/*
 *  /MathJax/jax/output/HTML-CSS/jax.js
 *
 *  Copyright (c) 2009-2015 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,comparisonFont:["sans-serif","monospace","script","Times","Courier","Arial","Helvetica"],testSize:["40px","50px","60px","30px","20px"],FedoraSTIXcheck:{family:"STIXSizeOneSym",testString:"abcABC",noStyleChar:true},Init:function(){this.div=MathJax.HTML.addElement(document.body,"div",{style:{position:"absolute",width:0,height:0,overflow:"hidden",padding:0,border:0,margin:0}},[["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"}},[""]]]).firstChild;this.text=this.div.firstChild},findFont:function(p,l){var o=null;if(l&&this.testCollection(l)){o=l}else{for(var n=0,k=p.length;n<k;n++){if(p[n]===l){continue}if(this.testCollection(p[n])){o=p[n];break}}}if(o==="STIX"&&this.testFont(this.FedoraSTIXcheck)){o=null}return o},testCollection:function(l){var k={testString:"() {} []"};k.family={TeX:"MathJax_Size1",STIX:"STIXSizeOneSym"}[l]||l.replace(/-(Math)?/,"")+"MathJax_Size1";if(l==="STIX"){k.noStyleChar=true}return this.testFont(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 p=n.familyFixed||n.family;if(!n.isWebFont&&!p.match(/^(STIX|MathJax)|'/)){p=p.replace(/_/g," ").replace(/([a-z])([A-Z])/g,"$1 $2").replace(/ Jax/,"Jax")+"','"+p+"','"+p+"-";if(n.weight){p+="Bold"}if(n.style){p+="Italic"}if(!n.weight&&!n.style){p+="Regular"}n.familyFixed=p="'"+p+"'"}var l=this.getComparisonWidths(n.testString,n.noStyleChar);var q=null;if(l){this.div.style.fontFamily=p+","+this.comparisonFont[0];if(this.div.offsetWidth==l[0]){this.div.style.fontFamily=p+","+this.comparisonFont[l[2]];if(this.div.offsetWidth==l[1]){q=false}}if(q===null&&(this.div.offsetWidth!=l[3]||this.div.offsetHeight!=l[4])){if(!n.noStyleChar&&d.FONTDATA&&d.FONTDATA.hasStyleChar){for(var o=0,k=this.testSize.length;o<k;o++){if(this.testStyleChar(n,this.testSize[o])){q=true;k=0}}}else{q=true}}}if(d.safariTextNodeBug){this.div.innerHTML=""}else{this.text.nodeValue=""}return q},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(o){var p=d.allowWebFonts;var r=d.FONTDATA.FONTS[o];if(d.msieFontCSSBug&&!r.family.match(/-Web$/)){r.family+="-Web"}if(r.isWebFont){delete r.familyFixed}var k=d.webfontDir+"/"+p;var n=h.fileURL(k);var m=o.replace(/-b/,"-B").replace(/-i/,"-I").replace(/-Bold-/,"-Bold");if(!m.match(/-/)){m+="-Regular"}if(p==="svg"){m+=".svg#"+m}else{m+="."+p}var l=h.fileRev(k+"/"+m.replace(/#.*/,""));var q={"font-family":r.family,src:"url('"+n+"/"+m+l+"')"};if(p==="otf"){m=m.replace(/otf$/,"woff");l=h.fileRev(k+"/"+m);q.src+=" format('opentype')";n=h.fileURL(d.webfontDir+"/woff");q.src="url('"+n+"/"+m+l+"') format('woff'), "+q.src}else{if(p!=="eot"){q.src+=" format('"+p+"')"}}if(!(d.FontFaceBug&&r.isWebFont)){if(o.match(/-bold/)){q["font-weight"]="bold"}if(o.match(/-italic/)){q["font-style"]="italic"}}return q}});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","max-width":"none","max-height":"none","min-width":0,"min-height":0,border:0,padding:0,margin:0},".MathJax:focus, body :focus .MathJax":{display:"inline-table"},".MathJax_Display":{position:"relative",display:"block!important","text-indent":0,"max-width":"none","max-height":"none","min-width":0,"min-height":0,width:"100%"},".MathJax img, .MathJax nobr, .MathJax a":{border:0,padding:0,margin:0,"max-width":"none","max-height":"none","min-width":0,"min-height":0,"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!important",overflow:"hidden",width:"1px",height:"60ex","min-height":0,"max-height":"none"},".MathJax .MathJax_EmBox":{display:"block!important",overflow:"hidden",width:"1px",height:"60em","min-height":0,"max-height":"none"},".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,Font:null,webFontDefault:"MathJax_Blank",allowWebFonts:"otf",maxStretchyParts:1000,fontName:{TeXLocal:"TeX",TeXWeb:["","TeX"],TeXImage:["",""],STIXLocal:["STIX","STIX-Web"],STIXWeb:"STIX-Web",AsanaMathWeb:"Asana-Math",GyrePagellaWeb:"Gyre-Pagella",GyreTermesWeb:"Gyre-Termes",LatinModernWeb:"Latin-Modern",NeoEulerWeb:"Neo-Euler"},fontInUse:"generic",FONTDATA:{TeX_factor:1,baselineskip:1.2,lineH:0.8,lineD:0.2,ffLineH:0.8,FONTS:{},VARIANT:{normal:{fonts:[]},"-generic-variant":{},"-largeOp":{},"-smallOp":{}},RANGES:[],DELIMITERS:{},RULECHAR:45,REMAP:{}},Config:function(){if(!this.require){this.require=[]}this.Font=f();this.SUPER(arguments).Config.call(this);var m=this.settings,l=this.config,k=m.font;if(this.adjustAvailableFonts){this.adjustAvailableFonts(l.availableFonts)}if(m.scale){l.scale=m.scale}if(k&&k!=="Auto"&&this.fontName[k]){l.availableFonts=[];delete l.fonts;if(this.fontName[k] instanceof Array){l.preferredFont=this.fontName[k][0];l.webFont=this.fontName[k][1]}else{l.preferredFont=l.webFont=this.fontName[k]}if(l.preferredFont){l.availableFonts[0]=l.preferredFont}}if(l.fonts){l.availableFonts=l.fonts;l.preferredFont=l.webFont=l.fonts[0];if(l.webFont==="STIX"){l.webFont+="-Web"}}k=this.Font.findFont(l.availableFonts,l.preferredFont);if(!k&&this.allowWebFonts){k=l.webFont;if(k){this.webFonts=true}}if(!k&&this.config.imageFont){k=l.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);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();this.getDefaultExEm();if(this.defaultEm){return}var k=MathJax.Callback();h.timer.start(h,function(l){if(l.time(k)){b.signal.Post(["HTML-CSS Jax - no default em size"]);return}d.getDefaultExEm();if(d.defaultEm){k()}else{setTimeout(l,l.delay)}},this.defaultEmDelay,this.defaultEmTimeout);return k},defaultEmDelay:100,defaultEmTimeout:1000,getDefaultExEm:function(){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(q){var p=q.jax[this.id],B,x=p.length,w,E,u,A,s,C,l,D,k,F,t,r=false,y,o=this.config.linebreaks.automatic,v=this.config.linebreaks.width;if(o){r=(v.match(/^\s*(\d+(\.\d*)?%\s*)?container\s*$/)!=null);if(r){v=v.replace(/\s*container\s*/,"")}else{t=this.defaultWidth}if(v===""){v="100%"}}else{t=100000}for(B=0;B<x;B++){E=p[B];if(!E.parentNode){continue}u=E.previousSibling;if(u&&String(u.className).match(/^MathJax(_Display)?( MathJax_Processing)?$/)){u.parentNode.removeChild(u)}l=E.MathJax.elementJax;if(!l){continue}l.HTMLCSS={display:(l.root.Get("display")==="block")};A=s=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,onkeydown:j.Keydown,tabIndex:"0"});if(b.Browser.noContextMenu){A.ontouchstart=a.start;A.ontouchend=a.end}if(l.HTMLCSS.display){s=this.Element("div",{className:"MathJax_Display"});s.appendChild(A)}else{if(this.msieDisappearingBug){A.style.display="inline-block"}}s.className+=" MathJax_Processing";E.parentNode.insertBefore(s,E);E.parentNode.insertBefore(this.EmExSpan.cloneNode(true),E);s.parentNode.insertBefore(this.linebreakSpan.cloneNode(true),s)}var z=[];for(B=0;B<x;B++){E=p[B];if(!E.parentNode){continue}C=E.previousSibling;s=C.previousSibling;l=E.MathJax.elementJax;if(!l){continue}D=C.firstChild.offsetHeight/60;k=C.lastChild.firstChild.offsetHeight/60;y=s.previousSibling.firstChild.offsetWidth;if(r){t=y}if(D===0||D==="NaN"){z.push(s);l.HTMLCSS.isHidden=true;D=this.defaultEx;k=this.defaultEm;y=this.defaultWidth;if(r){t=y}}F=(this.config.matchFontHeight?D/this.TeX.x_height/k:1);F=Math.floor(Math.max(this.config.minScaleAdjust/100,F)*this.config.scale);l.HTMLCSS.scale=F/100;l.HTMLCSS.fontSize=F+"%";l.HTMLCSS.em=l.HTMLCSS.outerEm=k;this.em=k*F/100;l.HTMLCSS.ex=D;l.HTMLCSS.cwidth=y/this.em;l.HTMLCSS.lineWidth=(o?this.length2em(v,1,t/this.em):1000000)}for(B=0,w=z.length;B<w;B++){this.hiddenDiv.appendChild(z[B]);this.addElement(this.hiddenDiv,"br")}for(B=0;B<x;B++){E=p[B];if(!E.parentNode){continue}C=p[B].previousSibling;l=p[B].MathJax.elementJax;if(!l){continue}A=C.previousSibling;if(!l.HTMLCSS.isHidden){A=A.previousSibling}A.parentNode.removeChild(A);C.parentNode.removeChild(C)}q.HTMLCSSeqn=q.HTMLCSSlast=0;q.HTMLCSSi=-1;q.HTMLCSSchunk=this.config.EqnChunk;q.HTMLCSSdelay=false},PHASE:{I:1,II:2,III:3},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);if(!q){return}this.getMetrics(k);if(this.scale!==1){m.style.fontSize=k.HTMLCSS.fontSize}this.initImg(m);this.initHTML(o,m);this.savePreview(l);try{o.setTeXclass();k.HTMLCSS.span=m;k.HTMLCSS.div=q;o.toHTML(m,q,this.PHASE.I)}catch(n){if(n.restart){while(m.firstChild){m.removeChild(m.firstChild)}}this.restorePreview(l);throw n}this.restorePreview(l);q.className=q.className.split(/ /)[0]+" MathJax_Processed";b.signal.Post(["New Math Pending",k.inputID]);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}return false},savePreview:function(k){var l=k.MathJax.preview;if(l){k.MathJax.tmpPreview=document.createElement("span");l.parentNode.replaceChild(k.MathJax.tmpPreview,l)}},restorePreview:function(k){var l=k.MathJax.tmpPreview;if(l){l.parentNode.replaceChild(k.MathJax.preview,l);delete k.MathJax.tmpPreview}},getMetrics:function(k){var l=k.HTMLCSS;this.em=g.mbase.prototype.em=l.em*l.scale;this.outerEm=l.em;this.scale=l.scale;this.cwidth=l.cwidth;this.linebreakWidth=l.lineWidth},postTranslate:function(l,s){var p=l.jax[this.id],t,n,q,o;for(q=l.HTMLCSSlast,o=l.HTMLCSSeqn;q<o;q++){t=p[q];if(t&&t.MathJax.elementJax){var k=t.MathJax.elementJax.HTMLCSS.div;k.className=k.className.split(/ /)[0];if(t.MathJax.preview){t.MathJax.preview.innerHTML=""}}}for(q=l.HTMLCSSlast,o=l.HTMLCSSeqn;q<o;q++){t=p[q];if(t&&t.MathJax.elementJax){n=t.MathJax.elementJax;this.getMetrics(n);n.root.toHTML(n.HTMLCSS.span,n.HTMLCSS.div,this.PHASE.II)}}for(q=l.HTMLCSSlast,o=l.HTMLCSSeqn;q<o;q++){t=p[q];if(t&&t.MathJax.elementJax){n=t.MathJax.elementJax;this.getMetrics(n);n.root.toHTML(n.HTMLCSS.span,n.HTMLCSS.div,this.PHASE.III);if(n.HTMLCSS.isHidden){t.parentNode.insertBefore(n.HTMLCSS.div,t)}delete n.HTMLCSS.span;delete n.HTMLCSS.div;t.MathJax.state=n.STATE.PROCESSED;b.signal.Post(["New Math",t.MathJax.elementJax.inputID])}}if(this.forceReflow){var r=(document.styleSheets||[])[0]||{};r.disabled=true;r.disabled=false}l.HTMLCSSlast=l.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,w,v,k,t){w.className="MathJax";w.style.fontSize=l.HTMLCSS.fontSize;var z=w.appendChild(this.EmExSpan.cloneNode(true));var o=z.lastChild.firstChild.offsetHeight/60;this.em=g.mbase.prototype.em=o;this.outerEm=o/l.HTMLCSS.scale;z.parentNode.removeChild(z);this.scale=l.HTMLCSS.scale;this.linebreakWidth=l.HTMLCSS.lineWidth;this.cwidth=l.HTMLCSS.cwidth;this.zoomScale=parseInt(b.config.menuSettings.zscale)/100;this.idPostfix="-zoom";l.root.toHTML(w,w);this.idPostfix="";this.zoomScale=1;var x=l.root.HTMLspanElement().bbox,n=x.width;if(n){if(x.tw){k=x.tw*o}if(x.w*o<k){k=x.w*o}w.style.width=Math.floor(k-1.5*d.em)+"px";w.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){var s=p.offsetWidth;p.style.width="100%";if(s>k){w.style.width=(s+100)+"px"}}}p=w.firstChild.firstChild.style;if(x.H!=null&&x.H>x.h){p.marginTop=d.Em(x.H-Math.max(x.h,d.FONTDATA.lineH))}if(x.D!=null&&x.D>x.d){p.marginBottom=d.Em(x.D-Math.max(x.d,d.FONTDATA.lineD))}if(x.lw<0){p.paddingLeft=d.Em(-x.lw)}if(x.rw>x.w){p.marginRight=d.Em(x.rw-x.w)}w.style.position="absolute";if(!n){v.style.position="absolute"}var u=w.offsetWidth,r=w.offsetHeight,y=v.offsetHeight,q=v.offsetWidth;w.style.position=v.style.position="";return{Y:-j.getBBox(w).h,mW:q,mH:y,zW:u,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;if(m[k].familyFixed){m[k].family=m[k].familyFixed;delete m[k].familyFixed}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,m){if(l.bbox&&this.config.noReflows&&!m){return{h:l.bbox.h,d:l.bbox.d}}var k=l.style.position;l.style.position="absolute";this.HDimg.style.height="0px";l.appendChild(this.HDspan);var n={h:l.offsetHeight};this.HDimg.style.height=n.h+"px";n.d=l.offsetHeight-n.h;n.h-=n.d;n.h/=this.em;n.d/=this.em;l.removeChild(this.HDspan);l.style.position=k;return n},getW:function(o){var l,n,m=(o.bbox||{}).w,p=o;if(o.bbox&&this.config.noReflows&&o.bbox.exactW!==false){if(!o.bbox.exactW){if(o.style.paddingLeft){m+=this.unEm(o.style.paddingLeft)*(o.scale||1)}if(o.style.paddingRight){m+=this.unEm(o.style.paddingRight)*(o.scale||1)}}return m}if(o.bbox&&o.bbox.exactW){return m}if((o.bbox&&m>=0&&!this.initialSkipBug&&!this.msieItalicWidthBug)||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{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);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||(this.config.noReflows&&u.exactW!==false)){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+$/,"")+"%"},length2em:function(r,l,p){if(typeof(r)!=="string"){r=r.toString()}if(r===""){return""}if(r===g.SIZE.NORMAL){return 1}if(r===g.SIZE.BIG){return 2}if(r===g.SIZE.SMALL){return 0.71}if(r==="infinity"){return d.BIGDIMEN}var o=this.FONTDATA.TeX_factor,s=(d.zoomScale||1)/d.em;if(r.match(/mathspace$/)){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*s}if(q==="pt"){return k/10*o}if(q==="pc"){return k*1.2*o}if(q==="in"){return k*this.pxPerInch*s}if(q==="cm"){return k*this.pxPerInch*s/2.54}if(q==="mm"){return k*this.pxPerInch*s/25.4}if(q==="mu"){return k/18*o*l}return k*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(k<0){n.style.marginRight=n.style.width;n.style.width=0}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,true).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}var k={display:"inline-block",overflow:"hidden",verticalAlign:this.Em(-p)};if(s>n+p){k.borderTop=this.Px(n+p)+" "+l;k.width=this.Em(s);k.height=(this.msieRuleBug&&n+p>0?this.Em(n+p):0)}else{k.borderLeft=this.Px(s)+" "+l;k.width=(this.msieRuleBug&&s>0?this.Em(s):0);k.height=this.Em(n+p)}var q=this.addElement(r,"span",{style:k,noAdjust:true,HH:n+p,isMathJax:true,bbox:{h:n,d:p,w:s,rw:s,lw:0,exactW:true}});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.Px(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=-1000,k=C.rw+1000;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}if(C.tw){z.tw=C.tw}}},alignBox:function(s,o,q,v){if(v==null){v=0}this.placeBox(s,v,q);if(this.msiePlaceBoxBug){var m=s.lastChild;while(m&&m.nodeName!=="#text"){m=m.previousSibling}if(m){s.removeChild(m)}}var u=s.bbox;if(u.isMultiline){return}var t=u.width!=null&&!u.isFixed;var k=0,p=v-u.w/2,n="50%";if(this.initialSkipBug){k=u.w-u.rw-0.1;p+=u.lw}if(this.msieMarginScaleBug){p=(p*this.em)+"px"}else{p=this.Em(p)}if(t){p=(v===0?"":this.Em(v));n=(50-parseFloat(u.width)/2)+"%"}b.Insert(s.style,({right:{left:"",right:this.Em(k-v)},center:{left:n,marginLeft:p}})[o])},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),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);delete l.parentNode.bbox}}}},handleVariant:function(z,o,r){var y="",w,B,s,C,k=z,l=!!z.style.fontFamily;if(r.length===0){return}if(!z.bbox){z.bbox={w:0,h:-this.BIGDIMEN,d:-this.BIGDIMEN,rw:-this.BIGDIMEN,lw:this.BIGDIMEN}}if(!o){o=this.FONTDATA.VARIANT[g.VARIANT.NORMAL]}C=o;for(var A=0,x=r.length;A<x;A++){o=C;w=r.charCodeAt(A);B=r.charAt(A);if(w>=55296&&w<56319){A++;w=(((w-55296)<<10)+(r.charCodeAt(A)-56320))+65536;if(this.FONTDATA.RemapPlane1){var D=this.FONTDATA.RemapPlane1(w,o);w=D.n;o=D.variant}}else{var t,q,u=this.FONTDATA.RANGES;for(t=0,q=u.length;t<q;t++){if(u[t].name==="alpha"&&o.noLowerCase){continue}var p=o["offset"+u[t].offset];if(p&&w>=u[t].low&&w<=u[t].high){if(u[t].remap&&u[t].remap[w]){w=p+u[t].remap[w]}else{w=w-u[t].low+p;if(u[t].add){w+=u[t].add}}if(o["variant"+u[t].offset]){o=this.FONTDATA.VARIANT[o["variant"+u[t].offset]]}break}}}if(o.remap&&o.remap[w]){w=o.remap[w];if(o.remap.variant){o=this.FONTDATA.VARIANT[o.remap.variant]}}else{if(this.FONTDATA.REMAP[w]&&!o.noRemap){w=this.FONTDATA.REMAP[w]}}if(w instanceof Array){o=this.FONTDATA.VARIANT[w[1]];w=w[0]}if(typeof(w)==="string"){r=w+r.substr(A+1);x=r.length;A=-1;continue}s=this.lookupChar(o,w);B=s[w];if(l||(!this.checkFont(s,k.style)&&!B[5].img)){if(y.length){this.addText(k,y);y=""}var v=!!k.style.fontFamily||!!z.style.fontStyle||!!z.style.fontWeight||!s.directory||l;l=false;if(k!==z){v=!this.checkFont(s,z.style);k=z}if(v){k=this.addElement(z,"span",{isMathJax:true,subSpan:true})}this.handleFont(k,s,k!==z)}y=this.handleChar(k,s,B,w,y);if(!(B[5]||{}).space){if(B[0]/1000>z.bbox.h){z.bbox.h=B[0]/1000}if(B[1]/1000>z.bbox.d){z.bbox.d=B[1]/1000}}if(z.bbox.w+B[3]/1000<z.bbox.lw){z.bbox.lw=z.bbox.w+B[3]/1000}if(z.bbox.w+B[4]/1000>z.bbox.rw){z.bbox.rw=z.bbox.w+B[4]/1000}z.bbox.w+=B[2]/1000;if((B[5]||{}).isUnknown){z.bbox.exactW=false}}if(y.length){this.addText(k,y)}if(z.scale&&z.scale!==1){z.bbox.h*=z.scale;z.bbox.d*=z.scale;z.bbox.w*=z.scale;z.bbox.lw*=z.scale;z.bbox.rw*=z.scale}if(r.length==1&&s.skew&&s.skew[w]){z.bbox.skew=s.skew[w]}},checkFont:function(k,l){var m=(l.fontWeight||"normal");if(m.match(/^\d+$/)){m=(parseInt(m)>=600?"bold":"normal")}return(k.family.replace(/'/g,"")===l.fontFamily.replace(/'/g,"")&&(k.style||"normal")===(l.fontStyle||"normal")&&(k.weight||"normal")===m)},handleFont:function(m,k,o){m.style.fontFamily=k.family;if(!k.directory){m.style.fontSize=Math.floor(d.config.scale/d.scale+0.5)+"%"}if(!(d.FontFaceBug&&k.isWebFont)){var l=k.style||"normal",n=k.weight||"normal";if(l!=="normal"||o){m.style.fontStyle=l}if(n!=="normal"||o){m.style.fontWeight=n}}},handleChar:function(l,k,s,r,q){var p=s[5];if(p.space){if(q.length){this.addText(l,q)}d.createShift(l,s[2]/1000);return""}if(p.img){return this.handleImg(l,k,s,r,q)}if(p.isUnknown&&this.FONTDATA.DELIMITERS[r]){if(q.length){this.addText(l,q)}var o=l.scale;d.createDelimiter(l,r,0,1,k);if(this.FONTDATA.DELIMITERS[r].dir==="V"){l.style.verticalAlign=this.Em(l.bbox.d);l.bbox.h+=l.bbox.d;l.bbox.d=0}l.scale=o;s[0]=l.bbox.h*1000;s[1]=l.bbox.d*1000;s[2]=l.bbox.w*1000;s[3]=l.bbox.lw*1000;s[4]=l.bbox.rw*1000;return""}if(p.c==null){if(r<=65535){p.c=String.fromCharCode(r)}else{var m=r-65536;p.c=String.fromCharCode((m>>10)+55296)+String.fromCharCode((m&1023)+56320)}}if(p.rfix){this.addText(l,q+p.c);d.createShift(l,p.rfix/1000);return""}if(s[2]||!this.msieAccentBug||q.length){return q+p.c}d.createShift(l,s[3]/1000);d.createShift(l,(s[4]-s[3])/1000);this.addText(l,p.c);d.createShift(l,-s[4]/1000);return""},handleImg:function(l,k,p,o,m){return m},lookupChar:function(p,s){var o,k;if(!p.FONTS){var r=this.FONTDATA.FONTS;var q=(p.fonts||this.FONTDATA.VARIANT.normal.fonts);if(!(q instanceof Array)){q=[q]}if(p.fonts!=q){p.fonts=q}p.FONTS=[];for(o=0,k=q.length;o<k;o++){if(r[q[o]]){p.FONTS.push(r[q[o]]);r[q[o]].name=q[o]}}}for(o=0,k=p.FONTS.length;o<k;o++){var l=p.FONTS[o];if(typeof(l)==="string"){delete p.FONTS;this.loadFont(l)}if(l[s]){if(l[s].length===5){l[s][5]={}}if(d.allowWebFonts&&!l.available){this.loadWebFont(l)}else{return l}}else{this.findBlock(l,s)}}return this.unknownChar(p,s)},unknownChar:function(k,m){var l=(k.defaultFont||{family:d.config.undefinedFamily});if(k.bold){l.weight="bold"}if(k.italic){l.style="italic"}if(!l[m]){l[m]=[800,200,500,0,500,{isUnknown:true}]}b.signal.Post(["HTML-CSS Jax - unknown char",m,k]);return l},findBlock:function(l,q){if(l.Ranges){for(var p=0,k=l.Ranges.length;p<k;p++){if(q<l.Ranges[p][0]){return}if(q<=l.Ranges[p][1]){var o=l.Ranges[p][2];for(var n=l.Ranges.length-1;n>=0;n--){if(l.Ranges[n][2]==o){l.Ranges.splice(n,1)}}this.loadFont(l.directory+"/"+o+".js")}}}},loadFont:function(l){var k=MathJax.Callback.Queue();k.Push(["Require",h,this.fontDir+"/"+l]);if(this.imgFonts){if(!MathJax.isPacked){l=l.replace(/\/([^\/]*)$/,d.imgPacked+"/$1")}k.Push(["Require",h,this.webfontDir+"/png/"+l])}b.RestartAfter(k.Push({}))},loadWebFont:function(k){k.available=k.isWebFont=true;if(d.FontFaceBug){k.family=k.name;if(d.msieFontCSSBug){k.family+="-Web"}}b.RestartAfter(this.Font.loadWebFont(k))},loadWebFontError:function(l,k){b.Startup.signal.Post("HTML-CSS Jax - disable web fonts");l.isWebFont=false;if(this.config.imageFont&&this.config.imageFont===this.fontInUse){this.imgFonts=true;b.Startup.signal.Post("HTML-CSS Jax - switch to image fonts");b.Startup.signal.Post("HTML-CSS Jax - using image fonts");e(["WebFontNotAvailable","Web-Fonts not available -- using image fonts instead"],null,3000);h.Require(this.directory+"/imageFonts.js",k)}else{this.allowWebFonts=false;k()}},Element:MathJax.HTML.Element,addElement:MathJax.HTML.addElement,TextNode:MathJax.HTML.TextNode,addText:MathJax.HTML.addText,ucMatch:MathJax.HTML.ucMatch,BIGDIMEN:10000000,ID:0,idPostfix:"",GetID:function(){this.ID++;return this.ID},MATHSPACE:{veryverythinmathspace:1/18,verythinmathspace:2/18,thinmathspace:3/18,mediummathspace:4/18,thickmathspace:5/18,verythickmathspace:6/18,veryverythickmathspace:7/18,negativeveryverythinmathspace:-1/18,negativeverythinmathspace:-2/18,negativethinmathspace:-3/18,negativemediummathspace:-4/18,negativethickmathspace:-5/18,negativeverythickmathspace:-6/18,negativeveryverythickmathspace:-7/18},TeX:{x_height:0.430554,quad:1,num1:0.676508,num2:0.393732,num3:0.44373,denom1:0.685951,denom2:0.344841,sup1:0.412892,sup2:0.362892,sup3:0.288888,sub1:0.15,sub2:0.247217,sup_drop:0.386108,sub_drop:0.05,delim1:2.39,delim2:1,axis_height:0.25,rule_thickness:0.06,big_op_spacing1:0.111111,big_op_spacing2:0.166666,big_op_spacing3:0.2,big_op_spacing4:0.6,big_op_spacing5:0.1,scriptspace:0.1,nulldelimiterspace:0.12,delimiterfactor:901,delimitershortfall:0.3,min_rule_thickness:1.25},NBSP:"\u00A0",rfuzz:0});MathJax.Hub.Register.StartupHook("mml Jax Ready",function(){g=MathJax.ElementJax.mml;g.mbase.Augment({toHTML:function(o){o=this.HTMLcreateSpan(o);if(this.type!="mrow"){o=this.HTMLhandleSize(o)}for(var l=0,k=this.data.length;l<k;l++){if(this.data[l]){this.data[l].toHTML(o)}}var s=this.HTMLcomputeBBox(o);var n=o.bbox.h,r=o.bbox.d,p=false,q;for(l=0,k=s.length;l<k;l++){q=s[l].HTMLspanElement().bbox;if(s[l].forceStretch||q.h!==n||q.d!==r){s[l].HTMLstretchV(o,n,r);p=true}else{if(s[l].needsBBox){p=true}}}if(p){this.HTMLcomputeBBox(o,true)}if(this.HTMLlineBreaks(o)){o=this.HTMLmultiline(o)}this.HTMLhandleSpace(o);this.HTMLhandleColor(o);if(this.data.length===1&&this.data[0]){q=this.data[0].HTMLspanElement().bbox;if(q.skew){o.bbox.skew=q.skew}}return o},HTMLlineBreaks:function(){return false},HTMLmultiline:function(){g.mbase.HTMLautoloadFile("multiline")},HTMLcomputeBBox:function(q,p,o,k){if(o==null){o=0}if(k==null){k=this.data.length}var n=q.bbox={exactW:true},r=[];while(o<k){var l=this.data[o];if(!l){continue}if(!p&&l.HTMLcanStretch("Vertical")){r.push(l);l=(l.CoreMO()||l);r[r.length-1].needsBBox=(l!==this.data[o])}this.HTMLcombineBBoxes(l,n);o++}this.HTMLcleanBBox(n);return r},HTMLcombineBBoxes:function(k,l){if(l.w==null){this.HTMLemptyBBox(l)}var n=(k.bbox?k:k.HTMLspanElement());if(!n||!n.bbox){return}var m=n.bbox;if(m.d>l.d){l.d=m.d}if(m.h>l.h){l.h=m.h}if(m.D!=null&&m.D>l.D){l.D=m.D}if(m.H!=null&&m.H>l.H){l.H=m.H}if(n.style.paddingLeft){l.w+=d.unEm(n.style.paddingLeft)*(n.scale||1)}if(l.w+m.lw<l.lw){l.lw=l.w+m.lw}if(l.w+m.rw>l.rw){l.rw=l.w+m.rw}l.w+=m.w;if(n.style.paddingRight){l.w+=d.unEm(n.style.paddingRight)*(n.scale||1)}if(m.width){l.width=m.width;l.minWidth=m.minWidth}if(m.tw){l.tw=m.tw}if(m.ic){l.ic=m.ic}else{delete l.ic}if(l.exactW&&!m.exactW){l.exactW=m.exactW}},HTMLemptyBBox:function(k){k.h=k.d=k.H=k.D=k.rw=-d.BIGDIMEN;k.w=0;k.lw=d.BIGDIMEN;return k},HTMLcleanBBox:function(k){if(k.h===this.BIGDIMEN){k.h=k.d=k.H=k.D=k.w=k.rw=k.lw=0}if(k.D<=k.d){delete k.D}if(k.H<=k.h){delete k.H}},HTMLzeroBBox:function(){return{h:0,d:0,w:0,lw:0,rw:0}},HTMLcanStretch:function(l){if(this.isEmbellished()){var k=this.Core();if(k&&k!==this){return k.HTMLcanStretch(l)}}return false},HTMLstretchH:function(l,k){return this.HTMLspanElement()},HTMLstretchV:function(l,k,m){return this.HTMLspanElement()},HTMLnotEmpty:function(k){while(k){if((k.type!=="mrow"&&k.type!=="texatom")||k.data.length>1){return true}k=k.data[0]}return false},HTMLmeasureChild:function(l,k){if(this.data[l]){d.Measured(this.data[l].toHTML(k),k)}else{k.bbox=this.HTMLzeroBBox()}},HTMLboxChild:function(l,k){if(!this.data[l]){this.SetData(l,g.mrow())}return this.data[l].toHTML(k)},HTMLcreateSpan:function(k){if(this.spanID){var l=this.HTMLspanElement();if(l&&(l.parentNode===k||(l.parentNode||{}).parentNode===k)){while(l.firstChild){l.removeChild(l.firstChild)}l.bbox=this.HTMLzeroBBox();l.scale=1;l.isMultChar=l.HH=null;l.style.cssText="";return l}}if(this.href){k=d.addElement(k,"a",{href:this.href,isMathJax:true})}k=d.addElement(k,"span",{className:this.type,isMathJax:true});if(d.imgHeightBug){k.style.display="inline-block"}if(this["class"]){k.className+=" "+this["class"]}if(!this.spanID){this.spanID=d.GetID()}k.id=(this.id||"MathJax-Span-"+this.spanID)+d.idPostfix;k.bbox=this.HTMLzeroBBox();this.styles={};if(this.style){k.style.cssText=this.style;if(k.style.fontSize){this.mathsize=k.style.fontSize;k.style.fontSize=""}this.styles={border:d.getBorders(k),padding:d.getPadding(k)};if(this.styles.border){k.style.border=""}if(this.styles.padding){k.style.padding=""}}if(this.href){k.parentNode.bbox=k.bbox}this.HTMLaddAttributes(k);return k},HTMLaddAttributes:function(n){if(this.attrNames){var s=this.attrNames,o=g.nocopyAttributes,r=b.config.ignoreMMLattributes;var p=(this.type==="mstyle"?g.math.prototype.defaults:this.defaults);for(var l=0,k=s.length;l<k;l++){var q=s[l];if(r[q]==false||(!o[q]&&!r[q]&&p[q]==null&&typeof(n[q])==="undefined")){n.setAttribute(q,this.attr[q])}}}},HTMLspanElement:function(){if(!this.spanID){return null}return document.getElementById((this.id||"MathJax-Span-"+this.spanID)+d.idPostfix)},HTMLhandleVariant:function(l,k,m){d.handleVariant(l,k,m)},HTMLhandleSize:function(k){if(!k.scale){k.scale=this.HTMLgetScale();if(k.scale!==1){k.style.fontSize=d.Percent(k.scale)}}return k},HTMLhandleDir:function(l){var k=this.Get("dir",true);if(k){l.dir=k}return l},HTMLhandleColor:function(w){var y=this.getValues("mathcolor","color");if(this.mathbackground){y.mathbackground=this.mathbackground}if(this.background){y.background=this.background}if(this.style&&w.style.backgroundColor){y.mathbackground=w.style.backgroundColor;w.style.backgroundColor="transparent"}var t=(this.styles||{}).border,v=(this.styles||{}).padding;if(y.color&&!this.mathcolor){y.mathcolor=y.color}if(y.background&&!this.mathbackground){y.mathbackground=y.background}if(y.mathcolor){w.style.color=y.mathcolor}if((y.mathbackground&&y.mathbackground!==g.COLOR.TRANSPARENT)||t||v){var A=w.bbox,z=(A.exact?0:1/d.em),u=0,s=0,m=w.style.paddingLeft,q=w.style.paddingRight;if(this.isToken){u=A.lw;s=A.rw-A.w}if(m!==""){u+=d.unEm(m)*(w.scale||1)}if(q!==""){s-=d.unEm(q)*(w.scale||1)}var l=(d.PaddingWidthBug||A.keepPadding||A.exactW?0:s-u);var o=Math.max(0,d.getW(w)+l);var x=A.h+A.d,k=-A.d,r=0,p=0;if(o>0){o+=2*z;u-=z}if(x>0){x+=2*z;k-=z}s=-o-u;if(t){s-=t.right;k-=t.bottom;r+=t.left;p+=t.right;A.h+=t.top;A.d+=t.bottom;A.w+=t.left+t.right;A.lw-=t.left;A.rw+=t.right}if(v){x+=v.top+v.bottom;o+=v.left+v.right;s-=v.right;k-=v.bottom;r+=v.left;p+=v.right;A.h+=v.top;A.d+=v.bottom;A.w+=v.left+v.right;A.lw-=v.left;A.rw+=v.right}if(p){w.style.paddingRight=d.Em(p)}var n=d.Element("span",{id:"MathJax-Color-"+this.spanID+d.idPostfix,isMathJax:true,style:{display:"inline-block",backgroundColor:y.mathbackground,width:d.Em(o),height:d.Em(x),verticalAlign:d.Em(k),marginLeft:d.Em(u),marginRight:d.Em(s)}});d.setBorders(n,t);if(A.width){n.style.width=A.width;n.style.marginRight="-"+A.width}if(d.msieInlineBlockAlignBug){n.style.position="relative";n.style.width=n.style.height=0;n.style.verticalAlign=n.style.marginLeft=n.style.marginRight="";n.style.border=n.style.padding="";if(t&&d.msieBorderWidthBug){x+=t.top+t.bottom;o+=t.left+t.right}n.style.width=d.Em(r+z);d.placeBox(d.addElement(n,"span",{noAdjust:true,isMathJax:true,style:{display:"inline-block",position:"absolute",overflow:"hidden",background:(y.mathbackground||"transparent"),width:d.Em(o),height:d.Em(x)}}),u,A.h+z);d.setBorders(n.firstChild,t)}w.parentNode.insertBefore(n,w);if(d.msieColorPositionBug){w.style.position="relative"}return n}return null},HTMLremoveColor:function(){var k=document.getElementById("MathJax-Color-"+this.spanID+d.idPostfix);if(k){k.parentNode.removeChild(k)}},HTMLhandleSpace:function(o){if(this.useMMLspacing){if(this.type!=="mo"){return}var m=this.getValues("scriptlevel","lspace","rspace");if(m.scriptlevel<=0||this.hasValue("lspace")||this.hasValue("rspace")){var l=this.HTMLgetMu(o);m.lspace=Math.max(0,d.length2em(m.lspace,l));m.rspace=Math.max(0,d.length2em(m.rspace,l));var k=this,n=this.Parent();while(n&&n.isEmbellished()&&n.Core()===k){k=n;n=n.Parent();o=k.HTMLspanElement()}if(m.lspace){o.style.paddingLeft=d.Em(m.lspace)}if(m.rspace){o.style.paddingRight=d.Em(m.rspace)}}}else{var p=this.texSpacing();if(p!==""){this.HTMLgetScale();p=d.length2em(p,this.scale)/(o.scale||1)*this.mscale;if(o.style.paddingLeft){p+=d.unEm(o.style.paddingLeft)}o.style.paddingLeft=d.Em(p)}}},HTMLgetScale:function(){if(this.scale){return this.scale*this.mscale}var m=1,k=this.getValues("scriptlevel","fontsize");k.mathsize=(this.isToken?this:this.Parent()).Get("mathsize");if(this.style){var 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}}this.scale=m;this.mscale=d.length2em(k.mathsize);return m*this.mscale},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 m=this.HTMLspanElement();if(!k.family&&m.style.fontFamily){k.family=m.style.fontFamily}if(!k.weight&&m.style.fontWeight){k.weight=m.style.fontWeight}if(!k.style&&m.style.fontStyle){k.style=m.style.fontStyle}}if(k.weight&&k.weight.match(/^\d+$/)){k.weight=(parseInt(k.weight)>600?"bold":"normal")}var l=k.mathvariant;if(this.variantForm){l="-"+d.fontInUse+"-variant"}if(k.family&&!k.hasVariant){if(!k.weight&&k.mathvariant.match(/bold/)){k.weight="bold"}if(!k.style&&k.mathvariant.match(/italic/)){k.style="italic"}return{FONTS:[],fonts:[],noRemap:true,defaultFont:{family:k.family,style:k.style,weight:k.weight}}}if(k.weight==="bold"){l={normal:g.VARIANT.BOLD,italic:g.VARIANT.BOLDITALIC,fraktur:g.VARIANT.BOLDFRAKTUR,script:g.VARIANT.BOLDSCRIPT,"sans-serif":g.VARIANT.BOLDSANSSERIF,"sans-serif-italic":g.VARIANT.SANSSERIFBOLDITALIC}[l]||l}else{if(k.weight==="normal"){l={bold:g.VARIANT.normal,"bold-italic":g.VARIANT.ITALIC,"bold-fraktur":g.VARIANT.FRAKTUR,"bold-script":g.VARIANT.SCRIPT,"bold-sans-serif":g.VARIANT.SANSSERIF,"sans-serif-bold-italic":g.VARIANT.SANSSERIFITALIC}[l]||l}}if(k.style==="italic"){l={normal:g.VARIANT.ITALIC,bold:g.VARIANT.BOLDITALIC,"sans-serif":g.VARIANT.SANSSERIFITALIC,"bold-sans-serif":g.VARIANT.SANSSERIFBOLDITALIC}[l]||l}else{if(k.style==="normal"){l={italic:g.VARIANT.NORMAL,"bold-italic":g.VARIANT.BOLD,"sans-serif-italic":g.VARIANT.SANSSERIF,"sans-serif-bold-italic":g.VARIANT.BOLDSANSSERIF}[l]||l}}if(!(l in d.FONTDATA.VARIANT)){l="normal"}return d.FONTDATA.VARIANT[l]},HTMLdrawBBox:function(k){var m=k.bbox;var l=d.Element("span",{style:{"font-size":k.style.fontSize,display:"inline-block",opacity:0.25,"margin-left":d.Em(-m.w)}},[["span",{style:{height:d.Em(m.h),width:d.Em(m.w),"background-color":"red",display:"inline-block"}}],["span",{style:{height:d.Em(m.d),width:d.Em(m.w),"margin-left":d.Em(-m.w),"vertical-align":d.Em(-m.d),"background-color":"green",display:"inline-block"}}]]);if(k.nextSibling){k.parentNode.insertBefore(l,k.nextSibling)}else{k.parentNode.appendChild(l)}}},{HTMLautoload:function(){var k=d.autoloadDir+"/"+this.type+".js";b.RestartAfter(h.Require(k))},HTMLautoloadFile:function(k){var l=d.autoloadDir+"/"+k+".js";b.RestartAfter(h.Require(l))},HTMLstretchH:function(l,k){this.HTMLremoveColor();return this.toHTML(l,k)},HTMLstretchV:function(l,k,m){this.HTMLremoveColor();return this.toHTML(l,k,m)}});g.chars.Augment({toHTML:function(n,m,l,o){var r=this.data.join("").replace(/[\u2061-\u2064]/g,"");if(l){r=l(r,o)}if(m.fontInherit){var q=Math.floor(d.config.scale/d.scale+0.5)+"%";d.addElement(n,"span",{style:{"font-size":q}},[r]);if(m.bold){n.lastChild.style.fontWeight="bold"}if(m.italic){n.lastChild.style.fontStyle="italic"}n.bbox=null;var p=d.getHD(n),k=d.getW(n);n.bbox={h:p.h,d:p.d,w:k,lw:0,rw:k,exactW:true}}else{this.HTMLhandleVariant(n,m,r)}}});g.entity.Augment({toHTML:function(n,m,l,o){var r=this.toString().replace(/[\u2061-\u2064]/g,"");if(l){r=l(r,o)}if(m.fontInherit){var q=Math.floor(d.config.scale/d.scale+0.5)+"%";d.addElement(n,"span",{style:{"font-size":q}},[r]);if(m.bold){n.lastChild.style.fontWeight="bold"}if(m.italic){n.lastChild.style.fontStyle="italic"}delete n.bbox;var p=d.getHD(n),k=d.getW(n);n.bbox={h:p.h,d:p.d,w:k,lw:0,rw:k,exactW:true}}else{this.HTMLhandleVariant(n,m,r)}}});g.mi.Augment({toHTML:function(o){o=this.HTMLhandleSize(this.HTMLcreateSpan(o));o.bbox=null;var n=this.HTMLgetVariant();for(var l=0,k=this.data.length;l<k;l++){if(this.data[l]){this.data[l].toHTML(o,n)}}if(!o.bbox){o.bbox=this.HTMLzeroBBox()}var q=this.data.join(""),p=o.bbox;if(p.skew&&q.length!==1){delete p.skew}if(p.rw>p.w&&q.length===1&&!n.noIC){p.ic=p.rw-p.w;d.createBlank(o,p.ic/this.mscale);p.w=p.rw}this.HTMLhandleSpace(o);this.HTMLhandleColor(o);this.HTMLhandleDir(o);return o}});g.mn.Augment({toHTML:function(o){o=this.HTMLhandleSize(this.HTMLcreateSpan(o));o.bbox=null;var n=this.HTMLgetVariant();for(var l=0,k=this.data.length;l<k;l++){if(this.data[l]){this.data[l].toHTML(o,n)}}if(!o.bbox){o.bbox=this.HTMLzeroBBox()}if(this.data.join("").length!==1){delete o.bbox.skew}this.HTMLhandleSpace(o);this.HTMLhandleColor(o);this.HTMLhandleDir(o);return o}});g.mo.Augment({toHTML:function(v){v=this.HTMLhandleSize(this.HTMLcreateSpan(v));if(this.data.length==0){return v}else{v.bbox=null}var y=this.data.join("");var q=this.HTMLgetVariant();var x=this.getValues("largeop","displaystyle");if(x.largeop){q=d.FONTDATA.VARIANT[x.displaystyle?"-largeOp":"-smallOp"]}var w=this.CoreParent(),o=(w&&w.isa(g.msubsup)&&this!==w.data[w.base]),l=(o?this.remapChars:null);if(y.length===1&&w&&w.isa(g.munderover)&&this.CoreText(w.data[w.base]).length===1){var s=w.data[w.over],u=w.data[w.under];if(s&&this===s.CoreMO()&&w.Get("accent")){l=d.FONTDATA.REMAPACCENT}else{if(u&&this===u.CoreMO()&&w.Get("accentunder")){l=d.FONTDATA.REMAPACCENTUNDER}}}if(o&&y.match(/['`"\u00B4\u2032-\u2037\u2057]/)){q=d.FONTDATA.VARIANT["-"+d.fontInUse+"-variant"]}for(var r=0,n=this.data.length;r<n;r++){if(this.data[r]){this.data[r].toHTML(v,q,this.remap,l)}}if(!v.bbox){v.bbox=this.HTMLzeroBBox()}if(y.length!==1){delete v.bbox.skew}if(d.AccentBug&&v.bbox.w===0&&y.length===1&&v.firstChild){v.firstChild.nodeValue+=d.NBSP;d.createSpace(v,0,0,-v.offsetWidth/d.em)}if(x.largeop){var t=d.TeX.axis_height*this.scale*this.mscale;var k=(v.bbox.h-v.bbox.d)/2-t;if(d.safariVerticalAlignBug&&v.lastChild.nodeName==="IMG"){v.lastChild.style.verticalAlign=d.Em(d.unEm(v.lastChild.style.verticalAlign||0)/d.em-k/v.scale)}else{if(d.konquerorVerticalAlignBug&&v.lastChild.nodeName==="IMG"){v.style.position="relative";v.lastChild.style.position="relative";v.lastChild.style.top=d.Em(k/v.scale)}else{v.style.verticalAlign=d.Em(-k/v.scale)}}v.bbox.h-=k;v.bbox.d+=k;if(v.bbox.rw>v.bbox.w){v.bbox.ic=v.bbox.rw-v.bbox.w;d.createBlank(v,v.bbox.ic/this.mscale);v.bbox.w=v.bbox.rw}}this.HTMLhandleSpace(v);this.HTMLhandleColor(v);this.HTMLhandleDir(v);return v},HTMLcanStretch:function(o){if(!this.Get("stretchy")){return false}var p=this.data.join("");if(p.length>1){return false}var m=this.CoreParent();if(m&&m.isa(g.munderover)&&this.CoreText(m.data[m.base]).length===1){var n=m.data[m.over],l=m.data[m.under];if(n&&this===n.CoreMO()&&m.Get("accent")){p=d.FONTDATA.REMAPACCENT[p]||p}else{if(l&&this===l.CoreMO()&&m.Get("accentunder")){p=d.FONTDATA.REMAPACCENTUNDER[p]||p}}}p=d.FONTDATA.DELIMITERS[p.charCodeAt(0)];var k=(p&&p.dir===o.substr(0,1));this.forceStretch=(k&&(this.Get("minsize",true)||this.Get("maxsize",true)));return k},HTMLstretchV:function(m,n,o){this.HTMLremoveColor();var r=this.getValues("symmetric","maxsize","minsize");var p=this.HTMLspanElement(),s=this.HTMLgetMu(p),q;var l=this.HTMLgetScale(),k=d.TeX.axis_height*l;if(r.symmetric){q=2*Math.max(n-k,o+k)}else{q=n+o}r.maxsize=d.length2em(r.maxsize,s,p.bbox.h+p.bbox.d);r.minsize=d.length2em(r.minsize,s,p.bbox.h+p.bbox.d);q=Math.max(r.minsize,Math.min(r.maxsize,q));if(q!=r.minsize){q=[Math.max(q*d.TeX.delimiterfactor/1000,q-d.TeX.delimitershortfall),q]}p=this.HTMLcreateSpan(m);d.createDelimiter(p,this.data.join("").charCodeAt(0),q,l);if(r.symmetric){q=(p.bbox.h+p.bbox.d)/2+k}else{q=(p.bbox.h+p.bbox.d)*n/(n+o)}d.positionDelimiter(p,q);this.HTMLhandleSpace(p);this.HTMLhandleColor(p);return p},HTMLstretchH:function(o,k){this.HTMLremoveColor();var m=this.getValues("maxsize","minsize","mathvariant","fontweight");if((m.fontweight==="bold"||parseInt(m.fontweight)>=600)&&!this.Get("mathvariant",true)){m.mathvariant=g.VARIANT.BOLD}var n=this.HTMLspanElement(),l=this.HTMLgetMu(n),p=n.scale;m.maxsize=d.length2em(m.maxsize,l,n.bbox.w);m.minsize=d.length2em(m.minsize,l,n.bbox.w);k=Math.max(m.minsize,Math.min(m.maxsize,k));n=this.HTMLcreateSpan(o);d.createDelimiter(n,this.data.join("").charCodeAt(0),k,p,m.mathvariant);this.HTMLhandleSpace(n);this.HTMLhandleColor(n);return n}});g.mtext.Augment({toHTML:function(o){o=this.HTMLhandleSize(this.HTMLcreateSpan(o));var n=this.HTMLgetVariant();if(d.config.mtextFontInherit||this.Parent().type==="merror"){var p=this.Get("mathvariant");if(p==="monospace"){o.className+=" MJX-monospace"}else{if(p.match(/sans-serif/)){o.className+=" MJX-sans-serif"}}n={bold:n.bold,italic:n.italic,fontInherit:true}}for(var l=0,k=this.data.length;l<k;l++){if(this.data[l]){this.data[l].toHTML(o,n)}}if(!o.bbox){o.bbox=this.HTMLzeroBBox()}if(this.data.join("").length!==1){delete o.bbox.skew}this.HTMLhandleSpace(o);this.HTMLhandleColor(o);this.HTMLhandleDir(o);return o}});g.merror.Augment({toHTML:function(l){var n=MathJax.HTML.addElement(l,"span",{style:{display:"inline-block"}});l=this.SUPER(arguments).toHTML.call(this,n);var m=d.getHD(n),k=d.getW(n);n.bbox={h:m.h,d:m.d,w:k,lw:0,rw:k,exactW:true};n.id=l.id;l.id=null;return n}});g.ms.Augment({toHTML:g.mbase.HTMLautoload});g.mglyph.Augment({toHTML:g.mbase.HTMLautoload});g.mspace.Augment({toHTML:function(o){o=this.HTMLcreateSpan(o);var m=this.getValues("height","depth","width");var l=this.HTMLgetMu(o);this.HTMLgetScale();m.mathbackground=this.mathbackground;if(this.background&&!this.mathbackground){m.mathbackground=this.background}var n=d.length2em(m.height,l)*this.mscale,p=d.length2em(m.depth,l)*this.mscale,k=d.length2em(m.width,l)*this.mscale;d.createSpace(o,n,p,k,m.mathbackground,true);return o}});g.mphantom.Augment({toHTML:function(o,l,q){o=this.HTMLcreateSpan(o);if(this.data[0]!=null){var p=this.data[0].toHTML(o);if(q!=null){d.Remeasured(this.data[0].HTMLstretchV(o,l,q),o)}else{if(l!=null){d.Remeasured(this.data[0].HTMLstretchH(o,l),o)}else{p=d.Measured(p,o)}}o.bbox={w:p.bbox.w,h:p.bbox.h,d:p.bbox.d,lw:0,rw:0,exactW:true};for(var n=0,k=o.childNodes.length;n<k;n++){o.childNodes[n].style.visibility="hidden"}}this.HTMLhandleSpace(o);this.HTMLhandleColor(o);return o},HTMLstretchH:g.mbase.HTMLstretchH,HTMLstretchV:g.mbase.HTMLstretchV});g.mpadded.Augment({toHTML:function(s,m,k){s=this.HTMLcreateSpan(s);if(this.data[0]!=null){var q=d.createStack(s,true);var n=d.createBox(q);var l=this.data[0].toHTML(n);if(k!=null){d.Remeasured(this.data[0].HTMLstretchV(n,m,k),n)}else{if(m!=null){d.Remeasured(this.data[0].HTMLstretchH(n,m),n)}else{d.Measured(l,n)}}var t=this.getValues("height","depth","width","lspace","voffset"),r=0,p=0,u=this.HTMLgetMu(s);this.HTMLgetScale();if(t.lspace){r=this.HTMLlength2em(n,t.lspace,u)}if(t.voffset){p=this.HTMLlength2em(n,t.voffset,u)}d.placeBox(n,r,p);r/=this.mscale;p/=this.mscale;s.bbox={h:n.bbox.h,d:n.bbox.d,w:n.bbox.w,exactW:true,lw:n.bbox.lw+r,rw:n.bbox.rw+r,H:Math.max((n.bbox.H==null?-d.BIGDIMEN:n.bbox.H+p),n.bbox.h+p),D:Math.max((n.bbox.D==null?-d.BIGDIMEN:n.bbox.D-p),n.bbox.d-p)};if(t.height!==""){s.bbox.h=this.HTMLlength2em(n,t.height,u,"h",0)}if(t.depth!==""){s.bbox.d=this.HTMLlength2em(n,t.depth,u,"d",0)}if(t.width!==""){s.bbox.w=this.HTMLlength2em(n,t.width,u,"w",0)}if(s.bbox.H<=s.bbox.h){delete s.bbox.H}if(s.bbox.D<=s.bbox.d){delete s.bbox.D}var o=/^\s*(\d+(\.\d*)?|\.\d+)\s*(pt|em|ex|mu|px|pc|in|mm|cm)\s*$/;s.bbox.exact=!!((this.data[0]&&this.data[0].data.length==0)||o.exec(t.height)||o.exec(t.width)||o.exec(t.depth));d.setStackWidth(q,s.bbox.w)}this.HTMLhandleSpace(s);this.HTMLhandleColor(s);return s},HTMLlength2em:function(q,r,l,s,k){if(k==null){k=-d.BIGDIMEN}var o=String(r).match(/width|height|depth/);var p=(o?q.bbox[o[0].charAt(0)]:(s?q.bbox[s]:0));var n=d.length2em(r,l,p/this.mscale)*this.mscale;if(s&&String(r).match(/^\s*[-+]/)){return Math.max(k,q.bbox[s]+n)}else{return n}},HTMLstretchH:g.mbase.HTMLstretchH,HTMLstretchV:g.mbase.HTMLstretchV});g.mrow.Augment({HTMLlineBreaks:function(k){if(!this.parent.linebreakContainer){return false}return(d.config.linebreaks.automatic&&k.bbox.w>d.linebreakWidth)||this.hasNewline()},HTMLstretchH:function(m,k){this.HTMLremoveColor();var l=this.HTMLspanElement();this.data[this.core].HTMLstretchH(l,k);this.HTMLcomputeBBox(l,true);this.HTMLhandleColor(l);return l},HTMLstretchV:function(m,l,n){this.HTMLremoveColor();var k=this.HTMLspanElement();this.data[this.core].HTMLstretchV(k,l,n);this.HTMLcomputeBBox(k,true);this.HTMLhandleColor(k);return k}});g.mstyle.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);this.HTMLhandleColor(l);return l},HTMLstretchH:g.mbase.HTMLstretchH,HTMLstretchV:g.mbase.HTMLstretchV});g.mfrac.Augment({toHTML:function(D){D=this.HTMLcreateSpan(D);var m=d.createStack(D);var r=d.createBox(m),o=d.createBox(m);d.MeasureSpans([this.HTMLboxChild(0,r),this.HTMLboxChild(1,o)]);var k=this.getValues("displaystyle","linethickness","numalign","denomalign","bevelled");var I=this.HTMLgetScale(),C=k.displaystyle;var G=d.TeX.axis_height*I;if(k.bevelled){var F=(C?0.4:0.15);var s=Math.max(r.bbox.h+r.bbox.d,o.bbox.h+o.bbox.d)+2*F;var E=d.createBox(m);d.createDelimiter(E,47,s);d.placeBox(r,0,(r.bbox.d-r.bbox.h)/2+G+F);d.placeBox(E,r.bbox.w-F/2,(E.bbox.d-E.bbox.h)/2+G);d.placeBox(o,r.bbox.w+E.bbox.w-F,(o.bbox.d-o.bbox.h)/2+G-F)}else{var l=Math.max(r.bbox.w,o.bbox.w);var y=d.thickness2em(k.linethickness,this.scale)*this.mscale,A,z,x,w;var B=d.TeX.min_rule_thickness/this.em;if(C){x=d.TeX.num1;w=d.TeX.denom1}else{x=(y===0?d.TeX.num3:d.TeX.num2);w=d.TeX.denom2}x*=I;w*=I;if(y===0){A=Math.max((C?7:3)*d.TeX.rule_thickness,2*B);z=(x-r.bbox.d)-(o.bbox.h-w);if(z<A){x+=(A-z)/2;w+=(A-z)/2}}else{A=Math.max((C?2:0)*B+y,y/2+1.5*B);z=(x-r.bbox.d)-(G+y/2);if(z<A){x+=A-z}z=(G-y/2)-(o.bbox.h-w);if(z<A){w+=A-z}var n=d.createBox(m);d.createRule(n,y,0,l+2*y);d.placeBox(n,0,G-y/2)}d.alignBox(r,k.numalign,x);d.alignBox(o,k.denomalign,-w)}this.HTMLhandleSpace(D);this.HTMLhandleColor(D);return D},HTMLcanStretch:function(k){return false},HTMLhandleSpace:function(l){if(!this.texWithDelims&&!this.useMMLspacing){var m=d.TeX.nulldelimiterspace*this.mscale;var k=l.childNodes[d.msiePaddingWidthBug?1:0].style;k.marginLeft=k.marginRight=d.Em(m);l.bbox.w+=2*m;l.bbox.rw+=2*m}this.SUPER(arguments).HTMLhandleSpace.call(this,l)}});g.msqrt.Augment({toHTML:function(w){w=this.HTMLcreateSpan(w);var z=d.createStack(w);var n=d.createBox(z),u=d.createBox(z),s=d.createBox(z);var r=this.HTMLgetScale();var A=d.TeX.rule_thickness*r,m,l,y,o;if(this.Get("displaystyle")){m=d.TeX.x_height*r}else{m=A}l=Math.max(A+m/4,1.5*d.TeX.min_rule_thickness/this.em);var k=this.HTMLboxChild(0,n);y=k.bbox.h+k.bbox.d+l+A;d.createDelimiter(s,8730,y,r);d.MeasureSpans([k,s]);o=k.bbox.w;var v=0;if(s.isMultiChar||(d.AdjustSurd&&d.imgFonts)){s.bbox.w*=0.95}if(s.bbox.h+s.bbox.d>y){l=((s.bbox.h+s.bbox.d)-(y-A))/2}var B=d.FONTDATA.DELIMITERS[d.FONTDATA.RULECHAR];if(!B||o<B.HW[0][0]*r||r<0.75){d.createRule(u,0,A,o)}else{d.createDelimiter(u,d.FONTDATA.RULECHAR,o,r)}y=k.bbox.h+l+A;l=y*d.rfuzz;if(s.isMultiChar){l=d.rfuzz}v=this.HTMLaddRoot(z,s,v,s.bbox.h+s.bbox.d-y,r);d.placeBox(s,v,y-s.bbox.h);d.placeBox(u,v+s.bbox.w,y-u.bbox.h+l);d.placeBox(n,v+s.bbox.w,0);this.HTMLhandleSpace(w);this.HTMLhandleColor(w);return w},HTMLaddRoot:function(m,l,k,o,n){return k}});g.mroot.Augment({toHTML:g.msqrt.prototype.toHTML,HTMLaddRoot:function(s,l,q,o,k){var m=d.createBox(s);if(this.data[1]){var 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");o[M].style.paddingLeft=o[M].style.paddingRight=""}}}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(M!==this.base){o[M].style.paddingLeft=o[M].style.paddingRight=""}}if(w.bbox.w>K){K=w.bbox.w}}}var E=d.TeX.rule_thickness*this.mscale,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;L.bbox.skew=p.bbox.skew;if(v+w.bbox.w>K){L.bbox.skew+=(K-w.bbox.w-v)/2}}}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=N;if(k){m=this.data[this.sup].HTMLgetScale()}else{if(x){m=this.data[this.sub].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]&&I==null&&C==null&&(this.data[this.base].type==="mi"||this.data[this.base].type==="mo")){if(this.data[this.base].data.join("").length===1&&n[0].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.annotation.Augment({toHTML:function(k){return this.HTMLcreateSpan(k)}});g.math.Augment({toHTML:function(B,y,q){var r,t,u,n,k=B;if(!q||q===d.PHASE.I){var z=d.addElement(B,"nobr",{isMathJax:true});B=this.HTMLcreateSpan(z);var l=this.Get("alttext");if(l&&!B.getAttribute("aria-label")){B.setAttribute("aria-label",l)}if(!B.getAttribute("role")){B.setAttribute("role","math")}r=d.createStack(B);t=d.createBox(r);r.style.fontSize=z.parentNode.style.fontSize;z.parentNode.style.fontSize="";if(this.data[0]!=null){g.mbase.prototype.displayAlign=b.config.displayAlign;g.mbase.prototype.displayIndent=b.config.displayIndent;if(String(b.config.displayIndent).match(/^0($|[a-z%])/i)){g.mbase.prototype.displayIndent="0"}u=this.data[0].toHTML(t);u.bbox.exactW=false}}else{B=B.firstChild.firstChild;if(this.href){B=B.firstChild}r=B.firstChild;if(r.style.position!=="relative"){r=r.nextSibling}t=r.firstChild;u=t.firstChild}n=((!q||q===d.PHASE.II)?d.Measured(u,t):u);if(!q||q===d.PHASE.III){d.placeBox(t,0,0);B.style.width=d.Em(Math.max(0,Math.round(n.bbox.w*this.em)+0.25)/d.outerEm);B.style.display="inline-block";var x=1/d.em,D=d.em/d.outerEm;d.em/=D;B.bbox.h*=D;B.bbox.d*=D;B.bbox.w*=D;B.bbox.lw*=D;B.bbox.rw*=D;if(B.bbox.H){B.bbox.H*=D}if(B.bbox.D){B.bbox.D*=D}if(n&&n.bbox.width!=null){B.style.minWidth=(n.bbox.minWidth||B.style.width);B.style.width=n.bbox.width;t.style.width=r.style.width=k.style.width="100%"}var A=this.HTMLhandleColor(B);if(n){d.createRule(B,(n.bbox.h+x)*D,(n.bbox.d+x)*D,0)}if(!this.isMultiline&&this.Get("display")==="block"&&B.bbox.width==null){var m=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift");if(m.indentalignfirst!==g.INDENTALIGN.INDENTALIGN){m.indentalign=m.indentalignfirst}if(m.indentalign===g.INDENTALIGN.AUTO){m.indentalign=this.displayAlign}if(m.indentshiftfirst!==g.INDENTSHIFT.INDENTSHIFT){m.indentshift=m.indentshiftfirst}if(m.indentshift==="auto"){m.indentshift="0"}var C=d.length2em(m.indentshift,1,d.scale*d.cwidth);if(this.displayIndent!=="0"){var v=d.length2em(this.displayIndent,1,d.scale*d.cwidth);C+=(m.indentalign===g.INDENTALIGN.RIGHT?-v:v)}y.style.textAlign=m.indentalign;if(C){b.Insert(B.style,({left:{marginLeft:d.Em(C)},right:{marginRight:d.Em(-C)},center:{marginLeft:d.Em(C),marginRight:d.Em(-C)}})[m.indentalign]);if(A){var s=parseFloat(A.style.marginLeft||"0")+C,o=parseFloat(A.style.marginRight||"0")-C;A.style.marginLeft=d.Em(s);A.style.marginRight=d.Em(o+(m.indentalign==="right"?B.bbox.w+C-B.bbox.w:0));if(d.msieColorBug&&m.indentalign==="right"){if(parseFloat(A.style.marginLeft)>0){var w=MathJax.HTML.addElement(A.parentNode,"span");w.style.marginLeft=d.Em(o+Math.min(0,B.bbox.w+C));A.nextSibling.style.marginRight="0em"}A.nextSibling.style.marginLeft="0em";A.style.marginRight=A.style.marginLeft="0em"}}}}}return B},HTMLspanElement:g.mbase.prototype.HTMLspanElement});g.TeXAtom.Augment({toHTML:function(o,m,q){o=this.HTMLcreateSpan(o);if(this.data[0]!=null){if(this.texClass===g.TEXCLASS.VCENTER){var k=d.createStack(o);var p=d.createBox(k);var r=this.data[0].toHTML(p);if(q!=null){d.Remeasured(this.data[0].HTMLstretchV(p,m,q),p)}else{if(m!=null){d.Remeasured(this.data[0].HTMLstretchH(p,m),p)}else{d.Measured(r,p)}}var l=d.TeX.axis_height*this.HTMLgetScale();d.placeBox(p,0,l-(p.bbox.h+p.bbox.d)/2+p.bbox.d)}else{var n=this.data[0].toHTML(o,m,q);if(q!=null){n=this.data[0].HTMLstretchV(p,m,q)}else{if(m!=null){n=this.data[0].HTMLstretchH(p,m)}}o.bbox=n.bbox}}this.HTMLhandleSpace(o);this.HTMLhandleColor(o);return o},HTMLstretchH:g.mbase.HTMLstretchH,HTMLstretchV:g.mbase.HTMLstretchV});b.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:(o<8),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,msieRuleBug:(o<7),cloneNodeBug:(m&&k.version==="8.0"),msieItalicWidthBug:true,initialSkipBug:(o<8),msieNegativeBBoxBug:(o>=8),msieIE6:!n,msieItalicWidthBug:true,FontFaceBug:(o<9),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:!l.versionAtLeast("20.0"),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"}}},Em:((p.webkit||0)>=538?d.EmRounded:d.Em),rfuzz:0.011,AccentBug:true,AdjustSurd:true,negativeBBoxes:true,safariNegativeSpaceBug:true,safariVerticalAlignBug:!m,safariTextNodeBug:!n,forceReflow:true,FontFaceBug: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:-0.02,AccentBug:true,AdjustSurd:true,FontFaceBug:k.versionAtLeast("32.0"),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"]);
