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# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Linq;
using System.Collections.Generic;

namespace ABC
{
    class ProgramB
    {
        static void Main(string[] args)
        {
            var inputs = Console.ReadLine().Split(" ");
            var w = int.Parse(inputs[0]);
            var h = int.Parse(inputs[1]);
            var n = int.Parse(inputs[2]);

            var left = 0;
            var right = w;
            var bottom = 0;
            var top = h;

            for (var i = 0; i < n; i++)
            {
                var inputs1 = Console.ReadLine().Split(" ");
                var x = int.Parse(inputs1[0]);
                var y = int.Parse(inputs1[1]);
                var a = int.Parse(inputs1[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 nw = right - left;
            var nh = top - bottom;
            if (nw < 0 || nh < 0)
            {
                Console.WriteLine(0);
            }
            else
            {
                var result = Math.Max(0, nw * nh);
                Console.WriteLine(result);
            }
        }
    }
}