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;
int X;
int main() {
    cin >> X;
    vector<bool> beki(X+1, false);
    beki.at(1) = true;

    for(int i = 2; i <= X; ++i) {
        int v = i * i;
        while(v <= X) {
            beki.at(v) = true;
            v *= i;
        }
    }

    for(int j = X; j >= 1; --j) {
        if(beki.at(j)) {
            cout << j << endl;
            return 0;
        }
    }
}