Fizz and Buzz

Two dwarves, Fizz and Buzz, build a sequence of $n$ integers. Each element is constructed as follows. First, the friends toss a fair coin to choose who creates the next number: with probability $\frac{1}{2}$ it is Fizz, and with probability $\frac{1}{2}$ it is Buzz. Then, if the toss favors Fizz, he considers all integers from $1$ to $10\,000$ that are divisible by $3$ and selects one of them at random. All these integers are equally likely to be selected. If the toss favors Buzz, he considers all integers from $1$ to $10\,000$ that are divisible by $5$ and selects one of them at random. All these integers are equally likely to be selected as well. All coin tosses and all integer selections are independent events.

The dwarves built a sequence of $n$ integers by the rules above. Given the resulting sequence, guess who created which number, without making too many errors.

The first line contains an integer $n$, the length of the sequence ($1 \le n \le 10\,000$). The second line contains the sequence itself: the integers $a_1$, $a_2$, $\ldots$, $a_n$ ($1 \le a_i \le 10\,000$). It is guaranteed that the sequence was built according to the statement using a random number generator.

Print a single line with $n$ characters, each of which is either "F" or "B". In the perfect answer, the character at position $i$ must be "F" if the number $a_i$ was created by Fizz, or "B" if the number $a_i$ was created by Buzz. Your answer may contain at most $1200$ errors. In other words, it may differ from the perfect answer at no more than $1200$ positions.

The example above shows the perfect answer. In this example a solution cannot make more than ten errors, so any correctly formatted answer is accepted.