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++14 (Clang 3.8.0) (judge verdict: Accepted)

#include<cstdio>
#include<map>
#include<algorithm>
using namespace std;
#define MAXN 100000000
int h,w,k,x,y;
long long memory[MAXN], ans[12];
int Sep,tot;
long long z;
int main() {
	scanf("%d%d%d",&h,&w,&k);
	z=1ll*(h-2)*(w-2);
	for(int p=1;p<=k;p++) {
		scanf("%d%d",&x,&y);
		for(int i=0;i<3;i++)
			for(int j=0;j<3;j++)
				if(1<=x-i&&x-i<=h-2 && 1<=y-j&&y-j<=w-2)
					memory[++tot]=MAXN*(x-i)+(y-j);
	}
	sort(memory+1,memory+1+tot);
	int cnt=1;
	for(int i=1;i<=tot;i++) {
		if(memory[i]==memory[i+1])
			cnt++;
		else
			ans[cnt]++, cnt=1, z--;
	}
	printf("%lld\n",z);
	for(int i=1;i<=9;i++)
		printf("%lld\n",ans[i]);
}