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;

class Solution
{
    static void Main()
    {
        var N = long.Parse(Console.ReadLine());
        for (long h = 1; h <= 3500; h++)
        {
            for (long w = 1; w <= 3500; w++)
            {
                var numer = N * h * w;
                var denom = 4 * h * w - N * (w + h);
                if (denom > 0 && numer % denom == 0)
                {

                    long n = numer / denom;
                    if (4 * n * h * w == (n * w + w * h + n * h) * N)
                    {
                        Console.WriteLine($"{h} {n} {w}");
                        return;
                    }
                }
            }
        }
    }
}