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;
using System.Collections.Generic;
using System.Collections.ObjectModel;
using System.Diagnostics;
using System.IO;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

public static class TemplateExtension
{
    public static X[] MakeArray<X>(this int count, Func<int, X> func)
    {
        var xs = new X[count];
        for (var i = 0; i < count; i++)
        {
            xs[i] = func(i);
        }
        return xs;
    }

    public static int[] Range(this int count, int start = 0)
    {
        return count.MakeArray(i => i + start);
    }

    public static string Intercalate<X>(this IEnumerable<X> @this, string separator)
    {
        return string.Join(separator, @this);
    }

    public sealed class ValueIndexPair<T>
        : Tuple<T, int>
    {
        public T Value { get { return Item1; } }
        public int Index { get { return Item2; } }

        public ValueIndexPair(T value, int index)
            : base(value, index)
        {
        }
    }

    public static IEnumerable<ValueIndexPair<X>> Indexed<X>(this IEnumerable<X> @this)
    {
        var i = 0;
        foreach (var x in @this)
        {
            yield return new ValueIndexPair<X>(x, i);
            i++;
        }
    }
}

public sealed class Scanner
{
    readonly TextReader reader;
    readonly StringBuilder sb = new StringBuilder();

    /// <summary>
    /// Reads next word separated by spaces.
    /// </summary>
    public string Word()
    {
        sb.Clear();

        while (true)
        {
            var r = reader.Read();

            if (r == '\r')
            {
                if (reader.Peek() == '\n') reader.Read();
                break;
            }
            else if (r == -1 || r == ' ' || r == '\n')
            {
                break;
            }
            else
            {
                sb.Append((char)r);
            }
        }

        return sb.ToString();
    }

    /// <summary>
    /// Reads next word as <see cref="int"/>.
    /// </summary>
    public int N()
    {
        return int.Parse(Word());
    }

    /// <summary>
    /// Reads next word as <see cref="long"/>.
    /// </summary>
    public long L()
    {
        return long.Parse(Word());
    }

    /// <summary>
    /// Reads next word as <see cref="double"/>.
    /// </summary>
    public double F()
    {
        return double.Parse(Word());
    }

    public int[] Ns(int count)
    {
        return count.MakeArray(_ => N());
    }

    public long[] Ls(int count)
    {
        return count.MakeArray(_ => L());
    }

    public double[] Fs(int count)
    {
        return count.MakeArray(_ => F());
    }

    /// <summary>
    /// Reads next line and splits it by spaces.
    /// </summary>
    public X[] Words<X>(Func<string, X> func)
    {
        return reader.ReadLine().Split(' ').Select(func).ToArray();
    }

    public Scanner(TextReader reader)
    {
        this.reader = reader;
    }
}

public partial class Program
{
    readonly TextReader input;
    readonly TextWriter output;
    readonly Scanner scanner;

    void WriteLine(int value)
    {
        output.WriteLine(value);
    }

    void WriteLine(long value)
    {
        output.WriteLine(value);
    }

    void WriteLine(double value)
    {
        output.WriteLine(value);
    }

    void WriteLine(char value)
    {
        output.WriteLine(value);
    }

    void WriteLine(string value)
    {
        output.WriteLine(value);
    }

    public Program(TextReader input, TextWriter output)
    {
        this.input = input;
        this.output = output;
        scanner = new Scanner(input);
    }

    public static void Main(string[] args)
    {
#if DEBUG
        using (var writer = new VainZero.IO.DebugTextWriter(Console.Out))
#else
        var writer = Console.Out;
#endif
        {
            new Program(Console.In, writer).EntryPoint();
        }
    }
}

public sealed partial class Program
{
    long n;

    long[] Solve()
    {
        for (var a = 1L; a <= 3500; a++)
        {
            for (var b = a; b <= 3500; b++)
            {
                var p = n * a * b;
                var q = 4 * a * b - n * b - n * a;
                if (p > 0 && q > 0 && p % q == 0)
                {
                    var c = p / q;
                    return new[] { a, b, c };
                }
            }
        }

        throw new InvalidOperationException();
    }

    void Read()
    {
        var a = scanner;
        n = a.L();
    }

    public void EntryPoint()
    {
        Read();
        WriteLine(Solve().Intercalate(" "));
    }
}