+ محدودیت زمان: ۱ ثانیه + محدودیت حافظه: ۲۵۶ مگابایت ---------- A histogram is a simple rectilinear polygon $H$ (i.e. the interior angle at each vertex is either $90$° or $270$°) that has a horizontal edge seeing every point $q$ inside (i.e. the interior or the boundary of) $H$. Here, we say that an edge sees a point $q \in H$ if there is a vertical segment $s$ connecting $e$ to $q$ that is lying inside $H$. Let $H$ be a histogram with $n$ vertices, and consider a decomposition $R$ of $H$ into rectangles whose sides are vertical or horizontal. The vertices of the rectangles need not all be vertices of $H$: it is allowed to introduce additional vertices, on the boundary of $H$ and/or in its interior. The stabbing number of a horizontal or vertical segment $s$ inside $H$ with respect to such a decomposition $R$ is the number of rectangles from $R$ whose interior (not just their boundaries) are intersected by $s$. The stabbing number of $R$ is the maximum stabbing number of any horizontal or vertical segment $s$ that lies inside $H$. The goal is to compute a decomposition $R$ with the minimum stabbing number. # ورودی The first line of the input contains two positive integers $m$ and $n$ ($1 \leq m,n \leq 50$) denoting the number of rows and the number of columns of the table illustrating the histogram, respectively. The next $m$ lines, each contains exactly n characters. `*`s denote the boundary of the histogram. The rest is filled with dots (`.`). Each edge of the histogram contains at least three `*`s. You can assume the given histogram has at least four and at most 16 edges, and edges do not overlap, intersect or touch each other; i.e. each `*` is adjacent to exactly two other `*` characters. # خروجی Print the stabbing number of the given histogram in one line. # مثال‌ها ## ورودی نمونه ۱ ``` 10 13 .....****.... .....*..*.... .....*..***.. .....*....*.. .....*....*** ...***......* ...*........* ****........* *...........* ************* ```` ## خروجی نمونه ۱ ``` 2 ```` ## ورودی نمونه ۲ ``` 8 15 ............... .........*****. ....***..*...*. ....*.*..*...*. .****.****...*. .*...........*. .*************. ............... ```` ## خروجی نمونه ۲ ``` 2 ````