Day 1 Question 3: The Game of 31

Your solution: N:\game\game.{pas,c,cpp}
Input file:
Output file: game.out

The game of 31 was a favourite of con artists who rode the railroads in days of yore. The game is played with a deck of 24 cards: four labelled each of 1, 2, 3, 4, 5, 6. (That is, there are four cards labelled '1', four cards labelled '2', and so on.) Initially all of the cards are spread, face up, on a table and the "discard pile" is empty. The players then take turns. During each turn, a player picks up one unused card from the table and lays it on the discard pile. The object of the game is to be the last player to lay a card such that the sum of the cards in the pile does not exceed 31. Your task is to determine the eventual winner of a partially played game, assuming each player plays the remainder of the game using a perfect strategy.

For example, in the following game player B wins:

   Player A plays 3
   Player B plays 5
   Player A plays 6
   Player B plays 6
   Player A plays 5
   Player B plays 6


The first line of the input file is the number of test cases. It is followed by one line for each test case. Each such line consists of a sequence of zero or more digits representing a partially completed game. The first digit is player A's move; the second player B's move; and so on. You are to complete the game using a perfect strategy for both players and to determine who wins.


For each game, output A or B on a single line to indicate the eventual winner of the game.

Sample Input


Output for Sample Input