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.