Problem:
Score : 300 points

Problem Statement

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

Sample Input 1

2

Sample Output 1

1 2 2

4/2 = 1/1 + 1/2 + 1/2.

Sample Input 2

3485

Sample Output 2

872 1012974 1539173474040

It is allowed to use an integer exceeding 3500 in a solution.

Sample Input 3

4664

Sample Output 3

3498 3498 3498

Solution in Python (3.4.3) (judge verdict: Runtime Error)

N = int(input())
if N % 4 == 0:
  h, n, w = (3 * N) // 4, (3 * N) // 4, (3 * N) // 4
elif N % 4 == 2:
  h, n, w = N, N, N // 2
elif N % 4 == 3:
  s = N // 4 + 1
  h, n, w = 2 * s, 2 * s, s * N
elif N % 4 == 1:
  s = (N // 4) + 1
  if s % 3 == 0:
    h = s
    n = 2 * (s // 3) * (4 * s - 3)
    w = 2 * (s // 3) * (4 * s - 3)
  elif s % 3 == 2:
    h = N
    n = 4 * (s // 3) + 2
    w = (4 * (s // 3) + 2) * (12 * (s // 3) + 5)
  elif s % 3 == 1:
    h = 
print(h, n, w)