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: Wrong Answer)

using System;
using System.Collections.Generic;

namespace ABC045Coloring
{
    class Program
    {
        static void Main(string[] args)
        {
            long H, W;
            int N;
            string[] vals = Console.ReadLine().Split(' ');
            H = long.Parse(vals[0]);
            W = long.Parse(vals[1]);
            N = int.Parse(vals[2]);
            long[,] ab;
            if (N >= 1)
                ab = new long[N, 2];
            else
                ab = new long[1, 2];
            for(int i=0; i < N; i++)
            {
                vals = Console.ReadLine().Split(' ');
                ab[i, 0] = long.Parse(vals[0]);
                ab[i, 1] = long.Parse(vals[1]); 
            }

            long[] totalCount = new long[10];
            totalCount[0] = (W - 2) * (H - 2);

            Dictionary<long, int> count = new Dictionary<long, int>();
            for(int i=0; i < N; i++)
            {
                long a, b, n;
                for(int y=0; y < 3; y++)
                {
                    for(int x=0; x < 3; x++)
                    {
                        a = ab[i, 0] - y;
                        b = ab[i, 1] - x;
                        if (a < 1 || a > H - 2 || b < 1 || b > W - 2)
                            continue;
                 
                        n = (b - 1) * (W - 2) + (a - 1);
                        //Console.WriteLine("Square " + i + " is in (" + a + "," + b + ") n=" + n);

                        if (count.ContainsKey(n))
                        {
                            count[n]++;
                        }
                        else
                        {
                            totalCount[0]--;
                            count[n] = 1;
                        }
                    }
                }
            }

            foreach(var n in count.Keys)
            {
                if(count[n] <= 9)
                    totalCount[count[n]]++;
            }
            for (int i = 0; i <= 9; i++)
                Console.WriteLine(totalCount[i]);

        }
    }
}