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 ll = long long;
using namespace std;
ll mod=1e9+7;
ll inf=1e10;

int main(){
  ll N;
  cin>>N;
  for (ll h(1);h<=3500;h++){
    for (ll n(1);n<=3500;n++){
      ll ue = N*h*n;
      ll sita = 4*h*n - n*N - h*N;
      if (sita!=0&&ue%sita==0&&sita>=0){
        cout << h <<" "<< n <<" "<< ue/sita << endl;
        return 0;
      }
    }
  }
  return 0;
}