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(){
  long long N;
  cin >> N;
  long long n,w,h;
  for(n=1;n<=3500;n++){
    for(w=1;w<=3500;w++){
      if((4*n*w-w*N-n*N)>0&&(N*n*w)%(4*n*w-w*N-n*N)==0){
        cout << (N*n*w)/(4*n*w-w*N-n*N) << " " << n << " " << w << endl;
        return 0;
      }
    }
  }
  return 0;
}