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 Ruby (2.3.3) (judge verdict: Runtime Error)

def main
  w, h, n = gets.split.map{|s| s.to_i}

  arr = []
  (0...n).each do |i|
    x, y, a = gets.split.map{|s| s.to_i}
    arr << Area.new(x, y, w, h, a)
  end

  require 'pp'
  puresum = arr.inject(0) {|sum, a| sum + a.area }
  subtract = 0
  (0...(arr.size - 1)).each do |i|
    subtract += arr[i].overlay(arr[i+1])
  end
  puts puresum - subtract
end

class Area
  attr_accessor :from, :to
  def initialize(x, y, limit_x, limit_y, a)
    case a
    when 1 then
      @from = Point.new(0, 0)
      @to = Point.new(x, limit_y)
    when 2 then
      @from = Point.new(x, 0)
      @to = Point.new(x, litmi_y)
    when 3 then
      @from = Point.new(0, 0)
      @to = Point.new(limit_x, y)
    when 4 then
      @from = Point.new(0, y)
      @to = Point.new(limit_x, limit_y)
    end
    @a = a
  end

  def overlay area
    if (@from.x..@to.x).include?(area.from.x) && (@from.y..@to.y).include?(area.from.y)
      minx = (@to.x - @from.x) > (area.to.x - area.from.x) ? (area.to.x - area.from.x) : (@to.x - @from.x)
      miny = (@to.y - @from.y) > (area.to.y - area.from.y)? (area.to.y - area.from.y) : (@to.y - @from.y)
      minx * miny
    else
      0
    end
  end

  def area
    (@to.x - @from.x) * (@to.y - @from.y)
  end
end


class Point
  attr_accessor :x, :y
  def initialize(x, y)
    @x = x
    @y = y
  end
end

main