log = console.log;

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 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;
  }
  BigInteger.prototype = Object.create(Integer.prototype);

  function SmallInteger(value) {
      this.value = value;
      this.sign = value < 0;
      this.isSmall = true;
  }
  SmallInteger.prototype = Object.create(Integer.prototype);

  function NativeBigInt(value) {
      this.value = value;
  }
  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;
})();

var stdin = require("fs").readFileSync("/dev/stdin", "UTF-8");
var lines = stdin.split("\n");
var N = lines[0].split(" ").map(Number)[0];
var T = lines
  .slice(1)
  .filter(v => v !== "")
  .map(Number);


for(var i=1; i<N;i++){
  T[i] = bigInt.lcm(T[i],T[i-1]).toString() 
}

log(T[N-1])