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]
N=0
ans=1000000000000000000

def dfs(i,x,n):
    global ans
    if n>N: return
    if n==N and x<ans: ans=x
    for j in range(1,61):
        if ans<=x*p[i]: return
        x*=p[i]
        dfs(i+1,x, n*(j+1))

N=int(input())
dfs(0,1,1)
print(ans)
