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>
#include<stdlib.h>
int main(void){
    int height,width;
    int n;
    int count[10]={0};
    int count2=0;
    int **board;
    int i,j,k,l;

    //printf("Input height:");
    scanf("%d",&height);
    //printf("Input width:");
    scanf("%d",&width);
    //printf("Input the number of painting:");
    scanf("%d",&n);

    board=(int **)malloc(height*sizeof(int *));
    for(i=0;i<height;i++){
        board[i]=(int *)malloc(width*sizeof(int));
    }
    for(i=0;i<height;i++){
        for(j=0;j<width;j++){
            board[i][j]=0;
        }
    }
    int x,y;
    for(i=0;i<n;i++){    
        //printf("Input the coodinate(%d):",i+1);
        scanf("%d %d",&x,&y);
        board[x-1][y-1]=1;
    }
    int check=0;
    for(i=0;i<height-2;i++){
        count2=0;
        for(k=0;k<width-2;k++){
            count2=0;
            for(j=i;j<i+3;j++){
                for(l=k;l<k+3;l++){
                    if(board[j][l]==1){
                        count2++;
                        //printf("count2:%d\n",count2);
                    }
                }
            }
            count[count2]++;
        }

    }
    for(i=0;i<10;i++){
        printf("%d\n",count[i]);
    }
    return 0;
}