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)

#region using
using System;
using System.Collections.Generic;
using System.Linq;
using IEnumerable = System.Collections.IEnumerable;
using IEnumerator = System.Collections.IEnumerator;
using BitArray = System.Collections.BitArray;
using BigInteger = System.Numerics.BigInteger;
using TextReader = System.IO.TextReader;
using System.Text;
#endregion

namespace AtCoderProject
{
    public class Program
    {
        public object Calc()
        {
            H = consoleReader.Int;
            W = consoleReader.Int;
            var N = consoleReader.Int;
            res[0] = (long)(H - 2) * (W - 2);
            foreach (var cr in consoleReader.Repeat(N))
            {
                var a = cr.Int - 1;
                var b = cr.Int - 1;
                Update(b, a);
            }
            return AllLines(res);
        }
        void Update(int x, int y)
        {
            var tmp = new bool[5, 5];
            for (int i = 0; i < 5; i++)
                for (int j = 0; j < 5; j++)
                    tmp[i, j] = blacks.ContainsKey(new Point(x + i - 2, y + j - 2));
            var sumsHorisontal = new int[5, 3];
            for (int i = 0; i < 5; i++)
                for (int j = 0; j < 3; j++)
                    sumsHorisontal[i, j] = (tmp[i, j] ? 1 : 0) + (tmp[i, j + 1] ? 1 : 0) + (tmp[i, j + 2] ? 1 : 0);

            var xStart = Math.Max(0, 2 - x);
            var yStart = Math.Max(0, 2 - y);
            var xEnd = Math.Min(3, W - x);
            var yEnd = Math.Min(3, H - y);

            for (int i = xStart; i < xEnd; i++)
                for (int j = yStart; j < yEnd; j++)
                {
                    var sum = sumsHorisontal[i, j] + sumsHorisontal[i + 1, j] + sumsHorisontal[i + 2, j];
                    res[sum]--;
                    res[sum + 1]++;
                }
            blacks.Add(new Point(x, y), true);
        }
        int H;
        int W;
        long[] res = new long[10];
        Dictionary<Point, bool> blacks = new Dictionary<Point, bool>(100000);
        struct Point : IEquatable<Point>
        {
            public int x;
            public int y;
            public Point(int[] arr) : this(arr[0], arr[1]) { }
            public Point(int x, int y)
            {
                this.x = x;
                this.y = y;
            }
            public bool Equals(Point other) => this.x == other.x && this.y == other.y;
            public override bool Equals(object obj)
            {
                if (obj is Point) return Equals((Point)obj);
                return false;
            }
            public override int GetHashCode() => x ^ y;
            public override string ToString() => $"({x}, {y})";
        }

        #region いつもの
#pragma warning disable
        [System.Diagnostics.DebuggerBrowsable(System.Diagnostics.DebuggerBrowsableState.Never)] private ConsoleReader consoleReader;
        public Program(ConsoleReader consoleReader) { this.consoleReader = consoleReader; }
        static void Main() => Console.WriteLine(new Program(new ConsoleReader(Console.In)).Calc()); static string AllLines<T>(IEnumerable<T> source) => string.Join("\n", source);
    }
    static class Ext
    {
        public static IComparer<T> Reverse<T>(this IComparer<T> comparer) => Comparer<T>.Create((x, y) => comparer.Compare(y, x));
        public static Dictionary<TKey, int> GroupCount<TSource, TKey>(this IEnumerable<TSource> source, Func<TSource, TKey> keySelector) => source.GroupBy(keySelector).ToDictionary(g => g.Key, g => g.Count());
        public static Dictionary<TKey, int> GroupCount<TKey>(this IEnumerable<TKey> source) => source.GroupCount(i => i);
    }
    public class ConsoleReader { private string[] ReadLineSplit() => textReader.ReadLine().Split(Array.Empty<char>(), StringSplitOptions.RemoveEmptyEntries); private string[] line = Array.Empty<string>(); private int linePosition; private TextReader textReader; public ConsoleReader(TextReader tr) { textReader = tr; } public int Int => int.Parse(String); public long Long => long.Parse(String); public double Double => double.Parse(String); public string String { get { if (linePosition >= line.Length) { linePosition = 0; line = ReadLineSplit(); } return line[linePosition++]; } } public class SplitLine { private string[] splited; public SplitLine(ConsoleReader cr) { splited = cr.ReadLineSplit(); cr.line = Array.Empty<string>(); } public int[] Int => String.Select(x => int.Parse(x)).ToArray(); public int[] Int0 => String.Select(x => int.Parse(x) - 1).ToArray(); public long[] Long => String.Select(x => long.Parse(x)).ToArray(); public double[] Double => String.Select(x => double.Parse(x)).ToArray(); public string[] String => splited; } public SplitLine Split => new SplitLine(this); public class RepeatReader : IEnumerable<ConsoleReader> { ConsoleReader cr; int count; public RepeatReader(ConsoleReader cr, int count) { this.cr = cr; this.count = count; } public IEnumerator<ConsoleReader> GetEnumerator() => Enumerable.Repeat(cr, count).GetEnumerator(); System.Collections.IEnumerator System.Collections.IEnumerable.GetEnumerator() => GetEnumerator(); public IEnumerable<string> String => this.Select(cr => cr.String); public IEnumerable<int> Int => this.Select(cr => cr.Int); public IEnumerable<int> Int0 => this.Select(cr => cr.Int - 1); public IEnumerable<long> Long => this.Select(cr => cr.Long); public IEnumerable<double> Double => this.Select(cr => cr.Double); } public RepeatReader Repeat(int count) => new RepeatReader(this, count); }
    #endregion
}