/*
 *  ../SourceForge/trunk/mathjax/jax/output/HTML-CSS/jax.js
 *  
 *  Copyright (c) 2010 Design Science, Inc.
 *
 *  Part of the MathJax library.
 *  See http://www.mathjax.org for details.
 * 
 *  Licensed under the Apache License, Version 2.0;
 *  you may not use this file except in compliance with the License.
 *
 *      http://www.apache.org/licenses/LICENSE-2.0
 */

MathJax.Unpack([
  ['(','function(','a,c,d,e){var b=','MathJax','.Object.Subclass({FontInfo:{STIX:{family:"STIXSizeOneSym",','testString',':"() {} []"},TeX:{family:"MathJax_Size1",',5,':"() {} []"}},comparisonFont:["sans-serif","monospace","script","Times","Courier","Arial","Helvetica"],testSize:["40px","50px","60px","30px","20px"],Init:','function(){','this.div','=','MathJax.HTML.','addElement','(','document.body',',"div','",{style:{','position:"absolute','",','visibility:"hidden",','top:0,left:0,','fontSize',':','this.testSize','[0],','fontWeight',':"normal",','fontStyle',':"normal"}},[""]);this.text=',10,'.firstChild','},findFont:',1,'j,g){if(g&&this.','testCollection','(g)){','return g','}for(var ','h=0,f=j','.length;h<f;h++){','if(j[h]===g','){continue}','if(this.',35,'(j[h])){return j[h',']}}return null},',35,':',1,'f','){return',' this.testFont(this.FontInfo[f])},testFont:',1,'h){if(h.','isWebFont','&&e.FontFaceBug){','this.div.style.',26,'=',57,28,'="normal"}else{',57,26,'=(h.weight||"normal");',57,28,'=(h.style||"normal")}','var g=this.','getComparisonWidths','(h.',5,',','h.noStyleChar',');if(g){',57,'fontFamily','="\'"+h.family+"\',"+','this.comparisonFont','[0];if(','this.div.offsetWidth','==g[0]){',57,77,'="\'"+h.family+"\',"+',79,'[g[2]];if(',81,'==g[1]){','return false','}}if(',81,'!=g[3]){if(',74,'||!e.FONTDATA||!','e.FONTDATA.','hasStyleChar',51,' true',38,'j=0,f=',24,'.length;','j<f;j++){',43,'testStyleChar','(h,',24,'[j])){return true}}}}',90,'},styleChar:','String.fromCharCode(','61437),','versionChar',':',112,'61438),compChar:',112,'61439),',106,':',1,'h,j){var m=3+(h.weight?2:0)+(h.style?4:0);var g="",i=0;var l=',57,22,';',57,22,'=j;if(e.msieItalicWidthBug&&h.style==="italic"){this.text.nodeValue=g=','this.compChar',';i=',81,'}','if(e.safariTextNodeBug){this.div.innerHTML=',130,'+g','}else{this.text.nodeValue=',130,'+g}','var f=',81,'-i;',134,'this.styleChar','+g',137,144,'+g}var k','=Math.floor((',81,'-i)/f+0.5);if(k===m){',134,'this.',114,'+g',137,'this.',114,'+g}h.version',149,81,'-i)/f+1.5)/2}',57,22,'=l;return(k===m)},',70,':',1,'j,h){if(e.FONTDATA&&',96,97,'&&!h){j+=',144,'+" "+',130,'}',134,'j',137,'j}',57,77,'=',79,'[0];var g=',81,',l=-1;if(','e.safariWebFontSerif','){',57,77,'=',188,'[0];l=',81,38,'k=1,f=',79,103,'k<f;k++){',57,77,'=',79,'[k];if(',81,'!=g',51,'[g,',81,',k,l',46,'loadWebFont',':',1,'f){','d.Startup.signal.Post("HTML-CSS Jax - ','Web-Font',' "+e.fontInUse+"/"+f.directory',');var h','=','MathJax.Message.','File("Web-Font',219,');var g=',3,'.Callback','(["loadComplete",this,f,h]);c.timer.start(c,[this.checkWebFont,f,g],1);',37,'},loadComplete:',1,'g,i,f){if(f!==c.STATUS.OK){this.loadError(g);if(d.Browser.isFirefox&&e','.allowWebFonts','){var h=','document.location.','protocol+"//"+',235,'hostname;if(',235,'port!=""){h+=":"+',235,'port}h+="/";if(','c.fileURL(e.webfontDir',').substr(0,h.length)!==h){this.','firefoxFontError','(g)}}}',222,'Clear(i)},loadError:',1,'f){',222,'Set("Can\'t ','load web font',219,',null,2000)},',245,':',1,'f){',222,'Set("Firefox can\'t load web fonts from a remote host",null,3000)},checkWebFont:',1,'f,g,h){if(f.time(h)){return}if(','e.Font.testFont(','g)){h(f.STATUS.OK',')}else{','setTimeout(f,f.delay)}},fontFace:',1,'h){var i=','e',233,';var g=',243,'+"/"+i);',140,'h.replace(/-b/,"-B").replace(/-i/,"-I").replace(/-Bold-/,"-Bold");if(!f.match(/-/)){f+="-Regular"}if(i==="svg"){f+=".svg#"+f}else{f+="."+i}var j={"','font-family":',96,'FONTS[h].','family,src:"url(\'"+g+"/"+f+"\')"};if(i==="svg"){j.src+=" format(\'svg\')"}','if(!(e.FontFaceBug&&',96,279,55,')){if(h.match(/-bold/)){j["','font-weight','"]="bold"}if(h.match(/-italic/)){j["font-style"]="italic"}}return j}});e.Augment({config:{useOldImageData:true,styles:{".',3,'":{display:"inline','","font-family":"serif","font-style','":"normal","',286,291,'line-height',291,'font-size":"100%","','font-size-adjust":"none','","text-indent":0,"text-align":"left","text-transform":"none","letter-spacing',291,'word-spacing',291,'word-wrap',291,'white-space":"nowrap","float":"none",','border:0,padding:0,margin:0','},".','MathJax_Display','":{','position:"relative','",display:"block",width:"100%"},".',3,' img, .',3,' nobr, .',3,' a":{',305,',"','max-width":"none","max-height":"none','","','vertical-align":0,"line-height":"normal","text-decoration":"none','"},"img.','MathJax_strut','":{border:"','0 !important','",padding:"',325,'",margin:"',325,'","vertical-align":"',325,'"},".',3,' span',289,'",',305,',"',321,'"},".',3,' .MathJax_HitBox":{cursor:"text','"},"#MathJax_Tooltip','":{',18,'",left:0,top:0,width:"auto",height:"auto",display:"none',343,' *":{filter:"none",background:"transparent"}}},settings:d.config.menuSettings,LEFTBUTTON:(d.Browser.isMSIE?1:0),MENUKEY:"altKey",Font:b(),Config:',9,'this.SUPER(arguments).Config.call(this);',69,'settings;if(g.scale){','this.config.','scale=g.scale}if(g.font&&g.font!=="Auto"){if(g.font==="TeX (local)"){','this.config.availableFonts','=["TeX"];','this.config.preferredFont','="TeX";','this.config.webFont="TeX"}else{if(g.font==="','STIX (local)"){',355,'=["STIX"];',357,'="STIX";',359,'TeX (web)"){',355,'=[];',357,'="";',359,'TeX (image)"){',355,'=[];',357,370,353,'webFont=""}}}}}',140,'this.Font.','findFont(',355,',',357,');if(!f&&this',233,'){f=',353,'webFont;if(f){this.webFonts=true}}if(!f&&',353,'imageFont','){f=',353,391,';this.imgFonts=true}if(f){this.fontInUse=f;this.fontDir+="/"+f;this.webfontDir+="/"+f;if(!this.require){this.require=[]}','this.require.push(this.','fontDir+"/fontdata.js");',43,'imgFonts){',396,'directory+"/imageFonts.js");',217,'using image fonts")}}else{',222,252,'find a valid font using ["+',355,'.join(", ")+"]",null,3000);this.FONTDATA={TeX_factor:1,baselineskip:1.2,lineH:0.8,lineD:0.2,ffLineH:0.8,FONTS:{},VARIANT:{normal:{fonts:[]}},RANGES:[],','DEFAULTFAMILY',':"serif",','DEFAULTWEIGHT',27,'DEFAULTSTYLE',27,'DELIMITERS',':{},RULECHAR:45,REMAP:{}};if(',3,'.InputJax.TeX&&','MathJax.InputJax.TeX.Definitions','){',419,'.macros.overline[1]="002D";',419,'.macros.underline[1]="002D"}',217,'no valid font")}},Startup:',9,'var h=[],l=','this.FONTDATA.','VARIANT.normal.fonts',';if(!(l ','instanceof Array',')){l=[l]}','for(var g=0,f=l',103,'g<f;g++){','h[g]=',429,'FONTS[l[g]].family;if(!h[g]){h[g]=l[g]}}',353,'styles[".',3,' .math span"]=',353,'styles["#','MathJax_getScales','"]={"',277,'h.join(",")};','this.hiddenDiv','=','this.Element("','div',17,20,'overflow:"hidden",','height:"1px",',18,'",top:0}});if(!',15,31,'){',15,'.appendChild(',450,266,15,'.insertBefore(',450,',',15,31,')}',450,'=','this.addElement(',450,',"div",{id:"MathJax_Hidden"});var k=',476,450,',"div',17,'width:"5in"}});this.pxPerInch=k','.offsetWidth','/5;',450,'.removeChild(','k);','this.startMarker','=e','.createStrut(',452,'span"),10,true);','this.endMarker','=','this.addText(',452,'span"),"x").parentNode;','this.HDspan','=',452,'span");',43,'operaHeightBug){this',491,499,',0)}','if(this.msieInlineBlockAlignBug){','this.HDimg','=',476,499,',"img',17,'height:"0px",width:"1px','"}});try{',509,'.src="about:blank"}catch(j){}}else{this.','HDimg=e',491,499,',0)}','this.HDMspan','=',452,'span',17,18,'","',297,'"}});',508,'this.HDMimg','=',476,523,',"img',17,515,'","',319,'",',305,'}});try{',533,518,'HDMimg=e',491,523,',0);',533,'.style.','marginRight=""}','this.marginCheck','=e.Element("span",null,[["','span",{style:{display:"inline-block",','width:"5em','"}}]]);','this.marginMove','=e.',13,'(',554,',"',556,557,'",','marginLeft',':"-5em"}});return c.Styles(',353,'styles,["','PreloadWebFonts','",this])},',572,':',9,'if(!e',233,'||!','e.config.preloadWebFonts',51,38,'g=0,f=',580,103,436,'var h=',96,'FONTS[',580,'[g]];if(!h','.available){',264,'h)}}},Translate:',1,'f){if(!f','.parentNode',51,'}var k=f','.previousSibling;if','(k&&String(k','.className',').match(/^',3,'(_MathML|_Display)?$/)){k',597,487,'k)}var j=f.',3,'.elementJax.root,h,l;h=l=',452,'span','",{className:"',3,'",oncontextmenu:this.ContextMenu,onmousedown:this.Mousedown,onmouseover:this.Mouseover,onclick:this.Click,ondblclick:this.DblClick});if(j.Get("display")==="block"){l=',452,'div',613,307,'",style:{width:"100%",',309,'"}});l',464,'h)}','l.setAttribute("','role","textbox");',625,'aria-readonly","true");f',597,468,'l,f);var g;try{','this.getScales(l,h',');g=(this.em===0||String(this.em)==="NaN")}catch(i){g=true}if(g){',450,464,'l);',632,')}this.initImg(h);this.initHTML(j,h);j.setTeXclass();try{j.toHTML(h,l)}catch(i){if(i.restart){l',597,487,'l)}throw i}if(g){f',597,468,'l,f)}},ContextMenu:',1,'i,j','){if(e.config.showMathMenu','&&(e.settings.context==="',3,'"||j)){if(e.safariContextMenuBug){setTimeout("window.getSelection().empty()",0)}',140,3,'.Menu;if(f){var h=(this',597,602,'==="',307,'"?this',597,':this);f.jax=d.getJaxFor(h.nextSibling);f.menu.items[1].menu.items[1].name=(','f.jax.inputJax.name','==="MathML"?"Original":',661,');return ','f.menu.Post(i',266,'if(!','c.loadingMathMenu','){',668,'=true;','if(!i){i=window.event}','var g={pageX:i.pageX,pageY:i.pageY,clientX:i.clientX,clientY:i.clientY};',3,227,'.Queue(c.Require("[',3,']/extensions/MathMenu.js"),',9,'delete ',668,'},[this,arguments.callee,g,j])}',672,'if(','i.preventDefault','){',685,'()}if(','i.stopPropagation','){',689,'()}i.cancelBubble=true;i.returnValue=false;',90,'}}},Mousedown:',1,'f',647,'){if(!f){f=window.event}if(e.settings.context==="',3,'"){if(!e.noContextMenuBug||f.button!==2',51,'}}else{if(!f[e.MENUKEY]||f.button!==e.LEFTBUTTON',51,'}}return e.ContextMenu.call(this,f,true)}},Mouseover:',1,'f){e.HandleEvent(f,"','Mouseover",this)},Click:',1,706,'Click",this)},DblClick:',1,706,'DblClick",this)},HandleEvent:',1,'h,f,g){},initImg:',1,'f){},initHTML:',1,'g,f){},initFont:',1,'f',234,96,'FONTS,g=e.config.availableFonts;if(g&&g.length&&',264,'h[f])){h[f].available=true;return null}if(!this',233,51,' null}h[f].','isWebFont=true;if(e.FontFaceBug){','h[f].family','=f}return ','c.Styles({"@font-face":',380,'fontFace(f)})},Remove:',1,'f){var g=','f.SourceElement();if(!g',51,'}g=g',600,'(!g',51,'}if(g',602,'.match(/^',3,'/)){g',597,487,'g)}},getScales:',1,'i,f){i',597,468,523,',i);',523,602,370,499,'.id',370,523,'.style.fontSize',370,533,'.style.height','="1px";',533,'.style.width','="60ex";var h=',523,484,'/60;',523,602,'="',3,'";',499,'.id="',446,'";',533,771,'="60em";',69,'outerEm=',523,484,'/60;var j',149,'h/this.TeX.x_height)/g*',353,'scale);f',765,'=',523,765,'=j+"%";this.em=a.mbase.prototype.em=',523,484,'/60;i',597,487,523,');','this.msieMarginScale','=this.getMarginScale(f)},getMarginScale:',1,'f',51,' 1},getMSIEmarginScale:',1,'h){h',464,554,');',140,554,484,',g=',559,484,';var i=g/(2*g-f);h',487,554,664,'i},getHD:',1,'g){',140,'g','.style.position',';g',835,'="absolute";',509,768,'="0px";g',464,499,220,'={h:g','.offsetHeight','};',509,768,'=h.h+"px";h.d=g',846,'-h.h;h.h-=h.d;h.h/=this.em;h.d/=this.em;g',487,499,');g',835,'=f;return h},getW:',1,'i){var g=i',484,',h=(i.bbox?i.bbox.w:-1),j=i;if((h<0||this.negativeSkipBug)&&g>=0){','if(this.negativeSkipBug){',140,'i',835,';i',835,838,'j=',489,';if(i',31,'){i',468,'j,i',31,266,'i',464,'j)}j=',489,'}i',464,494,');g=',494,'.offsetLeft-j.offsetLeft;i',487,494,');',862,'i',487,'j);i',835,'=f}}',37,'/this.em},Measured:',1,'h,g){if(h','.bbox.width','==null&&h.bbox.w&&!h.bbox.isMultiline){',140,'this.getW(h);h.bbox.rw+=f-h.bbox.w;h.bbox.w=f}if(!g){g=h',597,'}if(!','g.bbox){g.bbox','=h.bbox}return h},Remeasured:',1,'g,f){f.bbox=this.Measured(g,f).bbox},Em:',1,'f){if(Math.abs(f)<0.0006',51,'"0em"}return f.toFixed(3',').replace(/\\.?0','+$/,"")+"em"},Percent:',1,'f',51,'(100*f).toFixed(1',915,'+$/,"")+"%"},length2percent:',1,'f',51,' ','this.Percent(','this.length2em(f','))},length2em:',1,'k,i){if(typeof(k)!=="string"){k=k.toString()}if(k===""){return""}','if(k===a.SIZE.','NORMAL',51,' 1}',932,'BIG',51,' 2}',932,'SMALL',51,' 0.71}if(k==="infinity"){return e.BIGDIMEN}var h=',429,'TeX_factor;if(k.match(/mathspace$/)){return e.MATHSPACE[k]*h}var g=k.match(/^\\s*([-+]?(?:\\.\\d+|\\d+(?:\\.\\d*)?))?(pt|em|ex|mu|px|in|mm|cm|%)?/);',140,'parseFloat(g','[1]||"1"),j=g[2];if(i==null){i=1','}if(j==="','em','"){return f','*h',949,'ex',951,'*e.TeX.x_height*h}if(j==="%"){return f/100*i',949,'px',951,'/e.em',949,'pt',951,'/10*h',949,'in','"){return f*this.pxPerInch/e.em',949,'cm',967,'/2.54',949,'mm',967,'/25.4',949,'pc',967,'/12',949,'mu',951,'/18*h}return f*h*i},thickness2em:',1,737,'e.TeX.rule_thickness;','if(f===a.LINETHICKNESS.','MEDIUM',51,' g}',987,'THIN',51,' 0.67*g}',987,'THICK',51,' 1.67*g}return ',928,',g)},createStrut:',1,'i,g,j){',140,452,556,456,'height:g+"px",width:"1px",marginRight:"-1px"}});if(j){i',468,'f,i',31,266,'i',464,'f)}return f},createBlank:',1,'g,f,',269,452,556,456,457,'width',':this.Em(f)}});if(','h){g',468,'i,g',31,266,'g',464,'i)}return i},createShift:',1,'g,f,i',234,452,'span',17,568,1023,'i){g',468,'h,g',31,266,'g',464,'h)}return h},createSpace:',1,'k,j,m,f,g){var i','=this.Em(','Math.max(','0,j+m)),l','=this.Em(-m);',508,'l',1050,'e.getHD(k',597,').d-m)}if(k.isBox||k',602,'=="mspace"){','k.bbox={h:j*k.scale,d:m*k.scale,w:f*k.scale,rw:f*k.scale,lw:0};k',768,'=i;k',552,'verticalAlign','=l}else{k=',476,'k,"span',17,'height:i,',1066,':l}})}if(f>=0){k',771,1050,'f);k',552,'display="inline-block"}else{',43,'msieNegativeSpaceBug){k',768,'=""}k',552,568,1050,'f);if(e.safariNegativeSpaceBug&&k',597,31,'==k){this','.createBlank(','k,0,true)}}if(g&&g!==a.COLOR.TRANSPARENT){k',552,'backgroundColor=g}return k},createRule:',1,'o,k,m,p,i){var j=e.TeX.','min_rule_thickness',';if(p>0&&p*this.em<j){p=j/this.em}if(k+m>0&&(k+m)*this.em<j){var l=1/(k+m)*(j/this.em);k*=l;m*=l}if(!i){i="solid"}else{i="solid "+i}i',1050,'p)+" "+i;var q',1050,'k+m),g',1053,'var n=',476,'o,"span',17,'borderLeft:i,','display:"inline-block",',456,'width:0,height:','q,',1066,':g},bbox:{h:k,d:m',',w:p,rw:p,lw:0},noAdjust:true});if(','p>0&&n',484,'==0){n',771,1050,'p)}if(o.isBox||o',602,1061,'o.bbox=n.bbox}','return n},createFrame:',1,'o,m,n,p,r,g){var l=(this.msieBorderWidthBug?0:2*r);var q',1050,'m+n-l),f=this.Em(-n-r),k',1050,'p-l);var i',1050,'r)+" "+g;var j=',476,'o,"span',17,'border:i,',1108,456,'width:k,height:q},bbox:{h:m,d:n',1114,'f){j',552,1066,732,'j},createStack:',1,'h,j,g){',43,'msiePaddingWidthBug){this',491,'h,0)}var i=String(g).match(/%$/);var f=(!i&&g!=null?g:0);h=',476,'h,"span",{noAdjust:true,style:{',1108,309,'",width:(i?"100%":this.Em(f)),height:0}});if(!j){h',597,'.bbox=h.bbox={','h:-this.BIGDIMEN,d:-this.BIGDIMEN',',w:f,lw:','this.BIGDIMEN',',rw:(!i&&g!=null?g:-',1161,')};if(i){h',901,'=g}}return h},createBox:',1,'g,f',234,476,'g,"span',17,18,'"},isBox:true});if(f!=null){h',771,732,'h},addBox:',1,'f,g){g',835,838,'g.isBox=true;return f',464,'g)},placeBox:',1,'n,m,k,i){var o=n',597,',v=n.bbox,q=o.bbox;',43,'msiePlaceBoxBug){',496,'n,this.NBSP)}',43,'imgSpaceBug){',496,'n,this.imgSpace)}var p=n',846,'/this.em+1,z=0;if(n.noAdjust){p-=1}else{',508,476,'n,"img',613,323,'",border:0,src:"about:blank",style:{',1110,'this.Em(p',')}})}else{',476,'n,"',556,1110,1206,')}})}}n','.style.top=this.Em(-','k-p);n',552,'left',1050,'m+z);if(v){',862,'if(v.lw<0){z=v.lw;e',1090,'n,-z,true);h=0}if(v.rw>v.w){e',1090,'n,v.rw-v.w+0.1)}}if(!this.msieClipRectBug&&!v.noclip&&!i){var u=3/this.em;var s=(v.H==null?v.h:v.H),g=(v.D==null?v.d:v.D);var w=p-s-u,j=p+g+u,h=v.lw-3*u,f=1000;if(v.isFixed){f=v.width-h}n',552,'clip="rect("+this.Em(w',')+" "+this.Em(','f',1228,'j',1228,'h)+")"}}if(v&&q){if(v.H!=null&&(q.H==null||v.H+k>q.H)){q.H=v.H+k}if(v.D!=null&&(q.D==null||v.D-k>q.D)){q.D=v.D-k}if(v.h+k>q.h){q.h=v.h+k}if(v.d-k>q.d){q.d=v.d-k}if(q.H!=null&&q.H<=q.h){delete q.H}if(q.D!=null&&q.D<=q.d){delete q.D}if(v.w+m>q.w){q.w=v.w+m;if(q.width==null){o',771,1050,'q.w)}}if(v.rw+m>q.rw){q.rw=v.rw+m}if(v.lw+m<q.lw){q.lw=v.lw+m}if(v','.width!=null&&!','v.isFixed){if(q.width==null){o',771,'=q.width="100%"}n',771,'=v.width}}},alignBox:',1,'h,n,m){','this.placeBox(','h,0,m);var j=h.bbox;if(j.isMultiline',51,'}var g=j',1237,'j.isFixed;var i=0,k=-j.w/2,f="50%";',862,'i=j.w-j.rw-0.1;k+=j.lw}k',1050,'k*',809,75,'k',370,'f=(50-parseFloat(j.width)/2)+"%"}d.Insert(h.style,({right:{left:"",right:this.Em(i)},center:{left:f,',568,':k}})[n])},setStackWidth:',1,'g,f){if(typeof(f)==="number"){g',771,1050,1051,'0,f));if(',907,'.w=f}if(g',597,'.bbox){g',597,'.bbox.w=f}}else{g',771,'=g',597,771,'="100%";if(',907,'.width=f}if(g',597,'.bbox){g',597,901,'=f}}},createDelimiter:',1,'q,f,h,l,j){if(!f){q.bbox={h:0,d:0,w:this.TeX.','nulldelimiterspace',',lw:0};q.bbox.rw=q.bbox.w;this.createSpace(q,q.bbox.h,q.bbox.d,q.bbox.w);return}if(!l){l=1}if(!(h ',432,')){h=[h,h]}var p=h[1];h=h[0];var g={alias:f};while(g.alias){f=g.alias;g=',429,415,'[f];if(!g){g={HW:[0,',429,'VARIANT[a.VARIANT.NORMAL',']]}}}for(var o=0,k=g.HW',103,'o<k;o++){if(g.HW[o][0]*l>=h-0.01||(o==k-1&&!g.stretch)){if(g.HW[o][2]){l*=g.HW[o][2]}if(g.HW[o][3]){f=g.HW[o][3]}var n=',476,'q,"',502,'this.createChar(','n,[f,g.HW[o][1]],l,j);q.bbox=n.bbox;q.offset=0.65*q.bbox.w;q.scale=l;return}}if(g.stretch){this["extendDelimiter"+g.dir](q,p,g.stretch,l,j)}},extendDelimiterV:',1,'u,o,z,A,r){var i','=this.createStack(','u,true);var q','=this.createBox(','i),p',1309,'i);',1303,'q,(z.top','||z.ext),A,r);',1303,'p,(z.bot',1315,'var g={bbox:{w:0,lw:0,rw:0}},x=g;var v=q.bbox.h+q.bbox.d+','p.bbox.h+p.bbox.d;','var l=-q.bbox.h;',1245,'q,0,l,true);l-=q','.bbox.d;if(z.mid','){x',1309,'i);',1303,'x,z.mid,A,r);v+=','x.bbox.h+x.bbox.d','}if(o>v){g=',452,502,1303,'g,z.ext,A,r);var w=g.bbox.h+g.bbox.d,f=w-0.05,s,j,t=(z.mid?2:1);j=s=Math.ceil((o-v)/(t*f));if(!z.fullExtenders){f=(o-v)/(t*s)}var m=(s/(s+1))*(w-f);f=w-m;l+=m+f-g.bbox.h;while(t-->0){while(s-->0){l-=f;',1245,'this.addBox(','i,g','.cloneNode(true)),','0,l,true)}l+=m-g',1324,'&&t){',1245,'x,0,l-x.bbox.h,true);','s=j;l+=-(',1330,')+m+f-g.bbox.h}}}else{l+=(v-o)/2;if(z.mid){',1245,1344,'l+=-(',1330,')}l+=(v-o)/2}',1245,'p,0,l-p.bbox.h,true);l-=',1320,'u.bbox={w:',1051,'q.bbox.w,g.bbox.w,p.bbox.w,x.bbox.w),lw:Math.min(q.bbox.lw,g.bbox.lw,p.bbox.lw,x.bbox.lw),rw:',1051,'q.bbox.rw,g.bbox.rw,p.bbox.rw,x.bbox.rw),h:0,d:-l};u.scale=A;u.offset=0.55*u.bbox.w;u','.isMultiChar=true;this.setStackWidth(','i,u.bbox.w)},extendDelimiterH:',1,'t,g,y,A,q){var j',1307,'t,true',220,1309,'j),u',1309,'j);',1303,'h,(y.left','||y.rep),A,q);',1303,'u,(y.right',1374,140,452,502,1303,'f,y.rep,A,q);var v={bbox:{',1159,'}};',1245,'h,-h.bbox.lw,0,true);var o=(','h.bbox.rw-h.bbox.lw',')+(u.bbox.rw-u.bbox.lw)-0.05,m=',1387,'-0.025;if(y.mid){v',1309,'j);',1303,'v,y.mid,A,q);o+=v.bbox.w}if(g>o){var z=f.bbox.rw-f.bbox.lw,i=z-0.05,r,l,s=(y.mid?2:1);l=r=Math.ceil((g-o)/(s*i));i=(g-o)/(s*r);var p=(r/(r+1))*(z-i);i=z-p;m-=f.bbox.lw+p;while(s-->0){while(r-->0){',1245,1337,'j,f',1339,'m,0,true);m+=i}if(y.mid&&s){',1245,'v,m,0,true);m+=v.bbox.w','-p;r=l}}}else{m-=(o-g)/2;if(y.mid){',1245,1401,'}m-=(o-g)/2}',1245,'u,m,0,true);t.bbox={w:m+u.bbox.rw,lw:0,rw:m+u.bbox.rw,H:',1051,'h.bbox.h,f.bbox.h,u.bbox.h,v.bbox.h),D:',1051,'h.bbox.d,f.bbox.d,u.bbox.d,v.bbox.d),h:f.bbox.h,d:f.bbox.d};t.scale=A;t',1361,'j,t.bbox.w)},createChar:',1,'o,k,h,f){var n=o,p="",j={fonts:[k[1]],noRemap:true};if(f&&f===a.VARIANT.BOLD){j.fonts=[k[1]+"-bold",k[1]]}if(typeof(k[1])!=="string"){j=k[1]}if(k[0] ',432,'){for(var l=0,','g=k[0].length;l<g;l++){p+=',112,'k[0][l])}}else{p=',112,'k[0])}if(h!==1){n=',476,'o,"span',17,22,':',927,'h)},scale:h});','this.handleVariant(','n,j,p);',1123,'else{',1430,'o,j,p)}if(k[2]){o',552,568,1050,'k[2])}',43,'AccentBug&&o.bbox.w===0){n',31,'.nodeValue+=this.NBSP;e.createSpace(o,0,0,-o',484,'/e.em)}},positionDelimiter:',1,'g,f){f-=g.bbox.h;g.bbox.d-=f;g.bbox.h+=f;if(f){',43,'safariVerticalAlignBug||this.msieVerticalAlignBug||this.konquerorVerticalAlignBug||(this.operaVerticalAlignBug&&g.isMultiChar)){if(g',31,552,'display===""&&g',552,'top!==""){g=g',31,';f-=',947,552,'top)}g',835,'="relative";g',1214,'f',266,'g',552,1066,1050,'f);if(e.ffVerticalAlignBug){e.createRule(g',597,',g.bbox.h,0,0)}}}},handleVariant:',1,'v,j,o){var u="",s,y,p,g,x,z,f=v;if(o.length===0',51,'}if(!v.bbox){v.bbox={w:0,',1159,',rw:-',1161,',lw:',1161,'}}if(!j){j=',429,1296,']}z=j;for(var w=0,t=o',103,'w<t;w++){j=z;','s=o.charCodeAt(w',');y=o.charAt(w);if(y===this.PLANE1){w++;',1487,')+119808-56320;if(',429,'RemapPlane1','){var A=',429,1492,'(s,j);s=A.n;j=A.variant}}else{var q,l,r=',429,'RANGES;for(q=0,l=r',103,'q<l;q++){if(r[q].name==="alpha"&&j.noLowerCase',42,'var k=j["offset"+r[q].offset];if(k&&s>=r[q].low&&s<=r[q].high){if(r[q].remap&&r[q].remap[s]){s=k+r[q].remap[s]}else{s=s-r[q].low+k;if(r[q].add){s+=r[q].add}}if(','j["variant"+r[q].offset',']){j=',429,'VARIANT[',1503,']]}break}}}if(j.remap&&j.remap[s]){if(j.remap[s] ',432,234,'j.remap[s];s=h[0];j=',429,1506,'h[1]]}else{s=j.remap[s];if(','j.remap.variant','){j=',429,1506,1515,']}}}if(',429,'REMAP[s]&&!j.noRemap){s=',429,'REMAP[s]}p=this.lookupChar(j,s);y=p[s];if(j!==x&&!y[5].img){if(u','.length){',496,'f,u);u=""}f=v;x=g;if(j!==x){if(x){f=',476,'v,"span")}else{g=j}}this.handleFont(f,p,f!==v);x=j}u=this.handleChar(f,p,y,s,u);if(y[0',']/1000>v.bbox.','h){v.bbox.h=y[0]/1000}if(y[1',1530,'d){v.bbox.d=y[1',']/1000}if(v.bbox.w+y[','3]/1000<v.bbox.lw){v.bbox.lw=v.bbox.w+y[3',1534,'4',1530,'rw){v.bbox.rw=v.bbox.w+y[4]/1000}v.bbox.w+=y[2]/1000}if(u',1525,496,'f,u)}if(v.scale&&v.scale!==1){v.bbox.h','*=v.scale;v.bbox.','d',1543,'w',1543,'lw',1543,'rw*=v.scale}if(o.length==1&&p.skew&&p.skew[s]){v.bbox.skew=p.skew[s]}},handleFont:',1,'h,f,j){h',552,77,'=f.family;',281,'f.',55,')){var g=f.style||',429,413,',i=f.weight||',429,411,';if(g','!=="normal"||j){h.style.',28,'=g}if(i',1566,26,'=i}}},handleChar:',1,'g,f,k,j,i',234,'k[5];if(h.img',51,' this.handleImg(',1573,')}if(h.c==null){if(j<=65535){h.c=',112,'j',266,'h.c=this.PLANE1+',112,'j-119808+56320)}}if(k[2]||!this.msieAccentBug||i.length',51,' i+h.c}','e.createShift(g',',k[3]/1000);',1588,',(k[4]-k[3])/1000);',496,'g,h.c);',1588,',-k[4]/1000);return""},handleImg:',1,'g,f,j,i,h',51,' h},lookupChar:',1,'j,p){var h,f;if(!j.FONTS){var o=',429,'FONTS;var l=(j.fonts||',429,430,');if(!(l ',432,433,'if(j.fonts!=l){j.fonts=l}j.FONTS=[];for(h=0,f=l',40,'if(o[l[h]]){j.FONTS.push(o[l[h]]);o[l[h]].name=l[h]}}}for(h=0,f=j.FONTS',40,'var g=j.FONTS[h];if(typeof(g)==="string"){delete j.FONTS;this.loadFont(g)}if(g[p]){if(g[p].length===5){g[p][5]={}}if(e',233,'&&!g',592,'this.',213,'(g',266,37,'}}else{this.findBlock(g,p)}}var k=(j.defaultFont||{family:',96,409,'+",serif"});k[p]=[800,200,500,0,500,{isUnknown:true}];return k},findBlock:',1,'g,n){if(g.Ranges',1417,'f=g.Ranges',103,'l<f;l++){if(n<g.Ranges[l][0]){return}if(n<=g.Ranges[l][1]){var k=g.Ranges[l][2];for(var h=g.Ranges.length-1;h>=0;h--){if(g.Ranges[h][2]==k){g.Ranges.splice(h,1)}}this.loadFont(g.directory+"/"+k+".js")}}}},loadFont:',1,'g){',140,3,227,'.Queue();','f.Push(["Require",c,this.','fontDir+"/"+g]);',43,399,'if(!',3,'.isPacked){g=g.replace(/\\/([^\\/]*)$/,e.imgPacked+"/$1")}',1638,'webfontDir+"/png/"+g])}','d.RestartAfter(','f.Push({}))},',213,':',1,'f){f.available=f.',730,'f.family=f.name}',1647,380,213,'(f))},Element:',12,'Element,',13,':',12,13,',TextNode:',12,'TextNode,addText:',12,'addText,ucMatch:',12,'ucMatch,BIGDIMEN:10000000,ID:0,idPostfix:"",GetID:',9,'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},TeX:{x_height:0.430554,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_spacing4:0.6,big_op_spacing5:0.1,scriptspace:0.1,',1288,':0.12,delimiterfactor:901,delimitershortfall:0.1,',1096,':1.25},PLANE1:String.fromCharCo'],
  ['de(55349),NBSP:String.fromCharCode(160),rfuzz:0});a.mbase','.Augment({toHTML:function(','l){var j','=this.','HTMLlineBreaks','();if(','j','.length','>2){','return ','this.','toHTMLmultiline','(l,j)}l=','this.HTMLcreateSpan(','l);','if(this.','type!="mrow"){l','=this.HTMLhandleSize(','l)}','for(var ','g=0,f=','this.data','.length;g<f;g++){','if(',21,'[g]){',21,'[g].toHTML(','l)}}var o=','this.HTMLcomputeBBox(','l);var k=l.bbox.h,n=l.bbox.d;for(',20,'o',22,'o[g].','HTMLstretchV','(l,k,n)}if(o',7,'){',29,'l,true)}','this.HTMLhandleSpace(','l',');this.HTMLhandleColor(','l);',9,'l},',4,':function(){','var k=[[0,this]];','for(var h=0,f=',21,'.length;h<f;h++){','if(',21,'[h]){','var l=',21,'[h].lineBreak',5,'l!=="none"){var g=(l==="after"?h+1:h);if(k',7,'===0||k[k',7,'-1]!==g){k.push([g,',21,'[h]])}else{k[k',7,'-1]=[g,',21,'[h]]}}}}k.push([',21,7,',k[k',7,'-1][1]]);',9,'k},',11,':function(','f){a.mbase.','HTMLautoloadFile','("multiline")},','HTMLcomputeBBox',79,'l,k,j,','f){if(','j','==null){','j=0}if(f',88,'f=',21,7,'}var h=','l.bbox={},n=[];while(j<f','){var g','=',21,'[j];if(!g){continue}if(!k&&g.','HTMLcanStretch','("Vertical")){','n.push(g);g=(g.CoreMO()||g)}',10,'HTMLcombineBBoxes','(g,h);j++}',10,'HTMLcleanBBox','(h);',9,'n},',104,79,'f,g){if(g.w',88,10,'HTMLemptyBBox','(g)}var i=f.','HTMLspanElement','();if(!i||!i.bbox){return',94,'i.bbox;if(h.d>g.d){g.d=h.d}if(h.h>g.h){g.h=h.h}if(h.D!=null&&h.D>g.D){g.D=h.D}if(h.H!=null&&h.H>g.H){g.H=h.H}if(i','.style.paddingLeft','){g.w+=','parseFloat(','i',122,')*(i.scale||1)}if(','g.w+h.lw<g.lw){g.lw=g.w+h.lw}if(g.w+h.rw>g.rw){g.rw=g.w+h.rw}g.w+=h.w;if(i','.style.paddingRight','){g.w+=',124,'i',129,127,'h.width){g.width=h.width}},',116,79,'f','){f.h=f.d=f.H=f.D=f.','rw=-','e.BIGDIMEN',';f.w=0;f.lw=',141,';',9,'f},',107,79,86,'f.h===',10,'BIGDIMEN',139,'w=f.rw=f.lw=0}if(f.D<=f.d){delete f.D}if(f.H<=f.h){delete f.H}},','HTMLzeroBBox',48,'return{h:0,d:0,w:0,lw:0,rw:0}},',100,79,'f){',15,'isEmbellished','()){',9,10,'Core().',100,'(f)}',9,'false},','HTMLstretchH',79,'g,f){',9,10,118,'()},',35,79,'g,f,i){',9,10,118,177,'HTMLnotEmpty',79,'f){while(f){if((f.type!=="mrow"&&f.type!=="texatom")||f.data',7,'>1){',9,'true}f=f.data[0]}',9,170,'HTMLmeasureChild',79,173,'if(',21,'[g]!=null){','e.Measured(',21,27,'f),f)}else{f.bbox',3,155,'()}},HTMLcreateSpan',79,'f){',15,'spanID',96,3,118,5,'g){while(g','.firstChild','){g','.removeChild(','g',216,')}g','.bbox={w:0,h:0,d:0,lw:0,','rw:0};g.scale=1;g.isMultChar=null;g','.style.cssText','="";',9,'g}}',15,'href){f','=','e.addElement(','f,"a",{href:',10,'href})}f=',231,'f,"span",{className:',10,'type});if(e.imgHeightBug){f.style.display="inline-block"}if(this["class"]!=null){f.className+=" "+this["class"]}',15,'style){f',224,3,'style;if(f','.style.fontSize','){',10,'mathsize','=f',244,';f',244,'=""}}',10,'spanID=','e.GetID();f.id=(','this.id||"MathJax-Span-"+this.spanID)+e.idPostfix',';f',222,'lr:0};',15,229,'.parentNode','.bbox=f.bbox}',9,'f},',118,48,'if(!',10,210,'){',9,'null}',9,'document.getElementById','((',256,')},','HTMLhandleVariant',79,'g,f,h){e.handleVariant(g,f,h)},HTMLhandleSize',79,'f){if(!','f.scale){f.scale','=this.HTMLgetScale',5,'f.scale!==1){f',244,'=e.Percent(f.scale)}}',9,'f},','HTMLhandleColor',79,'k){var m','=this.getValues("','mathcolor','","color");if(this','.mathbackground','){m',298,'=this',298,'}if(','this.background','){m.','background','=',304,'}',15,'style&&k.style.','backgroundColor','){m',298,'=k.style.',312,'}if(m.','color&&!',10,296,305,296,'=m.color',317,306,'&&!this',298,'){m',298,'=m.',306,317,296,'){k.style.color=m.',296,'}if(m',298,'&&m',298,'!==a.COLOR.TRANSPARENT){','var n=','1/e.em,j=0,i=0;',15,'isToken){j=k.bbox.lw;i=','k.bbox.rw','-k.bbox.w','}if(k',122,'!==""){j+=',124,'k',122,')*(k.scale||1)}','if(k',129,'!==""){i-=',124,'k',129,353,'var h','=Math.max(','0,e.getW(k)+(e.PaddingWidthBug?0:i-j));if(e.','msieCharPaddingWidthBug','&&k',122,'!==""){h+=',124,'k',122,353,56,'k.bbox.h+k.bbox.d',',f=-k.bbox.d;if(h>0){h+=2*n;j-=n}if(l>0){l+=2*n;f-=n}i=-h-j;var g=e.Element("span",{id:"','MathJax-Color-"+this.spanID+e.idPostfix',',style:{display:"inline-block",',312,':m',298,',','width:e.Em(h),height:e.Em(l),','verticalAlign:e.Em(f),','marginLeft',':e.Em(j),','marginRight',':e.Em(i)}});if(e.','msieInlineBlockAlignBug','){g','.style.position="relative";','g','.style.width','=g.style.','height=0;g','.style.verticalAlign',392,383,392,385,225,'e.placeBox(',231,'g,"span",{noAdjust:true',376,'position:"absolute",overflow:"hidden",',381,306,':m',298,'}}),j,k.bbox.h+n)}k',262,'.insertBefore(','g,k);',9,'g}',9,'null},HTMLremoveColor',48,'var f=',275,'("',375,');if(f){f',262,218,'f)}},','HTMLhandleSpace',79,'i){',15,'useMMLspacing','){',15,'type!=="mo"){return}var g',295,'scriptlevel','","lspace","','rspace','");if(g.',435,'<=0||',10,'hasValue("','lspace")||',10,442,437,'")){','g.lspace',362,'0,','e.length2em(',448,'));','g.rspace',362,'0,',451,454,'));var f=this,h',3,'Parent();while(h&&h.',162,'()&&h.Core()===f){f=h;h=h.Parent();i=f.',118,'()}if(',448,'){i',122,'=e.Em(',448,')}if(',454,'){i',129,469,454,')}}}else{var j',3,'texSpacing',5,'j!==""){j=',451,'j)/(i.scale||1);if(i',122,'){j+=',124,'i',122,')}i',122,469,'j)}}},','HTMLgetScale',48,'var h=1,f',295,247,'","',435,'","fontsize","scriptminsize");',15,'style',96,3,118,5,'g',244,'!=""){f.fontsize=g',244,'}}if(f.fontsize&&!',10,247,'){f.',247,'=f.fontsize}if(f.',435,'!==0){if(f.',435,8,'f.',435,'=2}h=Math.pow(',10,'Get("scriptsizemultiplier"),f.',435,');','f.scriptminsize','=',451,528,');if(h<',528,'){h=',528,'}}h*=',451,'f.',247,');',9,'h},','HTMLgetVariant',48,'var f',295,'mathvariant','","fontfamily","','fontweight','","','fontstyle','");',15,'style){var h',3,118,5,'h.style.fontFamily','){','f.fontfamily','=',558,'}if(','h.style.fontWeight','){f.',549,'=',564,'}if(','h.style.fontStyle','){f.fontStyle=',570,'}}var g=f.',547,';',15,'variantForm){g="-"+e.fontInUse+"-variant"}if(',560,'&&!',10,547,'){if(!f.',549,'&&f.',547,'.match(/bold/)){f.',549,'="bold"}if(!f.',551,584,547,'.match(/italic/)){f.',551,'="italic"}return{FONTS:[],fonts:[],noRemap:true,defaultFont:{family:',560,',style:f.',551,',weight:f.',549,'}}}if(f.',549,'==="bold"){g={normal',':a.VARIANT.','BOLD,italic',603,'BOLDITALIC',',fraktur',603,'BOLDFRAKTUR,script',603,'BOLDSCRIPT,"','sans-serif":a.VARIANT.','BOLDSANSSERIF',',"sans-serif','-italic":a.VARIANT.','SANSSERIFBOLDITALIC}[g]||g}else{if(f.',549,'==="normal"){g={','bold',603,'normal,"bold',615,'ITALIC,"bold-fraktur":a.VARIANT.FRAKTUR,"bold-script":a.VARIANT.SCRIPT,"bold-',612,'SANSSERIF',614,'-bold',615,'SANSSERIFITALIC','}[g]||g}}','if(f.',551,'==="italic"){g={normal',603,'ITALIC,bold',603,606,',"',612,629,',"bold-',612,616,551,618,'italic',603,'NORMAL,"bold',615,'BOLD',614,615,'SANSSERIF',614,'-bold',615,613,630,9,'e.FONTDATA.','VARIANT[g',']}},{HTMLautoload',48,'var f','=e.autoloadDir+"/"+',10,'type','+".js";d.RestartAfter(c.Require(','f))},',81,79,'f',96,665,'f',668,'g))},',171,79,'g,f','){this.HTMLremoveColor();',9,10,'toHTML(g,f',')},',35,79,'g,f,i',681,9,10,684,',i)}});a.chars',1,173,10,279,'(g,f,',21,'.join("").','replace(/[\\u2061-\\u2064]/g,""))}});a.','entity',1,173,10,279,'(g,f,',10,'toString().',701,'mi',1,'j){j',17,13,'j));j','.bbox=null;','var h','=this.HTMLgetVariant();for(var ',20,21,22,'if(',21,25,21,27,'j,h)}}if(!j.bbox){j','.bbox={w:0,h:0,d:0,rw:0,lw:0}}if(',21,'.join("").length!==1){delete ','j','.bbox.skew}',41,'j',43,'j);',9,'j}});a.','mn',1,'j){j',17,13,'j));j',717,'var h',719,20,21,22,'if(',21,25,21,27,'j,h)}}if(!j.bbox){j',729,21,731,'j',733,41,'j',43,'j);',9,739,'mo',1,'k){k',17,13,'k));if(',21,7,'==0){',9,'k}else{k.bbox=null}',341,21,'.join("");','var j',3,543,'();var ','g',295,'largeop","','displaystyle',438,'largeop){j=',660,661,'.',790,'?"-largeOp":"-smallOp"]}',50,21,52,'if(',21,55,21,'[h].toHTML(k,j)}}if(!k.bbox){k',729,'n',7,'!==1){delete k',733,'if(e.AccentBug&&k.bbox.w===0&&n',7,'===1&&k',216,'){k',216,'.nodeValue+=e.NBSP;','e.createSpace(','k,0,0,-k.offsetWidth/e.em)}if(g.largeop){var l=(k.bbox.h-k.bbox.d)/2-','e.TeX.axis_height','*k.scale;if(e.','safariVerticalAlignBug','&&','k.lastChild.','nodeName==="IMG"){k.lastChild',394,469,124,'k.lastChild',394,'||0)/e.em-','l/k.scale)}else{','if(e.','konquerorVerticalAlignBug','&&',824,'nodeName==="IMG"){k',389,'k.lastChild',389,824,'style.top',469,832,'k',394,'=e.Em(-l/k.scale)}}k.bbox.h-=l;k.bbox.d+=l;if(',345,'>k.bbox.w){k.bbox.ic=',345,346,';e.createBlank(k,k.bbox.ic);k.bbox.w=',345,'}}',41,'k',43,'k);',9,'k},',100,79,283,10,'Get("stretchy")){',9,'false}var g=',21,782,'if(g',7,'>1){',9,'false}g=',660,'DELIMITERS[','g.charCodeAt(0)];','return(','g&&g.dir==f.substr(0,1))},',35,79,'l,k,n',681,'var f',295,'symmetric","','maxsize","minsize','");var j',3,118,'(),g;var i=',820,',m=j.scale;','if(f.symmetric){g','=2*','Math.max(','k-i,n+i)}else{g=k+n}f.maxsize=',451,'f.maxsize,','j.bbox.h+j.bbox.d',');f.minsize=',451,'f.minsize,',900,');g',362,903,'Math.min(',899,'g));j=',13,'l);','e.createDelimiter(','j,',21,'.join("").charCodeAt(0),','g,m);',894,'=(',900,')/2+i}else{g=(',900,')*k/(k+n)}e.positionDelimiter(j,g);',41,'j',43,'j);',9,'j},',171,79,'i,f',681,'var g',295,887,'","',547,'","',549,438,549,'==="bold"&&!',10,547,'){g.',547,'=a.VARIANT.BOLD}var h',3,118,'(),j=h.scale;','g.maxsize','=',451,952,',h.bbox.w);g.minsize=',451,'g.minsize,','h.bbox.w);f',362,958,908,952,',f));h=',13,'i);',913,'h,',21,916,'f,j,g.',547,');',41,'h',43,'h);',9,'h}});a.mtext',1,'k){k',17,13,'k));k',717,15,'Parent().type==="merror"){e.addText(k,',21,'.join(""));',56,'e.getHD(k),g=e.getW(k);k.bbox={h:l.h,d:l.d,w:g,lw:0,rw:g}}else{var j',719,'h=0,f=',21,52,'if(',21,55,21,'[h].toHTML(k,j)}}if(!k.bbox){k',729,21,731,'k','.bbox.skew}}',41,'k',43,'k);',9,'k}});a.ms','.Augment({toHTML:a.mbase.HTMLautoload});a.','mglyph',1012,'mspace',1,'j){j',17,13,'j));var g',295,'height","depth","width','");g',298,'=this',298,';if(',304,'&&!this',298,'){g',298,'=',304,'}var i=',451,'g.height),k=',451,'g.depth),f=',451,'g.width);',818,'j,i,k,f,g',298,');',9,739,'mphantom',1,'j,g,l){j=',13,'j);if(',21,'[0]!=null','){var k=',200,21,'[0].toHTML(','j),',1052,'l!=null){e.Remeasured(',21,'[0].',35,'(j,g,l),j)}else{if(g!=null){e.Remeasured(',21,1063,171,'(j,g),j)}}j.bbox={w:','k.bbox.w,','h:k.bbox.h,d:k.bbox.d,','lw:0,rw:0};',50,'j.childNodes',52,1074,'[h].','style.visibility','="hidden"}}',41,'j',43,'j);',9,'j},','HTMLstretchH:a.mbase.HTMLstretchH,HTMLstretchV:a.mbase.HTMLstretchV});a.','mpadded',1,'j,h,l){j=',13,1052,21,1054,96,'=e.createStack(','j,true);var k','=e.createBox(','g);',200,21,1058,'k),k);if(l!=null){e.Remeasured(',21,1063,35,'(k,h,l),k)}else{if(h!=null){e.Remeasured(',21,1063,171,'(k,h),k)}}var i',295,1022,436,'voffset"),f=0,m=0;if(i.lspace){f','=this.HTMLlength2em(k,i.','lspace)}if(i.voffset){m',1115,'voffset)}',400,'k,f,m);j.bbox={',1071,'w:',1070,'lw:',908,'0,k.bbox.lw+f),rw:',896,1070,345,'+f),H',':Math.max((k.bbox.','H==null?-',141,':k.bbox.H),k.bbox.h+m),D',1131,'D==null?-',141,':k.bbox.D),k.bbox.d-m)};if(i.height','!==""){j.bbox.','h',1115,'height,"h",0)}if(i.depth',1139,'d',1115,'depth,"d",0)}if(i.width',1139,'w',1115,'width,"w",0)}if(j.bbox.H<=j.bbox.h','){delete j.bbox.','H}if(j.bbox.D<=j.bbox.d',1151,'D}e.setStackWidth(g,j.bbox.w)}',41,'j',43,'j);',9,'j},HTMLlength2em',79,'j,k,l,',86,'f',88,'f=-',141,94,'String(k).match','(/width|height|depth/);var i=(h?j.bbox[h',1063,'charAt(0)]:(l?j.bbox[l]:null));var g=',451,'k,i);if(l&&',1169,'(/^\\s*[-+]/)){',9,896,'f,j.bbox[l]+g)}else{',9,'g}},',1086,'mrow','.Augment({',171,79,'h,f',681,'var g',3,118,'();',21,'[this.core].',171,'(g,f);',29,'g,true',43,'g);',9,'g},',35,79,'i,g,j',681,'var f',3,118,'();',21,1194,35,'(f,g,j);',29,'f,true',43,'f);',9,'f}});a.mstyle',1,86,21,1054,'){f=',21,1058,'f);',10,254,21,1063,210,';',41,'f',43,'f)}',9,'f},',118,48,878,21,1054,'?',21,1063,118,'():null)},',171,79,173,878,21,1054,'?',21,1063,171,'(g,f):g)},',35,79,180,878,21,1054,'?',21,1063,35,'(g,f,i):g)}});a.','mfrac',1,'y){y=',13,'y',');var h',1095,'y);var k',1097,'h),j',1097,'h',');this.HTMLmeasureChild(','0,k',1285,'1,j);var f',295,790,'","linethickness","numalign","denomalign","bevelled");var C',285,'(),x=f.',790,';var B=',820,'*C;if(f.bevelled){var A=(x?0.4:0.15);var l',362,373,',',900,')+2*A;var z',1097,'h);',913,'z,47,l);',400,'k,0,(k.bbox.d-k','.bbox.h)/2+B','+A);',400,'z,k.bbox.w-A/2,(z.bbox.d-z',1309,');',400,'j,k.bbox.w+z.bbox.w-A,(j.bbox.d-j',1309,'-A)}else{var g',362,1070,'j.bbox.w);var o=e.thickness2em(f.linethickness),s,r,n,m;var w=','e.TeX.min_rule_thickness/this.em',';if(x){n=e.TeX.num1;m=e.TeX.denom1}else{n=(o===0?e.TeX.num3:e.TeX.num2);m=e.TeX.denom2}n*=C;m*=C;if(o===0){s=Math.max((x?7:3)*','e.TeX.rule_thickness',',2*w);r=(n-k.bbox.d',')-(j.bbox.h-m);if(r<s){','n+=(s-r)/2;m+=(s-r)/2}}else{s=Math.max((x?2:0)*w+o,o/2+1.5*w);r=(n-k.bbox.d)-(B+o/2);if(r<s){n+=s-r}r=(B-o/2',1326,'m+=s-r}var i',1097,'h);','e.createRule(','i,o,0,g+2*o);',400,'i,0,B-o/2)}e.alignBox(k,f.numalign,n);e.alignBox(j,f.denomalign,-m)}',41,'y',43,'y);',9,'y},',100,79,'f){',9,170,426,79,283,10,'texWithDelims',96,'=(',10,430,'?0:',451,10,479,'()||0))+0.12;f',122,469,'g);f',129,'=".12em"}}});a.msqrt',1,'n){n=',13,'n);var r',1095,'n',1278,1097,'r),l',1097,'r),k',1097,'r',1285,'0,h);var j',285,786,'s=',1324,'*j,g,f,o,i;',15,'Get("',790,'")){g','=e.TeX.x_height*','j}else{g=s}f',362,'s+g/4,2*',1322,');o=','h.bbox.h+h.bbox.d','+f+s;i=h.bbox.w;',913,'k,8730,o,j);',200,'k);var m=0;if(k.isMultiChar||(e.AdjustSurd&&e.imgFonts)){k.bbox.w*=0.95}if(',373,'>o){f+=((',373,')-(o-s))/2}var u=',660,876,660,'RULECHAR];if(!u||i<u.HW[0][0]*j||j<0.75){',1332,'l,s,0,i)}else{',913,'l,',660,'RULECHAR,i,j)}o=h.bbox.h+f+s;m',3,'HTMLaddRoot','(r,k,m,',373,'-o,j);',400,'k,m,o-k.bbox.h);',400,'l,m+',1070,'o-l.bbox.h+e.rfuzz);',400,'h,m+',1070,'0);n.bbox.h+=s;',41,'n',43,'n);',9,'n},',1417,79,'h,g,f,j,i){',9,'f}});a.mroot',1184,'toHTML:a.msqrt','.prototype.toHTML',',',1417,79,'o,g,m,k,f){var i',1097,'o);if(',21,'[1]){',56,21,'[1].toHTML(i);l',129,'=l',122,225,200,'l,i)}else{i.bbox',3,155,'()}var j',3,'HTMLrootHeight','(g.bbox.h+g.bbox.d,f,i)-k;',341,908,'i.bbox.w,i.bbox.rw);m',362,'n,g.offset);',400,'i,m-n,j);',9,'m-g.offset},',1466,79,'h,',173,9,'0.45*(h-0.9*g)+0.6*g+',896,'0,f.bbox.d-0.075)}});a.mfenced',1,'k){k=',13,'k);if(',21,'.open){',21,'.open.','toHTML(k)}','if(',21,1054,'){',21,1058,'k)}',19,'g=1,f=',21,22,'if(',21,25,'if(',21,'["sep"+','g]){',21,1510,'g].',1493,21,27,'k)}}if(',21,'.close){',21,'.close.',1493,341,29,'k);var j=k.bbox.h,l=k.bbox.d;for(',20,'n',22,'n[g].',35,'(k,j,l)}if(n',7,'){',29,'k,true)}',41,'k',43,'k);',9,'k},',83,79,'k,j',96,'=k.bbox={},l=[];',10,'HTMLcheckStretchy','(',21,'.open,','g,l,j);',10,1549,'(',21,'[0],',1553,19,'h=1,f=',21,52,'if(',21,55,10,1549,'(',21,1510,'h],',1553,10,1549,'(',21,'[h],g,l,j)}}',10,1549,'(',21,'.close,',1553,10,107,'(g);',9,'l},',1549,79,'f,g,i,h){if(',283,'h',584,100,101,'i.push(f);f=(f.CoreMO()||f)}',10,104,'(f,g)}}});a.menclose',1012,'maction',1012,'semantics',1,86,21,1054,'){f=',21,1058,'f);',10,254,21,1063,210,';',41,'f)}',9,'f},',118,48,878,21,1054,'?',21,1063,118,'():null)},',171,79,173,878,21,1054,'?',21,1063,171,'(g,f):g)},',35,79,180,878,21,1054,'?',21,1063,35,1272,'munderover',1,'G,B,z){var f',295,790,'","accent","accentunder","align");if(!f.',790,'&&',21,'[this.base',']!=null&&',21,'[this.base].','Get("movablelimits")){',9,'a.msubsup',1444,'.call(this,G)}G=',13,'G);var K',285,786,'j',1095,'G);var l=[],I=[],q,H,C,g=-',141,',F=g;for(H=0,C=',21,7,';H<C;H++){if(',21,'[H]!=null){q=l[H',']=e.createBox(j);',200,21,'[H].','toHTML(q),q);if(H==',10,'base){if(z!=null){e.Remeasured(',21,1668,35,'(q,B,z),q)}else{if(B!=null){e.Remeasured(',21,1668,171,'(q,B),q)}}I[H]=(','z==null&&B!=null','?false:',21,1691,100,'("Horizontal','"))}else{I[H]=',21,1691,100,1708,'")}if(q.bbox.w>F){F=q.bbox.w}if(!I[H]&&F>g){g=F}}}if(g==-',141,'){g=F}if(',1703,'){g=F=B}var w=',1324,',A=',660,'TeX_factor;var h=l',1665,']||{bbox:',10,155,177,'J=(h.bbox.ic||0);var p,n,s,r,o,v,E;for(H=0,C=',21,7,';H<C;H++){if(',21,1687,'];if(I[H]){q.bbox=',21,1691,171,'(q,g).bbox}o=e.TeX.big_op_spacing5*K;var u=(H!=',10,'base&&f[',10,'ACCENTS[H]]);if(u&&q.bbox.w<=1/e.em+0.0001){q.bbox.w=q.bbox.rw-q.bbox.lw;q.bbox.noclip=true;if(q.bbox.lw&&!e.zeroWidthBug){q',411,818,'q',262,',0,0,-q.bbox.lw),q',216,')}e.createBlank(q,0,0,q.bbox.rw+0.1)}v={left:0,center:(g-q.bbox.w)/2,right:g-q.bbox.w}[f.align];p=v;n=0;if(H==',10,'over){if(u){E',362,'w*K*A,2.5/',10,'em);o=0;if(h.bbox.skew){p+=h',1005,'else{s=e.TeX.','big_op_spacing1*K*A;r=e.TeX.big_op_spacing3*K*A;E',362,'s,r-',896,'0,q.bbox.d))}E',362,'E,1.5/',10,'em);p+=J;n=h.bbox.h+q.bbox.d+E;q.bbox.h+=o}else{if(H==',10,'under){if(u){E=3*w*K*A;o=0}',1757,'big_op_spacing2*K*A;r=e.TeX.big_op_spacing4*K*A;E',362,'s,r-q.bbox.h)}E',362,'E,1.5/',10,'em);p-=J;n=-(h.bbox.d+q.bbox.h+E);q.bbox.d+=o}}',400,'q,p,n)}}',41,'G',43,'G);',9,'G},',1086,'msubsup',1,'C,A,w){C=',13,'C);var G',285,786,'j',1095,'C),g;var i',1097,'j',1285,10,'base,i);if(',21,1665,']){if(w!=null){e.Remeasured(',21,1668,35,'(i,A,w),i)}else{if(A!=null){e.Remeasured(',21,1668,171,'(i,A),i)}}}',400,'i,0,0);var ','h=(',21,'[',10,'sup]||',21,'[',10,'sub]||this).',493,786,'E',1390,'G,o=e.TeX.scriptspace*G*0.75;var f,k;',15,185,'(',21,'[',10,'sup])){f',1097,'j);',200,21,'[',10,'sup].toHTML(f),f);f.bbox.w+=o;f.bbox.rw',362,'f.bbox.w,f.bbox.rw)}',15,185,'(',21,'[',10,'sub])){k',1097,'j);',200,21,'[',10,'sub].toHTML(k),k);k.bbox.w+=o;',345,362,1070,345,')}var y=e.TeX.sup_drop*h,x=e.TeX.sub_drop*h;var m=i.bbox.h-y,l=i.bbox.d+x,F=0,z;if(i.bbox.ic){F=i.bbox.ic}if(',21,1665,']&&(',21,1668,'type==="mi"||',21,1668,'type==="mo")){if(',21,1668,'data',700,'length===1&&i.bbox.scale===1&&!',21,1668,'Get("largeop")){m=l=0}}var B',295,'subscriptshift","superscriptshift");','B.subscriptshift','=(',1882,'===""?0:',451,1882,'));','B.superscriptshift','=(',1889,'===""?0:',451,1889,'));if(!',86,'k){l',362,'l,e.TeX.sub1*G,k.bbox.h-(4/5)*E,',1882,');',400,'k,i.bbox.w+o-F,-','l,k.bbox)}}else{if(!k){g',295,790,'","texprimestyle");z=e.TeX[(g.',790,'?"sup1":(g.texprimestyle?"sup3":"sup2"))];m',362,'m,z*G,f.bbox.d+(1/4)*E,',1889,');',400,'f,i.bbox.w+o,','m,f.bbox)}else{l',362,'l,e.TeX.sub2*G);',341,1324,'*G;if((m-f.bbox.d)-(k.bbox.h-l)<3*n){l=3*n-m+f.bbox.d+k.bbox.h;y=(4/5)*E-(m-f.bbox.d);if(y>0){m+=y;l-=y}}',400,1915,896,'m,',1889,'));',400,1903,896,'l,',1882,'))}}',41,'C',43,'C);',9,'C},',1086,'mmultiscripts',1012,'mtable',1012,'math',1,'n,g){var k',3,'Get("alttext");if(k){g.setAttribute("aria-label",k)}var h=',231,'n,"nobr",{style:{visibility:"hidden"}});n=',13,'h);var l',1095,'n),i',1097,'l),m;l',244,'=h',262,244,';h',262,244,225,'if(',21,1054,'){if(e.msieColorBug){if(',304,'){',21,1063,306,'=',304,';delete ',304,'}if(this',298,'){',21,1063,'mathbackground=this',298,';delete this',298,'}}','a.mbase.prototype.','displayAlign','=d.config.',1990,';',1989,'displayIndent',1991,1995,';m=',200,21,1058,'i),i)}',400,1813,'j=e.em/e.outerEm;e.em/=j;n.bbox.h','*=j;n.bbox.','d',2006,'w',2006,'lw',2006,'rw*=j;if(m&&m','.bbox.width','!=null){l',391,'=m',2014,';i',391,'="100%"}',10,292,'(n);if(m){',1332,'n,m.bbox.h*j,m.bbox.d*j,0)}if(!',10,'isMultiline&&',10,'Get("display")==="block"&&n',2014,88,'var o',295,'indentalignfirst','","','indentshiftfirst','","indentalign","indentshift");if(o.',2035,'!==a.INDENTALIGN.','INDENTALIGN){','o.indentalign','=o.',2035,'}if(',2042,'===a.INDENTALIGN.AUTO){',2042,3,1990,'}g.style.textAlign=',2042,';if(o.',2037,'!==a.INDENTSHIFT.INDENTSHIFT){','o.indentshift','=o.',2037,'}if(',2056,'==="auto"){',2056,3,1995,'}if(',2056,'&&',2042,2040,'CENTER){n.style[{left:"',383,'",right:"',385,'"}[',2042,']]=e.Em(',451,2056,'))}}h.',1078,225,9,'n}});a.TeXAtom',1,'g){g=',13,'g);if(',21,1054,'){',15,'texClass===a.TEXCLASS.VCENTER){var f',1095,'g',1278,1097,'f);',200,21,1058,'h),h);',400,'h,0,',820,'-(',1396,')/2+h.bbox.d)}else{g.bbox=',21,1058,'g).bbox}}',41,'g',43,'g);',9,'g}});d.Browser.Select({MSIE',79,'f){var i=f','.versionAtLeast("','7.0");var h=f',2119,'8.0")&&document.documentMode>7;var g=(document.compatMode==="BackCompat");','e.config.styles[".MathJax',' span"]={position:"relative"};',2123,' .MathJax_HitBox','"]["',306,'-color"]="white";',2123,2126,'"].opacity=0;',2123,2126,'"].filter="alpha(opacity=0)";e',1184,'getMarginScale:e.getMSIEmarginScale,','PaddingWidthBug:true,','msieAccentBug:true,msieColorBug:true,msieRelativeWidthBug:g,msieMarginWidthBug:true,msiePaddingWidthBug:true,',364,':(h&&!g),msieBorderWidthBug:g,',387,':(!h||g),msieVerticalAlignBug:(h&&!g),msiePlaceBoxBug:(h&&!g),msieClipRectBug:!h,msieNegativeSpaceBug:g,negativeSkipBug:true,msieIE6:!i,msieItalicWidthBug',':true,zeroWidthBug:true,FontFaceBug:true,','allowWebFonts',':"eot"})},Firefox',79,'g){var h=false;if(g',2119,'3.5")){var f=String','(document.location',').replace(/[^\\/]*$/,"");if',2151,'.protocol!=="file:"||(d.config.root+"/").substr(0,f',7,')===f){h="otf"}}e',1184,'ffVerticalAlignBug:true,AccentBug:true,',2145,':h})},Safari',79,'i',96,'=i',2119,'3.0");var f=i',2119,'3.1");i.isMobile','=(navigator.appVersion.match','(/Mobile/i)!=null);e',1184,'config:{styles:{".MathJax img, .MathJax nobr, .MathJax a":{"max-width":"5000em","max-height":"5000em"}}},','rfuzz:0.05,AccentBug:true,AdjustSurd:true,','safariContextMenuBug:true,','safariNegativeSpaceBug:true,',822,':!f,safariTextNodeBug:!g,','safariWebFontSerif',':["serif"],',2145,':(f&&!i.isMobile?(i.isPC?"svg":"otf"):false)});if(i.isMobile){var h=','MathJax.Hub.config["HTML-CSS','"];if(h){h.availableFonts=[];h.preferredFont=null}else{',2182,'"]={availableFonts:[],preferredFont:null}}}},Chrome',79,'f){e',1184,2173,2145,':"svg",',2175,2178,':[""]})},Opera',79,'f){f.isMini',2169,'("Opera Mini")!=null);',2123,' .merror"]["vertical-align"]=null;e',1184,'operaHeightBug:true,operaVerticalAlignBug:true,negativeSkipBug',2144,2138,2145,':(f',2119,'10.0")&&!f.isMini?"otf":false)})},Konqueror',79,'f){e',1184,834,':true,noContextMenuBug:true})}});if(d.config.menuSettings.zoom!=="None"){c.Require("[MathJax]/extensions/MathZoom.js")}e.loadComplete("jax.js")})(MathJax.ElementJax.mml,MathJax.Ajax,MathJax.Hub,MathJax.OutputJax["HTML-CSS"]);']
]);