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 Scala (2.11.7) (judge verdict: Runtime Error)

object Main extends App {
  val inputs: Seq[String] = scala.io.Source.stdin.getLines().toList
  // val inputs = Seq("5 4 3", "2 1 1", "3 3 4", "1 4 2")
  val nums   = inputs.head.split(" ").map(_.toInt)
  val pointSeq = inputs.tail
  val width  = nums(0)
  val height = nums(1)
  val point  = nums(2)

  println(solve(width, height, pointSeq))

  private def solve(w: Int, h: Int, points: Seq[String]): Int = {
    val hash = scala.collection.mutable.HashMap((1,0), (2, w), (3, 0), (4 ,h))
    points.map(point => point.split(" ").map(_.toInt))

    points.foreach { str =>
      val inputs = str.split(" ").map(_.toInt)
      val x = inputs(0)
      val y = inputs(1)
      val a = inputs(2)

      a match {
        case 1 if(hash(a) < x) => hash.update(a, x)
        case 2 if(hash(a) > x) => hash.update(a, x)
        case 3 if(hash(a) < y) => hash.update(a, y)
        case 4 if(hash(a) > y) => hash.update(a, y)
      }
    }
    val whiteX = hash(2) - hash(1)
    val whiteY = hash(2) - hash(1)

    (whiteX, whiteY) match {
      case (x, y) if (0 <= x && 0 <= y) => whiteX * whiteY
      case _ => 0
    }
  }
}