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: Time Limit Exceeded)

n = gets.to_i

ans  = nil
max  = 3500
left = Rational(4, n)
1.upto(max) do |h|
  if ans != nil
    break
  end

  1.upto(max) do |n|
    if ans != nil
      break
    end

    1.upto(max) do |w|
      if ans != nil
        break
      end

      right = Rational(1, h) + Rational(1, n) + Rational(1, w)
      if left == right
        ans = [h, n, w]
        break
      end
    end
  end
end

puts ans.map(&:to_s).join(" ")