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 <vector>

using namespace std;

int main()
{
    int x;
    cin >> x;
    vector<bool> expo(x + 1);
    expo[1] = 1;
    for (int b = 2; b <= x; b++)
    {
        int v = b * b;
        while (v <= x)
        {
            expo[v] = 1;
            v *= b;
        }
    }
    for (int i = x; x >= 1; i--)
    {
        if (expo[i] == 1)
        {
            cout << i << endl;
            return 0;
        }
    }
}