CF1534G.A New Beginning

Annie has gotten bored of winning every coding contest and farming unlimited rating. Today, she is going to farm potatoes instead.

Annie's garden is an infinite 2D plane. She has $n$ potatoes to plant, and the $i$-th potato must be planted at $(x_i,y_i)$. Starting at the point $(0, 0)$, Annie begins walking, in one step she can travel one unit right or up (increasing her $x$ or $y$ coordinate by $1$ respectively). At any point $(X,Y)$ during her walk she can plant some potatoes at arbitrary points using her potato gun, consuming $\max(|X-x|,|Y-y|)$ units of energy in order to plant a potato at $(x,y)$. Find the minimum total energy required to plant every potato.

Note that Annie may plant any number of potatoes from any point.

安妮已经厌倦了在每场编程竞赛中获胜以及刷无限的评分。今天，她决定改种土豆。

安妮的菜园是一个无限大的二维平面。她有 $n$ 个土豆需要种植，其中第 $i$ 个土豆必须种在点 $(x_i, y_i)$ 处。安妮从点 $(0, 0)$ 出发开始行走；每一步，她只能向右或向上移动一个单位（即分别使她的 $x$ 或 $y$ 坐标增加 $1$）。在行走途中的任意一点 $(X, Y)$，她都可以使用她的“土豆枪”在任意位置种植若干土豆，但要在点 $(x, y)$ 处种植一个土豆需消耗 $\max(|X - x|, |Y - y|)$ 单位的能量。求种植所有土豆所需的最小总能量。

注意：安妮可以在任意一个位置种植任意数量的土豆。

The first line contains the integer $n$ ($1 \le n \le 800\,000$).

The next $n$ lines contain two integers $x_i$ and $y_i$ ($0 \le x_i,y_i \le 10^9$), representing the location of the $i$-th potato. It is possible that some potatoes should be planted in the same location.

第一行包含一个整数 $n$（$1 \le n \le 800\,000$）。

接下来的 $n$ 行每行包含两个整数 $x_i$ 和 $y_i$（$0 \le x_i,y_i \le 10^9$），表示第 $i$ 个土豆的种植位置。可能存在多个土豆需种植在同一位置的情况。

Print the minimum total energy to plant all potatoes.

输出种植所有土豆所需的最小总能量。

In example $1$, Annie can travel to each spot directly and plant a potato with no energy required.

In example $2$, moving to $(1,0)$, Annie plants the second potato using $1$ energy. Next, she travels to $(1,1)$ and plants the first potato with $0$ energy.

在示例 $1$ 中，安妮可以直接到达每个地点，并且无需消耗能量即可种植一个土豆。

在示例 $2$ 中，安妮移动到 $(1,0)$，并消耗 $1$ 单位能量种植第二个土豆。接着，她前往 $(1,1)$，并以 $0$ 单位能量种植第一个土豆。