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.Collections.Generic;
using System.Linq;

class D {
    static ulong Hash(int a1, int a2) {
        return (ulong)a1 * 0x9ddfea08eb382d69 + (ulong)a2;
    }

    public static void Main() {
        var line = Console.ReadLine().Split();
        var h = int.Parse(line[0]);
        var w = int.Parse(line[1]);
        var n = int.Parse(line[2]);
        var blocks = new Dictionary<ulong, int>();
        for (int i = 0; i < n; ++i) {
            line = Console.ReadLine().Split();
            var x1 = int.Parse(line[0]) - 1;
            var x2 = int.Parse(line[1]) - 1;
            for (int j1 = x1 - 2; j1 <= x1; ++j1)
                if (0 <= j1 && j1 + 2 < h)
                    for (int j2 = x2 - 2; j2 <= x2; ++j2)
                        if (0 <= j2 && j2 + 2 < w) {
                            var hash = Hash(j1, j2);
                            var v = 0;
                            blocks.TryGetValue(hash, out v);
                            blocks[hash] = v + 1;
                        }
        }
        var answer = new long[10];
        foreach (var i in blocks) ++answer[i.Value];
        answer[0] = (long)(h - 2) * (w - 2) - answer.Sum();
        for (int i = 0; i < answer.Length; ++i) Console.WriteLine(answer[i]);
    }
}