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: Runtime Error)

N=gets.to_i
a = case N%4
when 0,2
  [N/2, N, N]
when 1
  a=4r/N
  (N/4+1).upto(N/4+1){|i|
    b=a-1r/i
    i.upto(3500){|j|
      c=b-1r/j
      if c.numerator==1
        puts [i, j, c.denominator] * ?\s
        exit
      end
    }
  }
when 3
  g=N/4+1
  [g, N*g+1, N*g*(N*g+1)]
end
puts a * ?\s