CF27E：Number With The Given Amount Of Divisors（反素数）

E. Number With The Given Amount Of Divisors

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

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

题意：给出n，输出最小的有n个因子的数。

思路：深搜答案，2^64就超过1018了，每个数枚举64次即可。

# include <iostream>
# define ULL unsigned long long

using namespace std;
int n, p[16] = {2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53};
ULL ans;

void dfs(int depth, ULL tmp, int num)
{
    if(num > n || depth >= 16) return;
    if(num == n && tmp < ans) ans = tmp;
    for(int i=1; i<=64; ++i)
    {
        if(ans < tmp) break;
        dfs(depth+1, tmp *= p[depth], num*(i+1));
    }
}

int main()
{

    while(cin >> n)
    {
        ans = ~0ULL;
        dfs(0, 1, 1);
        cout << ans << endl;
    }
    return 0;
}