#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ull = unsigned long long;
constexpr int MOD = 1000 * 1000 * 1000 + 7;
constexpr int ALPHABET_SIZE = 26;
constexpr ll INF = 1e18;
int main() {
  ios_base::sync_with_stdio(false);
  int n;
  cin >> n;
  vector<pair<int, int>> p(n);
  for (int i = 0; i < n; ++i) {
    cin >> p[i].first;
  }
  for (int i = 0; i < n; ++i) {
    cin >> p[i].second;
  }
  sort(p.begin(), p.end());
  ll ans = 0, cur_sum = 0;
  priority_queue<int> q;
  int pos = 0;
  ll cur_lev = 0;
  while (!q.empty() || pos < n) {
    if (!q.empty()) {
      cur_sum -= q.top();
      q.pop();
      ++cur_lev;
      ans += cur_sum;
    } else {
      cur_lev = p[pos].first;
    }
    int new_pos = pos;
    while (new_pos < n && p[new_pos].first == cur_lev) {
      q.push(p[new_pos].second);
      cur_sum += p[new_pos].second;
      ++new_pos;
    }
    pos = new_pos;
  }
  cout << ans << "\n";
  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;
using ll = long long;
using ull = unsigned long long;
constexpr int MOD = 1000 * 1000 * 1000 + 7;
constexpr int ALPHABET_SIZE = 26;
constexpr ll INF = 1e18;
int main() {
  ios_base::sync_with_stdio(false);
  int n;
  cin >> n;
  vector<pair<int, int>> p(n);
  for (int i = 0; i < n; ++i) {
    cin >> p[i].first;
  }
  for (int i = 0; i < n; ++i) {
    cin >> p[i].second;
  }
  sort(p.begin(), p.end());
  ll ans = 0, cur_sum = 0;
  priority_queue<int> q;
  int pos = 0;
  ll cur_lev = 0;
  while (!q.empty() || pos < n) {
    if (!q.empty()) {
      cur_sum -= q.top();
      q.pop();
      ++cur_lev;
      ans += cur_sum;
    } else {
      cur_lev = p[pos].first;
    }
    int new_pos = pos;
    while (new_pos < n && p[new_pos].first == cur_lev) {
      q.push(p[new_pos].second);
      cur_sum += p[new_pos].second;
      ++new_pos;
    }
    pos = new_pos;
  }
  cout << ans << "\n";
  return 0;
}

```