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;

namespace SnukesColoring
{
    class Program
    {
        static void Main(string[] args)
        {
            long W, H, N;
            var read = Console.ReadLine();
            var ary = read.Split(' ');
            H = long.Parse(ary[0]);
            W = long.Parse(ary[1]);
            N = long.Parse(ary[2]);

            var blacks = new Tuple<long, long>[N];
            for (long i = 0; i < N; i++)
            {
                read = Console.ReadLine();
                ary = read.Split(' ');
                blacks[i] = new Tuple<long, long>(long.Parse(ary[0]) - 1, long.Parse(ary[1]) - 1);
            }

            //var sw = System.Diagnostics.Stopwatch.StartNew();

            var counts = new Dictionary<Tuple<long, long>, int>();
            System.Threading.Tasks.Parallel.ForEach(blacks, black =>
            {
                for (var y = 0; y < 3; y++)
                {
                    var wy = black.Item1 - y;
                    if (wy < 0 || wy + 2 >= H) continue;
                    for (var x = 0; x < 3; x++)
                    {
                        var wx = black.Item2 - x;
                        if (wx < 0 || wx + 2 >= W) continue;

                        var pt = new Tuple<long, long>(wx, wy);
                        lock (counts)
                        {
                            int value = 0;
                            if (counts.TryGetValue(pt, out value))
                            {
                                counts[pt] = value + 1;
                            }
                            else
                            {
                                counts.Add(pt, 1);
                            }
                        }
                    }
                }
            });

            //sw.Stop();
            //Console.WriteLine("counting. {0}ms", (double)sw.ElapsedTicks / System.Diagnostics.Stopwatch.Frequency * 1000.0);

            //sw.Reset();
            //sw.Restart();

            var results = new long[10];
            results[0] = (W - 2) * (H - 2) - counts.Count;
            foreach (var t in counts)
                results[t.Value]++;
            for (var j = 0; j <= 9; j++)
                Console.WriteLine(results[j]);

            //sw.Stop();
            //Console.WriteLine("result. {0}ms", sw.ElapsedMilliseconds);

            //Console.ReadKey();
        }
    }
}