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, *rest = $stdin.read.split.map(&:to_i)
BS = rest.each_slice(2)
BLACKS_Y = {}
BS.each{|y, x| BLACKS_Y[y] ||= []; BLACKS_Y[y] << x}
BLACKS_Y.each{|k, v| v.sort!}
ct = Array.new(10, 0)

def count(y1, x1, y2, x2)
  n = 0
  (y1..y2).each do |y|
    if BLACKS_Y.key?(y)
      i = BLACKS_Y[y].bsearch_index{|x| x >= x1}
      next if i.nil?
      (i...BLACKS_Y[y].length).each do |i|
        x = BLACKS_Y[y][i]
        break if x > x2
        n += 1
      end
    end
  end
  return n
end

BS.each do |y, x|
  (-2..0).each do |dy|
    (-2..0).each do |dx|
      if (1..(H-2)).cover?(y+dy) && (1..(W-2)).cover?(x+dx)
        n = count(y+dy, x+dx, y+dy+2, x+dx+2)
        ct[n] += 1
      end
    end
  end
end

ans = ct.map.with_index{|k, n| n == 0 ? nil : k / n}
ans[0] = (W-2)*(H-2) - ans[1..9].inject(:+)
puts ans