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 System.Text;

namespace AtCoder
{
    class Program
    {
        private const int MODULO = 1000000007;
        private static string Read() { return Console.ReadLine(); }
        private static int ReadInt() { return int.Parse(Read()); }
        private static long ReadLong() { return long.Parse(Read()); }
        private static double ReadDouble() { return double.Parse(Read()); }
        private static int[] ReadInts() { return Array.ConvertAll(Read().Split(), int.Parse); }
        private static long[] ReadLongs() { return Array.ConvertAll(Read().Split(), long.Parse); }
        private static double[] ReadDoubles() { return Array.ConvertAll(Read().Split(), double.Parse); }

        static IEnumerable<long> Solve(int H, int W, IEnumerable<Tuple<int, int>> points)
        {
            var dict = new Dictionary<Tuple<int, int>, int>();
            foreach (var p in points)
            {
                int i1 = Math.Max(p.Item1 - 2, 0);
                int i2 = Math.Min(p.Item1, H - 3);
                int j1 = Math.Max(p.Item2 - 2, 0);
                int j2 = Math.Min(p.Item2, W - 3);
                for (int i = i1; i <= i2; ++i)
                {
                    for (int j = j1; j <= j2; ++j)
                    {
                        var key = new Tuple<int, int>(i, j);
                        if (!dict.ContainsKey(key)) { dict[key] = 0; }
                        ++dict[key];
                    }
                }
            }
            long[] counts = new long[10];
            foreach (int n in dict.Values) { ++counts[n]; }
            counts[0] = Math.BigMul(H - 2, W - 2) - counts.Sum();
            return counts;
        }
        static void Main(string[] args)
        {
            int[] v1 = ReadInts();
            int H = v1[0];
            int W = v1[1];
            var list = new List<Tuple<int, int>>();
            for (int i = 0; i < v1[2]; ++i)
            {
                int[] v2 = ReadInts();
                list.Add(new Tuple<int, int>(v2[0] - 1, v2[1] - 1));
            }
            foreach (long count in Solve(H, W, list))
            {
                Console.WriteLine(count);
            }
        }
    }
}