哈密顿 - المسألة

#7993. 哈密顿

الإحصائيات

This problem is prepared by Itst .

题目描述

给出 $n$ 个二元组 $(a_i,b_i)$。

考虑 $n$ 个节点的带权有向完全图 $G$，其中从 $i (1 \le i \le n)$ 到 $j (1 \le j \le n)$ 的边边权为 $|a_i-b_j|$。

求 $G$ 的一条哈密顿回路使得其经过的边的边权和最大，并给出这个最大值。

输入格式

从标准输入读入数据。

输入的第一行一个整数 $n(2 \le n \le 10^5)$ 表示二元组个数，接下来 $n$ 行每行两个整数 $a_i,b_i(0 \le a_i,b_i \le 10^9)$ 表示每个二元组。保证输入的 $n$ 个二元组中的总共 $2n$ 个数两两不同。

输出格式

输出到标准输出。

输出一行一个整数表示最大的哈密顿回路边权和。

样例

输入

输出

解释

考察哈密顿回路 $1 \to 2 \to 3 \to 1$，其边权和为 $|1-2| + | 8-5| + |4-10| = 10$。可以证明不存在哈密顿回路边权和超过 $10$，因此答案为 $10$。

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