Problem:
Score : 200 points

Problem Statement

There is a rectangle in the xy-plane, with its lower left corner at (0, 0) and its upper right corner at (W, H). Each of its sides is parallel to the x-axis or y-axis. Initially, the whole region within the rectangle is painted white.

Snuke plotted N points into the rectangle. The coordinate of the i-th (1 ≦ i ≦ N) point was (x_i, y_i).

Then, he created an integer sequence a of length N, and for each 1 ≦ i ≦ N, he painted some region within the rectangle black, as follows:

If a_i = 1, he painted the region satisfying x < x_i within the rectangle.

If a_i = 2, he painted the region satisfying x > x_i within the rectangle.

If a_i = 3, he painted the region satisfying y < y_i within the rectangle.

If a_i = 4, he painted the region satisfying y > y_i within the rectangle.

Find the area of the white region within the rectangle after he finished painting.

Constraints

1 ≦ W, H ≦ 100

1 ≦ N ≦ 100

0 ≦ x_i ≦ W (1 ≦ i ≦ N)

0 ≦ y_i ≦ H (1 ≦ i ≦ N)

W, H (21:32, added), x_i and y_i are integers.

a_i (1 ≦ i ≦ N) is 1, 2, 3 or 4.

Input

The input is given from Standard Input in the following format:

W H N
x_1 y_1 a_1
x_2 y_2 a_2
:
x_N y_N a_N

Output

Print the area of the white region within the rectangle after Snuke finished painting.

Sample Input 1

5 4 2
2 1 1
3 3 4

Sample Output 1

9

The figure below shows the rectangle before Snuke starts painting.

First, as (x_1, y_1) = (2, 1) and a_1 = 1, he paints the region satisfying x < 2 within the rectangle:

Then, as (x_2, y_2) = (3, 3) and a_2 = 4, he paints the region satisfying y > 3 within the rectangle:

Now, the area of the white region within the rectangle is 9.

Sample Input 2

5 4 3
2 1 1
3 3 4
1 4 2

Sample Output 2

0

It is possible that the whole region within the rectangle is painted black.

Sample Input 3

10 10 5
1 6 1
4 1 3
6 9 4
9 4 2
3 1 3

Sample Output 3

64

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

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

namespace B_014_47
{
    internal class Program
    {
        private static void Main(string[] args)
        {
            //new Logic_A().Start();
            new Logic_B().Start();
            Console.ReadLine();
        }

        public class Logic_B
        {
            public void Start()
            {
                var str = Console.ReadLine().Split(' ');
                var W = Convert.ToInt32(str[0]);
                var H = Convert.ToInt32(str[1]);
                var N = Convert.ToInt32(str[2]);

                var maxX1 = 0;
                var minX2 = W;
                var maxY1 = 0;
                var minY2 = H;
                for (int i = 0; i < N; i++)
                {
                    var info = Console.ReadLine().Split(' ');

                    var a = Convert.ToInt32(info[2]);
                    switch (a)
                    {
                        case 1: maxX1 = Math.Max(maxX1, Convert.ToInt32(info[0])); break;
                        case 2: minX2 = Math.Min(minX2, Convert.ToInt32(info[0])); break;
                        case 3: maxY1 = Math.Max(maxY1, Convert.ToInt32(info[1])); break;
                        case 4: minY2 = Math.Min(minY2, Convert.ToInt32(info[1])); break;
                        default: break;
                    }
                }

                var result = (minX2 - maxX1) * (minY2 - maxY1);
                if ((minX2 - maxX1) < 0 || (minY2 - maxY1) < 0)
                {
                    result = 0;
                }
                Console.WriteLine(result);
            }
        }

        public class Logic_A
        {
            public void Start()
            {
                var str = Console.ReadLine().Split(' ');
                var a = Convert.ToInt32(str[0]);
                var b = Convert.ToInt32(str[1]);
                var c = Convert.ToInt32(str[2]);

                Console.WriteLine((a == b + c || b == a + c || c == a + b) ? "Yes" : "No");
            }
        }
    }
}