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/*
 *  big.js v5.2.2
 *  A small, fast, easy-to-use library for arbitrary-precision decimal arithmetic.
 *  Copyright (c) 2018 Michael Mclaughlin <M8ch88l@gmail.com>
 *  https://github.com/MikeMcl/big.js/LICENCE
 */
;(function (GLOBAL) {
  'use strict';
  var Big,


/************************************** EDITABLE DEFAULTS *****************************************/


    // The default values below must be integers within the stated ranges.

    /*
     * The maximum number of decimal places (DP) of the results of operations involving division:
     * div and sqrt, and pow with negative exponents.
     */
    DP = 20,          // 0 to MAX_DP

    /*
     * The rounding mode (RM) used when rounding to the above decimal places.
     *
     *  0  Towards zero (i.e. truncate, no rounding).       (ROUND_DOWN)
     *  1  To nearest neighbour. If equidistant, round up.  (ROUND_HALF_UP)
     *  2  To nearest neighbour. If equidistant, to even.   (ROUND_HALF_EVEN)
     *  3  Away from zero.                                  (ROUND_UP)
     */
    RM = 1,             // 0, 1, 2 or 3

    // The maximum value of DP and Big.DP.
    MAX_DP = 1E6,       // 0 to 1000000

    // The maximum magnitude of the exponent argument to the pow method.
    MAX_POWER = 1E6,    // 1 to 1000000

    /*
     * The negative exponent (NE) at and beneath which toString returns exponential notation.
     * (JavaScript numbers: -7)
     * -1000000 is the minimum recommended exponent value of a Big.
     */
    NE = -7,            // 0 to -1000000

    /*
     * The positive exponent (PE) at and above which toString returns exponential notation.
     * (JavaScript numbers: 21)
     * 1000000 is the maximum recommended exponent value of a Big.
     * (This limit is not enforced or checked.)
     */
    PE = 21,            // 0 to 1000000


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


    // Error messages.
    NAME = '[big.js] ',
    INVALID = NAME + 'Invalid ',
    INVALID_DP = INVALID + 'decimal places',
    INVALID_RM = INVALID + 'rounding mode',
    DIV_BY_ZERO = NAME + 'Division by zero',

    // The shared prototype object.
    P = {},
    UNDEFINED = void 0,
    NUMERIC = /^-?(\d+(\.\d*)?|\.\d+)(e[+-]?\d+)?$/i;


  /*
   * Create and return a Big constructor.
   *
   */
  function _Big_() {

    /*
     * The Big constructor and exported function.
     * Create and return a new instance of a Big number object.
     *
     * n {number|string|Big} A numeric value.
     */
    function Big(n) {
      var x = this;

      // Enable constructor usage without new.
      if (!(x instanceof Big)) return n === UNDEFINED ? _Big_() : new Big(n);

      // Duplicate.
      if (n instanceof Big) {
        x.s = n.s;
        x.e = n.e;
        x.c = n.c.slice();
      } else {
        parse(x, n);
      }

      /*
       * Retain a reference to this Big constructor, and shadow Big.prototype.constructor which
       * points to Object.
       */
      x.constructor = Big;
    }

    Big.prototype = P;
    Big.DP = DP;
    Big.RM = RM;
    Big.NE = NE;
    Big.PE = PE;
    Big.version = '5.2.2';

    return Big;
  }


  /*
   * Parse the number or string value passed to a Big constructor.
   *
   * x {Big} A Big number instance.
   * n {number|string} A numeric value.
   */
  function parse(x, n) {
    var e, i, nl;

    // Minus zero?
    if (n === 0 && 1 / n < 0) n = '-0';
    else if (!NUMERIC.test(n += '')) throw Error(INVALID + 'number');

    // Determine sign.
    x.s = n.charAt(0) == '-' ? (n = n.slice(1), -1) : 1;

    // Decimal point?
    if ((e = n.indexOf('.')) > -1) n = n.replace('.', '');

    // Exponential form?
    if ((i = n.search(/e/i)) > 0) {

      // Determine exponent.
      if (e < 0) e = i;
      e += +n.slice(i + 1);
      n = n.substring(0, i);
    } else if (e < 0) {

      // Integer.
      e = n.length;
    }

    nl = n.length;

    // Determine leading zeros.
    for (i = 0; i < nl && n.charAt(i) == '0';) ++i;

    if (i == nl) {

      // Zero.
      x.c = [x.e = 0];
    } else {

      // Determine trailing zeros.
      for (; nl > 0 && n.charAt(--nl) == '0';);
      x.e = e - i - 1;
      x.c = [];

      // Convert string to array of digits without leading/trailing zeros.
      for (e = 0; i <= nl;) x.c[e++] = +n.charAt(i++);
    }

    return x;
  }


  /*
   * Round Big x to a maximum of dp decimal places using rounding mode rm.
   * Called by stringify, P.div, P.round and P.sqrt.
   *
   * x {Big} The Big to round.
   * dp {number} Integer, 0 to MAX_DP inclusive.
   * rm {number} 0, 1, 2 or 3 (DOWN, HALF_UP, HALF_EVEN, UP)
   * [more] {boolean} Whether the result of division was truncated.
   */
  function round(x, dp, rm, more) {
    var xc = x.c,
      i = x.e + dp + 1;

    if (i < xc.length) {
      if (rm === 1) {

        // xc[i] is the digit after the digit that may be rounded up.
        more = xc[i] >= 5;
      } else if (rm === 2) {
        more = xc[i] > 5 || xc[i] == 5 &&
          (more || i < 0 || xc[i + 1] !== UNDEFINED || xc[i - 1] & 1);
      } else if (rm === 3) {
        more = more || !!xc[0];
      } else {
        more = false;
        if (rm !== 0) throw Error(INVALID_RM);
      }

      if (i < 1) {
        xc.length = 1;

        if (more) {

          // 1, 0.1, 0.01, 0.001, 0.0001 etc.
          x.e = -dp;
          xc[0] = 1;
        } else {

          // Zero.
          xc[0] = x.e = 0;
        }
      } else {

        // Remove any digits after the required decimal places.
        xc.length = i--;

        // Round up?
        if (more) {

          // Rounding up may mean the previous digit has to be rounded up.
          for (; ++xc[i] > 9;) {
            xc[i] = 0;
            if (!i--) {
              ++x.e;
              xc.unshift(1);
            }
          }
        }

        // Remove trailing zeros.
        for (i = xc.length; !xc[--i];) xc.pop();
      }
    } else if (rm < 0 || rm > 3 || rm !== ~~rm) {
      throw Error(INVALID_RM);
    }

    return x;
  }


  /*
   * Return a string representing the value of Big x in normal or exponential notation.
   * Handles P.toExponential, P.toFixed, P.toJSON, P.toPrecision, P.toString and P.valueOf.
   *
   * x {Big}
   * id? {number} Caller id.
   *         1 toExponential
   *         2 toFixed
   *         3 toPrecision
   *         4 valueOf
   * n? {number|undefined} Caller's argument.
   * k? {number|undefined}
   */
  function stringify(x, id, n, k) {
    var e, s,
      Big = x.constructor,
      z = !x.c[0];

    if (n !== UNDEFINED) {
      if (n !== ~~n || n < (id == 3) || n > MAX_DP) {
        throw Error(id == 3 ? INVALID + 'precision' : INVALID_DP);
      }

      x = new Big(x);

      // The index of the digit that may be rounded up.
      n = k - x.e;

      // Round?
      if (x.c.length > ++k) round(x, n, Big.RM);

      // toFixed: recalculate k as x.e may have changed if value rounded up.
      if (id == 2) k = x.e + n + 1;

      // Append zeros?
      for (; x.c.length < k;) x.c.push(0);
    }

    e = x.e;
    s = x.c.join('');
    n = s.length;

    // Exponential notation?
    if (id != 2 && (id == 1 || id == 3 && k <= e || e <= Big.NE || e >= Big.PE)) {
      s = s.charAt(0) + (n > 1 ? '.' + s.slice(1) : '') + (e < 0 ? 'e' : 'e+') + e;

    // Normal notation.
    } else if (e < 0) {
      for (; ++e;) s = '0' + s;
      s = '0.' + s;
    } else if (e > 0) {
      if (++e > n) for (e -= n; e--;) s += '0';
      else if (e < n) s = s.slice(0, e) + '.' + s.slice(e);
    } else if (n > 1) {
      s = s.charAt(0) + '.' + s.slice(1);
    }

    return x.s < 0 && (!z || id == 4) ? '-' + s : s;
  }


  // Prototype/instance methods


  /*
   * Return a new Big whose value is the absolute value of this Big.
   */
  P.abs = function () {
    var x = new this.constructor(this);
    x.s = 1;
    return x;
  };


  /*
   * Return 1 if the value of this Big is greater than the value of Big y,
   *       -1 if the value of this Big is less than the value of Big y, or
   *        0 if they have the same value.
  */
  P.cmp = function (y) {
    var isneg,
      x = this,
      xc = x.c,
      yc = (y = new x.constructor(y)).c,
      i = x.s,
      j = y.s,
      k = x.e,
      l = y.e;

    // Either zero?
    if (!xc[0] || !yc[0]) return !xc[0] ? !yc[0] ? 0 : -j : i;

    // Signs differ?
    if (i != j) return i;

    isneg = i < 0;

    // Compare exponents.
    if (k != l) return k > l ^ isneg ? 1 : -1;

    j = (k = xc.length) < (l = yc.length) ? k : l;

    // Compare digit by digit.
    for (i = -1; ++i < j;) {
      if (xc[i] != yc[i]) return xc[i] > yc[i] ^ isneg ? 1 : -1;
    }

    // Compare lengths.
    return k == l ? 0 : k > l ^ isneg ? 1 : -1;
  };


  /*
   * Return a new Big whose value is the value of this Big divided by the value of Big y, rounded,
   * if necessary, to a maximum of Big.DP decimal places using rounding mode Big.RM.
   */
  P.div = function (y) {
    var x = this,
      Big = x.constructor,
      a = x.c,                  // dividend
      b = (y = new Big(y)).c,   // divisor
      k = x.s == y.s ? 1 : -1,
      dp = Big.DP;

    if (dp !== ~~dp || dp < 0 || dp > MAX_DP) throw Error(INVALID_DP);

    // Divisor is zero?
    if (!b[0]) throw Error(DIV_BY_ZERO);

    // Dividend is 0? Return +-0.
    if (!a[0]) return new Big(k * 0);

    var bl, bt, n, cmp, ri,
      bz = b.slice(),
      ai = bl = b.length,
      al = a.length,
      r = a.slice(0, bl),   // remainder
      rl = r.length,
      q = y,                // quotient
      qc = q.c = [],
      qi = 0,
      d = dp + (q.e = x.e - y.e) + 1;    // number of digits of the result

    q.s = k;
    k = d < 0 ? 0 : d;

    // Create version of divisor with leading zero.
    bz.unshift(0);

    // Add zeros to make remainder as long as divisor.
    for (; rl++ < bl;) r.push(0);

    do {

      // n is how many times the divisor goes into current remainder.
      for (n = 0; n < 10; n++) {

        // Compare divisor and remainder.
        if (bl != (rl = r.length)) {
          cmp = bl > rl ? 1 : -1;
        } else {
          for (ri = -1, cmp = 0; ++ri < bl;) {
            if (b[ri] != r[ri]) {
              cmp = b[ri] > r[ri] ? 1 : -1;
              break;
            }
          }
        }

        // If divisor < remainder, subtract divisor from remainder.
        if (cmp < 0) {

          // Remainder can't be more than 1 digit longer than divisor.
          // Equalise lengths using divisor with extra leading zero?
          for (bt = rl == bl ? b : bz; rl;) {
            if (r[--rl] < bt[rl]) {
              ri = rl;
              for (; ri && !r[--ri];) r[ri] = 9;
              --r[ri];
              r[rl] += 10;
            }
            r[rl] -= bt[rl];
          }

          for (; !r[0];) r.shift();
        } else {
          break;
        }
      }

      // Add the digit n to the result array.
      qc[qi++] = cmp ? n : ++n;

      // Update the remainder.
      if (r[0] && cmp) r[rl] = a[ai] || 0;
      else r = [a[ai]];

    } while ((ai++ < al || r[0] !== UNDEFINED) && k--);

    // Leading zero? Do not remove if result is simply zero (qi == 1).
    if (!qc[0] && qi != 1) {

      // There can't be more than one zero.
      qc.shift();
      q.e--;
    }

    // Round?
    if (qi > d) round(q, dp, Big.RM, r[0] !== UNDEFINED);

    return q;
  };


  /*
   * Return true if the value of this Big is equal to the value of Big y, otherwise return false.
   */
  P.eq = function (y) {
    return !this.cmp(y);
  };


  /*
   * Return true if the value of this Big is greater than the value of Big y, otherwise return
   * false.
   */
  P.gt = function (y) {
    return this.cmp(y) > 0;
  };


  /*
   * Return true if the value of this Big is greater than or equal to the value of Big y, otherwise
   * return false.
   */
  P.gte = function (y) {
    return this.cmp(y) > -1;
  };


  /*
   * Return true if the value of this Big is less than the value of Big y, otherwise return false.
   */
  P.lt = function (y) {
    return this.cmp(y) < 0;
  };


  /*
   * Return true if the value of this Big is less than or equal to the value of Big y, otherwise
   * return false.
   */
  P.lte = function (y) {
    return this.cmp(y) < 1;
  };


  /*
   * Return a new Big whose value is the value of this Big minus the value of Big y.
   */
  P.minus = P.sub = function (y) {
    var i, j, t, xlty,
      x = this,
      Big = x.constructor,
      a = x.s,
      b = (y = new Big(y)).s;

    // Signs differ?
    if (a != b) {
      y.s = -b;
      return x.plus(y);
    }

    var xc = x.c.slice(),
      xe = x.e,
      yc = y.c,
      ye = y.e;

    // Either zero?
    if (!xc[0] || !yc[0]) {

      // y is non-zero? x is non-zero? Or both are zero.
      return yc[0] ? (y.s = -b, y) : new Big(xc[0] ? x : 0);
    }

    // Determine which is the bigger number. Prepend zeros to equalise exponents.
    if (a = xe - ye) {

      if (xlty = a < 0) {
        a = -a;
        t = xc;
      } else {
        ye = xe;
        t = yc;
      }

      t.reverse();
      for (b = a; b--;) t.push(0);
      t.reverse();
    } else {

      // Exponents equal. Check digit by digit.
      j = ((xlty = xc.length < yc.length) ? xc : yc).length;

      for (a = b = 0; b < j; b++) {
        if (xc[b] != yc[b]) {
          xlty = xc[b] < yc[b];
          break;
        }
      }
    }

    // x < y? Point xc to the array of the bigger number.
    if (xlty) {
      t = xc;
      xc = yc;
      yc = t;
      y.s = -y.s;
    }

    /*
     * Append zeros to xc if shorter. No need to add zeros to yc if shorter as subtraction only
     * needs to start at yc.length.
     */
    if ((b = (j = yc.length) - (i = xc.length)) > 0) for (; b--;) xc[i++] = 0;

    // Subtract yc from xc.
    for (b = i; j > a;) {
      if (xc[--j] < yc[j]) {
        for (i = j; i && !xc[--i];) xc[i] = 9;
        --xc[i];
        xc[j] += 10;
      }

      xc[j] -= yc[j];
    }

    // Remove trailing zeros.
    for (; xc[--b] === 0;) xc.pop();

    // Remove leading zeros and adjust exponent accordingly.
    for (; xc[0] === 0;) {
      xc.shift();
      --ye;
    }

    if (!xc[0]) {

      // n - n = +0
      y.s = 1;

      // Result must be zero.
      xc = [ye = 0];
    }

    y.c = xc;
    y.e = ye;

    return y;
  };


  /*
   * Return a new Big whose value is the value of this Big modulo the value of Big y.
   */
  P.mod = function (y) {
    var ygtx,
      x = this,
      Big = x.constructor,
      a = x.s,
      b = (y = new Big(y)).s;

    if (!y.c[0]) throw Error(DIV_BY_ZERO);

    x.s = y.s = 1;
    ygtx = y.cmp(x) == 1;
    x.s = a;
    y.s = b;

    if (ygtx) return new Big(x);

    a = Big.DP;
    b = Big.RM;
    Big.DP = Big.RM = 0;
    x = x.div(y);
    Big.DP = a;
    Big.RM = b;

    return this.minus(x.times(y));
  };


  /*
   * Return a new Big whose value is the value of this Big plus the value of Big y.
   */
  P.plus = P.add = function (y) {
    var t,
      x = this,
      Big = x.constructor,
      a = x.s,
      b = (y = new Big(y)).s;

    // Signs differ?
    if (a != b) {
      y.s = -b;
      return x.minus(y);
    }

    var xe = x.e,
      xc = x.c,
      ye = y.e,
      yc = y.c;

    // Either zero? y is non-zero? x is non-zero? Or both are zero.
    if (!xc[0] || !yc[0]) return yc[0] ? y : new Big(xc[0] ? x : a * 0);

    xc = xc.slice();

    // Prepend zeros to equalise exponents.
    // Note: reverse faster than unshifts.
    if (a = xe - ye) {
      if (a > 0) {
        ye = xe;
        t = yc;
      } else {
        a = -a;
        t = xc;
      }

      t.reverse();
      for (; a--;) t.push(0);
      t.reverse();
    }

    // Point xc to the longer array.
    if (xc.length - yc.length < 0) {
      t = yc;
      yc = xc;
      xc = t;
    }

    a = yc.length;

    // Only start adding at yc.length - 1 as the further digits of xc can be left as they are.
    for (b = 0; a; xc[a] %= 10) b = (xc[--a] = xc[a] + yc[a] + b) / 10 | 0;

    // No need to check for zero, as +x + +y != 0 && -x + -y != 0

    if (b) {
      xc.unshift(b);
      ++ye;
    }

    // Remove trailing zeros.
    for (a = xc.length; xc[--a] === 0;) xc.pop();

    y.c = xc;
    y.e = ye;

    return y;
  };


  /*
   * Return a Big whose value is the value of this Big raised to the power n.
   * If n is negative, round to a maximum of Big.DP decimal places using rounding
   * mode Big.RM.
   *
   * n {number} Integer, -MAX_POWER to MAX_POWER inclusive.
   */
  P.pow = function (n) {
    var x = this,
      one = new x.constructor(1),
      y = one,
      isneg = n < 0;

    if (n !== ~~n || n < -MAX_POWER || n > MAX_POWER) throw Error(INVALID + 'exponent');
    if (isneg) n = -n;

    for (;;) {
      if (n & 1) y = y.times(x);
      n >>= 1;
      if (!n) break;
      x = x.times(x);
    }

    return isneg ? one.div(y) : y;
  };


  /*
   * Return a new Big whose value is the value of this Big rounded using rounding mode rm
   * to a maximum of dp decimal places, or, if dp is negative, to an integer which is a
   * multiple of 10**-dp.
   * If dp is not specified, round to 0 decimal places.
   * If rm is not specified, use Big.RM.
   *
   * dp? {number} Integer, -MAX_DP to MAX_DP inclusive.
   * rm? 0, 1, 2 or 3 (ROUND_DOWN, ROUND_HALF_UP, ROUND_HALF_EVEN, ROUND_UP)
   */
  P.round = function (dp, rm) {
    var Big = this.constructor;
    if (dp === UNDEFINED) dp = 0;
    else if (dp !== ~~dp || dp < -MAX_DP || dp > MAX_DP) throw Error(INVALID_DP);
    return round(new Big(this), dp, rm === UNDEFINED ? Big.RM : rm);
  };


  /*
   * Return a new Big whose value is the square root of the value of this Big, rounded, if
   * necessary, to a maximum of Big.DP decimal places using rounding mode Big.RM.
   */
  P.sqrt = function () {
    var r, c, t,
      x = this,
      Big = x.constructor,
      s = x.s,
      e = x.e,
      half = new Big(0.5);

    // Zero?
    if (!x.c[0]) return new Big(x);

    // Negative?
    if (s < 0) throw Error(NAME + 'No square root');

    // Estimate.
    s = Math.sqrt(x + '');

    // Math.sqrt underflow/overflow?
    // Re-estimate: pass x coefficient to Math.sqrt as integer, then adjust the result exponent.
    if (s === 0 || s === 1 / 0) {
      c = x.c.join('');
      if (!(c.length + e & 1)) c += '0';
      s = Math.sqrt(c);
      e = ((e + 1) / 2 | 0) - (e < 0 || e & 1);
      r = new Big((s == 1 / 0 ? '1e' : (s = s.toExponential()).slice(0, s.indexOf('e') + 1)) + e);
    } else {
      r = new Big(s);
    }

    e = r.e + (Big.DP += 4);

    // Newton-Raphson iteration.
    do {
      t = r;
      r = half.times(t.plus(x.div(t)));
    } while (t.c.slice(0, e).join('') !== r.c.slice(0, e).join(''));

    return round(r, Big.DP -= 4, Big.RM);
  };


  /*
   * Return a new Big whose value is the value of this Big times the value of Big y.
   */
  P.times = P.mul = function (y) {
    var c,
      x = this,
      Big = x.constructor,
      xc = x.c,
      yc = (y = new Big(y)).c,
      a = xc.length,
      b = yc.length,
      i = x.e,
      j = y.e;

    // Determine sign of result.
    y.s = x.s == y.s ? 1 : -1;

    // Return signed 0 if either 0.
    if (!xc[0] || !yc[0]) return new Big(y.s * 0);

    // Initialise exponent of result as x.e + y.e.
    y.e = i + j;

    // If array xc has fewer digits than yc, swap xc and yc, and lengths.
    if (a < b) {
      c = xc;
      xc = yc;
      yc = c;
      j = a;
      a = b;
      b = j;
    }

    // Initialise coefficient array of result with zeros.
    for (c = new Array(j = a + b); j--;) c[j] = 0;

    // Multiply.

    // i is initially xc.length.
    for (i = b; i--;) {
      b = 0;

      // a is yc.length.
      for (j = a + i; j > i;) {

        // Current sum of products at this digit position, plus carry.
        b = c[j] + yc[i] * xc[j - i - 1] + b;
        c[j--] = b % 10;

        // carry
        b = b / 10 | 0;
      }

      c[j] = (c[j] + b) % 10;
    }

    // Increment result exponent if there is a final carry, otherwise remove leading zero.
    if (b) ++y.e;
    else c.shift();

    // Remove trailing zeros.
    for (i = c.length; !c[--i];) c.pop();
    y.c = c;

    return y;
  };


  /*
   * Return a string representing the value of this Big in exponential notation to dp fixed decimal
   * places and rounded using Big.RM.
   *
   * dp? {number} Integer, 0 to MAX_DP inclusive.
   */
  P.toExponential = function (dp) {
    return stringify(this, 1, dp, dp);
  };


  /*
   * Return a string representing the value of this Big in normal notation to dp fixed decimal
   * places and rounded using Big.RM.
   *
   * dp? {number} Integer, 0 to MAX_DP inclusive.
   *
   * (-0).toFixed(0) is '0', but (-0.1).toFixed(0) is '-0'.
   * (-0).toFixed(1) is '0.0', but (-0.01).toFixed(1) is '-0.0'.
   */
  P.toFixed = function (dp) {
    return stringify(this, 2, dp, this.e + dp);
  };


  /*
   * Return a string representing the value of this Big rounded to sd significant digits using
   * Big.RM. Use exponential notation if sd is less than the number of digits necessary to represent
   * the integer part of the value in normal notation.
   *
   * sd {number} Integer, 1 to MAX_DP inclusive.
   */
  P.toPrecision = function (sd) {
    return stringify(this, 3, sd, sd - 1);
  };


  /*
   * Return a string representing the value of this Big.
   * Return exponential notation if this Big has a positive exponent equal to or greater than
   * Big.PE, or a negative exponent equal to or less than Big.NE.
   * Omit the sign for negative zero.
   */
  P.toString = function () {
    return stringify(this);
  };


  /*
   * Return a string representing the value of this Big.
   * Return exponential notation if this Big has a positive exponent equal to or greater than
   * Big.PE, or a negative exponent equal to or less than Big.NE.
   * Include the sign for negative zero.
   */
  P.valueOf = P.toJSON = function () {
    return stringify(this, 4);
  };


  // Export


  Big = _Big_();

  Big['default'] = Big.Big = Big;

  //AMD.
  if (typeof define === 'function' && define.amd) {
    define(function () { return Big; });

  // Node and other CommonJS-like environments that support module.exports.
  } else if (typeof module !== 'undefined' && module.exports) {
    module.exports = Big;

  //Browser.
  } else {
    GLOBAL.Big = Big;
  }
})(this);