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: Wrong Answer)

import java.util.HashMap;
import java.util.Scanner;
import java.awt.Point;
public class Main{

   public static void main(String[] args){
      new Main().solve();  
   }

   public void solve(){
      Scanner scanner = new Scanner(System.in);
      long H = scanner.nextLong();
      long W = scanner.nextLong();
      int N = scanner.nextInt();

      Point[] point = new Point[N];
      for(int i=0; i<N; i++){
         int row = scanner.nextInt();
         int col = scanner.nextInt();
         point[i] = new Point(col, row);
      }

      HashMap<Point,Integer> hashmap = new HashMap<Point,Integer>();

      for(int i=0; i<N; i++){
         for(int y=-1; y<2; y++){
            for(int x=-1; x<2; x++){
               Point p = new Point(point[i].x+x, point[i].y+y);
               if(hashmap.get(p) == null){
                  hashmap.put(p,1);
               }else{
                  hashmap.put(p,hashmap.get(p)+1);
               }
            }
         }
      }

      long[] counter = new long[10];
      for(int i=0; i<counter.length; i++){
         counter[i] = 0;
      }
      for(HashMap.Entry<Point,Integer> map : hashmap.entrySet()){
         if(1<map.getKey().x && map.getKey().x<W && 1<map.getKey().y && map.getKey().y<H){
            counter[map.getValue()]++;
         }
      }
      for(int i=0; i<counter.length; i++){
         System.out.println(counter[i]);
      }

   }

}