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: Wrong Answer)

#include <stdio.h>
#include <stdlib.h>

int main(void) {
	int h,w,n,i,j,k,a,b;
	int **map;
	long long cnt[9] = {};
	
	scanf("%d %d %d",&h,&w,&n);
	
	map = (int**)calloc(h,sizeof(int));
	for (i = 0;i < h;i++) {
		map[i] = (int*)calloc(w,sizeof(int));
	}
	
	for (i = 0;i < n;i++) {
		scanf("%d %d",&a,&b);
		for (j = 0;j < 3;j++) {
			if (a+j-1 == h) {
				break;
			}
			for (k = 0;k < 3;k++) {
				if (b+k-1 == w) {
					break;
				}
				map[a+j-1][b+k-1]++;
			}
		}
	}
	
	for (i = 2;i < h;i++) {
		for (j = 2;j < w;j++) {
			cnt[map[i][j]]++;
		}
	}
	
	for (i = 0;i < 9;i++) {
		printf("%lld\n",cnt[i]);
	}
	
	return 0;
}