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.Text;
using System.Linq;

namespace atcoder
{
    class Program
    {
        static void Main(string[] args)
        {
            string[] s = Console.ReadLine().Split();
            long h = long.Parse(s[0]);
            long w = long.Parse(s[1]);
            int n = int.Parse(s[2]);
            long[] cnt = new long[10];
            Dictionary<Tuple<int, int>, int> board = new Dictionary<Tuple<int, int>, int>();
            for (int m = 0; m < n; m++)
            {
                string[] ab = Console.ReadLine().Split();

                int ph = int.Parse(ab[0]);
                int pw = int.Parse(ab[1]);

                for (int i = ph - 1; i <= ph + 1; i++)
                {
                    for (int j = pw - 1; j <= pw + 1; j++)
                    {
                        if (i > 1 && i < h && j > 1 && j < w)
                        {
                            var masu = new Tuple<int, int>(i, j);
                            if (board.ContainsKey(masu) == false)
                            {
                                board.Add(masu,1);
                            }
                            else
                            {
                                board[masu]++;
                            }
                        }
                    }
                }
            }
            
            foreach (var item in board)
            {
                cnt[item.Value]++;
            }
            cnt[0] = (h - 2) * (w - 2) - cnt.Sum();
            foreach (var item in cnt)
            {
                Console.WriteLine(item);
            }
        }
    }
}