Two Strings Swaps
Contest: Codeforces Round 498 (Div. 3)
Difficulty rating: 1700
Tags: implementation

You are given two strings $$$a$$$ and $$$b$$$ consisting of lowercase English letters, both of length $$$n$$$. The characters of both strings have indices from $$$1$$$ to $$$n$$$, inclusive.

You are allowed to do the following changes:

- Choose any index $$$i$$$ ($$$1 \le i \le n$$$) and swap characters $$$a_i$$$ and $$$b_i$$$;
- Choose any index $$$i$$$ ($$$1 \le i \le n$$$) and swap characters $$$a_i$$$ and $$$a_{n - i + 1}$$$;
- Choose any index $$$i$$$ ($$$1 \le i \le n$$$) and swap characters $$$b_i$$$ and $$$b_{n - i + 1}$$$.

Note that if $$$n$$$ is odd, you are formally allowed to swap $$$a_{\lceil\frac{n}{2}\rceil}$$$ with $$$a_{\lceil\frac{n}{2}\rceil}$$$ (and the same with the string $$$b$$$) but this move is useless. Also you can swap two equal characters but this operation is useless as well.

You have to make these strings equal by applying any number of changes described above, in any order. But it is obvious that it may be impossible to make two strings equal by these swaps.

In one preprocess move you can replace a character in $$$a$$$ with another character. In other words, in a single preprocess move you can choose any index $$$i$$$ ($$$1 \le i \le n$$$), any character $$$c$$$ and set $$$a_i := c$$$.

Your task is to find the minimum number of preprocess moves to apply in such a way that after them you can make strings $$$a$$$ and $$$b$$$ equal by applying some number of changes described in the list above.

Note that the number of changes you make after the preprocess moves does not matter. Also note that you cannot apply preprocess moves to the string $$$b$$$ or make any preprocess moves after the first change is made.

Input format:
The first line of the input contains one integer $$$n$$$ ($$$1 \le n \le 10^5$$$) — the length of strings $$$a$$$ and $$$b$$$.

The second line contains the string $$$a$$$ consisting of exactly $$$n$$$ lowercase English letters.

The third line contains the string $$$b$$$ consisting of exactly $$$n$$$ lowercase English letters.

Output format:
Print a single integer — the minimum number of preprocess moves to apply before changes, so that it is possible to make the string $$$a$$$ equal to string $$$b$$$ with a sequence of changes from the list above.

Constraints:
Time limit: 2.0 s
Memory limit: 256.0 MB

Note:
In the first example preprocess moves are as follows: $$$a_1 := $$$'b', $$$a_3 := $$$'c', $$$a_4 := $$$'a' and $$$a_5:=$$$'b'. Afterwards, $$$a = $$$"bbcabba". Then we can obtain equal strings by the following sequence of changes: $$$swap(a_2, b_2)$$$ and $$$swap(a_2, a_6)$$$. There is no way to use fewer than $$$4$$$ preprocess moves before a sequence of changes to make string equal, so the answer in this example is $$$4$$$.

In the second example no preprocess moves are required. We can use the following sequence of changes to make $$$a$$$ and $$$b$$$ equal: $$$swap(b_1, b_5)$$$, $$$swap(a_2, a_4)$$$.

Example input:
7
abacaba
bacabaa

Example output:
4

Example input:
5
zcabd
dbacz

Example output:
0

Editorial:
Let's divide all characters of both strings into groups in such a way that characters in each group can be swapped with each other with changes. So, there will be following groups: $$$\{a_1, a_n, b_1, b_n\}$$$, $$$\{a_2, a_{n - 1}, b_2, b_{n - 1}\}$$$ and so on. Since these groups don't affect each other, we can calculate the number of preprocess moves in each group and then sum it up.
How to determine if a group does not need any preprocess moves? For a group consisting of $$$2$$$ characters (there will be one such group if $$$n$$$ is odd, it will contain $$$a_{\lceil\frac{n}{2}\rceil}$$$ and $$$b_{\lceil\frac{n}{2}\rceil}$$$), that's easy — if the characters in this group are equal, the answer is $$$0$$$, otherwise it's $$$1$$$.
To determine the required number of preprocess moves for a group consising of four characters, we may use the following fact: this group doesn't require preprocess moves iff the characters in this group can be divided into pairs. So if the group contains four equal characters, or two pairs of equal characters, then the answer for this group is $$$0$$$. Otherwise we may check that replacing only one character of $$$a_i$$$ and $$$a_{n - i + 1}$$$ will be enough; if so, then the answer is $$$1$$$, otherwise it's $$$2$$$.
Overall complexity is $$$O(n)$$$.