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)
ans = 10**18
def g(a, n, i):
    global ans
    if a < ans:
        if n == 1:
            ans = a
        else:
            for j in range(2, n + 1):
                if n % j == 0:
                    g(a * (p[i] ** (j - 1) ), n / j, i + 1)
g(1, input(), 0)
print ans