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;
using ll = long long;
int main () {
  ll N;
  cin >> N;
  for(ll h = 1; h <= 3500; h++) {
    for(ll w = h; w <= 3500; w++) {
      ll a = 4 * h * w - N * w - N  * h;
      ll b = N * h * w;
      if (a > 0 && (b % a) == 0) {
        cout << h << ' ' << w << ' ' << b / a << endl;
        return 0;
      }
    }
  }
}