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 OCaml (4.02.3) (judge verdict: Accepted)

module M = Map.Make(struct type t = int * int let compare = compare end)

let rec seq a b = if a > b then [] else a :: seq (a+1) b
let (>>=) xs f = List.map f xs |> List.concat

let inc x y m =
  try M.add (x, y) (1 + M.find (x, y) m) m
  with Not_found -> M.add (x, y) 1 m

let () =
  Scanf.scanf "%d %d %d" @@ fun h w n ->
  let a = Array.init n (fun _ -> Scanf.scanf " %d %d" (fun x y -> x, y)) in
  let ret = Array.make 10 0 in
  a |> Array.fold_left (fun m1 (x, y) ->
    seq (max 1 (x-2)) (min (h-2) x) >>= (fun i -> seq (max 1 (y-2)) (min (w-2) y) >>= (fun j -> [(i, j)]))
    |> List.fold_left (fun m2 (i, j) -> inc i j m2) m1
  ) M.empty
  |> M.iter (fun (x, y) v ->
      ret.(v) <- ret.(v) + 1);
  
  let cur = Array.fold_left (+) 0 ret in
  ret.(0) <- (h-2)*(w-2) - cur;
  Array.iter (Printf.printf "%d\n") ret