#include <bits/stdc++.h>
using namespace std;
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  ;
  {
    int n;
    cin >> n;
    int arr[n];
    for (int i = 0; i < n; i++) {
      cin >> arr[i];
    }
    vector<pair<int, int>> a;
    for (int i = 0; i < n; i++) {
      int x;
      cin >> x;
      a.push_back({arr[i], x});
    }
    sort(a.begin(), a.end());
    priority_queue<int> pq;
    long long sum = 0, ans = 0;
    for (int i = 0; i < n; i++) {
      int current = a[i].first;
      pq.push(a[i].second);
      sum += a[i].second;
      while (!pq.empty() && (i == n - 1 || current != a[i + 1].first)) {
        sum -= pq.top();
        pq.pop();
        ans += sum;
        current++;
      }
    }
    cout << ans << endl;
  }
  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;
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  ;
  {
    int n;
    cin >> n;
    int arr[n];
    for (int i = 0; i < n; i++) {
      cin >> arr[i];
    }
    vector<pair<int, int>> a;
    for (int i = 0; i < n; i++) {
      int x;
      cin >> x;
      a.push_back({arr[i], x});
    }
    sort(a.begin(), a.end());
    priority_queue<int> pq;
    long long sum = 0, ans = 0;
    for (int i = 0; i < n; i++) {
      int current = a[i].first;
      pq.push(a[i].second);
      sum += a[i].second;
      while (!pq.empty() && (i == n - 1 || current != a[i + 1].first)) {
        sum -= pq.top();
        pq.pop();
        ans += sum;
        current++;
      }
    }
    cout << ans << endl;
  }
  return 0;
}

```