#include <bits/stdc++.h>
using namespace std;
int n;
pair<int, int> A[200005];
long long ans = 0;
void pro(int s, int e) {
  int idx = s;
  priority_queue<int> pq;
  long long sum = 0;
  for (int i = s; i < e; i++) {
    while (idx < e && A[idx].first <= i - s + A[s].first) {
      pq.push(A[idx].second);
      sum += A[idx].second;
      idx++;
    }
    sum -= (long long)pq.top();
    pq.pop();
    ans += sum;
  }
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  cin >> n;
  for (int i = 1; i <= n; i++) cin >> A[i].first;
  for (int i = 1; i <= n; i++) cin >> A[i].second;
  sort(A + 1, A + n + 1);
  int st = 1, ed = 2;
  while (st <= n && ed <= n) {
    if (A[ed].first - A[st].first > ed - st) {
      pro(st, ed);
      st = ed;
      ed = st + 1;
    } else
      ed++;
  }
  if (st <= n) pro(st, ed);
  cout << ans;
  return 0;
}

### 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;
int n;
pair<int, int> A[200005];
long long ans = 0;
void pro(int s, int e) {
  int idx = s;
  priority_queue<int> pq;
  long long sum = 0;
  for (int i = s; i < e; i++) {
    while (idx < e && A[idx].first <= i - s + A[s].first) {
      pq.push(A[idx].second);
      sum += A[idx].second;
      idx++;
    }
    sum -= (long long)pq.top();
    pq.pop();
    ans += sum;
  }
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  cin >> n;
  for (int i = 1; i <= n; i++) cin >> A[i].first;
  for (int i = 1; i <= n; i++) cin >> A[i].second;
  sort(A + 1, A + n + 1);
  int st = 1, ed = 2;
  while (st <= n && ed <= n) {
    if (A[ed].first - A[st].first > ed - st) {
      pro(st, ed);
      st = ed;
      ed = st + 1;
    } else
      ed++;
  }
  if (st <= n) pro(st, ed);
  cout << ans;
  return 0;
}

```