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{|i| i.to_i}

@hash = {}

for i in 0...@n
  a, b = gets.chomp.split(" ").map{|j| j.to_i}
  a -= 1
  b -= 1
  @hash[[a, b]] = 1
end

def valid(x, y)
  return 0 <= x && x < @h && 0 <= y && y < @w
end

@ans = Array.new(10){0}

@hash.each{|key, val|
  x = key[0]
  y = key[1]
  for i in 0...3
    for j in 0...3
      nx = x - i
      ny = y - j
      cnt = 0
      out = false
      for k in 0...3
        for l in 0...3
          sx = nx + k
          sy = ny + l
          if !valid(sx, sy)
            out = true
          elsif @hash.has_key?([sx, sy])
            cnt += 1
          end
        end
      end
      if !out
        @ans[cnt] += 1
      end
    end
  end
}

sum = 0
for i in 1..9
  @ans[i] /= i
  sum += @ans[i]
end

@ans[0] = (@h-2) * (@w-2) - sum;

for i in 0..9
  puts @ans[i]
end