#include <bits/stdc++.h>
using namespace std;
int n, cur = -1;
long long sum = 0, ans = 0;
vector<pair<int, int>> v;
multiset<int> s;
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cin >> n;
  v.resize(n);
  for (int i = 0; i < n; ++i) cin >> v[i].first;
  for (int i = 0; i < n; ++i) cin >> v[i].second;
  sort(v.rbegin(), v.rend());
  auto add = [&]() {
    assert(v.size());
    s.insert(v.back().second);
    cur = v.back().first;
    sum += v.back().second;
    v.pop_back();
  };
  while (v.size() || s.size()) {
    if (s.empty())
      add();
    else
      ++cur;
    while (v.size() && v.back().first <= cur) {
      assert(v.back().first == cur);
      add();
    }
    assert(s.size());
    sum -= *s.rbegin();
    s.erase(prev(s.end()));
    ans += sum;
  }
  cout << ans;
  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;
int n, cur = -1;
long long sum = 0, ans = 0;
vector<pair<int, int>> v;
multiset<int> s;
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cin >> n;
  v.resize(n);
  for (int i = 0; i < n; ++i) cin >> v[i].first;
  for (int i = 0; i < n; ++i) cin >> v[i].second;
  sort(v.rbegin(), v.rend());
  auto add = [&]() {
    assert(v.size());
    s.insert(v.back().second);
    cur = v.back().first;
    sum += v.back().second;
    v.pop_back();
  };
  while (v.size() || s.size()) {
    if (s.empty())
      add();
    else
      ++cur;
    while (v.size() && v.back().first <= cur) {
      assert(v.back().first == cur);
      add();
    }
    assert(s.size());
    sum -= *s.rbegin();
    s.erase(prev(s.end()));
    ans += sum;
  }
  cout << ans;
  return 0;
}

```