#include <bits/stdc++.h>
using namespace std;
template <typename T>
T abs(T x) {
  return x > 0 ? x : -x;
}
template <typename T>
T sqr(T x) {
  return x * x;
}
template <typename T>
ostream &operator<<(ostream &s, const vector<T> &x) {
  s << "[";
  for (auto it : x) {
    s << it << ", ";
  }
  s << "]";
  return s;
}
template <typename T>
ostream &operator<<(ostream &s, const set<T> &x) {
  s << "{";
  for (auto it : x) {
    s << it << ", ";
  }
  s << "}";
  return s;
}
template <typename U, typename V>
ostream &operator<<(ostream &s, const pair<U, V> &x) {
  s << "(" << x.first << ", " << x.second << ")";
  return s;
}
template <typename T>
bool chmax(T &x, const T &y) {
  if (x < y) {
    x = y;
    return true;
  }
  return false;
}
template <typename T>
bool chmin(T &x, const T &y) {
  if (x > y) {
    x = y;
    return true;
  }
  return false;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  srand(time(NULL));
  int n;
  cin >> n;
  vector<int> a(n), t(n);
  vector<pair<int, int>> v;
  for (int i = 0; i < n; ++i) {
    cin >> a[i];
  }
  for (int i = 0; i < n; ++i) {
    cin >> t[i];
  }
  for (int i = 0; i < n; ++i) {
    v.push_back({a[i], t[i]});
  }
  sort(v.begin(), v.end());
  long long ans = 0;
  priority_queue<int> ms;
  long long sum = 0;
  const int INF = 2e9;
  for (int i = 0; i < n;) {
    int j = i;
    while (i < n && v[i].first == v[j].first) {
      ms.push(v[i].second);
      sum += v[i].second;
      ++i;
    }
    int cur = v[j].first;
    int nxt = INF;
    if (i < n) {
      nxt = v[i].first;
    }
    while (!ms.empty() && cur != nxt) {
      sum -= ms.top();
      ms.pop();
      ans += sum;
      ++cur;
    }
  }
  cout << ans << "\n";
  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;
template <typename T>
T abs(T x) {
  return x > 0 ? x : -x;
}
template <typename T>
T sqr(T x) {
  return x * x;
}
template <typename T>
ostream &operator<<(ostream &s, const vector<T> &x) {
  s << "[";
  for (auto it : x) {
    s << it << ", ";
  }
  s << "]";
  return s;
}
template <typename T>
ostream &operator<<(ostream &s, const set<T> &x) {
  s << "{";
  for (auto it : x) {
    s << it << ", ";
  }
  s << "}";
  return s;
}
template <typename U, typename V>
ostream &operator<<(ostream &s, const pair<U, V> &x) {
  s << "(" << x.first << ", " << x.second << ")";
  return s;
}
template <typename T>
bool chmax(T &x, const T &y) {
  if (x < y) {
    x = y;
    return true;
  }
  return false;
}
template <typename T>
bool chmin(T &x, const T &y) {
  if (x > y) {
    x = y;
    return true;
  }
  return false;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  srand(time(NULL));
  int n;
  cin >> n;
  vector<int> a(n), t(n);
  vector<pair<int, int>> v;
  for (int i = 0; i < n; ++i) {
    cin >> a[i];
  }
  for (int i = 0; i < n; ++i) {
    cin >> t[i];
  }
  for (int i = 0; i < n; ++i) {
    v.push_back({a[i], t[i]});
  }
  sort(v.begin(), v.end());
  long long ans = 0;
  priority_queue<int> ms;
  long long sum = 0;
  const int INF = 2e9;
  for (int i = 0; i < n;) {
    int j = i;
    while (i < n && v[i].first == v[j].first) {
      ms.push(v[i].second);
      sum += v[i].second;
      ++i;
    }
    int cur = v[j].first;
    int nxt = INF;
    if (i < n) {
      nxt = v[i].first;
    }
    while (!ms.empty() && cur != nxt) {
      sum -= ms.top();
      ms.pop();
      ans += sum;
      ++cur;
    }
  }
  cout << ans << "\n";
  return 0;
}

```