Aboard the spaceship Skeld are you — the ship's commander — along with $$$N$$$ crewmates. The voyage from Earth to Polus was meant to be peaceful... until it wasn't. A series of strange incidents occurs: oxygen runs low, the reactor nearly melts down, the lights flicker, and the doors jam shut. Suspicion spreads — there might be impostors among us.

Moments of crisis were handled with the crewmates' unity, but the tension lingered. Each crewmate now secretly suspects exactly one crewmate of being the impostor. Remarkably, no crewmate is suspected by more than one person. Formally, there exists a permutation $$$P$$$ of length $$$N$$$, where $$$P[i]$$$ is the crewmate whom the $$$i$$$-th crewmate suspects.

Overseeing this chaos from the commander's room, you, however, are not actually concerned with finding the impostors. Rather, your only goal is to determine the hidden permutation $$$P$$$.

Naturally, to achieve this, you may call emergency meetings. In each meeting, you can choose the order in which the crewmates speak.

Given a crewmate speaking, they will accuse the crewmate they suspect. If the speaker has not yet been marked as sus, their accusation is valid, and the accused crewmate becomes sus. However, if the speaker is already sus, their accusation is ignored.

Unfortunately, as the commander, you cannot attend the meetings yourself. Instead, after each meeting, the ship's log reports the sus status of all crewmates as a binary array, where 1 indicates sus and 0 indicates not sus.

Since time is limited, you may hold at most $$$400$$$ emergency meetings. Your task is to determine the hidden permutation $$$P$$$ within this limit.

Your program first reads a single integer $$$N$$$ ($$$2 \le N \le 100$$$) — the number of crewmates.

Then, you may repeatedly perform queries (call emergency meetings). To make a query, print a line in the following format:

• ? $$$q_1$$$ $$$q_2$$$ $$$\dots$$$ $$$q_N$$$

Here, $$$(q_1, q_2, \dots, q_N)$$$ is the order in which the crewmates will speak during the meeting. The sequence must be a permutation of length $$$N$$$.

After printing a query, flush the output and read a line containing $$$N$$$ integers:

• $$$s_1$$$ $$$s_2$$$ $$$\dots$$$ $$$s_N$$$

Here, $$$s_i$$$ indicates the status of the $$$i$$$-th crewmate after the meeting ends:

• $$$s_i = 0$$$ — the $$$i$$$-th crewmate is not sus.
• $$$s_i = 1$$$ — the $$$i$$$-th crewmate is sus.

Each emergency meeting is independent; all crewmates start as not sus.

When you have determined the hidden permutation $$$P$$$, print it in the following format:

• ! $$$p_1$$$ $$$p_2$$$ $$$\dots$$$ $$$p_N$$$

Printing the answer does not count as a query. After printing the final answer, your program should immediately terminate. Failure to do so may result in an undefined verdict.

You may perform at most 400 queries. If your program performs more than $$$400$$$ queries or outputs an invalid format, you may receive a Wrong Answer verdict.

The interactor is not adaptive, which means that the hidden permutation does not depend on the queries you make.

After printing a query or an answer, do not forget to output the end of line and flush the output. Otherwise, you may get an Idleness Limit Exceeded verdict. To do this, use:

• fflush(stdout) or cout.flush() in C/C++;
• System.out.flush() in Java and Kotlin;
• sys.stdout.flush() in Python;