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
n = int(input())
g = lambda n: [q for q in range(2, n + 1) if n % q == 0]
t = {k: g(k) for k in g(n)}
p = [2, 3, 5, 7, 11, 13, 17, 19, 23]
def f(i, k): return min(f(i + 1, k // s) * p[i] ** (s - 1) for s in t[k]) if k > 1 else 1
print(f(0, n))