#include <bits/stdc++.h>
using namespace std;
int main() {
  int n;
  cin >> n;
  vector<int> a(n), cost(n);
  for (int& p : a) cin >> p;
  for (int& p : cost) cin >> p;
  priority_queue<pair<int, int> > q;
  priority_queue<int> t;
  for (int i = 0; i < n; i++) {
    q.push({-a[i], cost[i]});
  }
  int index = 0;
  long long sol = 0, total = 0;
  while (q.size() > 0) {
    while (t.size() > 0 && index + 1 < -q.top().first) {
      index++;
      sol += total - t.top();
      total -= t.top();
      t.pop();
    }
    total += q.top().second;
    index = -q.top().first - 1;
    t.push(q.top().second);
    q.pop();
  }
  while (t.size() > 0) {
    sol += total - t.top();
    total -= t.top();
    t.pop();
  }
  cout << sol << "\n";
}

### Prompt

Generate 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() {
  int n;
  cin >> n;
  vector<int> a(n), cost(n);
  for (int& p : a) cin >> p;
  for (int& p : cost) cin >> p;
  priority_queue<pair<int, int> > q;
  priority_queue<int> t;
  for (int i = 0; i < n; i++) {
    q.push({-a[i], cost[i]});
  }
  int index = 0;
  long long sol = 0, total = 0;
  while (q.size() > 0) {
    while (t.size() > 0 && index + 1 < -q.top().first) {
      index++;
      sol += total - t.top();
      total -= t.top();
      t.pop();
    }
    total += q.top().second;
    index = -q.top().first - 1;
    t.push(q.top().second);
    q.pop();
  }
  while (t.size() > 0) {
    sol += total - t.top();
    total -= t.top();
    t.pop();
  }
  cout << sol << "\n";
}

```