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 C# (.NET Core 3.1.201) (judge verdict: Runtime Error)

using System;
using static System.Console;


    public class point
    {
        public int blackflag;
        public point(){
            blackflag=0;
        }
        public void setflag()
        {
            blackflag = 1;
        }
    }

    class At
    {
        public static void Main()
        {
            int h, w, n;
            var str = ReadLine().Split(' ');
            h = int.Parse(str[0]);
            w = int.Parse(str[1]);
            n = int.Parse(str[2]);

            int count = 0, x = 0, y = 0;
            int[] ans = new int[10];

            point[,] P = new point[h, w];   //箱を準備


        for (int i = 0; i < h;i++){
            for (int j = 0; j < w;j++){
                P[i, j] = new point();
            }   //箱の中身を入れる準備
        }

            for (int i = 0; i < n; i++)
            {
                var str2 = ReadLine().Split(' ');
                x = int.Parse(str2[0]) - 1;
                y = int.Parse(str2[1]) - 1;

                P[x, y].setflag();
            }


        for (int a = 0; a < h - 2; a++)
            {
                for (int b = 0; b < w - 2; b++)
                {
                    for (int i = a; i < a + 3; i++)
                    {
                        for (int j = b; j < b + 3; j++)
                        {
                            if (P[i, j].blackflag == 1) count++;
                        }
                    }
                    ans[count]++;
                    count = 0;
                }
            }

            for (int i = 0; i < 10; i++)
            {
                WriteLine(ans[i]);
            }
        }
    }