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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int W = sc.nextInt();
		int H = sc.nextInt();
		int N = sc.nextInt();

		Field field = new Field(W, H);

		for (int i = 0; i < N; i++) {
			int x = sc.nextInt();
			int y = sc.nextInt();
			int a = sc.nextInt();
			field.draw(x, y, a);
		}

		System.out.println(field.calcWhiteArea());
	}

	static class Field {
		final int W, H;
		final boolean[] fieldArray;

		public Field(int W, int H) {
			this.fieldArray = new boolean[W * H];
			this.W = W;
			this.H = H;
			for (int i = 0; i < W * H; i++) {
				fieldArray[i] = true;
			}
		}

		public void draw(int x, int y, int a) {
			switch (a) {
			case 1:
				drawRect(0, x, 0, H);
				break;
			case 2:
				drawRect(x, W, 0, H);
				break;
			case 3:
				drawRect(0, W, 0, y);
				break;
			case 4:
				drawRect(0, W, y, H);
				break;
			}
		}

		private void drawRect(int x1, int x2, int y1, int y2) {
			for (int x = x1; x < x2; x++) {
				for (int y = y1; y < y2; y++) {
					drawPoint(x, y);
				}
			}
		}

		private void drawPoint(int x, int y) {
			this.fieldArray[x * H + y] = false;
		}

		public int calcWhiteArea() {
			int ans = 0;
			for (int i = 0; i < W * H; i++) {
				if (this.fieldArray[i]) {
					ans++;
				}
			}
			return ans;
		}
	}
}