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>
#define REP(i, a, n) for(ll i = ((ll) a); i < ((ll) n); i++)
using namespace std;
typedef long long ll;

ll N;

int main(void) {
  cin >> N;

  REP(h, 1, 3501) REP(w, 1, 3501) {
    ll p = h * w * N;
    ll q = 4 * h * w - N * (h + w);
    if(q != 0 && p % q == 0 && p / q > 0) {
      cout << h << " " << p / q << " " << w << endl;
      return 0;
    }
  }
}