#include <bits/stdc++.h>
using namespace std;
map<int, int> mxl;
int n, t;
struct db {
  long long cost;
  int data;
  bool operator<(const db &b) const {
    if (cost == b.cost)
      return data < b.data;
    else
      return cost > b.cost;
  }
};
struct db a[3000000];
int srch(int a) {
  if (mxl[a] == 0)
    return a;
  else
    return mxl[a] = srch(mxl[a]);
}
void scl(int x, int y) {
  x = srch(x);
  y = srch(y);
  if (x != y) mxl[x] = y;
}
int main() {
  cin >> n;
  mxl.clear();
  int i;
  long long ans = 0;
  for (i = 0; i < n; i++) scanf("%d", &a[i].data);
  for (i = 0; i < n; i++) scanf("%lld", &a[i].cost);
  sort(a, a + n);
  for (i = 0; i < n; i++) {
    int x = srch(a[i].data);
    ans += a[i].cost * (x - a[i].data);
    scl(x, x + 1);
  }
  cout << ans << endl;
}

### 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;
map<int, int> mxl;
int n, t;
struct db {
  long long cost;
  int data;
  bool operator<(const db &b) const {
    if (cost == b.cost)
      return data < b.data;
    else
      return cost > b.cost;
  }
};
struct db a[3000000];
int srch(int a) {
  if (mxl[a] == 0)
    return a;
  else
    return mxl[a] = srch(mxl[a]);
}
void scl(int x, int y) {
  x = srch(x);
  y = srch(y);
  if (x != y) mxl[x] = y;
}
int main() {
  cin >> n;
  mxl.clear();
  int i;
  long long ans = 0;
  for (i = 0; i < n; i++) scanf("%d", &a[i].data);
  for (i = 0; i < n; i++) scanf("%lld", &a[i].cost);
  sort(a, a + n);
  for (i = 0; i < n; i++) {
    int x = srch(a[i].data);
    ans += a[i].cost * (x - a[i].data);
    scl(x, x + 1);
  }
  cout << ans << endl;
}

```