#include <bits/stdc++.h>
using namespace std;
const int maxd = 1e6 + 10;
int d[maxd], v[maxd], ls[maxd], rs[maxd], fa[maxd];
int n, m;
struct node {
  int x, y;
} a[maxd];
bool cmp(const node a, const node b) { return a.x < b.x; }
priority_queue<int> que;
int main() {
  scanf("%d", &n);
  d[0] = -1;
  for (int i = 1; i <= n; i++) scanf("%d", &a[i].x);
  for (int i = 1; i <= n; i++) scanf("%d", &a[i].y);
  sort(a + 1, a + 1 + n, cmp);
  long long ans = 0, res = 0;
  int now = 0, pos = 0, sz = 0;
  a[n + 1].x = 2e9;
  for (int i = 1; i <= n + 1; i++) {
    while (que.size() && a[i].x != now) {
      res -= que.top();
      que.pop();
      now++;
      ans += res;
    }
    if (que.size()) {
      que.push(a[i].y);
      res += a[i].y;
    } else {
      que.push(a[i].y);
      now = a[i].x;
      res = a[i].y;
    }
  }
  printf("%lld", ans);
  return 0;
}

### Prompt

Your task is to create 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;
const int maxd = 1e6 + 10;
int d[maxd], v[maxd], ls[maxd], rs[maxd], fa[maxd];
int n, m;
struct node {
  int x, y;
} a[maxd];
bool cmp(const node a, const node b) { return a.x < b.x; }
priority_queue<int> que;
int main() {
  scanf("%d", &n);
  d[0] = -1;
  for (int i = 1; i <= n; i++) scanf("%d", &a[i].x);
  for (int i = 1; i <= n; i++) scanf("%d", &a[i].y);
  sort(a + 1, a + 1 + n, cmp);
  long long ans = 0, res = 0;
  int now = 0, pos = 0, sz = 0;
  a[n + 1].x = 2e9;
  for (int i = 1; i <= n + 1; i++) {
    while (que.size() && a[i].x != now) {
      res -= que.top();
      que.pop();
      now++;
      ans += res;
    }
    if (que.size()) {
      que.push(a[i].y);
      res += a[i].y;
    } else {
      que.push(a[i].y);
      now = a[i].x;
      res = a[i].y;
    }
  }
  printf("%lld", ans);
  return 0;
}

```