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 Perl (v5.18.2) (judge verdict: Time Limit Exceeded)

use bigint;
use Data::Dumper;

my $input = <STDIN>;
chomp $input;

my ($W, $H, $N) = split(/\s/, $input);
my @squares;
for (my $i = 0; $i < $H; $i++) {
    $squares[$i] = 0;
}

my $w = 2**$W;

for (my $i = 0; $i < $N; $i++) {
    $input = <STDIN>;
    chomp $input;

    my ($x, $y, $a) = split(/\s/, $input);
    
    if ($a == 1) {
        for (my $j = 0; $j < $H; $j++) {
            $squares[$j] = $squares[$j] | (2**($x)-1);
        }
    } elsif ($a == 2) {
        for (my $j = 0; $j < $H; $j++) {
            $squares[$j] = $squares[$j] | (($w - 1) ^ ((2**$x) - 1));
        }
    } elsif ($a == 3) {
        for (my $j = 0; $j < $y; $j++) {
            $squares[$j] = $squares[$j] | ($w - 1);
        }
    } else {
        for (my $j = $y; $j < $H; $j++) {
            $squares[$j] = $squares[$j] | ($w - 1);
        }
    }
}

my $count = 0;
for (my $i = 0; $i < $H; $i++) {
    for (my $j = 0; $j < $W; $j++) {
        if (($squares[$i] & 1) == 0) {
            $count++;
        }
        $squares[$i] = $squares[$i] >> 1;
    }
}

print $count, "\n";

exit;