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;

namespace tenka1_2017_c
{
    class Program
    {
        static void Main(string[] args)
        {
            long n = long.Parse(Console.ReadLine());
            bool found = false;
            for (long i = 1; i < 3500 && !found; i++)
            {
                for (long j = i; j < 3500 && !found; j++)
                {
                    double x = n * i * j;
                    x /= 4 * i * j - n * (i + j);
                    if (x % 1 == 0 && x > 0)
                    {
                        Console.WriteLine(x + " " + i + " " + j);
                        found = true;
                    }
                }
            }
        }
    }
}