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 PyPy3 (7.3.0) (judge verdict: Time Limit Exceeded)

import sys
from collections import deque

sys.setrecursionlimit(10 ** 7)
input = sys.stdin.readline
f_inf = float('inf')
mod = 10 ** 9 + 7


def resolve():
    H, W, n = map(int, input().split())
    AB = set(tuple(tuple(map(lambda x: int(x) - 1, input().split())) for _ in range(n)))

    d = ((1, 1), (1, 0), (1, -1), (0, 1), (0, 0), (0, -1), (-1, 1), (-1, 0), (-1, -1))
    total = (H - 2) * (W - 2)
    res = [0] * 10
    used = set()
    for a, b in AB:
        if (a, b) in used:
            continue
        que = deque([(a, b)])
        while que:
            h, w = que.popleft()
            if (h, w) in used:
                continue
            used.add((h, w))
            cnt = 0
            flg = True
            for dh, dw in d:
                next_h, next_w = h + dh, w + dw
                if next_h < 0 or next_h >= H or next_w < 0 or next_w >= W:
                    flg = False
                else:
                    if (next_h, next_w) in AB:
                        cnt += 1
                    if (next_h, next_w) not in used:
                        que.append((next_h, next_w))
            if flg:
                res[cnt] += 1
    t = total - sum(res)
    res[0] += t
    print(*res, sep="\n")


if __name__ == '__main__':
    resolve()