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e=document.documentMode||0,i=t.versionAtLeast("8.0");l.msieBorderWidthBug="BackCompat"===document.compatMode,l.msieEventBug=t.isIE9,l.msieAlignBug=!i||e<8,e<9&&(u.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=d=t.CombineConfig("MathEvents",d),a.Queue(t.Register.StartupHook("End Config",{}),[function(){var t=d.styles[".MathJax_Hover_Frame"];t.border=d.frame.bwidth+"px solid "+d.frame.bcolor+" ! important",t["box-shadow"]=t["-webkit-box-shadow"]=t["-moz-box-shadow"]=t["-khtml-box-shadow"]="0px 0px "+d.frame.hwidth+" "+d.frame.hcolor}],["getImages",c],["Styles",i,d.styles],["Post",t.Startup.signal,"MathEvents 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h=MathJax.Extension.MathZoom={version:"2.7.9",settings:t.config.menuSettings,scrollSize:18,HandleEvent:function(t,e,i){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,i)},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(i,a){this.Remove(),o.ClearHoverTimer(),r.ClearSelection();var s=MathJax.OutputJax[a.jaxID],h=s.getJaxFromMath(a);h.hover&&o.UnHover(h);var d=this.findContainer(a),u=Math.floor(.85*d.clientWidth),c=Math.max(document.body.clientHeight,document.documentElement.clientHeight);"visible"!==this.getOverflow(d)&&(c=Math.min(d.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;a.parentNode.insertBefore(m,a),a.parentNode.insertBefore(a,m),M.addEventListener&&M.addEventListener("mousedown",this.Remove,!0);var g=p.offsetWidth||p.clientWidth;if(u-=g,c-=g,p.style.maxWidth=u+"px",p.style.maxHeight=c+"px",this.msieTrapEventBug){var b=e.Element("span",{id:"MathJax_ZoomEventTrap",onmousedown:this.Remove});m.insertBefore(b,p)}if(this.msieZIndexBug){var x=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=x}var v=s.Zoom(h,M,a,u,c);return 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i=this.Resize(),a=i.x,s=i.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-a)+"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"),i=document.getElementById("MathJax_ZoomOverlay"),a=h.getXY(e),s=h.findContainer(e);if("visible"!==h.getOverflow(s)){i.scroll_parent=s;var n=h.getXY(s);a.x-=n.x,a.y-=n.y,n=h.getBorder(s),a.x-=n.x,a.y-=n.y}return i.style.left=-a.x+"px",i.style.top=-a.y+"px",h.msiePositionBug?setTimeout(h.SetWH,0):h.SetWH(),a},SetWH:function(){var t=document.getElementById("MathJax_ZoomOverlay");if(t){t.style.display="none";var 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a=document.getElementById("MathJax_ZoomFrame");if(a){var s=MathJax.OutputJax[a.previousSibling.jaxID].getJaxFromMath(a.previousSibling);if(t.signal.Post(["math unzoomed",s]),a.parentNode.removeChild(a),(a=document.getElementById("MathJax_ZoomTracker"))&&a.parentNode.removeChild(a),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(i)}};t.Browser.Select({MSIE:function(t){var e=document.documentMode||0,i=e>=9;h.msiePositionBug=!i,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),i&&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",i,l.styles],["Post",t.Startup.signal,"MathZoom Ready"],["loadComplete",i,"[MathJax]/extensions/MathZoom.js"])}(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.OutputJax["HTML-CSS"],MathJax.OutputJax.NativeMML),function(t,e,i,a,s){var 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L=window.pageXOffset||document.documentElement.scrollLeft,E=window.pageYOffset||document.documentElement.scrollTop,y=T.getBoundingClientRect();d=(y.right+y.left)/2+L,u=(y.bottom+y.top)/2+E}d+n.offsetWidth>M-this.margin&&(d=M-n.offsetWidth-this.margin),b.isMobile&&(d=Math.max(5,d-Math.floor(n.offsetWidth/2)),u-=20),b.skipUp=t.isContextMenu}n.style.left=d+"px",n.style.top=u+"px",document.selection&&document.selection.empty&&document.selection.empty();var C=window.pageXOffset||document.documentElement.scrollLeft,S=window.pageYOffset||document.documentElement.scrollTop;return b.Focus(n),"keydown"===t.type&&(b.skipMouseoverFromKey=!0,setTimeout((function(){delete b.skipMouseoverFromKey}),f.delay)),window.scrollTo(C,S),r(t)},Remove:function(t,e){o.Post(["unpost",b.jax]);var i=document.getElementById("MathJax_MenuFrame");return i&&(i.parentNode.removeChild(i),this.msieFixedPositionBug&&detachEvent("onresize",b.Resize)),b.jax.hover&&(delete 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r=document.documentElement||{},l=window.innerHeight||r.clientHeight||r.scrollHeight||0;b.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")},b.About.Remove=function(t){b.About.div&&(document.body.removeChild(b.About.div),delete b.About.div)},b.About.Keydown=function(t){t.keyCode!==h.ESCAPE&&("MathJax_AboutClose"!==this.id||t.keyCode!==h.SPACE&&t.keyCode!==h.RETURN)||(b.About.Remove(t),b.CurrentNode().focus(),r(t))},b.About.GetJax=function(t,e,i,a){var s=[];for(var n in e)e.hasOwnProperty(n)&&e[n]&&(a&&e[n].version||e[n].isa&&e[n].isa(e))&&s.push(d(i[0],i[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},b.About.GetFont=function(){var 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t=e.config.displayAlign,i=e.config.displayIndent,a={"text-align":t+"!important"};a["margin-"+t]=i+"!important",e.Insert(this.config.styles,{"div.MathJax_MathML":a,"div.MathJax_MathML math":{"text-align":t},"div.MathJax_MathContainer > span":{"text-align":t+"!important"}})}this.require||(this.require=[]),this.require.push(MathJax.OutputJax.extensionDir+"/MathEvents.js")},Startup:function(){return 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,e.Browser.hasMathPlayer||(this.EmExSpan=a.Element("span",{style:{position:"absolute","font-size-adjust":"none"}},[["div",{className:"MathJax_mmlExBox"}],["span",{className:"MathJax_MathML"}]]),s.math(s.mspace().With({width:"60ex"})).toNativeMML(this.EmExSpan.lastChild)),i.Styles(this.config.styles)},InitializeMML:function(){if(this.initialized=!0,e.Browser.hasMathPlayer)try{if(!e.Browser.mpNamespace){var t=document.createElement("object");t.id="mathplayer",t.classid="clsid:32F66A20-7614-11D4-BD11-00104BD3F987",document.getElementsByTagName("head")[0].appendChild(t),document.namespaces.add("m","http://www.w3.org/1998/Math/MathML"),e.Browser.mpNamespace=!0}e.Browser.mpImported||(document.namespaces.m.doImport("#mathplayer"),e.Browser.mpImported=!0)}catch(t){this.config.noMathPlayerWarning||alert(MathJax.Localization._(["MathML","MathPlayer"],"MathJax was not able to set up MathPlayer.\n\nIf MathPlayer is not installed, you need to install it first.\nOtherwise, your security settings may be preventing ActiveX     \ncontrols from running.  Use the Internet Options item under\nthe Tools menu and select the Security tab, then press the\nCustom Level button. Check that the settings for\n'Run ActiveX Controls', and 'Binary and script behaviors'\nare enabled.\n\nCurrently you will see error messages rather than\ntypeset mathematics."))}else document.body.appendChild(this.EmExSpan),this.defaultEx=this.EmExSpan.firstChild.offsetWidth/60,this.defaultMEx=this.EmExSpan.lastChild.offsetWidth/60,document.body.removeChild(this.EmExSpan)},preTranslate:function(t){var e,i,s,n,o,r,l,d,u,c,m=t.jax[this.id],p=m.length;for(e=0;e<p;e++)if((i=m[e]).parentNode&&(this.initialized||this.InitializeMML(),(s=i.previousSibling)&&"MathJax_MathML"===s.className&&s.parentNode.removeChild(s),l=i.MathJax.elementJax)){r=l.root,l.NativeMML={};var M="block"===r.Get("display")?"div":"span";n=a.Element(M,{className:"MathJax_MathML",id:l.inputID+"-Frame"},[["span",{className:"MathJax_MathContainer",isMathJax:!0,jaxID:this.id,style:{position:"relative",display:"inline-block","white-space":"nowrap"}},[["span",{isMathJax:!0,style:{display:"inline-block"}}]]]]),i.parentNode.insertBefore(n,i),h||i.parentNode.insertBefore(this.EmExSpan.cloneNode(!0),i)}for(e=0;e<p;e++)(i=m[e]).parentNode&&(l=i.MathJax.elementJax)&&(h?c=100:(d=(o=i.previousSibling).firstChild.offsetWidth/60,u=o.lastChild.offsetWidth/60,0!==d&&"NaN"!==d||(d=this.defaultEx,u=this.defaultMEx),c=this.config.matchFontHeight&&u>1?d/u:1,c=Math.floor(Math.max(this.config.minScaleAdjust/100,c)*this.config.scale),l.NativeMML.ex=d,l.NativeMML.mex=u),l.NativeMML.fontSize=c+"%",l.NativeMML.scale=c/100);if(!h)for(e=0;e<p;e++)(i=m[e]).parentNode&&i.MathJax.elementJax&&i.parentNode.removeChild(i.previousSibling)},Translate:function(t){if(t.parentNode){var i=t.MathJax.elementJax,a=i.root,s=document.getElementById(i.inputID+"-Frame");if(s){var r=s.firstChild,l=r.firstChild;this.ex=i.NativeMML.ex||this.defaultEx,this.scale=i.NativeMML.scale||1,1!==this.scale&&(s.style.fontSize=i.NativeMML.fontSize);try{a.toNativeMML(l,i)}catch(t){if(t.restart)for(;l.firstChild;)l.removeChild(l.firstChild);throw t}if(h)if(r.addEventListener)for(var d in this.MSIE9events)this.MSIE9events.hasOwnProperty(d)&&r.addEventListener(d,this.MSIE9event,!0);else!(null!=this.config.showMathMenuMSIE?this:e).config.showMathMenuMSIE||this.settings.mpContext||this.settings.mpMouse?(r.style.position="",l.firstChild.onmousedown=this.MSIEaltMenu):this.MSIEoverlay(r);else r.oncontextmenu=n.Menu,r.onmouseover=n.Mouseover,r.onmouseout=n.Mouseout,r.onmousedown=n.Mousedown,r.onclick=n.Click,r.ondblclick=n.DblClick,r.onkeydown=n.Keydown,r.tabIndex=e.getTabOrder(i),e.Browser.noContextMenu&&(r.ontouchstart=o.start,r.ontouchend=o.end)}}},postTranslate:function(t){if(this.forceReflow){var e=(document.styleSheets||[])[0]||{};e.disabled=!0,e.disabled=!1}},Remove:function(t){var e=t.SourceElement();e&&(e=e.previousSibling)&&e.className.match(/MathJax_MathML/)&&e.parentNode.removeChild(e)},MMLnamespace:"http://www.w3.org/1998/Math/MathML",isFullWidth:function(t){if(t){var e=t.getAttribute("width")||(String(t.getAttribute("style")).match(/(?:^| )width: *([^; ]*)/)||[])[1];if(e)return!!e.match(/%/);if(t.nodeName.match(/^(semantics|math|mstyle)$/))e=this.isFullWidth(t.firstChild);else if("mrow"===t.nodeName.toLowerCase())for(var i=0,a=t.childNodes.length;i<a&&!e;i++)e=this.isFullWidth(t.childNodes[i]);if(e){var s="width:100%; "+(t.getAttribute("style")||"");t.setAttribute("style",s.replace(/ +$/,""))}return e}},MSIEoverlay:function(t){var i=t.firstChild;"span"===i.nodeName.toLowerCase()&&(i=i.firstChild);var s=this.getHoverBBox(null,i,{});a.addElement(t,"span",{style:{display:"inline-block",width:0,height:0,position:"relative"}},[["span",{isMathJax:!0,className:"MathJax_MathPlayer_Overlay",style:{display:"inline-block",position:"absolute",left:r.Px(-s.w),top:r.Px(-s.h-(s.y||0)-1),width:r.Px(s.w),height:r.Px(s.h+s.d),cursor:"pointer","background-color":"white",filter:"alpha(opacity=0)"}}]]),e.Insert(t,{msieMath:i,onmousedown:this.MSIEevent,oncontextmenu:this.MSIEevent,onclick:this.MSIEevent,onmouseup:this.MSIEevent,onmousemove:this.MSIEevent,ondblclick:this.MSIEevent,onmouseover:this.MSIEevent,onmouseout:this.MSIEevent})},MSIEevents:{mousedown:"Mousedown",contextmenu:"ContextMenu",click:"Click",mouseup:"Mouseup",mousemove:"Mousemove",dblclick:"DblClick",mouseover:"Mouseover",mouseout:"Mouseout"},MSIEevent:function(){var e=window.event,i=t.MSIEevents[e.type];return(!t[i]||!1!==t[i](e,this))&&(!l||!1!==l.HandleEvent(e,i,this))&&("MathJax_MathPlayer_Overlay"===e.srcElement.className&&this.msieMath.fireEvent&&("ContextMenu"!==i&&"Mouseover"!==i&&"Mouseout"!==i||this.msieMath.fireEvent("on"+e.type,e)),n.False(e))},MSIEaltMenu:function(){for(var t=this.parentNode.parentNode;!t.jaxID;)t=t.parentNode;n.AltContextMenu(window.event,t)},MSIE9events:{contextmenu:"Menu",click:"Click",dblclick:"DblClick",mouseup:"False",mouseover:"Mouseover",mouseout:"Mouseout"},MSIE9event:function(e){if("contextmenu"===e.type&&t.settings.mpContext)return!0;if("mouseup"===e.type&&t.settings.mpMouse)return!0;if("click"===e.type&&t.settings.mpContext)return n.AltContextMenu(e,this);var i=t.MSIE9events[e.type];return n[i].call(this,e)},getJaxFromMath:function(t){t=t.parentNode;do{t=t.nextSibling}while(t&&"script"!==t.nodeName.toLowerCase());return e.getJaxFor(t)},getHoverSpan:function(t,e){return e.firstChild},getHoverBBox:function(t,e,i){return n.getBBox(e.parentNode)},Zoom:function(e,i,a,s,o){e.root.toNativeMML(i),this.msieIE8HeightBug&&(i.style.position="absolute"),t.widthBug&&(i.style.width=i.parentNode.style.width=""),i.parentNode.style.width.match(/%$/)&&(i.parentNode.style.minWidth=Math.ceil(3*o/4)+"px");var r=a.offsetWidth||a.scrollWidth,l=a.offsetHeight||a.scrollHeight,h=i.offsetWidth,d=i.offsetHeight;if(t.widthBug||i.style.width.match(/%/)){var u=i.firstChild.firstChild.scrollWidth;u>h&&(h=u,i.parentNode.style.width=i.style.minWidth=h+"px")}return this.msieIE8HeightBug&&(i.style.position=""),{Y:-n.getBBox(i.parentNode).h,mW:r,mH:l,zW:h,zH:d}},NAMEDSPACE:{negativeveryverythinmathspace:"-.0556em",negativeverythinmathspace:"-.1111em",negativethinmathspace:"-.1667em",negativemediummathspace:"-.2222em",negativethickmathspace:"-.2778em",negativeverythickmathspace:"-.3333em",negativeveryverythickmathspace:"-.3889em",veryverythinmathspace:".0556em",verythinmathspace:".1111em",thinmathspace:".1667em",mediummathspace:".2222em",thickmathspace:".2778em",verythickmathspace:".3333em",veryverythickmathspace:".3889em"}}),e.Register.StartupHook("mml Jax Ready",(function(){if((s=MathJax.ElementJax.mml).mbase.Augment({toNativeMML:function(t){var e=this.NativeMMLelement(this.type);this.NativeMMLattributes(e);for(var i=0,a=this.data.length;i<a;i++)this.data[i]?this.data[i].toNativeMML(e):e.appendChild(this.NativeMMLelement("mrow"));t.appendChild(e)},NativeMMLattributes:function(t){var e="mstyle"===this.type?s.math.prototype.defaults:this.defaults,i=this.attrNames||s.copyAttributeNames,a=s.skipAttributes,n=s.copyAttributes;if(!this.attrNames)for(var o in e)a[o]||n[o]||!e.hasOwnProperty(o)||null!=this[o]&&this[o]!==e[o]&&this.Get(o,null,1)!==this[o]&&t.setAttribute(o,this.NativeMMLattribute(this[o]));for(var r=0,l=i.length;r<l;r++)if(1!==n[i[r]]||e.hasOwnProperty(i[r])){var h=(this.attr||{})[i[r]];null==h&&(h=this[i[r]]),null!=h&&t.setAttribute(i[r],this.NativeMMLattribute(h))}this.NativeMMLclass(t)},NativeMMLclass:function(t){var e=[];if(this.class&&e.push(this.class),this.isa(s.TeXAtom)){var i=["ORD","OP","BIN","REL","OPEN","CLOSE","PUNCT","INNER","VCENTER"][this.texClass];i&&(e.push("MJX-TeXAtom-"+i),"OP"!==i||this.movablelimits||e.push("MJX-fixedlimits"))}this.mathvariant&&this.NativeMMLvariants[this.mathvariant]&&e.push("MJX"+this.mathvariant),this.variantForm&&e.push("MJX-variant"),e.length&&t.setAttribute("class",e.join(" "))},NativeMMLattribute:function(e){return e=String(e),t.NAMEDSPACE[e]?e=t.NAMEDSPACE[e]:e.match(/^\s*(([-+])?(\d+(\.\d*)?|\.\d+))\s*mu\s*$/)?e=(RegExp.$2||"")+(1/18*RegExp.$3).toFixed(3).replace(/\.?0+$/,"")+"em":this.NativeMMLvariants[e]&&(e=this.NativeMMLvariants[e]),e},NativeMMLvariants:{"-tex-caligraphic":s.VARIANT.SCRIPT,"-tex-caligraphic-bold":s.VARIANT.BOLDSCRIPT,"-tex-oldstyle":s.VARIANT.NORMAL,"-tex-oldstyle-bold":s.VARIANT.BOLD,"-tex-mathit":s.VARIANT.ITALIC},NativeMMLelement:function(i){var a=e.Browser.mpNamespace?document.createElement("m:"+i):document.createElementNS?document.createElementNS(t.MMLnamespace,i):document.createElement(i);return a.isMathJax=!0,a}}),s.mrow.Augment({toNativeMML:function(e){var i,a;if(this.inferred&&this.parent.inferRow)for(i=0,a=this.data.length;i<a;i++)this.data[i]?this.data[i].toNativeMML(e):e.appendChild(this.NativeMMLelement("mrow"));else if(t.stretchyMoBug&&(this.open||this.close)){var s=this.NativeMMLelement("mfenced");this.NativeMMLattributes(s),i=0,a=this.data.length,this.open&&(s.setAttribute("open",this.open),i++),this.close&&(s.setAttribute("close",this.close),a--);var n=s;for(a-i+1>1&&(n=this.NativeMMLelement("mrow"),e.appendChild(s),e=s);i<a;i++)this.data[i]?this.data[i].toNativeMML(n):n.appendChild(this.NativeMMLelement("mrow"));e.appendChild(n)}else this.SUPER(arguments).toNativeMML.call(this,e)}}),s.msubsup.Augment({toNativeMML:function(t){var e=this.type;null==this.data[this.sup]&&(e="msub"),null==this.data[this.sub]&&(e="msup");var i=this.NativeMMLelement(e);this.NativeMMLattributes(i),this.data[0]&&delete this.data[0].inferred;for(var a=0,s=this.data.length;a<s;a++)this.data[a]&&this.data[a].toNativeMML(i);t.appendChild(i)}}),s.munderover.Augment({toNativeMML:function(t){var e=this.type,i=this.data[this.base];i&&i.isa(s.TeXAtom)&&i.movablelimits&&!i.Get("displaystyle")?(e="msubsup",null==this.data[this.under]&&(e="msup"),null==this.data[this.over]&&(e="msub")):(null==this.data[this.under]&&(e="mover"),null==this.data[this.over]&&(e="munder"));var a=this.NativeMMLelement(e);this.NativeMMLattributes(a),this.data[0]&&delete this.data[0].inferred;for(var n=0,o=this.data.length;n<o;n++)this.data[n]&&this.data[n].toNativeMML(a);t.appendChild(a)}}),!h){var n=e.SplitList;s.mtable.Augment({toNativeMML:function(i){var a,o;if(t.tableSpacingBug){var r=this.getValues("rowspacing","columnspacing");this.nMMLtopPadding=n("0px "+r.rowspacing),this.nMMLleftPadding=n("0px "+r.columnspacing);var l=this.nMMLtopPadding,h=l.length;for(a=0,o=this.data.length;a<o;a++)this.data[a]&&(this.data[a].nMMLtopPadding=l[a<h?a:h-1])}if(t.tableLabelBug)for(a=0,o=this.data.length;a<o;a++)if(this.data[a]&&this.data[a].isa(s.mlabeledtr)){var d=e.config.displayAlign.charAt(0),u=this.Get("side").charAt(0);this.nMMLhasLabels=!0,this.nMMLlaMatch=d===u,this.nMMLforceWidth="c"===d||!!(this.width||"").match("%");break}if(this.width&&this.ffTableWidthBug){var c=(this.style||"").replace(/;\s*$/,"").split(";");""===c[0]&&c.shift(),c.push("width:"+this.width),this.style=c.join(";")}if(this.SUPER(arguments).toNativeMML.call(this,i),this.nMMLhasLabels){var m=i.firstChild;if(this.nMMLforceWidth||"r"!==u){var p=("l"!==d?1:0)+("l"===u?1:0);if(p){var M={columnalign:"left",columnwidth:"auto",columnspacing:"0px",columnlines:"none"};for(var f in M)if(M.hasOwnProperty(f)&&this[f]){var g=[M[f],M[f]].slice(2-p).join(" ")+" ";m.setAttribute(f,g+m.getAttribute(f))}}}!this.nMMLforceWidth&&this.nMMLlaMatch||m.setAttribute("width","100%")}}}),s.mtr.Augment({toNativeMML:function(i){this.SUPER(arguments).toNativeMML.call(this,i);var a=i.lastChild;if(t.tableSpacingBug)for(var s=this.parent.nMMLleftPadding,n=s.length,o=a.firstChild,r=0;o;o=o.nextSibling,r++)u(o,this.nMMLtopPadding,s[r<n?r:n-1]);if(t.tableLabelBug){var l=this.parent.nMMLforceWidth,h=this.parent.Get("side").charAt(0),c=e.config.displayAlign.charAt(0);this.parent.nMMLhasLabels&&a.firstChild&&((l||"r"!==h)&&(d("Left",a.firstChild),"l"!==c&&a.insertBefore(this.NativeMMLelement("mtd"),a.firstChild).setAttribute("style","padding:0"),"l"===h&&a.insertBefore(this.NativeMMLelement("mtd"),a.firstChild).setAttribute("style","padding:0")),(l||"l"!==h)&&d("Right",a.lastChild))}}}),s.mlabeledtr.Augment({toNativeMML:function(i){var a=this.NativeMMLelement("mtr");this.NativeMMLattributes(a);for(var s=1,n=this.data.length;s<n;s++)this.data[s]?this.data[s].toNativeMML(a):a.appendChild(this.NativeMMLelement("mtd"));if(t.tableSpacingBug){var o=this.parent.nMMLleftPadding,r=o.length;s=0;for(var l=a.firstChild;l;l=l.nextSibling,s++)u(l,this.nMMLtopPadding,o[s<r?s:r-1])}if(t.tableLabelBug&&this.data[0]){var h=this.parent.Get("side").charAt(0),c=e.config.displayAlign.charAt(0),m=e.config.displayIndent;this.data[0].toNativeMML(a);var p=a.lastChild,M=p;h===c?(p.setAttribute("style","width:"+m),p.setAttribute("columnalign",e.config.displayAlign)):((M=this.NativeMMLelement("mpadded")).setAttribute("style","width:0"),M.setAttribute("width","0px"),M.appendChild(p.firstChild),p.appendChild(M)),d("",p),a.removeChild(p);var f=100,g=this.parent.nMMLforceWidth;(this.parent.width||"").match(/%/)&&(f-=parseFloat(this.parent.width));var b=f;(g||"r"!==h)&&(d("Left",a.firstChild),"l"!==c&&("c"===c&&(b/=2),f-=b,a.insertBefore(this.NativeMMLelement("mtd"),a.firstChild).setAttribute("style","padding:0;width:"+b+"%")),"l"===h&&a.insertBefore(p,a.firstChild)),(g||"l"!==h)&&(d("Right",a.lastChild),"r"!==c&&a.appendChild(this.NativeMMLelement("mtd")).setAttribute("style","padding:0;width:"+f+"%"),"r"===h&&(h!==c&&M.setAttribute("lspace","-1width"),a.appendChild(p)))}i.appendChild(a)}}),s.mtd.Augment({toNativeMML:function(e){var i=e.appendChild(this.NativeMMLelement(this.type));this.NativeMMLattributes(i),t.mtdWidthBug&&(t.adjustWidths.push(i),i=i.appendChild(this.NativeMMLelement("mrow")));for(var a=0,s=this.data.length;a<s;a++)this.data[a]?this.data[a].toNativeMML(i):i.appendChild(this.NativeMMLelement("mrow"))}}),s.mspace.Augment({toNativeMML:function(e){if(this.SUPER(arguments).toNativeMML.call(this,e),t.spaceWidthBug&&this.width){var i=e.lastChild,a=i.getAttribute("width"),s=(i.getAttribute("style")||"").replace(/;?\s*/,"; ");i.setAttribute("style",s+"width:"+a)}}}),s.mn.Augment({NativeMMLremapMinus:function(t){return t.replace(/^-/,"−")},toNativeMML:function(t){var e=this.NativeMMLelement(this.type);this.NativeMMLattributes(e);for(var i=this.NativeMMLremapMinus,a=0,s=this.data.length;a<s;a++)this.data[a]&&(this.data[a].toNativeMML(e,i),i=null);t.appendChild(e)}});var o=i.fileURL(MathJax.OutputJax.fontDir+"/HTML-CSS/TeX/otf");t.Augment({config:{styles:{'[class="MJX-tex-oldstyle"]':{"font-family":"MathJax_Caligraphic, MathJax_Caligraphic-WEB"},'[class="MJX-tex-oldstyle-bold"]':{"font-family":"MathJax_Caligraphic, MathJax_Caligraphic-WEB","font-weight":"bold"},'[class="MJX-tex-caligraphic"]':{"font-family":"MathJax_Caligraphic, MathJax_Caligraphic-WEB"},'[class="MJX-tex-caligraphic-bold"]':{"font-family":"MathJax_Caligraphic, MathJax_Caligraphic-WEB","font-weight":"bold"},"@font-face /*1*/":{"font-family":"MathJax_Caligraphic-WEB",src:"url('"+o+"/MathJax_Caligraphic-Regular.otf')"},"@font-face /*2*/":{"font-family":"MathJax_Caligraphic-WEB","font-weight":"bold",src:"url('"+o+"/MathJax_Caligraphic-Bold.otf')"}}}}),this.handlesVariants||t.Augment({config:{styles:{'[mathvariant="double-struck"]':{"font-family":"MathJax_AMS, MathJax_AMS-WEB"},'[mathvariant="script"]':{"font-family":"MathJax_Script, MathJax_Script-WEB"},'[mathvariant="fraktur"]':{"font-family":"MathJax_Fraktur, MathJax_Fraktur-WEB"},'[mathvariant="bold-script"]':{"font-family":"MathJax_Script, MathJax_Caligraphic-WEB","font-weight":"bold"},'[mathvariant="bold-fraktur"]':{"font-family":"MathJax_Fraktur, MathJax_Fraktur-WEB","font-weight":"bold"},'[mathvariant="monospace"]':{"font-family":"monospace"},'[mathvariant="sans-serif"]':{"font-family":"sans-serif"},'[mathvariant="bold-sans-serif"]':{"font-family":"sans-serif","font-weight":"bold"},'[mathvariant="sans-serif-italic"]':{"font-family":"sans-serif","font-style":"italic"},'[mathvariant="sans-serif-bold-italic"]':{"font-family":"sans-serif","font-style":"italic","font-weight":"bold"},"@font-face /*3*/":{"font-family":"MathJax_AMS-WEB",src:"url('"+o+"/MathJax_AMS-Regular.otf')"},"@font-face /*4*/":{"font-family":"MathJax_Script-WEB",src:"url('"+o+"/MathJax_Script-Regular.otf')"},"@font-face /*5*/":{"font-family":"MathJax_Fraktur-WEB",src:"url('"+o+"/MathJax_Fraktur-Regular.otf')"},"@font-face /*6*/":{"font-family":"MathJax_Fraktur-WEB","font-weight":"bold",src:"url('"+o+"/MathJax_Fraktur-Bold.otf')"}}}})}s.math.Augment({toNativeMML:function(i,a){var s,n,o=this.NativeMMLelement(this.type),r=o,l=a?MathJax.InputJax[a.inputJax].annotationEncoding:null;if(t.adjustWidths=[],o.setAttribute("xmlns",t.MMLnamespace),this.NativeMMLattributes(o),t.widthBug&&(o=o.appendChild(this.NativeMMLelement("mrow"))),l){(o=o.appendChild(this.NativeMMLelement("semantics"))).appendChild(this.NativeMMLelement("mrow"));var h=o.appendChild(this.NativeMMLelement("annotation"));h.appendChild(document.createTextNode(a.originalText)),h.setAttribute("encoding",l),o=o.firstChild}for(s=0,n=this.data.length;s<n;s++)this.data[s]?this.data[s].toNativeMML(o):o.appendChild(this.NativeMMLelement("mrow"));var d=(this.data[0]||{data:[]}).data[0]||{};d.nMMLhasLabels&&(!d.nMMLforceWidth&&d.nMMLlaMatch||(o.setAttribute("style","width:100%"),l&&o.parentNode.setAttribute("style","width:100%")),d.nMMLlaMatch&&"div"===i.parentNode.parentNode.nodeName.toLowerCase()&&i.parentNode.parentNode.style.setProperty("margin-"+e.config.displayAlign,"0px","important"));var u=t.isFullWidth(r);if(u&&(i.style.width=i.parentNode.style.width="100%"),i.appendChild(r),t.widthBug&&!u&&(i.style.width=(r.firstChild.scrollWidth/t.ex/t.scale).toFixed(3)+"ex",a&&(a.NativeMML.scrollWidth=r.firstChild.scrollWidth)),t.adjustWidths.length){var c=[];for(s=0,n=t.adjustWidths.length;s<n;s++){var m=(o=t.adjustWidths[s]).getAttribute("style")||"";if(!m.match(/(^|;)\s*min-width:/)){var p=o.firstChild.scrollWidth;c.push(p),p=(p/t.ex).toFixed(3)+"ex",m=m.replace(/;?\s*$/,"; "),o.setAttribute("style",m+"min-width:"+p)}}a||(a=e.getJaxFor(i)),a&&(a.NativeMML.mtds=c),r.MathJaxMtds=t.adjustWidths,t.adjustWidths=[]}}}),s.mfenced.Augment({toNativeMML:function(i){if(t.mfencedBug){var a,s,n,o=e.Browser.isOpera,r=this.getValues("open","close","separators");if(r.open=r.open.replace(/^\s+/,"").replace(/\s+$/,""),r.close=r.close.replace(/^\s+/,"").replace(/\s+$/,""),r.separators=r.separators.replace(/\s+/g,"").split(""),0==r.separators.length)r.separators=null;else if(r.separators.length<this.data.length-1){var l=r.separators[r.separators.length-1];for(a=this.data.length-1-r.separators.length;a>0;a--)r.separators.push(l)}var h=this.NativeMMLelement(o?this.type:"mrow");for(this.NativeMMLattributes(h),h.removeAttribute("separators"),o?(h.setAttribute("open",r.open),h.setAttribute("close",r.close),this.data.length>1&&(i.appendChild(h),i=h,h=this.NativeMMLelement("mrow"))):(h.removeAttribute("open"),h.removeAttribute("close")),o||((n=this.NativeMMLelement("mo")).setAttribute("fence","true"),n.textContent=r.open,h.appendChild(n)),a=0,s=this.data.length;a<s;a++)r.separators&&a>0&&((n=this.NativeMMLelement("mo")).setAttribute("separator","true"),n.textContent=r.separators[a-1],h.appendChild(n)),this.data[a]?this.data[a].toNativeMML(h):h.appendChild(this.NativeMMLelement("mrow"));o||((n=this.NativeMMLelement("mo")).setAttribute("fence","true"),n.textContent=r.close,h.appendChild(n)),i.appendChild(h)}else this.SUPER(arguments).toNativeMML.call(this,i)}}),s.TeXAtom.Augment({toNativeMML:function(t){var e=this.NativeMMLelement("mrow");this.NativeMMLattributes(e),this.data[0].toNativeMML(e),t.appendChild(e)}}),s.chars.Augment({toNativeMML:function(t,e){var i=this.toString();e&&(i=e(i)),t.appendChild(document.createTextNode(i))}}),s.entity.Augment({toNativeMML:function(t){t.appendChild(document.createTextNode(this.toString()))}}),s.xml.Augment({toNativeMML:function(t){for(var e=0,i=this.data.length;e<i;e++)t.appendChild(this.data[e].cloneNode(!0))}}),s.mi.Augment({toNativeMML:function(e){if(this.SUPER(arguments).toNativeMML.call(this,e),t.miItalicBug&&this.Get("mathvariant")===s.VARIANT.NORMAL){var i=e.lastChild;i.setAttribute("mathvariant",s.VARIANT.NORMAL)}}}),s.mo.Augment({toNativeMML:function(e){if(this.SUPER(arguments).toNativeMML.call(this,e),t.webkitMoSpacingBug){var i=0,s=0,n=this.parent;if(n&&"mrow"===n.type&&(n.inferred||!n.isEmbellished())){var o=this.getValues("lspace","rspace");i=o.lspace,s=o.rspace,t.NAMEDSPACE[i]&&(i=t.NAMEDSPACE[i]),t.NAMEDSPACE[s]&&(s=t.NAMEDSPACE[s])}var r=e.lastChild,l=a.Element("span");l.style.cssText=r.getAttribute("style")||"",l.style.setProperty("-webkit-margin-start",i),l.style.setProperty("-webkit-margin-end",s),r.setAttribute("style",l.style.cssText)}}}),s.mmultiscripts.Augment({toNativeMML:function(e){if(t.mmultiscriptsBug&&0!==this.data.length){var i=this.NativeMMLelement("mrow");this.NativeMMLattributes(i),this.data[0]?this.data[0].toNativeMML(i):i.appendChild(this.NativeMMLelement("mrow"));var a,s,n=i.removeChild(i.lastChild),o=this.data.length;for(a=1;a<o&&"mprescripts"!==this.data[a].type;a+=2)(s=this.NativeMMLelement("msubsup")).appendChild(n),this.data[a]?this.data[a].toNativeMML(s):s.appendChild(this.NativeMMLelement("mrow")),a+1<o&&this.data[a+1]?this.data[a+1].toNativeMML(s):s.appendChild(this.NativeMMLelement("mrow")),n=s;for(i.appendChild(n),a++;a<o;a+=2)(s=this.NativeMMLelement("msubsup")).appendChild(this.NativeMMLelement("mrow")),this.data[a]?this.data[a].toNativeMML(s):s.appendChild(this.NativeMMLelement("mrow")),a+1<o&&this.data[a+1]?this.data[a+1].toNativeMML(s):s.appendChild(this.NativeMMLelement("mrow")),i.insertBefore(s,n);e.appendChild(i)}else this.SUPER(arguments).toNativeMML.call(this,e)}}),e.Register.StartupHook("TeX mathchoice Ready",(function(){s.TeXmathchoice.Augment({toNativeMML:function(t){this.Core().toNativeMML(t)}})})),setTimeout(MathJax.Callback(["loadComplete",t,"jax.js"]),0)})),e.Browser.Select({MSIE:function(e){var i=document.documentMode||0;t.msieIE8HeightBug=8===i},Opera:function(e){t.stretchyMoBug=!0,t.tableLabelBug=!0,t.mfencedBug=!0,t.miBug=!0,t.mmultiscriptsBug=!0},Firefox:function(e){var i=e.versionAtLeast("29.0");t.ffTableWidthBug=!e.versionAtLeast("13.0"),t.forceReflow=!i,t.widthBug=!i,t.mtdWidthBug=!0,t.handlesVariants=i,t.spaceWidthBug=!e.versionAtLeast("20.0"),t.tableSpacingBug=!e.versionAtLeast("33.0"),t.tableLabelBug=!0,t.mfencedBug=!0},Chrome:function(e){t.tableSpacingBug=!0,t.tableLabelBug=!0,t.mfencedBug=!0},Safari:function(e){t.tableSpacingBug=!0,t.tableLabelBug=!0,t.mfencedBug=!0,t.miItalicBug=!0,t.webkitMoSpacingBug=!0,t.spaceWidthBug=!0,t.mmultiscriptsBug=!0}}),e.Register.StartupHook("End Cookie",(function(){"None"!==e.config.menuSettings.zoom&&i.Require("[MathJax]/extensions/MathZoom.js")}))}(MathJax.OutputJax.NativeMML,MathJax.Hub,MathJax.Ajax,MathJax.HTML),function(t,e,i){var a,s,n,o,r=e.Browser.isMobile,l=MathJax.Object.isArray,h=function(){var t=[].slice.call(arguments,0);return t[0][0]=["HTML-CSS",t[0][0]],MathJax.Message.Set.apply(MathJax.Message,t)},d=MathJax.Object.Subclass({timeout:1e3*(r?15:8),comparisonFont:["sans-serif","monospace","script","Times","Courier","Arial","Helvetica"],testSize:["40px","50px","60px","30px","20px"],FedoraSTIXcheck:{family:"STIXSizeOneSym",testString:"abcABC",noStyleChar:!0},Init:function(){this.div=MathJax.HTML.addElement(document.body,"div",{style:{position:"absolute",width:0,height:0,overflow:"hidden",padding:0,border:0,margin:0}},[["div",{id:"MathJax_Font_Test",style:{position:"absolute",visibility:"hidden",top:0,left:0,width:"auto","min-width":0,"max-width":"none",padding:0,border:0,margin:0,whiteSpace:"nowrap",textAlign:"left",textIndent:0,textTransform:"none",lineHeight:"normal",letterSpacing:"normal",wordSpacing:"normal",fontSize:this.testSize[0],fontWeight:"normal",fontStyle:"normal",fontSizeAdjust:"none"}},[""]]]).firstChild,this.text=this.div.firstChild},findFont:function(t,e){var i=null;if(e&&this.testCollection(e))i=e;else for(var a=0,s=t.length;a<s;a++)if(t[a]!==e&&this.testCollection(t[a])){i=t[a];break}return"STIX"===i&&this.testFont(this.FedoraSTIXcheck)&&(i=null),i},testCollection:function(t){var e={testString:"() {} []"};return e.family={TeX:"MathJax_Size1",STIX:"STIXSizeOneSym"}[t]||t.replace(/-(Math)?/,"")+"MathJax_Size1","STIX"===t&&(e.noStyleChar=!0),this.testFont(e)},testFont:function(t){t.isWebFont&&i.FontFaceBug?this.div.style.fontWeight=this.div.style.fontStyle="normal":(this.div.style.fontWeight=t.weight||"normal",this.div.style.fontStyle=t.style||"normal");var e=t.familyFixed||t.family;t.isWebFont||e.match(/^(STIX|MathJax)|'/)||(e=e.replace(/_/g," ").replace(/([a-z])([A-Z])/g,"$1 $2").replace(/ Jax/,"Jax")+"','"+e+"','"+e+"-",t.weight&&(e+="Bold"),t.style&&(e+="Italic"),t.weight||t.style||(e+="Regular"),t.familyFixed=e="'"+e+"'");var a=this.getComparisonWidths(t.testString,t.noStyleChar),s=null;if(a&&(this.div.style.fontFamily=e+","+this.comparisonFont[0],this.div.offsetWidth==a[0]&&(this.div.style.fontFamily=e+","+this.comparisonFont[a[2]],this.div.offsetWidth==a[1]&&(s=!1)),null===s&&(this.div.offsetWidth!=a[3]||this.div.offsetHeight!=a[4])))if(!t.noStyleChar&&i.FONTDATA&&i.FONTDATA.hasStyleChar)for(var n=0,o=this.testSize.length;n<o;n++)this.testStyleChar(t,this.testSize[n])&&(s=!0,o=0);else s=!0;return i.safariTextNodeBug?this.div.innerHTML="":this.text.nodeValue="",s},styleChar:"",versionChar:"",compChar:"",testStyleChar:function(t,e){var a=3+(t.weight?2:0)+(t.style?4:0),s="",n=0,o=this.div.style.fontSize;this.div.style.fontSize=e,i.msieItalicWidthBug&&"italic"===t.style&&(this.text.nodeValue=s=this.compChar,n=this.div.offsetWidth),i.safariTextNodeBug?this.div.innerHTML=this.compChar+s:this.text.nodeValue=this.compChar+s;var r=this.div.offsetWidth-n;i.safariTextNodeBug?this.div.innerHTML=this.styleChar+s:this.text.nodeValue=this.styleChar+s;var l=Math.floor((this.div.offsetWidth-n)/r+.5);return l===a&&(i.safariTextNodeBug?this.div.innerHTML=this.versionChar+s:this.text.nodeValue=this.versionChar+s,t.version=Math.floor((this.div.offsetWidth-n)/r+1.5)/2),this.div.style.fontSize=o,l===a},getComparisonWidths:function(t,e){i.FONTDATA&&i.FONTDATA.hasStyleChar&&!e&&(t+=this.styleChar+" "+this.compChar),i.safariTextNodeBug?this.div.innerHTML=t:this.text.nodeValue=t,this.div.style.fontFamily=this.comparisonFont[0];var a=this.div.offsetWidth;this.div.style.fontFamily=i.webFontDefault;for(var s=this.div.offsetWidth,n=this.div.offsetHeight,o=1,r=this.comparisonFont.length;o<r;o++)if(this.div.style.fontFamily=this.comparisonFont[o],this.div.offsetWidth!=a)return[a,this.div.offsetWidth,o,s,n];return null},loadWebFont:function(a){e.Startup.signal.Post("HTML-CSS Jax - Web-Font "+i.fontInUse+"/"+a.directory);var s=h(["LoadWebFont","Loading web-font %1",i.fontInUse+"/"+a.directory]),n=MathJax.Callback({}),o=MathJax.Callback(["loadComplete",this,a,s,n]);return t.timer.start(t,[this.checkWebFont,a,o],0,this.timeout),n},loadComplete:function(a,s,n,o){if(MathJax.Message.Clear(s),o===t.STATUS.OK)return this.webFontLoaded=!0,void n();if(this.loadError(a),e.Browser.isFirefox&&i.allowWebFonts){var r=document.location.protocol+"//"+document.location.hostname;""!=document.location.port&&(r+=":"+document.location.port),r+="/",t.fileURL(i.webfontDir).substr(0,r.length)!==r&&this.firefoxFontError(a)}this.webFontLoaded?n():i.loadWebFontError(a,n)},loadError:function(t){h(["CantLoadWebFont","Can't load web font %1",i.fontInUse+"/"+t.directory],null,2e3),e.Startup.signal.Post("HTML-CSS Jax - web font error for "+i.fontInUse+"/"+t.directory)},firefoxFontError:function(t){h(["FirefoxCantLoadWebFont","Firefox can't load web fonts from a remote host"],null,3e3),e.Startup.signal.Post("HTML-CSS Jax - Firefox web 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.MathJax":{display:"inline-table"},".MathJax_Display":{position:"relative",display:"block!important","text-indent":0,"max-width":"none","max-height":"none","min-width":0,"min-height":0,width:"100%"},".MathJax.MathJax_FullWidth":{"text-align":"center",display:(u?"block":"table-cell")+"!important",width:(u?"100%":"10000em")+"!important"},".MathJax img, .MathJax nobr, .MathJax a":{border:0,padding:0,margin:0,"max-width":"none","max-height":"none","min-width":0,"min-height":0,"vertical-align":0,"line-height":"normal","text-decoration":"none"},"img.MathJax_strut":{border:"0!important",padding:"0!important",margin:"0!important","vertical-align":"0!important"},".MathJax span":{display:"inline",position:"static",border:0,padding:0,margin:0,"vertical-align":0,"line-height":"normal","text-decoration":"none","box-sizing":"content-box"},".MathJax nobr":{"white-space":"nowrap!important"},".MathJax img":{display:"inline!important",float:"none!important"},".MathJax *":{transition:"none","-webkit-transition":"none","-moz-transition":"none","-ms-transition":"none","-o-transition":"none"},".MathJax_Processing":{visibility:"hidden",position:"fixed",width:0,height:0,overflow:"hidden"},".MathJax_Processed":{display:"none!important"},".MathJax_test":{"font-style":"normal","font-weight":"normal","font-size":"100%","font-size-adjust":"none","text-indent":0,"text-transform":"none","letter-spacing":"normal","word-spacing":"normal",overflow:"hidden",height:"1px"},".MathJax_test.mjx-test-display":{display:(u?"block":"table")+"!important"},".MathJax_test.mjx-test-inline":{display:"inline!important","margin-right":"-1px"},".MathJax_test.mjx-test-default":{display:"block!important",clear:"both"},".MathJax_ex_box":{display:"inline-block!important",position:"absolute",overflow:"hidden","min-height":0,"max-height":"none",padding:0,border:0,margin:0,width:"1px",height:"60ex"},".MathJax_em_box":{display:"inline-block!important",position:"absolute",overflow:"hidden","min-height":0,"max-height":"none",padding:0,border:0,margin:0,width:"1px",height:"60em"},".mjx-test-inline .MathJax_left_box":{display:"inline-block",width:0,float:"left"},".mjx-test-inline .MathJax_right_box":{display:"inline-block",width:0,float:"right"},".mjx-test-display .MathJax_right_box":{display:(u?"block":"table-cell")+"!important",width:(u?"100%":"10000em")+"!important","min-width":0,"max-width":"none",padding:0,border:0,margin:0},".MathJax .MathJax_HitBox":{cursor:"text",background:"white",opacity:0,filter:"alpha(opacity=0)"},".MathJax .MathJax_HitBox *":{filter:"none",opacity:1,background:"transparent"},"#MathJax_Tooltip":{position:"absolute",left:0,top:0,width:"auto",height:"auto",display:"none"},"#MathJax_Tooltip *":{filter:"none",opacity:1,background:"transparent"},"@font-face":{"font-family":"MathJax_Blank",src:"url('about:blank')"}}},settings:e.config.menuSettings,Font:null,webFontDefault:"MathJax_Blank",allowWebFonts:"otf",maxStretchyParts:1e3,fontName:{TeXLocal:"TeX",TeXWeb:["","TeX"],TeXImage:["",""],STIXLocal:["STIX","STIX-Web"],STIXWeb:"STIX-Web",AsanaMathWeb:"Asana-Math",GyrePagellaWeb:"Gyre-Pagella",GyreTermesWeb:"Gyre-Termes",LatinModernWeb:"Latin-Modern",NeoEulerWeb:"Neo-Euler"},fontInUse:"generic",FONTDATA:{TeX_factor:1,baselineskip:1.2,lineH:.8,lineD:.2,ffLineH:.8,FONTS:{},VARIANT:{normal:{fonts:[]},"-generic-variant":{},"-largeOp":{},"-smallOp":{}},RANGES:[],DELIMITERS:{},RULECHAR:45,REMAP:{}},Config:function(){this.require||(this.require=[]),this.Font=d(),this.SUPER(arguments).Config.call(this);var t=this.settings,i=this.config,a=t.font;this.adjustAvailableFonts&&this.adjustAvailableFonts(i.availableFonts),t.scale&&(i.scale=t.scale),a&&"Auto"!==a&&this.fontName[a]&&(i.availableFonts=[],delete i.fonts,l(this.fontName[a])?(i.preferredFont=this.fontName[a][0],i.webFont=this.fontName[a][1]):i.preferredFont=i.webFont=this.fontName[a],i.preferredFont&&(i.availableFonts[0]=i.preferredFont)),i.fonts&&(i.availableFonts=i.fonts,i.preferredFont=i.webFont=i.fonts[0],"STIX"===i.webFont&&(i.webFont+="-Web")),!(a=this.Font.findFont(i.availableFonts,i.preferredFont))&&this.allowWebFonts&&(a=i.webFont)&&(this.webFonts=!0),!a&&this.config.imageFont&&(a=i.imageFont,this.imgFonts=!0),a?(this.fontInUse=a,this.fontDir+="/"+a,this.webfontDir+="/"+a,this.require.push(this.fontDir+"/fontdata.js"),this.imgFonts&&(this.require.push(this.directory+"/imageFonts.js"),e.Startup.signal.Post("HTML-CSS Jax - using image fonts"))):(h(["CantFindFontUsing","Can't find a valid font using 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e=this.addElement(this.hiddenDiv,"div",{style:{width:"5in"}});if(this.pxPerInch=e.offsetWidth/5,this.hiddenDiv.removeChild(e),this.startMarker=this.createStrut(this.Element("span"),10,!0),this.endMarker=this.addText(this.Element("span"),"x").parentNode,this.HDspan=this.Element("span"),this.operaHeightBug&&this.createStrut(this.HDspan,0),this.msieInlineBlockAlignBug){this.HDimg=this.addElement(this.HDspan,"img",{style:{height:"0px",width:"1px"}});try{this.HDimg.src="about:blank"}catch(t){}}else this.HDimg=this.createStrut(this.HDspan,0);return this.TestSpan=this.Element("span",{className:"MathJax_test"},[["span",{className:"MathJax_left_box"}],["span",{className:"MathJax_ex_box"}],["span",{className:"MathJax_em_box"}],["span",{className:"MathJax_right_box"}]]),t.Styles(this.config.styles,["InitializeHTML",this])},removeSTIXfonts:function(t){for(var e=0,i=t.length;e<i;e++)"STIX"===t[e]&&(t.splice(e,1),i--,e--);"STIX"===this.config.preferredFont&&(this.config.preferredFont=t[0])},PreloadWebFonts:function(){if(i.allowWebFonts&&i.config.preloadWebFonts)for(var t=0,e=i.config.preloadWebFonts.length;t<e;t++){var a=i.FONTDATA.FONTS[i.config.preloadWebFonts[t]];a.available||i.Font.testFont(a)}},InitializeHTML:function(){if(this.PreloadWebFonts(),this.getDefaultExEm(),!this.defaultEm){var a=MathJax.Callback();return t.timer.start(t,(function(t){t.time(a)?e.signal.Post(["HTML-CSS Jax - no default em size"]):(i.getDefaultExEm(),i.defaultEm?a():setTimeout(t,t.delay))}),this.defaultEmDelay,this.defaultEmTimeout),a}},defaultEmDelay:100,defaultEmTimeout:1e3,getDefaultExEm:function(){var t=document.body.appendChild(this.TestSpan.cloneNode(!0));t.className+=" mjx-test-inline mjx-test-default",this.defaultEx=t.childNodes[1].offsetHeight/60,this.defaultEm=t.childNodes[2].offsetHeight/60,this.defaultWidth=Math.max(0,t.lastChild.offsetLeft-t.firstChild.offsetLeft-2),document.body.removeChild(t)},preTranslate:function(t){var i,a,o,r,l,h,d,u,c,m,p,M,f,g=t.jax[this.id],b=g.length,x=!1,v=this.config.linebreaks.automatic,T=this.config.linebreaks.width;for(v?((x=null!=T.match(/^\s*(\d+(\.\d*)?%\s*)?container\s*$/))?T=T.replace(/\s*container\s*/,""):M=this.defaultWidth,""===T&&(T="100%")):M=1e5,i=0;i<b;i++)(o=g[i]).parentNode&&((r=o.previousSibling)&&String(r.className).match(/^MathJax(_Display)?( 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L=[];for(i=0;i<b;i++)(o=g[i]).parentNode&&(h=(d=o.previousSibling).previousSibling,(u=o.MathJax.elementJax)&&(c=d.childNodes[1].offsetHeight/60,m=d.childNodes[2].offsetHeight/60,f=Math.max(0,u.HTMLCSS.display?d.lastChild.offsetWidth-1:d.lastChild.offsetLeft-d.firstChild.offsetLeft-2),0!==c&&"NaN"!==c||(L.push(h),u.HTMLCSS.isHidden=!0,c=this.defaultEx,m=this.defaultEm,f=this.defaultWidth),0!==f||u.HTMLCSS.display||(f=this.defaultWidth),x&&(M=f),p=this.config.matchFontHeight?c/this.TeX.x_height/m:1,p=Math.floor(Math.max(this.config.minScaleAdjust/100,p)*this.config.scale),u.HTMLCSS.scale=p/100,u.HTMLCSS.fontSize=p+"%",u.HTMLCSS.em=u.HTMLCSS.outerEm=m,this.em=m*p/100,u.HTMLCSS.ex=c,u.HTMLCSS.cwidth=f/this.em,u.HTMLCSS.lineWidth=v?this.length2em(T,1,M/this.em):1e6));for(i=0,a=L.length;i<a;i++)this.hiddenDiv.appendChild(L[i]),this.addElement(this.hiddenDiv,"br");for(i=0;i<b;i++)(o=g[i]).parentNode&&(u=g[i].MathJax.elementJax)&&(o.parentNode.removeChild(o.previousSibling),o.MathJax.preview&&(o.MathJax.preview.style.display=""));t.HTMLCSSeqn=t.HTMLCSSlast=0,t.HTMLCSSi=-1,t.HTMLCSSchunk=this.config.EqnChunk,t.HTMLCSSdelay=!1},PHASE:{I:1,II:2,III:3},Translate:function(t,i){if(t.parentNode){i.HTMLCSSdelay&&(i.HTMLCSSdelay=!1,e.RestartAfter(MathJax.Callback.Delay(this.config.EqnChunkDelay)));var a=t.MathJax.elementJax,s=a.root,n=a.HTMLCSS.div,o=a.HTMLCSS.span;if(document.getElementById(o.id)){this.getMetrics(a),1!==this.scale&&(o.style.fontSize=a.HTMLCSS.fontSize),this.initImg(o),this.initHTML(s,o),this.savePreview(t);try{s.setTeXclass(),s.toHTML(o,n,this.PHASE.I)}catch(e){if(e.restart)for(;o.firstChild;)o.removeChild(o.firstChild);throw this.restorePreview(t),e}return this.restorePreview(t),n.className=n.className.split(/ /)[0]+" MathJax_Processed",e.signal.Post(["New Math Pending",a.inputID]),i.HTMLCSSeqn+=i.i-i.HTMLCSSi,i.HTMLCSSi=i.i,i.HTMLCSSeqn>=i.HTMLCSSlast+i.HTMLCSSchunk&&(this.postTranslate(i,!0),i.HTMLCSSchunk=Math.floor(i.HTMLCSSchunk*this.config.EqnChunkFactor),i.HTMLCSSdelay=!0),!1}}},savePreview:function(t){var e=t.MathJax.preview;e&&(t.MathJax.tmpPreview=document.createElement("span"),e.parentNode.replaceChild(t.MathJax.tmpPreview,e))},restorePreview:function(t){var e=t.MathJax.tmpPreview;e&&(e.parentNode.replaceChild(t.MathJax.preview,e),delete t.MathJax.tmpPreview)},getMetrics:function(t){var e=t.HTMLCSS;this.em=a.mbase.prototype.em=e.em*e.scale,this.outerEm=e.em,this.scale=e.scale,this.cwidth=e.cwidth,this.linebreakWidth=e.lineWidth},postTranslate:function(t,i){var a,s,n,o,r=t.jax[this.id];for(n=t.HTMLCSSlast,o=t.HTMLCSSeqn;n<o;n++)if((a=r[n])&&a.parentNode&&a.MathJax.elementJax){var l=(a.MathJax.elementJax.HTMLCSS||{}).div;l&&(l.className=l.className.split(/ /)[0]),a.MathJax.preview&&(a.MathJax.preview.innerHTML="")}for(n=t.HTMLCSSlast,o=t.HTMLCSSeqn;n<o;n++)(a=r[n])&&a.parentNode&&a.MathJax.elementJax&&(s=a.MathJax.elementJax,this.getMetrics(s),s.HTMLCSS.span&&s.HTMLCSS.div&&s.root.toHTML(s.HTMLCSS.span,s.HTMLCSS.div,this.PHASE.II));for(n=t.HTMLCSSlast,o=t.HTMLCSSeqn;n<o;n++)(a=r[n])&&a.parentNode&&a.MathJax.elementJax&&(s=a.MathJax.elementJax,this.getMetrics(s),s.HTMLCSS.span&&s.HTMLCSS.div&&(s.root.toHTML(s.HTMLCSS.span,s.HTMLCSS.div,this.PHASE.III),s.HTMLCSS.isHidden&&a.parentNode.insertBefore(s.HTMLCSS.div,a),delete s.HTMLCSS.span,delete s.HTMLCSS.div,a.MathJax.state=s.STATE.PROCESSED,e.signal.Post(["New Math",a.MathJax.elementJax.inputID])));if(this.forceReflow){var h=(document.styleSheets||[])[0]||{};h.disabled=!0,h.disabled=!1}t.HTMLCSSlast=t.HTMLCSSeqn},getJaxFromMath:function(t){t.parentNode.className.match(/MathJax_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.HTMLspanElement()},getHoverBBox:function(t,e,i){var a=e.bbox,s=t.HTMLCSS.outerEm,n={w:a.w*s,h:a.h*s,d:a.d*s};return a.width&&(n.width=a.width),n},Zoom:function(t,n,o,r,l){n.className="MathJax",n.style.fontSize=t.HTMLCSS.fontSize;var h=n.appendChild(this.TestSpan.cloneNode(!0)),d=h.childNodes[2].offsetHeight/60;this.em=a.mbase.prototype.em=d,this.outerEm=d/t.HTMLCSS.scale,h.parentNode.removeChild(h),this.scale=t.HTMLCSS.scale,this.linebreakWidth=t.HTMLCSS.lineWidth,this.cwidth=t.HTMLCSS.cwidth,this.zoomScale=parseInt(e.config.menuSettings.zscale)/100,this.idPostfix="-zoom",t.root.toHTML(n,n),this.idPostfix="",this.zoomScale=1;var u=t.root.HTMLspanElement().bbox,c=u.width;if(c){u.tw&&(r=u.tw*d),u.w*d<r&&(r=u.w*d),n.style.width=Math.floor(r-1.5*i.em)+"px",n.style.display="inline-block";for(var m=(t.root.id||"MathJax-Span-"+t.root.spanID)+"-zoom",p=document.getElementById(m).firstChild;p&&p.style.width!==c;)p=p.nextSibling;if(p){var M=p.offsetWidth;p.style.width="100%",M>r&&(n.style.width=M+100+"px")}}p=n.firstChild.firstChild.style,null!=u.H&&u.H>u.h&&(p.marginTop=i.Em(u.H-Math.max(u.h,i.FONTDATA.lineH))),null!=u.D&&u.D>u.d&&(p.marginBottom=i.Em(u.D-Math.max(u.d,i.FONTDATA.lineD))),u.lw<0&&(p.paddingLeft=i.Em(-u.lw)),u.rw>u.w&&(p.marginRight=i.Em(u.rw-u.w)),n.style.position="absolute",c||(o.style.position="absolute");var f=n.offsetWidth,g=n.offsetHeight,b=o.offsetHeight,x=o.offsetWidth;return n.style.position=o.style.position="",{Y:-s.getBBox(n).h,mW:x,mH:b,zW:f,zH:g}},initImg:function(t){},initHTML:function(t,e){},initFont:function(e){var a=i.FONTDATA.FONTS,s=i.config.availableFonts;return s&&s.length&&i.Font.testFont(a[e])?(a[e].available=!0,a[e].familyFixed&&(a[e].family=a[e].familyFixed,delete a[e].familyFixed),null):this.allowWebFonts?(a[e].isWebFont=!0,i.FontFaceBug&&(a[e].family=e,i.msieFontCSSBug&&(a[e].family+="-Web")),t.Styles({"@font-face":this.Font.fontFace(e)})):null},Remove:function(t){var e=document.getElementById(t.inputID+"-Frame");e&&(t.HTMLCSS.display&&(e=e.parentNode),e.parentNode.removeChild(e)),delete t.HTMLCSS},getHD:function(t,e){if(t.bbox&&this.config.noReflows&&!e)return{h:t.bbox.h,d:t.bbox.d};var i=t.style.position;t.style.position="absolute",this.HDimg.style.height="0px",t.appendChild(this.HDspan);var a={h:t.offsetHeight};return this.HDimg.style.height=a.h+"px",a.d=t.offsetHeight-a.h,a.h-=a.d,a.h/=this.em,a.d/=this.em,t.removeChild(this.HDspan),t.style.position=i,a},getW:function(t){var e,i,a=(t.bbox||{}).w,s=t;if(t.bbox&&this.config.noReflows&&!1!==t.bbox.exactW)return t.bbox.exactW||(t.style.paddingLeft&&(a+=this.unEm(t.style.paddingLeft)*(t.scale||1)),t.style.paddingRight&&(a+=this.unEm(t.style.paddingRight)*(t.scale||1))),a;if(t.bbox&&t.bbox.exactW)return a;if(t.bbox&&a>=0&&!this.initialSkipBug&&!this.msieItalicWidthBug||this.negativeBBoxes||!t.firstChild)e=t.offsetWidth,i=t.parentNode.offsetHeight;else if(t.bbox&&a<0&&this.msieNegativeBBoxBug)e=-t.offsetWidth,i=t.parentNode.offsetHeight;else{var n=t.style.position;t.style.position="absolute",s=this.startMarker,t.insertBefore(s,t.firstChild),t.appendChild(this.endMarker),e=this.endMarker.offsetLeft-s.offsetLeft,t.removeChild(this.endMarker),t.removeChild(s),t.style.position=n}return null!=i&&(t.parentNode.HH=i/this.em),e/this.em},Measured:function(t,e){var i=t.bbox;if(null==i.width&&i.w&&!i.isMultiline){var a=this.getW(t);i.rw+=a-i.w,i.w=a,i.exactW=!0}return e||(e=t.parentNode),e.bbox||(e.bbox=i),t},Remeasured:function(t,e){e.bbox=this.Measured(t,e).bbox},MeasureSpans:function(t){var e,i,a,s,n,o,r,l,h=[];for(i=0,a=t.length;i<a;i++)(e=t[i])&&(s=e.bbox,l=this.parentNode(e),s.exactW||s.width||0===s.w||s.isMultiline||this.config.noReflows&&!1!==s.exactW?l.bbox||(l.bbox=s):this.negativeBBoxes||!e.firstChild||s.w>=0&&!this.initialSkipBug||s.w<0&&this.msieNegativeBBoxBug?h.push([e]):this.initialSkipBug?(n=this.startMarker.cloneNode(!0),o=this.endMarker.cloneNode(!0),e.insertBefore(n,e.firstChild),e.appendChild(o),h.push([e,n,o,e.style.position]),e.style.position="absolute"):(o=this.endMarker.cloneNode(!0),e.appendChild(o),h.push([e,null,o])));for(i=0,a=h.length;i<a;i++)s=(e=h[i][0]).bbox,l=this.parentNode(e),s.w>=0&&!this.initialSkipBug||this.negativeBBoxes||!e.firstChild?(r=e.offsetWidth,l.HH=l.offsetHeight/this.em):s.w<0&&this.msieNegativeBBoxBug?(r=-e.offsetWidth,l.HH=l.offsetHeight/this.em):r=h[i][2].offsetLeft-((h[i][1]||{}).offsetLeft||0),r/=this.em,s.rw+=r-s.w,s.w=r,s.exactW=!0,l.bbox||(l.bbox=s);for(i=0,a=h.length;i<a;i++)(e=h[i])[1]&&(e[1].parentNode.removeChild(e[1]),e[0].style.position=e[3]),e[2]&&e[2].parentNode.removeChild(e[2])},Em:function(t){return 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null==s&&(s=1),null==e&&(e=1),"em"===h?l*n:"ex"===h?l*i.TeX.x_height*n:"%"===h?l/100*s:"px"===h?l*o:"pt"===h?l/10*n:"pc"===h?1.2*l*n:"in"===h?l*this.pxPerInch*o:"cm"===h?l*this.pxPerInch*o/2.54:"mm"===h?l*this.pxPerInch*o/25.4:"mu"===h?l/18*n*e:l*s},thickness2em:function(t,e){var s=i.TeX.rule_thickness;return t===a.LINETHICKNESS.MEDIUM?s:t===a.LINETHICKNESS.THIN?.67*s:t===a.LINETHICKNESS.THICK?1.67*s:this.length2em(t,e,s)},border2em:function(t,e){return t===a.LINETHICKNESS.THIN&&(t="1px"),t===a.LINETHICKNESS.MEDIUM&&(t="3px"),t===a.LINETHICKNESS.THICK&&(t="5px"),this.length2em(t,e)},getPadding:function(t){var e={top:0,right:0,bottom:0,left:0},i=!1;for(var a in e)if(e.hasOwnProperty(a)){var s=t.style["padding"+a.charAt(0).toUpperCase()+a.substr(1)];s&&(e[a]=this.length2em(s),i=!0)}return!!i&&e},getBorders:function(t){var e={top:0,right:0,bottom:0,left:0},i={},s=!1;for(var n in e)if(e.hasOwnProperty(n)){var o="border"+n.charAt(0).toUpperCase()+n.substr(1);t.style[o+"Style"]&&(s=!0,e[n]=this.border2em(t.style[o+"Width"]||a.LINETHICKNESS.MEDIUM),i[o]=[t.style[o+"Width"],t.style[o+"Style"],t.style[o+"Color"]].join(" "))}return e.css=i,!!s&&e},setBorders:function(t,e){if(e)for(var i in e.css)e.css.hasOwnProperty(i)&&(t.style[i]=e.css[i])},createStrut:function(t,e,i){var a=this.Element("span",{isMathJax:!0,style:{display:"inline-block",overflow:"hidden",height:e+"px",width:"1px",marginRight:"-1px"}});return i?t.insertBefore(a,t.firstChild):t.appendChild(a),a},createBlank:function(t,e,i){var a=this.Element("span",{isMathJax:!0,style:{display:"inline-block",overflow:"hidden",height:"1px",width:this.Em(e)}});return e<0&&(a.style.marginRight=a.style.width,a.style.width=0),i?t.insertBefore(a,t.firstChild):t.appendChild(a),a},createShift:function(t,e,i){var a=this.Element("span",{style:{marginLeft:this.Em(e)},isMathJax:!0});return i?t.insertBefore(a,t.firstChild):t.appendChild(a),a},createSpace:function(t,e,s,n,o,r){e<-s&&(s=-e);var l=this.Em(e+s),h=this.Em(-s);if(this.msieInlineBlockAlignBug&&(h=this.Em(i.getHD(t.parentNode,!0).d-s)),t.isBox||r){var d=null==t.scale?1:t.scale;t.bbox={exactW:!0,h:e*d,d:s*d,w:n*d,rw:n*d,lw:0},t.style.height=l,t.style.verticalAlign=h,t.HH=(e+s)*d}else t=this.addElement(t,"span",{style:{height:l,verticalAlign:h},isMathJax:!0});return n>=0?(t.style.width=this.Em(n),t.style.display="inline-block",t.style.overflow="hidden"):(this.msieNegativeSpaceBug&&(t.style.height=""),t.style.marginLeft=this.Em(n),i.safariNegativeSpaceBug&&t.parentNode.firstChild==t&&this.createBlank(t,0,!0)),o&&o!==a.COLOR.TRANSPARENT&&(t.style.backgroundColor=o,t.style.position="relative"),t},createRule:function(t,e,a,s,n){e<-a&&(a=-e);var o=i.TeX.min_rule_thickness,r=1;s>0&&s*this.em<o&&(s=o/this.em),e+a>0&&(e+a)*this.em<o&&(e*=r=1/(e+a)*(o/this.em),a*=r),n=n?"solid "+n:"solid";var 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e=t.parentNode;return"a"===e.nodeName.toLowerCase()&&(e=e.parentNode),e},createStack:function(t,e,i){this.msiePaddingWidthBug&&this.createStrut(t,0);var a=String(i).match(/%$/),s=a||null==i?0:i;return t=this.addElement(t,"span",{noAdjust:!0,HH:0,isMathJax:!0,style:{display:"inline-block",position:"relative",width:a?"100%":this.Em(s),height:0}}),e||(t.parentNode.bbox=t.bbox={exactW:!0,h:-this.BIGDIMEN,d:-this.BIGDIMEN,w:s,lw:this.BIGDIMEN,rw:a||null==i?-this.BIGDIMEN:i},a&&(t.bbox.width=i)),t},createBox:function(t,e){var i=this.addElement(t,"span",{style:{position:"absolute"},isBox:!0,isMathJax:!0});return null!=e&&(i.style.width=e),i},addBox:function(t,e){return e.style.position="absolute",e.isBox=e.isMathJax=!0,t.appendChild(e)},placeBox:function(t,e,a,s){t.isMathJax=!0;var n=i.parentNode(t),o=t.bbox,r=n.bbox;this.msiePlaceBoxBug&&this.addText(t,this.NBSP),this.imgSpaceBug&&this.addText(t,this.imgSpace);var l,h=0;if(null!=t.HH)l=t.HH;else if(o){var d=t.firstChild;l=Math.max(3,3*(d&&d.scale||1),o.h+o.d)}else l=t.offsetHeight/this.em;if(t.noAdjust||(l+=1,l=Math.round(l*this.em)/this.em,this.msieInlineBlockAlignBug?this.addElement(t,"img",{className:"MathJax_strut",border:0,src:"about:blank",isMathJax:!0,style:{width:0,height:this.Em(l)}}):(this.addElement(t,"span",{isMathJax:!0,style:{display:"inline-block",width:0,height:this.Em(l)}}),i.chromeHeightBug&&(l-=(t.lastChild.offsetHeight-Math.round(l*this.em))/this.em))),o&&(this.initialSkipBug&&(o.lw<0&&(h=o.lw,i.createBlank(t,-h,!0)),o.rw>o.w&&i.createBlank(t,o.rw-o.w+.1)),!this.msieClipRectBug&&!o.noclip&&!s)){var u=3/this.em,c=l-(null==o.H?o.h:o.H)-u,m=l+(null==o.D?o.d:o.D)+u,p=o.rw+1e3;t.style.clip="rect("+this.Em(c)+" "+this.Em(p)+" "+this.Em(m)+" "+this.Em(-1e3)+")"}t.style.top=this.Em(-a-l),t.style.left=this.Em(e+h),o&&r&&(null!=o.H&&(null==r.H||o.H+a>r.H)&&(r.H=o.H+a),null!=o.D&&(null==r.D||o.D-a>r.D)&&(r.D=o.D-a),o.h+a>r.h&&(r.h=o.h+a),o.d-a>r.d&&(r.d=o.d-a),null!=r.H&&r.H<=r.h&&delete r.H,null!=r.D&&r.D<=r.d&&delete r.D,o.w+e>r.w&&(r.w=o.w+e,null==r.width&&(n.style.width=this.Em(r.w))),o.rw+e>r.rw&&(r.rw=o.rw+e),o.lw+e<r.lw&&(r.lw=o.lw+e),null==o.width||o.isFixed||(null==r.width&&(n.style.width=r.width="100%",o.minWidth&&(n.style.minWidth=r.minWidth=o.minWidth)),t.style.width=o.width),o.tw&&(r.tw=o.tw))},alignBox:function(t,i,a,s,n){if(null==s&&(s=0),this.placeBox(t,s,a),this.msiePlaceBoxBug){for(var o=t.lastChild;o&&"#text"!==o.nodeName;)o=o.previousSibling;o&&t.removeChild(o)}var r=t.bbox;if(!r.isMultiline||n){var l=null!=r.width&&!r.isFixed,h=0,d=s-r.w/2,u="50%";this.initialSkipBug&&(h=r.w-r.rw-.1,d+=r.lw),d=this.msieMarginScaleBug?d*this.em+"px":this.Em(d),l&&(d=0===s?"":this.Em(s),u=50-parseFloat(r.width)/2+"%"),e.Insert(t.style,{right:{left:"",right:this.Em(h-s)},center:{left:u,marginLeft:d}}[i])}},setStackWidth:function(t,e){if("number"==typeof e){t.style.width=this.Em(Math.max(0,e));var i=t.bbox;i&&(i.w=e,i.exactW=!0),(i=t.parentNode.bbox)&&(i.w=e,i.exactW=!0)}else t.style.width=t.parentNode.style.width="100%",t.bbox&&(t.bbox.width=e),t.parentNode.bbox&&(t.parentNode.bbox.width=e)},createDelimiter:function(i,s,n,o,r){if(!s)return i.bbox={h:0,d:0,w:this.TeX.nulldelimiterspace,lw:0},i.bbox.rw=i.bbox.w,void this.createSpace(i,i.bbox.h,i.bbox.d,i.bbox.w);o||(o=1),n instanceof Array||(n=[n,n]);var l=n[1];n=n[0];for(var h={alias:s};h.alias;)s=h.alias,(h=this.FONTDATA.DELIMITERS[s])||(h={HW:[0,this.FONTDATA.VARIANT[a.VARIANT.NORMAL]]});h.load&&e.RestartAfter(t.Require(this.fontDir+"/fontdata-"+h.load+".js"));for(var d=0,u=h.HW.length;d<u;d++)if(h.HW[d][0]*o>=n-.01||d==u-1&&!h.stretch){h.HW[d][2]&&(o*=h.HW[d][2]),h.HW[d][3]&&(s=h.HW[d][3]);var c=this.addElement(i,"span");return this.createChar(c,[s,h.HW[d][1]],o,r),i.bbox=c.bbox,i.offset=.65*i.bbox.w,void(i.scale=o)}h.stretch&&this["extendDelimiter"+h.dir](i,l,h.stretch,o,r)},extendDelimiterV:function(t,e,i,a,s){var n=this.createStack(t,!0),o=this.createBox(n),r=this.createBox(n);this.createChar(o,i.top||i.ext,a,s),this.createChar(r,i.bot||i.ext,a,s);var l,h={bbox:{w:0,lw:0,rw:0}},d=h,u=o.bbox.h+o.bbox.d+r.bbox.h+r.bbox.d,c=-o.bbox.h;if(this.placeBox(o,0,c,!0),c-=o.bbox.d,i.mid&&(d=this.createBox(n),this.createChar(d,i.mid,a,s),u+=d.bbox.h+d.bbox.d),i.min&&e<u*i.min&&(e=u*i.min),e>u){h=this.Element("span"),this.createChar(h,i.ext,a,s);var m,p,M=h.bbox.h+h.bbox.d,f=M-.05,g=i.mid?2:1;p=m=Math.min(Math.ceil((e-u)/(g*f)),this.maxStretchyParts),i.fullExtenders||(f=(e-u)/(g*m));var b=m/(m+1)*(M-f);for(c+=b+(f=M-b)-h.bbox.h;g-- >0;){for(;m-- >0;)this.msieCloneNodeBug?(l=this.Element("span"),this.createChar(l,i.ext,a,s)):l=h.cloneNode(!0),l.bbox=h.bbox,c-=f,this.placeBox(this.addBox(n,l),0,c,!0);c+=b-h.bbox.d,i.mid&&g&&(this.placeBox(d,0,c-d.bbox.h,!0),m=p,c+=-(d.bbox.h+d.bbox.d)+b+f-h.bbox.h)}}else c+=(u-e)/2,i.mid&&(this.placeBox(d,0,c-d.bbox.h,!0),c+=-(d.bbox.h+d.bbox.d)),c+=(u-e)/2;this.placeBox(r,0,c-r.bbox.h,!0),c-=r.bbox.h+r.bbox.d,t.bbox={w:Math.max(o.bbox.w,h.bbox.w,r.bbox.w,d.bbox.w),lw:Math.min(o.bbox.lw,h.bbox.lw,r.bbox.lw,d.bbox.lw),rw:Math.max(o.bbox.rw,h.bbox.rw,r.bbox.rw,d.bbox.rw),h:0,d:-c,exactW:!0},t.scale=a,t.offset=.55*t.bbox.w,t.isMultiChar=!0,this.setStackWidth(n,t.bbox.w)},extendDelimiterH:function(t,e,i,a,s){var n=this.createStack(t,!0),o=this.createBox(n),r=this.createBox(n);this.createChar(o,i.left||i.rep,a,s),this.createChar(r,i.right||i.rep,a,s);var l=this.Element("span");this.createChar(l,i.rep,a,s);var h,d={bbox:{h:-this.BIGDIMEN,d:-this.BIGDIMEN}};this.placeBox(o,-o.bbox.lw,0,!0);var u,c=o.bbox.rw-o.bbox.lw+(r.bbox.rw-r.bbox.lw)-.05,m=o.bbox.rw-o.bbox.lw-.025;if(i.mid&&(d=this.createBox(n),this.createChar(d,i.mid,a,s),c+=d.bbox.w),i.min&&e<c*i.min&&(e=c*i.min),e>c){var p,M,f=l.bbox.rw-l.bbox.lw,g=f-.05,b=i.mid?2:1;for(M=p=Math.min(Math.ceil((e-c)/(b*g)),this.maxStretchyParts),i.fillExtenders||(g=(e-c)/(b*p)),g=f-(u=p/(p+1)*(f-g)),m-=l.bbox.lw+u;b-- >0;){for(;p-- >0;)this.cloneNodeBug?(h=this.Element("span"),this.createChar(h,i.rep,a,s)):h=l.cloneNode(!0),h.bbox=l.bbox,this.placeBox(this.addBox(n,h),m,0,!0),m+=g;i.mid&&b&&(this.placeBox(d,m,0,!0),m+=d.bbox.w-u,p=M)}}else m-=(c-e)/2,i.mid&&(this.placeBox(d,m,0,!0),m+=d.bbox.w),m-=(c-e)/2;m-=r.bbox.lw,this.placeBox(r,m,0,!0),t.bbox={w:m+r.bbox.rw,lw:0,rw:m+r.bbox.rw,h:Math.max(o.bbox.h,l.bbox.h,r.bbox.h,d.bbox.h),d:Math.max(o.bbox.d,l.bbox.d,r.bbox.d,d.bbox.d),exactW:!0},t.scale=a,t.isMultiChar=!0,this.setStackWidth(n,t.bbox.w)},createChar:function(t,e,i,s){t.isMathJax=!0;var n=t,o="",r={fonts:[e[1]],noRemap:!0};if(s&&s===a.VARIANT.BOLD&&(r.fonts=[e[1]+"-bold",e[1]]),"string"!=typeof e[1]&&(r=e[1]),e[0]instanceof Array)for(var l=0,h=e[0].length;l<h;l++)o+=String.fromCharCode(e[0][l]);else o=String.fromCharCode(e[0]);e[4]&&(i*=e[4]),1!==i||e[3]?(n=this.addElement(t,"span",{style:{fontSize:this.Percent(i)},scale:i,isMathJax:!0}),this.handleVariant(n,r,o),t.bbox=n.bbox):this.handleVariant(t,r,o),e[2]&&(t.style.marginLeft=this.Em(e[2])),e[3]&&(t.firstChild.style.verticalAlign=this.Em(e[3]),t.bbox.h+=e[3],t.bbox.h<0&&(t.bbox.h=0)),e[5]&&(t.bbox.h+=e[5]),e[6]&&(t.bbox.d+=e[6]),this.AccentBug&&0===t.bbox.w&&(n.firstChild.nodeValue+=this.NBSP)},positionDelimiter:function(t,e){e-=t.bbox.h,t.bbox.d-=e,t.bbox.h+=e,e&&(this.safariVerticalAlignBug||this.konquerorVerticalAlignBug||this.operaVerticalAlignBug&&t.isMultiChar?(""===t.firstChild.style.display&&""!==t.style.top&&(t=t.firstChild,e-=i.unEm(t.style.top)),t.style.position="relative",t.style.top=this.Em(-e)):(t.style.verticalAlign=this.Em(e),i.ffVerticalAlignBug&&(i.createRule(t.parentNode,t.bbox.h,0,0),delete t.parentNode.bbox)))},handleVariant:function(t,e,s){var n,o,r,h,d="",u=t,c=!!t.style.fontFamily;if(0!==s.length){t.bbox||(t.bbox={w:0,h:-this.BIGDIMEN,d:-this.BIGDIMEN,rw:-this.BIGDIMEN,lw:this.BIGDIMEN}),e||(e=this.FONTDATA.VARIANT[a.VARIANT.NORMAL]),h=e;for(var m=0,p=s.length;m<p;m++){if(e=h,n=s.charCodeAt(m),s.charAt(m),n>=55296&&n<56319){if(m++,n=(n-55296<<10)+(s.charCodeAt(m)-56320)+65536,this.FONTDATA.RemapPlane1){var M=this.FONTDATA.RemapPlane1(n,e);n=M.n,e=M.variant}}else{var f,g,b=this.FONTDATA.RANGES;for(f=0,g=b.length;f<g;f++)if("alpha"!==b[f].name||!e.noLowerCase){var x=e["offset"+b[f].offset];if(x&&n>=b[f].low&&n<=b[f].high){if(b[f].remap&&b[f].remap[n])n=x+b[f].remap[n];else{if(b[f].remapOnly)break;n=n-b[f].low+x,b[f].add&&(n+=b[f].add)}e["variant"+b[f].offset]&&(e=this.FONTDATA.VARIANT[e["variant"+b[f].offset]]);break}}}if(e.remap&&e.remap[n]?(n=e.remap[n],e.remap.variant&&(e=this.FONTDATA.VARIANT[e.remap.variant])):this.FONTDATA.REMAP[n]&&!e.noRemap&&(n=this.FONTDATA.REMAP[n]),l(n)&&(e=this.FONTDATA.VARIANT[n[1]],n=n[0]),"string"!=typeof n){if(o=(r=this.lookupChar(e,n))[n],c||!this.checkFont(r,u.style)&&!o[5].img){d.length&&(this.addText(u,d),d="");var v=!!u.style.fontFamily||!!t.style.fontStyle||!!t.style.fontWeight||!r.directory||c;c=!1,u!==t&&(v=!this.checkFont(r,t.style),u=t),v&&(u=this.addElement(t,"span",{isMathJax:!0,subSpan:!0})),this.handleFont(u,r,u!==t)}d=this.handleChar(u,r,o,n,d),(o[5]||{}).space||(o[0]/1e3>t.bbox.h&&(t.bbox.h=o[0]/1e3),o[1]/1e3>t.bbox.d&&(t.bbox.d=o[1]/1e3)),t.bbox.w+o[3]/1e3<t.bbox.lw&&(t.bbox.lw=t.bbox.w+o[3]/1e3),t.bbox.w+o[4]/1e3>t.bbox.rw&&(t.bbox.rw=t.bbox.w+o[4]/1e3),t.bbox.w+=o[2]/1e3,(o[5]||{}).isUnknown&&(t.bbox.exactW=!1)}else p=(s=n+s.substr(m+1)).length,m=-1}d.length&&this.addText(u,d),t.scale&&1!==t.scale&&(t.bbox.h*=t.scale,t.bbox.d*=t.scale,t.bbox.w*=t.scale,t.bbox.lw*=t.scale,t.bbox.rw*=t.scale),i.isChar(s)&&r.skew&&r.skew[n]&&(t.bbox.skew=r.skew[n])}},checkFont:function(t,e){var i=e.fontWeight||"normal";return i.match(/^\d+$/)&&(i=parseInt(i)>=600?"bold":"normal"),t.family.replace(/'/g,"")===e.fontFamily.replace(/'/g,"")&&((t.style||"normal")===(e.fontStyle||"normal")&&(t.weight||"normal")===i||this.FontFaceBug&&""!==e.fontFamily)},handleFont:function(t,e,a){if(t.style.fontFamily=e.family,e.directory||(t.style.fontSize=Math.floor(i.config.scale/i.scale+.5)+"%"),!i.FontFaceBug||!e.isWebFont){var s=e.style||"normal",n=e.weight||"normal";("normal"!==s||a)&&(t.style.fontStyle=s),("normal"!==n||a)&&(t.style.fontWeight=n)}},handleChar:function(t,e,a,s,n){var o=a[5];if(o.space)return n.length&&this.addText(t,n),i.createShift(t,a[2]/1e3),"";if(o.img)return this.handleImg(t,e,a,s,n);if(o.isUnknown&&this.FONTDATA.DELIMITERS[s]){n.length&&this.addText(t,n);var r=t.scale;return i.createDelimiter(t,s,0,1,e),"V"===this.FONTDATA.DELIMITERS[s].dir&&(t.style.verticalAlign=this.Em(t.bbox.d),t.bbox.h+=t.bbox.d,t.bbox.d=0),t.scale=r,a[0]=1e3*t.bbox.h,a[1]=1e3*t.bbox.d,a[2]=1e3*t.bbox.w,a[3]=1e3*t.bbox.lw,a[4]=1e3*t.bbox.rw,""}if(null==o.c)if(s<=65535)o.c=String.fromCharCode(s);else{var l=s-65536;o.c=String.fromCharCode(55296+(l>>10))+String.fromCharCode(56320+(1023&l))}return i.ffFontOptimizationBug&&a[4]-a[2]>125&&(t.style.textRendering="optimizeLegibility"),o.rfix?(this.addText(t,n+o.c),i.createShift(t,o.rfix/1e3),""):a[2]||!this.msieAccentBug&&!this.combiningCharBug||n.length?n+o.c:this.combiningCharBug?(i.addElement(t,"span",{style:{marginLeft:i.Em(a[3]/1e3)}},[o.c]),""):(i.createShift(t,a[3]/1e3),i.createShift(t,(a[4]-a[3])/1e3),this.addText(t,o.c),i.createShift(t,-a[4]/1e3),"")},handleImg:function(t,e,i,a,s){return s},lookupChar:function(t,e){var a,s;if(!t.FONTS){var n=this.FONTDATA.FONTS,o=t.fonts||this.FONTDATA.VARIANT.normal.fonts;for(o instanceof Array||(o=[o]),t.fonts!=o&&(t.fonts=o),t.FONTS=[],a=0,s=o.length;a<s;a++)n[o[a]]&&(t.FONTS.push(n[o[a]]),n[o[a]].name=o[a])}for(a=0,s=t.FONTS.length;a<s;a++){var r=t.FONTS[a];if("string"==typeof r&&(delete t.FONTS,this.loadFont(r)),r[e]){if(5===r[e].length&&(r[e][5]={}),!i.allowWebFonts||r.available)return r;this.loadWebFont(r)}else this.findBlock(r,e)}return this.unknownChar(t,e)},unknownChar:function(t,a){var s=t.defaultFont||{family:i.config.undefinedFamily};return t.bold&&(s.weight="bold"),t.italic&&(s.style="italic"),s[a]||(s[a]=[800,200,500,0,500,{isUnknown:!0}]),e.signal.Post(["HTML-CSS Jax - unknown char",a,t]),s},isChar:function(t){if(1===t.length)return!0;if(2!==t.length)return!1;var e=t.charCodeAt(0);return e>=55296&&e<56319},findBlock:function(t,e){if(t.Ranges)for(var i=0,a=t.Ranges.length;i<a;i++){if(e<t.Ranges[i][0])return;if(e<=t.Ranges[i][1]){for(var s=t.Ranges[i][2],n=t.Ranges.length-1;n>=0;n--)t.Ranges[n][2]==s&&t.Ranges.splice(n,1);this.loadFont(t.directory+"/"+s+".js")}}},loadFont:function(a){var s=MathJax.Callback.Queue();s.Push(["Require",t,this.fontDir+"/"+a]),this.imgFonts&&(MathJax.isPacked||(a=a.replace(/\/([^\/]*)$/,i.imgPacked+"/$1")),s.Push(["Require",t,this.webfontDir+"/png/"+a])),e.RestartAfter(s.Push({}))},loadWebFont:function(t){t.available=t.isWebFont=!0,i.FontFaceBug&&(t.family=t.name,i.msieFontCSSBug&&(t.family+="-Web")),e.RestartAfter(this.Font.loadWebFont(t))},loadWebFontError:function(i,a){e.Startup.signal.Post("HTML-CSS Jax - disable web fonts"),i.isWebFont=!1,this.config.imageFont&&this.config.imageFont===this.fontInUse?(this.imgFonts=!0,e.Startup.signal.Post("HTML-CSS Jax - switch to image fonts"),e.Startup.signal.Post("HTML-CSS Jax - using image fonts"),h(["WebFontNotAvailable","Web-Fonts not available -- using image fonts instead"],null,3e3),t.Require(this.directory+"/imageFonts.js",a)):(this.allowWebFonts=!1,a())},Element:MathJax.HTML.Element,addElement:MathJax.HTML.addElement,TextNode:MathJax.HTML.TextNode,addText:MathJax.HTML.addText,ucMatch:MathJax.HTML.ucMatch,BIGDIMEN:1e7,ID:0,idPostfix:"",GetID:function(){return this.ID++,this.ID},MATHSPACE:{veryverythinmathspace:1/18,verythinmathspace:2/18,thinmathspace:3/18,mediummathspace:4/18,thickmathspace:5/18,verythickmathspace:6/18,veryverythickmathspace:7/18,negativeveryverythinmathspace:-1/18,negativeverythinmathspace:-2/18,negativethinmathspace:-3/18,negativemediummathspace:-4/18,negativethickmathspace:-5/18,negativeverythickmathspace:-6/18,negativeveryverythickmathspace:-7/18},TeX:{x_height:.430554,quad:1,num1:.676508,num2:.393732,num3:.44373,denom1:.685951,denom2:.344841,sup1:.412892,sup2:.362892,sup3:.288888,sub1:.15,sub2:.247217,sup_drop:.386108,sub_drop:.05,delim1:2.39,delim2:1,axis_height:.25,rule_thickness:.06,big_op_spacing1:.111111,big_op_spacing2:.166666,big_op_spacing3:.2,big_op_spacing4:.6,big_op_spacing5:.1,scriptspace:.1,nulldelimiterspace:.12,delimiterfactor:901,delimitershortfall:.3,min_rule_thickness:1.25},NBSP:" ",rfuzz:0}),MathJax.Hub.Register.StartupHook("mml Jax Ready",(function(){(a=MathJax.ElementJax.mml).mbase.Augment({toHTML:function(t){t=this.HTMLcreateSpan(t),"mrow"!=this.type&&(t=this.HTMLhandleSize(t));for(var e=0,i=this.data.length;e<i;e++)this.data[e]&&this.data[e].toHTML(t);var a,s=this.HTMLcomputeBBox(t),n=t.bbox.h,o=t.bbox.d,r=!1;for(e=0,i=s.length;e<i;e++)a=s[e].HTMLspanElement().bbox,s[e].forceStretch||a.h!==n||a.d!==o?(s[e].HTMLstretchV(t,n,o),r=!0):s[e].needsBBox&&(r=!0);return r&&this.HTMLcomputeBBox(t,!0),this.HTMLlineBreaks(t)&&(t=this.HTMLmultiline(t)),this.HTMLhandleSpace(t),this.HTMLhandleColor(t),1===this.data.length&&this.data[0]&&(a=this.data[0].HTMLspanElement().bbox).skew&&(t.bbox.skew=a.skew),t},HTMLlineBreaks:function(){return!1},HTMLmultiline:function(){a.mbase.HTMLautoloadFile("multiline")},HTMLcomputeBBox:function(t,e,i,a){null==i&&(i=0),null==a&&(a=this.data.length);for(var s=t.bbox={exactW:!0},n=[];i<a;){var 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this.href&&(t=i.addElement(t,"a",{href:this.href,isMathJax:!0})),t=i.addElement(t,"span",{className:this.type,isMathJax:!0}),i.imgHeightBug&&(t.style.display="inline-block"),this.class&&(t.className+=" "+this.class),this.spanID||(this.spanID=i.GetID()),t.id=(this.id||"MathJax-Span-"+this.spanID)+i.idPostfix,t.bbox=this.HTMLzeroBBox(),this.styles={},this.style&&(t.style.cssText=this.style,t.style.fontSize&&(this.mathsize=t.style.fontSize,t.style.fontSize=""),this.styles={border:i.getBorders(t),padding:i.getPadding(t)},this.styles.border&&(t.style.border=""),this.styles.padding&&(t.style.padding="")),this.href&&(t.parentNode.bbox=t.bbox),this.HTMLaddAttributes(t),t},HTMLaddAttributes:function(t){if(this.attrNames)for(var i=this.attrNames,s=a.nocopyAttributes,n=e.config.ignoreMMLattributes,o="mstyle"===this.type?a.math.prototype.defaults:this.defaults,r=0,l=i.length;r<l;r++){var h=i[r];0!=n[h]&&(s[h]||n[h]||null!=o[h]||void 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s=(this.styles||{}).border,n=(this.styles||{}).padding;if(e.color&&!this.mathcolor&&(e.mathcolor=e.color),e.background&&!this.mathbackground&&(e.mathbackground=e.background),e.mathcolor&&(t.style.color=e.mathcolor),e.mathbackground&&e.mathbackground!==a.COLOR.TRANSPARENT||s||n){var o=t.bbox,r=o.exact?0:1/i.em,l=0,h=0,d=t.style.paddingLeft,u=t.style.paddingRight;this.isToken&&(l=o.lw,h=o.rw-o.w),""!==d&&(l+=i.unEm(d)*(t.scale||1)),""!==u&&(h-=i.unEm(u)*(t.scale||1));var c=i.PaddingWidthBug||o.keepPadding||o.exactW?0:h-l,m=Math.max(0,i.getW(t)+c),p=o.h+o.d,M=-o.d,f=0,g=0;m>0&&(m+=2*r,l-=r),p>0&&(p+=2*r,M-=r),h=-m-l,s&&(h-=s.right,M-=s.bottom,f+=s.left,g+=s.right,o.h+=s.top,o.d+=s.bottom,o.w+=s.left+s.right,o.lw-=s.left,o.rw+=s.right),n&&(p+=n.top+n.bottom,m+=n.left+n.right,h-=n.right,M-=n.bottom,f+=n.left,g+=n.right,o.h+=n.top,o.d+=n.bottom,o.w+=n.left+n.right,o.lw-=n.left,o.rw+=n.right),g&&(t.style.paddingRight=i.Em(g));var 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s=n.symmetric?2*Math.max(e-h,a+h):e+a,n.maxsize=i.length2em(n.maxsize,r,o.bbox.h+o.bbox.d),n.minsize=i.length2em(n.minsize,r,o.bbox.h+o.bbox.d),(s=Math.max(n.minsize,Math.min(n.maxsize,s)))!=n.minsize&&(s=[Math.max(s*i.TeX.delimiterfactor/1e3,s-i.TeX.delimitershortfall),s]),o=this.HTMLcreateSpan(t),i.createDelimiter(o,this.data.join("").charCodeAt(0),s,l),s=n.symmetric?(o.bbox.h+o.bbox.d)/2+h:(o.bbox.h+o.bbox.d)*e/(e+a),i.positionDelimiter(o,s),this.HTMLhandleSpace(o),this.HTMLhandleColor(o),o},HTMLstretchH:function(t,e){this.HTMLremoveColor();var s=this.getValues("maxsize","minsize","mathvariant","fontweight");("bold"===s.fontweight||parseInt(s.fontweight)>=600)&&!this.Get("mathvariant",!0)&&(s.mathvariant=a.VARIANT.BOLD);var n=this.HTMLspanElement(),o=this.HTMLgetMu(n),r=n.scale;return s.maxsize=i.length2em(s.maxsize,o,n.bbox.w),s.minsize=i.length2em(s.minsize,o,n.bbox.w),e=Math.max(s.minsize,Math.min(s.maxsize,e)),n=this.HTMLcreateSpan(t),i.createDelimiter(n,this.data.join("").charCodeAt(0),e,r,s.mathvariant),this.HTMLhandleSpace(n),this.HTMLhandleColor(n),n}}),a.mtext.Augment({toHTML:function(t){t=this.HTMLhandleSize(this.HTMLcreateSpan(t));var e=this.HTMLgetVariant();if(i.config.mtextFontInherit||"merror"===this.Parent().type){var a=this.Get("mathvariant");"monospace"===a?t.className+=" MJX-monospace":a.match(/sans-serif/)&&(t.className+=" MJX-sans-serif"),e={bold:e.bold,italic:e.italic,fontInherit:!0}}for(var s=0,n=this.data.length;s<n;s++)this.data[s]&&this.data[s].toHTML(t,e);return t.bbox||(t.bbox=this.HTMLzeroBBox()),i.isChar(this.data.join(""))||delete t.bbox.skew,this.HTMLhandleSpace(t),this.HTMLhandleColor(t),this.HTMLhandleDir(t),t}}),a.merror.Augment({toHTML:function(t){var e=MathJax.HTML.addElement(t,"span",{style:{display:"inline-block"}});t=this.SUPER(arguments).toHTML.call(this,e);var a=i.getHD(e),s=i.getW(e);return e.bbox={h:a.h,d:a.d,w:s,lw:0,rw:s,exactW:!0},e.id=t.id,t.id=null,e}}),a.ms.Augment({toHTML:a.mbase.HTMLautoload}),a.mglyph.Augment({toHTML:a.mbase.HTMLautoload}),a.mspace.Augment({toHTML:function(t){t=this.HTMLcreateSpan(t);var e=this.getValues("height","depth","width"),a=this.HTMLgetMu(t);this.HTMLgetScale(),e.mathbackground=this.mathbackground,this.background&&!this.mathbackground&&(e.mathbackground=this.background);var s=i.length2em(e.height,a)*this.mscale,n=i.length2em(e.depth,a)*this.mscale,o=i.length2em(e.width,a)*this.mscale;return i.createSpace(t,s,n,o,e.mathbackground,!0),t}}),a.mphantom.Augment({toHTML:function(t,e,a){if(t=this.HTMLcreateSpan(t),null!=this.data[0]){var s=this.data[0].toHTML(t);null!=a?i.Remeasured(this.data[0].HTMLstretchV(t,e,a),t):null!=e?i.Remeasured(this.data[0].HTMLstretchH(t,e),t):s=i.Measured(s,t),t.bbox={w:s.bbox.w,h:s.bbox.h,d:s.bbox.d,lw:0,rw:0,exactW:!0};for(var n=0,o=t.childNodes.length;n<o;n++)t.childNodes[n].style.visibility="hidden"}return this.HTMLhandleSpace(t),this.HTMLhandleColor(t),t},HTMLstretchH:a.mbase.HTMLstretchH,HTMLstretchV:a.mbase.HTMLstretchV}),a.mpadded.Augment({toHTML:function(t,e,a){if(t=this.HTMLcreateSpan(t),null!=this.data[0]){var s=i.createStack(t,!0),n=i.createBox(s),o=this.data[0].toHTML(n);null!=a?i.Remeasured(this.data[0].HTMLstretchV(n,e,a),n):null!=e?i.Remeasured(this.data[0].HTMLstretchH(n,e),n):i.Measured(o,n);var r=this.getValues("height","depth","width","lspace","voffset"),l=0,h=0,d=this.HTMLgetMu(t);this.HTMLgetScale(),r.lspace&&(l=this.HTMLlength2em(n,r.lspace,d)),r.voffset&&(h=this.HTMLlength2em(n,r.voffset,d)),i.placeBox(n,l,h),l/=this.mscale,h/=this.mscale,t.bbox={h:n.bbox.h,d:n.bbox.d,w:n.bbox.w,exactW:!0,lw:n.bbox.lw+l,rw:n.bbox.rw+l,H:Math.max(null==n.bbox.H?-i.BIGDIMEN:n.bbox.H+h,n.bbox.h+h),D:Math.max(null==n.bbox.D?-i.BIGDIMEN:n.bbox.D-h,n.bbox.d-h)},""!==r.height&&(t.bbox.h=this.HTMLlength2em(n,r.height,d,"h",0)),""!==r.depth&&(t.bbox.d=this.HTMLlength2em(n,r.depth,d,"d",0)),""!==r.width&&(t.bbox.w=this.HTMLlength2em(n,r.width,d,"w",0)),t.bbox.H<=t.bbox.h&&delete t.bbox.H,t.bbox.D<=t.bbox.d&&delete t.bbox.D;var u=/^\s*(\d+(\.\d*)?|\.\d+)\s*(pt|em|ex|mu|px|pc|in|mm|cm)\s*$/;t.bbox.exact=!!(this.data[0]&&0==this.data[0].data.length||u.exec(r.height)||u.exec(r.width)||u.exec(r.depth)),i.setStackWidth(s,t.bbox.w)}return this.HTMLhandleSpace(t),this.HTMLhandleColor(t),t},HTMLlength2em:function(t,e,a,s,n){null==n&&(n=-i.BIGDIMEN);var o=String(e).match(/width|height|depth/),r=o?t.bbox[o[0].charAt(0)]:s?t.bbox[s]:0,l=i.length2em(e,a,r/this.mscale)*this.mscale;return s&&String(e).match(/^\s*[-+]/)?Math.max(n,t.bbox[s]+l):l},HTMLstretchH:a.mbase.HTMLstretchH,HTMLstretchV:a.mbase.HTMLstretchV}),a.mrow.Augment({HTMLlineBreaks:function(t){return!!this.parent.linebreakContainer&&(i.config.linebreaks.automatic&&t.bbox.w>i.linebreakWidth||this.hasNewline())},HTMLstretchH:function(t,e){this.HTMLremoveColor();var i=this.HTMLspanElement();return this.data[this.core].HTMLstretchH(i,e),this.HTMLcomputeBBox(i,!0),this.HTMLhandleColor(i),i},HTMLstretchV:function(t,e,i){this.HTMLremoveColor();var a=this.HTMLspanElement();return this.data[this.core].HTMLstretchV(a,e,i),this.HTMLcomputeBBox(a,!0),this.HTMLhandleColor(a),a}}),a.mstyle.Augment({toHTML:function(t,e,i){if(t=this.HTMLcreateSpan(t),null!=this.data[0]){var a=this.data[0].toHTML(t);null!=i?this.data[0].HTMLstretchV(t,e,i):null!=e&&this.data[0].HTMLstretchH(t,e),t.bbox=a.bbox}return this.HTMLhandleSpace(t),this.HTMLhandleColor(t),t},HTMLstretchH:a.mbase.HTMLstretchH,HTMLstretchV:a.mbase.HTMLstretchV}),a.mfrac.Augment({toHTML:function(t){t=this.HTMLcreateSpan(t);var e=i.createStack(t),a=i.createBox(e),s=i.createBox(e);i.MeasureSpans([this.HTMLboxChild(0,a),this.HTMLboxChild(1,s)]);var n=this.getValues("displaystyle","linethickness","numalign","denomalign","bevelled"),o=this.HTMLgetScale(),r=n.displaystyle,l=i.TeX.axis_height*o;if(n.bevelled){var h=r?.4:.15,d=Math.max(a.bbox.h+a.bbox.d,s.bbox.h+s.bbox.d)+2*h,u=i.createBox(e);i.createDelimiter(u,47,d),i.placeBox(a,0,(a.bbox.d-a.bbox.h)/2+l+h),i.placeBox(u,a.bbox.w-h/2,(u.bbox.d-u.bbox.h)/2+l),i.placeBox(s,a.bbox.w+u.bbox.w-h,(s.bbox.d-s.bbox.h)/2+l-h)}else{var c,m,p,M,f=Math.max(a.bbox.w,s.bbox.w),g=i.thickness2em(n.linethickness,this.scale)*this.mscale,b=i.TeX.min_rule_thickness/this.em;if(r?(p=i.TeX.num1,M=i.TeX.denom1):(p=0===g?i.TeX.num3:i.TeX.num2,M=i.TeX.denom2),p*=o,M*=o,0===g)c=Math.max((r?7:3)*i.TeX.rule_thickness,2*b),(m=p-a.bbox.d-(s.bbox.h-M))<c&&(p+=(c-m)/2,M+=(c-m)/2);else{c=Math.max((r?2:0)*b+g,g/2+1.5*b),(m=p-a.bbox.d-(l+g/2))<c&&(p+=c-m),(m=l-g/2-(s.bbox.h-M))<c&&(M+=c-m);var x=i.createBox(e);i.createRule(x,g,0,f+2*g),i.placeBox(x,0,l-g/2)}i.alignBox(a,n.numalign,p,0,!0),i.alignBox(s,n.denomalign,-M,0,!0)}return this.HTMLhandleSpace(t),this.HTMLhandleColor(t),t},HTMLcanStretch:function(t){return!1},HTMLhandleSpace:function(t){if(!this.texWithDelims){var e=i.TeX.nulldelimiterspace*this.mscale,a=t.childNodes[i.msiePaddingWidthBug?1:0].style;a.marginLeft=a.marginRight=i.Em(e),t.bbox.w+=2*e,t.bbox.rw+=2*e}this.SUPER(arguments).HTMLhandleSpace.call(this,t)}}),a.msqrt.Augment({toHTML:function(t){t=this.HTMLcreateSpan(t);var e,a,s,n,o=i.createStack(t),r=i.createBox(o),l=i.createBox(o),h=i.createBox(o),d=this.HTMLgetScale(),u=i.TeX.rule_thickness*d;e=this.Get("displaystyle")?i.TeX.x_height*d:u,a=Math.max(u+e/4,1.5*i.TeX.min_rule_thickness/this.em);var c=this.HTMLboxChild(0,r);s=c.bbox.h+c.bbox.d+a+u,i.createDelimiter(h,8730,s,d),i.MeasureSpans([c,h]),n=c.bbox.w;var m=0;(h.isMultiChar||i.AdjustSurd&&i.imgFonts)&&(h.bbox.w*=.95),h.bbox.h+h.bbox.d>s&&(a=(h.bbox.h+h.bbox.d-(s-u))/2);var p=i.FONTDATA.DELIMITERS[i.FONTDATA.RULECHAR];return!p||n<(p.HW[0]||[0])[0]*d||d<.75?(i.createRule(l,0,u,n),l.bbox.h=-u):i.createDelimiter(l,i.FONTDATA.RULECHAR,n,d),a=(s=c.bbox.h+a+u)*i.rfuzz,h.isMultiChar&&(a=i.rfuzz),m=this.HTMLaddRoot(o,h,m,h.bbox.h+h.bbox.d-s,d),i.placeBox(h,m,s-h.bbox.h),i.placeBox(l,m+h.bbox.w,s-l.bbox.h+a),i.placeBox(r,m+h.bbox.w,0),this.HTMLhandleSpace(t),this.HTMLhandleColor(t),t},HTMLaddRoot:function(t,e,i,a,s){return i}}),a.mroot.Augment({toHTML:a.msqrt.prototype.toHTML,HTMLaddRoot:function(t,e,a,s,n){var o=i.createBox(t);if(this.data[1]){var r=this.data[1].toHTML(o);r.style.paddingRight=r.style.paddingLeft="",i.Measured(r,o)}else o.bbox=this.HTMLzeroBBox();var l=this.HTMLrootHeight(e.bbox.h+e.bbox.d,n,o)-s,h=Math.min(o.bbox.w,o.bbox.rw);return a=Math.max(h,e.offset),i.placeBox(o,a-h,l),a-e.offset},HTMLrootHeight:function(t,e,i){return.45*(t-.9*e)+.6*e+Math.max(0,i.bbox.d-.075)}}),a.mfenced.Augment({toHTML:function(t){t=this.HTMLcreateSpan(t),this.data.open&&this.data.open.toHTML(t),null!=this.data[0]&&this.data[0].toHTML(t);for(var e=1,i=this.data.length;e<i;e++)this.data[e]&&(this.data["sep"+e]&&this.data["sep"+e].toHTML(t),this.data[e].toHTML(t));this.data.close&&this.data.close.toHTML(t);var a=this.HTMLcomputeBBox(t),s=t.bbox.h,n=t.bbox.d;for(e=0,i=a.length;e<i;e++)a[e].HTMLstretchV(t,s,n);return a.length&&this.HTMLcomputeBBox(t,!0),this.HTMLhandleSpace(t),this.HTMLhandleColor(t),t},HTMLcomputeBBox:function(t,e){var i=t.bbox={},a=[];this.HTMLcheckStretchy(this.data.open,i,a,e),this.HTMLcheckStretchy(this.data[0],i,a,e);for(var s=1,n=this.data.length;s<n;s++)this.data[s]&&(this.HTMLcheckStretchy(this.data["sep"+s],i,a,e),this.HTMLcheckStretchy(this.data[s],i,a,e));return this.HTMLcheckStretchy(this.data.close,i,a,e),this.HTMLcleanBBox(i),a},HTMLcheckStretchy:function(t,e,i,a){t&&(!a&&t.HTMLcanStretch("Vertical")&&(i.push(t),t=t.CoreMO()||t),this.HTMLcombineBBoxes(t,e))}}),a.menclose.Augment({toHTML:a.mbase.HTMLautoload}),a.maction.Augment({toHTML:a.mbase.HTMLautoload}),a.semantics.Augment({toHTML:function(t,e,i){if(t=this.HTMLcreateSpan(t),null!=this.data[0]){var a=this.data[0].toHTML(t);null!=i?this.data[0].HTMLstretchV(t,e,i):null!=e&&this.data[0].HTMLstretchH(t,e),t.bbox=a.bbox}return this.HTMLhandleSpace(t),t},HTMLstretchH:a.mbase.HTMLstretchH,HTMLstretchV:a.mbase.HTMLstretchV}),a.munderover.Augment({toHTML:function(t,e,s){var n=this.getValues("displaystyle","accent","accentunder","align"),o=this.data[this.base];if(!n.displaystyle&&null!=o&&(o.movablelimits||o.CoreMO().Get("movablelimits")))return a.msubsup.prototype.toHTML.call(this,t);t=this.HTMLcreateSpan(t);var r,l,h,d=this.HTMLgetScale(),u=i.createStack(t),c=[],m=[],p=[];for(l=0,h=this.data.length;l<h;l++)null!=this.data[l]&&(r=c[l]=i.createBox(u),m[l]=this.data[l].toHTML(r),l==this.base?(null!=s?this.data[this.base].HTMLstretchV(r,e,s):null!=e&&this.data[this.base].HTMLstretchH(r,e),p[l]=(null!=s||null==e)&&this.data[l].HTMLcanStretch("Horizontal"),this.data[this.over]&&n.accent&&(m[l].bbox.h=Math.max(m[l].bbox.h,d*i.TeX.x_height))):(p[l]=this.data[l].HTMLcanStretch("Horizontal"),m[l].style.paddingLeft=m[l].style.paddingRight=""));i.MeasureSpans(m);var M=-i.BIGDIMEN,f=M;for(l=0,h=this.data.length;l<h;l++)this.data[l]&&(c[l].bbox.w>f&&(f=c[l].bbox.w),!p[l]&&f>M&&(M=f));for(null==s&&null!=e?M=e:M==-i.BIGDIMEN&&(M=f),l=f=0,h=this.data.length;l<h;l++)this.data[l]&&(r=c[l],p[l]&&(r.bbox=this.data[l].HTMLstretchH(r,M).bbox,l!==this.base&&(m[l].style.paddingLeft=m[l].style.paddingRight="")),r.bbox.w>f&&(f=r.bbox.w));var g,b,x,v,T,L,E=i.TeX.rule_thickness*this.mscale,y=i.FONTDATA.TeX_factor,C=0;for((o=c[this.base]||{bbox:this.HTMLzeroBBox()}).bbox.ic&&(C=1.3*o.bbox.ic+.05),l=0,h=this.data.length;l<h;l++)if(null!=this.data[l]){r=c[l],T=i.TeX.big_op_spacing5*d;var S=l!=this.base&&n[this.ACCENTS[l]];S&&r.bbox.w<=1/i.em+1e-4&&(r.bbox.w=r.bbox.rw-r.bbox.lw,r.bbox.noclip=!0,r.bbox.lw&&r.insertBefore(i.createSpace(r.parentNode,0,0,-r.bbox.lw),r.firstChild),i.createBlank(r,0,0,r.bbox.rw+.1)),g={left:0,center:(f-r.bbox.w)/2,right:f-r.bbox.w}[n.align],b=0,l==this.over?(S?(L=Math.max(E*d*y,2.5/this.em),T=0,o.bbox.skew&&(g+=o.bbox.skew,t.bbox.skew=o.bbox.skew,g+r.bbox.w>f&&(t.bbox.skew+=(f-r.bbox.w-g)/2))):(x=i.TeX.big_op_spacing1*d*y,v=i.TeX.big_op_spacing3*d*y,L=Math.max(x,v-Math.max(0,r.bbox.d))),L=Math.max(L,1.5/this.em),g+=C/2,b=o.bbox.h+r.bbox.d+L,r.bbox.h+=T):l==this.under&&(S?(L=3*E*d*y,T=0):(x=i.TeX.big_op_spacing2*d*y,v=i.TeX.big_op_spacing4*d*y,L=Math.max(x,v-r.bbox.h)),L=Math.max(L,1.5/this.em),g-=C/2,b=-(o.bbox.d+r.bbox.h+L),r.bbox.d+=T),i.placeBox(r,g,b)}return this.HTMLhandleSpace(t),this.HTMLhandleColor(t),t},HTMLstretchH:a.mbase.HTMLstretchH,HTMLstretchV:a.mbase.HTMLstretchV}),a.msubsup.Augment({toHTML:function(t,e,a){t=this.HTMLcreateSpan(t);var s,n=this.HTMLgetScale(),o=this.HTMLgetMu(t),r=i.createStack(t),l=[],h=i.createBox(r);this.data[this.base]?(l.push(this.data[this.base].toHTML(h)),null!=a?this.data[this.base].HTMLstretchV(h,e,a):null!=e&&this.data[this.base].HTMLstretchH(h,e)):h.bbox=this.HTMLzeroBBox();var d,u,c=i.TeX.x_height*n,m=i.TeX.scriptspace*n*.75;this.HTMLnotEmpty(this.data[this.sup])&&(d=i.createBox(r),l.push(this.data[this.sup].toHTML(d))),this.HTMLnotEmpty(this.data[this.sub])&&(u=i.createBox(r),l.push(this.data[this.sub].toHTML(u))),i.MeasureSpans(l),d&&(d.bbox.w+=m,d.bbox.rw=Math.max(d.bbox.w,d.bbox.rw)),u&&(u.bbox.w+=m,u.bbox.rw=Math.max(u.bbox.w,u.bbox.rw)),i.placeBox(h,0,0);var p=n;d?p=this.data[this.sup].HTMLgetScale():u&&(p=this.data[this.sub].HTMLgetScale());var M,f=i.TeX.sup_drop*p,g=i.TeX.sub_drop*p,b=h.bbox.h-f,x=h.bbox.d+g,v=0;h.bbox.ic&&(h.bbox.w-=h.bbox.ic,v=1.3*h.bbox.ic+.05),!this.data[this.base]||null!=e||null!=a||"mi"!==this.data[this.base].type&&"mo"!==this.data[this.base].type||i.isChar(this.data[this.base].data.join(""))&&1===l[0].scale&&!this.data[this.base].Get("largeop")&&(b=x=0);var T=this.getValues("subscriptshift","superscriptshift");if(T.subscriptshift=""===T.subscriptshift?0:i.length2em(T.subscriptshift,o),T.superscriptshift=""===T.superscriptshift?0:i.length2em(T.superscriptshift,o),d)if(u){x=Math.max(x,i.TeX.sub2*n);var L=i.TeX.rule_thickness*n;b-d.bbox.d-(u.bbox.h-x)<3*L&&(x=3*L-b+d.bbox.d+u.bbox.h,(f=.8*c-(b-d.bbox.d))>0&&(b+=f,x-=f)),i.placeBox(d,h.bbox.w+v,Math.max(b,T.superscriptshift)),i.placeBox(u,h.bbox.w,-Math.max(x,T.subscriptshift))}else 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c=this.Get("alttext");c&&!t.getAttribute("aria-label")&&t.setAttribute("aria-label",c),o=i.createStack(t),r=i.createBox(o),o.style.fontSize=u.parentNode.style.fontSize,u.parentNode.style.fontSize="",null!=this.data[0]&&(a.mbase.prototype.displayAlign=e.config.displayAlign,a.mbase.prototype.displayIndent=e.config.displayIndent,String(e.config.displayIndent).match(/^0($|[a-z%])/i)&&(a.mbase.prototype.displayIndent="0"),(l=this.data[0].toHTML(r)).bbox.exactW=!1)}if(h=n&&n!==i.PHASE.II?l:i.Measured(l,r),!n||n===i.PHASE.III){i.placeBox(r,0,0);var m=h.bbox.w;m=Math.abs(m)<.006?0:Math.max(0,Math.round(m*this.em)+.25),t.style.width=i.EmRounded(m/i.outerEm),t.style.display="inline-block";var p=1/i.em,M=i.em/i.outerEm;i.em/=M,t.bbox.h*=M,t.bbox.d*=M,t.bbox.w*=M,t.bbox.lw*=M,t.bbox.rw*=M,t.bbox.H&&(t.bbox.H*=M),t.bbox.D&&(t.bbox.D*=M),h&&null!=h.bbox.width&&(t.style.minWidth=h.bbox.minWidth||t.style.width,t.style.width=h.bbox.width,r.style.width=o.style.width="100%",d.className+=" 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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,d=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 u=i.Element("span",{},[["span",{className:"MJXp-over"}]]);u.firstChild.appendChild(t.lastChild),t.childNodes.length>(this.data[this.under]?1:0)&&u.firstChild.appendChild(t.firstChild),this.data[this.over].PHTMLhandleScriptlevel(u.firstChild.firstChild),null!=d&&(o.vec&&(u.firstChild.firstChild.firstChild.style.fontSize="60%",o.h*=.6,o.d*=.6,o.w*=.6),d=d-o.d+.1,null!=l.t&&(d+=l.t-l.h),u.firstChild.firstChild.style.marginBottom=a.Em(d)),t.firstChild?t.insertBefore(u,t.firstChild):t.appendChild(u)}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+(d||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(i.Element("span"),t.firstChild):t.appendChild(i.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=i.Element("span",{className:"MJXp-script-box",style:{height:a.Em(o+.8*n.PHTML.h+r+.8*s.PHTML.d),"vertical-align":a.Em(-r-.8*s.PHTML.d)}},[["span",{},[["span",{},[["span",{style:{"margin-bottom":a.Em(-(n.PHTML.d-.05))}}]]]]],["span",{},[["span",{},[["span",{style:{"margin-top":a.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=a.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=a.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=i.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,a.length2em(e.linethickness||"0",0)),e.linethickness){var l=s.firstChild.firstChild.firstChild,h=a.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=a.Em(3*h-1.2),t.style.verticalAlign=a.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=a.Em(14/n),r=i.Element("span",{className:"MJXp-surd"},[["span",{style:{"font-size":n+"%","margin-top":o}},["√"]]]),l=i.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 d=Math.ceil(150/n*10);r.firstChild.className="MJXp-right MJXp-scale"+d,r.firstChild.style.marginLeft=a.Em(h*(d/10-1)/n*100),h=h*d/10,l.firstChild.style.borderTopWidth=a.Em(.08/Math.sqrt(d/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(i.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=a.Em(l),s.style.verticalAlign=a.Em(r),-l>.8*e.w&&(s.style.marginLeft=a.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,i=this.data.length;e<i;e++)this.PHTMLaddChild(t,"sep"+e,{}),this.PHTMLaddChild(t,e,{});this.PHTMLaddChild(t,"close",{});var a=this.PHTML.h,s=this.PHTML.d;for(this.PHTMLstretchChild("open",a,s),e=0,i=this.data.length;e<i;e++)this.PHTMLstretchChild("sep"+e,a,s),this.PHTMLstretchChild(e,a,s);return this.PHTMLstretchChild("close",a,s),t}}),s.mrow.Augment({toPreviewHTML:function(t){t=this.PHTMLdefaultSpan(t);for(var e=this.PHTML.h,i=this.PHTML.d,a=0,s=this.data.length;a<s;a++)this.PHTMLstretchChild(a,e,i);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),d=l(r.rowspacing),u=l(r.columnalign),c=l(r.rowalign);for(e=0,s=h.length;e<s;e++)h[e]=a.length2em(h[e]);for(e=0,s=d.length;e<s;e++)d[e]=a.length2em(d[e]);for(var m=i.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=a.arrayEntry(d,e-1),b=a.arrayEntry(c,e),x=f.PHTML;f.PHTMLspanElement().style.verticalAlign=b;var v="mlabeledtr"===f.type?1:0;for(n=0,o=f.data.length;n<o-v;n++){var T=f.data[n+v];if(T){var L=a.arrayEntry(h,n-1),E=a.arrayEntry(u,n),y=T.PHTMLspanElement();n&&(x.w+=L,y.style.paddingLeft=a.Em(L)),e&&(y.style.paddingTop=a.Em(g)),y.style.textAlign=E}}p+=x.h+x.d,e&&(p+=g),x.w>M&&(M=x.w)}}var C=this.PHTML;return C.w=M,C.h=p/2+.25,C.d=p/2-.25,C.l=C.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 i=1,a=this.data.length;i<a;i++)this.PHTMLaddChild(t,i,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",a,"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,i){var a=t.config.menuSettings,s=MathJax.OutputJax,n=i.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:i.isMSIE&&!i.versionAtLeast("8.0")}),Config:function(){var e,i,s,n,r;t.config["CHTML-preview"]&&MathJax.Hub.Config({"fast-preview":t.config["CHTML-preview"]});var l=this.config;l.disabled||null!=a.FastPreview||t.Config({menuSettings:{FastPreview:!0}}),a.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,i=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=i,t.Config({messageStyle:s}),n=!0)}))},Disable:function(){this.enabled=!1},Enable:function(){this.enabled=!0},Active:function(){return a.FastPreview&&this.enabled&&!(s[a.renderer]||{}).noFastPreview},Preview:function(t){if(this.Active()&&t.script.parentNode){var i=t.script.MathJax.preview||t.script.previousSibling;return i&&i.className===MathJax.Hub.config.preRemoveClass||(i=e.Element("span",{className:MathJax.Hub.config.preRemoveClass}),t.script.parentNode.insertBefore(i,t.script),t.script.MathJax.preview=i),i.innerHTML="",i.style.color=n?"black":"inherit",this.postFilter(i,t)}},postFilter:function(e,i){if(!i.math.root.toPreviewHTML){var a=MathJax.Callback.Queue();a.Push(["Require",MathJax.Ajax,"[MathJax]/jax/output/PreviewHTML/config.js"],["Require",MathJax.Ajax,"[MathJax]/jax/output/PreviewHTML/jax.js"]),t.RestartAfter(a.Push({}))}i.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,i,a){var s=i.config.menuSettings,n=MathJax.Extension.AssistiveMML={version:"2.7.9",config:i.CombineConfig("AssistiveMML",{disabled:!1,styles:{".MJX_Assistive_MathML":{position:"absolute!important",top:0,left:0,clip:i.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||i.Config({menuSettings:{assistiveMML:!0}}),t.Styles(this.config.styles),i.Register.MessageHook("End Math",(function(t){if(s.assistiveMML)return n.AddAssistiveMathML(t[1])}))},AddAssistiveMathML:function(t){var e={jax:i.getAllJax(t),i:0,callback:MathJax.Callback({})};return this.HandleMML(e),e.callback},RemoveAssistiveMathML:function(t){for(var e,a=i.getAllJax(t),s=0,n=a.length;s<n;s++)(e=document.getElementById(a[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,i,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{i=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",i),n=a.addElement(s,"span",{isMathJax:!0,unselectable:"on",className:"MJX_Assistive_MathML"+("block"===e.root.Get("display")?" MJX_Assistive_MathML_Block":"")});try{n.innerHTML=i}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()}};i.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 i,a,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 i in t)t.hasOwnProperty(i)&&e.push(i);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),i=0;t=e[i];i++){var a=l.MakeOption(t);void 0===s[a]&&(s[a]=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=a.FindId("Accessibility");r?(e.unshift(i.RULE()),r.submenu.items.push.apply(r.submenu.items,e)):((n=(a.FindId("Settings","Renderer")||{}).submenu)&&(e.unshift(i.RULE()),e.unshift(n.items.pop()),e.unshift(n.items.pop())),e.unshift("Accessibility"),r=i.SUBMENU.apply(i.SUBMENU,e),(o=a.IndexOfId("Locale"))?a.items.splice(o,0,r):a.items.push(i.RULE(),r))},Register:function(t){l.defaults[t.option]=!1,l.modules.push(t)},Startup:function(){i=MathJax.Menu.ITEM,a=MathJax.Menu.menu;for(var t,e=0;t=this.modules[e];e++)t.CreateMenu();this.AddMenu()},LoadExtensions:function(){for(var e,i=[],a=0;e=this.modules[a];a++)s[e.option]&&i.push(e.module);return i.length?t.Startup.loadArray(i):null}},h=MathJax.Extension.ModuleLoader=MathJax.Object.Subclass({option:"",name:["",""],module:"",placeHolder:null,submenu:!1,extension:null,Init:function(t,e,i,a,s){this.option=t,this.name=[e.replace(/ /g,""),e],this.module=i,this.extension=a,this.submenu=s||!1},CreateMenu:function(){var t=n(this.Load,this);this.submenu?this.placeHolder=i.SUBMENU(this.name,i.CHECKBOX(["Activate","Activate"],l.MakeOption(this.option),{action:t}),i.RULE(),i.COMMAND(["OptionsWhenActive","(Options when Active)"],null,{disabled:!0})):this.placeHolder=i.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-full.js");