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();
        long n = 0, h = 0, w = 0;
        for (int i = 1; i < 3501; i++) {
            for (int j = 1; j < 3501; j++) {
                long a = N * i * j;
                long b = 4*i*j - N*i - N*j;
                if(0 < b && b < a && a % b == 0){
                    h = i; w = j; n = a/b; break;
                }
            }
        }
        System.out.println(n + " " + h + " " + w);
        sc.close();

    }

}