P17052 [NWERC 2022] Delft Distance

You are currently in your hotel at the north-west corner of Delft, and want to go to the contest site at the university in the south-east corner of Delft. To get there, you have to go right through the historical centre of the city. Like Manhattan, the city consists of a grid of $h\times w$ buildings. But unlike Manhattan, the city does not only contain square residential buildings but also some round medieval towers. All the square buildings are axis aligned with a side length of $10~\text{m}$ and all round towers have a diameter of $10~\text{m}$. There is just enough space for a small alley of negligible width between two neighbouring buildings. Since you are already late for the contest start, you need to find a shortest path from your hotel to the contest site. Fortunately, you have a map of the city. :::align{center}  ::: Figure: Illustration of Sample Input 1, with a shortest path shown in red.

The input consists of: - One line with two integers $h$ and $w$ ($1 \leq h,w \leq 700$), the number of rows and the number of columns of buildings shown on the map of the city. - $h$ lines, each with $w$ characters which are either `O` for round towers or `X` for square buildings, describing the shapes of the buildings. The map is oriented with the north side up.

Output the length of a shortest path from the north-west corner to the south-east corner of Delft in metres. Your answer may have a relative or absolute error of at most $10^{-6}$.