CF1066F.Yet another 2D Walking

Maksim walks on a Cartesian plane. Initially, he stands at the point $(0, 0)$ and in one move he can go to any of four adjacent points (left, right, up, down). For example, if Maksim is currently at the point $(0, 0)$, he can go to any of the following points in one move:

• $(1, 0)$;
• $(0, 1)$;
• $(-1, 0)$;
• $(0, -1)$.

There are also $n$ distinct key points at this plane. The $i$-th point is $p_i = (x_i, y_i)$. It is guaranteed that $0 \le x_i$ and $0 \le y_i$ and there is no key point $(0, 0)$.

Let the first level points be such points that $max(x_i, y_i) = 1$, the second level points be such points that $max(x_i, y_i) = 2$ and so on. Maksim wants to visit all the key points. But he shouldn't visit points of level $i + 1$ if he does not visit all the points of level $i$. He starts visiting the points from the minimum level of point from the given set.

The distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ is $|x_1 - x_2| + |y_1 - y_2|$ where $|v|$ is the absolute value of $v$.

Maksim wants to visit all the key points in such a way that the total distance he walks will be minimum possible. Your task is to find this distance.

If you are Python programmer, consider using PyPy instead of Python when you submit your code.

马克西姆在笛卡尔平面上行走。初始时，他位于点 $(0, 0)$，每次移动可前往四个相邻点之一（左、右、上、下）。例如，若马克西姆当前位于点 $(0, 0)$，则他可在一次移动中到达以下任意一点：

• $(1, 0)$；
• $(0, 1)$；
• $(-1, 0)$；
• $(0, -1)$。

平面上还有 $n$ 个互异的关键点。第 $i$ 个点为 $p_i = (x_i, y_i)$。保证对所有 $i$ 有 $0 \le x_i$ 且 $0 \le y_i$，且不存在关键点 $(0, 0)$。

定义“第一层”点为满足 $\max(x_i, y_i) = 1$ 的点，“第二层”点为满足 $\max(x_i, y_i) = 2$ 的点，依此类推。马克西姆需访问所有关键点，但在未访问完第 $i$ 层的所有点之前，不得访问第 $i+1$ 层的任何点。他从给定关键点集合中最小的层数开始访问。

两点 $(x_1, y_1)$ 与 $(x_2, y_2)$ 之间的距离定义为 $|x_1 - x_2| + |y_1 - y_2|$，其中 $|v|$ 表示 $v$ 的绝对值。

马克西姆希望以总行走距离最小的方式访问全部关键点。你的任务是求出该最小总距离。

如果你使用 Python 编程，请在提交代码时考虑使用 PyPy 而非 Python。

The first line of the input contains one integer $n$ ($1 \le n \le 2 \cdot 10^5$) — the number of key points.

Each of the next $n$ lines contains two integers $x_i$, $y_i$ ($0 \le x_i, y_i \le 10^9$) — $x$-coordinate of the key point $p_i$ and $y$-coordinate of the key point $p_i$. It is guaranteed that all the points are distinct and the point $(0, 0)$ is not in this set.

输入的第一行包含一个整数 $n$（$1 \le n \le 2 \cdot 10^5$）—— 关键点的数量。

接下来的 $n$ 行中，每行包含两个整数 $x_i$、$y_i$（$0 \le x_i, y_i \le 10^9$）—— 关键点 $p_i$ 的 $x$ 坐标和 $y$ 坐标。保证所有点互不相同，且点 $(0, 0)$ 不在该集合中。

Print one integer — the minimum possible total distance Maksim has to travel if he needs to visit all key points in a way described above.

输出一个整数——即马克西姆按上述方式访问所有关键点所需经过的最小总距离。

The picture corresponding to the first example:

There is one of the possible answers of length $15$.

The picture corresponding to the second example:

There is one of the possible answers of length $9$.

第一个示例对应的图片：

存在一个长度为 $15$ 的可能答案。

第二个示例对应的图片：

存在一个长度为 $9$ 的可能答案。