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: Wrong Answer)

H, W, N = gets.split.map(&:to_i)
if N == 0
  puts (H - 2) * (W - 2)
  exit
end
dir = [-2, -1, 0].repeated_permutation(2)
arr = []
N.times do
  a, b = gets.split.map(&:to_i)
  dir.each do |x, y|
    r, c = a + x - 1, b + y - 1
    arr << [r, c] unless r < 0 || r >= H - 2 || c < 0 || c >= W - 2
  end
end
arr.sort! { |a, b| a[0] == b[0] ? a[1] <=> b[1] : a[0] <=> b[0] }
x = arr[0]
c = 1
h = (1..9).map { |i| [i, 0] }.to_h
arr[1..-1].each do |y|
  if y == x
    c += 1
  else
    h[c] += 1
    x, c = y, 1
  end
end
h[c] += 1
h[0] = (H - 2) * (W - 2) - arr.uniq.size
10.times { |i| puts h[i] }