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++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;
#define rep(i,n) for(int i=0; i<(n); i++)
#define FOR(i,a,b) for(int i=a; i<=b; i++)
#define all(v) v.begin(), v.end()
#define F first
#define S second
#define INF 1000000000000
#define MOD 10000007
typedef long long ll;
//
int main(){
   int h,w,n;cin>>h>>w>>n;
   vector<pair<int,int>> vp,check;
   rep(i,n){
      int a,b;cin>>a>>b;
      vp.push_back(pair<int,int>(a,b));
   }
   rep(i,n){
      int x=vp[i].F,y=vp[i].S;
       rep(a,3){
            rep(b,3){
               if(x-a>0&&y-b>0&&x-a+2<=h&&y-b+2<=w){
                  check.push_back(pair<int,int>(x-a,y-b));
               }
            }
         }
      
   }
   map<pair<int,int>,int> mp;
   for(auto e:check){
      mp[e]++;
   }
   sort(all(check));
   check.erase(unique(all(check)),check.end());
   vector<ll> count;
   FOR(i,1,9){
      ll a=0;
      for(auto e:check){
         if(mp[e]==i){
            a++;
         }
      }
      count.push_back(a);
   }
   int aa=(h-2)*(w-2);
   rep(i,count.size()){
      aa-=count[i];
   }
   cout<<aa<<endl;
   for(auto e:count)cout<<e<<endl;

}