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 static AtCoder.Io;
namespace AtCoder
{
    class Program
    {
        static void Main()
        {
            var whn = ReadIntArray();
            var w = whn[0];
            var h = whn[1];
            var n = whn[2];
            var left = 0;
            var right = w;
            var bottom = 0;
            var top = h;

            for (var i = 0; i < n; i++)
            {
                var xya = ReadIntArray();
                var x = xya[0];
                var y = xya[1];
                var a = xya[2];
                switch (a)
                {
                    case 1: left = Math.Max(left, x); break;
                    case 2: right = Math.Min(right, x); break;
                    case 3: bottom = Math.Max(bottom, y); break;
                    case 4: top = Math.Min(top, y); break;
                }
            }

            var width = Math.Max(right - left, 0);
            var height = Math.Max(top - bottom, 0);
            Console.WriteLine(width * height);
        }
    }

    public static class Io
    {
        public static string ReadString() => Console.ReadLine();
        public static string[] ReadStringArray() => ReadString().Split(' ');
        public static int ReadInt() => int.Parse(ReadString());
        public static long ReadLong() => long.Parse(ReadString());
        public static int[] ReadIntArray() => ReadStringArray().ParseInt().ToArray();
        public static long[] ReadLongArray() => ReadStringArray().ParseLong().ToArray();
        public static IEnumerable<int> ParseInt(this IEnumerable<string> source) => source.Select(int.Parse);
        public static IEnumerable<long> ParseLong(this IEnumerable<string> source) => source.Select(long.Parse);
    }
}