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: Wrong Answer)

# xy  平面上に、左下の座標が (0,0)、右上の座標が (W,H) で、各辺が x 軸か y 軸に平行な長方形があります。
# 最初、長方形の内部は白く塗られています。すぬけ君はこの長方形の中に N 個の点を打ちました。
# i 個目 (1≦i≦N) 点の座標は (xi,yi) でした。
# また、すぬけ君は長さ N の数列 a を決めて、各 1≦i≦N に対し、
# ai=1 のときは長方形の x<xi をみたす領域
# ai=2 のときは長方形の x>xi をみたす領域
# ai=3 のときは長方形の y<yi をみたす領域
# ai=4 のときは長方形の y>yi をみたす領域
# を黒く塗りました。塗りつぶしが終わったあとの長方形内での白い部分の面積を求めてください。

whn = gets.chomp.split
w = whn[0].to_i
h = whn[1].to_i
n = whn[2].to_i

x = Array.new
y = Array.new
a = Array.new
n.times do
    xya = gets.chomp.split
    x << xya[0].to_i
    y << xya[1].to_i
    a << xya[2].to_i
end

white = [[0, 0], [w, h]]

n.times do |i|
    case a[i]
    when 1
        white[0][0] = x[i] if white[0][0] < x[i]
    when 2
        white[1][0] = x[i] if white[1][0] > x[i]
    when 3
        white[0][1] = y[i] if white[0][1] < y[i]
    when 4
        white[1][1] = y[i] if white[1][1] > y[i]
    end
end

height = white[1][0] - white[0][0]
width = white[1][1] - white[0][1]
area = height * width

if area < 0
    area = 0
end

puts area