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;

/**
 *  http://abc047.contest.atcoder.jp/tasks/abc047_b
 * @author おとうさん
 */
public class Main {
    public static void main(String[] args) {
        int W, H, N ;
        Scanner sc = new Scanner(System.in);
        W = sc.nextInt();
        H = sc.nextInt();
        N = sc.nextInt();
        int x[]=new int[N] ;
        int y[]=new int[N] ;
        int a[]=new int[N] ;
        for (int i=0 ; i<N; i++){
            x[i]=sc.nextInt() ;
            y[i]=sc.nextInt() ;
            a[i]=sc.nextInt() ;            
        }
        int x_low, x_high, y_low, y_high ;
        x_high = W ;
        y_high = H ;
        x_low = 0 ;
        y_low = 0 ;
        for (int i=0 ; i<N ;i++) {
            switch (a[i]) {
                case 1 :
                    if (x[i]>x_low) x_low = x[i] ;
                    break ;
                case 2 :
                    if (x_high>x[i]) x_high = x[i] ;
                    break ;
                case 3 :
                    if (y[i]>y_low) y_low = y[i] ;
                    break ;
                case 4 :
                    if (y_high>y[i]) y_high = y[i] ;
                    break ;
            }
        }
        int ans ;
        if (x_high < x_low ) x_high = x_low ;
        if (y_high < y_low ) y_high = y_low ;
        ans = (x_high - x_low) * (y_high - y_low) ;
        if (ans<0) ans = 0 ;
        System.out.println(ans) ;      

    }
    
}