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: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;

namespace ARC061_D___すぬけ君の塗り絵
{
    class Program
    {
        static void Main(string[] args)
        {
            var HWN = Array.ConvertAll(Console.ReadLine().Split(' '), long.Parse);
            var H = HWN[0];
            var W = HWN[1];
            var N = HWN[2];
            long MOD = 1000000007;

            var colored = new HashSet<long>();
            for (int i = 0; i < N; i++)
            {
                var ab = Array.ConvertAll(Console.ReadLine().Split(' '), int.Parse);
                colored.Add(ab[0] + ab[1] * MOD);
            }

            var checking = new HashSet<long>();
            foreach (long p in colored)
            {
                var h = p % MOD;
                var w = p / MOD;
                for (long a = h - 1; a <= h + 1; a++)
                {
                    for (long b = w - 1; b <= w + 1; b++)
                    {
                        if (a <= 1 || a >= H || b <= 1 || b >= W) continue;
                        checking.Add(a + b * MOD);
                    }
                }
            }

            var result = new long[10];
            foreach (long p in checking)
            {
                var count = 0;
                var height = p % MOD;
                var width = p / MOD;
                for (long h = height - 1; h <= height + 1; h++)
                {
                    for (long w = width - 1; w <= width + 1; w++)
                    {
                        if (colored.Contains(h + w * MOD)) count++;
                    }
                }
                result[count]++;
            }

            result[0] = (H - 2) * (W - 2);
            for (int i = 1; i < 10; i++) result[0] -= result[i];
            for (int i = 0; i < 10; i++) Console.WriteLine(result[i]);
        }
    }
}