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)

import sys
input = sys.stdin.readline

h,w,n = map(int,input().split())
dg = 10**10
d = dict()

def f(z):
    x,y = z//dg,z%dg
    if 2 <= x <= h-1 and 2 <= y <= w-1:
        return True
    else:
        False

for i in range(n):
    a,b = map(int,input().split())
    
    if f((a-1)*dg + b-1):
        if (a-1)*dg + b-1 in d:
            d[(a-1)*dg + b-1] += 1
        else:
            d[(a-1)*dg + b-1] = 1
    
    if f((a-1)*dg + b):
        if (a-1)*dg + b in d:
            d[(a-1)*dg + b] += 1
        else:
            d[(a-1)*dg + b] = 1
    
    if f((a-1)*dg + b+1):
        if (a-1)*dg + b+1 in d:
            d[(a-1)*dg + b+1] += 1
        else:
            d[(a-1)*dg + b+1] = 1

    if f((a)*dg + b-1):
        if (a)*dg + b-1 in d:
            d[(a)*dg + b-1] += 1
        else:
            d[(a)*dg + b-1] = 1
    
    if f(a*dg + b):
        if a*dg + b in d:
            d[a*dg + b] += 1
        else:
            d[a*dg + b] = 1
    
    if f((a)*dg + b+1):
        if (a)*dg + b+1 in d:
            d[(a)*dg + b+1] += 1
        else:
            d[(a)*dg + b+1] = 1
    
    if f((a+1)*dg + b+1):
        if (a+1)*dg + b+1 in d:
            d[(a+1)*dg + b+1] += 1
        else:
            d[(a+1)*dg + b+1] = 1
    
    if f((a+1)*dg + b):
        if (a+1)*dg + b in d:
            d[(a+1)*dg + b] += 1
        else:
            d[(a+1)*dg + b] = 1
    
    if f((a+1)*dg + b-1):
        if (a+1)*dg + b-1 in d:
            d[(a+1)*dg + b-1] += 1
        else:
            d[(a+1)*dg + b-1] = 1
    
    
    
    
res = [0]*10

for e in d:
    res[d[e]] += 1

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

for e in res:
    print(e)