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;

struct coord
{
    public int a;
    public int b;
}
class Board
{
    int H;
    int W;
    int N;
    Dictionary<coord, int> dic;
    public Board(int H, int W, int N)
    {
        this.H = H;
        this.W = W;
        this.N = N;
        dic = new Dictionary<coord, int>();
    }
    public void add(int a, int b)
    {
        if (a < 2 || b < 2) return;
        if (a >= H || b >= W) return;
        coord ab;
        ab.a = a;
        ab.b = b;
        if (dic.ContainsKey(ab))
        {
            dic[ab]++;
        }
        else
        {
            dic[ab] = 1;
        }
    }
    public void calc()
    {
        ulong[] count = new ulong[10];
        count[0] = ((ulong)H - 2) * ((ulong)W - 2);
        foreach (var x in dic)
        {
            count[x.Value]++;
            count[0]--;
        }
        for (int i = 0; i < 10; ++i)
        {
            Console.WriteLine(count[i]);
        }
    }
}
class Program
{
    public static int Main()
    {
        string[] HWN = Console.ReadLine().Split(' ');
        int H = int.Parse(HWN[0]);
        int W = int.Parse(HWN[1]);
        int N = int.Parse(HWN[2]);

        //int[,] board = new int[H + 2, W + 2];
        Board board = new Board(H, W, N);
        for (int i = 0; i < N; ++i)
        {
            string[] ab = Console.ReadLine().Split(' ');
            int a = int.Parse(ab[0]) - 1;
            int b = int.Parse(ab[1]) - 1;
            board.add(a + 0, b + 0); board.add(a + 1, b + 0); board.add(a + 2, b + 0);
            board.add(a + 0, b + 1); board.add(a + 1, b + 1); board.add(a + 2, b + 1);
            board.add(a + 0, b + 2); board.add(a + 1, b + 2); board.add(a + 2, b + 2);
        }

        board.calc();
        return 0;
    }
}