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)

n = gets.to_i
if(n.even?)
  a = n/2 
  b = c = n
  puts "#{a} #{b} #{c}"
else
  a = n / 4 + 1
  ee = Rational(4, n)  - Rational(1, a)   
  b = (1 / ee.to_f).to_i + 1 
  if(1 / ee.to_f - (1 / ee.to_f).to_i < 0.00001)
    b *= 2
    c = b
    puts "#{a} #{b} #{c}"
    exit
  end
  ee = ee  - Rational(1, b)   
  c = (1 / ee.to_f).to_i 
  puts "#{a} #{b} #{c}"
end