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 fn(n, index, primes):
    if(n==1): return 1
    ans = 10**19
    for i in range(2, n+1):
        if(n%i==0):
            ans = min(ans, primes[index]**(i-1)*fn(n//i, index+1, primes))
    return ans

primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29]
n = int(input())
print(fn(n, 0, primes))