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: Accepted)

<?php
fscanf(STDIN,"%d %d %d",$H,$W,$N);
$ans = array(1 => 0,2 => 0,3 => 0,4 => 0,5 => 0,6 => 0,7 => 0,8 => 0,9 => 0);
$count = ($H - 2) * ($W - 2);
if($N >= 1){
$i = 1;
while($i <= $N){
fscanf(STDIN,"%d %d",$a,$b);
$j = -1;
while($j <= 1){
if($a + $j >= 2){
if($a + $j <= $H - 1){
$k = -1;
while($k <= 1){
if($b + $k >= 2){
if($b + $k <= $W - 1){
if(isset($map[$a + $j][$b + $k])){
++$map[$a + $j][$b + $k];
}else{
$map[$a + $j][$b + $k] = 1;
}
}
}
++$k;
}
}
}
++$j;
}
++$i;
}
foreach($map as $val){
foreach($val as $val2){
++$ans[$val2];
--$count;
}
}
}
echo $count , PHP_EOL , join(PHP_EOL,$ans);
?>