## Day 1 Question 3: The Game of 31

**Your solution:** N:\game\game.{pas,c,cpp}

**Input file:** game.in

**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

### Input

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.
### Output

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

5
356656
35665
3566
111126666
552525

### Output for Sample Input

B
B
A
A
A