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 Java7 (OpenJDK 1.7.0) (judge verdict: Time Limit Exceeded)

/* Filename: ABC045D.java
 * Author: Mushiyo
 */

import java.util.Set;
import java.util.HashSet;
import java.util.Scanner;
import java.awt.Point;

public class Main{
	static int[] dx = { -1, -1, -1, 0, 0, 0, 1, 1, 1 };
	static int[] dy = { -1, 0, 1, -1, 0, 1, -1, 0, 1 };

	public static void main(String[] args) {
		Scanner input = new Scanner(System.in);

		while (input.hasNext()) {
			int H = input.nextInt(), W = input.nextInt(), N = input.nextInt();

			if (N == 0) {
				System.out.println((long) (H - 2) * (W - 2));

				for (int i = 1; i <= 9; ++i) {
					System.out.println(0);
				}

				continue;
			}

			Set<Point> blackCell = new HashSet<Point>();
			for (int i = 0; i < N; ++i) {
				blackCell.add(new Point(input.nextInt(), input.nextInt()));
			}

			long[] count = new long[10];
			for (int i = 2; i < H; ++i) {
				for (int j = 2; j < W; ++j) {
					int countBlack = 0;
					for (int d = 0; d < dx.length; ++d) {
						int a = i + dx[d];
						int b = j + dy[d];

						if (blackCell.contains(new Point(a, b))) {
							++countBlack;
						}
					}

					++count[countBlack];
				}
			}

			for (long i : count) {
				System.out.println(i);
			}
		}
	}
}