#include <bits/stdc++.h>
using namespace std;
const int N = 2e5 + 5;
int n;
vector<pair<int, int>> a;
multiset<int> q;
long long ans = 0;
long long sum = 0;
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  scanf("%d", &n);
  a.resize(n);
  int x;
  for (int i = 0; i < n; ++i) {
    scanf("%d", &x);
    a[i].first = x;
  }
  for (int i = 0; i < n; ++i) {
    scanf("%d", &x);
    a[i].second = x;
  }
  sort(a.begin(), a.end());
  int cur, prev = -1;
  for (int i = 0; i < n; ++i) {
    cur = a[i].first;
    while (q.size() && (cur - prev++)) {
      sum -= *(--q.end());
      q.erase(--q.end());
      ans += sum;
    }
    sum += (long long)a[i].second;
    ;
    q.insert(a[i].second);
    prev = cur;
  }
  while (q.size() > 1) {
    sum -= *(--q.end());
    q.erase(--q.end());
    ans += sum;
  }
  cout << ans << endl;
  return 0;
}

### 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 int N = 2e5 + 5;
int n;
vector<pair<int, int>> a;
multiset<int> q;
long long ans = 0;
long long sum = 0;
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  scanf("%d", &n);
  a.resize(n);
  int x;
  for (int i = 0; i < n; ++i) {
    scanf("%d", &x);
    a[i].first = x;
  }
  for (int i = 0; i < n; ++i) {
    scanf("%d", &x);
    a[i].second = x;
  }
  sort(a.begin(), a.end());
  int cur, prev = -1;
  for (int i = 0; i < n; ++i) {
    cur = a[i].first;
    while (q.size() && (cur - prev++)) {
      sum -= *(--q.end());
      q.erase(--q.end());
      ans += sum;
    }
    sum += (long long)a[i].second;
    ;
    q.insert(a[i].second);
    prev = cur;
  }
  while (q.size() > 1) {
    sum -= *(--q.end());
    q.erase(--q.end());
    ans += sum;
  }
  cout << ans << endl;
  return 0;
}

```