#include <bits/stdc++.h>
using namespace std;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  long long int t, n, k, i, j, lvl, ans;
  cin >> n;
  pair<long long int, long long int> p[n];
  for (i = 0; i < n; i++) cin >> p[i].first;
  for (i = 0; i < n; i++) cin >> p[i].second;
  sort(p, p + n);
  priority_queue<pair<int, int> > pq;
  ans = 0;
  k = p[0].second;
  lvl = p[0].first;
  pq.push({p[0].second, p[0].first});
  for (i = 1; i < n; i++) {
    while (lvl < p[i].first && pq.size() > 0) {
      k -= pq.top().first;
      pq.pop();
      ans += k;
      lvl++;
    }
    if (lvl < p[i].first) ans += k * (p[i].first - lvl);
    lvl = p[i].first;
    pq.push({p[i].second, p[i].first});
    k += p[i].second;
  }
  while (pq.size() > 0) {
    k -= pq.top().first;
    pq.pop();
    ans += k;
    lvl++;
  }
  cout << ans;
  return 0;
}

### 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 main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  long long int t, n, k, i, j, lvl, ans;
  cin >> n;
  pair<long long int, long long int> p[n];
  for (i = 0; i < n; i++) cin >> p[i].first;
  for (i = 0; i < n; i++) cin >> p[i].second;
  sort(p, p + n);
  priority_queue<pair<int, int> > pq;
  ans = 0;
  k = p[0].second;
  lvl = p[0].first;
  pq.push({p[0].second, p[0].first});
  for (i = 1; i < n; i++) {
    while (lvl < p[i].first && pq.size() > 0) {
      k -= pq.top().first;
      pq.pop();
      ans += k;
      lvl++;
    }
    if (lvl < p[i].first) ans += k * (p[i].first - lvl);
    lvl = p[i].first;
    pq.push({p[i].second, p[i].first});
    k += p[i].second;
  }
  while (pq.size() > 0) {
    k -= pq.top().first;
    pq.pop();
    ans += k;
    lvl++;
  }
  cout << ans;
  return 0;
}

```