#include <bits/stdc++.h>
using namespace std;
const int maxn = 2e5 + 50;
const int INF = 0x3f3f3f3f;
struct node {
  int num;
  long long t;
} a[maxn];
bool cmp(node x, node y) { return x.t > y.t; }
map<int, int> fa;
int findfa(int x) {
  if (fa[x] == 0) return fa[x] = x;
  if (fa[x] == x) return x;
  return fa[x] = findfa(fa[x]);
}
void uni(int x, int y) {
  int fax = findfa(x);
  int fay = findfa(y);
  if (fax != fay) fa[fax] = fay;
}
int main() {
  int n;
  scanf("%d", &n);
  for (int i = 1; i <= n; i++) scanf("%d", &a[i].num);
  for (int i = 1; i <= n; i++) scanf("%lld", &a[i].t);
  sort(a + 1, a + 1 + n, cmp);
  long long ans = 0;
  for (int i = 1; i <= n; i++) {
    int k = a[i].num;
    if (findfa(k) == k) {
      uni(k, k + 1);
    } else {
      int p = findfa(k);
      uni(p, p + 1);
      ans += (p - k) * a[i].t;
    }
  }
  cout << ans << endl;
}

### 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;
const int maxn = 2e5 + 50;
const int INF = 0x3f3f3f3f;
struct node {
  int num;
  long long t;
} a[maxn];
bool cmp(node x, node y) { return x.t > y.t; }
map<int, int> fa;
int findfa(int x) {
  if (fa[x] == 0) return fa[x] = x;
  if (fa[x] == x) return x;
  return fa[x] = findfa(fa[x]);
}
void uni(int x, int y) {
  int fax = findfa(x);
  int fay = findfa(y);
  if (fax != fay) fa[fax] = fay;
}
int main() {
  int n;
  scanf("%d", &n);
  for (int i = 1; i <= n; i++) scanf("%d", &a[i].num);
  for (int i = 1; i <= n; i++) scanf("%lld", &a[i].t);
  sort(a + 1, a + 1 + n, cmp);
  long long ans = 0;
  for (int i = 1; i <= n; i++) {
    int k = a[i].num;
    if (findfa(k) == k) {
      uni(k, k + 1);
    } else {
      int p = findfa(k);
      uni(p, p + 1);
      ans += (p - k) * a[i].t;
    }
  }
  cout << ans << endl;
}

```