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 Haskell (GHC 7.10.3) (judge verdict: Accepted)

import qualified Data.ByteString.Char8 as C
import Data.Maybe (fromJust)
import Control.Monad (replicateM)

cReadLn :: IO Int
cReadLn = fst . fromJust . C.readInt <$> C.getLine

getParms :: IO [Int]
getParms = map (fst . fromJust . C.readInt) . C.words <$> C.getLine

main :: IO ()
main = do
  [w,h,n] <- getParms
  xya     <- replicateM n getParms
  print $ area $ f w h xya

initialize
  :: Int -> Int -> ([Int],[Int])
initialize w h = ([0 .. w-1], [0 .. h-1])

cut :: ([Int],[Int]) -> [Int] -> ([Int], [Int])
cut (xs,ys) [x,y,a]
  | a == 1 = (xs1, ys)
  | a == 2 = (xs2, ys)
  | a == 3 = (xs,  ys3)
  | a == 4 = (xs,  ys4)
  where
    xs1 = dropWhile (< x) xs
    xs2 = takeWhile (< x) xs
    ys3 = dropWhile (< y) ys
    ys4 = takeWhile (< y) ys

f :: Int -> Int -> [[Int]] -> ([Int], [Int])
f w h = foldl cut (initialize w h) 

area (xs,ys) = length xs * length ys