#include <bits/stdc++.h>
using namespace std;
const int N = 200009;
pair<int, int> a[N];
priority_queue<int> f;
int main(void) {
  int n;
  int i, j, k;
  long long o, s;
  scanf("%d", &n);
  for (i = 0; i < n; i++) scanf("%d", &a[i].first);
  for (i = 0; i < n; i++) scanf("%d", &a[i].second);
  a[n].first = 2000000000;
  sort(a, a + n);
  for (i = o = s = 0; i < n; i = j) {
    for (j = i; j < n && a[j].first == a[i].first; j++) {
      s += a[j].second;
      f.push(a[j].second);
    }
    for (k = 0; k < a[j].first - a[i].first && !f.empty(); k++) {
      s -= f.top();
      o += s;
      f.pop();
    }
  }
  cout << o << "\n";
  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;
const int N = 200009;
pair<int, int> a[N];
priority_queue<int> f;
int main(void) {
  int n;
  int i, j, k;
  long long o, s;
  scanf("%d", &n);
  for (i = 0; i < n; i++) scanf("%d", &a[i].first);
  for (i = 0; i < n; i++) scanf("%d", &a[i].second);
  a[n].first = 2000000000;
  sort(a, a + n);
  for (i = o = s = 0; i < n; i = j) {
    for (j = i; j < n && a[j].first == a[i].first; j++) {
      s += a[j].second;
      f.push(a[j].second);
    }
    for (k = 0; k < a[j].first - a[i].first && !f.empty(); k++) {
      s -= f.top();
      o += s;
      f.pop();
    }
  }
  cout << o << "\n";
  return 0;
}

```