#include <bits/stdc++.h>
using namespace std;
pair<long long, long long> arr[200100];
vector<long long> barr;
multiset<pair<long long, long long> > st;
int main() {
  long long t, n, i, j, K, k, l, m;
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  t = 1;
  while (t--) {
    cin >> n;
    for (i = 0; i < n; i++) cin >> arr[i].first;
    for (i = 0; i < n; i++) cin >> arr[i].second;
    sort(arr, arr + n);
    int maxi = -1;
    for (i = 0; i < n; i++) {
      if (maxi < arr[i].first)
        maxi = arr[i].first;
      else
        maxi++;
      barr.push_back(maxi);
    }
    j = 0;
    long long ans = 0;
    for (i = 0; i < n; i++) {
      while (j < n && arr[j].first <= barr[i]) {
        st.insert(pair<long long, long long>(-arr[j].second, arr[j].first));
        j++;
      }
      pair<long long, long long> op = *(st.begin());
      st.erase(st.begin());
      ans += (barr[i] - op.second) * (-op.first);
    }
    cout << ans << '\n';
  }
  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;
pair<long long, long long> arr[200100];
vector<long long> barr;
multiset<pair<long long, long long> > st;
int main() {
  long long t, n, i, j, K, k, l, m;
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  t = 1;
  while (t--) {
    cin >> n;
    for (i = 0; i < n; i++) cin >> arr[i].first;
    for (i = 0; i < n; i++) cin >> arr[i].second;
    sort(arr, arr + n);
    int maxi = -1;
    for (i = 0; i < n; i++) {
      if (maxi < arr[i].first)
        maxi = arr[i].first;
      else
        maxi++;
      barr.push_back(maxi);
    }
    j = 0;
    long long ans = 0;
    for (i = 0; i < n; i++) {
      while (j < n && arr[j].first <= barr[i]) {
        st.insert(pair<long long, long long>(-arr[j].second, arr[j].first));
        j++;
      }
      pair<long long, long long> op = *(st.begin());
      st.erase(st.begin());
      ans += (barr[i] - op.second) * (-op.first);
    }
    cout << ans << '\n';
  }
  return 0;
}

```