#include <bits/stdc++.h>
using namespace std;
map<long long, priority_queue<long long> > mp;
map<long long, bool> vis;
map<long long, long long> sum;
set<long long> st;
vector<long long> ara;
vector<long long> tim;
priority_queue<long long> pq;
int main() {
  long long n;
  scanf("%lld", &n);
  for (long long i = 0; i < n; i++) {
    long long a;
    scanf("%lld", &a);
    ara.push_back(a);
    vis[a] = true;
    st.insert(a);
  }
  for (long long i = 0; i < n; i++) {
    long long a;
    scanf("%lld", &a);
    long long val = ara[i];
    mp[val].push(a);
  }
  long long ans = 0;
  long long tot = 0;
  for (auto it = st.begin(); it != st.end(); it++) {
    long long val = (*it);
    long long cur = val;
    while (mp[val].size()) {
      pq.push(mp[val].top());
      tot += mp[val].top();
      mp[val].pop();
    }
    while (pq.size()) {
      long long tt = pq.top();
      tot -= tt;
      pq.pop();
      ans += tot;
      cur++;
      if (mp[cur].size()) {
        break;
      }
    }
  }
  cout << ans << endl;
  return 0;
}

### Prompt

Your task is to create 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;
map<long long, priority_queue<long long> > mp;
map<long long, bool> vis;
map<long long, long long> sum;
set<long long> st;
vector<long long> ara;
vector<long long> tim;
priority_queue<long long> pq;
int main() {
  long long n;
  scanf("%lld", &n);
  for (long long i = 0; i < n; i++) {
    long long a;
    scanf("%lld", &a);
    ara.push_back(a);
    vis[a] = true;
    st.insert(a);
  }
  for (long long i = 0; i < n; i++) {
    long long a;
    scanf("%lld", &a);
    long long val = ara[i];
    mp[val].push(a);
  }
  long long ans = 0;
  long long tot = 0;
  for (auto it = st.begin(); it != st.end(); it++) {
    long long val = (*it);
    long long cur = val;
    while (mp[val].size()) {
      pq.push(mp[val].top());
      tot += mp[val].top();
      mp[val].pop();
    }
    while (pq.size()) {
      long long tt = pq.top();
      tot -= tt;
      pq.pop();
      ans += tot;
      cur++;
      if (mp[cur].size()) {
        break;
      }
    }
  }
  cout << ans << endl;
  return 0;
}

```