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 PYTHON3):

Solution:
N = int(input())
f = True
for h in range(1,3501):
  for n in range(1,3501):
    w_ = (-(h+n)/(h*n) + 4/N)
    if w_ > 0:
      w = (1/w_)
      if w%1 < 10E-8:
        print(h,n,int(w))
        f = False
        break
  if not f:
    break