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.Linq;//リストの使用
using System.Collections.Generic;
using System.Text;//テキストの高速出力に必要
class Program 
{
  static void Main() 
  {
    int[] input = Console.ReadLine().Split(' ').Select(s => int.Parse(s)).ToArray();
    int H = input[0];
    int W = input[1];
    int N = input[2];
    
    List<long> list = new List<long>();
    for (int i = 0; i < N; i++)//黒い箇所全て
    {
      int[] inputb = Console.ReadLine().Split(' ').Select(s => int.Parse(s)).ToArray();
      for (int j = inputb[0] - 1; j <= inputb[0] + 1; j++)//黒いxの前後3箇所
      {
        for (int k = inputb[1] - 1; k <= inputb[1] + 1; k++)//黒いyの前後3箇所
        {
          if (j >= 2 && j <= H - 1 && k >= 2 && k <= W - 1)//中央に9周囲が存在するならば
          {
            list.Add((long)(j-1)*W + k);//マスの番号（1~）
          }
        }
      }
    }
    list.Sort();
    long temp = 0;
    int num = 0;
    long[] ans = new long[10];
    ans[0] = (long)(H-2) * (W-2);//黒がない場合で解答を初期化
            
    for (int i = 0; i < list.Count; i++)//リストを全探索
    {
      if (list[i] != temp)//座標が変わったならば
      {
        if (temp != 0) 
        {
          ans[num]++;
          ans[0]--;
        }
        temp = list[i];
        num = 1;
      }else num++;//同じ座標ならば       
    }
    ans[num]++;
    ans[0]--;
    
    for (int i = 0; i < 10; i++) Console.WriteLine(ans[i]);
  }
}