#include <bits/stdc++.h>
using namespace std;
map<long long, set<pair<long long, long long>>> dic;
long long mas[200010];
int main() {
  long long n;
  cin >> n;
  long long a;
  for (long long i = 0; i < n; i++) {
    cin >> mas[i];
  }
  for (long long i = 0; i < n; i++) {
    cin >> a;
    dic[mas[i]].insert({a, i});
  }
  long long ans = 0;
  set<pair<long long, long long>, greater<pair<long long, long long>>> vec;
  set<pair<long long, long long>> todel;
  long long kil = 0;
  long long prev = -1;
  dic[9999999999999].insert({0, -10});
  for (auto x : dic) {
    if (prev != -1) {
      auto y = vec.begin();
      for (long long i = 0; i < min(x.first - prev - 1, (long long)vec.size());
           i++) {
        kil -= y->first;
        todel.insert(*y);
        y++;
        ans += kil;
      }
    }
    for (auto y : todel) {
      vec.erase(y);
    }
    todel.clear();
    for (auto y : x.second) {
      vec.insert(y);
      kil += y.first;
    }
    for (auto y : vec) {
      vec.erase(y);
      kil -= y.first;
      ans += kil;
      prev = x.first;
      break;
    }
  }
  cout << ans << endl;
  return 0;
}

### Prompt

Your challenge is to write 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;
map<long long, set<pair<long long, long long>>> dic;
long long mas[200010];
int main() {
  long long n;
  cin >> n;
  long long a;
  for (long long i = 0; i < n; i++) {
    cin >> mas[i];
  }
  for (long long i = 0; i < n; i++) {
    cin >> a;
    dic[mas[i]].insert({a, i});
  }
  long long ans = 0;
  set<pair<long long, long long>, greater<pair<long long, long long>>> vec;
  set<pair<long long, long long>> todel;
  long long kil = 0;
  long long prev = -1;
  dic[9999999999999].insert({0, -10});
  for (auto x : dic) {
    if (prev != -1) {
      auto y = vec.begin();
      for (long long i = 0; i < min(x.first - prev - 1, (long long)vec.size());
           i++) {
        kil -= y->first;
        todel.insert(*y);
        y++;
        ans += kil;
      }
    }
    for (auto y : todel) {
      vec.erase(y);
    }
    todel.clear();
    for (auto y : x.second) {
      vec.insert(y);
      kil += y.first;
    }
    for (auto y : vec) {
      vec.erase(y);
      kil -= y.first;
      ans += kil;
      prev = x.first;
      break;
    }
  }
  cout << ans << endl;
  return 0;
}

```