#include <bits/stdc++.h>
using namespace std;
const long long MAX = 300005;
long long inf = (long long)1e13;
long long n, m, k;
int main() {
  long long n;
  cin >> n;
  vector<pair<long long, long long>> a, c;
  multiset<long long> nums;
  for (int i = 0; i < n; i++) {
    long long b;
    cin >> b;
    a.push_back({b, -1});
  }
  for (int i = 0; i < n; i++) {
    cin >> a[i].second;
  }
  a.push_back({0, 0});
  sort(a.begin(), a.end());
  a.push_back({(long long)1e10, 0});
  long long ans = 0;
  long long mus = 0;
  for (int i = 1; i <= n + 1; i++) {
    long long cnt = 0;
    while (nums.size() && a[i - 1].first + cnt < a[i].first) {
      ans -= *(nums.rbegin());
      ans += mus;
      mus -= *(nums.rbegin());
      nums.erase(nums.find(*nums.rbegin()));
      cnt++;
    }
    nums.insert(a[i].second);
    mus += a[i].second;
  }
  cout << ans;
  return 0;
}

### Prompt

Your task is to create 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 long long MAX = 300005;
long long inf = (long long)1e13;
long long n, m, k;
int main() {
  long long n;
  cin >> n;
  vector<pair<long long, long long>> a, c;
  multiset<long long> nums;
  for (int i = 0; i < n; i++) {
    long long b;
    cin >> b;
    a.push_back({b, -1});
  }
  for (int i = 0; i < n; i++) {
    cin >> a[i].second;
  }
  a.push_back({0, 0});
  sort(a.begin(), a.end());
  a.push_back({(long long)1e10, 0});
  long long ans = 0;
  long long mus = 0;
  for (int i = 1; i <= n + 1; i++) {
    long long cnt = 0;
    while (nums.size() && a[i - 1].first + cnt < a[i].first) {
      ans -= *(nums.rbegin());
      ans += mus;
      mus -= *(nums.rbegin());
      nums.erase(nums.find(*nums.rbegin()));
      cnt++;
    }
    nums.insert(a[i].second);
    mus += a[i].second;
  }
  cout << ans;
  return 0;
}

```