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>
typedef long long int ll;
using namespace std;

int main(){
  ll N,h,n,w;
  cin>>N;

  w=-1;
  for(h=1;w==-1&&h<=3500;h++){
    for(n=h;w==-1&&n<=3500;n++){
      ll factor1 = N * h * n;
      ll factor2 = 4*h*n-N*n-N*h;
      if(factor2>0&&(factor1%factor2)==0){
        w=factor1/factor2;
        goto XX;
      }
    }
  }
 XX:
  cout<<h<<" "<<n<<" "<<w<<endl;
  return 0;
}