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: Time Limit Exceeded)

import java.util.Arrays;
import java.util.HashMap;
import java.util.Map;
import java.util.Objects;
import java.util.Scanner;
import java.util.stream.IntStream;

/**
 * 解説通り実装したソースコード
 */
public class Main {

	public static void main(String[] args) {
		try (Scanner scanner = new Scanner(System.in)) {
			int h = scanner.nextInt(), w = scanner.nextInt(), n = scanner.nextInt();
			Map<Dimesion, Integer> map = new HashMap<>();
			IntStream.range(0, n).forEach(i -> {
				int a = scanner.nextInt(), b = scanner.nextInt();
				IntStream.rangeClosed(0, 2).filter(j -> (a - j > 0) && (a - j <= h - 2)).forEach(
						j -> IntStream.rangeClosed(0, 2).filter(k -> (b - k > 0) && (b - k <= w - 2)).forEach(k -> {
							Dimesion key = new Dimesion(a - j, b - k);
							map.put(key, map.getOrDefault(key, 0) + 1);
						}));
			});
			long[] results = new long[10];
			map.entrySet().stream().forEach(entry -> results[entry.getValue()]++);
			results[0] = (h - 2L) * (w - 2L) - map.size();
			Arrays.stream(results).forEach(System.out::println);
		}
	}

	/**
	 * Mapのキーとなるクラス
	 */
	private static class Dimesion {
		int x;
		int y;

		Dimesion(int x, int y) {
			super();
			this.x = x;
			this.y = y;
		}

		@Override
		public int hashCode() {
			return Objects.hash(x, y);
		}

		@Override
		public boolean equals(Object obj) {
			if (obj instanceof Dimesion) {
				Dimesion dimesion = (Dimesion) obj;
				return (x == dimesion.x) && (y == dimesion.y);
			}
			return false;
		}
	}
}