// empty line needed here

 Number.prototype.add32 = function(x) { return (this + x) | 0; };

 Number.prototype.sub32 = function(x) { return (this - x) | 0; };

 Number.prototype.mul32 = function(x) { 

     return (((this * (x >> 16)) << 16) + this * (x & 0xFFFF)) | 0;

 };

 Number.prototype.toInt8 = function()  { return (this << 24) >> 24; };

 Number.prototype.toInt16 = function() { return (this << 16) >> 16; };

 var __m32 = 0xFFFFFFFF;

 Number.prototype.next32 = function(low) {

   if (this === 0) {

     return low;

   }

   var l = new Number(low);

   l.hi = this | 0;

   return l;

 };

 Number.prototype.high32 = function() { 

     return this.hi ? this.hi : (Math.floor(this / (__m32+1))) | 0;

 };

 Number.prototype.toInt32 = function() { return this | 0; };

 Number.prototype.toFP = function() {

     return this.hi ? this.hi * (__m32+1) + this : this;

 };

 Number.prototype.toLong = function() {

     var hi = (this > __m32) ? (Math.floor(this / (__m32+1))) | 0 : 0;

     return hi.next32(Math.floor(this % (__m32+1)));

 };

 Number.prototype.toExactString = function() {

     if (this.hi) {

         var res = 0;

         var a = [ 6,9,2,7,6,9,4,9,2,4 ];

         var s = '';

         var digit;

         var neg = this.hi < 0;

         if (neg) {

             var x = this.neg64();

             var hi = x.hi;

             var low = x;

         } else {

             var hi = this.hi;

             var low = this;

         }

         for (var i = 0; i < a.length; i++) {

             res += hi * a[i];

             var low_digit = low % 10;

             digit = (res % 10) + low_digit;

             low = Math.floor(low / 10);

             res = Math.floor(res / 10);

             if (digit >= 10) {

                 digit -= 10;

                 res++;

             }

             s = String(digit).concat(s);

         }

         return (neg ? '-' : '').concat(res).concat(s);

     }

     return String(this);

 };

 Number.prototype.add64 = function(x) {

     var low = this + x;

     carry = 0;

     if (low > __m32) {

         carry = 1;

         low -= (__m32+1);

     }

     var hi = (this.high32() + x.high32() + carry) | 0;

     return hi.next32(low);

 };

 Number.prototype.sub64 = function(x) {

     var low = this - x;

     carry = 0;

     if (low < 0) {

         carry = 1;

         low += (__m32+1);

     }

     var hi = (this.high32() - x.high32() - carry) | 0;

     return hi.next32(low);

 };

 Number.prototype.mul64 = function(x) {

     var low = this.mul32(x);

     low += (low < 0) ? (__m32+1) : 0;

     // first count upper 32 bits of (this.low * x.low)

     var hi_hi = 0;

     var hi_low = 0;

     var m = 1;

     for (var i = 0; i < 32; i++) {

         if (x & m) {

             hi_hi += this >>> 16;

             hi_low += this & 0xFFFF

         }

         hi_low >>= 1;

         hi_low += (hi_hi & 1) ? 0x8000 : 0;

         hi_hi >>= 1;

         m <<= 1;

     }

     var hi = (hi_hi << 16) + hi_low;

     var m1 = this.high32().mul32(x);

     var m2 = this.mul32(x.high32());

     hi = hi.add32(m1).add32(m2);

     return hi.next32(low);

 };

 Number.prototype.and64 = function(x) {

     var low = this & x;

     low += (low < 0) ? (__m32+1) : 0;

     if (this.hi && x.hi) {

         var hi = this.hi & x.hi;

         return hi.next32(low);

     };

     return low;

 };

 Number.prototype.or64 = function(x) {

     var low = this | x;

     low += (low < 0) ? (__m32+1) : 0;

     if (this.hi || x.hi) {

         var hi = this.hi | x.hi;

         return hi.next32(low);

     };

     return low;

 };

 Number.prototype.xor64 = function(x) {

     var low = this ^ x;

     low += (low < 0) ? (__m32+1) : 0;

     if (this.hi || x.hi) {

         var hi = this.hi ^ x.hi;

         return hi.next32(low);

     };

     return low;

 };

 Number.prototype.shl64 = function(x) {

     if (x >= 32) {

         var hi = this << (x - 32);

         return hi.next32(0);

     } else {

         var hi = this.high32() << x;

         var low_reminder = this >> (32 - x);

         hi |= low_reminder;

         var low = this << x;

         low += (low < 0) ? (__m32+1) : 0;

         return hi.next32(low);

     }

 };

 Number.prototype.shr64 = function(x) {

     if (x >= 32) {

         var low = this.high32() >> (x - 32);

         low += (low < 0) ? (__m32+1) : 0;

         return low;

     } else {

         var low = this >> x;

         var hi_reminder = this.high32() << (32 - x);

         low |= hi_reminder;

         low += (low < 0) ? (__m32+1) : 0;

         var hi = this.high32() >> x;

         return hi.next32(low);

     }

 };

 Number.prototype.ushr64 = function(x) {

     if (x >= 32) {

         var low = this.high32() >>> (x - 32);

         low += (low < 0) ? (__m32+1) : 0;

         return low;

     } else {

         var low = this >>> x;

         var hi_reminder = this.high32() << (32 - x);

         low |= hi_reminder;

         low += (low < 0) ? (__m32+1) : 0;

         var hi = this.high32() >>> x;

         return hi.next32(low);

     }

 };

 Number.prototype.compare64 = function(x) {

     if (this.hi == x.hi) {

         return (this == x) ? 0 : ((this < x) ? -1 : 1);

     }

     return (this.hi < x.hi) ? -1 : 1;

 };

 Number.prototype.neg64 = function() {

     var hi = this.high32();

     var low = this;

     if ((hi === 0) && (low < 0)) { return -low; }

     hi = ~hi;

     low = ~low;

     low += (low < 0) ? (__m32+1) : 0;

     var ret = hi.next32(low);

     return ret.add64(1);

 };

 function __initDivMod(numberPrototype) {

     function __Int64(hi32, lo32) {

         this.hi32 = hi32 | 0;

         this.lo32 = lo32 | 0;

         this.get32 = function(bitIndex) {

             var v0;

             var v1;

             bitIndex += 32;

             var selector = bitIndex >>> 5;

             switch (selector) {

                 case 0:

                     v0 = 0;

                     v1 = this.lo32;

                     break;

                 case 1:

                     v0 = this.lo32;

                     v1 = this.hi32;

                     break;

                 case 2:

                     v0 = this.hi32;

                     v1 = 0;

                     break

                 default:

                     return 0;

             }

             var shift = bitIndex & 31;

             if (shift === 0) {

                 return v0;

             }

             return (v1 << (32 - shift)) | (v0 >>> shift);

         }

         this.get16 = function(bitIndex) {

             return this.get32(bitIndex) & 0xffff;

         }

         this.set16 = function(bitIndex, value) {

             bitIndex += 32;

             var shift = bitIndex & 15;

             var svalue = (value & 0xffff) << shift; 

             var smask = 0xffff << shift;

             var selector = bitIndex >>> 4;

             switch (selector) {

                 case 0:

                     break;

                 case 1:

                     this.lo32 = (this.lo32 & ~(smask >>> 16))

                                     | (svalue >>> 16);

                     break;

                 case 2:

                     this.lo32 = (this.lo32 & ~smask) | svalue;

                     break;

                 case 3:

                     this.lo32 = (this.lo32 & ~(smask << 16))

                                     | (svalue << 16);

                     this.hi32 = (this.hi32 & ~(smask >>> 16))

                                     | (svalue >>> 16);

                     break;

                 case 4:

                     this.hi32 = (this.hi32 & ~smask) | svalue;

                     break;

                 case 5:

                     this.hi32 = (this.hi32 & ~(smask << 16))

                                     | (svalue << 16);

                     break;

             }

         }

         this.getDigit = function(index, shift) {

             return this.get16((index << 4) - shift);

         }

         this.getTwoDigits = function(index, shift) {

             return this.get32(((index - 1) << 4) - shift);

         }

         this.setDigit = function(index, shift, value) {

             this.set16((index << 4) - shift, value);

         }

         this.countSignificantDigits = function() {

             var sd;

             var remaining;

             if (this.hi32 === 0) {

                 if (this.lo32 === 0) {

                     return 0;

                 }

                 sd = 2;

                 remaining = this.lo32;

             } else {

                 sd = 4;

                 remaining = this.hi32;

             }

             if (remaining < 0) {

                 return sd;

             }

             return (remaining < 65536) ? sd - 1 : sd;

         }

         this.toNumber = function() {

             var lo32 = this.lo32;

             if (lo32 < 0) {

                 lo32 += 0x100000000;

             }

             return this.hi32.next32(lo32);

         }

     }

     function __countLeadingZeroes16(number) {

         var nlz = 0;

         if (number < 256) {

             nlz += 8;

             number <<= 8;

         }

         if (number < 4096) {

             nlz += 4;

             number <<= 4;

         }

         if (number < 16384) {

             nlz += 2;

             number <<= 2;

         }

         return (number < 32768) ? nlz + 1 : nlz;

     }

     // q = u / v; r = u - q * v;

     // v != 0

     function __div64(q, r, u, v) {

         var m = u.countSignificantDigits();

         var n = v.countSignificantDigits();

         q.hi32 = q.lo32 = 0;

         if (n === 1) {

             // v has single digit

             var vd = v.getDigit(0, 0);

             var carry = 0;

             for (var i = m - 1; i >= 0; --i) {

                 var ui = (carry << 16) | u.getDigit(i, 0);

                 if (ui < 0) {

                     ui += 0x100000000;

                 }

                 var qi = (ui / vd) | 0;

                 q.setDigit(i, 0, qi);

                 carry = ui - qi * vd;

             }

             r.hi32 = 0;

             r.lo32 = carry;

             return;

         }

         r.hi32 = u.hi32;  

         r.lo32 = u.lo32;

         if (m < n) {

             return;

         }

         // Normalize

         var nrm = __countLeadingZeroes16(v.getDigit(n - 1, 0));

         var vd1 = v.getDigit(n - 1, nrm);                

         var vd0 = v.getDigit(n - 2, nrm);

         for (var j = m - n; j >= 0; --j) {

             // Calculate qj estimate

             var ud21 = r.getTwoDigits(j + n, nrm);

             var ud2 = ud21 >>> 16;

             if (ud21 < 0) {

                 ud21 += 0x100000000;

             }

             var qest = (ud2 === vd1) ? 0xFFFF : ((ud21 / vd1) | 0);

             var rest = ud21 - qest * vd1;

             // 0 <= (qest - qj) <= 2

             // Refine qj estimate

             var ud0 = r.getDigit(j + n - 2, nrm);

             while ((qest * vd0) > ((rest * 0x10000) + ud0)) {

                 --qest;

                 rest += vd1;

             }

             // 0 <= (qest - qj) <= 1

             // Multiply and subtract

             var carry = 0;

             for (var i = 0; i < n; ++i) {

                 var vi = qest * v.getDigit(i, nrm);

                 var ui = r.getDigit(i + j, nrm) - carry - (vi & 0xffff);

                 r.setDigit(i + j, nrm, ui);

                 carry = (vi >>> 16) - (ui >> 16);

             }

             var uj = ud2 - carry;

             if (uj < 0) {

                 // qest - qj = 1

                 // Add back

                 --qest;

                 var carry = 0;

                 for (var i = 0; i < n; ++i) {

                     var ui = r.getDigit(i + j, nrm) + v.getDigit(i, nrm)

                                  + carry;

                     r.setDigit(i + j, nrm, ui);

                     carry = ui >> 16;

                 }

                 uj += carry;

             }

             q.setDigit(j, 0, qest);

             r.setDigit(j + n, nrm, uj);

         }

     }

     numberPrototype.div64 = function(x) {

         var negateResult = false;

         var u, v;

         if ((this.high32() & 0x80000000) != 0) {

             u = this.neg64();

             negateResult = !negateResult;

         } else {

             u = this;        

         }

         if ((x.high32() & 0x80000000) != 0) {

             v = x.neg64();

             negateResult = !negateResult;

         } else {

             v = x;

         }

         if ((v === 0) && (v.high32() === 0)) {

             // TODO: throw

         }

         if (u.high32() === 0) {

             if (v.high32() === 0) {

                 var result = (u / v) | 0;

                 return negateResult ? result.neg64() : result; 

             }

             return 0;

         }

         var u64 = new __Int64(u.high32(), u);

         var v64 = new __Int64(v.high32(), v);

         var q64 = new __Int64(0, 0);

         var r64 = new __Int64(0, 0);

         __div64(q64, r64, u64, v64);

         var result = q64.toNumber();

         return negateResult ? result.neg64() : result; 

     }

     numberPrototype.mod64 = function(x) {

         var negateResult = false;

         var u, v;

         if ((this.high32() & 0x80000000) != 0) {

             u = this.neg64();

             negateResult = !negateResult;

         } else {

             u = this;        

         }

         if ((x.high32() & 0x80000000) != 0) {

             v = x.neg64();

         } else {

             v = x;

         }

         if ((v === 0) && (v.high32() === 0)) {

             // TODO: throw

         }

         if (u.high32() === 0) {

             var result = (v.high32() === 0) ? (u % v) : u;

             return negateResult ? result.neg64() : result; 

         }

         var u64 = new __Int64(u.high32(), u);

         var v64 = new __Int64(v.high32(), v);

         var q64 = new __Int64(0, 0);

         var r64 = new __Int64(0, 0);

         __div64(q64, r64, u64, v64);

         var result = r64.toNumber();

         return negateResult ? result.neg64() : result; 

     }

 };

 __initDivMod(Number.prototype);