/*! KaTeX v0.16.8 - Local minimal version */
.katex {
  font: normal 1.21em KaTeX_Main, Times, serif;
  line-height: 1.2;
  text-indent: 0;
  text-rendering: auto;
  border-color: currentColor;
}

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

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

.katex .katex-html {
  /* IE8 - IE11 do not add the font-feature-settings. */
  font-feature-settings: "kern";
}

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

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

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

.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: bold;
}

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

.katex .amsrm {
  font-family: KaTeX_AMS;
}

.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: bold;
}

.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 .hlist {
  display: inline-flex;
  flex-direction: row;
}

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

.katex .thinspace {
  width: 0.16667em;
}

.katex .mediumspace {
  width: 0.22222em;
}

.katex .thickspace {
  width: 0.27778em;
}

.katex .enspace {
  width: 0.5em;
}

.katex .quad {
  width: 1em;
}

.katex .qquad {
  width: 2em;
}

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

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

.katex .mord {
  color: inherit;
}

.katex .mop {
  color: inherit;
}

.katex .mbin {
  color: inherit;
}

.katex .mrel {
  color: inherit;
}

.katex .mopen {
  color: inherit;
}

.katex .mclose {
  color: inherit;
}

.katex .mpunct {
  color: inherit;
}

.katex .minner {
  color: inherit;
}

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

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

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

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

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

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

.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:before,
.katex .stretchy:after {
  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 .cd-arrow-pad {
  padding: 0 0.55556em 0 0.27778em;
}

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

.katex .mmlToken {
  font-family: math;
}

.katex .mml-table {
  display: inline-table;
}

.katex .mml-row {
  display: table-row;
}

.katex .mml-cell {
  display: table-cell;
  text-align: center;
  padding: 0 0.5em;
}

.katex .mml-tiled-table {
  display: inline-block;
}

.katex .mml-tiled-row {
  display: block;
}

.katex .mml-tiled-cell {
  display: inline-block;
  text-align: center;
  padding: 0 0.5em;
}

.katex .mml-script {
  font-size: 0.7em;
}

.katex .mml-root {
  vertical-align: baseline;
  border-top: 1px solid;
  margin-top: 0.6em;
  padding-left: 0.2em;
}

/* Dark mode optimization */
@media (prefers-color-scheme: dark) {
  .katex {
    color: #e5e7eb;
  }
}