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.*;

public class Main {
	public static void main (String[] args) {
		Scanner sc = new Scanner(System.in);
		long N = sc.nextLong();
		for (long h = 1; h <= 3500; h++) {
			for (long n = 1; n <= 3500; n++) {
				long bunbo = 4 * h * n - N * n - N * h;
				if (bunbo == 0) {
					continue;
				}
				if ((N * h * n) % bunbo == 0) {
					long w = (N * h * n) / bunbo ;
					if (w <= 0) {
						continue;
					}
					System.out.println(h + " " + n + " " + w);
					return;
				}
			}
		}
	}
}