A13360 | 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.

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 $i$ ( $1 \le t_i \le 10^5)$ .

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