/*
 *  /MathJax/config/TeX-AMS_HTML-full.js
 *  
 *  Copyright (c) 2010-11 Design Science, Inc.
 *
 *  Part of the MathJax library.
 *  See http://www.mathjax.org for details.
 * 
 *  Licensed under the Apache License, Version 2.0;
 *  you may not use this file except in compliance with the License.
 *
 *      http://www.apache.org/licenses/LICENSE-2.0
 */

MathJax.Ajax.Preloading(
  "[MathJax]/jax/input/TeX/config.js",
  "[MathJax]/jax/output/HTML-CSS/config.js",
  "[MathJax]/extensions/tex2jax.js",
  "[MathJax]/extensions/MathZoom.js",
  "[MathJax]/extensions/MathMenu.js",
  "[MathJax]/jax/element/mml/jax.js",
  "[MathJax]/extensions/toMathML.js",
  "[MathJax]/extensions/TeX/noErrors.js",
  "[MathJax]/extensions/TeX/noUndefined.js",
  "[MathJax]/jax/input/TeX/jax.js",
  "[MathJax]/extensions/TeX/AMSmath.js",
  "[MathJax]/extensions/TeX/AMSsymbols.js",
  "[MathJax]/jax/output/HTML-CSS/jax.js",
  "[MathJax]/jax/output/HTML-CSS/autoload/mtable.js"
);

MathJax.Hub.Config({"v1.0-compatible":false});

MathJax.InputJax.TeX=MathJax.InputJax({id:"TeX",version:"1.1.1",directory:MathJax.InputJax.directory+"/TeX",extensionDir:MathJax.InputJax.extensionDir+"/TeX",config:{TagSide:"right",TagIndent:"0.8em",MultLineWidth:"85%"}});MathJax.InputJax.TeX.Register("math/tex");MathJax.InputJax.TeX.loadComplete("config.js");

MathJax.OutputJax["HTML-CSS"]=MathJax.OutputJax({id:"HTML-CSS",version:"1.1.5",directory:MathJax.OutputJax.directory+"/HTML-CSS",extensionDir:MathJax.OutputJax.extensionDir+"/HTML-CSS",autoloadDir:MathJax.OutputJax.directory+"/HTML-CSS/autoload",fontDir:MathJax.OutputJax.directory+"/HTML-CSS/fonts",webfontDir:MathJax.OutputJax.fontDir+"/HTML-CSS",config:{scale:100,minScaleAdjust:50,availableFonts:["STIX","TeX"],preferredFont:"TeX",webFont:"TeX",imageFont:"TeX",undefinedFamily:"STIXGeneral,'Arial Unicode MS',serif",showMathMenu:true,styles:{".MathJax_Display":{"text-align":"center",margin:"1em 0em"},".MathJax .merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"1px 3px","font-family":"serif","font-style":"normal","font-size":"90%"},".MathJax_Preview":{color:"#888888"},"#MathJax_Tooltip":{"background-color":"InfoBackground",color:"InfoText",border:"1px solid black","box-shadow":"2px 2px 5px #AAAAAA","-webkit-box-shadow":"2px 2px 5px #AAAAAA","-moz-box-shadow":"2px 2px 5px #AAAAAA","-khtml-box-shadow":"2px 2px 5px #AAAAAA",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')",padding:"3px 4px"}}}});if(MathJax.Hub.Browser.isMSIE&&document.documentMode>=9){delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}MathJax.Hub.Register.StartupHook("End Config",[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=["[Math]"],j;var h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax.id==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;g<d;g++){h.appendChild(document.createTextNode(k[g]));if(g<d-1){h.appendChild(document.createElement("br"))}}f.parentNode.insertBefore(h,f)}},(b.config["HTML-CSS"]||{}));if(b.Browser.version!=="0.0"&&!b.Browser.versionAtLeast(a.minBrowserVersion[b.Browser]||0)){c.Translate=a.minBrowserTranslate;b.Config({showProcessingMessages:false});MathJax.Message.Set("Your browser does not support MathJax",null,4000);b.Startup.signal.Post("MathJax not supported")}},MathJax.Hub,MathJax.OutputJax["HTML-CSS"]]);MathJax.OutputJax["HTML-CSS"].loadComplete("config.js");

MathJax.Extension.tex2jax={version:"1.1.3",config:{inlineMath:[["\\(","\\)"]],displayMath:[["$$","$$"],["\\[","\\]"]],skipTags:["script","noscript","style","textarea","pre","code"],ignoreClass:"tex2jax_ignore",processClass:"tex2jax_process",processEscapes:false,processEnvironments:true,preview:"TeX"},PreProcess:function(a){if(!this.configured){this.config=MathJax.Hub.CombineConfig("tex2jax",this.config);if(this.config.Augment){MathJax.Hub.Insert(this,this.config.Augment)}if(typeof(this.config.previewTeX)!=="undefined"&&!this.config.previewTeX){this.config.preview="none"}this.configured=true}if(typeof(a)==="string"){a=document.getElementById(a)}if(!a){a=document.body}this.createPatterns();this.scanElement(a,a.nextSibling)},createPatterns:function(){var d=[],c,a,b=this.config;this.match={};for(c=0,a=b.inlineMath.length;c<a;c++){d.push(this.patternQuote(b.inlineMath[c][0]));this.match[b.inlineMath[c][0]]={mode:"",end:b.inlineMath[c][1],pattern:this.endPattern(b.inlineMath[c][1])}}for(c=0,a=b.displayMath.length;c<a;c++){d.push(this.patternQuote(b.displayMath[c][0]));this.match[b.displayMath[c][0]]={mode:"; mode=display",end:b.displayMath[c][1],pattern:this.endPattern(b.displayMath[c][1])}}this.start=new RegExp(d.sort(this.sortLength).join("|")+(b.processEnvironments?"|\\\\begin\\{([^}]*)\\}":"")+(b.processEscapes?"|\\\\*\\\\\\$":""),"g");this.skipTags=new RegExp("^("+b.skipTags.join("|")+")$","i");this.ignoreClass=new RegExp("(^| )("+b.ignoreClass+")( |$)");this.processClass=new RegExp("(^| )("+b.processClass+")( |$)")},patternQuote:function(a){return a.replace(/([\^$(){}+*?\-|\[\]\:\\])/g,"\\$1")},endPattern:function(a){return new RegExp(this.patternQuote(a)+"|\\\\.","g")},sortLength:function(d,c){if(d.length!==c.length){return c.length-d.length}return(d==c?0:(d<c?-1:1))},scanElement:function(c,b,f){var a,e,d;while(c&&c!=b){if(c.nodeName.toLowerCase()==="#text"){if(!f){c=this.scanText(c)}}else{a=(typeof(c.className)==="undefined"?"":c.className);e=(typeof(c.tagName)==="undefined"?"":c.tagName);if(typeof(a)!=="string"){a=String(a)}if(c.firstChild&&!a.match(/(^| )MathJax/)&&!this.skipTags.exec(e)){d=(f||this.ignoreClass.exec(a))&&!this.processClass.exec(a);this.scanElement(c.firstChild,b,d)}}if(c){c=c.nextSibling}}},scanText:function(b){if(b.nodeValue.replace(/\s+/,"")==""){return b}var a,c;this.search={start:true};this.pattern=this.start;while(b){this.pattern.lastIndex=0;while(b&&b.nodeName.toLowerCase()==="#text"&&(a=this.pattern.exec(b.nodeValue))){if(this.search.start){b=this.startMatch(a,b)}else{b=this.endMatch(a,b)}}if(this.search.matched){b=this.encloseMath(b)}if(b){do{c=b;b=b.nextSibling}while(b&&(b.nodeName.toLowerCase()==="br"||b.nodeName.toLowerCase()==="#comment"));if(!b||b.nodeName!=="#text"){return c}}}return b},startMatch:function(a,b){var f=this.match[a[0]];if(f!=null){this.search={end:f.end,mode:f.mode,open:b,olen:a[0].length,opos:this.pattern.lastIndex-a[0].length};this.switchPattern(f.pattern)}else{if(a[0].substr(0,6)==="\\begin"){this.search={end:"\\end{"+a[1]+"}",mode:"; mode=display",open:b,olen:0,opos:this.pattern.lastIndex-a[0].length,isBeginEnd:true};this.switchPattern(this.endPattern(this.search.end))}else{var d=a[0].substr(0,a[0].length-1),g,c;if(d.length%2===0){c=[d.replace(/\\\\/g,"\\")];g=1}else{c=[d.substr(1).replace(/\\\\/g,"\\"),"$"];g=0}c=MathJax.HTML.Element("span",null,c);var e=MathJax.HTML.TextNode(b.nodeValue.substr(0,a.index));b.nodeValue=b.nodeValue.substr(a.index+a[0].length-g);b.parentNode.insertBefore(c,b);b.parentNode.insertBefore(e,c);this.pattern.lastIndex=g}}return b},endMatch:function(a,b){if(a[0]==this.search.end){this.search.close=b;this.search.cpos=this.pattern.lastIndex;this.search.clen=(this.search.isBeginEnd?0:a[0].length);this.search.matched=true;b=this.encloseMath(b);this.switchPattern(this.start)}return b},switchPattern:function(a){a.lastIndex=this.pattern.lastIndex;this.pattern=a;this.search.start=(a===this.start)},encloseMath:function(b){var a=this.search,f=a.close,e,c;if(a.cpos===f.length){f=f.nextSibling}else{f=f.splitText(a.cpos)}if(!f){e=f=MathJax.HTML.addText(a.close.parentNode,"")}a.close=f;c=(a.opos?a.open.splitText(a.opos):a.open);while(c.nextSibling&&c.nextSibling!==f){if(c.nextSibling.nodeValue!==null){if(c.nextSibling.nodeName==="#comment"){c.nodeValue+=c.nextSibling.nodeValue.replace(/^\[CDATA\[((.|\n|\r)*)\]\]$/,"$1")}else{c.nodeValue+=c.nextSibling.nodeValue}}else{if(this.msieNewlineBug){c.nodeValue+=(c.nextSibling.nodeName.toLowerCase()==="br"?"\n":" ")}else{c.nodeValue+=" "}}c.parentNode.removeChild(c.nextSibling)}var d=c.nodeValue.substr(a.olen,c.nodeValue.length-a.olen-a.clen);c.parentNode.removeChild(c);if(this.config.preview!=="none"){this.createPreview(a.mode,d)}c=this.createMathTag(a.mode,d);this.search={};this.pattern.lastIndex=0;if(e){e.parentNode.removeChild(e)}return c},insertNode:function(b){var a=this.search;a.close.parentNode.insertBefore(b,a.close)},createPreview:function(c,a){var b;if(this.config.preview==="TeX"){b=[this.filterTeX(a)]}else{if(this.config.preview instanceof Array){b=this.config.preview}}if(b){b=MathJax.HTML.Element("span",{className:MathJax.Hub.config.preRemoveClass},b);this.insertNode(b)}},createMathTag:function(c,b){var a=document.createElement("script");a.type="math/tex"+c;MathJax.HTML.setScript(a,b);this.insertNode(a);return a},filterTeX:function(a){return a},msieNewlineBug:(MathJax.Hub.Browser.isMSIE&&document.documentMode<9)};MathJax.Hub.Register.PreProcessor(["PreProcess",MathJax.Extension.tex2jax]);MathJax.Ajax.loadComplete("[MathJax]/extensions/tex2jax.js");

(function(a,c,e,b,h){var i="1.1";var g=a.CombineConfig("MathZoom",{delay:400,styles:{"#MathJax_Zoom":{position:"absolute","background-color":"#F0F0F0",overflow:"auto",display:"block","z-index":301,padding:".5em",border:"1px solid black",margin:0,"font-family":"serif","font-size":"85%","font-weight":"normal","font-style":"normal","text-align":"left","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","box-shadow":"5px 5px 15px #AAAAAA","-webkit-box-shadow":"5px 5px 15px #AAAAAA","-moz-box-shadow":"5px 5px 15px #AAAAAA","-khtml-box-shadow":"5px 5px 15px #AAAAAA",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},"#MathJax_ZoomOverlay":{position:"absolute",left:0,top:0,"z-index":300,display:"inline-block",width:"100%",height:"100%",border:0,padding:0,margin:0,"background-color":"white",opacity:0,filter:"alpha(opacity=0)"}}});var d=function(j){if(!j){j=window.event}if(j){if(j.preventDefault){j.preventDefault()}if(j.stopPropagation){j.stopPropagation()}j.cancelBubble=true;j.returnValue=false}return false};var f=MathJax.Extension.MathZoom={version:i,settings:a.config.menuSettings,HandleEvent:function(l,j,k){if(!l){l=window.event}if(f.settings.CTRL&&!l.ctrlKey){return true}if(f.settings.ALT&&!l.altKey){return true}if(f.settings.CMD&&!l.metaKey){return true}if(f.settings.Shift&&!l.shiftKey){return true}return f[j](l,k)},Click:function(k,j){if(this.settings.zoom==="Click"){return this.Zoom(j,k)}},DblClick:function(k,j){if(this.settings.zoom==="Double-Click"){return this.Zoom(j,k)}},Mouseover:function(k,j){if(this.settings.zoom==="Hover"){f.oldMouseOver=j.onmouseover;j.onmouseover=null;j.onmousemove=this.Mousemove;j.onmouseout=this.Mouseout;return f.Timer(k,j)}},Mouseout:function(j){this.onmouseover=f.oldMouseOver;delete f.oldMouseOver;this.onmousemove=this.onmouseout=null;f.ClearTimer();return d(j)},Mousemove:function(j){return f.Timer(j||window.event,this)},Timer:function(k,j){this.ClearTimer();this.timer=setTimeout(MathJax.Callback(["Zoom",this,j,{}]),g.delay);return d(k)},ClearTimer:function(){if(this.timer){clearTimeout(this.timer);delete this.timer}},Zoom:function(s,l){this.ClearTimer();this.Remove();var v=s.parentNode;if(v.className==="MathJax_MathContainer"){v=v.parentNode}if(v.parentNode.className==="MathJax_MathContainer"){v=v.parentNode.parentNode}var q=(String(v.className).match(/^MathJax_(MathML|Display)$/)?v:s).nextSibling;var m=a.getJaxFor(q),r=m.root;var o=(b&&m.outputJax.isa(b.constructor)?"HTMLCSS":(h&&m.outputJax.isa(h.constructor)?"MathML":null));if(!o){return}var j=Math.floor(0.85*document.body.clientWidth),p=Math.floor(0.85*document.body.clientHeight);var k=c.Element("span",{style:{position:"relative",display:"inline-block",height:0,width:0},id:"MathJax_ZoomFrame"},[["span",{id:"MathJax_ZoomOverlay",onmousedown:this.Remove}],["span",{id:"MathJax_Zoom",onclick:this.Remove,style:{visibility:"hidden",fontSize:this.settings.zscale,"max-width":j+"px","max-height":p+"px"}},[["span"]]]]);var x=k.lastChild,u=x.firstChild,n=k.firstChild;s.parentNode.insertBefore(k,s);if(this.msieZIndexBug){var t=c.Element("img",{src:"about:blank",id:"MathJax_ZoomTracker",style:{width:0,height:0,position:"relative"}});document.body.appendChild(k);k.style.position="absolute";k.style.zIndex=g.styles["#MathJax_ZoomOverlay"]["z-index"];k=t}var w=(this["Zoom"+o])(r,u,s);if(this.msiePositionBug){if(this.msieIE8Bug){u.style.position="absolute";x.style.height=u.offsetHeight;u.style.position="";if(x.offsetHeight<=p&&x.offsetWidth<=j){x.style.overflow="visible"}}if(this.msieWidthBug){x.style.width=Math.min(j,w.w)}else{if(w.w>j){x.style.width=j}}if(x.offsetHeight>p){x.style.Height=p+"px"}if(s.nextSibling){s.parentNode.insertBefore(k,s.nextSibling)}else{v.appendChild(k)}}else{if(this.operaPositionBug){x.style.width=Math.min(j,u.offsetWidth)+"px"}}this.Position(x,w,(o==="MathML"&&v.nodeName.toLowerCase()==="div"));x.style.visibility="";if(this.settings.zoom==="Hover"){n.onmouseover=this.Remove}if(window.addEventListener){addEventListener("resize",this.Resize,false)}else{if(window.attachEvent){attachEvent("onresize",this.Resize)}else{this.onresize=window.onresize;window.onresize=this.Resize}}return d(l)},ZoomHTMLCSS:function(o,q,p){q.className="MathJax";b.idPostfix="-zoom";b.getScales(q,q);o.toHTML(q,q);var r=o.HTMLspanElement().bbox;b.idPostfix="";if(r.width&&r.width!=="100%"){var j=Math.floor(0.85*document.body.clientWidth);q.style.width=j+"px";q.style.display="inline-block";var k=(o.id||"MathJax-Span-"+o.spanID)+"-zoom";var l=document.getElementById(k).firstChild;while(l&&l.style.width!==r.width){l=l.nextSibling}if(l){l.style.width="100%"}}q.appendChild(this.topImg);var n=this.topImg.offsetTop;q.removeChild(this.topImg);var m=(this.msieWidthBug?b.getW(p)*b.em:p.offsetWidth);return{w:r.w*b.em,Y:-n,W:m}},ZoomMathML:function(k,l,m){k.toNativeMML(l,l);var n;l.appendChild(this.topImg);n=this.topImg.offsetTop;l.removeChild(this.topImg);var j=(this.ffMMLwidthBug?m.parentNode:m).offsetWidth;return{w:l.offsetWidth,Y:-n,W:j}},Position:function(p,n,r){var k=this.Resize(),m=k.x,l=k.y,j=n.W;if(this.msiePositionBug){j=-j}if(r&&this.ffMMLcenterBug){j=0}var q=-Math.floor((p.offsetWidth-j)/2),o=n.Y;p.style.left=Math.max(q,20-m)+"px";p.style.top=Math.max(o,20-l)+"px"},Resize:function(l){if(f.onresize){f.onresize(l)}var j=0,o=0,n=document.getElementById("MathJax_ZoomFrame"),k=document.getElementById("MathJax_ZoomOverlay");var m=(f.msieZIndexBug?document.getElementById("MathJax_ZoomTracker"):n);if(f.operaPositionBug){n.style.border="1px solid"}if(m.offsetParent){do{j+=m.offsetLeft;o+=m.offsetTop}while(m=m.offsetParent)}if(f.operaPositionBug){n.style.border=""}if(f.msieZIndexBug){n.style.left=j+"px";n.style.top=o+"px"}k.style.left=(-j)+"px";k.style.top=(-o)+"px";if(f.msiePositionBug){setTimeout(f.SetWH,0)}else{f.SetWH()}return{x:j,y:o}},SetWH:function(){var j=document.getElementById("MathJax_ZoomOverlay");j.style.width=j.style.height="1px";j.style.width=document.body.scrollWidth+"px";j.style.height=document.body.scrollHeight+"px"},Remove:function(k){var l=document.getElementById("MathJax_ZoomFrame");if(l){l.parentNode.removeChild(l);l=document.getElementById("MathJax_ZoomTracker");if(l){l.parentNode.removeChild(l)}if(f.operaRefreshBug){var j=c.addElement(document.body,"div",{style:{position:"fixed",left:0,top:0,width:"100%",height:"100%",backgroundColor:"white",opacity:0},id:"MathJax_OperaDiv"});document.body.removeChild(j)}if(window.removeEventListener){removeEventListener("resize",f.Resize,false)}else{if(window.detachEvent){detachEvent("onresize",f.Resize)}else{window.onresize=f.onresize;delete f.onresize}}}return d(k)}};a.Register.StartupHook("HTML-CSS Jax Ready",function(){b=MathJax.OutputJax["HTML-CSS"];b.Augment({HandleEvent:f.HandleEvent})});a.Register.StartupHook("NativeMML Jax Ready",function(){h=MathJax.OutputJax.NativeMML;h.Augment({HandleEvent:f.HandleEvent,MSIEmouseup:function(l,k,j){if(this.trapUp){delete this.trapUp;return true}if(this.MSIEzoomKeys(l)){return true}return false},MSIEclick:function(l,k,j){if(this.trapClick){delete this.trapClick;return true}if(!this.MSIEzoomKeys(l)){return false}if(!this.settings.zoom.match(/Click/)){return false}return(f.Click(l,k)===false)},MSIEdblclick:function(l,k,j){if(!this.MSIEzoomKeys(l)){return false}return(f.DblClick(l,k)===false)},MSIEmouseover:function(l,k,j){if(this.settings.zoom!=="Hover"){return false}f.Timer(l,k);return true},MSIEmouseout:function(l,k,j){if(this.settings.zoom!=="Hover"){return false}f.ClearTimer();return true},MSIEmousemove:function(l,k,j){if(this.settings.zoom!=="Hover"){return false}f.Timer(l,k);return true},MSIEzoomKeys:function(j){if(this.settings.CTRL&&!j.ctrlKey){return false}if(this.settings.CMD&&!j.metaKey){return false}if(this.settings.ALT&&!j.altKey){return false}if(this.settings.Shift&&!j.shiftKey){return false}return true}})});a.Browser.Select({MSIE:function(j){var k=(document.compatMode==="BackCompat");var l=j.versionAtLeast("8.0")&&document.documentMode>7;f.msiePositionBug=true;f.msieWidthBug=!k;f.msieIE8Bug=l;f.msieZIndexBug=!l;f.msieInlineBlockAlignBug=(!l||k);if(document.documentMode>=9){delete g.styles["#MathJax_Zoom"].filter}},Opera:function(j){f.operaPositionBug=true;f.operaRefreshBug=true},Firefox:function(j){f.ffMMLwidthBug=true;f.ffMMLcenterBug=true}});f.topImg=(f.msieInlineBlockAlignBug?c.Element("img",{style:{width:0,height:0},src:"about:blank"}):c.Element("span",{style:{width:0,height:0,display:"inline-block"}}));if(f.operaPositionBug){f.topImg.style.border="1px solid"}MathJax.Callback.Queue(["Styles",e,g.styles],["Post",a.Startup.signal,"MathZoom Ready"],["loadComplete",e,"[MathJax]/extensions/MathZoom.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.OutputJax["HTML-CSS"],MathJax.OutputJax.NativeMML);

(function(b,c,f){var k="1.1.4";MathJax.Extension.MathMenu={version:k};var i=b.Browser.isPC,g=b.Browser.isMSIE;var e=(i?null:"5px");var j=b.CombineConfig("MathMenu",{delay:150,helpURL:"http://www.mathjax.org/help/user/",showRenderer:true,showFontMenu:false,showContext:false,windowSettings:{status:"no",toolbar:"no",locationbar:"no",menubar:"no",directories:"no",personalbar:"no",resizable:"yes",scrollbars:"yes",width:100,height:50},styles:{"#MathJax_About":{position:"fixed",left:"50%",width:"auto","text-align":"center",border:"3px outset",padding:"1em 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l=this.div.style.fontSize;this.div.style.fontSize=j;if(e.msieItalicWidthBug&&h.style==="italic"){this.text.nodeValue=g=this.compChar;i=this.div.offsetWidth}if(e.safariTextNodeBug){this.div.innerHTML=this.compChar+g}else{this.text.nodeValue=this.compChar+g}var f=this.div.offsetWidth-i;if(e.safariTextNodeBug){this.div.innerHTML=this.styleChar+g}else{this.text.nodeValue=this.styleChar+g}var k=Math.floor((this.div.offsetWidth-i)/f+0.5);if(k===m){if(e.safariTextNodeBug){this.div.innerHTML=this.versionChar+g}else{this.text.nodeValue=this.versionChar+g}h.version=Math.floor((this.div.offsetWidth-i)/f+1.5)/2}this.div.style.fontSize=l;return(k===m)},getComparisonWidths:function(j,h){if(e.FONTDATA&&e.FONTDATA.hasStyleChar&&!h){j+=this.styleChar+" "+this.compChar}if(e.safariTextNodeBug){this.div.innerHTML=j}else{this.text.nodeValue=j}this.div.style.fontFamily=this.comparisonFont[0];var g=this.div.offsetWidth,l=-1;if(e.safariWebFontSerif){this.div.style.fontFamily=e.safariWebFontSerif[0];l=this.div.offsetWidth}for(var k=1,f=this.comparisonFont.length;k<f;k++){this.div.style.fontFamily=this.comparisonFont[k];if(this.div.offsetWidth!=g){return[g,this.div.offsetWidth,k,l]}}return null},loadWebFont:function(g){d.Startup.signal.Post("HTML-CSS Jax - Web-Font "+e.fontInUse+"/"+g.directory);var i=MathJax.Message.File("Web-Font "+e.fontInUse+"/"+g.directory);var f=MathJax.Callback({});var h=MathJax.Callback(["loadComplete",this,g,i,f]);c.timer.start(c,[this.checkWebFont,g,h],1,this.timeout);return f},loadComplete:function(h,j,g,f){MathJax.Message.Clear(j);if(f===c.STATUS.OK){g();return}this.loadError(h);if(d.Browser.isFirefox&&e.allowWebFonts){var i=document.location.protocol+"//"+document.location.hostname;if(document.location.port!=""){i+=":"+document.location.port}i+="/";if(c.fileURL(e.webfontDir).substr(0,i.length)!==i){this.firefoxFontError(h)}}e.loadWebFontError(h,g)},loadError:function(f){MathJax.Message.Set("Can't load web font "+e.fontInUse+"/"+f.directory,null,2000)},firefoxFontError:function(f){MathJax.Message.Set("Firefox can't load web fonts from a remote host",null,3000)},checkWebFont:function(f,g,h){if(f.time(h)){return}if(e.Font.testFont(g)){h(f.STATUS.OK)}else{setTimeout(f,f.delay)}},fontFace:function(h){var i=e.allowWebFonts;var k=e.FONTDATA.FONTS[h];if(e.msieFontCSSBug&&!k.family.match(/-Web$/)){k.family+="-Web"}var g=c.fileURL(e.webfontDir+"/"+i);var f=h.replace(/-b/,"-B").replace(/-i/,"-I").replace(/-Bold-/,"-Bold");if(!f.match(/-/)){f+="-Regular"}if(i==="svg"){f+=".svg#"+f}else{f+="."+i}var j={"font-family":k.family,src:"url('"+g+"/"+f+"')"};if(i==="svg"){j.src+=" format('svg')"}if(!(e.FontFaceBug&&k.isWebFont)){if(h.match(/-bold/)){j["font-weight"]="bold"}if(h.match(/-italic/)){j["font-style"]="italic"}}return j}});e.Augment({config:{styles:{".MathJax":{display:"inline","font-family":"serif","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"},".MathJax img":{display:"inline ! important"},".MathJax_Processing":{visibility:"hidden",position:"fixed",width:0,height:0,overflow:"hidden"},".MathJax .MathJax_HitBox":{cursor:"text"},"#MathJax_Tooltip":{position:"absolute",left:0,top:0,width:"auto",height:"auto",display:"none"},"#MathJax_Tooltip *":{filter:"none",background:"transparent"}}},settings:d.config.menuSettings,LEFTBUTTON:(d.Browser.isMSIE?1:0),MENUKEY:"altKey",Font:null,Config:function(){this.Font=b();this.SUPER(arguments).Config.call(this);var g=this.settings;if(this.adjustAvailableFonts){this.adjustAvailableFonts(this.config.availableFonts)}if(g.scale){this.config.scale=g.scale}if(g.font&&g.font!=="Auto"){if(g.font==="TeX (local)"){this.config.availableFonts=["TeX"];this.config.preferredFont="TeX";this.config.webFont="TeX"}else{if(g.font==="STIX (local)"){this.config.availableFonts=["STIX"];this.config.preferredFont="STIX";this.config.webFont="TeX"}else{if(g.font==="TeX (web)"){this.config.availableFonts=[];this.config.preferredFont="";this.config.webFont="TeX"}else{if(g.font==="TeX (image)"){this.config.availableFonts=[];this.config.preferredFont="";this.config.webFont=""}}}}}var f=this.Font.findFont(this.config.availableFonts,this.config.preferredFont);if(!f&&this.allowWebFonts){f=this.config.webFont;if(f){this.webFonts=true}}if(!f&&this.config.imageFont){f=this.config.imageFont;this.imgFonts=true}if(f){this.fontInUse=f;this.fontDir+="/"+f;this.webfontDir+="/"+f;if(!this.require){this.require=[]}this.require.push(this.fontDir+"/fontdata.js");if(this.imgFonts){this.require.push(this.directory+"/imageFonts.js");d.Startup.signal.Post("HTML-CSS Jax - using image fonts")}}else{MathJax.Message.Set("Can't find a valid font using ["+this.config.availableFonts.join(", ")+"]",null,3000);this.FONTDATA={TeX_factor:1,baselineskip:1.2,lineH:0.8,lineD:0.2,ffLineH:0.8,FONTS:{},VARIANT:{normal:{fonts:[]}},RANGES:[],DELIMITERS:{},RULECHAR:45,REMAP:{}};if(MathJax.InputJax.TeX&&MathJax.InputJax.TeX.Definitions){MathJax.InputJax.TeX.Definitions.macros.overline[1]="002D";MathJax.InputJax.TeX.Definitions.macros.underline[1]="002D"}d.Startup.signal.Post("HTML-CSS Jax - no valid font")}},Startup:function(){var h=[],l=this.FONTDATA.VARIANT.normal.fonts;if(!(l instanceof Array)){l=[l]}for(var g=0,f=l.length;g<f;g++){h[g]=this.FONTDATA.FONTS[l[g]].family;if(!h[g]){h[g]=l[g]}}this.config.styles[".MathJax .math span"]=this.config.styles["#MathJax_getScales"]={"font-family":h.join(",")};this.hiddenDiv=this.Element("div",{style:{visibility:"hidden",overflow:"hidden",position:"absolute",top:0,height:"1px",width:"auto",padding:0,border:0,margin:0,textAlign:"left",textIndent:0,textTransform:"none",lineHeight:"normal",letterSpacing:"normal",wordSpacing:"normal"}});if(!document.body.firstChild){document.body.appendChild(this.hiddenDiv)}else{document.body.insertBefore(this.hiddenDiv,document.body.firstChild)}this.hiddenDiv=this.addElement(this.hiddenDiv,"div",{id:"MathJax_Hidden"});var k=this.addElement(this.hiddenDiv,"div",{style:{width:"5in"}});this.pxPerInch=k.offsetWidth/5;this.hiddenDiv.removeChild(k);this.startMarker=e.createStrut(this.Element("span"),10,true);this.endMarker=this.addText(this.Element("span"),"x").parentNode;this.HDspan=this.Element("span");if(this.operaHeightBug){this.createStrut(this.HDspan,0)}if(this.msieInlineBlockAlignBug){this.HDimg=this.addElement(this.HDspan,"img",{style:{height:"0px",width:"1px"}});try{this.HDimg.src="about:blank"}catch(j){}}else{this.HDimg=e.createStrut(this.HDspan,0)}this.HDMspan=this.Element("span",{style:{position:"absolute","font-size-adjust":"none"}});if(this.msieInlineBlockAlignBug){this.HDMimg=this.addElement(this.HDMspan,"img",{style:{height:"0px",width:"1px","max-width":"none","max-height":"none",border:0,padding:0,margin:0}});try{this.HDMimg.src="about:blank"}catch(j){}}else{this.HDMimg=e.createStrut(this.HDMspan,0);this.HDMimg.style.marginRight=""}this.marginCheck=e.Element("span",null,[["span",{style:{display:"inline-block",width:"5em"}}]]);this.marginMove=e.addElement(this.marginCheck,"span",{style:{display:"inline-block",width:"5em",marginLeft:"-5em"}});return c.Styles(this.config.styles,["PreloadWebFonts",this])},PreloadWebFonts:function(){if(!e.allowWebFonts||!e.config.preloadWebFonts){return}for(var g=0,f=e.config.preloadWebFonts.length;g<f;g++){var h=e.FONTDATA.FONTS[e.config.preloadWebFonts[g]];if(!h.available){e.Font.testFont(h)}}},Translate:function(l){if(!l.parentNode){return}var j=l.previousSibling;if(j&&String(j.className).match(/^MathJax(_MathML|_Display)?$/)){j.parentNode.removeChild(j)}var m=l.MathJax.elementJax.root,n,f,h;n=f=h=this.Element("span",{className:"MathJax",oncontextmenu:this.ContextMenu,onmousedown:this.Mousedown,onmouseover:this.Mouseover,onclick:this.Click,ondblclick:this.DblClick});var i=(m.Get("display")==="block");if(i){f=h=this.Element("div",{className:"MathJax_Display",style:{width:"100%",position:"relative"}});f.appendChild(n)}f.setAttribute("role","textbox");f.setAttribute("aria-readonly","true");if(this.useProcessingFrame){h=this.Element((i?"div":"span"),{className:"MathJax_Processing"});h.appendChild(f)}l.parentNode.insertBefore(h,l);var g;try{this.getScales(n);g=(this.em===0||String(this.em)==="NaN")}catch(k){g=true}if(g){this.hiddenDiv.appendChild(h);this.getScales(n)}this.initImg(n);this.initHTML(m,n);m.setTeXclass();try{m.toHTML(n,f)}catch(k){if(k.restart){h.parentNode.removeChild(h)}throw k}if(g){l.parentNode.insertBefore(h,l)}if(this.useProcessingFrame){h.parentNode.replaceChild(f,h)}},ContextMenu:function(i,j){if(e.config.showMathMenu&&(e.settings.context==="MathJax"||j)){if(e.safariContextMenuBug){setTimeout("window.getSelection().empty()",0)}if(!i||e.msieEventBug){i=window.event}var f=MathJax.Menu;if(f){var h=(this.parentNode.className==="MathJax_Display"?this.parentNode:this);f.jax=d.getJaxFor(h.nextSibling);f.menu.items[1].menu.items[1].name=(f.jax.inputJax.id==="MathML"?"Original":f.jax.inputJax.id);return f.menu.Post(i)}else{if(!c.loadingMathMenu){c.loadingMathMenu=true;var g={pageX:i.pageX,pageY:i.pageY,clientX:i.clientX,clientY:i.clientY};MathJax.Callback.Queue(c.Require("[MathJax]/extensions/MathMenu.js"),function(){delete c.loadingMathMenu},[this,arguments.callee,g,j])}if(!i){i=window.event}if(i.preventDefault){i.preventDefault()}if(i.stopPropagation){i.stopPropagation()}i.cancelBubble=true;i.returnValue=false;return false}}},Mousedown:function(f){if(e.config.showMathMenu){if(!f){f=window.event}if(e.settings.context==="MathJax"){if(!e.noContextMenuBug||f.button!==2){return}}else{if(!f[e.MENUKEY]||f.button!==e.LEFTBUTTON){return}}return e.ContextMenu.call(this,f,true)}},Mouseover:function(f){e.HandleEvent(f,"Mouseover",this)},Click:function(f){e.HandleEvent(f,"Click",this)},DblClick:function(f){e.HandleEvent(f,"DblClick",this)},HandleEvent:function(h,f,g){},initImg:function(f){},initHTML:function(g,f){},initFont:function(f){var h=e.FONTDATA.FONTS,g=e.config.availableFonts;if(g&&g.length&&e.Font.testFont(h[f])){h[f].available=true;return null}if(!this.allowWebFonts){return null}h[f].isWebFont=true;if(e.FontFaceBug){h[f].family=f;if(e.msieFontCSSBug){h[f].family+="-Web"}}return c.Styles({"@font-face":this.Font.fontFace(f)})},Remove:function(f){var g=f.SourceElement();if(!g){return}g=g.previousSibling;if(!g){return}if(g.className.match(/^MathJax/)){g.parentNode.removeChild(g)}},getScales:function(h){h.parentNode.insertBefore(this.HDMspan,h);this.HDMspan.className="";this.HDMspan.id="";this.HDMspan.style.fontSize="";this.HDMimg.style.height="1px";this.HDMimg.style.width="60ex";var g=this.HDMspan.offsetWidth/60;this.HDMspan.className="MathJax";this.HDMspan.id="MathJax_getScales";this.HDMimg.style.width="60em";var f=this.outerEm=this.HDMspan.offsetWidth/60;this.scale=Math.floor(Math.max(this.config.minScaleAdjust/100,(g/this.TeX.x_height)/f)*this.config.scale);h.style.fontSize=this.HDMspan.style.fontSize=this.scale+"%";this.em=a.mbase.prototype.em=this.HDMspan.offsetWidth/60;if(this.operaFontSizeBug&&f===this.em&&this.scale!==100){this.em=a.mbase.prototype.em=f*this.scale/100}h.parentNode.removeChild(this.HDMspan);this.msieMarginScale=this.getMarginScale(h)},getMarginScale:function(f){return 1},getMSIEmarginScale:function(h){h.appendChild(this.marginCheck);var f=this.marginCheck.offsetWidth,g=this.marginMove.offsetWidth;var i=(2*g-f?g/(2*g-f):1);h.removeChild(this.marginCheck);return i},getHD:function(g){var f=g.style.position;g.style.position="absolute";this.HDimg.style.height="0px";g.appendChild(this.HDspan);var h={h:g.offsetHeight};this.HDimg.style.height=h.h+"px";h.d=g.offsetHeight-h.h;h.h-=h.d;h.h/=this.em;h.d/=this.em;g.removeChild(this.HDspan);g.style.position=f;return h},getW:function(i){var g=i.offsetWidth,h=(i.bbox?i.bbox.w:-1),j=i;if((h<0||this.negativeSkipBug)&&g>=0){if(this.negativeSkipBug){var f=i.style.position;i.style.position="absolute";j=this.startMarker;if(i.firstChild){i.insertBefore(j,i.firstChild)}else{i.appendChild(j)}j=this.startMarker}i.appendChild(this.endMarker);g=this.endMarker.offsetLeft-j.offsetLeft;i.removeChild(this.endMarker);if(this.negativeSkipBug){i.removeChild(j);i.style.position=f}}return g/this.em},Measured:function(h,g){if(h.bbox.width==null&&h.bbox.w&&!h.bbox.isMultiline){var f=this.getW(h);h.bbox.rw+=f-h.bbox.w;h.bbox.w=f}if(!g){g=h.parentNode}if(!g.bbox){g.bbox=h.bbox}return h},Remeasured:function(g,f){f.bbox=this.Measured(g,f).bbox},Em:function(f){if(Math.abs(f)<0.0006){return"0em"}return f.toFixed(3).replace(/\.?0+$/,"")+"em"},Percent:function(f){return(100*f).toFixed(1).replace(/\.?0+$/,"")+"%"},length2percent:function(f){return this.Percent(this.length2em(f))},length2em:function(k,i){if(typeof(k)!=="string"){k=k.toString()}if(k===""){return""}if(k===a.SIZE.NORMAL){return 1}if(k===a.SIZE.BIG){return 2}if(k===a.SIZE.SMALL){return 0.71}if(k==="infinity"){return e.BIGDIMEN}var h=this.FONTDATA.TeX_factor;if(k.match(/mathspace$/)){return e.MATHSPACE[k]*h}var g=k.match(/^\s*([-+]?(?:\.\d+|\d+(?:\.\d*)?))?(pt|em|ex|mu|px|pc|in|mm|cm|%)?/);var f=parseFloat(g[1]||"1"),j=g[2];if(i==null){i=1}if(j==="em"){return f*h}if(j==="ex"){return f*e.TeX.x_height*h}if(j==="%"){return f/100*i}if(j==="px"){return f/e.em}if(j==="pt"){return f/10*h}if(j==="pc"){return f*1.2*h}if(j==="in"){return f*this.pxPerInch/e.em}if(j==="cm"){return f*this.pxPerInch/e.em/2.54}if(j==="mm"){return f*this.pxPerInch/e.em/25.4}if(j==="mu"){return f/18*h}return f*h*i},thickness2em:function(f){var g=e.TeX.rule_thickness;if(f===a.LINETHICKNESS.MEDIUM){return g}if(f===a.LINETHICKNESS.THIN){return 0.67*g}if(f===a.LINETHICKNESS.THICK){return 1.67*g}return this.length2em(f,g)},createStrut:function(i,g,j){var f=this.Element("span",{style:{display:"inline-block",overflow:"hidden",height:g+"px",width:"1px",marginRight:"-1px"}});if(j){i.insertBefore(f,i.firstChild)}else{i.appendChild(f)}return f},createBlank:function(g,f,h){var i=this.Element("span",{style:{display:"inline-block",overflow:"hidden",height:"1px",width:this.Em(f)}});if(h){g.insertBefore(i,g.firstChild)}else{g.appendChild(i)}return i},createShift:function(g,f,i){var h=this.Element("span",{style:{marginLeft:this.Em(f)}});if(i){g.insertBefore(h,g.firstChild)}else{g.appendChild(h)}return h},createSpace:function(k,j,m,f,g){var i=this.Em(Math.max(0,j+m)),l=this.Em(-m);if(this.msieInlineBlockAlignBug){l=this.Em(e.getHD(k.parentNode).d-m)}if(k.isBox||k.className=="mspace"){k.bbox={h:j*k.scale,d:m*k.scale,w:f*k.scale,rw:f*k.scale,lw:0};k.style.height=i;k.style.verticalAlign=l}else{k=this.addElement(k,"span",{style:{height:i,verticalAlign:l}})}if(f>=0){k.style.width=this.Em(f);k.style.display="inline-block"}else{if(this.msieNegativeSpaceBug){k.style.height=""}k.style.marginLeft=this.Em(f);if(e.safariNegativeSpaceBug&&k.parentNode.firstChild==k){this.createBlank(k,0,true)}}if(g&&g!==a.COLOR.TRANSPARENT){k.style.backgroundColor=g}return k},createRule:function(o,k,m,p,i){var j=e.TeX.min_rule_thickness;if(p>0&&p*this.em<j){p=j/this.em}if(k+m>0&&(k+m)*this.em<j){var l=1/(k+m)*(j/this.em);k*=l;m*=l}if(!i){i="solid"}else{i="solid "+i}i=this.Em(p)+" "+i;var q=this.Em(k+m),g=this.Em(-m);var n=this.addElement(o,"span",{style:{borderLeft:i,display:"inline-block",overflow:"hidden",width:0,height:q,verticalAlign:g},bbox:{h:k,d:m,w:p,rw:p,lw:0},noAdjust:true});if(p>0&&n.offsetWidth==0){n.style.width=this.Em(p)}if(o.isBox||o.className=="mspace"){o.bbox=n.bbox}return n},createFrame:function(o,m,n,p,r,g){var l=(this.msieBorderWidthBug?0:2*r);var q=this.Em(m+n-l),f=this.Em(-n-r),k=this.Em(p-l);var i=this.Em(r)+" "+g;var j=this.addElement(o,"span",{style:{border:i,display:"inline-block",overflow:"hidden",width:k,height:q},bbox:{h:m,d:n,w:p,rw:p,lw:0},noAdjust:true});if(f){j.style.verticalAlign=f}return j},createStack:function(h,j,g){if(this.msiePaddingWidthBug){this.createStrut(h,0)}var i=String(g).match(/%$/);var f=(!i&&g!=null?g:0);h=this.addElement(h,"span",{noAdjust:true,style:{display:"inline-block",position:"relative",width:(i?"100%":this.Em(f)),height:0}});if(!j){h.parentNode.bbox=h.bbox={h:-this.BIGDIMEN,d:-this.BIGDIMEN,w:f,lw:this.BIGDIMEN,rw:(!i&&g!=null?g:-this.BIGDIMEN)};if(i){h.bbox.width=g}}return h},createBox:function(g,f){var h=this.addElement(g,"span",{style:{position:"absolute"},isBox:true});if(f!=null){h.style.width=f}return h},addBox:function(f,g){g.style.position="absolute";g.isBox=true;return f.appendChild(g)},placeBox:function(n,m,k,i){var o=n.parentNode,v=n.bbox,q=o.bbox;if(this.msiePlaceBoxBug){this.addText(n,this.NBSP)}if(this.imgSpaceBug){this.addText(n,this.imgSpace)}var p=n.offsetHeight/this.em+1,z=0;if(n.noAdjust){p-=1}else{if(this.msieInlineBlockAlignBug){this.addElement(n,"img",{className:"MathJax_strut",border:0,src:"about:blank",style:{width:0,height:this.Em(p)}})}else{this.addElement(n,"span",{style:{display:"inline-block",width:0,height:this.Em(p)}})}}n.style.top=this.Em(-k-p);n.style.left=this.Em(m+z);if(v){if(this.negativeSkipBug){if(v.lw<0){z=v.lw;e.createBlank(n,-z,true);h=0}if(v.rw>v.w){e.createBlank(n,v.rw-v.w+0.1)}}if(!this.msieClipRectBug&&!v.noclip&&!i){var u=3/this.em;var s=(v.H==null?v.h:v.H),g=(v.D==null?v.d:v.D);var w=p-s-u,j=p+g+u,h=v.lw-3*u,f=1000;if(v.isFixed){f=v.width-h}n.style.clip="rect("+this.Em(w)+" "+this.Em(f)+" "+this.Em(j)+" "+this.Em(h)+")"}}if(v&&q){if(v.H!=null&&(q.H==null||v.H+k>q.H)){q.H=v.H+k}if(v.D!=null&&(q.D==null||v.D-k>q.D)){q.D=v.D-k}if(v.h+k>q.h){q.h=v.h+k}if(v.d-k>q.d){q.d=v.d-k}if(q.H!=null&&q.H<=q.h){delete q.H}if(q.D!=null&&q.D<=q.d){delete q.D}if(v.w+m>q.w){q.w=v.w+m;if(q.width==null){o.style.width=this.Em(q.w)}}if(v.rw+m>q.rw){q.rw=v.rw+m}if(v.lw+m<q.lw){q.lw=v.lw+m}if(v.width!=null&&!v.isFixed){if(q.width==null){o.style.width=q.width="100%"}n.style.width=v.width}}},alignBox:function(h,n,m){this.placeBox(h,0,m);var j=h.bbox;if(j.isMultiline){return}var g=j.width!=null&&!j.isFixed;var i=0,k=-j.w/2,f="50%";if(this.negativeSkipBug){i=j.w-j.rw-0.1;k+=j.lw}k=this.Em(k*this.msieMarginScale);if(g){k="";f=(50-parseFloat(j.width)/2)+"%"}d.Insert(h.style,({right:{left:"",right:this.Em(i)},center:{left:f,marginLeft:k}})[n])},setStackWidth:function(g,f){if(typeof(f)==="number"){g.style.width=this.Em(Math.max(0,f));if(g.bbox){g.bbox.w=f}if(g.parentNode.bbox){g.parentNode.bbox.w=f}}else{g.style.width=g.parentNode.style.width="100%";if(g.bbox){g.bbox.width=f}if(g.parentNode.bbox){g.parentNode.bbox.width=f}}},createDelimiter:function(q,f,h,l,j){if(!f){q.bbox={h:0,d:0,w:this.TeX.nulldelimiterspace,lw:0};q.bbox.rw=q.bbox.w;this.createSpace(q,q.bbox.h,q.bbox.d,q.bbox.w);return}if(!l){l=1}if(!(h instanceof Array)){h=[h,h]}var p=h[1];h=h[0];var g={alias:f};while(g.alias){f=g.alias;g=this.FONTDATA.DELIMITERS[f];if(!g){g={HW:[0,this.FONTDATA.VARIANT[a.VARIANT.NORMAL]]}}}for(var o=0,k=g.HW.length;o<k;o++){if(g.HW[o][0]*l>=h-0.01||(o==k-1&&!g.stretch)){if(g.HW[o][2]){l*=g.HW[o][2]}if(g.HW[o][3]){f=g.HW[o][3]}var n=this.addElement(q,"span");this.createChar(n,[f,g.HW[o][1]],l,j);q.bbox=n.bbox;q.offset=0.65*q.bbox.w;q.scale=l;return}}if(g.stretch){this["extendDelimiter"+g.dir](q,p,g.stretch,l,j)}},extendDelimiterV:function(v,p,A,B,s){var i=this.createStack(v,true);var r=this.createBox(i),q=this.createBox(i);this.createChar(r,(A.top||A.ext),B,s);this.createChar(q,(A.bot||A.ext),B,s);var g={bbox:{w:0,lw:0,rw:0}},z=g,j;var w=r.bbox.h+r.bbox.d+q.bbox.h+q.bbox.d;var m=-r.bbox.h;this.placeBox(r,0,m,true);m-=r.bbox.d;if(A.mid){z=this.createBox(i);this.createChar(z,A.mid,B,s);w+=z.bbox.h+z.bbox.d}if(p>w){g=this.Element("span");this.createChar(g,A.ext,B,s);var x=g.bbox.h+g.bbox.d,f=x-0.05,t,l,u=(A.mid?2:1);l=t=Math.ceil((p-w)/(u*f));if(!A.fullExtenders){f=(p-w)/(u*t)}var o=(t/(t+1))*(x-f);f=x-o;m+=o+f-g.bbox.h;while(u-->0){while(t-->0){if(!this.msieCloneNodeBug){j=g.cloneNode(true)}else{j=this.Element("span");this.createChar(j,A.ext,B,s)}m-=f;this.placeBox(this.addBox(i,j),0,m,true)}m+=o-g.bbox.d;if(A.mid&&u){this.placeBox(z,0,m-z.bbox.h,true);t=l;m+=-(z.bbox.h+z.bbox.d)+o+f-g.bbox.h}}}else{m+=(w-p)/2;if(A.mid){this.placeBox(z,0,m-z.bbox.h,true);m+=-(z.bbox.h+z.bbox.d)}m+=(w-p)/2}this.placeBox(q,0,m-q.bbox.h,true);m-=q.bbox.h+q.bbox.d;v.bbox={w:Math.max(r.bbox.w,g.bbox.w,q.bbox.w,z.bbox.w),lw:Math.min(r.bbox.lw,g.bbox.lw,q.bbox.lw,z.bbox.lw),rw:Math.max(r.bbox.rw,g.bbox.rw,q.bbox.rw,z.bbox.rw),h:0,d:-m};v.scale=B;v.offset=0.55*v.bbox.w;v.isMultiChar=true;this.setStackWidth(i,v.bbox.w)},extendDelimiterH:function(u,h,z,B,r){var l=this.createStack(u,true);var i=this.createBox(l),v=this.createBox(l);this.createChar(i,(z.left||z.rep),B,r);this.createChar(v,(z.right||z.rep),B,r);var f=this.Element("span");this.createChar(f,z.rep,B,r);var y={bbox:{h:-this.BIGDIMEN,d:-this.BIGDIMEN}},g;this.placeBox(i,-i.bbox.lw,0,true);var p=(i.bbox.rw-i.bbox.lw)+(v.bbox.rw-v.bbox.lw)-0.05,o=i.bbox.rw-i.bbox.lw-0.025,q;if(z.mid){y=this.createBox(l);this.createChar(y,z.mid,B,r);p+=y.bbox.w}if(h>p){var A=f.bbox.rw-f.bbox.lw,j=A-0.05,s,m,t=(z.mid?2:1);m=s=Math.ceil((h-p)/(t*j));j=(h-p)/(t*s);q=(s/(s+1))*(A-j);j=A-q;o-=f.bbox.lw+q;while(t-->0){while(s-->0){if(!this.msieCloneNodeBug){g=f.cloneNode(true)}else{g=this.Element("span");this.createChar(g,z.rep,B,r)}this.placeBox(this.addBox(l,g),o,0,true);o+=j}if(z.mid&&t){this.placeBox(y,o,0,true);o+=y.bbox.w-q;s=m}}}else{q=Math.min(p-h,i.bbox.w/2);o-=q/2;if(z.mid){this.placeBox(y,o,0,true);o+=y.bbox.w}o-=q/2}this.placeBox(v,o,0,true);u.bbox={w:o+v.bbox.rw,lw:0,rw:o+v.bbox.rw,H:Math.max(i.bbox.h,f.bbox.h,v.bbox.h,y.bbox.h),D:Math.max(i.bbox.d,f.bbox.d,v.bbox.d,y.bbox.d),h:f.bbox.h,d:f.bbox.d};u.scale=B;u.isMultiChar=true;this.setStackWidth(l,u.bbox.w)},createChar:function(o,k,h,f){var n=o,p="",j={fonts:[k[1]],noRemap:true};if(f&&f===a.VARIANT.BOLD){j.fonts=[k[1]+"-bold",k[1]]}if(typeof(k[1])!=="string"){j=k[1]}if(k[0] instanceof Array){for(var l=0,g=k[0].length;l<g;l++){p+=String.fromCharCode(k[0][l])}}else{p=String.fromCharCode(k[0])}if(h!==1){n=this.addElement(o,"span",{style:{fontSize:this.Percent(h)},scale:h});this.handleVariant(n,j,p);o.bbox=n.bbox}else{this.handleVariant(o,j,p)}if(k[2]){o.style.marginLeft=this.Em(k[2])}if(this.AccentBug&&o.bbox.w===0){n.firstChild.nodeValue+=this.NBSP;e.createSpace(o,0,0,-o.offsetWidth/e.em)}},positionDelimiter:function(g,f){f-=g.bbox.h;g.bbox.d-=f;g.bbox.h+=f;if(f){if(this.safariVerticalAlignBug||this.msieVerticalAlignBug||this.konquerorVerticalAlignBug||(this.operaVerticalAlignBug&&g.isMultiChar)){if(g.firstChild.style.display===""&&g.style.top!==""){g=g.firstChild;f-=parseFloat(g.style.top)}g.style.position="relative";g.style.top=this.Em(-f)}else{g.style.verticalAlign=this.Em(f);if(e.ffVerticalAlignBug){e.createRule(g.parentNode,g.bbox.h,0,0)}}}},handleVariant:function(v,j,o){var u="",s,y,p,g,x,z,f=v;if(o.length===0){return}if(!v.bbox){v.bbox={w:0,h:-this.BIGDIMEN,d:-this.BIGDIMEN,rw:-this.BIGDIMEN,lw:this.BIGDIMEN}}if(!j){j=this.FONTDATA.VARIANT[a.VARIANT.NORMAL]}z=j;for(var w=0,t=o.length;w<t;w++){j=z;s=o.charCodeAt(w);y=o.charAt(w);if(y===this.PLANE1){w++;s=o.charCodeAt(w)+119808-56320;if(this.FONTDATA.RemapPlane1){var A=this.FONTDATA.RemapPlane1(s,j);s=A.n;j=A.variant}}else{var q,l,r=this.FONTDATA.RANGES;for(q=0,l=r.length;q<l;q++){if(r[q].name==="alpha"&&j.noLowerCase){continue}var k=j["offset"+r[q].offset];if(k&&s>=r[q].low&&s<=r[q].high){if(r[q].remap&&r[q].remap[s]){s=k+r[q].remap[s]}else{s=s-r[q].low+k;if(r[q].add){s+=r[q].add}}if(j["variant"+r[q].offset]){j=this.FONTDATA.VARIANT[j["variant"+r[q].offset]]}break}}}if(j.remap&&j.remap[s]){if(j.remap[s] instanceof Array){var h=j.remap[s];s=h[0];j=this.FONTDATA.VARIANT[h[1]]}else{s=j.remap[s];if(j.remap.variant){j=this.FONTDATA.VARIANT[j.remap.variant]}}}if(this.FONTDATA.REMAP[s]&&!j.noRemap){s=this.FONTDATA.REMAP[s]}p=this.lookupChar(j,s);y=p[s];if(j!==x&&!y[5].img){if(u.length){this.addText(f,u);u=""}f=v;x=g;if(j!==x){if(x){f=this.addElement(v,"span")}else{g=j}}this.handleFont(f,p,f!==v);x=j}u=this.handleChar(f,p,y,s,u);if(y[0]/1000>v.bbox.h){v.bbox.h=y[0]/1000}if(y[1]/1000>v.bbox.d){v.bbox.d=y[1]/1000}if(v.bbox.w+y[3]/1000<v.bbox.lw){v.bbox.lw=v.bbox.w+y[3]/1000}if(v.bbox.w+y[4]/1000>v.bbox.rw){v.bbox.rw=v.bbox.w+y[4]/1000}v.bbox.w+=y[2]/1000}if(u.length){this.addText(f,u)}if(v.scale&&v.scale!==1){v.bbox.h*=v.scale;v.bbox.d*=v.scale;v.bbox.w*=v.scale;v.bbox.lw*=v.scale;v.bbox.rw*=v.scale}if(o.length==1&&p.skew&&p.skew[s]){v.bbox.skew=p.skew[s]}},handleFont:function(h,f,j){h.style.fontFamily=f.family;if(!(e.FontFaceBug&&f.isWebFont)){var g=f.style||"normal",i=f.weight||"normal";if(g!=="normal"||j){h.style.fontStyle=g}if(i!=="normal"||j){h.style.fontWeight=i}}},handleChar:function(g,f,l,k,j){var i=l[5];if(i.img){return this.handleImg(g,f,l,k,j)}if(i.isUnknown&&this.FONTDATA.DELIMITERS[k]){if(j.length){this.addText(g,j)}var h=g.scale;e.createDelimiter(g,k,0,1,f);g.scale=h;l[0]=g.bbox.h*1000;l[1]=g.bbox.d*1000;l[2]=g.bbox.w*1000;l[3]=g.bbox.lw*1000;l[4]=g.bbox.rw*1000;return""}if(i.c==null){if(k<=65535){i.c=String.fromCharCode(k)}else{i.c=this.PLANE1+String.fromCharCode(k-119808+56320)}}if(l[2]||!this.msieAccentBug||j.length){return j+i.c}e.createShift(g,l[3]/1000);e.createShift(g,(l[4]-l[3])/1000);this.addText(g,i.c);e.createShift(g,-l[4]/1000);return""},handleImg:function(g,f,j,i,h){return h},lookupChar:function(j,p){var h,f;if(!j.FONTS){var o=this.FONTDATA.FONTS;var l=(j.fonts||this.FONTDATA.VARIANT.normal.fonts);if(!(l instanceof Array)){l=[l]}if(j.fonts!=l){j.fonts=l}j.FONTS=[];for(h=0,f=l.length;h<f;h++){if(o[l[h]]){j.FONTS.push(o[l[h]]);o[l[h]].name=l[h]}}}for(h=0,f=j.FONTS.length;h<f;h++){var g=j.FONTS[h];if(typeof(g)==="string"){delete j.FONTS;this.loadFont(g)}if(g[p]){if(g[p].length===5){g[p][5]={}}if(e.allowWebFonts&&!g.available){this.loadWebFont(g)}else{return g}}else{this.findBlock(g,p)}}var k=(j.defaultFont||{family:e.config.undefinedFamily});if(j.bold){k.weight="bold"}if(j.italic){k.style="italic"}k[p]=[800,200,500,0,500,{isUnknown:true}];return k},findBlock:function(g,n){if(g.Ranges){for(var l=0,f=g.Ranges.length;l<f;l++){if(n<g.Ranges[l][0]){return}if(n<=g.Ranges[l][1]){var k=g.Ranges[l][2];for(var h=g.Ranges.length-1;h>=0;h--){if(g.Ranges[h][2]==k){g.Ranges.splice(h,1)}}this.loadFont(g.directory+"/"+k+".js")}}}},loadFont:function(g){var f=MathJax.Callback.Queue();f.Push(["Require",c,this.fontDir+"/"+g]);if(this.imgFonts){if(!MathJax.isPacked){g=g.replace(/\/([^\/]*)$/,e.imgPacked+"/$1")}f.Push(["Require",c,this.webfontDir+"/png/"+g])}d.RestartAfter(f.Push({}))},loadWebFont:function(f){f.available=f.isWebFont=true;if(e.FontFaceBug){f.family=f.name;if(e.msieFontCSSBug){f.family+="-Web"}}d.RestartAfter(this.Font.loadWebFont(f))},loadWebFontError:function(g,f){d.Startup.signal.Post("HTML-CSS Jax - disable web fonts");g.isWebFont=false;if(this.config.imageFont&&this.config.imageFont===this.fontInUse){this.imgFonts=true;d.Startup.signal.Post("HTML-CSS Jax - switch to image fonts");d.Startup.signal.Post("HTML-CSS Jax - using image fonts");MathJax.Message.Set("Web-Fonts not available -- using image fonts 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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:0.1,min_rule_thickness:1.25},PLANE1:String.fromCharCode(55349),NBSP:String.fromCharCode(160),rfuzz:0});MathJax.Hub.Register.StartupHook("mml Jax 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h=l.bbox={},n=[];while(j<f){var g=this.data[j];if(!g){continue}if(!k&&g.HTMLcanStretch("Vertical")){n.push(g);g=(g.CoreMO()||g)}this.HTMLcombineBBoxes(g,h);j++}this.HTMLcleanBBox(h);return n},HTMLcombineBBoxes:function(f,g){if(g.w==null){this.HTMLemptyBBox(g)}var i=f.HTMLspanElement();if(!i||!i.bbox){return}var h=i.bbox;if(h.d>g.d){g.d=h.d}if(h.h>g.h){g.h=h.h}if(h.D!=null&&h.D>g.D){g.D=h.D}if(h.H!=null&&h.H>g.H){g.H=h.H}if(i.style.paddingLeft){g.w+=parseFloat(i.style.paddingLeft)*(i.scale||1)}if(g.w+h.lw<g.lw){g.lw=g.w+h.lw}if(g.w+h.rw>g.rw){g.rw=g.w+h.rw}g.w+=h.w;if(i.style.paddingRight){g.w+=parseFloat(i.style.paddingRight)*(i.scale||1)}if(h.width){g.width=h.width}},HTMLemptyBBox:function(f){f.h=f.d=f.H=f.D=f.rw=-e.BIGDIMEN;f.w=0;f.lw=e.BIGDIMEN;return f},HTMLcleanBBox:function(f){if(f.h===this.BIGDIMEN){f.h=f.d=f.H=f.D=f.w=f.rw=f.lw=0}if(f.D<=f.d){delete f.D}if(f.H<=f.h){delete f.H}},HTMLzeroBBox:function(){return{h:0,d:0,w:0,lw:0,rw:0}},HTMLcanStretch:function(f){if(this.isEmbellished()){return this.Core().HTMLcanStretch(f)}return false},HTMLstretchH:function(g,f){return this.HTMLspanElement()},HTMLstretchV:function(g,f,i){return this.HTMLspanElement()},HTMLnotEmpty:function(f){while(f){if((f.type!=="mrow"&&f.type!=="texatom")||f.data.length>1){return true}f=f.data[0]}return false},HTMLmeasureChild:function(g,f){if(this.data[g]!=null){e.Measured(this.data[g].toHTML(f),f)}else{f.bbox=this.HTMLzeroBBox()}},HTMLcreateSpan:function(f){if(this.spanID){var g=this.HTMLspanElement();if(g){while(g.firstChild){g.removeChild(g.firstChild)}g.bbox={w:0,h:0,d:0,lw:0,rw:0};g.scale=1;g.isMultChar=null;g.style.cssText="";return g}}if(this.href){f=e.addElement(f,"a",{href:this.href})}f=e.addElement(f,"span",{className:this.type});if(e.imgHeightBug){f.style.display="inline-block"}if(this["class"]!=null){f.className+=" "+this["class"]}if(this.style){f.style.cssText=this.style;if(f.style.fontSize){this.mathsize=f.style.fontSize;f.style.fontSize=""}}this.spanID=e.GetID();f.id=(this.id||"MathJax-Span-"+this.spanID)+e.idPostfix;f.bbox={w:0,h:0,d:0,lw:0,lr:0};if(this.href){f.parentNode.bbox=f.bbox}return f},HTMLspanElement:function(){if(!this.spanID){return null}return document.getElementById((this.id||"MathJax-Span-"+this.spanID)+e.idPostfix)},HTMLhandleVariant:function(g,f,h){e.handleVariant(g,f,h)},HTMLhandleSize:function(f){if(!f.scale){f.scale=this.HTMLgetScale();if(f.scale!==1){f.style.fontSize=e.Percent(f.scale)}}return f},HTMLhandleColor:function(k){var 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