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)

#pragma warning disable

using System;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Runtime.Serialization.Formatters.Binary;
using System.Text;
using System.Text.RegularExpressions;
using System.Diagnostics;
using System.Numerics;
using System.Collections;
using System.Timers;

static class MainClass
{
    // 深さ優先探索 ?
    // 10^9*10^9 -> TLE,MLE(grid)
    public static void Main(string[] args)
    {
        var HWN = Console.ReadLine().SplittedStringToInt32List();
        var H = HWN[0];
        var W = HWN[1];
        var N = HWN[2];

        var ls = new Dictionary<string,int>();

        for (int i = 0; i < N; i++)
        {
            var ab = Console.ReadLine().SplittedStringToInt32List();
            var a = ab[0];
            var b = ab[1];
            for (int j = 0; j < 3; j++)
            {
                for (int k = 0; k < 3; k++)
                {
                    var x = a - j;
                    var y = b - k;
                    if (x + 2 > H || y+ 2 > W || x <= 0 || y <= 0)
                    {

                    }
                    else
                    {
                        var key = $"{a-j}:{b-k}";
                        if (ls.ContainsKey(key))
                            ls[key]++;
                        else
                            ls.Add(key, 1);
                    }
                }
            }
        }
        var dic = new Dictionary<int, int>();
        for (int i = 1; i < 10; i++)
        {
            dic.Add(i, 0);
        }
        foreach (var item in ls.Values)
        {
            dic[item]++;
        }
        var sum = dic.ToList().Sum(x => x.Value);
        Console.WriteLine((BigInteger)(H-2)*(BigInteger)(W-2)-sum);
        foreach (var item in dic)
        {
            Console.WriteLine(item.Value);
        }

        Console.ReadLine();
    }


    #region ライブラリ
    public static long ToInt64(this string str) => long.Parse(str);
    public static int ToInt32(this string str) => int.Parse(str);
    public static BigInteger ToBigInteger(this string str) => BigInteger.Parse(str);
    public static List<string> SplittedStringToList(this string str) => str.Split(new[] { ' ' }, StringSplitOptions.RemoveEmptyEntries).ToList();
    public static List<int> SplittedStringToInt32List(this string str) => str.Split(new[] { ' ' }, StringSplitOptions.RemoveEmptyEntries).Select(x => int.Parse(x)).ToList();
    public static List<BigInteger> SplittedStringToBigInteger(this string str) => str.Split(new[] { ' ' }, StringSplitOptions.RemoveEmptyEntries).Select(x => BigInteger.Parse(x)).ToList();

    public const int INF = int.MaxValue / 2;
    #endregion
}