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++14 (Clang 3.8.0) (judge verdict: Wrong Answer)

#include <vector>
#include <iostream>
#include <algorithm>
#include <string>
#include <sstream>
#include <functional>
#include <unordered_map>

#include <cassert>
using namespace std;


long long f_hs(long long a,long long b){
    return a*1000000000+b;
}
pair<long long,long long> i_hs(long long k){
    return pair<long long,long long>(k/1000000000,k%1000000000);
}
 
std::unordered_map<long long,bool> blacks, well_known;
std::vector<long long> result;

int main(void){
	result.assign(10,0);

	long long h=0,w=0,n=0;
	cin >> h>>w>>n;
	for(int ni=0;ni<n;ni++){
		long long ia,ib;
		cin >> ia>>ib;
		blacks[ f_hs(ia-1,ib-1) ] = true;
	}

	for(auto bitr : blacks){
		auto ip = i_hs(bitr.first);
		auto ia=ip.first,ib=ip.second;

		for(auto ca=ia-1;ca<=ia+1;ca++){
			if(ca+1>=h || ca-1<0){continue;}
			for(auto cb=ib-1;cb<=ib+1;cb++){
				if(cb+1>=h || cb-1<0){continue;}
				if(well_known[f_hs(ca,cb)]){continue;}

				long long cnt=0;
				for(auto fa=ca-1;fa<=ca+1;fa++){
					for(auto fb=cb-1;fb<=cb+1;fb++){
						if(blacks[f_hs(fa,fb)]){cnt++;}
					}
				}
				result[cnt]++;
				well_known[f_hs(ca,cb)]=true;
			}
		}
	}

	result[0] = (h-2)*(w-2);
	for(int i=1;i<=9;++i){ result[0]-=result[i];}
	for(int i=0;i<=9;++i){ cout << result[i] << endl; }

	return 0;
}