.xtxdoc .input.multiplechoice .content .choices,
.xtxdoc .input.multiplechoice .help .choices {
  list-style-type: none;
  display: flex;
  flex-wrap: wrap;
  margin: 0;
  padding: 0;
}

.xtxdoc .input.multiplechoice .content .choices .choice,
.xtxdoc .input.multiplechoice .help .choices .choice {
  display: flex;
  white-space: pre;
  list-style-type: none;
  list-style-position: inside;
  background-color: #ecf0f1;
  border: 0.05em solid #bdc3c7;
  padding: 0.25em 0.55em 0.25em 0.55em;
  margin: 0.225em 0.45em 0.225em 0;
  flex-direction: row;
  align-items: center;
  cursor: pointer;
}

.xtxdoc .input.multiplechoice .content .choices .choice.active,
.xtxdoc .input.multiplechoice .help .choices .choice.active {
  border: 0.05em solid #2980b9;
  box-shadow: 0 0 0em 0.1em #3498db;
}
.xtxdoc .input.number .content input.text {
  background-color: #ecf0f1;
  border: 0.05em solid #bdc3c7;
  padding: 0.25em 0.55em 0.25em 0.55em;
  margin: 0;
  font-family: KaTeX_Typewriter, SFMono-Regular, Menlo, Monaco, Consolas, "Liberation Mono", "Courier New", monospace;
  width: 10em;
}

.xtxdoc .input.number .content input.text:focus {
  border: 0.05em solid #2980b9;
  box-shadow: 0 0 0em 0.1em #3498db;
  outline: none;
}

.xtxdoc .input.number .content .subcontent input.text {
  width: 2em;
}
.xtxdoc .input.sequence .content .choices,
.xtxdoc .input.sequence .help .choices {
  list-style-type: none;
  display: flex;
  flex-wrap: wrap;
  margin: 0;
  padding: 0;
}

.xtxdoc .input.sequence .content .choices .choice,
.xtxdoc .input.sequence .help .choices .choice {
  display: flex;
  white-space: pre;
  list-style-type: none;
  list-style-position: inside;
  background-color: #ecf0f1;
  border: 0.05em solid #bdc3c7;
  padding: 0.25em 0.55em 0.25em 0.55em;
  margin: 0.225em 0.45em 0.225em 0;
  flex-direction: row;
  align-items: center;
  cursor: pointer;
}

.xtxdoc .input.sequence .content .choices .choice.active,
.xtxdoc .input.sequence .help .choices .choice.active {
  border: 0.05em solid #2980b9;
  box-shadow: 0 0 0em 0.1em #3498db;
}

.xtxdoc .input.sequence .content .choices .choice,
.xtxdoc .input.sequence .help .choices .choice {
  cursor: grab;
}

.xtxdoc .input.sequence .content .choices .choice.gu-mirror,
.xtxdoc .input.sequence .help .choices .choice.gu-mirror {
  cursor: grabbing;
}
.xtxdoc .input.singlechoice .content .choices,
.xtxdoc .input.singlechoice .help .choices {
  list-style-type: none;
  display: flex;
  flex-wrap: wrap;
  margin: 0;
  padding: 0;
}

.xtxdoc .input.singlechoice .content .choices .choice,
.xtxdoc .input.singlechoice .help .choices .choice {
  display: flex;
  white-space: pre;
  list-style-type: none;
  list-style-position: inside;
  background-color: #ecf0f1;
  border: 0.05em solid #bdc3c7;
  padding: 0.25em 0.55em 0.25em 0.55em;
  margin: 0.225em 0.45em 0.225em 0;
  flex-direction: row;
  align-items: center;
  cursor: pointer;
}

.xtxdoc .input.singlechoice .content .choices .choice.active,
.xtxdoc .input.singlechoice .help .choices .choice.active {
  border: 0.05em solid #2980b9;
  box-shadow: 0 0 0em 0.1em #3498db;
}
.xtxdoc > .control > .lesson-control .input-status {
  display: flex;
  justify-content: space-between;
  margin: 0.5em 0;
}

.xtxdoc > .control > .lesson-control .input-status .key {
  order: 1;
}

.xtxdoc > .control > .lesson-control .input-status .value {
  order: 2;
}

.xtxdoc > .control > .lesson-control .input-status .correct {
  color: #1B7A43;
}

.xtxdoc > .control > .lesson-control .input-status .wrong {
  color: #e74c3c;
}

.xtxdoc > .control > .lesson-control .input-status .total {
  color: #3498db;
}

.xtxdoc > .control > .lesson-control .actions {
  display: flex;
  justify-content: space-between;
  margin: 0.5em 0;
}

.xtxdoc > .control > .lesson-control .actions .key {
  order: 1;
}

.xtxdoc > .control > .lesson-control .actions .value {
  order: 2;
}

.xtxdoc > .control > .lesson-control .actions button {
  vertical-align: text-bottom;
  border-radius: 0.2em;
  background-color: #E6F2FB;
  border: 0.05em solid #3498db;
  color: #3498db;
  text-align: center;
  font-size: 0.65em;
  padding-top: 0.1em;
  padding-bottom: 0.1em;
  padding-left: 0.4em;
  padding-right: 0.4em;
  cursor: pointer;
  margin: 0.2em;
}

.xtxdoc > .control > .lesson-control .actions button:hover {
  background-color: #3498db;
  color: #E6F2FB;
}
.xtxdoc .input.string .content input.text {
  background-color: #ecf0f1;
  border: 0.05em solid #bdc3c7;
  padding: 0.25em 0.55em 0.25em 0.55em;
  margin: 0;
  font-family: KaTeX_Typewriter, SFMono-Regular, Menlo, Monaco, Consolas, "Liberation Mono", "Courier New", monospace;
  width: 10em;
}

.xtxdoc .input.string .content input.text:focus {
  border: 0.05em solid #2980b9;
  box-shadow: 0 0 0em 0.1em #3498db;
  outline: none;
}

.xtxdoc .input.string .content .subcontent input.text {
  width: 2em;
}
.xtxdoc .floating {
  margin-top: 3em;
  margin-bottom: 3em;
  text-align: center;
}

.xtxdoc .floating .meta {
  margin-top: 0.75em;
  margin-bottom: 0.75em;
  margin-left: 2em;
  margin-right: 2em;
  text-align: justify;
}

.xtxdoc .floating .meta .caption {
  display: inline-block;
  margin-right: 0.75em;
}

.xtxdoc .floating .meta .caption {
  font-weight: bold;
  font-style: normal;
}

.xtxdoc .floating .meta .caption .subcaption {
  font-weight: normal;
}

.xtxdoc .floating .meta .meta-inner {
  width: fit-content;
  margin-left: auto;
  margin-right: auto;
}
.xtxdoc > .meta {
  display: none;
}

.xtxdoc > .control {
  display: none;
}

.xtxdoc > .document {
  display: block;
  width: 100%;
  max-width: 21cm;
  min-width: 21cm;
  box-sizing: border-box;
  background-color: #ffffff;
  color: #2c3e50;
  padding: 1cm 2cm;
  font-family: KaTeX_Main, "CMU Serif", cmr10, LMRoman10-Regular, "Latin Modern Math", "Georgia", "Nimbus Roman No9 L", serif;
  font-size: 0.4cm;
  text-align: justify;
  hyphens: auto;
  -ms-hyphens: auto;
  -moz-hyphens: auto;
  -webkit-hyphens: auto;
  font-style: normal;
}

.xtxdoc > .document em {
  font-style: italic;
}

.xtxdoc > .document > p.paragraph {
  margin-top: 0.75em;
}

.xtxdoc > .document > p.paragraph .caption {
  display: inline-block;
  margin-right: 0.75em;
}

.xtxdoc > .document > p.paragraph .caption {
  font-weight: bold;
  font-style: normal;
}

.xtxdoc > .document > p.paragraph .caption .subcaption {
  font-weight: normal;
}

.xtxdoc > .document p {
  margin-top: 0.5em;
  margin-bottom: 0.5em;
  text-indent: 0em;
}

.xtxdoc > .document .title {
  margin-top: 4em;
  margin-bottom: 4em;
}

.xtxdoc > .document .title h1 {
  margin-top: 0em;
  margin-bottom: 0.5em;
  font-size: 2.5em;
  font-weight: bold;
}

.xtxdoc > .document .title .meta {
  margin-top: 0.5em;
  color: #95a5a6;
  font-family: KaTeX_SansSerif, -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, "Helvetica Neue", Arial, "Noto Sans", sans-serif, "Apple Color Emoji", "Segoe UI Emoji", "Segoe UI Symbol", "Noto Color Emoji";
  font-size: 0.75em;
}

.xtxdoc > .document .title .meta .author {
  margin-right: 0.35em;
}

.xtxdoc > .document h2 {
  margin-top: 2em;
  margin-bottom: 1em;
  font-weight: bold;
  font-size: 2em;
}

.xtxdoc > .document h2 .number {
  margin-right: 1em;
}

.xtxdoc > .document h3 {
  margin-top: 2em;
  margin-bottom: 1em;
  font-weight: bold;
  font-size: 1.75em;
}

.xtxdoc > .document h3 .number {
  margin-right: 1em;
}

.xtxdoc > .document h4 {
  margin-top: 2em;
  margin-bottom: 1em;
  font-weight: bold;
  font-size: 1.5em;
}

.xtxdoc > .document h4 .number {
  margin-right: 1em;
}

.xtxdoc > .document h5 {
  margin-top: 2em;
  margin-bottom: 1em;
  font-weight: bold;
  font-size: 1.25em;
}

.xtxdoc > .document h5 .number {
  margin-right: 1em;
}

.xtxdoc > .document h6 {
  margin-top: 2em;
  margin-bottom: 1em;
  font-weight: bold;
  font-size: 1em;
}

.xtxdoc > .document h6 .number {
  margin-right: 1em;
}

.xtxdoc > .document .center {
  text-align: center;
}

.xtxdoc > .document .textbf {
  font-weight: bold;
}

.xtxdoc > .document .texttt {
  font-family: KaTeX_Typewriter, SFMono-Regular, Menlo, Monaco, Consolas, "Liberation Mono", "Courier New", monospace;
  text-justify: none;
  width: min-content;
}

.xtxdoc > .document .thinspace {
  display: inline-block;
  width: 1.666em;
}

.xtxdoc > .document .enspace {
  display: inline-block;
  width: 0.5em;
}

.xtxdoc > .document .quad {
  display: inline-block;
  width: 1em;
}

.xtxdoc > .document .qquad {
  display: inline-block;
  width: 2em;
}

.xtxdoc > .document .katex .base {
  display: inline;
}

.xtxdoc > .document .katex .katex-mathml {
  display: none;
}

.xtxdoc > .document .inline-math {
  display: contents;
}

.xtxdoc > .document .display-math {
  margin-top: 0.75em;
  margin-bottom: 0.75em;
  display: block;
  text-align: center;
}
.xtxdoc .includegraphics {
  display: inline-block;
  max-width: 100%;
  overflow-x: auto;
  overflow-y: hidden;
}

.xtxdoc .includegraphics img {
  display: block;
}

.xtxdoc .includegraphics img {
  width: inherit;
  height: inherit;
  object-fit: fill;
}
.xtxdoc a.url {
  color: #3498db;
  text-decoration: none;
  font-family: KaTeX_Typewriter, SFMono-Regular, Menlo, Monaco, Consolas, "Liberation Mono", "Courier New", monospace;
}

.xtxdoc a.href {
  color: #3498db;
  text-decoration: none;
}
.xtxdoc .input {
  margin-top: 0.75em;
  margin-bottom: 0.75em;
  border-left: 0.15em solid #3498db;
  padding-left: 1.5em;
  padding-right: 1.5em;
  padding-top: 0.5em;
  padding-bottom: 0.5em;
}

.xtxdoc .input .title-dots-buttons {
  display: inline-flex;
  overflow: hidden;
  width: 100%;
  color: #3498db;
  font-family: KaTeX_SansSerif, -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, "Helvetica Neue", Arial, "Noto Sans", sans-serif, "Apple Color Emoji", "Segoe UI Emoji", "Segoe UI Symbol", "Noto Color Emoji";
  font-style: normal;
  font-weight: bold;
  margin-bottom: 0.5em;
}

.xtxdoc .input .title-dots-buttons .title {
  flex-grow: 0;
  flex-shrink: 1;
  margin: 0;
  margin-right: 0.5em;
  white-space: nowrap;
  min-width: 2em;
  overflow: hidden;
  text-overflow: ellipsis;
}

.xtxdoc .input .title-dots-buttons .dots {
  flex-grow: 1;
  flex-shrink: 1000000;
  white-space: nowrap;
  direction: rtl;
  min-width: 1.5em;
  overflow: hidden;
}

.xtxdoc .input .title-dots-buttons .dots:before {
  content: ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ";
}

.xtxdoc .input .title-dots-buttons .buttons {
  flex-grow: 0;
  flex-shrink: 0;
  margin-left: 0.5em;
  white-space: nowrap;
  vertical-align: baseline;
}

.xtxdoc .input .title-dots-buttons .buttons > form {
  display: inline;
}

.xtxdoc .input .title-dots-buttons .buttons button {
  vertical-align: text-bottom;
  border-radius: 0.2em;
  background-color: #E6F2FB;
  border: 0.05em solid #3498db;
  color: #3498db;
  text-align: center;
  font-size: 0.65em;
  padding-top: 0.1em;
  padding-bottom: 0.1em;
  padding-left: 0.4em;
  padding-right: 0.4em;
  cursor: pointer;
  margin: 0.2em;
}

.xtxdoc .input .title-dots-buttons .buttons button:hover {
  background-color: #3498db;
  color: #E6F2FB;
}

.xtxdoc .input .back-button,
.xtxdoc .input .help {
  display: none;
}

.xtxdoc .input .content {
  position: relative;
}

.xtxdoc .input .content:after {
  position: absolute;
  right: -0.9em;
  bottom: -0.3em;
  font-weight: bold;
  font-style: normal;
  font-size: 2em;
}

.xtxdoc .input .help {
  font-style: normal;
}

.xtxdoc .input .help > p.paragraph {
  margin-top: 0.75em;
}

.xtxdoc .input .help > p.paragraph .caption {
  display: inline-block;
  margin-right: 0.75em;
}

.xtxdoc .input .help > p.paragraph .caption {
  font-weight: bold;
  font-style: normal;
}

.xtxdoc .input .help > p.paragraph .caption .subcaption {
  font-weight: normal;
}

.xtxdoc .input .help p {
  margin-top: 0.5em;
  margin-bottom: 0.5em;
  text-indent: 0em;
}

.xtxdoc .input .help em {
  font-style: italic;
}

.xtxdoc .input .solution {
  margin-top: 0.5em;
}

.xtxdoc .input .solution > p:first-of-type {
  margin-top: 0.75em;
}

.xtxdoc .input .solution > p:first-of-type:before {
  display: inline-block;
  color: #1B7A43;
  padding-right: 0.1em;
  display: inline-block;
  text-decoration: inherit;
  margin: 0;
  width: 1em;
  line-height: 1em;
  text-align: center;
  font-family: "fontello";
  font-style: normal;
  font-weight: normal;
  font-variant: normal;
  speak: never;
  text-transform: none;
  -webkit-font-smoothing: antialiased;
  -moz-osx-font-smoothing: grayscale;
  content: "\f138";
  margin: 0 0.2em 0 0;
}

.xtxdoc .input .solution.hidden {
  display: none;
}

.xtxdoc .input .feedback {
  margin-top: 0.5em;
}

.xtxdoc .input .feedback > p:first-of-type {
  margin-top: 0.75em;
}

.xtxdoc .input .feedback > p:first-of-type:before {
  display: inline-block;
  color: #e74c3c;
  padding-right: 0.1em;
  display: inline-block;
  text-decoration: inherit;
  margin: 0;
  width: 1em;
  line-height: 1em;
  text-align: center;
  font-family: "fontello";
  font-style: normal;
  font-weight: normal;
  font-variant: normal;
  speak: never;
  text-transform: none;
  -webkit-font-smoothing: antialiased;
  -moz-osx-font-smoothing: grayscale;
  content: "\f138";
  margin: 0 0.2em 0 0;
}

.xtxdoc .input.correct .content:after {
  color: #1B7A43;
  display: inline-block;
  text-decoration: inherit;
  margin: 0;
  width: 1em;
  line-height: 1em;
  text-align: center;
  font-family: "fontello";
  font-style: normal;
  font-weight: normal;
  font-variant: normal;
  speak: never;
  text-transform: none;
  -webkit-font-smoothing: antialiased;
  -moz-osx-font-smoothing: grayscale;
  content: "\e801";
  margin: 0 0 0 0.2em;
}

.xtxdoc .input.wrong .content:after {
  color: #e74c3c;
  display: inline-block;
  text-decoration: inherit;
  margin: 0;
  width: 1em;
  line-height: 1em;
  text-align: center;
  font-family: "fontello";
  font-style: normal;
  font-weight: normal;
  font-variant: normal;
  speak: never;
  text-transform: none;
  -webkit-font-smoothing: antialiased;
  -moz-osx-font-smoothing: grayscale;
  content: "\e802";
  margin: 0 0 0 0.2em;
}

.xtxdoc .input.pending .content:after {
  color: #3498db;
  display: inline-block;
  text-decoration: inherit;
  margin: 0;
  width: 1em;
  line-height: 1em;
  text-align: center;
  font-family: "fontello";
  font-style: normal;
  font-weight: normal;
  font-variant: normal;
  speak: never;
  text-transform: none;
  -webkit-font-smoothing: antialiased;
  -moz-osx-font-smoothing: grayscale;
  content: "\f110";
  animation: spin 2s infinite linear;
  margin: 0 0 0 0.2em;
}

@keyframes spin {
  0% {
    transform: rotate(0deg);
  }

  100% {
    transform: rotate(359deg);
  }
}

.xtxdoc .input.hidden .content:after {
  color: #3498db;
  display: inline-block;
  text-decoration: inherit;
  margin: 0;
  width: 1em;
  line-height: 1em;
  text-align: center;
  font-family: "fontello";
  font-style: normal;
  font-weight: normal;
  font-variant: normal;
  speak: never;
  text-transform: none;
  -webkit-font-smoothing: antialiased;
  -moz-osx-font-smoothing: grayscale;
  content: "\e807";
  margin: 0 0 0 0.2em;
}

.xtxdoc .input.helping .back-button {
  display: initial;
}

.xtxdoc .input.helping .help {
  display: block;
}

.xtxdoc .input.helping .help-button,
.xtxdoc .input.helping .reset-button,
.xtxdoc .input.helping .submit-button,
.xtxdoc .input.helping .normal {
  display: none;
}
.xtxdoc .itemize,
.xtxdoc .description,
.xtxdoc .enumerate {
  margin-top: 0.75em;
  margin-bottom: 0.75em;
  padding-inline-start: 0;
}

.xtxdoc .itemize > li,
.xtxdoc .description > li,
.xtxdoc .enumerate > li {
  margin-top: 0.5em;
  margin-bottom: 0.5em;
  margin-left: 2em;
  margin-right: 2em;
}

.xtxdoc .itemize > li > p.paragraph,
.xtxdoc .description > li > p.paragraph,
.xtxdoc .enumerate > li > p.paragraph {
  margin-top: 0.75em;
}

.xtxdoc .itemize > li > p.paragraph .caption,
.xtxdoc .description > li > p.paragraph .caption,
.xtxdoc .enumerate > li > p.paragraph .caption {
  display: inline-block;
  margin-right: 0.75em;
}

.xtxdoc .itemize > li > p.paragraph .caption,
.xtxdoc .description > li > p.paragraph .caption,
.xtxdoc .enumerate > li > p.paragraph .caption {
  font-weight: bold;
  font-style: normal;
}

.xtxdoc .itemize > li > p.paragraph .caption .subcaption,
.xtxdoc .description > li > p.paragraph .caption .subcaption,
.xtxdoc .enumerate > li > p.paragraph .caption .subcaption {
  font-weight: normal;
}

.xtxdoc .itemize > li p,
.xtxdoc .description > li p,
.xtxdoc .enumerate > li p {
  margin-top: 0em;
  margin-bottom: 0em;
  line-height: 1.25em;
}

.xtxdoc .itemize > li p + p,
.xtxdoc .description > li p + p,
.xtxdoc .enumerate > li p + p {
  text-indent: 1.5em;
}

.xtxdoc .itemize > li p.paragraph,
.xtxdoc .description > li p.paragraph,
.xtxdoc .enumerate > li p.paragraph {
  text-indent: 0;
}

.xtxdoc .itemize > li p.paragraph,
.xtxdoc .description > li p.paragraph,
.xtxdoc .enumerate > li p.paragraph {
  margin-top: 0.75em;
}

.xtxdoc .description {
  list-style-type: none;
}

.xtxdoc .enumerate {
  list-style: decimal;
}

.xtxdoc .itemize {
  list-style-type: disc;
}

.xtxdoc .description .caption {
  display: inline-block;
  margin-right: 0.75em;
}

.xtxdoc .description .caption {
  font-weight: bold;
  font-style: normal;
}

.xtxdoc .description .caption .subcaption {
  font-weight: normal;
}
.xtxdoc .mdp {
  margin-top: 0.75em;
  margin-bottom: 0.75em;
  display: grid;
  align-items: baseline;
  width: 100%;
  overflow-x: auto;
  overflow-y: hidden;
}

.xtxdoc .mdp .cell,
.xtxdoc .mdp .eqno {
  margin: 0.25em 0.125em;
  white-space: nowrap;
}

.xtxdoc .mdp .eqno {
  margin-right: 0;
}

.xtxdoc .mdp .row1 {
  grid-row: 1;
}

.xtxdoc .mdp .row2 {
  grid-row: 2;
}

.xtxdoc .mdp .row3 {
  grid-row: 3;
}

.xtxdoc .mdp .row4 {
  grid-row: 4;
}

.xtxdoc .mdp .row5 {
  grid-row: 5;
}

.xtxdoc .mdp .row6 {
  grid-row: 6;
}

.xtxdoc .mdp .row7 {
  grid-row: 7;
}

.xtxdoc .mdp .row8 {
  grid-row: 8;
}

.xtxdoc .mdp .row9 {
  grid-row: 9;
}

.xtxdoc .mdp .row10 {
  grid-row: 10;
}

.xtxdoc .mdp .row11 {
  grid-row: 11;
}

.xtxdoc .mdp .row12 {
  grid-row: 12;
}

.xtxdoc .mdp .row13 {
  grid-row: 13;
}

.xtxdoc .mdp .row14 {
  grid-row: 14;
}

.xtxdoc .mdp .row15 {
  grid-row: 15;
}

.xtxdoc .mdp .row16 {
  grid-row: 16;
}

.xtxdoc .mdp .row17 {
  grid-row: 17;
}

.xtxdoc .mdp .row18 {
  grid-row: 18;
}

.xtxdoc .mdp .row19 {
  grid-row: 19;
}

.xtxdoc .mdp .row20 {
  grid-row: 20;
}

.xtxdoc .mdp .inline-math {
  display: inline-block;
  width: max-content;
}

.xtxdoc .mdp .eqno {
  text-align: right;
  font-style: normal;
}

.xtxdoc .mdp.equation {
  grid-template-columns: 1fr max-content;
}

.xtxdoc .mdp.equation .cell {
  text-align: center;
}

.xtxdoc .mdp.align .cell.odd {
  text-align: right;
}

.xtxdoc .mdp.align .cell.even {
  text-align: left;
}

.xtxdoc .mdp.eqnarray .cell {
  text-align: left;
}
.xtxdoc a.reference {
  color: #3498db;
  text-decoration: none;
}
.xtxdoc .toc {
  margin-top: 2em;
  margin-bottom: 2em;
}

.xtxdoc .toc .entry.part {
  display: flex;
  color: #2c3e50;
  text-decoration: none;
  padding-top: 0.2em;
  padding-bottom: 0.2em;
  font-weight: bold;
}

.xtxdoc .toc .entry.part:hover {
  color: #3498db;
}

.xtxdoc .toc .entry.part .number {
  display: inline-block;
  min-width: 2em;
}

.xtxdoc .toc .entry.part .text {
  flex-grow: 1;
}

.xtxdoc .toc .entry.chapter {
  display: flex;
  color: #2c3e50;
  text-decoration: none;
  padding-top: 0.15em;
  padding-bottom: 0.15em;
  font-weight: bold;
}

.xtxdoc .toc .entry.chapter:hover {
  color: #3498db;
}

.xtxdoc .toc .entry.chapter .number {
  display: inline-block;
  min-width: 2em;
}

.xtxdoc .toc .entry.chapter .text {
  flex-grow: 1;
}

.xtxdoc .toc .entry.section {
  display: flex;
  color: #2c3e50;
  text-decoration: none;
  padding-top: 0.1em;
  padding-bottom: 0.1em;
  margin-left: 2em;
}

.xtxdoc .toc .entry.section:hover {
  color: #3498db;
}

.xtxdoc .toc .entry.section .number {
  display: inline-block;
  min-width: 2.5em;
}

.xtxdoc .toc .entry.section .text {
  flex-grow: 1;
}

.xtxdoc .toc .entry.subsection {
  display: flex;
  color: #2c3e50;
  text-decoration: none;
  padding-top: 0.05em;
  padding-bottom: 0.05em;
  margin-left: 4.5em;
}

.xtxdoc .toc .entry.subsection:hover {
  color: #3498db;
}

.xtxdoc .toc .entry.subsection .number {
  display: inline-block;
  min-width: 3em;
}

.xtxdoc .toc .entry.subsection .text {
  flex-grow: 1;
}

.xtxdoc .toc .entry.subsubsection {
  display: flex;
  color: #2c3e50;
  text-decoration: none;
  padding-top: 0em;
  padding-bottom: 0em;
  margin-left: 7.5em;
}

.xtxdoc .toc .entry.subsubsection:hover {
  color: #3498db;
}

.xtxdoc .toc .entry.subsubsection .number {
  display: inline-block;
  min-width: 3.5em;
}

.xtxdoc .toc .entry.subsubsection .text {
  flex-grow: 1;
}
.xtxdoc .tabular {
  display: inline-table;
  border-collapse: collapse;
}

.xtxdoc .tabular.l1 tr td.normal.col1 {
  text-align: left;
}

.xtxdoc .tabular.c1 tr td.normal.col1 {
  text-align: center;
}

.xtxdoc .tabular.r1 tr td.normal.col1 {
  text-align: right;
}

.xtxdoc .tabular.b1 tr td.col1 {
  border-left: 0.075em solid var(--color-text);
}

.xtxdoc .tabular.l2 tr td.normal.col2 {
  text-align: left;
}

.xtxdoc .tabular.c2 tr td.normal.col2 {
  text-align: center;
}

.xtxdoc .tabular.r2 tr td.normal.col2 {
  text-align: right;
}

.xtxdoc .tabular.b2 tr td.col2 {
  border-left: 0.075em solid var(--color-text);
}

.xtxdoc .tabular.l3 tr td.normal.col3 {
  text-align: left;
}

.xtxdoc .tabular.c3 tr td.normal.col3 {
  text-align: center;
}

.xtxdoc .tabular.r3 tr td.normal.col3 {
  text-align: right;
}

.xtxdoc .tabular.b3 tr td.col3 {
  border-left: 0.075em solid var(--color-text);
}

.xtxdoc .tabular.l4 tr td.normal.col4 {
  text-align: left;
}

.xtxdoc .tabular.c4 tr td.normal.col4 {
  text-align: center;
}

.xtxdoc .tabular.r4 tr td.normal.col4 {
  text-align: right;
}

.xtxdoc .tabular.b4 tr td.col4 {
  border-left: 0.075em solid var(--color-text);
}

.xtxdoc .tabular.l5 tr td.normal.col5 {
  text-align: left;
}

.xtxdoc .tabular.c5 tr td.normal.col5 {
  text-align: center;
}

.xtxdoc .tabular.r5 tr td.normal.col5 {
  text-align: right;
}

.xtxdoc .tabular.b5 tr td.col5 {
  border-left: 0.075em solid var(--color-text);
}

.xtxdoc .tabular.l6 tr td.normal.col6 {
  text-align: left;
}

.xtxdoc .tabular.c6 tr td.normal.col6 {
  text-align: center;
}

.xtxdoc .tabular.r6 tr td.normal.col6 {
  text-align: right;
}

.xtxdoc .tabular.b6 tr td.col6 {
  border-left: 0.075em solid var(--color-text);
}

.xtxdoc .tabular.l7 tr td.normal.col7 {
  text-align: left;
}

.xtxdoc .tabular.c7 tr td.normal.col7 {
  text-align: center;
}

.xtxdoc .tabular.r7 tr td.normal.col7 {
  text-align: right;
}

.xtxdoc .tabular.b7 tr td.col7 {
  border-left: 0.075em solid var(--color-text);
}

.xtxdoc .tabular.l8 tr td.normal.col8 {
  text-align: left;
}

.xtxdoc .tabular.c8 tr td.normal.col8 {
  text-align: center;
}

.xtxdoc .tabular.r8 tr td.normal.col8 {
  text-align: right;
}

.xtxdoc .tabular.b8 tr td.col8 {
  border-left: 0.075em solid var(--color-text);
}

.xtxdoc .tabular.l9 tr td.normal.col9 {
  text-align: left;
}

.xtxdoc .tabular.c9 tr td.normal.col9 {
  text-align: center;
}

.xtxdoc .tabular.r9 tr td.normal.col9 {
  text-align: right;
}

.xtxdoc .tabular.b9 tr td.col9 {
  border-left: 0.075em solid var(--color-text);
}

.xtxdoc .tabular.l10 tr td.normal.col10 {
  text-align: left;
}

.xtxdoc .tabular.c10 tr td.normal.col10 {
  text-align: center;
}

.xtxdoc .tabular.r10 tr td.normal.col10 {
  text-align: right;
}

.xtxdoc .tabular.b10 tr td.col10 {
  border-left: 0.075em solid var(--color-text);
}

.xtxdoc .tabular.l11 tr td.normal.col11 {
  text-align: left;
}

.xtxdoc .tabular.c11 tr td.normal.col11 {
  text-align: center;
}

.xtxdoc .tabular.r11 tr td.normal.col11 {
  text-align: right;
}

.xtxdoc .tabular.b11 tr td.col11 {
  border-left: 0.075em solid var(--color-text);
}

.xtxdoc .tabular.l12 tr td.normal.col12 {
  text-align: left;
}

.xtxdoc .tabular.c12 tr td.normal.col12 {
  text-align: center;
}

.xtxdoc .tabular.r12 tr td.normal.col12 {
  text-align: right;
}

.xtxdoc .tabular.b12 tr td.col12 {
  border-left: 0.075em solid var(--color-text);
}

.xtxdoc .tabular.l13 tr td.normal.col13 {
  text-align: left;
}

.xtxdoc .tabular.c13 tr td.normal.col13 {
  text-align: center;
}

.xtxdoc .tabular.r13 tr td.normal.col13 {
  text-align: right;
}

.xtxdoc .tabular.b13 tr td.col13 {
  border-left: 0.075em solid var(--color-text);
}

.xtxdoc .tabular.l14 tr td.normal.col14 {
  text-align: left;
}

.xtxdoc .tabular.c14 tr td.normal.col14 {
  text-align: center;
}

.xtxdoc .tabular.r14 tr td.normal.col14 {
  text-align: right;
}

.xtxdoc .tabular.b14 tr td.col14 {
  border-left: 0.075em solid var(--color-text);
}

.xtxdoc .tabular.l15 tr td.normal.col15 {
  text-align: left;
}

.xtxdoc .tabular.c15 tr td.normal.col15 {
  text-align: center;
}

.xtxdoc .tabular.r15 tr td.normal.col15 {
  text-align: right;
}

.xtxdoc .tabular.b15 tr td.col15 {
  border-left: 0.075em solid var(--color-text);
}

.xtxdoc .tabular.l16 tr td.normal.col16 {
  text-align: left;
}

.xtxdoc .tabular.c16 tr td.normal.col16 {
  text-align: center;
}

.xtxdoc .tabular.r16 tr td.normal.col16 {
  text-align: right;
}

.xtxdoc .tabular.b16 tr td.col16 {
  border-left: 0.075em solid var(--color-text);
}

.xtxdoc .tabular.l17 tr td.normal.col17 {
  text-align: left;
}

.xtxdoc .tabular.c17 tr td.normal.col17 {
  text-align: center;
}

.xtxdoc .tabular.r17 tr td.normal.col17 {
  text-align: right;
}

.xtxdoc .tabular.b17 tr td.col17 {
  border-left: 0.075em solid var(--color-text);
}

.xtxdoc .tabular.l18 tr td.normal.col18 {
  text-align: left;
}

.xtxdoc .tabular.c18 tr td.normal.col18 {
  text-align: center;
}

.xtxdoc .tabular.r18 tr td.normal.col18 {
  text-align: right;
}

.xtxdoc .tabular.b18 tr td.col18 {
  border-left: 0.075em solid var(--color-text);
}

.xtxdoc .tabular.l19 tr td.normal.col19 {
  text-align: left;
}

.xtxdoc .tabular.c19 tr td.normal.col19 {
  text-align: center;
}

.xtxdoc .tabular.r19 tr td.normal.col19 {
  text-align: right;
}

.xtxdoc .tabular.b19 tr td.col19 {
  border-left: 0.075em solid var(--color-text);
}

.xtxdoc .tabular.l20 tr td.normal.col20 {
  text-align: left;
}

.xtxdoc .tabular.c20 tr td.normal.col20 {
  text-align: center;
}

.xtxdoc .tabular.r20 tr td.normal.col20 {
  text-align: right;
}

.xtxdoc .tabular.b20 tr td.col20 {
  border-left: 0.075em solid var(--color-text);
}

.xtxdoc .tabular.l21 tr td.normal.col21 {
  text-align: left;
}

.xtxdoc .tabular.c21 tr td.normal.col21 {
  text-align: center;
}

.xtxdoc .tabular.r21 tr td.normal.col21 {
  text-align: right;
}

.xtxdoc .tabular.b21 tr td.col21 {
  border-left: 0.075em solid var(--color-text);
}

.xtxdoc .tabular.l22 tr td.normal.col22 {
  text-align: left;
}

.xtxdoc .tabular.c22 tr td.normal.col22 {
  text-align: center;
}

.xtxdoc .tabular.r22 tr td.normal.col22 {
  text-align: right;
}

.xtxdoc .tabular.b22 tr td.col22 {
  border-left: 0.075em solid var(--color-text);
}

.xtxdoc .tabular.l23 tr td.normal.col23 {
  text-align: left;
}

.xtxdoc .tabular.c23 tr td.normal.col23 {
  text-align: center;
}

.xtxdoc .tabular.r23 tr td.normal.col23 {
  text-align: right;
}

.xtxdoc .tabular.b23 tr td.col23 {
  border-left: 0.075em solid var(--color-text);
}

.xtxdoc .tabular.l24 tr td.normal.col24 {
  text-align: left;
}

.xtxdoc .tabular.c24 tr td.normal.col24 {
  text-align: center;
}

.xtxdoc .tabular.r24 tr td.normal.col24 {
  text-align: right;
}

.xtxdoc .tabular.b24 tr td.col24 {
  border-left: 0.075em solid var(--color-text);
}

.xtxdoc .tabular.l25 tr td.normal.col25 {
  text-align: left;
}

.xtxdoc .tabular.c25 tr td.normal.col25 {
  text-align: center;
}

.xtxdoc .tabular.r25 tr td.normal.col25 {
  text-align: right;
}

.xtxdoc .tabular.b25 tr td.col25 {
  border-left: 0.075em solid var(--color-text);
}

.xtxdoc .tabular tr td:last-of-type {
  padding: 0;
}

.xtxdoc .tabular td {
  padding: 0.125em 0.5em;
  white-space: nowrap;
}

.xtxdoc .tabular td.multicolumn.l {
  text-align: left;
}

.xtxdoc .tabular td.multicolumn.c {
  text-align: center;
}

.xtxdoc .tabular td.multicolumn.r {
  text-align: right;
}

.xtxdoc .tabular tr.hline td {
  border-top: 0.075em solid var(--color-text);
}
.xtxdoc .theorem {
  margin-top: 1em;
  margin-bottom: 1em;
  font-style: italic;
  background-color: #F6F8F8;
  box-shadow: 0.35em 0.25em 0 0 #F6F8F8, -0.35em 0.25em 0 0 #F6F8F8, 0.35em -0.25em 0 0 #F6F8F8, -0.35em -0.25em 0 0 #F6F8F8;
}

.xtxdoc .theorem .caption {
  display: inline-block;
  margin-right: 0.75em;
}

.xtxdoc .theorem .caption {
  font-weight: bold;
  font-style: normal;
}

.xtxdoc .theorem .caption .subcaption {
  font-weight: normal;
}

.xtxdoc .theorem > p.paragraph {
  margin-top: 0.75em;
}

.xtxdoc .theorem > p.paragraph .caption {
  display: inline-block;
  margin-right: 0.75em;
}

.xtxdoc .theorem > p.paragraph .caption {
  font-weight: bold;
  font-style: normal;
}

.xtxdoc .theorem > p.paragraph .caption .subcaption {
  font-weight: normal;
}

.xtxdoc .theorem p {
  margin-top: 0em;
  margin-bottom: 0em;
  line-height: 1.25em;
}

.xtxdoc .theorem p + p {
  text-indent: 1.5em;
}

.xtxdoc .theorem p.paragraph {
  text-indent: 0;
}

.xtxdoc .theorem p.paragraph {
  margin-top: 0.75em;
}

.xtxdoc .theorem em {
  font-style: normal;
}

.xtxdoc .theorem p:nth-of-type(1),
.xtxdoc .theorem p:nth-of-type(2) {
  display: inline;
}

.xtxdoc .proof > p.paragraph {
  margin-top: 0.75em;
}

.xtxdoc .proof > p.paragraph .caption {
  display: inline-block;
  margin-right: 0.75em;
}

.xtxdoc .proof > p.paragraph .caption {
  font-weight: bold;
  font-style: normal;
}

.xtxdoc .proof > p.paragraph .caption .subcaption {
  font-weight: normal;
}

.xtxdoc .proof p {
  margin-top: 0.5em;
  margin-bottom: 0.5em;
  text-indent: 0em;
}

.xtxdoc .proof > p:first-of-type .caption {
  display: inline-block;
  margin-right: 0.75em;
}

.xtxdoc .proof > p:first-of-type .caption {
  font-style: italic;
  font-weight: normal;
}

.xtxdoc .proof > p:first-of-type .caption .subcaption {
  font-style: normal;
}

.xtxdoc .proof .qed {
  float: right;
  font-size: 1.15em;
  position: relative;
}
.xtxdoc .tikz {
  display: inline-block;
  max-width: 100%;
  overflow-x: auto;
  overflow-y: hidden;
}

.xtxdoc .tikz img {
  display: block;
}
.verb {
  font-family: KaTeX_Typewriter, SFMono-Regular, Menlo, Monaco, Consolas, "Liberation Mono", "Courier New", monospace;
  width: min-content;
}

.verbatim {
  font-family: KaTeX_Typewriter, SFMono-Regular, Menlo, Monaco, Consolas, "Liberation Mono", "Courier New", monospace;
  margin-top: 1em;
  margin-bottom: 1em;
  white-space: pre;
}
.gu-mirror {
  position: fixed !important;
  margin: 0 !important;
  z-index: 9999 !important;
  opacity: 0.8;
  -ms-filter: "progid:DXImageTransform.Microsoft.Alpha(Opacity=80)";
  filter: alpha(opacity=80);
}

.gu-hide {
  display: none !important;
}

.gu-unselectable {
  -webkit-user-select: none !important;
  -moz-user-select: none !important;
  -ms-user-select: none !important;
  user-select: none !important;
}

.gu-transit {
  opacity: 0.2;
  -ms-filter: "progid:DXImageTransform.Microsoft.Alpha(Opacity=20)";
  filter: alpha(opacity=20);
}
.katex {
  font: normal 1em KaTeX_Main, Times New Roman, serif;
  line-height: 1.2;
  text-indent: 0;
  text-rendering: auto;
  border-color: currentColor;
}

.katex * {
  -ms-high-contrast-adjust: none !important;
}

.katex .katex-version:after {
  content: "0.12.0";
}

.katex .katex-mathml {
  position: absolute;
  clip: rect(1px, 1px, 1px, 1px);
  padding: 0;
  border: 0;
  height: 1px;
  width: 1px;
  overflow: hidden;
}

.katex .katex-html > .newline {
  display: block;
}

.katex .base {
  position: relative;
  white-space: nowrap;
  width: min-content;
}

.katex .base,
.katex .strut {
  display: inline-block;
}

.katex .textbf {
  font-weight: 700;
}

.katex .textit {
  font-style: italic;
}

.katex .textrm {
  font-family: KaTeX_Main;
}

.katex .textsf {
  font-family: KaTeX_SansSerif;
}

.katex .texttt {
  font-family: KaTeX_Typewriter;
}

.katex .mathnormal {
  font-family: KaTeX_Math;
  font-style: italic;
}

.katex .mathit {
  font-family: KaTeX_Main;
  font-style: italic;
}

.katex .mathrm {
  font-style: normal;
}

.katex .mathbf {
  font-family: KaTeX_Main;
  font-weight: 700;
}

.katex .boldsymbol {
  font-family: KaTeX_Math;
  font-weight: 700;
  font-style: italic;
}

.katex .amsrm,
.katex .mathbb,
.katex .textbb {
  font-family: KaTeX_AMS;
}

.katex .mathcal {
  font-family: KaTeX_Caligraphic;
}

.katex .mathfrak,
.katex .textfrak {
  font-family: KaTeX_Fraktur;
}

.katex .mathtt {
  font-family: KaTeX_Typewriter;
}

.katex .mathscr,
.katex .textscr {
  font-family: KaTeX_Script;
}

.katex .mathsf,
.katex .textsf {
  font-family: KaTeX_SansSerif;
}

.katex .mathboldsf,
.katex .textboldsf {
  font-family: KaTeX_SansSerif;
  font-weight: 700;
}

.katex .mathitsf,
.katex .textitsf {
  font-family: KaTeX_SansSerif;
  font-style: italic;
}

.katex .mainrm {
  font-family: KaTeX_Main;
  font-style: normal;
}

.katex .vlist-t {
  display: inline-table;
  table-layout: fixed;
  border-collapse: collapse;
}

.katex .vlist-r {
  display: table-row;
}

.katex .vlist {
  display: table-cell;
  vertical-align: bottom;
  position: relative;
}

.katex .vlist > span {
  display: block;
  height: 0;
  position: relative;
}

.katex .vlist > span > span {
  display: inline-block;
}

.katex .vlist > span > .pstrut {
  overflow: hidden;
  width: 0;
}

.katex .vlist-t2 {
  margin-right: -2px;
}

.katex .vlist-s {
  display: table-cell;
  vertical-align: bottom;
  font-size: 1px;
  width: 2px;
  min-width: 2px;
}

.katex .vbox {
  -ms-flex-direction: column;
  flex-direction: column;
  align-items: baseline;
}

.katex .hbox,
.katex .vbox {
  display: -ms-inline-flexbox;
  display: inline-flex;
}

.katex .hbox {
  -ms-flex-direction: row;
  flex-direction: row;
  width: 100%;
}

.katex .thinbox {
  display: inline-flex;
  flex-direction: row;
  width: 0;
  max-width: 0;
}

.katex .msupsub {
  text-align: left;
}

.katex .mfrac > span > span {
  text-align: center;
}

.katex .mfrac .frac-line {
  display: inline-block;
  width: 100%;
  border-bottom-style: solid;
}

.katex .hdashline,
.katex .hline,
.katex .mfrac .frac-line,
.katex .overline .overline-line,
.katex .rule,
.katex .underline .underline-line {
  min-height: 1px;
}

.katex .mspace {
  display: inline-block;
}

.katex .clap,
.katex .llap,
.katex .rlap {
  width: 0;
  position: relative;
}

.katex .clap > .inner,
.katex .llap > .inner,
.katex .rlap > .inner {
  position: absolute;
}

.katex .clap > .fix,
.katex .llap > .fix,
.katex .rlap > .fix {
  display: inline-block;
}

.katex .llap > .inner {
  right: 0;
}

.katex .clap > .inner,
.katex .rlap > .inner {
  left: 0;
}

.katex .clap > .inner > span {
  margin-left: -50%;
  margin-right: 50%;
}

.katex .rule {
  display: inline-block;
  border: 0 solid;
  position: relative;
}

.katex .hline,
.katex .overline .overline-line,
.katex .underline .underline-line {
  display: inline-block;
  width: 100%;
  border-bottom-style: solid;
}

.katex .hdashline {
  display: inline-block;
  width: 100%;
  border-bottom-style: dashed;
}

.katex .sqrt > .root {
  margin-left: 0.27777778em;
  margin-right: -0.55555556em;
}

.katex .fontsize-ensurer.reset-size1.size1,
.katex .sizing.reset-size1.size1 {
  font-size: 1em;
}

.katex .fontsize-ensurer.reset-size1.size2,
.katex .sizing.reset-size1.size2 {
  font-size: 1.2em;
}

.katex .fontsize-ensurer.reset-size1.size3,
.katex .sizing.reset-size1.size3 {
  font-size: 1.4em;
}

.katex .fontsize-ensurer.reset-size1.size4,
.katex .sizing.reset-size1.size4 {
  font-size: 1.6em;
}

.katex .fontsize-ensurer.reset-size1.size5,
.katex .sizing.reset-size1.size5 {
  font-size: 1.8em;
}

.katex .fontsize-ensurer.reset-size1.size6,
.katex .sizing.reset-size1.size6 {
  font-size: 2em;
}

.katex .fontsize-ensurer.reset-size1.size7,
.katex .sizing.reset-size1.size7 {
  font-size: 2.4em;
}

.katex .fontsize-ensurer.reset-size1.size8,
.katex .sizing.reset-size1.size8 {
  font-size: 2.88em;
}

.katex .fontsize-ensurer.reset-size1.size9,
.katex .sizing.reset-size1.size9 {
  font-size: 3.456em;
}

.katex .fontsize-ensurer.reset-size1.size10,
.katex .sizing.reset-size1.size10 {
  font-size: 4.148em;
}

.katex .fontsize-ensurer.reset-size1.size11,
.katex .sizing.reset-size1.size11 {
  font-size: 4.976em;
}

.katex .fontsize-ensurer.reset-size2.size1,
.katex .sizing.reset-size2.size1 {
  font-size: 0.83333333em;
}

.katex .fontsize-ensurer.reset-size2.size2,
.katex .sizing.reset-size2.size2 {
  font-size: 1em;
}

.katex .fontsize-ensurer.reset-size2.size3,
.katex .sizing.reset-size2.size3 {
  font-size: 1.16666667em;
}

.katex .fontsize-ensurer.reset-size2.size4,
.katex .sizing.reset-size2.size4 {
  font-size: 1.33333333em;
}

.katex .fontsize-ensurer.reset-size2.size5,
.katex .sizing.reset-size2.size5 {
  font-size: 1.5em;
}

.katex .fontsize-ensurer.reset-size2.size6,
.katex .sizing.reset-size2.size6 {
  font-size: 1.66666667em;
}

.katex .fontsize-ensurer.reset-size2.size7,
.katex .sizing.reset-size2.size7 {
  font-size: 2em;
}

.katex .fontsize-ensurer.reset-size2.size8,
.katex .sizing.reset-size2.size8 {
  font-size: 2.4em;
}

.katex .fontsize-ensurer.reset-size2.size9,
.katex .sizing.reset-size2.size9 {
  font-size: 2.88em;
}

.katex .fontsize-ensurer.reset-size2.size10,
.katex .sizing.reset-size2.size10 {
  font-size: 3.45666667em;
}

.katex .fontsize-ensurer.reset-size2.size11,
.katex .sizing.reset-size2.size11 {
  font-size: 4.14666667em;
}

.katex .fontsize-ensurer.reset-size3.size1,
.katex .sizing.reset-size3.size1 {
  font-size: 0.71428571em;
}

.katex .fontsize-ensurer.reset-size3.size2,
.katex .sizing.reset-size3.size2 {
  font-size: 0.85714286em;
}

.katex .fontsize-ensurer.reset-size3.size3,
.katex .sizing.reset-size3.size3 {
  font-size: 1em;
}

.katex .fontsize-ensurer.reset-size3.size4,
.katex .sizing.reset-size3.size4 {
  font-size: 1.14285714em;
}

.katex .fontsize-ensurer.reset-size3.size5,
.katex .sizing.reset-size3.size5 {
  font-size: 1.28571429em;
}

.katex .fontsize-ensurer.reset-size3.size6,
.katex .sizing.reset-size3.size6 {
  font-size: 1.42857143em;
}

.katex .fontsize-ensurer.reset-size3.size7,
.katex .sizing.reset-size3.size7 {
  font-size: 1.71428571em;
}

.katex .fontsize-ensurer.reset-size3.size8,
.katex .sizing.reset-size3.size8 {
  font-size: 2.05714286em;
}

.katex .fontsize-ensurer.reset-size3.size9,
.katex .sizing.reset-size3.size9 {
  font-size: 2.46857143em;
}

.katex .fontsize-ensurer.reset-size3.size10,
.katex .sizing.reset-size3.size10 {
  font-size: 2.96285714em;
}

.katex .fontsize-ensurer.reset-size3.size11,
.katex .sizing.reset-size3.size11 {
  font-size: 3.55428571em;
}

.katex .fontsize-ensurer.reset-size4.size1,
.katex .sizing.reset-size4.size1 {
  font-size: 0.625em;
}

.katex .fontsize-ensurer.reset-size4.size2,
.katex .sizing.reset-size4.size2 {
  font-size: 0.75em;
}

.katex .fontsize-ensurer.reset-size4.size3,
.katex .sizing.reset-size4.size3 {
  font-size: 0.875em;
}

.katex .fontsize-ensurer.reset-size4.size4,
.katex .sizing.reset-size4.size4 {
  font-size: 1em;
}

.katex .fontsize-ensurer.reset-size4.size5,
.katex .sizing.reset-size4.size5 {
  font-size: 1.125em;
}

.katex .fontsize-ensurer.reset-size4.size6,
.katex .sizing.reset-size4.size6 {
  font-size: 1.25em;
}

.katex .fontsize-ensurer.reset-size4.size7,
.katex .sizing.reset-size4.size7 {
  font-size: 1.5em;
}

.katex .fontsize-ensurer.reset-size4.size8,
.katex .sizing.reset-size4.size8 {
  font-size: 1.8em;
}

.katex .fontsize-ensurer.reset-size4.size9,
.katex .sizing.reset-size4.size9 {
  font-size: 2.16em;
}

.katex .fontsize-ensurer.reset-size4.size10,
.katex .sizing.reset-size4.size10 {
  font-size: 2.5925em;
}

.katex .fontsize-ensurer.reset-size4.size11,
.katex .sizing.reset-size4.size11 {
  font-size: 3.11em;
}

.katex .fontsize-ensurer.reset-size5.size1,
.katex .sizing.reset-size5.size1 {
  font-size: 0.55555556em;
}

.katex .fontsize-ensurer.reset-size5.size2,
.katex .sizing.reset-size5.size2 {
  font-size: 0.66666667em;
}

.katex .fontsize-ensurer.reset-size5.size3,
.katex .sizing.reset-size5.size3 {
  font-size: 0.77777778em;
}

.katex .fontsize-ensurer.reset-size5.size4,
.katex .sizing.reset-size5.size4 {
  font-size: 0.88888889em;
}

.katex .fontsize-ensurer.reset-size5.size5,
.katex .sizing.reset-size5.size5 {
  font-size: 1em;
}

.katex .fontsize-ensurer.reset-size5.size6,
.katex .sizing.reset-size5.size6 {
  font-size: 1.11111111em;
}

.katex .fontsize-ensurer.reset-size5.size7,
.katex .sizing.reset-size5.size7 {
  font-size: 1.33333333em;
}

.katex .fontsize-ensurer.reset-size5.size8,
.katex .sizing.reset-size5.size8 {
  font-size: 1.6em;
}

.katex .fontsize-ensurer.reset-size5.size9,
.katex .sizing.reset-size5.size9 {
  font-size: 1.92em;
}

.katex .fontsize-ensurer.reset-size5.size10,
.katex .sizing.reset-size5.size10 {
  font-size: 2.30444444em;
}

.katex .fontsize-ensurer.reset-size5.size11,
.katex .sizing.reset-size5.size11 {
  font-size: 2.76444444em;
}

.katex .fontsize-ensurer.reset-size6.size1,
.katex .sizing.reset-size6.size1 {
  font-size: 0.5em;
}

.katex .fontsize-ensurer.reset-size6.size2,
.katex .sizing.reset-size6.size2 {
  font-size: 0.6em;
}

.katex .fontsize-ensurer.reset-size6.size3,
.katex .sizing.reset-size6.size3 {
  font-size: 0.7em;
}

.katex .fontsize-ensurer.reset-size6.size4,
.katex .sizing.reset-size6.size4 {
  font-size: 0.8em;
}

.katex .fontsize-ensurer.reset-size6.size5,
.katex .sizing.reset-size6.size5 {
  font-size: 0.9em;
}

.katex .fontsize-ensurer.reset-size6.size6,
.katex .sizing.reset-size6.size6 {
  font-size: 1em;
}

.katex .fontsize-ensurer.reset-size6.size7,
.katex .sizing.reset-size6.size7 {
  font-size: 1.2em;
}

.katex .fontsize-ensurer.reset-size6.size8,
.katex .sizing.reset-size6.size8 {
  font-size: 1.44em;
}

.katex .fontsize-ensurer.reset-size6.size9,
.katex .sizing.reset-size6.size9 {
  font-size: 1.728em;
}

.katex .fontsize-ensurer.reset-size6.size10,
.katex .sizing.reset-size6.size10 {
  font-size: 2.074em;
}

.katex .fontsize-ensurer.reset-size6.size11,
.katex .sizing.reset-size6.size11 {
  font-size: 2.488em;
}

.katex .fontsize-ensurer.reset-size7.size1,
.katex .sizing.reset-size7.size1 {
  font-size: 0.41666667em;
}

.katex .fontsize-ensurer.reset-size7.size2,
.katex .sizing.reset-size7.size2 {
  font-size: 0.5em;
}

.katex .fontsize-ensurer.reset-size7.size3,
.katex .sizing.reset-size7.size3 {
  font-size: 0.58333333em;
}

.katex .fontsize-ensurer.reset-size7.size4,
.katex .sizing.reset-size7.size4 {
  font-size: 0.66666667em;
}

.katex .fontsize-ensurer.reset-size7.size5,
.katex .sizing.reset-size7.size5 {
  font-size: 0.75em;
}

.katex .fontsize-ensurer.reset-size7.size6,
.katex .sizing.reset-size7.size6 {
  font-size: 0.83333333em;
}

.katex .fontsize-ensurer.reset-size7.size7,
.katex .sizing.reset-size7.size7 {
  font-size: 1em;
}

.katex .fontsize-ensurer.reset-size7.size8,
.katex .sizing.reset-size7.size8 {
  font-size: 1.2em;
}

.katex .fontsize-ensurer.reset-size7.size9,
.katex .sizing.reset-size7.size9 {
  font-size: 1.44em;
}

.katex .fontsize-ensurer.reset-size7.size10,
.katex .sizing.reset-size7.size10 {
  font-size: 1.72833333em;
}

.katex .fontsize-ensurer.reset-size7.size11,
.katex .sizing.reset-size7.size11 {
  font-size: 2.07333333em;
}

.katex .fontsize-ensurer.reset-size8.size1,
.katex .sizing.reset-size8.size1 {
  font-size: 0.34722222em;
}

.katex .fontsize-ensurer.reset-size8.size2,
.katex .sizing.reset-size8.size2 {
  font-size: 0.41666667em;
}

.katex .fontsize-ensurer.reset-size8.size3,
.katex .sizing.reset-size8.size3 {
  font-size: 0.48611111em;
}

.katex .fontsize-ensurer.reset-size8.size4,
.katex .sizing.reset-size8.size4 {
  font-size: 0.55555556em;
}

.katex .fontsize-ensurer.reset-size8.size5,
.katex .sizing.reset-size8.size5 {
  font-size: 0.625em;
}

.katex .fontsize-ensurer.reset-size8.size6,
.katex .sizing.reset-size8.size6 {
  font-size: 0.69444444em;
}

.katex .fontsize-ensurer.reset-size8.size7,
.katex .sizing.reset-size8.size7 {
  font-size: 0.83333333em;
}

.katex .fontsize-ensurer.reset-size8.size8,
.katex .sizing.reset-size8.size8 {
  font-size: 1em;
}

.katex .fontsize-ensurer.reset-size8.size9,
.katex .sizing.reset-size8.size9 {
  font-size: 1.2em;
}

.katex .fontsize-ensurer.reset-size8.size10,
.katex .sizing.reset-size8.size10 {
  font-size: 1.44027778em;
}

.katex .fontsize-ensurer.reset-size8.size11,
.katex .sizing.reset-size8.size11 {
  font-size: 1.72777778em;
}

.katex .fontsize-ensurer.reset-size9.size1,
.katex .sizing.reset-size9.size1 {
  font-size: 0.28935185em;
}

.katex .fontsize-ensurer.reset-size9.size2,
.katex .sizing.reset-size9.size2 {
  font-size: 0.34722222em;
}

.katex .fontsize-ensurer.reset-size9.size3,
.katex .sizing.reset-size9.size3 {
  font-size: 0.40509259em;
}

.katex .fontsize-ensurer.reset-size9.size4,
.katex .sizing.reset-size9.size4 {
  font-size: 0.46296296em;
}

.katex .fontsize-ensurer.reset-size9.size5,
.katex .sizing.reset-size9.size5 {
  font-size: 0.52083333em;
}

.katex .fontsize-ensurer.reset-size9.size6,
.katex .sizing.reset-size9.size6 {
  font-size: 0.5787037em;
}

.katex .fontsize-ensurer.reset-size9.size7,
.katex .sizing.reset-size9.size7 {
  font-size: 0.69444444em;
}

.katex .fontsize-ensurer.reset-size9.size8,
.katex .sizing.reset-size9.size8 {
  font-size: 0.83333333em;
}

.katex .fontsize-ensurer.reset-size9.size9,
.katex .sizing.reset-size9.size9 {
  font-size: 1em;
}

.katex .fontsize-ensurer.reset-size9.size10,
.katex .sizing.reset-size9.size10 {
  font-size: 1.20023148em;
}

.katex .fontsize-ensurer.reset-size9.size11,
.katex .sizing.reset-size9.size11 {
  font-size: 1.43981481em;
}

.katex .fontsize-ensurer.reset-size10.size1,
.katex .sizing.reset-size10.size1 {
  font-size: 0.24108004em;
}

.katex .fontsize-ensurer.reset-size10.size2,
.katex .sizing.reset-size10.size2 {
  font-size: 0.28929605em;
}

.katex .fontsize-ensurer.reset-size10.size3,
.katex .sizing.reset-size10.size3 {
  font-size: 0.33751205em;
}

.katex .fontsize-ensurer.reset-size10.size4,
.katex .sizing.reset-size10.size4 {
  font-size: 0.38572806em;
}

.katex .fontsize-ensurer.reset-size10.size5,
.katex .sizing.reset-size10.size5 {
  font-size: 0.43394407em;
}

.katex .fontsize-ensurer.reset-size10.size6,
.katex .sizing.reset-size10.size6 {
  font-size: 0.48216008em;
}

.katex .fontsize-ensurer.reset-size10.size7,
.katex .sizing.reset-size10.size7 {
  font-size: 0.57859209em;
}

.katex .fontsize-ensurer.reset-size10.size8,
.katex .sizing.reset-size10.size8 {
  font-size: 0.69431051em;
}

.katex .fontsize-ensurer.reset-size10.size9,
.katex .sizing.reset-size10.size9 {
  font-size: 0.83317261em;
}

.katex .fontsize-ensurer.reset-size10.size10,
.katex .sizing.reset-size10.size10 {
  font-size: 1em;
}

.katex .fontsize-ensurer.reset-size10.size11,
.katex .sizing.reset-size10.size11 {
  font-size: 1.19961427em;
}

.katex .fontsize-ensurer.reset-size11.size1,
.katex .sizing.reset-size11.size1 {
  font-size: 0.20096463em;
}

.katex .fontsize-ensurer.reset-size11.size2,
.katex .sizing.reset-size11.size2 {
  font-size: 0.24115756em;
}

.katex .fontsize-ensurer.reset-size11.size3,
.katex .sizing.reset-size11.size3 {
  font-size: 0.28135048em;
}

.katex .fontsize-ensurer.reset-size11.size4,
.katex .sizing.reset-size11.size4 {
  font-size: 0.32154341em;
}

.katex .fontsize-ensurer.reset-size11.size5,
.katex .sizing.reset-size11.size5 {
  font-size: 0.36173633em;
}

.katex .fontsize-ensurer.reset-size11.size6,
.katex .sizing.reset-size11.size6 {
  font-size: 0.40192926em;
}

.katex .fontsize-ensurer.reset-size11.size7,
.katex .sizing.reset-size11.size7 {
  font-size: 0.48231511em;
}

.katex .fontsize-ensurer.reset-size11.size8,
.katex .sizing.reset-size11.size8 {
  font-size: 0.57877814em;
}

.katex .fontsize-ensurer.reset-size11.size9,
.katex .sizing.reset-size11.size9 {
  font-size: 0.69453376em;
}

.katex .fontsize-ensurer.reset-size11.size10,
.katex .sizing.reset-size11.size10 {
  font-size: 0.83360129em;
}

.katex .fontsize-ensurer.reset-size11.size11,
.katex .sizing.reset-size11.size11 {
  font-size: 1em;
}

.katex .delimsizing.size1 {
  font-family: KaTeX_Size1;
}

.katex .delimsizing.size2 {
  font-family: KaTeX_Size2;
}

.katex .delimsizing.size3 {
  font-family: KaTeX_Size3;
}

.katex .delimsizing.size4 {
  font-family: KaTeX_Size4;
}

.katex .delimsizing.mult .delim-size1 > span {
  font-family: KaTeX_Size1;
}

.katex .delimsizing.mult .delim-size4 > span {
  font-family: KaTeX_Size4;
}

.katex .nulldelimiter {
  display: inline-block;
  width: 0.12em;
}

.katex .delimcenter,
.katex .op-symbol {
  position: relative;
}

.katex .op-symbol.small-op {
  font-family: KaTeX_Size1;
}

.katex .op-symbol.large-op {
  font-family: KaTeX_Size2;
}

.katex .op-limits > .vlist-t {
  text-align: center;
}

.katex .accent > .vlist-t {
  text-align: center;
}

.katex .accent .accent-body {
  position: relative;
}

.katex .accent .accent-body:not(.accent-full) {
  width: 0;
}

.katex .overlay {
  display: block;
}

.katex .mtable .vertical-separator {
  display: inline-block;
  min-width: 1px;
}

.katex .mtable .arraycolsep {
  display: inline-block;
}

.katex .mtable .col-align-c > .vlist-t {
  text-align: center;
}

.katex .mtable .col-align-l > .vlist-t {
  text-align: left;
}

.katex .mtable .col-align-r > .vlist-t {
  text-align: right;
}

.katex .svg-align {
  text-align: left;
}

.katex svg {
  display: block;
  position: absolute;
  width: 100%;
  height: inherit;
  fill: currentColor;
  stroke: currentColor;
  fill-rule: nonzero;
  fill-opacity: 1;
  stroke-width: 1;
  stroke-linecap: butt;
  stroke-linejoin: miter;
  stroke-miterlimit: 4;
  stroke-dasharray: none;
  stroke-dashoffset: 0;
  stroke-opacity: 1;
}

.katex svg path {
  stroke: none;
}

.katex img {
  border-style: none;
  min-width: 0;
  min-height: 0;
  max-width: none;
  max-height: none;
}

.katex .stretchy {
  width: 100%;
  display: block;
  position: relative;
  overflow: hidden;
}

.katex .stretchy:after,
.katex .stretchy:before {
  content: "";
}

.katex .hide-tail {
  width: 100%;
  position: relative;
  overflow: hidden;
}

.katex .halfarrow-left {
  position: absolute;
  left: 0;
  width: 50.2%;
  overflow: hidden;
}

.katex .halfarrow-right {
  position: absolute;
  right: 0;
  width: 50.2%;
  overflow: hidden;
}

.katex .brace-left {
  position: absolute;
  left: 0;
  width: 25.1%;
  overflow: hidden;
}

.katex .brace-center {
  position: absolute;
  left: 25%;
  width: 50%;
  overflow: hidden;
}

.katex .brace-right {
  position: absolute;
  right: 0;
  width: 25.1%;
  overflow: hidden;
}

.katex .x-arrow-pad {
  padding: 0 0.5em;
}

.katex .mover,
.katex .munder,
.katex .x-arrow {
  text-align: center;
}

.katex .boxpad {
  padding: 0 0.3em;
}

.katex .fbox,
.katex .fcolorbox {
  box-sizing: border-box;
  border: 0.04em solid;
}

.katex .cancel-pad {
  padding: 0 0.2em;
}

.katex .cancel-lap {
  margin-left: -0.2em;
  margin-right: -0.2em;
}

.katex .sout {
  border-bottom-style: solid;
  border-bottom-width: 0.08em;
}

.katex-display {
  display: block;
  margin: 1em 0;
  text-align: center;
}

.katex-display > .katex {
  display: block;
  text-align: center;
  white-space: nowrap;
}

.katex-display > .katex > .katex-html {
  display: block;
  position: relative;
}

.katex-display > .katex > .katex-html > .tag {
  position: absolute;
  right: 0;
}

.katex-display.leqno > .katex > .katex-html > .tag {
  left: 0;
  right: auto;
}

.katex-display.fleqn > .katex {
  text-align: left;
  padding-left: 2em;
}