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)

$w,$h,$n = gets.chomp.map{|i| i.to_i}
x = []
y = []
z = []
n.times do |i|
	p,q,r = gets.chomp.map{|i| i.to_i}
	x << p
	y << q
	z << r
end

$rect = Array.new(h,1).map{|i| i = Array.new(w,1)}#[h][w]

def draw(nw,nh,na)
	rx = 0..($w)
	ry = 0..($h)
	case a then
		when 1 then
			rx = 0..(nw-1)
		when 2 then
			rx = nw..($w-1)
		when 3 then
			ry = 0..(nh-1)
		when 4 then
			ry = nh..($h-1)
		else
	end
	rx.each do |x|
		ry.each do |y|
			$rect[y][x] = 0
		end
	end
end

n.times do |i|
	draw(x[i],y[i],a[i])
end

res = 0
$rect.each do |i|
	res+=i.inject{|sum,i|sum+=i}
end

puts res