Canadian Computing Competition: 2000 Stage 2, Day 1, Problem 3

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:

1. Player ~A~ plays 3.
2. Player ~B~ plays 5.
3. Player ~A~ plays 6.
4. Player ~B~ plays 6.
5. Player ~A~ plays 5.
6. Player ~B~ plays 6.

Input Specification

The first line of the input 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 Specification

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

Sample Output

B
B
A
A
A