/*
 *  /MathJax/config/TeX-AMS_CHTML-full.js
 *  
 *  Copyright (c) 2010-2015 The MathJax Consortium
 *
 *  Part of the MathJax library.
 *  See http://www.mathjax.org for details.
 * 
 *  Licensed under the Apache License, Version 2.0;
 *  you may not use this file except in compliance with the License.
 *
 *      http://www.apache.org/licenses/LICENSE-2.0
 */

MathJax.Ajax.Preloading(
  "[MathJax]/jax/input/TeX/config.js",
  "[MathJax]/jax/output/CommonHTML/config.js",
  "[MathJax]/extensions/tex2jax.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/TeX/jax.js",
  "[MathJax]/extensions/TeX/AMSmath.js",
  "[MathJax]/extensions/TeX/AMSsymbols.js",
  "[MathJax]/jax/output/CommonHTML/jax.js",
  "[MathJax]/jax/output/CommonHTML/autoload/mtable.js",
  "[MathJax]/extensions/AssistiveMML.js"
);

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

MathJax.InputJax.TeX=MathJax.InputJax({id:"TeX",version:"2.6.0-beta",directory:MathJax.InputJax.directory+"/TeX",extensionDir:MathJax.InputJax.extensionDir+"/TeX",config:{TagSide:"right",TagIndent:"0.8em",MultLineWidth:"85%",equationNumbers:{autoNumber:"none",formatNumber:function(a){return a},formatTag:function(a){return"("+a+")"},formatID:function(a){return"mjx-eqn-"+String(a).replace(/[:"'<>&]/g,"")},formatURL:function(a){return"#"+escape(a)},useLabelIds:true}}});MathJax.InputJax.TeX.Register("math/tex");MathJax.InputJax.TeX.loadComplete("config.js");
MathJax.OutputJax.CommonHTML=MathJax.OutputJax({id:"CommonHTML",version:"2.6.0-beta",directory:MathJax.OutputJax.directory+"/CommonHTML",extensionDir:MathJax.OutputJax.extensionDir+"/CommonHTML",autoloadDir:MathJax.OutputJax.directory+"/CommonHTML/autoload",fontDir:MathJax.OutputJax.directory+"/CommonHTML/fonts",webfontDir:MathJax.OutputJax.fontDir+"/HTML-CSS",config:{matchFontHeight:true,scale:100,minScaleAdjust:50,mtextFontInherit:false,undefinedFamily:"STIXGeneral,'Cambria Math','Arial Unicode MS',serif",EqnChunk:(MathJax.Hub.Browser.isMobile?20:100),EqnChunkFactor:1.5,EqnChunkDelay:100,linebreaks:{automatic:false,width:"container"}}});if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax.CommonHTML.Register("jax/mml")}MathJax.OutputJax.CommonHTML.loadComplete("config.js");
MathJax.Extension.tex2jax={version:"2.6.0-beta",config:{inlineMath:[["\\(","\\)"]],displayMath:[["$$","$$"],["\\[","\\]"]],balanceBraces:true,skipTags:["script","noscript","style","textarea","pre","code","annotation","annotation-xml"],ignoreClass:"tex2jax_ignore",processClass:"tex2jax_process",processEscapes:false,processEnvironments:true,processRefs:true,preview:"TeX"},PreProcess:function(a){if(!this.configured){this.config=MathJax.Hub.CombineConfig("tex2jax",this.config);if(this.config.Augment){MathJax.Hub.Insert(this,this.config.Augment)}if(typeof(this.config.previewTeX)!=="undefined"&&!this.config.previewTeX){this.config.preview="none"}this.configured=true}if(typeof(a)==="string"){a=document.getElementById(a)}if(!a){a=document.body}if(this.createPatterns()){this.scanElement(a,a.nextSibling)}},createPatterns:function(){var d=[],e=[],c,a,b=this.config;this.match={};for(c=0,a=b.inlineMath.length;c<a;c++){d.push(this.patternQuote(b.inlineMath[c][0]));this.match[b.inlineMath[c][0]]={mode:"",end:b.inlineMath[c][1],pattern:this.endPattern(b.inlineMath[c][1])}}for(c=0,a=b.displayMath.length;c<a;c++){d.push(this.patternQuote(b.displayMath[c][0]));this.match[b.displayMath[c][0]]={mode:"; mode=display",end:b.displayMath[c][1],pattern:this.endPattern(b.displayMath[c][1])}}if(d.length){e.push(d.sort(this.sortLength).join("|"))}if(b.processEnvironments){e.push("\\\\begin\\{([^}]*)\\}")}if(b.processEscapes){e.push("\\\\*\\\\\\$")}if(b.processRefs){e.push("\\\\(eq)?ref\\{[^}]*\\}")}this.start=new RegExp(e.join("|"),"g");this.skipTags=new RegExp("^("+b.skipTags.join("|")+")$","i");var f=[];if(MathJax.Hub.config.preRemoveClass){f.push(MathJax.Hub.config.preRemoveClass)}if(b.ignoreClass){f.push(b.ignoreClass)}this.ignoreClass=(f.length?new RegExp("(^| )("+f.join("|")+")( |$)"):/^$/);this.processClass=new RegExp("(^| )("+b.processClass+")( |$)");return(e.length>0)},patternQuote:function(a){return a.replace(/([\^$(){}+*?\-|\[\]\:\\])/g,"\\$1")},endPattern:function(a){return new RegExp(this.patternQuote(a)+"|\\\\.|[{}]","g")},sortLength:function(d,c){if(d.length!==c.length){return c.length-d.length}return(d==c?0:(d<c?-1:1))},scanElement:function(c,b,g){var a,e,d,f;while(c&&c!=b){if(c.nodeName.toLowerCase()==="#text"){if(!g){c=this.scanText(c)}}else{a=(typeof(c.className)==="undefined"?"":c.className);e=(typeof(c.tagName)==="undefined"?"":c.tagName);if(typeof(a)!=="string"){a=String(a)}f=this.processClass.exec(a);if(c.firstChild&&!a.match(/(^| )MathJax/)&&(f||!this.skipTags.exec(e))){d=(g||this.ignoreClass.exec(a))&&!f;this.scanElement(c.firstChild,b,d)}}if(c){c=c.nextSibling}}},scanText:function(b){if(b.nodeValue.replace(/\s+/,"")==""){return b}var a,c;this.search={start:true};this.pattern=this.start;while(b){this.pattern.lastIndex=0;while(b&&b.nodeName.toLowerCase()==="#text"&&(a=this.pattern.exec(b.nodeValue))){if(this.search.start){b=this.startMatch(a,b)}else{b=this.endMatch(a,b)}}if(this.search.matched){b=this.encloseMath(b)}if(b){do{c=b;b=b.nextSibling}while(b&&(b.nodeName.toLowerCase()==="br"||b.nodeName.toLowerCase()==="#comment"));if(!b||b.nodeName!=="#text"){return(this.search.close?this.prevEndMatch():c)}}}return b},startMatch:function(a,b){var f=this.match[a[0]];if(f!=null){this.search={end:f.end,mode:f.mode,pcount:0,open:b,olen:a[0].length,opos:this.pattern.lastIndex-a[0].length};this.switchPattern(f.pattern)}else{if(a[0].substr(0,6)==="\\begin"){this.search={end:"\\end{"+a[1]+"}",mode:"; mode=display",pcount:0,open:b,olen:0,opos:this.pattern.lastIndex-a[0].length,isBeginEnd:true};this.switchPattern(this.endPattern(this.search.end))}else{if(a[0].substr(0,4)==="\\ref"||a[0].substr(0,6)==="\\eqref"){this.search={mode:"",end:"",open:b,pcount:0,olen:0,opos:this.pattern.lastIndex-a[0].length};return this.endMatch([""],b)}else{var d=a[0].substr(0,a[0].length-1),g,c;if(d.length%2===0){c=[d.replace(/\\\\/g,"\\")];g=1}else{c=[d.substr(1).replace(/\\\\/g,"\\"),"$"];g=0}c=MathJax.HTML.Element("span",null,c);var e=MathJax.HTML.TextNode(b.nodeValue.substr(0,a.index));b.nodeValue=b.nodeValue.substr(a.index+a[0].length-g);b.parentNode.insertBefore(c,b);b.parentNode.insertBefore(e,c);this.pattern.lastIndex=g}}}return b},endMatch:function(a,c){var b=this.search;if(a[0]==b.end){if(!b.close||b.pcount===0){b.close=c;b.cpos=this.pattern.lastIndex;b.clen=(b.isBeginEnd?0:a[0].length)}if(b.pcount===0){b.matched=true;c=this.encloseMath(c);this.switchPattern(this.start)}}else{if(a[0]==="{"){b.pcount++}else{if(a[0]==="}"&&b.pcount){b.pcount--}}}return c},prevEndMatch:function(){this.search.matched=true;var a=this.encloseMath(this.search.close);this.switchPattern(this.start);return a},switchPattern:function(a){a.lastIndex=this.pattern.lastIndex;this.pattern=a;this.search.start=(a===this.start)},encloseMath:function(b){var a=this.search,f=a.close,e,c;if(a.cpos===f.length){f=f.nextSibling}else{f=f.splitText(a.cpos)}if(!f){e=f=MathJax.HTML.addText(a.close.parentNode,"")}a.close=f;c=(a.opos?a.open.splitText(a.opos):a.open);while(c.nextSibling&&c.nextSibling!==f){if(c.nextSibling.nodeValue!==null){if(c.nextSibling.nodeName==="#comment"){c.nodeValue+=c.nextSibling.nodeValue.replace(/^\[CDATA\[((.|\n|\r)*)\]\]$/,"$1")}else{c.nodeValue+=c.nextSibling.nodeValue}}else{if(this.msieNewlineBug){c.nodeValue+=(c.nextSibling.nodeName.toLowerCase()==="br"?"\n":" ")}else{c.nodeValue+=" "}}c.parentNode.removeChild(c.nextSibling)}var d=c.nodeValue.substr(a.olen,c.nodeValue.length-a.olen-a.clen);c.parentNode.removeChild(c);if(this.config.preview!=="none"){this.createPreview(a.mode,d)}c=this.createMathTag(a.mode,d);this.search={};this.pattern.lastIndex=0;if(e){e.parentNode.removeChild(e)}return c},insertNode:function(b){var a=this.search;a.close.parentNode.insertBefore(b,a.close)},createPreview:function(c,a){var b=this.config.preview;if(b==="none"){return}if(b==="TeX"){b=[this.filterPreview(a)]}if(b){b=MathJax.HTML.Element("span",{className:MathJax.Hub.config.preRemoveClass},b);this.insertNode(b)}},createMathTag:function(c,b){var a=document.createElement("script");a.type="math/tex"+c;MathJax.HTML.setScript(a,b);this.insertNode(a);return a},filterPreview:function(a){return a},msieNewlineBug:(MathJax.Hub.Browser.isMSIE&&document.documentMode<9)};MathJax.Hub.Register.PreProcessor(["PreProcess",MathJax.Extension.tex2jax]);MathJax.Ajax.loadComplete("[MathJax]/extensions/tex2jax.js");
(function(d,h,l,g,m,b,j){var p="2.6.0-beta";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="2.6.0-beta";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);
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g=MathJax.Menu=h.Subclass({version:o,items:[],posted:false,title:null,margin:5,Init:function(t){this.items=[].slice.call(arguments,0)},With:function(t){if(t){f.Insert(this,t)}return this},Post:function(u,I,G){if(!u){u=window.event||{}}var t=document.getElementById("MathJax_MenuFrame");if(!t){t=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=n.Element("div",{onmouseup:g.Mouseup,ondblclick:m,ondragstart:m,onselectstart:m,oncontextmenu:m,menuItem:this,className:"MathJax_Menu",onkeydown:g.Keydown,role:"menu"});if(u.type==="contextmenu"||u.type==="mouseover"){v.className+=" MathJax_ContextMenu"}if(!G){MathJax.Localization.setCSS(v)}for(var 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v=window.innerHeight||y.clientHeight||y.scrollHeight||0;if(g.prototype.msieAboutBug){w.style.width="20em";w.style.position="absolute";w.style.left=Math.floor((document.documentElement.scrollWidth-w.offsetWidth)/2)+"px";w.style.top=(Math.floor((v-w.offsetHeight)/3)+document.body.scrollTop)+"px"}else{w.style.marginLeft=Math.floor(-w.offsetWidth/2)+"px";w.style.top=Math.floor((v-w.offsetHeight)/3)+"px"}};g.About.Remove=function(t){if(g.About.div){document.body.removeChild(g.About.div);delete g.About.div}};g.About.Keydown=function(t){if(t.keyCode===b.ESCAPE||(this.id==="MathJax_AboutClose"&&(t.keyCode===b.SPACE||t.keyCode===b.RETURN))){g.About.Remove(t);g.CurrentNode().focus();m(t)}},g.About.GetJax=function(u,z,x,w){var y=[];for(var A in z){if(z.hasOwnProperty(A)&&z[A]){if((w&&z[A].version)||(z[A].isa&&z[A].isa(z))){y.push(s(x[0],x[1],(z[A].id||A),z[A].version))}}}y.sort();for(var v=0,t=y.length;v<t;v++){u.push(y[v],["br"])}return u};g.About.GetFont=function(){var t=MathJax.Hub.outputJax["jax/mml"][0]||{};var u={SVG:"web SVG",CommonHTML:"web TeX","HTML-CSS":(t.imgFonts?"image":(t.webFonts?"web":"local")+" "+t.fontInUse)}[t.id]||"generic";return u+" fonts"};g.About.GetFormat=function(){var t=MathJax.Hub.outputJax["jax/mml"][0]||{};if(t.id!=="HTML-CSS"||!t.webFonts||t.imgFonts){return}return t.allowWebFonts.replace(/otf/,"woff or otf")+" fonts"};g.Help=function(t){p.Require("[MathJax]/extensions/HelpDialog.js",function(){MathJax.Extension.Help.Dialog({type:t.type})})};g.ShowSource=function(x){if(!x){x=window.event}var w={screenX:x.screenX,screenY:x.screenY};if(!g.jax){return}if(this.format==="MathML"){var u=MathJax.ElementJax.mml;if(u&&typeof(u.mbase.prototype.toMathML)!=="undefined"){try{g.ShowSource.Text(g.jax.root.toMathML("",g.jax),x)}catch(v){if(!v.restart){throw 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A=(t.outerHeight-t.innerHeight)||30,z=(t.outerWidth-t.innerWidth)||30,w,D;z=Math.max(140,Math.min(Math.floor(0.5*screen.width),u.offsetWidth+z+25));A=Math.max(40,Math.min(Math.floor(0.5*screen.height),u.offsetHeight+A+25));if(g.prototype.msieHeightBug){A+=35}t.resizeTo(z,A);var C;try{C=v.screenX}catch(B){}if(v&&C!=null){w=Math.max(0,Math.min(v.screenX-Math.floor(z/2),screen.width-z-20));D=Math.max(0,Math.min(v.screenY-Math.floor(A/2),screen.height-A-20));t.moveTo(w,D)}},50)}};g.Scale=function(){var u=q["HTML-CSS"],t=q.NativeMML,x=q.SVG;var w=(u||t||x||{config:{scale:100}}).config.scale;var v=prompt(s("ScaleMath","Scale all mathematics (compared to surrounding text) by"),w+"%");if(v){if(v.match(/^\s*\d+(\.\d*)?\s*%?\s*$/)){v=parseFloat(v);if(v){if(v!==w){if(u){u.config.scale=v}if(t){t.config.scale=v}if(x){x.config.scale=v}g.cookie.scale=v;g.saveCookie();f.Rerender()}}else{alert(s("NonZeroScale","The scale should not be zero"))}}else{alert(s("PercentScale","The scale should be a 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Switching to SVG output will cause the mathematics to not display properly."]}};g.Font=function(){var t=q["HTML-CSS"];if(!t){return}document.location.reload()};g.Locale=function(){MathJax.Localization.setLocale(r.settings.locale);MathJax.Hub.Queue(["Reprocess",MathJax.Hub])};g.LoadLocale=function(){var t=prompt(s("LoadURL","Load translation data from this URL:"));if(t){if(!t.match(/\.js$/)){alert(s("BadURL","The URL should be for a javascript file that defines MathJax translation data.  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m},Comment:function(l){while(this.i<this.string.length&&this.string.charAt(this.i)!="\n"){this.i++}},Hash:function(l){d.Error(["CantUseHash1","You can't use 'macro parameter character #' in math mode"])},Other:function(n){var m,l;if(this.stack.env.font){m={mathvariant:this.stack.env.font}}if(f.remap[n]){n=f.remap[n];if(n instanceof Array){m=n[1];n=n[0]}l=h.mo(h.entity("#x"+n)).With(m)}else{l=h.mo(n).With(m)}if(l.autoDefault("stretchy",true)){l.stretchy=false}if(l.autoDefault("texClass",true)==""){l=h.TeXAtom(l)}this.Push(this.mmlToken(l))},SetFont:function(m,l){this.stack.env.font=l},SetStyle:function(m,l,n,o){this.stack.env.style=l;this.stack.env.level=o;this.Push(b.style().With({styles:{displaystyle:n,scriptlevel:o}}))},SetSize:function(l,m){this.stack.env.size=m;this.Push(b.style().With({styles:{mathsize:m+"em"}}))},Color:function(n){var m=this.GetArgument(n);var l=this.stack.env.color;this.stack.env.color=m;var o=this.ParseArg(n);if(l){this.stack.env.color}else{delete this.stack.env.color}this.Push(h.mstyle(o).With({mathcolor:m}))},Spacer:function(l,m){this.Push(h.mspace().With({width:m,mathsize:h.SIZE.NORMAL,scriptlevel:0}))},LeftRight:function(l){this.Push(b[l.substr(1)]().With({delim:this.GetDelimiter(l)}))},Middle:function(l){var m=this.GetDelimiter(l);if(this.stack.Top().type!=="left"){d.Error(["MisplacedMiddle","%1 must be within \\left and \\right",l])}this.Push(h.mo(m).With({stretchy:true}))},NamedFn:function(m,n){if(!n){n=m.substr(1)}var l=h.mi(n).With({texClass:h.TEXCLASS.OP});this.Push(b.fn(this.mmlToken(l)))},NamedOp:function(m,n){if(!n){n=m.substr(1)}n=n.replace(/&thinsp;/,"\u2006");var l=h.mo(n).With({movablelimits:true,movesupsub:true,form:h.FORM.PREFIX,texClass:h.TEXCLASS.OP});l.useMMLspacing&=~l.SPACE_ATTR.form;this.Push(this.mmlToken(l))},Limits:function(m,l){var o=this.stack.Prev("nopop");if(!o||(o.Get("texClass")!==h.TEXCLASS.OP&&o.movesupsub==null)){d.Error(["MisplacedLimits","%1 is allowed only on operators",m])}var n=this.stack.Top();if(o.type==="munderover"&&!l){o=n.data[n.data.length-1]=h.msubsup.apply(h.subsup,o.data)}else{if(o.type==="msubsup"&&l){o=n.data[n.data.length-1]=h.munderover.apply(h.underover,o.data)}}o.movesupsub=(l?true:false);o.Core().movablelimits=false},Over:function(n,m,o){var l=b.over().With({name:n});if(m||o){l.open=m;l.close=o}else{if(n.match(/withdelims$/)){l.open=this.GetDelimiter(n);l.close=this.GetDelimiter(n)}}if(n.match(/^\\above/)){l.thickness=this.GetDimen(n)}else{if(n.match(/^\\atop/)||m||o){l.thickness=0}}this.Push(l)},Frac:function(m){var l=this.ParseArg(m);var n=this.ParseArg(m);this.Push(h.mfrac(l,n))},Sqrt:function(o){var p=this.GetBrackets(o),l=this.GetArgument(o);if(l==="\\frac"){l+="{"+this.GetArgument(l)+"}{"+this.GetArgument(l)+"}"}var m=d.Parse(l,this.stack.env).mml();if(!p){m=h.msqrt.apply(h,m.array())}else{m=h.mroot(m,this.parseRoot(p))}this.Push(m)},Root:function(m){var o=this.GetUpTo(m,"\\of");var l=this.ParseArg(m);this.Push(h.mroot(l,this.parseRoot(o)))},parseRoot:function(q){var m=this.stack.env,l=m.inRoot;m.inRoot=true;var p=d.Parse(q,m);q=p.mml();var o=p.stack.global;if(o.leftRoot||o.upRoot){q=h.mpadded(q);if(o.leftRoot){q.width=o.leftRoot}if(o.upRoot){q.voffset=o.upRoot;q.height=o.upRoot}}m.inRoot=l;return q},MoveRoot:function(l,o){if(!this.stack.env.inRoot){d.Error(["MisplacedMoveRoot","%1 can appear only within a root",l])}if(this.stack.global[o]){d.Error(["MultipleMoveRoot","Multiple use of %1",l])}var m=this.GetArgument(l);if(!m.match(/-?[0-9]+/)){d.Error(["IntegerArg","The argument to %1 must be an integer",l])}m=(m/15)+"em";if(m.substr(0,1)!=="-"){m="+"+m}this.stack.global[o]=m},Accent:function(n,l,q){var p=this.ParseArg(n);var o={accent:true};if(this.stack.env.font){o.mathvariant=this.stack.env.font}var m=this.mmlToken(h.mo(h.entity("#x"+l)).With(o));m.stretchy=(q?true:false);this.Push(h.TeXAtom(h.munderover(p,null,m).With({accent:true})))},UnderOver:function(n,q,l){var p={o:"over",u:"under"}[n.charAt(1)];var o=this.ParseArg(n);if(o.Get("movablelimits")){o.movablelimits=false}if(o.isa(h.munderover)&&o.isEmbellished()){o.Core().With({lspace:0,rspace:0});o=h.mrow(h.mo().With({rspace:0}),o)}var m=h.munderover(o,null,null);m.SetData(m[p],this.mmlToken(h.mo(h.entity("#x"+q)).With({stretchy:true,accent:(p==="under")})));if(l){m=h.TeXAtom(m).With({texClass:h.TEXCLASS.OP,movesupsub:true})}this.Push(m.With({subsupOK:true}))},Overset:function(l){var n=this.ParseArg(l),m=this.ParseArg(l);this.Push(h.mover(m,n))},Underset:function(l){var n=this.ParseArg(l),m=this.ParseArg(l);this.Push(h.munder(m,n))},TeXAtom:function(o,q){var p={texClass:q},n;if(q==h.TEXCLASS.OP){p.movesupsub=p.movablelimits=true;var l=this.GetArgument(o);var m=l.match(/^\s*\\rm\s+([a-zA-Z0-9 ]+)$/);if(m){p.mathvariant=h.VARIANT.NORMAL;n=b.fn(this.mmlToken(h.mi(m[1]).With(p)))}else{n=b.fn(h.TeXAtom(d.Parse(l,this.stack.env).mml()).With(p))}}else{n=h.TeXAtom(this.ParseArg(o)).With(p)}this.Push(n)},MmlToken:function(n){var o=this.GetArgument(n),l=this.GetBrackets(n,"").replace(/^\s+/,""),r=this.GetArgument(n),q={attrNames:[]},m;if(!h[o]||!h[o].prototype.isToken){d.Error(["NotMathMLToken","%1 is not a token element",o])}while(l!==""){m=l.match(/^([a-z]+)\s*=\s*('[^']*'|"[^"]*"|[^ ,]*)\s*,?\s*/i);if(!m){d.Error(["InvalidMathMLAttr","Invalid MathML attribute: %1",l])}if(h[o].prototype.defaults[m[1]]==null&&!this.MmlTokenAllow[m[1]]){d.Error(["UnknownAttrForElement","%1 is not a recognized attribute for %2",m[1],o])}var p=this.MmlFilterAttribute(m[1],m[2].replace(/^(['"])(.*)\1$/,"$2"));if(p){if(p.toLowerCase()==="true"){p=true}else{if(p.toLowerCase()==="false"){p=false}}q[m[1]]=p;q.attrNames.push(m[1])}l=l.substr(m[0].length)}this.Push(this.mmlToken(h[o](r).With(q)))},MmlFilterAttribute:function(l,m){return m},MmlTokenAllow:{fontfamily:1,fontsize:1,fontweight:1,fontstyle:1,color:1,background:1,id:1,"class":1,href:1,style:1},Strut:function(l){this.Push(h.mpadded(h.mrow()).With({height:"8.6pt",depth:"3pt",width:0}))},Phantom:function(m,l,n){var o=h.mphantom(this.ParseArg(m));if(l||n){o=h.mpadded(o);if(n){o.height=o.depth=0}if(l){o.width=0}}this.Push(h.TeXAtom(o))},Smash:function(n){var m=this.trimSpaces(this.GetBrackets(n,""));var l=h.mpadded(this.ParseArg(n));switch(m){case"b":l.depth=0;break;case"t":l.height=0;break;default:l.height=l.depth=0}this.Push(h.TeXAtom(l))},Lap:function(m){var l=h.mpadded(this.ParseArg(m)).With({width:0});if(m==="\\llap"){l.lspace="-1width"}this.Push(h.TeXAtom(l))},RaiseLower:function(l){var m=this.GetDimen(l);var n=b.position().With({name:l,move:"vertical"});if(m.charAt(0)==="-"){m=m.slice(1);l={raise:"\\lower",lower:"\\raise"}[l.substr(1)]}if(l==="\\lower"){n.dh="-"+m;n.dd="+"+m}else{n.dh="+"+m;n.dd="-"+m}this.Push(n)},MoveLeftRight:function(l){var o=this.GetDimen(l);var n=(o.charAt(0)==="-"?o.slice(1):"-"+o);if(l==="\\moveleft"){var m=o;o=n;n=m}this.Push(b.position().With({name:l,move:"horizontal",left:h.mspace().With({width:o,mathsize:h.SIZE.NORMAL}),right:h.mspace().With({width:n,mathsize:h.SIZE.NORMAL})}))},Hskip:function(l){this.Push(h.mspace().With({width:this.GetDimen(l),mathsize:h.SIZE.NORMAL}))},Rule:function(n,p){var l=this.GetDimen(n),o=this.GetDimen(n),r=this.GetDimen(n);var m,q={width:l,height:o,depth:r};if(p!=="blank"){if(parseFloat(l)&&parseFloat(o)+parseFloat(r)){q.mathbackground=(this.stack.env.color||"black")}m=h.mpadded(h.mrow()).With(q)}else{m=h.mspace().With(q)}this.Push(m)},MakeBig:function(l,o,m){m*=f.p_height;m=String(m).replace(/(\.\d\d\d).+/,"$1")+"em";var n=this.GetDelimiter(l,true);this.Push(h.TeXAtom(h.mo(n).With({minsize:m,maxsize:m,fence:true,stretchy:true,symmetric:true})).With({texClass:o}))},BuildRel:function(l){var m=this.ParseUpTo(l,"\\over");var n=this.ParseArg(l);this.Push(h.TeXAtom(h.munderover(n,null,m)).With({texClass:h.TEXCLASS.REL}))},HBox:function(l,m){this.Push.apply(this,this.InternalMath(this.GetArgument(l),m))},FBox:function(l){this.Push(h.menclose.apply(h,this.InternalMath(this.GetArgument(l))).With({notation:"box"}))},Not:function(l){this.Push(b.not())},Dots:function(l){this.Push(b.dots().With({ldots:this.mmlToken(h.mo(h.entity("#x2026")).With({stretchy:false})),cdots:this.mmlToken(h.mo(h.entity("#x22EF")).With({stretchy:false}))}))},Require:function(l){var m=this.GetArgument(l).replace(/.*\//,"").replace(/[^a-z0-9_.-]/ig,"");this.Extension(null,m)},Extension:function(l,m,n){if(l&&!typeof(l)==="string"){l=l.name}m=d.extensionDir+"/"+m;if(!m.match(/\.js$/)){m+=".js"}if(!i.loaded[i.fileURL(m)]){if(l!=null){delete f[n||"macros"][l.replace(/^\\/,"")]}c.RestartAfter(i.Require(m))}},Macro:function(n,q,p,r){if(p){var m=[];if(r!=null){var l=this.GetBrackets(n);m.push(l==null?r:l)}for(var o=m.length;o<p;o++){m.push(this.GetArgument(n))}q=this.SubstituteArgs(m,q)}this.string=this.AddArgs(q,this.string.slice(this.i));this.i=0;if(++this.macroCount>d.config.MAXMACROS){d.Error(["MaxMacroSub1","MathJax maximum macro substitution count exceeded; is there a recursive macro call?"])}},Matrix:function(m,o,u,q,t,n,l,v,s){var r=this.GetNext();if(r===""){d.Error(["MissingArgFor","Missing argument for %1",m])}if(r==="{"){this.i++}else{this.string=r+"}"+this.string.slice(this.i+1);this.i=0}var p=b.array().With({requireClose:true,arraydef:{rowspacing:(n||"4pt"),columnspacing:(t||"1em")}});if(v){p.isCases=true}if(s){p.isNumbered=true;p.arraydef.side=s}if(o||u){p.open=o;p.close=u}if(l==="D"){p.arraydef.displaystyle=true}if(q!=null){p.arraydef.columnalign=q}this.Push(p)},Entry:function(o){this.Push(b.cell().With({isEntry:true,name:o}));if(this.stack.Top().isCases){var n=this.string;var r=0,p=this.i,l=n.length;while(p<l){var s=n.charAt(p);if(s==="{"){r++;p++}else{if(s==="}"){if(r===0){l=0}else{r--;p++}}else{if(s==="&"&&r===0){d.Error(["ExtraAlignTab","Extra alignment tab in \\cases text"])}else{if(s==="\\"){if(n.substr(p).match(/^((\\cr)[^a-zA-Z]|\\\\)/)){l=0}else{p+=2}}else{p++}}}}}var q=n.substr(this.i,p-this.i);if(!q.match(/^\s*\\text[^a-zA-Z]/)){this.Push.apply(this,this.InternalMath(q,0));this.i=p}}},Cr:function(l){this.Push(b.cell().With({isCR:true,name:l}))},CrLaTeX:function(l){var p;if(this.string.charAt(this.i)==="["){p=this.GetBrackets(l,"").replace(/ /g,"").replace(/,/,".");if(p&&!this.matchDimen(p)){d.Error(["BracketMustBeDimension","Bracket argument to %1 must be a dimension",l])}}this.Push(b.cell().With({isCR:true,name:l,linebreak:true}));var o=this.stack.Top();if(o.isa(b.array)){if(p&&o.arraydef.rowspacing){var m=o.arraydef.rowspacing.split(/ /);if(!o.rowspacing){o.rowspacing=this.dimen2em(m[0])}while(m.length<o.table.length){m.push(this.Em(o.rowspacing))}m[o.table.length-1]=this.Em(Math.max(0,o.rowspacing+this.dimen2em(p)));o.arraydef.rowspacing=m.join(" ")}}else{if(p){this.Push(h.mspace().With({depth:p}))}this.Push(h.mspace().With({linebreak:h.LINEBREAK.NEWLINE}))}},emPerInch:7.2,pxPerInch:72,matchDimen:function(l){return l.match(/^(-?(?:\.\d+|\d+(?:\.\d*)?))(px|pt|em|ex|mu|pc|in|mm|cm)$/)},dimen2em:function(p){var n=this.matchDimen(p);var l=parseFloat(n[1]||"1"),o=n[2];if(o==="em"){return l}if(o==="ex"){return l*0.43}if(o==="pt"){return l/10}if(o==="pc"){return l*1.2}if(o==="px"){return l*this.emPerInch/this.pxPerInch}if(o==="in"){return l*this.emPerInch}if(o==="cm"){return l*this.emPerInch/2.54}if(o==="mm"){return l*this.emPerInch/25.4}if(o==="mu"){return l/18}return 0},Em:function(l){if(Math.abs(l)<0.0006){return"0em"}return l.toFixed(3).replace(/\.?0+$/,"")+"em"},HLine:function(m,n){if(n==null){n="solid"}var o=this.stack.Top();if(!o.isa(b.array)||o.data.length){d.Error(["Misplaced","Misplaced %1",m])}if(o.table.length==0){o.frame.push("top")}else{var l=(o.arraydef.rowlines?o.arraydef.rowlines.split(/ /):[]);while(l.length<o.table.length){l.push("none")}l[o.table.length-1]=n;o.arraydef.rowlines=l.join(" ")}},HFill:function(l){var m=this.stack.Top();if(m.isa(b.array)){m.hfill.push(m.data.length)}else{d.Error(["UnsupportedHFill","Unsupported use of %1",l])}},BeginEnd:function(n){var o=this.GetArgument(n),q=false;if(o.match(/^\\end\\/)){q=true;o=o.substr(5)}if(o.match(/\\/i)){d.Error(["InvalidEnv","Invalid environment name '%1'",o])}var p=this.envFindName(o);if(!p){d.Error(["UnknownEnv","Unknown environment '%1'",o])}if(!(p instanceof Array)){p=[p]}var l=(p[1] instanceof Array?p[1][0]:p[1]);var m=b.begin().With({name:o,end:l,parse:this});if(n==="\\end"){if(!q&&p[1] instanceof Array&&this[p[1][1]]){m=this[p[1][1]].apply(this,[m].concat(p.slice(2)))}else{m=b.end().With({name:o})}}else{if(++this.macroCount>d.config.MAXMACROS){d.Error(["MaxMacroSub2","MathJax maximum substitution count exceeded; is there a recursive latex environment?"])}if(p[0]&&this[p[0]]){m=this[p[0]].apply(this,[m].concat(p.slice(2)))}}this.Push(m)},envFindName:function(l){return f.environment[l]},Equation:function(l,m){return m},ExtensionEnv:function(m,l){this.Extension(m.name,l,"environment")},Array:function(m,o,t,r,s,n,l,p){if(!r){r=this.GetArgument("\\begin{"+m.name+"}")}var u=("c"+r).replace(/[^clr|:]/g,"").replace(/[^|:]([|:])+/g,"$1");r=r.replace(/[^clr]/g,"").split("").join(" ");r=r.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");var q=b.array().With({arraydef:{columnalign:r,columnspacing:(s||"1em"),rowspacing:(n||"4pt")}});if(u.match(/[|:]/)){if(u.charAt(0).match(/[|:]/)){q.frame.push("left");q.frame.dashed=u.charAt(0)===":"}if(u.charAt(u.length-1).match(/[|:]/)){q.frame.push("right")}u=u.substr(1,u.length-2);q.arraydef.columnlines=u.split("").join(" ").replace(/[^|: ]/g,"none").replace(/\|/g,"solid").replace(/:/g,"dashed")}if(o){q.open=this.convertDelimiter(o)}if(t){q.close=this.convertDelimiter(t)}if(l==="D"){q.arraydef.displaystyle=true}else{if(l){q.arraydef.displaystyle=false}}if(l==="S"){q.arraydef.scriptlevel=1}if(p){q.arraydef.useHeight=false}this.Push(m);return q},AlignedArray:function(l){var m=this.GetBrackets("\\begin{"+l.name+"}");return this.setArrayAlign(this.Array.apply(this,arguments),m)},setArrayAlign:function(m,l){l=this.trimSpaces(l||"");if(l==="t"){m.arraydef.align="baseline 1"}else{if(l==="b"){m.arraydef.align="baseline -1"}else{if(l==="c"){m.arraydef.align="center"}else{if(l){m.arraydef.align=l}}}}return m},convertDelimiter:function(l){if(l){l=f.delimiter[l]}if(l==null){return null}if(l instanceof Array){l=l[0]}if(l.length===4){l=String.fromCharCode(parseInt(l,16))}return l},trimSpaces:function(l){if(typeof(l)!="string"){return l}return l.replace(/^\s+|\s+$/g,"")},nextIsSpace:function(){return this.string.charAt(this.i).match(/\s/)},GetNext:function(){while(this.nextIsSpace()){this.i++}return this.string.charAt(this.i)},GetCS:function(){var l=this.string.slice(this.i).match(/^([a-z]+|.) ?/i);if(l){this.i+=l[1].length;return l[1]}else{this.i++;return" "}},GetArgument:function(m,n){switch(this.GetNext()){case"":if(!n){d.Error(["MissingArgFor","Missing argument for %1",m])}return null;case"}":if(!n){d.Error(["ExtraCloseMissingOpen","Extra close brace or missing open brace"])}return null;case"\\":this.i++;return"\\"+this.GetCS();case"{":var l=++this.i,o=1;while(this.i<this.string.length){switch(this.string.charAt(this.i++)){case"\\":this.i++;break;case"{":o++;break;case"}":if(--o==0){return this.string.slice(l,this.i-1)}break}}d.Error(["MissingCloseBrace","Missing close brace"]);break}return this.string.charAt(this.i++)},GetBrackets:function(m,o){if(this.GetNext()!="["){return o}var l=++this.i,n=0;while(this.i<this.string.length){switch(this.string.charAt(this.i++)){case"{":n++;break;case"\\":this.i++;break;case"}":if(n--<=0){d.Error(["ExtraCloseLooking","Extra close brace while looking for %1","']'"])}break;case"]":if(n==0){return this.string.slice(l,this.i-1)}break}}d.Error(["MissingCloseBracket","Couldn't find closing ']' for argument to %1",m])},GetDelimiter:function(l,m){while(this.nextIsSpace()){this.i++}var n=this.string.charAt(this.i);this.i++;if(this.i<=this.string.length){if(n=="\\"){n+=this.GetCS(l)}else{if(n==="{"&&m){this.i--;n=this.GetArgument(l)}}if(f.delimiter[n]!=null){return this.convertDelimiter(n)}}d.Error(["MissingOrUnrecognizedDelim","Missing or unrecognized delimiter for %1",l])},GetDimen:function(m){var n;if(this.nextIsSpace()){this.i++}if(this.string.charAt(this.i)=="{"){n=this.GetArgument(m);if(n.match(/^\s*([-+]?([.,]\d+|\d+([.,]\d*)?))\s*(pt|em|ex|mu|px|mm|cm|in|pc)\s*$/)){return n.replace(/ /g,"").replace(/,/,".")}}else{n=this.string.slice(this.i);var l=n.match(/^\s*(([-+]?([.,]\d+|\d+([.,]\d*)?))\s*(pt|em|ex|mu|px|mm|cm|in|pc)) ?/);if(l){this.i+=l[0].length;return l[1].replace(/ /g,"").replace(/,/,".")}}d.Error(["MissingDimOrUnits","Missing dimension or its units for %1",m])},GetUpTo:function(n,o){while(this.nextIsSpace()){this.i++}var m=this.i,l,q,p=0;while(this.i<this.string.length){l=this.i;q=this.string.charAt(this.i++);switch(q){case"\\":q+=this.GetCS();break;case"{":p++;break;case"}":if(p==0){d.Error(["ExtraCloseLooking","Extra close brace while looking for %1",o])}p--;break}if(p==0&&q==o){return 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String.fromCharCode(p)}p-=65536;return String.fromCharCode((p>>10)+55296)+String.fromCharCode((p&1023)+56320)},getUnicode:function(p){var q=p.text.charCodeAt(p.i);p.i++;if(q>=55296&&q<56319){q=(((q-55296)<<10)+(p.text.charCodeAt(p.i)-56320))+65536;p.i++}return q},getCharList:function(t,s){var r,x,w=[],p=t.cache,A=s;if(p[s]){return p[s]}var q=this.FONTDATA.RANGES,z=this.FONTDATA.VARIANT;if(s>=q[0].low&&s<=q[q.length-1].high){for(r=0,x=q.length;r<x;r++){if(q[r].name==="alpha"&&t.noLowerCase){continue}var v=t["offset"+q[r].offset];if(v&&s>=q[r].low&&s<=q[r].high){if(q[r].remap&&q[r].remap[s]){s=v+q[r].remap[s]}else{s=s-q[r].low+v;if(q[r].add){s+=q[r].add}}if(t["variant"+q[r].offset]){t=z[t["variant"+q[r].offset]]}break}}}if(t.remap&&t.remap[s]){s=t.remap[s];if(t.remap.variant){t=z[t.remap.variant]}}else{if(this.FONTDATA.REMAP[s]&&!t.noRemap){s=this.FONTDATA.REMAP[s]}}if(s instanceof Array){t=z[s[1]];s=s[0]}if(typeof(s)==="string"){var u={text:s,i:0,length:s.length};while(u.i<u.length){s=this.getUnicode(u);var y=this.getCharList(t,s);if(y){w.push.apply(w,y)}}}else{if(t.cache[s]){w=t.cache[s]}else{t.cache[s]=w=[this.lookupChar(t,s)]}}p[A]=w;return w},lookupChar:function(s,v){var u=s;while(s){for(var r=0,p=s.fonts.length;r<p;r++){var q=this.FONTDATA.FONTS[s.fonts[r]];if(typeof(q)==="string"){this.loadFont(q)}var t=q[v];if(t){if(t.length===5){t[5]={}}if(t.c==null){t[0]/=1000;t[1]/=1000;t[2]/=1000;t[3]/=1000;t[4]/=1000;t.c=this.unicodeChar(v)}if(t[5].space){return{type:"space",w:t[2],font:q}}return{type:"char",font:q,n:v}}else{if(q.Extra){this.findBlock(q,v)}}}s=this.FONTDATA.VARIANT[s.chain]}return this.unknownChar(u,v)},findBlock:function(r,v){var q=r.Extra,s=r.file,u;for(var t=0,p=q.length;t<p;t++){if(typeof(q[t])==="number"){if(v===q[t]){u=s;break}}else{if(v<q[t][0]){return}if(v<=q[t][1]){u=s;break}}}if(u){delete r.Extra;this.loadFont(s)}},unknownChar:function(p,s){c.signal.Post(["CommonHTML Jax - unknown char",s,p]);var r="";if(p.bold){r+="B"}if(p.italic){r+="I"}var q=this.FONTDATA.UNKNOWN[r||"R"];if(!q[s]){this.getUnknownChar(q,s)}return{type:"unknown",n:s,font:q}},getUnknownChar:function(q,s){var r=this.unicodeChar(s);var p=this.getHDW(r,q.className);q[s]=[0.8,0.2,p.w,0,p.w,{a:(p.h-p.d)/2,h:p.h,d:p.d}];q[s].c=r},styledText:function(q,t){c.signal.Post(["CommonHTML Jax - styled text",t,q]);var r=q.style;var u="_"+(r["font-family"]||q.className||"");if(r["font-weight"]){u+="_"+r["font-weight"]}if(r["font-style"]){u+="_"+r["font-style"]}if(!this.STYLEDTEXT){this.STYLEDTEXT={}}if(!this.STYLEDTEXT[u]){this.STYLEDTEXT[u]={className:q.className||""}}var s=this.STYLEDTEXT[u];if(!s["_"+t]){var p=this.getHDW(t,q.className||"",r);s["_"+t]=[0.8,0.2,p.w,0,p.w,{a:(p.h-p.d)/2,h:p.h,d:p.d}];s["_"+t].c=t}return{type:"unknown",n:"_"+t,font:s,style:r,rscale:q.rscale}},getHDW:function(v,r,y){var q=g.addElement(g.CHTMLnode,"mjx-chartest",{className:r},[["mjx-char",{style:y},[v]]]);var p=g.addElement(g.CHTMLnode,"mjx-chartest",{className:r},[["mjx-char",{style:y},[v,["mjx-box"]]]]);q.firstChild.style.fontSize=p.firstChild.style.fontSize="";var s=5*g.em;var u=(p.offsetHeight-1000)/s;var x=q.offsetWidth/s,t=q.offsetHeight/s-u;g.CHTMLnode.removeChild(q);g.CHTMLnode.removeChild(p);return{h:t,d:u,w:x}},addCharList:function(s,u,v){var t={text:"",className:null,a:0};for(var q=0,p=u.length;q<p;q++){var r=u[q];if(this.charList[r.type]){(this.charList[r.type])(r,s,v,t,p)}}if(t.text!==""){if(s.childNodes.length){this.charList.flushText(s,t)}else{f.addText(s,t.text);if(s.className){s.className+=" "+t.className}else{s.className=t.className}}}v.b=(t.flushed?0:v.a)},charList:{"char":function(s,r,v,t,p){var q=s.font;if(t.className&&q.className!==t.className){this.flushText(r,t)}if(!t.a){t.a=q.centerline/1000}if(t.a>(v.a||0)){v.a=t.a}var u=q[s.n];t.text+=u.c;t.className=q.className;if(v.h<u[0]+j){v.t=v.h=u[0]+j}if(v.d<u[1]+a){v.b=v.d=u[1]+a}if(v.l>v.w+u[3]){v.l=v.w+u[3]}if(v.r<v.w+u[4]){v.r=v.w+u[4]}v.w+=u[2]*(s.rscale||1);if(p==1&&q.skew&&q.skew[s.n]){v.skew=q.skew[s.n]}if(u[5].rfix){this.flushText(r,t).style.marginRight=g.Em(u[5].rfix/1000)}},space:function(q,p,s,r){if(q.w){if(r.text===""){r.className=q.font.className}this.flushText(p,r).style.marginRight=g.Em(q.w);s.w+=q.w}},unknown:function(q,p,t,r){(this["char"])(q,p,t,r,0);var s=q.font[q.n];if(s[5].a){r.a=s[5].a;if(t.a==null||r.a>t.a){t.a=r.a}}p=this.flushText(p,r,q.style);p.style.width=g.Em(s[2])},flushText:function(q,r,p){q=g.addElement(q,"mjx-charbox",{className:r.className,style:p},[r.text]);if(r.a){q.style.paddingBottom=g.Em(r.a)}r.text="";r.className=null;r.a=0;r.flushed=true;return q}},handleText:function(r,u,q,t){if(r.childNodes.length===0){g.addElement(r,"mjx-char");t=g.BBOX.empty(t)}if(typeof(q)==="string"){q=this.FONTDATA.VARIANT[q]}if(!q){q=this.FONTDATA.VARIANT[h.VARIANT.NORMAL]}var p={text:u,i:0,length:u.length},s=[];if(q.style&&p.length){s.push(this.styledText(q,u))}else{while(p.i<p.length){var v=this.getUnicode(p);s.push.apply(s,this.getCharList(q,v))}}if(s.length){this.addCharList(r.firstChild,s,t)}t.clean();if(t.d<0){t.D=t.d;t.d=0}if(t.h-t.a){r.firstChild.style[t.h-t.a<0?"marginTop":"paddingTop"]=this.Em(t.h-t.a)}if(t.d>-t.b){r.firstChild.style.paddingBottom=this.Em(t.d+t.b)}return t},createDelimiter:function(u,p,r,x,s){if(!p){var y=this.BBOX.zero();y.w=y.r=this.TEX.nulldelimiterspace;g.addElement(u,"mjx-box",{style:{width:y.w}});return y}if(!(r instanceof Array)){r=[r,r]}var w=r[1];r=r[0];var q={alias:p};while(q.alias){p=q.alias;q=this.FONTDATA.DELIMITERS[p];if(!q){q={HW:[0,this.FONTDATA.VARIANT[h.VARIANT.NORMAL]]}}}if(q.load){c.RestartAfter(i.Require(this.fontDir+"/TeX/fontdata-"+q.load+".js"))}for(var v=0,t=q.HW.length;v<t;v++){if(q.HW[v][0]>=r-0.01||(v==t-1&&!q.stretch)){if(q.HW[v][3]){p=q.HW[v][3]}y=this.createChar(u,[p,q.HW[v][1]],(q.HW[v][2]||1),s);y.offset=0.6*y.w;if(x){y.scale=x.scale;x.rscale=x.rscale}return y}}if(!q.stretch){return y}return this["extendDelimiter"+q.dir](u,w,q.stretch,x,s)},extendDelimiterV:function(B,u,J,t,z){B=g.addElement(B,"mjx-delim-v");var G=g.Element("span");var y,w,I,r,E,q,C,v,D=1;E=this.createChar(G,(J.top||J.ext),1,z);y=G.removeChild(G.firstChild);q=this.createChar(G,(J.bot||J.ext),1,z);w=G.removeChild(G.firstChild);C=v=g.BBOX.zero();var F=E.h+E.d+q.h+q.d;B.appendChild(y);if(J.mid){C=this.createChar(G,J.mid,1,z);I=G.removeChild(G.firstChild);F+=C.h+C.d;D=2}if(J.min&&u<F*J.min){u=F*J.min}if(u>F){v=this.createChar(G,J.ext,1,z);r=G.removeChild(G.firstChild);if(J.fullExtenders){var A=Math.ceil((u-F)/(D*(v.h+v.d)*0.9));u=0.9*A*D*(v.h+v.d)+F}var x=1.1*(u-F)/D+0.3;x/=(v.h+v.d);this.Transform(r,"translateY("+g.Em(-v.d+0.25-x*v.a)+") scaleY("+x.toFixed(3).replace(/0+$/,"")+")","left "+g.Em(v.d));r.style.paddingTop=r.style.paddingBottom=0;y.style.marginBottom=g.Em((u-F)/D);B.appendChild(r);if(J.mid){B.appendChild(I);I.style.marginBottom=y.style.marginBottom;B.appendChild(r.cloneNode(true))}}else{u=F-0.25;y.style.marginBottom="-.25em";if(J.mid){B.appendChild(I);I.style.marginBottom="-.3em";u-=0.1}}B.appendChild(w);var p=g.BBOX({w:Math.max(E.w,v.w,q.w,C.w),l:Math.min(E.l,v.l,q.l,C.l),r:Math.max(E.r,v.r,q.r,C.r),h:u-q.d,d:q.d,t:u-q.d,b:q.d});p.offset=0.5*p.w;if(t){p.scale=t.scale;p.rscale=t.rscale}return p},extendDelimiterH:function(D,q,K,u,B){D=g.addElement(D,"mjx-delim-h");var I=g.Element("span");var r,H,J,t,G,z,v,E,y,F=1;z=this.createChar(I,(K.left||K.rep),1,B);r=I.removeChild(I.firstChild);v=this.createChar(I,(K.right||K.rep),1,B);H=I.removeChild(I.firstChild);y=this.createChar(I,K.rep,1,B);t=I.removeChild(I.firstChild);D.appendChild(r);var L=g.BBOX.zero();L.h=Math.max(z.h,v.h);L.d=Math.max(z.d,v.d);r.style.marginLeft=g.Em(-z.l);r.style.marginRight=g.Em(z.r-z.w);H.style.marginleft=g.Em(-v.l);H.style.marginRight=g.Em(v.r-v.w);var x=(z.r-z.l)+(v.r-v.l)-0.05;if(K.mid){E=this.createChar(I,K.mid,1,B);J=I.removeChild(I.firstChild);x+=E.w;F=2;if(E.h>L.h){L.h=E.h}if(E.d>L.d){L.d=E.d}}if(K.min&&q<x*K.min){q=x*K.min}H.style.marginLeft=g.Em((q-x-v.l)/F);L.w=L.r=q;if(q>x){if(y.h>L.h){L.h=y.h}if(y.d>L.d){L.d=y.d}var A=(q-x)/F+0.2;A/=(y.r-y.l);this.Transform(t,"translateX("+g.Em(-y.l-0.1)+") scaleX("+A.toFixed(3).replace(/0+$/,"")+")",g.Em(y.l)+" 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x=this.handleText(r,y,u),p=r.firstChild.style;if(t!==1){p.fontSize=this.Percent(t)}if(v[2]){p.paddingLeft=this.Em(v[2]);x.w+=v[2];x.r+=v[2]}if(v[3]){p.verticalAlign=this.Em(v[3]);x.h+=v[3];if(x.h<0){x.h=0}}if(v[5]){p.marginTop=this.Em(v[5]);x.h+=v[5];x.t+=v[5]}if(v[6]){p.marginBottom=this.Em(v[6]);x.d+=v[6];x.b+=v[6]}return x},length2em:function(t,r,u){if(typeof(t)!=="string"){t=t.toString()}if(t===""){return""}if(t===h.SIZE.NORMAL){return 1}if(t===h.SIZE.BIG){return 2}if(t===h.SIZE.SMALL){return 0.71}if(this.MATHSPACE[t]){return this.MATHSPACE[t]}var q=t.match(/^\s*([-+]?(?:\.\d+|\d+(?:\.\d*)?))?(pt|em|ex|mu|px|pc|in|mm|cm|%)?/);var p=parseFloat(q[1]||"1"),s=q[2];if(r==null){r=1}if(!u){u=1}u=1/this.em/u;if(s==="em"){return p}if(s==="ex"){return p*this.TEX.x_height}if(s==="%"){return p/100*r}if(s==="px"){return p*u}if(s==="pt"){return p/10}if(s==="pc"){return p*1.2}u*=this.pxPerInch;if(s==="in"){return p*u}if(s==="cm"){return p*u/2.54}if(s==="mm"){return p*u/25.4}if(s==="mu"){return p/18}return p*r},thickness2em:function(p,q){var r=g.TEX.rule_thickness/(q||1);if(p===h.LINETHICKNESS.MEDIUM){return r}if(p===h.LINETHICKNESS.THIN){return 0.67*r}if(p===h.LINETHICKNESS.THICK){return 1.67*r}return this.length2em(p,r,q)},Em:function(p){if(Math.abs(p)<0.001){return"0"}return(p.toFixed(3).replace(/\.?0+$/,""))+"em"},unEm:function(p){return parseFloat(p)},Px:function(p){p*=this.em;if(Math.abs(p)<0.1){return"0"}return p.toFixed(1).replace(/\.0$/,"")+"px"},Percent:function(p){return(100*p).toFixed(1).replace(/\.?0+$/,"")+"%"},Transform:function(s,q,p){var r=s.style;r.transform=r.WebkitTransform=r.MozTransform=r["-ms-transform"]=q;if(p){r.transformOrigin=r.WebkitTransformOrigin=r.MozTransformOrigin=r["-ms-transform-origin"]=p}},arrayEntry:function(p,q){return p[Math.max(0,Math.min(q,p.length-1))]},removeStyles:["fontSize","fontFamily","fontWeight","fontStyle","fontVariant","font"]});g.BBOX=MathJax.Object.Subclass({Init:function(p){for(var q in p){if(p.hasOwnProperty(q)){this[q]=p[q]}}},clean:function(){if(this.h===-m){this.h=0}if(this.d===-m){this.d=0}if(this.l===m){this.l=0}if(this.r===-m){this.r=0}if(this.t===-m){this.t=0}if(this.b===-m){this.b=0}if(this.D&&this.d>0){delete this.D}},rescale:function(p){this.w*=p;this.h*=p;this.d*=p;this.l*=p;this.r*=p;this.t*=p;this.b*=p;if(this.L){this.L*=p}if(this.R){this.R*=p}if(this.D){this.D*=p}},combine:function(q,p,r){q.X=p;q.Y=r;scale=q.rscale;if(p+scale*q.r>this.r){this.r=p+scale*q.r}if(p+scale*q.l<this.l){this.l=p+scale*q.l}if(p+scale*(q.w+(q.L||0)+(q.R||0))>this.w){this.w=p+scale*(q.w+(q.L||0)+(q.R||0))}if(r+scale*q.h>this.h){this.h=r+scale*q.h}if(q.D&&(this.D==null||scale*q.D-r>this.D)&&scale*q.D>this.d){this.D=scale*q.D-r}else{if(q.D==null&&this.D){delete this.D}}if(scale*q.d-r>this.d){this.d=scale*q.d-r}if(r+scale*q.t>this.t){this.t=r+scale*q.t}if(scale*q.b-r>this.b){this.b=scale*q.b-r}},append:function(q){scale=q.rscale;var p=this.w;if(p+scale*q.r>this.r){this.r=p+scale*q.r}if(p+scale*q.l<this.l){this.l=p+scale*q.l}this.w+=scale*(q.w+(q.L||0)+(q.R||0));if(scale*q.h>this.h){this.h=scale*q.h}if(q.D&&(this.D==null||scale*q.D>this.D)&&scale*q.D>this.d){this.D=scale*q.D}else{if(q.D==null&&this.D){delete this.D}}if(scale*q.d>this.d){this.d=scale*q.d}if(scale*q.t>this.t){this.t=scale*q.t}if(scale*q.b>this.b){this.b=scale*q.b}},updateFrom:function(p){this.h=p.h;this.d=p.d;this.w=p.w;this.r=p.r;this.l=p.l;this.t=p.t;this.b=p.b;if(p.D){this.D=p.D}else{delete this.D}},adjust:function(q,p,s,r){this[p]+=g.length2em(q,1,this.scale);if(r==null){if(this[p]>this[s]){this[s]=this[p]}}else{if(this[s]<r){this[s]=r}}}},{zero:function(){return g.BBOX({h:0,d:0,w:0,l:0,r:0,t:0,b:0,scale:1,rscale:1})},empty:function(p){if(!p){p=g.BBOX.zero()}p.h=p.d=p.r=p.t=p.b=-m;p.w=0;p.l=m;return p},styleAdjust:[["borderTopWidth","h","t"],["borderRightWidth","w","r"],["borderBottomWidth","d","b"],["borderLeftWidth","w","l",0],["paddingTop","h","t"],["paddingRight","w","r"],["paddingBottom","d","b"],["paddingLeft","w","l",0],]});MathJax.Hub.Register.StartupHook("mml Jax Ready",function(){h=MathJax.ElementJax.mml;h.mbase.Augment({toCommonHTML:function(q,p){return this.CHTMLdefaultNode(q,p)},CHTMLmultiline:function(){h.mbase.CHTMLautoloadFile("multiline")},CHTMLdefaultNode:function(s,q){if(!q){q={}}s=this.CHTMLcreateNode(s);this.CHTML=g.BBOX.empty();this.CHTMLhandleStyle(s);this.CHTMLhandleScale(s);if(this.isToken){this.CHTMLgetVariant()}var p=Math.max((q.minChildren||0),this.data.length);for(var r=0;r<p;r++){this.CHTMLaddChild(s,r,q)}if(!q.noBBox){this.CHTML.clean()}this.CHTMLhandleSpace(s);this.CHTMLhandleBBox(s);this.CHTMLhandleColor(s);return s},CHTMLaddChild:function(u,q,p){var w=this.data[q],t;if(w){var r=p.childNodes;if(r){if(r instanceof 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v=this.CHTML,r=u.CHTML;if(r.stretch||(r.stretch==null&&u.CHTMLcanStretch("Horizontal",p))){var q=r.w;r=u.CHTMLstretchH(this.CHTMLchildNode(t,s),p);v.w+=r.w-q;if(v.w>v.r){v.r=v.w}if(r.h>v.h){v.h=r.h}if(r.d>v.d){v.d=r.d}if(r.t>v.t){v.t=r.t}if(r.b>v.b){v.b=r.b}}}},CHTMLcanStretch:function(t,r,s){var q=false;if(this.isEmbellished()){var p=this.Core();if(p&&p!==this){q=p.CHTMLcanStretch(t,r,s)}}this.CHTML.stretch=q;return q},CHTMLstretchV:function(p,q){this.CHTML.updateFrom(this.Core().CHTMLstretchV(p,q));return this.CHTML},CHTMLstretchH:function(q,p){this.CHTML.updateFrom(this.CHTMLstretchCoreH(q,p));return this.CHTML},CHTMLstretchCoreH:function(q,p){return this.Core().CHTMLstretchH(this.CHTMLcoreNode(q),p)},CHTMLcreateNode:function(p){if(!this.CHTML){this.CHTML={}}this.CHTML=g.BBOX.zero();if(this.href){p=g.addElement(p,"a",{href:this.href,isMathJax:true})}if(!this.CHTMLnodeID){this.CHTMLnodeID=g.GetID()}var q=(this.id||"MJXc-Node-"+this.CHTMLnodeID)+g.idPostfix;return this.CHTMLhandleAttributes(g.addElement(p,"mjx-"+this.type,{id:q}))},CHTMLnodeElement:function(){if(!this.CHTMLnodeID){return null}return document.getElementById((this.id||"MJXc-Node-"+this.CHTMLnodeID)+g.idPostfix)},CHTMLlength2em:function(q,p){return g.length2em(q,p,this.CHTML.scale)},CHTMLhandleAttributes:function(s){if(this["class"]){if(s.className){s.className+=" "+this["class"]}else{s.className=this["class"]}}if(this.attrNames){var w=this.attrNames,r=h.nocopyAttributes,v=c.config.ignoreMMLattributes;var t=(this.type==="mstyle"?h.math.prototype.defaults:this.defaults);for(var q=0,p=w.length;q<p;q++){var u=w[q];if(v[u]==false||(!r[u]&&!v[u]&&t[u]==null&&typeof(s[u])==="undefined")){s.setAttribute(u,this.attr[u])}}}return s},CHTMLhandleScale:function(r){var t=1,q=this.parent,s=(q?q.CHTML.scale:1);var p=this.getValues("scriptlevel","fontsize","mathsize");if(!this.isToken){p.mathsize=1}if(p.scriptlevel!==0){if(p.scriptlevel>2){p.scriptlevel=2}t=Math.pow(this.Get("scriptsizemultiplier"),p.scriptlevel);p.scriptminsize=g.length2em(this.Get("scriptminsize"),0.8,1);if(t<p.scriptminsize){t=p.scriptminsize}}if(this.removedStyles&&this.removedStyles.fontSize&&!p.fontsize){p.fontsize=this.removedStyles.fontSize}if(p.fontsize&&!this.mathsize){p.mathsize=p.fontsize}if(p.mathsize!==1){t*=g.length2em(p.mathsize,1,1)}this.CHTML.scale=t;s=this.CHTML.rscale=t/s;if(Math.abs(s-1)<0.001){s=1}if(r&&s!==1){r.style.fontSize=g.Percent(s)}return t},CHTMLhandleStyle:function(s){if(!this.style){return}var r=s.style;r.cssText=this.style;this.removedStyles={};for(var q=0,p=g.removeStyles.length;q<p;q++){var t=g.removeStyles[q];if(r[t]){this.removedStyles[t]=r[t];r[t]=""}}},CHTMLhandleBBox:function(t){var q=this.CHTML,s=t.style;if(this.data.length===1&&(this.data[0].CHTML||{}).pwidth){q.pwidth=this.data[0].CHTML.pwidth;q.mwidth=this.data[0].CHTML.mwidth;s.width="100%"}else{if(q.pwidth){q.mwidth=q.w;s.width="100%"}}if(!this.style){return}for(var r=0,p=g.BBOX.styleAdjust.length;r<p;r++){var u=g.BBOX.styleAdjust[r];if(s[u[0]]){q.adjust(s[u[0]],u[1],u[2],u[3])}}},CHTMLhandleColor:function(p){if(this.mathcolor){p.style.color=this.mathcolor}else{if(this.color){p.style.color=this.color}}if(this.mathbackground){p.style.backgroundColor=this.mathbackground}else{if(this.background){p.style.backgroundColor=this.background}}},CHTMLhandleSpace:function(p){if(!this.useMMLspacing){var q=this.texSpacing();if(q!==""){this.CHTML.L=this.CHTMLlength2em(q);p.className+=" "+g.SPACECLASS[q]}}},CHTMLhandleText:function(q,r,p){if(q.firstChild&&!this.CHTML){this.CHTML=g.BBOX.empty()}this.CHTML=g.handleText(q,r,p,this.CHTML)},CHTMLgetVariant:function(){var p=this.getValues("mathvariant","fontfamily","fontweight","fontstyle"),r;p.hasVariant=this.Get("mathvariant",true);if(this.removedStyles){r=this.removedStyles;if(r.fontFamily){p.family=r.fontFamily}if(r.fontWeight){p.weight=r.fontWeight}if(r.fontStyle){p.style=r.fontStyle}}if(!p.hasVariant){if(p.fontfamily){p.family=p.fontfamily}if(p.fontweight){p.weight=p.fontweight}if(p.fontstyle){p.style=p.fontstyle}}if(p.weight&&p.weight.match(/^\d+$/)){p.weight=(parseInt(p.weight)>600?"bold":"normal")}var q=p.mathvariant;if(this.variantForm){q="-TeX-variant"}if(p.family&&!p.hasVariant){if(!p.weight&&p.mathvariant.match(/bold/)){p.weight="bold"}if(!p.style&&p.mathvariant.match(/italic/)){p.style="italic"}this.CHTMLvariant={fonts:[],noRemap:true,cache:{},style:{"font-family":p.family,"font-weight":p.weight,"font-style":p.style}};return}if(p.weight==="bold"){q={normal:h.VARIANT.BOLD,italic:h.VARIANT.BOLDITALIC,fraktur:h.VARIANT.BOLDFRAKTUR,script:h.VARIANT.BOLDSCRIPT,"sans-serif":h.VARIANT.BOLDSANSSERIF,"sans-serif-italic":h.VARIANT.SANSSERIFBOLDITALIC}[q]||q}else{if(p.weight==="normal"){q={bold:h.VARIANT.normal,"bold-italic":h.VARIANT.ITALIC,"bold-fraktur":h.VARIANT.FRAKTUR,"bold-script":h.VARIANT.SCRIPT,"bold-sans-serif":h.VARIANT.SANSSERIF,"sans-serif-bold-italic":h.VARIANT.SANSSERIFITALIC}[q]||q}}if(p.style==="italic"){q={normal:h.VARIANT.ITALIC,bold:h.VARIANT.BOLDITALIC,"sans-serif":h.VARIANT.SANSSERIFITALIC,"bold-sans-serif":h.VARIANT.SANSSERIFBOLDITALIC}[q]||q}else{if(p.style==="normal"){q={italic:h.VARIANT.NORMAL,"bold-italic":h.VARIANT.BOLD,"sans-serif-italic":h.VARIANT.SANSSERIF,"sans-serif-bold-italic":h.VARIANT.BOLDSANSSERIF}[q]||q}}this.CHTMLvariant=g.FONTDATA.VARIANT[q]||g.FONTDATA.VARIANT[h.VARIANT.NORMAL]},CHTMLbboxFor:function(p){if(this.data[p]&&this.data[p].CHTML){return this.data[p].CHTML}return g.BBOX.zero()},CHTMLdrawBBox:function(q,r){if(!r){r=this.CHTML}var p=g.Element("mjx-box",{style:{"font-size":q.style.fontSize,opacity:0.25,"margin-left":g.Em(-(r.w+(r.R||0)))}},[["mjx-box",{style:{height:g.Em(r.h),width:g.Em(r.w),"background-color":"red"}}],["mjx-box",{style:{height:g.Em(r.d),width:g.Em(r.w),"margin-left":g.Em(-r.w),"vertical-align":g.Em(-r.d),"background-color":"green"}}]]);if(q.nextSibling){q.parentNode.insertBefore(p,q.nextSibling)}else{q.parentNode.appendChild(p)}},CHTMLnotEmpty:function(p){while(p&&p.data.length<2&&(p.type==="mrow"||p.type==="texatom")){p=p.data[0]}return !!p}},{CHTMLautoload:function(){var p=g.autoloadDir+"/"+this.type+".js";c.RestartAfter(i.Require(p))},CHTMLautoloadFile:function(p){var q=g.autoloadDir+"/"+p+".js";c.RestartAfter(i.Require(q))},CHTMLstretchV:function(p,q){this.Core().CHTMLstretchV(p,q);this.toCommonHTML(this.CHTMLnodeElement(),true);return this.CHTML},CHTMLstretchH:function(q,p){this.CHTMLstretchCoreH(q,p);this.toCommonHTML(q,true);return this.CHTML}});h.chars.Augment({toCommonHTML:function(q,p){if(p==null){p={}}var r=this.toString();if(p.remap){r=p.remap(r,p.remapchars)}this.CHTMLhandleText(q,r,p.variant||this.parent.CHTMLvariant)}});h.entity.Augment({toCommonHTML:function(q,p){if(p==null){p={}}var r=this.toString();if(p.remapchars){r=p.remap(r,p.remapchars)}this.CHTMLhandleText(q,r,p.variant||this.parent.CHTMLvariant)}});h.math.Augment({toCommonHTML:function(u){u=this.CHTMLdefaultNode(u);var s=this.Get("alttext");if(s&&!u.getAttribute("aria-label")){u.setAttribute("aria-label",s)}if(!u.getAttribute("role")){u.setAttribute("role","math")}if(this.CHTML.pwidth){u.parentNode.style.width=this.CHTML.pwidth;u.parentNode.style.minWidth=this.CHTML.mwidth}else{if(!this.isMultiline&&this.Get("display")==="block"){var r=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift");if(r.indentalignfirst!==h.INDENTALIGN.INDENTALIGN){r.indentalign=r.indentalignfirst}if(r.indentalign===h.INDENTALIGN.AUTO){r.indentalign=n.displayAlign}if(r.indentshiftfirst!==h.INDENTSHIFT.INDENTSHIFT){r.indentshift=r.indentshiftfirst}if(r.indentshift==="auto"){r.indentshift="0"}var q=this.CHTMLlength2em(r.indentshift,g.cwidth);if(n.displayIndent!=="0"){var p=this.CHTMLlength2em(n.displayIndent,g.cwidth);q+=(r.indentalign===h.INDENTALIGN.RIGHT?-p:p)}var t=u.parentNode.parentNode.style;t.textAlign=r.indentalign;if(q){q*=g.em/g.outerEm;c.Insert(t,({left:{marginLeft:g.Em(q)},right:{marginRight:g.Em(-q)},center:{marginLeft:g.Em(q),marginRight:g.Em(-q)}})[r.indentalign])}}}return u}});h.mi.Augment({toCommonHTML:function(p){p=this.CHTMLdefaultNode(p);var r=this.CHTML,q=this.data.join("");if(r.skew!=null&&q.length!==1){delete r.skew}if(r.r>r.w&&q.length===1&&!this.CHTMLvariant.noIC){r.ic=r.r-r.w;r.w=r.r;p.lastChild.style.paddingRight=g.Em(r.ic)}return p}});h.mn.Augment({toCommonHTML:function(p){p=this.CHTMLdefaultNode(p);var r=this.CHTML,q=this.data.join("");if(r.skew!=null&&q.length!==1){delete r.skew}if(r.r>r.w&&q.length===1&&!this.CHTMLvariant.noIC){r.ic=r.r-r.w;r.w=r.r;p.lastChild.style.paddingRight=g.Em(r.ic)}return p}});h.mo.Augment({toCommonHTML:function(s){s=this.CHTMLcreateNode(s);this.CHTMLhandleStyle(s);this.CHTMLhandleScale(s);this.CHTMLgetVariant();g.BBOX.empty(this.CHTML);var q=this.getValues("displaystyle","largeop");q.variant=this.CHTMLvariant;q.text=this.data.join("");if(q.text==""){if(this.fence){s.style.width=g.Em(g.TEX.nulldelimiterspace)}}else{this.CHTMLadjustAccent(q);this.CHTMLadjustVariant(q);for(var r=0,p=this.data.length;r<p;r++){this.CHTMLaddChild(s,r,{childOptions:{variant:q.mathvariant,remap:this.remap,remapchars:q.remapchars}})}if(q.text.length!==1){delete this.CHTML.skew}else{if(this.CHTML.w===0&&this.CHTML.l<0){this.CHTMLfixCombiningChar(s)}}if(q.largeop){this.CHTMLcenterOp(s)}}this.CHTML.clean();this.CHTMLhandleBBox(s);this.CHTMLhandleSpace(s);this.CHTMLhandleColor(s);return s},CHTMLhandleSpace:function(s){if(this.useMMLspacing){var q=this.getValues("scriptlevel","lspace","rspace");q.lspace=Math.max(0,this.CHTMLlength2em(q.lspace));q.rspace=Math.max(0,this.CHTMLlength2em(q.rspace));if(q.scriptlevel>0){if(!this.hasValue("lspace")){q.lspace=0.15}if(!this.hasValue("rspace")){q.rspace=0.15}}var p=this,r=this.Parent();while(r&&r.isEmbellished()&&r.Core()===p){p=r;r=r.Parent();s=p.CHTMLnodeElement()}if(q.lspace){s.style.paddingLeft=g.Em(q.lspace)}if(q.rspace){s.style.paddingRight=g.Em(q.rspace)}this.CHTML.L=q.lspace;this.CHTML.R=q.rspace}else{this.SUPER(arguments).CHTMLhandleSpace.apply(this,arguments)}},CHTMLadjustAccent:function(r){var q=this.CoreParent();r.parent=q;if(r.text.length===1&&q&&q.isa(h.munderover)&&this.CoreText(q.data[q.base]).length===1){var s=q.data[q.over],p=q.data[q.under];if(s&&this===s.CoreMO()&&q.Get("accent")){r.remapchars=g.FONTDATA.REMAPACCENT}else{if(p&&this===p.CoreMO()&&q.Get("accentunder")){r.remapchars=g.FONTDATA.REMAPACCENTUNDER}}}},CHTMLadjustVariant:function(q){var p=q.parent,r=(p&&p.isa(h.msubsup)&&this!==p.data[p.base]);if(q.largeop){q.mathvariant=(q.displaystyle?"-largeOp":"-smallOp")}if(r){q.remapchars=this.remapChars;if(q.text.match(/['`"\u00B4\u2032-\u2037\u2057]/)){q.mathvariant="-TeX-variant"}}},CHTMLfixCombiningChar:function(p){p=p.firstChild;var q=g.Element("mjx-span",{style:{width:".25em","margin-left":"-.25em"}});p.insertBefore(q,p.firstChild)},CHTMLcenterOp:function(q){var s=this.CHTML;var r=(s.h-s.d)/2-g.TEX.axis_height;if(Math.abs(r)>0.001){q.style.verticalAlign=g.Em(-r)}s.h-=r;s.d+=r;if(s.r>s.w){s.ic=s.r-s.w;s.w=s.r;q.style.paddingRight=g.Em(s.ic)}},CHTMLcanStretch:function(t,r,s){if(!this.Get("stretchy")){return false}var u=this.data.join("");if(u.length!==1){return false}var q={text:u};this.CHTMLadjustAccent(q);if(q.remapchars){u=q.remapchars[u]||u}u=g.FONTDATA.DELIMITERS[u.charCodeAt(0)];var p=(u&&u.dir===t.substr(0,1));if(p){p=(this.CHTML.h!==r||this.CHTML.d!==s||!!this.Get("minsize",true)||!!this.Get("maxsize",true));if(p){this.CHTML.stretch=true}}return p},CHTMLstretchV:function(s,v){var t=this.CHTMLnodeElement(),u=this.CHTML;var q=this.getValues("symmetric","maxsize","minsize");var r,p=g.TEX.axis_height;if(q.symmetric){r=2*Math.max(s-p,v+p)}else{r=s+v}q.maxsize=this.CHTMLlength2em(q.maxsize,u.h+u.d);q.minsize=this.CHTMLlength2em(q.minsize,u.h+u.d);r=Math.max(q.minsize,Math.min(q.maxsize,r));if(r!==u.sH){if(r!=q.minsize){r=[Math.max(r*g.TEX.delimiterfactor/1000,r-g.TEX.delimitershortfall),r]}while(t.firstChild){t.removeChild(t.firstChild)}this.CHTML=u=g.createDelimiter(t,this.data.join("").charCodeAt(0),r,u);u.sH=(r instanceof Array?r[1]:r);if(q.symmetric){r=(u.h+u.d)/2+p}else{r=(u.h+u.d)*s/(s+v)}r-=u.h;if(Math.abs(r)>0.05){t.style.verticalAlign=g.Em(r);u.h+=r;u.d-=r;u.t+=r;u.b-=r}}return this.CHTML},CHTMLstretchH:function(r,p){var s=this.CHTML;var q=this.getValues("maxsize","minsize","mathvariant","fontweight");if((q.fontweight==="bold"||(this.removedStyles||{}).fontWeight==="bold"||parseInt(q.fontweight)>=600)&&!this.Get("mathvariant",true)){q.mathvariant=h.VARIANT.BOLD}q.maxsize=this.CHTMLlength2em(q.maxsize,s.w);q.minsize=this.CHTMLlength2em(q.minsize,s.w);p=Math.max(q.minsize,Math.min(q.maxsize,p));if(p!==s.sW){while(r.firstChild){r.removeChild(r.firstChild)}this.CHTML=s=g.createDelimiter(r,this.data.join("").charCodeAt(0),p,s,q.mathvariant);s.sW=p}return this.CHTML}});h.mtext.Augment({CHTMLgetVariant:function(){if(g.config.mtextFontInherit||this.Parent().type==="merror"){var r=(g.config.scale/100)/g.scale;var q={cache:{},fonts:[],className:"MJXc-font-inherit",rscale:r,style:{"font-size":g.Percent(r)}};var p=this.Get("mathvariant");if(p.match(/bold/)){q.style["font-weight"]="bold"}if(p.match(/italic|-tex-mathit/)){q.style["font-style"]="italic"}if(p==="monospace"){q.className+=" MJXc-monospace-font"}if(p==="double-struck"){q.className+=" MJXc-double-struck-font"}if(p.match(/fraktur/)){q.className+=" MJXc-fraktur-font"}if(p.match(/sans-serif/)){q.className+=" MJXc-sans-serif-font"}if(p.match(/script/)){q.className+=" MJXc-script-font"}this.CHTMLvariant=q}else{this.SUPER(arguments).CHTMLgetVariant.call(this)}}});h.merror.Augment({toCommonHTML:function(p){p=this.CHTMLdefaultNode(p);var q=this.CHTML;q.rescale(0.9);q.h+=3/g.em;if(q.h>q.t){q.t=q.h}q.d+=3/g.em;if(q.d>q.b){q.b=q.d}q.w+=8/g.em;q.r=q.w;q.l=0;return p}});h.mspace.Augment({toCommonHTML:function(s){s=this.CHTMLcreateNode(s);this.CHTMLhandleStyle(s);this.CHTMLhandleScale(s);var q=this.getValues("height","depth","width");var p=this.CHTMLlength2em(q.width),r=this.CHTMLlength2em(q.height),u=this.CHTMLlength2em(q.depth);var t=this.CHTML;t.w=t.r=p;t.h=t.t=r;t.d=t.b=u;t.l=0;if(p<0){s.style.marginRight=g.Em(p);p=0}s.style.width=g.Em(p);s.style.height=g.Em(r+u);if(u){s.style.verticalAlign=g.Em(-u)}this.CHTMLhandleBBox(s);this.CHTMLhandleColor(s);return s}});h.mpadded.Augment({toCommonHTML:function(r,p){var q;if(p){r=r.firstChild;q=r.firstChild}else{r=this.CHTMLdefaultNode(r,{childNodes:"mjx-box",forceChild:true});q=r.firstChild;r=g.addElement(r,"mjx-block");r.appendChild(q);g.addElement(r,"mjx-strut")}var u=this.CHTMLbboxFor(0);var B=this.getValues("width","height","depth","lspace","voffset");var z=0,v=0,A=u.w,s=u.h,t=u.d;q.style.width=0;q.style.margin=g.Em(-s)+" 0 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s}});h.munderover.Augment({toCommonHTML:function(t,p){var B=this.getValues("displaystyle","accent","accentunder","align");if(!B.displaystyle&&this.data[this.base]!=null&&this.data[this.base].CoreMO().Get("movablelimits")){return h.msubsup.prototype.toCommonHTML.call(this,t,p)}var r,y,w,q=[];if(p){r=g.getNode(t,"mjx-op");y=g.getNode(t,"mjx-under");w=g.getNode(t,"mjx-over");q[0]=r;q[1]=y||w;q[2]=w}else{var v=["mjx-op","mjx-under","mjx-over"];if(this.over===1){v[1]=v[2]}t=this.CHTMLdefaultNode(t,{childNodes:v,noBBox:true,forceChild:true,minChildren:2});q[0]=r=t.removeChild(t.firstChild);q[1]=y=w=t.removeChild(t.firstChild);if(t.firstChild){q[2]=w=t.removeChild(t.firstChild)}}var u=[],s=this.CHTMLgetBBoxes(u,q,B);var C=u[this.base],z=this.CHTML;z.w=s;z.h=C.h;z.d=C.d;var x=r,A=0;if(C.ic){A=1.3*C.ic+0.05}if(this.data[this.over]){x=this.CHTMLaddOverscript(w,u,B,A,r,p)}if(this.data[this.under]){this.CHTMLaddUnderscript(y,u,B,A,t,x,p)}else{if(!p){t.appendChild(x)}}this.CHTMLplaceBoxes(r,y,w,B,u);return t},CHTMLgetBBoxes:function(x,t,s){var u,q=this.data.length,v,r=-m,p=r;for(u=0;u<q;u++){x[u]=this.CHTMLbboxFor(u);x[u].x=x[u].y=0;if(this.data[u]){x[u].stretch=this.data[u].CHTMLcanStretch("Horizontal")}v=(u===this.base?1:x[u].rscale);p=Math.max(p,v*(x[u].w+(x[u].L||0)+(x[u].R||0)));if(!x[u].stretch&&p>r){r=p}}if(r===-m){r=p}for(u=0;u<q;u++){if(x[u].stretch){v=(u===this.base?1:x[u].rscale);x[u]=this.data[u].CHTMLstretchH(t[u].firstChild,r/v);x[u].x=x[u].y=0;p=Math.max(p,v*(x[u].w+(x[u].L||0)+(x[u].R||0)))}}if(!x[this.base]){x[this.base]=g.BBOX.empty()}return p},CHTMLaddOverscript:function(y,w,C,B,q,p){var A=this.CHTML;var v,u,t=g.TEX.big_op_spacing5,s;var x=w[this.over],D=w[this.base],r=x.rscale;if(!p){var z=g.Element("mjx-stack");z.appendChild(y);z.appendChild(q)}if(x.D){x.d=x.D}if(x.d<0){y.firstChild.style.verticalAlign="top";y.style.height=g.Em(x.h+x.d)}x.x=0;if(C.accent){if(x.w<0.001){x.x+=(x.r-x.l)/2}s=g.TEX.rule_thickness;t=0;if(D.skew){x.x+=r*D.skew;A.skew=r*D.skew;if(x.x+r*x.w>A.w){A.skew+=(A.w-(x.x+r*x.w))/2}}}else{v=g.TEX.big_op_spacing1;u=g.TEX.big_op_spacing3;s=Math.max(v,u-Math.max(0,r*x.d))}x.x+=B/2;x.y=A.h+s+t+r*x.d;if(s){y.style.paddingBottom=g.Em(s/r)}if(t){y.style.paddingTop=g.Em(t/r)}return z},CHTMLaddUnderscript:function(y,w,B,A,q,x,p){var z=this.CHTML;var v,u,t=g.TEX.big_op_spacing5,s;var C=w[this.under],r=C.rscale;if(!p){g.addElement(q,"mjx-itable",{},[["mjx-row",{},[["mjx-cell"]]],["mjx-row"]]);q.firstChild.firstChild.firstChild.appendChild(x);q.firstChild.lastChild.appendChild(y)}if(C.D){C.d=C.D}if(C.d<0){y.firstChild.style.verticalAlign="top";q.firstChild.style.marginBottom=g.Em(C.d)}if(B.accentunder){s=2*g.TEX.rule_thickness;t=0}else{v=g.TEX.big_op_spacing2;u=g.TEX.big_op_spacing4;s=Math.max(v,u-r*C.h)}C.x=-A/2;C.y=-(z.d+s+t+r*C.h);if(s){y.style.paddingTop=g.Em(s/r)}if(t){y.style.paddingBottom=g.Em(t/r)}},CHTMLplaceBoxes:function(p,y,x,B,v){var q=this.CHTML.w,u,s=v.length,t;var A=g.BBOX.zero();A.scale=this.CHTML.scale;A.rscale=this.CHTML.rscale;v[this.base].x=v[this.base].y=0;var C=m;for(u=0;u<s;u++){t=(u===this.base?1:v[u].rscale);var z=t*(v[u].w+(v[u].L||0)+(v[u].R||0));v[u].x+={left:0,center:(q-z)/2,right:q-z}[B.align];if(v[u].x<C){C=v[u].x}}for(u=0;u<s;u++){if(this.data[u]){t=(u===this.base?1:v[u].rscale);if(v[u].x-C){var r=(u===this.base?p:u===this.over?x:y);r.style.paddingLeft=g.Em((v[u].x-C)/t)}A.combine(v[u],v[u].x-C,v[u].y)}}this.CHTML=A},CHTMLstretchV:h.mbase.CHTMLstretchV,CHTMLstretchH:h.mbase.CHTMLstretchH});h.msubsup.Augment({toCommonHTML:function(R,X){var A=this.getValues("displaystyle","subscriptshift","superscriptshift","texprimestyle");var C,G,z;if(X){C=g.getNode(R,"mjx-base");G=g.getNode(R,"mjx-sub");z=g.getNode(R,"mjx-sup")}else{var J=["mjx-base","mjx-sub","mjx-sup"];if(this.sup===1){J[1]=J[2]}R=this.CHTMLdefaultNode(R,{childNodes:J,noBBox:true,forceChild:true,minChildren:3});C=R.childNodes[this.base];G=R.childNodes[this.sub];z=R.childNodes[this.sup];if(!this.CHTMLnotEmpty(this.data[this.sub])){R.removeChild(G);G=null}if(!this.CHTMLnotEmpty(this.data[this.sup])){R.removeChild(z);z=null}if(R.childNodes.length===3){var D=g.addElement(R,"mjx-stack");D.appendChild(z);D.appendChild(G)}}var E=[],F=g.BBOX.empty(this.CHTML);for(var U=0,S=this.data.length;U<S;U++){E[U]=this.CHTMLbboxFor(U)}var y=E[this.base]||g.BBOX.empty(),O=E[this.sub],V=E[this.sup];var B=(G?O.rscale:1),w=(z?V.rscale:1);F.combine(y,0,0);var W=g.TEX.x_height,M=g.TEX.scriptspace;var P=g.TEX.sup_drop*w,N=g.TEX.sub_drop*B;var K=y.h-P,I=y.d+N,Y=0,Q;if(y.ic){F.w-=y.ic;C.style.marginRight=g.Em(-y.ic);Y=1.3*y.ic+0.05}var T=this.data[this.base];if(T){if((T.type==="mrow"||T.type==="mstyle")&&T.data.length===1){T=T.data[0]}if(T.type==="mi"||T.type==="mo"){if(T.data.join("").length===1&&y.rscale===1&&!y.sH&&!T.Get("largeop")){K=I=0}}}A.subscriptshift=(A.subscriptshift===""?0:this.CHTMLlength2em(A.subscriptshift));A.superscriptshift=(A.superscriptshift===""?0:this.CHTMLlength2em(A.superscriptshift));var H=F.w;if(G){O.w+=M}if(z){V.w+=M}if(!z){if(G){I=Math.max(I,g.TEX.sub1,B*O.h-(4/5)*W,A.subscriptshift);G.style.verticalAlign=g.Em(-I/B);G.style.paddingRight=g.Em(M/B);F.combine(O,H,-I)}}else{if(!G){Q=g.TEX[(A.displaystyle?"sup1":(A.texprimestyle?"sup3":"sup2"))];K=Math.max(K,Q,w*V.d+(1/4)*W,A.superscriptshift);z.style.verticalAlign=g.Em(K/w);z.style.paddingLeft=g.Em(Y/w);z.style.paddingRight=g.Em(M/w);F.combine(V,H+Y,K)}else{I=Math.max(I,g.TEX.sub2);var L=g.TEX.rule_thickness;if((K-w*V.d)-(B*O.h-I)<3*L){I=3*L-K+w*V.d+B*O.h;P=(4/5)*W-(K-w*V.d);if(P>0){K+=P;I-=P}}K=Math.max(K,A.superscriptshift);I=Math.max(I,A.subscriptshift);G.style.paddingRight=g.Em(M/B);z.style.paddingBottom=g.Em(K/w+I/B-V.d-O.h/B*w);z.style.paddingLeft=g.Em(Y/w);z.style.paddingRight=g.Em(M/w);D.style.verticalAlign=g.Em(-I);F.combine(V,H+Y,K);F.combine(O,H,-I)}}F.clean();return R},CHTMLstretchV:h.mbase.CHTMLstretchV,CHTMLstretchH:h.mbase.CHTMLstretchH});h.mfrac.Augment({toCommonHTML:function(L){L=this.CHTMLdefaultNode(L,{childNodes:["mjx-numerator","mjx-denominator"],forceChild:true,noBBox:true,minChildren:2});var w=this.getValues("linethickness","displaystyle","numalign","denomalign","bevelled");var M=w.displaystyle;var B=L.firstChild,s=L.lastChild;var x=g.addElement(L,"mjx-box");x.appendChild(B);x.appendChild(s);L.appendChild(x);if(w.numalign!=="center"){B.style.textAlign=w.numalign}if(w.denomalign!=="center"){s.style.textAlign=w.denomalign}var N=this.CHTMLbboxFor(0),z=this.CHTMLbboxFor(1),A=g.BBOX.empty(this.CHTML),D=N.rscale,y=z.rscale;w.linethickness=Math.max(0,g.thickness2em(w.linethickness||"0",A.scale));var K=g.TEX.min_rule_thickness/g.em/A.scale,R=g.TEX.axis_height;var G=w.linethickness,J,I,F,E;if(w.bevelled){x.className+=" MJXc-bevelled";var Q=(M?0.4:0.15);var C=Math.max(D*(N.h+N.d),y*(z.h+z.d))+2*Q;var P=g.Element("mjx-bevel");x.insertBefore(P,s);var r=g.createDelimiter(P,47,C);F=D*(N.d-N.h)/2+R+Q;E=y*(z.d-z.h)/2+R-Q;if(F){B.style.verticalAlign=g.Em(F/D)}if(E){s.style.verticalAlign=g.Em(E/y)}P.style.marginLeft=P.style.marginRight=g.Em(-Q/2);A.combine(N,0,F);A.combine(r,D*N.w-Q/2,0);A.combine(z,D*N.w+r.w-Q,E);A.clean()}else{if(M){F=g.TEX.num1;E=g.TEX.denom1}else{F=(G===0?g.TEX.num3:g.TEX.num2);E=g.TEX.denom2}if(G===0){J=Math.max((M?7:3)*g.TEX.rule_thickness,2*K);I=(F-N.d*D)-(z.h*y-E);if(I<J){F+=(J-I)/2;E+=(J-I)/2}x.style.verticalAlign=g.Em(-E)}else{J=Math.max((M?2:0)*K+G,G/2+1.5*K);G=Math.max(G,K);I=(F-N.d*D)-(R+G/2);if(I<J){F+=(J-I)}I=(R-G/2)-(z.h*y-E);if(I<J){E+=(J-I)}x.style.verticalAlign=g.Em(G/2-E);B.style.borderBottom=g.Em(G/D)+" solid";B.className+=" MJXc-fpad";N.L=N.R=0.1;s.className+=" MJXc-fpad";z.L=z.R=0.1}A.combine(N,0,F);A.combine(z,0,-E);A.clean();F-=D*N.d+R+G/2;E-=y*z.h-R+G/2;if(F){B.style[F>0?"paddingBottom":"marginBottom"]=g.Em(F/D)}if(E){s.style[E>0?"paddingTop":"marginTop"]=g.Em(E/y)}}if(!this.texWithDelims&&!this.useMMLspacing){var O=g.TEX.nulldelimiterspace;x.style.padding="0 "+g.Em(O);A.l+=O;A.r+=O;A.w+=2*O}return L},CHTMLcanStretch:function(p){return false}});h.msqrt.Augment({toCommonHTML:function(v){v=this.CHTMLdefaultNode(v,{childNodes:["mjx-box","mjx-root"],forceChild:true,noBBox:true});var u=v.firstChild||g.Element("mjx-box");var D=g.addElement(v,"mjx-box");D.appendChild(u);var E=this.CHTMLbboxFor(0),B=g.BBOX.empty(this.CHTML);var F=g.TEX.rule_thickness,w=g.TEX.surd_height,s=F,r,C;if(this.Get("displaystyle")){s=g.TEX.x_height}r=F+s/4;C=E.h+E.d+r+F;var y=g.Element("mjx-surd");D.insertBefore(y,u);var z=g.createDelimiter(y,8730,[C-0.04,C]);if(z.h+z.d>C){r=((z.h+z.d)-(C-F))/2}C=E.h+r+F;var A=this.CHTMLaddRoot(v,z,z.h+z.d-C);u.style.paddingTop=g.Em(r);u.style.borderTop=g.Em(w)+" solid";D.style.paddingTop=g.Em(2*F-w);E.h+=r+2*F;B.combine(z,A,C-z.h);B.combine(E,A+z.w,0);B.clean();return v},CHTMLaddRoot:function(){return 0}});h.mroot.Augment({toCommonHTML:h.msqrt.prototype.toCommonHTML,CHTMLaddRoot:function(x,r,s){if(!this.data[1]){return}var v=this.CHTML,y=this.data[1].CHTML,t=x.firstChild;var p=y.rscale;var q=this.CHTMLrootHeight(y,r,p)-s;var u=Math.min(y.w,y.r);var z=Math.max(u,r.offset/p);if(q){t.style.verticalAlign=g.Em(q/p)}if(z>u){t.firstChild.style.paddingLeft=g.Em(z-u)}z-=r.offset/p;t.style.width=g.Em(z);v.combine(y,0,q);return z*p},CHTMLrootHeight:function(r,p,q){return 0.45*(p.h+p.d-0.9)+p.offset+Math.max(0,r.d-0.075)}});h.mfenced.Augment({toCommonHTML:function(s){s=this.CHTMLcreateNode(s);this.CHTMLhandleStyle(s);this.CHTMLhandleScale(s);this.CHTMLaddChild(s,"open",{});for(var r=0,p=this.data.length;r<p;r++){this.CHTMLaddChild(s,"sep"+r,{});this.CHTMLaddChild(s,r,{})}this.CHTMLaddChild(s,"close",{});var q=this.CHTML.h,t=this.CHTML.d;this.CHTMLstretchChildV("open",q,t);for(r=0,p=this.data.length;r<p;r++){this.CHTMLstretchChildV("sep"+r,q,t);this.CHTMLstretchChildV(r,q,t)}this.CHTMLstretchChildV("close",q,t);this.CHTMLhandleSpace(s);this.CHTMLhandleBBox(s);this.CHTMLhandleColor(s);return s}});h.mrow.Augment({toCommonHTML:function(s){s=this.CHTMLdefaultNode(s);var u=this.CHTML,r=u.h,t=u.d;for(var q=0,p=this.data.length;q<p;q++){this.CHTMLstretchChildV(q,r,t)}if(this.CHTMLlineBreaks()){this.CHTMLmultiline(s)}return s},CHTMLlineBreaks:function(){if(!this.parent.linebreakContainer){return false}return(k.automatic&&this.CHTML.w>g.linebreakWidth)||this.hasNewline()},CHTMLstretchV:function(p,q){this.CHTMLstretchChildV(this.CoreIndex(),p,q);return this.CHTML},CHTMLstretchH:function(q,p){this.CHTMLstretchChildH(this.CoreIndex(),p,q);return this.CHTML}});h.mstyle.Augment({toCommonHTML:function(p){p=this.CHTMLdefaultNode(p);if(this.scriptlevel&&this.data[0]){this.CHTML.rescale(this.data[0].CHTML.rscale)}return p}});h.TeXAtom.Augment({toCommonHTML:function(t,r){if(!r){t=this.CHTMLdefaultNode(t)}if(this.texClass===h.TEXCLASS.VCENTER){var p=g.TEX.axis_height,s=this.CHTML;var q=p-(s.h+s.d)/2+s.d;if(Math.abs(q)>0.001){t.style.verticalAlign=g.Em(q);s.h+=q;s.t+=q;s.d-=q;s.b-=q}}return t},CHTMLstretchV:function(p,q){this.CHTML.updateFrom(this.Core().CHTMLstretchV(p,q));this.toCommonHTML(this.CHTMLnodeElement(),true);return this.CHTML},CHTMLstretchH:function(q,p){this.CHTML.updateFrom(this.CHTMLstretchCoreH(q,p));this.toCommonHTML(q,true);return this.CHTML}});h.semantics.Augment({toCommonHTML:function(p){p=this.CHTMLcreateNode(p);if(this.data[0]){this.data[0].toCommonHTML(p);this.CHTML.updateFrom(this.data[0].CHTML)}return p}});h.annotation.Augment({toCommonHTML:function(p){return this.CHTMLcreateNode(p)}});h["annotation-xml"].Augment({toCommonHTML:h.mbase.CHTMLautoload});h.ms.Augment({toCommonHTML:h.mbase.CHTMLautoload});h.mglyph.Augment({toCommonHTML:h.mbase.CHTMLautoload});h.menclose.Augment({toCommonHTML:h.mbase.CHTMLautoload});h.maction.Augment({toCommonHTML:h.mbase.CHTMLautoload});h.mmultiscripts.Augment({toCommonHTML:h.mbase.CHTMLautoload});h.mtable.Augment({toCommonHTML:h.mbase.CHTMLautoload});MathJax.Hub.Register.StartupHook("onLoad",function(){setTimeout(MathJax.Callback(["loadComplete",g,"jax.js"]),0)})});MathJax.Hub.Register.StartupHook("End Cookie",function(){if(c.config.menuSettings.zoom!=="None"){i.Require("[MathJax]/extensions/MathZoom.js")}})})(MathJax.Ajax,MathJax.Hub,MathJax.HTML,MathJax.OutputJax.CommonHTML);
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