// 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.div64 = function(x) {

     var low = Math.floor(this.toFP() / x.toFP()); // TODO: not exact enough

     if (low > __m32) {

         var hi = Math.floor(low / (__m32+1)) | 0;

         return hi.next32(low % (__m32+1));

     }

     return 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);

 };