#include <bits/stdc++.h>
using namespace std;
int main() {
  multiset<long long> s;
  vector<pair<long long, long long>> v;
  long long i, j, nw, od, cursum = 0, k, a[200005], n, b, ans = 0;
  cin >> n;
  for (i = 0; i < n; i++) cin >> a[i];
  for (i = 0; i < n; i++) {
    cin >> b;
    v.push_back({a[i], b});
  }
  sort(v.begin(), v.end());
  v.push_back({1000000000000000, -1});
  for (i = 0; i < n; i++) {
    cursum += v[i].second;
    s.insert(v[i].second);
    if (v[i].first != v[i + 1].first) {
      nw = v[i + 1].first;
      od = v[i].first;
      while (s.size() > 0 && od < nw) {
        auto t = s.end();
        t--;
        cursum -= *t;
        ans += cursum;
        s.erase(t);
        od++;
      }
    }
  }
  cout << ans << endl;
}

### 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;
int main() {
  multiset<long long> s;
  vector<pair<long long, long long>> v;
  long long i, j, nw, od, cursum = 0, k, a[200005], n, b, ans = 0;
  cin >> n;
  for (i = 0; i < n; i++) cin >> a[i];
  for (i = 0; i < n; i++) {
    cin >> b;
    v.push_back({a[i], b});
  }
  sort(v.begin(), v.end());
  v.push_back({1000000000000000, -1});
  for (i = 0; i < n; i++) {
    cursum += v[i].second;
    s.insert(v[i].second);
    if (v[i].first != v[i + 1].first) {
      nw = v[i + 1].first;
      od = v[i].first;
      while (s.size() > 0 && od < nw) {
        auto t = s.end();
        t--;
        cursum -= *t;
        ans += cursum;
        s.erase(t);
        od++;
      }
    }
  }
  cout << ans << endl;
}

```