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 Kotlin (1.0.0) (judge verdict: Accepted)

fun main(args: Array<String>) {
    abc047b()
}

// 黒く塗らない方向
private enum class Direction { RIGHT, LEFT, ABOVE, BELOW }

private data class Xya(val x: Int, val y: Int, val direction: Direction)

fun abc047b() {
    val (w, h, n) = readLine()!!.split(" ").map { it.toInt() }
    val xyaList = (1..n).map { readLine()!!.split(" ").map { it.toInt() } }
        .map {
            Xya(
                it[0], it[1], when (it[2]) {
                    1 -> Direction.RIGHT
                    2 -> Direction.LEFT
                    3 -> Direction.ABOVE
                    else -> Direction.BELOW
                }
            )
        }

    val left = xyaList.filter { it.direction == Direction.RIGHT }
        .maxBy { it.x }?.x ?: 0
    val right = xyaList.filter { it.direction == Direction.LEFT }
        .minBy { it.x }?.x ?: w
    val below = xyaList.filter { it.direction == Direction.ABOVE }
        .maxBy { it.y }?.y ?: 0
    val above = xyaList.filter { it.direction == Direction.BELOW }
        .minBy { it.y }?.y ?: h

    val answer = Math.max(0, (right - left)) * Math.max(0, (above - below))

    println(answer)
}