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: Wrong Answer)

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

namespace ABC047
{
	class Q2
	{
		static void Main()
		{
			var buff = Console.ReadLine().Split(' ').Select(x => int.Parse(x)).ToList();
			int W = buff[0], H = buff[1], N = buff[2];
			var buff2 = Enumerable.Range(1, N).Select(x => Console.ReadLine().Split(' ').Select(y => int.Parse(y)).ToList()).ToList();
			var A1 = buff2.Where(x => x[2] == 1);
			var A2 = buff2.Where(x => x[2] == 2);
			var A3 = buff2.Where(x => x[2] == 3);
			var A4 = buff2.Where(x => x[2] == 4);

			int x1 = A1.Count() == 0 ? 0 : A1.Select(x => x[0]).Min();
			int x2 = A2.Count() == 0 ? W : A2.Select(x => x[0]).Max();
			int y1 = A3.Count() == 0 ? 0 : A3.Select(x => x[1]).Min();
			int y2 = A4.Count() == 0 ? H : A4.Select(x => x[1]).Max();

			int w = x2 - x1, h = y2 - y1;
			w = w < 0 ? 0 : w; h = h < 0 ? 0 : h;

			Console.WriteLine(w * h);
		}
	}
}