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)

h,w,n = gets.chomp.split(" ").map(&:to_i)
coord = Hash.new{|h,k|h[k] = Hash.new(false)}
dot = n.times.map{gets.chomp.split(" ").map{|i|i.to_i-1}}
ans = Array.new(10,0)
list = []
dot.each do |a,b|
  coord[a][b] = true
end
dot.each do |a,b|
  o = [1-a,-1].max
  p = [h-a-2,1].min
  q = [1-b,-1].max
  r = [w-b-2,1].min
  for i in o..p
    for j in q..r
      list << [a+i-1,b+j-1]
    end
  end
end
list.uniq!
list.each do |a,b|
  temp = 0
  for i in 0..2
    for j in 0..2
      if coord[a+i][b+j] == true
        temp += 1
      end
    end
  end
  ans[temp] += 1
end
puts (h-2)*(w-2)-ans.inject(:+)
puts ans[1..-1]