#include <bits/stdc++.h>
using namespace std;
const int maxn = 2e5 + 5;
struct node {
  long long a;
  long long t;
  bool friend operator<(node x, node y) { return x.t > y.t; }
} p[maxn];
unordered_map<long long, long long> fa;
long long find(int x) {
  if (fa[x] == 0)
    return x;
  else {
    return fa[x] = find(fa[x]);
  }
}
void Merge(int x, int y) {
  int xx = find(x);
  int yy = find(y);
  if (yy == 0) {
    yy = xx + 1;
  }
  if (xx != yy) {
    fa[xx] = yy;
  }
  return;
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int n;
  cin >> n;
  for (int i = 1; i <= n; i++) {
    cin >> p[i].a;
  }
  for (int i = 1; i <= n; i++) {
    cin >> p[i].t;
  }
  sort(p + 1, p + n + 1);
  long long ans = 0;
  for (int i = 1; i <= n; i++) {
    long long xx = find(p[i].a);
    ans += (xx - p[i].a) * p[i].t;
    Merge(xx, xx + 1);
  }
  cout << ans << endl;
  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;
const int maxn = 2e5 + 5;
struct node {
  long long a;
  long long t;
  bool friend operator<(node x, node y) { return x.t > y.t; }
} p[maxn];
unordered_map<long long, long long> fa;
long long find(int x) {
  if (fa[x] == 0)
    return x;
  else {
    return fa[x] = find(fa[x]);
  }
}
void Merge(int x, int y) {
  int xx = find(x);
  int yy = find(y);
  if (yy == 0) {
    yy = xx + 1;
  }
  if (xx != yy) {
    fa[xx] = yy;
  }
  return;
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int n;
  cin >> n;
  for (int i = 1; i <= n; i++) {
    cin >> p[i].a;
  }
  for (int i = 1; i <= n; i++) {
    cin >> p[i].t;
  }
  sort(p + 1, p + n + 1);
  long long ans = 0;
  for (int i = 1; i <= n; i++) {
    long long xx = find(p[i].a);
    ans += (xx - p[i].a) * p[i].t;
    Merge(xx, xx + 1);
  }
  cout << ans << endl;
  return 0;
}

```