CF1370E.Binary Subsequence Rotation

Naman has two binary strings $s$ and $t$ of length $n$ (a binary string is a string which only consists of the characters "0" and "1"). He wants to convert $s$ into $t$ using the following operation as few times as possible.

In one operation, he can choose any subsequence of $s$ and rotate it clockwise once.

For example, if $s = 1\textbf{1}101\textbf{00}$, he can choose a subsequence corresponding to indices ($1$-based) ${2, 6, 7 }$ and rotate them clockwise. The resulting string would then be $s = 1\textbf{0}101\textbf{10}$.

A string $a$ is said to be a subsequence of string $b$ if $a$ can be obtained from $b$ by deleting some characters without changing the ordering of the remaining characters.

To perform a clockwise rotation on a sequence $c$ of size $k$ is to perform an operation which sets $c_1:=c_k, c_2:=c_1, c_3:=c_2, \ldots, c_k:=c_{k-1}$ simultaneously.

Determine the minimum number of operations Naman has to perform to convert $s$ into $t$ or say that it is impossible.

纳曼有两条长度为 $n$ 的二进制字符串 $s$ 和 $t$（二进制字符串仅由字符 "0" 和 "1" 构成）。他希望用尽可能少的操作次数将 $s$ 转换为 $t$。

每次操作中，他可以任选 $s$ 的一个子序列，并将其顺时针旋转一次。

例如，若 $s = 1\textbf{1}101\textbf{00}$，他可选取对应下标（从 1 开始计数）为 $\{2, 6, 7\}$ 的子序列并进行顺时针旋转，结果字符串变为 $s = 1\textbf{0}101\textbf{10}$。

字符串 $a$ 称为字符串 $b$ 的子序列，当且仅当 $a$ 可通过从 $b$ 中删除若干字符（不改变其余字符的相对顺序）而得到。

对长度为 $k$ 的序列 $c$ 进行一次顺时针旋转，是指同时执行如下赋值操作：$c_1:=c_k,\ c_2:=c_1,\ c_3:=c_2,\ \ldots,\ c_k:=c_{k-1}$。

请确定将 $s$ 转换为 $t$ 所需的最少操作次数；若不可能实现，则说明这一点。

The first line contains a single integer $n$ $(1 \le n \le 10^6)$ — the length of the strings.

The second line contains the binary string $s$ of length $n$.

The third line contains the binary string $t$ of length $n$.

第一行包含一个整数 $n$ $(1 \le n \le 10^6)$ —— 字符串的长度。

第二行包含一个长度为 $n$ 的二进制字符串 $s$。

第三行包含一个长度为 $n$ 的二进制字符串 $t$。

If it is impossible to convert $s$ to $t$ after any number of operations, print $-1$.

Otherwise, print the minimum number of operations required.

如果经过任意次数的操作都无法将 $s$ 转换为 $t$，则输出 $-1$。

否则，输出所需的最少操作次数。

In the first test, Naman can choose the subsequence corresponding to indices ${2, 6}$ and rotate it once to convert $s$ into $t$.

In the second test, he can rotate the subsequence corresponding to all indices $5$ times. It can be proved, that it is the minimum required number of operations.

In the last test, it is impossible to convert $s$ into $t$.

在第一个测试用例中，Naman 可以选择对应下标 $\{2, 6\}$ 的子序列，并将其旋转一次，从而将 $s$ 转换为 $t$。

在第二个测试用例中，他可以将对应所有下标的子序列旋转 $5$ 次。可以证明，这是所需的最少操作次数。

在最后一个测试用例中，无法将 $s$ 转换为 $t$。