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 (GCC 5.4.1) (judge verdict: Accepted)

#include<iostream>
#include<vector>
#include<string>
#include<array>
#include<algorithm>
#include<list>
#include<cmath>
#include<iomanip>
#include<queue>
#include<functional>
#include<climits>
#include<iterator>
#include<unordered_set>
#include<unordered_map>
#include<map>
#include<set>
using namespace std;

const double pi=4*atan(1.0);

constexpr long long mod=static_cast<long long>(1e9+7);

using cEdges=vector<vector<int>>;

int main() {
	long long H,W,N;
	cin>>H>>W>>N;

	auto compare=[](pair<int,int> x,pair<int,int> y)->bool{return x.first<y.first?true:(x.first==y.first?x.second<y.second:false);};
	set<pair<int,int>,decltype(compare)> Set(compare);
	for(int i=0;i<N;++i){
		int a,b;
		cin>>a>>b;
		--a,--b;
		Set.insert(make_pair(a,b));
	}

	array<long long,10> ans;
	ans.fill(0);

	for(const auto& p:Set){
		bool arr[5][5];
		for(int i=0;i<5;++i){
			for(int j=0;j<5;++j){
				if(Set.find(make_pair(p.first+i-2,p.second+j-2))!=Set.end())arr[i][j]=true;
				else arr[i][j]=false;
			}
		}

		for(int i=0;i<3;++i){
			for(int j=0;j<3;++j){
				if(0<=p.first+i-2 && p.first+i<H && 0<=p.second+j-2 && p.second+j<W){
					int num=0;
					for(int k=0;k<3;++k){
						for(int l=0;l<3;++l){
							if(arr[i+k][j+l])++num;
						}
					}
					++ans[num];
				}
			}
		}
	}
	long long sum=0;
	for(int i=1;i<10;++i){
		ans[i]/=i;
		sum+=ans[i];
	}
	
	ans[0]=(H-2)*(W-2)-sum;
	for(const auto& val:ans)
		cout<<val<<endl;

	return 0;
}