You and your friends like to play chess and backgammon  every day.  But now you are bored of these games, and you would like to play a new game.  So you decided to make your own game, which will be played using a backgammon  die (singular of dice) on a board similar to the chess board, and it will be a single player game.

The game is played on a board of N rows and M columns.  Each cell is either empty or contains a number from 0 to 9, and  there  is a single die (a die with six faces containing the numbers from 1 to 6) placed in one of the empty cells (the borders of the bottom face is aligned to the

axes of the board),  and your goal is to move it to a target  empty cell.

The initial orientation of the die is defined by a string S which is a permutation of the digits from 1 to 6. Each digit represents  the number written  on a face of the die according to this order: right, left, back, front, top, bottom.  Moving the die is defined by the following rules:

1. You can move the die from a cell to one of its four adjacent cells by flipping it on the corresponding face. For example, if the current orientation  of the die is 136425 and you will move it to the cell on its right,  you should flip the die on its right face and it will become the bottom  face in the right cell, so the orientation of the die will be 256431. (This is the example in the figure).

2. Your score is initially  zero.  By moving the  die to another  cell, if the  number  on the bottom  face is the same as the number in the cell you just moved to, your score will be increased by the sum of these two numbers,  otherwise your score will be decreased by the sum of these two numbers.  Entering  the target  cell will not affect your score.

3. You can not leave the board.

4. Once you leave the starting  cell, you can not enter it again.

5. Once you enter the target  cell, you can not leave it.

6. You can not enter an empty cell, except the target  one.

Given the board configuration, the starting  cell, the target cell and the die’s initial orientation, your task is to move the die from the starting  cell to the target  cell according the rules above, such that  you end up with the maximum  possible score.  Can you write a program  to help you?

Input

Your program  will be tested  on one or more test cases. The first line of the input  will be a single integer T , the number of test cases (1 ≤ T ≤ 200). After that  follow the specifications of T test  cases.

Each  test  case is specified in N + 2 lines.  The  first line contains  two  integers  N  and  M (1 ≤ N, M  ≤ 10) representing  the  number  of rows and  number  of columns of the  board, respectively.  The second line contains the string S representing  the initial orientation  of the die in the starting  cell as described above.  Each line of the remaining  N  lines contains  M characters,  the j-th character  in the i-th line represents  the value of the j-th cell in the i-th row of the board.  Each character  will be one of the following values:

1. '.' means an empty cell.

2. 'S' means the starting  cell (which will appear  exactly once in the board).

3. 'T' means the target  cell (which will appear  exactly once in the board).

4. A digit from '0' to '9' means the value written  in this cell.

Output

For each test  case, output, on a single line, one of these values:

1. "Impossible" if you can not reach the target  cell from the starting  cell.

2. "Infinity" if there  is no limit  for your final score, and  you can increase it  with  no limit.

3. Otherwise,  output the maximum score which you can get.

Example

Input:
3
4 4
123456
S789
0987
789.
09.T
3 6
153462
S16521
.46324
.....T
4 4
623451
S6T.
....
....
....
Output:
Impossible
Infinity
12