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;

#define int long long
#define For(i, a, b) for(int i = a; i <= b; ++ i)
#define fi first
#define se second

typedef pair < int, int > ii;

int r, c, n;
int ans[10];
map < ii, int > ma;

signed main(){
	ios_base::sync_with_stdio(false); cin.tie(0);
	cin >> r >> c >> n;
	For(k, 1, n){
		int x, y; cin >> x >> y;
		For(i, - 2, 0) For(j, -2, 0)
			if(1 <= x + i && x + i <= r - 2 && 1 <= y + j && y + j <= c - 2) ma[ii(x + i, y + j )] ++;
	}
	for(auto i : ma) ans[i.se] ++;
	ans[0] = (r - 2) * (c - 2);
	For(i, 1, 9)  ans[0] -= ans[i];
	For(i, 0, 9) cout << ans[i] << "\n";
}
/*
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
*/