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;
using System.Collections.Generic;
using System.Linq;
using System.IO;
using System.Text;

class Myon
{
    public Myon() { }
    public static int Main()
    {
        new Myon().calc();
        return 0;
    }

    Scanner cin;

    int H, W, N;
    int[] a, b;

    Dictionary<long, bool> dic = new Dictionary<long, bool>();
    Dictionary<long, bool> dic2 = new Dictionary<long, bool>();

    const int MAX = 7654321;
    bool[] minitable = new bool[MAX];
    bool[] minitable2 = new bool[MAX];

    long[] ans;
    public void calc()
    {
        cin = new Scanner();
        H = cin.nextInt();
        W = cin.nextInt();
        N = cin.nextInt();
        a = new int[N];
        b = new int[N];
        
        for (int i = 0; i < N; i++)
        {
            a[i] = cin.nextInt() - 1;
            b[i] = cin.nextInt() - 1;
            dic[gethash(a[i], b[i])] = true;
            minitable[(int)((a[i] * 1235641L + b[i] * 124517L) % MAX)] = true;
        }

        long allans = (H - 2L) * (W - 2L);
        ans = new long[10];

        for (int i = 0; i < N; i++)
        {
            for (int vy = -2; vy <= 0; vy++)
            {
                for (int vx = -2; vx <= 0; vx++)
                {
                    int by = a[i] + vy;
                    int bx = b[i] + vx;
                    if (!inside(by, bx)) continue;
                    if (!inside(by + 2, bx + 2)) continue;
                    if (checkhash2(by,bx)) continue;
                    int cnt = 0;
                    for (int dy = 0; dy < 3; dy++)
                    {
                        for (int dx = 0; dx < 3; dx++)
                        {
                            int y = by + dy;
                            int x = bx + dx;
                            if (checkhash(y, x)) cnt++;
                        }
                    }
                    allans--;
                    ans[cnt]++;
                    dic2[gethash(by, bx)] = true;
                    minitable2[(int)((by * 1235641L + bx * 124517L) % MAX)] = true;

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

    bool inside(int y, int x)
    {
        return y >= 0 && x >= 0 && y < H && x < W;
    } 

    long gethash(int a, int b)
    {
        return ((long)a << 31) + b;
    }


    bool checkhash(int a, int b)
    {
        int minihash = (int)((a * 1235641L + b * 124517L) % MAX);
        if (!minitable[minihash]) return false;
        return dic.ContainsKey(gethash(a, b));
    }



    bool checkhash2(int a, int b)
    {
        int minihash = (int)((a * 1235641L + b * 124517L) % MAX);
        if (!minitable2[minihash]) return false;
        return dic2.ContainsKey(gethash(a, b));
    }
}


class Scanner
{
    string[] s;
    int i;

    char[] cs = new char[] { ' ' };

    public Scanner()
    {
        s = new string[0];
        i = 0;
    }

    public string next()
    {
        while (i >= s.Length)
        {
            string st = Console.ReadLine();
            while (st == "") st = Console.ReadLine();
            s = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
            i = 0;
        }
        return s[i++];
    }

    public int nextInt()
    {
        return int.Parse(next());
    }

    public long nextLong()
    {
        return long.Parse(next());
    }

    public double nextDouble()
    {
        return double.Parse(next());
    }

}