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: Accepted)

<?php
    list($width, $height, $num) = explode(" ", trim(fgets(STDIN)));
//    $width = 10;
//    $height = 10;

    $map = array();

    for($i = 0; $i < $width; $i++){
        for($k = 0; $k < $height; $k++){
            $map[$i][$k] = 1;
        }
    }
    
//    $testcase = array(array(1,6,1), array(4,1,3), array(6,9,4), array(9,4,2), array(3,1,3));
    
/*
    for($i = 0; $i < $width; $i++){
        for($k = 0; $k < $height; $k++){
            echo $map[$i][$k];
        }
        echo PHP_EOL;
    }
*/

    for($i = 0; $i < $num; $i++){
//    for($ite = 0; $ite < 5; $ite++){
        list($x, $y, $a) = explode(" ", trim(fgets(STDIN)));
//        $x = $testcase[$ite][0];
//        $y = $testcase[$ite][1];
//        $a = $testcase[$ite][2];

        switch ($a) {
            case '1':
                for($n = 0; $n < $height; $n++){
                    for($m = 0; $m < $x; $m++){
                        $map[$m][$n] = 0;
                    }
                }
                break;

            case '2':
                for($n = 0; $n < $height; $n++){
                    for($m = $width - 1; $m >= $x; $m--){
                        $map[$m][$n] = 0;
                    }
                }
                break;
            
            case '3':
                for($n = 0; $n < $width; $n++){
                    for($m = 0; $m < $y; $m++){
                        $map[$n][$m] = 0;
                    }
                }
                break;

            case '4':
                for($n = 0; $n < $width; $n++){
                    for($m = $height - 1; $m >= $y; $m--){
                        $map[$n][$m] = 0;
                    }
                }
                break;
            default:
                break;
        }
/*
    for($k = $height - 1 ; $k >= 0; $k--){
        for($i = 0 ; $i < $width; $i++){
            echo $map[$i][$k];
        }
        echo PHP_EOL;
    }
    echo PHP_EOL;
*/        
    }
    
    $ans = 0;

    for($k = $height - 1 ; $k >= 0; $k--){
        for($i = 0 ; $i < $width; $i++){
            $ans += $map[$i][$k];
        }
    }
    echo $ans;
?>