/*
 *  /MathJax/config/TeX-AMS-MML_SVG-full.js
 *  
 *  Copyright (c) 2010-2013 The MathJax Consortium
 *
 *  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/input/MathML/config.js","[MathJax]/jax/output/SVG/config.js","[MathJax]/extensions/tex2jax.js","[MathJax]/extensions/mml2jax.js","[MathJax]/extensions/MathEvents.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/input/MathML/jax.js","[MathJax]/jax/output/SVG/jax.js","[MathJax]/jax/output/SVG/autoload/mtable.js");MathJax.Hub.Config({"v1.0-compatible":!1});MathJax.InputJax.TeX=MathJax.InputJax({id:"TeX",version:"2.2.1",directory:MathJax.InputJax.directory+"/TeX",extensionDir:MathJax.InputJax.extensionDir+"/TeX",config:{TagSide:"right",TagIndent:"0.8em",MultLineWidth:"85%",equationNumbers:{autoNumber:"none",formatNumber:function(a){return a},formatTag:function(a){return"("+a+")"},formatID:function(a){return"mjx-eqn-"+String(a).replace(/[:"'<>&]/g,"")},formatURL:function(a){return"#"+escape(a)},useLabelIds:!0}}});MathJax.InputJax.TeX.Register("math/tex");MathJax.InputJax.TeX.loadComplete("config.js");MathJax.InputJax.MathML=MathJax.InputJax({id:"MathML",version:"2.2",directory:MathJax.InputJax.directory+"/MathML",extensionDir:MathJax.InputJax.extensionDir+"/MathML",entityDir:MathJax.InputJax.directory+"/MathML/entities",config:{useMathMLspacing:!1}});MathJax.InputJax.MathML.Register("math/mml");MathJax.InputJax.MathML.loadComplete("config.js");MathJax.OutputJax.SVG=MathJax.OutputJax({id:"SVG",version:"2.2",directory:MathJax.OutputJax.directory+"/SVG",extensionDir:MathJax.OutputJax.extensionDir+"/SVG",autoloadDir:MathJax.OutputJax.directory+"/SVG/autoload",fontDir:MathJax.OutputJax.directory+"/SVG/fonts",config:{scale:100,minScaleAdjust:50,font:"TeX",blacker:10,mtextFontInherit:!1,undefinedFamily:"STIXGeneral,'Arial Unicode MS',serif",addMMLclasses:!1,EqnChunk:MathJax.Hub.Browser.isMobile?10:50,EqnChunkFactor:1.5,EqnChunkDelay:100,linebreaks:{automatic:!1,width:"container"},styles:{".MathJax_SVG_Display":{"text-align":"center",margin:"1em 0em"},"#MathJax_SVG_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",padding:"3px 4px","z-index":401}}}});MathJax.Hub.config.delayJaxRegistration||MathJax.OutputJax.SVG.Register("jax/mml");MathJax.OutputJax.SVG.loadComplete("config.js");MathJax.Extension.tex2jax={version:"2.2",config:{inlineMath:[["\\(","\\)"]],displayMath:[["$$","$$"],["\\[","\\]"]],balanceBraces:!0,skipTags:"script noscript style textarea pre code".split(" "),ignoreClass:"tex2jax_ignore",processClass:"tex2jax_process",processEscapes:!1,processEnvironments:!0,processRefs:!0,preview:"TeX"},PreProcess:function(a){this.configured||(this.config=MathJax.Hub.CombineConfig("tex2jax",this.config),this.config.Augment&&MathJax.Hub.Insert(this,this.config.Augment),"undefined"===typeof this.config.previewTeX||this.config.previewTeX||(this.config.preview="none"),this.configured=!0);"string"===typeof a&&(a=document.getElementById(a));a||(a=document.body);this.createPatterns()&&this.scanElement(a,a.nextSibling)},createPatterns:function(){var a=[],f=[],e,d,g=this.config;this.match={};e=0;for(d=g.inlineMath.length;e<d;e++)a.push(this.patternQuote(g.inlineMath[e][0])),this.match[g.inlineMath[e][0]]={mode:"",end:g.inlineMath[e][1],pattern:this.endPattern(g.inlineMath[e][1])};e=0;for(d=g.displayMath.length;e<d;e++)a.push(this.patternQuote(g.displayMath[e][0])),this.match[g.displayMath[e][0]]={mode:"; mode\x3ddisplay",end:g.displayMath[e][1],pattern:this.endPattern(g.displayMath[e][1])};a.length&&f.push(a.sort(this.sortLength).join("|"));g.processEnvironments&&f.push("\\\\begin\\{([^}]*)\\}");g.processEscapes&&f.push("\\\\*\\\\\\$");g.processRefs&&f.push("\\\\(eq)?ref\\{[^}]*\\}");this.start=new RegExp(f.join("|"),"g");this.skipTags=new RegExp("^("+g.skipTags.join("|")+")$","i");a=[];MathJax.Hub.config.preRemoveClass&&a.push(MathJax.Hub.config.preRemoveClass);g.ignoreClass&&a.push(g.ignoreClass);this.ignoreClass=a.length?new RegExp("(^| )("+a.join("|")+")( |$)"):/^$/;this.processClass=new RegExp("(^| )("+g.processClass+")( |$)");return 0<f.length},patternQuote:function(a){return a.replace(/([\^$(){}+*?\-|\[\]\:\\])/g,"\\$1")},endPattern:function(a){return new RegExp(this.patternQuote(a)+"|\\\\.|[{}]","g")},sortLength:function(a,f){return a.length!==f.length?f.length-a.length:a==f?0:a<f?-1:1},scanElement:function(a,f,e){for(var d,g,p;a&&a!=f;)"#text"===a.nodeName.toLowerCase()?e||(a=this.scanText(a)):(d="undefined"===typeof a.className?"":a.className,g="undefined"===typeof a.tagName?"":a.tagName,"string"!==typeof d&&(d=String(d)),p=this.processClass.exec(d),!a.firstChild||d.match(/(^| )MathJax/)||!p&&this.skipTags.exec(g)||(d=(e||this.ignoreClass.exec(d))&&!p,this.scanElement(a.firstChild,f,d))),a&&(a=a.nextSibling)},scanText:function(a){if(""==a.nodeValue.replace(/\s+/,""))return a;var f,e;this.search={start:!0};for(this.pattern=this.start;a;){for(this.pattern.lastIndex=0;a&&"#text"===a.nodeName.toLowerCase()&&(f=this.pattern.exec(a.nodeValue));)a=this.search.start?this.startMatch(f,a):this.endMatch(f,a);this.search.matched&&(a=this.encloseMath(a));if(a){do e=a,a=a.nextSibling;while(a&&("br"===a.nodeName.toLowerCase()||"#comment"===a.nodeName.toLowerCase()));if(!a||"#text"!==a.nodeName)return this.search.close?this.prevEndMatch():e}}return a},startMatch:function(a,f){var e=this.match[a[0]];if(null!=e)this.search={end:e.end,mode:e.mode,pcount:0,open:f,olen:a[0].length,opos:this.pattern.lastIndex-a[0].length},this.switchPattern(e.pattern);else if("\\begin"===a[0].substr(0,6))this.search={end:"\\end{"+a[1]+"}",mode:"; mode\x3ddisplay",pcount:0,open:f,olen:0,opos:this.pattern.lastIndex-a[0].length,isBeginEnd:!0},this.switchPattern(this.endPattern(this.search.end));else{if("\\ref"===a[0].substr(0,4)||"\\eqref"===a[0].substr(0,6))return this.search={mode:"",end:"",open:f,pcount:0,olen:0,opos:this.pattern.lastIndex-a[0].length},this.endMatch([""],f);var e=a[0].substr(0,a[0].length-1),d;0===e.length%2?(d=[e.replace(/\\\\/g,"\\")],e=1):(d=[e.substr(1).replace(/\\\\/g,"\\"),"$"],e=0);d=MathJax.HTML.Element("span",null,d);var g=MathJax.HTML.TextNode(f.nodeValue.substr(0,a.index));f.nodeValue=f.nodeValue.substr(a.index+a[0].length-e);f.parentNode.insertBefore(d,f);f.parentNode.insertBefore(g,d);this.pattern.lastIndex=e}return f},endMatch:function(a,f){var e=this.search;a[0]==e.end?(e.close&&0!==e.pcount||(e.close=f,e.cpos=this.pattern.lastIndex,e.clen=e.isBeginEnd?0:a[0].length),0===e.pcount&&(e.matched=!0,f=this.encloseMath(f),this.switchPattern(this.start))):"{"===a[0]?e.pcount++:"}"===a[0]&&e.pcount&&e.pcount--;return f},prevEndMatch:function(){this.search.matched=!0;var a=this.encloseMath(this.search.close);this.switchPattern(this.start);return a},switchPattern:function(a){a.lastIndex=this.pattern.lastIndex;this.pattern=a;this.search.start=a===this.start},encloseMath:function(a){a=this.search;var f=a.close,e,d;(f=a.cpos===f.length?f.nextSibling:f.splitText(a.cpos))||(e=f=MathJax.HTML.addText(a.close.parentNode,""));a.close=f;for(d=a.opos?a.open.splitText(a.opos):a.open;d.nextSibling&&d.nextSibling!==f;)d.nodeValue=null!==d.nextSibling.nodeValue?"#comment"===d.nextSibling.nodeName?d.nodeValue+d.nextSibling.nodeValue.replace(/^\[CDATA\[((.|\n|\r)*)\]\]$/,"$1"):d.nodeValue+d.nextSibling.nodeValue:this.msieNewlineBug?d.nodeValue+("br"===d.nextSibling.nodeName.toLowerCase()?"\n":" "):d.nodeValue+" ",d.parentNode.removeChild(d.nextSibling);f=d.nodeValue.substr(a.olen,d.nodeValue.length-a.olen-a.clen);d.parentNode.removeChild(d);"none"!==this.config.preview&&this.createPreview(a.mode,f);d=this.createMathTag(a.mode,f);this.search={};this.pattern.lastIndex=0;e&&e.parentNode.removeChild(e);return d},insertNode:function(a){var f=this.search;f.close.parentNode.insertBefore(a,f.close)},createPreview:function(a,f){var e=this.config.preview;"none"!==e&&("TeX"===e&&(e=[this.filterPreview(f)]),e&&(e=MathJax.HTML.Element("span",{className:MathJax.Hub.config.preRemoveClass},e),this.insertNode(e)))},createMathTag:function(a,f){var e=document.createElement("script");e.type="math/tex"+a;MathJax.HTML.setScript(e,f);this.insertNode(e);return e},filterPreview:function(a){return a},msieNewlineBug:MathJax.Hub.Browser.isMSIE&&9>document.documentMode};MathJax.Hub.Register.PreProcessor(["PreProcess",MathJax.Extension.tex2jax]);MathJax.Ajax.loadComplete("[MathJax]/extensions/tex2jax.js");MathJax.Extension.mml2jax={version:"2.2",config:{preview:"alttext"},MMLnamespace:"http://www.w3.org/1998/Math/MathML",PreProcess:function(a){this.configured||(this.config=MathJax.Hub.CombineConfig("mml2jax",this.config),this.config.Augment&&MathJax.Hub.Insert(this,this.config.Augment),this.InitBrowser(),this.configured=!0);"string"===typeof a&&(a=document.getElementById(a));a||(a=document.body);this.ProcessMathArray(a.getElementsByTagName("math"));a.getElementsByTagNameNS&&this.ProcessMathArray(a.getElementsByTagNameNS(this.MMLnamespace,"math"));var f,e;if("undefined"!==typeof document.namespaces)try{for(f=0,e=document.namespaces.length;f<e;f++){var d=document.namespaces[f];d.urn===this.MMLnamespace&&this.ProcessMathArray(a.getElementsByTagName(d.name+":math"))}}catch(p){}else if(d=document.getElementsByTagName("html")[0])for(f=0,e=d.attributes.length;f<e;f++){var g=d.attributes[f];"xmlns:"===g.nodeName.substr(0,6)&&g.nodeValue===this.MMLnamespace&&this.ProcessMathArray(a.getElementsByTagName(g.nodeName.substr(6)+":math"))}},ProcessMathArray:function(a){var f;if(a.length)if(this.MathTagBug)for(f=a.length-1;0<=f;f--)"MATH"===a[f].nodeName?this.ProcessMathFlattened(a[f]):this.ProcessMath(a[f]);else for(f=a.length-1;0<=f;f--)this.ProcessMath(a[f])},ProcessMath:function(a){var f=a.parentNode,e=document.createElement("script");e.type="math/mml";f.insertBefore(e,a);if(this.AttributeBug){var d=this.OuterHTML(a);this.CleanupHTML&&(d=d.replace(/<\?import .*?>/i,"").replace(/<\?xml:namespace .*?\/>/i,""),d=d.replace(/&nbsp;/g,"\x26#xA0;"));MathJax.HTML.setScript(e,d);f.removeChild(a)}else f=MathJax.HTML.Element("span"),f.appendChild(a),MathJax.HTML.setScript(e,f.innerHTML);"none"!==this.config.preview&&this.createPreview(a,e)},ProcessMathFlattened:function(a){var f=a.parentNode,e=document.createElement("script");e.type="math/mml";f.insertBefore(e,a);for(var f="",d,g=a;a&&"/MATH"!==a.nodeName;)d=a,a=a.nextSibling,f+=this.NodeHTML(d),d.parentNode.removeChild(d);a&&"/MATH"===a.nodeName&&a.parentNode.removeChild(a);e.text=f+"\x3c/math\x3e";"none"!==this.config.preview&&this.createPreview(g,e)},NodeHTML:function(a){var f,e,d;if("#text"===a.nodeName)f=this.quoteHTML(a.nodeValue);else 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e=this.config.preview;"none"!==e&&("alttext"===e&&(e=a.getAttribute("alttext"),e=null!=e?[this.filterPreview(e)]:null),e&&(e=MathJax.HTML.Element("span",{className:MathJax.Hub.config.preRemoveClass},e),f.parentNode.insertBefore(e,f)))},filterPreview:function(a){return a},InitBrowser:function(){var a=MathJax.HTML.Element("span",{id:"\x3c",className:"mathjax",innerHTML:"\x3cmath\x3e\x3cmi\x3ex\x3c/mi\x3e\x3cmspace /\x3e\x3c/math\x3e"}),f=a.outerHTML||"";this.AttributeBug=""!==f&&!(f.match(/id="&lt;"/)&&f.match(/class="mathjax"/)&&f.match(/<\/math>/));this.MathTagBug=1<a.childNodes.length;this.CleanupHTML=MathJax.Hub.Browser.isMSIE}};MathJax.Hub.Register.PreProcessor(["PreProcess",MathJax.Extension.mml2jax]);MathJax.Ajax.loadComplete("[MathJax]/extensions/mml2jax.js");(function(a,f,e,d,g,p,n){var l=MathJax.Extension,c=l.MathEvents={version:"2.2"},b=a.config.menuSettings,m={hover:500,frame:{x:3.5,y:5,bwidth:1,bcolor:"#A6D",hwidth:"15px",hcolor:"#83A"},button:{x:-4,y:-3,wx:-2,src:e.fileURL(p.imageDir+"/MenuArrow-15.png")},fadeinInc:.2,fadeoutInc:.05,fadeDelay:50,fadeoutStart:400,fadeoutDelay:15E3,styles:{".MathJax_Hover_Frame":{"border-radius":".25em","-webkit-border-radius":".25em","-moz-border-radius":".25em","-khtml-border-radius":".25em","box-shadow":"0px 0px 15px #83A","-webkit-box-shadow":"0px 0px 15px #83A","-moz-box-shadow":"0px 0px 15px #83A","-khtml-box-shadow":"0px 0px 15px #83A",border:"1px solid #A6D ! important",display:"inline-block",position:"absolute"},".MathJax_Hover_Arrow":{position:"absolute",width:"15px",height:"11px",cursor:"pointer"}}},t=c.Event={LEFTBUTTON:0,RIGHTBUTTON:2,MENUKEY:"altKey",Mousedown:function(b){return t.Handler(b,"Mousedown",this)},Mouseup:function(b){return t.Handler(b,"Mouseup",this)},Mousemove:function(b){return t.Handler(b,"Mousemove",this)},Mouseover:function(b){return t.Handler(b,"Mouseover",this)},Mouseout:function(b){return t.Handler(b,"Mouseout",this)},Click:function(b){return t.Handler(b,"Click",this)},DblClick:function(b){return t.Handler(b,"DblClick",this)},Menu:function(b){return t.Handler(b,"ContextMenu",this)},Handler:function(b,m,c){if(e.loadingMathMenu)return t.False(b);var d=p[c.jaxID];b||(b=window.event);b.isContextMenu="ContextMenu"===m;if(d[m])return d[m](b,c);if(l.MathZoom)return l.MathZoom.HandleEvent(b,m,c)},False:function(b){b||(b=window.event);b&&(b.preventDefault&&b.preventDefault(),b.stopPropagation&&b.stopPropagation(),b.cancelBubble=!0,b.returnValue=!1);return!1},ContextMenu:function(m,k,r){var f=p[k.jaxID],l=f.getJaxFromMath(k);if((null!=f.config.showMathMenu?f:a).config.showMathMenu&&("MathJax"===b.context||r)){c.msieEventBug&&(m=window.event||m);t.ClearSelection();h.ClearHoverTimer();l.hover&&(l.hover.remove&&(clearTimeout(l.hover.remove),delete 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h=p[d.jaxID],g=(null!=h.config.showMathMenu?h:a).config.showMathMenu;if(g){g=(null!=h.config.showMathMenuMSIE?h:a).config.showMathMenuMSIE;if("MathJax"===b.context&&!b.mpContext&&g){if(!c.noContextMenuBug||m.button!==t.RIGHTBUTTON)return}else if(!m[t.MENUKEY]||m.button!==t.LEFTBUTTON)return;return h.ContextMenu(m,d,!0)}},ClearSelection:function(){c.safariContextMenuBug&&setTimeout("window.getSelection().empty()",0);document.selection&&setTimeout("document.selection.empty()",0)},getBBox:function(b){b.appendChild(c.topImg);var m=c.topImg.offsetTop,d=b.offsetHeight-m,a=b.offsetWidth;b.removeChild(c.topImg);return{w:a,h:m,d:d}}},h=c.Hover={Mouseover:function(m,c){if(b.discoverable||"Hover"===b.zoom){var d=m.fromElement||m.relatedTarget,g=m.toElement||m.target;if(d&&g&&(d.isMathJax!=g.isMathJax||a.getJaxFor(d)!==a.getJaxFor(g)))return d=this.getJaxFromMath(c),d.hover?h.ReHover(d):h.HoverTimer(d,c),t.False(m)}},Mouseout:function(m,c){if(b.discoverable||"Hover"===b.zoom){var d=m.fromElement||m.relatedTarget,g=m.toElement||m.target;if(d&&g&&(d.isMathJax!=g.isMathJax||a.getJaxFor(d)!==a.getJaxFor(g)))return d=this.getJaxFromMath(c),d.hover?h.UnHover(d):h.ClearHoverTimer(),t.False(m)}},Mousemove:function(m,c){if(b.discoverable||"Hover"===b.zoom){var d=this.getJaxFromMath(c);if(!d.hover&&(h.lastX!=m.clientX||h.lastY!=m.clientY))return h.lastX=m.clientX,h.lastY=m.clientY,h.HoverTimer(d,c),t.False(m)}},HoverTimer:function(b,c){this.ClearHoverTimer();this.hoverTimer=setTimeout(d(["Hover",this,b,c]),m.hover)},ClearHoverTimer:function(){this.hoverTimer&&(clearTimeout(this.hoverTimer),delete this.hoverTimer)},Hover:function(b,d){if(!l.MathZoom||!l.MathZoom.Hover({},d)){var t=p[b.outputJax],h=t.getHoverSpan(b,d),g=t.getHoverBBox(b,h,d),e=(null!=t.config.showMathMenu?t:a).config.showMathMenu,k=m.frame.x,r=m.frame.y,n=m.frame.bwidth;c.msieBorderWidthBug&&(n=0);b.hover={opacity:0,id:b.inputID+"-Hover"};var 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m=document.documentMode||0,d=b.versionAtLeast("8.0");c.msieBorderWidthBug="BackCompat"===document.compatMode;c.msieEventBug=b.isIE9;c.msieAlignBug=!d||8>m;9>m&&(t.LEFTBUTTON=1)},Safari:function(b){c.safariContextMenuBug=!0},Opera:function(b){c.operaPositionBug=!0},Konqueror:function(b){c.noContextMenuBug=!0}});c.topImg=c.msieAlignBug?f.Element("img",{style:{width:0,height:0,position:"relative"},src:"about:blank"}):f.Element("span",{style:{width:0,height:0,display:"inline-block"}});c.operaPositionBug&&(c.topImg.style.border="1px solid");c.config=m=a.CombineConfig("MathEvents",m);d.Queue(a.Register.StartupHook("End Config",{}),[function(){var b=m.styles[".MathJax_Hover_Frame"];b.border=m.frame.bwidth+"px solid "+m.frame.bcolor+" ! important";b["box-shadow"]=b["-webkit-box-shadow"]=b["-moz-box-shadow"]=b["-khtml-box-shadow"]="0px 0px "+m.frame.hwidth+" "+m.frame.hcolor}],["getImages",h],["Styles",e,m.styles],["Post",a.Startup.signal,"MathEvents 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b.settings.CTRL&&!m.ctrlKey||b.settings.ALT&&!m.altKey||b.settings.CMD&&!m.metaKey||b.settings.Shift&&!m.shiftKey||!b[c]?!0:b[c](m,d)},Click:function(b,c){if("Click"===this.settings.zoom)return this.Zoom(b,c)},DblClick:function(b,c){if("Double-Click"===this.settings.zoom)return this.Zoom(b,c)},Hover:function(b,c){return"Hover"===this.settings.zoom?(this.Zoom(b,c),!0):!1},Zoom:function(b,d){this.Remove();l.ClearHoverTimer();c.ClearSelection();var h=MathJax.OutputJax[d.jaxID],g=h.getJaxFromMath(d);g.hover&&l.UnHover(g);var e=Math.floor(.85*document.body.clientWidth),q=Math.floor(.85*Math.max(document.body.clientHeight,document.documentElement.clientHeight)),A=f.Element("span",{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":e+"px","max-height":q+"px"}},[["span",{style:{display:"inline-block","white-space":"nowrap"}}]]]]),u=A.lastChild,w=u.firstChild,v=A.firstChild;d.parentNode.insertBefore(A,d);d.parentNode.insertBefore(d,A);w.addEventListener&&w.addEventListener("mousedown",this.Remove,!0);if(this.msieTrapEventBug){var x=f.Element("span",{id:"MathJax_ZoomEventTrap",onmousedown:this.Remove});A.insertBefore(x,u)}this.msieZIndexBug&&(f.addElement(document.body,"img",{src:"about:blank",id:"MathJax_ZoomTracker",width:0,height:0,style:{width:0,height:0,position:"relative"}}),A.style.position="relative",A.style.zIndex=p.styles["#MathJax_ZoomOverlay"]["z-index"]);h=h.Zoom(g,w,d,e,q);this.msiePositionBug&&(this.msieSizeBug&&(u.style.height=h.zH+"px",u.style.width=h.zW+"px"),u.offsetHeight>q&&(u.style.height=q+"px",u.style.width=h.zW+this.scrollSize+"px"),u.offsetWidth>e&&(u.style.width=e+"px",u.style.height=h.zH+this.scrollSize+"px"));this.operaPositionBug&&(u.style.width=Math.min(e,h.zW)+"px");u.offsetWidth&&u.offsetWidth<e&&u.offsetHeight<q&&(u.style.overflow="visible");this.Position(u,h);this.msieTrapEventBug&&(x.style.height=u.clientHeight+"px",x.style.width=u.clientWidth+"px",x.style.left=parseFloat(u.style.left)+u.clientLeft+"px",x.style.top=parseFloat(u.style.top)+u.clientTop+"px");u.style.visibility="";"Hover"===this.settings.zoom&&(v.onmouseover=this.Remove);window.addEventListener?addEventListener("resize",this.Resize,!1):window.attachEvent?attachEvent("onresize",this.Resize):(this.onresize=window.onresize,window.onresize=this.Resize);a.signal.Post(["math zoomed",g]);return n(b)},Position:function(m,c){var d=this.Resize(),a=d.y,g=c.mW,e=c.Y;m.style.left=Math.max(-g-Math.floor((m.offsetWidth-g)/2),10-d.x)+"px";m.style.top=Math.max(e,10-a)+"px";b.msiePositionBug||b.SetWH()},Resize:function(m){if(b.onresize)b.onresize(m);var c=document.getElementById("MathJax_ZoomFrame");m=document.getElementById("MathJax_ZoomOverlay");for(var d=b.getXY(c),c=c.parentNode,a=b.getOverflow(c);c.parentNode&&c!==document.body&&"visible"===a;)c=c.parentNode,a=b.getOverflow(c);"visible"!==a&&(m.scroll_parent=c,a=b.getXY(c),d.x-=a.x,d.y-=a.y,a=b.getBorder(c),d.x-=a.x,d.y-=a.y);m.style.left=-d.x+"px";m.style.top=-d.y+"px";b.msiePositionBug?setTimeout(b.SetWH,0):b.SetWH();return d},SetWH:function(){var b=document.getElementById("MathJax_ZoomOverlay");b.style.width=b.style.height="1px";var c=b.scroll_parent||document.documentElement||document.body;b.style.width=c.scrollWidth+"px";b.style.height=Math.max(c.clientHeight,c.scrollHeight)+"px"},getOverflow:window.getComputedStyle?function(b){return getComputedStyle(b).overflow}:function(b){return(b.currentStyle||{overflow:"visible"}).overflow},getBorder:function(b){var c={thin:1,medium:2,thick:3},d=window.getComputedStyle?getComputedStyle(b):b.currentStyle||{borderLeftWidth:0,borderTopWidth:0};b=d.borderLeftWidth;d=d.borderTopWidth;b=c[b]?c[b]:parseInt(b);d=c[d]?c[d]:parseInt(d);return{x:b,y:d}},getXY:function(c){var d=0,a=0,g;for(g=c;g.offsetParent;)d+=g.offsetLeft,g=g.offsetParent;b.operaPositionBug&&(c.style.border="1px solid");for(g=c;g.offsetParent;)a+=g.offsetTop,g=g.offsetParent;b.operaPositionBug&&(c.style.border="");return{x:d,y:a}},Remove:function(c){var d=document.getElementById("MathJax_ZoomFrame");if(d){var h=MathJax.OutputJax[d.previousSibling.jaxID].getJaxFromMath(d.previousSibling);a.signal.Post(["math unzoomed",h]);d.parentNode.removeChild(d);(d=document.getElementById("MathJax_ZoomTracker"))&&d.parentNode.removeChild(d);b.operaRefreshBug&&(d=f.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(d));window.removeEventListener?removeEventListener("resize",b.Resize,!1):window.detachEvent?detachEvent("onresize",b.Resize):(window.onresize=b.onresize,delete b.onresize)}return n(c)}};a.Browser.Select({MSIE:function(c){var d=document.documentMode||0,a=9<=d;b.msiePositionBug=!a;b.msieSizeBug=c.versionAtLeast("7.0")&&(!document.documentMode||7===d||8===d);b.msieZIndexBug=7>=d;b.msieInlineBlockAlignBug=7>=d;b.msieTrapEventBug=!window.addEventListener;"BackCompat"===document.compatMode&&(b.scrollSize=52);a&&delete p.styles["#MathJax_Zoom"].filter},Opera:function(c){b.operaPositionBug=!0;b.operaRefreshBug=!0}});b.topImg=b.msieInlineBlockAlignBug?f.Element("img",{style:{width:0,height:0,position:"relative"},src:"about:blank"}):f.Element("span",{style:{width:0,height:0,display:"inline-block"}});if(b.operaPositionBug||b.msieTopBug)b.topImg.style.border="1px solid";MathJax.Callback.Queue(["StartupHook",MathJax.Hub.Register,"Begin Styles",{}],["Styles",e,p.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(a,f,e,d,g){var p=MathJax.Callback.Signal("menu");MathJax.Extension.MathMenu={version:"2.2",signal:p};var n=function(b){return MathJax.Localization._.apply(MathJax.Localization,[["MathMenu",b]].concat([].slice.call(arguments,1)))},l=a.Browser.isPC,c=a.Browser.isMSIE,b=8<(document.documentMode||0),m=l?null:"5px",t=a.CombineConfig("MathMenu",{delay:150,closeImg:e.fileURL(g.imageDir+"/CloseX-31.png"),showRenderer:!0,showMathPlayer:!0,showFontMenu:!1,showContext:!1,showDiscoverable:!1,showLocale:!0,showLocaleURL:!1,windowSettings:{status:"no",toolbar:"no",locationbar:"no",menubar:"no",directories:"no",personalbar:"no",resizable:"yes",scrollbars:"yes",width:400,height:300,left:Math.round((screen.width-400)/2),top:Math.round((screen.height-300)/3)},styles:{"#MathJax_About":{position:"fixed",left:"50%",width:"auto","text-align":"center",border:"3px outset",padding:"1em 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q.lastItem,delete q.lastMenu,delete k.skipUp,p.Post(["post",k.jax]));var d=f.addElement(m,"div",{onmouseup:k.Mouseup,ondblclick:h,ondragstart:h,onselectstart:h,oncontextmenu:h,menuItem:this,className:"MathJax_Menu"});MathJax.Localization.setCSS(d);for(var a=0,g=this.items.length;a<g;a++)this.items[a].Create(d);k.isMobile&&f.addElement(d,"span",{className:"MathJax_Menu_Close",menu:c,ontouchstart:k.Close,ontouchend:h,onmousedown:k.Close,onmouseup:h},[["img",{src:t.closeImg,style:{width:"100%",height:"100%"}}]]);this.posted=!0;d.style.width=d.offsetWidth+2+"px";a=b.pageX;g=b.pageY;a||g||(a=b.clientX+document.body.scrollLeft+document.documentElement.scrollLeft,g=b.clientY+document.body.scrollTop+document.documentElement.scrollTop);if(c){for(var e="left",r=c.offsetWidth,a=k.isMobile?30:r-2,g=0;c&&c!==m;)a+=c.offsetLeft,g+=c.offsetTop,c=c.parentNode;a+d.offsetWidth>document.body.offsetWidth-this.margin&&!k.isMobile&&(e="right",a=Math.max(this.margin,a-r-d.offsetWidth+6));l||(d.style["borderRadiusTop"+e]=0,d.style["WebkitBorderRadiusTop"+e]=0,d.style["MozBorderRadiusTop"+e]=0,d.style["KhtmlBorderRadiusTop"+e]=0)}else a+d.offsetWidth>document.body.offsetWidth-this.margin&&(a=document.body.offsetWidth-d.offsetWidth-this.margin),k.isMobile&&(a=Math.max(5,a-Math.floor(d.offsetWidth/2)),g-=20),k.skipUp=b.isContextMenu;d.style.left=a+"px";d.style.top=g+"px";document.selection&&document.selection.empty&&document.selection.empty();return h(b)},Remove:function(b,c){p.Post(["unpost",k.jax]);var m=document.getElementById("MathJax_MenuFrame");m&&(m.parentNode.removeChild(m),this.msieFixedPositionBug&&detachEvent("onresize",k.Resize));k.jax.hover&&(delete k.jax.hover.nofade,r.UnHover(k.jax));return h(b)},Find:function(b){return this.FindN(1,b,[].slice.call(arguments,1))},FindId:function(b){return this.FindN(0,b,[].slice.call(arguments,1))},FindN:function(b,c,m){for(var d=0,a=this.items.length;d<a;d++)if(this.items[d].name[b]===c){if(m.length){if(!this.items[d].menu)break;return this.items[d].menu.FindN(b,m[0],m.slice(1))}return this.items[d]}return null},IndexOf:function(b){return this.IndexOfN(1,b)},IndexOfId:function(b){return this.IndexOfN(0,b)},IndexOfN:function(b,c){for(var m=0,d=this.items.length;m<d;m++)if(this.items[m].name[b]===c)return m;return null}},{config:t,div:null,Close:function(b){return k.Event(b,this.menu||this.parentNode,this.menu?"Touchend":"Remove")},Remove:function(b){return k.Event(b,this,"Remove")},Mouseover:function(b){return k.Event(b,this,"Mouseover")},Mouseout:function(b){return k.Event(b,this,"Mouseout")},Mousedown:function(b){return k.Event(b,this,"Mousedown")},Mouseup:function(b){return k.Event(b,this,"Mouseup")},Touchstart:function(b){return k.Event(b,this,"Touchstart")},Touchend:function(b){return k.Event(b,this,"Touchend")},Event:function(b,c,m,d){if(k.skipMouseover&&"Mouseover"===m&&!d)return h(b);if(k.skipUp){if(m.match(/Mouseup|Touchend/))return delete k.skipUp,h(b);("Touchstart"===m||"Mousedown"===m&&!k.skipMousedown)&&delete k.skipUp}b||(b=window.event);return(d=c.menuItem)&&d[m]?d[m](b,c):null},BGSTYLE:{position:"absolute",left:0,top:0,"z-index":200,width:"100%",height:"100%",border:0,padding:0,margin:0},Background:function(b){b=f.addElement(document.body,"div",{style:this.BGSTYLE,id:"MathJax_MenuFrame"},[["div",{style:this.BGSTYLE,menuItem:b,onmousedown:this.Remove}]]);var c=b.firstChild;k.msieBackgroundBug&&(c.style.backgroundColor="white",c.style.filter="alpha(opacity\x3d0)");k.msieFixedPositionBug?(b.width=b.height=0,this.Resize(),attachEvent("onresize",this.Resize)):c.style.position="fixed";return b},Resize:function(){setTimeout(k.SetWH,0)},SetWH:function(){var 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m=document.getElementById("MathJax_MenuFrame").childNodes,d=c.parentNode.childNodes,a=0,h=d.length;a<h;a++){var t=d[a].menuItem;t&&t.menu&&t.menu.posted&&t.Deactivate(d[a])}for(h=m.length-1;0<=h&&c.parentNode.menuItem!==m[h].menuItem;)m[h].menuItem.posted=!1,m[h].parentNode.removeChild(m[h]),h--;this.Timer&&!k.isMobile&&this.Timer(b,c)}},Mouseout:function(b,c){this.menu&&this.menu.posted||this.Deactivate(c);this.timer&&(clearTimeout(this.timer),delete this.timer)},Mouseup:function(b,c){return this.Remove(b,c)},Touchstart:function(b,c){return this.TouchEvent(b,c,"Mousedown")},Touchend:function(b,c){return this.TouchEvent(b,c,"Mouseup")},TouchEvent:function(b,c,m){this!==q.lastItem&&(q.lastMenu&&k.Event(b,q.lastMenu,"Mouseout"),k.Event(b,c,"Mouseover",!0),q.lastItem=this,q.lastMenu=c);if(this.nativeTouch)return null;k.Event(b,c,m);return!1},Remove:function(b,c){c=c.parentNode.menuItem;return c.Remove(b,c)},Activate:function(b){this.Deactivate(b);b.className+=" 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m={className:"MathJax_MenuRadioCheck"};t.settings[this.variable]!==this.value&&(m={style:{display:"none"}});return[["span",m,[this.marker]]," "+this.Name()]},Mouseup:function(b,c){if(!this.disabled){for(var m=c.parentNode.childNodes,d=0,a=m.length;d<a;d++){var g=m[d].menuItem;g&&g.variable===this.variable&&(m[d].firstChild.style.display="none")}c.firstChild.display="";t.settings[this.variable]=this.value;k.cookie[this.variable]=t.settings[this.variable];k.saveCookie();p.Post(["radio button",this])}this.Remove(b,c);this.action&&!this.disabled&&this.action.call(k,this);return h(b)}});k.ITEM.CHECKBOX=k.ITEM.Subclass({variable:null,marker:"\u2713",Init:function(b,c,m){b instanceof Array||(b=[b,b]);this.name=b;this.variable=c;this.With(m)},Label:function(b,c){var m={className:"MathJax_MenuCheck"};t.settings[this.variable]||(m={style:{display:"none"}});return[["span",m,[this.marker]]," 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b=g["HTML-CSS"],c=g.NativeMML,m=g.SVG,d=(b||c||m||{config:{scale:100}}).config.scale,h=prompt(n("ScaleMath","Scale all mathematics (compared to surrounding text) by"),d+"%");h&&(h.match(/^\s*\d+(\.\d*)?\s*%?\s*$/)?(h=parseFloat(h))?h!==d&&(b&&(b.config.scale=h),c&&(c.config.scale=h),m&&(m.config.scale=h),k.cookie.scale=h,k.saveCookie(),a.Reprocess()):alert(n("NonZeroScale","The scale should not be zero")):alert(n("PercentScale","The scale should be a percentage (e.g., 120%%)")))};k.Zoom=function(){MathJax.Extension.MathZoom||e.Require("[MathJax]/extensions/MathZoom.js")};k.Renderer=function(){var c=a.outputJax["jax/mml"];if(c[0]!==t.settings.renderer){var m=a.Browser,d,h=k.Renderer.Messages,g;switch(t.settings.renderer){case "NativeMML":t.settings.warnedMML||(m.isChrome&&"24."!==m.version.substr(0,3)?d=h.MML.WebKit:m.isSafari&&!m.versionAtLeast("5.0")?d=h.MML.WebKit:m.isMSIE?m.hasMathPlayer||(d=h.MML.MSIE):d=h.MML[m],g="warnedMML");break;case 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c=this.ParseUpTo(b,"\\over");b=this.ParseArg(b);this.Push(d.TeXAtom(d.munderover(b,null,c)).With({mclass:d.TEXCLASS.REL}))},HBox:function(b,c){this.Push.apply(this,this.InternalMath(this.GetArgument(b),c))},FBox:function(b){this.Push(d.menclose.apply(d,this.InternalMath(this.GetArgument(b))).With({notation:"box"}))},Not:function(b){this.Push(n.not())},Dots:function(b){this.Push(n.dots().With({ldots:this.mmlToken(d.mo(d.entity("#x2026")).With({stretchy:!1})),cdots:this.mmlToken(d.mo(d.entity("#x22EF")).With({stretchy:!1}))}))},Require:function(b){b=this.GetArgument(b).replace(/.*\//,"").replace(/[^a-z0-9_.-]/ig,"");this.Extension(null,b)},Extension:function(b,c,d){c=a.extensionDir+"/"+c;c.match(/\.js$/)||(c+=".js");e.loaded[e.fileURL(c)]||(null!=b&&delete l[d||"macros"][b.replace(/^\\/,"")],f.RestartAfter(e.Require(c)))},Macro:function(b,c,d,e){if(d){var g=[];if(null!=e){var k=this.GetBrackets(b);g.push(null==k?e:k)}for(e=g.length;e<d;e++)g.push(this.GetArgument(b));c=this.SubstituteArgs(g,c)}this.string=this.AddArgs(c,this.string.slice(this.i));this.i=0;++this.macroCount>a.config.MAXMACROS&&a.Error(["MaxMacroSub1","MathJax maximum macro substitution count exceeded; is there a recursive macro call?"])},Matrix:function(b,c,d,e,g,k,f,l){var p=this.GetNext();""===p&&a.Error(["MissingArgFor","Missing argument for %1",b]);"{"===p?this.i++:(this.string=p+"}"+this.string.slice(this.i+1),this.i=0);b=n.array().With({requireClose:!0,arraydef:{rowspacing:k||"4pt",columnspacing:g||"1em"}});l&&(b.isCases=!0);if(c||d)b.open=c,b.close=d;"D"===f&&(b.arraydef.displaystyle=!0);null!=e&&(b.arraydef.columnalign=e);this.Push(b)},Entry:function(b){this.Push(n.cell().With({isEntry:!0,name:b}));if(this.stack.Top().isCases){var c=this.string,d=0;b=this.i;for(var e=c.length;b<e;){var 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d=++this.i,e=1;this.i<this.string.length;)switch(this.string.charAt(this.i++)){case "\\":this.i++;break;case "{":e++;break;case "}":if(0==e&&a.Error(["ExtraClose","Extra close brace"]),0==--e)return this.string.slice(d,this.i-1)}a.Error(["MissingCloseBrace","Missing close brace"])}return this.string.charAt(this.i++)},GetBrackets:function(b,c){if("["!=this.GetNext())return c;for(var d=++this.i,e=0;this.i<this.string.length;)switch(this.string.charAt(this.i++)){case "{":e++;break;case "\\":this.i++;break;case "}":0>=e--&&a.Error(["ExtraCloseLooking","Extra close brace while looking for %1","']'"]);break;case "]":if(0==e)return this.string.slice(d,this.i-1)}a.Error(["MissingCloseBracket","Couldn't find closing ']' for argument to %1",b])},GetDelimiter:function(b){for(;this.nextIsSpace();)this.i++;var c=this.string.charAt(this.i);if(this.i<this.string.length&&(this.i++,"\\"==c&&(c+=this.GetCS(b)),null!=l.delimiter[c]))return 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c=e.addElement(this.hiddenDiv,"div",{style:{width:"5in"}});this.pxPerInch=c.offsetWidth/5;this.hiddenDiv.removeChild(c);this.textSVG=this.Element("svg");l=this.addElement(this.addElement(this.hiddenDiv.parentNode,"svg"),"defs",{id:"MathJax_SVG_glyphs"});n={};this.ExSpan=e.Element("span",{style:{position:"absolute","font-size-adjust":"none"}},[["span",{className:"MathJax_SVG_ExBox"}]]);this.linebreakSpan=e.Element("span",null,[["hr",{style:{width:"auto",size:1,padding:0,border:0,margin:0}}]]);return a.Styles(this.config.styles,["InitializeSVG",this])},InitializeSVG:function(){document.body.appendChild(this.ExSpan);document.body.appendChild(this.linebreakSpan);this.defaultEx=this.ExSpan.firstChild.offsetHeight/60;this.defaultWidth=this.linebreakSpan.firstChild.offsetWidth;document.body.removeChild(this.linebreakSpan);document.body.removeChild(this.ExSpan)},preTranslate:function(c){var 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a=c.MathJax.elementJax,d=a.root,e=document.getElementById(a.inputID+"-Frame"),r=a.SVG.display?e.parentNode:e;this.em=g.mbase.prototype.em=a.SVG.em;this.ex=a.SVG.ex;this.linebreakWidth=1E3*a.SVG.lineWidth;this.cwidth=a.SVG.cwidth;this.mathDiv=r;e.appendChild(this.textSVG);this.initSVG(d,e);d.setTeXclass();try{d.toSVG(e,r)}catch(k){if(k.restart)for(;e.firstChild;)e.removeChild(e.firstChild);throw k;}e.removeChild(this.textSVG);a.SVG.isHidden&&c.parentNode.insertBefore(r,c);r.className=r.className.split(/ /)[0];this.hideProcessedMath&&(r.className+=" MathJax_SVG_Processed",c.MathJax.preview&&(a.SVG.preview=c.MathJax.preview,delete c.MathJax.preview),b.SVGeqn+=b.i-b.SVGi,b.SVGi=b.i,b.SVGeqn>=b.SVGlast+b.SVGchunk&&(this.postTranslate(b),b.SVGchunk=Math.floor(b.SVGchunk*this.config.EqnChunkFactor),b.SVGdelay=!0))}},postTranslate:function(c){var b=c.jax[this.id];if(this.hideProcessedMath){for(var a=c.SVGlast,d=c.SVGeqn;a<d;a++){var 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p=d.BBOX=MathJax.Object.Subclass({type:"g",removeable:!0,Init:function(c){this.h=this.d=-d.BIGDIMEN;this.w=this.r=this.H=this.D=0;this.l=d.BIGDIMEN;this.x=this.y=0;this.scale=1;this.n=0;this.type&&(this.element=d.Element(this.type,c))},With:function(c){return f.Insert(this,c)},Add:function(c,b,a,d,e){b&&(c.x+=b);a&&(c.y+=a);if(c.element){c.removeable&&1===c.element.childNodes.length&&1===c.n&&(b=c.element.firstChild,"use"===b.nodeName||"rect"===b.nodeName)&&(c.element=b,c.scale=c.childScale,b=c.childX,a=c.childY,c.x+=b,c.y+=a,c.h-=a,c.d+=a,c.H-=a,c.D+=a,c.w-=b,c.r-=b,c.l+=b,c.removeable=!1);1>Math.abs(c.x)&&1>Math.abs(c.y)?c.remove=c.removeable:"g"===c.element.nodeName?c.element.firstChild?c.element.setAttribute("transform","translate("+Math.floor(c.x)+","+Math.floor(c.y)+")"):c.remove=c.removeable:"line"===c.element.nodeName||"polygon"===c.element.nodeName||"path"===c.element.nodeName||"a"===c.element.nodeName?c.element.setAttribute("transform","translate("+Math.floor(c.x)+","+Math.floor(c.y)+")"):(c.element.setAttribute("x",Math.floor(c.x/c.scale)),c.element.setAttribute("y",Math.floor(c.y/c.scale)));if(c.remove)for(this.n+=c.n;c.element.firstChild;)e&&this.element.firstChild?this.element.insertBefore(c.element.firstChild,this.element.firstChild):this.element.appendChild(c.element.firstChild);else e?this.element.insertBefore(c.element,this.element.firstChild):this.element.appendChild(c.element);delete c.element}c.hasIndent&&(this.hasIndent=c.hasIndent);c.d-c.y>this.d&&(this.d=c.d-c.y,this.d>this.D&&(this.D=this.d));c.y+c.h>this.h&&(this.h=c.y+c.h,this.h>this.H&&(this.H=this.h));c.D-c.y>this.D&&(this.D=c.D-c.y);c.y+c.H>this.H&&(this.H=c.y+c.H);c.x+c.l<this.l&&(this.l=c.x+c.l);c.x+c.r>this.r&&(this.r=c.x+c.r);if(d||c.x+c.w+(c.X||0)>this.w)this.w=c.x+c.w+(c.X||0);this.childScale=c.scale;this.childX=c.x;this.childY=c.y;this.n++;return c},Align:function(c,b,a,d){a={left:a,center:(this.w-c.w)/2,right:this.w-c.w-a}[b]||0;this.Add(c,a,d)},Clean:function(){this.h===-d.BIGDIMEN&&(this.h=this.d=this.l=0);return this}});p.ROW=p.Subclass({Init:function(){this.SUPER(arguments).Init.call(this);this.svg=[];this.sh=this.sd=0},Check:function(c){var b=c.toSVG();this.svg.push(b);c.SVGcanStretch("Vertical")&&(b.mml=c);b.h>this.sh&&(this.sh=b.h);b.d>this.sd&&(this.sd=b.d)},Stretch:function(){for(var c=0,b=this.svg.length;c<b;c++){var a=this.svg[c],d=a.mml;d&&(a=d.SVGstretchV(this.sh,this.sd),d.SVGdata.HW=this.sh,d.SVGdata.D=this.sd);a.ic?this.ic=a.ic:delete this.ic;this.Add(a,this.w,0,!0)}delete this.svg}});p.RECT=p.Subclass({type:"rect",removeable:!1,Init:function(c,b,a,d){null==d&&(d={stroke:"none"});d.width=Math.floor(a);d.height=Math.floor(c+b);this.SUPER(arguments).Init.call(this,d);this.w=this.r=a;this.h=this.H=c+b;this.d=this.D=this.l=0;this.y=-b}});p.FRAME=p.Subclass({type:"rect",removeable:!1,Init:function(c,b,a,e,h,f,k){null==k&&(k={});k.fill="none";k["stroke-width"]=e.toFixed(2).replace(/\.?0+$/,"");k.width=Math.floor(a-e);k.height=Math.floor(c+b-e);k.transform="translate("+Math.floor(e/2)+","+Math.floor(-b+e/2)+")";"dashed"===h&&(k["stroke-dasharray"]=[Math.floor(6*d.em),Math.floor(6*d.em)].join(" "));this.SUPER(arguments).Init.call(this,k);this.w=this.r=a;this.h=this.H=c;this.d=this.D=b;this.l=0}});p.HLINE=p.Subclass({type:"line",removeable:!1,Init:function(c,b,a,d,e){null==e&&(e={});d&&""!==d&&(e.stroke=d);e["stroke-width"]=b.toFixed(2).replace(/\.?0+$/,"");e.x1=0;e.y1=e.y2=b/2;e.x2=Math.floor(c);if("dashed"===a){var f=Math.floor(c/(2*Math.floor(c/(6*b))+1));e["stroke-dasharray"]=f+" "+f}this.SUPER(arguments).Init.call(this,e);this.w=this.r=c;this.l=0;this.h=this.H=b;this.d=this.D=0}});p.VLINE=p.Subclass({type:"line",removeable:!1,Init:function(c,b,a,d,e){null==e&&(e={});d&&""!==d&&(e.stroke=d);e["stroke-width"]=b.toFixed(2).replace(/\.?0+$/,"");e.x1=e.x2=b/2;e.y1=0;e.y2=Math.floor(c);if("dashed"===a){var f=Math.floor(c/(2*Math.floor(c/(6*b))+1));e["stroke-dasharray"]=f+" "+f}this.SUPER(arguments).Init.call(this,e);this.w=this.r=b;this.l=0;this.h=this.H=c;this.d=this.D=0}});p.TEXT=p.Subclass({type:"text",removeable:!1,Init:function(c,b,a){a||(a={});a.stroke="none";this.SUPER(arguments).Init.call(this,a);d.addText(this.element,b);d.textSVG.appendChild(this.element);var e=this.element.getBBox();d.textSVG.removeChild(this.element);c*=1E3/d.em;this.element.setAttribute("transform","scale("+c+") matrix(1 0 0 -1 0 0)");this.w=this.r=e.width*c;this.l=0;this.h=this.H=-e.y*c;this.d=this.D=(e.height+e.y)*c}});p.G=p;p.NULL=p.Subclass({Init:function(){this.SUPER(arguments).Init.apply(this,arguments);this.Clean()}});var n,l;p.GLYPH=p.Subclass({type:"path",removeable:!1,Init:function(c,b,a,e,h,f,k,g){var p,u=d.config.blacker;n[b]||(p={id:b,"stroke-width":u},""!==g&&(p.d="M"+g+"Z"),this.SUPER(arguments).Init.call(this,p),l.appendChild(this.element),n[b]=!0);p={};1!==c&&(p.transform="scale("+c+")");this.element=d.Element("use",p);this.element.setAttributeNS("http://www.w3.org/1999/xlink","href","#"+b);this.h=(a+u)*c;this.d=(e+u)*c;this.w=(h+u/2)*c;this.l=(f+u/2)*c;this.r=(k+u/2)*c;this.H=Math.max(0,this.h);this.D=Math.max(0,this.d);this.x=this.y=0;this.scale=c}});f.Register.StartupHook("mml Jax Ready",function(){g=MathJax.ElementJax.mml;g.mbase.Augment({SVG:p,toSVG:function(){this.SVGgetStyles();var c=this.SVGgetVariant(),b=this.SVG();b.scale=this.SVGgetScale();this.SVGhandleSpace(b);for(var a=0,d=this.data.length;a<d;a++)if(this.data[a]){var e=b.Add(this.data[a].toSVG(c,b.scale),b.w,0,!0);e.skew&&(b.skew=e.skew)}b.Clean();a=this.data.join("");b.skew&&1!==a.length&&delete b.skew;b.r>b.w&&1===a.length&&!c.noIC&&(b.ic=b.r-b.w,b.w=b.r);this.SVGhandleColor(b);this.SVGsaveData(b);return b},SVGchildSVG:function(c){return this.data[c]?this.data[c].toSVG():p()},SVGdataStretched:function(c,b,a){this.SVGdata={HW:b,D:a};return this.data[c]?null!=a?this.data[c].SVGstretchV(b,a):null!=b?this.data[c].SVGstretchH(b):this.data[c].toSVG():p()},SVGsaveData:function(c){this.SVGdata||(this.SVGdata={});this.SVGdata.w=c.w;this.SVGdata.x=c.x;this.SVGdata.h=c.h;this.SVGdata.d=c.d;null!=c.X&&(this.SVGdata.X=c.X);this["class"]&&(c.removeable=!1,d.Element(c.element,{"class":this["class"]}));this.id&&(c.removeable=!1,d.Element(c.element,{id:this.id}));if(this.href){var b=d.Element("a",{"class":"mjx-svg-href"});b.setAttributeNS("http://www.w3.org/1999/xlink","href",this.href);b.onclick=this.SVGlink;d.addElement(b,"rect",{width:c.w,height:c.h+c.d,y:-c.d,fill:"none",stroke:"none","pointer-events":"all"});if("svg"===c.type){for(var a=c.element.firstChild;a.firstChild;)b.appendChild(a.firstChild);a.appendChild(b)}else b.appendChild(c.element),c.element=b;c.removeable=!1}d.config.addMMLclasses&&(this.SVGaddClass(c.element,"mjx-svg-"+this.type),c.removeable=!1);(b=this.style)&&c.element&&(c.element.style.cssText=b,c.element.style.fontSize&&(c.element.style.fontSize=""),c.element.style.border=c.element.style.padding="",c.removeable&&(c.removeable=""===c.element.style.cssText))},SVGaddClass:function(c,b){var a=c.getAttribute("class");c.setAttribute("class",(a?a+" ":"")+b)},SVGlink:function(){var c=this.href.animVal;if("#"===c.charAt(0)){var b=d.hashCheck(document.getElementById(c.substr(1)));b&&b.scrollIntoView&&setTimeout(function(){b.parentNode.scrollIntoView(!0)},1)}document.location=c},SVGgetStyles:function(){if(this.style){var c=e.Element("span");c.style.cssText=this.style;this.styles={border:d.getBorders(c),padding:d.getPadding(c)};c.style.fontSize&&(this.styles.fontSize=c.style.fontSize);c.style.color&&(this.styles.color=c.style.color);c.style.backgroundColor&&(this.styles.background=c.style.backgroundColor);c.style.fontStyle&&(this.styles.fontStyle=c.style.fontStyle);c.style.fontWeight&&(this.styles.fontWeight=c.style.fontWeight);c.style.fontFamily&&(this.styles.fontFamily=c.style.fontFamily);this.styles.fontWeight&&this.styles.fontWeight.match(/^\d+$/)&&(this.styles.fontWeight=600<parseInt(this.styles.fontWeight)?"bold":"normal")}},SVGhandleSpace:function(c){if(this.useMMLspacing){if("mo"===this.type){var b=this.getValues("scriptlevel","lspace","rspace");if(0>=b.scriptlevel||this.hasValue("lspace")||this.hasValue("rspace")){var a=this.SVGgetMu(c);b.lspace=Math.max(0,d.length2em(b.lspace,a));b.rspace=Math.max(0,d.length2em(b.rspace,a));for(var a=this,e=this.Parent();e&&e.isEmbellished()&&e.Core()===a;)a=e,e=e.Parent();b.lspace&&(c.x+=b.lspace);b.rspace&&(c.X=b.rspace)}}}else b=this.texSpacing(),""!==b&&(c.x+=d.length2em(b,this.SVGgetScale())/c.scale)},SVGhandleColor:function(c){var b=this.getValues("mathcolor","color");this.styles&&this.styles.color&&!b.color&&(b.color=this.styles.color);b.color&&!this.mathcolor&&(b.mathcolor=b.color);b.mathcolor&&(d.Element(c.element,{fill:b.mathcolor,stroke:b.mathcolor}),c.removeable=!1);var a=(this.styles||{}).border,e=(this.styles||{}).padding,h=(a||{}).left||0,f=(e||{}).left||0,k;b.background=this.mathbackground||this.background||(this.styles||{}).background||g.COLOR.TRANSPARENT;if(h+f){var n=p();for(k in c)c.hasOwnProperty(k)&&(n[k]=c[k]);n.x=0;n.y=0;c.element=d.Element("g");c.removeable=!0;c.Add(n,h+f,0)}e&&(c.w+=e.right,c.h+=e.top,c.d+=e.bottom);a&&(c.w+=a.right,c.h+=a.top,c.d+=a.bottom);b.background!==g.COLOR.TRANSPARENT&&("g"!==c.element.nodeName&&"svg"!==c.element.nodeName&&(e=d.Element("g"),e.appendChild(c.element),c.element=e,c.removeable=!0),c.Add(p.RECT(c.h,c.d,c.w,{fill:b.background,stroke:"none"}),0,0,!1,!0));if(a)for(k in b={left:["V",c.h+c.d,-5,-c.d],right:["V",c.h+c.d,c.w-a.right+5,-c.d],top:["H",c.w,0,c.h-a.top+5],bottom:["H",c.w,0,-c.d-5]},b)b.hasOwnProperty(k)&&a[k]&&(e=b[k],c.Add((0,p[e[0]+"LINE"])(e[1],a[k],a[k+"Style"],a[k+"Color"]),e[2],e[3]))},SVGhandleVariant:function(c,b,a){return d.HandleVariant(c,b,a)},SVGgetVariant:function(){var c=this.getValues("mathvariant","fontfamily","fontweight","fontstyle"),b=c.mathvariant;this.variantForm&&(b="-TeX-variant");c.hasVariant=this.Get("mathvariant",!0);c.hasVariant||(c.family=c.fontfamily,c.weight=c.fontweight,c.style=c.fontstyle);this.styles&&(!c.style&&this.styles.fontStyle&&(c.style=this.styles.fontStyle),!c.weight&&this.styles.fontWeight&&(c.weight=this.styles.fontWeight),!c.family&&this.styles.fontFamily&&(c.family=this.styles.fontFamily));if(c.family&&!c.hasVariant)return!c.weight&&c.mathvariant.match(/bold/)&&(c.weight="bold"),!c.style&&c.mathvariant.match(/italic/)&&(c.style="italic"),b={forceFamily:!0,font:{"font-family":c.family}},c.style&&(b.font["font-style"]=c.style),c.weight&&(b.font["font-weight"]=c.weight),b;"bold"===c.weight?b={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}[b]||b:"normal"===c.weight&&(b={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}[b]||b);"italic"===c.style?b={normal:g.VARIANT.ITALIC,bold:g.VARIANT.BOLDITALIC,"sans-serif":g.VARIANT.SANSSERIFITALIC,"bold-sans-serif":g.VARIANT.SANSSERIFBOLDITALIC}[b]||b:"normal"===c.style&&(b={italic:g.VARIANT.NORMAL,"bold-italic":g.VARIANT.BOLD,"sans-serif-italic":g.VARIANT.SANSSERIF,"sans-serif-bold-italic":g.VARIANT.BOLDSANSSERIF}[b]||b);b in d.FONTDATA.VARIANT||(b="normal");return d.FONTDATA.VARIANT[b]},SVGgetScale:function(){var c=1,b=this.getValues("mathsize","scriptlevel","fontsize");(this.styles||{}).fontSize&&!b.fontsize&&(b.fontsize=this.styles.fontSize);b.fontsize&&!this.mathsize&&(b.mathsize=b.fontsize);0!==b.scriptlevel&&(2<b.scriptlevel&&(b.scriptlevel=2),c=Math.pow(this.Get("scriptsizemultiplier"),b.scriptlevel),b.scriptminsize=d.length2em(this.Get("scriptminsize"))/1E3,c<b.scriptminsize&&(c=b.scriptminsize));this.isToken&&(c*=d.length2em(b.mathsize)/1E3);return c},SVGgetMu:function(c){var b=1,a=this.getValues("scriptlevel","scriptsizemultiplier");c.scale&&1!==c.scale&&(b=1/c.scale);0!==a.scriptlevel&&(2<a.scriptlevel&&(a.scriptlevel=2),b=Math.sqrt(Math.pow(a.scriptsizemultiplier,a.scriptlevel)));return b},SVGnotEmpty:function(c){for(;c;){if("mrow"!==c.type&&"texatom"!==c.type||1<c.data.length)return!0;c=c.data[0]}return!1},SVGcanStretch:function(c){return this.isEmbellished()?this.Core().SVGcanStretch(c):!1},SVGstretchV:function(c,b){return this.toSVG(c,b)},SVGstretchH:function(c){return this.toSVG(c)},SVGlineBreaks:function(){return!1}},{SVGautoload:function(){f.RestartAfter(a.Require(d.autoloadDir+"/"+this.type+".js"))},SVGautoloadFile:function(c){f.RestartAfter(a.Require(d.autoloadDir+"/"+c+".js"))}});g.chars.Augment({toSVG:function(c,b,a,d){var e=this.data.join("").replace(/[\u2061-\u2064]/g,"");a&&(e=a(e,d));return this.SVGhandleVariant(c,b,e)}});g.entity.Augment({toSVG:function(c,b,a,d){var e=this.toString().replace(/[\u2061-\u2064]/g,"");a&&(e=a(e,d));return this.SVGhandleVariant(c,b,e)}});g.mo.Augment({toSVG:function(c,b){this.SVGgetStyles();var a=this.svg=this.SVG();this.SVGhandleSpace(a);if(0==this.data.length)return a.Clean(),this.SVGsaveData(a),a;if(null!=b)return this.SVGstretchV(c,b);if(null!=c)return this.SVG.strechH(c);var e=this.SVGgetScale(),f=this.SVGgetVariant(),n=this.getValues("largeop","displaystyle");n.largeop&&(f=d.FONTDATA.VARIANT[n.displaystyle?"-largeOp":"-smallOp"]);var k=this.CoreParent(),q=k&&k.isa(g.msubsup)&&this!==k.data[0],l=q?this.SVGremapChars:null;if(1===this.data.join("").length&&k&&k.isa(g.munderover)&&1===this.CoreText(k.data[k.base]).length){var p=k.data[k.over],w=k.data[k.under];p&&this===p.CoreMO()&&k.Get("accent")?l=d.FONTDATA.REMAPACCENT:w&&this===w.CoreMO()&&k.Get("accentunder")&&(l=d.FONTDATA.REMAPACCENTUNDER)}q&&this.data.join("").match(/['`"\u00B4\u2032-\u2037\u2057]/)&&(f=d.FONTDATA.VARIANT["-TeX-variant"]);k=0;for(q=this.data.length;k<q;k++)this.data[k]&&(p=this.data[k].toSVG(f,e,this.SVGremap,l),w=a.w,0===w&&-p.l>10*p.w&&(w+=-p.l),a.Add(p,w,0,!0),p.skew&&(a.skew=p.skew));a.Clean();1!==this.data.join("").length&&delete a.skew;n.largeop&&(a.y=(a.h-a.d)/2/e-d.TeX.axis_height,a.r>a.w&&(a.ic=a.r-a.w,a.w=a.r));this.SVGhandleColor(a);this.SVGsaveData(a);return a},CoreParent:function(){for(var c=this;c&&c.isEmbellished()&&c.CoreMO()===this&&!c.isa(g.math);)c=c.Parent();return c},CoreText:function(c){if(!c)return"";if(c.isEmbellished())return c.CoreMO().data.join("");for(;(c.isa(g.mrow)||c.isa(g.TeXAtom)||c.isa(g.mstyle)||c.isa(g.mphantom))&&1===c.data.length&&c.data[0];)c=c.data[0];return c.isToken?c.data.join(""):""},SVGremapChars:{"*":"\u2217",'"':"\u2033","\u00b0":"\u2218","\u00b2":"2","\u00b3":"3","\u00b4":"\u2032","\u00b9":"1"},SVGremap:function(c,b){c=c.replace(/-/g,"\u2212");b&&(c=c.replace(/'/g,"\u2032").replace(/`/g,"\u2035"),1===c.length&&(c=b[c]||c));return c},SVGcanStretch:function(c){if(!this.Get("stretchy"))return!1;var b=this.data.join("");if(1<b.length)return!1;var a=this.CoreParent();if(a&&a.isa(g.munderover)&&1===this.CoreText(a.data[a.base]).length){var e=a.data[a.over],f=a.data[a.under];e&&this===e.CoreMO()&&a.Get("accent")?b=d.FONTDATA.REMAPACCENT[b]||b:f&&this===f.CoreMO()&&a.Get("accentunder")&&(b=d.FONTDATA.REMAPACCENTUNDER[b]||b)}(c=(b=d.FONTDATA.DELIMITERS[b.charCodeAt(0)])&&b.dir==c.substr(0,1))||delete this.svg;return c},SVGstretchV:function(c,b){var a=this.svg||this.toSVG(),e=this.getValues("symmetric","maxsize","minsize"),f=d.TeX.axis_height,g=this.SVGgetMu(a),k;k=e.symmetric?2*Math.max(c-f,b+f):c+b;e.maxsize=d.length2em(e.maxsize,g,a.h+a.d);e.minsize=d.length2em(e.minsize,g,a.h+a.d);k=Math.max(e.minsize,Math.min(e.maxsize,k));a=d.createDelimiter(this.data.join("").charCodeAt(0),k,a.scale);k=e.symmetric?(a.h+a.d)/2+f:(a.h+a.d)*c/(c+b);a.y=k-a.h;this.SVGhandleSpace(a);this.SVGhandleColor(a);delete this.svg.element;this.SVGsaveData(a);return a},SVGstretchH:function(c){var b=this.svg||this.toSVG(),a=this.SVGgetMu(b),e=this.getValues("maxsize","minsize","mathvariant","fontweight");("bold"===e.fontweight||600<=parseInt(e.fontweight))&&!this.Get("mathvariant",!0)&&(e.mathvariant=g.VARIANT.BOLD);e.maxsize=d.length2em(e.maxsize,a,b.w);e.minsize=d.length2em(e.minsize,a,b.w);c=Math.max(e.minsize,Math.min(e.maxsize,c));b=d.createDelimiter(this.data.join("").charCodeAt(0),c,b.scale,e.mathvariant);this.SVGhandleSpace(b);this.SVGhandleColor(b);delete this.svg.element;this.SVGsaveData(b);return b}});g.mtext.Augment({toSVG:function(){this.SVGgetStyles();var c,b,a=this.SVGgetScale();if("merror"===this.Parent().type)return c=this.SVG(),this.SVGhandleSpace(c),b=p.G(),b.Add(p.TEXT(.9*a,this.data.join(""),{fill:"#C00"})),c.Add(p.RECT(b.h+100,b.d+100,b.w+200,{fill:"#FF8",stroke:"#C00","stroke-width":50}),0,0),c.Add(b,150,0),c.H+=150,c.D+=50,c.Clean(),this.SVGsaveData(c),c;if(d.config.mtextFontInherit){c=this.SVG();this.SVGhandleSpace(c);b=this.SVGgetVariant();var e={};b.bold&&(e["font-weight"]="bold");b.italic&&(e["font-style"]="italic");c.Add(p.TEXT(a,this.data.join(""),e));c.Clean();this.SVGhandleColor(c);this.SVGsaveData(c);return c}return this.SUPER(arguments).toSVG.call(this)}});g.ms.Augment({toSVG:g.mbase.SVGautoload});g.mglyph.Augment({toSVG:g.mbase.SVGautoload});g.mspace.Augment({toSVG:function(){this.SVGgetStyles();var c=this.getValues("height","depth","width");c.mathbackground=this.mathbackground;this.background&&!this.mathbackground&&(c.mathbackground=this.background);var b=this.SVG(),a=this.SVGgetMu(b);b.h=d.length2em(c.height,a)/b.scale;b.d=d.length2em(c.depth,a)/b.scale;b.w=b.r=d.length2em(c.width,a)/b.scale;0>b.w&&(b.x=b.w,b.w=b.r=0);b.h<-b.d&&(b.d=-b.h);b.l=0;b.Clean();this.SVGhandleColor(b);this.SVGsaveData(b);return b}});g.mphantom.Augment({toSVG:function(c,b){this.SVGgetStyles();var a=this.SVG();if(null!=this.data[0])for(this.SVGhandleSpace(a),a.Add(this.SVGdataStretched(0,c,b)),a.Clean();a.element.firstChild;)a.element.removeChild(a.element.firstChild);this.SVGhandleColor(a);this.SVGsaveData(a);a.removeable&&!a.element.firstChild&&delete a.element;return a}});g.mpadded.Augment({toSVG:function(a,b){this.SVGgetStyles();var d=this.SVG();if(null!=this.data[0]){this.SVGhandleSpace(d);var e=this.SVGdataStretched(0,a,b),f=this.SVGgetMu(d),g=this.getValues("height","depth","width","lspace","voffset"),k=0,n=0;g.lspace&&(k=this.SVGlength2em(e,g.lspace,f));g.voffset&&(n=this.SVGlength2em(e,g.voffset,f));var l=e.h,p=e.d,w=e.w;d.Add(e,k,n);d.Clean();d.h=l;d.d=p;d.w=w;d.removeable=!1;""!==g.height&&(d.h=this.SVGlength2em(d,g.height,f,"h",0));""!==g.depth&&(d.d=this.SVGlength2em(d,g.depth,f,"d",0));""!==g.width&&(d.w=this.SVGlength2em(d,g.width,f,"w",0));d.h>d.H&&(d.H=d.h);d.d>d.D&&(d.D=d.d)}this.SVGhandleColor(d);this.SVGsaveData(d);return d},SVGlength2em:function(a,b,e,f,h){null==h&&(h=-d.BIGDIMEN);var g=String(b).match(/width|height|depth/),g=g?a[g[0].charAt(0)]:f?a[f]:0;e=d.length2em(b,e,g);return f&&String(b).match(/^\s*[-+]/)?Math.max(h,a[f]+e):e}});g.mrow.Augment({SVG:p.ROW,toSVG:function(){this.SVGgetStyles();var a=this.SVG();this.SVGhandleSpace(a);for(var b=0,d=this.data.length;b<d;b++)this.data[b]&&a.Check(this.data[b]);a.Stretch();a.Clean();this.SVGlineBreaks(a)&&(a=this.SVGmultiline(a));this.SVGhandleColor(a);this.SVGsaveData(a);return a},SVGlineBreaks:function(a){return this.parent.linebreakContainer?d.config.linebreaks.automatic&&a.w>d.linebreakWidth||this.hasNewline():!1},SVGmultiline:function(a){g.mbase.SVGautoloadFile("multiline")},SVGstretchH:function(a){a=this.data[this.core].SVGstretchH(a);this.SVGhandleColor(a);this.SVGsaveData(a);return a},SVGstretchV:function(a,b){var d=this.data[this.core].SVGstretchV(a,b);this.SVGhandleColor(d);this.SVGsaveData(d);return d}});g.mstyle.Augment({toSVG:function(){this.SVGgetStyles();var a=this.SVG();if(null!=this.data[0]){this.SVGhandleSpace(a);var b=a.Add(this.data[0].toSVG());a.Clean();b.ic&&(a.ic=b.ic);this.SVGhandleColor(a)}this.SVGsaveData(a);return a},SVGstretchH:function(a){return null!=this.data[0]?this.data[0].SVGstretchH(a):p.NULL()},SVGstretchV:function(a,b){return null!=this.data[0]?this.data[0].SVGstretchV(a,b):p.NULL()}});g.mfrac.Augment({toSVG:function(){this.SVGgetStyles();var a=this.SVG();this.SVGhandleSpace(a);var b=this.SVGchildSVG(0),e=this.SVGchildSVG(1),f=this.getValues("displaystyle","linethickness","numalign","denomalign","bevelled"),h=a.scale=this.SVGgetScale(),g=f.displaystyle,k=d.TeX.axis_height*h;if(f.bevelled){var f=g?400:150,n=d.createDelimiter(47,Math.max(b.h+b.d,e.h+e.d)+2*f);a.Add(b,0,(b.d-b.h)/2+k+f);a.Add(n,b.w-f/2,(n.d-n.h)/2+k);a.Add(e,b.w+n.w-f,(e.d-e.h)/2+k-f)}else{var n=Math.max(b.w,e.w),l=d.thickness2em(f.linethickness,h),u,w,v=d.TeX.min_rule_thickness/d.em*1E3;g?(u=d.TeX.num1,w=d.TeX.denom1):(u=0===l?d.TeX.num3:d.TeX.num2,w=d.TeX.denom2);u*=h;w*=h;0===l?(h=Math.max((g?7:3)*d.TeX.rule_thickness,2*v),g=u-b.d-(e.h-w),g<h&&(u+=(h-g)/2,w+=(h-g)/2),a.w=n,l=0):(h=Math.max((g?2:0)*v+l,l/2+1.5*v),g=u-b.d-(k+l/2),g<h&&(u+=h-g),g=k-l/2-(e.h-w),g<h&&(w+=h-g),a.Add(p.RECT(l/2,l/2,n+2*l),0,k));a.Align(b,f.numalign,l,u);a.Align(e,f.denomalign,l,-w)}a.Clean();this.SVGhandleColor(a);this.SVGsaveData(a);return a},SVGcanStretch:function(a){return!1},SVGhandleSpace:function(a){this.texWithDelims||(a.x=(this.useMMLspacing?0:d.length2em(this.texSpacing()||0))+120,a.X=120)}});g.msqrt.Augment({toSVG:function(){this.SVGgetStyles();var a=this.SVG();this.SVGhandleSpace(a);var b=this.SVGchildSVG(0),e,f,h=this.SVGgetScale(),g=d.TeX.rule_thickness*h,k,n,l=0;e=this.Get("displaystyle")?d.TeX.x_height*h:g;k=Math.max(g+e/4,1E3*d.TeX.min_root_space/d.em);n=b.h+b.d+k+g;f=d.createDelimiter(8730,n,h);f.h+f.d>n&&(k=(f.h+f.d-(n-g))/2);e=p.RECT(g,0,b.w);n=b.h+k+g;l=this.SVGaddRoot(a,f,l,f.h+f.d-n,h);a.Add(f,l,n-f.h);a.Add(e,l+f.w,n-e.h);a.Add(b,l+f.w,0);a.Clean();a.h+=g;a.H+=g;this.SVGhandleColor(a);this.SVGsaveData(a);return a},SVGaddRoot:function(a,b,d,e,f){return d}});g.mroot.Augment({toSVG:g.msqrt.prototype.toSVG,SVGaddRoot:function(a,b,d,e,f){var g=(b.isMultiChar?.55:.65)*b.w;if(this.data[1]){var k=this.data[1].toSVG();k.x=0;b=this.SVGrootHeight(b.h+b.d,f,k)-e;e=Math.min(k.w,k.r);d=Math.max(e,g);a.Add(k,d-e,b)}else g=d;return d-g},SVGrootHeight:function(a,b,d){return.45*(a-900*b)+600*b+Math.max(0,d.d-75)}});g.mfenced.Augment({SVG:p.ROW,toSVG:function(){this.SVGgetStyles();var a=this.SVG();this.SVGhandleSpace(a);this.data.open&&a.Check(this.data.open);null!=this.data[0]&&a.Check(this.data[0]);for(var b=1,d=this.data.length;b<d;b++)this.data[b]&&(this.data["sep"+b]&&a.Check(this.data["sep"+b]),a.Check(this.data[b]));this.data.close&&a.Check(this.data.close);a.Stretch();a.Clean();this.SVGhandleColor(a);this.SVGsaveData(a);return a}});g.menclose.Augment({toSVG:g.mbase.SVGautoload});g.maction.Augment({toSVG:g.mbase.SVGautoload});g.semantics.Augment({toSVG:function(){this.SVGgetStyles();var a=this.SVG();null!=this.data[0]&&(this.SVGhandleSpace(a),a.Add(this.data[0].toSVG()));a.Clean();this.SVGsaveData(a);return a},SVGstretchH:function(a){return null!=this.data[0]?this.data[0].SVGstretchH(a):p.NULL()},SVGstretchV:function(a,b){return null!=this.data[0]?this.data[0].SVGstretchV(a,b):p.NULL()}});g.munderover.Augment({toSVG:function(a,b){this.SVGgetStyles();var e=this.getValues("displaystyle","accent","accentunder","align");if(!e.displaystyle&&null!=this.data[this.base]&&this.data[this.base].CoreMO().Get("movablelimits"))return g.msubsup.prototype.toSVG.call(this);var f=this.SVG();this.SVGhandleSpace(f);var h=f.scale=this.SVGgetScale(),n=[],k=[],l,A,u=-d.BIGDIMEN,w=u;l=0;for(A=this.data.length;l<A;l++)null!=this.data[l]&&(l==this.base?(n[l]=this.SVGdataStretched(l,a,b),k[l]=(null!=b||null==a)&&this.data[l].SVGcanStretch("Horizontal")):(n[l]=this.data[l].toSVG(),k[l]=this.data[l].SVGcanStretch("Horizontal")),n[l].w>w&&(w=n[l].w),!k[l]&&w>u&&(u=w));null==b&&null!=a?u=a:u==-d.BIGDIMEN&&(u=w);l=w=0;for(A=this.data.length;l<A;l++)this.data[l]&&(k[l]&&(n[l]=this.data[l].SVGstretchH(u)),n[l].w>w&&(w=n[l].w));var u=d.TeX.rule_thickness,v=n[this.base]||{w:0,h:0,d:0,H:0,D:0,l:0,r:0,scale:h},x,B,z,F,y=0;v.ic&&(y=1.3*v.ic+.05);l=0;for(A=this.data.length;l<A;l++)null!=this.data[l]&&(k=n[l],F=d.TeX.big_op_spacing5*h,(z=l!=this.base&&e[this.ACCENTS[l]])&&1>=k.w&&(k.x=-k.l,n[l]=p.G().With({removeable:!1}),n[l].Add(k),n[l].Clean(),n[l].w=-k.l,k=n[l]),x={left:0,center:(w-k.w)/2,right:w-k.w}[e.align],B=0,l==this.over?(z?(z=u*h,F=0,v.skew&&(x+=v.skew)):(z=d.TeX.big_op_spacing1*h,B=d.TeX.big_op_spacing3*h,z=Math.max(z,B-Math.max(0,k.d))),z=Math.max(z,1500/d.em),x+=y/2,B=v.h+k.d+z,k.h+=F,k.h>k.H&&(k.H=k.h)):l==this.under&&(z?(z=3*u*h,F=0):(z=d.TeX.big_op_spacing2*h,B=d.TeX.big_op_spacing4*h,z=Math.max(z,B-k.h)),z=Math.max(z,1500/d.em),x-=y/2,B=-(v.d+k.h+z),k.d+=F,k.d>k.D&&(k.D=k.d)),f.Add(k,x,B));f.Clean();this.SVGhandleColor(f);this.SVGsaveData(f);return f}});g.msubsup.Augment({toSVG:function(a,b){this.SVGgetStyles();var e=this.SVG();this.SVGhandleSpace(e);var f=e.scale=this.SVGgetScale(),h=this.SVGgetMu(e),g=e.Add(this.SVGdataStretched(this.base,a,b)),k=(this.data[this.sup]||this.data[this.sub]||this).SVGgetScale(),n=d.TeX.x_height*f,l=d.TeX.scriptspace*f,p,w;this.SVGnotEmpty(this.data[this.sup])&&(p=this.data[this.sup].toSVG(),p.w+=l,p.r=Math.max(p.w,p.r));this.SVGnotEmpty(this.data[this.sub])&&(w=this.data[this.sub].toSVG(),w.w+=l,w.r=Math.max(w.w,w.r));var v=d.TeX.sup_drop*k,l=g.h+(g.y||0)-v,x=g.d-(g.y||0)+d.TeX.sub_drop*k,k=0;g.ic&&(g.w-=g.ic,k=1.3*g.ic+.05);!this.data[this.base]||"mi"!==this.data[this.base].type&&"mo"!==this.data[this.base].type||1!==this.data[this.base].data.join("").length||1!==g.scale||g.stretched||this.data[this.base].Get("largeop")||(l=x=0);var B=this.getValues("subscriptshift","superscriptshift");B.subscriptshift=""===B.subscriptshift?0:d.length2em(B.subscriptshift,h);B.superscriptshift=""===B.superscriptshift?0:d.length2em(B.superscriptshift,h);p?w?(x=Math.max(x,d.TeX.sub2*f),f*=d.TeX.rule_thickness,l-p.d-(w.h-x)<3*f&&(x=3*f-l+p.d+w.h,v=.8*n-(l-p.d),0<v&&(l+=v,x-=v)),e.Add(p,g.w+k,Math.max(l,B.superscriptshift)),e.Add(w,g.w,-Math.max(x,B.subscriptshift)),this.data[this.sup].SVGdata.dx=k,this.data[this.sup].SVGdata.dy=Math.max(l,B.superscriptshift),this.data[this.sub].SVGdata.dy=-Math.max(x,B.subscriptshift)):(values=this.getValues("displaystyle","texprimestyle"),w=d.TeX[values.displaystyle?"sup1":values.texprimestyle?"sup3":"sup2"],l=Math.max(l,w*f,p.d+.25*n,B.superscriptshift),e.Add(p,g.w+k,l),this.data[this.sup].SVGdata.dx=k,this.data[this.sup].SVGdata.dy=l):w&&(x=Math.max(x,d.TeX.sub1*f,w.h-.8*n,B.subscriptshift),e.Add(w,g.w,-x),this.data[this.sub].SVGdata.dy=-x);e.Clean();this.SVGhandleColor(e);this.SVGsaveData(e);return e}});g.mmultiscripts.Augment({toSVG:g.mbase.SVGautoload});g.mtable.Augment({toSVG:g.mbase.SVGautoload});g["annotation-xml"].Augment({toSVG:g.mbase.SVGautoload});g.math.Augment({SVG:p.Subclass({type:"svg",removeable:!1}),toSVG:function(a,b){if(this.data[0]){this.SVGgetStyles();g.mbase.prototype.displayAlign=f.config.displayAlign;g.mbase.prototype.displayIndent=f.config.displayIndent;var m=p.G({stroke:"black",fill:"black","stroke-width":0,transform:"matrix(1 0 0 -1 0 0)"}).With({removeable:!1});m.Add(this.data[0].toSVG(),0,0,!0);m.Clean();this.SVGhandleColor(m);var l=this.SVG();l.element.setAttribute("xmlns:xlink","http://www.w3.org/1999/xlink");l.Add(m);l.Clean();this.SVGsaveData(l);var h=Math.max(-l.l,0),n=Math.max(l.r-l.w,0),m=l.element.style;m.width=d.Ex(h+l.w+n);m.height=d.Ex(l.H+l.D+2*d.em);m.verticalAlign=d.Ex(-l.D-3*d.em);m.marginLeft=d.Ex(-h);m.marginRight=d.Ex(-n);l.element.setAttribute("viewBox",-h+" "+(-l.H-d.em)+" "+(h+l.w+n)+" "+(l.H+l.D+2*d.em));l.element.style.margin="1px 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a}});g.TeXAtom.Augment({toSVG:function(){this.SVGgetStyles();var a=this.SVG();this.SVGhandleSpace(a);if(null!=this.data[0]){var b=this.data[0].toSVG(),e=0;this.texClass===g.TEXCLASS.VCENTER&&(e=d.TeX.axis_height-(b.h+b.d)/2+b.d);a.Add(b,0,e);a.ic=b.ic}this.SVGhandleColor(a);this.SVGsaveData(a);return a}});f.Register.StartupHook("onLoad",function(){setTimeout(MathJax.Callback(["loadComplete",d,"jax.js"]),0)})});f.Browser.Select({Opera:function(a){d.Augment({operaZoomRefresh:!0})}});f.Register.StartupHook("End Cookie",function(){"None"!==f.config.menuSettings.zoom&&a.Require("[MathJax]/extensions/MathZoom.js")});document.createElementNS||(document.namespaces.svg||document.namespaces.add("svg","http://www.w3.org/2000/svg"),d.Augment({Element:function(a,b){var d="string"===typeof a?document.createElement("svg:"+a):a;d.isMathJax=!0;if(b)for(var e in b)b.hasOwnProperty(e)&&d.setAttribute(e,b[e].toString());return d}}))})(MathJax.Ajax,MathJax.Hub,MathJax.HTML,MathJax.OutputJax.SVG);MathJax.Hub.Register.StartupHook("SVG Jax Ready",function(){var a=MathJax.ElementJax.mml,f=MathJax.OutputJax.SVG,e=f.BBOX;a.mtable.Augment({toSVG:function(d){this.SVGgetStyles();d=this.SVG();if(0===this.data.length)return this.SVGsaveData(d),d;var g=this.getValues("columnalign","rowalign","columnspacing","rowspacing","columnwidth","equalcolumns","equalrows","columnlines","rowlines","frame","framespacing","align","useHeight","width","side","minlabelspacing");g.width.match(/%$/)&&(d.width=g.width=Math.floor(f.cwidth*parseFloat(g.width)/100)+"px");var p=this.SVGgetScale(),n=this.SVGgetMu(d),l=[],c=[],b=[],m=[],t=[],h,r,k=-1,q,A,u,w,v,x,B=f.FONTDATA.baselineskip*p*g.useHeight,z=f.FONTDATA.lineH*p,F=f.FONTDATA.lineD*p;h=0;for(q=this.data.length;h<q;h++)for(w=this.data[h],u="mlabeledtr"===w.type?-1:0,m[h]=[],l[h]=c[h]=0,r=u,A=w.data.length+u;r<A;r++){null==b[r]&&(r>k&&(k=r),t[r]=e.G(),b[r]=-f.BIGDIMEN);v=w.data[r-u];m[h][r]=v.toSVG();if(v.isEmbellished()){x=v.CoreMO();var y=x.Get("minsize",!0);if(y)if(x.SVGcanStretch("Vertical")){if(v=x.SVGdata.h+x.SVGdata.d)y=f.length2em(y,n,v),y*x.SVGdata.h/v>l[r]&&(l[r]=y*x.SVGdata.h/v),y*x.SVGdata.d/v>c[r]&&(c[r]=y*x.SVGdata.d/v)}else x.SVGcanStretch("Horizontal")&&(y=f.length2em(y,n,x.SVGdata.w),y>b[r]&&(b[r]=y))}m[h][r].h>l[h]&&(l[h]=m[h][r].h);m[h][r].d>c[h]&&(c[h]=m[h][r].d);m[h][r].w>b[r]&&(b[r]=m[h][r].w)}l[0]+c[0]&&(l[0]=Math.max(l[0],z));l[m.length-1]+c[m.length-1]&&(c[m.length-1]=Math.max(c[m.length-1],F));var E=MathJax.Hub.SplitList,y=E(g.columnspacing),z=E(g.rowspacing);A=E(g.columnalign);var D=E(g.rowalign),J=E(g.columnlines),F=E(g.rowlines);r=E(g.columnwidth);var I=[];h=0;for(q=y.length;h<q;h++)y[h]=f.length2em(y[h],n);h=0;for(q=z.length;h<q;h++)z[h]=f.length2em(z[h],n);for(;y.length<k;)y.push(y[y.length-1]);for(;A.length<=k;)A.push(A[A.length-1]);for(;J.length<k;)J.push(J[J.length-1]);for(;r.length<=k;)r.push(r[r.length-1]);for(;z.length<m.length;)z.push(z[z.length-1]);for(;D.length<=m.length;)D.push(D[D.length-1]);for(;F.length<m.length;)F.push(F[F.length-1]);t[-1]&&(A[-1]="l"===g.side.substr(0,1)?"left":"right",y[-1]=-b[-1]);h=0;for(q=m.length;h<q;h++)if(w=this.data[h],I[h]=[],w.rowalign&&(D[h]=w.rowalign),w.columnalign)for(I[h]=E(w.columnalign);I[h].length<=k;)I[h].push(I[h][I[h].length-1]);if(g.equalrows){w=Math.max.apply(Math,l);var 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