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: Runtime Error)

using System;
using System.Collections;
using System.IO;
using System.Linq;

namespace CompetitiveProgramming
{
  
  class Solve
  {
    const int INF = (int)(1e9) + 10;

    private void Main()
    {
      long[] HWN = Console.ReadLine().Split().Select(long.Parse).ToArray();
      long H = HWN[0], W = HWN[1], N = HWN[2];

      long[] count = new long[10];
      long sum = 0;
      long[,] nums = new long[H, W];

      count[0] = (H - 2) * (W - 2) - sum;

      for (long i = 0; i < N; i++)
      {
        long[] ab = Console.ReadLine().Split().Select(long.Parse).ToArray();
        long a = ab[0] - 1, b = ab[1] - 1;

        for (long j = -2; j <= 0; j++)
        {
          for (long k = -2; k <= 0; k++)
          {
            long t = a + j;
            long u = b + k;
            if (t >= 0 && t + 2 < H && u >= 0 && u + 2 < W)
            {
              long tmp = ++nums[t, u];
              count[tmp - 1]--;
              count[tmp]++;
            }
          }
        }
      }
      for (int i = 0; i < 10; i++)
      {
        Console.WriteLine(count[i]);
      }
    }

    public Solve()
    {
      Console.SetOut(new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false });
      Main();
      Console.Out.Flush();
    }
  }

  class Program
  {
    static void Main(string[] args)
    {
      new Solve();
    }
  }
}