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: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;

int main() {
    int X;
    cin >> X;
    int ans = 0;
    vector<bool>ok(X+1);
    ok[1] = 1;
    for(int i = 2; i*i < X; i++) {
        ok[i*i] = 1;
        int cnt = i*i;
        while(cnt < X) {
            ok[cnt] = 1;
            cnt *= i;
        }
    }
    for(int i = X; i >= 1; i--) {
        if(ok[i]) {
            cout << i << endl;
            break;
        }
    }
}