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 Java7 (OpenJDK 1.7.0) (judge verdict: Accepted)

import java.util.ArrayList;
import java.util.HashMap;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		
		// 入力を読み込む
		Scanner sc = new Scanner(System.in);

		// 取得
		int maxX = sc.nextInt();
		int maxY = sc.nextInt();
		int squearNum = sc.nextInt();
		
		// 長方形作成
		boolean[][] squear = new boolean[maxX][maxY];
		// 長方形の色を塗っていく
		int x;
		int y;
		int positionPaint;
		for (int i = 0; i < squearNum; i++) {
			x = sc.nextInt();
			y = sc.nextInt();
			positionPaint = sc.nextInt();
			
			// 条件によって色を塗る
			switch (positionPaint) {
			case 1 :
				paintX(squear, x, 0, maxY);
				break;
			case 2 :
				paintX(squear, maxX, x, maxY);
				break;
			case 3 :
				paintY(squear, y, 0, maxX);
				break;
			case 4 :
				paintY(squear, maxY, y, maxX);
				break;
			default :
			}
			
		}
		int count = 0;
		// 塗られていない箇所を求める
		for (int i = 0; i < maxX; i++) {
			for (int j = 0; j < maxY; j++) {
				if (!squear[i][j]) {
					count++;
				}
			}
		}
		System.out.println(count);
	}
	
	public static void paintX(boolean[][] square, int maxX, int x, int maxY) {
		for (int i = x; i < maxX; i++) {
			for (int j = 0; j < maxY; j++) {
				// 塗りつぶす
				square[i][j] = true;
			}
		}
	}
	
	public static void paintY(boolean[][] square, int maxY, int y, int maxX) {
		for (int i = 0; i < maxX; i++) {
			for (int j = y; j < maxY; j++) {
				// 塗りつぶす
				square[i][j] = true;
			}
		}
	}

}