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.

Examples

Input

4 5 8
1 1
1 4
1 5
2 3
3 1
3 2
3 4
4 4


Output

0
0
0
2
4
0
0
0
0
0


Input

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


Output

4
26
22
10
2
0
0
0
0
0


Input

1000000000 1000000000 0


Output

999999996000000004
0
0
0
0
0
0
0
0
0
#include <bits/stdc++.h>

using namespace std;
typedef long long ll;

const int N=2e5+100;
typedef pair<int,int>pa;
map<pa,int>mp;
ll ans[10];
int main()
{
    ios::sync_with_stdio(0);cin.tie(0);
    int h,w,n;
    cin>>h>>w>>n;
    for(int i=1;i<=n;i++){
        int a,b;
        cin>>a>>b;
        for(int i=-2;i<=0;i++)
         for(int j=-2;j<=0;j++){
             int aa=a+i;
             int bb=b+j;
             if(aa>=1&&aa<=h-2&&bb>=1&&bb<=w-2){
                mp[make_pair(aa,bb)]++;
             }
        }
    }
    ans[0]=1ll*(h-2)*(w-2);
    for(auto it=mp.begin();it!=mp.end();it++){
        ans[it->second]++;
        ans[0]--;
    }
    for(int i=0;i<=9;i++){
        cout<<ans[i]<<endl;
    }
    return 0;
}
