#include <bits/stdc++.h>
using namespace std;
struct node {
  int a, t;
  bool operator<(const node &b) const { return a < b.a; }
} a[200009];
priority_queue<int> qu;
int main() {
  int n;
  scanf("%d", &n);
  for (int i = 0; i < n; i++) scanf("%d", &a[i].a);
  for (int i = 0; i < n; i++) scanf("%d", &a[i].t);
  sort(a, a + n);
  long long sum = 0, ans = 0;
  int last = 0, cur = -1;
  while (!qu.empty() || last < n) {
    if (!qu.empty()) {
      sum -= qu.top();
      ans += sum;
      qu.pop();
      cur++;
    } else
      cur = a[last].a;
    int pos = last;
    while (pos < n && a[pos].a == cur) {
      qu.push(a[pos].t);
      sum += a[pos].t;
      pos++;
    }
    last = pos;
  }
  printf("%lld\n", ans);
  return 0;
}

### Prompt

Please formulate 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;
struct node {
  int a, t;
  bool operator<(const node &b) const { return a < b.a; }
} a[200009];
priority_queue<int> qu;
int main() {
  int n;
  scanf("%d", &n);
  for (int i = 0; i < n; i++) scanf("%d", &a[i].a);
  for (int i = 0; i < n; i++) scanf("%d", &a[i].t);
  sort(a, a + n);
  long long sum = 0, ans = 0;
  int last = 0, cur = -1;
  while (!qu.empty() || last < n) {
    if (!qu.empty()) {
      sum -= qu.top();
      ans += sum;
      qu.pop();
      cur++;
    } else
      cur = a[last].a;
    int pos = last;
    while (pos < n && a[pos].a == cur) {
      qu.push(a[pos].t);
      sum += a[pos].t;
      pos++;
    }
    last = pos;
  }
  printf("%lld\n", ans);
  return 0;
}

```