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 CPP):

Solution:

#include<iostream>

using namespace std;
int main(void){
  long N;
  cin >> N;
  bool exitFlag=false;
  for(int h=1;h<=3500;h++){
    for(int n=1;n<=3500;n++){
      long num=N*h*n;
      long den=4*h*n-N*(h+n);
      if(den<=0) continue;
      if(num%den==0){
	cout << h << " " << n << " " << num/den << endl;
	exitFlag=true;
	break;
      }
    }
    if(exitFlag) break;
  }
  return 0;
}