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 OCaml (4.02.3) (judge verdict: Accepted)

let () = Scanf.scanf "%d" (fun n ->
  try
    for h = 1 to 3500 do
      for w = h to 3500 do
        if 4 * h * w > n * w + n * h && (n * h * w) mod (4 * h * w - n * w - n * h) = 0
        then (Printf.printf "%d %d %d\n" h ((n * h * w) / (4 * h * w - n * w - n * h)) w; raise Not_found)
      done
    done
  with Not_found -> ())