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 a;
    cin >> a;
    vector<int> pri = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31};
    vector<int> x = {1,1,1,1,1,1,1,1,1,1,1};
    for(int i=0; i < 11; i++){
        while (x[i] <= a){
            x[i] *= pri[i];
        }
        if(x[i] != 1){
            x[i] /= pri[i];
        }
    }
    sort(x.begin(), x.end());
    cout << x[10];
}