#include <bits/stdc++.h>
using namespace std;
long long int gcd(long long int a, long long int b) {
  return (!b) ? a : gcd(b, a % b);
}
int n;
map<int, vector<int> > mp;
pair<int, int> cat[200005];
void solve() {
  cin >> n;
  priority_queue<int> pq;
  for (int i = 1; i <= n; i++) cin >> cat[i].first;
  for (int i = 1; i <= n; i++) cin >> cat[i].second;
  sort(cat + 1, cat + 1 + n);
  long long int sum = 0, ans = 0;
  int curi = 1;
  long long int curr = 0;
  while (curi <= n || !pq.empty()) {
    while (curi <= n && cat[curi].first == curr) {
      pq.push(cat[curi].second);
      sum += cat[curi].second;
      curi++;
    }
    if (!pq.empty()) {
      sum -= pq.top();
      pq.pop();
      ans += sum;
      curr += 1;
    } else {
      curr = cat[curi].first;
    }
  }
  cout << ans;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  if (fopen("input.txt", "r")) {
    freopen("input.txt", "r", stdin);
    freopen("output.txt", "w", stdout);
  }
  int t = 1;
  while (t--) {
    solve();
  }
}

### Prompt

Construct a CPP code solution to the problem outlined:

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;
long long int gcd(long long int a, long long int b) {
  return (!b) ? a : gcd(b, a % b);
}
int n;
map<int, vector<int> > mp;
pair<int, int> cat[200005];
void solve() {
  cin >> n;
  priority_queue<int> pq;
  for (int i = 1; i <= n; i++) cin >> cat[i].first;
  for (int i = 1; i <= n; i++) cin >> cat[i].second;
  sort(cat + 1, cat + 1 + n);
  long long int sum = 0, ans = 0;
  int curi = 1;
  long long int curr = 0;
  while (curi <= n || !pq.empty()) {
    while (curi <= n && cat[curi].first == curr) {
      pq.push(cat[curi].second);
      sum += cat[curi].second;
      curi++;
    }
    if (!pq.empty()) {
      sum -= pq.top();
      pq.pop();
      ans += sum;
      curr += 1;
    } else {
      curr = cat[curi].first;
    }
  }
  cout << ans;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  if (fopen("input.txt", "r")) {
    freopen("input.txt", "r", stdin);
    freopen("output.txt", "w", stdout);
  }
  int t = 1;
  while (t--) {
    solve();
  }
}

```