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 × 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 m and all round towers have a diameter of 10 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.

The input consists of:
• One line with two integers h and w (1 \le H,W \le 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.