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.Linq;
using static System.Console;
using static System.Convert;
using static System.Math;
//using static System.Globalization.CultureInfo;

class Program
{
    struct P
    {
        public int h;
        public int w;
        public P(int h,int w)
        {
            this.h = h;
            this.w = w;
        }
    }
    static void Main(string[] args)
    {
        var hwn = Array.ConvertAll(ReadLine().Split(' '), int.Parse);
        var point = new long[10];
        point[0] = (long)(hwn[0] - 2) * (hwn[1] - 2);
        var dic = new Dictionary<P, int>();
        for(var i = 0; i < hwn[2]; i++)
        {
            var input = Array.ConvertAll(ReadLine().Split(' '), int.Parse);
            for(var j = 0; j < 3; j++)
                for(var h = 0; h < 3; h++)
                {
                    var hh = input[0] - j;
                    var ww = input[1] - h;
                    if (1 > hh || hh > hwn[0]-2 || 1 > ww || ww > hwn[1]-2)
                        continue;
                    var p = new P(hh, ww);
                    if (dic.ContainsKey(p))
                        dic[p]++;
                    else dic[p] = 1;
                    point[dic[p]]++;
                }
        }
        for (var i = 0; i < 9; i++)
            WriteLine(point[i] - point[i + 1]);
        WriteLine(point[9]);
    }
    private const string ALFA = "abcdefghijklmnopqrstuvwxyz";
    private const int MOD = 1000000007;
}