File "mathlive.min-1.js"

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/** MathLive 0.95.4 */
    (function(global,factory){typeof exports === 'object' && typeof module !== 'undefined' ? factory(exports) : typeof define === 'function' && define.amd ? define(['exports'],factory):(global = typeof globalThis !== 'undefined' ? globalThis : global || self, factory(global.MathLive = {}));})(this, (function (exports) { 'use strict';
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this.atomIdsSettings.seed+=1,t}scale(t){return t*this.effectiveFontSize}get scalingFactor(){return this.parent?this.effectiveFontSize/this.parent.effectiveFontSize:1}get isDisplayStyle(){return this.mathstyle.id===Jn||this.mathstyle.id===ho}get isCramped(){return this.mathstyle.cramped}get isTight(){return this.mathstyle.isTight}get metrics(){return this.mathstyle.metrics}get effectiveFontSize(){return Math.max(uo[Math.max(1,this.size+this.mathstyle.sizeDelta)],this.minFontScale)}getRegister(t){var r;if((r=this.registers)!=null&&r[t])return this.registers[t];if(this.parent)return this.parent.getRegister(t)}getRegisterAsNumber(t){let r=this.getRegister(t);if(typeof r=="number")return r;if(typeof r=="string")return Number(r)}getRegisterAsGlue(t){var r;if((r=this.registers)!=null&&r[t]){let i=this.registers[t];return typeof i=="object"&&"glue"in i?i:typeof i=="object"&&"dimension"in i?{glue:{dimension:i.dimension}}:typeof i=="number"?{glue:{dimension:i}}:void 0}if(this.parent)return this.parent.getRegisterAsGlue(t)}getRegisterAsEm(t,r){return Gn(this.getRegisterAsDimension(t),r)}getRegisterAsDimension(t){var r;if((r=this.registers)!=null&&r[t]){let i=this.registers[t];return typeof i=="object"&&"glue"in i?i.glue:typeof i=="object"&&"dimension"in i?i:typeof i=="number"?{dimension:i}:void 0}if(this.parent)return this.parent.getRegisterAsDimension(t)}setRegister(t,r){if(r===void 0){delete this.registers[t];return}this.registers[t]=r}evaluate(t){if(!t||!("register"in t))return t;let r=this;if("global"in t&&t.global)for(;r.parent;)r=r.parent;let i=1;"factor"in t&&t.factor!==1&&t.factor!==void 0&&(i=t.factor);let o=r.getRegister(t.register);if(o===void 0)return;if(typeof o=="string")return{string:Number(o).toString()+o};if(typeof o=="number")return{number:i*o};let n=r.evaluate(o);if(n!==void 0)return"string"in n?{string:Number(o).toString()+n.string}:"number"in n?{number:i*n.number}:"dimension"in n?g(m({},n),{dimension:i*n.dimension}):"glue"in n?g(m({},n),{glue:g(m({},n.glue),{dimension:i*n.glue.dimension}),shrink:n.shrink?g(m({},n.shrink),{dimension:i*n.shrink.dimension}):void 0,grow:n.grow?g(m({},n.grow),{dimension:i*n.grow.dimension}):void 0}):t}toDimension(t){let r=this.evaluate(t);return r===void 0?null:"dimension"in r?r:"glue"in r?r.glue:"number"in r?{dimension:r.number}:null}toEm(t,r){if(t===null)return 0;let i=this.toDimension(t);return i===null?0:Bs(i,r)/ht}toNumber(t){if(t===null)return null;let r=this.evaluate(t);return r===void 0?null:"number"in r?r.number:"dimension"in r?r.dimension:"glue"in r?r.glue.dimension:"string"in r?Number(r.string):null}toColor(t){var i,o;if(t===null)return null;let r=this.evaluate(t);return r===void 0?null:"string"in r?(o=(i=this.colorMap)==null?void 0:i.call(this,r.string))!=null?o:r.string:null}toBackgroundColor(t){var i,o;if(t===null)return null;let r=this.evaluate(t);return r===void 0?null:"string"in r?(o=(i=this.backgroundColorMap)==null?void 0:i.call(this,r.string))!=null?o:r.string:null}};var nr=["body","above","below","superscript","subscript"];function or(e){return typeof e=="string"&&nr.includes(e)}function yo(e){return e!==void 0&&Array.isArray(e)&&e.length===2}var y=class e{constructor(t){this.subsupPlacement=void 0;this.explicitSubsupPlacement=!1;var r,i,o,n,a,s,l,c,u;this.type=t.type,typeof t.value=="string"&&(this.value=t.value),this.command=(i=(r=t.command)!=null?r:this.value)!=null?i:"",this.mode=(o=t.mode)!=null?o:"math",this.isFunction=(n=t.isFunction)!=null?n:!1,this.subsupPlacement=t.limits,this.style=(a=m({},t.style))!=null?a:{},this.displayContainsHighlight=(s=t.displayContainsHighlight)!=null?s:!1,this.captureSelection=(l=t.captureSelection)!=null?l:!1,this.skipBoundary=(c=t.skipBoundary)!=null?c:!1,this.verbatimLatex=(u=t.verbatimLatex)!=null?u:void 0,t.args&&(this.args=t.args),t.body&&(this.body=t.body),this._changeCounter=0}static createBox(t,r,i){var s;if(!r)return null;let o=rp(r),n=[];for(let l of 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0&&(t.verbatimLatex=this.verbatimLatex),this.subsupPlacement&&(t.subsupPlacement=this.subsupPlacement),this.explicitSubsupPlacement&&(t.explicitSubsupPlacement=!0),this.isFunction&&(t.isFunction=!0),this.displayContainsHighlight&&(t.displayContainsHighlight=!0),this.isExtensibleSymbol&&(t.isExtensibleSymbol=!0),this.skipBoundary&&(t.skipBoundary=!0),this.captureSelection&&(t.captureSelection=!0),this.args&&(t.args=op(this.args)),this._branches)for(let r of Object.keys(this._branches))this._branches[r]&&(t[r]=this._branches[r].filter(i=>i.type!=="first").map(i=>i.toJson()));return t.type==="mord"&&Object.keys(t).length===2&&"value"in t?t.value:t}get changeCounter(){return this.parent?this.parent.changeCounter:this._changeCounter}set isDirty(t){if(t){this.parent||this._changeCounter++,"verbatimLatex"in this&&(this.verbatimLatex=void 0),this._children=void 0;let{parent:r}=this;for(;r;)r.parent||r._changeCounter++,"verbatimLatex"in r&&(r.verbatimLatex=void 0),r._children=void 0,r=r.parent}}_serialize(t){var i;if(!(t.expandMacro||t.skipStyles)&&typeof this.verbatimLatex=="string")return this.verbatimLatex;let r=ee(this.command,this.mode);return r!=null&&r.serialize?r.serialize(this,t):this.body&&this.command?B([O(this.command,this.bodyToLatex(t)),this.supsubToLatex(t)]):this.body?B([this.bodyToLatex(t),this.supsubToLatex(t)]):!this.value||this.value==="\u200B"?"":(i=this.command)!=null?i:Hl(this.mode,this.value)}bodyToLatex(t){var r;return se.serialize(this.body,g(m({},t),{defaultMode:(r=t.defaultMode)!=null?r:this.latexMode}))}aboveToLatex(t){return se.serialize(this.above,t)}belowToLatex(t){return se.serialize(this.below,t)}supsubToLatex(t){let r="";if(t=g(m({},t),{defaultMode:"math"}),this.branch("subscript")!==void 0){let i=se.serialize(this.subscript,t);i.length===0?r+="_{}":i.length===1?/^[0-9]$/.test(i)?r+=`_${i}`:r+=`_{${i}}`:r+=`_{${i}}`}if(this.branch("superscript")!==void 0){let 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r?(r.length>0,r[0].type,r.length===1):!0}setChildren(t,r){var o;if(!t||(or(r),!or(r)))return;(o=t[0])==null||o.type;let i=[this.makeFirstAtom(r),...t];this._branches?this._branches[r]=i:this._branches={[r]:i};for(let n of t)n.parent=this,n.parentBranch=r;this.isDirty=!0}makeFirstAtom(t){let r=new e({type:"first",mode:this.mode});return r.parent=this,r.parentBranch=t,r}addChild(t,r){t.type,this.createBranch(r).push(t),this.isDirty=!0,t.parent=this,t.parentBranch=r}addChildBefore(t,r){r.parentBranch;let i=this.createBranch(r.parentBranch);i.splice(i.indexOf(r),0,t),this.isDirty=!0,t.parent=this,t.parentBranch=r.parentBranch}addChildAfter(t,r){r.parentBranch;let i=this.createBranch(r.parentBranch);i.splice(i.indexOf(r)+1,0,t),this.isDirty=!0,t.parent=this,t.parentBranch=r.parentBranch}addChildren(t,r){let i=this.createBranch(r);for(let o of t)o.parent=this,o.parentBranch=r,i.push(o);this.isDirty=!0}addChildrenAfter(t,r){t.length===0||t[0].type,r.parentBranch;let 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a=null,s=null,l=(f=r.isCharacterBox)!=null?f:this.isCharacterBox(),c=0;if(o){let x=new P({parent:t,mathstyle:"superscript"});a=e.createBox(x,o),l||(c=i.height-t.metrics.supDrop*x.scalingFactor)}let u=0;if(n){let x=new P({parent:t,mathstyle:"subscript"});s=e.createBox(x,n),l||(u=i.depth+t.metrics.subDrop*x.scalingFactor)}let d;t.isDisplayStyle?d=t.metrics.sup1:t.isCramped?d=t.metrics.sup3:d=t.metrics.sup2;let p=.5/ht/t.scalingFactor,h=null;if(s&&a){c=Math.max(c,d,a.depth+.25*t.metrics.xHeight),u=Math.max(u,t.metrics.sub2);let x=t.metrics.defaultRuleThickness;if(c-a.depth-(s.height-u)<4*x){u=4*x-(c-a.depth)+s.height;let v=.8*t.metrics.xHeight-(c-a.depth);v>0&&(c+=v,u-=v)}let M=this.isExtensibleSymbol&&i.italic?-i.italic:0;h=new W({individualShift:[{box:s,shift:u,marginLeft:M},{box:a,shift:-c}]}).wrap(t)}else s&&!a?(u=Math.max(u,t.metrics.sub1,s.height-.8*pt),h=new 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i=="string"||i===void 0?new k(i!=null?i:null,{type:o,isSelected:this.isSelected,mode:this.mode,maxFontSize:t.scalingFactor,style:g(m({variant:"normal"},this.style),{fontSize:Math.max(1,t.size+t.mathstyle.sizeDelta)}),letterShapeStyle:t.letterShapeStyle,classes:n}):(u=e.createBox(t,i,{type:o,classes:n}))!=null?u:new k(null);return t.isTight&&(a.isTight=!0),(this.mode!=="math"||this.style.variant==="main")&&(a.italic=0),a.right=a.italic,this.bind(t,a),this.caret&&!this.superscript&&!this.subscript&&(a.caret=this.caret),a}isDigit(){var t;return this.type==="mord"&&this.value?/^[\d,\.]$/.test(this.value):this.type==="group"&&((t=this.body)==null?void 0:t.length)===2?this.body[0].type==="first"&&this.body[1].value===",":!1}asDigit(){var t;return this.type==="mord"&&this.value&&/^[\d,\.]$/.test(this.value)?this.value:this.type==="group"&&((t=this.body)==null?void 0:t.length)===2&&this.body[0].type==="first"&&this.body[1].value===","?".":""}};function rp(e){let t,r=[],i=[];for(let o of e)if(!t&&!o.style)i.push(o);else{let n=o.computedStyle;t&&n.color===t.color&&n.backgroundColor===t.backgroundColor&&n.fontSize===t.fontSize?i.push(o):(i.length>0&&r.push(i),i=[o],t=n)}return i.length>0&&r.push(i),r}function ip(e,t,r){var s,l,c,u,d;if(!t||t.length===0)return null;let i=new P({parent:e},r.style),o=!((s=i.atomIdsSettings)!=null&&s.groupNumbers),n=[];if(t.length===1){let p=t[0],h=p.render(i);h&&(o&&p.isSelected&&h.selected(!0),n=[h])}else{let p="",h=!0;for(let f of t){(l=i.atomIdsSettings)!=null&&l.groupNumbers&&p&&(h&&f.isDigit()||!h&&Ds(f))&&(i.atomIdsSettings.overrideID=p);let x=f.render(i);i.atomIdsSettings&&(i.atomIdsSettings.overrideID=void 0),x&&((c=i.atomIdsSettings)!=null&&c.groupNumbers&&((f.isDigit()||Ds(f))&&(!p||h!==f.isDigit())&&(h=f.isDigit(),p=(u=f.id)!=null?u:""),p&&(!(f.isDigit()||Ds(f))||!f.hasEmptyBranch("superscript")||!f.hasEmptyBranch("subscript"))&&(p="")),o&&f.isSelected&&x.selected(!0),n.push(x))}}if(n.length===0)return null;let a=new 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  100% {
    opacity: 1;
  }
  50% {
    opacity: 0;
  }
}
.ML__container {
  display: inline-flex;
  flex-flow: row;
  justify-content: space-between;
  align-items: flex-end;
  min-height: 39px;
  /* Need some room for the virtual keyboard toggle */
  width: 100%;
  /* Encourage browsers to consider allocating a hardware accelerated
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  isolation: isolate;
  /* Prevent the browser from trying to interpret touch gestures in the field */
  /* "Disabling double-tap to zoom removes the need for browsers to
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  touch-action: none;
  --_caret-color: var(--caret-color, hsl(var(--_hue), 40%, 49%));
  --_selection-color: var(--selection-color, #000);
  --_selection-background-color: var(--selection-background-color, hsl(var(--_hue), 70%, 85%));
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  --_correct-color: var(--correct-color, #10a000);
  --_incorrect-color: var(--incorrect-color, #a01b00);
  --_composition-background-color: var(--composition-background-color, #fff1c2);
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}
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.ML__content {
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  align-self: center;
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}
.ML__virtual-keyboard-toggle {
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  display: flex;
  align-self: center;
  align-items: center;
  flex-shrink: 0;
  flex-direction: column;
  justify-content: center;
  width: 34px;
  height: 34px;
  padding: 0;
  margin-right: 4px;
  cursor: pointer;
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  border: 1px solid transparent;
  transition: background 0.2s cubic-bezier(0.64, 0.09, 0.08, 1);
  color: hsl(var(--_hue), 40%, 50%);
  fill: currentColor;
  background: transparent;
}
.ML__virtual-keyboard-toggle:hover {
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  color: #333;
  fill: currentColor;
}
.ML__virtual-keyboard-toggle > span {
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}
/* The invisible element used to capture keyboard events. We're just trying
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  font-size: 1em;
  font-family: KaTeX_Main;
}
.ML__composition {
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}
.ML__caret:after {
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  position: relative;
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  animation: ML__caret-blink 1.05s step-end forwards infinite;
}
.ML__text-caret:after {
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  border: none;
  border-radius: 1px;
  border-right: 1px solid var(--_caret-color);
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  animation: ML__caret-blink 1.05s step-end forwards infinite;
}
.ML__latex-caret:after {
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  margin-right: 0;
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}
.ML__focused .ML__text {
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}
/* When using smartFence, the anticipated closing fence is displayed
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.ML__smart-fence__close {
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}
.ML__selected,
.ML__focused .ML__selected .ML__contains-caret,
.ML__focused .ML__selected .ML__smart-fence__close,
.ML__focused .ML__selected .ML__placeholder {
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  opacity: 1;
}
:host(:focus) .ML__selection {
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}
.ML__contains-caret.ML__close,
.ML__contains-caret.ML__open,
.ML__contains-caret > .ML__close,
.ML__contains-caret > .ML__open,
.ML__contains-caret .ML__sqrt-sign,
.ML__contains-caret .ML__sqrt-line {
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}
.ML__contains-highlight {
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.ML__latex {
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  color: var(--_latex-color);
}
.ML__suggestion {
  opacity: 0.5;
}
.ML__virtual-keyboard-toggle.is-visible.is-pressed:hover {
  background: hsl(var(--_hue), 25%, 35%);
  color: #fafafa;
  fill: currentColor;
}
.ML__virtual-keyboard-toggle:focus {
  outline: none;
  border-radius: 8px;
  border: 2px solid hsl(var(--_hue), 40%, 50%);
}
.ML__virtual-keyboard-toggle.is-pressed,
.ML__virtual-keyboard-toggle.is-active:hover,
.ML__virtual-keyboard-toggle.is-active {
  background: hsl(var(--_hue), 25%, 35%);
  color: #fafafa;
  fill: currentColor;
}
/* Add an attribute 'data-ML__tooltip' to automatically show a
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   Use 'data-delay' to delay the triggering of the tooltip.
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[data-ML__tooltip] {
  position: relative;
}
[data-ML__tooltip][data-placement='top']::after {
  top: inherit;
  bottom: 100%;
}
[data-ML__tooltip]::after {
  content: attr(data-ML__tooltip);
  position: absolute;
  display: none;
  z-index: 2;
  right: 110%;
  left: calc(100% + 8px);
  width: max-content;
  max-width: 200px;
  padding: 8px 8px;
  border-radius: 2px;
  background: #616161;
  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);
  text-align: center;
  font-family: system-ui, -apple-system, BlinkMacSystemFont, 'Segoe UI', 'Roboto', 'Oxygen', 'Ubuntu', 'Cantarell', 'Fira Sans', 'Droid Sans', 'Helvetica Neue', sans-serif;
  font-style: normal;
  font-weight: 400;
  font-size: 12px;
  /* Phone */
  opacity: 0;
  transform: scale(0.5);
  transition: all 0.15s cubic-bezier(0.4, 0, 1, 1);
}
@media only screen and (max-width: 767px) {
  [data-ML__tooltip]::after {
    padding: 8px 16px;
    font-size: 16px;
  }
}
:not(.tracking) [data-ML__tooltip]:hover {
  position: relative;
}
:not(.tracking) [data-ML__tooltip]:hover::after {
  visibility: visible;
  display: inline-table;
  opacity: 1;
  transform: scale(1);
}
[data-ML__tooltip][data-delay]::after {
  transition-delay: 0s;
}
[data-ML__tooltip][data-delay]:hover::after {
  transition-delay: 1s;
  /* attr(data-delay); Should work. But doesn't. */
}
.ML__prompt {
  border-radius: 2px;
}
.ML__editablePromptBox {
  outline: 1px solid #acacac;
  border-radius: 2px;
  z-index: -1;
}
.ML__focusedPromptBox {
  outline: highlight auto 1px;
}
.ML__lockedPromptBox {
  background-color: rgba(142, 142, 141, 0.4);
  z-index: -1;
}
.ML__correctPromptBox {
  outline: 1px solid var(--_correct-color);
  box-shadow: 0 0 5px var(--_correct-color);
}
.ML__incorrectPromptBox {
  outline: 1px solid var(--_incorrect-color);
  box-shadow: 0 0 5px var(--_incorrect-color);
}
`;var Yd=`.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 
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.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__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;
}
.ML__mathlive {
  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__mathlive .style-wrap {
  position: relative;
}
.ML__mathlive .mfrac,
.ML__mathlive .left-right {
  display: inline-block;
}
.ML__mathlive .vlist-t {
  display: inline-table;
  table-layout: fixed;
  border-collapse: collapse;
}
.ML__mathlive .vlist-r {
  display: table-row;
}
.ML__mathlive .vlist {
  display: table-cell;
  vertical-align: bottom;
  position: relative;
}
.ML__mathlive .vlist > span {
  display: block;
  height: 0;
  position: relative;
}
.ML__mathlive .vlist > span > span {
  display: inline-block;
}
.ML__mathlive .vlist > span > .pstrut {
  overflow: hidden;
  width: 0;
}
.ML__mathlive .vlist-t2 {
  margin-right: -2px;
}
.ML__mathlive .vlist-s {
  display: table-cell;
  vertical-align: bottom;
  font-size: 1px;
  width: 2px;
  min-width: 2px;
}
.ML__mathlive .msubsup {
  text-align: left;
}
.ML__mathlive .negativethinspace {
  display: inline-block;
  margin-left: -0.16667em;
  height: 0.71em;
}
.ML__mathlive .thinspace {
  display: inline-block;
  width: 0.16667em;
  height: 0.71em;
}
.ML__mathlive .mediumspace {
  display: inline-block;
  width: 0.22222em;
  height: 0.71em;
}
.ML__mathlive .thickspace {
  display: inline-block;
  width: 0.27778em;
  height: 0.71em;
}
.ML__mathlive .enspace {
  display: inline-block;
  width: 0.5em;
  height: 0.71em;
}
.ML__mathlive .quad {
  display: inline-block;
  width: 1em;
  height: 0.71em;
}
.ML__mathlive .qquad {
  display: inline-block;
  width: 2em;
  height: 0.71em;
}
.ML__mathlive .llap,
.ML__mathlive .rlap {
  width: 0;
  position: relative;
  display: inline-block;
}
.ML__mathlive .llap > .inner,
.ML__mathlive .rlap > .inner {
  position: absolute;
}
.ML__mathlive .llap > .fix,
.ML__mathlive .rlap > .fix {
  display: inline-block;
}
.ML__mathlive .llap > .inner {
  right: 0;
}
.ML__mathlive .rlap > .inner {
  left: 0;
}
.ML__mathlive .rule {
  display: inline-block;
  border: solid 0;
  position: relative;
  box-sizing: border-box;
}
.ML__mathlive .overline .overline-line,
.ML__mathlive .underline .underline-line {
  width: 100%;
}
.ML__mathlive .overline .overline-line:before,
.ML__mathlive .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__mathlive .overline .overline-line:after,
.ML__mathlive .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__mathlive .stretchy {
  display: block;
  position: absolute;
  width: 100%;
  left: 0;
  overflow: hidden;
}
.ML__mathlive .stretchy:before,
.ML__mathlive .stretchy:after {
  content: '';
}
.ML__mathlive .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__mathlive .slice-1-of-2 {
  display: inline-flex;
  position: absolute;
  left: 0;
  width: 50.2%;
  overflow: hidden;
}
.ML__mathlive .slice-2-of-2 {
  display: inline-flex;
  position: absolute;
  right: 0;
  width: 50.2%;
  overflow: hidden;
}
.ML__mathlive .slice-1-of-3 {
  display: inline-flex;
  position: absolute;
  left: 0;
  width: 25.1%;
  overflow: hidden;
}
.ML__mathlive .slice-2-of-3 {
  display: inline-flex;
  position: absolute;
  left: 25%;
  width: 50%;
  overflow: hidden;
}
.ML__mathlive .slice-3-of-3 {
  display: inline-flex;
  position: absolute;
  right: 0;
  width: 25.1%;
  overflow: hidden;
}
.ML__mathlive .slice-1-of-1 {
  display: inline-flex;
  position: absolute;
  width: 100%;
  left: 0;
  overflow: hidden;
}
.ML__mathlive .nulldelimiter {
  display: inline-block;
}
.ML__mathlive .op-group {
  display: inline-block;
}
.ML__mathlive .op-symbol {
  position: relative;
}
.ML__mathlive .op-symbol.small-op {
  font-family: KaTeX_Size1;
}
.ML__mathlive .op-symbol.large-op {
  font-family: KaTeX_Size2;
}
.ML__mathlive .mtable .vertical-separator {
  display: inline-block;
  min-width: 1px;
  box-sizing: border-box;
}
.ML__mathlive .mtable .arraycolsep {
  display: inline-block;
}
.ML__mathlive .mtable .col-align-m > .vlist-t {
  text-align: center;
}
.ML__mathlive .mtable .col-align-c > .vlist-t {
  text-align: center;
}
.ML__mathlive .mtable .col-align-l > .vlist-t {
  text-align: left;
}
.ML__mathlive .mtable .col-align-r > .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);
}
`;var Qd=`#mathlive-environment-popover.is-visible {
  visibility: visible;
}
#mathlive-environment-popover {
  --_environment-panel-height: var(--environment-panel-height, 70px);
  --_accent-color: var(--accent-color, #0c75d8);
  --_background: var(--environment-panel-background, #0c75d8);
  --_button-background: var(--environment-panel-button-background, white);
  --_button-background-hover: var(--environment-panel-button-background-hover, #f5f5f7);
  --_button-background-active: var(--environment-panel-button-background-active, #f5f5f7);
  --_button-text: var(--environment-panel-button-text, #e3e4e8);
  position: absolute;
  width: calc(var(--_environment-panel-height) * 2);
  height: var(--_environment-panel-height);
  border-radius: 4px;
  border: 1.5px solid var(--_accent-color);
  background-color: var(--_background);
  box-shadow: 0 0 30px 0 var(--environment-shadow, rgba(0, 0, 0, 0.4));
  pointer-events: all;
  visibility: hidden;
}
#mathlive-environment-popover .MLEP__array-buttons {
  height: calc(var(--_environment-panel-height) * 5/4);
  width: calc(var(--_environment-panel-height) * 5/4);
  margin-left: calc(0px - var(--_environment-panel-height) * 0.16);
  margin-top: calc(0px - var(--_environment-panel-height) * 0.19);
}
#mathlive-environment-popover .MLEP__array-buttons .font {
  fill: white;
}
#mathlive-environment-popover .MLEP__array-buttons circle {
  fill: #7f7f7f;
  transition: fill 300ms;
}
#mathlive-environment-popover .MLEP__array-buttons .MLEP__array-insert-background {
  fill-opacity: 1;
  fill: var(--_background);
  stroke: var(--_accent-color);
  stroke-width: 3px;
}
#mathlive-environment-popover .MLEP__array-buttons line {
  stroke: var(--_accent-color);
  stroke-opacity: 0;
  stroke-width: 40;
  pointer-events: none;
  transition: stroke-opacity 300ms;
  stroke-linecap: round;
}
#mathlive-environment-popover .MLEP__array-buttons g[data-command]:hover circle {
  fill: var(--_accent-color);
}
#mathlive-environment-popover .MLEP__array-buttons g[data-command]:hover line {
  stroke-opacity: 1;
}
#mathlive-environment-popover .MLEP__environment-delimiter-controls {
  height: 100%;
  width: 50%;
}
#mathlive-environment-popover .MLEP__environment-delimiter-controls .MLEP__array-delimiter-options {
  width: var(--_environment-panel-height);
  height: var(--_environment-panel-height);
  display: flex;
  flex-wrap: wrap;
  flex-direction: row;
  justify-content: space-around;
}
#mathlive-environment-popover .MLEP__environment-delimiter-controls .MLEP__array-delimiter-options svg {
  pointer-events: all;
  margin-top: 2px;
  width: calc(var(--_environment-panel-height) / 3 * 28 / 24);
  height: calc(var(--_environment-panel-height) / 3 - 2px);
  border-radius: calc(var(--_environment-panel-height) / 25);
  background-color: var(--_button-background);
}
#mathlive-environment-popover .MLEP__environment-delimiter-controls .MLEP__array-delimiter-options svg:hover {
  background-color: var(--_button-background-hover);
}
#mathlive-environment-popover .MLEP__environment-delimiter-controls .MLEP__array-delimiter-options svg path,
#mathlive-environment-popover .MLEP__environment-delimiter-controls .MLEP__array-delimiter-options svg line {
  stroke: var(--_button-text);
  stroke-width: 2;
  stroke-linecap: round;
}
#mathlive-environment-popover .MLEP__environment-delimiter-controls .MLEP__array-delimiter-options svg rect,
#mathlive-environment-popover .MLEP__environment-delimiter-controls .MLEP__array-delimiter-options svg path {
  fill-opacity: 0;
}
#mathlive-environment-popover .MLEP__environment-delimiter-controls .MLEP__array-delimiter-options svg.active {
  pointer-events: none;
  background-color: var(--_button-background-active);
}
#mathlive-environment-popover .MLEP__environment-delimiter-controls .MLEP__array-delimiter-options svg.active path,
#mathlive-environment-popover .MLEP__environment-delimiter-controls .MLEP__array-delimiter-options svg.active line {
  stroke: var(--_accent-color);
}
#mathlive-environment-popover .MLEP__environment-delimiter-controls .MLEP__array-delimiter-options svg.active circle {
  fill: var(--_accent-color);
}
`;var e0=`/* The element that display info while in latex mode */
#mathlive-suggestion-popover {
  background-color: rgba(97, 97, 97);
  color: #fff;
  text-align: center;
  border-radius: 8px;
  position: fixed;
  z-index: 1;
  display: none;
  flex-direction: column;
  justify-content: center;
  box-shadow: 0 14px 28px rgba(0, 0, 0, 0.25), 0 10px 10px rgba(0, 0, 0, 0.22);
}
#mathlive-suggestion-popover.top-tip::after {
  content: '';
  position: absolute;
  top: -15px;
  left: calc(50% - 15px);
  width: 0;
  height: 0;
  border-left: 15px solid transparent;
  border-right: 15px solid transparent;
  border-bottom: 15px solid rgba(97, 97, 97);
  font-size: 1rem;
}
#mathlive-suggestion-popover.bottom-tip::after {
  content: '';
  position: absolute;
  bottom: -15px;
  left: calc(50% - 15px);
  width: 0;
  height: 0;
  border-left: 15px solid transparent;
  border-right: 15px solid transparent;
  border-top: 15px solid rgba(97, 97, 97);
  font-size: 1rem;
}
#mathlive-suggestion-popover.is-animated {
  transition: all 0.2s cubic-bezier(0.64, 0.09, 0.08, 1);
  animation: ML__fade-in cubic-bezier(0, 0, 0.2, 1) 0.15s;
}
#mathlive-suggestion-popover.is-visible {
  display: flex;
}
@keyframes ML__fade-in {
  from {
    opacity: 0;
  }
  to {
    opacity: 1;
  }
}
/* The wrapper class for the entire content of the popover panel */
#mathlive-suggestion-popover ul {
  display: flex;
  flex-flow: column;
  list-style: none;
  margin: 0;
  padding: 0;
  align-items: flex-start;
  max-height: 400px;
  overflow-y: auto;
}
#mathlive-suggestion-popover li {
  display: flex;
  flex-direction: row;
  justify-content: space-between;
  margin: 8px;
  padding: 8px;
  width: calc(100% - 16px - 16px);
  column-gap: 1em;
  border-radius: 8px;
  cursor: pointer;
  /* Since the content can be clicked on, provide feedback on hover */
}
#mathlive-suggestion-popover li a {
  color: #5ea6fd;
  padding-top: 0.3em;
  margin-top: 0.4em;
  display: block;
}
#mathlive-suggestion-popover li a:hover {
  color: #5ea6fd;
  text-decoration: underline;
}
#mathlive-suggestion-popover li:hover,
#mathlive-suggestion-popover li.is-pressed,
#mathlive-suggestion-popover li.is-active {
  background: rgba(255, 255, 255, 0.1);
}
/* The command inside a popover (inside a #mathlive-suggestion-popover) */
.ML__popover__command {
  font-size: 1.6rem;
  font-family: KaTeX_Main;
}
.ML__popover__current {
  background: #5ea6fd;
  color: #fff;
}
.ML__popover__latex {
  font-family: 'IBM Plex Mono', 'Source Code Pro', Consolas, 'Roboto Mono', Menlo, 'Bitstream Vera Sans Mono', 'DejaVu Sans Mono', Monaco, Courier, monospace;
  align-self: center;
}
/* The keyboard shortcuts for a symbol as displayed in the popover */
.ML__popover__keybinding {
  font-family: system-ui, -apple-system, BlinkMacSystemFont, 'Segoe UI', 'Roboto', 'Oxygen', 'Ubuntu', 'Cantarell', 'Fira Sans', 'Droid Sans', 'Helvetica Neue', sans-serif;
  font-size: 0.8em;
  opacity: 0.7;
}
/* Style for the character that joins the modifiers of a keyboard shortcut 
(usually a "+" sign)*/
.ML__shortcut-join {
  opacity: 0.5;
}
`;var t0=`/* The element that displays the keys as the user type them */
#mathlive-keystroke-caption-panel {
  visibility: hidden;
  /*min-width: 160px;*/
  /*background-color: rgba(97, 97, 200, .95);*/
  background: var(--secondary, hsl(var(--_hue), 19%, 26%));
  border-color: var(--secondary-border, hsl(0, 0%, 91%));
  box-shadow: 0 3px 6px rgba(0, 0, 0, 0.16), 0 3px 6px rgba(0, 0, 0, 0.23);
  text-align: center;
  border-radius: 6px;
  padding: 16px;
  position: absolute;
  z-index: 1;
  display: flex;
  flex-direction: row-reverse;
  justify-content: center;
  --keystroke: white;
  --on-keystroke: #555;
  --keystroke-border: #f7f7f7;
}
@media (prefers-color-scheme: dark) {
  body:not([theme='light']) #mathlive-keystroke-caption-panel {
    --keystroke: hsl(var(--_hue), 50%, 30%);
    --on-keystroke: hsl(0, 0%, 98%);
    --keystroke-border: hsl(var(--_hue), 50%, 25%);
  }
}
body[theme='dark'] #mathlive-keystroke-caption-panel {
  --keystroke: hsl(var(--_hue), 50%, 30%);
  --on-keystroke: hsl(0, 0%, 98%);
  --keystroke-border: hsl(var(--_hue), 50%, 25%);
}
#mathlive-keystroke-caption-panel > span {
  min-width: 14px;
  /*height: 8px;*/
  margin: 0 8px 0 0;
  padding: 4px;
  background-color: var(--keystroke);
  color: var(--on-keystroke);
  fill: currentColor;
  font-family: system-ui, -apple-system, BlinkMacSystemFont, 'Segoe UI', 'Roboto', 'Oxygen', 'Ubuntu', 'Cantarell', 'Fira Sans', 'Droid Sans', 'Helvetica Neue', sans-serif;
  font-size: 1em;
  border-radius: 6px;
  border: 2px solid var(--keystroke-border);
  /*box-shadow: 0 7px 14px rgba(0,0,0,0.25), 0 5px 5px rgba(0,0,0,0.22);*/
}
`;var r0=`.ML__keyboard {
  --_keyboard-height: 0;
  --_keyboard-zindex: var(--keyboard-zindex, 105);
  --_accent-color: var(--keyboard-accent-color, #0c75d8);
  --_background: var(--keyboard-background, #cacfd7);
  --_border: var(--keyboard-border, #ddd);
  --_padding-horizontal: var(--keyboard-padding-horizontal, 0px);
  --_padding-top: var(--keyboard-padding-top, 5px);
  --_padding-bottom: var(--keyboard-padding-bottom, 0px);
  --_row-padding-left: var(--keyboard-row-padding-left, 0px);
  --_row-padding-right: var(--keyboard-row-padding-right, 0px);
  --_toolbar-text: var(--keyboard-toolbar-text, #2c2e2f);
  --_toolbar-text-active: var(--keyboard-toolbar-text-active, var(--_accent-color));
  --_toolbar-background: var(--keyboard-toolbar-background, transparent);
  --_toolbar-background-hover: var(--keyboard-toolbar-background-hover, #eee);
  --_toolbar-background-selected: var(--keyboard-toolbar-background-selected, transparent);
  --_toolbar-font-size: var(--keyboard-toolbar-font-size, '135%');
  --_horizontal-rule: var(--keyboard-horizontal-rule, 1px solid #fff);
  --_keycap-background: var(--keycap-background, white);
  --_keycap-background-hover: var(--keycap-background-hover, #f5f5f7);
  --_keycap-background-active: var(--keycap-background-active, var(--_accent-color));
  --_keycap-background-pressed: var(--keycap-background-pressed, var(--_accent-color));
  --_keycap-border: var(--keycap-border, #e5e6e9);
  --_keycap-border-bottom: var(--keycap-border-bottom, #8d8f92);
  --_keycap-text: var(--keycap-text, #000);
  --_keycap-text-active: var(--keycap-text-active, #fff);
  --_keycap-text-hover: var(--keycap-text-hover, var(--_keycap-text));
  --_keycap-text-pressed: var(--keycap-text-pressed, #fff);
  --_keycap-shift-text: var(--keycap-shift-text, var(--_accent-color));
  --_keycap-primary-background: var(--keycap-primary-background, var(--_accent-color));
  --_keycap-primary-text: var(--keycap-primary-text, #ddd);
  --_keycap-primary-background-hover: var(--keycap-primary-background-hover, #0d80f2);
  --_keycap-secondary-background: var(--keycap-secondary-background, #a0a9b8);
  --_keycap-secondary-background-hover: var(--keycap-secondary-background-hover, #7d8795);
  --_keycap-secondary-text: var(--keycap-secondary-text, #060707);
  --_keycap-secondary-border: var(--keycap-secondary-border, #c5c9d0);
  --_keycap-secondary-border-bottom: var(--keycap-secondary-border-bottom, #989da6);
  --_keycap-height: var(--keycap-height, 60px);
  /* Keycap width (incl. margin) */
  --_keycap-max-width: var(--keycap-max-width, 100px);
  --_keycap-gap: var(--keycap-gap, 8px);
  --_keycap-font-size: var(--keycap-font-size, clamp(16px, 4cqw, 24px));
  --_keycap-small-font-size: var(--keycap-small-font-size, calc(var(--keycap-font-size) * 0.8));
  --_keycap-extra-small-font-size: var(--keycap-extra-small-font-size, calc(var(--keycap-font-size) / 1.42));
  --_variant-panel-background: var(--variant-panel-background, #fff);
  --_variant-keycap-text: var(--variant-keycap-text, var(--_keycap-text));
  --_variant-keycap-text-active: var(--variant-keycap-text-active, var(--_keycap-text-active));
  --_variant-keycap-background-active: var(--variant-keycap-background-active, var(--_accent-color));
  --_variant-keycap-length: var(--variant-keycap-length, 70px);
  --_variant-keycap-font-size: var(--variant-keycap-font-size, 30px);
  --_variant-keycap-aside-font-size: var(--variant-keycap-aside-font-size, 12px);
  --_keycap-shift-font-size: var(--keycap-shift-font-size, 16px);
  --_keycap-shift-color: var(--keycap-shift-color, var(--_accent-color));
  --_box-placeholder-color: var(--box-placeholder-color, var(--_accent-color));
}
.is-math-mode .MLK__rows .if-text-mode,
.is-text-mode .MLK__rows .if-math-mode {
  display: none;
}
.if-can-undo,
.if-can-redo,
.if-can-copy,
.if-can-cut,
.if-can-paste {
  opacity: 0.4;
  pointer-events: none;
}
.can-undo .if-can-undo,
.can-redo .if-can-redo,
.can-copy .if-can-copy,
.can-cut .if-can-cut,
.can-paste .if-can-paste {
  opacity: 1;
  pointer-events: all;
}
body > .ML__keyboard {
  position: fixed;
  --_padding-bottom: calc(var(--keyboard-padding-bottom, 0px) + env(safe-area-inset-bottom, 0));
}
body > .ML__keyboard.is-visible > .MLK__backdrop {
  box-shadow: 0 -5px 6px rgba(0, 0, 0, 0.08);
  border-top: 1px solid var(--_border);
}
body > .ML__keyboard.backdrop-is-transparent.is-visible > .MLK__backdrop {
  box-shadow: none;
  border: none;
}
body > .ML__keyboard.is-visible.animate > .MLK__backdrop {
  transition: 0.28s cubic-bezier(0, 0, 0.2, 1);
  transition-property: transform, opacity;
  transition-timing-function: cubic-bezier(0.4, 0, 1, 1);
}
.ML__keyboard {
  position: relative;
  overflow: hidden;
  top: 0;
  left: 0;
  height: 100%;
  width: 100%;
  z-index: var(--_keyboard-zindex);
  box-sizing: border-box;
  outline: none;
  border: none;
  margin: 0;
  padding: 0;
  line-height: 1;
  overflow-wrap: unset;
  text-align: left;
  vertical-align: baseline;
  cursor: auto;
  white-space: pre;
  box-shadow: none;
  opacity: 1;
  transform: none;
  pointer-events: none;
}
.ML__keyboard :where(div) {
  box-sizing: border-box;
  outline: none;
  border: none;
  margin: 0;
  padding: 0;
  line-height: 1;
  overflow-wrap: unset;
  text-align: left;
  vertical-align: baseline;
  cursor: auto;
  white-space: pre;
  box-shadow: none;
  transform: none;
}
.MLK__backdrop {
  position: absolute;
  bottom: calc(-1 * var(--_keyboard-height));
  width: 100%;
  height: var(--_keyboard-height);
  box-sizing: border-box;
  padding-top: var(--_padding-top);
  padding-bottom: var(--_padding-bottom);
  padding-left: var(--_padding-horizontal);
  padding-right: var(--_padding-horizontal);
  opacity: 0;
  visibility: hidden;
  transform: translate(0, 0);
  background: var(--_background);
}
.backdrop-is-transparent .MLK__backdrop {
  background: transparent;
}
/* If a custom layout has a custom container/backdrop
  (backdrop-is-transparent), make sure to let pointer event go through. */
.backdrop-is-transparent .MLK__plate {
  background: transparent;
  pointer-events: none;
}
/* If a custom layout has a custom container/backdrop, make sure to 
   allow pointer events on it. */
.backdrop-is-transparent .MLK__layer > div > div {
  pointer-events: all;
}
.ML__keyboard.is-visible > .MLK__backdrop {
  transform: translate(0, calc(-1 * var(--_keyboard-height)));
  opacity: 1;
  visibility: visible;
}
.caps-lock-indicator {
  display: none;
  width: 8px;
  height: 8px;
  background: #0cbc0c;
  box-shadow: inset 0 0 4px 0 #13ca13, 0 0 4px 0 #a9ef48;
  border-radius: 8px;
  right: 8px;
  top: 8px;
  position: absolute;
}
.ML__keyboard.is-caps-lock .caps-lock-indicator {
  display: block;
}
.ML__keyboard.is-caps-lock .shift {
  background: var(--_keycap-background-active);
  color: var(--_keycap-text-active);
}
.MLK__plate {
  position: absolute;
  top: var(--_padding-top);
  left: var(--_padding-horizontal);
  width: calc(100% - 2 * var(--_padding-horizontal));
  margin: 0;
  padding: 0;
  box-sizing: border-box;
  container-type: inline-size;
  touch-action: none;
  -webkit-user-select: none;
  user-select: none;
  pointer-events: all;
  font-family: system-ui, -apple-system, BlinkMacSystemFont, 'Segoe UI', 'Roboto', 'Oxygen', 'Ubuntu', 'Cantarell', 'Fira Sans', 'Droid Sans', 'Helvetica Neue', sans-serif;
  font-size: 16px;
  /* Size of toolbar labels */
  font-weight: 400;
  text-shadow: none;
}
.ML__box-placeholder {
  color: var(--_box-placeholder-color);
}
.MLK__tex {
  font-family: KaTeX_Main, KaTeX_Math, 'Cambria Math', 'Asana Math', OpenSymbol, Symbola, STIX, Times, serif !important;
}
.MLK__tex-math {
  font-family: KaTeX_Math, KaTeX_Main, 'Cambria Math', 'Asana Math', OpenSymbol, Symbola, STIX, Times, serif !important;
  font-style: italic;
}
.MLK__layer {
  display: none;
  outline: none;
}
.MLK__layer.is-visible {
  display: flex;
  flex-flow: column;
}
/* Keyboard layouts are made or rows of keys... */
.MLK__rows {
  --_keycap-width: min(var(--_keycap-max-width), 10cqw);
  display: flex;
  flex-flow: column;
  align-items: center;
  border-collapse: separate;
  clear: both;
  border: 0;
  margin: 0;
  margin-bottom: var(--_keycap-gap);
  gap: var(--_keycap-gap);
  /* If the styling include, e.g., some shadows, they will be
  cut off by the overflow. In that case, set the padding to 
  compensate. */
  padding-left: var(--_row-padding-left);
  padding-right: var(--_row-padding-right);
  overflow-x: auto;
  touch-action: none;
}
.MLK__rows > .row {
  display: flex;
  flex-flow: row;
  justify-content: center;
  width: 100%;
  gap: var(--_keycap-gap);
  margin: 0;
  padding: 0;
  /* For the alignment of the text on some modifiers (e.g. shift) */
  /* Extra spacing between two adjacent keys */
  /** A regular keycap */
}
.MLK__rows > .row .tex {
  font-family: KaTeX_Math, KaTeX_Main, 'Cambria Math', 'Asana Math', OpenSymbol, Symbola, STIX, Times, serif !important;
}
.MLK__rows > .row .tex-math {
  font-family: KaTeX_Math, 'Cambria Math', 'Asana Math', OpenSymbol, Symbola, STIX, Times, serif !important;
}
.MLK__rows > .row .big-op {
  font-size: calc(1.25 * var(--_keycap-font-size));
}
.MLK__rows > .row .small {
  font-size: var(--_keycap-small-font-size);
}
.MLK__rows > .row .bottom {
  justify-content: flex-end;
}
.MLK__rows > .row .left {
  align-items: flex-start;
  padding-left: 12px;
}
.MLK__rows > .row .right {
  align-items: flex-end;
  padding-right: 12px;
}
.MLK__rows > .row .w0 {
  width: 0;
}
.MLK__rows > .row .w5 {
  width: calc(0.5 * var(--_keycap-width) - var(--_keycap-gap));
}
.MLK__rows > .row .w15 {
  width: calc(1.5 * var(--_keycap-width) - var(--_keycap-gap));
}
.MLK__rows > .row .w20 {
  width: calc(2 * var(--_keycap-width) - var(--_keycap-gap));
}
.MLK__rows > .row .w50 {
  width: calc(5 * var(--_keycap-width) - var(--_keycap-gap));
}
.MLK__rows > .row .MLK__keycap.w50 {
  font-size: 80%;
  padding-top: 10px;
  font-weight: 100;
}
.MLK__rows > .row .separator {
  background: transparent;
  border: none;
  pointer-events: none;
}
.MLK__rows > .row .horizontal-rule {
  height: 6px;
  margin-top: 3px;
  margin-bottom: 0;
  width: 100%;
  border-radius: 0;
  border-top: var(--_horizontal-rule);
}
.MLK__rows > .row .ghost {
  background: var(--_toolbar-background);
  border: none;
  color: var(--_toolbar-text);
}
.MLK__rows > .row .ghost:hover {
  background: var(--_toolbar-background-hover);
}
.MLK__rows > .row .bigfnbutton {
  font-size: var(--_keycap-extra-small-font-size);
}
.MLK__rows > .row .shift,
.MLK__rows > .row .action {
  color: var(--_keycap-secondary-text);
  background: var(--_keycap-secondary-background);
  border-color: var(--_keycap-secondary-border);
  border-bottom-color: var(--_keycap-secondary-border-bottom);
  line-height: 0.8;
  font-size: min(1rem, var(--_keycap-small-font-size));
  font-weight: 600;
  padding: 8px 12px 8px 12px;
}
.MLK__rows > .row .shift:hover,
.MLK__rows > .row .action:hover {
  background: var(--_keycap-secondary-background-hover);
}
.MLK__rows > .row .action.primary {
  background: var(--_keycap-primary-background);
  color: var(--_keycap-primary-text);
}
.MLK__rows > .row .action.primary:hover {
  background: var(--_keycap-primary-background-hover);
  color: var(--_keycap-primary-text);
}
.MLK__rows > .row .shift.selected,
.MLK__rows > .row .action.selected {
  color: var(--_toolbar-text-active);
}
.MLK__rows > .row .shift.selected.is-pressed,
.MLK__rows > .row .action.selected.is-pressed,
.MLK__rows > .row .shift.selected.is-active,
.MLK__rows > .row .action.selected.is-active {
  color: white;
}
.MLK__rows > .row .warning {
  background: #cd0030;
  color: white;
}
.MLK__rows > .row .warning svg.svg-glyph {
  width: 24px;
  height: 24px;
  min-height: 24px;
}
.MLK__rows > .row div {
  display: flex;
  flex-flow: column;
  align-items: center;
  justify-content: space-evenly;
  width: calc(var(--_keycap-width) - var(--_keycap-gap));
  height: var(--_keycap-height);
  box-sizing: border-box;
  padding: 0;
  vertical-align: top;
  text-align: center;
  float: left;
  color: var(--_keycap-text);
  fill: currentColor;
  font-size: var(--_keycap-font-size);
  background: var(--_keycap-background);
  border: 1px solid var(--_keycap-border);
  border-bottom-color: var(--_keycap-border-bottom);
  border-radius: 6px;
  cursor: pointer;
  touch-action: none;
  /* Keys with a variants panel */
  position: relative;
  overflow: hidden;
  -webkit-user-select: none;
  user-select: none;
  -webkit-tap-highlight-color: transparent;
}
.MLK__rows > .row div:hover {
  background: var(--_keycap-background-hover);
}
.MLK__rows > .row div .ML__mathlive {
  pointer-events: none;
  touch-action: none;
}
.MLK__rows > .row div svg.svg-glyph {
  margin: 8px 0;
  width: 20px;
  height: 20px;
  min-height: 20px;
}
.MLK__rows > .row div svg.svg-glyph-lg {
  margin: 8px 0;
  width: 24px;
  height: 24px;
  min-height: 24px;
}
.MLK__rows > .row div.MLK__tex-math {
  font-size: 25px;
}
.MLK__rows > .row div.is-pressed {
  background: var(--_keycap-background-pressed);
  color: var(--_keycap-text-pressed);
}
.MLK__rows > .row div.MLK__keycap.is-active,
.MLK__rows > .row div.action.is-active,
.MLK__rows > .row div.MLK__keycap.is-pressed,
.MLK__rows > .row div.action.is-pressed {
  z-index: calc(var(--_keyboard-zindex) - 5);
}
.MLK__rows > .row div.MLK__keycap.is-active aside,
.MLK__rows > .row div.action.is-active aside,
.MLK__rows > .row div.MLK__keycap.is-pressed aside,
.MLK__rows > .row div.action.is-pressed aside {
  display: none;
}
.MLK__rows > .row div.MLK__keycap.is-active .MLK__shift,
.MLK__rows > .row div.action.is-active .MLK__shift,
.MLK__rows > .row div.MLK__keycap.is-pressed .MLK__shift,
.MLK__rows > .row div.action.is-pressed .MLK__shift {
  display: none;
}
.MLK__rows > .row div.shift.is-pressed,
.MLK__rows > .row div.MLK__keycap.is-pressed,
.MLK__rows > .row div.action.is-pressed {
  background: var(--_keycap-background-pressed);
  color: var(--_keycap-text-pressed);
}
.MLK__rows > .row div.shift.is-active,
.MLK__rows > .row div.MLK__keycap.is-active,
.MLK__rows > .row div.action.is-active {
  background: var(--_keycap-background-active);
  color: var(--_keycap-text-active);
}
.MLK__rows > .row div small {
  color: var(--_keycap-secondary-text);
}
.MLK__rows > .row div aside {
  font-family: system-ui, -apple-system, BlinkMacSystemFont, 'Segoe UI', 'Roboto', 'Oxygen', 'Ubuntu', 'Cantarell', 'Fira Sans', 'Droid Sans', 'Helvetica Neue', sans-serif;
  font-size: 10px;
  line-height: 10px;
  color: var(--_keycap-secondary-text);
}
/* Add an attribute 'data-tooltip' to display a tooltip on hover.
Note there are a different set of tooltip rules for the keyboard toggle
(it's in a different CSS tree) */
.MLK__tooltip {
  position: relative;
}
.MLK__tooltip::after {
  position: absolute;
  display: inline-table;
  content: attr(data-tooltip);
  top: inherit;
  bottom: 100%;
  width: max-content;
  max-width: 200px;
  padding: 8px 8px;
  background: #616161;
  color: #fff;
  text-align: center;
  z-index: 2;
  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);
  border-radius: 2px;
  font-family: system-ui, -apple-system, BlinkMacSystemFont, 'Segoe UI', 'Roboto', 'Oxygen', 'Ubuntu', 'Cantarell', 'Fira Sans', 'Droid Sans', 'Helvetica Neue', sans-serif;
  font-weight: 400;
  font-size: 12px;
  transition: all 0.15s cubic-bezier(0.4, 0, 1, 1) 1s;
  opacity: 0;
  transform: scale(0.5);
}
.MLK__tooltip:hover {
  position: relative;
}
.MLK__tooltip:hover::after {
  opacity: 1;
  transform: scale(1);
}
.MLK__toolbar {
  align-self: center;
  display: flex;
  flex-flow: row;
  justify-content: space-between;
  width: 100%;
  max-width: 996px;
  min-height: 32px;
  /* Icons for undo/redo, etc. */
}
.MLK__toolbar svg {
  height: 20px;
  width: 20px;
}
.MLK__toolbar > .left {
  position: relative;
  display: flex;
  justify-content: flex-start;
  flex-flow: row;
}
.MLK__toolbar > .right {
  display: flex;
  justify-content: flex-end;
  flex-flow: row;
}
.MLK__toolbar > div > div {
  /* "button" in the toolbar */
  display: flex;
  align-items: center;
  justify-content: center;
  color: var(--_toolbar-text);
  fill: currentColor;
  background: var(--_toolbar-background);
  font-size: var(--_toolbar-font-size);
  padding: 4px 15px;
  cursor: pointer;
  width: max-content;
  min-width: 42px;
  min-height: 22px;
  border: none;
  padding-left: 10px;
  padding-right: 10px;
  padding-bottom: 8px;
  padding-top: 8px;
  margin-top: 7px;
  margin-bottom: 8px;
  margin-left: 4px;
  margin-right: 4px;
  border-radius: 8px;
  box-shadow: none;
  border-bottom: 2px solid transparent;
}
.MLK__toolbar > div > div:not(.disabled):not(.selected):hover {
  background: var(--_toolbar-background-hover);
}
.MLK__toolbar > div > div.disabled svg,
.MLK__toolbar > div > div.disabled:hover svg,
.MLK__toolbar > div > div.disabled.is-pressed svg {
  color: var(--_toolbar-text);
  opacity: 0.2;
}
.MLK__toolbar > div > div:hover,
.MLK__toolbar > div > div:active,
.MLK__toolbar > div > div.is-pressed,
.MLK__toolbar > div > div.is-active {
  color: var(--_toolbar-text-active);
}
.MLK__toolbar > div > div.selected {
  color: var(--_toolbar-text-active);
  background: var(--_toolbar-background-selected);
  border-radius: 0;
  border-bottom-color: var(--_toolbar-text-active);
  padding-bottom: 4px;
  margin-bottom: 12px;
}
/* This is the element that displays variants on press+hold */
.MLK__variant-panel {
  visibility: hidden;
  position: fixed;
  display: flex;
  flex-flow: row wrap-reverse;
  justify-content: center;
  align-content: center;
  margin: 0;
  padding: 0;
  bottom: auto;
  top: 0;
  box-sizing: content-box;
  transform: none;
  z-index: calc(var(--_keyboard-zindex) + 1);
  touch-action: none;
  max-width: 350px;
  background: var(--_variant-panel-background);
  text-align: center;
  border-radius: 6px;
  padding: 6px;
  box-shadow: 0 14px 28px rgba(0, 0, 0, 0.25), 0 10px 10px rgba(0, 0, 0, 0.22);
  transition: none;
}
.MLK__variant-panel.is-visible {
  visibility: visible;
}
.MLK__variant-panel.compact {
  --_variant-keycap-length: var(--variant-keycap-length, 50px);
  --_variant-keycap-font-size: var(--variant-keycap-font-size, 24px);
  --_variant-keycap-aside-font-size: var(--variant-keycap-aside-font-size, 10px);
}
.MLK__variant-panel .item {
  display: flex;
  flex-flow: column;
  align-items: center;
  justify-content: center;
  font-size: var(--_variant-keycap-font-size);
  height: var(--_variant-keycap-length);
  width: var(--_variant-keycap-length);
  margin: 0;
  box-sizing: border-box;
  border-radius: 5px;
  border: 1px solid transparent;
  background: transparent;
  pointer-events: all;
  cursor: pointer;
  color: var(--_variant-keycap-text);
  fill: currentColor;
}
@media (max-height: 412px) {
  .MLK__variant-panel .item {
    --_variant-keycap-font-size: var(--variant-keycap-font-size, 24px);
    --_variant-keycap-length: var(--variant-keycap-length, 50px);
  }
}
.MLK__variant-panel .item .ML__mathlive {
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}
.MLK__variant-panel .item.is-active {
  background: var(--_variant-keycap-background-active);
  color: var(--_variant-keycap-text-active);
}
.MLK__variant-panel .item.is-pressed {
  background: var(--_variant-keycap-background-pressed);
  color: var(--_variant-keycap-text-pressed);
}
.MLK__variant-panel .item.small {
  font-size: var(--_keycap-small-font-size);
}
.MLK__variant-panel .item.swatch-button {
  box-sizing: border-box;
  background: #fbfbfb;
}
.MLK__variant-panel .item.swatch-button > span {
  display: inline-block;
  margin: 6px;
  width: calc(100% - 12px);
  height: calc(100% - 12px);
  border-radius: 50%;
}
.MLK__variant-panel .item.swatch-button:hover {
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}
.MLK__variant-panel .item.swatch-button:hover > span {
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}
.MLK__variant-panel .item.box > div,
.MLK__variant-panel .item.box > span {
  border: 1px dashed rgba(0, 0, 0, 0.24);
}
.MLK__variant-panel .item .warning {
  min-height: 60px;
  min-width: 60px;
  background: #cd0030;
  color: white;
  padding: 5px;
  display: flex;
  align-items: center;
  justify-content: center;
  border-radius: 5px;
}
.MLK__variant-panel .item .warning.is-pressed,
.MLK__variant-panel .item .warning.is-active {
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}
.MLK__variant-panel .item .warning svg.svg-glyph {
  width: 50px;
  height: 50px;
}
.MLK__variant-panel .item aside {
  font-size: var(--_variant-keycap-aside-font-size);
  line-height: 12px;
  opacity: 0.78;
  padding-top: 2px;
}
.MLK__keycap {
  position: relative;
}
.MLK__shift {
  display: block;
  position: absolute;
  right: 4px;
  top: 4px;
  font-size: var(--_keycap-shift-font-size);
  color: var(--_keycap-shift-color);
}
.hide-shift .MLK__shift {
  display: none;
}
@media (max-width: 414px) {
  .MLK__variant-panel {
    max-width: 350px;
    --_variant-keycap-font-size: var(--variant-keycap-font-size, 24px);
    --_variant-keycap-length: var(--variant-keycap-length, 50px);
  }
}
/* @xs breakpoint: iPhone 5 */
@container (max-width: 414px) {
  .MLK__rows {
    --_keycap-gap: max(var(--_keycap-gap, 2px), 2px);
    --_keycap-height: max(var(--_keycap-height), 42px);
    --_keycap-width: min(min(var(--_keycap-max-width), 10cqw), 62px);
  }
  .MLK__toolbar > div > div {
    font-size: 100%;
    padding: 0;
    margin-left: 2px;
    margin-right: 2px;
  }
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  .MLK__rows .action {
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  }
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    height: 14px;
    min-height: 14px;
  }
}
@container (max-width: 744px) {
  .MLK__rows {
    --_keycap-gap: max(var(--keycap-gap, 2px), 2px);
    --_keycap-height: max(var(--keycap-height, 52px), 52px);
    --_keycap-width: min(min(var(--_keycap-max-width), 10cqw), 62px);
  }
  .MLK__toolbar > div > div {
    padding-left: 0;
    padding-right: 0;
  }
  .MLK__tooltip::after {
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    font-size: 16px;
  }
  .MLK__rows > .row > div.fnbutton {
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  }
  .MLK__rows > .row > div.bigfnbutton {
    font-size: calc(var(--_keycap-extra-small-font-size) / 1.55);
  }
  .MLK__rows > .row > div.small {
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  }
  .MLK__rows > .row > div > aside {
    display: none;
  }
  .MLK__shift {
    display: none;
  }
}
/* Medium breakpoint: larger phones */
@container (max-width: 768px) {
  .MLK__rows {
    --_keycap-height: max(var(--keycap-height, 42px), 42px);
  }
  .MLK__rows > .row > div > small {
    font-size: 14px;
  }
}
@media (max-height: 768px) {
  .MLK__rows {
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  }
  .MLK__rows > .row > div > small {
    font-size: 14px;
  }
}
@container (max-width: 1444px) {
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    display: none;
  }
}
@media (prefers-color-scheme: dark) {
  .ML__keyboard {
    --_accent-color: var(--keyboard-accent-color, #0b5c9c);
    --_background: var(--keyboard-background, #151515);
    --_border: var(--keyboard-border, transparent);
    --_toolbar-text: var(--keyboard-toolbar-text, #e3e4e8);
    --_toolbar-background-hover: var(--keyboard-toolbar-background-hover, #303030);
    --keyboard-toolbar-background-hover: #303030;
    --_horizontal-rule: var(--keyboard-horizontal-rule, 1px solid #303030);
    --_keycap-background: var(--keycap-background, #1f2022);
    --_keycap-background-hover: var(--keycap-background, #2f3032);
    --_keycap-border: var(--_keycap-border, transparent);
    --_keycap-border-bottom: var(--_keycap-border-bottom, transparent);
    --_keycap-text: var(--keycap-text, #e3e4e8);
    --_keycap-secondary-background: var(--keycap-secondary-background, #3d4144);
    --_keycap-secondary-background-hover: var(--keycap-secondary-background-hover, #4d5154);
    --_keycap-secondary-text: var(--keycap-secondary-text, #e7ebee);
    --keycap-secondary-border: transparent;
    --keycap-secondary-border-bottom: transparent;
    --_keycap-secondary-border: var(--keycap-secondary-border, transparent);
    --_keycap-secondary-border-bottom: var(--keycap-secondary-border-bottom, transparent);
    --_variant-panel-background: var(--variant-panel-background, #303030);
    --_variant-keycap-text-active: var(--variant-keycap-text-active, #fff);
  }
}
/* Same as the media query, but with a class */
[theme='dark'] .ML__keyboard .ML__keyboard {
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  --_background: var(--keyboard-background, #151515);
  --_border: var(--keyboard-border, transparent);
  --_toolbar-text: var(--keyboard-toolbar-text, #e3e4e8);
  --_toolbar-background-hover: var(--keyboard-toolbar-background-hover, #303030);
  --keyboard-toolbar-background-hover: #303030;
  --_horizontal-rule: var(--keyboard-horizontal-rule, 1px solid #303030);
  --_keycap-background: var(--keycap-background, #1f2022);
  --_keycap-background-hover: var(--keycap-background, #2f3032);
  --_keycap-border: var(--_keycap-border, transparent);
  --_keycap-border-bottom: var(--_keycap-border-bottom, transparent);
  --_keycap-text: var(--keycap-text, #e3e4e8);
  --_keycap-secondary-background: var(--keycap-secondary-background, #3d4144);
  --_keycap-secondary-background-hover: var(--keycap-secondary-background-hover, #4d5154);
  --_keycap-secondary-text: var(--keycap-secondary-text, #e7ebee);
  --keycap-secondary-border: transparent;
  --keycap-secondary-border-bottom: transparent;
  --_keycap-secondary-border: var(--keycap-secondary-border, transparent);
  --_keycap-secondary-border-bottom: var(--keycap-secondary-border-bottom, transparent);
  --_variant-panel-background: var(--variant-panel-background, #303030);
  --_variant-keycap-text-active: var(--variant-keycap-text-active, #fff);
}
[theme='light'] .ML__keyboard {
  --_accent-color: var(--keyboard-accent-color, #0c75d8);
  --_background: var(--keyboard-background, #cacfd7);
  --_border: var(--keyboard-border, #ddd);
  --_toolbar-text: var(--keyboard-toolbar-text, #2c2e2f);
  --_toolbar-background: var(--keyboard-toolbar-background, transparent);
  --_toolbar-background-hover: var(--keyboard-toolbar-background-hover, #eee);
  --_toolbar-background-selected: var(--keyboard-toolbar-background-selected, transparent);
  --_horizontal-rule: var(--keyboard-horizontal-rule, 1px solid #fff);
  --_keycap-background: var(--keycap-background, white);
  --_keycap-background-hover: var(--keycap-background, #f5f5f7);
  --_keycap-background-active: var(--keycap-background-active, var(--_accent-color));
  --_keycap-background-pressed: var(--keycap-background-pressed, var(--_accent-color));
  --_keycap-border: var(--_keycap-border, #e5e6e9);
  --_keycap-border-bottom: var(--_keycap-border-bottom, #8d8f92);
  --_keycap-text: var(--keycap-text, #000);
  --_keycap-text-active: var(--keycap-text-active, #fff);
  --_keycap-text-hover: var(--keycap-text-hover, var(--_keycap-text));
  --_keycap-text-pressed: var(--keycap-text-pressed, #fff);
  --_keycap-shift-text: var(--keycap-shift-text, var(--_accent-color));
  --_keycap-secondary-background: var(--keycap-secondary-background, #a0a9b8);
  --_keycap-secondary-background-hover: var(--keycap-secondary-background-hover, #7d8795);
  --_keycap-secondary-text: var(--keycap-secondary-text, #060707);
  --_keycap-secondary-border: var(--keycap-secondary-border, #c5c9d0);
  --_keycap-secondary-border-bottom: var(--keycap-secondary-border-bottom, #989da6);
  --_variant-panel-background: var(--variant-panel-background, #fff);
  --_variant-keycap-text: var(--variant-keycap-textvar, var(--_keycap-text));
  --_variant-keycap-text-active: var(--variant-keycap-text-active, var(--_keycap-text-active));
  --_variant-keycap-background-active: var(--variant-keycap-background-active, var(--_accent-color));
}
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ym(e){if(e&&(e.classList.remove("ML__highlight"),e.children))for(let t of e.children)ym(t)}function Ml(e,t){var r;e&&(!t||((r=e.dataset)==null?void 0:r.atomId)===t?(e.classList.add("ML__highlight"),e.children&&e.children.length>0&&[...e.children].forEach(i=>{i instanceof HTMLElement&&Ml(i)})):(e.classList.remove("ML__highlight"),e.children&&e.children.length>0&&[...e.children].forEach(i=>{i instanceof HTMLElement&&Ml(i,t)})))}function bm(e,t){var o;if(!ue())return;if(window.MathfieldElement.speechEngine!=="amazon"){console.error("MathLive 0.95.4: Use Amazon TTS Engine for synchronized highlighting"),typeof window.MathfieldElement.speakHook=="function"&&window.MathfieldElement.speakHook(t);return}if(!window.AWS){console.error("MathLive 0.95.4: AWS SDK not loaded. 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Use `"thinmuskip"`, `"medmuskip"`, and `"thickmuskip"` registers ',macros:"mf.macros = ...",registers:"mf.registers = ...",backgroundColorMap:"mf.backgroundColorMap = ...",colorMap:"mf.colorMap = ...",enablePopover:"mf.popoverPolicy = ...",mathModeSpace:"mf.mathModeSpace = ...",placeholderSymbol:"mf.placeholderSymbol = ...",readOnly:"mf.readOnly = ...",removeExtraneousParentheses:"mf.removeExtraneousParentheses = ...",scriptDepth:"mf.scriptDepth = ...",smartFence:"mf.smartFence = ...",smartMode:"mf.smartMode = ...",smartSuperscript:"mf.smartSuperscript = ...",inlineShortcutTimeout:"mf.inlineShortcutTimeout = ...",inlineShortcuts:"mf.inlineShortcuts = ...",keybindings:"mf.keybindings = ...",virtualKeyboardMode:"mf.mathVirtualKeyboardPolicy = ...",customVirtualKeyboardLayers:"mathVirtualKeyboard.layers = ...",customVirtualKeyboards:"mathVirtualKeyboard.layouts = ...",keypressSound:"mathVirtualKeyboard.keypressSound = ...",keypressVibration:"mathVirtualKeyboard.keypressVibration = ...",plonkSound:"mathVirtualKeyboard.plonkSound = ...",virtualKeyboardContainer:"mathVirtualKeyboard.container = ...",virtualKeyboardLayout:"mathVirtualKeyboard.alphabeticLayout = ...",virtualKeyboardTheme:"No longer supported",virtualKeyboardToggleGlyph:"No longer supported",virtualKeyboardToolbar:"mathVirtualKeyboard.editToolbar = ...",virtualKeyboards:"Use `mathVirtualKeyboard.layouts`",speechEngine:"`MathfieldElement.speechEngine`",speechEngineRate:"`MathfieldElement.speechEngineRate`",speechEngineVoice:"`MathfieldElement.speechEngineVoice`",textToSpeechMarkup:"`MathfieldElement.textToSpeechMarkup`",textToSpeechRules:"`MathfieldElement.textToSpeechRules`",textToSpeechRulesOptions:"`MathfieldElement.textToSpeechRulesOptions`",readAloudHook:"`MathfieldElement.readAloudHook`",speakHook:"`MathfieldElement.speakHook`",computeEngine:"`MathfieldElement.computeEngine`",fontsDirectory:"`MathfieldElement.fontsDirectory`",soundsDirectory:"`MathfieldElement.soundsDirectory`",createHTML:"`MathfieldElement.createHTML`",onExport:"`MathfieldElement.onExport`",onInlineShortcut:"`MathfieldElement.onInlineShortcut`",onScrollIntoView:"`MathfieldElement.onScrollIntoView`",locale:"MathfieldElement.locale = ...",strings:"MathfieldElement.strings = ...",decimalSeparator:"MathfieldElement.decimalSeparator = ...",fractionNavigationOrder:"MathfieldElement.fractionNavigationOrder = ..."},re=class re extends HTMLElement{constructor(r){super();if(r){let i=[];for(let o of Object.keys(r))if(fr[o])if(fr[o].startsWith("mf."))if(fr[o].startsWith(`mf.${o}`))i.push(`Option \`${o}\` cannot be used as a constructor option. Use ${fr[o]}`);else{let n=fr[o].match(/([a-zA-Z]+) =/);i.push(`Option \`${o}\` has been renamed \`${n[1]}\``)}else i.push(`Option \`${o}\` cannot be used as a constructor option. Use ${fr[o]}`);if(i.length>0){console.group("%cMathLive 0.95.4: %cInvalid Options","color:#12b; font-size: 1.1rem","color:#db1111; font-size: 1.1rem"),console.warn("Some of the options passed to `new MathFieldElement(...)` are invalid. \n          See https://cortexjs.io/mathlive/changelog/ for details.");for(let o of i)console.warn(o);console.groupEnd()}}Ii()&&(this._internals=this.attachInternals(),this._internals.role="math",this._internals.ariaLabel="math input field",this._internals.ariaMultiLine="false"),this.attachShadow({mode:"open",delegatesFocus:!0}),this.shadowRoot&&"adoptedStyleSheets"in this.shadowRoot?(this.shadowRoot.adoptedStyleSheets=[vo("core"),vo("mathfield"),vo("mathfield-element")],this.shadowRoot.innerHTML='<span style="pointer-events:auto"></span><slot style="display:none"></slot>'):this.shadowRoot.innerHTML=`<style>${gi("core")}${gi("mathfield")}${gi("mathfield-element")}</style><span style="pointer-events:auto"></span><slot style="display:none"></slot>`,r&&this._setOptions(r)}static get formAssociated(){return Ii()}static get optionsAttributes(){return{"default-mode":"string","letter-shape-style":"string","min-font-scale":"number","popover-policy":"string","math-mode-space":"string","read-only":"boolean","remove-extraneous-parentheses":"on/off","smart-fence":"on/off","smart-mode":"on/off","smart-superscript":"on/off","inline-shortcut-timeout":"string","script-depth":"string","virtual-keyboard-target-origin":"string","math-virtual-keyboard-policy":"string"}}static get observedAttributes(){return[...Object.keys(this.optionsAttributes),"contenteditable","disabled","readonly","read-only"]}static get fontsDirectory(){return this._fontsDirectory}static set fontsDirectory(r){r!==this._fontsDirectory&&(this._fontsDirectory=r,D0())}static get soundsDirectory(){return this._soundsDirectory}static set soundsDirectory(r){this._soundsDirectory=r,this.audioBuffers={}}static get keypressSound(){return this._keypressSound}static set keypressSound(r){var i,o,n;this.audioBuffers={},r===null?this._keypressSound={spacebar:null,return:null,delete:null,default:null}:typeof r=="string"?this._keypressSound={spacebar:r,return:r,delete:r,default:r}:typeof r=="object"&&"default"in r&&(this._keypressSound={spacebar:(i=r.spacebar)!=null?i:r.default,return:(o=r.return)!=null?o:r.default,delete:(n=r.delete)!=null?n:r.default,default:r.default})}static get plonkSound(){return this._plonkSound}static set plonkSound(r){this.audioBuffers={},this._plonkSound=r}static get audioContext(){return this._audioContext||(this._audioContext=new AudioContext),this._audioContext}static get speechEngine(){return this._speechEngine}static set speechEngine(r){this._speechEngine=r}static get speechEngineRate(){return this._speechEngineRate}static set speechEngineRate(r){this._speechEngineRate=r}static get speechEngineVoice(){return this._speechEngineVoice}static set speechEngineVoice(r){this._speechEngineVoice=r}static get textToSpeechMarkup(){return this._textToSpeechMarkup}static set textToSpeechMarkup(r){this._textToSpeechMarkup=r}static get textToSpeechRules(){return this._textToSpeechRules}static set textToSpeechRules(r){this._textToSpeechRules=r}static get textToSpeechRulesOptions(){return this._textToSpeechRulesOptions}static set textToSpeechRulesOptions(r){this._textToSpeechRulesOptions=r}static get locale(){return j.locale}static set locale(r){r==="auto"&&(r=navigator.language.slice(0,5)),j.locale=r}static get decimalSeparator(){return this._decimalSeparator}static set decimalSeparator(r){this._decimalSeparator=r,this._computeEngine&&(this._computeEngine.latexOptions.decimalMarker=this.decimalSeparator===","?"{,}":".")}static get strings(){return j.strings}static set strings(r){j.merge(r)}static get computeEngine(){var r,i;if(this._computeEngine===void 0){let o=(r=window[Symbol.for("io.cortexjs.compute-engine")])==null?void 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r;return(r=this.getAttribute("name"))!=null?r:""}get type(){return this.localName}get mode(){var r,i;return(i=(r=this._mathfield)==null?void 0:r.model.mode)!=null?i:this.defaultMode==="text"?"text":"math"}set mode(r){this._mathfield&&(this._mathfield.model.mode=r)}get expression(){if(this._mathfield)return window[Symbol.for("io.cortexjs.compute-engine")]?this._mathfield.expression:(console.error(`MathLive 0.95.4: The CortexJS Compute Engine library is not available.
        
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Read the property directly on the mathfield instead.\n      See https://cortexjs.io/mathlive/changelog/ for details.","color:#12b; font-size: 1.1rem","color:#db1111; font-size: 1.1rem","color: inherit, font-size: 1rem"),this._getOptions([r])[r]}_getOption(r){return this._getOptions([r])[r]}_setOptions(r){if(this._mathfield)this._mathfield.setOptions(r);else if(V.has(this)){let i=m(m({},V.get(this).options),r);V.set(this,g(m({},V.get(this)),{selection:{ranges:i.readOnly?[[0,0]]:[[0,-1]]},options:i}))}else V.set(this,{value:void 0,selection:{ranges:[[0,0]]},options:r});this.reflectAttributes()}setOptions(r){console.group("%cMathLive 0.95.4: %cDeprecated Usage","color:#12b; font-size: 1.1rem","color:#db1111; font-size: 1.1rem"),console.warn(" `mf.setOptions()` is deprecated. Set the property directly on the mathfield instead.\n      See https://cortexjs.io/mathlive/changelog/ for details.");for(let i of Object.keys(r))fr[i]&&console.warn(`\`mf.setOptions({${i}:...})\` -> ${fr[i]}`);console.groupEnd(),this._setOptions(r)}executeCommand(r){var i,o;return(o=(i=this._mathfield)==null?void 0:i.executeCommand(r))!=null?o:!1}getValue(r,i,o){var n,a;if(this._mathfield)return this._mathfield.model.getValue(r,i,o);if(V.has(this)){let s,l,c;if(Ri(r)?([s,l]=r.ranges[0],c=i):Rr(r)?([s,l]=r,c=i):Mt(r)&&Mt(i)?(s=r,l=i,c=o):(s=0,l=-1,c=r),(c===void 0||c==="latex")&&s===0&&l===-1)return(a=(n=V.get(this).value)!=null?n:this.textContent)!=null?a:""}return""}setValue(r,i){if(this._mathfield&&r!==void 0){i!=null||(i={silenceNotifications:!0,mode:"math"}),this._mathfield.setValue(r,i);return}if(V.has(this)){let n=V.get(this).options;V.set(this,{value:r,selection:{ranges:n.readOnly?[[0,0]]:[[0,-1]],direction:"forward"},options:n});return}let 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field"),this.setAttribute("aria-multiline","false")),this.hasAttribute("contenteditable")||this.setAttribute("contenteditable","true"),this.hasAttribute("tabindex")||this.setAttribute("tabindex","0");let r=this.shadowRoot.querySelector("slot:not([name])"),i="";if(this.hasAttribute("value")?i=(o=this.getAttribute("value"))!=null?o:"":i=(n=r==null?void 0:r.assignedNodes().map(s=>s.nodeType===3?s.textContent:"").join("").trim())!=null?n:"",this._mathfield=new Ea(this.shadowRoot.querySelector(":host > span"),g(m({},V.has(this)?V.get(this).options:Da(this)),{eventSink:this,value:i})),!V.has(this)){this.upgradeProperty("disabled"),this.upgradeProperty("readonly");for(let s of Object.keys(re.optionsAttributes))this.upgradeProperty(Rt(s))}if(!((a=this._mathfield)!=null&&a.model)){this._mathfield=null;return}V.has(this)&&this._mathfield.model.deferNotifications({content:!1,selection:!1},()=>{let s=V.get(this).value;s!==void 0&&this._mathfield.setValue(s),this._mathfield.model.selection=V.get(this).selection,V.delete(this)}),window.queueMicrotask(()=>{this.isConnected&&this.dispatchEvent(new Event("mount",{cancelable:!1,bubbles:!0,composed:!0}))}),Dr()}disconnectedCallback(){if(this.shadowRoot.host.removeEventListener("pointerdown",this,!0),!this._mathfield)return;window.queueMicrotask(()=>this.dispatchEvent(new Event("unmount",{cancelable:!1,bubbles:!0,composed:!0})));let r=Ot(this._mathfield.options,Object.keys(re.optionsAttributes).map(i=>Rt(i)));V.set(this,{value:this._mathfield.getValue(),selection:this._mathfield.model.selection,options:r}),this._mathfield.dispose(),this._mathfield=null}upgradeProperty(r){if(this.hasOwnProperty(r)){let i=this[r];delete this[r],(r==="readonly"||r==="read-only")&&(r="readOnly"),this[r]=i}}attributeChangedCallback(r,i,o){if(i===o)return;let n=o!==null;switch(r){case"contenteditable":this._mathfield&&U(this._mathfield);break;case"disabled":this.disabled=n;break;case"read-only":case"readonly":this.readOnly=n;break;default:}}get readonly(){return this.hasAttribute("readonly")||this.hasAttribute("read-only")}set readonly(r){let i=!!r;i?(this.setAttribute("readonly",""),Ii()?this._internals.ariaReadOnly="true":this.setAttribute("aria-readonly","true"),this.setAttribute("aria-readonly","true")):(Ii()?this._internals.ariaReadOnly="false":this.removeAttribute("aria-readonly"),this.removeAttribute("readonly"),this.removeAttribute("read-only")),this._setOptions({readOnly:i})}get disabled(){return this.hasAttribute("disabled")}set disabled(r){var o;let i=!!r;i?this.setAttribute("disabled",""):this.removeAttribute("disabled"),Ii()?this._internals.ariaDisabled=i?"true":"false":this.setAttribute("aria-disabled",i?"true":"false"),i&&((o=this._mathfield)!=null&&o.hasFocus)&&window.mathVirtualKeyboard.visible&&this._mathfield.executeCommand("hideVirtualKeyboard")}get value(){return this.getValue()}set value(r){this.setValue(r)}get defaultMode(){return this._getOption("defaultMode")}set defaultMode(r){this._setOptions({defaultMode:r})}get macros(){return this._getOption("macros")}set macros(r){this._setOptions({macros:r})}get registers(){return this._getOption("registers")}set registers(r){this._setOptions({registers:r})}get colorMap(){return this._getOption("colorMap")}set colorMap(r){this._setOptions({colorMap:r})}get backgroundColorMap(){return this._getOption("backgroundColorMap")}set backgroundColorMap(r){this._setOptions({backgroundColorMap:r})}get letterShapeStyle(){return this._getOption("letterShapeStyle")}set letterShapeStyle(r){this._setOptions({letterShapeStyle:r})}get minFontScale(){return this._getOption("minFontScale")}set minFontScale(r){this._setOptions({minFontScale:r})}get smartMode(){return this._getOption("smartMode")}set smartMode(r){this._setOptions({smartMode:r})}get smartFence(){return this._getOption("smartFence")}set smartFence(r){this._setOptions({smartFence:r})}get smartSuperscript(){return this._getOption("smartSuperscript")}set smartSuperscript(r){this._setOptions({smartSuperscript:r})}get scriptDepth(){return this._getOption("scriptDepth")}set scriptDepth(r){this._setOptions({scriptDepth:r})}get removeExtraneousParentheses(){return this._getOption("removeExtraneousParentheses")}set removeExtraneousParentheses(r){this._setOptions({removeExtraneousParentheses:r})}get mathModeSpace(){return this._getOption("mathModeSpace")}set mathModeSpace(r){this._setOptions({mathModeSpace:r})}get placeholderSymbol(){return this._getOption("placeholderSymbol")}set 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