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;
using ll = long long;

int main(){
  ll N;
  cin >> N;

  for(ll h = 1; h <= 3500; h++){
    for(ll w = 1; w <= 3500; w++){
      ll num = N * h * w;
      ll den = 4 * h * w - N * w - N * h;
      if((den != 0) && (num % den == 0) && (num / den > 0)){
	cout << h << ' ' << (num / den) << ' ' << w << endl;
	return 0;
      }
    }
  }
}