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 Julia (0.5.0) (judge verdict: Memory Limit Exceeded)

const D=Dict{Pair{Int,Int},Int}()
function f(H,W,x,y,cnt)
	for (dx,dy)=zip([1,1,1,0,0,0,-1,-1,-1],[1,0,-1,1,0,-1,1,0,-1])
		tx,ty=x+dx,y+dy
		if 1<tx<H&&1<ty<W
			t=get(D,tx=>ty,0)
			cnt[t+1]-=1
			cnt[t+2]+=1
			D[tx=>ty]=t+1
		end
	end
end
function main()
	H,W,N=map(x->parse(Int,x),split(readline()))
	cnt=zeros(Int,10)
	cnt[1]=(H-2)*(W-2)
	for s=readlines()
		x,y=map(x->parse(Int,x),split(s))
		f(H,W,x,y,cnt)
	end
	println(join(cnt,'\n'))
end
main()