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;
#define MOD 1000000007

int main() {
  
  long long N;
  cin >> N;

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