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: Memory Limit Exceeded)

import java.util.HashMap;
import java.util.Map;
import java.util.Scanner;
import java.util.Vector;

public class Main {

	public static int[] results = new int[10];

	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		int a = in.nextInt();
		int b = in.nextInt();
		boolean[][] points = new boolean[a][b];
		for (int i = 0; i < a; ++i) {

			for (int j = 0; j < b; ++j) {
				points[i][j] = false;
			}
		}
		int n = in.nextInt();
		for (int i = 0; i < n; ++i) {
			int x = in.nextInt();
			int y = in.nextInt();
			points[x - 1][y - 1] = true;

		}
		display(points, a, b);
		test(points, a, b);
		for (int i = 0; i < 10; ++i) {
			System.out.println(results[i]);
		}

	}

	public static void test(boolean[][] points, int a, int b) {
		for (int i = 0; i < a - 2; ++i) {
			for (int j = 0; j < b - 2; ++j) {
				int k = 0;
				for (int p = 0; p < 3; ++p) {
					for (int q = 0; q < 3; ++q) {
						if (points[i+p][j+q] == true) {
							k += 1;
						}
					}
				}

				results[k] += 1;
			}
		}
	}

	public static void display(boolean[][] points, int a, int b) {
		// System.out.println(a);
		// System.out.println(b);
		for (int i = 0; i < a; ++i) {
			for (int j = 0; j < b; ++j) {

				// 0 for white, 1 for black
				boolean flag = points[i][j];
				// System.out.println(i + "," + j + " " + flag);
			}
		}
	}

}