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 $P_X$ does not lie on $\Pi$.
• No three distinct points on $\Pi$ are collinear.

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.

$?\ k\ a_1\ a_2\ \cdots\ a_k$

Every query must satisfy $1 \leq k \leq N$ and $1 \leq a_i \leq N$. You must flush the output after printing a query.

The interactor prints YES if all selected points lie on one plane, and NO otherwise. This plane does not have to be $\Pi$. In particular, selecting at most three points always results in YES.

After determining the index $X$ of the point outside the plane, print the following line.

$!\ X$

You must flush the output after printing the final answer.

If your program exceeds a query limit specified by the problem or prints an invalid command, the interactor prints -1 and terminates. Your program must terminate immediately after reading -1.

• $5 \leq N \leq 100\,000$.
• $1 \leq X \leq N$.
• $P_i$ and $P_j$ are distinct points. ($1 \leq i < j \leq N$.)
• No three distinct points on $\Pi$ are collinear.
• All point indices printed in one query must be distinct.
• The sum of $k$ over all queries must not exceed $200\,000$.
• At most $80$ queries may be used.