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: Accepted)

import qualified Data.ByteString.Char8 as BC
import qualified Data.IntMap as M
import Data.Array.IO
import Data.Maybe (fromJust)
import Data.List
import Control.Monad

main = do
  [h,w,n] <- map read . words <$> getLine :: IO [Int]
  painted <- getInt2DListBC
  let sub = map (\x -> (head x, length x)) . group . sort . map length . group . sort . concat $ map (solve h w) painted
  memo <- newArray (1, 9) 0 :: IO (IOUArray Int Int)
  foldM count memo sub
  ans <- getElems memo
  let zero = (h-2)*(w-2) - (sum ans)
  print zero
  putStr $ unlines . map show $ ans

bsToInt :: BC.ByteString -> Int
bsToInt = fst . fromJust . BC.readInt

getInt2DListBC :: IO [[Int]]
getInt2DListBC = map (map bsToInt . BC.words) . BC.lines <$> BC.getContents

solve :: Int -> Int -> [Int] -> [(Int, Int)]
solve h w [x, y] = [(i, j) | i <- [x-1..x+1], j <- [y-1..y+1], 2 <= i, i <= h-1, 2 <= j, j <= w-1]

count :: IOUArray Int Int -> (Int, Int) -> IO (IOUArray Int Int)
count memo (i, c) = do
  writeArray memo i c
  return memo