1730D · Prefixes and Suffixes

Problem: You have two strings $s_1$ and $s_2$ of length $n$, consisting of lowercase English letters. You can perform the following operation any (possibly zero) number of times:

• Choose a positive integer $1 \leq k \leq n$.
• Swap the prefix of the string $s_1$ and the suffix of the string $s_2$ of length $k$.

Is it possible to make these two strings equal by doing described operations?

Input Format: The first line contains a single integer $t$ ($1 \le t \le 10^4$) — the number of test cases. Then the test cases follow.

Each test case consists of three lines.

The first line contains a single integer $n$ ($1 \le n \le 10^5$) — the length of the strings $s_1$ and $s_2$.

The second line contains the string $s_1$ of length $n$, consisting of lowercase English letters.

The third line contains the string $s_2$ of length $n$, consisting of lowercase English letters.

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

Output Format: For each test case, print "YES" if it is possible to make the strings equal, and "NO" otherwise.

Note: In the first test case:

• Initially $s_1 = \mathtt{cbc}$, $s_2 = \mathtt{aba}$.
• Operation with $k = 1$, after the operation $s_1 = \mathtt{abc}$, $s_2 = \mathtt{abc}$.

In the second test case:

• Initially $s_1 = \mathtt{abcaa}$, $s_2 = \mathtt{cbabb}$.
• Operation with $k = 2$, after the operation $s_1 = \mathtt{bbcaa}$, $s_2 = \mathtt{cbaab}$.
• Operation with $k = 3$, after the operation $s_1 = \mathtt{aabaa}$, $s_2 = \mathtt{cbbbc}$.
• Operation with $k = 1$, after the operation $s_1 = \mathtt{cabaa}$, $s_2 = \mathtt{cbbba}$.
• Operation with $k = 2$, after the operation $s_1 = \mathtt{babaa}$, $s_2 = \mathtt{cbbca}$.
• Operation with $k = 1$, after the operation $s_1 = \mathtt{aabaa}$, $s_2 = \mathtt{cbbcb}$.
• Operation with $k = 2$, after the operation $s_1 = \mathtt{cbbaa}$, $s_2 = \mathtt{cbbaa}$.

In the third test case, it's impossible to make strings equal.