A14830 | Division by Two and Permutation

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 $a = [1, 4, 3, 2]$ .

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 $a_1, a_2, \dots, a_n$ ( $1 \le a_i \le 10^9$ ).

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).