CF1310A.Recommendations

VK news recommendation system daily selects interesting publications of one of $n$ disjoint categories for each user. Each publication belongs to exactly one category. For each category $i$ batch algorithm selects $a_i$ publications.

The latest A/B test suggests that users are reading recommended publications more actively if each category has a different number of publications within daily recommendations. The targeted algorithm can find a single interesting publication of $i$-th category within $t_i$ seconds.

What is the minimum total time necessary to add publications to the result of batch algorithm execution, so all categories have a different number of publications? You can't remove publications recommended by the batch algorithm.

VK 新闻推荐系统每天为每位用户从 $n$ 个互不相交的类别中，各选择若干篇有趣的文章进行推荐。每篇文章恰好属于一个类别。对于每个类别 $i$，批处理算法会选出 $a_i$ 篇文章。

最近的一次 A/B 测试表明：若每日推荐中每个类别的文章数量互不相同，则用户阅读推荐文章的积极性更高。目标算法可在 $t_i$ 秒内为第 $i$ 个类别找到一篇有趣的文章。

在不能移除批处理算法已推荐的文章的前提下，为使所有类别的文章数量互不相同，最少需要额外添加多少总时间？

The first line of input consists of single integer $n$ — the number of news categories ($1 \le n \le 200\,000$).

The second line of input consists of $n$ integers $a_i$ — the number of publications of $i$-th category selected by the batch algorithm ($1 \le a_i \le 10^9$).

The third line of input consists of $n$ integers $t_i$ — time it takes for targeted algorithm to find one new publication of category $i$ ($1 \le t_i \le 10^5)$.

输入的第一行包含一个整数 $n$ —— 新闻类别的数量（$1 \le n \le 200\,000$）。

输入的第二行包含 $n$ 个整数 $a_i$ —— 批处理算法为第 $i$ 类新闻所选择的发布数量（$1 \le a_i \le 10^9$）。

输入的第三行包含 $n$ 个整数 $t_i$ —— 目标算法为第 $i$ 类新闻找到一篇新发布的所需时间（$1 \le t_i \le 10^5$）。

Print one integer — the minimal required time for the targeted algorithm to get rid of categories with the same size.

输出一个整数——目标算法消除所有相同大小类别的最短所需时间。

In the first example, it is possible to find three publications of the second type, which will take 6 seconds.

In the second example, all news categories contain a different number of publications.

在第一个例子中，可以找到三篇第二类出版物，耗时 6 秒。

在第二个例子中，所有新闻类别包含的出版物数量均不相同。