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;
using static Input;

public class Prog
{
    private const int INF = 1000000007;
    public struct Pair<T> { public T x, y; public Pair(T x, T y) { this.x = x; this.y = y; } }
    public static void Solve()
    {
        long H = NextLong();
        long W = NextLong();
        int N = NextInt();
        Dictionary<int, Dictionary<int, bool>> d = new Dictionary<int, Dictionary<int, bool>>();
        long[] ans = new long[10];
        ans[0] = (H - 2) * (W - 2);
        for (int i = 0; i < N; i++)
        {
            int a = NextInt();
            int b = NextInt();
            //置く
            if (!d.ContainsKey(a)) d[a] = new Dictionary<int, bool>();
            if (!d[a].ContainsKey(b)) d[a][b] = true;

            //(a,b)を始点に9パターン考えてみる
            for (int x = -1; x <= 1; x++)
            {
                int xx = b + x;
                if (xx < 1 || W < xx) continue;
                for (int y = -1; y <= 1; y++)
                {
                    int yy = a + y;
                    if (yy < 1 || H < yy) continue;
                    int count = 0;
                    for (int dx = -1; dx <= 1; dx++)
                    {
                        int xdx = xx + dx;
                        if(xdx < 1 || W < xdx) { count = -1; break; }
                        for (int dy = -1; dy <= 1; dy++)
                        {
                            if ((yy + dy) < 1 || H < (yy + dy)) { count = -1; break; }
                            if (d.ContainsKey(yy + dy) && d[yy + dy].ContainsKey(xdx)) count++;
                        }
                    }
                    if (count != -1) { ans[count]++; ans[count - 1]--; }
                }
            }
        }
        ans.ToList().ForEach(Console.WriteLine);
    }
    public static void Main()
    {
        var sw = new System.IO.StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
        Console.SetOut(sw);
        Solve();
        Console.Out.Flush();
    }
}
public class Input
{
    private static Queue<string> q = new Queue<string>();
    private static void Confirm() { if (q.Count == 0) foreach (var s in Console.ReadLine().Split(' ')) q.Enqueue(s); }
    public static int NextInt() { Confirm(); return int.Parse(q.Dequeue()); }
    public static long NextLong() { Confirm(); return long.Parse(q.Dequeue()); }
    public static char NextChar() { Confirm(); return char.Parse(q.Dequeue()); }
    public static string NextString() { Confirm(); return q.Dequeue(); }
    public static double NextDouble() { Confirm(); return double.Parse(q.Dequeue()); }
    public static int[] LineInt() { return Console.ReadLine().Split(' ').Select(int.Parse).ToArray(); }
    public static long[] LineLong() { return Console.ReadLine().Split(' ').Select(long.Parse).ToArray(); }
    public static string[] LineString() { return Console.ReadLine().Split(' ').ToArray(); }
    public static double[] LineDouble() { return Console.ReadLine().Split(' ').Select(double.Parse).ToArray(); }
}