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 (2.4.0) (judge verdict: Accepted)

def main():
    import sys
    # readline = sys.stdin.readline
    readlines = sys.stdin.readlines
    H, W, N = map(int, input().split())
    grid = {}
    P = set()
    for s in readlines():
        a, b = map(int, s.split())
        a -= 1; b -= 1
        if a in grid:
            grid[a].add(b)
        else:
            grid[a] = set([b])
        P.add((a, b))

    ans = [0] * 10
    done = set()
    for a, b in P:
        for oa in range(a - 2, a + 1):
            for ob in range(b - 2, b + 1):
                if 0 <= oa <= H - 3 and 0 <= ob <= W - 3 and (oa, ob) not in done:
                    tmp = 0
                    for i in range(3):
                        for j in range(3):
                            na = oa + i
                            nb = ob + j
                            if (na, nb) in P:
                                tmp += 1
                    ans[tmp] += 1
                    done.add((oa, ob))
    
    ans[0] = (H - 2) * (W - 2) - sum(ans[1:])

    print(*ans, sep='\n')


if __name__ == "__main__":
    main()