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;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using Console = System.Console;

namespace Atcoder
{
    class Program
    {
        static void Main(string[] args)
        {
            var WHN = ReadIntArray();
            int[] rect = new int[4];
            rect[0] = 0;
            rect[1] = WHN[0];
            rect[2] = 0;
            rect[3] = WHN[1];

            for (int i = 0; i < WHN[2]; i++)
            {
                var xya = ReadIntArray();
                switch (xya[2])
                {
                    case 1:
                        rect[0] = Math.Max(xya[0], rect[0]);
                        break;
                    case 2:
                        rect[1] = Math.Min(xya[0], rect[1]);
                        break;
                    case 3:
                        rect[2] = Math.Max(xya[1], rect[2]);
                        break;
                    case 4:
                        rect[3] = Math.Min(xya[1],rect[3]);
                        break;
                }
            }

            // -width * -heightの場合にプラスになって不正な値になってしまう
            var ret = Math.Max(0, (rect[1] - rect[0]) * Math.Max(0, (rect[3] - rect[2])));
            Console.WriteLine(ret);
        }


        private static readonly Func<string> Read = () => Console.ReadLine();
        private static readonly Func<string[]> ReadStringArray = () => Console.ReadLine().Split();
        private static readonly Func<int> ReadInt = () => int.Parse(Console.ReadLine());
        private static readonly Func<long> ReadLong = () => long.Parse(Console.ReadLine());
        private static readonly Func<int[]> ReadIntArray = () => Console.ReadLine().Split().Select(int.Parse).ToArray();
        private static readonly Func<long[]> ReadLongArray = () => Console.ReadLine().Split().Select(long.Parse).ToArray();
        private static readonly Action<string> Cw = str => Console.WriteLine(str);
    }
}