homework

There are $N$ ($2 \le N \le 1000$) students in line, name them $s\_0, s\_1, \cdots, s\_{N-1}$ by their order.

For each student, you have to check whether he/she did the homework or not, and you can ask:

• Q1 defined as 0 standing for "Have you finished the homework?" or
• Q2 defined as 1 standing for "Are you late for the homework?".

However, due to the weird culture in the school, if a student has to answer "no" then he/she will hesitate to answer until the class ends. (Of course, you know that this student expressed "no".)

You prepare the questions $q\_0, q\_1, \cdots, q\_{N-1}$ for the students and they will come to answer in order, and you have to wait for their answers.

• i.e., if $s\_0, s\_1, \cdots s\_{M-1}$ answer YES and $s\_M$ expresses "no", then you will only receive $M$ YES's.
• so if $s\_0, s\_1, \cdots s\_{N-1}$ answer YES then you will receive $N$ YES's.

Here, for the COVID-19 situation, you write the questions on the computer and upload them online and what you receive is a big YES on the monitor. You can only get the sequence of answers.

However, the online system was broken so the questions get arranged by a pre-chosen order $i\_0, i\_1, \cdots, i\_{N-1}$.

• i.e., if you input $q\_0, q\_1, \cdots, q\_{N-1}$, then the questions will be asked by the order $q\_{i\_0}, q\_{i\_1}, \cdots, q\_{i\_{N-1}}$.

You can have at most $\lceil N + N\log\_2 N \rceil$ classes to ask the questions.

Write a function question:

• input parameter: a Student object containing the information of the students' state and the order

• $\cdot$.n() returns the number of students; i.e., $N$

  • $\cdot$.ask(Q) returns the list of 'YES'’s (need not be a length of $N$) based on the question list Q

    • input parameter: a list of length $N$, consisting of Q1 and Q2
    • return value: ['YES' for j in range($M$)] where $M$ is the number of YES's: i.e., M = \max\\{m \le N \\,\vert\\, j < m \Longrightarrow s\_j \textrm{ answers } YES$\textrm{ on }$Q[$i\_j$]\\}

• output: the list of input questions $q\_0, q\_1, \cdots, q\_{N-1}$ that gets $N$ YES's and the order $i\_0, i\_1, \cdots, i\_{N-1}$

  • in the order that you need to input to computer, and the order that $q\_i$ is asked, respectively.

Assume every student either finished or was late for the homework, and the states do not change as the classes proceed.

Caution: The protected attributes in Student are named differently in the judging code.