#include <bits/stdc++.h>
using namespace std;
const int N = 2e5 + 2;
pair<int, int> a[N];
priority_queue<int> q;
long long n, i, d, second, ans;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  cin >> n;
  for (i = 1; i <= n; i++) {
    cin >> a[i].first;
  }
  for (i = 1; i <= n; i++) {
    cin >> a[i].second;
  }
  sort(a + 1, a + n + 1);
  a[n + 1] = make_pair(2e9, 0);
  for (i = 1; i <= n + 1; i++) {
    d = a[i].first - a[i - 1].first;
    while (!q.empty() && d) {
      second -= q.top();
      ans += second;
      d--;
      q.pop();
    }
    q.push(a[i].second);
    second += a[i].second;
  }
  cout << ans << "\n";
  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;
const int N = 2e5 + 2;
pair<int, int> a[N];
priority_queue<int> q;
long long n, i, d, second, ans;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  cin >> n;
  for (i = 1; i <= n; i++) {
    cin >> a[i].first;
  }
  for (i = 1; i <= n; i++) {
    cin >> a[i].second;
  }
  sort(a + 1, a + n + 1);
  a[n + 1] = make_pair(2e9, 0);
  for (i = 1; i <= n + 1; i++) {
    d = a[i].first - a[i - 1].first;
    while (!q.empty() && d) {
      second -= q.top();
      ans += second;
      d--;
      q.pop();
    }
    q.push(a[i].second);
    second += a[i].second;
  }
  cout << ans << "\n";
  return 0;
}

```