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++14 (GCC 5.4.1) (judge verdict: Accepted)

#define _CRT_SECURE_NO_WARNINGS
#include <stdio.h>
#include <algorithm>
#include <utility>
#include <functional>
#include <cstring>
#include <queue>
#include <stack>
#include <math.h>
#include <iterator>
#include <vector>
#include <string>
#include <set>
#include <math.h>
#include <iostream> 
#include<map>
#include <iomanip>
#include <stdlib.h>
#include <list>
#include <typeinfo>
#include <list>
#include <set>
using namespace std;
#define MAX_MOD 1000000007
#define REP(i,n) for(int i = 0;i < n;++i)
#define LONGINF 1000000000000000000
map<pair<int, int>,int> tizu;
long long h, w, n;
long long ans[100] = {};
pair<int, int> go_through[9] = { pair<int,int>(-1,-1),pair<int,int>(1,-1),pair<int,int>(0,-1),pair<int,int>(-1,0),pair<int,int>(0,0),pair<int,int>(1,0),pair<int,int>(-1,1),pair<int,int>(0,1),pair<int,int>(1,1) };
bool suit(pair<int, int> a) {
	if (a.first+1 <= h&&a.second+1 <= w&&a.first-1 > 0&&a.second-1 > 0) return true;
	return false;
}
int main() {
	scanf("%d%d%d", &h,&w,&n);
	REP(i, n) {
		int a, b;
		scanf("%d%d", &a, &b);
		for (int i = 0;i < 9;++i) {
			a += go_through[i].first;
			b += go_through[i].second;
			pair<int, int> hoge = pair<int,int>(a,b);
			if (suit(hoge) == true) {
				ans[tizu[hoge]]--;
				tizu[hoge]++;
				ans[tizu[hoge]]++;
			}
			a -= go_through[i].first;
			b -= go_through[i].second;
		}
	}
	long long cal = (h-2)*(w-2);
	for (int i = 1;i <= 9;++i) {
		cal -= ans[i];
	}
	ans[0] = cal;
	for (int i = 0;i <= 9;++i) {
		printf("%lld\n", ans[i]);
	}
	return 0;
}