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;

class Main{
	public static void main(String args[]){
		int x, a, b, c;
		Scanner sc = new Scanner(System.in);
		x = sc.nextInt();
		while(x > 2) {
			x -= 1;
			a = b = x;
			while(true) {
				b--;
				while(a > 0) {
					a -= b;
					if(a == 0) {
						System.out.print(b);
					}
				}
			}
		}
		System.out.print(1);
	}
}