#include <bits/stdc++.h>
using namespace std;
using ll = long long;
const int N = 2e5;
pair<int, int> arr[N];
int main() {
  ios_base::sync_with_stdio();
  cin.tie(0);
  cout.tie(0);
  int n;
  scanf("%d", &n);
  for (int i = 0; i < n; ++i) scanf("%d", &arr[i].first);
  for (int i = 0; i < n; ++i) scanf("%d", &arr[i].second);
  sort(arr, arr + n);
  multiset<int> s;
  ll ans = 0, sum = 0;
  int cur = arr[0].first, idx = 0;
  while (idx < n or not s.empty()) {
    while (idx < n and arr[idx].first == cur) {
      s.insert(arr[idx].second);
      sum += arr[idx].second;
      ++idx;
    }
    auto it = s.end();
    --it;
    int temp = *it;
    s.erase(it);
    sum -= temp;
    ans += sum;
    if (not s.empty())
      ++cur;
    else if (idx < n)
      cur = arr[idx].first;
  }
  cout << ans;
}

### Prompt

Your task is to create 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;
using ll = long long;
const int N = 2e5;
pair<int, int> arr[N];
int main() {
  ios_base::sync_with_stdio();
  cin.tie(0);
  cout.tie(0);
  int n;
  scanf("%d", &n);
  for (int i = 0; i < n; ++i) scanf("%d", &arr[i].first);
  for (int i = 0; i < n; ++i) scanf("%d", &arr[i].second);
  sort(arr, arr + n);
  multiset<int> s;
  ll ans = 0, sum = 0;
  int cur = arr[0].first, idx = 0;
  while (idx < n or not s.empty()) {
    while (idx < n and arr[idx].first == cur) {
      s.insert(arr[idx].second);
      sum += arr[idx].second;
      ++idx;
    }
    auto it = s.end();
    --it;
    int temp = *it;
    s.erase(it);
    sum -= temp;
    ans += sum;
    if (not s.empty())
      ++cur;
    else if (idx < n)
      cur = arr[idx].first;
  }
  cout << ans;
}

```