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e,f,g,h,i,j,k,l,m,n,o,p;if(!vLi(a.k)||!(a.j.Fv(($jj(),ljj))||a.j.Fv(xij))){return null}o=new Nnd;g=fMi(a.j);e=eMi(a.j);if(g.Fv(($jj(),ljj))){for(n=new aOi(g);n.g<n.i.g.length;){l=_Ni(n);_wd(o.B,l)}}else{_wd(o.B,g)}if(!!e&&e.Fv(ljj)){for(n=new aOi(e);n.g<n.i.g.length;){l=_Ni(n);_wd(o.B,l)}}else !!e&&(_wd(o.B,e),true);h=new Nnd;for(m=new Tnd(o);m.g<m.j.B.length;){l=Rnd(m);if(l.p3(null)){continue}wNi(new xNi(l,ZMi(0),false,a.i),b,c,new qKi);f=new tNi(l,ZMi(0));for(j=rNi(f,b,new Dyi,new qKi).tf();j.$i();){i=j._i();p=rOi(i);if(!p||!p.h3()){throw Ttc(new Mxi)}_wd(h.B,p)}}Ood();Lnd(h,new BHi);vnd(h,0,(UMi(),QMi));wnd(h,SMi);k=Xxi(b,h,o);Wxi(k,g,e);!c.g?(c.g=k):c.g.V2(k);c.i=k;return new HJi(fyi(k,a,b,d))}\nfunction NNi(a,b,c){var d,e,f,g,h,i,j,k,l;switch(a.i.v){case 20:l=0;for(f=a.g,h=0,j=f.length;h<j;++h){d=f[h];l+=d.n3(b,c)}return l;case 21:return -a.g[0].n3(b,c);case 24:k=1;for(e=a.g,g=0,i=e.length;g<i;++g){d=e[g];k*=d.n3(b,c)}return k;case 26:return a.g[0].n3(b,c)/a.g[1].n3(b,c);case 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null}e=r.g[0];q=ELi(eLi(($jj(),Ljj),e),ZMi(2));l=ELi(eLi(nij,e),ZMi(2));j=YLi(f,q);h=YLi(f,l);o=a;if(!!j&&Vb(j,h)){o=_Mi(o,$Li(o.k,q),c);m=xMi(ILi(o.j,bLi($Li(o.j,q),$Li(o.j,l))),null);n=ILi(o.k,CLi(j,cLi(vjj,q,l)));o=o.v3(m,n);o=o.z3(cLi(vjj,q,l),ZMi(1),c);o=o.x3(c)}f=xMi(ILi(o.j,o.k),null);p=eLi(Ljj,e);k=eLi(nij,e);i=YLi(f,p);g=YLi(f,k);j=YLi(f,q);h=YLi(f,l);if(!!i&&!g&&!!j&&!!h){o=o.z3(l,ILi(ZMi(1),q),c);o=o.x3(c)}if(!i&&!!g&&!!j&&!!h){o=o.z3(q,ILi(ZMi(1),l),c);o=o.x3(c)}if(!!i&&!!g&&!j&&!h){if(vLi($Li(o.j,p))){o=_Mi(o,$Li(o.k,k),c)}else{o=_Mi(o,$Li(o.j,k),c);o=_Mi(o,$Li(o.k,p),c)}o=iNi(o,2,c,d)}return new IJi(o)}\nfunction tKi(a,b,c,d,e){var f,g,h,i,j,k,l,m;g=new Dyi;vyi(c,new Fyi((fDi(),LAi)));Ysd(c.j,c.g);c.g=c.i;Vb(nKi(e),(BNi(),ANi))?vyi(c,new Hyi(vCi,me(fe(grb,1),f5n,135,0,[a,b]))):vyi(c,new Hyi(wCi,me(fe(grb,1),f5n,135,0,[a,nKi(e)])));Ysd(c.j,c.g);c.g=c.i;i=a;m=null;h=0;do{f=false;for(k=0;k<d.length&&!f;k++){l=d[k].$2(i,b,g,e);if(l){nyj(o6n+d[k]);!!kyj&&lyj(kyj,(Dyj(),wyj),'to: '+l);if(l.g){wyi(c,Byi(g));Cyi(g);m=l.g;f=true}else{f=!Vb(i,l.i);i=l.i}}}}while(!m&&f&&h++<10);if(m){j=CEi(a,m,g,e);wyi(c,Byi(g));c.i=c.g=Xsd(c.j);if(j.size()==0){vyi(c,new Fyi(mBi));return new Nnd}else j.size()==1?vyi(c,new Hyi(sCi,j.Ih(me(fe(Fub,1),f5n,650,0,[])))):vyi(c,new Hyi(tCi,j.Ih(me(fe(Fub,1),f5n,650,0,[]))));c.i=c.g=Xsd(c.j);return j}throw Ttc((Byi(c),new Nxi))}\nfunction RLi(a,b){var c,d,e,f,g,h,i,j,k,l,m,n;if(Vb(a,b)||!(!a||a.r3()&&$wnd.Math.abs(a.A_())<C4m)&&a.q3()&&(!b||b.q3()&&$wnd.Math.abs(a.A_()%b.A_())<C4m)){return true}if(a.Fv(($jj(),vjj))&&b.Fv(vjj)){m=LNi(a);n=LNi(b);e=0;for(i=m,j=0,l=i.length;j<l;++j){h=i[j];e<n.length&&Vb(h,n[e])&&++e}return e==n.length}if(a.Fv(ljj)&&b.Fv(ljj)){c=a.l3();d=b.l3();if(!!c&&!!d&&c.q3()&&d.q3()){if(!(c.q3()&&(!d||d.q3()&&$wnd.Math.abs(c.A_()%d.A_())<C4m))){return false}f=a.m3();g=b.m3();if(!f){return !g}return RLi(f,g)}m=LNi(a);n=LNi(b);e=0;for(i=m,j=0,l=i.length;j<l;++j){h=i[j];e<n.length&&Vb(h,n[e])&&++e}return e==n.length}if(a.Fv(vjj)||a.Fv(ljj)){for(k=new aOi(a);k.g<k.i.g.length;){h=_Ni(k);if(Vb(h,b)){return true}}return false}return a.Fv(kjj)&&RLi(a.g[0],b)}\nfunction MNi(a){var b,c,d,e,f,g,h,i,j,k,l;switch(a.i.v){case 20:l=0;for(f=a.g,h=0,j=f.length;h<j;++h){d=f[h];l+=d.A_()}return l;case 21:return -a.g[0].A_();case 24:k=1;for(e=a.g,g=0,i=e.length;g<i;++g){d=e[g];k*=d.A_()}return k;case 26:return a.g[0].A_()/a.g[1].A_();case 28:return $wnd.Math.pow(a.g[0].A_(),a.g[1].A_());case 44:b=a.g[0].A_();c=a.g[1].A_();if(b<0){if($wnd.Math.abs(c%2-1)<C4m){return -$wnd.Math.pow(-b,1/c)}}return $wnd.Math.pow(b,1/c);case 47:return $wnd.Math.abs(a.g[0].A_());case 32:return $wnd.Math.sin(a.g[0].A_());case 31:return $wnd.Math.cos(a.g[0].A_());case 33:return $wnd.Math.tan(a.g[0].A_());case 38:return $wnd.Math.asin(a.g[0].A_());case 36:return $wnd.Math.acos(a.g[0].A_());case 40:return $wnd.Math.atan(a.g[0].A_());}return NaN}\nfunction LGi(a,b,c,d,e){var f,g,h,i,j,k,l,m,n,o,p,q,r,s;b.Fv(($jj(),xij))?(p=b.d3(BGi,c,d)):(p=b.d3(a,c,d));if(!Vb(p,b)){return p}if(b.Fv(vjj)){o=b;h=null;for(n=new aOi(o);n.g<n.i.g.length;){m=_Ni(n);!!eMi(m)&&(!h?(h=eMi(m)):(h=dyi(h,eMi(m))))}if(!h||h.r3()&&$wnd.Math.abs(h.A_()-1)<C4m||e&&!h.q3()){return b.d3(a,c,d)}e&&MGi(o,d);q=d.i;h.f3(q++);j=je(vub,g5n,137,o.g.length,0,1);s=false;for(g=0;g<o.g.length;g++){f=eMi(o.g[g]);if((nMi(o.g[g])||!e||wJi(d,o.g[g],(DJi(),AJi)))&&!Vb(h,f)){s=true;r=vMi(h,f);r.f3(q++);o.g[g].Fv(kjj)?(l=fMi(tMi(o.g[g]))):(l=fMi(o.g[g]));k=GMi(r,l);vJi(d,k,(DJi(),zJi));i=lLi(k,h);o.g[g].Fv(kjj)?(j[g]=tMi(i)):(j[g]=i)}else{j[g]=o.g[g]}}if(s){d.i=q;vyi(c,new Hyi((fDi(),pAi),me(fe(grb,1),f5n,135,0,[h])));return new WNi(vjj,j)}}return b}\nfunction NIi(a,b,c,d,e){var f,g,h,i,j,k,l,m,n,o,p,q,r;if(b.Fv(($jj(),ljj))){r=b;i=new Nnd;j=1;p=je(vub,g5n,137,r.g.length,0,1);for(m=0;m<r.g.length;m++){q=r.g[m];if(q.r3()){_wd(i.B,q);j*=q.A_()}else{p[m]=q}}if(i.B.length==1&&$wnd.Math.abs(j-1)<C4m){(sxd(0,i.B.length),i.B[0]).f3(d.i);vyi(c,new Gyi((fDi(),ZAi),d.i++));return YNi(ljj,p)}if(i.B.length<2){return b.d3(a,c,d)}f=new Nnd;k=new Nnd;aMi(r,f,k);for(l=0;l<f.B.length;l++){for(n=l+1;n<f.B.length;n++){if(sxd(l,f.B.length),Vb(f.B[l],(sxd(n,f.B.length),f.B[n]))){if(e||!sLi((sxd(l,k.B.length),k.B[l]),1)||!sLi((sxd(n,k.B.length),k.B[n]),1)){return b}}}}o=ZMi($wnd.Math.abs(j));if(i.B.length>1){for(h=new Tnd(i);h.g<h.j.B.length;){g=Rnd(h);g.f3(d.i)}vyi(c,new Gyi((fDi(),bBi),d.i));o.f3(d.i++)}return j<0?ALi(CLi(o,YNi(ljj,p))):CLi(o,YNi(ljj,p))}return b.d3(a,c,d)}\nfunction IEi(a,b,c,d){var e,f,g,h;if(!OLi(a.j)||!a.k.p3(b)){return null}h=a.j;if(QNi(h,($jj(),Zhj))){if(a.k.h3()){if(a.k.A_()<Omn||a.k.A_()>Tdn){vyi(c,new 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GDi(j.g));i=j.g.length;0<i?(j.g=Gid(j.g,0,0)):0>i&&(j.g+=Sid(je(pf,tZm,5,-i,15,1)));h=f.g.length;0<h?(f.g=Gid(f.g,0,0)):0>h&&(f.g+=Sid(je(pf,tZm,5,-h,15,1)))}}g=!g}else if(d==37){++e;k=(Axd(e,a.length),a.charCodeAt(e)-48);if(g){if(k>=0&&k<b.length){f.g+=''+b[k];j.g+=''+c[k]}}else{if(j.g.length!=0){wnd(l,new GDi(j.g));h=j.g.length;0<h?(j.g=Gid(j.g,0,0)):0>h&&(j.g+=Sid(je(pf,tZm,5,-h,15,1)))}k>=0&&k<b.length&&wnd(l,new HDi(b[k],c[k]))}}else{j.g+=String.fromCharCode(d);g&&(f.g+=String.fromCharCode(d),f)}}nid('',j.g)||wnd(l,new GDi(j.g));return l}\nfunction _Ei(a,b,c,d){var e,f,g,h,i,j,k,l,m;if(cNi(a,b)!=2){return null}i=a;YLi(i.j,ELi(b,ZMi(2))).Fv(($jj(),kjj))&&(i=fNi(i,ZMi(-1),c));e=YLi(i.j,ELi(b,ZMi(2)));f=YLi(i.j,b);g=ZLi(i.j,b);e.f3(1);f.f3(2);g.f3(3);h=ILi(ELi(f,ZMi(2)),BLi(4,cLi(ljj,e,g)));m=new Dyi;vyi(m,new Hyi((fDi(),HBi),me(fe(grb,1),f5n,135,0,[b])));i=new tNi(b,lLi(bLi(eLi(kjj,f),DLi(FLi(h,ZMi(2)))),CLi(ZMi(2),e)));vyi(m,new Hyi(cAi,me(fe(grb,1),f5n,135,0,[i])));i=i.x3(m);xyi(c,new Hyi(UCi,me(fe(grb,1),f5n,135,0,[e,f,g])),m,i);h=kJi((uIi(),KHi),h,null,new xJi);if(h.h3()&&h.A_()<0){return new GJi}e.f3(0);f.f3(0);g.f3(0);l=new Nnd;if(!e.p3(null)){wnd(l,vOi(b,lLi(tMi(g),f),d));nOi((sxd(0,l.B.length),l.B[0]),new tNi(e,ZMi(0)));lKi(d,pNi(new tNi(e,ZMi(0))))}AMi(h)<=0&&!(h.h3()&&h.A_()>0)&&lKi(d,new xNi(h,ZMi(0),false,false));j=lLi(bLi(eLi(kjj,f),FLi(h,ZMi(2))),CLi(ZMi(2),e));k=lLi(ILi(eLi(kjj,f),FLi(h,ZMi(2))),CLi(ZMi(2),e));wnd(l,vOi(b,LLi(j),d));wnd(l,vOi(b,LLi(k),d));return new HJi(l)}\nfunction BFi(a,b,c){var d,e,f;f=a.g[0];for(e=new aOi(f);e.g<e.i.g.length;){d=_Ni(e);d.f3(c.i++)}if(sLi(a.g[1],2)&&f.g.length==2&&f.g[1].Fv(($jj(),kjj))){vyi(b,new Fyi((fDi(),Ryi)));return new WNi(($jj(),vjj),me(fe(vub,1),g5n,137,0,[ELi(f.g[0],ZMi(2)),BLi(-2,CLi(f.g[0],tMi(f.g[1]))),ELi(tMi(f.g[1]),ZMi(2))]))}else if(sLi(a.g[1],2)&&f.g.length==2){vyi(b,new Fyi((fDi(),Tyi)));return new WNi(($jj(),vjj),me(fe(vub,1),g5n,137,0,[ELi(f.g[0],ZMi(2)),BLi(2,CLi(f.g[0],f.g[1])),ELi(f.g[1],ZMi(2))]))}else if(sLi(a.g[1],2)&&f.g.length==3){vyi(b,new Fyi((fDi(),QCi)));return new WNi(($jj(),vjj),me(fe(vub,1),g5n,137,0,[ELi(f.g[0],ZMi(2)),ELi(f.g[1],ZMi(2)),ELi(f.g[2],ZMi(2)),BLi(2,CLi(f.g[0],f.g[1])),BLi(2,CLi(f.g[1],f.g[2])),BLi(2,CLi(f.g[0],f.g[2]))]))}else if(sLi(a.g[1],3)&&f.g.length==2){vyi(b,new Fyi((fDi(),Oyi)));return new WNi(($jj(),vjj),me(fe(vub,1),g5n,137,0,[ELi(f.g[0],ZMi(3)),BLi(3,CLi(ELi(f.g[0],ZMi(2)),f.g[1])),BLi(3,CLi(f.g[0],ELi(f.g[1],ZMi(2)))),ELi(f.g[1],ZMi(3))]))}return null}\nfunction iDi(){fDi();return me(fe(jrb,1),n$m,66,0,[XCi,LAi,ICi,MCi,cAi,YAi,rCi,oAi,uAi,uCi,vCi,wCi,xCi,RCi,mBi,MAi,sCi,tCi,HCi,GCi,xBi,yBi,zBi,ABi,aDi,bDi,dDi,eDi,BBi,DBi,hBi,gBi,WAi,VAi,XAi,nAi,vBi,Xyi,VCi,NAi,WCi,OAi,HAi,ezi,nCi,$Bi,SAi,QAi,fBi,ECi,czi,rBi,DCi,IBi,Myi,Nyi,JCi,KCi,_Ai,aBi,Tzi,Uzi,wAi,KBi,UCi,HBi,$yi,_yi,qBi,oBi,nBi,pBi,ZBi,XBi,YBi,pAi,FBi,KAi,VBi,qCi,azi,Zzi,JBi,dBi,Ozi,Qzi,Nzi,Iyi,Yyi,Kyi,Lyi,Zyi,Wyi,$Ai,UBi,bBi,ZAi,jAi,sBi,kAi,tBi,iBi,jBi,LBi,MBi,eAi,gAi,hAi,$Ci,IAi,JAi,oCi,mAi,uBi,pCi,gCi,BCi,yCi,ACi,CCi,$zi,tAi,cDi,_Ci,dAi,Rzi,Szi,Wzi,Vzi,_Bi,bCi,EBi,kBi,GAi,sAi,rAi,Tyi,Ryi,Oyi,QCi,gzi,xAi,LCi,Uyi,Syi,fzi,hzi,Qyi,Pyi,TAi,RAi,UAi,PAi,FAi,BAi,vAi,EAi,yAi,AAi,zAi,WBi,aCi,Pzi,FCi,qAi,GBi,wBi,iAi,OCi,NCi,PCi,CAi,DAi,aAi,_zi,bAi,QBi,RBi,SBi,NBi,OBi,PBi,TBi,zCi,kCi,jCi,fCi,eCi,iCi,hCi,dCi,cCi,mCi,lCi,fAi,CBi,lBi,lAi,izi,Jzi,pzi,qzi,Ezi,xzi,Mzi,Czi,vzi,tzi,Fzi,yzi,Azi,Hzi,rzi,Kzi,lzi,jzi,nzi,Dzi,wzi,uzi,Gzi,zzi,Bzi,Izi,szi,Lzi,mzi,kzi,ozi,Jyi,SCi,dzi,bzi,TCi,Vyi,YCi,ZCi,eBi,cBi,Yzi,Xzi])}\nfunction hLi(a){var b,c,d,e,f;if(cf(a,22)){d=a;e=hLi(d.u);f=hLi(d.C);switch(a.A.v){case 0:case 32:case 31:case 33:case 61:case 62:case 63:case 38:case 36:case 40:return eLi(d.A,e);case 45:return FLi(e,ZMi(2));case 21:return bLi(e,eLi(($jj(),kjj),f));case 22:if(cf(d.C,329)){return eLi(($jj(),wjj),e)}return bLi(e,eLi(($jj(),wjj),f));case 47:return eLi(($jj(),Phj),e);case 86:return dLi(($jj(),fjj),e,f);case 35:return zLi((UMi(),PMi),e);case 84:return zLi(ZMi(10),e);case 85:return zLi(ZMi(2),e);case 34:return ELi((UMi(),PMi),e);case 10:return new xNi(e,f,true,true);case 12:return new xNi(e,f,true,false);case 11:return new xNi(e,f,false,true);case 13:return new xNi(e,f,false,false);case 110:return new OMi('k',mf(d.u.cs()));case 24:if(cf(d.u,38)&&d.u.cs()==-1){return eLi(($jj(),kjj),f)}default:return YNi(d.A,me(fe(vub,1),g5n,137,0,[e,f]));}}if(cf(a,121)){b=hLi(a.u);c=hLi(a.A);return new tNi(b,c)}if(cf(a,190)&&nid('e',a.i)){return UMi(),PMi}if(cf(a,56)||cf(a,190)){return new AOi(a.ln((xrg(),Vqg)))}if(cf(a,38)){return ZMi(a.s)}return null}\nfunction GIi(a,b,c,d){var e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t;e=je(vub,g5n,137,a.g.length,0,1);t=je(vub,g5n,137,a.g.length,0,1);for(l=0;l<a.g.length;l++){if(d){e[l]=a.g[l].l3();t[l]=a.g[l].m3()}else{e[l]=a.g[l].k3(null);t[l]=a.g[l].o3(null)}}s=je(Qtc,YZm,5,a.g.length,16,1);h=new Nnd;i=0;for(m=0;m<a.g.length;m++){if(!!e[m]&&!t[m]&&(e[m].r3()||c.j&&e[m].t3())){_wd(h.B,e[m]);i+=e[m].A_();s[m]=true}}for(n=0;n<a.g.length;n++){if(!s[n]&&!!t[n]){j=false;for(o=n+1;o<a.g.length;o++){if(!s[o]&&Vb(t[n],t[o])){j=true;a.g[o].f3(c.i);e[n]=!e[n]?ZMi(1):e[n];e[o]=!e[o]?ZMi(1):e[o];e[n]=bLi(e[n],e[o]);s[o]=true}}if(j){a.g[n].f3(c.i);e[n].f3(c.i);t[n].f3(c.i);vyi(b,new Hyi((fDi(),Yyi),me(fe(grb,1),f5n,135,0,[t[n]])));++c.i}}}q=je(vub,g5n,137,a.g.length+1,0,1);for(k=0;k<a.g.length;k++){s[k]||(q[k]=JMi(e[k],t[k]))}p=ZMi(i);if(h.B.length>1){for(g=new Tnd(h);g.g<g.j.B.length;){f=Rnd(g);f.f3(c.i)}vyi(b,new Gyi((fDi(),Iyi),c.i));p.f3(c.i);++c.i}if($wnd.Math.abs(i)<C4m&&h.B.length==1){(sxd(0,h.B.length),h.B[0]).f3(c.i);vyi(b,new Gyi((fDi(),cDi),c.i++))}$wnd.Math.abs(i)<C4m||(q[a.g.length]=p);r=YNi(($jj(),vjj),q);return !r?ZMi(0):r}\nfunction xHi(a,b,c,d){var e,f,g,h,i,j;j=new Nnd;if(AMi(a.j)>0&&vLi(a.k)){if(a.g){if(a.i){vyi(c,new Hyi((fDi(),ABi),me(fe(grb,1),f5n,135,0,[b])))}else{g=new tNi(a.j,a.k);vyi(c,new Hyi((fDi(),zBi),me(fe(grb,1),f5n,135,0,[g])));return new HJi(rNi(g,b,c,new qKi))}}else{if(a.i){g=new tNi(a.j,a.k);vyi(c,new Hyi((fDi(),yBi),me(fe(grb,1),f5n,135,0,[g])));e=rNi(g,b,c,new qKi);f=new gOi(me(fe(vub,1),g5n,137,0,[]));for(i=e.tf();i.$i();){h=i._i();cOi(f,rOi(h))}wnd(j,vOi(b,JLi(nKi(d),f),d))}else{vyi(c,new Hyi((fDi(),xBi),me(fe(grb,1),f5n,135,0,[b])));wnd(j,vOi(b,nKi(d),d))}}return new HJi(j)}if(vLi(a.j)&&AMi(a.k)>0){if(a.g){if(a.i){g=new tNi(a.j,a.k);vyi(c,new Hyi((fDi(),eDi),me(fe(grb,1),f5n,135,0,[g])));e=rNi(g,b,c,new qKi);f=new gOi(me(fe(vub,1),g5n,137,0,[]));for(i=e.tf();i.$i();){h=i._i();cOi(f,rOi(h))}wnd(j,vOi(b,JLi(nKi(d),f),d))}else{vyi(c,new Hyi((fDi(),dDi),me(fe(grb,1),f5n,135,0,[b])));wnd(j,vOi(b,nKi(d),d))}}else{if(a.i){vyi(c,new Hyi((fDi(),bDi),me(fe(grb,1),f5n,135,0,[b])))}else{g=new tNi(a.j,a.k);vyi(c,new Hyi((fDi(),aDi),me(fe(grb,1),f5n,135,0,[g])));return new HJi(rNi(g,b,c,new qKi))}}return new HJi(j)}return null}\nfunction GEi(a,b,c,d){var e,f,g,h,i,j,k,l,m,n,o,p,q;if(!PLi(a.j)||!a.k.p3(b)){return null}q=a.j;if(q.i!=($jj(),Rjj)){if(a.k.h3()){if(a.k.A_()<-1||a.k.A_()>1){vyi(c,new Hyi((fDi(),qBi),me(fe(grb,1),f5n,135,0,[q,b])));return new GJi}}else{lKi(d,new xNi(ZMi(-1),a.k,true,false));lKi(d,new xNi(a.k,ZMi(1),true,false))}}j=CMi(q.i);h=q.g[0];if(QNi(q,Rjj)){i=bLi(eLi(j,a.k),CLi(new OMi('k',++d.i),(UMi(),RMi)));g=nNi(a,h,i);return new HJi((o=me(fe(Qtb,1),qZm,286,0,[(XJi(),QJi),MJi,lEi,RJi,mEi,jEi,zEi,qEi,SJi,PJi,VJi,vEi,TJi,WJi,oEi,UJi,KJi,kEi,OJi,LJi,iEi,sEi,nEi,yEi,rEi,uEi,xEi,wEi,NJi,tEi,pEi]),tKi(g,b,c,o,d)))}f=bLi(eLi(j,a.k),CLi(BLi(2,new OMi('k',++d.i)),(UMi(),RMi)));e=new tNi(h,f);m=(p=me(fe(Qtb,1),qZm,286,0,[(XJi(),QJi),MJi,lEi,RJi,mEi,jEi,zEi,qEi,SJi,PJi,VJi,vEi,TJi,WJi,oEi,UJi,KJi,kEi,OJi,LJi,iEi,sEi,nEi,yEi,rEi,uEi,xEi,wEi,NJi,tEi,pEi]),tKi(e,b,c,p,d));if(!sLi(a.k,1)&&!sLi(a.k,-1)){l=bLi(eLi(j,a.k),CLi(BLi(2,new OMi('k',++d.i)),RMi));QNi(q,Ljj)?(k=new tNi(ILi(RMi,h),l)):(k=new tNi(ILi(BLi(2,RMi),h),l));m.addAll((n=me(fe(Qtb,1),qZm,286,0,[QJi,MJi,lEi,RJi,mEi,jEi,zEi,qEi,SJi,PJi,VJi,vEi,TJi,WJi,oEi,UJi,KJi,kEi,OJi,LJi,iEi,sEi,nEi,yEi,rEi,uEi,xEi,wEi,NJi,tEi,pEi]),tKi(k,b,c,n,d)))}return new HJi(m)}\nfunction vFi(a,b,c,d,e){var f,g,h,i,j,k,l,m,n,o,p,q,r;if(b.Fv(($jj(),ljj))){o=b;f=null;n=null;m=null;for(k=new aOi(o);k.g<k.i.g.length;){i=_Ni(k);!f||!n&&!f.Fv(vjj)&&!i.Fv(vjj)?(f=YNi(ljj,me(fe(vub,1),g5n,137,0,[f,i]))):!n||!n.Fv(vjj)&&!i.Fv(vjj)?(n=YNi(ljj,me(fe(vub,1),g5n,137,0,[n,i]))):(m=YNi(ljj,me(fe(vub,1),g5n,137,0,[m,i])))}if(!!f&&!!n&&(f.Fv(vjj)||n.Fv(vjj))){if(!(e!=null&&(txd(e),e)||f.q3()&&!m||wJi(d,b,(DJi(),zJi)))){return b}if(f.Fv(vjj)){for(j=new aOi(f);j.g<j.i.g.length;){i=_Ni(j);i.f3(d.i++)}}else{f.f3(d.i++)}if(n.Fv(vjj)){for(j=new aOi(n);j.g<j.i.g.length;){i=_Ni(j);i.f3(d.i++)}}else{n.f3(d.i++)}l=null;if(f.Fv(vjj)&&n.Fv(vjj)){p=f;q=n;r=je(vub,g5n,137,p.g.length*q.g.length,0,1);for(g=0;g<p.g.length;g++){for(h=0;h<q.g.length;h++){r[g*q.g.length+h]=CLi(p.g[g],q.g[h])}}l=new WNi(vjj,r);vyi(c,new Fyi((fDi(),sAi)))}else if(f.Fv(vjj)){p=f;r=je(vub,g5n,137,p.g.length,0,1);for(g=0;g<p.g.length;g++){r[g]=CLi(p.g[g],n)}l=new WNi(vjj,r);vyi(c,new Hyi((fDi(),rAi),me(fe(grb,1),f5n,135,0,[n])))}else if(n.Fv(vjj)){q=n;r=je(vub,g5n,137,q.g.length,0,1);for(g=0;g<q.g.length;g++){r[g]=CLi(f,q.g[g])}l=new WNi(vjj,r);vyi(c,new Hyi((fDi(),rAi),me(fe(grb,1),f5n,135,0,[f])))}return cLi(ljj,l,m)}}return b.d3(a,c,d)}\nfunction KMi(a){var b,c,d,e,f,g,h,i,j,k;f=(UMi(),RMi);k=ZMi(0);e=ZMi(1);h=FLi(ZMi(2),ZMi(2));i=FLi(ZMi(3),ZMi(2));d=new KQc;EQc(d,($jj(),Ljj),me(fe(vub,1),g5n,137,0,[eLi(kjj,e),ALi(lLi(i,ZMi(2))),ALi(lLi(h,ZMi(2))),ALi(lLi(ZMi(1),ZMi(2))),k,lLi(ZMi(1),ZMi(2)),lLi(h,ZMi(2)),lLi(i,ZMi(2)),e,k,eLi(kjj,e),k]));EQc(d,nij,me(fe(vub,1),g5n,137,0,[eLi(kjj,e),ALi(lLi(i,ZMi(2))),ALi(lLi(h,ZMi(2))),ALi(lLi(ZMi(1),ZMi(2))),k,lLi(ZMi(1),ZMi(2)),lLi(h,ZMi(2)),lLi(i,ZMi(2)),e,eLi(kjj,e),k,e]));EQc(d,Rjj,me(fe(vub,1),g5n,137,0,[eLi(kjj,i),eLi(kjj,e),ALi(lLi(ZMi(1),i)),k,lLi(ZMi(1),i),e,i]));EQc(d,Zhj,me(fe(vub,1),g5n,137,0,[ALi(lLi(f,ZMi(2))),ALi(lLi(f,ZMi(3))),ALi(lLi(f,ZMi(4))),ALi(lLi(f,ZMi(6))),k,lLi(f,ZMi(6)),lLi(f,ZMi(4)),lLi(f,ZMi(3)),lLi(f,ZMi(2)),f,lLi(CLi(ZMi(3),f),ZMi(2)),CLi(ZMi(2),f)]));EQc(d,Xhj,me(fe(vub,1),g5n,137,0,[f,lLi(CLi(ZMi(5),f),ZMi(6)),lLi(CLi(ZMi(3),f),ZMi(4)),lLi(CLi(ZMi(2),f),ZMi(3)),lLi(f,ZMi(2)),lLi(f,ZMi(3)),lLi(f,ZMi(4)),lLi(f,ZMi(6)),k,f,lLi(CLi(ZMi(3),f),ZMi(2)),CLi(ZMi(2),f)]));EQc(d,_hj,me(fe(vub,1),g5n,137,0,[ALi(lLi(f,ZMi(3))),ALi(lLi(f,ZMi(4))),ALi(lLi(f,ZMi(6))),k,lLi(f,ZMi(6)),lLi(f,ZMi(4)),lLi(f,ZMi(3))]));b=a.g[0];j=BQc(d,CMi(a.i));g=BQc(d,a.i);for(c=0;c<j.length;c++){if(Vb(j[c],b)){return g[c]}}return null}\nfunction OEi(a,b,c,d){var e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,A,B,C,D,F;g=aNi(a,($jj(),Phj),b);if(g==0){return null}if(!Vb(nKi(d),(BNi(),ANi))){D=new Dyi;k=me(fe(sf,1),TZm,5,15,[0]);e=jyi(a.j,nKi(d),b,D,k);f=jyi(a.k,nKi(d),b,D,k);q=nNi(a,e,f);Ayi(c,a,q,D);q=EFi((tFi(),q),c,new xJi);return new IJi(q)}n=ayi(xMi(ILi(a.j,a.k),null),(Vxi(),Oxi));if(g==2&&(!n||n.r3()&&$wnd.Math.abs(n.A_())<C4m)){q=_Mi(a,n,c);VLi(q.k,Phj,b)>VLi(q.j,Phj,b)&&(q=q.B3());if(VLi(q.j,Phj,b)==2){o=byi(q.j,Phj);q=_Mi(q,o,c)}q.j.Fv(kjj)&&q.k.Fv(kjj)&&(q=gNi(q,ZMi(-1),c));if(q.j.Fv(kjj)||q.k.Fv(kjj)){throw Ttc((Byi(c),new Nxi))}return new IJi(q)}j=new L9c;_xi(a,j,Txi);vyi(c,new Fyi((fDi(),nCi)));Ysd(c.j,c.g);c.g=c.i;C=new Nnd;for(i=(p=(new Gmd(j.g)).g._g().tf(),new Hmd(p));i.g.$i();){h=(l=i.g._i(),l.Ji());B=new tNi(h,ZMi(0));ynd(C,rNi(B,b,c,new qKi))}c.i=c.g=Xsd(c.j);s=new Nnd;for(w=new Tnd(C);w.g<w.j.B.length;){v=Rnd(w);r=BQc(v.i,b);if(!r.h3()){throw Ttc((Byi(c),new Nxi))}Bnd(s,r,0)!=-1||(_wd(s.B,r),true)}Ood();Lnd(s,new QEi);vnd(s,0,(UMi(),QMi));wnd(s,SMi);t=Xxi(b,s,new Pnd(j));!c.g?(c.g=t):c.g.V2(t);c.i=t;u=new Nnd;for(m=1;m<s.B.length;m++){F=new qKi;mKi(F,new ENi((sxd(m-1,s.B.length),s.B[m-1]),(sxd(m,s.B.length),s.B[m]),false,m!=s.B.length-1));ynd(u,(A=me(fe(Qtb,1),qZm,286,0,[(XJi(),QJi),MJi,lEi,RJi,mEi,jEi,zEi,qEi,SJi,PJi,VJi,vEi,TJi,WJi,oEi,UJi,KJi,kEi,OJi,LJi,iEi,sEi,nEi,yEi,rEi,uEi,xEi,wEi,NJi,tEi,pEi]),tKi(a,b,c,A,F)))}return new HJi(u)}\nfunction FNi(a,b,c){var d,e,f,g,h,i,j,k,l;switch(a.i.v){case 18:return a.g[0].U2(b,c)+r6n+a.g[1].U2(b,c);case 20:l=new sjd;for(g=0;g<a.g.length;g++){g!=0&&$Ni(a.g[g])&&(l.g+=Jhn,l);hjd(l,a.g[g].U2(b,c))}a.g.length==0&&(l.g+='0',l);return l.g;case 21:if(a.g[0].Fv(($jj(),vjj))||a.g[0].Fv(kjj)){return '-\\\\left('+a.g[0].U2(b,c)+R0m}return '-'+a.g[0].U2(b,c);case 22:if(a.g[0].Fv(($jj(),vjj))||a.g[0].Fv(kjj)){return '\\\\pm\\\\left('+a.g[0].U2(b,c)+R0m}return '\\\\pm '+a.g[0].U2(b,c);case 24:k=new sjd;for(f=0;f<a.g.length;f++){e=a.g[f];f!=0&&ZNi(a.g[f-1],e)?(k.g+=' \\\\cdot ',k):f!=0&&(k.g+=' ',k);h=f==a.g.length-1;i=e.Fv(($jj(),vjj))||e.Fv(kjj)||e.Fv(vij)&&!h;i&&(k.g+=Q0m,k);hjd(k,e.U2(b,c));i&&(k.g+=R0m,k)}return k.g;case 26:return vEn+a.g[0].U2(b,c)+Q1m+a.g[1].U2(b,c)+'}';case 28:if(a.g[0].Fv(($jj(),kjj))||cf(a.g[0],202)&&!a.g[0].Fv(rjj)){return Q0m+a.g[0].U2(b,c)+'\\\\right)^{'+a.g[1].U2(b,c)+'}'}return a.g[0].U2(b,c)+'^{'+a.g[1].U2(b,c)+'}';case 44:if(QNi(a,($jj(),rjj))&&sLi(a.g[1],2)){return '\\\\sqrt{'+a.g[0].U2(b,c)+'}'}return '\\\\sqrt['+a.g[1].U2(b,c)+']{'+a.g[0].U2(b,c)+'}';case 47:return X1m+a.g[0].U2(b,c)+Y1m;case 32:case 31:case 33:case 61:case 62:case 63:case 38:case 36:case 40:return EZm+JUi(b,Kvc(a.i).toLowerCase(),true)+Q0m+a.g[0].U2(b,c)+R0m;case 35:if(QNi(a,($jj(),fjj))&&Vb(a.g[0],(UMi(),PMi))){return '\\\\ln \\\\left('+a.g[1].U2(b,c)+R0m}return '\\\\log_{'+a.g[0].U2(b,c)+'} \\\\left('+a.g[1].U2(b,c)+R0m;case 117:j=new sjd;if(!nid(b.i.k,fKn)){j.g+=Q0m;hjd(j,a.g[0].U2(b,c));j.g+=R0m;j.g+=\"'\";return j.g}j.g+='\\\\frac{d}{d';hjd(j,a.g[1].U2(b,c));j.g+='}';d=a.g[0].Fv(($jj(),kjj))||a.g[0].Fv(vjj)||a.g[0].Fv(ljj);d&&(j.g+=Q0m,j);hjd(j,a.g[0].U2(b,c));d&&(j.g+=R0m,j);return j.g;}return ''}\nfunction fDi(){fDi=Auc;XCi=new gDi('WRAPPER',0,'','');LAi=new gDi('GROUP_WRAPPER',1,'','');ICi=new gDi('SUBSTEP_WRAPPER',2,'','');MCi=new gDi(LDn,3,'','');cAi=new gDi('EQUATION',4,'',Rjn);YAi=new gDi(lzn,5,'',Rjn);rCi=new gDi('SIMPLIFY',6,'SimplifyA','Simplify %0');oAi=new gDi(h5n,7,'ExpandA','Expand %0');uAi=new gDi(i5n,8,'FactorA','Factor %0');uCi=new gDi('SOLVE',9,kjn,'Solve %0');vCi=new gDi('SOLVE_FOR',10,'SolveFor','Solve %0 for %1');wCi=new gDi('SOLVE_IN',11,'SolveIn','Solve %0 in %1');xCi=new gDi('SOLVE_WHEN',12,'SolveWhen','Solve %0 when %1');RCi=new gDi('TRUE_FOR_ALL',13,'TrueForAllAInB','The equation is true for all %0');mBi=new gDi('NO_REAL_SOLUTION',14,'NoRealSolutions','No Real Solutions');MAi=new gDi('INVALID_NOT_IN_RANGE',15,'InvalidNotInRange','%0 is not a valid solution, because $%0 \\\\notin %1$');sCi=new gDi('SOLUTION',16,'SolutionA','Solution: %0');tCi=new gDi('SOLUTIONS',17,'SolutionsA','Solutions: %0');HCi=new gDi('STATEMENT_IS_TRUE',18,'StatementIsTrue','The statement is true');GCi=new gDi('STATEMENT_IS_FALSE',19,'StatementIsFalse','The statement is false');xBi=new gDi('POSITIVE_GE_ZERO',20,j5n,k5n);yBi=new gDi('POSITIVE_GT_ZERO',21,l5n,m5n);zBi=new gDi('POSITIVE_LE_ZERO',22,n5n,o5n);ABi=new gDi('POSITIVE_LT_ZERO',23,p5n,q5n);aDi=new gDi('ZERO_GE_POSITIVE',24,j5n,o5n);bDi=new gDi('ZERO_GT_POSITIVE',25,l5n,q5n);dDi=new gDi('ZERO_LE_POSITIVE',26,n5n,k5n);eDi=new gDi('ZERO_LT_POSITIVE',27,p5n,m5n);BBi=new gDi('POSITIVE_L_NEGATIVE',28,'PositiveLNegative',q5n);DBi=new gDi('POSTIVE_G_NEGATIVE',29,'PositiveGNegative',k5n);hBi=new gDi('NEGATIVE_L_POSITIVE',30,'NegativeLPositive',k5n);gBi=new gDi('NEGATIVE_G_POSITIVE',31,'NegativeGPositive',q5n);WAi=new gDi('LEADING_COEFFICIENT_POSITIVE',32,'LeadingCoefficientPositive','$a = %0 > 0$ therefore $%1 > 0$ for all %2');VAi=new gDi('LEADING_COEFFICIENT_NEGATIVE',33,'LeadingCoefficientNegative','$a = %0 < 0$ therefore $%1 < 0$ for all %2');XAi=new gDi('LEFT_POSITIVE_RIGHT_NEGATIVE',34,'LeftPositiveRightNegative','The left hand side is always positive, the right is always negative');nAi=new hDi('EXCLUDE_UNDEFINED_POINTS',35,'ExcludeUndefinedPoints','Exclude undefined points: %0');vBi=new gDi('PLUG_IN_AND_CHECK',36,'PlugInAndCheck','Plug in and check if %0 is a correct solution');Xyi=new gDi('CHECK_VALIDITY',37,'CheckingValidityOfSolutions','Checking validity of solutions');VCi=new gDi('VALID_SOLUTION',38,'ValidSolution','Valid Solution: %0');NAi=new gDi('INVALID_SOLUTION',39,'InvalidSolution','Invalid Solution: %0');WCi=new gDi('VALID_SOLUTION_ABS',40,r5n,'$%0 \\\\in %1$');OAi=new gDi('INVALID_SOLUTION_ABS',41,r5n,'$%0 \\\\notin %1$');HAi=new gDi('FIND_UNDEFINED_POINTS',42,'FindUndefinedPoints','Find undefined points');ezi=new gDi('DETERMINE_THE_DEFINED_RANGE',43,'DetermineTheDefinedRange','Determine the defined range');nCi=new gDi('ROOTS_AND_SIGN_TABLE',44,'FindRootsAndCreateSignTable','Find the roots of the absolute values and create sign table');$Bi=new hDi('RESOLVE_ABSOLUTE_VALUES',45,'ResolveAbsoluteValues','$\\\\left|a\\\\right| = \\\\left|b\\\\right| \\\\implies a = \\\\pm b$');SAi=new hDi('IS_POSITIVE_IN',46,'IsPositiveIn','$%0 \\\\ge 0$ in %1');QAi=new hDi('IS_NEGATIVE_IN',47,'IsNegativeIn','$%0 \\\\le 0$ in %1');fBi=new gDi(s5n,48,'NegateBothSides','Negate both sides');ECi=new gDi('SQUARE_ROOT',49,'TakeSquareRoot','Take square root of both sides');czi=new gDi('CUBE_ROOT',50,'TakeCubeRoot','Take cube root of both sides');rBi=new gDi('NTH_ROOT',51,'TakeNthRoot','Take %0 root of both sides');DCi=new gDi('SQUARE_BOTH_SIDES',52,'SquareBothSides','Square both sides');IBi=new gDi(t5n,53,'RaiseToPower','Raise both sides to the %0 power');Myi=new gDi('ADD_TO_BOTH_SIDES',54,'AddAToBothSides','Add %0 to both sides');Nyi=new gDi('ADD_TO_BOTH_SIDES_NUM',55,'AddToBithSidesNum','Add %0 to the %1 equation');JCi=new gDi('SUBTRACT_FROM_BOTH_SIDES',56,'SubtractAFromBothSides','Subtract %0 from both sides');KCi=new gDi('SUBTRACT_FROM_BOTH_SIDES_NUM',57,'SubtractFromBothSidesNum','Subtract %0 from both sides of equation %1');_Ai=new gDi('MULTIPLY_BOTH_SIDES',58,'MultiplyBothSidesByA','Multiply both sides by %0');aBi=new gDi('MULTIPLY_BOTH_SIDES_NUM',59,'MultiplyBothSidesNum','Multiply both sides by %0 of equation %1');Tzi=new gDi('DIVIDE_BOTH_SIDES',60,'DivideBothSidesByA','Divide both sides by %0');Uzi=new gDi('DIVIDE_BOTH_SIDES_NUM',61,'DivideBothSidesNum','Divide both sides by %0 of equation %1');wAi=new gDi('FACTOR_EQUATION',62,'FactorEquation','Factor equation');KBi=new gDi('RECIPROCATE_BOTH_SIDES',63,'ReciprocateBothSides','Reciprocate  both sides');UCi=new gDi('USE_QUADRATIC_FORMULA',64,'UseQuadraticFormulaWithABC','Use quadratic formula with $a = %0$, $b = %1$, $c = %2$');HBi=new gDi('QUADRATIC_FORMULA',65,'QuadraticFormula','$%0 = \\\\frac{-b \\\\pm \\\\sqrt{b^2-4ac}}{2a}$');$yi=new gDi('COMPLETE_THE_CUBE',66,'CompleteCube','Complete the cube');_yi=new gDi(u5n,67,DHn,'Complete the square');qBi=new gDi('NO_SOLUTION_SIN_COS',68,'NoSolutionSinCos','$%0 \\\\in \\\\left[-1, 1\\\\right]$ for all $%1 \\\\in \\\\mathbb{R}$');oBi=new gDi('NO_SOLUTION_ARCSIN',69,'NoSolutionArcsin',v5n);nBi=new gDi('NO_SOLUTION_ARCCOS',70,'NoSolutionArccos','$%0 \\\\in \\\\left[0, \\\\pi\\\\right]$ for all $%1 \\\\in \\\\mathbb{R}$');pBi=new gDi('NO_SOLUTION_ARCTAN',71,'NoSolutionArctan',v5n);ZBi=new gDi('REPLACE_WITH',72,'ReplaceAWithB','Replace %0 with %1');XBi=new gDi('REPLACE_AND_REGROUP',73,'ReplaceAndRegroup','Replace %0 in %1 and regroup');YBi=new gDi('REPLACE_AND_SOLVE',74,'ReplaceAndSolve','Replace %0 with %1 in %2 and solve the equation');pAi=new gDi(w5n,75,'ExpandFractions','Expand Fractions, the common denominator is: %0');FBi=new gDi(x5n,76,'ProductIsZero','Product is zero');KAi=new hDi(y5n,77,'FractionIsZero','When the quotient of expressions equals 0, the numerator has to be 0');VBi=new gDi('REGROUP_WRAPPER',78,'RegroupExpression','Regroup Expression');qCi=new gDi('SIMPLIFICATION_WRAPPER',79,'SimplifyExpression','Simplify Expression');azi=new gDi('CONVERT_DECIMALS',80,'ConvertDecimals','Convert decimals to fractions');Zzi=new gDi(z5n,81,'DoubleMinus','A double negative is a positive');JBi=new gDi('RATIONALIZE_DENOMINATOR',82,'RationalizeDenominator','Rationalize the denominator.');dBi=new gDi('MULTIPLY_NUM_DENOM',83,'MultiplyNumeratorAndDenominator','Mutiply the numerator and denominator by %0');Ozi=new gDi('DISTRIBUTE_POWER_FRAC',84,'DistributePowerOverFraction','Distribute power over fraction');Qzi=new gDi('DISTRIBUTE_ROOT_FRAC',85,'DistributeRootOverFraction','Distribute the root over the fraction');Nzi=new gDi(A5n,86,'DistributeMinus','Distribute minus');Iyi=new gDi('ADD_CONSTANTS',87,'AddConstants','Add constants');Yyi=new hDi('COLLECT_LIKE_TERMS',88,'CollectLikeTerms','Collect like terms: %0');Kyi=new gDi(B5n,89,'AddFractions','Add fractions');Lyi=new gDi(C5n,90,'AddNumerators','Add numerators');Zyi=new gDi(D5n,91,'CommonFraction','Write the product as a single fraction');Wyi=new hDi(E5n,92,'CancelFraction','Cancel %0 in the fraction');$Ai=new gDi(F5n,93,'MultipliedByZero','Anything multiplied by zero is zero');UBi=new gDi(G5n,94,'RegroupProducts','Regroup products');bBi=new gDi(H5n,95,'MultiplyConstants','Multiply constants');ZAi=new hDi('MULTIPLIED_BY_ONE',96,'MultipliedByOne','Any expression multiplied by one is itself');jAi=new hDi('EVEN_NUMBER_OF_NEGATIVES',97,'EvenNumberOfNegative','Multiplying an even number of negative numbers gives a positive');sBi=new hDi('ODD_NUMBER_OF_NEGATIVES',98,'OddNumberOfNegative','Multiplying an odd number of negative numbers gives a negative');kAi=new gDi('EVEN_POWER_NEGATIVE',99,'EvenPowerNegative','An even power of a negative number is a positive');tBi=new gDi('ODD_POWER_NEGATIVE',100,'OddPowerNegative','An odd power of a negative number is a negative');iBi=new gDi('NEGATIVE_NUM_AND_DENOM',101,'NegativeNumeratorAndDenominator','Use $\\\\frac{-a}{-b} = \\\\frac{a}{b}$');jBi=new gDi('NEGATIVE_NUM_OR_DENOM',102,'NegativeNumeratorOrDenominator','Use $\\\\frac{-a}{b} = \\\\frac{a}{-b} = -\\\\frac{a}{b}$');LBi=new hDi('REDUCE_ROOT_AND_POWER',103,'ReduceRootAndPower',I5n);MBi=new hDi('REDUCE_ROOT_AND_POWER_EVEN',104,'ReduceRootAndPowerEven',I5n);eAi=new gDi('EVALUATE_FRACTION',105,'EvaluateFraction','Evaluate fraction');gAi=new gDi('EVALUATE_POWER',106,'EvaluatePower','Evaluate powers');hAi=new gDi('EVALUATE_ROOT',107,'EvaluateRoot','Evaluate roots');$Ci=new hDi('ZEROTH_POWER',108,'ZerothPower','The zeroth power of anything is one');IAi=new hDi('FIRST_POWER',109,'FirstPower','The first power of anything is itself');JAi=new hDi('FIRST_ROOT',110,'FirstRoot','The first root of anything is itself');oCi=new gDi('ROOT_OF_ONE',111,'RootOfOne','Any root of 1 is 1');mAi=new hDi('EVEN_ROOT_OF_NEGATIVE',112,'EvenRootOfNegative','The square root of a negative number is undefined in the set of the real numbers');uBi=new gDi('ODD_ROOT_OF_NEGATIVE',113,'OddRootOfNegative','An odd root of a negative radicand is always negative');pCi=new gDi(J5n,114,'RootOfRoot','Use $\\\\sqrt[m]{\\\\sqrt[n]{a}} \\\\equiv \\\\sqrt[mn]{a}$ to simplify the expression');gCi=new gDi('REWRITE_DECIMAL_AS_COMMON_FRACTION',115,'RewriteDecimalAsCommonFraction','Rewrite decimal as common fraction');BCi=new gDi(K5n,116,'SplitProducts','Split products for factoring');yCi=new gDi(L5n,117,'SplitFractions','Split fractions');ACi=new hDi('SPLIT_POWERS',118,'SplitPowers',M5n);CCi=new hDi(N5n,119,'SplitRoots','The root of a product is equal to the product of the roots of each factor');$zi=new gDi(O5n,120,'EliminateOpposites','Eliminate the opposites');tAi=new gDi(P5n,121,'ExponentialOfLog','Exponential of logarithm');cDi=new gDi('ZERO_IN_ADDITION',122,'AddingOrSubtractionZero','When adding or subtracting zero, the quantity does not change');_Ci=new hDi('ZERO_DIVIDED',123,'ZeroDivided','Zero divided by anything is zero');dAi=new hDi('EVALUATE_DIVISION',124,'EvaluateDivision','Evaluate the division');Rzi=new hDi('DIVIDED_BY_ITSELF',125,'DividedByItself','Any expression divided by itself equals 1');Szi=new hDi('DIVIDED_BY_ZERO',126,'DividedByZero','Any expression divided by zero is undefined');Wzi=new hDi('DIVIDE_BY_ONE',127,'DividedByOne','Any expression divided by one remains the same');Vzi=new hDi('DIVIDE_BY_NEGATVE_ONE',128,'DividedByNegativeOne','Any expression divided by negative one negates the expression');_Bi=new gDi('REWRITE_AS',129,'RewriteAAsB',M5n);bCi=new gDi('REWRITE_COMPLEX_FRACTION',130,'RewriteComplexFraction','Rewrite complex fraction');EBi=new gDi(Q5n,131,'MultiplyExponents','Simplify the expression by multiplying the exponents');kBi=new hDi('NEGATIVE_POWER',132,'NegativePower','Express with a positive exponent using $a^{-n} \\\\equiv \\\\frac{1}{a^n}$');GAi=new gDi('FACTOR_SQUARE',133,'FactorSquare','Factor out the perfect square');sAi=new hDi('EXPAND_SUM_TIMES_SUM',134,'ExpandSumTimesSum','Multiply everything in the first parentheses with everything in the second parentheses');rAi=new hDi('EXPAND_SIMPLE_TIMES_SUM',135,'ExpandSimpleTimesSum','Multiply %0 with everything in the parentheses');Tyi=new gDi('BINOM_SQUARED_SUM',136,R5n,'Use $(a+b)^2 \\\\equiv a^2 + 2ab + b^2$ to expand');Ryi=new gDi('BINOM_SQUARED_DIFF',137,S5n,'Use $(a-b)^2 \\\\equiv a^2 - 2ab + b^2$ to expand');Oyi=new gDi('BINOM_CUBED',138,T5n,'Use $(a+b)^3 \\\\equiv a^3 + 3a^2b + 3ab^2 + b^3$ to expand');QCi=new gDi('TRINOM_SQUARED',139,'TrinomSquared','Use $(a+b+c)^2 \\\\equiv a^2 + b^2 + c^2 + 2ab + 2bc + 2ac$ to expand');gzi=new gDi('DIFFERENCE_OF_SQUARES',140,'DifferenceOfSquares','Use $(a+b)(a-b) \\\\equiv a^2-b^2$ to expand');xAi=new gDi(U5n,141,'FactorFractions','Factor fractions');LCi=new gDi('SUM_OF_CUBES',142,'SumOfCubes','Use $a^3 + b^3 = (a + b)(a^2 - ab + b^2)$ to factor');Uyi=new gDi('BINOM_SQUARED_SUM_FACTOR',143,R5n,'Use $a^2 + 2ab + b^2 \\\\equiv (a+b)^2$ to factor');Syi=new gDi('BINOM_SQUARED_DIFF_FACTOR',144,S5n,'Use $a^2 - 2ab + b^2 \\\\equiv (a-b)^2$ to factor');fzi=new gDi('DIFFERENCE_OF_CUBES_FACTOR',145,'DifferenceOfCubes','Use $a^3 - b^3 = (a - b)(a^2 + ab + b^2)$ to factor');hzi=new gDi('DIFFERENCE_OF_SQUARES_FACTOR',146,'DifferenceOfSquaresFactor','Use $a^2-b^2 \\\\equiv (a+b)(a-b)$ to factor');Qyi=new gDi('BINOM_CUBED_SUM_FACTOR',147,T5n,'Use $a^3 + 3a^2b + 3ab^2 + b^3 \\\\equiv (a+b)^3$ to factor');Pyi=new gDi('BINOM_CUBED_DIFF_FACTOR',148,T5n,'Use $a^3 - 3a^2b + 3ab^2 - b^3 \\\\equiv (a+b)^3$ to factor');TAi=new gDi('IS_POSITIVE_IN_INEQUALITY',149,'IsPositiveInInequality','%0 is positive in %1, because there are an even number of negative values in the product');RAi=new gDi('IS_NEGATIVE_IN_INEQUALITY',150,'IsNegativeInInequality','%0 is negative in %1, because there are an odd number of negative values in the product');UAi=new gDi('IS_ZERO_IN',151,'IsZeroIn','%0 is zero in %1, because at least one of the multiplicands is zero');PAi=new gDi('IS_INVALID_IN',152,'IsInvalidIn','%0 is invalid in %1, because there is a zero in the denominator');FAi=new hDi('FACTOR_QUADRATIC',153,'FactorQuadratic','Use $ax^2+bx+c = a\\\\left(x - x_{1}\\\\right)\\\\left(x - x_{2}\\\\right)$ to factor the expression');BAi=new hDi('FACTOR_OUT',154,'FactorOutA','Factor out %0');vAi=new gDi(V5n,155,'FactorCommon','Factor common');EAi=new gDi(W5n,156,'FactorPolynomial','Factor polynomial');yAi=new gDi('FACTOR_FROM_PAIR',157,'FactorOutAFromEveryPair','Factor out %0 from every pair');AAi=new gDi('FACTOR_MINUS',158,'FactorMinus','Factor out the minus sign');zAi=new gDi('FACTOR_GCD',159,'FactorGCD','Factor out the greatest common divisor of %0 and %1: %2');WBi=new gDi('REORGANIZE_EXPRESSION',160,'ReorganizeExpression','Reorganize expression');aCi=new gDi('REWRITE_AS_MULTIPLICATION',161,'RewriteAsMultiplication','Rewrite as multiplication');Pzi=new gDi(X5n,162,'DistributePowerOverProduct','Distribute power over product');FCi=new gDi(Y5n,163,'SquareRootMultipliedByItself','When the square root of an expression in multiplied by itself, the result is that expression');qAi=new gDi(Z5n,164,'ExpandRoot','Using $\\\\sqrt[n]{a} \\\\equiv \\\\sqrt[mn]{a^m}$, expand the expression');GBi=new gDi('PRODUCT_OF_ROOTS',165,'ProductOfRoots','The product of roots with the same index is equal to the root of the product');wBi=new gDi('POLYNOMIAL_DIVISION',166,'DivideAByBToGetC','Divide %0 by %1 to get %2');iAi=new gDi('EVALUATE_TRIGO',167,'EvaluateTrigo','Evaluate trigonometric function');OCi=new hDi('TRIGO_ODD_SIN',168,'TrigoOddSin','$\\\\sin(-x) = -\\\\sin(x)$');NCi=new hDi('TRIGO_EVEN_COS',169,'TrigoEvenCos','$\\\\cos(-x) = \\\\cos(x)$');PCi=new hDi('TRIGO_ODD_TAN',170,'TrigoOddTan','$\\\\tan(-x) = \\\\tan(x)$');CAi=new gDi('FACTOR_OUT_2PI',171,$5n,'Factor out $2 \\\\pi$ where possible');DAi=new gDi('FACTOR_OUT_PI',172,$5n,'Factor out $\\\\pi$ where possible');aAi=new hDi('ELIMINATE_THE_PERIOD_SIN',173,_5n,'$\\\\sin(x + k \\\\cdot 2 \\\\pi) = \\\\sin(x)$, for any $k \\\\in \\\\mathbb{Z}$');_zi=new hDi('ELIMINATE_THE_PERIOD_COS',174,_5n,'$\\\\cos(x + k \\\\cdot 2 \\\\pi) = \\\\cos(x)$, for any $k \\\\in \\\\mathbb{Z}$');bAi=new hDi('ELIMINATE_THE_PERIOD_TAN',175,_5n,'$\\\\tan(x + k \\\\cdot \\\\pi) = \\\\tan(x)$, for any $k \\\\in \\\\mathbb{Z}$');QBi=new hDi('REDUCE_TO_FRIST_QUADRANT_SIN_II',176,'ReduceToFirstQuadrantSinII','Use $\\\\sin(x) = \\\\sin(\\\\pi - x)$');RBi=new hDi('REDUCE_TO_FRIST_QUADRANT_SIN_III',177,'ReduceToFirstQuadrantSinIII','Use $\\\\sin(x) = -\\\\sin(x - \\\\pi)$');SBi=new hDi('REDUCE_TO_FRIST_QUADRANT_SIN_IV',178,'ReduceToFirstQuadrantSinIV','Use $\\\\sin(x) = -\\\\sin(2 \\\\pi - x)$');NBi=new hDi('REDUCE_TO_FRIST_QUADRANT_COS_II',179,'ReduceToFirstQuadrantCosII','Use $\\\\cos(x) = -\\\\cos(\\\\pi - x)$');OBi=new hDi('REDUCE_TO_FRIST_QUADRANT_COS_III',180,'ReduceToFirstQuadrantCosIII','Use $\\\\cos(x) = -\\\\cos(x - \\\\pi)$');PBi=new hDi('REDUCE_TO_FRIST_QUADRANT_COS_IV',181,'ReduceToFirstQuadrantCosIV','Use $\\\\cos(x) = \\\\cos(2 \\\\pi - x)$');TBi=new hDi('REDUCE_TO_FRIST_QUADRANT_TAN',182,'ReduceToFirstQuadrantTan','Use $\\\\tan(x) = -\\\\tan(\\\\pi - x)$');zCi=new gDi(a6n,183,'SplitFractionsWithPi','Split fractions with $\\\\pi$');kCi=new hDi('REWRITE_SIN_PI_POSITIVE',184,'RewriteSinPiPositive','$\\\\sin(x + \\\\pi) = -\\\\sin(x)$');jCi=new hDi('REWRITE_SIN_PI_NEGATIVE',185,'RewriteSinPiNegative','$\\\\sin(\\\\pi - x) = \\\\sin(x)$');fCi=new hDi('REWRITE_COS_PI_POSITIVE',186,'RewriteCosPiPositive','$\\\\cos(x + \\\\pi) = -\\\\cos(x)$');eCi=new hDi('REWRITE_COS_PI_NEGATIVE',187,'RewriteCosPiNegative','$\\\\cos(\\\\pi - x) = -\\\\cos(x)$');iCi=new hDi('REWRITE_SIN_PI_HALF_POSITIVE',188,'RewriteSinPiHalfPositive','$\\\\sin\\\\left(x + \\\\frac{\\\\pi}{2}\\\\right) = \\\\cos(x)$');hCi=new hDi('REWRITE_SIN_PI_HALF_NEGATIVE',189,'RewriteSinPiHalfNegative','$\\\\sin\\\\left(\\\\frac{\\\\pi}{2} - x\\\\right) = \\\\cos(x)$');dCi=new hDi('REWRITE_COS_PI_HALF_POSITIVE',190,'RewriteCosPiHalfPositive','$\\\\cos\\\\left(x + \\\\frac{\\\\pi}{2}\\\\right) = -\\\\sin(x)$');cCi=new hDi('REWRITE_COS_PI_HALF_NEGATIVE',191,'RewriteCosPiHalfNegative','$\\\\cos\\\\left(\\\\frac{\\\\pi}{2} - x\\\\right) = \\\\sin(x)$');mCi=new hDi('REWRITE_TAN_PI_HALF_POSITIVE',192,'RewriteTanPiHalfPositive','$\\\\tan\\\\left(x + \\\\frac{\\\\pi}{2}\\\\right) = -\\\\frac{1}{\\\\tan(x)}$');lCi=new hDi('REWRITE_TAN_PI_HALF_NEGATIVE',193,'RewriteTanPiHalfNegative','$\\\\tan\\\\left(\\\\frac{\\\\pi}{2} - x\\\\right) = \\\\frac{1}{\\\\tan(x)}$');fAi=new gDi('EVALUATE_INVERSE_TRIGO',194,'EvaluateInverseTrigo','Evaluate inverse trigonometric function');CBi=new hDi('POSITIVE_UNDER_ABSOLUTE_VALUE',195,'PositiveUnderAbsoluteValue','The absolute value of a positive value is itself');lBi=new hDi('NEGATIVE_UNDER_ABSOLUTE_VALUE',196,'NegativeUnderAbsoluteValue','The absolute value of a negative value is the negation of itself');lAi=new hDi(b6n,197,'EvenPowerOfAbsoluteValue','An even power of an absolute value is already positive');izi=new gDi('DIFFERENTIATE',198,'Differentiate','Differentiate %0');Jzi=new hDi('DIFF_SUM',199,'SumRule','$\\\\frac{d}{dx} \\\\left[f(x) + g(x)\\\\right] = \\\\frac{d}{dx}f(x) + \\\\frac{d}{dx}g(x)$');pzi=new gDi('DIFF_CONSTANT',200,'ConstantRule','The derivative of a constant is zero');qzi=new hDi('DIFF_CONSTANT_COEFFICIENT',201,'ConstantCoefficientRule','$\\\\frac{d}{dx} \\\\left[k \\\\cdot f(x) \\\\right] = k \\\\cdot \\\\frac{d}{dx} f(x)$');Ezi=new hDi('DIFF_PRODUCT',202,'ProductRule','$\\\\frac{d}{dx}\\\\left[f(x) \\\\cdot g(x)\\\\right] = \\\\frac{d}{dx} f(x) \\\\cdot g(x) + f(x) \\\\cdot \\\\frac{d}{dx} g(x)$');xzi=new hDi('DIFF_FRACTION',203,'QuotientRule','$\\\\frac{d}{dx} \\\\frac{f(x)}{g(x)} = \\\\frac{\\\\frac{d}{dx} f(x) \\\\cdot g(x) - f(x) \\\\cdot \\\\frac{d}{dx} g(x)}{(g(x))^2}$');Mzi=new hDi('DIFF_VARIABLE',204,'DifferentiateVariable','$\\\\frac{d}{dx} x = 1$');Czi=new hDi('DIFF_POWER',205,'PowerRule','$\\\\frac{d}{dx} x^n = n x^{n-1}$');vzi=new hDi('DIFF_EXPONENTIAL_E',206,'ExponentialRuleE','$\\\\frac{d}{dx} e^x = e^x$');tzi=new hDi('DIFF_EXPONENTIAL',207,'ExponentialRule','$\\\\frac{d}{dx} a^x = \\\\ln(a) a^x$');Fzi=new hDi('DIFF_ROOT',208,'RootRule','$\\\\frac{d}{dx} \\\\sqrt[n]{x} = \\\\frac{1}{n \\\\sqrt[n]{x^{n-1}}}$');yzi=new hDi('DIFF_LOG',209,'LogRule','$\\\\frac{d}{dx} \\\\( \\\\log_{a} \\\\left(x\\\\right) \\\\) = \\\\frac{1}{\\\\ln(a) \\\\cdot x}$');Azi=new hDi('DIFF_NATURAL_LOG',210,'NaturalLogRule','$\\\\frac{d}{dx} \\\\ln(x) = \\\\frac{1}{x}$');Hzi=new hDi('DIFF_SIN',211,'SinRule','$\\\\frac{d}{dx} sin(x) = cos(x)$');rzi=new hDi('DIFF_COS',212,'CosRule','$\\\\frac{d}{dx} cos(x) = -sin(x)$');Kzi=new hDi('DIFF_TAN',213,'TanRule','$\\\\frac{d}{dx} tan(x) = \\\\frac{1}{cos^2(x)}$');lzi=new hDi('DIFF_ARCSIN',214,'ArcsinRule','$\\\\frac{d}{dx} arcsin(x) = \\\\frac{1}{\\\\sqrt{1-x^2}}$');jzi=new hDi('DIFF_ARCCOS',215,'ArccosRule','$\\\\frac{d}{dx} arccos(x) = -\\\\frac{1}{\\\\sqrt{1-x^2}}$');nzi=new hDi('DIFF_ARCTAN',216,'ArctanRule','$\\\\frac{d}{dx} arctan(x) = \\\\frac{1}{x^2+1}$');Dzi=new hDi('DIFF_POWER_CHAIN',217,'PowerRuleChain','$\\\\frac{d}{dx} (u(x))^n = n (u(x))^{n-1} \\\\cdot \\\\frac{d}{dx} u(x)$');wzi=new hDi('DIFF_EXPONENTIAL_E_CHAIN',218,'ExponentialRuleEChain','$\\\\frac{d}{dx} a^{u(x)} = \\\\ln(a) a^{u(x)} \\\\cdot \\\\frac{d}{dx} u(x)$');uzi=new hDi('DIFF_EXPONENTIAL_CHAIN',219,'ExponentialRuleChain','$\\\\frac{d}{dx} e^{u(x)} = e^{u(x)} \\\\cdot \\\\frac{d}{dx} u(x)$');Gzi=new hDi('DIFF_ROOT_CHAIN',220,'RootRuleChain','$\\\\frac{d}{dx} \\\\sqrt[n]{u(x)} = \\\\frac{1}{n \\\\sqrt[n]{(u(x))^{n-1}}} \\\\cdot \\\\frac{d}{dx} u(x)$');zzi=new hDi('DIFF_LOG_CHAIN',221,'LogRuleChain','$\\\\frac{d}{dx} \\\\log_{a}(u(x)) = \\\\frac{1}{\\\\ln(a) \\\\cdot u(x)} \\\\cdot \\\\frac{d}{dx} u(x)$');Bzi=new hDi('DIFF_NATURAL_LOG_CHAIN',222,'NaturalLogRuleChain','$\\\\frac{d}{dx} \\\\ln(u(x)) = \\\\frac{1}{u(x)} \\\\cdot \\\\frac{d}{dx} u(x)$');Izi=new hDi('DIFF_SIN_CHAIN',223,'SinRuleChain','$\\\\frac{d}{dx} sin(u(x)) = cos(u(x)) \\\\cdot \\\\frac{d}{dx} u(x)$');szi=new hDi('DIFF_COS_CHAIN',224,'CosRuleChain','$\\\\frac{d}{dx} cos(u(x)) = -sin(u(x)) \\\\cdot \\\\frac{d}{dx} u(x)$');Lzi=new hDi('DIFF_TAN_CHAIN',225,'TanRuleChain','$\\\\frac{d}{dx} tan(u(x)) = \\\\frac{1}{cos^2(u(x))} \\\\cdot \\\\frac{d}{dx} u(x)$');mzi=new hDi('DIFF_ARCSIN_CHAIN',226,'ArcsinRuleChain','$\\\\frac{d}{dx} arcsin(u(x)) = \\\\frac{1}{\\\\sqrt{1-(u(x))^2}} \\\\cdot \\\\frac{d}{dx} u(x)$');kzi=new hDi('DIFF_ARCCOS_CHAIN',227,'ArccosRuleChain','\\\\frac{d}{dx} arccos(u(x)) = -\\\\frac{1}{\\\\sqrt{1-(u(x))^2}} \\\\cdot \\\\frac{d}{dx} u(x)');ozi=new hDi('DIFF_ARCTAN_CHAIN',228,'ArctanRuleChain','\\\\frac{d}{dx} arctan(u(x)) = \\\\frac{1}{(u(x))^2+1} \\\\cdot \\\\frac{d}{dx} u(x)');Jyi=new gDi('ADD_EQUATIONS',229,'AddEquations','Add the equations to eliminate %0');SCi=new gDi('USE_CRAMERS_RULE',230,'UseCramersRule',\"Use Cramer's rule to solve the equation system\");dzi=new gDi('DETERMINANTS',231,'','$D = %3$, $D_{1} = %0$, $D_{2} = %1$, $D_{3} = %2$');bzi=new gDi('CRAMER_VARIABLE',232,'','$%0 = \\\\frac{D_{%1}}{D} = \\\\frac{%2}{%3}$');TCi=new hDi('USE_LEIBNIZ_FORMULA',233,'UseLeibnizFormula','Use the Leibniz formula to evaluate the determinant');Vyi=new gDi('CALCULATE_DETERINANT',234,'CalculateDeterminant','Calculate the determinant %0');YCi=new gDi('WRITE_IN_MATRIX_FORM',235,'WriteInMatrixForm','Write the equation system in matrix form');ZCi=new gDi('WRITE_IN_SYSTEM_FORM',236,'WriteInSystemForm','Write the matrix in equation system form');eBi=new gDi('MULTIPLY_ROW_AND_ADD',237,'MultiplyRowAndAdd','Multiply row %0 by %1 and add it to row %2');cBi=new gDi('MULTIPLY_EACH_ELEMENT_AND_ADD',238,'MultiplyEachElementAndAdd','Multiply each element in row %0 by %1 and add that product to row %2');Yzi=new gDi('DIVIDE_ROW',239,'DivideRow','Divide row %0 by %1');Xzi=new gDi('DIVIDE_EACH_ELEMENT',240,'DivideEachElement','Divide each element in row %0 by %1')}\nvar f5n={3:1,4:1,7:1,76:1},g5n={3:1,4:1,8:1,7:1,76:1,154:1},h5n='EXPAND',i5n='FACTOR',j5n='PositiveGEZero',k5n='The statement is true for all values of %0',l5n='PositiveGTZero',m5n='The statement is true, except when %0',n5n='PositiveLEZero',o5n='The statement is only true when %0',p5n='PositiveLTZero',q5n='The statement is false for all values of %0',r5n='ValidSolutionAbs',s5n='NEGATE_BOTH_SIDES',t5n='RAISE_TO_POWER',u5n='COMPLETE_THE_SQUARE',v5n='$%0 \\\\in \\\\left[-\\\\frac{\\\\pi}{2}, \\\\frac{\\\\pi}{2}\\\\right]$ for all $%1 \\\\in 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%1',N5n='SPLIT_ROOTS',O5n='ELIMINATE_OPPOSITES',P5n='EXPONENTIAL_OF_LOG',Q5n='POWER_OF_POWER',R5n='BinomSquaredSum',S5n='BinomSquaredDiff',T5n='BinomCubed',U5n='FACTOR_FRACTIONS',V5n='FACTOR_COMMON',W5n='FACTOR_POLYNOMIAL',X5n='DISTRIBUTE_POWER_OVER_PRODUCT',Y5n='SQUARE_ROOT_MULTIPLIED_BY_ITSELF',Z5n='EXPAND_ROOT',$5n='FactorOut2Pi',_5n='EliminatePeriodSin',a6n='SPLIT_FRACTIONS_WITH_PI',b6n='EVEN_POWER_OF_ABSOLUTE_VALUE',c6n='\\\\fgcolor{',d6n={3:1,16:1,23:1,445:1,105:1},e6n={3:1,16:1,23:1,337:1,286:1},f6n='SOLVE_QUADRATIC',g6n='SIMPLIFY_TRIGONOMETRIC',h6n={3:1,16:1,23:1,616:1,105:1},i6n={3:1,16:1,23:1,348:1,105:1},j6n={3:1,16:1,23:1,338:1,105:1},k6n='SIMPLIFY_FRACTIONS',l6n={3:1,16:1,23:1,680:1,286:1},m6n={3:1,16:1,23:1,150:1,105:1},n6n={3:1,16:1,23:1,286:1,422:1},o6n='changed at ',p6n={3:1,16:1,23:1,105:1,490:1},q6n=4.71238898038469,r6n=' \\\\in ',s6n=' \\\\text{ and } ';zuc(6406,1,{},u$f);_.He=function(){return i9i(this.i)};var 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WNi(vjj,me(fe(vub,1),g5n,137,0,[CLi(d,dLi(vij,i,k)),CLi(dLi(vij,d,k),i)]));vyi(b,new Fyi((fDi(),Ezi)));return h}}return a.d3(this,b,c)};var urb=Ngd(7100,Arb,null);zuc(7101,445,d6n,dEi);_.Y2=function(a,b,c){var d,e,f,g,h,i,j;if(a.Fv(($jj(),vij))){i=a;if(i.g[0].Fv(xij)){e=i.g[0];j=i.g[1];f=e.g[0];d=e.g[1];f.f3(c.i++);d.f3(c.i++);h=ILi(CLi(dLi(vij,f,j),d),CLi(f,dLi(vij,d,j)));g=lLi(h,ELi(d,ZMi(2)));vyi(b,new Fyi((fDi(),xzi)));return g}}return a.d3(this,b,c)};var vrb=Ngd(7101,Arb,null);zuc(7102,445,d6n,eEi);_.Y2=function(a,b,c){var d,e,f,g,h,i;if(a.Fv(($jj(),vij))){h=a;if(Vb(h.g[0],h.g[1])){g=ZMi(1);h.g[0].f3(c.i);g.f3(c.i);vyi(b,new Gyi((fDi(),Mzi),c.i++));return g}if(h.g[0].Fv(yjj)){f=h.g[0];i=h.g[1];d=f.g[0];e=f.g[1];if(e.p3(i)){d.f3(c.i++);e.f3(c.i++);g=CLi(e,EMi(d,ZMi(e.A_()-1)));if(Vb(d,i)){vyi(b,new Fyi((fDi(),Czi)))}else{g=CLi(g,dLi(vij,d,i));vyi(b,new Fyi((fDi(),Dzi)))}return g}}}return a.d3(this,b,c)};var wrb=Ngd(7102,Arb,null);zuc(7103,445,d6n,fEi);_.Y2=function(a,b,c){var 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Drb=Ngd(7679,Urb,null);zuc(7680,337,e6n,NEi);_.$2=function(a,b,c,d){return MEi(a,c,d)};var Erb=Ngd(7680,Urb,null);zuc(7681,337,e6n,PEi);_.$2=function(a,b,c,d){return OEi(a,b,c,d)};var Grb=Ngd(7681,Urb,null);zuc(7682,1,{},QEi);_.Gi=Mqo;_.Fe=Nqo;_.Hi=Oqo;var Frb=Mgd(7682);zuc(7683,337,e6n,SEi);_.$2=function(a,b,c,d){return REi(a,b,c,d)};var Hrb=Ngd(7683,Urb,null);zuc(7684,337,e6n,UEi);_.$2=function(a,b,c,d){return TEi(a,b,c)};var Irb=Ngd(7684,Urb,null);zuc(7685,337,e6n,WEi);_.$2=function(a,b,c,d){return VEi(a,b,c,d)};var Jrb=Ngd(7685,Urb,null);zuc(7686,337,e6n,YEi);_.$2=function(a,b,c,d){return XEi(a,b,c)};var Krb=Ngd(7686,Urb,null);zuc(7669,337,e6n,$Ei);_.$2=function(a,b,c,d){return ZEi(a,c)};var Mrb=Ngd(7669,Urb,null);zuc(7670,337,e6n,aFi);_.$2=function(a,b,c,d){return _Ei(a,b,c,d)};var Nrb=Ngd(7670,Urb,null);zuc(7671,337,e6n,cFi);_.$2=function(a,b,c,d){return bFi(a,b,c)};var Orb=Ngd(7671,Urb,null);zuc(7672,337,e6n,eFi);_.$2=function(a,b,c,d){return dFi(a,b,c)};var Prb=Ngd(7672,Urb,null);zuc(7673,337,e6n,gFi);_.$2=function(a,b,c,d){return fFi(a,c)};var Qrb=Ngd(7673,Urb,null);zuc(7674,337,e6n,hFi);_.$2=function(a,b,c,d){var e;return e=ZMi(1),!a.j.p3(null)&&!!eMi(a.j)&&(e=eMi(a.j)),!a.k.p3(null)&&!!eMi(a.k)&&(e=dyi(eMi(a.k),e)),new IJi(fNi(a,e,c))};var Rrb=Ngd(7674,Urb,null);zuc(7675,337,e6n,jFi);_.$2=function(a,b,c,d){return iFi(a,c)};var Srb=Ngd(7675,Urb,null);zuc(7676,337,e6n,lFi);_.$2=function(a,b,c,d){return kFi(a,b,c,d)};var Trb=Ngd(7676,Urb,null);zuc(616,23,h6n);_.Z2=function(){return this==nFi||this==mFi};var mFi,nFi,oFi,pFi,qFi,rFi,sFi;var asb=Ngd(616,Ru,wFi);zuc(7073,616,h6n,xFi);_.Y2=function(a,b,c){var d,e,f,g;if(a.Fv(($jj(),ljj))){f=a;if(f.g.length!=2||!f.g[0].Fv(vjj)||!f.g[1].Fv(vjj)){return a.d3(this,b,c)}d=f.g[0];e=f.g[1];if(d.g.length!=2||e.g.length!=2){return a.d3(this,b,c)}if(Vb(d.g[0],e.g[0])&&Vb(d.g[1],tMi(e.g[1]))){d.g[0].f3(c.i);e.g[0].f3(c.i++);d.g[1].f3(c.i);e.g[1].f3(c.i++);g=je(vub,g5n,137,2,0,1);g[0]=ELi(d.g[0],ZMi(2));d.g[1].Fv(kjj)?(g[1]=ALi(ELi(tMi(d.g[1]),ZMi(2)))):(g[1]=ALi(ELi(d.g[1],ZMi(2))));vyi(b,new Fyi((fDi(),gzi)));return new WNi(vjj,g)}if(Vb(d.g[1],e.g[1])&&Vb(d.g[0],tMi(e.g[0]))){d.g[1].f3(c.i);e.g[1].f3(c.i++);d.g[0].f3(c.i);e.g[0].f3(c.i++);vyi(b,new Fyi((fDi(),WBi)));return new WNi(ljj,me(fe(vub,1),g5n,137,0,[bLi(d.g[1],d.g[0]),bLi(e.g[1],e.g[0])]))}}return a.d3(this,b,c)};var Vrb=Ngd(7073,asb,null);zuc(7074,616,h6n,yFi);_.Y2=function(a,b,c){return vFi(this,a,b,c,null)};var Wrb=Ngd(7074,asb,null);zuc(7075,616,h6n,zFi);_.Y2=function(a,b,c){return vFi(this,a,b,c,(Ofd(),false))};var Xrb=Ngd(7075,asb,null);zuc(7076,616,h6n,AFi);_.Y2=function(a,b,c){return vFi(this,a,b,c,(Ofd(),true))};var Yrb=Ngd(7076,asb,null);zuc(7077,616,h6n,CFi);_.Y2=function(a,b,c){var d,e,f,g,h;if(cf(a,202)&&!a.Fv(($jj(),Phj))){g=a;if(QNi(g,($jj(),yjj))&&g.g[0].Fv(vjj)&&g.g[1].A_()>0&&g.g[1].q3()){h=g.g[0];if(g.g[1].A_()+h.g.length<6){return BFi(g,b,c)}e=puc($tc($wnd.Math.round(g.g[1].A_())));d=je(vub,g5n,137,e,0,1);for(f=0;f<e;f++){d[f]=GNi(h)}return new WNi(ljj,d)}}return a.d3(this,b,c)};var Zrb=Ngd(7077,asb,null);zuc(7078,616,h6n,DFi);_.Y2=function(a,b,c){var d;d=me(fe(Ptb,1),qZm,105,0,[(uIi(),IHi),oFi,qFi,rFi]);return sKi(a,null,d,b,c)};var $rb=Ngd(7078,asb,null);zuc(7079,616,h6n,FFi);_.Y2=function(a,b,c){return EFi(a,b,c)};var _rb=Ngd(7079,asb,null);zuc(348,23,i6n);_.Z2=function(){return this==KFi||this==HFi||this==WFi||this==SFi||this==RFi||this==MFi};var GFi,HFi,IFi,JFi,KFi,LFi,MFi,NFi,OFi,PFi,QFi,RFi,SFi,TFi,UFi,VFi,WFi;var ssb=Ngd(348,Ru,ZFi);zuc(7080,348,i6n,$Fi);_.Y2=function(a,b,c){var d,e,f,g,h,i,j,k,l,m,n,o,p,q,r;if(a.Fv(($jj(),vjj))&&!wJi(c,a,(DJi(),BJi))){r=a;f=new Nnd;g=new Nnd;e=r.g[0];for(m=1;m<r.g.length;m++){e=iyi(e,r.g[m])}if(!e||e.r3()&&$wnd.Math.abs(e.A_()-1)<C4m||e.r3()&&$wnd.Math.abs(e.A_()- -1)<C4m){return a.d3(this,b,c)}e=e.i3();d=c.i;aMi(e,f,g);i=new Nnd;j=new Nnd;p=je(vub,g5n,137,r.g.length,0,1);for(l=0;l<r.g.length;l++){wnd(i,new Nnd);wnd(j,new Nnd);aMi(r.g[l],(sxd(l,i.B.length),i.B[l]),(sxd(l,j.B.length),j.B[l]));h=null;for(o=0;o<(sxd(l,i.B.length),i.B[l]).size();o++){n=Bnd(f,(sxd(l,i.B.length),i.B[l]).getAtIndex(o),0);if(n!=-1&&!vLi((sxd(n,g.B.length),g.B[n]))){k=ILi((sxd(l,j.B.length),j.B[l]).getAtIndex(o),(sxd(n,g.B.length),g.B[n]));k=gJi((uIi(),tIi),k,null,new 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d,e,f,g,h,i,j,k,l,m,n,o,p,q,r;if(a.Fv(($jj(),vjj))&&wJi(c,a,(DJi(),zJi))){q=a;r=And(_Ki(q),0);p=ULi(q,r);m=je(tf,$_m,5,p.length,14,1);for(k=0;k<p.length;k++){!p[k]?(m[k]=0):(m[k]=$tc($wnd.Math.round(p[k].A_())))}g=Ghd(m[0]);i=Ghd(m[m.length-1]);for(j=guc(g);Wtc(j,g)<=0;e=j,j=Utc(j,1),e){for(n=1;Wtc(n,i)<=0;d=n,n=Utc(n,1),d){if(Wtc(j,0)!=0&&Ztc(euc(g,j),0)&&Ztc(euc(i,n),0)&&$wnd.Math.abs(NNi(q,r,ouc(j)/ouc(n)))<C4m){h=je(vub,g5n,137,p.length,0,1);l=bLi(GMi(ZMi(ouc(n)),r),ZMi(ouc(guc(j))));l.f3(c.i++);for(o=p.length-1;o>0;o--){f=Ytc(m[o],n);Wtc(f,0)<0?(h[p.length-o]=tMi(CLi(FMi(ouc(guc(f)),EMi(r,ZMi(o-1))),l))):(h[p.length-o]=CLi(FMi(ouc(f),EMi(r,ZMi(o-1))),l));m[o-1]=Utc(m[o-1],Ytc(fuc(j,m[o]),n))}vyi(b,new Hyi((fDi(),yAi),me(fe(grb,1),f5n,135,0,[l])));return YNi(vjj,h)}}}}return a.d3(this,b,c)};var bsb=Ngd(7089,ssb,null);zuc(7090,348,i6n,aGi);_.Y2=function(a,b,c){var d;d=me(fe(Ptb,1),qZm,105,0,[GFi,JFi]);return sKi(a,null,d,b,c)};var 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d,e;if(a.Fv(($jj(),xij))){d=a;if(d.g[0].r3()&&d.g[1].r3()){e=ZMi(MNi(d));RNi(d,c.i);e.f3(c.i);vyi(b,new Gyi((fDi(),eAi),c.i++));return e}}return a.d3(this,b,c)};var Dsb=Ngd(7697,Lsb,null);zuc(7698,338,j6n,aHi);_.Y2=function(a,b,c){var d,e,f,g,h;if(cf(a,137)){h=a;if(h.r3()&&!h.q3()){d=Did(''+h.A_(),'\\\\.',0)[1].length;f=$tc(h.A_()*$wnd.Math.pow(10,d));e=$tc($wnd.Math.pow(10,d));g=lLi(ZMi(ouc(f)),ZMi(ouc(e)));h.f3(c.i);g.f3(c.i);vyi(b,new Gyi((fDi(),gCi),c.i++));return g}}return a.d3(this,b,c)};var Esb=Ngd(7698,Lsb,null);zuc(7699,338,j6n,cHi);_.Y2=function(a,b,c){return bHi(a,b,c)};var Fsb=Ngd(7699,Lsb,null);zuc(7700,338,j6n,dHi);_.Y2=function(a,b,c){var d,e,f;if(a.Fv(($jj(),xij))){e=a;f=new Dyi;d=dGi((XFi(),e),f,new xJi);if(!uLi(kyi(d.g[0],d.g[1]))&&!INi(e,d)){yyi(b,(fDi(),uAi),f,d,me(fe(grb,1),f5n,135,0,[a]));++c.i;return d}}return a.d3(this,b,c)};var Gsb=Ngd(7700,Lsb,null);zuc(7701,338,j6n,eHi);_.Y2=function(a,b,c){var d,e,f,g,h,i,j,k,l,m;if(a.Fv(($jj(),xij))){l=a;e=new Nnd;h=new 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d,e;if(a.Fv(($jj(),xij))){e=a;if(nMi(e.g[0])||nMi(e.g[1])){d=GMi(e.g[0],wMi(e.g[1]));RNi(e,c.i);d.f3(c.i);vyi(b,new Gyi((fDi(),bCi),c.i++));return d}}return a.d3(this,b,c)};var Jsb=Ngd(7703,Lsb,null);zuc(7704,338,j6n,hHi);_.Y2=function(a,b,c){var d,e;if(a.Fv(($jj(),xij))){e=a;if(Vb(e.g[0],e.g[1])){d=ZMi(1);RNi(e,c.i);d.f3(c.i);vyi(b,new Gyi((fDi(),Rzi),c.i++));return d}if(e.g[0].q3()&&e.g[1].q3()&&jMi(e.g[0],e.g[1])){d=vMi(e.g[0],e.g[1]);RNi(e,c.i);d.f3(c.i);vyi(b,new Gyi((fDi(),dAi),c.i++));return d}if(sLi(e.g[0],0)){d=ZMi(0);RNi(e,c.i);d.f3(c.i);vyi(b,new Gyi((fDi(),_Ci),c.i++));return d}if(sLi(e.g[1],0)){d=(UMi(),TMi);RNi(e,c.i);MMi(d,c.i);vyi(b,new Gyi((fDi(),Szi),c.i++));return d}if(sLi(e.g[1],1)){e.g[1].f3(c.i);vyi(b,new Gyi((fDi(),Wzi),c.i++));return e.g[0]}if(sLi(e.g[1],-1)){e.g[1].f3(c.i);vyi(b,new Gyi((fDi(),Vzi),c.i++));return ALi(e.g[0])}}return a.d3(this,b,c)};var Ksb=Ngd(7704,Lsb,null);zuc(680,23,l6n);var iHi,jHi,kHi,lHi,mHi,nHi;var Tsb=Ngd(680,Ru,qHi);zuc(7661,680,l6n,sHi);_.$2=function(a,b,c,d){return rHi(a,b,d)};var Msb=Ngd(7661,Tsb,null);zuc(7662,680,l6n,uHi);_.$2=function(a,b,c,d){return tHi(a,c)};var Nsb=Ngd(7662,Tsb,null);zuc(7663,680,l6n,wHi);_.$2=function(a,b,c,d){return vHi(a,b,c,d)};var Osb=Ngd(7663,Tsb,null);zuc(7664,680,l6n,yHi);_.$2=function(a,b,c,d){return xHi(a,b,c,d)};var Psb=Ngd(7664,Tsb,null);zuc(7665,680,l6n,AHi);_.$2=function(a,b,c,d){return zHi(a,b,c,d)};var Rsb=Ngd(7665,Tsb,null);zuc(7666,1,{},BHi);_.Gi=Mqo;_.Fe=Nqo;_.Hi=Oqo;var Qsb=Mgd(7666);zuc(7667,680,l6n,DHi);_.$2=function(a,b,c,d){return CHi(a,b,c,d)};var Ssb=Ngd(7667,Tsb,null);zuc(150,23,m6n);_.Z2=function(){return this==mIi||this==kIi||this==KHi||this==tIi||this==$Hi||this==aIi||this==jIi};var EHi,FHi,GHi,HHi,IHi,JHi,KHi,LHi,MHi,NHi,OHi,PHi,QHi,RHi,SHi,THi,UHi,VHi,WHi,XHi,YHi,ZHi,$Hi,_Hi,aIi,bIi,cIi,dIi,eIi,fIi,gIi,hIi,iIi,jIi,kIi,lIi,mIi,nIi,oIi,pIi,qIi,rIi,sIi,tIi;var Ktb=Ngd(150,Ru,wIi);zuc(7029,150,m6n,xIi);_.Y2=function(a,b,c){var d,e,f,g,h,i,j;if(a.Fv(($jj(),rjj))){h=a;j=h.g[0];d=j.l3();f=j.m3();if(!!d&&!!f){e=FLi(d,h.g[1]);i=FLi(f,h.g[1]);g=cLi(ljj,e,i);RNi(h,c.i);g.f3(c.i);vyi(b,new Gyi((fDi(),CCi),c.i++));return g}if(d){g=ZMi(MNi(h));RNi(h,c.i);g.f3(c.i);vyi(b,new Gyi((fDi(),hAi),c.i++));return g}}return a.d3(this,b,c)};var ctb=Ngd(7029,Ktb,null);zuc(7038,150,m6n,yIi);_.Y2=function(a,b,c){var d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s;if(a.Fv(($jj(),xij))){r=a;g=new Nnd;r.g[1].Fv(rjj)&&wnd(g,r.g[1]);if(r.g[1].Fv(ljj)){for(k=new aOi(r.g[1]);k.g<k.i.g.length;){j=_Ni(k);j.Fv(rjj)&&(_wd(g.B,j),true)}}l=je(vub,g5n,137,g.B.length,0,1);for(f=0;f<g.B.length;f++){p=(sxd(f,g.B.length),g.B[f]).g[1];d=(sxd(f,g.B.length),g.B[f]).g[0];m=null;if(d.Fv(yjj)){m=d.g[1];d=d.g[0]}if((!m||m.q3())&&p.q3()){n=!m?1:m.A_();q=p.A_();h=q-n%q;l[f]=FLi(EMi(d,ZMi(h)),p)}}s=YNi(ljj,l);if(s){s.f3(c.i++);i=GMi(r.g[0],s);e=CLi(r.g[1],s);o=lLi(i,e);vyi(b,new 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Nnd;if(s.Fv(ljj)){for(m=new aOi(s);m.g<m.i.g.length;){l=_Ni(m);_wd(g.B,l)}}else{_wd(g.B,s)}p=$tc($wnd.Math.round(o.A_()));i=je(vub,g5n,137,g.B.length,0,1);for(f=0;f<g.B.length;f++){if((sxd(f,g.B.length),g.B[f]).q3()&&!(sxd(f,g.B.length),g.B[f]).Fv(kjj)){n=pLi($tc($wnd.Math.round((sxd(f,g.B.length),g.B[f]).A_())));e=nLi(p,n);j=0;Wtc(e,1)>0&&g.B.length==1?(j=e):Wtc(n,p)>=0&&(j=n);if(Wtc(j,0)!=0){i[f]=ELi(ZMi($wnd.Math.pow((sxd(f,g.B.length),g.B[f]).A_(),1/ouc(j))),ZMi(ouc(j)));(sxd(f,g.B.length),g.B[f]).f3(c.i);i[f].f3(c.i++);vyi(b,new Hyi((fDi(),_Bi),me(fe(grb,1),f5n,135,0,[(sxd(f,g.B.length),g.B[f]),i[f]])));continue}h=wLi((sxd(f,g.B.length),g.B[f]),ouc(p));if(Wtc(h,1)!=0){d=ZMi(ouc(h));q=ZMi((sxd(f,g.B.length),g.B[f]).A_()/ouc(h));d.f3(c.i);q.f3(c.i++);i[f]=cLi(ljj,d,q);vyi(b,new Hyi((fDi(),_Bi),me(fe(grb,1),f5n,135,0,[(sxd(f,g.B.length),g.B[f]),i[f]])));continue}}i[f]=(sxd(f,g.B.length),g.B[f])}k=FLi(YNi(ljj,i),o);if(!INi(r,k)){return k}}return a.d3(this,b,c)};var Xsb=Ngd(7041,Ktb,null);zuc(7042,150,m6n,CIi);_.Y2=function(a,b,c){var d,e,f,g,h,i;if(a.Fv(($jj(),yjj))&&a.g[0].Fv(rjj)){e=a;i=e.g[0];f=vMi(e.g[1],i.g[1]);g=yMi(e.g[1],i.g[1]);if(!(!f||f.r3()&&$wnd.Math.abs(f.A_())<C4m)&&!(!g||g.r3()&&$wnd.Math.abs(g.A_())<C4m)){d=GMi(f,i.g[1]);h=CLi(EMi(i,d),EMi(i,g));a.f3(c.i);h.f3(c.i++);vyi(b,new Hyi((fDi(),_Bi),me(fe(grb,1),f5n,135,0,[a,h])));return h}}return a.d3(this,b,c)};var Ysb=Ngd(7042,Ktb,null);zuc(7043,150,m6n,DIi);_.Y2=function(a,b,c){var d,e,f,g,h,i,j,k,l,m,n,o,p,q;if(a.Fv(($jj(),rjj))){o=a;q=o.g[0];m=o.g[1];g=new Nnd;if(q.Fv(ljj)){for(j=new aOi(q);j.g<j.i.g.length;){i=_Ni(j);_wd(g.B,i)}}else{_wd(g.B,q)}h=null;for(f=new Tnd(g);f.g<f.j.B.length;){e=Rnd(f);if(e.Fv(yjj)){p=e.g[0];k=vMi(gMi(e),m);l=yMi(gMi(e),m);if(!(!k||k.r3()&&$wnd.Math.abs(k.A_())<C4m)&&!(!l||l.r3()&&$wnd.Math.abs(l.A_())<C4m)){d=ELi(p,GMi(m,k));n=EMi(p,l);e.f3(c.i);d.f3(c.i);n.f3(c.i++);h=CLi(h,cLi(ljj,d,n));vyi(b,new 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mtb=Ngd(7057,Ktb,null);zuc(7031,150,m6n,WIi);_.Y2=function(a,b,c){var d,e,f;if(a.Fv(($jj(),yjj))){e=a.g[0];f=a.g[1];if(f.Fv(fjj)&&Vb(f.g[0],e)){vyi(b,new Gyi((fDi(),tAi),c.i++));d=f.g[1];d.f3(c.i);return d}}return a.d3(this,b,c)};var ytb=Ngd(7031,Ktb,null);zuc(7058,150,m6n,XIi);_.Y2=function(a,b,c){var d,e;if(a.Fv(($jj(),yjj))){e=a;if(e.g[1].Fv(kjj)){d=kLi(EMi(e.g[0],tMi(e.g[1])));RNi(e,c.i);d.f3(c.i);vyi(b,new Gyi((fDi(),kBi),c.i++));return d}if(e.g[0].r3()&&e.g[1].q3()){d=ZMi($wnd.Math.pow(e.g[0].A_(),e.g[1].A_()));RNi(e,c.i);d.f3(c.i);vyi(b,new Gyi((fDi(),gAi),c.i++));return d}}return a.d3(this,b,c)};var otb=Ngd(7058,Ktb,null);zuc(7059,150,m6n,YIi);_.Y2=function(a,b,c){var d,e;if(a.Fv(($jj(),rjj))){e=a;if(mMi(e.g[1])&&e.g[0].r3()&&e.g[0].Fv(kjj)){d=(UMi(),TMi);RNi(e,c.i);MMi(d,c.i);vyi(b,new Gyi((fDi(),mAi),c.i++));return d}if(sLi(e.g[0],1)){d=ZMi(1);RNi(e,c.i);d.f3(c.i);vyi(b,new Gyi((fDi(),oCi),c.i++));return d}if(sLi(e.g[1],1)){d=e.g[0];RNi(e,c.i);d.f3(c.i);vyi(b,new 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