Delft Distance

You are staying at a hotel in the north-west corner of Delft and want to reach the contest site at the university in the south-east corner. The route goes straight through the historical centre of the city. Like Manhattan, the city is a grid of $h \times w$ buildings. Unlike Manhattan, the grid also contains round medieval towers. Every square building is axis aligned with a side length of $10 \text{m}$, and every round tower has a diameter of $10 \text{m}$. Between two neighbouring buildings there is just enough room for a small alley of negligible width. The contest has already started and you are late, so you need a shortest path from the hotel to the contest site. Fortunately, you have a map of the city. See Figure D.1.

Figure D.1: The city map from the first input, with a shortest path shown in red.

The first line contains two integers $h$ and $w$ ($1 \leq h,w \leq 700$), the number of rows and the number of columns of buildings on the map. Each of the next $h$ lines contains $w$ characters, each either 'O' (a round tower) or 'X' (a square building). The map is oriented with north 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 $10^{-6}$.