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 deque,defaultdict
printn = lambda x: print(x,end='')
inn = lambda : int(input())
inl   = lambda: list(map(int, input().split()))
inm   = lambda:      map(int, input().split())
ins = lambda : input().strip()
DBG = True # and False
BIG = 10**18
R = 10**9 + 7

def ddprint(x):
  if DBG:
    print(x)

def foo(a,b,ans):
    z = d[a][b]
    for p in range(3):
        for q in range(3):
            if a-2+p<0 or a+p>=h or b-2+q<0 or b+q>=w:
                continue
            ok = True
            reachorig = False
            v = 0
            for i in range(3):
                for j in range(3):
                    if p+i==q+j==2:
                        reachorig = True
                    if z[p+i][q+j]==1:
                        if reachorig:
                            v += 1
                        else:
                            ok = False
                            break
            if ok:
                ans[v] += 1

h,w,n = inm()
d = {}
ab = []
for i in range(n):
    a,b = inm()
    a -= 1
    b -= 1
    ab.append((a,b))
    if a not in d:
        d[a] = {}
    d[a][b] = [[0]*5 for j in range(5)]
    d[a][b][2][2] = 1
for a,b in ab:
    for dx in range(-2,3):
        for dy in range(-2,3):
            if a+dx in d and b+dy in d[a+dx] and not (dx==dy==0):
                d[a+dx][b+dy][2-dx][2-dy] = 1

if False and DBG:
    for i in range(h):
        for j in range(w):
            if i in d and j in d[i]:
                #print(f"{i=} {j=}")
                for k in range(5):
                    print(d[i][j][k])
ans = [0]*10
for a,b in ab:
    foo(a,b,ans)
print((h-2)*(w-2)-sum(ans))
for i in range(1,10):
    print(ans[i])