Problem: You are given an integer N.

Find a triple of positive integers h, n and w such that 4/N = 1/h + 1/n + 1/w.

If there are multiple solutions, any of them will be accepted.

Constraints

* It is guaranteed that, for the given integer N, there exists a solution such that h,n,w \leq 3500.

Inputs

Input is given from Standard Input in the following format:


N


Outputs

Print a triple of positive integers h, n and w that satisfies the condition, in the following format:


h n w

Examples

Input

2


Output

1 2 2


Input

3485


Output

872 1012974 1539173474040


Input

4664


Output

3498 3498 3498

Solution (in JAVA):

Solution:
import java.util.Scanner;

public class Main {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		long N = sc.nextInt();
		for(long n = 1; n <= 3500; n++) {
			for(long w = 1; w <= 3500; w++) {
				long k1 = N * n * w;
				long k2 = 4 * n * w - N * (n + w);
				if(k2 >= 1 && k1 % k2 == 0) {
					System.out.printf("%d %d %d", k1 / k2, n, w);
					System.exit(0);
				}
			}
		}
		sc.close();
	}
}