You are given a positive integer X. Find the largest perfect power that is at most X. Here, a perfect power is an integer that can be represented as b^p, where b is an integer not less than 1 and p is an integer not less than 2.

Constraints

* 1 ≤ X ≤ 1000
* X is an integer.

Input

Input is given from Standard Input in the following format:


X


Output

Print the largest perfect power that is at most X.

Examples

Input

10


Output

9


Input

1


Output

1


Input

999


Output

961
#include<bits/stdc++.h>
using namespace std;
int main (){
	int x,j,ans,s=9999;
	cin>>x;
	if(x==1){cout<<x;return 0;}
	for(int i=2;i*i<=x;i++){
		for(j=i;j*i<=x;j=j*i){}
		if(x-j<s) s=x-j;
	}
	ans=x-s;
	cout<<ans;
	return 0;
}