You need to move a chess knight between the points B and E.

A chess knight moves in an L shaped pattern, like so:

.X.X. X...X ..B.. X...X .X.X.

The Xs mark where the knight in position B can move.

There may be other chess pieces on the board, blocking the knight's movement, but for clarity, you will only be notified of where you cannot go by # characters. You cannot land on these marked spaces, but you can go over them. You also cannot go outside of the board.

Your goal is to find how many turns N are needed to go from B to E, or return Impossible if it can't be done.

Input

Line 1: Two integers W and H giving the width and height of the board. H next lines: A row of the board, containing the characters B, E, . and #

Output

One line, giving the minimum number of turns N needed to go from B to E, or Impossible.