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: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;
map<pair<int, int>, int> mp;
int main(){
  cin.tie(0);
  ios::sync_with_stdio(false);
  int H, W, N;
  cin >> H >> W >> N;
  int count[10];
  for(int i = 0; i < 10; i++){count[i] = 0;}
  for(int i = 0; i < N; i++){
    int a, b;
    cin >> a >> b;
    pair<int, int> p = pair<int, int>(a, b);
    for(int dh = -1; dh < 2; dh++){
      for(int dw = -1; dw < 2;dw++){
        int h = a + dh;
        int w = b + dw;
        if (!((h > 1) && (h < H) && (w > 1) && (w < W))){continue;}
        pair<int,int> p = pair<int, int>(h,w);
        if(mp[p]){
          mp[p] += 1;
        }
        else{
          mp[p] = 1;
        }
      }
    }
  }
  for(map<pair<int,int>,int>::iterator itr = mp.begin(); itr != mp.end(); itr++){
    count[itr->second] += 1;
  }
  int max = (H - 2) * (W - 2);
  for(int i = 1; i < 10; i++){
    max -= count[i];
  }
  count[0] = max;
  for(int i = 0; i < 10; i++){
    cout << count[i] << endl;
  }
}