## Day 1, Problem 3: The Game of 31

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.

```5
356656
35665
3566
111126666
552525```

### Sample Output

```B
B
A
A
A```

Point Value: 10
Time Limit: 2.00s
Memory Limit: 16M

Languages Allowed:
C++03, PAS, C, HASK, ASM, RUBY, PYTH2, JAVA, PHP, SCM, CAML, PERL, C#, C++11, PYTH3

• (0/0)
There aren't enough lines.

• (0/0)
The test case is valid according to the description:
 Each such line consists of a sequence of zero or more digits representing a partially completed game.

• (1/0)
Test case 3 has N lines, but the first line has the integer N instead of N-1. Furthermore, the input says that there is a line per input case, so I should expect N lines after the first one. I don't accept azneye's interpretation that a nonexistent line should be the same as a blank line, because that doesn't conform to the input specification.

Submission 193441 crashes because I try to read in a line and don't get one.

Submission 193442 breaks if it hits EOF, and it does not crash, unlike 193441.

• (0/0)
Oh I guess you're right. It's fixed now.