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: Runtime Error)

#include <bits/stdc++.h>
#define rep(i,n)for(long long i=0;i<(n);i++)
using namespace std;
typedef long long ll;
typedef pair<int,int> P;

const int MOD=1000000007;
const int INF=0x3f3f3f3f;
const ll INFL=0x3f3f3f3f3f3f3f3f;

char maze[50][50];
int  dist[50][50];

int dx[4]={1,0,-1,0},dy[4]={0,1,0,-1};

int main(){
  cin.tie(nullptr);
  ios::sync_with_stdio(false);
  
  ll h,w,n;
  cin>>h>>w>>n;
  
  int field[h][w];
  rep(i,h){
    rep(j,w){
      field[i][j]=0;
    }
  }
  
  rep(i,n){
    ll a,b;
    cin>>a>>b;
    a--;
    b--;
    field[a][b]=1;
  }
  ll s1[h][w+1];
  rep(i,h){
    s1[i][0]=0;
  }
  rep(i,h){
    rep(j,w){
      s1[i][j+1]=s1[i][j]+field[i][j];
    }
  }
  ll s3[h][w-2];
  rep(i,h){
    rep(j,w-2){
      s3[i][j]=s1[i][j+3]-s1[i][j];
    }
  }
  ll s2[w-2][h];
  rep(i,w-2){
    rep(j,h){
      s2[i][j]=s3[j][i];
    }
  }
  
  ll H=w-2,W=h;
  ll s4[H][W+1];
  rep(i,H){
    s4[i][0]=0;
  }
  rep(i,H){
    rep(j,W){
      s4[i][j+1]=s4[i][j]+s2[i][j];
    }
  }
  ll s6[H][W-2];
  rep(i,H){
    rep(j,W-2){
      s6[i][j]=s4[i][j+3]-s4[i][j];
    }
  }
  ll s7[W-2][H];
  ll ans[10]={};
  rep(i,W-2){
    rep(j,H){
      s7[i][j]=s6[j][i];
      ans[s7[i][j]]++;
    }
  }
  rep(i,10){
    cout<<ans[i]<<endl;
  }
}