#include <bits/stdc++.h>
using namespace std;
const long long N = 1001;
signed main() {
  long long n;
  cin >> n;
  vector<long long> a(n), t(n);
  map<long long, vector<long long> > mp;
  for (long long i = 0; i < n; i++) cin >> a[i];
  for (long long i = 0; i < n; i++) cin >> t[i];
  for (long long i = 0; i < n; i++) {
    mp[a[i]].push_back(t[i]);
  }
  priority_queue<long long> pq;
  long long pos = 0;
  long long T = 0;
  long long del = 0;
  long long cost = 0;
  while (true) {
    if (del == n) break;
    if (!pq.size()) {
      auto data = *mp.lower_bound(pos);
      long long new_pos = data.first;
      cost += (new_pos - pos) * T;
      pos = new_pos;
    }
    for (long long u : mp[pos]) {
      pq.push(u);
      T += u;
    }
    T -= pq.top();
    pq.pop();
    del++;
    pos++;
    cost += T;
  }
  cout << cost;
}

### 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 long long N = 1001;
signed main() {
  long long n;
  cin >> n;
  vector<long long> a(n), t(n);
  map<long long, vector<long long> > mp;
  for (long long i = 0; i < n; i++) cin >> a[i];
  for (long long i = 0; i < n; i++) cin >> t[i];
  for (long long i = 0; i < n; i++) {
    mp[a[i]].push_back(t[i]);
  }
  priority_queue<long long> pq;
  long long pos = 0;
  long long T = 0;
  long long del = 0;
  long long cost = 0;
  while (true) {
    if (del == n) break;
    if (!pq.size()) {
      auto data = *mp.lower_bound(pos);
      long long new_pos = data.first;
      cost += (new_pos - pos) * T;
      pos = new_pos;
    }
    for (long long u : mp[pos]) {
      pq.push(u);
      T += u;
    }
    T -= pq.top();
    pq.pop();
    del++;
    pos++;
    cost += T;
  }
  cout << cost;
}

```