You are given an array of positive integers $$$a_1, a_2, \ldots, a_n$$$.

Make the product of all the numbers in the array (that is, $$$a_1 \cdot a_2 \cdot \ldots \cdot a_n$$$) divisible by $$$2^n$$$.

You can perform the following operation as many times as you like:

select an arbitrary index $$$i$$$ ($$$1 \leq i \leq n$$$) and replace the value $$$a_i$$$ with $$$a_i=a_i \cdot i$$$.

You cannot apply the operation repeatedly to a single index. In other words, all selected values of $$$i$$$ must be different.

Find the smallest number of operations you need to perform to make the product of all the elements in the array divisible by $$$2^n$$$. Note that such a set of operations does not always exist.

Input

The first line of the input contains a single integer $$$t$$$ $$$(1 \leq t \leq 10^4$$$) — the number test cases.

Then the descriptions of the input data sets follow.

The first line of each test case contains a single integer $$$n$$$ ($$$1 \leq n \leq 2 \cdot 10^5$$$) — the length of array $$$a$$$.

The second line of each test case contains exactly $$$n$$$ integers: $$$a_1, a_2, \ldots, a_n$$$ ($$$1 \leq a_i \leq 10^9$$$).

It is guaranteed that the sum of $$$n$$$ values over all test cases in a test does not exceed $$$2 \cdot 10^5$$$.

Output

For each test case, print the least number of operations to make the product of all numbers in the array divisible by $$$2^n$$$. If the answer does not exist, print -1.

Note

In the first test case, the product of all elements is initially $$$2$$$, so no operations needed.

In the second test case, the product of elements initially equals $$$6$$$. We can apply the operation for $$$i = 2$$$, and then $$$a_2$$$ becomes $$$2\cdot2=4$$$, and the product of numbers becomes $$$3\cdot4=12$$$, and this product of numbers is divided by $$$2^n=2^2=4$$$.

In the fourth test case, even if we apply all possible operations, we still cannot make the product of numbers divisible by $$$2^n$$$ — it will be $$$(13\cdot1)\cdot(17\cdot2)\cdot(1\cdot3)\cdot(1\cdot4)=5304$$$, which does not divide by $$$2^n=2^4=16$$$.

In the fifth test case, we can apply operations for $$$i = 2$$$ and $$$i = 4$$$.

Divisibility by 2^n

Examples