@font-face {
  font-family: 'KaTeX_AMS';
  src: url('/fonts/KaTeX_AMS-Regular.woff2') format('woff2');
  font-weight: normal;
  font-style: normal;
  font-display: 'swap';
}
@font-face {
  font-family: 'KaTeX_Caligraphic';
  src: url('/fonts/KaTeX_Caligraphic-Bold.woff2') format('woff2');
  font-weight: bold;
  font-style: normal;
  font-display: 'swap';
}
@font-face {
  font-family: 'KaTeX_Caligraphic';
  src: url('/fonts/KaTeX_Caligraphic-Regular.woff2') format('woff2');
  font-weight: normal;
  font-style: normal;
  font-display: 'swap';
}
@font-face {
  font-family: 'KaTeX_Fraktur';
  src: url('/fonts/KaTeX_Fraktur-Bold.woff2') format('woff2');
  font-weight: bold;
  font-style: normal;
  font-display: 'swap';
}
@font-face {
  font-family: 'KaTeX_Fraktur';
  src: url('/fonts/KaTeX_Fraktur-Regular.woff2') format('woff2');
  font-weight: normal;
  font-style: normal;
  font-display: 'swap';
}
@font-face {
  font-family: 'KaTeX_Main';
  src: url('/fonts/KaTeX_Main-BoldItalic.woff2') format('woff2');
  font-weight: bold;
  font-style: italic;
  font-display: 'swap';
}
@font-face {
  font-family: 'KaTeX_Main';
  src: url('/fonts/KaTeX_Main-Bold.woff2') format('woff2');
  font-weight: bold;
  font-style: normal;
  font-display: 'swap';
}
@font-face {
  font-family: 'KaTeX_Main';
  src: url('/fonts/KaTeX_Main-Italic.woff2') format('woff2');
  font-weight: normal;
  font-style: italic;
  font-display: 'swap';
}
@font-face {
  font-family: 'KaTeX_Main';
  src: url('/fonts/KaTeX_Main-Regular.woff2') format('woff2');
  font-weight: normal;
  font-style: normal;
  font-display: 'swap';
}
@font-face {
  font-family: 'KaTeX_Math';
  src: url('/fonts/KaTeX_Math-BoldItalic.woff2') format('woff2');
  font-weight: bold;
  font-style: italic;
  font-display: 'swap';
}
@font-face {
  font-family: 'KaTeX_Math';
  src: url('/fonts/KaTeX_Math-Italic.woff2') format('woff2');
  font-weight: normal;
  font-style: italic;
  font-display: 'swap';
}
@font-face {
  font-family: 'KaTeX_SansSerif';
  src: url('/fonts/KaTeX_SansSerif-Bold.woff2') format('woff2');
  font-weight: bold;
  font-style: normal;
  font-display: 'swap';
}
@font-face {
  font-family: 'KaTeX_SansSerif';
  src: url('/fonts/KaTeX_SansSerif-Italic.woff2') format('woff2');
  font-weight: normal;
  font-style: italic;
  font-display: 'swap';
}
@font-face {
  font-family: 'KaTeX_SansSerif';
  src: url('/fonts/KaTeX_SansSerif-Regular.woff2') format('woff2');
  font-weight: normal;
  font-style: normal;
  font-display: 'swap';
}
@font-face {
  font-family: 'KaTeX_Script';
  src: url('/fonts/KaTeX_Script-Regular.woff2') format('woff2');
  font-weight: normal;
  font-style: normal;
  font-display: 'swap';
}
@font-face {
  font-family: 'KaTeX_Size1';
  src: url('/fonts/KaTeX_Size1-Regular.woff2') format('woff2');
  font-weight: normal;
  font-style: normal;
  font-display: 'swap';
}
@font-face {
  font-family: 'KaTeX_Size2';
  src: url('/fonts/KaTeX_Size2-Regular.woff2') format('woff2');
  font-weight: normal;
  font-style: normal;
  font-display: 'swap';
}
@font-face {
  font-family: 'KaTeX_Size3';
  src: url('/fonts/KaTeX_Size3-Regular.woff2') format('woff2');
  font-weight: normal;
  font-style: normal;
  font-display: 'swap';
}
@font-face {
  font-family: 'KaTeX_Size4';
  src: url('/fonts/KaTeX_Size4-Regular.woff2') format('woff2');
  font-weight: normal;
  font-style: normal;
  font-display: 'swap';
}
@font-face {
  font-family: 'KaTeX_Typewriter';
  src: url('/fonts/KaTeX_Typewriter-Regular.woff2') format('woff2');
  font-weight: normal;
  font-style: normal;
  font-display: 'swap';
}
:root {
  --ML__static-fonts: true;
}
.ML__container {
  min-height: auto !important;
  --_hue: var(--hue, 212);
  --_placeholder-color: var(--placeholder-color, hsl(var(--_hue), 40%, 49%));
  --_placeholder-opacity: var(--placeholder-opacity, 0.4);
  --_text-font-family: var(--text-font-family, system-ui, -apple-system, BlinkMacSystemFont, 'Segoe UI', 'Roboto', 'Oxygen', 'Ubuntu', 'Cantarell', 'Fira Sans', 'Droid Sans', 'Helvetica Neue', sans-serif);
}
.ML__sr-only {
  position: absolute;
  width: 1px;
  height: 1px;
  margin: -1px;
  padding: 0;
  overflow: hidden;
  clip: rect(0, 0, 0, 0);
  clip-path: inset(50%);
  white-space: nowrap;
  border: 0;
}
.ML__is-inline {
  display: inline-block;
}
.ML__base {
  visibility: inherit;
  display: inline-block;
  position: relative;
  cursor: text;
  padding: 0;
  margin: 0;
  box-sizing: content-box;
  border: 0;
  outline: 0;
  vertical-align: baseline;
  font-weight: inherit;
  font-family: inherit;
  font-style: inherit;
  text-decoration: none;
  width: min-content;
}
.ML__strut,
.ML__strut--bottom {
  display: inline-block;
  min-height: 0.5em;
}
.ML__small-delim {
  font-family: KaTeX_Main;
}
/* Text mode */
.ML__text {
  font-family: var(--_text-font-family);
  white-space: pre;
}
/* Use cmr for 'math upright' */
.ML__cmr {
  font-family: KaTeX_Main;
  font-style: normal;
}
.ML__mathit {
  font-family: KaTeX_Math;
  /* The KaTeX_Math font is italic by default, so the font-style below is only 
     useful when a fallback font is used
  */
  font-style: italic;
}
.ML__mathbf {
  font-family: KaTeX_Main;
  font-weight: bold;
}
/* Lowercase greek symbols should stick to math font when \mathbf is applied 
   to match TeX idiosyncratic behavior */
.lcGreek.ML__mathbf {
  font-family: KaTeX_Math;
  font-weight: normal;
}
.ML__mathbfit {
  font-family: KaTeX_Math;
  font-weight: bold;
  font-style: italic;
}
.ML__ams {
  font-family: KaTeX_AMS;
}
/* Blackboard */
.ML__bb {
  font-family: KaTeX_AMS;
}
.ML__cal {
  font-family: KaTeX_Caligraphic;
}
.ML__frak {
  font-family: KaTeX_Fraktur;
}
.ML__tt {
  font-family: KaTeX_Typewriter;
}
.ML__script {
  font-family: KaTeX_Script;
}
.ML__sans {
  font-family: KaTeX_SansSerif;
}
.ML__series_ul {
  font-weight: 100;
}
.ML__series_el {
  font-weight: 100;
}
.ML__series_l {
  font-weight: 200;
}
.ML__series_sl {
  font-weight: 300;
}
.ML__series_sb {
  font-weight: 500;
}
.ML__bold,
.ML__boldsymbol {
  font-weight: 700;
}
.ML__series_eb {
  font-weight: 800;
}
.ML__series_ub {
  font-weight: 900;
}
.ML__series_uc {
  font-stretch: ultra-condensed;
}
.ML__series_ec {
  font-stretch: extra-condensed;
}
.ML__series_c {
  font-stretch: condensed;
}
.ML__series_sc {
  font-stretch: semi-condensed;
}
.ML__series_sx {
  font-stretch: semi-expanded;
}
.ML__series_x {
  font-stretch: expanded;
}
.ML__series_ex {
  font-stretch: extra-expanded;
}
.ML__series_ux {
  font-stretch: ultra-expanded;
}
.ML__it {
  font-style: italic;
}
.ML__shape_ol {
  -webkit-text-stroke: 1px black;
  text-stroke: 1px black;
  color: transparent;
}
.ML__shape_sc {
  font-variant: small-caps;
}
.ML__shape_sl {
  font-style: oblique;
}
/* First level emphasis */
.ML__emph {
  color: #bc2612;
}
/* Second level emphasis */
.ML__emph .ML__emph {
  color: #0c7f99;
}
.ML__highlight {
  color: #007cb2;
  background: #edd1b0;
}
.ML__center {
  text-align: center;
}
.ML__left {
  text-align: left;
}
.ML__right {
  text-align: right;
}
.ML__label_padding {
  padding: 0 0.5em;
}
.ML__frac-line {
  width: 100%;
  min-height: 1px;
}
.ML__frac-line:after {
  content: '';
  display: block;
  margin-top: max(-1px, -0.04em);
  min-height: max(1px, 0.04em);
  /* Ensure the line is visible when printing even if "turn off background images" is on*/
  -webkit-print-color-adjust: exact;
  print-color-adjust: exact;
  /* There's a bug since Chrome 62 where 
      sub-pixel border lines don't draw at some zoom 
      levels (110%, 90%). 
      Setting the min-height used to work around it, but that workaround
      broke in Chrome 84 or so.
      Setting the background (and the min-height) seems to work for now.
      */
  background: currentColor;
  box-sizing: content-box;
  /* Vuetify sets the box-sizing to inherit 
            causes the fraction line to not draw at all sizes (see #26) */
  /* On some versions of Firefox on Windows, the line fails to 
            draw at some zoom levels, but setting the transform triggers
            the hardware accelerated path, which works */
  transform: translate(0, 0);
}
.ML__sqrt {
  display: inline-block;
}
.ML__sqrt-sign {
  display: inline-block;
  position: relative;
}
.ML__sqrt-line {
  display: inline-block;
  height: max(1px, 0.04em);
  width: 100%;
}
.ML__sqrt-line:before {
  content: '';
  display: block;
  margin-top: min(-1px, -0.04em);
  min-height: max(1px, 0.04em);
  /* Ensure the line is visible when printing even if "turn off background images" is on*/
  -webkit-print-color-adjust: exact;
  print-color-adjust: exact;
  background: currentColor;
  /* On some versions of Firefox on Windows, the line fails to 
            draw at some zoom levels, but setting the transform triggers
            the hardware accelerated path, which works */
  transform: translate(0, 0);
}
.ML__sqrt-line:after {
  border-bottom-width: 1px;
  content: ' ';
  display: block;
  margin-top: -0.1em;
}
.ML__sqrt-index {
  margin-left: 0.27777778em;
  margin-right: -0.55555556em;
}
.ML__delim-size1 {
  font-family: KaTeX_Size1;
}
.ML__delim-size2 {
  font-family: KaTeX_Size2;
}
.ML__delim-size3 {
  font-family: KaTeX_Size3;
}
.ML__delim-size4 {
  font-family: KaTeX_Size4;
}
.ML__delim-mult .delim-size1 > span {
  font-family: KaTeX_Size1;
}
.ML__delim-mult .delim-size4 > span {
  font-family: KaTeX_Size4;
}
.ML__accent-body > span {
  font-family: KaTeX_Main;
  width: 0;
}
.ML__accent-vec {
  position: relative;
  left: 0.24em;
}
/** The markup for a LaTeX formula, either in an editable mathfield or 
    in a static display.
*/
.ML__latex {
  display: inline-block;
  direction: ltr;
  text-align: left;
  text-indent: 0;
  text-rendering: auto;
  font-family: KaTeX_Main, 'Times New Roman', serif;
  font-style: normal;
  font-size-adjust: none;
  font-stretch: normal;
  font-variant-caps: normal;
  letter-spacing: normal;
  line-height: 1.2;
  word-wrap: normal;
  word-spacing: normal;
  white-space: nowrap;
  text-shadow: none;
  -webkit-user-select: none;
  user-select: none;
  width: min-content;
}
.ML__latex .style-wrap {
  position: relative;
}
.ML__latex .ML__mfrac {
  display: inline-block;
}
.ML__latex .ML__left-right {
  display: inline-block;
}
.ML__latex .ML__vlist-t {
  display: inline-table;
  table-layout: fixed;
  border-collapse: collapse;
}
.ML__latex .ML__vlist-r {
  display: table-row;
}
.ML__latex .ML__vlist {
  display: table-cell;
  vertical-align: bottom;
  position: relative;
}
.ML__latex .ML__vlist > span {
  display: block;
  height: 0;
  position: relative;
}
.ML__latex .ML__vlist > span > span {
  display: inline-block;
}
.ML__latex .ML__vlist > span > .ML__pstrut {
  overflow: hidden;
  width: 0;
}
.ML__latex .ML__vlist-t2 {
  margin-right: -2px;
}
.ML__latex .ML__vlist-s {
  display: table-cell;
  vertical-align: bottom;
  font-size: 1px;
  width: 2px;
  min-width: 2px;
}
.ML__latex .ML__msubsup {
  text-align: left;
}
.ML__latex .ML__negativethinspace {
  display: inline-block;
  margin-left: -0.16667em;
  height: 0.71em;
}
.ML__latex .ML__thinspace {
  display: inline-block;
  width: 0.16667em;
  height: 0.71em;
}
.ML__latex .ML__mediumspace {
  display: inline-block;
  width: 0.22222em;
  height: 0.71em;
}
.ML__latex .ML__thickspace {
  display: inline-block;
  width: 0.27778em;
  height: 0.71em;
}
.ML__latex .ML__enspace {
  display: inline-block;
  width: 0.5em;
  height: 0.71em;
}
.ML__latex .ML__quad {
  display: inline-block;
  width: 1em;
  height: 0.71em;
}
.ML__latex .ML__qquad {
  display: inline-block;
  width: 2em;
  height: 0.71em;
}
.ML__latex .ML__llap,
.ML__latex .ML__rlap {
  width: 0;
  position: relative;
  display: inline-block;
}
.ML__latex .ML__llap > .ML__inner,
.ML__latex .ML__rlap > .ML__inner {
  position: absolute;
}
.ML__latex .ML__llap > .ML__fix,
.ML__latex .ML__rlap > .ML__fix {
  display: inline-block;
}
.ML__latex .ML__llap > .ML__inner {
  right: 0;
}
.ML__latex .ML__rlap > .ML__inner {
  left: 0;
}
.ML__latex .ML__rule {
  display: inline-block;
  border: solid 0;
  position: relative;
  box-sizing: border-box;
}
.ML__latex .overline .overline-line,
.ML__latex .underline .underline-line {
  width: 100%;
}
.ML__latex .overline .overline-line:before,
.ML__latex .underline .underline-line:before {
  content: '';
  border-bottom-style: solid;
  border-bottom-width: max(1px, 0.04em);
  -webkit-print-color-adjust: exact;
  print-color-adjust: exact;
  display: block;
}
.ML__latex .overline .overline-line:after,
.ML__latex .underline .underline-line:after {
  border-bottom-style: solid;
  border-bottom-width: max(1px, 0.04em);
  -webkit-print-color-adjust: exact;
  print-color-adjust: exact;
  content: '';
  display: block;
  margin-top: -1px;
}
.ML__latex .ML__stretchy {
  display: block;
  position: absolute;
  width: 100%;
  left: 0;
  overflow: hidden;
}
.ML__latex .ML__stretchy:before,
.ML__latex .ML__stretchy:after {
  content: '';
}
.ML__latex .ML__stretchy 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;
}
.ML__latex .slice-1-of-2 {
  display: inline-flex;
  position: absolute;
  left: 0;
  width: 50.2%;
  overflow: hidden;
}
.ML__latex .slice-2-of-2 {
  display: inline-flex;
  position: absolute;
  right: 0;
  width: 50.2%;
  overflow: hidden;
}
.ML__latex .slice-1-of-3 {
  display: inline-flex;
  position: absolute;
  left: 0;
  width: 25.1%;
  overflow: hidden;
}
.ML__latex .slice-2-of-3 {
  display: inline-flex;
  position: absolute;
  left: 25%;
  width: 50%;
  overflow: hidden;
}
.ML__latex .slice-3-of-3 {
  display: inline-flex;
  position: absolute;
  right: 0;
  width: 25.1%;
  overflow: hidden;
}
.ML__latex .slice-1-of-1 {
  display: inline-flex;
  position: absolute;
  width: 100%;
  left: 0;
  overflow: hidden;
}
.ML__latex .ML__nulldelimiter {
  display: inline-block;
}
.ML__latex .ML__op-group {
  display: inline-block;
}
.ML__latex .ML__op-symbol {
  position: relative;
}
.ML__latex .ML__op-symbol.ML__small-op {
  font-family: KaTeX_Size1;
}
.ML__latex .ML__op-symbol.ML__large-op {
  font-family: KaTeX_Size2;
}
.ML__latex .ML__mtable .ML__vertical-separator {
  display: inline-block;
  min-width: 1px;
  box-sizing: border-box;
}
.ML__latex .ML__mtable .ML__arraycolsep {
  display: inline-block;
}
.ML__latex .ML__mtable .col-align-m > .ML__vlist-t {
  text-align: center;
}
.ML__latex .ML__mtable .col-align-c > .ML__vlist-t {
  text-align: center;
}
.ML__latex .ML__mtable .col-align-l > .ML__vlist-t {
  text-align: left;
}
.ML__latex .ML__mtable .col-align-r > .ML__vlist-t {
  text-align: right;
}
.ML__error {
  display: inline-block;
  background-image: radial-gradient(ellipse at center, hsl(341, 100%, 40%), rgba(0, 0, 0, 0) 70%);
  background-color: hsla(341, 100%, 40%, 0.1);
  background-repeat: repeat-x;
  background-size: 3px 3px;
  padding-bottom: 3px;
  background-position: 0 100%;
}
.ML__error > .ML__error {
  background: transparent;
  padding: 0;
}
.ML__placeholder {
  color: var(--_placeholder-color);
  opacity: var(--_placeholder-opacity);
  padding-left: 0.4ex;
  padding-right: 0.4ex;
  font-family: system-ui, -apple-system, BlinkMacSystemFont, 'Segoe UI', 'Roboto', 'Oxygen', 'Ubuntu', 'Cantarell', 'Fira Sans', 'Droid Sans', 'Helvetica Neue', sans-serif;
}
.ML__notation {
  position: absolute;
  box-sizing: border-box;
  line-height: 0;
}
/* This class is used to implement the `\mathtip` and `\texttip` commands
   For UI elements, see `[data-ML__tooltip]`
*/
.ML__tooltip-container {
  position: relative;
  transform: scale(0);
}
.ML__tooltip-container .ML__tooltip-content {
  position: fixed;
  display: inline-table;
  visibility: hidden;
  z-index: 2;
  width: max-content;
  max-width: 400px;
  padding: 12px 12px;
  border-radius: 8px;
  background: #616161;
  --_selection-color: #fff;
  color: #fff;
  box-shadow: 0 2px 2px 0 rgba(0, 0, 0, 0.14), 0 1px 5px 0 rgba(0, 0, 0, 0.12), 0 3px 1px -2px rgba(0, 0, 0, 0.2);
  opacity: 0;
  transition: opacity 0.15s cubic-bezier(0.4, 0, 1, 1);
}
.ML__tooltip-container .ML__tooltip-content .ML__text {
  white-space: normal;
}
.ML__tooltip-container .ML__tooltip-content .ML__base {
  display: contents;
}
.ML__tooltip-container:hover .ML__tooltip-content {
  visibility: visible;
  opacity: 1;
  font-size: 0.75em;
  transform: scale(1) translate(0, 3em);
}