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 <cmath>
#include <iomanip>
#include <limits>
#include <string>
#include <vector>
#include <algorithm>
using namespace std;

int main() {
    int x;
    cin >> x;
    int cur=1;
    for(int i=x;;i--){
        for(int b=1;b<32;b++){
            for(int p=2;p<10;p++){
                cur = 1;
                for(int j=0;j<p;j++) cur *= b;
                if(cur == i){
                    cout << i << endl;
                    return 0;
                }
            }
        }
    }
}