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.io.*;
import java.util.*;
import java.lang.Math;

public class Main {
    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);
        long N = sc.nextLong();
        for(long h = 1; h < 3501; ++h){
            for(long n = 1; n < 3501; ++n){
                long u = N * h * n;
                long d = 4 * h * n - N * n - N * h;
                if(d <= 0) continue;
                if(u < d) continue;
                if(u%d!=0) continue;
                long w = u/d;
                if(4 * h * n * w == N * n * w + N * h * w + N * h * n){
                    System.out.println(h + " " + n + " " + w);
                    return;
                }
            }
        }
        System.out.println("NO!");
    }
}