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 Java (OpenJDK 11.0.6) (judge verdict: Accepted)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.HashMap;
import java.util.Map;
 
// https://atcoder.jp/contests/abc045/submissions/878750
public class Main {
 
	public static void main(String[] args) throws IOException {
		BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
		String[] tmp = in.readLine().split(" ");
		Integer h = Integer.parseInt(tmp[0]);
		Integer w = Integer.parseInt(tmp[1]);
		Integer n = Integer.parseInt(tmp[2]);
		Integer a, b;
		Map<String, Integer> candidates = new HashMap<>();
		long[] result = new long[10];
		
		for (int i = 0; i < n; i++) {
			tmp = in.readLine().split(" ");
			a = Integer.parseInt(tmp[0]);
			b = Integer.parseInt(tmp[1]);
			for (int x = 2; x >= 0; x--) {
				for (int y = 2; y >= 0; y--) {
					if (a - x >= 1 && b - y >= 1 && (a - x + 2) <= h && (b - y + 2) <= w) {
						String key = (a - x) + "+" + (b - y);
						if (candidates.containsKey(key)) {
							candidates.put(key, candidates.get(key) + 1);
						} else {
							candidates.put(key, 1);
						}
					}
				}
			}
		}
		
		result[0] = (long) (h - 2) * (w - 2) - candidates.size();
		for (Map.Entry<String, Integer> candidate : candidates.entrySet()) {
			result[candidate.getValue()]++;
		}
		
		for (int j = 0; j <= 9; j++) {
			System.out.println(result[j]);
		}
	}
}