# Pushing Boxes

Description

Imagine you are standing inside a two-dimensional maze composed of square cells which may or may not be filled with rock. You can move north, south, east or west one cell at a step. These moves are called *walks*.

*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).

Print asequence as "**Pushbox times:a Free_walk times:b**", a is the number of pushes,and b is the number of walks .

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 Pushbox times:5 Free_walk times:0 Maze #2 Impossible. Maze #3 Pushbox times:6 Free_walk times:22 Maze #4 Pushbox times:3 Free_walk times:16

Hint

**eennwwWWWWeeeeeesswwwwwwwnNN**" is one best solution of the third case's , and they need 6 times to push and 22 times to walk, so the right answer is

"

**Pushbox times:6 Free_walk times:22**".

Editor