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 Python (3.4.3) (judge verdict: Runtime Error)

h,w,n = map(int,input().split())
coord = [list(map(int,input().split())) for i in range(n)]

num = {}

for i in range(n):
  for j,k in [[0,0],[0,1],[0,-1],[1,0],[1,1],[1,-1],[-1,0],[-1,1],[-1,-1]]:
    if not(2<=coord[i][0]+j<=h-1) or not(2<=coord[i][1]+k<=w-1):
      continue
    if not coord[i][0]+j in num:
      num[coord[i][0]+j] = {}
    if not coord[i][1]+k in num[coord[i][0]+j]:
      num[coord[i][0]+j][coord[i][1]+k] = 1
    else:
      num[coord[i][0]+j][coord[i][1]+k] += 1

ans = [0]*9
for i in num:
  for value in num[i].values():
    ans[value] +=1

print((h-2)*(w-2)-sum(ans))
for i in range(1,9):
  print(ans[i])