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: Runtime Error)

n = gets.to_i
from = [3500 * n / (14000 - 2 * n), 1].max
to_x = (3 * n + 3) / 4

from.upto(to_x) do |x|
  to_y = (2.0 / (4.0 / n - 1.0 / x)).to_i
  from.upto(to_y) do |y|
    next if x.zero? || y.zero?
    z = 4r / n - 1r / x - 1r / y
    if z.numerator == 1
      puts [x, y, z.denominator].join(" ")
      exit
    end
  end
end