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;
using System.Linq;

namespace ABC045D{
    public class Program{
        public static void Main(string[] args){
            var sr = new StreamReader();
            //---------------------------------
            var H = sr.Next<int>();
            var W = sr.Next<int>();
            var N = sr.Next<int>();
            var P = sr.Next<int>(N, 2);

            Func<int, int, long> hash = (s, t) => s * 1000000L + t;
            Func<int, int, bool> isInside = (x, y) => 1 <= x && x < W - 1 && 1 <= y && y < H - 1;
            var dx = new[]{0, 1, 0, -1, 1, 1, -1, -1, 0};
            var dy = new[]{1, 0, -1, 0, 1, -1, 1, -1, 0};
            var area = new List<long>();

            foreach(var p in P){
                for(var i = 0; i < 9; i++){
                    var x = p[0] + dx[i] - 1;
                    var y = p[1] + dy[i] - 1;
                    if(isInside(x, y)){
                        area.Add(hash(x, y));
                    }
                }
            }

            var res = new int[10];
            foreach(var ag in area.GroupBy(x => x)){
                Console.WriteLine($"x = {ag.Key / 1000000}, y = {ag.Key % 1000000}, cnt = {ag.Count()}");
                res[ag.Count()]++;
            }

            res[0] = (W - 2) * (H - 2) - res.Sum();
            Array.ForEach(res, Console.WriteLine);
            //---------------------------------
        }
    }

    public class StreamReader{
        private readonly char[] _c = {' '};
        private int _index = -1;
        private string[] _input = new string[0];
        private readonly System.IO.StreamReader _sr = new System.IO.StreamReader(Console.OpenStandardInput());

        public T Next<T>(){
            if(_index == _input.Length - 1){
                _index = -1;
                while(true){
                    string rl = _sr.ReadLine();
                    if(rl == null){
                        if(typeof(T).IsClass) return default(T);
                        return (T)typeof(T).GetField("MinValue").GetValue(null);
                    }
                    if(rl != ""){
                        _input = rl.Split(_c, StringSplitOptions.RemoveEmptyEntries);
                        break;
                    }
                }
            }
            return (T)Convert.ChangeType(_input[++_index], typeof(T), System.Globalization.CultureInfo.InvariantCulture);
        }

        public T[] Next<T>(int x){
            var ret = new T[x];
            for(var i = 0; i < x; ++i) ret[i] = Next<T>();
            return ret;
        }

        public T[][] Next<T>(int y, int x){
            var ret = new T[y][];
            for(var i = 0; i < y; ++i) ret[i] = Next<T>(x);
            return ret;
        }
    }
}