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;

class Program
    {
        static void Main(string[] args)
        {
            // 入力
            var N = long.Parse(Console.ReadLine());

            var min = Math.Max((long)(N / 4), 1);

            // h <= n <= w としてよい。ただし、 h = den/num
            var den = 1l;
            var num = 1l;

            for (long w = min;w <= 3500; w++)
            {
                for (long n = min; n <= w; n++)
                {
                    den = 4 * n * w - N * n - N * w;
                    num = N * n * w;
                    
                    if (den > 0 && num % den == 0)
                    {
                        Console.WriteLine("{0} {1} {2}", ((int)(num / den)).ToString(), n.ToString(), w.ToString());
                        return;
                    }
                }
            }
        }
    }