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

### Prompt

Please provide a cpp coded solution to the problem described below:

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(false);
  cin.tie(0);
  cout.tie(0);
  int TESTS = 1;
  while (TESTS--) {
    long long n;
    cin >> n;
    long long vec[n];
    for (long long i = 0; i < n; i++) {
      cin >> vec[i];
    }
    vector<pair<long long, long long> > arr;
    for (long long i = 0; i < n; i++) {
      long long x;
      cin >> x;
      arr.push_back({vec[i], x});
    }
    sort(arr.begin(), arr.end());
    priority_queue<long long> pq;
    long long id = -1;
    long long sum = 0;
    long long maxi;
    long long curr = 0;
    long long i = 0;
    while (i < n || !pq.empty()) {
      while (i < n && arr[i].first == id) {
        curr += arr[i].second;
        pq.push(arr[i].second);
        i++;
      }
      if (pq.size() > 0) {
        id++;
        curr -= pq.top();
        sum += curr;
        pq.pop();
      } else {
        if (i < n) {
          id = arr[i].first;
          curr = 0;
        }
      }
    }
    cout << sum << endl;
  }
  return 0;
}

```