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)

#include<bits/stdc++.h>

using namespace std;

#define mp make_pair
#define ll long long

int
main(void){
	int h, w, n;
	cin >> h >> w >> n;
	map<pair<int, int>, int> black;
	map<pair<int, int>, int> used;
	vector<pair<int, int> > vec(n);
	for(int i = 0; i < n; i++){
		cin >> vec[i].first >> vec[i].second;
		black[vec[i]] = 1;
	}
	vector<int> ans(10, 0);
	for(int i = 0; i < n; i++){
		int x = vec[i].first;
		int y = vec[i].second;
		for(int r = x; x - r < 3; r--){
			for(int c = y; y - c < 3; c--){
				if(r < 1 || c < 1 || r > h || c > w || used[mp(r, c)] == 1 || r + 2 > h || c + 2 > w){
					continue;
				}
				int count = 0;
				for(int j = 0; j < 3; j++){
					for(int k = 0; k < 3; k++){
						count += black[mp(r + j, c + k)];
					}
				}
				used[mp(r, c)] = 1;
				ans[count]++; 
			}
		}
	}
	ll zero = (h - 2) * 1ll * (w - 2);
	for(int i = 1; i <= 9; i++) zero -= ans[i];
	cout << zero << "\n";
	for(int i = 1; i <= 9; i++) cout << ans[i] << "\n";
	
}