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 C (GCC 5.4.1) (judge verdict: Accepted)

#include<stdio.h>
#define M 100000
long long H,W,A[10],q;
int p[M];
struct{int a,b,n,q;}d[900001];

void f(int a,int b){
	int h,t,i;
	if(1<a&&a<H&&1<b&&b<W){
		i=p[h=(a/M+a+b/M+b)%M];
		if(i){
			for(;;){
				if(d[i].a==a&&d[i].b==b){
					break;
				}else if(d[i].q){
					i=d[i].q;
				}else{
					d[i=d[i].q=++q].a=a;
					d[i].b=b;
					break;
				}
			}
		}else{
			d[i=p[h]=++q].a=a;
			d[i].b=b;
		}
		--A[t=d[i].n++];
		++A[t+1];
	}
}
int main(){
	int a,b,i,j;
	scanf("%lld%lld%d",&H,&W,&i);
	A[0]=(H-2)*(W-2);
	for(;~scanf("%d%d",&a,&b);)
		for(i=-1;i<=1;++i)
			for(j=-1;j<=1;++j)
				f(a+i,b+j);
	for(i=0;i<=9;++i)printf("%lld\n",A[i]);
	return 0;
}