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 ABC037B {
	class Program {
		static void Main(string[] args) {
			int W, H, N, answer;
			int[] x, y, a, coordinate;
			x = new int[100];
			y = new int[100];
			a = new int[100];
			string[] input;
			input = Console.ReadLine().Split(' ');
			W = int.Parse(input[0]);
			H = int.Parse(input[1]);
			N = int.Parse(input[2]);
			coordinate = new int[4] { 0, 0, W, H};
			for (int i = 0; i < N; i++) {
				input = Console.ReadLine().Split(' ');
				x[i] = int.Parse(input[0]);
				y[i] = int.Parse(input[1]);
				a[i] = int.Parse(input[2]);
			}
			for (int i = 0; i < N; i++) {
				switch (a[i]) {
					case 1:
						coordinate[0] = coordinate[0] < x[i] ? x[i] : coordinate[0];
						break;
					case 2:
						coordinate[1] = coordinate[1] > x[i] ? x[i] : coordinate[1];
						break;
					case 3:
						coordinate[2] = coordinate[2] < y[i] ? y[i] : coordinate[2];
						break;
					case 4:
						coordinate[3] = coordinate[3] > y[i] ? y[i] : coordinate[3];
						break;
				}
			}
			answer = (coordinate[2] - coordinate[0]) * (coordinate[3] - coordinate[1]);
			answer = answer < 0 ? 0 : answer;
			Console.WriteLine(answer);
		}
	}
}