### Day 2 Question 3

# Derek's Dilemma

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Input file: derek.in

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Output file: derek.out

There once were two sad people who were named, oddly enough, A and B.
They were sad because they were always being talked about, often quite
slanderously, in math problems by the callous, faceless mathematical
institution. Whenever they would talk to other people, the mean people
would say "Hey, I read about you! You're always collecting and losing
apples, aren't you?" They could not get jobs, because the mean
interviewers would say "Didn't I read that at one point you two were
prisoners? Hmmm, this is a dilemma..."

While the author feels deeply for them, unfortunately he lacks any
semblance of an imagination and none of the other letters could make
it, so he will be using them yet again. However, to prevent the
standard misconceptions, please read the disclaimer.

A and B are playing a game. They have n tokens, inscribed with the
numbers 1 to n. A takes token 1 and places it in one of two piles. B
then takes token 2 and places it in one of the two piles. A does this
with token 3, and so on, until the last player places token n in one of
the two piles.

The numbers on the tokens in each of the piles are summed up, and A
wins if the two totals are relatively prime. (Two numbers are
relatively prime if there is no integer greater than 1 which evenly
divides both of them) Otherwise, B wins. (Note: an empty pile has
total 0, and every integer evenly divides 0)

Your goal is to figure out, if both A and B play perfectly, which one
of them will win for a given n.

Note: This question is for the sole purpose of cruelty to participants
of the CCC. Any resemblance to real or imagined persons, living or
dead, is purely coincidental.

### The Input

Several lines containing the number of tokens for different games to be
analyzed. Each line consists of a single number n, 1 <= n <= 30,
except for the last line, which contains the number 0.
### The Output

For each non-zero n, you are to print out who will win the game (A or
B) with n tokens, assuming both play as well as possible.
Note that efficiency may be an issue here for large n - your program
will not have forever to run.

### Sample Input

2
5
10
0

### Sample Output

When n=2, B will win.
When n=5, A will win.
When n=10, A will win.