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 PHP (5.6.30) (judge verdict: Time Limit Exceeded)

<?php
list($H,$W,$N) = explode(" ",trim(fgets(STDIN)));

$ans = array(0,0,0,0,0,0,0,0,0,0);

if($N > 0){
    for($i = 1;$i <= $N;$i++){
        list($a,$b) = explode(" ",trim(fgets(STDIN)));
        for($j = -1;$j <= 1;$j++){
            if($a + $j > 1 && $a + $j < $H){
                for($k = -1;$k <= 1;$k++){
                    if($b + $k > 1 && $b + $k < $W){
                        if(isset($map[$a + $j][$b + $k])){
                            $map[$a + $j][$b + $k] ++;
                        }else{
                            $map[$a + $j][$b + $k] = 1;
                        }
                    }
                }
            }
        }
    }
    
    foreach($map as $val){
        foreach($val as $val2){
            $ans[$val2] ++;
        }
    }
}

echo ($H - 2) * ($W - 2) - array_sum($ans) . PHP_EOL;

for($i = 1;$i <= 9;$i++){
    echo $ans[$i] . PHP_EOL;
}
?>