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.IO;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace ConsoleApplication2
{
    class Program
    {
        static void Main(string[] args)
        {
            int minX = 0;
            int minY = 0;
            int maxX = 0;
            int maxY = 0;
            int startX = 0;
            int startY = 0;
            int tempX = 0;
            int tempY = 0;
            int readCount = 0;
            int result = 0;
            int calcFLG = 0;
            
            string readValue =Console.ReadLine();
            int[] tokens = readValue.Split(' ').Select(int.Parse).ToArray();
            maxX = tokens[0];
            maxY = tokens[1];
            startX = maxX;
            startY = maxY;
            readCount = tokens[2];

            for (int i = 0; i < readCount; i++)
            {
                readValue = Console.ReadLine();
                tokens = readValue.Split(' ').Select(int.Parse).ToArray();
                tempX = tokens[0];
                tempY = tokens[1];
                calcFLG = tokens[2];

                switch (calcFLG)
                {
                    case 1:
                        if (minX < tempX)
                        {
                            minX = tempX;
                        }
                        break;
                    case 2:
                        if (startX > tempX && maxX > tempX)
                        {
                            maxX = tempX;
                        }
                        break;
                    case 3:
                        if (minY < tempY)
                        {
                            minY = tempY;
                        }
                        break;
                    case 4:
                        if (startY > tempY && maxY > tempY)
                        {
                            maxY = tempY;
                        }
                        break;
                    default:
                        break;  
                }
            }

            if (maxX - minX > 0 && maxY - minY > 0)
            {
                result = (maxX - minX) * (maxY - minY);
            }

            Console.WriteLine(result.ToString());
            //Console.ReadLine();
        }
    }
}