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: Time Limit Exceeded)

n = gets.to_i

K = (3*n/4).ceil

MAX = 3500

if K > MAX/2
  MAX.downto(K) do |c|
    K.downto(1) do |a|
      bb = Rational(4,n) - Rational(1,c) -Rational(1,a)
      next if bb <= 0r
      b = Rational(1,bb)
      if b.denominator == 1
        puts "#{a} #{b.to_i} #{c}"
        exit
      end
    end
  end
else
  1.upto(K) do |a|
    K.upto(MAX) do |c|
      bb = Rational(4,n) - Rational(1,c) -Rational(1,a)
      next if bb <= 0r
      b = Rational(1,bb)
      if b.denominator == 1
        puts "#{a} #{b.to_i} #{c}"
        exit
      end
    end
  end
end