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: Accepted)

from collections import defaultdict
H, W, N = map( int, input().split())
D = defaultdict( int)
def check(t):
    a, b = t
    if a == 0 or a == H-1:
        return False
    if b == 0 or b == W-1:
        return False
    return True
for _ in range(N):
    a, b = map( int, input().split())
    a, b = a-1, b-1
    if a >= 1:
        if b >= 1:
            D[(a-1,b-1)] += 1
        if b < W-1:
            D[(a-1,b+1)] += 1
        D[(a-1,b)] += 1
    if a < H-1:
        if b >= 1:
            D[(a+1,b-1)] += 1
        if b < W-1:
            D[(a+1,b+1)] += 1
        D[(a+1,b)] += 1
    if b >= 1:
        D[(a,b-1)] += 1
    if b < W-1:
        D[(a,b+1)] += 1
    D[(a,b)] += 1
ANS = [0]*10
for c in D:
    if check(c):
        ANS[D[c]] += 1
ANS[0] = (H-2)*(W-2)- sum(ANS)
for ans in ANS:
    print(ans)