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 <bits/stdc++.h>
# define INF 1e9
using namespace std;

int main(){

  long int N;
  cin >> N;
  for(int n=1; n<3501; n++){
    for(int h=1; h<3501; h++){
      long int num = N * h * n;
      long int den = 4*h*n - N*(n+h);
      if (den > 0 && num % den == 0){
        cout << n <<" "<< h <<" " << num / den << endl;
        exit(0);
      }
    }
  }

}