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;

int main(){
  long N;
  int c=0;
  cin >> N;
  for(long h=N/4;h<=3500;h++){
    for(long n=N/4;n<=3500;n++){
      if(4*h*n-N*n-h*N>0&&N*h*n%(4*h*n-N*n-h*N)==0&&c==0){
        cout << h <<' '<< n <<' '<< N*h*n/(4*h*n-N*n-h*N) << endl;
        c = 1;
      }
    }
  }
}