Mocha likes arrays, so before her departure, Chamo gave her an array $$$a$$$ consisting of $$$n$$$ positive integers as a gift.

Mocha doesn't like arrays containing different numbers, so Mocha decides to use magic to change the array. Mocha can perform the following three-step operation some (possibly, zero) times:

Choose indices $$$l$$$ and $$$r$$$ ($$$1 \leq l \lt r \leq n$$$)
Let $$$x$$$ be the median$$$^\dagger$$$ of the subarray $$$[a_l, a_{l+1},\ldots, a_r]$$$
Set all values $$$a_l, a_{l+1},\ldots, a_r$$$ to $$$x$$$

Suppose $$$a=[1,2,3,4,5]$$$ initially:

If Mocha chooses $$$(l,r)=(3,4)$$$ in the first operation, then $$$x=3$$$, the array will be changed into $$$a=[1,2,3,3,5]$$$.
If Mocha chooses $$$(l,r)=(1,3)$$$ in the first operation, then $$$x=2$$$, the array will be changed into $$$a=[2,2,2,4,5]$$$.

Mocha will perform the operation until the array contains only the same number. Mocha wants to know what is the maximum possible value of this number.

$$$^\dagger$$$ The median in an array $$$b$$$ of length $$$m$$$ is an element that occupies position number $$$\lfloor \frac{m+1}{2} \rfloor$$$ after we sort the elements in non-decreasing order. For example, the median of $$$[3,1,4,1,5]$$$ is $$$3$$$ and the median of $$$[5,25,20,24]$$$ is $$$20$$$.

Input

Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1\leq t\leq 500$$$). The description of the test cases follows.

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

The second line of each test case contains $$$n$$$ integers $$$a_1,a_2,\ldots,a_n$$$ ($$$1\leq a_i \leq 10^9$$$) — the elements of the array $$$a$$$.

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

Output

For each test case, output the maximum value of the number.

Note

In the first test case, $$$a=[1,2]$$$. Mocha can only choose the interval $$$(l,r)=(1,2)$$$. The array will be changed to $$$a=[1,1]$$$. Therefore, the answer is $$$1$$$.

In the second test case, Mocha can perform the following operations:

Choose the interval $$$(l,r)=(4,5)$$$, then $$$a=[1,2,3,4,4]$$$.
Choose the interval $$$(l,r)=(3,5)$$$, then $$$a=[1,2,4,4,4]$$$.
Choose the interval $$$(l,r)=(1,5)$$$, then $$$a=[4,4,4,4,4]$$$.

The array contains only the same number, which is $$$4$$$. It can be proven that the maximum value of the final number cannot be greater than $$$4$$$.

Chamo and Mocha's Array

Examples