#include <bits/stdc++.h>
using namespace std;
const int maxn = 2e5 + 1;
map<int, pair<bool, priority_queue<int>>> pbs;
int n;
int main() {
  cin >> n;
  int a[maxn];
  for (int i = 0; i < n; i++) {
    cin >> a[i];
    pbs[a[i]].first = true;
  }
  int t;
  for (int i = 0; i < n; i++) {
    cin >> t;
    pbs[a[i]].second.push(t);
  }
  priority_queue<int> buf;
  long long sum = 0;
  long long ans = 0;
  for (auto i : pbs) {
    while (!i.second.second.empty()) {
      int tmp = i.second.second.top();
      i.second.second.pop();
      sum += tmp;
      buf.push(tmp);
    }
    if (!buf.empty()) {
      sum -= buf.top();
      ans += sum;
      buf.pop();
    }
    if (!buf.empty()) {
      pbs[i.first + 1].first = 1;
    }
  }
  cout << ans << endl;
  return 0;
}

### Prompt

Develop a solution in cpp 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 maxn = 2e5 + 1;
map<int, pair<bool, priority_queue<int>>> pbs;
int n;
int main() {
  cin >> n;
  int a[maxn];
  for (int i = 0; i < n; i++) {
    cin >> a[i];
    pbs[a[i]].first = true;
  }
  int t;
  for (int i = 0; i < n; i++) {
    cin >> t;
    pbs[a[i]].second.push(t);
  }
  priority_queue<int> buf;
  long long sum = 0;
  long long ans = 0;
  for (auto i : pbs) {
    while (!i.second.second.empty()) {
      int tmp = i.second.second.top();
      i.second.second.pop();
      sum += tmp;
      buf.push(tmp);
    }
    if (!buf.empty()) {
      sum -= buf.top();
      ans += sum;
      buf.pop();
    }
    if (!buf.empty()) {
      pbs[i.first + 1].first = 1;
    }
  }
  cout << ans << endl;
  return 0;
}

```