#include <bits/stdc++.h>
using namespace std;
signed main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  long long n;
  cin >> n;
  map<long long, vector<long long>> mp;
  long long ans = 0;
  vector<long long> ax(n), bx(n);
  for (long long i = 0; i < n; ++i) {
    cin >> ax[i];
  }
  for (long long j = 0; j < n; ++j) {
    cin >> bx[j];
    mp[ax[j]].push_back(bx[j]);
  }
  multiset<long long> st;
  long long sum = 0;
  while (!mp.empty()) {
    auto i = *mp.begin();
    for (auto j : i.second) {
      st.insert(j);
      sum += j;
    }
    if (!st.empty()) {
      long long x = *prev(st.end());
      sum -= x;
      ans += sum;
      st.erase(st.find(x));
      if (!st.empty()) {
        if (mp[i.first + 1].empty()) mp[i.first + 1] = {};
      }
    }
    mp.erase(mp.begin());
  }
  cout << ans << '\n';
}

### Prompt

Generate 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;
signed main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  long long n;
  cin >> n;
  map<long long, vector<long long>> mp;
  long long ans = 0;
  vector<long long> ax(n), bx(n);
  for (long long i = 0; i < n; ++i) {
    cin >> ax[i];
  }
  for (long long j = 0; j < n; ++j) {
    cin >> bx[j];
    mp[ax[j]].push_back(bx[j]);
  }
  multiset<long long> st;
  long long sum = 0;
  while (!mp.empty()) {
    auto i = *mp.begin();
    for (auto j : i.second) {
      st.insert(j);
      sum += j;
    }
    if (!st.empty()) {
      long long x = *prev(st.end());
      sum -= x;
      ans += sum;
      st.erase(st.find(x));
      if (!st.empty()) {
        if (mp[i.first + 1].empty()) mp[i.first + 1] = {};
      }
    }
    mp.erase(mp.begin());
  }
  cout << ans << '\n';
}

```