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 Lua (LuaJIT 2.1.0) (judge verdict: Accepted)

local read = io.read

local W, H, N = read("*n", "*n", "*n")
local rectangle = {}
for x = 1, W do
	rectangle[x] = {}
	for y = 1, H do
		rectangle[x][y] = true
	end
end

local function paint(x_i, y_i, a_i)
	if a_i == 1 then
		for x = 1, x_i do
			for y = 1, H do
				rectangle[x][y] = false
			end
		end
	elseif a_i == 2 then
		for x = x_i + 1, W do
			for y = 1, H do
				rectangle[x][y] = false
			end
		end
	elseif a_i == 3 then
		for x = 1, W do
			for y = 1, y_i do
				rectangle[x][y] = false
			end
		end
	else
		for x = 1, W do
			for y = y_i + 1, H do
				rectangle[x][y] = false
			end
		end
	end
end

for i = 1, N do
	paint(read("*n", "*n", "*n"))
end

local out = 0
for x = 1, W do
	for y = 1, H do
		if rectangle[x][y] then
			out = out + 1
		end
	end
end

print(out)