#include <bits/stdc++.h>
#pragma optimize("TKACHENKO-GORYACHENKO")
#pragma GCC optimize("O3")
using namespace std;
const long long maxn = 1e6;
const long long inf = 1e15;
long long n, m, k, t;
long long A[maxn];
long long T[maxn];
int main() {
  long long q, w, e, a, b, c;
  string s;
  cin >> n;
  for (q = 0; q < n; q++) {
    cin >> A[q];
  }
  for (q = 0; q < n; q++) {
    cin >> T[q];
  }
  vector<pair<long long, long long> > P;
  for (q = 0; q < n; q++) {
    P.push_back(make_pair(A[q], q));
  }
  sort(P.begin(), P.end());
  P.push_back(make_pair(inf, n));
  long long sum = 0;
  set<pair<long long, long long> > S;
  long long cur = 0;
  long long ans = 0;
  for (q = 0; q < P.size(); q++) {
    long long first = P[q].first;
    while (first > cur && !S.empty()) {
      cur++;
      pair<long long, long long> p = *(S.begin());
      sum += p.first;
      ans += sum;
      S.erase(S.begin());
    }
    cur = first;
    long long i = P[q].second;
    S.insert(make_pair(-T[i], i));
    sum += T[i];
  }
  cout << ans;
  return 0;
}

### Prompt

Construct a Cpp code solution to the problem outlined:

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>
#pragma optimize("TKACHENKO-GORYACHENKO")
#pragma GCC optimize("O3")
using namespace std;
const long long maxn = 1e6;
const long long inf = 1e15;
long long n, m, k, t;
long long A[maxn];
long long T[maxn];
int main() {
  long long q, w, e, a, b, c;
  string s;
  cin >> n;
  for (q = 0; q < n; q++) {
    cin >> A[q];
  }
  for (q = 0; q < n; q++) {
    cin >> T[q];
  }
  vector<pair<long long, long long> > P;
  for (q = 0; q < n; q++) {
    P.push_back(make_pair(A[q], q));
  }
  sort(P.begin(), P.end());
  P.push_back(make_pair(inf, n));
  long long sum = 0;
  set<pair<long long, long long> > S;
  long long cur = 0;
  long long ans = 0;
  for (q = 0; q < P.size(); q++) {
    long long first = P[q].first;
    while (first > cur && !S.empty()) {
      cur++;
      pair<long long, long long> p = *(S.begin());
      sum += p.first;
      ans += sum;
      S.erase(S.begin());
    }
    cur = first;
    long long i = P[q].second;
    S.insert(make_pair(-T[i], i));
    sum += T[i];
  }
  cout << ans;
  return 0;
}

```