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 static System.Console;
using static System.Math;
using static ConsoleApplication.Utils;

namespace ConsoleApplication
{
    public class Program
    {
        public static void Main(string[] args)
        {
            var hwn = ReadInts().ToArray();
            var lst = new List<Tuple<int, int>>();
            foreach (var i in Enumerable.Range(0, hwn[2]))
            {
                var ab = ReadInts().ToArray();
                for (var j = 0; j <= 2; ++j)
                {
                    for (var k = 0; k <= 2; ++k)
                    {
                        var a = ab[0] - j;
                        var b = ab[1] - k;
                        if (a < 1 || b < 1 || a > hwn[0] - 2 || b > hwn[1] - 2) continue;
                        lst.Add(Tuple.Create(ab[0] - j, ab[1] - k));
                    }
                }
            }
            var res = lst.GroupBy(p => p)
                .Select(g => g.Count())
                .OrderBy(i => i)
                .GroupBy(i => i)
                .ToDictionary(g => g.Key, g => g.LongCount());
            res.Add(0, (long)(hwn[0] - 2) * (long)(hwn[1] - 2) - res.Select(t => t.Value).Sum());
            foreach (var i in Enumerable.Range(0, 10))
            {
                if (res.ContainsKey(i)) WriteLine(res[i]);
                else WriteLine(0);
            }
        }
    }

    public static class Utils
    {
        #region Extensions for IO

        public static long ReadLong()
            => ReadLine().ToLong();
        public static int ReadInt()
            => ReadLine().ToInt();

        public static IEnumerable<int> ReadInts()
            => ReadStrings().Select(int.Parse);

        public static IEnumerable<string> ReadStrings()
            => ReadLine().Split(' ');

        public static IEnumerable<string> ReadLines(int n)
        {
            foreach (var i in Enumerable.Range(0, n))
            {
                yield return ReadLine();
            }
        }

        #endregion

        #region Extensions of int

        public static bool IsOdd(this int n)
            => !n.IsEven();

        public static bool IsEven(this int n)
            => n % 2 == 0;

        public static bool CanDivideWith(this int n, int divisor)
            => n % divisor == 0;

        #endregion

        #region Extensions of string

        public static int ToInt(this string str)
            => int.Parse(str);

        public static long ToLong(this string str)
            => long.Parse(str);

        public static double ToDouble(this string str)
            => double.Parse(str);

        public static bool IsNullOrEmpty(this string str)
            => string.IsNullOrEmpty(str);

        #endregion

        public static TSource Min<TSource, TKey>(this IEnumerable<TSource> source, Func<TSource, TKey> keySelector)
            where TKey : IComparable
            => source.OrderBy(keySelector).First();

        public static TSource Max<TSource, TKey>(this IEnumerable<TSource> source, Func<TSource, TKey> keySelector)
            where TKey : IComparable
            => source.OrderByDescending(keySelector).First();

        public static void ForEach<T>(this IEnumerable<T> source, Action<T> action)
        {
            foreach (var item in source)
            {
                action(item);
            }
        }

        public static IEnumerable<T> Peek<T>(this IEnumerable<T> source, Action<T> action)
        {
            foreach (var item in source)
            {
                action(item);
            }
            return source;
        }
    }
}