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.