#include <bits/stdc++.h>
using namespace std;
const long long logN = 20;
const long long M = 1000000007;
const long long INF = 1e12;
int main() {
  long long n;
  cin >> n;
  vector<long long> a(n + 1);
  for (long long i = 0; i < n; i++) cin >> a[i];
  vector<long long> t(n + 1);
  for (long long i = 0; i < n; i++) cin >> t[i];
  t[n] = 0;
  a[n] = 1e10;
  ++n;
  vector<long long> ord(n);
  iota(ord.begin(), ord.end(), 0);
  sort(ord.begin(), ord.end(),
       [&](long long i, long long j) { return a[i] < a[j]; });
  long long ans = 0;
  long long last = 0;
  multiset<long long> s;
  long long sum = 0;
  for (auto i : ord) {
    while (a[i] > last && !s.empty()) {
      ++last;
      auto it = prev(s.end());
      sum -= *it;
      s.erase(it);
      ans += sum;
    }
    last = a[i];
    s.insert(t[i]);
    sum += t[i];
  }
  cout << ans;
}

### Prompt

Please formulate 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 long long logN = 20;
const long long M = 1000000007;
const long long INF = 1e12;
int main() {
  long long n;
  cin >> n;
  vector<long long> a(n + 1);
  for (long long i = 0; i < n; i++) cin >> a[i];
  vector<long long> t(n + 1);
  for (long long i = 0; i < n; i++) cin >> t[i];
  t[n] = 0;
  a[n] = 1e10;
  ++n;
  vector<long long> ord(n);
  iota(ord.begin(), ord.end(), 0);
  sort(ord.begin(), ord.end(),
       [&](long long i, long long j) { return a[i] < a[j]; });
  long long ans = 0;
  long long last = 0;
  multiset<long long> s;
  long long sum = 0;
  for (auto i : ord) {
    while (a[i] > last && !s.empty()) {
      ++last;
      auto it = prev(s.end());
      sum -= *it;
      s.erase(it);
      ans += sum;
    }
    last = a[i];
    s.insert(t[i]);
    sum += t[i];
  }
  cout << ans;
}

```