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 System.Text;
using System.Threading.Tasks;

namespace ARC061D {
    class Program {
        static void Main(string[] args) {
            int[] input = Console.ReadLine().Split(' ').Select(s => int.Parse(s)).ToArray();
            int H = input[0];
            int W = input[1];
            int N = input[2];
            List<long> list = new List<long>();
            for (int i = 0; i < N; i++) {
                int[] inputb = Console.ReadLine().Split(' ').Select(s => int.Parse(s)).ToArray();
                for (int j = inputb[0] - 1; j <= inputb[0] + 1; j++) {
                    for (int k = inputb[1] - 1; k <= inputb[1] + 1; k++) {
                        if (j >= 2 && j <= H - 1 && k >= 2 && k <= W - 1) {
                            list.Add((long)(j - 1) * W + k);
                        }
                    }
                }
            }
            list.Sort();
            long temp = 0;
            int num = 0;
            long[] ans = new long[10];
            ans[0] = (long)(H - 2) * (W - 2);
            for (int i = 0; i < list.Count; i++) {
                if (list[i] != temp) {
                    if (temp != 0) {
                        ans[num]++;
                        ans[0]--;
                    }
                    temp = list[i];
                    num = 1;
                } else {
                    num++;
                }
            }
            ans[num]++;
            ans[0]--;
            for (int i = 0; i < 10; i++) {
                Console.WriteLine(ans[i]);
            }
        }
    }
}