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
prime = [0, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29]
min_value = round(1e18)
n = int(input())
def search(value, total_factor, i):
    global min_value
    if total_factor == n:
        min_value = min(value, min_value)
        return 
    for k in range(1, 65):
        value *= prime[i]
        if value > min_value:
            break
        if total_factor * (k + 1) <= n:
            search(value, total_factor * (k + 1), i+1)
search(1, 1, 1)    
print(min_value)