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>
#include <string.h>
#include <stdbool.h>
#include <math.h>
#include <limits.h>

typedef struct {
    int x;
    int y;
} squr_t;

int sort(const void *a, const void *b){
    if ( ((squr_t*)a)->x - ((squr_t*)b)->x >0 ) {
        return 1;
    }
    if ( ((squr_t*)a)->x - ((squr_t*)b)->x <0 ) {
        return -1;
    }
    if ( ((squr_t*)a)->x - ((squr_t*)b)->x ==0 ) {
        if ( ((squr_t*)a)->y - ((squr_t*)b)->y >=0 ) {
            return 1;
        }
        if ( ((squr_t*)a)->y - ((squr_t*)b)->y <0 ) {
            return -1;
        }
    }
    return 0;
}

int main(void){
    int h,w,n,a,b,count=0;
    scanf("%d%d%d",&h,&w,&n);
    squr_t s[n*9];
    for (int i=0; i<n; i++){
        scanf("%d%d",&a,&b);
        a--;
        b--;
        for (int j=-1; j<2; j++){
            if(a+j>=1 && a+j<h-1){
                for (int k=-1; k<2; k++){
                    if (b+k>=1 && b+k<w-1){
                        s[count].x=a+j;
                        s[count].y=b+k;
                        count++;
                    }
                }
            }
        }
    }
    qsort (s,count,sizeof(squr_t),sort);
    long long ans[10],am=0;
    for (int i=0; i<10; i++){
        ans[i]=0;
    }
    for (int i=0; i<count; i++){
        if (i==0){
            am++;
        } else if (s[i].x==s[i-1].x && s[i].y==s[i-1].y){
            am++;
        } else {
            ans[am]++;
            am=1;
        }
        if (i==count-1){
            ans[am]++;
        }
    }
    ans[0]=(h-2)*(w-2);
    for (int i=1; i<10; i++){
        ans[0]-=ans[i];
    }
    for (int i=0; i<10; i++){
        printf("%lld\n",ans[i]);
    }

    
	return 0 ;
}