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 <iostream>
#include <vector>
#include <cstring>
#include <string>
#include <algorithm>
#include <iomanip>
#include <cmath>
#include <cassert>
#include <unordered_map>
#include <set>
using namespace std;
typedef long long ll;
typedef pair<int, int> P;
ll H, W, N;
ll ans[10];
int a[100000];
int b[100000];
set<P> s;

int find(int i, int x, int y) {
	int sum = 1;
	for(int yy = 0; yy < 3; yy++) {
		for(int xx = 0; xx < 3; xx++) {
			if(y == yy && x == xx) continue;
			int dx = xx - x, dy = yy - y;
			int na = a[i] + dy, nb = b[i] + dx;
			if(na < 0 || H <= na || nb < 0 || W <= nb) return -1;
			if(s.find(P(na, nb)) != s.end()) sum++;
		}
	}
	return sum;
}

int main() {
	cin.tie(0);
	ios::sync_with_stdio(false);

	cin >> H >> W >> N;

	for(int i = 0; i < N; i++) {
		cin >> a[i] >> b[i];
		a[i]--, b[i]--;
		s.insert(P(a[i], b[i]));
	}

	for(int i = 0; i < N; i++) {
		for(int y = 0; y < 3; y++) {
			for(int x = 0; x < 3; x++) {
				int res = find(i, x, y);
				if(res != -1) ans[res]++;
			}
		}
	}

	ll s = (W - 2) * (H - 2);
	for(int i = 1; i <= 9; i++) {
		ans[i] /= i;
		s -= ans[i];
	}
	ans[0] = s;
	for(int i = 0; i <= 9; i++) {
		cout << ans[i] << endl;
	}
}