| var bigInt=function(E){function k(a,b){if("undefined"===typeof a)return k[0];if("undefined"!==typeof b){var c;if(10===+b)c=l(a);else{c=b;var n=k[0],f=k[1],d=a.length;if(2<=c&&36>=c&&d<=ga/Math.log(c))c=new e(parseInt(a,c));else{c=l(c);var d=[],g,h="-"===a[0];for(g=h?1:0;g<a.length;g++){var q=a[g].toLowerCase(),u=q.charCodeAt(0);if(48<=u&&57>=u)d.push(l(q));else if(97<=u&&122>=u)d.push(l(q.charCodeAt(0)-87));else if("<"===q){q=g;do g++;while(">"!==a[g]);d.push(l(a.slice(q+1,g)))}else throw Error(q+ |
| " is not a valid character");}d.reverse();for(g=0;g<d.length;g++)n=n.add(d[g].times(f)),f=f.times(c);c=h?n.negate():n}}return c}return l(a)}function d(a,b){this.value=a;this.sign=b;this.isSmall=!1}function e(a){this.value=a;this.sign=0>a;this.isSmall=!0}function w(a){return-9007199254740992<a&&9007199254740992>a}function z(a){return 1E7>a?[a]:1E14>a?[a%1E7,Math.floor(a/1E7)]:[a%1E7,Math.floor(a/1E7)%1E7,Math.floor(a/1E14)]}function y(a){D(a);var b=a.length;if(4>b&&0>A(a,P))switch(b){case 0:return 0; |
| case 1:return a[0];case 2:return a[0]+1E7*a[1];default:return a[0]+1E7*(a[1]+1E7*a[2])}return a}function D(a){for(var b=a.length;0===a[--b];);a.length=b+1}function K(a){for(var b=Array(a),c=-1;++c<a;)b[c]=0;return b}function B(a){return 0<a?Math.floor(a):Math.ceil(a)}function S(a,b){var c=a.length,d=b.length,f=Array(c),m=0,g,e;for(e=0;e<d;e++)g=a[e]+b[e]+m,m=1E7<=g?1:0,f[e]=g-1E7*m;for(;e<c;)g=a[e]+m,m=1E7===g?1:0,f[e++]=g-1E7*m;0<m&&f.push(m);return f}function F(a,b){return a.length>=b.length?S(a, |
| b):S(b,a)}function L(a,b){var c=a.length,d=Array(c),f,e;for(e=0;e<c;e++)f=a[e]-1E7+b,b=Math.floor(f/1E7),d[e]=f-1E7*b,b+=1;for(;0<b;)d[e++]=b%1E7,b=Math.floor(b/1E7);return d}function G(a,b){var c=a.length,d=b.length,f=Array(c),e=0,g,h;for(g=0;g<d;g++)h=a[g]-e-b[g],0>h?(h+=1E7,e=1):e=0,f[g]=h;for(g=d;g<c;g++){h=a[g]-e;if(0>h)h+=1E7;else{f[g++]=h;break}f[g]=h}for(;g<c;g++)f[g]=a[g];D(f);return f}function M(a,b,c){var n=a.length,f=Array(n);b=-b;var m,g;for(m=0;m<n;m++)g=a[m]+b,b=Math.floor(g/1E7),g%= |
| 1E7,f[m]=0>g?g+1E7:g;f=y(f);return"number"===typeof f?(c&&(f=-f),new e(f)):new d(f,c)}function Q(a,b){var c=a.length,d=b.length,f=K(c+d),e,g,h,k;for(h=0;h<c;++h){k=a[h];for(var l=0;l<d;++l)e=b[l],e=k*e+f[h+l],g=Math.floor(e/1E7),f[h+l]=e-1E7*g,f[h+l+1]+=g}D(f);return f}function H(a,b){var c=a.length,d=Array(c),f=0,e,g;for(g=0;g<c;g++)e=a[g]*b+f,f=Math.floor(e/1E7),d[g]=e-1E7*f;for(;0<f;)d[g++]=f%1E7,f=Math.floor(f/1E7);return d}function T(a,b){for(var c=[];0<b--;)c.push(0);return c.concat(a)}function N(a, |
| b){var c=Math.max(a.length,b.length);if(30>=c)return Q(a,b);var c=Math.ceil(c/2),d=a.slice(c),f=a.slice(0,c),e=b.slice(c),g=b.slice(0,c),h=N(f,g),k=N(d,e),d=N(F(f,d),F(g,e)),c=F(F(h,T(G(G(d,h),k),c)),T(k,2*c));D(c);return c}function U(a,b,c){return 1E7>a?new d(H(b,a),c):new d(Q(b,z(a)),c)}function V(a){var b=a.length,c=K(b+b),d,f,e,g;for(e=0;e<b;e++){g=a[e];for(var h=0;h<b;h++)d=a[h],d=g*d+c[e+h],f=Math.floor(d/1E7),c[e+h]=d-1E7*f,c[e+h+1]+=f}D(c);return c}function W(a,b){var c=a.length,d=K(c),f, |
| e;e=0;for(--c;0<=c;--c)e=1E7*e+a[c],f=B(e/b),e-=f*b,d[c]=f|0;return[d,e|0]}function I(a,b){var c,n=l(b),f=a.value;c=n.value;if(0===c)throw Error("Cannot divide by zero");if(a.isSmall)return n.isSmall?[new e(B(f/c)),new e(f%c)]:[k[0],a];if(n.isSmall){if(1===c)return[a,k[0]];if(-1==c)return[a.negate(),k[0]];c=Math.abs(c);if(1E7>c)return c=W(f,c),f=y(c[0]),c=c[1],a.sign&&(c=-c),"number"===typeof f?(a.sign!==n.sign&&(f=-f),[new e(f),new e(c)]):[new d(f,a.sign!==n.sign),new e(c)];c=z(c)}var m=A(f,c);if(-1=== |
| m)return[k[0],a];if(0===m)return[k[a.sign===n.sign?1:-1],k[0]];if(200>=f.length+c.length){var g=c,h=f.length;c=g.length;var m=K(g.length),q=g[c-1],u=Math.ceil(1E7/(2*q)),f=H(f,u),g=H(g,u),p,r,x,t,v,w;f.length<=h&&f.push(0);g.push(0);q=g[c-1];for(p=h-c;0<=p;p--){h=9999999;f[p+c]!==q&&(h=Math.floor((1E7*f[p+c]+f[p+c-1])/q));x=r=0;v=g.length;for(t=0;t<v;t++)r+=h*g[t],w=Math.floor(r/1E7),x+=f[p+t]-(r-1E7*w),r=w,0>x?(f[p+t]=x+1E7,x=-1):(f[p+t]=x,x=0);for(;0!==x;){--h;for(t=r=0;t<v;t++)r+=f[p+t]-1E7+g[t], |
| 0>r?(f[p+t]=r+1E7,r=0):(f[p+t]=r,r=1);x+=r}m[p]=h}f=W(f,u)[0];c=[y(m),y(f)]}else{m=f.length;q=c.length;u=[];for(g=[];m;)if(g.unshift(f[--m]),0>A(g,c))u.push(0);else{h=g.length;p=1E7*g[h-1]+g[h-2];r=1E7*c[q-1]+c[q-2];h>q&&(p=1E7*(p+1));h=Math.ceil(p/r);do{p=H(c,h);if(0>=A(p,g))break;h--}while(h);u.push(h);g=G(g,p)}u.reverse();c=[y(u),y(g)]}f=c[0];n=a.sign!==n.sign;c=c[1];m=a.sign;"number"===typeof f?(n&&(f=-f),f=new e(f)):f=new d(f,n);"number"===typeof c?(m&&(c=-c),c=new e(c)):c=new d(c,m);return[f, |
| c]}function A(a,b){if(a.length!==b.length)return a.length>b.length?1:-1;for(var c=a.length-1;0<=c;c--)if(a[c]!==b[c])return a[c]>b[c]?1:-1;return 0}function X(a){a=a.abs();if(a.isUnit())return!1;if(a.equals(2)||a.equals(3)||a.equals(5))return!0;if(a.isEven()||a.isDivisibleBy(3)||a.isDivisibleBy(5))return!1;if(a.lesser(25))return!0}function Y(a){return("number"===typeof a||"string"===typeof a)&&1E7>=+Math.abs(a)||a instanceof d&&1>=a.value.length}function R(a,b,c){b=l(b);var d=a.isNegative(),e=b.isNegative(), |
| m=d?a.not():a,g=e?b.not():b;b=[];a=[];for(var h=!1,k=!1;!h||!k;)m.isZero()?(h=!0,b.push(d?1:0)):d?b.push(m.isEven()?1:0):b.push(m.isEven()?0:1),g.isZero()?(k=!0,a.push(e?1:0)):e?a.push(g.isEven()?1:0):a.push(g.isEven()?0:1),m=m.over(2),g=g.over(2);d=[];for(e=0;e<b.length;e++)d.push(c(b[e],a[e]));for(c=bigInt(d.pop()).negate().times(bigInt(2).pow(d.length));d.length;)c=c.add(bigInt(d.pop()).times(bigInt(2).pow(d.length)));return c}function O(a){a=a.value;a="number"===typeof a?a|1073741824:a[0]+1E7* |
| a[1]|1073758208;return a&-a}function Z(a,b){a=l(a);b=l(b);return a.greater(b)?a:b}function aa(a,b){a=l(a);b=l(b);return a.lesser(b)?a:b}function ba(a,b){a=l(a).abs();b=l(b).abs();if(a.equals(b))return a;if(a.isZero())return b;if(b.isZero())return a;for(var c=k[1],d;a.isEven()&&b.isEven();)d=Math.min(O(a),O(b)),a=a.divide(d),b=b.divide(d),c=c.multiply(d);for(;a.isEven();)a=a.divide(O(a));do{for(;b.isEven();)b=b.divide(O(b));a.greater(b)&&(d=b,b=a,a=d);b=b.subtract(a)}while(!b.isZero());return c.isUnit()? |
| a:a.multiply(c)}function ca(a){a=a.value;"number"===typeof a&&(a=[a]);return 1===a.length&&35>=a[0]?"0123456789abcdefghijklmnopqrstuvwxyz".charAt(a[0]):"<"+a+">"}function da(a,b){b=bigInt(b);if(b.isZero()){if(a.isZero())return"0";throw Error("Cannot convert nonzero numbers to base 0.");}if(b.equals(-1))return a.isZero()?"0":a.isNegative()?Array(1-a).join("10"):"1"+Array(+a).join("01");var c="";a.isNegative()&&b.isPositive()&&(c="-",a=a.abs());if(b.equals(1))return a.isZero()?"0":c+Array(+a+1).join(1); |
| for(var d=[],e=a,k;e.isNegative()||0<=e.compareAbs(b);)k=e.divmod(b),e=k.quotient,k=k.remainder,k.isNegative()&&(k=b.minus(k).abs(),e=e.next()),d.push(ca(k));d.push(ca(e));return c+d.reverse().join("")}function ea(a){if(w(+a)){var b=+a;if(b===B(b))return new e(b);throw"Invalid integer: "+a;}(b="-"===a[0])&&(a=a.slice(1));var c=a.split(/e/i);if(2<c.length)throw Error("Invalid integer: "+c.join("e"));if(2===c.length){a=c[1];"+"===a[0]&&(a=a.slice(1));a=+a;if(a!==B(a)||!w(a))throw Error("Invalid integer: "+ |
| a+" is not a valid exponent.");var c=c[0],n=c.indexOf(".");0<=n&&(a-=c.length-n-1,c=c.slice(0,n)+c.slice(n+1));if(0>a)throw Error("Cannot include negative exponent part for integers");a=c+=Array(a+1).join("0")}if(!/^([0-9][0-9]*)$/.test(a))throw Error("Invalid integer: "+a);for(var c=[],n=a.length,f=n-7;0<n;)c.push(+a.slice(f,n)),f-=7,0>f&&(f=0),n-=7;D(c);return new d(c,b)}function l(a){if("number"===typeof a){if(w(a)){if(a!==B(a))throw Error(a+" is not an integer.");a=new e(a)}else a=ea(a.toString()); |
| return a}return"string"===typeof a?ea(a):a}var P=z(9007199254740992),ga=Math.log(9007199254740992);d.prototype=Object.create(k.prototype);e.prototype=Object.create(k.prototype);d.prototype.add=function(a){a=l(a);if(this.sign!==a.sign)return this.subtract(a.negate());var b=this.value,c=a.value;return a.isSmall?new d(L(b,Math.abs(c)),this.sign):new d(F(b,c),this.sign)};d.prototype.plus=d.prototype.add;e.prototype.add=function(a){a=l(a);var b=this.value;if(0>b!==a.sign)return this.subtract(a.negate()); |
| var c=a.value;if(a.isSmall){if(w(b+c))return new e(b+c);c=z(Math.abs(c))}return new d(L(c,Math.abs(b)),0>b)};e.prototype.plus=e.prototype.add;d.prototype.subtract=function(a){var b=l(a);if(this.sign!==b.sign)return this.add(b.negate());a=this.value;var c=b.value;if(b.isSmall)return M(a,Math.abs(c),this.sign);b=this.sign;0<=A(a,c)?a=G(a,c):(a=G(c,a),b=!b);a=y(a);"number"===typeof a?(b&&(a=-a),a=new e(a)):a=new d(a,b);return a};d.prototype.minus=d.prototype.subtract;e.prototype.subtract=function(a){a= |
| l(a);var b=this.value;if(0>b!==a.sign)return this.add(a.negate());var c=a.value;return a.isSmall?new e(b-c):M(c,Math.abs(b),0<=b)};e.prototype.minus=e.prototype.subtract;d.prototype.negate=function(){return new d(this.value,!this.sign)};e.prototype.negate=function(){var a=this.sign,b=new e(-this.value);b.sign=!a;return b};d.prototype.abs=function(){return new d(this.value,!1)};e.prototype.abs=function(){return new e(Math.abs(this.value))};d.prototype.multiply=function(a){var b=l(a);a=this.value;var c= |
| b.value,e=this.sign!==b.sign;if(b.isSmall){if(0===c)return k[0];if(1===c)return this;if(-1===c)return this.negate();c=Math.abs(c);if(1E7>c)return new d(H(a,c),e);c=z(c)}var b=a.length,f=c.length;return 0<-.012*b-.012*f+1.5E-5*b*f?new d(N(a,c),e):new d(Q(a,c),e)};d.prototype.times=d.prototype.multiply;e.prototype._multiplyBySmall=function(a){return w(a.value*this.value)?new e(a.value*this.value):U(Math.abs(a.value),z(Math.abs(this.value)),this.sign!==a.sign)};d.prototype._multiplyBySmall=function(a){return 0=== |
| a.value?k[0]:1===a.value?this:-1===a.value?this.negate():U(Math.abs(a.value),this.value,this.sign!==a.sign)};e.prototype.multiply=function(a){return l(a)._multiplyBySmall(this)};e.prototype.times=e.prototype.multiply;d.prototype.square=function(){return new d(V(this.value),!1)};e.prototype.square=function(){var a=this.value*this.value;return w(a)?new e(a):new d(V(z(Math.abs(this.value))),!1)};d.prototype.divmod=function(a){a=I(this,a);return{quotient:a[0],remainder:a[1]}};e.prototype.divmod=d.prototype.divmod; |
| d.prototype.divide=function(a){return I(this,a)[0]};e.prototype.over=e.prototype.divide=d.prototype.over=d.prototype.divide;d.prototype.mod=function(a){return I(this,a)[1]};e.prototype.remainder=e.prototype.mod=d.prototype.remainder=d.prototype.mod;d.prototype.pow=function(a){var b=l(a),c=this.value;a=b.value;var d;if(0===a)return k[1];if(0===c)return k[0];if(1===c)return k[1];if(-1===c)return b.isEven()?k[1]:k[-1];if(b.sign)return k[0];if(!b.isSmall)throw Error("The exponent "+b.toString()+" is too large."); |
| if(this.isSmall&&w(d=Math.pow(c,a)))return new e(B(d));d=this;for(b=k[1];;){a&1&&(b=b.times(d),--a);if(0===a)break;a/=2;d=d.square()}return b};e.prototype.pow=d.prototype.pow;d.prototype.modPow=function(a,b){a=l(a);b=l(b);if(b.isZero())throw Error("Cannot take modPow with modulus 0");for(var c=k[1],d=this.mod(b);a.isPositive();){if(d.isZero())return k[0];a.isOdd()&&(c=c.multiply(d).mod(b));a=a.divide(2);d=d.square().mod(b)}return c};e.prototype.modPow=d.prototype.modPow;d.prototype.compareAbs=function(a){a= |
| l(a);return a.isSmall?1:A(this.value,a.value)};e.prototype.compareAbs=function(a){a=l(a);var b=Math.abs(this.value),c=a.value;return a.isSmall?(c=Math.abs(c),b===c?0:b>c?1:-1):-1};d.prototype.compare=function(a){if(Infinity===a)return-1;if(-Infinity===a)return 1;a=l(a);return this.sign!==a.sign?a.sign?1:-1:a.isSmall?this.sign?-1:1:A(this.value,a.value)*(this.sign?-1:1)};d.prototype.compareTo=d.prototype.compare;e.prototype.compare=function(a){if(Infinity===a)return-1;if(-Infinity===a)return 1;a=l(a); |
| var b=this.value,c=a.value;return a.isSmall?b==c?0:b>c?1:-1:0>b!==a.sign?0>b?-1:1:0>b?1:-1};e.prototype.compareTo=e.prototype.compare;d.prototype.equals=function(a){return 0===this.compare(a)};e.prototype.eq=e.prototype.equals=d.prototype.eq=d.prototype.equals;d.prototype.notEquals=function(a){return 0!==this.compare(a)};e.prototype.neq=e.prototype.notEquals=d.prototype.neq=d.prototype.notEquals;d.prototype.greater=function(a){return 0<this.compare(a)};e.prototype.gt=e.prototype.greater=d.prototype.gt= |
| d.prototype.greater;d.prototype.lesser=function(a){return 0>this.compare(a)};e.prototype.lt=e.prototype.lesser=d.prototype.lt=d.prototype.lesser;d.prototype.greaterOrEquals=function(a){return 0<=this.compare(a)};e.prototype.geq=e.prototype.greaterOrEquals=d.prototype.geq=d.prototype.greaterOrEquals;d.prototype.lesserOrEquals=function(a){return 0>=this.compare(a)};e.prototype.leq=e.prototype.lesserOrEquals=d.prototype.leq=d.prototype.lesserOrEquals;d.prototype.isEven=function(){return 0===(this.value[0]& |
| 1)};e.prototype.isEven=function(){return 0===(this.value&1)};d.prototype.isOdd=function(){return 1===(this.value[0]&1)};e.prototype.isOdd=function(){return 1===(this.value&1)};d.prototype.isPositive=function(){return!this.sign};e.prototype.isPositive=function(){return 0<this.value};d.prototype.isNegative=function(){return this.sign};e.prototype.isNegative=function(){return 0>this.value};d.prototype.isUnit=function(){return!1};e.prototype.isUnit=function(){return 1===Math.abs(this.value)};d.prototype.isZero= |
| function(){return!1};e.prototype.isZero=function(){return 0===this.value};d.prototype.isDivisibleBy=function(a){a=l(a);var b=a.value;return 0===b?!1:1===b?!0:2===b?this.isEven():this.mod(a).equals(k[0])};e.prototype.isDivisibleBy=d.prototype.isDivisibleBy;d.prototype.isPrime=function(){var a=X(this);if(a!==E)return a;for(var a=this.abs(),b=a.prev(),c=[2,3,5,7,11,13,17,19],d=b,e,l,g,h;d.isEven();)d=d.divide(2);for(g=0;g<c.length;g++)if(h=bigInt(c[g]).modPow(d,a),!h.equals(k[1])&&!h.equals(b)){l=!0; |
| for(e=d;l&&e.lesser(b);e=e.multiply(2))h=h.square().mod(a),h.equals(b)&&(l=!1);if(l)return!1}return!0};e.prototype.isPrime=d.prototype.isPrime;d.prototype.isProbablePrime=function(a){var b=X(this);if(b!==E)return b;b=this.abs();a=a===E?5:a;for(var c=0;c<a;c++)if(!bigInt.randBetween(2,b.minus(2)).modPow(b.prev(),b).isUnit())return!1;return!0};e.prototype.isProbablePrime=d.prototype.isProbablePrime;d.prototype.next=function(){var a=this.value;return this.sign?M(a,1,this.sign):new d(L(a,1),this.sign)}; |
| e.prototype.next=function(){var a=this.value;return 9007199254740992>a+1?new e(a+1):new d(P,!1)};d.prototype.prev=function(){var a=this.value;return this.sign?new d(L(a,1),!0):M(a,1,this.sign)};e.prototype.prev=function(){var a=this.value;return-9007199254740992<a-1?new e(a-1):new d(P,!0)};for(var v=[1];1E7>=v[v.length-1];)v.push(2*v[v.length-1]);var J=v.length,fa=v[J-1];d.prototype.shiftLeft=function(a){if(!Y(a))throw Error(String(a)+" is too large for shifting.");a=+a;if(0>a)return this.shiftRight(-a); |
| for(var b=this;a>=J;)b=b.multiply(fa),a-=J-1;return b.multiply(v[a])};e.prototype.shiftLeft=d.prototype.shiftLeft;d.prototype.shiftRight=function(a){var b;if(!Y(a))throw Error(String(a)+" is too large for shifting.");a=+a;if(0>a)return this.shiftLeft(-a);for(b=this;a>=J;){if(b.isZero())return b;b=I(b,fa);b=b[1].isNegative()?b[0].prev():b[0];a-=J-1}b=I(b,v[a]);return b[1].isNegative()?b[0].prev():b[0]};e.prototype.shiftRight=d.prototype.shiftRight;d.prototype.not=function(){return this.negate().prev()}; |
| e.prototype.not=d.prototype.not;d.prototype.and=function(a){return R(this,a,function(a,c){return a&c})};e.prototype.and=d.prototype.and;d.prototype.or=function(a){return R(this,a,function(a,c){return a|c})};e.prototype.or=d.prototype.or;d.prototype.xor=function(a){return R(this,a,function(a,c){return a^c})};e.prototype.xor=d.prototype.xor;d.prototype.toString=function(a){a===E&&(a=10);if(10!==a)return da(this,a);a=this.value;for(var b=a.length,c=String(a[--b]),d;0<=--b;)d=String(a[b]),c+="0000000".slice(d.length)+ |
| d;return(this.sign?"-":"")+c};e.prototype.toString=function(a){a===E&&(a=10);return 10!=a?da(this,a):String(this.value)};d.prototype.valueOf=function(){return+this.toString()};d.prototype.toJSNumber=d.prototype.valueOf;e.prototype.valueOf=function(){return this.value};e.prototype.toJSNumber=e.prototype.valueOf;for(var C=0;1E3>C;C++)k[C]=new e(C),0<C&&(k[-C]=new e(-C));k.one=k[1];k.zero=k[0];k.minusOne=k[-1];k.max=Z;k.min=aa;k.gcd=ba;k.lcm=function(a,b){a=l(a).abs();b=l(b).abs();return a.divide(ba(a, |
| b)).multiply(b)};k.isInstance=function(a){return a instanceof d||a instanceof e};k.randBetween=function(a,b){a=l(a);b=l(b);var c=aa(a,b),k=Z(a,b).subtract(c);if(k.isSmall)return c.add(Math.round(Math.random()*k));for(var f=[],m=!0,g=k.value.length-1;0<=g;g--){var h=m?k.value[g]:1E7,q=B(Math.random()*h);f.unshift(q);q<h&&(m=!1)}f=y(f);return c.add("number"===typeof f?new e(f):new d(f,!1))};return k}();"undefined"!==typeof module&&module.hasOwnProperty("exports")&&(module.exports=bigInt); |
