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.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Scanner;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Scanner in = new Scanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        B solver = new B();
        solver.solve(1, in, out);
        out.close();
    }

    static class B {
        public void solve(int testNumber, Scanner in, PrintWriter out) {
            // 入力
            int w = Integer.parseInt(in.next());
            int h = Integer.parseInt(in.next());
            int n = Integer.parseInt(in.next());
            int points[][] = new int[n][3];
            for (int i = 0; i < n; i++) {
                points[i][0] = Integer.parseInt(in.next());
                points[i][1] = Integer.parseInt(in.next());
                points[i][2] = Integer.parseInt(in.next());
            }

            int board[][] = new int[w][h];  // 0 : white 1 : black
            long ans = 0;

            for (int i = 0; i < n; i++) {
                if (points[i][2] == 1) {
                    for (int j = 0; j < points[i][0]; j++) {
                        for (int k = 0; k < h; k++) {
                            board[j][k] = 1;
                        }
                    }
                } else if (points[i][2] == 2) {
                    for (int j = points[i][0]; j < w; j++) {
                        for (int k = 0; k < h; k++) {
                            board[j][k] = 1;
                        }
                    }
                } else if (points[i][2] == 3) {
                    for (int j = 0; j < w; j++) {
                        for (int k = 0; k < points[i][1]; k++) {
                            board[j][k] = 1;
                        }
                    }
                } else if (points[i][2] == 4) {
                    for (int j = 0; j < w; j++) {
                        for (int k = points[i][1]; k < h; k++) {
                            board[j][k] = 1;
                        }
                    }
                }
            }

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

            out.println(ans);
        }

    }
}