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<bits/stdc++.h>
#define mod 1000000007
#define ll long long int
#define ar(n) array<int,n>
#define mp make_pair
using namespace std;

int main()
{
	ios::sync_with_stdio(false);
	cin.tie(NULL);
	ll h,w,n;
	cin>>h>>w>>n;
	set<ar(2)> st;
	set<ar(2)> s;
	ll ans [10]={0};
	ans [0]= (h-2)*(w-2);
	for(int i = 0; i<n; i++)
	{
		int a,b;
		cin>>a>>b, --a,--b;
		st.insert({a,b});
		for(int j =0; j<3; j++)
			for(int k =0; k<3; k++)
			{
				int x = a-j;
				int y = b-k;
				if(x<0 || y<0 || x+3>h || y+3>w)continue;
				s.insert({x,y});
			}
	}
	for(auto it: s)
	{
		int cnt =0;
		for(int i =0; i<3; i++)
			for(int  j =0; j<3; j++)
			{
				int x = it[0]+i;
				int y = it[1]+j;
				if(st.count({x,y}))cnt++;
			}
		ans[0]--;
		ans[cnt]++;
	}
	for(int i =0; i<10; i++)
		cout<<ans[i]<<endl;
	return 0;
}