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]

black = Array.new(n){}

0.upto(n - 1) do |i|
	s = gets().split().map(&:to_i)
	black[i] = [s[1] - 1, s[0] - 1]
end

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

list = Array.new(10){[]}
sum = (h - 2) * (w - 2)
0.upto(n - 1) do |i|
	p = black[i]
	0.upto(8) do |j|
		x = p[0] + vx[j]
		y = p[1] + vy[j]
		cnt = 0
		ok = true
		0.upto(2) do |k|
			if y + k < 0 || y + k > h - 1
				ok = false
				break
			end
			0.upto(2) do |l|
				if x + l < 0 || x + l > w - 1
					ok = false
					break
				end
				if black.include?([x + l, y + k])
					cnt += 1
				end
			end
			break if !ok
		end
		if ok
			list[cnt] << [p[0] + vx[j], p[1] + vy[j]]
		end
	end
end

def Object.eql? a
	self == a
end

all = Array.new(10){}
1.upto(9) do |i|
	list[i] = list[i].uniq
	sum -= list[i].length
	all[i] = list[i].length
end
all[0] = sum

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