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<iostream>
#include<vector>
#include<set>
#include<algorithm>

using namespace std;

struct Point{
  long long  xy;
  int num;
  bool operator==(const Point a) const {
    return xy == a.xy;
  }
  bool operator< (const Point& a) const {
    return xy < a.xy;
  }
};

int main(int argc, char* argv[]){
  long long h,w,n;
  cin >> h >> w >> n;
  set<Point> p;
  for(int i = 0 ; i < n ; i++){
    int a,b;
    cin >> a >> b;
    a--; b--;
    for(int s = -1; s < 2; s++){
      for(int t = -1; t < 2; t++){
        if(a+s<1 || a+s >= h-1 || b+t < 1 || b+t >= w-1) continue;
        int x = a+s;
        int y = b+t;
        auto it = p.find((Point){x*1000000007+y, 0});
        if(it != p.end()){
          int tmp = it->num;
          p.erase(it);
          p.insert({x*1000000007+y, tmp+1});
        }
        else{
          p.insert((Point){x*1000000007+y, 1});
          // cout << x << " " << y << endl;
        }
      }
    }
  }
  vector<long long> ans(10, 0);
  ans[0] = (h-2)*(w-2);
  for(auto v:p){
    ans[0]--;
    ans[v.num]++;
  }
  for(int i = 0; i < 10; i++){
    cout << ans[i] << endl;
  }
}