#include <bits/stdc++.h>
using namespace std;
pair<long long, long long> arr[200001];
int main(void) {
  int n;
  scanf("%d\n", &n);
  for (int i = 0; i < n; i++) {
    int x;
    scanf("%lld ", &x);
    arr[i].first = x;
  }
  scanf("\n");
  for (int i = 0; i < n; i++) {
    int x;
    scanf("%lld ", &x);
    arr[i].second = x;
  }
  scanf("\n");
  sort(arr, arr + n);
  arr[n].first = 2e9;
  priority_queue<long long> pq;
  long long ret = 0;
  long long sum = 0;
  int ind = 0;
  while (1) {
    do {
      pq.push(arr[ind].second);
      sum += arr[ind].second;
      ind++;
    } while (ind < n && arr[ind - 1].first == arr[ind].first);
    for (int i = arr[ind - 1].first; i < arr[ind].first && (!pq.empty()); i++) {
      sum -= pq.top();
      pq.pop();
      ret += sum;
    }
    if (ind == n) {
      break;
    }
  }
  printf("%lld", ret);
}

### Prompt

Construct a Cpp code solution to the problem outlined:

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;
pair<long long, long long> arr[200001];
int main(void) {
  int n;
  scanf("%d\n", &n);
  for (int i = 0; i < n; i++) {
    int x;
    scanf("%lld ", &x);
    arr[i].first = x;
  }
  scanf("\n");
  for (int i = 0; i < n; i++) {
    int x;
    scanf("%lld ", &x);
    arr[i].second = x;
  }
  scanf("\n");
  sort(arr, arr + n);
  arr[n].first = 2e9;
  priority_queue<long long> pq;
  long long ret = 0;
  long long sum = 0;
  int ind = 0;
  while (1) {
    do {
      pq.push(arr[ind].second);
      sum += arr[ind].second;
      ind++;
    } while (ind < n && arr[ind - 1].first == arr[ind].first);
    for (int i = arr[ind - 1].first; i < arr[ind].first && (!pq.empty()); i++) {
      sum -= pq.top();
      pq.pop();
      ret += sum;
    }
    if (ind == n) {
      break;
    }
  }
  printf("%lld", ret);
}

```