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>
using namespace std;
using lint = long long;

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