@font-face {
  font-family: KaTeX_AMS;
  src: url(fonts/KaTeX_AMS-Regular.eot);
  src:
    url(fonts/KaTeX_AMS-Regular.eot#iefix) format("embedded-opentype"),
    url(fonts/KaTeX_AMS-Regular.woff2) format("woff2"),
    url(fonts/KaTeX_AMS-Regular.woff) format("woff"),
    url(fonts/KaTeX_AMS-Regular.ttf) format("ttf");
  font-weight: 400;
  font-style: normal;
}
@font-face {
  font-family: KaTeX_Caligraphic;
  src: url(fonts/KaTeX_Caligraphic-Bold.eot);
  src:
    url(fonts/KaTeX_Caligraphic-Bold.eot#iefix) format("embedded-opentype"),
    url(fonts/KaTeX_Caligraphic-Bold.woff2) format("woff2"),
    url(fonts/KaTeX_Caligraphic-Bold.woff) format("woff"),
    url(fonts/KaTeX_Caligraphic-Bold.ttf) format("ttf");
  font-weight: 700;
  font-style: normal;
}
@font-face {
  font-family: KaTeX_Caligraphic;
  src: url(fonts/KaTeX_Caligraphic-Regular.eot);
  src:
    url(fonts/KaTeX_Caligraphic-Regular.eot#iefix) format("embedded-opentype"),
    url(fonts/KaTeX_Caligraphic-Regular.woff2) format("woff2"),
    url(fonts/KaTeX_Caligraphic-Regular.woff) format("woff"),
    url(fonts/KaTeX_Caligraphic-Regular.ttf) format("ttf");
  font-weight: 400;
  font-style: normal;
}
@font-face {
  font-family: KaTeX_Fraktur;
  src: url(fonts/KaTeX_Fraktur-Bold.eot);
  src:
    url(fonts/KaTeX_Fraktur-Bold.eot#iefix) format("embedded-opentype"),
    url(fonts/KaTeX_Fraktur-Bold.woff2) format("woff2"),
    url(fonts/KaTeX_Fraktur-Bold.woff) format("woff"),
    url(fonts/KaTeX_Fraktur-Bold.ttf) format("ttf");
  font-weight: 700;
  font-style: normal;
}
@font-face {
  font-family: KaTeX_Fraktur;
  src: url(fonts/KaTeX_Fraktur-Regular.eot);
  src:
    url(fonts/KaTeX_Fraktur-Regular.eot#iefix) format("embedded-opentype"),
    url(fonts/KaTeX_Fraktur-Regular.woff2) format("woff2"),
    url(fonts/KaTeX_Fraktur-Regular.woff) format("woff"),
    url(fonts/KaTeX_Fraktur-Regular.ttf) format("ttf");
  font-weight: 400;
  font-style: normal;
}
@font-face {
  font-family: KaTeX_Main;
  src: url(fonts/KaTeX_Main-Bold.eot);
  src:
    url(fonts/KaTeX_Main-Bold.eot#iefix) format("embedded-opentype"),
    url(fonts/KaTeX_Main-Bold.woff2) format("woff2"),
    url(fonts/KaTeX_Main-Bold.woff) format("woff"),
    url(fonts/KaTeX_Main-Bold.ttf) format("ttf");
  font-weight: 700;
  font-style: normal;
}
@font-face {
  font-family: KaTeX_Main;
  src: url(fonts/KaTeX_Main-Italic.eot);
  src:
    url(fonts/KaTeX_Main-Italic.eot#iefix) format("embedded-opentype"),
    url(fonts/KaTeX_Main-Italic.woff2) format("woff2"),
    url(fonts/KaTeX_Main-Italic.woff) format("woff"),
    url(fonts/KaTeX_Main-Italic.ttf) format("ttf");
  font-weight: 400;
  font-style: italic;
}
@font-face {
  font-family: KaTeX_Main;
  src: url(fonts/KaTeX_Main-Regular.eot);
  src:
    url(fonts/KaTeX_Main-Regular.eot#iefix) format("embedded-opentype"),
    url(fonts/KaTeX_Main-Regular.woff2) format("woff2"),
    url(fonts/KaTeX_Main-Regular.woff) format("woff"),
    url(fonts/KaTeX_Main-Regular.ttf) format("ttf");
  font-weight: 400;
  font-style: normal;
}
@font-face {
  font-family: KaTeX_Math;
  src: url(fonts/KaTeX_Math-Italic.eot);
  src:
    url(fonts/KaTeX_Math-Italic.eot#iefix) format("embedded-opentype"),
    url(fonts/KaTeX_Math-Italic.woff2) format("woff2"),
    url(fonts/KaTeX_Math-Italic.woff) format("woff"),
    url(fonts/KaTeX_Math-Italic.ttf) format("ttf");
  font-weight: 400;
  font-style: italic;
}
@font-face {
  font-family: KaTeX_SansSerif;
  src: url(fonts/KaTeX_SansSerif-Regular.eot);
  src:
    url(fonts/KaTeX_SansSerif-Regular.eot#iefix) format("embedded-opentype"),
    url(fonts/KaTeX_SansSerif-Regular.woff2) format("woff2"),
    url(fonts/KaTeX_SansSerif-Regular.woff) format("woff"),
    url(fonts/KaTeX_SansSerif-Regular.ttf) format("ttf");
  font-weight: 400;
  font-style: normal;
}
@font-face {
  font-family: KaTeX_Script;
  src: url(fonts/KaTeX_Script-Regular.eot);
  src:
    url(fonts/KaTeX_Script-Regular.eot#iefix) format("embedded-opentype"),
    url(fonts/KaTeX_Script-Regular.woff2) format("woff2"),
    url(fonts/KaTeX_Script-Regular.woff) format("woff"),
    url(fonts/KaTeX_Script-Regular.ttf) format("ttf");
  font-weight: 400;
  font-style: normal;
}
@font-face {
  font-family: KaTeX_Size1;
  src: url(fonts/KaTeX_Size1-Regular.eot);
  src:
    url(fonts/KaTeX_Size1-Regular.eot#iefix) format("embedded-opentype"),
    url(fonts/KaTeX_Size1-Regular.woff2) format("woff2"),
    url(fonts/KaTeX_Size1-Regular.woff) format("woff"),
    url(fonts/KaTeX_Size1-Regular.ttf) format("ttf");
  font-weight: 400;
  font-style: normal;
}
@font-face {
  font-family: KaTeX_Size2;
  src: url(fonts/KaTeX_Size2-Regular.eot);
  src:
    url(fonts/KaTeX_Size2-Regular.eot#iefix) format("embedded-opentype"),
    url(fonts/KaTeX_Size2-Regular.woff2) format("woff2"),
    url(fonts/KaTeX_Size2-Regular.woff) format("woff"),
    url(fonts/KaTeX_Size2-Regular.ttf) format("ttf");
  font-weight: 400;
  font-style: normal;
}
@font-face {
  font-family: KaTeX_Size3;
  src: url(fonts/KaTeX_Size3-Regular.eot);
  src:
    url(fonts/KaTeX_Size3-Regular.eot#iefix) format("embedded-opentype"),
    url(fonts/KaTeX_Size3-Regular.woff2) format("woff2"),
    url(fonts/KaTeX_Size3-Regular.woff) format("woff"),
    url(fonts/KaTeX_Size3-Regular.ttf) format("ttf");
  font-weight: 400;
  font-style: normal;
}
@font-face {
  font-family: KaTeX_Size4;
  src: url(fonts/KaTeX_Size4-Regular.eot);
  src:
    url(fonts/KaTeX_Size4-Regular.eot#iefix) format("embedded-opentype"),
    url(fonts/KaTeX_Size4-Regular.woff2) format("woff2"),
    url(fonts/KaTeX_Size4-Regular.woff) format("woff"),
    url(fonts/KaTeX_Size4-Regular.ttf) format("ttf");
  font-weight: 400;
  font-style: normal;
}
@font-face {
  font-family: KaTeX_Typewriter;
  src: url(fonts/KaTeX_Typewriter-Regular.eot);
  src:
    url(fonts/KaTeX_Typewriter-Regular.eot#iefix) format("embedded-opentype"),
    url(fonts/KaTeX_Typewriter-Regular.woff2) format("woff2"),
    url(fonts/KaTeX_Typewriter-Regular.woff) format("woff"),
    url(fonts/KaTeX_Typewriter-Regular.ttf) format("ttf");
  font-weight: 400;
  font-style: normal;
}
.katex-display {
  display: block;
  margin: 1em 0;
  text-align: center;
}
.katex-display > .katex {
  display: inline-block;
}
.katex {
  font: 400 1.21em KaTeX_Main;
  line-height: 1.2;
  white-space: nowrap;
  text-indent: 0;
}
.katex .katex-html {
  display: inline-block;
}
.katex .katex-mathml {
  position: absolute;
  clip: rect(1px, 1px, 1px, 1px);
  padding: 0;
  border: 0;
  height: 1px;
  width: 1px;
  overflow: hidden;
}
.katex .base, .katex .strut {
  display: inline-block;
}
.katex .mathit {
  font-family: KaTeX_Math;
  font-style: italic;
}
.katex .mathbf {
  font-family: KaTeX_Main;
  font-weight: 700;
}
.katex .amsrm, .katex .mathbb {
  font-family: KaTeX_AMS;
}
.katex .mathcal {
  font-family: KaTeX_Caligraphic;
}
.katex .mathfrak {
  font-family: KaTeX_Fraktur;
}
.katex .mathtt {
  font-family: KaTeX_Typewriter;
}
.katex .mathscr {
  font-family: KaTeX_Script;
}
.katex .mathsf {
  font-family: KaTeX_SansSerif;
}
.katex .mainit {
  font-family: KaTeX_Main;
  font-style: italic;
}
.katex .textstyle > .mord + .mop {
  margin-left: 0.16667em;
}
.katex .textstyle > .mord + .mbin {
  margin-left: 0.22222em;
}
.katex .textstyle > .mord + .mrel {
  margin-left: 0.27778em;
}
.katex .textstyle > .mop + .mop,
.katex .textstyle > .mop + .mord,
.katex .textstyle > .mord + .minner {
  margin-left: 0.16667em;
}
.katex .textstyle > .mop + .mrel {
  margin-left: 0.27778em;
}
.katex .textstyle > .mop + .minner {
  margin-left: 0.16667em;
}
.katex .textstyle > .mbin + .minner,
.katex .textstyle > .mbin + .mop,
.katex .textstyle > .mbin + .mopen,
.katex .textstyle > .mbin + .mord {
  margin-left: 0.22222em;
}
.katex .textstyle > .mrel + .minner,
.katex .textstyle > .mrel + .mop,
.katex .textstyle > .mrel + .mopen,
.katex .textstyle > .mrel + .mord {
  margin-left: 0.27778em;
}
.katex .textstyle > .mclose + .mop {
  margin-left: 0.16667em;
}
.katex .textstyle > .mclose + .mbin {
  margin-left: 0.22222em;
}
.katex .textstyle > .mclose + .mrel {
  margin-left: 0.27778em;
}
.katex .textstyle > .mclose + .minner,
.katex .textstyle > .minner + .mop,
.katex .textstyle > .minner + .mord,
.katex .textstyle > .mpunct + .mclose,
.katex .textstyle > .mpunct + .minner,
.katex .textstyle > .mpunct + .mop,
.katex .textstyle > .mpunct + .mopen,
.katex .textstyle > .mpunct + .mord,
.katex .textstyle > .mpunct + .mpunct,
.katex .textstyle > .mpunct + .mrel {
  margin-left: 0.16667em;
}
.katex .textstyle > .minner + .mbin {
  margin-left: 0.22222em;
}
.katex .textstyle > .minner + .mrel {
  margin-left: 0.27778em;
}
.katex .mclose + .mop,
.katex .minner + .mop,
.katex .mop + .mop,
.katex .mop + .mord,
.katex .mord + .mop,
.katex .textstyle > .minner + .minner,
.katex .textstyle > .minner + .mopen,
.katex .textstyle > .minner + .mpunct {
  margin-left: 0.16667em;
}
.katex .reset-textstyle.textstyle {
  font-size: 1em;
}
.katex .reset-textstyle.scriptstyle {
  font-size: 0.7em;
}
.katex .reset-textstyle.scriptscriptstyle {
  font-size: 0.5em;
}
.katex .reset-scriptstyle.textstyle {
  font-size: 1.42857em;
}
.katex .reset-scriptstyle.scriptstyle {
  font-size: 1em;
}
.katex .reset-scriptstyle.scriptscriptstyle {
  font-size: 0.71429em;
}
.katex .reset-scriptscriptstyle.textstyle {
  font-size: 2em;
}
.katex .reset-scriptscriptstyle.scriptstyle {
  font-size: 1.4em;
}
.katex .reset-scriptscriptstyle.scriptscriptstyle {
  font-size: 1em;
}
.katex .style-wrap {
  position: relative;
}
.katex .vlist {
  display: inline-block;
}
.katex .vlist > span {
  display: block;
  height: 0;
  position: relative;
}
.katex .vlist > span > span {
  display: inline-block;
}
.katex .vlist .baseline-fix {
  display: inline-table;
  table-layout: fixed;
}
.katex .msupsub {
  text-align: left;
}
.katex .mfrac > span > span {
  text-align: center;
}
.katex .mfrac .frac-line {
  width: 100%;
}
.katex .mfrac .frac-line:before {
  border-bottom-style: solid;
  border-bottom-width: 1px;
  content: "";
  display: block;
}
.katex .mfrac .frac-line:after {
  border-bottom-style: solid;
  border-bottom-width: 0.04em;
  content: "";
  display: block;
  margin-top: -1px;
}
.katex .mspace {
  display: inline-block;
}
.katex .mspace.negativethinspace {
  margin-left: -0.16667em;
}
.katex .mspace.thinspace {
  width: 0.16667em;
}
.katex .mspace.mediumspace {
  width: 0.22222em;
}
.katex .mspace.thickspace {
  width: 0.27778em;
}
.katex .mspace.enspace {
  width: 0.5em;
}
.katex .mspace.quad {
  width: 1em;
}
.katex .mspace.qquad {
  width: 2em;
}
.katex .llap, .katex .rlap {
  width: 0;
  position: relative;
}
.katex .llap > .inner, .katex .rlap > .inner {
  position: absolute;
}
.katex .llap > .fix, .katex .rlap > .fix {
  display: inline-block;
}
.katex .llap > .inner {
  right: 0;
}
.katex .rlap > .inner {
  left: 0;
}
.katex .katex-logo .a {
  font-size: 0.75em;
  margin-left: -0.32em;
  position: relative;
  top: -0.2em;
}
.katex .katex-logo .t {
  margin-left: -0.23em;
}
.katex .katex-logo .e {
  margin-left: -0.1667em;
  position: relative;
  top: 0.2155em;
}
.katex .katex-logo .x {
  margin-left: -0.125em;
}
.katex .rule {
  display: inline-block;
  border-style: solid;
  position: relative;
}
.katex .overline .overline-line {
  width: 100%;
}
.katex .overline .overline-line:before {
  border-bottom-style: solid;
  border-bottom-width: 1px;
  content: "";
  display: block;
}
.katex .overline .overline-line:after {
  border-bottom-style: solid;
  border-bottom-width: 0.04em;
  content: "";
  display: block;
  margin-top: -1px;
}
.katex .sqrt > .sqrt-sign {
  position: relative;
}
.katex .sqrt .sqrt-line {
  width: 100%;
}
.katex .sqrt .sqrt-line:before {
  border-bottom-style: solid;
  border-bottom-width: 1px;
  content: "";
  display: block;
}
.katex .sqrt .sqrt-line:after {
  border-bottom-style: solid;
  border-bottom-width: 0.04em;
  content: "";
  display: block;
  margin-top: -1px;
}
.katex .sqrt > .root {
  margin-left: 0.27777778em;
  margin-right: -0.55555556em;
}
.katex .fontsize-ensurer, .katex .sizing {
  display: inline-block;
}
.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: 1.4em;
}
.katex .fontsize-ensurer.reset-size1.size3, .katex .sizing.reset-size1.size3 {
  font-size: 1.6em;
}
.katex .fontsize-ensurer.reset-size1.size4, .katex .sizing.reset-size1.size4 {
  font-size: 1.8em;
}
.katex .fontsize-ensurer.reset-size1.size5, .katex .sizing.reset-size1.size5 {
  font-size: 2em;
}
.katex .fontsize-ensurer.reset-size1.size6, .katex .sizing.reset-size1.size6 {
  font-size: 2.4em;
}
.katex .fontsize-ensurer.reset-size1.size7, .katex .sizing.reset-size1.size7 {
  font-size: 2.88em;
}
.katex .fontsize-ensurer.reset-size1.size8, .katex .sizing.reset-size1.size8 {
  font-size: 3.46em;
}
.katex .fontsize-ensurer.reset-size1.size9, .katex .sizing.reset-size1.size9 {
  font-size: 4.14em;
}
.katex .fontsize-ensurer.reset-size1.size10, .katex .sizing.reset-size1.size10 {
  font-size: 4.98em;
}
.katex .fontsize-ensurer.reset-size2.size1, .katex .sizing.reset-size2.size1 {
  font-size: 0.71428571em;
}
.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: 1.14285714em;
}
.katex .fontsize-ensurer.reset-size2.size4, .katex .sizing.reset-size2.size4 {
  font-size: 1.28571429em;
}
.katex .fontsize-ensurer.reset-size2.size5, .katex .sizing.reset-size2.size5 {
  font-size: 1.42857143em;
}
.katex .fontsize-ensurer.reset-size2.size6, .katex .sizing.reset-size2.size6 {
  font-size: 1.71428571em;
}
.katex .fontsize-ensurer.reset-size2.size7, .katex .sizing.reset-size2.size7 {
  font-size: 2.05714286em;
}
.katex .fontsize-ensurer.reset-size2.size8, .katex .sizing.reset-size2.size8 {
  font-size: 2.47142857em;
}
.katex .fontsize-ensurer.reset-size2.size9, .katex .sizing.reset-size2.size9 {
  font-size: 2.95714286em;
}
.katex .fontsize-ensurer.reset-size2.size10, .katex .sizing.reset-size2.size10 {
  font-size: 3.55714286em;
}
.katex .fontsize-ensurer.reset-size3.size1, .katex .sizing.reset-size3.size1 {
  font-size: 0.625em;
}
.katex .fontsize-ensurer.reset-size3.size2, .katex .sizing.reset-size3.size2 {
  font-size: 0.875em;
}
.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: 1.125em;
}
.katex .fontsize-ensurer.reset-size3.size5, .katex .sizing.reset-size3.size5 {
  font-size: 1.25em;
}
.katex .fontsize-ensurer.reset-size3.size6, .katex .sizing.reset-size3.size6 {
  font-size: 1.5em;
}
.katex .fontsize-ensurer.reset-size3.size7, .katex .sizing.reset-size3.size7 {
  font-size: 1.8em;
}
.katex .fontsize-ensurer.reset-size3.size8, .katex .sizing.reset-size3.size8 {
  font-size: 2.1625em;
}
.katex .fontsize-ensurer.reset-size3.size9, .katex .sizing.reset-size3.size9 {
  font-size: 2.5875em;
}
.katex .fontsize-ensurer.reset-size3.size10, .katex .sizing.reset-size3.size10 {
  font-size: 3.1125em;
}
.katex .fontsize-ensurer.reset-size4.size1, .katex .sizing.reset-size4.size1 {
  font-size: 0.55555556em;
}
.katex .fontsize-ensurer.reset-size4.size2, .katex .sizing.reset-size4.size2 {
  font-size: 0.77777778em;
}
.katex .fontsize-ensurer.reset-size4.size3, .katex .sizing.reset-size4.size3 {
  font-size: 0.88888889em;
}
.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: 1.11111111em;
}
.katex .fontsize-ensurer.reset-size4.size6, .katex .sizing.reset-size4.size6 {
  font-size: 1.33333333em;
}
.katex .fontsize-ensurer.reset-size4.size7, .katex .sizing.reset-size4.size7 {
  font-size: 1.6em;
}
.katex .fontsize-ensurer.reset-size4.size8, .katex .sizing.reset-size4.size8 {
  font-size: 1.92222222em;
}
.katex .fontsize-ensurer.reset-size4.size9, .katex .sizing.reset-size4.size9 {
  font-size: 2.3em;
}
.katex .fontsize-ensurer.reset-size4.size10, .katex .sizing.reset-size4.size10 {
  font-size: 2.76666667em;
}
.katex .fontsize-ensurer.reset-size5.size1, .katex .sizing.reset-size5.size1 {
  font-size: 0.5em;
}
.katex .fontsize-ensurer.reset-size5.size2, .katex .sizing.reset-size5.size2 {
  font-size: 0.7em;
}
.katex .fontsize-ensurer.reset-size5.size3, .katex .sizing.reset-size5.size3 {
  font-size: 0.8em;
}
.katex .fontsize-ensurer.reset-size5.size4, .katex .sizing.reset-size5.size4 {
  font-size: 0.9em;
}
.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: 1.2em;
}
.katex .fontsize-ensurer.reset-size5.size7, .katex .sizing.reset-size5.size7 {
  font-size: 1.44em;
}
.katex .fontsize-ensurer.reset-size5.size8, .katex .sizing.reset-size5.size8 {
  font-size: 1.73em;
}
.katex .fontsize-ensurer.reset-size5.size9, .katex .sizing.reset-size5.size9 {
  font-size: 2.07em;
}
.katex .fontsize-ensurer.reset-size5.size10, .katex .sizing.reset-size5.size10 {
  font-size: 2.49em;
}
.katex .fontsize-ensurer.reset-size6.size1, .katex .sizing.reset-size6.size1 {
  font-size: 0.41666667em;
}
.katex .fontsize-ensurer.reset-size6.size2, .katex .sizing.reset-size6.size2 {
  font-size: 0.58333333em;
}
.katex .fontsize-ensurer.reset-size6.size3, .katex .sizing.reset-size6.size3 {
  font-size: 0.66666667em;
}
.katex .fontsize-ensurer.reset-size6.size4, .katex .sizing.reset-size6.size4 {
  font-size: 0.75em;
}
.katex .fontsize-ensurer.reset-size6.size5, .katex .sizing.reset-size6.size5 {
  font-size: 0.83333333em;
}
.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: 1.44166667em;
}
.katex .fontsize-ensurer.reset-size6.size9, .katex .sizing.reset-size6.size9 {
  font-size: 1.725em;
}
.katex .fontsize-ensurer.reset-size6.size10, .katex .sizing.reset-size6.size10 {
  font-size: 2.075em;
}
.katex .fontsize-ensurer.reset-size7.size1, .katex .sizing.reset-size7.size1 {
  font-size: 0.34722222em;
}
.katex .fontsize-ensurer.reset-size7.size2, .katex .sizing.reset-size7.size2 {
  font-size: 0.48611111em;
}
.katex .fontsize-ensurer.reset-size7.size3, .katex .sizing.reset-size7.size3 {
  font-size: 0.55555556em;
}
.katex .fontsize-ensurer.reset-size7.size4, .katex .sizing.reset-size7.size4 {
  font-size: 0.625em;
}
.katex .fontsize-ensurer.reset-size7.size5, .katex .sizing.reset-size7.size5 {
  font-size: 0.69444444em;
}
.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: 1.20138889em;
}
.katex .fontsize-ensurer.reset-size7.size9, .katex .sizing.reset-size7.size9 {
  font-size: 1.4375em;
}
.katex .fontsize-ensurer.reset-size7.size10, .katex .sizing.reset-size7.size10 {
  font-size: 1.72916667em;
}
.katex .fontsize-ensurer.reset-size8.size1, .katex .sizing.reset-size8.size1 {
  font-size: 0.28901734em;
}
.katex .fontsize-ensurer.reset-size8.size2, .katex .sizing.reset-size8.size2 {
  font-size: 0.40462428em;
}
.katex .fontsize-ensurer.reset-size8.size3, .katex .sizing.reset-size8.size3 {
  font-size: 0.46242775em;
}
.katex .fontsize-ensurer.reset-size8.size4, .katex .sizing.reset-size8.size4 {
  font-size: 0.52023121em;
}
.katex .fontsize-ensurer.reset-size8.size5, .katex .sizing.reset-size8.size5 {
  font-size: 0.57803468em;
}
.katex .fontsize-ensurer.reset-size8.size6, .katex .sizing.reset-size8.size6 {
  font-size: 0.69364162em;
}
.katex .fontsize-ensurer.reset-size8.size7, .katex .sizing.reset-size8.size7 {
  font-size: 0.83236994em;
}
.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: 1.19653179em;
}
.katex .fontsize-ensurer.reset-size8.size10, .katex .sizing.reset-size8.size10 {
  font-size: 1.43930636em;
}
.katex .fontsize-ensurer.reset-size9.size1, .katex .sizing.reset-size9.size1 {
  font-size: 0.24154589em;
}
.katex .fontsize-ensurer.reset-size9.size2, .katex .sizing.reset-size9.size2 {
  font-size: 0.33816425em;
}
.katex .fontsize-ensurer.reset-size9.size3, .katex .sizing.reset-size9.size3 {
  font-size: 0.38647343em;
}
.katex .fontsize-ensurer.reset-size9.size4, .katex .sizing.reset-size9.size4 {
  font-size: 0.43478261em;
}
.katex .fontsize-ensurer.reset-size9.size5, .katex .sizing.reset-size9.size5 {
  font-size: 0.48309179em;
}
.katex .fontsize-ensurer.reset-size9.size6, .katex .sizing.reset-size9.size6 {
  font-size: 0.57971014em;
}
.katex .fontsize-ensurer.reset-size9.size7, .katex .sizing.reset-size9.size7 {
  font-size: 0.69565217em;
}
.katex .fontsize-ensurer.reset-size9.size8, .katex .sizing.reset-size9.size8 {
  font-size: 0.83574879em;
}
.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: 1.20289855em;
}
.katex .fontsize-ensurer.reset-size10.size1, .katex .sizing.reset-size10.size1 {
  font-size: 0.20080321em;
}
.katex .fontsize-ensurer.reset-size10.size2, .katex .sizing.reset-size10.size2 {
  font-size: 0.2811245em;
}
.katex .fontsize-ensurer.reset-size10.size3, .katex .sizing.reset-size10.size3 {
  font-size: 0.32128514em;
}
.katex .fontsize-ensurer.reset-size10.size4, .katex .sizing.reset-size10.size4 {
  font-size: 0.36144578em;
}
.katex .fontsize-ensurer.reset-size10.size5, .katex .sizing.reset-size10.size5 {
  font-size: 0.40160643em;
}
.katex .fontsize-ensurer.reset-size10.size6, .katex .sizing.reset-size10.size6 {
  font-size: 0.48192771em;
}
.katex .fontsize-ensurer.reset-size10.size7, .katex .sizing.reset-size10.size7 {
  font-size: 0.57831325em;
}
.katex .fontsize-ensurer.reset-size10.size8, .katex .sizing.reset-size10.size8 {
  font-size: 0.69477912em;
}
.katex .fontsize-ensurer.reset-size10.size9, .katex .sizing.reset-size10.size9 {
  font-size: 0.8313253em;
}
.katex .fontsize-ensurer.reset-size10.size10,
.katex .sizing.reset-size10.size10 {
  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 .op-symbol {
  position: relative;
}
.katex .op-symbol.small-op {
  font-family: KaTeX_Size1;
}
.katex .op-symbol.large-op {
  font-family: KaTeX_Size2;
}
.katex .accent > .vlist > span, .katex .op-limits > .vlist > span {
  text-align: center;
}
.katex .accent .accent-body > span {
  width: 0;
}
.katex .accent .accent-body.accent-vec > span {
  position: relative;
  left: 0.326em;
}
.katex .mtable .vertical-separator {
  display: inline-block;
  margin: 0 -0.025em;
  border-right: 0.05em solid #000;
}
.katex .mtable .arraycolsep {
  display: inline-block;
}
.katex .mtable .col-align-c > .vlist {
  text-align: center;
}
.katex .mtable .col-align-l > .vlist {
  text-align: left;
}
.katex .mtable .col-align-r > .vlist {
  text-align: right;
}