Chocolate Bunny

This is an interactive problem.

We hid from you a permutation $$$p$$$ of length $$$n$$$, consisting of the elements from $$$1$$$ to $$$n$$$. You want to guess it. To do that, you can give us 2 different indices $$$i$$$ and $$$j$$$, and we will reply with $$$p_{i} \bmod p_{j}$$$ (remainder of division $$$p_{i}$$$ by $$$p_{j}$$$).

We have enough patience to answer at most $$$2 \cdot n$$$ queries, so you should fit in this constraint. Can you do it?

As a reminder, a permutation of length $$$n$$$ is an array consisting of $$$n$$$ distinct integers from $$$1$$$ to $$$n$$$ in arbitrary order. For example, $$$[2,3,1,5,4]$$$ is a permutation, but $$$[1,2,2]$$$ is not a permutation ($$$2$$$ appears twice in the array) and $$$[1,3,4]$$$ is also not a permutation ($$$n=3$$$ but there is $$$4$$$ in the array).

The interaction starts with reading $$$n$$$.

Then you are allowed to make at most $$$2 \cdot n$$$ queries in the following way:

• "? x y" ($$$1 \le x, y \le n, x \ne y$$$).

After each one, you should read an integer $$$k$$$, that equals $$$p_x \bmod p_y$$$.

When you have guessed the permutation, print a single line "! " (without quotes), followed by array $$$p$$$ and quit.

After printing a query do not forget to output end of line and flush the output. Otherwise, you will get Idleness limit exceeded. To do this, use:

• fflush(stdout) or cout.flush() in C++;
• System.out.flush() in Java;
• flush(output) in Pascal;
• stdout.flush() in Python;
• see documentation for other languages.

Exit immediately after receiving "-1" and you will see Wrong answer verdict. Otherwise you can get an arbitrary verdict because your solution will continue to read from a closed stream.

Hack format

In the first line output $$$n$$$ ($$$1 \le n \le 10^4$$$). In the second line print the permutation of $$$n$$$ integers $$$p_1, p_2, \ldots, p_n$$$.