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.Collections.Generic;
using System;

public struct P
{
    public int x { get; set; }
    public int y { get; set; }
}

public class Hello
{
    public static void Main()
    {
        var d = new Dictionary<P, int>();
        string[] line = Console.ReadLine().Trim().Split(' ');
        var h = int.Parse(line[0]);
        var w = int.Parse(line[1]);
        var n = int.Parse(line[2]);
        for (int i = 0; i < n; i++)
        {
            line = Console.ReadLine().Trim().Split(' ');
            var a = int.Parse(line[0]) - 1;
            var b = int.Parse(line[1]) - 1;
            putDict(d, h, w, a, b);
        }
        var ret = new long[10];
        var rsum = 0;
        foreach (var x in d)
        {
            ret[x.Value]++;
            rsum++;
        }
        ret[0] = (long)(w - 2) * (h - 2) - rsum;
        foreach (var x in ret) Console.WriteLine(x);
    }
    public static void putDict(Dictionary<P, int> d, int h, int w, int a, int b)
    {
        if (a - 2 >= 0)
        {
            if (b - 2 >= 0) putDict2(d, a - 2, b - 2);
            if (b - 1 >= 0 && b + 1 < w) putDict2(d, a - 2, b - 1);
            if (b + 2 < w) putDict2(d, a - 2, b);
        }
        if (a - 1 >= 0 && a + 1 < h)
        {
            if (b - 2 >= 0) putDict2(d, a - 1, b - 2);
            if (b - 1 >= 0 && b + 1 < w) putDict2(d, a - 1, b - 1);
            if (b + 2 < w) putDict2(d, a - 1, b);
        }
        if (a + 2 < h)
        {
            if (b - 2 >= 0) putDict2(d, a, b - 2);
            if (b - 1 >= 0 && b + 1 < w) putDict2(d, a, b - 1);
            if (b + 2 < w) putDict2(d, a, b);
        }
    }
    public static void putDict2(Dictionary<P, int> d, int a, int b)
    {
        var w = new P { x = a, y = b };
        if (d.ContainsKey(w)) d[w]++;
        else d[w] = 1;
    }
}