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())
max_int = 3500
for n in range(1,max_int+1):
  for w in range(1,max_int+1):
    a1 = N*n*w
    a2 = 4*n*w-w*N-N*n
    if a2<=0:continue
    if a1%a2==0 and a1//a2<=max_int:
      print(N*n*w//(4*n*w-w*N-N*n), n, w)
      exit()