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: Runtime Error)

#include <stdio.h>
#include <stdlib.h>
#include <assert.h>

int main(int argc, char * argv[]){
    int W,H,N;
    scanf("%d %d %d",&W,&H,&N);
    
    char ** rectangle = malloc(H*sizeof(char));
    int i,j;
    for(i = 0; i < H; i++){
        rectangle[i] = malloc(W*sizeof(char));
        assert(rectangle[i] != NULL);
        for(j = 0; j<W; j++){
            rectangle[i][j] = 0;
        }
    }
    //printf("A\n");
    
    int x,y,a;
    while(N > 0){
        N--;
        scanf("%d %d %d",&x,&y,&a);
        switch (a) {
            case 1 :
                for(i = 0; i < x; i++){
                    for(j = 0; j < H; j++){
                        rectangle[j][i] = 1;
                    }
                }
                break;
            case 2 :
                for(i = x; i < W; i++){
                    for(j = 0; j < H; j++){
                        rectangle[j][i] = 1;
                    }
                }
                break;
            case 3 :
                for(i = 0; i < y; i++){
                    for(j = 0; j < W; j++){
                        rectangle[i][j] = 1;
                    }
                }
                break;
            case 4 :
                for(i = y; i < H; i++){
                    for(j = 0; j < W; j++){
                        rectangle[i][j] = 1;
                    }
                }
                break;
        }
    }
    //printf("A\n");
    int area = 0;
    for(i = 0; i < H; i++){
        for(j = 0; j<W; j++){
            if(rectangle[i][j]==0)area++;
        }
        free(rectangle[i]);
    }
    free(rectangle);
    printf("%d\n",area);
    
    return EXIT_SUCCESS;
}