#include <bits/stdc++.h>
using namespace std;
const int oo = 1e9 + 9;
const long long inf = 1e18 + 18;
const int max6 = 2e6 + 6;
const int modx = 1e9 + 123;
const int mody = 997;
const int base = 137;
pair<int, int> a[max6];
map<int, int> lt, cnt;
int Find(int u) {
  if (!lt.count(u) || cnt[lt[u] + 1] != 1) return lt[u];
  return lt[u] = Find(lt[u] + 1);
}
int main() {
  int n;
  cin >> n;
  for (int i = 1; i <= n; ++i) cin >> a[i].second;
  for (int i = 1; i <= n; ++i) cin >> a[i].first;
  sort(a + 1, a + n + 1);
  reverse(a + 1, a + n + 1);
  long long res = 0;
  for (int i = 1; i <= n; ++i) {
    int id = a[i].second;
    if (cnt[id] == 1) {
      int u = Find(id) + 1;
      cnt[u] = 1;
      lt[u] = u;
      res += 1ll * (u - id) * a[i].first;
    } else {
      lt[id] = id;
      cnt[id] = 1;
    }
  }
  cout << res;
}

### Prompt

Generate 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;
const int oo = 1e9 + 9;
const long long inf = 1e18 + 18;
const int max6 = 2e6 + 6;
const int modx = 1e9 + 123;
const int mody = 997;
const int base = 137;
pair<int, int> a[max6];
map<int, int> lt, cnt;
int Find(int u) {
  if (!lt.count(u) || cnt[lt[u] + 1] != 1) return lt[u];
  return lt[u] = Find(lt[u] + 1);
}
int main() {
  int n;
  cin >> n;
  for (int i = 1; i <= n; ++i) cin >> a[i].second;
  for (int i = 1; i <= n; ++i) cin >> a[i].first;
  sort(a + 1, a + n + 1);
  reverse(a + 1, a + n + 1);
  long long res = 0;
  for (int i = 1; i <= n; ++i) {
    int id = a[i].second;
    if (cnt[id] == 1) {
      int u = Find(id) + 1;
      cnt[u] = 1;
      lt[u] = u;
      res += 1ll * (u - id) * a[i].first;
    } else {
      lt[id] = id;
      cnt[id] = 1;
    }
  }
  cout << res;
}

```