100471: [AtCoder]ABC047 B - Snuke's Coloring 2 (ABC Edit)

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