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: Accepted)

using System;

namespace T1PC2017
{
    class C
    {
        static void Main(string[] args)
        {
            long N = long.Parse(Console.ReadLine());
            for (int h = 1; h <= 3500; h++)
            {
                for (int n = 1; n <= 3500; n++)
                {
                    if (4 * h * n - N * n - N * h > 0)
                    {
                        if ((N * h * n) % (4 * h * n - N * n - N * h) == 0)
                        {
                            Console.WriteLine("{0} {1} {2}", h, n, (N * h * n) / (4 * h * n - N * n - N * h));
                            return;
                        }
                    }
                }
            }
        }
    }
}