Lexicographically Small Enough

1000ms

262144K

Description:

You are given two strings $$$s$$$ and $$$t$$$ of equal length $$$n$$$. In one move, you can swap any two adjacent characters of the string $$$s$$$.

You need to find the minimal number of operations you need to make string $$$s$$$ lexicographically smaller than string $$$t$$$.

A string $$$a$$$ is lexicographically smaller than a string $$$b$$$ if and only if one of the following holds:

$$$a$$$ is a prefix of $$$b$$$, but $$$a \ne b$$$;
in the first position where $$$a$$$ and $$$b$$$ differ, the string $$$a$$$ has a letter that appears earlier in the alphabet than the corresponding letter in $$$b$$$.

Input:

The first line of input contains one integer $$$q$$$ ($$$1 \le q \le 10\,000$$$): the number of test cases.

The first line of each test case contains a single integer $$$n$$$ ($$$1 \le n \le 10^5$$$).

The second line of each test case contains the string $$$s$$$ consisting of $$$n$$$ lowercase English letters.

The third line of each test case contains the string $$$t$$$ consisting of $$$n$$$ lowercase English letters.

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

Output:

For each test case, print in a separate line the minimal number of operations you need to make string $$$s$$$ lexicographically smaller than string $$$t$$$, or $$$-1$$$, if it's impossible.

Sample Input:

4
1
a
a
3
rll
rrr
3
caa
aca
5
ababa
aabba

Sample Output:

Informação

Provedor Codeforces

Código CF1616E