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.*;

class Main{
  public static void main(String[] args){
    Scanner sc=new Scanner(System.in);
    long x=sc.nextLong();
    for(long h=1;h<=3500;h++){
      for(long n=h;n<=3500;n++){
        if((4*h*n-n*x-h*x)>0&&(h*n*x)%(4*h*n-n*x-h*x)==0){
          System.out.println(h+" "+n+" "+((h*n*x)/(4*h*n-n*x-h*x)));
          return;
        }
      }
    }
  }
}