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f=1;for(c=l(t,u,t.length,e),u=0;u<o;u++)f*=e;this.imuln(f),this.words[0]+c<67108864?this.words[0]+=c:this._iaddn(c)}},a.prototype.copy=function(t){t.words=new Array(this.length);for(var e=0;e<this.length;e++)t.words[e]=this.words[e];t.length=this.length,t.negative=this.negative,t.red=this.red},a.prototype.clone=function(){var t=new a(null);return this.copy(t),t},a.prototype._expand=function(t){for(;this.length<t;)this.words[this.length++]=0;return this},a.prototype.strip=function(){for(;this.length>1&&0===this.words[this.length-1];)this.length--;return this._normSign()},a.prototype._normSign=function(){return 1===this.length&&0===this.words[0]&&(this.negative=0),this},a.prototype.inspect=function(){return(this.red?"<BN-R: ":"<BN: ")+this.toString(16)+">"};var 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u=l>>>26,f=67108863&l,h=Math.min(c,e.length-1),p=Math.max(0,c-t.length+1);p<=h;p++){var d=c-p|0;u+=(o=(i=0|t.words[d])*(a=0|e.words[p])+f)/67108864|0,f=67108863&o}r.words[c]=0|f,l=0|u}return 0!==l?r.words[c]=0|l:r.length--,r.strip()}a.prototype.toString=function(t,e){var r;if(e=0|e||1,16===(t=t||10)||"hex"===t){r="";for(var i=0,a=0,o=0;o<this.length;o++){var s=this.words[o],l=(16777215&(s<<i|a)).toString(16);r=0!==(a=s>>>24-i&16777215)||o!==this.length-1?c[6-l.length]+l+r:l+r,(i+=2)>=26&&(i-=26,o--)}for(0!==a&&(r=a.toString(16)+r);r.length%e!=0;)r="0"+r;return 0!==this.negative&&(r="-"+r),r}if(t===(0|t)&&t>=2&&t<=36){var h=u[t],p=f[t];r="";var d=this.clone();for(d.negative=0;!d.isZero();){var g=d.modn(p).toString(t);r=(d=d.idivn(p)).isZero()?g+r:c[h-g.length]+g+r}for(this.isZero()&&(r="0"+r);r.length%e!=0;)r="0"+r;return 0!==this.negative&&(r="-"+r),r}n(!1,"Base should be between 2 and 36")},a.prototype.toNumber=function(){var t=this.words[0];return 2===this.length?t+=67108864*this.words[1]:3===this.length&&1===this.words[2]?t+=4503599627370496+67108864*this.words[1]:this.length>2&&n(!1,"Number can only safely store up to 53 bits"),0!==this.negative?-t:t},a.prototype.toJSON=function(){return this.toString(16)},a.prototype.toBuffer=function(t,e){return n(void 0!==o),this.toArrayLike(o,t,e)},a.prototype.toArray=function(t,e){return this.toArrayLike(Array,t,e)},a.prototype.toArrayLike=function(t,e,r){var i=this.byteLength(),a=r||Math.max(1,i);n(i<=a,"byte array longer than desired length"),n(a>0,"Requested array length <= 0"),this.strip();var o,s,l="le"===e,c=new t(a),u=this.clone();if(l){for(s=0;!u.isZero();s++)o=u.andln(255),u.iushrn(8),c[s]=o;for(;s<a;s++)c[s]=0}else{for(s=0;s<a-i;s++)c[s]=0;for(s=0;!u.isZero();s++)o=u.andln(255),u.iushrn(8),c[a-s-1]=o}return c},Math.clz32?a.prototype._countBits=function(t){return 32-Math.clz32(t)}:a.prototype._countBits=function(t){var e=t,r=0;return 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this.isZero()||(this.negative^=1),this},a.prototype.iuor=function(t){for(;this.length<t.length;)this.words[this.length++]=0;for(var e=0;e<t.length;e++)this.words[e]=this.words[e]|t.words[e];return this.strip()},a.prototype.ior=function(t){return n(0==(this.negative|t.negative)),this.iuor(t)},a.prototype.or=function(t){return this.length>t.length?this.clone().ior(t):t.clone().ior(this)},a.prototype.uor=function(t){return this.length>t.length?this.clone().iuor(t):t.clone().iuor(this)},a.prototype.iuand=function(t){var e;e=this.length>t.length?t:this;for(var r=0;r<e.length;r++)this.words[r]=this.words[r]&t.words[r];return this.length=e.length,this.strip()},a.prototype.iand=function(t){return n(0==(this.negative|t.negative)),this.iuand(t)},a.prototype.and=function(t){return this.length>t.length?this.clone().iand(t):t.clone().iand(this)},a.prototype.uand=function(t){return this.length>t.length?this.clone().iuand(t):t.clone().iuand(this)},a.prototype.iuxor=function(t){var e,r;this.length>t.length?(e=this,r=t):(e=t,r=this);for(var n=0;n<r.length;n++)this.words[n]=e.words[n]^r.words[n];if(this!==e)for(;n<e.length;n++)this.words[n]=e.words[n];return this.length=e.length,this.strip()},a.prototype.ixor=function(t){return n(0==(this.negative|t.negative)),this.iuxor(t)},a.prototype.xor=function(t){return this.length>t.length?this.clone().ixor(t):t.clone().ixor(this)},a.prototype.uxor=function(t){return this.length>t.length?this.clone().iuxor(t):t.clone().iuxor(this)},a.prototype.inotn=function(t){n("number"==typeof t&&t>=0);var e=0|Math.ceil(t/26),r=t%26;this._expand(e),r>0&&e--;for(var i=0;i<e;i++)this.words[i]=67108863&~this.words[i];return r>0&&(this.words[i]=~this.words[i]&67108863>>26-r),this.strip()},a.prototype.notn=function(t){return this.clone().inotn(t)},a.prototype.setn=function(t,e){n("number"==typeof t&&t>=0);var r=t/26|0,i=t%26;return this._expand(r+1),this.words[r]=e?this.words[r]|1<<i:this.words[r]&~(1<<i),this.strip()},a.prototype.iadd=function(t){var e,r,n;if(0!==this.negative&&0===t.negative)return this.negative=0,e=this.isub(t),this.negative^=1,this._normSign();if(0===this.negative&&0!==t.negative)return t.negative=0,e=this.isub(t),t.negative=1,e._normSign();this.length>t.length?(r=this,n=t):(r=t,n=this);for(var i=0,a=0;a<n.length;a++)e=(0|r.words[a])+(0|n.words[a])+i,this.words[a]=67108863&e,i=e>>>26;for(;0!==i&&a<r.length;a++)e=(0|r.words[a])+i,this.words[a]=67108863&e,i=e>>>26;if(this.length=r.length,0!==i)this.words[this.length]=i,this.length++;else if(r!==this)for(;a<r.length;a++)this.words[a]=r.words[a];return this},a.prototype.add=function(t){var e;return 0!==t.negative&&0===this.negative?(t.negative=0,e=this.sub(t),t.negative^=1,e):0===t.negative&&0!==this.negative?(this.negative=0,e=t.sub(this),this.negative=1,e):this.length>t.length?this.clone().iadd(t):t.clone().iadd(this)},a.prototype.isub=function(t){if(0!==t.negative){t.negative=0;var e=this.iadd(t);return t.negative=1,e._normSign()}if(0!==this.negative)return this.negative=0,this.iadd(t),this.negative=1,this._normSign();var r,n,i=this.cmp(t);if(0===i)return this.negative=0,this.length=1,this.words[0]=0,this;i>0?(r=this,n=t):(r=t,n=this);for(var a=0,o=0;o<n.length;o++)a=(e=(0|r.words[o])-(0|n.words[o])+a)>>26,this.words[o]=67108863&e;for(;0!==a&&o<r.length;o++)a=(e=(0|r.words[o])+a)>>26,this.words[o]=67108863&e;if(0===a&&o<r.length&&r!==this)for(;o<r.length;o++)this.words[o]=r.words[o];return this.length=Math.max(this.length,o),r!==this&&(this.negative=1),this.strip()},a.prototype.sub=function(t){return this.clone().isub(t)};var p=function(t,e,r){var 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xt=(c+(n=n+Math.imul(f,J)|0)|0)+((8191&(i=(i=i+Math.imul(f,K)|0)+Math.imul(h,J)|0))<<13)|0;c=((a=a+Math.imul(h,K)|0)+(i>>>13)|0)+(xt>>>26)|0,xt&=67108863,n=Math.imul(T,U),i=(i=Math.imul(T,V))+Math.imul(k,U)|0,a=Math.imul(k,V),n=n+Math.imul(b,H)|0,i=(i=i+Math.imul(b,G)|0)+Math.imul(_,H)|0,a=a+Math.imul(_,G)|0,n=n+Math.imul(v,W)|0,i=(i=i+Math.imul(v,X)|0)+Math.imul(y,W)|0,a=a+Math.imul(y,X)|0,n=n+Math.imul(d,J)|0,i=(i=i+Math.imul(d,K)|0)+Math.imul(g,J)|0,a=a+Math.imul(g,K)|0;var bt=(c+(n=n+Math.imul(f,$)|0)|0)+((8191&(i=(i=i+Math.imul(f,tt)|0)+Math.imul(h,$)|0))<<13)|0;c=((a=a+Math.imul(h,tt)|0)+(i>>>13)|0)+(bt>>>26)|0,bt&=67108863,n=Math.imul(M,U),i=(i=Math.imul(M,V))+Math.imul(S,U)|0,a=Math.imul(S,V),n=n+Math.imul(T,H)|0,i=(i=i+Math.imul(T,G)|0)+Math.imul(k,H)|0,a=a+Math.imul(k,G)|0,n=n+Math.imul(b,W)|0,i=(i=i+Math.imul(b,X)|0)+Math.imul(_,W)|0,a=a+Math.imul(_,X)|0,n=n+Math.imul(v,J)|0,i=(i=i+Math.imul(v,K)|0)+Math.imul(y,J)|0,a=a+Math.imul(y,K)|0,n=n+Math.imul(d,$)|0,i=(i=i+Math.imul(d,tt)|0)+Math.imul(g,$)|0,a=a+Math.imul(g,tt)|0;var _t=(c+(n=n+Math.imul(f,rt)|0)|0)+((8191&(i=(i=i+Math.imul(f,nt)|0)+Math.imul(h,rt)|0))<<13)|0;c=((a=a+Math.imul(h,nt)|0)+(i>>>13)|0)+(_t>>>26)|0,_t&=67108863,n=Math.imul(L,U),i=(i=Math.imul(L,V))+Math.imul(C,U)|0,a=Math.imul(C,V),n=n+Math.imul(M,H)|0,i=(i=i+Math.imul(M,G)|0)+Math.imul(S,H)|0,a=a+Math.imul(S,G)|0,n=n+Math.imul(T,W)|0,i=(i=i+Math.imul(T,X)|0)+Math.imul(k,W)|0,a=a+Math.imul(k,X)|0,n=n+Math.imul(b,J)|0,i=(i=i+Math.imul(b,K)|0)+Math.imul(_,J)|0,a=a+Math.imul(_,K)|0,n=n+Math.imul(v,$)|0,i=(i=i+Math.imul(v,tt)|0)+Math.imul(y,$)|0,a=a+Math.imul(y,tt)|0,n=n+Math.imul(d,rt)|0,i=(i=i+Math.imul(d,nt)|0)+Math.imul(g,rt)|0,a=a+Math.imul(g,nt)|0;var wt=(c+(n=n+Math.imul(f,at)|0)|0)+((8191&(i=(i=i+Math.imul(f,ot)|0)+Math.imul(h,at)|0))<<13)|0;c=((a=a+Math.imul(h,ot)|0)+(i>>>13)|0)+(wt>>>26)|0,wt&=67108863,n=Math.imul(I,U),i=(i=Math.imul(I,V))+Math.imul(O,U)|0,a=Math.imul(O,V),n=n+Math.imul(L,H)|0,i=(i=i+Math.imul(L,G)|0)+Math.imul(C,H)|0,a=a+Math.imul(C,G)|0,n=n+Math.imul(M,W)|0,i=(i=i+Math.imul(M,X)|0)+Math.imul(S,W)|0,a=a+Math.imul(S,X)|0,n=n+Math.imul(T,J)|0,i=(i=i+Math.imul(T,K)|0)+Math.imul(k,J)|0,a=a+Math.imul(k,K)|0,n=n+Math.imul(b,$)|0,i=(i=i+Math.imul(b,tt)|0)+Math.imul(_,$)|0,a=a+Math.imul(_,tt)|0,n=n+Math.imul(v,rt)|0,i=(i=i+Math.imul(v,nt)|0)+Math.imul(y,rt)|0,a=a+Math.imul(y,nt)|0,n=n+Math.imul(d,at)|0,i=(i=i+Math.imul(d,ot)|0)+Math.imul(g,at)|0,a=a+Math.imul(g,ot)|0;var Tt=(c+(n=n+Math.imul(f,lt)|0)|0)+((8191&(i=(i=i+Math.imul(f,ct)|0)+Math.imul(h,lt)|0))<<13)|0;c=((a=a+Math.imul(h,ct)|0)+(i>>>13)|0)+(Tt>>>26)|0,Tt&=67108863,n=Math.imul(D,U),i=(i=Math.imul(D,V))+Math.imul(R,U)|0,a=Math.imul(R,V),n=n+Math.imul(I,H)|0,i=(i=i+Math.imul(I,G)|0)+Math.imul(O,H)|0,a=a+Math.imul(O,G)|0,n=n+Math.imul(L,W)|0,i=(i=i+Math.imul(L,X)|0)+Math.imul(C,W)|0,a=a+Math.imul(C,X)|0,n=n+Math.imul(M,J)|0,i=(i=i+Math.imul(M,K)|0)+Math.imul(S,J)|0,a=a+Math.imul(S,K)|0,n=n+Math.imul(T,$)|0,i=(i=i+Math.imul(T,tt)|0)+Math.imul(k,$)|0,a=a+Math.imul(k,tt)|0,n=n+Math.imul(b,rt)|0,i=(i=i+Math.imul(b,nt)|0)+Math.imul(_,rt)|0,a=a+Math.imul(_,nt)|0,n=n+Math.imul(v,at)|0,i=(i=i+Math.imul(v,ot)|0)+Math.imul(y,at)|0,a=a+Math.imul(y,ot)|0,n=n+Math.imul(d,lt)|0,i=(i=i+Math.imul(d,ct)|0)+Math.imul(g,lt)|0,a=a+Math.imul(g,ct)|0;var kt=(c+(n=n+Math.imul(f,ft)|0)|0)+((8191&(i=(i=i+Math.imul(f,ht)|0)+Math.imul(h,ft)|0))<<13)|0;c=((a=a+Math.imul(h,ht)|0)+(i>>>13)|0)+(kt>>>26)|0,kt&=67108863,n=Math.imul(B,U),i=(i=Math.imul(B,V))+Math.imul(N,U)|0,a=Math.imul(N,V),n=n+Math.imul(D,H)|0,i=(i=i+Math.imul(D,G)|0)+Math.imul(R,H)|0,a=a+Math.imul(R,G)|0,n=n+Math.imul(I,W)|0,i=(i=i+Math.imul(I,X)|0)+Math.imul(O,W)|0,a=a+Math.imul(O,X)|0,n=n+Math.imul(L,J)|0,i=(i=i+Math.imul(L,K)|0)+Math.imul(C,J)|0,a=a+Math.imul(C,K)|0,n=n+Math.imul(M,$)|0,i=(i=i+Math.imul(M,tt)|0)+Math.imul(S,$)|0,a=a+Math.imul(S,tt)|0,n=n+Math.imul(T,rt)|0,i=(i=i+Math.imul(T,nt)|0)+Math.imul(k,rt)|0,a=a+Math.imul(k,nt)|0,n=n+Math.imul(b,at)|0,i=(i=i+Math.imul(b,ot)|0)+Math.imul(_,at)|0,a=a+Math.imul(_,ot)|0,n=n+Math.imul(v,lt)|0,i=(i=i+Math.imul(v,ct)|0)+Math.imul(y,lt)|0,a=a+Math.imul(y,ct)|0,n=n+Math.imul(d,ft)|0,i=(i=i+Math.imul(d,ht)|0)+Math.imul(g,ft)|0,a=a+Math.imul(g,ht)|0;var At=(c+(n=n+Math.imul(f,dt)|0)|0)+((8191&(i=(i=i+Math.imul(f,gt)|0)+Math.imul(h,dt)|0))<<13)|0;c=((a=a+Math.imul(h,gt)|0)+(i>>>13)|0)+(At>>>26)|0,At&=67108863,n=Math.imul(B,H),i=(i=Math.imul(B,G))+Math.imul(N,H)|0,a=Math.imul(N,G),n=n+Math.imul(D,W)|0,i=(i=i+Math.imul(D,X)|0)+Math.imul(R,W)|0,a=a+Math.imul(R,X)|0,n=n+Math.imul(I,J)|0,i=(i=i+Math.imul(I,K)|0)+Math.imul(O,J)|0,a=a+Math.imul(O,K)|0,n=n+Math.imul(L,$)|0,i=(i=i+Math.imul(L,tt)|0)+Math.imul(C,$)|0,a=a+Math.imul(C,tt)|0,n=n+Math.imul(M,rt)|0,i=(i=i+Math.imul(M,nt)|0)+Math.imul(S,rt)|0,a=a+Math.imul(S,nt)|0,n=n+Math.imul(T,at)|0,i=(i=i+Math.imul(T,ot)|0)+Math.imul(k,at)|0,a=a+Math.imul(k,ot)|0,n=n+Math.imul(b,lt)|0,i=(i=i+Math.imul(b,ct)|0)+Math.imul(_,lt)|0,a=a+Math.imul(_,ct)|0,n=n+Math.imul(v,ft)|0,i=(i=i+Math.imul(v,ht)|0)+Math.imul(y,ft)|0,a=a+Math.imul(y,ht)|0;var Mt=(c+(n=n+Math.imul(d,dt)|0)|0)+((8191&(i=(i=i+Math.imul(d,gt)|0)+Math.imul(g,dt)|0))<<13)|0;c=((a=a+Math.imul(g,gt)|0)+(i>>>13)|0)+(Mt>>>26)|0,Mt&=67108863,n=Math.imul(B,W),i=(i=Math.imul(B,X))+Math.imul(N,W)|0,a=Math.imul(N,X),n=n+Math.imul(D,J)|0,i=(i=i+Math.imul(D,K)|0)+Math.imul(R,J)|0,a=a+Math.imul(R,K)|0,n=n+Math.imul(I,$)|0,i=(i=i+Math.imul(I,tt)|0)+Math.imul(O,$)|0,a=a+Math.imul(O,tt)|0,n=n+Math.imul(L,rt)|0,i=(i=i+Math.imul(L,nt)|0)+Math.imul(C,rt)|0,a=a+Math.imul(C,nt)|0,n=n+Math.imul(M,at)|0,i=(i=i+Math.imul(M,ot)|0)+Math.imul(S,at)|0,a=a+Math.imul(S,ot)|0,n=n+Math.imul(T,lt)|0,i=(i=i+Math.imul(T,ct)|0)+Math.imul(k,lt)|0,a=a+Math.imul(k,ct)|0,n=n+Math.imul(b,ft)|0,i=(i=i+Math.imul(b,ht)|0)+Math.imul(_,ft)|0,a=a+Math.imul(_,ht)|0;var St=(c+(n=n+Math.imul(v,dt)|0)|0)+((8191&(i=(i=i+Math.imul(v,gt)|0)+Math.imul(y,dt)|0))<<13)|0;c=((a=a+Math.imul(y,gt)|0)+(i>>>13)|0)+(St>>>26)|0,St&=67108863,n=Math.imul(B,J),i=(i=Math.imul(B,K))+Math.imul(N,J)|0,a=Math.imul(N,K),n=n+Math.imul(D,$)|0,i=(i=i+Math.imul(D,tt)|0)+Math.imul(R,$)|0,a=a+Math.imul(R,tt)|0,n=n+Math.imul(I,rt)|0,i=(i=i+Math.imul(I,nt)|0)+Math.imul(O,rt)|0,a=a+Math.imul(O,nt)|0,n=n+Math.imul(L,at)|0,i=(i=i+Math.imul(L,ot)|0)+Math.imul(C,at)|0,a=a+Math.imul(C,ot)|0,n=n+Math.imul(M,lt)|0,i=(i=i+Math.imul(M,ct)|0)+Math.imul(S,lt)|0,a=a+Math.imul(S,ct)|0,n=n+Math.imul(T,ft)|0,i=(i=i+Math.imul(T,ht)|0)+Math.imul(k,ft)|0,a=a+Math.imul(k,ht)|0;var Et=(c+(n=n+Math.imul(b,dt)|0)|0)+((8191&(i=(i=i+Math.imul(b,gt)|0)+Math.imul(_,dt)|0))<<13)|0;c=((a=a+Math.imul(_,gt)|0)+(i>>>13)|0)+(Et>>>26)|0,Et&=67108863,n=Math.imul(B,$),i=(i=Math.imul(B,tt))+Math.imul(N,$)|0,a=Math.imul(N,tt),n=n+Math.imul(D,rt)|0,i=(i=i+Math.imul(D,nt)|0)+Math.imul(R,rt)|0,a=a+Math.imul(R,nt)|0,n=n+Math.imul(I,at)|0,i=(i=i+Math.imul(I,ot)|0)+Math.imul(O,at)|0,a=a+Math.imul(O,ot)|0,n=n+Math.imul(L,lt)|0,i=(i=i+Math.imul(L,ct)|0)+Math.imul(C,lt)|0,a=a+Math.imul(C,ct)|0,n=n+Math.imul(M,ft)|0,i=(i=i+Math.imul(M,ht)|0)+Math.imul(S,ft)|0,a=a+Math.imul(S,ht)|0;var Lt=(c+(n=n+Math.imul(T,dt)|0)|0)+((8191&(i=(i=i+Math.imul(T,gt)|0)+Math.imul(k,dt)|0))<<13)|0;c=((a=a+Math.imul(k,gt)|0)+(i>>>13)|0)+(Lt>>>26)|0,Lt&=67108863,n=Math.imul(B,rt),i=(i=Math.imul(B,nt))+Math.imul(N,rt)|0,a=Math.imul(N,nt),n=n+Math.imul(D,at)|0,i=(i=i+Math.imul(D,ot)|0)+Math.imul(R,at)|0,a=a+Math.imul(R,ot)|0,n=n+Math.imul(I,lt)|0,i=(i=i+Math.imul(I,ct)|0)+Math.imul(O,lt)|0,a=a+Math.imul(O,ct)|0,n=n+Math.imul(L,ft)|0,i=(i=i+Math.imul(L,ht)|0)+Math.imul(C,ft)|0,a=a+Math.imul(C,ht)|0;var Ct=(c+(n=n+Math.imul(M,dt)|0)|0)+((8191&(i=(i=i+Math.imul(M,gt)|0)+Math.imul(S,dt)|0))<<13)|0;c=((a=a+Math.imul(S,gt)|0)+(i>>>13)|0)+(Ct>>>26)|0,Ct&=67108863,n=Math.imul(B,at),i=(i=Math.imul(B,ot))+Math.imul(N,at)|0,a=Math.imul(N,ot),n=n+Math.imul(D,lt)|0,i=(i=i+Math.imul(D,ct)|0)+Math.imul(R,lt)|0,a=a+Math.imul(R,ct)|0,n=n+Math.imul(I,ft)|0,i=(i=i+Math.imul(I,ht)|0)+Math.imul(O,ft)|0,a=a+Math.imul(O,ht)|0;var Pt=(c+(n=n+Math.imul(L,dt)|0)|0)+((8191&(i=(i=i+Math.imul(L,gt)|0)+Math.imul(C,dt)|0))<<13)|0;c=((a=a+Math.imul(C,gt)|0)+(i>>>13)|0)+(Pt>>>26)|0,Pt&=67108863,n=Math.imul(B,lt),i=(i=Math.imul(B,ct))+Math.imul(N,lt)|0,a=Math.imul(N,ct),n=n+Math.imul(D,ft)|0,i=(i=i+Math.imul(D,ht)|0)+Math.imul(R,ft)|0,a=a+Math.imul(R,ht)|0;var It=(c+(n=n+Math.imul(I,dt)|0)|0)+((8191&(i=(i=i+Math.imul(I,gt)|0)+Math.imul(O,dt)|0))<<13)|0;c=((a=a+Math.imul(O,gt)|0)+(i>>>13)|0)+(It>>>26)|0,It&=67108863,n=Math.imul(B,ft),i=(i=Math.imul(B,ht))+Math.imul(N,ft)|0,a=Math.imul(N,ht);var Ot=(c+(n=n+Math.imul(D,dt)|0)|0)+((8191&(i=(i=i+Math.imul(D,gt)|0)+Math.imul(R,dt)|0))<<13)|0;c=((a=a+Math.imul(R,gt)|0)+(i>>>13)|0)+(Ot>>>26)|0,Ot&=67108863;var zt=(c+(n=Math.imul(B,dt))|0)+((8191&(i=(i=Math.imul(B,gt))+Math.imul(N,dt)|0))<<13)|0;return c=((a=Math.imul(N,gt))+(i>>>13)|0)+(zt>>>26)|0,zt&=67108863,l[0]=mt,l[1]=vt,l[2]=yt,l[3]=xt,l[4]=bt,l[5]=_t,l[6]=wt,l[7]=Tt,l[8]=kt,l[9]=At,l[10]=Mt,l[11]=St,l[12]=Et,l[13]=Lt,l[14]=Ct,l[15]=Pt,l[16]=It,l[17]=Ot,l[18]=zt,0!==c&&(l[19]=c,r.length++),r};function d(t,e,r){return(new g).mulp(t,e,r)}function g(t,e){this.x=t,this.y=e}Math.imul||(p=h),a.prototype.mulTo=function(t,e){var r=this.length+t.length;return 10===this.length&&10===t.length?p(this,t,e):r<63?h(this,t,e):r<1024?function(t,e,r){r.negative=e.negative^t.negative,r.length=t.length+e.length;for(var n=0,i=0,a=0;a<r.length-1;a++){var o=i;i=0;for(var s=67108863&n,l=Math.min(a,e.length-1),c=Math.max(0,a-t.length+1);c<=l;c++){var u=a-c,f=(0|t.words[u])*(0|e.words[c]),h=67108863&f;s=67108863&(h=h+s|0),i+=(o=(o=o+(f/67108864|0)|0)+(h>>>26)|0)>>>26,o&=67108863}r.words[a]=s,n=o,o=i}return 0!==n?r.words[a]=n:r.length--,r.strip()}(this,t,e):d(this,t,e)},g.prototype.makeRBT=function(t){for(var e=new Array(t),r=a.prototype._countBits(t)-1,n=0;n<t;n++)e[n]=this.revBin(n,r,t);return e},g.prototype.revBin=function(t,e,r){if(0===t||t===r-1)return t;for(var n=0,i=0;i<e;i++)n|=(1&t)<<e-i-1,t>>=1;return n},g.prototype.permute=function(t,e,r,n,i,a){for(var o=0;o<a;o++)n[o]=e[t[o]],i[o]=r[t[o]]},g.prototype.transform=function(t,e,r,n,i,a){this.permute(a,t,e,r,n,i);for(var o=1;o<i;o<<=1)for(var s=o<<1,l=Math.cos(2*Math.PI/s),c=Math.sin(2*Math.PI/s),u=0;u<i;u+=s)for(var f=l,h=c,p=0;p<o;p++){var d=r[u+p],g=n[u+p],m=r[u+p+o],v=n[u+p+o],y=f*m-h*v;v=f*v+h*m,m=y,r[u+p]=d+m,n[u+p]=g+v,r[u+p+o]=d-m,n[u+p+o]=g-v,p!==s&&(y=l*f-c*h,h=l*h+c*f,f=y)}},g.prototype.guessLen13b=function(t,e){var r=1|Math.max(e,t),n=1&r,i=0;for(r=r/2|0;r;r>>>=1)i++;return 1<<i+1+n},g.prototype.conjugate=function(t,e,r){if(!(r<=1))for(var n=0;n<r/2;n++){var i=t[n];t[n]=t[r-n-1],t[r-n-1]=i,i=e[n],e[n]=-e[r-n-1],e[r-n-1]=-i}},g.prototype.normalize13b=function(t,e){for(var r=0,n=0;n<e/2;n++){var i=8192*Math.round(t[2*n+1]/e)+Math.round(t[2*n]/e)+r;t[n]=67108863&i,r=i<67108864?0:i/67108864|0}return t},g.prototype.convert13b=function(t,e,r,i){for(var a=0,o=0;o<e;o++)a+=0|t[o],r[2*o]=8191&a,a>>>=13,r[2*o+1]=8191&a,a>>>=13;for(o=2*e;o<i;++o)r[o]=0;n(0===a),n(0==(-8192&a))},g.prototype.stub=function(t){for(var e=new Array(t),r=0;r<t;r++)e[r]=0;return e},g.prototype.mulp=function(t,e,r){var n=2*this.guessLen13b(t.length,e.length),i=this.makeRBT(n),a=this.stub(n),o=new Array(n),s=new Array(n),l=new Array(n),c=new Array(n),u=new Array(n),f=new Array(n),h=r.words;h.length=n,this.convert13b(t.words,t.length,o,n),this.convert13b(e.words,e.length,c,n),this.transform(o,a,s,l,n,i),this.transform(c,a,u,f,n,i);for(var p=0;p<n;p++){var d=s[p]*u[p]-l[p]*f[p];l[p]=s[p]*f[p]+l[p]*u[p],s[p]=d}return this.conjugate(s,l,n),this.transform(s,l,h,a,n,i),this.conjugate(h,a,n),this.normalize13b(h,n),r.negative=t.negative^e.negative,r.length=t.length+e.length,r.strip()},a.prototype.mul=function(t){var e=new a(null);return e.words=new Array(this.length+t.length),this.mulTo(t,e)},a.prototype.mulf=function(t){var e=new a(null);return e.words=new Array(this.length+t.length),d(this,t,e)},a.prototype.imul=function(t){return this.clone().mulTo(t,this)},a.prototype.imuln=function(t){n("number"==typeof t),n(t<67108864);for(var e=0,r=0;r<this.length;r++){var i=(0|this.words[r])*t,a=(67108863&i)+(67108863&e);e>>=26,e+=i/67108864|0,e+=a>>>26,this.words[r]=67108863&a}return 0!==e&&(this.words[r]=e,this.length++),this},a.prototype.muln=function(t){return this.clone().imuln(t)},a.prototype.sqr=function(){return this.mul(this)},a.prototype.isqr=function(){return this.imul(this.clone())},a.prototype.pow=function(t){var e=function(t){for(var e=new Array(t.bitLength()),r=0;r<e.length;r++){var n=r/26|0,i=r%26;e[r]=(t.words[n]&1<<i)>>>i}return e}(t);if(0===e.length)return new a(1);for(var r=this,n=0;n<e.length&&0===e[n];n++,r=r.sqr());if(++n<e.length)for(var i=r.sqr();n<e.length;n++,i=i.sqr())0!==e[n]&&(r=r.mul(i));return r},a.prototype.iushln=function(t){n("number"==typeof t&&t>=0);var e,r=t%26,i=(t-r)/26,a=67108863>>>26-r<<26-r;if(0!==r){var o=0;for(e=0;e<this.length;e++){var s=this.words[e]&a,l=(0|this.words[e])-s<<r;this.words[e]=l|o,o=s>>>26-r}o&&(this.words[e]=o,this.length++)}if(0!==i){for(e=this.length-1;e>=0;e--)this.words[e+i]=this.words[e];for(e=0;e<i;e++)this.words[e]=0;this.length+=i}return this.strip()},a.prototype.ishln=function(t){return n(0===this.negative),this.iushln(t)},a.prototype.iushrn=function(t,e,r){var i;n("number"==typeof t&&t>=0),i=e?(e-e%26)/26:0;var a=t%26,o=Math.min((t-a)/26,this.length),s=67108863^67108863>>>a<<a,l=r;if(i-=o,i=Math.max(0,i),l){for(var c=0;c<o;c++)l.words[c]=this.words[c];l.length=o}if(0===o);else if(this.length>o)for(this.length-=o,c=0;c<this.length;c++)this.words[c]=this.words[c+o];else this.words[0]=0,this.length=1;var u=0;for(c=this.length-1;c>=0&&(0!==u||c>=i);c--){var f=0|this.words[c];this.words[c]=u<<26-a|f>>>a,u=f&s}return l&&0!==u&&(l.words[l.length++]=u),0===this.length&&(this.words[0]=0,this.length=1),this.strip()},a.prototype.ishrn=function(t,e,r){return n(0===this.negative),this.iushrn(t,e,r)},a.prototype.shln=function(t){return this.clone().ishln(t)},a.prototype.ushln=function(t){return this.clone().iushln(t)},a.prototype.shrn=function(t){return this.clone().ishrn(t)},a.prototype.ushrn=function(t){return this.clone().iushrn(t)},a.prototype.testn=function(t){n("number"==typeof t&&t>=0);var e=t%26,r=(t-e)/26,i=1<<e;return!(this.length<=r)&&!!(this.words[r]&i)},a.prototype.imaskn=function(t){n("number"==typeof t&&t>=0);var e=t%26,r=(t-e)/26;if(n(0===this.negative,"imaskn works only with positive numbers"),this.length<=r)return this;if(0!==e&&r++,this.length=Math.min(r,this.length),0!==e){var i=67108863^67108863>>>e<<e;this.words[this.length-1]&=i}return this.strip()},a.prototype.maskn=function(t){return this.clone().imaskn(t)},a.prototype.iaddn=function(t){return n("number"==typeof t),n(t<67108864),t<0?this.isubn(-t):0!==this.negative?1===this.length&&(0|this.words[0])<t?(this.words[0]=t-(0|this.words[0]),this.negative=0,this):(this.negative=0,this.isubn(t),this.negative=1,this):this._iaddn(t)},a.prototype._iaddn=function(t){this.words[0]+=t;for(var e=0;e<this.length&&this.words[e]>=67108864;e++)this.words[e]-=67108864,e===this.length-1?this.words[e+1]=1:this.words[e+1]++;return this.length=Math.max(this.length,e+1),this},a.prototype.isubn=function(t){if(n("number"==typeof t),n(t<67108864),t<0)return this.iaddn(-t);if(0!==this.negative)return this.negative=0,this.iaddn(t),this.negative=1,this;if(this.words[0]-=t,1===this.length&&this.words[0]<0)this.words[0]=-this.words[0],this.negative=1;else for(var e=0;e<this.length&&this.words[e]<0;e++)this.words[e]+=67108864,this.words[e+1]-=1;return this.strip()},a.prototype.addn=function(t){return this.clone().iaddn(t)},a.prototype.subn=function(t){return this.clone().isubn(t)},a.prototype.iabs=function(){return this.negative=0,this},a.prototype.abs=function(){return this.clone().iabs()},a.prototype._ishlnsubmul=function(t,e,r){var i,a,o=t.length+r;this._expand(o);var s=0;for(i=0;i<t.length;i++){a=(0|this.words[i+r])+s;var l=(0|t.words[i])*e;s=((a-=67108863&l)>>26)-(l/67108864|0),this.words[i+r]=67108863&a}for(;i<this.length-r;i++)s=(a=(0|this.words[i+r])+s)>>26,this.words[i+r]=67108863&a;if(0===s)return this.strip();for(n(-1===s),s=0,i=0;i<this.length;i++)s=(a=-(0|this.words[i])+s)>>26,this.words[i]=67108863&a;return this.negative=1,this.strip()},a.prototype._wordDiv=function(t,e){var r=(this.length,t.length),n=this.clone(),i=t,o=0|i.words[i.length-1];0!==(r=26-this._countBits(o))&&(i=i.ushln(r),n.iushln(r),o=0|i.words[i.length-1]);var s,l=n.length-i.length;if("mod"!==e){(s=new a(null)).length=l+1,s.words=new Array(s.length);for(var c=0;c<s.length;c++)s.words[c]=0}var u=n.clone()._ishlnsubmul(i,1,l);0===u.negative&&(n=u,s&&(s.words[l]=1));for(var f=l-1;f>=0;f--){var h=67108864*(0|n.words[i.length+f])+(0|n.words[i.length+f-1]);for(h=Math.min(h/o|0,67108863),n._ishlnsubmul(i,h,f);0!==n.negative;)h--,n.negative=0,n._ishlnsubmul(i,1,f),n.isZero()||(n.negative^=1);s&&(s.words[f]=h)}return s&&s.strip(),n.strip(),"div"!==e&&0!==r&&n.iushrn(r),{div:s||null,mod:n}},a.prototype.divmod=function(t,e,r){return n(!t.isZero()),this.isZero()?{div:new a(0),mod:new a(0)}:0!==this.negative&&0===t.negative?(s=this.neg().divmod(t,e),"mod"!==e&&(i=s.div.neg()),"div"!==e&&(o=s.mod.neg(),r&&0!==o.negative&&o.iadd(t)),{div:i,mod:o}):0===this.negative&&0!==t.negative?(s=this.divmod(t.neg(),e),"mod"!==e&&(i=s.div.neg()),{div:i,mod:s.mod}):0!=(this.negative&t.negative)?(s=this.neg().divmod(t.neg(),e),"div"!==e&&(o=s.mod.neg(),r&&0!==o.negative&&o.isub(t)),{div:s.div,mod:o}):t.length>this.length||this.cmp(t)<0?{div:new a(0),mod:this}:1===t.length?"div"===e?{div:this.divn(t.words[0]),mod:null}:"mod"===e?{div:null,mod:new a(this.modn(t.words[0]))}:{div:this.divn(t.words[0]),mod:new a(this.modn(t.words[0]))}:this._wordDiv(t,e);var i,o,s},a.prototype.div=function(t){return this.divmod(t,"div",!1).div},a.prototype.mod=function(t){return this.divmod(t,"mod",!1).mod},a.prototype.umod=function(t){return this.divmod(t,"mod",!0).mod},a.prototype.divRound=function(t){var e=this.divmod(t);if(e.mod.isZero())return e.div;var r=0!==e.div.negative?e.mod.isub(t):e.mod,n=t.ushrn(1),i=t.andln(1),a=r.cmp(n);return a<0||1===i&&0===a?e.div:0!==e.div.negative?e.div.isubn(1):e.div.iaddn(1)},a.prototype.modn=function(t){n(t<=67108863);for(var e=(1<<26)%t,r=0,i=this.length-1;i>=0;i--)r=(e*r+(0|this.words[i]))%t;return r},a.prototype.idivn=function(t){n(t<=67108863);for(var e=0,r=this.length-1;r>=0;r--){var i=(0|this.words[r])+67108864*e;this.words[r]=i/t|0,e=i%t}return this.strip()},a.prototype.divn=function(t){return this.clone().idivn(t)},a.prototype.egcd=function(t){n(0===t.negative),n(!t.isZero());var e=this,r=t.clone();e=0!==e.negative?e.umod(t):e.clone();for(var i=new a(1),o=new a(0),s=new a(0),l=new a(1),c=0;e.isEven()&&r.isEven();)e.iushrn(1),r.iushrn(1),++c;for(var u=r.clone(),f=e.clone();!e.isZero();){for(var h=0,p=1;0==(e.words[0]&p)&&h<26;++h,p<<=1);if(h>0)for(e.iushrn(h);h-- >0;)(i.isOdd()||o.isOdd())&&(i.iadd(u),o.isub(f)),i.iushrn(1),o.iushrn(1);for(var d=0,g=1;0==(r.words[0]&g)&&d<26;++d,g<<=1);if(d>0)for(r.iushrn(d);d-- >0;)(s.isOdd()||l.isOdd())&&(s.iadd(u),l.isub(f)),s.iushrn(1),l.iushrn(1);e.cmp(r)>=0?(e.isub(r),i.isub(s),o.isub(l)):(r.isub(e),s.isub(i),l.isub(o))}return{a:s,b:l,gcd:r.iushln(c)}},a.prototype._invmp=function(t){n(0===t.negative),n(!t.isZero());var e=this,r=t.clone();e=0!==e.negative?e.umod(t):e.clone();for(var i,o=new a(1),s=new a(0),l=r.clone();e.cmpn(1)>0&&r.cmpn(1)>0;){for(var c=0,u=1;0==(e.words[0]&u)&&c<26;++c,u<<=1);if(c>0)for(e.iushrn(c);c-- >0;)o.isOdd()&&o.iadd(l),o.iushrn(1);for(var f=0,h=1;0==(r.words[0]&h)&&f<26;++f,h<<=1);if(f>0)for(r.iushrn(f);f-- >0;)s.isOdd()&&s.iadd(l),s.iushrn(1);e.cmp(r)>=0?(e.isub(r),o.isub(s)):(r.isub(e),s.isub(o))}return(i=0===e.cmpn(1)?o:s).cmpn(0)<0&&i.iadd(t),i},a.prototype.gcd=function(t){if(this.isZero())return t.abs();if(t.isZero())return this.abs();var e=this.clone(),r=t.clone();e.negative=0,r.negative=0;for(var n=0;e.isEven()&&r.isEven();n++)e.iushrn(1),r.iushrn(1);for(;;){for(;e.isEven();)e.iushrn(1);for(;r.isEven();)r.iushrn(1);var i=e.cmp(r);if(i<0){var a=e;e=r,r=a}else if(0===i||0===r.cmpn(1))break;e.isub(r)}return r.iushln(n)},a.prototype.invm=function(t){return this.egcd(t).a.umod(t)},a.prototype.isEven=function(){return 0==(1&this.words[0])},a.prototype.isOdd=function(){return 1==(1&this.words[0])},a.prototype.andln=function(t){return this.words[0]&t},a.prototype.bincn=function(t){n("number"==typeof t);var e=t%26,r=(t-e)/26,i=1<<e;if(this.length<=r)return this._expand(r+1),this.words[r]|=i,this;for(var a=i,o=r;0!==a&&o<this.length;o++){var s=0|this.words[o];a=(s+=a)>>>26,s&=67108863,this.words[o]=s}return 0!==a&&(this.words[o]=a,this.length++),this},a.prototype.isZero=function(){return 1===this.length&&0===this.words[0]},a.prototype.cmpn=function(t){var e,r=t<0;if(0!==this.negative&&!r)return-1;if(0===this.negative&&r)return 1;if(this.strip(),this.length>1)e=1;else{r&&(t=-t),n(t<=67108863,"Number is too big");var i=0|this.words[0];e=i===t?0:i<t?-1:1}return 0!==this.negative?0|-e:e},a.prototype.cmp=function(t){if(0!==this.negative&&0===t.negative)return-1;if(0===this.negative&&0!==t.negative)return 1;var e=this.ucmp(t);return 0!==this.negative?0|-e:e},a.prototype.ucmp=function(t){if(this.length>t.length)return 1;if(this.length<t.length)return-1;for(var e=0,r=this.length-1;r>=0;r--){var n=0|this.words[r],i=0|t.words[r];if(n!==i){n<i?e=-1:n>i&&(e=1);break}}return e},a.prototype.gtn=function(t){return 1===this.cmpn(t)},a.prototype.gt=function(t){return 1===this.cmp(t)},a.prototype.gten=function(t){return this.cmpn(t)>=0},a.prototype.gte=function(t){return this.cmp(t)>=0},a.prototype.ltn=function(t){return-1===this.cmpn(t)},a.prototype.lt=function(t){return-1===this.cmp(t)},a.prototype.lten=function(t){return this.cmpn(t)<=0},a.prototype.lte=function(t){return this.cmp(t)<=0},a.prototype.eqn=function(t){return 0===this.cmpn(t)},a.prototype.eq=function(t){return 0===this.cmp(t)},a.red=function(t){return new w(t)},a.prototype.toRed=function(t){return n(!this.red,"Already a number in reduction context"),n(0===this.negative,"red works only with positives"),t.convertTo(this)._forceRed(t)},a.prototype.fromRed=function(){return n(this.red,"fromRed works only with numbers in reduction context"),this.red.convertFrom(this)},a.prototype._forceRed=function(t){return this.red=t,this},a.prototype.forceRed=function(t){return n(!this.red,"Already a number in reduction context"),this._forceRed(t)},a.prototype.redAdd=function(t){return n(this.red,"redAdd works only with red numbers"),this.red.add(this,t)},a.prototype.redIAdd=function(t){return n(this.red,"redIAdd works only with red numbers"),this.red.iadd(this,t)},a.prototype.redSub=function(t){return n(this.red,"redSub works only with red numbers"),this.red.sub(this,t)},a.prototype.redISub=function(t){return n(this.red,"redISub works only with red numbers"),this.red.isub(this,t)},a.prototype.redShl=function(t){return n(this.red,"redShl works only with red numbers"),this.red.shl(this,t)},a.prototype.redMul=function(t){return n(this.red,"redMul works only with red numbers"),this.red._verify2(this,t),this.red.mul(this,t)},a.prototype.redIMul=function(t){return n(this.red,"redMul works only with red numbers"),this.red._verify2(this,t),this.red.imul(this,t)},a.prototype.redSqr=function(){return n(this.red,"redSqr works only with red numbers"),this.red._verify1(this),this.red.sqr(this)},a.prototype.redISqr=function(){return n(this.red,"redISqr works only with red numbers"),this.red._verify1(this),this.red.isqr(this)},a.prototype.redSqrt=function(){return n(this.red,"redSqrt works only with red numbers"),this.red._verify1(this),this.red.sqrt(this)},a.prototype.redInvm=function(){return n(this.red,"redInvm works only with red numbers"),this.red._verify1(this),this.red.invm(this)},a.prototype.redNeg=function(){return n(this.red,"redNeg works only with red numbers"),this.red._verify1(this),this.red.neg(this)},a.prototype.redPow=function(t){return n(this.red&&!t.red,"redPow(normalNum)"),this.red._verify1(this),this.red.pow(this,t)};var m={k256:null,p224:null,p192:null,p25519:null};function v(t,e){this.name=t,this.p=new a(e,16),this.n=this.p.bitLength(),this.k=new a(1).iushln(this.n).isub(this.p),this.tmp=this._tmp()}function y(){v.call(this,"k256","ffffffff ffffffff ffffffff ffffffff ffffffff ffffffff fffffffe fffffc2f")}function x(){v.call(this,"p224","ffffffff ffffffff ffffffff ffffffff 00000000 00000000 00000001")}function b(){v.call(this,"p192","ffffffff ffffffff ffffffff fffffffe ffffffff ffffffff")}function _(){v.call(this,"25519","7fffffffffffffff ffffffffffffffff ffffffffffffffff ffffffffffffffed")}function w(t){if("string"==typeof t){var e=a._prime(t);this.m=e.p,this.prime=e}else n(t.gtn(1),"modulus must be greater than 1"),this.m=t,this.prime=null}function T(t){w.call(this,t),this.shift=this.m.bitLength(),this.shift%26!=0&&(this.shift+=26-this.shift%26),this.r=new a(1).iushln(this.shift),this.r2=this.imod(this.r.sqr()),this.rinv=this.r._invmp(this.m),this.minv=this.rinv.mul(this.r).isubn(1).div(this.m),this.minv=this.minv.umod(this.r),this.minv=this.r.sub(this.minv)}v.prototype._tmp=function(){var t=new a(null);return t.words=new Array(Math.ceil(this.n/13)),t},v.prototype.ireduce=function(t){var e,r=t;do{this.split(r,this.tmp),e=(r=(r=this.imulK(r)).iadd(this.tmp)).bitLength()}while(e>this.n);var n=e<this.n?-1:r.ucmp(this.p);return 0===n?(r.words[0]=0,r.length=1):n>0?r.isub(this.p):r.strip(),r},v.prototype.split=function(t,e){t.iushrn(this.n,0,e)},v.prototype.imulK=function(t){return t.imul(this.k)},i(y,v),y.prototype.split=function(t,e){for(var r=Math.min(t.length,9),n=0;n<r;n++)e.words[n]=t.words[n];if(e.length=r,t.length<=9)return t.words[0]=0,void(t.length=1);var i=t.words[9];for(e.words[e.length++]=4194303&i,n=10;n<t.length;n++){var a=0|t.words[n];t.words[n-10]=(4194303&a)<<4|i>>>22,i=a}i>>>=22,t.words[n-10]=i,0===i&&t.length>10?t.length-=10:t.length-=9},y.prototype.imulK=function(t){t.words[t.length]=0,t.words[t.length+1]=0,t.length+=2;for(var e=0,r=0;r<t.length;r++){var n=0|t.words[r];e+=977*n,t.words[r]=67108863&e,e=64*n+(e/67108864|0)}return 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/*!
* The buffer module from node.js, for the browser.
*
* @author Feross Aboukhadijeh <https://feross.org>
* @license MIT
*/
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f=1;for(c=l(t,u,t.length,e),u=0;u<o;u++)f*=e;this.imuln(f),this.words[0]+c<67108864?this.words[0]+=c:this._iaddn(c)}},a.prototype.copy=function(t){t.words=new Array(this.length);for(var e=0;e<this.length;e++)t.words[e]=this.words[e];t.length=this.length,t.negative=this.negative,t.red=this.red},a.prototype.clone=function(){var t=new a(null);return this.copy(t),t},a.prototype._expand=function(t){for(;this.length<t;)this.words[this.length++]=0;return this},a.prototype.strip=function(){for(;this.length>1&&0===this.words[this.length-1];)this.length--;return this._normSign()},a.prototype._normSign=function(){return 1===this.length&&0===this.words[0]&&(this.negative=0),this},a.prototype.inspect=function(){return(this.red?"<BN-R: ":"<BN: ")+this.toString(16)+">"};var c=["","0","00","000","0000","00000","000000","0000000","00000000","000000000","0000000000","00000000000","000000000000","0000000000000","00000000000000","000000000000000","0000000000000000","00000000000000000","000000000000000000","0000000000000000000","00000000000000000000","000000000000000000000","0000000000000000000000","00000000000000000000000","000000000000000000000000","0000000000000000000000000"],u=[0,0,25,16,12,11,10,9,8,8,7,7,7,7,6,6,6,6,6,6,6,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5],f=[0,0,33554432,43046721,16777216,48828125,60466176,40353607,16777216,43046721,1e7,19487171,35831808,62748517,7529536,11390625,16777216,24137569,34012224,47045881,64e6,4084101,5153632,6436343,7962624,9765625,11881376,14348907,17210368,20511149,243e5,28629151,33554432,39135393,45435424,52521875,60466176];function h(t,e,r){r.negative=e.negative^t.negative;var n=t.length+e.length|0;r.length=n,n=n-1|0;var i=0|t.words[0],a=0|e.words[0],o=i*a,s=67108863&o,l=o/67108864|0;r.words[0]=s;for(var c=1;c<n;c++){for(var u=l>>>26,f=67108863&l,h=Math.min(c,e.length-1),p=Math.max(0,c-t.length+1);p<=h;p++){var d=c-p|0;u+=(o=(i=0|t.words[d])*(a=0|e.words[p])+f)/67108864|0,f=67108863&o}r.words[c]=0|f,l=0|u}return 0!==l?r.words[c]=0|l:r.length--,r.strip()}a.prototype.toString=function(t,e){var r;if(e=0|e||1,16===(t=t||10)||"hex"===t){r="";for(var i=0,a=0,o=0;o<this.length;o++){var s=this.words[o],l=(16777215&(s<<i|a)).toString(16);r=0!==(a=s>>>24-i&16777215)||o!==this.length-1?c[6-l.length]+l+r:l+r,(i+=2)>=26&&(i-=26,o--)}for(0!==a&&(r=a.toString(16)+r);r.length%e!=0;)r="0"+r;return 0!==this.negative&&(r="-"+r),r}if(t===(0|t)&&t>=2&&t<=36){var h=u[t],p=f[t];r="";var d=this.clone();for(d.negative=0;!d.isZero();){var g=d.modn(p).toString(t);r=(d=d.idivn(p)).isZero()?g+r:c[h-g.length]+g+r}for(this.isZero()&&(r="0"+r);r.length%e!=0;)r="0"+r;return 0!==this.negative&&(r="-"+r),r}n(!1,"Base should be between 2 and 36")},a.prototype.toNumber=function(){var t=this.words[0];return 2===this.length?t+=67108864*this.words[1]:3===this.length&&1===this.words[2]?t+=4503599627370496+67108864*this.words[1]:this.length>2&&n(!1,"Number can only safely store up to 53 bits"),0!==this.negative?-t:t},a.prototype.toJSON=function(){return this.toString(16)},a.prototype.toBuffer=function(t,e){return n(void 0!==o),this.toArrayLike(o,t,e)},a.prototype.toArray=function(t,e){return this.toArrayLike(Array,t,e)},a.prototype.toArrayLike=function(t,e,r){var i=this.byteLength(),a=r||Math.max(1,i);n(i<=a,"byte array longer than desired length"),n(a>0,"Requested array length <= 0"),this.strip();var o,s,l="le"===e,c=new t(a),u=this.clone();if(l){for(s=0;!u.isZero();s++)o=u.andln(255),u.iushrn(8),c[s]=o;for(;s<a;s++)c[s]=0}else{for(s=0;s<a-i;s++)c[s]=0;for(s=0;!u.isZero();s++)o=u.andln(255),u.iushrn(8),c[a-s-1]=o}return c},Math.clz32?a.prototype._countBits=function(t){return 32-Math.clz32(t)}:a.prototype._countBits=function(t){var e=t,r=0;return e>=4096&&(r+=13,e>>>=13),e>=64&&(r+=7,e>>>=7),e>=8&&(r+=4,e>>>=4),e>=2&&(r+=2,e>>>=2),r+e},a.prototype._zeroBits=function(t){if(0===t)return 26;var e=t,r=0;return 0==(8191&e)&&(r+=13,e>>>=13),0==(127&e)&&(r+=7,e>>>=7),0==(15&e)&&(r+=4,e>>>=4),0==(3&e)&&(r+=2,e>>>=2),0==(1&e)&&r++,r},a.prototype.bitLength=function(){var t=this.words[this.length-1],e=this._countBits(t);return 26*(this.length-1)+e},a.prototype.zeroBits=function(){if(this.isZero())return 0;for(var t=0,e=0;e<this.length;e++){var r=this._zeroBits(this.words[e]);if(t+=r,26!==r)break}return t},a.prototype.byteLength=function(){return Math.ceil(this.bitLength()/8)},a.prototype.toTwos=function(t){return 0!==this.negative?this.abs().inotn(t).iaddn(1):this.clone()},a.prototype.fromTwos=function(t){return this.testn(t-1)?this.notn(t).iaddn(1).ineg():this.clone()},a.prototype.isNeg=function(){return 0!==this.negative},a.prototype.neg=function(){return this.clone().ineg()},a.prototype.ineg=function(){return this.isZero()||(this.negative^=1),this},a.prototype.iuor=function(t){for(;this.length<t.length;)this.words[this.length++]=0;for(var e=0;e<t.length;e++)this.words[e]=this.words[e]|t.words[e];return this.strip()},a.prototype.ior=function(t){return n(0==(this.negative|t.negative)),this.iuor(t)},a.prototype.or=function(t){return this.length>t.length?this.clone().ior(t):t.clone().ior(this)},a.prototype.uor=function(t){return this.length>t.length?this.clone().iuor(t):t.clone().iuor(this)},a.prototype.iuand=function(t){var e;e=this.length>t.length?t:this;for(var r=0;r<e.length;r++)this.words[r]=this.words[r]&t.words[r];return this.length=e.length,this.strip()},a.prototype.iand=function(t){return n(0==(this.negative|t.negative)),this.iuand(t)},a.prototype.and=function(t){return this.length>t.length?this.clone().iand(t):t.clone().iand(this)},a.prototype.uand=function(t){return this.length>t.length?this.clone().iuand(t):t.clone().iuand(this)},a.prototype.iuxor=function(t){var e,r;this.length>t.length?(e=this,r=t):(e=t,r=this);for(var n=0;n<r.length;n++)this.words[n]=e.words[n]^r.words[n];if(this!==e)for(;n<e.length;n++)this.words[n]=e.words[n];return this.length=e.length,this.strip()},a.prototype.ixor=function(t){return n(0==(this.negative|t.negative)),this.iuxor(t)},a.prototype.xor=function(t){return this.length>t.length?this.clone().ixor(t):t.clone().ixor(this)},a.prototype.uxor=function(t){return this.length>t.length?this.clone().iuxor(t):t.clone().iuxor(this)},a.prototype.inotn=function(t){n("number"==typeof t&&t>=0);var e=0|Math.ceil(t/26),r=t%26;this._expand(e),r>0&&e--;for(var i=0;i<e;i++)this.words[i]=67108863&~this.words[i];return r>0&&(this.words[i]=~this.words[i]&67108863>>26-r),this.strip()},a.prototype.notn=function(t){return this.clone().inotn(t)},a.prototype.setn=function(t,e){n("number"==typeof t&&t>=0);var r=t/26|0,i=t%26;return this._expand(r+1),this.words[r]=e?this.words[r]|1<<i:this.words[r]&~(1<<i),this.strip()},a.prototype.iadd=function(t){var e,r,n;if(0!==this.negative&&0===t.negative)return this.negative=0,e=this.isub(t),this.negative^=1,this._normSign();if(0===this.negative&&0!==t.negative)return t.negative=0,e=this.isub(t),t.negative=1,e._normSign();this.length>t.length?(r=this,n=t):(r=t,n=this);for(var i=0,a=0;a<n.length;a++)e=(0|r.words[a])+(0|n.words[a])+i,this.words[a]=67108863&e,i=e>>>26;for(;0!==i&&a<r.length;a++)e=(0|r.words[a])+i,this.words[a]=67108863&e,i=e>>>26;if(this.length=r.length,0!==i)this.words[this.length]=i,this.length++;else if(r!==this)for(;a<r.length;a++)this.words[a]=r.words[a];return this},a.prototype.add=function(t){var e;return 0!==t.negative&&0===this.negative?(t.negative=0,e=this.sub(t),t.negative^=1,e):0===t.negative&&0!==this.negative?(this.negative=0,e=t.sub(this),this.negative=1,e):this.length>t.length?this.clone().iadd(t):t.clone().iadd(this)},a.prototype.isub=function(t){if(0!==t.negative){t.negative=0;var e=this.iadd(t);return t.negative=1,e._normSign()}if(0!==this.negative)return this.negative=0,this.iadd(t),this.negative=1,this._normSign();var r,n,i=this.cmp(t);if(0===i)return this.negative=0,this.length=1,this.words[0]=0,this;i>0?(r=this,n=t):(r=t,n=this);for(var a=0,o=0;o<n.length;o++)a=(e=(0|r.words[o])-(0|n.words[o])+a)>>26,this.words[o]=67108863&e;for(;0!==a&&o<r.length;o++)a=(e=(0|r.words[o])+a)>>26,this.words[o]=67108863&e;if(0===a&&o<r.length&&r!==this)for(;o<r.length;o++)this.words[o]=r.words[o];return this.length=Math.max(this.length,o),r!==this&&(this.negative=1),this.strip()},a.prototype.sub=function(t){return this.clone().isub(t)};var p=function(t,e,r){var n,i,a,o=t.words,s=e.words,l=r.words,c=0,u=0|o[0],f=8191&u,h=u>>>13,p=0|o[1],d=8191&p,g=p>>>13,m=0|o[2],v=8191&m,y=m>>>13,x=0|o[3],b=8191&x,_=x>>>13,w=0|o[4],T=8191&w,k=w>>>13,A=0|o[5],M=8191&A,S=A>>>13,E=0|o[6],L=8191&E,C=E>>>13,P=0|o[7],I=8191&P,O=P>>>13,z=0|o[8],D=8191&z,R=z>>>13,F=0|o[9],B=8191&F,N=F>>>13,j=0|s[0],U=8191&j,V=j>>>13,q=0|s[1],H=8191&q,G=q>>>13,Y=0|s[2],W=8191&Y,X=Y>>>13,Z=0|s[3],J=8191&Z,K=Z>>>13,Q=0|s[4],$=8191&Q,tt=Q>>>13,et=0|s[5],rt=8191&et,nt=et>>>13,it=0|s[6],at=8191&it,ot=it>>>13,st=0|s[7],lt=8191&st,ct=st>>>13,ut=0|s[8],ft=8191&ut,ht=ut>>>13,pt=0|s[9],dt=8191&pt,gt=pt>>>13;r.negative=t.negative^e.negative,r.length=19;var mt=(c+(n=Math.imul(f,U))|0)+((8191&(i=(i=Math.imul(f,V))+Math.imul(h,U)|0))<<13)|0;c=((a=Math.imul(h,V))+(i>>>13)|0)+(mt>>>26)|0,mt&=67108863,n=Math.imul(d,U),i=(i=Math.imul(d,V))+Math.imul(g,U)|0,a=Math.imul(g,V);var vt=(c+(n=n+Math.imul(f,H)|0)|0)+((8191&(i=(i=i+Math.imul(f,G)|0)+Math.imul(h,H)|0))<<13)|0;c=((a=a+Math.imul(h,G)|0)+(i>>>13)|0)+(vt>>>26)|0,vt&=67108863,n=Math.imul(v,U),i=(i=Math.imul(v,V))+Math.imul(y,U)|0,a=Math.imul(y,V),n=n+Math.imul(d,H)|0,i=(i=i+Math.imul(d,G)|0)+Math.imul(g,H)|0,a=a+Math.imul(g,G)|0;var yt=(c+(n=n+Math.imul(f,W)|0)|0)+((8191&(i=(i=i+Math.imul(f,X)|0)+Math.imul(h,W)|0))<<13)|0;c=((a=a+Math.imul(h,X)|0)+(i>>>13)|0)+(yt>>>26)|0,yt&=67108863,n=Math.imul(b,U),i=(i=Math.imul(b,V))+Math.imul(_,U)|0,a=Math.imul(_,V),n=n+Math.imul(v,H)|0,i=(i=i+Math.imul(v,G)|0)+Math.imul(y,H)|0,a=a+Math.imul(y,G)|0,n=n+Math.imul(d,W)|0,i=(i=i+Math.imul(d,X)|0)+Math.imul(g,W)|0,a=a+Math.imul(g,X)|0;var xt=(c+(n=n+Math.imul(f,J)|0)|0)+((8191&(i=(i=i+Math.imul(f,K)|0)+Math.imul(h,J)|0))<<13)|0;c=((a=a+Math.imul(h,K)|0)+(i>>>13)|0)+(xt>>>26)|0,xt&=67108863,n=Math.imul(T,U),i=(i=Math.imul(T,V))+Math.imul(k,U)|0,a=Math.imul(k,V),n=n+Math.imul(b,H)|0,i=(i=i+Math.imul(b,G)|0)+Math.imul(_,H)|0,a=a+Math.imul(_,G)|0,n=n+Math.imul(v,W)|0,i=(i=i+Math.imul(v,X)|0)+Math.imul(y,W)|0,a=a+Math.imul(y,X)|0,n=n+Math.imul(d,J)|0,i=(i=i+Math.imul(d,K)|0)+Math.imul(g,J)|0,a=a+Math.imul(g,K)|0;var bt=(c+(n=n+Math.imul(f,$)|0)|0)+((8191&(i=(i=i+Math.imul(f,tt)|0)+Math.imul(h,$)|0))<<13)|0;c=((a=a+Math.imul(h,tt)|0)+(i>>>13)|0)+(bt>>>26)|0,bt&=67108863,n=Math.imul(M,U),i=(i=Math.imul(M,V))+Math.imul(S,U)|0,a=Math.imul(S,V),n=n+Math.imul(T,H)|0,i=(i=i+Math.imul(T,G)|0)+Math.imul(k,H)|0,a=a+Math.imul(k,G)|0,n=n+Math.imul(b,W)|0,i=(i=i+Math.imul(b,X)|0)+Math.imul(_,W)|0,a=a+Math.imul(_,X)|0,n=n+Math.imul(v,J)|0,i=(i=i+Math.imul(v,K)|0)+Math.imul(y,J)|0,a=a+Math.imul(y,K)|0,n=n+Math.imul(d,$)|0,i=(i=i+Math.imul(d,tt)|0)+Math.imul(g,$)|0,a=a+Math.imul(g,tt)|0;var _t=(c+(n=n+Math.imul(f,rt)|0)|0)+((8191&(i=(i=i+Math.imul(f,nt)|0)+Math.imul(h,rt)|0))<<13)|0;c=((a=a+Math.imul(h,nt)|0)+(i>>>13)|0)+(_t>>>26)|0,_t&=67108863,n=Math.imul(L,U),i=(i=Math.imul(L,V))+Math.imul(C,U)|0,a=Math.imul(C,V),n=n+Math.imul(M,H)|0,i=(i=i+Math.imul(M,G)|0)+Math.imul(S,H)|0,a=a+Math.imul(S,G)|0,n=n+Math.imul(T,W)|0,i=(i=i+Math.imul(T,X)|0)+Math.imul(k,W)|0,a=a+Math.imul(k,X)|0,n=n+Math.imul(b,J)|0,i=(i=i+Math.imul(b,K)|0)+Math.imul(_,J)|0,a=a+Math.imul(_,K)|0,n=n+Math.imul(v,$)|0,i=(i=i+Math.imul(v,tt)|0)+Math.imul(y,$)|0,a=a+Math.imul(y,tt)|0,n=n+Math.imul(d,rt)|0,i=(i=i+Math.imul(d,nt)|0)+Math.imul(g,rt)|0,a=a+Math.imul(g,nt)|0;var wt=(c+(n=n+Math.imul(f,at)|0)|0)+((8191&(i=(i=i+Math.imul(f,ot)|0)+Math.imul(h,at)|0))<<13)|0;c=((a=a+Math.imul(h,ot)|0)+(i>>>13)|0)+(wt>>>26)|0,wt&=67108863,n=Math.imul(I,U),i=(i=Math.imul(I,V))+Math.imul(O,U)|0,a=Math.imul(O,V),n=n+Math.imul(L,H)|0,i=(i=i+Math.imul(L,G)|0)+Math.imul(C,H)|0,a=a+Math.imul(C,G)|0,n=n+Math.imul(M,W)|0,i=(i=i+Math.imul(M,X)|0)+Math.imul(S,W)|0,a=a+Math.imul(S,X)|0,n=n+Math.imul(T,J)|0,i=(i=i+Math.imul(T,K)|0)+Math.imul(k,J)|0,a=a+Math.imul(k,K)|0,n=n+Math.imul(b,$)|0,i=(i=i+Math.imul(b,tt)|0)+Math.imul(_,$)|0,a=a+Math.imul(_,tt)|0,n=n+Math.imul(v,rt)|0,i=(i=i+Math.imul(v,nt)|0)+Math.imul(y,rt)|0,a=a+Math.imul(y,nt)|0,n=n+Math.imul(d,at)|0,i=(i=i+Math.imul(d,ot)|0)+Math.imul(g,at)|0,a=a+Math.imul(g,ot)|0;var Tt=(c+(n=n+Math.imul(f,lt)|0)|0)+((8191&(i=(i=i+Math.imul(f,ct)|0)+Math.imul(h,lt)|0))<<13)|0;c=((a=a+Math.imul(h,ct)|0)+(i>>>13)|0)+(Tt>>>26)|0,Tt&=67108863,n=Math.imul(D,U),i=(i=Math.imul(D,V))+Math.imul(R,U)|0,a=Math.imul(R,V),n=n+Math.imul(I,H)|0,i=(i=i+Math.imul(I,G)|0)+Math.imul(O,H)|0,a=a+Math.imul(O,G)|0,n=n+Math.imul(L,W)|0,i=(i=i+Math.imul(L,X)|0)+Math.imul(C,W)|0,a=a+Math.imul(C,X)|0,n=n+Math.imul(M,J)|0,i=(i=i+Math.imul(M,K)|0)+Math.imul(S,J)|0,a=a+Math.imul(S,K)|0,n=n+Math.imul(T,$)|0,i=(i=i+Math.imul(T,tt)|0)+Math.imul(k,$)|0,a=a+Math.imul(k,tt)|0,n=n+Math.imul(b,rt)|0,i=(i=i+Math.imul(b,nt)|0)+Math.imul(_,rt)|0,a=a+Math.imul(_,nt)|0,n=n+Math.imul(v,at)|0,i=(i=i+Math.imul(v,ot)|0)+Math.imul(y,at)|0,a=a+Math.imul(y,ot)|0,n=n+Math.imul(d,lt)|0,i=(i=i+Math.imul(d,ct)|0)+Math.imul(g,lt)|0,a=a+Math.imul(g,ct)|0;var kt=(c+(n=n+Math.imul(f,ft)|0)|0)+((8191&(i=(i=i+Math.imul(f,ht)|0)+Math.imul(h,ft)|0))<<13)|0;c=((a=a+Math.imul(h,ht)|0)+(i>>>13)|0)+(kt>>>26)|0,kt&=67108863,n=Math.imul(B,U),i=(i=Math.imul(B,V))+Math.imul(N,U)|0,a=Math.imul(N,V),n=n+Math.imul(D,H)|0,i=(i=i+Math.imul(D,G)|0)+Math.imul(R,H)|0,a=a+Math.imul(R,G)|0,n=n+Math.imul(I,W)|0,i=(i=i+Math.imul(I,X)|0)+Math.imul(O,W)|0,a=a+Math.imul(O,X)|0,n=n+Math.imul(L,J)|0,i=(i=i+Math.imul(L,K)|0)+Math.imul(C,J)|0,a=a+Math.imul(C,K)|0,n=n+Math.imul(M,$)|0,i=(i=i+Math.imul(M,tt)|0)+Math.imul(S,$)|0,a=a+Math.imul(S,tt)|0,n=n+Math.imul(T,rt)|0,i=(i=i+Math.imul(T,nt)|0)+Math.imul(k,rt)|0,a=a+Math.imul(k,nt)|0,n=n+Math.imul(b,at)|0,i=(i=i+Math.imul(b,ot)|0)+Math.imul(_,at)|0,a=a+Math.imul(_,ot)|0,n=n+Math.imul(v,lt)|0,i=(i=i+Math.imul(v,ct)|0)+Math.imul(y,lt)|0,a=a+Math.imul(y,ct)|0,n=n+Math.imul(d,ft)|0,i=(i=i+Math.imul(d,ht)|0)+Math.imul(g,ft)|0,a=a+Math.imul(g,ht)|0;var At=(c+(n=n+Math.imul(f,dt)|0)|0)+((8191&(i=(i=i+Math.imul(f,gt)|0)+Math.imul(h,dt)|0))<<13)|0;c=((a=a+Math.imul(h,gt)|0)+(i>>>13)|0)+(At>>>26)|0,At&=67108863,n=Math.imul(B,H),i=(i=Math.imul(B,G))+Math.imul(N,H)|0,a=Math.imul(N,G),n=n+Math.imul(D,W)|0,i=(i=i+Math.imul(D,X)|0)+Math.imul(R,W)|0,a=a+Math.imul(R,X)|0,n=n+Math.imul(I,J)|0,i=(i=i+Math.imul(I,K)|0)+Math.imul(O,J)|0,a=a+Math.imul(O,K)|0,n=n+Math.imul(L,$)|0,i=(i=i+Math.imul(L,tt)|0)+Math.imul(C,$)|0,a=a+Math.imul(C,tt)|0,n=n+Math.imul(M,rt)|0,i=(i=i+Math.imul(M,nt)|0)+Math.imul(S,rt)|0,a=a+Math.imul(S,nt)|0,n=n+Math.imul(T,at)|0,i=(i=i+Math.imul(T,ot)|0)+Math.imul(k,at)|0,a=a+Math.imul(k,ot)|0,n=n+Math.imul(b,lt)|0,i=(i=i+Math.imul(b,ct)|0)+Math.imul(_,lt)|0,a=a+Math.imul(_,ct)|0,n=n+Math.imul(v,ft)|0,i=(i=i+Math.imul(v,ht)|0)+Math.imul(y,ft)|0,a=a+Math.imul(y,ht)|0;var Mt=(c+(n=n+Math.imul(d,dt)|0)|0)+((8191&(i=(i=i+Math.imul(d,gt)|0)+Math.imul(g,dt)|0))<<13)|0;c=((a=a+Math.imul(g,gt)|0)+(i>>>13)|0)+(Mt>>>26)|0,Mt&=67108863,n=Math.imul(B,W),i=(i=Math.imul(B,X))+Math.imul(N,W)|0,a=Math.imul(N,X),n=n+Math.imul(D,J)|0,i=(i=i+Math.imul(D,K)|0)+Math.imul(R,J)|0,a=a+Math.imul(R,K)|0,n=n+Math.imul(I,$)|0,i=(i=i+Math.imul(I,tt)|0)+Math.imul(O,$)|0,a=a+Math.imul(O,tt)|0,n=n+Math.imul(L,rt)|0,i=(i=i+Math.imul(L,nt)|0)+Math.imul(C,rt)|0,a=a+Math.imul(C,nt)|0,n=n+Math.imul(M,at)|0,i=(i=i+Math.imul(M,ot)|0)+Math.imul(S,at)|0,a=a+Math.imul(S,ot)|0,n=n+Math.imul(T,lt)|0,i=(i=i+Math.imul(T,ct)|0)+Math.imul(k,lt)|0,a=a+Math.imul(k,ct)|0,n=n+Math.imul(b,ft)|0,i=(i=i+Math.imul(b,ht)|0)+Math.imul(_,ft)|0,a=a+Math.imul(_,ht)|0;var St=(c+(n=n+Math.imul(v,dt)|0)|0)+((8191&(i=(i=i+Math.imul(v,gt)|0)+Math.imul(y,dt)|0))<<13)|0;c=((a=a+Math.imul(y,gt)|0)+(i>>>13)|0)+(St>>>26)|0,St&=67108863,n=Math.imul(B,J),i=(i=Math.imul(B,K))+Math.imul(N,J)|0,a=Math.imul(N,K),n=n+Math.imul(D,$)|0,i=(i=i+Math.imul(D,tt)|0)+Math.imul(R,$)|0,a=a+Math.imul(R,tt)|0,n=n+Math.imul(I,rt)|0,i=(i=i+Math.imul(I,nt)|0)+Math.imul(O,rt)|0,a=a+Math.imul(O,nt)|0,n=n+Math.imul(L,at)|0,i=(i=i+Math.imul(L,ot)|0)+Math.imul(C,at)|0,a=a+Math.imul(C,ot)|0,n=n+Math.imul(M,lt)|0,i=(i=i+Math.imul(M,ct)|0)+Math.imul(S,lt)|0,a=a+Math.imul(S,ct)|0,n=n+Math.imul(T,ft)|0,i=(i=i+Math.imul(T,ht)|0)+Math.imul(k,ft)|0,a=a+Math.imul(k,ht)|0;var Et=(c+(n=n+Math.imul(b,dt)|0)|0)+((8191&(i=(i=i+Math.imul(b,gt)|0)+Math.imul(_,dt)|0))<<13)|0;c=((a=a+Math.imul(_,gt)|0)+(i>>>13)|0)+(Et>>>26)|0,Et&=67108863,n=Math.imul(B,$),i=(i=Math.imul(B,tt))+Math.imul(N,$)|0,a=Math.imul(N,tt),n=n+Math.imul(D,rt)|0,i=(i=i+Math.imul(D,nt)|0)+Math.imul(R,rt)|0,a=a+Math.imul(R,nt)|0,n=n+Math.imul(I,at)|0,i=(i=i+Math.imul(I,ot)|0)+Math.imul(O,at)|0,a=a+Math.imul(O,ot)|0,n=n+Math.imul(L,lt)|0,i=(i=i+Math.imul(L,ct)|0)+Math.imul(C,lt)|0,a=a+Math.imul(C,ct)|0,n=n+Math.imul(M,ft)|0,i=(i=i+Math.imul(M,ht)|0)+Math.imul(S,ft)|0,a=a+Math.imul(S,ht)|0;var Lt=(c+(n=n+Math.imul(T,dt)|0)|0)+((8191&(i=(i=i+Math.imul(T,gt)|0)+Math.imul(k,dt)|0))<<13)|0;c=((a=a+Math.imul(k,gt)|0)+(i>>>13)|0)+(Lt>>>26)|0,Lt&=67108863,n=Math.imul(B,rt),i=(i=Math.imul(B,nt))+Math.imul(N,rt)|0,a=Math.imul(N,nt),n=n+Math.imul(D,at)|0,i=(i=i+Math.imul(D,ot)|0)+Math.imul(R,at)|0,a=a+Math.imul(R,ot)|0,n=n+Math.imul(I,lt)|0,i=(i=i+Math.imul(I,ct)|0)+Math.imul(O,lt)|0,a=a+Math.imul(O,ct)|0,n=n+Math.imul(L,ft)|0,i=(i=i+Math.imul(L,ht)|0)+Math.imul(C,ft)|0,a=a+Math.imul(C,ht)|0;var Ct=(c+(n=n+Math.imul(M,dt)|0)|0)+((8191&(i=(i=i+Math.imul(M,gt)|0)+Math.imul(S,dt)|0))<<13)|0;c=((a=a+Math.imul(S,gt)|0)+(i>>>13)|0)+(Ct>>>26)|0,Ct&=67108863,n=Math.imul(B,at),i=(i=Math.imul(B,ot))+Math.imul(N,at)|0,a=Math.imul(N,ot),n=n+Math.imul(D,lt)|0,i=(i=i+Math.imul(D,ct)|0)+Math.imul(R,lt)|0,a=a+Math.imul(R,ct)|0,n=n+Math.imul(I,ft)|0,i=(i=i+Math.imul(I,ht)|0)+Math.imul(O,ft)|0,a=a+Math.imul(O,ht)|0;var Pt=(c+(n=n+Math.imul(L,dt)|0)|0)+((8191&(i=(i=i+Math.imul(L,gt)|0)+Math.imul(C,dt)|0))<<13)|0;c=((a=a+Math.imul(C,gt)|0)+(i>>>13)|0)+(Pt>>>26)|0,Pt&=67108863,n=Math.imul(B,lt),i=(i=Math.imul(B,ct))+Math.imul(N,lt)|0,a=Math.imul(N,ct),n=n+Math.imul(D,ft)|0,i=(i=i+Math.imul(D,ht)|0)+Math.imul(R,ft)|0,a=a+Math.imul(R,ht)|0;var It=(c+(n=n+Math.imul(I,dt)|0)|0)+((8191&(i=(i=i+Math.imul(I,gt)|0)+Math.imul(O,dt)|0))<<13)|0;c=((a=a+Math.imul(O,gt)|0)+(i>>>13)|0)+(It>>>26)|0,It&=67108863,n=Math.imul(B,ft),i=(i=Math.imul(B,ht))+Math.imul(N,ft)|0,a=Math.imul(N,ht);var Ot=(c+(n=n+Math.imul(D,dt)|0)|0)+((8191&(i=(i=i+Math.imul(D,gt)|0)+Math.imul(R,dt)|0))<<13)|0;c=((a=a+Math.imul(R,gt)|0)+(i>>>13)|0)+(Ot>>>26)|0,Ot&=67108863;var zt=(c+(n=Math.imul(B,dt))|0)+((8191&(i=(i=Math.imul(B,gt))+Math.imul(N,dt)|0))<<13)|0;return c=((a=Math.imul(N,gt))+(i>>>13)|0)+(zt>>>26)|0,zt&=67108863,l[0]=mt,l[1]=vt,l[2]=yt,l[3]=xt,l[4]=bt,l[5]=_t,l[6]=wt,l[7]=Tt,l[8]=kt,l[9]=At,l[10]=Mt,l[11]=St,l[12]=Et,l[13]=Lt,l[14]=Ct,l[15]=Pt,l[16]=It,l[17]=Ot,l[18]=zt,0!==c&&(l[19]=c,r.length++),r};function d(t,e,r){return(new g).mulp(t,e,r)}function g(t,e){this.x=t,this.y=e}Math.imul||(p=h),a.prototype.mulTo=function(t,e){var r=this.length+t.length;return 10===this.length&&10===t.length?p(this,t,e):r<63?h(this,t,e):r<1024?function(t,e,r){r.negative=e.negative^t.negative,r.length=t.length+e.length;for(var n=0,i=0,a=0;a<r.length-1;a++){var o=i;i=0;for(var s=67108863&n,l=Math.min(a,e.length-1),c=Math.max(0,a-t.length+1);c<=l;c++){var u=a-c,f=(0|t.words[u])*(0|e.words[c]),h=67108863&f;s=67108863&(h=h+s|0),i+=(o=(o=o+(f/67108864|0)|0)+(h>>>26)|0)>>>26,o&=67108863}r.words[a]=s,n=o,o=i}return 0!==n?r.words[a]=n:r.length--,r.strip()}(this,t,e):d(this,t,e)},g.prototype.makeRBT=function(t){for(var e=new Array(t),r=a.prototype._countBits(t)-1,n=0;n<t;n++)e[n]=this.revBin(n,r,t);return e},g.prototype.revBin=function(t,e,r){if(0===t||t===r-1)return t;for(var n=0,i=0;i<e;i++)n|=(1&t)<<e-i-1,t>>=1;return n},g.prototype.permute=function(t,e,r,n,i,a){for(var o=0;o<a;o++)n[o]=e[t[o]],i[o]=r[t[o]]},g.prototype.transform=function(t,e,r,n,i,a){this.permute(a,t,e,r,n,i);for(var o=1;o<i;o<<=1)for(var s=o<<1,l=Math.cos(2*Math.PI/s),c=Math.sin(2*Math.PI/s),u=0;u<i;u+=s)for(var f=l,h=c,p=0;p<o;p++){var d=r[u+p],g=n[u+p],m=r[u+p+o],v=n[u+p+o],y=f*m-h*v;v=f*v+h*m,m=y,r[u+p]=d+m,n[u+p]=g+v,r[u+p+o]=d-m,n[u+p+o]=g-v,p!==s&&(y=l*f-c*h,h=l*h+c*f,f=y)}},g.prototype.guessLen13b=function(t,e){var r=1|Math.max(e,t),n=1&r,i=0;for(r=r/2|0;r;r>>>=1)i++;return 1<<i+1+n},g.prototype.conjugate=function(t,e,r){if(!(r<=1))for(var n=0;n<r/2;n++){var i=t[n];t[n]=t[r-n-1],t[r-n-1]=i,i=e[n],e[n]=-e[r-n-1],e[r-n-1]=-i}},g.prototype.normalize13b=function(t,e){for(var r=0,n=0;n<e/2;n++){var i=8192*Math.round(t[2*n+1]/e)+Math.round(t[2*n]/e)+r;t[n]=67108863&i,r=i<67108864?0:i/67108864|0}return t},g.prototype.convert13b=function(t,e,r,i){for(var a=0,o=0;o<e;o++)a+=0|t[o],r[2*o]=8191&a,a>>>=13,r[2*o+1]=8191&a,a>>>=13;for(o=2*e;o<i;++o)r[o]=0;n(0===a),n(0==(-8192&a))},g.prototype.stub=function(t){for(var e=new Array(t),r=0;r<t;r++)e[r]=0;return e},g.prototype.mulp=function(t,e,r){var n=2*this.guessLen13b(t.length,e.length),i=this.makeRBT(n),a=this.stub(n),o=new Array(n),s=new Array(n),l=new Array(n),c=new Array(n),u=new Array(n),f=new Array(n),h=r.words;h.length=n,this.convert13b(t.words,t.length,o,n),this.convert13b(e.words,e.length,c,n),this.transform(o,a,s,l,n,i),this.transform(c,a,u,f,n,i);for(var p=0;p<n;p++){var d=s[p]*u[p]-l[p]*f[p];l[p]=s[p]*f[p]+l[p]*u[p],s[p]=d}return this.conjugate(s,l,n),this.transform(s,l,h,a,n,i),this.conjugate(h,a,n),this.normalize13b(h,n),r.negative=t.negative^e.negative,r.length=t.length+e.length,r.strip()},a.prototype.mul=function(t){var e=new a(null);return e.words=new Array(this.length+t.length),this.mulTo(t,e)},a.prototype.mulf=function(t){var e=new a(null);return e.words=new Array(this.length+t.length),d(this,t,e)},a.prototype.imul=function(t){return this.clone().mulTo(t,this)},a.prototype.imuln=function(t){n("number"==typeof t),n(t<67108864);for(var e=0,r=0;r<this.length;r++){var i=(0|this.words[r])*t,a=(67108863&i)+(67108863&e);e>>=26,e+=i/67108864|0,e+=a>>>26,this.words[r]=67108863&a}return 0!==e&&(this.words[r]=e,this.length++),this},a.prototype.muln=function(t){return this.clone().imuln(t)},a.prototype.sqr=function(){return this.mul(this)},a.prototype.isqr=function(){return this.imul(this.clone())},a.prototype.pow=function(t){var e=function(t){for(var e=new Array(t.bitLength()),r=0;r<e.length;r++){var n=r/26|0,i=r%26;e[r]=(t.words[n]&1<<i)>>>i}return e}(t);if(0===e.length)return new a(1);for(var r=this,n=0;n<e.length&&0===e[n];n++,r=r.sqr());if(++n<e.length)for(var i=r.sqr();n<e.length;n++,i=i.sqr())0!==e[n]&&(r=r.mul(i));return r},a.prototype.iushln=function(t){n("number"==typeof t&&t>=0);var e,r=t%26,i=(t-r)/26,a=67108863>>>26-r<<26-r;if(0!==r){var o=0;for(e=0;e<this.length;e++){var s=this.words[e]&a,l=(0|this.words[e])-s<<r;this.words[e]=l|o,o=s>>>26-r}o&&(this.words[e]=o,this.length++)}if(0!==i){for(e=this.length-1;e>=0;e--)this.words[e+i]=this.words[e];for(e=0;e<i;e++)this.words[e]=0;this.length+=i}return this.strip()},a.prototype.ishln=function(t){return n(0===this.negative),this.iushln(t)},a.prototype.iushrn=function(t,e,r){var i;n("number"==typeof t&&t>=0),i=e?(e-e%26)/26:0;var a=t%26,o=Math.min((t-a)/26,this.length),s=67108863^67108863>>>a<<a,l=r;if(i-=o,i=Math.max(0,i),l){for(var c=0;c<o;c++)l.words[c]=this.words[c];l.length=o}if(0===o);else if(this.length>o)for(this.length-=o,c=0;c<this.length;c++)this.words[c]=this.words[c+o];else this.words[0]=0,this.length=1;var u=0;for(c=this.length-1;c>=0&&(0!==u||c>=i);c--){var f=0|this.words[c];this.words[c]=u<<26-a|f>>>a,u=f&s}return l&&0!==u&&(l.words[l.length++]=u),0===this.length&&(this.words[0]=0,this.length=1),this.strip()},a.prototype.ishrn=function(t,e,r){return n(0===this.negative),this.iushrn(t,e,r)},a.prototype.shln=function(t){return this.clone().ishln(t)},a.prototype.ushln=function(t){return this.clone().iushln(t)},a.prototype.shrn=function(t){return this.clone().ishrn(t)},a.prototype.ushrn=function(t){return this.clone().iushrn(t)},a.prototype.testn=function(t){n("number"==typeof t&&t>=0);var e=t%26,r=(t-e)/26,i=1<<e;return!(this.length<=r)&&!!(this.words[r]&i)},a.prototype.imaskn=function(t){n("number"==typeof t&&t>=0);var e=t%26,r=(t-e)/26;if(n(0===this.negative,"imaskn works only with positive numbers"),this.length<=r)return this;if(0!==e&&r++,this.length=Math.min(r,this.length),0!==e){var i=67108863^67108863>>>e<<e;this.words[this.length-1]&=i}return this.strip()},a.prototype.maskn=function(t){return this.clone().imaskn(t)},a.prototype.iaddn=function(t){return n("number"==typeof t),n(t<67108864),t<0?this.isubn(-t):0!==this.negative?1===this.length&&(0|this.words[0])<t?(this.words[0]=t-(0|this.words[0]),this.negative=0,this):(this.negative=0,this.isubn(t),this.negative=1,this):this._iaddn(t)},a.prototype._iaddn=function(t){this.words[0]+=t;for(var e=0;e<this.length&&this.words[e]>=67108864;e++)this.words[e]-=67108864,e===this.length-1?this.words[e+1]=1:this.words[e+1]++;return this.length=Math.max(this.length,e+1),this},a.prototype.isubn=function(t){if(n("number"==typeof t),n(t<67108864),t<0)return this.iaddn(-t);if(0!==this.negative)return this.negative=0,this.iaddn(t),this.negative=1,this;if(this.words[0]-=t,1===this.length&&this.words[0]<0)this.words[0]=-this.words[0],this.negative=1;else for(var e=0;e<this.length&&this.words[e]<0;e++)this.words[e]+=67108864,this.words[e+1]-=1;return this.strip()},a.prototype.addn=function(t){return this.clone().iaddn(t)},a.prototype.subn=function(t){return this.clone().isubn(t)},a.prototype.iabs=function(){return this.negative=0,this},a.prototype.abs=function(){return this.clone().iabs()},a.prototype._ishlnsubmul=function(t,e,r){var i,a,o=t.length+r;this._expand(o);var s=0;for(i=0;i<t.length;i++){a=(0|this.words[i+r])+s;var l=(0|t.words[i])*e;s=((a-=67108863&l)>>26)-(l/67108864|0),this.words[i+r]=67108863&a}for(;i<this.length-r;i++)s=(a=(0|this.words[i+r])+s)>>26,this.words[i+r]=67108863&a;if(0===s)return this.strip();for(n(-1===s),s=0,i=0;i<this.length;i++)s=(a=-(0|this.words[i])+s)>>26,this.words[i]=67108863&a;return this.negative=1,this.strip()},a.prototype._wordDiv=function(t,e){var r=(this.length,t.length),n=this.clone(),i=t,o=0|i.words[i.length-1];0!==(r=26-this._countBits(o))&&(i=i.ushln(r),n.iushln(r),o=0|i.words[i.length-1]);var s,l=n.length-i.length;if("mod"!==e){(s=new a(null)).length=l+1,s.words=new Array(s.length);for(var c=0;c<s.length;c++)s.words[c]=0}var u=n.clone()._ishlnsubmul(i,1,l);0===u.negative&&(n=u,s&&(s.words[l]=1));for(var f=l-1;f>=0;f--){var h=67108864*(0|n.words[i.length+f])+(0|n.words[i.length+f-1]);for(h=Math.min(h/o|0,67108863),n._ishlnsubmul(i,h,f);0!==n.negative;)h--,n.negative=0,n._ishlnsubmul(i,1,f),n.isZero()||(n.negative^=1);s&&(s.words[f]=h)}return s&&s.strip(),n.strip(),"div"!==e&&0!==r&&n.iushrn(r),{div:s||null,mod:n}},a.prototype.divmod=function(t,e,r){return n(!t.isZero()),this.isZero()?{div:new a(0),mod:new a(0)}:0!==this.negative&&0===t.negative?(s=this.neg().divmod(t,e),"mod"!==e&&(i=s.div.neg()),"div"!==e&&(o=s.mod.neg(),r&&0!==o.negative&&o.iadd(t)),{div:i,mod:o}):0===this.negative&&0!==t.negative?(s=this.divmod(t.neg(),e),"mod"!==e&&(i=s.div.neg()),{div:i,mod:s.mod}):0!=(this.negative&t.negative)?(s=this.neg().divmod(t.neg(),e),"div"!==e&&(o=s.mod.neg(),r&&0!==o.negative&&o.isub(t)),{div:s.div,mod:o}):t.length>this.length||this.cmp(t)<0?{div:new a(0),mod:this}:1===t.length?"div"===e?{div:this.divn(t.words[0]),mod:null}:"mod"===e?{div:null,mod:new a(this.modn(t.words[0]))}:{div:this.divn(t.words[0]),mod:new a(this.modn(t.words[0]))}:this._wordDiv(t,e);var i,o,s},a.prototype.div=function(t){return this.divmod(t,"div",!1).div},a.prototype.mod=function(t){return this.divmod(t,"mod",!1).mod},a.prototype.umod=function(t){return this.divmod(t,"mod",!0).mod},a.prototype.divRound=function(t){var e=this.divmod(t);if(e.mod.isZero())return e.div;var r=0!==e.div.negative?e.mod.isub(t):e.mod,n=t.ushrn(1),i=t.andln(1),a=r.cmp(n);return a<0||1===i&&0===a?e.div:0!==e.div.negative?e.div.isubn(1):e.div.iaddn(1)},a.prototype.modn=function(t){n(t<=67108863);for(var e=(1<<26)%t,r=0,i=this.length-1;i>=0;i--)r=(e*r+(0|this.words[i]))%t;return r},a.prototype.idivn=function(t){n(t<=67108863);for(var e=0,r=this.length-1;r>=0;r--){var i=(0|this.words[r])+67108864*e;this.words[r]=i/t|0,e=i%t}return this.strip()},a.prototype.divn=function(t){return this.clone().idivn(t)},a.prototype.egcd=function(t){n(0===t.negative),n(!t.isZero());var e=this,r=t.clone();e=0!==e.negative?e.umod(t):e.clone();for(var i=new a(1),o=new a(0),s=new a(0),l=new a(1),c=0;e.isEven()&&r.isEven();)e.iushrn(1),r.iushrn(1),++c;for(var u=r.clone(),f=e.clone();!e.isZero();){for(var h=0,p=1;0==(e.words[0]&p)&&h<26;++h,p<<=1);if(h>0)for(e.iushrn(h);h-- >0;)(i.isOdd()||o.isOdd())&&(i.iadd(u),o.isub(f)),i.iushrn(1),o.iushrn(1);for(var d=0,g=1;0==(r.words[0]&g)&&d<26;++d,g<<=1);if(d>0)for(r.iushrn(d);d-- >0;)(s.isOdd()||l.isOdd())&&(s.iadd(u),l.isub(f)),s.iushrn(1),l.iushrn(1);e.cmp(r)>=0?(e.isub(r),i.isub(s),o.isub(l)):(r.isub(e),s.isub(i),l.isub(o))}return{a:s,b:l,gcd:r.iushln(c)}},a.prototype._invmp=function(t){n(0===t.negative),n(!t.isZero());var e=this,r=t.clone();e=0!==e.negative?e.umod(t):e.clone();for(var i,o=new a(1),s=new a(0),l=r.clone();e.cmpn(1)>0&&r.cmpn(1)>0;){for(var c=0,u=1;0==(e.words[0]&u)&&c<26;++c,u<<=1);if(c>0)for(e.iushrn(c);c-- >0;)o.isOdd()&&o.iadd(l),o.iushrn(1);for(var f=0,h=1;0==(r.words[0]&h)&&f<26;++f,h<<=1);if(f>0)for(r.iushrn(f);f-- >0;)s.isOdd()&&s.iadd(l),s.iushrn(1);e.cmp(r)>=0?(e.isub(r),o.isub(s)):(r.isub(e),s.isub(o))}return(i=0===e.cmpn(1)?o:s).cmpn(0)<0&&i.iadd(t),i},a.prototype.gcd=function(t){if(this.isZero())return t.abs();if(t.isZero())return this.abs();var e=this.clone(),r=t.clone();e.negative=0,r.negative=0;for(var n=0;e.isEven()&&r.isEven();n++)e.iushrn(1),r.iushrn(1);for(;;){for(;e.isEven();)e.iushrn(1);for(;r.isEven();)r.iushrn(1);var i=e.cmp(r);if(i<0){var a=e;e=r,r=a}else if(0===i||0===r.cmpn(1))break;e.isub(r)}return r.iushln(n)},a.prototype.invm=function(t){return this.egcd(t).a.umod(t)},a.prototype.isEven=function(){return 0==(1&this.words[0])},a.prototype.isOdd=function(){return 1==(1&this.words[0])},a.prototype.andln=function(t){return this.words[0]&t},a.prototype.bincn=function(t){n("number"==typeof t);var e=t%26,r=(t-e)/26,i=1<<e;if(this.length<=r)return this._expand(r+1),this.words[r]|=i,this;for(var a=i,o=r;0!==a&&o<this.length;o++){var s=0|this.words[o];a=(s+=a)>>>26,s&=67108863,this.words[o]=s}return 0!==a&&(this.words[o]=a,this.length++),this},a.prototype.isZero=function(){return 1===this.length&&0===this.words[0]},a.prototype.cmpn=function(t){var e,r=t<0;if(0!==this.negative&&!r)return-1;if(0===this.negative&&r)return 1;if(this.strip(),this.length>1)e=1;else{r&&(t=-t),n(t<=67108863,"Number is too big");var i=0|this.words[0];e=i===t?0:i<t?-1:1}return 0!==this.negative?0|-e:e},a.prototype.cmp=function(t){if(0!==this.negative&&0===t.negative)return-1;if(0===this.negative&&0!==t.negative)return 1;var e=this.ucmp(t);return 0!==this.negative?0|-e:e},a.prototype.ucmp=function(t){if(this.length>t.length)return 1;if(this.length<t.length)return-1;for(var e=0,r=this.length-1;r>=0;r--){var n=0|this.words[r],i=0|t.words[r];if(n!==i){n<i?e=-1:n>i&&(e=1);break}}return e},a.prototype.gtn=function(t){return 1===this.cmpn(t)},a.prototype.gt=function(t){return 1===this.cmp(t)},a.prototype.gten=function(t){return this.cmpn(t)>=0},a.prototype.gte=function(t){return this.cmp(t)>=0},a.prototype.ltn=function(t){return-1===this.cmpn(t)},a.prototype.lt=function(t){return-1===this.cmp(t)},a.prototype.lten=function(t){return this.cmpn(t)<=0},a.prototype.lte=function(t){return this.cmp(t)<=0},a.prototype.eqn=function(t){return 0===this.cmpn(t)},a.prototype.eq=function(t){return 0===this.cmp(t)},a.red=function(t){return new w(t)},a.prototype.toRed=function(t){return n(!this.red,"Already a number in reduction context"),n(0===this.negative,"red works only with positives"),t.convertTo(this)._forceRed(t)},a.prototype.fromRed=function(){return n(this.red,"fromRed works only with numbers in reduction context"),this.red.convertFrom(this)},a.prototype._forceRed=function(t){return this.red=t,this},a.prototype.forceRed=function(t){return n(!this.red,"Already a number in reduction context"),this._forceRed(t)},a.prototype.redAdd=function(t){return n(this.red,"redAdd works only with red numbers"),this.red.add(this,t)},a.prototype.redIAdd=function(t){return n(this.red,"redIAdd works only with red numbers"),this.red.iadd(this,t)},a.prototype.redSub=function(t){return n(this.red,"redSub works only with red numbers"),this.red.sub(this,t)},a.prototype.redISub=function(t){return n(this.red,"redISub works only with red numbers"),this.red.isub(this,t)},a.prototype.redShl=function(t){return n(this.red,"redShl works only with red numbers"),this.red.shl(this,t)},a.prototype.redMul=function(t){return n(this.red,"redMul works only with red numbers"),this.red._verify2(this,t),this.red.mul(this,t)},a.prototype.redIMul=function(t){return n(this.red,"redMul works only with red numbers"),this.red._verify2(this,t),this.red.imul(this,t)},a.prototype.redSqr=function(){return n(this.red,"redSqr works only with red numbers"),this.red._verify1(this),this.red.sqr(this)},a.prototype.redISqr=function(){return n(this.red,"redISqr works only with red numbers"),this.red._verify1(this),this.red.isqr(this)},a.prototype.redSqrt=function(){return n(this.red,"redSqrt works only with red numbers"),this.red._verify1(this),this.red.sqrt(this)},a.prototype.redInvm=function(){return n(this.red,"redInvm works only with red numbers"),this.red._verify1(this),this.red.invm(this)},a.prototype.redNeg=function(){return n(this.red,"redNeg works only with red numbers"),this.red._verify1(this),this.red.neg(this)},a.prototype.redPow=function(t){return n(this.red&&!t.red,"redPow(normalNum)"),this.red._verify1(this),this.red.pow(this,t)};var m={k256:null,p224:null,p192:null,p25519:null};function v(t,e){this.name=t,this.p=new a(e,16),this.n=this.p.bitLength(),this.k=new a(1).iushln(this.n).isub(this.p),this.tmp=this._tmp()}function y(){v.call(this,"k256","ffffffff ffffffff ffffffff ffffffff ffffffff ffffffff fffffffe fffffc2f")}function x(){v.call(this,"p224","ffffffff ffffffff ffffffff ffffffff 00000000 00000000 00000001")}function b(){v.call(this,"p192","ffffffff ffffffff ffffffff fffffffe ffffffff ffffffff")}function _(){v.call(this,"25519","7fffffffffffffff ffffffffffffffff ffffffffffffffff ffffffffffffffed")}function w(t){if("string"==typeof t){var e=a._prime(t);this.m=e.p,this.prime=e}else n(t.gtn(1),"modulus must be greater than 1"),this.m=t,this.prime=null}function T(t){w.call(this,t),this.shift=this.m.bitLength(),this.shift%26!=0&&(this.shift+=26-this.shift%26),this.r=new a(1).iushln(this.shift),this.r2=this.imod(this.r.sqr()),this.rinv=this.r._invmp(this.m),this.minv=this.rinv.mul(this.r).isubn(1).div(this.m),this.minv=this.minv.umod(this.r),this.minv=this.r.sub(this.minv)}v.prototype._tmp=function(){var t=new a(null);return t.words=new Array(Math.ceil(this.n/13)),t},v.prototype.ireduce=function(t){var e,r=t;do{this.split(r,this.tmp),e=(r=(r=this.imulK(r)).iadd(this.tmp)).bitLength()}while(e>this.n);var n=e<this.n?-1:r.ucmp(this.p);return 0===n?(r.words[0]=0,r.length=1):n>0?r.isub(this.p):r.strip(),r},v.prototype.split=function(t,e){t.iushrn(this.n,0,e)},v.prototype.imulK=function(t){return t.imul(this.k)},i(y,v),y.prototype.split=function(t,e){for(var r=Math.min(t.length,9),n=0;n<r;n++)e.words[n]=t.words[n];if(e.length=r,t.length<=9)return t.words[0]=0,void(t.length=1);var i=t.words[9];for(e.words[e.length++]=4194303&i,n=10;n<t.length;n++){var a=0|t.words[n];t.words[n-10]=(4194303&a)<<4|i>>>22,i=a}i>>>=22,t.words[n-10]=i,0===i&&t.length>10?t.length-=10:t.length-=9},y.prototype.imulK=function(t){t.words[t.length]=0,t.words[t.length+1]=0,t.length+=2;for(var e=0,r=0;r<t.length;r++){var n=0|t.words[r];e+=977*n,t.words[r]=67108863&e,e=64*n+(e/67108864|0)}return 0===t.words[t.length-1]&&(t.length--,0===t.words[t.length-1]&&t.length--),t},i(x,v),i(b,v),i(_,v),_.prototype.imulK=function(t){for(var e=0,r=0;r<t.length;r++){var n=19*(0|t.words[r])+e,i=67108863&n;n>>>=26,t.words[r]=i,e=n}return 0!==e&&(t.words[t.length++]=e),t},a._prime=function(t){if(m[t])return m[t];var e;if("k256"===t)e=new y;else if("p224"===t)e=new x;else if("p192"===t)e=new b;else{if("p25519"!==t)throw new Error("Unknown prime "+t);e=new _}return m[t]=e,e},w.prototype._verify1=function(t){n(0===t.negative,"red works only with positives"),n(t.red,"red works only with red numbers")},w.prototype._verify2=function(t,e){n(0==(t.negative|e.negative),"red works only with positives"),n(t.red&&t.red===e.red,"red works only with red numbers")},w.prototype.imod=function(t){return this.prime?this.prime.ireduce(t)._forceRed(this):t.umod(this.m)._forceRed(this)},w.prototype.neg=function(t){return t.isZero()?t.clone():this.m.sub(t)._forceRed(this)},w.prototype.add=function(t,e){this._verify2(t,e);var r=t.add(e);return r.cmp(this.m)>=0&&r.isub(this.m),r._forceRed(this)},w.prototype.iadd=function(t,e){this._verify2(t,e);var r=t.iadd(e);return r.cmp(this.m)>=0&&r.isub(this.m),r},w.prototype.sub=function(t,e){this._verify2(t,e);var r=t.sub(e);return r.cmpn(0)<0&&r.iadd(this.m),r._forceRed(this)},w.prototype.isub=function(t,e){this._verify2(t,e);var r=t.isub(e);return r.cmpn(0)<0&&r.iadd(this.m),r},w.prototype.shl=function(t,e){return this._verify1(t),this.imod(t.ushln(e))},w.prototype.imul=function(t,e){return this._verify2(t,e),this.imod(t.imul(e))},w.prototype.mul=function(t,e){return this._verify2(t,e),this.imod(t.mul(e))},w.prototype.isqr=function(t){return this.imul(t,t.clone())},w.prototype.sqr=function(t){return this.mul(t,t)},w.prototype.sqrt=function(t){if(t.isZero())return t.clone();var e=this.m.andln(3);if(n(e%2==1),3===e){var r=this.m.add(new a(1)).iushrn(2);return this.pow(t,r)}for(var i=this.m.subn(1),o=0;!i.isZero()&&0===i.andln(1);)o++,i.iushrn(1);n(!i.isZero());var s=new a(1).toRed(this),l=s.redNeg(),c=this.m.subn(1).iushrn(1),u=this.m.bitLength();for(u=new a(2*u*u).toRed(this);0!==this.pow(u,c).cmp(l);)u.redIAdd(l);for(var f=this.pow(u,i),h=this.pow(t,i.addn(1).iushrn(1)),p=this.pow(t,i),d=o;0!==p.cmp(s);){for(var g=p,m=0;0!==g.cmp(s);m++)g=g.redSqr();n(m<d);var v=this.pow(f,new a(1).iushln(d-m-1));h=h.redMul(v),f=v.redSqr(),p=p.redMul(f),d=m}return h},w.prototype.invm=function(t){var e=t._invmp(this.m);return 0!==e.negative?(e.negative=0,this.imod(e).redNeg()):this.imod(e)},w.prototype.pow=function(t,e){if(e.isZero())return new a(1).toRed(this);if(0===e.cmpn(1))return t.clone();var r=new Array(16);r[0]=new a(1).toRed(this),r[1]=t;for(var n=2;n<r.length;n++)r[n]=this.mul(r[n-1],t);var i=r[0],o=0,s=0,l=e.bitLength()%26;for(0===l&&(l=26),n=e.length-1;n>=0;n--){for(var c=e.words[n],u=l-1;u>=0;u--){var 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/*!
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*
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27. Error Minimization, untuk meningkatkan akurasi hasil simulasi, jumlah data yang digunakan perlu diperbanyak, karena visualisasi hanya merupakan pendekatan dari dataset yang tersedia. Dengan semakin banyaknya titik data, pola distribusi suhu dapat lebih jelas terbaca, sehingga kesalahan dalam interpolasi atau aproksimasi dapat dikurangi. Selain itu, pemilihan metode curve fitting yang sesuai, seperti polinomial orde lebih tinggi atau spline interpolation, juga dapat membantu meningkatkan ketepatan hasil.
28. Verification and Validation, keabsahan hasil simulasi harus dikonfirmasi dengan membandingkannya terhadap teori yang sudah ada, seperti hukum Fourier dalam perpindahan panas. Validasi dapat dilakukan dengan membandingkan hasil numerik dengan data eksperimen atau solusi analitis yang telah terbukti kebenarannya. Manusia, dengan anugerah akal sehat dari Allah SWT, memiliki kemampuan untuk menilai apakah hasil simulasi ini masuk akal dan sesuai dengan prinsip fisika yang berlaku.
29. Iterative Approach, metode iteratif memungkinkan simulasi dijalankan secara berulang dengan berbagai parameter, seperti perubahan konduktivitas termal, suhu awal, atau kondisi batas, untuk memastikan keakuratan dan stabilitas hasil. Selain itu, iterasi juga dapat digunakan untuk menyempurnakan model dengan menyesuaikan grid atau resolusi numerik, sehingga solusi yang diperoleh lebih presisi dan sesuai dengan kondisi nyata.
30. Sustainability Integration, pendekatan simulasi ini mendukung keberlanjutan karena mengurangi kebutuhan akan eksperimen fisik yang mahal dan berpotensi menghasilkan limbah. Dengan memanfaatkan model numerik, analisis dapat dilakukan dengan lebih cepat dan efisien tanpa memerlukan bahan uji nyata. Selain itu, penggunaan daya komputasi yang rendah juga menjadikan metode ini lebih hemat energi dibandingkan simulasi dengan resolusi yang sangat tinggi.
31. Communication Effectiveness, penyajian hasil dalam bentuk curve fitting plot dan heatmap bertujuan untuk mempermudah interpretasi distribusi temperatur. Heatmap memberikan gambaran menyeluruh mengenai pola perpindahan panas pada seluruh plat, sementara curve fitting plot berfungsi untuk menganalisis perubahan suhu secara lebih detail pada titik-titik tertentu. Dengan kombinasi kedua metode ini, hasil simulasi dapat dikomunikasikan dengan lebih efektif kepada berbagai kalangan, termasuk insinyur, peneliti, dan praktisi industri.
32. Alignment with DAI5 Framework, seluruh proses analisis dan penyelesaian masalah dalam simulasi distribusi temperatur pada plat ini telah dilakukan sesuai dengan framework DAI5. Tidak hanya mempertimbangkan aspek teknis, metode ini juga memperhatikan nilai etika, kebermanfaatan, dan keberlanjutan. Dengan pendekatan ini, ilmu teknik tidak hanya menjadi alat pemecahan masalah, tetapi juga bagian dari refleksi terhadap keteraturan alam yang telah Allah SWT ciptakan.
33. Documentation Quality, dokumentasi hasil simulasi disajikan melalui curve fitting plot gabungan dan heatmap untuk memberikan gambaran yang lebih komprehensif. Curve fitting plot gabungan digunakan untuk membandingkan pola distribusi suhu dari berbagai titik dalam satu visualisasi, sementara heatmap menampilkan sebaran temperatur secara menyeluruh di seluruh plat. Dengan kombinasi kedua metode ini, analisis menjadi lebih jelas, terstruktur, dan mudah dipahami.




https://drive.google.com/drive/folders/1_YtKPPp-oXs6sePybN1SbhzbT108n6B4?usp=sharing
Energi panas yang dialirkan dari sumber panas di ujung plat akan menyebar ke seluruh permukaan, dengan suhu yang perlahan menurun seiring bertambahnya jarak dari sumbernya. Proses ini menunjukkan bagaimana panas berpindah melalui material sesuai dengan hukum fisika, di mana energi cenderung mengalir dari daerah bersuhu tinggi ke daerah bersuhu lebih rendah hingga mencapai kesetimbangan termal. Analisis numerik memungkinkan kita untuk memahami pola penyebaran ini secara lebih detail, membantu dalam memvisualisasikan bagaimana panas bergerak dan berinteraksi dengan lingkungan sekitarnya.
Dengan pendekatan Integrasi Numerik dan 33 Kriteria Evaluasi Framework DAI5, fenomena perpindahan panas dapat dianalisis secara lebih sistematis dan akurat. Melalui metode seperti curve fitting plot dan heatmap, kita dapat melihat bagaimana distribusi suhu terbentuk dan bagaimana parameter fisik memengaruhi hasilnya. Pemahaman ini tidak hanya berguna dalam dunia akademik, tetapi juga dalam berbagai aplikasi teknik dan industri. Semoga tulisan ini memberikan wawasan yang lebih mendalam serta menginspirasi pendekatan yang lebih analitis dalam menyelesaikan permasalahan teknik.
Link Part 1: https://ccitonline.com/wp/2025/03/16/memahami-perpindahan-panas-dengan-33-kriteria-dai5-curve-fitting-heatmap-dan-pendekatan-numerik-rafi-radityatama-prasetyo-2306155376-metode-numerik-01/
Link Part 2: https://ccitonline.com/wp/2025/03/16/memahami-perpindahan-panas-dengan-33-kriteria-dai5-curve-fitting-heatmap-dan-pendekatan-numerik-rafi-radityatama-prasetyo-2306155376-metode-numerik-01-part-2/
Wassalamualaikum Warahmatullahi Wabarakatuh.
What we observe is not nature itself, but nature exposed to our method of questioning
Werner Heisenberg