This is an interactive problem.

Upon clearing the Waterside Area, Gretel has found a monster named Genokraken, and she's keeping it contained for her scientific studies.

The monster's nerve system can be structured as a tree$$$^{\dagger}$$$ of $$$n$$$ nodes (really, everything should stop resembling trees all the time$$$\ldots$$$), numbered from $$$0$$$ to $$$n-1$$$, with node $$$0$$$ as the root.

Gretel's objective is to learn the exact structure of the monster's nerve system — more specifically, she wants to know the values $$$p_1, p_2, \ldots, p_{n-1}$$$ of the tree, where $$$p_i$$$ ($$$0 \le p_i < i$$$) is the direct parent node of node $$$i$$$ ($$$1 \le i \le n - 1$$$).

She doesn't know exactly how the nodes are placed, but she knows a few convenient facts:

- If we remove root node $$$0$$$ and all adjacent edges, this tree will turn into a forest consisting of only paths$$$^{\ddagger}$$$. Each node that was initially adjacent to the node $$$0$$$ will be the end of some path.
- The nodes are indexed in a way that if $$$1 \le x \le y \le n - 1$$$, then $$$p_x \le p_y$$$.
- Node $$$1$$$ has exactly two adjacent nodes (including the node $$$0$$$).

The tree in this picture does not satisfy the condition, because if we remove node $$$0$$$, then node $$$2$$$ (which was initially adjacent to the node $$$0$$$) will not be the end of the path $$$4-2-5$$$.The tree in this picture does not satisfy the condition, because $$$p_3 \le p_4$$$ must hold.The tree in this picture does not satisfy the condition, because node $$$1$$$ has only one adjacent node.

Gretel can make queries to the containment cell:

- "? a b" ($$$1 \le a, b < n$$$, $$$a \ne b$$$) — the cell will check if the simple path between nodes $$$a$$$ and $$$b$$$ contains the node $$$0$$$.

However, to avoid unexpected consequences by overstimulating the creature, Gretel wants to query at most $$$2n - 6$$$ times. Though Gretel is gifted, she can't do everything all at once, so can you give her a helping hand?

$$$^{\dagger}$$$A tree is a connected graph where every pair of distinct nodes has exactly one simple path connecting them.

$$$^{\ddagger}$$$A path is a tree whose vertices can be listed in the order $$$v_1, v_2, \ldots, v_k$$$ such that the edges are $$$(v_i, v_{i+1})$$$ ($$$1 \le i < k$$$).

Input format:
Each test consists of multiple test cases. The first line contains a single integer $$$t$$$ ($$$1 \le t \le 500$$$) — the number of test cases. The description of the test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$4 \le n \le 10^4$$$) — the number of nodes in Genokraken's nerve system.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$10^4$$$.
Example Input 0:
3
4

1

5

1

0

9

Example Output 0:
? 2 3

! 0 0 1

? 2 3

? 2 4

! 0 0 1 2

! 0 0 0 1 3 5 6 7

Notes:
In the first test case, Genokraken's nerve system forms the following tree:

- The answer to "? 2 3" is $$$1$$$. This means that the simple path between nodes $$$2$$$ and $$$3$$$ contains node $$$0$$$.

In the second test case, Genokraken's nerve system forms the following tree:

- The answer to "? 2 3" is $$$1$$$. This means that the simple path between nodes $$$2$$$ and $$$3$$$ contains node $$$0$$$.
- The answer to "? 2 4" is $$$0$$$. This means that the simple path between nodes $$$2$$$ and $$$4$$$ doesn't contain node $$$0$$$.

In the third test case, Genokraken's nerve system forms the following tree:

Example input:
3
4

1

5

1

0

9


Example output:
? 2 3

! 0 0 1

? 2 3

? 2 4

! 0 0 1 2

! 0 0 0 1 3 5 6 7