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);
		double n = sc.nextInt();
		sc.close();
		for (double c = 1; c <= 3500; c++) {
			double t1 = 4 * c / n - 1;
			if (t1 <= 0) {
				continue;
			}
			for (double b = 1; b <= 3500; b++) {
				double t2 =b * (4 * c / n - 1) - c ;
				if(t2 <= 0 ) {
					continue;
				}
				double t3 = b * c / (b * (4 * c / n - 1) - c);
				if (t3 < 1) {
					continue;
				}
				int t4 =(int) (b * c / (b * (4 * c / n - 1) - c));
				if (t3 == t4) {
					int a = t4;
					System.out.println(a + " " + (int)b + " " + (int)c);
					return;
				}
			}
		}
	}
}