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<cstdio>
#include<cstdlib>
#include<cmath>

int main(){
    int x;
    std::cin >> x;
    int max = 1;
    if(x == 1){
        std::cout << 1 << std::endl;
        return 0;
    }
    for(int b = 2; b < sqrt(x); b++){
        int p = 1;
        while(1){
            if(std::pow(b, p) > x){
                break;
            }
            if(max < std::pow(b, p)){
                max = std::pow(b, p);
            }
            p++;
        }
    }
    std::cout << max << std::endl;
    return 0;
}