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)

{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE BangPatterns #-}

import Control.Applicative
import Control.Monad
import Control.Arrow
import Data.List
import Data.Maybe
import Data.Char
import qualified Data.ByteString.Char8 as B
import Text.Printf

readInt = ( readLn :: IO Int )
readInts = map ( read :: String -> Int ) . words <$> getLine

getList = map ( fst . fromJust . B.readInt ) . B.words <$> B.getLine

which a b f = if f then a else b
mp [ a, b ] = ( a, b )

main = do
	[ w, h, n ] <- readInts
	queries <- replicateM n $ do
		[ x, y, a ] <- readInts
		return ( x, y, a )
	let	
		( x1, y1, x2, y2 ) = foldl solve ( 0, 0, w, h ) queries
	print $ ( max 0 $ x2 - x1 ) * ( max 0 $ y2 - y1 )

solve ( x1, y1, x2, y2 ) ( x, y, a )
	| a == 1 = ( ( max x1 x ), y1, x2, y2 )
	| a == 2 = ( x1, y1, ( min x2 x ), y2 )
	| a == 3 = ( x1, ( max y1 y ), x2, y2 )
	| a == 4 = ( x1, y1, x2, ( min y2 y ) )