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 k = 1; k <= 3500; k++) {
                if (4 * h * k - n * (h + k) == 0) {
                    continue;
                }
                if (n * h * k % (4 * h * k - n * (h + k)) != 0) {
                    continue;
                }
                long w = n * h * k / (4 * h * k - n * (h + k));
                if(w <= 0){
                    continue;
                }
                System.out.printf("%d %d %d%n", h, k, w);
                return;
            }
        }
    }
}