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())
# 4/n = 1/h+1/n+1/w
for h in range(1,3501):
  for n in range(h,3501):
    w1 = N*h*n
    w2 = 4*h*n-N*n-N*h
    if w2 == 0:
      continue
    if w1%w2 == 0:
      w = w1//w2
      if w > 0:
        print(h,n,w)
        exit()