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: Wrong Answer)

#include <iostream>
#include <algorithm>
#include <set>

using P=std::pair<int,int>;
using ll=long long int;

constexpr int dx[]={1,0,-1,-1,-1,0,1,1},
dy[]={1,1,1,0,-1,-1,-1,0};

int h,w;
int n;

std::set<P> set,used;
ll ans[10];

void solve(int x,int y,bool flag) {
	int res=flag;
	used.emplace(P(x,y));
	for(int i=0;i<8;++i){
		int tx=x+dx[i];
		int ty=y+dy[i];
		if(0<=tx&&tx<w&&
			0<=ty&&ty<h){
			if(set.count(P(tx,ty)))
				++res;
			if(1<=tx&&tx<w-1&&
			1<=ty&&ty<h-1&&
			flag&&!used.count(P(tx,ty)))
				solve(tx,ty,set.count(P(tx,ty)));
		}
	}
	if(res!=0){
		++ans[res];
		--ans[0];
	}
	std::cout<<x<<' '<<y<<' '<<res<<std::endl;
}

int main(){
	std::cin>>h>>w>>n;
	int a,b;
	for(int i=0;i<n;++i){
		std::cin>>a>>b;
		--a;
		--b;
		set.emplace(b,a);
	}
	ans[0]=((ll)h-2)*((ll)w-2);
	for(auto it=set.cbegin();it!=set.cend();++it){
		if(!used.count(P(it->first,it->second))){
			if(1<=it->first&&it->first<w-1&&
				1<=it->second&&it->second<h-1)
				solve(it->first,it->second,true);
		}
	}
	for(int i=0;i<10;++i)
		std::cout<<ans[i]<<std::endl;
	return 0;
}