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 PyPy3 (2.4.0) (judge verdict: Time Limit Exceeded)

H,W,N = map(int,input().split())
if N == 0:
  print((H-2)*(W-2))
  for i in range(9):
    print(0)
  exit()

AB = [list(map(int,input().split())) for _ in range(N)]

Board = [[0 for _ in range(W)] for _ in range(H)]
Done = [[0 for _ in range(W)] for _ in range(H)]
Count = [0 for _ in range(10)]

for a,b in AB:
  Board[a-1][b-1] = 1
for a,b in AB:
  a -= 1
  b -= 1
  for i in range(-1,2):
    for j in range(-1,2):
      if 1 <= a+i <= H-2 and 1 <= b+j <= W-2:
        if Done[a+i][b+j] == 1:
          continue
        c = 0
        for k in range(-1,2):
          for l in range(-1,2):
            c += Board[a+i+k][b+j+l]
        Count[c] += 1
        Done[a+i][b+j] = 1
Count[0] = (H-2)*(W-2)-sum(Count[1:])
for c in Count:
  print(c)