#include <bits/stdc++.h>
using namespace std;
const long long N = 200001;
const long long MOD = 1000000007;
const long long INF = LLONG_MAX;
int main() {
  ios::sync_with_stdio(false), cin.tie(0), cout.tie(0);
  int t = 1, cs = 0;
  while (t--) {
    long long n, i, last, sum = 0, ans = 0;
    cin >> n;
    vector<pair<long long, long long> > v(n);
    for (i = 0; i < n; i++) cin >> v[i].first;
    for (i = 0; i < n; i++) cin >> v[i].second;
    sort(v.begin(), v.end());
    v.push_back(make_pair(INT_MAX, 0LL));
    priority_queue<long long> p;
    for (i = 0; i <= n; i++) {
      while (p.size() && v[i].first > last) {
        sum -= p.top();
        p.pop();
        ans += sum;
        last++;
      }
      last = v[i].first;
      sum += v[i].second;
      p.push(v[i].second);
    }
    cout << ans << '\n';
  }
}

### Prompt

Your challenge is to write 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 N = 200001;
const long long MOD = 1000000007;
const long long INF = LLONG_MAX;
int main() {
  ios::sync_with_stdio(false), cin.tie(0), cout.tie(0);
  int t = 1, cs = 0;
  while (t--) {
    long long n, i, last, sum = 0, ans = 0;
    cin >> n;
    vector<pair<long long, long long> > v(n);
    for (i = 0; i < n; i++) cin >> v[i].first;
    for (i = 0; i < n; i++) cin >> v[i].second;
    sort(v.begin(), v.end());
    v.push_back(make_pair(INT_MAX, 0LL));
    priority_queue<long long> p;
    for (i = 0; i <= n; i++) {
      while (p.size() && v[i].first > last) {
        sum -= p.top();
        p.pop();
        ans += sum;
        last++;
      }
      last = v[i].first;
      sum += v[i].second;
      p.push(v[i].second);
    }
    cout << ans << '\n';
  }
}

```