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: Time Limit Exceeded)

H, W , N = map(int,input().split())
from bisect import bisect_left
from bisect import bisect_right
matrix = []
for _ in range(N):
    x,y = map(int,input().split())
    x -= 1
    y -= 1
    matrix.append([x,y])
matrix.sort()
ans = [0 for _ in range(10)]
from bisect import bisect_left
cand = {}
for l in matrix:
    for x_r in [-2, -1 , 0]:
        for y_r in [-2, -1 , 0]:
            nowx = l[0] + x_r
            nowy = l[1] + y_r
            if nowx < 0 or nowy < 0 or nowx + 2>= H or nowy+ 2 >= W:
                continue
            #ここで起点(左上)nowx, nowy として　 9マスに着目する
            name = str(nowx) + str(nowy)
            try: cand[name] += 1
            except: cand[name] = 1
tmp = ((H - 2) * (W - 2))
for x in cand.values():
    if x > 9:
        while True:
            print(W)
    ans[x] += 1
    tmp -= 1
ans[0] = tmp
for x in ans:
    print(x)