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: Accepted)

N = gets.to_i
MAX_NUM = 3500

1.upto(MAX_NUM) do |h|
  1.upto(MAX_NUM) do |n|
    numerator = N * h * n
    denominator = 4 * h * n - N * n - N * h
    next if denominator.zero? || !(numerator % denominator).zero?

    w = numerator / denominator
    if w.positive?
      puts "#{h} #{n} #{w}"
      exit
    end
  end
end