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# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Linq;
using System.Collections.Generic;
using static System.Console;
using System.Text;
using System.IO;
using static System.Math;
using System.Numerics;

namespace AtCoder
{
    class Program
    {
        static public long[] Sarray() { return ReadLine().Split().Select(long.Parse).ToArray(); }
        static public List<long> Slist() { return ReadLine().Split().Select(long.Parse).ToList(); }
        static long Mod = (long)1e9 + 7;
        static void Main(string[] args)
        {
            SetOut(new StreamWriter(OpenStandardOutput()) { AutoFlush = false });
            Solve();
            Out.Flush();
            Read();
        }
        static void Solve()
        {
            var HWN = Sarray();
            var H = HWN[0];
            var W = HWN[1];
            var N = HWN[2];
            var bMasu = new HashSet<(long h, long w)>();
            for (var i = 0; i < N; ++i)
            {
                var ab = Sarray();
                bMasu.Add((ab[0], ab[1]));
            }
            var used = new HashSet<(long h, long w)>();
            var zah = new long[] { -1, 0, 1, -1, 0, 1, -1, 0, 1 };
            var zaw = new long[] { -1, -1, -1, 0, 0, 0, 1, 1, 1 };

            var nums = new long[10];
            foreach (var b in bMasu)
            {
                for (var i = 0; i < 9; ++i)//中心
                {
                    var ch = b.h + zah[i];
                    var cw = b.w + zaw[i];
                    if (1 < ch && ch < H && 1 < cw && cw < W && !used.Contains((ch, cw)))
                    {
                        var cnt = 0;
                        for (var j = 0; j < 9; ++j)//フィルタ
                        {
                            var h = ch + zah[j];
                            var w = cw + zaw[j];
                            if (bMasu.Contains((h, w))) ++cnt;
                        }
                        ++nums[cnt];
                    }
                    used.Add((ch, cw));
                }
            }
            var square = (H - 2) * (W - 2);
            nums[0] = square - nums.Skip(1).Sum();
            foreach (var n in nums)
                WriteLine(n);
        }
    }
}