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.IO;
using System.Linq;
using System.Numerics;
using System.Collections.Generic;
using System.Text;
using System.Text.RegularExpressions;
using static System.Math;
using Debug = System.Diagnostics.Debug;


static class P
{
    static void Main()
    {
        var hwn = Console.ReadLine().Split().Select(int.Parse).ToArray();
        SortedSet<Tuple<int, int>> candidateCenter = new SortedSet<Tuple<int, int>>();
        SortedSet<Tuple<int, int>> black = new SortedSet<Tuple<int, int>>();
        for (int iterate = 0; iterate < hwn[2]; iterate++)
        {
            var ab = Console.ReadLine().Split().Select(int.Parse).ToArray();
            for (int i = -1; i <= 1; i++)
            {
                for (int j = -1; j <= 1; j++)
                {
                    Tuple<int, int> point = new Tuple<int, int>(ab[0] + i, ab[1] + j);
                    if (point.Item1 <= 1 || hwn[0] - 1 < point.Item1 || point.Item2 <= 1 || hwn[1] - 1 < point.Item2)
                        continue;
                    candidateCenter.Add(point);
                }
            }
            black.Add(new Tuple<int, int>(ab[0], ab[1]));
        }
        var res = new long[10];
        res[0] = (long)(hwn[0] - 2) * (hwn[1] - 2);
        foreach (var cand in candidateCenter)
        {
            res[0]--;
            int count = 0;
            for (int i = -1; i <= 1; i++)
            {
                for (int j = -1; j <= 1; j++)
                {
                    if (black.Contains(new Tuple<int, int>(cand.Item1 + i, cand.Item2 + j)))
                        count++;
                }
            }
            res[count]++;
        }
        Console.WriteLine(string.Join("\n", res));
    }
}