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: Accepted)

MIN_H = 3
MIN_W = 3

h, w, n = gets.split(" ").map(&:to_i)

count_map = {}
# 黒マスを起点として、影響範囲を数える
(0...n).each{
  black_y, black_x = gets.split(" ").map(&:to_i)
  (0...MIN_H).each{ |y|
    (0...MIN_W).each{ |x|
      # 各影響範囲の左上のマス
      sub_y = black_y - y
      sub_x = black_x - x
      in_y = (1 <= sub_y && sub_y <= (h-2))
      in_x = (1 <= sub_x && sub_x <= (w-2))
      if in_x && in_y
        # 左上のマスごとにマッピング
        if !count_map.key?(sub_y)
          count_map[sub_y] = {}
        end
        if !count_map[sub_y].key?(sub_x)
          count_map[sub_y][sub_x] = 0
        end
        count_map[sub_y][sub_x] += 1
      end
    }
  }
}

# 0～9までの件数
counts = Array.new(MIN_W * MIN_H + 1, 0)
count_map.each{ |k, in_count_map|
  in_count_map.each { |k2, v|
    counts[v] += 1
  }
}
counts[0] = (w - 2) * (h - 2) - counts.inject(0, &:+)

puts counts