This is an interactive problem.

Returning from a restful vacation on Australia's Gold Coast, Penchick forgot to bring home gifts for his pet duck Duong Canh! But perhaps a beautiful problem crafted through deep thought on the scenic beaches could be the perfect souvenir.

There is a hidden permutation$$$^{\text{∗}}$$$ $$$p$$$ of length $$$n$$$, where $$$n$$$ is even. You are allowed to make the following query:

- Choose a subsequence$$$^{\text{†}}$$$ of the permutation $$$p$$$ with even length $$$4\le k\le n$$$. The interactor will return the value of the two medians$$$^{\text{‡}}$$$ in the chosen subsequence.

Find the index of the two medians in permutation $$$p$$$ using at most $$$80$$$ queries.

Note that the interactor is non-adaptive. This means that the permutation $$$p$$$ is fixed at the beginning and will not change based on your queries.

Input format:
Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 1000$$$). The description of the test cases follows.

The only line of each test case contains a single integer $$$n$$$ ($$$6 \le n \le 100$$$, $$$n$$$ is even) — the length of the hidden permutation $$$p$$$.

For each test case, after reading the integer $$$n$$$, you should begin the interaction and find the answer before reading $$$n$$$ for the next test case.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$10^4$$$.
Example Input 0:
2
6

3 4

3 4

2 3

10

3 4

6 7

Example Output 0:
? 6 1 2 3 4 5 6

? 4 3 6 1 5

? 4 3 6 2 5

! 3 6

? 6 1 3 7 8 9 10

? 8 1 2 3 4 5 6 7 8

! 6 5

Notes:
In the first test case, the hidden permutation is $$$p = [6, 2, 3, 5, 1, 4]$$$.

1. The entire permutation was chosen for the first query. The two medians of the entire permutation $$$p$$$ are $$$3$$$ and $$$4$$$.
2. The indices of the chosen subsequence in the second query are $$$3$$$, $$$6$$$, $$$1$$$, and $$$5$$$. The interactor returns the two medians of the subsequence $$$[p_3, p_6, p_1, p_5] = [3, 4, 6, 1]$$$, which are $$$3$$$ and $$$4$$$.
3. The indices of the chosen subsequence in the second query are $$$3$$$, $$$6$$$, $$$2$$$, and $$$5$$$. The interactor returns the two medians of the subsequence $$$[p_3, p_6, p_2, p_5] = [3, 4, 2, 1]$$$, which are $$$2$$$ and $$$3$$$.

The answer "! 3 6" is valid as $$$p_3 = 3$$$ and $$$p_6 = 4$$$.

In the second test case, the hidden permutation is $$$p = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1]$$$.

1. The indices of the chosen subsequence in the second query are $$$1$$$, $$$3$$$, $$$7$$$, $$$8$$$, $$$9$$$, and $$$10$$$. The interactor returns the two medians of the subsequence $$$[p_1, p_3, p_7, p_8, p_9, p_{10}] = [10, 8, 4, 3, 2, 1]$$$, which are $$$3$$$ and $$$4$$$.
2. The indices of the chosen subsequence in the second query are $$$1$$$, $$$2$$$, $$$3$$$, $$$4$$$, $$$5$$$, $$$6$$$, $$$7$$$, and $$$8$$$. The interactor returns the two medians of the subsequence $$$[p_1, p_2, p_3, p_4, p_5, p_6, p_7, p_8] = [10, 9, 8, 7, 6, 5, 4, 3]$$$, which are $$$6$$$ and $$$7$$$.

The answer "! 5 6" is valid as $$$p_5 = 6$$$ and $$$p_6 = 5$$$.

Example input:
2
6

3 4

3 4

2 3

10

3 4

6 7


Example output:
? 6 1 2 3 4 5 6

? 4 3 6 1 5

? 4 3 6 2 5

! 3 6

? 6 1 3 7 8 9 10

? 8 1 2 3 4 5 6 7 8

! 6 5