#include <bits/stdc++.h>
using namespace std;
priority_queue<pair<long long, long long> > pq;
pair<long long, long long> ara[200006];
int main() {
  long long n, i, ans, now;
  bool flag;
  pair<long long, long long> val;
  scanf("%lld", &n);
  for (i = 1; i <= n; i++) scanf("%lld", &ara[i].first);
  for (i = 1; i <= n; i++) scanf("%lld", &ara[i].second);
  sort(ara + 1, ara + n + 1);
  ara[n + 1].first = 2e9, ans = 0;
  for (i = 1; i <= n; i++) {
    while (ara[i].first == ara[i + 1].first)
      pq.push({ara[i].second, ara[i].first}), i++;
    if (!pq.empty()) {
      pq.push({ara[i].second, ara[i].first});
      now = ara[i].first;
      while (now < ara[i + 1].first && !pq.empty()) {
        val = pq.top();
        ans += ((now - val.second) * val.first);
        now++, pq.pop();
      }
    }
  }
  printf("%lld\n", ans);
  return 0;
}

### Prompt

Construct a cpp code solution to the problem outlined:

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.

Input

The first line of input consists of single integer n — the number of news categories (1 ≤ n ≤ 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 ≤ a_i ≤ 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 ≤ t_i ≤ 10^5).

Output

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

Examples

Input


5
3 7 9 7 8
5 2 5 7 5


Output


6


Input


5
1 2 3 4 5
1 1 1 1 1


Output


0

Note

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.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
priority_queue<pair<long long, long long> > pq;
pair<long long, long long> ara[200006];
int main() {
  long long n, i, ans, now;
  bool flag;
  pair<long long, long long> val;
  scanf("%lld", &n);
  for (i = 1; i <= n; i++) scanf("%lld", &ara[i].first);
  for (i = 1; i <= n; i++) scanf("%lld", &ara[i].second);
  sort(ara + 1, ara + n + 1);
  ara[n + 1].first = 2e9, ans = 0;
  for (i = 1; i <= n; i++) {
    while (ara[i].first == ara[i + 1].first)
      pq.push({ara[i].second, ara[i].first}), i++;
    if (!pq.empty()) {
      pq.push({ara[i].second, ara[i].first});
      now = ara[i].first;
      while (now < ara[i + 1].first && !pq.empty()) {
        val = pq.top();
        ans += ((now - val.second) * val.first);
        now++, pq.pop();
      }
    }
  }
  printf("%lld\n", ans);
  return 0;
}

```