This is an interactive problem.

There is a secret sequence $$$a_1, a_2, \ldots, a_{2n-1},a_{2n}$$$, which contains each integer from $$$1$$$ to $$$n$$$ exactly twice.

Your task is to guess the sequence by using queries of the following type:

"? $$$k\;j_1\;j_2\;\ldots\;j_k$$$" — select the integer $$$k$$$ ($$$1 \le k \le 2n$$$) and $$$k$$$ distinct indices $$$j_1, j_2, \ldots, j_k$$$ ($$$1 \le j_1 , j_2 , \ldots , j_k \le 2n$$$). In response to the query, the jury will return $$$\text{MAD}([a_{j_1}, a_{j_2}, \ldots, a_{j_k}])$$$.

We define the $$$\operatorname{MAD}$$$ (Maximum Appearing Duplicate) of an integer sequence as the largest integer that appears at least twice. Specifically, if there is no number that appears at least twice, the $$$\operatorname{MAD}$$$ value is $$$0$$$. Some examples are as follows:

$$$\operatorname{MAD}([1, 2, 1]) = 1$$$;
$$$\operatorname{MAD}([2, 2, 3, 3]) = 3$$$;
$$$\operatorname{MAD}([1, 2, 3, 4]) = 0$$$.

Please identify the secret sequence using at most $$$3n$$$ queries.

Input

Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 3000$$$). The description of the test cases follows.

The first line of each test case contains one integer $$$n$$$ ($$$2 \le n \le 300$$$).

It is guaranteed that the sum of $$$n^2$$$ over all test cases does not exceed $$$10^5$$$.

After you read this line of input, the interaction begins with your first query.

Interaction

To make a query, output a line (without quotes) in the following format:

"? $$$k\;j_1\;j_2\;\ldots\;j_k$$$" ($$$1 \le k \le 2n$$$, $$$1 \le j_1 , j_2 , \ldots , j_k \le 2n$$$)

Here, the indices $$$j_1 , j_2 , \ldots , j_k$$$ which you selected must be pairwise distinct.

Then, after each query, read a single integer — the answer to your query.

You can make at most $$$3n$$$ queries of this type.

If your program has found the sequence $$$a$$$, print the line (without quotes) in the following format:

"! $$$a_1\;a_2\;\ldots\;a_{2n-1}\;a_{2n}$$$" ($$$1 \le a_i \le n$$$)

Note that this does not count towards the query limit.

After this, proceed to the next test case, or exit if this is the last test case.

The interactor in this task is not adaptive. In other words, the sequence $$$a$$$ does not change during the interaction.

If you make more than $$$3n$$$ queries during an interaction, your program must terminate immediately, and you will receive the Wrong Answer verdict. Otherwise, you can get an arbitrary verdict because your solution will continue to read from a closed stream.

After printing each line, do not forget to output the end of line and flush the output buffer. Otherwise, you will receive the Idleness Limit Exceeded verdict. To flush, use:

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

Hacks

To make a hack, please use the following format:

The first line should contain the number of test cases $$$t$$$ ($$$1 \leq t \leq 3000$$$).

The first line of each test case should contain an integer $$$n$$$ ($$$2 \leq n \leq 300$$$).

The following line should contain $$$2n$$$ integers $$$a_1,a_2,\ldots,a_{2n}$$$ ($$$1 \leq a_i \leq n$$$). Each number from $$$1$$$ through $$$n$$$ must appear exactly twice.

The sum of $$$n^2$$$ over all test cases should not exceed $$$10^5$$$.

For example, the hack format corresponding to the example interaction is as follows.

Note

In the first test case, the hidden sequence is $$$a=[2,2,1,1]$$$.

For the query "? 2 2 1", the jury returns $$$2$$$ because $$$\operatorname{MAD}([a_2, a_1]) = \operatorname{MAD}([2, 2]) = 2$$$.

For the query "? 2 1 3", the jury returns $$$0$$$ because $$$\operatorname{MAD}([a_1, a_3]) = \operatorname{MAD}([2, 1]) = 0$$$.

For the query "? 3 1 3 4", the jury returns $$$1$$$ because $$$\operatorname{MAD}([a_1, a_3, a_4]) = \operatorname{MAD}([2 ,1, 1]) = 1$$$.

Note that the example interaction is only for understanding statements and does not guarantee finding a unique sequence $$$a$$$.

MAD Interactive Problem

Examples