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;
using System.Collections.Generic;
using System.Collections.Specialized;
using System.Text;
using System.Text.RegularExpressions;
using System.Linq;

class Magatro
{
    static int H, W, N;
    static xy[] Points;
    static void Main()
    {
        string[] s = Console.ReadLine().Split(' ');
        H = int.Parse(s[0]);
        W = int.Parse(s[1]);
        N = int.Parse(s[2]);
        HashSet<xy> Hs = new HashSet<xy>();
        Dictionary<xy, int> Dic = new Dictionary<xy, int>();
        long[] cnt = new long[10];
        Points = new xy[N];
        for(int i = 0; i < N; i++)
        {
            s = Console.ReadLine().Split(' ');
            Points[i] = new xy(int.Parse(s[0]), int.Parse(s[1]));
        }
        int[] q = new int[] { -2, -1, 0, -2, -1, 0, -2, -1, 0 };
        int[] w = new int[] { -2, -2, -2, -1, -1, -1, 0, 0, 0 };
        for(int i = 0; i < N; i++)
        {
            for(int j = 0; j < 9; j++)
            {
                xy p = Points[i];
                p.X += q[j];
                p.Y += w[j];
                if (p.X <= 0 || p.Y <= 0 || p.X > W - 2 || p.Y > H - 2)
                {
                    continue;
                }
                //    Console.WriteLine(p.toString());
                if (Hs.Add(p))
                {
                    Dic.Add(p, 1);
                }
                else
                {
                    Dic[p]++;
                }
            }

        }
       foreach(xy pp in Hs)
        {
            cnt[Dic[pp]]++;
        }
        cnt[0] = ((long)W - 2) * ((long)H - 2) - cnt.Sum();
        for(int i = 0; i < 10; i++)
        {
            Console.WriteLine(cnt[i]);
        }
    }
   
}
struct xy
{
    public int Y;
    public int X;
    public xy(int y, int x)
    {
        Y = y;
        X = x;
        
    }
    public string toString()
    {
        return Y + " " + X;
    }
}