#include <bits/stdc++.h>
using namespace std;
multiset<long long, greater<long long>> s;
map<long long, vector<long long>> m;
long long cur = 0, ans = 0;
const long long N = 2e5 + 7, INF = 1e18;
long long a[N], t[N];
void add(long long val) {
  s.insert(val);
  cur += val;
}
void eras() {
  if (s.empty()) return;
  long long x = *s.begin();
  s.erase(s.begin());
  cur -= x;
}
signed main() {
  ios_base ::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  long long n;
  cin >> n;
  for (long long i = 0; i < n; i++) cin >> a[i];
  for (long long i = 0; i < n; i++) cin >> t[i];
  for (long long i = 0; i < n; i++) m[a[i]].push_back(t[i]);
  for (long long i = 0; i < INF; i++) {
    if (s.empty()) {
      if (m.empty()) break;
      i = (*m.begin()).first;
    }
    for (long long elem : m[i]) add(elem);
    if (m.find(i) != m.end()) m.erase(i);
    eras();
    ans += cur;
  }
  cout << ans << "\n";
  return 0;
}

### Prompt

Create a solution in Cpp for 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;
multiset<long long, greater<long long>> s;
map<long long, vector<long long>> m;
long long cur = 0, ans = 0;
const long long N = 2e5 + 7, INF = 1e18;
long long a[N], t[N];
void add(long long val) {
  s.insert(val);
  cur += val;
}
void eras() {
  if (s.empty()) return;
  long long x = *s.begin();
  s.erase(s.begin());
  cur -= x;
}
signed main() {
  ios_base ::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  long long n;
  cin >> n;
  for (long long i = 0; i < n; i++) cin >> a[i];
  for (long long i = 0; i < n; i++) cin >> t[i];
  for (long long i = 0; i < n; i++) m[a[i]].push_back(t[i]);
  for (long long i = 0; i < INF; i++) {
    if (s.empty()) {
      if (m.empty()) break;
      i = (*m.begin()).first;
    }
    for (long long elem : m[i]) add(elem);
    if (m.find(i) != m.end()) m.erase(i);
    eras();
    ans += cur;
  }
  cout << ans << "\n";
  return 0;
}

```