[Solution] Mark and the Online Exam Codeforces Solution

F. Mark and the Online Exam

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

Mark is administering an online exam consisting of n$n$ 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$n$ 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$675$ times. Help Mark determine the answer keys.

Note that answer keys are fixed in advance and will not change

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depending on your queries.

Input

The first line of the input consists of an integer n$n$ (1≤n≤1000$1\le n\le 1000$) — the number of questions.

Interaction

After reading n$n$, you can start making queries to the grading system. For each query, print a line containing a

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 string s$s$ of length n$n$ consisting of only letters 'T' and 'F'.

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

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

If your program reads k=−1$k=-1$ 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$-1$, 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$n$ (1≤n≤1000$1\le n\le 1000$) — the number of questions.

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