/*
 *  /MathJax/config/MML_CHTML.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/MathML/config.js",
  "[MathJax]/jax/output/CommonHTML/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]/extensions/AssistiveMML.js"
);

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

MathJax.InputJax.MathML=MathJax.InputJax({id:"MathML",version:"2.6.0-beta",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.CommonHTML=MathJax.OutputJax({id:"CommonHTML",version:"2.6.0-beta.2",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.mml2jax={version:"2.6.0-beta",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(f,b){var g=this.config.preview;if(g==="none"){return}var a=false;if(g==="mathml"){a=true;if(this.MathTagBug){g="alttext"}else{g=f.cloneNode(true)}}if(g==="alttext"||g==="altimg"){a=true;var c=this.filterPreview(f.getAttribute("alttext"));if(g==="alttext"){if(c!=null){g=MathJax.HTML.TextNode(c)}else{g=null}}else{var h=f.getAttribute("altimg");if(h!=null){var e={width:f.getAttribute("altimg-width"),height:f.getAttribute("altimg-height")};g=MathJax.HTML.Element("img",{src:h,alt:c,style:e})}else{g=null}}}if(g){var d;if(a){d=MathJax.HTML.Element("span",{className:MathJax.Hub.config.preRemoveClass});d.appendChild(g)}else{d=MathJax.HTML.Element("span",{className:MathJax.Hub.config.preRemoveClass},g)}b.parentNode.insertBefore(d,b)}},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="2.6.0-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);
(function(f,n,p,e,q){var o="2.6.0-beta.2";var d=MathJax.Callback.Signal("menu");MathJax.Extension.MathMenu={version:o,signal:d};var s=function(t){return MathJax.Localization._.apply(MathJax.Localization,[["MathMenu",t]].concat([].slice.call(arguments,1)))};var a=f.Browser.isPC,k=f.Browser.isMSIE,l=((document.documentMode||0)>8);var i=(a?null:"5px");var r=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":i,"-webkit-border-radius":i,"-moz-border-radius":i,"-khtml-border-radius":i,"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":(k?"'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":(k?"'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 m,j,b;f.Register.StartupHook("MathEvents Ready",function(){m=MathJax.Extension.MathEvents.Event.False;j=MathJax.Extension.MathEvents.Hover;b=MathJax.Extension.MathEvents.Event.KEY});var h=MathJax.Object.Subclass({Keydown:function(t,u){switch(t.keyCode){case b.ESCAPE:this.Remove(t,u);break;case b.RIGHT:this.Right(t,u);break;case b.LEFT:this.Left(t,u);break;case b.UP:this.Up(t,u);break;case b.DOWN:this.Down(t,u);break;case b.RETURN:case b.SPACE:this.Space(t,u);break;default:return;break}return m(t)},Escape:function(t,u){},Right:function(t,u){},Left:function(t,u){},Up:function(t,u){},Down:function(t,u){},Space:function(t,u){}},{});var 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 B=0,z=this.items.length;B<z;B++){this.items[B].Create(v)}if(g.isMobile){n.addElement(v,"span",{className:"MathJax_MenuClose",menu:I,ontouchstart:g.Close,ontouchend:m,onmousedown:g.Close,onmouseup:m},[["span",{},"\u00D7"]])}t.appendChild(v);this.posted=true;if(v.offsetWidth){v.style.width=(v.offsetWidth+2)+"px"}var H=u.pageX,F=u.pageY;if(!H&&!F&&"clientX" in u){H=u.clientX+document.body.scrollLeft+document.documentElement.scrollLeft;F=u.clientY+document.body.scrollTop+document.documentElement.scrollTop}if(!I){var w=g.CurrentNode()||u.target;if((u.type==="keydown"||(!H&&!F))&&w){var C=window.pageXOffset||document.documentElement.scrollLeft;var A=window.pageYOffset||document.documentElement.scrollTop;var E=w.getBoundingClientRect();H=(E.right+E.left)/2+C;F=(E.bottom+E.top)/2+A}if(H+v.offsetWidth>document.body.offsetWidth-this.margin){H=document.body.offsetWidth-v.offsetWidth-this.margin}if(g.isMobile){H=Math.max(5,H-Math.floor(v.offsetWidth/2));F-=20}g.skipUp=u.isContextMenu}else{var D="left",L=I.offsetWidth;H=(g.isMobile?30:L-2);F=0;while(I&&I!==t){H+=I.offsetLeft;F+=I.offsetTop;I=I.parentNode}if(!g.isMobile){if((g.isRTL&&H-L-v.offsetWidth>this.margin)||(!g.isRTL&&H+v.offsetWidth>document.body.offsetWidth-this.margin)){D="right";H=Math.max(this.margin,H-L-v.offsetWidth+6)}}if(!a){v.style["borderRadiusTop"+D]=0;v.style["WebkitBorderRadiusTop"+D]=0;v.style["MozBorderRadiusTop"+D]=0;v.style["KhtmlBorderRadiusTop"+D]=0}}v.style.left=H+"px";v.style.top=F+"px";if(document.selection&&document.selection.empty){document.selection.empty()}var K=window.pageXOffset||document.documentElement.scrollLeft;var J=window.pageYOffset||document.documentElement.scrollTop;g.Focus(v);if(u.type==="keydown"){g.skipMouseoverFromKey=true;setTimeout(function(){delete g.skipMouseoverFromKey},r.delay)}window.scrollTo(K,J);return m(u)},Remove:function(t,u){d.Post(["unpost",g.jax]);var v=document.getElementById("MathJax_MenuFrame");if(v){v.parentNode.removeChild(v);if(this.msieFixedPositionBug){detachEvent("onresize",g.Resize)}}if(g.jax.hover){delete g.jax.hover.nofade;j.UnHover(g.jax)}g.Unfocus(u);if(t.type==="mousedown"){g.CurrentNode().blur()}return m(t)},Find:function(t){return this.FindN(1,t,[].slice.call(arguments,1))},FindId:function(t){return this.FindN(0,t,[].slice.call(arguments,1))},FindN:function(x,u,w){for(var v=0,t=this.items.length;v<t;v++){if(this.items[v].name[x]===u){if(w.length){if(!this.items[v].submenu){return null}return this.items[v].submenu.FindN(x,w[0],w.slice(1))}return this.items[v]}}return null},IndexOf:function(t){return this.IndexOfN(1,t)},IndexOfId:function(t){return this.IndexOfN(0,t)},IndexOfN:function(w,u){for(var v=0,t=this.items.length;v<t;v++){if(this.items[v].name[w]===u){return v}}return null},Right:function(t,u){g.Right(t,u)},Left:function(t,u){g.Left(t,u)},Up:function(u,v){var t=v.lastChild;t.menuItem.Activate(u,t)},Down:function(u,v){var t=v.firstChild;t.menuItem.Activate(u,t)},Space:function(t,u){this.Remove(t,u)}},{config:r,Remove:function(t){return g.Event(t,this,"Remove")},Mouseover:function(t){return g.Event(t,this,"Mouseover")},Mouseout:function(t){return g.Event(t,this,"Mouseout")},Mousedown:function(t){return g.Event(t,this,"Mousedown")},Mouseup:function(t){return g.Event(t,this,"Mouseup")},Keydown:function(t){return g.Event(t,this,"Keydown")},Touchstart:function(t){return g.Event(t,this,"Touchstart")},Touchend:function(t){return g.Event(t,this,"Touchend")},Close:function(t){return g.Event(t,this.menu||this.parentNode,(this.menu?"Touchend":"Remove"))},Event:function(v,x,t,w){if(g.skipMouseover&&t==="Mouseover"&&!w){return m(v)}if(g.skipMouseoverFromKey&&t==="Mouseover"){delete g.skipMouseoverFromKey;return m(v)}if(g.skipUp){if(t.match(/Mouseup|Touchend/)){delete g.skipUp;return m(v)}if(t==="Touchstart"||(t==="Mousedown"&&!g.skipMousedown)){delete g.skipUp}}if(!v){v=window.event}var u=x.menuItem;if(u&&u[t]){return u[t](v,x)}return null},BGSTYLE:{position:"absolute",left:0,top:0,"z-index":200,width:"100%",height:"100%",border:0,padding:0,margin:0},Background:function(u){var v=n.addElement(document.body,"div",{style:this.BGSTYLE,id:"MathJax_MenuFrame"},[["div",{style:this.BGSTYLE,menuItem:u,onmousedown:this.Remove}]]);var t=v.firstChild;if(g.msieBackgroundBug){t.style.backgroundColor="white";t.style.filter="alpha(opacity=0)"}if(g.msieFixedPositionBug){v.width=v.height=0;this.Resize();attachEvent("onresize",this.Resize)}else{t.style.position="fixed"}return v},Resize:function(){setTimeout(g.SetWH,0)},SetWH:function(){var t=document.getElementById("MathJax_MenuFrame");if(t){t=t.firstChild;t.style.width=t.style.height="1px";t.style.width=document.body.scrollWidth+"px";t.style.height=document.body.scrollHeight+"px"}},posted:false,active:null,GetNode:function(t){var u=document.getElementById(t.inputID+"-Frame");return u.isMathJax?u:u.firstChild},CurrentNode:function(){return g.GetNode(g.jax)},AllNodes:function(){var u=MathJax.Hub.getAllJax();var v=[];for(var w=0,t;t=u[w];w++){v.push(g.GetNode(t))}return v},ActiveNode:function(){return g.active},FocusNode:function(t){g.active=t;t.focus()},Focus:function(t){!g.posted?g.Activate(t):g.ActiveNode().tabIndex=-1;t.tabIndex=0;g.FocusNode(t)},Activate:function(w,x){var u=g.AllNodes();for(var v=0,t;t=u[v];v++){t.tabIndex=-1}g.posted=true},Unfocus:function(){g.ActiveNode().tabIndex=-1;var u=g.AllNodes();for(var v=0,t;t=u[v];v++){t.tabIndex=0}g.FocusNode(g.CurrentNode());g.posted=false},MoveHorizontal:function(x,y,v){if(!x.shiftKey){return}var u=g.AllNodes();var t=u.length;if(t===0){return}var w=u[g.Mod(v(g.IndexOf(u,g.CurrentNode())),t)];if(w===g.CurrentNode()){return}g.menu.Remove(x,y);g.jax=MathJax.Hub.getJaxFor(w);g.FocusNode(w);g.menu.Post(null)},Right:function(t,u){g.MoveHorizontal(t,u,function(v){return v+1})},Left:function(t,u){g.MoveHorizontal(t,u,function(v){return v-1})},Mod:function(t,u){return((t%u)+u)%u},IndexOf:(Array.prototype.indexOf?function(t,u,v){return t.indexOf(u,v)}:function(t,w,x){for(var v=(x||0),u=t.length;v<u;v++){if(w===t[v]){return v}}return -1}),saveCookie:function(){n.Cookie.Set("menu",this.cookie)},getCookie:function(){this.cookie=n.Cookie.Get("menu")}});MathJax.Menu.NAV=h;var c=g.ITEM=h.Subclass({name:"",node:null,menu:null,Attributes:function(t){return f.Insert({onmouseup:g.Mouseup,ondragstart:m,onselectstart:m,onselectend:m,ontouchstart:g.Touchstart,ontouchend:g.Touchend,className:"MathJax_MenuItem",role:this.role,menuItem:this},t)},Create:function(v){if(!this.hidden){var u=this.Attributes();var t=this.Label(u,v);n.addElement(v,"div",u,t)}},Name:function(){return s(this.name[0],this.name[1])},Mouseover:function(t,u){if(u.parentNode===g.ActiveNode().parentNode){this.Deactivate(g.ActiveNode())}this.Activate(t,u)},Mouseout:function(t,u){this.Deactivate(u)},Mouseup:function(t,u){return this.Remove(t,u)},DeactivateSubmenus:function(y){var x=document.getElementById("MathJax_MenuFrame").childNodes,u=c.GetMenuNode(y).childNodes;for(var v=0,t=u.length;v<t;v++){var w=u[v].menuItem;if(w&&w.submenu&&w.submenu.posted&&w!==y.menuItem){w.Deactivate(u[v])}}this.RemoveSubmenus(y,x)},RemoveSubmenus:function(v,u){u=u||document.getElementById("MathJax_MenuFrame").childNodes;var t=u.length-1;while(t>=0&&c.GetMenuNode(v).menuItem!==u[t].menuItem){u[t].menuItem.posted=false;u[t].parentNode.removeChild(u[t]);t--}},Touchstart:function(t,u){return this.TouchEvent(t,u,"Mousedown")},Touchend:function(t,u){return this.TouchEvent(t,u,"Mouseup")},TouchEvent:function(u,v,t){if(this!==c.lastItem){if(c.lastMenu){g.Event(u,c.lastMenu,"Mouseout")}g.Event(u,v,"Mouseover",true);c.lastItem=this;c.lastMenu=v}if(this.nativeTouch){return null}g.Event(u,v,t);return false},Remove:function(t,u){u=u.parentNode.menuItem;return u.Remove(t,u)},With:function(t){if(t){f.Insert(this,t)}return this},isRTL:function(){return g.isRTL},rtlClass:function(){return(this.isRTL()?" RTL":"")}},{GetMenuNode:function(t){return t.parentNode}});g.ENTRY=g.ITEM.Subclass({role:"menuitem",Attributes:function(t){t=f.Insert({onmouseover:g.Mouseover,onmouseout:g.Mouseout,onmousedown:g.Mousedown,onkeydown:g.Keydown,"aria-disabled":!!this.disabled},t);t=this.SUPER(arguments).Attributes.call(this,t);if(this.disabled){t.className+=" MathJax_MenuDisabled"}return t},MoveVertical:function(t,D,v){var w=c.GetMenuNode(D);var C=[];for(var y=0,B=w.menuItem.items,x;x=B[y];y++){if(!x.hidden){C.push(x)}}var A=g.IndexOf(C,this);if(A===-1){return}var z=C.length;var u=w.childNodes;do{A=g.Mod(v(A),z)}while(C[A].hidden||!u[A].role||u[A].role==="separator");this.Deactivate(D);C[A].Activate(t,u[A])},Up:function(u,t){this.MoveVertical(u,t,function(v){return v-1})},Down:function(u,t){this.MoveVertical(u,t,function(v){return v+1})},Right:function(u,t){this.MoveHorizontal(u,t,g.Right,!this.isRTL())},Left:function(u,t){this.MoveHorizontal(u,t,g.Left,this.isRTL())},MoveHorizontal:function(z,y,t,A){var w=c.GetMenuNode(y);if(w.menuItem===g.menu&&z.shiftKey){t(z,y)}if(A){return}if(w.menuItem!==g.menu){this.Deactivate(y)}var u=w.previousSibling.childNodes;var x=u.length;while(x--){var v=u[x];if(v.menuItem.submenu&&v.menuItem.submenu===w.menuItem){g.Focus(v);break}}this.RemoveSubmenus(y)},Space:function(t,u){this.Mouseup(t,u)},Activate:function(t,u){this.Deactivate(u);if(!this.disabled){u.className+=" MathJax_MenuActive"}this.DeactivateSubmenus(u);g.Focus(u)},Deactivate:function(t){t.className=t.className.replace(/ MathJax_MenuActive/,"")}});g.ITEM.COMMAND=g.ENTRY.Subclass({action:function(){},Init:function(t,v,u){if(!(t instanceof Array)){t=[t,t]}this.name=t;this.action=v;this.With(u)},Label:function(t,u){return[this.Name()]},Mouseup:function(t,u){if(!this.disabled){this.Remove(t,u);d.Post(["command",this]);this.action.call(this,t)}return m(t)}});g.ITEM.SUBMENU=g.ENTRY.Subclass({submenu:null,marker:"\u25BA",markerRTL:"\u25C4",Attributes:function(t){t=f.Insert({"aria-haspopup":"true"},t);t=this.SUPER(arguments).Attributes.call(this,t);return t},Init:function(t,v){if(!(t instanceof Array)){t=[t,t]}this.name=t;var u=1;if(!(v instanceof g.ITEM)){this.With(v),u++}this.submenu=g.apply(g,[].slice.call(arguments,u))},Label:function(t,u){this.submenu.posted=false;return[this.Name()+" ",["span",{className:"MathJax_MenuArrow"+this.rtlClass()},[this.isRTL()?this.markerRTL:this.marker]]]},Timer:function(t,u){this.ClearTimer();t={type:t.type,clientX:t.clientX,clientY:t.clientY};this.timer=setTimeout(e(["Mouseup",this,t,u]),r.delay)},ClearTimer:function(){if(this.timer){clearTimeout(this.timer)}},Touchend:function(u,w){var v=this.submenu.posted;var t=this.SUPER(arguments).Touchend.apply(this,arguments);if(v){this.Deactivate(w);delete c.lastItem;delete c.lastMenu}return t},Mouseout:function(t,u){if(!this.submenu.posted){this.Deactivate(u)}this.ClearTimer()},Mouseover:function(t,u){this.Activate(t,u)},Mouseup:function(t,u){if(!this.disabled){if(!this.submenu.posted){this.ClearTimer();this.submenu.Post(t,u,this.ltr);g.Focus(u)}else{this.DeactivateSubmenus(u)}}return m(t)},Activate:function(t,u){if(!this.disabled){this.Deactivate(u);u.className+=" MathJax_MenuActive"}if(!this.submenu.posted){this.DeactivateSubmenus(u);if(!g.isMobile){this.Timer(t,u)}}g.Focus(u)},MoveVertical:function(v,u,t){this.ClearTimer();this.SUPER(arguments).MoveVertical.apply(this,arguments)},MoveHorizontal:function(v,x,u,w){if(!w){this.SUPER(arguments).MoveHorizontal.apply(this,arguments);return}if(this.disabled){return}if(!this.submenu.posted){this.Activate(v,x);return}var t=c.GetMenuNode(x).nextSibling.childNodes;if(t.length>0){this.submenu.items[0].Activate(v,t[0])}}});g.ITEM.RADIO=g.ENTRY.Subclass({variable:null,marker:(a?"\u25CF":"\u2713"),role:"menuitemradio",Attributes:function(u){var t=r.settings[this.variable]===this.value?"true":"false";u=f.Insert({"aria-checked":t},u);u=this.SUPER(arguments).Attributes.call(this,u);return u},Init:function(u,t,v){if(!(u instanceof Array)){u=[u,u]}this.name=u;this.variable=t;this.With(v);if(this.value==null){this.value=this.name[0]}},Label:function(u,v){var t={className:"MathJax_MenuRadioCheck"+this.rtlClass()};if(r.settings[this.variable]!==this.value){t={style:{display:"none"}}}return[["span",t,[this.marker]]," "+this.Name()]},Mouseup:function(w,x){if(!this.disabled){var y=x.parentNode.childNodes;for(var u=0,t=y.length;u<t;u++){var v=y[u].menuItem;if(v&&v.variable===this.variable){y[u].firstChild.style.display="none"}}x.firstChild.display="";r.settings[this.variable]=this.value;g.cookie[this.variable]=r.settings[this.variable];g.saveCookie();d.Post(["radio button",this])}this.Remove(w,x);if(this.action&&!this.disabled){this.action.call(g,this)}return m(w)}});g.ITEM.CHECKBOX=g.ENTRY.Subclass({variable:null,marker:"\u2713",role:"menuitemcheckbox",Attributes:function(u){var t=r.settings[this.variable]?"true":"false";u=f.Insert({"aria-checked":t},u);u=this.SUPER(arguments).Attributes.call(this,u);return u},Init:function(u,t,v){if(!(u instanceof Array)){u=[u,u]}this.name=u;this.variable=t;this.With(v)},Label:function(u,v){var t={className:"MathJax_MenuCheck"+this.rtlClass()};if(!r.settings[this.variable]){t={style:{display:"none"}}}return[["span",t,[this.marker]]," "+this.Name()]},Mouseup:function(t,u){if(!this.disabled){u.firstChild.display=(r.settings[this.variable]?"none":"");r.settings[this.variable]=!r.settings[this.variable];g.cookie[this.variable]=r.settings[this.variable];g.saveCookie();d.Post(["checkbox",this])}this.Remove(t,u);if(this.action&&!this.disabled){this.action.call(g,this)}return m(t)}});g.ITEM.LABEL=g.ENTRY.Subclass({role:"menuitem",Init:function(t,u){if(!(t instanceof Array)){t=[t,t]}this.name=t;this.With(u)},Label:function(t,u){t.className+=" MathJax_MenuLabel";return[this.Name()]},Activate:function(t,u){this.Deactivate(u);g.Focus(u)},Mouseup:function(t,u){}});g.ITEM.RULE=g.ITEM.Subclass({role:"separator",Attributes:function(t){t=f.Insert({"aria-orientation":"vertical"},t);t=this.SUPER(arguments).Attributes.call(this,t);return t},Label:function(t,u){t.className+=" MathJax_MenuRule";return null}});g.About=function(x){var u=g.About.GetFont();var z=g.About.GetFormat();var t=["MathJax.js v"+MathJax.fileversion,["br"]];t.push(["div",{style:{"border-top":"groove 2px",margin:".25em 0"}}]);g.About.GetJax(t,MathJax.InputJax,["InputJax","%1 Input Jax v%2"]);g.About.GetJax(t,MathJax.OutputJax,["OutputJax","%1 Output Jax v%2"]);g.About.GetJax(t,MathJax.ElementJax,["ElementJax","%1 Element Jax v%2"]);t.push(["div",{style:{"border-top":"groove 2px",margin:".25em 0"}}]);g.About.GetJax(t,MathJax.Extension,["Extension","%1 Extension v%2"],true);t.push(["div",{style:{"border-top":"groove 2px",margin:".25em 0"}}],["center",{},[f.Browser+" v"+f.Browser.version+(z?" \u2014 "+s(z.replace(/ /g,""),z):"")]]);g.About.div=g.Background(g.About);var w=n.addElement(g.About.div,"div",{id:"MathJax_About",tabIndex:0,onkeydown:g.About.Keydown},[["b",{style:{fontSize:"120%"}},["MathJax"]]," v"+MathJax.version,["br"],s(u.replace(/ /g,""),"using "+u),["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},t],["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":s("CloseAboutDialog","Close about MathJax dialog")},[["span",{},"\u00D7"]]]]);if(x.type==="mouseup"){w.className+=" MathJax_MousePost"}w.focus();MathJax.Localization.setCSS(w);var y=(document.documentElement||{});var 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 v}e.After([this,g.ShowSource,w],v.restart)}}else{if(!p.loadingToMathML){p.loadingToMathML=true;g.ShowSource.Window(x);e.Queue(p.Require("[MathJax]/extensions/toMathML.js"),function(){delete p.loadingToMathML;if(!u.mbase.prototype.toMathML){u.mbase.prototype.toMathML=function(){}}},[this,g.ShowSource,w]);return}}}else{if(this.format==="Error"){g.ShowSource.Text(g.jax.errorText,x)}else{if(r.semanticsAnnotations[this.format]){var t=g.jax.root.getAnnotation(this.format);if(t.data[0]){g.ShowSource.Text(t.data[0].toString())}}else{if(g.jax.originalText==null){alert(s("NoOriginalForm","No original form available"));return}g.ShowSource.Text(g.jax.originalText,x)}}}};g.ShowSource.Window=function(u){if(!g.ShowSource.w){var v=[],t=r.windowSettings;for(var w in t){if(t.hasOwnProperty(w)){v.push(w+"="+t[w])}}g.ShowSource.w=window.open("","_blank",v.join(","))}return g.ShowSource.w};g.ShowSource.Text=function(y,v){var t=g.ShowSource.Window(v);delete g.ShowSource.w;y=y.replace(/^\s*/,"").replace(/\s*$/,"");y=y.replace(/&/g,"&amp;").replace(/</g,"&lt;").replace(/>/g,"&gt;");var x=s("EqSource","MathJax Equation Source");if(g.isMobile){t.document.open();t.document.write("<html><head><meta name='viewport' content='width=device-width, initial-scale=1.0' /><title>"+x+"</title></head><body style='font-size:85%'>");t.document.write("<pre>"+y+"</pre>");t.document.write("<hr><input type='button' value='"+s("Close","Close")+"' onclick='window.close()' />");t.document.write("</body></html>");t.document.close()}else{t.document.open();t.document.write("<html><head><title>"+x+"</title></head><body style='font-size:85%'>");t.document.write("<table><tr><td><pre>"+y+"</pre></td></tr></table>");t.document.write("</body></html>");t.document.close();var u=t.document.body.firstChild;setTimeout(function(){var A=(t.outerHeight-t.innerHeight)||30,z=(t.outerWidth-t.innerWidth)||30,w,D;z=Math.max(140,Math.min(Math.floor(0.5*screen.width),u.offsetWidth+z+25));A=Math.max(40,Math.min(Math.floor(0.5*screen.height),u.offsetHeight+A+25));if(g.prototype.msieHeightBug){A+=35}t.resizeTo(z,A);var C;try{C=v.screenX}catch(B){}if(v&&C!=null){w=Math.max(0,Math.min(v.screenX-Math.floor(z/2),screen.width-z-20));D=Math.max(0,Math.min(v.screenY-Math.floor(A/2),screen.height-A-20));t.moveTo(w,D)}},50)}};g.Scale=function(){var y=["CommonHTML","HTML-CSS","SVG","NativeMML","PreviewHTML"],t=y.length,x=100,v,u;for(v=0;v<t;v++){u=q[y[v]];if(u){x=u.config.scale;break}}var w=prompt(s("ScaleMath","Scale all mathematics (compared to surrounding text) by"),x+"%");if(w){if(w.match(/^\s*\d+(\.\d*)?\s*%?\s*$/)){w=parseFloat(w);if(w){if(w!==x){for(v=0;v<t;v++){u=q[y[v]];if(u){u.config.scale=w}}g.cookie.scale=f.config.scale=w;g.saveCookie();f.Queue(["Rerender",f])}}else{alert(s("NonZeroScale","The scale should not be zero"))}}else{alert(s("PercentScale","The scale should be a percentage (e.g., 120%%)"))}}};g.Zoom=function(){if(!MathJax.Extension.MathZoom){p.Require("[MathJax]/extensions/MathZoom.js")}};g.Renderer=function(){var u=f.outputJax["jax/mml"];if(u[0]!==r.settings.renderer){var x=f.Browser,w,t=g.Renderer.Messages,v;switch(r.settings.renderer){case"NativeMML":if(!r.settings.warnedMML){if(x.isChrome&&x.version.substr(0,3)!=="24."){w=t.MML.WebKit}else{if(x.isSafari&&!x.versionAtLeast("5.0")){w=t.MML.WebKit}else{if(x.isMSIE){if(!x.hasMathPlayer){w=t.MML.MSIE}}else{if(x.isEdge){w=t.MML.WebKit}else{w=t.MML[x]}}}}v="warnedMML"}break;case"SVG":if(!r.settings.warnedSVG){if(x.isMSIE&&!l){w=t.SVG.MSIE}}break}if(w){w=s(w[0],w[1]);w+="\n\n";w+=s("SwitchAnyway","Switch the renderer anyway?\n\n(Press OK to switch, CANCEL to continue with the current renderer)");g.cookie.renderer=u[0].id;g.saveCookie();if(!confirm(w)){g.cookie.renderer=r.settings.renderer=n.Cookie.Get("menu").renderer;g.saveCookie();return}if(v){g.cookie.warned=r.settings.warned=true}g.cookie.renderer=r.settings.renderer;g.saveCookie()}f.Queue(["setRenderer",f,r.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.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.  Javascript file names should end with '.js'"))}p.Require(t,function(u){if(u!=p.STATUS.OK){alert(s("BadData","Failed to load translation data from %1",t))}})}};g.MPEvents=function(v){var u=r.settings.discoverable,t=g.MPEvents.Messages;if(!l){if(r.settings.mpMouse&&!confirm(s.apply(s,t.IE8warning))){delete g.cookie.mpContext;delete r.settings.mpContext;delete g.cookie.mpMouse;delete r.settings.mpMouse;g.saveCookie();return}r.settings.mpContext=r.settings.mpMouse;g.cookie.mpContext=g.cookie.mpMouse=r.settings.mpMouse;g.saveCookie();MathJax.Hub.Queue(["Rerender",MathJax.Hub])}else{if(!u&&v.name[1]==="Menu Events"&&r.settings.mpContext){alert(s.apply(s,t.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(t){var u=(document.compatMode==="BackCompat");var v=t.versionAtLeast("8.0")&&document.documentMode>7;g.Augment({margin:20,msieBackgroundBug:((document.documentMode||0)<9),msieFixedPositionBug:(u||!v),msieAboutBug:u,msieHeightBug:((document.documentMode||0)<9)});if(l){delete r.styles["#MathJax_About"].filter;delete r.styles[".MathJax_Menu"].filter}},Firefox:function(t){g.skipMouseover=t.isMobile&&t.versionAtLeast("6.0");g.skipMousedown=t.isMobile}});g.isMobile=f.Browser.isMobile;g.noContextMenu=f.Browser.noContextMenu;g.CreateLocaleMenu=function(){if(!g.menu){return}var y=g.menu.Find("Language").submenu,v=y.items;var u=[],A=MathJax.Localization.strings;for(var z in A){if(A.hasOwnProperty(z)){u.push(z)}}u=u.sort();y.items=[];for(var w=0,t=u.length;w<t;w++){var x=A[u[w]].menuTitle;if(x){x+=" ("+u[w]+")"}else{x=u[w]}y.items.push(c.RADIO([u[w],x],"locale",{action:g.Locale}))}y.items.push(v[v.length-2],v[v.length-1])};g.CreateAnnotationMenu=function(){if(!g.menu){return}var v=g.menu.Find("Show Math As","Annotation").submenu;var u=r.semanticsAnnotations;for(var t in u){if(u.hasOwnProperty(t)){v.items.push(c.COMMAND([t,t],g.ShowSource,{hidden:true,nativeTouch:true,format:t}))}}};f.Register.StartupHook("End Config",function(){r.settings=f.config.menuSettings;if(typeof(r.settings.showRenderer)!=="undefined"){r.showRenderer=r.settings.showRenderer}if(typeof(r.settings.showFontMenu)!=="undefined"){r.showFontMenu=r.settings.showFontMenu}if(typeof(r.settings.showContext)!=="undefined"){r.showContext=r.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:!r.showRenderer},c.RADIO("HTML-CSS","renderer",{action:g.Renderer}),c.RADIO("Common HTML","renderer",{action:g.Renderer,value:"CommonHTML"}),c.RADIO("Fast HTML","renderer",{action:g.Renderer,value:"PreviewHTML"}),c.RADIO("MathML","renderer",{action:g.Renderer,value:"NativeMML"}),c.RADIO("SVG","renderer",{action:g.Renderer}),c.RULE(),c.CHECKBOX("Fast Preview","FastPreview"),c.CHECKBOX("Assistive MathML","assistiveMML",{hidden:!r.showAssistiveMML})),c.SUBMENU("MathPlayer",{hidden:!f.Browser.isMSIE||!r.showMathPlayer,disabled:!f.Browser.hasMathPlayer},c.LABEL(["MPHandles","Let MathPlayer Handle:"]),c.CHECKBOX(["MenuEvents","Menu Events"],"mpContext",{action:g.MPEvents,hidden:!l}),c.CHECKBOX(["MouseEvents","Mouse Events"],"mpMouse",{action:g.MPEvents,hidden:!l}),c.CHECKBOX(["MenuAndMouse","Mouse and Menu Events"],"mpMouse",{action:g.MPEvents,hidden:l})),c.SUBMENU(["FontPrefs","Font Preference"],{hidden:!r.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:!r.showContext},c.RADIO("MathJax","context"),c.RADIO(["Browser","Browser"],"context")),c.COMMAND(["Scale","Scale All Math ..."],g.Scale),c.RULE().With({hidden:!r.showDiscoverable,name:["","discover_rule"]}),c.CHECKBOX(["Discoverable","Highlight on Hover"],"discoverable",{hidden:!r.showDiscoverable})),c.SUBMENU(["Locale","Language"],{hidden:!r.showLocale,ltr:true},c.RADIO("en","locale",{action:g.Locale}),c.RULE().With({hidden:!r.showLocaleURL,name:["","localURL_rule"]}),c.COMMAND(["LoadLocale","Load from URL ..."],g.LoadLocale,{hidden:!r.showLocaleURL})),c.RULE(),c.COMMAND(["About","About MathJax"],g.About),c.COMMAND(["Help","MathJax Help"],g.Help));if(g.isMobile){(function(){var u=r.settings;var t=g.menu.Find("Math Settings","Zoom Trigger").submenu;t.items[0].disabled=t.items[1].disabled=true;if(u.zoom==="Hover"||u.zoom=="Click"){u.zoom="None"}t.items=t.items.slice(0,4);if(navigator.appVersion.match(/[ (]Android[) ]/)){g.ITEM.SUBMENU.Augment({marker:"\u00BB"})}})()}g.CreateLocaleMenu();g.CreateAnnotationMenu()});g.showRenderer=function(t){g.cookie.showRenderer=r.showRenderer=t;g.saveCookie();g.menu.Find("Math Settings","Math Renderer").hidden=!t};g.showMathPlayer=function(t){g.cookie.showMathPlayer=r.showMathPlayer=t;g.saveCookie();g.menu.Find("Math Settings","MathPlayer").hidden=!t};g.showFontMenu=function(t){g.cookie.showFontMenu=r.showFontMenu=t;g.saveCookie();g.menu.Find("Math Settings","Font Preference").hidden=!t};g.showContext=function(t){g.cookie.showContext=r.showContext=t;g.saveCookie();g.menu.Find("Math Settings","Contextual Menu").hidden=!t};g.showDiscoverable=function(t){g.cookie.showDiscoverable=r.showDiscoverable=t;g.saveCookie();g.menu.Find("Math Settings","Highlight on Hover").hidden=!t;g.menu.Find("Math Settings","discover_rule").hidden=!t};g.showLocale=function(t){g.cookie.showLocale=r.showLocale=t;g.saveCookie();g.menu.Find("Language").hidden=!t};g.showAssistiveMML=function(t){g.cookie.showAssistiveMML=r.showAssistiveMML=t;g.saveCookie();g.menu.Find("Math Settings","Math Renderer","Assistive MathML").hidden=!t};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",p,r.styles],["Post",f.Startup.signal,"MathMenu Ready"],["loadComplete",p,"[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:"2.6.0-beta",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:"inital",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)},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,form:4},useMMLspacing:7,autoDefault:function(g,n){var l=this.def;if(!l){if(g==="form"){this.useMMLspacing&=~this.SPACE_ATTR.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.useMMLspacing){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}));this.data.open.useMMLspacing=0}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}));this.data["sep"+g].useMMLspacing=0}}}if(f.close!==""){this.SetData("close",a.mo(f.close).With({fence:true,form:a.FORM.POSTFIX,texClass:a.TEXCLASS.CLOSE}));this.data.close.useMMLspacing=0}},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",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="2.6.0-beta";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||!this.attr.xmlns)){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(this.mathvariant&&this.toMathMLvariants[this.mathvariant]){f.push("MJX"+this.mathvariant)}if(this.variantForm){f.push("MJX-variant")}if(f.length){d.unshift('class="'+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="'+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(j){var f=this.type;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(j+"  "))}}return j+"<"+f+e+">\n"+h.join("\n")+"\n"+j+"</"+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.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])}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(f){var e=a.TeXAtom().With({texClass:a.TEXCLASS[f]});if(e.texClass===a.TEXCLASS.OP){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){if(k.toLowerCase()==="true"){k=true}else{if(k.toLowerCase()==="false"){k=false}}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(e instanceof Array){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(a,e,b,f){var c=b.config.menuSettings;var d=MathJax.Extension.AssistiveMML={version:"2.6.0-beta.2",config:{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"},".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){d.EndMathHook(g[1])})},EndMathHook:function(g){if(!c.assistiveMML){return}var h={jax:b.getAllJax(g),i:0,callback:MathJax.Callback({})};this.HandleMML(h);return h.callback},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"&&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,className:"MJX_Assistive_MathML"+(h.root.Get("display")==="block"?" MJX_Assistive_MathML_Block":"")});j.innerHTML=i;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])});
MathJax.Ajax.loadComplete("[MathJax]/config/MML_CHTML.js");