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>

typedef struct {
    int x,y,a;
} data;

int main()
{
    int w,h,n,maxmin[4] = {0,100,0,100};
    data data[100];
    int i,j;

    scanf("%d %d %d",&w,&h,&n);
    for (i = 0; i < n; i++)scanf("%d %d %d",&data[i].x,&data[i].y,&data[i].a);

    int ans = w * h;

    for (i = 0; i < n; i++)
    {
        switch (data[i].a)
        {
        case 1:
            if(maxmin[0] < data[i].x)maxmin[0] = data[i].x;
            break;
        case 2:
            if(maxmin[1] > data[i].x)maxmin[1] = data[i].x;
            break;
        case 3:
            if(maxmin[2] < data[i].y)maxmin[2] = data[i].y;
            break;
        default:
            if(maxmin[3] > data[i].y)maxmin[3] = data[i].y;
            break;
        }
    }
    if(maxmin[0] < maxmin[1] && maxmin[2] < maxmin[3])
    {
        printf("%d",(maxmin[1] - maxmin[0]) * (maxmin[3] - maxmin[2]));
    }
    else
    {
        printf("0");
    }
    
}