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.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace atcoder
{
	class Program
	{
		static int[] In => Console.ReadLine().Split(' ').Select(int.Parse).ToArray();

		static void Main(string[] args)
		{
			var N = int.Parse(Console.ReadLine());
			for (int i = 1; i <= 3500; i++)
			{
				for (int j = 1; j <= 3500; j++)
				{
					double b = 1 / ((4 / (double)N) - (1 / (double)i + 1 / (double)j));
					for (long k = (long)(b - 1); k <= (long)(b + 1); k++)
					{
						if (k <= 0) continue;
						long a = 4 * (long)i * j * k;
						if (a == N * ((long)i * j + (long)j * k + (long)i * k))
						{
							Console.WriteLine(i + " " + j + " " + k);
							//Console.ReadLine();
							return;
						}
					}
				}
			}
		}
	}
}