Pak Chanek has an array $a$ of $n$ positive integers. Since he is currently learning how to calculate the floored average of two numbers, he wants to practice it on his array $a$.

While the array $a$ has at least two elements, Pak Chanek will perform the following three-step operation:

1. Pick two different indices $i$ and $j$ ($1 \leq i, j \leq |a|$; $i \neq j$), note that $|a|$ denotes the current size of the array $a$.
2. Append $\lfloor \frac{a_i+a_j}{2} \rfloor$$^{\text{∗}}$ to the end of the array.
3. Remove elements $a_i$ and $a_j$ from the array and concatenate the remaining parts of the array.

For example, suppose that $a=[5,4,3,2,1,1]$. If we choose $i=1$ and $j=5$, the resulting array will be $a=[4,3,2,1,3]$. If we choose $i=4$ and $j=3$, the resulting array will be $a=[5,4,1,1,2]$.

After all operations, the array will consist of a single element $x$. Find the maximum possible value of $x$ if Pak Chanek performs the operations optimally.

$^{\text{∗}}$$\lfloor x \rfloor$ denotes the floor function of $x$, which is the greatest integer that is less than or equal to $x$. For example, $\lfloor 6 \rfloor = 6$, $\lfloor 2.5 \rfloor=2$, $\lfloor -3.6 \rfloor=-4$ and $\lfloor \pi \rfloor=3$

Input

Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \le t \le 5000$). The description of the test cases follows.

The first line of each test case contains a single integer $n$ ($2 \le n \le 50$) — the length of the array $a$.

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

Do note that the sum of $n$ over all test cases is not bounded.

Output

For each test case, output a single integer: the maximum possible value of $x$ after all numbers have been picked.

Note

In the first test case, the array is initially $a=[1,7,8,4,5]$. Pak Chanek will perform the following operations:

1. Pick $i=1$ and $j=2$, then $a=[8,4,5,4]$.
2. Pick $i=3$ and $j=2$, then $a=[8,4,4]$.
3. Pick $i=2$ and $j=3$, then $a=[8,4]$.
4. Pick $i=1$ and $j=2$, then $a=[6]$.

After all the operations, the array consists of a single element $x=6$. It can be proven that there is no series of operations that results in $x$ greater than $6$ in the end.