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)

import math

H, W, N = map(int, input().split())
count = [0]*10
count[0] = (H-2)*(W-2)
rectmap=[]

#print(board)
for i in range(0,N):
    a, b = list(map(int, input().split()))
    for j in range(a-1, a+2):
        for k in range(b-1, b+2):
            if j>1 and j<H and k>1 and k<W:
                rectmap.append([j-1, k-1])
#    print(rectmap)
rectmap.sort()
while rectmap!=[] :
#    print(rectmap[0])
#    print(rectmap)
    count[rectmap.count(rectmap[0])]+=1
    count[0]-=1
    del rectmap[:rectmap.count(rectmap[0])]
for i in range(0, 10):
    print(count[i])    
#print(H,W,N)
#print(ab)