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 PHP (7.4.4) (judge verdict: Accepted)

<?php
$whn = explode(' ', trim(fgets(STDIN)));

$w          = (int)$whn[0];
$h          = (int)$whn[1];
$n          = (int)$whn[2];
$coordinate = [];
$sequence   = [];

while (count($sequence) < $n) {
    $xya          = explode(' ', trim(fgets(STDIN)));
    $coordinate[] = [(int)$xya[0], (int)$xya[1]];
    $sequence[]   = (int)$xya[2];
}

$map = [];
for ($x = 0; $x < $w; $x++) {
    for ($y = 0; $y < $h; $y++) {
        $map[$x][$y] = 1;
    }
}

for ($i = 0; $i < count($sequence); $i++) {
    switch ($sequence[$i]) {
        case 1:
            for ($x = 0; $x < $coordinate[$i][0]; $x++) {
                for ($y = 0; $y < $h; $y++) {
                    $map[$x][$y] = 0;
                }
            }
            break;
        case 2:
            for ($x = $w - 1; $x >= $coordinate[$i][0]; $x--) {
                for ($y = 0; $y < $h; $y++) {
                    $map[$x][$y] = 0;
                }
            }
            break;
        case 3:
            for ($x = 0; $x < $w; $x++) {
                for ($y = 0; $y < $coordinate[$i][1]; $y++) {
                    $map[$x][$y] = 0;
                }
            }
            break;
        case 4:
            for ($x = 0; $x < $w; $x++) {
                for ($y = $h - 1; $y >= $coordinate[$i][1]; $y--) {
                    $map[$x][$y] = 0;
                }
            }
            break;
    }
}

$ans = 0;
foreach ($map as $value) {
    $ans = $ans + array_sum($value);
}
echo $ans;