/*!
 ************************************************************
 *
 *  MathJax.js
 *
 *  The main support code for the MathJax Hub, including the
 *  Ajax, Callback, Messaging, and Object-Oriented Programming
 *  libraries, as well as the base Jax classes, and startup
 *  processing code.
 *
 *  ---------------------------------------------------------------------
 *
 *  Copyright (c) 2009-2018 The MathJax Consortium
 *
 *  Licensed under the Apache License, Version 2.0 (the "License");
 *  you may not use this file except in compliance with the License.
 *  You may obtain a copy of the License at
 *
 *      http://www.apache.org/licenses/LICENSE-2.0
 *
 *  Unless required by applicable law or agreed to in writing, software
 *  distributed under the License is distributed on an "AS IS" BASIS,
 *  WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 *  See the License for the specific language governing permissions and
 *  limitations under the License.
 */
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e=t.MathJax.elementJax;e&&e.needsUpdate()?(e.Remove(!0),t.MathJax.state=e.STATE.UPDATE):t.MathJax.state=e.STATE.PROCESSED},Reprocess:function(t){var e=t.MathJax.elementJax;e&&(e.Remove(!0),t.MathJax.state=e.STATE.UPDATE)},Rerender:function(t){var e=t.MathJax.elementJax;e&&(e.Remove(!0),t.MathJax.state=e.STATE.OUTPUT)}},prepareScripts:function(t,e,a){if(!arguments.callee.disabled)for(var i=this.elementScripts(e),s=MathJax.ElementJax.STATE,n=0,r=i.length;n<r;n++){var o=i[n];o.type&&this.inputJax[o.type.replace(/ *;(.|\n)*/,"")]&&(o.MathJax&&(o.MathJax.elementJax&&o.MathJax.elementJax.hover&&MathJax.Extension.MathEvents.Hover.ClearHover(o.MathJax.elementJax),o.MathJax.state!==s.PENDING&&this.scriptAction[t](o)),o.MathJax||(o.MathJax={state:s.PENDING}),o.MathJax.error&&delete o.MathJax.error,o.MathJax.state!==s.PROCESSED&&a.scripts.push(o))}},checkScriptSiblings:function(t){if(!t.MathJax.checked){var e=this.config,a=t.previousSibling;if(a&&"#text"===a.nodeName){var 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f=e.Element("span",{id:a.hover.id,isMathJax:!0,style:{display:"inline-block",width:0,height:0,position:"relative"}},[["span",{className:"MathJax_Hover_Frame",isMathJax:!0,style:{display:"inline-block",position:"absolute",top:this.Px(-h.h-d-p-(h.y||0)),left:this.Px(-u-p+(h.x||0)),width:this.Px(h.w+2*u),height:this.Px(h.h+h.d+2*d),opacity:0,filter:"alpha(opacity=0)"}}]]),x=e.Element("span",{isMathJax:!0,id:a.hover.id+"Menu",className:"MathJax_Menu_Button",style:{display:"inline-block","z-index":1,width:0,height:0,position:"relative"}},[["span",{className:"MathJax_Hover_Arrow",isMathJax:!0,math:i,onclick:this.HoverMenu,jax:s.id,style:{left:this.Px(h.w+u+p+(h.x||0)+c.button.x),top:this.Px(-h.h-d-p-(h.y||0)-c.button.y),opacity:0,filter:"alpha(opacity=0)"}},[["span",{isMathJax:!0},"▼"]]]]);h.width&&(f.style.width=x.style.width=h.width,f.style.marginRight=x.style.marginRight="-"+h.width,f.firstChild.style.width=h.width,x.firstChild.style.left="",x.firstChild.style.right=this.Px(c.button.wx)),r.parentNode.insertBefore(f,r),m&&r.parentNode.insertBefore(x,r),r.style&&(r.style.position="relative"),this.ReHover(a)}},ReHover:function(t){t.hover.remove&&clearTimeout(t.hover.remove),t.hover.remove=setTimeout(i(["UnHover",this,t]),c.fadeoutDelay),this.HoverFadeTimer(t,c.fadeinInc)},UnHover:function(t){t.hover.nofade||this.HoverFadeTimer(t,-c.fadeoutInc,c.fadeoutStart)},HoverFade:function(t){delete 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t.hover},Px:function(t){return Math.abs(t)<.006?"0px":t.toFixed(2).replace(/\.?0+$/,"")+"px"},getImages:function(){h.discoverable&&((new Image).src=c.button.src)}},d=l.Touch={last:0,delay:500,start:function(t){var e=(new Date).getTime(),a=e-d.last<d.delay&&d.up;d.last=e,d.up=!1,a&&(d.timeout=setTimeout(d.menu,d.delay,t,this),t.preventDefault())},end:function(t){var e=(new Date).getTime();if(d.up=e-d.last<d.delay,d.timeout)return clearTimeout(d.timeout),delete d.timeout,d.last=0,d.up=!1,t.preventDefault(),m.Handler(t.touches[0]||t.touch,"DblClick",this)},menu:function(t,e){return delete d.timeout,d.last=0,d.up=!1,m.Handler(t.touches[0]||t.touch,"ContextMenu",e)}};t.Browser.Select({MSIE:function(t){var e=document.documentMode||0,a=t.versionAtLeast("8.0");l.msieBorderWidthBug="BackCompat"===document.compatMode,l.msieEventBug=t.isIE9,l.msieAlignBug=!a||e<8,e<9&&(m.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=c=t.CombineConfig("MathEvents",c);i.Queue(t.Register.StartupHook("End Config",{}),[function(){var t=c.styles[".MathJax_Hover_Frame"];t.border=c.frame.bwidth+"px solid "+c.frame.bcolor+" ! important",t["box-shadow"]=t["-webkit-box-shadow"]=t["-moz-box-shadow"]=t["-khtml-box-shadow"]="0px 0px "+c.frame.hwidth+" "+c.frame.hcolor}],["getImages",u],["Styles",a,c.styles],["Post",t.Startup.signal,"MathEvents Ready"],["loadComplete",a,"[MathJax]/extensions/MathEvents.js"])}(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.Callback,MathJax.Localization,MathJax.OutputJax,MathJax.InputJax),function(t,e,a,i,s){var n,r,o,l=t.CombineConfig("MathZoom",{styles:{"#MathJax_Zoom":{position:"absolute","background-color":"#F0F0F0",overflow:"auto",display:"block","z-index":301,padding:".5em",border:"1px solid black",margin:0,"font-weight":"normal","font-style":"normal","text-align":"left","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap",float:"none","-webkit-box-sizing":"content-box","-moz-box-sizing":"content-box","box-sizing":"content-box","box-shadow":"5px 5px 15px #AAAAAA","-webkit-box-shadow":"5px 5px 15px #AAAAAA","-moz-box-shadow":"5px 5px 15px #AAAAAA","-khtml-box-shadow":"5px 5px 15px #AAAAAA",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},"#MathJax_ZoomOverlay":{position:"absolute",left:0,top:0,"z-index":300,display:"inline-block",width:"100%",height:"100%",border:0,padding:0,margin:0,"background-color":"white",opacity:0,filter:"alpha(opacity=0)"},"#MathJax_ZoomFrame":{position:"relative",display:"inline-block",height:0,width:0},"#MathJax_ZoomEventTrap":{position:"absolute",left:0,top:0,"z-index":302,display:"inline-block",border:0,padding:0,margin:0,"background-color":"white",opacity:0,filter:"alpha(opacity=0)"}}});MathJax.Hub.Register.StartupHook("MathEvents Ready",function(){o=MathJax.Extension.MathEvents.Event,n=MathJax.Extension.MathEvents.Event.False,r=MathJax.Extension.MathEvents.Hover});var h=MathJax.Extension.MathZoom={version:"2.7.5",settings:t.config.menuSettings,scrollSize:18,HandleEvent:function(t,e,a){return!(!h.settings.CTRL||t.ctrlKey)||(!(!h.settings.ALT||t.altKey)||(!(!h.settings.CMD||t.metaKey)||(!(!h.settings.Shift||t.shiftKey)||(!h[e]||h[e](t,a)))))},Click:function(t,e){if("Click"===this.settings.zoom)return this.Zoom(t,e)},DblClick:function(t,e){if("Double-Click"===this.settings.zoom||"DoubleClick"===this.settings.zoom)return this.Zoom(t,e)},Hover:function(t,e){return"Hover"===this.settings.zoom&&(this.Zoom(t,e),!0)},Zoom:function(a,i){this.Remove(),r.ClearHoverTimer(),o.ClearSelection();var s=MathJax.OutputJax[i.jaxID],h=s.getJaxFromMath(i);h.hover&&r.UnHover(h);var c=this.findContainer(i),m=Math.floor(.85*c.clientWidth),u=Math.max(document.body.clientHeight,document.documentElement.clientHeight);"visible"!==this.getOverflow(c)&&(u=Math.min(c.clientHeight,u)),u=Math.floor(.85*u);var d=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=d.lastChild,f=p.firstChild,x=d.firstChild;i.parentNode.insertBefore(d,i),i.parentNode.insertBefore(i,d),f.addEventListener&&f.addEventListener("mousedown",this.Remove,!0);var M=p.offsetWidth||p.clientWidth;if(m-=M,u-=M,p.style.maxWidth=m+"px",p.style.maxHeight=u+"px",this.msieTrapEventBug){var g=e.Element("span",{id:"MathJax_ZoomEventTrap",onmousedown:this.Remove});d.insertBefore(g,p)}if(this.msieZIndexBug){var T=e.addElement(document.body,"img",{src:"about:blank",id:"MathJax_ZoomTracker",width:0,height:0,style:{width:0,height:0,position:"relative"}});d.style.position="relative",d.style.zIndex=l.styles["#MathJax_ZoomOverlay"]["z-index"],d=T}var E=s.Zoom(h,f,i,m,u);return this.msiePositionBug&&(this.msieSizeBug&&(p.style.height=E.zH+"px",p.style.width=E.zW+"px"),p.offsetHeight>u&&(p.style.height=u+"px",p.style.width=E.zW+this.scrollSize+"px"),p.offsetWidth>m&&(p.style.width=m+"px",p.style.height=E.zH+this.scrollSize+"px")),this.operaPositionBug&&(p.style.width=Math.min(m,E.zW)+"px"),p.offsetWidth>M&&p.offsetWidth-M<m&&p.offsetHeight-M<u&&(p.style.overflow="visible"),this.Position(p,E),this.msieTrapEventBug&&(g.style.height=p.clientHeight+"px",g.style.width=p.clientWidth+"px",g.style.left=parseFloat(p.style.left)+p.clientLeft+"px",g.style.top=parseFloat(p.style.top)+p.clientTop+"px"),p.style.visibility="","Hover"===this.settings.zoom&&(x.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{x:i=e[i]?e[i]:parseInt(i),y:s=e[s]?e[s]:parseInt(s)}},getXY:function(t){var e,a=0,i=0;for(e=t;e.offsetParent;)a+=e.offsetLeft,e=e.offsetParent;for(h.operaPositionBug&&(t.style.border="1px solid"),e=t;e.offsetParent;)i+=e.offsetTop,e=e.offsetParent;return h.operaPositionBug&&(t.style.border=""),{x:a,y:i}},Remove:function(a){var i=document.getElementById("MathJax_ZoomFrame");if(i){var s=MathJax.OutputJax[i.previousSibling.jaxID].getJaxFromMath(i.previousSibling);if(t.signal.Post(["math unzoomed",s]),i.parentNode.removeChild(i),(i=document.getElementById("MathJax_ZoomTracker"))&&i.parentNode.removeChild(i),h.operaRefreshBug){var 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:"2.7.5",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,m=t.Browser.isPC,u=t.Browser.isMSIE,d=(document.documentMode||0)>8,p=m?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:m?"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:m?"2px 2em":"1px 2em",background:"transparent"},".MathJax_MenuArrow":{position:"absolute",right:".5em","padding-top":".25em",color:"#666666","font-family":u?"'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":u?"'Arial unicode MS'":null},".MathJax_MenuCheck.RTL":{right:".7em",left:"auto"},".MathJax_MenuRadioCheck":{position:"absolute",left:m?"1em":".7em"},".MathJax_MenuRadioCheck.RTL":{right:m?"1em":".7em",left:"auto"},".MathJax_MenuLabel":{padding:m?"2px 2em 4px 1.33em":"1px 2em 3px 1.33em","font-style":"italic"},".MathJax_MenuRule":{"border-top":m?"1px solid #CCCCCC":"1px solid #DDDDDD",margin:m?"4px 1px 0px":"4px 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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 x=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 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t,i,n,r=a.outerHeight-a.innerHeight||30,o=a.outerWidth-a.innerWidth||30;o=Math.max(140,Math.min(Math.floor(.5*screen.width),s.offsetWidth+o+25)),r=Math.max(40,Math.min(Math.floor(.5*screen.height),s.offsetHeight+r+25)),M.prototype.msieHeightBug&&(r+=35),a.resizeTo(o,r);try{n=e.screenX}catch(t){}e&&null!=n&&(t=Math.max(0,Math.min(e.screenX-Math.floor(o/2),screen.width-o-20)),i=Math.max(0,Math.min(e.screenY-Math.floor(r/2),screen.height-r-20)),a.moveTo(t,i))},50)}},M.Scale=function(){var e,a,i=["CommonHTML","HTML-CSS","SVG","NativeMML","PreviewHTML"],n=i.length,r=100;for(e=0;e<n;e++)if(a=s[i[e]]){r=a.config.scale;break}var o=prompt(h("ScaleMath","Scale all mathematics (compared to surrounding text) by"),r+"%");if(o)if(o.match(/^\s*\d+(\.\d*)?\s*%?\s*$/))if(o=parseFloat(o)){if(o!==r){for(e=0;e<n;e++)(a=s[i[e]])&&(a.config.scale=o);M.cookie.scale=t.config.scale=o,M.saveCookie(),t.Queue(["Rerender",t])}}else alert(h("NonZeroScale","The scale should not be zero"));else alert(h("PercentScale","The scale should be a percentage (e.g., 120%%)"))},M.Zoom=function(){MathJax.Extension.MathZoom||a.Require("[MathJax]/extensions/MathZoom.js")},M.Renderer=function(){var a=t.outputJax["jax/mml"];if(a[0]!==f.settings.renderer){var 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&&!d&&(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 mathematics on the page to become unreadable."],MSIE:["MSIENativeMMLWarning","Internet Explorer requires the MathPlayer plugin in order to process MathML output."],Opera:["OperaNativeMMLWarning","Opera's support for MathML is limited, so switching to MathML output may cause some expressions to render poorly."],Safari:["SafariNativeMMLWarning","Your browser's native MathML does not implement all the features used by MathJax, so some expressions may not render properly."],Firefox:["FirefoxNativeMMLWarning","Your browser's native MathML does not implement all the features used by MathJax, so some expressions may not render properly."]},SVG:{MSIE:["MSIESVGWarning","SVG is not implemented in Internet Explorer prior to IE9 or when it is emulating IE8 or below. Switching to SVG output will cause the mathematics to not display properly."]}},M.AssistiveMML=function(t,e){var i=MathJax.Extension.AssistiveMML;i?MathJax.Hub.Queue([(f.settings.assistiveMML?"Add":"Remove")+"AssistiveMathML",i]):e||a.Require("[MathJax]/extensions/AssistiveMML.js",["AssistiveMML",M,t,!0])},M.Font=function(){s["HTML-CSS"]&&document.location.reload()},M.Locale=function(){MathJax.Localization.setLocale(f.settings.locale),MathJax.Hub.Queue(["Reprocess",MathJax.Hub])},M.LoadLocale=function(){var t=prompt(h("LoadURL","Load translation data from this URL:"));t&&(t.match(/\.js$/)||alert(h("BadURL","The URL should be for a javascript file that defines MathJax translation data.  Javascript file names should end with '.js'")),a.Require(t,function(e){e!=a.STATUS.OK&&alert(h("BadData","Failed to load translation data from %1",t))}))},M.MPEvents=function(t){var e=f.settings.discoverable,a=M.MPEvents.Messages;if(d)!e&&"Menu Events"===t.name[1]&&f.settings.mpContext&&alert(h.apply(h,a.IE9warning));else{if(f.settings.mpMouse&&!confirm(h.apply(h,a.IE8warning)))return delete M.cookie.mpContext,delete f.settings.mpContext,delete M.cookie.mpMouse,delete f.settings.mpMouse,void M.saveCookie();f.settings.mpContext=f.settings.mpMouse,M.cookie.mpContext=M.cookie.mpMouse=f.settings.mpMouse,M.saveCookie(),MathJax.Hub.Queue(["Rerender",MathJax.Hub])}},M.MPEvents.Messages={IE8warning:["IE8warning","This will disable the MathJax menu and zoom features, but you can Alt-Click on an expression to obtain the MathJax menu instead.\n\nReally change the MathPlayer settings?"],IE9warning:["IE9warning","The MathJax contextual menu will be disabled, but you can Alt-Click on an expression to obtain the MathJax menu instead."]},t.Browser.Select({MSIE:function(t){var e="BackCompat"===document.compatMode,a=t.versionAtLeast("8.0")&&document.documentMode>7;M.Augment({margin:20,msieBackgroundBug:(document.documentMode||0)<9,msieFixedPositionBug:e||!a,msieAboutBug:e,msieHeightBug:(document.documentMode||0)<9}),d&&(delete f.styles["#MathJax_About"].filter,delete f.styles[".MathJax_Menu"].filter)},Firefox:function(t){M.skipMouseover=t.isMobile&&t.versionAtLeast("6.0"),M.skipMousedown=t.isMobile}}),M.isMobile=t.Browser.isMobile,M.noContextMenu=t.Browser.noContextMenu,M.CreateLocaleMenu=function(){if(M.menu){var t=M.menu.Find("Language").submenu,e=t.items,a=[],i=MathJax.Localization.strings;for(var s in i)i.hasOwnProperty(s)&&a.push(s);a=a.sort(),t.items=[];for(var n=0,r=a.length;n<r;n++){var o=i[a[n]].menuTitle;o?o+=" 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Events"],"mpMouse",{action:M.MPEvents,hidden:d})),g.SUBMENU(["FontPrefs","Font Preference"],{hidden:!f.showFontMenu},g.LABEL(["ForHTMLCSS","For HTML-CSS:"]),g.RADIO(["Auto","Auto"],"font",{action:M.Font}),g.RULE(),g.RADIO(["TeXLocal","TeX (local)"],"font",{action:M.Font}),g.RADIO(["TeXWeb","TeX (web)"],"font",{action:M.Font}),g.RADIO(["TeXImage","TeX (image)"],"font",{action:M.Font}),g.RULE(),g.RADIO(["STIXLocal","STIX (local)"],"font",{action:M.Font}),g.RADIO(["STIXWeb","STIX (web)"],"font",{action:M.Font}),g.RULE(),g.RADIO(["AsanaMathWeb","Asana Math (web)"],"font",{action:M.Font}),g.RADIO(["GyrePagellaWeb","Gyre Pagella (web)"],"font",{action:M.Font}),g.RADIO(["GyreTermesWeb","Gyre Termes (web)"],"font",{action:M.Font}),g.RADIO(["LatinModernWeb","Latin Modern (web)"],"font",{action:M.Font}),g.RADIO(["NeoEulerWeb","Neo Euler (web)"],"font",{action:M.Font})),g.SUBMENU(["ContextMenu","Contextual Menu"],{hidden:!f.showContext},g.RADIO(["MathJax","MathJax"],"context"),g.RADIO(["Browser","Browser"],"context")),g.COMMAND(["Scale","Scale All Math ..."],M.Scale),g.RULE().With({hidden:!f.showDiscoverable,name:["","discover_rule"]}),g.CHECKBOX(["Discoverable","Highlight on Hover"],"discoverable",{hidden:!f.showDiscoverable})),g.SUBMENU(["Accessibility","Accessibility"],g.CHECKBOX(["AssistiveMML","Assistive MathML"],"assistiveMML",{action:M.AssistiveMML}),g.CHECKBOX(["InTabOrder","Include in Tab Order"],"inTabOrder")),g.SUBMENU(["Locale","Language"],{hidden:!f.showLocale,ltr:!0},g.RADIO("en","locale",{action:M.Locale}),g.RULE().With({hidden:!f.showLocaleURL,name:["","localURL_rule"]}),g.COMMAND(["LoadLocale","Load from URL ..."],M.LoadLocale,{hidden:!f.showLocaleURL})),g.RULE(),g.COMMAND(["About","About MathJax"],M.About),g.COMMAND(["Help","MathJax Help"],M.Help)),M.isMobile&&(e=f.settings,(a=M.menu.Find("Math Settings","Zoom Trigger").submenu).items[0].disabled=a.items[1].disabled=!0,"Hover"!==e.zoom&&"Click"!=e.zoom||(e.zoom="None"),a.items=a.items.slice(0,4),navigator.appVersion.match(/[ (]Android[) ]/)&&M.ITEM.SUBMENU.Augment({marker:"»"})),M.CreateLocaleMenu(),M.CreateAnnotationMenu()}),M.showRenderer=function(t){M.cookie.showRenderer=f.showRenderer=t,M.saveCookie(),M.menu.Find("Math Settings","Math Renderer").hidden=!t},M.showMathPlayer=function(t){M.cookie.showMathPlayer=f.showMathPlayer=t,M.saveCookie(),M.menu.Find("Math Settings","MathPlayer").hidden=!t},M.showFontMenu=function(t){M.cookie.showFontMenu=f.showFontMenu=t,M.saveCookie(),M.menu.Find("Math Settings","Font Preference").hidden=!t},M.showContext=function(t){M.cookie.showContext=f.showContext=t,M.saveCookie(),M.menu.Find("Math Settings","Contextual Menu").hidden=!t},M.showDiscoverable=function(t){M.cookie.showDiscoverable=f.showDiscoverable=t,M.saveCookie(),M.menu.Find("Math Settings","Highlight on Hover").hidden=!t,M.menu.Find("Math Settings","discover_rule").hidden=!t},M.showLocale=function(t){M.cookie.showLocale=f.showLocale=t,M.saveCookie(),M.menu.Find("Language").hidden=!t},MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function(){MathJax.OutputJax["HTML-CSS"].config.imageFont||(M.menu.Find("Math Settings","Font Preference","TeX (image)").disabled=!0)}),i.Queue(t.Register.StartupHook("End Config",{}),["Styles",a,f.styles],["Post",t.Startup.signal,"MathMenu Ready"],["loadComplete",a,"[MathJax]/extensions/MathMenu.js"])}(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.CallBack,MathJax.OutputJax),MathJax.Hub.Register.LoadHook("[MathJax]/jax/element/mml/jax.js",function(){var t=MathJax.ElementJax.mml,e=MathJax.Hub.config.menuSettings;t.mbase.Augment({toMathML:function(t){var e=this.inferred&&this.parent.inferRow;null==t&&(t="");var a=this.type,i=this.toMathMLattributes();if("mspace"===a)return t+"<"+a+i+" />";for(var s=[],n=this.isToken?"":t+(e?"":"  "),r=0,o=this.data.length;r<o;r++)this.data[r]?s.push(this.data[r].toMathML(n)):this.isToken||this.isChars||s.push(n+"<mrow />");return this.isToken||this.isChars?t+"<"+a+i+">"+s.join("")+"</"+a+">":e?s.join("\n"):0===s.length||1===s.length&&""===s[0]?t+"<"+a+i+" />":t+"<"+a+i+">\n"+s.join("\n")+"\n"+t+"</"+a+">"},toMathMLattributes:function(){var e="mstyle"===this.type?t.math.prototype.defaults:this.defaults,a=this.attrNames||t.copyAttributeNames,i=t.skipAttributes,s=t.copyAttributes,n=[];if("math"!==this.type||this.attr&&"xmlns"in this.attr||n.push('xmlns="http://www.w3.org/1998/Math/MathML"'),!this.attrNames)for(var r in e)i[r]||s[r]||!e.hasOwnProperty(r)||null!=this[r]&&this[r]!==e[r]&&this.Get(r,null,1)!==this[r]&&n.push(r+'="'+this.toMathMLattribute(this[r])+'"');for(var o=0,l=a.length;o<l;o++)(1!==s[a[o]]||e.hasOwnProperty(a[o]))&&(value=(this.attr||{})[a[o]],null==value&&(value=this[a[o]]),null!=value&&n.push(a[o]+'="'+this.toMathMLquote(value)+'"'));return this.toMathMLclass(n),n.length?" 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t:"§",sharp:"♯",sigma:"σ",sigmav:"ς",simne:"≆",smile:"⌣",spades:"♠",sub:"⊂",subE:"⫅",subnE:"⫋",subne:"⊊",supE:"⫆",supnE:"⫌",supne:"⊋",swarr:"↙",tau:"τ",theta:"θ",thetav:"ϑ",tilde:"˜",times:"×",triangle:"▵",triangleq:"≜",upsi:"υ",upuparrows:"⇈",veebar:"⊻",vellip:"⋮",weierp:"℘",xi:"ξ",yen:"¥",zeta:"ζ",zigrarr:"⇝"},y.loadComplete("jax.js"),H=MathJax.InputJax.MathML,MathJax.Hub.Insert(H.Parse.Entity,{Ascr:"𝒜",Bscr:"ℬ",Cscr:"𝒞",Dscr:"𝒟",Escr:"ℰ",Fscr:"ℱ",Gscr:"𝒢",Hscr:"ℋ",Iscr:"ℐ",Jscr:"𝒥",Kscr:"𝒦",Lscr:"ℒ",Mscr:"ℳ",Nscr:"𝒩",Oscr:"𝒪",Pscr:"𝒫",Qscr:"𝒬",Rscr:"ℛ",Sscr:"𝒮",Tscr:"𝒯",Uscr:"𝒰",Vscr:"𝒱",Wscr:"𝒲",Xscr:"𝒳",Yscr:"𝒴",Zscr:"𝒵",ascr:"𝒶",bscr:"𝒷",cscr:"𝒸",dscr:"𝒹",escr:"ℯ",fscr:"𝒻",gscr:"ℊ",hscr:"𝒽",iscr:"𝒾",jscr:"𝒿",kscr:"𝓀",lscr:"𝓁",mscr:"𝓂",nscr:"𝓃",oscr:"ℴ",pscr:"𝓅",qscr:"𝓆",rscr:"𝓇",sscr:"𝓈",tscr:"𝓉",uscr:"𝓊",vscr:"𝓋",wscr:"𝓌",xscr:"𝓍",yscr:"𝓎",zscr:"𝓏"}),MathJax.Ajax.loadComplete(H.entityDir+"/scr.js"),w=MathJax.InputJax.MathML,MathJax.Hub.Insert(w.Parse.Entity,{Aopf:"𝔸",Bopf:"𝔹",Copf:"ℂ",Dopf:"𝔻",Eopf:"𝔼",Fopf:"𝔽",Gopf:"𝔾",Hopf:"ℍ",Iopf:"𝕀",Jopf:"𝕁",Kopf:"𝕂",Lopf:"𝕃",Mopf:"𝕄",Nopf:"ℕ",Oopf:"𝕆",Popf:"ℙ",Qopf:"ℚ",Ropf:"ℝ",Sopf:"𝕊",Topf:"𝕋",Uopf:"𝕌",Vopf:"𝕍",Wopf:"𝕎",Xopf:"𝕏",Yopf:"𝕐",Zopf:"ℤ",aopf:"𝕒",bopf:"𝕓",copf:"𝕔",dopf:"𝕕",eopf:"𝕖",fopf:"𝕗",gopf:"𝕘",hopf:"𝕙",iopf:"𝕚",jopf:"𝕛",kopf:"𝕜",lopf:"𝕝",mopf:"𝕞",nopf:"𝕟",oopf:"𝕠",popf:"𝕡",qopf:"𝕢",ropf:"𝕣",sopf:"𝕤",topf:"𝕥",uopf:"𝕦",vopf:"𝕧",wopf:"𝕨",xopf:"𝕩",yopf:"𝕪",zopf:"𝕫"}),MathJax.Ajax.loadComplete(w.entityDir+"/opf.js"),S=MathJax.InputJax.MathML,MathJax.Hub.Insert(S.Parse.Entity,{ZHcy:"Ж",Zacute:"Ź",Zcaron:"Ž",Zcy:"З",Zdot:"Ż",ZeroWidthSpace:"​",Zeta:"Ζ",zacute:"ź",zcaron:"ž",zcy:"з",zdot:"ż",zeetrf:"ℨ",zhcy:"ж",zwj:"‍",zwnj:"‌"}),MathJax.Ajax.loadComplete(S.entityDir+"/z.js"),I=MathJax.InputJax.MathML,MathJax.Hub.Insert(I.Parse.Entity,{GJcy:"Ѓ",GT:">",Gammad:"Ϝ",Gbreve:"Ğ",Gcedil:"Ģ",Gcirc:"Ĝ",Gcy:"Г",Gdot:"Ġ",GreaterGreater:"⪢",Gt:"≫",gE:"≧",gacute:"ǵ",gammad:"ϝ",gbreve:"ğ",gcirc:"ĝ",gcy:"г",gdot:"ġ",ge:"≥",gel:"⋛",geq:"≥",geqq:"≧",geqslant:"⩾",ges:"⩾",gescc:"⪩",gesdot:"⪀",gesdoto:"⪂",gesdotol:"⪄",gesl:"⋛︀",gesles:"⪔",gg:"≫",ggg:"⋙",gjcy:"ѓ",gl:"≷",glE:"⪒",gla:"⪥",glj:"⪤",gnapprox:"⪊",gneq:"⪈",gneqq:"≩",grave:"`",gsim:"≳",gsime:"⪎",gsiml:"⪐",gtcc:"⪧",gtcir:"⩺",gtlPar:"⦕",gtquest:"⩼",gtrapprox:"⪆",gtrarr:"⥸",gtrdot:"⋗",gtreqless:"⋛",gtreqqless:"⪌",gtrless:"≷",gtrsim:"≳",gvertneqq:"≩︀",gvnE:"≩︀"}),MathJax.Ajax.loadComplete(I.entityDir+"/g.js"),J=MathJax.InputJax.MathML,MathJax.Hub.Insert(J.Parse.Entity,{RBarr:"⤐",REG:"®",Racute:"Ŕ",Rang:"⟫",Rarrtl:"⤖",Rcaron:"Ř",Rcedil:"Ŗ",Rcy:"Р",ReverseElement:"∋",ReverseUpEquilibrium:"⥯",Rho:"Ρ",RightArrowBar:"⇥",RightDoubleBracket:"⟧",RightDownTeeVector:"⥝",RightDownVectorBar:"⥕",RightTeeVector:"⥛",RightTriangleBar:"⧐",RightUpDownVector:"⥏",RightUpTeeVector:"⥜",RightUpVectorBar:"⥔",RightVectorBar:"⥓",RoundImplies:"⥰",RuleDelayed:"⧴",rAarr:"⇛",rArr:"⇒",rAtail:"⤜",rBarr:"⤏",rHar:"⥤",race:"∽̱",racute:"ŕ",radic:"√",raemptyv:"⦳",rang:"⟩",rangd:"⦒",range:"⦥",rangle:"⟩",raquo:"»",rarr:"→",rarrap:"⥵",rarrb:"⇥",rarrbfs:"⤠",rarrc:"⤳",rarrfs:"⤞",rarrhk:"↪",rarrlp:"↬",rarrpl:"⥅",rarrsim:"⥴",rarrw:"↝",ratail:"⤚",ratio:"∶",rationals:"ℚ",rbarr:"⤍",rbbrk:"❳",rbrke:"⦌",rbrksld:"⦎",rbrkslu:"⦐",rcaron:"ř",rcedil:"ŗ",rceil:"⌉",rcub:"}",rcy:"р",rdca:"⤷",rdldhar:"⥩",rdquo:"”",rdquor:"”",rdsh:"↳",real:"ℜ",realine:"ℛ",realpart:"ℜ",reals:"ℝ",rect:"▭",reg:"®",rfisht:"⥽",rfloor:"⌋",rhard:"⇁",rharu:"⇀",rharul:"⥬",rightarrow:"→",rightarrowtail:"↣",rightharpoondown:"⇁",rightharpoonup:"⇀",rightleftarrows:"⇄",rightleftharpoons:"⇌",rightsquigarrow:"↝",risingdotseq:"≓",rlarr:"⇄",rlhar:"⇌",rlm:"‏",rmoustache:"⎱",rnmid:"⫮",roang:"⟭",roarr:"⇾",robrk:"⟧",ropar:"⦆",roplus:"⨮",rotimes:"⨵",rpar:")",rpargt:"⦔",rppolint:"⨒",rrarr:"⇉",rsaquo:"›",rsh:"↱",rsqb:"]",rsquo:"’",rsquor:"’",rthree:"⋌",rtrie:"⊵",rtrif:"▸",rtriltri:"⧎",ruluhar:"⥨",rx:"℞"}),MathJax.Ajax.loadComplete(J.entityDir+"/r.js"),O=MathJax.InputJax.MathML,MathJax.Hub.Insert(O.Parse.Entity,{Pcy:"П",Poincareplane:"ℌ",Pr:"⪻",Prime:"″",Proportion:"∷",par:"∥",para:"¶",parallel:"∥",parsim:"⫳",parsl:"⫽",part:"∂",pcy:"п",percnt:"%",permil:"‰",perp:"⊥",pertenk:"‱",phmmat:"ℳ",phone:"☎",pitchfork:"⋔",planck:"ℏ",planckh:"ℎ",plankv:"ℏ",plus:"+",plusacir:"⨣",plusb:"⊞",pluscir:"⨢",plusdo:"∔",plusdu:"⨥",pluse:"⩲",plusmn:"±",plussim:"⨦",plustwo:"⨧",pm:"±",pointint:"⨕",pound:"£",pr:"≺",prE:"⪳",prcue:"≼",pre:"⪯",prec:"≺",precapprox:"⪷",preccurlyeq:"≼",preceq:"⪯",precsim:"≾",primes:"ℙ",prnE:"⪵",prnap:"⪹",prnsim:"⋨",prod:"∏",profalar:"⌮",profline:"⌒",profsurf:"⌓",prop:"∝",propto:"∝",prsim:"≾",prurel:"⊰",puncsp:" "}),MathJax.Ajax.loadComplete(O.entityDir+"/p.js"),k=MathJax.InputJax.MathML,MathJax.Hub.Insert(k.Parse.Entity,{Map:"⤅",Mcy:"М",MediumSpace:" ",Mellintrf:"ℳ",Mu:"Μ",mDDot:"∺",male:"♂",maltese:"✠",map:"↦",mapsto:"↦",mapstodown:"↧",mapstoleft:"↤",mapstoup:"↥",marker:"▮",mcomma:"⨩",mcy:"м",mdash:"—",measuredangle:"∡",micro:"µ",mid:"∣",midast:"*",midcir:"⫰",middot:"·",minus:"−",minusb:"⊟",minusd:"∸",minusdu:"⨪",mlcp:"⫛",mldr:"…",mnplus:"∓",models:"⊧",mp:"∓",mstpos:"∾",mumap:"⊸"}),MathJax.Ajax.loadComplete(k.entityDir+"/m.js"),D=MathJax.InputJax.MathML,MathJax.Hub.Insert(D.Parse.Entity,{QUOT:'"',qint:"⨌",qprime:"⁗",quaternions:"ℍ",quatint:"⨖",quest:"?",questeq:"≟",quot:'"'}),MathJax.Ajax.loadComplete(D.entityDir+"/q.js"),B=MathJax.InputJax.MathML,MathJax.Hub.Insert(B.Parse.Entity,{THORN:"Þ",TRADE:"™",TSHcy:"Ћ",TScy:"Ц",Tab:"\t",Tau:"Τ",Tcaron:"Ť",Tcedil:"Ţ",Tcy:"Т",ThickSpace:"  ",ThinSpace:" ",TripleDot:"⃛",Tstrok:"Ŧ",target:"⌖",tbrk:"⎴",tcaron:"ť",tcedil:"ţ",tcy:"т",tdot:"⃛",telrec:"⌕",there4:"∴",therefore:"∴",thetasym:"ϑ",thickapprox:"≈",thicksim:"∼",thinsp:" ",thkap:"≈",thksim:"∼",thorn:"þ",timesb:"⊠",timesbar:"⨱",timesd:"⨰",tint:"∭",toea:"⤨",top:"⊤",topbot:"⌶",topcir:"⫱",topfork:"⫚",tosa:"⤩",tprime:"‴",trade:"™",triangledown:"▿",triangleleft:"◃",trianglelefteq:"⊴",triangleright:"▹",trianglerighteq:"⊵",tridot:"◬",trie:"≜",triminus:"⨺",triplus:"⨹",trisb:"⧍",tritime:"⨻",trpezium:"⏢",tscy:"ц",tshcy:"ћ",tstrok:"ŧ",twixt:"≬",twoheadleftarrow:"↞",twoheadrightarrow:"↠"}),MathJax.Ajax.loadComplete(B.entityDir+"/t.js"),P=MathJax.InputJax.MathML,MathJax.Hub.Insert(P.Parse.Entity,{Wcirc:"Ŵ",wcirc:"ŵ",wedbar:"⩟",wedge:"∧",wedgeq:"≙",wp:"℘",wr:"≀",wreath:"≀"}),MathJax.Ajax.loadComplete(P.entityDir+"/w.js"),j=MathJax.InputJax.MathML,MathJax.Hub.Insert(j.Parse.Entity,{Fcy:"Ф",FilledSmallSquare:"◼",Fouriertrf:"ℱ",fallingdotseq:"≒",fcy:"ф",female:"♀",ffilig:"ﬃ",fflig:"ﬀ",ffllig:"ﬄ",filig:"ﬁ",fjlig:"fj",fllig:"ﬂ",fltns:"▱",fnof:"ƒ",forall:"∀",forkv:"⫙",fpartint:"⨍",frac12:"½",frac13:"⅓",frac14:"¼",frac15:"⅕",frac16:"⅙",frac18:"⅛",frac23:"⅔",frac25:"⅖",frac34:"¾",frac35:"⅗",frac38:"⅜",frac45:"⅘",frac56:"⅚",frac58:"⅝",frac78:"⅞",frasl:"⁄"}),MathJax.Ajax.loadComplete(j.entityDir+"/f.js"),F=MathJax.InputJax.MathML,MathJax.Hub.Insert(F.Parse.Entity,{VDash:"⊫",Vbar:"⫫",Vcy:"В",Vdashl:"⫦",Verbar:"‖",Vert:"‖",VerticalLine:"|",VerticalSeparator:"❘",VeryThinSpace:" ",vArr:"⇕",vBar:"⫨",vBarv:"⫩",vDash:"⊨",vangrt:"⦜",varepsilon:"ϵ",varkappa:"ϰ",varnothing:"∅",varphi:"ϕ",varpi:"ϖ",varpropto:"∝",varr:"↕",varrho:"ϱ",varsigma:"ς",varsubsetneq:"⊊︀",varsubsetneqq:"⫋︀",varsupsetneq:"⊋︀",varsupsetneqq:"⫌︀",vartheta:"ϑ",vartriangleleft:"⊲",vartriangleright:"⊳",vcy:"в",vdash:"⊢",vee:"∨",veeeq:"≚",verbar:"|",vert:"|",vltri:"⊲",vnsub:"⊂⃒",vnsup:"⊃⃒",vprop:"∝",vrtri:"⊳",vsubnE:"⫋︀",vsubne:"⊊︀",vsupnE:"⫌︀",vsupne:"⊋︀",vzigzag:"⦚"}),MathJax.Ajax.loadComplete(F.entityDir+"/v.js"),X=MathJax.InputJax.MathML,MathJax.Hub.Insert(X.Parse.Entity,{ENG:"Ŋ",ETH:"Ð",Eacute:"É",Ecaron:"Ě",Ecirc:"Ê",Ecy:"Э",Edot:"Ė",Egrave:"È",Emacr:"Ē",EmptySmallSquare:"◻",EmptyVerySmallSquare:"▫",Eogon:"Ę",Epsilon:"Ε",Equal:"⩵",Esim:"⩳",Eta:"Η",Euml:"Ë",eDDot:"⩷",eDot:"≑",eacute:"é",easter:"⩮",ecaron:"ě",ecirc:"ê",ecolon:"≕",ecy:"э",edot:"ė",ee:"ⅇ",eg:"⪚",egrave:"è",egsdot:"⪘",el:"⪙",elinters:"⏧",elsdot:"⪗",emacr:"ē",emptyset:"∅",emptyv:"∅",emsp:" ",emsp13:" ",emsp14:" ",eng:"ŋ",ensp:" ",eogon:"ę",epar:"⋕",eparsl:"⧣",eplus:"⩱",epsilon:"ε",eqcirc:"≖",eqcolon:"≕",eqsim:"≂",eqslantgtr:"⪖",eqslantless:"⪕",equals:"=",equest:"≟",equiv:"≡",equivDD:"⩸",eqvparsl:"⧥",erarr:"⥱",esdot:"≐",esim:"≂",euml:"ë",euro:"€",excl:"!",exist:"∃",expectation:"ℰ",exponentiale:"ⅇ"}),MathJax.Ajax.loadComplete(X.entityDir+"/e.js"),W=MathJax.InputJax.MathML,MathJax.Hub.Insert(W.Parse.Entity,{KHcy:"Х",KJcy:"Ќ",Kappa:"Κ",Kcedil:"Ķ",Kcy:"К",kcedil:"ķ",kcy:"к",kgreen:"ĸ",khcy:"х",kjcy:"ќ"}),MathJax.Ajax.loadComplete(W.entityDir+"/k.js"),_=MathJax.InputJax.MathML,MathJax.Hub.Insert(_.Parse.Entity,{xcap:"⋂",xcirc:"◯",xcup:"⋃",xdtri:"▽",xhArr:"⟺",xharr:"⟷",xlArr:"⟸",xlarr:"⟵",xmap:"⟼",xnis:"⋻",xodot:"⨀",xoplus:"⨁",xotime:"⨂",xrArr:"⟹",xrarr:"⟶",xsqcup:"⨆",xuplus:"⨄",xutri:"△",xvee:"⋁",xwedge:"⋀"}),MathJax.Ajax.loadComplete(_.entityDir+"/x.js"),U=MathJax.InputJax.MathML,MathJax.Hub.Insert(U.Parse.Entity,{CHcy:"Ч",COPY:"©",Cacute:"Ć",CapitalDifferentialD:"ⅅ",Cayleys:"ℭ",Ccaron:"Č",Ccedil:"Ç",Ccirc:"Ĉ",Cconint:"∰",Cdot:"Ċ",Cedilla:"¸",Chi:"Χ",ClockwiseContourIntegral:"∲",CloseCurlyDoubleQuote:"”",CloseCurlyQuote:"’",Colon:"∷",Colone:"⩴",Conint:"∯",CounterClockwiseContourIntegral:"∳",cacute:"ć",capand:"⩄",capbrcup:"⩉",capcap:"⩋",capcup:"⩇",capdot:"⩀",caps:"∩︀",caret:"⁁",caron:"ˇ",ccaps:"⩍",ccaron:"č",ccedil:"ç",ccirc:"ĉ",ccups:"⩌",ccupssm:"⩐",cdot:"ċ",cedil:"¸",cemptyv:"⦲",cent:"¢",centerdot:"·",chcy:"ч",checkmark:"✓",cir:"○",cirE:"⧃",cire:"≗",cirfnint:"⨐",cirmid:"⫯",cirscir:"⧂",clubsuit:"♣",colone:"≔",coloneq:"≔",comma:",",commat:"@",compfn:"∘",complement:"∁",complexes:"ℂ",cong:"≅",congdot:"⩭",conint:"∮",coprod:"∐",copy:"©",copysr:"℗",crarr:"↵",cross:"✗",csub:"⫏",csube:"⫑",csup:"⫐",csupe:"⫒",cudarrl:"⤸",cudarrr:"⤵",cularrp:"⤽",cupbrcap:"⩈",cupcap:"⩆",cupcup:"⩊",cupdot:"⊍",cupor:"⩅",cups:"∪︀",curarrm:"⤼",curlyeqprec:"⋞",curlyeqsucc:"⋟",curren:"¤",curvearrowleft:"↶",curvearrowright:"↷",cuvee:"⋎",cuwed:"⋏",cwconint:"∲",cwint:"∱",cylcty:"⌭"}),MathJax.Ajax.loadComplete(U.entityDir+"/c.js"),q=MathJax.InputJax.MathML,MathJax.Hub.Insert(q.Parse.Entity,{NJcy:"Њ",Nacute:"Ń",Ncaron:"Ň",Ncedil:"Ņ",Ncy:"Н",NegativeMediumSpace:"​",NegativeThickSpace:"​",NegativeThinSpace:"​",NegativeVeryThinSpace:"​",NewLine:"\n",NoBreak:"⁠",NonBreakingSpace:" ",Not:"⫬",NotCongruent:"≢",NotCupCap:"≭",NotEqualTilde:"≂̸",NotGreaterFullEqual:"≧̸",NotGreaterGreater:"≫̸",NotGreaterLess:"≹",NotGreaterSlantEqual:"⩾̸",NotGreaterTilde:"≵",NotHumpDownHump:"≎̸",NotHumpEqual:"≏̸",NotLeftTriangleBar:"⧏̸",NotLessGreater:"≸",NotLessLess:"≪̸",NotLessSlantEqual:"⩽̸",NotLessTilde:"≴",NotNestedGreaterGreater:"⪢̸",NotNestedLessLess:"⪡̸",NotPrecedesEqual:"⪯̸",NotReverseElement:"∌",NotRightTriangleBar:"⧐̸",NotSquareSubset:"⊏̸",NotSquareSubsetEqual:"⋢",NotSquareSuperset:"⊐̸",NotSquareSupersetEqual:"⋣",NotSubset:"⊂⃒",NotSucceedsEqual:"⪰̸",NotSucceedsTilde:"≿̸",NotSuperset:"⊃⃒",NotTildeEqual:"≄",NotTildeFullEqual:"≇",NotTildeTilde:"≉",Ntilde:"Ñ",Nu:"Ν",nGg:"⋙̸",nGt:"≫⃒",nGtv:"≫̸",nLl:"⋘̸",nLt:"≪⃒",nLtv:"≪̸",nabla:"∇",nacute:"ń",nang:"∠⃒",nap:"≉",napE:"⩰̸",napid:"≋̸",napos:"ŉ",napprox:"≉",natural:"♮",naturals:"ℕ",nbsp:" ",nbump:"≎̸",nbumpe:"≏̸",ncap:"⩃",ncaron:"ň",ncedil:"ņ",ncong:"≇",ncongdot:"⩭̸",ncup:"⩂",ncy:"н",ndash:"–",ne:"≠",neArr:"⇗",nearhk:"⤤",nearrow:"↗",nedot:"≐̸",nequiv:"≢",nesear:"⤨",nesim:"≂̸",nexist:"∄",nexists:"∄",ngE:"≧̸",nge:"≱",ngeq:"≱",ngeqq:"≧̸",ngeqslant:"⩾̸",nges:"⩾̸",ngsim:"≵",ngt:"≯",ngtr:"≯",nhArr:"⇎",nhpar:"⫲",ni:"∋",nis:"⋼",nisd:"⋺",niv:"∋",njcy:"њ",nlArr:"⇍",nlE:"≦̸",nldr:"‥",nle:"≰",nleftarrow:"↚",nleftrightarrow:"↮",nleq:"≰",nleqq:"≦̸",nleqslant:"⩽̸",nles:"⩽̸",nless:"≮",nlsim:"≴",nlt:"≮",nltri:"⋪",nltrie:"⋬",nmid:"∤",notin:"∉",notinE:"⋹̸",notindot:"⋵̸",notinva:"∉",notinvb:"⋷",notinvc:"⋶",notni:"∌",notniva:"∌",notnivb:"⋾",notnivc:"⋽",npar:"∦",nparallel:"∦",nparsl:"⫽⃥",npart:"∂̸",npolint:"⨔",npr:"⊀",nprcue:"⋠",npre:"⪯̸",nprec:"⊀",npreceq:"⪯̸",nrArr:"⇏",nrarrc:"⤳̸",nrarrw:"↝̸",nrightarrow:"↛",nrtri:"⋫",nrtrie:"⋭",nsc:"⊁",nsccue:"⋡",nsce:"⪰̸",nshortmid:"∤",nshortparallel:"∦",nsim:"≁",nsime:"≄",nsimeq:"≄",nsmid:"∤",nspar:"∦",nsqsube:"⋢",nsqsupe:"⋣",nsub:"⊄",nsubE:"⫅̸",nsube:"⊈",nsubset:"⊂⃒",nsubseteq:"⊈",nsubseteqq:"⫅̸",nsucc:"⊁",nsucceq:"⪰̸",nsup:"⊅",nsupE:"⫆̸",nsupe:"⊉",nsupset:"⊃⃒",nsupseteq:"⊉",nsupseteqq:"⫆̸",ntgl:"≹",ntilde:"ñ",ntlg:"≸",ntriangleleft:"⋪",ntrianglelefteq:"⋬",ntriangleright:"⋫",ntrianglerighteq:"⋭",num:"#",numero:"№",numsp:" ",nvHarr:"⤄",nvap:"≍⃒",nvge:"≥⃒",nvgt:">⃒",nvinfin:"⧞",nvlArr:"⤂",nvle:"≤⃒",nvlt:"<⃒",nvltrie:"⊴⃒",nvrArr:"⤃",nvrtrie:"⊵⃒",nvsim:"∼⃒",nwArr:"⇖",nwarhk:"⤣",nwarrow:"↖",nwnear:"⤧"}),MathJax.Ajax.loadComplete(q.entityDir+"/n.js"),V=MathJax.InputJax.MathML,MathJax.Hub.Insert(V.Parse.Entity,{AElig:"Æ",AMP:"&",Aacute:"Á",Abreve:"Ă",Acirc:"Â",Acy:"А",Agrave:"À",Alpha:"Α",Amacr:"Ā",And:"⩓",Aogon:"Ą",Aring:"Å",Assign:"≔",Atilde:"Ã",Auml:"Ä",aacute:"á",abreve:"ă",ac:"∾",acE:"∾̳",acd:"∿",acirc:"â",acy:"а",aelig:"æ",af:"⁡",agrave:"à",alefsym:"ℵ",amacr:"ā",amp:"&",andand:"⩕",andd:"⩜",andslope:"⩘",andv:"⩚",ange:"⦤",angle:"∠",angmsdaa:"⦨",angmsdab:"⦩",angmsdac:"⦪",angmsdad:"⦫",angmsdae:"⦬",angmsdaf:"⦭",angmsdag:"⦮",angmsdah:"⦯",angrt:"∟",angrtvb:"⊾",angrtvbd:"⦝",angst:"Å",angzarr:"⍼",aogon:"ą",ap:"≈",apE:"⩰",apacir:"⩯",apid:"≋",apos:"'",approx:"≈",approxeq:"≊",aring:"å",ast:"*",asymp:"≈",asympeq:"≍",atilde:"ã",auml:"ä",awconint:"∳",awint:"⨑"}),MathJax.Ajax.loadComplete(V.entityDir+"/a.js"),z=MathJax.InputJax.MathML,MathJax.Hub.Insert(z.Parse.Entity,{Jcirc:"Ĵ",Jcy:"Й",Jsercy:"Ј",Jukcy:"Є",jcirc:"ĵ",jcy:"й",jsercy:"ј",jukcy:"є"}),MathJax.Ajax.loadComplete(z.entityDir+"/j.js"),G=MathJax.InputJax.MathML,MathJax.Hub.Insert(G.Parse.Entity,{Uacute:"Ú",Uarr:"↟",Uarrocir:"⥉",Ubrcy:"Ў",Ubreve:"Ŭ",Ucirc:"Û",Ucy:"У",Udblac:"Ű",Ugrave:"Ù",Umacr:"Ū",UnderBracket:"⎵",UnderParenthesis:"⏝",Uogon:"Ų",UpArrowBar:"⤒",UpArrowDownArrow:"⇅",UpEquilibrium:"⥮",UpTeeArrow:"↥",UpperLeftArrow:"↖",UpperRightArrow:"↗",Upsi:"ϒ",Uring:"Ů",Utilde:"Ũ",Uuml:"Ü",uArr:"⇑",uHar:"⥣",uacute:"ú",uarr:"↑",ubrcy:"ў",ubreve:"ŭ",ucirc:"û",ucy:"у",udarr:"⇅",udblac:"ű",udhar:"⥮",ufisht:"⥾",ugrave:"ù",uharl:"↿",uharr:"↾",uhblk:"▀",ulcorn:"⌜",ulcorner:"⌜",ulcrop:"⌏",ultri:"◸",umacr:"ū",uml:"¨",uogon:"ų",uparrow:"↑",updownarrow:"↕",upharpoonleft:"↿",upharpoonright:"↾",uplus:"⊎",upsih:"ϒ",upsilon:"υ",urcorn:"⌝",urcorner:"⌝",urcrop:"⌎",uring:"ů",urtri:"◹",utdot:"⋰",utilde:"ũ",utri:"▵",utrif:"▴",uuarr:"⇈",uuml:"ü",uwangle:"⦧"}),MathJax.Ajax.loadComplete(G.entityDir+"/u.js"),$=MathJax.InputJax.MathML,MathJax.Hub.Insert($.Parse.Entity,{Barv:"⫧",Barwed:"⌆",Bcy:"Б",Bernoullis:"ℬ",Beta:"Β",Bumpeq:"≎",bNot:"⫭",backcong:"≌",backepsilon:"϶",barvee:"⊽",barwed:"⌅",barwedge:"⌅",bbrk:"⎵",bbrktbrk:"⎶",bcong:"≌",bcy:"б",bdquo:"„",becaus:"∵",because:"∵",bemptyv:"⦰",bepsi:"϶",bernou:"ℬ",bigcap:"⋂",bigcup:"⋃",bigvee:"⋁",bigwedge:"⋀",bkarow:"⤍",blacksquare:"▪",blacktriangleright:"▸",blank:"␣",blk12:"▒",blk14:"░",blk34:"▓",block:"█",bne:"=⃥",bnequiv:"≡⃥",bnot:"⌐",bot:"⊥",bottom:"⊥",boxDL:"╗",boxDR:"╔",boxDl:"╖",boxDr:"╓",boxH:"═",boxHD:"╦",boxHU:"╩",boxHd:"╤",boxHu:"╧",boxUL:"╝",boxUR:"╚",boxUl:"╜",b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i=[],s=this.FONTDATA.VARIANT;if(t.remap&&t.remap[e]?(e=t.remap[e],t.remap.variant&&(t=s[t.remap.variant])):this.FONTDATA.REMAP[e]&&!t.noRemap&&(e=this.FONTDATA.REMAP[e]),ut(e)&&(e[2]&&(a=5),t=s[e[1]],e=e[0]),"string"==typeof e)for(var n={text:e,i:0,length:e.length};n.i<n.length;){e=this.getUnicode(n);var r=this.getCharList(t,e);r&&i.push.apply(i,r)}else t.cache[e]?i=t.cache[e]:t.cache[e]=i=this.lookupChar(t,e,a);return i},lookupChar:function(t,e,a){for(var i=t;t;){for(var s=0,n=t.fonts.length;s<n;s++){var r=this.FONTDATA.FONTS[t.fonts[s]];"string"==typeof r&&this.loadFont(r);var o=r[e];if(o)return this.fixChar(o,e),o[5].space?[{type:"space",w:o[2],font:r}]:[{type:"char",font:r,n:e}];r.Extra&&this.findBlock(r,e)}if((t=this.FONTDATA.VARIANT[t.chain])&&t.remap&&t.remap[e]&&a++<5)return this.remapChar(t,e,a)}return[this.unknownChar(i,e)]},fixChar:function(t,e){return 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x=h.h+h.d+c.h+c.d-.1;if(t.appendChild(n),a.mid&&(m=this.createChar(p,a.mid,1,s),o=p.removeChild(p.firstChild),x+=m.h+m.d,f=2),a.min&&e<x*a.min&&(e=x*a.min),e>x){u=this.createChar(p,a.ext,1,s),l=p.removeChild(p.firstChild);var M=u.h+u.d,g=M-.1,T=Math.min(Math.ceil((e-x)/(f*g)),this.maxStretchyParts);a.fullExtenders?e=T*f*g+x:g=(e-x)/(f*T),d=u.d+u.a-M/2,l.style.margin=l.style.padding="",l.style.lineHeight=ot.Em(g),l.style.marginBottom=ot.Em(d-.05/f),l.style.marginTop=ot.Em(-d-.05/f);for(var E=l.textContent,L="\n"+E;--T>0;)E+=L;l.textContent=E,t.appendChild(l),a.mid&&(t.appendChild(o),t.appendChild(l.cloneNode(!0)))}else d=(e-x-.1)/f,n.style.marginBottom=ot.Em(d+parseFloat(n.style.marginBottom||"0")),a.mid&&t.appendChild(o),r.style.marginTop=ot.Em(d+parseFloat(r.style.marginTop||"0"));t.appendChild(r);var C=ot.BBOX({w:Math.max(h.w,u.w,c.w,m.w),l:Math.min(h.l,u.l,c.l,m.l),r:Math.max(h.r,u.r,c.r,m.r),h:e-c.d,d:c.d,t:e-c.d,b:c.d});return 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i=t.style;i.transform=i.WebkitTransform=i.MozTransform=i["-ms-transform"]=e,a&&(i.transformOrigin=i.WebkitTransformOrigin=i.MozTransformOrigin=i["-ms-transform-origin"]=a)},arrayEntry:function(t,e){return t[Math.max(0,Math.min(e,t.length-1))]},removeStyles:["fontSize","fontFamily","fontWeight","fontStyle","fontVariant","font"]}),ot.BBOX=MathJax.Object.Subclass({Init:function(t){for(var e in t)t.hasOwnProperty(e)&&(this[e]=t[e])},clean:function(){this.h===-pt&&(this.h=0),this.d===-pt&&(this.d=0),this.l===pt&&(this.l=0),this.r===-pt&&(this.r=0),this.t===-pt&&(this.t=0),this.b===-pt&&(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;var i=t.rscale;e+i*t.r>this.r&&(this.r=e+i*t.r),e+i*t.l<this.l&&(this.l=e+i*t.l),e+i*(t.w+(t.L||0)+(t.R||0))>this.w&&(this.w=e+i*(t.w+(t.L||0)+(t.R||0))),a+i*t.h>this.h&&(this.h=a+i*t.h),t.D&&(null==this.D||i*t.D-a>this.D)&&i*t.D>this.d?this.D=i*t.D-a:null==t.D&&this.D&&delete this.D,i*t.d-a>this.d&&(this.d=i*t.d-a),a+i*t.t>this.t&&(this.t=a+i*t.t),i*t.b-a>this.b&&(this.b=i*t.b-a)},append:function(t){var e=t.rscale,a=this.w;a+e*t.r>this.r&&(this.r=a+e*t.r),a+e*t.l<this.l&&(this.l=a+e*t.l),this.w+=e*(t.w+(t.L||0)+(t.R||0)),e*t.h>this.h&&(this.h=e*t.h),t.D&&(null==this.D||e*t.D>this.D)&&e*t.D>this.d?this.D=e*t.D:null==t.D&&this.D&&delete this.D,e*t.d>this.d&&(this.d=e*t.d),e*t.t>this.t&&(this.t=e*t.t),e*t.b>this.b&&(this.b=e*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,i){this[e]+=ot.length2em(t,1,this.scale),null==i?this[e]>this[a]&&(this[a]=this[e]):this[a]<i&&(this[a]=i)}},{zero:function(){return ot.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=ot.BBOX.zero()),t.h=t.d=t.r=t.t=t.b=-pt,t.w=0,t.l=pt,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(){(lt=MathJax.ElementJax.mml).mbase.Augment({toCommonHTML:function(t,e){return this.CHTMLdefaultNode(t,e)},CHTMLmultiline:function(){lt.mbase.CHTMLautoloadFile("multiline")},CHTMLdefaultNode:function(t,e){e||(e={}),t=this.CHTMLcreateNode(t),this.CHTML=ot.BBOX.empty(),this.CHTMLhandleStyle(t),this.isToken&&this.CHTMLgetVariant(),this.CHTMLhandleScale(t);for(var a=Math.max(e.minChildren||0,this.data.length),i=0;i<a;i++)this.CHTMLaddChild(t,i,e);return e.noBBox||this.CHTML.clean(),this.CHTMLhandleSpace(t),this.CHTMLhandleBBox(t),this.CHTMLhandleColor(t),t},CHTMLaddChild:function(t,e,a){var i,s=this.data[e],n=a.childNodes;if(n instanceof Array&&(n=n[e]||"span"),s){if(n&&(t=ot.addElement(t,n)),i=s.toCommonHTML(t,a.childOptions),n&&1!==s.CHTML.rscale&&(t.style.fontSize=t.firstChild.style.fontSize,t.firstChild.style.fontSize=""),!a.noBBox){var r=this.CHTML,o=s.CHTML;r.append(o),1===this.data.length?(o.ic&&(r.ic=o.ic),o.skew&&(r.skew=o.skew)):(delete r.ic,delete r.skew),o.pwidth&&(r.pwidth=o.pwidth)}}else a.forceChild&&(i=ot.addElement(t,n||"mjx-box"));return i},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)}}},CHTMLupdateFrom:function(t){this.CHTML.updateFrom(t),this.inferRow&&this.data[0].CHTML.updateFrom(t)},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.CHTMLupdateFrom(this.Core().CHTMLstretchV(t,e)),this.CHTML},CHTMLstretchH:function(t,e){return this.CHTMLupdateFrom(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=ot.BBOX.zero(),this.href&&(t=ot.addElement(t,"a",{href:this.href,isMathJax:!0})),this.CHTMLnodeID||(this.CHTMLnodeID=ot.GetID());var e=(this.id||"MJXc-Node-"+this.CHTMLnodeID)+ot.idPostfix;return this.CHTMLhandleAttributes(ot.addElement(t,"mjx-"+this.type,{id:e}))},CHTMLnodeElement:function(){return this.CHTMLnodeID?document.getElementById((this.id||"MJXc-Node-"+this.CHTMLnodeID)+ot.idPostfix):null},CHTMLlength2em:function(t,e){return ot.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 e=this.attrNames,a=lt.nocopyAttributes,i=nt.config.ignoreMMLattributes,s="mstyle"===this.type?lt.math.prototype.defaults:this.defaults,n=0,r=e.length;n<r;n++){var o=e[n];0!=i[o]&&(a[o]||i[o]||null!=s[o]||void 0!==t[o])||t.setAttribute(o,this.attr[o])}return t},CHTMLhandleScale:function(t){var e=1,a=this.parent,i=a?a.CHTML.scale:1,s=this.getValues("scriptlevel","fontsize");s.mathsize=this.Get("mathsize",null,!this.isToken),0!==s.scriptlevel&&(s.scriptlevel>2&&(s.scriptlevel=2),e=Math.pow(this.Get("scriptsizemultiplier"),s.scriptlevel),s.scriptminsize=ot.length2em(this.Get("scriptminsize"),.8,1),e<s.scriptminsize&&(e=s.scriptminsize)),this.removedStyles&&this.removedStyles.fontSize&&!s.fontsize&&(s.fontsize=this.removedStyles.fontSize),s.fontsize&&!this.mathsize&&(s.mathsize=s.fontsize),1!==s.mathsize&&(e*=ot.length2em(s.mathsize,1,1));var n=this.CHTMLvariant;return n&&n.style&&n.style["font-family"]&&(e*=ot.config.scale/100/ot.scale),this.CHTML.scale=e,i=this.CHTML.rscale=e/i,Math.abs(i-1)<.001&&(i=1),t&&1!==i&&(t.style.fontSize=ot.Percent(i)),e},CHTMLhandleStyle:function(t){if(this.style){var e=t.style;e.cssText=this.style,this.removedStyles={};for(var a=0,i=ot.removeStyles.length;a<i;a++){var s=ot.removeStyles[a];e[s]&&(this.removedStyles[s]=e[s],e[s]="")}}},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=ot.Em(e.w),a.width="100%"):e.w<0&&(a.width="0px",a.marginRight=ot.Em(e.w)),this.style)for(var i=0,s=ot.BBOX.styleAdjust.length;i<s;i++){var n=ot.BBOX.styleAdjust[i];n&&a[n[0]]&&e.adjust(a[n[0]],n[1],n[2],n[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+=" "+ot.SPACECLASS[e])}},CHTMLhandleText:function(t,e,a){t.firstChild&&!this.CHTML&&(this.CHTML=ot.BBOX.empty()),this.CHTML=ot.handleText(t,e,a,this.CHTML)},CHTMLgetVariant:function(){var t,e=this.getValues("mathvariant","fontfamily","fontweight","fontstyle");e.hasVariant=this.Get("mathvariant",!0),this.removedStyles&&((t=this.removedStyles).fontFamily&&(e.family=t.fontFamily),t.fontWeight&&(e.weight=t.fontWeight),t.fontStyle&&(e.style=t.fontStyle)),e.hasVariant||(e.fontfamily&&(e.family=e.fontfamily),e.fontweight&&(e.weight=e.fontweight),e.fontstyle&&(e.style=e.fontstyle)),e.weight&&e.weight.match(/^\d+$/)&&(e.weight=parseInt(e.weight)>600?"bold":"normal");var 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:lt.VARIANT.BOLD,italic:lt.VARIANT.BOLDITALIC,fraktur:lt.VARIANT.BOLDFRAKTUR,script:lt.VARIANT.BOLDSCRIPT,"sans-serif":lt.VARIANT.BOLDSANSSERIF,"sans-serif-italic":lt.VARIANT.SANSSERIFBOLDITALIC}[a]||a:"normal"===e.weight&&(a={bold:lt.VARIANT.normal,"bold-italic":lt.VARIANT.ITALIC,"bold-fraktur":lt.VARIANT.FRAKTUR,"bold-script":lt.VARIANT.SCRIPT,"bold-sans-serif":lt.VARIANT.SANSSERIF,"sans-serif-bold-italic":lt.VARIANT.SANSSERIFITALIC}[a]||a),"italic"===e.style?a={normal:lt.VARIANT.ITALIC,bold:lt.VARIANT.BOLDITALIC,"sans-serif":lt.VARIANT.SANSSERIFITALIC,"bold-sans-serif":lt.VARIANT.SANSSERIFBOLDITALIC}[a]||a:"normal"===e.style&&(a={italic:lt.VARIANT.NORMAL,"bold-italic":lt.VARIANT.BOLD,"sans-serif-italic":lt.VARIANT.SANSSERIF,"sans-serif-bold-italic":lt.VARIANT.BOLDSANSSERIF}[a]||a),this.CHTMLvariant=ot.FONTDATA.VARIANT[a]||ot.FONTDATA.VARIANT[lt.VARIANT.NORMAL]},CHTMLbboxFor:function(t){return this.data[t]&&this.data[t].CHTML?this.data[t].CHTML:ot.BBOX.zero()},CHTMLdrawBBox:function(t,e){e||(e=this.CHTML);var a=ot.Element("mjx-box",{style:{opacity:.25,"margin-left":ot.Em(-(e.w+(e.R||0)))}},[["mjx-box",{style:{height:ot.Em(e.h),width:ot.Em(e.w),"background-color":"red"}}],["mjx-box",{style:{height:ot.Em(e.d),width:ot.Em(e.w),"margin-left":ot.Em(-e.w),"vertical-align":ot.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(){this.constructor.Augment({toCommonHTML:lt.mbase.CHTMLautoloadFail});var t=ot.autoloadDir+"/"+this.type+".js";nt.RestartAfter(st.Require(t))},CHTMLautoloadFail:function(){throw Error("CommonHTML can't autoload '"+this.type+"'")},CHTMLautoloadList:{},CHTMLautoloadFile:function(t){if(lt.mbase.CHTMLautoloadList.hasOwnProperty(t))throw Error("CommonHTML can't autoload file '"+t+"'");lt.mbase.CHTMLautoloadList[t]=!0;var e=ot.autoloadDir+"/"+t+".js";nt.RestartAfter(st.Require(e))},CHTMLstretchV:function(t,e){return this.Core().CHTMLstretchV(t,e),this.toCommonHTML(this.CHTMLnodeElement(),{stretch:!0}),this.CHTML},CHTMLstretchH:function(t,e){return this.CHTMLupdateFrom(this.CHTMLstretchCoreH(t,e)),this.toCommonHTML(t,{stretch:!0}),this.CHTML}}),lt.chars.Augment({toCommonHTML:function(t,e){this.CHTML=null,null==e&&(e={});var a=this.toString();e.remap&&(a=e.remap(a,e.remapchars)),this.CHTMLhandleText(t,a,e.variant||this.parent.CHTMLvariant)}}),lt.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)}}),lt.math.Augment({toCommonHTML:function(t){t=this.CHTMLdefaultNode(t),this.CHTML.w<0&&(t.parentNode.style.width="0px",t.parentNode.style.marginRight=ot.Em(this.CHTML.w));var e=this.Get("alttext");if(e&&!t.getAttribute("aria-label")&&t.setAttribute("aria-label",e),this.CHTML.pwidth)t.parentNode.style.minWidth=this.CHTML.mwidth||ot.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 a=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift");a.indentalignfirst!==lt.INDENTALIGN.INDENTALIGN&&(a.indentalign=a.indentalignfirst),a.indentalign===lt.INDENTALIGN.AUTO&&(a.indentalign=xt.displayAlign),a.indentshiftfirst!==lt.INDENTSHIFT.INDENTSHIFT&&(a.indentshift=a.indentshiftfirst),"auto"===a.indentshift&&(a.indentshift="0");var i=this.CHTMLlength2em(a.indentshift,ot.cwidth);if("0"!==xt.displayIndent){var s=this.CHTMLlength2em(xt.displayIndent,ot.cwidth);i+=a.indentalign===lt.INDENTALIGN.RIGHT?-s:s}var n=t.parentNode.parentNode.style;t.parentNode.style.textAlign=n.textAlign=a.indentalign,i&&(i*=ot.em/ot.outerEm,nt.Insert(n,{left:{marginLeft:ot.Em(i)},right:{marginRight:ot.Em(-i)},center:{marginLeft:ot.Em(i),marginRight:ot.Em(-i)}}[a.indentalign]))}return t}}),lt.mi.Augment({toCommonHTML:function(t){t=this.CHTMLdefaultNode(t);var e=this.CHTML,a=this.data.join("");return null==e.skew||ot.isChar(a)||delete e.skew,e.r>e.w&&ot.isChar(a)&&!this.CHTMLvariant.noIC&&(e.ic=e.r-e.w,e.w=e.r,t.lastChild.style.paddingRight=ot.Em(e.ic)),t}}),lt.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||ot.isChar(a)||delete e.skew,e.r>e.w&&ot.isChar(a)&&!this.CHTMLvariant.noIC&&(e.ic=e.r-e.w,e.w=e.r,t.lastChild.style.paddingRight=ot.Em(e.ic)),t}}),lt.mo.Augment({toCommonHTML:function(t){t=this.CHTMLcreateNode(t),this.CHTMLhandleStyle(t),this.CHTMLgetVariant(),this.CHTMLhandleScale(t),ot.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=ot.Em(ot.TEX.nulldelimiterspace));else{this.CHTMLadjustAccent(e),this.CHTMLadjustVariant(e);for(var a=0,i=this.data.length;a<i;a++)this.CHTMLaddChild(t,a,{childOptions:{variant:e.mathvariant,remap:this.remap,remapchars:e.remapchars}});ot.isChar(e.text)?0===this.CHTML.w&&this.CHTML.l<0&&this.CHTMLfixCombiningChar(t):delete this.CHTML.skew,e.largeop&&this.CHTMLcenterOp(t)}return this.CHTML.clean(),this.CHTMLhandleBBox(t),this.CHTMLhandleSpace(t),this.CHTMLhandleColor(t),t},CHTMLhandleSpace:function(t){if(this.hasMMLspacing()){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,i=this.Parent();i&&i.isEmbellished()&&i.Core()===a;)a=i,i=i.Parent(),t=a.CHTMLnodeElement();e.lspace&&(t.style.paddingLeft=ot.Em(e.lspace)),e.rspace&&(t.style.paddingRight=ot.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,ot.isChar(t.text)&&e&&e.isa(lt.munderover)){var a=e.data[e.over],i=e.data[e.under];a&&this===a.CoreMO()&&e.Get("accent")?t.remapchars=ot.FONTDATA.REMAPACCENT:i&&this===i.CoreMO()&&e.Get("accentunder")&&(t.remapchars=ot.FONTDATA.REMAPACCENTUNDER)}},CHTMLadjustVariant:function(t){var e=t.parent,a=e&&e.isa(lt.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=ot.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-ot.TEX.axis_height;Math.abs(a)>.001&&(t.style.verticalAlign=ot.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=ot.Em(e.ic))},CHTMLcanStretch:function(t,e,a){if(!this.Get("stretchy"))return!1;var i=this.data.join("");if(!ot.isChar(i))return!1;var s={text:i};this.CHTMLadjustAccent(s),s.remapchars&&(i=s.remapchars[i]||i);var n=(i=ot.FONTDATA.DELIMITERS[i.charCodeAt(0)])&&i.dir===t.substr(0,1);return n&&(n=this.CHTML.h!==e||this.CHTML.d!==a||!!this.Get("minsize",!0)||!!this.Get("maxsize",!0))&&(this.CHTML.stretch=!0),n},CHTMLstretchV:function(t,e){var a,i=this.CHTMLnodeElement(),s=this.CHTML,n=this.getValues("symmetric","maxsize","minsize"),r=ot.TEX.axis_height;if(a=n.symmetric?2*Math.max(t-r,e+r):t+e,n.maxsize=this.CHTMLlength2em(n.maxsize,s.h+s.d),n.minsize=this.CHTMLlength2em(n.minsize,s.h+s.d),(a=Math.max(n.minsize,Math.min(n.maxsize,a)))!==s.sH){for(a!=n.minsize&&(a=[Math.max(a*ot.TEX.delimiterfactor/1e3,a-ot.TEX.delimitershortfall),a]);i.firstChild;)i.removeChild(i.firstChild);this.CHTML=s=ot.createDelimiter(i,this.data.join("").charCodeAt(0),a,s),s.sH=a instanceof Array?a[1]:a,a=n.symmetric?(s.h+s.d)/2+r:(s.h+s.d)*t/(t+e),a-=s.h,Math.abs(a)>.05&&(i.style.verticalAlign=ot.Em(a),s.h+=a,s.d-=a,s.t+=a,s.b-=a)}return this.CHTML},CHTMLstretchH:function(t,e){var a=this.CHTML,i=this.getValues("maxsize","minsize","mathvariant","fontweight");if(("bold"===i.fontweight||"bold"===(this.removedStyles||{}).fontWeight||parseInt(i.fontweight)>=600)&&!this.Get("mathvariant",!0)&&(i.mathvariant=lt.VARIANT.BOLD),i.maxsize=this.CHTMLlength2em(i.maxsize,a.w),i.minsize=this.CHTMLlength2em(i.minsize,a.w),(e=Math.max(i.minsize,Math.min(i.maxsize,e)))!==a.sW){for(;t.firstChild;)t.removeChild(t.firstChild);this.CHTML=a=ot.createDelimiter(t,this.data.join("").charCodeAt(0),e,a,i.mathvariant),a.sW=e}return this.CHTML}}),lt.mtext.Augment({CHTMLgetVariant:function(){if(ot.config.mtextFontInherit||"merror"===this.Parent().type){var t=ot.config.scale/100/ot.scale,e={cache:{},fonts:[],className:"MJXc-font-inherit",rscale:t,style:{"font-size":ot.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)}}),lt.merror.Augment({toCommonHTML:function(t){t=this.CHTMLdefaultNode(t);var e=this.CHTML;return e.rescale(.9),e.h+=3/ot.em,e.h>e.t&&(e.t=e.h),e.d+=3/ot.em,e.d>e.b&&(e.b=e.d),e.w+=8/ot.em,e.r=e.w,e.l=0,t}}),lt.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),i=this.CHTMLlength2em(e.height),s=this.CHTMLlength2em(e.depth),n=this.CHTML;return n.w=n.r=a,n.h=n.t=i,n.d=n.b=s,n.l=0,a<0&&(t.style.marginRight=ot.Em(a),a=0),t.style.width=ot.Em(a),t.style.height=ot.Em(Math.max(0,i+s)),s&&(t.style.verticalAlign=ot.Em(-s)),this.CHTMLhandleBBox(t),this.CHTMLhandleColor(t),t}}),lt.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=ot.addElement(t,"mjx-block")).appendChild(a),ot.addElement(t,"mjx-strut"));var i=this.CHTMLbboxFor(0),s=this.getValues("width","height","depth","lspace","voffset"),n=0,r=0,o=i.w,l=i.h,h=i.d;a.style.width=0,a.style.margin=ot.Em(-l)+" 0 "+ot.Em(-h),""!==s.width&&(o=this.CHTMLdimen(s.width,"w",o,0)),""!==s.height&&(l=this.CHTMLdimen(s.height,"h",l,0)),""!==s.depth&&(h=this.CHTMLdimen(s.depth,"d",h,0)),""!==s.voffset&&(r=this.CHTMLdimen(s.voffset))&&(a.style.position="relative",a.style.top=ot.Em(-r)),""!==s.lspace&&(n=this.CHTMLdimen(s.lspace))&&(a.style.position="relative",a.style.left=ot.Em(n)),t.style.width=0,t.style.marginTop=ot.Em(l-1),t.style.padding="0 "+ot.Em(o)+" "+ot.Em(h)+" 0";var c=ot.BBOX({w:o,h:l,d:h,l:0,r:o,t:l,b:h,scale:this.CHTML.scale,rscale:this.CHTML.rscale});return c.combine(i,n,r),c.w=o,c.h=l,c.d=h,this.CHTML=c,t.parentNode},CHTMLstretchV:lt.mbase.CHTMLstretchV,CHTMLstretchH:lt.mbase.CHTMLstretchH,CHTMLdimen:function(t,e,a,i){null==i&&(i=-pt);var s=(t=String(t)).match(/width|height|depth/),n=s?this.CHTML[s[0].charAt(0)]:e?this.CHTML[e]:0,r=this.CHTMLlength2em(t,n)||0;return t.match(/^[-+]/)&&null!=a&&(r+=a),null!=i&&(r=Math.max(i,r)),r}}),lt.munderover.Augment({toCommonHTML:function(t,e){var a=this.getValues("displaystyle","accent","accentunder","align"),i=this.data[this.base];if(!a.displaystyle&&null!=i&&(i.movablelimits||i.CoreMO().Get("movablelimits")))return lt.msubsup.prototype.toCommonHTML.call(this,t,o);var s,n,r=[],o=!1;if(e&&e.stretch)this.data[this.base]&&(i=ot.getNode(t,"mjx-op")),this.data[this.under]&&(s=ot.getNode(t,"mjx-under")),this.data[this.over]&&(n=ot.getNode(t,"mjx-over")),r[0]=i,r[1]=s||n,r[2]=n,o=!0;else{var l=["mjx-op","mjx-under","mjx-over"];1===this.over&&(l[1]=l[2]),t=this.CHTMLdefaultNode(t,{childNodes:l,noBBox:!0,forceChild:!0,minChildren:2}),r[0]=i=t.removeChild(t.firstChild),r[1]=s=n=t.removeChild(t.firstChild),t.firstChild&&(r[2]=n=t.removeChild(t.firstChild))}var h=[],c=this.CHTMLgetBBoxes(h,r,a),m=h[this.base],u=this.CHTML;u.w=c,u.h=m.h,u.d=m.d,m.h<.35&&(i.style.marginTop=ot.Em(m.h-.35)),a.accent&&m.h<ot.TEX.x_height&&(u.h+=ot.TEX.x_height-m.h,i.style.marginTop=ot.Em(ot.TEX.x_height-Math.max(m.h,.35)),m.h=ot.TEX.x_height);var d=i,p=0;return m.ic&&(p=1.3*m.ic+.05),this.data[this.over]&&(d=this.CHTMLaddOverscript(n,h,a,p,i,o)),this.data[this.under]?this.CHTMLaddUnderscript(s,h,a,p,t,d,o):o||t.appendChild(d),this.CHTMLplaceBoxes(i,s,n,a,h),t},CHTMLgetBBoxes:function(t,e,a){var i,s,n=this.data.length,r=-pt,o=r;for(i=0;i<n;i++)t[i]=this.CHTMLbboxFor(i),t[i].x=t[i].y=0,this.data[i]&&(t[i].stretch=this.data[i].CHTMLcanStretch("Horizontal")),s=i===this.base?1:t[i].rscale,i!==this.base&&(delete t[i].L,delete t[i].R),o=Math.max(o,s*(t[i].w+(t[i].L||0)+(t[i].R||0))),!t[i].stretch&&o>r&&(r=o);for(r===-pt&&(r=o),i=0;i<n;i++)t[i].stretch&&(s=i===this.base?1:t[i].rscale,t[i]=this.data[i].CHTMLstretchH(e[i].firstChild,r/s),t[i].x=t[i].y=0,o=Math.max(o,s*(t[i].w+(t[i].L||0)+(t[i].R||0))));return t[this.base]||(t[this.base]=ot.BBOX.empty()),o},CHTMLaddOverscript:function(t,e,a,i,s,n){var r,o,l,h=this.CHTML,c=ot.TEX.big_op_spacing5,m=e[this.over],u=e[this.base],d=m.rscale;if(!n){var p=ot.Element("mjx-stack");p.appendChild(t),p.appendChild(s)}return m.D&&(m.d=m.D),m.d<0&&(t.firstChild.style.verticalAlign="top",t.style.height=ot.Em(m.h+m.d)),m.x=0,a.accent?(m.w<.001&&(m.x+=(m.r-m.l)/2),l=ot.TEX.rule_thickness,c=0,u.skew&&(m.x+=d*u.skew,h.skew=d*u.skew,m.x+d*m.w>h.w&&(h.skew+=(h.w-(m.x+d*m.w))/2))):(r=ot.TEX.big_op_spacing1,o=ot.TEX.big_op_spacing3,l=Math.max(r,o-Math.max(0,d*m.d))),m.x+=i/2,m.y=h.h+l+c+d*m.d,l&&(t.style.paddingBottom=ot.Em(l/d)),c&&(t.style.paddingTop=ot.Em(c/d)),p},CHTMLaddUnderscript:function(t,e,a,i,s,n,r){var o,l,h,c=this.CHTML,m=ot.TEX.big_op_spacing5,u=e[this.under],d=u.rscale;r||(ot.addElement(s,"mjx-itable",{},[["mjx-row",{},[["mjx-cell"]]],["mjx-row"]]),s.firstChild.firstChild.firstChild.appendChild(n),s.firstChild.lastChild.appendChild(t)),u.D&&(u.d=u.D),u.d<0&&(t.firstChild.style.verticalAlign="top",s.firstChild.style.marginBottom=ot.Em(u.d)),a.accentunder?(h=2*ot.TEX.rule_thickness,m=0):(o=ot.TEX.big_op_spacing2,l=ot.TEX.big_op_spacing4,h=Math.max(o,l-d*u.h)),u.x=-i/2,u.y=-(c.d+h+m+d*u.h),h&&(t.style.paddingTop=ot.Em(h/d)),m&&(t.style.paddingBottom=ot.Em(m/d))},CHTMLplaceBoxes:function(t,e,a,i,s){var n,r,o=this.CHTML.w,l=s.length,h=ot.BBOX.zero();h.scale=this.CHTML.scale,h.rscale=this.CHTML.rscale,s[this.base].x=s[this.base].y=0;var c=pt;for(n=0;n<l;n++){var m=(r=n===this.base?1:s[n].rscale)*(s[n].w+(s[n].L||0)+(s[n].R||0));s[n].x+={left:0,center:(o-m)/2,right:o-m}[i.align],s[n].x<c&&(c=s[n].x)}for(n=0;n<l;n++)this.data[n]&&(r=n===this.base?1:s[n].rscale,s[n].x-c&&((n===this.base?t:n===this.over?a:e).style.paddingLeft=ot.Em((s[n].x-c)/r)),h.combine(s[n],s[n].x-c,s[n].y));this.CHTML=h},CHTMLstretchV:lt.mbase.CHTMLstretchV,CHTMLstretchH:lt.mbase.CHTMLstretchH,CHTMLchildNode:function(t,e){var a=["mjx-op","mjx-under","mjx-over"];return 1===this.over&&(a[1]=a[2]),ot.getNode(t,a[e])}}),lt.msubsup.Augment({toCommonHTML:function(t,e){var a,i,s,n=this.getValues("displaystyle","subscriptshift","superscriptshift","texprimestyle");if(e&&e.stretch)this.data[this.base]&&(a=ot.getNode(t,"mjx-base")),this.data[this.sub]&&(i=ot.getNode(t,"mjx-sub")),this.data[this.sup]&&(s=ot.getNode(t,"mjx-sup")),o=ot.getNode(t,"mjx-stack");else{var r=["mjx-base","mjx-sub","mjx-sup"];if(1===this.sup&&(r[1]=r[2]),a=(t=this.CHTMLdefaultNode(t,{childNodes:r,noBBox:!0,forceChild:!0,minChildren:3})).childNodes[this.base],i=t.childNodes[this.sub],s=t.childNodes[this.sup],this.CHTMLnotEmpty(this.data[this.sub])||(t.removeChild(i),i=null),this.CHTMLnotEmpty(this.data[this.sup])||(t.removeChild(s),s=null),3===t.childNodes.length){var o=ot.addElement(t,"mjx-stack");o.appendChild(s),o.appendChild(i)}}for(var l=[],h=ot.BBOX.empty(this.CHTML),c=0,m=this.data.length;c<m;c++)l[c]=this.CHTMLbboxFor(c);var u=l[this.base]||ot.BBOX.empty(),d=l[this.sub],p=l[this.sup],f=i?d.rscale:1,x=s?p.rscale:1;h.combine(u,0,0);var M,g=ot.TEX.x_height,T=ot.TEX.scriptspace,E=ot.TEX.sup_drop*x,L=ot.TEX.sub_drop*f,C=u.h-E,b=u.d+L,v=0;u.ic&&(h.w-=u.ic,a.style.marginRight=ot.Em(-u.ic),v=1.3*u.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||!ot.isChar(y.data.join(""))||1!==u.rscale||u.sH||y.Get("largeop")||(C=b=0)),n.subscriptshift=""===n.subscriptshift?0:this.CHTMLlength2em(n.subscriptshift),n.superscriptshift=""===n.superscriptshift?0:this.CHTMLlength2em(n.superscriptshift);var R=h.w;if(i&&(d.w+=T),s&&(p.w+=T),s)if(i){b=Math.max(b,ot.TEX.sub2);var A=ot.TEX.rule_thickness;C-x*p.d-(f*d.h-b)<3*A&&(b=3*A-C+x*p.d+f*d.h,(E=.8*g-(C-x*p.d))>0&&(C+=E,b-=E)),C=Math.max(C,n.superscriptshift),b=Math.max(b,n.subscriptshift),i.style.paddingRight=ot.Em(T/f),s.style.paddingBottom=ot.Em(C/x+b/f-p.d-d.h/f*x),s.style.paddingLeft=ot.Em(v/x),s.style.paddingRight=ot.Em(T/x),o.style.verticalAlign=ot.Em(-b),h.combine(p,R+v,C),h.combine(d,R,-b)}else M=ot.TEX[n.displaystyle?"sup1":n.texprimestyle?"sup3":"sup2"],C=Math.max(C,M,x*p.d+.25*g,n.superscriptshift),s.style.verticalAlign=ot.Em(C/x),s.style.paddingLeft=ot.Em(v/x),s.style.paddingRight=ot.Em(T/x),h.combine(p,R+v,C);else i&&(b=Math.max(b,ot.TEX.sub1,f*d.h-.8*g,n.subscriptshift),i.style.verticalAlign=ot.Em(-b/f),i.style.paddingRight=ot.Em(T/f),h.combine(d,R,-b));return h.clean(),t},CHTMLstretchV:lt.mbase.CHTMLstretchV,CHTMLstretchH:lt.mbase.CHTMLstretchH,CHTMLchildNode:function(t,e){var a=["mjx-base","mjx-sub","mjx-sup"];return 1===this.over&&(a[1]=a[2]),ot.getNode(t,a[e])}}),lt.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,i=t.firstChild,s=t.lastChild,n=ot.addElement(t,"mjx-box");n.appendChild(i),n.appendChild(s),t.appendChild(n),"center"!==e.numalign&&(i.style.textAlign=e.numalign),"center"!==e.denomalign&&(s.style.textAlign=e.denomalign);var r=this.CHTMLbboxFor(0),o=this.CHTMLbboxFor(1),l=ot.BBOX.empty(this.CHTML),h=r.rscale,c=o.rscale;e.linethickness=Math.max(0,ot.thickness2em(e.linethickness||"0",l.scale));var m,u,d,p,f=ot.TEX.min_rule_thickness/ot.em,x=ot.TEX.axis_height,M=e.linethickness;if(e.bevelled){n.className+=" MJXc-bevelled";var g=a?.4:.15,T=Math.max(h*(r.h+r.d),c*(o.h+o.d))+2*g,E=ot.Element("mjx-bevel");n.insertBefore(E,s);var L=ot.createDelimiter(E,47,T);d=h*(r.d-r.h)/2+x+g,p=c*(o.d-o.h)/2+x-g,d&&(i.style.verticalAlign=ot.Em(d/h)),p&&(s.style.verticalAlign=ot.Em(p/c)),E.style.marginLeft=E.style.marginRight=ot.Em(-g/2),l.combine(r,0,d),l.combine(L,h*r.w-g/2,0),l.combine(o,h*r.w+L.w-g,p),l.clean()}else{if(n.className+=" MJXc-stacked",a?(d=ot.TEX.num1,p=ot.TEX.denom1):(d=0===M?ot.TEX.num3:ot.TEX.num2,p=ot.TEX.denom2),0===M)m=Math.max((a?7:3)*ot.TEX.rule_thickness,2*f),(u=d-r.d*h-(o.h*c-p))<m&&(d+=(m-u)/2,p+=(m-u)/2);else{m=Math.max((a?2:0)*f+M,M/2+1.5*f),M=Math.max(M,f),(u=d-r.d*h-(x+M/2))<m&&(d+=m-u),(u=x-M/2-(o.h*c-p))<m&&(p+=m-u),r.L=r.R=o.L=o.R=.1;var C=ot.addElement(n,"mjx-line",{style:{"border-bottom":ot.Px(M*l.scale,1)+" solid",top:ot.Em(-M/2-x)}})}l.combine(r,0,d),l.combine(o,0,-p),l.clean(),n.style.width=ot.Em(l.w),i.style.width=ot.Em(l.w/h),s.style.width=ot.Em(l.w/c),C&&(C.style.width=n.style.width),i.style.top=ot.Em(-l.h/h),s.style.bottom=ot.Em(-l.d/c),ot.addElement(t,"mjx-vsize",{style:{height:ot.Em(l.h+l.d),verticalAlign:ot.Em(-l.d)}})}if(!this.texWithDelims){var b=ot.TEX.nulldelimiterspace;n.style.padding="0 "+ot.Em(b),l.l+=b,l.r+=b,l.w+=2*b}return t},CHTMLcanStretch:function(t){return!1}}),lt.msqrt.Augment({toCommonHTML:function(t){var e=(t=this.CHTMLdefaultNode(t,{childNodes:["mjx-box","mjx-root"],forceChild:!0,noBBox:!0})).firstChild||ot.Element("mjx-box"),a=ot.addElement(t,"mjx-box");a.appendChild(e);var i,s,n=this.CHTMLbboxFor(0),r=ot.BBOX.empty(this.CHTML),o=ot.TEX.rule_thickness,l=ot.TEX.surd_height,h=o;this.Get("displaystyle")&&(h=ot.TEX.x_height),i=o+h/4,s=n.h+n.d+i+o;var c=ot.Element("mjx-surd");a.insertBefore(c,e);var m=ot.createDelimiter(c,8730,[s-.04,s]);m.h+m.d>s&&(i=(m.h+m.d-(s-o))/2),s=n.h+i+o;var u=this.CHTMLaddRoot(t,m,m.h+m.d-s);return e.style.paddingTop=ot.Em(i),e.style.borderTop=ot.Px(l*n.scale,1)+" solid",a.style.paddingTop=ot.Em(2*o-l),n.h+=i+2*o,r.combine(m,u,s-m.h),r.combine(n,u+m.w,0),r.clean(),t},CHTMLaddRoot:function(){return 0},CHTMLhandleBBox:function(t){delete this.CHTMLbboxFor(0).pwidth,this.SUPER(arguments).CHTMLhandleBBox.apply(this,arguments)}}),lt.mroot.Augment({toCommonHTML:lt.msqrt.prototype.toCommonHTML,CHTMLhandleBBox:lt.msqrt.prototype.CHTMLhandleBBox,CHTMLaddRoot:function(t,e,a){if(this.data[1]){var i=this.CHTML,s=this.data[1].CHTML,n=t.firstChild,r=s.rscale,o=this.CHTMLrootHeight(s,e,r)-a,l=Math.min(s.w,s.r),h=Math.max(l,e.offset/r);return o&&(n.style.verticalAlign=ot.Em(o/r)),h>l&&(n.firstChild.style.paddingLeft=ot.Em(h-l)),h-=e.offset/r,n.style.width=ot.Em(h),i.combine(s,0,o),h*r}},CHTMLrootHeight:function(t,e,a){return.45*(e.h+e.d-.9)+e.offset+Math.max(0,t.d-.075)}}),lt.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}}),lt.mrow.Augment({toCommonHTML:function(t,e){e=e||{},t=this.CHTMLdefaultNode(t);for(var a,i=this.CHTML,s=i.h,n=i.d,r=0,o=this.data.length;r<o;r++)this.CHTMLstretchChildV(r,s,n),this.data[r]&&this.data[r].CHTML&&this.data[r].CHTML.w<0&&(a=!0);return this.CHTMLlineBreaks()?(this.CHTMLmultiline(t),e.autowidth&&(t.style.width="")):(a&&i.w&&(t.style.width=ot.Em(Math.max(0,i.w))),i.w<0&&(t.style.marginRight=ot.Em(i.w))),t},CHTMLlineBreaks:function(){return!!this.parent.linebreakContainer&&(ft.automatic&&this.CHTML.w>ot.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}}),lt.TeXAtom.Augment({toCommonHTML:function(t,e){if(e&&e.stretch||(t=this.CHTMLdefaultNode(t)),this.texClass===lt.TEXCLASS.VCENTER){var a=ot.TEX.axis_height,i=this.CHTML,s=a-(i.h+i.d)/2+i.d;Math.abs(s)>.001&&(t.style.verticalAlign=ot.Em(s),i.h+=s,i.t+=s,i.d-=s,i.b-=s)}return t},CHTMLstretchV:function(t,e){return this.CHTMLupdateFrom(this.Core().CHTMLstretchV(t,e)),this.toCommonHTML(this.CHTMLnodeElement(),{stretch:!0}),this.CHTML},CHTMLstretchH:function(t,e){return this.CHTMLupdateFrom(this.CHTMLstretchCoreH(t,e)),this.toCommonHTML(t,{stretch:!0}),this.CHTML}}),lt.semantics.Augment({toCommonHTML:function(t){return t=this.CHTMLcreateNode(t),this.data[0]&&(this.data[0].toCommonHTML(t),this.CHTMLupdateFrom(this.data[0].CHTML),this.CHTMLhandleBBox(t)),t}}),lt.annotation.Augment({toCommonHTML:function(t){return this.CHTMLcreateNode(t)}}),lt["annotation-xml"].Augment({toCommonHTML:lt.mbase.CHTMLautoload}),lt.ms.Augment({toCommonHTML:lt.mbase.CHTMLautoload}),lt.mglyph.Augment({toCommonHTML:lt.mbase.CHTMLautoload}),lt.menclose.Augment({toCommonHTML:lt.mbase.CHTMLautoload}),lt.maction.Augment({toCommonHTML:lt.mbase.CHTMLautoload}),lt.mmultiscripts.Augment({toCommonHTML:lt.mbase.CHTMLautoload}),lt.mtable.Augment({toCommonHTML:lt.mbase.CHTMLautoload}),MathJax.Hub.Register.StartupHook("onLoad",function(){setTimeout(MathJax.Callback(["loadComplete",ot,"jax.js"]),0)})}),MathJax.Hub.Register.StartupHook("End Cookie",function(){"None"!==nt.config.menuSettings.zoom&&st.Require("[MathJax]/extensions/MathZoom.js")}),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.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="http://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),m={},u=0,d=c.length;u<d;u++)m[c[u]]=!0;m[t.NOTATION.UPDIAGONALARROW]&&delete m[t.NOTATION.UPDIAGONALSTRIKE];for(var p in m)m.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),m=this.CHTMLsvg(t,i,n),u=this.CHTMLsvgElement(m.firstChild,"g",{fill:"currentColor",transform:"translate("+this.CHTMLpx(n/2)+" "+this.CHTMLpx(o+n/2)+") rotate("+h+")"}),d=4*n,p=1*n,f=2*n;this.CHTMLsvgElement(u,"line",{x1:e.Px(n/2),y1:0,x2:e.Px(c-d),y2:0}),this.CHTMLsvgElement(u,"path",{d:"M "+this.CHTMLpx(c-d)+",0 L "+this.CHTMLpx(c-d-p)+","+this.CHTMLpx(f)+"L "+this.CHTMLpx(c)+",0 L "+this.CHTMLpx(c-d-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 m=this.CHTMLsvg(t,i,n);this.CHTMLsvgElement(m.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,m=n.height,u=o.img.img.width/e.em,d=o.img.img.height/e.em,p=u,f=d;""!==c&&(u=this.CHTMLlength2em(c,p),d=p?u/p*f:0),""!==m&&(d=this.CHTMLlength2em(m,f),""===c&&(u=f?d/f*p:0)),h.style.width=e.Em(u),o.w=o.r=u,h.style.height=e.Em(d),o.h=o.t=d,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,s,n=(a||{}).stretch;n||(t=this.CHTMLcreateNode(t),this.CHTMLhandleStyle(t),this.CHTMLgetVariant(),this.CHTMLhandleScale(t)),e.BBOX.empty(this.CHTML),n?i=e.getNode(t,"mjx-base"):(this.CHTMLaddChild(t,0,{type:"mjx-base",noBBox:!0,forceChild:!0}),i=t.firstChild),(s=this.CHTMLbboxFor(0)).ic&&(s.R-=s.ic,n||(i.style.marginRight=e.Em(-s.ic)),y=1.3*s.ic+.05);var r={},o={};this.CHTMLgetScripts(r,o,n,t);var l=r.sub,h=r.sup,c=r.presub,m=r.presup,u=o.sub,d=o.sup,p=o.presub,f=o.presup;n||this.CHTMLaddBoxes(t,i,r);var x,M=this.getValues("scriptlevel","scriptsizemultiplier"),g=this.Get("scriptlevel")<3?M.scriptsizemultiplier:1,T=e.TEX.x_height,E=e.TEX.scriptspace,L=e.TEX.sup_drop*g,C=e.TEX.sub_drop*g,b=s.h-L,v=s.d+C,y=0,R=this.data[this.base];!R||"mi"!==R.type&&"mo"!==R.type||!e.isChar(R.data.join(""))||1!==s.rscale||s.sH||R.Get("largeop")||(b=v=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 A=c?E+p.w:m?E+f.w-y:0;this.CHTML.combine(s,A,0);var N=this.CHTML.w;if(h||m)if(l||c){v=Math.max(v,e.TEX.sub2);var H=e.TEX.rule_thickness,w=(u||p).h,S=(d||f).d;c&&(w=Math.max(w,p.h)),m&&(S=Math.max(S,f.d)),b-S-(w-v)<3*H&&(v=3*H-b+S+w,(L=.8*T-(b-S))>0&&(b+=L,v-=L)),b=Math.max(b,M.superscriptshift),v=Math.max(v,M.subscriptshift),h?l?this.CHTMLplaceSubSup(l,u,h,d,N,y,b,v,E):this.CHTMLplaceSupOnly(h,d,N,y,b,E):l&&this.CHTMLplaceSubOnly(l,u,N,v,E),m?c?this.CHTMLplacePresubPresup(c,p,m,f,y,b,v,E):this.CHTMLplacePresupOnly(m,f,y,b,E):c&&this.CHTMLplacePresubOnly(c,p,v,E)}else x=e.TEX[M.displaystyle?"sup1":M.texprimestyle?"sup3":"sup2"],b=Math.max(b,x,M.superscriptshift),h&&(b=Math.max(b,d.d+.25*T)),m&&(b=Math.max(b,f.d+.25*T)),h&&this.CHTMLplaceSupOnly(h,d,N,y,b,E),m&&this.CHTMLplacePresupOnly(m,f,y,b,E);else v=Math.max(v,e.TEX.sub1,M.subscriptshift),l&&(v=Math.max(v,u.h-.8*T)),c&&(v=Math.max(v,p.h-.8*T)),l&&this.CHTMLplaceSubOnly(l,u,N,v,E),c&&this.CHTMLplacePresubOnly(c,p,v,E);return 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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 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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 m=this.data[i],u="mtr"===m.type?0:-1;o[i]=n,l[i]=r;for(var d=u,p=m.data.length+u;d<p;d++){null==h[d]&&(h[d]=-1e6,d>c&&(c=d));var f=m.data[d-u].CHTML;f.h>o[i]&&(o[i]=f.h),f.d>l[i]&&(l[i]=f.d),f.w>h[d]&&(h[d]=f.w)}}if(t.equalrows){e.HD=!0;var x=Math.max.apply(Math,o),M=Math.max.apply(Math,l);for(i=0,s=o.length;i<s;i++)o[i]=x,l[i]=M}e.H=o,e.D=l,e.W=h,e.J=c},CHTMLgetAttributes:function(e,a){var s,n,r=i(e.columnspacing),o=i(e.rowspacing),l=i(e.columnalign),h=i(e.rowalign),c=i(e.columnlines),m=i(e.rowlines),u=i(e.columnwidth),d=[],p=a.J,f=a.rows.length-1;for(s=0,n=r.length;s<n;s++)r[s]=this.CHTMLlength2em(r[s]);for(s=0,n=o.length;s<n;s++)o[s]=this.CHTMLlength2em(o[s]);for(;r.length<p;)r.push(r[r.length-1]);for(;l.length<=p;)l.push(l[l.length-1]);for(;c.length<p;)c.push(c[c.length-1]);for(;u.length<=p;)u.push(u[u.length-1]);for(;o.length<f;)o.push(o[o.length-1]);for(;h.length<=f;)h.push(h[h.length-1]);for(;m.length<f;)m.push(m[m.length-1]);for(l[-1]="l"===e.side.substr(0,1)?"left":"right",s=0;s<=f;s++){var x=this.data[s];if(d[s]=[],x.rowalign&&(h[s]=x.rowalign),x.columnalign)for(d[s]=i(x.columnalign);d[s].length<=p;)d[s].push(d[s][d[s].length-1])}var M=i(e.framespacing);2!=M.length&&(M=i(this.defaults.framespacing)),M[0]=Math.max(0,this.CHTMLlength2em(M[0])),M[1]=Math.max(0,this.CHTMLlength2em(M[1])),""===e.columnlines.replace(/none/g,"").replace(/ 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R="mtr"===b.type?0:-1,A=b.data[v-R]||{CHTML:a.BBOX.zero()},N=C[v].style;x=A.CHTML,d=n[v]/2,r[v]!==t.LINES.NONE&&(N.borderRight=i.t+" "+r[v],d-=1/a.em/2),d=a.Em(Math.max(0,d)),N.padding=g+" "+d+" 0px "+p,f&&(N.borderBottom=f),p=d,M=A.rowalign||(this.data[E]||{}).rowalign||c[E];var H=Math.max(1,x.h),w=Math.max(.2,x.d),S=i.H[E]+i.D[E]-(H+w),I=C[v].firstChild.style;M===t.ALIGN.TOP?(S&&(I.marginBottom=a.Em(S)),N.verticalAlign="top"):M===t.ALIGN.BOTTOM?(N.verticalAlign="bottom",S&&(I.marginTop=a.Em(S))):M===t.ALIGN.CENTER?(S&&(I.marginTop=I.marginBottom=a.Em(S/2)),N.verticalAlign="middle"):H!==i.H[E]&&(I.marginTop=a.Em(i.H[E]-H)),(M=A.columnalign||m[E][v]||h[v])!==t.ALIGN.CENTER&&(N.textAlign=M)}C.node.style.height=a.Em(i.RHD[E]),g=u}n[i.J]/=2,o[s.length-1]/=2},CHTMLalignV:function(t,e,i){var s,n=e.rows.length,r=e.H,o=e.D,l=e.RSPACE;"string"!=typeof t.align&&(t.align=String(t.align)),t.align.match(/(top|bottom|center|baseline|axis)( 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M=[],g=[],T=[],E=[],L=e.rows[0];for(s=0;s<=c;s++)E[s]=e.W[s],"auto"===l[s]?M.push(s):"fit"===l[s]?g.push(s):l[s].match(/%$/)?T.push(s):E[s]=this.CHTMLlength2em(l[s],E[s]),x+=E[s]+h[s],L[s]&&(L[s].style.width=a.Em(E[s]));t.frame&&(x+=2/a.em);var C=g.length>0;if(u)if(d)for(s=0;s<=c;s++)cell=L[s].style,"auto"!==l[s]||C?"fit"===l[s]?cell.width="":l[s].match(/%$/)?cell.width=l[s]:cell.minWidth=cell.maxWidth=cell.width:cell.width="";else{if(m>x){var b=0;for(n=0,r=T.length;n<r;n++)s=T[n],b+=(o=Math.max(E[s],this.CHTMLlength2em(l[s],m)))-E[s],E[s]=o,L[s].style.width=a.Em(o);x+=b}if(C||(g=M),m>x&&g.length){var v=(m-x)/g.length;for(n=0,r=g.length;n<r;n++)E[s=g[n]]+=v,L[s].style.width=a.Em(E[s]);x=m}}E[-1]=e.W[-1],e.W=E,e.R=x,d&&(i.style.width=this.CHTML.pwidth="100%",this.CHTML.mwidth=a.Em(x),i.firstChild.style.width=t.width,i.firstChild.style.margin="auto")},CHTMLstretchCells:function(t,e){for(var a=e.rows,i=e.H,s=e.D,n=e.W,r=e.J,o=a.length-1,l=0;l<=o;l++)for(var h=a[l],c=this.data[l],m=i[l],u=s[l],d=0;d<=r;d++){var p=h[d],f=c.data[d];f&&("V"===f.CHTML.stretch?f.CHTMLstretchV(m,u):"H"===f.CHTML.stretch&&f.CHTMLstretchH(p,n[d]))}},CHTMLaddLabels:function(i,s,n,r){var o=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift");o.indentalignfirst!==t.INDENTALIGN.INDENTALIGN&&(o.indentalign=o.indentalignfirst),o.indentalign===t.INDENTALIGN.AUTO&&(o.indentalign=e.displayAlign),o.indentshiftfirst!==t.INDENTSHIFT.INDENTSHIFT&&(o.indentshift=o.indentshiftfirst),"auto"===o.indentshift&&(o.indentshift="0");var l=this.CHTMLlength2em(o.indentshift,a.cwidth),h=this.CHTMLlength2em(i.minlabelspacing,.8)+s.W[-1],c=0,m=s.R,u=this.CHTMLlength2em(e.displayIndent,a.cwidth),d=s.CALIGN[-1]===t.INDENTALIGN.RIGHT?-1:1;o.indentalign===t.INDENTALIGN.CENTER?(m+=2*(h-d*(l+u)),l+=u):s.CALIGN[-1]===o.indentalign?(u<0&&(c=d*u,u=0),h>d*(l+=d*u)&&(l=d*h),l+=c,m+=l*=d):(m+=h-d*l+u,l-=d*u,l*=-d);var 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r=a.addElement(i,"mjx-base");t.length>1?this.data[this.base].CHTMLmoveSlice(t.slice(1),e.slice(1),r,s,n,"marginLeft"):e.length<=1?this.data[this.base].CHTMLmoveNode(r,s,n):this.data[this.base].CHTMLmoveSlice([],e.slice(1),r,s,n,"marginRight")}if(0===e.length){var o=this.CHTMLnodeElement(),l=a.getNode(o,"mjx-stack"),h=a.getNode(o,"mjx-sup"),c=a.getNode(o,"mjx-sub");l?i.appendChild(l):h?i.appendChild(h):c&&i.appendChild(c);var m,u=s.bbox.w;h&&(m=this.data[this.sup].CHTML,s.bbox.combine(m,u,m.Y)),c&&(m=this.data[this.sub].CHTML,s.bbox.combine(m,u,m.Y))}}}),t.mmultiscripts.Augment({CHTMLbetterBreak:function(t,e){if(!this.data[this.base])return!1;var a=t.index.slice(0);t.index.shift();var i,n,r,o=t.index.length>0,l=!1;o||(t.W+=t.w,t.w=0),t.scanW=t.W;var h=this.CHTML,c=this.data[this.base].CHTML,m=h.w-c.w-(h.X||0);return 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l=a.linebreakWidth-r;if(0===i.n&&(n.indentshiftfirst!==i.VALUES.indentshiftfirst||n.indentalignfirst!==i.VALUES.indentalignfirst)){var h=this.CHTMLgetAlign(i,n),c=this.CHTMLgetShift(i,n,h);l+=e.shift-c}var m=Math.floor(l/a.linebreakWidth*1e3);m<0&&(m=s.toobig-3*m),n.fence&&(m+=s.fence),(n.linebreakstyle===t.LINEBREAKSTYLE.AFTER&&n.texClass===t.TEXCLASS.OPEN||n.texClass===t.TEXCLASS.CLOSE)&&(m+=s.close),m+=e.nest*s.nestfactor;var u=s[n.linebreak||t.LINEBREAK.AUTO]||0;return MathJax.Object.isArray(u)?m=Math.max(1,m+u[0]*e.nest):(u||l>=0)&&(m=u*e.nest),!(m>=e.penalty)&&(e.penalty=m,e.values=n,e.W=r,e.w=o,n.lineleading=this.CHTMLlength2em(n.lineleading,i.VALUES.lineleading),n.id=this.CHTMLnodeID,!0)}}),t.mspace.Augment({CHTMLbetterBreak:function(e,i){if(e.values&&e.values.id===this.CHTMLnodeID)return!1;var n=this.getValues("linebreak"),r=n.linebreak;r&&!this.hasDimAttr()||(r=t.LINEBREAK.AUTO);var o=e.scanW,l=this.CHTML.w+(this.CHTML.L||0)+(this.CHTML.R||0);if(o-e.shift==0)return!1;var h=a.linebreakWidth-o,c=Math.floor(h/a.linebreakWidth*1e3);c<0&&(c=s.toobig-3*c),c+=e.nest*s.nestfactor;var m=s[r]||0;return r===t.LINEBREAK.AUTO&&l>=s.spacelimit&&!this.mathbackground&&!this.background&&(m=[(l+s.spaceoffset)*s.spacefactor]),MathJax.Object.isArray(m)?c=Math.max(1,c+m[0]*e.nest):(m||h>=0)&&(c=m*e.nest),!(c>=e.penalty)&&(e.penalty=c,e.values=n,e.W=o,e.w=l,n.lineleading=i.VALUES.lineleading,n.linebreakstyle="before",n.id=this.CHTMLnodeID,!0)}}),MathJax.Hub.Register.StartupHook("TeX mathchoice Ready",function(){t.TeXmathchoice.Augment({CHTMLbetterBreak:function(t,e){return this.Core().CHTMLbetterBreak(t,e)},CHTMLmoveLine:function(t,e,a,i,s){return this.Core().CHTMLmoveSlice(t,e,a,i,s)}})}),t.maction.Augment({CHTMLbetterBreak:function(t,e){return this.Core().CHTMLbetterBreak(t,e)},CHTMLmoveLine:function(t,e,a,i,s){return 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