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)

h, w, n = gets.strip.split.map(&:to_i)
ab = readlines.map {|line| line.strip.split.map(&:to_i) }

blacks = Array.new(n+1) { [false]*(n+1) }
ab.each do |a, b|
  blacks[a][b]=true
end

checker = {}
count_array = [0]*10
ab.each do |a, b|

  [a-2, a-1, a].each do |ca|
    next if ca<1 || ca > h-2
    [b-2, b-1, b].each do |cb|
      next if cb < 1 || cb > w-2
      key = [ca, cb].to_s
      next if checker[key]
      checker[key] = true

#p [ca, cb, '-']

      count = 0
      3.times do |i|
        3.times do |j|
          next if ca+i >h || cb+j > w

          count += 1 if blacks[ca+i][cb+j]
#p [ca+i, cb+j].to_s if blacks[ca+i][cb+j]
        end
      end
      count_array[count] += 1

    end
  end
end

all_count = (h-2)*(w-2)

#p [all_count, count_array.inject(:+)]
#blacks.each {|b|p b}

count_array[0] = all_count - count_array.inject(:+)

count_array.each do |cc|
  p cc
end