#include <bits/stdc++.h>
using namespace std;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  int n;
  cin >> n;
  vector<pair<int, int> > a(n);
  for (pair<int, int>& x : a) cin >> x.first;
  for (pair<int, int>& x : a) cin >> x.second;
  sort(a.begin(), a.end());
  priority_queue<int> pq;
  int idx = 0;
  long long tot = 0, ans = 0;
  while (idx < n) {
    int nxt = a[idx].first;
    tot += a[idx].second;
    pq.push(a[idx].second);
    idx++;
    while (!pq.empty()) {
      while (idx < n && a[idx].first == nxt) {
        tot += a[idx].second;
        pq.push(a[idx].second);
        idx++;
      }
      int t = pq.top();
      pq.pop();
      nxt++;
      tot -= t;
      ans += tot;
    }
  }
  cout << ans << '\n';
}

### Prompt

Please create a solution in cpp 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() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  int n;
  cin >> n;
  vector<pair<int, int> > a(n);
  for (pair<int, int>& x : a) cin >> x.first;
  for (pair<int, int>& x : a) cin >> x.second;
  sort(a.begin(), a.end());
  priority_queue<int> pq;
  int idx = 0;
  long long tot = 0, ans = 0;
  while (idx < n) {
    int nxt = a[idx].first;
    tot += a[idx].second;
    pq.push(a[idx].second);
    idx++;
    while (!pq.empty()) {
      while (idx < n && a[idx].first == nxt) {
        tot += a[idx].second;
        pq.push(a[idx].second);
        idx++;
      }
      int t = pq.top();
      pq.pop();
      nxt++;
      tot -= t;
      ans += tot;
    }
  }
  cout << ans << '\n';
}

```