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: Wrong Answer)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.List;

public class Main {

	public static void main(String[] args) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		int X = Integer.parseInt(br.readLine());
		int[] prime = {2,3, 5, 7, 11, 13, 17, 19, 23, 29, 31};
		List<Integer> beki = new ArrayList<Integer>();
		beki.add(1);

		for(int i = 0;i<prime.length;i++){
			int p = 2;
			int now = (int)Math.pow(prime[i], p);
			while(now <= X){
				beki.add(now);
				p++;
				now = (int)Math.pow(prime[i], p);

			}
		}

		beki.sort(null);
		System.out.println(beki.get(beki.size()-1));

	}


}