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
a = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29]

def rec(n, pos):
    if n == 1:
        return 1
    cur = 10**20
    for i in range(2, n + 1):
        if n % i == 0:
            cur = min(cur, a[pos] ** (i - 1) * rec(n // i, pos + 1))
    return cur

n = int(input())
print(rec(n, 0))


