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);
        int n = sc.nextInt();
        for (int i = 1 ; i <= 3500 ; i++) {
            for (int j = 1 ; j <= 3500 ; j++) {
                if (4 * i * j - (long) n * (i + j) > 0 && (long) n * i * j % (4 * i * j - n * (i + j)) == 0) {
                    System.out.println(i + " " + j + " " + (long) n * i * j / (4 * i * j - n * (i + j)));
                    return;
                }
            }
        }

        System.out.println("NG");



    }
}