#include <bits/stdc++.h>
using namespace std;
int main() {
  long long i, f, s, n, cnt = 0, ans = 0;
  cin >> n;
  long long a[n], b[n];
  map<long long, vector<long long>> mp;
  map<long long, long long> ch;
  map<long long, long long>::iterator it;
  for (i = 0; i < n; i++) {
    cin >> a[i];
  }
  for (i = 0; i < n; i++) {
    cin >> b[i];
    mp[a[i]].push_back(b[i]);
    ch[a[i]] = 1;
  }
  priority_queue<long long> pq;
  while (ch.size()) {
    it = ch.begin();
    f = it->first;
    vector<long long> v = mp[f];
    for (i = 0; i < v.size(); i++) {
      pq.push(v[i]);
      cnt = cnt + v[i];
    }
    cnt = cnt - pq.top();
    ans = ans + cnt;
    pq.pop();
    if (pq.size()) {
      ch[f + 1] = 1;
    }
    ch.erase(f);
  }
  cout << ans;
  return 0;
}

### 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;
int main() {
  long long i, f, s, n, cnt = 0, ans = 0;
  cin >> n;
  long long a[n], b[n];
  map<long long, vector<long long>> mp;
  map<long long, long long> ch;
  map<long long, long long>::iterator it;
  for (i = 0; i < n; i++) {
    cin >> a[i];
  }
  for (i = 0; i < n; i++) {
    cin >> b[i];
    mp[a[i]].push_back(b[i]);
    ch[a[i]] = 1;
  }
  priority_queue<long long> pq;
  while (ch.size()) {
    it = ch.begin();
    f = it->first;
    vector<long long> v = mp[f];
    for (i = 0; i < v.size(); i++) {
      pq.push(v[i]);
      cnt = cnt + v[i];
    }
    cnt = cnt - pq.top();
    ans = ans + cnt;
    pq.pop();
    if (pq.size()) {
      ch[f + 1] = 1;
    }
    ch.erase(f);
  }
  cout << ans;
  return 0;
}

```