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 Scala (2.11.7) (judge verdict: Accepted)

import io.StdIn.{ readLong }

object Main extends App {
  val largeN = readLong

  val hnws = for {
    h <- 1 to 3500
    n <- 1 to 3500
    den = largeN * h * n
    num = 4 * h * n - largeN * n - largeN * h
    if num != 0 && den * num > 0 && den % num == 0
  } yield (h, n, den / num)

  val (h, n, w) = hnws(0)

  assert(4 * h * n * w == n * w * largeN + w * largeN * h + largeN * h * n)

  println("%d %d %d".format(h, n, w))
}