# Pushing Boxes

Time Limit: 10 Seconds Memory Limit: 32768 KB

Special Judge

One of the empty cells contains a box which can be moved to an adjacent free cell by standing next to the box and then moving in the direction of the box. Such a move is called a push. The box cannot be moved in any other way than by pushing, which means that if you push it into a corner you can never get it out of the corner again.

One of the empty cells is marked as the target cell. Your job is to bring the box to the target cell by a sequence of walks and pushes. As the box is very heavy, you would like to minimize the number of pushes. Can you write a program that will work out the best such sequence?

## Input

The input contains the descriptions of several mazes. Each maze description
starts with a line containing two integers r and c (both <= 20) representing
the number of rows and columns of the maze.

Following this are r lines each containing c characters. Each character describes
one cell of the maze. A cell full of rock is indicated by a `#' and an empty
cell is represented by a `.'. Your starting position is symbolized by `S', the
starting position of the box by `B' and the target cell by `T'.

Input is terminated by two zeroes for r and c.

## Output

For each maze in the input, first print the number of the maze, as shown in
the sample output. Then, if it is impossible to bring the box to the target
cell, print ``Impossible.''.

Otherwise, output a sequence that minimizes the number of pushes. If there is
more than one such sequence, choose the one that minimizes the number of total
moves (walks and pushes). If there is still more than one such sequence, any
one is acceptable.

Print the sequence as a string of the characters N, S, E, W, n, s, e and w where uppercase letters stand for pushes, lowercase letters stand for walks and the different letters stand for the directions north, south, east and west.

Output a single blank line after each test case.

## Sample Input

1 7 SB....T 1 7 SB..#.T 7 11 ########### #T##......# #.#.#..#### #....B....# #.######..# #.....S...# ########### 8 4 .... .##. .#.. .#.. .#.B .##S .... ###T 0 0

## Sample Output

Maze #1 EEEEE Maze #2 Impossible. Maze #3 eennwwWWWWeeeeeesswwwwwwwnNN Maze #4 swwwnnnnnneeesssSSSSubmit

Source: Southwestern Europe 1997