/*
 *  /MathJax/jax/output/HTML-CSS/jax.js
 *  
 *  Copyright (c) 2012 Design Science, Inc.
 *
 *  Part of the MathJax library.
 *  See http://www.mathjax.org for details.
 * 
 *  Licensed under the Apache License, Version 2.0;
 *  you may not use this file except in compliance with the License.
 *
 *      http://www.apache.org/licenses/LICENSE-2.0
 */

(function(g,b,d){var f,h=b.Browser.isMobile;var e=MathJax.Object.Subclass({timeout:(h?15:8)*1000,FontInfo:{STIX:{family:"STIXSizeOneSym",testString:"() {} []"},TeX:{family:"MathJax_Size1",testString:"() {} []"}},comparisonFont:["sans-serif","monospace","script","Times","Courier","Arial","Helvetica"],testSize:["40px","50px","60px","30px","20px"],Init:function(){this.div=MathJax.HTML.addElement(document.body,"div",{id:"MathJax_Font_Test",style:{position:"absolute",visibility:"hidden",top:0,left:0,width:"auto",padding:0,border:0,margin:0,whiteSpace:"nowrap",textAlign:"left",textIndent:0,textTransform:"none",lineHeight:"normal",letterSpacing:"normal",wordSpacing:"normal",fontSize:this.testSize[0],fontWeight:"normal",fontStyle:"normal",fontSizeAdjust:"none"}},[""]);this.text=this.div.firstChild},findFont:function(n,k){if(k&&this.testCollection(k)){return k}for(var l=0,j=n.length;l<j;l++){if(n[l]===k){continue}if(this.testCollection(n[l])){return n[l]}}return null},testCollection:function(j){return this.testFont(this.FontInfo[j])},testFont:function(l){if(l.isWebFont&&d.FontFaceBug){this.div.style.fontWeight=this.div.style.fontStyle="normal"}else{this.div.style.fontWeight=(l.weight||"normal");this.div.style.fontStyle=(l.style||"normal")}var k=this.getComparisonWidths(l.testString,l.noStyleChar);if(k){this.div.style.fontFamily="'"+l.family+"',"+this.comparisonFont[0];if(this.div.offsetWidth==k[0]){this.div.style.fontFamily="'"+l.family+"',"+this.comparisonFont[k[2]];if(this.div.offsetWidth==k[1]){return false}}if(this.div.offsetWidth!=k[3]||this.div.offsetHeight!=k[4]){if(l.noStyleChar||!d.FONTDATA||!d.FONTDATA.hasStyleChar){return true}for(var n=0,j=this.testSize.length;n<j;n++){if(this.testStyleChar(l,this.testSize[n])){return true}}}}return false},styleChar:"\uEFFD",versionChar:"\uEFFE",compChar:"\uEFFF",testStyleChar:function(l,o){var r=3+(l.weight?2:0)+(l.style?4:0);var k="",m=0;var q=this.div.style.fontSize;this.div.style.fontSize=o;if(d.msieItalicWidthBug&&l.style==="italic"){this.text.nodeValue=k=this.compChar;m=this.div.offsetWidth}if(d.safariTextNodeBug){this.div.innerHTML=this.compChar+k}else{this.text.nodeValue=this.compChar+k}var j=this.div.offsetWidth-m;if(d.safariTextNodeBug){this.div.innerHTML=this.styleChar+k}else{this.text.nodeValue=this.styleChar+k}var p=Math.floor((this.div.offsetWidth-m)/j+0.5);if(p===r){if(d.safariTextNodeBug){this.div.innerHTML=this.versionChar+k}else{this.text.nodeValue=this.versionChar+k}l.version=Math.floor((this.div.offsetWidth-m)/j+1.5)/2}this.div.style.fontSize=q;return(p===r)},getComparisonWidths:function(o,l){if(d.FONTDATA&&d.FONTDATA.hasStyleChar&&!l){o+=this.styleChar+" "+this.compChar}if(d.safariTextNodeBug){this.div.innerHTML=o}else{this.text.nodeValue=o}this.div.style.fontFamily=this.comparisonFont[0];var k=this.div.offsetWidth;this.div.style.fontFamily=d.webFontDefault;var q=this.div.offsetWidth,n=this.div.offsetHeight;for(var p=1,j=this.comparisonFont.length;p<j;p++){this.div.style.fontFamily=this.comparisonFont[p];if(this.div.offsetWidth!=k){return[k,this.div.offsetWidth,p,q,n]}}return null},loadWebFont:function(k){b.Startup.signal.Post("HTML-CSS Jax - Web-Font "+d.fontInUse+"/"+k.directory);var m=MathJax.Message.File("Web-Font "+d.fontInUse+"/"+k.directory);var j=MathJax.Callback({});var l=MathJax.Callback(["loadComplete",this,k,m,j]);g.timer.start(g,[this.checkWebFont,k,l],0,this.timeout);return j},loadComplete:function(l,o,k,j){MathJax.Message.Clear(o);if(j===g.STATUS.OK){this.webFontLoaded=true;k();return}this.loadError(l);if(b.Browser.isFirefox&&d.allowWebFonts){var m=document.location.protocol+"//"+document.location.hostname;if(document.location.port!=""){m+=":"+document.location.port}m+="/";if(g.fileURL(d.webfontDir).substr(0,m.length)!==m){this.firefoxFontError(l)}}if(!this.webFontLoaded){d.loadWebFontError(l,k)}else{k()}},loadError:function(j){MathJax.Message.Set("Can't load web font "+d.fontInUse+"/"+j.directory,null,2000);b.Startup.signal.Post(["HTML-CSS Jax - web font error",d.fontInUse+"/"+j.directory,j])},firefoxFontError:function(j){MathJax.Message.Set("Firefox can't load web fonts from a remote host",null,3000);b.Startup.signal.Post("HTML-CSS Jax - Firefox web fonts on remote host error")},checkWebFont:function(j,k,l){if(j.time(l)){return}if(d.Font.testFont(k)){l(j.STATUS.OK)}else{setTimeout(j,j.delay)}},fontFace:function(l){var m=d.allowWebFonts;var o=d.FONTDATA.FONTS[l];if(d.msieFontCSSBug&&!o.family.match(/-Web$/)){o.family+="-Web"}var k=g.fileURL(d.webfontDir+"/"+m);var j=l.replace(/-b/,"-B").replace(/-i/,"-I").replace(/-Bold-/,"-Bold");if(!j.match(/-/)){j+="-Regular"}if(m==="svg"){j+=".svg#"+j}else{j+="."+m}var n={"font-family":o.family,src:"url('"+k+"/"+j+"')"};if(m==="otf"){n.src+=" format('opentype')";k=g.fileURL(d.webfontDir+"/woff");n.src="url('"+k+"/"+j.replace(/otf$/,"woff")+"') format('woff'), "+n.src}else{if(m!=="eot"){n.src+=" format('"+m+"')"}}if(!(d.FontFaceBug&&o.isWebFont)){if(l.match(/-bold/)){n["font-weight"]="bold"}if(l.match(/-italic/)){n["font-style"]="italic"}}return n}});var i,a,c;d.Augment({config:{styles:{".MathJax":{display:"inline","font-style":"normal","font-weight":"normal","line-height":"normal","font-size":"100%","font-size-adjust":"none","text-indent":0,"text-align":"left","text-transform":"none","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none",direction:"ltr",border:0,padding:0,margin:0},".MathJax_Display":{position:"relative",display:"block",width:"100%"},".MathJax img, .MathJax nobr, .MathJax a":{border:0,padding:0,margin:0,"max-width":"none","max-height":"none","vertical-align":0,"line-height":"normal","text-decoration":"none"},"img.MathJax_strut":{border:"0 !important",padding:"0 !important",margin:"0 !important","vertical-align":"0 !important"},".MathJax span":{display:"inline",position:"static",border:0,padding:0,margin:0,"vertical-align":0,"line-height":"normal","text-decoration":"none"},".MathJax nobr":{"white-space":"nowrap ! important"},".MathJax img":{display:"inline ! important","float":"none ! important"},".MathJax_Processing":{visibility:"hidden",position:"fixed",width:0,height:0,overflow:"hidden"},".MathJax_Processed":{display:"none!important"},".MathJax_ExBox":{display:"block",overflow:"hidden",width:"1px",height:"60ex"},".MathJax .MathJax_EmBox":{display:"block",overflow:"hidden",width:"1px",height:"60em"},".MathJax .MathJax_HitBox":{cursor:"text",background:"white",opacity:0,filter:"alpha(opacity=0)"},".MathJax .MathJax_HitBox *":{filter:"none",opacity:1,background:"transparent"},"#MathJax_Tooltip":{position:"absolute",left:0,top:0,width:"auto",height:"auto",display:"none"},"#MathJax_Tooltip *":{filter:"none",opacity:1,background:"transparent"},"@font-face":{"font-family":"MathJax_Blank",src:"url('about:blank')"}}},settings:b.config.menuSettings,hideProcessedMath:true,Font:null,webFontDefault:"MathJax_Blank",Config:function(){if(!this.require){this.require=[]}this.Font=e();this.SUPER(arguments).Config.call(this);var k=this.settings;if(this.adjustAvailableFonts){this.adjustAvailableFonts(this.config.availableFonts)}if(k.scale){this.config.scale=k.scale}if(k.font&&k.font!=="Auto"){if(k.font==="TeX (local)"){this.config.availableFonts=["TeX"];this.config.preferredFont="TeX";this.config.webFont="TeX"}else{if(k.font==="STIX (local)"){this.config.availableFonts=["STIX"];this.config.preferredFont="STIX";this.config.webFont="TeX"}else{if(k.font==="TeX (web)"){this.config.availableFonts=[];this.config.preferredFont="";this.config.webFont="TeX"}else{if(k.font==="TeX (image)"){this.config.availableFonts=[];this.config.preferredFont="";this.config.webFont=""}}}}}var j=this.Font.findFont(this.config.availableFonts,this.config.preferredFont);if(!j&&this.allowWebFonts){j=this.config.webFont;if(j){this.webFonts=true}}if(!j&&this.config.imageFont){j=this.config.imageFont;this.imgFonts=true}if(j){this.fontInUse=j;this.fontDir+="/"+j;this.webfontDir+="/"+j;this.require.push(this.fontDir+"/fontdata.js");if(this.imgFonts){this.require.push(this.directory+"/imageFonts.js");b.Startup.signal.Post("HTML-CSS Jax - using image fonts")}}else{MathJax.Message.Set("Can't find a valid font using ["+this.config.availableFonts.join(", ")+"]",null,3000);this.FONTDATA={TeX_factor:1,baselineskip:1.2,lineH:0.8,lineD:0.2,ffLineH:0.8,FONTS:{},VARIANT:{normal:{fonts:[]}},RANGES:[],DELIMITERS:{},RULECHAR:45,REMAP:{}};if(MathJax.InputJax.TeX&&MathJax.InputJax.TeX.Definitions){MathJax.InputJax.TeX.Definitions.macros.overline[1]="002D";MathJax.InputJax.TeX.Definitions.macros.underline[1]="002D"}b.Startup.signal.Post("HTML-CSS Jax - no valid font")}this.require.push(MathJax.OutputJax.extensionDir+"/MathEvents.js")},Startup:function(){i=MathJax.Extension.MathEvents.Event;a=MathJax.Extension.MathEvents.Touch;c=MathJax.Extension.MathEvents.Hover;this.ContextMenu=i.ContextMenu;this.Mousedown=i.AltContextMenu;this.Mouseover=c.Mouseover;this.Mouseout=c.Mouseout;this.Mousemove=c.Mousemove;this.hiddenDiv=this.Element("div",{style:{visibility:"hidden",overflow:"hidden",position:"absolute",top:0,height:"1px",width:"auto",padding:0,border:0,margin:0,textAlign:"left",textIndent:0,textTransform:"none",lineHeight:"normal",letterSpacing:"normal",wordSpacing:"normal"}});if(!document.body.firstChild){document.body.appendChild(this.hiddenDiv)}else{document.body.insertBefore(this.hiddenDiv,document.body.firstChild)}this.hiddenDiv=this.addElement(this.hiddenDiv,"div",{id:"MathJax_Hidden"});var k=this.addElement(this.hiddenDiv,"div",{style:{width:"5in"}});this.pxPerInch=k.offsetWidth/5;this.hiddenDiv.removeChild(k);this.startMarker=this.createStrut(this.Element("span"),10,true);this.endMarker=this.addText(this.Element("span"),"x").parentNode;this.HDspan=this.Element("span");if(this.operaHeightBug){this.createStrut(this.HDspan,0)}if(this.msieInlineBlockAlignBug){this.HDimg=this.addElement(this.HDspan,"img",{style:{height:"0px",width:"1px"}});try{this.HDimg.src="about:blank"}catch(j){}}else{this.HDimg=this.createStrut(this.HDspan,0)}this.EmExSpan=this.Element("span",{style:{position:"absolute","font-size-adjust":"none"}},[["span",{className:"MathJax_ExBox"}],["span",{className:"MathJax"},[["span",{className:"MathJax_EmBox"}]]]]);this.linebreakSpan=this.Element("span",null,[["hr",{style:{width:"100%",size:1,padding:0,border:0,margin:0}}]]);return g.Styles(this.config.styles,["InitializeHTML",this])},removeSTIXfonts:function(l){for(var k=0,j=l.length;k<j;k++){if(l[k]==="STIX"){l.splice(k,1);j--;k--}}if(this.config.preferredFont==="STIX"){this.config.preferredFont=l[0]}},PreloadWebFonts:function(){if(!d.allowWebFonts||!d.config.preloadWebFonts){return}for(var k=0,j=d.config.preloadWebFonts.length;k<j;k++){var l=d.FONTDATA.FONTS[d.config.preloadWebFonts[k]];if(!l.available){d.Font.testFont(l)}}},InitializeHTML:function(){this.PreloadWebFonts();document.body.appendChild(this.EmExSpan);document.body.appendChild(this.linebreakSpan);this.defaultEx=this.EmExSpan.firstChild.offsetHeight/60;this.defaultEm=this.EmExSpan.lastChild.firstChild.offsetHeight/60;this.defaultWidth=this.linebreakSpan.firstChild.offsetWidth;document.body.removeChild(this.linebreakSpan);document.body.removeChild(this.EmExSpan)},preTranslate:function(n){var t=n.jax[this.id],u,q=t.length,y,s,z,l,x,k,w,p,r,j,v=false,A=this.config.linebreaks.automatic,o=this.config.linebreaks.width;if(A){v=(o.match(/^\s*(\d+(\.\d*)?%\s*)?container\s*$/)!=null);if(v){o=o.replace(/\s*container\s*/,"")}else{j=this.defaultWidth}if(o===""){o="100%"}}else{j=100000}for(u=0;u<q;u++){y=t[u];if(!y.parentNode){continue}s=y.previousSibling;if(s&&String(s.className).match(/^MathJax(_Display)?$/)){s.parentNode.removeChild(s)}k=y.MathJax.elementJax;k.HTMLCSS={display:(k.root.Get("display")==="block")};z=l=this.Element("span",{className:"MathJax",id:k.inputID+"-Frame",isMathJax:true,jaxID:this.id,oncontextmenu:i.Menu,onmousedown:i.Mousedown,onmouseover:i.Mouseover,onmouseout:i.Mouseout,onmousemove:i.Mousemove,onclick:i.Click,ondblclick:i.DblClick});if(b.Browser.noContextMenu){z.ontouchstart=a.start;z.ontouchend=a.end}if(k.HTMLCSS.display){l=this.Element("div",{className:"MathJax_Display"});l.appendChild(z)}else{if(this.msieDisappearingBug){z.style.display="inline-block"}}l.setAttribute("role","textbox");l.setAttribute("aria-readonly","true");l.className+=" MathJax_Processing";y.parentNode.insertBefore(l,y);y.parentNode.insertBefore(this.EmExSpan.cloneNode(true),y);if(v){l.parentNode.insertBefore(this.linebreakSpan.cloneNode(true),l)}}for(u=0;u<q;u++){y=t[u];if(!y.parentNode){continue}x=y.previousSibling;l=x.previousSibling;k=y.MathJax.elementJax;w=x.firstChild.offsetHeight/60;p=x.lastChild.firstChild.offsetHeight/60;if(v){j=l.previousSibling.firstChild.offsetWidth}if(w===0||w==="NaN"){this.hiddenDiv.appendChild(l);k.HTMLCSS.isHidden=true;w=this.defaultEx;p=this.defaultEm;if(v){j=this.defaultWidth}}r=Math.floor(Math.max(this.config.minScaleAdjust/100,(w/this.TeX.x_height)/p)*this.config.scale);k.HTMLCSS.scale=r/100;k.HTMLCSS.fontSize=r+"%";k.HTMLCSS.em=k.HTMLCSS.outerEm=p;this.em=p*r/100;k.HTMLCSS.ex=w;k.HTMLCSS.lineWidth=(A?this.length2em(o,1,j/this.em):1000000)}for(u=0;u<q;u++){y=t[u];if(!y.parentNode){continue}x=t[u].previousSibling;k=t[u].MathJax.elementJax;if(v){z=x.previousSibling;if(!k.HTMLCSS.isHidden){z=z.previousSibling}z.parentNode.removeChild(z)}x.parentNode.removeChild(x)}n.HTMLCSSeqn=n.HTMLCSSlast=0;n.HTMLCSSchunk=this.config.EqnChunk;n.HTMLCSSdelay=false},Translate:function(k,o){if(!k.parentNode){return}if(o.HTMLCSSdelay){o.HTMLCSSdelay=false;b.RestartAfter(MathJax.Callback.Delay(this.config.EqnChunkDelay))}var j=k.MathJax.elementJax,n=j.root,l=document.getElementById(j.inputID+"-Frame"),p=(j.HTMLCSS.display?l.parentNode:l);this.em=f.mbase.prototype.em=j.HTMLCSS.em*j.HTMLCSS.scale;this.outerEm=j.HTMLCSS.em;this.scale=j.HTMLCSS.scale;this.linebreakWidth=j.HTMLCSS.lineWidth;l.style.fontSize=j.HTMLCSS.fontSize;this.initImg(l);this.initHTML(n,l);n.setTeXclass();try{n.toHTML(l,p)}catch(m){if(m.restart){while(l.firstChild){l.removeChild(l.firstChild)}}throw m}if(j.HTMLCSS.isHidden){k.parentNode.insertBefore(p,k)}p.className=p.className.split(/ /)[0];if(this.hideProcessedMath){p.className+=" MathJax_Processed";if(k.MathJax.preview){j.HTMLCSS.preview=k.MathJax.preview;delete k.MathJax.preview}o.HTMLCSSeqn++;if(o.HTMLCSSeqn>=o.HTMLCSSlast+o.HTMLCSSchunk){this.postTranslate(o);o.HTMLCSSchunk=Math.floor(o.HTMLCSSchunk*this.config.EqnChunkFactor);o.HTMLCSSdelay=true}}},postTranslate:function(q){var k=q.jax[this.id];if(!this.hideProcessedMath){return}for(var o=q.HTMLCSSlast,j=q.HTMLCSSeqn;o<j;o++){var l=k[o];if(l){l.previousSibling.className=l.previousSibling.className.split(/ /)[0];var p=l.MathJax.elementJax.HTMLCSS;if(p.preview){p.preview.innerHTML="";l.MathJax.preview=p.preview;delete p.preview}}}if(this.forceReflow){var n=(document.styleSheets||[])[0]||{};n.disabled=true;n.disabled=false}q.HTMLCSSlast=q.HTMLCSSeqn},getJaxFromMath:function(j){if(j.parentNode.className==="MathJax_Display"){j=j.parentNode}return b.getJaxFor(j.nextSibling)},getHoverSpan:function(j,k){return j.root.HTMLspanElement()},getHoverBBox:function(j,m,n){var o=m.bbox,l=j.HTMLCSS.outerEm;var k={w:o.w*l,h:o.h*l,d:o.d*l};if(o.width){k.width=o.width}return k},Zoom:function(k,u,t,j,r){u.className="MathJax";u.style.fontSize=k.HTMLCSS.fontSize;var w=u.appendChild(this.EmExSpan.cloneNode(true));var n=w.lastChild.firstChild.offsetHeight/60;this.em=f.mbase.prototype.em=n;this.outerEm=n/k.HTMLCSS.scale;w.parentNode.removeChild(w);this.idPostfix="-zoom";k.root.toHTML(u,u);this.idPostfix="";var m=k.root.HTMLspanElement().bbox.width;if(m){u.style.width=Math.floor(j-1.5*d.em)+"px";u.style.display="inline-block";var l=(k.root.id||"MathJax-Span-"+k.root.spanID)+"-zoom";var o=document.getElementById(l).firstChild;while(o&&o.style.width!==m){o=o.nextSibling}if(o){o.style.width="100%"}}u.style.position=t.style.position="absolute";var s=u.offsetWidth,q=u.offsetHeight,v=t.offsetHeight,p=t.offsetWidth;if(p===0){p=t.parentNode.offsetWidth}u.style.position=t.style.position="";return{Y:-i.getBBox(u).h,mW:p,mH:v,zW:s,zH:q}},initImg:function(j){},initHTML:function(k,j){},initFont:function(j){var l=d.FONTDATA.FONTS,k=d.config.availableFonts;if(k&&k.length&&d.Font.testFont(l[j])){l[j].available=true;return null}if(!this.allowWebFonts){return null}l[j].isWebFont=true;if(d.FontFaceBug){l[j].family=j;if(d.msieFontCSSBug){l[j].family+="-Web"}}return g.Styles({"@font-face":this.Font.fontFace(j)})},Remove:function(j){var k=document.getElementById(j.inputID+"-Frame");if(k){if(j.HTMLCSS.display){k=k.parentNode}k.parentNode.removeChild(k)}delete j.HTMLCSS},getHD:function(k){var j=k.style.position;k.style.position="absolute";this.HDimg.style.height="0px";k.appendChild(this.HDspan);var l={h:k.offsetHeight};this.HDimg.style.height=l.h+"px";l.d=k.offsetHeight-l.h;l.h-=l.d;l.h/=this.em;l.d/=this.em;k.removeChild(this.HDspan);k.style.position=j;return l},getW:function(n){var k,m,l=(n.bbox||{}).w,o=n;if(n.bbox&&n.bbox.exactW){return l}if((n.bbox&&l>=0&&!this.initialSkipBug)||this.negativeBBoxes||!n.firstChild){k=n.offsetWidth;m=n.parentNode.offsetHeight}else{if(n.bbox&&l<0&&this.msieNegativeBBoxBug){k=-n.offsetWidth,m=n.parentNode.offsetHeight}else{if(this.initialSkipBug){var j=n.style.position;n.style.position="absolute";o=this.startMarker;n.insertBefore(o,n.firstChild)}n.appendChild(this.endMarker);k=this.endMarker.offsetLeft-o.offsetLeft;n.removeChild(this.endMarker);if(this.initialSkipBug){n.removeChild(o);n.style.position=j}}}if(m!=null){n.parentNode.HH=m/this.em}return k/this.em},Measured:function(l,k){var m=l.bbox;if(m.width==null&&m.w&&!m.isMultiline){var j=this.getW(l);m.rw+=j-m.w;m.w=j;m.exactW=true}if(!k){k=l.parentNode}if(!k.bbox){k.bbox=m}return l},Remeasured:function(k,j){j.bbox=this.Measured(k,j).bbox},MeasureSpans:function(n){var q=[],s,p,l,t,j,o,k;for(p=0,l=n.length;p<l;p++){s=n[p];if(!s){continue}t=s.bbox;if(t.exactW||t.width||t.w===0||t.isMultiline){if(!s.parentNode.bbox){s.parentNode.bbox=t}continue}if(this.negativeBBoxes||!s.firstChild||(t.w>=0&&!this.initialSkipBug)||(t.w<0&&this.msieNegativeBBoxBug)){q.push([s])}else{if(this.initialSkipBug){j=this.startMarker.cloneNode(true);o=this.endMarker.cloneNode(true);s.insertBefore(j,s.firstChild);s.appendChild(o);q.push([s,j,o,s.style.position]);s.style.position="absolute"}else{o=this.endMarker.cloneNode(true);s.appendChild(o);q.push([s,null,o])}}}for(p=0,l=q.length;p<l;p++){s=q[p][0];t=s.bbox;var r=s.parentNode;if((t.w>=0&&!this.initialSkipBug)||this.negativeBBoxes||!s.firstChild){k=s.offsetWidth;r.HH=s.parentNode.offsetHeight/this.em}else{if(t.w<0&&this.msieNegativeBBoxBug){k=-s.offsetWidth,r.HH=s.parentNode.offsetHeight/this.em}else{k=q[p][2].offsetLeft-((q[p][1]||{}).offsetLeft||0)}}k/=this.em;t.rw+=k-t.w;t.w=k;t.exactW=true;if(!r.bbox){r.bbox=t}}for(p=0,l=q.length;p<l;p++){s=q[p];if(s[1]){s[1].parentNode.removeChild(s[1]),s[0].style.position=s[3]}if(s[2]){s[2].parentNode.removeChild(s[2])}}},Em:function(j){if(Math.abs(j)<0.0006){return"0em"}return j.toFixed(3).replace(/\.?0+$/,"")+"em"},Percent:function(j){return(100*j).toFixed(1).replace(/\.?0+$/,"")+"%"},length2em:function(q,k,o){if(typeof(q)!=="string"){q=q.toString()}if(q===""){return""}if(q===f.SIZE.NORMAL){return 1}if(q===f.SIZE.BIG){return 2}if(q===f.SIZE.SMALL){return 0.71}if(q==="infinity"){return d.BIGDIMEN}var n=this.FONTDATA.TeX_factor;if(q.match(/mathspace$/)){return d.MATHSPACE[q]*n}var 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l=this.HTMLspanElement();if(!j.family&&l.style.fontFamily){j.family=l.style.fontFamily}if(!j.weight&&l.style.fontWeight){j.weight=l.style.fontWeight}if(!j.style&&l.style.fontStyle){j.style=l.style.fontStyle}}if(j.weight&&j.weight.match(/^\d+$/)){j.weight=(parseInt(j.weight)>600?"bold":"normal")}var 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q=this.getValues("symmetric","maxsize","minsize");var o=this.HTMLspanElement(),r=this.HTMLgetMu(o),p;var j=d.TeX.axis_height,k=o.scale;if(q.symmetric){p=2*Math.max(m-j,n+j)}else{p=m+n}q.maxsize=d.length2em(q.maxsize,r,o.bbox.h+o.bbox.d);q.minsize=d.length2em(q.minsize,r,o.bbox.h+o.bbox.d);p=Math.max(q.minsize,Math.min(q.maxsize,p));o=this.HTMLcreateSpan(l);d.createDelimiter(o,this.data.join("").charCodeAt(0),p,k);if(q.symmetric){p=(o.bbox.h+o.bbox.d)/2+j}else{p=(o.bbox.h+o.bbox.d)*m/(m+n)}d.positionDelimiter(o,p);this.HTMLhandleSpace(o);this.HTMLhandleColor(o);return o},HTMLstretchH:function(n,j){this.HTMLremoveColor();var l=this.getValues("maxsize","minsize","mathvariant","fontweight");if((l.fontweight==="bold"||parseInt(l.fontweight)>=600)&&!this.Get("mathvariant",true)){l.mathvariant=f.VARIANT.BOLD}var m=this.HTMLspanElement(),k=this.HTMLgetMu(m),o=m.scale;l.maxsize=d.length2em(l.maxsize,k,m.bbox.w);l.minsize=d.length2em(l.minsize,k,m.bbox.w);j=Math.max(l.minsize,Math.min(l.maxsize,j));m=this.HTMLcreateSpan(n);d.createDelimiter(m,this.data.join("").charCodeAt(0),j,o,l.mathvariant);this.HTMLhandleSpace(m);this.HTMLhandleColor(m);return m}});f.mtext.Augment({toHTML:function(n){n=this.HTMLhandleSize(this.HTMLcreateSpan(n));var l=this.HTMLgetVariant();if(d.config.mtextFontInherit||this.Parent().type==="merror"){l=null}for(var k=0,j=this.data.length;k<j;k++){if(this.data[k]){this.data[k].toHTML(n,l)}}if(!n.bbox){n.bbox={w:0,h:0,d:0,rw:0,lw:0}}if(this.data.join("").length!==1){delete n.bbox.skew}this.HTMLhandleSpace(n);this.HTMLhandleColor(n);return n}});f.merror.Augment({toHTML:function(k){var m=MathJax.HTML.addElement(k,"span",{style:{display:"inline-block"}});k=this.SUPER(arguments).toHTML.call(this,m);var l=d.getHD(m),j=d.getW(m);m.bbox={h:l.h,d:l.d,w:j,lw:0,rw:j,exactW:true};m.id=k.id;k.id=null;return m}});f.ms.Augment({toHTML:f.mbase.HTMLautoload});f.mglyph.Augment({toHTML:f.mbase.HTMLautoload});f.mspace.Augment({toHTML:function(n){n=this.HTMLhandleSize(this.HTMLcreateSpan(n));var l=this.getValues("height","depth","width");var k=this.HTMLgetMu(n);l.mathbackground=this.mathbackground;if(this.background&&!this.mathbackground){l.mathbackground=this.background}var m=d.length2em(l.height,k)/n.scale,o=d.length2em(l.depth,k)/n.scale,j=d.length2em(l.width,k)/n.scale;d.createSpace(n,m,o,j,l.mathbackground);return n}});f.mphantom.Augment({toHTML:function(n,k,p){n=this.HTMLcreateSpan(n);if(this.data[0]!=null){var o=this.data[0].toHTML(n);if(p!=null){d.Remeasured(this.data[0].HTMLstretchV(n,k,p),n)}else{if(k!=null){d.Remeasured(this.data[0].HTMLstretchH(n,k),n)}else{o=d.Measured(o,n)}}n.bbox={w:o.bbox.w,h:o.bbox.h,d:o.bbox.d,lw:0,rw:0,exactW:true};for(var 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s=this.getValues("height","depth","width","lspace","voffset"),q=0,o=0,t=this.HTMLgetMu(r);if(s.lspace){q=this.HTMLlength2em(m,s.lspace,t)}if(s.voffset){o=this.HTMLlength2em(m,s.voffset,t)}d.placeBox(m,q,o);r.bbox={h:m.bbox.h,d:m.bbox.d,w:m.bbox.w,exactW:true,lw:Math.min(0,m.bbox.lw+q),rw:Math.max(m.bbox.w,m.bbox.rw+q),H:Math.max((m.bbox.H==null?-d.BIGDIMEN:m.bbox.H),m.bbox.h+o),D:Math.max((m.bbox.D==null?-d.BIGDIMEN:m.bbox.D),m.bbox.d-o)};if(s.height!==""){r.bbox.h=this.HTMLlength2em(m,s.height,t,"h",0)}if(s.depth!==""){r.bbox.d=this.HTMLlength2em(m,s.depth,t,"d",0)}if(s.width!==""){r.bbox.w=this.HTMLlength2em(m,s.width,t,"w",0)}if(r.bbox.H<=r.bbox.h){delete r.bbox.H}if(r.bbox.D<=r.bbox.d){delete r.bbox.D}var n=/^\s*(\d+(\.\d*)?|\.\d+)\s*(pt|em|ex|mu|px|pc|in|mm|cm)\s*$/;r.bbox.exact=!!((this.data[0]&&this.data[0].data.length==0)||n.exec(s.height)||n.exec(s.width)||n.exec(s.depth));d.setStackWidth(p,r.bbox.w)}this.HTMLhandleSpace(r);this.HTMLhandleColor(r);return 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m=this.data[0].toHTML(k);if(l!=null){this.data[0].HTMLstretchV(k,j,l)}else{if(j!=null){this.data[0].HTMLstretchH(k,j)}}k.bbox=m.bbox}this.HTMLhandleSpace(k);this.HTMLhandleColor(k);return k},HTMLstretchH:f.mbase.HTMLstretchH,HTMLstretchV:f.mbase.HTMLstretchV});f.mfrac.Augment({toHTML:function(C){C=this.HTMLcreateSpan(C);var l=d.createStack(C);var o=d.createBox(l),n=d.createBox(l);d.MeasureSpans([this.HTMLboxChild(0,o),this.HTMLboxChild(1,n)]);var j=this.getValues("displaystyle","linethickness","numalign","denomalign","bevelled");var G=this.HTMLgetScale(),B=j.displaystyle;var F=d.TeX.axis_height*G;if(j.bevelled){var E=(B?0.4:0.15);var r=Math.max(o.bbox.h+o.bbox.d,n.bbox.h+n.bbox.d)+2*E;var D=d.createBox(l);d.createDelimiter(D,47,r);d.placeBox(o,0,(o.bbox.d-o.bbox.h)/2+F+E);d.placeBox(D,o.bbox.w-E/2,(D.bbox.d-D.bbox.h)/2+F);d.placeBox(n,o.bbox.w+D.bbox.w-E,(n.bbox.d-n.bbox.h)/2+F-E)}else{var k=Math.max(o.bbox.w,n.bbox.w);var x=d.thickness2em(j.linethickness,G),z,y,w,s;var A=d.TeX.min_rule_thickness/this.em;if(B){w=d.TeX.num1;s=d.TeX.denom1}else{w=(x===0?d.TeX.num3:d.TeX.num2);s=d.TeX.denom2}w*=G;s*=G;if(x===0){z=Math.max((B?7:3)*d.TeX.rule_thickness,2*A);y=(w-o.bbox.d)-(n.bbox.h-s);if(y<z){w+=(z-y)/2;s+=(z-y)/2}}else{z=Math.max((B?2:0)*A+x,x/2+1.5*A);y=(w-o.bbox.d)-(F+x/2);if(y<z){w+=z-y}y=(F-x/2)-(n.bbox.h-s);if(y<z){s+=z-y}var m=d.createBox(l);d.createRule(m,x,0,k+2*x);d.placeBox(m,0,F-x/2)}d.alignBox(o,j.numalign,w);d.alignBox(n,j.denomalign,-s)}this.HTMLhandleSpace(C);this.HTMLhandleColor(C);return C},HTMLcanStretch:function(j){return false},HTMLhandleSpace:function(j){if(!this.texWithDelims){var k=(this.useMMLspacing?0:d.length2em(this.texSpacing()||0))+0.12;j.style.paddingLeft=d.Em(k);j.style.paddingRight=".12em"}}});f.msqrt.Augment({toHTML:function(v){v=this.HTMLcreateSpan(v);var y=d.createStack(v);var m=d.createBox(y),s=d.createBox(y),r=d.createBox(y);var o=this.HTMLgetScale();var z=d.TeX.rule_thickness*o,l,k,w,n;if(this.Get("displaystyle")){l=d.TeX.x_height*o}else{l=z}k=Math.max(z+l/4,1.5*d.TeX.min_rule_thickness/this.em);var j=this.HTMLboxChild(0,m);w=j.bbox.h+j.bbox.d+k+z;d.createDelimiter(r,8730,w,o);d.MeasureSpans([j,r]);n=j.bbox.w;var u=0;if(r.isMultiChar||(d.AdjustSurd&&d.imgFonts)){r.bbox.w*=0.95}if(r.bbox.h+r.bbox.d>w){k=((r.bbox.h+r.bbox.d)-(w-z))/2}var A=d.FONTDATA.DELIMITERS[d.FONTDATA.RULECHAR];if(!A||n<A.HW[0][0]*o||o<0.75){d.createRule(s,z,0,n)}else{d.createDelimiter(s,d.FONTDATA.RULECHAR,n,o)}w=j.bbox.h+k+z;k=w*d.rfuzz;if(r.isMultiChar){k=d.rfuzz}u=this.HTMLaddRoot(y,r,u,r.bbox.h+r.bbox.d-w,o);d.placeBox(r,u,w-r.bbox.h);d.placeBox(s,u+r.bbox.w,w-s.bbox.h+k);d.placeBox(m,u+r.bbox.w,0);this.HTMLhandleSpace(v);this.HTMLhandleColor(v);return v},HTMLaddRoot:function(l,k,j,n,m){return j}});f.mroot.Augment({toHTML:f.msqrt.prototype.toHTML,HTMLaddRoot:function(r,k,p,n,j){var l=d.createBox(r);if(this.data[1]){var o=this.data[1].toHTML(l);o.style.paddingRight=o.style.paddingLeft="";d.Measured(o,l)}else{l.bbox=this.HTMLzeroBBox()}var m=this.HTMLrootHeight(k.bbox.h+k.bbox.d,j,l)-n;var q=Math.min(l.bbox.w,l.bbox.rw);p=Math.max(q,k.offset);d.placeBox(l,p-q,m);return p-k.offset},HTMLrootHeight:function(l,k,j){return 0.45*(l-0.9*k)+0.6*k+Math.max(0,j.bbox.d-0.075)}});f.mfenced.Augment({toHTML:function(n){n=this.HTMLcreateSpan(n);if(this.data.open){this.data.open.toHTML(n)}if(this.data[0]!=null){this.data[0].toHTML(n)}for(var k=1,j=this.data.length;k<j;k++){if(this.data[k]){if(this.data["sep"+k]){this.data["sep"+k].toHTML(n)}this.data[k].toHTML(n)}}if(this.data.close){this.data.close.toHTML(n)}var p=this.HTMLcomputeBBox(n);var l=n.bbox.h,o=n.bbox.d;for(k=0,j=p.length;k<j;k++){p[k].HTMLstretchV(n,l,o)}if(p.length){this.HTMLcomputeBBox(n,true)}this.HTMLhandleSpace(n);this.HTMLhandleColor(n);return n},HTMLcomputeBBox:function(o,n){var k=o.bbox={},p=[];this.HTMLcheckStretchy(this.data.open,k,p,n);this.HTMLcheckStretchy(this.data[0],k,p,n);for(var l=1,j=this.data.length;l<j;l++){if(this.data[l]){this.HTMLcheckStretchy(this.data["sep"+l],k,p,n);this.HTMLcheckStretchy(this.data[l],k,p,n)}}this.HTMLcheckStretchy(this.data.close,k,p,n);this.HTMLcleanBBox(k);return p},HTMLcheckStretchy:function(j,k,m,l){if(j){if(!l&&j.HTMLcanStretch("Vertical")){m.push(j);j=(j.CoreMO()||j)}this.HTMLcombineBBoxes(j,k)}}});f.menclose.Augment({toHTML:f.mbase.HTMLautoload});f.maction.Augment({toHTML:f.mbase.HTMLautoload});f.semantics.Augment({toHTML:function(j){if(this.data[0]!=null){j=this.data[0].toHTML(j);this.spanID=this.data[0].spanID;this.HTMLhandleSpace(j)}return j},HTMLspanElement:function(){return(this.data[0]!=null?this.data[0].HTMLspanElement():null)},HTMLstretchH:function(k,j){return(this.data[0]!=null?this.data[0].HTMLstretchH(k,j):k)},HTMLstretchV:function(k,j,l){return(this.data[0]!=null?this.data[0].HTMLstretchV(k,j,l):k)}});f.munderover.Augment({toHTML:function(K,G,E){var j=this.getValues("displaystyle","accent","accentunder","align");if(!j.displaystyle&&this.data[this.base]!=null&&this.data[this.base].CoreMO().Get("movablelimits")){return f.msubsup.prototype.toHTML.call(this,K)}K=this.HTMLcreateSpan(K);var O=this.HTMLgetScale();var p=d.createStack(K);var q=[],n=[],M=[],v,L,H;for(L=0,H=this.data.length;L<H;L++){if(this.data[L]!=null){v=q[L]=d.createBox(p);n[L]=this.data[L].toHTML(v);if(L==this.base){if(E!=null){this.data[this.base].HTMLstretchV(v,G,E)}else{if(G!=null){this.data[this.base].HTMLstretchH(v,G)}}M[L]=(E==null&&G!=null?false:this.data[L].HTMLcanStretch("Horizontal"))}else{M[L]=this.data[L].HTMLcanStretch("Horizontal")}}}d.MeasureSpans(n);var l=-d.BIGDIMEN,J=l;for(L=0,H=this.data.length;L<H;L++){if(this.data[L]){if(q[L].bbox.w>J){J=q[L].bbox.w}if(!M[L]&&J>l){l=J}}}if(E==null&&G!=null){l=G}else{if(l==-d.BIGDIMEN){l=J}}for(L=J=0,H=this.data.length;L<H;L++){if(this.data[L]){v=q[L];if(M[L]){v.bbox=this.data[L].HTMLstretchH(v,l).bbox}if(v.bbox.w>J){J=v.bbox.w}}}var C=d.TeX.rule_thickness,F=d.FONTDATA.TeX_factor;var o=q[this.base]||{bbox:this.HTMLzeroBBox()};var u,r,z,w,s,B,I,N=0;if(o.bbox.ic){N=1.3*o.bbox.ic+0.05}for(L=0,H=this.data.length;L<H;L++){if(this.data[L]!=null){v=q[L];s=d.TeX.big_op_spacing5*O;var A=(L!=this.base&&j[this.ACCENTS[L]]);if(A&&v.bbox.w<=1/d.em+0.0001){v.bbox.w=v.bbox.rw-v.bbox.lw;v.bbox.noclip=true;if(v.bbox.lw&&!d.zeroWidthBug){v.insertBefore(d.createSpace(v.parentNode,0,0,-v.bbox.lw),v.firstChild)}d.createBlank(v,0,0,v.bbox.rw+0.1)}B={left:0,center:(J-v.bbox.w)/2,right:J-v.bbox.w}[j.align];u=B;r=0;if(L==this.over){if(A){I=Math.max(C*O*F,2.5/this.em);s=0;if(o.bbox.skew){u+=o.bbox.skew}}else{z=d.TeX.big_op_spacing1*O*F;w=d.TeX.big_op_spacing3*O*F;I=Math.max(z,w-Math.max(0,v.bbox.d))}I=Math.max(I,1.5/this.em);u+=N/2;r=o.bbox.h+v.bbox.d+I;v.bbox.h+=s}else{if(L==this.under){if(A){I=3*C*O*F;s=0}else{z=d.TeX.big_op_spacing2*O*F;w=d.TeX.big_op_spacing4*O*F;I=Math.max(z,w-v.bbox.h)}I=Math.max(I,1.5/this.em);u-=N/2;r=-(o.bbox.d+v.bbox.h+I);v.bbox.d+=s}}d.placeBox(v,u,r)}}this.HTMLhandleSpace(K);this.HTMLhandleColor(K);return K},HTMLstretchH:f.mbase.HTMLstretchH,HTMLstretchV:f.mbase.HTMLstretchV});f.msubsup.Augment({toHTML:function(J,H,B){J=this.HTMLcreateSpan(J);var M=this.HTMLgetScale(),G=this.HTMLgetMu(J);var o=d.createStack(J),k,m=[];var n=d.createBox(o);if(this.data[this.base]){m.push(this.data[this.base].toHTML(n));if(B!=null){this.data[this.base].HTMLstretchV(n,H,B)}else{if(H!=null){this.data[this.base].HTMLstretchH(n,H)}}}else{n.bbox=this.HTMLzeroBBox()}var K=d.TeX.x_height*M,A=d.TeX.scriptspace*M*0.75;var j,w;if(this.HTMLnotEmpty(this.data[this.sup])){j=d.createBox(o);m.push(this.data[this.sup].toHTML(j))}if(this.HTMLnotEmpty(this.data[this.sub])){w=d.createBox(o);m.push(this.data[this.sub].toHTML(w))}d.MeasureSpans(m);if(j){j.bbox.w+=A;j.bbox.rw=Math.max(j.bbox.w,j.bbox.rw)}if(w){w.bbox.w+=A;w.bbox.rw=Math.max(w.bbox.w,w.bbox.rw)}d.placeBox(n,0,0);var l=(this.data[this.sup]||this.data[this.sub]||this).HTMLgetScale();var E=d.TeX.sup_drop*l,C=d.TeX.sub_drop*l;var 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this.background}if(this.mathbackground){this.data[0].mathbackground=this.mathbackground;delete this.mathbackground}}f.mbase.prototype.displayAlign=b.config.displayAlign;f.mbase.prototype.displayIndent=b.config.displayIndent;r=d.Measured(this.data[0].toHTML(m),m)}d.placeBox(m,0,0);var j=1/d.em,n=d.em/d.outerEm;d.em/=n;s.bbox.h*=n;s.bbox.d*=n;s.bbox.w*=n;s.bbox.lw*=n;s.bbox.rw*=n;if(r&&r.bbox.width!=null){q.style.width=r.bbox.width;m.style.width="100%"}this.HTMLhandleColor(s);if(r){d.createRule(s,(r.bbox.h+j)*n,(r.bbox.d+j)*n,0)}if(!this.isMultiline&&this.Get("display")==="block"&&s.bbox.width==null){var t=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift");if(t.indentalignfirst!==f.INDENTALIGN.INDENTALIGN){t.indentalign=t.indentalignfirst}if(t.indentalign===f.INDENTALIGN.AUTO){t.indentalign=this.displayAlign}k.style.textAlign=t.indentalign;if(t.indentshiftfirst!==f.INDENTSHIFT.INDENTSHIFT){t.indentshift=t.indentshiftfirst}if(t.indentshift==="auto"){t.indentshift=this.displayIndent}if(t.indentshift&&t.indentalign!==f.INDENTALIGN.CENTER){s.style[{left:"marginLeft",right:"marginRight"}[t.indentalign]]=d.Em(d.length2em(t.indentshift))}}return s},HTMLspanElement:f.mbase.prototype.HTMLspanElement});f.TeXAtom.Augment({toHTML:function(k){k=this.HTMLcreateSpan(k);if(this.data[0]!=null){if(this.texClass===f.TEXCLASS.VCENTER){var j=d.createStack(k);var l=d.createBox(j);d.Measured(this.data[0].toHTML(l),l);d.placeBox(l,0,d.TeX.axis_height-(l.bbox.h+l.bbox.d)/2+l.bbox.d)}else{k.bbox=this.data[0].toHTML(k).bbox}}this.HTMLhandleSpace(k);this.HTMLhandleColor(k);return k}});MathJax.Hub.Register.StartupHook("onLoad",function(){setTimeout(MathJax.Callback(["loadComplete",d,"jax.js"]),0)})});b.Register.StartupHook("End Config",function(){b.Browser.Select({MSIE:function(j){var n=(document.documentMode||0);var m=j.versionAtLeast("7.0");var l=j.versionAtLeast("8.0")&&n>7;var k=(document.compatMode==="BackCompat");if(n<9){d.config.styles[".MathJax .MathJax_HitBox"]["background-color"]="white";d.config.styles[".MathJax .MathJax_HitBox"].opacity=0;d.config.styles[".MathJax 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j=navigator.appVersion.match(/ Safari\/\d/)&&navigator.appVersion.match(/ Version\/\d/)&&navigator.vendor.match(/Apple/);var k=(navigator.appVersion.match(/ Android (\d+)\.(\d+)/));var p=(l&&o.isMobile&&((navigator.platform.match(/iPad|iPod|iPhone/)&&!o.versionAtLeast("5.0"))||(k!=null&&(k[1]<2||(k[1]==2&&k[2]<2)))));d.Augment({config:{styles:{".MathJax img, .MathJax nobr, .MathJax a":{"max-width":"5000em","max-height":"5000em"}}},rfuzz:0.011,AccentBug:true,AdjustSurd:true,negativeBBoxes:true,safariNegativeSpaceBug:true,safariVerticalAlignBug:!l,safariTextNodeBug:!m,forceReflow:true,allowWebFonts:(l&&!p?"otf":false)});if(j){d.Augment({webFontDefault:(o.isMobile?"sans-serif":"serif")})}if(o.isPC){d.Augment({adjustAvailableFonts:d.removeSTIXfonts,checkWebFontsTwice:true})}if(p){var 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