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var BI_RM="0123456789abcdefghijklmnopqrstuvwxyz",BI_RC=[],rr,vv;rr="0".charCodeAt(0);for(vv=0;vv<=9;++vv)BI_RC[rr++]=vv;rr="a".charCodeAt(0);for(vv=10;vv<36;++vv)BI_RC[rr++]=vv;rr="A".charCodeAt(0);for(vv=10;vv<36;++vv)BI_RC[rr++]=vv;function int2char(c){return BI_RM.charAt(c)}function intAt(c,k){c=BI_RC[c.charCodeAt(k)];return c==null?-1:c}function bnpCopyTo(c){for(var k=this.t-1;k>=0;--k)c[k]=this[k];c.t=this.t;c.s=this.s}
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function bnpFromString(c,k){if(k==16)k=4;else if(k==8)k=3;else if(k==256)k=8;else if(k==2)k=1;else if(k==32)k=5;else if(k==4)k=2;else{this.fromRadix(c,k);return}this.s=this.t=0;for(var n=c.length,u=false,I=0;--n>=0;){var D=k==8?c[n]&255:intAt(c,n);if(D<0){if(c.charAt(n)=="-")u=true}else{u=false;if(I==0)this[this.t++]=D;else if(I+k>this.DB){this[this.t-1]|=(D&(1<<this.DB-I)-1)<<I;this[this.t++]=D>>this.DB-I}else this[this.t-1]|=D<<I;I+=k;if(I>=this.DB)I-=this.DB}}if(k==8&&(c[0]&128)!=0){this.s=-1;
if(I>0)this[this.t-1]|=(1<<this.DB-I)-1<<I}this.clamp();u&&BigInteger.ZERO.subTo(this,this)}function bnpClamp(){for(var c=this.s&this.DM;this.t>0&&this[this.t-1]==c;)--this.t}
function bnToString(c){if(this.s<0)return"-"+this.negate().toString(c);if(c==16)c=4;else if(c==8)c=3;else if(c==2)c=1;else if(c==32)c=5;else if(c==4)c=2;else return this.toRadix(c);var k=(1<<c)-1,n,u=false,I="",D=this.t,T=this.DB-D*this.DB%c;if(D-- >0){if(T<this.DB&&(n=this[D]>>T)>0){u=true;I=int2char(n)}for(;D>=0;){if(T<c){n=(this[D]&(1<<T)-1)<<c-T;n|=this[--D]>>(T+=this.DB-c)}else{n=this[D]>>(T-=c)&k;if(T<=0){T+=this.DB;--D}}if(n>0)u=true;if(u)I+=int2char(n)}}return u?I:"0"}
function bnNegate(){var c=nbi();BigInteger.ZERO.subTo(this,c);return c}function bnAbs(){return this.s<0?this.negate():this}function bnCompareTo(c){var k=this.s-c.s;if(k!=0)return k;var n=this.t;k=n-c.t;if(k!=0)return k;for(;--n>=0;)if((k=this[n]-c[n])!=0)return k;return 0}function nbits(c){var k=1,n;if((n=c>>>16)!=0){c=n;k+=16}if((n=c>>8)!=0){c=n;k+=8}if((n=c>>4)!=0){c=n;k+=4}if((n=c>>2)!=0){c=n;k+=2}if(c>>1!=0)k+=1;return k}
function bnBitLength(){if(this.t<=0)return 0;return this.DB*(this.t-1)+nbits(this[this.t-1]^this.s&this.DM)}function bnpDLShiftTo(c,k){var n;for(n=this.t-1;n>=0;--n)k[n+c]=this[n];for(n=c-1;n>=0;--n)k[n]=0;k.t=this.t+c;k.s=this.s}function bnpDRShiftTo(c,k){for(var n=c;n<this.t;++n)k[n-c]=this[n];k.t=Math.max(this.t-c,0);k.s=this.s}
function bnpLShiftTo(c,k){var n=c%this.DB,u=this.DB-n,I=(1<<u)-1;c=Math.floor(c/this.DB);var D=this.s<<n&this.DM,T;for(T=this.t-1;T>=0;--T){k[T+c+1]=this[T]>>u|D;D=(this[T]&I)<<n}for(T=c-1;T>=0;--T)k[T]=0;k[c]=D;k.t=this.t+c+1;k.s=this.s;k.clamp()}
function bnpRShiftTo(c,k){k.s=this.s;var n=Math.floor(c/this.DB);if(n>=this.t)k.t=0;else{c=c%this.DB;var u=this.DB-c,I=(1<<c)-1;k[0]=this[n]>>c;for(var D=n+1;D<this.t;++D){k[D-n-1]|=(this[D]&I)<<u;k[D-n]=this[D]>>c}if(c>0)k[this.t-n-1]|=(this.s&I)<<u;k.t=this.t-n;k.clamp()}}
function bnpSubTo(c,k){for(var n=0,u=0,I=Math.min(c.t,this.t);n<I;){u+=this[n]-c[n];k[n++]=u&this.DM;u>>=this.DB}if(c.t<this.t){for(u-=c.s;n<this.t;){u+=this[n];k[n++]=u&this.DM;u>>=this.DB}u+=this.s}else{for(u+=this.s;n<c.t;){u-=c[n];k[n++]=u&this.DM;u>>=this.DB}u-=c.s}k.s=u<0?-1:0;if(u<-1)k[n++]=this.DV+u;else if(u>0)k[n++]=u;k.t=n;k.clamp()}
function bnpMultiplyTo(c,k){var n=this.abs(),u=c.abs(),I=n.t;for(k.t=I+u.t;--I>=0;)k[I]=0;for(I=0;I<u.t;++I)k[I+n.t]=n.am(0,u[I],k,I,0,n.t);k.s=0;k.clamp();this.s!=c.s&&BigInteger.ZERO.subTo(k,k)}function bnpSquareTo(c){for(var k=this.abs(),n=c.t=2*k.t;--n>=0;)c[n]=0;for(n=0;n<k.t-1;++n){var u=k.am(n,k[n],c,2*n,0,1);if((c[n+k.t]+=k.am(n+1,2*k[n],c,2*n+1,u,k.t-n-1))>=k.DV){c[n+k.t]-=k.DV;c[n+k.t+1]=1}}if(c.t>0)c[c.t-1]+=k.am(n,k[n],c,2*n,0,1);c.s=0;c.clamp()}
function bnpDivRemTo(c,k,n){var u=c.abs();if(!(u.t<=0)){var I=this.abs();if(I.t<u.t){k!=null&&k.fromInt(0);n!=null&&this.copyTo(n)}else{if(n==null)n=nbi();var D=nbi(),T=this.s;c=c.s;var x=this.DB-nbits(u[u.t-1]);if(x>0){u.lShiftTo(x,D);I.lShiftTo(x,n)}else{u.copyTo(D);I.copyTo(n)}u=D.t;I=D[u-1];if(I!=0){var G=I*(1<<this.F1)+(u>1?D[u-2]>>this.F2:0),R=this.FV/G;G=(1<<this.F1)/G;var U=1<<this.F2,X=n.t,K=X-u,V=k==null?nbi():k;D.dlShiftTo(K,V);if(n.compareTo(V)>=0){n[n.t++]=1;n.subTo(V,n)}BigInteger.ONE.dlShiftTo(u,
V);for(V.subTo(D,D);D.t<u;)D[D.t++]=0;for(;--K>=0;){var P=n[--X]==I?this.DM:Math.floor(n[X]*R+(n[X-1]+U)*G);if((n[X]+=D.am(0,P,n,K,0,u))<P){D.dlShiftTo(K,V);for(n.subTo(V,n);n[X]<--P;)n.subTo(V,n)}}if(k!=null){n.drShiftTo(u,k);T!=c&&BigInteger.ZERO.subTo(k,k)}n.t=u;n.clamp();x>0&&n.rShiftTo(x,n);T<0&&BigInteger.ZERO.subTo(n,n)}}}}function bnMod(c){var k=nbi();this.abs().divRemTo(c,null,k);this.s<0&&k.compareTo(BigInteger.ZERO)>0&&c.subTo(k,k);return k}function Classic(c){this.m=c}
function cConvert(c){return c.s<0||c.compareTo(this.m)>=0?c.mod(this.m):c}function cRevert(c){return c}function cReduce(c){c.divRemTo(this.m,null,c)}function cMulTo(c,k,n){c.multiplyTo(k,n);this.reduce(n)}function cSqrTo(c,k){c.squareTo(k);this.reduce(k)}a=Classic.prototype;a.convert=cConvert;a.revert=cRevert;a.reduce=cReduce;a.mulTo=cMulTo;a.sqrTo=cSqrTo;
function bnpInvDigit(){if(this.t<1)return 0;var c=this[0];if((c&1)==0)return 0;var k=c&3;k=k*(2-(c&15)*k)&15;k=k*(2-(c&255)*k)&255;k=k*(2-((c&65535)*k&65535))&65535;k=k*(2-c*k%this.DV)%this.DV;return k>0?this.DV-k:-k}function Montgomery(c){this.m=c;this.mp=c.invDigit();this.mpl=this.mp&32767;this.mph=this.mp>>15;this.um=(1<<c.DB-15)-1;this.mt2=2*c.t}
function montConvert(c){var k=nbi();c.abs().dlShiftTo(this.m.t,k);k.divRemTo(this.m,null,k);c.s<0&&k.compareTo(BigInteger.ZERO)>0&&this.m.subTo(k,k);return k}function montRevert(c){var k=nbi();c.copyTo(k);this.reduce(k);return k}
function montReduce(c){for(;c.t<=this.mt2;)c[c.t++]=0;for(var k=0;k<this.m.t;++k){var n=c[k]&32767,u=n*this.mpl+((n*this.mph+(c[k]>>15)*this.mpl&this.um)<<15)&c.DM;n=k+this.m.t;for(c[n]+=this.m.am(0,u,c,k,0,this.m.t);c[n]>=c.DV;){c[n]-=c.DV;c[++n]++}}c.clamp();c.drShiftTo(this.m.t,c);c.compareTo(this.m)>=0&&c.subTo(this.m,c)}function montSqrTo(c,k){c.squareTo(k);this.reduce(k)}function montMulTo(c,k,n){c.multiplyTo(k,n);this.reduce(n)}a=Montgomery.prototype;a.convert=montConvert;a.revert=montRevert;
a.reduce=montReduce;a.mulTo=montMulTo;a.sqrTo=montSqrTo;function bnpIsEven(){return(this.t>0?this[0]&1:this.s)==0}function bnpExp(c,k){if(c>4294967295||c<1)return BigInteger.ONE;var n=nbi(),u=nbi(),I=k.convert(this),D=nbits(c)-1;for(I.copyTo(n);--D>=0;){k.sqrTo(n,u);if((c&1<<D)>0)k.mulTo(u,I,n);else{var T=n;n=u;u=T}}return k.revert(n)}function bnModPowInt(c,k){k=c<256||k.isEven()?new Classic(k):new Montgomery(k);return this.exp(c,k)}a=BigInteger.prototype;a.copyTo=bnpCopyTo;a.fromInt=bnpFromInt;
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