/*
 *  /MathJax/config/MML_SVG-full.js
 *  
 *  Copyright (c) 2010-2018 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/MathML/config.js",
  "[MathJax]/jax/output/SVG/config.js",
  "[MathJax]/jax/output/PreviewHTML/config.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]/jax/input/MathML/jax.js",
  "[MathJax]/jax/output/SVG/jax.js",
  "[MathJax]/jax/output/SVG/autoload/mtable.js",
  "[MathJax]/jax/output/PreviewHTML/jax.js",
  "[MathJax]/extensions/fast-preview.js",
  "[MathJax]/extensions/AssistiveMML.js",
  "[MathJax]/extensions/a11y/accessibility-menu.js"
);

MathJax.Hub.Config({
  extensions: ['[a11y]/accessibility-menu.js']
});

MathJax.InputJax.MathML=MathJax.InputJax({id:"MathML",version:"2.7.5",directory:MathJax.InputJax.directory+"/MathML",extensionDir:MathJax.InputJax.extensionDir+"/MathML",entityDir:MathJax.InputJax.directory+"/MathML/entities",config:{useMathMLspacing:false}});MathJax.InputJax.MathML.Register("math/mml");MathJax.InputJax.MathML.loadComplete("config.js");
MathJax.OutputJax.SVG=MathJax.OutputJax({id:"SVG",version:"2.7.5",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:1,mtextFontInherit:false,undefinedFamily:"STIXGeneral,'Arial Unicode MS',serif",addMMLclasses:false,useFontCache:true,useGlobalCache:true,EqnChunk:(MathJax.Hub.Browser.isMobile?10:50),EqnChunkFactor:1.5,EqnChunkDelay:100,linebreaks:{automatic:false,width:"container"},merrorStyle:{fontSize:"90%",color:"#C00",background:"#FF8",border:"1px solid #C00",padding:"3px"},styles:{".MathJax_SVG_Display":{"text-align":"center",margin:"1em 0em"},".MathJax_SVG .MJX-monospace":{"font-family":"monospace"},".MathJax_SVG .MJX-sans-serif":{"font-family":"sans-serif"},"#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}}}});if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax.SVG.Register("jax/mml")}MathJax.OutputJax.SVG.loadComplete("config.js");
MathJax.OutputJax.PreviewHTML=MathJax.OutputJax({id:"PreviewHTML",version:"2.7.5",directory:MathJax.OutputJax.directory+"/PreviewHTML",extensionDir:MathJax.OutputJax.extensionDir+"/PreviewHTML",noFastPreview:true,config:{scale:100,minScaleAdjust:50,mtextFontInherit:false,linebreaks:{automatic:false,width:"container"}}});if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax.PreviewHTML.Register("jax/mml")}MathJax.OutputJax.PreviewHTML.loadComplete("config.js");
MathJax.Extension.mml2jax={version:"2.7.5",config:{preview:"mathml"},MMLnamespace:"http://www.w3.org/1998/Math/MathML",PreProcess:function(e){if(!this.configured){this.config=MathJax.Hub.CombineConfig("mml2jax",this.config);if(this.config.Augment){MathJax.Hub.Insert(this,this.config.Augment)}this.InitBrowser();this.configured=true}if(typeof(e)==="string"){e=document.getElementById(e)}if(!e){e=document.body}var h=[];this.PushMathElements(h,e,"math");this.PushMathElements(h,e,"math",this.MMLnamespace);var d,b;if(typeof(document.namespaces)!=="undefined"){try{for(d=0,b=document.namespaces.length;d<b;d++){var f=document.namespaces[d];if(f.urn===this.MMLnamespace){this.PushMathElements(h,e,f.name+":math")}}}catch(g){}}else{var c=document.getElementsByTagName("html")[0];if(c){for(d=0,b=c.attributes.length;d<b;d++){var a=c.attributes[d];if(a.nodeName.substr(0,6)==="xmlns:"&&a.nodeValue===this.MMLnamespace){this.PushMathElements(h,e,a.nodeName.substr(6)+":math")}}}}this.ProcessMathArray(h)},PushMathElements:function(f,d,a,c){var h,g=MathJax.Hub.config.preRemoveClass;if(c){if(!d.getElementsByTagNameNS){return}h=d.getElementsByTagNameNS(c,a)}else{h=d.getElementsByTagName(a)}for(var e=0,b=h.length;e<b;e++){var j=h[e].parentNode;if(j&&j.className!==g&&!j.isMathJax&&!h[e].prefix===!c){f.push(h[e])}}},ProcessMathArray:function(c){var b,a=c.length;if(a){if(this.MathTagBug){for(b=0;b<a;b++){if(c[b].nodeName==="MATH"){this.ProcessMathFlattened(c[b])}else{this.ProcessMath(c[b])}}}else{for(b=0;b<a;b++){this.ProcessMath(c[b])}}}},ProcessMath:function(e){var d=e.parentNode;if(!d||d.className===MathJax.Hub.config.preRemoveClass){return}var a=document.createElement("script");a.type="math/mml";d.insertBefore(a,e);if(this.AttributeBug){var b=this.OuterHTML(e);if(this.CleanupHTML){b=b.replace(/<\?import .*?>/i,"").replace(/<\?xml:namespace .*?\/>/i,"");b=b.replace(/&nbsp;/g,"&#xA0;")}MathJax.HTML.setScript(a,b);d.removeChild(e)}else{var c=MathJax.HTML.Element("span");c.appendChild(e);MathJax.HTML.setScript(a,c.innerHTML)}if(this.config.preview!=="none"){this.createPreview(e,a)}},ProcessMathFlattened:function(f){var d=f.parentNode;if(!d||d.className===MathJax.Hub.config.preRemoveClass){return}var b=document.createElement("script");b.type="math/mml";d.insertBefore(b,f);var c="",e,a=f;while(f&&f.nodeName!=="/MATH"){e=f;f=f.nextSibling;c+=this.NodeHTML(e);e.parentNode.removeChild(e)}if(f&&f.nodeName==="/MATH"){f.parentNode.removeChild(f)}b.text=c+"</math>";if(this.config.preview!=="none"){this.createPreview(a,b)}},NodeHTML:function(e){var c,b,a;if(e.nodeName==="#text"){c=this.quoteHTML(e.nodeValue)}else{if(e.nodeName==="#comment"){c="<!--"+e.nodeValue+"-->"}else{c="<"+e.nodeName.toLowerCase();for(b=0,a=e.attributes.length;b<a;b++){var d=e.attributes[b];if(d.specified&&d.nodeName.substr(0,10)!=="_moz-math-"){c+=" "+d.nodeName.toLowerCase().replace(/xmlns:xmlns/,"xmlns")+"=";var f=d.nodeValue;if(f==null&&d.nodeName==="style"&&e.style){f=e.style.cssText}c+='"'+this.quoteHTML(f)+'"'}}c+=">";if(e.outerHTML!=null&&e.outerHTML.match(/(.<\/[A-Z]+>|\/>)$/)){for(b=0,a=e.childNodes.length;b<a;b++){c+=this.OuterHTML(e.childNodes[b])}c+="</"+e.nodeName.toLowerCase()+">"}}}return c},OuterHTML:function(d){if(d.nodeName.charAt(0)==="#"){return this.NodeHTML(d)}if(!this.AttributeBug){return d.outerHTML}var c=this.NodeHTML(d);for(var b=0,a=d.childNodes.length;b<a;b++){c+=this.OuterHTML(d.childNodes[b])}c+="</"+d.nodeName.toLowerCase()+">";return c},quoteHTML:function(a){if(a==null){a=""}return a.replace(/&/g,"&#x26;").replace(/</g,"&lt;").replace(/>/g,"&gt;").replace(/\"/g,"&quot;")},createPreview:function(g,f){var e=this.config.preview;if(e==="none"){return}var i=false;var c=MathJax.Hub.config.preRemoveClass;if((f.previousSibling||{}).className===c){return}if(e==="mathml"){i=true;if(this.MathTagBug){e="alttext"}else{e=g.cloneNode(true)}}if(e==="alttext"||e==="altimg"){i=true;var d=this.filterPreview(g.getAttribute("alttext"));if(e==="alttext"){if(d!=null){e=MathJax.HTML.TextNode(d)}else{e=null}}else{var a=g.getAttribute("altimg");if(a!=null){var b={width:g.getAttribute("altimg-width"),height:g.getAttribute("altimg-height")};e=MathJax.HTML.Element("img",{src:a,alt:d,style:b})}else{e=null}}}if(e){var h;if(i){h=MathJax.HTML.Element("span",{className:c});h.appendChild(e)}else{h=MathJax.HTML.Element("span",{className:c},e)}f.parentNode.insertBefore(h,f)}},filterPreview:function(a){return a},InitBrowser:function(){var b=MathJax.HTML.Element("span",{id:"<",className:"mathjax",innerHTML:"<math><mi>x</mi><mspace /></math>"});var a=b.outerHTML||"";this.AttributeBug=a!==""&&!(a.match(/id="&lt;"/)&&a.match(/class="mathjax"/)&&a.match(/<\/math>/));this.MathTagBug=b.childNodes.length>1;this.CleanupHTML=MathJax.Hub.Browser.isMSIE}};MathJax.Hub.Register.PreProcessor(["PreProcess",MathJax.Extension.mml2jax],5);MathJax.Ajax.loadComplete("[MathJax]/extensions/mml2jax.js");
(function(d,h,l,g,m,b,j){var p="2.7.5";var i=MathJax.Extension;var c=i.MathEvents={version:p};var k=d.config.menuSettings;var o={hover:500,frame:{x:3.5,y:5,bwidth:1,bcolor:"#A6D",hwidth:"15px",hcolor:"#83A"},button:{x:-6,y:-3,wx:-2},fadeinInc:0.2,fadeoutInc:0.05,fadeDelay:50,fadeoutStart:400,fadeoutDelay:15*1000,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_Menu_Button .MathJax_Hover_Arrow":{position:"absolute",cursor:"pointer",display:"inline-block",border:"2px solid #AAA","border-radius":"4px","-webkit-border-radius":"4px","-moz-border-radius":"4px","-khtml-border-radius":"4px","font-family":"'Courier New',Courier","font-size":"9px",color:"#F0F0F0"},".MathJax_Menu_Button .MathJax_Hover_Arrow span":{display:"block","background-color":"#AAA",border:"1px solid","border-radius":"3px","line-height":0,padding:"4px"},".MathJax_Hover_Arrow:hover":{color:"white!important",border:"2px solid #CCC!important"},".MathJax_Hover_Arrow:hover span":{"background-color":"#CCC!important"}}};var n=c.Event={LEFTBUTTON:0,RIGHTBUTTON:2,MENUKEY:"altKey",KEY:{RETURN:13,ESCAPE:27,SPACE:32,LEFT:37,UP:38,RIGHT:39,DOWN:40},Mousedown:function(q){return n.Handler(q,"Mousedown",this)},Mouseup:function(q){return n.Handler(q,"Mouseup",this)},Mousemove:function(q){return n.Handler(q,"Mousemove",this)},Mouseover:function(q){return n.Handler(q,"Mouseover",this)},Mouseout:function(q){return n.Handler(q,"Mouseout",this)},Click:function(q){return n.Handler(q,"Click",this)},DblClick:function(q){return n.Handler(q,"DblClick",this)},Menu:function(q){return n.Handler(q,"ContextMenu",this)},Handler:function(t,r,s){if(l.loadingMathMenu){return n.False(t)}var q=b[s.jaxID];if(!t){t=window.event}t.isContextMenu=(r==="ContextMenu");if(q[r]){return q[r](t,s)}if(i.MathZoom){return i.MathZoom.HandleEvent(t,r,s)}},False:function(q){if(!q){q=window.event}if(q){if(q.preventDefault){q.preventDefault()}else{q.returnValue=false}if(q.stopPropagation){q.stopPropagation()}q.cancelBubble=true}return false},Keydown:function(r,q){if(!r){r=window.event}if(r.keyCode===n.KEY.SPACE){n.ContextMenu(r,this)}},ContextMenu:function(t,E,w){var B=b[E.jaxID],v=B.getJaxFromMath(E);var F=(B.config.showMathMenu!=null?B:d).config.showMathMenu;if(!F||(k.context!=="MathJax"&&!w)){return}if(c.msieEventBug){t=window.event||t}n.ClearSelection();f.ClearHoverTimer();if(v.hover){if(v.hover.remove){clearTimeout(v.hover.remove);delete v.hover.remove}v.hover.nofade=true}var u=MathJax.Menu;var G,D;if(u){if(u.loadingDomain){return n.False(t)}G=m.loadDomain("MathMenu");if(!G){u.jax=v;var r=u.menu.Find("Show Math As").submenu;r.items[0].name=v.sourceMenuTitle;r.items[0].format=(v.sourceMenuFormat||"MathML");r.items[1].name=j[v.inputJax].sourceMenuTitle;r.items[5].disabled=!j[v.inputJax].annotationEncoding;var A=r.items[2];A.disabled=true;var q=A.submenu.items;annotationList=MathJax.Hub.Config.semanticsAnnotations;for(var z=0,y=q.length;z<y;z++){var s=q[z].name[1];if(v.root&&v.root.getAnnotation(s)!==null){A.disabled=false;q[z].hidden=false}else{q[z].hidden=true}}var x=u.menu.Find("Math Settings","MathPlayer");x.hidden=!(v.outputJax==="NativeMML"&&d.Browser.hasMathPlayer);return u.menu.Post(t)}u.loadingDomain=true;D=function(){delete u.loadingDomain}}else{if(l.loadingMathMenu){return n.False(t)}l.loadingMathMenu=true;G=l.Require("[MathJax]/extensions/MathMenu.js");D=function(){delete l.loadingMathMenu;if(!MathJax.Menu){MathJax.Menu={}}}}var C={pageX:t.pageX,pageY:t.pageY,clientX:t.clientX,clientY:t.clientY};g.Queue(G,D,["ContextMenu",n,C,E,w]);return n.False(t)},AltContextMenu:function(s,r){var t=b[r.jaxID];var q=(t.config.showMathMenu!=null?t:d).config.showMathMenu;if(q){q=(t.config.showMathMenuMSIE!=null?t:d).config.showMathMenuMSIE;if(k.context==="MathJax"&&!k.mpContext&&q){if(!c.noContextMenuBug||s.button!==n.RIGHTBUTTON){return}}else{if(!s[n.MENUKEY]||s.button!==n.LEFTBUTTON){return}}return t.ContextMenu(s,r,true)}},ClearSelection:function(){if(c.safariContextMenuBug){setTimeout("window.getSelection().empty()",0)}if(document.selection){setTimeout("document.selection.empty()",0)}},getBBox:function(s){s.appendChild(c.topImg);var r=c.topImg.offsetTop,t=s.offsetHeight-r,q=s.offsetWidth;s.removeChild(c.topImg);return{w:q,h:r,d:t}}};var f=c.Hover={Mouseover:function(s,r){if(k.discoverable||k.zoom==="Hover"){var u=s.fromElement||s.relatedTarget,t=s.toElement||s.target;if(u&&t&&(d.isMathJaxNode(u)!==d.isMathJaxNode(t)||d.getJaxFor(u)!==d.getJaxFor(t))){var q=this.getJaxFromMath(r);if(q.hover){f.ReHover(q)}else{f.HoverTimer(q,r)}return n.False(s)}}},Mouseout:function(s,r){if(k.discoverable||k.zoom==="Hover"){var u=s.fromElement||s.relatedTarget,t=s.toElement||s.target;if(u&&t&&(d.isMathJaxNode(u)!==d.isMathJaxNode(t)||d.getJaxFor(u)!==d.getJaxFor(t))){var q=this.getJaxFromMath(r);if(q.hover){f.UnHover(q)}else{f.ClearHoverTimer()}return n.False(s)}}},Mousemove:function(s,r){if(k.discoverable||k.zoom==="Hover"){var q=this.getJaxFromMath(r);if(q.hover){return}if(f.lastX==s.clientX&&f.lastY==s.clientY){return}f.lastX=s.clientX;f.lastY=s.clientY;f.HoverTimer(q,r);return n.False(s)}},HoverTimer:function(q,r){this.ClearHoverTimer();this.hoverTimer=setTimeout(g(["Hover",this,q,r]),o.hover)},ClearHoverTimer:function(){if(this.hoverTimer){clearTimeout(this.hoverTimer);delete this.hoverTimer}},Hover:function(q,u){if(i.MathZoom&&i.MathZoom.Hover({},u)){return}var t=b[q.outputJax],v=t.getHoverSpan(q,u),y=t.getHoverBBox(q,v,u),w=(t.config.showMathMenu!=null?t:d).config.showMathMenu;var A=o.frame.x,z=o.frame.y,x=o.frame.bwidth;if(c.msieBorderWidthBug){x=0}q.hover={opacity:0,id:q.inputID+"-Hover"};var r=h.Element("span",{id:q.hover.id,isMathJax:true,style:{display:"inline-block",width:0,height:0,position:"relative"}},[["span",{className:"MathJax_Hover_Frame",isMathJax:true,style:{display:"inline-block",position:"absolute",top:this.Px(-y.h-z-x-(y.y||0)),left:this.Px(-A-x+(y.x||0)),width:this.Px(y.w+2*A),height:this.Px(y.h+y.d+2*z),opacity:0,filter:"alpha(opacity=0)"}}]]);var s=h.Element("span",{isMathJax:true,id:q.hover.id+"Menu",className:"MathJax_Menu_Button",style:{display:"inline-block","z-index":1,width:0,height:0,position:"relative"}},[["span",{className:"MathJax_Hover_Arrow",isMathJax:true,math:u,onclick:this.HoverMenu,jax:t.id,style:{left:this.Px(y.w+A+x+(y.x||0)+o.button.x),top:this.Px(-y.h-z-x-(y.y||0)-o.button.y),opacity:0,filter:"alpha(opacity=0)"}},[["span",{isMathJax:true},"\u25BC"]]]]);if(y.width){r.style.width=s.style.width=y.width;r.style.marginRight=s.style.marginRight="-"+y.width;r.firstChild.style.width=y.width;s.firstChild.style.left="";s.firstChild.style.right=this.Px(o.button.wx)}v.parentNode.insertBefore(r,v);if(w){v.parentNode.insertBefore(s,v)}if(v.style){v.style.position="relative"}this.ReHover(q)},ReHover:function(q){if(q.hover.remove){clearTimeout(q.hover.remove)}q.hover.remove=setTimeout(g(["UnHover",this,q]),o.fadeoutDelay);this.HoverFadeTimer(q,o.fadeinInc)},UnHover:function(q){if(!q.hover.nofade){this.HoverFadeTimer(q,-o.fadeoutInc,o.fadeoutStart)}},HoverFade:function(q){delete q.hover.timer;q.hover.opacity=Math.max(0,Math.min(1,q.hover.opacity+q.hover.inc));q.hover.opacity=Math.floor(1000*q.hover.opacity)/1000;var s=document.getElementById(q.hover.id),r=document.getElementById(q.hover.id+"Menu");s.firstChild.style.opacity=q.hover.opacity;s.firstChild.style.filter="alpha(opacity="+Math.floor(100*q.hover.opacity)+")";if(r){r.firstChild.style.opacity=q.hover.opacity;r.firstChild.style.filter=s.style.filter}if(q.hover.opacity===1){return}if(q.hover.opacity>0){this.HoverFadeTimer(q,q.hover.inc);return}s.parentNode.removeChild(s);if(r){r.parentNode.removeChild(r)}if(q.hover.remove){clearTimeout(q.hover.remove)}delete q.hover},HoverFadeTimer:function(q,s,r){q.hover.inc=s;if(!q.hover.timer){q.hover.timer=setTimeout(g(["HoverFade",this,q]),(r||o.fadeDelay))}},HoverMenu:function(q){if(!q){q=window.event}return b[this.jax].ContextMenu(q,this.math,true)},ClearHover:function(q){if(q.hover.remove){clearTimeout(q.hover.remove)}if(q.hover.timer){clearTimeout(q.hover.timer)}f.ClearHoverTimer();delete q.hover},Px:function(q){if(Math.abs(q)<0.006){return"0px"}return q.toFixed(2).replace(/\.?0+$/,"")+"px"},getImages:function(){if(k.discoverable){var q=new Image();q.src=o.button.src}}};var a=c.Touch={last:0,delay:500,start:function(r){var q=new Date().getTime();var s=(q-a.last<a.delay&&a.up);a.last=q;a.up=false;if(s){a.timeout=setTimeout(a.menu,a.delay,r,this);r.preventDefault()}},end:function(r){var q=new Date().getTime();a.up=(q-a.last<a.delay);if(a.timeout){clearTimeout(a.timeout);delete a.timeout;a.last=0;a.up=false;r.preventDefault();return n.Handler((r.touches[0]||r.touch),"DblClick",this)}},menu:function(r,q){delete a.timeout;a.last=0;a.up=false;return n.Handler((r.touches[0]||r.touch),"ContextMenu",q)}};d.Browser.Select({MSIE:function(q){var s=(document.documentMode||0);var r=q.versionAtLeast("8.0");c.msieBorderWidthBug=(document.compatMode==="BackCompat");c.msieEventBug=q.isIE9;c.msieAlignBug=(!r||s<8);if(s<9){n.LEFTBUTTON=1}},Safari:function(q){c.safariContextMenuBug=true},Opera:function(q){c.operaPositionBug=true},Konqueror:function(q){c.noContextMenuBug=true}});c.topImg=(c.msieAlignBug?h.Element("img",{style:{width:0,height:0,position:"relative"},src:"about:blank"}):h.Element("span",{style:{width:0,height:0,display:"inline-block"}}));if(c.operaPositionBug){c.topImg.style.border="1px solid"}c.config=o=d.CombineConfig("MathEvents",o);var e=function(){var q=o.styles[".MathJax_Hover_Frame"];q.border=o.frame.bwidth+"px solid "+o.frame.bcolor+" ! important";q["box-shadow"]=q["-webkit-box-shadow"]=q["-moz-box-shadow"]=q["-khtml-box-shadow"]="0px 0px "+o.frame.hwidth+" "+o.frame.hcolor};g.Queue(d.Register.StartupHook("End Config",{}),[e],["getImages",f],["Styles",l,o.styles],["Post",d.Startup.signal,"MathEvents Ready"],["loadComplete",l,"[MathJax]/extensions/MathEvents.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.Callback,MathJax.Localization,MathJax.OutputJax,MathJax.InputJax);
(function(a,d,f,c,j){var k="2.7.5";var i=a.CombineConfig("MathZoom",{styles:{"#MathJax_Zoom":{position:"absolute","background-color":"#F0F0F0",overflow:"auto",display:"block","z-index":301,padding:".5em",border:"1px solid black",margin:0,"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","-webkit-box-sizing":"content-box","-moz-box-sizing":"content-box","box-sizing":"content-box","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)"},"#MathJax_ZoomFrame":{position:"relative",display:"inline-block",height:0,width:0},"#MathJax_ZoomEventTrap":{position:"absolute",left:0,top:0,"z-index":302,display:"inline-block",border:0,padding:0,margin:0,"background-color":"white",opacity:0,filter:"alpha(opacity=0)"}}});var e,b,g;MathJax.Hub.Register.StartupHook("MathEvents Ready",function(){g=MathJax.Extension.MathEvents.Event;e=MathJax.Extension.MathEvents.Event.False;b=MathJax.Extension.MathEvents.Hover});var h=MathJax.Extension.MathZoom={version:k,settings:a.config.menuSettings,scrollSize:18,HandleEvent:function(n,l,m){if(h.settings.CTRL&&!n.ctrlKey){return true}if(h.settings.ALT&&!n.altKey){return true}if(h.settings.CMD&&!n.metaKey){return true}if(h.settings.Shift&&!n.shiftKey){return true}if(!h[l]){return true}return h[l](n,m)},Click:function(m,l){if(this.settings.zoom==="Click"){return this.Zoom(m,l)}},DblClick:function(m,l){if(this.settings.zoom==="Double-Click"||this.settings.zoom==="DoubleClick"){return this.Zoom(m,l)}},Hover:function(m,l){if(this.settings.zoom==="Hover"){this.Zoom(m,l);return true}return false},Zoom:function(o,u){this.Remove();b.ClearHoverTimer();g.ClearSelection();var s=MathJax.OutputJax[u.jaxID];var p=s.getJaxFromMath(u);if(p.hover){b.UnHover(p)}var q=this.findContainer(u);var l=Math.floor(0.85*q.clientWidth),t=Math.max(document.body.clientHeight,document.documentElement.clientHeight);if(this.getOverflow(q)!=="visible"){t=Math.min(q.clientHeight,t)}t=Math.floor(0.85*t);var n=d.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}},[["span",{style:{display:"inline-block","white-space":"nowrap"}}]]]]);var z=n.lastChild,w=z.firstChild,r=n.firstChild;u.parentNode.insertBefore(n,u);u.parentNode.insertBefore(u,n);if(w.addEventListener){w.addEventListener("mousedown",this.Remove,true)}var m=z.offsetWidth||z.clientWidth;l-=m;t-=m;z.style.maxWidth=l+"px";z.style.maxHeight=t+"px";if(this.msieTrapEventBug){var y=d.Element("span",{id:"MathJax_ZoomEventTrap",onmousedown:this.Remove});n.insertBefore(y,z)}if(this.msieZIndexBug){var v=d.addElement(document.body,"img",{src:"about:blank",id:"MathJax_ZoomTracker",width:0,height:0,style:{width:0,height:0,position:"relative"}});n.style.position="relative";n.style.zIndex=i.styles["#MathJax_ZoomOverlay"]["z-index"];n=v}var x=s.Zoom(p,w,u,l,t);if(this.msiePositionBug){if(this.msieSizeBug){z.style.height=x.zH+"px";z.style.width=x.zW+"px"}if(z.offsetHeight>t){z.style.height=t+"px";z.style.width=(x.zW+this.scrollSize)+"px"}if(z.offsetWidth>l){z.style.width=l+"px";z.style.height=(x.zH+this.scrollSize)+"px"}}if(this.operaPositionBug){z.style.width=Math.min(l,x.zW)+"px"}if(z.offsetWidth>m&&z.offsetWidth-m<l&&z.offsetHeight-m<t){z.style.overflow="visible"}this.Position(z,x);if(this.msieTrapEventBug){y.style.height=z.clientHeight+"px";y.style.width=z.clientWidth+"px";y.style.left=(parseFloat(z.style.left)+z.clientLeft)+"px";y.style.top=(parseFloat(z.style.top)+z.clientTop)+"px"}z.style.visibility="";if(this.settings.zoom==="Hover"){r.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}}a.signal.Post(["math zoomed",p]);return e(o)},Position:function(p,r){p.style.display="none";var q=this.Resize(),m=q.x,s=q.y,l=r.mW;p.style.display="";var o=-l-Math.floor((p.offsetWidth-l)/2),n=r.Y;p.style.left=Math.max(o,10-m)+"px";p.style.top=Math.max(n,10-s)+"px";if(!h.msiePositionBug){h.SetWH()}},Resize:function(m){if(h.onresize){h.onresize(m)}var q=document.getElementById("MathJax_ZoomFrame"),l=document.getElementById("MathJax_ZoomOverlay");var o=h.getXY(q),n=h.findContainer(q);if(h.getOverflow(n)!=="visible"){l.scroll_parent=n;var p=h.getXY(n);o.x-=p.x;o.y-=p.y;p=h.getBorder(n);o.x-=p.x;o.y-=p.y}l.style.left=(-o.x)+"px";l.style.top=(-o.y)+"px";if(h.msiePositionBug){setTimeout(h.SetWH,0)}else{h.SetWH()}return o},SetWH:function(){var l=document.getElementById("MathJax_ZoomOverlay");if(!l){return}l.style.display="none";var m=l.scroll_parent||document.documentElement||document.body;l.style.width=m.scrollWidth+"px";l.style.height=Math.max(m.clientHeight,m.scrollHeight)+"px";l.style.display=""},findContainer:function(l){l=l.parentNode;while(l.parentNode&&l!==document.body&&h.getOverflow(l)==="visible"){l=l.parentNode}return l},getOverflow:(window.getComputedStyle?function(l){return getComputedStyle(l).overflow}:function(l){return(l.currentStyle||{overflow:"visible"}).overflow}),getBorder:function(o){var m={thin:1,medium:2,thick:3};var n=(window.getComputedStyle?getComputedStyle(o):(o.currentStyle||{borderLeftWidth:0,borderTopWidth:0}));var l=n.borderLeftWidth,p=n.borderTopWidth;if(m[l]){l=m[l]}else{l=parseInt(l)}if(m[p]){p=m[p]}else{p=parseInt(p)}return{x:l,y:p}},getXY:function(o){var l=0,n=0,m;m=o;while(m.offsetParent){l+=m.offsetLeft;m=m.offsetParent}if(h.operaPositionBug){o.style.border="1px solid"}m=o;while(m.offsetParent){n+=m.offsetTop;m=m.offsetParent}if(h.operaPositionBug){o.style.border=""}return{x:l,y:n}},Remove:function(n){var p=document.getElementById("MathJax_ZoomFrame");if(p){var o=MathJax.OutputJax[p.previousSibling.jaxID];var l=o.getJaxFromMath(p.previousSibling);a.signal.Post(["math unzoomed",l]);p.parentNode.removeChild(p);p=document.getElementById("MathJax_ZoomTracker");if(p){p.parentNode.removeChild(p)}if(h.operaRefreshBug){var m=d.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(m)}if(window.removeEventListener){removeEventListener("resize",h.Resize,false)}else{if(window.detachEvent){detachEvent("onresize",h.Resize)}else{window.onresize=h.onresize;delete h.onresize}}}return e(n)}};a.Browser.Select({MSIE:function(l){var n=(document.documentMode||0);var m=(n>=9);h.msiePositionBug=!m;h.msieSizeBug=l.versionAtLeast("7.0")&&(!document.documentMode||n===7||n===8);h.msieZIndexBug=(n<=7);h.msieInlineBlockAlignBug=(n<=7);h.msieTrapEventBug=!window.addEventListener;if(document.compatMode==="BackCompat"){h.scrollSize=52}if(m){delete i.styles["#MathJax_Zoom"].filter}},Opera:function(l){h.operaPositionBug=true;h.operaRefreshBug=true}});h.topImg=(h.msieInlineBlockAlignBug?d.Element("img",{style:{width:0,height:0,position:"relative"},src:"about:blank"}):d.Element("span",{style:{width:0,height:0,display:"inline-block"}}));if(h.operaPositionBug||h.msieTopBug){h.topImg.style.border="1px solid"}MathJax.Callback.Queue(["StartupHook",MathJax.Hub.Register,"Begin Styles",{}],["Styles",f,i.styles],["Post",a.Startup.signal,"MathZoom Ready"],["loadComplete",f,"[MathJax]/extensions/MathZoom.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.OutputJax["HTML-CSS"],MathJax.OutputJax.NativeMML);
(function(f,o,q,e,r){var p="2.7.5";var d=MathJax.Callback.Signal("menu");MathJax.Extension.MathMenu={version:p,signal:d};var t=function(u){return MathJax.Localization._.apply(MathJax.Localization,[["MathMenu",u]].concat([].slice.call(arguments,1)))};var i=MathJax.Object.isArray;var a=f.Browser.isPC,l=f.Browser.isMSIE,m=((document.documentMode||0)>8);var j=(a?null:"5px");var s=f.CombineConfig("MathMenu",{delay:150,showRenderer:true,showMathPlayer:true,showFontMenu:false,showContext:false,showDiscoverable:false,showLocale:true,showLocaleURL:false,semanticsAnnotations:{TeX:["TeX","LaTeX","application/x-tex"],StarMath:["StarMath 5.0"],Maple:["Maple"],ContentMathML:["MathML-Content","application/mathml-content+xml"],OpenMath:["OpenMath"]},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 2em","background-color":"#DDDDDD",color:"black",cursor:"default","font-family":"message-box","font-size":"120%","font-style":"normal","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":"15px","-webkit-border-radius":"15px","-moz-border-radius":"15px","-khtml-border-radius":"15px","box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},"#MathJax_About.MathJax_MousePost":{outline:"none"},".MathJax_Menu":{position:"absolute","background-color":"white",color:"black",width:"auto",padding:(a?"2px":"5px 0px"),border:"1px solid #CCCCCC",margin:0,cursor:"default",font:"menu","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","z-index":201,"border-radius":j,"-webkit-border-radius":j,"-moz-border-radius":j,"-khtml-border-radius":j,"box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},".MathJax_MenuItem":{padding:(a?"2px 2em":"1px 2em"),background:"transparent"},".MathJax_MenuArrow":{position:"absolute",right:".5em","padding-top":".25em",color:"#666666","font-family":(l?"'Arial unicode MS'":null),"font-size":".75em"},".MathJax_MenuActive .MathJax_MenuArrow":{color:"white"},".MathJax_MenuArrow.RTL":{left:".5em",right:"auto"},".MathJax_MenuCheck":{position:"absolute",left:".7em","font-family":(l?"'Arial unicode MS'":null)},".MathJax_MenuCheck.RTL":{right:".7em",left:"auto"},".MathJax_MenuRadioCheck":{position:"absolute",left:(a?"1em":".7em")},".MathJax_MenuRadioCheck.RTL":{right:(a?"1em":".7em"),left:"auto"},".MathJax_MenuLabel":{padding:(a?"2px 2em 4px 1.33em":"1px 2em 3px 1.33em"),"font-style":"italic"},".MathJax_MenuRule":{"border-top":(a?"1px solid #CCCCCC":"1px solid #DDDDDD"),margin:(a?"4px 1px 0px":"4px 3px")},".MathJax_MenuDisabled":{color:"GrayText"},".MathJax_MenuActive":{"background-color":(a?"Highlight":"#606872"),color:(a?"HighlightText":"white")},".MathJax_MenuDisabled:focus, .MathJax_MenuLabel:focus":{"background-color":"#E8E8E8"},".MathJax_ContextMenu:focus":{outline:"none"},".MathJax_ContextMenu .MathJax_MenuItem:focus":{outline:"none"},"#MathJax_AboutClose":{top:".2em",right:".2em"},".MathJax_Menu .MathJax_MenuClose":{top:"-10px",left:"-10px"},".MathJax_MenuClose":{position:"absolute",cursor:"pointer",display:"inline-block",border:"2px solid #AAA","border-radius":"18px","-webkit-border-radius":"18px","-moz-border-radius":"18px","-khtml-border-radius":"18px","font-family":"'Courier New',Courier","font-size":"24px",color:"#F0F0F0"},".MathJax_MenuClose span":{display:"block","background-color":"#AAA",border:"1.5px solid","border-radius":"18px","-webkit-border-radius":"18px","-moz-border-radius":"18px","-khtml-border-radius":"18px","line-height":0,padding:"8px 0 6px"},".MathJax_MenuClose:hover":{color:"white!important",border:"2px solid #CCC!important"},".MathJax_MenuClose:hover span":{"background-color":"#CCC!important"},".MathJax_MenuClose:hover:focus":{outline:"none"}}});var n,k,b;f.Register.StartupHook("MathEvents Ready",function(){n=MathJax.Extension.MathEvents.Event.False;k=MathJax.Extension.MathEvents.Hover;b=MathJax.Extension.MathEvents.Event.KEY});var h=MathJax.Object.Subclass({Keydown:function(u,v){switch(u.keyCode){case b.ESCAPE:this.Remove(u,v);break;case b.RIGHT:this.Right(u,v);break;case b.LEFT:this.Left(u,v);break;case b.UP:this.Up(u,v);break;case b.DOWN:this.Down(u,v);break;case b.RETURN:case b.SPACE:this.Space(u,v);break;default:return;break}return n(u)},Escape:function(u,v){},Right:function(u,v){},Left:function(u,v){},Up:function(u,v){},Down:function(u,v){},Space:function(u,v){}},{});var g=MathJax.Menu=h.Subclass({version:p,items:[],posted:false,title:null,margin:5,Init:function(u){this.items=[].slice.call(arguments,0)},With:function(u){if(u){f.Insert(this,u)}return this},Post:function(M,E,B){if(!M){M=window.event||{}}var I=document.getElementById("MathJax_MenuFrame");if(!I){I=g.Background(this);delete c.lastItem;delete c.lastMenu;delete g.skipUp;d.Post(["post",g.jax]);g.isRTL=(MathJax.Localization.fontDirection()==="rtl")}var v=o.Element("div",{onmouseup:g.Mouseup,ondblclick:n,ondragstart:n,onselectstart:n,oncontextmenu:n,menuItem:this,className:"MathJax_Menu",onkeydown:g.Keydown,role:"menu"});if(M.type==="contextmenu"||M.type==="mouseover"){v.className+=" MathJax_ContextMenu"}if(!B){MathJax.Localization.setCSS(v)}for(var N=0,K=this.items.length;N<K;N++){this.items[N].Create(v)}if(g.isMobile){o.addElement(v,"span",{className:"MathJax_MenuClose",menu:E,ontouchstart:g.Close,ontouchend:n,onmousedown:g.Close,onmouseup:n},[["span",{},"\u00D7"]])}I.appendChild(v);this.posted=true;if(v.offsetWidth){v.style.width=(v.offsetWidth+2)+"px"}var H=M.pageX,F=M.pageY;var u=document.body.getBoundingClientRect();var C=(window.getComputedStyle?window.getComputedStyle(document.body):{marginLeft:"0px"});var A=u.right-Math.min(0,u.left)+parseFloat(C.marginLeft);if(!H&&!F&&"clientX" in M){H=M.clientX+document.body.scrollLeft+document.documentElement.scrollLeft;F=M.clientY+document.body.scrollTop+document.documentElement.scrollTop}if(!E){var L=g.CurrentNode()||M.target;if((M.type==="keydown"||(!H&&!F))&&L){var P=window.pageXOffset||document.documentElement.scrollLeft;var O=window.pageYOffset||document.documentElement.scrollTop;var w=L.getBoundingClientRect();H=(w.right+w.left)/2+P;F=(w.bottom+w.top)/2+O}if(H+v.offsetWidth>A-this.margin){H=A-v.offsetWidth-this.margin}if(g.isMobile){H=Math.max(5,H-Math.floor(v.offsetWidth/2));F-=20}g.skipUp=M.isContextMenu}else{var z="left",J=E.offsetWidth;H=(g.isMobile?30:J-2);F=0;while(E&&E!==I){H+=E.offsetLeft;F+=E.offsetTop;E=E.parentNode}if(!g.isMobile){if((g.isRTL&&H-J-v.offsetWidth>this.margin)||(!g.isRTL&&H+v.offsetWidth>A-this.margin)){z="right";H=Math.max(this.margin,H-J-v.offsetWidth+6)}}if(!a){v.style["borderRadiusTop"+z]=0;v.style["WebkitBorderRadiusTop"+z]=0;v.style["MozBorderRadiusTop"+z]=0;v.style["KhtmlBorderRadiusTop"+z]=0}}v.style.left=H+"px";v.style.top=F+"px";if(document.selection&&document.selection.empty){document.selection.empty()}var G=window.pageXOffset||document.documentElement.scrollLeft;var D=window.pageYOffset||document.documentElement.scrollTop;g.Focus(v);if(M.type==="keydown"){g.skipMouseoverFromKey=true;setTimeout(function(){delete g.skipMouseoverFromKey},s.delay)}window.scrollTo(G,D);return n(M)},Remove:function(u,v){d.Post(["unpost",g.jax]);var w=document.getElementById("MathJax_MenuFrame");if(w){w.parentNode.removeChild(w);if(this.msieFixedPositionBug){detachEvent("onresize",g.Resize)}}if(g.jax.hover){delete g.jax.hover.nofade;k.UnHover(g.jax)}g.Unfocus(v);if(u.type==="mousedown"){g.CurrentNode().blur()}return n(u)},Find:function(u){return this.FindN(1,u,[].slice.call(arguments,1))},FindId:function(u){return this.FindN(0,u,[].slice.call(arguments,1))},FindN:function(y,v,x){for(var w=0,u=this.items.length;w<u;w++){if(this.items[w].name[y]===v){if(x.length){if(!this.items[w].submenu){return null}return this.items[w].submenu.FindN(y,x[0],x.slice(1))}return this.items[w]}}return null},IndexOf:function(u){return this.IndexOfN(1,u)},IndexOfId:function(u){return this.IndexOfN(0,u)},IndexOfN:function(x,v){for(var w=0,u=this.items.length;w<u;w++){if(this.items[w].name[x]===v){return w}}return null},Right:function(u,v){g.Right(u,v)},Left:function(u,v){g.Left(u,v)},Up:function(v,w){var u=w.lastChild;u.menuItem.Activate(v,u)},Down:function(v,w){var u=w.firstChild;u.menuItem.Activate(v,u)},Space:function(u,v){this.Remove(u,v)}},{config:s,Remove:function(u){return g.Event(u,this,"Remove")},Mouseover:function(u){return g.Event(u,this,"Mouseover")},Mouseout:function(u){return g.Event(u,this,"Mouseout")},Mousedown:function(u){return g.Event(u,this,"Mousedown")},Mouseup:function(u){return g.Event(u,this,"Mouseup")},Keydown:function(u){return g.Event(u,this,"Keydown")},Touchstart:function(u){return g.Event(u,this,"Touchstart")},Touchend:function(u){return g.Event(u,this,"Touchend")},Close:function(u){return g.Event(u,this.menu||this.parentNode,(this.menu?"Touchend":"Remove"))},Event:function(w,y,u,x){if(g.skipMouseover&&u==="Mouseover"&&!x){return n(w)}if(g.skipMouseoverFromKey&&u==="Mouseover"){delete g.skipMouseoverFromKey;return n(w)}if(g.skipUp){if(u.match(/Mouseup|Touchend/)){delete g.skipUp;return n(w)}if(u==="Touchstart"||(u==="Mousedown"&&!g.skipMousedown)){delete g.skipUp}}if(!w){w=window.event}var v=y.menuItem;if(v&&v[u]){return v[u](w,y)}return null},BGSTYLE:{position:"absolute",left:0,top:0,"z-index":200,width:"100%",height:"100%",border:0,padding:0,margin:0},Background:function(v){var w=o.addElement(document.body,"div",{style:this.BGSTYLE,id:"MathJax_MenuFrame"},[["div",{style:this.BGSTYLE,menuItem:v,onmousedown:this.Remove}]]);var u=w.firstChild;if(g.msieBackgroundBug){u.style.backgroundColor="white";u.style.filter="alpha(opacity=0)"}if(g.msieFixedPositionBug){w.width=w.height=0;this.Resize();attachEvent("onresize",this.Resize)}else{u.style.position="fixed"}return w},Resize:function(){setTimeout(g.SetWH,0)},SetWH:function(){var u=document.getElementById("MathJax_MenuFrame");if(u){u=u.firstChild;u.style.width=u.style.height="1px";u.style.width=document.body.scrollWidth+"px";u.style.height=document.body.scrollHeight+"px"}},posted:false,active:null,GetNode:function(u){var v=document.getElementById(u.inputID+"-Frame");return v.isMathJax?v:v.firstChild},CurrentNode:function(){return g.GetNode(g.jax)},AllNodes:function(){var v=MathJax.Hub.getAllJax();var w=[];for(var x=0,u;u=v[x];x++){w.push(g.GetNode(u))}return w},ActiveNode:function(){return g.active},FocusNode:function(u){g.active=u;u.focus()},Focus:function(u){!g.posted?g.Activate(u):g.ActiveNode().tabIndex=-1;u.tabIndex=0;g.FocusNode(u)},Activate:function(u,v){g.UnsetTabIndex();g.posted=true},Unfocus:function(){g.ActiveNode().tabIndex=-1;g.SetTabIndex();g.FocusNode(g.CurrentNode());g.posted=false},MoveHorizontal:function(y,z,w){if(!y.shiftKey){return}var v=g.AllNodes();var u=v.length;if(u===0){return}var x=v[g.Mod(w(g.IndexOf(v,g.CurrentNode())),u)];if(x===g.CurrentNode()){return}g.menu.Remove(y,z);g.jax=MathJax.Hub.getJaxFor(x);g.FocusNode(x);g.menu.Post(null)},Right:function(u,v){g.MoveHorizontal(u,v,function(w){return w+1})},Left:function(u,v){g.MoveHorizontal(u,v,function(w){return w-1})},UnsetTabIndex:function(){var v=g.AllNodes();for(var w=0,u;u=v[w];w++){if(u.tabIndex>0){u.oldTabIndex=u.tabIndex}u.tabIndex=-1}},SetTabIndex:function(){var v=g.AllNodes();for(var w=0,u;u=v[w];w++){if(u.oldTabIndex!==undefined){u.tabIndex=u.oldTabIndex;delete u.oldTabIndex}else{u.tabIndex=f.getTabOrder(u)}}},Mod:function(u,v){return((u%v)+v)%v},IndexOf:(Array.prototype.indexOf?function(u,v,w){return u.indexOf(v,w)}:function(u,x,y){for(var w=(y||0),v=u.length;w<v;w++){if(x===u[w]){return w}}return -1}),saveCookie:function(){o.Cookie.Set("menu",this.cookie)},getCookie:function(){this.cookie=o.Cookie.Get("menu")}});MathJax.Menu.NAV=h;var c=g.ITEM=h.Subclass({name:"",node:null,menu:null,Attributes:function(u){return f.Insert({onmouseup:g.Mouseup,ondragstart:n,onselectstart:n,onselectend:n,ontouchstart:g.Touchstart,ontouchend:g.Touchend,className:"MathJax_MenuItem",role:this.role,menuItem:this},u)},Create:function(w){if(!this.hidden){var v=this.Attributes();var u=this.Label(v,w);o.addElement(w,"div",v,u)}},Name:function(){return t(this.name[0],this.name[1])},Mouseover:function(u,v){if(v.parentNode===g.ActiveNode().parentNode){this.Deactivate(g.ActiveNode())}this.Activate(u,v)},Mouseout:function(u,v){this.Deactivate(v)},Mouseup:function(u,v){return this.Remove(u,v)},DeactivateSubmenus:function(z){var y=document.getElementById("MathJax_MenuFrame").childNodes,v=c.GetMenuNode(z).childNodes;for(var w=0,u=v.length;w<u;w++){var x=v[w].menuItem;if(x&&x.submenu&&x.submenu.posted&&x!==z.menuItem){x.Deactivate(v[w])}}this.RemoveSubmenus(z,y)},RemoveSubmenus:function(w,v){v=v||document.getElementById("MathJax_MenuFrame").childNodes;var u=v.length-1;while(u>=0&&c.GetMenuNode(w).menuItem!==v[u].menuItem){v[u].menuItem.posted=false;v[u].parentNode.removeChild(v[u]);u--}},Touchstart:function(u,v){return this.TouchEvent(u,v,"Mousedown")},Touchend:function(u,v){return this.TouchEvent(u,v,"Mouseup")},TouchEvent:function(v,w,u){if(this!==c.lastItem){if(c.lastMenu){g.Event(v,c.lastMenu,"Mouseout")}g.Event(v,w,"Mouseover",true);c.lastItem=this;c.lastMenu=w}if(this.nativeTouch){return null}g.Event(v,w,u);return false},Remove:function(u,v){v=v.parentNode.menuItem;return v.Remove(u,v)},With:function(u){if(u){f.Insert(this,u)}return this},isRTL:function(){return g.isRTL},rtlClass:function(){return(this.isRTL()?" RTL":"")}},{GetMenuNode:function(u){return u.parentNode}});g.ENTRY=g.ITEM.Subclass({role:"menuitem",Attributes:function(u){u=f.Insert({onmouseover:g.Mouseover,onmouseout:g.Mouseout,onmousedown:g.Mousedown,onkeydown:g.Keydown,"aria-disabled":!!this.disabled},u);u=this.SUPER(arguments).Attributes.call(this,u);if(this.disabled){u.className+=" MathJax_MenuDisabled"}return u},MoveVertical:function(u,E,w){var x=c.GetMenuNode(E);var D=[];for(var z=0,C=x.menuItem.items,y;y=C[z];z++){if(!y.hidden){D.push(y)}}var B=g.IndexOf(D,this);if(B===-1){return}var A=D.length;var v=x.childNodes;do{B=g.Mod(w(B),A)}while(D[B].hidden||!v[B].role||v[B].role==="separator");this.Deactivate(E);D[B].Activate(u,v[B])},Up:function(v,u){this.MoveVertical(v,u,function(w){return w-1})},Down:function(v,u){this.MoveVertical(v,u,function(w){return w+1})},Right:function(v,u){this.MoveHorizontal(v,u,g.Right,!this.isRTL())},Left:function(v,u){this.MoveHorizontal(v,u,g.Left,this.isRTL())},MoveHorizontal:function(A,z,u,B){var x=c.GetMenuNode(z);if(x.menuItem===g.menu&&A.shiftKey){u(A,z)}if(B){return}if(x.menuItem!==g.menu){this.Deactivate(z)}var v=x.previousSibling.childNodes;var y=v.length;while(y--){var w=v[y];if(w.menuItem.submenu&&w.menuItem.submenu===x.menuItem){g.Focus(w);break}}this.RemoveSubmenus(z)},Space:function(u,v){this.Mouseup(u,v)},Activate:function(u,v){this.Deactivate(v);if(!this.disabled){v.className+=" MathJax_MenuActive"}this.DeactivateSubmenus(v);g.Focus(v)},Deactivate:function(u){u.className=u.className.replace(/ MathJax_MenuActive/,"")}});g.ITEM.COMMAND=g.ENTRY.Subclass({action:function(){},Init:function(u,w,v){if(!i(u)){u=[u,u]}this.name=u;this.action=w;this.With(v)},Label:function(u,v){return[this.Name()]},Mouseup:function(u,v){if(!this.disabled){this.Remove(u,v);d.Post(["command",this]);this.action.call(this,u)}return n(u)}});g.ITEM.SUBMENU=g.ENTRY.Subclass({submenu:null,marker:"\u25BA",markerRTL:"\u25C4",Attributes:function(u){u=f.Insert({"aria-haspopup":"true"},u);u=this.SUPER(arguments).Attributes.call(this,u);return u},Init:function(u,w){if(!i(u)){u=[u,u]}this.name=u;var v=1;if(!(w instanceof g.ITEM)){this.With(w),v++}this.submenu=g.apply(g,[].slice.call(arguments,v))},Label:function(u,v){this.submenu.posted=false;return[this.Name()+" ",["span",{className:"MathJax_MenuArrow"+this.rtlClass()},[this.isRTL()?this.markerRTL:this.marker]]]},Timer:function(u,v){this.ClearTimer();u={type:u.type,clientX:u.clientX,clientY:u.clientY};this.timer=setTimeout(e(["Mouseup",this,u,v]),s.delay)},ClearTimer:function(){if(this.timer){clearTimeout(this.timer)}},Touchend:function(v,x){var w=this.submenu.posted;var u=this.SUPER(arguments).Touchend.apply(this,arguments);if(w){this.Deactivate(x);delete c.lastItem;delete c.lastMenu}return u},Mouseout:function(u,v){if(!this.submenu.posted){this.Deactivate(v)}this.ClearTimer()},Mouseover:function(u,v){this.Activate(u,v)},Mouseup:function(u,v){if(!this.disabled){if(!this.submenu.posted){this.ClearTimer();this.submenu.Post(u,v,this.ltr);g.Focus(v)}else{this.DeactivateSubmenus(v)}}return n(u)},Activate:function(u,v){if(!this.disabled){this.Deactivate(v);v.className+=" MathJax_MenuActive"}if(!this.submenu.posted){this.DeactivateSubmenus(v);if(!g.isMobile){this.Timer(u,v)}}g.Focus(v)},MoveVertical:function(w,v,u){this.ClearTimer();this.SUPER(arguments).MoveVertical.apply(this,arguments)},MoveHorizontal:function(w,y,v,x){if(!x){this.SUPER(arguments).MoveHorizontal.apply(this,arguments);return}if(this.disabled){return}if(!this.submenu.posted){this.Activate(w,y);return}var u=c.GetMenuNode(y).nextSibling.childNodes;if(u.length>0){this.submenu.items[0].Activate(w,u[0])}}});g.ITEM.RADIO=g.ENTRY.Subclass({variable:null,marker:(a?"\u25CF":"\u2713"),role:"menuitemradio",Attributes:function(v){var u=s.settings[this.variable]===this.value?"true":"false";v=f.Insert({"aria-checked":u},v);v=this.SUPER(arguments).Attributes.call(this,v);return v},Init:function(v,u,w){if(!i(v)){v=[v,v]}this.name=v;this.variable=u;this.With(w);if(this.value==null){this.value=this.name[0]}},Label:function(v,w){var u={className:"MathJax_MenuRadioCheck"+this.rtlClass()};if(s.settings[this.variable]!==this.value){u={style:{display:"none"}}}return[["span",u,[this.marker]]," "+this.Name()]},Mouseup:function(x,y){if(!this.disabled){var z=y.parentNode.childNodes;for(var v=0,u=z.length;v<u;v++){var w=z[v].menuItem;if(w&&w.variable===this.variable){z[v].firstChild.style.display="none"}}y.firstChild.display="";s.settings[this.variable]=this.value;g.cookie[this.variable]=s.settings[this.variable];g.saveCookie();d.Post(["radio button",this])}this.Remove(x,y);if(this.action&&!this.disabled){this.action.call(g,this)}return n(x)}});g.ITEM.CHECKBOX=g.ENTRY.Subclass({variable:null,marker:"\u2713",role:"menuitemcheckbox",Attributes:function(v){var u=s.settings[this.variable]?"true":"false";v=f.Insert({"aria-checked":u},v);v=this.SUPER(arguments).Attributes.call(this,v);return v},Init:function(v,u,w){if(!i(v)){v=[v,v]}this.name=v;this.variable=u;this.With(w)},Label:function(v,w){var u={className:"MathJax_MenuCheck"+this.rtlClass()};if(!s.settings[this.variable]){u={style:{display:"none"}}}return[["span",u,[this.marker]]," "+this.Name()]},Mouseup:function(u,v){if(!this.disabled){v.firstChild.display=(s.settings[this.variable]?"none":"");s.settings[this.variable]=!s.settings[this.variable];g.cookie[this.variable]=s.settings[this.variable];g.saveCookie();d.Post(["checkbox",this])}this.Remove(u,v);if(this.action&&!this.disabled){this.action.call(g,this)}return n(u)}});g.ITEM.LABEL=g.ENTRY.Subclass({role:"menuitem",Init:function(u,v){if(!i(u)){u=[u,u]}this.name=u;this.With(v)},Label:function(u,v){u.className+=" MathJax_MenuLabel";return[this.Name()]},Activate:function(u,v){this.Deactivate(v);g.Focus(v)},Mouseup:function(u,v){}});g.ITEM.RULE=g.ITEM.Subclass({role:"separator",Attributes:function(u){u=f.Insert({"aria-orientation":"vertical"},u);u=this.SUPER(arguments).Attributes.call(this,u);return u},Label:function(u,v){u.className+=" MathJax_MenuRule";return null}});g.About=function(y){var v=g.About.GetFont();var A=g.About.GetFormat();var u=["MathJax.js v"+MathJax.fileversion,["br"]];u.push(["div",{style:{"border-top":"groove 2px",margin:".25em 0"}}]);g.About.GetJax(u,MathJax.InputJax,["InputJax","%1 Input Jax v%2"]);g.About.GetJax(u,MathJax.OutputJax,["OutputJax","%1 Output Jax v%2"]);g.About.GetJax(u,MathJax.ElementJax,["ElementJax","%1 Element Jax v%2"]);u.push(["div",{style:{"border-top":"groove 2px",margin:".25em 0"}}]);g.About.GetJax(u,MathJax.Extension,["Extension","%1 Extension v%2"],true);u.push(["div",{style:{"border-top":"groove 2px",margin:".25em 0"}}],["center",{},[f.Browser+" v"+f.Browser.version+(A?" \u2014 "+t(A.replace(/ /g,""),A):"")]]);g.About.div=g.Background(g.About);var x=o.addElement(g.About.div,"div",{id:"MathJax_About",tabIndex:0,onkeydown:g.About.Keydown},[["b",{style:{fontSize:"120%"}},["MathJax"]]," v"+MathJax.version,["br"],t(v.replace(/ /g,""),"using "+v),["br"],["br"],["span",{style:{display:"inline-block","text-align":"left","font-size":"80%","max-height":"20em",overflow:"auto","background-color":"#E4E4E4",padding:".4em .6em",border:"1px inset"},tabIndex:0},u],["br"],["br"],["a",{href:"http://www.mathjax.org/"},["www.mathjax.org"]],["span",{className:"MathJax_MenuClose",id:"MathJax_AboutClose",onclick:g.About.Remove,onkeydown:g.About.Keydown,tabIndex:0,role:"button","aria-label":t("CloseAboutDialog","Close about MathJax dialog")},[["span",{},"\u00D7"]]]]);if(y.type==="mouseup"){x.className+=" MathJax_MousePost"}x.focus();MathJax.Localization.setCSS(x);var z=(document.documentElement||{});var w=window.innerHeight||z.clientHeight||z.scrollHeight||0;if(g.prototype.msieAboutBug){x.style.width="20em";x.style.position="absolute";x.style.left=Math.floor((document.documentElement.scrollWidth-x.offsetWidth)/2)+"px";x.style.top=(Math.floor((w-x.offsetHeight)/3)+document.body.scrollTop)+"px"}else{x.style.marginLeft=Math.floor(-x.offsetWidth/2)+"px";x.style.top=Math.floor((w-x.offsetHeight)/3)+"px"}};g.About.Remove=function(u){if(g.About.div){document.body.removeChild(g.About.div);delete g.About.div}};g.About.Keydown=function(u){if(u.keyCode===b.ESCAPE||(this.id==="MathJax_AboutClose"&&(u.keyCode===b.SPACE||u.keyCode===b.RETURN))){g.About.Remove(u);g.CurrentNode().focus();n(u)}},g.About.GetJax=function(v,A,y,x){var z=[];for(var B in A){if(A.hasOwnProperty(B)&&A[B]){if((x&&A[B].version)||(A[B].isa&&A[B].isa(A))){z.push(t(y[0],y[1],(A[B].id||B),A[B].version))}}}z.sort();for(var w=0,u=z.length;w<u;w++){v.push(z[w],["br"])}return v};g.About.GetFont=function(){var u=MathJax.Hub.outputJax["jax/mml"][0]||{};var v={SVG:"web SVG",CommonHTML:"web TeX","HTML-CSS":(u.imgFonts?"image":(u.webFonts?"web":"local")+" "+u.fontInUse)}[u.id]||"generic";return v+" fonts"};g.About.GetFormat=function(){var u=MathJax.Hub.outputJax["jax/mml"][0]||{};if(u.id!=="HTML-CSS"||!u.webFonts||u.imgFonts){return}return u.allowWebFonts.replace(/otf/,"woff or otf")+" fonts"};g.Help=function(u){q.Require("[MathJax]/extensions/HelpDialog.js",function(){MathJax.Extension.Help.Dialog({type:u.type})})};g.ShowSource=function(y){if(!y){y=window.event}var x={screenX:y.screenX,screenY:y.screenY};if(!g.jax){return}if(this.format==="MathML"){var v=MathJax.ElementJax.mml;if(v&&typeof(v.mbase.prototype.toMathML)!=="undefined"){try{g.ShowSource.Text(g.jax.root.toMathML("",g.jax),y)}catch(w){if(!w.restart){throw w}e.After([this,g.ShowSource,x],w.restart)}}else{if(!q.loadingToMathML){q.loadingToMathML=true;g.ShowSource.Window(y);e.Queue(q.Require("[MathJax]/extensions/toMathML.js"),function(){delete q.loadingToMathML;if(!v.mbase.prototype.toMathML){v.mbase.prototype.toMathML=function(){}}},[this,g.ShowSource,x]);return}}}else{if(this.format==="Error"){g.ShowSource.Text(g.jax.errorText,y)}else{if(s.semanticsAnnotations[this.format]){var u=g.jax.root.getAnnotation(this.format);if(u.data[0]){g.ShowSource.Text(u.data[0].toString())}}else{if(g.jax.originalText==null){alert(t("NoOriginalForm","No original form available"));return}g.ShowSource.Text(g.jax.originalText,y)}}}};g.ShowSource.Window=function(v){if(!g.ShowSource.w){var w=[],u=s.windowSettings;for(var x in u){if(u.hasOwnProperty(x)){w.push(x+"="+u[x])}}g.ShowSource.w=window.open("","_blank",w.join(","))}return g.ShowSource.w};g.ShowSource.Text=function(z,x){var u=g.ShowSource.Window(x);delete g.ShowSource.w;z=z.replace(/^\s*/,"").replace(/\s*$/,"");z=z.replace(/&/g,"&amp;").replace(/</g,"&lt;").replace(/>/g,"&gt;");var y=t("EqSource","MathJax Equation Source");if(g.isMobile){u.document.open();u.document.write("<html><head><meta name='viewport' content='width=device-width, initial-scale=1.0' /><title>"+y+"</title></head><body style='font-size:85%'>");u.document.write("<pre>"+z+"</pre>");u.document.write("<hr><input type='button' value='"+t("Close","Close")+"' onclick='window.close()' />");u.document.write("</body></html>");u.document.close()}else{u.document.open();u.document.write("<html><head><title>"+y+"</title></head><body style='font-size:85%'>");u.document.write("<table><tr><td><pre>"+z+"</pre></td></tr></table>");u.document.write("</body></html>");u.document.close();var v=u.document.body.firstChild;setTimeout(function(){var B=(u.outerHeight-u.innerHeight)||30,A=(u.outerWidth-u.innerWidth)||30,w,E;A=Math.max(140,Math.min(Math.floor(0.5*screen.width),v.offsetWidth+A+25));B=Math.max(40,Math.min(Math.floor(0.5*screen.height),v.offsetHeight+B+25));if(g.prototype.msieHeightBug){B+=35}u.resizeTo(A,B);var D;try{D=x.screenX}catch(C){}if(x&&D!=null){w=Math.max(0,Math.min(x.screenX-Math.floor(A/2),screen.width-A-20));E=Math.max(0,Math.min(x.screenY-Math.floor(B/2),screen.height-B-20));u.moveTo(w,E)}},50)}};g.Scale=function(){var z=["CommonHTML","HTML-CSS","SVG","NativeMML","PreviewHTML"],u=z.length,y=100,w,v;for(w=0;w<u;w++){v=r[z[w]];if(v){y=v.config.scale;break}}var x=prompt(t("ScaleMath","Scale all mathematics (compared to surrounding text) by"),y+"%");if(x){if(x.match(/^\s*\d+(\.\d*)?\s*%?\s*$/)){x=parseFloat(x);if(x){if(x!==y){for(w=0;w<u;w++){v=r[z[w]];if(v){v.config.scale=x}}g.cookie.scale=f.config.scale=x;g.saveCookie();f.Queue(["Rerender",f])}}else{alert(t("NonZeroScale","The scale should not be zero"))}}else{alert(t("PercentScale","The scale should be a percentage (e.g., 120%%)"))}}};g.Zoom=function(){if(!MathJax.Extension.MathZoom){q.Require("[MathJax]/extensions/MathZoom.js")}};g.Renderer=function(){var v=f.outputJax["jax/mml"];if(v[0]!==s.settings.renderer){var y=f.Browser,x,u=g.Renderer.Messages,w;switch(s.settings.renderer){case"NativeMML":if(!s.settings.warnedMML){if(y.isChrome&&y.version.substr(0,3)!=="24."){x=u.MML.WebKit}else{if(y.isSafari&&!y.versionAtLeast("5.0")){x=u.MML.WebKit}else{if(y.isMSIE){if(!y.hasMathPlayer){x=u.MML.MSIE}}else{if(y.isEdge){x=u.MML.WebKit}else{x=u.MML[y]}}}}w="warnedMML"}break;case"SVG":if(!s.settings.warnedSVG){if(y.isMSIE&&!m){x=u.SVG.MSIE}}break}if(x){x=t(x[0],x[1]);x+="\n\n";x+=t("SwitchAnyway","Switch the renderer anyway?\n\n(Press OK to switch, CANCEL to continue with the current renderer)");g.cookie.renderer=v[0].id;g.saveCookie();if(!confirm(x)){g.cookie.renderer=s.settings.renderer=o.Cookie.Get("menu").renderer;g.saveCookie();return}if(w){g.cookie.warned=s.settings.warned=true}g.cookie.renderer=s.settings.renderer;g.saveCookie()}f.Queue(["setRenderer",f,s.settings.renderer,"jax/mml"],["Rerender",f])}};g.Renderer.Messages={MML:{WebKit:["WebkitNativeMMLWarning","Your browser doesn't seem to support MathML natively, so switching to MathML output may cause the mathematics on the page to become unreadable."],MSIE:["MSIENativeMMLWarning","Internet Explorer requires the MathPlayer plugin in order to process MathML output."],Opera:["OperaNativeMMLWarning","Opera's support for MathML is limited, so switching to MathML output may cause some expressions to render poorly."],Safari:["SafariNativeMMLWarning","Your browser's native MathML does not implement all the features used by MathJax, so some expressions may not render properly."],Firefox:["FirefoxNativeMMLWarning","Your browser's native MathML does not implement all the features used by MathJax, so some expressions may not render properly."]},SVG:{MSIE:["MSIESVGWarning","SVG is not implemented in Internet Explorer prior to IE9 or when it is emulating IE8 or below. Switching to SVG output will cause the mathematics to not display properly."]}};g.AssistiveMML=function(w,u){var v=MathJax.Extension.AssistiveMML;if(!v){if(!u){q.Require("[MathJax]/extensions/AssistiveMML.js",["AssistiveMML",g,w,true])}return}MathJax.Hub.Queue([(s.settings.assistiveMML?"Add":"Remove")+"AssistiveMathML",v])};g.Font=function(){var u=r["HTML-CSS"];if(!u){return}document.location.reload()};g.Locale=function(){MathJax.Localization.setLocale(s.settings.locale);MathJax.Hub.Queue(["Reprocess",MathJax.Hub])};g.LoadLocale=function(){var u=prompt(t("LoadURL","Load translation data from this URL:"));if(u){if(!u.match(/\.js$/)){alert(t("BadURL","The URL should be for a javascript file that defines MathJax translation data.  Javascript file names should end with '.js'"))}q.Require(u,function(v){if(v!=q.STATUS.OK){alert(t("BadData","Failed to load translation data from %1",u))}})}};g.MPEvents=function(w){var v=s.settings.discoverable,u=g.MPEvents.Messages;if(!m){if(s.settings.mpMouse&&!confirm(t.apply(t,u.IE8warning))){delete g.cookie.mpContext;delete s.settings.mpContext;delete g.cookie.mpMouse;delete s.settings.mpMouse;g.saveCookie();return}s.settings.mpContext=s.settings.mpMouse;g.cookie.mpContext=g.cookie.mpMouse=s.settings.mpMouse;g.saveCookie();MathJax.Hub.Queue(["Rerender",MathJax.Hub])}else{if(!v&&w.name[1]==="Menu Events"&&s.settings.mpContext){alert(t.apply(t,u.IE9warning))}}};g.MPEvents.Messages={IE8warning:["IE8warning","This will disable the MathJax menu and zoom features, but you can Alt-Click on an expression to obtain the MathJax menu instead.\n\nReally change the MathPlayer settings?"],IE9warning:["IE9warning","The MathJax contextual menu will be disabled, but you can Alt-Click on an expression to obtain the MathJax menu instead."]};f.Browser.Select({MSIE:function(u){var v=(document.compatMode==="BackCompat");var w=u.versionAtLeast("8.0")&&document.documentMode>7;g.Augment({margin:20,msieBackgroundBug:((document.documentMode||0)<9),msieFixedPositionBug:(v||!w),msieAboutBug:v,msieHeightBug:((document.documentMode||0)<9)});if(m){delete s.styles["#MathJax_About"].filter;delete s.styles[".MathJax_Menu"].filter}},Firefox:function(u){g.skipMouseover=u.isMobile&&u.versionAtLeast("6.0");g.skipMousedown=u.isMobile}});g.isMobile=f.Browser.isMobile;g.noContextMenu=f.Browser.noContextMenu;g.CreateLocaleMenu=function(){if(!g.menu){return}var z=g.menu.Find("Language").submenu,w=z.items;var v=[],B=MathJax.Localization.strings;for(var A in B){if(B.hasOwnProperty(A)){v.push(A)}}v=v.sort();z.items=[];for(var x=0,u=v.length;x<u;x++){var y=B[v[x]].menuTitle;if(y){y+=" ("+v[x]+")"}else{y=v[x]}z.items.push(c.RADIO([v[x],y],"locale",{action:g.Locale}))}z.items.push(w[w.length-2],w[w.length-1])};g.CreateAnnotationMenu=function(){if(!g.menu){return}var w=g.menu.Find("Show Math As","Annotation").submenu;var v=s.semanticsAnnotations;for(var u in v){if(v.hasOwnProperty(u)){w.items.push(c.COMMAND([u,u],g.ShowSource,{hidden:true,nativeTouch:true,format:u}))}}};f.Register.StartupHook("End Config",function(){s.settings=f.config.menuSettings;if(typeof(s.settings.showRenderer)!=="undefined"){s.showRenderer=s.settings.showRenderer}if(typeof(s.settings.showFontMenu)!=="undefined"){s.showFontMenu=s.settings.showFontMenu}if(typeof(s.settings.showContext)!=="undefined"){s.showContext=s.settings.showContext}g.getCookie();g.menu=g(c.SUBMENU(["Show","Show Math As"],c.COMMAND(["MathMLcode","MathML Code"],g.ShowSource,{nativeTouch:true,format:"MathML"}),c.COMMAND(["Original","Original Form"],g.ShowSource,{nativeTouch:true}),c.SUBMENU(["Annotation","Annotation"],{disabled:true}),c.RULE(),c.CHECKBOX(["texHints","Show TeX hints in MathML"],"texHints"),c.CHECKBOX(["semantics","Add original form as annotation"],"semantics")),c.RULE(),c.SUBMENU(["Settings","Math Settings"],c.SUBMENU(["ZoomTrigger","Zoom Trigger"],c.RADIO(["Hover","Hover"],"zoom",{action:g.Zoom}),c.RADIO(["Click","Click"],"zoom",{action:g.Zoom}),c.RADIO(["DoubleClick","Double-Click"],"zoom",{action:g.Zoom}),c.RADIO(["NoZoom","No Zoom"],"zoom",{value:"None"}),c.RULE(),c.LABEL(["TriggerRequires","Trigger Requires:"]),c.CHECKBOX((f.Browser.isMac?["Option","Option"]:["Alt","Alt"]),"ALT"),c.CHECKBOX(["Command","Command"],"CMD",{hidden:!f.Browser.isMac}),c.CHECKBOX(["Control","Control"],"CTRL",{hidden:f.Browser.isMac}),c.CHECKBOX(["Shift","Shift"],"Shift")),c.SUBMENU(["ZoomFactor","Zoom Factor"],c.RADIO("125%","zscale"),c.RADIO("133%","zscale"),c.RADIO("150%","zscale"),c.RADIO("175%","zscale"),c.RADIO("200%","zscale"),c.RADIO("250%","zscale"),c.RADIO("300%","zscale"),c.RADIO("400%","zscale")),c.RULE(),c.SUBMENU(["Renderer","Math Renderer"],{hidden:!s.showRenderer},c.RADIO(["HTML-CSS","HTML-CSS"],"renderer",{action:g.Renderer}),c.RADIO(["CommonHTML","Common HTML"],"renderer",{action:g.Renderer,value:"CommonHTML"}),c.RADIO(["PreviewHTML","Preview HTML"],"renderer",{action:g.Renderer,value:"PreviewHTML"}),c.RADIO(["MathML","MathML"],"renderer",{action:g.Renderer,value:"NativeMML"}),c.RADIO(["SVG","SVG"],"renderer",{action:g.Renderer}),c.RADIO(["PlainSource","Plain Source"],"renderer",{action:g.Renderer,value:"PlainSource"}),c.RULE(),c.CHECKBOX(["FastPreview","Fast Preview"],"FastPreview")),c.SUBMENU("MathPlayer",{hidden:!f.Browser.isMSIE||!s.showMathPlayer,disabled:!f.Browser.hasMathPlayer},c.LABEL(["MPHandles","Let MathPlayer Handle:"]),c.CHECKBOX(["MenuEvents","Menu Events"],"mpContext",{action:g.MPEvents,hidden:!m}),c.CHECKBOX(["MouseEvents","Mouse Events"],"mpMouse",{action:g.MPEvents,hidden:!m}),c.CHECKBOX(["MenuAndMouse","Mouse and Menu Events"],"mpMouse",{action:g.MPEvents,hidden:m})),c.SUBMENU(["FontPrefs","Font Preference"],{hidden:!s.showFontMenu},c.LABEL(["ForHTMLCSS","For HTML-CSS:"]),c.RADIO(["Auto","Auto"],"font",{action:g.Font}),c.RULE(),c.RADIO(["TeXLocal","TeX (local)"],"font",{action:g.Font}),c.RADIO(["TeXWeb","TeX (web)"],"font",{action:g.Font}),c.RADIO(["TeXImage","TeX (image)"],"font",{action:g.Font}),c.RULE(),c.RADIO(["STIXLocal","STIX (local)"],"font",{action:g.Font}),c.RADIO(["STIXWeb","STIX (web)"],"font",{action:g.Font}),c.RULE(),c.RADIO(["AsanaMathWeb","Asana Math (web)"],"font",{action:g.Font}),c.RADIO(["GyrePagellaWeb","Gyre Pagella (web)"],"font",{action:g.Font}),c.RADIO(["GyreTermesWeb","Gyre Termes (web)"],"font",{action:g.Font}),c.RADIO(["LatinModernWeb","Latin Modern (web)"],"font",{action:g.Font}),c.RADIO(["NeoEulerWeb","Neo Euler (web)"],"font",{action:g.Font})),c.SUBMENU(["ContextMenu","Contextual Menu"],{hidden:!s.showContext},c.RADIO(["MathJax","MathJax"],"context"),c.RADIO(["Browser","Browser"],"context")),c.COMMAND(["Scale","Scale All Math ..."],g.Scale),c.RULE().With({hidden:!s.showDiscoverable,name:["","discover_rule"]}),c.CHECKBOX(["Discoverable","Highlight on Hover"],"discoverable",{hidden:!s.showDiscoverable})),c.SUBMENU(["Accessibility","Accessibility"],c.CHECKBOX(["AssistiveMML","Assistive MathML"],"assistiveMML",{action:g.AssistiveMML}),c.CHECKBOX(["InTabOrder","Include in Tab Order"],"inTabOrder")),c.SUBMENU(["Locale","Language"],{hidden:!s.showLocale,ltr:true},c.RADIO("en","locale",{action:g.Locale}),c.RULE().With({hidden:!s.showLocaleURL,name:["","localURL_rule"]}),c.COMMAND(["LoadLocale","Load from URL ..."],g.LoadLocale,{hidden:!s.showLocaleURL})),c.RULE(),c.COMMAND(["About","About MathJax"],g.About),c.COMMAND(["Help","MathJax Help"],g.Help));if(g.isMobile){(function(){var v=s.settings;var u=g.menu.Find("Math Settings","Zoom Trigger").submenu;u.items[0].disabled=u.items[1].disabled=true;if(v.zoom==="Hover"||v.zoom=="Click"){v.zoom="None"}u.items=u.items.slice(0,4);if(navigator.appVersion.match(/[ (]Android[) ]/)){g.ITEM.SUBMENU.Augment({marker:"\u00BB"})}})()}g.CreateLocaleMenu();g.CreateAnnotationMenu()});g.showRenderer=function(u){g.cookie.showRenderer=s.showRenderer=u;g.saveCookie();g.menu.Find("Math Settings","Math Renderer").hidden=!u};g.showMathPlayer=function(u){g.cookie.showMathPlayer=s.showMathPlayer=u;g.saveCookie();g.menu.Find("Math Settings","MathPlayer").hidden=!u};g.showFontMenu=function(u){g.cookie.showFontMenu=s.showFontMenu=u;g.saveCookie();g.menu.Find("Math Settings","Font Preference").hidden=!u};g.showContext=function(u){g.cookie.showContext=s.showContext=u;g.saveCookie();g.menu.Find("Math Settings","Contextual Menu").hidden=!u};g.showDiscoverable=function(u){g.cookie.showDiscoverable=s.showDiscoverable=u;g.saveCookie();g.menu.Find("Math Settings","Highlight on Hover").hidden=!u;g.menu.Find("Math Settings","discover_rule").hidden=!u};g.showLocale=function(u){g.cookie.showLocale=s.showLocale=u;g.saveCookie();g.menu.Find("Language").hidden=!u};MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function(){if(!MathJax.OutputJax["HTML-CSS"].config.imageFont){g.menu.Find("Math Settings","Font Preference","TeX (image)").disabled=true}});e.Queue(f.Register.StartupHook("End Config",{}),["Styles",q,s.styles],["Post",f.Startup.signal,"MathMenu Ready"],["loadComplete",q,"[MathJax]/extensions/MathMenu.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.CallBack,MathJax.OutputJax);
MathJax.ElementJax.mml=MathJax.ElementJax({mimeType:"jax/mml"},{id:"mml",version:"2.7.5",directory:MathJax.ElementJax.directory+"/mml",extensionDir:MathJax.ElementJax.extensionDir+"/mml",optableDir:MathJax.ElementJax.directory+"/mml/optable"});MathJax.ElementJax.mml.Augment({Init:function(){if(arguments.length===1&&arguments[0].type==="math"){this.root=arguments[0]}else{this.root=MathJax.ElementJax.mml.math.apply(this,arguments)}if(this.root.attr&&this.root.attr.mode){if(!this.root.display&&this.root.attr.mode==="display"){this.root.display="block";this.root.attrNames.push("display")}delete this.root.attr.mode;for(var b=0,a=this.root.attrNames.length;b<a;b++){if(this.root.attrNames[b]==="mode"){this.root.attrNames.splice(b,1);break}}}}},{INHERIT:"_inherit_",AUTO:"_auto_",SIZE:{INFINITY:"infinity",SMALL:"small",NORMAL:"normal",BIG:"big"},COLOR:{TRANSPARENT:"transparent"},VARIANT:{NORMAL:"normal",BOLD:"bold",ITALIC:"italic",BOLDITALIC:"bold-italic",DOUBLESTRUCK:"double-struck",FRAKTUR:"fraktur",BOLDFRAKTUR:"bold-fraktur",SCRIPT:"script",BOLDSCRIPT:"bold-script",SANSSERIF:"sans-serif",BOLDSANSSERIF:"bold-sans-serif",SANSSERIFITALIC:"sans-serif-italic",SANSSERIFBOLDITALIC:"sans-serif-bold-italic",MONOSPACE:"monospace",INITIAL:"initial",TAILED:"tailed",LOOPED:"looped",STRETCHED:"stretched",CALIGRAPHIC:"-tex-caligraphic",OLDSTYLE:"-tex-oldstyle"},FORM:{PREFIX:"prefix",INFIX:"infix",POSTFIX:"postfix"},LINEBREAK:{AUTO:"auto",NEWLINE:"newline",NOBREAK:"nobreak",GOODBREAK:"goodbreak",BADBREAK:"badbreak"},LINEBREAKSTYLE:{BEFORE:"before",AFTER:"after",DUPLICATE:"duplicate",INFIXLINBREAKSTYLE:"infixlinebreakstyle"},INDENTALIGN:{LEFT:"left",CENTER:"center",RIGHT:"right",AUTO:"auto",ID:"id",INDENTALIGN:"indentalign"},INDENTSHIFT:{INDENTSHIFT:"indentshift"},LINETHICKNESS:{THIN:"thin",MEDIUM:"medium",THICK:"thick"},NOTATION:{LONGDIV:"longdiv",ACTUARIAL:"actuarial",RADICAL:"radical",BOX:"box",ROUNDEDBOX:"roundedbox",CIRCLE:"circle",LEFT:"left",RIGHT:"right",TOP:"top",BOTTOM:"bottom",UPDIAGONALSTRIKE:"updiagonalstrike",DOWNDIAGONALSTRIKE:"downdiagonalstrike",UPDIAGONALARROW:"updiagonalarrow",VERTICALSTRIKE:"verticalstrike",HORIZONTALSTRIKE:"horizontalstrike",PHASORANGLE:"phasorangle",MADRUWB:"madruwb"},ALIGN:{TOP:"top",BOTTOM:"bottom",CENTER:"center",BASELINE:"baseline",AXIS:"axis",LEFT:"left",RIGHT:"right"},LINES:{NONE:"none",SOLID:"solid",DASHED:"dashed"},SIDE:{LEFT:"left",RIGHT:"right",LEFTOVERLAP:"leftoverlap",RIGHTOVERLAP:"rightoverlap"},WIDTH:{AUTO:"auto",FIT:"fit"},ACTIONTYPE:{TOGGLE:"toggle",STATUSLINE:"statusline",TOOLTIP:"tooltip",INPUT:"input"},LENGTH:{VERYVERYTHINMATHSPACE:"veryverythinmathspace",VERYTHINMATHSPACE:"verythinmathspace",THINMATHSPACE:"thinmathspace",MEDIUMMATHSPACE:"mediummathspace",THICKMATHSPACE:"thickmathspace",VERYTHICKMATHSPACE:"verythickmathspace",VERYVERYTHICKMATHSPACE:"veryverythickmathspace",NEGATIVEVERYVERYTHINMATHSPACE:"negativeveryverythinmathspace",NEGATIVEVERYTHINMATHSPACE:"negativeverythinmathspace",NEGATIVETHINMATHSPACE:"negativethinmathspace",NEGATIVEMEDIUMMATHSPACE:"negativemediummathspace",NEGATIVETHICKMATHSPACE:"negativethickmathspace",NEGATIVEVERYTHICKMATHSPACE:"negativeverythickmathspace",NEGATIVEVERYVERYTHICKMATHSPACE:"negativeveryverythickmathspace"},OVERFLOW:{LINBREAK:"linebreak",SCROLL:"scroll",ELIDE:"elide",TRUNCATE:"truncate",SCALE:"scale"},UNIT:{EM:"em",EX:"ex",PX:"px",IN:"in",CM:"cm",MM:"mm",PT:"pt",PC:"pc"},TEXCLASS:{ORD:0,OP:1,BIN:2,REL:3,OPEN:4,CLOSE:5,PUNCT:6,INNER:7,VCENTER:8,NONE:-1},TEXCLASSNAMES:["ORD","OP","BIN","REL","OPEN","CLOSE","PUNCT","INNER","VCENTER"],skipAttributes:{texClass:true,useHeight:true,texprimestyle:true},copyAttributes:{displaystyle:1,scriptlevel:1,open:1,close:1,form:1,actiontype:1,fontfamily:true,fontsize:true,fontweight:true,fontstyle:true,color:true,background:true,id:true,"class":1,href:true,style:true},copyAttributeNames:["displaystyle","scriptlevel","open","close","form","actiontype","fontfamily","fontsize","fontweight","fontstyle","color","background","id","class","href","style"],nocopyAttributes:{fontfamily:true,fontsize:true,fontweight:true,fontstyle:true,color:true,background:true,id:true,"class":true,href:true,style:true,xmlns:true},Error:function(d,e){var c=this.merror(d),b=MathJax.Localization.fontDirection(),a=MathJax.Localization.fontFamily();if(e){c=c.With(e)}if(b||a){c=this.mstyle(c);if(b){c.dir=b}if(a){c.style.fontFamily="font-family: "+a}}return c}});(function(a){a.mbase=MathJax.Object.Subclass({type:"base",isToken:false,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,dir:a.INHERIT},noInherit:{},noInheritAttribute:{texClass:true},getRemoved:{},linebreakContainer:false,Init:function(){this.data=[];if(this.inferRow&&!(arguments.length===1&&arguments[0].inferred)){this.Append(a.mrow().With({inferred:true,notParent:true}))}this.Append.apply(this,arguments)},With:function(e){for(var f in e){if(e.hasOwnProperty(f)){this[f]=e[f]}}return this},Append:function(){if(this.inferRow&&this.data.length){this.data[0].Append.apply(this.data[0],arguments)}else{for(var f=0,e=arguments.length;f<e;f++){this.SetData(this.data.length,arguments[f])}}},SetData:function(e,f){if(f!=null){if(!(f instanceof a.mbase)){f=(this.isToken||this.isChars?a.chars(f):a.mtext(f))}f.parent=this;f.setInherit(this.inheritFromMe?this:this.inherit)}this.data[e]=f},Parent:function(){var e=this.parent;while(e&&e.notParent){e=e.parent}return e},Get:function(f,k,l){if(!l){if(this[f]!=null){return this[f]}if(this.attr&&this.attr[f]!=null){return this.attr[f]}}var g=this.Parent();if(g&&g["adjustChild_"+f]!=null){return(g["adjustChild_"+f])(this.childPosition(),k)}var j=this.inherit;var e=j;while(j){var i=j[f];if(i==null&&j.attr){i=j.attr[f]}if(j.removedStyles&&j.getRemoved[f]&&i==null){i=j.removedStyles[j.getRemoved[f]]}if(i!=null&&j.noInheritAttribute&&!j.noInheritAttribute[f]){var h=j.noInherit[this.type];if(!(h&&h[f])){return i}}e=j;j=j.inherit}if(!k){if(this.defaults[f]===a.AUTO){return this.autoDefault(f)}if(this.defaults[f]!==a.INHERIT&&this.defaults[f]!=null){return this.defaults[f]}if(e){return e.defaults[f]}}return null},hasValue:function(e){return(this.Get(e,true)!=null)},getValues:function(){var f={};for(var g=0,e=arguments.length;g<e;g++){f[arguments[g]]=this.Get(arguments[g])}return f},adjustChild_scriptlevel:function(f,e){return this.Get("scriptlevel",e)},adjustChild_displaystyle:function(f,e){return this.Get("displaystyle",e)},adjustChild_texprimestyle:function(f,e){return this.Get("texprimestyle",e)},hasMMLspacing:function(){return false},childPosition:function(){var h=this,g=h.parent;while(g.notParent){h=g;g=h.parent}for(var f=0,e=g.data.length;f<e;f++){if(g.data[f]===h){return f}}return null},setInherit:function(g){if(g!==this.inherit&&this.inherit==null){this.inherit=g;for(var f=0,e=this.data.length;f<e;f++){if(this.data[f]&&this.data[f].setInherit){this.data[f].setInherit(g)}}}},setTeXclass:function(e){this.getPrevClass(e);return(typeof(this.texClass)!=="undefined"?this:e)},getPrevClass:function(e){if(e){this.prevClass=e.Get("texClass");this.prevLevel=e.Get("scriptlevel")}},updateTeXclass:function(e){if(e){this.prevClass=e.prevClass;delete e.prevClass;this.prevLevel=e.prevLevel;delete e.prevLevel;this.texClass=e.Get("texClass")}},texSpacing:function(){var f=(this.prevClass!=null?this.prevClass:a.TEXCLASS.NONE);var e=(this.Get("texClass")||a.TEXCLASS.ORD);if(f===a.TEXCLASS.NONE||e===a.TEXCLASS.NONE){return""}if(f===a.TEXCLASS.VCENTER){f=a.TEXCLASS.ORD}if(e===a.TEXCLASS.VCENTER){e=a.TEXCLASS.ORD}var g=this.TEXSPACE[f][e];if((this.prevLevel>0||this.Get("scriptlevel")>0)&&g>=0){return""}return this.TEXSPACELENGTH[Math.abs(g)]},TEXSPACELENGTH:["",a.LENGTH.THINMATHSPACE,a.LENGTH.MEDIUMMATHSPACE,a.LENGTH.THICKMATHSPACE],TEXSPACE:[[0,-1,2,3,0,0,0,1],[-1,-1,0,3,0,0,0,1],[2,2,0,0,2,0,0,2],[3,3,0,0,3,0,0,3],[0,0,0,0,0,0,0,0],[0,-1,2,3,0,0,0,1],[1,1,0,1,1,1,1,1],[1,-1,2,3,1,0,1,1]],autoDefault:function(e){return""},isSpacelike:function(){return false},isEmbellished:function(){return false},Core:function(){return this},CoreMO:function(){return this},childIndex:function(g){if(g==null){return}for(var f=0,e=this.data.length;f<e;f++){if(g===this.data[f]){return f}}},CoreIndex:function(){return(this.inferRow?this.data[0]||this:this).childIndex(this.Core())},hasNewline:function(){if(this.isEmbellished()){return this.CoreMO().hasNewline()}if(this.isToken||this.linebreakContainer){return false}for(var f=0,e=this.data.length;f<e;f++){if(this.data[f]&&this.data[f].hasNewline()){return true}}return false},array:function(){if(this.inferred){return this.data}else{return[this]}},toString:function(){return this.type+"("+this.data.join(",")+")"},getAnnotation:function(){return null}},{childrenSpacelike:function(){for(var f=0,e=this.data.length;f<e;f++){if(!this.data[f].isSpacelike()){return false}}return true},childEmbellished:function(){return(this.data[0]&&this.data[0].isEmbellished())},childCore:function(){return(this.inferRow&&this.data[0]?this.data[0].Core():this.data[0])},childCoreMO:function(){return(this.data[0]?this.data[0].CoreMO():null)},setChildTeXclass:function(e){if(this.data[0]){e=this.data[0].setTeXclass(e);this.updateTeXclass(this.data[0])}return e},setBaseTeXclasses:function(g){this.getPrevClass(g);this.texClass=null;if(this.data[0]){if(this.isEmbellished()||this.data[0].isa(a.mi)){g=this.data[0].setTeXclass(g);this.updateTeXclass(this.Core())}else{this.data[0].setTeXclass();g=this}}else{g=this}for(var f=1,e=this.data.length;f<e;f++){if(this.data[f]){this.data[f].setTeXclass()}}return g},setSeparateTeXclasses:function(g){this.getPrevClass(g);for(var f=0,e=this.data.length;f<e;f++){if(this.data[f]){this.data[f].setTeXclass()}}if(this.isEmbellished()){this.updateTeXclass(this.Core())}return this}});a.mi=a.mbase.Subclass({type:"mi",isToken:true,texClass:a.TEXCLASS.ORD,defaults:{mathvariant:a.AUTO,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT,dir:a.INHERIT},autoDefault:function(f){if(f==="mathvariant"){var e=(this.data[0]||"").toString();return(e.length===1||(e.length===2&&e.charCodeAt(0)>=55296&&e.charCodeAt(0)<56320)?a.VARIANT.ITALIC:a.VARIANT.NORMAL)}return""},setTeXclass:function(f){this.getPrevClass(f);var e=this.data.join("");if(e.length>1&&e.match(/^[a-z][a-z0-9]*$/i)&&this.texClass===a.TEXCLASS.ORD){this.texClass=a.TEXCLASS.OP;this.autoOP=true}return this}});a.mn=a.mbase.Subclass({type:"mn",isToken:true,texClass:a.TEXCLASS.ORD,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT,dir:a.INHERIT}});a.mo=a.mbase.Subclass({type:"mo",isToken:true,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT,dir:a.INHERIT,form:a.AUTO,fence:a.AUTO,separator:a.AUTO,lspace:a.AUTO,rspace:a.AUTO,stretchy:a.AUTO,symmetric:a.AUTO,maxsize:a.AUTO,minsize:a.AUTO,largeop:a.AUTO,movablelimits:a.AUTO,accent:a.AUTO,linebreak:a.LINEBREAK.AUTO,lineleading:a.INHERIT,linebreakstyle:a.AUTO,linebreakmultchar:a.INHERIT,indentalign:a.INHERIT,indentshift:a.INHERIT,indenttarget:a.INHERIT,indentalignfirst:a.INHERIT,indentshiftfirst:a.INHERIT,indentalignlast:a.INHERIT,indentshiftlast:a.INHERIT,texClass:a.AUTO},defaultDef:{form:a.FORM.INFIX,fence:false,separator:false,lspace:a.LENGTH.THICKMATHSPACE,rspace:a.LENGTH.THICKMATHSPACE,stretchy:false,symmetric:false,maxsize:a.SIZE.INFINITY,minsize:"0em",largeop:false,movablelimits:false,accent:false,linebreak:a.LINEBREAK.AUTO,lineleading:"1ex",linebreakstyle:"before",indentalign:a.INDENTALIGN.AUTO,indentshift:"0",indenttarget:"",indentalignfirst:a.INDENTALIGN.INDENTALIGN,indentshiftfirst:a.INDENTSHIFT.INDENTSHIFT,indentalignlast:a.INDENTALIGN.INDENTALIGN,indentshiftlast:a.INDENTSHIFT.INDENTSHIFT,texClass:a.TEXCLASS.REL},SPACE_ATTR:{lspace:1,rspace:2},useMMLspacing:3,hasMMLspacing:function(){if(this.useMMLspacing){return true}return this.form&&(this.OPTABLE[this.form]||{})[this.data.join("")]},autoDefault:function(g,n){var l=this.def;if(!l){if(g==="form"){return this.getForm()}var k=this.data.join("");var f=[this.Get("form"),a.FORM.INFIX,a.FORM.POSTFIX,a.FORM.PREFIX];for(var h=0,e=f.length;h<e;h++){var j=this.OPTABLE[f[h]][k];if(j){l=this.makeDef(j);break}}if(!l){l=this.CheckRange(k)}if(!l&&n){l={}}else{if(!l){l=MathJax.Hub.Insert({},this.defaultDef)}if(this.parent){this.def=l}else{l=MathJax.Hub.Insert({},l)}l.form=f[0]}}this.useMMLspacing&=~(this.SPACE_ATTR[g]||0);if(l[g]!=null){return l[g]}else{if(!n){return this.defaultDef[g]}}return""},CheckRange:function(j){var k=j.charCodeAt(0);if(k>=55296&&k<56320){k=(((k-55296)<<10)+(j.charCodeAt(1)-56320))+65536}for(var g=0,e=this.RANGES.length;g<e&&this.RANGES[g][0]<=k;g++){if(k<=this.RANGES[g][1]){if(this.RANGES[g][3]){var f=a.optableDir+"/"+this.RANGES[g][3]+".js";this.RANGES[g][3]=null;MathJax.Hub.RestartAfter(MathJax.Ajax.Require(f))}var h=a.TEXCLASSNAMES[this.RANGES[g][2]];h=this.OPTABLE.infix[j]=a.mo.OPTYPES[h==="BIN"?"BIN3":h];return this.makeDef(h)}}return null},makeDef:function(f){if(f[2]==null){f[2]=this.defaultDef.texClass}if(!f[3]){f[3]={}}var e=MathJax.Hub.Insert({},f[3]);e.lspace=this.SPACE[f[0]];e.rspace=this.SPACE[f[1]];e.texClass=f[2];if(e.texClass===a.TEXCLASS.REL&&(this.movablelimits||this.data.join("").match(/^[a-z]+$/i))){e.texClass=a.TEXCLASS.OP}return e},getForm:function(){var e=this,g=this.parent,f=this.Parent();while(f&&f.isEmbellished()){e=g;g=f.parent;f=f.Parent()}if(g&&g.type==="mrow"&&g.NonSpaceLength()!==1){if(g.FirstNonSpace()===e){return a.FORM.PREFIX}if(g.LastNonSpace()===e){return a.FORM.POSTFIX}}return a.FORM.INFIX},isEmbellished:function(){return true},hasNewline:function(){return(this.Get("linebreak")===a.LINEBREAK.NEWLINE)},CoreParent:function(){var e=this;while(e&&e.isEmbellished()&&e.CoreMO()===this&&!e.isa(a.math)){e=e.Parent()}return e},CoreText:function(e){if(!e){return""}if(e.isEmbellished()){return e.CoreMO().data.join("")}while((((e.isa(a.mrow)||e.isa(a.TeXAtom)||e.isa(a.mstyle)||e.isa(a.mphantom))&&e.data.length===1)||e.isa(a.munderover))&&e.data[0]){e=e.data[0]}if(!e.isToken){return""}else{return e.data.join("")}},remapChars:{"*":"\u2217",'"':"\u2033","\u00B0":"\u2218","\u00B2":"2","\u00B3":"3","\u00B4":"\u2032","\u00B9":"1"},remap:function(f,e){f=f.replace(/-/g,"\u2212");if(e){f=f.replace(/'/g,"\u2032").replace(/`/g,"\u2035");if(f.length===1){f=e[f]||f}}return f},setTeXclass:function(f){var e=this.getValues("form","lspace","rspace","fence");if(this.hasMMLspacing()){this.texClass=a.TEXCLASS.NONE;return this}if(e.fence&&!this.texClass){if(e.form===a.FORM.PREFIX){this.texClass=a.TEXCLASS.OPEN}if(e.form===a.FORM.POSTFIX){this.texClass=a.TEXCLASS.CLOSE}}this.texClass=this.Get("texClass");if(this.data.join("")==="\u2061"){if(f){f.texClass=a.TEXCLASS.OP;f.fnOP=true}this.texClass=this.prevClass=a.TEXCLASS.NONE;return f}return this.adjustTeXclass(f)},adjustTeXclass:function(f){if(this.texClass===a.TEXCLASS.NONE){return f}if(f){if(f.autoOP&&(this.texClass===a.TEXCLASS.BIN||this.texClass===a.TEXCLASS.REL)){f.texClass=a.TEXCLASS.ORD}this.prevClass=f.texClass||a.TEXCLASS.ORD;this.prevLevel=f.Get("scriptlevel")}else{this.prevClass=a.TEXCLASS.NONE}if(this.texClass===a.TEXCLASS.BIN&&(this.prevClass===a.TEXCLASS.NONE||this.prevClass===a.TEXCLASS.BIN||this.prevClass===a.TEXCLASS.OP||this.prevClass===a.TEXCLASS.REL||this.prevClass===a.TEXCLASS.OPEN||this.prevClass===a.TEXCLASS.PUNCT)){this.texClass=a.TEXCLASS.ORD}else{if(this.prevClass===a.TEXCLASS.BIN&&(this.texClass===a.TEXCLASS.REL||this.texClass===a.TEXCLASS.CLOSE||this.texClass===a.TEXCLASS.PUNCT)){f.texClass=this.prevClass=a.TEXCLASS.ORD}else{if(this.texClass===a.TEXCLASS.BIN){var g=this,e=this.parent;while(e&&e.parent&&e.isEmbellished()&&(e.data.length===1||(e.type!=="mrow"&&e.Core()===g))){g=e;e=e.parent}if(e.data[e.data.length-1]===g){this.texClass=a.TEXCLASS.ORD}}}}return this}});a.mtext=a.mbase.Subclass({type:"mtext",isToken:true,isSpacelike:function(){return true},texClass:a.TEXCLASS.ORD,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT,dir:a.INHERIT}});a.mspace=a.mbase.Subclass({type:"mspace",isToken:true,isSpacelike:function(){return true},defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,width:"0em",height:"0ex",depth:"0ex",linebreak:a.LINEBREAK.AUTO},hasDimAttr:function(){return(this.hasValue("width")||this.hasValue("height")||this.hasValue("depth"))},hasNewline:function(){return(!this.hasDimAttr()&&this.Get("linebreak")===a.LINEBREAK.NEWLINE)}});a.ms=a.mbase.Subclass({type:"ms",isToken:true,texClass:a.TEXCLASS.ORD,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT,dir:a.INHERIT,lquote:'"',rquote:'"'}});a.mglyph=a.mbase.Subclass({type:"mglyph",isToken:true,texClass:a.TEXCLASS.ORD,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,alt:"",src:"",width:a.AUTO,height:a.AUTO,valign:"0em"}});a.mrow=a.mbase.Subclass({type:"mrow",isSpacelike:a.mbase.childrenSpacelike,inferred:false,notParent:false,isEmbellished:function(){var f=false;for(var g=0,e=this.data.length;g<e;g++){if(this.data[g]==null){continue}if(this.data[g].isEmbellished()){if(f){return false}f=true;this.core=g}else{if(!this.data[g].isSpacelike()){return false}}}return f},NonSpaceLength:function(){var g=0;for(var f=0,e=this.data.length;f<e;f++){if(this.data[f]&&!this.data[f].isSpacelike()){g++}}return g},FirstNonSpace:function(){for(var f=0,e=this.data.length;f<e;f++){if(this.data[f]&&!this.data[f].isSpacelike()){return this.data[f]}}return null},LastNonSpace:function(){for(var e=this.data.length-1;e>=0;e--){if(this.data[0]&&!this.data[e].isSpacelike()){return this.data[e]}}return null},Core:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core]},CoreMO:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core].CoreMO()},toString:function(){if(this.inferred){return"["+this.data.join(",")+"]"}return this.SUPER(arguments).toString.call(this)},setTeXclass:function(g){var f,e=this.data.length;if((this.open||this.close)&&(!g||!g.fnOP)){this.getPrevClass(g);g=null;for(f=0;f<e;f++){if(this.data[f]){g=this.data[f].setTeXclass(g)}}if(!this.hasOwnProperty("texClass")){this.texClass=a.TEXCLASS.INNER}return this}else{for(f=0;f<e;f++){if(this.data[f]){g=this.data[f].setTeXclass(g)}}if(this.data[0]){this.updateTeXclass(this.data[0])}return g}},getAnnotation:function(e){if(this.data.length!=1){return null}return this.data[0].getAnnotation(e)}});a.mfrac=a.mbase.Subclass({type:"mfrac",num:0,den:1,linebreakContainer:true,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,linethickness:a.LINETHICKNESS.MEDIUM,numalign:a.ALIGN.CENTER,denomalign:a.ALIGN.CENTER,bevelled:false},adjustChild_displaystyle:function(e){return false},adjustChild_scriptlevel:function(f){var e=this.Get("scriptlevel");if(!this.Get("displaystyle")||e>0){e++}return e},adjustChild_texprimestyle:function(e){if(e==this.den){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.msqrt=a.mbase.Subclass({type:"msqrt",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD,setTeXclass:a.mbase.setSeparateTeXclasses,adjustChild_texprimestyle:function(e){return true}});a.mroot=a.mbase.Subclass({type:"mroot",linebreakContainer:true,texClass:a.TEXCLASS.ORD,adjustChild_displaystyle:function(e){if(e===1){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(f){var e=this.Get("scriptlevel");if(f===1){e+=2}return e},adjustChild_texprimestyle:function(e){if(e===0){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.mstyle=a.mbase.Subclass({type:"mstyle",isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,inferRow:true,defaults:{scriptlevel:a.INHERIT,displaystyle:a.INHERIT,scriptsizemultiplier:Math.sqrt(1/2),scriptminsize:"8pt",mathbackground:a.INHERIT,mathcolor:a.INHERIT,dir:a.INHERIT,infixlinebreakstyle:a.LINEBREAKSTYLE.BEFORE,decimalseparator:"."},adjustChild_scriptlevel:function(g){var f=this.scriptlevel;if(f==null){f=this.Get("scriptlevel")}else{if(String(f).match(/^ *[-+]/)){var e=this.Get("scriptlevel",null,true);f=e+parseInt(f)}}return f},inheritFromMe:true,noInherit:{mpadded:{width:true,height:true,depth:true,lspace:true,voffset:true},mtable:{width:true,height:true,depth:true,align:true}},getRemoved:{fontfamily:"fontFamily",fontweight:"fontWeight",fontstyle:"fontStyle",fontsize:"fontSize"},setTeXclass:a.mbase.setChildTeXclass});a.merror=a.mbase.Subclass({type:"merror",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD});a.mpadded=a.mbase.Subclass({type:"mpadded",inferRow:true,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,width:"",height:"",depth:"",lspace:0,voffset:0},setTeXclass:a.mbase.setChildTeXclass});a.mphantom=a.mbase.Subclass({type:"mphantom",texClass:a.TEXCLASS.ORD,inferRow:true,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,setTeXclass:a.mbase.setChildTeXclass});a.mfenced=a.mbase.Subclass({type:"mfenced",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,open:"(",close:")",separators:","},addFakeNodes:function(){var f=this.getValues("open","close","separators");f.open=f.open.replace(/[ \t\n\r]/g,"");f.close=f.close.replace(/[ \t\n\r]/g,"");f.separators=f.separators.replace(/[ \t\n\r]/g,"");if(f.open!==""){this.SetData("open",a.mo(f.open).With({fence:true,form:a.FORM.PREFIX,texClass:a.TEXCLASS.OPEN}))}if(f.separators!==""){while(f.separators.length<this.data.length){f.separators+=f.separators.charAt(f.separators.length-1)}for(var g=1,e=this.data.length;g<e;g++){if(this.data[g]){this.SetData("sep"+g,a.mo(f.separators.charAt(g-1)).With({separator:true}))}}}if(f.close!==""){this.SetData("close",a.mo(f.close).With({fence:true,form:a.FORM.POSTFIX,texClass:a.TEXCLASS.CLOSE}))}},texClass:a.TEXCLASS.OPEN,setTeXclass:function(g){this.addFakeNodes();this.getPrevClass(g);if(this.data.open){g=this.data.open.setTeXclass(g)}if(this.data[0]){g=this.data[0].setTeXclass(g)}for(var f=1,e=this.data.length;f<e;f++){if(this.data["sep"+f]){g=this.data["sep"+f].setTeXclass(g)}if(this.data[f]){g=this.data[f].setTeXclass(g)}}if(this.data.close){g=this.data.close.setTeXclass(g)}this.updateTeXclass(this.data.open);this.texClass=a.TEXCLASS.INNER;return g}});a.menclose=a.mbase.Subclass({type:"menclose",inferRow:true,linebreakContainer:true,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,notation:a.NOTATION.LONGDIV,texClass:a.TEXCLASS.ORD},setTeXclass:a.mbase.setSeparateTeXclasses});a.msubsup=a.mbase.Subclass({type:"msubsup",base:0,sub:1,sup:2,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,subscriptshift:"",superscriptshift:"",texClass:a.AUTO},autoDefault:function(e){if(e==="texClass"){return(this.isEmbellished()?this.CoreMO().Get(e):a.TEXCLASS.ORD)}return 0},adjustChild_displaystyle:function(e){if(e>0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(f){var e=this.Get("scriptlevel");if(f>0){e++}return e},adjustChild_texprimestyle:function(e){if(e===this.sub){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.msub=a.msubsup.Subclass({type:"msub"});a.msup=a.msubsup.Subclass({type:"msup",sub:2,sup:1});a.mmultiscripts=a.msubsup.Subclass({type:"mmultiscripts",adjustChild_texprimestyle:function(e){if(e%2===1){return true}return this.Get("texprimestyle")}});a.mprescripts=a.mbase.Subclass({type:"mprescripts"});a.none=a.mbase.Subclass({type:"none"});a.munderover=a.mbase.Subclass({type:"munderover",base:0,under:1,over:2,sub:1,sup:2,ACCENTS:["","accentunder","accent"],linebreakContainer:true,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,accent:a.AUTO,accentunder:a.AUTO,align:a.ALIGN.CENTER,texClass:a.AUTO,subscriptshift:"",superscriptshift:""},autoDefault:function(e){if(e==="texClass"){return(this.isEmbellished()?this.CoreMO().Get(e):a.TEXCLASS.ORD)}if(e==="accent"&&this.data[this.over]){return this.data[this.over].CoreMO().Get("accent")}if(e==="accentunder"&&this.data[this.under]){return this.data[this.under].CoreMO().Get("accent")}return false},adjustChild_displaystyle:function(e){if(e>0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(g){var f=this.Get("scriptlevel");var e=(this.data[this.base]&&!this.Get("displaystyle")&&this.data[this.base].CoreMO().Get("movablelimits"));if(g==this.under&&(e||!this.Get("accentunder"))){f++}if(g==this.over&&(e||!this.Get("accent"))){f++}return f},adjustChild_texprimestyle:function(e){if(e===this.base&&this.data[this.over]){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.munder=a.munderover.Subclass({type:"munder"});a.mover=a.munderover.Subclass({type:"mover",over:1,under:2,sup:1,sub:2,ACCENTS:["","accent","accentunder"]});a.mtable=a.mbase.Subclass({type:"mtable",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,align:a.ALIGN.AXIS,rowalign:a.ALIGN.BASELINE,columnalign:a.ALIGN.CENTER,groupalign:"{left}",alignmentscope:true,columnwidth:a.WIDTH.AUTO,width:a.WIDTH.AUTO,rowspacing:"1ex",columnspacing:".8em",rowlines:a.LINES.NONE,columnlines:a.LINES.NONE,frame:a.LINES.NONE,framespacing:"0.4em 0.5ex",equalrows:false,equalcolumns:false,displaystyle:false,side:a.SIDE.RIGHT,minlabelspacing:"0.8em",texClass:a.TEXCLASS.ORD,useHeight:1},adjustChild_displaystyle:function(){return(this.displaystyle!=null?this.displaystyle:this.defaults.displaystyle)},inheritFromMe:true,noInherit:{mover:{align:true},munder:{align:true},munderover:{align:true},mtable:{align:true,rowalign:true,columnalign:true,groupalign:true,alignmentscope:true,columnwidth:true,width:true,rowspacing:true,columnspacing:true,rowlines:true,columnlines:true,frame:true,framespacing:true,equalrows:true,equalcolumns:true,displaystyle:true,side:true,minlabelspacing:true,texClass:true,useHeight:1}},linebreakContainer:true,Append:function(){for(var f=0,e=arguments.length;f<e;f++){if(!((arguments[f] instanceof a.mtr)||(arguments[f] instanceof a.mlabeledtr))){arguments[f]=a.mtr(arguments[f])}}this.SUPER(arguments).Append.apply(this,arguments)},setTeXclass:a.mbase.setSeparateTeXclasses});a.mtr=a.mbase.Subclass({type:"mtr",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,rowalign:a.INHERIT,columnalign:a.INHERIT,groupalign:a.INHERIT},inheritFromMe:true,noInherit:{mrow:{rowalign:true,columnalign:true,groupalign:true},mtable:{rowalign:true,columnalign:true,groupalign:true}},linebreakContainer:true,Append:function(){for(var f=0,e=arguments.length;f<e;f++){if(!(arguments[f] instanceof a.mtd)){arguments[f]=a.mtd(arguments[f])}}this.SUPER(arguments).Append.apply(this,arguments)},setTeXclass:a.mbase.setSeparateTeXclasses});a.mtd=a.mbase.Subclass({type:"mtd",inferRow:true,linebreakContainer:true,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,rowspan:1,columnspan:1,rowalign:a.INHERIT,columnalign:a.INHERIT,groupalign:a.INHERIT},setTeXclass:a.mbase.setSeparateTeXclasses});a.maligngroup=a.mbase.Subclass({type:"maligngroup",isSpacelike:function(){return true},defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,groupalign:a.INHERIT},inheritFromMe:true,noInherit:{mrow:{groupalign:true},mtable:{groupalign:true}}});a.malignmark=a.mbase.Subclass({type:"malignmark",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,edge:a.SIDE.LEFT},isSpacelike:function(){return true}});a.mlabeledtr=a.mtr.Subclass({type:"mlabeledtr"});a.maction=a.mbase.Subclass({type:"maction",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,actiontype:a.ACTIONTYPE.TOGGLE,selection:1},selected:function(){return this.data[this.Get("selection")-1]||a.NULL},isEmbellished:function(){return this.selected().isEmbellished()},isSpacelike:function(){return this.selected().isSpacelike()},Core:function(){return this.selected().Core()},CoreMO:function(){return this.selected().CoreMO()},setTeXclass:function(f){if(this.Get("actiontype")===a.ACTIONTYPE.TOOLTIP&&this.data[1]){this.data[1].setTeXclass()}var e=this.selected();f=e.setTeXclass(f);this.updateTeXclass(e);return f}});a.semantics=a.mbase.Subclass({type:"semantics",notParent:true,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{definitionURL:null,encoding:null},setTeXclass:a.mbase.setChildTeXclass,getAnnotation:function(g){var l=MathJax.Hub.config.MathMenu.semanticsAnnotations[g];if(l){for(var h=0,e=this.data.length;h<e;h++){var k=this.data[h].Get("encoding");if(k){for(var f=0,o=l.length;f<o;f++){if(l[f]===k){return this.data[h]}}}}}return null}});a.annotation=a.mbase.Subclass({type:"annotation",isChars:true,linebreakContainer:true,defaults:{definitionURL:null,encoding:null,cd:"mathmlkeys",name:"",src:null}});a["annotation-xml"]=a.mbase.Subclass({type:"annotation-xml",linebreakContainer:true,defaults:{definitionURL:null,encoding:null,cd:"mathmlkeys",name:"",src:null}});a.math=a.mstyle.Subclass({type:"math",defaults:{mathvariant:a.VARIANT.NORMAL,mathsize:a.SIZE.NORMAL,mathcolor:"",mathbackground:a.COLOR.TRANSPARENT,dir:"ltr",scriptlevel:0,displaystyle:a.AUTO,display:"inline",maxwidth:"",overflow:a.OVERFLOW.LINEBREAK,altimg:"","altimg-width":"","altimg-height":"","altimg-valign":"",alttext:"",cdgroup:"",scriptsizemultiplier:Math.sqrt(1/2),scriptminsize:"8px",infixlinebreakstyle:a.LINEBREAKSTYLE.BEFORE,lineleading:"1ex",indentshift:"auto",indentalign:a.INDENTALIGN.AUTO,indentalignfirst:a.INDENTALIGN.INDENTALIGN,indentshiftfirst:a.INDENTSHIFT.INDENTSHIFT,indentalignlast:a.INDENTALIGN.INDENTALIGN,indentshiftlast:a.INDENTSHIFT.INDENTSHIFT,decimalseparator:".",texprimestyle:false},autoDefault:function(e){if(e==="displaystyle"){return this.Get("display")==="block"}return""},linebreakContainer:true,setTeXclass:a.mbase.setChildTeXclass,getAnnotation:function(e){if(this.data.length!=1){return null}return this.data[0].getAnnotation(e)}});a.chars=a.mbase.Subclass({type:"chars",Append:function(){this.data.push.apply(this.data,arguments)},value:function(){return this.data.join("")},toString:function(){return this.data.join("")}});a.entity=a.mbase.Subclass({type:"entity",Append:function(){this.data.push.apply(this.data,arguments)},value:function(){if(this.data[0].substr(0,2)==="#x"){return parseInt(this.data[0].substr(2),16)}else{if(this.data[0].substr(0,1)==="#"){return parseInt(this.data[0].substr(1))}else{return 0}}},toString:function(){var e=this.value();if(e<=65535){return String.fromCharCode(e)}e-=65536;return String.fromCharCode((e>>10)+55296)+String.fromCharCode((e&1023)+56320)}});a.xml=a.mbase.Subclass({type:"xml",Init:function(){this.div=document.createElement("div");return this.SUPER(arguments).Init.apply(this,arguments)},Append:function(){for(var f=0,e=arguments.length;f<e;f++){var g=this.Import(arguments[f]);this.data.push(g);this.div.appendChild(g)}},Import:function(j){if(document.importNode){return document.importNode(j,true)}var f,g,e;if(j.nodeType===1){f=document.createElement(j.nodeName);for(g=0,e=j.attributes.length;g<e;g++){var h=j.attributes[g];if(h.specified&&h.nodeValue!=null&&h.nodeValue!=""){f.setAttribute(h.nodeName,h.nodeValue)}if(h.nodeName==="style"){f.style.cssText=h.nodeValue}}if(j.className){f.className=j.className}}else{if(j.nodeType===3||j.nodeType===4){f=document.createTextNode(j.nodeValue)}else{if(j.nodeType===8){f=document.createComment(j.nodeValue)}else{return document.createTextNode("")}}}for(g=0,e=j.childNodes.length;g<e;g++){f.appendChild(this.Import(j.childNodes[g]))}return f},value:function(){return this.div},toString:function(){return this.div.innerHTML}});a.TeXAtom=a.mbase.Subclass({type:"texatom",linebreakContainer:true,inferRow:true,notParent:true,texClass:a.TEXCLASS.ORD,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,isEmbellished:a.mbase.childEmbellished,setTeXclass:function(e){this.data[0].setTeXclass();return this.adjustTeXclass(e)},adjustTeXclass:a.mo.prototype.adjustTeXclass});a.NULL=a.mbase().With({type:"null"});var b=a.TEXCLASS;var d={ORD:[0,0,b.ORD],ORD11:[1,1,b.ORD],ORD21:[2,1,b.ORD],ORD02:[0,2,b.ORD],ORD55:[5,5,b.ORD],OP:[1,2,b.OP,{largeop:true,movablelimits:true,symmetric:true}],OPFIXED:[1,2,b.OP,{largeop:true,movablelimits:true}],INTEGRAL:[0,1,b.OP,{largeop:true,symmetric:true}],INTEGRAL2:[1,2,b.OP,{largeop:true,symmetric:true}],BIN3:[3,3,b.BIN],BIN4:[4,4,b.BIN],BIN01:[0,1,b.BIN],BIN5:[5,5,b.BIN],TALLBIN:[4,4,b.BIN,{stretchy:true}],BINOP:[4,4,b.BIN,{largeop:true,movablelimits:true}],REL:[5,5,b.REL],REL1:[1,1,b.REL,{stretchy:true}],REL4:[4,4,b.REL],RELSTRETCH:[5,5,b.REL,{stretchy:true}],RELACCENT:[5,5,b.REL,{accent:true}],WIDEREL:[5,5,b.REL,{accent:true,stretchy:true}],OPEN:[0,0,b.OPEN,{fence:true,stretchy:true,symmetric:true}],CLOSE:[0,0,b.CLOSE,{fence:true,stretchy:true,symmetric:true}],INNER:[0,0,b.INNER],PUNCT:[0,3,b.PUNCT],ACCENT:[0,0,b.ORD,{accent:true}],WIDEACCENT:[0,0,b.ORD,{accent:true,stretchy:true}]};a.mo.Augment({SPACE:["0em","0.1111em","0.1667em","0.2222em","0.2667em","0.3333em"],RANGES:[[32,127,b.REL,"BasicLatin"],[160,255,b.ORD,"Latin1Supplement"],[256,383,b.ORD],[384,591,b.ORD],[688,767,b.ORD,"SpacingModLetters"],[768,879,b.ORD,"CombDiacritMarks"],[880,1023,b.ORD,"GreekAndCoptic"],[7680,7935,b.ORD],[8192,8303,b.PUNCT,"GeneralPunctuation"],[8304,8351,b.ORD],[8352,8399,b.ORD],[8400,8447,b.ORD,"CombDiactForSymbols"],[8448,8527,b.ORD,"LetterlikeSymbols"],[8528,8591,b.ORD],[8592,8703,b.REL,"Arrows"],[8704,8959,b.BIN,"MathOperators"],[8960,9215,b.ORD,"MiscTechnical"],[9312,9471,b.ORD],[9472,9631,b.ORD],[9632,9727,b.ORD,"GeometricShapes"],[9984,10175,b.ORD,"Dingbats"],[10176,10223,b.ORD,"MiscMathSymbolsA"],[10224,10239,b.REL,"SupplementalArrowsA"],[10496,10623,b.REL,"SupplementalArrowsB"],[10624,10751,b.ORD,"MiscMathSymbolsB"],[10752,11007,b.BIN,"SuppMathOperators"],[11008,11263,b.ORD,"MiscSymbolsAndArrows"],[119808,120831,b.ORD]],OPTABLE:{prefix:{"\u2200":d.ORD21,"\u2202":d.ORD21,"\u2203":d.ORD21,"\u2207":d.ORD21,"\u220F":d.OP,"\u2210":d.OP,"\u2211":d.OP,"\u2212":d.BIN01,"\u2213":d.BIN01,"\u221A":[1,1,b.ORD,{stretchy:true}],"\u2220":d.ORD,"\u222B":d.INTEGRAL,"\u222E":d.INTEGRAL,"\u22C0":d.OP,"\u22C1":d.OP,"\u22C2":d.OP,"\u22C3":d.OP,"\u2308":d.OPEN,"\u230A":d.OPEN,"\u27E8":d.OPEN,"\u27EE":d.OPEN,"\u2A00":d.OP,"\u2A01":d.OP,"\u2A02":d.OP,"\u2A04":d.OP,"\u2A06":d.OP,"\u00AC":d.ORD21,"\u00B1":d.BIN01,"(":d.OPEN,"+":d.BIN01,"-":d.BIN01,"[":d.OPEN,"{":d.OPEN,"|":d.OPEN},postfix:{"!":[1,0,b.CLOSE],"&":d.ORD,"\u2032":d.ORD02,"\u203E":d.WIDEACCENT,"\u2309":d.CLOSE,"\u230B":d.CLOSE,"\u23DE":d.WIDEACCENT,"\u23DF":d.WIDEACCENT,"\u266D":d.ORD02,"\u266E":d.ORD02,"\u266F":d.ORD02,"\u27E9":d.CLOSE,"\u27EF":d.CLOSE,"\u02C6":d.WIDEACCENT,"\u02C7":d.WIDEACCENT,"\u02C9":d.WIDEACCENT,"\u02CA":d.ACCENT,"\u02CB":d.ACCENT,"\u02D8":d.ACCENT,"\u02D9":d.ACCENT,"\u02DC":d.WIDEACCENT,"\u0302":d.WIDEACCENT,"\u00A8":d.ACCENT,"\u00AF":d.WIDEACCENT,")":d.CLOSE,"]":d.CLOSE,"^":d.WIDEACCENT,_:d.WIDEACCENT,"`":d.ACCENT,"|":d.CLOSE,"}":d.CLOSE,"~":d.WIDEACCENT},infix:{"":d.ORD,"%":[3,3,b.ORD],"\u2022":d.BIN4,"\u2026":d.INNER,"\u2044":d.TALLBIN,"\u2061":d.ORD,"\u2062":d.ORD,"\u2063":[0,0,b.ORD,{linebreakstyle:"after",separator:true}],"\u2064":d.ORD,"\u2190":d.WIDEREL,"\u2191":d.RELSTRETCH,"\u2192":d.WIDEREL,"\u2193":d.RELSTRETCH,"\u2194":d.WIDEREL,"\u2195":d.RELSTRETCH,"\u2196":d.RELSTRETCH,"\u2197":d.RELSTRETCH,"\u2198":d.RELSTRETCH,"\u2199":d.RELSTRETCH,"\u21A6":d.WIDEREL,"\u21A9":d.WIDEREL,"\u21AA":d.WIDEREL,"\u21BC":d.WIDEREL,"\u21BD":d.WIDEREL,"\u21C0":d.WIDEREL,"\u21C1":d.WIDEREL,"\u21CC":d.WIDEREL,"\u21D0":d.WIDEREL,"\u21D1":d.RELSTRETCH,"\u21D2":d.WIDEREL,"\u21D3":d.RELSTRETCH,"\u21D4":d.WIDEREL,"\u21D5":d.RELSTRETCH,"\u2208":d.REL,"\u2209":d.REL,"\u220B":d.REL,"\u2212":d.BIN4,"\u2213":d.BIN4,"\u2215":d.TALLBIN,"\u2216":d.BIN4,"\u2217":d.BIN4,"\u2218":d.BIN4,"\u2219":d.BIN4,"\u221D":d.REL,"\u2223":d.REL,"\u2225":d.REL,"\u2227":d.BIN4,"\u2228":d.BIN4,"\u2229":d.BIN4,"\u222A":d.BIN4,"\u223C":d.REL,"\u2240":d.BIN4,"\u2243":d.REL,"\u2245":d.REL,"\u2248":d.REL,"\u224D":d.REL,"\u2250":d.REL,"\u2260":d.REL,"\u2261":d.REL,"\u2264":d.REL,"\u2265":d.REL,"\u226A":d.REL,"\u226B":d.REL,"\u227A":d.REL,"\u227B":d.REL,"\u2282":d.REL,"\u2283":d.REL,"\u2286":d.REL,"\u2287":d.REL,"\u228E":d.BIN4,"\u2291":d.REL,"\u2292":d.REL,"\u2293":d.BIN4,"\u2294":d.BIN4,"\u2295":d.BIN4,"\u2296":d.BIN4,"\u2297":d.BIN4,"\u2298":d.BIN4,"\u2299":d.BIN4,"\u22A2":d.REL,"\u22A3":d.REL,"\u22A4":d.ORD55,"\u22A5":d.REL,"\u22A8":d.REL,"\u22C4":d.BIN4,"\u22C5":d.BIN4,"\u22C6":d.BIN4,"\u22C8":d.REL,"\u22EE":d.ORD55,"\u22EF":d.INNER,"\u22F1":[5,5,b.INNER],"\u25B3":d.BIN4,"\u25B5":d.BIN4,"\u25B9":d.BIN4,"\u25BD":d.BIN4,"\u25BF":d.BIN4,"\u25C3":d.BIN4,"\u2758":d.REL,"\u27F5":d.WIDEREL,"\u27F6":d.WIDEREL,"\u27F7":d.WIDEREL,"\u27F8":d.WIDEREL,"\u27F9":d.WIDEREL,"\u27FA":d.WIDEREL,"\u27FC":d.WIDEREL,"\u2A2F":d.BIN4,"\u2A3F":d.BIN4,"\u2AAF":d.REL,"\u2AB0":d.REL,"\u00B1":d.BIN4,"\u00B7":d.BIN4,"\u00D7":d.BIN4,"\u00F7":d.BIN4,"*":d.BIN3,"+":d.BIN4,",":[0,3,b.PUNCT,{linebreakstyle:"after",separator:true}],"-":d.BIN4,".":[3,3,b.ORD],"/":d.ORD11,":":[1,2,b.REL],";":[0,3,b.PUNCT,{linebreakstyle:"after",separator:true}],"<":d.REL,"=":d.REL,">":d.REL,"?":[1,1,b.CLOSE],"\\":d.ORD,"^":d.ORD11,_:d.ORD11,"|":[2,2,b.ORD,{fence:true,stretchy:true,symmetric:true}],"#":d.ORD,"$":d.ORD,"\u002E":[0,3,b.PUNCT,{separator:true}],"\u02B9":d.ORD,"\u0300":d.ACCENT,"\u0301":d.ACCENT,"\u0303":d.WIDEACCENT,"\u0304":d.ACCENT,"\u0306":d.ACCENT,"\u0307":d.ACCENT,"\u0308":d.ACCENT,"\u030C":d.ACCENT,"\u0332":d.WIDEACCENT,"\u0338":d.REL4,"\u2015":[0,0,b.ORD,{stretchy:true}],"\u2017":[0,0,b.ORD,{stretchy:true}],"\u2020":d.BIN3,"\u2021":d.BIN3,"\u20D7":d.ACCENT,"\u2111":d.ORD,"\u2113":d.ORD,"\u2118":d.ORD,"\u211C":d.ORD,"\u2205":d.ORD,"\u221E":d.ORD,"\u2305":d.BIN3,"\u2306":d.BIN3,"\u2322":d.REL4,"\u2323":d.REL4,"\u2329":d.OPEN,"\u232A":d.CLOSE,"\u23AA":d.ORD,"\u23AF":[0,0,b.ORD,{stretchy:true}],"\u23B0":d.OPEN,"\u23B1":d.CLOSE,"\u2500":d.ORD,"\u25EF":d.BIN3,"\u2660":d.ORD,"\u2661":d.ORD,"\u2662":d.ORD,"\u2663":d.ORD,"\u3008":d.OPEN,"\u3009":d.CLOSE,"\uFE37":d.WIDEACCENT,"\uFE38":d.WIDEACCENT}}},{OPTYPES:d});var c=a.mo.prototype.OPTABLE;c.infix["^"]=d.WIDEREL;c.infix._=d.WIDEREL;c.prefix["\u2223"]=d.OPEN;c.prefix["\u2225"]=d.OPEN;c.postfix["\u2223"]=d.CLOSE;c.postfix["\u2225"]=d.CLOSE})(MathJax.ElementJax.mml);MathJax.ElementJax.mml.loadComplete("jax.js");
MathJax.Hub.Register.LoadHook("[MathJax]/jax/element/mml/jax.js",function(){var c="2.7.5";var a=MathJax.ElementJax.mml,b=MathJax.Hub.config.menuSettings;a.mbase.Augment({toMathML:function(l){var h=(this.inferred&&this.parent.inferRow);if(l==null){l=""}var f=this.type,e=this.toMathMLattributes();if(f==="mspace"){return l+"<"+f+e+" />"}var k=[],j=(this.isToken?"":l+(h?"":"  "));for(var g=0,d=this.data.length;g<d;g++){if(this.data[g]){k.push(this.data[g].toMathML(j))}else{if(!this.isToken&&!this.isChars){k.push(j+"<mrow />")}}}if(this.isToken||this.isChars){return l+"<"+f+e+">"+k.join("")+"</"+f+">"}if(h){return k.join("\n")}if(k.length===0||(k.length===1&&k[0]==="")){return l+"<"+f+e+" />"}return l+"<"+f+e+">\n"+k.join("\n")+"\n"+l+"</"+f+">"},toMathMLattributes:function(){var j=(this.type==="mstyle"?a.math.prototype.defaults:this.defaults);var h=(this.attrNames||a.copyAttributeNames),g=a.skipAttributes,l=a.copyAttributes;var e=[];if(this.type==="math"&&(!this.attr||!("xmlns" in this.attr))){e.push('xmlns="http://www.w3.org/1998/Math/MathML"')}if(!this.attrNames){for(var k in j){if(!g[k]&&!l[k]&&j.hasOwnProperty(k)){if(this[k]!=null&&this[k]!==j[k]){if(this.Get(k,null,1)!==this[k]){e.push(k+'="'+this.toMathMLattribute(this[k])+'"')}}}}}for(var f=0,d=h.length;f<d;f++){if(l[h[f]]===1&&!j.hasOwnProperty(h[f])){continue}value=(this.attr||{})[h[f]];if(value==null){value=this[h[f]]}if(value!=null){e.push(h[f]+'="'+this.toMathMLquote(value)+'"')}}this.toMathMLclass(e);if(e.length){return" "+e.join(" ")}else{return""}},toMathMLclass:function(d){var f=[];if(this["class"]){f.push(this["class"])}if(this.isa(a.TeXAtom)&&b.texHints){var e=["ORD","OP","BIN","REL","OPEN","CLOSE","PUNCT","INNER","VCENTER"][this.texClass];if(e){f.push("MJX-TeXAtom-"+e);if(e==="OP"&&!this.movablelimits){f.push("MJX-fixedlimits")}}}if(this.mathvariant&&this.toMathMLvariants[this.mathvariant]){f.push("MJX"+this.mathvariant)}if(this.variantForm){f.push("MJX-variant")}if(f.length){d.unshift('class="'+this.toMathMLquote(f.join(" "))+'"')}},toMathMLattribute:function(d){if(typeof(d)==="string"&&d.replace(/ /g,"").match(/^(([-+])?(\d+(\.\d*)?|\.\d+))mu$/)){return(RegExp.$2||"")+((1/18)*RegExp.$3).toFixed(3).replace(/\.?0+$/,"")+"em"}else{if(this.toMathMLvariants[d]){return this.toMathMLvariants[d]}}return this.toMathMLquote(d)},toMathMLvariants:{"-tex-caligraphic":a.VARIANT.SCRIPT,"-tex-caligraphic-bold":a.VARIANT.BOLDSCRIPT,"-tex-oldstyle":a.VARIANT.NORMAL,"-tex-oldstyle-bold":a.VARIANT.BOLD,"-tex-mathit":a.VARIANT.ITALIC},toMathMLquote:function(f){f=String(f).split("");for(var g=0,d=f.length;g<d;g++){var k=f[g].charCodeAt(0);if(k<=55295||57344<=k){if(k>126||(k<32&&k!==10&&k!==13&&k!==9)){f[g]="&#x"+k.toString(16).toUpperCase()+";"}else{var j={"&":"&amp;","<":"&lt;",">":"&gt;",'"':"&quot;"}[f[g]];if(j){f[g]=j}}}else{if(g+1<d){var h=f[g+1].charCodeAt(0);var e=(((k-55296)<<10)+(h-56320)+65536);f[g]="&#x"+e.toString(16).toUpperCase()+";";f[g+1]="";g++}else{f[g]=""}}}return f.join("")}});a.math.Augment({toMathML:function(d,e){var g;if(d==null){d=""}if(e&&e.originalText&&b.semantics){g=MathJax.InputJax[e.inputJax].annotationEncoding}var n=(this.data[0]&&this.data[0].data.length>1);var p=this.type,k=this.toMathMLattributes();var j=[],o=d+(g?"  "+(n?"  ":""):"")+"  ";for(var h=0,f=this.data.length;h<f;h++){if(this.data[h]){j.push(this.data[h].toMathML(o))}else{j.push(o+"<mrow />")}}if(j.length===0||(j.length===1&&j[0]==="")){if(!g){return"<"+p+k+" />"}j.push(o+"<mrow />")}if(g){if(n){j.unshift(d+"    <mrow>");j.push(d+"    </mrow>")}j.unshift(d+"  <semantics>");var l=e.originalText.replace(/[&<>]/g,function(i){return{">":"&gt;","<":"&lt;","&":"&amp;"}[i]});j.push(d+'    <annotation encoding="'+this.toMathMLquote(g)+'">'+l+"</annotation>");j.push(d+"  </semantics>")}return d+"<"+p+k+">\n"+j.join("\n")+"\n"+d+"</"+p+">"}});a.msubsup.Augment({toMathML:function(j){var f=this.type;if(this.data[this.sup]==null){f="msub"}if(this.data[this.sub]==null){f="msup"}var e=this.toMathMLattributes();delete this.data[0].inferred;var h=[];for(var g=0,d=this.data.length;g<d;g++){if(this.data[g]){h.push(this.data[g].toMathML(j+"  "))}}return j+"<"+f+e+">\n"+h.join("\n")+"\n"+j+"</"+f+">"}});a.munderover.Augment({toMathML:function(k){var f=this.type;var j=this.data[this.base];if(j&&j.isa(a.TeXAtom)&&j.movablelimits&&!j.Get("displaystyle")){type="msubsup";if(this.data[this.under]==null){f="msup"}if(this.data[this.over]==null){f="msub"}}else{if(this.data[this.under]==null){f="mover"}if(this.data[this.over]==null){f="munder"}}var e=this.toMathMLattributes();delete this.data[0].inferred;var h=[];for(var g=0,d=this.data.length;g<d;g++){if(this.data[g]){h.push(this.data[g].toMathML(k+"  "))}}return k+"<"+f+e+">\n"+h.join("\n")+"\n"+k+"</"+f+">"}});a.TeXAtom.Augment({toMathML:function(e){var d=this.toMathMLattributes();if(!d&&this.data[0].data.length===1){return e.substr(2)+this.data[0].toMathML(e)}return e+"<mrow"+d+">\n"+this.data[0].toMathML(e+"  ")+"\n"+e+"</mrow>"}});a.chars.Augment({toMathML:function(d){return(d||"")+this.toMathMLquote(this.toString())}});a.entity.Augment({toMathML:function(d){return(d||"")+"&"+this.toMathMLquote(this.data[0])+";<!-- "+this.toString()+" -->"}});a.xml.Augment({toMathML:function(d){return(d||"")+this.toString()}});MathJax.Hub.Register.StartupHook("TeX mathchoice Ready",function(){a.TeXmathchoice.Augment({toMathML:function(d){return this.Core().toMathML(d)}})});MathJax.Hub.Startup.signal.Post("toMathML Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/toMathML.js");
(function(c,d){var a;var b=function(e){return MathJax.Localization._.apply(MathJax.Localization,[["MathML",e]].concat([].slice.call(arguments,1)))};c.Parse=MathJax.Object.Subclass({Init:function(f,e){this.Parse(f,e)},Parse:function(h,e){var j;if(typeof h!=="string"){j=h.parentNode}else{j=c.ParseXML(this.preProcessMath.call(this,h));if(j==null){c.Error(["ErrorParsingMathML","Error parsing MathML"])}}var g=j.getElementsByTagName("parsererror")[0];if(g){c.Error(["ParsingError","Error parsing MathML: %1",g.textContent.replace(/This page.*?errors:|XML Parsing Error: |Below is a rendering of the page.*/g,"")])}if(j.childNodes.length!==1){c.Error(["MathMLSingleElement","MathML must be formed by a single element"])}if(j.firstChild.nodeName.toLowerCase()==="html"){var f=j.getElementsByTagName("h1")[0];if(f&&f.textContent==="XML parsing error"&&f.nextSibling){c.Error(["ParsingError","Error parsing MathML: %1",String(f.nextSibling.nodeValue).replace(/fatal parsing error: /,"")])}}if(j.firstChild.nodeName.toLowerCase().replace(/^[a-z]+:/,"")!=="math"){c.Error(["MathMLRootElement","MathML must be formed by a <math> element, not %1","<"+j.firstChild.nodeName+">"])}var i={math:j.firstChild,script:e};c.DOMfilterHooks.Execute(i);this.mml=this.MakeMML(i.math)},MakeMML:function(h){var i=String(h.getAttribute("class")||"");var f,g=h.nodeName.toLowerCase().replace(/^[a-z]+:/,"");var e=(i.match(/(^| )MJX-TeXAtom-([^ ]*)/));if(e){f=this.TeXAtom(e[2],e[2]==="OP"&&!i.match(/MJX-fixedlimits/))}else{if(!(a[g]&&a[g].isa&&a[g].isa(a.mbase))){MathJax.Hub.signal.Post(["MathML Jax - unknown node type",g]);return a.Error(b("UnknownNodeType","Unknown node type: %1",g))}else{f=a[g]()}}this.AddAttributes(f,h);this.CheckClass(f,f["class"]);this.AddChildren(f,h);if(c.config.useMathMLspacing){f.useMMLspacing=8}return f},TeXAtom:function(g,f){var e=a.TeXAtom().With({texClass:a.TEXCLASS[g]});if(f){e.movesupsub=e.movablelimits=true}return e},CheckClass:function(f,h){h=(h||"").split(/ /);var j=[];for(var g=0,e=h.length;g<e;g++){if(h[g].substr(0,4)==="MJX-"){if(h[g]==="MJX-arrow"){if(!f.notation.match("/"+a.NOTATION.UPDIAGONALARROW+"/")){f.notation+=" "+a.NOTATION.UPDIAGONALARROW}}else{if(h[g]==="MJX-variant"){f.variantForm=true;if(!MathJax.Extension["TeX/AMSsymbols"]){MathJax.Hub.RestartAfter(MathJax.Ajax.Require("[MathJax]/extensions/TeX/AMSsymbols.js"))}}else{if(h[g].substr(0,11)!=="MJX-TeXAtom"){f.mathvariant=h[g].substr(3);if(f.mathvariant==="-tex-caligraphic-bold"||f.mathvariant==="-tex-oldstyle-bold"){if(!MathJax.Extension["TeX/boldsymbol"]){MathJax.Hub.RestartAfter(MathJax.Ajax.Require("[MathJax]/extensions/TeX/boldsymbol.js"))}}}}}}else{j.push(h[g])}}if(j.length){f["class"]=j.join(" ")}else{delete f["class"]}},AddAttributes:function(g,j){g.attr={};g.attrNames=[];for(var h=0,e=j.attributes.length;h<e;h++){var f=j.attributes[h].name;if(f=="xlink:href"){f="href"}if(f.match(/:/)){continue}if(f.match(/^_moz-math-((column|row)(align|line)|font-style)$/)){continue}var k=j.attributes[h].value;k=this.filterAttribute(f,k);var l=(g.type==="mstyle"?a.math.prototype.defaults:g.defaults);if(k!=null){var n=k.toLowerCase();if(n==="true"||n==="false"){if(typeof(l[f])==="boolean"||l[f]===a.INHERIT||g.type==="math"||g.type==="mstyle"||(l[f]===a.AUTO&&(g.defaultDef==null||typeof(g.defaultDef[f])==="boolean"))){k=(n==="true")}}if(l[f]!=null||a.copyAttributes[f]){g[f]=k}else{g.attr[f]=k}g.attrNames.push(f)}}},filterAttribute:function(e,f){return f},AddChildren:function(e,g){for(var k=0,j=g.childNodes.length;k<j;k++){var f=g.childNodes[k];if(f.nodeName==="#comment"){continue}if(f.nodeName==="#text"){if((e.isToken||e.isChars)&&!e.mmlSelfClosing){var o=f.nodeValue;if(e.isToken){o=o.replace(/&([a-z][a-z0-9]*);/ig,this.replaceEntity);o=this.trimSpace(o)}e.Append(a.chars(o))}else{if(f.nodeValue.match(/\S/)){c.Error(["UnexpectedTextNode","Unexpected text node: %1","'"+f.nodeValue+"'"])}}}else{if(e.type==="annotation-xml"){e.Append(a.xml(f))}else{var h=this.MakeMML(f);e.Append(h);if(h.mmlSelfClosing&&h.data.length){e.Append.apply(e,h.data);h.data=[]}}}}if(e.type==="mrow"&&e.data.length>=2){var l=e.data[0],n=e.data[e.data.length-1];if(l.type==="mo"&&l.Get("fence")&&n.type==="mo"&&n.Get("fence")){if(l.data[0]){e.open=l.data.join("")}if(n.data[0]){e.close=n.data.join("")}}}},preProcessMath:function(f){if(f.match(/^<[a-z]+:/i)&&!f.match(/^<[^<>]* xmlns:/)){f=f.replace(/^<([a-z]+)(:math)/i,'<$1$2 xmlns:$1="http://www.w3.org/1998/Math/MathML"')}var e=f.match(/^(<math( ('.*?'|".*?"|[^>])+)>)/i);if(e&&e[2].match(/ (?!xmlns=)[a-z]+=\"http:/i)){f=e[1].replace(/ (?!xmlns=)([a-z]+=(['"])http:.*?\2)/ig," xmlns:$1 $1")+f.substr(e[0].length)}if(f.match(/^<math[ >]/i)&&!f.match(/^<[^<>]* xmlns=/)){f=f.replace(/^<(math)/i,'<math xmlns="http://www.w3.org/1998/Math/MathML"')}f=f.replace(/^\s*(?:\/\/)?<!(--)?\[CDATA\[((.|\n)*)(\/\/)?\]\]\1>\s*$/,"$2");return f.replace(/&([a-z][a-z0-9]*);/ig,this.replaceEntity)},trimSpace:function(e){return e.replace(/[\t\n\r]/g," ").replace(/^ +/,"").replace(/ +$/,"").replace(/  +/g," ")},replaceEntity:function(g,f){if(f.match(/^(lt|amp|quot)$/)){return g}if(c.Parse.Entity[f]){return c.Parse.Entity[f]}var h=f.charAt(0).toLowerCase();var e=f.match(/^[a-zA-Z](fr|scr|opf)$/);if(e){h=e[1]}if(!c.Parse.loaded[h]){c.Parse.loaded[h]=true;MathJax.Hub.RestartAfter(MathJax.Ajax.Require(c.entityDir+"/"+h+".js"))}return g}},{loaded:[]});c.Augment({sourceMenuTitle:["OriginalMathML","Original MathML"],prefilterHooks:MathJax.Callback.Hooks(true),DOMfilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Translate:function(e){if(!this.ParseXML){this.ParseXML=this.createParser()}var f,h,i={script:e};if(e.firstChild&&e.firstChild.nodeName.toLowerCase().replace(/^[a-z]+:/,"")==="math"){i.math=e.firstChild}else{h=MathJax.HTML.getScript(e);if(d.isMSIE){h=h.replace(/(&nbsp;)+$/,"")}i.math=h}var j=this.prefilterHooks.Execute(i);if(j){return j}h=i.math;try{f=c.Parse(h,e).mml}catch(g){if(!g.mathmlError){throw g}f=this.formatError(g,h,e)}i.math=a(f);return this.postfilterHooks.Execute(i)||i.math},prefilterMath:function(f,e){return f},prefilterMathML:function(f,e){return f},formatError:function(h,g,e){var f=h.message.replace(/\n.*/,"");MathJax.Hub.signal.Post(["MathML Jax - parse error",f,g,e]);return a.Error(f)},Error:function(e){if(MathJax.Object.isArray(e)){e=b.apply(b,e)}throw MathJax.Hub.Insert(Error(e),{mathmlError:true})},parseDOM:function(e){return this.parser.parseFromString(e,"text/xml")},parseMS:function(e){return(this.parser.loadXML(e)?this.parser:null)},parseDIV:function(e){this.div.innerHTML="<div>"+e.replace(/<([a-z]+)([^>]*)\/>/g,"<$1$2></$1>")+"</div>";var f=this.div.firstChild;this.div.innerHTML="";return f},parseError:function(e){return null},createMSParser:function(){var j=null;var f=["MSXML2.DOMDocument.6.0","MSXML2.DOMDocument.5.0","MSXML2.DOMDocument.4.0","MSXML2.DOMDocument.3.0","MSXML2.DOMDocument.2.0","Microsoft.XMLDOM"];for(var g=0,e=f.length;g<e&&!j;g++){try{j=new ActiveXObject(f[g])}catch(h){}}return j},createParser:function(){if(window.DOMParser){this.parser=new DOMParser();return(this.parseDOM)}else{if(window.ActiveXObject){this.parser=this.createMSParser();if(!this.parser){MathJax.Localization.Try(this.parserCreationError);return(this.parseError)}this.parser.async=false;return(this.parseMS)}}this.div=MathJax.Hub.Insert(document.createElement("div"),{style:{visibility:"hidden",overflow:"hidden",height:"1px",position:"absolute",top:0}});if(!document.body.firstChild){document.body.appendChild(this.div)}else{document.body.insertBefore(this.div,document.body.firstChild)}return(this.parseDIV)},parserCreationError:function(){alert(b("CantCreateXMLParser","MathJax can't create an XML parser for MathML.  Check that\nthe 'Script ActiveX controls marked safe for scripting' security\nsetting is enabled (use the Internet Options item in the Tools\nmenu, and select the Security panel, then press the Custom Level\nbutton to check this).\n\nMathML equations will not be able to be processed by MathJax."))},Startup:function(){a=MathJax.ElementJax.mml;a.mspace.Augment({mmlSelfClosing:true});a.none.Augment({mmlSelfClosing:true});a.mprescripts.Augment({mmlSelfClosing:true});a.maligngroup.Augment({mmlSelfClosing:true});a.malignmark.Augment({mmlSelfClosing:true})}});c.prefilterHooks.Add(function(e){e.math=(typeof(e.math)==="string"?c.prefilterMath(e.math,e.script):c.prefilterMathML(e.math,e.script))});c.Parse.Entity={ApplyFunction:"\u2061",Backslash:"\u2216",Because:"\u2235",Breve:"\u02D8",Cap:"\u22D2",CenterDot:"\u00B7",CircleDot:"\u2299",CircleMinus:"\u2296",CirclePlus:"\u2295",CircleTimes:"\u2297",Congruent:"\u2261",ContourIntegral:"\u222E",Coproduct:"\u2210",Cross:"\u2A2F",Cup:"\u22D3",CupCap:"\u224D",Dagger:"\u2021",Del:"\u2207",Delta:"\u0394",Diamond:"\u22C4",DifferentialD:"\u2146",DotEqual:"\u2250",DoubleDot:"\u00A8",DoubleRightTee:"\u22A8",DoubleVerticalBar:"\u2225",DownArrow:"\u2193",DownLeftVector:"\u21BD",DownRightVector:"\u21C1",DownTee:"\u22A4",Downarrow:"\u21D3",Element:"\u2208",EqualTilde:"\u2242",Equilibrium:"\u21CC",Exists:"\u2203",ExponentialE:"\u2147",FilledVerySmallSquare:"\u25AA",ForAll:"\u2200",Gamma:"\u0393",Gg:"\u22D9",GreaterEqual:"\u2265",GreaterEqualLess:"\u22DB",GreaterFullEqual:"\u2267",GreaterLess:"\u2277",GreaterSlantEqual:"\u2A7E",GreaterTilde:"\u2273",Hacek:"\u02C7",Hat:"\u005E",HumpDownHump:"\u224E",HumpEqual:"\u224F",Im:"\u2111",ImaginaryI:"\u2148",Integral:"\u222B",Intersection:"\u22C2",InvisibleComma:"\u2063",InvisibleTimes:"\u2062",Lambda:"\u039B",Larr:"\u219E",LeftAngleBracket:"\u27E8",LeftArrow:"\u2190",LeftArrowRightArrow:"\u21C6",LeftCeiling:"\u2308",LeftDownVector:"\u21C3",LeftFloor:"\u230A",LeftRightArrow:"\u2194",LeftTee:"\u22A3",LeftTriangle:"\u22B2",LeftTriangleEqual:"\u22B4",LeftUpVector:"\u21BF",LeftVector:"\u21BC",Leftarrow:"\u21D0",Leftrightarrow:"\u21D4",LessEqualGreater:"\u22DA",LessFullEqual:"\u2266",LessGreater:"\u2276",LessSlantEqual:"\u2A7D",LessTilde:"\u2272",Ll:"\u22D8",Lleftarrow:"\u21DA",LongLeftArrow:"\u27F5",LongLeftRightArrow:"\u27F7",LongRightArrow:"\u27F6",Longleftarrow:"\u27F8",Longleftrightarrow:"\u27FA",Longrightarrow:"\u27F9",Lsh:"\u21B0",MinusPlus:"\u2213",NestedGreaterGreater:"\u226B",NestedLessLess:"\u226A",NotDoubleVerticalBar:"\u2226",NotElement:"\u2209",NotEqual:"\u2260",NotExists:"\u2204",NotGreater:"\u226F",NotGreaterEqual:"\u2271",NotLeftTriangle:"\u22EA",NotLeftTriangleEqual:"\u22EC",NotLess:"\u226E",NotLessEqual:"\u2270",NotPrecedes:"\u2280",NotPrecedesSlantEqual:"\u22E0",NotRightTriangle:"\u22EB",NotRightTriangleEqual:"\u22ED",NotSubsetEqual:"\u2288",NotSucceeds:"\u2281",NotSucceedsSlantEqual:"\u22E1",NotSupersetEqual:"\u2289",NotTilde:"\u2241",NotVerticalBar:"\u2224",Omega:"\u03A9",OverBar:"\u203E",OverBrace:"\u23DE",PartialD:"\u2202",Phi:"\u03A6",Pi:"\u03A0",PlusMinus:"\u00B1",Precedes:"\u227A",PrecedesEqual:"\u2AAF",PrecedesSlantEqual:"\u227C",PrecedesTilde:"\u227E",Product:"\u220F",Proportional:"\u221D",Psi:"\u03A8",Rarr:"\u21A0",Re:"\u211C",ReverseEquilibrium:"\u21CB",RightAngleBracket:"\u27E9",RightArrow:"\u2192",RightArrowLeftArrow:"\u21C4",RightCeiling:"\u2309",RightDownVector:"\u21C2",RightFloor:"\u230B",RightTee:"\u22A2",RightTeeArrow:"\u21A6",RightTriangle:"\u22B3",RightTriangleEqual:"\u22B5",RightUpVector:"\u21BE",RightVector:"\u21C0",Rightarrow:"\u21D2",Rrightarrow:"\u21DB",Rsh:"\u21B1",Sigma:"\u03A3",SmallCircle:"\u2218",Sqrt:"\u221A",Square:"\u25A1",SquareIntersection:"\u2293",SquareSubset:"\u228F",SquareSubsetEqual:"\u2291",SquareSuperset:"\u2290",SquareSupersetEqual:"\u2292",SquareUnion:"\u2294",Star:"\u22C6",Subset:"\u22D0",SubsetEqual:"\u2286",Succeeds:"\u227B",SucceedsEqual:"\u2AB0",SucceedsSlantEqual:"\u227D",SucceedsTilde:"\u227F",SuchThat:"\u220B",Sum:"\u2211",Superset:"\u2283",SupersetEqual:"\u2287",Supset:"\u22D1",Therefore:"\u2234",Theta:"\u0398",Tilde:"\u223C",TildeEqual:"\u2243",TildeFullEqual:"\u2245",TildeTilde:"\u2248",UnderBar:"\u005F",UnderBrace:"\u23DF",Union:"\u22C3",UnionPlus:"\u228E",UpArrow:"\u2191",UpDownArrow:"\u2195",UpTee:"\u22A5",Uparrow:"\u21D1",Updownarrow:"\u21D5",Upsilon:"\u03A5",Vdash:"\u22A9",Vee:"\u22C1",VerticalBar:"\u2223",VerticalTilde:"\u2240",Vvdash:"\u22AA",Wedge:"\u22C0",Xi:"\u039E",acute:"\u00B4",aleph:"\u2135",alpha:"\u03B1",amalg:"\u2A3F",and:"\u2227",ang:"\u2220",angmsd:"\u2221",angsph:"\u2222",ape:"\u224A",backprime:"\u2035",backsim:"\u223D",backsimeq:"\u22CD",beta:"\u03B2",beth:"\u2136",between:"\u226C",bigcirc:"\u25EF",bigodot:"\u2A00",bigoplus:"\u2A01",bigotimes:"\u2A02",bigsqcup:"\u2A06",bigstar:"\u2605",bigtriangledown:"\u25BD",bigtriangleup:"\u25B3",biguplus:"\u2A04",blacklozenge:"\u29EB",blacktriangle:"\u25B4",blacktriangledown:"\u25BE",blacktriangleleft:"\u25C2",bowtie:"\u22C8",boxdl:"\u2510",boxdr:"\u250C",boxminus:"\u229F",boxplus:"\u229E",boxtimes:"\u22A0",boxul:"\u2518",boxur:"\u2514",bsol:"\u005C",bull:"\u2022",cap:"\u2229",check:"\u2713",chi:"\u03C7",circ:"\u02C6",circeq:"\u2257",circlearrowleft:"\u21BA",circlearrowright:"\u21BB",circledR:"\u00AE",circledS:"\u24C8",circledast:"\u229B",circledcirc:"\u229A",circleddash:"\u229D",clubs:"\u2663",colon:"\u003A",comp:"\u2201",ctdot:"\u22EF",cuepr:"\u22DE",cuesc:"\u22DF",cularr:"\u21B6",cup:"\u222A",curarr:"\u21B7",curlyvee:"\u22CE",curlywedge:"\u22CF",dagger:"\u2020",daleth:"\u2138",ddarr:"\u21CA",deg:"\u00B0",delta:"\u03B4",digamma:"\u03DD",div:"\u00F7",divideontimes:"\u22C7",dot:"\u02D9",doteqdot:"\u2251",dotplus:"\u2214",dotsquare:"\u22A1",dtdot:"\u22F1",ecir:"\u2256",efDot:"\u2252",egs:"\u2A96",ell:"\u2113",els:"\u2A95",empty:"\u2205",epsi:"\u03B5",epsiv:"\u03F5",erDot:"\u2253",eta:"\u03B7",eth:"\u00F0",flat:"\u266D",fork:"\u22D4",frown:"\u2322",gEl:"\u2A8C",gamma:"\u03B3",gap:"\u2A86",gimel:"\u2137",gnE:"\u2269",gnap:"\u2A8A",gne:"\u2A88",gnsim:"\u22E7",gt:"\u003E",gtdot:"\u22D7",harrw:"\u21AD",hbar:"\u210F",hellip:"\u2026",hookleftarrow:"\u21A9",hookrightarrow:"\u21AA",imath:"\u0131",infin:"\u221E",intcal:"\u22BA",iota:"\u03B9",jmath:"\u0237",kappa:"\u03BA",kappav:"\u03F0",lEg:"\u2A8B",lambda:"\u03BB",lap:"\u2A85",larrlp:"\u21AB",larrtl:"\u21A2",lbrace:"\u007B",lbrack:"\u005B",le:"\u2264",leftleftarrows:"\u21C7",leftthreetimes:"\u22CB",lessdot:"\u22D6",lmoust:"\u23B0",lnE:"\u2268",lnap:"\u2A89",lne:"\u2A87",lnsim:"\u22E6",longmapsto:"\u27FC",looparrowright:"\u21AC",lowast:"\u2217",loz:"\u25CA",lt:"\u003C",ltimes:"\u22C9",ltri:"\u25C3",macr:"\u00AF",malt:"\u2720",mho:"\u2127",mu:"\u03BC",multimap:"\u22B8",nLeftarrow:"\u21CD",nLeftrightarrow:"\u21CE",nRightarrow:"\u21CF",nVDash:"\u22AF",nVdash:"\u22AE",natur:"\u266E",nearr:"\u2197",nharr:"\u21AE",nlarr:"\u219A",not:"\u00AC",nrarr:"\u219B",nu:"\u03BD",nvDash:"\u22AD",nvdash:"\u22AC",nwarr:"\u2196",omega:"\u03C9",omicron:"\u03BF",or:"\u2228",osol:"\u2298",period:"\u002E",phi:"\u03C6",phiv:"\u03D5",pi:"\u03C0",piv:"\u03D6",prap:"\u2AB7",precnapprox:"\u2AB9",precneqq:"\u2AB5",precnsim:"\u22E8",prime:"\u2032",psi:"\u03C8",rarrtl:"\u21A3",rbrace:"\u007D",rbrack:"\u005D",rho:"\u03C1",rhov:"\u03F1",rightrightarrows:"\u21C9",rightthreetimes:"\u22CC",ring:"\u02DA",rmoust:"\u23B1",rtimes:"\u22CA",rtri:"\u25B9",scap:"\u2AB8",scnE:"\u2AB6",scnap:"\u2ABA",scnsim:"\u22E9",sdot:"\u22C5",searr:"\u2198",sect:"\u00A7",sharp:"\u266F",sigma:"\u03C3",sigmav:"\u03C2",simne:"\u2246",smile:"\u2323",spades:"\u2660",sub:"\u2282",subE:"\u2AC5",subnE:"\u2ACB",subne:"\u228A",supE:"\u2AC6",supnE:"\u2ACC",supne:"\u228B",swarr:"\u2199",tau:"\u03C4",theta:"\u03B8",thetav:"\u03D1",tilde:"\u02DC",times:"\u00D7",triangle:"\u25B5",triangleq:"\u225C",upsi:"\u03C5",upuparrows:"\u21C8",veebar:"\u22BB",vellip:"\u22EE",weierp:"\u2118",xi:"\u03BE",yen:"\u00A5",zeta:"\u03B6",zigrarr:"\u21DD"};c.loadComplete("jax.js")})(MathJax.InputJax.MathML,MathJax.Hub.Browser);
(function(j,e,g,a){var i;var h=MathJax.Object.isArray;var b="http://www.w3.org/2000/svg";var m="http://www.w3.org/1999/xlink";var k,c,f;var d=(document.getElementsByTagName("base").length===0)?"":String(document.location).replace(/#.*$/,"");a.Augment({HFUZZ:2,DFUZZ:2,config:{styles:{".MathJax_SVG":{display:"inline","font-style":"normal","font-weight":"normal","line-height":"normal","font-size":"100%","font-size-adjust":"none","text-indent":0,"text-align":"left","text-transform":"none","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none",direction:"ltr","max-width":"none","max-height":"none","min-width":0,"min-height":0,border:0,padding:0,margin:0},".MathJax_SVG_Display":{position:"relative",display:"block!important","text-indent":0,"max-width":"none","max-height":"none","min-width":0,"min-height":0,width:"100%"},".MathJax_SVG *":{transition:"none","-webkit-transition":"none","-moz-transition":"none","-ms-transition":"none","-o-transition":"none"},".MathJax_SVG > div":{display:"inline-block"},".mjx-svg-href":{fill:"blue",stroke:"blue"},".MathJax_SVG_Processing":{visibility:"hidden",position:"absolute",top:0,left:0,width:0,height:0,overflow:"hidden",display:"block!important"},".MathJax_SVG_Processed":{display:"none!important"},".MathJax_SVG_test":{"font-style":"normal","font-weight":"normal","font-size":"100%","font-size-adjust":"none","text-indent":0,"text-transform":"none","letter-spacing":"normal","word-spacing":"normal",overflow:"hidden",height:"1px"},".MathJax_SVG_test.mjx-test-display":{display:"table!important"},".MathJax_SVG_test.mjx-test-inline":{display:"inline!important","margin-right":"-1px"},".MathJax_SVG_test.mjx-test-default":{display:"block!important",clear:"both"},".MathJax_SVG_ex_box":{display:"inline-block!important",position:"absolute",overflow:"hidden","min-height":0,"max-height":"none",padding:0,border:0,margin:0,width:"1px",height:"60ex"},".mjx-test-inline .MathJax_SVG_left_box":{display:"inline-block",width:0,"float":"left"},".mjx-test-inline .MathJax_SVG_right_box":{display:"inline-block",width:0,"float":"right"},".mjx-test-display .MathJax_SVG_right_box":{display:"table-cell!important",width:"10000em!important","min-width":0,"max-width":"none",padding:0,border:0,margin:0},"#MathJax_SVG_Tooltip":{position:"absolute",left:0,top:0,width:"auto",height:"auto",display:"none"}}},hideProcessedMath:true,fontNames:["TeX","STIX","STIX-Web","Asana-Math","Gyre-Termes","Gyre-Pagella","Latin-Modern","Neo-Euler"],Config:function(){this.SUPER(arguments).Config.apply(this,arguments);var p=e.config.menuSettings,o=this.config,n=p.font;if(p.scale){o.scale=p.scale}if(n&&n!=="Auto"){n=n.replace(/(Local|Web|Image)$/i,"");n=n.replace(/([a-z])([A-Z])/,"$1-$2");this.fontInUse=n}else{this.fontInUse=o.font||"TeX"}if(this.fontNames.indexOf(this.fontInUse)<0){this.fontInUse="TeX"}this.fontDir+="/"+this.fontInUse;if(!this.require){this.require=[]}this.require.push(this.fontDir+"/fontdata.js");this.require.push(MathJax.OutputJax.extensionDir+"/MathEvents.js")},Startup:function(){k=MathJax.Extension.MathEvents.Event;c=MathJax.Extension.MathEvents.Touch;f=MathJax.Extension.MathEvents.Hover;this.ContextMenu=k.ContextMenu;this.Mousedown=k.AltContextMenu;this.Mouseover=f.Mouseover;this.Mouseout=f.Mouseout;this.Mousemove=f.Mousemove;this.hiddenDiv=g.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=g.addElement(this.hiddenDiv,"div",{id:"MathJax_SVG_Hidden"});var n=g.addElement(this.hiddenDiv,"div",{style:{width:"5in"}});this.pxPerInch=n.offsetWidth/5;this.hiddenDiv.removeChild(n);this.textSVG=this.Element("svg");l.GLYPH.defs=this.addElement(this.addElement(this.hiddenDiv.parentNode,"svg"),"defs",{id:"MathJax_SVG_glyphs"});this.TestSpan=g.Element("span",{className:"MathJax_SVG_test"},[["span",{className:"MathJax_SVG_left_box"}],["span",{className:"MathJax_SVG_ex_box"}],["span",{className:"MathJax_SVG_right_box"}]]);return j.Styles(this.config.styles,["InitializeSVG",this])},InitializeSVG:function(){var n=document.body.appendChild(this.TestSpan.cloneNode(true));n.className+=" mjx-test-inline mjx-test-default";this.defaultEx=n.childNodes[1].offsetHeight/60;this.defaultWidth=Math.max(0,n.lastChild.offsetLeft-n.firstChild.offsetLeft-2);document.body.removeChild(n)},preTranslate:function(s){var r=s.jax[this.id],D,z=r.length,y,G,w,C,u,E,p,F,o,v,t=false,A,q=this.config.linebreaks.automatic,x=this.config.linebreaks.width;if(q){t=(x.match(/^\s*(\d+(\.\d*)?%\s*)?container\s*$/)!=null);if(t){x=x.replace(/\s*container\s*/,"")}else{v=this.defaultWidth}if(x===""){x="100%"}}else{v=100000}for(D=0;D<z;D++){G=r[D];if(!G.parentNode){continue}w=G.previousSibling;if(w&&String(w.className).match(/^MathJax(_SVG)?(_Display)?( MathJax(_SVG)?_Process(ing|ed))?$/)){w.parentNode.removeChild(w)}if(G.MathJax.preview){G.MathJax.preview.style.display="none"}p=G.MathJax.elementJax;if(!p){continue}p.SVG={display:(p.root.Get("display")==="block"),preview:(p.SVG||{}).preview};C=u=g.Element("span",{style:{"font-size":this.config.scale+"%",display:"inline-block"},className:"MathJax_SVG",id:p.inputID+"-Frame",isMathJax:true,jaxID:this.id,oncontextmenu:k.Menu,onmousedown:k.Mousedown,onmouseover:k.Mouseover,onmouseout:k.Mouseout,onmousemove:k.Mousemove,onclick:k.Click,ondblclick:k.DblClick,onkeydown:k.Keydown,tabIndex:e.getTabOrder(p)});if(e.Browser.noContextMenu){C.ontouchstart=c.start;C.ontouchend=c.end}if(p.SVG.display){u=g.Element("div",{className:"MathJax_SVG_Display"});u.appendChild(C)}u.className+=" MathJax_SVG_Processing";G.parentNode.insertBefore(u,G);E=this.TestSpan.cloneNode(true);E.className+=" mjx-test-"+(p.SVG.display?"display":"inline");G.parentNode.insertBefore(E,G)}var B=[];for(D=0;D<z;D++){G=r[D];if(!G.parentNode){continue}E=G.previousSibling;u=E.previousSibling;p=G.MathJax.elementJax;if(!p){continue}F=E.childNodes[1].offsetHeight/60;A=Math.max(0,p.SVG.display?E.lastChild.offsetWidth-1:E.lastChild.offsetLeft-E.firstChild.offsetLeft-2)/this.config.scale*100;if(F===0||F==="NaN"){B.push(u);p.SVG.isHidden=true;F=this.defaultEx;A=this.defaultWidth}if(A===0&&!p.SVG.display){A=this.defaultWidth}if(t){v=A}p.SVG.ex=F;p.SVG.em=o=F/a.TeX.x_height*1000;p.SVG.cwidth=A/o*1000;p.SVG.lineWidth=(q?this.length2em(x,1,v/o*1000):a.BIGDIMEN)}for(D=0,y=B.length;D<y;D++){this.hiddenDiv.appendChild(B[D]);this.addElement(this.hiddenDiv,"br")}for(D=0;D<z;D++){G=r[D];if(!G.parentNode){continue}p=G.MathJax.elementJax;if(!p){continue}G.parentNode.removeChild(G.previousSibling);if(G.MathJax.preview){G.MathJax.preview.style.display=""}}s.SVGeqn=s.SVGlast=0;s.SVGi=-1;s.SVGchunk=this.config.EqnChunk;s.SVGdelay=false},Translate:function(o,s){if(!o.parentNode){return}if(s.SVGdelay){s.SVGdelay=false;e.RestartAfter(MathJax.Callback.Delay(this.config.EqnChunkDelay))}var n=o.MathJax.elementJax,r=n.root,u,p,t=(a.config.useFontCache&&!a.config.useGlobalCache);if(n.SVG.isHidden){p=document.getElementById(n.inputID+"-Frame");u=(n.SVG.display?p.parentElement:p)}else{u=o.previousSibling;p=(n.SVG.display?(u||{}).firstChild||u:u)}if(!u){return}this.em=i.mbase.prototype.em=n.SVG.em;this.ex=n.SVG.ex;this.linebreakWidth=n.SVG.lineWidth;this.cwidth=n.SVG.cwidth;this.mathDiv=u;p.appendChild(this.textSVG);if(t){a.resetGlyphs()}this.initSVG(r,p);r.setTeXclass();try{r.toSVG(p,u)}catch(q){if(q.restart){while(p.firstChild){p.removeChild(p.firstChild)}}if(t){l.GLYPH.n--}throw q}p.removeChild(this.textSVG);if(n.SVG.isHidden){o.parentNode.insertBefore(u,o)}u.className=u.className.split(/ /)[0];if(this.hideProcessedMath){u.className+=" MathJax_SVG_Processed";if(o.MathJax.preview){n.SVG.preview=o.MathJax.preview;delete o.MathJax.preview}s.SVGeqn+=(s.i-s.SVGi);s.SVGi=s.i;if(s.SVGeqn>=s.SVGlast+s.SVGchunk){this.postTranslate(s,true);s.SVGchunk=Math.floor(s.SVGchunk*this.config.EqnChunkFactor);s.SVGdelay=true}}},postTranslate:function(t,q){var o=t.jax[this.id];if(!this.hideProcessedMath){return}for(var r=t.SVGlast,n=t.SVGeqn;r<n;r++){var p=o[r];if(p&&p.MathJax.elementJax){p.previousSibling.className=p.previousSibling.className.split(/ /)[0];var s=p.MathJax.elementJax.SVG;if(s.preview){s.preview.innerHTML="";p.MathJax.preview=s.preview;delete s.preview}}}t.SVGlast=t.SVGeqn},resetGlyphs:function(o){if(this.config.useFontCache){var n=l.GLYPH;if(this.config.useGlobalCache){n.defs=document.getElementById("MathJax_SVG_glyphs");n.defs.innerHTML=""}else{n.defs=this.Element("defs");n.n++}n.glyphs={};if(o){n.n=0}}},hashCheck:function(n){if(n&&n.nodeName.toLowerCase()==="g"){do{n=n.parentNode}while(n&&n.firstChild.nodeName!=="svg")}return n},getJaxFromMath:function(n){if(n.parentNode.className.match(/MathJax_SVG_Display/)){n=n.parentNode}do{n=n.nextSibling}while(n&&n.nodeName.toLowerCase()!=="script");return e.getJaxFor(n)},getHoverSpan:function(n,o){o.style.position="relative";return o.firstChild},getHoverBBox:function(n,o,p){var q=k.getBBox(o.parentNode);q.h+=2;q.d-=2;return q},Zoom:function(o,x,w,n,u){x.className="MathJax_SVG";var z=x.appendChild(this.TestSpan.cloneNode(true));var t=z.childNodes[1].offsetHeight/60;this.em=i.mbase.prototype.em=t/a.TeX.x_height*1000;this.ex=t;this.linebreakWidth=o.SVG.lineWidth;this.cwidth=o.SVG.cwidth;z.parentNode.removeChild(z);x.appendChild(this.textSVG);this.mathDIV=x;this.zoomScale=parseInt(e.config.menuSettings.zscale)/100;var s=o.root.data[0].SVGdata.tw;if(s&&s<this.cwidth){this.cwidth=s}this.idPostfix="-zoom";o.root.toSVG(x,x);this.idPostfix="";this.zoomScale=1;x.removeChild(this.textSVG);var r=x.getElementsByTagName("svg")[0].style;r.marginTop=r.marginRight=r.marginLeft=0;if(r.marginBottom.charAt(0)==="-"){x.style.marginBottom=r.marginBottom.substr(1)}if(this.operaZoomRefresh){setTimeout(function(){x.firstChild.style.border="1px solid transparent"},1)}if(x.offsetWidth<x.firstChild.offsetWidth){x.style.minWidth=x.firstChild.offsetWidth+"px";w.style.minWidth=w.firstChild.offsetWidth+"px"}x.style.position=w.style.position="absolute";var v=x.offsetWidth,q=x.offsetHeight,y=w.offsetHeight,p=w.offsetWidth;x.style.position=w.style.position="";return{Y:-k.getBBox(x).h,mW:p,mH:y,zW:v,zH:q}},initSVG:function(o,n){},Remove:function(n){var o=document.getElementById(n.inputID+"-Frame");if(o){if(n.SVG.display){o=o.parentNode}o.parentNode.removeChild(o)}delete n.SVG},Em:function(n){if(Math.abs(n)<0.0006){return"0"}return n.toFixed(3).replace(/\.?0+$/,"")+"em"},Ex:function(n){n=n/this.TeX.x_height;if(Math.abs(n)<0.0006){return"0"}return n.toFixed(3).replace(/\.?0+$/,"")+"ex"},Percent:function(n){return(100*n).toFixed(1).replace(/\.?0+$/,"")+"%"},Fixed:function(o,p){if(Math.abs(o)<0.0006){return"0"}return o.toFixed(p||3).replace(/\.?0+$/,"")},length2em:function(s,o,q){if(typeof(s)!=="string"){s=s.toString()}if(s===""){return""}if(s===i.SIZE.NORMAL){return 1000}if(s===i.SIZE.BIG){return 2000}if(s===i.SIZE.SMALL){return 710}if(s==="infinity"){return a.BIGDIMEN}if(s.match(/mathspace$/)){return 1000*a.MATHSPACE[s]}var t=(this.zoomScale||1)/a.em;var p=s.match(/^\s*([-+]?(?:\.\d+|\d+(?:\.\d*)?))?(pt|em|ex|mu|px|pc|in|mm|cm|%)?/);var n=parseFloat(p[1]||"1")*1000,r=p[2];if(q==null){q=1000}if(o==null){o=1}if(r==="em"){return n}if(r==="ex"){return n*a.TeX.x_height/1000}if(r==="%"){return n/100*q/1000}if(r==="px"){return n*t}if(r==="pt"){return n/10}if(r==="pc"){return n*1.2}if(r==="in"){return n*this.pxPerInch*t}if(r==="cm"){return n*this.pxPerInch*t/2.54}if(r==="mm"){return n*this.pxPerInch*t/25.4}if(r==="mu"){return n/18*o}return n*q/1000},thickness2em:function(o,n){var p=a.TeX.rule_thickness;if(o===i.LINETHICKNESS.MEDIUM){return p}if(o===i.LINETHICKNESS.THIN){return 0.67*p}if(o===i.LINETHICKNESS.THICK){return 1.67*p}return this.length2em(o,n,p)},border2em:function(o,n){if(o===i.LINETHICKNESS.THIN){o="1px"}if(o===i.LINETHICKNESS.MEDIUM){o="3px"}if(o===i.LINETHICKNESS.THICK){o="5px"}return this.length2em(o,n)},getPadding:function(o){var q={top:0,right:0,bottom:0,left:0},n=false;for(var r in q){if(q.hasOwnProperty(r)){var p=o["padding"+r.charAt(0).toUpperCase()+r.substr(1)];if(p){q[r]=this.length2em(p);n=true}}}return(n?q:false)},getBorders:function(r){var p={top:0,right:0,bottom:0,left:0},o=false;for(var s in p){if(p.hasOwnProperty(s)){var n="border"+s.charAt(0).toUpperCase()+s.substr(1);var q=r[n+"Style"];if(q&&q!=="none"){o=true;p[s]=this.border2em(r[n+"Width"]||i.LINETHICKNESS.MEDIUM);p[s+"Style"]=r[n+"Style"];p[s+"Color"]=r[n+"Color"];if(p[s+"Color"]==="initial"){p[s+"Color"]=""}}else{delete p[s]}}}return(o?p:false)},Element:function(n,o){var p=(typeof(n)==="string"?document.createElementNS(b,n):n);p.isMathJax=true;if(o){for(var q in o){if(o.hasOwnProperty(q)){p.setAttribute(q,o[q].toString())}}}return p},addElement:function(o,n,p){return o.appendChild(this.Element(n,p))},TextNode:g.TextNode,addText:g.addText,ucMatch:g.ucMatch,HandleVariant:function(u,t,D){var x=l.G();var q,z,B,r,C,v,s,p,A,o;if(!u){u=this.FONTDATA.VARIANT[i.VARIANT.NORMAL]}if(u.forceFamily){D=l.TEXT(t,D,u.font);if(u.h!=null){D.h=u.h}if(u.d!=null){D.d=u.d}x.Add(D);D=""}C=u;for(v=0,s=D.length;v<s;v++){u=C;q=D.charCodeAt(v);B=D.charAt(v);if(q>=55296&&q<56319){v++;q=(((q-55296)<<10)+(D.charCodeAt(v)-56320))+65536;if(this.FONTDATA.RemapPlane1){var y=this.FONTDATA.RemapPlane1(q,u);q=y.n;u=y.variant}}else{o=this.FONTDATA.RANGES;for(p=0,A=o.length;p<A;p++){if(o[p].name==="alpha"&&u.noLowerCase){continue}z=u["offset"+o[p].offset];if(z&&q>=o[p].low&&q<=o[p].high){if(o[p].remap&&o[p].remap[q]){q=z+o[p].remap[q]}else{if(o[p].remapOnly){break}q=q-o[p].low+z;if(o[p].add){q+=o[p].add}}if(u["variant"+o[p].offset]){u=this.FONTDATA.VARIANT[u["variant"+o[p].offset]]}break}}}if(u.remap&&u.remap[q]){q=u.remap[q];if(u.remap.variant){u=this.FONTDATA.VARIANT[u.remap.variant]}}else{if(this.FONTDATA.REMAP[q]&&!u.noRemap){q=this.FONTDATA.REMAP[q]}}if(h(q)){u=this.FONTDATA.VARIANT[q[1]];q=q[0]}if(typeof(q)==="string"){D=q+D.substr(v+1);s=D.length;v=-1;continue}r=this.lookupChar(u,q);B=r[q];if(B){if((B[5]&&B[5].space)||(B[5]===""&&B[0]+B[1]===0)){x.w+=B[2]}else{B=[t,r.id+"-"+q.toString(16).toUpperCase()].concat(B);x.Add(l.GLYPH.apply(l,B),x.w,0)}}else{if(this.FONTDATA.DELIMITERS[q]){B=this.createDelimiter(q,0,1,r);x.Add(B,x.w,(this.FONTDATA.DELIMITERS[q].dir==="V"?B.d:0))}else{if(q<=65535){B=String.fromCharCode(q)}else{z=q-65536;B=String.fromCharCode((z>>10)+55296)+String.fromCharCode((z&1023)+56320)}var w=l.TEXT(t*100/a.config.scale,B,{"font-family":u.defaultFamily||a.config.undefinedFamily,"font-style":(u.italic?"italic":""),"font-weight":(u.bold?"bold":"")});if(u.h!=null){w.h=u.h}if(u.d!=null){w.d=u.d}B=l.G();B.Add(w);x.Add(B,x.w,0);e.signal.Post(["SVG Jax - unknown char",q,u])}}}if(a.isChar(D)&&r.skew&&r.skew[q]){x.skew=r.skew[q]*1000}if(x.element.childNodes.length===1&&!x.element.firstChild.getAttribute("x")){x.element=x.element.firstChild;x.removeable=false;x.scale=t}return x},lookupChar:function(r,u){var q,o;if(!r.FONTS){var t=this.FONTDATA.FONTS;var s=(r.fonts||this.FONTDATA.VARIANT.normal.fonts);if(!(s instanceof Array)){s=[s]}if(r.fonts!=s){r.fonts=s}r.FONTS=[];for(q=0,o=s.length;q<o;q++){if(t[s[q]]){r.FONTS.push(t[s[q]])}}}for(q=0,o=r.FONTS.length;q<o;q++){var p=r.FONTS[q];if(typeof(p)==="string"){delete r.FONTS;this.loadFont(p)}if(p[u]){return p}else{this.findBlock(p,u)}}return{id:"unknown"}},isChar:function(o){if(o.length===1){return true}if(o.length!==2){return false}var p=o.charCodeAt(0);return(p>=55296&&p<56319)},findBlock:function(o,s){if(o.Ranges){for(var r=0,n=o.Ranges.length;r<n;r++){if(s<o.Ranges[r][0]){return}if(s<=o.Ranges[r][1]){var q=o.Ranges[r][2];for(var p=o.Ranges.length-1;p>=0;p--){if(o.Ranges[p][2]==q){o.Ranges.splice(p,1)}}this.loadFont(o.directory+"/"+q+".js")}}}},loadFont:function(n){e.RestartAfter(j.Require(this.fontDir+"/"+n))},createDelimiter:function(n,p,s,q){if(!s){s=1}var u=l.G();if(!n){u.Clean();delete u.element;u.w=u.r=this.TeX.nulldelimiterspace*s;return u}if(!(p instanceof Array)){p=[p,p]}var v=p[1];p=p[0];var o={alias:n};while(o.alias){n=o.alias;o=this.FONTDATA.DELIMITERS[n];if(!o){o={HW:[0,this.FONTDATA.VARIANT[i.VARIANT.NORMAL]]}}}if(o.load){e.RestartAfter(j.Require(this.fontDir+"/fontdata-"+o.load+".js"))}for(var t=0,r=o.HW.length;t<r;t++){if(o.HW[t][0]*s>=p-10-a.config.blacker||(t==r-1&&!o.stretch)){if(o.HW[t][2]){s*=o.HW[t][2]}if(o.HW[t][3]){n=o.HW[t][3]}return this.createChar(s,[n,o.HW[t][1]],q).With({stretched:true})}}if(o.stretch){this["extendDelimiter"+o.dir](u,v,o.stretch,s,q)}return u},createChar:function(u,s,p){var t="",r={fonts:[s[1]],noRemap:true};if(p&&p===i.VARIANT.BOLD){r.fonts=[s[1]+"-bold",s[1]]}if(typeof(s[1])!=="string"){r=s[1]}if(s[0] instanceof Array){for(var q=0,n=s[0].length;q<n;q++){t+=String.fromCharCode(s[0][q])}}else{t=String.fromCharCode(s[0])}if(s[4]){u=u*s[4]}var o=this.HandleVariant(r,u,t);if(s[2]){o.x=s[2]*1000}if(s[3]){o.y=s[3]*1000}if(s[5]){o.h+=s[5]*1000}if(s[6]){o.d+=s[6]*1000}return o},extendDelimiterV:function(u,C,o,q,p){var A=this.createChar(q,(o.top||o.ext),p);var w=this.createChar(q,(o.bot||o.ext),p);var t=A.h+A.d+w.h+w.d;var z=-A.h;u.Add(A,0,z);z-=A.d;if(o.mid){var B=this.createChar(q,o.mid,p);t+=B.h+B.d}if(o.min&&C<t*o.min){C=t*o.min}if(C>t){var n=this.createChar(q,o.ext,p);var r=(o.mid?2:1),x=(C-t)/r,D=(x+100)/(n.h+n.d);while(r-->0){var v=a.Element("g",{transform:"translate("+n.y+","+(z-D*n.h+50+n.y)+") scale(1,"+D+")"});v.appendChild(n.element.cloneNode(false));u.element.appendChild(v);z-=x;if(o.mid&&r){u.Add(B,0,z-B.h);z-=(B.h+B.d)}}}else{if(o.mid){z+=(t-C)/2;u.Add(B,0,z-B.h);z+=-(B.h+B.d)+(t-C)/2}else{z+=(t-C)}}u.Add(w,0,z-w.h);u.Clean();u.scale=q;u.isMultiChar=true},extendDelimiterH:function(v,q,o,t,p){var r=this.createChar(t,(o.left||o.rep),p);var E=this.createChar(t,(o.right||o.rep),p);v.Add(r,-r.l,0);var D=(r.r-r.l)+(E.r-E.l),B=r.r-r.l;if(o.mid){var C=this.createChar(t,o.mid,p);D+=C.w}if(o.min&&q<D*o.min){q=D*o.min}if(q>D){var A=this.createChar(t,o.rep,p),n=o.fuzz||0;var u=(o.mid?2:1),z=(q-D)/u,F=(z+n)/(A.r-A.l);while(u-->0){var y=a.Element("g",{transform:"translate("+(B-n/2-F*A.l+A.x)+","+A.y+") scale("+F+",1)"});y.appendChild(A.element.cloneNode(false));v.element.appendChild(y);B+=z;if(o.mid&&u){v.Add(C,B,0);B+=C.w}}}else{if(o.mid){B-=(D-q)/2;v.Add(C,B,0);B+=C.w-(D-q)/2}else{B-=(D-q)}}v.Add(E,B-E.l,0);v.Clean();v.scale=t;v.isMultiChar=true},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:430.554,quad:1000,num1:676.508,num2:393.732,num3:443.73,denom1:685.951,denom2:344.841,sup1:412.892,sup2:362.892,sup3:288.888,sub1:150,sub2:247.217,sup_drop:386.108,sub_drop:50,delim1:2390,delim2:1000,axis_height:250,rule_thickness:60,big_op_spacing1:111.111,big_op_spacing2:166.666,big_op_spacing3:200,big_op_spacing4:600,big_op_spacing5:100,scriptspace:100,nulldelimiterspace:120,delimiterfactor:901,delimitershortfall:300,min_rule_thickness:1.25,min_root_space:1.5},BIGDIMEN:10000000,NBSP:"\u00A0"});var l=a.BBOX=MathJax.Object.Subclass({type:"g",removeable:true,Init:function(n){this.h=this.d=-a.BIGDIMEN;this.H=this.D=0;this.w=this.r=0;this.l=a.BIGDIMEN;this.x=this.y=0;this.scale=1;this.n=0;if(this.type){this.element=a.Element(this.type,n)}},With:function(n){return e.Insert(this,n)},Add:function(q,w,v,n,u){if(w){q.x+=w}if(v){q.y+=v}if(q.element){if(q.removeable&&q.element.childNodes.length===1&&q.n===1){var o=q.element.firstChild,s=o.nodeName.toLowerCase();if(s==="use"||s==="rect"){q.element=o;q.scale=q.childScale;var t=q.childX,r=q.childY;q.x+=t;q.y+=r;q.h-=r;q.d+=r;q.H-=r;q.D+=r;q.w-=t;q.r-=t;q.l+=t;q.removeable=false;o.setAttribute("x",Math.floor(q.x/q.scale));o.setAttribute("y",Math.floor(q.y/q.scale))}}if(Math.abs(q.x)<1&&Math.abs(q.y)<1){q.remove=q.removeable}else{s=q.element.nodeName.toLowerCase();if(s==="g"){if(!q.element.firstChild){q.remove=q.removeable}else{q.element.setAttribute("transform","translate("+Math.floor(q.x)+","+Math.floor(q.y)+")")}}else{if(s==="line"||s==="polygon"||s==="path"||s==="a"){var p=q.element.getAttribute("transform")||"";if(p){p=" "+p}p="translate("+Math.floor(q.x)+","+Math.floor(q.y)+")"+p;q.element.setAttribute("transform",p)}else{q.element.setAttribute("x",Math.floor(q.x/q.scale));q.element.setAttribute("y",Math.floor(q.y/q.scale))}}}if(q.remove){this.n+=q.n;while(q.element.firstChild){if(u&&this.element.firstChild){this.element.insertBefore(q.element.firstChild,this.element.firstChild)}else{this.element.appendChild(q.element.firstChild)}}}else{if(u){this.element.insertBefore(q.element,this.element.firstChild)}else{this.element.appendChild(q.element)}}delete q.element}if(q.hasIndent){this.hasIndent=q.hasIndent}if(q.tw!=null){this.tw=q.tw}if(q.d-q.y>this.d){this.d=q.d-q.y;if(this.d>this.D){this.D=this.d}}if(q.y+q.h>this.h){this.h=q.y+q.h;if(this.h>this.H){this.H=this.h}}if(q.D-q.y>this.D){this.D=q.D-q.y}if(q.y+q.H>this.H){this.H=q.y+q.H}if(q.x+q.l<this.l){this.l=q.x+q.l}if(q.x+q.r>this.r){this.r=q.x+q.r}if(n||q.x+q.w+(q.X||0)>this.w){this.w=q.x+q.w+(q.X||0)}this.childScale=q.scale;this.childX=q.x;this.childY=q.y;this.n++;return q},Align:function(r,s,q,p,o){q=({left:q,center:(this.w-r.w)/2,right:this.w-r.w-q})[s]||0;var n=this.w;this.Add(r,q+(o||0),p);this.w=n},Clean:function(){if(this.h===-a.BIGDIMEN){this.h=this.d=this.l=0}return this}});l.ROW=l.Subclass({Init:function(){this.SUPER(arguments).Init.call(this);this.svg=[];this.sh=this.sd=0},Check:function(o){var n=o.toSVG();this.svg.push(n);if(o.SVGcanStretch("Vertical")){n.mml=o}if(n.h+n.y>this.sh){this.sh=n.h+n.y}if(n.d-n.y>this.sd){this.sd=n.d-n.y}},Stretch:function(){for(var q=0,n=this.svg.length;q<n;q++){var o=this.svg[q],p=o.mml;if(p){if(p.forceStretch||p.SVGdata.h!==this.sh||p.SVGdata.d!==this.sd){o=p.SVGstretchV(this.sh,this.sd)}p.SVGdata.HW=this.sh;p.SVGdata.D=this.sd}if(o.ic){this.ic=o.ic}else{delete this.ic}this.Add(o,this.w,0,true)}delete this.svg}});l.RECT=l.Subclass({type:"rect",removeable:false,Init:function(o,q,n,p){if(p==null){p={stroke:"none"}}p.width=Math.floor(n);p.height=Math.floor(o+q);this.SUPER(arguments).Init.call(this,p);this.w=this.r=n;this.h=this.H=o+q;this.d=this.D=this.l=0;this.y=-q}});l.FRAME=l.Subclass({type:"rect",removeable:false,Init:function(q,u,n,p,s,o,r){if(r==null){r={}}r.fill="none";r["stroke-width"]=a.Fixed(p,2);r.width=Math.floor(n-p);r.height=Math.floor(q+u-p);r.transform="translate("+Math.floor(p/2)+","+Math.floor(-u+p/2)+")";if(s==="dashed"){r["stroke-dasharray"]=[Math.floor(6*a.em),Math.floor(6*a.em)].join(" ")}this.SUPER(arguments).Init.call(this,r);this.w=this.r=n;this.h=this.H=q;this.d=this.D=u;this.l=0}});l.HLINE=l.Subclass({type:"line",removeable:false,Init:function(p,r,u,q,s){if(s==null){s={"stroke-linecap":"square"}}if(q&&q!==""){s.stroke=q}s["stroke-width"]=a.Fixed(r,2);s.x1=s.y1=s.y2=Math.floor(r/2);s.x2=Math.floor(p-r/2);if(u==="dashed"){var v=Math.floor(Math.max(0,p-r)/(6*r)),o=Math.floor(Math.max(0,p-r)/(2*v+1));s["stroke-dasharray"]=o+" "+o}if(u==="dotted"){s["stroke-dasharray"]=[1,Math.max(150,Math.floor(2*r))].join(" ");s["stroke-linecap"]="round"}this.SUPER(arguments).Init.call(this,s);this.w=this.r=p;this.l=0;this.h=this.H=r;this.d=this.D=0}});l.VLINE=l.Subclass({type:"line",removeable:false,Init:function(r,q,u,p,s){if(s==null){s={"stroke-linecap":"square"}}if(p&&p!==""){s.stroke=p}s["stroke-width"]=a.Fixed(q,2);s.x1=s.x2=s.y1=Math.floor(q/2);s.y2=Math.floor(r-q/2);if(u==="dashed"){var v=Math.floor(Math.max(0,r-q)/(6*q)),o=Math.floor(Math.max(0,r-q)/(2*v+1));s["stroke-dasharray"]=o+" "+o}if(u==="dotted"){s["stroke-dasharray"]=[1,Math.max(150,Math.floor(2*q))].join(" ");s["stroke-linecap"]="round"}this.SUPER(arguments).Init.call(this,s);this.w=this.r=q;this.l=0;this.h=this.H=r;this.d=this.D=0}});l.TEXT=l.Subclass({type:"text",removeable:false,Init:function(q,p,n){if(!n){n={}}n.stroke="none";if(n["font-style"]===""){delete n["font-style"]}if(n["font-weight"]===""){delete n["font-weight"]}this.SUPER(arguments).Init.call(this,n);a.addText(this.element,p);a.textSVG.appendChild(this.element);var o=this.element.getBBox();a.textSVG.removeChild(this.element);q*=1000/a.em;this.element.setAttribute("transform","scale("+a.Fixed(q)+") matrix(1 0 0 -1 0 0)");this.w=this.r=o.width*q;this.l=0;this.h=this.H=-o.y*q;this.d=this.D=(o.height+o.y)*q}});l.G=l;l.NULL=l.Subclass({Init:function(){this.SUPER(arguments).Init.apply(this,arguments);this.Clean()}});l.GLYPH=l.Subclass({type:"path",removeable:false,Init:function(x,q,A,B,C,y,o,s){var u,D=a.config.blacker,z=l.GLYPH;var n=a.config.useFontCache;var v=(x===1?null:"scale("+a.Fixed(x)+")");if(n&&!a.config.useGlobalCache){q="E"+z.n+"-"+q}if(!n||!z.glyphs[q]){u={"stroke-width":D};if(n){u.id=q}else{if(v){u.transform=v}}u.d=(s?"M"+s+"Z":"");this.SUPER(arguments).Init.call(this,u);if(n){z.defs.appendChild(this.element);z.glyphs[q]=true}}if(n){u={};if(v){u.transform=v}this.element=a.Element("use",u);this.element.setAttributeNS(m,"href",d+"#"+q)}this.h=(A+D)*x;this.d=(B+D)*x;this.w=(C+D/2)*x;this.l=(y+D/2)*x;this.r=(o+D/2)*x;this.H=Math.max(0,this.h);this.D=Math.max(0,this.d);this.x=this.y=0;this.scale=x}},{glyphs:{},defs:null,n:0});e.Register.StartupHook("mml Jax Ready",function(){i=MathJax.ElementJax.mml;i.mbase.Augment({SVG:l,toSVG:function(){this.SVGgetStyles();var q=this.SVGgetVariant();var o=this.SVG();this.SVGgetScale(o);this.SVGhandleSpace(o);for(var p=0,n=this.data.length;p<n;p++){if(this.data[p]){var s=o.Add(this.data[p].toSVG(q,o.scale),o.w,0,true);if(s.skew){o.skew=s.skew}}}o.Clean();var r=this.data.join("");if(o.skew&&!a.isChar(r)){delete o.skew}if(o.r>o.w&&a.isChar(r)&&!q.noIC){o.ic=o.r-o.w;o.w=o.r}this.SVGhandleColor(o);this.SVGsaveData(o);return o},SVGchildSVG:function(n){return(this.data[n]?this.data[n].toSVG():l())},SVGdataStretched:function(o,n,p){this.SVGdata={HW:n,D:p};if(!this.data[o]){return l()}if(p!=null){return this.data[o].SVGstretchV(n,p)}if(n!=null){return this.data[o].SVGstretchH(n)}return this.data[o].toSVG()},SVGsaveData:function(n){if(!this.SVGdata){this.SVGdata={}}this.SVGdata.w=n.w,this.SVGdata.x=n.x;this.SVGdata.h=n.h,this.SVGdata.d=n.d;if(n.y){this.SVGdata.h+=n.y;this.SVGdata.d-=n.y}if(n.X!=null){this.SVGdata.X=n.X}if(n.tw!=null){this.SVGdata.tw=n.tw}if(n.skew){this.SVGdata.skew=n.skew}if(n.ic){this.SVGdata.ic=n.ic}if(this["class"]){n.removeable=false;a.Element(n.element,{"class":this["class"]})}if(this.id){n.removeable=false;a.Element(n.element,{id:this.id})}if(this.href){this.SVGaddHref(n)}if(a.config.addMMLclasses){this.SVGaddClass(n.element,"mjx-svg-"+this.type);n.removeable=false}var o=this.style;if(o&&n.element){n.element.style.cssText=o;if(n.element.style.fontSize){n.element.style.fontSize=""}n.element.style.border=n.element.style.padding="";if(n.removeable){n.removeable=(n.element.style.cssText==="")}}this.SVGaddAttributes(n)},SVGaddClass:function(p,n){var o=p.getAttribute("class");p.setAttribute("class",(o?o+" ":"")+n)},SVGaddAttributes:function(o){if(this.attrNames){var u=this.attrNames,q=i.nocopyAttributes,t=e.config.ignoreMMLattributes;var r=(this.type==="mstyle"?i.math.prototype.defaults:this.defaults);for(var p=0,n=u.length;p<n;p++){var s=u[p];if(t[s]==false||(!q[s]&&!t[s]&&r[s]==null&&typeof(o.element[s])==="undefined")){o.element.setAttribute(s,this.attr[s]);o.removeable=false}}}},SVGaddHref:function(o){var n=a.Element("a",{"class":"mjx-svg-href"});n.setAttributeNS(m,"href",this.href);n.onclick=this.SVGlink;a.addElement(n,"rect",{width:o.w,height:o.h+o.d,y:-o.d,fill:"none",stroke:"none","pointer-events":"all"});if(o.type==="svg"){var p=o.element.firstChild;while(p.firstChild){n.appendChild(p.firstChild)}p.appendChild(n)}else{n.appendChild(o.element);o.element=n}o.removeable=false},SVGlink:function(){var n=this.href.animVal;if(n.charAt(0)==="#"){var o=a.hashCheck(document.getElementById(n.substr(1)));if(o&&o.scrollIntoView){setTimeout(function(){o.parentNode.scrollIntoView(true)},1)}}document.location=n},SVGgetStyles:function(){if(this.style){var n=g.Element("span");n.style.cssText=this.style;this.styles=this.SVGprocessStyles(n.style)}},SVGprocessStyles:function(n){var o={border:a.getBorders(n),padding:a.getPadding(n)};if(!o.border){delete o.border}if(!o.padding){delete o.padding}if(n.fontSize){o.fontSize=n.fontSize}if(n.color){o.color=n.color}if(n.backgroundColor){o.background=n.backgroundColor}if(n.fontStyle){o.fontStyle=n.fontStyle}if(n.fontWeight){o.fontWeight=n.fontWeight}if(n.fontFamily){o.fontFamily=n.fontFamily}if(o.fontWeight&&o.fontWeight.match(/^\d+$/)){o.fontWeight=(parseInt(o.fontWeight)>600?"bold":"normal")}return o},SVGhandleSpace:function(q){if(this.hasMMLspacing()){if(this.type!=="mo"){return}var p=this.getValues("scriptlevel","lspace","rspace");if(p.scriptlevel<=0||this.hasValue("lspace")||this.hasValue("rspace")){var o=this.SVGgetMu(q);p.lspace=Math.max(0,a.length2em(p.lspace,o));p.rspace=Math.max(0,a.length2em(p.rspace,o));var n=this,r=this.Parent();while(r&&r.isEmbellished()&&r.Core()===n){n=r;r=r.Parent()}if(p.lspace){q.x+=p.lspace}if(p.rspace){q.X=p.rspace}}}else{var s=this.texSpacing();this.SVGgetScale();if(s!==""){q.x+=a.length2em(s,this.scale)*this.mscale}}},SVGhandleColor:function(r){var A=this.getValues("mathcolor","color");if(this.styles&&this.styles.color&&!A.color){A.color=this.styles.color}if(A.color&&!this.mathcolor){A.mathcolor=A.color}if(A.mathcolor){a.Element(r.element,{fill:A.mathcolor,stroke:A.mathcolor});r.removeable=false}var v=(this.styles||{}).border,y=(this.styles||{}).padding,w=((v||{}).left||0),t=((y||{}).left||0),n;A.background=(this.mathbackground||this.background||(this.styles||{}).background||i.COLOR.TRANSPARENT);if(w+t){var o=l();for(n in r){if(r.hasOwnProperty(n)){o[n]=r[n]}}o.x=0;o.y=0;r.element=a.Element("g");r.removeable=true;r.Add(o,w+t,0)}if(y){r.w+=y.right||0;r.h+=y.top||0;r.d+=y.bottom||0}if(v){r.w+=v.right||0;r.h+=v.top||0;r.d+=v.bottom||0}if(A.background!==i.COLOR.TRANSPARENT){var x=r.element.nodeName.toLowerCase();if(x!=="g"&&x!=="svg"){var s=a.Element("g");s.appendChild(r.element);r.element=s;r.removeable=true}r.Add(l.RECT(r.h,r.d,r.w,{fill:A.background,stroke:"none"}),0,0,false,true)}if(v){var z=5;var p={left:["V",r.h+r.d,-z,-r.d],right:["V",r.h+r.d,r.w-v.right+z,-r.d],top:["H",r.w,0,r.h-v.top+z],bottom:["H",r.w,0,-r.d-z]};for(n in p){if(p.hasOwnProperty(n)){if(v[n]){var u=p[n],q=l[u[0]+"LINE"];r.Add(q(u[1],v[n],v[n+"Style"],v[n+"Color"]),u[2],u[3])}}}}},SVGhandleVariant:function(n,p,o){return a.HandleVariant(n,p,o)},SVGgetVariant:function(){var n=this.getValues("mathvariant","fontfamily","fontweight","fontstyle");var o=n.mathvariant;if(this.variantForm){o="-"+a.fontInUse+"-variant"}n.hasVariant=this.Get("mathvariant",true);if(!n.hasVariant){n.family=n.fontfamily;n.weight=n.fontweight;n.style=n.fontstyle}if(this.styles){if(!n.style&&this.styles.fontStyle){n.style=this.styles.fontStyle}if(!n.weight&&this.styles.fontWeight){n.weight=this.styles.fontWeight}if(!n.family&&this.styles.fontFamily){n.family=this.styles.fontFamily}}if(n.family&&!n.hasVariant){if(!n.weight&&n.mathvariant.match(/bold/)){n.weight="bold"}if(!n.style&&n.mathvariant.match(/italic/)){n.style="italic"}o={forceFamily:true,font:{"font-family":n.family}};if(n.style){o.font["font-style"]=n.style}if(n.weight){o.font["font-weight"]=n.weight}return o}if(n.weight==="bold"){o={normal:i.VARIANT.BOLD,italic:i.VARIANT.BOLDITALIC,fraktur:i.VARIANT.BOLDFRAKTUR,script:i.VARIANT.BOLDSCRIPT,"sans-serif":i.VARIANT.BOLDSANSSERIF,"sans-serif-italic":i.VARIANT.SANSSERIFBOLDITALIC}[o]||o}else{if(n.weight==="normal"){o={bold:i.VARIANT.normal,"bold-italic":i.VARIANT.ITALIC,"bold-fraktur":i.VARIANT.FRAKTUR,"bold-script":i.VARIANT.SCRIPT,"bold-sans-serif":i.VARIANT.SANSSERIF,"sans-serif-bold-italic":i.VARIANT.SANSSERIFITALIC}[o]||o}}if(n.style==="italic"){o={normal:i.VARIANT.ITALIC,bold:i.VARIANT.BOLDITALIC,"sans-serif":i.VARIANT.SANSSERIFITALIC,"bold-sans-serif":i.VARIANT.SANSSERIFBOLDITALIC}[o]||o}else{if(n.style==="normal"){o={italic:i.VARIANT.NORMAL,"bold-italic":i.VARIANT.BOLD,"sans-serif-italic":i.VARIANT.SANSSERIF,"sans-serif-bold-italic":i.VARIANT.BOLDSANSSERIF}[o]||o}}if(!(o in a.FONTDATA.VARIANT)){o="normal"}return a.FONTDATA.VARIANT[o]},SVGgetScale:function(o){var p=1;if(this.mscale){p=this.scale}else{var n=this.getValues("scriptlevel","fontsize");n.mathsize=(this.isToken?this:this.Parent()).Get("mathsize");if((this.styles||{}).fontSize&&!n.fontsize){n.fontsize=this.styles.fontSize}if(n.fontsize&&!this.mathsize){n.mathsize=n.fontsize}if(n.scriptlevel!==0){if(n.scriptlevel>2){n.scriptlevel=2}p=Math.pow(this.Get("scriptsizemultiplier"),n.scriptlevel);n.scriptminsize=a.length2em(this.Get("scriptminsize"))/1000;if(p<n.scriptminsize){p=n.scriptminsize}}this.scale=p;this.mscale=a.length2em(n.mathsize)/1000}if(o){o.scale=p;if(this.isToken){o.scale*=this.mscale}}return p*this.mscale},SVGgetMu:function(p){var n=1,o=this.getValues("scriptlevel","scriptsizemultiplier");if(p.scale&&p.scale!==1){n=1/p.scale}if(o.scriptlevel!==0){if(o.scriptlevel>2){o.scriptlevel=2}n=Math.sqrt(Math.pow(o.scriptsizemultiplier,o.scriptlevel))}return n},SVGnotEmpty:function(n){while(n){if((n.type!=="mrow"&&n.type!=="texatom")||n.data.length>1){return true}n=n.data[0]}return false},SVGcanStretch:function(p){var o=false;if(this.isEmbellished()){var n=this.Core();if(n&&n!==this){o=n.SVGcanStretch(p);if(o&&n.forceStretch){this.forceStretch=true}}}return o},SVGstretchV:function(n,o){return this.toSVG(n,o)},SVGstretchH:function(n){return this.toSVG(n)},SVGlineBreaks:function(){return false}},{SVGemptySVG:function(){var n=this.SVG();n.Clean();this.SVGsaveData(n);return n},SVGautoload:function(){this.constructor.Augment({toSVG:i.mbase.SVGautoloadFail});var n=a.autoloadDir+"/"+this.type+".js";e.RestartAfter(j.Require(n))},SVGautoloadFail:function(){throw Error("SVG can't autoload '"+this.type+"'")},SVGautoloadList:{},SVGautoloadFile:function(n){if(i.mbase.SVGautoloadList.hasOwnProperty(n)){throw Error("SVG can't autoload file '"+n+"'")}i.mbase.SVGautoloadList[n]=true;var o=a.autoloadDir+"/"+n+".js";e.RestartAfter(j.Require(o))}});i.chars.Augment({toSVG:function(o,r,n,p){var q=this.data.join("").replace(/[\u2061-\u2064]/g,"");if(n){q=n(q,p)}return this.SVGhandleVariant(o,r,q)}});i.entity.Augment({toSVG:function(o,r,n,p){var q=this.toString().replace(/[\u2061-\u2064]/g,"");if(n){q=n(q,p)}return this.SVGhandleVariant(o,r,q)}});i.mo.Augment({toSVG:function(o,n){this.SVGgetStyles();var v=this.svg=this.SVG();var r=this.SVGgetScale(v);this.SVGhandleSpace(v);if(this.data.length==0){v.Clean();this.SVGsaveData(v);return v}if(n!=null){return this.SVGstretchV(o,n)}else{if(o!=null){return this.SVG.strechH(o)}}var t=this.SVGgetVariant();var B=this.getValues("largeop","displaystyle");if(B.largeop){t=a.FONTDATA.VARIANT[B.displaystyle?"-largeOp":"-smallOp"]}var A=this.CoreParent(),s=(A&&A.isa(i.msubsup)&&this!==A.data[0]),p=(s?this.remapChars:null);if(a.isChar(this.data.join(""))&&A&&A.isa(i.munderover)&&a.isChar(this.CoreText(A.data[A.base]))){var w=A.data[A.over],z=A.data[A.under];if(w&&this===w.CoreMO()&&A.Get("accent")){p=a.FONTDATA.REMAPACCENT}else{if(z&&this===z.CoreMO()&&A.Get("accentunder")){p=a.FONTDATA.REMAPACCENTUNDER}}}if(s&&this.data.join("").match(/['`"\u00B4\u2032-\u2037\u2057]/)){t=a.FONTDATA.VARIANT["-"+a.fontInUse+"-variant"]}for(var u=0,q=this.data.length;u<q;u++){if(this.data[u]){var C=this.data[u].toSVG(t,r,this.remap,p),y=v.w;if(y===0&&-C.l>10*C.w){y+=-C.l}v.Add(C,y,0,true);if(C.skew){v.skew=C.skew}}}v.Clean();if(!a.isChar(this.data.join(""))){delete v.skew}if(B.largeop){v.y=a.TeX.axis_height-(v.h-v.d)/2/r;if(v.r>v.w){v.ic=v.r-v.w;v.w=v.r}}this.SVGhandleColor(v);this.SVGsaveData(v);return v},SVGcanStretch:function(r){if(!this.Get("stretchy")){return false}var s=this.data.join("");if(s.length>1){return false}var o=this.CoreParent();if(o&&o.isa(i.munderover)&&a.isChar(this.CoreText(o.data[o.base]))){var q=o.data[o.over],n=o.data[o.under];if(q&&this===q.CoreMO()&&o.Get("accent")){s=a.FONTDATA.REMAPACCENT[s]||s}else{if(n&&this===n.CoreMO()&&o.Get("accentunder")){s=a.FONTDATA.REMAPACCENTUNDER[s]||s}}}s=a.FONTDATA.DELIMITERS[s.charCodeAt(0)];var p=(s&&s.dir==r.substr(0,1));if(!p){delete this.svg}this.forceStretch=p&&(this.Get("minsize",true)||this.Get("maxsize",true));return p},SVGstretchV:function(s,t){var p=this.svg||this.toSVG();var o=this.getValues("symmetric","maxsize","minsize");var r=a.TeX.axis_height*p.scale,n=this.SVGgetMu(p),q;if(o.symmetric){q=2*Math.max(s-r,t+r)}else{q=s+t}o.maxsize=a.length2em(o.maxsize,n,p.h+p.d);o.minsize=a.length2em(o.minsize,n,p.h+p.d);q=Math.max(o.minsize,Math.min(o.maxsize,q));if(q!=o.minsize){q=[Math.max(q*a.TeX.delimiterfactor/1000,q-a.TeX.delimitershortfall),q]}p=a.createDelimiter(this.data.join("").charCodeAt(0),q,p.scale);if(o.symmetric){q=(p.h+p.d)/2+r}else{q=(p.h+p.d)*s/(s+t)}p.y=q-p.h;this.SVGhandleSpace(p);this.SVGhandleColor(p);delete this.svg.element;this.SVGsaveData(p);p.stretched=true;return p},SVGstretchH:function(o){var q=this.svg||this.toSVG(),n=this.SVGgetMu(q);var p=this.getValues("maxsize","minsize","mathvariant","fontweight");if((p.fontweight==="bold"||parseInt(p.fontweight)>=600)&&!this.Get("mathvariant",true)){p.mathvariant=i.VARIANT.BOLD}p.maxsize=a.length2em(p.maxsize,n,q.w);p.minsize=a.length2em(p.minsize,n,q.w);o=Math.max(p.minsize,Math.min(p.maxsize,o));q=a.createDelimiter(this.data.join("").charCodeAt(0),o,q.scale,p.mathvariant);this.SVGhandleSpace(q);this.SVGhandleColor(q);delete this.svg.element;this.SVGsaveData(q);q.stretched=true;return q}});i.mn.Augment({SVGremapMinus:function(n){return n.replace(/^-/,"\u2212")},toSVG:function(){this.SVGgetStyles();var r=this.SVGgetVariant();var o=this.SVG();this.SVGgetScale(o);this.SVGhandleSpace(o);var q=this.SVGremapMinus;for(var p=0,n=this.data.length;p<n;p++){if(this.data[p]){var t=o.Add(this.data[p].toSVG(r,o.scale,q),o.w,0,true);if(t.skew){o.skew=t.skew}q=null}}o.Clean();var s=this.data.join("");if(o.skew&&!a.isChar(s)){delete o.skew}if(o.r>o.w&&a.isChar(s)&&!r.noIC){o.ic=o.r-o.w;o.w=o.r}this.SVGhandleColor(o);this.SVGsaveData(o);return o},}),i.mtext.Augment({toSVG:function(){if(a.config.mtextFontInherit||this.Parent().type==="merror"){this.SVGgetStyles();var n=this.SVG(),q=this.SVGgetScale(n);this.SVGhandleSpace(n);var o=this.SVGgetVariant(),p={direction:this.Get("dir")};if(o.bold){p["font-weight"]="bold"}if(o.italic){p["font-style"]="italic"}o=this.Get("mathvariant");if(o==="monospace"){p["class"]="MJX-monospace"}else{if(o.match(/sans-serif/)){p["class"]="MJX-sans-serif"}}n.Add(l.TEXT(q*100/a.config.scale,this.data.join(""),p));n.Clean();this.SVGhandleColor(n);this.SVGsaveData(n);return n}else{return this.SUPER(arguments).toSVG.call(this)}}});i.merror.Augment({toSVG:function(p,n){this.SVGgetStyles();var t=this.SVG(),r=a.length2em(this.styles.fontSize||1)/1000;this.SVGhandleSpace(t);var o=(r!==1?{transform:"scale("+a.Fixed(r)+")"}:{});var v=l(o);v.Add(this.SVGchildSVG(0));v.Clean();if(r!==1){v.removeable=false;var u=["w","h","d","l","r","D","H"];for(var s=0,q=u.length;s<q;s++){v[u[s]]*=r}}t.Add(v);t.Clean();this.SVGhandleColor(t);this.SVGsaveData(t);return t},SVGgetStyles:function(){var n=g.Element("span",{style:a.config.merrorStyle});this.styles=this.SVGprocessStyles(n.style);if(this.style){n.style.cssText=this.style;e.Insert(this.styles,this.SVGprocessStyles(n.style))}}});i.ms.Augment({toSVG:i.mbase.SVGautoload});i.mglyph.Augment({toSVG:i.mbase.SVGautoload});i.mspace.Augment({toSVG:function(){this.SVGgetStyles();var p=this.getValues("height","depth","width");p.mathbackground=this.mathbackground;if(this.background&&!this.mathbackground){p.mathbackground=this.background}var o=this.SVG();this.SVGgetScale(o);var q=this.mscale,n=this.SVGgetMu(o);o.h=a.length2em(p.height,n)*q;o.d=a.length2em(p.depth,n)*q;o.w=o.r=a.length2em(p.width,n)*q;if(o.w<0){o.x=o.w;o.w=o.r=0}if(o.h<-o.d){o.d=-o.h}o.l=0;o.Clean();this.SVGhandleColor(o);this.SVGsaveData(o);return o}});i.mphantom.Augment({toSVG:function(n,p){this.SVGgetStyles();var o=this.SVG();this.SVGgetScale(o);if(this.data[0]!=null){this.SVGhandleSpace(o);o.Add(this.SVGdataStretched(0,n,p));o.Clean();while(o.element.firstChild){o.element.removeChild(o.element.firstChild)}}this.SVGhandleColor(o);this.SVGsaveData(o);if(o.removeable&&!o.element.firstChild){delete o.element}return o}});i.mpadded.Augment({toSVG:function(q,n){this.SVGgetStyles();var t=this.SVG();if(this.data[0]!=null){this.SVGgetScale(t);this.SVGhandleSpace(t);var r=this.SVGdataStretched(0,q,n),A=this.SVGgetMu(t);var z=this.getValues("height","depth","width","lspace","voffset"),p=0,o=0;if(z.lspace){p=this.SVGlength2em(r,z.lspace,A)}if(z.voffset){o=this.SVGlength2em(r,z.voffset,A)}var s=r.h,u=r.d,x=r.w,v=r.y;t.Add(r,p,o);t.Clean();t.h=s+v;t.d=u-v;t.w=x;t.removeable=false;if(z.height!==""){t.h=this.SVGlength2em(t,z.height,A,"h",0)}if(z.depth!==""){t.d=this.SVGlength2em(t,z.depth,A,"d",0)}if(z.width!==""){t.w=this.SVGlength2em(t,z.width,A,"w",0)}if(t.h>t.H){t.H=t.h}if(t.d>t.D){t.D=t.d}}this.SVGhandleColor(t);this.SVGsaveData(t);return t},SVGlength2em:function(q,t,o,u,n){if(n==null){n=-a.BIGDIMEN}var r=String(t).match(/width|height|depth/);var s=(r?q[r[0].charAt(0)]:(u?q[u]:0));var p=a.length2em(t,o,s/this.mscale)*this.mscale;if(u&&String(t).match(/^\s*[-+]/)){return Math.max(n,q[u]+p)}else{return p}}});i.mrow.Augment({SVG:l.ROW,toSVG:function(q,s){this.SVGgetStyles();var o=this.SVG();this.SVGhandleSpace(o);if(s!=null){o.sh=q;o.sd=s}for(var p=0,n=this.data.length;p<n;p++){if(this.data[p]){o.Check(this.data[p])}}o.Stretch();o.Clean();if(this.data.length===1&&this.data[0]){var r=this.data[0].SVGdata;if(r.skew){o.skew=r.skew}}if(this.SVGlineBreaks(o)){o=this.SVGmultiline(o)}this.SVGhandleColor(o);this.SVGsaveData(o);return o},SVGlineBreaks:function(n){if(!this.parent.linebreakContainer){return false}return(a.config.linebreaks.automatic&&n.w>a.linebreakWidth)||this.hasNewline()},SVGmultiline:function(n){i.mbase.SVGautoloadFile("multiline")},SVGstretchH:function(o){var p=this.SVG();this.SVGhandleSpace(p);for(var q=0,n=this.data.length;q<n;q++){p.Add(this.SVGdataStretched(q,o),p.w,0)}p.Clean();this.SVGhandleColor(p);this.SVGsaveData(p);return p}});i.mstyle.Augment({toSVG:function(){this.SVGgetStyles();var n=this.SVG();if(this.data[0]!=null){this.SVGhandleSpace(n);var o=n.Add(this.data[0].toSVG());n.Clean();if(o.ic){n.ic=o.ic}this.SVGhandleColor(n)}this.SVGsaveData(n);return n},SVGstretchH:function(n){return(this.data[0]!=null?this.data[0].SVGstretchH(n):l.NULL())},SVGstretchV:function(n,o){return(this.data[0]!=null?this.data[0].SVGstretchV(n,o):l.NULL())}});i.mfrac.Augment({toSVG:function(){this.SVGgetStyles();var B=this.SVG(),K=this.SVGgetScale(B);var r=l();r.scale=B.scale;this.SVGhandleSpace(r);var w=this.SVGchildSVG(0),s=this.SVGchildSVG(1);var n=this.getValues("displaystyle","linethickness","numalign","denomalign","bevelled");var F=n.displaystyle;var J=a.TeX.axis_height*K;if(n.bevelled){var I=(F?400:150);var x=Math.max(w.h+w.d,s.h+s.d)+2*I;var G=a.createDelimiter(47,x);r.Add(w,0,(w.d-w.h)/2+J+I);r.Add(G,w.w-I/2,(G.d-G.h)/2+J);r.Add(s,w.w+G.w-I,(s.d-s.h)/2+J-I)}else{var o=Math.max(w.w,s.w);var A=a.thickness2em(n.linethickness,this.scale)*this.mscale,D,C,z,y;var E=a.TeX.min_rule_thickness/a.em*1000;if(F){z=a.TeX.num1;y=a.TeX.denom1}else{z=(A===0?a.TeX.num3:a.TeX.num2);y=a.TeX.denom2}z*=K;y*=K;if(A===0){D=Math.max((F?7:3)*a.TeX.rule_thickness,2*E);C=(z-w.d)-(s.h-y);if(C<D){z+=(D-C)/2;y+=(D-C)/2}r.w=o;A=0}else{D=Math.max((F?2:0)*E+A,A/2+1.5*E);C=(z-w.d)-(J+A/2);if(C<D){z+=D-C}C=(J-A/2)-(s.h-y);if(C<D){y+=D-C}r.Add(l.RECT(A/2,A/2,o+2*A),0,J)}r.Align(w,n.numalign,A,z);r.Align(s,n.denomalign,A,-y)}r.Clean();B.Add(r,0,0);B.Clean();this.SVGhandleColor(B);this.SVGsaveData(B);return B},SVGcanStretch:function(n){return false},SVGhandleSpace:function(n){if(!this.texWithDelims){n.x=n.X=a.TeX.nulldelimiterspace*this.mscale}this.SUPER(arguments).SVGhandleSpace.call(this,n)}});i.msqrt.Augment({toSVG:function(){this.SVGgetStyles();var v=this.SVG(),s=this.SVGgetScale(v);this.SVGhandleSpace(v);var r=this.SVGchildSVG(0),w,u;var A=a.TeX.rule_thickness*s,o,n,z,y=0;if(this.Get("displaystyle")){o=a.TeX.x_height*s}else{o=A}n=Math.max(A+o/4,1000*a.TeX.min_root_space/a.em);z=r.h+r.d+n+A;u=a.createDelimiter(8730,z,s);if(u.h+u.d>z){n=((u.h+u.d)-(z-A))/2}w=l.RECT(A,0,r.w);z=r.h+n+A;y=this.SVGaddRoot(v,u,y,u.h+u.d-z,s);v.Add(u,y,z-u.h);v.Add(w,y+u.w,z-w.h);v.Add(r,y+u.w,0);v.Clean();v.h+=A;v.H+=A;this.SVGhandleColor(v);this.SVGsaveData(v);return v},SVGaddRoot:function(o,p,n,r,q){return n}});i.mroot.Augment({toSVG:i.msqrt.prototype.toSVG,SVGaddRoot:function(q,o,t,r,n){var v=(o.isMultiChar?0.55:0.65)*o.w;if(this.data[1]){var s=this.data[1].toSVG();s.x=0;var p=this.SVGrootHeight(o.h+o.d,n,s)-r;var u=Math.min(s.w,s.r);t=Math.max(u,v);q.Add(s,t-u,p)}else{v=t}return t-v},SVGrootHeight:function(p,o,n){return 0.45*(p-900*o)+600*o+Math.max(0,n.d-75)}});i.mfenced.Augment({SVG:l.ROW,toSVG:function(){this.SVGgetStyles();var o=this.SVG();this.SVGhandleSpace(o);if(this.data.open){o.Check(this.data.open)}if(this.data[0]!=null){o.Check(this.data[0])}for(var p=1,n=this.data.length;p<n;p++){if(this.data[p]){if(this.data["sep"+p]){o.Check(this.data["sep"+p])}o.Check(this.data[p])}}if(this.data.close){o.Check(this.data.close)}o.Stretch();o.Clean();this.SVGhandleColor(o);this.SVGsaveData(o);return o}});i.menclose.Augment({toSVG:i.mbase.SVGautoload});i.maction.Augment({toSVG:i.mbase.SVGautoload});i.semantics.Augment({toSVG:function(){this.SVGgetStyles();var n=this.SVG();if(this.data[0]!=null){this.SVGhandleSpace(n);n.Add(this.data[0].toSVG());n.Clean()}else{n.Clean()}this.SVGsaveData(n);return n},SVGstretchH:function(n){return(this.data[0]!=null?this.data[0].SVGstretchH(n):l.NULL())},SVGstretchV:function(n,o){return(this.data[0]!=null?this.data[0].SVGstretchV(n,o):l.NULL())}});i.munderover.Augment({toSVG:function(G,E){this.SVGgetStyles();var n=this.getValues("displaystyle","accent","accentunder","align");var p=this.data[this.base];if(!n.displaystyle&&p!=null&&(p.movablelimits||p.CoreMO().Get("movablelimits"))){return i.msubsup.prototype.toSVG.call(this)}var F=this.SVG(),O=this.SVGgetScale(F);this.SVGhandleSpace(F);var q=[],L=[],v,K,H,o=-a.BIGDIMEN,J=o,N;for(K=0,H=this.data.length;K<H;K++){if(this.data[K]!=null){if(K==this.base){v=q[K]=this.SVGdataStretched(K,G,E);L[K]=(E!=null||G==null)&&this.data[K].SVGcanStretch("Horizontal");if(this.data[this.over]&&n.accent){v.h=Math.max(v.h,O*a.TeX.x_height)}}else{v=q[K]=this.data[K].toSVG();v.x=0;delete v.X;L[K]=this.data[K].SVGcanStretch("Horizontal")}N=v.w+v.x+(v.X||0);if(N>J){J=N}if(!L[K]&&J>o){o=J}}}if(E==null&&G!=null){o=G}else{if(o==-a.BIGDIMEN){o=J}}for(K=J=0,H=this.data.length;K<H;K++){if(this.data[K]){v=q[K];if(L[K]){v=q[K]=this.data[K].SVGstretchH(o);if(K!==this.base){v.x=0;delete v.X}}N=v.w+v.x+(v.X||0);if(N>J){J=N}}}var C=a.TeX.rule_thickness*this.mscale;var u,r,z,w,s,B,I,M=0;p=q[this.base]||{w:0,h:0,d:0,H:0,D:0,l:0,r:0,y:0,scale:O};if(p.ic){M=1.3*p.ic+0.05}for(K=0,H=this.data.length;K<H;K++){if(this.data[K]!=null){v=q[K];s=a.TeX.big_op_spacing5*O;var A=(K!=this.base&&n[this.ACCENTS[K]]);if(A&&v.w<=1){v.x=-v.l;q[K]=l.G().With({removeable:false});q[K].Add(v);q[K].Clean();q[K].w=-v.l;v=q[K]}N=v.w+v.x+(v.X||0);B={left:0,center:(J-N)/2,right:J-N}[n.align];u=B;r=0;if(K==this.over){if(A){I=C*O;s=0;if(p.skew){u+=p.skew;F.skew=p.skew;if(u+N>J){F.skew+=(J-N-u)/2}}}else{z=a.TeX.big_op_spacing1*O;w=a.TeX.big_op_spacing3*O;I=Math.max(z,w-Math.max(0,v.d))}I=Math.max(I,1500/a.em);u+=M/2;r=p.y+p.h+v.d+I;v.h+=s;if(v.h>v.H){v.H=v.h}}else{if(K==this.under){if(A){I=3*C*O;s=0}else{z=a.TeX.big_op_spacing2*O;w=a.TeX.big_op_spacing4*O;I=Math.max(z,w-v.h)}I=Math.max(I,1500/a.em);u-=M/2;r=p.y-(p.d+v.h+I);v.d+=s;if(v.d>v.D){v.D=v.d}}}F.Add(v,u,r)}}F.Clean();this.SVGhandleColor(F);this.SVGsaveData(F);return F}});i.msubsup.Augment({toSVG:function(M,G){this.SVGgetStyles();var I=this.SVG(),Q=this.SVGgetScale(I);this.SVGhandleSpace(I);var K=this.SVGgetMu(I);var y=I.Add(this.SVGdataStretched(this.base,M,G));var w=(this.data[this.sup]||this.data[this.sub]||this).SVGgetScale();var O=a.TeX.x_height*Q,F=a.TeX.scriptspace*Q;var n,z;if(this.SVGnotEmpty(this.data[this.sup])){n=this.data[this.sup].toSVG();n.w+=F;n.r=Math.max(n.w,n.r)}if(this.SVGnotEmpty(this.data[this.sub])){z=this.data[this.sub].toSVG();z.w+=F;z.r=Math.max(z.w,z.r)}var J=a.TeX.sup_drop*w,H=a.TeX.sub_drop*w;var C=y.h+(y.y||0)-J,B=y.d-(y.y||0)+H,P=0,L;if(y.ic){y.w-=y.ic;P=1.3*y.ic+0.05}if(this.data[this.base]&&(this.data[this.base].type==="mi"||this.data[this.base].type==="mo")){if(a.isChar(this.data[this.base].data.join(""))&&y.scale===1&&!y.stretched&&!this.data[this.base].Get("largeop")){C=B=0}}var N=this.getValues("subscriptshift","superscriptshift");N.subscriptshift=(N.subscriptshift===""?0:a.length2em(N.subscriptshift,K));N.superscriptshift=(N.superscriptshift===""?0:a.length2em(N.superscriptshift,K));var A=y.w+y.x;if(!n){if(z){B=Math.max(B,a.TeX.sub1*Q,z.h-(4/5)*O,N.subscriptshift);I.Add(z,A,-B);this.data[this.sub].SVGdata.dy=-B}}else{if(!z){var o=this.getValues("displaystyle","texprimestyle");L=a.TeX[(o.displaystyle?"sup1":(o.texprimestyle?"sup3":"sup2"))];C=Math.max(C,L*Q,n.d+(1/4)*O,N.superscriptshift);I.Add(n,A+P,C);this.data[this.sup].SVGdata.dx=P;this.data[this.sup].SVGdata.dy=C}else{B=Math.max(B,a.TeX.sub2*Q);var E=a.TeX.rule_thickness*Q;if((C-n.d)-(z.h-B)<3*E){B=3*E-C+n.d+z.h;J=(4/5)*O-(C-n.d);if(J>0){C+=J;B-=J}}I.Add(n,A+P,Math.max(C,N.superscriptshift));I.Add(z,A,-Math.max(B,N.subscriptshift));this.data[this.sup].SVGdata.dx=P;this.data[this.sup].SVGdata.dy=Math.max(C,N.superscriptshift);this.data[this.sub].SVGdata.dy=-Math.max(B,N.subscriptshift)}}I.Clean();this.SVGhandleColor(I);this.SVGsaveData(I);return I}});i.mmultiscripts.Augment({toSVG:i.mbase.SVGautoload});i.mtable.Augment({toSVG:i.mbase.SVGautoload});i["annotation-xml"].Augment({toSVG:i.mbase.SVGautoload});i.math.Augment({SVG:l.Subclass({type:"svg",removeable:false}),toSVG:function(B,p){var F=a.config;if(this.data[0]){this.SVGgetStyles();i.mbase.prototype.displayAlign=e.config.displayAlign;i.mbase.prototype.displayIndent=e.config.displayIndent;if(String(e.config.displayIndent).match(/^0($|[a-z%])/i)){i.mbase.prototype.displayIndent="0"}var v=l.G();v.Add(this.data[0].toSVG(),0,0,true);v.Clean();this.SVGhandleColor(v);a.Element(v.element,{stroke:"currentColor",fill:"currentColor","stroke-width":0,transform:"matrix(1 0 0 -1 0 0)"});v.removeable=false;var x=this.SVG();x.element.setAttribute("xmlns:xlink",m);if(F.useFontCache&&!F.useGlobalCache){x.element.appendChild(l.GLYPH.defs)}x.Add(v);x.Clean();this.SVGsaveData(x);if(!B){x.element=x.element.firstChild;x.element.removeAttribute("transform");x.removable=true;return x}var u=Math.max(-x.l,0),o=Math.max(x.r-x.w,0);var q=x.element.style,A=a.TeX.x_height/a.ex;var E=(Math.ceil(x.H/A)+1)*A+a.HFUZZ,n=(Math.ceil(x.D/A)+1)*A+a.DFUZZ;var z=u+x.w+o;x.element.setAttribute("width",a.Ex(z));x.element.setAttribute("height",a.Ex(E+n));q.verticalAlign=a.Ex(-n);if(u){q.marginLeft=a.Ex(-u)}if(o){q.marginRight=a.Ex(-o)}x.element.setAttribute("viewBox",a.Fixed(-u,1)+" "+a.Fixed(-E,1)+" "+a.Fixed(z,1)+" "+a.Fixed(E+n,1));if(x.H>x.h){q.marginTop=a.Ex(x.h-E)}if(x.D>x.d){q.marginBottom=a.Ex(x.d-n);q.verticalAlign=a.Ex(-x.d)}if(Math.abs(z-a.cwidth)<10){q.maxWidth=a.Fixed(a.cwidth*a.em/1000*a.config.scale)+"px"}var y=this.Get("alttext");if(y&&!x.element.getAttribute("aria-label")){x.element.setAttribute("aria-label",y)}if(!x.element.getAttribute("role")){x.element.setAttribute("role","img")}x.element.setAttribute("focusable","false");B.appendChild(x.element);x.element=null;if(!this.isMultiline&&this.Get("display")==="block"&&!x.hasIndent){var C=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift");if(C.indentalignfirst!==i.INDENTALIGN.INDENTALIGN){C.indentalign=C.indentalignfirst}if(C.indentalign===i.INDENTALIGN.AUTO){C.indentalign=this.displayAlign}if(C.indentshiftfirst!==i.INDENTSHIFT.INDENTSHIFT){C.indentshift=C.indentshiftfirst}if(C.indentshift==="auto"){C.indentshift="0"}var s=a.length2em(C.indentshift,1,a.cwidth);if(this.displayIndent!=="0"){var t=a.length2em(this.displayIndent,1,a.cwidth);s+=(C.indentalign===i.INDENTALIGN.RIGHT?-t:t)}p.style.textAlign=C.indentalign;if(s){e.Insert(q,({left:{marginLeft:a.Ex(s)},right:{marginRight:a.Ex(-s),marginLeft:a.Ex(Math.max(0,s-z))},center:{marginLeft:a.Ex(s),marginRight:a.Ex(-s)}})[C.indentalign])}}}return B}});i.TeXAtom.Augment({toSVG:function(n,q){this.SVGgetStyles();var o=this.SVG();this.SVGhandleSpace(o);if(this.data[0]!=null){var p=this.SVGdataStretched(0,n,q),r=0;if(this.texClass===i.TEXCLASS.VCENTER){r=a.TeX.axis_height-(p.h+p.d)/2+p.d}o.Add(p,0,r);o.ic=p.ic;o.skew=p.skew}this.SVGhandleColor(o);this.SVGsaveData(o);return o}});i.maligngroup.Augment({toSVG:i.mbase.SVGemptySVG});i.malignmark.Augment({toSVG:i.mbase.SVGemptySVG});i.mprescripts.Augment({toSVG:i.mbase.SVGemptySVG});i.none.Augment({toSVG:i.mbase.SVGemptySVG});e.Register.StartupHook("onLoad",function(){setTimeout(MathJax.Callback(["loadComplete",a,"jax.js"]),0)})});e.Browser.Select({Opera:function(n){a.Augment({operaZoomRefresh:true})}});e.Register.StartupHook("End Cookie",function(){if(e.config.menuSettings.zoom!=="None"){j.Require("[MathJax]/extensions/MathZoom.js")}});if(!document.createElementNS){if(!document.namespaces.svg){document.namespaces.add("svg",b)}a.Augment({Element:function(n,o){var p=(typeof(n)==="string"?document.createElement("svg:"+n):n);p.isMathJax=true;if(o){for(var q in o){if(o.hasOwnProperty(q)){p.setAttribute(q,o[q].toString())}}}return p}})}})(MathJax.Ajax,MathJax.Hub,MathJax.HTML,MathJax.OutputJax.SVG);
MathJax.Hub.Register.StartupHook("SVG Jax Ready",function(){var c="2.7.5";var a=MathJax.ElementJax.mml,d=MathJax.OutputJax.SVG,b=d.BBOX;a.mtable.Augment({toSVG:function(aa){this.SVGgetStyles();var o=this.SVG(),ap=this.SVGgetScale(o);if(this.data.length===0){this.SVGsaveData(o);return o}var aN=this.getValues("columnalign","rowalign","columnspacing","rowspacing","columnwidth","equalcolumns","equalrows","columnlines","rowlines","frame","framespacing","align","useHeight","width","side","minlabelspacing");if(aN.width.match(/%$/)){o.width=aN.width=d.Em((d.cwidth/1000)*(parseFloat(aN.width)/100))}var v=this.SVGgetMu(o);var aK=-1;var z=[],I=[],k=[],O=[],K=[],aI,aG,w=-1,aE,u,az,S,an,E,aA;var ac=d.FONTDATA.lineH*ap*aN.useHeight,ag=d.FONTDATA.lineD*ap*aN.useHeight;for(aI=0,aE=this.data.length;aI<aE;aI++){S=this.data[aI];az=(S.type==="mlabeledtr"?aK:0);O[aI]=[];z[aI]=ac;I[aI]=ag;for(aG=az,u=S.data.length+az;aG<u;aG++){if(k[aG]==null){if(aG>w){w=aG}K[aG]=b.G();k[aG]=-d.BIGDIMEN}an=S.data[aG-az];O[aI][aG]=an.toSVG();if(an.isEmbellished()){E=an.CoreMO();var aM=E.Get("minsize",true);if(aM){if(E.SVGcanStretch("Vertical")){aA=E.SVGdata.h+E.SVGdata.d;if(aA){aM=d.length2em(aM,v,aA);if(aM*E.SVGdata.h/aA>z[aI]){z[aI]=aM*E.SVGdata.h/aA}if(aM*E.SVGdata.d/aA>I[aI]){I[aI]=aM*E.SVGdata.d/aA}}}else{if(E.SVGcanStretch("Horizontal")){aM=d.length2em(aM,v,E.SVGdata.w);if(aM>k[aG]){k[aG]=aM}}}}}if(O[aI][aG].h>z[aI]){z[aI]=O[aI][aG].h}if(O[aI][aG].d>I[aI]){I[aI]=O[aI][aG].d}if(O[aI][aG].w>k[aG]){k[aG]=O[aI][aG].w}}}var ao=MathJax.Hub.SplitList;var am=ao(aN.columnspacing),T=ao(aN.rowspacing),ai=ao(aN.columnalign),L=ao(aN.rowalign),N=ao(aN.columnlines),h=ao(aN.rowlines),ar=ao(aN.columnwidth),aw=[];for(aI=0,aE=am.length;aI<aE;aI++){am[aI]=d.length2em(am[aI],v)}for(aI=0,aE=T.length;aI<aE;aI++){T[aI]=d.length2em(T[aI],v)}while(am.length<w){am.push(am[am.length-1])}while(ai.length<=w){ai.push(ai[ai.length-1])}while(N.length<w){N.push(N[N.length-1])}while(ar.length<=w){ar.push(ar[ar.length-1])}while(T.length<O.length){T.push(T[T.length-1])}while(L.length<=O.length){L.push(L[L.length-1])}while(h.length<O.length){h.push(h[h.length-1])}if(K[aK]){ai[aK]=(aN.side.substr(0,1)==="l"?"left":"right");am[aK]=-k[aK]}for(aI=0,aE=O.length;aI<aE;aI++){S=this.data[aI];aw[aI]=[];if(S.rowalign){L[aI]=S.rowalign}if(S.columnalign){aw[aI]=ao(S.columnalign);while(aw[aI].length<=w){aw[aI].push(aw[aI][aw[aI].length-1])}}}if(aN.equalrows){var U=Math.max.apply(Math,z),aq=Math.max.apply(Math,I);for(aI=0,aE=O.length;aI<aE;aI++){az=((U+aq)-(z[aI]+I[aI]))/2;z[aI]+=az;I[aI]+=az}}aA=z[0]+I[O.length-1];for(aI=0,aE=O.length-1;aI<aE;aI++){aA+=Math.max(0,I[aI]+z[aI+1]+T[aI])}var ae=0,ab=0,aB,aL=aA;if(aN.frame!=="none"||(aN.columnlines+aN.rowlines).match(/solid|dashed/)){var t=ao(aN.framespacing);if(t.length!=2){t=ao(this.defaults.framespacing)}ae=d.length2em(t[0],v);ab=d.length2em(t[1],v);aL=aA+2*ab}var g,ay,aD="";if(typeof(aN.align)!=="string"){aN.align=String(aN.align)}if(aN.align.match(/(top|bottom|center|baseline|axis)( +(-?\d+))?/)){aD=RegExp.$3||"";aN.align=RegExp.$1}else{aN.align=this.defaults.align}if(aD!==""){aD=parseInt(aD);if(aD<0){aD=O.length+1+aD}if(aD<1){aD=1}else{if(aD>O.length){aD=O.length}}g=0;ay=-(aA+ab)+z[0];for(aI=0,aE=aD-1;aI<aE;aI++){var Z=Math.max(0,I[aI]+z[aI+1]+T[aI]);g+=Z;ay+=Z}}else{g=({top:-(z[0]+ab),bottom:aA+ab-z[0],center:aA/2-z[0],baseline:aA/2-z[0],axis:aA/2+d.TeX.axis_height*ap-z[0]})[aN.align];ay=({top:-(aA+2*ab),bottom:0,center:-(aA/2+ab),baseline:-(aA/2+ab),axis:d.TeX.axis_height*ap-aA/2-ab})[aN.align]}var at,ax=0,V=0,X=0,aC=0,aJ=0,r=[],B=[],aj=1;if(aN.equalcolumns&&aN.width!=="auto"){at=d.length2em(aN.width,v);for(aI=0,aE=Math.min(w,am.length);aI<aE;aI++){at-=am[aI]}at/=w;for(aI=0,aE=Math.min(w+1,ar.length);aI<aE;aI++){k[aI]=at}}else{for(aI=0,aE=Math.min(w+1,ar.length);aI<aE;aI++){if(ar[aI]==="auto"){V+=k[aI]}else{if(ar[aI]==="fit"){B[aJ]=aI;aJ++;V+=k[aI]}else{if(ar[aI].match(/%$/)){r[aC]=aI;aC++;X+=k[aI];ax+=d.length2em(ar[aI],v,1)}else{k[aI]=d.length2em(ar[aI],v);V+=k[aI]}}}}if(aN.width==="auto"){if(ax>0.98){aj=X/(V+X);at=V+X}else{at=V/(1-ax)}}else{at=Math.max(V+X,d.length2em(aN.width,v));for(aI=0,aE=Math.min(w,am.length);aI<aE;aI++){at-=am[aI]}}for(aI=0,aE=r.length;aI<aE;aI++){k[r[aI]]=d.length2em(ar[r[aI]],v,at*aj);V+=k[r[aI]]}if(Math.abs(at-V)>0.01){if(aJ&&at>V){at=(at-V)/aJ;for(aI=0,aE=B.length;aI<aE;aI++){k[B[aI]]+=at}}else{at=at/V;for(aG=0;aG<=w;aG++){k[aG]*=at}}}if(aN.equalcolumns){var af=Math.max.apply(Math,k);for(aG=0;aG<=w;aG++){k[aG]=af}}}var au=g,l,aF;az=(K[aK]?aK:0);for(aG=az;aG<=w;aG++){K[aG].w=k[aG];for(aI=0,aE=O.length;aI<aE;aI++){if(O[aI][aG]){az=(this.data[aI].type==="mlabeledtr"?aK:0);an=this.data[aI].data[aG-az];if(an.SVGcanStretch("Horizontal")){O[aI][aG]=an.SVGstretchH(k[aG])}else{if(an.SVGcanStretch("Vertical")){E=an.CoreMO();var ad=E.symmetric;E.symmetric=false;O[aI][aG]=an.SVGstretchV(z[aI],I[aI]);E.symmetric=ad}}aF=an.rowalign||this.data[aI].rowalign||L[aI];l=({top:z[aI]-O[aI][aG].h,bottom:O[aI][aG].d-I[aI],center:((z[aI]-I[aI])-(O[aI][aG].h-O[aI][aG].d))/2,baseline:0,axis:0})[aF]||0;aF=(an.columnalign||aw[aI][aG]||ai[aG]);K[aG].Align(O[aI][aG],aF,0,au+l)}if(aI<O.length-1){au-=Math.max(0,I[aI]+z[aI+1]+T[aI])}}au=g}var ah=1.5*d.em;var av=ae-ah/2;for(aG=0;aG<=w;aG++){o.Add(K[aG],av,0);av+=k[aG]+am[aG];if(N[aG]!=="none"&&aG<w&&aG!==aK){o.Add(b.VLINE(aL,ah,N[aG]),av-am[aG]/2,ay)}}o.w+=ae;o.d=-ay;o.h=aL+ay;aB=o.w;if(aN.frame!=="none"){o.Add(b.HLINE(aB,ah,aN.frame),0,ay+aL-ah);o.Add(b.HLINE(aB,ah,aN.frame),0,ay);o.Add(b.VLINE(aL,ah,aN.frame),0,ay);o.Add(b.VLINE(aL,ah,aN.frame),aB-ah,ay)}au=g-ah/2;for(aI=0,aE=O.length-1;aI<aE;aI++){l=Math.max(0,I[aI]+z[aI+1]+T[aI]);if(h[aI]!==a.LINES.NONE&&h[aI]!==""){o.Add(b.HLINE(aB,ah,h[aI]),0,au-I[aI]-(l-I[aI]-z[aI+1])/2)}au-=l}o.Clean();this.SVGhandleSpace(o);this.SVGhandleColor(o);if(K[aK]){o.tw=Math.max(o.w,o.r)-Math.min(0,o.l);var R=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift");if(R.indentalignfirst!==a.INDENTALIGN.INDENTALIGN){R.indentalign=R.indentalignfirst}if(R.indentalign===a.INDENTALIGN.AUTO){R.indentalign=this.displayAlign}if(R.indentshiftfirst!==a.INDENTSHIFT.INDENTSHIFT){R.indentshift=R.indentshiftfirst}if(R.indentshift==="auto"||R.indentshift===""){R.indentshift="0"}var ak=d.length2em(R.indentshift,v,d.cwidth);var Q=d.length2em(aN.minlabelspacing,v,d.cwidth);var al=Q+K[aK].w,aO=0,aH=o.w;var e=d.length2em(this.displayIndent,v,d.cwidth);az=(ai[aK]===a.INDENTALIGN.RIGHT?-1:1);if(R.indentalign===a.INDENTALIGN.CENTER){var q=(d.cwidth-aH)/2;ak+=e;if(al+az*aO>q+az*ak){R.indentalign=ai[aK];ak=az*(al+az*aO);aH+=al+Math.max(0,ak)}}else{if(ai[aK]===R.indentalign){if(e<0){aO=az*e;e=0}ak+=az*e;if(al>az*ak){ak=az*al}ak+=aO;aH+=az*ak}else{ak-=az*e;if(aH-az*ak+al>d.cwidth){ak=az*(aH+al-d.cwidth);if(az*ak>0){aH=d.cwidth+az*ak;ak=0}}}}var G=o;o=this.SVG();o.hasIndent=true;o.w=o.r=Math.max(aH,d.cwidth);o.Align(K[aK],ai[aK],0,0,aO);o.Align(G,R.indentalign,0,0,ak);o.tw=aH}this.SVGsaveData(o);return o},SVGhandleSpace:function(e){if(!this.hasFrame&&!e.width){e.x=e.X=167}this.SUPER(arguments).SVGhandleSpace.call(this,e)}});a.mtd.Augment({toSVG:function(e,g){var f=this.svg=this.SVG();if(this.data[0]){f.Add(this.SVGdataStretched(0,e,g));f.Clean()}this.SVGhandleColor(f);this.SVGsaveData(f);return f}});MathJax.Hub.Startup.signal.Post("SVG mtable Ready");MathJax.Ajax.loadComplete(d.autoloadDir+"/mtable.js")});
(function(i,b,e,g){var h;var j,a,d;var f="'Times New Roman',Times,STIXGeneral,serif";var m={".MJXp-script":{"font-size":".8em"},".MJXp-right":{"-webkit-transform-origin":"right","-moz-transform-origin":"right","-ms-transform-origin":"right","-o-transform-origin":"right","transform-origin":"right"},".MJXp-bold":{"font-weight":"bold"},".MJXp-italic":{"font-style":"italic"},".MJXp-scr":{"font-family":"MathJax_Script,"+f},".MJXp-frak":{"font-family":"MathJax_Fraktur,"+f},".MJXp-sf":{"font-family":"MathJax_SansSerif,"+f},".MJXp-cal":{"font-family":"MathJax_Caligraphic,"+f},".MJXp-mono":{"font-family":"MathJax_Typewriter,"+f},".MJXp-largeop":{"font-size":"150%"},".MJXp-largeop.MJXp-int":{"vertical-align":"-.2em"},".MJXp-math":{display:"inline-block","line-height":"1.2","text-indent":"0","font-family":f,"white-space":"nowrap","border-collapse":"collapse"},".MJXp-display":{display:"block","text-align":"center",margin:"1em 0"},".MJXp-math span":{display:"inline-block"},".MJXp-box":{display:"block!important","text-align":"center"},".MJXp-box:after":{content:'" "'},".MJXp-rule":{display:"block!important","margin-top":".1em"},".MJXp-char":{display:"block!important"},".MJXp-mo":{margin:"0 .15em"},".MJXp-mfrac":{margin:"0 .125em","vertical-align":".25em"},".MJXp-denom":{display:"inline-table!important",width:"100%"},".MJXp-denom > *":{display:"table-row!important"},".MJXp-surd":{"vertical-align":"top"},".MJXp-surd > *":{display:"block!important"},".MJXp-script-box > * ":{display:"table!important",height:"50%"},".MJXp-script-box > * > *":{display:"table-cell!important","vertical-align":"top"},".MJXp-script-box > *:last-child > *":{"vertical-align":"bottom"},".MJXp-script-box > * > * > *":{display:"block!important"},".MJXp-mphantom":{visibility:"hidden"},".MJXp-munderover, .MJXp-munder":{display:"inline-table!important"},".MJXp-over":{display:"inline-block!important","text-align":"center"},".MJXp-over > *":{display:"block!important"},".MJXp-munderover > *, .MJXp-munder > *":{display:"table-row!important"},".MJXp-mtable":{"vertical-align":".25em",margin:"0 .125em"},".MJXp-mtable > *":{display:"inline-table!important","vertical-align":"middle"},".MJXp-mtr":{display:"table-row!important"},".MJXp-mtd":{display:"table-cell!important","text-align":"center",padding:".5em 0 0 .5em"},".MJXp-mtr > .MJXp-mtd:first-child":{"padding-left":0},".MJXp-mtr:first-child > .MJXp-mtd":{"padding-top":0},".MJXp-mlabeledtr":{display:"table-row!important"},".MJXp-mlabeledtr > .MJXp-mtd:first-child":{"padding-left":0},".MJXp-mlabeledtr:first-child > .MJXp-mtd":{"padding-top":0},".MJXp-merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"1px 3px","font-style":"normal","font-size":"90%"}};(function(){for(var n=0;n<10;n++){var o="scaleX(."+n+")";m[".MJXp-scale"+n]={"-webkit-transform":o,"-moz-transform":o,"-ms-transform":o,"-o-transform":o,transform:o}}})();var k=1000000;var c="V",l="H";g.Augment({settings:b.config.menuSettings,config:{styles:m},hideProcessedMath:false,maxStretchyParts:1000,Config:function(){if(!this.require){this.require=[]}this.SUPER(arguments).Config.call(this);var n=this.settings;if(n.scale){this.config.scale=n.scale}this.require.push(MathJax.OutputJax.extensionDir+"/MathEvents.js")},Startup:function(){j=MathJax.Extension.MathEvents.Event;a=MathJax.Extension.MathEvents.Touch;d=MathJax.Extension.MathEvents.Hover;this.ContextMenu=j.ContextMenu;this.Mousedown=j.AltContextMenu;this.Mouseover=d.Mouseover;this.Mouseout=d.Mouseout;this.Mousemove=d.Mousemove;var n=e.addElement(document.body,"div",{style:{width:"5in"}});this.pxPerInch=n.offsetWidth/5;n.parentNode.removeChild(n);return i.Styles(this.config.styles,["InitializePHTML",this])},InitializePHTML:function(){},preTranslate:function(p){var s=p.jax[this.id],t,q=s.length,u,r,v,o,n;for(t=0;t<q;t++){u=s[t];if(!u.parentNode){continue}r=u.previousSibling;if(r&&String(r.className).match(/^MathJax(_PHTML)?(_Display)?( MathJax_Process(ing|ed))?$/)){r.parentNode.removeChild(r)}n=u.MathJax.elementJax;if(!n){continue}n.PHTML={display:(n.root.Get("display")==="block")};v=o=e.Element("span",{className:"MathJax_PHTML",id:n.inputID+"-Frame",isMathJax:true,jaxID:this.id,oncontextmenu:j.Menu,onmousedown:j.Mousedown,onmouseover:j.Mouseover,onmouseout:j.Mouseout,onmousemove:j.Mousemove,onclick:j.Click,ondblclick:j.DblClick,onkeydown:j.Keydown,tabIndex:b.getTabOrder(n)});if(b.Browser.noContextMenu){v.ontouchstart=a.start;v.ontouchend=a.end}if(n.PHTML.display){o=e.Element("div",{className:"MathJax_PHTML_Display"});o.appendChild(v)}o.className+=" MathJax_Processing";u.parentNode.insertBefore(o,u)}},Translate:function(o,s){if(!o.parentNode){return}var n=o.MathJax.elementJax,r=n.root,p=document.getElementById(n.inputID+"-Frame"),t=(n.PHTML.display?p.parentNode:p);this.initPHTML(r,p);try{r.toPreviewHTML(p)}catch(q){if(q.restart){while(p.firstChild){p.removeChild(p.firstChild)}}throw q}t.className=t.className.split(/ /)[0];if(this.hideProcessedMath){t.className+=" MathJax_Processed";if(o.MathJax.preview){n.PHTML.preview=o.MathJax.preview;delete o.MathJax.preview}}},postTranslate:function(s){var o=s.jax[this.id];if(!this.hideProcessedMath){return}for(var q=0,n=o.length;q<n;q++){var p=o[q];if(p&&p.MathJax.elementJax){p.previousSibling.className=p.previousSibling.className.split(/ /)[0];var r=p.MathJax.elementJax.PHTML;if(r.preview){r.preview.innerHTML="";p.MathJax.preview=r.preview;delete r.preview}}}},getJaxFromMath:function(n){if(n.parentNode.className.match(/MathJax_PHTML_Display/)){n=n.parentNode}do{n=n.nextSibling}while(n&&n.nodeName.toLowerCase()!=="script");return b.getJaxFor(n)},getHoverSpan:function(n,o){return n.root.PHTMLspanElement()},getHoverBBox:function(n,q,r){var s=n.root.PHTML,p=n.PHTML.outerEm;var o={w:s.w*p,h:s.h*p,d:s.d*p};if(s.width){o.width=s.width}return o},Zoom:function(o,u,s,n,r){u.className="MathJax";this.idPostfix="-zoom";o.root.toPHTML(u,u);this.idPostfix="";u.style.position="absolute";if(!width){s.style.position="absolute"}var t=u.offsetWidth,q=u.offsetHeight,v=s.offsetHeight,p=s.offsetWidth;if(p===0){p=s.parentNode.offsetWidth}u.style.position=s.style.position="";return{Y:-j.getBBox(u).h,mW:p,mH:v,zW:t,zH:q}},initPHTML:function(o,n){},Remove:function(n){var o=document.getElementById(n.inputID+"-Frame");if(o){if(n.PHTML.display){o=o.parentNode}o.parentNode.removeChild(o)}delete n.PHTML},ID:0,idPostfix:"",GetID:function(){this.ID++;return this.ID},VARIANT:{bold:"MJXp-bold",italic:"MJXp-italic","bold-italic":"MJXp-bold MJXp-italic",script:"MJXp-scr","bold-script":"MJXp-scr MJXp-bold",fraktur:"MJXp-frak","bold-fraktur":"MJXp-frak MJXp-bold",monospace:"MJXp-mono","sans-serif":"MJXp-sf","-tex-caligraphic":"MJXp-cal"},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,thin:0.08,medium:0.1,thick:0.15,infinity:k},TeX:{x_height:0.430554},pxPerInch:72,em:16,DELIMITERS:{"(":{dir:c},"{":{dir:c,w:0.58},"[":{dir:c},"|":{dir:c,w:0.275},")":{dir:c},"}":{dir:c,w:0.58},"]":{dir:c},"/":{dir:c},"\\":{dir:c},"\u2223":{dir:c,w:0.275},"\u2225":{dir:c,w:0.55},"\u230A":{dir:c,w:0.5},"\u230B":{dir:c,w:0.5},"\u2308":{dir:c,w:0.5},"\u2309":{dir:c,w:0.5},"\u27E8":{dir:c,w:0.5},"\u27E9":{dir:c,w:0.5},"\u2191":{dir:c,w:0.65},"\u2193":{dir:c,w:0.65},"\u21D1":{dir:c,w:0.75},"\u21D3":{dir:c,w:0.75},"\u2195":{dir:c,w:0.65},"\u21D5":{dir:c,w:0.75},"\u27EE":{dir:c,w:0.275},"\u27EF":{dir:c,w:0.275},"\u23B0":{dir:c,w:0.6},"\u23B1":{dir:c,w:0.6}},REMAPACCENT:{"\u20D7":"\u2192","'":"\u02CB","`":"\u02CA",".":"\u02D9","^":"\u02C6","-":"\u02C9","~":"\u02DC","\u00AF":"\u02C9","\u00B0":"\u02DA","\u00B4":"\u02CA","\u0300":"\u02CB","\u0301":"\u02CA","\u0302":"\u02C6","\u0303":"\u02DC","\u0304":"\u02C9","\u0305":"\u02C9","\u0306":"\u02D8","\u0307":"\u02D9","\u0308":"\u00A8","\u030C":"\u02C7"},REMAPACCENTUNDER:{},length2em:function(r,p){if(typeof(r)!=="string"){r=r.toString()}if(r===""){return""}if(r===h.SIZE.NORMAL){return 1}if(r===h.SIZE.BIG){return 2}if(r===h.SIZE.SMALL){return 0.71}if(this.MATHSPACE[r]){return this.MATHSPACE[r]}var o=r.match(/^\s*([-+]?(?:\.\d+|\d+(?:\.\d*)?))?(pt|em|ex|mu|px|pc|in|mm|cm|%)?/);var n=parseFloat(o[1]||"1"),q=o[2];if(p==null){p=1}if(q==="em"){return n}if(q==="ex"){return n*this.TeX.x_height}if(q==="%"){return n/100*p}if(q==="px"){return n/this.em}if(q==="pt"){return n/10}if(q==="pc"){return n*1.2}if(q==="in"){return n*this.pxPerInch/this.em}if(q==="cm"){return n*this.pxPerInch/this.em/2.54}if(q==="mm"){return n*this.pxPerInch/this.em/25.4}if(q==="mu"){return n/18}return n*p},Em:function(n){if(Math.abs(n)<0.001){return"0em"}return(n.toFixed(3).replace(/\.?0+$/,""))+"em"},arrayEntry:function(n,o){return n[Math.max(0,Math.min(o,n.length-1))]}});MathJax.Hub.Register.StartupHook("mml Jax Ready",function(){h=MathJax.ElementJax.mml;h.mbase.Augment({toPreviewHTML:function(o,n){return this.PHTMLdefaultSpan(o,n)},PHTMLdefaultSpan:function(q,o){if(!o){o={}}q=this.PHTMLcreateSpan(q);this.PHTMLhandleStyle(q);this.PHTMLhandleColor(q);if(this.isToken){this.PHTMLhandleToken(q)}for(var p=0,n=this.data.length;p<n;p++){this.PHTMLaddChild(q,p,o)}return q},PHTMLaddChild:function(p,o,n){var q=this.data[o];if(q){if(n.childSpans){p=e.addElement(p,"span",{className:n.className})}q.toPreviewHTML(p);if(!n.noBBox){this.PHTML.w+=q.PHTML.w+q.PHTML.l+q.PHTML.r;if(q.PHTML.h>this.PHTML.h){this.PHTML.h=q.PHTML.h}if(q.PHTML.d>this.PHTML.d){this.PHTML.d=q.PHTML.d}if(q.PHTML.t>this.PHTML.t){this.PHTML.t=q.PHTML.t}if(q.PHTML.b>this.PHTML.b){this.PHTML.b=q.PHTML.b}}}else{if(n.forceChild){e.addElement(p,"span")}}},PHTMLstretchChild:function(q,p,s){var r=this.data[q];if(r&&r.PHTMLcanStretch("Vertical",p,s)){var t=this.PHTML,o=r.PHTML,n=o.w;r.PHTMLstretchV(p,s);t.w+=o.w-n;if(o.h>t.h){t.h=o.h}if(o.d>t.d){t.d=o.d}}},PHTMLcreateSpan:function(n){if(!this.PHTML){this.PHTML={}}this.PHTML={w:0,h:0,d:0,l:0,r:0,t:0,b:0};if(this.inferred){return n}if(this.type==="mo"&&this.data.join("")==="\u222B"){g.lastIsInt=true}else{if(this.type!=="mspace"||this.width!=="negativethinmathspace"){g.lastIsInt=false}}if(!this.PHTMLspanID){this.PHTMLspanID=g.GetID()}var o=(this.id||"MJXp-Span-"+this.PHTMLspanID);return e.addElement(n,"span",{className:"MJXp-"+this.type,id:o})},PHTMLspanElement:function(){if(!this.PHTMLspanID){return null}return document.getElementById(this.id||"MJXp-Span-"+this.PHTMLspanID)},PHTMLhandleToken:function(o){var n=this.getValues("mathvariant");if(n.mathvariant!==h.VARIANT.NORMAL){o.className+=" "+g.VARIANT[n.mathvariant]}},PHTMLhandleStyle:function(n){if(this.style){n.style.cssText=this.style}},PHTMLhandleColor:function(n){if(this.mathcolor){n.style.color=this.mathcolor}if(this.mathbackground){n.style.backgroundColor=this.mathbackground}},PHTMLhandleScriptlevel:function(n){var o=this.Get("scriptlevel");if(o){n.className+=" MJXp-script"}},PHTMLhandleText:function(y,A){var v,p;var z=0,o=0,q=0;for(var s=0,r=A.length;s<r;s++){p=A.charCodeAt(s);v=A.charAt(s);if(p>=55296&&p<56319){s++;p=(((p-55296)<<10)+(A.charCodeAt(s)-56320))+65536}var t=0.7,u=0.22,x=0.5;if(p<127){if(v.match(/[A-Za-ehik-or-xz0-9]/)){u=0}if(v.match(/[A-HK-Z]/)){x=0.67}else{if(v.match(/[IJ]/)){x=0.36}}if(v.match(/[acegm-su-z]/)){t=0.45}else{if(v.match(/[ij]/)){t=0.75}}if(v.match(/[ijlt]/)){x=0.28}}if(g.DELIMITERS[v]){x=g.DELIMITERS[v].w||0.4}if(t>z){z=t}if(u>o){o=u}q+=x}if(!this.CHML){this.PHTML={}}this.PHTML={h:0.9,d:0.3,w:q,l:0,r:0,t:z,b:o};e.addText(y,A)},PHTMLbboxFor:function(o){if(this.data[o]&&this.data[o].PHTML){return this.data[o].PHTML}return{w:0,h:0,d:0,l:0,r:0,t:0,b:0}},PHTMLcanStretch:function(q,o,p){if(this.isEmbellished()){var n=this.Core();if(n&&n!==this){return n.PHTMLcanStretch(q,o,p)}}return false},PHTMLstretchV:function(n,o){},PHTMLstretchH:function(n){},CoreParent:function(){var n=this;while(n&&n.isEmbellished()&&n.CoreMO()===this&&!n.isa(h.math)){n=n.Parent()}return n},CoreText:function(n){if(!n){return""}if(n.isEmbellished()){return n.CoreMO().data.join("")}while((n.isa(h.mrow)||n.isa(h.TeXAtom)||n.isa(h.mstyle)||n.isa(h.mphantom))&&n.data.length===1&&n.data[0]){n=n.data[0]}if(!n.isToken){return""}else{return n.data.join("")}}});h.chars.Augment({toPreviewHTML:function(n){var o=this.toString().replace(/[\u2061-\u2064]/g,"");this.PHTMLhandleText(n,o)}});h.entity.Augment({toPreviewHTML:function(n){var o=this.toString().replace(/[\u2061-\u2064]/g,"");this.PHTMLhandleText(n,o)}});h.math.Augment({toPreviewHTML:function(n){n=this.PHTMLdefaultSpan(n);if(this.Get("display")==="block"){n.className+=" MJXp-display"}return n}});h.mo.Augment({toPreviewHTML:function(o){o=this.PHTMLdefaultSpan(o);this.PHTMLadjustAccent(o);var n=this.getValues("lspace","rspace","scriptlevel","displaystyle","largeop");if(n.scriptlevel===0){this.PHTML.l=g.length2em(n.lspace);this.PHTML.r=g.length2em(n.rspace);o.style.marginLeft=g.Em(this.PHTML.l);o.style.marginRight=g.Em(this.PHTML.r)}else{this.PHTML.l=0.15;this.PHTML.r=0.1}if(n.displaystyle&&n.largeop){var p=e.Element("span",{className:"MJXp-largeop"});p.appendChild(o.firstChild);o.appendChild(p);this.PHTML.h*=1.2;this.PHTML.d*=1.2;if(this.data.join("")==="\u222B"){p.className+=" MJXp-int"}}return o},PHTMLadjustAccent:function(p){var o=this.CoreParent();if(o&&o.isa(h.munderover)&&this.CoreText(o.data[o.base]).length===1){var q=o.data[o.over],n=o.data[o.under];var s=this.data.join(""),r;if(q&&this===q.CoreMO()&&o.Get("accent")){r=g.REMAPACCENT[s]}else{if(n&&this===n.CoreMO()&&o.Get("accentunder")){r=g.REMAPACCENTUNDER[s]}}if(r){s=p.innerHTML=r}if(s.match(/[\u02C6-\u02DC\u00A8]/)){this.PHTML.acc=-0.52}else{if(s==="\u2192"){this.PHTML.acc=-0.15;this.PHTML.vec=true}}}},PHTMLcanStretch:function(q,o,p){if(!this.Get("stretchy")){return false}var r=this.data.join("");if(r.length>1){return false}r=g.DELIMITERS[r];var n=(r&&r.dir===q.substr(0,1));if(n){n=(this.PHTML.h!==o||this.PHTML.d!==p||(this.Get("minsize",true)||this.Get("maxsize",true)))}return n},PHTMLstretchV:function(p,u){var o=this.PHTMLspanElement(),t=this.PHTML;var n=this.getValues("symmetric","maxsize","minsize");if(n.symmetric){l=2*Math.max(p-0.25,u+0.25)}else{l=p+u}n.maxsize=g.length2em(n.maxsize,t.h+t.d);n.minsize=g.length2em(n.minsize,t.h+t.d);l=Math.max(n.minsize,Math.min(n.maxsize,l));var s=l/(t.h+t.d-0.3);var q=e.Element("span",{style:{"font-size":g.Em(s)}});if(s>1.25){var r=Math.ceil(1.25/s*10);q.className="MJXp-right MJXp-scale"+r;q.style.marginLeft=g.Em(t.w*(r/10-1)+0.07);t.w*=s*r/10}q.appendChild(o.firstChild);o.appendChild(q);if(n.symmetric){o.style.verticalAlign=g.Em(0.25*(1-s))}}});h.mspace.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q);var o=this.getValues("height","depth","width");var n=g.length2em(o.width),p=g.length2em(o.height),s=g.length2em(o.depth);var r=this.PHTML;r.w=n;r.h=p;r.d=s;if(n<0){if(!g.lastIsInt){q.style.marginLeft=g.Em(n)}n=0}q.style.width=g.Em(n);q.style.height=g.Em(p+s);if(s){q.style.verticalAlign=g.Em(-s)}return q}});h.mpadded.Augment({toPreviewHTML:function(u){u=this.PHTMLdefaultSpan(u,{childSpans:true,className:"MJXp-box",forceChild:true});var o=u.firstChild;var v=this.getValues("width","height","depth","lspace","voffset");var s=this.PHTMLdimen(v.lspace);var q=0,n=0,t=s.len,r=-s.len,p=0;if(v.width!==""){s=this.PHTMLdimen(v.width,"w",0);if(s.pm){r+=s.len}else{u.style.width=g.Em(s.len)}}if(v.height!==""){s=this.PHTMLdimen(v.height,"h",0);if(!s.pm){q+=-this.PHTMLbboxFor(0).h}q+=s.len}if(v.depth!==""){s=this.PHTMLdimen(v.depth,"d",0);if(!s.pm){n+=-this.PHTMLbboxFor(0).d;p+=-s.len}n+=s.len}if(v.voffset!==""){s=this.PHTMLdimen(v.voffset);q-=s.len;n+=s.len;p+=s.len}if(q){o.style.marginTop=g.Em(q)}if(n){o.style.marginBottom=g.Em(n)}if(t){o.style.marginLeft=g.Em(t)}if(r){o.style.marginRight=g.Em(r)}if(p){u.style.verticalAlign=g.Em(p)}return u},PHTMLdimen:function(q,r,n){if(n==null){n=-k}q=String(q);var o=q.match(/width|height|depth/);var p=(o?this.PHTML[o[0].charAt(0)]:(r?this.PHTML[r]:0));return{len:g.length2em(q,p)||0,pm:!!q.match(/^[-+]/)}}});h.munderover.Augment({toPreviewHTML:function(r){var t=this.getValues("displaystyle","accent","accentunder","align");var n=this.data[this.base];if(!t.displaystyle&&n!=null&&(n.movablelimits||n.CoreMO().Get("movablelimits"))){r=h.msubsup.prototype.toPreviewHTML.call(this,r);r.className=r.className.replace(/munderover/,"msubsup");return r}r=this.PHTMLdefaultSpan(r,{childSpans:true,className:"",noBBox:true});var p=this.PHTMLbboxFor(this.over),v=this.PHTMLbboxFor(this.under),u=this.PHTMLbboxFor(this.base),s=this.PHTML,o=p.acc;if(this.data[this.over]){if(r.lastChild.firstChild){r.lastChild.firstChild.style.marginLeft=p.l=r.lastChild.firstChild.style.marginRight=p.r=0}var q=e.Element("span",{},[["span",{className:"MJXp-over"}]]);q.firstChild.appendChild(r.lastChild);if(r.childNodes.length>(this.data[this.under]?1:0)){q.firstChild.appendChild(r.firstChild)}this.data[this.over].PHTMLhandleScriptlevel(q.firstChild.firstChild);if(o!=null){if(p.vec){q.firstChild.firstChild.firstChild.style.fontSize="60%";p.h*=0.6;p.d*=0.6;p.w*=0.6}o=o-p.d+0.1;if(u.t!=null){o+=u.t-u.h}q.firstChild.firstChild.style.marginBottom=g.Em(o)}if(r.firstChild){r.insertBefore(q,r.firstChild)}else{r.appendChild(q)}}if(this.data[this.under]){if(r.lastChild.firstChild){r.lastChild.firstChild.style.marginLeft=v.l=r.lastChild.firstChild.marginRight=v.r=0}this.data[this.under].PHTMLhandleScriptlevel(r.lastChild)}s.w=Math.max(0.8*p.w,0.8*v.w,u.w);s.h=0.8*(p.h+p.d+(o||0))+u.h;s.d=u.d+0.8*(v.h+v.d);return r}});h.msubsup.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q,{noBBox:true});if(!this.data[this.base]){if(q.firstChild){q.insertBefore(e.Element("span"),q.firstChild)}else{q.appendChild(e.Element("span"))}}var s=this.data[this.base],p=this.data[this.sub],n=this.data[this.sup];if(!s){s={bbox:{h:0.8,d:0.2}}}q.firstChild.style.marginRight=".05em";var o=Math.max(0.4,s.PHTML.h-0.4),u=Math.max(0.2,s.PHTML.d+0.1);var t=this.PHTML;if(n&&p){var r=e.Element("span",{className:"MJXp-script-box",style:{height:g.Em(o+n.PHTML.h*0.8+u+p.PHTML.d*0.8),"vertical-align":g.Em(-u-p.PHTML.d*0.8)}},[["span",{},[["span",{},[["span",{style:{"margin-bottom":g.Em(-(n.PHTML.d-0.05))}}]]]]],["span",{},[["span",{},[["span",{style:{"margin-top":g.Em(-(n.PHTML.h-0.05))}}]]]]]]);p.PHTMLhandleScriptlevel(r.firstChild);n.PHTMLhandleScriptlevel(r.lastChild);r.firstChild.firstChild.firstChild.appendChild(q.lastChild);r.lastChild.firstChild.firstChild.appendChild(q.lastChild);q.appendChild(r);t.h=Math.max(s.PHTML.h,n.PHTML.h*0.8+o);t.d=Math.max(s.PHTML.d,p.PHTML.d*0.8+u);t.w=s.PHTML.w+Math.max(n.PHTML.w,p.PHTML.w)+0.07}else{if(n){q.lastChild.style.verticalAlign=g.Em(o);n.PHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.PHTML.h,n.PHTML.h*0.8+o);t.d=Math.max(s.PHTML.d,n.PHTML.d*0.8-o);t.w=s.PHTML.w+n.PHTML.w+0.07}else{if(p){q.lastChild.style.verticalAlign=g.Em(-u);p.PHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.PHTML.h,p.PHTML.h*0.8-u);t.d=Math.max(s.PHTML.d,p.PHTML.d*0.8+u);t.w=s.PHTML.w+p.PHTML.w+0.07}}}return q}});h.mfrac.Augment({toPreviewHTML:function(r){r=this.PHTMLdefaultSpan(r,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});var o=this.getValues("linethickness","displaystyle");if(!o.displaystyle){if(this.data[0]){this.data[0].PHTMLhandleScriptlevel(r.firstChild)}if(this.data[1]){this.data[1].PHTMLhandleScriptlevel(r.lastChild)}}var n=e.Element("span",{className:"MJXp-box"},[["span",{className:"MJXp-denom"},[["span",{},[["span",{className:"MJXp-rule",style:{height:"1em"}}]]],["span"]]]]);n.firstChild.lastChild.appendChild(r.lastChild);r.appendChild(n);var s=this.PHTMLbboxFor(0),p=this.PHTMLbboxFor(1),v=this.PHTML;v.w=Math.max(s.w,p.w)*0.8;v.h=s.h+s.d+0.1+0.25;v.d=p.h+p.d-0.25;v.l=v.r=0.125;o.linethickness=Math.max(0,g.length2em(o.linethickness||"0",0));if(o.linethickness){var u=n.firstChild.firstChild.firstChild;var q=g.Em(o.linethickness);u.style.borderTop="none";u.style.borderBottom=(o.linethickness<0.15?"1px":q)+" solid";u.style.margin=q+" 0";q=o.linethickness;n.style.marginTop=g.Em(3*q-1.2);r.style.verticalAlign=g.Em(1.5*q+0.1);v.h+=1.5*q-0.1;v.d+=1.5*q}else{n.style.marginTop="-.7em"}return r}});h.msqrt.Augment({toPreviewHTML:function(n){n=this.PHTMLdefaultSpan(n,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});this.PHTMLlayoutRoot(n,n.firstChild);return n},PHTMLlayoutRoot:function(u,n){var v=this.PHTMLbboxFor(0);var q=Math.ceil((v.h+v.d+0.14)*100),w=g.Em(14/q);var r=e.Element("span",{className:"MJXp-surd"},[["span",{style:{"font-size":q+"%","margin-top":w}},["\u221A"]]]);var s=e.Element("span",{className:"MJXp-root"},[["span",{className:"MJXp-rule",style:{"border-top":".08em solid"}}]]);var p=(1.2/2.2)*q/100;if(q>150){var o=Math.ceil(150/q*10);r.firstChild.className="MJXp-right MJXp-scale"+o;r.firstChild.style.marginLeft=g.Em(p*(o/10-1)/q*100);p=p*o/10;s.firstChild.style.borderTopWidth=g.Em(0.08/Math.sqrt(o/10))}s.appendChild(n);u.appendChild(r);u.appendChild(s);this.PHTML.h=v.h+0.18;this.PHTML.d=v.d;this.PHTML.w=v.w+p;return u}});h.mroot.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});var p=this.PHTMLbboxFor(1),n=q.removeChild(q.lastChild);var t=this.PHTMLlayoutRoot(e.Element("span"),q.firstChild);n.className="MJXp-script";var u=parseInt(t.firstChild.firstChild.style.fontSize);var o=0.55*(u/120)+p.d*0.8,s=-0.6*(u/120);if(u>150){s*=0.95*Math.ceil(150/u*10)/10}n.style.marginRight=g.Em(s);n.style.verticalAlign=g.Em(o);if(-s>p.w*0.8){n.style.marginLeft=g.Em(-s-p.w*0.8)}q.appendChild(n);q.appendChild(t);this.PHTML.w+=Math.max(0,p.w*0.8+s);this.PHTML.h=Math.max(this.PHTML.h,p.h*0.8+o);return q},PHTMLlayoutRoot:h.msqrt.prototype.PHTMLlayoutRoot});h.mfenced.Augment({toPreviewHTML:function(q){q=this.PHTMLcreateSpan(q);this.PHTMLhandleStyle(q);this.PHTMLhandleColor(q);this.addFakeNodes();this.PHTMLaddChild(q,"open",{});for(var p=0,n=this.data.length;p<n;p++){this.PHTMLaddChild(q,"sep"+p,{});this.PHTMLaddChild(q,p,{})}this.PHTMLaddChild(q,"close",{});var o=this.PHTML.h,r=this.PHTML.d;this.PHTMLstretchChild("open",o,r);for(p=0,n=this.data.length;p<n;p++){this.PHTMLstretchChild("sep"+p,o,r);this.PHTMLstretchChild(p,o,r)}this.PHTMLstretchChild("close",o,r);return q}});h.mrow.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q);var p=this.PHTML.h,r=this.PHTML.d;for(var o=0,n=this.data.length;o<n;o++){this.PHTMLstretchChild(o,p,r)}return q}});h.mstyle.Augment({toPreviewHTML:function(n){n=this.PHTMLdefaultSpan(n);this.PHTMLhandleScriptlevel(n);return n}});h.TeXAtom.Augment({toPreviewHTML:function(n){n=this.PHTMLdefaultSpan(n);n.className="MJXp-mrow";return n}});h.mtable.Augment({toPreviewHTML:function(E){E=this.PHTMLdefaultSpan(E,{noBBox:true});var r=this.getValues("columnalign","rowalign","columnspacing","rowspacing","columnwidth","equalcolumns","equalrows","columnlines","rowlines","frame","framespacing","align","width");var u=MathJax.Hub.SplitList,F,A,D,z;var N=u(r.columnspacing),w=u(r.rowspacing),L=u(r.columnalign),t=u(r.rowalign);for(F=0,A=N.length;F<A;F++){N[F]=g.length2em(N[F])}for(F=0,A=w.length;F<A;F++){w[F]=g.length2em(w[F])}var K=e.Element("span");while(E.firstChild){K.appendChild(E.firstChild)}E.appendChild(K);var y=0,s=0;for(F=0,A=this.data.length;F<A;F++){var v=this.data[F];if(v){var J=g.arrayEntry(w,F-1),C=g.arrayEntry(t,F);var x=v.PHTML,q=v.PHTMLspanElement();q.style.verticalAlign=C;var B=(v.type==="mlabeledtr"?1:0);for(D=0,z=v.data.length;D<z-B;D++){var p=v.data[D+B];if(p){var M=g.arrayEntry(N,D-1),G=g.arrayEntry(L,D);var I=p.PHTMLspanElement();if(D){x.w+=M;I.style.paddingLeft=g.Em(M)}if(F){I.style.paddingTop=g.Em(J)}I.style.textAlign=G}}y+=x.h+x.d;if(F){y+=J}if(x.w>s){s=x.w}}}var o=this.PHTML;o.w=s;o.h=y/2+0.25;o.d=y/2-0.25;o.l=o.r=0.125;return E}});h.mlabeledtr.Augment({PHTMLdefaultSpan:function(q,o){if(!o){o={}}q=this.PHTMLcreateSpan(q);this.PHTMLhandleStyle(q);this.PHTMLhandleColor(q);if(this.isToken){this.PHTMLhandleToken(q)}for(var p=1,n=this.data.length;p<n;p++){this.PHTMLaddChild(q,p,o)}return q}});h.semantics.Augment({toPreviewHTML:function(n){n=this.PHTMLcreateSpan(n);if(this.data[0]){this.data[0].toPreviewHTML(n);MathJax.Hub.Insert(this.data[0].PHTML||{},this.PHTML)}return n}});h.annotation.Augment({toPreviewHTML:function(n){}});h["annotation-xml"].Augment({toPreviewHTML:function(n){}});MathJax.Hub.Register.StartupHook("onLoad",function(){setTimeout(MathJax.Callback(["loadComplete",g,"jax.js"]),0)})});MathJax.Hub.Register.StartupHook("End Cookie",function(){if(b.config.menuSettings.zoom!=="None"){i.Require("[MathJax]/extensions/MathZoom.js")}})})(MathJax.Ajax,MathJax.Hub,MathJax.HTML,MathJax.OutputJax.PreviewHTML);
(function(b,g,f){var c=b.config.menuSettings;var e=MathJax.OutputJax;var a=f.isMSIE&&(document.documentMode||0)<8;var d=MathJax.Extension["fast-preview"]={version:"2.7.5",enabled:true,config:b.CombineConfig("fast-preview",{Chunks:{EqnChunk:10000,EqnChunkFactor:1,EqnChunkDelay:0},color:"inherit!important",updateTime:30,updateDelay:6,messageStyle:"none",disabled:f.isMSIE&&!f.versionAtLeast("8.0")}),Config:function(){if(b.config["CHTML-preview"]){MathJax.Hub.Config({"fast-preview":b.config["CHTML-preview"]})}var m,j,k,h,l;var i=this.config;if(!i.disabled&&c.FastPreview==null){b.Config({menuSettings:{FastPreview:true}})}if(c.FastPreview){MathJax.Ajax.Styles({".MathJax_Preview .MJXf-math":{color:i.color}});b.Config({"HTML-CSS":i.Chunks,CommonHTML:i.Chunks,SVG:i.Chunks})}b.Register.MessageHook("Begin Math Output",function(){if(!h&&d.Active()){m=b.processUpdateTime;j=b.processUpdateDelay;k=b.config.messageStyle;b.processUpdateTime=i.updateTime;b.processUpdateDelay=i.updateDelay;b.Config({messageStyle:i.messageStyle});MathJax.Message.Clear(0,0);l=true}});b.Register.MessageHook("End Math Output",function(){if(!h&&l){b.processUpdateTime=m;b.processUpdateDelay=j;b.Config({messageStyle:k});h=true}})},Disable:function(){this.enabled=false},Enable:function(){this.enabled=true},Active:function(){return c.FastPreview&&this.enabled&&!(e[c.renderer]||{}).noFastPreview},Preview:function(h){if(!this.Active()||!h.script.parentNode){return}var i=h.script.MathJax.preview||h.script.previousSibling;if(!i||i.className!==MathJax.Hub.config.preRemoveClass){i=g.Element("span",{className:MathJax.Hub.config.preRemoveClass});h.script.parentNode.insertBefore(i,h.script);h.script.MathJax.preview=i}i.innerHTML="";i.style.color=(a?"black":"inherit");return this.postFilter(i,h)},postFilter:function(j,i){if(!i.math.root.toPreviewHTML){var h=MathJax.Callback.Queue();h.Push(["Require",MathJax.Ajax,"[MathJax]/jax/output/PreviewHTML/config.js"],["Require",MathJax.Ajax,"[MathJax]/jax/output/PreviewHTML/jax.js"]);b.RestartAfter(h.Push({}))}i.math.root.toPreviewHTML(j)},Register:function(h){b.Register.StartupHook(h+" Jax Require",function(){var i=MathJax.InputJax[h];i.postfilterHooks.Add(["Preview",MathJax.Extension["fast-preview"]],50)})}};d.Register("TeX");d.Register("MathML");d.Register("AsciiMath");b.Register.StartupHook("End Config",["Config",d]);b.Startup.signal.Post("fast-preview Ready")})(MathJax.Hub,MathJax.HTML,MathJax.Hub.Browser);MathJax.Ajax.loadComplete("[MathJax]/extensions/fast-preview.js");
(function(a,e,b,f){var c=b.config.menuSettings;var d=MathJax.Extension.AssistiveMML={version:"2.7.5",config:b.CombineConfig("AssistiveMML",{disabled:false,styles:{".MJX_Assistive_MathML":{position:"absolute!important",top:0,left:0,clip:(b.Browser.isMSIE&&(document.documentMode||0)<8?"rect(1px 1px 1px 1px)":"rect(1px, 1px, 1px, 1px)"),padding:"1px 0 0 0!important",border:"0!important",height:"1px!important",width:"1px!important",overflow:"hidden!important",display:"block!important","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none"},".MJX_Assistive_MathML.MJX_Assistive_MathML_Block":{width:"100%!important"}}}),Config:function(){if(!this.config.disabled&&c.assistiveMML==null){b.Config({menuSettings:{assistiveMML:true}})}a.Styles(this.config.styles);b.Register.MessageHook("End Math",function(g){if(c.assistiveMML){return d.AddAssistiveMathML(g[1])}})},AddAssistiveMathML:function(g){var h={jax:b.getAllJax(g),i:0,callback:MathJax.Callback({})};this.HandleMML(h);return h.callback},RemoveAssistiveMathML:function(k){var h=b.getAllJax(k),l;for(var j=0,g=h.length;j<g;j++){l=document.getElementById(h[j].inputID+"-Frame");if(l&&l.getAttribute("data-mathml")){l.removeAttribute("data-mathml");if(l.lastChild&&l.lastChild.className.match(/MJX_Assistive_MathML/)){l.removeChild(l.lastChild)}}}},HandleMML:function(l){var g=l.jax.length,h,i,n,j;while(l.i<g){h=l.jax[l.i];n=document.getElementById(h.inputID+"-Frame");if(h.outputJax!=="NativeMML"&&h.outputJax!=="PlainSource"&&n&&!n.getAttribute("data-mathml")){try{i=h.root.toMathML("").replace(/\n */g,"").replace(/<!--.*?-->/g,"")}catch(k){if(!k.restart){throw k}return MathJax.Callback.After(["HandleMML",this,l],k.restart)}n.setAttribute("data-mathml",i);j=f.addElement(n,"span",{isMathJax:true,unselectable:"on",className:"MJX_Assistive_MathML"+(h.root.Get("display")==="block"?" MJX_Assistive_MathML_Block":"")});try{j.innerHTML=i}catch(k){}n.style.position="relative";n.setAttribute("role","presentation");n.firstChild.setAttribute("aria-hidden","true");j.setAttribute("role","presentation")}l.i++}l.callback()}};b.Startup.signal.Post("AssistiveMML Ready")})(MathJax.Ajax,MathJax.Callback,MathJax.Hub,MathJax.HTML);MathJax.Callback.Queue(["Require",MathJax.Ajax,"[MathJax]/extensions/toMathML.js"],["loadComplete",MathJax.Ajax,"[MathJax]/extensions/AssistiveMML.js"],function(){MathJax.Hub.Register.StartupHook("End Config",["Config",MathJax.Extension.AssistiveMML])});
!function(a,b){var c,d,e=a.config.menuSettings,f=Function.prototype.bind?function(a,b){return a.bind(b)}:function(a,b){return function(){a.apply(b,arguments)}},g=Object.keys||function(a){var b=[];for(var c in a)a.hasOwnProperty(c)&&b.push(c);return b},h=MathJax.Ajax.config.path;h.a11y||(h.a11y=a.config.root+"/extensions/a11y");var i=b["accessibility-menu"]={version:"1.5.0",prefix:"",defaults:{},modules:[],MakeOption:function(a){return i.prefix+a},GetOption:function(a){return e[i.MakeOption(a)]},AddDefaults:function(){for(var a,b=g(i.defaults),c=0;a=b[c];c++){var d=i.MakeOption(a);void 0===e[d]&&(e[d]=i.defaults[a])}},AddMenu:function(){for(var a,b=Array(this.modules.length),e=0;a=this.modules[e];e++)b[e]=a.placeHolder;var f=d.FindId("Accessibility");if(f)b.unshift(c.RULE()),f.submenu.items.push.apply(f.submenu.items,b);else{var g=(d.FindId("Settings","Renderer")||{}).submenu;g&&(b.unshift(c.RULE()),b.unshift(g.items.pop()),b.unshift(g.items.pop())),b.unshift("Accessibility");var f=c.SUBMENU.apply(c.SUBMENU,b),h=d.IndexOfId("Locale");h?d.items.splice(h,0,f):d.items.push(c.RULE(),f)}},Register:function(a){i.defaults[a.option]=!1,i.modules.push(a)},Startup:function(){c=MathJax.Menu.ITEM,d=MathJax.Menu.menu;for(var a,b=0;a=this.modules[b];b++)a.CreateMenu();this.AddMenu()},LoadExtensions:function(){for(var b,c=[],d=0;b=this.modules[d];d++)e[b.option]&&c.push(b.module);return c.length?a.Startup.loadArray(c):null}},j=MathJax.Extension.ModuleLoader=MathJax.Object.Subclass({option:"",name:["",""],module:"",placeHolder:null,submenu:!1,extension:null,Init:function(a,b,c,d,e){this.option=a,this.name=[b.replace(/ /g,""),b],this.module=c,this.extension=d,this.submenu=e||!1},CreateMenu:function(){var a=f(this.Load,this);this.submenu?this.placeHolder=c.SUBMENU(this.name,c.CHECKBOX(["Activate","Activate"],i.MakeOption(this.option),{action:a}),c.RULE(),c.COMMAND(["OptionsWhenActive","(Options when Active)"],null,{disabled:!0})):this.placeHolder=c.CHECKBOX(this.name,i.MakeOption(this.option),{action:a})},Load:function(){a.Queue(["Require",MathJax.Ajax,this.module,["Enable",this]])},Enable:function(a){var b=MathJax.Extension[this.extension];b&&(b.Enable(!0,!0),MathJax.Menu.saveCookie())}});i.Register(j("collapsible","Collapsible Math","[a11y]/collapsible.js","collapsible")),i.Register(j("autocollapse","Auto Collapse","[a11y]/auto-collapse.js","auto-collapse")),i.Register(j("explorer","Explorer","[a11y]/explorer.js","explorer",!0)),i.AddDefaults(),a.Register.StartupHook("End Extensions",function(){a.Register.StartupHook("MathMenu Ready",function(){i.Startup(),a.Startup.signal.Post("Accessibility Menu Ready")},5)},5),MathJax.Hub.Register.StartupHook("End Cookie",function(){MathJax.Callback.Queue(["LoadExtensions",i],["loadComplete",MathJax.Ajax,"[a11y]/accessibility-menu.js"])})}(MathJax.Hub,MathJax.Extension);MathJax.Ajax.loadComplete("[MathJax]/config/MML_SVG-full.js");