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;

namespace AtCoder
{
    class Program
    {
        static void Main()
        {
            var HWN = Utility.ReadIntArray();
            var H = HWN[0];
            var W = HWN[1];
            var N = HWN[2];
            var ab = new Point[N];
            var ans = new long[10];
            for (int i = 0; i < N; i++)
            {
                var temp = Utility.ReadIntArray();
                ab[i] = new Point(temp[0] - 1, temp[1] - 1);
            }

            for (int i = 0; i < ab.Length; i++)
            {
                for (var baseX = Math.Max(0, ab[i].X - 2); baseX <= Math.Min(H - 3, ab[i].X); baseX++)
                {
                    for (var baseY = Math.Max(0, ab[i].Y - 2); baseY <= Math.Min(W - 3, ab[i].Y); baseY++)
                    {
                        var count = ab.Count(v => baseX <= v.X && v.X < baseX + 3 && baseY <= v.Y && v.Y < baseY + 3);
                        ans[count]++;
                    }
                }

            }
            for (int i = 1; i < ans.Length; i++)
            {
                ans[i] /= i;
            }

            ans[0] = ((long)H - 2) * (W - 2) - ans.Skip(1).Sum();
            foreach (var an in ans)
            {
                Console.WriteLine(an);
            }
        }
        struct Point
        {
            public readonly int X;
            public readonly int Y;
            public Point(int x, int y)
            {
                X = x;
                Y = y;
            }
        }
    }

    public static class Utility
    {
        public static string ReadString() => Console.ReadLine();
        public static string[] ReadStringArray() => ReadString().Split(' ');
        public static int ReadInt() => int.Parse(ReadString());
        public static int[] ReadIntArray() => ReadStringArray().ParseInt().ToArray();
        public static IEnumerable<int> ParseInt(this IEnumerable<string> source) => source.Select(v => int.Parse(v));

        public static IEnumerable<int> EnumerateDigits(int value)
        {
            while (value > 0)
            {
                yield return value % 10;
                value /= 10;
            }
        }

    }

    public class Factorial
    {
        public static long Number(long term)
        {
            return term > 1 ? Number(term - 1) * term : 1;
        }

        public static long[] Cache(long term)
        {
            var cache = new long[term + 1];
            cache[0] = 1;
            for (int i = 1; i < cache.Length; i++)
            {
                cache[i] = cache[i - 1] * i;
            }
            return cache;
        }

        public static long[] CacheMod(long term, long mod)
        {
            var cache = new long[term + 1];
            cache[0] = 1;
            for (int i = 1; i < cache.Length; i++)
            {
                cache[i] = cache[i - 1] * i % mod;
            }
            return cache;
        }
    }
}