MathJax.Hub.Config({delayJaxRegistration:!0}),MathJax.Ajax.Preloading("[MathJax]/jax/input/MathML/config.js","[MathJax]/jax/output/HTML-CSS/config.js","[MathJax]/jax/output/NativeMML/config.js","[MathJax]/jax/output/PreviewHTML/config.js","[MathJax]/config/MMLorHTML.js","[MathJax]/extensions/mml2jax.js","[MathJax]/extensions/MathEvents.js","[MathJax]/extensions/MathZoom.js","[MathJax]/extensions/MathMenu.js","[MathJax]/jax/element/mml/jax.js","[MathJax]/extensions/toMathML.js","[MathJax]/jax/input/MathML/jax.js","[MathJax]/jax/output/PreviewHTML/jax.js","[MathJax]/extensions/fast-preview.js","[MathJax]/extensions/AssistiveMML.js","[MathJax]/extensions/a11y/accessibility-menu.js"),MathJax.Hub.Config({extensions:["[a11y]/accessibility-menu.js"]}),MathJax.InputJax.MathML=MathJax.InputJax({id:"MathML",version:"2.7.9",directory:MathJax.InputJax.directory+"/MathML",extensionDir:MathJax.InputJax.extensionDir+"/MathML",entityDir:MathJax.InputJax.directory+"/MathML/entities",config:{useMathMLspacing:!1}}),MathJax.InputJax.MathML.Register("math/mml"),MathJax.InputJax.MathML.loadComplete("config.js"),MathJax.OutputJax["HTML-CSS"]=MathJax.OutputJax({id:"HTML-CSS",version:"2.7.9",directory:MathJax.OutputJax.directory+"/HTML-CSS",extensionDir:MathJax.OutputJax.extensionDir+"/HTML-CSS",autoloadDir:MathJax.OutputJax.directory+"/HTML-CSS/autoload",fontDir:MathJax.OutputJax.directory+"/HTML-CSS/fonts",webfontDir:MathJax.OutputJax.fontDir+"/HTML-CSS",config:{noReflows:!0,matchFontHeight:!0,scale:100,minScaleAdjust:50,availableFonts:["STIX","TeX"],preferredFont:"TeX",webFont:"TeX",imageFont:"TeX",undefinedFamily:"STIXGeneral,'Arial Unicode MS',serif",mtextFontInherit:!1,EqnChunk:MathJax.Hub.Browser.isMobile?10:50,EqnChunkFactor:1.5,EqnChunkDelay:100,linebreaks:{automatic:!1,width:"container"},styles:{".MathJax_Display":{"text-align":"center",margin:"1em 0em"},".MathJax .merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"1px 3px","font-style":"normal","font-size":"90%"},".MathJax .MJX-monospace":{"font-family":"monospace"},".MathJax .MJX-sans-serif":{"font-family":"sans-serif"},"#MathJax_Tooltip":{"background-color":"InfoBackground",color:"InfoText",border:"1px solid black","box-shadow":"2px 2px 5px #AAAAAA","-webkit-box-shadow":"2px 2px 5px #AAAAAA","-moz-box-shadow":"2px 2px 5px #AAAAAA","-khtml-box-shadow":"2px 2px 5px #AAAAAA",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')",padding:"3px 4px","z-index":401}}}}),MathJax.Hub.Browser.isMSIE&&document.documentMode>=9&&delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter,MathJax.Hub.config.delayJaxRegistration||MathJax.OutputJax["HTML-CSS"].Register("jax/mml"),MathJax.Hub.Register.StartupHook("End Config",[function(t,e){var a=t.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:!0,minBrowserTranslate:function(e){var i,s=t.getJaxFor(e),n=["[Math]"],o=document.createElement("span",{className:"MathJax_Preview"});"TeX"===s.inputJax&&(s.root.Get("displaystyle")?(n=[(i=a.displayMathDelimiters)[0]+s.originalText+i[1]],a.multilineDisplay&&(n=n[0].split(/\n/))):n=[(i=a.inlineMathDelimiters)[0]+s.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+i[1]]);for(var r=0,l=n.length;r<l;r++)o.appendChild(document.createTextNode(n[r])),r<l-1&&o.appendChild(document.createElement("br"));e.parentNode.insertBefore(o,e)}},t.config["HTML-CSS"]||{});"0.0"===t.Browser.version||t.Browser.versionAtLeast(a.minBrowserVersion[t.Browser]||0)||(e.Translate=a.minBrowserTranslate,t.Config({showProcessingMessages:!1}),MathJax.Message.Set(["MathJaxNotSupported","Your browser does not support MathJax"],null,4e3),t.Startup.signal.Post("MathJax not supported"))},MathJax.Hub,MathJax.OutputJax["HTML-CSS"]]),MathJax.OutputJax["HTML-CSS"].loadComplete("config.js"),MathJax.OutputJax.NativeMML=MathJax.OutputJax({id:"NativeMML",version:"2.7.9",directory:MathJax.OutputJax.directory+"/NativeMML",extensionDir:MathJax.OutputJax.extensionDir+"/NativeMML",config:{matchFontHeight:!0,scale:100,minScaleAdjust:50,styles:{"div.MathJax_MathML":{"text-align":"center",margin:".75em 0px"}}}}),MathJax.Hub.config.delayJaxRegistration||MathJax.OutputJax.NativeMML.Register("jax/mml"),MathJax.OutputJax.NativeMML.loadComplete("config.js"),MathJax.OutputJax.PreviewHTML=MathJax.OutputJax({id:"PreviewHTML",version:"2.7.9",directory:MathJax.OutputJax.directory+"/PreviewHTML",extensionDir:MathJax.OutputJax.extensionDir+"/PreviewHTML",noFastPreview:!0,config:{scale:100,minScaleAdjust:50,mtextFontInherit:!1,linebreaks:{automatic:!1,width:"container"}}}),MathJax.Hub.config.delayJaxRegistration||MathJax.OutputJax.PreviewHTML.Register("jax/mml"),MathJax.OutputJax.PreviewHTML.loadComplete("config.js"),function(t,e){var a=MathJax.Hub.CombineConfig("MMLorHTML",{prefer:{MSIE:"MML",Firefox:"HTML",Opera:"HTML",Chrome:"HTML",Safari:"HTML",other:"HTML"}}),i="0.0"===e.version||e.versionAtLeast({Firefox:3,Opera:9.52,MSIE:6,Chrome:.3,Safari:2,Konqueror:4}[e]||0),s=e.isFirefox&&e.versionAtLeast("1.5")||e.isMSIE&&e.hasMathPlayer||e.isSafari&&e.versionAtLeast("5.0")||e.isOpera&&e.versionAtLeast("9.52");t.Register.StartupHook("End Config",(function(){var e=a.prefer&&"object"==typeof a.prefer?a.prefer[MathJax.Hub.Browser]||a.prefer.other||"HTML":a.prefer;i||s?!s||"MML"!==e&&i?(MathJax.OutputJax["HTML-CSS"]?MathJax.OutputJax["HTML-CSS"].Register("jax/mml"):t.config.jax.unshift("output/HTML-CSS"),t.Startup.signal.Post("HTML-CSS output selected")):(MathJax.OutputJax.NativeMML?MathJax.OutputJax.NativeMML.Register("jax/mml"):t.config.jax.unshift("output/NativeMML"),t.Startup.signal.Post("NativeMML output selected")):(t.PreProcess.disabled=!0,t.prepareScripts.disabled=!0,MathJax.Message.Set(["MathJaxNotSupported","Your browser does not support MathJax"],null,4e3),t.Startup.signal.Post("MathJax not supported"))}))}(MathJax.Hub,MathJax.Hub.Browser),MathJax.Ajax.loadComplete("[MathJax]/config/MMLorHTML.js"),MathJax.Extension.mml2jax={version:"2.7.9",config:{preview:"mathml"},MMLnamespace:"http://www.w3.org/1998/Math/MathML",PreProcess:function(t){this.configured||(this.config=MathJax.Hub.CombineConfig("mml2jax",this.config),this.config.Augment&&MathJax.Hub.Insert(this,this.config.Augment),this.InitBrowser(),this.configured=!0),"string"==typeof t&&(t=document.getElementById(t)),t||(t=document.body);var e,a,i=[];if(this.PushMathElements(i,t,"math"),this.PushMathElements(i,t,"math",this.MMLnamespace),void 0!==document.namespaces)try{for(e=0,a=document.namespaces.length;e<a;e++){var s=document.namespaces[e];s.urn===this.MMLnamespace&&this.PushMathElements(i,t,s.name+":math")}}catch(t){}else{var n=document.getElementsByTagName("html")[0];if(n)for(e=0,a=n.attributes.length;e<a;e++){var o=n.attributes[e];"xmlns:"===o.nodeName.substr(0,6)&&o.nodeValue===this.MMLnamespace&&this.PushMathElements(i,t,o.nodeName.substr(6)+":math")}}this.ProcessMathArray(i)},PushMathElements:function(t,e,a,i){var s,n=MathJax.Hub.config.preRemoveClass;if(i){if(!e.getElementsByTagNameNS)return;s=e.getElementsByTagNameNS(i,a)}else s=e.getElementsByTagName(a);for(var o=0,r=s.length;o<r;o++){var l=s[o].parentNode;l&&l.className!==n&&!l.isMathJax&&!s[o].prefix==!i&&t.push(s[o])}},ProcessMathArray:function(t){var e,a=t.length;if(a)if(this.MathTagBug)for(e=0;e<a;e++)"MATH"===t[e].nodeName?this.ProcessMathFlattened(t[e]):this.ProcessMath(t[e]);else for(e=0;e<a;e++)this.ProcessMath(t[e])},ProcessMath:function(t){var e=t.parentNode;if(e&&e.className!==MathJax.Hub.config.preRemoveClass){var a=document.createElement("script");if(a.type="math/mml",e.insertBefore(a,t),this.AttributeBug){var i=this.OuterHTML(t);this.CleanupHTML&&(i=(i=i.replace(/<\?import .*?>/i,"").replace(/<\?xml:namespace .*?\/>/i,"")).replace(/&nbsp;/g,"&#xA0;")),MathJax.HTML.setScript(a,i),e.removeChild(t)}else{var s=MathJax.HTML.Element("span");s.appendChild(t),MathJax.HTML.setScript(a,s.innerHTML)}"none"!==this.config.preview&&this.createPreview(t,a)}},ProcessMathFlattened:function(t){var e=t.parentNode;if(e&&e.className!==MathJax.Hub.config.preRemoveClass){var a=document.createElement("script");a.type="math/mml",e.insertBefore(a,t);for(var i,s="",n=t;t&&"/MATH"!==t.nodeName;)i=t,t=t.nextSibling,s+=this.NodeHTML(i),i.parentNode.removeChild(i);t&&"/MATH"===t.nodeName&&t.parentNode.removeChild(t),a.text=s+"</math>","none"!==this.config.preview&&this.createPreview(n,a)}},NodeHTML:function(t){var e,a,i;if("#text"===t.nodeName)e=this.quoteHTML(t.nodeValue);else if("#comment"===t.nodeName)e="\x3c!--"+t.nodeValue+"--\x3e";else{for(e="<"+t.nodeName.toLowerCase(),a=0,i=t.attributes.length;a<i;a++){var s=t.attributes[a];if(s.specified&&"_moz-math-"!==s.nodeName.substr(0,10)){e+=" "+s.nodeName.toLowerCase().replace(/xmlns:xmlns/,"xmlns")+"=";var n=s.nodeValue;null==n&&"style"===s.nodeName&&t.style&&(n=t.style.cssText),e+='"'+this.quoteHTML(n)+'"'}}if(e+=">",null!=t.outerHTML&&t.outerHTML.match(/(.<\/[A-Z]+>|\/>)$/)){for(a=0,i=t.childNodes.length;a<i;a++)e+=this.OuterHTML(t.childNodes[a]);e+="</"+t.nodeName.toLowerCase()+">"}}return e},OuterHTML:function(t){if("#"===t.nodeName.charAt(0))return this.NodeHTML(t);if(!this.AttributeBug)return t.outerHTML;for(var e=this.NodeHTML(t),a=0,i=t.childNodes.length;a<i;a++)e+=this.OuterHTML(t.childNodes[a]);return e+"</"+t.nodeName.toLowerCase()+">"},quoteHTML:function(t){return null==t&&(t=""),t.replace(/&/g,"&#x26;").replace(/</g,"&lt;").replace(/>/g,"&gt;").replace(/\"/g,"&quot;")},createPreview:function(t,e){var a=this.config.preview;if("none"!==a){var i=!1,s=MathJax.Hub.config.preRemoveClass;if((e.previousSibling||{}).className!==s){if("mathml"===a&&(i=!0,a=this.MathTagBug?"alttext":t.cloneNode(!0)),"alttext"===a||"altimg"===a){i=!0;var n=this.filterPreview(t.getAttribute("alttext"));if("alttext"===a)a=null!=n?MathJax.HTML.TextNode(n):null;else{var o=t.getAttribute("altimg");if(null!=o){var r={width:t.getAttribute("altimg-width"),height:t.getAttribute("altimg-height")};a=MathJax.HTML.Element("img",{src:o,alt:n,style:r})}else a=null}}var l;a&&(i?(l=MathJax.HTML.Element("span",{className:s})).appendChild(a):l=MathJax.HTML.Element("span",{className:s},a),e.parentNode.insertBefore(l,e))}}},filterPreview:function(t){return t},InitBrowser:function(){var t=MathJax.HTML.Element("span",{id:"<",className:"mathjax",innerHTML:"<math><mi>x</mi><mspace /></math>"}),e=t.outerHTML||"";this.AttributeBug=""!==e&&!(e.match(/id="&lt;"/)&&e.match(/class="mathjax"/)&&e.match(/<\/math>/)),this.MathTagBug=t.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(t,e,a,i,s,n,o){var r=MathJax.Extension,l=r.MathEvents={version:"2.7.9"},h=t.config.menuSettings,u={hover:500,frame:{x:3.5,y:5,bwidth:1,bcolor:"#A6D",hwidth:"15px",hcolor:"#83A"},button:{x:-6,y:-3,wx:-2},fadeinInc:.2,fadeoutInc:.05,fadeDelay:50,fadeoutStart:400,fadeoutDelay:15e3,styles:{".MathJax_Hover_Frame":{"border-radius":".25em","-webkit-border-radius":".25em","-moz-border-radius":".25em","-khtml-border-radius":".25em","box-shadow":"0px 0px 15px #83A","-webkit-box-shadow":"0px 0px 15px #83A","-moz-box-shadow":"0px 0px 15px #83A","-khtml-box-shadow":"0px 0px 15px #83A",border:"1px solid #A6D ! important",display:"inline-block",position:"absolute"},".MathJax_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"}}},d=l.Event={LEFTBUTTON:0,RIGHTBUTTON:2,MENUKEY:"altKey",KEY:{RETURN:13,ESCAPE:27,SPACE:32,LEFT:37,UP:38,RIGHT:39,DOWN:40,LESS:188,GREATER:190,DASH:189},Mousedown:function(t){return d.Handler(t,"Mousedown",this)},Mouseup:function(t){return d.Handler(t,"Mouseup",this)},Mousemove:function(t){return d.Handler(t,"Mousemove",this)},Mouseover:function(t){return d.Handler(t,"Mouseover",this)},Mouseout:function(t){return d.Handler(t,"Mouseout",this)},Click:function(t){return d.Handler(t,"Click",this)},DblClick:function(t){return d.Handler(t,"DblClick",this)},Menu:function(t){return d.Handler(t,"ContextMenu",this)},Handler:function(t,e,i){if(a.loadingMathMenu)return d.False(t);var s=n[i.jaxID];return t||(t=window.event),t.isContextMenu="ContextMenu"===e,s[e]?s[e](t,i):r.MathZoom?r.MathZoom.HandleEvent(t,e,i):void 0},False:function(t){return t||(t=window.event),t&&(t.preventDefault?t.preventDefault():t.returnValue=!1,t.stopPropagation&&t.stopPropagation(),t.cancelBubble=!0),!1},Keydown:function(t,e){t||(t=window.event),t.keyCode===d.KEY.SPACE&&d.ContextMenu(t,this)},ContextMenu:function(e,r,u){var m=n[r.jaxID],p=m.getJaxFromMath(r);if((null!=m.config.showMathMenu?m:t).config.showMathMenu&&("MathJax"===h.context||u)){l.msieEventBug&&(e=window.event||e),d.ClearSelection(),c.ClearHoverTimer(),p.hover&&(p.hover.remove&&(clearTimeout(p.hover.remove),delete p.hover.remove),p.hover.nofade=!0);var M,f,g=MathJax.Menu;if(g){if(g.loadingDomain)return d.False(e);if(!(M=s.loadDomain("MathMenu"))){g.jax=p;var x=g.menu.Find("Show Math As").submenu;x.items[0].name=p.sourceMenuTitle,x.items[0].format=p.sourceMenuFormat||"MathML",x.items[1].name=o[p.inputJax].sourceMenuTitle,x.items[5].disabled=!o[p.inputJax].annotationEncoding;var v=x.items[2];v.disabled=!0;var T=v.submenu.items;annotationList=MathJax.Hub.Config.semanticsAnnotations;for(var E=0,b=T.length;E<b;E++){var C=T[E].name[1];p.root&&null!==p.root.getAnnotation(C)?(v.disabled=!1,T[E].hidden=!1):T[E].hidden=!0}return g.menu.Find("Math Settings","MathPlayer").hidden=!("NativeMML"===p.outputJax&&t.Browser.hasMathPlayer),g.menu.Post(e)}g.loadingDomain=!0,f=function(){delete g.loadingDomain}}else{if(a.loadingMathMenu)return d.False(e);a.loadingMathMenu=!0,M=a.Require("[MathJax]/extensions/MathMenu.js"),f=function(){delete a.loadingMathMenu,MathJax.Menu||(MathJax.Menu={})}}var L={pageX:e.pageX,pageY:e.pageY,clientX:e.clientX,clientY:e.clientY};return i.Queue(M,f,["ContextMenu",d,L,r,u]),d.False(e)}},AltContextMenu:function(e,a){var i=n[a.jaxID],s=(null!=i.config.showMathMenu?i:t).config.showMathMenu;if(s){if(s=(null!=i.config.showMathMenuMSIE?i:t).config.showMathMenuMSIE,"MathJax"===h.context&&!h.mpContext&&s){if(!l.noContextMenuBug||e.button!==d.RIGHTBUTTON)return}else if(!e[d.MENUKEY]||e.button!==d.LEFTBUTTON)return;return i.ContextMenu(e,a,!0)}},ClearSelection:function(){l.safariContextMenuBug&&setTimeout("window.getSelection().empty()",0),document.selection&&setTimeout("document.selection.empty()",0)},getBBox:function(t){t.appendChild(l.topImg);var e=l.topImg.offsetTop,a=t.offsetHeight-e,i=t.offsetWidth;return t.removeChild(l.topImg),{w:i,h:e,d:a}}},c=l.Hover={Mouseover:function(e,a){if(h.discoverable||"Hover"===h.zoom){var i=e.fromElement||e.relatedTarget,s=e.toElement||e.target;if(i&&s&&(t.isMathJaxNode(i)!==t.isMathJaxNode(s)||t.getJaxFor(i)!==t.getJaxFor(s))){var n=this.getJaxFromMath(a);return n.hover?c.ReHover(n):c.HoverTimer(n,a),d.False(e)}}},Mouseout:function(e,a){if(h.discoverable||"Hover"===h.zoom){var i=e.fromElement||e.relatedTarget,s=e.toElement||e.target;if(i&&s&&(t.isMathJaxNode(i)!==t.isMathJaxNode(s)||t.getJaxFor(i)!==t.getJaxFor(s))){var n=this.getJaxFromMath(a);return n.hover?c.UnHover(n):c.ClearHoverTimer(),d.False(e)}}},Mousemove:function(t,e){if(h.discoverable||"Hover"===h.zoom){var a=this.getJaxFromMath(e);if(a.hover)return;if(c.lastX==t.clientX&&c.lastY==t.clientY)return;return c.lastX=t.clientX,c.lastY=t.clientY,c.HoverTimer(a,e),d.False(t)}},HoverTimer:function(t,e){this.ClearHoverTimer(),this.hoverTimer=setTimeout(i(["Hover",this,t,e]),u.hover)},ClearHoverTimer:function(){this.hoverTimer&&(clearTimeout(this.hoverTimer),delete this.hoverTimer)},Hover:function(a,i){if(!r.MathZoom||!r.MathZoom.Hover({},i)){var s=n[a.outputJax],o=s.getHoverSpan(a,i),h=s.getHoverBBox(a,o,i),d=(null!=s.config.showMathMenu?s:t).config.showMathMenu,c=u.frame.x,m=u.frame.y,p=u.frame.bwidth;l.msieBorderWidthBug&&(p=0),a.hover={opacity:0,id:a.inputID+"-Hover"};var M=e.Element("span",{id:a.hover.id,isMathJax:!0,style:{display:"inline-block",width:0,height:0,position:"relative"}},[["span",{className:"MathJax_Hover_Frame",isMathJax:!0,style:{display:"inline-block",position:"absolute",top:this.Px(-h.h-m-p-(h.y||0)),left:this.Px(-c-p+(h.x||0)),width:this.Px(h.w+2*c),height:this.Px(h.h+h.d+2*m),opacity:0,filter:"alpha(opacity=0)"}}]]),f=e.Element("span",{isMathJax:!0,id:a.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:!0,math:i,onclick:this.HoverMenu,jax:s.id,style:{left:this.Px(h.w+c+p+(h.x||0)+u.button.x),top:this.Px(-h.h-m-p-(h.y||0)-u.button.y),opacity:0,filter:"alpha(opacity=0)"}},[["span",{isMathJax:!0},"▼"]]]]);h.width&&(M.style.width=f.style.width=h.width,M.style.marginRight=f.style.marginRight="-"+h.width,M.firstChild.style.width=h.width,f.firstChild.style.left="",f.firstChild.style.right=this.Px(u.button.wx)),o.parentNode.insertBefore(M,o),d&&o.parentNode.insertBefore(f,o),o.style&&(o.style.position="relative"),this.ReHover(a)}},ReHover:function(t){t.hover.remove&&clearTimeout(t.hover.remove),t.hover.remove=setTimeout(i(["UnHover",this,t]),u.fadeoutDelay),this.HoverFadeTimer(t,u.fadeinInc)},UnHover:function(t){t.hover.nofade||this.HoverFadeTimer(t,-u.fadeoutInc,u.fadeoutStart)},HoverFade:function(t){delete t.hover.timer,t.hover.opacity=Math.max(0,Math.min(1,t.hover.opacity+t.hover.inc)),t.hover.opacity=Math.floor(1e3*t.hover.opacity)/1e3;var e=document.getElementById(t.hover.id),a=document.getElementById(t.hover.id+"Menu");e.firstChild.style.opacity=t.hover.opacity,e.firstChild.style.filter="alpha(opacity="+Math.floor(100*t.hover.opacity)+")",a&&(a.firstChild.style.opacity=t.hover.opacity,a.firstChild.style.filter=e.style.filter),1!==t.hover.opacity&&(t.hover.opacity>0?this.HoverFadeTimer(t,t.hover.inc):(e.parentNode.removeChild(e),a&&a.parentNode.removeChild(a),t.hover.remove&&clearTimeout(t.hover.remove),delete t.hover))},HoverFadeTimer:function(t,e,a){t.hover.inc=e,t.hover.timer||(t.hover.timer=setTimeout(i(["HoverFade",this,t]),a||u.fadeDelay))},HoverMenu:function(t){return t||(t=window.event),n[this.jax].ContextMenu(t,this.math,!0)},ClearHover:function(t){t.hover.remove&&clearTimeout(t.hover.remove),t.hover.timer&&clearTimeout(t.hover.timer),c.ClearHoverTimer(),delete t.hover},Px:function(t){return Math.abs(t)<.006?"0px":t.toFixed(2).replace(/\.?0+$/,"")+"px"},getImages:function(){h.discoverable&&((new Image).src=u.button.src)}},m=l.Touch={last:0,delay:500,start:function(t){var e=(new Date).getTime(),a=e-m.last<m.delay&&m.up;m.last=e,m.up=!1,a&&(m.timeout=setTimeout(m.menu,m.delay,t,this),t.preventDefault())},end:function(t){var e=(new Date).getTime();if(m.up=e-m.last<m.delay,m.timeout)return clearTimeout(m.timeout),delete m.timeout,m.last=0,m.up=!1,t.preventDefault(),d.Handler(t.touches[0]||t.touch,"DblClick",this)},menu:function(t,e){return delete m.timeout,m.last=0,m.up=!1,d.Handler(t.touches[0]||t.touch,"ContextMenu",e)}};t.Browser.Select({MSIE:function(t){var e=document.documentMode||0,a=t.versionAtLeast("8.0");l.msieBorderWidthBug="BackCompat"===document.compatMode,l.msieEventBug=t.isIE9,l.msieAlignBug=!a||e<8,e<9&&(d.LEFTBUTTON=1)},Safari:function(t){l.safariContextMenuBug=!0},Opera:function(t){l.operaPositionBug=!0},Konqueror:function(t){l.noContextMenuBug=!0}}),l.topImg=l.msieAlignBug?e.Element("img",{style:{width:0,height:0,position:"relative"},src:"about:blank"}):e.Element("span",{style:{width:0,height:0,display:"inline-block"}}),l.operaPositionBug&&(l.topImg.style.border="1px solid"),l.config=u=t.CombineConfig("MathEvents",u),i.Queue(t.Register.StartupHook("End Config",{}),[function(){var t=u.styles[".MathJax_Hover_Frame"];t.border=u.frame.bwidth+"px solid "+u.frame.bcolor+" ! important",t["box-shadow"]=t["-webkit-box-shadow"]=t["-moz-box-shadow"]=t["-khtml-box-shadow"]="0px 0px "+u.frame.hwidth+" "+u.frame.hcolor}],["getImages",c],["Styles",a,u.styles],["Post",t.Startup.signal,"MathEvents Ready"],["loadComplete",a,"[MathJax]/extensions/MathEvents.js"])}(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.Callback,MathJax.Localization,MathJax.OutputJax,MathJax.InputJax),function(t,e,a,i,s){var n,o,r,l=t.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)"}}});MathJax.Hub.Register.StartupHook("MathEvents Ready",(function(){r=MathJax.Extension.MathEvents.Event,n=MathJax.Extension.MathEvents.Event.False,o=MathJax.Extension.MathEvents.Hover}));var h=MathJax.Extension.MathZoom={version:"2.7.9",settings:t.config.menuSettings,scrollSize:18,HandleEvent:function(t,e,a){return!(!h.settings.CTRL||t.ctrlKey)||!(!h.settings.ALT||t.altKey)||!(!h.settings.CMD||t.metaKey)||!(!h.settings.Shift||t.shiftKey)||!h[e]||h[e](t,a)},Click:function(t,e){if("Click"===this.settings.zoom)return this.Zoom(t,e)},DblClick:function(t,e){if("Double-Click"===this.settings.zoom||"DoubleClick"===this.settings.zoom)return this.Zoom(t,e)},Hover:function(t,e){return"Hover"===this.settings.zoom&&(this.Zoom(t,e),!0)},Zoom:function(a,i){this.Remove(),o.ClearHoverTimer(),r.ClearSelection();var s=MathJax.OutputJax[i.jaxID],h=s.getJaxFromMath(i);h.hover&&o.UnHover(h);var u=this.findContainer(i),d=Math.floor(.85*u.clientWidth),c=Math.max(document.body.clientHeight,document.documentElement.clientHeight);"visible"!==this.getOverflow(u)&&(c=Math.min(u.clientHeight,c)),c=Math.floor(.85*c);var m=e.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"}}]]]]),p=m.lastChild,M=p.firstChild,f=m.firstChild;i.parentNode.insertBefore(m,i),i.parentNode.insertBefore(i,m),M.addEventListener&&M.addEventListener("mousedown",this.Remove,!0);var g=p.offsetWidth||p.clientWidth;if(d-=g,c-=g,p.style.maxWidth=d+"px",p.style.maxHeight=c+"px",this.msieTrapEventBug){var x=e.Element("span",{id:"MathJax_ZoomEventTrap",onmousedown:this.Remove});m.insertBefore(x,p)}if(this.msieZIndexBug){var v=e.addElement(document.body,"img",{src:"about:blank",id:"MathJax_ZoomTracker",width:0,height:0,style:{width:0,height:0,position:"relative"}});m.style.position="relative",m.style.zIndex=l.styles["#MathJax_ZoomOverlay"]["z-index"],m=v}var T=s.Zoom(h,M,i,d,c);return this.msiePositionBug&&(this.msieSizeBug&&(p.style.height=T.zH+"px",p.style.width=T.zW+"px"),p.offsetHeight>c&&(p.style.height=c+"px",p.style.width=T.zW+this.scrollSize+"px"),p.offsetWidth>d&&(p.style.width=d+"px",p.style.height=T.zH+this.scrollSize+"px")),this.operaPositionBug&&(p.style.width=Math.min(d,T.zW)+"px"),p.offsetWidth>g&&p.offsetWidth-g<d&&p.offsetHeight-g<c&&(p.style.overflow="visible"),this.Position(p,T),this.msieTrapEventBug&&(x.style.height=p.clientHeight+"px",x.style.width=p.clientWidth+"px",x.style.left=parseFloat(p.style.left)+p.clientLeft+"px",x.style.top=parseFloat(p.style.top)+p.clientTop+"px"),p.style.visibility="","Hover"===this.settings.zoom&&(f.onmouseover=this.Remove),window.addEventListener?addEventListener("resize",this.Resize,!1):window.attachEvent?attachEvent("onresize",this.Resize):(this.onresize=window.onresize,window.onresize=this.Resize),t.signal.Post(["math zoomed",h]),n(a)},Position:function(t,e){t.style.display="none";var a=this.Resize(),i=a.x,s=a.y,n=e.mW;t.style.display="";var o=-n-Math.floor((t.offsetWidth-n)/2),r=e.Y;t.style.left=Math.max(o,10-i)+"px",t.style.top=Math.max(r,10-s)+"px",h.msiePositionBug||h.SetWH()},Resize:function(t){h.onresize&&h.onresize(t);var e=document.getElementById("MathJax_ZoomFrame"),a=document.getElementById("MathJax_ZoomOverlay"),i=h.getXY(e),s=h.findContainer(e);if("visible"!==h.getOverflow(s)){a.scroll_parent=s;var n=h.getXY(s);i.x-=n.x,i.y-=n.y,n=h.getBorder(s),i.x-=n.x,i.y-=n.y}return a.style.left=-i.x+"px",a.style.top=-i.y+"px",h.msiePositionBug?setTimeout(h.SetWH,0):h.SetWH(),i},SetWH:function(){var t=document.getElementById("MathJax_ZoomOverlay");if(t){t.style.display="none";var e=t.scroll_parent||document.documentElement||document.body;t.style.width=e.scrollWidth+"px",t.style.height=Math.max(e.clientHeight,e.scrollHeight)+"px",t.style.display=""}},findContainer:function(t){for(t=t.parentNode;t.parentNode&&t!==document.body&&"visible"===h.getOverflow(t);)t=t.parentNode;return t},getOverflow:window.getComputedStyle?function(t){return getComputedStyle(t).overflow}:function(t){return(t.currentStyle||{overflow:"visible"}).overflow},getBorder:function(t){var e={thin:1,medium:2,thick:3},a=window.getComputedStyle?getComputedStyle(t):t.currentStyle||{borderLeftWidth:0,borderTopWidth:0},i=a.borderLeftWidth,s=a.borderTopWidth;return{x:i=e[i]?e[i]:parseInt(i),y:s=e[s]?e[s]:parseInt(s)}},getXY:function(t){var e,a=0,i=0;for(e=t;e.offsetParent;)a+=e.offsetLeft,e=e.offsetParent;for(h.operaPositionBug&&(t.style.border="1px solid"),e=t;e.offsetParent;)i+=e.offsetTop,e=e.offsetParent;return h.operaPositionBug&&(t.style.border=""),{x:a,y:i}},Remove:function(a){var i=document.getElementById("MathJax_ZoomFrame");if(i){var s=MathJax.OutputJax[i.previousSibling.jaxID].getJaxFromMath(i.previousSibling);if(t.signal.Post(["math unzoomed",s]),i.parentNode.removeChild(i),(i=document.getElementById("MathJax_ZoomTracker"))&&i.parentNode.removeChild(i),h.operaRefreshBug){var o=e.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(o)}window.removeEventListener?removeEventListener("resize",h.Resize,!1):window.detachEvent?detachEvent("onresize",h.Resize):(window.onresize=h.onresize,delete h.onresize)}return n(a)}};t.Browser.Select({MSIE:function(t){var e=document.documentMode||0,a=e>=9;h.msiePositionBug=!a,h.msieSizeBug=t.versionAtLeast("7.0")&&(!document.documentMode||7===e||8===e),h.msieZIndexBug=e<=7,h.msieInlineBlockAlignBug=e<=7,h.msieTrapEventBug=!window.addEventListener,"BackCompat"===document.compatMode&&(h.scrollSize=52),a&&delete l.styles["#MathJax_Zoom"].filter},Opera:function(t){h.operaPositionBug=!0,h.operaRefreshBug=!0}}),h.topImg=h.msieInlineBlockAlignBug?e.Element("img",{style:{width:0,height:0,position:"relative"},src:"about:blank"}):e.Element("span",{style:{width:0,height:0,display:"inline-block"}}),(h.operaPositionBug||h.msieTopBug)&&(h.topImg.style.border="1px solid"),MathJax.Callback.Queue(["StartupHook",MathJax.Hub.Register,"Begin Styles",{}],["Styles",a,l.styles],["Post",t.Startup.signal,"MathZoom Ready"],["loadComplete",a,"[MathJax]/extensions/MathZoom.js"])}(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.OutputJax["HTML-CSS"],MathJax.OutputJax.NativeMML),function(t,e,a,i,s){var n="2.7.9",o=MathJax.Callback.Signal("menu");MathJax.Extension.MathMenu={version:n,signal:o};var r,l,h,u=function(t){return MathJax.Localization._.apply(MathJax.Localization,[["MathMenu",t]].concat([].slice.call(arguments,1)))},d=MathJax.Object.isArray,c=t.Browser.isPC,m=t.Browser.isMSIE,p=(document.documentMode||0)>8,M=c?null:"5px",f=t.CombineConfig("MathMenu",{delay:150,showRenderer:!0,showMathPlayer:!0,showFontMenu:!1,showContext:!1,showDiscoverable:!1,showLocale:!0,showLocaleURL:!1,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:c?"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":M,"-webkit-border-radius":M,"-moz-border-radius":M,"-khtml-border-radius":M,"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:c?"2px 2em":"1px 2em",background:"transparent"},".MathJax_MenuArrow":{position:"absolute",right:".5em","padding-top":".25em",color:"#666666","font-family":m?"'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":m?"'Arial unicode MS'":null},".MathJax_MenuCheck.RTL":{right:".7em",left:"auto"},".MathJax_MenuRadioCheck":{position:"absolute",left:c?"1em":".7em"},".MathJax_MenuRadioCheck.RTL":{right:c?"1em":".7em",left:"auto"},".MathJax_MenuLabel":{padding:c?"2px 2em 4px 1.33em":"1px 2em 3px 1.33em","font-style":"italic"},".MathJax_MenuRule":{"border-top":c?"1px solid #CCCCCC":"1px solid #DDDDDD",margin:c?"4px 1px 0px":"4px 3px"},".MathJax_MenuDisabled":{color:"GrayText"},".MathJax_MenuActive":{"background-color":c?"Highlight":"#606872",color:c?"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"}}});t.Register.StartupHook("MathEvents Ready",(function(){r=MathJax.Extension.MathEvents.Event.False,l=MathJax.Extension.MathEvents.Hover,h=MathJax.Extension.MathEvents.Event.KEY}));var g=MathJax.Object.Subclass({Keydown:function(t,e){switch(t.keyCode){case h.ESCAPE:this.Remove(t,e);break;case h.RIGHT:this.Right(t,e);break;case h.LEFT:this.Left(t,e);break;case h.UP:this.Up(t,e);break;case h.DOWN:this.Down(t,e);break;case h.RETURN:case h.SPACE:this.Space(t,e);break;default:return}return r(t)},Escape:function(t,e){},Right:function(t,e){},Left:function(t,e){},Up:function(t,e){},Down:function(t,e){},Space:function(t,e){}},{}),x=MathJax.Menu=g.Subclass({version:n,items:[],posted:!1,title:null,margin:5,Init:function(t){this.items=[].slice.call(arguments,0)},With:function(e){return e&&t.Insert(this,e),this},Post:function(t,a,i){t||(t=window.event||{});var s=document.getElementById("MathJax_MenuFrame");s||(s=x.Background(this),delete v.lastItem,delete v.lastMenu,delete x.skipUp,o.Post(["post",x.jax]),x.isRTL="rtl"===MathJax.Localization.fontDirection());var n=e.Element("div",{onmouseup:x.Mouseup,ondblclick:r,ondragstart:r,onselectstart:r,oncontextmenu:r,menuItem:this,className:"MathJax_Menu",onkeydown:x.Keydown,role:"menu"});"contextmenu"!==t.type&&"mouseover"!==t.type||(n.className+=" MathJax_ContextMenu"),i||MathJax.Localization.setCSS(n);for(var l=0,h=this.items.length;l<h;l++)this.items[l].Create(n);x.isMobile&&e.addElement(n,"span",{className:"MathJax_MenuClose",menu:a,ontouchstart:x.Close,ontouchend:r,onmousedown:x.Close,onmouseup:r},[["span",{},"×"]]),s.appendChild(n),this.posted=!0,n.offsetWidth&&(n.style.width=n.offsetWidth+2+"px");var u=t.pageX,d=t.pageY,m=document.body.getBoundingClientRect(),p=window.getComputedStyle?window.getComputedStyle(document.body):{marginLeft:"0px"},M=m.right-Math.min(0,m.left)+parseFloat(p.marginLeft);if(u||d||!("clientX"in t)||(u=t.clientX+document.body.scrollLeft+document.documentElement.scrollLeft,d=t.clientY+document.body.scrollTop+document.documentElement.scrollTop),a){var g="left",T=a.offsetWidth;for(u=x.isMobile?30:T-2,d=0;a&&a!==s;)u+=a.offsetLeft,d+=a.offsetTop,a=a.parentNode;x.isMobile||(x.isRTL&&u-T-n.offsetWidth>this.margin||!x.isRTL&&u+n.offsetWidth>M-this.margin)&&(g="right",u=Math.max(this.margin,u-T-n.offsetWidth+6)),c||(n.style["borderRadiusTop"+g]=0,n.style["WebkitBorderRadiusTop"+g]=0,n.style["MozBorderRadiusTop"+g]=0,n.style["KhtmlBorderRadiusTop"+g]=0)}else{var E=x.CurrentNode()||t.target;if(("keydown"===t.type||!u&&!d)&&E){var b=window.pageXOffset||document.documentElement.scrollLeft,C=window.pageYOffset||document.documentElement.scrollTop,L=E.getBoundingClientRect();u=(L.right+L.left)/2+b,d=(L.bottom+L.top)/2+C}u+n.offsetWidth>M-this.margin&&(u=M-n.offsetWidth-this.margin),x.isMobile&&(u=Math.max(5,u-Math.floor(n.offsetWidth/2)),d-=20),x.skipUp=t.isContextMenu}n.style.left=u+"px",n.style.top=d+"px",document.selection&&document.selection.empty&&document.selection.empty();var y=window.pageXOffset||document.documentElement.scrollLeft,S=window.pageYOffset||document.documentElement.scrollTop;return x.Focus(n),"keydown"===t.type&&(x.skipMouseoverFromKey=!0,setTimeout((function(){delete x.skipMouseoverFromKey}),f.delay)),window.scrollTo(y,S),r(t)},Remove:function(t,e){o.Post(["unpost",x.jax]);var a=document.getElementById("MathJax_MenuFrame");return a&&(a.parentNode.removeChild(a),this.msieFixedPositionBug&&detachEvent("onresize",x.Resize)),x.jax.hover&&(delete x.jax.hover.nofade,l.UnHover(x.jax)),x.Unfocus(e),"mousedown"===t.type&&x.CurrentNode().blur(),r(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(t,e,a){for(var i=0,s=this.items.length;i<s;i++)if(this.items[i].name[t]===e)return a.length?this.items[i].submenu?this.items[i].submenu.FindN(t,a[0],a.slice(1)):null:this.items[i];return null},IndexOf:function(t){return this.IndexOfN(1,t)},IndexOfId:function(t){return this.IndexOfN(0,t)},IndexOfN:function(t,e){for(var a=0,i=this.items.length;a<i;a++)if(this.items[a].name[t]===e)return a;return null},Right:function(t,e){x.Right(t,e)},Left:function(t,e){x.Left(t,e)},Up:function(t,e){var a=e.lastChild;a.menuItem.Activate(t,a)},Down:function(t,e){var a=e.firstChild;a.menuItem.Activate(t,a)},Space:function(t,e){this.Remove(t,e)}},{config:f,Remove:function(t){return x.Event(t,this,"Remove")},Mouseover:function(t){return x.Event(t,this,"Mouseover")},Mouseout:function(t){return x.Event(t,this,"Mouseout")},Mousedown:function(t){return x.Event(t,this,"Mousedown")},Mouseup:function(t){return x.Event(t,this,"Mouseup")},Keydown:function(t){return x.Event(t,this,"Keydown")},Touchstart:function(t){return x.Event(t,this,"Touchstart")},Touchend:function(t){return x.Event(t,this,"Touchend")},Close:function(t){return x.Event(t,this.menu||this.parentNode,this.menu?"Touchend":"Remove")},Event:function(t,e,a,i){if(x.skipMouseover&&"Mouseover"===a&&!i)return r(t);if(x.skipMouseoverFromKey&&"Mouseover"===a)return delete x.skipMouseoverFromKey,r(t);if(x.skipUp){if(a.match(/Mouseup|Touchend/))return delete x.skipUp,r(t);("Touchstart"===a||"Mousedown"===a&&!x.skipMousedown)&&delete x.skipUp}t||(t=window.event);var s=e.menuItem;return s&&s[a]?s[a](t,e):null},BGSTYLE:{position:"absolute",left:0,top:0,"z-index":200,width:"100%",height:"100%",border:0,padding:0,margin:0},Background:function(t){var a=e.addElement(document.body,"div",{style:this.BGSTYLE,id:"MathJax_MenuFrame"},[["div",{style:this.BGSTYLE,menuItem:t,onmousedown:this.Remove}]]),i=a.firstChild;return x.msieBackgroundBug&&(i.style.backgroundColor="white",i.style.filter="alpha(opacity=0)"),x.msieFixedPositionBug?(a.width=a.height=0,this.Resize(),attachEvent("onresize",this.Resize)):i.style.position="fixed",a},Resize:function(){setTimeout(x.SetWH,0)},SetWH:function(){var t=document.getElementById("MathJax_MenuFrame");t&&((t=t.firstChild).style.width=t.style.height="1px",t.style.width=document.body.scrollWidth+"px",t.style.height=document.body.scrollHeight+"px")},posted:!1,active:null,GetNode:function(t){var e=document.getElementById(t.inputID+"-Frame");return e.isMathJax?e:e.firstChild},CurrentNode:function(){return x.GetNode(x.jax)},AllNodes:function(){for(var t,e=MathJax.Hub.getAllJax(),a=[],i=0;t=e[i];i++)a.push(x.GetNode(t));return a},ActiveNode:function(){return x.active},FocusNode:function(t){x.active=t,t.focus()},Focus:function(t){x.posted?x.ActiveNode().tabIndex=-1:x.Activate(t),t.tabIndex=0,x.FocusNode(t)},Activate:function(t,e){x.UnsetTabIndex(),x.posted=!0},Unfocus:function(){x.ActiveNode().tabIndex=-1,x.SetTabIndex(),x.FocusNode(x.CurrentNode()),x.posted=!1},MoveHorizontal:function(t,e,a){if(t.shiftKey){var i=x.AllNodes(),s=i.length;if(0!==s){var n=i[x.Mod(a(x.IndexOf(i,x.CurrentNode())),s)];n!==x.CurrentNode()&&(x.menu.Remove(t,e),x.jax=MathJax.Hub.getJaxFor(n),x.FocusNode(n),x.menu.Post(null))}}},Right:function(t,e){x.MoveHorizontal(t,e,(function(t){return t+1}))},Left:function(t,e){x.MoveHorizontal(t,e,(function(t){return t-1}))},UnsetTabIndex:function(){for(var t,e=x.AllNodes(),a=0;t=e[a];a++)t.tabIndex>0&&(t.oldTabIndex=t.tabIndex),t.tabIndex=-1},SetTabIndex:function(){for(var e,a=x.AllNodes(),i=0;e=a[i];i++)void 0!==e.oldTabIndex?(e.tabIndex=e.oldTabIndex,delete e.oldTabIndex):e.tabIndex=t.getTabOrder(e)},Mod:function(t,e){return(t%e+e)%e},IndexOf:Array.prototype.indexOf?function(t,e,a){return t.indexOf(e,a)}:function(t,e,a){for(var i=a||0,s=t.length;i<s;i++)if(e===t[i])return i;return-1},saveCookie:function(){e.Cookie.Set("menu",this.cookie)},getCookie:function(){this.cookie=e.Cookie.Get("menu")}});MathJax.Menu.NAV=g;var v=x.ITEM=g.Subclass({name:"",node:null,menu:null,Attributes:function(e){return t.Insert({onmouseup:x.Mouseup,ondragstart:r,onselectstart:r,onselectend:r,ontouchstart:x.Touchstart,ontouchend:x.Touchend,className:"MathJax_MenuItem",role:this.role,menuItem:this},e)},Create:function(t){if(!this.hidden){var a=this.Attributes(),i=this.Label(a,t);e.addElement(t,"div",a,i)}},Name:function(){return u(this.name[0],this.name[1])},Mouseover:function(t,e){e.parentNode===x.ActiveNode().parentNode&&this.Deactivate(x.ActiveNode()),this.Activate(t,e)},Mouseout:function(t,e){this.Deactivate(e)},Mouseup:function(t,e){return this.Remove(t,e)},DeactivateSubmenus:function(t){for(var e=document.getElementById("MathJax_MenuFrame").childNodes,a=v.GetMenuNode(t).childNodes,i=0,s=a.length;i<s;i++){var n=a[i].menuItem;n&&n.submenu&&n.submenu.posted&&n!==t.menuItem&&n.Deactivate(a[i])}this.RemoveSubmenus(t,e)},RemoveSubmenus:function(t,e){for(var a=(e=e||document.getElementById("MathJax_MenuFrame").childNodes).length-1;a>=0&&v.GetMenuNode(t).menuItem!==e[a].menuItem;)e[a].menuItem.posted=!1,e[a].parentNode.removeChild(e[a]),a--},Touchstart:function(t,e){return this.TouchEvent(t,e,"Mousedown")},Touchend:function(t,e){return this.TouchEvent(t,e,"Mouseup")},TouchEvent:function(t,e,a){return this!==v.lastItem&&(v.lastMenu&&x.Event(t,v.lastMenu,"Mouseout"),x.Event(t,e,"Mouseover",!0),v.lastItem=this,v.lastMenu=e),this.nativeTouch?null:(x.Event(t,e,a),!1)},Remove:function(t,e){return(e=e.parentNode.menuItem).Remove(t,e)},With:function(e){return e&&t.Insert(this,e),this},isRTL:function(){return x.isRTL},rtlClass:function(){return this.isRTL()?" RTL":""}},{GetMenuNode:function(t){return t.parentNode}});x.ENTRY=x.ITEM.Subclass({role:"menuitem",Attributes:function(e){return e=t.Insert({onmouseover:x.Mouseover,onmouseout:x.Mouseout,onmousedown:x.Mousedown,onkeydown:x.Keydown,"aria-disabled":!!this.disabled},e),e=this.SUPER(arguments).Attributes.call(this,e),this.disabled&&(e.className+=" MathJax_MenuDisabled"),e},MoveVertical:function(t,e,a){for(var i,s=v.GetMenuNode(e),n=[],o=0,r=s.menuItem.items;i=r[o];o++)i.hidden||n.push(i);var l=x.IndexOf(n,this);if(-1!==l){var h=n.length,u=s.childNodes;do{l=x.Mod(a(l),h)}while(n[l].hidden||!u[l].role||"separator"===u[l].role);this.Deactivate(e),n[l].Activate(t,u[l])}},Up:function(t,e){this.MoveVertical(t,e,(function(t){return t-1}))},Down:function(t,e){this.MoveVertical(t,e,(function(t){return t+1}))},Right:function(t,e){this.MoveHorizontal(t,e,x.Right,!this.isRTL())},Left:function(t,e){this.MoveHorizontal(t,e,x.Left,this.isRTL())},MoveHorizontal:function(t,e,a,i){var s=v.GetMenuNode(e);if(s.menuItem===x.menu&&t.shiftKey&&a(t,e),!i){s.menuItem!==x.menu&&this.Deactivate(e);for(var n=s.previousSibling.childNodes,o=n.length;o--;){var r=n[o];if(r.menuItem.submenu&&r.menuItem.submenu===s.menuItem){x.Focus(r);break}}this.RemoveSubmenus(e)}},Space:function(t,e){this.Mouseup(t,e)},Activate:function(t,e){this.Deactivate(e),this.disabled||(e.className+=" MathJax_MenuActive"),this.DeactivateSubmenus(e),x.Focus(e)},Deactivate:function(t){t.className=t.className.replace(/ MathJax_MenuActive/,"")}}),x.ITEM.COMMAND=x.ENTRY.Subclass({action:function(){},Init:function(t,e,a){d(t)||(t=[t,t]),this.name=t,this.action=e,this.With(a)},Label:function(t,e){return[this.Name()]},Mouseup:function(t,e){return this.disabled||(this.Remove(t,e),o.Post(["command",this]),this.action.call(this,t)),r(t)}}),x.ITEM.SUBMENU=x.ENTRY.Subclass({submenu:null,marker:"►",markerRTL:"◄",Attributes:function(e){return e=t.Insert({"aria-haspopup":"true"},e),this.SUPER(arguments).Attributes.call(this,e)},Init:function(t,e){d(t)||(t=[t,t]),this.name=t;var a=1;e instanceof x.ITEM||(this.With(e),a++),this.submenu=x.apply(x,[].slice.call(arguments,a))},Label:function(t,e){return this.submenu.posted=!1,[this.Name()+" ",["span",{className:"MathJax_MenuArrow"+this.rtlClass()},[this.isRTL()?this.markerRTL:this.marker]]]},Timer:function(t,e){this.ClearTimer(),t={type:t.type,clientX:t.clientX,clientY:t.clientY},this.timer=setTimeout(i(["Mouseup",this,t,e]),f.delay)},ClearTimer:function(){this.timer&&clearTimeout(this.timer)},Touchend:function(t,e){var a=this.submenu.posted,i=this.SUPER(arguments).Touchend.apply(this,arguments);return a&&(this.Deactivate(e),delete v.lastItem,delete v.lastMenu),i},Mouseout:function(t,e){this.submenu.posted||this.Deactivate(e),this.ClearTimer()},Mouseover:function(t,e){this.Activate(t,e)},Mouseup:function(t,e){return this.disabled||(this.submenu.posted?this.DeactivateSubmenus(e):(this.ClearTimer(),this.submenu.Post(t,e,this.ltr),x.Focus(e))),r(t)},Activate:function(t,e){this.disabled||(this.Deactivate(e),e.className+=" MathJax_MenuActive"),this.submenu.posted||(this.DeactivateSubmenus(e),x.isMobile||this.Timer(t,e)),x.Focus(e)},MoveVertical:function(t,e,a){this.ClearTimer(),this.SUPER(arguments).MoveVertical.apply(this,arguments)},MoveHorizontal:function(t,e,a,i){if(i){if(!this.disabled)if(this.submenu.posted){var s=v.GetMenuNode(e).nextSibling.childNodes;s.length>0&&this.submenu.items[0].Activate(t,s[0])}else this.Activate(t,e)}else this.SUPER(arguments).MoveHorizontal.apply(this,arguments)}}),x.ITEM.RADIO=x.ENTRY.Subclass({variable:null,marker:c?"●":"✓",role:"menuitemradio",Attributes:function(e){var a=f.settings[this.variable]===this.value?"true":"false";return e=t.Insert({"aria-checked":a},e),this.SUPER(arguments).Attributes.call(this,e)},Init:function(t,e,a){d(t)||(t=[t,t]),this.name=t,this.variable=e,this.With(a),null==this.value&&(this.value=this.name[0])},Label:function(t,e){var a={className:"MathJax_MenuRadioCheck"+this.rtlClass()};return f.settings[this.variable]!==this.value&&(a={style:{display:"none"}}),[["span",a,[this.marker]]," "+this.Name()]},Mouseup:function(t,e){if(!this.disabled){for(var a=e.parentNode.childNodes,i=0,s=a.length;i<s;i++){var n=a[i].menuItem;n&&n.variable===this.variable&&(a[i].firstChild.style.display="none")}e.firstChild.display="",f.settings[this.variable]=this.value,x.cookie[this.variable]=f.settings[this.variable],x.saveCookie(),o.Post(["radio button",this])}return this.Remove(t,e),this.action&&!this.disabled&&this.action.call(x,this),r(t)}}),x.ITEM.CHECKBOX=x.ENTRY.Subclass({variable:null,marker:"✓",role:"menuitemcheckbox",Attributes:function(e){var a=f.settings[this.variable]?"true":"false";return e=t.Insert({"aria-checked":a},e),this.SUPER(arguments).Attributes.call(this,e)},Init:function(t,e,a){d(t)||(t=[t,t]),this.name=t,this.variable=e,this.With(a)},Label:function(t,e){var a={className:"MathJax_MenuCheck"+this.rtlClass()};return f.settings[this.variable]||(a={style:{display:"none"}}),[["span",a,[this.marker]]," "+this.Name()]},Mouseup:function(t,e){return this.disabled||(e.firstChild.display=f.settings[this.variable]?"none":"",f.settings[this.variable]=!f.settings[this.variable],x.cookie[this.variable]=f.settings[this.variable],x.saveCookie(),o.Post(["checkbox",this])),this.Remove(t,e),this.action&&!this.disabled&&this.action.call(x,this),r(t)}}),x.ITEM.LABEL=x.ENTRY.Subclass({role:"menuitem",Init:function(t,e){d(t)||(t=[t,t]),this.name=t,this.With(e)},Label:function(t,e){return t.className+=" MathJax_MenuLabel",[this.Name()]},Activate:function(t,e){this.Deactivate(e),x.Focus(e)},Mouseup:function(t,e){}}),x.ITEM.RULE=x.ITEM.Subclass({role:"separator",Attributes:function(e){return e=t.Insert({"aria-orientation":"vertical"},e),this.SUPER(arguments).Attributes.call(this,e)},Label:function(t,e){return t.className+=" MathJax_MenuRule",null}}),x.About=function(a){var i=x.About.GetFont(),s=x.About.GetFormat(),n=["MathJax.js v"+MathJax.fileversion,["br"]];n.push(["div",{style:{"border-top":"groove 2px",margin:".25em 0"}}]),x.About.GetJax(n,MathJax.InputJax,["InputJax","%1 Input Jax v%2"]),x.About.GetJax(n,MathJax.OutputJax,["OutputJax","%1 Output Jax v%2"]),x.About.GetJax(n,MathJax.ElementJax,["ElementJax","%1 Element Jax v%2"]),n.push(["div",{style:{"border-top":"groove 2px",margin:".25em 0"}}]),x.About.GetJax(n,MathJax.Extension,["Extension","%1 Extension v%2"],!0),n.push(["div",{style:{"border-top":"groove 2px",margin:".25em 0"}}],["center",{},[t.Browser+" v"+t.Browser.version+(s?" — "+u(s.replace(/ /g,""),s):"")]]),x.About.div=x.Background(x.About);var o=e.addElement(x.About.div,"div",{id:"MathJax_About",tabIndex:0,onkeydown:x.About.Keydown},[["b",{style:{fontSize:"120%"}},["MathJax"]]," v"+MathJax.version,["br"],u(i.replace(/ /g,""),"using "+i),["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},n],["br"],["br"],["a",{href:"http://www.mathjax.org/"},["www.mathjax.org"]],["span",{className:"MathJax_MenuClose",id:"MathJax_AboutClose",onclick:x.About.Remove,onkeydown:x.About.Keydown,tabIndex:0,role:"button","aria-label":u("CloseAboutDialog","Close about MathJax dialog")},[["span",{},"×"]]]]);"mouseup"===a.type&&(o.className+=" MathJax_MousePost"),o.focus(),MathJax.Localization.setCSS(o);var r=document.documentElement||{},l=window.innerHeight||r.clientHeight||r.scrollHeight||0;x.prototype.msieAboutBug?(o.style.width="20em",o.style.position="absolute",o.style.left=Math.floor((document.documentElement.scrollWidth-o.offsetWidth)/2)+"px",o.style.top=Math.floor((l-o.offsetHeight)/3)+document.body.scrollTop+"px"):(o.style.marginLeft=Math.floor(-o.offsetWidth/2)+"px",o.style.top=Math.floor((l-o.offsetHeight)/3)+"px")},x.About.Remove=function(t){x.About.div&&(document.body.removeChild(x.About.div),delete x.About.div)},x.About.Keydown=function(t){t.keyCode!==h.ESCAPE&&("MathJax_AboutClose"!==this.id||t.keyCode!==h.SPACE&&t.keyCode!==h.RETURN)||(x.About.Remove(t),x.CurrentNode().focus(),r(t))},x.About.GetJax=function(t,e,a,i){var s=[];for(var n in e)e.hasOwnProperty(n)&&e[n]&&(i&&e[n].version||e[n].isa&&e[n].isa(e))&&s.push(u(a[0],a[1],e[n].id||n,e[n].version));s.sort();for(var o=0,r=s.length;o<r;o++)t.push(s[o],["br"]);return t},x.About.GetFont=function(){var t=MathJax.Hub.outputJax["jax/mml"][0]||{};return({SVG:"web SVG",CommonHTML:"web TeX","HTML-CSS":t.imgFonts?"image":(t.webFonts?"web":"local")+" "+t.fontInUse}[t.id]||"generic")+" fonts"},x.About.GetFormat=function(){var t=MathJax.Hub.outputJax["jax/mml"][0]||{};if("HTML-CSS"===t.id&&t.webFonts&&!t.imgFonts)return t.allowWebFonts.replace(/otf/,"woff or otf")+" fonts"},x.Help=function(t){a.Require("[MathJax]/extensions/HelpDialog.js",(function(){MathJax.Extension.Help.Dialog({type:t.type})}))},x.ShowSource=function(t){t||(t=window.event);var e={screenX:t.screenX,screenY:t.screenY};if(x.jax)if("MathML"===this.format){var s=MathJax.ElementJax.mml;if(s&&void 0!==s.mbase.prototype.toMathML)try{x.ShowSource.Text(x.jax.root.toMathML("",x.jax),t)}catch(t){if(!t.restart)throw t;i.After([this,x.ShowSource,e],t.restart)}else if(!a.loadingToMathML)return a.loadingToMathML=!0,x.ShowSource.Window(t),void i.Queue(a.Require("[MathJax]/extensions/toMathML.js"),(function(){delete a.loadingToMathML,s.mbase.prototype.toMathML||(s.mbase.prototype.toMathML=function(){})}),[this,x.ShowSource,e])}else if("Error"===this.format)x.ShowSource.Text(x.jax.errorText,t);else if(f.semanticsAnnotations[this.format]){var n=x.jax.root.getAnnotation(this.format);n.data[0]&&x.ShowSource.Text(n.data[0].toString())}else{if(null==x.jax.originalText)return void alert(u("NoOriginalForm","No original form available"));x.ShowSource.Text(x.jax.originalText,t)}},x.ShowSource.Window=function(t){if(!x.ShowSource.w){var e=[],a=f.windowSettings;for(var i in a)a.hasOwnProperty(i)&&e.push(i+"="+a[i]);x.ShowSource.w=window.open("","_blank",e.join(","))}return x.ShowSource.w},x.ShowSource.Text=function(t,e){var a=x.ShowSource.Window(e);delete x.ShowSource.w,t=(t=t.replace(/^\s*/,"").replace(/\s*$/,"")).replace(/&/g,"&amp;").replace(/</g,"&lt;").replace(/>/g,"&gt;");var i=u("EqSource","MathJax Equation Source");if(x.isMobile)a.document.open(),a.document.write("<html><head><meta name='viewport' content='width=device-width, initial-scale=1.0' /><title>"+i+"</title></head><body style='font-size:85%'>"),a.document.write("<pre>"+t+"</pre>"),a.document.write("<hr><input type='button' value='"+u("Close","Close")+"' onclick='window.close()' />"),a.document.write("</body></html>"),a.document.close();else{a.document.open(),a.document.write("<html><head><title>"+i+"</title></head><body style='font-size:85%'>"),a.document.write("<table><tr><td><pre>"+t+"</pre></td></tr></table>"),a.document.write("</body></html>"),a.document.close();var s=a.document.body.firstChild;setTimeout((function(){var t,i,n,o=a.outerHeight-a.innerHeight||30,r=a.outerWidth-a.innerWidth||30;r=Math.max(140,Math.min(Math.floor(.5*screen.width),s.offsetWidth+r+25)),o=Math.max(40,Math.min(Math.floor(.5*screen.height),s.offsetHeight+o+25)),x.prototype.msieHeightBug&&(o+=35),a.resizeTo(r,o);try{n=e.screenX}catch(t){}e&&null!=n&&(t=Math.max(0,Math.min(e.screenX-Math.floor(r/2),screen.width-r-20)),i=Math.max(0,Math.min(e.screenY-Math.floor(o/2),screen.height-o-20)),a.moveTo(t,i))}),50)}},x.Scale=function(){var e,a,i=["CommonHTML","HTML-CSS","SVG","NativeMML","PreviewHTML"],n=i.length,o=100;for(e=0;e<n;e++)if(a=s[i[e]]){o=a.config.scale;break}var r=prompt(u("ScaleMath","Scale all mathematics (compared to surrounding text) by"),o+"%");if(r)if(r.match(/^\s*\d+(\.\d*)?\s*%?\s*$/))if(r=parseFloat(r)){if(r!==o){for(e=0;e<n;e++)(a=s[i[e]])&&(a.config.scale=r);x.cookie.scale=t.config.scale=r,x.saveCookie(),t.Queue(["Rerender",t])}}else alert(u("NonZeroScale","The scale should not be zero"));else alert(u("PercentScale","The scale should be a percentage (e.g., 120%%)"))},x.Zoom=function(){MathJax.Extension.MathZoom||a.Require("[MathJax]/extensions/MathZoom.js")},x.Renderer=function(){var a=t.outputJax["jax/mml"];if(a[0]!==f.settings.renderer){var i,s,n=t.Browser,o=x.Renderer.Messages;switch(f.settings.renderer){case"NativeMML":f.settings.warnedMML||(n.isChrome&&"24."!==n.version.substr(0,3)||n.isSafari&&!n.versionAtLeast("5.0")?i=o.MML.WebKit:n.isMSIE?n.hasMathPlayer||(i=o.MML.MSIE):i=n.isEdge?o.MML.WebKit:o.MML[n],s="warnedMML");break;case"SVG":f.settings.warnedSVG||n.isMSIE&&!p&&(i=o.SVG.MSIE)}if(i){if(i=u(i[0],i[1]),i+="\n\n",i+=u("SwitchAnyway","Switch the renderer anyway?\n\n(Press OK to switch, CANCEL to continue with the current renderer)"),x.cookie.renderer=a[0].id,x.saveCookie(),!confirm(i))return x.cookie.renderer=f.settings.renderer=e.Cookie.Get("menu").renderer,void x.saveCookie();s&&(x.cookie.warned=f.settings.warned=!0),x.cookie.renderer=f.settings.renderer,x.saveCookie()}t.Queue(["setRenderer",t,f.settings.renderer,"jax/mml"],["Rerender",t])}},x.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."]}},x.AssistiveMML=function(t,e){var i=MathJax.Extension.AssistiveMML;i?MathJax.Hub.Queue([(f.settings.assistiveMML?"Add":"Remove")+"AssistiveMathML",i]):e||a.Require("[MathJax]/extensions/AssistiveMML.js",["AssistiveMML",x,t,!0])},x.Font=function(){s["HTML-CSS"]&&document.location.reload()},x.Locale=function(){MathJax.Localization.setLocale(f.settings.locale),MathJax.Hub.Queue(["Reprocess",MathJax.Hub])},x.LoadLocale=function(){var t=prompt(u("LoadURL","Load translation data from this URL:"));t&&(t.match(/\.js$/)||alert(u("BadURL","The URL should be for a javascript file that defines MathJax translation data.  Javascript file names should end with '.js'")),a.Require(t,(function(e){e!=a.STATUS.OK&&alert(u("BadData","Failed to load translation data from %1",t))})))},x.MPEvents=function(t){var e=f.settings.discoverable,a=x.MPEvents.Messages;if(p)!e&&"Menu Events"===t.name[1]&&f.settings.mpContext&&alert(u.apply(u,a.IE9warning));else{if(f.settings.mpMouse&&!confirm(u.apply(u,a.IE8warning)))return delete x.cookie.mpContext,delete f.settings.mpContext,delete x.cookie.mpMouse,delete f.settings.mpMouse,void x.saveCookie();f.settings.mpContext=f.settings.mpMouse,x.cookie.mpContext=x.cookie.mpMouse=f.settings.mpMouse,x.saveCookie(),MathJax.Hub.Queue(["Rerender",MathJax.Hub])}},x.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."]},t.Browser.Select({MSIE:function(t){var e="BackCompat"===document.compatMode,a=t.versionAtLeast("8.0")&&document.documentMode>7;x.Augment({margin:20,msieBackgroundBug:(document.documentMode||0)<9,msieFixedPositionBug:e||!a,msieAboutBug:e,msieHeightBug:(document.documentMode||0)<9}),p&&(delete f.styles["#MathJax_About"].filter,delete f.styles[".MathJax_Menu"].filter)},Firefox:function(t){x.skipMouseover=t.isMobile&&t.versionAtLeast("6.0"),x.skipMousedown=t.isMobile}}),x.isMobile=t.Browser.isMobile,x.noContextMenu=t.Browser.noContextMenu,x.CreateLocaleMenu=function(){if(x.menu){var t=x.menu.Find("Language").submenu,e=t.items,a=[],i=MathJax.Localization.strings;for(var s in i)i.hasOwnProperty(s)&&a.push(s);a=a.sort(),t.items=[];for(var n=0,o=a.length;n<o;n++){var r=i[a[n]].menuTitle;r?r+=" ("+a[n]+")":r=a[n],t.items.push(v.RADIO([a[n],r],"locale",{action:x.Locale}))}t.items.push(e[e.length-2],e[e.length-1])}},x.CreateAnnotationMenu=function(){if(x.menu){var t=x.menu.Find("Show Math As","Annotation").submenu,e=f.semanticsAnnotations;for(var a in e)e.hasOwnProperty(a)&&t.items.push(v.COMMAND([a,a],x.ShowSource,{hidden:!0,nativeTouch:!0,format:a}))}},t.Register.StartupHook("End Config",(function(){var e,a;f.settings=t.config.menuSettings,void 0!==f.settings.showRenderer&&(f.showRenderer=f.settings.showRenderer),void 0!==f.settings.showFontMenu&&(f.showFontMenu=f.settings.showFontMenu),void 0!==f.settings.showContext&&(f.showContext=f.settings.showContext),x.getCookie(),x.menu=x(v.SUBMENU(["Show","Show Math As"],v.COMMAND(["MathMLcode","MathML Code"],x.ShowSource,{nativeTouch:!0,format:"MathML"}),v.COMMAND(["Original","Original Form"],x.ShowSource,{nativeTouch:!0}),v.SUBMENU(["Annotation","Annotation"],{disabled:!0}),v.RULE(),v.CHECKBOX(["texHints","Show TeX hints in MathML"],"texHints"),v.CHECKBOX(["semantics","Add original form as annotation"],"semantics")),v.RULE(),v.SUBMENU(["Settings","Math Settings"],v.SUBMENU(["ZoomTrigger","Zoom Trigger"],v.RADIO(["Hover","Hover"],"zoom",{action:x.Zoom}),v.RADIO(["Click","Click"],"zoom",{action:x.Zoom}),v.RADIO(["DoubleClick","Double-Click"],"zoom",{action:x.Zoom}),v.RADIO(["NoZoom","No Zoom"],"zoom",{value:"None"}),v.RULE(),v.LABEL(["TriggerRequires","Trigger Requires:"]),v.CHECKBOX(t.Browser.isMac?["Option","Option"]:["Alt","Alt"],"ALT"),v.CHECKBOX(["Command","Command"],"CMD",{hidden:!t.Browser.isMac}),v.CHECKBOX(["Control","Control"],"CTRL",{hidden:t.Browser.isMac}),v.CHECKBOX(["Shift","Shift"],"Shift")),v.SUBMENU(["ZoomFactor","Zoom Factor"],v.RADIO("125%","zscale"),v.RADIO("133%","zscale"),v.RADIO("150%","zscale"),v.RADIO("175%","zscale"),v.RADIO("200%","zscale"),v.RADIO("250%","zscale"),v.RADIO("300%","zscale"),v.RADIO("400%","zscale")),v.RULE(),v.SUBMENU(["Renderer","Math Renderer"],{hidden:!f.showRenderer},v.RADIO(["HTML-CSS","HTML-CSS"],"renderer",{action:x.Renderer}),v.RADIO(["CommonHTML","Common HTML"],"renderer",{action:x.Renderer,value:"CommonHTML"}),v.RADIO(["PreviewHTML","Preview HTML"],"renderer",{action:x.Renderer,value:"PreviewHTML"}),v.RADIO(["MathML","MathML"],"renderer",{action:x.Renderer,value:"NativeMML"}),v.RADIO(["SVG","SVG"],"renderer",{action:x.Renderer}),v.RADIO(["PlainSource","Plain Source"],"renderer",{action:x.Renderer,value:"PlainSource"}),v.RULE(),v.CHECKBOX(["FastPreview","Fast Preview"],"FastPreview")),v.SUBMENU("MathPlayer",{hidden:!t.Browser.isMSIE||!f.showMathPlayer,disabled:!t.Browser.hasMathPlayer},v.LABEL(["MPHandles","Let MathPlayer Handle:"]),v.CHECKBOX(["MenuEvents","Menu Events"],"mpContext",{action:x.MPEvents,hidden:!p}),v.CHECKBOX(["MouseEvents","Mouse Events"],"mpMouse",{action:x.MPEvents,hidden:!p}),v.CHECKBOX(["MenuAndMouse","Mouse and Menu Events"],"mpMouse",{action:x.MPEvents,hidden:p})),v.SUBMENU(["FontPrefs","Font Preference"],{hidden:!f.showFontMenu},v.LABEL(["ForHTMLCSS","For HTML-CSS:"]),v.RADIO(["Auto","Auto"],"font",{action:x.Font}),v.RULE(),v.RADIO(["TeXLocal","TeX (local)"],"font",{action:x.Font}),v.RADIO(["TeXWeb","TeX (web)"],"font",{action:x.Font}),v.RADIO(["TeXImage","TeX (image)"],"font",{action:x.Font}),v.RULE(),v.RADIO(["STIXLocal","STIX (local)"],"font",{action:x.Font}),v.RADIO(["STIXWeb","STIX (web)"],"font",{action:x.Font}),v.RULE(),v.RADIO(["AsanaMathWeb","Asana Math (web)"],"font",{action:x.Font}),v.RADIO(["GyrePagellaWeb","Gyre Pagella (web)"],"font",{action:x.Font}),v.RADIO(["GyreTermesWeb","Gyre Termes (web)"],"font",{action:x.Font}),v.RADIO(["LatinModernWeb","Latin Modern (web)"],"font",{action:x.Font}),v.RADIO(["NeoEulerWeb","Neo Euler (web)"],"font",{action:x.Font})),v.SUBMENU(["ContextMenu","Contextual Menu"],{hidden:!f.showContext},v.RADIO(["MathJax","MathJax"],"context"),v.RADIO(["Browser","Browser"],"context")),v.COMMAND(["Scale","Scale All Math ..."],x.Scale),v.RULE().With({hidden:!f.showDiscoverable,name:["","discover_rule"]}),v.CHECKBOX(["Discoverable","Highlight on Hover"],"discoverable",{hidden:!f.showDiscoverable})),v.SUBMENU(["Accessibility","Accessibility"],v.CHECKBOX(["AssistiveMML","Assistive MathML"],"assistiveMML",{action:x.AssistiveMML}),v.CHECKBOX(["InTabOrder","Include in Tab Order"],"inTabOrder")),v.SUBMENU(["Locale","Language"],{hidden:!f.showLocale,ltr:!0},v.RADIO("en","locale",{action:x.Locale}),v.RULE().With({hidden:!f.showLocaleURL,name:["","localURL_rule"]}),v.COMMAND(["LoadLocale","Load from URL ..."],x.LoadLocale,{hidden:!f.showLocaleURL})),v.RULE(),v.COMMAND(["About","About MathJax"],x.About),v.COMMAND(["Help","MathJax Help"],x.Help)),x.isMobile&&(e=f.settings,(a=x.menu.Find("Math Settings","Zoom Trigger").submenu).items[0].disabled=a.items[1].disabled=!0,"Hover"!==e.zoom&&"Click"!=e.zoom||(e.zoom="None"),a.items=a.items.slice(0,4),navigator.appVersion.match(/[ (]Android[) ]/)&&x.ITEM.SUBMENU.Augment({marker:"»"})),x.CreateLocaleMenu(),x.CreateAnnotationMenu()})),x.showRenderer=function(t){x.cookie.showRenderer=f.showRenderer=t,x.saveCookie(),x.menu.Find("Math Settings","Math Renderer").hidden=!t},x.showMathPlayer=function(t){x.cookie.showMathPlayer=f.showMathPlayer=t,x.saveCookie(),x.menu.Find("Math Settings","MathPlayer").hidden=!t},x.showFontMenu=function(t){x.cookie.showFontMenu=f.showFontMenu=t,x.saveCookie(),x.menu.Find("Math Settings","Font Preference").hidden=!t},x.showContext=function(t){x.cookie.showContext=f.showContext=t,x.saveCookie(),x.menu.Find("Math Settings","Contextual Menu").hidden=!t},x.showDiscoverable=function(t){x.cookie.showDiscoverable=f.showDiscoverable=t,x.saveCookie(),x.menu.Find("Math Settings","Highlight on Hover").hidden=!t,x.menu.Find("Math Settings","discover_rule").hidden=!t},x.showLocale=function(t){x.cookie.showLocale=f.showLocale=t,x.saveCookie(),x.menu.Find("Language").hidden=!t},MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",(function(){MathJax.OutputJax["HTML-CSS"].config.imageFont||(x.menu.Find("Math Settings","Font Preference","TeX (image)").disabled=!0)})),i.Queue(t.Register.StartupHook("End Config",{}),["Styles",a,f.styles],["Post",t.Startup.signal,"MathMenu Ready"],["loadComplete",a,"[MathJax]/extensions/MathMenu.js"])}(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.CallBack,MathJax.OutputJax),MathJax.ElementJax.mml=MathJax.ElementJax({mimeType:"jax/mml"},{id:"mml",version:"2.7.9",directory:MathJax.ElementJax.directory+"/mml",extensionDir:MathJax.ElementJax.extensionDir+"/mml",optableDir:MathJax.ElementJax.directory+"/mml/optable"}),MathJax.ElementJax.mml.Augment({Init:function(){if(1===arguments.length&&"math"===arguments[0].type?this.root=arguments[0]:this.root=MathJax.ElementJax.mml.math.apply(this,arguments),this.root.attr&&this.root.attr.mode){this.root.display||"display"!==this.root.attr.mode||(this.root.display="block",this.root.attrNames.push("display")),delete this.root.attr.mode;for(var t=0,e=this.root.attrNames.length;t<e;t++)if("mode"===this.root.attrNames[t]){this.root.attrNames.splice(t,1);break}}}},{INHERIT:"_inherit_",AUTO:"_auto_",SIZE:{INFINITY:"infinity",SMALL:"small",NORMAL:"normal",BIG:"big"},COLOR:{TRANSPARENT:"transparent"},VARIANT:{NORMAL:"normal",BOLD:"bold",ITALIC:"italic",BOLDITALIC:"bold-italic",DOUBLESTRUCK:"double-struck",FRAKTUR:"fraktur",BOLDFRAKTUR:"bold-fraktur",SCRIPT:"script",BOLDSCRIPT:"bold-script",SANSSERIF:"sans-serif",BOLDSANSSERIF:"bold-sans-serif",SANSSERIFITALIC:"sans-serif-italic",SANSSERIFBOLDITALIC:"sans-serif-bold-italic",MONOSPACE:"monospace",INITIAL:"initial",TAILED:"tailed",LOOPED:"looped",STRETCHED:"stretched",CALIGRAPHIC:"-tex-caligraphic",OLDSTYLE:"-tex-oldstyle"},FORM:{PREFIX:"prefix",INFIX:"infix",POSTFIX:"postfix"},LINEBREAK:{AUTO:"auto",NEWLINE:"newline",NOBREAK:"nobreak",GOODBREAK:"goodbreak",BADBREAK:"badbreak"},LINEBREAKSTYLE:{BEFORE:"before",AFTER:"after",DUPLICATE:"duplicate",INFIXLINBREAKSTYLE:"infixlinebreakstyle"},INDENTALIGN:{LEFT:"left",CENTER:"center",RIGHT:"right",AUTO:"auto",ID:"id",INDENTALIGN:"indentalign"},INDENTSHIFT:{INDENTSHIFT:"indentshift"},LINETHICKNESS:{THIN:"thin",MEDIUM:"medium",THICK:"thick"},NOTATION:{LONGDIV:"longdiv",ACTUARIAL:"actuarial",RADICAL:"radical",BOX:"box",ROUNDEDBOX:"roundedbox",CIRCLE:"circle",LEFT:"left",RIGHT:"right",TOP:"top",BOTTOM:"bottom",UPDIAGONALSTRIKE:"updiagonalstrike",DOWNDIAGONALSTRIKE:"downdiagonalstrike",UPDIAGONALARROW:"updiagonalarrow",VERTICALSTRIKE:"verticalstrike",HORIZONTALSTRIKE:"horizontalstrike",PHASORANGLE:"phasorangle",MADRUWB:"madruwb"},ALIGN:{TOP:"top",BOTTOM:"bottom",CENTER:"center",BASELINE:"baseline",AXIS:"axis",LEFT:"left",RIGHT:"right"},LINES:{NONE:"none",SOLID:"solid",DASHED:"dashed"},SIDE:{LEFT:"left",RIGHT:"right",LEFTOVERLAP:"leftoverlap",RIGHTOVERLAP:"rightoverlap"},WIDTH:{AUTO:"auto",FIT:"fit"},ACTIONTYPE:{TOGGLE:"toggle",STATUSLINE:"statusline",TOOLTIP:"tooltip",INPUT:"input"},LENGTH:{VERYVERYTHINMATHSPACE:"veryverythinmathspace",VERYTHINMATHSPACE:"verythinmathspace",THINMATHSPACE:"thinmathspace",MEDIUMMATHSPACE:"mediummathspace",THICKMATHSPACE:"thickmathspace",VERYTHICKMATHSPACE:"verythickmathspace",VERYVERYTHICKMATHSPACE:"veryverythickmathspace",NEGATIVEVERYVERYTHINMATHSPACE:"negativeveryverythinmathspace",NEGATIVEVERYTHINMATHSPACE:"negativeverythinmathspace",NEGATIVETHINMATHSPACE:"negativethinmathspace",NEGATIVEMEDIUMMATHSPACE:"negativemediummathspace",NEGATIVETHICKMATHSPACE:"negativethickmathspace",NEGATIVEVERYTHICKMATHSPACE:"negativeverythickmathspace",NEGATIVEVERYVERYTHICKMATHSPACE:"negativeveryverythickmathspace"},OVERFLOW:{LINBREAK:"linebreak",SCROLL:"scroll",ELIDE:"elide",TRUNCATE:"truncate",SCALE:"scale"},UNIT:{EM:"em",EX:"ex",PX:"px",IN:"in",CM:"cm",MM:"mm",PT:"pt",PC:"pc"},TEXCLASS:{ORD:0,OP:1,BIN:2,REL:3,OPEN:4,CLOSE:5,PUNCT:6,INNER:7,VCENTER:8,NONE:-1},TEXCLASSNAMES:["ORD","OP","BIN","REL","OPEN","CLOSE","PUNCT","INNER","VCENTER"],skipAttributes:{texClass:!0,useHeight:!0,texprimestyle:!0},copyAttributes:{displaystyle:1,scriptlevel:1,open:1,close:1,form:1,actiontype:1,fontfamily:!0,fontsize:!0,fontweight:!0,fontstyle:!0,color:!0,background:!0,id:!0,class:1,href:!0,style:!0},copyAttributeNames:["displaystyle","scriptlevel","open","close","form","actiontype","fontfamily","fontsize","fontweight","fontstyle","color","background","id","class","href","style"],nocopyAttributes:{fontfamily:!0,fontsize:!0,fontweight:!0,fontstyle:!0,color:!0,background:!0,id:!0,class:!0,href:!0,style:!0,xmlns:!0},Error:function(t,e){var a=this.merror(t),i=MathJax.Localization.fontDirection(),s=MathJax.Localization.fontFamily();return e&&(a=a.With(e)),(i||s)&&(a=this.mstyle(a),i&&(a.dir=i),s&&(a.style.fontFamily="font-family: "+s)),a}}),function(t){t.mbase=MathJax.Object.Subclass({type:"base",isToken:!1,defaults:{mathbackground:t.INHERIT,mathcolor:t.INHERIT,dir:t.INHERIT},noInherit:{},noInheritAttribute:{texClass:!0},getRemoved:{},linebreakContainer:!1,Init:function(){this.data=[],!this.inferRow||1===arguments.length&&arguments[0].inferred||this.Append(t.mrow().With({inferred:!0,notParent:!0})),this.Append.apply(this,arguments)},With:function(t){for(var e in t)t.hasOwnProperty(e)&&(this[e]=t[e]);return this},Append:function(){if(this.inferRow&&this.data.length)this.data[0].Append.apply(this.data[0],arguments);else for(var t=0,e=arguments.length;t<e;t++)this.SetData(this.data.length,arguments[t])},SetData:function(e,a){null!=a&&(a instanceof t.mbase||(a=this.isToken||this.isChars?t.chars(a):t.mtext(a)),a.parent=this,a.setInherit(this.inheritFromMe?this:this.inherit)),this.data[e]=a},Parent:function(){for(var t=this.parent;t&&t.notParent;)t=t.parent;return t},Get:function(e,a,i){if(!i){if(null!=this[e])return this[e];if(this.attr&&null!=this.attr[e])return this.attr[e]}var s=this.Parent();if(s&&null!=s["adjustChild_"+e])return s["adjustChild_"+e](this.childPosition(),a);for(var n=this.inherit,o=n;n;){var r=n[e];if(null==r&&n.attr&&(r=n.attr[e]),n.removedStyles&&n.getRemoved[e]&&null==r&&(r=n.removedStyles[n.getRemoved[e]]),null!=r&&n.noInheritAttribute&&!n.noInheritAttribute[e]){var l=n.noInherit[this.type];if(!l||!l[e])return r}o=n,n=n.inherit}if(!a){if(this.defaults[e]===t.AUTO)return this.autoDefault(e);if(this.defaults[e]!==t.INHERIT&&null!=this.defaults[e])return this.defaults[e];if(o)return o.defaults[e]}return null},hasValue:function(t){return null!=this.Get(t,!0)},getValues:function(){for(var t={},e=0,a=arguments.length;e<a;e++)t[arguments[e]]=this.Get(arguments[e]);return t},adjustChild_scriptlevel:function(t,e){return this.Get("scriptlevel",e)},adjustChild_displaystyle:function(t,e){return this.Get("displaystyle",e)},adjustChild_texprimestyle:function(t,e){return this.Get("texprimestyle",e)},hasMMLspacing:function(){return!1},childPosition:function(){for(var t=this,e=t.parent;e.notParent;)e=(t=e).parent;for(var a=0,i=e.data.length;a<i;a++)if(e.data[a]===t)return a;return null},setInherit:function(t){if(t!==this.inherit&&null==this.inherit){this.inherit=t;for(var e=0,a=this.data.length;e<a;e++)this.data[e]&&this.data[e].setInherit&&this.data[e].setInherit(t)}},setTeXclass:function(t){return this.getPrevClass(t),void 0!==this.texClass?this:t},getPrevClass:function(t){t&&(this.prevClass=t.Get("texClass"),this.prevLevel=t.Get("scriptlevel"))},updateTeXclass:function(t){t&&(this.prevClass=t.prevClass,delete t.prevClass,this.prevLevel=t.prevLevel,delete t.prevLevel,this.texClass=t.Get("texClass"))},texSpacing:function(){var e=null!=this.prevClass?this.prevClass:t.TEXCLASS.NONE,a=this.Get("texClass")||t.TEXCLASS.ORD;if(e===t.TEXCLASS.NONE||a===t.TEXCLASS.NONE)return"";e===t.TEXCLASS.VCENTER&&(e=t.TEXCLASS.ORD),a===t.TEXCLASS.VCENTER&&(a=t.TEXCLASS.ORD);var i=this.TEXSPACE[e][a];return(this.prevLevel>0||this.Get("scriptlevel")>0)&&i>=0?"":this.TEXSPACELENGTH[Math.abs(i)]},TEXSPACELENGTH:["",t.LENGTH.THINMATHSPACE,t.LENGTH.MEDIUMMATHSPACE,t.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(t){return""},isSpacelike:function(){return!1},isEmbellished:function(){return!1},Core:function(){return this},CoreMO:function(){return this},childIndex:function(t){if(null!=t)for(var e=0,a=this.data.length;e<a;e++)if(t===this.data[e])return e},CoreIndex:function(){return(this.inferRow&&this.data[0]||this).childIndex(this.Core())},hasNewline:function(){if(this.isEmbellished())return this.CoreMO().hasNewline();if(this.isToken||this.linebreakContainer)return!1;for(var t=0,e=this.data.length;t<e;t++)if(this.data[t]&&this.data[t].hasNewline())return!0;return!1},array:function(){return this.inferred?this.data:[this]},toString:function(){return this.type+"("+this.data.join(",")+")"},getAnnotation:function(){return null}},{childrenSpacelike:function(){for(var t=0,e=this.data.length;t<e;t++)if(!this.data[t].isSpacelike())return!1;return!0},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(t){return this.data[0]&&(t=this.data[0].setTeXclass(t),this.updateTeXclass(this.data[0])),t},setBaseTeXclasses:function(e){this.getPrevClass(e),this.texClass=null,this.data[0]?this.isEmbellished()||this.data[0].isa(t.mi)?(e=this.data[0].setTeXclass(e),this.updateTeXclass(this.Core())):(this.data[0].setTeXclass(),e=this):e=this;for(var a=1,i=this.data.length;a<i;a++)this.data[a]&&this.data[a].setTeXclass();return e},setSeparateTeXclasses:function(t){this.getPrevClass(t);for(var e=0,a=this.data.length;e<a;e++)this.data[e]&&this.data[e].setTeXclass();return this.isEmbellished()&&this.updateTeXclass(this.Core()),this}}),t.mi=t.mbase.Subclass({type:"mi",isToken:!0,texClass:t.TEXCLASS.ORD,defaults:{mathvariant:t.AUTO,mathsize:t.INHERIT,mathbackground:t.INHERIT,mathcolor:t.INHERIT,dir:t.INHERIT},autoDefault:function(e){if("mathvariant"===e){var a=(this.data[0]||"").toString();return 1===a.length||2===a.length&&a.charCodeAt(0)>=55296&&a.charCodeAt(0)<56320?t.VARIANT.ITALIC:t.VARIANT.NORMAL}return""},setTeXclass:function(e){this.getPrevClass(e);var a=this.data.join("");return a.length>1&&a.match(/^[a-z][a-z0-9]*$/i)&&this.texClass===t.TEXCLASS.ORD&&(this.texClass=t.TEXCLASS.OP,this.autoOP=!0),this}}),t.mn=t.mbase.Subclass({type:"mn",isToken:!0,texClass:t.TEXCLASS.ORD,defaults:{mathvariant:t.INHERIT,mathsize:t.INHERIT,mathbackground:t.INHERIT,mathcolor:t.INHERIT,dir:t.INHERIT}}),t.mo=t.mbase.Subclass({type:"mo",isToken:!0,defaults:{mathvariant:t.INHERIT,mathsize:t.INHERIT,mathbackground:t.INHERIT,mathcolor:t.INHERIT,dir:t.INHERIT,form:t.AUTO,fence:t.AUTO,separator:t.AUTO,lspace:t.AUTO,rspace:t.AUTO,stretchy:t.AUTO,symmetric:t.AUTO,maxsize:t.AUTO,minsize:t.AUTO,largeop:t.AUTO,movablelimits:t.AUTO,accent:t.AUTO,linebreak:t.LINEBREAK.AUTO,lineleading:t.INHERIT,linebreakstyle:t.AUTO,linebreakmultchar:t.INHERIT,indentalign:t.INHERIT,indentshift:t.INHERIT,indenttarget:t.INHERIT,indentalignfirst:t.INHERIT,indentshiftfirst:t.INHERIT,indentalignlast:t.INHERIT,indentshiftlast:t.INHERIT,texClass:t.AUTO},defaultDef:{form:t.FORM.INFIX,fence:!1,separator:!1,lspace:t.LENGTH.THICKMATHSPACE,rspace:t.LENGTH.THICKMATHSPACE,stretchy:!1,symmetric:!1,maxsize:t.SIZE.INFINITY,minsize:"0em",largeop:!1,movablelimits:!1,accent:!1,linebreak:t.LINEBREAK.AUTO,lineleading:"1ex",linebreakstyle:"before",indentalign:t.INDENTALIGN.AUTO,indentshift:"0",indenttarget:"",indentalignfirst:t.INDENTALIGN.INDENTALIGN,indentshiftfirst:t.INDENTSHIFT.INDENTSHIFT,indentalignlast:t.INDENTALIGN.INDENTALIGN,indentshiftlast:t.INDENTSHIFT.INDENTSHIFT,texClass:t.TEXCLASS.REL},SPACE_ATTR:{lspace:1,rspace:2},useMMLspacing:3,hasMMLspacing:function(){return!!this.useMMLspacing||this.form&&(this.OPTABLE[this.form]||{})[this.data.join("")]},autoDefault:function(e,a){var i=this.def;if(!i){if("form"===e)return this.getForm();for(var s=this.data.join(""),n=[this.Get("form"),t.FORM.INFIX,t.FORM.POSTFIX,t.FORM.PREFIX],o=0,r=n.length;o<r;o++){var l=this.OPTABLE[n[o]][s];if(l){i=this.makeDef(l);break}}i||(i=this.CheckRange(s)),!i&&a?i={}:(i||(i=MathJax.Hub.Insert({},this.defaultDef)),this.parent?this.def=i:i=MathJax.Hub.Insert({},i),i.form=n[0])}return this.useMMLspacing&=~(this.SPACE_ATTR[e]||0),null!=i[e]?i[e]:a?"":this.defaultDef[e]},CheckRange:function(e){var a=e.charCodeAt(0);a>=55296&&a<56320&&(a=(a-55296<<10)+(e.charCodeAt(1)-56320)+65536);for(var i=0,s=this.RANGES.length;i<s&&this.RANGES[i][0]<=a;i++)if(a<=this.RANGES[i][1]){if(this.RANGES[i][3]){var n=t.optableDir+"/"+this.RANGES[i][3]+".js";this.RANGES[i][3]=null,MathJax.Hub.RestartAfter(MathJax.Ajax.Require(n))}var o=t.TEXCLASSNAMES[this.RANGES[i][2]];return o=this.OPTABLE.infix[e]=t.mo.OPTYPES["BIN"===o?"BIN3":o],this.makeDef(o)}return null},makeDef:function(e){null==e[2]&&(e[2]=this.defaultDef.texClass),e[3]||(e[3]={});var a=MathJax.Hub.Insert({},e[3]);return a.lspace=this.SPACE[e[0]],a.rspace=this.SPACE[e[1]],a.texClass=e[2],a.texClass===t.TEXCLASS.REL&&(this.movablelimits||this.data.join("").match(/^[a-z]+$/i))&&(a.texClass=t.TEXCLASS.OP),a},getForm:function(){for(var e=this,a=this.parent,i=this.Parent();i&&i.isEmbellished();)e=a,a=i.parent,i=i.Parent();if(a&&"mrow"===a.type&&1!==a.NonSpaceLength()){if(a.FirstNonSpace()===e)return t.FORM.PREFIX;if(a.LastNonSpace()===e)return t.FORM.POSTFIX}return t.FORM.INFIX},isEmbellished:function(){return!0},hasNewline:function(){return this.Get("linebreak")===t.LINEBREAK.NEWLINE},CoreParent:function(){for(var e=this;e&&e.isEmbellished()&&e.CoreMO()===this&&!e.isa(t.math);)e=e.Parent();return e},CoreText:function(e){if(!e)return"";if(e.isEmbellished())return e.CoreMO().data.join("");for(;((e.isa(t.mrow)||e.isa(t.TeXAtom)||e.isa(t.mstyle)||e.isa(t.mphantom))&&1===e.data.length||e.isa(t.munderover))&&e.data[0];)e=e.data[0];return e.isToken?e.data.join(""):""},remapChars:{"*":"∗",'"':"″","°":"∘","²":"2","³":"3","´":"′","¹":"1"},remap:function(t,e){return t=t.replace(/-/g,"−"),e&&1===(t=t.replace(/'/g,"′").replace(/`/g,"‵")).length&&(t=e[t]||t),t},setTeXclass:function(e){var a=this.getValues("form","lspace","rspace","fence");return this.hasMMLspacing()?(this.texClass=t.TEXCLASS.NONE,this):(a.fence&&!this.texClass&&(a.form===t.FORM.PREFIX&&(this.texClass=t.TEXCLASS.OPEN),a.form===t.FORM.POSTFIX&&(this.texClass=t.TEXCLASS.CLOSE)),this.texClass=this.Get("texClass"),"⁡"===this.data.join("")?(e&&(e.texClass=t.TEXCLASS.OP,e.fnOP=!0),this.texClass=this.prevClass=t.TEXCLASS.NONE,e):this.adjustTeXclass(e))},adjustTeXclass:function(e){if(this.texClass===t.TEXCLASS.NONE)return e;if(e?(!e.autoOP||this.texClass!==t.TEXCLASS.BIN&&this.texClass!==t.TEXCLASS.REL||(e.texClass=t.TEXCLASS.ORD),this.prevClass=e.texClass||t.TEXCLASS.ORD,this.prevLevel=e.Get("scriptlevel")):this.prevClass=t.TEXCLASS.NONE,this.texClass!==t.TEXCLASS.BIN||this.prevClass!==t.TEXCLASS.NONE&&this.prevClass!==t.TEXCLASS.BIN&&this.prevClass!==t.TEXCLASS.OP&&this.prevClass!==t.TEXCLASS.REL&&this.prevClass!==t.TEXCLASS.OPEN&&this.prevClass!==t.TEXCLASS.PUNCT)if(this.prevClass!==t.TEXCLASS.BIN||this.texClass!==t.TEXCLASS.REL&&this.texClass!==t.TEXCLASS.CLOSE&&this.texClass!==t.TEXCLASS.PUNCT){if(this.texClass===t.TEXCLASS.BIN){for(var a=this,i=this.parent;i&&i.parent&&i.isEmbellished()&&(1===i.data.length||"mrow"!==i.type&&i.Core()===a);)a=i,i=i.parent;i.data[i.data.length-1]===a&&(this.texClass=t.TEXCLASS.ORD)}}else e.texClass=this.prevClass=t.TEXCLASS.ORD;else this.texClass=t.TEXCLASS.ORD;return this}}),t.mtext=t.mbase.Subclass({type:"mtext",isToken:!0,isSpacelike:function(){return!0},texClass:t.TEXCLASS.ORD,defaults:{mathvariant:t.INHERIT,mathsize:t.INHERIT,mathbackground:t.INHERIT,mathcolor:t.INHERIT,dir:t.INHERIT}}),t.mspace=t.mbase.Subclass({type:"mspace",isToken:!0,isSpacelike:function(){return!0},defaults:{mathbackground:t.INHERIT,mathcolor:t.INHERIT,width:"0em",height:"0ex",depth:"0ex",linebreak:t.LINEBREAK.AUTO},hasDimAttr:function(){return this.hasValue("width")||this.hasValue("height")||this.hasValue("depth")},hasNewline:function(){return!this.hasDimAttr()&&this.Get("linebreak")===t.LINEBREAK.NEWLINE}}),t.ms=t.mbase.Subclass({type:"ms",isToken:!0,texClass:t.TEXCLASS.ORD,defaults:{mathvariant:t.INHERIT,mathsize:t.INHERIT,mathbackground:t.INHERIT,mathcolor:t.INHERIT,dir:t.INHERIT,lquote:'"',rquote:'"'}}),t.mglyph=t.mbase.Subclass({type:"mglyph",isToken:!0,texClass:t.TEXCLASS.ORD,defaults:{mathbackground:t.INHERIT,mathcolor:t.INHERIT,alt:"",src:"",width:t.AUTO,height:t.AUTO,valign:"0em"}}),t.mrow=t.mbase.Subclass({type:"mrow",isSpacelike:t.mbase.childrenSpacelike,inferred:!1,notParent:!1,isEmbellished:function(){for(var t=!1,e=0,a=this.data.length;e<a;e++)if(null!=this.data[e])if(this.data[e].isEmbellished()){if(t)return!1;t=!0,this.core=e}else if(!this.data[e].isSpacelike())return!1;return t},NonSpaceLength:function(){for(var t=0,e=0,a=this.data.length;e<a;e++)this.data[e]&&!this.data[e].isSpacelike()&&t++;return t},FirstNonSpace:function(){for(var t=0,e=this.data.length;t<e;t++)if(this.data[t]&&!this.data[t].isSpacelike())return this.data[t];return null},LastNonSpace:function(){for(var t=this.data.length-1;t>=0;t--)if(this.data[0]&&!this.data[t].isSpacelike())return this.data[t];return null},Core:function(){return this.isEmbellished()&&void 0!==this.core?this.data[this.core]:this},CoreMO:function(){return this.isEmbellished()&&void 0!==this.core?this.data[this.core].CoreMO():this},toString:function(){return this.inferred?"["+this.data.join(",")+"]":this.SUPER(arguments).toString.call(this)},setTeXclass:function(e){var a,i=this.data.length;if(!this.open&&!this.close||e&&e.fnOP){for(a=0;a<i;a++)this.data[a]&&(e=this.data[a].setTeXclass(e));return this.data[0]&&this.updateTeXclass(this.data[0]),e}for(this.getPrevClass(e),e=null,a=0;a<i;a++)this.data[a]&&(e=this.data[a].setTeXclass(e));return this.hasOwnProperty("texClass")||(this.texClass=t.TEXCLASS.INNER),this},getAnnotation:function(t){return 1!=this.data.length?null:this.data[0].getAnnotation(t)}}),t.mfrac=t.mbase.Subclass({type:"mfrac",num:0,den:1,linebreakContainer:!0,isEmbellished:t.mbase.childEmbellished,Core:t.mbase.childCore,CoreMO:t.mbase.childCoreMO,defaults:{mathbackground:t.INHERIT,mathcolor:t.INHERIT,linethickness:t.LINETHICKNESS.MEDIUM,numalign:t.ALIGN.CENTER,denomalign:t.ALIGN.CENTER,bevelled:!1},adjustChild_displaystyle:function(t){return!1},adjustChild_scriptlevel:function(t){var e=this.Get("scriptlevel");return(!this.Get("displaystyle")||e>0)&&e++,e},adjustChild_texprimestyle:function(t){return t==this.den||this.Get("texprimestyle")},setTeXclass:t.mbase.setSeparateTeXclasses}),t.msqrt=t.mbase.Subclass({type:"msqrt",inferRow:!0,linebreakContainer:!0,texClass:t.TEXCLASS.ORD,setTeXclass:t.mbase.setSeparateTeXclasses,adjustChild_texprimestyle:function(t){return!0}}),t.mroot=t.mbase.Subclass({type:"mroot",linebreakContainer:!0,texClass:t.TEXCLASS.ORD,adjustChild_displaystyle:function(t){return 1!==t&&this.Get("displaystyle")},adjustChild_scriptlevel:function(t){var e=this.Get("scriptlevel");return 1===t&&(e+=2),e},adjustChild_texprimestyle:function(t){return 0===t||this.Get("texprimestyle")},setTeXclass:t.mbase.setSeparateTeXclasses}),t.mstyle=t.mbase.Subclass({type:"mstyle",isSpacelike:t.mbase.childrenSpacelike,isEmbellished:t.mbase.childEmbellished,Core:t.mbase.childCore,CoreMO:t.mbase.childCoreMO,inferRow:!0,defaults:{scriptlevel:t.INHERIT,displaystyle:t.INHERIT,scriptsizemultiplier:Math.sqrt(.5),scriptminsize:"8pt",mathbackground:t.INHERIT,mathcolor:t.INHERIT,dir:t.INHERIT,infixlinebreakstyle:t.LINEBREAKSTYLE.BEFORE,decimalseparator:"."},adjustChild_scriptlevel:function(t){var e=this.scriptlevel;return null==e?e=this.Get("scriptlevel"):String(e).match(/^ *[-+]/)&&(e=this.Get("scriptlevel",null,!0)+parseInt(e)),e},inheritFromMe:!0,noInherit:{mpadded:{width:!0,height:!0,depth:!0,lspace:!0,voffset:!0},mtable:{width:!0,height:!0,depth:!0,align:!0}},getRemoved:{fontfamily:"fontFamily",fontweight:"fontWeight",fontstyle:"fontStyle",fontsize:"fontSize"},setTeXclass:t.mbase.setChildTeXclass}),t.merror=t.mbase.Subclass({type:"merror",inferRow:!0,linebreakContainer:!0,texClass:t.TEXCLASS.ORD}),t.mpadded=t.mbase.Subclass({type:"mpadded",inferRow:!0,isSpacelike:t.mbase.childrenSpacelike,isEmbellished:t.mbase.childEmbellished,Core:t.mbase.childCore,CoreMO:t.mbase.childCoreMO,defaults:{mathbackground:t.INHERIT,mathcolor:t.INHERIT,width:"",height:"",depth:"",lspace:0,voffset:0},setTeXclass:t.mbase.setChildTeXclass}),t.mphantom=t.mbase.Subclass({type:"mphantom",texClass:t.TEXCLASS.ORD,inferRow:!0,isSpacelike:t.mbase.childrenSpacelike,isEmbellished:t.mbase.childEmbellished,Core:t.mbase.childCore,CoreMO:t.mbase.childCoreMO,setTeXclass:t.mbase.setChildTeXclass}),t.mfenced=t.mbase.Subclass({type:"mfenced",defaults:{mathbackground:t.INHERIT,mathcolor:t.INHERIT,open:"(",close:")",separators:","},addFakeNodes:function(){var e=this.getValues("open","close","separators");if(e.open=e.open.replace(/[ \t\n\r]/g,""),e.close=e.close.replace(/[ \t\n\r]/g,""),e.separators=e.separators.replace(/[ \t\n\r]/g,""),""!==e.open&&this.SetData("open",t.mo(e.open).With({fence:!0,form:t.FORM.PREFIX,texClass:t.TEXCLASS.OPEN})),""!==e.separators){for(;e.separators.length<this.data.length;)e.separators+=e.separators.charAt(e.separators.length-1);for(var a=1,i=this.data.length;a<i;a++)this.data[a]&&this.SetData("sep"+a,t.mo(e.separators.charAt(a-1)).With({separator:!0}))}""!==e.close&&this.SetData("close",t.mo(e.close).With({fence:!0,form:t.FORM.POSTFIX,texClass:t.TEXCLASS.CLOSE}))},texClass:t.TEXCLASS.OPEN,setTeXclass:function(e){this.addFakeNodes(),this.getPrevClass(e),this.data.open&&(e=this.data.open.setTeXclass(e)),this.data[0]&&(e=this.data[0].setTeXclass(e));for(var a=1,i=this.data.length;a<i;a++)this.data["sep"+a]&&(e=this.data["sep"+a].setTeXclass(e)),this.data[a]&&(e=this.data[a].setTeXclass(e));return this.data.close&&(e=this.data.close.setTeXclass(e)),this.updateTeXclass(this.data.open),this.texClass=t.TEXCLASS.INNER,e}}),t.menclose=t.mbase.Subclass({type:"menclose",inferRow:!0,linebreakContainer:!0,defaults:{mathbackground:t.INHERIT,mathcolor:t.INHERIT,notation:t.NOTATION.LONGDIV,texClass:t.TEXCLASS.ORD},setTeXclass:t.mbase.setSeparateTeXclasses}),t.msubsup=t.mbase.Subclass({type:"msubsup",base:0,sub:1,sup:2,isEmbellished:t.mbase.childEmbellished,Core:t.mbase.childCore,CoreMO:t.mbase.childCoreMO,defaults:{mathbackground:t.INHERIT,mathcolor:t.INHERIT,subscriptshift:"",superscriptshift:"",texClass:t.AUTO},autoDefault:function(e){return"texClass"===e?this.isEmbellished()?this.CoreMO().Get(e):t.TEXCLASS.ORD:0},adjustChild_displaystyle:function(t){return!(t>0)&&this.Get("displaystyle")},adjustChild_scriptlevel:function(t){var e=this.Get("scriptlevel");return t>0&&e++,e},adjustChild_texprimestyle:function(t){return t===this.sub||this.Get("texprimestyle")},setTeXclass:t.mbase.setBaseTeXclasses}),t.msub=t.msubsup.Subclass({type:"msub"}),t.msup=t.msubsup.Subclass({type:"msup",sub:2,sup:1}),t.mmultiscripts=t.msubsup.Subclass({type:"mmultiscripts",adjustChild_texprimestyle:function(t){return t%2==1||this.Get("texprimestyle")}}),t.mprescripts=t.mbase.Subclass({type:"mprescripts"}),t.none=t.mbase.Subclass({type:"none"}),t.munderover=t.mbase.Subclass({type:"munderover",base:0,under:1,over:2,sub:1,sup:2,ACCENTS:["","accentunder","accent"],linebreakContainer:!0,isEmbellished:t.mbase.childEmbellished,Core:t.mbase.childCore,CoreMO:t.mbase.childCoreMO,defaults:{mathbackground:t.INHERIT,mathcolor:t.INHERIT,accent:t.AUTO,accentunder:t.AUTO,align:t.ALIGN.CENTER,texClass:t.AUTO,subscriptshift:"",superscriptshift:""},autoDefault:function(e){return"texClass"===e?this.isEmbellished()?this.CoreMO().Get(e):t.TEXCLASS.ORD:"accent"===e&&this.data[this.over]?this.data[this.over].CoreMO().Get("accent"):!("accentunder"!==e||!this.data[this.under])&&this.data[this.under].CoreMO().Get("accent")},adjustChild_displaystyle:function(t){return!(t>0)&&this.Get("displaystyle")},adjustChild_scriptlevel:function(t){var e=this.Get("scriptlevel"),a=this.data[this.base]&&!this.Get("displaystyle")&&this.data[this.base].CoreMO().Get("movablelimits");return t!=this.under||!a&&this.Get("accentunder")||e++,t!=this.over||!a&&this.Get("accent")||e++,e},adjustChild_texprimestyle:function(t){return!(t!==this.base||!this.data[this.over])||this.Get("texprimestyle")},setTeXclass:t.mbase.setBaseTeXclasses}),t.munder=t.munderover.Subclass({type:"munder"}),t.mover=t.munderover.Subclass({type:"mover",over:1,under:2,sup:1,sub:2,ACCENTS:["","accent","accentunder"]}),t.mtable=t.mbase.Subclass({type:"mtable",defaults:{mathbackground:t.INHERIT,mathcolor:t.INHERIT,align:t.ALIGN.AXIS,rowalign:t.ALIGN.BASELINE,columnalign:t.ALIGN.CENTER,groupalign:"{left}",alignmentscope:!0,columnwidth:t.WIDTH.AUTO,width:t.WIDTH.AUTO,rowspacing:"1ex",columnspacing:".8em",rowlines:t.LINES.NONE,columnlines:t.LINES.NONE,frame:t.LINES.NONE,framespacing:"0.4em 0.5ex",equalrows:!1,equalcolumns:!1,displaystyle:!1,side:t.SIDE.RIGHT,minlabelspacing:"0.8em",texClass:t.TEXCLASS.ORD,useHeight:1},adjustChild_displaystyle:function(){return null!=this.displaystyle?this.displaystyle:this.defaults.displaystyle},inheritFromMe:!0,noInherit:{mover:{align:!0},munder:{align:!0},munderover:{align:!0},mtable:{align:!0,rowalign:!0,columnalign:!0,groupalign:!0,alignmentscope:!0,columnwidth:!0,width:!0,rowspacing:!0,columnspacing:!0,rowlines:!0,columnlines:!0,frame:!0,framespacing:!0,equalrows:!0,equalcolumns:!0,displaystyle:!0,side:!0,minlabelspacing:!0,texClass:!0,useHeight:1}},linebreakContainer:!0,Append:function(){for(var e=0,a=arguments.length;e<a;e++)arguments[e]instanceof t.mtr||arguments[e]instanceof t.mlabeledtr||(arguments[e]=t.mtr(arguments[e]));this.SUPER(arguments).Append.apply(this,arguments)},setTeXclass:t.mbase.setSeparateTeXclasses}),t.mtr=t.mbase.Subclass({type:"mtr",defaults:{mathbackground:t.INHERIT,mathcolor:t.INHERIT,rowalign:t.INHERIT,columnalign:t.INHERIT,groupalign:t.INHERIT},inheritFromMe:!0,noInherit:{mrow:{rowalign:!0,columnalign:!0,groupalign:!0},mtable:{rowalign:!0,columnalign:!0,groupalign:!0}},linebreakContainer:!0,Append:function(){for(var e=0,a=arguments.length;e<a;e++)arguments[e]instanceof t.mtd||(arguments[e]=t.mtd(arguments[e]));this.SUPER(arguments).Append.apply(this,arguments)},setTeXclass:t.mbase.setSeparateTeXclasses}),t.mtd=t.mbase.Subclass({type:"mtd",inferRow:!0,linebreakContainer:!0,isEmbellished:t.mbase.childEmbellished,Core:t.mbase.childCore,CoreMO:t.mbase.childCoreMO,defaults:{mathbackground:t.INHERIT,mathcolor:t.INHERIT,rowspan:1,columnspan:1,rowalign:t.INHERIT,columnalign:t.INHERIT,groupalign:t.INHERIT},setTeXclass:t.mbase.setSeparateTeXclasses}),t.maligngroup=t.mbase.Subclass({type:"maligngroup",isSpacelike:function(){return!0},defaults:{mathbackground:t.INHERIT,mathcolor:t.INHERIT,groupalign:t.INHERIT},inheritFromMe:!0,noInherit:{mrow:{groupalign:!0},mtable:{groupalign:!0}}}),t.malignmark=t.mbase.Subclass({type:"malignmark",defaults:{mathbackground:t.INHERIT,mathcolor:t.INHERIT,edge:t.SIDE.LEFT},isSpacelike:function(){return!0}}),t.mlabeledtr=t.mtr.Subclass({type:"mlabeledtr"}),t.maction=t.mbase.Subclass({type:"maction",defaults:{mathbackground:t.INHERIT,mathcolor:t.INHERIT,actiontype:t.ACTIONTYPE.TOGGLE,selection:1},selected:function(){return this.data[this.Get("selection")-1]||t.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(e){this.Get("actiontype")===t.ACTIONTYPE.TOOLTIP&&this.data[1]&&this.data[1].setTeXclass();var a=this.selected();return e=a.setTeXclass(e),this.updateTeXclass(a),e}}),t.semantics=t.mbase.Subclass({type:"semantics",notParent:!0,isEmbellished:t.mbase.childEmbellished,Core:t.mbase.childCore,CoreMO:t.mbase.childCoreMO,defaults:{definitionURL:null,encoding:null},setTeXclass:t.mbase.setChildTeXclass,getAnnotation:function(t){var e=MathJax.Hub.config.MathMenu.semanticsAnnotations[t];if(e)for(var a=0,i=this.data.length;a<i;a++){var s=this.data[a].Get("encoding");if(s)for(var n=0,o=e.length;n<o;n++)if(e[n]===s)return this.data[a]}return null}}),t.annotation=t.mbase.Subclass({type:"annotation",isChars:!0,linebreakContainer:!0,defaults:{definitionURL:null,encoding:null,cd:"mathmlkeys",name:"",src:null}}),t["annotation-xml"]=t.mbase.Subclass({type:"annotation-xml",linebreakContainer:!0,defaults:{definitionURL:null,encoding:null,cd:"mathmlkeys",name:"",src:null}}),t.math=t.mstyle.Subclass({type:"math",defaults:{mathvariant:t.VARIANT.NORMAL,mathsize:t.SIZE.NORMAL,mathcolor:"",mathbackground:t.COLOR.TRANSPARENT,dir:"ltr",scriptlevel:0,displaystyle:t.AUTO,display:"inline",maxwidth:"",overflow:t.OVERFLOW.LINEBREAK,altimg:"","altimg-width":"","altimg-height":"","altimg-valign":"",alttext:"",cdgroup:"",scriptsizemultiplier:Math.sqrt(.5),scriptminsize:"8px",infixlinebreakstyle:t.LINEBREAKSTYLE.BEFORE,lineleading:"1ex",indentshift:"auto",indentalign:t.INDENTALIGN.AUTO,indentalignfirst:t.INDENTALIGN.INDENTALIGN,indentshiftfirst:t.INDENTSHIFT.INDENTSHIFT,indentalignlast:t.INDENTALIGN.INDENTALIGN,indentshiftlast:t.INDENTSHIFT.INDENTSHIFT,decimalseparator:".",texprimestyle:!1},autoDefault:function(t){return"displaystyle"===t?"block"===this.Get("display"):""},linebreakContainer:!0,setTeXclass:t.mbase.setChildTeXclass,getAnnotation:function(t){return 1!=this.data.length?null:this.data[0].getAnnotation(t)}}),t.chars=t.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("")}}),t.entity=t.mbase.Subclass({type:"entity",Append:function(){this.data.push.apply(this.data,arguments)},value:function(){return"#x"===this.data[0].substr(0,2)?parseInt(this.data[0].substr(2),16):"#"===this.data[0].substr(0,1)?parseInt(this.data[0].substr(1)):0},toString:function(){var t=this.value();return t<=65535?String.fromCharCode(t):(t-=65536,String.fromCharCode(55296+(t>>10))+String.fromCharCode(56320+(1023&t)))}}),t.xml=t.mbase.Subclass({type:"xml",Init:function(){return this.div=document.createElement("div"),this.SUPER(arguments).Init.apply(this,arguments)},Append:function(){for(var t=0,e=arguments.length;t<e;t++){var a=this.Import(arguments[t]);this.data.push(a),this.div.appendChild(a)}},Import:function(t){if(document.importNode)return document.importNode(t,!0);var e,a,i;if(1===t.nodeType){for(e=document.createElement(t.nodeName),a=0,i=t.attributes.length;a<i;a++){var s=t.attributes[a];s.specified&&null!=s.nodeValue&&""!=s.nodeValue&&e.setAttribute(s.nodeName,s.nodeValue),"style"===s.nodeName&&(e.style.cssText=s.nodeValue)}t.className&&(e.className=t.className)}else if(3===t.nodeType||4===t.nodeType)e=document.createTextNode(t.nodeValue);else{if(8!==t.nodeType)return document.createTextNode("");e=document.createComment(t.nodeValue)}for(a=0,i=t.childNodes.length;a<i;a++)e.appendChild(this.Import(t.childNodes[a]));return e},value:function(){return this.div},toString:function(){return this.div.innerHTML}}),t.TeXAtom=t.mbase.Subclass({type:"texatom",linebreakContainer:!0,inferRow:!0,notParent:!0,texClass:t.TEXCLASS.ORD,Core:t.mbase.childCore,CoreMO:t.mbase.childCoreMO,isEmbellished:t.mbase.childEmbellished,setTeXclass:function(t){return this.data[0].setTeXclass(),this.adjustTeXclass(t)},adjustTeXclass:t.mo.prototype.adjustTeXclass}),t.NULL=t.mbase().With({type:"null"});var e=t.TEXCLASS,a={ORD:[0,0,e.ORD],ORD11:[1,1,e.ORD],ORD21:[2,1,e.ORD],ORD02:[0,2,e.ORD],ORD55:[5,5,e.ORD],OP:[1,2,e.OP,{largeop:!0,movablelimits:!0,symmetric:!0}],OPFIXED:[1,2,e.OP,{largeop:!0,movablelimits:!0}],INTEGRAL:[0,1,e.OP,{largeop:!0,symmetric:!0}],INTEGRAL2:[1,2,e.OP,{largeop:!0,symmetric:!0}],BIN3:[3,3,e.BIN],BIN4:[4,4,e.BIN],BIN01:[0,1,e.BIN],BIN5:[5,5,e.BIN],TALLBIN:[4,4,e.BIN,{stretchy:!0}],BINOP:[4,4,e.BIN,{largeop:!0,movablelimits:!0}],REL:[5,5,e.REL],REL1:[1,1,e.REL,{stretchy:!0}],REL4:[4,4,e.REL],RELSTRETCH:[5,5,e.REL,{stretchy:!0}],RELACCENT:[5,5,e.REL,{accent:!0}],WIDEREL:[5,5,e.REL,{accent:!0,stretchy:!0}],OPEN:[0,0,e.OPEN,{fence:!0,stretchy:!0,symmetric:!0}],CLOSE:[0,0,e.CLOSE,{fence:!0,stretchy:!0,symmetric:!0}],INNER:[0,0,e.INNER],PUNCT:[0,3,e.PUNCT],ACCENT:[0,0,e.ORD,{accent:!0}],WIDEACCENT:[0,0,e.ORD,{accent:!0,stretchy:!0}]};t.mo.Augment({SPACE:["0em","0.1111em","0.1667em","0.2222em","0.2667em","0.3333em"],RANGES:[[32,127,e.REL,"BasicLatin"],[160,255,e.ORD,"Latin1Supplement"],[256,383,e.ORD],[384,591,e.ORD],[688,767,e.ORD,"SpacingModLetters"],[768,879,e.ORD,"CombDiacritMarks"],[880,1023,e.ORD,"GreekAndCoptic"],[7680,7935,e.ORD],[8192,8303,e.PUNCT,"GeneralPunctuation"],[8304,8351,e.ORD],[8352,8399,e.ORD],[8400,8447,e.ORD,"CombDiactForSymbols"],[8448,8527,e.ORD,"LetterlikeSymbols"],[8528,8591,e.ORD],[8592,8703,e.REL,"Arrows"],[8704,8959,e.BIN,"MathOperators"],[8960,9215,e.ORD,"MiscTechnical"],[9312,9471,e.ORD],[9472,9631,e.ORD],[9632,9727,e.ORD,"GeometricShapes"],[9984,10175,e.ORD,"Dingbats"],[10176,10223,e.ORD,"MiscMathSymbolsA"],[10224,10239,e.REL,"SupplementalArrowsA"],[10496,10623,e.REL,"SupplementalArrowsB"],[10624,10751,e.ORD,"MiscMathSymbolsB"],[10752,11007,e.BIN,"SuppMathOperators"],[11008,11263,e.ORD,"MiscSymbolsAndArrows"],[119808,120831,e.ORD]],OPTABLE:{prefix:{"∀":a.ORD21,"∂":a.ORD21,"∃":a.ORD21,"∇":a.ORD21,"∏":a.OP,"∐":a.OP,"∑":a.OP,"−":a.BIN01,"∓":a.BIN01,"√":[1,1,e.ORD,{stretchy:!0}],"∠":a.ORD,"∫":a.INTEGRAL,"∮":a.INTEGRAL,"⋀":a.OP,"⋁":a.OP,"⋂":a.OP,"⋃":a.OP,"⌈":a.OPEN,"⌊":a.OPEN,"⟨":a.OPEN,"⟮":a.OPEN,"⨀":a.OP,"⨁":a.OP,"⨂":a.OP,"⨄":a.OP,"⨆":a.OP,"¬":a.ORD21,"±":a.BIN01,"(":a.OPEN,"+":a.BIN01,"-":a.BIN01,"[":a.OPEN,"{":a.OPEN,"|":a.OPEN},postfix:{"!":[1,0,e.CLOSE],"&":a.ORD,"′":a.ORD02,"‾":a.WIDEACCENT,"⌉":a.CLOSE,"⌋":a.CLOSE,"⏞":a.WIDEACCENT,"⏟":a.WIDEACCENT,"♭":a.ORD02,"♮":a.ORD02,"♯":a.ORD02,"⟩":a.CLOSE,"⟯":a.CLOSE,ˆ:a.WIDEACCENT,ˇ:a.WIDEACCENT,ˉ:a.WIDEACCENT,ˊ:a.ACCENT,ˋ:a.ACCENT,"˘":a.ACCENT,"˙":a.ACCENT,"˜":a.WIDEACCENT,"̂":a.WIDEACCENT,"¨":a.ACCENT,"¯":a.WIDEACCENT,")":a.CLOSE,"]":a.CLOSE,"^":a.WIDEACCENT,_:a.WIDEACCENT,"`":a.ACCENT,"|":a.CLOSE,"}":a.CLOSE,"~":a.WIDEACCENT},infix:{"":a.ORD,"%":[3,3,e.ORD],"•":a.BIN4,"…":a.INNER,"⁄":a.TALLBIN,"⁡":a.ORD,"⁢":a.ORD,"⁣":[0,0,e.ORD,{linebreakstyle:"after",separator:!0}],"⁤":a.ORD,"←":a.WIDEREL,"↑":a.RELSTRETCH,"→":a.WIDEREL,"↓":a.RELSTRETCH,"↔":a.WIDEREL,"↕":a.RELSTRETCH,"↖":a.RELSTRETCH,"↗":a.RELSTRETCH,"↘":a.RELSTRETCH,"↙":a.RELSTRETCH,"↦":a.WIDEREL,"↩":a.WIDEREL,"↪":a.WIDEREL,"↼":a.WIDEREL,"↽":a.WIDEREL,"⇀":a.WIDEREL,"⇁":a.WIDEREL,"⇌":a.WIDEREL,"⇐":a.WIDEREL,"⇑":a.RELSTRETCH,"⇒":a.WIDEREL,"⇓":a.RELSTRETCH,"⇔":a.WIDEREL,"⇕":a.RELSTRETCH,"∈":a.REL,"∉":a.REL,"∋":a.REL,"−":a.BIN4,"∓":a.BIN4,"∕":a.TALLBIN,"∖":a.BIN4,"∗":a.BIN4,"∘":a.BIN4,"∙":a.BIN4,"∝":a.REL,"∣":a.REL,"∥":a.REL,"∧":a.BIN4,"∨":a.BIN4,"∩":a.BIN4,"∪":a.BIN4,"∼":a.REL,"≀":a.BIN4,"≃":a.REL,"≅":a.REL,"≈":a.REL,"≍":a.REL,"≐":a.REL,"≠":a.REL,"≡":a.REL,"≤":a.REL,"≥":a.REL,"≪":a.REL,"≫":a.REL,"≺":a.REL,"≻":a.REL,"⊂":a.REL,"⊃":a.REL,"⊆":a.REL,"⊇":a.REL,"⊎":a.BIN4,"⊑":a.REL,"⊒":a.REL,"⊓":a.BIN4,"⊔":a.BIN4,"⊕":a.BIN4,"⊖":a.BIN4,"⊗":a.BIN4,"⊘":a.BIN4,"⊙":a.BIN4,"⊢":a.REL,"⊣":a.REL,"⊤":a.ORD55,"⊥":a.REL,"⊨":a.REL,"⋄":a.BIN4,"⋅":a.BIN4,"⋆":a.BIN4,"⋈":a.REL,"⋮":a.ORD55,"⋯":a.INNER,"⋱":[5,5,e.INNER],"△":a.BIN4,"▵":a.BIN4,"▹":a.BIN4,"▽":a.BIN4,"▿":a.BIN4,"◃":a.BIN4,"❘":a.REL,"⟵":a.WIDEREL,"⟶":a.WIDEREL,"⟷":a.WIDEREL,"⟸":a.WIDEREL,"⟹":a.WIDEREL,"⟺":a.WIDEREL,"⟼":a.WIDEREL,"⨯":a.BIN4,"⨿":a.BIN4,"⪯":a.REL,"⪰":a.REL,"±":a.BIN4,"·":a.BIN4,"×":a.BIN4,"÷":a.BIN4,"*":a.BIN3,"+":a.BIN4,",":[0,3,e.PUNCT,{linebreakstyle:"after",separator:!0}],"-":a.BIN4,".":[3,3,e.ORD],"/":a.ORD11,":":[1,2,e.REL],";":[0,3,e.PUNCT,{linebreakstyle:"after",separator:!0}],"<":a.REL,"=":a.REL,">":a.REL,"?":[1,1,e.CLOSE],"\\":a.ORD,"^":a.ORD11,_:a.ORD11,"|":[2,2,e.ORD,{fence:!0,stretchy:!0,symmetric:!0}],"#":a.ORD,$:a.ORD,".":[0,3,e.PUNCT,{separator:!0}],ʹ:a.ORD,"̀":a.ACCENT,"́":a.ACCENT,"̃":a.WIDEACCENT,"̄":a.ACCENT,"̆":a.ACCENT,"̇":a.ACCENT,"̈":a.ACCENT,"̌":a.ACCENT,"̲":a.WIDEACCENT,"̸":a.REL4,"―":[0,0,e.ORD,{stretchy:!0}],"‗":[0,0,e.ORD,{stretchy:!0}],"†":a.BIN3,"‡":a.BIN3,"⃗":a.ACCENT,ℑ:a.ORD,ℓ:a.ORD,℘:a.ORD,ℜ:a.ORD,"∅":a.ORD,"∞":a.ORD,"⌅":a.BIN3,"⌆":a.BIN3,"⌢":a.REL4,"⌣":a.REL4,"〈":a.OPEN,"〉":a.CLOSE,"⎪":a.ORD,"⎯":[0,0,e.ORD,{stretchy:!0}],"⎰":a.OPEN,"⎱":a.CLOSE,"─":a.ORD,"◯":a.BIN3,"♠":a.ORD,"♡":a.ORD,"♢":a.ORD,"♣":a.ORD,"〈":a.OPEN,"〉":a.CLOSE,"︷":a.WIDEACCENT,"︸":a.WIDEACCENT}}},{OPTYPES:a});var i=t.mo.prototype.OPTABLE;i.infix["^"]=a.WIDEREL,i.infix._=a.WIDEREL,i.prefix["∣"]=a.OPEN,i.prefix["∥"]=a.OPEN,i.postfix["∣"]=a.CLOSE,i.postfix["∥"]=a.CLOSE}(MathJax.ElementJax.mml),MathJax.ElementJax.mml.loadComplete("jax.js"),MathJax.Hub.Register.LoadHook("[MathJax]/jax/element/mml/jax.js",(function(){var t=MathJax.ElementJax.mml,e=MathJax.Hub.config.menuSettings;t.mbase.Augment({toMathML:function(t){var e=this.inferred&&this.parent.inferRow;null==t&&(t="");var a=this.type,i=this.toMathMLattributes();if("mspace"===a)return t+"<"+a+i+" />";for(var s=[],n=this.isToken?"":t+(e?"":"  "),o=0,r=this.data.length;o<r;o++)this.data[o]?s.push(this.data[o].toMathML(n)):this.isToken||this.isChars||s.push(n+"<mrow />");return this.isToken||this.isChars?t+"<"+a+i+">"+s.join("")+"</"+a+">":e?s.join("\n"):0===s.length||1===s.length&&""===s[0]?t+"<"+a+i+" />":t+"<"+a+i+">\n"+s.join("\n")+"\n"+t+"</"+a+">"},toMathMLattributes:function(){var e="mstyle"===this.type?t.math.prototype.defaults:this.defaults,a=this.attrNames||t.copyAttributeNames,i=t.skipAttributes,s=t.copyAttributes,n=[];if("math"!==this.type||this.attr&&"xmlns"in this.attr||n.push('xmlns="http://www.w3.org/1998/Math/MathML"'),!this.attrNames)for(var o in e)i[o]||s[o]||!e.hasOwnProperty(o)||null!=this[o]&&this[o]!==e[o]&&this.Get(o,null,1)!==this[o]&&n.push(o+'="'+this.toMathMLattribute(this[o])+'"');for(var r=0,l=a.length;r<l;r++)(1!==s[a[r]]||e.hasOwnProperty(a[r]))&&(value=(this.attr||{})[a[r]],null==value&&(value=this[a[r]]),null!=value&&n.push(a[r]+'="'+this.toMathMLquote(value)+'"'));return this.toMathMLclass(n),n.length?" "+n.join(" "):""},toMathMLclass:function(a){var i=[];if(this.class&&i.push(this.class),this.isa(t.TeXAtom)&&e.texHints){var s=["ORD","OP","BIN","REL","OPEN","CLOSE","PUNCT","INNER","VCENTER"][this.texClass];s&&(i.push("MJX-TeXAtom-"+s),"OP"!==s||this.movablelimits||i.push("MJX-fixedlimits"))}this.mathvariant&&this.toMathMLvariants[this.mathvariant]&&i.push("MJX"+this.mathvariant),this.variantForm&&i.push("MJX-variant"),i.length&&a.unshift('class="'+this.toMathMLquote(i.join(" "))+'"')},toMathMLattribute:function(t){return"string"==typeof t&&t.replace(/ /g,"").match(/^(([-+])?(\d+(\.\d*)?|\.\d+))mu$/)?(RegExp.$2||"")+(1/18*RegExp.$3).toFixed(3).replace(/\.?0+$/,"")+"em":this.toMathMLvariants[t]?this.toMathMLvariants[t]:this.toMathMLquote(t)},toMathMLvariants:{"-tex-caligraphic":t.VARIANT.SCRIPT,"-tex-caligraphic-bold":t.VARIANT.BOLDSCRIPT,"-tex-oldstyle":t.VARIANT.NORMAL,"-tex-oldstyle-bold":t.VARIANT.BOLD,"-tex-mathit":t.VARIANT.ITALIC},toMathMLquote:function(t){for(var e=0,a=(t=String(t).split("")).length;e<a;e++){var i=t[e].charCodeAt(0);if(i<=55295||57344<=i)if(i>126||i<32&&10!==i&&13!==i&&9!==i)t[e]="&#x"+i.toString(16).toUpperCase()+";";else{var s={"&":"&amp;","<":"&lt;",">":"&gt;",'"':"&quot;"}[t[e]];s&&(t[e]=s)}else if(e+1<a){var n=t[e+1].charCodeAt(0)-56320+(i-55296<<10)+65536;t[e]="&#x"+n.toString(16).toUpperCase()+";",t[e+1]="",e++}else t[e]=""}return t.join("")}}),t.math.Augment({toMathML:function(t,a){var i;null==t&&(t=""),a&&a.originalText&&e.semantics&&(i=MathJax.InputJax[a.inputJax].annotationEncoding);for(var s=this.data[0]&&this.data[0].data.length>1,n=this.type,o=this.toMathMLattributes(),r=[],l=t+(i?"  "+(s?"  ":""):"")+"  ",h=0,u=this.data.length;h<u;h++)this.data[h]?r.push(this.data[h].toMathML(l)):r.push(l+"<mrow />");if(0===r.length||1===r.length&&""===r[0]){if(!i)return"<"+n+o+" />";r.push(l+"<mrow />")}if(i){s&&(r.unshift(t+"    <mrow>"),r.push(t+"    </mrow>")),r.unshift(t+"  <semantics>");var d=a.originalText.replace(/[&<>]/g,(function(t){return{">":"&gt;","<":"&lt;","&":"&amp;"}[t]}));r.push(t+'    <annotation encoding="'+this.toMathMLquote(i)+'">'+d+"</annotation>"),r.push(t+"  </semantics>")}return t+"<"+n+o+">\n"+r.join("\n")+"\n"+t+"</"+n+">"}}),t.msubsup.Augment({toMathML:function(t){var e=this.type;null==this.data[this.sup]&&(e="msub"),null==this.data[this.sub]&&(e="msup");var a=this.toMathMLattributes();delete this.data[0].inferred;for(var i=[],s=0,n=this.data.length;s<n;s++)this.data[s]&&i.push(this.data[s].toMathML(t+"  "));return t+"<"+e+a+">\n"+i.join("\n")+"\n"+t+"</"+e+">"}}),t.munderover.Augment({toMathML:function(e){var a=this.type,i=this.data[this.base];i&&i.isa(t.TeXAtom)&&i.movablelimits&&!i.Get("displaystyle")?(type="msubsup",null==this.data[this.under]&&(a="msup"),null==this.data[this.over]&&(a="msub")):(null==this.data[this.under]&&(a="mover"),null==this.data[this.over]&&(a="munder"));var s=this.toMathMLattributes();delete this.data[0].inferred;for(var n=[],o=0,r=this.data.length;o<r;o++)this.data[o]&&n.push(this.data[o].toMathML(e+"  "));return e+"<"+a+s+">\n"+n.join("\n")+"\n"+e+"</"+a+">"}}),t.TeXAtom.Augment({toMathML:function(t){var e=this.toMathMLattributes();return e||1!==this.data[0].data.length?t+"<mrow"+e+">\n"+this.data[0].toMathML(t+"  ")+"\n"+t+"</mrow>":t.substr(2)+this.data[0].toMathML(t)}}),t.chars.Augment({toMathML:function(t){return(t||"")+this.toMathMLquote(this.toString())}}),t.entity.Augment({toMathML:function(t){return(t||"")+"&"+this.toMathMLquote(this.data[0])+";\x3c!-- "+this.toString()+" --\x3e"}}),t.xml.Augment({toMathML:function(t){return(t||"")+this.toString()}}),MathJax.Hub.Register.StartupHook("TeX mathchoice Ready",(function(){t.TeXmathchoice.Augment({toMathML:function(t){return this.Core().toMathML(t)}})})),MathJax.Hub.Startup.signal.Post("toMathML Ready")})),MathJax.Ajax.loadComplete("[MathJax]/extensions/toMathML.js"),function(t,e){var a,i=function(t){return MathJax.Localization._.apply(MathJax.Localization,[["MathML",t]].concat([].slice.call(arguments,1)))};t.Parse=MathJax.Object.Subclass({Init:function(t,e){this.Parse(t,e)},Parse:function(e,a){var i;"string"!=typeof e?i=e.parentNode:null==(i=t.ParseXML(this.preProcessMath.call(this,e)))&&t.Error(["ErrorParsingMathML","Error parsing MathML"]);var s=i.getElementsByTagName("parsererror")[0];if(s&&t.Error(["ParsingError","Error parsing MathML: %1",s.textContent.replace(/This page.*?errors:|XML Parsing Error: |Below is a rendering of the page.*/g,"")]),1!==i.childNodes.length&&t.Error(["MathMLSingleElement","MathML must be formed by a single element"]),"html"===i.firstChild.nodeName.toLowerCase()){var n=i.getElementsByTagName("h1")[0];n&&"XML parsing error"===n.textContent&&n.nextSibling&&t.Error(["ParsingError","Error parsing MathML: %1",String(n.nextSibling.nodeValue).replace(/fatal parsing error: /,"")])}"math"!==i.firstChild.nodeName.toLowerCase().replace(/^[a-z]+:/,"")&&t.Error(["MathMLRootElement","MathML must be formed by a <math> element, not %1","<"+i.firstChild.nodeName+">"]);var o={math:i.firstChild,script:a};t.DOMfilterHooks.Execute(o),this.mml=this.MakeMML(o.math)},MakeMML:function(e){var s,n=String(e.getAttribute("class")||""),o=e.nodeName.toLowerCase().replace(/^[a-z]+:/,""),r=n.match(/(^| )MJX-TeXAtom-([^ ]*)/);if(r)s=this.TeXAtom(r[2],"OP"===r[2]&&!n.match(/MJX-fixedlimits/));else{if(!(a[o]&&a[o].isa&&a[o].isa(a.mbase)))return MathJax.Hub.signal.Post(["MathML Jax - unknown node type",o]),a.Error(i("UnknownNodeType","Unknown node type: %1",o));s=a[o]()}return this.AddAttributes(s,e),this.CheckClass(s,s.class),this.AddChildren(s,e),t.config.useMathMLspacing&&(s.useMMLspacing=8),s},TeXAtom:function(t,e){var i=a.TeXAtom().With({texClass:a.TEXCLASS[t]});return e&&(i.movesupsub=i.movablelimits=!0),i},CheckClass:function(t,e){for(var i=[],s=0,n=(e=(e||"").split(/ /)).length;s<n;s++)"MJX-"===e[s].substr(0,4)?"MJX-arrow"===e[s]?t.notation.match("/"+a.NOTATION.UPDIAGONALARROW+"/")||(t.notation+=" "+a.NOTATION.UPDIAGONALARROW):"MJX-variant"===e[s]?(t.variantForm=!0,MathJax.Extension["TeX/AMSsymbols"]||MathJax.Hub.RestartAfter(MathJax.Ajax.Require("[MathJax]/extensions/TeX/AMSsymbols.js"))):"MJX-TeXAtom"!==e[s].substr(0,11)&&(t.mathvariant=e[s].substr(3),"-tex-caligraphic-bold"!==t.mathvariant&&"-tex-oldstyle-bold"!==t.mathvariant||MathJax.Extension["TeX/boldsymbol"]||MathJax.Hub.RestartAfter(MathJax.Ajax.Require("[MathJax]/extensions/TeX/boldsymbol.js"))):i.push(e[s]);i.length?t.class=i.join(" "):delete t.class},AddAttributes:function(t,e){t.attr={},t.attrNames=[];for(var i=0,s=e.attributes.length;i<s;i++){var n=e.attributes[i].name;if("xlink:href"==n&&(n="href"),!n.match(/:/)&&!n.match(/^_moz-math-((column|row)(align|line)|font-style)$/)){var o=e.attributes[i].value;o=this.filterAttribute(n,o);var r="mstyle"===t.type?a.math.prototype.defaults:t.defaults;if(null!=o){var l=o.toLowerCase();"true"!==l&&"false"!==l||"boolean"!=typeof r[n]&&r[n]!==a.INHERIT&&"math"!==t.type&&"mstyle"!==t.type&&(r[n]!==a.AUTO||null!=t.defaultDef&&"boolean"!=typeof t.defaultDef[n])||(o="true"===l),null!=r[n]||a.copyAttributes[n]?t[n]=o:t.attr[n]=o,t.attrNames.push(n)}}}},filterAttribute:function(t,e){return e},AddChildren:function(e,i){for(var s=0,n=i.childNodes.length;s<n;s++){var o=i.childNodes[s];if("#comment"!==o.nodeName)if("#text"===o.nodeName)if(!e.isToken&&!e.isChars||e.mmlSelfClosing)o.nodeValue.match(/\S/)&&t.Error(["UnexpectedTextNode","Unexpected text node: %1","'"+o.nodeValue+"'"]);else{var r=o.nodeValue;e.isToken&&(r=r.replace(/&([a-z][a-z0-9]*);/gi,this.replaceEntity),r=this.trimSpace(r)),e.Append(a.chars(r))}else if("annotation-xml"===e.type)e.Append(a.xml(o));else{var l=this.MakeMML(o);e.Append(l),l.mmlSelfClosing&&l.data.length&&(e.Append.apply(e,l.data),l.data=[])}}if("mrow"===e.type&&e.data.length>=2){var h=e.data[0],u=e.data[e.data.length-1];"mo"===h.type&&h.Get("fence")&&"mo"===u.type&&u.Get("fence")&&(h.data[0]&&(e.open=h.data.join("")),u.data[0]&&(e.close=u.data.join("")))}},preProcessMath:function(t){t.match(/^<[a-z]+:/i)&&!t.match(/^<[^<>]* xmlns:/)&&(t=t.replace(/^<([a-z]+)(:math)/i,'<$1$2 xmlns:$1="http://www.w3.org/1998/Math/MathML"'));var e=t.match(/^(<math( ('.*?'|".*?"|[^>])+)>)/i);return e&&e[2].match(/ (?!xmlns=)[a-z]+=\"http:/i)&&(t=e[1].replace(/ (?!xmlns=)([a-z]+=(['"])http:.*?\2)/gi," xmlns:$1 $1")+t.substr(e[0].length)),t.match(/^<math[ >]/i)&&!t.match(/^<[^<>]* xmlns=/)&&(t=t.replace(/^<(math)/i,'<math xmlns="http://www.w3.org/1998/Math/MathML"')),(t=t.replace(/^\s*(?:\/\/)?<!(--)?\[CDATA\[((.|\n)*)(\/\/)?\]\]\1>\s*$/,"$2")).replace(/&([a-z][a-z0-9]*);/gi,this.replaceEntity)},trimSpace:function(t){return t.replace(/[\t\n\r]/g," ").replace(/^ +/,"").replace(/ +$/,"").replace(/  +/g," ")},replaceEntity:function(e,a){if(a.match(/^(lt|amp|quot)$/))return e;if(t.Parse.Entity[a])return t.Parse.Entity[a];var i=a.charAt(0).toLowerCase(),s=a.match(/^[a-zA-Z](fr|scr|opf)$/);return s&&(i=s[1]),t.Parse.loaded[i]||(t.Parse.loaded[i]=!0,MathJax.Hub.RestartAfter(MathJax.Ajax.Require(t.entityDir+"/"+i+".js"))),e}},{loaded:[]}),t.Augment({sourceMenuTitle:["OriginalMathML","Original MathML"],prefilterHooks:MathJax.Callback.Hooks(!0),DOMfilterHooks:MathJax.Callback.Hooks(!0),postfilterHooks:MathJax.Callback.Hooks(!0),Translate:function(i){this.ParseXML||(this.ParseXML=this.createParser());var s,n,o={script:i};i.firstChild&&"math"===i.firstChild.nodeName.toLowerCase().replace(/^[a-z]+:/,"")?o.math=i.firstChild:(n=MathJax.HTML.getScript(i),e.isMSIE&&(n=n.replace(/(&nbsp;)+$/,"")),o.math=n);var r=this.prefilterHooks.Execute(o);if(r)return r;n=o.math;try{s=t.Parse(n,i).mml}catch(t){if(!t.mathmlError)throw t;s=this.formatError(t,n,i)}return o.math=a(s),this.postfilterHooks.Execute(o)||o.math},prefilterMath:function(t,e){return t},prefilterMathML:function(t,e){return t},formatError:function(t,e,i){var s=t.message.replace(/\n.*/,"");return MathJax.Hub.signal.Post(["MathML Jax - parse error",s,e,i]),a.Error(s)},Error:function(t){throw MathJax.Object.isArray(t)&&(t=i.apply(i,t)),MathJax.Hub.Insert(Error(t),{mathmlError:!0})},parseDOM:function(t){return this.parser.parseFromString(t,"text/xml")},parseMS:function(t){return this.parser.loadXML(t)?this.parser:null},parseDIV:function(t){this.div.innerHTML="<div>"+t.replace(/<([a-z]+)([^>]*)\/>/g,"<$1$2></$1>")+"</div>";var e=this.div.firstChild;return this.div.innerHTML="",e},parseError:function(t){return null},createMSParser:function(){for(var t=null,e=["MSXML2.DOMDocument.6.0","MSXML2.DOMDocument.5.0","MSXML2.DOMDocument.4.0","MSXML2.DOMDocument.3.0","MSXML2.DOMDocument.2.0","Microsoft.XMLDOM"],a=0,i=e.length;a<i&&!t;a++)try{t=new ActiveXObject(e[a])}catch(t){}return t},createParser:function(){return window.DOMParser?(this.parser=new DOMParser,this.parseDOM):window.ActiveXObject?(this.parser=this.createMSParser(),this.parser?(this.parser.async=!1,this.parseMS):(MathJax.Localization.Try(this.parserCreationError),this.parseError)):(this.div=MathJax.Hub.Insert(document.createElement("div"),{style:{visibility:"hidden",overflow:"hidden",height:"1px",position:"absolute",top:0}}),document.body.firstChild?document.body.insertBefore(this.div,document.body.firstChild):document.body.appendChild(this.div),this.parseDIV)},parserCreationError:function(){alert(i("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).mspace.Augment({mmlSelfClosing:!0}),a.none.Augment({mmlSelfClosing:!0}),a.mprescripts.Augment({mmlSelfClosing:!0}),a.maligngroup.Augment({mmlSelfClosing:!0}),a.malignmark.Augment({mmlSelfClosing:!0})}}),t.prefilterHooks.Add((function(e){e.math="string"==typeof e.math?t.prefilterMath(e.math,e.script):t.prefilterMathML(e.math,e.script)})),t.Parse.Entity={ApplyFunction:"⁡",Backslash:"∖",Because:"∵",Breve:"˘",Cap:"⋒",CenterDot:"·",CircleDot:"⊙",CircleMinus:"⊖",CirclePlus:"⊕",CircleTimes:"⊗",Congruent:"≡",ContourIntegral:"∮",Coproduct:"∐",Cross:"⨯",Cup:"⋓",CupCap:"≍",Dagger:"‡",Del:"∇",Delta:"Δ",Diamond:"⋄",DifferentialD:"ⅆ",DotEqual:"≐",DoubleDot:"¨",DoubleRightTee:"⊨",DoubleVerticalBar:"∥",DownArrow:"↓",DownLeftVector:"↽",DownRightVector:"⇁",DownTee:"⊤",Downarrow:"⇓",Element:"∈",EqualTilde:"≂",Equilibrium:"⇌",Exists:"∃",ExponentialE:"ⅇ",FilledVerySmallSquare:"▪",ForAll:"∀",Gamma:"Γ",Gg:"⋙",GreaterEqual:"≥",GreaterEqualLess:"⋛",GreaterFullEqual:"≧",GreaterLess:"≷",GreaterSlantEqual:"⩾",GreaterTilde:"≳",Hacek:"ˇ",Hat:"^",HumpDownHump:"≎",HumpEqual:"≏",Im:"ℑ",ImaginaryI:"ⅈ",Integral:"∫",Intersection:"⋂",InvisibleComma:"⁣",InvisibleTimes:"⁢",Lambda:"Λ",Larr:"↞",LeftAngleBracket:"⟨",LeftArrow:"←",LeftArrowRightArrow:"⇆",LeftCeiling:"⌈",LeftDownVector:"⇃",LeftFloor:"⌊",LeftRightArrow:"↔",LeftTee:"⊣",LeftTriangle:"⊲",LeftTriangleEqual:"⊴",LeftUpVector:"↿",LeftVector:"↼",Leftarrow:"⇐",Leftrightarrow:"⇔",LessEqualGreater:"⋚",LessFullEqual:"≦",LessGreater:"≶",LessSlantEqual:"⩽",LessTilde:"≲",Ll:"⋘",Lleftarrow:"⇚",LongLeftArrow:"⟵",LongLeftRightArrow:"⟷",LongRightArrow:"⟶",Longleftarrow:"⟸",Longleftrightarrow:"⟺",Longrightarrow:"⟹",Lsh:"↰",MinusPlus:"∓",NestedGreaterGreater:"≫",NestedLessLess:"≪",NotDoubleVerticalBar:"∦",NotElement:"∉",NotEqual:"≠",NotExists:"∄",NotGreater:"≯",NotGreaterEqual:"≱",NotLeftTriangle:"⋪",NotLeftTriangleEqual:"⋬",NotLess:"≮",NotLessEqual:"≰",NotPrecedes:"⊀",NotPrecedesSlantEqual:"⋠",NotRightTriangle:"⋫",NotRightTriangleEqual:"⋭",NotSubsetEqual:"⊈",NotSucceeds:"⊁",NotSucceedsSlantEqual:"⋡",NotSupersetEqual:"⊉",NotTilde:"≁",NotVerticalBar:"∤",Omega:"Ω",OverBar:"‾",OverBrace:"⏞",PartialD:"∂",Phi:"Φ",Pi:"Π",PlusMinus:"±",Precedes:"≺",PrecedesEqual:"⪯",PrecedesSlantEqual:"≼",PrecedesTilde:"≾",Product:"∏",Proportional:"∝",Psi:"Ψ",Rarr:"↠",Re:"ℜ",ReverseEquilibrium:"⇋",RightAngleBracket:"⟩",RightArrow:"→",RightArrowLeftArrow:"⇄",RightCeiling:"⌉",RightDownVector:"⇂",RightFloor:"⌋",RightTee:"⊢",RightTeeArrow:"↦",RightTriangle:"⊳",RightTriangleEqual:"⊵",RightUpVector:"↾",RightVector:"⇀",Rightarrow:"⇒",Rrightarrow:"⇛",Rsh:"↱",Sigma:"Σ",SmallCircle:"∘",Sqrt:"√",Square:"□",SquareIntersection:"⊓",SquareSubset:"⊏",SquareSubsetEqual:"⊑",SquareSuperset:"⊐",SquareSupersetEqual:"⊒",SquareUnion:"⊔",Star:"⋆",Subset:"⋐",SubsetEqual:"⊆",Succeeds:"≻",SucceedsEqual:"⪰",SucceedsSlantEqual:"≽",SucceedsTilde:"≿",SuchThat:"∋",Sum:"∑",Superset:"⊃",SupersetEqual:"⊇",Supset:"⋑",Therefore:"∴",Theta:"Θ",Tilde:"∼",TildeEqual:"≃",TildeFullEqual:"≅",TildeTilde:"≈",UnderBar:"_",UnderBrace:"⏟",Union:"⋃",UnionPlus:"⊎",UpArrow:"↑",UpDownArrow:"↕",UpTee:"⊥",Uparrow:"⇑",Updownarrow:"⇕",Upsilon:"Υ",Vdash:"⊩",Vee:"⋁",VerticalBar:"∣",VerticalTilde:"≀",Vvdash:"⊪",Wedge:"⋀",Xi:"Ξ",acute:"´",aleph:"ℵ",alpha:"α",amalg:"⨿",and:"∧",ang:"∠",angmsd:"∡",angsph:"∢",ape:"≊",backprime:"‵",backsim:"∽",backsimeq:"⋍",beta:"β",beth:"ℶ",between:"≬",bigcirc:"◯",bigodot:"⨀",bigoplus:"⨁",bigotimes:"⨂",bigsqcup:"⨆",bigstar:"★",bigtriangledown:"▽",bigtriangleup:"△",biguplus:"⨄",blacklozenge:"⧫",blacktriangle:"▴",blacktriangledown:"▾",blacktriangleleft:"◂",bowtie:"⋈",boxdl:"┐",boxdr:"┌",boxminus:"⊟",boxplus:"⊞",boxtimes:"⊠",boxul:"┘",boxur:"└",bsol:"\\",bull:"•",cap:"∩",check:"✓",chi:"χ",circ:"ˆ",circeq:"≗",circlearrowleft:"↺",circlearrowright:"↻",circledR:"®",circledS:"Ⓢ",circledast:"⊛",circledcirc:"⊚",circleddash:"⊝",clubs:"♣",colon:":",comp:"∁",ctdot:"⋯",cuepr:"⋞",cuesc:"⋟",cularr:"↶",cup:"∪",curarr:"↷",curlyvee:"⋎",curlywedge:"⋏",dagger:"†",daleth:"ℸ",ddarr:"⇊",deg:"°",delta:"δ",digamma:"ϝ",div:"÷",divideontimes:"⋇",dot:"˙",doteqdot:"≑",dotplus:"∔",dotsquare:"⊡",dtdot:"⋱",ecir:"≖",efDot:"≒",egs:"⪖",ell:"ℓ",els:"⪕",empty:"∅",epsi:"ε",epsiv:"ϵ",erDot:"≓",eta:"η",eth:"ð",flat:"♭",fork:"⋔",frown:"⌢",gEl:"⪌",gamma:"γ",gap:"⪆",gimel:"ℷ",gnE:"≩",gnap:"⪊",gne:"⪈",gnsim:"⋧",gt:">",gtdot:"⋗",harrw:"↭",hbar:"ℏ",hellip:"…",hookleftarrow:"↩",hookrightarrow:"↪",imath:"ı",infin:"∞",intcal:"⊺",iota:"ι",jmath:"ȷ",kappa:"κ",kappav:"ϰ",lEg:"⪋",lambda:"λ",lap:"⪅",larrlp:"↫",larrtl:"↢",lbrace:"{",lbrack:"[",le:"≤",leftleftarrows:"⇇",leftthreetimes:"⋋",lessdot:"⋖",lmoust:"⎰",lnE:"≨",lnap:"⪉",lne:"⪇",lnsim:"⋦",longmapsto:"⟼",looparrowright:"↬",lowast:"∗",loz:"◊",lt:"<",ltimes:"⋉",ltri:"◃",macr:"¯",malt:"✠",mho:"℧",mu:"μ",multimap:"⊸",nLeftarrow:"⇍",nLeftrightarrow:"⇎",nRightarrow:"⇏",nVDash:"⊯",nVdash:"⊮",natur:"♮",nearr:"↗",nharr:"↮",nlarr:"↚",not:"¬",nrarr:"↛",nu:"ν",nvDash:"⊭",nvdash:"⊬",nwarr:"↖",omega:"ω",omicron:"ο",or:"∨",osol:"⊘",period:".",phi:"φ",phiv:"ϕ",pi:"π",piv:"ϖ",prap:"⪷",precnapprox:"⪹",precneqq:"⪵",precnsim:"⋨",prime:"′",psi:"ψ",rarrtl:"↣",rbrace:"}",rbrack:"]",rho:"ρ",rhov:"ϱ",rightrightarrows:"⇉",rightthreetimes:"⋌",ring:"˚",rmoust:"⎱",rtimes:"⋊",rtri:"▹",scap:"⪸",scnE:"⪶",scnap:"⪺",scnsim:"⋩",sdot:"⋅",searr:"↘",sect:"§",sharp:"♯",sigma:"σ",sigmav:"ς",simne:"≆",smile:"⌣",spades:"♠",sub:"⊂",subE:"⫅",subnE:"⫋",subne:"⊊",supE:"⫆",supnE:"⫌",supne:"⊋",swarr:"↙",tau:"τ",theta:"θ",thetav:"ϑ",tilde:"˜",times:"×",triangle:"▵",triangleq:"≜",upsi:"υ",upuparrows:"⇈",veebar:"⊻",vellip:"⋮",weierp:"℘",xi:"ξ",yen:"¥",zeta:"ζ",zigrarr:"⇝"},t.loadComplete("jax.js")}(MathJax.InputJax.MathML,MathJax.Hub.Browser),function(t,e,a,i){var s,n,o,r,l="'Times New Roman',Times,STIXGeneral,serif",h={".MJXp-script":{"font-size":".8em"},".MJXp-right":{"-webkit-transform-origin":"right","-moz-transform-origin":"right","-ms-transform-origin":"right","-o-transform-origin":"right","transform-origin":"right"},".MJXp-bold":{"font-weight":"bold"},".MJXp-italic":{"font-style":"italic"},".MJXp-scr":{"font-family":"MathJax_Script,"+l},".MJXp-frak":{"font-family":"MathJax_Fraktur,"+l},".MJXp-sf":{"font-family":"MathJax_SansSerif,"+l},".MJXp-cal":{"font-family":"MathJax_Caligraphic,"+l},".MJXp-mono":{"font-family":"MathJax_Typewriter,"+l},".MJXp-largeop":{"font-size":"150%"},".MJXp-largeop.MJXp-int":{"vertical-align":"-.2em"},".MJXp-math":{display:"inline-block","line-height":"1.2","text-indent":"0","font-family":l,"white-space":"nowrap","border-collapse":"collapse"},".MJXp-display":{display:"block","text-align":"center",margin:"1em 0"},".MJXp-math span":{display:"inline-block"},".MJXp-box":{display:"block!important","text-align":"center"},".MJXp-box:after":{content:'" "'},".MJXp-rule":{display:"block!important","margin-top":".1em"},".MJXp-char":{display:"block!important"},".MJXp-mo":{margin:"0 .15em"},".MJXp-mfrac":{margin:"0 .125em","vertical-align":".25em"},".MJXp-denom":{display:"inline-table!important",width:"100%"},".MJXp-denom > *":{display:"table-row!important"},".MJXp-surd":{"vertical-align":"top"},".MJXp-surd > *":{display:"block!important"},".MJXp-script-box > * ":{display:"table!important",height:"50%"},".MJXp-script-box > * > *":{display:"table-cell!important","vertical-align":"top"},".MJXp-script-box > *:last-child > *":{"vertical-align":"bottom"},".MJXp-script-box > * > * > *":{display:"block!important"},".MJXp-mphantom":{visibility:"hidden"},".MJXp-munderover, .MJXp-munder":{display:"inline-table!important"},".MJXp-over":{display:"inline-block!important","text-align":"center"},".MJXp-over > *":{display:"block!important"},".MJXp-munderover > *, .MJXp-munder > *":{display:"table-row!important"},".MJXp-mtable":{"vertical-align":".25em",margin:"0 .125em"},".MJXp-mtable > *":{display:"inline-table!important","vertical-align":"middle"},".MJXp-mtr":{display:"table-row!important"},".MJXp-mtd":{display:"table-cell!important","text-align":"center",padding:".5em 0 0 .5em"},".MJXp-mtr > .MJXp-mtd:first-child":{"padding-left":0},".MJXp-mtr:first-child > .MJXp-mtd":{"padding-top":0},".MJXp-mlabeledtr":{display:"table-row!important"},".MJXp-mlabeledtr > .MJXp-mtd:first-child":{"padding-left":0},".MJXp-mlabeledtr:first-child > .MJXp-mtd":{"padding-top":0},".MJXp-merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"1px 3px","font-style":"normal","font-size":"90%"}};!function(){for(var t=0;t<10;t++){var e="scaleX(."+t+")";h[".MJXp-scale"+t]={"-webkit-transform":e,"-moz-transform":e,"-ms-transform":e,"-o-transform":e,transform:e}}}();var u=1e6,d="V",c="H";i.Augment({settings:e.config.menuSettings,config:{styles:h},hideProcessedMath:!1,maxStretchyParts:1e3,Config:function(){this.require||(this.require=[]),this.SUPER(arguments).Config.call(this);var t=this.settings;t.scale&&(this.config.scale=t.scale),this.require.push(MathJax.OutputJax.extensionDir+"/MathEvents.js")},Startup:function(){n=MathJax.Extension.MathEvents.Event,o=MathJax.Extension.MathEvents.Touch,r=MathJax.Extension.MathEvents.Hover,this.ContextMenu=n.ContextMenu,this.Mousedown=n.AltContextMenu,this.Mouseover=r.Mouseover,this.Mouseout=r.Mouseout,this.Mousemove=r.Mousemove;var e=a.addElement(document.body,"div",{style:{width:"5in"}});return this.pxPerInch=e.offsetWidth/5,e.parentNode.removeChild(e),t.Styles(this.config.styles,["InitializePHTML",this])},InitializePHTML:function(){},preTranslate:function(t){var i,s,r,l,h,u,d=t.jax[this.id],c=d.length;for(i=0;i<c;i++)(s=d[i]).parentNode&&((r=s.previousSibling)&&String(r.className).match(/^MathJax(_PHTML)?(_Display)?( MathJax_Process(ing|ed))?$/)&&r.parentNode.removeChild(r),(u=s.MathJax.elementJax)&&(u.PHTML={display:"block"===u.root.Get("display")},l=h=a.Element("span",{className:"MathJax_PHTML",id:u.inputID+"-Frame",isMathJax:!0,jaxID:this.id,oncontextmenu:n.Menu,onmousedown:n.Mousedown,onmouseover:n.Mouseover,onmouseout:n.Mouseout,onmousemove:n.Mousemove,onclick:n.Click,ondblclick:n.DblClick,onkeydown:n.Keydown,tabIndex:e.getTabOrder(u)}),e.Browser.noContextMenu&&(l.ontouchstart=o.start,l.ontouchend=o.end),u.PHTML.display&&(h=a.Element("div",{className:"MathJax_PHTML_Display"})).appendChild(l),h.className+=" MathJax_Processing",s.parentNode.insertBefore(h,s)))},Translate:function(t,e){if(t.parentNode){var a=t.MathJax.elementJax,i=a.root,s=document.getElementById(a.inputID+"-Frame"),n=a.PHTML.display?s.parentNode:s;this.initPHTML(i,s);try{i.toPreviewHTML(s)}catch(t){if(t.restart)for(;s.firstChild;)s.removeChild(s.firstChild);throw t}n.className=n.className.split(/ /)[0],this.hideProcessedMath&&(n.className+=" MathJax_Processed",t.MathJax.preview&&(a.PHTML.preview=t.MathJax.preview,delete t.MathJax.preview))}},postTranslate:function(t){var e=t.jax[this.id];if(this.hideProcessedMath)for(var a=0,i=e.length;a<i;a++){var s=e[a];if(s&&s.MathJax.elementJax){s.previousSibling.className=s.previousSibling.className.split(/ /)[0];var n=s.MathJax.elementJax.PHTML;n.preview&&(n.preview.innerHTML="",s.MathJax.preview=n.preview,delete n.preview)}}},getJaxFromMath:function(t){t.parentNode.className.match(/MathJax_PHTML_Display/)&&(t=t.parentNode);do{t=t.nextSibling}while(t&&"script"!==t.nodeName.toLowerCase());return e.getJaxFor(t)},getHoverSpan:function(t,e){return t.root.PHTMLspanElement()},getHoverBBox:function(t,e,a){var i=t.root.PHTML,s=t.PHTML.outerEm,n={w:i.w*s,h:i.h*s,d:i.d*s};return i.width&&(n.width=i.width),n},Zoom:function(t,e,a,i,s){e.className="MathJax",this.idPostfix="-zoom",t.root.toPHTML(e,e),this.idPostfix="",e.style.position="absolute",width||(a.style.position="absolute");var o=e.offsetWidth,r=e.offsetHeight,l=a.offsetHeight,h=a.offsetWidth;return 0===h&&(h=a.parentNode.offsetWidth),e.style.position=a.style.position="",{Y:-n.getBBox(e).h,mW:h,mH:l,zW:o,zH:r}},initPHTML:function(t,e){},Remove:function(t){var e=document.getElementById(t.inputID+"-Frame");e&&(t.PHTML.display&&(e=e.parentNode),e.parentNode.removeChild(e)),delete t.PHTML},ID:0,idPostfix:"",GetID:function(){return this.ID++,this.ID},VARIANT:{bold:"MJXp-bold",italic:"MJXp-italic","bold-italic":"MJXp-bold MJXp-italic",script:"MJXp-scr","bold-script":"MJXp-scr MJXp-bold",fraktur:"MJXp-frak","bold-fraktur":"MJXp-frak MJXp-bold",monospace:"MJXp-mono","sans-serif":"MJXp-sf","-tex-caligraphic":"MJXp-cal"},MATHSPACE:{veryverythinmathspace:1/18,verythinmathspace:2/18,thinmathspace:3/18,mediummathspace:4/18,thickmathspace:5/18,verythickmathspace:6/18,veryverythickmathspace:7/18,negativeveryverythinmathspace:-1/18,negativeverythinmathspace:-2/18,negativethinmathspace:-3/18,negativemediummathspace:-4/18,negativethickmathspace:-5/18,negativeverythickmathspace:-6/18,negativeveryverythickmathspace:-7/18,thin:.08,medium:.1,thick:.15,infinity:u},TeX:{x_height:.430554},pxPerInch:72,em:16,DELIMITERS:{"(":{dir:d},"{":{dir:d,w:.58},"[":{dir:d},"|":{dir:d,w:.275},")":{dir:d},"}":{dir:d,w:.58},"]":{dir:d},"/":{dir:d},"\\":{dir:d},"∣":{dir:d,w:.275},"∥":{dir:d,w:.55},"⌊":{dir:d,w:.5},"⌋":{dir:d,w:.5},"⌈":{dir:d,w:.5},"⌉":{dir:d,w:.5},"⟨":{dir:d,w:.5},"⟩":{dir:d,w:.5},"↑":{dir:d,w:.65},"↓":{dir:d,w:.65},"⇑":{dir:d,w:.75},"⇓":{dir:d,w:.75},"↕":{dir:d,w:.65},"⇕":{dir:d,w:.75},"⟮":{dir:d,w:.275},"⟯":{dir:d,w:.275},"⎰":{dir:d,w:.6},"⎱":{dir:d,w:.6}},REMAPACCENT:{"⃗":"→","'":"ˋ","`":"ˊ",".":"˙","^":"ˆ","-":"ˉ","~":"˜","¯":"ˉ","°":"˚","´":"ˊ","̀":"ˋ","́":"ˊ","̂":"ˆ","̃":"˜","̄":"ˉ","̅":"ˉ","̆":"˘","̇":"˙","̈":"¨","̌":"ˇ"},REMAPACCENTUNDER:{},length2em:function(t,e){if("string"!=typeof t&&(t=t.toString()),""===t)return"";if(t===s.SIZE.NORMAL)return 1;if(t===s.SIZE.BIG)return 2;if(t===s.SIZE.SMALL)return.71;if(this.MATHSPACE[t])return this.MATHSPACE[t];var a=t.match(/^\s*([-+]?(?:\.\d+|\d+(?:\.\d*)?))?(pt|em|ex|mu|px|pc|in|mm|cm|%)?/),i=parseFloat(a[1]||"1"),n=a[2];return null==e&&(e=1),"em"===n?i:"ex"===n?i*this.TeX.x_height:"%"===n?i/100*e:"px"===n?i/this.em:"pt"===n?i/10:"pc"===n?1.2*i:"in"===n?i*this.pxPerInch/this.em:"cm"===n?i*this.pxPerInch/this.em/2.54:"mm"===n?i*this.pxPerInch/this.em/25.4:"mu"===n?i/18:i*e},Em:function(t){return Math.abs(t)<.001?"0em":t.toFixed(3).replace(/\.?0+$/,"")+"em"},arrayEntry:function(t,e){return t[Math.max(0,Math.min(e,t.length-1))]}}),MathJax.Hub.Register.StartupHook("mml Jax Ready",(function(){(s=MathJax.ElementJax.mml).mbase.Augment({toPreviewHTML:function(t,e){return this.PHTMLdefaultSpan(t,e)},PHTMLdefaultSpan:function(t,e){e||(e={}),t=this.PHTMLcreateSpan(t),this.PHTMLhandleStyle(t),this.PHTMLhandleColor(t),this.isToken&&this.PHTMLhandleToken(t);for(var a=0,i=this.data.length;a<i;a++)this.PHTMLaddChild(t,a,e);return t},PHTMLaddChild:function(t,e,i){var s=this.data[e];s?(i.childSpans&&(t=a.addElement(t,"span",{className:i.className})),s.toPreviewHTML(t),i.noBBox||(this.PHTML.w+=s.PHTML.w+s.PHTML.l+s.PHTML.r,s.PHTML.h>this.PHTML.h&&(this.PHTML.h=s.PHTML.h),s.PHTML.d>this.PHTML.d&&(this.PHTML.d=s.PHTML.d),s.PHTML.t>this.PHTML.t&&(this.PHTML.t=s.PHTML.t),s.PHTML.b>this.PHTML.b&&(this.PHTML.b=s.PHTML.b))):i.forceChild&&a.addElement(t,"span")},PHTMLstretchChild:function(t,e,a){var i=this.data[t];if(i&&i.PHTMLcanStretch("Vertical",e,a)){var s=this.PHTML,n=i.PHTML,o=n.w;i.PHTMLstretchV(e,a),s.w+=n.w-o,n.h>s.h&&(s.h=n.h),n.d>s.d&&(s.d=n.d)}},PHTMLcreateSpan:function(t){if(this.PHTML||(this.PHTML={}),this.PHTML={w:0,h:0,d:0,l:0,r:0,t:0,b:0},this.inferred)return t;"mo"===this.type&&"∫"===this.data.join("")?i.lastIsInt=!0:"mspace"===this.type&&"negativethinmathspace"===this.width||(i.lastIsInt=!1),this.PHTMLspanID||(this.PHTMLspanID=i.GetID());var e=this.id||"MJXp-Span-"+this.PHTMLspanID;return a.addElement(t,"span",{className:"MJXp-"+this.type,id:e})},PHTMLspanElement:function(){return this.PHTMLspanID?document.getElementById(this.id||"MJXp-Span-"+this.PHTMLspanID):null},PHTMLhandleToken:function(t){var e=this.getValues("mathvariant");e.mathvariant!==s.VARIANT.NORMAL&&(t.className+=" "+i.VARIANT[e.mathvariant])},PHTMLhandleStyle:function(t){this.style&&(t.style.cssText=this.style)},PHTMLhandleColor:function(t){this.mathcolor&&(t.style.color=this.mathcolor),this.mathbackground&&(t.style.backgroundColor=this.mathbackground)},PHTMLhandleScriptlevel:function(t){this.Get("scriptlevel")&&(t.className+=" MJXp-script")},PHTMLhandleText:function(t,e){for(var s,n,o=0,r=0,l=0,h=0,u=e.length;h<u;h++){n=e.charCodeAt(h),s=e.charAt(h),n>=55296&&n<56319&&(h++,n=(n-55296<<10)+(e.charCodeAt(h)-56320)+65536);var d=.7,c=.22,m=.5;n<127&&(s.match(/[A-Za-ehik-or-xz0-9]/)&&(c=0),s.match(/[A-HK-Z]/)?m=.67:s.match(/[IJ]/)&&(m=.36),s.match(/[acegm-su-z]/)?d=.45:s.match(/[ij]/)&&(d=.75),s.match(/[ijlt]/)&&(m=.28)),i.DELIMITERS[s]&&(m=i.DELIMITERS[s].w||.4),d>o&&(o=d),c>r&&(r=c),l+=m}this.CHML||(this.PHTML={}),this.PHTML={h:.9,d:.3,w:l,l:0,r:0,t:o,b:r},a.addText(t,e)},PHTMLbboxFor:function(t){return this.data[t]&&this.data[t].PHTML?this.data[t].PHTML:{w:0,h:0,d:0,l:0,r:0,t:0,b:0}},PHTMLcanStretch:function(t,e,a){if(this.isEmbellished()){var i=this.Core();if(i&&i!==this)return i.PHTMLcanStretch(t,e,a)}return!1},PHTMLstretchV:function(t,e){},PHTMLstretchH:function(t){},CoreParent:function(){for(var t=this;t&&t.isEmbellished()&&t.CoreMO()===this&&!t.isa(s.math);)t=t.Parent();return t},CoreText:function(t){if(!t)return"";if(t.isEmbellished())return t.CoreMO().data.join("");for(;(t.isa(s.mrow)||t.isa(s.TeXAtom)||t.isa(s.mstyle)||t.isa(s.mphantom))&&1===t.data.length&&t.data[0];)t=t.data[0];return t.isToken?t.data.join(""):""}}),s.chars.Augment({toPreviewHTML:function(t){var e=this.toString().replace(/[\u2061-\u2064]/g,"");this.PHTMLhandleText(t,e)}}),s.entity.Augment({toPreviewHTML:function(t){var e=this.toString().replace(/[\u2061-\u2064]/g,"");this.PHTMLhandleText(t,e)}}),s.math.Augment({toPreviewHTML:function(t){return t=this.PHTMLdefaultSpan(t),"block"===this.Get("display")&&(t.className+=" MJXp-display"),t}}),s.mo.Augment({toPreviewHTML:function(t){t=this.PHTMLdefaultSpan(t),this.PHTMLadjustAccent(t);var e=this.getValues("lspace","rspace","scriptlevel","displaystyle","largeop");if(0===e.scriptlevel?(this.PHTML.l=i.length2em(e.lspace),this.PHTML.r=i.length2em(e.rspace),t.style.marginLeft=i.Em(this.PHTML.l),t.style.marginRight=i.Em(this.PHTML.r)):(this.PHTML.l=.15,this.PHTML.r=.1),e.displaystyle&&e.largeop){var s=a.Element("span",{className:"MJXp-largeop"});s.appendChild(t.firstChild),t.appendChild(s),this.PHTML.h*=1.2,this.PHTML.d*=1.2,"∫"===this.data.join("")&&(s.className+=" MJXp-int")}return t},PHTMLadjustAccent:function(t){var e=this.CoreParent();if(e&&e.isa(s.munderover)&&1===this.CoreText(e.data[e.base]).length){var a,n=e.data[e.over],o=e.data[e.under],r=this.data.join("");n&&this===n.CoreMO()&&e.Get("accent")?a=i.REMAPACCENT[r]:o&&this===o.CoreMO()&&e.Get("accentunder")&&(a=i.REMAPACCENTUNDER[r]),a&&(r=t.innerHTML=a),r.match(/[\u02C6-\u02DC\u00A8]/)?this.PHTML.acc=-.52:"→"===r&&(this.PHTML.acc=-.15,this.PHTML.vec=!0)}},PHTMLcanStretch:function(t,e,a){if(!this.Get("stretchy"))return!1;var s=this.data.join("");if(s.length>1)return!1;var n=(s=i.DELIMITERS[s])&&s.dir===t.substr(0,1);return n&&(n=this.PHTML.h!==e||this.PHTML.d!==a||this.Get("minsize",!0)||this.Get("maxsize",!0)),n},PHTMLstretchV:function(t,e){var s=this.PHTMLspanElement(),n=this.PHTML,o=this.getValues("symmetric","maxsize","minsize");c=o.symmetric?2*Math.max(t-.25,e+.25):t+e,o.maxsize=i.length2em(o.maxsize,n.h+n.d),o.minsize=i.length2em(o.minsize,n.h+n.d);var r=(c=Math.max(o.minsize,Math.min(o.maxsize,c)))/(n.h+n.d-.3),l=a.Element("span",{style:{"font-size":i.Em(r)}});if(r>1.25){var h=Math.ceil(1.25/r*10);l.className="MJXp-right MJXp-scale"+h,l.style.marginLeft=i.Em(n.w*(h/10-1)+.07),n.w*=r*h/10}l.appendChild(s.firstChild),s.appendChild(l),o.symmetric&&(s.style.verticalAlign=i.Em(.25*(1-r)))}}),s.mspace.Augment({toPreviewHTML:function(t){t=this.PHTMLdefaultSpan(t);var e=this.getValues("height","depth","width"),a=i.length2em(e.width),s=i.length2em(e.height),n=i.length2em(e.depth),o=this.PHTML;return o.w=a,o.h=s,o.d=n,a<0&&(i.lastIsInt||(t.style.marginLeft=i.Em(a)),a=0),t.style.width=i.Em(a),t.style.height=i.Em(s+n),n&&(t.style.verticalAlign=i.Em(-n)),t}}),s.mpadded.Augment({toPreviewHTML:function(t){var e=(t=this.PHTMLdefaultSpan(t,{childSpans:!0,className:"MJXp-box",forceChild:!0})).firstChild,a=this.getValues("width","height","depth","lspace","voffset"),s=this.PHTMLdimen(a.lspace),n=0,o=0,r=s.len,l=-s.len,h=0;return""!==a.width&&((s=this.PHTMLdimen(a.width,"w",0)).pm?l+=s.len:t.style.width=i.Em(s.len)),""!==a.height&&((s=this.PHTMLdimen(a.height,"h",0)).pm||(n+=-this.PHTMLbboxFor(0).h),n+=s.len),""!==a.depth&&((s=this.PHTMLdimen(a.depth,"d",0)).pm||(o+=-this.PHTMLbboxFor(0).d,h+=-s.len),o+=s.len),""!==a.voffset&&(n-=(s=this.PHTMLdimen(a.voffset)).len,o+=s.len,h+=s.len),n&&(e.style.marginTop=i.Em(n)),o&&(e.style.marginBottom=i.Em(o)),r&&(e.style.marginLeft=i.Em(r)),l&&(e.style.marginRight=i.Em(l)),h&&(t.style.verticalAlign=i.Em(h)),t},PHTMLdimen:function(t,e,a){null==a&&(a=-u);var s=(t=String(t)).match(/width|height|depth/),n=s?this.PHTML[s[0].charAt(0)]:e?this.PHTML[e]:0;return{len:i.length2em(t,n)||0,pm:!!t.match(/^[-+]/)}}}),s.munderover.Augment({toPreviewHTML:function(t){var e=this.getValues("displaystyle","accent","accentunder","align"),n=this.data[this.base];if(!e.displaystyle&&null!=n&&(n.movablelimits||n.CoreMO().Get("movablelimits")))return(t=s.msubsup.prototype.toPreviewHTML.call(this,t)).className=t.className.replace(/munderover/,"msubsup"),t;t=this.PHTMLdefaultSpan(t,{childSpans:!0,className:"",noBBox:!0});var o=this.PHTMLbboxFor(this.over),r=this.PHTMLbboxFor(this.under),l=this.PHTMLbboxFor(this.base),h=this.PHTML,u=o.acc;if(this.data[this.over]){t.lastChild.firstChild&&(t.lastChild.firstChild.style.marginLeft=o.l=t.lastChild.firstChild.style.marginRight=o.r=0);var d=a.Element("span",{},[["span",{className:"MJXp-over"}]]);d.firstChild.appendChild(t.lastChild),t.childNodes.length>(this.data[this.under]?1:0)&&d.firstChild.appendChild(t.firstChild),this.data[this.over].PHTMLhandleScriptlevel(d.firstChild.firstChild),null!=u&&(o.vec&&(d.firstChild.firstChild.firstChild.style.fontSize="60%",o.h*=.6,o.d*=.6,o.w*=.6),u=u-o.d+.1,null!=l.t&&(u+=l.t-l.h),d.firstChild.firstChild.style.marginBottom=i.Em(u)),t.firstChild?t.insertBefore(d,t.firstChild):t.appendChild(d)}return this.data[this.under]&&(t.lastChild.firstChild&&(t.lastChild.firstChild.style.marginLeft=r.l=t.lastChild.firstChild.marginRight=r.r=0),this.data[this.under].PHTMLhandleScriptlevel(t.lastChild)),h.w=Math.max(.8*o.w,.8*r.w,l.w),h.h=.8*(o.h+o.d+(u||0))+l.h,h.d=l.d+.8*(r.h+r.d),t}}),s.msubsup.Augment({toPreviewHTML:function(t){t=this.PHTMLdefaultSpan(t,{noBBox:!0}),this.data[this.base]||(t.firstChild?t.insertBefore(a.Element("span"),t.firstChild):t.appendChild(a.Element("span")));var e=this.data[this.base],s=this.data[this.sub],n=this.data[this.sup];e||(e={bbox:{h:.8,d:.2}}),t.firstChild.style.marginRight=".05em";var o=Math.max(.4,e.PHTML.h-.4),r=Math.max(.2,e.PHTML.d+.1),l=this.PHTML;if(n&&s){var h=a.Element("span",{className:"MJXp-script-box",style:{height:i.Em(o+.8*n.PHTML.h+r+.8*s.PHTML.d),"vertical-align":i.Em(-r-.8*s.PHTML.d)}},[["span",{},[["span",{},[["span",{style:{"margin-bottom":i.Em(-(n.PHTML.d-.05))}}]]]]],["span",{},[["span",{},[["span",{style:{"margin-top":i.Em(-(n.PHTML.h-.05))}}]]]]]]);s.PHTMLhandleScriptlevel(h.firstChild),n.PHTMLhandleScriptlevel(h.lastChild),h.firstChild.firstChild.firstChild.appendChild(t.lastChild),h.lastChild.firstChild.firstChild.appendChild(t.lastChild),t.appendChild(h),l.h=Math.max(e.PHTML.h,.8*n.PHTML.h+o),l.d=Math.max(e.PHTML.d,.8*s.PHTML.d+r),l.w=e.PHTML.w+Math.max(n.PHTML.w,s.PHTML.w)+.07}else n?(t.lastChild.style.verticalAlign=i.Em(o),n.PHTMLhandleScriptlevel(t.lastChild),l.h=Math.max(e.PHTML.h,.8*n.PHTML.h+o),l.d=Math.max(e.PHTML.d,.8*n.PHTML.d-o),l.w=e.PHTML.w+n.PHTML.w+.07):s&&(t.lastChild.style.verticalAlign=i.Em(-r),s.PHTMLhandleScriptlevel(t.lastChild),l.h=Math.max(e.PHTML.h,.8*s.PHTML.h-r),l.d=Math.max(e.PHTML.d,.8*s.PHTML.d+r),l.w=e.PHTML.w+s.PHTML.w+.07);return t}}),s.mfrac.Augment({toPreviewHTML:function(t){t=this.PHTMLdefaultSpan(t,{childSpans:!0,className:"MJXp-box",forceChild:!0,noBBox:!0});var e=this.getValues("linethickness","displaystyle");e.displaystyle||(this.data[0]&&this.data[0].PHTMLhandleScriptlevel(t.firstChild),this.data[1]&&this.data[1].PHTMLhandleScriptlevel(t.lastChild));var s=a.Element("span",{className:"MJXp-box"},[["span",{className:"MJXp-denom"},[["span",{},[["span",{className:"MJXp-rule",style:{height:"1em"}}]]],["span"]]]]);s.firstChild.lastChild.appendChild(t.lastChild),t.appendChild(s);var n=this.PHTMLbboxFor(0),o=this.PHTMLbboxFor(1),r=this.PHTML;if(r.w=.8*Math.max(n.w,o.w),r.h=n.h+n.d+.1+.25,r.d=o.h+o.d-.25,r.l=r.r=.125,e.linethickness=Math.max(0,i.length2em(e.linethickness||"0",0)),e.linethickness){var l=s.firstChild.firstChild.firstChild,h=i.Em(e.linethickness);l.style.borderTop="none",l.style.borderBottom=(e.linethickness<.15?"1px":h)+" solid",l.style.margin=h+" 0",h=e.linethickness,s.style.marginTop=i.Em(3*h-1.2),t.style.verticalAlign=i.Em(1.5*h+.1),r.h+=1.5*h-.1,r.d+=1.5*h}else s.style.marginTop="-.7em";return t}}),s.msqrt.Augment({toPreviewHTML:function(t){return t=this.PHTMLdefaultSpan(t,{childSpans:!0,className:"MJXp-box",forceChild:!0,noBBox:!0}),this.PHTMLlayoutRoot(t,t.firstChild),t},PHTMLlayoutRoot:function(t,e){var s=this.PHTMLbboxFor(0),n=Math.ceil(100*(s.h+s.d+.14)),o=i.Em(14/n),r=a.Element("span",{className:"MJXp-surd"},[["span",{style:{"font-size":n+"%","margin-top":o}},["√"]]]),l=a.Element("span",{className:"MJXp-root"},[["span",{className:"MJXp-rule",style:{"border-top":".08em solid"}}]]),h=1.2/2.2*n/100;if(n>150){var u=Math.ceil(150/n*10);r.firstChild.className="MJXp-right MJXp-scale"+u,r.firstChild.style.marginLeft=i.Em(h*(u/10-1)/n*100),h=h*u/10,l.firstChild.style.borderTopWidth=i.Em(.08/Math.sqrt(u/10))}return l.appendChild(e),t.appendChild(r),t.appendChild(l),this.PHTML.h=s.h+.18,this.PHTML.d=s.d,this.PHTML.w=s.w+h,t}}),s.mroot.Augment({toPreviewHTML:function(t){t=this.PHTMLdefaultSpan(t,{childSpans:!0,className:"MJXp-box",forceChild:!0,noBBox:!0});var e=this.PHTMLbboxFor(1),s=t.removeChild(t.lastChild),n=this.PHTMLlayoutRoot(a.Element("span"),t.firstChild);s.className="MJXp-script";var o=parseInt(n.firstChild.firstChild.style.fontSize),r=o/120*.55+.8*e.d,l=o/120*-.6;return o>150&&(l*=.95*Math.ceil(150/o*10)/10),s.style.marginRight=i.Em(l),s.style.verticalAlign=i.Em(r),-l>.8*e.w&&(s.style.marginLeft=i.Em(-l-.8*e.w)),t.appendChild(s),t.appendChild(n),this.PHTML.w+=Math.max(0,.8*e.w+l),this.PHTML.h=Math.max(this.PHTML.h,.8*e.h+r),t},PHTMLlayoutRoot:s.msqrt.prototype.PHTMLlayoutRoot}),s.mfenced.Augment({toPreviewHTML:function(t){t=this.PHTMLcreateSpan(t),this.PHTMLhandleStyle(t),this.PHTMLhandleColor(t),this.addFakeNodes(),this.PHTMLaddChild(t,"open",{});for(var e=0,a=this.data.length;e<a;e++)this.PHTMLaddChild(t,"sep"+e,{}),this.PHTMLaddChild(t,e,{});this.PHTMLaddChild(t,"close",{});var i=this.PHTML.h,s=this.PHTML.d;for(this.PHTMLstretchChild("open",i,s),e=0,a=this.data.length;e<a;e++)this.PHTMLstretchChild("sep"+e,i,s),this.PHTMLstretchChild(e,i,s);return this.PHTMLstretchChild("close",i,s),t}}),s.mrow.Augment({toPreviewHTML:function(t){t=this.PHTMLdefaultSpan(t);for(var e=this.PHTML.h,a=this.PHTML.d,i=0,s=this.data.length;i<s;i++)this.PHTMLstretchChild(i,e,a);return t}}),s.mstyle.Augment({toPreviewHTML:function(t){return t=this.PHTMLdefaultSpan(t),this.PHTMLhandleScriptlevel(t),t}}),s.TeXAtom.Augment({toPreviewHTML:function(t){return(t=this.PHTMLdefaultSpan(t)).className="MJXp-mrow",t}}),s.mtable.Augment({toPreviewHTML:function(t){t=this.PHTMLdefaultSpan(t,{noBBox:!0});var e,s,n,o,r=this.getValues("columnalign","rowalign","columnspacing","rowspacing","columnwidth","equalcolumns","equalrows","columnlines","rowlines","frame","framespacing","align","width"),l=MathJax.Hub.SplitList,h=l(r.columnspacing),u=l(r.rowspacing),d=l(r.columnalign),c=l(r.rowalign);for(e=0,s=h.length;e<s;e++)h[e]=i.length2em(h[e]);for(e=0,s=u.length;e<s;e++)u[e]=i.length2em(u[e]);for(var m=a.Element("span");t.firstChild;)m.appendChild(t.firstChild);t.appendChild(m);var p=0,M=0;for(e=0,s=this.data.length;e<s;e++){var f=this.data[e];if(f){var g=i.arrayEntry(u,e-1),x=i.arrayEntry(c,e),v=f.PHTML;f.PHTMLspanElement().style.verticalAlign=x;var T="mlabeledtr"===f.type?1:0;for(n=0,o=f.data.length;n<o-T;n++){var E=f.data[n+T];if(E){var b=i.arrayEntry(h,n-1),C=i.arrayEntry(d,n),L=E.PHTMLspanElement();n&&(v.w+=b,L.style.paddingLeft=i.Em(b)),e&&(L.style.paddingTop=i.Em(g)),L.style.textAlign=C}}p+=v.h+v.d,e&&(p+=g),v.w>M&&(M=v.w)}}var y=this.PHTML;return y.w=M,y.h=p/2+.25,y.d=p/2-.25,y.l=y.r=.125,t}}),s.mlabeledtr.Augment({PHTMLdefaultSpan:function(t,e){e||(e={}),t=this.PHTMLcreateSpan(t),this.PHTMLhandleStyle(t),this.PHTMLhandleColor(t),this.isToken&&this.PHTMLhandleToken(t);for(var a=1,i=this.data.length;a<i;a++)this.PHTMLaddChild(t,a,e);return t}}),s.semantics.Augment({toPreviewHTML:function(t){return t=this.PHTMLcreateSpan(t),this.data[0]&&(this.data[0].toPreviewHTML(t),MathJax.Hub.Insert(this.data[0].PHTML||{},this.PHTML)),t}}),s.annotation.Augment({toPreviewHTML:function(t){}}),s["annotation-xml"].Augment({toPreviewHTML:function(t){}}),MathJax.Hub.Register.StartupHook("onLoad",(function(){setTimeout(MathJax.Callback(["loadComplete",i,"jax.js"]),0)}))})),MathJax.Hub.Register.StartupHook("End Cookie",(function(){"None"!==e.config.menuSettings.zoom&&t.Require("[MathJax]/extensions/MathZoom.js")}))}(MathJax.Ajax,MathJax.Hub,MathJax.HTML,MathJax.OutputJax.PreviewHTML),function(t,e,a){var i=t.config.menuSettings,s=MathJax.OutputJax,n=a.isMSIE&&(document.documentMode||0)<8,o=MathJax.Extension["fast-preview"]={version:"2.7.9",enabled:!0,config:t.CombineConfig("fast-preview",{Chunks:{EqnChunk:1e4,EqnChunkFactor:1,EqnChunkDelay:0},color:"inherit!important",updateTime:30,updateDelay:6,messageStyle:"none",disabled:a.isMSIE&&!a.versionAtLeast("8.0")}),Config:function(){var e,a,s,n,r;t.config["CHTML-preview"]&&MathJax.Hub.Config({"fast-preview":t.config["CHTML-preview"]});var l=this.config;l.disabled||null!=i.FastPreview||t.Config({menuSettings:{FastPreview:!0}}),i.FastPreview&&(MathJax.Ajax.Styles({".MathJax_Preview .MJXf-math":{color:l.color}}),t.Config({"HTML-CSS":l.Chunks,CommonHTML:l.Chunks,SVG:l.Chunks})),t.Register.MessageHook("Begin Math Output",(function(){!n&&o.Active()&&(e=t.processUpdateTime,a=t.processUpdateDelay,s=t.config.messageStyle,t.processUpdateTime=l.updateTime,t.processUpdateDelay=l.updateDelay,t.Config({messageStyle:l.messageStyle}),MathJax.Message.Clear(0,0),r=!0)})),t.Register.MessageHook("End Math Output",(function(){!n&&r&&(t.processUpdateTime=e,t.processUpdateDelay=a,t.Config({messageStyle:s}),n=!0)}))},Disable:function(){this.enabled=!1},Enable:function(){this.enabled=!0},Active:function(){return i.FastPreview&&this.enabled&&!(s[i.renderer]||{}).noFastPreview},Preview:function(t){if(this.Active()&&t.script.parentNode){var a=t.script.MathJax.preview||t.script.previousSibling;return a&&a.className===MathJax.Hub.config.preRemoveClass||(a=e.Element("span",{className:MathJax.Hub.config.preRemoveClass}),t.script.parentNode.insertBefore(a,t.script),t.script.MathJax.preview=a),a.innerHTML="",a.style.color=n?"black":"inherit",this.postFilter(a,t)}},postFilter:function(e,a){if(!a.math.root.toPreviewHTML){var i=MathJax.Callback.Queue();i.Push(["Require",MathJax.Ajax,"[MathJax]/jax/output/PreviewHTML/config.js"],["Require",MathJax.Ajax,"[MathJax]/jax/output/PreviewHTML/jax.js"]),t.RestartAfter(i.Push({}))}a.math.root.toPreviewHTML(e)},Register:function(e){t.Register.StartupHook(e+" Jax Require",(function(){MathJax.InputJax[e].postfilterHooks.Add(["Preview",MathJax.Extension["fast-preview"]],50)}))}};o.Register("TeX"),o.Register("MathML"),o.Register("AsciiMath"),t.Register.StartupHook("End Config",["Config",o]),t.Startup.signal.Post("fast-preview Ready")}(MathJax.Hub,MathJax.HTML,MathJax.Hub.Browser),MathJax.Ajax.loadComplete("[MathJax]/extensions/fast-preview.js"),function(t,e,a,i){var s=a.config.menuSettings,n=MathJax.Extension.AssistiveMML={version:"2.7.9",config:a.CombineConfig("AssistiveMML",{disabled:!1,styles:{".MJX_Assistive_MathML":{position:"absolute!important",top:0,left:0,clip:a.Browser.isMSIE&&(document.documentMode||0)<8?"rect(1px 1px 1px 1px)":"rect(1px, 1px, 1px, 1px)",padding:"1px 0 0 0!important",border:"0!important",height:"1px!important",width:"1px!important",overflow:"hidden!important",display:"block!important","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none"},".MJX_Assistive_MathML.MJX_Assistive_MathML_Block":{width:"100%!important"}}}),Config:function(){this.config.disabled||null!=s.assistiveMML||a.Config({menuSettings:{assistiveMML:!0}}),t.Styles(this.config.styles),a.Register.MessageHook("End Math",(function(t){if(s.assistiveMML)return n.AddAssistiveMathML(t[1])}))},AddAssistiveMathML:function(t){var e={jax:a.getAllJax(t),i:0,callback:MathJax.Callback({})};return this.HandleMML(e),e.callback},RemoveAssistiveMathML:function(t){for(var e,i=a.getAllJax(t),s=0,n=i.length;s<n;s++)(e=document.getElementById(i[s].inputID+"-Frame"))&&e.getAttribute("data-mathml")&&(e.removeAttribute("data-mathml"),e.lastChild&&e.lastChild.className.match(/MJX_Assistive_MathML/)&&e.removeChild(e.lastChild))},HandleMML:function(t){var e,a,s,n,o=t.jax.length,r=MathJax.ElementJax.mml;for(r.copyAttributes.id=1;t.i<o;){if(e=t.jax[t.i],s=document.getElementById(e.inputID+"-Frame"),"NativeMML"!==e.outputJax&&"PlainSource"!==e.outputJax&&s&&!s.getAttribute("data-mathml")){try{a=e.root.toMathML("").replace(/\n */g,"").replace(/<!--.*?-->/g,"")}catch(e){if(r.copyAttributes.id=!0,!e.restart)throw e;return MathJax.Callback.After(["HandleMML",this,t],e.restart)}s.setAttribute("data-mathml",a),n=i.addElement(s,"span",{isMathJax:!0,unselectable:"on",className:"MJX_Assistive_MathML"+("block"===e.root.Get("display")?" MJX_Assistive_MathML_Block":"")});try{n.innerHTML=a}catch(t){}s.style.position="relative",s.setAttribute("role","presentation"),s.firstChild.setAttribute("aria-hidden","true"),n.setAttribute("role","presentation")}t.i++}r.copyAttributes.id=!0,t.callback()}};a.Startup.signal.Post("AssistiveMML Ready")}(MathJax.Ajax,MathJax.Callback,MathJax.Hub,MathJax.HTML),MathJax.Callback.Queue(["Require",MathJax.Ajax,"[MathJax]/extensions/toMathML.js"],["loadComplete",MathJax.Ajax,"[MathJax]/extensions/AssistiveMML.js"],(function(){MathJax.Hub.Register.StartupHook("End Config",["Config",MathJax.Extension.AssistiveMML])})),function(t,e){var a,i,s=t.config.menuSettings,n=Function.prototype.bind?function(t,e){return t.bind(e)}:function(t,e){return function(){t.apply(e,arguments)}},o=Object.keys||function(t){var e=[];for(var a in t)t.hasOwnProperty(a)&&e.push(a);return e},r=MathJax.Ajax.config.path;r.a11y||(r.a11y=t.config.root+"/extensions/a11y");var l=e["accessibility-menu"]={version:"1.6.0",prefix:"",defaults:{},modules:[],MakeOption:function(t){return l.prefix+t},GetOption:function(t){return s[l.MakeOption(t)]},AddDefaults:function(){for(var t,e=o(l.defaults),a=0;t=e[a];a++){var i=l.MakeOption(t);void 0===s[i]&&(s[i]=l.defaults[t])}},AddMenu:function(){for(var t,e=Array(this.modules.length),s=0;t=this.modules[s];s++)e[s]=t.placeHolder;var n,o,r=i.FindId("Accessibility");r?(e.unshift(a.RULE()),r.submenu.items.push.apply(r.submenu.items,e)):((n=(i.FindId("Settings","Renderer")||{}).submenu)&&(e.unshift(a.RULE()),e.unshift(n.items.pop()),e.unshift(n.items.pop())),e.unshift("Accessibility"),r=a.SUBMENU.apply(a.SUBMENU,e),(o=i.IndexOfId("Locale"))?i.items.splice(o,0,r):i.items.push(a.RULE(),r))},Register:function(t){l.defaults[t.option]=!1,l.modules.push(t)},Startup:function(){a=MathJax.Menu.ITEM,i=MathJax.Menu.menu;for(var t,e=0;t=this.modules[e];e++)t.CreateMenu();this.AddMenu()},LoadExtensions:function(){for(var e,a=[],i=0;e=this.modules[i];i++)s[e.option]&&a.push(e.module);return a.length?t.Startup.loadArray(a):null}},h=MathJax.Extension.ModuleLoader=MathJax.Object.Subclass({option:"",name:["",""],module:"",placeHolder:null,submenu:!1,extension:null,Init:function(t,e,a,i,s){this.option=t,this.name=[e.replace(/ /g,""),e],this.module=a,this.extension=i,this.submenu=s||!1},CreateMenu:function(){var t=n(this.Load,this);this.submenu?this.placeHolder=a.SUBMENU(this.name,a.CHECKBOX(["Activate","Activate"],l.MakeOption(this.option),{action:t}),a.RULE(),a.COMMAND(["OptionsWhenActive","(Options when Active)"],null,{disabled:!0})):this.placeHolder=a.CHECKBOX(this.name,l.MakeOption(this.option),{action:t})},Load:function(){t.Queue(["Require",MathJax.Ajax,this.module,["Enable",this]])},Enable:function(t){var e=MathJax.Extension[this.extension];e&&(e.Enable(!0,!0),MathJax.Menu.saveCookie())}});l.Register(h("collapsible","Collapsible Math","[a11y]/collapsible.js","collapsible")),l.Register(h("autocollapse","Auto Collapse","[a11y]/auto-collapse.js","auto-collapse")),l.Register(h("explorer","Explorer","[a11y]/explorer.js","explorer",!0)),l.AddDefaults(),t.Register.StartupHook("End Extensions",(function(){t.Register.StartupHook("MathMenu Ready",(function(){l.Startup(),t.Startup.signal.Post("Accessibility Menu Ready")}),5)}),5),MathJax.Hub.Register.StartupHook("End Cookie",(function(){MathJax.Callback.Queue(["LoadExtensions",l],["loadComplete",MathJax.Ajax,"[a11y]/accessibility-menu.js"])}))}(MathJax.Hub,MathJax.Extension),MathJax.Ajax.loadComplete("[MathJax]/config/MML_HTMLorMML.js");