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;
  cin >> N;
  for (long h = 1; h <= 3500; h++) {
    for (long n = 1; n <= 3500; n++) {
      long double w = (N * h * n) / (double) (4 * h * n - N * n - N * h);
      if (w < 0) continue;
      if (w == (long) w) return cout << h << " " << n << " " << (long) w << "\n", 0;
    }
  }
}