/*
 *  /MathJax/jax/output/HTML-CSS/jax.js
 *
 *  Copyright (c) 2009-2013 The MathJax Consortium
 *
 *  Licensed under the Apache License, Version 2.0 (the "License");
 *  you may not use this file except in compliance with the License.
 *  You may obtain a copy of the License at
 *
 *      http://www.apache.org/licenses/LICENSE-2.0
 *
 *  Unless required by applicable law or agreed to in writing, software
 *  distributed under the License is distributed on an "AS IS" BASIS,
 *  WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 *  See the License for the specific language governing permissions and
 *  limitations under the License.
 */

(function(h,b,d){var g,i=b.Browser.isMobile;var e=function(){var k=[].slice.call(arguments,0);k[0][0]=["HTML-CSS",k[0][0]];return MathJax.Message.Set.apply(MathJax.Message,k)};var f=MathJax.Object.Subclass({timeout:(i?15:8)*1000,FontInfo:{STIX:{family:"STIXSizeOneSym",testString:"() {} []"},TeX:{family:"MathJax_Size1",testString:"() {} []"},"STIX-Web":{family:"STIXWeb_Size1",testString:"() {} []"},"Asana-Math":{family:"AsanaMath_Size1",testString:"() {} []"},"Gyre-Pagella":{family:"GyrePagella_Size1",testString:"() {} []"},"Gyre-Termes":{family:"GyreTermes_Size1",testString:"() {} []"},"Latin-Modern":{family:"LatinModern_Size1",testString:"() {} []"},"Neo-Euler":{family:"NeoEuler_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(o,l){if(l&&this.testCollection(l)){return l}for(var n=0,k=o.length;n<k;n++){if(o[n]===l){continue}if(this.testCollection(o[n])){return o[n]}}return null},testCollection:function(k){return this.testFont(this.FontInfo[k])},testFont:function(n){if(n.isWebFont&&d.FontFaceBug){this.div.style.fontWeight=this.div.style.fontStyle="normal"}else{this.div.style.fontWeight=(n.weight||"normal");this.div.style.fontStyle=(n.style||"normal")}var l=this.getComparisonWidths(n.testString,n.noStyleChar);if(l){this.div.style.fontFamily="'"+n.family+"',"+this.comparisonFont[0];if(this.div.offsetWidth==l[0]){this.div.style.fontFamily="'"+n.family+"',"+this.comparisonFont[l[2]];if(this.div.offsetWidth==l[1]){return false}}if(this.div.offsetWidth!=l[3]||this.div.offsetHeight!=l[4]){if(n.noStyleChar||!d.FONTDATA||!d.FONTDATA.hasStyleChar){return true}for(var o=0,k=this.testSize.length;o<k;o++){if(this.testStyleChar(n,this.testSize[o])){return true}}}}return false},styleChar:"\uEFFD",versionChar:"\uEFFE",compChar:"\uEFFF",testStyleChar:function(m,p){var s=3+(m.weight?2:0)+(m.style?4:0);var l="",o=0;var r=this.div.style.fontSize;this.div.style.fontSize=p;if(d.msieItalicWidthBug&&m.style==="italic"){this.text.nodeValue=l=this.compChar;o=this.div.offsetWidth}if(d.safariTextNodeBug){this.div.innerHTML=this.compChar+l}else{this.text.nodeValue=this.compChar+l}var k=this.div.offsetWidth-o;if(d.safariTextNodeBug){this.div.innerHTML=this.styleChar+l}else{this.text.nodeValue=this.styleChar+l}var q=Math.floor((this.div.offsetWidth-o)/k+0.5);if(q===s){if(d.safariTextNodeBug){this.div.innerHTML=this.versionChar+l}else{this.text.nodeValue=this.versionChar+l}m.version=Math.floor((this.div.offsetWidth-o)/k+1.5)/2}this.div.style.fontSize=r;return(q===s)},getComparisonWidths:function(p,n){if(d.FONTDATA&&d.FONTDATA.hasStyleChar&&!n){p+=this.styleChar+" "+this.compChar}if(d.safariTextNodeBug){this.div.innerHTML=p}else{this.text.nodeValue=p}this.div.style.fontFamily=this.comparisonFont[0];var l=this.div.offsetWidth;this.div.style.fontFamily=d.webFontDefault;var r=this.div.offsetWidth,o=this.div.offsetHeight;for(var q=1,k=this.comparisonFont.length;q<k;q++){this.div.style.fontFamily=this.comparisonFont[q];if(this.div.offsetWidth!=l){return[l,this.div.offsetWidth,q,r,o]}}return null},loadWebFont:function(l){b.Startup.signal.Post("HTML-CSS Jax - Web-Font "+d.fontInUse+"/"+l.directory);var o=e(["LoadWebFont","Loading web-font %1",d.fontInUse+"/"+l.directory]);var k=MathJax.Callback({});var m=MathJax.Callback(["loadComplete",this,l,o,k]);h.timer.start(h,[this.checkWebFont,l,m],0,this.timeout);return k},loadComplete:function(m,p,l,k){MathJax.Message.Clear(p);if(k===h.STATUS.OK){this.webFontLoaded=true;l();return}this.loadError(m);if(b.Browser.isFirefox&&d.allowWebFonts){var o=document.location.protocol+"//"+document.location.hostname;if(document.location.port!=""){o+=":"+document.location.port}o+="/";if(h.fileURL(d.webfontDir).substr(0,o.length)!==o){this.firefoxFontError(m)}}if(!this.webFontLoaded){d.loadWebFontError(m,l)}else{l()}},loadError:function(k){e(["CantLoadWebFont","Can't load web font %1",d.fontInUse+"/"+k.directory],null,2000);b.Startup.signal.Post(["HTML-CSS Jax - web font error",d.fontInUse+"/"+k.directory,k])},firefoxFontError:function(k){e(["FirefoxCantLoadWebFont","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(k,l,m){if(k.time(m)){return}if(d.Font.testFont(l)){m(k.STATUS.OK)}else{setTimeout(k,k.delay)}},fontFace:function(m){var n=d.allowWebFonts;var p=d.FONTDATA.FONTS[m];if(d.msieFontCSSBug&&!p.family.match(/-Web$/)){p.family+="-Web"}var l=h.fileURL(d.webfontDir+"/"+n);var k=m.replace(/-b/,"-B").replace(/-i/,"-I").replace(/-Bold-/,"-Bold");if(!k.match(/-/)){k+="-Regular"}if(n==="svg"){k+=".svg#"+k}else{k+="."+n}var o={"font-family":p.family,src:"url('"+l+"/"+k+"')"};if(n==="otf"){o.src+=" format('opentype')";l=h.fileURL(d.webfontDir+"/woff");o.src="url('"+l+"/"+k.replace(/otf$/,"woff")+"') format('woff'), "+o.src}else{if(n!=="eot"){o.src+=" format('"+n+"')"}}if(!(d.FontFaceBug&&p.isWebFont)){if(m.match(/-bold/)){o["font-weight"]="bold"}if(m.match(/-italic/)){o["font-style"]="italic"}}return o}});var j,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 *":{transition:"none","-webkit-transition":"none","-moz-transition":"none","-ms-transition":"none","-o-transition":"none"},".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",allowWebFonts:"otf",maxStretchyParts:1000,Config:function(){if(!this.require){this.require=[]}this.Font=f();this.SUPER(arguments).Config.call(this);var l=this.settings;if(this.adjustAvailableFonts){this.adjustAvailableFonts(this.config.availableFonts)}if(l.scale){this.config.scale=l.scale}if(l.font&&l.font!=="Auto"){if(l.font==="TeXLocal"){this.config.availableFonts=["TeX"];this.config.preferredFont="TeX";this.config.webFont="TeX"}else{if(l.font==="TeXWeb"){this.config.availableFonts=[];this.config.preferredFont="";this.config.webFont="TeX"}else{if(l.font==="TeXimage"){this.config.availableFonts=[];this.config.preferredFont="";this.config.webFont=""}else{if(l.font==="STIXlocal"){this.config.availableFonts=["STIX"];this.config.preferredFont="STIX";this.config.webFont="STIX-Web"}else{if(l.font==="STIXWeb"){this.config.availableFonts=[];this.config.preferredFont="";this.config.webFont="STIX-Web"}else{if(l.font==="AsanaMathWeb"){this.config.availableFonts=[];this.config.preferredFont="";this.config.webFont="Asana-Math"}else{if(l.font==="GyrePagellaWeb"){this.config.availableFonts=[];this.config.preferredFont="";this.config.webFont="Gyre-Pagella"}else{if(l.font==="GyreTermesWeb"){this.config.availableFonts=[];this.config.preferredFont="";this.config.webFont="Gyre-Termes"}else{if(l.font==="LatinModernWeb"){this.config.availableFonts=[];this.config.preferredFont="";this.config.webFont="Latin-Modern"}else{if(l.font==="NeoEulerWeb"){this.config.availableFonts=[];this.config.preferredFont="";this.config.webFont="Neo-Euler"}}}}}}}}}}}var k=this.Font.findFont(this.config.availableFonts,this.config.preferredFont);if(!k&&this.allowWebFonts){k=this.config.webFont;if(k){this.webFonts=true}}if(!k&&this.config.imageFont){k=this.config.imageFont;this.imgFonts=true}if(k){this.fontInUse=k;this.fontDir+="/"+k;this.webfontDir+="/"+k;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{e(["CantFindFontUsing","Can't find a valid font using %1","["+this.config.availableFonts.join(", ")+"]"],null,3000);this.fontInUse="generic";this.FONTDATA={TeX_factor:1,baselineskip:1.2,lineH:0.8,lineD:0.2,ffLineH:0.8,FONTS:{},VARIANT:{normal:{fonts:[]},"-generic-variant":{fonts:[]},"-largeOp":{fonts:[]},"-smallOp":{fonts:[]}},RANGES:[],DELIMITERS:{},RULECHAR:45,REMAP:{}};b.Startup.signal.Post("HTML-CSS Jax - no valid font")}this.require.push(MathJax.OutputJax.extensionDir+"/MathEvents.js")},Startup:function(){j=MathJax.Extension.MathEvents.Event;a=MathJax.Extension.MathEvents.Touch;c=MathJax.Extension.MathEvents.Hover;this.ContextMenu=j.ContextMenu;this.Mousedown=j.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 l=this.addElement(this.hiddenDiv,"div",{style:{width:"5in"}});this.pxPerInch=l.offsetWidth/5;this.hiddenDiv.removeChild(l);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(k){}}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 h.Styles(this.config.styles,["InitializeHTML",this])},removeSTIXfonts:function(n){for(var l=0,k=n.length;l<k;l++){if(n[l]==="STIX"){n.splice(l,1);k--;l--}}if(this.config.preferredFont==="STIX"){this.config.preferredFont=n[0]}},PreloadWebFonts:function(){if(!d.allowWebFonts||!d.config.preloadWebFonts){return}for(var l=0,k=d.config.preloadWebFonts.length;l<k;l++){var n=d.FONTDATA.FONTS[d.config.preloadWebFonts[l]];if(!n.available){d.Font.testFont(n)}}},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(o){var u=o.jax[this.id],v,r=u.length,z,t,A,n,y,l,x,q,s,k,w=false,B=this.config.linebreaks.automatic,p=this.config.linebreaks.width;if(B){w=(p.match(/^\s*(\d+(\.\d*)?%\s*)?container\s*$/)!=null);if(w){p=p.replace(/\s*container\s*/,"")}else{k=this.defaultWidth}if(p===""){p="100%"}}else{k=100000}for(v=0;v<r;v++){z=u[v];if(!z.parentNode){continue}t=z.previousSibling;if(t&&String(t.className).match(/^MathJax(_Display)?( MathJax_Processing)?$/)){t.parentNode.removeChild(t)}l=z.MathJax.elementJax;if(!l){continue}l.HTMLCSS={display:(l.root.Get("display")==="block")};A=n=this.Element("span",{className:"MathJax",id:l.inputID+"-Frame",isMathJax:true,jaxID:this.id,oncontextmenu:j.Menu,onmousedown:j.Mousedown,onmouseover:j.Mouseover,onmouseout:j.Mouseout,onmousemove:j.Mousemove,onclick:j.Click,ondblclick:j.DblClick});if(b.Browser.noContextMenu){A.ontouchstart=a.start;A.ontouchend=a.end}if(l.HTMLCSS.display){n=this.Element("div",{className:"MathJax_Display"});n.appendChild(A)}else{if(this.msieDisappearingBug){A.style.display="inline-block"}}n.setAttribute("role","textbox");n.setAttribute("aria-readonly","true");n.className+=" MathJax_Processing";z.parentNode.insertBefore(n,z);z.parentNode.insertBefore(this.EmExSpan.cloneNode(true),z);if(w){n.parentNode.insertBefore(this.linebreakSpan.cloneNode(true),n)}}for(v=0;v<r;v++){z=u[v];if(!z.parentNode){continue}y=z.previousSibling;n=y.previousSibling;l=z.MathJax.elementJax;if(!l){continue}x=y.firstChild.offsetHeight/60;q=y.lastChild.firstChild.offsetHeight/60;if(w){k=n.previousSibling.firstChild.offsetWidth}if(x===0||x==="NaN"){this.hiddenDiv.appendChild(n);l.HTMLCSS.isHidden=true;x=this.defaultEx;q=this.defaultEm;if(w){k=this.defaultWidth}}s=(this.config.matchFontHeight?x/this.TeX.x_height/q:1);s=Math.floor(Math.max(this.config.minScaleAdjust/100,s)*this.config.scale);l.HTMLCSS.scale=s/100;l.HTMLCSS.fontSize=s+"%";l.HTMLCSS.em=l.HTMLCSS.outerEm=q;this.em=q*s/100;l.HTMLCSS.ex=x;l.HTMLCSS.lineWidth=(B?this.length2em(p,1,k/this.em):1000000)}for(v=0;v<r;v++){z=u[v];if(!z.parentNode){continue}y=u[v].previousSibling;l=u[v].MathJax.elementJax;if(!l){continue}if(w){A=y.previousSibling;if(!l.HTMLCSS.isHidden){A=A.previousSibling}A.parentNode.removeChild(A)}y.parentNode.removeChild(y)}o.HTMLCSSeqn=o.HTMLCSSlast=0;o.HTMLCSSi=-1;o.HTMLCSSchunk=this.config.EqnChunk;o.HTMLCSSdelay=false},Translate:function(l,p){if(!l.parentNode){return}if(p.HTMLCSSdelay){p.HTMLCSSdelay=false;b.RestartAfter(MathJax.Callback.Delay(this.config.EqnChunkDelay))}var k=l.MathJax.elementJax,o=k.root,m=document.getElementById(k.inputID+"-Frame"),q=(k.HTMLCSS.display?m.parentNode:m);this.em=g.mbase.prototype.em=k.HTMLCSS.em*k.HTMLCSS.scale;this.outerEm=k.HTMLCSS.em;this.scale=k.HTMLCSS.scale;this.linebreakWidth=k.HTMLCSS.lineWidth;if(this.scale!==1){m.style.fontSize=k.HTMLCSS.fontSize}this.initImg(m);this.initHTML(o,m);o.setTeXclass();try{o.toHTML(m,q)}catch(n){if(n.restart){while(m.firstChild){m.removeChild(m.firstChild)}}throw n}if(k.HTMLCSS.isHidden){l.parentNode.insertBefore(q,l)}q.className=q.className.split(/ /)[0];if(this.hideProcessedMath){q.className+=" MathJax_Processed";if(l.MathJax.preview){k.HTMLCSS.preview=l.MathJax.preview;delete l.MathJax.preview}p.HTMLCSSeqn+=(p.i-p.HTMLCSSi);p.HTMLCSSi=p.i;if(p.HTMLCSSeqn>=p.HTMLCSSlast+p.HTMLCSSchunk){this.postTranslate(p,true);p.HTMLCSSchunk=Math.floor(p.HTMLCSSchunk*this.config.EqnChunkFactor);p.HTMLCSSdelay=true}}},postTranslate:function(s,o){var l=s.jax[this.id];if(!this.hideProcessedMath){return}for(var q=s.HTMLCSSlast,k=s.HTMLCSSeqn;q<k;q++){var n=l[q];if(n&&n.MathJax.elementJax){n.previousSibling.className=n.previousSibling.className.split(/ /)[0];var r=n.MathJax.elementJax.HTMLCSS;if(r.preview){r.preview.innerHTML="";n.MathJax.preview=r.preview;delete r.preview}}}if(this.forceReflow){var p=(document.styleSheets||[])[0]||{};p.disabled=true;p.disabled=false}s.HTMLCSSlast=s.HTMLCSSeqn},getJaxFromMath:function(k){if(k.parentNode.className==="MathJax_Display"){k=k.parentNode}do{k=k.nextSibling}while(k&&k.nodeName.toLowerCase()!=="script");return b.getJaxFor(k)},getHoverSpan:function(k,l){return k.root.HTMLspanElement()},getHoverBBox:function(k,n,o){var p=n.bbox,m=k.HTMLCSS.outerEm;var l={w:p.w*m,h:p.h*m,d:p.d*m};if(p.width){l.width=p.width}return l},Zoom:function(l,v,u,k,s){v.className="MathJax";v.style.fontSize=l.HTMLCSS.fontSize;var x=v.appendChild(this.EmExSpan.cloneNode(true));var o=x.lastChild.firstChild.offsetHeight/60;this.em=g.mbase.prototype.em=o;this.outerEm=o/l.HTMLCSS.scale;x.parentNode.removeChild(x);this.idPostfix="-zoom";l.root.toHTML(v,v);this.idPostfix="";var n=l.root.HTMLspanElement().bbox.width;if(n){v.style.width=Math.floor(k-1.5*d.em)+"px";v.style.display="inline-block";var m=(l.root.id||"MathJax-Span-"+l.root.spanID)+"-zoom";var p=document.getElementById(m).firstChild;while(p&&p.style.width!==n){p=p.nextSibling}if(p){p.style.width="100%"}}v.style.position="absolute";if(!n){u.style.position="absolute"}var t=v.offsetWidth,r=v.offsetHeight,w=u.offsetHeight,q=u.offsetWidth;if(q===0){q=u.parentNode.offsetWidth}v.style.position=u.style.position="";return{Y:-j.getBBox(v).h,mW:q,mH:w,zW:t,zH:r}},initImg:function(k){},initHTML:function(l,k){},initFont:function(k){var m=d.FONTDATA.FONTS,l=d.config.availableFonts;if(l&&l.length&&d.Font.testFont(m[k])){m[k].available=true;return null}if(!this.allowWebFonts){return null}m[k].isWebFont=true;if(d.FontFaceBug){m[k].family=k;if(d.msieFontCSSBug){m[k].family+="-Web"}}return h.Styles({"@font-face":this.Font.fontFace(k)})},Remove:function(k){var l=document.getElementById(k.inputID+"-Frame");if(l){if(k.HTMLCSS.display){l=l.parentNode}l.parentNode.removeChild(l)}delete k.HTMLCSS},getHD:function(l){var k=l.style.position;l.style.position="absolute";this.HDimg.style.height="0px";l.appendChild(this.HDspan);var m={h:l.offsetHeight};this.HDimg.style.height=m.h+"px";m.d=l.offsetHeight-m.h;m.h-=m.d;m.h/=this.em;m.d/=this.em;l.removeChild(this.HDspan);l.style.position=k;return m},getW:function(o){var l,n,m=(o.bbox||{}).w,p=o;if(o.bbox&&o.bbox.exactW){return m}if((o.bbox&&m>=0&&!this.initialSkipBug)||this.negativeBBoxes||!o.firstChild){l=o.offsetWidth;n=o.parentNode.offsetHeight}else{if(o.bbox&&m<0&&this.msieNegativeBBoxBug){l=-o.offsetWidth,n=o.parentNode.offsetHeight}else{if(this.initialSkipBug){var k=o.style.position;o.style.position="absolute";p=this.startMarker;o.insertBefore(p,o.firstChild)}o.appendChild(this.endMarker);l=this.endMarker.offsetLeft-p.offsetLeft;o.removeChild(this.endMarker);if(this.initialSkipBug){o.removeChild(p);o.style.position=k}}}if(n!=null){o.parentNode.HH=n/this.em}return l/this.em},Measured:function(m,l){var n=m.bbox;if(n.width==null&&n.w&&!n.isMultiline){var k=this.getW(m);n.rw+=k-n.w;n.w=k;n.exactW=true}if(!l){l=m.parentNode}if(!l.bbox){l.bbox=n}return m},Remeasured:function(l,k){k.bbox=this.Measured(l,k).bbox},MeasureSpans:function(o){var r=[],t,q,n,u,k,p,l,s;for(q=0,n=o.length;q<n;q++){t=o[q];if(!t){continue}u=t.bbox;s=this.parentNode(t);if(u.exactW||u.width||u.w===0||u.isMultiline){if(!s.bbox){s.bbox=u}continue}if(this.negativeBBoxes||!t.firstChild||(u.w>=0&&!this.initialSkipBug)||(u.w<0&&this.msieNegativeBBoxBug)){r.push([t])}else{if(this.initialSkipBug){k=this.startMarker.cloneNode(true);p=this.endMarker.cloneNode(true);t.insertBefore(k,t.firstChild);t.appendChild(p);r.push([t,k,p,t.style.position]);t.style.position="absolute"}else{p=this.endMarker.cloneNode(true);t.appendChild(p);r.push([t,null,p])}}}for(q=0,n=r.length;q<n;q++){t=r[q][0];u=t.bbox;s=this.parentNode(t);if((u.w>=0&&!this.initialSkipBug)||this.negativeBBoxes||!t.firstChild){l=t.offsetWidth;s.HH=s.offsetHeight/this.em}else{if(u.w<0&&this.msieNegativeBBoxBug){l=-t.offsetWidth,s.HH=s.offsetHeight/this.em}else{l=r[q][2].offsetLeft-((r[q][1]||{}).offsetLeft||0)}}l/=this.em;u.rw+=l-u.w;u.w=l;u.exactW=true;if(!s.bbox){s.bbox=u}}for(q=0,n=r.length;q<n;q++){t=r[q];if(t[1]){t[1].parentNode.removeChild(t[1]),t[0].style.position=t[3]}if(t[2]){t[2].parentNode.removeChild(t[2])}}},Em:function(k){if(Math.abs(k)<0.0006){return"0em"}return k.toFixed(3).replace(/\.?0+$/,"")+"em"},EmRounded:function(k){k=(Math.round(k*d.em)+0.05)/d.em;if(Math.abs(k)<0.0006){return"0em"}return k.toFixed(3).replace(/\.?0+$/,"")+"em"},unEm:function(k){return parseFloat(k)},Px:function(k){k*=this.em;var l=(k<0?"-":"");return l+Math.abs(k).toFixed(1).replace(/\.?0+$/,"")+"px"},unPx:function(k){return parseFloat(k)/this.em},Percent:function(k){return(100*k).toFixed(1).replace(/\.?0+$/,"")+"%"},length2em:function(r,l,p){if(typeof(r)!=="string"){r=r.toString()}if(r===""){return""}if(r===g.SIZE.NORMAL){return 1}if(r===g.SIZE.BIG){return 2}if(r===g.SIZE.SMALL){return 0.71}if(r==="infinity"){return d.BIGDIMEN}var o=this.FONTDATA.TeX_factor;if(r.match(/mathspace$/)){return d.MATHSPACE[r]*o}var n=r.match(/^\s*([-+]?(?:\.\d+|\d+(?:\.\d*)?))?(pt|em|ex|mu|px|pc|in|mm|cm|%)?/);var k=parseFloat(n[1]||"1"),q=n[2];if(p==null){p=1}if(l==null){l=1}if(q==="em"){return k*o}if(q==="ex"){return k*d.TeX.x_height*o}if(q==="%"){return k/100*p}if(q==="px"){return k/d.em}if(q==="pt"){return k/10*o}if(q==="pc"){return k*1.2*o}if(q==="in"){return k*this.pxPerInch/d.em}if(q==="cm"){return k*this.pxPerInch/d.em/2.54}if(q==="mm"){return k*this.pxPerInch/d.em/25.4}if(q==="mu"){return k/18*o*l}return k*o*p},thickness2em:function(l,k){var m=d.TeX.rule_thickness;if(l===g.LINETHICKNESS.MEDIUM){return m}if(l===g.LINETHICKNESS.THIN){return 0.67*m}if(l===g.LINETHICKNESS.THICK){return 1.67*m}return this.length2em(l,k,m)},getPadding:function(l){var n={top:0,right:0,bottom:0,left:0},k=false;for(var o in n){if(n.hasOwnProperty(o)){var m=l.style["padding"+o.charAt(0).toUpperCase()+o.substr(1)];if(m){n[o]=this.length2em(m);k=true}}}return(k?n:false)},getBorders:function(p){var m={top:0,right:0,bottom:0,left:0},n={},l=false;for(var q in m){if(m.hasOwnProperty(q)){var k="border"+q.charAt(0).toUpperCase()+q.substr(1);var o=p.style[k+"Style"];if(o){l=true;m[q]=this.length2em(p.style[k+"Width"]);n[k]=[p.style[k+"Width"],p.style[k+"Style"],p.style[k+"Color"]].join(" ")}}}m.css=n;return(l?m:false)},setBorders:function(k,l){if(l){for(var m in l.css){if(l.css.hasOwnProperty(m)){k.style[m]=l.css[m]}}}},createStrut:function(m,l,n){var k=this.Element("span",{isMathJax:true,style:{display:"inline-block",overflow:"hidden",height:l+"px",width:"1px",marginRight:"-1px"}});if(n){m.insertBefore(k,m.firstChild)}else{m.appendChild(k)}return k},createBlank:function(l,k,m){var n=this.Element("span",{isMathJax:true,style:{display:"inline-block",overflow:"hidden",height:"1px",width:this.Em(k)}});if(m){l.insertBefore(n,l.firstChild)}else{l.appendChild(n)}return n},createShift:function(l,k,n){var m=this.Element("span",{style:{marginLeft:this.Em(k)},isMathJax:true});if(n){l.insertBefore(m,l.firstChild)}else{l.appendChild(m)}return m},createSpace:function(p,n,o,q,m,s){if(n<-o){o=-n}var r=this.Em(n+o),k=this.Em(-o);if(this.msieInlineBlockAlignBug){k=this.Em(d.getHD(p.parentNode).d-o)}if(p.isBox||s){var l=(p.scale==null?1:p.scale);p.bbox={exactW:true,h:n*l,d:o*l,w:q*l,rw:q*l,lw:0};p.style.height=r;p.style.verticalAlign=k;p.HH=(n+o)*l}else{p=this.addElement(p,"span",{style:{height:r,verticalAlign:k},isMathJax:true})}if(q>=0){p.style.width=this.Em(q);p.style.display="inline-block";p.style.overflow="hidden"}else{if(this.msieNegativeSpaceBug){p.style.height=""}p.style.marginLeft=this.Em(q);if(d.safariNegativeSpaceBug&&p.parentNode.firstChild==p){this.createBlank(p,0,true)}}if(m&&m!==g.COLOR.TRANSPARENT){p.style.backgroundColor=m;p.style.position="relative"}return p},createRule:function(r,n,p,s,l){if(n<-p){p=-n}var m=d.TeX.min_rule_thickness,o=1;if(s>0&&s*this.em<m){s=m/this.em}if(n+p>0&&(n+p)*this.em<m){o=1/(n+p)*(m/this.em);n*=o;p*=o}if(!l){l="solid"}else{l="solid "+l}l=this.Em(s)+" "+l;var t=(o===1?this.Em(n+p):m+"px"),k=this.Em(-p);var q=this.addElement(r,"span",{style:{borderLeft:l,display:"inline-block",overflow:"hidden",width:0,height:t,verticalAlign:k},bbox:{h:n,d:p,w:s,rw:s,lw:0,exactW:true},noAdjust:true,HH:n+p,isMathJax:true});if(s>0&&q.offsetWidth==0){q.style.width=this.Em(s)}if(r.isBox||r.className=="mspace"){r.bbox=q.bbox,r.HH=n+p}return q},createFrame:function(s,q,r,u,x,l){if(q<-r){r=-q}var p=2*x;if(this.msieFrameSizeBug){if(u<p){u=p}if(q+r<p){q=p-r}}if(this.msieBorderWidthBug){p=0}var v=this.Em(q+r-p),k=this.Em(-r-x),o=this.Em(u-p);var m=this.Em(x)+" "+l;var n=this.addElement(s,"span",{style:{border:m,display:"inline-block",overflow:"hidden",width:o,height:v},bbox:{h:q,d:r,w:u,rw:u,lw:0,exactW:true},noAdjust:true,HH:q+r,isMathJax:true});if(k){n.style.verticalAlign=k}return n},parentNode:function(l){var k=l.parentNode;if(k.nodeName.toLowerCase()==="a"){k=k.parentNode}return k},createStack:function(m,o,l){if(this.msiePaddingWidthBug){this.createStrut(m,0)}var n=String(l).match(/%$/);var k=(!n&&l!=null?l:0);m=this.addElement(m,"span",{noAdjust:true,HH:0,isMathJax:true,style:{display:"inline-block",position:"relative",width:(n?"100%":this.Em(k)),height:0}});if(!o){m.parentNode.bbox=m.bbox={exactW:true,h:-this.BIGDIMEN,d:-this.BIGDIMEN,w:k,lw:this.BIGDIMEN,rw:(!n&&l!=null?l:-this.BIGDIMEN)};if(n){m.bbox.width=l}}return m},createBox:function(l,k){var m=this.addElement(l,"span",{style:{position:"absolute"},isBox:true,isMathJax:true});if(k!=null){m.style.width=k}return m},addBox:function(k,l){l.style.position="absolute";l.isBox=l.isMathJax=true;return k.appendChild(l)},placeBox:function(u,s,q,o){u.isMathJax=true;var v=d.parentNode(u),C=u.bbox,z=v.bbox;if(this.msiePlaceBoxBug){this.addText(u,this.NBSP)}if(this.imgSpaceBug){this.addText(u,this.imgSpace)}var w,F=0;if(u.HH!=null){w=u.HH}else{if(C){w=Math.max(3,C.h+C.d)}else{w=u.offsetHeight/this.em}}if(!u.noAdjust){w+=1;w=Math.round(w*this.em)/this.em;if(this.msieInlineBlockAlignBug){this.addElement(u,"img",{className:"MathJax_strut",border:0,src:"about:blank",isMathJax:true,style:{width:0,height:this.Em(w)}})}else{this.addElement(u,"span",{isMathJax:true,style:{display:"inline-block",width:0,height:this.Em(w)}});if(d.chromeHeightBug){w-=(u.lastChild.offsetHeight-Math.round(w*this.em))/this.em}}}if(C){if(this.initialSkipBug){if(C.lw<0){F=C.lw;d.createBlank(u,-F,true)}if(C.rw>C.w){d.createBlank(u,C.rw-C.w+0.1)}}if(!this.msieClipRectBug&&!C.noclip&&!o){var B=3/this.em;var A=(C.H==null?C.h:C.H),m=(C.D==null?C.d:C.D);var E=w-A-B,p=w+m+B,n=C.lw-3*B,k=1000;if(this.initialSkipBug&&C.lw<0){n=-3*B}if(C.isFixed){k=C.width-n}u.style.clip="rect("+this.Em(E)+" "+this.Em(k)+" "+this.Em(p)+" "+this.Em(n)+")"}}u.style.top=this.Em(-q-w);u.style.left=this.Em(s+F);if(C&&z){if(C.H!=null&&(z.H==null||C.H+q>z.H)){z.H=C.H+q}if(C.D!=null&&(z.D==null||C.D-q>z.D)){z.D=C.D-q}if(C.h+q>z.h){z.h=C.h+q}if(C.d-q>z.d){z.d=C.d-q}if(z.H!=null&&z.H<=z.h){delete z.H}if(z.D!=null&&z.D<=z.d){delete z.D}if(C.w+s>z.w){z.w=C.w+s;if(z.width==null){v.style.width=this.Em(z.w)}}if(C.rw+s>z.rw){z.rw=C.rw+s}if(C.lw+s<z.lw){z.lw=C.lw+s}if(C.width!=null&&!C.isFixed){if(z.width==null){v.style.width=z.width="100%";if(C.minWidth){v.style.minWidth=z.minWidth=C.minWidth}}u.style.width=C.width}}},alignBox:function(n,t,s){this.placeBox(n,0,s);var p=n.bbox;if(p.isMultiline){return}var m=p.width!=null&&!p.isFixed;var o=0,q=-p.w/2,k="50%";if(this.initialSkipBug){o=p.w-p.rw-0.1;q+=p.lw}if(this.msieMarginScaleBug){q=(q*this.em)+"px"}else{q=this.Em(q)}if(m){q="";k=(50-parseFloat(p.width)/2)+"%"}b.Insert(n.style,({right:{left:"",right:this.Em(o)},center:{left:k,marginLeft:q}})[t])},setStackWidth:function(l,k){if(typeof(k)==="number"){l.style.width=this.Em(Math.max(0,k));var m=l.bbox;if(m){m.w=k;m.exactW=true}m=l.parentNode.bbox;if(m){m.w=k;m.exactW=true}}else{l.style.width=l.parentNode.style.width="100%";if(l.bbox){l.bbox.width=k}if(l.parentNode.bbox){l.parentNode.bbox.width=k}}},createDelimiter:function(u,k,n,q,o){if(!k){u.bbox={h:0,d:0,w:this.TeX.nulldelimiterspace,lw:0};u.bbox.rw=u.bbox.w;this.createSpace(u,u.bbox.h,u.bbox.d,u.bbox.w);return}if(!q){q=1}if(!(n instanceof Array)){n=[n,n]}var t=n[1];n=n[0];var l={alias:k};while(l.alias){k=l.alias;l=this.FONTDATA.DELIMITERS[k];if(!l){l={HW:[0,this.FONTDATA.VARIANT[g.VARIANT.NORMAL]]}}}if(l.load){b.RestartAfter(h.Require(this.fontDir+"/fontdata-"+l.load+".js"))}for(var s=0,p=l.HW.length;s<p;s++){if(l.HW[s][0]*q>=n-0.01||(s==p-1&&!l.stretch)){if(l.HW[s][2]){q*=l.HW[s][2]}if(l.HW[s][3]){k=l.HW[s][3]}var r=this.addElement(u,"span");this.createChar(r,[k,l.HW[s][1]],q,o);u.bbox=r.bbox;u.offset=0.65*u.bbox.w;u.scale=q;return}}if(l.stretch){this["extendDelimiter"+l.dir](u,t,l.stretch,q,o)}},extendDelimiterV:function(A,t,E,F,w){var o=this.createStack(A,true);var v=this.createBox(o),u=this.createBox(o);this.createChar(v,(E.top||E.ext),F,w);this.createChar(u,(E.bot||E.ext),F,w);var m={bbox:{w:0,lw:0,rw:0}},D=m,p;var B=v.bbox.h+v.bbox.d+u.bbox.h+u.bbox.d;var r=-v.bbox.h;this.placeBox(v,0,r,true);r-=v.bbox.d;if(E.mid){D=this.createBox(o);this.createChar(D,E.mid,F,w);B+=D.bbox.h+D.bbox.d}if(E.min&&t<B*E.min){t=B*E.min}if(t>B){m=this.Element("span");this.createChar(m,E.ext,F,w);var C=m.bbox.h+m.bbox.d,l=C-0.05,x,q,z=(E.mid?2:1);q=x=Math.min(Math.ceil((t-B)/(z*l)),this.maxStretchyParts);if(!E.fullExtenders){l=(t-B)/(z*x)}var s=(x/(x+1))*(C-l);l=C-s;r+=s+l-m.bbox.h;while(z-->0){while(x-->0){if(!this.msieCloneNodeBug){p=m.cloneNode(true)}else{p=this.Element("span");this.createChar(p,E.ext,F,w)}p.bbox=m.bbox;r-=l;this.placeBox(this.addBox(o,p),0,r,true)}r+=s-m.bbox.d;if(E.mid&&z){this.placeBox(D,0,r-D.bbox.h,true);x=q;r+=-(D.bbox.h+D.bbox.d)+s+l-m.bbox.h}}}else{r+=(B-t)/2;if(E.mid){this.placeBox(D,0,r-D.bbox.h,true);r+=-(D.bbox.h+D.bbox.d)}r+=(B-t)/2}this.placeBox(u,0,r-u.bbox.h,true);r-=u.bbox.h+u.bbox.d;A.bbox={w:Math.max(v.bbox.w,m.bbox.w,u.bbox.w,D.bbox.w),lw:Math.min(v.bbox.lw,m.bbox.lw,u.bbox.lw,D.bbox.lw),rw:Math.max(v.bbox.rw,m.bbox.rw,u.bbox.rw,D.bbox.rw),h:0,d:-r,exactW:true};A.scale=F;A.offset=0.55*A.bbox.w;A.isMultiChar=true;this.setStackWidth(o,A.bbox.w)},extendDelimiterH:function(B,o,E,G,y){var r=this.createStack(B,true);var p=this.createBox(r),C=this.createBox(r);this.createChar(p,(E.left||E.rep),G,y);this.createChar(C,(E.right||E.rep),G,y);var l=this.Element("span");this.createChar(l,E.rep,G,y);var D={bbox:{h:-this.BIGDIMEN,d:-this.BIGDIMEN}},m;this.placeBox(p,-p.bbox.lw,0,true);var u=(p.bbox.rw-p.bbox.lw)+(C.bbox.rw-C.bbox.lw)-0.05,t=p.bbox.rw-p.bbox.lw-0.025,v;if(E.mid){D=this.createBox(r);this.createChar(D,E.mid,G,y);u+=D.bbox.w}if(E.min&&o<u*E.min){o=u*E.min}if(o>u){var F=l.bbox.rw-l.bbox.lw,q=F-0.05,z,s,A=(E.mid?2:1);s=z=Math.min(Math.ceil((o-u)/(A*q)),this.maxStretchyParts);if(!E.fillExtenders){q=(o-u)/(A*z)}v=(z/(z+1))*(F-q);q=F-v;t-=l.bbox.lw+v;while(A-->0){while(z-->0){if(!this.cloneNodeBug){m=l.cloneNode(true)}else{m=this.Element("span");this.createChar(m,E.rep,G,y)}m.bbox=l.bbox;this.placeBox(this.addBox(r,m),t,0,true);t+=q}if(E.mid&&A){this.placeBox(D,t,0,true);t+=D.bbox.w-v;z=s}}}else{t-=(u-o)/2;if(E.mid){this.placeBox(D,t,0,true);t+=D.bbox.w}t-=(u-o)/2}this.placeBox(C,t,0,true);B.bbox={w:t+C.bbox.rw,lw:0,rw:t+C.bbox.rw,H:Math.max(p.bbox.h,l.bbox.h,C.bbox.h,D.bbox.h),D:Math.max(p.bbox.d,l.bbox.d,C.bbox.d,D.bbox.d),h:l.bbox.h,d:l.bbox.d,exactW:true};B.scale=G;B.isMultiChar=true;this.setStackWidth(r,B.bbox.w)},createChar:function(s,p,n,k){s.isMathJax=true;var r=s,t="",o={fonts:[p[1]],noRemap:true};if(k&&k===g.VARIANT.BOLD){o.fonts=[p[1]+"-bold",p[1]]}if(typeof(p[1])!=="string"){o=p[1]}if(p[0] instanceof Array){for(var q=0,l=p[0].length;q<l;q++){t+=String.fromCharCode(p[0][q])}}else{t=String.fromCharCode(p[0])}if(p[4]){n*=p[4]}if(n!==1||p[3]){r=this.addElement(s,"span",{style:{fontSize:this.Percent(n)},scale:n,isMathJax:true});this.handleVariant(r,o,t);s.bbox=r.bbox}else{this.handleVariant(s,o,t)}if(p[2]){s.style.marginLeft=this.Em(p[2])}if(p[3]){s.firstChild.style.verticalAlign=this.Em(p[3]);s.bbox.h+=p[3];if(s.bbox.h<0){s.bbox.h=0}}if(p[5]){s.bbox.h+=p[5]}if(p[6]){s.bbox.d+=p[6]}if(this.AccentBug&&s.bbox.w===0){r.firstChild.nodeValue+=this.NBSP}},positionDelimiter:function(l,k){k-=l.bbox.h;l.bbox.d-=k;l.bbox.h+=k;if(k){if(this.safariVerticalAlignBug||this.konquerorVerticalAlignBug||(this.operaVerticalAlignBug&&l.isMultiChar)){if(l.firstChild.style.display===""&&l.style.top!==""){l=l.firstChild;k-=d.unEm(l.style.top)}l.style.position="relative";l.style.top=this.Em(-k)}else{l.style.verticalAlign=this.Em(k);if(d.ffVerticalAlignBug){d.createRule(l.parentNode,l.bbox.h,0,0)}}}},handleVariant:function(A,p,s){var z="",x,C,t,D,k=A,l=!!A.style.fontFamily;if(s.length===0){return}if(!A.bbox){A.bbox={w:0,h:-this.BIGDIMEN,d:-this.BIGDIMEN,rw:-this.BIGDIMEN,lw:this.BIGDIMEN}}if(!p){p=this.FONTDATA.VARIANT[g.VARIANT.NORMAL]}D=p;for(var B=0,y=s.length;B<y;B++){p=D;x=s.charCodeAt(B);C=s.charAt(B);if(x>=55296&&x<56319){B++;x=(((x-55296)<<10)+(s.charCodeAt(B)-56320))+65536;if(this.FONTDATA.RemapPlane1){var E=this.FONTDATA.RemapPlane1(x,p);x=E.n;p=E.variant}}else{var u,r,v=this.FONTDATA.RANGES;for(u=0,r=v.length;u<r;u++){if(v[u].name==="alpha"&&p.noLowerCase){continue}var q=p["offset"+v[u].offset];if(q&&x>=v[u].low&&x<=v[u].high){if(v[u].remap&&v[u].remap[x]){x=q+v[u].remap[x]}else{x=x-v[u].low+q;if(v[u].add){x+=v[u].add}}if(p["variant"+v[u].offset]){p=this.FONTDATA.VARIANT[p["variant"+v[u].offset]]}break}}}if(p.remap&&p.remap[x]){if(p.remap[x] instanceof Array){var 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l=this.HTMLspanElement();if(l.style.fontSize!=""){k.fontsize=l.style.fontSize}}if(k.fontsize&&!this.mathsize){k.mathsize=k.fontsize}if(k.scriptlevel!==0){if(k.scriptlevel>2){k.scriptlevel=2}m=Math.pow(this.Get("scriptsizemultiplier"),k.scriptlevel);k.scriptminsize=d.length2em(this.Get("scriptminsize"));if(m<k.scriptminsize){m=k.scriptminsize}}if(this.isToken){m*=d.length2em(k.mathsize)}return m},HTMLgetMu:function(m){var k=1,l=this.getValues("scriptlevel","scriptsizemultiplier");if(m.scale&&m.scale!==1){k=1/m.scale}if(l.scriptlevel!==0){if(l.scriptlevel>2){l.scriptlevel=2}k=Math.sqrt(Math.pow(l.scriptsizemultiplier,l.scriptlevel))}return k},HTMLgetVariant:function(){var k=this.getValues("mathvariant","fontfamily","fontweight","fontstyle");k.hasVariant=this.Get("mathvariant",true);if(!k.hasVariant){k.family=k.fontfamily;k.weight=k.fontweight;k.style=k.fontstyle}if(this.style){var 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p=this.data[1].toHTML(m);p.style.paddingRight=p.style.paddingLeft="";d.Measured(p,m)}else{m.bbox=this.HTMLzeroBBox()}var n=this.HTMLrootHeight(l.bbox.h+l.bbox.d,k,m)-o;var r=Math.min(m.bbox.w,m.bbox.rw);q=Math.max(r,l.offset);d.placeBox(m,q-r,n);return q-l.offset},HTMLrootHeight:function(m,l,k){return 0.45*(m-0.9*l)+0.6*l+Math.max(0,k.bbox.d-0.075)}});g.mfenced.Augment({toHTML:function(o){o=this.HTMLcreateSpan(o);if(this.data.open){this.data.open.toHTML(o)}if(this.data[0]!=null){this.data[0].toHTML(o)}for(var l=1,k=this.data.length;l<k;l++){if(this.data[l]){if(this.data["sep"+l]){this.data["sep"+l].toHTML(o)}this.data[l].toHTML(o)}}if(this.data.close){this.data.close.toHTML(o)}var q=this.HTMLcomputeBBox(o);var n=o.bbox.h,p=o.bbox.d;for(l=0,k=q.length;l<k;l++){q[l].HTMLstretchV(o,n,p)}if(q.length){this.HTMLcomputeBBox(o,true)}this.HTMLhandleSpace(o);this.HTMLhandleColor(o);return o},HTMLcomputeBBox:function(p,o){var l=p.bbox={},q=[];this.HTMLcheckStretchy(this.data.open,l,q,o);this.HTMLcheckStretchy(this.data[0],l,q,o);for(var n=1,k=this.data.length;n<k;n++){if(this.data[n]){this.HTMLcheckStretchy(this.data["sep"+n],l,q,o);this.HTMLcheckStretchy(this.data[n],l,q,o)}}this.HTMLcheckStretchy(this.data.close,l,q,o);this.HTMLcleanBBox(l);return q},HTMLcheckStretchy:function(k,l,n,m){if(k){if(!m&&k.HTMLcanStretch("Vertical")){n.push(k);k=(k.CoreMO()||k)}this.HTMLcombineBBoxes(k,l)}}});g.menclose.Augment({toHTML:g.mbase.HTMLautoload});g.maction.Augment({toHTML:g.mbase.HTMLautoload});g.semantics.Augment({toHTML:function(l,k,m){l=this.HTMLcreateSpan(l);if(this.data[0]!=null){var n=this.data[0].toHTML(l);if(m!=null){this.data[0].HTMLstretchV(l,k,m)}else{if(k!=null){this.data[0].HTMLstretchH(l,k)}}l.bbox=n.bbox}this.HTMLhandleSpace(l);return l},HTMLstretchH:g.mbase.HTMLstretchH,HTMLstretchV:g.mbase.HTMLstretchV});g.munderover.Augment({toHTML:function(L,H,F){var l=this.getValues("displaystyle","accent","accentunder","align");if(!l.displaystyle&&this.data[this.base]!=null&&this.data[this.base].CoreMO().Get("movablelimits")){return g.msubsup.prototype.toHTML.call(this,L)}L=this.HTMLcreateSpan(L);var P=this.HTMLgetScale();var q=d.createStack(L);var r=[],o=[],N=[],w,M,I;for(M=0,I=this.data.length;M<I;M++){if(this.data[M]!=null){w=r[M]=d.createBox(q);o[M]=this.data[M].toHTML(w);if(M==this.base){if(F!=null){this.data[this.base].HTMLstretchV(w,H,F)}else{if(H!=null){this.data[this.base].HTMLstretchH(w,H)}}N[M]=(F==null&&H!=null?false:this.data[M].HTMLcanStretch("Horizontal"))}else{N[M]=this.data[M].HTMLcanStretch("Horizontal")}}}d.MeasureSpans(o);var n=-d.BIGDIMEN,K=n;for(M=0,I=this.data.length;M<I;M++){if(this.data[M]){if(r[M].bbox.w>K){K=r[M].bbox.w}if(!N[M]&&K>n){n=K}}}if(F==null&&H!=null){n=H}else{if(n==-d.BIGDIMEN){n=K}}for(M=K=0,I=this.data.length;M<I;M++){if(this.data[M]){w=r[M];if(N[M]){w.bbox=this.data[M].HTMLstretchH(w,n).bbox}if(w.bbox.w>K){K=w.bbox.w}}}var E=d.TeX.rule_thickness,G=d.FONTDATA.TeX_factor;var p=r[this.base]||{bbox:this.HTMLzeroBBox()};var v,s,A,z,u,C,J,O=0;if(p.bbox.ic){O=1.3*p.bbox.ic+0.05}for(M=0,I=this.data.length;M<I;M++){if(this.data[M]!=null){w=r[M];u=d.TeX.big_op_spacing5*P;var B=(M!=this.base&&l[this.ACCENTS[M]]);if(B&&w.bbox.w<=1/d.em+0.0001){w.bbox.w=w.bbox.rw-w.bbox.lw;w.bbox.noclip=true;if(w.bbox.lw){w.insertBefore(d.createSpace(w.parentNode,0,0,-w.bbox.lw),w.firstChild)}d.createBlank(w,0,0,w.bbox.rw+0.1)}C={left:0,center:(K-w.bbox.w)/2,right:K-w.bbox.w}[l.align];v=C;s=0;if(M==this.over){if(B){J=Math.max(E*P*G,2.5/this.em);u=0;if(p.bbox.skew){v+=p.bbox.skew}}else{A=d.TeX.big_op_spacing1*P*G;z=d.TeX.big_op_spacing3*P*G;J=Math.max(A,z-Math.max(0,w.bbox.d))}J=Math.max(J,1.5/this.em);v+=O/2;s=p.bbox.h+w.bbox.d+J;w.bbox.h+=u}else{if(M==this.under){if(B){J=3*E*P*G;u=0}else{A=d.TeX.big_op_spacing2*P*G;z=d.TeX.big_op_spacing4*P*G;J=Math.max(A,z-w.bbox.h)}J=Math.max(J,1.5/this.em);v-=O/2;s=-(p.bbox.d+w.bbox.h+J);w.bbox.d+=u}}d.placeBox(w,v,s)}}this.HTMLhandleSpace(L);this.HTMLhandleColor(L);return L},HTMLstretchH:g.mbase.HTMLstretchH,HTMLstretchV:g.mbase.HTMLstretchV});g.msubsup.Augment({toHTML:function(K,I,C){K=this.HTMLcreateSpan(K);var N=this.HTMLgetScale(),H=this.HTMLgetMu(K);var w=d.createStack(K),l,n=[];var o=d.createBox(w);if(this.data[this.base]){n.push(this.data[this.base].toHTML(o));if(C!=null){this.data[this.base].HTMLstretchV(o,I,C)}else{if(I!=null){this.data[this.base].HTMLstretchH(o,I)}}}else{o.bbox=this.HTMLzeroBBox()}var L=d.TeX.x_height*N,B=d.TeX.scriptspace*N*0.75;var k,x;if(this.HTMLnotEmpty(this.data[this.sup])){k=d.createBox(w);n.push(this.data[this.sup].toHTML(k))}if(this.HTMLnotEmpty(this.data[this.sub])){x=d.createBox(w);n.push(this.data[this.sub].toHTML(x))}d.MeasureSpans(n);if(k){k.bbox.w+=B;k.bbox.rw=Math.max(k.bbox.w,k.bbox.rw)}if(x){x.bbox.w+=B;x.bbox.rw=Math.max(x.bbox.w,x.bbox.rw)}d.placeBox(o,0,0);var m;if(k){m=this.data[this.sup].HTMLgetScale()}else{if(x){m=this.data[this.sub].HTMLgetScale()}else{m=this.HTMLgetScale()}}var F=d.TeX.sup_drop*m,E=d.TeX.sub_drop*m;var z=o.bbox.h-F,y=o.bbox.d+E,M=0,G;if(o.bbox.ic){o.bbox.w-=o.bbox.ic;M=1.3*o.bbox.ic+0.05}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&&o.bbox.scale===1&&!this.data[this.base].Get("largeop")){z=y=0}}var J=this.getValues("subscriptshift","superscriptshift");J.subscriptshift=(J.subscriptshift===""?0:d.length2em(J.subscriptshift,H));J.superscriptshift=(J.superscriptshift===""?0:d.length2em(J.superscriptshift,H));if(!k){if(x){y=Math.max(y,d.TeX.sub1*N,x.bbox.h-(4/5)*L,J.subscriptshift);d.placeBox(x,o.bbox.w,-y,x.bbox)}}else{if(!x){l=this.getValues("displaystyle","texprimestyle");G=d.TeX[(l.displaystyle?"sup1":(l.texprimestyle?"sup3":"sup2"))];z=Math.max(z,G*N,k.bbox.d+(1/4)*L,J.superscriptshift);d.placeBox(k,o.bbox.w+M,z,k.bbox)}else{y=Math.max(y,d.TeX.sub2*N);var A=d.TeX.rule_thickness*N;if((z-k.bbox.d)-(x.bbox.h-y)<3*A){y=3*A-z+k.bbox.d+x.bbox.h;F=(4/5)*L-(z-k.bbox.d);if(F>0){z+=F;y-=F}}d.placeBox(k,o.bbox.w+M,Math.max(z,J.superscriptshift));d.placeBox(x,o.bbox.w,-Math.max(y,J.subscriptshift))}}this.HTMLhandleSpace(K);this.HTMLhandleColor(K);return K},HTMLstretchH:g.mbase.HTMLstretchH,HTMLstretchV:g.mbase.HTMLstretchV});g.mmultiscripts.Augment({toHTML:g.mbase.HTMLautoload});g.mtable.Augment({toHTML:g.mbase.HTMLautoload});g["annotation-xml"].Augment({toHTML:g.mbase.HTMLautoload});g.math.Augment({toHTML:function(u,l){var r=this.Get("alttext");if(r&&r!==""){l.setAttribute("aria-label",r)}var m=d.addElement(u,"nobr",{isMathJax:true});u=this.HTMLcreateSpan(m);var s=d.createStack(u),n=d.createBox(s),t;s.style.fontSize=m.parentNode.style.fontSize;m.parentNode.style.fontSize="";if(this.data[0]!=null){if(d.msieColorBug){if(this.background){this.data[0].background=this.background;delete this.background}if(this.mathbackground){this.data[0].mathbackground=this.mathbackground;delete this.mathbackground}}g.mbase.prototype.displayAlign=b.config.displayAlign;g.mbase.prototype.displayIndent=b.config.displayIndent;var o=this.data[0].toHTML(n);o.bbox.exactW=false;t=d.Measured(o,n)}d.placeBox(n,0,0);u.style.width=d.Em((Math.round(t.bbox.w*this.em)+0.25)/d.outerEm);u.style.display="inline-block";var k=1/d.em,q=d.em/d.outerEm;d.em/=q;u.bbox.h*=q;u.bbox.d*=q;u.bbox.w*=q;u.bbox.lw*=q;u.bbox.rw*=q;if(t&&t.bbox.width!=null){u.style.minWidth=(t.bbox.minWidth||u.style.width);u.style.width=s.style.width=t.bbox.width;n.style.width="100%"}this.HTMLhandleColor(u);if(t){d.createRule(u,(t.bbox.h+k)*q,(t.bbox.d+k)*q,0)}if(!this.isMultiline&&this.Get("display")==="block"&&u.bbox.width==null){var v=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift");if(v.indentalignfirst!==g.INDENTALIGN.INDENTALIGN){v.indentalign=v.indentalignfirst}if(v.indentalign===g.INDENTALIGN.AUTO){v.indentalign=this.displayAlign}l.style.textAlign=v.indentalign;if(v.indentshiftfirst!==g.INDENTSHIFT.INDENTSHIFT){v.indentshift=v.indentshiftfirst}if(v.indentshift==="auto"){v.indentshift=this.displayIndent}if(v.indentshift&&v.indentalign!==g.INDENTALIGN.CENTER){u.style[{left:"marginLeft",right:"marginRight"}[v.indentalign]]=d.Em(d.length2em(v.indentshift))}}return u},HTMLspanElement:g.mbase.prototype.HTMLspanElement});g.TeXAtom.Augment({toHTML:function(l){l=this.HTMLcreateSpan(l);if(this.data[0]!=null){if(this.texClass===g.TEXCLASS.VCENTER){var k=d.createStack(l);var m=d.createBox(k);d.Measured(this.data[0].toHTML(m),m);d.placeBox(m,0,d.TeX.axis_height-(m.bbox.h+m.bbox.d)/2+m.bbox.d)}else{l.bbox=this.data[0].toHTML(l).bbox}}this.HTMLhandleSpace(l);this.HTMLhandleColor(l);return l}});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(k){var o=(document.documentMode||0);var n=k.versionAtLeast("7.0");var m=k.versionAtLeast("8.0")&&o>7;var l=(document.compatMode==="BackCompat");if(o<9){d.config.styles[".MathJax .MathJax_HitBox"]["background-color"]="white";d.config.styles[".MathJax .MathJax_HitBox"].opacity=0;d.config.styles[".MathJax .MathJax_HitBox"].filter="alpha(opacity=0)"}d.Augment({PaddingWidthBug:true,msieAccentBug:true,msieColorBug:true,msieColorPositionBug:true,msieRelativeWidthBug:l,msieDisappearingBug:(o>=8),msieMarginScaleBug:(o<8),msiePaddingWidthBug:true,msieBorderWidthBug:l,msieFrameSizeBug:(o<=8),msieInlineBlockAlignBug:(!m||l),msiePlaceBoxBug:(m&&!l),msieClipRectBug:!m,msieNegativeSpaceBug:l,cloneNodeBug:(m&&k.version==="8.0"),initialSkipBug:(o<8),msieNegativeBBoxBug:(o>=8),msieIE6:!n,msieItalicWidthBug:true,FontFaceBug:true,msieFontCSSBug:k.isIE9,allowWebFonts:(o>=9?"woff":"eot")})},Firefox:function(l){var m=false;if(l.versionAtLeast("3.5")){var k=String(document.location).replace(/[^\/]*$/,"");if(document.location.protocol!=="file:"||b.config.root.match(/^https?:\/\//)||(b.config.root+"/").substr(0,k.length)===k){m="otf"}}d.Augment({ffVerticalAlignBug:true,AccentBug:true,allowWebFonts:m})},Safari:function(p){var n=p.versionAtLeast("3.0");var m=p.versionAtLeast("3.1");var k=navigator.appVersion.match(/ Safari\/\d/)&&navigator.appVersion.match(/ Version\/\d/)&&navigator.vendor.match(/Apple/);var l=(navigator.appVersion.match(/ Android (\d+)\.(\d+)/));var q=(m&&p.isMobile&&((navigator.platform.match(/iPad|iPod|iPhone/)&&!p.versionAtLeast("5.0"))||(l!=null&&(l[1]<2||(l[1]==2&&l[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:!m,safariTextNodeBug:!n,forceReflow:true,allowWebFonts:(m&&!q?"otf":false)});if(k){d.Augment({webFontDefault:(p.isMobile?"sans-serif":"serif")})}if(p.isPC){d.Augment({adjustAvailableFonts:d.removeSTIXfonts,checkWebFontsTwice:true})}if(q){var o=b.config["HTML-CSS"];if(o){o.availableFonts=[];o.preferredFont=null}else{b.config["HTML-CSS"]={availableFonts:[],preferredFont:null}}}},Chrome:function(k){d.Augment({Em:d.EmRounded,cloneNodeBug:true,rfuzz:0.011,AccentBug:true,AdjustSurd:true,negativeBBoxes:true,safariNegativeSpaceBug:true,safariWebFontSerif:[""],forceReflow:true,allowWebFonts:(k.versionAtLeast("4.0")?"otf":"svg")})},Opera:function(k){k.isMini=(navigator.appVersion.match("Opera Mini")!=null);d.config.styles[".MathJax .merror"]["vertical-align"]=null;d.config.styles[".MathJax span"]["z-index"]=0;d.Augment({operaHeightBug:true,operaVerticalAlignBug:true,operaFontSizeBug:k.versionAtLeast("10.61"),initialSkipBug:true,FontFaceBug:true,PaddingWidthBug:true,allowWebFonts:(k.versionAtLeast("10.0")&&!k.isMini?"otf":false),adjustAvailableFonts:d.removeSTIXfonts})},Konqueror:function(k){d.Augment({konquerorVerticalAlignBug:true})}})});MathJax.Hub.Register.StartupHook("End Cookie",function(){if(b.config.menuSettings.zoom!=="None"){h.Require("[MathJax]/extensions/MathZoom.js")}})})(MathJax.Ajax,MathJax.Hub,MathJax.OutputJax["HTML-CSS"]);