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 Java (OpenJDK 11.0.6) (judge verdict: Accepted)

import java.util.Scanner;

public class Main {

  public static void main(String[] args) {

    Scanner sc = new Scanner(System.in);
    boolean[] b = new boolean[1001];
    b[1] = true;
    for (int i = 2; i <= 32; i++) {
      int tmp = i * i;
      while (tmp <= 1000) {
        b[tmp] = true;
        tmp *= i;
      }
    }

    int x = sc.nextInt();
    int i = x;
    while (true) {
      if (b[i]) {
        System.out.println(i);
        return;
      }
      i--;
    }

  }
}