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.*;

public class Main {
	public static void main(String[] args) {
		Scanner scn = new Scanner(System.in);
		Map<String, Byte> map = new HashMap<String, Byte>();
		int n = scn.nextInt();
		int n2 = scn.nextInt();
		int m, m2;
		for(int i = scn.nextInt();i>0;i--) {
			m = scn.nextInt();
			m2 = scn.nextInt();
			if(m<=n-2&m2<=n2-2)map.put(m+" "+m2,(byte) (map.getOrDefault(m+" "+m2, (byte) 0)+1));
			if(m>1&m<=n-1&m2<=n2-2) map.put((m-1)+" "+m2,(byte) (map.getOrDefault((m-1)+" "+m2, (byte) 0)+1));
			if(m>2&m2<=n2-2) map.put((m-2)+" "+m2,(byte) (map.getOrDefault((m-2)+" "+m2, (byte) 0)+1));
			if(m2>1&m<=n-2&m2<=n2-1) map.put(m+" "+(m2-1),(byte) (map.getOrDefault(m+" "+(m2-1), (byte) 0)+1));
			if(m2>2&m<=n-2) map.put(m+" "+(m2-2),(byte) (map.getOrDefault(m+" "+(m2-2), (byte)0)+1));
			if(m>1&m2>1&m<=n-1&m2<=n2-1) map.put((m-1)+" "+(m2-1),(byte) (map.getOrDefault((m-1)+" "+(m2-1), (byte)0)+1));
			if(m>2&m2>2) map.put((m-2)+" "+(m2-2),(byte) (map.getOrDefault((m-2)+" "+(m2-2), (byte) 0)+1));
			if(m>1&m2>2&m<=n-1) map.put((m-1)+" "+(m2-2),(byte) (map.getOrDefault((m-1)+" "+(m2-2), (byte) 0)+1));
			if(m>2&m2>1&m2<=n2-1) map.put((m-2)+" "+(m2-1),(byte) (map.getOrDefault((m-2)+" "+(m2-1), (byte) 0)+1));
		}
		long[] cc = new long[9];
		for (Object value : map.values()) {
		    if(value.toString().equals("1"))cc[0]++;
		    if(value.toString().equals("2"))cc[1]++;
		    if(value.toString().equals("3"))cc[2]++;
		    if(value.toString().equals("4"))cc[3]++;
		    if(value.toString().equals("5"))cc[4]++;
		    if(value.toString().equals("6"))cc[5]++;
		    if(value.toString().equals("7"))cc[6]++;
		    if(value.toString().equals("8"))cc[7]++;
		    if(value.toString().equals("9"))cc[8]++;
		}
		System.out.println((long)(n-2)*(n2-2)-cc[0]-cc[1]-cc[2]-cc[3]-cc[4]-cc[5]-cc[6]-cc[7]-cc[8]);
		for(int i = 0;i<9;i++)System.out.println(cc[i]);
		scn.close();
	}
}