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 Python (2.7.6) (judge verdict: Wrong Answer)

def read_nums():
    return map(int, raw_input().split(' '))


def is_in_the_map(x, y):
    return x < H-1 and x > 0 and y < W-1 and y > 0


def solve():
    res = [0 for _ in range(N)]
    for i in range(N):
        a = As[i]
        b = Bs[i]
        for j in [-1, 0, 1]:
            for k in [-1, 0, 1]:
                x_mid = a + j
                y_mid = b + k
                if not is_in_the_map(x_mid, y_mid) or memo[x_mid][y_mid] == 1:
                    continue
                memo[x_mid][y_mid] = 1
                count = 0
                for x_pad in [-1, 0, 1]:
                    for y_pad in [-1, 0, 1]:
                        x = x_mid + x_pad
                        y = y_mid + y_pad
                        if Map[x][y] == 1:
                            count += 1
                res[count] += 1
    res[0] = (H-2) * (W-2) - sum(res)
    return res


H, W, N = read_nums()
As = [0 for _ in range(N)]
Bs = [0 for _ in range(N)]
Map = [[0 for _ in range(W)] for _ in range(H)]
for i in range(N):
    a, b = read_nums()
    As[i] = a - 1
    Bs[i] = b - 1
    Map[a - 1][b - 1] = 1
As, Bs = zip(*sorted(zip(As, Bs), key=lambda x: (x[0], x[1])))
memo = [[0 for _ in range(W)] for _ in range(H)]
res = solve()
for i in res:
    print i