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 {

	private static final int VAL_LIMIT = 3500 + 1;

	public static void main(String[] args) {
		try (Scanner in = new Scanner(System.in)) {
			final int N = in.nextInt();

			int h0 = N / 4 + 1;
			for (int h = h0; h < VAL_LIMIT; ++h) {
				long a = (h << 2) - N;
				long b = N * h;
				int n0 = (int)(b / a + 1);
				for (int n = n0; n < VAL_LIMIT; ++n) {
					long c = a * n - b;
					long d = b * n;
					long w = d / c;
					if (w * c == d) {
						System.out.printf("%d %d %d%n", h, n, w);
						return;
					}
				}
			}
		}
	}
}