CF1705F 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.

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The empty lines in the example are just for you to better understand the interaction process. You're not required to print them. In the first example, there are $ 3 $ questions, and the answer to each question is 'true', 'true', and 'false', respectively. - The first query, guessing the answers to be 'false', 'true', and 'true', respectively, guesses only one question — the $ 2 $ -nd question — correctly. - Then, in the second query, the program correctly guesses the answer key. The interaction ends here. In the second example, there are $ 4 $ questions, and the answer to each question is 'true', 'false', 'true', and 'true', respectively. - The first query guessed none of the questions correctly, resulting in the answer $ 0 $ . - The second query guessed the $ 1 $ -st, $ 3 $ -rd, and $ 4 $ -th question correctly, resulting in the answer $ 3 $ . - In the third query, the program correctly guesses the answer key. Then, the interaction ends.