Description:
You are given an array $$$a$$$ consisting of $$$n$$$ positive integers. You can perform operations on it.
In one operation you can replace any element of the array $$$a_i$$$ with $$$\lfloor \frac{a_i}{2} \rfloor$$$, that is, by an integer part of dividing $$$a_i$$$ by $$$2$$$ (rounding down).
See if you can apply the operation some number of times (possible $$$0$$$) to make the array $$$a$$$ become a permutation of numbers from $$$1$$$ to $$$n$$$ —that is, so that it contains all numbers from $$$1$$$ to $$$n$$$, each exactly once.
For example, if $$$a = [1, 8, 25, 2]$$$, $$$n = 4$$$, then the answer is yes. You could do the following:
1. Replace $$$8$$$ with $$$\lfloor \frac{8}{2} \rfloor = 4$$$, then $$$a = [1, 4, 25, 2]$$$.
2. Replace $$$25$$$ with $$$\lfloor \frac{25}{2} \rfloor = 12$$$, then $$$a = [1, 4, 12, 2]$$$.
3. Replace $$$12$$$ with $$$\lfloor \frac{12}{2} \rfloor = 6$$$, then $$$a = [1, 4, 6, 2]$$$.
4. Replace $$$6$$$ with $$$\lfloor \frac{6}{2} \rfloor = 3$$$, then $$$a = [1, 4, 3, 2]$$$.
Input Format:
The first line of input data contains an integer $$$t$$$ ($$$1 \le t \le 10^4$$$) —the number of test cases.
Each test case contains exactly two lines. The first one contains an integer $$$n$$$ ($$$1 \le n \le 50$$$), the second one contains integers $$$a_1, a_2, \dots, a_n$$$ ($$$1 \le a_i \le 10^9$$$).
Output Format:
For each test case, output on a separate line:
- YES if you can make the array $$$a$$$ become a permutation of numbers from $$$1$$$ to $$$n$$$,
- NO otherwise.
You can output YES and NO in any case (for example, strings yEs, yes, Yes and YES will be recognized as a positive response).
Note:
The first test case is explained in the text of the problem statement.
In the second test case, it is not possible to get a permutation.