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

K = (3*n/4).ceil

MAX = 3500

MAX.downto(K) do |c|
  K.downto(1) do |a|
    b_bunbo = 4*c*a - a*n -c*n
    b_bunshi = n*c*a
    next if b_bunbo <= 0 || b_bunshi%b_bunbo != 0
    b = b_bunshi/b_bunbo
    puts "#{a} #{b} #{c}"
    exit
  end
end