Problem:
Score : 200 points

Problem Statement

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.

Sample Input 1

10

Sample Output 1

9

There are four perfect powers that are at most 10: 1, 4, 8 and 9.
We should print the largest among them, 9.

Sample Input 2

1

Sample Output 2

1

Sample Input 3

999

Sample Output 3

961

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include<bits/stdc++.h>
 
using namespace std;
 
#define INF 1000000007
#define LINF 1000000000000000007
 
typedef long long ll;
typedef pair<ll,ll> P;


int a;

int beki(int b, int c){
	int d = b;
	for(int i = 1; i < c; i++){
		d *= b;
		if(d > a) return 0;
	}
	return d;
}

int main(){
	cin >> a;
	
	int b = 0;
	for(int i = 1; i < 333; i++){
		for(int j = 2; j < 100; j++){
			int c = beki(i, j);
			b = max(b, c);
		}
	}
	
	cout << b << endl;
	
	return 0;
}