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 Java8 (OpenJDK 1.8.0) (judge verdict: Time Limit Exceeded)

import java.util.Scanner;

public class Main{
  public static void main(String[] args){
    Scanner scanner = new Scanner(System.in);
    int X = scanner.nextInt();
    int max = 0;

    while(true){
      int i = 0;
      int j = 0;
      for (i = 0; i <= Math.sqrt(X); i++){
        for (j = 0; j < 10; j++){
          if (max <= X){
          i *= i;
          max = Math.max(max, i);
          }
        }
      }
      if (i == Math.sqrt(X) && j == 9){break;}
    }
    System.out.println(max);
  }
}