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.Generic;

namespace ABC045_D_SnukesColoring
{
    class ABC045_D
    {
        static void Main(string[] args)
        {
            string[] first = Console.ReadLine().Split(' ');
            ulong H = ulong.Parse(first[0]);
            ulong W = ulong.Parse(first[1]);
            ulong N = ulong.Parse(first[2]);

            // マスを作る
            ulong[,] board = new ulong[H, W];
            for (ulong i = 0; i < N; i++)
            {
                string[] split = Console.ReadLine().Split(' ');
                board[ulong.Parse(split[0]) - 1, ulong.Parse(split[1]) - 1]++;
            }

            ulong[] counts = new ulong[10];
            for (ulong y = 0; y < H - 2; y++)
            {
                for (ulong x = 0; x < W - 2; x++)
                {
                    counts[Sum3x3(board, y, x)]++;
                }
            }

            for (int i = 0; i < counts.Length; i++)
            {
                Console.WriteLine(counts[i]);
            }

            Console.ReadKey();
        }

        static ulong Sum3x3(ulong[,] board, ulong top, ulong left)
        {
            ulong sum = 0;
            for (ulong y = 0; y < 3; y++)
            {
                for (ulong x = 0; x < 3; x++)
                {
                    sum += board[top + y, left + x];
                }
            }

            return sum;
        }
    }
}