Goal
You have an NxN grid consisting of white and black square pixels. White pixels are represented by . and black pixels are represented by #. The pixels on the outer edges of the grid are all white.
The black pixels form a single connected polygon without any holes (no group of white pixels is completely surrounded by black pixels).
How many sides does it have?
To be clear, the black area is a single region composed of one or more unit squares, and thus, all of its angles are 90 or 270 degree angles.
Input
Line 1: An integer N - the size of the grid
Next N lines: - the rows of the grid
Output
Line 1: The number of sides the black region has.
Constraints
- 3 ≤ N ≤ 10
- The pixels on the outer edge of the grid are all white.
- The black pixels form a single connected region.
- No group of white pixels is completely surrounded by black pixels.
Example
Input
4
....
.##.
.##.
....
