CF2247C.Inversion of a Subsequence

You are given two arrays $a$ and $b$ of length $n$, consisting only of $0$ and $1$.

You may perform the following operation on $a$ any number of times:

1. Choose $k$ indices $1 \le i_1 \lt i_2 \lt \ldots \lt i_k \le n$, where $1 \le k \le n$ and $\sum\limits_{j = 1}^k a_{i_j}$ is odd. In other words, choose a non-empty subsequence$^{\text{∗}}$ of $a$ with an odd sum.
2. For each $1 \le j \le k$, set $a_{i_j} = 1 - a_{i_j}$. In other words, invert all elements of the chosen subsequence.

Find the minimum number of operations needed to transform $a$ into $b$, or determine that it is impossible.

$^{\text{∗}}$A sequence $c$ is a subsequence of a sequence $d$ if $c$ can be obtained from $d$ by the deletion of several (possibly, zero or all) elements from arbitrary positions.

给你两个长度为 $n$ 的数组 $a$ 和 $b$，其中仅包含 $0$ 和 $1$。

你可以对数组 $a$ 执行以下操作任意多次：

1. 选择 $k$ 个下标 $1 \le i_1 \lt i_2 \lt \ldots \lt i_k \le n$，其中 $1 \le k \le n$，且 $\sum\limits_{j = 1}^k a_{i_j}$ 为奇数。换言之，选择 $a$ 的一个非空子序列$^{\text{∗}}$，其元素和为奇数。
2. 对每个 $1 \le j \le k$，令 $a_{i_j} = 1 - a_{i_j}$。换言之，将所选子序列中所有元素取反。

求将 $a$ 变为 $b$ 所需的最少操作次数；若不可能实现，则判定为不可行。

$^{\text{∗}}$ 序列 $c$ 是序列 $d$ 的子序列，当且仅当 $c$ 可通过从 $d$ 中删除若干（可能为零个或全部）任意位置的元素而得到。

Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \le t \le 10^4$). The description of the test cases follows.

The first line of each test case contains a single integer $n$ ($1 \le n \le 2 \cdot 10^5$) — the length of the arrays $a$ and $b$.

The second line of each test case contains $n$ integers $a_1, a_2, \ldots, a_n$ ($a_i \in {0, 1}$) — array $a$.

The third line of each test case contains $n$ integers $b_1, b_2, \ldots, b_n$ ($b_i \in {0, 1}$) — array $b$.

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

每个测试包含多个测试用例。第一行包含测试用例的数量 $t$（$1 \le t \le 10^4$）。随后是各测试用例的描述。

每个测试用例的第一行包含一个整数 $n$（$1 \le n \le 2 \cdot 10^5$）—— 数组 $a$ 和 $b$ 的长度。

每个测试用例的第二行包含 $n$ 个整数 $a_1, a_2, \ldots, a_n$（$a_i \in \{0, 1\}$）—— 数组 $a$。

每个测试用例的第三行包含 $n$ 个整数 $b_1, b_2, \ldots, b_n$（$b_i \in \{0, 1\}$）—— 数组 $b$。

保证所有测试用例中 $n$ 的总和不超过 $2 \cdot 10^5$。

For each test case, output a single integer — the minimum number of operations needed to transform $a$ into $b$, or $-1$ if it is impossible.

对于每个测试用例，输出一个整数——将 $a$ 变换为 $b$ 所需的最少操作次数；如果无法实现，则输出 $-1$。

In the first example, $a = b$, so no operations are needed. Therefore, the answer is $0$.

In the second example, we can perform an operation with the subsequence $[a_1, a_2]$. The sum of its elements is $1 + 0 = 1$, which is odd. This operation transforms $a$ as follows: $[\color{red}{1, 0}] \rightarrow [\color{red}{0, 1}]$. The resulting array equals $b$, so the answer is $1$.

在第一个例子中，$a = b$，因此无需执行任何操作。答案为 $0$。

在第二个例子中，我们可以对子序列 $[a_1, a_2]$ 执行一次操作。该子序列元素之和为 $1 + 0 = 1$，是奇数。该操作将 $a$ 变换如下：$[\color{red}{1, 0}] \rightarrow [\color{red}{0, 1}]$。变换后的数组等于 $b$，因此答案为 $1$。