#include <bits/stdc++.h>
using namespace std;
const int MAXN = 2e5 + 5;
int n;
pair<int, int> data[MAXN];
long long ans;
priority_queue<int> line;
long long cnt;
int niz;
int main() {
  scanf("%d", &n);
  for (register int i = 1; i <= n; ++i) scanf("%d", &data[i].first);
  for (register int i = 1; i <= n; ++i) scanf("%d", &data[i].second);
  sort(data + 1, data + 1 + n);
  for (register int i = 1; i <= n;) {
    niz = niz ? niz : data[i].first;
    while (i <= n && data[i].first == niz) {
      line.push(data[i].second);
      cnt += data[i].second;
      i++;
    }
    if (line.size() == 1) {
      niz = 0;
      cnt -= line.top();
      line.pop();
    } else {
      ans += cnt - (long long)line.top();
      cnt -= line.top();
      line.pop();
      niz++;
    }
  }
  while (line.size() >= 2) {
    ans += cnt - (long long)line.top();
    cnt -= line.top();
    line.pop();
  }
  printf("%lld\n", ans);
  return 0;
}

### Prompt

Please provide a Cpp coded solution 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 MAXN = 2e5 + 5;
int n;
pair<int, int> data[MAXN];
long long ans;
priority_queue<int> line;
long long cnt;
int niz;
int main() {
  scanf("%d", &n);
  for (register int i = 1; i <= n; ++i) scanf("%d", &data[i].first);
  for (register int i = 1; i <= n; ++i) scanf("%d", &data[i].second);
  sort(data + 1, data + 1 + n);
  for (register int i = 1; i <= n;) {
    niz = niz ? niz : data[i].first;
    while (i <= n && data[i].first == niz) {
      line.push(data[i].second);
      cnt += data[i].second;
      i++;
    }
    if (line.size() == 1) {
      niz = 0;
      cnt -= line.top();
      line.pop();
    } else {
      ans += cnt - (long long)line.top();
      cnt -= line.top();
      line.pop();
      niz++;
    }
  }
  while (line.size() >= 2) {
    ans += cnt - (long long)line.top();
    cnt -= line.top();
    line.pop();
  }
  printf("%lld\n", ans);
  return 0;
}

```