Snuke's Coloring 2 (ABC Edit)

AtCoder

IDabc047_b

Time2000ms

Memory256MB

Difficulty—

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: $W$ $H$ $N$ $x_1$ $y_1$ $a_1$ $x_2$ $y_2$ $a_2$ $:$ $x_N$ $y_N$ $a_N$ [samples]

Samples

Input #1

5 4 2
2 1 1
3 3 4

Output #1

9

The figure below shows the rectangle before Snuke starts painting.

![image](https://atcoder.jp/img/abc047/e19e673abcd0882783f635cce9d2f94d.png)

First, as $(x_1, y_1) = (2, 1)$ and $a_1 = 1$, he paints the region satisfying $x < 2$ within the rectangle:

![image](https://atcoder.jp/img/abc047/f25cd04bbac23c4e5426d70511a9762f.png)

Then, as $(x_2, y_2) = (3, 3)$ and $a_2 = 4$, he paints the region satisfying $y > 3$ within the rectangle:

![image](https://atcoder.jp/img/abc047/46b0c06fd9eee4f148e1f441f7abca53.png)

Now, the area of the white region within the rectangle is $9$.

Input #2

Output #2

0

It is possible that the whole region within the rectangle is painted black.

Input #3

Output #3

API Response (JSON)

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      "memory_limit": 262144
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      "statement_type": "Markdown",
      "content": "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 whol...",
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}

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