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: Accepted)

#include <limits.h>
#include <stdint.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <unistd.h>
#include <math.h>

#define P 1000000007

int comp(const void *a, const void *b){return *(int*)a-*(int*)b;}
int comp2(const void *a, const void *b){
	return (*(long*)a>*(long*)b)-(*(long*)a<*(long*)b);
}

int s[900000][2], S=0;
int ans[10];
int main(void){
	int h, w, n, i, j;
	scanf("%d%d%d", &h, &w, &n);
	for(i=0; i<n; i++){
		int a, b;
		scanf("%d%d", &a, &b);
		for(j=0; j<9; j++){
			int y=a-j/3, x=b-j%3;
			if(0<y && 0<x && y<=h-2 && x<=w-2){
				s[S][0]=y;
				s[S][1]=x;
				S++;
			}
		}
	}
	qsort(s, S, sizeof(int)*2, comp2);
	long ans0=(long)(h-2)*(w-2);
	int now=1;
	for(i=1; i<S; i++){
		if(s[i][0]==s[i-1][0] && s[i][1]==s[i-1][1]){
			now++;
		}else{
			ans[now]++; ans0--;
			now=1;
		}
	}
	if(S>0){
		ans[now]++; ans0--;
	}
	printf("%ld\n", ans0);
	for(i=1; i<=9; i++){
		printf("%d\n", ans[i]);
	}
}