#include <bits/stdc++.h>
using namespace std;
int main() {
  ios_base::sync_with_stdio(false), cin.tie(NULL);
  ;
  int n;
  cin >> n;
  vector<pair<int, int>> v(n);
  for (int i = 0; i < n; i++) cin >> v[i].first;
  for (int i = 0; i < n; i++) cin >> v[i].second;
  sort(v.begin(), v.end());
  multiset<int> st;
  long long sum = 0, res = 0;
  int c = 1;
  for (int i = 0; i < n;) {
    while (!st.empty() && v[i].first > c) {
      sum -= *(--st.end());
      res += sum;
      st.erase(--st.end());
      c++;
    }
    c = v[i].first;
    while (i < n && v[i].first == c) {
      st.insert(v[i].second);
      sum += v[i].second;
      i++;
    }
    sum -= *(--st.end());
    res += sum;
    st.erase(--st.end());
    c++;
  }
  while (!st.empty()) {
    sum -= *(--st.end());
    res += sum;
    st.erase(--st.end());
  }
  cout << res << endl;
  return 0;
}

### Prompt

Construct a CPP code solution to the problem outlined:

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);
  ;
  int n;
  cin >> n;
  vector<pair<int, int>> v(n);
  for (int i = 0; i < n; i++) cin >> v[i].first;
  for (int i = 0; i < n; i++) cin >> v[i].second;
  sort(v.begin(), v.end());
  multiset<int> st;
  long long sum = 0, res = 0;
  int c = 1;
  for (int i = 0; i < n;) {
    while (!st.empty() && v[i].first > c) {
      sum -= *(--st.end());
      res += sum;
      st.erase(--st.end());
      c++;
    }
    c = v[i].first;
    while (i < n && v[i].first == c) {
      st.insert(v[i].second);
      sum += v[i].second;
      i++;
    }
    sum -= *(--st.end());
    res += sum;
    st.erase(--st.end());
    c++;
  }
  while (!st.empty()) {
    sum -= *(--st.end());
    res += sum;
    st.erase(--st.end());
  }
  cout << res << endl;
  return 0;
}

```