Alice and Bob want to play a game. The game is played on a chessboard with R rows and C columns, for a total of RC squares. Some of these squares are burned.
A king will be placed on an unburned square of the board, and Alice and Bob will make successive moves with the king.
In a move, the player must move the king to any of its 8 neighboring squares, with the following two conditions:
If a player can't make a move, he or she loses the game. Alice will move first; you need to determine who will win, assuming both players play optimally.
The first line of input gives the number of cases, N.
N test cases follow. The first line of each case will contain two integers, R and C. The next R lines will contain strings of length C, representing the C squares of each row. Each string will contain only the characters '.', '#' and 'K':
There will be only one 'K' character in each test case.
For each test case, output one line containing "Case #X: " (where X is the case number, starting from 1) followed by A if Alice wins, or B if Bob wins.
1 ≤ N ≤ 100
1 ≤ R, C ≤ 4
1 ≤ R, C ≤ 15