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문제

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

Tile Meaning Passable
> Entrance Yes
< Exit Yes
a-z Key Yes
A-Z Door See rules
. Ground Yes
+ Wall No
Unstable floor See rules

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.

입력

The first line of input will contain the number of test cases, T (1 ≤ T ≤ 50). Each test case will begin with a line containing two integers R C (4 ≤ R, C ≤ 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.

출력

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.

예제 입력 1

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

예제 출력 1

2
Impossible