mw.loader.implement("ext.math.mathjax.jax.output.HTML-CSS.autoload",function($,jQuery){MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function(){var VERSION="2.3";var MML=MathJax.ElementJax.mml,HTMLCSS=MathJax.OutputJax["HTML-CSS"];MML["annotation-xml"].Augment({toHTML:function(span){span=this.HTMLhandleSize(this.HTMLcreateSpan(span));var encoding=this.Get("encoding");for(var i=0,m=this.data.length;i<m;i++){this.data[i].toHTML(span,encoding)}this.HTMLhandleSpace(span);this.HTMLhandleColor(span);return span;},HTMLgetScale:function(){return this.SUPER(arguments).HTMLgetScale.call(this)/HTMLCSS.scale;}});MML.xml.Augment({toHTML:function(span,encoding){for(var i=0,m=this.data.length;i<m;i++){span.appendChild(this.data[i].cloneNode(true))}span.bbox.w=HTMLCSS.getW(span);span.bbox.rw=span.bbox.w;var HD=HTMLCSS.getHD(span);span.bbox.h=HD.h;span.bbox.d=HD.d;}});MathJax.Hub.Startup.signal.Post("HTML-CSS annotation-xml Ready");MathJax.Ajax.loadComplete(HTMLCSS.autoloadDir+
"/annotation-xml.js");});MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function(){var VERSION="2.3";var MML=MathJax.ElementJax.mml,HTMLCSS=MathJax.OutputJax["HTML-CSS"];var currentTip,hover,clear;var CONFIG=HTMLCSS.config.tooltip=MathJax.Hub.Insert({delayPost:600,delayClear:600,offsetX:10,offsetY:5},HTMLCSS.config.tooltip||{});MML.maction.Augment({HTMLtooltip:HTMLCSS.addElement(document.body,"div",{id:"MathJax_Tooltip"}),toHTML:function(span,HW,D){var selected=this.selected();if(selected.type=="null"){span=this.HTMLcreateSpan(span);span.bbox=this.HTMLzeroBBox();return span;}span=this.HTMLhandleSize(this.HTMLcreateSpan(span));span.bbox=null;var box=selected.toHTML(span);if(D!=null){HTMLCSS.Remeasured(selected.HTMLstretchV(span,HW,D),span)}else if(HW!=null){HTMLCSS.Remeasured(selected.HTMLstretchH(span,HW),span)}else{HTMLCSS.Measured(box,span)}this.HTMLhandleHitBox(span);this.HTMLhandleSpace(span);this.HTMLhandleColor(span);return span;},HTMLhandleHitBox:function(span,postfix){
var frame;if(HTMLCSS.msieHitBoxBug){var box=HTMLCSS.addElement(span,"span",{isMathJax:true});frame=HTMLCSS.createFrame(box,span.bbox.h,span.bbox.d,span.bbox.w,0,"none");span.insertBefore(box,span.firstChild);box.style.marginRight=HTMLCSS.Em(-span.bbox.w);if(HTMLCSS.msieInlineBlockAlignBug){frame.style.verticalAlign=HTMLCSS.Em(HTMLCSS.getHD(span).d-span.bbox.d)}}else{frame=HTMLCSS.createFrame(span,span.bbox.h,span.bbox.d,span.bbox.w,0,"none");span.insertBefore(frame,span.firstChild);frame.style.marginRight=HTMLCSS.Em(-span.bbox.w);}frame.className="MathJax_HitBox";frame.id="MathJax-HitBox-"+this.spanID+(postfix||"")+HTMLCSS.idPostfix;var type=this.Get("actiontype");if(this.HTMLaction[type]){this.HTMLaction[type].call(this,span,frame,this.Get("selection"))}},HTMLstretchH:MML.mbase.HTMLstretchH,HTMLstretchV:MML.mbase.HTMLstretchV,HTMLaction:{toggle:function(span,frame,selection){this.selection=selection;frame.onclick=span.childNodes[1].onclick=MathJax.Callback(["HTMLclick",this]);frame.
style.cursor=span.childNodes[1].style.cursor="pointer";},statusline:function(span,frame,selection){frame.onmouseover=span.childNodes[1].onmouseover=MathJax.Callback(["HTMLsetStatus",this]);frame.onmouseout=span.childNodes[1].onmouseout=MathJax.Callback(["HTMLclearStatus",this]);frame.onmouseover.autoReset=frame.onmouseout.autoReset=true;},tooltip:function(span,frame,selection){if(this.data[1]&&this.data[1].isToken){frame.title=frame.alt=span.childNodes[1].title=span.childNodes[1].alt=this.data[1].data.join("");}else{frame.onmouseover=span.childNodes[1].onmouseover=MathJax.Callback(["HTMLtooltipOver",this]);frame.onmouseout=span.childNodes[1].onmouseout=MathJax.Callback(["HTMLtooltipOut",this]);frame.onmouseover.autoReset=frame.onmouseout.autoReset=true;}}},HTMLclick:function(event){this.selection++;if(this.selection>this.data.length){this.selection=1}var math=this;while(math.type!=="math"){math=math.inherit}var jax=MathJax.Hub.getJaxFor(math.inputID),hover=!!jax.hover;jax.Update();if(
hover){var span=document.getElementById(jax.inputID+"-Span");MathJax.Extension.MathEvents.Hover.Hover(jax,span);}return MathJax.Extension.MathEvents.Event.False(event);},HTMLsetStatus:function(event){this.messageID=MathJax.Message.Set((this.data[1]&&this.data[1].isToken)?this.data[1].data.join(""):this.data[1].toString());},HTMLclearStatus:function(event){if(this.messageID){MathJax.Message.Clear(this.messageID,0)}delete this.messageID;},HTMLtooltipOver:function(event){if(!event){event=window.event}if(clear){clearTimeout(clear);clear=null}if(hover){clearTimeout(hover)}var x=event.pageX;var y=event.pageY;if(x==null){x=event.clientX+document.body.scrollLeft+document.documentElement.scrollLeft;y=event.clientY+document.body.scrollTop+document.documentElement.scrollTop;}var callback=MathJax.Callback(["HTMLtooltipPost",this,x+CONFIG.offsetX,y+CONFIG.offsetY])
hover=setTimeout(callback,CONFIG.delayPost);},HTMLtooltipOut:function(event){if(hover){clearTimeout(hover);hover=null}if(clear){clearTimeout(clear)}var callback=MathJax.Callback(["HTMLtooltipClear",this,80]);clear=setTimeout(callback,CONFIG.delayClear);},HTMLtooltipPost:function(x,y){hover=null;if(clear){clearTimeout(clear);clear=null}var tip=this.HTMLtooltip;tip.style.display="block";tip.style.opacity="";tip.style.filter=HTMLCSS.config.styles["#MathJax_Tooltip"].filter;if(this===currentTip)return;tip.style.left=x+"px";tip.style.top=y+"px";tip.innerHTML='<span class="MathJax"><nobr></nobr></span>';var emex=tip.insertBefore(HTMLCSS.EmExSpan.cloneNode(true),tip.firstChild);var ex=emex.firstChild.offsetHeight/60,em=emex.lastChild.firstChild.offsetHeight/60;HTMLCSS.em=HTMLCSS.outerEm=MML.mbase.prototype.em=em;var scale=Math.floor(Math.max(HTMLCSS.config.minScaleAdjust/100,(ex/HTMLCSS.TeX.x_height)/em)*HTMLCSS.config.scale);tip.firstChild.style.fontSize=scale+"%";emex.parentNode.removeChild
(emex);var stack=HTMLCSS.createStack(tip.firstChild.firstChild);var box=HTMLCSS.createBox(stack);try{HTMLCSS.Measured(this.data[1].toHTML(box),box)}catch(err){if(!err.restart){throw err}tip.style.display="none";MathJax.Callback.After(["HTMLtooltipPost",this,x,y],err.restart);return;}HTMLCSS.placeBox(box,0,0);HTMLCSS.createRule(tip.firstChild.firstChild,box.bbox.h,box.bbox.d,0);currentTip=this;},HTMLtooltipClear:function(n){var tip=this.HTMLtooltip;if(n<=0){tip.style.display="none";tip.style.opacity=tip.style.filter="";clear=null;}else{tip.style.opacity=n/100;tip.style.filter="alpha(opacity="+n+")";clear=setTimeout(MathJax.Callback(["HTMLtooltipClear",this,n-20]),50);}}});MathJax.Hub.Browser.Select({MSIE:function(browser){HTMLCSS.msieHitBoxBug=true;}});MathJax.Hub.Startup.signal.Post("HTML-CSS maction Ready");MathJax.Ajax.loadComplete(HTMLCSS.autoloadDir+"/maction.js");});MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function(){var VERSION="2.3";var MML=MathJax.ElementJax.mml,
HTMLCSS=MathJax.OutputJax["HTML-CSS"];var SVGNS="http://www.w3.org/2000/svg";var VMLNS="urn:schemas-microsoft-com:vml";var vmlns="mjxvml";MML.menclose.Augment({toHTML:function(span){var values=this.getValues("notation","thickness","padding","mathcolor","color");if(values.color&&!this.mathcolor){values.mathcolor=values.color}if(values.thickness==null){values.thickness=".075em"}if(values.padding==null){values.padding=".2em"}span=this.HTMLcreateSpan(span);var mu=this.HTMLgetMu(span),scale=this.HTMLgetScale();var p=HTMLCSS.length2em(values.padding,mu,1/HTMLCSS.em)*scale;var t=HTMLCSS.length2em(values.thickness,mu,1/HTMLCSS.em);var SOLID=HTMLCSS.Em(t)+" solid";var stack=HTMLCSS.createStack(span);var base=HTMLCSS.createBox(stack);this.HTMLmeasureChild(0,base);var H=base.bbox.h+p+t,D=base.bbox.d+p+t,W=base.bbox.w+2*(p+t);var frame=HTMLCSS.createFrame(stack,H+D,0,W,t,"none");frame.id="MathJax-frame-"+this.spanID;HTMLCSS.addBox(stack,frame);stack.insertBefore(frame,base);var T=0,B=0,R=0,L=0,dx=
0,dy=0;var svg,vml;var w,h,r;if(!values.mathcolor){values.mathcolor="black"}else{span.style.color=values.mathcolor}var nl=MathJax.Hub.SplitList(values.notation),notation={};for(var i=0,m=nl.length;i<m;i++)notation[nl[i]]=true;if(notation[MML.NOTATION.UPDIAGONALARROW])notation[MML.NOTATION.UPDIAGONALSTRIKE]=false;var line;for(var n in notation){if(!notation.hasOwnProperty(n)||!notation[n])continue;switch(n){case MML.NOTATION.BOX:frame.style.border=SOLID;if(!HTMLCSS.msieBorderWidthBug){T=B=L=R=t}break;case MML.NOTATION.ROUNDEDBOX:if(HTMLCSS.useVML){if(!vml){vml=this.HTMLvml(stack,H,D,W,t,values.mathcolor)}r=Math.floor(1000*Math.min(W,H+D)-2*t);w=Math.floor(4000*(W-2*t)),h=Math.floor(4000*(H+D-2*t));this.HTMLvmlElement(vml,"shape",{style:{width:this.HTMLpx(W-2*t),height:this.HTMLpx(H+D-2*t),left:this.HTMLpx(t,.5),top:this.HTMLpx(t,.5)},path:"m "+r+",0 qx 0,"+r+" l 0,"+(h-r)+" qy "+r+","+h+" "+"l "+(w-r)+","+h+" qx "+w+","+(h-r)+" l "+w+","+r+" qy "+(w-r)+",0 x e",coordsize:w+","+h});}else
{if(!svg){svg=this.HTMLsvg(stack,H,D,W,t,values.mathcolor)}this.HTMLsvgElement(svg.firstChild,"rect",{x:1,y:1,width:this.HTMLpx(W-t)-1,height:this.HTMLpx(H+D-t)-1,rx:this.HTMLpx(Math.min(H+D,W)/4)});}break;case MML.NOTATION.CIRCLE:if(HTMLCSS.useVML){if(!vml){vml=this.HTMLvml(stack,H,D,W,t,values.mathcolor)}this.HTMLvmlElement(vml,"oval",{style:{width:this.HTMLpx(W-2*t),height:this.HTMLpx(H+D-2*t),left:this.HTMLpx(t,.5),top:this.HTMLpx(t,.5)}});}else{if(!svg){svg=this.HTMLsvg(stack,H,D,W,t,values.mathcolor)}this.HTMLsvgElement(svg.firstChild,"ellipse",{rx:this.HTMLpx(W/2-t),ry:this.HTMLpx((H+D)/2-t),cx:this.HTMLpx(W/2),cy:this.HTMLpx((H+D)/2)});}break;case MML.NOTATION.LEFT:frame.style.borderLeft=SOLID;if(!HTMLCSS.msieBorderWidthBug){L=t}break;case MML.NOTATION.ACTUARIAL:frame.style.borderTop=SOLID;if(!HTMLCSS.msieBorderWidthBug){T=t;frame.bbox.w+=p-t}case MML.NOTATION.RIGHT:frame.style.borderRight=SOLID;if(!HTMLCSS.msieBorderWidthBug){R=t}break;case MML.NOTATION.VERTICALSTRIKE:line=
HTMLCSS.createRule(stack,H+D-t/2,0,t);HTMLCSS.addBox(stack,line);HTMLCSS.placeBox(line,p+t+base.bbox.w/2,-D,true);break;case MML.NOTATION.TOP:frame.style.borderTop=SOLID;if(!HTMLCSS.msieBorderWidthBug){T=t}break;case MML.NOTATION.BOTTOM:frame.style.borderBottom=SOLID;if(!HTMLCSS.msieBorderWidthBug){B=t}break;case MML.NOTATION.HORIZONTALSTRIKE:line=HTMLCSS.createRule(stack,t,0,W-t/2);HTMLCSS.addBox(stack,line);HTMLCSS.placeBox(line,0,(H+D)/2-D,true);break;case MML.NOTATION.UPDIAGONALSTRIKE:if(HTMLCSS.useVML){if(!vml){vml=this.HTMLvml(stack,H,D,W,t,values.mathcolor)}line=this.HTMLvmlElement(vml,"line",{from:"0,"+this.HTMLpx(H+D-t),to:this.HTMLpx(W)+",0"});}else{if(!svg){svg=this.HTMLsvg(stack,H,D,W,t,values.mathcolor)}this.HTMLsvgElement(svg.firstChild,"line",{x1:1,y1:this.HTMLpx(H+D-t),x2:this.HTMLpx(W-t),y2:this.HTMLpx(t)});}break;case MML.NOTATION.UPDIAGONALARROW:if(HTMLCSS.useVML){if(!vml){vml=this.HTMLvml(stack,H,D,W,t,values.mathcolor)}line=this.HTMLvmlElement(vml,"line",{from:"0,"
+this.HTMLpx(H+D-t),to:this.HTMLpx(W)+","+this.HTMLpx(t)});this.HTMLvmlElement(line,"stroke",{endarrow:"classic"});}else{if(!svg){svg=this.HTMLsvg(stack,H,D,W,t,values.mathcolor)}var l=Math.sqrt(W*W+(H+D)*(H+D)),f=1/l*10*scale/HTMLCSS.em*t/.075;w=W*f;h=(H+D)*f;var x=W-t/2,y=t/2;if(y+h-.4*w<0){y=.4*w-h}this.HTMLsvgElement(svg.firstChild,"line",{x1:1,y1:this.HTMLpx(H+D-t),x2:this.HTMLpx(x-.7*w),y2:this.HTMLpx(y+.7*h)});this.HTMLsvgElement(svg.firstChild,"polygon",{points:this.HTMLpx(x)+","+this.HTMLpx(y)+" "+this.HTMLpx(x-w-.4*h)+","+this.HTMLpx(y+h-.4*w)+" "+this.HTMLpx(x-.7*w)+","+this.HTMLpx(y+.7*h)+" "+this.HTMLpx(x-w+.4*h)+","+this.HTMLpx(y+h+.4*w)+" "+this.HTMLpx(x)+","+this.HTMLpx(y),fill:values.mathcolor,stroke:"none"});}break;case MML.NOTATION.DOWNDIAGONALSTRIKE:if(HTMLCSS.useVML){if(!vml){vml=this.HTMLvml(stack,H,D,W,t,values.mathcolor)}this.HTMLvmlElement(vml,"line",{from:"0,0",to:this.HTMLpx(W)+","+this.HTMLpx(H+D-t)});}else{if(!svg){svg=this.HTMLsvg(stack,H,D,W,t,values.
mathcolor)}this.HTMLsvgElement(svg.firstChild,"line",{x1:1,y1:this.HTMLpx(t),x2:this.HTMLpx(W-t),y2:this.HTMLpx(H+D-t)});}break;case MML.NOTATION.MADRUWB:frame.style.borderBottom=SOLID;frame.style.borderRight=SOLID;if(!HTMLCSS.msieBorderWidthBug){B=R=t}break;case MML.NOTATION.RADICAL:if(HTMLCSS.useVML){if(!vml){vml=this.HTMLvml(stack,H,D,W,t,values.mathcolor)}this.HTMLvmlElement(vml,"shape",{style:{width:this.HTMLpx(W),height:this.HTMLpx(H+D)},path:"m "+this.HTMLpt(t/2,.6*(H+D))+" l "+this.HTMLpt(p,H+D-t)+" "+this.HTMLpt(2*p,t/2)+" "+this.HTMLpt(W,t/2)+" e",coordsize:this.HTMLpt(W,H+D)});dx=p;}else{if(!svg){svg=this.HTMLsvg(stack,H,D,W,t,values.mathcolor)}this.HTMLsvgElement(svg.firstChild,"path",{d:"M 1,"+this.HTMLpx(.6*(H+D))+" L "+this.HTMLpx(p)+","+this.HTMLpx(H+D)+" L "+this.HTMLpx(2*p)+",1 L "+this.HTMLpx(W)+",1"});HTMLCSS.placeBox(svg.parentNode,0,p/2-D,true);dx=p;dy=t;}break;case MML.NOTATION.LONGDIV:if(HTMLCSS.useVML){if(!vml){vml=this.HTMLvml(stack,H,D,W,t,values.mathcolor)}
this.HTMLvmlElement(vml,"line",{from:"0,"+this.HTMLpx(t/2),to:this.HTMLpx(W-t)+","+this.HTMLpx(t/2)});this.HTMLvmlElement(vml,"arc",{style:{width:this.HTMLpx(2*p),height:this.HTMLpx(H+D-2*t),left:this.HTMLpx(-p),top:this.HTMLpx(t)},startangle:"10",endangle:"170"});dx=p;}else{if(!svg){svg=this.HTMLsvg(stack,H,D,W,t,values.mathcolor)}this.HTMLsvgElement(svg.firstChild,"path",{d:"M "+this.HTMLpx(W)+",1 L 1,1 "+"a"+this.HTMLpx(p)+","+this.HTMLpx((H+D)/2-t)+" 0 0,1 1,"+this.HTMLpx(H+D-2*t)});HTMLCSS.placeBox(svg.parentNode,0,t-D,true);dx=p;dy=t;}break;}}frame.style.width=HTMLCSS.Em(W-L-R);frame.style.height=HTMLCSS.Em(H+D-T-B);HTMLCSS.placeBox(frame,0,dy-D,true);HTMLCSS.placeBox(base,dx+p+t,0);this.HTMLhandleSpace(span);this.HTMLhandleColor(span);return span;},HTMLpx:function(n){return(n*HTMLCSS.em)},HTMLpt:function(x,y){return Math.floor(1000*x)+','+Math.floor(1000*y)},HTMLhandleColor:function(span){var frame=document.getElementById("MathJax-frame-"+this.spanID);if(frame){var values=this.
getValues("mathbackground","background");if(this.style&&span.style.backgroundColor){values.mathbackground=span.style.backgroundColor;span.style.backgroundColor="";}if(values.background&&!this.mathbackground){values.mathbackground=values.background}if(values.mathbackground&&values.mathbackground!==MML.COLOR.TRANSPARENT){frame.style.backgroundColor=values.mathbackground}}else{this.SUPER(arguments).HTMLhandleColor.call(this,span)}},HTMLsvg:function(stack,H,D,W,t,color){var svg=document.createElementNS(SVGNS,"svg");if(svg.style){svg.style.width=HTMLCSS.Em(W);svg.style.height=HTMLCSS.Em(H+D)}var scale=HTMLCSS.createBox(stack);scale.appendChild(svg);HTMLCSS.placeBox(scale,0,-D,true);this.HTMLsvgElement(svg,"g",{fill:"none",stroke:color,"stroke-width":t*HTMLCSS.em});return svg;},HTMLsvgElement:function(svg,type,def){var obj=document.createElementNS(SVGNS,type);obj.isMathJax=true;if(def){for(var id in def){if(def.hasOwnProperty(id)){obj.setAttributeNS(null,id,def[id].toString())}}}svg.
appendChild(obj);return obj;},HTMLvml:function(stack,H,D,W,t,color){var vml=HTMLCSS.createFrame(stack,H+D,0,W,0,"none");HTMLCSS.addBox(stack,vml);HTMLCSS.placeBox(vml,0,-D,true);this.constructor.VMLcolor=color;this.constructor.VMLthickness=this.HTMLpx(t);return vml;},HTMLvmlElement:function(vml,type,def){var obj=HTMLCSS.addElement(vml,vmlns+":"+type,{isMathJax:true});obj.style.position="absolute";obj.style.left=obj.style.top=0;MathJax.Hub.Insert(obj,def);if(!def.fillcolor){obj.fillcolor="none"}if(!def.strokecolor){obj.strokecolor=this.constructor.VMLcolor}if(!def.strokeweight){obj.strokeweight=this.constructor.VMLthickness}return obj;}});MathJax.Hub.Browser.Select({MSIE:function(browser){if((document.documentMode||0)<9){MML.menclose.Augment({HTMLpx:function(n,d){return(n*HTMLCSS.em+(d||0))+"px"}});HTMLCSS.useVML=true;if(!document.namespaces[vmlns]){if(document.documentMode&&document.documentMode===8){document.namespaces.add(vmlns,VMLNS,"#default#VML");}else{document.namespaces.add(
vmlns,VMLNS);document.createStyleSheet().addRule(vmlns+"\\: *","{behavior: url(#default#VML)}");}}}}});MathJax.Hub.Startup.signal.Post("HTML-CSS menclose Ready");MathJax.Ajax.loadComplete(HTMLCSS.autoloadDir+"/menclose.js");});MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function(){var VERSION="2.3";var MML=MathJax.ElementJax.mml,HTMLCSS=MathJax.OutputJax["HTML-CSS"],LOCALE=MathJax.Localization;MML.mglyph.Augment({toHTML:function(span,variant){var SPAN=span,values=this.getValues("src","width","height","valign","alt"),err;span=this.HTMLcreateSpan(span);if(values.src===""){var index=this.Get("index");if(index){variant=this.HTMLgetVariant();var font=variant.defaultFont;if(font){font.noStyleChar=true;font.testString=String.fromCharCode(index)+'ABCabc';if(HTMLCSS.Font.testFont(font)){this.HTMLhandleVariant(span,variant,String.fromCharCode(index));}else{if(values.alt===""){values.alt=LOCALE._(["MathML","BadMglyphFont"],"Bad font: %1",font.family)}err=MML.Error(values.alt,{mathsize:
"75%"});this.Append(err);err.toHTML(span);this.data.pop();span.bbox=err.HTMLspanElement().bbox;}}}}else{if(!this.img){this.img=MML.mglyph.GLYPH[values.src]}if(!this.img){this.img=MML.mglyph.GLYPH[values.src]={img:new Image(),status:"pending"};var img=this.img.img;img.onload=MathJax.Callback(["HTMLimgLoaded",this]);img.onerror=MathJax.Callback(["HTMLimgError",this]);img.src=values.src;MathJax.Hub.RestartAfter(img.onload);}if(this.img.status!=="OK"){err=MML.Error(LOCALE._(["MathML","BadMglyph"],"Bad mglyph: %1",values.src),{mathsize:"75%"});this.Append(err);err.toHTML(span);this.data.pop();span.bbox=err.HTMLspanElement().bbox;}else{var mu=this.HTMLgetMu(span);img=HTMLCSS.addElement(span,"img",{isMathJax:true,src:values.src,alt:values.alt,title:values.alt});if(values.width){if(String(values.width).match(/^\s*-?\d+\s*$/)){values.width+="px"}img.style.width=HTMLCSS.Em(HTMLCSS.length2em(values.width,mu,this.img.img.width/HTMLCSS.em));}if(values.height){if(String(values.height).match(
/^\s*-?\d+\s*$/)){values.height+="px"}img.style.height=HTMLCSS.Em(HTMLCSS.length2em(values.height,mu,this.img.img.height/HTMLCSS.em));}span.bbox.w=span.bbox.rw=img.offsetWidth/HTMLCSS.em;span.bbox.h=img.offsetHeight/HTMLCSS.em;if(values.valign){if(String(values.valign).match(/^\s*-?\d+\s*$/)){values.valign+="px"}span.bbox.d=-HTMLCSS.length2em(values.valign,mu,this.img.img.height/HTMLCSS.em);img.style.verticalAlign=HTMLCSS.Em(-span.bbox.d);span.bbox.h-=span.bbox.d;}}}if(!SPAN.bbox){SPAN.bbox={w:span.bbox.w,h:span.bbox.h,d:span.bbox.d,rw:span.bbox.rw,lw:span.bbox.lw};}else if(span.bbox){SPAN.bbox.w+=span.bbox.w;if(SPAN.bbox.w>SPAN.bbox.rw){SPAN.bbox.rw=SPAN.bbox.w}if(span.bbox.h>SPAN.bbox.h){SPAN.bbox.h=span.bbox.h}if(span.bbox.d>SPAN.bbox.d){SPAN.bbox.d=span.bbox.d}}this.HTMLhandleSpace(span);this.HTMLhandleColor(span);return span;},HTMLimgLoaded:function(event,status){if(typeof(event)==="string"){status=event}this.img.status=(status||"OK")},HTMLimgError:function(){this.img.img.onload(
"error")}},{GLYPH:{}});MathJax.Hub.Startup.signal.Post("HTML-CSS mglyph Ready");MathJax.Ajax.loadComplete(HTMLCSS.autoloadDir+"/mglyph.js");});MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function(){var VERSION="2.3";var MML=MathJax.ElementJax.mml,HTMLCSS=MathJax.OutputJax["HTML-CSS"];MML.mmultiscripts.Augment({toHTML:function(span,HW,D){span=this.HTMLcreateSpan(span);var scale=this.HTMLgetScale();var stack=HTMLCSS.createStack(span),values;var base=HTMLCSS.createBox(stack);if(this.data[this.base]){var child=this.data[this.base].toHTML(base);if(D!=null){this.data[this.base].HTMLstretchV(base,HW,D)}else if(HW!=null){this.data[this.base].HTMLstretchH(base,HW)}HTMLCSS.Measured(child,base);}else{base.bbox=this.HTMLzeroBBox()}var x_height=HTMLCSS.TeX.x_height*scale,s=HTMLCSS.TeX.scriptspace*scale*.75;var BOX=this.HTMLgetScripts(stack,s);var sub=BOX[0],sup=BOX[1],presub=BOX[2],presup=BOX[3];var sscale=this.HTMLgetScale();for(var i=1;i<this.data.length;i++){if(this.data[i]&&this.data[
i].spanID){sscale=this.data[i].HTMLgetScale();break;}}var q=HTMLCSS.TeX.sup_drop*sscale,r=HTMLCSS.TeX.sub_drop*sscale;var u=base.bbox.h-q,v=base.bbox.d+r,delta=0,p;if(base.bbox.ic){delta=base.bbox.ic}if(this.data[this.base]&&(this.data[this.base].type==="mi"||this.data[this.base].type==="mo")){if(this.data[this.base].data.join("").length===1&&base.bbox.scale===1&&!this.data[this.base].Get("largeop")){u=v=0}}var min=this.getValues("subscriptshift","superscriptshift"),mu=this.HTMLgetMu(span);min.subscriptshift=(min.subscriptshift===""?0:HTMLCSS.length2em(min.subscriptshift,mu));min.superscriptshift=(min.superscriptshift===""?0:HTMLCSS.length2em(min.superscriptshift,mu));var dx=0;if(presub){dx=presub.bbox.w+delta}else if(presup){dx=presup.bbox.w-delta}if(dx<0){dx=0};HTMLCSS.placeBox(base,dx,0);if(!sup&&!presup){v=Math.max(v,HTMLCSS.TeX.sub1*scale,min.subscriptshift);if(sub){v=Math.max(v,sub.bbox.h-(4/5)*x_height)}if(presub){v=Math.max(v,presub.bbox.h-(4/5)*x_height)}if(sub){HTMLCSS.
placeBox(sub,dx+base.bbox.w+s-delta,-v)}if(presub){HTMLCSS.placeBox(presub,0,-v)}}else{if(!sub&&!presub){values=this.getValues("displaystyle","texprimestyle");p=HTMLCSS.TeX[(values.displaystyle?"sup1":(values.texprimestyle?"sup3":"sup2"))];u=Math.max(u,p*scale,min.superscriptshift);if(sup){u=Math.max(u,sup.bbox.d+(1/4)*x_height)}if(presup){u=Math.max(u,presup.bbox.d+(1/4)*x_height)}if(sup){HTMLCSS.placeBox(sup,dx+base.bbox.w+s,u)}if(presup){HTMLCSS.placeBox(presup,0,u)}}else{v=Math.max(v,HTMLCSS.TeX.sub2*scale);var t=HTMLCSS.TeX.rule_thickness*scale;var h=(sub||presub).bbox.h,d=(sup||presup).bbox.d;if(presub){h=Math.max(h,presub.bbox.h)}if(presup){d=Math.max(d,presup.bbox.d)}if((u-d)-(h-v)<3*t){v=3*t-u+d+h;q=(4/5)*x_height-(u-d);if(q>0){u+=q;v-=q}}u=Math.max(u,min.superscriptshift);v=Math.max(v,min.subscriptshift);if(sup){HTMLCSS.placeBox(sup,dx+base.bbox.w+s,u)}if(presup){HTMLCSS.placeBox(presup,dx+delta-presup.bbox.w,u)}if(sub){HTMLCSS.placeBox(sub,dx+base.bbox.w+s-delta,-v)}if(
presub){HTMLCSS.placeBox(presub,dx-presub.bbox.w,-v)}}}this.HTMLhandleSpace(span);this.HTMLhandleColor(span);return span;},HTMLgetScripts:function(stack,s){var sup,sub,BOX=[];var i=1,m=this.data.length,W=0;for(var k=0;k<4;k+=2){while(i<m&&this.data[i].type!=="mprescripts"){for(var j=k;j<k+2;j++){if(this.data[i]&&this.data[i].type!=="none"){if(!BOX[j]){BOX[j]=HTMLCSS.createBox(stack);BOX[j].bbox=this.HTMLemptyBBox({});if(W){HTMLCSS.createBlank(BOX[j],W);BOX[j].bbox.w=BOX[j].bbox.rw=W}}this.data[i].toHTML(BOX[j]);this.HTMLcombineBBoxes(this.data[i],BOX[j].bbox);}i++;}sub=BOX[k];sup=BOX[k+1];if(sub&&sup){if(sub.bbox.w<sup.bbox.w){HTMLCSS.createBlank(sub,sup.bbox.w-sub.bbox.w);sub.bbox.w=sup.bbox.w;sub.bbox.rw=Math.max(sub.bbox.w,sub.bbox.rw);}else if(sub.bbox.w>sup.bbox.w){HTMLCSS.createBlank(sup,sub.bbox.w-sup.bbox.w);sup.bbox.w=sub.bbox.w;sup.bbox.rw=Math.max(sup.bbox.w,sup.bbox.rw);}}if(sub){W=sub.bbox.w}else if(sup){W=sup.bbox.w}}i++;W=0;}for(j=0;j<4;j++){if(BOX[j]){BOX[j].bbox.w+=s;
BOX[j].bbox.rw=Math.max(BOX[j].bbox.w,BOX[j].bbox.rw);this.HTMLcleanBBox(BOX[j].bbox);}}return BOX;},HTMLstretchH:MML.mbase.HTMLstretchH,HTMLstretchV:MML.mbase.HTMLstretchV});MathJax.Hub.Startup.signal.Post("HTML-CSS mmultiscripts Ready");MathJax.Ajax.loadComplete(HTMLCSS.autoloadDir+"/mmultiscripts.js");});MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function(){var VERSION="2.3";var MML=MathJax.ElementJax.mml,HTMLCSS=MathJax.OutputJax["HTML-CSS"];MML.ms.Augment({toHTML:function(span){span=this.HTMLhandleSize(this.HTMLcreateSpan(span));var values=this.getValues("lquote","rquote");var text=this.data.join("");var pattern=[];if(values.lquote.length===1){pattern.push(this.HTMLquoteRegExp(values.lquote))}if(values.rquote.length===1){pattern.push(this.HTMLquoteRegExp(values.rquote))}if(pattern.length){text=text.replace(RegExp("("+pattern.join("|")+")","g"),"\\$1")}this.HTMLhandleVariant(span,this.HTMLgetVariant(),values.lquote+text+values.rquote);this.HTMLhandleSpace(span);this.
HTMLhandleColor(span);this.HTMLhandleDir(span);return span;},HTMLquoteRegExp:function(string){return string.replace(/([.*+?|{}()\[\]\\])/g,"\\$1");}});MML.ms.prototype.defaults.mathvariant='monospace';MathJax.Hub.Startup.signal.Post("HTML-CSS ms Ready");MathJax.Ajax.loadComplete(HTMLCSS.autoloadDir+"/ms.js");});MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function(){var VERSION="2.3";var MML=MathJax.ElementJax.mml,HTMLCSS=MathJax.OutputJax["HTML-CSS"];MML.mtable.Augment({toHTML:function(span){span=this.HTMLcreateSpan(span);if(this.data.length===0){return span}var values=this.getValues("columnalign","rowalign","columnspacing","rowspacing","columnwidth","equalcolumns","equalrows","columnlines","rowlines","frame","framespacing","align","useHeight","width","side","minlabelspacing");var hasRelativeWidth=values.width.match(/%$/);var stack=HTMLCSS.createStack(span);var scale=this.HTMLgetScale(),mu=this.HTMLgetMu(span),LABEL=-1;var H=[],D=[],W=[],A=[],C=[],i,j,J=-1,m,M,s,row,cell,mo,
entries=[];var LHD=HTMLCSS.FONTDATA.baselineskip*scale*values.useHeight,HD,LH=HTMLCSS.FONTDATA.lineH*scale,LD=HTMLCSS.FONTDATA.lineD*scale;for(i=0,m=this.data.length;i<m;i++){row=this.data[i];s=(row.type==="mlabeledtr"?LABEL:0);A[i]=[];H[i]=D[i]=0;for(j=s,M=row.data.length+s;j<M;j++){if(W[j]==null){if(j>J){J=j}C[j]=HTMLCSS.createStack(HTMLCSS.createBox(stack));W[j]=-HTMLCSS.BIGDIMEN;}A[i][j]=HTMLCSS.createBox(C[j]);entries.push(row.data[j-s].toHTML(A[i][j]));}}HTMLCSS.MeasureSpans(entries);for(i=0,m=this.data.length;i<m;i++){row=this.data[i];s=(row.type==="mlabeledtr"?LABEL:0);for(j=s,M=row.data.length+s;j<M;j++){cell=row.data[j-s];if(cell.isMultiline){A[i][j].style.width="100%"}if(cell.isEmbellished()){mo=cell.CoreMO();var min=mo.Get("minsize",true);if(min){var bbox=mo.HTMLspanElement().bbox;if(mo.HTMLcanStretch("Vertical")){HD=bbox.h+bbox.d;if(HD){min=HTMLCSS.length2em(min,mu,HD);if(min*bbox.h/HD>H[i]){H[i]=min*bbox.h/HD}if(min*bbox.d/HD>D[i]){D[i]=min*bbox.d/HD}}}else if(mo.
HTMLcanStretch("Horizontal")){min=HTMLCSS.length2em(min,mu,bbox.w);if(min>W[j]){W[j]=min}}}}if(A[i][j].bbox.h>H[i]){H[i]=A[i][j].bbox.h}if(A[i][j].bbox.d>D[i]){D[i]=A[i][j].bbox.d}if(A[i][j].bbox.w>W[j]){W[j]=A[i][j].bbox.w}}}if(H[0]+D[0]){H[0]=Math.max(H[0],LH)}if(H[A.length-1]+D[A.length-1]){D[A.length-1]=Math.max(D[A.length-1],LD)}var SPLIT=MathJax.Hub.SplitList;var CSPACE=SPLIT(values.columnspacing),RSPACE=SPLIT(values.rowspacing),CALIGN=SPLIT(values.columnalign),RALIGN=SPLIT(values.rowalign),CLINES=SPLIT(values.columnlines),RLINES=SPLIT(values.rowlines),CWIDTH=SPLIT(values.columnwidth),RCALIGN=[];for(i=0,m=CSPACE.length;i<m;i++){CSPACE[i]=HTMLCSS.length2em(CSPACE[i],mu)}for(i=0,m=RSPACE.length;i<m;i++){RSPACE[i]=HTMLCSS.length2em(RSPACE[i],mu)}while(CSPACE.length<J){CSPACE.push(CSPACE[CSPACE.length-1])}while(CALIGN.length<=J){CALIGN.push(CALIGN[CALIGN.length-1])}while(CLINES.length<J){CLINES.push(CLINES[CLINES.length-1])}while(CWIDTH.length<=J){CWIDTH.push(CWIDTH[CWIDTH.length-1])
}while(RSPACE.length<A.length){RSPACE.push(RSPACE[RSPACE.length-1])}while(RALIGN.length<=A.length){RALIGN.push(RALIGN[RALIGN.length-1])}while(RLINES.length<A.length){RLINES.push(RLINES[RLINES.length-1])}if(C[LABEL]){CALIGN[LABEL]=(values.side.substr(0,1)==="l"?"left":"right");CSPACE[LABEL]=-W[LABEL];}for(i=0,m=A.length;i<m;i++){row=this.data[i];RCALIGN[i]=[];if(row.rowalign){RALIGN[i]=row.rowalign}if(row.columnalign){RCALIGN[i]=SPLIT(row.columnalign);while(RCALIGN[i].length<=J){RCALIGN[i].push(RCALIGN[i][RCALIGN[i].length-1])}}}if(values.equalrows){var Hm=Math.max.apply(Math,H),Dm=Math.max.apply(Math,D);for(i=0,m=A.length;i<m;i++){s=((Hm+Dm)-(H[i]+D[i]))/2;H[i]+=s;D[i]+=s}}HD=H[0]+D[A.length-1];for(i=0,m=A.length-1;i<m;i++){HD+=Math.max((H[i]+D[i]?LHD:0),D[i]+H[i+1]+RSPACE[i])}var fx=0,fy=0,fW,fH=HD;if(values.frame!=="none"||(values.columnlines+values.rowlines).match(/solid|dashed/)){var frameSpacing=SPLIT(values.framespacing);if(frameSpacing.length!=2){frameSpacing=SPLIT(this.defaults
.framespacing);}fx=HTMLCSS.length2em(frameSpacing[0],mu);fy=HTMLCSS.length2em(frameSpacing[1],mu);fH=HD+2*fy;}var Y,fY,n="";if(typeof(values.align)!=="string"){values.align=String(values.align)}if(values.align.match(/(top|bottom|center|baseline|axis)( +(-?\d+))?/)){n=RegExp.$3;values.align=RegExp.$1}else{values.align=this.defaults.align}if(n!==""){n=parseInt(n);if(n<0){n=A.length+1+n}if(n<1){n=1}else if(n>A.length){n=A.length}Y=0;fY=-(HD+fy)+H[0];for(i=0,m=n-1;i<m;i++){var dY=Math.max((H[i]+D[i]?LHD:0),D[i]+H[i+1]+RSPACE[i]);Y+=dY;fY+=dY;}}else{Y=({top:-(H[0]+fy),bottom:HD+fy-H[0],center:HD/2-H[0],baseline:HD/2-H[0],axis:HD/2+HTMLCSS.TeX.axis_height*scale-H[0]})[values.align];fY=({top:-(HD+2*fy),bottom:0,center:-(HD/2+fy),baseline:-(HD/2+fy),axis:HTMLCSS.TeX.axis_height*scale-HD/2-fy})[values.align];}var WW,WP=0,Wt=0,Wp=0,p=0,f=0,P=[],F=[],Wf=1;if(values.equalcolumns&&values.width!=="auto"){if(hasRelativeWidth){WW=(100/(J+1)).toFixed(2).replace(/\.?0+$/,"")+"%";for(i=0,m=Math.min(J+1,
CWIDTH.length);i<m;i++){CWIDTH[i]=WW}WW=0;WP=1;f=J+1;for(i=0,m=Math.min(J+1,CSPACE.length);i<m;i++){WW+=CSPACE[i]}}else{WW=HTMLCSS.length2em(values.width,mu);for(i=0,m=Math.min(J+1,CSPACE.length);i<m;i++){WW-=CSPACE[i]}WW/=J+1;for(i=0,m=Math.min(J+1,CWIDTH.length);i<m;i++){W[i]=WW}}}else{for(i=0,m=Math.min(J+1,CWIDTH.length);i<m;i++){if(CWIDTH[i]==="auto"){Wt+=W[i]}else if(CWIDTH[i]==="fit"){F[f]=i;f++;Wt+=W[i]}else if(CWIDTH[i].match(/%$/)){P[p]=i;p++;Wp+=W[i];WP+=HTMLCSS.length2em(CWIDTH[i],mu,1)}else{W[i]=HTMLCSS.length2em(CWIDTH[i],mu);Wt+=W[i]}}if(hasRelativeWidth){WW=0;for(i=0,m=Math.min(J,CSPACE.length);i<m;i++){WW+=CSPACE[i]}if(WP>.98){Wf=.98/WP;WP=.98}}else{if(values.width==="auto"){if(WP>.98){Wf=Wp/(Wt+Wp);WW=Wt+Wp}else{WW=Wt/(1-WP)}}else{WW=HTMLCSS.length2em(values.width,mu);for(i=0,m=Math.min(J+1,CSPACE.length);i<m;i++){WW-=CSPACE[i]}}for(i=0,m=P.length;i<m;i++){W[P[i]]=HTMLCSS.length2em(CWIDTH[P[i]],mu,WW*Wf);Wt+=W[P[i]];}if(Math.abs(WW-Wt)>.01){if(f&&WW>Wt){WW=(WW-Wt)/f;
for(i=0,m=F.length;i<m;i++){W[F[i]]+=WW}}else{WW=WW/Wt;for(j=0;j<=J;j++){W[j]*=WW}}}if(values.equalcolumns){var Wm=Math.max.apply(Math,W);for(j=0;j<=J;j++){W[j]=Wm}}}}var y=Y,dy,line,align;s=(C[LABEL]?LABEL:0);for(j=s;j<=J;j++){for(i=0,m=A.length;i<m;i++){if(A[i][j]){s=(this.data[i].type==="mlabeledtr"?LABEL:0);cell=this.data[i].data[j-s];if(cell.HTMLcanStretch("Horizontal")){A[i][j].bbox=cell.HTMLstretchH(C[j],W[j]).bbox;}else if(cell.HTMLcanStretch("Vertical")){mo=cell.CoreMO();var symmetric=mo.symmetric;mo.symmetric=false;A[i][j].bbox=cell.HTMLstretchV(C[j],H[i],D[i]).bbox;A[i][j].HH=null;mo.symmetric=symmetric;}align=cell.rowalign||this.data[i].rowalign||RALIGN[i];dy=({top:H[i]-A[i][j].bbox.h,bottom:A[i][j].bbox.d-D[i],center:((H[i]-D[i])-(A[i][j].bbox.h-A[i][j].bbox.d))/2,baseline:0,axis:0})[align]||0;align=(cell.columnalign||RCALIGN[i][j]||CALIGN[j]);HTMLCSS.alignBox(A[i][j],align,y+dy);}if(i<A.length-1){y-=Math.max((H[i]+D[i]?LHD:0),D[i]+H[i+1]+RSPACE[i])}}y=Y;}if(
hasRelativeWidth){var box=HTMLCSS.createBox(stack);box.style.left=box.style.top=0;box.style.right=HTMLCSS.Em(WW+2*fx);box.style.display="inline-block";box.style.height="0px";if(HTMLCSS.msieRelativeWidthBug){box=HTMLCSS.createBox(box);box.style.position="relative";box.style.height="1em";box.style.width="100%";box.bbox=stack.bbox;}var xp=0,xf=fx,wp,wm;if(f){wp=100*(1-WP)/f,wm=Wt/f}else{wp=100*(1-WP)/(J+1);wm=Wt/(J+1)}for(j=0;j<=J;j++){HTMLCSS.placeBox(C[j].parentNode,0,0);C[j].style.position="relative";C[j].style.left=HTMLCSS.Em(xf);C[j].style.width="100%";C[j].parentNode.parentNode.removeChild(C[j].parentNode);var Cj=HTMLCSS.createBox(box);HTMLCSS.addBox(Cj,C[j]);C[j]=Cj;var CjStyle=Cj.style;CjStyle.display="inline-block";CjStyle.left=xp+"%";if(CWIDTH[j].match(/%$/)){var pp=parseFloat(CWIDTH[j])*Wf;if(f===0){CjStyle.width=(wp+pp)+"%";xp+=wp+pp;Cj=HTMLCSS.createBox(Cj);HTMLCSS.addBox(Cj,C[j].firstChild);Cj.style.left=0;Cj.style.right=HTMLCSS.Em(wm);xf-=wm;}else{CjStyle.width=pp+"%";xp+=
pp;}}else if(CWIDTH[j]==="fit"||f===0){CjStyle.width=wp+"%";Cj=HTMLCSS.createBox(Cj);HTMLCSS.addBox(Cj,C[j].firstChild);Cj.style.left=0;Cj.style.right=HTMLCSS.Em(wm-W[j]);xf+=W[j]-wm;xp+=wp;}else{CjStyle.width=HTMLCSS.Em(W[j]);xf+=W[j];}if(HTMLCSS.msieRelativeWidthBug){HTMLCSS.addText(Cj.firstChild,HTMLCSS.NBSP);Cj.firstChild.style.position="relative";}xf+=CSPACE[j];if(CLINES[j]!=="none"&&j<J&&j!==LABEL){line=HTMLCSS.createBox(box);line.style.left=xp+"%";line=HTMLCSS.createRule(line,fH,0,1.25/HTMLCSS.em);line.style.position="absolute";line.bbox={h:fH,d:0,w:0,rw:1.25/HTMLCSS.em,lw:0};line.parentNode.bbox=stack.bbox;HTMLCSS.placeBox(line,xf-CSPACE[j]/2,fY,true);line.style.borderStyle=CLINES[j];}}}else{var x=fx;for(j=0;j<=J;j++){if(!C[j].bbox.width){HTMLCSS.setStackWidth(C[j],W[j])}if(CWIDTH[j]!=="auto"&&CWIDTH[j]!=="fit"){C[j].bbox.width=W[j];C[j].bbox.isFixed=true}HTMLCSS.placeBox(C[j].parentNode,x,0);x+=W[j]+CSPACE[j];if(CLINES[j]!=="none"&&j<J&&j!==LABEL){line=HTMLCSS.createRule(stack
,fH,0,1.25/HTMLCSS.em);HTMLCSS.addBox(stack,line);line.bbox={h:fH,d:0,w:0,rw:1.25/HTMLCSS.em,lw:0};HTMLCSS.placeBox(line,x-CSPACE[j]/2,fY,true);line.style.borderStyle=CLINES[j];}}}stack.bbox.d=-fY;stack.bbox.h=fH+fY;HTMLCSS.setStackWidth(stack,stack.bbox.w+fx);fW=stack.bbox.w;var frame;if(values.frame!=="none"){frame=HTMLCSS.createFrame(stack,fH,0,fW,1.25/HTMLCSS.em,values.frame);HTMLCSS.addBox(stack,frame);HTMLCSS.placeBox(frame,0,fY,true);if(hasRelativeWidth){frame.style.width="100%"}}y=Y;for(i=0,m=A.length-1;i<m;i++){dy=Math.max(LHD,D[i]+H[i+1]+RSPACE[i]);if(RLINES[i]!=="none"){line=HTMLCSS.createRule(stack,1.25/HTMLCSS.em,0,fW);HTMLCSS.addBox(stack,line);line.bbox={h:1.25/HTMLCSS.em,d:0,w:fW,rw:fW,lw:0};HTMLCSS.placeBox(line,0,y-D[i]-(dy-D[i]-H[i+1])/2,true);if(RLINES[i]==="dashed"||hasRelativeWidth){line.style.borderTop=line.style.height+" "+RLINES[i];line.style.height=0;line.style.width=line.style.borderLeftWidth;line.style.borderLeft="";if(hasRelativeWidth){line.style.width=
"100%"}}}y-=dy;}if(hasRelativeWidth){span.bbox.width=values.width;stack.style.width="100%"}if(C[LABEL]){var mw=stack.bbox.w,dw;var indent=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift");if(indent.indentalignfirst!==MML.INDENTALIGN.INDENTALIGN){indent.indentalign=indent.indentalignfirst}if(indent.indentalign===MML.INDENTALIGN.AUTO){indent.indentalign=this.displayAlign}if(indent.indentshiftfirst!==MML.INDENTSHIFT.INDENTSHIFT){indent.indentshift=indent.indentshiftfirst}if(indent.indentshift==="auto"){indent.indentshift=this.displayIndent}var eqn=HTMLCSS.createStack(span,false,"100%");HTMLCSS.addBox(eqn,stack);HTMLCSS.alignBox(stack,indent.indentalign,0);if(indent.indentshift&&indent.indentalign!==MML.INDENTALIGN.CENTER){dw=HTMLCSS.length2em(indent.indentshift,mu);mw+=dw;stack.style[indent.indentalign]=HTMLCSS.Em(dw);}C[LABEL].parentNode.parentNode.removeChild(C[LABEL].parentNode);HTMLCSS.addBox(eqn,C[LABEL]);HTMLCSS.alignBox(C[LABEL],CALIGN[LABEL],0);if(
HTMLCSS.msieRelativeWidthBug){stack.style.top=C[LABEL].style.top=""}if(hasRelativeWidth){stack.style.width=values.width;span.bbox.width="100%"}dw=HTMLCSS.length2em(values.minlabelspacing,mu);C[LABEL].style.marginRight=C[LABEL].style.marginLeft=HTMLCSS.Em(dw);if(indent.indentalign===MML.INDENTALIGN.CENTER){mw+=4*dw+2*C[LABEL].bbox.w}else if(indent.indentalign!==CALIGN[LABEL]){mw+=2*dw+C[LABEL].bbox.w}span.style.minWidth=span.bbox.minWidth=eqn.style.minWidth=eqn.bbox.minWidth=HTMLCSS.Em(mw);}if(!hasRelativeWidth){this.HTMLhandleSpace(span)}var color=this.HTMLhandleColor(span);if(color&&hasRelativeWidth){if(!frame){frame=HTMLCSS.createFrame(stack,fH,0,fW,0,"none");HTMLCSS.addBox(stack,frame);HTMLCSS.placeBox(frame,0,fY,true);frame.style.width="100%";}frame.style.backgroundColor=color.style.backgroundColor;frame.parentNode.insertBefore(frame,frame.parentNode.firstChild);color.parentNode.removeChild(color);}return span;},HTMLhandleSpace:function(span){span.bbox.keepPadding=true;span.bbox.
exact=true;if(!this.hasFrame&&span.bbox.width==null){span.style.paddingLeft=span.style.paddingRight=HTMLCSS.Em(1/6)}this.SUPER(arguments).HTMLhandleSpace.call(this,span);}});MML.mtd.Augment({toHTML:function(span,HW,D){span=this.HTMLcreateSpan(span);if(this.data[0]){var box=this.data[0].toHTML(span);if(D!=null){box=this.data[0].HTMLstretchV(span,HW,D)}else if(HW!=null){box=this.data[0].HTMLstretchH(span,HW)}span.bbox=box.bbox;}this.HTMLhandleSpace(span);this.HTMLhandleColor(span);return span;},HTMLstretchH:MML.mbase.HTMLstretchH,HTMLstretchV:MML.mbase.HTMLstretchV});MathJax.Hub.Startup.signal.Post("HTML-CSS mtable Ready");MathJax.Ajax.loadComplete(HTMLCSS.autoloadDir+"/mtable.js");});MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function(){var VERSION="2.3";var MML=MathJax.ElementJax.mml,HTMLCSS=MathJax.OutputJax["HTML-CSS"];var PENALTY={newline:0,nobreak:1000000,goodbreak:[-200],badbreak:[+200],auto:[0],toobig:800,nestfactor:400,spacefactor:-100,spaceoffset:2,spacelimit:1,fence
:500,close:500};var ENDVALUES={linebreakstyle:"after"};MML.mbase.Augment({HTMLlinebreakPenalty:PENALTY,HTMLmultiline:function(span){var parent=this;while(parent.inferred||(parent.parent&&parent.parent.type==="mrow"&&parent.parent.data.length===1)){parent=parent.parent}var isTop=((parent.type==="math"&&parent.Get("display")==="block")||parent.type==="mtd");parent.isMultiline=true;var VALUES=this.getValues("linebreak","linebreakstyle","lineleading","linebreakmultchar","indentalign","indentshift","indentalignfirst","indentshiftfirst","indentalignlast","indentshiftlast");if(VALUES.linebreakstyle===MML.LINEBREAKSTYLE.INFIXLINEBREAKSTYLE){VALUES.linebreakstyle=this.Get("infixlinebreakstyle")}VALUES.lineleading=HTMLCSS.length2em(VALUES.lineleading,1,0.5);this.HTMLremoveColor(span);var stack=HTMLCSS.createStack(span);var state={n:0,Y:0,scale:this.HTMLgetScale(),isTop:isTop,values:{},VALUES:VALUES},align=this.HTMLgetAlign(state,{}),shift=this.HTMLgetShift(state,{},align),start=[],end={index:[],
penalty:PENALTY.nobreak,w:0,W:shift,shift:shift,scanW:shift,nest:0},broken=false;while(this.HTMLbetterBreak(end,state)&&(end.scanW>=HTMLCSS.linebreakWidth||end.penalty==PENALTY.newline)){this.HTMLaddLine(stack,start,end.index,state,end.values,broken);start=end.index.slice(0);broken=true;align=this.HTMLgetAlign(state,end.values);shift=this.HTMLgetShift(state,end.values,align);if(align===MML.INDENTALIGN.CENTER){shift=0}end.W=end.shift=end.scanW=shift;end.penalty=PENALTY.nobreak;}state.isLast=true;this.HTMLaddLine(stack,start,[],state,ENDVALUES,broken);if(isTop){stack.style.width="100%";if(parent.type==="math"){span.bbox.width="100%"}}this.HTMLhandleSpace(span);this.HTMLhandleColor(span);span.bbox.isMultiline=true;return span;},HTMLbetterBreak:function(info,state){if(this.isToken){return false}if(this.isEmbellished()){info.embellished=this;return this.CoreMO().HTMLbetterBreak(info,state);}if(this.linebreakContainer){return false}var index=info.index.slice(0),i=info.index.shift(),m=this.
data.length,W,w,scanW,broken=(info.index.length>0),better=false;if(i==null){i=-1};if(!broken){i++;info.W+=info.w;info.w=0}scanW=info.scanW=info.W;info.nest++;while(i<m&&info.scanW<1.33*HTMLCSS.linebreakWidth){if(this.data[i]){if(this.data[i].HTMLbetterBreak(info,state)){better=true;index=[i].concat(info.index);W=info.W;w=info.w;if(info.penalty===PENALTY.newline){info.index=index;if(info.nest){info.nest--}return true;}}scanW=(broken?info.scanW:this.HTMLaddWidth(i,info,scanW));}info.index=[];i++;broken=false;}if(info.nest){info.nest--}info.index=index;if(better){info.W=W;info.w=w}return better;},HTMLaddWidth:function(i,info,scanW){if(this.data[i]){var span=this.data[i].HTMLspanElement();scanW+=span.bbox.w;if(span.style.paddingLeft){scanW+=HTMLCSS.unEm(span.style.paddingLeft)}if(span.style.paddingRight){scanW+=HTMLCSS.unEm(span.style.paddingRight)}info.W=info.scanW=scanW;info.w=0;}return scanW;},HTMLaddLine:function(stack,start,end,state,values,broken){line=HTMLCSS.createBox(stack);line.
bbox=this.HTMLemptyBBox({});state.first=broken;state.last=true;this.HTMLmoveLine(start,end,line,state,values);this.HTMLcleanBBox(line.bbox);var align=this.HTMLgetAlign(state,values),shift=this.HTMLgetShift(state,values,align);if(shift){HTMLCSS.createBlank(line,shift,(align!==MML.INDENTALIGN.RIGHT));line.bbox.w+=shift;line.bbox.rw+=shift;}if(state.n>0){var LHD=HTMLCSS.FONTDATA.baselineskip*state.scale;var leading=(state.values.lineleading==null?state.VALUES:state.values).lineleading;state.Y-=Math.max(LHD,state.d+line.bbox.h+leading);}HTMLCSS.alignBox(line,align,state.Y);state.d=line.bbox.d;state.values=values;state.n++;},HTMLgetAlign:function(state,values){var cur=values,prev=state.values,def=state.VALUES,align;if(state.n===0){align=cur.indentalignfirst||prev.indentalignfirst||def.indentalignfirst}else if(state.isLast){align=prev.indentalignlast||def.indentalignlast}else{align=prev.indentalign||def.indentalign}if(align===MML.INDENTALIGN.INDENTALIGN){align=prev.indentalign||def.
indentalign}if(align===MML.INDENTALIGN.AUTO){align=(state.isTop?this.displayAlign:MML.INDENTALIGN.LEFT)}return align;},HTMLgetShift:function(state,values,align){if(align===MML.INDENTALIGN.CENTER){return 0}var cur=values,prev=state.values,def=state.VALUES,shift;if(state.n===0){shift=cur.indentshiftfirst||prev.indentshiftfirst||def.indentshiftfirst}else if(state.isLast){shift=prev.indentshiftlast||def.indentshiftlast}else{shift=prev.indentshift||def.indentshift}if(shift===MML.INDENTSHIFT.INDENTSHIFT){shift=prev.indentshift||def.indentshift}if(shift==="auto"||shift===""){shift=(state.isTSop?this.displayIndent:"0")}return HTMLCSS.length2em(shift,0);},HTMLmoveLine:function(start,end,span,state,values){var i=start[0],j=end[0];if(i==null){i=-1};if(j==null){j=this.data.length-1}if(i===j&&start.length>1){this.data[i].HTMLmoveSlice(start.slice(1),end.slice(1),span,state,values,"paddingLeft");}else{var last=state.last;state.last=false;while(i<j){if(this.data[i]){if(start.length<=1){this.data[i].
HTMLmoveSpan(span,state,values)}else{this.data[i].HTMLmoveSlice(start.slice(1),[],span,state,values,"paddingLeft")}}i++;state.first=false;start=[];}state.last=last;if(this.data[i]){if(end.length<=1){this.data[i].HTMLmoveSpan(span,state,values)}else{this.data[i].HTMLmoveSlice([],end.slice(1),span,state,values,"paddingRight")}}}},HTMLmoveSlice:function(start,end,span,state,values,padding){this.HTMLremoveColor();var slice=this.HTMLcreateSliceSpan(span);this.HTMLmoveLine(start,end,slice,state,values);slice.style[padding]="";this.HTMLcombineBBoxes(slice,span.bbox);this.HTMLcleanBBox(slice.bbox);if(end.length===0){span=this.HTMLspanElement();span.parentNode.removeChild(span);span.nextMathJaxSpan.id=span.id;var n=0;while(span=span.nextMathJaxSpan){var color=this.HTMLhandleColor(span);if(color){color.id+="-MathJax-Continue-"+n;n++}}}return slice;},HTMLcreateSliceSpan:function(span){var SPAN=this.HTMLspanElement(),n=0;var LAST=SPAN;while(LAST.nextMathJaxSpan){LAST=LAST.nextMathJaxSpan;n++}var
SLICE=SPAN.cloneNode(false);LAST.nextMathJaxSpan=SLICE;SLICE.nextMathJaxSpan=null;SLICE.id+="-MathJax-Continue-"+n;SLICE.bbox=this.HTMLemptyBBox({});return span.appendChild(SLICE);},HTMLmoveSpan:function(line,state,values){if(!(state.first||state.last)||(state.first&&state.values.linebreakstyle===MML.LINEBREAKSTYLE.BEFORE)||(state.last&&values.linebreakstyle===MML.LINEBREAKSTYLE.AFTER)){var color=document.getElementById("MathJax-Color-"+this.spanID+HTMLCSS.idPostfix);if(color){line.appendChild(color)}var span=this.HTMLspanElement();line.appendChild(span);if(state.last){span.style.paddingRight=""}if(state.first||state.nextIsFirst){delete state.nextIsFirst;span.style.paddingLeft="";if(color){this.HTMLremoveColor(span);this.HTMLhandleColor(span)}}this.HTMLcombineBBoxes(this,line.bbox);}else if(state.first){state.nextIsFirst=true}else{delete state.nextIsFirst}}});MML.mfenced.Augment({HTMLbetterBreak:function(info,state){var index=info.index.slice(0),i=info.index.shift(),m=this.data.length,
W,w,scanW,broken=(info.index.length>0),better=false;if(i==null){i=-1};if(!broken){i++;info.W+=info.w;info.w=0}scanW=info.scanW=info.W;info.nest++;if(!this.dataI){this.dataI=[];if(this.data.open){this.dataI.push("open")}if(m){this.dataI.push(0)}for(var j=1;j<m;j++){if(this.data["sep"+j]){this.dataI.push("sep"+j)}this.dataI.push(j);}if(this.data.close){this.dataI.push("close")}}m=this.dataI.length;while(i<m&&info.scanW<1.33*HTMLCSS.linebreakWidth){var k=this.dataI[i];if(this.data[k]){if(this.data[k].HTMLbetterBreak(info,state)){better=true;index=[i].concat(info.index);W=info.W;w=info.w;if(info.penalty===PENALTY.newline){info.index=index;if(info.nest){info.nest--}return true}}scanW=(broken?info.scanW:this.HTMLaddWidth(i,info,scanW));}info.index=[];i++;broken=false;}if(info.nest){info.nest--}info.index=index;if(better){info.W=W;info.w=w}return better;},HTMLmoveLine:function(start,end,span,state,values){var i=start[0],j=end[0];if(i==null){i=-1};if(j==null){j=this.dataI.length-1}if(i===j&&
start.length>1){this.data[this.dataI[i]].HTMLmoveSlice(start.slice(1),end.slice(1),span,state,values,"paddingLeft");}else{var last=state.last;state.last=false;var k=this.dataI[i];while(i<j){if(this.data[k]){if(start.length<=1){this.data[k].HTMLmoveSpan(span,state,values)}else{this.data[k].HTMLmoveSlice(start.slice(1),[],span,state,values,"paddingLeft")}}i++;k=this.dataI[i];state.first=false;start=[];}state.last=last;if(this.data[k]){if(end.length<=1){this.data[k].HTMLmoveSpan(span,state,values)}else{this.data[k].HTMLmoveSlice([],end.slice(1),span,state,values,"paddingRight")}}}}});MML.msubsup.Augment({HTMLbetterBreak:function(info,state){if(!this.data[this.base]){return false}var index=info.index.slice(0),i=info.index.shift(),W,w,scanW,broken=(info.index.length>0),better=false;if(!broken){info.W+=info.w;info.w=0}scanW=info.scanW=info.W;if(i==null){this.HTMLbaseW=this.data[this.base].HTMLspanElement().bbox.w;this.HTMLdw=this.HTMLspanElement().bbox.w-this.HTMLbaseW;}if(this.data[this.
base].HTMLbetterBreak(info,state)){better=true;index=[this.base].concat(info.index);W=info.W;w=info.w;if(info.penalty===PENALTY.newline){better=broken=true}}if(!broken){this.HTMLaddWidth(this.base,info,scanW)}info.scanW+=this.HTMLdw;info.W=info.scanW;info.index=[];if(better){info.W=W;info.w=w;info.index=index}return better;},HTMLmoveLine:function(start,end,span,state,values){if(this.data[this.base]){if(start.length>1){this.data[this.base].HTMLmoveSlice(start.slice(1),end.slice(1),span,state,values,"paddingLeft");}else{if(end.length<=1){this.data[this.base].HTMLmoveSpan(span,state,values)}else{this.data[this.base].HTMLmoveSlice([],end.slice(1),span,state,values,"paddingRight")}}}if(end.length===0){var s=this.data[this.sup]||this.data[this.sub];if(s){var box=s.HTMLspanElement().parentNode,stack=box.parentNode;if(this.data[this.base]){stack.removeChild(stack.firstChild)}for(box=stack.firstChild;box;box=box.nextSibling){box.style.left=HTMLCSS.Em(HTMLCSS.unEm(box.style.left)-this.HTMLbaseW)
}stack.bbox.w-=this.HTMLbaseW;stack.style.width=HTMLCSS.Em(stack.bbox.w);this.HTMLcombineBBoxes(stack,span.bbox);span.appendChild(stack);}}}});MML.mo.Augment({HTMLbetterBreak:function(info,state){if(info.values&&info.values.id===this.spanID){return false}var values=this.getValues("linebreak","linebreakstyle","lineleading","linebreakmultchar","indentalign","indentshift","indentalignfirst","indentshiftfirst","indentalignlast","indentshiftlast","texClass","fence");if(values.linebreakstyle===MML.LINEBREAKSTYLE.INFIXLINEBREAKSTYLE){values.linebreakstyle=this.Get("infixlinebreakstyle")}if(values.texClass===MML.TEXCLASS.OPEN){info.nest++}if(values.texClass===MML.TEXCLASS.CLOSE&&info.nest){info.nest--}var W=info.scanW,mo=(info.embellished||this);delete info.embellished;var span=mo.HTMLspanElement(),w=span.bbox.w;if(span.style.paddingLeft){w+=HTMLCSS.unEm(span.style.paddingLeft)}if(values.linebreakstyle===MML.LINEBREAKSTYLE.AFTER){W+=w;w=0}if(W-info.shift===0){return false}var offset=HTMLCSS.
linebreakWidth-W;if(state.n===0&&(values.indentshiftfirst!==state.VALUES.indentshiftfirst||values.indentalignfirst!==state.VALUES.indentalignfirst)){var align=this.HTMLgetAlign(state,values),shift=this.HTMLgetShift(state,values,align);offset+=(info.shift-shift);}var penalty=Math.floor(offset/HTMLCSS.linebreakWidth*1000);if(penalty<0){penalty=PENALTY.toobig-3*penalty}if(values.fence){penalty+=PENALTY.fence}if((values.linebreakstyle===MML.LINEBREAKSTYLE.AFTER&&values.texClass===MML.TEXCLASS.OPEN)||values.texClass===MML.TEXCLASS.CLOSE){penalty+=PENALTY.close}penalty+=info.nest*PENALTY.nestfactor;var linebreak=PENALTY[values.linebreak||MML.LINEBREAK.AUTO];if(!(linebreak instanceof Array)){if(offset>=0){penalty=linebreak*info.nest}}else{penalty=Math.max(1,penalty+linebreak[0]*info.nest)}if(penalty>=info.penalty){return false}info.penalty=penalty;info.values=values;info.W=W;info.w=w;values.lineleading=HTMLCSS.length2em(values.lineleading,state.VALUES.lineleading);values.id=this.spanID;return true
;}});MML.mspace.Augment({HTMLbetterBreak:function(info,state){if(info.values&&info.values.id===this.spanID){return false}var values=this.getValues("linebreak");var linebreakValue=values.linebreak;if(!linebreakValue||this.hasDimAttr()){linebreakValue=MML.LINEBREAK.AUTO;}var W=info.scanW,span=this.HTMLspanElement(),w=span.bbox.w;if(span.style.paddingLeft){w+=HTMLCSS.unEm(span.style.paddingLeft)}if(W-info.shift===0){return false}var offset=HTMLCSS.linebreakWidth-W;var penalty=Math.floor(offset/HTMLCSS.linebreakWidth*1000);if(penalty<0){penalty=PENALTY.toobig-3*penalty}penalty+=info.nest*PENALTY.nestfactor;var linebreak=PENALTY[linebreakValue];if(linebreakValue===MML.LINEBREAK.AUTO&&w>=PENALTY.spacelimit){linebreak=[(w+PENALTY.spaceoffset)*PENALTY.spacefactor]}if(!(linebreak instanceof Array)){if(offset>=0){penalty=linebreak*info.nest}}else{penalty=Math.max(1,penalty+linebreak[0]*info.nest)}if(penalty>=info.penalty){return false}info.penalty=penalty;info.values=values;info.W=W;info.w=w;
values.lineleading=state.VALUES.lineleading;values.linebreakstyle="before";values.id=this.spanID;return true;}});MathJax.Hub.Register.StartupHook("TeX mathchoice Ready",function(){MML.TeXmathchoice.Augment({HTMLbetterBreak:function(info,state){return this.Core().HTMLbetterBreak(info,state);},HTMLmoveLine:function(start,end,span,state,values){return this.Core().HTMLmoveSlice(start,end,span,state,values);}});});MML.maction.Augment({HTMLbetterBreak:function(info,state){return this.Core().HTMLbetterBreak(info,state);},HTMLmoveLine:function(start,end,span,state,values){return this.Core().HTMLmoveSlice(start,end,span,state,values);},HTMLmoveSlice:function(start,end,span,state,values,padding){var hitbox=document.getElementById("MathJax-HitBox-"+this.spanID+HTMLCSS.idPostfix);if(hitbox){hitbox.parentNode.removeChild(hitbox)}var slice=this.SUPER(arguments).HTMLmoveSlice.apply(this,arguments);if(end.length===0){span=this.HTMLspanElement();var n=0;while(span){hitbox=this.HTMLhandleHitBox(span,
"-Continue-"+n);span=span.nextMathJaxSpan;n++;}}return slice;}});MML.semantics.Augment({HTMLbetterBreak:function(info,state){return(this.data[0]?this.data[0].HTMLbetterBreak(info,state):false);},HTMLmoveLine:function(start,end,span,state,values){return(this.data[0]?this.data[0].HTMLmoveSlice(start,end,span,state,values):null);}});MathJax.Hub.Startup.signal.Post("HTML-CSS multiline Ready");MathJax.Ajax.loadComplete(HTMLCSS.autoloadDir+"/multiline.js");});},{},{});
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