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: Accepted)

import java.util.Arrays;
import java.util.HashMap;
import java.util.Map;
import java.util.Objects;
import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        Scanner stdin = new Scanner(System.in);
        long h = stdin.nextLong();
        long w = stdin.nextLong();
        int n = stdin.nextInt();
        
        Map<Tuple, Integer> counter = new HashMap<>();
        int[] d = new int[] { 0, 1, 2 };
        long[] ans = new long[10];
        ans[0] =  (h - 2) * (w - 2);
        
        
        for (int i = 0; i < n; i++) {
            int a = stdin.nextInt() - 1;
            int b = stdin.nextInt() - 1;
            
            for (int dx : d) {
                for (int dy : d) {
                    int x = a - dx;
                    int y = b - dy;
                    if (0 <= x && x < h - 2 && 0 <= y && y < w - 2) {
                        Tuple t = new Tuple(x, y);
                        int before = counter.getOrDefault(t, 0);
                        int after = before + 1;
                        
                        counter.put(t, after);
                        
                        ans[before]--;
                        ans[after]++;
                    }
                }
            }
        }
        
        Arrays.stream(ans).forEach(System.out::println);
    }
    
    public static class Tuple {
        private int x;
        private int y;
        
        public Tuple(int x, int y) {
            super();
            this.x = x;
            this.y = y;
        }

        @Override
        public int hashCode() {
            return Objects.hash(x, y);
        }
        
        @Override
        public boolean equals(Object obj) {
            if (obj == null || !(obj instanceof Tuple)) {
                return false;
            }
            
            Tuple other = (Tuple) obj;
            return this.x == other.x && this.y == other.y;
        }
    }
}