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