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

namespace Test
{
	class Program
	{
		static void Main(string[] args) {
			int N = Int32.Parse(Console.ReadLine());
			long w, h, n;
			w = 1;

			for (h = 1; h <= 3500; h++) {
				for (n = 1; n <= 3500; n++) {
					var x = (-N * n + 4 * h * n - h * N);
					if(x==0) continue;
					
					w = h * N * n / x;
					if(w<0) continue;
					if (4 * n * h * w == N * (h * n + n * w + h * w)) {
						Console.WriteLine(h+" "+n+" "+w);
						return;
						
					}
				}
			}
		}
	}
}