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
def main():

	primes = (2, 3, 5, 7, 11, 13, 17, 19, 23, 29)
	mmax = 29**1001
	mem = {}

	def solve(pos, n):

		if(pos >= len(primes) and n  > 1): return mmax
		if(pos >= len(primes) and n == 1): return 1

		if (pos, n) in mem:
			return mem[(pos, n)]

		ans = mmax
		for i in xrange(1, n+1):

			if n % i != 0: continue 

			res = primes[pos] ** (i-1) * solve(pos+1, n / i)
			ans = min(ans, res)
			
		mem[(pos, n)] = ans
		return ans


	n = input()

	print solve(0, n)

main()
