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 System.Text;
using System.Threading.Tasks;

namespace AtCoder
{
	class Program
	{
		static void Main(string[] args)
		{
			var firstLine = Console.ReadLine().Split(' ').Select(value => long.Parse(value)).ToList();
			var h = firstLine[0];
			var w = firstLine[1];
			var n = firstLine[2];
			
			var points = new List<Point>();

			for(long i = 0; i < n; i++)
			{
				var tmpList = Console.ReadLine().Split(' ').Select(value => long.Parse(value)).ToList();
				var point = new Point() { A = tmpList[0], B = tmpList[1] };
				points.Add(point);
			}

			var rectangleDictionary = new Dictionary<Point, int>();

			foreach(var point in points)
			{
				var tmpA = point.A - 1;
				var tmpB = point.B - 1;
				if (tmpA > 1 && tmpB > 1)
				{
					AddIfEmptyOrIncrement(rectangleDictionary, new Point() { A = tmpA, B = tmpB });
				}
				tmpB++;
				if (tmpA > 1 && tmpB > 1 && tmpB < w)
				{
					AddIfEmptyOrIncrement(rectangleDictionary, new Point() { A = tmpA, B = tmpB });
				}
				tmpB++;
				if (tmpA > 1 && tmpB < w)
				{
					AddIfEmptyOrIncrement(rectangleDictionary, new Point() { A = tmpA, B = tmpB });
				}
				tmpA++;
				tmpB -= 2;
				if (tmpA > 1 && tmpA < h && tmpB > 1)
				{
					AddIfEmptyOrIncrement(rectangleDictionary, new Point() { A = tmpA, B = tmpB });
				}
				tmpB++;
				if (tmpA > 1 && tmpA < h && tmpB > 1 && tmpB < w)
				{
					AddIfEmptyOrIncrement(rectangleDictionary, new Point() { A = tmpA, B = tmpB });
				}
				tmpB++;
				if (tmpA > 1 && tmpA < h &&  tmpB < w)
				{
					AddIfEmptyOrIncrement(rectangleDictionary, new Point() { A = tmpA, B = tmpB });
				}
				tmpA++;
				tmpB -= 2;
				if (tmpA < h && tmpB > 1)
				{
					AddIfEmptyOrIncrement(rectangleDictionary, new Point() { A = tmpA, B = tmpB });
				}
				tmpB++;
				if (tmpA < h && tmpB > 1 && tmpB < w)
				{
					AddIfEmptyOrIncrement(rectangleDictionary, new Point() { A = tmpA, B = tmpB });
				}
				tmpB++;
				if (tmpA < h && tmpB < w)
				{
					AddIfEmptyOrIncrement(rectangleDictionary, new Point() { A = tmpA, B = tmpB });
				}
			}

			var countList = new List<long>();
			countList.Add(0);

			for(int i = 1; i < 10; i++)
			{
				countList.Add(rectangleDictionary.Count(keyValuePair => keyValuePair.Value == i));
			}

			countList[0] = (h - 2) * (w - 2) - countList.Sum();

			foreach(var i in countList)
			{
				Console.WriteLine(i);
			}
		}

		private static void AddIfEmptyOrIncrement(Dictionary<Point, int> dictionary, Point point)
		{
			if(dictionary.ContainsKey(point))
			{
				dictionary[point]++;
			}
			else
			{
				dictionary.Add(point, 1);
			}
		}

		private struct Point
		{
			public long A;
			public long B;
		}
	}
}