CF1641C Anonymity Is Important

In the work of a doctor, it is important to maintain the anonymity of clients and the results of tests. The test results are sent to everyone personally by email, but people are very impatient and they want to know the results right away. That's why in the testing lab "De-vitro" doctors came up with an experimental way to report the results. Let's assume that $ n $ people took the tests in the order of the queue. Then the chief doctor Sam can make several statements, in each telling if there is a sick person among the people in the queue from $ l $ -th to $ r $ -th (inclusive), for some values $ l $ and $ r $ . During the process, Sam will check how well this scheme works and will be interested in whether it is possible to find out the test result of $ i $ -th person from the information he announced. And if it can be done, then is that patient sick or not. Help Sam to test his scheme.

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In the first test for the five first queries: 1. Initially Sam tells that people $ 4 $ , $ 5 $ are not sick. 2. In the next query Sam asks the status of the patient $ 5 $ . From the previous query, we know that the patient is definitely not sick. 3. In the next query Sam asks the status of the patient $ 6 $ . We don't know any information about that patient now. 4. After that Sam tells that there exists a sick patient among $ 4 $ , $ 5 $ , $ 6 $ . 5. In the next query Sam asks the status of the patient $ 6 $ . Now we can tell that this patient is definitely sick.