/*******************************************************************************

*                                                                              *

* Author    :  Angus Johnson                                                   *

* Version   :  5.0.2                                                           *

* Date      :  30 December 2012                                                *

* Website   :  http://www.angusj.com                                           *

* Copyright :  Angus Johnson 2010-2012                                         *

*                                                                              *

* License:                                                                     *

* Use, modification & distribution is subject to Boost Software License Ver 1. *

* http://www.boost.org/LICENSE_1_0.txt                                         *

*                                                                              *

* Attributions:                                                                *

* The code in this library is an extension of Bala Vatti's clipping algorithm: *

* "A generic solution to polygon clipping"                                     *

* Communications of the ACM, Vol 35, Issue 7 (July 1992) pp 56-63.             *

* http://portal.acm.org/citation.cfm?id=129906                                 *

*                                                                              *

* Computer graphics and geometric modeling: implementation and algorithms      *

* By Max K. Agoston                                                            *

* Springer; 1 edition (January 4, 2005)                                        *

* http://books.google.com/books?q=vatti+clipping+agoston                       *

*                                                                              *

* See also:                                                                    *

* "Polygon Offsetting by Computing Winding Numbers"                            *

* Paper no. DETC2005-85513 pp. 565-575                                         *

* ASME 2005 International Design Engineering Technical Conferences             *

* and Computers and Information in Engineering Conference (IDETC/CIE2005)      *

* September 24–28, 2005 , Long Beach, California, USA                          *

* http://www.me.berkeley.edu/~mcmains/pubs/DAC05OffsetPolygon.pdf              *

*                                                                              *

*******************************************************************************/

​

/*******************************************************************************

*                                                                              *

* Author    :  Timo                                                            *

* Version   :  5.0.2.2                                                         *

* Date      :  11 September 2013                                               *

*                                                                              *

* This is a translation of the C# Clipper library to Javascript.               *

* Int128 struct of C# is implemented using JSBN of Tom Wu.                     *

* Because Javascript lacks support for 64-bit integers, the space              *

* is a little more restricted than in C# version.                              *

*                                                                              *

* C# version has support for coordinate space:                                 *

* +-4611686018427387903 ( sqrt(2^127 -1)/2 )                                   *

* while Javascript version has support for space:                              *

* +-4503599627370495 ( sqrt(2^106 -1)/2 )                                      *

*                                                                              *

* Tom Wu's JSBN proved to be the fastest big integer library:                  *

* http://jsperf.com/big-integer-library-test                                   *

*                                                                              *

* This class can be made simpler when (if ever) 64-bit integer support comes.  *

*                                                                              *

*******************************************************************************/

​

/*******************************************************************************

*                                                                              *

* Basic JavaScript BN library - subset useful for RSA encryption.              *

* http://www-cs-students.stanford.edu/~tjw/jsbn/                               *

* Copyright (c) 2005  Tom Wu                                                   *

* All Rights Reserved.                                                         *

* See "LICENSE" for details:                                                   *

* http://www-cs-students.stanford.edu/~tjw/jsbn/LICENSE                        *

*                                                                              *

*******************************************************************************/

(function ()

{

  // "use strict";

  // Browser test to speedup performance critical functions

  var nav = navigator.userAgent.toString().toLowerCase();

  var browser = {};

  if ( nav.indexOf("chrome") != -1 && nav.indexOf("chromium") == -1 ) browser.chrome = 1; else browser.chrome = 0;

  if ( nav.indexOf("chromium") != -1 ) browser.chromium = 1; else browser.chromium = 0;

  if ( nav.indexOf("safari") != -1 && nav.indexOf("chrome") == -1 && nav.indexOf("chromium") == -1 ) browser.safari = 1; else browser.safari = 0;

  if ( nav.indexOf("firefox") != -1 ) browser.firefox = 1; else browser.firefox = 0;

  if ( nav.indexOf("firefox/17") != -1 ) browser.firefox17 = 1; else browser.firefox17 = 0;   

  if ( nav.indexOf("firefox/15") != -1 ) browser.firefox15 = 1; else browser.firefox15 = 0;

  if ( nav.indexOf("firefox/3") != -1 ) browser.firefox3 = 1; else browser.firefox3 = 0;

  if ( nav.indexOf("opera") != -1 ) browser.opera = 1; else browser.opera = 0;

  if ( nav.indexOf("msie 10") != -1 ) browser.msie10 = 1; else browser.msie10 = 0;

  if ( nav.indexOf("msie 9") != -1 ) browser.msie9 = 1; else browser.msie9 = 0;

  if ( nav.indexOf("msie 8") != -1 ) browser.msie8 = 1; else browser.msie8 = 0;

  if ( nav.indexOf("msie 7") != -1 ) browser.msie7 = 1; else browser.msie7 = 0;

  if ( nav.indexOf("msie ") != -1 ) browser.msie = 1; else browser.msie = 0;

​

  var ClipperLib = {};

  ClipperLib.biginteger_used = null;

  // Bits per digit

  var dbits;

  // JavaScript engine analysis

  var canary = 0xdeadbeefcafe;

  var j_lm = ((canary & 0xffffff) == 0xefcafe);

  // (public) Constructor

  function Int128(a, b, c)

  {

    // This test variable can be removed,

    // but at least for performance tests it is useful piece of knowledge

    // This is the only ClipperLib related variable in Int128 library

    ClipperLib.biginteger_used = 1;

    if (a != null) if ("number" == typeof a)

    {

        this.fromString(Math.floor(a)

        .toString(), 10); //this.fromNumber(a,b,c);

    }

    else if (b == null && "string" != typeof a) this.fromString(a, 256);

    else

    {

      if (a.indexOf(".") != -1) a = a.substring(0, a.indexOf("."));

      this.fromString(a, b);

    }

  }

  // return new, unset Int128

  function nbi()

  {

    return new Int128(null);

  }

  // am: Compute w_j += (x*this_i), propagate carries,

  // c is initial carry, returns final carry.

  // c < 3*dvalue, x < 2*dvalue, this_i < dvalue

  // We need to select the fastest one that works in this environment.

  // am1: use a single mult and divide to get the high bits,

  // max digit bits should be 26 because

  // max internal value = 2*dvalue^2-2*dvalue (< 2^53)

  function am1(i, x, w, j, c, n)

  {

    while (--n >= 0)

    {

      var v = x * this[i++] + w[j] + c;

      c = Math.floor(v / 0x4000000);

      w[j++] = v & 0x3ffffff;

    }

    return c;

  }

  // am2 avoids a big mult-and-extract completely.

  // Max digit bits should be <= 30 because we do bitwise ops

  // on values up to 2*hdvalue^2-hdvalue-1 (< 2^31)

  function am2(i, x, w, j, c, n)

  {

    var xl = x & 0x7fff,

      xh = x >> 15;

    while (--n >= 0)

    {

      var l = this[i] & 0x7fff;

      var h = this[i++] >> 15;

      var m = xh * l + h * xl;

      l = xl * l + ((m & 0x7fff) << 15) + w[j] + (c & 0x3fffffff);

      c = (l >>> 30) + (m >>> 15) + xh * h + (c >>> 30);

      w[j++] = l & 0x3fffffff;

    }

    return c;

  }

  // Alternately, set max digit bits to 28 since some

  // browsers slow down when dealing with 32-bit numbers.

  function am3(i, x, w, j, c, n)

  {

    var xl = x & 0x3fff,

      xh = x >> 14;

    while (--n >= 0)

    {

      var l = this[i] & 0x3fff;

      var h = this[i++] >> 14;

      var m = xh * l + h * xl;

      l = xl * l + ((m & 0x3fff) << 14) + w[j] + c;

      c = (l >> 28) + (m >> 14) + xh * h;

      w[j++] = l & 0xfffffff;

    }

    return c;

  }

  if (j_lm && (navigator.appName == "Microsoft Internet Explorer"))

  {

    Int128.prototype.am = am2;

    dbits = 30;

  }

  else if (j_lm && (navigator.appName != "Netscape"))

  {

    Int128.prototype.am = am1;

    dbits = 26;

  }

  else

  { // Mozilla/Netscape seems to prefer am3

    Int128.prototype.am = am3;

    dbits = 28;

  }

  Int128.prototype.DB = dbits;

  Int128.prototype.DM = ((1 << dbits) - 1);

  Int128.prototype.DV = (1 << dbits);

  var BI_FP = 52;

  Int128.prototype.FV = Math.pow(2, BI_FP);

  Int128.prototype.F1 = BI_FP - dbits;

  Int128.prototype.F2 = 2 * dbits - BI_FP;

  // Digit conversions

  var BI_RM = "0123456789abcdefghijklmnopqrstuvwxyz";

  var BI_RC = [];

  var rr, vv;

  rr = "0".charCodeAt(0);

  for (vv = 0; vv <= 9; ++vv) BI_RC[rr++] = vv;

  rr = "a".charCodeAt(0);

  for (vv = 10; vv < 36; ++vv) BI_RC[rr++] = vv;

  rr = "A".charCodeAt(0);

  for (vv = 10; vv < 36; ++vv) BI_RC[rr++] = vv;

​

  function int2char(n)

  {

    return BI_RM.charAt(n);

  }

​

  function intAt(s, i)

  {

    var c = BI_RC[s.charCodeAt(i)];

    return (c == null) ? -1 : c;

  }

  // (protected) copy this to r

  function bnpCopyTo(r)

  {

    for (var i = this.t - 1; i >= 0; --i) r[i] = this[i];

    r.t = this.t;

    r.s = this.s;

  }

  // (protected) set from integer value x, -DV <= x < DV

  function bnpFromInt(x)

  {

    this.t = 1;

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

    if (x > 0) this[0] = x;

    else if (x < -1) this[0] = x + this.DV;

    else this.t = 0;

  }

  // return bigint initialized to value

  function nbv(i)

  {

    var r = nbi();

    r.fromInt(i);

    return r;

  }

  // (protected) set from string and radix

  function bnpFromString(s, b)

  {

    var k;

    if (b == 16) k = 4;

    else if (b == 8) k = 3;

    else if (b == 256) k = 8; // byte array

    else if (b == 2) k = 1;

    else if (b == 32) k = 5;

    else if (b == 4) k = 2;

    else

    {

      this.fromRadix(s, b);

      return;

    }

    this.t = 0;

    this.s = 0;

    var i = s.length,

      mi = false,

      sh = 0;

    while (--i >= 0)

    {

      var x = (k == 8) ? s[i] & 0xff : intAt(s, i);

      if (x < 0)

      {

        if (s.charAt(i) == "-") mi = true;

        continue;

      }

      mi = false;

      if (sh == 0) this[this.t++] = x;

      else if (sh + k > this.DB)

      {

        this[this.t - 1] |= (x & ((1 << (this.DB - sh)) - 1)) << sh;

        this[this.t++] = (x >> (this.DB - sh));

      }

      else this[this.t - 1] |= x << sh;

      sh += k;

      if (sh >= this.DB) sh -= this.DB;

    }

    if (k == 8 && (s[0] & 0x80) != 0)

    {

      this.s = -1;

      if (sh > 0) this[this.t - 1] |= ((1 << (this.DB - sh)) - 1) << sh;

    }

    this.clamp();

    if (mi) Int128.ZERO.subTo(this, this);

  }

  // (protected) clamp off excess high words

  function bnpClamp()

  {

    var c = this.s & this.DM;

    while (this.t > 0 && this[this.t - 1] == c)--this.t;

  }

  // (public) return string representation in given radix

  function bnToString(b)

  {

    if (this.s < 0) return "-" + this.negate()

      .toString(b);

    var k;

    if (b == 16) k = 4;

    else if (b == 8) k = 3;

    else if (b == 2) k = 1;

    else if (b == 32) k = 5;

    else if (b == 4) k = 2;

    else return this.toRadix(b);

    var km = (1 << k) - 1,

      d, m = false,

      r = "",

      i = this.t;

    var p = this.DB - (i * this.DB) % k;

    if (i-- > 0)

    {

      if (p < this.DB && (d = this[i] >> p) > 0)

      {

        m = true;

        r = int2char(d);

      }

      while (i >= 0)

      {

        if (p < k)

        {

          d = (this[i] & ((1 << p) - 1)) << (k - p);

          d |= this[--i] >> (p += this.DB - k);

        }

        else

        {

          d = (this[i] >> (p -= k)) & km;

          if (p <= 0)

          {

            p += this.DB;

            --i;

          }

        }

        if (d > 0) m = true;

        if (m) r += int2char(d);

      }

    }

    return m ? r : "0";

  }

  // (public) -this

  function bnNegate()

  {

    var r = nbi();

    Int128.ZERO.subTo(this, r);

    return r;

  }

  // (public) |this|

  function bnAbs()

  {

    return (this.s < 0) ? this.negate() : this;

  }

  // (public) return + if this > a, - if this < a, 0 if equal

  function bnCompareTo(a)

  {

    var r = this.s - a.s;

    if (r != 0) return r;

    var i = this.t;

    r = i - a.t;

    if (r != 0) return (this.s < 0) ? -r : r;

    while (--i >= 0) if ((r = this[i] - a[i]) != 0) return r;

    return 0;

  }

  // returns bit length of the integer x

  function nbits(x)

  {

    var r = 1,

      t;

    if ((t = x >>> 16) != 0)

    {

      x = t;

      r += 16;

    }

    if ((t = x >> 8) != 0)

    {

      x = t;

      r += 8;

    }

    if ((t = x >> 4) != 0)

    {

      x = t;

      r += 4;

    }

    if ((t = x >> 2) != 0)

    {

      x = t;

      r += 2;

    }

    if ((t = x >> 1) != 0)

    {

      x = t;

      r += 1;

    }

    return r;

  }

  // (public) return the number of bits in "this"

  function bnBitLength()

  {

    if (this.t <= 0) return 0;

    return this.DB * (this.t - 1) + nbits(this[this.t - 1] ^ (this.s & this.DM));

  }

  // (protected) r = this << n*DB

  function bnpDLShiftTo(n, r)

  {

    var i;

    for (i = this.t - 1; i >= 0; --i) r[i + n] = this[i];

    for (i = n - 1; i >= 0; --i) r[i] = 0;

    r.t = this.t + n;

    r.s = this.s;

  }

  // (protected) r = this >> n*DB

  function bnpDRShiftTo(n, r)

  {

    for (var i = n; i < this.t; ++i) r[i - n] = this[i];

    r.t = Math.max(this.t - n, 0);

    r.s = this.s;

  }

  // (protected) r = this << n

  function bnpLShiftTo(n, r)

  {

    var bs = n % this.DB;

    var cbs = this.DB - bs;

    var bm = (1 << cbs) - 1;

    var ds = Math.floor(n / this.DB),

      c = (this.s << bs) & this.DM,

      i;

    for (i = this.t - 1; i >= 0; --i)

    {

      r[i + ds + 1] = (this[i] >> cbs) | c;

      c = (this[i] & bm) << bs;

    }

    for (i = ds - 1; i >= 0; --i) r[i] = 0;

    r[ds] = c;

    r.t = this.t + ds + 1;

    r.s = this.s;

    r.clamp();

  }

  // (protected) r = this >> n

  function bnpRShiftTo(n, r)

  {

    r.s = this.s;

    var ds = Math.floor(n / this.DB);

    if (ds >= this.t)

    {

      r.t = 0;

      return;

    }

    var bs = n % this.DB;

    var cbs = this.DB - bs;

    var bm = (1 << bs) - 1;

    r[0] = this[ds] >> bs;

    for (var i = ds + 1; i < this.t; ++i)

    {

      r[i - ds - 1] |= (this[i] & bm) << cbs;

      r[i - ds] = this[i] >> bs;

    }

    if (bs > 0) r[this.t - ds - 1] |= (this.s & bm) << cbs;

    r.t = this.t - ds;

    r.clamp();

  }

  // (protected) r = this - a

  function bnpSubTo(a, r)

  {

    var i = 0,

      c = 0,

      m = Math.min(a.t, this.t);

    while (i < m)

    {

      c += this[i] - a[i];

      r[i++] = c & this.DM;

      c >>= this.DB;

    }

    if (a.t < this.t)

    {

      c -= a.s;

      while (i < this.t)

      {

        c += this[i];

        r[i++] = c & this.DM;

        c >>= this.DB;

      }

      c += this.s;

    }

    else

    {

      c += this.s;

      while (i < a.t)

      {

        c -= a[i];

        r[i++] = c & this.DM;

        c >>= this.DB;

      }

      c -= a.s;

    }

    r.s = (c < 0) ? -1 : 0;

    if (c < -1) r[i++] = this.DV + c;

    else if (c > 0) r[i++] = c;

    r.t = i;

    r.clamp();

  }

  // (protected) r = this * a, r != this,a (HAC 14.12)

  // "this" should be the larger one if appropriate.

  function bnpMultiplyTo(a, r)

  {

    var x = this.abs(),

      y = a.abs();

    var i = x.t;

    r.t = i + y.t;

    while (--i >= 0) r[i] = 0;

    for (i = 0; i < y.t; ++i) r[i + x.t] = x.am(0, y[i], r, i, 0, x.t);

    r.s = 0;

    r.clamp();

    if (this.s != a.s) Int128.ZERO.subTo(r, r);

  }

  // (protected) r = this^2, r != this (HAC 14.16)

  function bnpSquareTo(r)

  {

    var x = this.abs();

    var i = r.t = 2 * x.t;

    while (--i >= 0) r[i] = 0;

    for (i = 0; i < x.t - 1; ++i)

    {

      var c = x.am(i, x[i], r, 2 * i, 0, 1);

      if ((r[i + x.t] += x.am(i + 1, 2 * x[i], r, 2 * i + 1, c, x.t - i - 1)) >= x.DV)

      {

        r[i + x.t] -= x.DV;

        r[i + x.t + 1] = 1;

      }

    }

    if (r.t > 0) r[r.t - 1] += x.am(i, x[i], r, 2 * i, 0, 1);

    r.s = 0;

    r.clamp();

  }

  // (protected) divide this by m, quotient and remainder to q, r (HAC 14.20)

  // r != q, this != m.  q or r may be null.

  function bnpDivRemTo(m, q, r)

  {

    var pm = m.abs();

    if (pm.t <= 0) return;

    var pt = this.abs();

    if (pt.t < pm.t)

    {

      if (q != null) q.fromInt(0);

      if (r != null) this.copyTo(r);

      return;

    }

    if (r == null) r = nbi();

    var y = nbi(),

      ts = this.s,

      ms = m.s;

    var nsh = this.DB - nbits(pm[pm.t - 1]); // normalize modulus

    if (nsh > 0)

    {

      pm.lShiftTo(nsh, y);

      pt.lShiftTo(nsh, r);

    }

    else

    {

      pm.copyTo(y);

      pt.copyTo(r);

    }

    var ys = y.t;

    var y0 = y[ys - 1];

    if (y0 == 0) return;

    var yt = y0 * (1 << this.F1) + ((ys > 1) ? y[ys - 2] >> this.F2 : 0);

    var d1 = this.FV / yt,

      d2 = (1 << this.F1) / yt,

      e = 1 << this.F2;

    var i = r.t,

      j = i - ys,

      t = (q == null) ? nbi() : q;

    y.dlShiftTo(j, t);

    if (r.compareTo(t) >= 0)

    {

      r[r.t++] = 1;

      r.subTo(t, r);

    }

    Int128.ONE.dlShiftTo(ys, t);

    t.subTo(y, y); // "negative" y so we can replace sub with am later

    while (y.t < ys) y[y.t++] = 0;

    while (--j >= 0)

    {

      // Estimate quotient digit

      var qd = (r[--i] == y0) ? this.DM : Math.floor(r[i] * d1 + (r[i - 1] + e) * d2);

      if ((r[i] += y.am(0, qd, r, j, 0, ys)) < qd)

      { // Try it out

        y.dlShiftTo(j, t);

        r.subTo(t, r);

        while (r[i] < --qd) r.subTo(t, r);

      }

    }

    if (q != null)

    {

      r.drShiftTo(ys, q);

      if (ts != ms) Int128.ZERO.subTo(q, q);

    }

    r.t = ys;

    r.clamp();

    if (nsh > 0) r.rShiftTo(nsh, r); // Denormalize remainder

    if (ts < 0) Int128.ZERO.subTo(r, r);

  }

  // (public) this mod a

  function bnMod(a)

  {

    var r = nbi();

    this.abs()

      .divRemTo(a, null, r);

    if (this.s < 0 && r.compareTo(Int128.ZERO) > 0) a.subTo(r, r);

    return r;

  }

  // Modular reduction using "classic" algorithm

  function Classic(m)

  {

    this.m = m;

  }

​

  function cConvert(x)

  {

    if (x.s < 0 || x.compareTo(this.m) >= 0) return x.mod(this.m);

    else return x;

  }

​

  function cRevert(x)

  {

    return x;

  }

​

  function cReduce(x)

  {

    x.divRemTo(this.m, null, x);

  }

​

  function cMulTo(x, y, r)

  {

    x.multiplyTo(y, r);

    this.reduce(r);

  }

​

  function cSqrTo(x, r)

  {

    x.squareTo(r);

    this.reduce(r);

  }

  Classic.prototype.convert = cConvert;

  Classic.prototype.revert = cRevert;

  Classic.prototype.reduce = cReduce;

  Classic.prototype.mulTo = cMulTo;

  Classic.prototype.sqrTo = cSqrTo;

  // (protected) return "-1/this % 2^DB"; useful for Mont. reduction

  // justification:

  //         xy == 1 (mod m)

  //         xy =  1+km

  //   xy(2-xy) = (1+km)(1-km)

  // x[y(2-xy)] = 1-k^2m^2

  // x[y(2-xy)] == 1 (mod m^2)

  // if y is 1/x mod m, then y(2-xy) is 1/x mod m^2

  // should reduce x and y(2-xy) by m^2 at each step to keep size bounded.

  // JS multiply "overflows" differently from C/C++, so care is needed here.

  function bnpInvDigit()

  {

    if (this.t < 1) return 0;

    var x = this[0];

    if ((x & 1) == 0) return 0;

    var y = x & 3; // y == 1/x mod 2^2

    y = (y * (2 - (x & 0xf) * y)) & 0xf; // y == 1/x mod 2^4

    y = (y * (2 - (x & 0xff) * y)) & 0xff; // y == 1/x mod 2^8

    y = (y * (2 - (((x & 0xffff) * y) & 0xffff))) & 0xffff; // y == 1/x mod 2^16

    // last step - calculate inverse mod DV directly;

    // assumes 16 < DB <= 32 and assumes ability to handle 48-bit ints

    y = (y * (2 - x * y % this.DV)) % this.DV; // y == 1/x mod 2^dbits

    // we really want the negative inverse, and -DV < y < DV

    return (y > 0) ? this.DV - y : -y;

  }

  // Montgomery reduction

  function Montgomery(m)

  {

    this.m = m;

    this.mp = m.invDigit();

    this.mpl = this.mp & 0x7fff;

    this.mph = this.mp >> 15;

    this.um = (1 << (m.DB - 15)) - 1;

    this.mt2 = 2 * m.t;

  }

  // xR mod m

  function montConvert(x)

  {

    var r = nbi();

    x.abs()

      .dlShiftTo(this.m.t, r);

    r.divRemTo(this.m, null, r);

    if (x.s < 0 && r.compareTo(Int128.ZERO) > 0) this.m.subTo(r, r);

    return r;

  }

  // x/R mod m

  function montRevert(x)

  {

    var r = nbi();

    x.copyTo(r);

    this.reduce(r);

    return r;

  }

  // x = x/R mod m (HAC 14.32)

  function montReduce(x)

  {

    while (x.t <= this.mt2) // pad x so am has enough room later

    x[x.t++] = 0;

    for (var i = 0; i < this.m.t; ++i)

    {

      // faster way of calculating u0 = x[i]*mp mod DV

      var j = x[i] & 0x7fff;

      var u0 = (j * this.mpl + (((j * this.mph + (x[i] >> 15) * this.mpl) & this.um) << 15)) & x.DM;

      // use am to combine the multiply-shift-add into one call

      j = i + this.m.t;

      x[j] += this.m.am(0, u0, x, i, 0, this.m.t);

      // propagate carry

      while (x[j] >= x.DV)

      {

        x[j] -= x.DV;

        x[++j]++;

      }

    }

    x.clamp();

    x.drShiftTo(this.m.t, x);

    if (x.compareTo(this.m) >= 0) x.subTo(this.m, x);

  }

  // r = "x^2/R mod m"; x != r

  function montSqrTo(x, r)

  {

    x.squareTo(r);

    this.reduce(r);

  }

  // r = "xy/R mod m"; x,y != r

  function montMulTo(x, y, r)

  {

    x.multiplyTo(y, r);

    this.reduce(r);

  }

  Montgomery.prototype.convert = montConvert;

  Montgomery.prototype.revert = montRevert;

  Montgomery.prototype.reduce = montReduce;

  Montgomery.prototype.mulTo = montMulTo;

  Montgomery.prototype.sqrTo = montSqrTo;

  // (protected) true iff this is even

  function bnpIsEven()

  {

    return ((this.t > 0) ? (this[0] & 1) : this.s) == 0;

  }

  // (protected) this^e, e < 2^32, doing sqr and mul with "r" (HAC 14.79)

  function bnpExp(e, z)

  {

    if (e > 0xffffffff || e < 1) return Int128.ONE;

    var r = nbi(),

      r2 = nbi(),

      g = z.convert(this),

      i = nbits(e) - 1;

    g.copyTo(r);

    while (--i >= 0)

    {

      z.sqrTo(r, r2);

      if ((e & (1 << i)) > 0) z.mulTo(r2, g, r);

      else

      {

        var t = r;

        r = r2;

        r2 = t;

      }

    }

    return z.revert(r);

  }

  // (public) this^e % m, 0 <= e < 2^32

  function bnModPowInt(e, m)

  {

    var z;

    if (e < 256 || m.isEven()) z = new Classic(m);

    else z = new Montgomery(m);

    return this.exp(e, z);

  }

  // protected

  Int128.prototype.copyTo = bnpCopyTo;

  Int128.prototype.fromInt = bnpFromInt;

  Int128.prototype.fromString = bnpFromString;

  Int128.prototype.clamp = bnpClamp;

  Int128.prototype.dlShiftTo = bnpDLShiftTo;

  Int128.prototype.drShiftTo = bnpDRShiftTo;

  Int128.prototype.lShiftTo = bnpLShiftTo;

  Int128.prototype.rShiftTo = bnpRShiftTo;

  Int128.prototype.subTo = bnpSubTo;

  Int128.prototype.multiplyTo = bnpMultiplyTo;

  Int128.prototype.squareTo = bnpSquareTo;

  Int128.prototype.divRemTo = bnpDivRemTo;

  Int128.prototype.invDigit = bnpInvDigit;

  Int128.prototype.isEven = bnpIsEven;

  Int128.prototype.exp = bnpExp;

  // public

  Int128.prototype.toString = bnToString;

  Int128.prototype.negate = bnNegate;

  Int128.prototype.abs = bnAbs;

  Int128.prototype.compareTo = bnCompareTo;

  Int128.prototype.bitLength = bnBitLength;

  Int128.prototype.mod = bnMod;

  Int128.prototype.modPowInt = bnModPowInt;

  // "constants"

  Int128.ZERO = nbv(0);

  Int128.ONE = nbv(1);

  // Copyright (c) 2005-2009  Tom Wu

  // All Rights Reserved.

  // See "LICENSE" for details.

  // Extended JavaScript BN functions, required for RSA private ops.

  // Version 1.1: new Int128("0", 10) returns "proper" zero

  // Version 1.2: square() API, isProbablePrime fix

  // (public)

  function bnClone()

  {

    var r = nbi();

    this.copyTo(r);

    return r;

  }

  // (public) return value as integer

  function bnIntValue()

  {

    if (this.s < 0)

    {

      if (this.t == 1) return this[0] - this.DV;

      else if (this.t == 0) return -1;

    }

    else if (this.t == 1) return this[0];

    else if (this.t == 0) return 0;

    // assumes 16 < DB < 32

    return ((this[1] & ((1 << (32 - this.DB)) - 1)) << this.DB) | this[0];

  }

  // (public) return value as byte

  function bnByteValue()

  {

    return (this.t == 0) ? this.s : (this[0] << 24) >> 24;

  }

  // (public) return value as short (assumes DB>=16)

  function bnShortValue()

  {

    return (this.t == 0) ? this.s : (this[0] << 16) >> 16;

  }

  // (protected) return x s.t. r^x < DV

  function bnpChunkSize(r)

  {

    return Math.floor(Math.LN2 * this.DB / Math.log(r));

  }

  // (public) 0 if this == 0, 1 if this > 0

  function bnSigNum()

  {

    if (this.s < 0) return -1;

    else if (this.t <= 0 || (this.t == 1 && this[0] <= 0)) return 0;

    else return 1;

  }

  // (protected) convert to radix string

  function bnpToRadix(b)

  {

    if (b == null) b = 10;

    if (this.signum() == 0 || b < 2 || b > 36) return "0";

    var cs = this.chunkSize(b);

    var a = Math.pow(b, cs);

    var d = nbv(a),

      y = nbi(),

      z = nbi(),

      r = "";

    this.divRemTo(d, y, z);

    while (y.signum() > 0)

    {

      r = (a + z.intValue())

        .toString(b)

        .substr(1) + r;

      y.divRemTo(d, y, z);

    }

    return z.intValue()

      .toString(b) + r;

  }

  // (protected) convert from radix string

  function bnpFromRadix(s, b)

  {

    this.fromInt(0);

    if (b == null) b = 10;

    var cs = this.chunkSize(b);

    var d = Math.pow(b, cs),

      mi = false,

      j = 0,

      w = 0;

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

    {

      var x = intAt(s, i);

      if (x < 0)

      {

        if (s.charAt(i) == "-" && this.signum() == 0) mi = true;

        continue;

      }

      w = b * w + x;

      if (++j >= cs)

      {

        this.dMultiply(d);

        this.dAddOffset(w, 0);

        j = 0;

        w = 0;

      }

    }

    if (j > 0)

    {

      this.dMultiply(Math.pow(b, j));

      this.dAddOffset(w, 0);

    }

    if (mi) Int128.ZERO.subTo(this, this);

  }

  // (protected) alternate constructor

  function bnpFromNumber(a, b, c)

  {

    if ("number" == typeof b)

    {

      // new Int128(int,int,RNG)

      if (a < 2) this.fromInt(1);

      else

      {

        this.fromNumber(a, c);

        if (!this.testBit(a - 1)) // force MSB set

        this.bitwiseTo(Int128.ONE.shiftLeft(a - 1), op_or, this);

        if (this.isEven()) this.dAddOffset(1, 0); // force odd

        while (!this.isProbablePrime(b))

        {

          this.dAddOffset(2, 0);

          if (this.bitLength() > a) this.subTo(Int128.ONE.shiftLeft(a - 1), this);

        }

      }

    }

    else

    {

      // new Int128(int,RNG)

      var x = [],

        t = a & 7;

      x.length = (a >> 3) + 1;

      b.nextBytes(x);

      if (t > 0) x[0] &= ((1 << t) - 1);

      else x[0] = 0;

      this.fromString(x, 256);

    }

  }

  // (public) convert to bigendian byte array

  function bnToByteArray()

  {

    var i = this.t,

      r = [];

    r[0] = this.s;

    var p = this.DB - (i * this.DB) % 8,

      d, k = 0;

    if (i-- > 0)

    {

      if (p < this.DB && (d = this[i] >> p) != (this.s & this.DM) >> p) r[k++] = d | (this.s << (this.DB - p));

      while (i >= 0)

      {

        if (p < 8)

        {

          d = (this[i] & ((1 << p) - 1)) << (8 - p);

          d |= this[--i] >> (p += this.DB - 8);

        }

        else

        {

          d = (this[i] >> (p -= 8)) & 0xff;

          if (p <= 0)

          {

            p += this.DB;

            --i;

          }

        }

        if ((d & 0x80) != 0) d |= -256;

        if (k == 0 && (this.s & 0x80) != (d & 0x80))++k;

        if (k > 0 || d != this.s) r[k++] = d;

      }

    }

    return r;

  }

​

  function bnEquals(a)

  {

    return (this.compareTo(a) == 0);

  }

​

  function bnMin(a)

  {

    return (this.compareTo(a) < 0) ? this : a;

  }

​

  function bnMax(a)

  {

    return (this.compareTo(a) > 0) ? this : a;

  }

  // (protected) r = this op a (bitwise)

  function bnpBitwiseTo(a, op, r)

  {

    var i, f, m = Math.min(a.t, this.t);

    for (i = 0; i < m; ++i) r[i] = op(this[i], a[i]);

    if (a.t < this.t)

    {

      f = a.s & this.DM;

      for (i = m; i < this.t; ++i) r[i] = op(this[i], f);

      r.t = this.t;

    }

    else

    {

      f = this.s & this.DM;

      for (i = m; i < a.t; ++i) r[i] = op(f, a[i]);

      r.t = a.t;

    }

    r.s = op(this.s, a.s);

    r.clamp();

  }

  // (public) this & a

  function op_and(x, y)

  {

    return x & y;

  }

​

  function bnAnd(a)

  {

    var r = nbi();

    this.bitwiseTo(a, op_and, r);

    return r;

  }

  // (public) this | a

  function op_or(x, y)

  {

    return x | y;

  }

​

  function bnOr(a)

  {

    var r = nbi();

    this.bitwiseTo(a, op_or, r);

    return r;