/*
 *  /MathJax/jax/output/CommonHTML/jax.js
 *
 *  Copyright (c) 2009-2016 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.
 */

(function(j,c,f,h){var i;var g=MathJax.Object.isArray;var m,b,d;var e=1,q=0.1,k=0.025,a=0.025;var p={".mjx-chtml":{display:"inline-block","line-height":0,"text-indent":0,"text-align":"left","text-transform":"none","font-style":"normal","font-weight":"normal","font-size":"100%","font-size-adjust":"none","letter-spacing":"normal","word-wrap":"normal","word-spacing":"normal","white-space":"nowrap","float":"none",direction:"ltr","max-width":"none","max-height":"none","min-width":0,"min-height":0,border:0,margin:0,padding:"1px 0"},".MJXc-display":{display:"block","text-align":"center",margin:"1em 0",padding:0},".mjx-chtml[tabindex]:focus, body :focus .mjx-chtml[tabindex]":{display:"inline-table"},".mjx-full-width":{"text-align":"center",display:"table-cell!important",width:"10000em"},".mjx-math":{display:"inline-block","border-collapse":"separate","border-spacing":0,},".mjx-math *":{display:"inline-block","-webkit-box-sizing":"content-box!important","-moz-box-sizing":"content-box!important","box-sizing":"content-box!important","text-align":"left"},".mjx-numerator":{display:"block","text-align":"center"},".mjx-denominator":{display:"block","text-align":"center"},".MJXc-stacked":{height:0,position:"relative"},".MJXc-stacked > *":{position:"absolute"},".MJXc-bevelled > *":{display:"inline-block"},".mjx-stack":{display:"inline-block"},".mjx-op":{display:"block"},".mjx-under":{display:"table-cell"},".mjx-over":{display:"block"},".mjx-over > *":{"padding-left":"0px!important","padding-right":"0px!important"},".mjx-under > *":{"padding-left":"0px!important","padding-right":"0px!important"},".mjx-stack > .mjx-sup":{display:"block"},".mjx-stack > .mjx-sub":{display:"block"},".mjx-prestack > .mjx-presup":{display:"block"},".mjx-prestack > .mjx-presub":{display:"block"},".mjx-delim-h > .mjx-char":{display:"inline-block"},".mjx-surd":{"vertical-align":"top"},".mjx-mphantom *":{visibility:"hidden"},".mjx-merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"2px 3px","font-style":"normal","font-size":"90%"},".mjx-annotation-xml":{"line-height":"normal"},".mjx-menclose > svg":{fill:"none",stroke:"currentColor"},".mjx-mtr":{display:"table-row"},".mjx-mlabeledtr":{display:"table-row"},".mjx-mtd":{display:"table-cell","text-align":"center"},".mjx-label":{display:"table-row"},".mjx-box":{display:"inline-block"},".mjx-block":{display:"block"},".mjx-span":{display:"inline"},".mjx-char":{display:"block","white-space":"pre"},".mjx-itable":{display:"inline-table",width:"auto"},".mjx-row":{display:"table-row"},".mjx-cell":{display:"table-cell"},".mjx-table":{display:"table",width:"100%"},".mjx-line":{display:"block",height:0},".mjx-strut":{width:0,"padding-top":e+"em"},".mjx-vsize":{width:0},".MJXc-space1":{"margin-left":".167em"},".MJXc-space2":{"margin-left":".222em"},".MJXc-space3":{"margin-left":".278em"},".mjx-chartest":{display:"block",visibility:"hidden",position:"absolute",top:0,"line-height":"normal","font-size":"500%"},".mjx-chartest .mjx-char":{display:"inline"},".mjx-chartest .mjx-box":{"padding-top":"1000px"},".MJXc-processing":{visibility:"hidden",position:"fixed",width:0,height:0,overflow:"hidden"},".MJXc-processed":{display:"none"},".mjx-test":{display:"block","font-style":"normal","font-weight":"normal","font-size":"100%","font-size-adjust":"none","text-indent":0,"text-transform":"none","letter-spacing":"normal","word-spacing":"normal",overflow:"hidden",height:"1px"},".mjx-ex-box-test":{position:"absolute",width:"1px",height:"60ex"},".mjx-line-box-test":{display:"table!important"},".mjx-line-box-test span":{display:"table-cell!important",width:"10000em!important","min-width":0,"max-width":"none",padding:0,border:0,margin:0},"#MathJax_CHTML_Tooltip":{"background-color":"InfoBackground",color:"InfoText",border:"1px solid black","box-shadow":"2px 2px 5px #AAAAAA","-webkit-box-shadow":"2px 2px 5px #AAAAAA","-moz-box-shadow":"2px 2px 5px #AAAAAA","-khtml-box-shadow":"2px 2px 5px #AAAAAA",padding:"3px 4px","z-index":401,position:"absolute",left:0,top:0,width:"auto",height:"auto",display:"none"}};var n=1000000;var l={},o=MathJax.Hub.config;h.Augment({settings:c.config.menuSettings,config:{styles:p},Config:function(){if(!this.require){this.require=[]}this.SUPER(arguments).Config.call(this);var r=this.settings;if(r.scale){this.config.scale=r.scale}this.require.push(this.fontDir+"/TeX/fontdata.js");this.require.push(MathJax.OutputJax.extensionDir+"/MathEvents.js");l=this.config.linebreaks},Startup:function(){m=MathJax.Extension.MathEvents.Event;b=MathJax.Extension.MathEvents.Touch;d=MathJax.Extension.MathEvents.Hover;this.ContextMenu=m.ContextMenu;this.Mousedown=m.AltContextMenu;this.Mouseover=d.Mouseover;this.Mouseout=d.Mouseout;this.Mousemove=d.Mousemove;var r=h.addElement(document.body,"mjx-block",{style:{display:"block",width:"5in"}});this.pxPerInch=r.offsetWidth/5;r.parentNode.removeChild(r);this.TestSpan=h.Element("mjx-test",{style:{left:"1em"}},[["mjx-ex-box-test"]]);this.linebreakSpan=f.Element("span",{className:"mjx-line-box-test"},[["span"]]);return j.Styles(this.config.styles,["InitializeCHTML",this])},InitializeCHTML:function(){this.getDefaultExEm();if(this.defaultEm){return}var r=MathJax.Callback();j.timer.start(j,function(s){if(s.time(r)){c.signal.Post(["CommonHTML Jax - no default em size"]);return}h.getDefaultExEm();if(h.defaultEm){r()}else{setTimeout(s,s.delay)}},this.defaultEmDelay,this.defaultEmTimeout);return r},defaultEmDelay:100,defaultEmTimeout:1000,getDefaultExEm:function(){document.body.appendChild(this.TestSpan);document.body.appendChild(this.linebreakSpan);this.defaultEm=this.getFontSize(this.TestSpan);this.defaultEx=this.TestSpan.firstChild.offsetHeight/60;this.defaultWidth=this.linebreakSpan.firstChild.offsetWidth;document.body.removeChild(this.linebreakSpan);document.body.removeChild(this.TestSpan)},getFontSize:(window.getComputedStyle?function(s){var r=window.getComputedStyle(s);return parseFloat(r.fontSize)}:function(r){return r.style.pixelLeft}),getMaxWidth:(window.getComputedStyle?function(s){var r=window.getComputedStyle(s);if(r.maxWidth!=="none"){return parseFloat(r.maxWidth)}return 0}:function(s){var r=s.currentStyle.maxWidth;if(r!=="none"){if(r.match(/\d*px/)){return parseFloat(r)}var t=s.style.left;s.style.left=r;r=s.style.pixelLeft;s.style.left=t;return r}return 0}),loadFont:function(r){c.RestartAfter(j.Require(this.fontDir+"/"+r))},fontLoaded:function(r){if(!r.match(/-|fontdata/)){r+="-Regular"}if(!r.match(/\.js$/)){r+=".js"}MathJax.Callback.Queue(["Post",c.Startup.signal,["CommonHTML - font data loaded",r]],["loadComplete",j,this.fontDir+"/"+r])},Element:function(r,t,s){if(r.substr(0,4)==="mjx-"){if(!t){t={}}if(t.isMathJax==null){t.isMathJax=true}if(t.className){t.className=r+" "+t.className}else{t.className=r}r="span"}return this.HTMLElement(r,t,s)},addElement:function(t,r,u,s){return t.appendChild(this.Element(r,u,s))},HTMLElement:f.Element,ucMatch:f.ucMatch,setScript:f.setScript,getNode:function(v,u){var s=RegExp("\\b"+u+"\\b");while(v){for(var t=0,r=v.childNodes.length;t<r;t++){var w=v.childNodes[t];if(s.test(w.className)){return w}}v=(v.firstChild&&(v.firstChild.id||"")===""?v.firstChild:null)}return null},preTranslate:function(v){var u=v.jax[this.id],E,A=u.length,H,y,B,F,D,s,G,r;var x=100000,w=false,C=0,t=l.automatic,z=l.width;if(t){w=!!z.match(/^\s*(\d+(\.\d*)?%\s*)?container\s*$/);if(w){z=z.replace(/\s*container\s*/,"")}else{x=this.defaultWidth}if(z===""){z="100%"}}for(E=0;E<A;E++){H=u[E];if(!H.parentNode){continue}y=H.previousSibling;if(y&&y.className&&String(y.className).substr(0,9)==="mjx-chtml"){y.parentNode.removeChild(y)}if(H.MathJax.preview){H.MathJax.preview.style.display="none"}s=H.MathJax.elementJax;if(!s){continue}s.CHTML={display:(s.root.Get("display")==="block"),preview:(s.CHTML||{}).preview};B=h.Element("mjx-chtml",{id:s.inputID+"-Frame",className:"MathJax_CHTML",isMathJax:true,jaxID:this.id,oncontextmenu:m.Menu,onmousedown:m.Mousedown,onmouseover:m.Mouseover,onmouseout:m.Mouseout,onmousemove:m.Mousemove,onclick:m.Click,ondblclick:m.DblClick,onkeydown:m.Keydown,tabIndex:c.getTabOrder(s)});if(s.CHTML.display){var I=h.Element("mjx-chtml",{className:"MJXc-display",isMathJax:false});I.appendChild(B);B=I}if(c.Browser.noContextMenu){B.ontouchstart=b.start;B.ontouchend=b.end}B.className+=" MJXc-processing";H.parentNode.insertBefore(B,H);H.parentNode.insertBefore(this.linebreakSpan.cloneNode(true),H);H.parentNode.insertBefore(this.TestSpan.cloneNode(true),H)}for(E=0;E<A;E++){H=u[E];if(!H.parentNode){continue}F=H.previousSibling;s=H.MathJax.elementJax;if(!s){continue}r=h.getFontSize(F);G=F.firstChild.offsetHeight/60;C=Math.max(0,F.previousSibling.firstChild.offsetWidth-2);if(G===0||G==="NaN"){G=this.defaultEx;C=this.defaultWidth}if(w){x=C}scale=(this.config.matchFontHeight?G/this.TEX.x_height/r:1);scale=Math.floor(Math.max(this.config.minScaleAdjust/100,scale)*this.config.scale);s.CHTML.scale=scale/100;s.CHTML.fontSize=scale+"%";s.CHTML.outerEm=r;s.CHTML.em=this.em=r*scale/100;s.CHTML.ex=G;s.CHTML.cwidth=C/this.em;s.CHTML.lineWidth=(t?this.length2em(z,x/this.em,1):x)}for(E=0;E<A;E++){H=u[E];if(!H.parentNode){continue}F=H.previousSibling;D=F.previousSibling;s=H.MathJax.elementJax;if(!s){continue}D.parentNode.removeChild(D);F.parentNode.removeChild(F);if(H.MathJax.preview){H.MathJax.preview.style.display=""}}v.CHTMLeqn=v.CHTMLlast=0;v.CHTMLi=-1;v.CHTMLchunk=this.config.EqnChunk;v.CHTMLdelay=false},Translate:function(s,w){if(!s.parentNode){return}if(w.CHTMLdelay){w.CHTMLdelay=false;c.RestartAfter(MathJax.Callback.Delay(this.config.EqnChunkDelay))}var r=s.MathJax.elementJax,v=r.root,u=document.getElementById(r.inputID+"-Frame");if(!u){return}this.getMetrics(r);if(this.scale!==1){u.style.fontSize=r.CHTML.fontSize}this.initCHTML(v,u);this.savePreview(s);this.CHTMLnode=u;try{v.setTeXclass();v.toCommonHTML(u)}catch(t){while(u.firstChild){u.removeChild(u.firstChild)}delete this.CHTMLnode;this.restorePreview(s);throw t}delete this.CHTMLnode;this.restorePreview(s);if(r.CHTML.display){u=u.parentNode}u.className=u.className.replace(/ [^ ]+$/,"");u.className+=" MJXc-processed";if(s.MathJax.preview){r.CHTML.preview=s.MathJax.preview;delete s.MathJax.preview}w.CHTMLeqn+=(w.i-w.CHTMLi);w.CHTMLi=w.i;if(w.CHTMLeqn>=w.CHTMLlast+w.CHTMLchunk){this.postTranslate(w);w.CHTMLchunk=Math.floor(w.CHTMLchunk*this.config.EqnChunkFactor);w.CHTMLdelay=true}},initCHTML:function(s,r){},savePreview:function(r){var s=r.MathJax.preview;if(s&&s.parentNode){r.MathJax.tmpPreview=document.createElement("span");s.parentNode.replaceChild(r.MathJax.tmpPreview,s)}},restorePreview:function(r){var s=r.MathJax.tmpPreview;if(s){s.parentNode.replaceChild(r.MathJax.preview,s);delete r.MathJax.tmpPreview}},getMetrics:function(r){var s=r.CHTML;this.jax=r;this.em=s.em;this.outerEm=s.outerEm;this.scale=s.scale;this.cwidth=s.cwidth;this.linebreakWidth=s.lineWidth},postTranslate:function(w){var s=w.jax[this.id];for(var u=w.CHTMLlast,r=w.CHTMLeqn;u<r;u++){var t=s[u];if(t&&t.MathJax.elementJax){t.previousSibling.className=t.previousSibling.className.replace(/ [^ ]+$/,"");var v=t.MathJax.elementJax.CHTML;if(v.preview){v.preview.innerHTML="";v.preview.style.display="none";t.MathJax.preview=v.preview;delete v.preview}}}w.CHTMLlast=w.CHTMLeqn},getJaxFromMath:function(r){if(r.parentNode.className.match(/MJXc-display/)){r=r.parentNode}do{r=r.nextSibling}while(r&&r.nodeName.toLowerCase()!=="script");return c.getJaxFor(r)},getHoverSpan:function(r,s){return r.root.CHTMLnodeElement()},getHoverBBox:function(r,u,v){var w=r.root.CHTML,t=r.CHTML.outerEm;var s={w:w.w*t,h:w.h*t,d:w.d*t};if(w.width){s.width=w.width}return s},Zoom:function(t,A,z,r,x){this.getMetrics(t);var u=h.addElement(A,"mjx-chtml",{style:{"font-size":Math.floor(h.scale*100)+"%"},isMathJax:false});h.CHTMLnode=u;this.idPostfix="-zoom";t.root.toCommonHTML(u);this.idPostfix="";var s=u.style,B=t.root.CHTML;if(B.t>B.h){s.marginTop=h.Em(B.t-B.h)}if(B.b>B.d){s.marginBottom=h.Em(B.b-B.d)}if(B.l<0){s.paddingLeft=h.Em(-B.l)}if(B.r>B.w){s.marginRight=h.Em(B.r-B.w)}s.position="absolute";var y=u.offsetWidth,w=u.offsetHeight,C=z.firstChild.offsetHeight,v=z.firstChild.offsetWidth;u.style.position="";return{Y:-m.getBBox(A).h,mW:v,mH:C,zW:y,zH:w}},Remove:function(r){var s=document.getElementById(r.inputID+"-Frame");if(s&&r.CHTML.display){s=s.parentNode}if(s){s.parentNode.removeChild(s)}delete r.CHTML},ID:0,idPostfix:"",GetID:function(){this.ID++;return this.ID},MATHSPACE:{veryverythinmathspace:1/18,verythinmathspace:2/18,thinmathspace:3/18,mediummathspace:4/18,thickmathspace:5/18,verythickmathspace:6/18,veryverythickmathspace:7/18,negativeveryverythinmathspace:-1/18,negativeverythinmathspace:-2/18,negativethinmathspace:-3/18,negativemediummathspace:-4/18,negativethickmathspace:-5/18,negativeverythickmathspace:-6/18,negativeveryverythickmathspace:-7/18,thin:0.04,medium:0.06,thick:0.1,infinity:n},SPACECLASS:{thinmathspace:"MJXc-space1",mediummathspace:"MJXc-space2",thickmathspace:"MJXc-space3"},pxPerInch:96,em:16,maxStretchyParts:1000,FONTDEF:{},TEXDEF:{x_height:0.442,quad:1,num1:0.676508,num2:0.393732,num3:0.44373,denom1:0.685951,denom2:0.344841,sup1:0.412892,sup2:0.362892,sup3:0.288888,sub1:0.15,sub2:0.247217,sup_drop:0.386108,sub_drop:0.05,delim1:2.39,delim2:1,axis_height:0.25,rule_thickness:0.06,big_op_spacing1:0.111111,big_op_spacing2:0.166666,big_op_spacing3:0.2,big_op_spacing4:0.45,big_op_spacing5:0.1,surd_height:0.075,scriptspace:0.05,nulldelimiterspace:0.12,delimiterfactor:901,delimitershortfall:0.3,min_rule_thickness:1.25},unicodeChar:function(r){if(r<65535){return String.fromCharCode(r)}r-=65536;return String.fromCharCode((r>>10)+55296)+String.fromCharCode((r&1023)+56320)},getUnicode:function(r){var s=r.text.charCodeAt(r.i);r.i++;if(s>=55296&&s<56319){s=(((s-55296)<<10)+(r.text.charCodeAt(r.i)-56320))+65536;r.i++}return s},getCharList:function(v,u){var t,A,y=[],s=v.cache,D=u;if(s[u]){return s[u]}if(u>65535&&this.FONTDATA.RemapPlane1){var z=this.FONTDATA.RemapPlane1(u,v);u=z.n;v=z.variant}var r=this.FONTDATA.RANGES,C=this.FONTDATA.VARIANT;if(u>=r[0].low&&u<=r[r.length-1].high){for(t=0,A=r.length;t<A;t++){if(r[t].name==="alpha"&&v.noLowerCase){continue}var x=v["offset"+r[t].offset];if(x&&u>=r[t].low&&u<=r[t].high){if(r[t].remap&&r[t].remap[u]){u=x+r[t].remap[u]}else{u=u-r[t].low+x;if(r[t].add){u+=r[t].add}}if(v["variant"+r[t].offset]){v=C[v["variant"+r[t].offset]]}break}}}if(v.remap&&v.remap[u]){u=v.remap[u];if(v.remap.variant){v=C[v.remap.variant]}}else{if(this.FONTDATA.REMAP[u]&&!v.noRemap){u=this.FONTDATA.REMAP[u]}}if(g(u)){v=C[u[1]];u=u[0]}if(typeof(u)==="string"){var w={text:u,i:0,length:u.length};while(w.i<w.length){u=this.getUnicode(w);var B=this.getCharList(v,u);if(B){y.push.apply(y,B)}}}else{if(v.cache[u]){y=v.cache[u]}else{v.cache[u]=y=[this.lookupChar(v,u)]}}s[D]=y;return y},lookupChar:function(u,x){var w=u;while(u){for(var t=0,r=u.fonts.length;t<r;t++){var s=this.FONTDATA.FONTS[u.fonts[t]];if(typeof(s)==="string"){this.loadFont(s)}var v=s[x];if(v){if(v.length===5){v[5]={}}if(v.c==null){v[0]/=1000;v[1]/=1000;v[2]/=1000;v[3]/=1000;v[4]/=1000;v.c=this.unicodeChar(x)}if(v[5].space){return{type:"space",w:v[2],font:s}}return{type:"char",font:s,n:x}}else{if(s.Extra){this.findBlock(s,x)}}}u=this.FONTDATA.VARIANT[u.chain]}return this.unknownChar(w,x)},findBlock:function(t,x){var s=t.Extra,u=t.file,w;for(var v=0,r=s.length;v<r;v++){if(typeof(s[v])==="number"){if(x===s[v]){w=u;break}}else{if(x<s[v][0]){return}if(x<=s[v][1]){w=u;break}}}if(w){delete t.Extra;this.loadFont(u)}},unknownChar:function(r,u){c.signal.Post(["CommonHTML Jax - unknown char",u,r]);var t="";if(r.bold){t+="B"}if(r.italic){t+="I"}var s=this.FONTDATA.UNKNOWN[t||"R"];if(!s[u]){this.getUnknownChar(s,u)}return{type:"unknown",n:u,font:s}},getUnknownChar:function(s,u){var t=this.unicodeChar(u);var r=this.getHDW(t,s.className);s[u]=[0.8,0.2,r.w,0,r.w,{a:Math.max(0,(r.h-r.d)/2),h:r.h,d:r.d}];s[u].c=t},styledText:function(s,v){c.signal.Post(["CommonHTML Jax - styled 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s}},handleText:function(t,w,s,v){if(t.childNodes.length===0){h.addElement(t,"mjx-char");v=h.BBOX.empty(v)}if(typeof(s)==="string"){s=this.FONTDATA.VARIANT[s]}if(!s){s=this.FONTDATA.VARIANT[i.VARIANT.NORMAL]}var r={text:w,i:0,length:w.length},u=[];if(s.style&&r.length){u.push(this.styledText(s,w))}else{while(r.i<r.length){var x=this.getUnicode(r);u.push.apply(u,this.getCharList(s,x))}}if(u.length){this.addCharList(t.firstChild,u,v)}v.clean();if(v.d<0){v.D=v.d;v.d=0}if(v.h-v.a){t.firstChild.style[v.h-v.a<0?"marginTop":"paddingTop"]=this.EmRounded(v.h-v.a)}if(v.d>-v.b){t.firstChild.style.paddingBottom=this.EmRounded(v.d+v.b)}return v},createDelimiter:function(w,r,t,z,u){if(!r){var A=this.BBOX.zero();A.w=A.r=this.TEX.nulldelimiterspace;h.addElement(w,"mjx-box",{style:{width:A.w}});return A}if(!(t instanceof Array)){t=[t,t]}var y=t[1];t=t[0];var s={alias:r};while(s.alias){r=s.alias;s=this.FONTDATA.DELIMITERS[r];if(!s){s={HW:[0,this.FONTDATA.VARIANT[i.VARIANT.NORMAL]]}}}if(s.load){c.RestartAfter(j.Require(this.fontDir+"/TeX/fontdata-"+s.load+".js"))}for(var x=0,v=s.HW.length;x<v;x++){if(s.HW[x][0]>=t-0.01||(x==v-1&&!s.stretch)){if(s.HW[x][3]){r=s.HW[x][3]}A=this.createChar(w,[r,s.HW[x][1]],(s.HW[x][2]||1),u);A.offset=0.6*A.w;if(z){A.scale=z.scale;z.rscale=z.rscale}return A}}if(!s.stretch){return A}return this["extendDelimiter"+s.dir](w,y,s.stretch,z,u)},extendDelimiterV:function(D,w,O,v,B){D=h.addElement(D,"mjx-delim-v");var M=h.Element("span");var A,z,N,u,G,s,E,x,F=1,L;G=this.createChar(M,(O.top||O.ext),1,B);A=M.removeChild(M.firstChild);s=this.createChar(M,(O.bot||O.ext),1,B);z=M.removeChild(M.firstChild);E=x=h.BBOX.zero();var 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r=h.BBOX({w:Math.max(G.w,x.w,s.w,E.w),l:Math.min(G.l,x.l,s.l,E.l),r:Math.max(G.r,x.r,s.r,E.r),h:w-s.d,d:s.d,t:w-s.d,b:s.d});r.offset=0.5*r.w;if(v){r.scale=v.scale;r.rscale=v.rscale}return r},extendDelimiterH:function(E,r,O,u,C){E=h.addElement(E,"mjx-delim-h");var M=h.Element("span");var s,L,N,t,J,B,v,F,y,G=1;B=this.createChar(M,(O.left||O.rep),1,C);s=M.removeChild(M.firstChild);v=this.createChar(M,(O.right||O.rep),1,C);L=M.removeChild(M.firstChild);y=this.createChar(M,O.rep,1,C);t=M.removeChild(M.firstChild);s.style.marginLeft=h.Em(-B.l);L.style.marginRight=h.Em(v.r-v.w);E.appendChild(s);var P=h.BBOX.zero();P.h=Math.max(B.h,v.h,y.h);P.d=Math.max(B.D||B.d,v.D||v.d,y.D||y.d);var x=(B.r-B.l)+(v.r-v.l)-q;if(O.mid){F=this.createChar(M,O.mid,1,C);N=M.removeChild(M.firstChild);N.style.marginleft=h.Em(-F.l);N.style.marginRight=h.Em(F.r-F.w);x+=F.r-F.l+q;G=2;if(F.h>P.h){P.h=F.h}if(F.d>P.d){P.d=F.d}}if(O.min&&r<x*O.min){r=x*O.min}P.w=P.r=r;if(r>x){var A=y.r-y.l,I=A-q;var 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r=this.Core();if(r&&r!==this){s=r.CHTMLcanStretch(v,t,u)}}this.CHTML.stretch=s;return s},CHTMLstretchV:function(r,s){this.CHTML.updateFrom(this.Core().CHTMLstretchV(r,s));return this.CHTML},CHTMLstretchH:function(s,r){this.CHTML.updateFrom(this.CHTMLstretchCoreH(s,r));return this.CHTML},CHTMLstretchCoreH:function(s,r){return this.Core().CHTMLstretchH(this.CHTMLcoreNode(s),r)},CHTMLcreateNode:function(r){if(!this.CHTML){this.CHTML={}}this.CHTML=h.BBOX.zero();if(this.href){r=h.addElement(r,"a",{href:this.href,isMathJax:true})}if(!this.CHTMLnodeID){this.CHTMLnodeID=h.GetID()}var s=(this.id||"MJXc-Node-"+this.CHTMLnodeID)+h.idPostfix;return this.CHTMLhandleAttributes(h.addElement(r,"mjx-"+this.type,{id:s}))},CHTMLnodeElement:function(){if(!this.CHTMLnodeID){return null}return document.getElementById((this.id||"MJXc-Node-"+this.CHTMLnodeID)+h.idPostfix)},CHTMLlength2em:function(s,r){return h.length2em(s,r,this.CHTML.scale)},CHTMLhandleAttributes:function(u){if(this["class"]){if(u.className){u.className+=" "+this["class"]}else{u.className=this["class"]}}if(this.attrNames){var y=this.attrNames,t=i.nocopyAttributes,x=c.config.ignoreMMLattributes;var v=(this.type==="mstyle"?i.math.prototype.defaults:this.defaults);for(var s=0,r=y.length;s<r;s++){var w=y[s];if(x[w]==false||(!t[w]&&!x[w]&&v[w]==null&&typeof(u[w])==="undefined")){u.setAttribute(w,this.attr[w])}}}return u},CHTMLhandleScale:function(u){var w=1,t=this.parent,v=(t?t.CHTML.scale:1);var r=this.getValues("scriptlevel","fontsize");r.mathsize=this.Get("mathsize",null,!this.isToken);if(r.scriptlevel!==0){if(r.scriptlevel>2){r.scriptlevel=2}w=Math.pow(this.Get("scriptsizemultiplier"),r.scriptlevel);r.scriptminsize=h.length2em(this.Get("scriptminsize"),0.8,1);if(w<r.scriptminsize){w=r.scriptminsize}}if(this.removedStyles&&this.removedStyles.fontSize&&!r.fontsize){r.fontsize=this.removedStyles.fontSize}if(r.fontsize&&!this.mathsize){r.mathsize=r.fontsize}if(r.mathsize!==1){w*=h.length2em(r.mathsize,1,1)}var s=this.CHTMLvariant;if(s&&s.style&&s.style["font-family"]){w*=(h.config.scale/100)/h.scale}this.CHTML.scale=w;v=this.CHTML.rscale=w/v;if(Math.abs(v-1)<0.001){v=1}if(u&&v!==1){u.style.fontSize=h.Percent(v)}return w},CHTMLhandleStyle:function(u){if(!this.style){return}var t=u.style;t.cssText=this.style;this.removedStyles={};for(var s=0,r=h.removeStyles.length;s<r;s++){var v=h.removeStyles[s];if(t[v]){this.removedStyles[v]=t[v];t[v]=""}}},CHTMLhandleBBox:function(v){var s=this.CHTML,u=v.style;if(this.data.length===1&&(this.data[0].CHTML||{}).pwidth){s.pwidth=this.data[0].CHTML.pwidth;s.mwidth=this.data[0].CHTML.mwidth;u.width="100%"}else{if(s.pwidth){s.mwidth=h.Em(s.w);u.width="100%"}else{if(s.w<0){u.width="0px";u.marginRight=h.Em(s.w)}}}if(!this.style){return}for(var t=0,r=h.BBOX.styleAdjust.length;t<r;t++){var w=h.BBOX.styleAdjust[t];if(w&&u[w[0]]){s.adjust(u[w[0]],w[1],w[2],w[3])}}},CHTMLhandleColor:function(r){if(this.mathcolor){r.style.color=this.mathcolor}else{if(this.color){r.style.color=this.color}}if(this.mathbackground){r.style.backgroundColor=this.mathbackground}else{if(this.background){r.style.backgroundColor=this.background}}},CHTMLhandleSpace:function(r){if(!this.useMMLspacing){var s=this.texSpacing();if(s!==""){this.CHTML.L=this.CHTMLlength2em(s);r.className+=" 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s=r.mathvariant;if(this.variantForm){s="-TeX-variant"}if(r.family&&!r.hasVariant){if(!r.weight&&r.mathvariant.match(/bold/)){r.weight="bold"}if(!r.style&&r.mathvariant.match(/italic/)){r.style="italic"}this.CHTMLvariant={fonts:[],noRemap:true,cache:{},style:{"font-family":r.family,"font-weight":r.weight||"normal","font-style":r.style||"normal"}};return}if(r.weight==="bold"){s={normal:i.VARIANT.BOLD,italic:i.VARIANT.BOLDITALIC,fraktur:i.VARIANT.BOLDFRAKTUR,script:i.VARIANT.BOLDSCRIPT,"sans-serif":i.VARIANT.BOLDSANSSERIF,"sans-serif-italic":i.VARIANT.SANSSERIFBOLDITALIC}[s]||s}else{if(r.weight==="normal"){s={bold:i.VARIANT.normal,"bold-italic":i.VARIANT.ITALIC,"bold-fraktur":i.VARIANT.FRAKTUR,"bold-script":i.VARIANT.SCRIPT,"bold-sans-serif":i.VARIANT.SANSSERIF,"sans-serif-bold-italic":i.VARIANT.SANSSERIFITALIC}[s]||s}}if(r.style==="italic"){s={normal:i.VARIANT.ITALIC,bold:i.VARIANT.BOLDITALIC,"sans-serif":i.VARIANT.SANSSERIFITALIC,"bold-sans-serif":i.VARIANT.SANSSERIFBOLDITALIC}[s]||s}else{if(r.style==="normal"){s={italic:i.VARIANT.NORMAL,"bold-italic":i.VARIANT.BOLD,"sans-serif-italic":i.VARIANT.SANSSERIF,"sans-serif-bold-italic":i.VARIANT.BOLDSANSSERIF}[s]||s}}this.CHTMLvariant=h.FONTDATA.VARIANT[s]||h.FONTDATA.VARIANT[i.VARIANT.NORMAL]},CHTMLbboxFor:function(r){if(this.data[r]&&this.data[r].CHTML){return this.data[r].CHTML}return h.BBOX.zero()},CHTMLdrawBBox:function(s,t){if(!t){t=this.CHTML}var r=h.Element("mjx-box",{style:{opacity:0.25,"margin-left":h.Em(-(t.w+(t.R||0)))}},[["mjx-box",{style:{height:h.Em(t.h),width:h.Em(t.w),"background-color":"red"}}],["mjx-box",{style:{height:h.Em(t.d),width:h.Em(t.w),"margin-left":h.Em(-t.w),"vertical-align":h.Em(-t.d),"background-color":"green"}}]]);if(s.nextSibling){s.parentNode.insertBefore(r,s.nextSibling)}else{s.parentNode.appendChild(r)}},CHTMLnotEmpty:function(r){while(r&&r.data.length<2&&(r.type==="mrow"||r.type==="texatom")){r=r.data[0]}return !!r}},{CHTMLautoload:function(){var r=h.autoloadDir+"/"+this.type+".js";c.RestartAfter(j.Require(r))},CHTMLautoloadFile:function(r){var s=h.autoloadDir+"/"+r+".js";c.RestartAfter(j.Require(s))},CHTMLstretchV:function(r,s){this.Core().CHTMLstretchV(r,s);this.toCommonHTML(this.CHTMLnodeElement(),{stretch:true});return this.CHTML},CHTMLstretchH:function(s,r){this.CHTMLstretchCoreH(s,r);this.toCommonHTML(s,{stretch:true});return this.CHTML}});i.chars.Augment({toCommonHTML:function(s,r){if(r==null){r={}}var t=this.toString();if(r.remap){t=r.remap(t,r.remapchars)}this.CHTMLhandleText(s,t,r.variant||this.parent.CHTMLvariant)}});i.entity.Augment({toCommonHTML:function(s,r){if(r==null){r={}}var t=this.toString();if(r.remapchars){t=r.remap(t,r.remapchars)}this.CHTMLhandleText(s,t,r.variant||this.parent.CHTMLvariant)}});i.math.Augment({toCommonHTML:function(w){w=this.CHTMLdefaultNode(w);if(this.CHTML.w<0){w.parentNode.style.width="0px";w.parentNode.style.marginRight=h.Em(this.CHTML.w)}var u=this.Get("alttext");if(u&&!w.getAttribute("aria-label")){w.setAttribute("aria-label",u)}if(this.CHTML.pwidth){w.parentNode.style.minWidth=this.CHTML.mwidth||h.Em(this.CHTML.w);w.parentNode.className="mjx-full-width 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t=this.CHTML,s=this.data.join("");if(t.skew!=null&&s.length!==1){delete t.skew}if(t.r>t.w&&s.length===1&&!this.CHTMLvariant.noIC){t.ic=t.r-t.w;t.w=t.r;r.lastChild.style.paddingRight=h.Em(t.ic)}return r}});i.mn.Augment({CHTMLremapMinus:function(r){return r.replace(/^-/,"\u2212")},toCommonHTML:function(r){r=this.CHTMLdefaultNode(r,{childOptions:{remap:this.CHTMLremapMinus}});var t=this.CHTML,s=this.data.join("");if(t.skew!=null&&s.length!==1){delete t.skew}if(t.r>t.w&&s.length===1&&!this.CHTMLvariant.noIC){t.ic=t.r-t.w;t.w=t.r;r.lastChild.style.paddingRight=h.Em(t.ic)}return r}});i.mo.Augment({toCommonHTML:function(u){u=this.CHTMLcreateNode(u);this.CHTMLhandleStyle(u);this.CHTMLgetVariant();this.CHTMLhandleScale(u);h.BBOX.empty(this.CHTML);var s=this.getValues("displaystyle","largeop");s.variant=this.CHTMLvariant;s.text=this.data.join("");if(s.text==""){if(this.fence){u.style.width=h.Em(h.TEX.nulldelimiterspace)}}else{this.CHTMLadjustAccent(s);this.CHTMLadjustVariant(s);for(var t=0,r=this.data.length;t<r;t++){this.CHTMLaddChild(u,t,{childOptions:{variant:s.mathvariant,remap:this.remap,remapchars:s.remapchars}})}if(s.text.length!==1){delete this.CHTML.skew}else{if(this.CHTML.w===0&&this.CHTML.l<0){this.CHTMLfixCombiningChar(u)}}if(s.largeop){this.CHTMLcenterOp(u)}}this.CHTML.clean();this.CHTMLhandleBBox(u);this.CHTMLhandleSpace(u);this.CHTMLhandleColor(u);return u},CHTMLhandleSpace:function(u){if(this.useMMLspacing){var s=this.getValues("scriptlevel","lspace","rspace");s.lspace=Math.max(0,this.CHTMLlength2em(s.lspace));s.rspace=Math.max(0,this.CHTMLlength2em(s.rspace));if(s.scriptlevel>0){if(!this.hasValue("lspace")){s.lspace=0.15}if(!this.hasValue("rspace")){s.rspace=0.15}}var r=this,t=this.Parent();while(t&&t.isEmbellished()&&t.Core()===r){r=t;t=t.Parent();u=r.CHTMLnodeElement()}if(s.lspace){u.style.paddingLeft=h.Em(s.lspace)}if(s.rspace){u.style.paddingRight=h.Em(s.rspace)}this.CHTML.L=s.lspace;this.CHTML.R=s.rspace}else{this.SUPER(arguments).CHTMLhandleSpace.apply(this,arguments)}},CHTMLadjustAccent:function(t){var s=this.CoreParent();t.parent=s;if(t.text.length===1&&s&&s.isa(i.munderover)&&this.CoreText(s.data[s.base]).length===1){var u=s.data[s.over],r=s.data[s.under];if(u&&this===u.CoreMO()&&s.Get("accent")){t.remapchars=h.FONTDATA.REMAPACCENT}else{if(r&&this===r.CoreMO()&&s.Get("accentunder")){t.remapchars=h.FONTDATA.REMAPACCENTUNDER}}}},CHTMLadjustVariant:function(s){var r=s.parent,t=(r&&r.isa(i.msubsup)&&this!==r.data[r.base]);if(s.largeop){s.mathvariant=(s.displaystyle?"-largeOp":"-smallOp")}if(t){s.remapchars=this.remapChars;if(s.text.match(/['`"\u00B4\u2032-\u2037\u2057]/)){s.mathvariant="-TeX-variant"}}},CHTMLfixCombiningChar:function(r){r=r.firstChild;var s=h.Element("mjx-box",{style:{width:".25em","margin-left":"-.25em"}});r.insertBefore(s,r.firstChild)},CHTMLcenterOp:function(r){var t=this.CHTML;var s=(t.h-t.d)/2-h.TEX.axis_height;if(Math.abs(s)>0.001){r.style.verticalAlign=h.Em(-s)}t.h-=s;t.d+=s;if(t.r>t.w){t.ic=t.r-t.w;t.w=t.r;r.style.paddingRight=h.Em(t.ic)}},CHTMLcanStretch:function(v,t,u){if(!this.Get("stretchy")){return false}var w=this.data.join("");if(w.length!==1){return false}var s={text:w};this.CHTMLadjustAccent(s);if(s.remapchars){w=s.remapchars[w]||w}w=h.FONTDATA.DELIMITERS[w.charCodeAt(0)];var r=(w&&w.dir===v.substr(0,1));if(r){r=(this.CHTML.h!==t||this.CHTML.d!==u||!!this.Get("minsize",true)||!!this.Get("maxsize",true));if(r){this.CHTML.stretch=true}}return r},CHTMLstretchV:function(u,x){var v=this.CHTMLnodeElement(),w=this.CHTML;var s=this.getValues("symmetric","maxsize","minsize");var t,r=h.TEX.axis_height;if(s.symmetric){t=2*Math.max(u-r,x+r)}else{t=u+x}s.maxsize=this.CHTMLlength2em(s.maxsize,w.h+w.d);s.minsize=this.CHTMLlength2em(s.minsize,w.h+w.d);t=Math.max(s.minsize,Math.min(s.maxsize,t));if(t!==w.sH){if(t!=s.minsize){t=[Math.max(t*h.TEX.delimiterfactor/1000,t-h.TEX.delimitershortfall),t]}while(v.firstChild){v.removeChild(v.firstChild)}this.CHTML=w=h.createDelimiter(v,this.data.join("").charCodeAt(0),t,w);w.sH=(t instanceof Array?t[1]:t);if(s.symmetric){t=(w.h+w.d)/2+r}else{t=(w.h+w.d)*u/(u+x)}t-=w.h;if(Math.abs(t)>0.05){v.style.verticalAlign=h.Em(t);w.h+=t;w.d-=t;w.t+=t;w.b-=t}}return this.CHTML},CHTMLstretchH:function(t,r){var u=this.CHTML;var s=this.getValues("maxsize","minsize","mathvariant","fontweight");if((s.fontweight==="bold"||(this.removedStyles||{}).fontWeight==="bold"||parseInt(s.fontweight)>=600)&&!this.Get("mathvariant",true)){s.mathvariant=i.VARIANT.BOLD}s.maxsize=this.CHTMLlength2em(s.maxsize,u.w);s.minsize=this.CHTMLlength2em(s.minsize,u.w);r=Math.max(s.minsize,Math.min(s.maxsize,r));if(r!==u.sW){while(t.firstChild){t.removeChild(t.firstChild)}this.CHTML=u=h.createDelimiter(t,this.data.join("").charCodeAt(0),r,u,s.mathvariant);u.sW=r}return this.CHTML}});i.mtext.Augment({CHTMLgetVariant:function(){if(h.config.mtextFontInherit||this.Parent().type==="merror"){var t=(h.config.scale/100)/h.scale;var s={cache:{},fonts:[],className:"MJXc-font-inherit",rscale:t,style:{"font-size":h.Percent(t)}};var r=this.Get("mathvariant");if(r.match(/bold/)){s.style["font-weight"]="bold"}if(r.match(/italic|-tex-mathit/)){s.style["font-style"]="italic"}if(r==="monospace"){s.className+=" 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v=this.CHTML;v.w=v.r=r;v.h=v.t=t;v.d=v.b=x;v.l=0;if(r<0){u.style.marginRight=h.Em(r);r=0}u.style.width=h.Em(r);u.style.height=h.Em(Math.max(0,t+x));if(x){u.style.verticalAlign=h.Em(-x)}this.CHTMLhandleBBox(u);this.CHTMLhandleColor(u);return u}});i.mpadded.Augment({toCommonHTML:function(s,E){var r;if(E&&E.stretch){s=s.firstChild;r=s.firstChild}else{s=this.CHTMLdefaultNode(s,{childNodes:"mjx-box",forceChild:true});r=s.firstChild;s=h.addElement(s,"mjx-block");s.appendChild(r);h.addElement(s,"mjx-strut")}var v=this.CHTMLbboxFor(0);var C=this.getValues("width","height","depth","lspace","voffset");var A=0,z=0,B=v.w,t=v.h,u=v.d;r.style.width=0;r.style.margin=h.Em(-t)+" 0 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u}});i.munderover.Augment({toCommonHTML:function(v,F){var D=this.getValues("displaystyle","accent","accentunder","align");var t=this.data[this.base];if(!D.displaystyle&&t!=null&&(t.movablelimits||t.CoreMO().Get("movablelimits"))){return i.msubsup.prototype.toCommonHTML.call(this,v,s)}var A,y,r=[],s=false;if(F&&F.stretch){if(this.data[this.base]){t=h.getNode(v,"mjx-op")}if(this.data[this.under]){A=h.getNode(v,"mjx-under")}if(this.data[this.over]){y=h.getNode(v,"mjx-over")}r[0]=t;r[1]=A||y;r[2]=y;s=true}else{var x=["mjx-op","mjx-under","mjx-over"];if(this.over===1){x[1]=x[2]}v=this.CHTMLdefaultNode(v,{childNodes:x,noBBox:true,forceChild:true,minChildren:2});r[0]=t=v.removeChild(v.firstChild);r[1]=A=y=v.removeChild(v.firstChild);if(v.firstChild){r[2]=y=v.removeChild(v.firstChild)}}var w=[],u=this.CHTMLgetBBoxes(w,r,D);var E=w[this.base],B=this.CHTML;B.w=u;B.h=E.h;B.d=E.d;var z=t,C=0;if(E.ic){C=1.3*E.ic+0.05}if(this.data[this.over]){z=this.CHTMLaddOverscript(y,w,D,C,t,s)}if(this.data[this.under]){this.CHTMLaddUnderscript(A,w,D,C,v,z,s)}else{if(!s){v.appendChild(z)}}this.CHTMLplaceBoxes(t,A,y,D,w);return v},CHTMLgetBBoxes:function(z,v,u){var x,s=this.data.length,y,t=-n,r=t;for(x=0;x<s;x++){z[x]=this.CHTMLbboxFor(x);z[x].x=z[x].y=0;if(this.data[x]){z[x].stretch=this.data[x].CHTMLcanStretch("Horizontal")}y=(x===this.base?1:z[x].rscale);if(x!==this.base){delete z[x].L;delete z[x].R}r=Math.max(r,y*(z[x].w+(z[x].L||0)+(z[x].R||0)));if(!z[x].stretch&&r>t){t=r}}if(t===-n){t=r}for(x=0;x<s;x++){if(z[x].stretch){y=(x===this.base?1:z[x].rscale);z[x]=this.data[x].CHTMLstretchH(v[x].firstChild,t/y);z[x].x=z[x].y=0;r=Math.max(r,y*(z[x].w+(z[x].L||0)+(z[x].R||0)))}}if(!z[this.base]){z[this.base]=h.BBOX.empty()}return r},CHTMLaddOverscript:function(A,y,E,D,s,r){var C=this.CHTML;var x,w,v=h.TEX.big_op_spacing5,u;var z=y[this.over],F=y[this.base],t=z.rscale;if(!r){var B=h.Element("mjx-stack");B.appendChild(A);B.appendChild(s)}if(z.D){z.d=z.D}if(z.d<0){A.firstChild.style.verticalAlign="top";A.style.height=h.Em(z.h+z.d)}z.x=0;if(E.accent){if(z.w<0.001){z.x+=(z.r-z.l)/2}u=h.TEX.rule_thickness;v=0;if(F.skew){z.x+=t*F.skew;C.skew=t*F.skew;if(z.x+t*z.w>C.w){C.skew+=(C.w-(z.x+t*z.w))/2}}}else{x=h.TEX.big_op_spacing1;w=h.TEX.big_op_spacing3;u=Math.max(x,w-Math.max(0,t*z.d))}z.x+=D/2;z.y=C.h+u+v+t*z.d;if(u){A.style.paddingBottom=h.Em(u/t)}if(v){A.style.paddingTop=h.Em(v/t)}return B},CHTMLaddUnderscript:function(A,y,D,C,s,z,r){var B=this.CHTML;var x,w,v=h.TEX.big_op_spacing5,u;var E=y[this.under],t=E.rscale;if(!r){h.addElement(s,"mjx-itable",{},[["mjx-row",{},[["mjx-cell"]]],["mjx-row"]]);s.firstChild.firstChild.firstChild.appendChild(z);s.firstChild.lastChild.appendChild(A)}if(E.D){E.d=E.D}if(E.d<0){A.firstChild.style.verticalAlign="top";s.firstChild.style.marginBottom=h.Em(E.d)}if(D.accentunder){u=2*h.TEX.rule_thickness;v=0}else{x=h.TEX.big_op_spacing2;w=h.TEX.big_op_spacing4;u=Math.max(x,w-t*E.h)}E.x=-C/2;E.y=-(B.d+u+v+t*E.h);if(u){A.style.paddingTop=h.Em(u/t)}if(v){A.style.paddingBottom=h.Em(v/t)}},CHTMLplaceBoxes:function(r,A,z,D,y){var s=this.CHTML.w,x,u=y.length,v;var C=h.BBOX.zero();C.scale=this.CHTML.scale;C.rscale=this.CHTML.rscale;y[this.base].x=y[this.base].y=0;var E=n;for(x=0;x<u;x++){v=(x===this.base?1:y[x].rscale);var B=v*(y[x].w+(y[x].L||0)+(y[x].R||0));y[x].x+={left:0,center:(s-B)/2,right:s-B}[D.align];if(y[x].x<E){E=y[x].x}}for(x=0;x<u;x++){if(this.data[x]){v=(x===this.base?1:y[x].rscale);if(y[x].x-E){var t=(x===this.base?r:x===this.over?z:A);t.style.paddingLeft=h.Em((y[x].x-E)/v)}C.combine(y[x],y[x].x-E,y[x].y)}}this.CHTML=C},CHTMLstretchV:i.mbase.CHTMLstretchV,CHTMLstretchH:i.mbase.CHTMLstretchH,CHTMLchildNode:function(t,s){var r=["mjx-op","mjx-under","mjx-over"];if(this.over===1){r[1]=r[2]}return h.getNode(t,r[s])}});i.msubsup.Augment({toCommonHTML:function(S,C){var A=this.getValues("displaystyle","subscriptshift","superscriptshift","texprimestyle");var D,H,z;if(C&&C.stretch){if(this.data[this.base]){D=h.getNode(S,"mjx-base")}if(this.data[this.sub]){H=h.getNode(S,"mjx-sub")}if(this.data[this.sup]){z=h.getNode(S,"mjx-sup")}E=h.getNode(S,"mjx-stack")}else{var K=["mjx-base","mjx-sub","mjx-sup"];if(this.sup===1){K[1]=K[2]}S=this.CHTMLdefaultNode(S,{childNodes:K,noBBox:true,forceChild:true,minChildren:3});D=S.childNodes[this.base];H=S.childNodes[this.sub];z=S.childNodes[this.sup];if(!this.CHTMLnotEmpty(this.data[this.sub])){S.removeChild(H);H=null}if(!this.CHTMLnotEmpty(this.data[this.sup])){S.removeChild(z);z=null}if(S.childNodes.length===3){var E=h.addElement(S,"mjx-stack");E.appendChild(z);E.appendChild(H)}}var F=[],G=h.BBOX.empty(this.CHTML);for(var V=0,T=this.data.length;V<T;V++){F[V]=this.CHTMLbboxFor(V)}var y=F[this.base]||h.BBOX.empty(),P=F[this.sub],W=F[this.sup];var B=(H?P.rscale:1),w=(z?W.rscale:1);G.combine(y,0,0);var X=h.TEX.x_height,N=h.TEX.scriptspace;var Q=h.TEX.sup_drop*w,O=h.TEX.sub_drop*B;var L=y.h-Q,J=y.d+O,Y=0,R;if(y.ic){G.w-=y.ic;D.style.marginRight=h.Em(-y.ic);Y=1.3*y.ic+0.05}var U=this.data[this.base];if(U){if((U.type==="mrow"||U.type==="mstyle")&&U.data.length===1){U=U.data[0]}if(U.type==="mi"||U.type==="mo"){if(U.data.join("").length===1&&y.rscale===1&&!y.sH&&!U.Get("largeop")){L=J=0}}}A.subscriptshift=(A.subscriptshift===""?0:this.CHTMLlength2em(A.subscriptshift));A.superscriptshift=(A.superscriptshift===""?0:this.CHTMLlength2em(A.superscriptshift));var I=G.w;if(H){P.w+=N}if(z){W.w+=N}if(!z){if(H){J=Math.max(J,h.TEX.sub1,B*P.h-(4/5)*X,A.subscriptshift);H.style.verticalAlign=h.Em(-J/B);H.style.paddingRight=h.Em(N/B);G.combine(P,I,-J)}}else{if(!H){R=h.TEX[(A.displaystyle?"sup1":(A.texprimestyle?"sup3":"sup2"))];L=Math.max(L,R,w*W.d+(1/4)*X,A.superscriptshift);z.style.verticalAlign=h.Em(L/w);z.style.paddingLeft=h.Em(Y/w);z.style.paddingRight=h.Em(N/w);G.combine(W,I+Y,L)}else{J=Math.max(J,h.TEX.sub2);var M=h.TEX.rule_thickness;if((L-w*W.d)-(B*P.h-J)<3*M){J=3*M-L+w*W.d+B*P.h;Q=(4/5)*X-(L-w*W.d);if(Q>0){L+=Q;J-=Q}}L=Math.max(L,A.superscriptshift);J=Math.max(J,A.subscriptshift);H.style.paddingRight=h.Em(N/B);z.style.paddingBottom=h.Em(L/w+J/B-W.d-P.h/B*w);z.style.paddingLeft=h.Em(Y/w);z.style.paddingRight=h.Em(N/w);E.style.verticalAlign=h.Em(-J);G.combine(W,I+Y,L);G.combine(P,I,-J)}}G.clean();return S},CHTMLstretchV:i.mbase.CHTMLstretchV,CHTMLstretchH:i.mbase.CHTMLstretchH,CHTMLchildNode:function(t,s){var r=["mjx-base","mjx-sub","mjx-sup"];if(this.over===1){r[1]=r[2]}return h.getNode(t,r[s])}});i.mfrac.Augment({toCommonHTML:function(M){M=this.CHTMLdefaultNode(M,{childNodes:["mjx-numerator","mjx-denominator"],childOptions:{autowidth:true},forceChild:true,noBBox:true,minChildren:2});var w=this.getValues("linethickness","displaystyle","numalign","denomalign","bevelled");var N=w.displaystyle;var C=M.firstChild,s=M.lastChild;var x=h.addElement(M,"mjx-box");x.appendChild(C);x.appendChild(s);M.appendChild(x);if(w.numalign!=="center"){C.style.textAlign=w.numalign}if(w.denomalign!=="center"){s.style.textAlign=w.denomalign}var O=this.CHTMLbboxFor(0),A=this.CHTMLbboxFor(1),B=h.BBOX.empty(this.CHTML),E=O.rscale,y=A.rscale;w.linethickness=Math.max(0,h.thickness2em(w.linethickness||"0",B.scale));var L=h.TEX.min_rule_thickness/h.em,S=h.TEX.axis_height;var I=w.linethickness,K,J,G,F;if(w.bevelled){x.className+=" MJXc-bevelled";var R=(N?0.4:0.15);var D=Math.max(E*(O.h+O.d),y*(A.h+A.d))+2*R;var Q=h.Element("mjx-bevel");x.insertBefore(Q,s);var r=h.createDelimiter(Q,47,D);G=E*(O.d-O.h)/2+S+R;F=y*(A.d-A.h)/2+S-R;if(G){C.style.verticalAlign=h.Em(G/E)}if(F){s.style.verticalAlign=h.Em(F/y)}Q.style.marginLeft=Q.style.marginRight=h.Em(-R/2);B.combine(O,0,G);B.combine(r,E*O.w-R/2,0);B.combine(A,E*O.w+r.w-R,F);B.clean()}else{x.className+=" MJXc-stacked";if(N){G=h.TEX.num1;F=h.TEX.denom1}else{G=(I===0?h.TEX.num3:h.TEX.num2);F=h.TEX.denom2}if(I===0){K=Math.max((N?7:3)*h.TEX.rule_thickness,2*L);J=(G-O.d*E)-(A.h*y-F);if(J<K){G+=(K-J)/2;F+=(K-J)/2}}else{K=Math.max((N?2:0)*L+I,I/2+1.5*L);I=Math.max(I,L);J=(G-O.d*E)-(S+I/2);if(J<K){G+=(K-J)}J=(S-I/2)-(A.h*y-F);if(J<K){F+=(K-J)}O.L=O.R=A.L=A.R=0.1;var z=h.addElement(x,"mjx-line",{style:{"border-bottom":h.Px(I*B.scale,1)+" solid",top:h.Em(-I/2-S)}})}B.combine(O,0,G);B.combine(A,0,-F);B.clean();x.style.width=h.Em(B.w);C.style.width=h.Em(B.w/E);s.style.width=h.Em(B.w/y);if(z){z.style.width=x.style.width}C.style.top=h.Em(-B.h/E);s.style.bottom=h.Em(-B.d/y);h.addElement(M,"mjx-vsize",{style:{height:h.Em(B.h+B.d),verticalAlign:h.Em(-B.d)}})}if(!this.texWithDelims&&!this.useMMLspacing){var P=h.TEX.nulldelimiterspace;x.style.padding="0 "+h.Em(P);B.l+=P;B.r+=P;B.w+=2*P}return M},CHTMLcanStretch:function(r){return false}});i.msqrt.Augment({toCommonHTML:function(v){v=this.CHTMLdefaultNode(v,{childNodes:["mjx-box","mjx-root"],forceChild:true,noBBox:true});var u=v.firstChild||h.Element("mjx-box");var D=h.addElement(v,"mjx-box");D.appendChild(u);var E=this.CHTMLbboxFor(0),B=h.BBOX.empty(this.CHTML);var F=h.TEX.rule_thickness,w=h.TEX.surd_height,s=F,r,C;if(this.Get("displaystyle")){s=h.TEX.x_height}r=F+s/4;C=E.h+E.d+r+F;var y=h.Element("mjx-surd");D.insertBefore(y,u);var z=h.createDelimiter(y,8730,[C-0.04,C]);if(z.h+z.d>C){r=((z.h+z.d)-(C-F))/2}C=E.h+r+F;var A=this.CHTMLaddRoot(v,z,z.h+z.d-C);u.style.paddingTop=h.Em(r);u.style.borderTop=h.Px(w*E.scale,1)+" solid";D.style.paddingTop=h.Em(2*F-w);E.h+=r+2*F;B.combine(z,A,C-z.h);B.combine(E,A+z.w,0);B.clean();return v},CHTMLaddRoot:function(){return 0}});i.mroot.Augment({toCommonHTML:i.msqrt.prototype.toCommonHTML,CHTMLaddRoot:function(z,t,u){if(!this.data[1]){return}var y=this.CHTML,A=this.data[1].CHTML,v=z.firstChild;var r=A.rscale;var s=this.CHTMLrootHeight(A,t,r)-u;var x=Math.min(A.w,A.r);var B=Math.max(x,t.offset/r);if(s){v.style.verticalAlign=h.Em(s/r)}if(B>x){v.firstChild.style.paddingLeft=h.Em(B-x)}B-=t.offset/r;v.style.width=h.Em(B);y.combine(A,0,s);return B*r},CHTMLrootHeight:function(t,r,s){return 0.45*(r.h+r.d-0.9)+r.offset+Math.max(0,t.d-0.075)}});i.mfenced.Augment({toCommonHTML:function(u){u=this.CHTMLcreateNode(u);this.CHTMLhandleStyle(u);this.CHTMLhandleScale(u);this.CHTMLaddChild(u,"open",{});for(var t=0,r=this.data.length;t<r;t++){this.CHTMLaddChild(u,"sep"+t,{});this.CHTMLaddChild(u,t,{})}this.CHTMLaddChild(u,"close",{});var s=this.CHTML.h,v=this.CHTML.d;this.CHTMLstretchChildV("open",s,v);for(t=0,r=this.data.length;t<r;t++){this.CHTMLstretchChildV("sep"+t,s,v);this.CHTMLstretchChildV(t,s,v)}this.CHTMLstretchChildV("close",s,v);this.CHTMLhandleSpace(u);this.CHTMLhandleBBox(u);this.CHTMLhandleColor(u);return u}});i.mrow.Augment({toCommonHTML:function(v,s){s=s||{};v=this.CHTMLdefaultNode(v);var y=this.CHTML,u=y.h,w=y.d,x;for(var t=0,r=this.data.length;t<r;t++){this.CHTMLstretchChildV(t,u,w);if(this.data[t]&&this.data[t].CHTML&&this.data[t].CHTML.w<0){x=true}}if(this.CHTMLlineBreaks()){this.CHTMLmultiline(v);if(s.autowidth){v.style.width=""}}else{if(x&&y.w){v.style.width=h.Em(Math.max(0,y.w))}if(y.w<0){v.style.marginRight=h.Em(y.w)}}return v},CHTMLlineBreaks:function(){if(!this.parent.linebreakContainer){return false}return(l.automatic&&this.CHTML.w>h.linebreakWidth)||this.hasNewline()},CHTMLstretchV:function(r,s){this.CHTMLstretchChildV(this.CoreIndex(),r,s);return this.CHTML},CHTMLstretchH:function(s,r){this.CHTMLstretchChildH(this.CoreIndex(),r,s);return this.CHTML}});i.mstyle.Augment({toCommonHTML:function(r){r=this.CHTMLdefaultNode(r);if(this.scriptlevel&&this.data[0]){this.CHTML.rescale(this.data[0].CHTML.rscale)}return r}});i.TeXAtom.Augment({toCommonHTML:function(w,u){if(!u||!u.stretch){w=this.CHTMLdefaultNode(w)}if(this.texClass===i.TEXCLASS.VCENTER){var r=h.TEX.axis_height,t=this.CHTML;var s=r-(t.h+t.d)/2+t.d;if(Math.abs(s)>0.001){w.style.verticalAlign=h.Em(s);t.h+=s;t.t+=s;t.d-=s;t.b-=s}}return w},CHTMLstretchV:function(r,s){this.CHTML.updateFrom(this.Core().CHTMLstretchV(r,s));this.toCommonHTML(this.CHTMLnodeElement(),{stretch:true});return this.CHTML},CHTMLstretchH:function(s,r){this.CHTML.updateFrom(this.CHTMLstretchCoreH(s,r));this.toCommonHTML(s,{stretch:true});return this.CHTML}});i.semantics.Augment({toCommonHTML:function(r){r=this.CHTMLcreateNode(r);if(this.data[0]){this.data[0].toCommonHTML(r);this.CHTML.updateFrom(this.data[0].CHTML);this.CHTMLhandleBBox(r)}return r}});i.annotation.Augment({toCommonHTML:function(r){return this.CHTMLcreateNode(r)}});i["annotation-xml"].Augment({toCommonHTML:i.mbase.CHTMLautoload});i.ms.Augment({toCommonHTML:i.mbase.CHTMLautoload});i.mglyph.Augment({toCommonHTML:i.mbase.CHTMLautoload});i.menclose.Augment({toCommonHTML:i.mbase.CHTMLautoload});i.maction.Augment({toCommonHTML:i.mbase.CHTMLautoload});i.mmultiscripts.Augment({toCommonHTML:i.mbase.CHTMLautoload});i.mtable.Augment({toCommonHTML:i.mbase.CHTMLautoload});MathJax.Hub.Register.StartupHook("onLoad",function(){setTimeout(MathJax.Callback(["loadComplete",h,"jax.js"]),0)})});MathJax.Hub.Register.StartupHook("End Cookie",function(){if(c.config.menuSettings.zoom!=="None"){j.Require("[MathJax]/extensions/MathZoom.js")}})})(MathJax.Ajax,MathJax.Hub,MathJax.HTML,MathJax.OutputJax.CommonHTML);