#include <bits/stdc++.h>
using namespace std;
const int mod = 1e9 + 7;
const int maxn = 2e5 + 5;
const double PI = acos(-1.0);
struct node {
  long long t, v;
} arr[maxn];
bool cmp(node a, node b) {
  if (a.t == b.t)
    return a.v < b.v;
  else
    return a.t > b.t;
}
map<long long, long long> pp;
long long seek(long long pos) {
  if (pp[pos] == 0)
    return pos;
  else
    return pp[pos] = seek(pp[pos]);
}
void mix(long long son, long long fa) {
  son = seek(son);
  fa = seek(fa);
  pp[son] = fa;
}
int main() {
  ios::sync_with_stdio(false), cin.tie(NULL);
  long long n;
  cin >> n;
  for (int i = 1; i <= n; i++) {
    cin >> arr[i].v;
  }
  for (int i = 1; i <= n; i++) {
    cin >> arr[i].t;
  }
  sort(arr + 1, arr + n + 1, cmp);
  long long ans = 0;
  for (int i = 1; i <= n; i++) {
    long long pos = seek(arr[i].v);
    ans += (pos - arr[i].v) * arr[i].t;
    mix(pos, pos + 1);
  }
  cout << ans << '\n';
  return 0;
}

### Prompt

Develop a solution in Cpp to the problem described below:

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 mod = 1e9 + 7;
const int maxn = 2e5 + 5;
const double PI = acos(-1.0);
struct node {
  long long t, v;
} arr[maxn];
bool cmp(node a, node b) {
  if (a.t == b.t)
    return a.v < b.v;
  else
    return a.t > b.t;
}
map<long long, long long> pp;
long long seek(long long pos) {
  if (pp[pos] == 0)
    return pos;
  else
    return pp[pos] = seek(pp[pos]);
}
void mix(long long son, long long fa) {
  son = seek(son);
  fa = seek(fa);
  pp[son] = fa;
}
int main() {
  ios::sync_with_stdio(false), cin.tie(NULL);
  long long n;
  cin >> n;
  for (int i = 1; i <= n; i++) {
    cin >> arr[i].v;
  }
  for (int i = 1; i <= n; i++) {
    cin >> arr[i].t;
  }
  sort(arr + 1, arr + n + 1, cmp);
  long long ans = 0;
  for (int i = 1; i <= n; i++) {
    long long pos = seek(arr[i].v);
    ans += (pos - arr[i].v) * arr[i].t;
    mix(pos, pos + 1);
  }
  cout << ans << '\n';
  return 0;
}

```