Solve the programming task below in a Python markdown code block.
An array $b$ is good if the sum of elements of $b$ is even.

You are given an array $a$ consisting of $n$ positive integers. In one operation, you can select an index $i$ and change $a_i := \lfloor \frac{a_i}{2} \rfloor$. $^\dagger$

Find the minimum number of operations (possibly $0$) needed to make $a$ good. It can be proven that it is always possible to make $a$ good.

$^\dagger$ $\lfloor x \rfloor$ denotes the floor function — the largest integer less than or equal to $x$. For example, $\lfloor 2.7 \rfloor = 2$, $\lfloor \pi \rfloor = 3$ and $\lfloor 5 \rfloor =5$.


-----Input-----

Each test contains multiple test cases. The first line contains a single integer $t$ ($1 \leq t \leq 1000$) — the number of test cases. The description of the test cases follows.

The first line of each test case contains a single integer $n$ ($1 \leq n \leq 50$) — the length of the array $a$.

The second line of each test case contains $n$ space-separated integers $a_1,a_2,\ldots,a_n$ ($1 \leq a_i \leq 10^6$) — representing the array $a$.

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


-----Output-----

For each test case, output the minimum number of operations needed to make $a$ good.


-----Examples-----

Input
4
4
1 1 1 1
2
7 4
3
1 2 4
1
15
Output
0
2
1
4


-----Note-----

In the first test case, array $a$ is already good.

In the second test case, we can perform on index $2$ twice. After the first operation, array $a$ becomes $[7,2]$. After performing on index $2$ again, $a$ becomes $[7,1]$, which is good. It can be proved that it is not possible to make $a$ good in less number of operations.

In the third test case, $a$ becomes $[0,2,4]$ if we perform the operation on index $1$ once. As $[0,2,4]$ is good, answer is $1$.

In the fourth test case, we need to perform the operation on index $1$ four times. After all operations, $a$ becomes $[0]$. It can be proved that it is not possible to make $a$ good in less number of operations.