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 long n;
  cin >> n;
  
  for(int i = 1; i < 3501; i++){
    for(int j = i; j < 3501; j++){
      long long now = n * i * j;
      long long c = 4 * i * j - n * i - n * j;
      if(c <= 0) continue;
      if(now % c ) continue;
      cout << i << " " << j << " " << now / c << endl;
      return 0;
    }
  }
}