405018: GYM101741 H Compressed Spanning Subtrees

This is an interactive problem. Make sure that your output does not get buffered after each query. Use, for instance, fflush(stdout) in C++, System.out.flush() in Java, or sys.stdout.flush() in Python.

For a tree T consisting of n vertices numbered from 1 to n, the compressed spanning subtree S(X) of a set X of spanned vertices (vertices that are not in X are called not spanned) can be defined by the following algorithm:

1. Assign S(X) ≤ ftarrow T;
2. If there is any not spanned vertex that has exactly one edge incident to it, remove it along with the edge;
3. Repeat step 2 while its condition stays true;
4. If there is any not spanned vertex that has exactly two edges incident to it, remove it along with the edges and add a new edge connecting the two remaining endpoints of the removed edges;
5. Repeat step 4 while its condition stays true.

Formally, S(X) is the smallest subgraph of T containing all vertices in X and then having all other vertices of degree two or less smoothed out.

The tree from test 1, and its compressed spanning subtrees for X = {3, 4, 6} and for X = {2, 5, 6}.

You are not given the tree T. Instead, your task is to find it. You can ask questions of the following form: "How many vertices does the compressed spanning subtree of X contain?". And since otherwise finding the tree by asking such questions would be impossible, there are no vertices incident to exactly two edges in T.

The first line of input contains a single integer n (2 ≤ n ≤ 100).

Your program can ask a question by printing a line in the format "? k x₁ x₂ ... x_k" where integer k (1 ≤ k ≤ n) equals to the number of vertices in X and distinct integers x_i (1 ≤ x_i ≤ n) represent these vertices in any order. You can ask no more than 2550 questions.

The answer for such question is an integer given on a separate line: the number of vertices in the compressed spanning subtree in question.

After asking sufficient questions, your program must give the answer by printing a line in the format "! p₂ p₃ ... p_n". Here, considering T as a rooted tree with root at vertex 1, p_i must be the parent vertex of vertex i. After giving the answer, the program must immediately terminate gracefully.

6 



3 



4 



4

? 3 4 3 6 




? 4 1 2 3 6 



? 3 2 5 6 



! 1 2 2 3 3