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

class TEST{
	static void Main(){
		Sol mySol =new Sol();
		mySol.Solve();
	}
}

class Sol{
	public void Solve(){
		
		
		long[] sum = new long[10];
		sum[0] = (H-2)*(W-2);
		HashSet<long> Hs = new HashSet<long>();
		for(int i=0;i<N;i++){
			
			for(int rc=-2;rc<=0;rc++){
				if(!InRange(rc+A[i],1,H))continue;
				if(!InRange(rc+A[i]+2,1,H))continue;
				for(int cc=-2;cc<=0;cc++){
					if(!InRange(cc+B[i],1,W))continue;
					if(!InRange(cc+B[i]+2,1,W))continue;
					
					long br = A[i] + rc;
					long bc = B[i] + cc;
					int cnt = 1;
					for(int ii=0;ii<3;ii++){
						for(int jj=0;jj<3;jj++){
							if(br+ii == A[i] && bc+jj == B[i])continue;
							if(Hs.Contains(enc(br+ii,bc+jj)))cnt++;
						}
					}
					sum[cnt]++;
					sum[cnt-1]--;
				}
			}
			Hs.Add(enc(A[i],B[i]));
		}
		
		for(int i=0;i<10;i++){
			Console.WriteLine(sum[i]);
		}
		
	}
	long H;
	long W;
	int N;
	long[] A,B;
	
	bool InRange(long n,long l,long u){
		return l <= n && n <= u ;
	}
	
	long enc(long r,long c){ return (r*1000000200L)+c ;}
	long decR(long s){ return s/1000000200L;}
	long decC(long s){ return s%1000000200L;}
	
	public Sol(){
		var d = ria();
		H = d[0]; W = d[1]; N = d[2];
		A = new long[N];
		B = new long[N];
		for(int i=0;i<N;i++){
			var dd = rla();
			A[i] = dd[0];
			B[i] = dd[1];
		}
	}
	
	static String rs(){return Console.ReadLine();}
	static int ri(){return int.Parse(Console.ReadLine());}
	static long rl(){return long.Parse(Console.ReadLine());}
	static double rd(){return double.Parse(Console.ReadLine());}
	static String[] rsa(char sep=' '){return Console.ReadLine().Split(sep);}
	static int[] ria(char sep=' '){return Array.ConvertAll(Console.ReadLine().Split(sep),e=>int.Parse(e));}
	static long[] rla(char sep=' '){return Array.ConvertAll(Console.ReadLine().Split(sep),e=>long.Parse(e));}
	static double[] rda(char sep=' '){return Array.ConvertAll(Console.ReadLine().Split(sep),e=>double.Parse(e));}
}