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 Data.Sequence
import Data.Array.ST
import Data.Array
import Data.Foldable

point_to_rect_id::Int->Int->(Int,Int)->[(Int,Int)]
point_to_rect_id h w (x,y) = [(x-i,y-j)|i<-[0,1,2],j<-[0,1,2],is_inside h w (x-i,y-j) ]

is_inside::Int->Int->(Int,Int)->Bool
is_inside h w (x,y) = ((x>=1)&&(y>=1))&&(((x+2)<=h)&&((y+2)<=w))

get_rect_id::Int->Int->[(Int,Int)]->[(Int,Int)]
get_rect_id h w xs = toList (unstableSort (fromList (concat (map (point_to_rect_id h w) xs))))

sep_counter::(Eq a)=>[a]->[Int]
sep_counter []     =  []
sep_counter (x:[])   =  1:[]
sep_counter (x:y:xs) =let h:r = sep_counter (y:xs) in
                      if x==y then  (h+1):r
                              else  1:h:r

num_count::(Int,Int)->[Int]->Array Int Int
num_count (mn,mx) xs = runSTArray $ do
                  ar<-newArray (mn,mx) 0
                  mapM (write ar) xs
                  return ar
                where write ar x = do
                              v<-readArray ar x
                              writeArray ar x (v+1)

solver::Int->Int->[(Int,Int)]->[Int]
solver h w xs = let one_nine = elems (num_count (1,9) (sep_counter (get_rect_id h w xs))) in
                (((h-2)*(w-2))-(sum one_nine)):one_nine

main::IO()
main =do
  d<-getLine
  let h:w:n:[] = map read (words d) ::[Int]
  dat<-get_dat n
  print_n (solver h w dat)

get_dat:: Int -> IO [(Int,Int)]
get_dat 0 = return []
get_dat n = do
  abc<-getLine
  let a:b:[]= map read (words abc)::[Int]
  rest<-get_dat (n-1)
  return ((a,b):rest)

print_n::[Int]->IO()
print_n [] = return ()
print_n (x:xs) =do
  print x
  print_n xs