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 int long long

using namespace std;
typedef pair<int,int> ii;
map<ii,int> mp;
set<ii> s;
int dx[] = {0,0,0,-1,-1,-1,-2,-2,-2};
int dy[] = {0,-1,-2,0,-1,-2,0,-1,-2};
int ans[10];

signed main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(0); cout.tie(0);

    int n,m,q;
    cin>>n>>m>>q;

    while(q--)
    {
        int x,y;
        cin>>x>>y;

        for(int i=0;i<9;i++)
        {
            if(x+dx[i]<1||x+dx[i]>n-2)
                continue;
            if(y+dy[i]<1||y+dy[i]>m-2)
                continue;
            mp[ii(x+dx[i],y+dy[i])] ++;
            s.insert(ii(x+dx[i],y+dy[i]));
        }
    }

    long long res = (n-2)*(m-2);
    for(auto it:s)
    {
        int x = it.first;
        int y = it.second;
        //cout<<x<<" "<<y<<" = "<<mp[ii(x,y)]<<'\n';

        ans[mp[ii(x,y)]]++;
        res --;
    }

    ans[0] = res;
    for(int i=0;i<=9;i++)
        cout<<ans[i]<<'\n';
}