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.Text;

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

class Sol{
	public void Solve(){
		
		
		int[] sum = new int[10];
		HashSet<long> Hs = new HashSet<long>();
		HashSet<long> Hp = new HashSet<long>();
		for(int i=0;i<N;i++){
			Hp.Add(enc(A[i],B[i]));
			for(int ii=-2;ii<=0;ii++){
				if(!InRange(A[i]+ii,1,H))continue;
				if(!InRange(A[i]+ii+2,1,H))continue;
				for(int jj=-2;jj<=0;jj++){
					if(!InRange(B[i]+jj,1,W))continue;
					if(!InRange(B[i]+jj+2,1,W))continue;
					Hs.Add(enc(A[i]+ii,B[i]+jj));
				}
			}
		}
		
		foreach(var sq in Hs){
			int r = decR(sq);
			int c = decC(sq);
			int cnt = 0;
			for(int i=0;i<3;i++){
				for(int j=0;j<3;j++){
					if(Hp.Contains(enc(r+i,c+j))){
						cnt++;
					}
				}
			}
			sum[cnt]++;
		}
		
		long[] ans = new long[10];
		for(int i=0;i<10;i++){
			ans[i] = sum[i];
		}
		ans[0] = ((long)H-2)*((long)W-2);
		for(int i=1;i<10;i++)ans[0] -= ans[i];
		
		
		
		for(int i=0;i<10;i++){
			Console.WriteLine(ans[i]);
		}
		
	}
	int H;
	int W;
	int N;
	int[] A,B;
	
	bool InRange(int n,int l,int u){
		return l <= n && n <= u ;
	}
	
	long enc(int r,int c){ return ((long)r<<32)+(long)c ;}
	int decR(long s){ return (int)(s>>32);}
	int decC(long s){ return (int)(s&0xFFFFFFFF);}
	
	public Sol(){
		var d = ria();
		H = d[0]; W = d[1]; N = d[2];
		A = new int[N];
		B = new int[N];
		for(int i=0;i<N;i++){
			var dd = ria();
			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));}
}