/*
 *  /MathJax/jax/output/SVG/jax.js
 *
 *  Copyright (c) 2009-2015 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(b,c,g,h){var a;var e="http://www.w3.org/2000/svg";var f="http://www.w3.org/1999/xlink";h.Augment({config:{styles:{".MathJax_SVG":{display:"inline","font-style":"normal","font-weight":"normal","line-height":"normal","font-size":"100%","font-size-adjust":"none","text-indent":0,"text-align":"left","text-transform":"none","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none",direction:"ltr","max-width":"none","max-height":"none","min-width":0,"min-height":0,border:0,padding:0,margin:0},".MathJax_SVG_Display":{position:"relative",display:"block!important","text-indent":0,"max-width":"none","max-height":"none","min-width":0,"min-height":0,width:"100%"},".MathJax_SVG *":{transition:"none","-webkit-transition":"none","-moz-transition":"none","-ms-transition":"none","-o-transition":"none"},".mjx-svg-href":{fill:"blue",stroke:"blue"},".MathJax_SVG_Processing":{visibility:"hidden",position:"absolute",top:0,left:0,width:0,height:0,overflow:"hidden",display:"block!important"},".MathJax_SVG_Processed":{display:"none!important"},".MathJax_SVG_ExBox":{display:"block!important",overflow:"hidden",width:"1px",height:"60ex","min-height":0,"max-height":"none",padding:0,border:0,margin:0},"#MathJax_SVG_Tooltip":{position:"absolute",left:0,top:0,width:"auto",height:"auto",display:"none"}}},hideProcessedMath:true,fontNames:["TeX","STIX","STIX-Web","Asana-Math","Gyre-Termes","Gyre-Pagella","Latin-Modern","Neo-Euler"],Config:function(){this.SUPER(arguments).Config.apply(this,arguments);var k=c.config.menuSettings,j=this.config,i=k.font;if(k.scale){j.scale=k.scale}if(i&&i!=="Auto"){i=i.replace(/(Local|Web|Image)$/i,"");i=i.replace(/([a-z])([A-Z])/,"$1-$2");this.fontInUse=i}else{this.fontInUse=j.font||"TeX"}if(this.fontNames.indexOf(this.fontInUse)<0){this.fontInUse="TeX"}this.fontDir+="/"+this.fontInUse;if(!this.require){this.require=[]}this.require.push(this.fontDir+"/fontdata.js");this.require.push(MathJax.OutputJax.extensionDir+"/MathEvents.js")},Startup:function(){EVENT=MathJax.Extension.MathEvents.Event;TOUCH=MathJax.Extension.MathEvents.Touch;HOVER=MathJax.Extension.MathEvents.Hover;this.ContextMenu=EVENT.ContextMenu;this.Mousedown=EVENT.AltContextMenu;this.Mouseover=HOVER.Mouseover;this.Mouseout=HOVER.Mouseout;this.Mousemove=HOVER.Mousemove;this.hiddenDiv=g.Element("div",{style:{visibility:"hidden",overflow:"hidden",position:"absolute",top:0,height:"1px",width:"auto",padding:0,border:0,margin:0,textAlign:"left",textIndent:0,textTransform:"none",lineHeight:"normal",letterSpacing:"normal",wordSpacing:"normal"}});if(!document.body.firstChild){document.body.appendChild(this.hiddenDiv)}else{document.body.insertBefore(this.hiddenDiv,document.body.firstChild)}this.hiddenDiv=g.addElement(this.hiddenDiv,"div",{id:"MathJax_SVG_Hidden"});var i=g.addElement(this.hiddenDiv,"div",{style:{width:"5in"}});this.pxPerInch=i.offsetWidth/5;this.hiddenDiv.removeChild(i);this.textSVG=this.Element("svg");d.GLYPH.defs=this.addElement(this.addElement(this.hiddenDiv.parentNode,"svg"),"defs",{id:"MathJax_SVG_glyphs"});this.ExSpan=g.Element("span",{style:{position:"absolute","font-size-adjust":"none"}},[["span",{className:"MathJax_SVG_ExBox"}]]);this.linebreakSpan=g.Element("span",null,[["hr",{style:{width:"auto",size:1,padding:0,border:0,margin:0}}]]);return b.Styles(this.config.styles,["InitializeSVG",this])},InitializeSVG:function(){document.body.appendChild(this.ExSpan);document.body.appendChild(this.linebreakSpan);this.defaultEx=this.ExSpan.firstChild.offsetHeight/60;this.defaultWidth=this.linebreakSpan.firstChild.offsetWidth;document.body.removeChild(this.linebreakSpan);document.body.removeChild(this.ExSpan)},preTranslate:function(n){var s=n.jax[this.id],t,q=s.length,y,r,z,l,x,k,w,p,j,v=false,u,A=this.config.linebreaks.automatic,o=this.config.linebreaks.width;if(A){v=(o.match(/^\s*(\d+(\.\d*)?%\s*)?container\s*$/)!=null);if(v){o=o.replace(/\s*container\s*/,"")}else{j=this.defaultWidth}if(o===""){o="100%"}}else{j=100000}for(t=0;t<q;t++){y=s[t];if(!y.parentNode){continue}r=y.previousSibling;if(r&&String(r.className).match(/^MathJax(_SVG)?(_Display)?( MathJax(_SVG)?_Processing)?$/)){r.parentNode.removeChild(r)}k=y.MathJax.elementJax;if(!k){continue}k.SVG={display:(k.root.Get("display")==="block")};z=l=g.Element("span",{style:{"font-size":this.config.scale+"%",display:"inline-block"},className:"MathJax_SVG",id:k.inputID+"-Frame",isMathJax:true,jaxID:this.id,oncontextmenu:EVENT.Menu,onmousedown:EVENT.Mousedown,onmouseover:EVENT.Mouseover,onmouseout:EVENT.Mouseout,onmousemove:EVENT.Mousemove,onclick:EVENT.Click,ondblclick:EVENT.DblClick});if(c.Browser.noContextMenu){z.ontouchstart=TOUCH.start;z.ontouchend=TOUCH.end}if(k.SVG.display){l=g.Element("div",{className:"MathJax_SVG_Display"});l.appendChild(z)}l.className+=" MathJax_SVG_Processing";y.parentNode.insertBefore(l,y);y.parentNode.insertBefore(this.ExSpan.cloneNode(true),y);l.parentNode.insertBefore(this.linebreakSpan.cloneNode(true),l)}for(t=0;t<q;t++){y=s[t];if(!y.parentNode){continue}x=y.previousSibling;l=x.previousSibling;k=y.MathJax.elementJax;if(!k){continue}w=x.firstChild.offsetHeight/60;u=l.previousSibling.firstChild.offsetWidth;if(v){j=u}if(w===0||w==="NaN"){this.hiddenDiv.appendChild(l);k.SVG.isHidden=true;w=this.defaultEx;u=this.defaultWidth;if(v){j=u}}k.SVG.ex=w;k.SVG.em=p=w/h.TeX.x_height*1000;k.SVG.cwidth=u/p*1000;k.SVG.lineWidth=(A?this.length2em(o,1,j/p*1000):h.BIGDIMEN)}for(t=0;t<q;t++){y=s[t];if(!y.parentNode){continue}x=s[t].previousSibling;z=x.previousSibling;k=s[t].MathJax.elementJax;if(!k){continue}if(!k.SVG.isHidden){z=z.previousSibling}z.parentNode.removeChild(z);x.parentNode.removeChild(x)}n.SVGeqn=n.SVGlast=0;n.SVGi=-1;n.SVGchunk=this.config.EqnChunk;n.SVGdelay=false},Translate:function(j,n){if(!j.parentNode){return}if(n.SVGdelay){n.SVGdelay=false;c.RestartAfter(MathJax.Callback.Delay(this.config.EqnChunkDelay))}var i=j.MathJax.elementJax,m=i.root,k=document.getElementById(i.inputID+"-Frame"),p=(i.SVG.display?(k||{}).parentNode:k),o=(h.config.useFontCache&&!h.config.useGlobalCache);if(!p){return}this.em=a.mbase.prototype.em=i.SVG.em;this.ex=i.SVG.ex;this.linebreakWidth=i.SVG.lineWidth;this.cwidth=i.SVG.cwidth;this.mathDiv=p;k.appendChild(this.textSVG);if(o){h.resetGlyphs()}this.initSVG(m,k);m.setTeXclass();try{m.toSVG(k,p)}catch(l){if(l.restart){while(k.firstChild){k.removeChild(k.firstChild)}}if(o){d.GLYPH.n--}throw l}k.removeChild(this.textSVG);if(i.SVG.isHidden){j.parentNode.insertBefore(p,j)}p.className=p.className.split(/ /)[0];if(this.hideProcessedMath){p.className+=" MathJax_SVG_Processed";if(j.MathJax.preview){i.SVG.preview=j.MathJax.preview;delete j.MathJax.preview}n.SVGeqn+=(n.i-n.SVGi);n.SVGi=n.i;if(n.SVGeqn>=n.SVGlast+n.SVGchunk){this.postTranslate(n,true);n.SVGchunk=Math.floor(n.SVGchunk*this.config.EqnChunkFactor);n.SVGdelay=true}}},postTranslate:function(q,n){var k=q.jax[this.id];if(!this.hideProcessedMath){return}for(var o=q.SVGlast,j=q.SVGeqn;o<j;o++){var l=k[o];if(l&&l.MathJax.elementJax){l.previousSibling.className=l.previousSibling.className.split(/ /)[0];var p=l.MathJax.elementJax.SVG;if(p.preview){p.preview.innerHTML="";l.MathJax.preview=p.preview;delete p.preview}}}q.SVGlast=q.SVGeqn},resetGlyphs:function(j){if(this.config.useFontCache){var i=d.GLYPH;if(this.config.useGlobalCache){i.defs=document.getElementById("MathJax_SVG_glyphs");i.defs.innerHTML=""}else{i.defs=this.Element("defs");i.n++}i.glyphs={};if(j){i.n=0}}},hashCheck:function(i){if(i&&i.nodeName.toLowerCase()==="g"){do{i=i.parentNode}while(i&&i.firstChild.nodeName!=="svg")}return i},getJaxFromMath:function(i){if(i.parentNode.className==="MathJax_SVG_Display"){i=i.parentNode}do{i=i.nextSibling}while(i&&i.nodeName.toLowerCase()!=="script");return c.getJaxFor(i)},getHoverSpan:function(i,j){j.style.position="relative";return j.firstChild},getHoverBBox:function(i,j,k){var l=EVENT.getBBox(j.parentNode);l.h+=2;l.d-=2;return l},Zoom:function(j,s,r,i,p){s.className="MathJax_SVG";var u=s.appendChild(this.ExSpan.cloneNode(true));var o=u.firstChild.offsetHeight/60;this.em=a.mbase.prototype.em=o/h.TeX.x_height*1000;this.ex=o;this.linebreakWidth=j.SVG.lineWidth;this.cwidth=j.SVG.cwidth;u.parentNode.removeChild(u);s.appendChild(this.textSVG);this.mathDIV=s;this.zoomScale=parseInt(c.config.menuSettings.zscale)/100;var n=j.root.data[0].SVGdata.tw;if(n&&n<this.cwidth){this.cwidth=n}this.idPostfix="-zoom";j.root.toSVG(s,s);this.idPostfix="";this.zoomScale=1;s.removeChild(this.textSVG);var m=s.getElementsByTagName("svg")[0].style;m.marginTop=m.marginRight=m.marginLeft=0;if(m.marginBottom.charAt(0)==="-"){s.style.marginBottom=m.marginBottom.substr(1)}if(this.operaZoomRefresh){setTimeout(function(){s.firstChild.style.border="1px solid transparent"},1)}if(s.offsetWidth<s.firstChild.offsetWidth){s.style.minWidth=s.firstChild.offsetWidth+"px";r.style.minWidth=r.firstChild.offsetWidth+"px"}s.style.position=r.style.position="absolute";var q=s.offsetWidth,l=s.offsetHeight,t=r.offsetHeight,k=r.offsetWidth;s.style.position=r.style.position="";return{Y:-EVENT.getBBox(s).h,mW:k,mH:t,zW:q,zH:l}},initSVG:function(j,i){},Remove:function(i){var j=document.getElementById(i.inputID+"-Frame");if(j){if(i.SVG.display){j=j.parentNode}j.parentNode.removeChild(j)}delete i.SVG},Em:function(i){if(Math.abs(i)<0.0006){return"0em"}return i.toFixed(3).replace(/\.?0+$/,"")+"em"},Ex:function(i){i=Math.round(i/this.TeX.x_height*this.ex)/this.ex;if(Math.abs(i)<0.0006){return"0ex"}return i.toFixed(3).replace(/\.?0+$/,"")+"ex"},Percent:function(i){return(100*i).toFixed(1).replace(/\.?0+$/,"")+"%"},Fixed:function(i,j){if(Math.abs(i)<0.0006){return"0"}return i.toFixed(j||3).replace(/\.?0+$/,"")},length2em:function(o,j,l){if(typeof(o)!=="string"){o=o.toString()}if(o===""){return""}if(o===a.SIZE.NORMAL){return 1000}if(o===a.SIZE.BIG){return 2000}if(o===a.SIZE.SMALL){return 710}if(o==="infinity"){return h.BIGDIMEN}if(o.match(/mathspace$/)){return 1000*h.MATHSPACE[o]}var p=(this.zoomScale||1)/h.em;var k=o.match(/^\s*([-+]?(?:\.\d+|\d+(?:\.\d*)?))?(pt|em|ex|mu|px|pc|in|mm|cm|%)?/);var i=parseFloat(k[1]||"1")*1000,n=k[2];if(l==null){l=1000}if(j==null){j=1}if(n==="em"){return i}if(n==="ex"){return i*h.TeX.x_height/1000}if(n==="%"){return i/100*l/1000}if(n==="px"){return i*p}if(n==="pt"){return i/10}if(n==="pc"){return i*1.2}if(n==="in"){return i*this.pxPerInch*p}if(n==="cm"){return i*this.pxPerInch*p/2.54}if(n==="mm"){return i*this.pxPerInch*p/25.4}if(n==="mu"){return i/18*j}return i*l/1000},thickness2em:function(j,i){var k=h.TeX.rule_thickness;if(j===a.LINETHICKNESS.MEDIUM){return k}if(j===a.LINETHICKNESS.THIN){return 0.67*k}if(j===a.LINETHICKNESS.THICK){return 1.67*k}return this.length2em(j,i,k)},getPadding:function(j){var l={top:0,right:0,bottom:0,left:0},i=false;for(var m in l){if(l.hasOwnProperty(m)){var k=j["padding"+m.charAt(0).toUpperCase()+m.substr(1)];if(k){l[m]=this.length2em(k);i=true}}}return(i?l:false)},getBorders:function(m){var k={top:0,right:0,bottom:0,left:0},j=false;for(var n in k){if(k.hasOwnProperty(n)){var i="border"+n.charAt(0).toUpperCase()+n.substr(1);var l=m[i+"Style"];if(l&&l!=="none"){j=true;k[n]=this.length2em(m[i+"Width"]);k[n+"Style"]=m[i+"Style"];k[n+"Color"]=m[i+"Color"];if(k[n+"Color"]==="initial"){k[n+"Color"]=""}}else{delete k[n]}}}return(j?k:false)},Element:function(i,j){var k=(typeof(i)==="string"?document.createElementNS(e,i):i);k.isMathJax=true;if(j){for(var l in j){if(j.hasOwnProperty(l)){k.setAttribute(l,j[l].toString())}}}return k},addElement:function(j,i,k){return j.appendChild(this.Element(i,k))},TextNode:g.TextNode,addText:g.addText,ucMatch:g.ucMatch,HandleVariant:function(r,q,A){var u=d.G();var l,w,y,o,z,s,p,k,x,j;if(!r){r=this.FONTDATA.VARIANT[a.VARIANT.NORMAL]}if(r.forceFamily){A=d.TEXT(q,A,r.font);if(r.h!=null){A.h=r.h}if(r.d!=null){A.d=r.d}u.Add(A);A=""}z=r;for(s=0,p=A.length;s<p;s++){r=z;l=A.charCodeAt(s);y=A.charAt(s);if(l>=55296&&l<56319){s++;l=(((l-55296)<<10)+(A.charCodeAt(s)-56320))+65536;if(this.FONTDATA.RemapPlane1){var v=this.FONTDATA.RemapPlane1(l,r);l=v.n;r=v.variant}}else{j=this.FONTDATA.RANGES;for(k=0,x=j.length;k<x;k++){if(j[k].name==="alpha"&&r.noLowerCase){continue}w=r["offset"+j[k].offset];if(w&&l>=j[k].low&&l<=j[k].high){if(j[k].remap&&j[k].remap[l]){l=w+j[k].remap[l]}else{l=l-j[k].low+w;if(j[k].add){l+=j[k].add}}if(r["variant"+j[k].offset]){r=this.FONTDATA.VARIANT[r["variant"+j[k].offset]]}break}}}if(r.remap&&r.remap[l]){l=r.remap[l];if(r.remap.variant){r=this.FONTDATA.VARIANT[r.remap.variant]}}else{if(this.FONTDATA.REMAP[l]&&!r.noRemap){l=this.FONTDATA.REMAP[l]}}if(l instanceof Array){r=this.FONTDATA.VARIANT[l[1]];l=l[0]}if(typeof(l)==="string"){A=l+A.substr(s+1);p=A.length;s=-1;continue}o=this.lookupChar(r,l);y=o[l];if(y){if((y[5]&&y[5].space)||(y[5]===""&&y[0]+y[1]===0)){u.w+=y[2]}else{y=[q,o.id+"-"+l.toString(16).toUpperCase()].concat(y);u.Add(d.GLYPH.apply(d,y),u.w,0)}}else{if(this.FONTDATA.DELIMITERS[l]){y=this.createDelimiter(l,0,1,o);u.Add(y,u.w,(this.FONTDATA.DELIMITERS[l].dir==="V"?y.d:0))}else{if(l<=65535){y=String.fromCharCode(l)}else{w=l-65536;y=String.fromCharCode((w>>10)+55296)+String.fromCharCode((w&1023)+56320)}var t=d.TEXT(q*100/h.config.scale,y,{"font-family":r.defaultFamily||h.config.undefinedFamily,"font-style":(r.italic?"italic":""),"font-weight":(r.bold?"bold":"")});if(r.h!=null){t.h=r.h}if(r.d!=null){t.d=r.d}y=d.G();y.Add(t);u.Add(y,u.w,0);c.signal.Post(["SVG Jax - unknown char",l,r])}}}if(A.length==1&&o.skew&&o.skew[l]){u.skew=o.skew[l]*1000}if(u.element.childNodes.length===1){u.element=u.element.firstChild;u.removeable=false;u.scale=q}return u},lookupChar:function(o,r){var l,j;if(!o.FONTS){var q=this.FONTDATA.FONTS;var p=(o.fonts||this.FONTDATA.VARIANT.normal.fonts);if(!(p instanceof Array)){p=[p]}if(o.fonts!=p){o.fonts=p}o.FONTS=[];for(l=0,j=p.length;l<j;l++){if(q[p[l]]){o.FONTS.push(q[p[l]])}}}for(l=0,j=o.FONTS.length;l<j;l++){var k=o.FONTS[l];if(typeof(k)==="string"){delete o.FONTS;this.loadFont(k)}if(k[r]){return k}else{this.findBlock(k,r)}}return{id:"unknown"}},findBlock:function(l,q){if(l.Ranges){for(var p=0,k=l.Ranges.length;p<k;p++){if(q<l.Ranges[p][0]){return}if(q<=l.Ranges[p][1]){var o=l.Ranges[p][2];for(var n=l.Ranges.length-1;n>=0;n--){if(l.Ranges[n][2]==o){l.Ranges.splice(n,1)}}this.loadFont(l.directory+"/"+o+".js")}}}},loadFont:function(i){c.RestartAfter(b.Require(this.fontDir+"/"+i))},createDelimiter:function(j,l,p,n){if(!p){p=1}var r=d.G();if(!j){r.Clean();delete r.element;r.w=r.r=this.TeX.nulldelimiterspace*p;return r}if(!(l instanceof Array)){l=[l,l]}var s=l[1];l=l[0];var k={alias:j};while(k.alias){j=k.alias;k=this.FONTDATA.DELIMITERS[j];if(!k){k={HW:[0,this.FONTDATA.VARIANT[a.VARIANT.NORMAL]]}}}if(k.load){c.RestartAfter(b.Require(this.fontDir+"/fontdata-"+k.load+".js"))}for(var q=0,o=k.HW.length;q<o;q++){if(k.HW[q][0]*p>=l-10-h.config.blacker||(q==o-1&&!k.stretch)){if(k.HW[q][2]){p*=k.HW[q][2]}if(k.HW[q][3]){j=k.HW[q][3]}return this.createChar(p,[j,k.HW[q][1]],n).With({stretched:true})}}if(k.stretch){this["extendDelimiter"+k.dir](r,s,k.stretch,p,n)}return r},createChar:function(r,p,l){var q="",o={fonts:[p[1]],noRemap:true};if(l&&l===a.VARIANT.BOLD){o.fonts=[p[1]+"-bold",p[1]]}if(typeof(p[1])!=="string"){o=p[1]}if(p[0] instanceof Array){for(var n=0,j=p[0].length;n<j;n++){q+=String.fromCharCode(p[0][n])}}else{q=String.fromCharCode(p[0])}if(p[4]){r=r*p[4]}var k=this.HandleVariant(o,r,q);if(p[2]){k.x=p[2]*1000}if(p[3]){k.y=p[3]*1000}if(p[5]){k.h+=p[5]*1000}if(p[6]){k.d+=p[6]*1000}return k},extendDelimiterV:function(p,x,j,m,l){var v=this.createChar(m,(j.top||j.ext),l);var r=this.createChar(m,(j.bot||j.ext),l);var o=v.h+v.d+r.h+r.d;var u=-v.h;p.Add(v,0,u);u-=v.d;if(j.mid){var w=this.createChar(m,j.mid,l);o+=w.h+w.d}if(j.min&&x<o*j.min){x=o*j.min}if(x>o){var i=this.createChar(m,j.ext,l);var n=(j.mid?2:1),t=(x-o)/n,z=(t+100)/(i.h+i.d);while(n-->0){var q=h.Element("g",{transform:"translate("+i.y+","+(u-z*i.h+50+i.y)+") scale(1,"+z+")"});q.appendChild(i.element.cloneNode(false));p.element.appendChild(q);u-=t;if(j.mid&&n){p.Add(w,0,u-w.h);u-=(w.h+w.d)}}}else{if(j.mid){u+=(o-x)/2;p.Add(w,0,u-w.h);u+=-(w.h+w.d)+(o-x)/2}else{u+=(o-x)}}p.Add(r,0,u-r.h);p.Clean();p.scale=m;p.isMultiChar=true},extendDelimiterH:function(q,m,j,o,l){var n=this.createChar(o,(j.left||j.rep),l);var A=this.createChar(o,(j.right||j.rep),l);q.Add(n,-n.l,0);var z=(n.r-n.l)+(A.r-A.l),v=n.r-n.l;if(j.mid){var y=this.createChar(o,j.mid,l);z+=y.w}if(j.min&&m<z*j.min){m=z*j.min}if(m>z){var u=this.createChar(o,j.rep,l),i=j.fuzz||0;var p=(j.mid?2:1),t=(m-z)/p,B=(t+i)/(u.r-u.l);while(p-->0){var r=h.Element("g",{transform:"translate("+(v-i/2-B*u.l+u.x)+","+u.y+") scale("+B+",1)"});r.appendChild(u.element.cloneNode(false));q.element.appendChild(r);v+=t;if(j.mid&&p){q.Add(y,v,0);v+=y.w}}}else{if(j.mid){v-=(z-m)/2;q.Add(y,v,0);v+=y.w-(z-m)/2}else{v-=(z-m)}}q.Add(A,v-A.l,0);q.Clean();q.scale=o;q.isMultiChar=true},MATHSPACE:{veryverythinmathspace:1/18,verythinmathspace:2/18,thinmathspace:3/18,mediummathspace:4/18,thickmathspace:5/18,verythickmathspace:6/18,veryverythickmathspace:7/18,negativeveryverythinmathspace:-1/18,negativeverythinmathspace:-2/18,negativethinmathspace:-3/18,negativemediummathspace:-4/18,negativethickmathspace:-5/18,negativeverythickmathspace:-6/18,negativeveryverythickmathspace:-7/18},TeX:{x_height:430.554,quad:1000,num1:676.508,num2:393.732,num3:443.73,denom1:685.951,denom2:344.841,sup1:412.892,sup2:362.892,sup3:288.888,sub1:150,sub2:247.217,sup_drop:386.108,sub_drop:50,delim1:2390,delim2:1000,axis_height:250,rule_thickness:60,big_op_spacing1:111.111,big_op_spacing2:166.666,big_op_spacing3:200,big_op_spacing4:600,big_op_spacing5:100,scriptspace:100,nulldelimiterspace:120,delimiterfactor:901,delimitershortfall:300,min_rule_thickness:1.25,min_root_space:1.5},BIGDIMEN:10000000,NBSP:"\u00A0"});var d=h.BBOX=MathJax.Object.Subclass({type:"g",removeable:true,Init:function(i){this.h=this.d=-h.BIGDIMEN;this.H=this.D=0;this.w=this.r=0;this.l=h.BIGDIMEN;this.x=this.y=0;this.scale=1;this.n=0;if(this.type){this.element=h.Element(this.type,i)}},With:function(i){return c.Insert(this,i)},Add:function(k,q,p,i,o){if(q){k.x+=q}if(p){k.y+=p}if(k.element){if(k.removeable&&k.element.childNodes.length===1&&k.n===1){var j=k.element.firstChild,m=j.nodeName.toLowerCase();if(m==="use"||m==="rect"){k.element=j;k.scale=k.childScale;var n=k.childX,l=k.childY;k.x+=n;k.y+=l;k.h-=l;k.d+=l;k.H-=l;k.D+=l;k.w-=n;k.r-=n;k.l+=n;k.removeable=false;j.setAttribute("x",Math.floor(k.x/k.scale));j.setAttribute("y",Math.floor(k.y/k.scale))}}if(Math.abs(k.x)<1&&Math.abs(k.y)<1){k.remove=k.removeable}else{m=k.element.nodeName.toLowerCase();if(m==="g"){if(!k.element.firstChild){k.remove=k.removeable}else{k.element.setAttribute("transform","translate("+Math.floor(k.x)+","+Math.floor(k.y)+")")}}else{if(m==="line"||m==="polygon"||m==="path"||m==="a"){k.element.setAttribute("transform","translate("+Math.floor(k.x)+","+Math.floor(k.y)+")")}else{k.element.setAttribute("x",Math.floor(k.x/k.scale));k.element.setAttribute("y",Math.floor(k.y/k.scale))}}}if(k.remove){this.n+=k.n;while(k.element.firstChild){if(o&&this.element.firstChild){this.element.insertBefore(k.element.firstChild,this.element.firstChild)}else{this.element.appendChild(k.element.firstChild)}}}else{if(o){this.element.insertBefore(k.element,this.element.firstChild)}else{this.element.appendChild(k.element)}}delete k.element}if(k.hasIndent){this.hasIndent=k.hasIndent}if(k.tw!=null){this.tw=k.tw}if(k.d-k.y>this.d){this.d=k.d-k.y;if(this.d>this.D){this.D=this.d}}if(k.y+k.h>this.h){this.h=k.y+k.h;if(this.h>this.H){this.H=this.h}}if(k.D-k.y>this.D){this.D=k.D-k.y}if(k.y+k.H>this.H){this.H=k.y+k.H}if(k.x+k.l<this.l){this.l=k.x+k.l}if(k.x+k.r>this.r){this.r=k.x+k.r}if(i||k.x+k.w+(k.X||0)>this.w){this.w=k.x+k.w+(k.X||0)}this.childScale=k.scale;this.childX=k.x;this.childY=k.y;this.n++;return k},Align:function(m,n,l,k,j){l=({left:l,center:(this.w-m.w)/2,right:this.w-m.w-l})[n]||0;var i=this.w;this.Add(m,l+(j||0),k);this.w=i},Clean:function(){if(this.h===-h.BIGDIMEN){this.h=this.d=this.l=0}return this}});d.ROW=d.Subclass({Init:function(){this.SUPER(arguments).Init.call(this);this.svg=[];this.sh=this.sd=0},Check:function(j){var i=j.toSVG();this.svg.push(i);if(j.SVGcanStretch("Vertical")){i.mml=j}if(i.h>this.sh){this.sh=i.h}if(i.d>this.sd){this.sd=i.d}},Stretch:function(){for(var n=0,j=this.svg.length;n<j;n++){var k=this.svg[n],l=k.mml;if(l){if(l.forceStretch||l.SVGdata.h!==this.sh||l.SVGdata.d!==this.sd){k=l.SVGstretchV(this.sh,this.sd)}l.SVGdata.HW=this.sh;l.SVGdata.D=this.sd}if(k.ic){this.ic=k.ic}else{delete this.ic}this.Add(k,this.w,0,true)}delete this.svg}});d.RECT=d.Subclass({type:"rect",removeable:false,Init:function(j,l,i,k){if(k==null){k={stroke:"none"}}k.width=Math.floor(i);k.height=Math.floor(j+l);this.SUPER(arguments).Init.call(this,k);this.w=this.r=i;this.h=this.H=j+l;this.d=this.D=this.l=0;this.y=-l}});d.FRAME=d.Subclass({type:"rect",removeable:false,Init:function(l,o,i,k,n,j,m){if(m==null){m={}}m.fill="none";m["stroke-width"]=h.Fixed(k,2);m.width=Math.floor(i-k);m.height=Math.floor(l+o-k);m.transform="translate("+Math.floor(k/2)+","+Math.floor(-o+k/2)+")";if(n==="dashed"){m["stroke-dasharray"]=[Math.floor(6*h.em),Math.floor(6*h.em)].join(" ")}this.SUPER(arguments).Init.call(this,m);this.w=this.r=i;this.h=this.H=l;this.d=this.D=o;this.l=0}});d.HLINE=d.Subclass({type:"line",removeable:false,Init:function(j,l,p,k,o){if(o==null){o={"stroke-linecap":"square"}}if(k&&k!==""){o.stroke=k}o["stroke-width"]=h.Fixed(l,2);o.x1=o.y1=o.y2=Math.floor(l/2);o.x2=Math.floor(j-l/2);if(p==="dashed"){var q=Math.floor(Math.max(0,j-l)/(6*l)),i=Math.floor(Math.max(0,j-l)/(2*q+1));o["stroke-dasharray"]=i+" "+i}if(p==="dotted"){o["stroke-dasharray"]=[1,Math.max(150,Math.floor(2*l))].join(" ");o["stroke-linecap"]="round"}this.SUPER(arguments).Init.call(this,o);this.w=this.r=j;this.l=0;this.h=this.H=l;this.d=this.D=0}});d.VLINE=d.Subclass({type:"line",removeable:false,Init:function(l,k,p,j,o){if(o==null){o={"stroke-linecap":"square"}}if(j&&j!==""){o.stroke=j}o["stroke-width"]=h.Fixed(k,2);o.x1=o.x2=o.y1=Math.floor(k/2);o.y2=Math.floor(l-k/2);if(p==="dashed"){var q=Math.floor(Math.max(0,l-k)/(6*k)),i=Math.floor(Math.max(0,l-k)/(2*q+1));o["stroke-dasharray"]=i+" "+i}if(p==="dotted"){o["stroke-dasharray"]=[1,Math.max(150,Math.floor(2*k))].join(" ");o["stroke-linecap"]="round"}this.SUPER(arguments).Init.call(this,o);this.w=this.r=k;this.l=0;this.h=this.H=l;this.d=this.D=0}});d.TEXT=d.Subclass({type:"text",removeable:false,Init:function(l,k,i){if(!i){i={}}i.stroke="none";if(i["font-style"]===""){delete i["font-style"]}if(i["font-weight"]===""){delete i["font-weight"]}this.SUPER(arguments).Init.call(this,i);h.addText(this.element,k);h.textSVG.appendChild(this.element);var j=this.element.getBBox();h.textSVG.removeChild(this.element);l*=1000/h.em;this.element.setAttribute("transform","scale("+h.Fixed(l)+") matrix(1 0 0 -1 0 0)");this.w=this.r=j.width*l;this.l=0;this.h=this.H=-j.y*l;this.d=this.D=(j.height+j.y)*l}});d.G=d;d.NULL=d.Subclass({Init:function(){this.SUPER(arguments).Init.apply(this,arguments);this.Clean()}});d.GLYPH=d.Subclass({type:"path",removeable:false,Init:function(q,k,v,x,y,s,j,m){var n,z=h.config.blacker,u=d.GLYPH;var i=h.config.useFontCache;var o=(q===1?null:"scale("+h.Fixed(q)+")");if(i&&!h.config.useGlobalCache){k="E"+u.n+"-"+k}if(!i||!u.glyphs[k]){n={"stroke-width":z};if(i){n.id=k}else{if(o){n.transform=o}}n.d=(m?"M"+m+"Z":"");this.SUPER(arguments).Init.call(this,n);if(i){u.defs.appendChild(this.element);u.glyphs[k]=true}}if(i){n={};if(o){n.transform=o}this.element=h.Element("use",n);this.element.setAttributeNS(f,"href","#"+k)}this.h=(v+z)*q;this.d=(x+z)*q;this.w=(y+z/2)*q;this.l=(s+z/2)*q;this.r=(j+z/2)*q;this.H=Math.max(0,this.h);this.D=Math.max(0,this.d);this.x=this.y=0;this.scale=q}},{glyphs:{},defs:null,n:0});c.Register.StartupHook("mml Jax Ready",function(){a=MathJax.ElementJax.mml;a.mbase.Augment({SVG:d,toSVG:function(){this.SVGgetStyles();var n=this.SVGgetVariant();var k=this.SVG();this.SVGgetScale(k);this.SVGhandleSpace(k);for(var l=0,j=this.data.length;l<j;l++){if(this.data[l]){var p=k.Add(this.data[l].toSVG(n,k.scale),k.w,0,true);if(p.skew){k.skew=p.skew}}}k.Clean();var o=this.data.join("");if(k.skew&&o.length!==1){delete k.skew}if(k.r>k.w&&o.length===1&&!n.noIC){k.ic=k.r-k.w;k.w=k.r}this.SVGhandleColor(k);this.SVGsaveData(k);return k},SVGchildSVG:function(j){return(this.data[j]?this.data[j].toSVG():d())},SVGdataStretched:function(k,j,l){this.SVGdata={HW:j,D:l};if(!this.data[k]){return d()}if(l!=null){return this.data[k].SVGstretchV(j,l)}if(j!=null){return this.data[k].SVGstretchH(j)}return this.data[k].toSVG()},SVGsaveData:function(j){if(!this.SVGdata){this.SVGdata={}}this.SVGdata.w=j.w,this.SVGdata.x=j.x;this.SVGdata.h=j.h,this.SVGdata.d=j.d;if(j.y){this.SVGdata.h+=j.y;this.SVGdata.d-=j.y}if(j.X!=null){this.SVGdata.X=j.X}if(j.tw!=null){this.SVGdata.tw=j.tw}if(j.skew){this.SVGdata.skew=j.skew}if(j.ic){this.SVGdata.ic=j.ic}if(this["class"]){j.removeable=false;h.Element(j.element,{"class":this["class"]})}if(this.id){j.removeable=false;h.Element(j.element,{id:this.id})}if(this.href){var i=h.Element("a",{"class":"mjx-svg-href"});i.setAttributeNS(f,"href",this.href);i.onclick=this.SVGlink;h.addElement(i,"rect",{width:j.w,height:j.h+j.d,y:-j.d,fill:"none",stroke:"none","pointer-events":"all"});if(j.type==="svg"){var l=j.element.firstChild;while(l.firstChild){i.appendChild(l.firstChild)}l.appendChild(i)}else{i.appendChild(j.element);j.element=i}j.removeable=false}if(h.config.addMMLclasses){this.SVGaddClass(j.element,"mjx-svg-"+this.type);j.removeable=false}var k=this.style;if(k&&j.element){j.element.style.cssText=k;if(j.element.style.fontSize){j.element.style.fontSize=""}j.element.style.border=j.element.style.padding="";if(j.removeable){j.removeable=(j.element.style.cssText==="")}}this.SVGaddAttributes(j)},SVGaddClass:function(k,i){var j=k.getAttribute("class");k.setAttribute("class",(j?j+" ":"")+i)},SVGaddAttributes:function(k){if(this.attrNames){var r=this.attrNames,n=a.nocopyAttributes,q=c.config.ignoreMMLattributes;var o=(this.type==="mstyle"?a.math.prototype.defaults:this.defaults);for(var l=0,j=r.length;l<j;l++){var p=r[l];if(q[p]==false||(!n[p]&&!q[p]&&o[p]==null&&typeof(k.element[p])==="undefined")){k.element.setAttribute(p,this.attr[p]);k.removeable=false}}}},SVGlink:function(){var i=this.href.animVal;if(i.charAt(0)==="#"){var j=h.hashCheck(document.getElementById(i.substr(1)));if(j&&j.scrollIntoView){setTimeout(function(){j.parentNode.scrollIntoView(true)},1)}}document.location=i},SVGgetStyles:function(){if(this.style){var i=g.Element("span");i.style.cssText=this.style;this.styles=this.SVGprocessStyles(i.style)}},SVGprocessStyles:function(i){var j={border:h.getBorders(i),padding:h.getPadding(i)};if(!j.border){delete j.border}if(!j.padding){delete j.padding}if(i.fontSize){j.fontSize=i.fontSize}if(i.color){j.color=i.color}if(i.backgroundColor){j.background=i.backgroundColor}if(i.fontStyle){j.fontStyle=i.fontStyle}if(i.fontWeight){j.fontWeight=i.fontWeight}if(i.fontFamily){j.fontFamily=i.fontFamily}if(j.fontWeight&&j.fontWeight.match(/^\d+$/)){j.fontWeight=(parseInt(j.fontWeight)>600?"bold":"normal")}return j},SVGhandleSpace:function(l){if(this.useMMLspacing){if(this.type!=="mo"){return}var k=this.getValues("scriptlevel","lspace","rspace");if(k.scriptlevel<=0||this.hasValue("lspace")||this.hasValue("rspace")){var j=this.SVGgetMu(l);k.lspace=Math.max(0,h.length2em(k.lspace,j));k.rspace=Math.max(0,h.length2em(k.rspace,j));var i=this,m=this.Parent();while(m&&m.isEmbellished()&&m.Core()===i){i=m;m=m.Parent()}if(k.lspace){l.x+=k.lspace}if(k.rspace){l.X=k.rspace}}}else{var n=this.texSpacing();this.SVGgetScale();if(n!==""){l.x+=h.length2em(n,this.scale)*this.mscale}}},SVGhandleColor:function(m){var v=this.getValues("mathcolor","color");if(this.styles&&this.styles.color&&!v.color){v.color=this.styles.color}if(v.color&&!this.mathcolor){v.mathcolor=v.color}if(v.mathcolor){h.Element(m.element,{fill:v.mathcolor,stroke:v.mathcolor});m.removeable=false}var q=(this.styles||{}).border,t=(this.styles||{}).padding,r=((q||{}).left||0),o=((t||{}).left||0),i;v.background=(this.mathbackground||this.background||(this.styles||{}).background||a.COLOR.TRANSPARENT);if(r+o){var j=d();for(i in m){if(m.hasOwnProperty(i)){j[i]=m[i]}}j.x=0;j.y=0;m.element=h.Element("g");m.removeable=true;m.Add(j,r+o,0)}if(t){m.w+=t.right||0;m.h+=t.top||0;m.d+=t.bottom||0}if(q){m.w+=q.right||0;m.h+=q.top||0;m.d+=q.bottom||0}if(v.background!==a.COLOR.TRANSPARENT){var s=m.element.nodeName.toLowerCase();if(s!=="g"&&s!=="svg"){var n=h.Element("g");n.appendChild(m.element);m.element=n;m.removeable=true}m.Add(d.RECT(m.h,m.d,m.w,{fill:v.background,stroke:"none"}),0,0,false,true)}if(q){var u=5;var k={left:["V",m.h+m.d,-u,-m.d],right:["V",m.h+m.d,m.w-q.right+u,-m.d],top:["H",m.w,0,m.h-q.top+u],bottom:["H",m.w,0,-m.d-u]};for(i in k){if(k.hasOwnProperty(i)){if(q[i]){var p=k[i],l=d[p[0]+"LINE"];m.Add(l(p[1],q[i],q[i+"Style"],q[i+"Color"]),p[2],p[3])}}}}},SVGhandleVariant:function(i,k,j){return h.HandleVariant(i,k,j)},SVGgetVariant:function(){var i=this.getValues("mathvariant","fontfamily","fontweight","fontstyle");var j=i.mathvariant;if(this.variantForm){j="-TeX-variant"}i.hasVariant=this.Get("mathvariant",true);if(!i.hasVariant){i.family=i.fontfamily;i.weight=i.fontweight;i.style=i.fontstyle}if(this.styles){if(!i.style&&this.styles.fontStyle){i.style=this.styles.fontStyle}if(!i.weight&&this.styles.fontWeight){i.weight=this.styles.fontWeight}if(!i.family&&this.styles.fontFamily){i.family=this.styles.fontFamily}}if(i.family&&!i.hasVariant){if(!i.weight&&i.mathvariant.match(/bold/)){i.weight="bold"}if(!i.style&&i.mathvariant.match(/italic/)){i.style="italic"}j={forceFamily:true,font:{"font-family":i.family}};if(i.style){j.font["font-style"]=i.style}if(i.weight){j.font["font-weight"]=i.weight}return j}if(i.weight==="bold"){j={normal:a.VARIANT.BOLD,italic:a.VARIANT.BOLDITALIC,fraktur:a.VARIANT.BOLDFRAKTUR,script:a.VARIANT.BOLDSCRIPT,"sans-serif":a.VARIANT.BOLDSANSSERIF,"sans-serif-italic":a.VARIANT.SANSSERIFBOLDITALIC}[j]||j}else{if(i.weight==="normal"){j={bold:a.VARIANT.normal,"bold-italic":a.VARIANT.ITALIC,"bold-fraktur":a.VARIANT.FRAKTUR,"bold-script":a.VARIANT.SCRIPT,"bold-sans-serif":a.VARIANT.SANSSERIF,"sans-serif-bold-italic":a.VARIANT.SANSSERIFITALIC}[j]||j}}if(i.style==="italic"){j={normal:a.VARIANT.ITALIC,bold:a.VARIANT.BOLDITALIC,"sans-serif":a.VARIANT.SANSSERIFITALIC,"bold-sans-serif":a.VARIANT.SANSSERIFBOLDITALIC}[j]||j}else{if(i.style==="normal"){j={italic:a.VARIANT.NORMAL,"bold-italic":a.VARIANT.BOLD,"sans-serif-italic":a.VARIANT.SANSSERIF,"sans-serif-bold-italic":a.VARIANT.BOLDSANSSERIF}[j]||j}}if(!(j in h.FONTDATA.VARIANT)){j="normal"}return h.FONTDATA.VARIANT[j]},SVGgetScale:function(j){var k=1;if(this.mscale){k=this.scale}else{var i=this.getValues("scriptlevel","fontsize");i.mathsize=(this.isToken?this:this.Parent()).Get("mathsize");if((this.styles||{}).fontSize&&!i.fontsize){i.fontsize=this.styles.fontSize}if(i.fontsize&&!this.mathsize){i.mathsize=i.fontsize}if(i.scriptlevel!==0){if(i.scriptlevel>2){i.scriptlevel=2}k=Math.pow(this.Get("scriptsizemultiplier"),i.scriptlevel);i.scriptminsize=h.length2em(this.Get("scriptminsize"))/1000;if(k<i.scriptminsize){k=i.scriptminsize}}this.scale=k;this.mscale=h.length2em(i.mathsize)/1000}if(j){j.scale=k;if(this.isToken){j.scale*=this.mscale}}return k*this.mscale},SVGgetMu:function(k){var i=1,j=this.getValues("scriptlevel","scriptsizemultiplier");if(k.scale&&k.scale!==1){i=1/k.scale}if(j.scriptlevel!==0){if(j.scriptlevel>2){j.scriptlevel=2}i=Math.sqrt(Math.pow(j.scriptsizemultiplier,j.scriptlevel))}return i},SVGnotEmpty:function(i){while(i){if((i.type!=="mrow"&&i.type!=="texatom")||i.data.length>1){return true}i=i.data[0]}return false},SVGcanStretch:function(k){var j=false;if(this.isEmbellished()){var i=this.Core();if(i&&i!==this){j=i.SVGcanStretch(k);if(j&&i.forceStretch){this.forceStretch=true}}}return j},SVGstretchV:function(i,j){return this.toSVG(i,j)},SVGstretchH:function(i){return this.toSVG(i)},SVGlineBreaks:function(){return false}},{SVGautoload:function(){var i=h.autoloadDir+"/"+this.type+".js";c.RestartAfter(b.Require(i))},SVGautoloadFile:function(i){var j=h.autoloadDir+"/"+i+".js";c.RestartAfter(b.Require(j))}});a.chars.Augment({toSVG:function(j,m,i,k){var l=this.data.join("").replace(/[\u2061-\u2064]/g,"");if(i){l=i(l,k)}return this.SVGhandleVariant(j,m,l)}});a.entity.Augment({toSVG:function(j,m,i,k){var l=this.toString().replace(/[\u2061-\u2064]/g,"");if(i){l=i(l,k)}return this.SVGhandleVariant(j,m,l)}});a.mo.Augment({toSVG:function(k,j){this.SVGgetStyles();var s=this.svg=this.SVG();var o=this.SVGgetScale(s);this.SVGhandleSpace(s);if(this.data.length==0){s.Clean();this.SVGsaveData(s);return s}if(j!=null){return this.SVGstretchV(k,j)}else{if(k!=null){return this.SVG.strechH(k)}}var q=this.SVGgetVariant();var y=this.getValues("largeop","displaystyle");if(y.largeop){q=h.FONTDATA.VARIANT[y.displaystyle?"-largeOp":"-smallOp"]}var w=this.CoreParent(),p=(w&&w.isa(a.msubsup)&&this!==w.data[0]),l=(p?this.remapChars:null);if(this.data.join("").length===1&&w&&w.isa(a.munderover)&&this.CoreText(w.data[w.base]).length===1){var t=w.data[w.over],v=w.data[w.under];if(t&&this===t.CoreMO()&&w.Get("accent")){l=h.FONTDATA.REMAPACCENT}else{if(v&&this===v.CoreMO()&&w.Get("accentunder")){l=h.FONTDATA.REMAPACCENTUNDER}}}if(p&&this.data.join("").match(/['`"\u00B4\u2032-\u2037\u2057]/)){q=h.FONTDATA.VARIANT["-TeX-variant"]}for(var r=0,n=this.data.length;r<n;r++){if(this.data[r]){var z=this.data[r].toSVG(q,o,this.remap,l),u=s.w;if(u===0&&-z.l>10*z.w){u+=-z.l}s.Add(z,u,0,true);if(z.skew){s.skew=z.skew}}}s.Clean();if(this.data.join("").length!==1){delete s.skew}if(y.largeop){s.y=h.TeX.axis_height-(s.h-s.d)/2/o;if(s.r>s.w){s.ic=s.r-s.w;s.w=s.r}}this.SVGhandleColor(s);this.SVGsaveData(s);return s},SVGcanStretch:function(m){if(!this.Get("stretchy")){return false}var n=this.data.join("");if(n.length>1){return false}var j=this.CoreParent();if(j&&j.isa(a.munderover)&&this.CoreText(j.data[j.base]).length===1){var l=j.data[j.over],i=j.data[j.under];if(l&&this===l.CoreMO()&&j.Get("accent")){n=h.FONTDATA.REMAPACCENT[n]||n}else{if(i&&this===i.CoreMO()&&j.Get("accentunder")){n=h.FONTDATA.REMAPACCENTUNDER[n]||n}}}n=h.FONTDATA.DELIMITERS[n.charCodeAt(0)];var k=(n&&n.dir==m.substr(0,1));if(!k){delete this.svg}this.forceStretch=k&&(this.Get("minsize",true)||this.Get("maxsize",true));return k},SVGstretchV:function(n,o){var k=this.svg||this.toSVG();var j=this.getValues("symmetric","maxsize","minsize");var m=h.TeX.axis_height*k.scale,i=this.SVGgetMu(k),l;if(j.symmetric){l=2*Math.max(n-m,o+m)}else{l=n+o}j.maxsize=h.length2em(j.maxsize,i,k.h+k.d);j.minsize=h.length2em(j.minsize,i,k.h+k.d);l=Math.max(j.minsize,Math.min(j.maxsize,l));if(l!=j.minsize){l=[Math.max(l*h.TeX.delimiterfactor/1000,l-h.TeX.delimitershortfall),l]}k=h.createDelimiter(this.data.join("").charCodeAt(0),l,k.scale);if(j.symmetric){l=(k.h+k.d)/2+m}else{l=(k.h+k.d)*n/(n+o)}k.y=l-k.h;this.SVGhandleSpace(k);this.SVGhandleColor(k);delete this.svg.element;this.SVGsaveData(k);k.stretched=true;return k},SVGstretchH:function(j){var l=this.svg||this.toSVG(),i=this.SVGgetMu(l);var k=this.getValues("maxsize","minsize","mathvariant","fontweight");if((k.fontweight==="bold"||parseInt(k.fontweight)>=600)&&!this.Get("mathvariant",true)){k.mathvariant=a.VARIANT.BOLD}k.maxsize=h.length2em(k.maxsize,i,l.w);k.minsize=h.length2em(k.minsize,i,l.w);j=Math.max(k.minsize,Math.min(k.maxsize,j));l=h.createDelimiter(this.data.join("").charCodeAt(0),j,l.scale,k.mathvariant);this.SVGhandleSpace(l);this.SVGhandleColor(l);delete this.svg.element;this.SVGsaveData(l);l.stretched=true;return l}});a.mtext.Augment({toSVG:function(){if(h.config.mtextFontInherit||this.Parent().type==="merror"){this.SVGgetStyles();var i=this.SVG(),l=this.SVGgetScale(i);this.SVGhandleSpace(i);var j=this.SVGgetVariant(),k={direction:this.Get("dir")};if(j.bold){k["font-weight"]="bold"}if(j.italic){k["font-style"]="italic"}j=this.Get("mathvariant");if(j==="monospace"){k["class"]="MJX-monospace"}else{if(j.match(/sans-serif/)){k["class"]="MJX-sans-serif"}}i.Add(d.TEXT(l*100/h.config.scale,this.data.join(""),k));i.Clean();this.SVGhandleColor(i);this.SVGsaveData(i);return i}else{return this.SUPER(arguments).toSVG.call(this)}}});a.merror.Augment({toSVG:function(l,j){this.SVGgetStyles();var q=this.SVG(),o=h.length2em(this.styles.fontSize||1)/1000;this.SVGhandleSpace(q);var k=(o!==1?{transform:"scale("+h.Fixed(o)+")"}:{});var s=d(k);s.Add(this.SVGchildSVG(0));s.Clean();if(o!==1){s.removeable=false;var r=["w","h","d","l","r","D","H"];for(var p=0,n=r.length;p<n;p++){s[r[p]]*=o}}q.Add(s);q.Clean();this.SVGhandleColor(q);this.SVGsaveData(q);return q},SVGgetStyles:function(){var i=g.Element("span",{style:h.config.merrorStyle});this.styles=this.SVGprocessStyles(i.style);if(this.style){i.style.cssText=this.style;c.Insert(this.styles,this.SVGprocessStyles(i.style))}}});a.ms.Augment({toSVG:a.mbase.SVGautoload});a.mglyph.Augment({toSVG:a.mbase.SVGautoload});a.mspace.Augment({toSVG:function(){this.SVGgetStyles();var k=this.getValues("height","depth","width");k.mathbackground=this.mathbackground;if(this.background&&!this.mathbackground){k.mathbackground=this.background}var j=this.SVG();this.SVGgetScale(j);var l=this.mscale,i=this.SVGgetMu(j);j.h=h.length2em(k.height,i)*l;j.d=h.length2em(k.depth,i)*l;j.w=j.r=h.length2em(k.width,i)*l;if(j.w<0){j.x=j.w;j.w=j.r=0}if(j.h<-j.d){j.d=-j.h}j.l=0;j.Clean();this.SVGhandleColor(j);this.SVGsaveData(j);return j}});a.mphantom.Augment({toSVG:function(i,k){this.SVGgetStyles();var j=this.SVG();this.SVGgetScale(j);if(this.data[0]!=null){this.SVGhandleSpace(j);j.Add(this.SVGdataStretched(0,i,k));j.Clean();while(j.element.firstChild){j.element.removeChild(j.element.firstChild)}}this.SVGhandleColor(j);this.SVGsaveData(j);if(j.removeable&&!j.element.firstChild){delete j.element}return j}});a.mpadded.Augment({toSVG:function(l,i){this.SVGgetStyles();var o=this.SVG();if(this.data[0]!=null){this.SVGgetScale(o);this.SVGhandleSpace(o);var m=this.SVGdataStretched(0,l,i),t=this.SVGgetMu(o);var s=this.getValues("height","depth","width","lspace","voffset"),k=0,j=0;if(s.lspace){k=this.SVGlength2em(m,s.lspace,t)}if(s.voffset){j=this.SVGlength2em(m,s.voffset,t)}var n=m.h,p=m.d,r=m.w,q=m.y;o.Add(m,k,j);o.Clean();o.h=n+q;o.d=p-q;o.w=r;o.removeable=false;if(s.height!==""){o.h=this.SVGlength2em(o,s.height,t,"h",0)}if(s.depth!==""){o.d=this.SVGlength2em(o,s.depth,t,"d",0)}if(s.width!==""){o.w=this.SVGlength2em(o,s.width,t,"w",0)}if(o.h>o.H){o.H=o.h}if(o.d>o.D){o.D=o.d}}this.SVGhandleColor(o);this.SVGsaveData(o);return o},SVGlength2em:function(l,p,j,q,i){if(i==null){i=-h.BIGDIMEN}var n=String(p).match(/width|height|depth/);var o=(n?l[n[0].charAt(0)]:(q?l[q]:0));var k=h.length2em(p,j,o/this.mscale)*this.mscale;if(q&&String(p).match(/^\s*[-+]/)){return Math.max(i,l[q]+k)}else{return k}}});a.mrow.Augment({SVG:d.ROW,toSVG:function(n,p){this.SVGgetStyles();var k=this.SVG();this.SVGhandleSpace(k);if(p!=null){k.sh=n;k.sd=p}for(var l=0,j=this.data.length;l<j;l++){if(this.data[l]){k.Check(this.data[l])}}k.Stretch();k.Clean();if(this.data.length===1&&this.data[0]){var o=this.data[0].SVGdata;if(o.skew){k.skew=o.skew}}if(this.SVGlineBreaks(k)){k=this.SVGmultiline(k)}this.SVGhandleColor(k);this.SVGsaveData(k);return k},SVGlineBreaks:function(i){if(!this.parent.linebreakContainer){return false}return(h.config.linebreaks.automatic&&i.w>h.linebreakWidth)||this.hasNewline()},SVGmultiline:function(i){a.mbase.SVGautoloadFile("multiline")},SVGstretchH:function(k){var l=this.SVG();this.SVGhandleSpace(l);for(var n=0,j=this.data.length;n<j;n++){l.Add(this.SVGdataStretched(n,k),l.w,0)}l.Clean();this.SVGhandleColor(l);this.SVGsaveData(l);return l}});a.mstyle.Augment({toSVG:function(){this.SVGgetStyles();var i=this.SVG();if(this.data[0]!=null){this.SVGhandleSpace(i);var j=i.Add(this.data[0].toSVG());i.Clean();if(j.ic){i.ic=j.ic}this.SVGhandleColor(i)}this.SVGsaveData(i);return i},SVGstretchH:function(i){return(this.data[0]!=null?this.data[0].SVGstretchH(i):d.NULL())},SVGstretchV:function(i,j){return(this.data[0]!=null?this.data[0].SVGstretchV(i,j):d.NULL())}});a.mfrac.Augment({toSVG:function(){this.SVGgetStyles();var w=this.SVG(),E=this.SVGgetScale(w);var k=d();k.scale=w.scale;this.SVGhandleSpace(k);var m=this.SVGchildSVG(0),l=this.SVGchildSVG(1);var i=this.getValues("displaystyle","linethickness","numalign","denomalign","bevelled");var A=i.displaystyle;var D=h.TeX.axis_height*E;if(i.bevelled){var C=(A?400:150);var n=Math.max(m.h+m.d,l.h+l.d)+2*C;var B=h.createDelimiter(47,n);k.Add(m,0,(m.d-m.h)/2+D+C);k.Add(B,m.w-C/2,(B.d-B.h)/2+D);k.Add(l,m.w+B.w-C,(l.d-l.h)/2+D-C)}else{var j=Math.max(m.w,l.w);var s=h.thickness2em(i.linethickness,this.scale)*this.mscale,y,x,r,o;var z=h.TeX.min_rule_thickness/h.em*1000;if(A){r=h.TeX.num1;o=h.TeX.denom1}else{r=(s===0?h.TeX.num3:h.TeX.num2);o=h.TeX.denom2}r*=E;o*=E;if(s===0){y=Math.max((A?7:3)*h.TeX.rule_thickness,2*z);x=(r-m.d)-(l.h-o);if(x<y){r+=(y-x)/2;o+=(y-x)/2}k.w=j;s=0}else{y=Math.max((A?2:0)*z+s,s/2+1.5*z);x=(r-m.d)-(D+s/2);if(x<y){r+=y-x}x=(D-s/2)-(l.h-o);if(x<y){o+=y-x}k.Add(d.RECT(s/2,s/2,j+2*s),0,D)}k.Align(m,i.numalign,s,r);k.Align(l,i.denomalign,s,-o)}k.Clean();w.Add(k,0,0);w.Clean();this.SVGhandleColor(w);this.SVGsaveData(w);return w},SVGcanStretch:function(i){return false},SVGhandleSpace:function(i){if(!this.texWithDelims&&!this.useMMLspacing){i.x=i.X=h.TeX.nulldelimiterspace*this.mscale}this.SUPER(arguments).SVGhandleSpace.call(this,i)}});a.msqrt.Augment({toSVG:function(){this.SVGgetStyles();var n=this.SVG(),l=this.SVGgetScale(n);this.SVGhandleSpace(n);var k=this.SVGchildSVG(0),o,m;var u=h.TeX.rule_thickness*l,j,i,s,r=0;if(this.Get("displaystyle")){j=h.TeX.x_height*l}else{j=u}i=Math.max(u+j/4,1000*h.TeX.min_root_space/h.em);s=k.h+k.d+i+u;m=h.createDelimiter(8730,s,l);if(m.h+m.d>s){i=((m.h+m.d)-(s-u))/2}o=d.RECT(u,0,k.w);s=k.h+i+u;r=this.SVGaddRoot(n,m,r,m.h+m.d-s,l);n.Add(m,r,s-m.h);n.Add(o,r+m.w,s-o.h);n.Add(k,r+m.w,0);n.Clean();n.h+=u;n.H+=u;this.SVGhandleColor(n);this.SVGsaveData(n);return n},SVGaddRoot:function(j,k,i,m,l){return i}});a.mroot.Augment({toSVG:a.msqrt.prototype.toSVG,SVGaddRoot:function(l,j,o,m,i){var q=(j.isMultiChar?0.55:0.65)*j.w;if(this.data[1]){var n=this.data[1].toSVG();n.x=0;var k=this.SVGrootHeight(j.h+j.d,i,n)-m;var p=Math.min(n.w,n.r);o=Math.max(p,q);l.Add(n,o-p,k)}else{q=o}return o-q},SVGrootHeight:function(k,j,i){return 0.45*(k-900*j)+600*j+Math.max(0,i.d-75)}});a.mfenced.Augment({SVG:d.ROW,toSVG:function(){this.SVGgetStyles();var k=this.SVG();this.SVGhandleSpace(k);if(this.data.open){k.Check(this.data.open)}if(this.data[0]!=null){k.Check(this.data[0])}for(var l=1,j=this.data.length;l<j;l++){if(this.data[l]){if(this.data["sep"+l]){k.Check(this.data["sep"+l])}k.Check(this.data[l])}}if(this.data.close){k.Check(this.data.close)}k.Stretch();k.Clean();this.SVGhandleColor(k);this.SVGsaveData(k);return k}});a.menclose.Augment({toSVG:a.mbase.SVGautoload});a.maction.Augment({toSVG:a.mbase.SVGautoload});a.semantics.Augment({toSVG:function(){this.SVGgetStyles();var i=this.SVG();if(this.data[0]!=null){this.SVGhandleSpace(i);i.Add(this.data[0].toSVG());i.Clean()}else{i.Clean()}this.SVGsaveData(i);return i},SVGstretchH:function(i){return(this.data[0]!=null?this.data[0].SVGstretchH(i):d.NULL())},SVGstretchV:function(i,j){return(this.data[0]!=null?this.data[0].SVGstretchV(i,j):d.NULL())}});a.munderover.Augment({toSVG:function(E,B){this.SVGgetStyles();var j=this.getValues("displaystyle","accent","accentunder","align");if(!j.displaystyle&&this.data[this.base]!=null&&this.data[this.base].CoreMO().Get("movablelimits")){return a.msubsup.prototype.toSVG.call(this)}var C=this.SVG(),L=this.SVGgetScale(C);this.SVGhandleSpace(C);var o=[],J=[],s,I,F,l=-h.BIGDIMEN,H=l;for(I=0,F=this.data.length;I<F;I++){if(this.data[I]!=null){if(I==this.base){o[I]=this.SVGdataStretched(I,E,B);J[I]=(B!=null||E==null)&&this.data[I].SVGcanStretch("Horizontal")}else{o[I]=this.data[I].toSVG();o[I].x=0;delete o[I].X;J[I]=this.data[I].SVGcanStretch("Horizontal")}if(o[I].w>H){H=o[I].w}if(!J[I]&&H>l){l=H}}}if(B==null&&E!=null){l=E}else{if(l==-h.BIGDIMEN){l=H}}for(I=H=0,F=this.data.length;I<F;I++){if(this.data[I]){if(J[I]){o[I]=this.data[I].SVGstretchH(l);if(I!==this.base){o[I].x=0;delete o[I].X}}if(o[I].w>H){H=o[I].w}}}var A=h.TeX.rule_thickness*this.mscale;var n=o[this.base]||{w:0,h:0,d:0,H:0,D:0,l:0,r:0,y:0,scale:L};var r,p,v,u,q,z,G,K=0;if(n.ic){K=1.3*n.ic+0.05}for(I=0,F=this.data.length;I<F;I++){if(this.data[I]!=null){s=o[I];q=h.TeX.big_op_spacing5*L;var w=(I!=this.base&&j[this.ACCENTS[I]]);if(w&&s.w<=1){s.x=-s.l;o[I]=d.G().With({removeable:false});o[I].Add(s);o[I].Clean();o[I].w=-s.l;s=o[I]}z={left:0,center:(H-s.w)/2,right:H-s.w}[j.align];r=z;p=0;if(I==this.over){if(w){G=A*L;q=0;if(n.skew){r+=n.skew;C.skew=n.skew;if(r+s.w>H){C.skew+=(H-s.w-r)/2}}}else{v=h.TeX.big_op_spacing1*L;u=h.TeX.big_op_spacing3*L;G=Math.max(v,u-Math.max(0,s.d))}G=Math.max(G,1500/h.em);r+=K/2;p=n.y+n.h+s.d+G;s.h+=q;if(s.h>s.H){s.H=s.h}}else{if(I==this.under){if(w){G=3*A*L;q=0}else{v=h.TeX.big_op_spacing2*L;u=h.TeX.big_op_spacing4*L;G=Math.max(v,u-s.h)}G=Math.max(G,1500/h.em);r-=K/2;p=n.y-(n.d+s.h+G);s.d+=q;if(s.d>s.D){s.D=s.d}}}C.Add(s,r,p)}}C.Clean();this.SVGhandleColor(C);this.SVGsaveData(C);return C}});a.msubsup.Augment({toSVG:function(G,z){this.SVGgetStyles();var B=this.SVG(),K=this.SVGgetScale(B);this.SVGhandleSpace(B);var E=this.SVGgetMu(B);var k=B.Add(this.SVGdataStretched(this.base,G,z));var j=(this.data[this.sup]||this.data[this.sub]||this).SVGgetScale();var I=h.TeX.x_height*K,y=h.TeX.scriptspace*K;var i,l;if(this.SVGnotEmpty(this.data[this.sup])){i=this.data[this.sup].toSVG();i.w+=y;i.r=Math.max(i.w,i.r)}if(this.SVGnotEmpty(this.data[this.sub])){l=this.data[this.sub].toSVG();l.w+=y;l.r=Math.max(l.w,l.r)}var C=h.TeX.sup_drop*j,A=h.TeX.sub_drop*j;var o=k.h+(k.y||0)-C,n=k.d-(k.y||0)+A,J=0,F;if(k.ic){k.w-=k.ic;J=1.3*k.ic+0.05}if(this.data[this.base]&&(this.data[this.base].type==="mi"||this.data[this.base].type==="mo")){if(this.data[this.base].data.join("").length===1&&k.scale===1&&!k.stretched&&!this.data[this.base].Get("largeop")){o=n=0}}var H=this.getValues("subscriptshift","superscriptshift");H.subscriptshift=(H.subscriptshift===""?0:h.length2em(H.subscriptshift,E));H.superscriptshift=(H.superscriptshift===""?0:h.length2em(H.superscriptshift,E));var m=k.w+k.x;if(!i){if(l){n=Math.max(n,h.TeX.sub1*K,l.h-(4/5)*I,H.subscriptshift);B.Add(l,m,-n);this.data[this.sub].SVGdata.dy=-n}}else{if(!l){values=this.getValues("displaystyle","texprimestyle");F=h.TeX[(values.displaystyle?"sup1":(values.texprimestyle?"sup3":"sup2"))];o=Math.max(o,F*K,i.d+(1/4)*I,H.superscriptshift);B.Add(i,m+J,o);this.data[this.sup].SVGdata.dx=J;this.data[this.sup].SVGdata.dy=o}else{n=Math.max(n,h.TeX.sub2*K);var w=h.TeX.rule_thickness*K;if((o-i.d)-(l.h-n)<3*w){n=3*w-o+i.d+l.h;C=(4/5)*I-(o-i.d);if(C>0){o+=C;n-=C}}B.Add(i,m+J,Math.max(o,H.superscriptshift));B.Add(l,m,-Math.max(n,H.subscriptshift));this.data[this.sup].SVGdata.dx=J;this.data[this.sup].SVGdata.dy=Math.max(o,H.superscriptshift);this.data[this.sub].SVGdata.dy=-Math.max(n,H.subscriptshift)}}B.Clean();this.SVGhandleColor(B);this.SVGsaveData(B);return B}});a.mmultiscripts.Augment({toSVG:a.mbase.SVGautoload});a.mtable.Augment({toSVG:a.mbase.SVGautoload});a["annotation-xml"].Augment({toSVG:a.mbase.SVGautoload});a.math.Augment({SVG:d.Subclass({type:"svg",removeable:false}),toSVG:function(t,j){var v=h.config;if(this.data[0]){this.SVGgetStyles();a.mbase.prototype.displayAlign=c.config.displayAlign;a.mbase.prototype.displayIndent=c.config.displayIndent;if(String(c.config.displayIndent).match(/^0($|[a-z%])/i)){a.mbase.prototype.displayIndent="0"}var p=d.G();p.Add(this.data[0].toSVG(),0,0,true);p.Clean();this.SVGhandleColor(p);h.Element(p.element,{stroke:"currentColor",fill:"currentColor","stroke-width":0,transform:"matrix(1 0 0 -1 0 0)"});p.removeable=false;var q=this.SVG();q.element.setAttribute("xmlns:xlink",f);if(v.useFontCache&&!v.useGlobalCache){q.element.appendChild(d.GLYPH.defs)}q.Add(p);q.Clean();this.SVGsaveData(q);if(!t){q.element=q.element.firstChild;q.element.removeAttribute("transform");q.removable=true;return q}var o=Math.max(-q.l,0),i=Math.max(q.r-q.w,0);var k=q.element.style;q.element.setAttribute("width",h.Ex(o+q.w+i));q.element.setAttribute("height",h.Ex(q.H+q.D+2*h.em));k.verticalAlign=h.Ex(-q.D-2*h.em);k.marginLeft=h.Ex(-o);k.marginRight=h.Ex(-i);q.element.setAttribute("viewBox",h.Fixed(-o,1)+" "+h.Fixed(-q.H-h.em,1)+" "+h.Fixed(o+q.w+i,1)+" "+h.Fixed(q.H+q.D+2*h.em,1));k.marginTop=k.marginBottom="1px";if(q.H>q.h){k.marginTop=h.Ex(q.h-q.H)}if(q.D>q.d){k.marginBottom=h.Ex(q.d-q.D);k.verticalAlign=h.Ex(-q.d)}var s=this.Get("alttext");if(s&&!q.element.getAttribute("aria-label")){t.setAttribute("aria-label",s)}if(!q.element.getAttribute("role")){t.setAttribute("role","math")}t.appendChild(q.element);q.element=null;if(!this.isMultiline&&this.Get("display")==="block"&&!q.hasIndent){var u=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift");if(u.indentalignfirst!==a.INDENTALIGN.INDENTALIGN){u.indentalign=u.indentalignfirst}if(u.indentalign===a.INDENTALIGN.AUTO){u.indentalign=this.displayAlign}if(u.indentshiftfirst!==a.INDENTSHIFT.INDENTSHIFT){u.indentshift=u.indentshiftfirst}if(u.indentshift==="auto"){u.indentshift="0"}var m=h.length2em(u.indentshift,1,h.cwidth);if(this.displayIndent!=="0"){var n=h.length2em(this.displayIndent,1,h.cwidth);m+=(u.indentalign===a.INDENTALIGN.RIGHT?-n:n)}j.style.textAlign=u.indentalign;if(m){c.Insert(k,({left:{marginLeft:h.Ex(m)},right:{marginRight:h.Ex(-m)},center:{marginLeft:h.Ex(m),marginRight:h.Ex(-m)}})[u.indentalign])}}}return t}});a.TeXAtom.Augment({toSVG:function(i,l){this.SVGgetStyles();var j=this.SVG();this.SVGhandleSpace(j);if(this.data[0]!=null){var k=this.SVGdataStretched(0,i,l),m=0;if(this.texClass===a.TEXCLASS.VCENTER){m=h.TeX.axis_height-(k.h+k.d)/2+k.d}j.Add(k,0,m);j.ic=k.ic;j.skew=k.skew}this.SVGhandleColor(j);this.SVGsaveData(j);return j}});c.Register.StartupHook("onLoad",function(){setTimeout(MathJax.Callback(["loadComplete",h,"jax.js"]),0)})});c.Browser.Select({Opera:function(i){h.Augment({operaZoomRefresh:true})}});c.Register.StartupHook("End Cookie",function(){if(c.config.menuSettings.zoom!=="None"){b.Require("[MathJax]/extensions/MathZoom.js")}});if(!document.createElementNS){if(!document.namespaces.svg){document.namespaces.add("svg",e)}h.Augment({Element:function(i,j){var k=(typeof(i)==="string"?document.createElement("svg:"+i):i);k.isMathJax=true;if(j){for(var l in j){if(j.hasOwnProperty(l)){k.setAttribute(l,j[l].toString())}}}return k}})}})(MathJax.Ajax,MathJax.Hub,MathJax.HTML,MathJax.OutputJax.SVG);