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 bisect
import heapq
H,W,N = map(int,input().split())
P = list(list(map(int,input().split()))for i in range(N))
P.sort()

def index(a,x):
    i = bisect.bisect_left(a,x)
    if i != len(a) and a[i] == x:
        return 0
    return -1

def around(a,b):
    out = []
    for i in [-1,0,1]:
        if not 1 < a+i < H:
            continue
        for j in [-1,0,1]:
            if not 1 < b+j < W:
                continue
            out.append([a+i,b+j])
    return out



def search(a,b):
    hoge = 0
    for i in [-1,0,1]:
        for j in [-1,0,1]:
            x,y = a+i,b+j
            if index(P,[x,y]) != -1:
                hoge += 1
    return hoge

A = []
for a,b in P:
    for x,y in around(a,b):
        heapq.heappush(A,[search(x,y),x,y])
a,b = 0,0
ans = [0]*10

while A:
    a = heapq.heappop(A)
    if a != b:
        ans[a[0]] += 1
    b = a[:]

ans[0] = (H-2)*(W-2)-sum(ans[1:])

for i in ans:
    print(i)