#include <bits/stdc++.h>
using namespace std;
const int N = 200010;
struct news {
  int a, t;
  bool operator<(const news &o) const { return t > o.t; }
} num[N];
map<int, int> fa;
int find(int a) { return (fa[a] == 0) ? a : (fa[a] = find(fa[a])); }
inline void merge(int a, int b) {
  int f = find(b);
  if (f != a) fa[a] = f;
}
int main() {
  int n;
  scanf("%d", &n);
  for (int i = 0; i < n; i++) scanf("%d", &num[i].a);
  for (int i = 0; i < n; i++) scanf("%d", &num[i].t);
  long long ans = 0;
  sort(num, num + n);
  for (int i = 0; i < n; i++) {
    int f = find(num[i].a);
    if (f == num[i].a) {
      merge(f, f + 1);
    } else {
      merge(f, f + 1);
      ans = ans + 1ll * (f - num[i].a) * num[i].t;
    }
  }
  printf("%lld\n", ans);
  return 0;
}

### Prompt

Please provide a CPP coded solution to the problem described below:

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 N = 200010;
struct news {
  int a, t;
  bool operator<(const news &o) const { return t > o.t; }
} num[N];
map<int, int> fa;
int find(int a) { return (fa[a] == 0) ? a : (fa[a] = find(fa[a])); }
inline void merge(int a, int b) {
  int f = find(b);
  if (f != a) fa[a] = f;
}
int main() {
  int n;
  scanf("%d", &n);
  for (int i = 0; i < n; i++) scanf("%d", &num[i].a);
  for (int i = 0; i < n; i++) scanf("%d", &num[i].t);
  long long ans = 0;
  sort(num, num + n);
  for (int i = 0; i < n; i++) {
    int f = find(num[i].a);
    if (f == num[i].a) {
      merge(f, f + 1);
    } else {
      merge(f, f + 1);
      ans = ans + 1ll * (f - num[i].a) * num[i].t;
    }
  }
  printf("%lld\n", ans);
  return 0;
}

```