CodeForces - 27E Number With The Given Amount Of Divisors （反素数入门）

CodeForces - 27E

Number With The Given Amount Of Divisors

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Description

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.

Sample Input

Input

4

Output

6

Input

6

Output

12

#include<stdio.h>#include<string.h>#include<algorithm>using namespace std;typedef unsigned long long ll;const ll INF = (ll)1<<63;int n;ll ans;int p[16]={2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53};void dfs(int gen,ll tmp,int num){if(num>n)return ;if(num==n&&ans>tmp)ans=tmp;for(int i=1;i<=63;i++){if(ans/p[gen]<tmp)break;dfs(gen+1,tmp*=p[gen],num*(i+1));}}int main(){while(scanf("%d",&n)!=EOF){ans=INF;dfs(0,1,1);printf("%lld\n",ans);}return 0;}