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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Deque;
import java.util.List;

/**
 *
 * @author Node2
 */
public class Main {


    public static void main(String[] args) throws IOException {
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));

        String str = in.readLine();

        String[] s = str.split(" ");
        int h=Integer.parseInt(s[0]);
        int w=Integer.parseInt(s[1]);
        int n=Integer.parseInt(s[2]);
        
        int[][] sq = new int[h][w];
        for(int i=0;i<h;i++){
            Arrays.fill(sq[i], 0);
        }
        
        for(int i=0;i<n;i++){
        str = in.readLine();
            String[] q = str.split(" ");
            sq[Integer.parseInt(q[0])-1][Integer.parseInt(q[1])-1] = 1;
        }
        
        int[][] an = new int[h][w-2];

        for(int j=0;j<h;j++){
        for(int i=0;i<w-2;i++){
            an[j][i] = sq[j][i] + sq[j][i+1] + sq[j][i+2];
        }
        }
        
        int[] anser = new int[10];
        for(int i=0;i<w-2;i++){
        for(int j=0;j<h-2;j++){
            int k = an[j][i] + an[j+1][i] + an[j+2][i];
            anser[k]++;
        }
        }
        
        for(int i=0;i<10;i++){
            System.out.println(anser[i]);
        }
    }


    
}