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 <cstdio>

int main() {
  long N, h = 0, n = 0, w = 0;
  scanf("%ld", &N);
  for (h = 1; h <= 3500; h++) {
    for (n = 1; n <= 3500; n++) {
      if ((4 * h * n - N * n - N * h) > 0 && (N * h * n) % (4 * h * n - N * n - N * h) == 0) {
        w = (N * h * n) / (4 * h * n - N * n - N * h);
        printf("%ld %ld %ld\n", h, n, w);
        return 0;
      }
    }
  }
}