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: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Linq;
class Program
{
    public static bool f = false, t = true;
    static void Main(string[] args)
    {
         long n = long.Parse(Console.ReadLine());
        if (n % 4 == 0) { Console.WriteLine(n / 4 * 3 + " " + n / 4 * 3 + " " + n * 3 / 4); Console.ReadLine(); return; }
        if (n % 4 == 1)
        {
            long dd = (n + 3) / 4;
            long hh = (dd + 2) * (dd - 1);
            Console.Write(dd + " " + hh + " " );

            for (long i = 1; ; i++)
            {
                if ((hh * dd + hh * i + dd * i)*n==4*i*hh*dd) { Console.WriteLine(i);Console.ReadLine(); return; }
            }
        }

        if (n % 4 == 2) { Console.WriteLine((n / 4 + 1) + " " + (n / 4 + 1) * n + " " + (n / 4 + 1) * n); Console.ReadLine(); return; }
        else { Console.WriteLine((((n + 1) / 4) * 2) + " " + (((n + 1) / 4) * 2) + " " + (((n + 1) / 4) * 2) * n / 2); Console.ReadLine(); return; }

    }

    public static long gcd(long a, long b)
    {
        while (true)
        {
            if (a == 0) { return b; }
            if (b == 0) { return a; }
            if (a > b) { a -= b; }
            else { b -= a; }
        }
    }
    public static long lcm(long a, long b)
    {
        return a / gcd(a, b) * b;
    }
    public static bool IsPrime(long n)
    {
        if (n < 2) return false;
        if (n == 2) return true;

        for (long i = 2; i < n; i++)
        {
            if (n % i == 0) return false;
        }
        return true;
    }

}
public static class Read
{
    public static void outl(string n = "") { Console.WriteLine(n); return; }
    public static long Long()
    {
        return long.Parse(Console.ReadLine());
    }
    public static long[] longs()
    {
        return Console.ReadLine().Split().Select(long.Parse).ToArray();
    }
    public static int Int()
    {
        return int.Parse(Console.ReadLine());
    }
    public static int[] ints()
    {
        return Console.ReadLine().Split().Select(int.Parse).ToArray();
    }
    public static string Str() { return Console.ReadLine(); }
    public static string[] Strs() { return Console.ReadLine().Split(); }
}