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)

h, w, n = map(int, input().split())
ab = [list(map(int, input().split())) for _ in range(n)]

d = dict()
for i in range(len(ab)):
    a = ab[i][0] - 1
    b = ab[i][0] - 1
    d[a] = set()

dp = [0] * 10
dp[0] = (h - 2) * (w - 2)
for i in range(n):
    a = ab[i][0] - 1
    b = ab[i][1] - 1
    for dx in [-1, 0, 1]:
        for dy in [-1, 0, 1]:
            nx, ny = a + dx, b + dy # center
            if nx >= 1 and nx <= h - 2 and ny >= 1 and ny <= w - 2:
                # print(nx, ny)
                tmp = 0
                for dx2 in [-1, 0, 1]:
                    for dy2 in [-1, 0, 1]:
                        if nx + dx2 in d and ny + dy2 in d[nx + dx2]:
                            tmp += 1

                dp[tmp] -= 1
                dp[tmp + 1] += 1

    d[a].add(b)

for x in dp:
    print(x)