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 == 1:
            return 1
        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]
        return min(p ** (d - 1) * f(x // d, i + 1, bb) for d in bb)

    n = int(input())
    print(f(n, 0, [d for d in range(2, n + 1) if not n % d]))


if __name__ == '__main__':
    main()
