#include <bits/stdc++.h>
using namespace std;
int main() {
  long long int n, i, dsr, pt, ans, curr;
  cin >> n;
  long long int a[n + 5], b[n + 5];
  vector<pair<long long int, long long int> > v;
  multiset<long long int, greater<long long int> > ms;
  for (i = 0; i < n; i++) cin >> a[i];
  for (i = 0; i < n; i++) cin >> b[i];
  for (i = 0; i < n; i++) v.push_back({a[i], b[i]});
  sort(v.begin(), v.end());
  dsr = 1;
  pt = 0;
  ans = 0;
  curr = 0;
  while (1) {
    if (pt >= n) break;
    ans += curr;
    if (ms.size() == 0) {
      dsr = v[pt].first;
      ms.insert(v[pt].second);
      curr += v[pt].second;
      pt++;
    }
    while (1) {
      if (v[pt].first == dsr) {
        ms.insert(v[pt].second);
        curr += v[pt].second;
      } else {
        break;
      }
      pt++;
    }
    curr -= (*(ms.begin()));
    ms.erase(ms.begin());
    dsr++;
    if (pt >= n) break;
  }
  while (1) {
    if (ms.size() == 0) break;
    ans += curr;
    curr -= (*(ms.begin()));
    ms.erase(ms.begin());
  }
  cout << ans;
}

### Prompt

Generate 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;
int main() {
  long long int n, i, dsr, pt, ans, curr;
  cin >> n;
  long long int a[n + 5], b[n + 5];
  vector<pair<long long int, long long int> > v;
  multiset<long long int, greater<long long int> > ms;
  for (i = 0; i < n; i++) cin >> a[i];
  for (i = 0; i < n; i++) cin >> b[i];
  for (i = 0; i < n; i++) v.push_back({a[i], b[i]});
  sort(v.begin(), v.end());
  dsr = 1;
  pt = 0;
  ans = 0;
  curr = 0;
  while (1) {
    if (pt >= n) break;
    ans += curr;
    if (ms.size() == 0) {
      dsr = v[pt].first;
      ms.insert(v[pt].second);
      curr += v[pt].second;
      pt++;
    }
    while (1) {
      if (v[pt].first == dsr) {
        ms.insert(v[pt].second);
        curr += v[pt].second;
      } else {
        break;
      }
      pt++;
    }
    curr -= (*(ms.begin()));
    ms.erase(ms.begin());
    dsr++;
    if (pt >= n) break;
  }
  while (1) {
    if (ms.size() == 0) break;
    ans += curr;
    curr -= (*(ms.begin()));
    ms.erase(ms.begin());
  }
  cout << ans;
}

```