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 i = 1; i <= 3500; ++i) {
    for (ll j = 1; j <= 3500; ++j) {
      ll x = n * i * j;
      ll y = 4 * i * j - n * (i + j);
      if (y > 0 && x % y == 0) {
        printf("%lld %lld %lld\n", i, j, x / y);
        return 0;
      }
    }
  }
}