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: Runtime Error)

#include <stdio.h>
int main(void)
{
    int H,W,N,res[10]={0};
    scanf("%d%d%d", &H, &W, &N);

    int matrix[H][W], black[N][2];
    for(int i=0; i<H; i++)
    {
        for(int j=0; j<W; j++)
        {
            matrix[i][j]=0;
        }
    }
    for(int i=0; i<N; i++)
    {
        scanf("%d%d", &black[i][0], &black[i][1]);
    }
    for(int i=0; i<N; i++)
    {
        matrix[black[i][0]][black[i][1]]=1;
    }

    for(int i=0; i<H-2; i++)
    {
        for(int j=0; j<W-2; j++)//ここまで座標指定
        {
            int check=0;
            for(int k=0; k<3; k++)
            {
                for(int l=0; l<3; l++)
                {
                    if(matrix[i+k][j+l]==1) check++;
                }
            }
            res[check]++;
        }
    }
    for(int i; i<10; i++) printf("%d\n", res[i]);
    return 0;
}