100453: [AtCoder]ABC045 D - Snuke's Coloring

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