Find the Plane

This is an interactive problem.

There are $N$ distinct points $P_1, P_2, \cdots, P_N$ in three-dimensional space. Their coordinates are not given to you.

There exist a plane $\Pi$ and a unique integer $X$ satisfying all of the following conditions.

• For every $i \neq X$, the point $P_i$ lies on $\Pi$.
• The point $$ does not lie on .

You may choose a set of point indices and ask whether the selected points lie on one plane. Find $X$ using these queries.

Each subtask has a different maximum number of queries. Refer to the restrictions by score group below for details.

At the beginning, the contestant program receives the following integer.

$N$

This problem consists of a single test case.

To ask a query, choose an integer $k$ and distinct point indices $a_1, a_2, \cdots, a_k$, then print the following line.

• $5 \leq N \leq 100\,000$.
• $1 \leq X \leq N$.
• $P_i$ and are distinct points. (.)