#include <bits/stdc++.h>
using namespace std;
const int M = 2e5 + 5;
int a[M], t[M];
int main() {
  int n;
  scanf("%d", &n);
  for (int i = 0; i < n; i++) scanf("%d", a + i);
  for (int i = 0; i < n; i++) scanf("%d", t + i);
  vector<pair<int, int> > vec;
  for (int i = 0; i < n; i++) vec.emplace_back(t[i], a[i]);
  sort(vec.begin(), vec.end());
  long long ans = 0;
  set<int> used, unused;
  for (int i = n - 1; i >= 0; i--) {
    int v = vec[i].second;
    if (!used.count(v)) {
      used.insert(v);
      if (unused.count(v)) unused.erase(v);
      if (!used.count(v + 1)) unused.insert(v + 1);
    } else {
      int vv = *(unused.lower_bound(v));
      ans += 1LL * (vv - v) * vec[i].first;
      used.insert(vv);
      unused.erase(vv);
      if (!used.count(vv + 1)) unused.insert(vv + 1);
    }
  }
  printf("%lld\n", ans);
  return 0;
}

### 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 int M = 2e5 + 5;
int a[M], t[M];
int main() {
  int n;
  scanf("%d", &n);
  for (int i = 0; i < n; i++) scanf("%d", a + i);
  for (int i = 0; i < n; i++) scanf("%d", t + i);
  vector<pair<int, int> > vec;
  for (int i = 0; i < n; i++) vec.emplace_back(t[i], a[i]);
  sort(vec.begin(), vec.end());
  long long ans = 0;
  set<int> used, unused;
  for (int i = n - 1; i >= 0; i--) {
    int v = vec[i].second;
    if (!used.count(v)) {
      used.insert(v);
      if (unused.count(v)) unused.erase(v);
      if (!used.count(v + 1)) unused.insert(v + 1);
    } else {
      int vv = *(unused.lower_bound(v));
      ans += 1LL * (vv - v) * vec[i].first;
      used.insert(vv);
      unused.erase(vv);
      if (!used.count(vv + 1)) unused.insert(vv + 1);
    }
  }
  printf("%lld\n", ans);
  return 0;
}

```