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 Java8 (OpenJDK 1.8.0) (judge verdict: Time Limit Exceeded)

import java.util.*;
import java.lang.*;
import java.io.*;
class Counter<T> extends HashMap<T,Integer>{
    public Counter(){
        super();
    }
    public Integer get(Object elm){
        return getOrDefault(elm,0);
    }
    public void add(T elm){
        put(elm, get(elm)+1);
    }
    
}
class Pair<E,F>{
    E first;
    F second;
    public Pair(E first, F second){
        this.first=first;
        this.second=second;
    }
    public E getFirst(){return first;}
    public F getSecond(){return second;}
    public String toString(){
        return "<"+first.toString()+","+second.toString()+">";
    }
    public int hashCode(){
        return first.hashCode()+second.hashCode()+2;
    }
    public boolean equals(Object obj) {
        if (this == obj)
            return true;
        if (obj == null)
            return false;
        if (getClass() != obj.getClass())
            return false;
        Pair another = (Pair) obj;
        return this.getFirst().equals(another.getFirst())&&this.getSecond().equals(another.getSecond());
    }
}

public class Main {
    
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        long H = sc.nextLong();
        long W = sc.nextLong();
        int N = sc.nextInt();
        Counter<Pair<Long,Long>> count = new Counter<>();
        for(int n=0;n<N;n++){
        	long A = sc.nextLong();
        	long B = sc.nextLong();
        	for(long a=A-1;a<=A+1;a++)for(long b=B-1;b<=B+1;b++){
        	    if(a>=2 && a<=H-1 && b>=2 && b<=W-1)
        	        count.add(new Pair<Long,Long>(a,b));
        	}
        }
        //System.out.println(count);
        long[] ans = new long[10];
        ans[0] = (H-2)*(W-2);
        for(Pair<Long,Long> p:count.keySet()){
        	ans[count.get(p)]++;
        	ans[0]--;
        }
        for(int i=0;i<10;i++) System.out.println(ans[i]);
        
    }
}