A14850. Hidden Permutations

This is an interactive problem.

The jury has a permutation $p$ of length $n$ and wants you to guess it. For this, the jury created another permutation $q$ of length $n$ . Initially, $q$ is an identity permutation ( $q_i = i$ for all $i$ ).

You can ask queries to get $q_i$ for any $i$ you want. After each query, the jury will change $q$ in the following way:

- At first, the jury will create a new permutation $q'$ of length $n$ such that $q'_i = q_{p_i}$ for all $i$ .
- Then the jury will replace permutation $q$ with pemutation $q'$ .

You can make no more than $2n$ queries in order to quess $p$ .

The first line of input contains a single integer $t$ ( $1 \leq t \leq 1000$ ) — the number of test cases.

Interaction in each test case starts after reading the single integer $n$ ( $1 \leq n \leq 10^4$ ) — the length of permutations $p$ and $q$ .

To get the value of $q_i$ , output the query in the format $?$ $i$ ( $1 \leq i \leq n$ ). After that you will receive the value of $q_i$ .

You can make at most $2n$ queries. After the incorrect query you will receive $0$ and you should exit immediately to get Wrong answer verdict.

When you will be ready to determine $p$ , output $p$ in format $!$ $p_1$ $p_2$ $\ldots$ $p_n$ . After this you should go to the next test case or exit if it was the last test case. Printing the permutation is not counted as one of $2n$ queries.

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.

It is guaranteed that the sum of $n$ over all test cases doesn't exceed $10^4$ . The interactor is not adaptive in this problem.

Hacks:

To hack, use the following format:

The first line contains the single integer $t$ — the number of test cases.

The first line of each test case contains the single integer $n$ — the length of the permutations $p$ and $q$ . The second line of each test case contains $n$ integers $p_1, p_2, \ldots, p_n$ — the hidden permutation for this test case.

In the first test case the hidden permutation $p = [4, 2, 1, 3]$ .

Before the first query $q = [1, 2, 3, 4]$ so answer for the query will be $q_3 = 3$ .

Before the second query $q = [4, 2, 1, 3]$ so answer for the query will be $q_2 = 2$ .

Before the third query $q = [3, 2, 4, 1]$ so answer for the query will be $q_4 = 1$ .

In the second test case the hidden permutation $p = [1, 3, 4, 2]$ .

Empty strings are given only for better readability. There will be no empty lines in the testing system.