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 C (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <stdio.h>                                                                                                                                                                                        
#include <stdlib.h>                                                                                                                                                                                       
#include <string.h>                                                                                                                                                                                       
                                                                                                                                                                                                          
int main(void)                                                                              
{                                                                                           
        int max_x, max_y, num, now_x = 0, now_y = 0, i, ans;                                
        int **point, *mode;                                                                 
                                                                                            
        scanf("%d %d %d", &max_x, &max_y, &num);                                        
                                                                                        
        point = calloc(sizeof(int *), num);                                             
        mode = calloc(sizeof(int), num);                                                
                                                                                        
        for (i = 0; i < num; i++) {                                                     
                point[i] = calloc(sizeof(int), 2);                                      
                scanf("%d %d %d", &point[i][0], &point[i][1], &mode[i]);                
        }                                                                               
                                                                                        
        for (i = 0; i < num; i++) {                                                     
                if (mode[i] == 1) {                                                     
                        now_x = now_x < point[i][0] ? point[i][0] : now_x;              
                } else if (mode[i] == 2) {                                              
                        max_x = max_x < point[i][0] ? max_x : point[i][0];              
                } else if (mode[i] == 3) {                                              
                        now_y = now_y < point[i][1] ? point[i][1] : now_y;              
                } else if (mode[i] == 4) {                                               
                        max_y = max_y < point[i][1] ? max_x : point[i][1];              
                }                                                                       
        }                                                                               
                                                                                        
        ans = (max_x - now_x) * (max_y - now_y);                                        
        if (ans <= 0) {                                                                 
                ans = 0;                                                                
        }                                                                               
        printf("%d\n", ans);                                                            
        return 0;                                                                       
}