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: Wrong Answer)


import java.util.Scanner;

public class Main {
    private static int W, H, N;
    private static int x1 = 0, y1 = 0, x2, y2;
    private static int[] x, y, a;
    private static Scanner scanner = new Scanner(System.in);


    public static void main(String[] args){
        input();
        solve();
    }

    private static void solve() {
        for (int i = 0; i < N; i++) {
            update_xy(x[i], y[i], a[i]);
            if (x2 <= x1 || y2 <= y1)
                break;
        }

        if (x2 > x1 && y2 > y1)
            System.out.println((x2-x1)*(y2-y1));
        else
            System.out.println(0);
    }

    private static void update_xy(int xi, int yi, int ai) {
        if (ai == 1)
            x1 = xi;
        else if (ai == 2)
            x2 = xi;
        else if (ai == 3)
            y1 = yi;
        else
            y2 = yi;
    }

    private static void input() {
        W = scanner.nextInt();
        H = scanner.nextInt();
        N = scanner.nextInt();

        x2 = W;
        y2 = H;

        x = new int[N];
        y = new int[N];
        a = new int[N];

        for (int i = 0; i < N; i++) {
            x[i] = scanner.nextInt();
            y[i] = scanner.nextInt();
            a[i] = scanner.nextInt();
        }
    }

    private static void test_input() {
        W = 5;
        H = 4;
        N = 2;

        x2 = W;
        y2 = H;

        x = new int[]{2, 3};
        y = new int[]{1, 3};
        a = new int[]{1, 4};

    }
}