#include <bits/stdc++.h>
using namespace std;
const int mxN = 3e5 + 5;
const long long INF = 1e18;
const long long mod = 1e9 + 7;
int main() {
  multiset<int> s;
  int n;
  cin >> n;
  vector<pair<long long, long long> > v(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).begin(), (v).end());
  long long cur = 0;
  long long sum = 0;
  long long ans = 0;
  int i = 0;
  while (i < n || !s.empty()) {
    if (s.empty()) cur = v[i].first;
    while (i < n && v[i].first == cur) {
      sum += v[i].second;
      s.insert(v[i].second);
      i++;
    }
    long long x = *s.rbegin();
    sum -= x;
    ans += sum;
    s.erase(s.find(x));
    cur++;
  }
  cout << ans;
}

### Prompt

Please formulate 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 int mxN = 3e5 + 5;
const long long INF = 1e18;
const long long mod = 1e9 + 7;
int main() {
  multiset<int> s;
  int n;
  cin >> n;
  vector<pair<long long, long long> > v(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).begin(), (v).end());
  long long cur = 0;
  long long sum = 0;
  long long ans = 0;
  int i = 0;
  while (i < n || !s.empty()) {
    if (s.empty()) cur = v[i].first;
    while (i < n && v[i].first == cur) {
      sum += v[i].second;
      s.insert(v[i].second);
      i++;
    }
    long long x = *s.rbegin();
    sum -= x;
    ans += sum;
    s.erase(s.find(x));
    cur++;
  }
  cout << ans;
}

```