AT_abc479_f.Narrow Passage

There are $N$ people standing on a number line. The people are numbered $1, 2, \ldots, N$, and initially person $i$ is at coordinate $S_i$. Here, the $S_i$ are pairwise distinct.

You can repeatedly perform the following operation.

• Choose one person. Let $x$ be the coordinate where that person currently is, and move them to $x - 1$ or $x + 1$. If there is a person at the destination, that person is simultaneously moved to coordinate $x$.

Find the minimum number of operations required to reach a state where each person $i$ is at coordinate $T_i$. Here, the $T_i$ are pairwise distinct.

数轴上有 $N$ 个人。这些人编号为 $1, 2, \ldots, N$，初始时第 $i$ 个人位于坐标 $S_i$。其中，所有 $S_i$ 两两互不相同。

你可以重复执行以下操作：

• 选择一个人。设该人当前所在坐标为 $x$，将其移动至 $x - 1$ 或 $x + 1$。若目标位置上已有一人，则该人将同时被移至坐标 $x$。

求达到如下状态所需的最少操作次数：每个人 $i$ 均位于坐标 $T_i$。其中，所有 $T_i$ 两两互不相同。

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

$N$
$S_1$ $S_2$ $\ldots$ $S_N$
$T_1$ $T_2$ $\ldots$ $T_N$

输入从标准输入中按以下格式给出：

$N$
$S_1$ $S_2$ $\ldots$ $S_N$
$T_1$ $T_2$ $\ldots$ $T_N$

Output the answer.

输出答案。

Sample 1 Explanation:
Initially, persons $1, 2, 3$ are at coordinates $4, 2, 5$, respectively. By performing the operations as follows, persons $1, 2, 3$ end up at coordinates $3, 4, 1$, respectively, in six operations.

• Move person $1$ from coordinate $4$ to $3$. After this operation, persons $1, 2, 3$ are at coordinates $3, 2, 5$, respectively.

• Move person $1$ from coordinate $3$ to $2$. Since person $2$ is at coordinate $2$, person $2$ simultaneously moves to coordinate $3$. After this operation, persons $1, 2, 3$ are at coordinates $2, 3, 5$, respectively.

• Move person $3$ from coordinate $5$ to $4$. After this operation, persons $1, 2, 3$ are at coordinates $2, 3, 4$, respectively.

• Move person $3$ from coordinate $4$ to $3$. Since person $2$ is at coordinate $3$, person $2$ simultaneously moves to coordinate $4$. After this operation, persons $1, 2, 3$ are at coordinates $2, 4, 3$, respectively.

• Move person $3$ from coordinate $3$ to $2$. Since person $1$ is at coordinate $2$, person $1$ simultaneously moves to coordinate $3$. After this operation, persons $1, 2, 3$ are at coordinates $3, 4, 2$, respectively.

• Move person $3$ from coordinate $2$ to $1$. After this operation, persons $1, 2, 3$ are at coordinates $3, 4, 1$, respectively.

Constraints

• $1 \leq N \leq 2 \times 10^5$
• $0 \leq S_i, T_i \leq 10^9$
• $S_i \neq S_j$ and $T_i \neq T_j$ if $i \neq j$.
• All input values are integers.

样例 1 解释：
初始时，人员 $1, 2, 3$ 分别位于坐标 $4, 2, 5$。通过执行如下六次操作，人员 $1, 2, 3$ 最终分别到达坐标 $3, 4, 1$。

• 将人员 $1$ 从坐标 $4$ 移动到 $3$。该操作后，人员 $1, 2, 3$ 分别位于坐标 $3, 2, 5$。
• 将人员 $1$ 从坐标 $3$ 移动到 $2$。由于人员 $2$ 当前位于坐标 $2$，因此人员 $2$ 同时移动至坐标 $3$。该操作后，人员 $1, 2, 3$ 分别位于坐标 $2, 3, 5$。
• 将人员 $3$ 从坐标 $5$ 移动到 $4$。该操作后，人员 $1, 2, 3$ 分别位于坐标 $2, 3, 4$。
• 将人员 $3$ 从坐标 $4$ 移动到 $3$。由于人员 $2$ 当前位于坐标 $3$，因此人员 $2$ 同时移动至坐标 $4$。该操作后，人员 $1, 2, 3$ 分别位于坐标 $2, 4, 3$。
• 将人员 $3$ 从坐标 $3$ 移动到 $2$。由于人员 $1$ 当前位于坐标 $2$，因此人员 $1$ 同时移动至坐标 $3$。该操作后，人员 $1, 2, 3$ 分别位于坐标 $3, 4, 2$。
• 将人员 $3$ 从坐标 $2$ 移动到 $1$。该操作后，人员 $1, 2, 3$ 分别位于坐标 $3, 4, 1$。

约束条件

• $1 \leq N \leq 2 \times 10^5$
• $0 \leq S_i, T_i \leq 10^9$
• 若 $i \neq j$，则 $S_i \neq S_j$ 且 $T_i \neq T_j$。
• 所有输入值均为整数。