Turtle and Piggy are playing a game on a sequence. They are given a sequence $$$a_1, a_2, \ldots, a_n$$$, and Turtle goes first. Turtle and Piggy alternate in turns (so, Turtle does the first turn, Piggy does the second, Turtle does the third, etc.).

The game goes as follows:

Let the current length of the sequence be $$$m$$$. If $$$m = 1$$$, the game ends.
If the game does not end and it's Turtle's turn, then Turtle must choose an integer $$$i$$$ such that $$$1 \le i \le m - 1$$$, set $$$a_i$$$ to $$$\max(a_i, a_{i + 1})$$$, and remove $$$a_{i + 1}$$$.
If the game does not end and it's Piggy's turn, then Piggy must choose an integer $$$i$$$ such that $$$1 \le i \le m - 1$$$, set $$$a_i$$$ to $$$\min(a_i, a_{i + 1})$$$, and remove $$$a_{i + 1}$$$.

Turtle wants to maximize the value of $$$a_1$$$ in the end, while Piggy wants to minimize the value of $$$a_1$$$ in the end. Find the value of $$$a_1$$$ in the end if both players play optimally.

You can refer to notes for further clarification.

Input

Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 10^4$$$). The description of the test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$2 \le n \le 10^5$$$) — the length of the sequence.

The second line of each test case contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$1 \le a_i \le 10^5$$$) — the elements of the sequence $$$a$$$.

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

Output

For each test case, output a single integer — the value of $$$a_1$$$ in the end if both players play optimally.

Note

In the first test case, initially $$$a = [1, 2]$$$. Turtle can only choose $$$i = 1$$$. Then he will set $$$a_1$$$ to $$$\max(a_1, a_2) = 2$$$ and remove $$$a_2$$$. The sequence $$$a$$$ becomes $$$[2]$$$. Then the length of the sequence becomes $$$1$$$, and the game will end. The value of $$$a_1$$$ is $$$2$$$, so you should output $$$2$$$.

In the second test case, one of the possible game processes is as follows:

Initially $$$a = [1, 1, 2]$$$.
Turtle can choose $$$i = 2$$$. Then he will set $$$a_2$$$ to $$$\max(a_2, a_3) = 2$$$ and remove $$$a_3$$$. The sequence $$$a$$$ will become $$$[1, 2]$$$.
Piggy can choose $$$i = 1$$$. Then he will set $$$a_1$$$ to $$$\min(a_1, a_2) = 1$$$ and remove $$$a_2$$$. The sequence $$$a$$$ will become $$$[1]$$$.
The length of the sequence becomes $$$1$$$, so the game will end. The value of $$$a_1$$$ will be $$$1$$$ in the end.

In the fourth test case, one of the possible game processes is as follows:

Initially $$$a = [3, 1, 2, 2, 3]$$$.
Turtle can choose $$$i = 4$$$. Then he will set $$$a_4$$$ to $$$\max(a_4, a_5) = 3$$$ and remove $$$a_5$$$. The sequence $$$a$$$ will become $$$[3, 1, 2, 3]$$$.
Piggy can choose $$$i = 3$$$. Then he will set $$$a_3$$$ to $$$\min(a_3, a_4) = 2$$$ and remove $$$a_4$$$. The sequence $$$a$$$ will become $$$[3, 1, 2]$$$.
Turtle can choose $$$i = 2$$$. Then he will set $$$a_2$$$ to $$$\max(a_2, a_3) = 2$$$ and remove $$$a_3$$$. The sequence $$$a$$$ will become $$$[3, 2]$$$.
Piggy can choose $$$i = 1$$$. Then he will set $$$a_1$$$ to $$$\min(a_1, a_2) = 2$$$ and remove $$$a_2$$$. The sequence $$$a$$$ will become $$$[2]$$$.
The length of the sequence becomes $$$1$$$, so the game will end. The value of $$$a_1$$$ will be $$$2$$$ in the end.

Turtle and Piggy Are Playing a Game 2

Examples