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: Accepted)

#include <bits/stdc++.h>
#define rep(i,n) for(int (i)=0;(i)<(n);(i)++)
#define repr(i,from,to) for(int (i)=(from);(i)<(to);(i)++)
// const bool debug=true;
const bool debug=false;
#define DEBUG if(debug==true)
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
const ll MOD = 1000000007;
int main(void) {
    set<pair<int, int>> st,checked;
    ll h,w,n;
    cin>>h>>w>>n;
    rep(i,n){
        int a,b;cin>>a>>b;
        a--;b--;
        st.emplace(a,b);
    }
    vector<ll> count(10,0);
    function<int(int,int)> check = [&](int x,int y){
        if(x<2||y<2||x>=h||y>=w){return -1;}
        int cnt = 0;
        repr(i,-2,1){
            repr(j,-2,1){
                if(st.find(pair<int, int>(x+i,y+j))!=st.end()){
                    cnt++;
                }
            }
        }
        DEBUG{
            printf("cnt: %d\n",cnt);;
        }
        return cnt;
    };
    for(auto x:st){
        repr(i,-2,3){
            repr(j,-2,3){
                if(checked.find(pair<int, int>(x.first+i,x.second+j))==checked.end()){
                    int tmp = check(x.first+i,x.second+j);
                    if(tmp!=-1){
                        count[tmp]++;
                    }
                    checked.emplace(x.first+i,x.second+j);
                }
            }
        }
    }
    ll res0 = (h-2)*(w-2);
    repr(i,1,10){
        res0 -= count[i];
    }
    cout << res0 << endl;
    repr(i,1,10){
        cout << count[i] << endl;
    }
    return 0;
}