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:
from itertools import product
n = int(input())
if n%2 == 0:
  print(n,n,n//2)
else:
  for h,l in product(range(max(2, n//4),3501),repeat=2):
    m = n*h*l
    c = 4*h*l - n*(h+l)
    if c > 0 and m%c == 0:
      w = m//c
      break
  print(h,l,w)