #fff;
  text-decoration: none;
  cursor: pointer;
}
.label:empty {
  display: none;
}
.btn .label {
  position: relative;
  top: -1px;
}
.label-default {
  background-color: #777777;
}
.label-default[href]:hover,
.label-default[href]:focus {
  background-color: #5e5e5e;
}
.label-primary {
  background-color: #337ab7;
}
.label-primary[href]:hover,
.label-primary[href]:focus {
  background-color: #286090;
}
.label-success {
  background-color: #5cb85c;
}
.label-success[href]:hover,
.label-success[href]:focus {
  background-color: #449d44;
}
.label-info {
  background-color: #5bc0de;
}
.label-info[href]:hover,
.label-info[href]:focus {
  background-color: #31b0d5;
}
.label-warning {
  background-color: #f0ad4e;
}
.label-warning[href]:hover,
.label-warning[href]:focus {
  background-color: #ec971f;
}
.label-danger {
  background-color: #d9534f;
}
.label-danger[href]:hover,
.label-danger[href]:focus {
  background-color: #c9302c;
}
.badge {
  display: inline-block;
  min-width: 10px;
  padding: 3px 7px;
  font-size: 12px;
  font-weight: bold;
  color: #fff;
  line-height: 1;
  vertical-align: middle;
  white-space: nowrap;
  text-align: center;
  background-color: #777777;
  border-radius: 10px;
}
.badge:empty {
  display: none;
}
.btn .badge {
  position: relative;
  top: -1px;
}
.btn-xs .badge,
.btn-group-xs > .btn .badge {
  top: 0;
  padding: 1px 5px;
}
a.badge:hover,
a.badge:focus {
  color: #fff;
  text-decoration: none;
  cursor: pointer;
}
.list-group-item.active > .badge,
.nav-pills > .active > a > .badge {
  color: #337ab7;
  background-color: #fff;
}
.list-group-item > .badge {
  float: right;
}
.list-group-item > .badge + .badge {
  margin-right: 5px;
}
.nav-pills > li > a > .badge {
  margin-left: 3px;
}
.jumbotron {
  padding-top: 30px;
  padding-bottom: 30px;
  margin-bottom: 30px;
  color: inherit;
  background-color: #eeeeee;
}
.jumbotron h1,
.jumbotron .h1 {
  color: inherit;
}
.jumbotron p {
  margin-bottom: 15px;
  font-size: 20px;
  font-weight: 200;
}
.jumbotron > hr {
  border-top-color: #d5d5d5;
}
.container .jumbotron,
.container-fluid .jumbotron {
  border-radius: 3px;
  padding-left: 0px;
  padding-right: 0px;
}
.jumbotron .container {
  max-width: 100%;
}
@media screen and (min-width: 768px) {
  .jumbotron {
    padding-top: 48px;
    padding-bottom: 48px;
  }
  .container .jumbotron,
  .container-fluid .jumbotron {
    padding-left: 60px;
    padding-right: 60px;
  }
  .jumbotron h1,
  .jumbotron .h1 {
    font-size: 59px;
  }
}
.thumbnail {
  display: block;
  padding: 4px;
  margin-bottom: 18px;
  line-height: 1.42857143;
  background-color: #fff;
  border: 1px solid #ddd;
  border-radius: 2px;
  -webkit-transition: border 0.2s ease-in-out;
  -o-transition: border 0.2s ease-in-out;
  transition: border 0.2s ease-in-out;
}
.thumbnail > img,
.thumbnail a > img {
  margin-left: auto;
  margin-right: auto;
}
a.thumbnail:hover,
a.thumbnail:focus,
a.thumbnail.active {
  border-color: #337ab7;
}
.thumbnail .caption {
  padding: 9px;
  color: #000;
}
.alert {
  padding: 15px;
  margin-bottom: 18px;
  border: 1px solid transparent;
  border-radius: 2px;
}
.alert h4 {
  margin-top: 0;
  color: inherit;
}
.alert .alert-link {
  font-weight: bold;
}
.alert > p,
.alert > ul {
  margin-bottom: 0;
}
.alert > p + p {
  margin-top: 5px;
}
.alert-dismissable,
.alert-dismissible {
  padding-right: 35px;
}
.alert-dismissable .close,
.alert-dismissible .close {
  position: relative;
  top: -2px;
  right: -21px;
  color: inherit;
}
.alert-success {
  background-color: #dff0d8;
  border-color: #d6e9c6;
  color: #3c763d;
}
.alert-success hr {
  border-top-color: #c9e2b3;
}
.alert-success .alert-link {
  color: #2b542c;
}
.alert-info {
  background-color: #d9edf7;
  border-color: #bce8f1;
  color: #31708f;
}
.alert-info hr {
  border-top-color: #a6e1ec;
}
.alert-info .alert-link {
  color: #245269;
}
.alert-warning {
  background-color: #fcf8e3;
  border-color: #faebcc;
  color: #8a6d3b;
}
.alert-warning hr {
  border-top-color: #f7e1b5;
}
.alert-warning .alert-link {
  color: #66512c;
}
.alert-danger {
  background-color: #f2dede;
  border-color: #ebccd1;
  color: #a94442;
}
.alert-danger hr {
  border-top-color: #e4b9c0;
}
.alert-danger .alert-link {
  color: #843534;
}
@-webkit-keyframes progress-bar-stripes {
  from {
    background-position: 40px 0;
  }
  to {
    background-position: 0 0;
  }
}
@keyframes progress-bar-stripes {
  from {
    background-position: 40px 0;
  }
  to {
    background-position: 0 0;
  }
}
.progress {
  overflow: hidden;
  height: 18px;
  margin-bottom: 18px;
  background-color: #f5f5f5;
  border-radius: 2px;
  -webkit-box-shadow: inset 0 1px 2px rgba(0, 0, 0, 0.1);
  box-shadow: inset 0 1px 2px rgba(0, 0, 0, 0.1);
}
.progress-bar {
  float: left;
  width: 0%;
  height: 100%;
  font-size: 12px;
  line-height: 18px;
  color: #fff;
  text-align: center;
  background-color: #337ab7;
  -webkit-box-shadow: inset 0 -1px 0 rgba(0, 0, 0, 0.15);
  box-shadow: inset 0 -1px 0 rgba(0, 0, 0, 0.15);
  -webkit-transition: width 0.6s ease;
  -o-transition: width 0.6s ease;
  transition: width 0.6s ease;
}
.progress-striped .progress-bar,
.progress-bar-striped {
  background-image: -webkit-linear-gradient(45deg, rgba(255, 255, 255, 0.15) 25%, transparent 25%, transparent 50%, rgba(255, 255, 255, 0.15) 50%, rgba(255, 255, 255, 0.15) 75%, transparent 75%, transparent);
  background-image: -o-linear-gradient(45deg, rgba(255, 255, 255, 0.15) 25%, transparent 25%, transparent 50%, rgba(255, 255, 255, 0.15) 50%, rgba(255, 255, 255, 0.15) 75%, transparent 75%, transparent);
  background-image: linear-gradient(45deg, rgba(255, 255, 255, 0.15) 25%, transparent 25%, transparent 50%, rgba(255, 255, 255, 0.15) 50%, rgba(255, 255, 255, 0.15) 75%, transparent 75%, transparent);
  background-size: 40px 40px;
}
.progress.active .progress-bar,
.progress-bar.active {
  -webkit-animation: progress-bar-stripes 2s linear infinite;
  -o-animation: progress-bar-stripes 2s linear infinite;
  animation: progress-bar-stripes 2s linear infinite;
}
.progress-bar-success {
  background-color: #5cb85c;
}
.progress-striped .progress-bar-success {
  background-image: -webkit-linear-gradient(45deg, rgba(255, 255, 255, 0.15) 25%, transparent 25%, transparent 50%, rgba(255, 255, 255, 0.15) 50%, rgba(255, 255, 255, 0.15) 75%, transparent 75%, transparent);
  background-image: -o-linear-gradient(45deg, rgba(255, 255, 255, 0.15) 25%, transparent 25%, transparent 50%, rgba(255, 255, 255, 0.15) 50%, rgba(255, 255, 255, 0.15) 75%, transparent 75%, transparent);
  background-image: linear-gradient(45deg, rgba(255, 255, 255, 0.15) 25%, transparent 25%, transparent 50%, rgba(255, 255, 255, 0.15) 50%, rgba(255, 255, 255, 0.15) 75%, transparent 75%, transparent);
}
.progress-bar-info {
  background-color: #5bc0de;
}
.progress-striped .progress-bar-info {
  background-image: -webkit-linear-gradient(45deg, rgba(255, 255, 255, 0.15) 25%, transparent 25%, transparent 50%, rgba(255, 255, 255, 0.15) 50%, rgba(255, 255, 255, 0.15) 75%, transparent 75%, transparent);
  background-image: -o-linear-gradient(45deg, rgba(255, 255, 255, 0.15) 25%, transparent 25%, transparent 50%, rgba(255, 255, 255, 0.15) 50%, rgba(255, 255, 255, 0.15) 75%, transparent 75%, transparent);
  background-image: linear-gradient(45deg, rgba(255, 255, 255, 0.15) 25%, transparent 25%, transparent 50%, rgba(255, 255, 255, 0.15) 50%, rgba(255, 255, 255, 0.15) 75%, transparent 75%, transparent);
}
.progress-bar-warning {
  background-color: #f0ad4e;
}
.progress-striped .progress-bar-warning {
  background-image: -webkit-linear-gradient(45deg, rgba(255, 255, 255, 0.15) 25%, transparent 25%, transparent 50%, rgba(255, 255, 255, 0.15) 50%, rgba(255, 255, 255, 0.15) 75%, transparent 75%, transparent);
  background-image: -o-linear-gradient(45deg, rgba(255, 255, 255, 0.15) 25%, transparent 25%, transparent 50%, rgba(255, 255, 255, 0.15) 50%, rgba(255, 255, 255, 0.15) 75%, transparent 75%, transparent);
  background-image: linear-gradient(45deg, rgba(255, 255, 255, 0.15) 25%, transparent 25%, transparent 50%, rgba(255, 255, 255, 0.15) 50%, rgba(255, 255, 255, 0.15) 75%, transparent 75%, transparent);
}
.progress-bar-danger {
  background-color: #d9534f;
}
.progress-striped .progress-bar-danger {
  background-image: -webkit-linear-gradient(45deg, rgba(255, 255, 255, 0.15) 25%, transparent 25%, transparent 50%, rgba(255, 255, 255, 0.15) 50%, rgba(255, 255, 255, 0.15) 75%, transparent 75%, transparent);
  background-image: -o-linear-gradient(45deg, rgba(255, 255, 255, 0.15) 25%, transparent 25%, transparent 50%, rgba(255, 255, 255, 0.15) 50%, rgba(255, 255, 255, 0.15) 75%, transparent 75%, transparent);
  background-image: linear-gradient(45deg, rgba(255, 255, 255, 0.15) 25%, transparent 25%, transparent 50%, rgba(255, 255, 255, 0.15) 50%, rgba(255, 255, 255, 0.15) 75%, transparent 75%, transparent);
}
.media {
  margin-top: 15px;
}
.media:first-child {
  margin-top: 0;
}
.media,
.media-body {
  zoom: 1;
  overflow: hidden;
}
.media-body {
  width: 10000px;
}
.media-object {
  display: block;
}
.media-object.img-thumbnail {
  max-width: none;
}
.media-right,
.media > .pull-right {
  padding-left: 10px;
}
.media-left,
.media > .pull-left {
  padding-right: 10px;
}
.media-left,
.media-right,
.media-body {
  display: table-cell;
  vertical-align: top;
}
.media-middle {
  vertical-align: middle;
}
.media-bottom {
  vertical-align: bottom;
}
.media-heading {
  margin-top: 0;
  margin-bottom: 5px;
}
.media-list {
  padding-left: 0;
  list-style: none;
}
.list-group {
  margin-bottom: 20px;
  padding-left: 0;
}
.list-group-item {
  position: relative;
  display: block;
  padding: 10px 15px;
  margin-bottom: -1px;
  background-color: #fff;
  border: 1px solid #ddd;
}
.list-group-item:first-child {
  border-top-right-radius: 2px;
  border-top-left-radius: 2px;
}
.list-group-item:last-child {
  margin-bottom: 0;
  border-bottom-right-radius: 2px;
  border-bottom-left-radius: 2px;
}
a.list-group-item,
button.list-group-item {
  color: #555;
}
a.list-group-item .list-group-item-heading,
button.list-group-item .list-group-item-heading {
  color: #333;
}
a.list-group-item:hover,
button.list-group-item:hover,
a.list-group-item:focus,
button.list-group-item:focus {
  text-decoration: none;
  color: #555;
  background-color: #f5f5f5;
}
button.list-group-item {
  width: 100%;
  text-align: left;
}
.list-group-item.disabled,
.list-group-item.disabled:hover,
.list-group-item.disabled:focus {
  background-color: #eeeeee;
  color: #777777;
  cursor: not-allowed;
}
.list-group-item.disabled .list-group-item-heading,
.list-group-item.disabled:hover .list-group-item-heading,
.list-group-item.disabled:focus .list-group-item-heading {
  color: inherit;
}
.list-group-item.disabled .list-group-item-text,
.list-group-item.disabled:hover .list-group-item-text,
.list-group-item.disabled:focus .list-group-item-text {
  color: #777777;
}
.list-group-item.active,
.list-group-item.active:hover,
.list-group-item.active:focus {
  z-index: 2;
  color: #fff;
  background-color: #337ab7;
  border-color: #337ab7;
}
.list-group-item.active .list-group-item-heading,
.list-group-item.active:hover .list-group-item-heading,
.list-group-item.active:focus .list-group-item-heading,
.list-group-item.active .list-group-item-heading > small,
.list-group-item.active:hover .list-group-item-heading > small,
.list-group-item.active:focus .list-group-item-heading > small,
.list-group-item.active .list-group-item-heading > .small,
.list-group-item.active:hover .list-group-item-heading > .small,
.list-group-item.active:focus .list-group-item-heading > .small {
  color: inherit;
}
.list-group-item.active .list-group-item-text,
.list-group-item.active:hover .list-group-item-text,
.list-group-item.active:focus .list-group-item-text {
  color: #c7ddef;
}
.list-group-item-success {
  color: #3c763d;
  background-color: #dff0d8;
}
a.list-group-item-success,
button.list-group-item-success {
  color: #3c763d;
}
a.list-group-item-success .list-group-item-heading,
button.list-group-item-success .list-group-item-heading {
  color: inherit;
}
a.list-group-item-success:hover,
button.list-group-item-success:hover,
a.list-group-item-success:focus,
button.list-group-item-success:focus {
  color: #3c763d;
  background-color: #d0e9c6;
}
a.list-group-item-success.active,
button.list-group-item-success.active,
a.list-group-item-success.active:hover,
button.list-group-item-success.active:hover,
a.list-group-item-success.active:focus,
button.list-group-item-success.active:focus {
  color: #fff;
  background-color: #3c763d;
  border-color: #3c763d;
}
.list-group-item-info {
  color: #31708f;
  background-color: #d9edf7;
}
a.list-group-item-info,
button.list-group-item-info {
  color: #31708f;
}
a.list-group-item-info .list-group-item-heading,
button.list-group-item-info .list-group-item-heading {
  color: inherit;
}
a.list-group-item-info:hover,
button.list-group-item-info:hover,
a.list-group-item-info:focus,
button.list-group-item-info:focus {
  color: #31708f;
  background-color: #c4e3f3;
}
a.list-group-item-info.active,
button.list-group-item-info.active,
a.list-group-item-info.active:hover,
button.list-group-item-info.active:hover,
a.list-group-item-info.active:focus,
button.list-group-item-info.active:focus {
  color: #fff;
  background-color: #31708f;
  border-color: #31708f;
}
.list-group-item-warning {
  color: #8a6d3b;
  background-color: #fcf8e3;
}
a.list-group-item-warning,
button.list-group-item-warning {
  color: #8a6d3b;
}
a.list-group-item-warning .list-group-item-heading,
button.list-group-item-warning .list-group-item-heading {
  color: inherit;
}
a.list-group-item-warning:hover,
button.list-group-item-warning:hover,
a.list-group-item-warning:focus,
button.list-group-item-warning:focus {
  color: #8a6d3b;
  background-color: #faf2cc;
}
a.list-group-item-warning.active,
button.list-group-item-warning.active,
a.list-group-item-warning.active:hover,
button.list-group-item-warning.active:hover,
a.list-group-item-warning.active:focus,
button.list-group-item-warning.active:focus {
  color: #fff;
  background-color: #8a6d3b;
  border-color: #8a6d3b;
}
.list-group-item-danger {
  color: #a94442;
  background-color: #f2dede;
}
a.list-group-item-danger,
button.list-group-item-danger {
  color: #a94442;
}
a.list-group-item-danger .list-group-item-heading,
button.list-group-item-danger .list-group-item-heading {
  color: inherit;
}
a.list-group-item-danger:hover,
button.list-group-item-danger:hover,
a.list-group-item-danger:focus,
button.list-group-item-danger:focus {
  color: #a94442;
  background-color: #ebcccc;
}
a.list-group-item-danger.active,
button.list-group-item-danger.active,
a.list-group-item-danger.active:hover,
button.list-group-item-danger.active:hover,
a.list-group-item-danger.active:focus,
button.list-group-item-danger.active:focus {
  color: #fff;
  background-color: #a94442;
  border-color: #a94442;
}
.list-group-item-heading {
  margin-top: 0;
  margin-bottom: 5px;
}
.list-group-item-text {
  margin-bottom: 0;
  line-height: 1.3;
}
.panel {
  margin-bottom: 18px;
  background-color: #fff;
  border: 1px solid transparent;
  border-radius: 2px;
  -webkit-box-shadow: 0 1px 1px rgba(0, 0, 0, 0.05);
  box-shadow: 0 1px 1px rgba(0, 0, 0, 0.05);
}
.panel-body {
  padding: 15px;
}
.panel-heading {
  padding: 10px 15px;
  border-bottom: 1px solid transparent;
  border-top-right-radius: 1px;
  border-top-left-radius: 1px;
}
.panel-heading > .dropdown .dropdown-toggle {
  color: inherit;
}
.panel-title {
  margin-top: 0;
  margin-bottom: 0;
  font-size: 15px;
  color: inherit;
}
.panel-title > a,
.panel-title > small,
.panel-title > .small,
.panel-title > small > a,
.panel-title > .small > a {
  color: inherit;
}
.panel-footer {
  padding: 10px 15px;
  background-color: #f5f5f5;
  border-top: 1px solid #ddd;
  border-bottom-right-radius: 1px;
  border-bottom-left-radius: 1px;
}
.panel > .list-group,
.panel > .panel-collapse > .list-group {
  margin-bottom: 0;
}
.panel > .list-group .list-group-item,
.panel > .panel-collapse > .list-group .list-group-item {
  border-width: 1px 0;
  border-radius: 0;
}
.panel > .list-group:first-child .list-group-item:first-child,
.panel > .panel-collapse > .list-group:first-child .list-group-item:first-child {
  border-top: 0;
  border-top-right-radius: 1px;
  border-top-left-radius: 1px;
}
.panel > .list-group:last-child .list-group-item:last-child,
.panel > .panel-collapse > .list-group:last-child .list-group-item:last-child {
  border-bottom: 0;
  border-bottom-right-radius: 1px;
  border-bottom-left-radius: 1px;
}
.panel > .panel-heading + .panel-collapse > .list-group .list-group-item:first-child {
  border-top-right-radius: 0;
  border-top-left-radius: 0;
}
.panel-heading + .list-group .list-group-item:first-child {
  border-top-width: 0;
}
.list-group + .panel-footer {
  border-top-width: 0;
}
.panel > .table,
.panel > .table-responsive > .table,
.panel > .panel-collapse > .table {
  margin-bottom: 0;
}
.panel > .table caption,
.panel > .table-responsive > .table caption,
.panel > .panel-collapse > .table caption {
  padding-left: 15px;
  padding-right: 15px;
}
.panel > .table:first-child,
.panel > .table-responsive:first-child > .table:first-child {
  border-top-right-radius: 1px;
  border-top-left-radius: 1px;
}
.panel > .table:first-child > thead:first-child > tr:first-child,
.panel > .table-responsive:first-child > .table:first-child > thead:first-child > tr:first-child,
.panel > .table:first-child > tbody:first-child > tr:first-child,
.panel > .table-responsive:first-child > .table:first-child > tbody:first-child > tr:first-child {
  border-top-left-radius: 1px;
  border-top-right-radius: 1px;
}
.panel > .table:first-child > thead:first-child > tr:first-child td:first-child,
.panel > .table-responsive:first-child > .table:first-child > thead:first-child > tr:first-child td:first-child,
.panel > .table:first-child > tbody:first-child > tr:first-child td:first-child,
.panel > .table-responsive:first-child > .table:first-child > tbody:first-child > tr:first-child td:first-child,
.panel > .table:first-child > thead:first-child > tr:first-child th:first-child,
.panel > .table-responsive:first-child > .table:first-child > thead:first-child > tr:first-child th:first-child,
.panel > .table:first-child > tbody:first-child > tr:first-child th:first-child,
.panel > .table-responsive:first-child > .table:first-child > tbody:first-child > tr:first-child th:first-child {
  border-top-left-radius: 1px;
}
.panel > .table:first-child > thead:first-child > tr:first-child td:last-child,
.panel > .table-responsive:first-child > .table:first-child > thead:first-child > tr:first-child td:last-child,
.panel > .table:first-child > tbody:first-child > tr:first-child td:last-child,
.panel > .table-responsive:first-child > .table:first-child > tbody:first-child > tr:first-child td:last-child,
.panel > .table:first-child > thead:first-child > tr:first-child th:last-child,
.panel > .table-responsive:first-child > .table:first-child > thead:first-child > tr:first-child th:last-child,
.panel > .table:first-child > tbody:first-child > tr:first-child th:last-child,
.panel > .table-responsive:first-child > .table:first-child > tbody:first-child > tr:first-child th:last-child {
  border-top-right-radius: 1px;
}
.panel > .table:last-child,
.panel > .table-responsive:last-child > .table:last-child {
  border-bottom-right-radius: 1px;
  border-bottom-left-radius: 1px;
}
.panel > .table:last-child > tbody:last-child > tr:last-child,
.panel > .table-responsive:last-child > .table:last-child > tbody:last-child > tr:last-child,
.panel > .table:last-child > tfoot:last-child > tr:last-child,
.panel > .table-responsive:last-child > .table:last-child > tfoot:last-child > tr:last-child {
  border-bottom-left-radius: 1px;
  border-bottom-right-radius: 1px;
}
.panel > .table:last-child > tbody:last-child > tr:last-child td:first-child,
.panel > .table-responsive:last-child > .table:last-child > tbody:last-child > tr:last-child td:first-child,
.panel > .table:last-child > tfoot:last-child > tr:last-child td:first-child,
.panel > .table-responsive:last-child > .table:last-child > tfoot:last-child > tr:last-child td:first-child,
.panel > .table:last-child > tbody:last-child > tr:last-child th:first-child,
.panel > .table-responsive:last-child > .table:last-child > tbody:last-child > tr:last-child th:first-child,
.panel > .table:last-child > tfoot:last-child > tr:last-child th:first-child,
.panel > .table-responsive:last-child > .table:last-child > tfoot:last-child > tr:last-child th:first-child {
  border-bottom-left-radius: 1px;
}
.panel > .table:last-child > tbody:last-child > tr:last-child td:last-child,
.panel > .table-responsive:last-child > .table:last-child > tbody:last-child > tr:last-child td:last-child,
.panel > .table:last-child > tfoot:last-child > tr:last-child td:last-child,
.panel > .table-responsive:last-child > .table:last-child > tfoot:last-child > tr:last-child td:last-child,
.panel > .table:last-child > tbody:last-child > tr:last-child th:last-child,
.panel > .table-responsive:last-child > .table:last-child > tbody:last-child > tr:last-child th:last-child,
.panel > .table:last-child > tfoot:last-child > tr:last-child th:last-child,
.panel > .table-responsive:last-child > .table:last-child > tfoot:last-child > tr:last-child th:last-child {
  border-bottom-right-radius: 1px;
}
.panel > .panel-body + .table,
.panel > .panel-body + .table-responsive,
.panel > .table + .panel-body,
.panel > .table-responsive + .panel-body {
  border-top: 1px solid #ddd;
}
.panel > .table > tbody:first-child > tr:first-child th,
.panel > .table > tbody:first-child > tr:first-child td {
  border-top: 0;
}
.panel > .table-bordered,
.panel > .table-responsive > .table-bordered {
  border: 0;
}
.panel > .table-bordered > thead > tr > th:first-child,
.panel > .table-responsive > .table-bordered > thead > tr > th:first-child,
.panel > .table-bordered > tbody > tr > th:first-child,
.panel > .table-responsive > .table-bordered > tbody > tr > th:first-child,
.panel > .table-bordered > tfoot > tr > th:first-child,
.panel > .table-responsive > .table-bordered > tfoot > tr > th:first-child,
.panel > .table-bordered > thead > tr > td:first-child,
.panel > .table-responsive > .table-bordered > thead > tr > td:first-child,
.panel > .table-bordered > tbody > tr > td:first-child,
.panel > .table-responsive > .table-bordered > tbody > tr > td:first-child,
.panel > .table-bordered > tfoot > tr > td:first-child,
.panel > .table-responsive > .table-bordered > tfoot > tr > td:first-child {
  border-left: 0;
}
.panel > .table-bordered > thead > tr > th:last-child,
.panel > .table-responsive > .table-bordered > thead > tr > th:last-child,
.panel > .table-bordered > tbody > tr > th:last-child,
.panel > .table-responsive > .table-bordered > tbody > tr > th:last-child,
.panel > .table-bordered > tfoot > tr > th:last-child,
.panel > .table-responsive > .table-bordered > tfoot > tr > th:last-child,
.panel > .table-bordered > thead > tr > td:last-child,
.panel > .table-responsive > .table-bordered > thead > tr > td:last-child,
.panel > .table-bordered > tbody > tr > td:last-child,
.panel > .table-responsive > .table-bordered > tbody > tr > td:last-child,
.panel > .table-bordered > tfoot > tr > td:last-child,
.panel > .table-responsive > .table-bordered > tfoot > tr > td:last-child {
  border-right: 0;
}
.panel > .table-bordered > thead > tr:first-child > td,
.panel > .table-responsive > .table-bordered > thead > tr:first-child > td,
.panel > .table-bordered > tbody > tr:first-child > td,
.panel > .table-responsive > .table-bordered > tbody > tr:first-child > td,
.panel > .table-bordered > thead > tr:first-child > th,
.panel > .table-responsive > .table-bordered > thead > tr:first-child > th,
.panel > .table-bordered > tbody > tr:first-child > th,
.panel > .table-responsive > .table-bordered > tbody > tr:first-child > th {
  border-bottom: 0;
}
.panel > .table-bordered > tbody > tr:last-child > td,
.panel > .table-responsive > .table-bordered > tbody > tr:last-child > td,
.panel > .table-bordered > tfoot > tr:last-child > td,
.panel > .table-responsive > .table-bordered > tfoot > tr:last-child > td,
.panel > .table-bordered > tbody > tr:last-child > th,
.panel > .table-responsive > .table-bordered > tbody > tr:last-child > th,
.panel > .table-bordered > tfoot > tr:last-child > th,
.panel > .table-responsive > .table-bordered > tfoot > tr:last-child > th {
  border-bottom: 0;
}
.panel > .table-responsive {
  border: 0;
  margin-bottom: 0;
}
.panel-group {
  margin-bottom: 18px;
}
.panel-group .panel {
  margin-bottom: 0;
  border-radius: 2px;
}
.panel-group .panel + .panel {
  margin-top: 5px;
}
.panel-group .panel-heading {
  border-bottom: 0;
}
.panel-group .panel-heading + .panel-collapse > .panel-body,
.panel-group .panel-heading + .panel-collapse > .list-group {
  border-top: 1px solid #ddd;
}
.panel-group .panel-footer {
  border-top: 0;
}
.panel-group .panel-footer + .panel-collapse .panel-body {
  border-bottom: 1px solid #ddd;
}
.panel-default {
  border-color: #ddd;
}
.panel-default > .panel-heading {
  color: #333333;
  background-color: #f5f5f5;
  border-color: #ddd;
}
.panel-default > .panel-heading + .panel-collapse > .panel-body {
  border-top-color: #ddd;
}
.panel-default > .panel-heading .badge {
  color: #f5f5f5;
  background-color: #333333;
}
.panel-default > .panel-footer + .panel-collapse > .panel-body {
  border-bottom-color: #ddd;
}
.panel-primary {
  border-color: #337ab7;
}
.panel-primary > .panel-heading {
  color: #fff;
  background-color: #337ab7;
  border-color: #337ab7;
}
.panel-primary > .panel-heading + .panel-collapse > .panel-body {
  border-top-color: #337ab7;
}
.panel-primary > .panel-heading .badge {
  color: #337ab7;
  background-color: #fff;
}
.panel-primary > .panel-footer + .panel-collapse > .panel-body {
  border-bottom-color: #337ab7;
}
.panel-success {
  border-color: #d6e9c6;
}
.panel-success > .panel-heading {
  color: #3c763d;
  background-color: #dff0d8;
  border-color: #d6e9c6;
}
.panel-success > .panel-heading + .panel-collapse > .panel-body {
  border-top-color: #d6e9c6;
}
.panel-success > .panel-heading .badge {
  color: #dff0d8;
  background-color: #3c763d;
}
.panel-success > .panel-footer + .panel-collapse > .panel-body {
  border-bottom-color: #d6e9c6;
}
.panel-info {
  border-color: #bce8f1;
}
.panel-info > .panel-heading {
  color: #31708f;
  background-color: #d9edf7;
  border-color: #bce8f1;
}
.panel-info > .panel-heading + .panel-collapse > .panel-body {
  border-top-color: #bce8f1;
}
.panel-info > .panel-heading .badge {
  color: #d9edf7;
  background-color: #31708f;
}
.panel-info > .panel-footer + .panel-collapse > .panel-body {
  border-bottom-color: #bce8f1;
}
.panel-warning {
  border-color: #faebcc;
}
.panel-warning > .panel-heading {
  color: #8a6d3b;
  background-color: #fcf8e3;
  border-color: #faebcc;
}
.panel-warning > .panel-heading + .panel-collapse > .panel-body {
  border-top-color: #faebcc;
}
.panel-warning > .panel-heading .badge {
  color: #fcf8e3;
  background-color: #8a6d3b;
}
.panel-warning > .panel-footer + .panel-collapse > .panel-body {
  border-bottom-color: #faebcc;
}
.panel-danger {
  border-color: #ebccd1;
}
.panel-danger > .panel-heading {
  color: #a94442;
  background-color: #f2dede;
  border-color: #ebccd1;
}
.panel-danger > .panel-heading + .panel-collapse > .panel-body {
  border-top-color: #ebccd1;
}
.panel-danger > .panel-heading .badge {
  color: #f2dede;
  background-color: #a94442;
}
.panel-danger > .panel-footer + .panel-collapse > .panel-body {
  border-bottom-color: #ebccd1;
}
.embed-responsive {
  position: relative;
  display: block;
  height: 0;
  padding: 0;
  overflow: hidden;
}
.embed-responsive .embed-responsive-item,
.embed-responsive iframe,
.embed-responsive embed,
.embed-responsive object,
.embed-responsive video {
  position: absolute;
  top: 0;
  left: 0;
  bottom: 0;
  height: 100%;
  width: 100%;
  border: 0;
}
.embed-responsive-16by9 {
  padding-bottom: 56.25%;
}
.embed-responsive-4by3 {
  padding-bottom: 75%;
}
.well {
  min-height: 20px;
  padding: 19px;
  margin-bottom: 20px;
  background-color: #f5f5f5;
  border: 1px solid #e3e3e3;
  border-radius: 2px;
  -webkit-box-shadow: inset 0 1px 1px rgba(0, 0, 0, 0.05);
  box-shadow: inset 0 1px 1px rgba(0, 0, 0, 0.05);
}
.well blockquote {
  border-color: #ddd;
  border-color: rgba(0, 0, 0, 0.15);
}
.well-lg {
  padding: 24px;
  border-radius: 3px;
}
.well-sm {
  padding: 9px;
  border-radius: 1px;
}
.close {
  float: right;
  font-size: 19.5px;
  font-weight: bold;
  line-height: 1;
  color: #000;
  text-shadow: 0 1px 0 #fff;
  opacity: 0.2;
  filter: alpha(opacity=20);
}
.close:hover,
.close:focus {
  color: #000;
  text-decoration: none;
  cursor: pointer;
  opacity: 0.5;
  filter: alpha(opacity=50);
}
button.close {
  padding: 0;
  cursor: pointer;
  background: transparent;
  border: 0;
  -webkit-appearance: none;
}
.modal-open {
  overflow: hidden;
}
.modal {
  display: none;
  overflow: hidden;
  position: fixed;
  top: 0;
  right: 0;
  bottom: 0;
  left: 0;
  z-index: 1050;
  -webkit-overflow-scrolling: touch;
  outline: 0;
}
.modal.fade .modal-dialog {
  -webkit-transform: translate(0, -25%);
  -ms-transform: translate(0, -25%);
  -o-transform: translate(0, -25%);
  transform: translate(0, -25%);
  -webkit-transition: -webkit-transform 0.3s ease-out;
  -moz-transition: -moz-transform 0.3s ease-out;
  -o-transition: -o-transform 0.3s ease-out;
  transition: transform 0.3s ease-out;
}
.modal.in .modal-dialog {
  -webkit-transform: translate(0, 0);
  -ms-transform: translate(0, 0);
  -o-transform: translate(0, 0);
  transform: translate(0, 0);
}
.modal-open .modal {
  overflow-x: hidden;
  overflow-y: auto;
}
.modal-dialog {
  position: relative;
  width: auto;
  margin: 10px;
}
.modal-content {
  position: relative;
  background-color: #fff;
  border: 1px solid #999;
  border: 1px solid rgba(0, 0, 0, 0.2);
  border-radius: 3px;
  -webkit-box-shadow: 0 3px 9px rgba(0, 0, 0, 0.5);
  box-shadow: 0 3px 9px rgba(0, 0, 0, 0.5);
  background-clip: padding-box;
  outline: 0;
}
.modal-backdrop {
  position: fixed;
  top: 0;
  right: 0;
  bottom: 0;
  left: 0;
  z-index: 1040;
  background-color: #000;
}
.modal-backdrop.fade {
  opacity: 0;
  filter: alpha(opacity=0);
}
.modal-backdrop.in {
  opacity: 0.5;
  filter: alpha(opacity=50);
}
.modal-header {
  padding: 15px;
  border-bottom: 1px solid #e5e5e5;
}
.modal-header .close {
  margin-top: -2px;
}
.modal-title {
  margin: 0;
  line-height: 1.42857143;
}
.modal-body {
  position: relative;
  padding: 15px;
}
.modal-footer {
  padding: 15px;
  text-align: right;
  border-top: 1px solid #e5e5e5;
}
.modal-footer .btn + .btn {
  margin-left: 5px;
  margin-bottom: 0;
}
.modal-footer .btn-group .btn + .btn {
  margin-left: -1px;
}
.modal-footer .btn-block + .btn-block {
  margin-left: 0;
}
.modal-scrollbar-measure {
  position: absolute;
  top: -9999px;
  width: 50px;
  height: 50px;
  overflow: scroll;
}
@media (min-width: 768px) {
  .modal-dialog {
    width: 600px;
    margin: 30px auto;
  }
  .modal-content {
    -webkit-box-shadow: 0 5px 15px rgba(0, 0, 0, 0.5);
    box-shadow: 0 5px 15px rgba(0, 0, 0, 0.5);
  }
  .modal-sm {
    width: 300px;
  }
}
@media (min-width: 992px) {
  .modal-lg {
    width: 900px;
  }
}
.tooltip {
  position: absolute;
  z-index: 1070;
  display: block;
  font-family: "Helvetica Neue", Helvetica, Arial, sans-serif;
  font-style: normal;
  font-weight: normal;
  letter-spacing: normal;
  line-break: auto;
  line-height: 1.42857143;
  text-align: left;
  text-align: start;
  text-decoration: none;
  text-shadow: none;
  text-transform: none;
  white-space: normal;
  word-break: normal;
  word-spacing: normal;
  word-wrap: normal;
  font-size: 12px;
  opacity: 0;
  filter: alpha(opacity=0);
}
.tooltip.in {
  opacity: 0.9;
  filter: alpha(opacity=90);
}
.tooltip.top {
  margin-top: -3px;
  padding: 5px 0;
}
.tooltip.right {
  margin-left: 3px;
  padding: 0 5px;
}
.tooltip.bottom {
  margin-top: 3px;
  padding: 5px 0;
}
.tooltip.left {
  margin-left: -3px;
  padding: 0 5px;
}
.tooltip-inner {
  max-width: 200px;
  padding: 3px 8px;
  color: #fff;
  text-align: center;
  background-color: #000;
  border-radius: 2px;
}
.tooltip-arrow {
  position: absolute;
  width: 0;
  height: 0;
  border-color: transparent;
  border-style: solid;
}
.tooltip.top .tooltip-arrow {
  bottom: 0;
  left: 50%;
  margin-left: -5px;
  border-width: 5px 5px 0;
  border-top-color: #000;
}
.tooltip.top-left .tooltip-arrow {
  bottom: 0;
  right: 5px;
  margin-bottom: -5px;
  border-width: 5px 5px 0;
  border-top-color: #000;
}
.tooltip.top-right .tooltip-arrow {
  bottom: 0;
  left: 5px;
  margin-bottom: -5px;
  border-width: 5px 5px 0;
  border-top-color: #000;
}
.tooltip.right .tooltip-arrow {
  top: 50%;
  left: 0;
  margin-top: -5px;
  border-width: 5px 5px 5px 0;
  border-right-color: #000;
}
.tooltip.left .tooltip-arrow {
  top: 50%;
  right: 0;
  margin-top: -5px;
  border-width: 5px 0 5px 5px;
  border-left-color: #000;
}
.tooltip.bottom .tooltip-arrow {
  top: 0;
  left: 50%;
  margin-left: -5px;
  border-width: 0 5px 5px;
  border-bottom-color: #000;
}
.tooltip.bottom-left .tooltip-arrow {
  top: 0;
  right: 5px;
  margin-top: -5px;
  border-width: 0 5px 5px;
  border-bottom-color: #000;
}
.tooltip.bottom-right .tooltip-arrow {
  top: 0;
  left: 5px;
  margin-top: -5px;
  border-width: 0 5px 5px;
  border-bottom-color: #000;
}
.popover {
  position: absolute;
  top: 0;
  left: 0;
  z-index: 1060;
  display: none;
  max-width: 276px;
  padding: 1px;
  font-family: "Helvetica Neue", Helvetica, Arial, sans-serif;
  font-style: normal;
  font-weight: normal;
  letter-spacing: normal;
  line-break: auto;
  line-height: 1.42857143;
  text-align: left;
  text-align: start;
  text-decoration: none;
  text-shadow: none;
  text-transform: none;
  white-space: normal;
  word-break: normal;
  word-spacing: normal;
  word-wrap: normal;
  font-size: 13px;
  background-color: #fff;
  background-clip: padding-box;
  border: 1px solid #ccc;
  border: 1px solid rgba(0, 0, 0, 0.2);
  border-radius: 3px;
  -webkit-box-shadow: 0 5px 10px rgba(0, 0, 0, 0.2);
  box-shadow: 0 5px 10px rgba(0, 0, 0, 0.2);
}
.popover.top {
  margin-top: -10px;
}
.popover.right {
  margin-left: 10px;
}
.popover.bottom {
  margin-top: 10px;
}
.popover.left {
  margin-left: -10px;
}
.popover-title {
  margin: 0;
  padding: 8px 14px;
  font-size: 13px;
  background-color: #f7f7f7;
  border-bottom: 1px solid #ebebeb;
  border-radius: 2px 2px 0 0;
}
.popover-content {
  padding: 9px 14px;
}
.popover > .arrow,
.popover > .arrow:after {
  position: absolute;
  display: block;
  width: 0;
  height: 0;
  border-color: transparent;
  border-style: solid;
}
.popover > .arrow {
  border-width: 11px;
}
.popover > .arrow:after {
  border-width: 10px;
  content: "";
}
.popover.top > .arrow {
  left: 50%;
  margin-left: -11px;
  border-bottom-width: 0;
  border-top-color: #999999;
  border-top-color: rgba(0, 0, 0, 0.25);
  bottom: -11px;
}
.popover.top > .arrow:after {
  content: " ";
  bottom: 1px;
  margin-left: -10px;
  border-bottom-width: 0;
  border-top-color: #fff;
}
.popover.right > .arrow {
  top: 50%;
  left: -11px;
  margin-top: -11px;
  border-left-width: 0;
  border-right-color: #999999;
  border-right-color: rgba(0, 0, 0, 0.25);
}
.popover.right > .arrow:after {
  content: " ";
  left: 1px;
  bottom: -10px;
  border-left-width: 0;
  border-right-color: #fff;
}
.popover.bottom > .arrow {
  left: 50%;
  margin-left: -11px;
  border-top-width: 0;
  border-bottom-color: #999999;
  border-bottom-color: rgba(0, 0, 0, 0.25);
  top: -11px;
}
.popover.bottom > .arrow:after {
  content: " ";
  top: 1px;
  margin-left: -10px;
  border-top-width: 0;
  border-bottom-color: #fff;
}
.popover.left > .arrow {
  top: 50%;
  right: -11px;
  margin-top: -11px;
  border-right-width: 0;
  border-left-color: #999999;
  border-left-color: rgba(0, 0, 0, 0.25);
}
.popover.left > .arrow:after {
  content: " ";
  right: 1px;
  border-right-width: 0;
  border-left-color: #fff;
  bottom: -10px;
}
.carousel {
  position: relative;
}
.carousel-inner {
  position: relative;
  overflow: hidden;
  width: 100%;
}
.carousel-inner > .item {
  display: none;
  position: relative;
  -webkit-transition: 0.6s ease-in-out left;
  -o-transition: 0.6s ease-in-out left;
  transition: 0.6s ease-in-out left;
}
.carousel-inner > .item > img,
.carousel-inner > .item > a > img {
  line-height: 1;
}
@media all and (transform-3d), (-webkit-transform-3d) {
  .carousel-inner > .item {
    -webkit-transition: -webkit-transform 0.6s ease-in-out;
    -moz-transition: -moz-transform 0.6s ease-in-out;
    -o-transition: -o-transform 0.6s ease-in-out;
    transition: transform 0.6s ease-in-out;
    -webkit-backface-visibility: hidden;
    -moz-backface-visibility: hidden;
    backface-visibility: hidden;
    -webkit-perspective: 1000px;
    -moz-perspective: 1000px;
    perspective: 1000px;
  }
  .carousel-inner > .item.next,
  .carousel-inner > .item.active.right {
    -webkit-transform: translate3d(100%, 0, 0);
    transform: translate3d(100%, 0, 0);
    left: 0;
  }
  .carousel-inner > .item.prev,
  .carousel-inner > .item.active.left {
    -webkit-transform: translate3d(-100%, 0, 0);
    transform: translate3d(-100%, 0, 0);
    left: 0;
  }
  .carousel-inner > .item.next.left,
  .carousel-inner > .item.prev.right,
  .carousel-inner > .item.active {
    -webkit-transform: translate3d(0, 0, 0);
    transform: translate3d(0, 0, 0);
    left: 0;
  }
}
.carousel-inner > .active,
.carousel-inner > .next,
.carousel-inner > .prev {
  display: block;
}
.carousel-inner > .active {
  left: 0;
}
.carousel-inner > .next,
.carousel-inner > .prev {
  position: absolute;
  top: 0;
  width: 100%;
}
.carousel-inner > .next {
  left: 100%;
}
.carousel-inner > .prev {
  left: -100%;
}
.carousel-inner > .next.left,
.carousel-inner > .prev.right {
  left: 0;
}
.carousel-inner > .active.left {
  left: -100%;
}
.carousel-inner > .active.right {
  left: 100%;
}
.carousel-control {
  position: absolute;
  top: 0;
  left: 0;
  bottom: 0;
  width: 15%;
  opacity: 0.5;
  filter: alpha(opacity=50);
  font-size: 20px;
  color: #fff;
  text-align: center;
  text-shadow: 0 1px 2px rgba(0, 0, 0, 0.6);
  background-color: rgba(0, 0, 0, 0);
}
.carousel-control.left {
  background-image: -webkit-linear-gradient(left, rgba(0, 0, 0, 0.5) 0%, rgba(0, 0, 0, 0.0001) 100%);
  background-image: -o-linear-gradient(left, rgba(0, 0, 0, 0.5) 0%, rgba(0, 0, 0, 0.0001) 100%);
  background-image: linear-gradient(to right, rgba(0, 0, 0, 0.5) 0%, rgba(0, 0, 0, 0.0001) 100%);
  background-repeat: repeat-x;
  filter: progid:DXImageTransform.Microsoft.gradient(startColorstr='#80000000', endColorstr='#00000000', GradientType=1);
}
.carousel-control.right {
  left: auto;
  right: 0;
  background-image: -webkit-linear-gradient(left, rgba(0, 0, 0, 0.0001) 0%, rgba(0, 0, 0, 0.5) 100%);
  background-image: -o-linear-gradient(left, rgba(0, 0, 0, 0.0001) 0%, rgba(0, 0, 0, 0.5) 100%);
  background-image: linear-gradient(to right, rgba(0, 0, 0, 0.0001) 0%, rgba(0, 0, 0, 0.5) 100%);
  background-repeat: repeat-x;
  filter: progid:DXImageTransform.Microsoft.gradient(startColorstr='#00000000', endColorstr='#80000000', GradientType=1);
}
.carousel-control:hover,
.carousel-control:focus {
  outline: 0;
  color: #fff;
  text-decoration: none;
  opacity: 0.9;
  filter: alpha(opacity=90);
}
.carousel-control .icon-prev,
.carousel-control .icon-next,
.carousel-control .glyphicon-chevron-left,
.carousel-control .glyphicon-chevron-right {
  position: absolute;
  top: 50%;
  margin-top: -10px;
  z-index: 5;
  display: inline-block;
}
.carousel-control .icon-prev,
.carousel-control .glyphicon-chevron-left {
  left: 50%;
  margin-left: -10px;
}
.carousel-control .icon-next,
.carousel-control .glyphicon-chevron-right {
  right: 50%;
  margin-right: -10px;
}
.carousel-control .icon-prev,
.carousel-control .icon-next {
  width: 20px;
  height: 20px;
  line-height: 1;
  font-family: serif;
}
.carousel-control .icon-prev:before {
  content: '\2039';
}
.carousel-control .icon-next:before {
  content: '\203a';
}
.carousel-indicators {
  position: absolute;
  bottom: 10px;
  left: 50%;
  z-index: 15;
  width: 60%;
  margin-left: -30%;
  padding-left: 0;
  list-style: none;
  text-align: center;
}
.carousel-indicators li {
  display: inline-block;
  width: 10px;
  height: 10px;
  margin: 1px;
  text-indent: -999px;
  border: 1px solid #fff;
  border-radius: 10px;
  cursor: pointer;
  background-color: #000 \9;
  background-color: rgba(0, 0, 0, 0);
}
.carousel-indicators .active {
  margin: 0;
  width: 12px;
  height: 12px;
  background-color: #fff;
}
.carousel-caption {
  position: absolute;
  left: 15%;
  right: 15%;
  bottom: 20px;
  z-index: 10;
  padding-top: 20px;
  padding-bottom: 20px;
  color: #fff;
  text-align: center;
  text-shadow: 0 1px 2px rgba(0, 0, 0, 0.6);
}
.carousel-caption .btn {
  text-shadow: none;
}
@media screen and (min-width: 768px) {
  .carousel-control .glyphicon-chevron-left,
  .carousel-control .glyphicon-chevron-right,
  .carousel-control .icon-prev,
  .carousel-control .icon-next {
    width: 30px;
    height: 30px;
    margin-top: -10px;
    font-size: 30px;
  }
  .carousel-control .glyphicon-chevron-left,
  .carousel-control .icon-prev {
    margin-left: -10px;
  }
  .carousel-control .glyphicon-chevron-right,
  .carousel-control .icon-next {
    margin-right: -10px;
  }
  .carousel-caption {
    left: 20%;
    right: 20%;
    padding-bottom: 30px;
  }
  .carousel-indicators {
    bottom: 20px;
  }
}
.clearfix:before,
.clearfix:after,
.dl-horizontal dd:before,
.dl-horizontal dd:after,
.container:before,
.container:after,
.container-fluid:before,
.container-fluid:after,
.row:before,
.row:after,
.form-horizontal .form-group:before,
.form-horizontal .form-group:after,
.btn-toolbar:before,
.btn-toolbar:after,
.btn-group-vertical > .btn-group:before,
.btn-group-vertical > .btn-group:after,
.nav:before,
.nav:after,
.navbar:before,
.navbar:after,
.navbar-header:before,
.navbar-header:after,
.navbar-collapse:before,
.navbar-collapse:after,
.pager:before,
.pager:after,
.panel-body:before,
.panel-body:after,
.modal-header:before,
.modal-header:after,
.modal-footer:before,
.modal-footer:after,
.item_buttons:before,
.item_buttons:after {
  content: " ";
  display: table;
}
.clearfix:after,
.dl-horizontal dd:after,
.container:after,
.container-fluid:after,
.row:after,
.form-horizontal .form-group:after,
.btn-toolbar:after,
.btn-group-vertical > .btn-group:after,
.nav:after,
.navbar:after,
.navbar-header:after,
.navbar-collapse:after,
.pager:after,
.panel-body:after,
.modal-header:after,
.modal-footer:after,
.item_buttons:after {
  clear: both;
}
.center-block {
  display: block;
  margin-left: auto;
  margin-right: auto;
}
.pull-right {
  float: right !important;
}
.pull-left {
  float: left !important;
}
.hide {
  display: none !important;
}
.show {
  display: block !important;
}
.invisible {
  visibility: hidden;
}
.text-hide {
  font: 0/0 a;
  color: transparent;
  text-shadow: none;
  background-color: transparent;
  border: 0;
}
.hidden {
  display: none !important;
}
.affix {
  position: fixed;
}
@-ms-viewport {
  width: device-width;
}
.visible-xs,
.visible-sm,
.visible-md,
.visible-lg {
  display: none !important;
}
.visible-xs-block,
.visible-xs-inline,
.visible-xs-inline-block,
.visible-sm-block,
.visible-sm-inline,
.visible-sm-inline-block,
.visible-md-block,
.visible-md-inline,
.visible-md-inline-block,
.visible-lg-block,
.visible-lg-inline,
.visible-lg-inline-block {
  display: none !important;
}
@media (max-width: 767px) {
  .visible-xs {
    display: block !important;
  }
  table.visible-xs {
    display: table !important;
  }
  tr.visible-xs {
    display: table-row !important;
  }
  th.visible-xs,
  td.visible-xs {
    display: table-cell !important;
  }
}
@media (max-width: 767px) {
  .visible-xs-block {
    display: block !important;
  }
}
@media (max-width: 767px) {
  .visible-xs-inline {
    display: inline !important;
  }
}
@media (max-width: 767px) {
  .visible-xs-inline-block {
    display: inline-block !important;
  }
}
@media (min-width: 768px) and (max-width: 991px) {
  .visible-sm {
    display: block !important;
  }
  table.visible-sm {
    display: table !important;
  }
  tr.visible-sm {
    display: table-row !important;
  }
  th.visible-sm,
  td.visible-sm {
    display: table-cell !important;
  }
}
@media (min-width: 768px) and (max-width: 991px) {
  .visible-sm-block {
    display: block !important;
  }
}
@media (min-width: 768px) and (max-width: 991px) {
  .visible-sm-inline {
    display: inline !important;
  }
}
@media (min-width: 768px) and (max-width: 991px) {
  .visible-sm-inline-block {
    display: inline-block !important;
  }
}
@media (min-width: 992px) and (max-width: 1199px) {
  .visible-md {
    display: block !important;
  }
  table.visible-md {
    display: table !important;
  }
  tr.visible-md {
    display: table-row !important;
  }
  th.visible-md,
  td.visible-md {
    display: table-cell !important;
  }
}
@media (min-width: 992px) and (max-width: 1199px) {
  .visible-md-block {
    display: block !important;
  }
}
@media (min-width: 992px) and (max-width: 1199px) {
  .visible-md-inline {
    display: inline !important;
  }
}
@media (min-width: 992px) and (max-width: 1199px) {
  .visible-md-inline-block {
    display: inline-block !important;
  }
}
@media (min-width: 1200px) {
  .visible-lg {
    display: block !important;
  }
  table.visible-lg {
    display: table !important;
  }
  tr.visible-lg {
    display: table-row !important;
  }
  th.visible-lg,
  td.visible-lg {
    display: table-cell !important;
  }
}
@media (min-width: 1200px) {
  .visible-lg-block {
    display: block !important;
  }
}
@media (min-width: 1200px) {
  .visible-lg-inline {
    display: inline !important;
  }
}
@media (min-width: 1200px) {
  .visible-lg-inline-block {
    display: inline-block !important;
  }
}
@media (max-width: 767px) {
  .hidden-xs {
    display: none !important;
  }
}
@media (min-width: 768px) and (max-width: 991px) {
  .hidden-sm {
    display: none !important;
  }
}
@media (min-width: 992px) and (max-width: 1199px) {
  .hidden-md {
    display: none !important;
  }
}
@media (min-width: 1200px) {
  .hidden-lg {
    display: none !important;
  }
}
.visible-print {
  display: none !important;
}
@media print {
  .visible-print {
    display: block !important;
  }
  table.visible-print {
    display: table !important;
  }
  tr.visible-print {
    display: table-row !important;
  }
  th.visible-print,
  td.visible-print {
    display: table-cell !important;
  }
}
.visible-print-block {
  display: none !important;
}
@media print {
  .visible-print-block {
    display: block !important;
  }
}
.visible-print-inline {
  display: none !important;
}
@media print {
  .visible-print-inline {
    display: inline !important;
  }
}
.visible-print-inline-block {
  display: none !important;
}
@media print {
  .visible-print-inline-block {
    display: inline-block !important;
  }
}
@media print {
  .hidden-print {
    display: none !important;
  }
}
/*!
*
* Font Awesome
*
*/
/*!
 *  Font Awesome 4.7.0 by @davegandy - http://fontawesome.io - @fontawesome
 *  License - http://fontawesome.io/license (Font: SIL OFL 1.1, CSS: MIT License)
 */
/* FONT PATH
 * -------------------------- */
@font-face {
  font-family: 'FontAwesome';
  src: url('../components/font-awesome/fonts/fontawesome-webfont.eot?v=4.7.0');
  src: url('../components/font-awesome/fonts/fontawesome-webfont.eot?#iefix&v=4.7.0') format('embedded-opentype'), url('../components/font-awesome/fonts/fontawesome-webfont.woff2?v=4.7.0') format('woff2'), url('../components/font-awesome/fonts/fontawesome-webfont.woff?v=4.7.0') format('woff'), url('../components/font-awesome/fonts/fontawesome-webfont.ttf?v=4.7.0') format('truetype'), url('../components/font-awesome/fonts/fontawesome-webfont.svg?v=4.7.0#fontawesomeregular') format('svg');
  font-weight: normal;
  font-style: normal;
}
.fa {
  display: inline-block;
  font: normal normal normal 14px/1 FontAwesome;
  font-size: inherit;
  text-rendering: auto;
  -webkit-font-smoothing: antialiased;
  -moz-osx-font-smoothing: grayscale;
}
/* makes the font 33% larger relative to the icon container */
.fa-lg {
  font-size: 1.33333333em;
  line-height: 0.75em;
  vertical-align: -15%;
}
.fa-2x {
  font-size: 2em;
}
.fa-3x {
  font-size: 3em;
}
.fa-4x {
  font-size: 4em;
}
.fa-5x {
  font-size: 5em;
}
.fa-fw {
  width: 1.28571429em;
  text-align: center;
}
.fa-ul {
  padding-left: 0;
  margin-left: 2.14285714em;
  list-style-type: none;
}
.fa-ul > li {
  position: relative;
}
.fa-li {
  position: absolute;
  left: -2.14285714em;
  width: 2.14285714em;
  top: 0.14285714em;
  text-align: center;
}
.fa-li.fa-lg {
  left: -1.85714286em;
}
.fa-border {
  padding: .2em .25em .15em;
  border: solid 0.08em #eee;
  border-radius: .1em;
}
.fa-pull-left {
  float: left;
}
.fa-pull-right {
  float: right;
}
.fa.fa-pull-left {
  margin-right: .3em;
}
.fa.fa-pull-right {
  margin-left: .3em;
}
/* Deprecated as of 4.4.0 */
.pull-right {
  float: right;
}
.pull-left {
  float: left;
}
.fa.pull-left {
  margin-right: .3em;
}
.fa.pull-right {
  margin-left: .3em;
}
.fa-spin {
  -webkit-animation: fa-spin 2s infinite linear;
  animation: fa-spin 2s infinite linear;
}
.fa-pulse {
  -webkit-animation: fa-spin 1s infinite steps(8);
  animation: fa-spin 1s infinite steps(8);
}
@-webkit-keyframes fa-spin {
  0% {
    -webkit-transform: rotate(0deg);
    transform: rotate(0deg);
  }
  100% {
    -webkit-transform: rotate(359deg);
    transform: rotate(359deg);
  }
}
@keyframes fa-spin {
  0% {
    -webkit-transform: rotate(0deg);
    transform: rotate(0deg);
  }
  100% {
    -webkit-transform: rotate(359deg);
    transform: rotate(359deg);
  }
}
.fa-rotate-90 {
  -ms-filter: "progid:DXImageTransform.Microsoft.BasicImage(rotation=1)";
  -webkit-transform: rotate(90deg);
  -ms-transform: rotate(90deg);
  transform: rotate(90deg);
}
.fa-rotate-180 {
  -ms-filter: "progid:DXImageTransform.Microsoft.BasicImage(rotation=2)";
  -webkit-transform: rotate(180deg);
  -ms-transform: rotate(180deg);
  transform: rotate(180deg);
}
.fa-rotate-270 {
  -ms-filter: "progid:DXImageTransform.Microsoft.BasicImage(rotation=3)";
  -webkit-transform: rotate(270deg);
  -ms-transform: rotate(270deg);
  transform: rotate(270deg);
}
.fa-flip-horizontal {
  -ms-filter: "progid:DXImageTransform.Microsoft.BasicImage(rotation=0, mirror=1)";
  -webkit-transform: scale(-1, 1);
  -ms-transform: scale(-1, 1);
  transform: scale(-1, 1);
}
.fa-flip-vertical {
  -ms-filter: "progid:DXImageTransform.Microsoft.BasicImage(rotation=2, mirror=1)";
  -webkit-transform: scale(1, -1);
  -ms-transform: scale(1, -1);
  transform: scale(1, -1);
}
:root .fa-rotate-90,
:root .fa-rotate-180,
:root .fa-rotate-270,
:root .fa-flip-horizontal,
:root .fa-flip-vertical {
  filter: none;
}
.fa-stack {
  position: relative;
  display: inline-block;
  width: 2em;
  height: 2em;
  line-height: 2em;
  vertical-align: middle;
}
.fa-stack-1x,
.fa-stack-2x {
  position: absolute;
  left: 0;
  width: 100%;
  text-align: center;
}
.fa-stack-1x {
  line-height: inherit;
}
.fa-stack-2x {
  font-size: 2em;
}
.fa-inverse {
  color: #fff;
}
/* Font Awesome uses the Unicode Private Use Area (PUA) to ensure screen
   readers do not read off random characters that represent icons */
.fa-glass:before {
  content: "\f000";
}
.fa-music:before {
  content: "\f001";
}
.fa-search:before {
  content: "\f002";
}
.fa-envelope-o:before {
  content: "\f003";
}
.fa-heart:before {
  content: "\f004";
}
.fa-star:before {
  content: "\f005";
}
.fa-star-o:before {
  content: "\f006";
}
.fa-user:before {
  content: "\f007";
}
.fa-film:before {
  content: "\f008";
}
.fa-th-large:before {
  content: "\f009";
}
.fa-th:before {
  content: "\f00a";
}
.fa-th-list:before {
  content: "\f00b";
}
.fa-check:before {
  content: "\f00c";
}
.fa-remove:before,
.fa-close:before,
.fa-times:before {
  content: "\f00d";
}
.fa-search-plus:before {
  content: "\f00e";
}
.fa-search-minus:before {
  content: "\f010";
}
.fa-power-off:before {
  content: "\f011";
}
.fa-signal:before {
  content: "\f012";
}
.fa-gear:before,
.fa-cog:before {
  content: "\f013";
}
.fa-trash-o:before {
  content: "\f014";
}
.fa-home:before {
  content: "\f015";
}
.fa-file-o:before {
  content: "\f016";
}
.fa-clock-o:before {
  content: "\f017";
}
.fa-road:before {
  content: "\f018";
}
.fa-download:before {
  content: "\f019";
}
.fa-arrow-circle-o-down:before {
  content: "\f01a";
}
.fa-arrow-circle-o-up:before {
  content: "\f01b";
}
.fa-inbox:before {
  content: "\f01c";
}
.fa-play-circle-o:before {
  content: "\f01d";
}
.fa-rotate-right:before,
.fa-repeat:before {
  content: "\f01e";
}
.fa-refresh:before {
  content: "\f021";
}
.fa-list-alt:before {
  content: "\f022";
}
.fa-lock:before {
  content: "\f023";
}
.fa-flag:before {
  content: "\f024";
}
.fa-headphones:before {
  content: "\f025";
}
.fa-volume-off:before {
  content: "\f026";
}
.fa-volume-down:before {
  content: "\f027";
}
.fa-volume-up:before {
  content: "\f028";
}
.fa-qrcode:before {
  content: "\f029";
}
.fa-barcode:before {
  content: "\f02a";
}
.fa-tag:before {
  content: "\f02b";
}
.fa-tags:before {
  content: "\f02c";
}
.fa-book:before {
  content: "\f02d";
}
.fa-bookmark:before {
  content: "\f02e";
}
.fa-print:before {
  content: "\f02f";
}
.fa-camera:before {
  content: "\f030";
}
.fa-font:before {
  content: "\f031";
}
.fa-bold:before {
  content: "\f032";
}
.fa-italic:before {
  content: "\f033";
}
.fa-text-height:before {
  content: "\f034";
}
.fa-text-width:before {
  content: "\f035";
}
.fa-align-left:before {
  content: "\f036";
}
.fa-align-center:before {
  content: "\f037";
}
.fa-align-right:before {
  content: "\f038";
}
.fa-align-justify:before {
  content: "\f039";
}
.fa-list:before {
  content: "\f03a";
}
.fa-dedent:before,
.fa-outdent:before {
  content: "\f03b";
}
.fa-indent:before {
  content: "\f03c";
}
.fa-video-camera:before {
  content: "\f03d";
}
.fa-photo:before,
.fa-image:before,
.fa-picture-o:before {
  content: "\f03e";
}
.fa-pencil:before {
  content: "\f040";
}
.fa-map-marker:before {
  content: "\f041";
}
.fa-adjust:before {
  content: "\f042";
}
.fa-tint:before {
  content: "\f043";
}
.fa-edit:before,
.fa-pencil-square-o:before {
  content: "\f044";
}
.fa-share-square-o:before {
  content: "\f045";
}
.fa-check-square-o:before {
  content: "\f046";
}
.fa-arrows:before {
  content: "\f047";
}
.fa-step-backward:before {
  content: "\f048";
}
.fa-fast-backward:before {
  content: "\f049";
}
.fa-backward:before {
  content: "\f04a";
}
.fa-play:before {
  content: "\f04b";
}
.fa-pause:before {
  content: "\f04c";
}
.fa-stop:before {
  content: "\f04d";
}
.fa-forward:before {
  content: "\f04e";
}
.fa-fast-forward:before {
  content: "\f050";
}
.fa-step-forward:before {
  content: "\f051";
}
.fa-eject:before {
  content: "\f052";
}
.fa-chevron-left:before {
  content: "\f053";
}
.fa-chevron-right:before {
  content: "\f054";
}
.fa-plus-circle:before {
  content: "\f055";
}
.fa-minus-circle:before {
  content: "\f056";
}
.fa-times-circle:before {
  content: "\f057";
}
.fa-check-circle:before {
  content: "\f058";
}
.fa-question-circle:before {
  content: "\f059";
}
.fa-info-circle:before {
  content: "\f05a";
}
.fa-crosshairs:before {
  content: "\f05b";
}
.fa-times-circle-o:before {
  content: "\f05c";
}
.fa-check-circle-o:before {
  content: "\f05d";
}
.fa-ban:before {
  content: "\f05e";
}
.fa-arrow-left:before {
  content: "\f060";
}
.fa-arrow-right:before {
  content: "\f061";
}
.fa-arrow-up:before {
  content: "\f062";
}
.fa-arrow-down:before {
  content: "\f063";
}
.fa-mail-forward:before,
.fa-share:before {
  content: "\f064";
}
.fa-expand:before {
  content: "\f065";
}
.fa-compress:before {
  content: "\f066";
}
.fa-plus:before {
  content: "\f067";
}
.fa-minus:before {
  content: "\f068";
}
.fa-asterisk:before {
  content: "\f069";
}
.fa-exclamation-circle:before {
  content: "\f06a";
}
.fa-gift:before {
  content: "\f06b";
}
.fa-leaf:before {
  content: "\f06c";
}
.fa-fire:before {
  content: "\f06d";
}
.fa-eye:before {
  content: "\f06e";
}
.fa-eye-slash:before {
  content: "\f070";
}
.fa-warning:before,
.fa-exclamation-triangle:before {
  content: "\f071";
}
.fa-plane:before {
  content: "\f072";
}
.fa-calendar:before {
  content: "\f073";
}
.fa-random:before {
  content: "\f074";
}
.fa-comment:before {
  content: "\f075";
}
.fa-magnet:before {
  content: "\f076";
}
.fa-chevron-up:before {
  content: "\f077";
}
.fa-chevron-down:before {
  content: "\f078";
}
.fa-retweet:before {
  content: "\f079";
}
.fa-shopping-cart:before {
  content: "\f07a";
}
.fa-folder:before {
  content: "\f07b";
}
.fa-folder-open:before {
  content: "\f07c";
}
.fa-arrows-v:before {
  content: "\f07d";
}
.fa-arrows-h:before {
  content: "\f07e";
}
.fa-bar-chart-o:before,
.fa-bar-chart:before {
  content: "\f080";
}
.fa-twitter-square:before {
  content: "\f081";
}
.fa-facebook-square:before {
  content: "\f082";
}
.fa-camera-retro:before {
  content: "\f083";
}
.fa-key:before {
  content: "\f084";
}
.fa-gears:before,
.fa-cogs:before {
  content: "\f085";
}
.fa-comments:before {
  content: "\f086";
}
.fa-thumbs-o-up:before {
  content: "\f087";
}
.fa-thumbs-o-down:before {
  content: "\f088";
}
.fa-star-half:before {
  content: "\f089";
}
.fa-heart-o:before {
  content: "\f08a";
}
.fa-sign-out:before {
  content: "\f08b";
}
.fa-linkedin-square:before {
  content: "\f08c";
}
.fa-thumb-tack:before {
  content: "\f08d";
}
.fa-external-link:before {
  content: "\f08e";
}
.fa-sign-in:before {
  content: "\f090";
}
.fa-trophy:before {
  content: "\f091";
}
.fa-github-square:before {
  content: "\f092";
}
.fa-upload:before {
  content: "\f093";
}
.fa-lemon-o:before {
  content: "\f094";
}
.fa-phone:before {
  content: "\f095";
}
.fa-square-o:before {
  content: "\f096";
}
.fa-bookmark-o:before {
  content: "\f097";
}
.fa-phone-square:before {
  content: "\f098";
}
.fa-twitter:before {
  content: "\f099";
}
.fa-facebook-f:before,
.fa-facebook:before {
  content: "\f09a";
}
.fa-github:before {
  content: "\f09b";
}
.fa-unlock:before {
  content: "\f09c";
}
.fa-credit-card:before {
  content: "\f09d";
}
.fa-feed:before,
.fa-rss:before {
  content: "\f09e";
}
.fa-hdd-o:before {
  content: "\f0a0";
}
.fa-bullhorn:before {
  content: "\f0a1";
}
.fa-bell:before {
  content: "\f0f3";
}
.fa-certificate:before {
  content: "\f0a3";
}
.fa-hand-o-right:before {
  content: "\f0a4";
}
.fa-hand-o-left:before {
  content: "\f0a5";
}
.fa-hand-o-up:before {
  content: "\f0a6";
}
.fa-hand-o-down:before {
  content: "\f0a7";
}
.fa-arrow-circle-left:before {
  content: "\f0a8";
}
.fa-arrow-circle-right:before {
  content: "\f0a9";
}
.fa-arrow-circle-up:before {
  content: "\f0aa";
}
.fa-arrow-circle-down:before {
  content: "\f0ab";
}
.fa-globe:before {
  content: "\f0ac";
}
.fa-wrench:before {
  content: "\f0ad";
}
.fa-tasks:before {
  content: "\f0ae";
}
.fa-filter:before {
  content: "\f0b0";
}
.fa-briefcase:before {
  content: "\f0b1";
}
.fa-arrows-alt:before {
  content: "\f0b2";
}
.fa-group:before,
.fa-users:before {
  content: "\f0c0";
}
.fa-chain:before,
.fa-link:before {
  content: "\f0c1";
}
.fa-cloud:before {
  content: "\f0c2";
}
.fa-flask:before {
  content: "\f0c3";
}
.fa-cut:before,
.fa-scissors:before {
  content: "\f0c4";
}
.fa-copy:before,
.fa-files-o:before {
  content: "\f0c5";
}
.fa-paperclip:before {
  content: "\f0c6";
}
.fa-save:before,
.fa-floppy-o:before {
  content: "\f0c7";
}
.fa-square:before {
  content: "\f0c8";
}
.fa-navicon:before,
.fa-reorder:before,
.fa-bars:before {
  content: "\f0c9";
}
.fa-list-ul:before {
  content: "\f0ca";
}
.fa-list-ol:before {
  content: "\f0cb";
}
.fa-strikethrough:before {
  content: "\f0cc";
}
.fa-underline:before {
  content: "\f0cd";
}
.fa-table:before {
  content: "\f0ce";
}
.fa-magic:before {
  content: "\f0d0";
}
.fa-truck:before {
  content: "\f0d1";
}
.fa-pinterest:before {
  content: "\f0d2";
}
.fa-pinterest-square:before {
  content: "\f0d3";
}
.fa-google-plus-square:before {
  content: "\f0d4";
}
.fa-google-plus:before {
  content: "\f0d5";
}
.fa-money:before {
  content: "\f0d6";
}
.fa-caret-down:before {
  content: "\f0d7";
}
.fa-caret-up:before {
  content: "\f0d8";
}
.fa-caret-left:before {
  content: "\f0d9";
}
.fa-caret-right:before {
  content: "\f0da";
}
.fa-columns:before {
  content: "\f0db";
}
.fa-unsorted:before,
.fa-sort:before {
  content: "\f0dc";
}
.fa-sort-down:before,
.fa-sort-desc:before {
  content: "\f0dd";
}
.fa-sort-up:before,
.fa-sort-asc:before {
  content: "\f0de";
}
.fa-envelope:before {
  content: "\f0e0";
}
.fa-linkedin:before {
  content: "\f0e1";
}
.fa-rotate-left:before,
.fa-undo:before {
  content: "\f0e2";
}
.fa-legal:before,
.fa-gavel:before {
  content: "\f0e3";
}
.fa-dashboard:before,
.fa-tachometer:before {
  content: "\f0e4";
}
.fa-comment-o:before {
  content: "\f0e5";
}
.fa-comments-o:before {
  content: "\f0e6";
}
.fa-flash:before,
.fa-bolt:before {
  content: "\f0e7";
}
.fa-sitemap:before {
  content: "\f0e8";
}
.fa-umbrella:before {
  content: "\f0e9";
}
.fa-paste:before,
.fa-clipboard:before {
  content: "\f0ea";
}
.fa-lightbulb-o:before {
  content: "\f0eb";
}
.fa-exchange:before {
  content: "\f0ec";
}
.fa-cloud-download:before {
  content: "\f0ed";
}
.fa-cloud-upload:before {
  content: "\f0ee";
}
.fa-user-md:before {
  content: "\f0f0";
}
.fa-stethoscope:before {
  content: "\f0f1";
}
.fa-suitcase:before {
  content: "\f0f2";
}
.fa-bell-o:before {
  content: "\f0a2";
}
.fa-coffee:before {
  content: "\f0f4";
}
.fa-cutlery:before {
  content: "\f0f5";
}
.fa-file-text-o:before {
  content: "\f0f6";
}
.fa-building-o:before {
  content: "\f0f7";
}
.fa-hospital-o:before {
  content: "\f0f8";
}
.fa-ambulance:before {
  content: "\f0f9";
}
.fa-medkit:before {
  content: "\f0fa";
}
.fa-fighter-jet:before {
  content: "\f0fb";
}
.fa-beer:before {
  content: "\f0fc";
}
.fa-h-square:before {
  content: "\f0fd";
}
.fa-plus-square:before {
  content: "\f0fe";
}
.fa-angle-double-left:before {
  content: "\f100";
}
.fa-angle-double-right:before {
  content: "\f101";
}
.fa-angle-double-up:before {
  content: "\f102";
}
.fa-angle-double-down:before {
  content: "\f103";
}
.fa-angle-left:before {
  content: "\f104";
}
.fa-angle-right:before {
  content: "\f105";
}
.fa-angle-up:before {
  content: "\f106";
}
.fa-angle-down:before {
  content: "\f107";
}
.fa-desktop:before {
  content: "\f108";
}
.fa-laptop:before {
  content: "\f109";
}
.fa-tablet:before {
  content: "\f10a";
}
.fa-mobile-phone:before,
.fa-mobile:before {
  content: "\f10b";
}
.fa-circle-o:before {
  content: "\f10c";
}
.fa-quote-left:before {
  content: "\f10d";
}
.fa-quote-right:before {
  content: "\f10e";
}
.fa-spinner:before {
  content: "\f110";
}
.fa-circle:before {
  content: "\f111";
}
.fa-mail-reply:before,
.fa-reply:before {
  content: "\f112";
}
.fa-github-alt:before {
  content: "\f113";
}
.fa-folder-o:before {
  content: "\f114";
}
.fa-folder-open-o:before {
  content: "\f115";
}
.fa-smile-o:before {
  content: "\f118";
}
.fa-frown-o:before {
  content: "\f119";
}
.fa-meh-o:before {
  content: "\f11a";
}
.fa-gamepad:before {
  content: "\f11b";
}
.fa-keyboard-o:before {
  content: "\f11c";
}
.fa-flag-o:before {
  content: "\f11d";
}
.fa-flag-checkered:before {
  content: "\f11e";
}
.fa-terminal:before {
  content: "\f120";
}
.fa-code:before {
  content: "\f121";
}
.fa-mail-reply-all:before,
.fa-reply-all:before {
  content: "\f122";
}
.fa-star-half-empty:before,
.fa-star-half-full:before,
.fa-star-half-o:before {
  content: "\f123";
}
.fa-location-arrow:before {
  content: "\f124";
}
.fa-crop:before {
  content: "\f125";
}
.fa-code-fork:before {
  content: "\f126";
}
.fa-unlink:before,
.fa-chain-broken:before {
  content: "\f127";
}
.fa-question:before {
  content: "\f128";
}
.fa-info:before {
  content: "\f129";
}
.fa-exclamation:before {
  content: "\f12a";
}
.fa-superscript:before {
  content: "\f12b";
}
.fa-subscript:before {
  content: "\f12c";
}
.fa-eraser:before {
  content: "\f12d";
}
.fa-puzzle-piece:before {
  content: "\f12e";
}
.fa-microphone:before {
  content: "\f130";
}
.fa-microphone-slash:before {
  content: "\f131";
}
.fa-shield:before {
  content: "\f132";
}
.fa-calendar-o:before {
  content: "\f133";
}
.fa-fire-extinguisher:before {
  content: "\f134";
}
.fa-rocket:before {
  content: "\f135";
}
.fa-maxcdn:before {
  content: "\f136";
}
.fa-chevron-circle-left:before {
  content: "\f137";
}
.fa-chevron-circle-right:before {
  content: "\f138";
}
.fa-chevron-circle-up:before {
  content: "\f139";
}
.fa-chevron-circle-down:before {
  content: "\f13a";
}
.fa-html5:before {
  content: "\f13b";
}
.fa-css3:before {
  content: "\f13c";
}
.fa-anchor:before {
  content: "\f13d";
}
.fa-unlock-alt:before {
  content: "\f13e";
}
.fa-bullseye:before {
  content: "\f140";
}
.fa-ellipsis-h:before {
  content: "\f141";
}
.fa-ellipsis-v:before {
  content: "\f142";
}
.fa-rss-square:before {
  content: "\f143";
}
.fa-play-circle:before {
  content: "\f144";
}
.fa-ticket:before {
  content: "\f145";
}
.fa-minus-square:before {
  content: "\f146";
}
.fa-minus-square-o:before {
  content: "\f147";
}
.fa-level-up:before {
  content: "\f148";
}
.fa-level-down:before {
  content: "\f149";
}
.fa-check-square:before {
  content: "\f14a";
}
.fa-pencil-square:before {
  content: "\f14b";
}
.fa-external-link-square:before {
  content: "\f14c";
}
.fa-share-square:before {
  content: "\f14d";
}
.fa-compass:before {
  content: "\f14e";
}
.fa-toggle-down:before,
.fa-caret-square-o-down:before {
  content: "\f150";
}
.fa-toggle-up:before,
.fa-caret-square-o-up:before {
  content: "\f151";
}
.fa-toggle-right:before,
.fa-caret-square-o-right:before {
  content: "\f152";
}
.fa-euro:before,
.fa-eur:before {
  content: "\f153";
}
.fa-gbp:before {
  content: "\f154";
}
.fa-dollar:before,
.fa-usd:before {
  content: "\f155";
}
.fa-rupee:before,
.fa-inr:before {
  content: "\f156";
}
.fa-cny:before,
.fa-rmb:before,
.fa-yen:before,
.fa-jpy:before {
  content: "\f157";
}
.fa-ruble:before,
.fa-rouble:before,
.fa-rub:before {
  content: "\f158";
}
.fa-won:before,
.fa-krw:before {
  content: "\f159";
}
.fa-bitcoin:before,
.fa-btc:before {
  content: "\f15a";
}
.fa-file:before {
  content: "\f15b";
}
.fa-file-text:before {
  content: "\f15c";
}
.fa-sort-alpha-asc:before {
  content: "\f15d";
}
.fa-sort-alpha-desc:before {
  content: "\f15e";
}
.fa-sort-amount-asc:before {
  content: "\f160";
}
.fa-sort-amount-desc:before {
  content: "\f161";
}
.fa-sort-numeric-asc:before {
  content: "\f162";
}
.fa-sort-numeric-desc:before {
  content: "\f163";
}
.fa-thumbs-up:before {
  content: "\f164";
}
.fa-thumbs-down:before {
  content: "\f165";
}
.fa-youtube-square:before {
  content: "\f166";
}
.fa-youtube:before {
  content: "\f167";
}
.fa-xing:before {
  content: "\f168";
}
.fa-xing-square:before {
  content: "\f169";
}
.fa-youtube-play:before {
  content: "\f16a";
}
.fa-dropbox:before {
  content: "\f16b";
}
.fa-stack-overflow:before {
  content: "\f16c";
}
.fa-instagram:before {
  content: "\f16d";
}
.fa-flickr:before {
  content: "\f16e";
}
.fa-adn:before {
  content: "\f170";
}
.fa-bitbucket:before {
  content: "\f171";
}
.fa-bitbucket-square:before {
  content: "\f172";
}
.fa-tumblr:before {
  content: "\f173";
}
.fa-tumblr-square:before {
  content: "\f174";
}
.fa-long-arrow-down:before {
  content: "\f175";
}
.fa-long-arrow-up:before {
  content: "\f176";
}
.fa-long-arrow-left:before {
  content: "\f177";
}
.fa-long-arrow-right:before {
  content: "\f178";
}
.fa-apple:before {
  content: "\f179";
}
.fa-windows:before {
  content: "\f17a";
}
.fa-android:before {
  content: "\f17b";
}
.fa-linux:before {
  content: "\f17c";
}
.fa-dribbble:before {
  content: "\f17d";
}
.fa-skype:before {
  content: "\f17e";
}
.fa-foursquare:before {
  content: "\f180";
}
.fa-trello:before {
  content: "\f181";
}
.fa-female:before {
  content: "\f182";
}
.fa-male:before {
  content: "\f183";
}
.fa-gittip:before,
.fa-gratipay:before {
  content: "\f184";
}
.fa-sun-o:before {
  content: "\f185";
}
.fa-moon-o:before {
  content: "\f186";
}
.fa-archive:before {
  content: "\f187";
}
.fa-bug:before {
  content: "\f188";
}
.fa-vk:before {
  content: "\f189";
}
.fa-weibo:before {
  content: "\f18a";
}
.fa-renren:before {
  content: "\f18b";
}
.fa-pagelines:before {
  content: "\f18c";
}
.fa-stack-exchange:before {
  content: "\f18d";
}
.fa-arrow-circle-o-right:before {
  content: "\f18e";
}
.fa-arrow-circle-o-left:before {
  content: "\f190";
}
.fa-toggle-left:before,
.fa-caret-square-o-left:before {
  content: "\f191";
}
.fa-dot-circle-o:before {
  content: "\f192";
}
.fa-wheelchair:before {
  content: "\f193";
}
.fa-vimeo-square:before {
  content: "\f194";
}
.fa-turkish-lira:before,
.fa-try:before {
  content: "\f195";
}
.fa-plus-square-o:before {
  content: "\f196";
}
.fa-space-shuttle:before {
  content: "\f197";
}
.fa-slack:before {
  content: "\f198";
}
.fa-envelope-square:before {
  content: "\f199";
}
.fa-wordpress:before {
  content: "\f19a";
}
.fa-openid:before {
  content: "\f19b";
}
.fa-institution:before,
.fa-bank:before,
.fa-university:before {
  content: "\f19c";
}
.fa-mortar-board:before,
.fa-graduation-cap:before {
  content: "\f19d";
}
.fa-yahoo:before {
  content: "\f19e";
}
.fa-google:before {
  content: "\f1a0";
}
.fa-reddit:before {
  content: "\f1a1";
}
.fa-reddit-square:before {
  content: "\f1a2";
}
.fa-stumbleupon-circle:before {
  content: "\f1a3";
}
.fa-stumbleupon:before {
  content: "\f1a4";
}
.fa-delicious:before {
  content: "\f1a5";
}
.fa-digg:before {
  content: "\f1a6";
}
.fa-pied-piper-pp:before {
  content: "\f1a7";
}
.fa-pied-piper-alt:before {
  content: "\f1a8";
}
.fa-drupal:before {
  content: "\f1a9";
}
.fa-joomla:before {
  content: "\f1aa";
}
.fa-language:before {
  content: "\f1ab";
}
.fa-fax:before {
  content: "\f1ac";
}
.fa-building:before {
  content: "\f1ad";
}
.fa-child:before {
  content: "\f1ae";
}
.fa-paw:before {
  content: "\f1b0";
}
.fa-spoon:before {
  content: "\f1b1";
}
.fa-cube:before {
  content: "\f1b2";
}
.fa-cubes:before {
  content: "\f1b3";
}
.fa-behance:before {
  content: "\f1b4";
}
.fa-behance-square:before {
  content: "\f1b5";
}
.fa-steam:before {
  content: "\f1b6";
}
.fa-steam-square:before {
  content: "\f1b7";
}
.fa-recycle:before {
  content: "\f1b8";
}
.fa-automobile:before,
.fa-car:before {
  content: "\f1b9";
}
.fa-cab:before,
.fa-taxi:before {
  content: "\f1ba";
}
.fa-tree:before {
  content: "\f1bb";
}
.fa-spotify:before {
  content: "\f1bc";
}
.fa-deviantart:before {
  content: "\f1bd";
}
.fa-soundcloud:before {
  content: "\f1be";
}
.fa-database:before {
  content: "\f1c0";
}
.fa-file-pdf-o:before {
  content: "\f1c1";
}
.fa-file-word-o:before {
  content: "\f1c2";
}
.fa-file-excel-o:before {
  content: "\f1c3";
}
.fa-file-powerpoint-o:before {
  content: "\f1c4";
}
.fa-file-photo-o:before,
.fa-file-picture-o:before,
.fa-file-image-o:before {
  content: "\f1c5";
}
.fa-file-zip-o:before,
.fa-file-archive-o:before {
  content: "\f1c6";
}
.fa-file-sound-o:before,
.fa-file-audio-o:before {
  content: "\f1c7";
}
.fa-file-movie-o:before,
.fa-file-video-o:before {
  content: "\f1c8";
}
.fa-file-code-o:before {
  content: "\f1c9";
}
.fa-vine:before {
  content: "\f1ca";
}
.fa-codepen:before {
  content: "\f1cb";
}
.fa-jsfiddle:before {
  content: "\f1cc";
}
.fa-life-bouy:before,
.fa-life-buoy:before,
.fa-life-saver:before,
.fa-support:before,
.fa-life-ring:before {
  content: "\f1cd";
}
.fa-circle-o-notch:before {
  content: "\f1ce";
}
.fa-ra:before,
.fa-resistance:before,
.fa-rebel:before {
  content: "\f1d0";
}
.fa-ge:before,
.fa-empire:before {
  content: "\f1d1";
}
.fa-git-square:before {
  content: "\f1d2";
}
.fa-git:before {
  content: "\f1d3";
}
.fa-y-combinator-square:before,
.fa-yc-square:before,
.fa-hacker-news:before {
  content: "\f1d4";
}
.fa-tencent-weibo:before {
  content: "\f1d5";
}
.fa-qq:before {
  content: "\f1d6";
}
.fa-wechat:before,
.fa-weixin:before {
  content: "\f1d7";
}
.fa-send:before,
.fa-paper-plane:before {
  content: "\f1d8";
}
.fa-send-o:before,
.fa-paper-plane-o:before {
  content: "\f1d9";
}
.fa-history:before {
  content: "\f1da";
}
.fa-circle-thin:before {
  content: "\f1db";
}
.fa-header:before {
  content: "\f1dc";
}
.fa-paragraph:before {
  content: "\f1dd";
}
.fa-sliders:before {
  content: "\f1de";
}
.fa-share-alt:before {
  content: "\f1e0";
}
.fa-share-alt-square:before {
  content: "\f1e1";
}
.fa-bomb:before {
  content: "\f1e2";
}
.fa-soccer-ball-o:before,
.fa-futbol-o:before {
  content: "\f1e3";
}
.fa-tty:before {
  content: "\f1e4";
}
.fa-binoculars:before {
  content: "\f1e5";
}
.fa-plug:before {
  content: "\f1e6";
}
.fa-slideshare:before {
  content: "\f1e7";
}
.fa-twitch:before {
  content: "\f1e8";
}
.fa-yelp:before {
  content: "\f1e9";
}
.fa-newspaper-o:before {
  content: "\f1ea";
}
.fa-wifi:before {
  content: "\f1eb";
}
.fa-calculator:before {
  content: "\f1ec";
}
.fa-paypal:before {
  content: "\f1ed";
}
.fa-google-wallet:before {
  content: "\f1ee";
}
.fa-cc-visa:before {
  content: "\f1f0";
}
.fa-cc-mastercard:before {
  content: "\f1f1";
}
.fa-cc-discover:before {
  content: "\f1f2";
}
.fa-cc-amex:before {
  content: "\f1f3";
}
.fa-cc-paypal:before {
  content: "\f1f4";
}
.fa-cc-stripe:before {
  content: "\f1f5";
}
.fa-bell-slash:before {
  content: "\f1f6";
}
.fa-bell-slash-o:before {
  content: "\f1f7";
}
.fa-trash:before {
  content: "\f1f8";
}
.fa-copyright:before {
  content: "\f1f9";
}
.fa-at:before {
  content: "\f1fa";
}
.fa-eyedropper:before {
  content: "\f1fb";
}
.fa-paint-brush:before {
  content: "\f1fc";
}
.fa-birthday-cake:before {
  content: "\f1fd";
}
.fa-area-chart:before {
  content: "\f1fe";
}
.fa-pie-chart:before {
  content: "\f200";
}
.fa-line-chart:before {
  content: "\f201";
}
.fa-lastfm:before {
  content: "\f202";
}
.fa-lastfm-square:before {
  content: "\f203";
}
.fa-toggle-off:before {
  content: "\f204";
}
.fa-toggle-on:before {
  content: "\f205";
}
.fa-bicycle:before {
  content: "\f206";
}
.fa-bus:before {
  content: "\f207";
}
.fa-ioxhost:before {
  content: "\f208";
}
.fa-angellist:before {
  content: "\f209";
}
.fa-cc:before {
  content: "\f20a";
}
.fa-shekel:before,
.fa-sheqel:before,
.fa-ils:before {
  content: "\f20b";
}
.fa-meanpath:before {
  content: "\f20c";
}
.fa-buysellads:before {
  content: "\f20d";
}
.fa-connectdevelop:before {
  content: "\f20e";
}
.fa-dashcube:before {
  content: "\f210";
}
.fa-forumbee:before {
  content: "\f211";
}
.fa-leanpub:before {
  content: "\f212";
}
.fa-sellsy:before {
  content: "\f213";
}
.fa-shirtsinbulk:before {
  content: "\f214";
}
.fa-simplybuilt:before {
  content: "\f215";
}
.fa-skyatlas:before {
  content: "\f216";
}
.fa-cart-plus:before {
  content: "\f217";
}
.fa-cart-arrow-down:before {
  content: "\f218";
}
.fa-diamond:before {
  content: "\f219";
}
.fa-ship:before {
  content: "\f21a";
}
.fa-user-secret:before {
  content: "\f21b";
}
.fa-motorcycle:before {
  content: "\f21c";
}
.fa-street-view:before {
  content: "\f21d";
}
.fa-heartbeat:before {
  content: "\f21e";
}
.fa-venus:before {
  content: "\f221";
}
.fa-mars:before {
  content: "\f222";
}
.fa-mercury:before {
  content: "\f223";
}
.fa-intersex:before,
.fa-transgender:before {
  content: "\f224";
}
.fa-transgender-alt:before {
  content: "\f225";
}
.fa-venus-double:before {
  content: "\f226";
}
.fa-mars-double:before {
  content: "\f227";
}
.fa-venus-mars:before {
  content: "\f228";
}
.fa-mars-stroke:before {
  content: "\f229";
}
.fa-mars-stroke-v:before {
  content: "\f22a";
}
.fa-mars-stroke-h:before {
  content: "\f22b";
}
.fa-neuter:before {
  content: "\f22c";
}
.fa-genderless:before {
  content: "\f22d";
}
.fa-facebook-official:before {
  content: "\f230";
}
.fa-pinterest-p:before {
  content: "\f231";
}
.fa-whatsapp:before {
  content: "\f232";
}
.fa-server:before {
  content: "\f233";
}
.fa-user-plus:before {
  content: "\f234";
}
.fa-user-times:before {
  content: "\f235";
}
.fa-hotel:before,
.fa-bed:before {
  content: "\f236";
}
.fa-viacoin:before {
  content: "\f237";
}
.fa-train:before {
  content: "\f238";
}
.fa-subway:before {
  content: "\f239";
}
.fa-medium:before {
  content: "\f23a";
}
.fa-yc:before,
.fa-y-combinator:before {
  content: "\f23b";
}
.fa-optin-monster:before {
  content: "\f23c";
}
.fa-opencart:before {
  content: "\f23d";
}
.fa-expeditedssl:before {
  content: "\f23e";
}
.fa-battery-4:before,
.fa-battery:before,
.fa-battery-full:before {
  content: "\f240";
}
.fa-battery-3:before,
.fa-battery-three-quarters:before {
  content: "\f241";
}
.fa-battery-2:before,
.fa-battery-half:before {
  content: "\f242";
}
.fa-battery-1:before,
.fa-battery-quarter:before {
  content: "\f243";
}
.fa-battery-0:before,
.fa-battery-empty:before {
  content: "\f244";
}
.fa-mouse-pointer:before {
  content: "\f245";
}
.fa-i-cursor:before {
  content: "\f246";
}
.fa-object-group:before {
  content: "\f247";
}
.fa-object-ungroup:before {
  content: "\f248";
}
.fa-sticky-note:before {
  content: "\f249";
}
.fa-sticky-note-o:before {
  content: "\f24a";
}
.fa-cc-jcb:before {
  content: "\f24b";
}
.fa-cc-diners-club:before {
  content: "\f24c";
}
.fa-clone:before {
  content: "\f24d";
}
.fa-balance-scale:before {
  content: "\f24e";
}
.fa-hourglass-o:before {
  content: "\f250";
}
.fa-hourglass-1:before,
.fa-hourglass-start:before {
  content: "\f251";
}
.fa-hourglass-2:before,
.fa-hourglass-half:before {
  content: "\f252";
}
.fa-hourglass-3:before,
.fa-hourglass-end:before {
  content: "\f253";
}
.fa-hourglass:before {
  content: "\f254";
}
.fa-hand-grab-o:before,
.fa-hand-rock-o:before {
  content: "\f255";
}
.fa-hand-stop-o:before,
.fa-hand-paper-o:before {
  content: "\f256";
}
.fa-hand-scissors-o:before {
  content: "\f257";
}
.fa-hand-lizard-o:before {
  content: "\f258";
}
.fa-hand-spock-o:before {
  content: "\f259";
}
.fa-hand-pointer-o:before {
  content: "\f25a";
}
.fa-hand-peace-o:before {
  content: "\f25b";
}
.fa-trademark:before {
  content: "\f25c";
}
.fa-registered:before {
  content: "\f25d";
}
.fa-creative-commons:before {
  content: "\f25e";
}
.fa-gg:before {
  content: "\f260";
}
.fa-gg-circle:before {
  content: "\f261";
}
.fa-tripadvisor:before {
  content: "\f262";
}
.fa-odnoklassniki:before {
  content: "\f263";
}
.fa-odnoklassniki-square:before {
  content: "\f264";
}
.fa-get-pocket:before {
  content: "\f265";
}
.fa-wikipedia-w:before {
  content: "\f266";
}
.fa-safari:before {
  content: "\f267";
}
.fa-chrome:before {
  content: "\f268";
}
.fa-firefox:before {
  content: "\f269";
}
.fa-opera:before {
  content: "\f26a";
}
.fa-internet-explorer:before {
  content: "\f26b";
}
.fa-tv:before,
.fa-television:before {
  content: "\f26c";
}
.fa-contao:before {
  content: "\f26d";
}
.fa-500px:before {
  content: "\f26e";
}
.fa-amazon:before {
  content: "\f270";
}
.fa-calendar-plus-o:before {
  content: "\f271";
}
.fa-calendar-minus-o:before {
  content: "\f272";
}
.fa-calendar-times-o:before {
  content: "\f273";
}
.fa-calendar-check-o:before {
  content: "\f274";
}
.fa-industry:before {
  content: "\f275";
}
.fa-map-pin:before {
  content: "\f276";
}
.fa-map-signs:before {
  content: "\f277";
}
.fa-map-o:before {
  content: "\f278";
}
.fa-map:before {
  content: "\f279";
}
.fa-commenting:before {
  content: "\f27a";
}
.fa-commenting-o:before {
  content: "\f27b";
}
.fa-houzz:before {
  content: "\f27c";
}
.fa-vimeo:before {
  content: "\f27d";
}
.fa-black-tie:before {
  content: "\f27e";
}
.fa-fonticons:before {
  content: "\f280";
}
.fa-reddit-alien:before {
  content: "\f281";
}
.fa-edge:before {
  content: "\f282";
}
.fa-credit-card-alt:before {
  content: "\f283";
}
.fa-codiepie:before {
  content: "\f284";
}
.fa-modx:before {
  content: "\f285";
}
.fa-fort-awesome:before {
  content: "\f286";
}
.fa-usb:before {
  content: "\f287";
}
.fa-product-hunt:before {
  content: "\f288";
}
.fa-mixcloud:before {
  content: "\f289";
}
.fa-scribd:before {
  content: "\f28a";
}
.fa-pause-circle:before {
  content: "\f28b";
}
.fa-pause-circle-o:before {
  content: "\f28c";
}
.fa-stop-circle:before {
  content: "\f28d";
}
.fa-stop-circle-o:before {
  content: "\f28e";
}
.fa-shopping-bag:before {
  content: "\f290";
}
.fa-shopping-basket:before {
  content: "\f291";
}
.fa-hashtag:before {
  content: "\f292";
}
.fa-bluetooth:before {
  content: "\f293";
}
.fa-bluetooth-b:before {
  content: "\f294";
}
.fa-percent:before {
  content: "\f295";
}
.fa-gitlab:before {
  content: "\f296";
}
.fa-wpbeginner:before {
  content: "\f297";
}
.fa-wpforms:before {
  content: "\f298";
}
.fa-envira:before {
  content: "\f299";
}
.fa-universal-access:before {
  content: "\f29a";
}
.fa-wheelchair-alt:before {
  content: "\f29b";
}
.fa-question-circle-o:before {
  content: "\f29c";
}
.fa-blind:before {
  content: "\f29d";
}
.fa-audio-description:before {
  content: "\f29e";
}
.fa-volume-control-phone:before {
  content: "\f2a0";
}
.fa-braille:before {
  content: "\f2a1";
}
.fa-assistive-listening-systems:before {
  content: "\f2a2";
}
.fa-asl-interpreting:before,
.fa-american-sign-language-interpreting:before {
  content: "\f2a3";
}
.fa-deafness:before,
.fa-hard-of-hearing:before,
.fa-deaf:before {
  content: "\f2a4";
}
.fa-glide:before {
  content: "\f2a5";
}
.fa-glide-g:before {
  content: "\f2a6";
}
.fa-signing:before,
.fa-sign-language:before {
  content: "\f2a7";
}
.fa-low-vision:before {
  content: "\f2a8";
}
.fa-viadeo:before {
  content: "\f2a9";
}
.fa-viadeo-square:before {
  content: "\f2aa";
}
.fa-snapchat:before {
  content: "\f2ab";
}
.fa-snapchat-ghost:before {
  content: "\f2ac";
}
.fa-snapchat-square:before {
  content: "\f2ad";
}
.fa-pied-piper:before {
  content: "\f2ae";
}
.fa-first-order:before {
  content: "\f2b0";
}
.fa-yoast:before {
  content: "\f2b1";
}
.fa-themeisle:before {
  content: "\f2b2";
}
.fa-google-plus-circle:before,
.fa-google-plus-official:before {
  content: "\f2b3";
}
.fa-fa:before,
.fa-font-awesome:before {
  content: "\f2b4";
}
.fa-handshake-o:before {
  content: "\f2b5";
}
.fa-envelope-open:before {
  content: "\f2b6";
}
.fa-envelope-open-o:before {
  content: "\f2b7";
}
.fa-linode:before {
  content: "\f2b8";
}
.fa-address-book:before {
  content: "\f2b9";
}
.fa-address-book-o:before {
  content: "\f2ba";
}
.fa-vcard:before,
.fa-address-card:before {
  content: "\f2bb";
}
.fa-vcard-o:before,
.fa-address-card-o:before {
  content: "\f2bc";
}
.fa-user-circle:before {
  content: "\f2bd";
}
.fa-user-circle-o:before {
  content: "\f2be";
}
.fa-user-o:before {
  content: "\f2c0";
}
.fa-id-badge:before {
  content: "\f2c1";
}
.fa-drivers-license:before,
.fa-id-card:before {
  content: "\f2c2";
}
.fa-drivers-license-o:before,
.fa-id-card-o:before {
  content: "\f2c3";
}
.fa-quora:before {
  content: "\f2c4";
}
.fa-free-code-camp:before {
  content: "\f2c5";
}
.fa-telegram:before {
  content: "\f2c6";
}
.fa-thermometer-4:before,
.fa-thermometer:before,
.fa-thermometer-full:before {
  content: "\f2c7";
}
.fa-thermometer-3:before,
.fa-thermometer-three-quarters:before {
  content: "\f2c8";
}
.fa-thermometer-2:before,
.fa-thermometer-half:before {
  content: "\f2c9";
}
.fa-thermometer-1:before,
.fa-thermometer-quarter:before {
  content: "\f2ca";
}
.fa-thermometer-0:before,
.fa-thermometer-empty:before {
  content: "\f2cb";
}
.fa-shower:before {
  content: "\f2cc";
}
.fa-bathtub:before,
.fa-s15:before,
.fa-bath:before {
  content: "\f2cd";
}
.fa-podcast:before {
  content: "\f2ce";
}
.fa-window-maximize:before {
  content: "\f2d0";
}
.fa-window-minimize:before {
  content: "\f2d1";
}
.fa-window-restore:before {
  content: "\f2d2";
}
.fa-times-rectangle:before,
.fa-window-close:before {
  content: "\f2d3";
}
.fa-times-rectangle-o:before,
.fa-window-close-o:before {
  content: "\f2d4";
}
.fa-bandcamp:before {
  content: "\f2d5";
}
.fa-grav:before {
  content: "\f2d6";
}
.fa-etsy:before {
  content: "\f2d7";
}
.fa-imdb:before {
  content: "\f2d8";
}
.fa-ravelry:before {
  content: "\f2d9";
}
.fa-eercast:before {
  content: "\f2da";
}
.fa-microchip:before {
  content: "\f2db";
}
.fa-snowflake-o:before {
  content: "\f2dc";
}
.fa-superpowers:before {
  content: "\f2dd";
}
.fa-wpexplorer:before {
  content: "\f2de";
}
.fa-meetup:before {
  content: "\f2e0";
}
.sr-only {
  position: absolute;
  width: 1px;
  height: 1px;
  padding: 0;
  margin: -1px;
  overflow: hidden;
  clip: rect(0, 0, 0, 0);
  border: 0;
}
.sr-only-focusable:active,
.sr-only-focusable:focus {
  position: static;
  width: auto;
  height: auto;
  margin: 0;
  overflow: visible;
  clip: auto;
}
.sr-only-focusable:active,
.sr-only-focusable:focus {
  position: static;
  width: auto;
  height: auto;
  margin: 0;
  overflow: visible;
  clip: auto;
}
/*!
*
* IPython base
*
*/
.modal.fade .modal-dialog {
  -webkit-transform: translate(0, 0);
  -ms-transform: translate(0, 0);
  -o-transform: translate(0, 0);
  transform: translate(0, 0);
}
code {
  color: #000;
}
pre {
  font-size: inherit;
  line-height: inherit;
}
label {
  font-weight: normal;
}
/* Make the page background atleast 100% the height of the view port */
/* Make the page itself atleast 70% the height of the view port */
.border-box-sizing {
  box-sizing: border-box;
  -moz-box-sizing: border-box;
  -webkit-box-sizing: border-box;
}
.corner-all {
  border-radius: 2px;
}
.no-padding {
  padding: 0px;
}
/* Flexible box model classes */
/* Taken from Alex Russell http://infrequently.org/2009/08/css-3-progress/ */
/* This file is a compatability layer.  It allows the usage of flexible box 
model layouts accross multiple browsers, including older browsers.  The newest,
universal implementation of the flexible box model is used when available (see
`Modern browsers` comments below).  Browsers that are known to implement this 
new spec completely include:

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

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

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

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


<div class="reveal">
<div class="slides">
<section><section>
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</div><div class="inner_cell">
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<h1 id="Concolic-Fuzzing">Concolic Fuzzing<a class="anchor-link" href="#Concolic-Fuzzing">&#182;</a></h1><p>We have previously seen how one can use dynamic taints to produce more intelligent test cases than simply looking for program crashes. We have also seen how one can use the taints to update the grammar, and hence focus more on the dangerous methods.</p>
<p>While taints are helpful, uninterpreted strings is only one of the attack vectors. Can we say anything more about the properties of variables at any point in the execution? For example, can we say for sure that a function will always receive the buffers with the correct length? Concolic execution offers a solution.</p>
<p>The idea of <em>concolic execution</em> over a function is as follows: We start with a sample input for the function, and execute the function under trace. At each point the execution passes through a conditional, we save the conditional encountered in an in the form of relations between symbolic variables.
(A <em>symbolic variable</em> can be thought of as a sort of placeholder for the real variable, sort of like the x in solving for x in Algebra. The symbolic variables can be used to specify relations without actually solving them.)</p>
<p>With concolic execution, one can collect the constraints that an execution path encounters, and use it to answer questions about the program behavior at any point we prefer along the program execution path. We can further use concolic execution to enhance fuzzing.</p>
<p>In this chapter, we explore in depth how to execute a Python function concolically, and how concolic execution can be used to enhance fuzzing.</p>

</div>
</div>
</div></section><section>
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<p><strong>Prerequisites</strong></p>
<ul>
<li>You should have read the <a href="Coverage.slides.html">chapter on coverage</a>.</li>
<li>You should have read the <a href="InformationFlow.slides.html">chapter on information flow</a>.</li>
<li>A familiarity with the basic idea of <a href="https://en.wikipedia.org/wiki/Satisfiability_modulo_theories">SMT solvers</a> would be useful.</li>
</ul>

</div>
</div>
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<p>We first setup our infrastructure so that we can make use of previously defined functions.</p>

</div>
</div>
</div></div></section></section><section><section>
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<h2 id="Synopsis">Synopsis<a class="anchor-link" href="#Synopsis">&#182;</a></h2><!-- Automatically generated. Do not edit. -->

<p>To <a href="Importing.slides.html">use the code provided in this chapter</a>, write</p>
<div class="highlight"><pre><span></span><span class="o">&gt;&gt;&gt;</span> <span class="kn">from</span> <span class="nn">fuzzingbook.ConcolicFuzzer</span> <span class="kn">import</span> <span class="o">&lt;</span><span class="n">identifier</span><span class="o">&gt;</span>
</pre></div>
<p>and then make use of the following features.</p>
<p>This chapter defines two main classes: <code>SimpleConcolicFuzzer</code> and <code>ConcolicGrammarFuzzer</code>. The <code>SimpleConcolicFuzzer</code> first uses a sample input to collect predicates encountered. The fuzzer then negates random predicates to generate new input constraints. These, when solved, produce inputs that explore paths that are close to the original path. It can be used as follows.</p>
<p>The <code>cgi_decode()</code> function <a href="Coverage.slides.html">from the chapter on coverage</a> is the subject program.</p>
<div class="highlight"><pre><span></span><span class="o">&gt;&gt;&gt;</span> <span class="kn">from</span> <span class="nn">Coverage</span> <span class="kn">import</span> <span class="n">cgi_decode</span>
</pre></div>
<p>We first obtain the constraints using <code>ConcolicTracer</code>.</p>
<div class="highlight"><pre><span></span><span class="o">&gt;&gt;&gt;</span> <span class="k">with</span> <span class="n">ConcolicTracer</span><span class="p">()</span> <span class="k">as</span> <span class="n">_</span><span class="p">:</span>
<span class="o">&gt;&gt;&gt;</span>     <span class="n">_</span><span class="p">[</span><span class="n">cgi_decode</span><span class="p">](</span><span class="s1">&#39;abcd&#39;</span><span class="p">)</span>
</pre></div>
<p>These constraints are added to the concolic fuzzer as follows:</p>
<div class="highlight"><pre><span></span><span class="o">&gt;&gt;&gt;</span> <span class="n">scf</span> <span class="o">=</span> <span class="n">SimpleConcolicFuzzer</span><span class="p">()</span>
<span class="o">&gt;&gt;&gt;</span> <span class="n">scf</span><span class="o">.</span><span class="n">add_trace</span><span class="p">(</span><span class="n">_</span><span class="p">)</span>
</pre></div>
<p>The concolic fuzzer then uses the constraints added to guide its fuzzing as follows:</p>
<div class="highlight"><pre><span></span><span class="o">&gt;&gt;&gt;</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">10</span><span class="p">):</span>
<span class="o">&gt;&gt;&gt;</span>     <span class="n">v</span> <span class="o">=</span> <span class="n">scf</span><span class="o">.</span><span class="n">fuzz</span><span class="p">()</span>
<span class="o">&gt;&gt;&gt;</span>     <span class="k">if</span> <span class="n">v</span> <span class="ow">is</span> <span class="bp">None</span><span class="p">:</span>
<span class="o">&gt;&gt;&gt;</span>         <span class="k">break</span>
<span class="o">&gt;&gt;&gt;</span>     <span class="k">print</span><span class="p">(</span><span class="n">v</span><span class="p">)</span>
<span class="o">%</span>\<span class="n">x00</span>
\<span class="n">x00</span>\<span class="n">x00</span><span class="o">+</span>\<span class="n">x00</span>
\<span class="n">x00</span>\<span class="n">x00</span><span class="o">+</span>\<span class="n">x04</span>
\<span class="n">x00</span>\<span class="n">x00</span><span class="o">+</span>\<span class="n">x02</span>
\<span class="n">x00</span>\<span class="n">x00</span>\<span class="n">x00</span><span class="o">+</span>\<span class="n">x00</span>
\<span class="n">x00</span><span class="o">+</span>\<span class="n">x00</span>
\<span class="n">x00</span>\<span class="n">x00</span><span class="o">+</span><span class="err">@</span>
\<span class="n">x00</span><span class="o">+</span> 
\<span class="n">x00</span><span class="o">%</span>\<span class="n">x00</span>
\<span class="n">x00</span><span class="o">+</span>\<span class="n">x08</span>
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<p>The <code>SimpleConcolicFuzzer</code> simply explores all paths near the original path traversed by the sample input. It does not use any kind of feedback from fuzzing.
The <code>ConcolicGrammarFuzzer</code> on the other hand, can collect feedback from the subject under fuzzing, and lift some of the constraints encountered to the grammar, enabling deeper fuzzing. It is used as follows:</p>
<div class="highlight"><pre><span></span><span class="o">&gt;&gt;&gt;</span> <span class="kn">from</span> <span class="nn">InformationFlow</span> <span class="kn">import</span> <span class="n">INVENTORY_GRAMMAR</span><span class="p">,</span> <span class="n">SQLException</span>
<span class="o">&gt;&gt;&gt;</span> <span class="n">cgf</span> <span class="o">=</span> <span class="n">ConcolicGrammarFuzzer</span><span class="p">(</span><span class="n">INVENTORY_GRAMMAR</span><span class="p">)</span>
<span class="o">&gt;&gt;&gt;</span> <span class="n">cgf</span><span class="o">.</span><span class="n">prune_tokens</span><span class="p">(</span><span class="n">prune_tokens</span><span class="p">)</span>
<span class="o">&gt;&gt;&gt;</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">10</span><span class="p">):</span>
<span class="o">&gt;&gt;&gt;</span>     <span class="n">query</span> <span class="o">=</span> <span class="n">cgf</span><span class="o">.</span><span class="n">fuzz</span><span class="p">()</span>
<span class="o">&gt;&gt;&gt;</span>     <span class="k">print</span><span class="p">(</span><span class="n">query</span><span class="p">)</span>
<span class="o">&gt;&gt;&gt;</span>     <span class="k">with</span> <span class="n">ConcolicTracer</span><span class="p">()</span> <span class="k">as</span> <span class="n">_</span><span class="p">:</span>
<span class="o">&gt;&gt;&gt;</span>         <span class="k">with</span> <span class="n">ExpectError</span><span class="p">():</span>
<span class="o">&gt;&gt;&gt;</span>             <span class="k">try</span><span class="p">:</span>
<span class="o">&gt;&gt;&gt;</span>                 <span class="n">res</span> <span class="o">=</span> <span class="n">_</span><span class="p">[</span><span class="n">db_select</span><span class="p">](</span><span class="n">query</span><span class="p">)</span>
<span class="o">&gt;&gt;&gt;</span>                 <span class="k">print</span><span class="p">(</span><span class="nb">repr</span><span class="p">(</span><span class="n">res</span><span class="p">))</span>
<span class="o">&gt;&gt;&gt;</span>             <span class="k">except</span> <span class="n">SQLException</span> <span class="k">as</span> <span class="n">e</span><span class="p">:</span>
<span class="o">&gt;&gt;&gt;</span>                 <span class="k">print</span><span class="p">(</span><span class="n">e</span><span class="p">)</span>
<span class="o">&gt;&gt;&gt;</span>         <span class="n">cgf</span><span class="o">.</span><span class="n">update_grammar</span><span class="p">(</span><span class="n">_</span><span class="p">)</span>
<span class="o">&gt;&gt;&gt;</span>         <span class="k">print</span><span class="p">()</span>
<span class="n">update</span> <span class="n">NK5f</span> <span class="nb">set</span> <span class="n">L</span><span class="o">=</span><span class="n">D</span><span class="p">,</span><span class="n">o</span><span class="o">=</span><span class="n">G</span><span class="p">,</span><span class="n">q</span><span class="o">=</span><span class="n">X</span> <span class="n">where</span> <span class="n">A</span><span class="o">!=</span><span class="n">S</span>
<span class="n">Table</span> <span class="p">(</span><span class="s1">&#39;NK5f&#39;</span><span class="p">)</span> <span class="n">was</span> <span class="ow">not</span> <span class="n">found</span>

<span class="n">update</span> <span class="n">vehicles</span> <span class="nb">set</span> <span class="n">V9</span><span class="o">=</span><span class="n">B</span><span class="p">,</span><span class="n">y</span><span class="o">=</span><span class="n">r</span><span class="p">,</span><span class="n">E</span><span class="o">=</span><span class="n">E</span> <span class="n">where</span> <span class="n">r</span><span class="p">(</span><span class="n">U</span><span class="p">)</span><span class="o">/</span><span class="n">x</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="o">&gt;</span><span class="n">b</span>
<span class="n">Column</span> <span class="p">(</span><span class="s1">&#39;V9&#39;</span><span class="p">)</span> <span class="n">was</span> <span class="ow">not</span> <span class="n">found</span>

<span class="n">insert</span> <span class="n">into</span> <span class="n">V6S</span> <span class="p">(</span><span class="n">V</span><span class="p">,</span><span class="n">R2</span><span class="p">,</span><span class="n">O</span><span class="p">)</span> <span class="n">values</span> <span class="p">(</span><span class="s1">&#39;2/&#39;</span><span class="p">,</span><span class="s1">&#39;@&#39;</span><span class="p">)</span>
<span class="n">Table</span> <span class="p">(</span><span class="s1">&#39;V6S&#39;</span><span class="p">)</span> <span class="n">was</span> <span class="ow">not</span> <span class="n">found</span>

<span class="n">update</span> <span class="n">months</span> <span class="nb">set</span> <span class="n">q</span><span class="o">=</span><span class="n">J1</span><span class="p">,</span><span class="n">Y</span><span class="o">=</span><span class="n">n</span><span class="p">,</span><span class="n">r</span><span class="o">=</span><span class="n">X</span> <span class="n">where</span> <span class="n">o</span><span class="o">-</span><span class="n">S</span><span class="o">*</span><span class="n">B</span><span class="o">!=</span><span class="p">(</span><span class="n">u</span><span class="o">!=</span><span class="n">q</span><span class="p">)</span>
<span class="n">Column</span> <span class="p">(</span><span class="s1">&#39;q&#39;</span><span class="p">)</span> <span class="n">was</span> <span class="ow">not</span> <span class="n">found</span>

<span class="n">select</span> <span class="n">e</span><span class="o">-</span><span class="n">e</span><span class="o">/</span><span class="n">B</span><span class="o">&gt;</span><span class="n">Z</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="o">-</span><span class="p">(</span><span class="n">_</span><span class="p">)</span> <span class="kn">from</span> <span class="nn">vehicles</span> <span class="nn">where</span> <span class="mf">59.2</span><span class="o">!=</span><span class="n">S</span><span class="o">==</span><span class="n">C</span>
<span class="n">Invalid</span> <span class="n">WHERE</span> <span class="p">(</span><span class="s1">&#39;(59.2!=S==C)&#39;</span><span class="p">)</span>

<span class="n">delete</span> <span class="kn">from</span> <span class="nn">months</span> <span class="nn">where</span> <span class="p">(</span><span class="n">M</span><span class="p">)</span><span class="o">*</span><span class="n">I</span><span class="o">&lt;</span><span class="n">p</span><span class="o">+</span><span class="n">e</span><span class="p">(</span><span class="n">S</span><span class="p">)</span><span class="o">-</span><span class="n">R</span><span class="o">*</span><span class="n">O</span><span class="p">(</span><span class="n">_</span><span class="p">)</span><span class="o">*</span><span class="n">p</span><span class="p">(</span><span class="mi">8</span><span class="p">,</span><span class="n">u</span><span class="p">)</span>
<span class="n">Invalid</span> <span class="n">WHERE</span> <span class="p">(</span><span class="s1">&#39;(M)*I&lt;p+e(S)-R*O(_)*p(8,u)&#39;</span><span class="p">)</span>

<span class="n">insert</span> <span class="n">into</span> <span class="n">months</span> <span class="p">(</span><span class="n">CRl</span><span class="p">,</span><span class="n">i</span><span class="p">,</span><span class="n">AW5</span><span class="p">,</span><span class="n">_j</span><span class="p">)</span> <span class="n">values</span> <span class="p">(</span><span class="s1">&#39;6&#39;</span><span class="p">)</span>
<span class="n">Column</span> <span class="p">(</span><span class="s1">&#39;CRl&#39;</span><span class="p">)</span> <span class="n">was</span> <span class="ow">not</span> <span class="n">found</span>

<span class="n">select</span> <span class="n">a</span><span class="p">(</span><span class="n">A</span><span class="p">),</span><span class="n">J</span> <span class="kn">from</span> <span class="nn">K8z</span> <span class="nn">where</span> <span class="nn">p</span><span class="o">-</span><span class="n">f</span><span class="o">-</span><span class="n">i</span><span class="o">&lt;</span><span class="n">H</span>
<span class="n">Table</span> <span class="p">(</span><span class="s1">&#39;K8z&#39;</span><span class="p">)</span> <span class="n">was</span> <span class="ow">not</span> <span class="n">found</span>

<span class="n">delete</span> <span class="kn">from</span> <span class="nn">vehicles</span> <span class="nn">where</span> <span class="nn">h</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span><span class="n">a</span><span class="p">)</span><span class="o">&gt;</span><span class="p">((</span><span class="n">Sg90</span><span class="p">))</span><span class="o">+</span><span class="n">M5</span><span class="p">((</span><span class="n">az1</span><span class="p">(</span><span class="n">p</span><span class="p">)</span><span class="o">*</span><span class="n">r</span><span class="o">/</span><span class="n">W</span><span class="o">/</span><span class="n">V</span><span class="o">+</span><span class="n">b9</span><span class="p">(</span><span class="n">H</span><span class="p">)))</span>
<span class="n">Invalid</span> <span class="n">WHERE</span> <span class="p">(</span><span class="s1">&#39;h(2,a)&gt;((Sg90))+M5((az1(p)*r/W/V+b9(H)))&#39;</span><span class="p">)</span>

<span class="n">select</span> <span class="mf">9.7</span> <span class="kn">from</span> <span class="nn">months</span>
<span class="p">[</span><span class="mf">9.7</span><span class="p">,</span> <span class="mf">9.7</span><span class="p">,</span> <span class="mf">9.7</span><span class="p">,</span> <span class="mf">9.7</span><span class="p">,</span> <span class="mf">9.7</span><span class="p">,</span> <span class="mf">9.7</span><span class="p">,</span> <span class="mf">9.7</span><span class="p">,</span> <span class="mf">9.7</span><span class="p">,</span> <span class="mf">9.7</span><span class="p">,</span> <span class="mf">9.7</span><span class="p">,</span> <span class="mf">9.7</span><span class="p">,</span> <span class="mf">9.7</span><span class="p">]</span>
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<h2 id="Tracking-Constraints">Tracking Constraints<a class="anchor-link" href="#Tracking-Constraints">&#182;</a></h2>
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<p>In the chapter on <a href="InformationFlow">information flow</a>, we have seen how dynamic taints can be used to direct fuzzing by indicating which part of input reached interesting places. However, dynamic taint tracking is limited in the information that it can propagate. For example, we might want to explore what happens when certain properties of the input changes.</p>

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<p>For example, say we have a function <code>factorial()</code> that returns the <em>factorial value</em> of its input.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">def</span> <span class="nf">factorial</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
    <span class="k">if</span> <span class="n">n</span> <span class="o">&lt;</span> <span class="mi">0</span><span class="p">:</span>
        <span class="k">return</span> <span class="kc">None</span>
    <span class="k">if</span> <span class="n">n</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
        <span class="k">return</span> <span class="mi">1</span>
    <span class="k">if</span> <span class="n">n</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
        <span class="k">return</span> <span class="mi">1</span>
    <span class="n">v</span> <span class="o">=</span> <span class="mi">1</span>
    <span class="k">while</span> <span class="n">n</span> <span class="o">!=</span> <span class="mi">0</span><span class="p">:</span>
        <span class="n">v</span> <span class="o">=</span> <span class="n">v</span> <span class="o">*</span> <span class="n">n</span>
        <span class="n">n</span> <span class="o">=</span> <span class="n">n</span> <span class="o">-</span> <span class="mi">1</span>
    <span class="k">return</span> <span class="n">v</span>
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<p>We exercise the function with a value of <code>5</code>.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">factorial</span><span class="p">(</span><span class="mi">5</span><span class="p">)</span>
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<pre>120</pre>
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<p>Is this sufficient to explore all the features of the function? How do we know? One way to verify that we have explored all features is to look at the coverage obtained. First we need to extend the <code>Coverage</code> class from the <a href="Coverage.slides.html">chapter on coverage</a> to provide us with coverage arcs.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">class</span> <span class="nc">ArcCoverage</span><span class="p">(</span><span class="n">Coverage</span><span class="p">):</span>
    <span class="k">def</span> <span class="nf">traceit</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">frame</span><span class="p">,</span> <span class="n">event</span><span class="p">,</span> <span class="n">args</span><span class="p">):</span>
        <span class="k">if</span> <span class="n">event</span> <span class="o">!=</span> <span class="s1">&#39;return&#39;</span><span class="p">:</span>
            <span class="n">f</span> <span class="o">=</span> <span class="n">inspect</span><span class="o">.</span><span class="n">getframeinfo</span><span class="p">(</span><span class="n">frame</span><span class="p">)</span>
            <span class="bp">self</span><span class="o">.</span><span class="n">_trace</span><span class="o">.</span><span class="n">append</span><span class="p">((</span><span class="n">f</span><span class="o">.</span><span class="n">function</span><span class="p">,</span> <span class="n">f</span><span class="o">.</span><span class="n">lineno</span><span class="p">))</span>
        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">traceit</span>

    <span class="k">def</span> <span class="nf">arcs</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
        <span class="n">t</span> <span class="o">=</span> <span class="p">[</span><span class="n">i</span> <span class="k">for</span> <span class="n">f</span><span class="p">,</span> <span class="n">i</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">_trace</span><span class="p">]</span>
        <span class="k">return</span> <span class="nb">list</span><span class="p">(</span><span class="nb">zip</span><span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="n">t</span><span class="p">[</span><span class="mi">1</span><span class="p">:]))</span>
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<p>Next, we use the <code>Tracer</code> to obtain the coverage arcs.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">with</span> <span class="n">ArcCoverage</span><span class="p">()</span> <span class="k">as</span> <span class="n">cov</span><span class="p">:</span>
    <span class="n">factorial</span><span class="p">(</span><span class="mi">5</span><span class="p">)</span>
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<p>We can now use the coverage arcs to visualize the coverage obtained.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">Source</span><span class="p">(</span><span class="n">to_graph</span><span class="p">(</span><span class="n">gen_cfg</span><span class="p">(</span><span class="n">inspect</span><span class="o">.</span><span class="n">getsource</span><span class="p">(</span><span class="n">factorial</span><span class="p">)),</span> <span class="n">arcs</span><span class="o">=</span><span class="n">cov</span><span class="o">.</span><span class="n">arcs</span><span class="p">()))</span>
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<p>We see that the path <code>[1, 2, 4, 6, 8, 9, 10, 11, 12]</code> is covered (green) but sub-paths such as  <code>[2, 3]</code>,  <code>[4, 5]</code> and <code>[6, 7]</code> are unexplored (red). What we need is the ability to generate inputs such that the <code>True</code> branch is taken at <code>2</code>. How do we do that?</p>

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<h2 id="Concolic-Execution">Concolic Execution<a class="anchor-link" href="#Concolic-Execution">&#182;</a></h2><p>One way is to look at the execution path being taken, and collect the conditional constraints that the path encounters. Then we can try to produce inputs that lead us to taking the non-traversed path.</p>

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<p>First, let us step through the function.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">lines</span> <span class="o">=</span> <span class="p">[</span><span class="n">i</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">cov</span><span class="o">.</span><span class="n">_trace</span> <span class="k">if</span> <span class="n">i</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">==</span> <span class="s1">&#39;factorial&#39;</span><span class="p">]</span>
<span class="n">src</span> <span class="o">=</span> <span class="p">{</span><span class="n">i</span> <span class="o">+</span> <span class="mi">1</span><span class="p">:</span> <span class="n">s</span> <span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">s</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span>
    <span class="n">inspect</span><span class="o">.</span><span class="n">getsource</span><span class="p">(</span><span class="n">factorial</span><span class="p">)</span><span class="o">.</span><span class="n">split</span><span class="p">(</span><span class="s1">&#39;</span><span class="se">\n</span><span class="s1">&#39;</span><span class="p">))}</span>
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<li>The line (1) is simply the entry point of the function. We know that the input is <code>n</code>, which is an integer.</li>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">src</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span>
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<pre>&#39;def factorial(n):&#39;</pre>
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<li>The line (2) is a predicate <code>n &lt; 0</code>. Since the next line taken is line (4), we know that at this point in the execution path, the predicate was <code>true</code>.</li>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">src</span><span class="p">[</span><span class="mi">2</span><span class="p">],</span> <span class="n">src</span><span class="p">[</span><span class="mi">3</span><span class="p">],</span> <span class="n">src</span><span class="p">[</span><span class="mi">4</span><span class="p">]</span>
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<pre>(&#39;    if n &lt; 0:&#39;, &#39;        return None&#39;, &#39;    if n == 0:&#39;)</pre>
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<p>We notice that this is one of the predicates where the <code>true</code> branch was not taken. How do we generate a value that takes the <code>true</code> branch here? One way is to use symbolic variables to represent the input, encode the constraint, and use an <em>SMT Solver</em> to solve the negation of the constraint.</p>

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<p>As we mentioned in the introduction to the chapter, a symbolic variable can be thought of as a sort of placeholder for the real variable, sort of like the <code>x</code> in solving for <code>x</code> in Algebra. These variables can be used to encode constraints placed on the variables in the program. We identify what constraints the variable is supposed to obey, and finally produce a value that obeys all constraints imposed.</p>

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<h2 id="SMT-Solvers">SMT Solvers<a class="anchor-link" href="#SMT-Solvers">&#182;</a></h2>
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<p>To solve these constraints, one can use a <em>Satisfiability Modulo Theories</em> (SMT) solver. An SMT solver is built on top of a <em>SATISFIABILITY</em> (SAT) solver. A SAT solver is be used to check whether boolean formulas in first order logic (e.g <code>(a | b ) &amp; (~a | ~b)</code>) can be satisfied using any assignments for the variables (e.g <code>a = true, b = false</code>). An SMT solver extends these SAT solvers to specific background theories -- for example, <em>theory of integers</em>, or <em>theory of strings</em>. That is, given a string constraint expressed as a formula with string variables (e.g <code>h + t == 'hello,world'</code>), an SMT solver that understands <em>theory of strings</em> can be used to check if that constraint can be satisfied, and if satisfiable, provide an instantiation of concrete values for the variables used in the formula (e.g <code>h = 'hello,', t = 'world'</code>).</p>
<p>We use the SMT solver, <code>Z3</code> in this chapter.</p>

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<p>To ensure that the string constraints we use in this chapter are successfully evaluated, we need to specify the <code>z3str3</code> solver. Further, we set the timeout for Z3 computations to to 30 seconds.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">assert</span> <span class="n">z3</span><span class="o">.</span><span class="n">get_version</span><span class="p">()</span> <span class="o">==</span> <span class="p">(</span><span class="mi">4</span><span class="p">,</span> <span class="mi">8</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span>
<span class="n">z3</span><span class="o">.</span><span class="n">set_option</span><span class="p">(</span><span class="s1">&#39;smt.string_solver&#39;</span><span class="p">,</span> <span class="s1">&#39;z3str3&#39;</span><span class="p">)</span>
<span class="n">z3</span><span class="o">.</span><span class="n">set_option</span><span class="p">(</span><span class="s1">&#39;timeout&#39;</span><span class="p">,</span> <span class="mi">30</span> <span class="o">*</span> <span class="mi">1000</span><span class="p">)</span>  <span class="c1"># milliseconds</span>
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<p>Encoding the constraint requires declaring a corresponding symbolic variable to the input <code>n</code>.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">zn</span> <span class="o">=</span> <span class="n">z3</span><span class="o">.</span><span class="n">Int</span><span class="p">(</span><span class="s1">&#39;n&#39;</span><span class="p">)</span>
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<p>Remember the constraint <code>(n &lt; 0)</code> from line 2 in <code>factorial()</code>? We can now encode the constraint as follows.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">zn</span> <span class="o">&lt;</span> <span class="mi">0</span>
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<pre>n &lt; 0</pre>
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<p>We previously traced <code>factorial(5)</code>. We saw that with input <code>5</code>, the execution took the <code>else</code> branch on the predicate <code>n &lt; 0</code>. We can express this observation as follows.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">z3</span><span class="o">.</span><span class="n">Not</span><span class="p">(</span><span class="n">zn</span> <span class="o">&lt;</span> <span class="mi">0</span><span class="p">)</span>
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<pre>Not(n &lt; 0)</pre>
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<p>The <code>z3.solve()</code> method can also be used to check if the constraints are satisfiable, and if it is, provide an values for variables such that the constraints are satisfied. For example, we can ask z3 for an input that will take the <code>else</code> branch as follows:</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">z3</span><span class="o">.</span><span class="n">solve</span><span class="p">(</span><span class="n">z3</span><span class="o">.</span><span class="n">Not</span><span class="p">(</span><span class="n">zn</span> <span class="o">&lt;</span> <span class="mi">0</span><span class="p">))</span>
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<pre>[n = 0]
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<p>This is <em>a solution</em> (albeit a trivial one). SMT solvers can be used to solve much harder problems. For example, here is how one can solve a quadratic equation.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">x</span> <span class="o">=</span> <span class="n">z3</span><span class="o">.</span><span class="n">Real</span><span class="p">(</span><span class="s1">&#39;x&#39;</span><span class="p">)</span>
<span class="n">eqn</span> <span class="o">=</span> <span class="p">(</span><span class="mi">2</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="mi">11</span> <span class="o">*</span> <span class="n">x</span> <span class="o">+</span> <span class="mi">5</span> <span class="o">==</span> <span class="mi">0</span><span class="p">)</span>
<span class="n">z3</span><span class="o">.</span><span class="n">solve</span><span class="p">(</span><span class="n">eqn</span><span class="p">)</span>
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<pre>[x = 5]
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<p>Again, this is <em>one solution</em>. We can ask z3 to give us another solution as follows.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">z3</span><span class="o">.</span><span class="n">solve</span><span class="p">(</span><span class="n">x</span> <span class="o">!=</span> <span class="mi">5</span><span class="p">,</span> <span class="n">eqn</span><span class="p">)</span>
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<pre>[x = 1/2]
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<p>Indeed, both <code>x = 5</code> and <code>x = 1/2</code> are solutions to the quadratic equation $ 2x^2 -11x + 5 = 0 $</p>

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<p>Similarly, we can ask <em>Z3</em> for an input that satisfies the constraint encoded in line 2 of <code>factorial()</code> so that we take the <code>if</code> branch.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">z3</span><span class="o">.</span><span class="n">solve</span><span class="p">(</span><span class="n">zn</span> <span class="o">&lt;</span> <span class="mi">0</span><span class="p">)</span>
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<pre>[n = -1]
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<p>That is, if one uses <code>-1</code> as an input to <code>factorial()</code>, it is guaranteed to take the <code>if</code> branch in line 2 during execution.</p>

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<p>Let us try using that with our coverage. Here, the <code>-1</code> is the solution from above.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">with</span> <span class="n">cov</span> <span class="k">as</span> <span class="n">cov</span><span class="p">:</span>
    <span class="n">factorial</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">Source</span><span class="p">(</span><span class="n">to_graph</span><span class="p">(</span><span class="n">gen_cfg</span><span class="p">(</span><span class="n">inspect</span><span class="o">.</span><span class="n">getsource</span><span class="p">(</span><span class="n">factorial</span><span class="p">)),</span> <span class="n">arcs</span><span class="o">=</span><span class="n">cov</span><span class="o">.</span><span class="n">arcs</span><span class="p">()))</span>
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<title>12&#45;&gt;10</title>
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<p>Ok, so we have managed to cover a little more of the graph. Let us continue with our original input of <code>factorial(5)</code>:</p>
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<li>In line (4) we encounter a new predicate <code>n == 0</code>, for which we again took the false branch.</li>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">src</span><span class="p">[</span><span class="mi">4</span><span class="p">]</span>
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<pre>&#39;    if n == 0:&#39;</pre>
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<p>The predicates required to follow the path until this point is as follows.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">predicates</span> <span class="o">=</span> <span class="p">[</span><span class="n">z3</span><span class="o">.</span><span class="n">Not</span><span class="p">(</span><span class="n">zn</span> <span class="o">&lt;</span> <span class="mi">0</span><span class="p">),</span> <span class="n">z3</span><span class="o">.</span><span class="n">Not</span><span class="p">(</span><span class="n">zn</span> <span class="o">==</span> <span class="mi">0</span><span class="p">)]</span>
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<li>If we continue to line (6), we encounter another predicate, for which again, we took the <code>false</code> branch</li>
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<pre>&#39;    if n == 1:&#39;</pre>
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<p>The predicates encountered so far is as follows</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">predicates</span> <span class="o">=</span> <span class="p">[</span><span class="n">z3</span><span class="o">.</span><span class="n">Not</span><span class="p">(</span><span class="n">zn</span> <span class="o">&lt;</span> <span class="mi">0</span><span class="p">),</span> <span class="n">z3</span><span class="o">.</span><span class="n">Not</span><span class="p">(</span><span class="n">zn</span> <span class="o">==</span> <span class="mi">0</span><span class="p">),</span> <span class="n">z3</span><span class="o">.</span><span class="n">Not</span><span class="p">(</span><span class="n">zn</span> <span class="o">==</span> <span class="mi">1</span><span class="p">)]</span>
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<p>To take the branch at (6), we essentially have to obey the predicates until that point, but invert the last predicate.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">last</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">predicates</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span>
<span class="n">z3</span><span class="o">.</span><span class="n">solve</span><span class="p">(</span><span class="n">predicates</span><span class="p">[</span><span class="mi">0</span><span class="p">:</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">+</span> <span class="p">[</span><span class="n">z3</span><span class="o">.</span><span class="n">Not</span><span class="p">(</span><span class="n">predicates</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">])])</span>
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<pre>[n = 1]
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<p>What we are doing here is tracing the execution corresponding to a particular input <code>factorial(5)</code>, using concrete values, and along with it, keeping <em>symbolic shadow variables</em> that enable us to capture the constraints. As we mentioned in the introduction, this particular method of execution where one tracks concrete  execution using symbolic variables is called <em>Concolic Execution</em>.</p>
<p>How do we automate this process? One method is to use a similar infrastructure as that of the chapter on <a href="InformationFlow.slides.html">information flow</a>, and use the Python inheritance to create symbolic proxy objects that can track the concrete execution.</p>

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<h2 id="A-Concolic-Tracer">A Concolic Tracer<a class="anchor-link" href="#A-Concolic-Tracer">&#182;</a></h2><p>Given that there is a symbolic context under which the program is executed (that is the symbolic variables that are used in the program execution) we define a context manager called <code>ConcolicTracer</code> that keeps track of the context.</p>

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<p>The <code>ConcolicTracer</code> accepts a single argument which contains the declarations for the symbolic variables seen so far, and the pre-conditions if any.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">class</span> <span class="nc">ConcolicTracer</span><span class="p">:</span>
    <span class="k">def</span> <span class="nf">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">context</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">context</span> <span class="o">=</span> <span class="n">context</span> <span class="k">if</span> <span class="n">context</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span> <span class="k">else</span> <span class="p">({},</span> <span class="p">[])</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">decls</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">path</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">context</span>
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<p>We add the <code>enter</code> and <code>exit</code> methods for the context manager.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">class</span> <span class="nc">ConcolicTracer</span><span class="p">(</span><span class="n">ConcolicTracer</span><span class="p">):</span>
    <span class="k">def</span> <span class="nf">__enter__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
        <span class="k">return</span> <span class="bp">self</span>

    <span class="k">def</span> <span class="nf">__exit__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">exc_type</span><span class="p">,</span> <span class="n">exc_value</span><span class="p">,</span> <span class="n">tb</span><span class="p">):</span>
        <span class="k">return</span>
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<p>We use introspection to determine the arguments to the function, which is hooked into the <code>getitem</code> method.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">class</span> <span class="nc">ConcolicTracer</span><span class="p">(</span><span class="n">ConcolicTracer</span><span class="p">):</span>
    <span class="k">def</span> <span class="nf">__getitem__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">fn</span><span class="p">):</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">fn</span> <span class="o">=</span> <span class="n">fn</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">fn_args</span> <span class="o">=</span> <span class="p">{</span><span class="n">i</span><span class="p">:</span> <span class="kc">None</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">inspect</span><span class="o">.</span><span class="n">signature</span><span class="p">(</span><span class="n">fn</span><span class="p">)</span><span class="o">.</span><span class="n">parameters</span><span class="p">}</span>
        <span class="k">return</span> <span class="bp">self</span>
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<p>Finally, the function itself is invoked using the <code>call</code> method.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">class</span> <span class="nc">ConcolicTracer</span><span class="p">(</span><span class="n">ConcolicTracer</span><span class="p">):</span>
    <span class="k">def</span> <span class="nf">__call__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="o">*</span><span class="n">args</span><span class="p">):</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">result</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">fn</span><span class="p">(</span><span class="o">*</span><span class="bp">self</span><span class="o">.</span><span class="n">concolic</span><span class="p">(</span><span class="n">args</span><span class="p">))</span>
        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">result</span>
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<p>For now, we define <code>concolic()</code> as a transparent function. It will be modified to produce symbolic variables later.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">class</span> <span class="nc">ConcolicTracer</span><span class="p">(</span><span class="n">ConcolicTracer</span><span class="p">):</span>
    <span class="k">def</span> <span class="nf">concolic</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">args</span><span class="p">):</span>
        <span class="k">return</span> <span class="n">args</span>
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<p>It can be used as follows</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">with</span> <span class="n">ConcolicTracer</span><span class="p">()</span> <span class="k">as</span> <span class="n">_</span><span class="p">:</span>
    <span class="n">_</span><span class="p">[</span><span class="n">factorial</span><span class="p">](</span><span class="mi">1</span><span class="p">)</span>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">_</span><span class="o">.</span><span class="n">context</span>
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<pre>({}, [])</pre>
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<p>The <code>context</code> is empty as we are yet to hook up the necessary infrastructure to <code>ConcolicTracer</code>.</p>

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<h3 id="Concolic-Proxy-Objects">Concolic Proxy Objects<a class="anchor-link" href="#Concolic-Proxy-Objects">&#182;</a></h3><p>We now define the concolic proxy objects that can be used for concolic tracing. First, we define the <code>zproxy_create()</code> method that given a class name, correctly creates an instance of that class, and the symbolic corresponding variable, and registers the symbolic variable in the context information <code>context</code>.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">def</span> <span class="nf">zproxy_create</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="n">sname</span><span class="p">,</span> <span class="n">z3var</span><span class="p">,</span> <span class="n">context</span><span class="p">,</span> <span class="n">zn</span><span class="p">,</span> <span class="n">v</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
    <span class="n">zv</span> <span class="o">=</span> <span class="bp">cls</span><span class="p">(</span><span class="n">context</span><span class="p">,</span> <span class="n">z3var</span><span class="p">(</span><span class="n">zn</span><span class="p">),</span> <span class="n">v</span><span class="p">)</span>
    <span class="n">context</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="n">zn</span><span class="p">]</span> <span class="o">=</span> <span class="n">sname</span>
    <span class="k">return</span> <span class="n">zv</span>
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<h4 id="A-Proxy-Class-for-Booleans">A Proxy Class for Booleans<a class="anchor-link" href="#A-Proxy-Class-for-Booleans">&#182;</a></h4><p>First, we define the <code>zbool</code> class which is used to track the predicates encountered. It is a wrapper class that contains both symbolic (<code>z</code>) as well as concrete (<code>v</code>) values. The concrete value is used to determine which path to take, and the symbolic value is used to collect the predicates encountered.</p>
<p>The initialization done in two parts. The first one is using <code>zproxy_create()</code> to correctly initialize and register the shadow symbolic variable corresponding to the passed argument. This is used exclusively when the symbolic variable needs to be initialized first. In all other cases, the constructor is called with the preexisting symbolic value.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">class</span> <span class="nc">zbool</span><span class="p">:</span>
    <span class="nd">@classmethod</span>
    <span class="k">def</span> <span class="nf">create</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="n">context</span><span class="p">,</span> <span class="n">zn</span><span class="p">,</span> <span class="n">v</span><span class="p">):</span>
        <span class="k">return</span> <span class="n">zproxy_create</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="s1">&#39;Bool&#39;</span><span class="p">,</span> <span class="n">z3</span><span class="o">.</span><span class="n">Bool</span><span class="p">,</span> <span class="n">context</span><span class="p">,</span> <span class="n">zn</span><span class="p">,</span> <span class="n">v</span><span class="p">)</span>

    <span class="k">def</span> <span class="nf">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">context</span><span class="p">,</span> <span class="n">z</span><span class="p">,</span> <span class="n">v</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">context</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">z</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">v</span> <span class="o">=</span> <span class="n">context</span><span class="p">,</span> <span class="n">z</span><span class="p">,</span> <span class="n">v</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">decl</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">path</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">context</span>
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<p>Here is how it can be used.</p>

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    <span class="n">za</span><span class="p">,</span> <span class="n">zb</span> <span class="o">=</span> <span class="n">z3</span><span class="o">.</span><span class="n">Ints</span><span class="p">(</span><span class="s1">&#39;a b&#39;</span><span class="p">)</span>
    <span class="n">val</span> <span class="o">=</span> <span class="n">zbool</span><span class="o">.</span><span class="n">create</span><span class="p">(</span><span class="n">_</span><span class="o">.</span><span class="n">context</span><span class="p">,</span> <span class="s1">&#39;my_bool_arg&#39;</span><span class="p">,</span> <span class="kc">True</span><span class="p">)</span>
    <span class="nb">print</span><span class="p">(</span><span class="n">val</span><span class="o">.</span><span class="n">z</span><span class="p">,</span> <span class="n">val</span><span class="o">.</span><span class="n">v</span><span class="p">)</span>
<span class="n">_</span><span class="o">.</span><span class="n">context</span>
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<pre>my_bool_arg True
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<pre>({&#39;my_bool_arg&#39;: &#39;Bool&#39;}, [])</pre>
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<h5 id="Negation-of-Encoded-formula">Negation of Encoded formula<a class="anchor-link" href="#Negation-of-Encoded-formula">&#182;</a></h5><p>The <code>zbool</code> class allows negation of its concrete and symbolic values.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">class</span> <span class="nc">zbool</span><span class="p">(</span><span class="n">zbool</span><span class="p">):</span>
    <span class="k">def</span> <span class="nf">__not__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
        <span class="k">return</span> <span class="n">zbool</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">context</span><span class="p">,</span> <span class="n">z3</span><span class="o">.</span><span class="n">Not</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">z</span><span class="p">),</span> <span class="ow">not</span> <span class="bp">self</span><span class="o">.</span><span class="n">v</span><span class="p">)</span>
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<p>Here is how it can be used.</p>

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    <span class="n">val</span> <span class="o">=</span> <span class="n">zbool</span><span class="o">.</span><span class="n">create</span><span class="p">(</span><span class="n">_</span><span class="o">.</span><span class="n">context</span><span class="p">,</span> <span class="s1">&#39;my_bool_arg&#39;</span><span class="p">,</span> <span class="kc">True</span><span class="p">)</span><span class="o">.</span><span class="n">__not__</span><span class="p">()</span>
    <span class="nb">print</span><span class="p">(</span><span class="n">val</span><span class="o">.</span><span class="n">z</span><span class="p">,</span> <span class="n">val</span><span class="o">.</span><span class="n">v</span><span class="p">)</span>
<span class="n">_</span><span class="o">.</span><span class="n">context</span>
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<pre>Not(my_bool_arg) False
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<pre>({&#39;my_bool_arg&#39;: &#39;Bool&#39;}, [])</pre>
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<h5 id="Registering-Predicates-on-Conditionals">Registering Predicates on Conditionals<a class="anchor-link" href="#Registering-Predicates-on-Conditionals">&#182;</a></h5><p>The <code>zbool</code> class is be used to track boolean conditions that arise during program execution. It tracks such conditions by registering the corresponding symbolic expressions in the context.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">class</span> <span class="nc">zbool</span><span class="p">(</span><span class="n">zbool</span><span class="p">):</span>
    <span class="k">def</span> <span class="nf">__bool__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
        <span class="n">r</span><span class="p">,</span> <span class="n">pred</span> <span class="o">=</span> <span class="p">(</span><span class="kc">True</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">z</span><span class="p">)</span> <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">v</span> <span class="k">else</span> <span class="p">(</span><span class="kc">False</span><span class="p">,</span> <span class="n">z3</span><span class="o">.</span><span class="n">Not</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">z</span><span class="p">))</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">path</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">pred</span><span class="p">)</span>
        <span class="k">return</span> <span class="n">r</span>
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<p>The <code>zbool</code> class can be used to keep track of boolean values and conditions encountered during the execution. For example, we can encode the conditions encountered by line 6 in <code>factorial()</code> as follows:</p>

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<p>First, we define the concrete value (<code>ca</code>), and its shadow symbolic variable (<code>za</code>).</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">ca</span><span class="p">,</span> <span class="n">za</span> <span class="o">=</span> <span class="mi">5</span><span class="p">,</span> <span class="n">z3</span><span class="o">.</span><span class="n">Int</span><span class="p">(</span><span class="s1">&#39;a&#39;</span><span class="p">)</span>
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<p>Then, we wrap it in <code>zbool</code>, and use it in a conditional, forcing the conditional to be registered in the context.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">with</span> <span class="n">ConcolicTracer</span><span class="p">()</span> <span class="k">as</span> <span class="n">_</span><span class="p">:</span>
    <span class="k">if</span> <span class="n">zbool</span><span class="p">(</span><span class="n">_</span><span class="o">.</span><span class="n">context</span><span class="p">,</span> <span class="n">za</span> <span class="o">==</span> <span class="n">z3</span><span class="o">.</span><span class="n">IntVal</span><span class="p">(</span><span class="mi">5</span><span class="p">),</span> <span class="n">ca</span> <span class="o">==</span> <span class="mi">5</span><span class="p">):</span>
        <span class="nb">print</span><span class="p">(</span><span class="s1">&#39;success&#39;</span><span class="p">)</span>
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<pre>success
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<p>We can retrieve the registered conditional as follows.</p>

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<pre>[5 == a]</pre>
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<h4 id="A-Proxy-Class-for-Integers">A Proxy Class for Integers<a class="anchor-link" href="#A-Proxy-Class-for-Integers">&#182;</a></h4>
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<p>Next, we define a symbolic wrapper <code>zint</code> for <code>int</code>.
This class keeps track of the int variables used and the predicates encountered in <code>context</code>. Finally, it also keeps the concrete value used so that it can be used to determine the path to take. As the <code>zint</code> extends the primitive <code>int</code> class, we have to define a <em>new</em> method to open it for extension.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">class</span> <span class="nc">zint</span><span class="p">(</span><span class="nb">int</span><span class="p">):</span>
    <span class="k">def</span> <span class="nf">__new__</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="n">context</span><span class="p">,</span> <span class="n">zn</span><span class="p">,</span> <span class="n">v</span><span class="p">,</span> <span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kw</span><span class="p">):</span>
        <span class="k">return</span> <span class="nb">int</span><span class="o">.</span><span class="fm">__new__</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="n">v</span><span class="p">,</span> <span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kw</span><span class="p">)</span>
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<p>As in the case of <code>zbool</code>, the initialization takes place in two parts. The first using <code>create()</code> if a new symbolic argument is being registered, and then the usual initialization.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">class</span> <span class="nc">zint</span><span class="p">(</span><span class="n">zint</span><span class="p">):</span>
    <span class="nd">@classmethod</span>
    <span class="k">def</span> <span class="nf">create</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="n">context</span><span class="p">,</span> <span class="n">zn</span><span class="p">,</span> <span class="n">v</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
        <span class="k">return</span> <span class="n">zproxy_create</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="s1">&#39;Int&#39;</span><span class="p">,</span> <span class="n">z3</span><span class="o">.</span><span class="n">Int</span><span class="p">,</span> <span class="n">context</span><span class="p">,</span> <span class="n">zn</span><span class="p">,</span> <span class="n">v</span><span class="p">)</span>

    <span class="k">def</span> <span class="nf">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">context</span><span class="p">,</span> <span class="n">z</span><span class="p">,</span> <span class="n">v</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">z</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">v</span> <span class="o">=</span> <span class="n">z</span><span class="p">,</span> <span class="n">v</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">context</span> <span class="o">=</span> <span class="n">context</span>
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<p>The <code>int</code> value of an <code>zint</code> object is its concrete value.</p>

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    <span class="k">def</span> <span class="nf">__int__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">v</span>

    <span class="k">def</span> <span class="nf">__pos__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">v</span>
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<p>Using these proxies are as follows.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">with</span> <span class="n">ConcolicTracer</span><span class="p">()</span> <span class="k">as</span> <span class="n">_</span><span class="p">:</span>
    <span class="n">val</span> <span class="o">=</span> <span class="n">zint</span><span class="o">.</span><span class="n">create</span><span class="p">(</span><span class="n">_</span><span class="o">.</span><span class="n">context</span><span class="p">,</span> <span class="s1">&#39;int_arg&#39;</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span>
    <span class="nb">print</span><span class="p">(</span><span class="n">val</span><span class="o">.</span><span class="n">z</span><span class="p">,</span> <span class="n">val</span><span class="o">.</span><span class="n">v</span><span class="p">)</span>
<span class="n">_</span><span class="o">.</span><span class="n">context</span>
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<pre>int_arg 0
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<pre>({&#39;int_arg&#39;: &#39;Int&#39;}, [])</pre>
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<p>The <code>zint</code> class is often used to do arithmetic with, or compare to other <code>int</code>s. These <code>int</code>s can be either a variable or a constant value. We define a helper method <code>_zv()</code> that checks what kind of <code>int</code> a given value is, and produces the correct symbolic equivalent.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">class</span> <span class="nc">zint</span><span class="p">(</span><span class="n">zint</span><span class="p">):</span>
    <span class="k">def</span> <span class="nf">_zv</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">o</span><span class="p">):</span>
        <span class="k">return</span> <span class="p">(</span><span class="n">o</span><span class="o">.</span><span class="n">z</span><span class="p">,</span> <span class="n">o</span><span class="o">.</span><span class="n">v</span><span class="p">)</span> <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">o</span><span class="p">,</span> <span class="n">zint</span><span class="p">)</span> <span class="k">else</span> <span class="p">(</span><span class="n">z3</span><span class="o">.</span><span class="n">IntVal</span><span class="p">(</span><span class="n">o</span><span class="p">),</span> <span class="n">o</span><span class="p">)</span>
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<p>It can be used as follows</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">with</span> <span class="n">ConcolicTracer</span><span class="p">()</span> <span class="k">as</span> <span class="n">_</span><span class="p">:</span>
    <span class="n">val</span> <span class="o">=</span> <span class="n">zint</span><span class="o">.</span><span class="n">create</span><span class="p">(</span><span class="n">_</span><span class="o">.</span><span class="n">context</span><span class="p">,</span> <span class="s1">&#39;int_arg&#39;</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span>
    <span class="nb">print</span><span class="p">(</span><span class="n">val</span><span class="o">.</span><span class="n">_zv</span><span class="p">(</span><span class="mi">0</span><span class="p">))</span>
    <span class="nb">print</span><span class="p">(</span><span class="n">val</span><span class="o">.</span><span class="n">_zv</span><span class="p">(</span><span class="n">val</span><span class="p">))</span>
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<pre>(0, 0)
(int_arg, 0)
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<h5 id="Equality-between-Integers">Equality between Integers<a class="anchor-link" href="#Equality-between-Integers">&#182;</a></h5><p>Two integers can be compared for equality using <em>ne</em> and <em>eq</em>.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">class</span> <span class="nc">zint</span><span class="p">(</span><span class="n">zint</span><span class="p">):</span>
    <span class="k">def</span> <span class="nf">__ne__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
        <span class="n">z</span><span class="p">,</span> <span class="n">v</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_zv</span><span class="p">(</span><span class="n">other</span><span class="p">)</span>
        <span class="k">return</span> <span class="n">zbool</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">context</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">z</span> <span class="o">!=</span> <span class="n">z</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">v</span> <span class="o">!=</span> <span class="n">v</span><span class="p">)</span>

    <span class="k">def</span> <span class="nf">__eq__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
        <span class="n">z</span><span class="p">,</span> <span class="n">v</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_zv</span><span class="p">(</span><span class="n">other</span><span class="p">)</span>
        <span class="k">return</span> <span class="n">zbool</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">context</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">z</span> <span class="o">==</span> <span class="n">z</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">v</span> <span class="o">==</span> <span class="n">v</span><span class="p">)</span>
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<p>We also define <em>req</em> using <em>eq</em> in case the int being compared is on the left hand side.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">class</span> <span class="nc">zint</span><span class="p">(</span><span class="n">zint</span><span class="p">):</span>
    <span class="k">def</span> <span class="nf">__req__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="fm">__eq__</span><span class="p">(</span><span class="n">other</span><span class="p">)</span>
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<p>It can be used as follows.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">with</span> <span class="n">ConcolicTracer</span><span class="p">()</span> <span class="k">as</span> <span class="n">_</span><span class="p">:</span>
    <span class="n">ia</span> <span class="o">=</span> <span class="n">zint</span><span class="o">.</span><span class="n">create</span><span class="p">(</span><span class="n">_</span><span class="o">.</span><span class="n">context</span><span class="p">,</span> <span class="s1">&#39;int_a&#39;</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span>
    <span class="n">ib</span> <span class="o">=</span> <span class="n">zint</span><span class="o">.</span><span class="n">create</span><span class="p">(</span><span class="n">_</span><span class="o">.</span><span class="n">context</span><span class="p">,</span> <span class="s1">&#39;int_b&#39;</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span>
    <span class="n">v1</span> <span class="o">=</span> <span class="n">ia</span> <span class="o">==</span> <span class="n">ib</span>
    <span class="n">v2</span> <span class="o">=</span> <span class="n">ia</span> <span class="o">!=</span> <span class="n">ib</span>
    <span class="n">v3</span> <span class="o">=</span> <span class="mi">0</span> <span class="o">!=</span> <span class="n">ib</span>
    <span class="nb">print</span><span class="p">(</span><span class="n">v1</span><span class="o">.</span><span class="n">z</span><span class="p">,</span> <span class="n">v2</span><span class="o">.</span><span class="n">z</span><span class="p">,</span> <span class="n">v3</span><span class="o">.</span><span class="n">z</span><span class="p">)</span>
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<pre>int_a == int_b int_a != int_b 0 != int_b
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<h5 id="Comparisons-between-Integers">Comparisons between Integers<a class="anchor-link" href="#Comparisons-between-Integers">&#182;</a></h5><p>Integers can also be compared for ordering, and the methods for this are defined below.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">class</span> <span class="nc">zint</span><span class="p">(</span><span class="n">zint</span><span class="p">):</span>
    <span class="k">def</span> <span class="nf">__lt__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
        <span class="n">z</span><span class="p">,</span> <span class="n">v</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_zv</span><span class="p">(</span><span class="n">other</span><span class="p">)</span>
        <span class="k">return</span> <span class="n">zbool</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">context</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">z</span> <span class="o">&lt;</span> <span class="n">z</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">v</span> <span class="o">&lt;</span> <span class="n">v</span><span class="p">)</span>

    <span class="k">def</span> <span class="nf">__gt__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
        <span class="n">z</span><span class="p">,</span> <span class="n">v</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_zv</span><span class="p">(</span><span class="n">other</span><span class="p">)</span>
        <span class="k">return</span> <span class="n">zbool</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">context</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">z</span> <span class="o">&gt;</span> <span class="n">z</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">v</span> <span class="o">&gt;</span> <span class="n">v</span><span class="p">)</span>
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<p>We use the comparisons and equality operators to provide the other missing operators.</p>

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    <span class="k">def</span> <span class="nf">__le__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
        <span class="n">z</span><span class="p">,</span> <span class="n">v</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_zv</span><span class="p">(</span><span class="n">other</span><span class="p">)</span>
        <span class="k">return</span> <span class="n">zbool</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">context</span><span class="p">,</span> <span class="n">z3</span><span class="o">.</span><span class="n">Or</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">z</span> <span class="o">&lt;</span> <span class="n">z</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">z</span> <span class="o">==</span> <span class="n">z</span><span class="p">),</span>
                     <span class="bp">self</span><span class="o">.</span><span class="n">v</span> <span class="o">&lt;</span> <span class="n">v</span> <span class="ow">or</span> <span class="bp">self</span><span class="o">.</span><span class="n">v</span> <span class="o">==</span> <span class="n">v</span><span class="p">)</span>

    <span class="k">def</span> <span class="nf">__ge__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
        <span class="n">z</span><span class="p">,</span> <span class="n">v</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_zv</span><span class="p">(</span><span class="n">other</span><span class="p">)</span>
        <span class="k">return</span> <span class="n">zbool</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">context</span><span class="p">,</span> <span class="n">z3</span><span class="o">.</span><span class="n">Or</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">z</span> <span class="o">&gt;</span> <span class="n">z</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">z</span> <span class="o">==</span> <span class="n">z</span><span class="p">),</span>
                     <span class="bp">self</span><span class="o">.</span><span class="n">v</span> <span class="o">&gt;</span> <span class="n">v</span> <span class="ow">or</span> <span class="bp">self</span><span class="o">.</span><span class="n">v</span> <span class="o">==</span> <span class="n">v</span><span class="p">)</span>
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<p>These functions can be used as follows.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">with</span> <span class="n">ConcolicTracer</span><span class="p">()</span> <span class="k">as</span> <span class="n">_</span><span class="p">:</span>
    <span class="n">ia</span> <span class="o">=</span> <span class="n">zint</span><span class="o">.</span><span class="n">create</span><span class="p">(</span><span class="n">_</span><span class="o">.</span><span class="n">context</span><span class="p">,</span> <span class="s1">&#39;int_a&#39;</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span>
    <span class="n">ib</span> <span class="o">=</span> <span class="n">zint</span><span class="o">.</span><span class="n">create</span><span class="p">(</span><span class="n">_</span><span class="o">.</span><span class="n">context</span><span class="p">,</span> <span class="s1">&#39;int_b&#39;</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
    <span class="n">v1</span> <span class="o">=</span> <span class="n">ia</span> <span class="o">&gt;</span> <span class="n">ib</span>
    <span class="n">v2</span> <span class="o">=</span> <span class="n">ia</span> <span class="o">&lt;</span> <span class="n">ib</span>
    <span class="nb">print</span><span class="p">(</span><span class="n">v1</span><span class="o">.</span><span class="n">z</span><span class="p">,</span> <span class="n">v2</span><span class="o">.</span><span class="n">z</span><span class="p">)</span>
    <span class="n">v3</span> <span class="o">=</span> <span class="n">ia</span> <span class="o">&gt;=</span> <span class="n">ib</span>
    <span class="n">v4</span> <span class="o">=</span> <span class="n">ia</span> <span class="o">&lt;=</span> <span class="n">ib</span>
    <span class="nb">print</span><span class="p">(</span><span class="n">v3</span><span class="o">.</span><span class="n">z</span><span class="p">,</span> <span class="n">v4</span><span class="o">.</span><span class="n">z</span><span class="p">)</span>
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<pre>int_a &gt; int_b int_a &lt; int_b
Or(int_a &gt; int_b, int_a == int_b) Or(int_a &lt; int_b, int_a == int_b)
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<h5 id="Binary-Operators-for-Integers">Binary Operators for Integers<a class="anchor-link" href="#Binary-Operators-for-Integers">&#182;</a></h5><p>We implement relevant arithmetic operators for integers as described in <a href="https://docs.python.org/3/reference/datamodel.html#object.__add__">Python documentation</a>. (The commented out operators are not directly available for <code>z3.ArithRef</code>. They need to be implemented separately if needed. See the exercises for how it can be done.)</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">INT_BINARY_OPS</span> <span class="o">=</span> <span class="p">[</span>
    <span class="s1">&#39;__add__&#39;</span><span class="p">,</span>
    <span class="s1">&#39;__sub__&#39;</span><span class="p">,</span>
    <span class="s1">&#39;__mul__&#39;</span><span class="p">,</span>
    <span class="s1">&#39;__truediv__&#39;</span><span class="p">,</span>
    <span class="c1"># &#39;__div__&#39;,</span>
    <span class="s1">&#39;__mod__&#39;</span><span class="p">,</span>
    <span class="c1"># &#39;__divmod__&#39;,</span>
    <span class="s1">&#39;__pow__&#39;</span><span class="p">,</span>
    <span class="c1"># &#39;__lshift__&#39;,</span>
    <span class="c1"># &#39;__rshift__&#39;,</span>
    <span class="c1"># &#39;__and__&#39;,</span>
    <span class="c1"># &#39;__xor__&#39;,</span>
    <span class="c1"># &#39;__or__&#39;,</span>
    <span class="s1">&#39;__radd__&#39;</span><span class="p">,</span>
    <span class="s1">&#39;__rsub__&#39;</span><span class="p">,</span>
    <span class="s1">&#39;__rmul__&#39;</span><span class="p">,</span>
    <span class="s1">&#39;__rtruediv__&#39;</span><span class="p">,</span>
    <span class="c1"># &#39;__rdiv__&#39;,</span>
    <span class="s1">&#39;__rmod__&#39;</span><span class="p">,</span>
    <span class="c1"># &#39;__rdivmod__&#39;,</span>
    <span class="s1">&#39;__rpow__&#39;</span><span class="p">,</span>
    <span class="c1"># &#39;__rlshift__&#39;,</span>
    <span class="c1"># &#39;__rrshift__&#39;,</span>
    <span class="c1"># &#39;__rand__&#39;,</span>
    <span class="c1"># &#39;__rxor__&#39;,</span>
    <span class="c1"># &#39;__ror__&#39;,</span>
<span class="p">]</span>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">def</span> <span class="nf">make_int_binary_wrapper</span><span class="p">(</span><span class="n">fname</span><span class="p">,</span> <span class="n">fun</span><span class="p">,</span> <span class="n">zfun</span><span class="p">):</span>
    <span class="k">def</span> <span class="nf">proxy</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
        <span class="n">z</span><span class="p">,</span> <span class="n">v</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_zv</span><span class="p">(</span><span class="n">other</span><span class="p">)</span>
        <span class="n">z_</span> <span class="o">=</span> <span class="n">zfun</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">z</span><span class="p">,</span> <span class="n">z</span><span class="p">)</span>
        <span class="n">v_</span> <span class="o">=</span> <span class="n">fun</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">v</span><span class="p">,</span> <span class="n">v</span><span class="p">)</span>
        <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">v_</span><span class="p">,</span> <span class="nb">float</span><span class="p">):</span>
            <span class="c1"># we do not implement float results yet.</span>
            <span class="k">assert</span> <span class="nb">round</span><span class="p">(</span><span class="n">v_</span><span class="p">)</span> <span class="o">==</span> <span class="n">v_</span>
            <span class="n">v_</span> <span class="o">=</span> <span class="nb">round</span><span class="p">(</span><span class="n">v_</span><span class="p">)</span>
        <span class="k">return</span> <span class="n">zint</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">context</span><span class="p">,</span> <span class="n">z_</span><span class="p">,</span> <span class="n">v_</span><span class="p">)</span>

    <span class="k">return</span> <span class="n">proxy</span>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">for</span> <span class="n">fname</span> <span class="ow">in</span> <span class="n">INT_BINARY_OPS</span><span class="p">:</span>
    <span class="n">fun</span> <span class="o">=</span> <span class="nb">getattr</span><span class="p">(</span><span class="nb">int</span><span class="p">,</span> <span class="n">fname</span><span class="p">)</span>
    <span class="n">zfun</span> <span class="o">=</span> <span class="nb">getattr</span><span class="p">(</span><span class="n">z3</span><span class="o">.</span><span class="n">ArithRef</span><span class="p">,</span> <span class="n">fname</span><span class="p">)</span>
    <span class="nb">setattr</span><span class="p">(</span><span class="n">zint</span><span class="p">,</span> <span class="n">fname</span><span class="p">,</span> <span class="n">make_int_binary_wrapper</span><span class="p">(</span><span class="n">fname</span><span class="p">,</span> <span class="n">fun</span><span class="p">,</span> <span class="n">zfun</span><span class="p">))</span>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">with</span> <span class="n">ConcolicTracer</span><span class="p">()</span> <span class="k">as</span> <span class="n">_</span><span class="p">:</span>
    <span class="n">ia</span> <span class="o">=</span> <span class="n">zint</span><span class="o">.</span><span class="n">create</span><span class="p">(</span><span class="n">_</span><span class="o">.</span><span class="n">context</span><span class="p">,</span> <span class="s1">&#39;int_a&#39;</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span>
    <span class="n">ib</span> <span class="o">=</span> <span class="n">zint</span><span class="o">.</span><span class="n">create</span><span class="p">(</span><span class="n">_</span><span class="o">.</span><span class="n">context</span><span class="p">,</span> <span class="s1">&#39;int_b&#39;</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
    <span class="nb">print</span><span class="p">((</span><span class="n">ia</span> <span class="o">+</span> <span class="n">ib</span><span class="p">)</span><span class="o">.</span><span class="n">z</span><span class="p">)</span>
    <span class="nb">print</span><span class="p">((</span><span class="n">ia</span> <span class="o">+</span> <span class="mi">10</span><span class="p">)</span><span class="o">.</span><span class="n">z</span><span class="p">)</span>
    <span class="nb">print</span><span class="p">((</span><span class="mi">11</span> <span class="o">+</span> <span class="n">ib</span><span class="p">)</span><span class="o">.</span><span class="n">z</span><span class="p">)</span>
    <span class="nb">print</span><span class="p">((</span><span class="n">ia</span> <span class="o">-</span> <span class="n">ib</span><span class="p">)</span><span class="o">.</span><span class="n">z</span><span class="p">)</span>
    <span class="nb">print</span><span class="p">((</span><span class="n">ia</span> <span class="o">*</span> <span class="n">ib</span><span class="p">)</span><span class="o">.</span><span class="n">z</span><span class="p">)</span>
    <span class="nb">print</span><span class="p">((</span><span class="n">ia</span> <span class="o">/</span> <span class="n">ib</span><span class="p">)</span><span class="o">.</span><span class="n">z</span><span class="p">)</span>
    <span class="nb">print</span><span class="p">((</span><span class="n">ia</span> <span class="o">**</span> <span class="n">ib</span><span class="p">)</span><span class="o">.</span><span class="n">z</span><span class="p">)</span>
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<pre>int_a + int_b
int_a + 10
11 + int_b
int_a - int_b
int_a*int_b
int_a/int_b
int_a**int_b
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<h5 id="Integer-Unary-Operators">Integer Unary Operators<a class="anchor-link" href="#Integer-Unary-Operators">&#182;</a></h5><p>We also implement the relevant unary operators as below.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">INT_UNARY_OPS</span> <span class="o">=</span> <span class="p">[</span>
    <span class="s1">&#39;__neg__&#39;</span><span class="p">,</span>
    <span class="s1">&#39;__pos__&#39;</span><span class="p">,</span>
    <span class="c1"># &#39;__abs__&#39;,</span>
    <span class="c1"># &#39;__invert__&#39;,</span>
    <span class="c1"># &#39;__round__&#39;,</span>
    <span class="c1"># &#39;__ceil__&#39;,</span>
    <span class="c1"># &#39;__floor__&#39;,</span>
    <span class="c1"># &#39;__trunc__&#39;,</span>
<span class="p">]</span>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">def</span> <span class="nf">make_int_unary_wrapper</span><span class="p">(</span><span class="n">fname</span><span class="p">,</span> <span class="n">fun</span><span class="p">,</span> <span class="n">zfun</span><span class="p">):</span>
    <span class="k">def</span> <span class="nf">proxy</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
        <span class="k">return</span> <span class="n">zint</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">context</span><span class="p">,</span> <span class="n">zfun</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">z</span><span class="p">),</span> <span class="n">fun</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">v</span><span class="p">))</span>

    <span class="k">return</span> <span class="n">proxy</span>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">for</span> <span class="n">fname</span> <span class="ow">in</span> <span class="n">INT_UNARY_OPS</span><span class="p">:</span>
    <span class="n">fun</span> <span class="o">=</span> <span class="nb">getattr</span><span class="p">(</span><span class="nb">int</span><span class="p">,</span> <span class="n">fname</span><span class="p">)</span>
    <span class="n">zfun</span> <span class="o">=</span> <span class="nb">getattr</span><span class="p">(</span><span class="n">z3</span><span class="o">.</span><span class="n">ArithRef</span><span class="p">,</span> <span class="n">fname</span><span class="p">)</span>
    <span class="nb">setattr</span><span class="p">(</span><span class="n">zint</span><span class="p">,</span> <span class="n">fname</span><span class="p">,</span> <span class="n">make_int_unary_wrapper</span><span class="p">(</span><span class="n">fname</span><span class="p">,</span> <span class="n">fun</span><span class="p">,</span> <span class="n">zfun</span><span class="p">))</span>
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<p>We can use the unary operators we defined above as follows:</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">with</span> <span class="n">ConcolicTracer</span><span class="p">()</span> <span class="k">as</span> <span class="n">_</span><span class="p">:</span>
    <span class="n">ia</span> <span class="o">=</span> <span class="n">zint</span><span class="o">.</span><span class="n">create</span><span class="p">(</span><span class="n">_</span><span class="o">.</span><span class="n">context</span><span class="p">,</span> <span class="s1">&#39;int_a&#39;</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span>
    <span class="nb">print</span><span class="p">((</span><span class="o">-</span><span class="n">ia</span><span class="p">)</span><span class="o">.</span><span class="n">z</span><span class="p">)</span>
    <span class="nb">print</span><span class="p">((</span><span class="o">+</span><span class="n">ia</span><span class="p">)</span><span class="o">.</span><span class="n">z</span><span class="p">)</span>
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<pre>-int_a
int_a
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<h5 id="Using-an-Integer-in-a-Boolean-Context">Using an Integer in a Boolean Context<a class="anchor-link" href="#Using-an-Integer-in-a-Boolean-Context">&#182;</a></h5><p>An integer may be converted to a boolean context in conditionals or as part of boolean predicates such as <code>or</code>, <code>and</code> and <code>not</code>. In these cases, the <code>__bool__()</code> method gets called. Unfortunately, this method requires a primitive boolean value. Hence, we force the current integer formula to a boolean predicate and register it in the current context.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">class</span> <span class="nc">zint</span><span class="p">(</span><span class="n">zint</span><span class="p">):</span>
    <span class="k">def</span> <span class="nf">__bool__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
        <span class="c1"># return zbool(self.context, self.z, self.v) &lt;-- not allowed</span>
        <span class="c1"># force registering boolean condition</span>
        <span class="k">if</span> <span class="bp">self</span> <span class="o">!=</span> <span class="mi">0</span><span class="p">:</span>
            <span class="k">return</span> <span class="kc">True</span>
        <span class="k">return</span> <span class="kc">False</span>
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<p>It is used as follows</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">with</span> <span class="n">ConcolicTracer</span><span class="p">()</span> <span class="k">as</span> <span class="n">_</span><span class="p">:</span>
    <span class="n">za</span> <span class="o">=</span> <span class="n">zint</span><span class="o">.</span><span class="n">create</span><span class="p">(</span><span class="n">_</span><span class="o">.</span><span class="n">context</span><span class="p">,</span> <span class="s1">&#39;int_a&#39;</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
    <span class="n">zb</span> <span class="o">=</span> <span class="n">zint</span><span class="o">.</span><span class="n">create</span><span class="p">(</span><span class="n">_</span><span class="o">.</span><span class="n">context</span><span class="p">,</span> <span class="s1">&#39;int_b&#39;</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span>
    <span class="k">if</span> <span class="n">za</span> <span class="ow">and</span> <span class="n">zb</span><span class="p">:</span>
        <span class="nb">print</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">_</span><span class="o">.</span><span class="n">context</span>
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<pre>({&#39;int_a&#39;: &#39;Int&#39;, &#39;int_b&#39;: &#39;Int&#39;}, [0 != int_a, Not(0 != int_b)])</pre>
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<h4 id="Remaining-Methods-of-the--ConcolicTracer">Remaining Methods of the  ConcolicTracer<a class="anchor-link" href="#Remaining-Methods-of-the--ConcolicTracer">&#182;</a></h4><p>We now complete some of the methods of the <code>ConcolicTracer</code>.</p>

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<h5 id="Translating-to-the-SMT-Expression-Format">Translating to the SMT Expression Format<a class="anchor-link" href="#Translating-to-the-SMT-Expression-Format">&#182;</a></h5><p>Given that we are using an SMT Solver z3, it is often useful to retrieve the corresponding SMT expression for a symbolic expression. This can be used as an argument to <code>z3</code> or other SMT solvers.</p>
<p>The format of the SMT expression (<a href="http://smtlib.github.io/jSMTLIB/SMTLIBTutorial.pdf">SMT-LIB</a>) is as follows:</p>
<ul>
<li>Variables declarations in <a href="https://en.wikipedia.org/wiki/S-expression">S-EXP</a> format.
E.g. The following declares a symbolic integer variable <code>x</code>
<pre><code>(declare-const x Int)</code></pre>
This declares a <code>bit vector</code> <code>b</code> of length <code>8</code>
<pre><code>(declare-const b (_ BitVec 8))</code></pre>
This declares a symbolic real variable <code>r</code>
<pre><code>(declare-const x Real)</code></pre>
This declares a symbolic string variable <code>s</code>
<pre><code>(declare-const s String)</code></pre>
</li>
</ul>
<p>The declared variables can be used in logical formulas that are encoded in <em>S-EXP</em> format. For example, here is a logical formula.</p>

<pre><code>(assert
    (and
        (= a b)
        (= a c)
        (! b c)))</code></pre>
<p>Here is another example, using string variables.</p>

<pre><code>(or (&lt; 0 (str.indexof (str.substr my_str1 7 19) " where " 0))
    (= (str.indexof (str.substr my_str1 7 19) " where " 0) 0))</code></pre>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">class</span> <span class="nc">ConcolicTracer</span><span class="p">(</span><span class="n">ConcolicTracer</span><span class="p">):</span>
    <span class="k">def</span> <span class="nf">smt_expr</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">show_decl</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="n">simplify</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="n">path</span><span class="o">=</span><span class="p">[]):</span>
        <span class="n">r</span> <span class="o">=</span> <span class="p">[]</span>
        <span class="k">if</span> <span class="n">show_decl</span><span class="p">:</span>
            <span class="k">for</span> <span class="n">decl</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">decls</span><span class="p">:</span>
                <span class="n">v</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">decls</span><span class="p">[</span><span class="n">decl</span><span class="p">]</span>
                <span class="n">v</span> <span class="o">=</span> <span class="s1">&#39;(_ BitVec 8)&#39;</span> <span class="k">if</span> <span class="n">v</span> <span class="o">==</span> <span class="s1">&#39;BitVec&#39;</span> <span class="k">else</span> <span class="n">v</span>
                <span class="n">r</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="s2">&quot;(declare-const </span><span class="si">%s</span><span class="s2"> </span><span class="si">%s</span><span class="s2">)&quot;</span> <span class="o">%</span> <span class="p">(</span><span class="n">decl</span><span class="p">,</span> <span class="n">v</span><span class="p">))</span>
        <span class="n">path</span> <span class="o">=</span> <span class="n">path</span> <span class="k">if</span> <span class="n">path</span> <span class="k">else</span> <span class="bp">self</span><span class="o">.</span><span class="n">path</span>
        <span class="k">if</span> <span class="n">path</span><span class="p">:</span>
            <span class="n">path</span> <span class="o">=</span> <span class="n">z3</span><span class="o">.</span><span class="n">And</span><span class="p">(</span><span class="n">path</span><span class="p">)</span>
            <span class="k">if</span> <span class="n">show_decl</span><span class="p">:</span>
                <span class="k">if</span> <span class="n">simplify</span><span class="p">:</span>
                    <span class="k">return</span> <span class="s1">&#39;</span><span class="se">\n</span><span class="s1">&#39;</span><span class="o">.</span><span class="n">join</span><span class="p">([</span>
                        <span class="o">*</span><span class="n">r</span><span class="p">,</span>
                        <span class="s2">&quot;(assert </span><span class="si">%s</span><span class="s2">)&quot;</span> <span class="o">%</span> <span class="n">z3</span><span class="o">.</span><span class="n">simplify</span><span class="p">(</span><span class="n">path</span><span class="p">)</span><span class="o">.</span><span class="n">sexpr</span><span class="p">()</span>
                    <span class="p">])</span>
                <span class="k">else</span><span class="p">:</span>
                    <span class="k">return</span> <span class="s1">&#39;</span><span class="se">\n</span><span class="s1">&#39;</span><span class="o">.</span><span class="n">join</span><span class="p">(</span>
                        <span class="p">[</span><span class="o">*</span><span class="n">r</span><span class="p">,</span> <span class="s2">&quot;(assert </span><span class="si">%s</span><span class="s2">)&quot;</span> <span class="o">%</span> <span class="n">path</span><span class="o">.</span><span class="n">sexpr</span><span class="p">()])</span>
            <span class="k">else</span><span class="p">:</span>
                <span class="k">return</span> <span class="n">z3</span><span class="o">.</span><span class="n">simplify</span><span class="p">(</span><span class="n">path</span><span class="p">)</span><span class="o">.</span><span class="n">sexpr</span><span class="p">()</span>
        <span class="k">else</span><span class="p">:</span>
            <span class="k">return</span> <span class="s1">&#39;&#39;</span>
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<p>To see how to use <code>smt_expr()</code>, let us consider an example. The <code>triangle()</code> function is used to determine if the given sides to a triangle result in an <code>equilateral</code> triangle, an <code>isosceles</code> triangle, or a <code>scalene</code> triangle. It is implemented as follows.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">def</span> <span class="nf">triangle</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">,</span> <span class="n">c</span><span class="p">):</span>
    <span class="k">if</span> <span class="n">a</span> <span class="o">==</span> <span class="n">b</span><span class="p">:</span>
        <span class="k">if</span> <span class="n">b</span> <span class="o">==</span> <span class="n">c</span><span class="p">:</span>
            <span class="k">return</span> <span class="s1">&#39;equilateral&#39;</span>
        <span class="k">else</span><span class="p">:</span>
            <span class="k">return</span> <span class="s1">&#39;isosceles&#39;</span>
    <span class="k">else</span><span class="p">:</span>
        <span class="k">if</span> <span class="n">b</span> <span class="o">==</span> <span class="n">c</span><span class="p">:</span>
            <span class="k">return</span> <span class="s1">&#39;isosceles&#39;</span>
        <span class="k">else</span><span class="p">:</span>
            <span class="k">if</span> <span class="n">a</span> <span class="o">==</span> <span class="n">c</span><span class="p">:</span>
                <span class="k">return</span> <span class="s1">&#39;isosceles&#39;</span>
            <span class="k">else</span><span class="p">:</span>
                <span class="k">return</span> <span class="s1">&#39;scalene&#39;</span>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">triangle</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
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<pre>&#39;isosceles&#39;</pre>
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<p>To translate make it run under <code>ConcolicTracer</code>, we first define the arguments. The triangle being defined has sides <code>1, 1, 1</code>. i.e. it is an <code>equilateral</code> triangle.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">with</span> <span class="n">ConcolicTracer</span><span class="p">()</span> <span class="k">as</span> <span class="n">_</span><span class="p">:</span>
    <span class="n">za</span> <span class="o">=</span> <span class="n">zint</span><span class="o">.</span><span class="n">create</span><span class="p">(</span><span class="n">_</span><span class="o">.</span><span class="n">context</span><span class="p">,</span> <span class="s1">&#39;int_a&#39;</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
    <span class="n">zb</span> <span class="o">=</span> <span class="n">zint</span><span class="o">.</span><span class="n">create</span><span class="p">(</span><span class="n">_</span><span class="o">.</span><span class="n">context</span><span class="p">,</span> <span class="s1">&#39;int_b&#39;</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
    <span class="n">zc</span> <span class="o">=</span> <span class="n">zint</span><span class="o">.</span><span class="n">create</span><span class="p">(</span><span class="n">_</span><span class="o">.</span><span class="n">context</span><span class="p">,</span> <span class="s1">&#39;int_c&#39;</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
    <span class="n">triangle</span><span class="p">(</span><span class="n">za</span><span class="p">,</span> <span class="n">zb</span><span class="p">,</span> <span class="n">zc</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="n">_</span><span class="o">.</span><span class="n">context</span><span class="p">)</span>
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<pre>({&#39;int_a&#39;: &#39;Int&#39;, &#39;int_b&#39;: &#39;Int&#39;, &#39;int_c&#39;: &#39;Int&#39;}, [int_a == int_b, int_b == int_c])
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<p>We can now call <code>smt_expr()</code> to retrieve the SMT expression as below.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="nb">print</span><span class="p">(</span><span class="n">_</span><span class="o">.</span><span class="n">smt_expr</span><span class="p">(</span><span class="n">show_decl</span><span class="o">=</span><span class="kc">True</span><span class="p">))</span>
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<pre>(declare-const int_a Int)
(declare-const int_b Int)
(declare-const int_c Int)
(assert (and (= int_a int_b) (= int_b int_c)))
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<p>The collected predicates can also be solved directly using the Python z3 API.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">z3</span><span class="o">.</span><span class="n">solve</span><span class="p">(</span><span class="n">_</span><span class="o">.</span><span class="n">path</span><span class="p">)</span>
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<pre>[int_c = 0, int_a = 0, int_b = 0]
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<h5 id="Generating-Fresh-Names">Generating Fresh Names<a class="anchor-link" href="#Generating-Fresh-Names">&#182;</a></h5><p>While using the proxy classes, we often will have to generate new symbolic variables, with names that have not been used before. For this, we define <code>fresh_name()</code> that always generates unique integers for names.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">COUNTER</span> <span class="o">=</span> <span class="mi">0</span>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">def</span> <span class="nf">fresh_name</span><span class="p">():</span>
    <span class="k">global</span> <span class="n">COUNTER</span>
    <span class="n">COUNTER</span> <span class="o">+=</span> <span class="mi">1</span>
    <span class="k">return</span> <span class="n">COUNTER</span>
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<p>It can be used as follows</p>

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<pre>1</pre>
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<h5 id="Translating-Arguments-to-Concolic-Proxies">Translating Arguments to Concolic Proxies<a class="anchor-link" href="#Translating-Arguments-to-Concolic-Proxies">&#182;</a></h5><p>We had previously defined <code>concolic()</code> as a transparent function. We now provide the full implementation of this function. It inspects a given function's parameters, and infers the parameter types from the concrete arguments passed in. It then uses this information to instantiate the correct proxy classes for each argument.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">class</span> <span class="nc">ConcolicTracer</span><span class="p">(</span><span class="n">ConcolicTracer</span><span class="p">):</span>
    <span class="k">def</span> <span class="nf">concolic</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">args</span><span class="p">):</span>
        <span class="n">my_args</span> <span class="o">=</span> <span class="p">[]</span>
        <span class="k">for</span> <span class="n">name</span><span class="p">,</span> <span class="n">arg</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">fn_args</span><span class="p">,</span> <span class="n">args</span><span class="p">):</span>
            <span class="n">t</span> <span class="o">=</span> <span class="nb">type</span><span class="p">(</span><span class="n">arg</span><span class="p">)</span><span class="o">.</span><span class="vm">__name__</span>
            <span class="n">zwrap</span> <span class="o">=</span> <span class="nb">globals</span><span class="p">()[</span><span class="s1">&#39;z&#39;</span> <span class="o">+</span> <span class="n">t</span><span class="p">]</span>
            <span class="n">vname</span> <span class="o">=</span> <span class="s2">&quot;</span><span class="si">%s</span><span class="s2">_</span><span class="si">%s</span><span class="s2">_</span><span class="si">%s</span><span class="s2">_</span><span class="si">%s</span><span class="s2">&quot;</span> <span class="o">%</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">fn</span><span class="o">.</span><span class="vm">__name__</span><span class="p">,</span> <span class="n">name</span><span class="p">,</span> <span class="n">t</span><span class="p">,</span> <span class="n">fresh_name</span><span class="p">())</span>
            <span class="n">my_args</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">zwrap</span><span class="o">.</span><span class="n">create</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">context</span><span class="p">,</span> <span class="n">vname</span><span class="p">,</span> <span class="n">arg</span><span class="p">))</span>
            <span class="bp">self</span><span class="o">.</span><span class="n">fn_args</span><span class="p">[</span><span class="n">name</span><span class="p">]</span> <span class="o">=</span> <span class="n">vname</span>
        <span class="k">return</span> <span class="n">my_args</span>
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<p>This is how it gets used:</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">with</span> <span class="n">ConcolicTracer</span><span class="p">()</span> <span class="k">as</span> <span class="n">_</span><span class="p">:</span>
    <span class="n">_</span><span class="p">[</span><span class="n">factorial</span><span class="p">](</span><span class="mi">5</span><span class="p">)</span>
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<p>With the new <code>concolic()</code> method, the arguments to the factorial are correctly associated with symbolic variables, which allows us to retrieve the predicates encountered.</p>

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<pre>({&#39;factorial_n_int_2&#39;: &#39;Int&#39;},
 [Not(0 &gt; factorial_n_int_2),
  Not(0 == factorial_n_int_2),
  Not(1 == factorial_n_int_2),
  0 != factorial_n_int_2,
  0 != factorial_n_int_2 - 1,
  0 != factorial_n_int_2 - 1 - 1,
  0 != factorial_n_int_2 - 1 - 1 - 1,
  0 != factorial_n_int_2 - 1 - 1 - 1 - 1,
  Not(0 != factorial_n_int_2 - 1 - 1 - 1 - 1 - 1)])</pre>
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<p>As before, we can also print out the SMT expression which can be passed directly to command line SMT solvers.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="nb">print</span><span class="p">(</span><span class="n">_</span><span class="o">.</span><span class="n">smt_expr</span><span class="p">(</span><span class="n">show_decl</span><span class="o">=</span><span class="kc">True</span><span class="p">))</span>
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<pre>(declare-const factorial_n_int_2 Int)
(assert (let ((a!1 (distinct 0 (- (- (- factorial_n_int_2 1) 1) 1)))
      (a!2 (- (- (- (- factorial_n_int_2 1) 1) 1) 1)))
  (and (not (&gt; 0 factorial_n_int_2))
       (not (= 0 factorial_n_int_2))
       (not (= 1 factorial_n_int_2))
       (distinct 0 factorial_n_int_2)
       (distinct 0 (- factorial_n_int_2 1))
       (distinct 0 (- (- factorial_n_int_2 1) 1))
       a!1
       (distinct 0 a!2)
       (not (distinct 0 (- a!2 1))))))
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<p>We next define methods to evaluate the SMT expression both in Python and from command line.</p>

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<h5 id="Evaluating-the-Concolic-Expressions">Evaluating the Concolic Expressions<a class="anchor-link" href="#Evaluating-the-Concolic-Expressions">&#182;</a></h5><p>We define <code>zeval()</code> to solve the predicates in a context, and return results. It has two modes. The <code>python</code> mode uses <code>z3</code> Python API to solve and return the results. If the <code>python</code> mode is false, it writes the SMT expression to a file, and invokes the command line <code>z3</code> for a solution.</p>

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    <span class="k">def</span> <span class="nf">zeval</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">python</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="n">log</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
        <span class="n">r</span><span class="p">,</span> <span class="n">sol</span> <span class="o">=</span> <span class="p">(</span><span class="n">zeval_py</span> <span class="k">if</span> <span class="n">python</span> <span class="k">else</span> <span class="n">zeval_smt</span><span class="p">)(</span><span class="bp">self</span><span class="o">.</span><span class="n">path</span><span class="p">,</span> <span class="bp">self</span><span class="p">,</span> <span class="n">log</span><span class="p">)</span>
        <span class="k">if</span> <span class="n">r</span> <span class="o">==</span> <span class="s1">&#39;sat&#39;</span><span class="p">:</span>
            <span class="k">return</span> <span class="n">r</span><span class="p">,</span> <span class="p">{</span><span class="n">k</span><span class="p">:</span> <span class="n">sol</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">fn_args</span><span class="p">[</span><span class="n">k</span><span class="p">],</span> <span class="kc">None</span><span class="p">)</span> <span class="k">for</span> <span class="n">k</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">fn_args</span><span class="p">}</span>
        <span class="k">else</span><span class="p">:</span>
            <span class="k">return</span> <span class="n">r</span><span class="p">,</span> <span class="kc">None</span>
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<h5 id="Using-the-Python-API">Using the Python API<a class="anchor-link" href="#Using-the-Python-API">&#182;</a></h5><p>Given a set of predicates that the function encountered, and the tracer under which the function was executed, the <code>zeval_py()</code> function first declares the relevant symbolic variables, and uses the <code>z3.Solver()</code>to provide a set of inputs that would trace the same path through the function.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">def</span> <span class="nf">zeval_py</span><span class="p">(</span><span class="n">path</span><span class="p">,</span> <span class="n">cc</span><span class="p">,</span> <span class="n">log</span><span class="p">):</span>
    <span class="k">for</span> <span class="n">decl</span> <span class="ow">in</span> <span class="n">cc</span><span class="o">.</span><span class="n">decls</span><span class="p">:</span>
        <span class="k">if</span> <span class="n">cc</span><span class="o">.</span><span class="n">decls</span><span class="p">[</span><span class="n">decl</span><span class="p">]</span> <span class="o">==</span> <span class="s1">&#39;BitVec&#39;</span><span class="p">:</span>
            <span class="n">v</span> <span class="o">=</span> <span class="s2">&quot;z3.</span><span class="si">%s</span><span class="s2">(&#39;</span><span class="si">%s</span><span class="s2">&#39;, 8)&quot;</span> <span class="o">%</span> <span class="p">(</span><span class="n">cc</span><span class="o">.</span><span class="n">decls</span><span class="p">[</span><span class="n">decl</span><span class="p">],</span> <span class="n">decl</span><span class="p">)</span>
        <span class="k">else</span><span class="p">:</span>
            <span class="n">v</span> <span class="o">=</span> <span class="s2">&quot;z3.</span><span class="si">%s</span><span class="s2">(&#39;</span><span class="si">%s</span><span class="s2">&#39;)&quot;</span> <span class="o">%</span> <span class="p">(</span><span class="n">cc</span><span class="o">.</span><span class="n">decls</span><span class="p">[</span><span class="n">decl</span><span class="p">],</span> <span class="n">decl</span><span class="p">)</span>
        <span class="n">exec</span><span class="p">(</span><span class="n">v</span><span class="p">)</span>
    <span class="n">s</span> <span class="o">=</span> <span class="n">z3</span><span class="o">.</span><span class="n">Solver</span><span class="p">()</span>
    <span class="n">s</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">z3</span><span class="o">.</span><span class="n">And</span><span class="p">(</span><span class="n">path</span><span class="p">))</span>
    <span class="k">if</span> <span class="n">s</span><span class="o">.</span><span class="n">check</span><span class="p">()</span> <span class="o">==</span> <span class="n">z3</span><span class="o">.</span><span class="n">unsat</span><span class="p">:</span>
        <span class="k">return</span> <span class="s1">&#39;No Solutions&#39;</span><span class="p">,</span> <span class="p">{}</span>
    <span class="k">elif</span> <span class="n">s</span><span class="o">.</span><span class="n">check</span><span class="p">()</span> <span class="o">==</span> <span class="n">z3</span><span class="o">.</span><span class="n">unknown</span><span class="p">:</span>
        <span class="k">return</span> <span class="s1">&#39;Gave up&#39;</span><span class="p">,</span> <span class="kc">None</span>
    <span class="k">assert</span> <span class="n">s</span><span class="o">.</span><span class="n">check</span><span class="p">()</span> <span class="o">==</span> <span class="n">z3</span><span class="o">.</span><span class="n">sat</span>
    <span class="n">m</span> <span class="o">=</span> <span class="n">s</span><span class="o">.</span><span class="n">model</span><span class="p">()</span>
    <span class="k">return</span> <span class="s1">&#39;sat&#39;</span><span class="p">,</span> <span class="p">{</span><span class="n">d</span><span class="o">.</span><span class="n">name</span><span class="p">():</span> <span class="n">m</span><span class="p">[</span><span class="n">d</span><span class="p">]</span> <span class="k">for</span> <span class="n">d</span> <span class="ow">in</span> <span class="n">m</span><span class="o">.</span><span class="n">decls</span><span class="p">()}</span>
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<p>It can be used as follows:</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">with</span> <span class="n">ConcolicTracer</span><span class="p">()</span> <span class="k">as</span> <span class="n">_</span><span class="p">:</span>
    <span class="n">_</span><span class="p">[</span><span class="n">factorial</span><span class="p">](</span><span class="mi">5</span><span class="p">)</span>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">_</span><span class="o">.</span><span class="n">zeval</span><span class="p">(</span><span class="n">python</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
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<pre>(&#39;sat&#39;, {&#39;n&#39;: 5})</pre>
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<p>That is, given the set of constraints, the assignment <code>n == 5</code> conforms to all constraints.</p>

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<h5 id="Using-the-Command-Line">Using the Command Line<a class="anchor-link" href="#Using-the-Command-Line">&#182;</a></h5><p>The <code>zeval_smt()</code> function writes the SMT expression to the file system, and calls the <code>z3</code> SMT solver command line to solve it. The result of SMT expression is again an <code>sexpr</code>. Hence, we first define <code>parse_sexp()</code> to parse and return the correct values.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">SEXPR_TOKEN</span> <span class="o">=</span> <span class="sa">r</span><span class="s1">&#39;&#39;&#39;(?mx)</span>
<span class="s1">    \s*(?:</span>
<span class="s1">        (?P&lt;bra&gt;\()|</span>
<span class="s1">        (?P&lt;ket&gt;\))|</span>
<span class="s1">        (?P&lt;token&gt;[^&quot;()\s]+)|</span>
<span class="s1">        (?P&lt;string&gt;&quot;[^&quot;]*&quot;)</span>
<span class="s1">       )&#39;&#39;&#39;</span>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">def</span> <span class="nf">parse_sexp</span><span class="p">(</span><span class="n">sexp</span><span class="p">):</span>
    <span class="n">stack</span><span class="p">,</span> <span class="n">res</span> <span class="o">=</span> <span class="p">[],</span> <span class="p">[]</span>
    <span class="k">for</span> <span class="n">elements</span> <span class="ow">in</span> <span class="n">re</span><span class="o">.</span><span class="n">finditer</span><span class="p">(</span><span class="n">SEXPR_TOKEN</span><span class="p">,</span> <span class="n">sexp</span><span class="p">):</span>
        <span class="n">kind</span><span class="p">,</span> <span class="n">value</span> <span class="o">=</span> <span class="p">[(</span><span class="n">t</span><span class="p">,</span> <span class="n">v</span><span class="p">)</span> <span class="k">for</span> <span class="n">t</span><span class="p">,</span> <span class="n">v</span> <span class="ow">in</span> <span class="n">elements</span><span class="o">.</span><span class="n">groupdict</span><span class="p">()</span><span class="o">.</span><span class="n">items</span><span class="p">()</span> <span class="k">if</span> <span class="n">v</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span>
        <span class="k">if</span> <span class="n">kind</span> <span class="o">==</span> <span class="s1">&#39;bra&#39;</span><span class="p">:</span>
            <span class="n">stack</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">res</span><span class="p">)</span>
            <span class="n">res</span> <span class="o">=</span> <span class="p">[]</span>
        <span class="k">elif</span> <span class="n">kind</span> <span class="o">==</span> <span class="s1">&#39;ket&#39;</span><span class="p">:</span>
            <span class="n">last</span><span class="p">,</span> <span class="n">res</span> <span class="o">=</span> <span class="n">res</span><span class="p">,</span> <span class="n">stack</span><span class="o">.</span><span class="n">pop</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span>
            <span class="n">res</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">last</span><span class="p">)</span>
        <span class="k">elif</span> <span class="n">kind</span> <span class="o">==</span> <span class="s1">&#39;token&#39;</span><span class="p">:</span>
            <span class="n">res</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">value</span><span class="p">)</span>
        <span class="k">elif</span> <span class="n">kind</span> <span class="o">==</span> <span class="s1">&#39;string&#39;</span><span class="p">:</span>
            <span class="n">res</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">value</span><span class="p">[</span><span class="mi">1</span><span class="p">:</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span>
        <span class="k">else</span><span class="p">:</span>
            <span class="k">assert</span> <span class="kc">False</span>
    <span class="k">return</span> <span class="n">res</span>
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<p>The <code>parse_sexp()</code> function can be used as follows</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">parse_sexp</span><span class="p">(</span><span class="s1">&#39;abcd (hello 123 (world &quot;hello world&quot;))&#39;</span><span class="p">)</span>
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<pre>[&#39;abcd&#39;, [&#39;hello&#39;, &#39;123&#39;, [&#39;world&#39;, &#39;hello world&#39;]]]</pre>
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<p>We now define <code>zeval_smt()</code> which uses the <code>z3</code> command line directly, and uses <code>parse_sexp()</code> to parse and return the solutions to function arguments if any.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">def</span> <span class="nf">zeval_smt</span><span class="p">(</span><span class="n">path</span><span class="p">,</span> <span class="n">cc</span><span class="p">,</span> <span class="n">log</span><span class="p">):</span>
    <span class="n">s</span> <span class="o">=</span> <span class="n">cc</span><span class="o">.</span><span class="n">smt_expr</span><span class="p">(</span><span class="kc">True</span><span class="p">,</span> <span class="kc">True</span><span class="p">,</span> <span class="n">path</span><span class="p">)</span>
    
    <span class="k">with</span> <span class="n">tempfile</span><span class="o">.</span><span class="n">NamedTemporaryFile</span><span class="p">(</span><span class="n">mode</span><span class="o">=</span><span class="s1">&#39;w&#39;</span><span class="p">,</span> <span class="n">suffix</span><span class="o">=</span><span class="s1">&#39;.smt&#39;</span><span class="p">)</span> <span class="k">as</span> <span class="n">f</span><span class="p">:</span>
        <span class="n">f</span><span class="o">.</span><span class="n">write</span><span class="p">(</span><span class="n">s</span><span class="p">)</span>
        <span class="n">f</span><span class="o">.</span><span class="n">write</span><span class="p">(</span><span class="s2">&quot;</span><span class="se">\n</span><span class="s2">(check-sat)&quot;</span><span class="p">)</span>
        <span class="n">f</span><span class="o">.</span><span class="n">write</span><span class="p">(</span><span class="s2">&quot;</span><span class="se">\n</span><span class="s2">(get-model)&quot;</span><span class="p">)</span>
        <span class="n">f</span><span class="o">.</span><span class="n">flush</span><span class="p">()</span>

        <span class="k">if</span> <span class="n">log</span><span class="p">:</span>
            <span class="nb">print</span><span class="p">(</span><span class="n">s</span><span class="p">,</span> <span class="s1">&#39;(check-sat)&#39;</span><span class="p">,</span> <span class="s1">&#39;(get-model)&#39;</span><span class="p">,</span> <span class="n">sep</span><span class="o">=</span><span class="s1">&#39;</span><span class="se">\n</span><span class="s1">&#39;</span><span class="p">)</span>
        <span class="n">output</span> <span class="o">=</span> <span class="n">subprocess</span><span class="o">.</span><span class="n">getoutput</span><span class="p">(</span><span class="s2">&quot;z3 &quot;</span> <span class="o">+</span> <span class="n">f</span><span class="o">.</span><span class="n">name</span><span class="p">)</span>
    
    <span class="k">if</span> <span class="n">log</span><span class="p">:</span>
        <span class="nb">print</span><span class="p">(</span><span class="n">output</span><span class="p">)</span>
    <span class="n">o</span> <span class="o">=</span> <span class="n">parse_sexp</span><span class="p">(</span><span class="n">output</span><span class="p">)</span>
    <span class="n">kind</span> <span class="o">=</span> <span class="n">o</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
    <span class="k">if</span> <span class="n">kind</span> <span class="o">==</span> <span class="s1">&#39;unknown&#39;</span><span class="p">:</span>
        <span class="k">return</span> <span class="s1">&#39;Gave up&#39;</span><span class="p">,</span> <span class="kc">None</span>
    <span class="k">elif</span> <span class="n">kind</span> <span class="o">==</span> <span class="s1">&#39;unsat&#39;</span><span class="p">:</span>
        <span class="k">return</span> <span class="s1">&#39;No Solutions&#39;</span><span class="p">,</span> <span class="p">{}</span>
    <span class="k">assert</span> <span class="n">kind</span> <span class="o">==</span> <span class="s1">&#39;sat&#39;</span>
    <span class="k">assert</span> <span class="n">o</span><span class="p">[</span><span class="mi">1</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span> <span class="o">==</span> <span class="s1">&#39;model&#39;</span>
    <span class="k">return</span> <span class="s1">&#39;sat&#39;</span><span class="p">,</span> <span class="p">{</span><span class="n">i</span><span class="p">[</span><span class="mi">1</span><span class="p">]:</span> <span class="n">i</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">o</span><span class="p">[</span><span class="mi">1</span><span class="p">][</span><span class="mi">1</span><span class="p">:]}</span>
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<p>We can now use <code>zeval()</code> as follows.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">with</span> <span class="n">ConcolicTracer</span><span class="p">()</span> <span class="k">as</span> <span class="n">_</span><span class="p">:</span>
    <span class="n">_</span><span class="p">[</span><span class="n">factorial</span><span class="p">](</span><span class="mi">5</span><span class="p">)</span>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">_</span><span class="o">.</span><span class="n">zeval</span><span class="p">()</span>
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<pre>(&#39;sat&#39;, {&#39;n&#39;: &#39;5&#39;})</pre>
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<p>Indeed, we get similar results (<code>n == 5</code>)  from using the command line as from using the Python API.</p>

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<h4 id="A-Proxy-Class-for-Strings">A Proxy Class for Strings<a class="anchor-link" href="#A-Proxy-Class-for-Strings">&#182;</a></h4><p>Here, we define the proxy string class <code>zstr</code>. First we define our initialization routines. Since <code>str</code> is a primitive type, we define <code>new</code> to extend it.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">class</span> <span class="nc">zstr</span><span class="p">(</span><span class="nb">str</span><span class="p">):</span>
    <span class="k">def</span> <span class="nf">__new__</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="n">context</span><span class="p">,</span> <span class="n">zn</span><span class="p">,</span> <span class="n">v</span><span class="p">):</span>
        <span class="k">return</span> <span class="nb">str</span><span class="o">.</span><span class="fm">__new__</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="n">v</span><span class="p">)</span>
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<p>As before, initialization proceeds with <code>create()</code> and the constructor.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">class</span> <span class="nc">zstr</span><span class="p">(</span><span class="n">zstr</span><span class="p">):</span>
    <span class="nd">@classmethod</span>
    <span class="k">def</span> <span class="nf">create</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="n">context</span><span class="p">,</span> <span class="n">zn</span><span class="p">,</span> <span class="n">v</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
        <span class="k">return</span> <span class="n">zproxy_create</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="s1">&#39;String&#39;</span><span class="p">,</span> <span class="n">z3</span><span class="o">.</span><span class="n">String</span><span class="p">,</span> <span class="n">context</span><span class="p">,</span> <span class="n">zn</span><span class="p">,</span> <span class="n">v</span><span class="p">)</span>

    <span class="k">def</span> <span class="nf">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">context</span><span class="p">,</span> <span class="n">z</span><span class="p">,</span> <span class="n">v</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">context</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">z</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">v</span> <span class="o">=</span> <span class="n">context</span><span class="p">,</span> <span class="n">z</span><span class="p">,</span> <span class="n">v</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">_len</span> <span class="o">=</span> <span class="n">zint</span><span class="p">(</span><span class="n">context</span><span class="p">,</span> <span class="n">z3</span><span class="o">.</span><span class="n">Length</span><span class="p">(</span><span class="n">z</span><span class="p">),</span> <span class="nb">len</span><span class="p">(</span><span class="n">v</span><span class="p">))</span>
        <span class="c1">#self.context[1].append(z3.Length(z) == z3.IntVal(len(v)))</span>
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<p>We also define <code>_zv()</code> helper to help us with methods that accept another string</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">class</span> <span class="nc">zstr</span><span class="p">(</span><span class="n">zstr</span><span class="p">):</span>
    <span class="k">def</span> <span class="nf">_zv</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">o</span><span class="p">):</span>
        <span class="k">return</span> <span class="p">(</span><span class="n">o</span><span class="o">.</span><span class="n">z</span><span class="p">,</span> <span class="n">o</span><span class="o">.</span><span class="n">v</span><span class="p">)</span> <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">o</span><span class="p">,</span> <span class="n">zstr</span><span class="p">)</span> <span class="k">else</span> <span class="p">(</span><span class="n">z3</span><span class="o">.</span><span class="n">StringVal</span><span class="p">(</span><span class="n">o</span><span class="p">),</span> <span class="n">o</span><span class="p">)</span>
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<h5 id="Retrieving-Ordinal-Value">Retrieving Ordinal Value<a class="anchor-link" href="#Retrieving-Ordinal-Value">&#182;</a></h5><p>We define <code>zord</code> that given a symbolic one character long string, obtains the <code>ord()</code> for that. It returns two values. The first one is the variable that corresponds to <code>ord()</code>, and second is the predicate that links the variable to the passed in single character string.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">def</span> <span class="nf">zord</span><span class="p">(</span><span class="n">context</span><span class="p">,</span> <span class="n">c</span><span class="p">):</span>
    <span class="n">bn</span> <span class="o">=</span> <span class="s2">&quot;bitvec_</span><span class="si">%d</span><span class="s2">&quot;</span> <span class="o">%</span> <span class="n">fresh_name</span><span class="p">()</span>
    <span class="n">v</span> <span class="o">=</span> <span class="n">z3</span><span class="o">.</span><span class="n">BitVec</span><span class="p">(</span><span class="n">bn</span><span class="p">,</span> <span class="mi">8</span><span class="p">)</span>
    <span class="n">context</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="n">bn</span><span class="p">]</span> <span class="o">=</span> <span class="s1">&#39;BitVec&#39;</span>
    <span class="n">z</span> <span class="o">=</span> <span class="p">(</span><span class="n">z3</span><span class="o">.</span><span class="n">Unit</span><span class="p">(</span><span class="n">v</span><span class="p">)</span> <span class="o">==</span> <span class="n">c</span><span class="p">)</span>
    <span class="n">context</span><span class="p">[</span><span class="mi">1</span><span class="p">]</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="k">return</span> <span class="n">v</span>
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<p>We use it as follows</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">zc</span> <span class="o">=</span> <span class="n">z3</span><span class="o">.</span><span class="n">String</span><span class="p">(</span><span class="s1">&#39;arg_</span><span class="si">%d</span><span class="s1">&#39;</span> <span class="o">%</span> <span class="n">fresh_name</span><span class="p">())</span>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">with</span> <span class="n">ConcolicTracer</span><span class="p">()</span> <span class="k">as</span> <span class="n">_</span><span class="p">:</span>
    <span class="n">zi</span> <span class="o">=</span> <span class="n">zord</span><span class="p">(</span><span class="n">_</span><span class="o">.</span><span class="n">context</span><span class="p">,</span> <span class="n">zc</span><span class="p">)</span>
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<p>The symbolic bitvector is in <code>zi</code>. It is linked to the passed in argument in <code>context</code></p>

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<pre>({&#39;bitvec_6&#39;: &#39;BitVec&#39;}, [seq.unit(bitvec_6) == arg_5])</pre>
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<p>We can specify what the result of <code>ord()</code> should be, and call <code>z3.solve()</code> to provide us with a solution that will provide the required result.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">z3</span><span class="o">.</span><span class="n">solve</span><span class="p">(</span><span class="n">_</span><span class="o">.</span><span class="n">path</span> <span class="o">+</span> <span class="p">[</span><span class="n">zi</span> <span class="o">==</span> <span class="mi">65</span><span class="p">])</span>
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<pre>[arg_5 = &#34;A&#34;, bitvec_6 = 65]
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<h5 id="Translating-an-Ordinal-Value-to-ASCII">Translating an Ordinal Value to ASCII<a class="anchor-link" href="#Translating-an-Ordinal-Value-to-ASCII">&#182;</a></h5><p>Similarly, we can convert the ASCII value back to a single character string using <code>zchr()</code></p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">def</span> <span class="nf">zchr</span><span class="p">(</span><span class="n">context</span><span class="p">,</span> <span class="n">i</span><span class="p">):</span>
    <span class="n">sn</span> <span class="o">=</span> <span class="s1">&#39;string_</span><span class="si">%d</span><span class="s1">&#39;</span> <span class="o">%</span> <span class="n">fresh_name</span><span class="p">()</span>
    <span class="n">s</span> <span class="o">=</span> <span class="n">z3</span><span class="o">.</span><span class="n">String</span><span class="p">(</span><span class="n">sn</span><span class="p">)</span>
    <span class="n">context</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="n">sn</span><span class="p">]</span> <span class="o">=</span> <span class="s1">&#39;String&#39;</span>
    <span class="n">z</span> <span class="o">=</span> <span class="n">z3</span><span class="o">.</span><span class="n">And</span><span class="p">([</span><span class="n">s</span> <span class="o">==</span> <span class="n">z3</span><span class="o">.</span><span class="n">Unit</span><span class="p">(</span><span class="n">i</span><span class="p">),</span> <span class="n">z3</span><span class="o">.</span><span class="n">Length</span><span class="p">(</span><span class="n">s</span><span class="p">)</span> <span class="o">==</span> <span class="mi">1</span><span class="p">])</span>
    <span class="n">context</span><span class="p">[</span><span class="mi">1</span><span class="p">]</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="k">return</span> <span class="n">s</span>
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<p>For using it, we first define a bitvector that is 8 bits long.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">i</span> <span class="o">=</span> <span class="n">z3</span><span class="o">.</span><span class="n">BitVec</span><span class="p">(</span><span class="s1">&#39;bv_</span><span class="si">%d</span><span class="s1">&#39;</span> <span class="o">%</span> <span class="n">fresh_name</span><span class="p">(),</span> <span class="mi">8</span><span class="p">)</span>
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<p>We can now retrieve the <code>chr()</code> representation as below.</p>

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    <span class="n">zc</span> <span class="o">=</span> <span class="n">zchr</span><span class="p">(</span><span class="n">_</span><span class="o">.</span><span class="n">context</span><span class="p">,</span> <span class="n">i</span><span class="p">)</span>
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<pre>({&#39;string_8&#39;: &#39;String&#39;},
 [And(string_8 == seq.unit(bv_7), str.len(string_8) == 1)])</pre>
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<p>As before, we can specify what the end result of calling <code>chr()</code> should be to get the original argument.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">z3</span><span class="o">.</span><span class="n">solve</span><span class="p">(</span><span class="n">_</span><span class="o">.</span><span class="n">path</span> <span class="o">+</span> <span class="p">[</span><span class="n">zc</span> <span class="o">==</span> <span class="n">z3</span><span class="o">.</span><span class="n">StringVal</span><span class="p">(</span><span class="s1">&#39;a&#39;</span><span class="p">)])</span>
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<pre>[bv_7 = 97, string_8 = &#34;a&#34;]
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<h5 id="Equality-between-Strings">Equality between Strings<a class="anchor-link" href="#Equality-between-Strings">&#182;</a></h5><p>The equality of <code>zstr</code> is defined similar to that of <code>zint</code></p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">class</span> <span class="nc">zstr</span><span class="p">(</span><span class="n">zstr</span><span class="p">):</span>
    <span class="k">def</span> <span class="nf">__eq__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
        <span class="n">z</span><span class="p">,</span> <span class="n">v</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_zv</span><span class="p">(</span><span class="n">other</span><span class="p">)</span>
        <span class="k">return</span> <span class="n">zbool</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">context</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">z</span> <span class="o">==</span> <span class="n">z</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">v</span> <span class="o">==</span> <span class="n">v</span><span class="p">)</span>

    <span class="k">def</span> <span class="nf">__req__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="fm">__eq__</span><span class="p">(</span><span class="n">other</span><span class="p">)</span>
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<p>The <code>zstr</code> class is used as follows.</p>

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    <span class="k">if</span> <span class="n">s</span> <span class="o">==</span> <span class="s1">&#39;h&#39;</span><span class="p">:</span>
        <span class="k">return</span> <span class="kc">True</span>
    <span class="k">else</span><span class="p">:</span>
        <span class="k">return</span> <span class="kc">False</span>
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    <span class="n">r</span> <span class="o">=</span> <span class="n">_</span><span class="p">[</span><span class="n">tstr1</span><span class="p">](</span><span class="s1">&#39;h&#39;</span><span class="p">)</span>
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<pre>(&#39;sat&#39;, {&#39;s&#39;: &#39;h&#39;})</pre>
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<p>It works even if we have more than one character.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">def</span> <span class="nf">tstr1</span><span class="p">(</span><span class="n">s</span><span class="p">):</span>
    <span class="k">if</span> <span class="n">s</span> <span class="o">==</span> <span class="s1">&#39;hello world&#39;</span><span class="p">:</span>
        <span class="k">return</span> <span class="kc">True</span>
    <span class="k">else</span><span class="p">:</span>
        <span class="k">return</span> <span class="kc">False</span>
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    <span class="n">r</span> <span class="o">=</span> <span class="n">_</span><span class="p">[</span><span class="n">tstr1</span><span class="p">](</span><span class="s1">&#39;hello world&#39;</span><span class="p">)</span>
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<pre>({&#39;tstr1_s_str_10&#39;: &#39;String&#39;}, [tstr1_s_str_10 == &#34;hello world&#34;])</pre>
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<pre>(&#39;sat&#39;, {&#39;s&#39;: &#39;hello world&#39;})</pre>
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<h5 id="Concatenation-of-Strings">Concatenation of Strings<a class="anchor-link" href="#Concatenation-of-Strings">&#182;</a></h5><p>What if we need to concatenate two strings? We need additional helpers to accomplish that.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">class</span> <span class="nc">zstr</span><span class="p">(</span><span class="n">zstr</span><span class="p">):</span>
    <span class="k">def</span> <span class="nf">__add__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
        <span class="n">z</span><span class="p">,</span> <span class="n">v</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_zv</span><span class="p">(</span><span class="n">other</span><span class="p">)</span>
        <span class="k">return</span> <span class="n">zstr</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">context</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">z</span> <span class="o">+</span> <span class="n">z</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">v</span> <span class="o">+</span> <span class="n">v</span><span class="p">)</span>

    <span class="k">def</span> <span class="nf">__radd__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="fm">__add__</span><span class="p">(</span><span class="n">other</span><span class="p">)</span>
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<p>Here is how it can be used. First, we create the wrapped arguments</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">with</span> <span class="n">ConcolicTracer</span><span class="p">()</span> <span class="k">as</span> <span class="n">_</span><span class="p">:</span>
    <span class="n">v1</span><span class="p">,</span> <span class="n">v2</span> <span class="o">=</span> <span class="p">[</span><span class="n">zstr</span><span class="o">.</span><span class="n">create</span><span class="p">(</span><span class="n">_</span><span class="o">.</span><span class="n">context</span><span class="p">,</span> <span class="s1">&#39;arg_</span><span class="si">%d</span><span class="s1">&#39;</span> <span class="o">%</span> <span class="n">fresh_name</span><span class="p">(),</span> <span class="n">s</span><span class="p">)</span>
              <span class="k">for</span> <span class="n">s</span> <span class="ow">in</span> <span class="p">[</span><span class="s1">&#39;hello&#39;</span><span class="p">,</span> <span class="s1">&#39;world&#39;</span><span class="p">]]</span>
    <span class="k">if</span> <span class="p">(</span><span class="n">v1</span> <span class="o">+</span> <span class="s1">&#39; &#39;</span> <span class="o">+</span> <span class="n">v2</span><span class="p">)</span> <span class="o">==</span> <span class="s1">&#39;hello world&#39;</span><span class="p">:</span>
        <span class="nb">print</span><span class="p">(</span><span class="s1">&#39;hello world&#39;</span><span class="p">)</span>
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<pre>hello world
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<p>The addition of symbolic variables is preserved in <code>context</code></p>

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<pre>({&#39;arg_11&#39;: &#39;String&#39;, &#39;arg_12&#39;: &#39;String&#39;},
 [str.++(str.++(arg_11, &#34; &#34;), arg_12) == &#34;hello world&#34;])</pre>
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<h5 id="Producing-Substrings">Producing Substrings<a class="anchor-link" href="#Producing-Substrings">&#182;</a></h5><p>Similarly, accessing substrings also require extra help.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">class</span> <span class="nc">zstr</span><span class="p">(</span><span class="n">zstr</span><span class="p">):</span>
    <span class="k">def</span> <span class="nf">__getitem__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">idx</span><span class="p">):</span>
        <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">idx</span><span class="p">,</span> <span class="nb">slice</span><span class="p">):</span>
            <span class="n">start</span><span class="p">,</span> <span class="n">stop</span><span class="p">,</span> <span class="n">step</span> <span class="o">=</span> <span class="n">idx</span><span class="o">.</span><span class="n">indices</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">v</span><span class="p">))</span>
            <span class="k">assert</span> <span class="n">step</span> <span class="o">==</span> <span class="mi">1</span>  <span class="c1"># for now</span>
            <span class="k">assert</span> <span class="n">stop</span> <span class="o">&gt;=</span> <span class="n">start</span>  <span class="c1"># for now</span>
            <span class="n">rz</span> <span class="o">=</span> <span class="n">z3</span><span class="o">.</span><span class="n">SubString</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">z</span><span class="p">,</span> <span class="n">start</span><span class="p">,</span> <span class="n">stop</span> <span class="o">-</span> <span class="n">start</span><span class="p">)</span>
            <span class="n">rv</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">v</span><span class="p">[</span><span class="n">idx</span><span class="p">]</span>
        <span class="k">elif</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">idx</span><span class="p">,</span> <span class="nb">int</span><span class="p">):</span>
            <span class="n">rz</span> <span class="o">=</span> <span class="n">z3</span><span class="o">.</span><span class="n">SubString</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">z</span><span class="p">,</span> <span class="n">idx</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
            <span class="n">rv</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">v</span><span class="p">[</span><span class="n">idx</span><span class="p">]</span>
        <span class="k">else</span><span class="p">:</span>
            <span class="k">assert</span> <span class="kc">False</span>  <span class="c1"># for now</span>
        <span class="k">return</span> <span class="n">zstr</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">context</span><span class="p">,</span> <span class="n">rz</span><span class="p">,</span> <span class="n">rv</span><span class="p">)</span>

    <span class="k">def</span> <span class="nf">__iter__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
        <span class="k">return</span> <span class="n">zstr_iterator</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">context</span><span class="p">,</span> <span class="bp">self</span><span class="p">)</span>
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<h5 id="An-Iterator-Class-for-Strings">An Iterator Class for Strings<a class="anchor-link" href="#An-Iterator-Class-for-Strings">&#182;</a></h5><p>We define the iterator as follows.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">class</span> <span class="nc">zstr_iterator</span><span class="p">():</span>
    <span class="k">def</span> <span class="nf">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">context</span><span class="p">,</span> <span class="n">zstr</span><span class="p">):</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">context</span> <span class="o">=</span> <span class="n">context</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">_zstr</span> <span class="o">=</span> <span class="n">zstr</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">_str_idx</span> <span class="o">=</span> <span class="mi">0</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">_str_max</span> <span class="o">=</span> <span class="n">zstr</span><span class="o">.</span><span class="n">_len</span>  <span class="c1"># intz is not an _int_</span>

    <span class="k">def</span> <span class="nf">__next__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">_str_idx</span> <span class="o">==</span> <span class="bp">self</span><span class="o">.</span><span class="n">_str_max</span><span class="p">:</span>  <span class="c1"># intz#eq</span>
            <span class="k">raise</span> <span class="ne">StopIteration</span>
        <span class="n">c</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_zstr</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">_str_idx</span><span class="p">]</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">_str_idx</span> <span class="o">+=</span> <span class="mi">1</span>
        <span class="k">return</span> <span class="n">c</span>

    <span class="k">def</span> <span class="nf">__len__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_len</span>
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<p>Here is how it can be used.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">def</span> <span class="nf">tstr2</span><span class="p">(</span><span class="n">s</span><span class="p">):</span>
    <span class="k">if</span> <span class="n">s</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">==</span> <span class="s1">&#39;h&#39;</span> <span class="ow">and</span> <span class="n">s</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">==</span> <span class="s1">&#39;e&#39;</span> <span class="ow">and</span> <span class="n">s</span><span class="p">[</span><span class="mi">3</span><span class="p">]</span> <span class="o">==</span> <span class="s1">&#39;l&#39;</span><span class="p">:</span>
        <span class="k">return</span> <span class="kc">True</span>
    <span class="k">else</span><span class="p">:</span>
        <span class="k">return</span> <span class="kc">False</span>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">with</span> <span class="n">ConcolicTracer</span><span class="p">()</span> <span class="k">as</span> <span class="n">_</span><span class="p">:</span>
    <span class="n">r</span> <span class="o">=</span> <span class="n">_</span><span class="p">[</span><span class="n">tstr2</span><span class="p">](</span><span class="s1">&#39;hello&#39;</span><span class="p">)</span>
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<p>Again, the context shows predicates encountered.</p>

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<pre>({&#39;tstr2_s_str_13&#39;: &#39;String&#39;},
 [str.substr(tstr2_s_str_13, 0, 1) == &#34;h&#34;,
  str.substr(tstr2_s_str_13, 1, 1) == &#34;e&#34;,
  str.substr(tstr2_s_str_13, 3, 1) == &#34;l&#34;])</pre>
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<p>The function <code>zeval()</code> returns a solution for the predicate. Note that the value returned is not exactly the argument that we passed in. This is a consequence of the predicates we have. That is, we have no constraints on what the character value on <code>s[2]</code> should be.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">_</span><span class="o">.</span><span class="n">zeval</span><span class="p">()</span>
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<pre>(&#39;sat&#39;, {&#39;s&#39;: &#39;he\\x00l&#39;})</pre>
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<h5 id="Translating-to-Upper-and-Lower-Equivalents">Translating to Upper and Lower Equivalents<a class="anchor-link" href="#Translating-to-Upper-and-Lower-Equivalents">&#182;</a></h5><p>A major complication is supporting <code>upper()</code> and <code>lower()</code> methods. We use the previously defined <code>zchr()</code> and <code>zord()</code> functions to accomplish this.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">class</span> <span class="nc">zstr</span><span class="p">(</span><span class="n">zstr</span><span class="p">):</span>
    <span class="k">def</span> <span class="nf">upper</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
        <span class="n">empty</span> <span class="o">=</span> <span class="s1">&#39;&#39;</span>
        <span class="n">ne</span> <span class="o">=</span> <span class="s1">&#39;empty_</span><span class="si">%d</span><span class="s1">&#39;</span> <span class="o">%</span> <span class="n">fresh_name</span><span class="p">()</span>
        <span class="n">result</span> <span class="o">=</span> <span class="n">zstr</span><span class="o">.</span><span class="n">create</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">context</span><span class="p">,</span> <span class="n">ne</span><span class="p">,</span> <span class="n">empty</span><span class="p">)</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">context</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">z3</span><span class="o">.</span><span class="n">StringVal</span><span class="p">(</span><span class="n">empty</span><span class="p">)</span> <span class="o">==</span> <span class="n">result</span><span class="o">.</span><span class="n">z</span><span class="p">)</span>
        <span class="n">cdiff</span> <span class="o">=</span> <span class="p">(</span><span class="nb">ord</span><span class="p">(</span><span class="s1">&#39;a&#39;</span><span class="p">)</span> <span class="o">-</span> <span class="nb">ord</span><span class="p">(</span><span class="s1">&#39;A&#39;</span><span class="p">))</span>
        <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="bp">self</span><span class="p">:</span>
            <span class="n">oz</span> <span class="o">=</span> <span class="n">zord</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">context</span><span class="p">,</span> <span class="n">i</span><span class="o">.</span><span class="n">z</span><span class="p">)</span>
            <span class="n">uz</span> <span class="o">=</span> <span class="n">zchr</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">context</span><span class="p">,</span> <span class="n">oz</span> <span class="o">-</span> <span class="n">cdiff</span><span class="p">)</span>
            <span class="n">rz</span> <span class="o">=</span> <span class="n">z3</span><span class="o">.</span><span class="n">And</span><span class="p">([</span><span class="n">oz</span> <span class="o">&gt;=</span> <span class="nb">ord</span><span class="p">(</span><span class="s1">&#39;a&#39;</span><span class="p">),</span> <span class="n">oz</span> <span class="o">&lt;=</span> <span class="nb">ord</span><span class="p">(</span><span class="s1">&#39;z&#39;</span><span class="p">)])</span>
            <span class="n">ov</span> <span class="o">=</span> <span class="nb">ord</span><span class="p">(</span><span class="n">i</span><span class="o">.</span><span class="n">v</span><span class="p">)</span>
            <span class="n">uv</span> <span class="o">=</span> <span class="nb">chr</span><span class="p">(</span><span class="n">ov</span> <span class="o">-</span> <span class="n">cdiff</span><span class="p">)</span>
            <span class="n">rv</span> <span class="o">=</span> <span class="n">ov</span> <span class="o">&gt;=</span> <span class="nb">ord</span><span class="p">(</span><span class="s1">&#39;a&#39;</span><span class="p">)</span> <span class="ow">and</span> <span class="n">ov</span> <span class="o">&lt;=</span> <span class="nb">ord</span><span class="p">(</span><span class="s1">&#39;z&#39;</span><span class="p">)</span>
            <span class="k">if</span> <span class="n">zbool</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">context</span><span class="p">,</span> <span class="n">rz</span><span class="p">,</span> <span class="n">rv</span><span class="p">):</span>
                <span class="n">i</span> <span class="o">=</span> <span class="n">zstr</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">context</span><span class="p">,</span> <span class="n">uz</span><span class="p">,</span> <span class="n">uv</span><span class="p">)</span>
            <span class="k">else</span><span class="p">:</span>
                <span class="n">i</span> <span class="o">=</span> <span class="n">zstr</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">context</span><span class="p">,</span> <span class="n">i</span><span class="o">.</span><span class="n">z</span><span class="p">,</span> <span class="n">i</span><span class="o">.</span><span class="n">v</span><span class="p">)</span>
            <span class="n">result</span> <span class="o">+=</span> <span class="n">i</span>
        <span class="k">return</span> <span class="n">result</span>
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<p>The <code>lower()</code> function is similar to <code>upper()</code> except that the character ranges are switched, and the lowercase is above uppercase. Hence, we add the difference to the ordinal to make a character to lowercase.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">class</span> <span class="nc">zstr</span><span class="p">(</span><span class="n">zstr</span><span class="p">):</span>
    <span class="k">def</span> <span class="nf">lower</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
        <span class="n">empty</span> <span class="o">=</span> <span class="s1">&#39;&#39;</span>
        <span class="n">ne</span> <span class="o">=</span> <span class="s1">&#39;empty_</span><span class="si">%d</span><span class="s1">&#39;</span> <span class="o">%</span> <span class="n">fresh_name</span><span class="p">()</span>
        <span class="n">result</span> <span class="o">=</span> <span class="n">zstr</span><span class="o">.</span><span class="n">create</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">context</span><span class="p">,</span> <span class="n">ne</span><span class="p">,</span> <span class="n">empty</span><span class="p">)</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">context</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">z3</span><span class="o">.</span><span class="n">StringVal</span><span class="p">(</span><span class="n">empty</span><span class="p">)</span> <span class="o">==</span> <span class="n">result</span><span class="o">.</span><span class="n">z</span><span class="p">)</span>
        <span class="n">cdiff</span> <span class="o">=</span> <span class="p">(</span><span class="nb">ord</span><span class="p">(</span><span class="s1">&#39;a&#39;</span><span class="p">)</span> <span class="o">-</span> <span class="nb">ord</span><span class="p">(</span><span class="s1">&#39;A&#39;</span><span class="p">))</span>
        <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="bp">self</span><span class="p">:</span>
            <span class="n">oz</span> <span class="o">=</span> <span class="n">zord</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">context</span><span class="p">,</span> <span class="n">i</span><span class="o">.</span><span class="n">z</span><span class="p">)</span>
            <span class="n">uz</span> <span class="o">=</span> <span class="n">zchr</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">context</span><span class="p">,</span> <span class="n">oz</span> <span class="o">+</span> <span class="n">cdiff</span><span class="p">)</span>
            <span class="n">rz</span> <span class="o">=</span> <span class="n">z3</span><span class="o">.</span><span class="n">And</span><span class="p">([</span><span class="n">oz</span> <span class="o">&gt;=</span> <span class="nb">ord</span><span class="p">(</span><span class="s1">&#39;A&#39;</span><span class="p">),</span> <span class="n">oz</span> <span class="o">&lt;=</span> <span class="nb">ord</span><span class="p">(</span><span class="s1">&#39;Z&#39;</span><span class="p">)])</span>
            <span class="n">ov</span> <span class="o">=</span> <span class="nb">ord</span><span class="p">(</span><span class="n">i</span><span class="o">.</span><span class="n">v</span><span class="p">)</span>
            <span class="n">uv</span> <span class="o">=</span> <span class="nb">chr</span><span class="p">(</span><span class="n">ov</span> <span class="o">+</span> <span class="n">cdiff</span><span class="p">)</span>
            <span class="n">rv</span> <span class="o">=</span> <span class="n">ov</span> <span class="o">&gt;=</span> <span class="nb">ord</span><span class="p">(</span><span class="s1">&#39;A&#39;</span><span class="p">)</span> <span class="ow">and</span> <span class="n">ov</span> <span class="o">&lt;=</span> <span class="nb">ord</span><span class="p">(</span><span class="s1">&#39;Z&#39;</span><span class="p">)</span>
            <span class="k">if</span> <span class="n">zbool</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">context</span><span class="p">,</span> <span class="n">rz</span><span class="p">,</span> <span class="n">rv</span><span class="p">):</span>
                <span class="n">i</span> <span class="o">=</span> <span class="n">zstr</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">context</span><span class="p">,</span> <span class="n">uz</span><span class="p">,</span> <span class="n">uv</span><span class="p">)</span>
            <span class="k">else</span><span class="p">:</span>
                <span class="n">i</span> <span class="o">=</span> <span class="n">zstr</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">context</span><span class="p">,</span> <span class="n">i</span><span class="o">.</span><span class="n">z</span><span class="p">,</span> <span class="n">i</span><span class="o">.</span><span class="n">v</span><span class="p">)</span>
            <span class="n">result</span> <span class="o">+=</span> <span class="n">i</span>
        <span class="k">return</span> <span class="n">result</span>
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<p>Here is how it is used.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">def</span> <span class="nf">tstr3</span><span class="p">(</span><span class="n">s</span><span class="p">):</span>
    <span class="k">if</span> <span class="n">s</span><span class="o">.</span><span class="n">upper</span><span class="p">()</span> <span class="o">==</span> <span class="s1">&#39;H&#39;</span><span class="p">:</span>
        <span class="k">return</span> <span class="kc">True</span>
    <span class="k">else</span><span class="p">:</span>
        <span class="k">return</span> <span class="kc">False</span>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">with</span> <span class="n">ConcolicTracer</span><span class="p">()</span> <span class="k">as</span> <span class="n">_</span><span class="p">:</span>
    <span class="n">r</span> <span class="o">=</span> <span class="n">_</span><span class="p">[</span><span class="n">tstr3</span><span class="p">](</span><span class="s1">&#39;h&#39;</span><span class="p">)</span>
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<p>Again, we use <code>zeval()</code> to solve the collected constraints, and verify that our constraints are correct.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">_</span><span class="o">.</span><span class="n">zeval</span><span class="p">()</span>
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<pre>(&#39;sat&#39;, {&#39;s&#39;: &#39;h&#39;})</pre>
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<p>Here is a larger example using <code>upper()</code></p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">def</span> <span class="nf">tstr4</span><span class="p">(</span><span class="n">s</span><span class="p">):</span>
    <span class="k">if</span> <span class="n">s</span><span class="o">.</span><span class="n">lower</span><span class="p">()</span> <span class="o">==</span> <span class="s1">&#39;hello world&#39;</span><span class="p">:</span>
        <span class="k">return</span> <span class="kc">True</span>
    <span class="k">else</span><span class="p">:</span>
        <span class="k">return</span> <span class="kc">False</span>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">with</span> <span class="n">ConcolicTracer</span><span class="p">()</span> <span class="k">as</span> <span class="n">_</span><span class="p">:</span>
    <span class="n">r</span> <span class="o">=</span> <span class="n">_</span><span class="p">[</span><span class="n">tstr4</span><span class="p">](</span><span class="s1">&#39;Hello World&#39;</span><span class="p">)</span>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">_</span><span class="o">.</span><span class="n">zeval</span><span class="p">()</span>
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<pre>(&#39;sat&#39;, {&#39;s&#39;: &#39;Hello World&#39;})</pre>
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<p>Again, we obtain the right input value.</p>

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<h5 id="Checking-for-String-Prefixes">Checking for String Prefixes<a class="anchor-link" href="#Checking-for-String-Prefixes">&#182;</a></h5><p>We define <code>startswith()</code>.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">class</span> <span class="nc">zstr</span><span class="p">(</span><span class="n">zstr</span><span class="p">):</span>
    <span class="k">def</span> <span class="nf">startswith</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">,</span> <span class="n">beg</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">end</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
        <span class="k">assert</span> <span class="n">end</span> <span class="ow">is</span> <span class="kc">None</span>  <span class="c1"># for now</span>
        <span class="k">assert</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">beg</span><span class="p">,</span> <span class="nb">int</span><span class="p">)</span>  <span class="c1"># for now</span>
        <span class="n">zb</span> <span class="o">=</span> <span class="n">z3</span><span class="o">.</span><span class="n">IntVal</span><span class="p">(</span><span class="n">beg</span><span class="p">)</span>

        <span class="n">others</span> <span class="o">=</span> <span class="n">other</span> <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">other</span><span class="p">,</span> <span class="nb">tuple</span><span class="p">)</span> <span class="k">else</span> <span class="p">(</span><span class="n">other</span><span class="p">,</span> <span class="p">)</span>

        <span class="n">last</span> <span class="o">=</span> <span class="kc">False</span>
        <span class="k">for</span> <span class="n">o</span> <span class="ow">in</span> <span class="n">others</span><span class="p">:</span>
            <span class="n">z</span><span class="p">,</span> <span class="n">v</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_zv</span><span class="p">(</span><span class="n">o</span><span class="p">)</span>
            <span class="n">r</span> <span class="o">=</span> <span class="n">z3</span><span class="o">.</span><span class="n">IndexOf</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">z</span><span class="p">,</span> <span class="n">z</span><span class="p">,</span> <span class="n">zb</span><span class="p">)</span>
            <span class="n">last</span> <span class="o">=</span> <span class="n">zbool</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">context</span><span class="p">,</span> <span class="n">r</span> <span class="o">==</span> <span class="n">zb</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">v</span><span class="o">.</span><span class="n">startswith</span><span class="p">(</span><span class="n">v</span><span class="p">))</span>
            <span class="k">if</span> <span class="n">last</span><span class="p">:</span>
                <span class="k">return</span> <span class="n">last</span>
        <span class="k">return</span> <span class="n">last</span>
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<p>An example.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">def</span> <span class="nf">tstr5</span><span class="p">(</span><span class="n">s</span><span class="p">):</span>
    <span class="k">if</span> <span class="n">s</span><span class="o">.</span><span class="n">startswith</span><span class="p">(</span><span class="s1">&#39;hello&#39;</span><span class="p">):</span>
        <span class="k">return</span> <span class="kc">True</span>
    <span class="k">else</span><span class="p">:</span>
        <span class="k">return</span> <span class="kc">False</span>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">with</span> <span class="n">ConcolicTracer</span><span class="p">()</span> <span class="k">as</span> <span class="n">_</span><span class="p">:</span>
    <span class="n">r</span> <span class="o">=</span> <span class="n">_</span><span class="p">[</span><span class="n">tstr5</span><span class="p">](</span><span class="s1">&#39;hello world&#39;</span><span class="p">)</span>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">_</span><span class="o">.</span><span class="n">zeval</span><span class="p">()</span>
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<pre>(&#39;sat&#39;, {&#39;s&#39;: &#39;hello&#39;})</pre>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">with</span> <span class="n">ConcolicTracer</span><span class="p">()</span> <span class="k">as</span> <span class="n">_</span><span class="p">:</span>
    <span class="n">r</span> <span class="o">=</span> <span class="n">_</span><span class="p">[</span><span class="n">tstr5</span><span class="p">](</span><span class="s1">&#39;my world&#39;</span><span class="p">)</span>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">_</span><span class="o">.</span><span class="n">zeval</span><span class="p">()</span>
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<pre>(&#39;sat&#39;, {&#39;s&#39;: &#39;\\x00hello&#39;})</pre>
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<p>As before, the predicates only ensure that the <code>startswith()</code> returned a true value. Hence, our solution reflects that.</p>

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<h5 id="Finding-Substrings">Finding Substrings<a class="anchor-link" href="#Finding-Substrings">&#182;</a></h5><p>We also define <code>find()</code></p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">class</span> <span class="nc">zstr</span><span class="p">(</span><span class="n">zstr</span><span class="p">):</span>
    <span class="k">def</span> <span class="nf">find</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">,</span> <span class="n">beg</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">end</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
        <span class="k">assert</span> <span class="n">end</span> <span class="ow">is</span> <span class="kc">None</span>  <span class="c1"># for now</span>
        <span class="k">assert</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">beg</span><span class="p">,</span> <span class="nb">int</span><span class="p">)</span>  <span class="c1"># for now</span>
        <span class="n">zb</span> <span class="o">=</span> <span class="n">z3</span><span class="o">.</span><span class="n">IntVal</span><span class="p">(</span><span class="n">beg</span><span class="p">)</span>
        <span class="n">z</span><span class="p">,</span> <span class="n">v</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_zv</span><span class="p">(</span><span class="n">other</span><span class="p">)</span>
        <span class="n">zi</span> <span class="o">=</span> <span class="n">z3</span><span class="o">.</span><span class="n">IndexOf</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">z</span><span class="p">,</span> <span class="n">z</span><span class="p">,</span> <span class="n">zb</span><span class="p">)</span>
        <span class="n">vi</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">v</span><span class="o">.</span><span class="n">find</span><span class="p">(</span><span class="n">v</span><span class="p">,</span> <span class="n">beg</span><span class="p">,</span> <span class="n">end</span><span class="p">)</span>
        <span class="k">return</span> <span class="n">zint</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">context</span><span class="p">,</span> <span class="n">zi</span><span class="p">,</span> <span class="n">vi</span><span class="p">)</span>
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<p>An example.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">def</span> <span class="nf">tstr6</span><span class="p">(</span><span class="n">s</span><span class="p">):</span>
    <span class="k">if</span> <span class="n">s</span><span class="o">.</span><span class="n">find</span><span class="p">(</span><span class="s1">&#39;world&#39;</span><span class="p">)</span> <span class="o">!=</span> <span class="o">-</span><span class="mi">1</span><span class="p">:</span>
        <span class="k">return</span> <span class="kc">True</span>
    <span class="k">else</span><span class="p">:</span>
        <span class="k">return</span> <span class="kc">False</span>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">with</span> <span class="n">ConcolicTracer</span><span class="p">()</span> <span class="k">as</span> <span class="n">_</span><span class="p">:</span>
    <span class="n">r</span> <span class="o">=</span> <span class="n">_</span><span class="p">[</span><span class="n">tstr6</span><span class="p">](</span><span class="s1">&#39;hello world&#39;</span><span class="p">)</span>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">_</span><span class="o">.</span><span class="n">zeval</span><span class="p">()</span>
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<pre>(&#39;sat&#39;, {&#39;s&#39;: &#39;\\x00world&#39;})</pre>
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<p>As before, the predicates only ensure that the <code>find()</code> returned a value greater than -1. Hence, our solution reflects that.</p>

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<h5 id="Remove-Space-from-Ends">Remove Space from Ends<a class="anchor-link" href="#Remove-Space-from-Ends">&#182;</a></h5>
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<p>We next implement <code>strip()</code>.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">class</span> <span class="nc">zstr</span><span class="p">(</span><span class="n">zstr</span><span class="p">):</span>
    <span class="k">def</span> <span class="nf">rstrip</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">chars</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
        <span class="k">if</span> <span class="n">chars</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
            <span class="n">chars</span> <span class="o">=</span> <span class="n">string</span><span class="o">.</span><span class="n">whitespace</span>
        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">_len</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
            <span class="k">return</span> <span class="bp">self</span>
        <span class="k">else</span><span class="p">:</span>
            <span class="n">last_idx</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_len</span> <span class="o">-</span> <span class="mi">1</span>
            <span class="n">cz</span> <span class="o">=</span> <span class="n">z3</span><span class="o">.</span><span class="n">SubString</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">z</span><span class="p">,</span> <span class="n">last_idx</span><span class="o">.</span><span class="n">z</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
            <span class="n">cv</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">v</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
            <span class="n">zcheck_space</span> <span class="o">=</span> <span class="n">z3</span><span class="o">.</span><span class="n">Or</span><span class="p">([</span><span class="n">cz</span> <span class="o">==</span> <span class="n">z3</span><span class="o">.</span><span class="n">StringVal</span><span class="p">(</span><span class="n">char</span><span class="p">)</span> <span class="k">for</span> <span class="n">char</span> <span class="ow">in</span> <span class="n">chars</span><span class="p">])</span>
            <span class="n">vcheck_space</span> <span class="o">=</span> <span class="nb">any</span><span class="p">(</span><span class="n">cv</span> <span class="o">==</span> <span class="n">char</span> <span class="k">for</span> <span class="n">char</span> <span class="ow">in</span> <span class="n">chars</span><span class="p">)</span>
            <span class="k">if</span> <span class="n">zbool</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">context</span><span class="p">,</span> <span class="n">zcheck_space</span><span class="p">,</span> <span class="n">vcheck_space</span><span class="p">):</span>
                <span class="k">return</span> <span class="n">zstr</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">context</span><span class="p">,</span> <span class="n">z3</span><span class="o">.</span><span class="n">SubString</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">z</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="n">last_idx</span><span class="o">.</span><span class="n">z</span><span class="p">),</span>
                            <span class="bp">self</span><span class="o">.</span><span class="n">v</span><span class="p">[</span><span class="mi">0</span><span class="p">:</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span><span class="o">.</span><span class="n">rstrip</span><span class="p">(</span><span class="n">chars</span><span class="p">)</span>
            <span class="k">else</span><span class="p">:</span>
                <span class="k">return</span> <span class="bp">self</span>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">def</span> <span class="nf">tstr7</span><span class="p">(</span><span class="n">s</span><span class="p">):</span>
    <span class="k">if</span> <span class="n">s</span><span class="o">.</span><span class="n">rstrip</span><span class="p">(</span><span class="s1">&#39; &#39;</span><span class="p">)</span> <span class="o">==</span> <span class="s1">&#39;a b&#39;</span><span class="p">:</span>
        <span class="k">return</span> <span class="kc">True</span>
    <span class="k">else</span><span class="p">:</span>
        <span class="k">return</span> <span class="kc">False</span>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">with</span> <span class="n">ConcolicTracer</span><span class="p">()</span> <span class="k">as</span> <span class="n">_</span><span class="p">:</span>
    <span class="n">r</span> <span class="o">=</span> <span class="n">_</span><span class="p">[</span><span class="n">tstr7</span><span class="p">](</span><span class="s1">&#39;a b   &#39;</span><span class="p">)</span>
    <span class="nb">print</span><span class="p">(</span><span class="n">r</span><span class="p">)</span>
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<pre>True
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<pre>(&#39;sat&#39;, {&#39;s&#39;: &#39;a b   &#39;})</pre>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">class</span> <span class="nc">zstr</span><span class="p">(</span><span class="n">zstr</span><span class="p">):</span>
    <span class="k">def</span> <span class="nf">lstrip</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">chars</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
        <span class="k">if</span> <span class="n">chars</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
            <span class="n">chars</span> <span class="o">=</span> <span class="n">string</span><span class="o">.</span><span class="n">whitespace</span>
        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">_len</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
            <span class="k">return</span> <span class="bp">self</span>
        <span class="k">else</span><span class="p">:</span>
            <span class="n">first_idx</span> <span class="o">=</span> <span class="mi">0</span>
            <span class="n">cz</span> <span class="o">=</span> <span class="n">z3</span><span class="o">.</span><span class="n">SubString</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">z</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
            <span class="n">cv</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">v</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
            <span class="n">zcheck_space</span> <span class="o">=</span> <span class="n">z3</span><span class="o">.</span><span class="n">Or</span><span class="p">([</span><span class="n">cz</span> <span class="o">==</span> <span class="n">z3</span><span class="o">.</span><span class="n">StringVal</span><span class="p">(</span><span class="n">char</span><span class="p">)</span> <span class="k">for</span> <span class="n">char</span> <span class="ow">in</span> <span class="n">chars</span><span class="p">])</span>
            <span class="n">vcheck_space</span> <span class="o">=</span> <span class="nb">any</span><span class="p">(</span><span class="n">cv</span> <span class="o">==</span> <span class="n">char</span> <span class="k">for</span> <span class="n">char</span> <span class="ow">in</span> <span class="n">chars</span><span class="p">)</span>
            <span class="k">if</span> <span class="n">zbool</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">context</span><span class="p">,</span> <span class="n">zcheck_space</span><span class="p">,</span> <span class="n">vcheck_space</span><span class="p">):</span>
                <span class="k">return</span> <span class="n">zstr</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">context</span><span class="p">,</span> <span class="n">z3</span><span class="o">.</span><span class="n">SubString</span><span class="p">(</span>
                    <span class="bp">self</span><span class="o">.</span><span class="n">z</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">_len</span><span class="o">.</span><span class="n">z</span><span class="p">),</span> <span class="bp">self</span><span class="o">.</span><span class="n">v</span><span class="p">[</span><span class="mi">1</span><span class="p">:])</span><span class="o">.</span><span class="n">lstrip</span><span class="p">(</span><span class="n">chars</span><span class="p">)</span>
            <span class="k">else</span><span class="p">:</span>
                <span class="k">return</span> <span class="bp">self</span>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">def</span> <span class="nf">tstr8</span><span class="p">(</span><span class="n">s</span><span class="p">):</span>
    <span class="k">if</span> <span class="n">s</span><span class="o">.</span><span class="n">lstrip</span><span class="p">(</span><span class="s1">&#39; &#39;</span><span class="p">)</span> <span class="o">==</span> <span class="s1">&#39;a b&#39;</span><span class="p">:</span>
        <span class="k">return</span> <span class="kc">True</span>
    <span class="k">else</span><span class="p">:</span>
        <span class="k">return</span> <span class="kc">False</span>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">with</span> <span class="n">ConcolicTracer</span><span class="p">()</span> <span class="k">as</span> <span class="n">_</span><span class="p">:</span>
    <span class="n">r</span> <span class="o">=</span> <span class="n">_</span><span class="p">[</span><span class="n">tstr8</span><span class="p">](</span><span class="s1">&#39;   a b&#39;</span><span class="p">)</span>
    <span class="nb">print</span><span class="p">(</span><span class="n">r</span><span class="p">)</span>
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<pre>True
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">_</span><span class="o">.</span><span class="n">zeval</span><span class="p">()</span>
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<pre>(&#39;sat&#39;, {&#39;s&#39;: &#39;   a b&#39;})</pre>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">class</span> <span class="nc">zstr</span><span class="p">(</span><span class="n">zstr</span><span class="p">):</span>
    <span class="k">def</span> <span class="nf">strip</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">chars</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">lstrip</span><span class="p">(</span><span class="n">chars</span><span class="p">)</span><span class="o">.</span><span class="n">rstrip</span><span class="p">(</span><span class="n">chars</span><span class="p">)</span>
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<p>Example usage.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">def</span> <span class="nf">tstr9</span><span class="p">(</span><span class="n">s</span><span class="p">):</span>
    <span class="k">if</span> <span class="n">s</span><span class="o">.</span><span class="n">strip</span><span class="p">()</span> <span class="o">==</span> <span class="s1">&#39;a b&#39;</span><span class="p">:</span>
        <span class="k">return</span> <span class="kc">True</span>
    <span class="k">else</span><span class="p">:</span>
        <span class="k">return</span> <span class="kc">False</span>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">with</span> <span class="n">ConcolicTracer</span><span class="p">()</span> <span class="k">as</span> <span class="n">_</span><span class="p">:</span>
    <span class="n">r</span> <span class="o">=</span> <span class="n">_</span><span class="p">[</span><span class="n">tstr9</span><span class="p">](</span><span class="s1">&#39;    a b  &#39;</span><span class="p">)</span>
    <span class="nb">print</span><span class="p">(</span><span class="n">r</span><span class="p">)</span>
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<pre>True
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">_</span><span class="o">.</span><span class="n">zeval</span><span class="p">()</span>
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<pre>(&#39;sat&#39;, {&#39;s&#39;: &#39;    a b  &#39;})</pre>
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<p>The <code>strip()</code> has generated the right constraints.</p>

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<h5 id="Splitting-Strings">Splitting Strings<a class="anchor-link" href="#Splitting-Strings">&#182;</a></h5><p>We implement string <code>split()</code> as follows.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">class</span> <span class="nc">zstr</span><span class="p">(</span><span class="n">zstr</span><span class="p">):</span>
    <span class="k">def</span> <span class="nf">split</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">sep</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">maxsplit</span><span class="o">=-</span><span class="mi">1</span><span class="p">):</span>
        <span class="k">assert</span> <span class="n">sep</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span>  <span class="c1"># default space based split is complicated</span>
        <span class="k">assert</span> <span class="n">maxsplit</span> <span class="o">==</span> <span class="o">-</span><span class="mi">1</span>  <span class="c1"># for now.</span>
        <span class="n">zsep</span> <span class="o">=</span> <span class="n">z3</span><span class="o">.</span><span class="n">StringVal</span><span class="p">(</span><span class="n">sep</span><span class="p">)</span>
        <span class="n">zl</span> <span class="o">=</span> <span class="n">z3</span><span class="o">.</span><span class="n">Length</span><span class="p">(</span><span class="n">zsep</span><span class="p">)</span>
        <span class="n">zi</span> <span class="o">=</span> <span class="n">z3</span><span class="o">.</span><span class="n">IndexOf</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">z</span><span class="p">,</span> <span class="n">zsep</span><span class="p">,</span> <span class="n">z3</span><span class="o">.</span><span class="n">IntVal</span><span class="p">(</span><span class="mi">0</span><span class="p">))</span>  <span class="c1"># zi would be the length of prefix</span>
        <span class="c1"># Z3Bug: There is a bug in the `z3.IndexOf` method which returns</span>
        <span class="c1"># `z3.SeqRef` instead of `z3.ArithRef`. So we need to fix it.</span>
        <span class="n">zi</span> <span class="o">=</span> <span class="n">z3</span><span class="o">.</span><span class="n">ArithRef</span><span class="p">(</span><span class="n">zi</span><span class="o">.</span><span class="n">ast</span><span class="p">,</span> <span class="n">zi</span><span class="o">.</span><span class="n">ctx</span><span class="p">)</span>

        <span class="n">vi</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">v</span><span class="o">.</span><span class="n">find</span><span class="p">(</span><span class="n">sep</span><span class="p">)</span>
        <span class="k">if</span> <span class="n">zbool</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">context</span><span class="p">,</span> <span class="n">zi</span> <span class="o">&gt;=</span> <span class="n">z3</span><span class="o">.</span><span class="n">IntVal</span><span class="p">(</span><span class="mi">0</span><span class="p">),</span> <span class="n">vi</span> <span class="o">&gt;=</span> <span class="mi">0</span><span class="p">):</span>
            <span class="n">zprefix</span> <span class="o">=</span> <span class="n">z3</span><span class="o">.</span><span class="n">SubString</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">z</span><span class="p">,</span> <span class="n">z3</span><span class="o">.</span><span class="n">IntVal</span><span class="p">(</span><span class="mi">0</span><span class="p">),</span> <span class="n">zi</span><span class="p">)</span>
            <span class="n">zmid</span> <span class="o">=</span> <span class="n">z3</span><span class="o">.</span><span class="n">SubString</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">z</span><span class="p">,</span> <span class="n">zi</span><span class="p">,</span> <span class="n">zl</span><span class="p">)</span>
            <span class="n">zsuffix</span> <span class="o">=</span> <span class="n">z3</span><span class="o">.</span><span class="n">SubString</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">z</span><span class="p">,</span> <span class="n">zi</span> <span class="o">+</span> <span class="n">zl</span><span class="p">,</span>
                                   <span class="n">z3</span><span class="o">.</span><span class="n">Length</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">z</span><span class="p">))</span>
            <span class="k">return</span> <span class="p">[</span><span class="n">zstr</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">context</span><span class="p">,</span> <span class="n">zprefix</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">v</span><span class="p">[</span><span class="mi">0</span><span class="p">:</span><span class="n">vi</span><span class="p">])]</span> <span class="o">+</span> <span class="n">zstr</span><span class="p">(</span>
                <span class="bp">self</span><span class="o">.</span><span class="n">context</span><span class="p">,</span> <span class="n">zsuffix</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">v</span><span class="p">[</span><span class="n">vi</span> <span class="o">+</span> <span class="nb">len</span><span class="p">(</span><span class="n">sep</span><span class="p">):])</span><span class="o">.</span><span class="n">split</span><span class="p">(</span>
                    <span class="n">sep</span><span class="p">,</span> <span class="n">maxsplit</span><span class="p">)</span>
        <span class="k">else</span><span class="p">:</span>
            <span class="k">return</span> <span class="p">[</span><span class="bp">self</span><span class="p">]</span>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">def</span> <span class="nf">tstr10</span><span class="p">(</span><span class="n">s</span><span class="p">):</span>
    <span class="k">if</span> <span class="n">s</span><span class="o">.</span><span class="n">split</span><span class="p">(</span><span class="s1">&#39;,&#39;</span><span class="p">)</span> <span class="o">==</span> <span class="p">[</span><span class="s1">&#39;a&#39;</span><span class="p">,</span> <span class="s1">&#39;b&#39;</span><span class="p">,</span> <span class="s1">&#39;c&#39;</span><span class="p">]:</span>
        <span class="k">return</span> <span class="kc">True</span>
    <span class="k">else</span><span class="p">:</span>
        <span class="k">return</span> <span class="kc">False</span>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">with</span> <span class="n">ConcolicTracer</span><span class="p">()</span> <span class="k">as</span> <span class="n">_</span><span class="p">:</span>
    <span class="n">r</span> <span class="o">=</span> <span class="n">_</span><span class="p">[</span><span class="n">tstr10</span><span class="p">](</span><span class="s1">&#39;a,b,c&#39;</span><span class="p">)</span>
    <span class="nb">print</span><span class="p">(</span><span class="n">r</span><span class="p">)</span>
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<pre>True
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">_</span><span class="o">.</span><span class="n">zeval</span><span class="p">()</span>
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<pre>(&#39;sat&#39;, {&#39;s&#39;: &#39;a,b,c&#39;})</pre>
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<h5 id="Trip-Wire">Trip Wire<a class="anchor-link" href="#Trip-Wire">&#182;</a></h5><p>For easier debugging, we abort any calls to methods in <code>str</code> that are not overridden by <code>zstr</code>.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">def</span> <span class="nf">make_str_abort_wrapper</span><span class="p">(</span><span class="n">fun</span><span class="p">):</span>
    <span class="k">def</span> <span class="nf">proxy</span><span class="p">(</span><span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
        <span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span> <span class="s1">&#39;</span><span class="si">%s</span><span class="s1"> Not implemented in `zstr`&#39;</span> <span class="o">%</span> <span class="n">fun</span><span class="o">.</span><span class="vm">__name__</span><span class="p">)</span>
    <span class="k">return</span> <span class="n">proxy</span>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">strmembers</span> <span class="o">=</span> <span class="n">inspect</span><span class="o">.</span><span class="n">getmembers</span><span class="p">(</span><span class="n">zstr</span><span class="p">,</span> <span class="n">callable</span><span class="p">)</span>
<span class="n">zstrmembers</span> <span class="o">=</span> <span class="p">{</span><span class="n">m</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="k">for</span> <span class="n">m</span> <span class="ow">in</span> <span class="n">strmembers</span> <span class="k">if</span> <span class="nb">len</span><span class="p">(</span>
    <span class="n">m</span><span class="p">)</span> <span class="o">==</span> <span class="mi">2</span> <span class="ow">and</span> <span class="s1">&#39;zstr&#39;</span> <span class="ow">in</span> <span class="n">m</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="vm">__qualname__</span><span class="p">}</span>
<span class="k">for</span> <span class="n">name</span><span class="p">,</span> <span class="n">fn</span> <span class="ow">in</span> <span class="n">inspect</span><span class="o">.</span><span class="n">getmembers</span><span class="p">(</span><span class="nb">str</span><span class="p">,</span> <span class="n">callable</span><span class="p">):</span>
    <span class="c1"># Omitted &#39;splitlines&#39; as this is needed for formatting output in</span>
    <span class="c1"># IPython/Jupyter</span>
    <span class="k">if</span> <span class="n">name</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">zstrmembers</span> <span class="ow">and</span> <span class="n">name</span> <span class="ow">not</span> <span class="ow">in</span> <span class="p">[</span>
        <span class="s1">&#39;splitlines&#39;</span><span class="p">,</span>
        <span class="s1">&#39;__class__&#39;</span><span class="p">,</span>
        <span class="s1">&#39;__contains__&#39;</span><span class="p">,</span>
        <span class="s1">&#39;__delattr__&#39;</span><span class="p">,</span>
        <span class="s1">&#39;__dir__&#39;</span><span class="p">,</span>
        <span class="s1">&#39;__format__&#39;</span><span class="p">,</span>
        <span class="s1">&#39;__ge__&#39;</span><span class="p">,</span>
        <span class="s1">&#39;__getattribute__&#39;</span><span class="p">,</span>
        <span class="s1">&#39;__getnewargs__&#39;</span><span class="p">,</span>
        <span class="s1">&#39;__gt__&#39;</span><span class="p">,</span>
        <span class="s1">&#39;__hash__&#39;</span><span class="p">,</span>
        <span class="s1">&#39;__le__&#39;</span><span class="p">,</span>
        <span class="s1">&#39;__len__&#39;</span><span class="p">,</span>
        <span class="s1">&#39;__lt__&#39;</span><span class="p">,</span>
        <span class="s1">&#39;__mod__&#39;</span><span class="p">,</span>
        <span class="s1">&#39;__mul__&#39;</span><span class="p">,</span>
        <span class="s1">&#39;__ne__&#39;</span><span class="p">,</span>
        <span class="s1">&#39;__reduce__&#39;</span><span class="p">,</span>
        <span class="s1">&#39;__reduce_ex__&#39;</span><span class="p">,</span>
        <span class="s1">&#39;__repr__&#39;</span><span class="p">,</span>
        <span class="s1">&#39;__rmod__&#39;</span><span class="p">,</span>
        <span class="s1">&#39;__rmul__&#39;</span><span class="p">,</span>
        <span class="s1">&#39;__setattr__&#39;</span><span class="p">,</span>
        <span class="s1">&#39;__sizeof__&#39;</span><span class="p">,</span>
        <span class="s1">&#39;__str__&#39;</span><span class="p">]:</span>
        <span class="nb">setattr</span><span class="p">(</span><span class="n">zstr</span><span class="p">,</span> <span class="n">name</span><span class="p">,</span> <span class="n">make_str_abort_wrapper</span><span class="p">(</span><span class="n">fn</span><span class="p">))</span>
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<h2 id="Examples">Examples<a class="anchor-link" href="#Examples">&#182;</a></h2>
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<h3 id="Triangle">Triangle<a class="anchor-link" href="#Triangle">&#182;</a></h3><p>We previously showed how to run <code>triangle()</code> under <code>ConcolicTracer</code>.</p>

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    <span class="nb">print</span><span class="p">(</span><span class="n">_</span><span class="p">[</span><span class="n">triangle</span><span class="p">](</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">))</span>
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<pre>scalene
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<p>The predicates are as follows:</p>

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<pre>[Not(triangle_a_int_49 == triangle_b_int_50),
 Not(triangle_b_int_50 == triangle_c_int_51),
 Not(triangle_a_int_49 == triangle_c_int_51)]</pre>
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<pre>(&#39;sat&#39;, {&#39;a&#39;: &#39;0&#39;, &#39;b&#39;: [&#39;-&#39;, &#39;2&#39;], &#39;c&#39;: [&#39;-&#39;, &#39;1&#39;]})</pre>
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<p>We can modify the predicates if necessary. First, we retrieve the symbolic variables.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">za</span><span class="p">,</span> <span class="n">zb</span><span class="p">,</span> <span class="n">zc</span> <span class="o">=</span> <span class="p">[</span><span class="n">z3</span><span class="o">.</span><span class="n">Int</span><span class="p">(</span><span class="n">s</span><span class="p">)</span> <span class="k">for</span> <span class="n">s</span> <span class="ow">in</span> <span class="n">_</span><span class="o">.</span><span class="n">context</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">keys</span><span class="p">()]</span>
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<p>Then, we pass a modified predicate to <code>zeval()</code>. The key determines which predicate the new predicate will replace.</p>

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<pre>(&#39;sat&#39;, {&#39;a&#39;: -1, &#39;b&#39;: -2, &#39;c&#39;: 0})</pre>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">triangle</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
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<pre>&#39;isosceles&#39;</pre>
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<p>The updated predicate returns <code>isosceles</code> as expected.</p>

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<h3 id="Round">Round<a class="anchor-link" href="#Round">&#182;</a></h3><p>Here is a function that gives you the nearest ten's multiplier</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">def</span> <span class="nf">round10</span><span class="p">(</span><span class="n">r</span><span class="p">):</span>
    <span class="k">while</span> <span class="n">r</span> <span class="o">%</span> <span class="mi">10</span> <span class="o">!=</span> <span class="mi">0</span><span class="p">:</span>
        <span class="n">r</span> <span class="o">+=</span> <span class="mi">1</span>
    <span class="k">return</span> <span class="n">r</span>
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<p>As before, we execute the function under the <code>ConcolicTracer</code> context.</p>

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    <span class="n">r</span> <span class="o">=</span> <span class="n">_</span><span class="p">[</span><span class="n">round10</span><span class="p">](</span><span class="mi">1</span><span class="p">)</span>
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<p>We verify that we were able to capture all the predicates</p>

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<pre>({&#39;round10_r_int_52&#39;: &#39;Int&#39;},
 [0 != round10_r_int_52%10,
  0 != (round10_r_int_52 + 1)%10,
  0 != (round10_r_int_52 + 1 + 1)%10,
  0 != (round10_r_int_52 + 1 + 1 + 1)%10,
  0 != (round10_r_int_52 + 1 + 1 + 1 + 1)%10,
  0 != (round10_r_int_52 + 1 + 1 + 1 + 1 + 1)%10,
  0 != (round10_r_int_52 + 1 + 1 + 1 + 1 + 1 + 1)%10,
  0 != (round10_r_int_52 + 1 + 1 + 1 + 1 + 1 + 1 + 1)%10,
  0 != (round10_r_int_52 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1)%10,
  Not(0 !=
      (round10_r_int_52 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1)%
      10)])</pre>
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<p>We use <code>zeval()</code> to obtain results.</p>

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<pre>(&#39;sat&#39;, {&#39;r&#39;: &#39;41&#39;})</pre>
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<h3 id="Absolute-Maximum">Absolute Maximum<a class="anchor-link" href="#Absolute-Maximum">&#182;</a></h3><p>Does our concolic proxies work across functions? Say we have a function <code>max_value()</code> as below.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">def</span> <span class="nf">abs_value</span><span class="p">(</span><span class="n">a</span><span class="p">):</span>
    <span class="k">if</span> <span class="n">a</span> <span class="o">&gt;</span> <span class="mi">0</span><span class="p">:</span>
        <span class="k">return</span> <span class="n">a</span>
    <span class="k">else</span><span class="p">:</span>
        <span class="k">return</span> <span class="o">-</span><span class="n">a</span>
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<p>It is called by another function <code>abs_max()</code></p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">def</span> <span class="nf">abs_max</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">):</span>
    <span class="n">a1</span> <span class="o">=</span> <span class="n">abs_value</span><span class="p">(</span><span class="n">a</span><span class="p">)</span>
    <span class="n">b1</span> <span class="o">=</span> <span class="n">abs_value</span><span class="p">(</span><span class="n">b</span><span class="p">)</span>
    <span class="k">if</span> <span class="n">a1</span> <span class="o">&gt;</span> <span class="n">b1</span><span class="p">:</span>
        <span class="n">c</span> <span class="o">=</span> <span class="n">a1</span>
    <span class="k">else</span><span class="p">:</span>
        <span class="n">c</span> <span class="o">=</span> <span class="n">b1</span>
    <span class="k">return</span> <span class="n">c</span>
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<p>Using the <code>Concolic()</code> context on <code>abs_max()</code>.</p>

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    <span class="n">_</span><span class="p">[</span><span class="n">abs_max</span><span class="p">](</span><span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
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<p>As expected, we have the predicates across functions.</p>

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<pre>({&#39;abs_max_a_int_53&#39;: &#39;Int&#39;, &#39;abs_max_b_int_54&#39;: &#39;Int&#39;},
 [0 &lt; abs_max_a_int_53,
  0 &lt; abs_max_b_int_54,
  abs_max_a_int_53 &gt; abs_max_b_int_54])</pre>
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<pre>(&#39;sat&#39;, {&#39;a&#39;: &#39;2&#39;, &#39;b&#39;: &#39;1&#39;})</pre>
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<p>Solving the predicates works as expected.</p>

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<p>Using negative numbers as arguments so that a different branch is taken in <code>abs_value()</code></p>

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    <span class="n">_</span><span class="p">[</span><span class="n">abs_max</span><span class="p">](</span><span class="o">-</span><span class="mi">2</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">)</span>
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<pre>({&#39;abs_max_a_int_55&#39;: &#39;Int&#39;, &#39;abs_max_b_int_56&#39;: &#39;Int&#39;},
 [Not(0 &lt; abs_max_a_int_55),
  Not(0 &lt; abs_max_b_int_56),
  -abs_max_a_int_55 &gt; -abs_max_b_int_56])</pre>
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<pre>(&#39;sat&#39;, {&#39;a&#39;: [&#39;-&#39;, &#39;1&#39;], &#39;b&#39;: &#39;0&#39;})</pre>
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<p>The solution reflects our predicates. (We used <code>a &gt; 0</code> in <code>abs_value()</code>).</p>

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<h3 id="Binomial-Coefficient">Binomial Coefficient<a class="anchor-link" href="#Binomial-Coefficient">&#182;</a></h3><p>For a larger example that uses different kinds of variables, say we want to compute the binomial coefficient by the following formulas</p>
$$ 
^nP_k=\frac{n!}{(n-k)!}
$$$$
\binom nk=\,^nC_k=\frac{^nP_k}{k!}
$$
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<p>we define the functions as follows.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">def</span> <span class="nf">factorial</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
    <span class="n">v</span> <span class="o">=</span> <span class="mi">1</span>
    <span class="k">while</span> <span class="n">n</span> <span class="o">!=</span> <span class="mi">0</span><span class="p">:</span>
        <span class="n">v</span> <span class="o">*=</span> <span class="n">n</span>
        <span class="n">n</span> <span class="o">-=</span> <span class="mi">1</span>
    <span class="k">return</span> <span class="n">v</span>
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    <span class="k">return</span> <span class="n">factorial</span><span class="p">(</span><span class="n">n</span><span class="p">)</span> <span class="o">/</span> <span class="n">factorial</span><span class="p">(</span><span class="n">n</span> <span class="o">-</span> <span class="n">k</span><span class="p">)</span>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">def</span> <span class="nf">combination</span><span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="n">k</span><span class="p">):</span>
    <span class="k">return</span> <span class="n">permutation</span><span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="n">k</span><span class="p">)</span> <span class="o">/</span> <span class="n">factorial</span><span class="p">(</span><span class="n">k</span><span class="p">)</span>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">def</span> <span class="nf">binomial</span><span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="n">k</span><span class="p">):</span>
    <span class="k">if</span> <span class="n">n</span> <span class="o">&lt;</span> <span class="mi">0</span> <span class="ow">or</span> <span class="n">k</span> <span class="o">&lt;</span> <span class="mi">0</span> <span class="ow">or</span> <span class="n">n</span> <span class="o">&lt;</span> <span class="n">k</span><span class="p">:</span>
        <span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s1">&#39;Invalid values&#39;</span><span class="p">)</span>
    <span class="k">return</span> <span class="n">combination</span><span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="n">k</span><span class="p">)</span>
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<p>As before, we run the function under <code>ConcolicTracer</code>.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">with</span> <span class="n">ConcolicTracer</span><span class="p">()</span> <span class="k">as</span> <span class="n">_</span><span class="p">:</span>
    <span class="n">v</span> <span class="o">=</span> <span class="n">_</span><span class="p">[</span><span class="n">binomial</span><span class="p">](</span><span class="mi">4</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
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<p>Then call <code>zeval()</code> to evaluate.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">_</span><span class="o">.</span><span class="n">zeval</span><span class="p">()</span>
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<pre>(&#39;sat&#39;, {&#39;n&#39;: &#39;4&#39;, &#39;k&#39;: &#39;2&#39;})</pre>
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<h3 id="Database">Database<a class="anchor-link" href="#Database">&#182;</a></h3>
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<p>For a larger example using the Concolic String class <code>zstr</code>, We use the DB class from the <a href="InformationFlow.slides.html">chapter on information flow</a>.</p>

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<p>We first populate our database.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">db</span> <span class="o">=</span> <span class="n">sample_db</span><span class="p">()</span>
<span class="k">for</span> <span class="n">V</span> <span class="ow">in</span> <span class="n">VEHICLES</span><span class="p">:</span>
    <span class="n">update_inventory</span><span class="p">(</span><span class="n">db</span><span class="p">,</span> <span class="n">V</span><span class="p">)</span>
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<pre>{&#39;inventory&#39;: ({&#39;year&#39;: int, &#39;kind&#39;: str, &#39;company&#39;: str, &#39;model&#39;: str},
  [{&#39;year&#39;: 1997, &#39;kind&#39;: &#39;van&#39;, &#39;company&#39;: &#39;Ford&#39;, &#39;model&#39;: &#39;E350&#39;},
   {&#39;year&#39;: 2000, &#39;kind&#39;: &#39;car&#39;, &#39;company&#39;: &#39;Mercury&#39;, &#39;model&#39;: &#39;Cougar&#39;},
   {&#39;year&#39;: 1999, &#39;kind&#39;: &#39;car&#39;, &#39;company&#39;: &#39;Chevy&#39;, &#39;model&#39;: &#39;Venture&#39;}])}</pre>
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<p>We are now ready to fuzz our <code>DB</code> class. Hash functions are difficult to handle directly (because they rely on internal C functions). Hence we modify <code>table()</code> slightly.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">class</span> <span class="nc">ConcolicDB</span><span class="p">(</span><span class="n">DB</span><span class="p">):</span>
    <span class="k">def</span> <span class="nf">table</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">t_name</span><span class="p">):</span>
        <span class="k">for</span> <span class="n">k</span><span class="p">,</span> <span class="n">v</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">db</span><span class="p">:</span>
            <span class="k">if</span> <span class="n">t_name</span> <span class="o">==</span> <span class="n">k</span><span class="p">:</span>
                <span class="k">return</span> <span class="n">v</span>
        <span class="k">raise</span> <span class="n">SQLException</span><span class="p">(</span><span class="s1">&#39;Table (</span><span class="si">%s</span><span class="s1">) was not found&#39;</span> <span class="o">%</span> <span class="nb">repr</span><span class="p">(</span><span class="n">t_name</span><span class="p">))</span>

    <span class="k">def</span> <span class="nf">column</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">decl</span><span class="p">,</span> <span class="n">c_name</span><span class="p">):</span>
        <span class="k">for</span> <span class="n">k</span> <span class="ow">in</span> <span class="n">decl</span><span class="p">:</span>
            <span class="k">if</span> <span class="n">c_name</span> <span class="o">==</span> <span class="n">k</span><span class="p">:</span>
                <span class="k">return</span> <span class="n">decl</span><span class="p">[</span><span class="n">k</span><span class="p">]</span>
        <span class="k">raise</span> <span class="n">SQLException</span><span class="p">(</span><span class="s1">&#39;Column (</span><span class="si">%s</span><span class="s1">) was not found&#39;</span> <span class="o">%</span> <span class="nb">repr</span><span class="p">(</span><span class="n">c_name</span><span class="p">))</span>
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<p>To make it easy, we define a single function <code>db_select()</code> that directly invokes <code>db.sql()</code>.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">def</span> <span class="nf">db_select</span><span class="p">(</span><span class="n">s</span><span class="p">):</span>
    <span class="n">my_db</span> <span class="o">=</span> <span class="n">ConcolicDB</span><span class="p">()</span>
    <span class="n">my_db</span><span class="o">.</span><span class="n">db</span> <span class="o">=</span> <span class="p">[(</span><span class="n">k</span><span class="p">,</span> <span class="n">v</span><span class="p">)</span> <span class="k">for</span> <span class="p">(</span><span class="n">k</span><span class="p">,</span> <span class="n">v</span><span class="p">)</span> <span class="ow">in</span> <span class="n">db</span><span class="o">.</span><span class="n">db</span><span class="o">.</span><span class="n">items</span><span class="p">()]</span>
    <span class="n">r</span> <span class="o">=</span> <span class="n">my_db</span><span class="o">.</span><span class="n">sql</span><span class="p">(</span><span class="n">s</span><span class="p">)</span>
    <span class="k">return</span> <span class="n">r</span>
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<p>We now want to run SQL statements under our <code>ConcolicTracer</code>, and collect predicates obtained.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">with</span> <span class="n">ConcolicTracer</span><span class="p">()</span> <span class="k">as</span> <span class="n">_</span><span class="p">:</span>
    <span class="n">_</span><span class="p">[</span><span class="n">db_select</span><span class="p">](</span><span class="s1">&#39;select kind from inventory&#39;</span><span class="p">)</span>
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<p>The predicates encountered during the execution are as follows:</p>

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<pre>[str.indexof(db_select_s_str_59, &#34;select &#34;, 0) == 0,
 str.indexof(db_select_s_str_59, &#34;select &#34;, 0) == 0,
 Not(0 &gt;
     str.indexof(str.substr(db_select_s_str_59, 7, 19),
                 &#34; from &#34;,
                 0)),
 Not(19 &lt;
     str.indexof(str.substr(db_select_s_str_59, 7, 19),
                 &#34; from &#34;,
                 0)),
 Or(0 &lt;
    str.indexof(str.substr(db_select_s_str_59, 7, 19),
                &#34; from &#34;,
                0),
    str.indexof(str.substr(db_select_s_str_59, 7, 19),
                &#34; from &#34;,
                0) ==
    0),
 Not(Or(0 &lt;
        str.indexof(str.substr(db_select_s_str_59, 7, 19),
                    &#34; where &#34;,
                    0),
        str.indexof(str.substr(db_select_s_str_59, 7, 19),
                    &#34; where &#34;,
                    0) ==
        0)),
 Not(19 &lt;
     str.indexof(str.substr(db_select_s_str_59, 7, 19),
                 &#34; from &#34;,
                 0) +
     6),
 Or(19 &gt;
    str.indexof(str.substr(db_select_s_str_59, 7, 19),
                &#34; from &#34;,
                0) +
    6,
    19 ==
    str.indexof(str.substr(db_select_s_str_59, 7, 19),
                &#34; from &#34;,
                0) +
    6),
 str.substr(str.substr(db_select_s_str_59, 7, 19), 10, 9) ==
 &#34;inventory&#34;]</pre>
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<p>We can use <code>zeval()</code> as before to solve the constraints.</p>

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<pre>(&#39;Gave up&#39;, None)</pre>
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<p><strong>Note:</strong> Due to the state of the <em>theory of strings</em> in SMT Solvers, you will mostly get <em>gave up</em> when executing the <code>zeval()</code>. This is perfectly fine. It just means that the SMT solver gave up before it reached an answer.</p>

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<h2 id="Fuzzing-with-Constraints">Fuzzing with Constraints<a class="anchor-link" href="#Fuzzing-with-Constraints">&#182;</a></h2><p>In this section, we show how to use the infrastructure we built for concolic execution for guiding fuzzing.</p>
<h3 id="SimpleConcolicFuzzer">SimpleConcolicFuzzer<a class="anchor-link" href="#SimpleConcolicFuzzer">&#182;</a></h3><p>The <code>SimpleConcolicFuzzer</code> starts with a sample input generated by some other fuzzer. It then runs the function being tested under <code>ConcolicTracer</code>, and collects the path predicates. It then negates random predicates within the path and solves it with <em>z3</em> to produce a new output that is guaranteed to take a different path than the original.</p>

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<p>First, we import the <code>Fuzzer</code> interface, and an example program <code>hang_if_no_space()</code></p>

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<p>The <code>SimpleConcolicFuzzer</code> is defined with the <code>Fuzzer</code> interface.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">class</span> <span class="nc">SimpleConcolicFuzzer</span><span class="p">(</span><span class="n">Fuzzer</span><span class="p">):</span>
    <span class="k">def</span> <span class="nf">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">ct</span> <span class="o">=</span> <span class="p">[]</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">seen</span> <span class="o">=</span> <span class="nb">set</span><span class="p">()</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">seen_strs</span> <span class="o">=</span> <span class="nb">set</span><span class="p">()</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">max_tries</span> <span class="o">=</span> <span class="mi">1000</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">last</span> <span class="o">=</span> <span class="kc">None</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">last_idx</span> <span class="o">=</span> <span class="kc">None</span>
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<p>The <code>add_trace()</code> method provides a way for new traces to be added. It is kept separate from the initialization as we might want to add more than one trace from the same function.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">class</span> <span class="nc">SimpleConcolicFuzzer</span><span class="p">(</span><span class="n">SimpleConcolicFuzzer</span><span class="p">):</span>
    <span class="k">def</span> <span class="nf">add_trace</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">tracer</span><span class="p">):</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">ct</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">tracer</span><span class="p">)</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">last</span> <span class="o">=</span> <span class="n">tracer</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">last_idx</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">tracer</span><span class="o">.</span><span class="n">context</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span> <span class="o">-</span> <span class="mi">1</span>
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<p>The <code>to_num()</code> method translates a series of predicates to a bit pattern that corresponds to the decision taken at each predicate. If the <code>if</code> branch is taken, the pattern is <code>1</code>, while <code>else</code> branch is indicated by <code>0</code>. This allows us to represent any execution path as a single integer.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">class</span> <span class="nc">SimpleConcolicFuzzer</span><span class="p">(</span><span class="n">SimpleConcolicFuzzer</span><span class="p">):</span>
    <span class="k">def</span> <span class="nf">to_num</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">arr</span><span class="p">):</span>
        <span class="k">return</span> <span class="nb">int</span><span class="p">(</span>
            <span class="s1">&#39;&#39;</span><span class="o">.</span><span class="n">join</span><span class="p">(</span>
                <span class="nb">reversed</span><span class="p">([</span>
                    <span class="s1">&#39;0&#39;</span> <span class="k">if</span> <span class="n">z3</span><span class="o">.</span><span class="n">simplify</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="o">.</span><span class="n">decl</span><span class="p">()</span><span class="o">.</span><span class="n">name</span><span class="p">()</span> <span class="o">==</span> <span class="s1">&#39;not&#39;</span> <span class="k">else</span> <span class="s1">&#39;1&#39;</span>
                    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">arr</span>
                <span class="p">]</span> <span class="o">+</span> <span class="p">[</span><span class="s1">&#39;1&#39;</span><span class="p">])),</span> <span class="mi">2</span><span class="p">)</span>
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<p>It is used as follows.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">scf</span> <span class="o">=</span> <span class="n">SimpleConcolicFuzzer</span><span class="p">()</span>
<span class="n">a</span><span class="p">,</span> <span class="n">b</span> <span class="o">=</span> <span class="n">z3</span><span class="o">.</span><span class="n">Ints</span><span class="p">(</span><span class="s1">&#39;a b&#39;</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="nb">bin</span><span class="p">(</span><span class="n">scf</span><span class="o">.</span><span class="n">to_num</span><span class="p">([</span><span class="n">z3</span><span class="o">.</span><span class="n">Not</span><span class="p">(</span><span class="n">a</span> <span class="o">==</span> <span class="n">b</span><span class="p">)])))</span>
<span class="nb">print</span><span class="p">(</span><span class="nb">bin</span><span class="p">(</span><span class="n">scf</span><span class="o">.</span><span class="n">to_num</span><span class="p">([</span><span class="n">z3</span><span class="o">.</span><span class="n">Not</span><span class="p">(</span><span class="n">a</span> <span class="o">==</span> <span class="n">b</span><span class="p">),</span> <span class="n">a</span> <span class="o">==</span> <span class="n">b</span><span class="p">])))</span>
<span class="nb">print</span><span class="p">(</span><span class="nb">bin</span><span class="p">(</span><span class="n">scf</span><span class="o">.</span><span class="n">to_num</span><span class="p">([</span><span class="n">z3</span><span class="o">.</span><span class="n">Not</span><span class="p">(</span><span class="n">a</span> <span class="o">==</span> <span class="n">b</span><span class="p">),</span> <span class="n">a</span> <span class="o">==</span> <span class="n">b</span><span class="p">,</span> <span class="n">z3</span><span class="o">.</span><span class="n">Not</span><span class="p">(</span><span class="n">a</span> <span class="o">==</span> <span class="n">b</span><span class="p">)])))</span>
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<pre>0b10
0b110
0b1010
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<p>The bit pattern is read from left to right. The first <code>0</code> indicates the first <code>else</code> branch (corresponding to <code>Not</code>), while the last <code>1</code> is added as a sentinel. The pattern <code>0b1010</code> indicates two <code>else</code> branches taken.</p>

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<p>The <code>get_newpath()</code> function chooses a random point in the list of predicates to negate. That is, it creates a new list with a prefix of random length (with same predicates as original), and a single negated value at the end. It also ensures that values seen once are never repeated.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">class</span> <span class="nc">SimpleConcolicFuzzer</span><span class="p">(</span><span class="n">SimpleConcolicFuzzer</span><span class="p">):</span>
    <span class="k">def</span> <span class="nf">get_newpath</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
        <span class="n">switch</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">last_idx</span><span class="p">)</span>
        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">seen</span><span class="p">:</span>
            <span class="n">param</span> <span class="o">=</span> <span class="nb">list</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">last</span><span class="o">.</span><span class="n">fn_args</span><span class="o">.</span><span class="n">values</span><span class="p">())[</span><span class="mi">0</span><span class="p">]</span>
            <span class="n">sparam</span> <span class="o">=</span> <span class="n">z3</span><span class="o">.</span><span class="n">String</span><span class="p">(</span><span class="n">param</span><span class="p">)</span>
            <span class="n">seen</span> <span class="o">=</span> <span class="p">[</span><span class="n">sparam</span> <span class="o">!=</span> <span class="n">z3</span><span class="o">.</span><span class="n">StringVal</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="bp">self</span><span class="o">.</span><span class="n">seen_strs</span><span class="p">]</span>
        <span class="k">else</span><span class="p">:</span>
            <span class="n">seen</span> <span class="o">=</span> <span class="p">[]</span>
        <span class="n">new_path</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">last</span><span class="o">.</span><span class="n">path</span><span class="p">[</span><span class="mi">0</span><span class="p">:</span><span class="n">switch</span><span class="p">]</span> <span class="o">+</span> \
            <span class="p">[</span><span class="n">z3</span><span class="o">.</span><span class="n">Not</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">last</span><span class="o">.</span><span class="n">path</span><span class="p">[</span><span class="n">switch</span><span class="p">])]</span> <span class="o">+</span> <span class="n">seen</span>
        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">to_num</span><span class="p">(</span><span class="n">new_path</span><span class="p">),</span> <span class="n">new_path</span>
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<p>The <code>fuzz()</code> method simply generates new lists of predicates, and solves them to produce new inputs.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">class</span> <span class="nc">SimpleConcolicFuzzer</span><span class="p">(</span><span class="n">SimpleConcolicFuzzer</span><span class="p">):</span>
    <span class="k">def</span> <span class="nf">fuzz</span><span class="p">(</span><span class="bp">self</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="bp">self</span><span class="o">.</span><span class="n">max_tries</span><span class="p">):</span>
            <span class="n">pattern</span><span class="p">,</span> <span class="n">path</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">get_newpath</span><span class="p">()</span>
            <span class="k">if</span> <span class="n">pattern</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">seen</span><span class="p">:</span>
                <span class="k">continue</span>
            <span class="bp">self</span><span class="o">.</span><span class="n">seen</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">pattern</span><span class="p">)</span>
            <span class="n">s</span><span class="p">,</span> <span class="n">v</span> <span class="o">=</span> <span class="n">zeval_smt</span><span class="p">(</span><span class="n">path</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">last</span><span class="p">,</span> <span class="n">log</span><span class="o">=</span><span class="kc">False</span><span class="p">)</span>
            <span class="k">if</span> <span class="n">s</span> <span class="o">!=</span> <span class="s1">&#39;sat&#39;</span><span class="p">:</span>
                <span class="k">continue</span>
            <span class="n">s</span> <span class="o">=</span> <span class="nb">list</span><span class="p">(</span><span class="n">v</span><span class="o">.</span><span class="n">values</span><span class="p">())[</span><span class="mi">0</span><span class="p">]</span>
            <span class="bp">self</span><span class="o">.</span><span class="n">seen_strs</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">s</span><span class="p">)</span>
            <span class="k">return</span> <span class="n">s</span>
        <span class="k">return</span> <span class="kc">None</span>
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<p>The <code>SimpleConcolicFuzzer</code> is used as follows. First, we use a random string to generate the concolic trace.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">with</span> <span class="n">ExpectTimeout</span><span class="p">(</span><span class="mi">2</span><span class="p">):</span>
    <span class="k">with</span> <span class="n">ConcolicTracer</span><span class="p">()</span> <span class="k">as</span> <span class="n">_</span><span class="p">:</span>
        <span class="n">_</span><span class="p">[</span><span class="n">hang_if_no_space</span><span class="p">](</span><span class="s1">&#39;abcd&#39;</span><span class="p">)</span>
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<pre>Traceback (most recent call last):
  File &#34;&lt;ipython-input-204-ff2b46f545ec&gt;&#34;, line 3, in &lt;module&gt;
    _[hang_if_no_space](&#39;abcd&#39;)
  File &#34;&lt;ipython-input-33-635d2b1b13c2&gt;&#34;, line 3, in __call__
    self.result = self.fn(*self.concolic(args))
  File &#34;&lt;string&gt;&#34;, line 4, in hang_if_no_space
  File &#34;&lt;string&gt;&#34;, line 4, in hang_if_no_space
  File &#34;&lt;string&gt;&#34;, line 16, in check_time
TimeoutError (expected)
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<p>Next, we initialize and add this trace to the fuzzer.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">scf</span> <span class="o">=</span> <span class="n">SimpleConcolicFuzzer</span><span class="p">()</span>
<span class="n">scf</span><span class="o">.</span><span class="n">add_trace</span><span class="p">(</span><span class="n">_</span><span class="p">)</span>
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<p>Finally, we fuzz.</p>

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<div class=" highlight hl-ipython3"><pre><span></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">10</span><span class="p">):</span>
    <span class="n">v</span> <span class="o">=</span> <span class="n">scf</span><span class="o">.</span><span class="n">fuzz</span><span class="p">()</span>
    <span class="k">if</span> <span class="n">v</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
        <span class="k">break</span>
    <span class="nb">print</span><span class="p">(</span><span class="n">v</span><span class="p">)</span>
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<pre> \x00
\x00\x00 \x00
 \x02
 \x80
 @
\x00 \x00
 \x10
\x00\x00 \x08
\x00\x00\x00 \x00
\x00  
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<p>Here is another example using <code>cgi_decode()</code></p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">with</span> <span class="n">ConcolicTracer</span><span class="p">()</span> <span class="k">as</span> <span class="n">_</span><span class="p">:</span>
    <span class="n">_</span><span class="p">[</span><span class="n">cgi_decode</span><span class="p">](</span><span class="s1">&#39;abcd&#39;</span><span class="p">)</span>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">scf</span> <span class="o">=</span> <span class="n">SimpleConcolicFuzzer</span><span class="p">()</span>
<span class="n">scf</span><span class="o">.</span><span class="n">add_trace</span><span class="p">(</span><span class="n">_</span><span class="p">)</span>
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<div class=" highlight hl-ipython3"><pre><span></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">10</span><span class="p">):</span>
    <span class="n">v</span> <span class="o">=</span> <span class="n">scf</span><span class="o">.</span><span class="n">fuzz</span><span class="p">()</span>
    <span class="k">if</span> <span class="n">v</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
        <span class="k">break</span>
    <span class="nb">print</span><span class="p">(</span><span class="n">v</span><span class="p">)</span>
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<pre>%\x00
\x00\x00\x00+\x00
%\x02
\x00\x00%\x00
\x00+\x00
\x00\x00\x00+\x02
\x00\x00\x00%\x00
\x00\x00% 
\x00\x00+\x00
\x00\x00\x00+\x80
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<p>The <code>SimpleConcolicFuzzer</code> is reasonably efficient at exploring paths near the path followed by a given sample input. However, it is not very intelligent when it comes to choosing which paths to follow. We look at another fuzzer that lifts the predicates obtained to the grammar and achieves better fuzzing.</p>

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<h3 id="ConcolicGrammarFuzzer">ConcolicGrammarFuzzer<a class="anchor-link" href="#ConcolicGrammarFuzzer">&#182;</a></h3><p>The concolic framework can be used directly in fuzzing. First, we extend our <code>GrammarFuzzer</code> with a a helper method <code>tree_to_string()</code> such that we can retrieve the derivation tree of the fuzz output. We also define <code>prune_tree()</code> and <code>coalesce()</code> to reduce the depth of sub trees. These methods accept a list of tokens types such that a node belonging to the token type gets converted from a tree to a leaf node by calling <code>tree_to_string()</code>.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">class</span> <span class="nc">ConcolicGrammarFuzzer</span><span class="p">(</span><span class="n">GrammarFuzzer</span><span class="p">):</span>
    <span class="k">def</span> <span class="nf">tree_to_string</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">tree</span><span class="p">):</span>
        <span class="n">symbol</span><span class="p">,</span> <span class="n">children</span><span class="p">,</span> <span class="o">*</span><span class="n">_</span> <span class="o">=</span> <span class="n">tree</span>
        <span class="n">e</span> <span class="o">=</span> <span class="s1">&#39;&#39;</span>
        <span class="k">if</span> <span class="n">children</span><span class="p">:</span>
            <span class="k">return</span> <span class="n">e</span><span class="o">.</span><span class="n">join</span><span class="p">([</span><span class="bp">self</span><span class="o">.</span><span class="n">tree_to_string</span><span class="p">(</span><span class="n">c</span><span class="p">)</span> <span class="k">for</span> <span class="n">c</span> <span class="ow">in</span> <span class="n">children</span><span class="p">])</span>
        <span class="k">else</span><span class="p">:</span>
            <span class="k">return</span> <span class="n">e</span> <span class="k">if</span> <span class="n">symbol</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">grammar</span> <span class="k">else</span> <span class="n">symbol</span>

    <span class="k">def</span> <span class="nf">prune_tree</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">tree</span><span class="p">,</span> <span class="n">tokens</span><span class="p">):</span>
        <span class="n">name</span><span class="p">,</span> <span class="n">children</span> <span class="o">=</span> <span class="n">tree</span>
        <span class="n">children</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">coalesce</span><span class="p">(</span><span class="n">children</span><span class="p">)</span>
        <span class="k">if</span> <span class="n">name</span> <span class="ow">in</span> <span class="n">tokens</span><span class="p">:</span>
            <span class="k">return</span> <span class="p">(</span><span class="n">name</span><span class="p">,</span> <span class="p">[(</span><span class="bp">self</span><span class="o">.</span><span class="n">tree_to_string</span><span class="p">(</span><span class="n">tree</span><span class="p">),</span> <span class="p">[])])</span>
        <span class="k">else</span><span class="p">:</span>
            <span class="k">return</span> <span class="p">(</span><span class="n">name</span><span class="p">,</span> <span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">prune_tree</span><span class="p">(</span><span class="n">c</span><span class="p">,</span> <span class="n">tokens</span><span class="p">)</span> <span class="k">for</span> <span class="n">c</span> <span class="ow">in</span> <span class="n">children</span><span class="p">])</span>

    <span class="k">def</span> <span class="nf">coalesce</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">children</span><span class="p">):</span>
        <span class="n">last</span> <span class="o">=</span> <span class="s1">&#39;&#39;</span>
        <span class="n">new_lst</span> <span class="o">=</span> <span class="p">[]</span>
        <span class="k">for</span> <span class="n">cn</span><span class="p">,</span> <span class="n">cc</span> <span class="ow">in</span> <span class="n">children</span><span class="p">:</span>
            <span class="k">if</span> <span class="n">cn</span> <span class="ow">not</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">grammar</span><span class="p">:</span>
                <span class="n">last</span> <span class="o">+=</span> <span class="n">cn</span>
            <span class="k">else</span><span class="p">:</span>
                <span class="k">if</span> <span class="n">last</span><span class="p">:</span>
                    <span class="n">new_lst</span><span class="o">.</span><span class="n">append</span><span class="p">((</span><span class="n">last</span><span class="p">,</span> <span class="p">[]))</span>
                    <span class="n">last</span> <span class="o">=</span> <span class="s1">&#39;&#39;</span>
                <span class="n">new_lst</span><span class="o">.</span><span class="n">append</span><span class="p">((</span><span class="n">cn</span><span class="p">,</span> <span class="n">cc</span><span class="p">))</span>
        <span class="k">if</span> <span class="n">last</span><span class="p">:</span>
            <span class="n">new_lst</span><span class="o">.</span><span class="n">append</span><span class="p">((</span><span class="n">last</span><span class="p">,</span> <span class="p">[]))</span>
        <span class="k">return</span> <span class="n">new_lst</span>
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<p>We can now use the fuzzer to produce inputs for our DB.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">tgf</span> <span class="o">=</span> <span class="n">ConcolicGrammarFuzzer</span><span class="p">(</span><span class="n">INVENTORY_GRAMMAR</span><span class="p">)</span>
<span class="k">while</span> <span class="kc">True</span><span class="p">:</span>
    <span class="n">qtree</span> <span class="o">=</span> <span class="n">tgf</span><span class="o">.</span><span class="n">fuzz_tree</span><span class="p">()</span>
    <span class="n">query</span> <span class="o">=</span> <span class="nb">str</span><span class="p">(</span><span class="n">tgf</span><span class="o">.</span><span class="n">tree_to_string</span><span class="p">(</span><span class="n">qtree</span><span class="p">))</span>
    <span class="k">if</span> <span class="n">query</span><span class="o">.</span><span class="n">startswith</span><span class="p">(</span><span class="s1">&#39;select&#39;</span><span class="p">):</span>
        <span class="k">break</span>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">with</span> <span class="n">ExpectError</span><span class="p">():</span>
    <span class="nb">print</span><span class="p">(</span><span class="nb">repr</span><span class="p">(</span><span class="n">query</span><span class="p">))</span>
    <span class="k">with</span> <span class="n">ConcolicTracer</span><span class="p">()</span> <span class="k">as</span> <span class="n">_</span><span class="p">:</span>
        <span class="n">res</span> <span class="o">=</span> <span class="n">_</span><span class="p">[</span><span class="n">db_select</span><span class="p">](</span><span class="nb">str</span><span class="p">(</span><span class="n">query</span><span class="p">))</span>
    <span class="nb">print</span><span class="p">(</span><span class="nb">repr</span><span class="p">(</span><span class="n">res</span><span class="p">))</span>
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<pre>&#39;select z,(k(w)+N) from W0 where T9(e)*i+b-E!=Yt&#39;
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<pre>Traceback (most recent call last):
  File &#34;&lt;ipython-input-216-6cbadb7bcf98&gt;&#34;, line 4, in &lt;module&gt;
    res = _[db_select](str(query))
  File &#34;&lt;ipython-input-33-635d2b1b13c2&gt;&#34;, line 3, in __call__
    self.result = self.fn(*self.concolic(args))
  File &#34;&lt;ipython-input-191-26b52b86ed9e&gt;&#34;, line 4, in db_select
    r = my_db.sql(s)
  File &#34;&lt;string&gt;&#34;, line 18, in sql
  File &#34;&lt;string&gt;&#34;, line 17, in do_select
  File &#34;&lt;ipython-input-190-d1ea3580462a&gt;&#34;, line 6, in table
    raise SQLException(&#39;Table (%s) was not found&#39; % repr(t_name))
InformationFlow.SQLException: Table (&#39;W0&#39;) was not found (expected)
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<p>Our fuzzer returns with an exception. It is unable to find the specified table. Let us examine the predicates it encountered.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">p</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">_</span><span class="o">.</span><span class="n">path</span><span class="p">):</span>
    <span class="nb">print</span><span class="p">(</span><span class="n">i</span><span class="p">,</span> <span class="n">p</span><span class="p">)</span>
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<pre>0 str.indexof(db_select_s_str_62, &#34;select &#34;, 0) == 0
1 str.indexof(db_select_s_str_62, &#34;select &#34;, 0) == 0
2 Not(0 &gt;
    str.indexof(str.substr(db_select_s_str_62, 7, 40),
                &#34; from &#34;,
                0))
3 Not(40 &lt;
    str.indexof(str.substr(db_select_s_str_62, 7, 40),
                &#34; from &#34;,
                0))
4 Or(0 &lt;
   str.indexof(str.substr(db_select_s_str_62, 7, 40),
               &#34; from &#34;,
               0),
   str.indexof(str.substr(db_select_s_str_62, 7, 40),
               &#34; from &#34;,
               0) ==
   0)
5 Or(0 &lt;
   str.indexof(str.substr(db_select_s_str_62, 7, 40),
               &#34; where &#34;,
               0),
   str.indexof(str.substr(db_select_s_str_62, 7, 40),
               &#34; where &#34;,
               0) ==
   0)
6 Not(40 &lt;
    str.indexof(str.substr(db_select_s_str_62, 7, 40),
                &#34; from &#34;,
                0) +
    6)
7 Not(40 &lt;
    str.indexof(str.substr(db_select_s_str_62, 7, 40),
                &#34; where &#34;,
                0))
8 Or(str.indexof(str.substr(db_select_s_str_62, 7, 40),
               &#34; from &#34;,
               0) +
   6 &lt;
   str.indexof(str.substr(db_select_s_str_62, 7, 40),
               &#34; where &#34;,
               0),
   str.indexof(str.substr(db_select_s_str_62, 7, 40),
               &#34; where &#34;,
               0) ==
   str.indexof(str.substr(db_select_s_str_62, 7, 40),
               &#34; from &#34;,
               0) +
   6)
9 Not(40 &lt;
    str.indexof(str.substr(db_select_s_str_62, 7, 40),
                &#34; where &#34;,
                0) +
    7)
10 Or(40 &gt;
   str.indexof(str.substr(db_select_s_str_62, 7, 40),
               &#34; where &#34;,
               0) +
   7,
   40 ==
   str.indexof(str.substr(db_select_s_str_62, 7, 40),
               &#34; where &#34;,
               0) +
   7)
11 Not(str.substr(str.substr(db_select_s_str_62, 7, 40), 16, 2) ==
    &#34;inventory&#34;)
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<p>Note that we can obtain constraints that are not present in the grammar from using the <code>ConcolicTracer</code>. In particular, see how we are able to obtain the condition that the table needs to be <code>inventory</code> (Predicate 11) for the fuzzing to succeed.</p>

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<p>How do we lift these to the grammar? and in particular how do we do it automatically? One option we have is to simply switch the last predicate obtained. In our case, the last predicate is (11). Can we simply invert the predicate and solve it again?</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">new_path</span> <span class="o">=</span> <span class="n">_</span><span class="o">.</span><span class="n">path</span><span class="p">[</span><span class="mi">0</span><span class="p">:</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">+</span> <span class="p">[</span><span class="n">z3</span><span class="o">.</span><span class="n">Not</span><span class="p">(</span><span class="n">_</span><span class="o">.</span><span class="n">path</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">])]</span>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">new_</span> <span class="o">=</span> <span class="n">ConcolicTracer</span><span class="p">((</span><span class="n">_</span><span class="o">.</span><span class="n">decls</span><span class="p">,</span> <span class="n">new_path</span><span class="p">))</span>
<span class="n">new_</span><span class="o">.</span><span class="n">fn</span> <span class="o">=</span> <span class="n">_</span><span class="o">.</span><span class="n">fn</span>
<span class="n">new_</span><span class="o">.</span><span class="n">fn_args</span> <span class="o">=</span> <span class="n">_</span><span class="o">.</span><span class="n">fn_args</span>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">new_</span><span class="o">.</span><span class="n">zeval</span><span class="p">()</span>
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<pre>(&#39;No Solutions&#39;, None)</pre>
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<p>Indeed, this will not work as the string lengths being compared to are different.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="nb">print</span><span class="p">(</span><span class="n">_</span><span class="o">.</span><span class="n">path</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span>
<span class="n">z3</span><span class="o">.</span><span class="n">solve</span><span class="p">(</span><span class="n">z3</span><span class="o">.</span><span class="n">Not</span><span class="p">(</span><span class="n">_</span><span class="o">.</span><span class="n">path</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]))</span>
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<pre>Not(str.substr(str.substr(db_select_s_str_62, 7, 40), 16, 2) ==
    &#34;inventory&#34;)
no solution
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<p>A better idea is to investigate what <em>string</em> comparisons are being made, and associate that with the corresponding nodes in the grammar. Let us examine our derivation tree (pruned to avoid recursive structures, and to focus on important parts).</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">prune_tokens</span> <span class="o">=</span> <span class="p">[</span>
    <span class="s1">&#39;&lt;value&gt;&#39;</span><span class="p">,</span> <span class="s1">&#39;&lt;table&gt;&#39;</span><span class="p">,</span> <span class="s1">&#39;&lt;column&gt;&#39;</span><span class="p">,</span> <span class="s1">&#39;&lt;literals&gt;&#39;</span><span class="p">,</span> <span class="s1">&#39;&lt;exprs&gt;&#39;</span><span class="p">,</span> <span class="s1">&#39;&lt;bexpr&gt;&#39;</span>
<span class="p">]</span>
<span class="n">dt</span> <span class="o">=</span> <span class="n">tgf</span><span class="o">.</span><span class="n">prune_tree</span><span class="p">(</span><span class="n">qtree</span><span class="p">,</span> <span class="n">prune_tokens</span><span class="p">)</span>
<span class="n">display_tree</span><span class="p">(</span><span class="n">dt</span><span class="p">)</span>
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<text text-anchor="middle" x="78" y="-3.8" font-family="Times,serif" font-size="14.00" fill="#000000">z,(k(w)+N)</text>
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<text text-anchor="middle" x="318" y="-3.8" font-family="Times,serif" font-size="14.00" fill="#000000">T9(e)*i+b&#45;E!=Yt</text>
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<p>Can we identify which part of the input was supplied by which part of the grammar? We define <code>span()</code> that can recover this information from the derivation tree. For a given node, let us assume that the start point is known. Then, for processing the children, we proceed as follows: We choose one child at a time from left to right, and compute the length of the child. The length of the children before the current child in addition to our starting point gives the starting point of the current child. The end point for each node is simply the end point of its last children (or the length of its node if it is a leaf).</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">def</span> <span class="nf">span</span><span class="p">(</span><span class="n">node</span><span class="p">,</span> <span class="n">g</span><span class="p">,</span> <span class="n">node_start</span><span class="o">=</span><span class="mi">0</span><span class="p">):</span>
    <span class="n">hm</span> <span class="o">=</span> <span class="p">{}</span>
    <span class="n">k</span><span class="p">,</span> <span class="n">cs</span> <span class="o">=</span> <span class="n">node</span>
    <span class="n">end_i</span> <span class="o">=</span> <span class="n">node_start</span>
    <span class="n">new_cs</span> <span class="o">=</span> <span class="p">[]</span>
    <span class="k">for</span> <span class="n">c</span> <span class="ow">in</span> <span class="n">cs</span><span class="p">:</span>
        <span class="n">chm</span><span class="p">,</span> <span class="p">(</span><span class="n">ck</span><span class="p">,</span> <span class="n">child_start</span><span class="p">,</span> <span class="n">child_end</span><span class="p">,</span> <span class="n">gcs</span><span class="p">)</span> <span class="o">=</span> <span class="n">span</span><span class="p">(</span><span class="n">c</span><span class="p">,</span> <span class="n">g</span><span class="p">,</span> <span class="n">end_i</span><span class="p">)</span>
        <span class="n">new_cs</span><span class="o">.</span><span class="n">append</span><span class="p">((</span><span class="n">ck</span><span class="p">,</span> <span class="n">child_start</span><span class="p">,</span> <span class="n">child_end</span><span class="p">,</span> <span class="n">gcs</span><span class="p">))</span>
        <span class="n">end_i</span> <span class="o">=</span> <span class="n">child_end</span>
        <span class="n">hm</span><span class="o">.</span><span class="n">update</span><span class="p">(</span><span class="n">chm</span><span class="p">)</span>
    <span class="n">node_end</span> <span class="o">=</span> <span class="n">end_i</span> <span class="k">if</span> <span class="n">cs</span> <span class="k">else</span> <span class="n">node_start</span> <span class="o">+</span> <span class="nb">len</span><span class="p">(</span><span class="n">k</span><span class="p">)</span>
    <span class="k">if</span> <span class="n">k</span> <span class="ow">in</span> <span class="n">g</span> <span class="ow">and</span> <span class="n">k</span> <span class="o">!=</span> <span class="n">START_SYMBOL</span><span class="p">:</span>
        <span class="n">hm</span><span class="p">[</span><span class="n">k</span><span class="p">]</span> <span class="o">=</span> <span class="p">(</span><span class="n">node_start</span><span class="p">,</span> <span class="n">node_end</span> <span class="o">-</span> <span class="n">node_start</span><span class="p">)</span>
    <span class="k">return</span> <span class="n">hm</span><span class="p">,</span> <span class="p">(</span><span class="n">k</span><span class="p">,</span> <span class="n">node_start</span><span class="p">,</span> <span class="n">node_end</span><span class="p">,</span> <span class="n">new_cs</span><span class="p">)</span>
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<p>We use it as follows:</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">span_hm</span><span class="p">,</span> <span class="n">_n</span> <span class="o">=</span> <span class="n">span</span><span class="p">(</span><span class="n">dt</span><span class="p">,</span> <span class="n">INVENTORY_GRAMMAR</span><span class="p">)</span>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">span_hm</span>
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<pre>{&#39;&lt;exprs&gt;&#39;: (7, 10),
 &#39;&lt;table&gt;&#39;: (23, 2),
 &#39;&lt;bexpr&gt;&#39;: (32, 15),
 &#39;&lt;query&gt;&#39;: (0, 47)}</pre>
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<p>We can check if we got the right values as follows.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="nb">print</span><span class="p">(</span><span class="s2">&quot;query:&quot;</span><span class="p">,</span> <span class="n">query</span><span class="p">)</span>
<span class="k">for</span> <span class="n">k</span> <span class="ow">in</span> <span class="n">span_hm</span><span class="p">:</span>
    <span class="n">start</span><span class="p">,</span> <span class="n">l</span> <span class="o">=</span> <span class="n">span_hm</span><span class="p">[</span><span class="n">k</span><span class="p">]</span>
    <span class="nb">print</span><span class="p">(</span><span class="n">k</span><span class="p">,</span> <span class="n">query</span><span class="p">[</span><span class="n">start</span><span class="p">:</span><span class="n">start</span> <span class="o">+</span> <span class="n">l</span><span class="p">])</span>
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<pre>query: select z,(k(w)+N) from W0 where T9(e)*i+b-E!=Yt
&lt;exprs&gt; z,(k(w)+N)
&lt;table&gt; W0
&lt;bexpr&gt; T9(e)*i+b-E!=Yt
&lt;query&gt; select z,(k(w)+N) from W0 where T9(e)*i+b-E!=Yt
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<p>Next, we need to obtain all the comparisons made in each predicate. For that, we define two helper functions. The first is <code>unwrap_substrings()</code> that translates multiple calls to <code>z3.SubString</code> and returns the start, and length of the given z3 string expression.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">def</span> <span class="nf">unwrap_substrings</span><span class="p">(</span><span class="n">s</span><span class="p">):</span>
    <span class="k">assert</span> <span class="n">s</span><span class="o">.</span><span class="n">decl</span><span class="p">()</span><span class="o">.</span><span class="n">name</span><span class="p">()</span> <span class="o">==</span> <span class="s1">&#39;str.substr&#39;</span>
    <span class="n">cs</span><span class="p">,</span> <span class="n">frm</span><span class="p">,</span> <span class="n">l</span> <span class="o">=</span> <span class="n">s</span><span class="o">.</span><span class="n">children</span><span class="p">()</span>
    <span class="n">fl</span> <span class="o">=</span> <span class="n">frm</span><span class="o">.</span><span class="n">as_long</span><span class="p">()</span>
    <span class="n">ll</span> <span class="o">=</span> <span class="n">l</span><span class="o">.</span><span class="n">as_long</span><span class="p">()</span>
    <span class="k">if</span> <span class="n">cs</span><span class="o">.</span><span class="n">decl</span><span class="p">()</span><span class="o">.</span><span class="n">name</span><span class="p">()</span> <span class="o">==</span> <span class="s1">&#39;str.substr&#39;</span><span class="p">:</span>
        <span class="n">newfrm</span><span class="p">,</span> <span class="n">_l</span> <span class="o">=</span> <span class="n">unwrap_substrings</span><span class="p">(</span><span class="n">cs</span><span class="p">)</span>
        <span class="k">return</span> <span class="p">(</span><span class="n">fl</span> <span class="o">+</span> <span class="n">newfrm</span><span class="p">,</span> <span class="n">ll</span><span class="p">)</span>
    <span class="k">else</span><span class="p">:</span>
        <span class="k">return</span> <span class="p">(</span><span class="n">fl</span><span class="p">,</span> <span class="n">ll</span><span class="p">)</span>
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<p>We define <code>traverse_z3()</code> that traverses a given z3 string expression, and collects all direct string comparisons to a substring of the original argument.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">def</span> <span class="nf">traverse_z3</span><span class="p">(</span><span class="n">p</span><span class="p">,</span> <span class="n">hm</span><span class="p">):</span>
    <span class="k">def</span> <span class="nf">z3_as_string</span><span class="p">(</span><span class="n">v</span><span class="p">):</span>
        <span class="n">s</span> <span class="o">=</span> <span class="n">v</span><span class="o">.</span><span class="n">as_string</span><span class="p">()</span>
        <span class="c1"># Z3 bug: Python z3 API returns quoted strings for as_string</span>
        <span class="k">assert</span> <span class="n">s</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">==</span> <span class="s1">&#39;&quot;&#39;</span> <span class="ow">and</span> <span class="n">s</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">==</span> <span class="s1">&#39;&quot;&#39;</span>
        <span class="k">return</span> <span class="n">s</span><span class="p">[</span><span class="mi">1</span><span class="p">:</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>

    <span class="n">n</span> <span class="o">=</span> <span class="n">p</span><span class="o">.</span><span class="n">decl</span><span class="p">()</span><span class="o">.</span><span class="n">name</span><span class="p">()</span>
    <span class="k">if</span> <span class="n">n</span> <span class="o">==</span> <span class="s1">&#39;not&#39;</span><span class="p">:</span>
        <span class="k">return</span> <span class="n">traverse_z3</span><span class="p">(</span><span class="n">p</span><span class="o">.</span><span class="n">children</span><span class="p">()[</span><span class="mi">0</span><span class="p">],</span> <span class="n">hm</span><span class="p">)</span>
    <span class="k">elif</span> <span class="n">n</span> <span class="o">==</span> <span class="s1">&#39;=&#39;</span><span class="p">:</span>
        <span class="n">i</span><span class="p">,</span> <span class="n">j</span> <span class="o">=</span> <span class="n">p</span><span class="o">.</span><span class="n">children</span><span class="p">()</span>
        <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">i</span><span class="p">,</span> <span class="p">(</span><span class="nb">int</span><span class="p">,</span> <span class="n">z3</span><span class="o">.</span><span class="n">IntNumRef</span><span class="p">)):</span>
            <span class="k">return</span> <span class="n">traverse_z3</span><span class="p">(</span><span class="n">j</span><span class="p">,</span> <span class="n">hm</span><span class="p">)</span>
        <span class="k">elif</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">j</span><span class="p">,</span> <span class="p">(</span><span class="nb">int</span><span class="p">,</span> <span class="n">z3</span><span class="o">.</span><span class="n">IntNumRef</span><span class="p">)):</span>
            <span class="k">return</span> <span class="n">traverse_z3</span><span class="p">(</span><span class="n">i</span><span class="p">,</span> <span class="n">hm</span><span class="p">)</span>
        <span class="k">else</span><span class="p">:</span>
            <span class="k">if</span> <span class="n">i</span><span class="o">.</span><span class="n">is_string</span><span class="p">()</span> <span class="ow">and</span> <span class="n">j</span><span class="o">.</span><span class="n">is_string</span><span class="p">():</span>
                <span class="k">if</span> <span class="n">i</span><span class="o">.</span><span class="n">is_string_value</span><span class="p">():</span>
                    <span class="n">cs</span><span class="p">,</span> <span class="n">frm</span><span class="p">,</span> <span class="n">l</span> <span class="o">=</span> <span class="n">j</span><span class="o">.</span><span class="n">children</span><span class="p">()</span>
                    <span class="k">if</span> <span class="p">(</span><span class="nb">isinstance</span><span class="p">(</span><span class="n">frm</span><span class="p">,</span> <span class="n">z3</span><span class="o">.</span><span class="n">IntNumRef</span><span class="p">)</span>
                            <span class="ow">and</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">l</span><span class="p">,</span> <span class="n">z3</span><span class="o">.</span><span class="n">IntNumRef</span><span class="p">)):</span>
                        <span class="n">hm</span><span class="p">[</span><span class="n">z3_as_string</span><span class="p">(</span><span class="n">i</span><span class="p">)]</span> <span class="o">=</span> <span class="n">unwrap_substrings</span><span class="p">(</span><span class="n">j</span><span class="p">)</span>
                <span class="k">elif</span> <span class="n">j</span><span class="o">.</span><span class="n">is_string_value</span><span class="p">():</span>
                    <span class="n">cs</span><span class="p">,</span> <span class="n">frm</span><span class="p">,</span> <span class="n">l</span> <span class="o">=</span> <span class="n">i</span><span class="o">.</span><span class="n">children</span><span class="p">()</span>
                    <span class="k">if</span> <span class="p">(</span><span class="nb">isinstance</span><span class="p">(</span><span class="n">frm</span><span class="p">,</span> <span class="n">z3</span><span class="o">.</span><span class="n">IntNumRef</span><span class="p">)</span>
                            <span class="ow">and</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">l</span><span class="p">,</span> <span class="n">z3</span><span class="o">.</span><span class="n">IntNumRef</span><span class="p">)):</span>
                        <span class="n">hm</span><span class="p">[</span><span class="n">z3_as_string</span><span class="p">(</span><span class="n">j</span><span class="p">)]</span> <span class="o">=</span> <span class="n">unwrap_substrings</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
            <span class="k">else</span><span class="p">:</span>
                <span class="k">assert</span> <span class="kc">False</span>  <span class="c1"># for now</span>
    <span class="k">elif</span> <span class="n">n</span> <span class="o">==</span> <span class="s1">&#39;&lt;&#39;</span> <span class="ow">or</span> <span class="n">n</span> <span class="o">==</span> <span class="s1">&#39;&gt;&#39;</span><span class="p">:</span>
        <span class="n">i</span><span class="p">,</span> <span class="n">j</span> <span class="o">=</span> <span class="n">p</span><span class="o">.</span><span class="n">children</span><span class="p">()</span>
        <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">i</span><span class="p">,</span> <span class="p">(</span><span class="nb">int</span><span class="p">,</span> <span class="n">z3</span><span class="o">.</span><span class="n">IntNumRef</span><span class="p">)):</span>
            <span class="k">return</span> <span class="n">traverse_z3</span><span class="p">(</span><span class="n">j</span><span class="p">,</span> <span class="n">hm</span><span class="p">)</span>
        <span class="k">elif</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">j</span><span class="p">,</span> <span class="p">(</span><span class="nb">int</span><span class="p">,</span> <span class="n">z3</span><span class="o">.</span><span class="n">IntNumRef</span><span class="p">)):</span>
            <span class="k">return</span> <span class="n">traverse_z3</span><span class="p">(</span><span class="n">i</span><span class="p">,</span> <span class="n">hm</span><span class="p">)</span>
        <span class="k">else</span><span class="p">:</span>
            <span class="k">assert</span> <span class="kc">False</span>
    <span class="k">return</span> <span class="n">p</span>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">comparisons</span> <span class="o">=</span> <span class="p">{}</span>
<span class="k">for</span> <span class="n">p</span> <span class="ow">in</span> <span class="n">_</span><span class="o">.</span><span class="n">path</span><span class="p">:</span>
    <span class="n">traverse_z3</span><span class="p">(</span><span class="n">p</span><span class="p">,</span> <span class="n">comparisons</span><span class="p">)</span>
<span class="n">comparisons</span>
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<pre>{&#39;inventory&#39;: (23, 2)}</pre>
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<p>All that we need now is to declare string variables that match the substrings in <code>comparisons</code>, and solve for them for each item in the path. For that, we define <code>find_alternatives()</code>.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">def</span> <span class="nf">find_alternatives</span><span class="p">(</span><span class="n">spans</span><span class="p">,</span> <span class="nb">cmp</span><span class="p">):</span>
    <span class="n">alts</span> <span class="o">=</span> <span class="p">{}</span>
    <span class="k">for</span> <span class="n">key</span> <span class="ow">in</span> <span class="n">spans</span><span class="p">:</span>
        <span class="n">start</span><span class="p">,</span> <span class="n">l</span> <span class="o">=</span> <span class="n">spans</span><span class="p">[</span><span class="n">key</span><span class="p">]</span>
        <span class="n">rset</span> <span class="o">=</span> <span class="nb">set</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="n">start</span><span class="p">,</span> <span class="n">start</span> <span class="o">+</span> <span class="n">l</span><span class="p">))</span>
        <span class="k">for</span> <span class="n">ckey</span> <span class="ow">in</span> <span class="nb">cmp</span><span class="p">:</span>
            <span class="n">cstart</span><span class="p">,</span> <span class="n">cl</span> <span class="o">=</span> <span class="nb">cmp</span><span class="p">[</span><span class="n">ckey</span><span class="p">]</span>
            <span class="n">cset</span> <span class="o">=</span> <span class="nb">set</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="n">cstart</span><span class="p">,</span> <span class="n">cstart</span> <span class="o">+</span> <span class="n">cl</span><span class="p">))</span>
            <span class="c1"># if rset.issubset(cset): &lt;- ignoring subsets for now.</span>
            <span class="k">if</span> <span class="n">rset</span> <span class="o">==</span> <span class="n">cset</span><span class="p">:</span>
                <span class="k">if</span> <span class="n">key</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">alts</span><span class="p">:</span>
                    <span class="n">alts</span><span class="p">[</span><span class="n">key</span><span class="p">]</span> <span class="o">=</span> <span class="nb">set</span><span class="p">()</span>
                <span class="n">alts</span><span class="p">[</span><span class="n">key</span><span class="p">]</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">ckey</span><span class="p">)</span>
    <span class="k">return</span> <span class="n">alts</span>
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<p>We use it as follows.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">alternatives</span> <span class="o">=</span> <span class="n">find_alternatives</span><span class="p">(</span><span class="n">span_hm</span><span class="p">,</span> <span class="n">comparisons</span><span class="p">)</span>
<span class="n">alternatives</span>
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<pre>{&#39;&lt;table&gt;&#39;: {&#39;inventory&#39;}}</pre>
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<p>So, we have our alternatives for each key in the grammar. We can now update our grammar as follows.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">INVENTORY_GRAMMAR_NEW</span> <span class="o">=</span> <span class="nb">dict</span><span class="p">(</span><span class="n">INVENTORY_GRAMMAR</span><span class="p">)</span>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">for</span> <span class="n">k</span> <span class="ow">in</span> <span class="n">alternatives</span><span class="p">:</span>
    <span class="n">INVENTORY_GRAMMAR_NEW</span><span class="p">[</span><span class="n">k</span><span class="p">]</span> <span class="o">=</span> <span class="n">INVENTORY_GRAMMAR_NEW</span><span class="p">[</span><span class="n">k</span><span class="p">]</span> <span class="o">+</span> <span class="nb">list</span><span class="p">(</span><span class="n">alternatives</span><span class="p">[</span><span class="n">k</span><span class="p">])</span>
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<p>We made a choice here. We could have completely overwritten the definition of <code>&lt;table&gt;</code> . Instead, we added our new alternatives to the existing definition. This way, our fuzzer will also attempt other values for <code>&lt;table&gt;</code> once in a while.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">INVENTORY_GRAMMAR_NEW</span><span class="p">[</span><span class="s1">&#39;&lt;table&gt;&#39;</span><span class="p">]</span>
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<pre>[&#39;&lt;word&gt;&#39;, &#39;inventory&#39;]</pre>
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<p>Let us try fuzzing with our new grammar.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">cgf</span> <span class="o">=</span> <span class="n">ConcolicGrammarFuzzer</span><span class="p">(</span><span class="n">INVENTORY_GRAMMAR_NEW</span><span class="p">)</span>
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<div class=" highlight hl-ipython3"><pre><span></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">10</span><span class="p">):</span>
    <span class="n">qtree</span> <span class="o">=</span> <span class="n">cgf</span><span class="o">.</span><span class="n">fuzz_tree</span><span class="p">()</span>
    <span class="n">query</span> <span class="o">=</span> <span class="n">cgf</span><span class="o">.</span><span class="n">tree_to_string</span><span class="p">(</span><span class="n">qtree</span><span class="p">)</span>
    <span class="nb">print</span><span class="p">(</span><span class="n">query</span><span class="p">)</span>
    <span class="k">with</span> <span class="n">ExpectError</span><span class="p">():</span>
        <span class="k">try</span><span class="p">:</span>
            <span class="k">with</span> <span class="n">ConcolicTracer</span><span class="p">()</span> <span class="k">as</span> <span class="n">_</span><span class="p">:</span>
                <span class="n">res</span> <span class="o">=</span> <span class="n">_</span><span class="p">[</span><span class="n">db_select</span><span class="p">](</span><span class="n">query</span><span class="p">)</span>
            <span class="nb">print</span><span class="p">(</span><span class="nb">repr</span><span class="p">(</span><span class="n">res</span><span class="p">))</span>
        <span class="k">except</span> <span class="n">SQLException</span> <span class="k">as</span> <span class="n">e</span><span class="p">:</span>
            <span class="nb">print</span><span class="p">(</span><span class="n">e</span><span class="p">)</span>
        <span class="nb">print</span><span class="p">()</span>
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<pre>select (A*S*l(e)+h) from inventory where l/j&lt;G(G)&lt;P
Invalid WHERE (&#39;(l/j&lt;G(G)&lt;P)&#39;)

update W5RhS set TT8=P7 where E!=b+e
Table (&#39;W5RhS&#39;) was not found

delete from inventory where Z(F)/y*W/v&lt;R/w/L(Y)/R
Invalid WHERE (&#39;Z(F)/y*W/v&lt;R/w/L(Y)/R&#39;)

delete from Y where -02==:
Table (&#39;Y&#39;) was not found

insert into ZQ (C3y,h4,o3) values (&#39;D&#39;,&#39;.{Y&#39;)
Table (&#39;ZQ&#39;) was not found

select oy((r42),K==_==D!=(:),((h&gt;N/W)),(k!=p)) from inventory
Invalid WHERE (&#39;(oy((r42),K==_==D!=(:),((h&gt;N/W)),(k!=p)))&#39;)

select X==(r),Y,l from inventory where J/x*f&gt;M(h)/B
Invalid WHERE (&#39;(J/x*f&gt;M(h)/B)&#39;)

select _6(U,K5)&gt;a-N-n+C*e+s-n from inventory
Invalid WHERE (&#39;(_6(U,K5)&gt;a-N-n+C*e+s-n)&#39;)

select n-V/X/X&lt;e(s),fqw(f+v) from inventory
Invalid WHERE (&#39;(n-V/X/X&lt;e(s),fqw(f+v))&#39;)

select (d769R090x1Of),(b9S9G89) from inventory
Invalid WHERE (&#39;((d769R090x1Of),(b9S9G89))&#39;)

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<p>That is, we were able to reach the dangerous method <code>my_eval()</code>.
In effect, what we have done is to lift parts of predicates to the grammar. The new grammar can generate inputs that reach deeper into the program than before. Note that we have only handled the equality predicate. One can also lift the '&lt;' and '&gt;' comparison operators to the grammar if required.</p>
<p>Compare the output of our fuzzer to the original <code>GrammarFuzzer</code> below.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">gf</span> <span class="o">=</span> <span class="n">GrammarFuzzer</span><span class="p">(</span><span class="n">INVENTORY_GRAMMAR</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">10</span><span class="p">):</span>
    <span class="n">query</span> <span class="o">=</span> <span class="n">gf</span><span class="o">.</span><span class="n">fuzz</span><span class="p">()</span>
    <span class="nb">print</span><span class="p">(</span><span class="n">query</span><span class="p">)</span>
    <span class="k">with</span> <span class="n">ExpectError</span><span class="p">():</span>
        <span class="k">try</span><span class="p">:</span>
            <span class="n">res</span> <span class="o">=</span> <span class="n">db_select</span><span class="p">(</span><span class="n">query</span><span class="p">)</span>
            <span class="nb">print</span><span class="p">(</span><span class="nb">repr</span><span class="p">(</span><span class="n">res</span><span class="p">))</span>
        <span class="k">except</span> <span class="n">SQLException</span> <span class="k">as</span> <span class="n">e</span><span class="p">:</span>
            <span class="nb">print</span><span class="p">(</span><span class="n">e</span><span class="p">)</span>
        <span class="nb">print</span><span class="p">()</span>
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<pre>select (D),j from _4 where N/d/I*o&gt;h
Table (&#39;_4&#39;) was not found

select r-u*Z/d*S/L-h,qN,T!=r from t
Table (&#39;t&#39;) was not found

delete from _04e where -5!=(X)*p(x)+w*l(J,i,b)/Y/d
Table (&#39;_04e&#39;) was not found

delete from c3 where --6!=o8M!=o==79156.443
Table (&#39;c3&#39;) was not found

insert into F (Lu9g:917s) values (&#39;B&#39;)
Table (&#39;F&#39;) was not found

delete from W where j/S*S+P/d/x&gt;a(a)+M(V)
Table (&#39;W&#39;) was not found

delete from NQ where D(u)-R+X(X,X)==x/w*s/R
Table (&#39;NQ&#39;) was not found

delete from C3 where A*q+u/M(z,X)&lt;v&lt;8+X*I(A)==821.2
Table (&#39;C3&#39;) was not found

delete from Tg06M6 where t+V/S&lt;s+.+S
Table (&#39;Tg06M6&#39;) was not found

select 5,G from z3 where W&gt;Z==l(W)/g*D-T
Table (&#39;z3&#39;) was not found

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<p>As can be seen, the original grammar fuzzer is unable to proceed beyond the table verification.</p>

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<h4 id="All-together">All together<a class="anchor-link" href="#All-together">&#182;</a></h4><p>We implement these methods in <code>ConcolicGrammarFuzzer</code>. The method <code>update_grammar()</code> allows <code>ConcolicGrammarFuzzer</code> to collect feedback from concolic fuzzing, and update the grammar used for fuzzing accordingly.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">class</span> <span class="nc">ConcolicGrammarFuzzer</span><span class="p">(</span><span class="n">ConcolicGrammarFuzzer</span><span class="p">):</span>
    <span class="k">def</span> <span class="nf">prune_tokens</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">tokens</span><span class="p">):</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">prune_tokens</span> <span class="o">=</span> <span class="n">tokens</span>

    <span class="k">def</span> <span class="nf">update_grammar</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">trace</span><span class="p">):</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">comparisons</span> <span class="o">=</span> <span class="p">{}</span>
        <span class="k">for</span> <span class="n">p</span> <span class="ow">in</span> <span class="n">trace</span><span class="o">.</span><span class="n">path</span><span class="p">:</span>
            <span class="n">traverse_z3</span><span class="p">(</span><span class="n">p</span><span class="p">,</span> <span class="n">comparisons</span><span class="p">)</span>
        <span class="n">alternatives</span> <span class="o">=</span> <span class="n">find_alternatives</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">span_range</span><span class="p">,</span> <span class="n">comparisons</span><span class="p">)</span>
        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">log</span><span class="p">:</span>
            <span class="nb">print</span><span class="p">(</span><span class="s1">&#39;Alternatives:&#39;</span><span class="p">,</span> <span class="n">alternatives</span><span class="p">,</span> <span class="s1">&#39;Span:&#39;</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">span_range</span><span class="p">)</span>
        <span class="n">new_grammar</span> <span class="o">=</span> <span class="nb">dict</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">grammar</span><span class="p">)</span>
        <span class="k">for</span> <span class="n">k</span> <span class="ow">in</span> <span class="n">alternatives</span><span class="p">:</span>
            <span class="n">new_grammar</span><span class="p">[</span><span class="n">k</span><span class="p">]</span> <span class="o">=</span> <span class="nb">list</span><span class="p">(</span><span class="nb">set</span><span class="p">(</span><span class="n">new_grammar</span><span class="p">[</span><span class="n">k</span><span class="p">]</span> <span class="o">+</span> <span class="nb">list</span><span class="p">(</span><span class="n">alternatives</span><span class="p">[</span><span class="n">k</span><span class="p">])))</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">grammar</span> <span class="o">=</span> <span class="n">new_grammar</span>
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<p>The <code>fuzz()</code> method simply generates the derivation tree, computes the span range, and returns the string generated from the derivation tree.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">class</span> <span class="nc">ConcolicGrammarFuzzer</span><span class="p">(</span><span class="n">ConcolicGrammarFuzzer</span><span class="p">):</span>
    <span class="k">def</span> <span class="nf">fuzz</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
        <span class="n">qtree</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">fuzz_tree</span><span class="p">()</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">pruned_tree</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">prune_tree</span><span class="p">(</span><span class="n">qtree</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">prune_tokens</span><span class="p">)</span>
        <span class="n">query</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">tree_to_string</span><span class="p">(</span><span class="n">qtree</span><span class="p">)</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">span_range</span><span class="p">,</span> <span class="n">_n</span> <span class="o">=</span> <span class="n">span</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">pruned_tree</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">grammar</span><span class="p">)</span>
        <span class="k">return</span> <span class="n">query</span>
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<p>To ensure that our approach works, let us update our tables slightly.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">inventory</span> <span class="o">=</span> <span class="n">db</span><span class="o">.</span><span class="n">db</span><span class="o">.</span><span class="n">pop</span><span class="p">(</span><span class="s1">&#39;inventory&#39;</span><span class="p">,</span> <span class="kc">None</span><span class="p">)</span>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">db</span><span class="o">.</span><span class="n">db</span><span class="p">[</span><span class="s1">&#39;vehicles&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="n">inventory</span>
<span class="n">db</span><span class="o">.</span><span class="n">db</span><span class="p">[</span><span class="s1">&#39;months&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="p">({</span>
    <span class="s1">&#39;month&#39;</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span>
    <span class="s1">&#39;name&#39;</span><span class="p">:</span> <span class="nb">str</span>
<span class="p">},</span> <span class="p">[{</span>
    <span class="s1">&#39;month&#39;</span><span class="p">:</span> <span class="n">i</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span>
    <span class="s1">&#39;name&#39;</span><span class="p">:</span> <span class="n">m</span>
<span class="p">}</span> <span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">m</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">([</span>
    <span class="s1">&#39;jan&#39;</span><span class="p">,</span> <span class="s1">&#39;feb&#39;</span><span class="p">,</span> <span class="s1">&#39;mar&#39;</span><span class="p">,</span> <span class="s1">&#39;apr&#39;</span><span class="p">,</span> <span class="s1">&#39;may&#39;</span><span class="p">,</span> <span class="s1">&#39;jun&#39;</span><span class="p">,</span> <span class="s1">&#39;jul&#39;</span><span class="p">,</span> <span class="s1">&#39;aug&#39;</span><span class="p">,</span> <span class="s1">&#39;sep&#39;</span><span class="p">,</span> <span class="s1">&#39;oct&#39;</span><span class="p">,</span>
    <span class="s1">&#39;nov&#39;</span><span class="p">,</span> <span class="s1">&#39;dec&#39;</span>
<span class="p">])])</span>
<span class="n">db</span><span class="o">.</span><span class="n">db</span>
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<pre>{&#39;vehicles&#39;: ({&#39;year&#39;: int, &#39;kind&#39;: str, &#39;company&#39;: str, &#39;model&#39;: str},
  [{&#39;year&#39;: 1997, &#39;kind&#39;: &#39;van&#39;, &#39;company&#39;: &#39;Ford&#39;, &#39;model&#39;: &#39;E350&#39;},
   {&#39;year&#39;: 2000, &#39;kind&#39;: &#39;car&#39;, &#39;company&#39;: &#39;Mercury&#39;, &#39;model&#39;: &#39;Cougar&#39;},
   {&#39;year&#39;: 1999, &#39;kind&#39;: &#39;car&#39;, &#39;company&#39;: &#39;Chevy&#39;, &#39;model&#39;: &#39;Venture&#39;}]),
 &#39;months&#39;: ({&#39;month&#39;: int, &#39;name&#39;: str},
  [{&#39;month&#39;: 1, &#39;name&#39;: &#39;jan&#39;},
   {&#39;month&#39;: 2, &#39;name&#39;: &#39;feb&#39;},
   {&#39;month&#39;: 3, &#39;name&#39;: &#39;mar&#39;},
   {&#39;month&#39;: 4, &#39;name&#39;: &#39;apr&#39;},
   {&#39;month&#39;: 5, &#39;name&#39;: &#39;may&#39;},
   {&#39;month&#39;: 6, &#39;name&#39;: &#39;jun&#39;},
   {&#39;month&#39;: 7, &#39;name&#39;: &#39;jul&#39;},
   {&#39;month&#39;: 8, &#39;name&#39;: &#39;aug&#39;},
   {&#39;month&#39;: 9, &#39;name&#39;: &#39;sep&#39;},
   {&#39;month&#39;: 10, &#39;name&#39;: &#39;oct&#39;},
   {&#39;month&#39;: 11, &#39;name&#39;: &#39;nov&#39;},
   {&#39;month&#39;: 12, &#39;name&#39;: &#39;dec&#39;}])}</pre>
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<p>The <code>ConcolicGrammarFuzzer</code> is used as follows.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">cgf</span> <span class="o">=</span> <span class="n">ConcolicGrammarFuzzer</span><span class="p">(</span><span class="n">INVENTORY_GRAMMAR</span><span class="p">)</span>
<span class="n">cgf</span><span class="o">.</span><span class="n">prune_tokens</span><span class="p">(</span><span class="n">prune_tokens</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">10</span><span class="p">):</span>
    <span class="n">query</span> <span class="o">=</span> <span class="n">cgf</span><span class="o">.</span><span class="n">fuzz</span><span class="p">()</span>
    <span class="nb">print</span><span class="p">(</span><span class="n">query</span><span class="p">)</span>
    <span class="k">with</span> <span class="n">ConcolicTracer</span><span class="p">()</span> <span class="k">as</span> <span class="n">_</span><span class="p">:</span>
        <span class="k">with</span> <span class="n">ExpectError</span><span class="p">():</span>
            <span class="k">try</span><span class="p">:</span>
                <span class="n">res</span> <span class="o">=</span> <span class="n">_</span><span class="p">[</span><span class="n">db_select</span><span class="p">](</span><span class="n">query</span><span class="p">)</span>
                <span class="nb">print</span><span class="p">(</span><span class="nb">repr</span><span class="p">(</span><span class="n">res</span><span class="p">))</span>
            <span class="k">except</span> <span class="n">SQLException</span> <span class="k">as</span> <span class="n">e</span><span class="p">:</span>
                <span class="nb">print</span><span class="p">(</span><span class="n">e</span><span class="p">)</span>
        <span class="n">cgf</span><span class="o">.</span><span class="n">update_grammar</span><span class="p">(</span><span class="n">_</span><span class="p">)</span>
        <span class="nb">print</span><span class="p">()</span>
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<pre>delete from b where m/C!=L-K*Q&lt;H+c(O)+-0*H/G
Table (&#39;b&#39;) was not found

update O8F set E=g,p=Z where y&gt;p
Table (&#39;O8F&#39;) was not found

update months set wz=w5 where _*E/O-K(U)&lt;Z+v/G/r/c
Column (&#39;wz&#39;) was not found

delete from months where r-z-Q-d*d-h-P!=r1R
Invalid WHERE (&#39;r-z-Q-d*d-h-P!=r1R&#39;)

insert into muc (n23f2W6sOP) values (&#39;y&#39;)
Table (&#39;muc&#39;) was not found

insert into months (.9) values (&#39;T|gi&#39;,&#39;O&#39;,1.86,-501.9,0.1,48199462.8)
Column (&#39;.9&#39;) was not found

select w&lt;O/X-S from months where Y/b&gt;Z*K*Z*B
Invalid WHERE (&#39;(Y/b&gt;Z*K*Z*B)&#39;)

insert into vehicles (name) values (5.0,25,4.0,&#39;/&#39;)
Column (&#39;name&#39;) was not found

update months set kind=kN,company=a,kind=O where (S&lt;S(Q))==I+t&lt;z
Column (&#39;kind&#39;) was not found

update vehicles set month=kU7,company=k,company=M,name=X where (((b+L)==0.4))==4
Column (&#39;month&#39;) was not found

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<p>As can be seen, the fuzzer starts with no knowledge of the tables <code>vehicles</code>, <code>months</code> and <code>years</code>, but identifies it from the concolic execution, and lifts it to the grammar. This allows us to improve the effectiveness of fuzzing.</p>

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<h2 id="Limitations">Limitations<a class="anchor-link" href="#Limitations">&#182;</a></h2><p>As with dynamic taint analysis, implicit control flow can obscure the predicates encountered during concolic execution. However, this limitation could be overcome to some extent by wrapping any constants in the source with their respective proxy objects. Similarly, calls to internal C functions can cause the symbolic information to be discarded, and only partial information may be obtained.</p>

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<h2 id="Synopsis">Synopsis<a class="anchor-link" href="#Synopsis">&#182;</a></h2>
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<p>This chapter defines two main classes: <code>SimpleConcolicFuzzer</code> and <code>ConcolicGrammarFuzzer</code>. The <code>SimpleConcolicFuzzer</code> first uses a sample input to collect predicates encountered. The fuzzer then negates random predicates to generate new input constraints. These, when solved, produce inputs that explore paths that are close to the original path. It can be used as follows.</p>

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<p>The <code>cgi_decode()</code> function <a href="Coverage.slides.html">from the chapter on coverage</a> is the subject program.</p>

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<p>We first obtain the constraints using <code>ConcolicTracer</code>.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">with</span> <span class="n">ConcolicTracer</span><span class="p">()</span> <span class="k">as</span> <span class="n">_</span><span class="p">:</span>
    <span class="n">_</span><span class="p">[</span><span class="n">cgi_decode</span><span class="p">](</span><span class="s1">&#39;abcd&#39;</span><span class="p">)</span>
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<p>These constraints are added to the concolic fuzzer as follows:</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">scf</span> <span class="o">=</span> <span class="n">SimpleConcolicFuzzer</span><span class="p">()</span>
<span class="n">scf</span><span class="o">.</span><span class="n">add_trace</span><span class="p">(</span><span class="n">_</span><span class="p">)</span>
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<p>The concolic fuzzer then uses the constraints added to guide its fuzzing as follows:</p>

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<div class=" highlight hl-ipython3"><pre><span></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">10</span><span class="p">):</span>
    <span class="n">v</span> <span class="o">=</span> <span class="n">scf</span><span class="o">.</span><span class="n">fuzz</span><span class="p">()</span>
    <span class="k">if</span> <span class="n">v</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
        <span class="k">break</span>
    <span class="nb">print</span><span class="p">(</span><span class="n">v</span><span class="p">)</span>
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<pre>%\x00
\x00\x00+\x00
\x00\x00+\x04
\x00\x00+\x02
\x00\x00\x00+\x00
\x00+\x00
\x00\x00+@
\x00+ 
\x00%\x00
\x00+\x08
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<p>The <code>SimpleConcolicFuzzer</code> simply explores all paths near the original path traversed by the sample input. It does not use any kind of feedback from fuzzing.
The <code>ConcolicGrammarFuzzer</code> on the other hand, can collect feedback from the subject under fuzzing, and lift some of the constraints encountered to the grammar, enabling deeper fuzzing. It is used as follows:</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">cgf</span> <span class="o">=</span> <span class="n">ConcolicGrammarFuzzer</span><span class="p">(</span><span class="n">INVENTORY_GRAMMAR</span><span class="p">)</span>
<span class="n">cgf</span><span class="o">.</span><span class="n">prune_tokens</span><span class="p">(</span><span class="n">prune_tokens</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">10</span><span class="p">):</span>
    <span class="n">query</span> <span class="o">=</span> <span class="n">cgf</span><span class="o">.</span><span class="n">fuzz</span><span class="p">()</span>
    <span class="nb">print</span><span class="p">(</span><span class="n">query</span><span class="p">)</span>
    <span class="k">with</span> <span class="n">ConcolicTracer</span><span class="p">()</span> <span class="k">as</span> <span class="n">_</span><span class="p">:</span>
        <span class="k">with</span> <span class="n">ExpectError</span><span class="p">():</span>
            <span class="k">try</span><span class="p">:</span>
                <span class="n">res</span> <span class="o">=</span> <span class="n">_</span><span class="p">[</span><span class="n">db_select</span><span class="p">](</span><span class="n">query</span><span class="p">)</span>
                <span class="nb">print</span><span class="p">(</span><span class="nb">repr</span><span class="p">(</span><span class="n">res</span><span class="p">))</span>
            <span class="k">except</span> <span class="n">SQLException</span> <span class="k">as</span> <span class="n">e</span><span class="p">:</span>
                <span class="nb">print</span><span class="p">(</span><span class="n">e</span><span class="p">)</span>
        <span class="n">cgf</span><span class="o">.</span><span class="n">update_grammar</span><span class="p">(</span><span class="n">_</span><span class="p">)</span>
        <span class="nb">print</span><span class="p">()</span>
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<pre>update NK5f set L=D,o=G,q=X where A!=S
Table (&#39;NK5f&#39;) was not found

update vehicles set V9=B,y=r,E=E where r(U)/x(i)&gt;b
Column (&#39;V9&#39;) was not found

insert into V6S (V,R2,O) values (&#39;2/&#39;,&#39;@&#39;)
Table (&#39;V6S&#39;) was not found

update months set q=J1,Y=n,r=X where o-S*B!=(u!=q)
Column (&#39;q&#39;) was not found

select e-e/B&gt;Z(i)-(_) from vehicles where 59.2!=S==C
Invalid WHERE (&#39;(59.2!=S==C)&#39;)

delete from months where (M)*I&lt;p+e(S)-R*O(_)*p(8,u)
Invalid WHERE (&#39;(M)*I&lt;p+e(S)-R*O(_)*p(8,u)&#39;)

insert into months (CRl,i,AW5,_j) values (&#39;6&#39;)
Column (&#39;CRl&#39;) was not found

select a(A),J from K8z where p-f-i&lt;H
Table (&#39;K8z&#39;) was not found

delete from vehicles where h(2,a)&gt;((Sg90))+M5((az1(p)*r/W/V+b9(H)))
Invalid WHERE (&#39;h(2,a)&gt;((Sg90))+M5((az1(p)*r/W/V+b9(H)))&#39;)

select 9.7 from months
[9.7, 9.7, 9.7, 9.7, 9.7, 9.7, 9.7, 9.7, 9.7, 9.7, 9.7, 9.7]

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<h2 id="Lessons-Learned">Lessons Learned<a class="anchor-link" href="#Lessons-Learned">&#182;</a></h2><ul>
<li><p>Concolic execution can often provide more information than taint analysis with respect to the program behavior. However, this comes at a much larger runtime cost. Hence, unlike taint analysis, real-time analysis is often not possible.</p>
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<li><p>Similar to taint analysis, concolic execution also suffers from limitations such as indirect control flow and internal function calls.</p>
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<li><p>Predicates from concolic execution can be used in conjunction with fuzzing to provide an even more robust indication of incorrect behavior than taints, and can be used to create grammars that are better at producing valid inputs.</p>
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<h2 id="Next-Steps">Next Steps<a class="anchor-link" href="#Next-Steps">&#182;</a></h2><p>A costlier but stronger alternative to concolic fuzzing is <a href="SymbolicFuzzer.slides.html">symbolic fuzzing</a>. Similarly, <a href="SearchBasedFuzzer.slides.html">search based fuzzing</a> can often provide a cheaper exploration strategy than relying on SMT solvers to provide inputs slightly different from the current path.</p>

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<h2 id="Background">Background<a class="anchor-link" href="#Background">&#182;</a></h2><p>The technique of concolic execution was originally used to inform and expand the scope of <em>symbolic execution</em> \cite{king1976symbolic}, a static analysis technique for program analysis. Laron et al. cite{Larson2003} was the first to use the concolic execution technique.</p>
<p>The idea of using proxy objects for collecting constraints was pioneered by Cadar et al. \cite{cadar2005execution}. The concolic execution technique for Python programs used in this chapter was pioneered by PeerCheck \cite{PeerCheck}, and Python Error Finder \cite{Barsotti2018}.</p>

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<h2 id="Exercises">Exercises<a class="anchor-link" href="#Exercises">&#182;</a></h2>
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<h3 id="Exercise-1:-Implment-a-Concolic-Float-Proxy-Class">Exercise 1: Implment a Concolic Float Proxy Class<a class="anchor-link" href="#Exercise-1:-Implment-a-Concolic-Float-Proxy-Class">&#182;</a></h3>
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<p>While implementing the <code>zint</code> binary operators, we asserted that the results were <code>int</code>. However, that need not be the case. For example, division can result in <code>float</code>. Hence, we need proxy objects for <code>float</code>. Can you implement a similar proxy object for <code>float</code> and fix the <code>zint</code> binary operator definition?</p>

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<p><strong>Solution.</strong> The solution is as follows.</p>

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<p>As in the case of <code>zint</code>, we first open up <code>zfloat</code> for extension.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">class</span> <span class="nc">zfloat</span><span class="p">(</span><span class="nb">float</span><span class="p">):</span>
    <span class="k">def</span> <span class="nf">__new__</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="n">context</span><span class="p">,</span> <span class="n">zn</span><span class="p">,</span> <span class="n">v</span><span class="p">,</span> <span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kw</span><span class="p">):</span>
        <span class="k">return</span> <span class="nb">float</span><span class="o">.</span><span class="fm">__new__</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="n">v</span><span class="p">,</span> <span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kw</span><span class="p">)</span>
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<p>We then implement the initialization methods.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">class</span> <span class="nc">zfloat</span><span class="p">(</span><span class="n">zfloat</span><span class="p">):</span>
    <span class="nd">@classmethod</span>
    <span class="k">def</span> <span class="nf">create</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="n">context</span><span class="p">,</span> <span class="n">zn</span><span class="p">,</span> <span class="n">v</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
        <span class="k">return</span> <span class="n">zproxy_create</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="s1">&#39;Real&#39;</span><span class="p">,</span> <span class="n">z3</span><span class="o">.</span><span class="n">Real</span><span class="p">,</span> <span class="n">context</span><span class="p">,</span> <span class="n">zn</span><span class="p">,</span> <span class="n">v</span><span class="p">)</span>

    <span class="k">def</span> <span class="nf">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">context</span><span class="p">,</span> <span class="n">z</span><span class="p">,</span> <span class="n">v</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">z</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">v</span> <span class="o">=</span> <span class="n">z</span><span class="p">,</span> <span class="n">v</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">context</span> <span class="o">=</span> <span class="n">context</span>
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<p>The helper for when one of the arguments in a binary operation is not <code>float</code>.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">class</span> <span class="nc">zfloat</span><span class="p">(</span><span class="n">zfloat</span><span class="p">):</span>
    <span class="k">def</span> <span class="nf">_zv</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">o</span><span class="p">):</span>
        <span class="k">return</span> <span class="p">(</span><span class="n">o</span><span class="o">.</span><span class="n">z</span><span class="p">,</span> <span class="n">o</span><span class="o">.</span><span class="n">v</span><span class="p">)</span> <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">o</span><span class="p">,</span> <span class="n">zfloat</span><span class="p">)</span> <span class="k">else</span> <span class="p">(</span><span class="n">z3</span><span class="o">.</span><span class="n">RealVal</span><span class="p">(</span><span class="n">o</span><span class="p">),</span> <span class="n">o</span><span class="p">)</span>
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<p>Coerce <code>float</code> into bool value for use in conditionals.</p>

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    <span class="k">def</span> <span class="nf">__bool__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
        <span class="c1"># force registering boolean condition</span>
        <span class="k">if</span> <span class="bp">self</span> <span class="o">!=</span> <span class="mf">0.0</span><span class="p">:</span>
            <span class="k">return</span> <span class="kc">True</span>
        <span class="k">return</span> <span class="kc">False</span>
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<p>Define the common proxy method for comparison methods</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">def</span> <span class="nf">make_float_bool_wrapper</span><span class="p">(</span><span class="n">fname</span><span class="p">,</span> <span class="n">fun</span><span class="p">,</span> <span class="n">zfun</span><span class="p">):</span>
    <span class="k">def</span> <span class="nf">proxy</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
        <span class="n">z</span><span class="p">,</span> <span class="n">v</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_zv</span><span class="p">(</span><span class="n">other</span><span class="p">)</span>
        <span class="n">z_</span> <span class="o">=</span> <span class="n">zfun</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">z</span><span class="p">,</span> <span class="n">z</span><span class="p">)</span>
        <span class="n">v_</span> <span class="o">=</span> <span class="n">fun</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">v</span><span class="p">,</span> <span class="n">v</span><span class="p">)</span>
        <span class="k">return</span> <span class="n">zbool</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">context</span><span class="p">,</span> <span class="n">z_</span><span class="p">,</span> <span class="n">v_</span><span class="p">)</span>

    <span class="k">return</span> <span class="n">proxy</span>
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<p>We apply the comparison methods on the defined <code>zfloat</code> class.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">FLOAT_BOOL_OPS</span> <span class="o">=</span> <span class="p">[</span>
    <span class="s1">&#39;__eq__&#39;</span><span class="p">,</span>
    <span class="c1"># &#39;__req__&#39;,</span>
    <span class="s1">&#39;__ne__&#39;</span><span class="p">,</span>
    <span class="c1"># &#39;__rne__&#39;,</span>
    <span class="s1">&#39;__gt__&#39;</span><span class="p">,</span>
    <span class="s1">&#39;__lt__&#39;</span><span class="p">,</span>
    <span class="s1">&#39;__le__&#39;</span><span class="p">,</span>
    <span class="s1">&#39;__ge__&#39;</span><span class="p">,</span>
<span class="p">]</span>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">for</span> <span class="n">fname</span> <span class="ow">in</span> <span class="n">FLOAT_BOOL_OPS</span><span class="p">:</span>
    <span class="n">fun</span> <span class="o">=</span> <span class="nb">getattr</span><span class="p">(</span><span class="nb">float</span><span class="p">,</span> <span class="n">fname</span><span class="p">)</span>
    <span class="n">zfun</span> <span class="o">=</span> <span class="nb">getattr</span><span class="p">(</span><span class="n">z3</span><span class="o">.</span><span class="n">ArithRef</span><span class="p">,</span> <span class="n">fname</span><span class="p">)</span>
    <span class="nb">setattr</span><span class="p">(</span><span class="n">zfloat</span><span class="p">,</span> <span class="n">fname</span><span class="p">,</span> <span class="n">make_float_bool_wrapper</span><span class="p">(</span><span class="n">fname</span><span class="p">,</span> <span class="n">fun</span><span class="p">,</span> <span class="n">zfun</span><span class="p">))</span>
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<p>Similarly, we define the common proxy method for binary operators.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">def</span> <span class="nf">make_float_binary_wrapper</span><span class="p">(</span><span class="n">fname</span><span class="p">,</span> <span class="n">fun</span><span class="p">,</span> <span class="n">zfun</span><span class="p">):</span>
    <span class="k">def</span> <span class="nf">proxy</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
        <span class="n">z</span><span class="p">,</span> <span class="n">v</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_zv</span><span class="p">(</span><span class="n">other</span><span class="p">)</span>
        <span class="n">z_</span> <span class="o">=</span> <span class="n">zfun</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">z</span><span class="p">,</span> <span class="n">z</span><span class="p">)</span>
        <span class="n">v_</span> <span class="o">=</span> <span class="n">fun</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">v</span><span class="p">,</span> <span class="n">v</span><span class="p">)</span>
        <span class="k">return</span> <span class="n">zfloat</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">context</span><span class="p">,</span> <span class="n">z_</span><span class="p">,</span> <span class="n">v_</span><span class="p">)</span>

    <span class="k">return</span> <span class="n">proxy</span>
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<p>And apply them on <code>zfloat</code></p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">FLOAT_BINARY_OPS</span> <span class="o">=</span> <span class="p">[</span>
    <span class="s1">&#39;__add__&#39;</span><span class="p">,</span>
    <span class="s1">&#39;__sub__&#39;</span><span class="p">,</span>
    <span class="s1">&#39;__mul__&#39;</span><span class="p">,</span>
    <span class="s1">&#39;__truediv__&#39;</span><span class="p">,</span>
    <span class="c1"># &#39;__div__&#39;,</span>
    <span class="s1">&#39;__mod__&#39;</span><span class="p">,</span>
    <span class="c1"># &#39;__divmod__&#39;,</span>
    <span class="s1">&#39;__pow__&#39;</span><span class="p">,</span>
    <span class="c1"># &#39;__lshift__&#39;,</span>
    <span class="c1"># &#39;__rshift__&#39;,</span>
    <span class="c1"># &#39;__and__&#39;,</span>
    <span class="c1"># &#39;__xor__&#39;,</span>
    <span class="c1"># &#39;__or__&#39;,</span>
    <span class="s1">&#39;__radd__&#39;</span><span class="p">,</span>
    <span class="s1">&#39;__rsub__&#39;</span><span class="p">,</span>
    <span class="s1">&#39;__rmul__&#39;</span><span class="p">,</span>
    <span class="s1">&#39;__rtruediv__&#39;</span><span class="p">,</span>
    <span class="c1"># &#39;__rdiv__&#39;,</span>
    <span class="s1">&#39;__rmod__&#39;</span><span class="p">,</span>
    <span class="c1"># &#39;__rdivmod__&#39;,</span>
    <span class="s1">&#39;__rpow__&#39;</span><span class="p">,</span>
    <span class="c1"># &#39;__rlshift__&#39;,</span>
    <span class="c1"># &#39;__rrshift__&#39;,</span>
    <span class="c1"># &#39;__rand__&#39;,</span>
    <span class="c1"># &#39;__rxor__&#39;,</span>
    <span class="c1"># &#39;__ror__&#39;,</span>
<span class="p">]</span>
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    <span class="n">fun</span> <span class="o">=</span> <span class="nb">getattr</span><span class="p">(</span><span class="nb">float</span><span class="p">,</span> <span class="n">fname</span><span class="p">)</span>
    <span class="n">zfun</span> <span class="o">=</span> <span class="nb">getattr</span><span class="p">(</span><span class="n">z3</span><span class="o">.</span><span class="n">ArithRef</span><span class="p">,</span> <span class="n">fname</span><span class="p">)</span>
    <span class="nb">setattr</span><span class="p">(</span><span class="n">zfloat</span><span class="p">,</span> <span class="n">fname</span><span class="p">,</span> <span class="n">make_float_binary_wrapper</span><span class="p">(</span><span class="n">fname</span><span class="p">,</span> <span class="n">fun</span><span class="p">,</span> <span class="n">zfun</span><span class="p">))</span>
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<p>These are used as follows.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">with</span> <span class="n">ConcolicTracer</span><span class="p">()</span> <span class="k">as</span> <span class="n">_</span><span class="p">:</span>
    <span class="n">za</span> <span class="o">=</span> <span class="n">zfloat</span><span class="o">.</span><span class="n">create</span><span class="p">(</span><span class="n">_</span><span class="o">.</span><span class="n">context</span><span class="p">,</span> <span class="s1">&#39;float_a&#39;</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">)</span>
    <span class="n">zb</span> <span class="o">=</span> <span class="n">zfloat</span><span class="o">.</span><span class="n">create</span><span class="p">(</span><span class="n">_</span><span class="o">.</span><span class="n">context</span><span class="p">,</span> <span class="s1">&#39;float_b&#39;</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">)</span>
    <span class="k">if</span> <span class="n">za</span> <span class="o">*</span> <span class="n">zb</span><span class="p">:</span>
        <span class="nb">print</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
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<pre>({&#39;float_a&#39;: &#39;Real&#39;, &#39;float_b&#39;: &#39;Real&#39;}, [Not(float_a*float_b != 0)])</pre>
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<p>Finally, we fix the <code>zint</code> binary wrapper to correctly create <code>zfloat</code> when needed.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">def</span> <span class="nf">make_int_binary_wrapper</span><span class="p">(</span><span class="n">fname</span><span class="p">,</span> <span class="n">fun</span><span class="p">,</span> <span class="n">zfun</span><span class="p">):</span>
    <span class="k">def</span> <span class="nf">proxy</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
        <span class="n">z</span><span class="p">,</span> <span class="n">v</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_zv</span><span class="p">(</span><span class="n">other</span><span class="p">)</span>
        <span class="n">z_</span> <span class="o">=</span> <span class="n">zfun</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">z</span><span class="p">,</span> <span class="n">z</span><span class="p">)</span>
        <span class="n">v_</span> <span class="o">=</span> <span class="n">fun</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">v</span><span class="p">,</span> <span class="n">v</span><span class="p">)</span>
        <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">v_</span><span class="p">,</span> <span class="nb">float</span><span class="p">):</span>
            <span class="k">return</span> <span class="n">zfloat</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">context</span><span class="p">,</span> <span class="n">z_</span><span class="p">,</span> <span class="n">v_</span><span class="p">)</span>
        <span class="k">elif</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">v_</span><span class="p">,</span> <span class="nb">int</span><span class="p">):</span>
            <span class="k">return</span> <span class="n">zint</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">context</span><span class="p">,</span> <span class="n">z_</span><span class="p">,</span> <span class="n">v_</span><span class="p">)</span>
        <span class="k">else</span><span class="p">:</span>
            <span class="k">assert</span> <span class="kc">False</span>

    <span class="k">return</span> <span class="n">proxy</span>
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    <span class="n">fun</span> <span class="o">=</span> <span class="nb">getattr</span><span class="p">(</span><span class="nb">int</span><span class="p">,</span> <span class="n">fname</span><span class="p">)</span>
    <span class="n">zfun</span> <span class="o">=</span> <span class="nb">getattr</span><span class="p">(</span><span class="n">z3</span><span class="o">.</span><span class="n">ArithRef</span><span class="p">,</span> <span class="n">fname</span><span class="p">)</span>
    <span class="nb">setattr</span><span class="p">(</span><span class="n">zint</span><span class="p">,</span> <span class="n">fname</span><span class="p">,</span> <span class="n">make_int_binary_wrapper</span><span class="p">(</span><span class="n">fname</span><span class="p">,</span> <span class="n">fun</span><span class="p">,</span> <span class="n">zfun</span><span class="p">))</span>
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<p>Checking whether it worked as expected.</p>

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    <span class="n">v</span> <span class="o">=</span> <span class="n">_</span><span class="p">[</span><span class="n">binomial</span><span class="p">](</span><span class="mi">4</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
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<pre>(&#39;sat&#39;, {&#39;n&#39;: &#39;4&#39;, &#39;k&#39;: &#39;2&#39;})</pre>
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<h3 id="Exercise-2:-Bit-Manipulation">Exercise 2: Bit Manipulation<a class="anchor-link" href="#Exercise-2:-Bit-Manipulation">&#182;</a></h3>
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<p>Similar to floats, implementing the bit manipulation functions such as <code>xor</code> involves converting <code>int</code> to its bit vector equivalents, performing operations on them, and converting it back to the original type. Can you implement the bit manipulation operations for <code>zint</code>?</p>

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<p><strong>Solution.</strong> The solution is as follows.</p>

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<p>We first define the proxy method as before.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">def</span> <span class="nf">make_int_bit_wrapper</span><span class="p">(</span><span class="n">fname</span><span class="p">,</span> <span class="n">fun</span><span class="p">,</span> <span class="n">zfun</span><span class="p">):</span>
    <span class="k">def</span> <span class="nf">proxy</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
        <span class="n">z</span><span class="p">,</span> <span class="n">v</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_zv</span><span class="p">(</span><span class="n">other</span><span class="p">)</span>
        <span class="n">z_</span> <span class="o">=</span> <span class="n">z3</span><span class="o">.</span><span class="n">BV2Int</span><span class="p">(</span>
            <span class="n">zfun</span><span class="p">(</span>
                <span class="n">z3</span><span class="o">.</span><span class="n">Int2BV</span><span class="p">(</span>
                    <span class="bp">self</span><span class="o">.</span><span class="n">z</span><span class="p">,</span> <span class="n">num_bits</span><span class="o">=</span><span class="mi">64</span><span class="p">),</span> <span class="n">z3</span><span class="o">.</span><span class="n">Int2BV</span><span class="p">(</span>
                    <span class="n">z</span><span class="p">,</span> <span class="n">num_bits</span><span class="o">=</span><span class="mi">64</span><span class="p">)))</span>
        <span class="n">v_</span> <span class="o">=</span> <span class="n">fun</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">v</span><span class="p">,</span> <span class="n">v</span><span class="p">)</span>
        <span class="k">return</span> <span class="n">zint</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">context</span><span class="p">,</span> <span class="n">z_</span><span class="p">,</span> <span class="n">v_</span><span class="p">)</span>

    <span class="k">return</span> <span class="n">proxy</span>
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<p>It is then applied to the <code>zint</code> class.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">BIT_OPS</span> <span class="o">=</span> <span class="p">[</span>
    <span class="s1">&#39;__lshift__&#39;</span><span class="p">,</span>
    <span class="s1">&#39;__rshift__&#39;</span><span class="p">,</span>
    <span class="s1">&#39;__and__&#39;</span><span class="p">,</span>
    <span class="s1">&#39;__xor__&#39;</span><span class="p">,</span>
    <span class="s1">&#39;__or__&#39;</span><span class="p">,</span>
    <span class="s1">&#39;__rlshift__&#39;</span><span class="p">,</span>
    <span class="s1">&#39;__rrshift__&#39;</span><span class="p">,</span>
    <span class="s1">&#39;__rand__&#39;</span><span class="p">,</span>
    <span class="s1">&#39;__rxor__&#39;</span><span class="p">,</span>
    <span class="s1">&#39;__ror__&#39;</span><span class="p">,</span>
<span class="p">]</span>
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    <span class="n">fun</span> <span class="o">=</span> <span class="nb">getattr</span><span class="p">(</span><span class="nb">int</span><span class="p">,</span> <span class="n">fname</span><span class="p">)</span>
    <span class="n">zfun</span> <span class="o">=</span> <span class="nb">getattr</span><span class="p">(</span><span class="n">z3</span><span class="o">.</span><span class="n">BitVecRef</span><span class="p">,</span> <span class="n">fname</span><span class="p">)</span>
    <span class="nb">setattr</span><span class="p">(</span><span class="n">zint</span><span class="p">,</span> <span class="n">fname</span><span class="p">,</span> <span class="n">make_int_bit_wrapper</span><span class="p">(</span><span class="n">fname</span><span class="p">,</span> <span class="n">fun</span><span class="p">,</span> <span class="n">zfun</span><span class="p">))</span>
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<p>Invert is the only unary bit manipulation method.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">class</span> <span class="nc">zint</span><span class="p">(</span><span class="n">zint</span><span class="p">):</span>
    <span class="k">def</span> <span class="nf">__invert__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
        <span class="k">return</span> <span class="n">zint</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">context</span><span class="p">,</span> <span class="n">z3</span><span class="o">.</span><span class="n">BV2Int</span><span class="p">(</span>
            <span class="o">~</span><span class="n">z3</span><span class="o">.</span><span class="n">Int2BV</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">z</span><span class="p">,</span> <span class="n">num_bits</span><span class="o">=</span><span class="mi">64</span><span class="p">)),</span> <span class="o">~</span><span class="bp">self</span><span class="o">.</span><span class="n">v</span><span class="p">)</span>
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<p>The <code>my_fn()</code> computes <code>xor</code> and returns <code>True</code> if the <code>xor</code> results in a non zero value.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">def</span> <span class="nf">my_fn</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">):</span>
    <span class="n">o_</span> <span class="o">=</span> <span class="p">(</span><span class="n">a</span> <span class="o">|</span> <span class="n">b</span><span class="p">)</span>
    <span class="n">a_</span> <span class="o">=</span> <span class="p">(</span><span class="n">a</span> <span class="o">&amp;</span> <span class="n">b</span><span class="p">)</span>
    <span class="k">if</span> <span class="n">o_</span> <span class="o">&amp;</span> <span class="o">~</span><span class="n">a_</span><span class="p">:</span>
        <span class="k">return</span> <span class="kc">True</span>
    <span class="k">else</span><span class="p">:</span>
        <span class="k">return</span> <span class="kc">False</span>
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<p>Using that under <code>ConcolicTracer</code></p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">with</span> <span class="n">ConcolicTracer</span><span class="p">()</span> <span class="k">as</span> <span class="n">_</span><span class="p">:</span>
    <span class="nb">print</span><span class="p">(</span><span class="n">_</span><span class="p">[</span><span class="n">my_fn</span><span class="p">](</span><span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">))</span>
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<pre>True
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<p>We log the computed SMT expression to verify that everything went well.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">_</span><span class="o">.</span><span class="n">zeval</span><span class="p">(</span><span class="n">log</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
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<pre>(declare-const my_fn_a_int_96 Int)
(declare-const my_fn_b_int_97 Int)
(assert (let ((a!1 (bvnot (bvor (bvnot ((_ int2bv 64) my_fn_a_int_96))
                        (bvnot ((_ int2bv 64) my_fn_b_int_97))))))
(let ((a!2 (bvor (bvnot (bvor ((_ int2bv 64) my_fn_a_int_96)
                              ((_ int2bv 64) my_fn_b_int_97)))
                 a!1)))
  (not (= 0 (bv2int (bvnot a!2)))))))
(check-sat)
(get-model)
sat
(model 
  (define-fun my_fn_a_int_96 () Int
    (- 18446744073709551617))
  (define-fun my_fn_b_int_97 () Int
    (- 2))
)
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    <div class="prompt output_prompt">Out[273]:</div>


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<pre>(&#39;sat&#39;, {&#39;a&#39;: [&#39;-&#39;, &#39;18446744073709551617&#39;], &#39;b&#39;: [&#39;-&#39;, &#39;2&#39;]})</pre>
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<p>We can confirm from the formulas generated that the bit manipulation functions worked correctly.</p>

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<h3 id="Exercise-3:-String-Translation-Functions">Exercise 3: String Translation Functions<a class="anchor-link" href="#Exercise-3:-String-Translation-Functions">&#182;</a></h3>
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<p>We have seen how to define <code>upper()</code> and <code>lower()</code>. Can you define the <code>capitalize()</code>, <code>title()</code>, and <code>swapcase()</code> methods?</p>

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<p><strong>Solution.</strong> Solution not yet available.</p>

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