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 Pair = System.Collections.Generic.KeyValuePair<int, int>;

namespace ABC045_D
{
    class Program
    {
        static sbyte[] dy = { -1, 0, 1, -1, 0, 1, -1, 0, 1 };
        static sbyte[] dx = { -1, -1, -1, 0, 0, 0, 1, 1, 1 };
        static void Main(string[] args)
        {
            var t = scan;
            var H = t[0];
            var W = t[1];
            var n = t[2];
            var G = new Dictionary<Pair, sbyte>();
            long all = (long)(H - 2) * (W - 2);
            for (int i = 0; i < n; i++)
            {
                t = scan;
                for (sbyte j = 0; j < 9; j++)
                {
                    int ty = t[0] + dy[j];
                    int tx = t[1] + dx[j];
                    if (ty <= 1 || tx <= 1 || ty >= H || tx >= W) continue;
                    var k = new Pair(ty, tx);
                    if (G.ContainsKey(k)) G[k]++;
                    else  G[k] = 1;
                }
            }           
            var A = new long[10];
            foreach (var g in G.Values)
            {
                A[g]++;
            }
            A[0] = all - G.Count;
            foreach (var a in A)
            {
                Console.WriteLine(a);
            }
        }

        static int[] scan { get { return Array.ConvertAll(Console.ReadLine().Split(), int.Parse); } }
    }
    
}