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)

using System;
using System.Collections.Generic;
using System.Linq;

namespace AtCoder
{
    class Program
    {
        static void Main()
        {

            var HWN = Utility.ReadLongArray();
            var H = HWN[0];
            var W = HWN[1];
            var N = HWN[2];
            var d = new Dictionary<long, long>();
            //for (var i = 0; i < N; i++)
            //{
            //    var ab = Utility.ReadLongArray();
            //    var x = ab[0] - 1;
            //    var y = ab[1] - 1;
            //    for (long j = 0; j < 3; j++)
            //    {
            //        var currentX = x - j;
            //        if (0 <= currentX && currentX < H - 2)
            //        {
            //            for (long k = 0; k < 3; k++)
            //            {
            //                var currentY = y - k;
            //                if (0 <= currentY && currentY < W - 2)
            //                {
            //                    var key = (currentX << 32) + currentY;
            //                    if (d.ContainsKey(key))
            //                    {
            //                        d[key]++;
            //                    }
            //                    else
            //                    {
            //                        d.Add(key, 1);
            //                    }
            //                }
            //            }
            //        }
            //    }

            //}


            for (long i = 0; i < N; ++i)
            {
                var y = Utility.ReadLongArray();
                long a = y[0] - 1;
                long b = y[1] - 1;

                for (long j = 0; j <= 2; ++j)
                {
                    for (long k = 0; k <= 2; ++k)
                    {
                        long Y = a - j;
                        long X = b - k;

                        long Key = X * 1000000000 + Y;

                        if (X < 0 || X >= W - 2 || Y < 0 || Y >= H - 2) continue;
                        if (!d.ContainsKey(Key))
                        {
                            d.Add(Key, 0);
                        }
                        d[Key]++;
                    }
                }


            }

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

            foreach (var an in ans)
            {
                Console.WriteLine(an);
            }
        }
    }

    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 long[] ReadLongArray() => ReadStringArray().ParseLong().ToArray();
        public static IEnumerable<int> ParseInt(this IEnumerable<string> source) => source.Select(int.Parse);
        public static IEnumerable<long> ParseLong(this IEnumerable<string> source) => source.Select(long.Parse);
    }
}