Given the number n, find the smallest positive integer which has exactly n divisors. It is guaranteed that for the given n the answer will not exceed 1018.

Input

The first line of the input contains integer n (1 ≤ n ≤ 1000).

Output

Output the smallest positive integer with exactly n divisors.

Examples

Input

4


Output

6


Input

6


Output

12
def main():
    def f(x, i, aa):
        if (x, i) not in cache:
            bb = [q for q in aa if not x % q]
            p = (2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43)[i]
            cache[x, i] = min(p ** (d - 1) * f(x // d, i + 1, bb) for d in bb)
        return cache[x, i]

    n, cache = int(input()), dict.fromkeys(((1, i) for i in range(14)), 1)
    print(f(n, 0, [d for d in range(2, n + 1) if not n % d]))


if __name__ == '__main__':
    main()
