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)

main::IO()
main =do
  whn<-getLine
  let w:h:n:[] = map read (words whn)::[Int]
  dats<-getn n
  print (solver w h dats)

getn::Int -> IO [(Int,(Int,Int))]
getn 0 = return []
getn n = do
  xya<-getLine
  let x:y:a:[]= map read (words xya)::[Int]
  rest<-getn (n-1)
  return ((a,(x,y)):rest)

folding::(Int,Int,Int,Int)->[(Int,(Int,Int))]->(Int,Int,Int,Int)
folding (x1,x2,y1,y2) []                =(x1,x2,y1,y2)
folding (x1,x2,y1,y2) ((a,(x,y)):dats)
                      | a==1 = let x1'= max x1 x in folding (x1',x2,y1,y2) dats
                      | a==2 = let x2'= min x2 x in folding (x1,x2',y1,y2) dats
                      | a==3 = let y1'= max y1 y in folding (x1,x2,y1',y2) dats
                      | a==4 = let y2'= min y2 y in folding (x1,x2,y1,y2') dats

solver::Int -> Int -> [(Int,(Int,Int))]->Int
solver w h dats = let (x1,x2,y1,y2) = folding (0,w,0,h) dats in (max (x2-x1) 0)*(max (y2-y1) 0)