#include <bits/stdc++.h>
using namespace std;
map<int, int> Fa;
struct Categories {
  long long a, t;
  bool operator<(const struct Categories c) const {
    if (t == c.t) return a < c.a;
    return t > c.t;
  }
};
int Find(int x) {
  if (Fa[x] == 0) return x;
  return Fa[x] = Find(Fa[x]);
}
void Un(int a, int b) {
  int aa = Find(a), bb = Find(b);
  if (aa != bb) Fa[aa] = bb;
}
Categories cate[200010];
int main() {
  int n;
  while (cin >> n) {
    Fa.clear();
    for (int i = 0; i < n; i++) {
      cin >> cate[i].a;
    }
    for (int i = 0; i < n; i++) {
      cin >> cate[i].t;
    }
    sort(cate, cate + n);
    long long ans = 0;
    for (int i = 0; i < n; i++) {
      int tmp = Find(cate[i].a);
      if (tmp == cate[i].a) {
        Un(tmp, tmp + 1);
      } else {
        ans += (tmp - cate[i].a) * cate[i].t;
        Un(tmp, tmp + 1);
      }
    }
    cout << ans << endl;
  }
  return 0;
}

### Prompt

In CPP, your task is to solve 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<int, int> Fa;
struct Categories {
  long long a, t;
  bool operator<(const struct Categories c) const {
    if (t == c.t) return a < c.a;
    return t > c.t;
  }
};
int Find(int x) {
  if (Fa[x] == 0) return x;
  return Fa[x] = Find(Fa[x]);
}
void Un(int a, int b) {
  int aa = Find(a), bb = Find(b);
  if (aa != bb) Fa[aa] = bb;
}
Categories cate[200010];
int main() {
  int n;
  while (cin >> n) {
    Fa.clear();
    for (int i = 0; i < n; i++) {
      cin >> cate[i].a;
    }
    for (int i = 0; i < n; i++) {
      cin >> cate[i].t;
    }
    sort(cate, cate + n);
    long long ans = 0;
    for (int i = 0; i < n; i++) {
      int tmp = Find(cate[i].a);
      if (tmp == cate[i].a) {
        Un(tmp, tmp + 1);
      } else {
        ans += (tmp - cate[i].a) * cate[i].t;
        Un(tmp, tmp + 1);
      }
    }
    cout << ans << endl;
  }
  return 0;
}

```