CF1060D.Social Circles

You invited $n$ guests to dinner! You plan to arrange one or more circles of chairs. Each chair is going to be either occupied by one guest, or be empty. You can make any number of circles.

Your guests happen to be a little bit shy, so the $i$-th guest wants to have a least $l_i$ free chairs to the left of his chair, and at least $r_i$ free chairs to the right. The "left" and "right" directions are chosen assuming all guests are going to be seated towards the center of the circle. Note that when a guest is the only one in his circle, the $l_i$ chairs to his left and $r_i$ chairs to his right may overlap.

What is smallest total number of chairs you have to use?

你邀请了 $n$ 位客人共进晚餐！你计划布置一个或多个圆形椅子排列。每把椅子要么坐一位客人，要么为空。你可以布置任意数量的圆圈。

你的客人恰好有点害羞，因此第 $i$ 位客人希望其椅子左侧至少有 $l_i$ 个空椅子，右侧至少有 $r_i$ 个空椅子。“左”和“右”的方向是基于所有客人均朝向圆心就座这一假设来确定的。注意：当某位客人是其所处圆圈中唯一一人时，其左侧的 $l_i$ 把空椅子与右侧的 $r_i$ 把空椅子可能重叠。

你最少需要准备多少把椅子？

First line contains one integer $n$ — number of guests, ($1 \leqslant n \leqslant 10^5$).

Next $n$ lines contain $n$ pairs of space-separated integers $l_i$ and $r_i$ ($0 \leqslant l_i, r_i \leqslant 10^9$).

第一行包含一个整数 $n$ —— 客人的数量（$1 \leqslant n \leqslant 10^5$）。

接下来的 $n$ 行，每行包含一对由空格分隔的整数 $l_i$ 和 $r_i$（$0 \leqslant l_i, r_i \leqslant 10^9$）。

Output a single integer — the smallest number of chairs you have to use.

输出一个整数——你需要使用的最少椅子数量。

In the second sample the only optimal answer is to use two circles: a circle with $5$ chairs accomodating guests $1$ and $2$, and another one with $10$ chairs accomodationg guests $3$ and $4$.

In the third sample, you have only one circle with one person. The guest should have at least five free chairs to his left, and at least six free chairs to his right to the next person, which is in this case the guest herself. So, overall number of chairs should be at least 6+1=7.

在第二个样例中，唯一的最优方案是使用两个圆圈：一个包含 5 把椅子的圆圈容纳客人 1 和 2，另一个包含 10 把椅子的圆圈容纳客人 3 和 4。

在第三个样例中，你只有一个圆圈，且圆圈中仅有一名客人。该客人左侧至少需要有 5 把空椅子，右侧（到下一位客人，即她本人）至少需要有 6 把空椅子。因此，椅子总数至少为 $6+1=7$。