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 Python (3.4.3) (judge verdict: Wrong Answer)

# coding: utf-8
# Here your code !
def scan(sx, sy, mp):
    cnt = 0
    for y in range(sy, sy + 3):
        for x in range(sx, sx + 3):
            if mp[y][x] == 1:
                cnt += 1
    return cnt

H, W, N = map(int, input().split())
mp = [[0 for i in range(W)] for j in range(H)]
input_ls = []
for i in range(N):
    a, b = map(int, input().split())
    input_ls.append((a,b))
    mp[a-1][b-1] = 1
    
print(mp, input_ls)

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

sx = 0
sy = 0
for y in range(H-2):
    for x in range(W-2):
        sx = x
        sy = y
        cnt = scan(sx, sy, mp)
        ans_list[cnt] += 1
print(ans_list)