Character Swap (Hard Version)
Contest: Codeforces Round 599 (Div. 2)
Difficulty rating: 1600
Tags: strings

This problem is different from the easy version. In this version Ujan makes at most $$$2n$$$ swaps. In addition, $$$k \le 1000, n \le 50$$$ and it is necessary to print swaps themselves. You can hack this problem if you solve it. But you can hack the previous problem only if you solve both problems.

After struggling and failing many times, Ujan decided to try to clean up his house again. He decided to get his strings in order first.

Ujan has two distinct strings $$$s$$$ and $$$t$$$ of length $$$n$$$ consisting of only of lowercase English characters. He wants to make them equal. Since Ujan is lazy, he will perform the following operation at most $$$2n$$$ times: he takes two positions $$$i$$$ and $$$j$$$ ($$$1 \le i,j \le n$$$, the values $$$i$$$ and $$$j$$$ can be equal or different), and swaps the characters $$$s_i$$$ and $$$t_j$$$.

Ujan's goal is to make the strings $$$s$$$ and $$$t$$$ equal. He does not need to minimize the number of performed operations: any sequence of operations of length $$$2n$$$ or shorter is suitable.

Input format:
The first line contains a single integer $$$k$$$ ($$$1 \leq k \leq 1000$$$), the number of test cases.

For each of the test cases, the first line contains a single integer $$$n$$$ ($$$2 \leq n \leq 50$$$), the length of the strings $$$s$$$ and $$$t$$$.

Each of the next two lines contains the strings $$$s$$$ and $$$t$$$, each having length exactly $$$n$$$. The strings consist only of lowercase English letters. It is guaranteed that strings are different.

Output format:
For each test case, output "Yes" if Ujan can make the two strings equal with at most $$$2n$$$ operations and "No" otherwise. You can print each letter in any case (upper or lower).

In the case of "Yes" print $$$m$$$ ($$$1 \le m \le 2n$$$) on the next line, where $$$m$$$ is the number of swap operations to make the strings equal. Then print $$$m$$$ lines, each line should contain two integers $$$i, j$$$ ($$$1 \le i, j \le n$$$) meaning that Ujan swaps $$$s_i$$$ and $$$t_j$$$ during the corresponding operation. You do not need to minimize the number of operations. Any sequence of length not more than $$$2n$$$ is suitable.

Constraints:
Time limit: 1.0 s
Memory limit: 256.0 MB

Example input:
4
5
souse
houhe
3
cat
dog
2
aa
az
3
abc
bca

Example output:
Yes
1
1 4
No
No
Yes
3
1 2
3 1
2 3

Editorial:
We claim that you can make the strings equal if and only if the total number of each character in both of the strings $$$s$$$ and $$$t$$$ is even.
Proof that this is a necessary condition. If we can make the strings equal, then for each position, the characters of $$$s$$$ and $$$t$$$ will be the same. Therefore, each character must appear an even number of times in both strings together.
Algorithm, if all characters appear even number of times. Iterate over the index $$$i$$$ from $$$1$$$ to $$$n$$$. If $$$s_i \neq t_i$$$, then one of the following cases holds:
• There is an index $$$j > i$$$ such that $$$s_i = s_j$$$. Then simply swap $$$s_j$$$ with $$$t_i$$$ and then the strings will have the same character at position $$$i$$$.
• There is an index $$$j > i$$$ such that $$$s_i = t_j$$$. Then first swap $$$t_j$$$ with $$$s_j$$$, and then swap $$$s_j$$$ with $$$t_i$$$. Again, the strings will have the same character at position $$$i$$$.
This problem was introduced by [user:MikeMirzayanov] inspired by the easier version of the problem (with a single swap).