Problem:
Score : 400 points

Problem Statement

We have a grid with H rows and W columns. At first, all cells were painted white.

Snuke painted N of these cells. The i-th ( 1 \leq i \leq N ) cell he painted is the cell at the a_i-th row and b_i-th column.

Compute the following:

For each integer j ( 0 \leq j \leq 9 ), how many subrectangles of size 3×3 of the grid contains exactly j black cells, after Snuke painted N cells?

Constraints

3 \leq H \leq 10^9

3 \leq W \leq 10^9

0 \leq N \leq min(10^5,H×W)

1 \leq a_i \leq H (1 \leq i \leq N)

1 \leq b_i \leq W (1 \leq i \leq N)

(a_i, b_i) \neq (a_j, b_j) (i \neq j)

Input

The input is given from Standard Input in the following format:

H W N
a_1 b_1
:
a_N b_N

Output

Print 10 lines.
The (j+1)-th ( 0 \leq j \leq 9 ) line should contain the number of the subrectangles of size 3×3 of the grid that contains exactly j black cells.

Sample Input 1

4 5 8
1 1
1 4
1 5
2 3
3 1
3 2
3 4
4 4

Sample Output 1

0
0
0
2
4
0
0
0
0
0

There are six subrectangles of size 3×3. Two of them contain three black cells each, and the remaining four contain four black cells each.

Sample Input 2

10 10 20
1 1
1 4
1 9
2 5
3 10
4 2
4 7
5 9
6 4
6 6
6 7
7 1
7 3
7 7
8 1
8 5
8 10
9 2
10 4
10 9

Sample Output 2

4
26
22
10
2
0
0
0
0
0

Sample Input 3

1000000000 1000000000 0

Sample Output 3

999999996000000004
0
0
0
0
0
0
0
0
0

Solution in Haskell (GHC 7.10.3) (judge verdict: Time Limit Exceeded)

import Control.Monad

type View = ((Int, Int), (Int, Int))
type Spot = (Int, Int)

views :: (Int, Int) -> [View]
views (w, h) = do
  y <- [0..(h - 3)]
  x <- [0..(w - 3)]
  return ((x + 1, y + 1), (x + 3, y + 3))

countSpots :: [Spot] -> View -> Int
countSpots spots ((x0, y0), (x1, y1)) = length $ filter isIn spots
  where isIn (x, y) = x0 <= x && x <= x1 && y0 <= y && y <= y1

readLine :: String -> (Int, Int)
readLine s = (x, y)
  where [y, x] = read <$> words s

main :: IO ()
main = do
  [h, w, n] <- (fmap read . words) <$> getLine
  spots <- replicateM n $ readLine <$> getLine
  let counts = countSpots spots <$> views (w, h)
  mapM_ (display counts) [0..9]
  where display counts i = print $ length $ filter (==i) counts