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 (5.6.30) (judge verdict: Wrong Answer)

<?php
//終端まで繰り返す
while ( ! feof(STDIN) ) {
  $line[] = trim(fgets(STDIN));
}

$split_line = explode(" ", $line[0]);
$x = $split_line[0];
$y = $split_line[1];
$n = $split_line[2];

for ($i = 1; $i <= $n; $i++) {
    $xy_list[] = $line[$i];
}

$white = $x * $y;
$black = 0;

for ($j = 0; $j < $n; $j++) {
    $xyn = explode(" ", $xy_list[$j]);
    if ($xyn[2] == 1) {
        $black = $black + ($xyn[0] * $y);
    } else if ($xyn[2] == 2) {
        $black = $black + ($y * ($x - $xyn[0]));
    } else if ($xyn[2] == 3) {
        $black = $black + ($xyn[1] * $x);
    } else if ($xyn[2] == 4) {
        $black = $black + ($x * ($y - $xyn[1]));
    }
    echo $black . "\n";
}

if (($white - ($black - $n)) <= 0) {
    echo "0";
} else {
    echo $white - ($black - $n);
}