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;
typedef long long ll;
#define INF (1<<30)
#define INFLL (1ll<<60)
typedef pair<int, int> P;
#define MOD (1000000007ll)
#define l_ength size
#define EPS (1e-10)

int main(void){
	int i,j,k,x;
	bool isexp[1234];
	fill(isexp,isexp+1234,false);
	for(i=2; i<10; ++i){
		for(j=1; j<=33; ++j){
			x = 1;
			for(k=0; k<i; ++k){
				x *= j;
				if(x > 1000){
					break;
				}
			}
			if(x > 1000){
				break;
			}
			isexp[x] = true;
		}
	}
	cin >> x;
	while(!isexp[x]){
		--x;
	}
	cout << x << endl;
	return 0;
}