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)

#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 point = new HashSet<Point>(new Point());
        
        var alreadyp = new HashSet<Point>(new Point());

        var nokorip = new HashSet<Point>(new Point());
        Point f = null;
        for (int i = 0; i < N; i++)
        {
            var ab = Console.ReadLine().SplittedStringToInt32List();
            var a = ab[0];
            var b = ab[1];
            point.Add(new Point() { X = a, Y = b });
            nokorip.Add(new Point() { X = a, Y = b });
            if (i == 0)
                f = new Point() { X = a, Y = b };
        }
        var dic = new Dictionary<int, int>();
        for (int i = 0; i <= 9; i++)
        {
            dic.Add(i, 0);
        }
        var dx = new int[] { -1, -1, -1, 0, 1, 1, 1, 0 };
        var dy = new int[] { 1, 0, -1, -1, -1, 0, 1, 1 };
        var stk = new Stack<Point>();
        while (nokorip.Count != 0)
        {
            //var addls = new List<Point>();

            //stk.Push(nokorip.First());
            //while (stk.Count != 0)
            //{
            var item = nokorip.First();//stk.Pop();
            var count = item.IsColored ? 1 : 0;
            var iscan = true;
            alreadyp.Add(item);
            nokorip.Remove(item);
            for (int i = 0; i < 8; i++)
            {
                var xx = item.X + dx[i];
                var yy = item.Y + dy[i];
                if (xx > H || yy > W || xx <= 0 || yy <= 0)
                {
                    iscan = false;
                    break;
                }
                var newp = new Point() { X = xx, Y = yy };
                if (point.Contains(newp))
                {
                    //if (!alreadyp.Contains(newp))
                    //  addls.Add(newp);
                    count++;
                }
                else
                {
                    newp.IsColored = false;
                    // point.Add(newp);
                    if (!alreadyp.Contains(newp))
                        nokorip.Add(newp);
                    //count++;
                }
            }
            if (iscan)
            {
                if (count != 0)
                    dic[count]++;
                // addls.ForEach(x => alreadyp.Add(x));
            }

            //}
        }

        var sum = dic.ToList().Sum(x => x.Value);
        var nums = (BigInteger)(H - 2) * (BigInteger)(W - 2);
        var rem = nums - sum;
        Console.WriteLine(rem);
        for (int i = 1; i <= 9; i++)
        {
            Console.WriteLine(dic[i]);
        }

        Console.ReadLine();
    }
    public class Point : IEqualityComparer<Point>
    {
        public int X;
        public int Y;
        public bool IsColored = true;

        public bool Equals(Point x, Point y)
        {
            return (x.X == y.X) && (x.Y == y.Y);
        }

        public int GetHashCode(Point obj)
        {
            return ($"X:{X} Y:{Y}").GetHashCode();
        }

        public override string ToString()
        {
            return ($"X:{X} Y:{Y}");
        }
    }


    #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
}