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.*;
import java.io.*;

public class Main {
    public static void main(String[] args) throws Exception {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        String[] first = br.readLine().split(" ", 3);
        long h = Integer.parseInt(first[0]);
        long w = Integer.parseInt(first[1]);
        int n = Integer.parseInt(first[2]);
        HashMap<Long, Integer> map = new HashMap<>();
        for (int i = 0; i < n; i++) {
            String[] line = br.readLine().split(" ", 2);
            int hh = Integer.parseInt(line[0]) - 1;
            int ww = Integer.parseInt(line[1]) - 1;
            for (int a = Math.max(hh - 2, 0); a <= hh && a + 2 < h; a++) {
                for (int b = Math.max(ww - 2, 0); b <= ww && b + 2 < w; b++) {
                    long key = a * w + b;
                    if (map.containsKey(key)) {
                        map.put(key, map.get(key) + 1);
                    } else {
                        map.put(key, 1);
                    }
                }
            }
        }
        long[] ans = new long[10];
        for (int x : map.values()) {
            ans[x]++;
        }
        ans[0] = (long)(h - 2) * (w - 2) - map.size();
        StringBuilder sb = new StringBuilder();
        for (long x : ans) {
            sb.append(x).append("\n");
        }
        System.out.print(sb);
    }
}