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 (7.3.0) (judge verdict: Accepted)


h,w,n = map(int,input().split())
d = {}
for i in range(n):
    a,b = map(int,input().split())
    a,b = a-1,b-1

    am1_f = a-1 > 0
    ap1_f = a+1 < h-1
    bm1_f = b-1 > 0
    bp1_f = b+1 < w-1
    a_f = a > 0 and a < h-1
    b_f = b > 0 and b < w-1

    am1 = a-1
    ap1 = a+1
    bm1 = b-1
    bp1 = b+1

    if am1_f:
        baseid = am1 * w
        if b_f:
            pid = baseid + b

            if pid not in d:
                d[pid] = 1
            else:
                d[pid] += 1

        if bm1_f:
            pid = baseid + bm1
            if pid not in d:
                d[pid] = 1
            else:
                d[pid] += 1

        if bp1_f:
            pid = baseid + bp1
            if pid not in d:
                d[pid] = 1
            else:
                d[pid] += 1

    if ap1_f:
        baseid = ap1*w
        if b_f:
            pid = baseid + b

            if pid not in d:
                d[pid] = 1
            else:
                d[pid] += 1

        if bm1_f:
            pid = baseid + bm1
            if pid not in d:
                d[pid] = 1
            else:
                d[pid] += 1

        if bp1_f:
            pid = baseid + bp1
            if pid not in d:
                d[pid] = 1
            else:
                d[pid] += 1
    if a_f:

        baseid = a * w
        if b_f:
            pid = baseid + b
            if pid not in d:
                d[pid] = 1
            else:
                d[pid] += 1

        if bm1_f:
            pid = baseid + bm1
            if pid not in d:
                d[pid] = 1
            else:
                d[pid] += 1

        if bp1_f:
            pid = baseid + bp1
            if pid not in d:
                d[pid] = 1
            else:
                d[pid] += 1
    # print(d)

ans = [0 for i in range(10)]

for val in d.values():
    ans[val] += 1

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

for a in ans:
    print(a)