Pac-man P87462

Given a rectangular board with Pac-Man in it, tell if Pac-man can eat any power pellet. To get there, Pac-Man can only move horizontally and vertically, never crossing a wall. Moreover, Pac-Man can never be too close to a ghost. There should always be a cell between them, either horizontally, vertically, or diagonally. Look at the input and output examples.

Input

Input consists of several cases. Every case begins with the number of rows $r$ and the number of columns $c$ of the board. Follow $r$ rows with $c$ characters each. A ‘P’ indicates the initial position of Pac-Man. An ‘F’ indicates the position of a ghost (which does not move). A ‘B’ indicates the position of a pellet. An ‘X’ indicates a wall. A dot indicates an empty position. Assume $3 \le r \le 100$ and $3 \le c \le 100$, that the rows and columns on the edge of the board only have walls, and that each board has exactly one ‘P’.

Output

For every case, tell if Pac-man can eat any pellet or not.