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
from = [4 / n, 1].max
to_x = (3 * n) / 4

from.upto(to_x) do |x|
  d = 4 * x - n
  to_y = d.zero? ? 3500 : 2 * n * x / d
  to_y = [to_y,3500].min
  from.upto(to_y) do |y|
    z = 4r / n - 1r / x - 1r / y
    if z.numerator == 1
      puts [x, y, z.denominator].join(" ")
      # puts [x, y, z.denominator].map{|i|"1/#{i}r"}.join("+")
      exit
    end
  end
end