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, 47]
def power(a, b):
	res = 1
	while (b):
		if (b & 1): res *= a
		a *= a
		b >>= 1
	return res
ans = []
ans.append(1e30)
def solve(pos, n, res):
	if (n == 1):
		ans[0] = min(ans[0], res)
	for i in range(2, 62):
		if (n % i == 0):
			solve(pos + 1, n / i, res * power(P[pos], i - 1))
n = int(input())
solve(0, n, 1)
print(ans[0])