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 OverloadedStrings #-}
-- AtCoder My Practice
-- author: Leonardone @ NEETSDKASU

import qualified Data.Set              as S
import qualified Data.Array            as A
import qualified Data.Text             as T
import qualified Text.Printf           as P
import qualified Data.ByteString.Char8 as C
import qualified Data.List             as L
import qualified Data.IntMap           as I
import qualified Data.Map              as M
import Data.Maybe (fromJust)
import Data.Ix    (inRange)
 
-- 解説読後
-- http://arc061.contest.atcoder.jp/data/arc/061/editorial.pdf


main = putStrLn . unlines . map show . solve . map (map (fst . fromJust . C.readInt) . C.words) . C.lines =<< C.getContents

solve ([h, w, n]:xs) = ans where
    ans = [I.findWithDefault 0 k res | k <- [0 .. 9]]
    f mp [y, x] = foldl (\m k -> M.insertWith (+) k 1 m) mp [(y - dy, x - dx) | dy <- [1 .. 3], dx <- [1 .. 3]]
    flt = M.filterWithKey (\(y, x) _ -> (inRange (0, h - 3) y) && (inRange (0, w - 3) x))
    g = foldl (\m c -> I.insertWith (+) c 1 m) I.empty . M.elems
    tmp = g . flt $ foldl f M.empty xs
    res = I.insert 0 ((-) ((h - 2) * (w - 2)) . sum $ I.elems tmp) tmp