Prefix and Suffix Array

Description:

Input:

Each test consists of multiple test cases. The first line contains a single integer $$$t$$$ ($$$1 \le t \le 120$$$) — the number of test cases. The description of test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$2\le n \le 20$$$) — the length of the string $$$s$$$.

The second line of each test case contains $$$2n-2$$$ strings $$$a_1, a_2, \cdots, a_{2n-2}$$$ — all non-empty prefixes and suffixes of $$$s$$$, not including itself, in arbitrary order.

It is guaranteed that these strings are all the non-empty prefixes and suffixes of some string consisting of lowercase English letters.

Output:

For each test case, output "YES" if $$$s$$$ is a palindrome, and "NO" otherwise.

You can output the answer in any case (upper or lower). For example, the strings "yEs", "yes", "Yes", and "YES" will be recognized as positive responses.

Sample Input:

5
4
bcd cd a d abc ab
3
i io i oi
2
g g
3
t al lt a
4
bba a ab a abb ba

Sample Output:

NO
YES
YES
NO
YES

Note:

In the first test case, $$$s$$$ is "abcd". Its prefixes are "a", "ab" and "abc", and its suffixes are "d", "cd" and "bcd". As the string "abcd" is not a palindrome, the answer is NO.

In the second test case, $$$s$$$ is "ioi". Its prefixes are "i" and "io", and its suffixes are "i" and "oi". As the string "ioi" is a palindrome, the answer is YES.

In the third test case, $$$s$$$ is "gg" which is a palindrome.

In the fourth test case, $$$s$$$ is "alt" which is not a palindrome.