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 <algorithm>

using namespace std;

int main(){
  int a;
  cin >> a;

  int max_v = 0;

  for(int i = 2; i < 32; i++){
    int tmp = i;
    if (tmp * i > a){
      tmp = i;
    }else{
      while(tmp <= a){
        tmp *= i;
      }
    }
    max_v = max(max_v, tmp/i);
  }

  cout << max_v <<endl;

  return 0;
}