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;
using System.Collections;
using System.Collections.Generic;

namespace ConsoleApplication6
{
    class Program
    {
        static void Main(string[] args)
        {
            int finish = 0;
            var read = Console.ReadLine();
            int N = int.Parse(read);
            for (long a = (N / 4) + 1; a <= 3500; a++)
            {
                for (long b = N * a / (4 * a - N)+1; b <= 3500; b++)
                {
                    long c = (N * a * b) / (4 * a * b - N * b - N * a);
                    if ((N * a * b) % (4 * a * b - N * b - N * a) == 0 && c<=3500)
                    {
                        
                        Console.WriteLine("{0} {1} {2}", a, b, (N * a * b) / (4 * a * b - N * b - N * a));
                        finish = 1;
                        break;
                    }
                    else if ((N * a * b) / (4 * a * b - N * b - N * a) > 3500) continue;
                    
                }
                if (finish == 1) break;

            }

        }
    }
}