(function(t){if("function"==typeof bootstrap)bootstrap("katex",t);else if("object"==typeof exports)module.exports=t();else if("function"==typeof define&&define.amd)define(t);else if("undefined"!=typeof ses){if(!ses.ok())return;ses.makeKatex=t}else"undefined"!=typeof window?window.katex=t():global.katex=t()})(function(){var t,i,e,h,a;return function l(t,i,e){function h(p,r){if(!i[p]){if(!t[p]){var c=typeof require=="function"&&require;if(!r&&c)return c(p,!0);if(a)return a(p,!0);throw new Error("Cannot find module '"+p+"'")}var g=i[p]={exports:{}};t[p][0].call(g.exports,function(i){var e=t[p][1][i];return h(e?e:i)},g,g.exports,l,t,i,e)}return i[p].exports}var a=typeof require=="function"&&require;for(var p=0;p<e.length;p++)h(e[p]);return h}({1:[function(t,i,e){var h=t("./ParseError");function a(t){this._input=t}function l(t,i,e){this.type=t;this.text=i;this.position=e}var p=[[/^[/|@."`0-9]/,"textord"],[/^[a-zA-Z]/,"mathord"],[/^[*+-]/,"bin"],[/^[=<>:]/,"rel"],[/^[,;]/,"punct"],[/^'/,"'"],[/^\^/,"^"],[/^_/,"_"],[/^{/,"{"],[/^}/,"}"],[/^[(\[]/,"open"],[/^[)\]?!]/,"close"],[/^~/,"spacing"]];var r=[[/^[a-zA-Z0-9`!@*()-=+\[\]'";:?\/.,]/,"textord"],[/^{/,"{"],[/^}/,"}"],[/^~/,"spacing"]];var c=/^\s*/;var g=/^( +|\\  +)/;var d=/^\\(?:[a-zA-Z]+|.)/;a.prototype._innerLex=function(t,i,e){var a=this._input.slice(t);if(e){var p=a.match(c)[0];t+=p.length;a=a.slice(p.length)}else{var p=a.match(g);if(p!==null){return new l(" "," ",t+p[0].length)}}if(a.length===0){return new l("EOF",null,t)}var r;if(r=a.match(d)){return new l(r[0],r[0],t+r[0].length)}else{for(var n=0;n<i.length;n++){var o=i[n];if(r=a.match(o[0])){return new l(o[1],r[0],t+r[0].length)}}}throw new h("Unexpected character: '"+a[0]+"'",this,t)};var n=/^(#[a-z0-9]+|[a-z]+)/i;a.prototype._innerLexColor=function(t){var i=this._input.slice(t);var e=i.match(c)[0];t+=e.length;i=i.slice(e.length);var a;if(a=i.match(n)){return new l("color",a[0],t+a[0].length)}throw new h("Invalid color",this,t)};var o=/^(\d+(?:\.\d*)?|\.\d+)\s*([a-z]{2})/;a.prototype._innerLexSize=function(t){var i=this._input.slice(t);var e=i.match(c)[0];t+=e.length;i=i.slice(e.length);var a;if(a=i.match(o)){var p=a[2];if(p!=="em"&&p!=="ex"){throw new h("Invalid unit: '"+p+"'",this,t)}return new l("size",{number:+a[1],unit:p},t+a[0].length)}throw new h("Invalid size",this,t)};a.prototype._innerLexWhitespace=function(t){var i=this._input.slice(t);var e=i.match(c)[0];t+=e.length;return new l("whitespace",e,t)};a.prototype.lex=function(t,i){if(i==="math"){return this._innerLex(t,p,true)}else if(i==="text"){return this._innerLex(t,r,false)}else if(i==="color"){return this._innerLexColor(t)}else if(i==="size"){return this._innerLexSize(t)}else if(i==="whitespace"){return this._innerLexWhitespace(t)}};i.exports=a},{"./ParseError":3}],2:[function(t,i,e){function h(t,i,e,h,a){this.style=t;this.color=e;this.size=i;if(h===undefined){h=t}this.parentStyle=h;if(a===undefined){a=i}this.parentSize=a}h.prototype.withStyle=function(t){return new h(t,this.size,this.color,this.style,this.size)};h.prototype.withSize=function(t){return new h(this.style,t,this.color,this.style,this.size)};h.prototype.withColor=function(t){return new h(this.style,this.size,t,this.style,this.size)};h.prototype.reset=function(){return new h(this.style,this.size,this.color,this.style,this.size)};var a={"katex-blue":"#6495ed","katex-orange":"#ffa500","katex-pink":"#ff00af","katex-red":"#df0030","katex-green":"#28ae7b","katex-gray":"gray","katex-purple":"#9d38bd"};h.prototype.getColor=function(){return a[this.color]||this.color};i.exports=h},{}],3:[function(t,i,e){function h(t,i,e){var a="KaTeX parse error: "+t;if(i!==undefined&&e!==undefined){a+=" at position "+e+": ";var l=i._input;l=l.slice(0,e)+"̲"+l.slice(e);var p=Math.max(0,e-15);var r=e+15;a+=l.slice(p,r)}var c=new Error(a);c.name="ParseError";c.__proto__=h.prototype;return c}h.prototype.__proto__=Error.prototype;i.exports=h},{}],4:[function(t,i,e){var h=t("./functions");var a=t("./Lexer");var l=t("./symbols");var p=t("./utils");var r=t("./ParseError");function c(t){this.lexer=new a(t)}function g(t,i,e){this.type=t;this.value=i;this.mode=e}function d(t,i){this.result=t;this.position=i}function n(t,i,e,h,a){this.result=t;this.isFunction=i;this.allowedInText=e;this.numArgs=h;this.argTypes=a}c.prototype.expect=function(t,i){if(t.type!==i){throw new r("Expected '"+i+"', got '"+t.type+"'",this.lexer,t.position)}};c.prototype.parse=function(t){var i=this.parseInput(0,"math");return i.result};c.prototype.parseInput=function(t,i){var e=this.parseExpression(t,i);var h=this.lexer.lex(e.position,i);this.expect(h,"EOF");return e};c.prototype.handleExpressionBody=function(t,i){var e=[];var h;while(h=this.parseAtom(t,i)){e.push(h.result);t=h.position}return{body:e,position:t}};c.prototype.parseExpression=function(t,i){var e=this.handleExpressionBody(t,i);return new d(e.body,e.position)};var o=1;c.prototype.handleSupSubscript=function(t,i,e,a){var l=this.parseGroup(t,i);if(!l){throw new r("Expected group after '"+e+"'",this.lexer,t)}else if(l.numArgs>0){var p=h.getGreediness(l.result.result);if(p>o){return this.parseFunction(t,i)}else{throw new r("Got function '"+l.result.result+"' with no arguments "+"as "+a,this.lexer,t)}}else{return l.result}};c.prototype.parseAtom=function(t,i){var e=this.parseImplicitGroup(t,i);if(i==="text"){return e}var h;if(!e){h=t;e=undefined}else{h=e.position}var a;var l;while(true){var p=this.lexer.lex(h,i);var c;if(p.type==="^"){if(a){throw new r("Double superscript",this.lexer,h)}var n=this.handleSupSubscript(p.position,i,p.type,"superscript");h=n.position;a=n.result}else if(p.type==="_"){if(l){throw new r("Double subscript",this.lexer,h)}var n=this.handleSupSubscript(p.position,i,p.type,"subscript");h=n.position;l=n.result}else if(p.type==="'"){var o=new g("textord","\\prime",i);var s=[o];h=p.position;while((p=this.lexer.lex(h,i)).type==="'"){s.push(o);h=p.position}a=new g("ordgroup",s,i)}else{break}}if(a||l){return new d(new g("supsub",{base:e&&e.result,sup:a,sub:l},i),h)}else{return e}};var s=["\\tiny","\\scriptsize","\\footnotesize","\\small","\\normalsize","\\large","\\Large","\\LARGE","\\huge","\\Huge"];var u=["\\displaystyle","\\textstyle","\\scriptstyle","\\scriptscriptstyle"];c.prototype.parseImplicitGroup=function(t,i){var e=this.parseSymbol(t,i);if(!e||!e.result){return this.parseFunction(t,i)}var h=e.result.result;if(h==="\\left"){var a=this.parseFunction(t,i);var l=this.handleExpressionBody(a.position,i);var c=this.parseSymbol(l.position,i);if(c&&c.result.result==="\\right"){var n=this.parseFunction(l.position,i);return new d(new g("leftright",{body:l.body,left:a.result.value.value,right:n.result.value.value},i),n.position)}else{throw new r("Missing \\right",this.lexer,l.position)}}else if(h==="\\right"){return null}else if(p.contains(s,h)){var l=this.handleExpressionBody(e.result.position,i);return new d(new g("sizing",{size:"size"+(p.indexOf(s,h)+1),value:l.body},i),l.position)}else if(p.contains(u,h)){var l=this.handleExpressionBody(e.result.position,i);return new d(new g("styling",{style:h.slice(1,h.length-5),value:l.body},i),l.position)}else{return this.parseFunction(t,i)}};c.prototype.parseFunction=function(t,i){var e=this.parseGroup(t,i);if(e){if(e.isFunction){var a=e.result.result;if(i==="text"&&!e.allowedInText){throw new r("Can't use function '"+a+"' in text mode",this.lexer,e.position)}var l=e.result.position;var p;if(e.numArgs>0){var c=h.getGreediness(a);var n=[a];var o=[l];for(var s=0;s<e.numArgs;s++){var u=e.argTypes&&e.argTypes[s];if(u){var m=this.parseSpecialGroup(l,u,i)}else{var m=this.parseGroup(l,i)}if(!m){throw new r("Expected group after '"+e.result.result+"'",this.lexer,l)}var f;if(m.numArgs>0){var v=h.getGreediness(m.result.result);if(v>c){f=this.parseFunction(l,i)}else{throw new r("Got function '"+m.result.result+"' as "+"argument to function '"+e.result.result+"'",this.lexer,m.result.position-1)}}else{f=m.result}n.push(f.result);o.push(f.position);l=f.position}n.push(o);p=h.funcs[a].handler.apply(this,n)}else{p=h.funcs[a].handler.apply(this,[a])}return new d(new g(p.type,p,i),l)}else{return e.result}}else{return null}};c.prototype.parseSpecialGroup=function(t,i,e){if(i==="color"||i==="size"){var h=this.lexer.lex(t,e);this.expect(h,"{");var a=this.lexer.lex(h.position,i);var l=this.lexer.lex(a.position,e);this.expect(l,"}");return new n(new d(new g("color",a.text,e),l.position),false)}else if(i==="text"){var p=this.lexer.lex(t,"whitespace");return this.parseGroup(p.position,i)}else{return this.parseGroup(t,i)}};c.prototype.parseGroup=function(t,i){var e=this.lexer.lex(t,i);if(e.type==="{"){var h=this.parseExpression(e.position,i);var a=this.lexer.lex(h.position,i);this.expect(a,"}");return new n(new d(new g("ordgroup",h.result,i),a.position),false)}else{return this.parseSymbol(t,i)}};c.prototype.parseSymbol=function(t,i){var e=this.lexer.lex(t,i);if(h.funcs[e.type]){var a=h.funcs[e.type];var p=a.argTypes;if(p){p=p.slice();for(var r=0;r<p.length;r++){if(p[r]==="original"){p[r]=i}}}return new n(new d(e.type,e.position),true,a.allowedInText,a.numArgs,p)}else if(l[i][e.text]){return new n(new d(new g(l[i][e.text].group,e.text,i),e.position),false)}else{return null}};i.exports=c},{"./Lexer":1,"./ParseError":3,"./functions":11,"./symbols":14,"./utils":15}],5:[function(t,i,e){function h(t,i,e,h){this.id=t;this.size=i;this.cramped=h;this.sizeMultiplier=e}h.prototype.sup=function(){return u[m[this.id]]};h.prototype.sub=function(){return u[f[this.id]]};h.prototype.fracNum=function(){return u[v[this.id]]};h.prototype.fracDen=function(){return u[y[this.id]]};h.prototype.cramp=function(){return u[x[this.id]]};h.prototype.cls=function(){return o[this.size]+(this.cramped?" cramped":" uncramped")};h.prototype.reset=function(){return s[this.size]};var a=0;var l=1;var p=2;var r=3;var c=4;var g=5;var d=6;var n=7;var o=["displaystyle textstyle","textstyle","scriptstyle","scriptscriptstyle"];var s=["reset-textstyle","reset-textstyle","reset-scriptstyle","reset-scriptscriptstyle"];var u=[new h(a,0,1,false),new h(l,0,1,true),new h(p,1,1,false),new h(r,1,1,true),new h(c,2,.7,false),new h(g,2,.7,true),new h(d,3,.5,false),new h(n,3,.5,true)];var m=[c,g,c,g,d,n,d,n];var f=[g,g,g,g,n,n,n,n];var v=[p,r,c,g,d,n,d,n];var y=[r,r,g,g,n,n,n,n];var x=[l,l,r,r,g,g,n,n];i.exports={DISPLAY:u[a],TEXT:u[p],SCRIPT:u[c],SCRIPTSCRIPT:u[d]}},{}],6:[function(t,i,e){var h=t("./domTree");var a=t("./fontMetrics");var l=t("./symbols");var p=function(t,i,e,p,r){if(l[e][t]&&l[e][t].replace){t=l[e][t].replace}var c=a.getCharacterMetrics(t,i);var g;if(c){g=new h.symbolNode(t,c.height,c.depth,c.italic,r)}else{console&&console.warn("No character metrics for '"+t+"' in style '"+i+"'");g=new h.symbolNode(t,0,0,0,r)}if(p){g.style.color=p}return g};var r=function(t,i,e,h){return p(t,"Math-Italic",i,e,h.concat(["mathit"]))};var c=function(t,i,e,h){if(l[i][t].font==="main"){return p(t,"Main-Regular",i,e,h)}else{return p(t,"AMS-Regular",i,e,h.concat(["amsrm"]))}};var g=function(t){var i=0;var e=0;var h=0;if(t.children){for(var a=0;a<t.children.length;a++){if(t.children[a].height>i){i=t.children[a].height}if(t.children[a].depth>e){e=t.children[a].depth}if(t.children[a].maxFontSize>h){h=t.children[a].maxFontSize}}}t.height=i;t.depth=e;t.maxFontSize=h};var d=function(t,i,e){var a=new h.span(t,i);g(a);if(e){a.style.color=e}return a};var n=function(t){var i=new h.documentFragment(t);g(i);return i};var o=function(t,i){var e=d([],[new h.symbolNode("​")]);e.style.fontSize=i/t.style.sizeMultiplier+"em";var a=d(["fontsize-ensurer","reset-"+t.size,"size5"],[e]);return a};var s=function(t,i,e,a){var l;if(i==="individualShift"){var p=t;t=[p[0]];l=-p[0].shift-p[0].elem.depth;var r=l;for(var c=1;c<p.length;c++){var g=-p[c].shift-r-p[c].elem.depth;var n=g-(p[c-1].elem.height+p[c-1].elem.depth);r=r+g;t.push({type:"kern",size:n});t.push(p[c])}}else if(i==="top"){var s=e;for(var c=0;c<t.length;c++){if(t[c].type==="kern"){s-=t[c].size}else{s-=t[c].elem.height+t[c].elem.depth}}l=s}else if(i==="bottom"){l=-e}else if(i==="shift"){l=-t[0].elem.depth-e}else if(i==="firstBaseline"){l=-t[0].elem.depth}else{l=0}var u=0;for(var c=0;c<t.length;c++){if(t[c].type==="elem"){u=Math.max(u,t[c].elem.maxFontSize)}}var m=o(a,u);var f=[];var r=l;for(var c=0;c<t.length;c++){if(t[c].type==="kern"){r+=t[c].size}else{var v=t[c].elem;var y=-v.depth-r;r+=v.height+v.depth;var x=d([],[m,v]);x.height-=y;x.depth+=y;x.style.top=y+"em";f.push(x)}}var b=d(["baseline-fix"],[m,new h.symbolNode("​")]);f.push(b);var z=d(["vlist"],f);z.height=Math.max(r,z.height);z.depth=Math.max(-l,z.depth);return z};i.exports={makeSymbol:p,mathit:r,mathrm:c,makeSpan:d,makeFragment:n,makeFontSizer:o,makeVList:s}},{"./domTree":9,"./fontMetrics":10,"./symbols":14}],7:[function(t,i,e){var h=t("./Options");var a=t("./ParseError");var l=t("./Style");var p=t("./buildCommon");var r=t("./delimiter");var c=t("./domTree");var g=t("./fontMetrics");var d=t("./parseTree");var n=t("./symbols");var o=t("./utils");var s=p.makeSpan;var u=function(t,i,e){var h=[];for(var a=0;a<t.length;a++){var l=t[a];h.push(z(l,i,e));e=l}return h};var m={mathord:"mord",textord:"mord",bin:"mbin",rel:"mrel",text:"mord",open:"mopen",close:"mclose",frac:"minner",spacing:"mord",punct:"mpunct",ordgroup:"mord",op:"mop",katex:"mord",overline:"mord",rule:"mord",leftright:"minner",sqrt:"mord"};var f=function(t){if(t==null){return m.mathord}else if(t.type==="supsub"){return f(t.value.base)}else if(t.type==="llap"||t.type==="rlap"){return f(t.value)}else if(t.type==="color"){return f(t.value.value)}else if(t.type==="sizing"){return f(t.value.value)}else if(t.type==="styling"){return f(t.value.value)}else if(t.type==="delimsizing"){return m[t.value.delimType]}else{return m[t.type]}};var v=function(t){if(t==null){return false}else if(t.type==="mathord"||t.type==="textord"||t.type==="bin"||t.type==="rel"||t.type==="open"||t.type==="close"||t.type==="punct"){return true}else if(t.type==="ordgroup"){return t.value.length===1&&v(t.value[0])}else{return false}};var y=function(t,i){if(t==null){return false}else if(t.type==="op"){return t.value.limits&&i.style.id===l.DISPLAY.id}else{return null}};var x={mathord:function(t,i,e){return p.mathit(t.value,t.mode,i.getColor(),["mord"])},textord:function(t,i,e){return p.mathrm(t.value,t.mode,i.getColor(),["mord"])},bin:function(t,i,e){var h="mbin";var a=e;while(a&&a.type=="color"){var l=a.value.value;a=l[l.length-1]}if(!e||o.contains(["mbin","mopen","mrel","mop","mpunct"],f(a))){t.type="ord";h="mord"}return p.mathrm(t.value,t.mode,i.getColor(),[h])},rel:function(t,i,e){return p.mathrm(t.value,t.mode,i.getColor(),["mrel"])},text:function(t,i,e){return s(["text","mord",i.style.cls()],u(t.value.body,i.reset()))},supsub:function(t,i,e){var h=t.value.base;if(y(t.value.base,i)){return x[t.value.base.type](t,i,e)}var a=z(t.value.base,i.reset());if(t.value.sup){var r=z(t.value.sup,i.withStyle(i.style.sup()));var d=s([i.style.reset(),i.style.sup().cls()],[r])}if(t.value.sub){var n=z(t.value.sub,i.withStyle(i.style.sub()));var o=s([i.style.reset(),i.style.sub().cls()],[n])}var u,m;if(v(t.value.base)){u=0;m=0}else{u=a.height-g.metrics.supDrop;m=a.depth+g.metrics.subDrop}var b;if(i.style===l.DISPLAY){b=g.metrics.sup1}else if(i.style.cramped){b=g.metrics.sup3}else{b=g.metrics.sup2}var w=l.TEXT.sizeMultiplier*i.style.sizeMultiplier;var S=.5/g.metrics.ptPerEm/w+"em";var k;if(!t.value.sup){m=Math.max(m,g.metrics.sub1,n.height-.8*g.metrics.xHeight);k=p.makeVList([{type:"elem",elem:o}],"shift",m,i);k.children[0].style.marginRight=S;if(a instanceof c.symbolNode){k.children[0].style.marginLeft=-a.italic+"em"}}else if(!t.value.sub){u=Math.max(u,b,r.depth+.25*g.metrics.xHeight);k=p.makeVList([{type:"elem",elem:d}],"shift",-u,i);k.children[0].style.marginRight=S}else{u=Math.max(u,b,r.depth+.25*g.metrics.xHeight);m=Math.max(m,g.metrics.sub2);var T=g.metrics.defaultRuleThickness;if(u-r.depth-(n.height-m)<4*T){m=4*T-(u-r.depth)+n.height;var M=.8*g.metrics.xHeight-(u-r.depth);if(M>0){u+=M;m-=M}}k=p.makeVList([{type:"elem",elem:o,shift:m},{type:"elem",elem:d,shift:-u}],"individualShift",null,i);if(a instanceof c.symbolNode){k.children[1].style.marginLeft=a.italic+"em";a.italic=0}k.children[0].style.marginRight=S;k.children[1].style.marginRight=S}return s([f(t.value.base)],[a,k])},open:function(t,i,e){return p.mathrm(t.value,t.mode,i.getColor(),["mopen"])},close:function(t,i,e){return p.mathrm(t.value,t.mode,i.getColor(),["mclose"])},frac:function(t,i,e){var h=i.style;if(t.value.size==="dfrac"){h=l.DISPLAY}else if(t.value.size==="tfrac"){h=l.TEXT}var a=h.fracNum();var r=h.fracDen();var c=z(t.value.numer,i.withStyle(a));var d=s([h.reset(),a.cls()],[c]);var n=z(t.value.denom,i.withStyle(r));var o=s([h.reset(),r.cls()],[n]);var u=g.metrics.defaultRuleThickness/i.style.sizeMultiplier;var m=s([i.style.reset(),l.TEXT.cls(),"frac-line"]);m.height=u;var f,v,y;if(h.size===l.DISPLAY.size){f=g.metrics.num1;v=g.metrics.denom1;y=3*u}else{f=g.metrics.num2;v=g.metrics.denom2;y=u}var x=g.metrics.axisHeight;if(f-c.depth-(x+.5*u)<y){f+=y-(f-c.depth-(x+.5*u))}if(x-.5*u-(n.height-v)<y){v+=y-(x-.5*u-(n.height-v))}var b=-(x-.5*u);var w=p.makeVList([{type:"elem",elem:o,shift:v},{type:"elem",elem:m,shift:b},{type:"elem",elem:d,shift:-f}],"individualShift",null,i);w.height*=h.sizeMultiplier/i.style.sizeMultiplier;w.depth*=h.sizeMultiplier/i.style.sizeMultiplier;return s(["minner","mfrac",i.style.reset(),h.cls()],[w],i.getColor())},color:function(t,i,e){var h=u(t.value.value,i.withColor(t.value.color),e);return new p.makeFragment(h)},spacing:function(t,i,e){if(t.value==="\\ "||t.value==="\\space"||t.value===" "||t.value==="~"){return s(["mord","mspace"],[p.mathrm(t.value,t.mode)])}else{var h={"\\qquad":"qquad","\\quad":"quad","\\enspace":"enspace","\\;":"thickspace","\\:":"mediumspace","\\,":"thinspace","\\!":"negativethinspace"};return s(["mord","mspace",h[t.value]])}},llap:function(t,i,e){var h=s(["inner"],[z(t.value.body,i.reset())]);var a=s(["fix"],[]);return s(["llap",i.style.cls()],[h,a])},rlap:function(t,i,e){var h=s(["inner"],[z(t.value.body,i.reset())]);var a=s(["fix"],[]);return s(["rlap",i.style.cls()],[h,a])},punct:function(t,i,e){return p.mathrm(t.value,t.mode,i.getColor(),["mpunct"])},ordgroup:function(t,i,e){return s(["mord",i.style.cls()],u(t.value,i.reset()))},op:function(t,i,e){var h;var a;var r=false;if(t.type==="supsub"){h=t.value.sup;a=t.value.sub;t=t.value.base;r=true}var c=["\\smallint"];var d=false;if(i.style.id===l.DISPLAY.id&&t.value.symbol&&!o.contains(c,t.value.body)){d=true}var n;var u=0;var m=0;if(t.value.symbol){var f=d?"Size2-Regular":"Size1-Regular";n=p.makeSymbol(t.value.body,f,"math",i.getColor(),["op-symbol",d?"large-op":"small-op","mop"]);u=(n.height-n.depth)/2-g.metrics.axisHeight*i.style.sizeMultiplier;m=n.italic}else{var v=[];for(var y=1;y<t.value.body.length;y++){v.push(p.mathrm(t.value.body[y],t.mode))}n=s(["mop"],v,i.getColor())}if(r){var n=s([],[n]);if(h){var x=z(h,i.withStyle(i.style.sup()));var b=s([i.style.reset(),i.style.sup().cls()],[x]);var w=Math.max(g.metrics.bigOpSpacing1,g.metrics.bigOpSpacing3-x.depth)}if(a){var S=z(a,i.withStyle(i.style.sub()));var k=s([i.style.reset(),i.style.sub().cls()],[S]);var T=Math.max(g.metrics.bigOpSpacing2,g.metrics.bigOpSpacing4-S.height)}var M;if(!h){var R=n.height-u;M=p.makeVList([{type:"kern",size:g.metrics.bigOpSpacing5},{type:"elem",elem:k},{type:"kern",size:T},{type:"elem",elem:n}],"top",R,i);M.children[0].style.marginLeft=-m+"em"}else if(!a){var C=n.depth+u;M=p.makeVList([{type:"elem",elem:n},{type:"kern",size:w},{type:"elem",elem:b},{type:"kern",size:g.metrics.bigOpSpacing5}],"bottom",C,i);M.children[1].style.marginLeft=m+"em"}else if(!h&&!a){return n}else{var C=g.metrics.bigOpSpacing5+k.height+k.depth+T+n.depth+u;M=p.makeVList([{type:"kern",size:g.metrics.bigOpSpacing5},{type:"elem",elem:k},{type:"kern",size:T},{type:"elem",elem:n},{type:"kern",size:w},{type:"elem",elem:b},{type:"kern",size:g.metrics.bigOpSpacing5}],"bottom",C,i);M.children[0].style.marginLeft=-m+"em";M.children[2].style.marginLeft=m+"em"}return s(["mop","op-limits"],[M])}else{if(t.value.symbol){n.style.top=u+"em"}return n}},katex:function(t,i,e){var h=s(["k"],[p.mathrm("K",t.mode)]);var a=s(["a"],[p.mathrm("A",t.mode)]);a.height=(a.height+.2)*.75;a.depth=(a.height-.2)*.75;var l=s(["t"],[p.mathrm("T",t.mode)]);var r=s(["e"],[p.mathrm("E",t.mode)]);r.height=r.height-.2155;r.depth=r.depth+.2155;var c=s(["x"],[p.mathrm("X",t.mode)]);return s(["katex-logo"],[h,a,l,r,c],i.getColor())},sqrt:function(t,i,e){var h=z(t.value.body,i.withStyle(i.style.cramp()));var a=g.metrics.defaultRuleThickness/i.style.sizeMultiplier;var c=s([i.style.reset(),l.TEXT.cls(),"sqrt-line"],[],i.getColor());c.height=a;c.maxFontSize=1;var d=a;if(i.style.id<l.TEXT.id){d=g.metrics.xHeight}var n=a+d/4;var o=(h.height+h.depth)*i.style.sizeMultiplier;var u=o+n+a;var m=s(["sqrt-sign"],[r.customSizedDelim("\\surd",u,false,i,t.mode)],i.getColor());var 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l={size1:.5,size2:.7,size3:.8,size4:.9,size5:1,size6:1.2,size7:1.44,size8:1.73,size9:2.07,size10:2.49};var p=l[t.value.size];a.maxFontSize=p*i.style.sizeMultiplier;return a},styling:function(t,i,e){var h={display:l.DISPLAY,text:l.TEXT,script:l.SCRIPT,scriptscript:l.SCRIPTSCRIPT};var a=h[t.value.style];var p=u(t.value.value,i.withStyle(a),e);return s([i.style.reset(),a.cls()],p)},delimsizing:function(t,i,e){var h=t.value.value;if(h==="."){return s([m[t.value.delimType]])}return s([m[t.value.delimType]],[r.sizedDelim(h,t.value.size,i,t.mode)])},leftright:function(t,i,e){var h=u(t.value.body,i.reset());var a=0;var l=0;for(var p=0;p<h.length;p++){a=Math.max(h[p].height,a);l=Math.max(h[p].depth,l)}a*=i.style.sizeMultiplier;l*=i.style.sizeMultiplier;var c;if(t.value.left==="."){c=s(["nulldelimiter"])}else{c=r.leftRightDelim(t.value.left,a,l,i,t.mode)}h.unshift(c);var g;if(t.value.right==="."){g=s(["nulldelimiter"])}else{g=r.leftRightDelim(t.value.right,a,l,i,t.mode)}h.push(g);return s(["minner",i.style.cls()],h,i.getColor())},rule:function(t,i,e){var h=s(["mord","rule"],[],i.getColor());var a=t.value.width.number;if(t.value.width.unit==="ex"){a*=g.metrics.xHeight}var l=t.value.height.number;if(t.value.height.unit==="ex"){l*=g.metrics.xHeight}a/=i.style.sizeMultiplier;l/=i.style.sizeMultiplier;h.style.borderRightWidth=a+"em";h.style.borderTopWidth=l+"em";h.width=a;h.height=l;return h}};var b={size1:.5,size2:.7,size3:.8,size4:.9,size5:1,size6:1.2,size7:1.44,size8:1.73,size9:2.07,size10:2.49};var z=function(t,i,e){if(!t){return s()}if(x[t.type]){var h=x[t.type](t,i,e);if(i.style!==i.parentStyle){var l=i.style.sizeMultiplier/i.parentStyle.sizeMultiplier;h.height*=l;h.depth*=l}if(i.size!==i.parentSize){var l=b[i.size]/b[i.parentSize];h.height*=l;h.depth*=l}return h}else{throw new a("Got group of unknown type: '"+t.type+"'")}};var w=function(t){var i=new h(l.TEXT,"size5","");var e=u(t,i);var a=s(["base",i.style.cls()],e);var p=s(["strut"]);var r=s(["strut","bottom"]);p.style.height=a.height+"em";r.style.height=a.height+a.depth+"em";r.style.verticalAlign=-a.depth+"em";var c=s(["katex"],[s(["katex-inner"],[p,r,a])]);return c};i.exports=w},{"./Options":2,"./ParseError":3,"./Style":5,"./buildCommon":6,"./delimiter":8,"./domTree":9,"./fontMetrics":10,"./parseTree":13,"./symbols":14,"./utils":15}],8:[function(t,i,e){var h=t("./Options");var a=t("./ParseError");var l=t("./Style");var p=t("./domTree");var r=t("./fontMetrics");var c=t("./parseTree");var g=t("./utils");var d=t("./symbols");var n=t("./buildCommon");var o=t("./buildCommon").makeSpan;var s=function(t,i){if(d["math"][t]&&d["math"][t].replace){return r.getCharacterMetrics(d["math"][t].replace,i)}else{return r.getCharacterMetrics(t,i)}};var u=function(t,i,e){return n.makeSymbol(t,"Size"+i+"-Regular",e)};var m=function(t,i,e){var h=o(["style-wrap",e.style.reset(),i.cls()],[t]);var a=i.sizeMultiplier/e.style.sizeMultiplier;h.height*=a;h.depth*=a;h.maxFontSize=i.sizeMultiplier;return h};var f=function(t,i,e,h,a){var l=n.makeSymbol(t,"Main-Regular",a);var p=m(l,i,h);if(e){var c=(1-h.style.sizeMultiplier/i.sizeMultiplier)*r.metrics.axisHeight;p.style.top=c+"em";p.height-=c;p.depth+=c}return p};var v=function(t,i,e,h,a){var p=u(t,i,a);var c=m(o(["delimsizing","size"+i],[p],h.getColor()),l.TEXT,h);if(e){var g=(1-h.style.sizeMultiplier)*r.metrics.axisHeight;c.style.top=g+"em";c.height-=g;c.depth+=g}return c};var y=function(t,i,e){var h;if(i==="Size1-Regular"){h="delim-size1"}else if(i==="Size4-Regular"){h="delim-size4"}var a=o(["delimsizinginner",h],[o([],[n.makeSymbol(t,i,e)])]);return{type:"elem",elem:a}};var x=function(t,i,e,h,a){var p,c,g,d;p=g=d=t;c=null;var u="Size1-Regular";if(t==="\\uparrow"){g=d="⏐"}else if(t==="\\Uparrow"){g=d="‖"}else if(t==="\\downarrow"){p=g="⏐"}else if(t==="\\Downarrow"){p=g="‖"}else if(t==="\\updownarrow"){p="\\uparrow";g="⏐";d="\\downarrow"}else if(t==="\\Updownarrow"){p="\\Uparrow";g="‖";d="\\Downarrow"}else if(t==="|"||t==="\\vert"){}else if(t==="\\|"||t==="\\Vert"){}else if(t==="["||t==="\\lbrack"){p="⎡";g="⎢";d="⎣";u="Size4-Regular"}else if(t==="]"||t==="\\rbrack"){p="⎤";g="⎥";d="⎦";u="Size4-Regular"}else if(t==="\\lfloor"){g=p="⎢";d="⎣";u="Size4-Regular"}else if(t==="\\lceil"){p="⎡";g=d="⎢";u="Size4-Regular"}else if(t==="\\rfloor"){g=p="⎥";d="⎦";u="Size4-Regular"}else if(t==="\\rceil"){p="⎤";g=d="⎥";u="Size4-Regular"}else if(t==="("){p="⎛";g="⎜";d="⎝";u="Size4-Regular"}else if(t===")"){p="⎞";g="⎟";d="⎠";u="Size4-Regular"}else if(t==="\\{"||t==="\\lbrace"){p="⎧";c="⎨";d="⎩";g="⎪";u="Size4-Regular"}else if(t==="\\}"||t==="\\rbrace"){p="⎫";c="⎬";d="⎭";g="⎪";u="Size4-Regular"}else if(t==="\\surd"){p="";d="⎷";g="";u="Size4-Regular"}var f=s(p,u);var v=f.height+f.depth;var x=s(g,u);var b=x.height+x.depth;var z=s(d,u);var w=z.height+z.depth;var S,k;if(c!==null){S=s(c,u);k=S.height+S.depth}var T=v+w;if(c!==null){T+=k}while(T<i){T+=b;if(c!==null){T+=b}}var M=r.metrics.axisHeight;if(e){M*=h.style.sizeMultiplier}var R=T/2+M;var C=T/2-M;var E=[];E.push(y(d,u,a));if(c===null){var P=T-v-w;var A=Math.ceil(P/b);for(var I=0;I<A;I++){E.push(y(g,u,a))}}else{var L=T/2-v-k/2;var O=Math.ceil(L/b);var q=T/2-v-k/2;var D=Math.ceil(q/b);for(var I=0;I<O;I++){E.push(y(g,u,a))}E.push(y(c,u,a));for(var I=0;I<D;I++){E.push(y(g,u,a))}}E.push(y(p,u,a));var F=n.makeVList(E,"bottom",C,h);return m(o(["delimsizing","mult"],[F],h.getColor()),l.TEXT,h)};var b=["(",")","[","\\lbrack","]","\\rbrack","\\{","\\lbrace","\\}","\\rbrace","\\lfloor","\\rfloor","\\lceil","\\rceil","<",">","\\langle","\\rangle","/","\\backslash","\\surd"];var z=["\\uparrow","\\downarrow","\\updownarrow","\\Uparrow","\\Downarrow","\\Updownarrow","|","\\|","\\vert","\\Vert"];var w=["<",">","\\langle","\\rangle","/","\\backslash"];var S=[0,1.2,1.8,2.4,3];var k=function(t,i,e,h){if(t==="<"){t="\\langle"}else if(t===">"){t="\\rangle"}var l;if(g.contains(b,t)){return v(t,i,false,e,h)}else if(g.contains(z,t)){return x(t,S[i],false,e,h)}else{throw new a("Illegal delimiter: '"+t+"'")}};var T=[{type:"small",style:l.SCRIPTSCRIPT},{type:"small",style:l.SCRIPT},{type:"small",style:l.TEXT},{type:"large",size:1},{type:"large",size:2},{type:"large",size:3},{type:"large",size:4}];var M=[{type:"small",style:l.SCRIPTSCRIPT},{type:"small",style:l.SCRIPT},{type:"small",style:l.TEXT},{type:"stack"}];var R=[{type:"small",style:l.SCRIPTSCRIPT},{type:"small",style:l.SCRIPT},{type:"small",style:l.TEXT},{type:"large",size:1},{type:"large",size:2},{type:"large",size:3},{type:"large",size:4},{type:"stack"}];var C=function(t){if(t.type==="small"){return"Main-Regular"}else if(t.type==="large"){return"Size"+t.size+"-Regular"}else if(t.type==="stack"){return"Size4-Regular"}};var E=function(t,i,e,h){var a=Math.min(2,3-h.style.size);for(var l=a;l<e.length;l++){if(e[l].type==="stack"){break}var p=s(t,C(e[l]));var r=p.height+p.depth;if(e[l].type==="small"){r*=e[l].style.sizeMultiplier}if(r>i){return e[l]}}return e[e.length-1]};var P=function(t,i,e,h,a){if(t==="<"){t="\\langle"}else if(t===">"){t="\\rangle"}var l;if(g.contains(w,t)){l=T}else if(g.contains(b,t)){l=R}else{l=M}var p=E(t,i,l,h);if(p.type==="small"){return f(t,p.style,e,h,a)}else if(p.type==="large"){return v(t,p.size,e,h,a)}else if(p.type==="stack"){return x(t,i,e,h,a)}};var A=function(t,i,e,h,a){var l=r.metrics.axisHeight*h.style.sizeMultiplier;var p=901;var c=5/r.metrics.ptPerEm;var g=Math.max(i-l,e+l);var d=Math.max(g/500*p,2*g-c);return P(t,d,true,h,a)};i.exports={sizedDelim:k,customSizedDelim:P,leftRightDelim:A}},{"./Options":2,"./ParseError":3,"./Style":5,"./buildCommon":6,"./domTree":9,"./fontMetrics":10,"./parseTree":13,"./symbols":14,"./utils":15}],9:[function(t,i,e){var h=t("./utils");var a=function(t){t=t.slice();for(var i=t.length-1;i>=0;i--){if(!t[i]){t.splice(i,1)}}return t.join(" ")};function l(t,i,e,h,a,l){this.classes=t||[];this.children=i||[];this.height=e||0;this.depth=h||0;this.maxFontSize=a||0;this.style=l||{}}l.prototype.toNode=function(){var t=document.createElement("span");t.className=a(this.classes);for(var i in this.style){if(this.style.hasOwnProperty(i)){t.style[i]=this.style[i]}}for(var e=0;e<this.children.length;e++){t.appendChild(this.children[e].toNode())}return t};l.prototype.toMarkup=function(){var t="<span";if(this.classes.length){t+=' class="';t+=h.escape(a(this.classes));t+='"'}var i="";for(var e in this.style){if(this.style.hasOwnProperty(e)){i+=h.hyphenate(e)+":"+this.style[e]+";"}}if(i){t+=' style="'+h.escape(i)+'"'}t+=">";for(var l=0;l<this.children.length;l++){t+=this.children[l].toMarkup()}t+="</span>";return t};function p(t,i,e,h){this.children=t||[];this.height=i||0;this.depth=e||0;this.maxFontSize=h||0}p.prototype.toNode=function(){var t=document.createDocumentFragment();for(var i=0;i<this.children.length;i++){t.appendChild(this.children[i].toNode())}return t};p.prototype.toMarkup=function(){var t="";for(var i=0;i<this.children.length;i++){t+=this.children[i].toMarkup()}return t};function r(t,i,e,h,a,l){this.value=t||"";this.height=i||0;this.depth=e||0;this.italic=h||0;this.classes=a||[];this.style=l||{};this.maxFontSize=0}r.prototype.toNode=function(){var t=document.createTextNode(this.value);var i=null;if(this.italic>0){i=document.createElement("span");i.style.marginRight=this.italic+"em"}if(this.classes.length>0){i=i||document.createElement("span");i.className=a(this.classes)}for(var e in this.style){if(this.style.hasOwnProperty(e)){i=i||document.createElement("span");i.style[e]=this.style[e]}}if(i){i.appendChild(t);return i}else{return t}};r.prototype.toMarkup=function(){var t=false;var i="<span";if(this.classes.length){t=true;i+=' class="';i+=h.escape(a(this.classes));i+='"'}var e="";if(this.italic>0){e+="margin-right:"+this.italic+"em;"}for(var l in this.style){if(this.style.hasOwnProperty(l)){e+=h.hyphenate(l)+":"+this.style[l]+";"}}if(e){t=true;i+=' style="'+h.escape(e)+'"'}var p=h.escape(this.value);if(t){i+=">";i+=p;i+="</span>";return i}else{return p}};i.exports={span:l,documentFragment:p,symbolNode:r}},{"./utils":15}],10:[function(t,i,e){var h=.025;var a=0;var l=0;var p=0;var r=.431;var c=1;var g=0;var d=.677;var n=.394;var o=.444;var s=.686;
var u=.345;var m=.413;var f=.363;var v=.289;var y=.15;var x=.247;var b=.386;var z=.05;var w=2.39;var S=.101;var k=.25;var T=0;var M=0;var R=0;var C=0;var E=.431;var P=1;var A=0;var I=.04;var L=.111;var O=.166;var q=.2;var D=.6;var F=.1;var _=10;var B={xHeight:r,quad:c,num1:d,num2:n,num3:o,denom1:s,denom2:u,sup1:m,sup2:f,sup3:v,sub1:y,sub2:x,supDrop:b,subDrop:z,delim1:w,delim2:S,axisHeight:k,defaultRuleThickness:I,bigOpSpacing1:L,bigOpSpacing2:O,bigOpSpacing3:q,bigOpSpacing4:D,bigOpSpacing5:F,ptPerEm:_};var 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var G=function(t,i){return N[i][t.charCodeAt(0)]};i.exports={metrics:B,getCharacterMetrics:G}},{}],11:[function(t,i,e){var h=t("./utils");var a=t("./ParseError");var l={"\\sqrt":{numArgs:1,handler:function(t,i){return{type:"sqrt",body:i}}},"\\text":{numArgs:1,argTypes:["text"],greediness:2,handler:function(t,i){var e;if(i.type==="ordgroup"){e=i.value}else{e=[i]}return{type:"text",body:e}}},"\\color":{numArgs:2,allowedInText:true,argTypes:["color","original"],handler:function(t,i,e){var h;if(e.type==="ordgroup"){h=e.value}else{h=[e]}return{type:"color",color:i.value,value:h}}},"\\overline":{numArgs:1,handler:function(t,i){return{type:"overline",body:i}}},"\\rule":{numArgs:2,argTypes:["size","size"],handler:function(t,i,e){return{type:"rule",width:i.value,height:e.value}}},"\\KaTeX":{numArgs:0,handler:function(t){return{type:"katex"}}}};var 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