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# (Mono 4.6.2.0) (judge verdict: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace ConsoleApplication1
{
    class Program
    {
        static void Main(string[] args)
        {
            string input = Console.ReadLine();
            string[] data = input.Split(' ');
            long H = long.Parse(data[0]);
            long W = long.Parse(data[1]);
            long N = long.Parse(data[2]);
            int[] a = new int[N];
            int[] b = new int[N];
            List<int> result = new List<int>();
            List<string> position = new List<String>();
            int ans = 0;
            long output = 0;

            for (long i = 0; i <= N - 1; i++)
            {
                input = Console.ReadLine();
                data = input.Split(' ');
                a[i] = int.Parse(data[0]);
                b[i] = int.Parse(data[1]);

                for (int x = a[i] - 2; x <= a[i]; x++)
                {
                    if (x > 0 && x + 2 < H + 1)
                    {
                        for (int y = b[i] - 2; y <= b[i]; y++)
                        {
                            if (y > 0 && y + 2 < W + 1)
                            {
                                if (position.Count == 0)
                                {
                                    position.Add(x.ToString() + "," + y.ToString());
                                }
                                else
                                {
                                    Boolean flg = false;
                                    foreach (string p in position)
                                    {
                                        if (p == x.ToString() + "," + y.ToString())
                                        {
                                            flg = true;
                                        }
                                    }
                                    if (flg == false)
                                    {
                                        position.Add(x.ToString() + "," + y.ToString());
                                    }
                                }
                            }
                        }
                    }
                }
            }


            foreach (string p in position)
            {
                data = p.Split(',');
                var row = int.Parse(data[0]);
                var column = int.Parse(data[1]);

                ans = 0;

                for (int i = row; i <= row + 2; i++)
                {
                    for (int j = column; j <= column + 2; j++)
                    {
                        for (int k = 0; k <= N - 1; k++)
                        {
                            if (i == a[k] && j == b[k])
                            {
                                ans += 1;
                            }
                        }
                    }
                }
                result.Add(ans);
            }

            output = (H - 2) * (W - 2) - result.Count;
            Console.WriteLine(output);

            for (int cnt = 1; cnt <= 9; cnt++)
            {
                output = 0;
                foreach (int r in result)
                {
                    if (r == cnt)
                    {
                        output += 1;
                    }
                }
                Console.WriteLine(output);
            }
        }
    }
}