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: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Linq;
using static System.Console;
using System.Runtime.CompilerServices;
using static MyUtil;

class MyUtil
{
    public static int[] ReadIntArray()
    {
	return ReadLine().Split().Select(x => int.Parse(x)).ToArray();
    }
}

class Program
{
    public static void Main()
    {
	var tmp = ReadIntArray();
	long h = tmp[0], w = tmp[1], n = tmp[2];

	var dict = new Dictionary<long, int>();
	for (int i = 0; i < n; i++)
	{
	    tmp = ReadIntArray();
	    int a = tmp[0], b = tmp[1];
	    for (int x = a-2; x <=a; x++)
	    {
		for (int y = b-2; y <=b; y++)
		{
		    if (x >= 1 && x <= h-2 && y >= 1 && y <= w-2)
		    {
			long key = x; key <<= 32; key += y;
			if (!dict.ContainsKey(key)){ dict.Add(key, 0); }
			dict[key]++;
		    }
		}
	    }
	}

	long[] ans = new long[10];
	foreach (long k in dict.Keys)
	{
	    int j = dict[k];
	    ans[j]++;
	}

	long m = 0;
	for (int i = 1; i <= 9; i++)
	    m += ans[i];
	ans[0] = (h-2)*(w-2) - m;
	
	for (int j = 0; j <= 9; j++)
	    WriteLine(ans[j]);
    }
}