#include <bits/stdc++.h>
using namespace std;
const int max_n = 200222, inf = 1000111222;
int n, a[max_n], b[max_n];
map<int, vector<int>> m;
set<int> all;
long long ans;
int main() {
  scanf("%d", &n);
  for (int i = 0; i < n; ++i) {
    scanf("%d", &a[i]);
  }
  for (int i = 0; i < n; ++i) {
    scanf("%d", &b[i]);
    m[a[i]].push_back(b[i]);
    all.insert(a[i]);
  }
  multiset<int> q;
  long long sum = 0;
  for (int x = 0;;) {
    auto it = m.find(x);
    if (it != m.end()) {
      for (int t : it->second) {
        q.insert(t);
        sum += t;
      }
    }
    if (!q.empty()) {
      sum -= *q.rbegin();
      q.erase(--q.end());
    }
    ans += sum;
    if (q.empty()) {
      auto it = all.upper_bound(x);
      if (it == all.end()) {
        break;
      }
      x = *it;
    } else {
      ++x;
    }
  }
  printf("%I64d\n", ans);
  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;
const int max_n = 200222, inf = 1000111222;
int n, a[max_n], b[max_n];
map<int, vector<int>> m;
set<int> all;
long long ans;
int main() {
  scanf("%d", &n);
  for (int i = 0; i < n; ++i) {
    scanf("%d", &a[i]);
  }
  for (int i = 0; i < n; ++i) {
    scanf("%d", &b[i]);
    m[a[i]].push_back(b[i]);
    all.insert(a[i]);
  }
  multiset<int> q;
  long long sum = 0;
  for (int x = 0;;) {
    auto it = m.find(x);
    if (it != m.end()) {
      for (int t : it->second) {
        q.insert(t);
        sum += t;
      }
    }
    if (!q.empty()) {
      sum -= *q.rbegin();
      q.erase(--q.end());
    }
    ans += sum;
    if (q.empty()) {
      auto it = all.upper_bound(x);
      if (it == all.end()) {
        break;
      }
      x = *it;
    } else {
      ++x;
    }
  }
  printf("%I64d\n", ans);
  return 0;
}

```