The ocean can be represented as a matrix $A$ of size $n \times n$. There are some storms, they are represented as character `X`. The storms have the radius of $r$. In other words, if a storm is at $(i, j)$, every $(i', j')$ with $|i-i'|+|j-j'| \le r$ will be affected.
Count the number of unaffected areas.
### Input
- The first line contains 2 integers $n, r$.
- The next $n$ lines represents $A$, each line contains a string of length $n$ consisting only characters `.` and `X`.
### Output
- Print the number of unaffected areas.
### Constraints
- $1 \le n \le 5000$.
### Example
Input:
```
4 1
..X.
X...
....
..X.
```
Output:
```
4
```
