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)

def solve
  ret = 0
  div = 1.0
  loop do
    div += 1.0
    ret = $l_n / div
    break if (1.0 / ret).floor == (1.0 / ret)
  end
  $l_n -= ret
  ret
end

$l_n = gets.to_i

h,n,w = 1
$l_n = 4.0 / $l_n

h = solve
n = solve
w = $l_n

puts "#{(1.0/h).to_i} #{(1.0/n).to_i} #{(1.0/w).to_i}"