#include <bits/stdc++.h>
using namespace std;
const int N = 2e5 + 5;
const int inf = 2e9;
int n;
long long a[N], t[N], sum, ans, lst = inf;
map<long long, vector<long long> > m;
priority_queue<long long> pq;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cin >> n;
  for (int i = 0; i < n; ++i) {
    cin >> a[i];
    lst = min(lst, a[i]) - 1;
  }
  for (int i = 0; i < n; ++i) {
    cin >> t[i];
    m[a[i]].push_back(t[i]);
  }
  auto it = m.begin();
  while (pq.size() || it != m.end()) {
    if (pq.size() && (it == m.end() || it->first != lst + 1)) {
      ans += sum;
      sum -= pq.top();
      pq.pop();
      lst++;
    } else {
      ans += (it->first - lst) * sum;
      lst = it->first;
      for (auto item : it->second) {
        sum += item;
        pq.push(item);
      }
      sum -= pq.top();
      pq.pop();
      it++;
    }
  }
  cout << ans << endl;
  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;
const int N = 2e5 + 5;
const int inf = 2e9;
int n;
long long a[N], t[N], sum, ans, lst = inf;
map<long long, vector<long long> > m;
priority_queue<long long> pq;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cin >> n;
  for (int i = 0; i < n; ++i) {
    cin >> a[i];
    lst = min(lst, a[i]) - 1;
  }
  for (int i = 0; i < n; ++i) {
    cin >> t[i];
    m[a[i]].push_back(t[i]);
  }
  auto it = m.begin();
  while (pq.size() || it != m.end()) {
    if (pq.size() && (it == m.end() || it->first != lst + 1)) {
      ans += sum;
      sum -= pq.top();
      pq.pop();
      lst++;
    } else {
      ans += (it->first - lst) * sum;
      lst = it->first;
      for (auto item : it->second) {
        sum += item;
        pq.push(item);
      }
      sum -= pq.top();
      pq.pop();
      it++;
    }
  }
  cout << ans << endl;
  return 0;
}

```