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 (2.13.1) (judge verdict: Wrong Answer)

object Main {

  def main(args: Array[String]): Unit = {
    val sc = new java.util.Scanner(System.in)

    val N = sc.nextInt()
    // 制約から, h, n, w <= 3500を探索することになる
    // しかし, 二つの整数を前探索すると普通に間に合わないので, 2nlognとかに落とすことができそう
    // だが, 解答例では3500を超える整数を使っても良い, とあり, そういう訳でもなさそう
    // 4/N = 1/N + 1/N + 2/N だから適当に N, N, 2Nと回答すれば良さそうだが, ダメという制約は特になさそうだがあまりにもひどい？
    println(s"$N $N ${2 * N}")
  }

}