#include <bits/stdc++.h>
using namespace std;
int main() {
  int n, F;
  long long int S = 0, s = 0;
  cin >> n;
  vector<pair<int, int> > X(n);
  for (int i = 0; i < n; i++) {
    cin >> X[i].first;
  }
  for (int i = 0; i < n; i++) {
    cin >> X[i].second;
  }
  sort(X.begin(), X.end());
  priority_queue<int> Y;
  Y.push(X[0].second);
  F = X[0].first;
  s += X[0].second;
  for (long long int i = 1; i < n; i++) {
    if (X[i].first == F) {
      Y.push(X[i].second);
      s += X[i].second;
    } else {
      for (long long int j = 0; j < X[i].first - F; j++) {
        if (!Y.empty()) {
          s -= Y.top();
          Y.pop();
          S += s;
        } else
          break;
      }
      F = X[i].first;
      Y.push(X[i].second);
      s += X[i].second;
    }
  }
  int N = Y.size();
  for (int i = 0; i < N; i++) {
    s -= Y.top();
    Y.pop();
    S += s;
  }
  cout << S;
  return 0;
}

### Prompt

In Cpp, your task is to solve 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() {
  int n, F;
  long long int S = 0, s = 0;
  cin >> n;
  vector<pair<int, int> > X(n);
  for (int i = 0; i < n; i++) {
    cin >> X[i].first;
  }
  for (int i = 0; i < n; i++) {
    cin >> X[i].second;
  }
  sort(X.begin(), X.end());
  priority_queue<int> Y;
  Y.push(X[0].second);
  F = X[0].first;
  s += X[0].second;
  for (long long int i = 1; i < n; i++) {
    if (X[i].first == F) {
      Y.push(X[i].second);
      s += X[i].second;
    } else {
      for (long long int j = 0; j < X[i].first - F; j++) {
        if (!Y.empty()) {
          s -= Y.top();
          Y.pop();
          S += s;
        } else
          break;
      }
      F = X[i].first;
      Y.push(X[i].second);
      s += X[i].second;
    }
  }
  int N = Y.size();
  for (int i = 0; i < N; i++) {
    s -= Y.top();
    Y.pop();
    S += s;
  }
  cout << S;
  return 0;
}

```