#include <bits/stdc++.h>
using namespace std;
int main() {
  std::ios::sync_with_stdio(false);
  std::cin.tie(0);
  int n;
  cin >> n;
  vector<int> a(n), t(n);
  long long res = 0;
  for (int i = 0; i < n; ++i) {
    cin >> a[i];
  }
  vector<pair<int, int> > w(1, pair<int, int>(2e9, 0));
  for (int i = 0; i < n; ++i) {
    cin >> t[i];
    w.emplace_back(a[i], t[i]);
  }
  sort(w.begin(), w.end());
  int val = -1;
  long long sumt = 0;
  multiset<int> q;
  for (int i = 0; i < w.size(); ++i) {
    while (val < w[i].first && !q.empty()) {
      auto it = q.end();
      --it;
      sumt -= *it;
      q.erase(it);
      res += sumt;
      ++val;
    }
    val = max(val, w[i].first);
    sumt += w[i].second;
    q.insert(w[i].second);
  }
  cout << res << endl;
  return 0;
}

### Prompt

Please formulate a cpp solution to the following problem:

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;
int main() {
  std::ios::sync_with_stdio(false);
  std::cin.tie(0);
  int n;
  cin >> n;
  vector<int> a(n), t(n);
  long long res = 0;
  for (int i = 0; i < n; ++i) {
    cin >> a[i];
  }
  vector<pair<int, int> > w(1, pair<int, int>(2e9, 0));
  for (int i = 0; i < n; ++i) {
    cin >> t[i];
    w.emplace_back(a[i], t[i]);
  }
  sort(w.begin(), w.end());
  int val = -1;
  long long sumt = 0;
  multiset<int> q;
  for (int i = 0; i < w.size(); ++i) {
    while (val < w[i].first && !q.empty()) {
      auto it = q.end();
      --it;
      sumt -= *it;
      q.erase(it);
      res += sumt;
      ++val;
    }
    val = max(val, w[i].first);
    sumt += w[i].second;
    q.insert(w[i].second);
  }
  cout << res << endl;
  return 0;
}

```