#include <bits/stdc++.h>
using namespace std;
map<long long int, vector<long long int>> arr;
void solve() {
  long long int n;
  cin >> n;
  vector<long long int> a(n);
  for (long long int &i : a) {
    cin >> i;
  }
  for (long long int i = 0; i < n; i++) {
    long long int x;
    cin >> x;
    arr[a[i]].push_back(x);
  }
  long long int res = 0;
  priority_queue<long long int> temp;
  sort(a.begin(), a.end());
  a.erase(unique(a.begin(), a.end()), a.end());
  bool done = false;
  long long int ans = 0;
  for (auto v : a) {
    if (arr[v].size() > 1 || !temp.empty()) {
      for (long long int i = 0; i < arr[v].size(); i++) {
        temp.push(arr[v][i]);
        ans += arr[v][i];
      }
      ans -= temp.top();
      temp.pop();
      long long int curr = v;
      while (!temp.empty()) {
        curr++;
        res += ans;
        if (arr[curr].size()) {
          break;
        } else {
          ans -= temp.top();
          temp.pop();
        }
      }
    }
  }
  cout << res << endl;
}
int main() {
  solve();
  return 0;
}

### Prompt

Create a solution in cpp for 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;
map<long long int, vector<long long int>> arr;
void solve() {
  long long int n;
  cin >> n;
  vector<long long int> a(n);
  for (long long int &i : a) {
    cin >> i;
  }
  for (long long int i = 0; i < n; i++) {
    long long int x;
    cin >> x;
    arr[a[i]].push_back(x);
  }
  long long int res = 0;
  priority_queue<long long int> temp;
  sort(a.begin(), a.end());
  a.erase(unique(a.begin(), a.end()), a.end());
  bool done = false;
  long long int ans = 0;
  for (auto v : a) {
    if (arr[v].size() > 1 || !temp.empty()) {
      for (long long int i = 0; i < arr[v].size(); i++) {
        temp.push(arr[v][i]);
        ans += arr[v][i];
      }
      ans -= temp.top();
      temp.pop();
      long long int curr = v;
      while (!temp.empty()) {
        curr++;
        res += ans;
        if (arr[curr].size()) {
          break;
        } else {
          ans -= temp.top();
          temp.pop();
        }
      }
    }
  }
  cout << res << endl;
}
int main() {
  solve();
  return 0;
}

```