#include <bits/stdc++.h>
using namespace std;
int n, i, j = 1;
pair<int, int> c[200000];
priority_queue<int> q;
long long s, ans;
inline void init_j() {
  if (q.empty()) j = c[i].first;
}
int main() {
  ios::sync_with_stdio(0), cin.tie(0);
  cin >> n;
  for (int i = 0; i < n; ++i) cin >> c[i].first;
  for (int i = 0; i < n; ++i) cin >> c[i].second;
  for (sort(c, c + n); !q.empty() || i < n;
       j++, s -= q.top(), ans += s, q.pop())
    for (init_j(); i < n && c[i].first == j; i++)
      q.push(c[i].second), s += c[i].second;
  cout << ans;
}

### Prompt

Please create a solution in cpp 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;
int n, i, j = 1;
pair<int, int> c[200000];
priority_queue<int> q;
long long s, ans;
inline void init_j() {
  if (q.empty()) j = c[i].first;
}
int main() {
  ios::sync_with_stdio(0), cin.tie(0);
  cin >> n;
  for (int i = 0; i < n; ++i) cin >> c[i].first;
  for (int i = 0; i < n; ++i) cin >> c[i].second;
  for (sort(c, c + n); !q.empty() || i < n;
       j++, s -= q.top(), ans += s, q.pop())
    for (init_j(); i < n && c[i].first == j; i++)
      q.push(c[i].second), s += c[i].second;
  cout << ans;
}

```