MathJax.min.js

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this.msiePositionBug&&(this.msieSizeBug&&(p.style.height=E.zH+"px",p.style.width=E.zW+"px"),p.offsetHeight>d&&(p.style.height=d+"px",p.style.width=E.zW+this.scrollSize+"px"),p.offsetWidth>u&&(p.style.width=u+"px",p.style.height=E.zH+this.scrollSize+"px")),this.operaPositionBug&&(p.style.width=Math.min(u,E.zW)+"px"),p.offsetWidth>M&&p.offsetWidth-M<u&&p.offsetHeight-M<d&&(p.style.overflow="visible"),this.Position(p,E),this.msieTrapEventBug&&(x.style.height=p.clientHeight+"px",x.style.width=p.clientWidth+"px",x.style.left=parseFloat(p.style.left)+p.clientLeft+"px",x.style.top=parseFloat(p.style.top)+p.clientTop+"px"),p.style.visibility="","Hover"===this.settings.zoom&&(g.onmouseover=this.Remove),window.addEventListener?addEventListener("resize",this.Resize,!1):window.attachEvent?attachEvent("onresize",this.Resize):(this.onresize=window.onresize,window.onresize=this.Resize),t.signal.Post(["math zoomed",h]),n(a)},Position:function(t,e){t.style.display="none";var a=this.Resize(),i=a.x,s=a.y,n=e.mW;t.style.display="";var r=-n-Math.floor((t.offsetWidth-n)/2),o=e.Y;t.style.left=Math.max(r,10-i)+"px",t.style.top=Math.max(o,10-s)+"px",h.msiePositionBug||h.SetWH()},Resize:function(t){h.onresize&&h.onresize(t);var e=document.getElementById("MathJax_ZoomFrame"),a=document.getElementById("MathJax_ZoomOverlay"),i=h.getXY(e),s=h.findContainer(e);if("visible"!==h.getOverflow(s)){a.scroll_parent=s;var n=h.getXY(s);i.x-=n.x,i.y-=n.y,n=h.getBorder(s),i.x-=n.x,i.y-=n.y}return a.style.left=-i.x+"px",a.style.top=-i.y+"px",h.msiePositionBug?setTimeout(h.SetWH,0):h.SetWH(),i},SetWH:function(){var t=document.getElementById("MathJax_ZoomOverlay");if(t){t.style.display="none";var e=t.scroll_parent||document.documentElement||document.body;t.style.width=e.scrollWidth+"px",t.style.height=Math.max(e.clientHeight,e.scrollHeight)+"px",t.style.display=""}},findContainer:function(t){for(t=t.parentNode;t.parentNode&&t!==document.body&&"visible"===h.getOverflow(t);)t=t.parentNode;return t},getOverflow:window.getComputedStyle?function(t){return getComputedStyle(t).overflow}:function(t){return(t.currentStyle||{overflow:"visible"}).overflow},getBorder:function(t){var e={thin:1,medium:2,thick:3},a=window.getComputedStyle?getComputedStyle(t):t.currentStyle||{borderLeftWidth:0,borderTopWidth:0},i=a.borderLeftWidth,s=a.borderTopWidth;return i=e[i]?e[i]:parseInt(i),s=e[s]?e[s]:parseInt(s),{x:i,y:s}},getXY:function(t){var e,a=0,i=0;for(e=t;e.offsetParent;)a+=e.offsetLeft,e=e.offsetParent;for(h.operaPositionBug&&(t.style.border="1px solid"),e=t;e.offsetParent;)i+=e.offsetTop,e=e.offsetParent;return h.operaPositionBug&&(t.style.border=""),{x:a,y:i}},Remove:function(a){var i=document.getElementById("MathJax_ZoomFrame");if(i){var s=MathJax.OutputJax[i.previousSibling.jaxID].getJaxFromMath(i.previousSibling);if(t.signal.Post(["math unzoomed",s]),i.parentNode.removeChild(i),(i=document.getElementById("MathJax_ZoomTracker"))&&i.parentNode.removeChild(i),h.operaRefreshBug){var r=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(r)}window.removeEventListener?removeEventListener("resize",h.Resize,!1):window.detachEvent?detachEvent("onresize",h.Resize):(window.onresize=h.onresize,delete h.onresize)}return n(a)}};t.Browser.Select({MSIE:function(t){var e=document.documentMode||0,a=e>=9;h.msiePositionBug=!a,h.msieSizeBug=t.versionAtLeast("7.0")&&(!document.documentMode||7===e||8===e),h.msieZIndexBug=e<=7,h.msieInlineBlockAlignBug=e<=7,h.msieTrapEventBug=!window.addEventListener,"BackCompat"===document.compatMode&&(h.scrollSize=52),a&&delete l.styles["#MathJax_Zoom"].filter},Opera:function(t){h.operaPositionBug=!0,h.operaRefreshBug=!0}}),h.topImg=h.msieInlineBlockAlignBug?e.Element("img",{style:{width:0,height:0,position:"relative"},src:"about:blank"}):e.Element("span",{style:{width:0,height:0,display:"inline-block"}}),(h.operaPositionBug||h.msieTopBug)&&(h.topImg.style.border="1px solid"),MathJax.Callback.Queue(["StartupHook",MathJax.Hub.Register,"Begin Styles",{}],["Styles",a,l.styles],["Post",t.Startup.signal,"MathZoom Ready"],["loadComplete",a,"[MathJax]/extensions/MathZoom.js"])}(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.OutputJax["HTML-CSS"],MathJax.OutputJax.NativeMML),function(t,e,a,i,s){var n=MathJax.Callback.Signal("menu");MathJax.Extension.MathMenu={version:"2.7.1",signal:n};var r,o,l,h=function(t){return MathJax.Localization._.apply(MathJax.Localization,[["MathMenu",t]].concat([].slice.call(arguments,1)))},c=MathJax.Object.isArray,u=t.Browser.isPC,d=t.Browser.isMSIE,m=(document.documentMode||0)>8,p=u?null:"5px",f=t.CombineConfig("MathMenu",{delay:150,showRenderer:!0,showMathPlayer:!0,showFontMenu:!1,showContext:!1,showDiscoverable:!1,showLocale:!0,showLocaleURL:!1,semanticsAnnotations:{TeX:["TeX","LaTeX","application/x-tex"],StarMath:["StarMath 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#808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},"#MathJax_About.MathJax_MousePost":{outline:"none"},".MathJax_Menu":{position:"absolute","background-color":"white",color:"black",width:"auto",padding:u?"2px":"5px 0px",border:"1px solid #CCCCCC",margin:0,cursor:"default",font:"menu","text-align":"left","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap",float:"none","z-index":201,"border-radius":p,"-webkit-border-radius":p,"-moz-border-radius":p,"-khtml-border-radius":p,"box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},".MathJax_MenuItem":{padding:u?"2px 2em":"1px 2em",background:"transparent"},".MathJax_MenuArrow":{position:"absolute",right:".5em","padding-top":".25em",color:"#666666","font-family":d?"'Arial unicode MS'":null,"font-size":".75em"},".MathJax_MenuActive .MathJax_MenuArrow":{color:"white"},".MathJax_MenuArrow.RTL":{left:".5em",right:"auto"},".MathJax_MenuCheck":{position:"absolute",left:".7em","font-family":d?"'Arial unicode MS'":null},".MathJax_MenuCheck.RTL":{right:".7em",left:"auto"},".MathJax_MenuRadioCheck":{position:"absolute",left:u?"1em":".7em"},".MathJax_MenuRadioCheck.RTL":{right:u?"1em":".7em",left:"auto"},".MathJax_MenuLabel":{padding:u?"2px 2em 4px 1.33em":"1px 2em 3px 1.33em","font-style":"italic"},".MathJax_MenuRule":{"border-top":u?"1px solid #CCCCCC":"1px solid #DDDDDD",margin:u?"4px 1px 0px":"4px 3px"},".MathJax_MenuDisabled":{color:"GrayText"},".MathJax_MenuActive":{"background-color":u?"Highlight":"#606872",color:u?"HighlightText":"white"},".MathJax_MenuDisabled:focus, .MathJax_MenuLabel:focus":{"background-color":"#E8E8E8"},".MathJax_ContextMenu:focus":{outline:"none"},".MathJax_ContextMenu .MathJax_MenuItem:focus":{outline:"none"},"#MathJax_AboutClose":{top:".2em",right:".2em"},".MathJax_Menu .MathJax_MenuClose":{top:"-10px",left:"-10px"},".MathJax_MenuClose":{position:"absolute",cursor:"pointer",display:"inline-block",border:"2px solid #AAA","border-radius":"18px","-webkit-border-radius":"18px","-moz-border-radius":"18px","-khtml-border-radius":"18px","font-family":"'Courier New',Courier","font-size":"24px",color:"#F0F0F0"},".MathJax_MenuClose span":{display:"block","background-color":"#AAA",border:"1.5px solid","border-radius":"18px","-webkit-border-radius":"18px","-moz-border-radius":"18px","-khtml-border-radius":"18px","line-height":0,padding:"8px 0 6px"},".MathJax_MenuClose:hover":{color:"white!important",border:"2px solid #CCC!important"},".MathJax_MenuClose:hover span":{"background-color":"#CCC!important"},".MathJax_MenuClose:hover:focus":{outline:"none"}}});t.Register.StartupHook("MathEvents Ready",function(){r=MathJax.Extension.MathEvents.Event.False,o=MathJax.Extension.MathEvents.Hover,l=MathJax.Extension.MathEvents.Event.KEY});var g=MathJax.Object.Subclass({Keydown:function(t,e){switch(t.keyCode){case l.ESCAPE:this.Remove(t,e);break;case l.RIGHT:this.Right(t,e);break;case l.LEFT:this.Left(t,e);break;case l.UP:this.Up(t,e);break;case l.DOWN:this.Down(t,e);break;case l.RETURN:case l.SPACE:this.Space(t,e);break;default:return}return r(t)},Escape:function(t,e){},Right:function(t,e){},Left:function(t,e){},Up:function(t,e){},Down:function(t,e){},Space:function(t,e){}},{}),M=MathJax.Menu=g.Subclass({version:"2.7.1",items:[],posted:!1,title:null,margin:5,Init:function(t){this.items=[].slice.call(arguments,0)},With:function(e){return e&&t.Insert(this,e),this},Post:function(t,a,i){t||(t=window.event||{});var s=document.getElementById("MathJax_MenuFrame");s||(s=M.Background(this),delete x.lastItem,delete x.lastMenu,delete M.skipUp,n.Post(["post",M.jax]),M.isRTL="rtl"===MathJax.Localization.fontDirection());var o=e.Element("div",{onmouseup:M.Mouseup,ondblclick:r,ondragstart:r,onselectstart:r,oncontextmenu:r,menuItem:this,className:"MathJax_Menu",onkeydown:M.Keydown,role:"menu"});"contextmenu"!==t.type&&"mouseover"!==t.type||(o.className+=" MathJax_ContextMenu"),i||MathJax.Localization.setCSS(o);for(var l=0,h=this.items.length;l<h;l++)this.items[l].Create(o);M.isMobile&&e.addElement(o,"span",{className:"MathJax_MenuClose",menu:a,ontouchstart:M.Close,ontouchend:r,onmousedown:M.Close,onmouseup:r},[["span",{},"×"]]),s.appendChild(o),this.posted=!0,o.offsetWidth&&(o.style.width=o.offsetWidth+2+"px");var c=t.pageX,d=t.pageY,m=document.body.getBoundingClientRect(),p=window.getComputedStyle?window.getComputedStyle(document.body):{marginLeft:"0px"},g=m.right-Math.min(0,m.left)+parseFloat(p.marginLeft);if(!c&&!d&&"clientX"in t&&(c=t.clientX+document.body.scrollLeft+document.documentElement.scrollLeft,d=t.clientY+document.body.scrollTop+document.documentElement.scrollTop),a){var T="left",E=a.offsetWidth;for(c=M.isMobile?30:E-2,d=0;a&&a!==s;)c+=a.offsetLeft,d+=a.offsetTop,a=a.parentNode;M.isMobile||(M.isRTL&&c-E-o.offsetWidth>this.margin||!M.isRTL&&c+o.offsetWidth>g-this.margin)&&(T="right",c=Math.max(this.margin,c-E-o.offsetWidth+6)),u||(o.style["borderRadiusTop"+T]=0,o.style["WebkitBorderRadiusTop"+T]=0,o.style["MozBorderRadiusTop"+T]=0,o.style["KhtmlBorderRadiusTop"+T]=0)}else{var C=M.CurrentNode()||t.target;if(("keydown"===t.type||!c&&!d)&&C){var v=window.pageXOffset||document.documentElement.scrollLeft,b=window.pageYOffset||document.documentElement.scrollTop,L=C.getBoundingClientRect();c=(L.right+L.left)/2+v,d=(L.bottom+L.top)/2+b}c+o.offsetWidth>g-this.margin&&(c=g-o.offsetWidth-this.margin),M.isMobile&&(c=Math.max(5,c-Math.floor(o.offsetWidth/2)),d-=20),M.skipUp=t.isContextMenu}o.style.left=c+"px",o.style.top=d+"px",document.selection&&document.selection.empty&&document.selection.empty();var A=window.pageXOffset||document.documentElement.scrollLeft,y=window.pageYOffset||document.documentElement.scrollTop;return M.Focus(o),"keydown"===t.type&&(M.skipMouseoverFromKey=!0,setTimeout(function(){delete M.skipMouseoverFromKey},f.delay)),window.scrollTo(A,y),r(t)},Remove:function(t,e){n.Post(["unpost",M.jax]);var a=document.getElementById("MathJax_MenuFrame");return a&&(a.parentNode.removeChild(a),this.msieFixedPositionBug&&detachEvent("onresize",M.Resize)),M.jax.hover&&(delete M.jax.hover.nofade,o.UnHover(M.jax)),M.Unfocus(e),"mousedown"===t.type&&M.CurrentNode().blur(),r(t)},Find:function(t){return this.FindN(1,t,[].slice.call(arguments,1))},FindId:function(t){return this.FindN(0,t,[].slice.call(arguments,1))},FindN:function(t,e,a){for(var i=0,s=this.items.length;i<s;i++)if(this.items[i].name[t]===e)return a.length?this.items[i].submenu?this.items[i].submenu.FindN(t,a[0],a.slice(1)):null:this.items[i];return null},IndexOf:function(t){return this.IndexOfN(1,t)},IndexOfId:function(t){return this.IndexOfN(0,t)},IndexOfN:function(t,e){for(var a=0,i=this.items.length;a<i;a++)if(this.items[a].name[t]===e)return a;return null},Right:function(t,e){M.Right(t,e)},Left:function(t,e){M.Left(t,e)},Up:function(t,e){var a=e.lastChild;a.menuItem.Activate(t,a)},Down:function(t,e){var a=e.firstChild;a.menuItem.Activate(t,a)},Space:function(t,e){this.Remove(t,e)}},{config:f,Remove:function(t){return M.Event(t,this,"Remove")},Mouseover:function(t){return M.Event(t,this,"Mouseover")},Mouseout:function(t){return M.Event(t,this,"Mouseout")},Mousedown:function(t){return M.Event(t,this,"Mousedown")},Mouseup:function(t){return M.Event(t,this,"Mouseup")},Keydown:function(t){return M.Event(t,this,"Keydown")},Touchstart:function(t){return M.Event(t,this,"Touchstart")},Touchend:function(t){return M.Event(t,this,"Touchend")},Close:function(t){return M.Event(t,this.menu||this.parentNode,this.menu?"Touchend":"Remove")},Event:function(t,e,a,i){if(M.skipMouseover&&"Mouseover"===a&&!i)return r(t);if(M.skipMouseoverFromKey&&"Mouseover"===a)return delete M.skipMouseoverFromKey,r(t);if(M.skipUp){if(a.match(/Mouseup|Touchend/))return delete M.skipUp,r(t);("Touchstart"===a||"Mousedown"===a&&!M.skipMousedown)&&delete M.skipUp}t||(t=window.event);var s=e.menuItem;return s&&s[a]?s[a](t,e):null},BGSTYLE:{position:"absolute",left:0,top:0,"z-index":200,width:"100%",height:"100%",border:0,padding:0,margin:0},Background:function(t){var a=e.addElement(document.body,"div",{style:this.BGSTYLE,id:"MathJax_MenuFrame"},[["div",{style:this.BGSTYLE,menuItem:t,onmousedown:this.Remove}]]),i=a.firstChild;return M.msieBackgroundBug&&(i.style.backgroundColor="white",i.style.filter="alpha(opacity=0)"),M.msieFixedPositionBug?(a.width=a.height=0,this.Resize(),attachEvent("onresize",this.Resize)):i.style.position="fixed",a},Resize:function(){setTimeout(M.SetWH,0)},SetWH:function(){var t=document.getElementById("MathJax_MenuFrame");t&&((t=t.firstChild).style.width=t.style.height="1px",t.style.width=document.body.scrollWidth+"px",t.style.height=document.body.scrollHeight+"px")},posted:!1,active:null,GetNode:function(t){var e=document.getElementById(t.inputID+"-Frame");return e.isMathJax?e:e.firstChild},CurrentNode:function(){return M.GetNode(M.jax)},AllNodes:function(){for(var t,e=MathJax.Hub.getAllJax(),a=[],i=0;t=e[i];i++)a.push(M.GetNode(t));return a},ActiveNode:function(){return M.active},FocusNode:function(t){M.active=t,t.focus()},Focus:function(t){M.posted?M.ActiveNode().tabIndex=-1:M.Activate(t),t.tabIndex=0,M.FocusNode(t)},Activate:function(t,e){M.UnsetTabIndex(),M.posted=!0},Unfocus:function(){M.ActiveNode().tabIndex=-1,M.SetTabIndex(),M.FocusNode(M.CurrentNode()),M.posted=!1},MoveHorizontal:function(t,e,a){if(t.shiftKey){var i=M.AllNodes(),s=i.length;if(0!==s){var n=i[M.Mod(a(M.IndexOf(i,M.CurrentNode())),s)];n!==M.CurrentNode()&&(M.menu.Remove(t,e),M.jax=MathJax.Hub.getJaxFor(n),M.FocusNode(n),M.menu.Post(null))}}},Right:function(t,e){M.MoveHorizontal(t,e,function(t){return t+1})},Left:function(t,e){M.MoveHorizontal(t,e,function(t){return t-1})},UnsetTabIndex:function(){for(var t,e=M.AllNodes(),a=0;t=e[a];a++)t.tabIndex>0&&(t.oldTabIndex=t.tabIndex),t.tabIndex=-1},SetTabIndex:function(){for(var e,a=M.AllNodes(),i=0;e=a[i];i++)void 0!==e.oldTabIndex?(e.tabIndex=e.oldTabIndex,delete e.oldTabIndex):e.tabIndex=t.getTabOrder(e)},Mod:function(t,e){return(t%e+e)%e},IndexOf:Array.prototype.indexOf?function(t,e,a){return t.indexOf(e,a)}:function(t,e,a){for(var i=a||0,s=t.length;i<s;i++)if(e===t[i])return i;return-1},saveCookie:function(){e.Cookie.Set("menu",this.cookie)},getCookie:function(){this.cookie=e.Cookie.Get("menu")}});MathJax.Menu.NAV=g;var x=M.ITEM=g.Subclass({name:"",node:null,menu:null,Attributes:function(e){return t.Insert({onmouseup:M.Mouseup,ondragstart:r,onselectstart:r,onselectend:r,ontouchstart:M.Touchstart,ontouchend:M.Touchend,className:"MathJax_MenuItem",role:this.role,menuItem:this},e)},Create:function(t){if(!this.hidden){var a=this.Attributes(),i=this.Label(a,t);e.addElement(t,"div",a,i)}},Name:function(){return h(this.name[0],this.name[1])},Mouseover:function(t,e){e.parentNode===M.ActiveNode().parentNode&&this.Deactivate(M.ActiveNode()),this.Activate(t,e)},Mouseout:function(t,e){this.Deactivate(e)},Mouseup:function(t,e){return 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o=document.documentElement||{},l=window.innerHeight||o.clientHeight||o.scrollHeight||0;M.prototype.msieAboutBug?(r.style.width="20em",r.style.position="absolute",r.style.left=Math.floor((document.documentElement.scrollWidth-r.offsetWidth)/2)+"px",r.style.top=Math.floor((l-r.offsetHeight)/3)+document.body.scrollTop+"px"):(r.style.marginLeft=Math.floor(-r.offsetWidth/2)+"px",r.style.top=Math.floor((l-r.offsetHeight)/3)+"px")},M.About.Remove=function(t){M.About.div&&(document.body.removeChild(M.About.div),delete M.About.div)},M.About.Keydown=function(t){t.keyCode!==l.ESCAPE&&("MathJax_AboutClose"!==this.id||t.keyCode!==l.SPACE&&t.keyCode!==l.RETURN)||(M.About.Remove(t),M.CurrentNode().focus(),r(t))},M.About.GetJax=function(t,e,a,i){var s=[];for(var n in e)e.hasOwnProperty(n)&&e[n]&&(i&&e[n].version||e[n].isa&&e[n].isa(e))&&s.push(h(a[0],a[1],e[n].id||n,e[n].version));s.sort();for(var r=0,o=s.length;r<o;r++)t.push(s[r],["br"]);return t},M.About.GetFont=function(){var t=MathJax.Hub.outputJax["jax/mml"][0]||{};return({SVG:"web SVG",CommonHTML:"web TeX","HTML-CSS":t.imgFonts?"image":(t.webFonts?"web":"local")+" "+t.fontInUse}[t.id]||"generic")+" fonts"},M.About.GetFormat=function(){var t=MathJax.Hub.outputJax["jax/mml"][0]||{};if("HTML-CSS"===t.id&&t.webFonts&&!t.imgFonts)return t.allowWebFonts.replace(/otf/,"woff or otf")+" fonts"},M.Help=function(t){a.Require("[MathJax]/extensions/HelpDialog.js",function(){MathJax.Extension.Help.Dialog({type:t.type})})},M.ShowSource=function(t){t||(t=window.event);var e={screenX:t.screenX,screenY:t.screenY};if(M.jax)if("MathML"===this.format){var s=MathJax.ElementJax.mml;if(s&&void 0!==s.mbase.prototype.toMathML)try{M.ShowSource.Text(M.jax.root.toMathML("",M.jax),t)}catch(t){if(!t.restart)throw t;i.After([this,M.ShowSource,e],t.restart)}else if(!a.loadingToMathML)return a.loadingToMathML=!0,M.ShowSource.Window(t),void i.Queue(a.Require("[MathJax]/extensions/toMathML.js"),function(){delete 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i,s,n=t.Browser,r=M.Renderer.Messages;switch(f.settings.renderer){case"NativeMML":f.settings.warnedMML||(n.isChrome&&"24."!==n.version.substr(0,3)?i=r.MML.WebKit:n.isSafari&&!n.versionAtLeast("5.0")?i=r.MML.WebKit:n.isMSIE?n.hasMathPlayer||(i=r.MML.MSIE):i=n.isEdge?r.MML.WebKit:r.MML[n],s="warnedMML");break;case"SVG":f.settings.warnedSVG||n.isMSIE&&!m&&(i=r.SVG.MSIE)}if(i){if(i=h(i[0],i[1]),i+="\n\n",i+=h("SwitchAnyway","Switch the renderer anyway?\n\n(Press OK to switch, CANCEL to continue with the current renderer)"),M.cookie.renderer=a[0].id,M.saveCookie(),!confirm(i))return M.cookie.renderer=f.settings.renderer=e.Cookie.Get("menu").renderer,void M.saveCookie();s&&(M.cookie.warned=f.settings.warned=!0),M.cookie.renderer=f.settings.renderer,M.saveCookie()}t.Queue(["setRenderer",t,f.settings.renderer,"jax/mml"],["Rerender",t])}},M.Renderer.Messages={MML:{WebKit:["WebkitNativeMMLWarning","Your browser doesn't seem to support MathML natively, so switching to MathML output may cause the 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e.getJaxFor(t)},getHoverSpan:function(t,e){return t.root.CHTMLnodeElement()},getHoverBBox:function(t,e,a){var i=t.root.CHTML,s=t.CHTML.outerEm,n={w:i.w*s,h:i.h*s,d:i.d*s};return i.width&&(n.width=i.width),n},Zoom:function(t,e,a,s,r){this.getMetrics(t);var o=i.addElement(e,"mjx-chtml",{style:{"font-size":Math.floor(100*i.scale)+"%"},isMathJax:!1});i.CHTMLnode=o,this.idPostfix="-zoom",t.root.toCommonHTML(o),this.idPostfix="";var l=o.style,h=t.root.CHTML;h.t>h.h&&(l.marginTop=i.Em(h.t-h.h)),h.b>h.d&&(l.marginBottom=i.Em(h.b-h.d)),h.l<0&&(l.paddingLeft=i.Em(-h.l)),h.r>h.w&&(l.marginRight=i.Em(h.r-h.w)),l.position="absolute";var c=o.offsetWidth,u=o.offsetHeight,d=a.firstChild.offsetHeight,m=a.firstChild.offsetWidth;return o.style.position="",{Y:-n.getBBox(e).h,mW:m,mH:d,zW:c,zH:u}},Remove:function(t){var e=document.getElementById(t.inputID+"-Frame");e&&t.CHTML.display&&(e=e.parentNode),e&&e.parentNode.removeChild(e),delete 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t<65535?String.fromCharCode(t):(t-=65536,String.fromCharCode(55296+(t>>10))+String.fromCharCode(56320+(1023&t)))},getUnicode:function(t){var e=t.text.charCodeAt(t.i);return t.i++,e>=55296&&e<56319&&(e=(e-55296<<10)+(t.text.charCodeAt(t.i)-56320)+65536,t.i++),e},getCharList:function(t,e){var a,i,s=[],n=t.cache,r=e;if(n[e])return n[e];if(e>65535&&this.FONTDATA.RemapPlane1){var o=this.FONTDATA.RemapPlane1(e,t);e=o.n,t=o.variant}var h=this.FONTDATA.RANGES,c=this.FONTDATA.VARIANT;if(e>=h[0].low&&e<=h[h.length-1].high)for(a=0,i=h.length;a<i;a++)if("alpha"!==h[a].name||!t.noLowerCase){var u=t["offset"+h[a].offset];if(u&&e>=h[a].low&&e<=h[a].high){h[a].remap&&h[a].remap[e]?e=u+h[a].remap[e]:(e=e-h[a].low+u,h[a].add&&(e+=h[a].add)),t["variant"+h[a].offset]&&(t=c[t["variant"+h[a].offset]]);break}}if(t.remap&&t.remap[e]?(e=t.remap[e],t.remap.variant&&(t=c[t.remap.variant])):this.FONTDATA.REMAP[e]&&!t.noRemap&&(e=this.FONTDATA.REMAP[e]),l(e)&&(t=c[e[1]],e=e[0]),"string"==typeof e)for(var d={text:e,i:0,length:e.length};d.i<d.length;){e=this.getUnicode(d);var m=this.getCharList(t,e);m&&s.push.apply(s,m)}else t.cache[e]?s=t.cache[e]:t.cache[e]=s=[this.lookupChar(t,e)];return n[r]=s,s},lookupChar:function(t,e){for(var a=t;t;){for(var i=0,s=t.fonts.length;i<s;i++){var n=this.FONTDATA.FONTS[t.fonts[i]];"string"==typeof n&&this.loadFont(n);var r=n[e];if(r)return 5===r.length&&(r[5]={}),null==r.c&&(r[0]/=1e3,r[1]/=1e3,r[2]/=1e3,r[3]/=1e3,r[4]/=1e3,r.c=this.unicodeChar(e)),r[5].space?{type:"space",w:r[2],font:n}:{type:"char",font:n,n:e};n.Extra&&this.findBlock(n,e)}t=this.FONTDATA.VARIANT[t.chain]}return this.unknownChar(a,e)},findBlock:function(t,e){for(var a,i=t.Extra,s=t.file,n=0,r=i.length;n<r;n++)if("number"==typeof i[n]){if(e===i[n]){a=s;break}}else{if(e<i[n][0])return;if(e<=i[n][1]){a=s;break}}a&&(delete t.Extra,this.loadFont(s))},unknownChar:function(t,a){e.signal.Post(["CommonHTML Jax - unknown char",a,t]);var i="";t.bold&&(i+="B"),t.italic&&(i+="I");var s=this.FONTDATA.UNKNOWN[i||"R"];return s[a]||this.getUnknownChar(s,a),{type:"unknown",n:a,font:s}},getUnknownChar:function(t,e){var a=this.unicodeChar(e),i=this.getHDW(a,t.className);t[e]=[.8,.2,i.w,0,i.w,{a:Math.max(0,(i.h-i.d)/2),h:i.h,d:i.d}],t[e].c=a},styledText:function(t,a){e.signal.Post(["CommonHTML Jax - styled text",a,t]);var i=t.style,s="_"+(i["font-family"]||t.className||"");i["font-weight"]&&(s+="_"+i["font-weight"]),i["font-style"]&&(s+="_"+i["font-style"]),this.STYLEDTEXT||(this.STYLEDTEXT={}),this.STYLEDTEXT[s]||(this.STYLEDTEXT[s]={className:t.className||""});var n=this.STYLEDTEXT[s];if(!n["_"+a]){var r=this.getHDW(a,t.className||"",i);n["_"+a]=[.8,.2,r.w,0,r.w,{a:Math.max(0,(r.h-r.d)/2),h:r.h,d:r.d}],n["_"+a].c=a}return{type:"unknown",n:"_"+a,font:n,style:i,rscale:t.rscale}},getHDW:function(t,e,a){var s=i.addElement(i.CHTMLnode,"mjx-chartest",{className:e},[["mjx-char",{style:a},[t]]]),n=i.addElement(i.CHTMLnode,"mjx-chartest",{className:e},[["mjx-char",{style:a},[t,["mjx-box"]]]]);s.firstChild.style.fontSize=n.firstChild.style.fontSize="";var r=5*i.em,o=s.offsetHeight,l=n.offsetHeight,h=s.offsetWidth;if(i.CHTMLnode.removeChild(s),i.CHTMLnode.removeChild(n),0===l){r=5*i.defaultEm;var c=document.body.appendChild(document.createElement("div"));c.appendChild(s),c.appendChild(n),o=s.offsetHeight,l=n.offsetHeight,h=s.offsetWidth,document.body.removeChild(c)}var u=(l-1e3)/r;return{h:o/r-u,d:u,w:h/r}},addCharList:function(t,e,i){for(var s={text:"",className:null,a:0},n=0,r=e.length;n<r;n++){var o=e[n];this.charList[o.type]&&this.charList[o.type](o,t,i,s,r)}""!==s.text&&(t.childNodes.length?this.charList.flushText(t,s):(a.addText(t,s.text),t.className?t.className+=" "+s.className:t.className=s.className)),i.b=s.flushed?0:i.a},charList:{char:function(t,e,a,s,n){var 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t=i.addElement(t,"mjx-charbox",{className:e.className,style:a},[e.text]),e.a&&(t.style.paddingBottom=i.Em(e.a)),e.text="",e.className=null,e.a=0,e.flushed=!0,t}},handleText:function(t,e,a,n){0===t.childNodes.length&&(i.addElement(t,"mjx-char"),n=i.BBOX.empty(n)),"string"==typeof a&&(a=this.FONTDATA.VARIANT[a]),a||(a=this.FONTDATA.VARIANT[s.VARIANT.NORMAL]);var r={text:e,i:0,length:e.length},o=[];if(a.style&&r.length)o.push(this.styledText(a,e));else for(;r.i<r.length;){var l=this.getUnicode(r);o.push.apply(o,this.getCharList(a,l))}return o.length&&this.addCharList(t.firstChild,o,n),n.clean(),n.d<0&&(n.D=n.d,n.d=0),n.h-n.a&&(t.firstChild.style[n.h-n.a<0?"marginTop":"paddingTop"]=this.EmRounded(n.h-n.a)),n.d>-n.b&&(t.firstChild.style.paddingBottom=this.EmRounded(n.d+n.b)),n},createDelimiter:function(a,n,r,o,l){if(!n){var h=this.BBOX.zero();return h.w=h.r=this.TEX.nulldelimiterspace,i.addElement(a,"mjx-box",{style:{width:h.w}}),h}r instanceof Array||(r=[r,r]);var c=r[1];r=r[0];for(var 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x=m.h+m.d,T=x-.1,E=Math.min(Math.ceil((e-M)/(g*T)),this.maxStretchyParts);a.fullExtenders?e=E*g*T+M:T=(e-M)/(g*E),p=m.d+m.a-x/2,h.style.margin=h.style.padding="",h.style.lineHeight=i.Em(T),h.style.marginBottom=i.Em(p-.05/g),h.style.marginTop=i.Em(-p-.05/g);for(var C=h.textContent,v="\n"+C;--E>0;)C+=v;h.textContent=C,t.appendChild(h),a.mid&&(t.appendChild(l),t.appendChild(h.cloneNode(!0)))}else p=(e-M-.1)/g,r.style.marginBottom=i.Em(p+parseFloat(r.style.marginBottom||"0")),a.mid&&t.appendChild(l),o.style.marginTop=i.Em(p+parseFloat(o.style.marginTop||"0"));t.appendChild(o);var b=i.BBOX({w:Math.max(c.w,m.w,u.w,d.w),l:Math.min(c.l,m.l,u.l,d.l),r:Math.max(c.r,m.r,u.r,d.r),h:e-u.d,d:u.d,t:e-u.d,b:u.d});return b.offset=.5*b.w,s&&(b.scale=s.scale,b.rscale=s.rscale),b},extendDelimiterH:function(t,e,a,s,n){t=i.addElement(t,"mjx-delim-h");var r,o,l,h,c,u,d,m,p,f=i.Element("span"),g=1;u=this.createChar(f,a.left||a.rep,1,n),r=f.removeChild(f.firstChild),d=this.createChar(f,a.right||a.rep,1,n),o=f.removeChild(f.firstChild),p=this.createChar(f,a.rep,1,n),h=f.removeChild(f.firstChild),r.style.marginLeft=i.Em(-u.l),o.style.marginRight=i.Em(d.r-d.w),t.appendChild(r);var M=i.BBOX.zero();M.h=Math.max(u.h,d.h,p.h),M.d=Math.max(u.D||u.d,d.D||d.d,p.D||p.d);var x=u.r-u.l+(d.r-d.l)-.1;if(a.mid&&(m=this.createChar(f,a.mid,1,n),(l=f.removeChild(f.firstChild)).style.marginleft=i.Em(-m.l),l.style.marginRight=i.Em(m.r-m.w),x+=m.r-m.l+.1,g=2,m.h>M.h&&(M.h=m.h),m.d>M.d&&(M.d=m.d)),a.min&&e<x*a.min&&(e=x*a.min),M.w=M.r=e,e>x){var T=p.r-p.l,E=T-.1,C=Math.min(Math.ceil((e-x)/(g*E)),this.maxStretchyParts);a.fullExtenders?e=C*g*E+x:E=(e-x)/(g*C);var v=(T-E+.1/g)/2;h.style.marginLeft=i.Em(-p.l-v),h.style.marginRight=i.Em(p.r-p.w+v),h.style.letterSpacing=i.Em(-(p.w-E)),r.style.marginRight=i.Em(u.r-u.w),o.style.marginleft=i.Em(-d.l);for(var 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t)t.hasOwnProperty(e)&&(this[e]=t[e])},clean:function(){-1e6===this.h&&(this.h=0),-1e6===this.d&&(this.d=0),1e6===this.l&&(this.l=0),-1e6===this.r&&(this.r=0),-1e6===this.t&&(this.t=0),-1e6===this.b&&(this.b=0),this.D&&this.d>0&&delete this.D},rescale:function(t){this.w*=t,this.h*=t,this.d*=t,this.l*=t,this.r*=t,this.t*=t,this.b*=t,this.L&&(this.L*=t),this.R&&(this.R*=t),this.D&&(this.D*=t)},combine:function(t,e,a){t.X=e,t.Y=a,scale=t.rscale,e+scale*t.r>this.r&&(this.r=e+scale*t.r),e+scale*t.l<this.l&&(this.l=e+scale*t.l),e+scale*(t.w+(t.L||0)+(t.R||0))>this.w&&(this.w=e+scale*(t.w+(t.L||0)+(t.R||0))),a+scale*t.h>this.h&&(this.h=a+scale*t.h),t.D&&(null==this.D||scale*t.D-a>this.D)&&scale*t.D>this.d?this.D=scale*t.D-a:null==t.D&&this.D&&delete this.D,scale*t.d-a>this.d&&(this.d=scale*t.d-a),a+scale*t.t>this.t&&(this.t=a+scale*t.t),scale*t.b-a>this.b&&(this.b=scale*t.b-a)},append:function(t){scale=t.rscale;var e=this.w;e+scale*t.r>this.r&&(this.r=e+scale*t.r),e+scale*t.l<this.l&&(this.l=e+scale*t.l),this.w+=scale*(t.w+(t.L||0)+(t.R||0)),scale*t.h>this.h&&(this.h=scale*t.h),t.D&&(null==this.D||scale*t.D>this.D)&&scale*t.D>this.d?this.D=scale*t.D:null==t.D&&this.D&&delete this.D,scale*t.d>this.d&&(this.d=scale*t.d),scale*t.t>this.t&&(this.t=scale*t.t),scale*t.b>this.b&&(this.b=scale*t.b)},updateFrom:function(t){this.h=t.h,this.d=t.d,this.w=t.w,this.r=t.r,this.l=t.l,this.t=t.t,this.b=t.b,t.pwidth&&(this.pwidth=t.pwidth),t.D?this.D=t.D:delete this.D},adjust:function(t,e,a,s){this[e]+=i.length2em(t,1,this.scale),null==s?this[e]>this[a]&&(this[a]=this[e]):this[a]<s&&(this[a]=s)}},{zero:function(){return i.BBOX({h:0,d:0,w:0,l:0,r:0,t:0,b:0,scale:1,rscale:1})},empty:function(t){return t||(t=i.BBOX.zero()),t.h=t.d=t.r=t.t=t.b=-1e6,t.w=0,t.l=1e6,delete t.pwidth,t},styleAdjust:[["borderTopWidth","h","t"],["borderRightWidth","w","r"],["borderBottomWidth","d","b"],["borderLeftWidth","w","l",0],["paddingTop","h","t"],["paddingRight","w","r"],["paddingBottom","d","b"],["paddingLeft","w","l",0]]}),MathJax.Hub.Register.StartupHook("mml Jax Ready",function(){(s=MathJax.ElementJax.mml).mbase.Augment({toCommonHTML:function(t,e){return this.CHTMLdefaultNode(t,e)},CHTMLmultiline:function(){s.mbase.CHTMLautoloadFile("multiline")},CHTMLdefaultNode:function(t,e){e||(e={}),t=this.CHTMLcreateNode(t),this.CHTML=i.BBOX.empty(),this.CHTMLhandleStyle(t),this.isToken&&this.CHTMLgetVariant(),this.CHTMLhandleScale(t);for(var a=Math.max(e.minChildren||0,this.data.length),s=0;s<a;s++)this.CHTMLaddChild(t,s,e);return e.noBBox||this.CHTML.clean(),this.CHTMLhandleSpace(t),this.CHTMLhandleBBox(t),this.CHTMLhandleColor(t),t},CHTMLaddChild:function(t,e,a){var s,n=this.data[e],r=a.childNodes;if(r instanceof Array&&(r=r[e]||"span"),n){if(r&&(t=i.addElement(t,r)),s=n.toCommonHTML(t,a.childOptions),r&&1!==n.CHTML.rscale&&(t.style.fontSize=t.firstChild.style.fontSize,t.firstChild.style.fontSize=""),!a.noBBox){var o=this.CHTML,l=n.CHTML;o.append(l),l.ic?o.ic=l.ic:delete o.ic,l.skew&&(o.skew=l.skew),l.pwidth&&(o.pwidth=l.pwidth)}}else a.forceChild&&(s=i.addElement(t,r||"mjx-box"));return s},CHTMLchildNode:function(t,e){return"a"===(t=t.childNodes[e]).nodeName.toLowerCase()&&(t=t.firstChild),t},CHTMLcoreNode:function(t){return this.inferRow&&this.data[0]?this.data[0].CHTMLcoreNode(t.firstChild):this.CHTMLchildNode(t,this.CoreIndex())},CHTMLstretchChildV:function(t,e,a){var i=this.data[t];if(i){var s=this.CHTML,n=i.CHTML;if(n.stretch||null==n.stretch&&i.CHTMLcanStretch("Vertical",e,a)){var r=n.w;n=i.CHTMLstretchV(e,a),s.w+=n.w-r,s.w>s.r&&(s.r=s.w),n.h>s.h&&(s.h=n.h),n.d>s.d&&(s.d=n.d),n.t>s.t&&(s.t=n.t),n.b>s.b&&(s.b=n.b)}}},CHTMLstretchChildH:function(t,e,a){var i=this.data[t];if(i){var s=this.CHTML,n=i.CHTML;if(n.stretch||null==n.stretch&&i.CHTMLcanStretch("Horizontal",e)){var r=n.w;n=i.CHTMLstretchH(this.CHTMLchildNode(a,t),e),s.w+=n.w-r,s.w>s.r&&(s.r=s.w),n.h>s.h&&(s.h=n.h),n.d>s.d&&(s.d=n.d),n.t>s.t&&(s.t=n.t),n.b>s.b&&(s.b=n.b)}}},CHTMLcanStretch:function(t,e,a){var i=!1;if(this.isEmbellished()){var s=this.Core();s&&s!==this&&(i=s.CHTMLcanStretch(t,e,a))}return this.CHTML.stretch=i,i},CHTMLstretchV:function(t,e){return this.CHTML.updateFrom(this.Core().CHTMLstretchV(t,e)),this.CHTML},CHTMLstretchH:function(t,e){return this.CHTML.updateFrom(this.CHTMLstretchCoreH(t,e)),this.CHTML},CHTMLstretchCoreH:function(t,e){return this.Core().CHTMLstretchH(this.CHTMLcoreNode(t),e)},CHTMLcreateNode:function(t){this.CHTML||(this.CHTML={}),this.CHTML=i.BBOX.zero(),this.href&&(t=i.addElement(t,"a",{href:this.href,isMathJax:!0})),this.CHTMLnodeID||(this.CHTMLnodeID=i.GetID());var e=(this.id||"MJXc-Node-"+this.CHTMLnodeID)+i.idPostfix;return this.CHTMLhandleAttributes(i.addElement(t,"mjx-"+this.type,{id:e}))},CHTMLnodeElement:function(){return this.CHTMLnodeID?document.getElementById((this.id||"MJXc-Node-"+this.CHTMLnodeID)+i.idPostfix):null},CHTMLlength2em:function(t,e){return i.length2em(t,e,this.CHTML.scale)},CHTMLhandleAttributes:function(t){if(this.class&&(t.className?t.className+=" "+this.class:t.className=this.class),this.attrNames)for(var a=this.attrNames,i=s.nocopyAttributes,n=e.config.ignoreMMLattributes,r="mstyle"===this.type?s.math.prototype.defaults:this.defaults,o=0,l=a.length;o<l;o++){var h=a[o];0!=n[h]&&(i[h]||n[h]||null!=r[h]||void 0!==t[h])||t.setAttribute(h,this.attr[h])}return t},CHTMLhandleScale:function(t){var e=1,a=this.parent,s=a?a.CHTML.scale:1,n=this.getValues("scriptlevel","fontsize");n.mathsize=this.Get("mathsize",null,!this.isToken),0!==n.scriptlevel&&(n.scriptlevel>2&&(n.scriptlevel=2),e=Math.pow(this.Get("scriptsizemultiplier"),n.scriptlevel),n.scriptminsize=i.length2em(this.Get("scriptminsize"),.8,1),e<n.scriptminsize&&(e=n.scriptminsize)),this.removedStyles&&this.removedStyles.fontSize&&!n.fontsize&&(n.fontsize=this.removedStyles.fontSize),n.fontsize&&!this.mathsize&&(n.mathsize=n.fontsize),1!==n.mathsize&&(e*=i.length2em(n.mathsize,1,1));var r=this.CHTMLvariant;return r&&r.style&&r.style["font-family"]&&(e*=i.config.scale/100/i.scale),this.CHTML.scale=e,s=this.CHTML.rscale=e/s,Math.abs(s-1)<.001&&(s=1),t&&1!==s&&(t.style.fontSize=i.Percent(s)),e},CHTMLhandleStyle:function(t){if(this.style){var e=t.style;e.cssText=this.style,this.removedStyles={};for(var a=0,s=i.removeStyles.length;a<s;a++){var n=i.removeStyles[a];e[n]&&(this.removedStyles[n]=e[n],e[n]="")}}},CHTMLhandleBBox:function(t){var e=this.CHTML,a=t.style;if(1===this.data.length&&(this.data[0].CHTML||{}).pwidth?(e.pwidth=this.data[0].CHTML.pwidth,e.mwidth=this.data[0].CHTML.mwidth,a.width="100%"):e.pwidth?(e.mwidth=i.Em(e.w),a.width="100%"):e.w<0&&(a.width="0px",a.marginRight=i.Em(e.w)),this.style)for(var s=0,n=i.BBOX.styleAdjust.length;s<n;s++){var r=i.BBOX.styleAdjust[s];r&&a[r[0]]&&e.adjust(a[r[0]],r[1],r[2],r[3])}},CHTMLhandleColor:function(t){this.mathcolor?t.style.color=this.mathcolor:this.color&&(t.style.color=this.color),this.mathbackground?t.style.backgroundColor=this.mathbackground:this.background&&(t.style.backgroundColor=this.background)},CHTMLhandleSpace:function(t){if(!this.useMMLspacing){var e=this.texSpacing();""!==e&&(this.CHTML.L=this.CHTMLlength2em(e),t.className+=" 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a=e.mathvariant;if(this.variantForm&&(a="-TeX-variant"),e.family&&!e.hasVariant)return!e.weight&&e.mathvariant.match(/bold/)&&(e.weight="bold"),!e.style&&e.mathvariant.match(/italic/)&&(e.style="italic"),void(this.CHTMLvariant={fonts:[],noRemap:!0,cache:{},style:{"font-family":e.family,"font-weight":e.weight||"normal","font-style":e.style||"normal"}});"bold"===e.weight?a={normal:s.VARIANT.BOLD,italic:s.VARIANT.BOLDITALIC,fraktur:s.VARIANT.BOLDFRAKTUR,script:s.VARIANT.BOLDSCRIPT,"sans-serif":s.VARIANT.BOLDSANSSERIF,"sans-serif-italic":s.VARIANT.SANSSERIFBOLDITALIC}[a]||a:"normal"===e.weight&&(a={bold:s.VARIANT.normal,"bold-italic":s.VARIANT.ITALIC,"bold-fraktur":s.VARIANT.FRAKTUR,"bold-script":s.VARIANT.SCRIPT,"bold-sans-serif":s.VARIANT.SANSSERIF,"sans-serif-bold-italic":s.VARIANT.SANSSERIFITALIC}[a]||a),"italic"===e.style?a={normal:s.VARIANT.ITALIC,bold:s.VARIANT.BOLDITALIC,"sans-serif":s.VARIANT.SANSSERIFITALIC,"bold-sans-serif":s.VARIANT.SANSSERIFBOLDITALIC}[a]||a:"normal"===e.style&&(a={italic:s.VARIANT.NORMAL,"bold-italic":s.VARIANT.BOLD,"sans-serif-italic":s.VARIANT.SANSSERIF,"sans-serif-bold-italic":s.VARIANT.BOLDSANSSERIF}[a]||a),this.CHTMLvariant=i.FONTDATA.VARIANT[a]||i.FONTDATA.VARIANT[s.VARIANT.NORMAL]},CHTMLbboxFor:function(t){return this.data[t]&&this.data[t].CHTML?this.data[t].CHTML:i.BBOX.zero()},CHTMLdrawBBox:function(t,e){e||(e=this.CHTML);var a=i.Element("mjx-box",{style:{opacity:.25,"margin-left":i.Em(-(e.w+(e.R||0)))}},[["mjx-box",{style:{height:i.Em(e.h),width:i.Em(e.w),"background-color":"red"}}],["mjx-box",{style:{height:i.Em(e.d),width:i.Em(e.w),"margin-left":i.Em(-e.w),"vertical-align":i.Em(-e.d),"background-color":"green"}}]]);t.nextSibling?t.parentNode.insertBefore(a,t.nextSibling):t.parentNode.appendChild(a)},CHTMLnotEmpty:function(t){for(;t&&t.data.length<2&&("mrow"===t.type||"texatom"===t.type);)t=t.data[0];return!!t}},{CHTMLautoload:function(){var a=i.autoloadDir+"/"+this.type+".js";e.RestartAfter(t.Require(a))},CHTMLautoloadFile:function(a){var s=i.autoloadDir+"/"+a+".js";e.RestartAfter(t.Require(s))},CHTMLstretchV:function(t,e){return this.Core().CHTMLstretchV(t,e),this.toCommonHTML(this.CHTMLnodeElement(),{stretch:!0}),this.CHTML},CHTMLstretchH:function(t,e){return this.CHTMLstretchCoreH(t,e),this.toCommonHTML(t,{stretch:!0}),this.CHTML}}),s.chars.Augment({toCommonHTML:function(t,e){null==e&&(e={});var a=this.toString();e.remap&&(a=e.remap(a,e.remapchars)),this.CHTMLhandleText(t,a,e.variant||this.parent.CHTMLvariant)}}),s.entity.Augment({toCommonHTML:function(t,e){null==e&&(e={});var a=this.toString();e.remapchars&&(a=e.remap(a,e.remapchars)),this.CHTMLhandleText(t,a,e.variant||this.parent.CHTMLvariant)}}),s.math.Augment({toCommonHTML:function(t){t=this.CHTMLdefaultNode(t),this.CHTML.w<0&&(t.parentNode.style.width="0px",t.parentNode.style.marginRight=i.Em(this.CHTML.w));var a=this.Get("alttext");if(a&&!t.getAttribute("aria-label")&&t.setAttribute("aria-label",a),this.CHTML.pwidth)t.parentNode.style.minWidth=this.CHTML.mwidth||i.Em(this.CHTML.w),t.parentNode.className="mjx-full-width "+t.parentNode.className,t.style.width=this.CHTML.pwidth;else if(!this.isMultiline&&"block"===this.Get("display")){var n=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift");n.indentalignfirst!==s.INDENTALIGN.INDENTALIGN&&(n.indentalign=n.indentalignfirst),n.indentalign===s.INDENTALIGN.AUTO&&(n.indentalign=u.displayAlign),n.indentshiftfirst!==s.INDENTSHIFT.INDENTSHIFT&&(n.indentshift=n.indentshiftfirst),"auto"===n.indentshift&&(n.indentshift="0");var r=this.CHTMLlength2em(n.indentshift,i.cwidth);if("0"!==u.displayIndent){var o=this.CHTMLlength2em(u.displayIndent,i.cwidth);r+=n.indentalign===s.INDENTALIGN.RIGHT?-o:o}var l=t.parentNode.parentNode.style;t.parentNode.style.textAlign=l.textAlign=n.indentalign,r&&(r*=i.em/i.outerEm,e.Insert(l,{left:{marginLeft:i.Em(r)},right:{marginRight:i.Em(-r)},center:{marginLeft:i.Em(r),marginRight:i.Em(-r)}}[n.indentalign]))}return t}}),s.mi.Augment({toCommonHTML:function(t){t=this.CHTMLdefaultNode(t);var e=this.CHTML,a=this.data.join("");return null!=e.skew&&1!==a.length&&delete e.skew,e.r>e.w&&1===a.length&&!this.CHTMLvariant.noIC&&(e.ic=e.r-e.w,e.w=e.r,t.lastChild.style.paddingRight=i.Em(e.ic)),t}}),s.mn.Augment({CHTMLremapMinus:function(t){return t.replace(/^-/,"−")},toCommonHTML:function(t){t=this.CHTMLdefaultNode(t,{childOptions:{remap:this.CHTMLremapMinus}});var e=this.CHTML,a=this.data.join("");return null!=e.skew&&1!==a.length&&delete e.skew,e.r>e.w&&1===a.length&&!this.CHTMLvariant.noIC&&(e.ic=e.r-e.w,e.w=e.r,t.lastChild.style.paddingRight=i.Em(e.ic)),t}}),s.mo.Augment({toCommonHTML:function(t){t=this.CHTMLcreateNode(t),this.CHTMLhandleStyle(t),this.CHTMLgetVariant(),this.CHTMLhandleScale(t),i.BBOX.empty(this.CHTML);var e=this.getValues("displaystyle","largeop");if(e.variant=this.CHTMLvariant,e.text=this.data.join(""),""==e.text)this.fence&&(t.style.width=i.Em(i.TEX.nulldelimiterspace));else{this.CHTMLadjustAccent(e),this.CHTMLadjustVariant(e);for(var a=0,s=this.data.length;a<s;a++)this.CHTMLaddChild(t,a,{childOptions:{variant:e.mathvariant,remap:this.remap,remapchars:e.remapchars}});1!==e.text.length?delete this.CHTML.skew:0===this.CHTML.w&&this.CHTML.l<0&&this.CHTMLfixCombiningChar(t),e.largeop&&this.CHTMLcenterOp(t)}return this.CHTML.clean(),this.CHTMLhandleBBox(t),this.CHTMLhandleSpace(t),this.CHTMLhandleColor(t),t},CHTMLhandleSpace:function(t){if(this.useMMLspacing){var e=this.getValues("scriptlevel","lspace","rspace");e.lspace=Math.max(0,this.CHTMLlength2em(e.lspace)),e.rspace=Math.max(0,this.CHTMLlength2em(e.rspace)),e.scriptlevel>0&&(this.hasValue("lspace")||(e.lspace=.15),this.hasValue("rspace")||(e.rspace=.15));for(var a=this,s=this.Parent();s&&s.isEmbellished()&&s.Core()===a;)a=s,s=s.Parent(),t=a.CHTMLnodeElement();e.lspace&&(t.style.paddingLeft=i.Em(e.lspace)),e.rspace&&(t.style.paddingRight=i.Em(e.rspace)),this.CHTML.L=e.lspace,this.CHTML.R=e.rspace}else this.SUPER(arguments).CHTMLhandleSpace.apply(this,arguments)},CHTMLadjustAccent:function(t){var e=this.CoreParent();if(t.parent=e,1===t.text.length&&e&&e.isa(s.munderover)&&1===this.CoreText(e.data[e.base]).length){var a=e.data[e.over],n=e.data[e.under];a&&this===a.CoreMO()&&e.Get("accent")?t.remapchars=i.FONTDATA.REMAPACCENT:n&&this===n.CoreMO()&&e.Get("accentunder")&&(t.remapchars=i.FONTDATA.REMAPACCENTUNDER)}},CHTMLadjustVariant:function(t){var e=t.parent,a=e&&e.isa(s.msubsup)&&this!==e.data[e.base];t.largeop&&(t.mathvariant=t.displaystyle?"-largeOp":"-smallOp"),a&&(t.remapchars=this.remapChars,t.text.match(/['`"\u00B4\u2032-\u2037\u2057]/)&&(t.mathvariant="-TeX-variant"))},CHTMLfixCombiningChar:function(t){t=t.firstChild;var e=i.Element("mjx-box",{style:{width:".25em","margin-left":"-.25em"}});t.insertBefore(e,t.firstChild)},CHTMLcenterOp:function(t){var e=this.CHTML,a=(e.h-e.d)/2-i.TEX.axis_height;Math.abs(a)>.001&&(t.style.verticalAlign=i.Em(-a)),e.h-=a,e.d+=a,e.r>e.w&&(e.ic=e.r-e.w,e.w=e.r,t.style.paddingRight=i.Em(e.ic))},CHTMLcanStretch:function(t,e,a){if(!this.Get("stretchy"))return!1;var s=this.data.join("");if(1!==s.length)return!1;var n={text:s};this.CHTMLadjustAccent(n),n.remapchars&&(s=n.remapchars[s]||s);var r=(s=i.FONTDATA.DELIMITERS[s.charCodeAt(0)])&&s.dir===t.substr(0,1);return r&&(r=this.CHTML.h!==e||this.CHTML.d!==a||!!this.Get("minsize",!0)||!!this.Get("maxsize",!0))&&(this.CHTML.stretch=!0),r},CHTMLstretchV:function(t,e){var a,s=this.CHTMLnodeElement(),n=this.CHTML,r=this.getValues("symmetric","maxsize","minsize"),o=i.TEX.axis_height;if(a=r.symmetric?2*Math.max(t-o,e+o):t+e,r.maxsize=this.CHTMLlength2em(r.maxsize,n.h+n.d),r.minsize=this.CHTMLlength2em(r.minsize,n.h+n.d),(a=Math.max(r.minsize,Math.min(r.maxsize,a)))!==n.sH){for(a!=r.minsize&&(a=[Math.max(a*i.TEX.delimiterfactor/1e3,a-i.TEX.delimitershortfall),a]);s.firstChild;)s.removeChild(s.firstChild);this.CHTML=n=i.createDelimiter(s,this.data.join("").charCodeAt(0),a,n),n.sH=a instanceof Array?a[1]:a,a=r.symmetric?(n.h+n.d)/2+o:(n.h+n.d)*t/(t+e),a-=n.h,Math.abs(a)>.05&&(s.style.verticalAlign=i.Em(a),n.h+=a,n.d-=a,n.t+=a,n.b-=a)}return this.CHTML},CHTMLstretchH:function(t,e){var a=this.CHTML,n=this.getValues("maxsize","minsize","mathvariant","fontweight");if(("bold"===n.fontweight||"bold"===(this.removedStyles||{}).fontWeight||parseInt(n.fontweight)>=600)&&!this.Get("mathvariant",!0)&&(n.mathvariant=s.VARIANT.BOLD),n.maxsize=this.CHTMLlength2em(n.maxsize,a.w),n.minsize=this.CHTMLlength2em(n.minsize,a.w),(e=Math.max(n.minsize,Math.min(n.maxsize,e)))!==a.sW){for(;t.firstChild;)t.removeChild(t.firstChild);this.CHTML=a=i.createDelimiter(t,this.data.join("").charCodeAt(0),e,a,n.mathvariant),a.sW=e}return this.CHTML}}),s.mtext.Augment({CHTMLgetVariant:function(){if(i.config.mtextFontInherit||"merror"===this.Parent().type){var t=i.config.scale/100/i.scale,e={cache:{},fonts:[],className:"MJXc-font-inherit",rscale:t,style:{"font-size":i.Percent(t)}},a=this.Get("mathvariant");a.match(/bold/)&&(e.style["font-weight"]="bold"),a.match(/italic|-tex-mathit/)&&(e.style["font-style"]="italic"),"monospace"===a&&(e.className+=" MJXc-monospace-font"),"double-struck"===a&&(e.className+=" MJXc-double-struck-font"),a.match(/fraktur/)&&(e.className+=" MJXc-fraktur-font"),a.match(/sans-serif/)&&(e.className+=" MJXc-sans-serif-font"),a.match(/script/)&&(e.className+=" MJXc-script-font"),this.CHTMLvariant=e}else this.SUPER(arguments).CHTMLgetVariant.call(this)}}),s.merror.Augment({toCommonHTML:function(t){t=this.CHTMLdefaultNode(t);var e=this.CHTML;return e.rescale(.9),e.h+=3/i.em,e.h>e.t&&(e.t=e.h),e.d+=3/i.em,e.d>e.b&&(e.b=e.d),e.w+=8/i.em,e.r=e.w,e.l=0,t}}),s.mspace.Augment({toCommonHTML:function(t){t=this.CHTMLcreateNode(t),this.CHTMLhandleStyle(t),this.CHTMLhandleScale(t);var e=this.getValues("height","depth","width"),a=this.CHTMLlength2em(e.width),s=this.CHTMLlength2em(e.height),n=this.CHTMLlength2em(e.depth),r=this.CHTML;return r.w=r.r=a,r.h=r.t=s,r.d=r.b=n,r.l=0,a<0&&(t.style.marginRight=i.Em(a),a=0),t.style.width=i.Em(a),t.style.height=i.Em(Math.max(0,s+n)),n&&(t.style.verticalAlign=i.Em(-n)),this.CHTMLhandleBBox(t),this.CHTMLhandleColor(t),t}}),s.mpadded.Augment({toCommonHTML:function(t,e){var a;e&&e.stretch?a=(t=t.firstChild).firstChild:(a=(t=this.CHTMLdefaultNode(t,{childNodes:"mjx-box",forceChild:!0})).firstChild,(t=i.addElement(t,"mjx-block")).appendChild(a),i.addElement(t,"mjx-strut"));var s=this.CHTMLbboxFor(0),n=this.getValues("width","height","depth","lspace","voffset"),r=0,o=0,l=s.w,h=s.h,c=s.d;a.style.width=0,a.style.margin=i.Em(-h)+" 0 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a=this.getValues("displaystyle","accent","accentunder","align"),n=this.data[this.base];if(!a.displaystyle&&null!=n&&(n.movablelimits||n.CoreMO().Get("movablelimits")))return s.msubsup.prototype.toCommonHTML.call(this,t,h);var r,o,l=[],h=!1;if(e&&e.stretch)this.data[this.base]&&(n=i.getNode(t,"mjx-op")),this.data[this.under]&&(r=i.getNode(t,"mjx-under")),this.data[this.over]&&(o=i.getNode(t,"mjx-over")),l[0]=n,l[1]=r||o,l[2]=o,h=!0;else{var c=["mjx-op","mjx-under","mjx-over"];1===this.over&&(c[1]=c[2]),t=this.CHTMLdefaultNode(t,{childNodes:c,noBBox:!0,forceChild:!0,minChildren:2}),l[0]=n=t.removeChild(t.firstChild),l[1]=r=o=t.removeChild(t.firstChild),t.firstChild&&(l[2]=o=t.removeChild(t.firstChild))}var u=[],d=this.CHTMLgetBBoxes(u,l,a),m=u[this.base],p=this.CHTML;p.w=d,p.h=m.h,p.d=m.d;var f=n,g=0;return m.ic&&(g=1.3*m.ic+.05),this.data[this.over]&&(f=this.CHTMLaddOverscript(o,u,a,g,n,h)),this.data[this.under]?this.CHTMLaddUnderscript(r,u,a,g,t,f,h):h||t.appendChild(f),this.CHTMLplaceBoxes(n,r,o,a,u),t},CHTMLgetBBoxes:function(t,e,a){var s,n,r=this.data.length,o=-1e6,l=o;for(s=0;s<r;s++)t[s]=this.CHTMLbboxFor(s),t[s].x=t[s].y=0,this.data[s]&&(t[s].stretch=this.data[s].CHTMLcanStretch("Horizontal")),n=s===this.base?1:t[s].rscale,s!==this.base&&(delete t[s].L,delete t[s].R),l=Math.max(l,n*(t[s].w+(t[s].L||0)+(t[s].R||0))),!t[s].stretch&&l>o&&(o=l);for(-1e6===o&&(o=l),s=0;s<r;s++)t[s].stretch&&(n=s===this.base?1:t[s].rscale,t[s]=this.data[s].CHTMLstretchH(e[s].firstChild,o/n),t[s].x=t[s].y=0,l=Math.max(l,n*(t[s].w+(t[s].L||0)+(t[s].R||0))));return t[this.base]||(t[this.base]=i.BBOX.empty()),l},CHTMLaddOverscript:function(t,e,a,s,n,r){var o,l,h,c=this.CHTML,u=i.TEX.big_op_spacing5,d=e[this.over],m=e[this.base],p=d.rscale;if(!r){var f=i.Element("mjx-stack");f.appendChild(t),f.appendChild(n)}return d.D&&(d.d=d.D),d.d<0&&(t.firstChild.style.verticalAlign="top",t.style.height=i.Em(d.h+d.d)),d.x=0,a.accent?(d.w<.001&&(d.x+=(d.r-d.l)/2),h=i.TEX.rule_thickness,u=0,m.skew&&(d.x+=p*m.skew,c.skew=p*m.skew,d.x+p*d.w>c.w&&(c.skew+=(c.w-(d.x+p*d.w))/2))):(o=i.TEX.big_op_spacing1,l=i.TEX.big_op_spacing3,h=Math.max(o,l-Math.max(0,p*d.d))),d.x+=s/2,d.y=c.h+h+u+p*d.d,h&&(t.style.paddingBottom=i.Em(h/p)),u&&(t.style.paddingTop=i.Em(u/p)),f},CHTMLaddUnderscript:function(t,e,a,s,n,r,o){var l,h,c,u=this.CHTML,d=i.TEX.big_op_spacing5,m=e[this.under],p=m.rscale;o||(i.addElement(n,"mjx-itable",{},[["mjx-row",{},[["mjx-cell"]]],["mjx-row"]]),n.firstChild.firstChild.firstChild.appendChild(r),n.firstChild.lastChild.appendChild(t)),m.D&&(m.d=m.D),m.d<0&&(t.firstChild.style.verticalAlign="top",n.firstChild.style.marginBottom=i.Em(m.d)),a.accentunder?(c=2*i.TEX.rule_thickness,d=0):(l=i.TEX.big_op_spacing2,h=i.TEX.big_op_spacing4,c=Math.max(l,h-p*m.h)),m.x=-s/2,m.y=-(u.d+c+d+p*m.h),c&&(t.style.paddingTop=i.Em(c/p)),d&&(t.style.paddingBottom=i.Em(d/p))},CHTMLplaceBoxes:function(t,e,a,s,n){var r,o,l=this.CHTML.w,h=n.length,c=i.BBOX.zero();c.scale=this.CHTML.scale,c.rscale=this.CHTML.rscale,n[this.base].x=n[this.base].y=0;var u=1e6;for(r=0;r<h;r++){var d=(o=r===this.base?1:n[r].rscale)*(n[r].w+(n[r].L||0)+(n[r].R||0));n[r].x+={left:0,center:(l-d)/2,right:l-d}[s.align],n[r].x<u&&(u=n[r].x)}for(r=0;r<h;r++)this.data[r]&&(o=r===this.base?1:n[r].rscale,n[r].x-u&&((r===this.base?t:r===this.over?a:e).style.paddingLeft=i.Em((n[r].x-u)/o)),c.combine(n[r],n[r].x-u,n[r].y));this.CHTML=c},CHTMLstretchV:s.mbase.CHTMLstretchV,CHTMLstretchH:s.mbase.CHTMLstretchH,CHTMLchildNode:function(t,e){var a=["mjx-op","mjx-under","mjx-over"];return 1===this.over&&(a[1]=a[2]),i.getNode(t,a[e])}}),s.msubsup.Augment({toCommonHTML:function(t,e){var a,s,n,r=this.getValues("displaystyle","subscriptshift","superscriptshift","texprimestyle");if(e&&e.stretch)this.data[this.base]&&(a=i.getNode(t,"mjx-base")),this.data[this.sub]&&(s=i.getNode(t,"mjx-sub")),this.data[this.sup]&&(n=i.getNode(t,"mjx-sup")),l=i.getNode(t,"mjx-stack");else{var o=["mjx-base","mjx-sub","mjx-sup"];if(1===this.sup&&(o[1]=o[2]),t=this.CHTMLdefaultNode(t,{childNodes:o,noBBox:!0,forceChild:!0,minChildren:3}),a=t.childNodes[this.base],s=t.childNodes[this.sub],n=t.childNodes[this.sup],this.CHTMLnotEmpty(this.data[this.sub])||(t.removeChild(s),s=null),this.CHTMLnotEmpty(this.data[this.sup])||(t.removeChild(n),n=null),3===t.childNodes.length){var l=i.addElement(t,"mjx-stack");l.appendChild(n),l.appendChild(s)}}for(var h=[],c=i.BBOX.empty(this.CHTML),u=0,d=this.data.length;u<d;u++)h[u]=this.CHTMLbboxFor(u);var m=h[this.base]||i.BBOX.empty(),p=h[this.sub],f=h[this.sup],g=s?p.rscale:1,M=n?f.rscale:1;c.combine(m,0,0);var x,T=i.TEX.x_height,E=i.TEX.scriptspace,C=i.TEX.sup_drop*M,v=i.TEX.sub_drop*g,b=m.h-C,L=m.d+v,A=0;m.ic&&(c.w-=m.ic,a.style.marginRight=i.Em(-m.ic),A=1.3*m.ic+.05);var y=this.data[this.base];y&&("mrow"!==y.type&&"mstyle"!==y.type||1!==y.data.length||(y=y.data[0]),"mi"!==y.type&&"mo"!==y.type||1!==y.data.join("").length||1!==m.rscale||m.sH||y.Get("largeop")||(b=L=0)),r.subscriptshift=""===r.subscriptshift?0:this.CHTMLlength2em(r.subscriptshift),r.superscriptshift=""===r.superscriptshift?0:this.CHTMLlength2em(r.superscriptshift);var R=c.w;if(s&&(p.w+=E),n&&(f.w+=E),n)if(s){L=Math.max(L,i.TEX.sub2);var S=i.TEX.rule_thickness;b-M*f.d-(g*p.h-L)<3*S&&(L=3*S-b+M*f.d+g*p.h,(C=.8*T-(b-M*f.d))>0&&(b+=C,L-=C)),b=Math.max(b,r.superscriptshift),L=Math.max(L,r.subscriptshift),s.style.paddingRight=i.Em(E/g),n.style.paddingBottom=i.Em(b/M+L/g-f.d-p.h/g*M),n.style.paddingLeft=i.Em(A/M),n.style.paddingRight=i.Em(E/M),l.style.verticalAlign=i.Em(-L),c.combine(f,R+A,b),c.combine(p,R,-L)}else x=i.TEX[r.displaystyle?"sup1":r.texprimestyle?"sup3":"sup2"],b=Math.max(b,x,M*f.d+.25*T,r.superscriptshift),n.style.verticalAlign=i.Em(b/M),n.style.paddingLeft=i.Em(A/M),n.style.paddingRight=i.Em(E/M),c.combine(f,R+A,b);else s&&(L=Math.max(L,i.TEX.sub1,g*p.h-.8*T,r.subscriptshift),s.style.verticalAlign=i.Em(-L/g),s.style.paddingRight=i.Em(E/g),c.combine(p,R,-L));return c.clean(),t},CHTMLstretchV:s.mbase.CHTMLstretchV,CHTMLstretchH:s.mbase.CHTMLstretchH,CHTMLchildNode:function(t,e){var a=["mjx-base","mjx-sub","mjx-sup"];return 1===this.over&&(a[1]=a[2]),i.getNode(t,a[e])}}),s.mfrac.Augment({toCommonHTML:function(t){t=this.CHTMLdefaultNode(t,{childNodes:["mjx-numerator","mjx-denominator"],childOptions:{autowidth:!0},forceChild:!0,noBBox:!0,minChildren:2});var e=this.getValues("linethickness","displaystyle","numalign","denomalign","bevelled"),a=e.displaystyle,s=t.firstChild,n=t.lastChild,r=i.addElement(t,"mjx-box");r.appendChild(s),r.appendChild(n),t.appendChild(r),"center"!==e.numalign&&(s.style.textAlign=e.numalign),"center"!==e.denomalign&&(n.style.textAlign=e.denomalign);var o=this.CHTMLbboxFor(0),l=this.CHTMLbboxFor(1),h=i.BBOX.empty(this.CHTML),c=o.rscale,u=l.rscale;e.linethickness=Math.max(0,i.thickness2em(e.linethickness||"0",h.scale));var d,m,p,f,g=i.TEX.min_rule_thickness/i.em,M=i.TEX.axis_height,x=e.linethickness;if(e.bevelled){r.className+=" MJXc-bevelled";var T=a?.4:.15,E=Math.max(c*(o.h+o.d),u*(l.h+l.d))+2*T,C=i.Element("mjx-bevel");r.insertBefore(C,n);var v=i.createDelimiter(C,47,E);p=c*(o.d-o.h)/2+M+T,f=u*(l.d-l.h)/2+M-T,p&&(s.style.verticalAlign=i.Em(p/c)),f&&(n.style.verticalAlign=i.Em(f/u)),C.style.marginLeft=C.style.marginRight=i.Em(-T/2),h.combine(o,0,p),h.combine(v,c*o.w-T/2,0),h.combine(l,c*o.w+v.w-T,f),h.clean()}else{if(r.className+=" MJXc-stacked",a?(p=i.TEX.num1,f=i.TEX.denom1):(p=0===x?i.TEX.num3:i.TEX.num2,f=i.TEX.denom2),0===x)d=Math.max((a?7:3)*i.TEX.rule_thickness,2*g),(m=p-o.d*c-(l.h*u-f))<d&&(p+=(d-m)/2,f+=(d-m)/2);else{d=Math.max((a?2:0)*g+x,x/2+1.5*g),x=Math.max(x,g),(m=p-o.d*c-(M+x/2))<d&&(p+=d-m),(m=M-x/2-(l.h*u-f))<d&&(f+=d-m),o.L=o.R=l.L=l.R=.1;var b=i.addElement(r,"mjx-line",{style:{"border-bottom":i.Px(x*h.scale,1)+" 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d=i.createDelimiter(u,8730,[n-.04,n]);d.h+d.d>n&&(s=(d.h+d.d-(n-l))/2),n=r.h+s+l;var m=this.CHTMLaddRoot(t,d,d.h+d.d-n);return e.style.paddingTop=i.Em(s),e.style.borderTop=i.Px(h*r.scale,1)+" solid",a.style.paddingTop=i.Em(2*l-h),r.h+=s+2*l,o.combine(d,m,n-d.h),o.combine(r,m+d.w,0),o.clean(),t},CHTMLaddRoot:function(){return 0}}),s.mroot.Augment({toCommonHTML:s.msqrt.prototype.toCommonHTML,CHTMLaddRoot:function(t,e,a){if(this.data[1]){var s=this.CHTML,n=this.data[1].CHTML,r=t.firstChild,o=n.rscale,l=this.CHTMLrootHeight(n,e,o)-a,h=Math.min(n.w,n.r),c=Math.max(h,e.offset/o);return l&&(r.style.verticalAlign=i.Em(l/o)),c>h&&(r.firstChild.style.paddingLeft=i.Em(c-h)),c-=e.offset/o,r.style.width=i.Em(c),s.combine(n,0,l),c*o}},CHTMLrootHeight:function(t,e,a){return.45*(e.h+e.d-.9)+e.offset+Math.max(0,t.d-.075)}}),s.mfenced.Augment({toCommonHTML:function(t){t=this.CHTMLcreateNode(t),this.CHTMLhandleStyle(t),this.CHTMLhandleScale(t),this.CHTMLaddChild(t,"open",{});for(var e=0,a=this.data.length;e<a;e++)this.CHTMLaddChild(t,"sep"+e,{}),this.CHTMLaddChild(t,e,{});this.CHTMLaddChild(t,"close",{});var i=this.CHTML.h,s=this.CHTML.d;for(this.CHTMLstretchChildV("open",i,s),e=0,a=this.data.length;e<a;e++)this.CHTMLstretchChildV("sep"+e,i,s),this.CHTMLstretchChildV(e,i,s);return this.CHTMLstretchChildV("close",i,s),this.CHTMLhandleSpace(t),this.CHTMLhandleBBox(t),this.CHTMLhandleColor(t),t}}),s.mrow.Augment({toCommonHTML:function(t,e){e=e||{},t=this.CHTMLdefaultNode(t);for(var a,s=this.CHTML,n=s.h,r=s.d,o=0,l=this.data.length;o<l;o++)this.CHTMLstretchChildV(o,n,r),this.data[o]&&this.data[o].CHTML&&this.data[o].CHTML.w<0&&(a=!0);return this.CHTMLlineBreaks()?(this.CHTMLmultiline(t),e.autowidth&&(t.style.width="")):(a&&s.w&&(t.style.width=i.Em(Math.max(0,s.w))),s.w<0&&(t.style.marginRight=i.Em(s.w))),t},CHTMLlineBreaks:function(){return!!this.parent.linebreakContainer&&(c.automatic&&this.CHTML.w>i.linebreakWidth||this.hasNewline())},CHTMLstretchV:function(t,e){return this.CHTMLstretchChildV(this.CoreIndex(),t,e),this.CHTML},CHTMLstretchH:function(t,e){return this.CHTMLstretchChildH(this.CoreIndex(),e,t),this.CHTML}}),s.mstyle.Augment({toCommonHTML:function(t){return t=this.CHTMLdefaultNode(t),this.scriptlevel&&this.data[0]&&this.CHTML.rescale(this.data[0].CHTML.rscale),t}}),s.TeXAtom.Augment({toCommonHTML:function(t,e){if(e&&e.stretch||(t=this.CHTMLdefaultNode(t)),this.texClass===s.TEXCLASS.VCENTER){var a=i.TEX.axis_height,n=this.CHTML,r=a-(n.h+n.d)/2+n.d;Math.abs(r)>.001&&(t.style.verticalAlign=i.Em(r),n.h+=r,n.t+=r,n.d-=r,n.b-=r)}return t},CHTMLstretchV:function(t,e){return this.CHTML.updateFrom(this.Core().CHTMLstretchV(t,e)),this.toCommonHTML(this.CHTMLnodeElement(),{stretch:!0}),this.CHTML},CHTMLstretchH:function(t,e){return this.CHTML.updateFrom(this.CHTMLstretchCoreH(t,e)),this.toCommonHTML(t,{stretch:!0}),this.CHTML}}),s.semantics.Augment({toCommonHTML:function(t){return t=this.CHTMLcreateNode(t),this.data[0]&&(this.data[0].toCommonHTML(t),this.CHTML.updateFrom(this.data[0].CHTML),this.CHTMLhandleBBox(t)),t}}),s.annotation.Augment({toCommonHTML:function(t){return this.CHTMLcreateNode(t)}}),s["annotation-xml"].Augment({toCommonHTML:s.mbase.CHTMLautoload}),s.ms.Augment({toCommonHTML:s.mbase.CHTMLautoload}),s.mglyph.Augment({toCommonHTML:s.mbase.CHTMLautoload}),s.menclose.Augment({toCommonHTML:s.mbase.CHTMLautoload}),s.maction.Augment({toCommonHTML:s.mbase.CHTMLautoload}),s.mmultiscripts.Augment({toCommonHTML:s.mbase.CHTMLautoload}),s.mtable.Augment({toCommonHTML:s.mbase.CHTMLautoload}),MathJax.Hub.Register.StartupHook("onLoad",function(){setTimeout(MathJax.Callback(["loadComplete",i,"jax.js"]),0)})}),MathJax.Hub.Register.StartupHook("End Cookie",function(){"None"!==e.config.menuSettings.zoom&&t.Require("[MathJax]/extensions/MathZoom.js")})}(MathJax.Ajax,MathJax.Hub,MathJax.HTML,MathJax.OutputJax.CommonHTML),MathJax.Hub.Register.StartupHook("CommonHTML Jax Ready",function(){var t=MathJax.ElementJax.mml,e=MathJax.OutputJax.CommonHTML;t["annotation-xml"].Augment({toCommonHTML:function(t){var e=this.Get("encoding");return t=this.CHTMLdefaultNode(t,{childOptions:{encoding:e}}),1!==this.CHTML.rscale&&this.CHTML.rescale(1/this.CHTML.rscale),t}}),t.xml.Augment({toCommonHTML:function(t,a){for(var i=this.CHTML=e.BBOX.zero(),s=0,n=this.data.length;s<n;s++)t.appendChild(this.data[s].cloneNode(!0));var r=t.offsetWidth,o=t.offsetHeight,l=e.addElement(t,"mjx-hd-test",{style:{height:o+"px"}});i.d=i.b=(t.offsetHeight-o)/e.em,i.w=i.r=r/e.em,i.h=i.t=o/e.em-i.d,t.removeChild(l)}}),MathJax.Hub.Startup.signal.Post("CommonHTML annotation-xml Ready"),MathJax.Ajax.loadComplete(e.autoloadDir+"/annotation-xml.js")}),MathJax.Hub.Register.StartupHook("CommonHTML Jax Ready",function(){var t,e,a,i=MathJax.ElementJax.mml,s=MathJax.OutputJax.CommonHTML,n=s.config.tooltip=MathJax.Hub.Insert({delayPost:600,delayClear:600,offsetX:10,offsetY:5},s.config.tooltip||{});i.maction.Augment({CHTMLtooltip:s.addElement(document.body,"div",{id:"MathJax_CHTML_Tooltip"}),toCommonHTML:function(t){var e=this.Get("selection");t=this.CHTMLcreateNode(t),this.CHTML=s.BBOX.empty(),this.CHTMLhandleStyle(t),this.CHTMLhandleScale(t),this.CHTMLaddChild(t,e-1,{}),this.CHTML.clean(),this.CHTMLhandleSpace(t),this.CHTMLhandleBBox(t),this.CHTMLhandleColor(t);var a=this.Get("actiontype");return this.CHTMLaction[a]&&this.CHTMLaction.hasOwnProperty(a)&&this.CHTMLaction[a].call(this,t,e),t},CHTMLcoreNode:function(t){return this.CHTMLchildNode(t,0)},CHTMLaction:{toggle:function(t,e){this.selection=e,t.onclick=MathJax.Callback(["CHTMLclick",this,s.jax]),t.style.cursor="pointer"},statusline:function(t,e){t.onmouseover=MathJax.Callback(["CHTMLsetStatus",this]),t.onmouseout=MathJax.Callback(["CHTMLclearStatus",this]),t.onmouseover.autoReset=t.onmouseout.autoReset=!0},tooltip:function(t,e){this.data[1]&&this.data[1].isToken?t.title=t.alt=this.data[1].data.join(""):(t.onmouseover=MathJax.Callback(["CHTMLtooltipOver",this,s.jax]),t.onmouseout=MathJax.Callback(["CHTMLtooltipOut",this,s.jax]),t.onmouseover.autoReset=t.onmouseout.autoReset=!0)}},CHTMLclick:function(t,e){++this.selection>this.data.length&&(this.selection=1);var a=!!t.hover;if(t.Update(),a){var i=document.getElementById(t.inputID+"-Span");MathJax.Extension.MathEvents.Hover.Hover(t,i)}return MathJax.Extension.MathEvents.Event.False(e)},CHTMLsetStatus:function(t){this.messageID=MathJax.Message.Set(this.data[1]&&this.data[1].isToken?this.data[1].data.join(""):this.data[1].toString())},CHTMLclearStatus:function(t){this.messageID&&MathJax.Message.Clear(this.messageID,0),delete this.messageID},CHTMLtooltipOver:function(t,i){i||(i=window.event),a&&(clearTimeout(a),a=null),e&&clearTimeout(e);var s=i.pageX,r=i.pageY;null==s&&(s=i.clientX+document.body.scrollLeft+document.documentElement.scrollLeft,r=i.clientY+document.body.scrollTop+document.documentElement.scrollTop);var o=MathJax.Callback(["CHTMLtooltipPost",this,t,s+n.offsetX,r+n.offsetY]);e=setTimeout(o,n.delayPost)},CHTMLtooltipOut:function(t,i){e&&(clearTimeout(e),e=null),a&&clearTimeout(a);var s=MathJax.Callback(["CHTMLtooltipClear",this,80]);a=setTimeout(s,n.delayClear)},CHTMLtooltipPost:function(i,n,r){e=null,a&&(clearTimeout(a),a=null);var o=this.CHTMLtooltip;if(o.style.display="block",o.style.opacity="",this!==t){o.style.left=n+"px",o.style.top=r+"px",o.innerHTML='<span class="mjx-chtml"><span class="mjx-math"></span></span>',s.getMetrics(i);try{this.data[1].toCommonHTML(o.firstChild.firstChild)}catch(t){if(!t.restart)throw t;return o.style.display="none",void MathJax.Callback.After(["CHTMLtooltipPost",this,i,n,r],t.restart)}t=this}},CHTMLtooltipClear:function(t){var e=this.CHTMLtooltip;t<=0?(e.style.display="none",e.style.opacity=e.style.filter="",a=null):(e.style.opacity=t/100,e.style.filter="alpha(opacity="+t+")",a=setTimeout(MathJax.Callback(["CHTMLtooltipClear",this,t-20]),50))}}),MathJax.Hub.Startup.signal.Post("CommonHTML maction Ready"),MathJax.Ajax.loadComplete(s.autoloadDir+"/maction.js")}),MathJax.Hub.Register.StartupHook("CommonHTML Jax Ready",function(){var t=MathJax.ElementJax.mml,e=MathJax.OutputJax.CommonHTML,a="https://www.w3.org/2000/svg";t.menclose.Augment({toCommonHTML:function(a){var i=this.getValues("notation","thickness","padding");null==i.thickness&&(i.thickness=".075em"),null==i.padding&&(i.padding=".2em");var s=(a=this.CHTMLdefaultNode(a,{childNodes:"mjx-box",forceChild:!0})).firstChild,n=this.CHTMLbboxFor(0),r=this.CHTMLlength2em(i.padding,1/e.em),o=this.CHTMLlength2em(i.thickness,1/e.em);o=Math.max(1,Math.round(o*e.em))/e.em;var l=e.Px(o)+" solid",h={L:r,R:r,T:r,B:r,H:n.h+r,D:n.d+r,W:n.w+2*r};s.style.padding=e.Em(r);for(var c=MathJax.Hub.SplitList(i.notation),u={},d=0,m=c.length;d<m;d++)u[c[d]]=!0;u[t.NOTATION.UPDIAGONALARROW]&&delete u[t.NOTATION.UPDIAGONALSTRIKE];for(var p in u)u.hasOwnProperty(p)&&this.CHTMLnotation[p]&&this.CHTMLnotation.hasOwnProperty(p)&&this.CHTMLnotation[p].call(this,s,n,h,r,o,l);var f=this.CHTML;return f.w+=h.L+h.R,f.r+=f.L,f.w>f.r&&(f.r=f.w),f.h+=h.T,f.h>f.t&&(f.t=f.h),f.d+=h.B,f.d>f.b&&(f.b=f.d),a},CHTMLnotation:{box:function(t,a,i,s,n,r){s-=n,t.style.padding=e.Em(s),t.style.border=r},roundedbox:function(t,a,i,s,n,r){var o=Math.min(a.w,a.h+a.d+2*s)/4;e.addElement(t.parentNode,"mjx-box",{style:{padding:e.Em(s-n),border:r,"border-radius":e.Em(o),height:e.Em(a.h+a.d),"vertical-align":e.Em(-i.D),width:e.Em(a.w),"margin-left":e.Em(-i.W)}})},circle:function(t,a,i,s,n,r){var o=i.H,l=i.D,h=i.W,c=this.CHTMLsvg(t,i,n);this.CHTMLsvgElement(c.firstChild,"ellipse",{rx:e.Px(h/2-n/2),ry:e.Px((o+l)/2-n/2),cx:e.Px(h/2),cy:e.Px((o+l)/2)})},left:function(t,a,i,s,n,r){t.style.borderLeft=r,t.style.paddingLeft=e.Em(s-n)},right:function(t,a,i,s,n,r){t.style.borderRight=r,t.style.paddingRight=e.Em(s-n)},top:function(t,a,i,s,n,r){t.style.borderTop=r,t.style.paddingTop=e.Em(s-n)},bottom:function(t,a,i,s,n,r){t.style.borderBottom=r,t.style.paddingBottom=e.Em(s-n)},actuarial:function(t,a,i,s,n,r){t.style.borderTop=t.style.borderRight=r,t.style.paddingTop=t.style.paddingRight=e.Em(s-n)},madruwb:function(t,a,i,s,n,r){t.style.borderBottom=t.style.borderRight=r,t.style.paddingBottom=t.style.paddingRight=e.Em(s-n)},verticalstrike:function(t,a,i,s,n,r){e.addElement(t.parentNode,"mjx-box",{style:{"border-left":r,height:e.Em(i.H+i.D),"vertical-align":e.Em(-i.D),width:e.Em(a.w/2+s-n/2),"margin-left":e.Em(-a.w/2-s-n/2)}})},horizontalstrike:function(t,a,i,s,n,r){e.addElement(t.parentNode,"mjx-box",{style:{"border-top":r,height:e.Em((i.H+i.D)/2-n/2),"vertical-align":e.Em(-i.D),width:e.Em(i.W),"margin-left":e.Em(-i.W)}})},updiagonalstrike:function(t,a,i,s,n,r){var o=i.H,l=i.D,h=i.W,c=this.CHTMLsvg(t,i,n);this.CHTMLsvgElement(c.firstChild,"line",{x1:e.Px(n/2),y1:e.Px(o+l-n),x2:e.Px(h-n),y2:e.Px(n/2)})},downdiagonalstrike:function(t,a,i,s,n,r){var o=i.H,l=i.D,h=i.W,c=this.CHTMLsvg(t,i,n);this.CHTMLsvgElement(c.firstChild,"line",{x1:e.Px(n/2),y1:e.Px(n/2),x2:e.Px(h-n),y2:e.Px(o+l-n)})},updiagonalarrow:function(t,a,i,s,n,r){var o=i.H+i.D-n,l=i.W-n/2,h=Math.atan2(o,l)*(-180/Math.PI).toFixed(3),c=Math.sqrt(o*o+l*l),u=this.CHTMLsvg(t,i,n),d=this.CHTMLsvgElement(u.firstChild,"g",{fill:"currentColor",transform:"translate("+this.CHTMLpx(n/2)+" "+this.CHTMLpx(o+n/2)+") rotate("+h+")"}),m=4*n,p=1*n,f=2*n;this.CHTMLsvgElement(d,"line",{x1:e.Px(n/2),y1:0,x2:e.Px(c-m),y2:0}),this.CHTMLsvgElement(d,"path",{d:"M "+this.CHTMLpx(c-m)+",0 L "+this.CHTMLpx(c-m-p)+","+this.CHTMLpx(f)+"L "+this.CHTMLpx(c)+",0 L "+this.CHTMLpx(c-m-p)+","+this.CHTMLpx(-f),stroke:"none"})},phasorangle:function(t,a,i,s,n,r){var o=s,l=i.H,h=i.D;s=(l+h)/2;var c=i.W+s-o;i.W=c,i.L=s,t.style.margin="0 0 0 "+e.Em(s-o);var u=this.CHTMLsvg(t,i,n);this.CHTMLsvgElement(u.firstChild,"path",{d:"M "+this.CHTMLpx(s)+",1 L 1,"+this.CHTMLpx(l+h-n)+" L "+this.CHTMLpx(c)+","+this.CHTMLpx(l+h-n)})},longdiv:function(t,a,i,s,n,r){i.W+=1.5*s,i.L+=1.5*s;var o=i.H,l=i.D,h=i.W;t.style.margin="0 0 0 "+e.Em(1.5*s);var c=this.CHTMLsvg(t,i,n);this.CHTMLsvgElement(c.firstChild,"path",{d:"M "+this.CHTMLpx(h)+",1 L 1,1 a"+this.CHTMLpx(s)+","+this.CHTMLpx((o+l)/2-n/2)+" 0 0,1 1,"+this.CHTMLpx(o+l-1.5*n)})},radical:function(t,a,i,s,n,r){i.W+=1.5*s,i.L+=1.5*s;var o=i.H,l=i.D,h=i.W;t.style.margin="0 0 0 "+e.Em(1.5*s);var c=this.CHTMLsvg(t,i,n);this.CHTMLsvgElement(c.firstChild,"path",{d:"M 1,"+this.CHTMLpx(.6*(o+l))+" L "+this.CHTMLpx(s)+","+this.CHTMLpx(o+l)+" L "+this.CHTMLpx(2*s)+",1 L "+this.CHTMLpx(h)+",1"})}},CHTMLpx:function(t){return t*=e.em,Math.abs(t)<.1?"0":t.toFixed(1).replace(/\.0$/,"")},CHTMLsvg:function(t,i,s){if(!n){var n=document.createElementNS(a,"svg");n.style&&(n.style.width=e.Em(i.W),n.style.height=e.Em(i.H+i.D),n.style.verticalAlign=e.Em(-i.D),n.style.marginLeft=e.Em(-i.W)),this.CHTMLsvgElement(n,"g",{"stroke-width":e.Px(s)}),t.parentNode.appendChild(n)}return n},CHTMLsvgElement:function(t,e,i){var s=document.createElementNS(a,e);if(s.isMathJax=!0,i)for(var n in i)i.hasOwnProperty(n)&&s.setAttributeNS(null,n,i[n].toString());return t.appendChild(s),s}}),document.createElementNS||delete t.menclose.prototype.toCommonHTML,MathJax.Hub.Startup.signal.Post("CommonHTML menclose Ready"),MathJax.Ajax.loadComplete(e.autoloadDir+"/menclose.js")}),MathJax.Hub.Register.StartupHook("CommonHTML Jax Ready",function(){var t=MathJax.ElementJax.mml,e=MathJax.OutputJax.CommonHTML,a=MathJax.Localization;t.mglyph.Augment({toCommonHTML:function(i,s){var n=this.getValues("src","width","height","valign","alt");if(i=this.CHTMLcreateNode(i),this.CHTMLhandleStyle(i),this.CHTMLhandleScale(i),""===n.src){var r=this.Get("index");this.CHTMLgetVariant(),r&&this.CHTMLvariant.style&&this.CHTMLhandleText(i,String.fromCharCode(r),this.CHTMLvariant)}else{var o=this.CHTML;if(o.img||(o.img=t.mglyph.GLYPH[n.src]),o.img||(o.img=t.mglyph.GLYPH[n.src]={img:new Image,status:"pending"},o.img.img.onload=MathJax.Callback(["CHTMLimgLoaded",this]),o.img.img.onerror=MathJax.Callback(["CHTMLimgError",this]),o.img.img.src=n.src,MathJax.Hub.RestartAfter(o.img.img.onload)),"OK"!==o.img.status){var l=t.Error(a._(["MathML","BadMglyph"],"Bad mglyph: %1",n.src));l.data[0].data[0].mathsize="75%",this.Append(l),l.toCommonHTML(i),this.data.pop(),o.combine(l.CHTML,0,0,1)}else{var h=e.addElement(i,"img",{isMathJax:!0,src:n.src,alt:n.alt,title:n.alt}),c=n.width,u=n.height,d=o.img.img.width/e.em,m=o.img.img.height/e.em,p=d,f=m;""!==c&&(d=this.CHTMLlength2em(c,p),m=p?d/p*f:0),""!==u&&(m=this.CHTMLlength2em(u,f),""===c&&(d=f?m/f*p:0)),h.style.width=e.Em(d),o.w=o.r=d,h.style.height=e.Em(m),o.h=o.t=m,n.valign&&(o.d=o.b=-this.CHTMLlength2em(n.valign,f),h.style.verticalAlign=e.Em(-o.d),o.h-=o.d,o.t=o.h)}}return this.CHTMLhandleSpace(i),this.CHTMLhandleBBox(i),this.CHTMLhandleColor(i),i},CHTMLimgLoaded:function(t,e){"string"==typeof t&&(e=t),this.CHTML.img.status=e||"OK"},CHTMLimgError:function(){this.CHTML.img.img.onload("error")}},{GLYPH:{}}),MathJax.Hub.Startup.signal.Post("CommonHTML mglyph Ready"),MathJax.Ajax.loadComplete(e.autoloadDir+"/mglyph.js")}),MathJax.Hub.Register.StartupHook("CommonHTML Jax Ready",function(){var t=MathJax.ElementJax.mml,e=MathJax.OutputJax.CommonHTML;t.mmultiscripts.Augment({toCommonHTML:function(t,a){var i=(a||{}).stretch;i||(t=this.CHTMLcreateNode(t),this.CHTMLhandleStyle(t),this.CHTMLgetVariant(),this.CHTMLhandleScale(t)),e.BBOX.empty(this.CHTML);var s,n;i?s=e.getNode(t,"mjx-base"):(this.CHTMLaddChild(t,0,{type:"mjx-base",noBBox:!0,forceChild:!0}),s=t.firstChild),(n=this.CHTMLbboxFor(0)).ic&&(n.R-=n.ic,i||(s.style.marginRight=e.Em(-n.ic)),A=1.3*n.ic+.05);var r={},o={};this.CHTMLgetScripts(r,o,i,t);var l=r.sub,h=r.sup,c=r.presub,u=r.presup,d=o.sub,m=o.sup,p=o.presub,f=o.presup;i||this.CHTMLaddBoxes(t,s,r);var g,M=this.getValues("scriptlevel","scriptsizemultiplier"),x=this.Get("scriptlevel")<3?M.scriptsizemultiplier:1,T=e.TEX.x_height,E=e.TEX.scriptspace,C=e.TEX.sup_drop*x,v=e.TEX.sub_drop*x,b=n.h-C,L=n.d+v,A=0,y=this.data[this.base];!y||"mi"!==y.type&&"mo"!==y.type||1!==y.data.join("").length||1!==n.rscale||n.sH||y.Get("largeop")||(b=L=0),(M=this.getValues("displaystyle","subscriptshift","superscriptshift","texprimestyle")).subscriptshift=""===M.subscriptshift?0:this.CHTMLlength2em(M.subscriptshift),M.superscriptshift=""===M.superscriptshift?0:this.CHTMLlength2em(M.superscriptshift);var R=c?E+p.w:u?E+f.w-A:0;this.CHTML.combine(n,R,0);var S=this.CHTML.w;if(h||u)if(l||c){L=Math.max(L,e.TEX.sub2);var N=e.TEX.rule_thickness,I=(d||p).h,H=(m||f).d;c&&(I=Math.max(I,p.h)),u&&(H=Math.max(H,f.d)),b-H-(I-L)<3*N&&(L=3*N-b+H+I,(C=.8*T-(b-H))>0&&(b+=C,L-=C)),b=Math.max(b,M.superscriptshift),L=Math.max(L,M.subscriptshift),h?l?this.CHTMLplaceSubSup(l,d,h,m,S,A,b,L,E):this.CHTMLplaceSupOnly(h,m,S,A,b,E):l&&this.CHTMLplaceSubOnly(l,d,S,L,E),u?c?this.CHTMLplacePresubPresup(c,p,u,f,A,b,L,E):this.CHTMLplacePresupOnly(u,f,A,b,E):c&&this.CHTMLplacePresubOnly(c,p,L,E)}else g=e.TEX[M.displaystyle?"sup1":M.texprimestyle?"sup3":"sup2"],b=Math.max(b,g,M.superscriptshift),h&&(b=Math.max(b,m.d+.25*T)),u&&(b=Math.max(b,f.d+.25*T)),h&&this.CHTMLplaceSupOnly(h,m,S,A,b,E),u&&this.CHTMLplacePresupOnly(u,f,A,b,E);else L=Math.max(L,e.TEX.sub1,M.subscriptshift),l&&(L=Math.max(L,d.h-.8*T)),c&&(L=Math.max(L,p.h-.8*T)),l&&this.CHTMLplaceSubOnly(l,d,S,L,E),c&&this.CHTMLplacePresubOnly(c,p,L,E);return this.CHTML.clean(),this.CHTMLhandleSpace(t),this.CHTMLhandleBBox(t),this.CHTMLhandleColor(t),t},CHTMLgetScripts:function(t,a,i,s){if(i)return t.sub=e.getNode(s,"mjx-sub"),t.sup=e.getNode(s,"mjx-sup"),t.presub=e.getNode(s,"mjx-presub"),t.presup=e.getNode(s,"mjx-presup"),a.sub=this.CHTMLbbox.sub,a.sup=this.CHTMLbbox.sup,a.presub=this.CHTMLbbox.presub,void(a.presup=this.CHTMLbbox.presup);this.CHTMLbbox=a;for(var n={i:1,w:0,BOX:t,BBOX:a},r=this.data.length,o="sub",l="sup";n.i<r;)if("mprescripts"===(this.data[n.i]||{}).type)n.i++,n.w=0,o="presub",l="presup";else{var h=this.CHTMLaddScript(o,n,s),c=this.CHTMLaddScript(l,n,s),u=Math.max(h?h.rscale*h.w:0,c?c.rscale*c.w:0);this.CHTMLpadScript(o,u,h,n),this.CHTMLpadScript(l,u,c,n),n.w+=u}a.sub&&a.sub.clean(),a.sup&&a.sup.clean(),a.presub&&a.presub.clean(),a.presup&&a.presup.clean()},CHTMLaddScript:function(t,a,i){var s,n,r=this.data[a.i];return r&&"none"!==r.type&&"mprescripts"!==r.type&&((s=a.BOX[t])||(s=a.BOX[t]=e.addElement(i,"mjx-"+t),n=a.BBOX[t]=e.BBOX.empty(),a.w&&(s.style.paddingLeft=e.Em(a.w),n.w=n.r=a.w,n.x=a.w)),r.toCommonHTML(s),n=r.CHTML),r&&"mprescripts"!==r.type&&a.i++,n},CHTMLpadScript:function(t,a,i,s){i||(i={w:0,fake:1,rscale:1});var n=s.BBOX[t],r=0,o=0;if(n){if(i.rscale*i.w<a){var l=s.BOX[t];o=a-i.rscale*i.w;var h=e.Element("mjx-spacer",{style:{width:e.Em(o)}});"pre"!==t.substr(0,3)||i.fake?l.appendChild(h):(l.insertBefore(h,l.lastChild),r=o,o=0)}i.fake?n.w+=r:n.combine(i,n.w+r,0),n.w+=o}},CHTMLaddBoxes:function(t,a,i){var s=i.sub,n=i.sup,r=i.presub,o=i.presup;if(r&&o){var l=e.Element("mjx-prestack");t.insertBefore(l,a),l.appendChild(o),l.appendChild(r)}else r&&t.insertBefore(r,a),o&&t.insertBefore(o,a);if(s&&n){var h=e.addElement(t,"mjx-stack");h.appendChild(n),h.appendChild(s)}else s&&t.appendChild(s),n&&t.appendChild(n)},CHTMLplaceSubOnly:function(t,a,i,s,n){t.style.verticalAlign=e.Em(-s),t.style.marginRight=e.Em(n),a.w+=n,this.CHTML.combine(a,i,-s)},CHTMLplaceSupOnly:function(t,a,i,s,n,r){t.style.verticalAlign=e.Em(n),t.style.paddingLeft=e.Em(s),t.style.paddingRight=e.Em(r),a.w+=r,this.CHTML.combine(a,i+s,n)},CHTMLplaceSubSup:function(t,a,i,s,n,r,o,l,h){t.style.paddingRight=e.Em(h),a.w+=h,i.style.paddingBottom=e.Em(o+l-s.d-a.h),i.style.paddingLeft=e.Em(r+(s.x||0)),i.style.paddingRight=e.Em(h),s.w+=h,i.parentNode.style.verticalAlign=e.Em(-l),this.CHTML.combine(a,n,-l),this.CHTML.combine(s,n+r,o)},CHTMLplacePresubOnly:function(t,a,i,s){t.style.verticalAlign=e.Em(-i),t.style.marginLeft=e.Em(s),this.CHTML.combine(a,s,-i)},CHTMLplacePresupOnly:function(t,a,i,s,n){t.style.verticalAlign=e.Em(s),t.style.paddingLeft=e.Em(n),t.style.paddingRight=e.Em(-i),this.CHTML.combine(a,n,s)},CHTMLplacePresubPresup:function(t,a,i,s,n,r,o,l){t.style.paddingLeft=e.Em(l),i.style.paddingBottom=e.Em(r+o-s.d-a.h),i.style.paddingLeft=e.Em(n+l+(s.x||0)),i.style.paddingRight=e.Em(-n),i.parentNode.style.verticalAlign=e.Em(-o),this.CHTML.combine(a,l,-o),this.CHTML.combine(s,l+n,r)},CHTMLstretchH:t.mbase.CHTMLstretchH,CHTMLstretchV:t.mbase.CHTMLstretchV}),MathJax.Hub.Startup.signal.Post("CommonHTML mmultiscripts Ready"),MathJax.Ajax.loadComplete(e.autoloadDir+"/mmultiscripts.js")}),MathJax.Hub.Register.StartupHook("CommonHTML Jax Ready",function(){var t=MathJax.ElementJax.mml,e=MathJax.OutputJax.CommonHTML;t.ms.Augment({toCommonHTML:function(t){t=this.CHTMLcreateNode(t),this.CHTMLhandleStyle(t),this.CHTMLgetVariant(),this.CHTMLhandleScale(t),e.BBOX.empty(this.CHTML);var a=this.getValues("lquote","rquote","mathvariant");this.hasValue("lquote")&&'"'!==a.lquote||(a.lquote="“"),this.hasValue("rquote")&&'"'!==a.rquote||(a.rquote="”"),"“"===a.lquote&&"monospace"===a.mathvariant&&(a.lquote='"'),"”"===a.rquote&&"monospace"===a.mathvariant&&(a.rquote='"');var i=a.lquote+this.data.join("")+a.rquote;return this.CHTMLhandleText(t,i,this.CHTMLvariant),this.CHTML.clean(),this.CHTMLhandleSpace(t),this.CHTMLhandleBBox(t),this.CHTMLhandleColor(t),t}}),MathJax.Hub.Startup.signal.Post("CommonHTML ms Ready"),MathJax.Ajax.loadComplete(e.autoloadDir+"/ms.js")}),MathJax.Hub.Register.StartupHook("CommonHTML Jax Ready",function(){var t=MathJax.ElementJax.mml,e=MathJax.Hub.config,a=MathJax.OutputJax.CommonHTML,i=MathJax.Hub.SplitList;t.mtable.Augment({toCommonHTML:function(t){var e={rows:[],labels:[],labeled:!1};t=this.CHTMLdefaultNode(t,{noBBox:!0,childOptions:e});for(var i=a.Element("mjx-table");t.firstChild;)i.appendChild(t.firstChild);t.appendChild(i);var s=this.getValues("columnalign","rowalign","columnspacing","rowspacing","columnwidth","equalcolumns","equalrows","columnlines","rowlines","frame","framespacing","align","width","side","minlabelspacing","useHeight"),n=a.TEX.min_rule_thickness/a.em;e.t=a.Px(n*this.CHTML.scale,1),this.CHTMLgetBoxSizes(s,e),this.CHTMLgetAttributes(s,e),this.CHTMLadjustCells(s,e),s.frame&&(i.style.border=e.t+" "+s.frame),this.CHTMLalignV(s,e,t),this.CHTMLcolumnWidths(s,e,t),this.CHTMLstretchCells(s,e),e.labeled&&this.CHTMLaddLabels(s,e,t,i);var r=this.CHTML;return r.w=r.r=e.R,r.h=r.t=e.T-e.B,r.d=r.b=e.B,s.frame||r.pwidth||(t.style.padding="0 "+a.Em(1/6),r.L=r.R=1/6),this.CHTMLhandleSpace(t),this.CHTMLhandleBBox(t),this.CHTMLhandleColor(t),t},CHTMLgetBoxSizes:function(t,e){var i,s,n=a.FONTDATA.lineH*t.useHeight,r=a.FONTDATA.lineD*t.useHeight,o=[],l=[],h=[],c=-1;for(i=0,s=this.data.length;i<s;i++){var u=this.data[i],d="mtr"===u.type?0:-1;o[i]=n,l[i]=r;for(var m=d,p=u.data.length+d;m<p;m++){null==h[m]&&(h[m]=-1e6,m>c&&(c=m));var f=u.data[m-d].CHTML;f.h>o[i]&&(o[i]=f.h),f.d>l[i]&&(l[i]=f.d),f.w>h[m]&&(h[m]=f.w)}}if(t.equalrows){e.HD=!0;var g=Math.max.apply(Math,o),M=Math.max.apply(Math,l);for(i=0,s=o.length;i<s;i++)o[i]=g,l[i]=M}e.H=o,e.D=l,e.W=h,e.J=c},CHTMLgetAttributes:function(e,a){var 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o,l=s,h=i.values,c=i.VALUES;if((o=0===i.n?l.indentshiftfirst||h.indentshiftfirst||c.indentshiftfirst:i.isLast?h.indentshiftlast||c.indentshiftlast:h.indentshift||c.indentshift)===t.INDENTSHIFT.INDENTSHIFT&&(o=h.indentshift||c.indentshift),"auto"!==o&&""!==o||(o="0"),o=this.CHTMLlength2em(o,a.cwidth),i.isTop&&"0"!==e.displayIndent){var u=this.CHTMLlength2em(e.displayIndent,a.cwidth);o+=n===t.INDENTALIGN.RIGHT?-u:u}return n!==t.INDENTALIGN.RIGHT||r?o:-o},CHTMLmoveLine:function(t,e,a,i,s){var n=t[0],r=e[0];if(null==n&&(n=-1),null==r&&(r=this.data.length-1),n===r&&t.length>1)this.data[n].CHTMLmoveSlice(t.slice(1),e.slice(1),a,i,s,"marginLeft");else{var o=i.last;for(i.last=!1;n<r;)this.data[n]&&(t.length<=1?this.data[n].CHTMLmoveNode(a,i,s):this.data[n].CHTMLmoveSlice(t.slice(1),[],a,i,s,"marginLeft")),n++,i.first=!1,t=[];i.last=o,this.data[n]&&(e.length<=1?this.data[n].CHTMLmoveNode(a,i,s):this.data[n].CHTMLmoveSlice([],e.slice(1),a,i,s,"marginRight"))}},CHTMLmoveSlice:function(t,e,a,i,s,n){var r=this.CHTMLcreateSliceNode(a);return this.CHTMLmoveLine(t,e,r,i,s),r.style[n]&&(r.style[n]=""),this.CHTML.L&&("marginLeft"!==n?i.bbox.w+=this.CHTML.L:r.className=r.className.replace(/ MJXc-space\d/,"")),this.CHTML.R&&"marginRight"!==n&&(i.bbox.w+=this.CHTML.R),0===e.length&&(a=this.CHTMLnodeElement(),this.href&&(a=a.parentNode),a.parentNode.removeChild(a),a.nextMathJaxNode.id=a.id),r},CHTMLcreateSliceNode:function(t){var e=this.CHTMLnodeElement(),a=0;this.href&&(e=e.parentNode);for(var i=e;i.nextMathJaxNode;)i=i.nextMathJaxNode,a++;var s=e.cloneNode(!1);return 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