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 Ruby (2.3.3) (judge verdict: Wrong Answer)

N   = gets.to_i
MAX = 3500

1.upto(MAX) do |h|
  1.upto(MAX) do |n|
    a = N*h*n
    b = 4*h*n - N*n - N*h
    if b != 0
      w = a / b
      if w.floor == w and w > 0
        puts "#{h.to_i} #{n.to_i} #{w.to_i}"
        exit
      end
    end
  end
end