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.
#include <bits/stdc++.h>
using namespace std;
struct pii {
  long long a;
  long long t;
};
bool cmp(pii a, pii b) {
  if (a.a == b.a)
    return a.t > b.t;
  else
    return a.a < b.a;
}
struct cmpmap {
  bool operator()(const pii& a, const pii& b) const {
    if (a.t == b.t)
      return a.a < b.a;
    else
      return a.t < b.t;
  }
};
struct cmpqueue {
  bool operator()(pii const& p1, pii const& p2) { return p1.t < p2.t; }
};
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  long long n;
  cin >> n;
  pii arr[n];
  for (long long i = 0; i < n; i++) cin >> arr[i].a;
  for (long long j = 0; j < n; j++) cin >> arr[j].t;
  sort(arr, arr + n, cmp);
  priority_queue<pii, vector<pii>, cmpqueue> q;
  long long cnt = 0;
  long long max = 0;
  long long sum = 0;
  for (long long i = 1; i < n; i++) {
    if (arr[i].a == arr[i - 1].a && cnt == 0) {
      q.push(arr[i]);
      cnt++;
      sum = sum + arr[i].t;
    } else if (arr[i].a == arr[i - 1].a && cnt > 0) {
      q.push(arr[i]);
      sum = sum + arr[i].t;
      cnt++;
    } else if (arr[i].a != arr[i - 1].a && cnt > 0) {
      max = max + sum;
      q.push(arr[i]);
      pii x = q.top();
      sum = sum + arr[i].t - x.t;
      q.pop();
    }
    if (i + 1 < n && arr[i + 1].a > arr[i].a) {
      long long start = arr[i].a + 1;
      while (start < arr[i + 1].a && cnt > 0) {
        max = max + sum;
        pii r = q.top();
        q.pop();
        sum = sum - r.t;
        cnt--;
        start++;
      }
    }
  }
  long long start = arr[n - 1].a + 1;
  while (!q.empty()) {
    max = max + sum;
    ;
    pii z = q.top();
    sum = sum - z.t;
    q.pop();
  }
  cout << max << endl;
}
