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 rep(i,n) for(int i=0;i<(n);++i)
#define ALL(A) A.begin(), A.end()

using namespace std;

typedef long long ll;
typedef pair<int, int> P;

int main()
{
	ios_base::sync_with_stdio(0);
	cin.tie(0);

	int H, W, N; cin >> H >> W >> N;
	vector<int> a(N, 0), b(N, 0);
	rep (i, N){
		cin >> a[i] >> b[i];
		--a[i], --b[i];
	} // end rep

	map<ll,int> cnt;cnt.clear();
	rep (i, N){
		int p = a[i], q = b[i];
		rep (k, 3){
			rep (l, 3){
				if (p - k < 0 || q - l < 0 || p - k + 2 >= H || q - l + 2 >= W) continue;
				++cnt[(ll)(p - k) * (ll)W + (ll)(q - l)];
			} // end rep
		} // end rep
	} // end rep

	vector<ll> res(10,0LL);
	ll total = 0LL;
	map<ll,int>::iterator it = cnt.begin();
	for(; it != cnt.end(); ++it){
		ll p = (*it).first;
		int c = (*it).second;
//		cerr << "pos:(" << (p/W) << ',' << (p%W) << ")" << " c: " << c << endl;
		++res[c];
		++total;
	} // end for

	res[0] = ((ll)H - 2LL)*((ll)W - 2LL) - total;
	rep (i, 10){
		cout << res[i] << endl;
	} // end rep

	return 0;
}