#include <bits/stdc++.h>
using namespace std;
void fun() {
  long long n;
  cin >> n;
  map<long long, vector<long long> > m;
  long long b[n], c[n];
  for (auto &i : b) cin >> i;
  for (auto &i : c) cin >> i;
  for (int i = 0; i < n; i++) m[b[i]].push_back(c[i]);
  priority_queue<long long> pq;
  long long t = m.begin()->first, s = 0, ans = 0;
  for (auto it = m.begin(); it != m.end(); it++) {
    while (!pq.empty() && (t != (it->first))) {
      ans += s;
      s -= (pq.top());
      pq.pop();
      t++;
    }
    ans += s;
    t = (it->first) + 1;
    for (auto i : (it->second)) s += i, pq.push(i);
    s -= (pq.top());
    pq.pop();
  }
  while (!pq.empty()) {
    ans += s;
    s -= (pq.top());
    pq.pop();
  }
  cout << ans;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  srand(time(0));
  ;
  int t = 1;
  while (t--) {
    fun();
  }
}

### 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;
void fun() {
  long long n;
  cin >> n;
  map<long long, vector<long long> > m;
  long long b[n], c[n];
  for (auto &i : b) cin >> i;
  for (auto &i : c) cin >> i;
  for (int i = 0; i < n; i++) m[b[i]].push_back(c[i]);
  priority_queue<long long> pq;
  long long t = m.begin()->first, s = 0, ans = 0;
  for (auto it = m.begin(); it != m.end(); it++) {
    while (!pq.empty() && (t != (it->first))) {
      ans += s;
      s -= (pq.top());
      pq.pop();
      t++;
    }
    ans += s;
    t = (it->first) + 1;
    for (auto i : (it->second)) s += i, pq.push(i);
    s -= (pq.top());
    pq.pop();
  }
  while (!pq.empty()) {
    ans += s;
    s -= (pq.top());
    pq.pop();
  }
  cout << ans;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  srand(time(0));
  ;
  int t = 1;
  while (t--) {
    fun();
  }
}

```