Permutation Reconstruction

$Q$ must be a permutation containing each integer from $1$ to $N$ exactly once. The same permutation may be queried more than once. After printing a query, flush the output buffer.

After each valid query, the program receives an integer $L$. It is the length of the longest cycle of the permutation $R$ defined by $R_i=P_{Q_i}$.

Once you have determined $P$, print the final answer in the following format.

$!\ P_1\ P_2\ \cdots\ P_N$

The final ! output does not count toward the limit of $1600$ queries. If the final answer differs from the hidden permutation $P$, the submission is incorrect. Flush the output buffer after printing the final answer and terminate the program immediately.

If you print an invalid query or ask more than $1600$ queries of the ? form, you may receive -1. In that case, terminate the program immediately.

Example interaction

Consider $N=3$ and the hidden permutation $P=(2,3,1)$. The actual interaction does not reveal $P$.

• The interactor sends 3.
• The contestant prints ? 1 2 3 and flushes. Here $R=(2,3,1)$, so the interactor sends 3.
• The contestant prints ? 3 1 2 and flushes. Here $R=(1,2,3)$, so the interactor sends 1.
• The contestant prints ! 2 3 1, flushes, and terminates.

This example illustrates the communication format and the meaning of responses; it does not describe a general method for recovering the permutation.