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;

typedef long long ll;

int main()
{
  ll n;
  cin >> n;
  for (int h = 1; h <= 3500; h++)
  {
    for (int w = 1; w < 3500; w++)
    {
      ll x = 4 * h * w - n * (w + h);
      if (x > 0 && (n * h * w) % x == 0)
      {
        ll y = (n * h * w) / x;
        cout << h << " " << w << " " << y << endl;
        return 0;
      }
    }
  }
}