#include <bits/stdc++.h>
using namespace std;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  long long int n;
  cin >> n;
  vector<long long int> a(n), b(n);
  for (int i = 0; i < n; ++i) cin >> a[i];
  for (int i = 0; i < n; ++i) cin >> b[i];
  map<long long int, vector<long long int> > m;
  for (int i = 0; i < n; ++i) {
    m[a[i]].push_back(b[i]);
  }
  priority_queue<long long int> q;
  long long int ans = 0, sm = 0;
  for (auto &i : m) {
    ans += sm;
    vector<long long int> v = i.second;
    for (int i = 0; i < v.size(); ++i) {
      if (v[i] == -1) {
        continue;
      }
      q.push(v[i]);
      sm += v[i];
    }
    sm -= (q.top());
    q.pop();
    if (sm != 0) {
      m[i.first + 1].push_back(-1);
    }
  }
  cout << ans << "\n";
  return 0;
}

### Prompt

Your task is to create 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() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  long long int n;
  cin >> n;
  vector<long long int> a(n), b(n);
  for (int i = 0; i < n; ++i) cin >> a[i];
  for (int i = 0; i < n; ++i) cin >> b[i];
  map<long long int, vector<long long int> > m;
  for (int i = 0; i < n; ++i) {
    m[a[i]].push_back(b[i]);
  }
  priority_queue<long long int> q;
  long long int ans = 0, sm = 0;
  for (auto &i : m) {
    ans += sm;
    vector<long long int> v = i.second;
    for (int i = 0; i < v.size(); ++i) {
      if (v[i] == -1) {
        continue;
      }
      q.push(v[i]);
      sm += v[i];
    }
    sm -= (q.top());
    q.pop();
    if (sm != 0) {
      m[i.first + 1].push_back(-1);
    }
  }
  cout << ans << "\n";
  return 0;
}

```