#include <bits/stdc++.h>
using namespace std;
using ll = long long;
const int MAX_N = 200002;
int n;
int a[MAX_N], t[MAX_N];
void solve() {
  vector<pair<int, int>> v;
  for (int i = 0; i < n; ++i) v.emplace_back(a[i], t[i]);
  sort(v.begin(), v.end());
  ll cur = -1;
  int idx = 0;
  multiset<ll> eq;
  ll ans = 0, sum = 0;
  while (idx < n || !eq.empty()) {
    if (eq.empty()) cur = v[idx].first;
    while (idx < n && v[idx].first == cur) {
      sum += v[idx].second;
      eq.insert(-v[idx].second);
      idx++;
    }
    sum += *eq.begin();
    eq.erase(eq.begin());
    ans += sum;
    cur++;
  }
  cout << ans << '\n';
}
int main() {
  cin >> n;
  for (int i = 0; i < n; ++i) cin >> a[i];
  for (int i = 0; i < n; ++i) cin >> t[i];
  solve();
  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;
using ll = long long;
const int MAX_N = 200002;
int n;
int a[MAX_N], t[MAX_N];
void solve() {
  vector<pair<int, int>> v;
  for (int i = 0; i < n; ++i) v.emplace_back(a[i], t[i]);
  sort(v.begin(), v.end());
  ll cur = -1;
  int idx = 0;
  multiset<ll> eq;
  ll ans = 0, sum = 0;
  while (idx < n || !eq.empty()) {
    if (eq.empty()) cur = v[idx].first;
    while (idx < n && v[idx].first == cur) {
      sum += v[idx].second;
      eq.insert(-v[idx].second);
      idx++;
    }
    sum += *eq.begin();
    eq.erase(eq.begin());
    ans += sum;
    cur++;
  }
  cout << ans << '\n';
}
int main() {
  cin >> n;
  for (int i = 0; i < n; ++i) cin >> a[i];
  for (int i = 0; i < n; ++i) cin >> t[i];
  solve();
  return 0;
}

```