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;

class Program
{
    static string InputPattern = "InputX";

    static List<string> GetInputList()
    {
        var WillReturn = new List<string>();

        if (InputPattern == "Input1") {
            WillReturn.Add("4 5 8");
            WillReturn.Add("1 1");
            WillReturn.Add("1 4");
            WillReturn.Add("1 5");
            WillReturn.Add("2 3");
            WillReturn.Add("3 1");
            WillReturn.Add("3 2");
            WillReturn.Add("3 4");
            WillReturn.Add("4 4");
            //0
            //0
            //0
            //2
            //4
            //0
            //0
            //0
            //0
            //0
        }
        else if (InputPattern == "Input2") {
            WillReturn.Add("10 10 20");
            WillReturn.Add("1 1");
            WillReturn.Add("1 4");
            WillReturn.Add("1 9");
            WillReturn.Add("2 5");
            WillReturn.Add("3 10");
            WillReturn.Add("4 2");
            WillReturn.Add("4 7");
            WillReturn.Add("5 9");
            WillReturn.Add("6 4");
            WillReturn.Add("6 6");
            WillReturn.Add("6 7");
            WillReturn.Add("7 1");
            WillReturn.Add("7 3");
            WillReturn.Add("7 7");
            WillReturn.Add("8 1");
            WillReturn.Add("8 5");
            WillReturn.Add("8 10");
            WillReturn.Add("9 2");
            WillReturn.Add("10 4");
            WillReturn.Add("10 9");
            //4
            //26
            //22
            //10
            //2
            //0
            //0
            //0
            //0
            //0
        }
        else if (InputPattern == "Input3") {
            WillReturn.Add("1000000000 1000000000 0");
            //999999996000000004
            //0
            //0
            //0
            //0
            //0
            //0
            //0
            //0
            //0
        }
        else {
            string wkStr;
            while ((wkStr = Console.ReadLine()) != null) WillReturn.Add(wkStr);
        }
        return WillReturn;
    }

    static void Main()
    {
        List<string> InputList = GetInputList();

        long[] wkArr = { };
        Action<string> SplitAct = pStr =>
            wkArr = pStr.Split(' ').Select(X => long.Parse(X)).ToArray();

        SplitAct(InputList[0]);
        long H = wkArr[0];
        long W = wkArr[1];

        //そのマスを始点としての黒マスの数[座標のhash値]
        var CntDict = new Dictionary<Tuple<long, long>, long>();

        foreach (string EachStr in InputList.Skip(1)) {
            SplitAct(EachStr);

            long a = wkArr[0];
            long b = wkArr[1];

            for (long LoopX = b - 2; LoopX <= b; LoopX++) {
                if (LoopX < 1) continue;
                if (LoopX + 2 > W) break;

                for (long LoopY = a - 2; LoopY <= a; LoopY++) {
                    if (LoopY < 1) continue;
                    if (LoopY + 2 > H) break;

                    var Hash = Tuple.Create(LoopX, LoopY);
                    if (CntDict.ContainsKey(Hash))
                        CntDict[Hash]++;
                    else CntDict[Hash] = 1;
                }
            }
        }

        //foreach (var EachPair in CntDict.OrderBy(X => X.Key)) {
        //    Console.WriteLine("CntDict[{0}]={1}", EachPair.Key, EachPair.Value);
        //}

        long[] CntArr = new long[10];
        long CntSum = 0;
        foreach (int EachValee in CntDict.Values) {
            CntArr[EachValee]++;
            CntSum++;
        }
        CntArr[0] = (long)(H - 2) * (W - 2) - CntSum;
        Array.ForEach(CntArr, X => Console.WriteLine(X));
    }
}