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 C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
 
class Program
    {
        static void Main(string[] args)
        {
            // 入力
            var N = long.Parse(Console.ReadLine());

            // h <= n <= w としてよい。
            for (long w = N;w >= N && w <= 3500; w++)
            {
                for (long n = N; n <= w; n++)
                {
                    for (long h = 1; h <= n &&  4 * h <= 3 * N; h++)
                    {
                        if (4 * h * n * w == N * (h * n + n * w + w * h))
                        {
                            Console.WriteLine("{0} {1} {2}",h.ToString(), n.ToString(), w.ToString());
                            goto exitLoop;
                        }
                           
                    }
                }
            }
            exitLoop:;
            }
    }