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 Ruby (2.3.3) (judge verdict: Time Limit Exceeded)

s = gets().split().map(&:to_i)
h = s[0]
w = s[1]
n = s[2]

vx = [-2, -1, 0, -2, -1, 0, -2, -1, 0]
vy = [-2, -2, -2, -1, -1, -1, 0, 0, 0]
list = []

j = 0
0.upto(n - 1) do |i|
	s = gets().split().map(&:to_i)
	0.upto(8) do |k|
		x = s[1] - 1 + vx[k]
		y = s[0] - 1 + vy[k]
		if x >= 0 && x + 2 < w && y >= 0 && y + 2 < h
			list << [x, y]
			j += 1
		end
	end
end

list.sort!{|a, b| (a[0] <=> b[0]).nonzero? || (a[1] <=> b[1])}

all = Array.new(10){0}
all[0] = (h - 2) * (w - 2)
i, k = 0, 0
loop{
	break if j <= i
	cnt = 0
	loop {
		break if j <= i
		if list[k][0] == list[i][0] && list[k][1] == list[i][1]
			cnt += 1
			i += 1
		else
			k = i
			i -= 1
			break
		end
	}
	all[cnt] += 1
	all[0] -= 1
	i += 1
}

0.upto(9) do |i|
	puts all[i]
end