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)

{-# LANGUAGE TupleSections #-}
import Control.Monad
import Data.List
import Data.Map.Strict (Map)
import qualified Data.Map.Strict as Map
import Data.IntMap.Strict (IntMap)
import qualified Data.IntMap.Strict as IntMap

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

putSpot :: CountMap -> Spot -> CountMap
putSpot counts spot = foldl' inc counts $ viewsFor spot
  where viewsFor (x, y) = do
          j <- [(max 0 (y - 2)) .. y]
          i <- [(max 0 (x - 2)) .. x]
          return (i, j)
        inc counts spot = Map.adjust (+1) spot counts

views :: (Int, Int) -> [View]
views (w, h) = do
  y <- [1..(h - 2)]
  x <- [1..(w - 2)]
  return (x, y)

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 init = Map.fromList $ (,0) <$> views (w, h)
      counts = foldl' putSpot init spots
      res = Map.foldl' (\a b -> IntMap.insertWith (+) b 1 a) IntMap.empty counts
      display i = print $ IntMap.findWithDefault 0 i res
  mapM_ display [0..9]