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 <sstream>
#include <cstdio>
#include <cmath>
#include <vector>
#include <string>
#include <algorithm>
#include <map>
#include <set>
#include <queue>

#ifdef _DEBUG
#define DMP(x) cerr << #x << ": " << x << "\n"
#else
#define DMP(x) ((void)0)
#endif

using namespace std;
typedef long long lint;

int main() {

	cin.tie(nullptr);
	ios::sync_with_stdio(false);

	lint H, W, N;
	cin >> H >> W >> N;

	vector<pair<int, int>> blk(N);
	for (int i = 0; i < N; i++) cin >> blk[i].first >> blk[i].second;

	map<lint, lint> sqmap;
	vector<int> dxdy{-1, 0, 1};

	for (int i = 0; i < N; i++) {

		for (const auto &dx : dxdy) {
			for (const auto &dy : dxdy) {

				lint x = blk[i].second + dx;
				lint y = blk[i].first + dy;

				if (1 < x && x < W && 1 < y && y < H) {
					sqmap[(y - 1) * W + x - 1]++;
				}

			}
		}

	}

	vector<lint> ans(10);
	for (const auto &elem : sqmap) ans[elem.second]++;

	ans[0] = (H - 2) * (W - 2) - (lint)(sqmap.size());

	for (const auto &elem : ans) cout << elem << "\n";

	return 0;
}