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(){
  long long n;cin>>n;
  for(long long i = 1; 3500 >= i; i++){
    for(long long j = 1; 3500 >= j; j++){
      if(!(4*i*j-n*j-n*i))continue;
      if(!((n*i*j)%(4*i*j-n*j-n*i)) && (n*i*j)/(4*i*j-n*j-n*i) > 0){
        cout << i << " " << j << " " << (n*i*j)/(4*i*j-n*j-n*i) << endl;
        return 0;
      }
    }
  }
}