Mark and the Online Exam

Mark is administering an online exam consisting of $$$n$$$ true-false questions. However, he has lost all answer keys. He needs a way to retrieve the answers before his client gets infuriated.

Fortunately, he has access to the grading system. Thus, for each query, you can input the answers to all $$$n$$$ questions, and the grading system will output how many of them are correct.

He doesn't have much time, so he can use the grading system at most $$$675$$$ times. Help Mark determine the answer keys.

Note that answer keys are fixed in advance and will not change depending on your queries.

After reading $$$n$$$, you can start making queries to the grading system. For each query, print a line containing a string $$$s$$$ of length $$$n$$$ consisting of only letters 'T' and 'F'.

• $$$s_i = $$$'T' means that you answer the $$$i$$$-question true.
• $$$s_i = $$$'F' means that you answer the $$$i$$$-question false.

After a successful query, you should read an integer $$$k$$$ ($$$0\leq k\leq n$$$) — the number of correct answers. If you read $$$n$$$, then you found the answers, and your program should not make any more queries.

If your program reads $$$k = -1$$$ instead of the number of correct answers, it means that you either made an invalid query or exceeded the query limits. Exit immediately after receiving $$$-1$$$, and you will see Wrong answer verdict. Otherwise, you can get an arbitrary verdict because your solution will continue to read from a closed stream.

After printing a query do not forget to output end of line and flush the output. Otherwise, you will get Idleness limit exceeded. To do this, use:

• fflush(stdout) or cout.flush() in C++;
• System.out.flush() in Java;
• flush(output) in Pascal;
• stdout.flush() in Python;
• see documentation for other languages.

Hacks

To hack, use the following format:

The first line contains an integer $$$n$$$ ($$$1\leq n\leq 1000$$$) — the number of questions.

The second line contains a string $$$s$$$ of length $$$n$$$ consisting of only 'T' and 'F' — the answer key.