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 <algorithm>
#include <functional>
#include<vector>
#include<math.h>
#include<bitset>
#include<string>
#include <deque>
#include<queue>
#include<map>


long long int Q[10];
using namespace std;
typedef pair <long long int, long long int> Edge;
Edge D[900008];

int main() {
	long long int n = 0;
	long long int k = 0;
	long long int H, W, N;
	cin >> H >> W >> N;
	long long int a, b;
	for (int i = 0; i < N; i++) {
		cin >> a >> b;
		if (a != 1 && b != 1 && a != H && b != W) {
			D[k].first = a;
			D[k].second = b;
			
			k++;
		}
		if (a - 1>1&&b!=1&&b!=W) {
			D[k].first = a - 1;
			D[k].second = b;
			
			k++;
		}
		else n++;
		if (a + 1 < H&&b!=1&&b!=W) {
			D[k].first = a + 1;
			D[k].second = b;
			
			k++;
		}
		else n++;
		if (b - 1 > 1&&a!=H&&a!=1) {
			D[k].first = a;
			D[k].second = b - 1;
		
			k++;
		}
		else n++;
		if (b + 1 < W&&a!=1&&a!=H) {
			D[k].first = a;
			D[k].second = b + 1;
			
			k++;
		}
		else n++;
		if (a - 1 >1 && b - 1 >1) {
			D[k].first = a - 1;
			D[k].second = b - 1;
			
			k++;
		}
		else n++; 
		if (a + 1 <H && b + 1<W) {
			D[k].first = a + 1;
			D[k].second = b + 1;
			
			k++;
		}
		else n++;
		if (a - 1 >1 && b + 1 <W) {
			D[k].first = a - 1;
			D[k].second = b + 1;
			
			k++;
		}
		else n++;
		if (a + 1 <H && b - 1 >1) {
			D[k].first = a + 1;
			D[k].second = b - 1;
			
			k++;
		}
		else n++;
	}
	sort(D, D +k,greater<Edge>());
	
	
	long long int d = 0;
	for (int i = 0; i <k ; i++) {


		if (D[i].first == D[i + 1].first&&D[i].second == D[i + 1].second) {
			d++;
		}
		else {
			Q[d+1]++;
			d = 0;
		}
	}
	int q = 0;
	for (int i = 0; i < 10; i++) {
		q += Q[i];
	}
	Q[0] = H * W - q-2*H-2*W+4;


	for (int i = 0; i < 10; i++) {
		cout << Q[i] << endl;
	}

	return 0;
}