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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.BufferedReader;
import java.io.InputStreamReader;

public class Main {

	private static int[][] buf = null;

	public static void main(String[] args) throws Exception {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		String line = br.readLine();
		String[] sp = line.split(" ");
		int h = Integer.parseInt(sp[0]);
		int w = Integer.parseInt(sp[1]);
		int n = Integer.parseInt(sp[2]);

		if (n == 0) {
			for (int j = 0; j < 10; j++) {
				System.out.println("0");
			}
			return;
		}

		buf = new int[h][w];
		for (int i = 0; i < n; i++) {
			line = br.readLine();
			sp = line.split(" ");
			int y = Integer.parseInt(sp[0]);
			int x = Integer.parseInt(sp[1]);
			buf[y - 1][x - 1] = 1;
		}

		for (int j = 0; j < 10; j++) {
			int sum = 0;
			for (int y = 0; y < h - 2; y++) {
				for (int x = 0; x < w - 2; x++) {
					sum += Main.check(y, x, j);
				}
			}
			System.out.println(sum);
		}
	}

	private static int check(int y, int x, int n) {
		int sum = 0;
		for (int a = 0; a < 3; a++) {
			for (int b = 0; b < 3; b++) {
				if (buf[y + a][x + b] == 1) {
					sum++;
				}
			}
		}
		return (sum == n) ? 1 : 0;
	}
}