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;

namespace AtCoder
{
    class Program
    {
        static void Main()
        {
            var HWN = Utility.ReadIntArray();
            var H = HWN[0];
            var W = HWN[1];
            var N = HWN[2];
            var dic = new Dictionary<long, int>();
            for (var i = 0; i < N; i++)
            {
                var ab = Utility.ReadIntArray();
                var x = ab[0] - 1;
                var y = ab[1] - 1;

                for (var baseX = Math.Max(0, x - 2); baseX <= Math.Min(H - 3, x); baseX++)
                {
                    for (var baseY = Math.Max(0, y - 2); baseY <= Math.Min(W - 3, y); baseY++)
                    {
                        var key = ((long)baseX << 32) + baseY;
                        if (!dic.ContainsKey(key))
                        {
                            dic.Add(key, 1);
                        }
                        else
                        {
                            dic[key]++;
                        }
                    }
                }

            }
            var ans = new long[10];
            foreach (var p in dic.GroupBy(v => v.Value))
            {
                ans[p.Key] = p.Count();
            }
            ans[0] = ((long)H - 2) * (W - 2) - ans.Skip(1).Sum();

            foreach (var an in ans)
            {
                Console.WriteLine(an);
            }
        }
        struct Point
        {
            public readonly int X;
            public readonly int Y;
            public Point(int x, int y)
            {
                X = x;
                Y = y;
            }
        }
    }

    public static class Utility
    {
        public static string ReadString() => Console.ReadLine();
        public static string[] ReadStringArray() => ReadString().Split(' ');
        public static int ReadInt() => int.Parse(ReadString());
        public static int[] ReadIntArray() => ReadStringArray().ParseInt().ToArray();
        public static IEnumerable<int> ParseInt(this IEnumerable<string> source) => source.Select(v => int.Parse(v));
    }
}