Practice Coding with the exercise "Chess cavalry"

Statement

Goal

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.

Constraints

2 ≤ W, H ≤ 8

Example

Input

3 2
..E
B..

Output

Solve it

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