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 (4.10.0) (judge verdict: Accepted)

Scanf.scanf "%d %d %d" (fun h w n ->
    let f a b = a lsl 30 + b in
    let module M = Map.Make (struct type t = int let compare = compare end) in

    let hist = Array.make 10 0 in
    hist.(0) <- (h - 2) * (w - 2);

    let rec loop i map =
        if i = n then hist else
            let map = Scanf.scanf " %d %d" (fun a b ->
                List.fold_left (fun map (vx, vy) ->
                    let x = b + vx in
                    let y = a + vy in
                    if x > 1 && x < w && y > 1 && y < h then (
                        let key = f x y in
                        let v = try M.find key map with _ -> 0 in
                        hist.(v) <- hist.(v) - 1;
                        hist.(v + 1) <- hist.(v + 1) + 1;
                        M.add key (v + 1) map
                    ) else map
                ) map [ -1, -1; -1, 0; -1, 1; 0, -1; 0, 0; 0, 1; 1, -1; 1, 0; 1, 1 ]
            ) in
            loop (i + 1) map
    in
    Array.iter (Printf.printf "%d\n") @@ loop 0 M.empty
)