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())

for h in range(N//4 +1, min(3501, 3*N//4 +1)):
  for n in range((N*h)//(4*h-N), min(3501, ((2*N*h)//(4*h-N))+1)):
    #print(h,n)
    x = 4*h*n - N*n - N*h
    y = N*h*n
    if x>0 and not y%x:
      print('{} {} {}'.format(h,n,y//x))
      exit()