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: Runtime Error)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Arrays;

public class Main {

    public static void main(String[] argv) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        String[] str = br.readLine().split(" ");

        int w = Integer.parseInt(str[0]);
        int h = Integer.parseInt(str[1]);
        int n = Integer.parseInt(str[2]);

        int[][] map = new int[h][w];
        for(int i=0; i<h; i++) Arrays.fill(map[i], 0);

        for(int i=0; i<n; i++){
            str = br.readLine().split(" ");
            int x = Integer.parseInt(str[0]);
            int y = Integer.parseInt(str[1]);
            int a = Integer.parseInt(str[2]);
            switch (a){
                case 1:
                    map[h-1][0]++;
                    map[h-1][x]--;
                    break;
                case 2:
                    map[h-1][x]++;
                    break;
                case 3:
                    map[y-1][0]++;
                    break;
                case 4:
                    map[h-1][0]++;
                    map[y-1][0]--;
                    break;
            }
        }

        for(int i=0; i<h; i++){
            for(int j=1; j<w; j++){
                map[i][j] += map[i][j-1];
            }
        }

        for(int i=h-2; i>=0; i--){
            for(int j=0; j<w; j++){
                map[i][j] += map[i+1][j];
            }
        }

        int cnt = 0;
        for(int i=0; i<h; i++){
            for(int j=0; j<w; j++){
                if(map[i][j] <= 0) cnt++;
            }
        }

        System.out.println(cnt);
    }
}