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
p = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43]


def dfs(n, pos):
    v = [1, 10 ** 18][n > 1]
    for i in range(2, n + 1):
        if n % i == 0:
            v = min(v, p[pos] ** (i - 1) * dfs(n // i, pos + 1))
    return v

print(dfs(int(input()), 0))
