Chuck's Challenge is a game in which a player navigates a maze consisting of various tiles in a grid. The player can encounter doors that may be unlocked using keys they acquire along the way. You must write a program to determine the minimum number of doors that must be opened to reach the exit of the maze.

Key

Rules

• Tiles that are diagonal to each other are not considered to be adjacent (only up, down, left, and right).
• The player begins the maze visiting the entrance tile.
• The player may only visit passable tiles that are adjacent to the tile the player is currently visiting.
• Doors are considered impassable until a tile with a matching key ('A' matches 'a', 'B' matches 'b', etc.) has been visited.
• At first, unstable floors are considered passable; however, if the player leaves an unstable floor and visits any other type of tile, it becomes impassable.
• When an unstable floor tile becomes impassable, all adjacent unstable floor tiles become impassable.
• The external edge of the maze is an impassable wall.

Input

The first line of input will contain the number of test cases, $T$ ($1 \leq T \leq 50$). Each test case will begin with a line containing two integers R C ($4 \leq R, C \leq 50$). Following that will be a maze with $R$ rows and $C$ columns. Only the characters in the key will be present in the maze.

Output

Each test case will have a single line of output. Print the minimum number of doors that must be opened to reach the exit or print "Impossible" if the exit cannot be reached.

Sample Input

2
8 15
+++++++++++++++
+>............+
+...a...+~+~+B+
+~+++++++~+~+.+
+~++..b..C+~+.+
+~++A++++++~+.+
+....~~~~~~c+<+
+++++++++++++++
8 6
++++++
+>.A<+
+.++++
+.+.a+
+~~..+
+~~..+
+~~..+
++++++

Sample Output

2
Impossible