Problem:
Score : 400 points

Problem Statement

There is a bar of chocolate with a height of H blocks and a width of W blocks.
Snuke is dividing this bar into exactly three pieces.
He can only cut the bar along borders of blocks, and the shape of each piece must be a rectangle.

Snuke is trying to divide the bar as evenly as possible.
More specifically, he is trying to minimize S_{max} - S_{min}, where S_{max} is the area (the number of blocks contained) of the largest piece, and S_{min} is the area of the smallest piece.
Find the minimum possible value of S_{max} - S_{min}.

Constraints

2 ≤ H, W ≤ 10^5

Input

Input is given from Standard Input in the following format:

H W

Output

Print the minimum possible value of S_{max} - S_{min}.

Sample Input 1

3 5

Sample Output 1

0

In the division below, S_{max} - S_{min} = 5 - 5 = 0.

Sample Input 2

4 5

Sample Output 2

2

In the division below, S_{max} - S_{min} = 8 - 6 = 2.

Sample Input 3

5 5

Sample Output 3

4

In the division below, S_{max} - S_{min} = 10 - 6 = 4.

Sample Input 4

100000 2

Sample Output 4

1

Sample Input 5

100000 100000

Sample Output 5

50000

Solution in C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace Chocolate_Bar
{
    class Program
    {
        static void Main(string[] args)
        {
            string[] line = Console.ReadLine().Split(' ');
            int H = Int32.Parse(line[0]);
            int W = Int32.Parse(line[1]);

           int Sdiff = H * W;

            if (H % 3 == 0 || W % 3 == 0)
            {
                Console.WriteLine(0);
            }

            else
            {
                int w = 0;
                int h = 0;
                 

                for (w = 0; w < W; w++) {
                    for (h = 0; h < H; h++)
                    {
                        int[] S = { H * w, (W - w) * h, (W - w) * (H - h) };

                        int Smax = Math.Max(S[0], S[1]);
                        Smax = Math.Max(Smax, S[2]);

                        int Smin = Math.Min(S[0], S[1]);
                        Smin = Math.Min(Smin, S[2]);

                        if (Smax - Smin < Sdiff)
                        {
                            Sdiff = Smax - Smin;
                        }

                    }
                }
                   Console.WriteLine(Sdiff.ToString());
            }

           
            Console.ReadLine();
        }
    }
}