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 <iostream>
#include <vector>
#include <cmath>
#include <algorithm>
#define rep(i,n) Rep(i,0,n)
#define Rep(i,k,n) for(int i=k ; i<n ; i++)
#define vii vector<int,int>
#define Sort(v) sort(v.begin(),v.end())

const int MOD = 1000000007;
const int INF = 1<<30;
using namespace std;

bool judge(int x,int y){
    int a = y;
    while(x > a){
        a *= y;
    }
    return x == a;
}


int main(){
    
    int x;
    cin >> x;
    
    int ans = 1;
    for(int i=x ; i>=0 ; i--){
        for(int j=2 ; j*j<x ; j++){
            if(judge(i,j)) {
                ans = i;
                break;
            }
        }
        if(ans != 1) break;
    }
    
    cout << ans << endl;
}