P7597 "EZEC-8" Guess the Tree (Enhanced Version).

This is an interactive problem.

There is a rooted tree with $n$ nodes, rooted at $1$. You need to determine the structure of this tree through several queries. You can use two types of queries: 1. `? 1 u v` With this query, you can get the distance between $u$ and $v$. 2. `? 2 u` With this query, you can get the size of the subtree of $u$ and all nodes in the subtree of $u$. Please determine the structure of the tree while making the interactive library output no more than $40000$ numbers. ### Interaction Input the size of the tree $n$ to start the interaction. During the interaction, you may make the two types of queries described above. For the first type of query, the interactive library will return a non-negative integer, which is the distance between node $u$ and node $v$. For the second type of query, the interactive library will first return a positive integer $num$, which is the size of the subtree of $u$. Then, on the same line, it will return $num$ positive integers, which are all nodes in the subtree of $u$ (the order of the nodes will be shuffled). After you have determined the answer, output one line in the form `! fa[2] fa[3] ... fa[n]` to stop the interaction, where $fa[i]$ denotes the parent of node $i$ in this tree. After you output a line, please flush the buffer: - In C++, use `fflush(stdout)` or `cout.flush()`. - In Pascal, use `flush(output)`. - In Python, use `stdout.flush()`. - For other languages, please check the documentation by yourself.

See "Interaction".

See "Interaction".

For $100\%$ of the testdata: $2 \leq n \leq 5000$, $1 \le u, v \le n$. Translated by ChatGPT 5