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: Runtime Error)

# require 'pry'
Y = [-2,-2,-2,-1,-1,-1,0,0,0]
X = [-2,-1,0,-2,-1,0,-2,-1,0]
H, W, N = gets.split.map(&:to_i)
areas = []
H.times do
  areas << Array.new(W, 0)
end
memos = Array.new(H){Array.new(W, 0)}
lists = []
N.times do
  a, b = gets.split.map(&:to_i)
  areas[a-1][b-1] = 1
  lists << [a-1, b-1]
end
# areas.each do |a|
#   p a
# end
ans = Hash.new(0)
# binding.pry
lists.each do |list|
  9.times do |i|
    nowy = list[0] + Y[i]
    nowx = list[1] + X[i]
    next if 0 > nowy || nowy > H-3 || 0 > nowx || nowx > W-3 || memos[nowy][nowx] == 1
    pre = 0
    3.times do |j|
      pre += areas[nowy + j][nowx, 3].inject(:+)
    end
    # binding.pry
    ans[pre] += 1
    memos[nowy][nowx] = 1
  end
end
# puts ans
sum = 0
ans.each do |k, v|
  sum += v
end
# puts sum
ans[0] = (H-2) * (W-2) - sum
# puts ans
10.times do |i|
  next if ans[i] != 0
  ans[i] = 0
end
ans.sort_by{|k, v|k}.each do |_, v|
  puts v
end