Score: $400$ points

问题陈述

给定两个由 A 和 B 组成的字符串 $S$ 和 $T$，它们的长度都为 $N$。设 $S_i$ 表示 $S$ 从左数第 $i$ 个字符。

你可以重复执行以下操作任意次，包括零次：

• 选择整数 $i$ 和 $j$，使得 $1\leq i < j \leq N$。将 $S_i$ 替换为 A，将 $S_j$ 替换为 B。

确定是否可能使 $S$ 等于 $T$。如果可能，找出所需的最小操作次数。

以上为大语言模型 kimi 翻译，仅供参考。

Problem Statement

You are given two strings $S$ and $T$ of length $N$ consisting of A and B. Let $S_i$ denote the $i$-th character from the left of $S$.

You can repeat the following operation any number of times, possibly zero:

• Choose integers $i$ and $j$ such that $1\leq i < j \leq N$. Replace $S_i$ with A and $S_j$ with B.

Determine if it is possible to make $S$ equal $T$. If it is possible, find the minimum number of operations required.

Constraints

• $2 \leq N \leq 2 \times 10^5$
• Each of $S$ and $T$ is a string of length $N$ consisting of A and B.
• All input numbers are integers.

Input

The input is given from Standard Input in the following format:

$N$

$S$

$T$

Output

If it is impossible to make $S$ equal $T$, print -1.

Otherwise, print the minimum number of operations required to do so.

Sample Input 1

5
BAABA
AABAB

Sample Output 1

2

Performing the operation with $i=1$ and $j=3$ changes $S$ to AABBA.

Performing the operation with $i=4$ and $j=5$ changes $S$ to AABAB.

Thus, you can make $S$ equal $T$ with two operations. It can be proved that this is the minimum number of operations required, so the answer is $2$.

Sample Input 2

2
AB
BA

Sample Output 2

-1

It can be proved that no matter how many operations you perform, you cannot make $S$ equal $T$.