D. Prefixes and Suffixes
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

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

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

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

Example
Input
7
3
cbc
aba
5
abcaa
cbabb
5
abcaa
cbabz
1
a
a
1
a
b
6
abadaa
adaaba
8
abcabdaa
adabcaba
Output
YES
YES
NO
YES
NO
NO
YES
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.