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 (2.7.1) (judge verdict: Time Limit Exceeded)

N = gets.to_i

(1 .. 3500).each do |a|
  (a .. 3500).each do |b|
    c = (b .. 3500).bsearch{|_| 4 * a * b * _ >= (a * b + b * _ + _ * a) * N }
    next unless c
    next unless 4 * a * b * c == (a * b + b * c + c * a) * N
    puts [a,b,c].join(" ") 
    exit
  end
end