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: Accepted)

import java.util.Scanner;
public class Main {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int X = sc.nextInt();
		sc.close();
		
		int limit = (int) Math.floor(Math.sqrt(X));
		int ans = 1;
		int max = 1;
		
		for(int i=1; i<=limit; i++) {
			for(int j=2; j<1000; j++) {
				max = (int)Math.pow(i, j);
				if(max <= X) {
					if(ans < max) {
						ans = max;
					}else {
						ans += 0;
					}
				}
			}
		}
		System.out.println(ans);

	}

}