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 ScopedTypeVariables #-}
import Control.Applicative
import Data.List
import qualified Data.IntMap as M

includingBoxes h w [a, b] = (,) <$> range h a <*> range w b
    where range max = filter (cond max) . sequence ((+) <$> [-2..0])
          cond max  = (&&) <$> (>= 0) <*> (<= max - 3)

frequencies :: Ord a => [a] -> [(a, Int)]
frequencies = map keyAndLen . group . sort
    where keyAndLen grp = (head grp, length grp)

solve h w ls = find <$> [0..9]
    where boxes     = ls >>= includingBoxes h w
          boxFreqs  = frequencies $ boxes
          freqs     = frequencies . filter (<= 9) . map snd $ boxFreqs
          zeros     = (h - 2) * (w - 2) - length boxFreqs
          find v    = M.findWithDefault 0 v $ M.fromList $ (0, zeros):freqs

main = do
    [h, w, _] <- map read . words <$> getLine
    ls      <- map (map (pred . read) . words) . lines <$> getContents
    mapM print $ solve h w ls