text: //Imported from https://github.com/peterolson/BigInteger.js#4e99b15b7951338f164728377c906caae5a78202
  
  //Provides: bigInt const
  var bigInt = (function (undefined) {
      "use strict";
  
      var BASE = 1e7,
          LOG_BASE = 7,
          MAX_INT = 9007199254740992,
          MAX_INT_ARR = smallToArray(MAX_INT),
          DEFAULT_ALPHABET = "0123456789abcdefghijklmnopqrstuvwxyz";
  
      var BigInt = joo_global_object.BigInt;
  
      var supportsNativeBigInt = typeof BigInt === "function";
  
      function Integer(v, radix, alphabet, caseSensitive) {
          if (typeof v === "undefined") return Integer[0];
          if (typeof radix !== "undefined") return +radix === 10 && !alphabet ? parseValue(v) : parseBase(v, radix, alphabet, caseSensitive);
          return parseValue(v);
      }
  
      function BigInteger(value, sign) {
          this.value = value;
          this.sign = sign;
          this.isSmall = false;
          this.caml_custom = '_z';
      }
      BigInteger.prototype = Object.create(Integer.prototype);
  
      function SmallInteger(value) {
          this.value = value;
          this.sign = value < 0;
          this.isSmall = true;
          this.caml_custom = '_z';
      }
      SmallInteger.prototype = Object.create(Integer.prototype);
  
      function NativeBigInt(value) {
          this.value = value;
          this.caml_custom = '_z';
      }
      NativeBigInt.prototype = Object.create(Integer.prototype);
  
      function isPrecise(n) {
          return -MAX_INT < n && n < MAX_INT;
      }
  
      function smallToArray(n) { // For performance reasons doesn't reference BASE, need to change this function if BASE changes
          if (n < 1e7)
              return [n];
          if (n < 1e14)
              return [n % 1e7, Math.floor(n / 1e7)];
          return [n % 1e7, Math.floor(n / 1e7) % 1e7, Math.floor(n / 1e14)];
      }
  
      function arrayToSmall(arr) { // If BASE changes this function may need to change
          trim(arr);
          var length = arr.length;
          if (length < 4 && compareAbs(arr, MAX_INT_ARR) < 0) {
              switch (length) {
                  case 0: return 0;
                  case 1: return arr[0];
                  case 2: return arr[0] + arr[1] * BASE;
                  default: return arr[0] + (arr[1] + arr[2] * BASE) * BASE;
              }
          }
          return arr;
      }
  
      function trim(v) {
          var i = v.length;
          while (v[--i] === 0);
          v.length = i + 1;
      }
  
      function createArray(length) { // function shamelessly stolen from Yaffle's library https://github.com/Yaffle/BigInteger
          var x = new Array(length);
          var i = -1;
          while (++i < length) {
              x[i] = 0;
          }
          return x;
      }
  
      function truncate(n) {
          if (n > 0) return Math.floor(n);
          return Math.ceil(n);
      }
  
      function add(a, b) { // assumes a and b are arrays with a.length >= b.length
          var l_a = a.length,
              l_b = b.length,
              r = new Array(l_a),
              carry = 0,
              base = BASE,
              sum, i;
          for (i = 0; i < l_b; i++) {
              sum = a[i] + b[i] + carry;
              carry = sum >= base ? 1 : 0;
              r[i] = sum - carry * base;
          }
          while (i < l_a) {
              sum = a[i] + carry;
              carry = sum === base ? 1 : 0;
              r[i++] = sum - carry * base;
          }
          if (carry > 0) r.push(carry);
          return r;
      }
  
      function addAny(a, b) {
          if (a.length >= b.length) return add(a, b);
          return add(b, a);
      }
  
      function addSmall(a, carry) { // assumes a is array, carry is number with 0 <= carry < MAX_INT
          var l = a.length,
              r = new Array(l),
              base = BASE,
              sum, i;
          for (i = 0; i < l; i++) {
              sum = a[i] - base + carry;
              carry = Math.floor(sum / base);
              r[i] = sum - carry * base;
              carry += 1;
          }
          while (carry > 0) {
              r[i++] = carry % base;
              carry = Math.floor(carry / base);
          }
          return r;
      }
  
      BigInteger.prototype.add = function (v) {
          var n = parseValue(v);
          if (this.sign !== n.sign) {
              return this.subtract(n.negate());
          }
          var a = this.value, b = n.value;
          if (n.isSmall) {
              return new BigInteger(addSmall(a, Math.abs(b)), this.sign);
          }
          return new BigInteger(addAny(a, b), this.sign);
      };
      BigInteger.prototype.plus = BigInteger.prototype.add;
  
      SmallInteger.prototype.add = function (v) {
          var n = parseValue(v);
          var a = this.value;
          if (a < 0 !== n.sign) {
              return this.subtract(n.negate());
          }
          var b = n.value;
          if (n.isSmall) {
              if (isPrecise(a + b)) return new SmallInteger(a + b);
              b = smallToArray(Math.abs(b));
          }
          return new BigInteger(addSmall(b, Math.abs(a)), a < 0);
      };
      SmallInteger.prototype.plus = SmallInteger.prototype.add;
  
      NativeBigInt.prototype.add = function (v) {
          return new NativeBigInt(this.value + parseValue(v).value);
      }
      NativeBigInt.prototype.plus = NativeBigInt.prototype.add;
  
      function subtract(a, b) { // assumes a and b are arrays with a >= b
          var a_l = a.length,
              b_l = b.length,
              r = new Array(a_l),
              borrow = 0,
              base = BASE,
              i, difference;
          for (i = 0; i < b_l; i++) {
              difference = a[i] - borrow - b[i];
              if (difference < 0) {
                  difference += base;
                  borrow = 1;
              } else borrow = 0;
              r[i] = difference;
          }
          for (i = b_l; i < a_l; i++) {
              difference = a[i] - borrow;
              if (difference < 0) difference += base;
              else {
                  r[i++] = difference;
                  break;
              }
              r[i] = difference;
          }
          for (; i < a_l; i++) {
              r[i] = a[i];
          }
          trim(r);
          return r;
      }
  
      function subtractAny(a, b, sign) {
          var value;
          if (compareAbs(a, b) >= 0) {
              value = subtract(a, b);
          } else {
              value = subtract(b, a);
              sign = !sign;
          }
          value = arrayToSmall(value);
          if (typeof value === "number") {
              if (sign) value = -value;
              return new SmallInteger(value);
          }
          return new BigInteger(value, sign);
      }
  
      function subtractSmall(a, b, sign) { // assumes a is array, b is number with 0 <= b < MAX_INT
          var l = a.length,
              r = new Array(l),
              carry = -b,
              base = BASE,
              i, difference;
          for (i = 0; i < l; i++) {
              difference = a[i] + carry;
              carry = Math.floor(difference / base);
              difference %= base;
              r[i] = difference < 0 ? difference + base : difference;
          }
          r = arrayToSmall(r);
          if (typeof r === "number") {
              if (sign) r = -r;
              return new SmallInteger(r);
          } return new BigInteger(r, sign);
      }
  
      BigInteger.prototype.subtract = function (v) {
          var n = parseValue(v);
          if (this.sign !== n.sign) {
              return this.add(n.negate());
          }
          var a = this.value, b = n.value;
          if (n.isSmall)
              return subtractSmall(a, Math.abs(b), this.sign);
          return subtractAny(a, b, this.sign);
      };
      BigInteger.prototype.minus = BigInteger.prototype.subtract;
  
      SmallInteger.prototype.subtract = function (v) {
          var n = parseValue(v);
          var a = this.value;
          if (a < 0 !== n.sign) {
              return this.add(n.negate());
          }
          var b = n.value;
          if (n.isSmall) {
              return new SmallInteger(a - b);
          }
          return subtractSmall(b, Math.abs(a), a >= 0);
      };
      SmallInteger.prototype.minus = SmallInteger.prototype.subtract;
  
      NativeBigInt.prototype.subtract = function (v) {
          return new NativeBigInt(this.value - parseValue(v).value);
      }
      NativeBigInt.prototype.minus = NativeBigInt.prototype.subtract;
  
      BigInteger.prototype.negate = function () {
          return new BigInteger(this.value, !this.sign);
      };
      SmallInteger.prototype.negate = function () {
          var sign = this.sign;
          var small = new SmallInteger(-this.value);
          small.sign = !sign;
          return small;
      };
      NativeBigInt.prototype.negate = function () {
          return new NativeBigInt(-this.value);
      }
  
      BigInteger.prototype.abs = function () {
          return new BigInteger(this.value, false);
      };
      SmallInteger.prototype.abs = function () {
          return new SmallInteger(Math.abs(this.value));
      };
      NativeBigInt.prototype.abs = function () {
          return new NativeBigInt(this.value >= 0 ? this.value : -this.value);
      }
  
  
      function multiplyLong(a, b) {
          var a_l = a.length,
              b_l = b.length,
              l = a_l + b_l,
              r = createArray(l),
              base = BASE,
              product, carry, i, a_i, b_j;
          for (i = 0; i < a_l; ++i) {
              a_i = a[i];
              for (var j = 0; j < b_l; ++j) {
                  b_j = b[j];
                  product = a_i * b_j + r[i + j];
                  carry = Math.floor(product / base);
                  r[i + j] = product - carry * base;
                  r[i + j + 1] += carry;
              }
          }
          trim(r);
          return r;
      }
  
      function multiplySmall(a, b) { // assumes a is array, b is number with |b| < BASE
          var l = a.length,
              r = new Array(l),
              base = BASE,
              carry = 0,
              product, i;
          for (i = 0; i < l; i++) {
              product = a[i] * b + carry;
              carry = Math.floor(product / base);
              r[i] = product - carry * base;
          }
          while (carry > 0) {
              r[i++] = carry % base;
              carry = Math.floor(carry / base);
          }
          return r;
      }
  
      function shiftLeft(x, n) {
          var r = [];
          while (n-- > 0) r.push(0);
          return r.concat(x);
      }
  
      function multiplyKaratsuba(x, y) {
          var n = Math.max(x.length, y.length);
  
          if (n <= 30) return multiplyLong(x, y);
          n = Math.ceil(n / 2);
  
          var b = x.slice(n),
              a = x.slice(0, n),
              d = y.slice(n),
              c = y.slice(0, n);
  
          var ac = multiplyKaratsuba(a, c),
              bd = multiplyKaratsuba(b, d),
              abcd = multiplyKaratsuba(addAny(a, b), addAny(c, d));
  
          var product = addAny(addAny(ac, shiftLeft(subtract(subtract(abcd, ac), bd), n)), shiftLeft(bd, 2 * n));
          trim(product);
          return product;
      }
  
      // The following function is derived from a surface fit of a graph plotting the performance difference
      // between long multiplication and karatsuba multiplication versus the lengths of the two arrays.
      function useKaratsuba(l1, l2) {
          return -0.012 * l1 - 0.012 * l2 + 0.000015 * l1 * l2 > 0;
      }
  
      BigInteger.prototype.multiply = function (v) {
          var n = parseValue(v),
              a = this.value, b = n.value,
              sign = this.sign !== n.sign,
              abs;
          if (n.isSmall) {
              if (b === 0) return Integer[0];
              if (b === 1) return this;
              if (b === -1) return this.negate();
              abs = Math.abs(b);
              if (abs < BASE) {
                  return new BigInteger(multiplySmall(a, abs), sign);
              }
              b = smallToArray(abs);
          }
          if (useKaratsuba(a.length, b.length)) // Karatsuba is only faster for certain array sizes
              return new BigInteger(multiplyKaratsuba(a, b), sign);
          return new BigInteger(multiplyLong(a, b), sign);
      };
  
      BigInteger.prototype.times = BigInteger.prototype.multiply;
  
      function multiplySmallAndArray(a, b, sign) { // a >= 0
          if (a < BASE) {
              return new BigInteger(multiplySmall(b, a), sign);
          }
          return new BigInteger(multiplyLong(b, smallToArray(a)), sign);
      }
      SmallInteger.prototype._multiplyBySmall = function (a) {
          if (isPrecise(a.value * this.value)) {
              return new SmallInteger(a.value * this.value);
          }
          return multiplySmallAndArray(Math.abs(a.value), smallToArray(Math.abs(this.value)), this.sign !== a.sign);
      };
      BigInteger.prototype._multiplyBySmall = function (a) {
          if (a.value === 0) return Integer[0];
          if (a.value === 1) return this;
          if (a.value === -1) return this.negate();
          return multiplySmallAndArray(Math.abs(a.value), this.value, this.sign !== a.sign);
      };
      SmallInteger.prototype.multiply = function (v) {
          return parseValue(v)._multiplyBySmall(this);
      };
      SmallInteger.prototype.times = SmallInteger.prototype.multiply;
  
      NativeBigInt.prototype.multiply = function (v) {
          return new NativeBigInt(this.value * parseValue(v).value);
      }
      NativeBigInt.prototype.times = NativeBigInt.prototype.multiply;
  
      function square(a) {
          //console.assert(2 * BASE * BASE < MAX_INT);
          var l = a.length,
              r = createArray(l + l),
              base = BASE,
              product, carry, i, a_i, a_j;
          for (i = 0; i < l; i++) {
              a_i = a[i];
              carry = 0 - a_i * a_i;
              for (var j = i; j < l; j++) {
                  a_j = a[j];
                  product = 2 * (a_i * a_j) + r[i + j] + carry;
                  carry = Math.floor(product / base);
                  r[i + j] = product - carry * base;
              }
              r[i + l] = carry;
          }
          trim(r);
          return r;
      }
  
      BigInteger.prototype.square = function () {
          return new BigInteger(square(this.value), false);
      };
  
      SmallInteger.prototype.square = function () {
          var value = this.value * this.value;
          if (isPrecise(value)) return new SmallInteger(value);
          return new BigInteger(square(smallToArray(Math.abs(this.value))), false);
      };
  
      NativeBigInt.prototype.square = function (v) {
          return new NativeBigInt(this.value * this.value);
      }
  
      function divMod1(a, b) { // Left over from previous version. Performs faster than divMod2 on smaller input sizes.
          var a_l = a.length,
              b_l = b.length,
              base = BASE,
              result = createArray(b.length),
              divisorMostSignificantDigit = b[b_l - 1],
              // normalization
              lambda = Math.ceil(base / (2 * divisorMostSignificantDigit)),
              remainder = multiplySmall(a, lambda),
              divisor = multiplySmall(b, lambda),
              quotientDigit, shift, carry, borrow, i, l, q;
          if (remainder.length <= a_l) remainder.push(0);
          divisor.push(0);
          divisorMostSignificantDigit = divisor[b_l - 1];
          for (shift = a_l - b_l; shift >= 0; shift--) {
              quotientDigit = base - 1;
              if (remainder[shift + b_l] !== divisorMostSignificantDigit) {
                  quotientDigit = Math.floor((remainder[shift + b_l] * base + remainder[shift + b_l - 1]) / divisorMostSignificantDigit);
              }
              // quotientDigit <= base - 1
              carry = 0;
              borrow = 0;
              l = divisor.length;
              for (i = 0; i < l; i++) {
                  carry += quotientDigit * divisor[i];
                  q = Math.floor(carry / base);
                  borrow += remainder[shift + i] - (carry - q * base);
                  carry = q;
                  if (borrow < 0) {
                      remainder[shift + i] = borrow + base;
                      borrow = -1;
                  } else {
                      remainder[shift + i] = borrow;
                      borrow = 0;
                  }
              }
              while (borrow !== 0) {
                  quotientDigit -= 1;
                  carry = 0;
                  for (i = 0; i < l; i++) {
                      carry += remainder[shift + i] - base + divisor[i];
                      if (carry < 0) {
                          remainder[shift + i] = carry + base;
                          carry = 0;
                      } else {
                          remainder[shift + i] = carry;
                          carry = 1;
                      }
                  }
                  borrow += carry;
              }
              result[shift] = quotientDigit;
          }
          // denormalization
          remainder = divModSmall(remainder, lambda)[0];
          return [arrayToSmall(result), arrayToSmall(remainder)];
      }
  
      function divMod2(a, b) { // Implementation idea shamelessly stolen from Silent Matt's library http://silentmatt.com/biginteger/
          // Performs faster than divMod1 on larger input sizes.
          var a_l = a.length,
              b_l = b.length,
              result = [],
              part = [],
              base = BASE,
              guess, xlen, highx, highy, check;
          while (a_l) {
              part.unshift(a[--a_l]);
              trim(part);
              if (compareAbs(part, b) < 0) {
                  result.push(0);
                  continue;
              }
              xlen = part.length;
              highx = part[xlen - 1] * base + part[xlen - 2];
              highy = b[b_l - 1] * base + b[b_l - 2];
              if (xlen > b_l) {
                  highx = (highx + 1) * base;
              }
              guess = Math.ceil(highx / highy);
              do {
                  check = multiplySmall(b, guess);
                  if (compareAbs(check, part) <= 0) break;
                  guess--;
              } while (guess);
              result.push(guess);
              part = subtract(part, check);
          }
          result.reverse();
          return [arrayToSmall(result), arrayToSmall(part)];
      }
  
      function divModSmall(value, lambda) {
          var length = value.length,
              quotient = createArray(length),
              base = BASE,
              i, q, remainder, divisor;
          remainder = 0;
          for (i = length - 1; i >= 0; --i) {
              divisor = remainder * base + value[i];
              q = truncate(divisor / lambda);
              remainder = divisor - q * lambda;
              quotient[i] = q | 0;
          }
          return [quotient, remainder | 0];
      }
  
      function divModAny(self, v) {
          var value, n = parseValue(v);
          if (supportsNativeBigInt) {
              return [new NativeBigInt(self.value / n.value), new NativeBigInt(self.value % n.value)];
          }
          var a = self.value, b = n.value;
          var quotient;
          if (b === 0) throw new Error("Cannot divide by zero");
          if (self.isSmall) {
              if (n.isSmall) {
                  return [new SmallInteger(truncate(a / b)), new SmallInteger(a % b)];
              }
              return [Integer[0], self];
          }
          if (n.isSmall) {
              if (b === 1) return [self, Integer[0]];
              if (b == -1) return [self.negate(), Integer[0]];
              var abs = Math.abs(b);
              if (abs < BASE) {
                  value = divModSmall(a, abs);
                  quotient = arrayToSmall(value[0]);
                  var remainder = value[1];
                  if (self.sign) remainder = -remainder;
                  if (typeof quotient === "number") {
                      if (self.sign !== n.sign) quotient = -quotient;
                      return [new SmallInteger(quotient), new SmallInteger(remainder)];
                  }
                  return [new BigInteger(quotient, self.sign !== n.sign), new SmallInteger(remainder)];
              }
              b = smallToArray(abs);
          }
          var comparison = compareAbs(a, b);
          if (comparison === -1) return [Integer[0], self];
          if (comparison === 0) return [Integer[self.sign === n.sign ? 1 : -1], Integer[0]];
  
          // divMod1 is faster on smaller input sizes
          if (a.length + b.length <= 200)
              value = divMod1(a, b);
          else value = divMod2(a, b);
  
          quotient = value[0];
          var qSign = self.sign !== n.sign,
              mod = value[1],
              mSign = self.sign;
          if (typeof quotient === "number") {
              if (qSign) quotient = -quotient;
              quotient = new SmallInteger(quotient);
          } else quotient = new BigInteger(quotient, qSign);
          if (typeof mod === "number") {
              if (mSign) mod = -mod;
              mod = new SmallInteger(mod);
          } else mod = new BigInteger(mod, mSign);
          return [quotient, mod];
      }
  
      BigInteger.prototype.divmod = function (v) {
          var result = divModAny(this, v);
          return {
              quotient: result[0],
              remainder: result[1]
          };
      };
      NativeBigInt.prototype.divmod = SmallInteger.prototype.divmod = BigInteger.prototype.divmod;
  
  
      BigInteger.prototype.divide = function (v) {
          return divModAny(this, v)[0];
      };
      NativeBigInt.prototype.over = NativeBigInt.prototype.divide = function (v) {
          return new NativeBigInt(this.value / parseValue(v).value);
      };
      SmallInteger.prototype.over = SmallInteger.prototype.divide = BigInteger.prototype.over = BigInteger.prototype.divide;
  
      BigInteger.prototype.mod = function (v) {
          return divModAny(this, v)[1];
      };
      NativeBigInt.prototype.mod = NativeBigInt.prototype.remainder = function (v) {
          return new NativeBigInt(this.value % parseValue(v).value);
      };
      SmallInteger.prototype.remainder = SmallInteger.prototype.mod = BigInteger.prototype.remainder = BigInteger.prototype.mod;
  
      BigInteger.prototype.pow = function (v) {
          var n = parseValue(v),
              a = this.value,
              b = n.value,
              value, x, y;
          if (b === 0) return Integer[1];
          if (a === 0) return Integer[0];
          if (a === 1) return Integer[1];
          if (a === -1) return n.isEven() ? Integer[1] : Integer[-1];
          if (n.sign) {
              return Integer[0];
          }
          if (!n.isSmall) throw new Error("The exponent " + n.toString() + " is too large.");
          if (this.isSmall) {
              if (isPrecise(value = Math.pow(a, b)))
                  return new SmallInteger(truncate(value));
          }
          x = this;
          y = Integer[1];
          while (true) {
              if (b & 1 === 1) {
                  y = y.times(x);
                  --b;
              }
              if (b === 0) break;
              b /= 2;
              x = x.square();
          }
          return y;
      };
      SmallInteger.prototype.pow = BigInteger.prototype.pow;
  
      NativeBigInt.prototype.pow = function (v) {
          var n = parseValue(v);
          var a = this.value, b = n.value;
          var _0 = BigInt(0), _1 = BigInt(1), _2 = BigInt(2);
          if (b === _0) return Integer[1];
          if (a === _0) return Integer[0];
          if (a === _1) return Integer[1];
          if (a === BigInt(-1)) return n.isEven() ? Integer[1] : Integer[-1];
          if (n.isNegative()) return new NativeBigInt(_0);
          var x = this;
          var y = Integer[1];
          while (true) {
              if ((b & _1) === _1) {
                  y = y.times(x);
                  --b;
              }
              if (b === _0) break;
              b /= _2;
              x = x.square();
          }
          return y;
      }
  
      BigInteger.prototype.modPow = function (exp, mod) {
          exp = parseValue(exp);
          mod = parseValue(mod);
          if (mod.isZero()) throw new Error("Cannot take modPow with modulus 0");
          var r = Integer[1],
              base = this.mod(mod);
          if (exp.isNegative()) {
              exp = exp.multiply(Integer[-1]);
              base = base.modInv(mod);
          }
          while (exp.isPositive()) {
              if (base.isZero()) return Integer[0];
              if (exp.isOdd()) r = r.multiply(base).mod(mod);
              exp = exp.divide(2);
              base = base.square().mod(mod);
          }
          return r;
      };
      NativeBigInt.prototype.modPow = SmallInteger.prototype.modPow = BigInteger.prototype.modPow;
  
      function compareAbs(a, b) {
          if (a.length !== b.length) {
              return a.length > b.length ? 1 : -1;
          }
          for (var i = a.length - 1; i >= 0; i--) {
              if (a[i] !== b[i]) return a[i] > b[i] ? 1 : -1;
          }
          return 0;
      }
  
      BigInteger.prototype.compareAbs = function (v) {
          var n = parseValue(v),
              a = this.value,
              b = n.value;
          if (n.isSmall) return 1;
          return compareAbs(a, b);
      };
      SmallInteger.prototype.compareAbs = function (v) {
          var n = parseValue(v),
              a = Math.abs(this.value),
              b = n.value;
          if (n.isSmall) {
              b = Math.abs(b);
              return a === b ? 0 : a > b ? 1 : -1;
          }
          return -1;
      };
      NativeBigInt.prototype.compareAbs = function (v) {
          var a = this.value;
          var b = parseValue(v).value;
          a = a >= 0 ? a : -a;
          b = b >= 0 ? b : -b;
          return a === b ? 0 : a > b ? 1 : -1;
      }
  
      BigInteger.prototype.compare = function (v) {
          // See discussion about comparison with Infinity:
          // https://github.com/peterolson/BigInteger.js/issues/61
          if (v === Infinity) {
              return -1;
          }
          if (v === -Infinity) {
              return 1;
          }
  
          var n = parseValue(v),
              a = this.value,
              b = n.value;
          if (this.sign !== n.sign) {
              return n.sign ? 1 : -1;
          }
          if (n.isSmall) {
              return this.sign ? -1 : 1;
          }
          return compareAbs(a, b) * (this.sign ? -1 : 1);
      };
      BigInteger.prototype.compareTo = BigInteger.prototype.compare;
  
      SmallInteger.prototype.compare = function (v) {
          if (v === Infinity) {
              return -1;
          }
          if (v === -Infinity) {
              return 1;
          }
  
          var n = parseValue(v),
              a = this.value,
              b = n.value;
          if (n.isSmall) {
              return a == b ? 0 : a > b ? 1 : -1;
          }
          if (a < 0 !== n.sign) {
              return a < 0 ? -1 : 1;
          }
          return a < 0 ? 1 : -1;
      };
      SmallInteger.prototype.compareTo = SmallInteger.prototype.compare;
  
      NativeBigInt.prototype.compare = function (v) {
          if (v === Infinity) {
              return -1;
          }
          if (v === -Infinity) {
              return 1;
          }
          var a = this.value;
          var b = parseValue(v).value;
          return a === b ? 0 : a > b ? 1 : -1;
      }
      NativeBigInt.prototype.compareTo = NativeBigInt.prototype.compare;
  
      BigInteger.prototype.equals = function (v) {
          return this.compare(v) === 0;
      };
      NativeBigInt.prototype.eq = NativeBigInt.prototype.equals = SmallInteger.prototype.eq = SmallInteger.prototype.equals = BigInteger.prototype.eq = BigInteger.prototype.equals;
  
      BigInteger.prototype.notEquals = function (v) {
          return this.compare(v) !== 0;
      };
      NativeBigInt.prototype.neq = NativeBigInt.prototype.notEquals = SmallInteger.prototype.neq = SmallInteger.prototype.notEquals = BigInteger.prototype.neq = BigInteger.prototype.notEquals;
  
      BigInteger.prototype.greater = function (v) {
          return this.compare(v) > 0;
      };
      NativeBigInt.prototype.gt = NativeBigInt.prototype.greater = SmallInteger.prototype.gt = SmallInteger.prototype.greater = BigInteger.prototype.gt = BigInteger.prototype.greater;
  
      BigInteger.prototype.lesser = function (v) {
          return this.compare(v) < 0;
      };
      NativeBigInt.prototype.lt = NativeBigInt.prototype.lesser = SmallInteger.prototype.lt = SmallInteger.prototype.lesser = BigInteger.prototype.lt = BigInteger.prototype.lesser;
  
      BigInteger.prototype.greaterOrEquals = function (v) {
          return this.compare(v) >= 0;
      };
      NativeBigInt.prototype.geq = NativeBigInt.prototype.greaterOrEquals = SmallInteger.prototype.geq = SmallInteger.prototype.greaterOrEquals = BigInteger.prototype.geq = BigInteger.prototype.greaterOrEquals;
  
      BigInteger.prototype.lesserOrEquals = function (v) {
          return this.compare(v) <= 0;
      };
      NativeBigInt.prototype.leq = NativeBigInt.prototype.lesserOrEquals = SmallInteger.prototype.leq = SmallInteger.prototype.lesserOrEquals = BigInteger.prototype.leq = BigInteger.prototype.lesserOrEquals;
  
      BigInteger.prototype.isEven = function () {
          return (this.value[0] & 1) === 0;
      };
      SmallInteger.prototype.isEven = function () {
          return (this.value & 1) === 0;
      };
      NativeBigInt.prototype.isEven = function () {
          return (this.value & BigInt(1)) === BigInt(0);
      }
  
      BigInteger.prototype.isOdd = function () {
          return (this.value[0] & 1) === 1;
      };
      SmallInteger.prototype.isOdd = function () {
          return (this.value & 1) === 1;
      };
      NativeBigInt.prototype.isOdd = function () {
          return (this.value & BigInt(1)) === BigInt(1);
      }
  
      BigInteger.prototype.isPositive = function () {
          return !this.sign;
      };
      SmallInteger.prototype.isPositive = function () {
          return this.value > 0;
      };
      NativeBigInt.prototype.isPositive = SmallInteger.prototype.isPositive;
  
      BigInteger.prototype.isNegative = function () {
          return this.sign;
      };
      SmallInteger.prototype.isNegative = function () {
          return this.value < 0;
      };
      NativeBigInt.prototype.isNegative = SmallInteger.prototype.isNegative;
  
      BigInteger.prototype.isUnit = function () {
          return false;
      };
      SmallInteger.prototype.isUnit = function () {
          return Math.abs(this.value) === 1;
      };
      NativeBigInt.prototype.isUnit = function () {
          return this.abs().value === BigInt(1);
      }
  
      BigInteger.prototype.isZero = function () {
          return false;
      };
      SmallInteger.prototype.isZero = function () {
          return this.value === 0;
      };
      NativeBigInt.prototype.isZero = function () {
          return this.value === BigInt(0);
      }
  
      BigInteger.prototype.isDivisibleBy = function (v) {
          var n = parseValue(v);
          if (n.isZero()) return false;
          if (n.isUnit()) return true;
          if (n.compareAbs(2) === 0) return this.isEven();
          return this.mod(n).isZero();
      };
      NativeBigInt.prototype.isDivisibleBy = SmallInteger.prototype.isDivisibleBy = BigInteger.prototype.isDivisibleBy;
  
      function isBasicPrime(v) {
          var n = v.abs();
          if (n.isUnit()) return false;
          if (n.equals(2) || n.equals(3) || n.equals(5)) return true;
          if (n.isEven() || n.isDivisibleBy(3) || n.isDivisibleBy(5)) return false;
          if (n.lesser(49)) return true;
          // we don't know if it's prime: let the other functions figure it out
      }
  
      function millerRabinTest(n, a) {
          var nPrev = n.prev(),
              b = nPrev,
              r = 0,
              d, t, i, x;
          while (b.isEven()) b = b.divide(2), r++;
          next: for (i = 0; i < a.length; i++) {
              if (n.lesser(a[i])) continue;
              x = bigInt(a[i]).modPow(b, n);
              if (x.isUnit() || x.equals(nPrev)) continue;
              for (d = r - 1; d != 0; d--) {
                  x = x.square().mod(n);
                  if (x.isUnit()) return false;
                  if (x.equals(nPrev)) continue next;
              }
              return false;
          }
          return true;
      }
  
      // Set "strict" to true to force GRH-supported lower bound of 2*log(N)^2
      BigInteger.prototype.isPrime = function (strict) {
          var isPrime = isBasicPrime(this);
          if (isPrime !== undefined) return isPrime;
          var n = this.abs();
          var bits = n.bitLength();
          if (bits <= 64)
              return millerRabinTest(n, [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37]);
          var logN = Math.log(2) * bits.toJSNumber();
          var t = Math.ceil((strict === true) ? (2 * Math.pow(logN, 2)) : logN);
          for (var a = [], i = 0; i < t; i++) {
              a.push(bigInt(i + 2));
          }
          return millerRabinTest(n, a);
      };
      NativeBigInt.prototype.isPrime = SmallInteger.prototype.isPrime = BigInteger.prototype.isPrime;
  
      BigInteger.prototype.isProbablePrime = function (iterations) {
          var isPrime = isBasicPrime(this);
          if (isPrime !== undefined) return isPrime;
          var n = this.abs();
          var t = iterations === undefined ? 5 : iterations;
          for (var a = [], i = 0; i < t; i++) {
              a.push(bigInt.randBetween(2, n.minus(2)));
          }
          return millerRabinTest(n, a);
      };
      NativeBigInt.prototype.isProbablePrime = SmallInteger.prototype.isProbablePrime = BigInteger.prototype.isProbablePrime;
  
      BigInteger.prototype.modInv = function (n) {
          var t = bigInt.zero, newT = bigInt.one, r = parseValue(n), newR = this.abs(), q, lastT, lastR;
          while (!newR.isZero()) {
              q = r.divide(newR);
              lastT = t;
              lastR = r;
              t = newT;
              r = newR;
              newT = lastT.subtract(q.multiply(newT));
              newR = lastR.subtract(q.multiply(newR));
          }
          if (!r.isUnit()) throw new Error(this.toString() + " and " + n.toString() + " are not co-prime");
          if (t.compare(0) === -1) {
              t = t.add(n);
          }
          if (this.isNegative()) {
              return t.negate();
          }
          return t;
      };
  
      NativeBigInt.prototype.modInv = SmallInteger.prototype.modInv = BigInteger.prototype.modInv;
  
      BigInteger.prototype.next = function () {
          var value = this.value;
          if (this.sign) {
              return subtractSmall(value, 1, this.sign);
          }
          return new BigInteger(addSmall(value, 1), this.sign);
      };
      SmallInteger.prototype.next = function () {
          var value = this.value;
          if (value + 1 < MAX_INT) return new SmallInteger(value + 1);
          return new BigInteger(MAX_INT_ARR, false);
      };
      NativeBigInt.prototype.next = function () {
          return new NativeBigInt(this.value + BigInt(1));
      }
  
      BigInteger.prototype.prev = function () {
          var value = this.value;
          if (this.sign) {
              return new BigInteger(addSmall(value, 1), true);
          }
          return subtractSmall(value, 1, this.sign);
      };
      SmallInteger.prototype.prev = function () {
          var value = this.value;
          if (value - 1 > -MAX_INT) return new SmallInteger(value - 1);
          return new BigInteger(MAX_INT_ARR, true);
      };
      NativeBigInt.prototype.prev = function () {
          return new NativeBigInt(this.value - BigInt(1));
      }
  
      var powersOfTwo = [1];
      while (2 * powersOfTwo[powersOfTwo.length - 1] <= BASE) powersOfTwo.push(2 * powersOfTwo[powersOfTwo.length - 1]);
      var powers2Length = powersOfTwo.length, highestPower2 = powersOfTwo[powers2Length - 1];
  
      function shift_isSmall(n) {
          return Math.abs(n) <= BASE;
      }
  
      BigInteger.prototype.shiftLeft = function (v) {
          var n = parseValue(v).toJSNumber();
          if (!shift_isSmall(n)) {
              throw new Error(String(n) + " is too large for shifting.");
          }
          if (n < 0) return this.shiftRight(-n);
          var result = this;
          if (result.isZero()) return result;
          while (n >= powers2Length) {
              result = result.multiply(highestPower2);
              n -= powers2Length - 1;
          }
          return result.multiply(powersOfTwo[n]);
      };
      NativeBigInt.prototype.shiftLeft = SmallInteger.prototype.shiftLeft = BigInteger.prototype.shiftLeft;
  
      BigInteger.prototype.shiftRight = function (v) {
          var remQuo;
          var n = parseValue(v).toJSNumber();
          if (!shift_isSmall(n)) {
              throw new Error(String(n) + " is too large for shifting.");
          }
          if (n < 0) return this.shiftLeft(-n);
          var result = this;
          while (n >= powers2Length) {
              if (result.isZero() || (result.isNegative() && result.isUnit())) return result;
              remQuo = divModAny(result, highestPower2);
              result = remQuo[1].isNegative() ? remQuo[0].prev() : remQuo[0];
              n -= powers2Length - 1;
          }
          remQuo = divModAny(result, powersOfTwo[n]);
          return remQuo[1].isNegative() ? remQuo[0].prev() : remQuo[0];
      };
      NativeBigInt.prototype.shiftRight = SmallInteger.prototype.shiftRight = BigInteger.prototype.shiftRight;
  
      function bitwise(x, y, fn) {
          y = parseValue(y);
          var xSign = x.isNegative(), ySign = y.isNegative();
          var xRem = xSign ? x.not() : x,
              yRem = ySign ? y.not() : y;
          var xDigit = 0, yDigit = 0;
          var xDivMod = null, yDivMod = null;
          var result = [];
          while (!xRem.isZero() || !yRem.isZero()) {
              xDivMod = divModAny(xRem, highestPower2);
              xDigit = xDivMod[1].toJSNumber();
              if (xSign) {
                  xDigit = highestPower2 - 1 - xDigit; // two's complement for negative numbers
              }
  
              yDivMod = divModAny(yRem, highestPower2);
              yDigit = yDivMod[1].toJSNumber();
              if (ySign) {
                  yDigit = highestPower2 - 1 - yDigit; // two's complement for negative numbers
              }
  
              xRem = xDivMod[0];
              yRem = yDivMod[0];
              result.push(fn(xDigit, yDigit));
          }
          var sum = fn(xSign ? 1 : 0, ySign ? 1 : 0) !== 0 ? bigInt(-1) : bigInt(0);
          for (var i = result.length - 1; i >= 0; i -= 1) {
              sum = sum.multiply(highestPower2).add(bigInt(result[i]));
          }
          return sum;
      }
  
      BigInteger.prototype.not = function () {
          return this.negate().prev();
      };
      NativeBigInt.prototype.not = SmallInteger.prototype.not = BigInteger.prototype.not;
  
      BigInteger.prototype.and = function (n) {
          return bitwise(this, n, function (a, b) { return a & b; });
      };
      NativeBigInt.prototype.and = SmallInteger.prototype.and = BigInteger.prototype.and;
  
      BigInteger.prototype.or = function (n) {
          return bitwise(this, n, function (a, b) { return a | b; });
      };
      NativeBigInt.prototype.or = SmallInteger.prototype.or = BigInteger.prototype.or;
  
      BigInteger.prototype.xor = function (n) {
          return bitwise(this, n, function (a, b) { return a ^ b; });
      };
      NativeBigInt.prototype.xor = SmallInteger.prototype.xor = BigInteger.prototype.xor;
  
      var LOBMASK_I = 1 << 30, LOBMASK_BI = (BASE & -BASE) * (BASE & -BASE) | LOBMASK_I;
      function roughLOB(n) { // get lowestOneBit (rough)
          // SmallInteger: return Min(lowestOneBit(n), 1 << 30)
          // BigInteger: return Min(lowestOneBit(n), 1 << 14) [BASE=1e7]
          var v = n.value,
              x = typeof v === "number" ? v | LOBMASK_I :
                  typeof v === "bigint" ? v | BigInt(LOBMASK_I) :
                      v[0] + v[1] * BASE | LOBMASK_BI;
          return x & -x;
      }
  
      function integerLogarithm(value, base) {
          if (base.compareTo(value) <= 0) {
              var tmp = integerLogarithm(value, base.square(base));
              var p = tmp.p;
              var e = tmp.e;
              var t = p.multiply(base);
              return t.compareTo(value) <= 0 ? { p: t, e: e * 2 + 1 } : { p: p, e: e * 2 };
          }
          return { p: bigInt(1), e: 0 };
      }
  
      BigInteger.prototype.bitLength = function () {
          var n = this;
          if (n.compareTo(bigInt(0)) < 0) {
              n = n.negate().subtract(bigInt(1));
          }
          if (n.compareTo(bigInt(0)) === 0) {
              return bigInt(0);
          }
          return bigInt(integerLogarithm(n, bigInt(2)).e).add(bigInt(1));
      }
      NativeBigInt.prototype.bitLength = SmallInteger.prototype.bitLength = BigInteger.prototype.bitLength;
  
      function max(a, b) {
          a = parseValue(a);
          b = parseValue(b);
          return a.greater(b) ? a : b;
      }
      function min(a, b) {
          a = parseValue(a);
          b = parseValue(b);
          return a.lesser(b) ? a : b;
      }
      function gcd(a, b) {
          a = parseValue(a).abs();
          b = parseValue(b).abs();
          if (a.equals(b)) return a;
          if (a.isZero()) return b;
          if (b.isZero()) return a;
          var c = Integer[1], d, t;
          while (a.isEven() && b.isEven()) {
              d = min(roughLOB(a), roughLOB(b));
              a = a.divide(d);
              b = b.divide(d);
              c = c.multiply(d);
          }
          while (a.isEven()) {
              a = a.divide(roughLOB(a));
          }
          do {
              while (b.isEven()) {
                  b = b.divide(roughLOB(b));
              }
              if (a.greater(b)) {
                  t = b; b = a; a = t;
              }
              b = b.subtract(a);
          } while (!b.isZero());
          return c.isUnit() ? a : a.multiply(c);
      }
      function lcm(a, b) {
          a = parseValue(a).abs();
          b = parseValue(b).abs();
          return a.divide(gcd(a, b)).multiply(b);
      }
      function randBetween(a, b) {
          a = parseValue(a);
          b = parseValue(b);
          var low = min(a, b), high = max(a, b);
          var range = high.subtract(low).add(1);
          if (range.isSmall) return low.add(Math.floor(Math.random() * range));
          var digits = toBase(range, BASE).value;
          var result = [], restricted = true;
          for (var i = 0; i < digits.length; i++) {
              var top = restricted ? digits[i] : BASE;
              var digit = truncate(Math.random() * top);
              result.push(digit);
              if (digit < top) restricted = false;
          }
          return low.add(Integer.fromArray(result, BASE, false));
      }
  
      var parseBase = function (text, base, alphabet, caseSensitive) {
          alphabet = alphabet || DEFAULT_ALPHABET;
          text = String(text);
          if (!caseSensitive) {
              text = text.toLowerCase();
              alphabet = alphabet.toLowerCase();
          }
          var length = text.length;
          var i;
          var absBase = Math.abs(base);
          var alphabetValues = {};
          for (i = 0; i < alphabet.length; i++) {
              alphabetValues[alphabet[i]] = i;
          }
          for (i = 0; i < length; i++) {
              var c = text[i];
              if (c === "-") continue;
              if (c in alphabetValues) {
                  if (alphabetValues[c] >= absBase) {
                      if (c === "1" && absBase === 1) continue;
                      throw new Error(c + " is not a valid digit in base " + base + ".");
                  }
              }
          }
          base = parseValue(base);
          var digits = [];
          var isNegative = text[0] === "-";
          for (i = isNegative ? 1 : 0; i < text.length; i++) {
              var c = text[i];
              if (c in alphabetValues) digits.push(parseValue(alphabetValues[c]));
              else if (c === "<") {
                  var start = i;
                  do { i++; } while (text[i] !== ">" && i < text.length);
                  digits.push(parseValue(text.slice(start + 1, i)));
              }
              else throw new Error(c + " is not a valid character");
          }
          return parseBaseFromArray(digits, base, isNegative);
      };
  
      function parseBaseFromArray(digits, base, isNegative) {
          var val = Integer[0], pow = Integer[1], i;
          for (i = digits.length - 1; i >= 0; i--) {
              val = val.add(digits[i].times(pow));
              pow = pow.times(base);
          }
          return isNegative ? val.negate() : val;
      }
  
      function stringify(digit, alphabet) {
          alphabet = alphabet || DEFAULT_ALPHABET;
          if (digit < alphabet.length) {
              return alphabet[digit];
          }
          return "<" + digit + ">";
      }
  
      function toBase(n, base) {
          base = bigInt(base);
          if (base.isZero()) {
              if (n.isZero()) return { value: [0], isNegative: false };
              throw new Error("Cannot convert nonzero numbers to base 0.");
          }
          if (base.equals(-1)) {
              if (n.isZero()) return { value: [0], isNegative: false };
              if (n.isNegative())
                  return {
                      value: [].concat.apply([], Array.apply(null, Array(-n.toJSNumber()))
                          .map(Array.prototype.valueOf, [1, 0])
                      ),
                      isNegative: false
                  };
  
              var arr = Array.apply(null, Array(n.toJSNumber() - 1))
                  .map(Array.prototype.valueOf, [0, 1]);
              arr.unshift([1]);
              return {
                  value: [].concat.apply([], arr),
                  isNegative: false
              };
          }
  
          var neg = false;
          if (n.isNegative() && base.isPositive()) {
              neg = true;
              n = n.abs();
          }
          if (base.isUnit()) {
              if (n.isZero()) return { value: [0], isNegative: false };
  
              return {
                  value: Array.apply(null, Array(n.toJSNumber()))
                      .map(Number.prototype.valueOf, 1),
                  isNegative: neg
              };
          }
          var out = [];
          var left = n, divmod;
          while (left.isNegative() || left.compareAbs(base) >= 0) {
              divmod = left.divmod(base);
              left = divmod.quotient;
              var digit = divmod.remainder;
              if (digit.isNegative()) {
                  digit = base.minus(digit).abs();
                  left = left.next();
              }
              out.push(digit.toJSNumber());
          }
          out.push(left.toJSNumber());
          return { value: out.reverse(), isNegative: neg };
      }
  
      function toBaseString(n, base, alphabet) {
          var arr = toBase(n, base);
          return (arr.isNegative ? "-" : "") + arr.value.map(function (x) {
              return stringify(x, alphabet);
          }).join('');
      }
  
      BigInteger.prototype.toArray = function (radix) {
          return toBase(this, radix);
      };
  
      SmallInteger.prototype.toArray = function (radix) {
          return toBase(this, radix);
      };
  
      NativeBigInt.prototype.toArray = function (radix) {
          return toBase(this, radix);
      };
  
      BigInteger.prototype.toString = function (radix, alphabet) {
          if (radix === undefined) radix = 10;
          if (radix !== 10) return toBaseString(this, radix, alphabet);
          var v = this.value, l = v.length, str = String(v[--l]), zeros = "0000000", digit;
          while (--l >= 0) {
              digit = String(v[l]);
              str += zeros.slice(digit.length) + digit;
          }
          var sign = this.sign ? "-" : "";
          return sign + str;
      };
  
      SmallInteger.prototype.toString = function (radix, alphabet) {
          if (radix === undefined) radix = 10;
          if (radix != 10) return toBaseString(this, radix, alphabet);
          return String(this.value);
      };
  
      NativeBigInt.prototype.toString = SmallInteger.prototype.toString;
  
      NativeBigInt.prototype.toJSON = BigInteger.prototype.toJSON = SmallInteger.prototype.toJSON = function () { return this.toString(); }
  
      BigInteger.prototype.valueOf = function () {
          return parseInt(this.toString(), 10);
      };
      BigInteger.prototype.toJSNumber = BigInteger.prototype.valueOf;
  
      SmallInteger.prototype.valueOf = function () {
          return this.value;
      };
      SmallInteger.prototype.toJSNumber = SmallInteger.prototype.valueOf;
      NativeBigInt.prototype.valueOf = NativeBigInt.prototype.toJSNumber = function () {
          return parseInt(this.toString(), 10);
      }
  
      function parseStringValue(v) {
          if (isPrecise(+v)) {
              var x = +v;
              if (x === truncate(x))
                  return supportsNativeBigInt ? new NativeBigInt(BigInt(x)) : new SmallInteger(x);
              throw new Error("Invalid integer: " + v);
          }
          var sign = v[0] === "-";
          if (sign) v = v.slice(1);
          var split = v.split(/e/i);
          if (split.length > 2) throw new Error("Invalid integer: " + split.join("e"));
          if (split.length === 2) {
              var exp = split[1];
              if (exp[0] === "+") exp = exp.slice(1);
              exp = +exp;
              if (exp !== truncate(exp) || !isPrecise(exp)) throw new Error("Invalid integer: " + exp + " is not a valid exponent.");
              var text = split[0];
              var decimalPlace = text.indexOf(".");
              if (decimalPlace >= 0) {
                  exp -= text.length - decimalPlace - 1;
                  text = text.slice(0, decimalPlace) + text.slice(decimalPlace + 1);
              }
              if (exp < 0) throw new Error("Cannot include negative exponent part for integers");
              text += (new Array(exp + 1)).join("0");
              v = text;
          }
          var isValid = /^([0-9][0-9]*)$/.test(v);
          if (!isValid) throw new Error("Invalid integer: " + v);
          if (supportsNativeBigInt) {
              return new NativeBigInt(BigInt(sign ? "-" + v : v));
          }
          var r = [], max = v.length, l = LOG_BASE, min = max - l;
          while (max > 0) {
              r.push(+v.slice(min, max));
              min -= l;
              if (min < 0) min = 0;
              max -= l;
          }
          trim(r);
          return new BigInteger(r, sign);
      }
  
      function parseNumberValue(v) {
          if (supportsNativeBigInt) {
              return new NativeBigInt(BigInt(v));
          }
          if (isPrecise(v)) {
              if (v !== truncate(v)) throw new Error(v + " is not an integer.");
              return new SmallInteger(v);
          }
          return parseStringValue(v.toString());
      }
  
      function parseValue(v) {
          if (typeof v === "number") {
              return parseNumberValue(v);
          }
          if (typeof v === "string") {
              return parseStringValue(v);
          }
          if (typeof v === "bigint") {
              return new NativeBigInt(v);
          }
          return v;
      }
      // Pre-define numbers in range [-999,999]
      for (var i = 0; i < 1000; i++) {
          Integer[i] = parseValue(i);
          if (i > 0) Integer[-i] = parseValue(-i);
      }
      // Backwards compatibility
      Integer.one = Integer[1];
      Integer.zero = Integer[0];
      Integer.minusOne = Integer[-1];
      Integer.max = max;
      Integer.min = min;
      Integer.gcd = gcd;
      Integer.lcm = lcm;
      Integer.isInstance = function (x) { return x instanceof BigInteger || x instanceof SmallInteger || x instanceof NativeBigInt; };
      Integer.randBetween = randBetween;
  
      Integer.fromArray = function (digits, base, isNegative) {
          return parseBaseFromArray(digits.map(parseValue), parseValue(base || 10), isNegative);
      };
  
      return Integer;
  })();
  