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: Accepted)

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


class Program
{
    public void Proc()
    {
        Reader.IsDebug = false;
        long[] inpt = Reader.ReadLine().Split(' ').Select(a => long.Parse(a)).ToArray();
        this.H = inpt[0];
        this.W = inpt[1];

        int queryCount = (int)inpt[2];

        Dictionary<long, Dictionary<long, int>> map = new Dictionary<long, Dictionary<long, int>>();

        for (int i = 0; i < queryCount; i++)
        {
            Pos p = new Pos(Reader.ReadLine());

            list.Add(p);

            for (long j = p.H - 2; j <= p.H; j++)
            {
                if (j < 0)
                {
                    continue;
                }
                if (j + 2 >= this.H)
                {
                    break;
                }
                if (!map.ContainsKey(j))
                {
                    map.Add(j, new Dictionary<long, int>());
                }
                for (long k = p.W - 2; k <= p.W; k++)
                {
                    if (k < 0)
                    {
                        continue;
                    }
                    if (k + 2 >= this.W)
                    {
                        break;
                    }
                    if (map[j].ContainsKey(k))
                    {
                        map[j][k]++;
                    }
                    else
                    {
                        map[j].Add(k, 1);
                    }
                }
            }
        }



        long[] ans = new long[10];
        ans[0] = ((this.H - 2) * (this.W - 2)) - map.Sum(a=>a.Value.Count());
        foreach (long key in map.Keys)
        {
            foreach (long k2 in map[key].Keys)
            {
                int num = map[key][k2];
                ans[num]++;
            }
        }
      
        for (int i = 0; i <= 9; i++)
        {
            Console.WriteLine(ans[i]);
        }
    
    }

    public List<Pos> list = new List<Pos>();
    
    public class Pos
    {
        public long H;
        public long W;
        public Pos(string inpt)
        {
            long[] tmp = inpt.Split(' ').Select(a => long.Parse(a)).ToArray();
            this.H = tmp[0] - 1;
            this.W = tmp[1] - 1;
        }
    }
    private long H;
    private long W;


    public class Reader
    {
        public static bool IsDebug = true;
        private static String PlainInput = @"

4 5 8
1 1
1 4
1 5
2 3
3 1
3 2
3 4
4 4

";
        private static System.IO.StringReader Sr = null;
        public static string ReadLine()
        {
            if (IsDebug)
            {
                if (Sr == null)
                {
                    Sr = new System.IO.StringReader(PlainInput.Trim());
                }
                return Sr.ReadLine();
            }
            else
            {
                return Console.ReadLine();
            }
        }
    }
    static void Main()
    {
        Program prg = new Program();
        prg.Proc();
    }
}