Description:
Marcos loves strings a lot, so he has a favorite string $$$s$$$ consisting of lowercase English letters. For this string, he wrote down all its non-empty prefixes and suffixes (except for $$$s$$$) on a piece of paper in arbitrary order. You see all these strings and wonder if Marcos' favorite string is a palindrome or not. So, your task is to decide whether $$$s$$$ is a palindrome by just looking at the piece of paper.
A string $$$a$$$ is a prefix of a string $$$b$$$ if $$$a$$$ can be obtained from $$$b$$$ by deletion of several (possibly, zero or all) characters from the end.
A string $$$a$$$ is a suffix of a string $$$b$$$ if $$$a$$$ can be obtained from $$$b$$$ by deletion of several (possibly, zero or all) characters from the beginning.
A palindrome is a string that reads the same backward as forward, for example, strings "gg", "ioi", "abba", "icpci" are palindromes, but strings "codeforces", "abcd", "alt" are not.
Input Format:
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 Format:
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.
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.