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: Time Limit Exceeded)

#include <bits/stdc++.h>
#define SVLL set<vector<LL>>
#define VLL vector<LL>
using namespace std;
typedef long long LL;
int countBlack(SVLL black, LL a, LL b, LL h, LL w){
    int count = 0;
    for(int i = a - 1; i <= a + 1; i++){
        for(int j = b - 1; j <= b + 1; j++){
            count += black.find(VLL {i, j}) != black.end();
        }
    }
    return count;
}
void updateBox(SVLL black, LL *box, LL a, LL b, LL h, LL w){
    for(int i = max((LL)2, a - 1); i <= min(h - 1, a + 1); i++){
        for(int j = max((LL)2, b - 1); j <= min(w - 1, b + 1); j++){
            int t = countBlack(black, i, j, h, w);
            box[t]--;
            box[t + 1]++;
        }
    }
}
int main(){
    LL h, w, n, a, b;
    LL box[10] = {};
    SVLL black;

    cin >> h >> w >> n;
    box[0] = (h - 2) * (w - 2);
    for(int i = 0; i < n; i++){
        cin >> a >> b;
        updateBox(black, box, a, b, h, w);
        black.insert(VLL {a, b});
    }
    for(auto v: box){
        cout << v << endl;
    }
    return 0;
}