#include <bits/stdc++.h>
#pragma GCC optimize("O3")
using namespace std;
using ll = long long;
using vi = vector<int>;
using pii = pair<int, int>;
using ld = long double;
int32_t main() {
  ios::sync_with_stdio(0), cin.tie(0), cout.tie(0);
  int n;
  cin >> n;
  vi a(n);
  for (int& x : a) cin >> x;
  vi b(n);
  for (int& x : b) cin >> x;
  vi ord(n);
  iota((ord).begin(), (ord).end(), 0);
  sort((ord).begin(), (ord).end(), [&](int i, int j) { return a[i] < a[j]; });
  ll sum = 0;
  ll ans = 0;
  multiset<int> ts;
  int pt = 0;
  for (int c = 0;; c++) {
    if (ts.empty()) {
      if (pt == n) break;
      c = a[ord[pt]];
    }
    while (pt < n && a[ord[pt]] == c) {
      sum += b[ord[pt]];
      ts.insert(b[ord[pt++]]);
    }
    sum -= *(--ts.end());
    ts.erase(--ts.end());
    ans += sum;
  }
  cout << ans;
}

### Prompt

Your challenge is to write a Cpp solution to 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>
#pragma GCC optimize("O3")
using namespace std;
using ll = long long;
using vi = vector<int>;
using pii = pair<int, int>;
using ld = long double;
int32_t main() {
  ios::sync_with_stdio(0), cin.tie(0), cout.tie(0);
  int n;
  cin >> n;
  vi a(n);
  for (int& x : a) cin >> x;
  vi b(n);
  for (int& x : b) cin >> x;
  vi ord(n);
  iota((ord).begin(), (ord).end(), 0);
  sort((ord).begin(), (ord).end(), [&](int i, int j) { return a[i] < a[j]; });
  ll sum = 0;
  ll ans = 0;
  multiset<int> ts;
  int pt = 0;
  for (int c = 0;; c++) {
    if (ts.empty()) {
      if (pt == n) break;
      c = a[ord[pt]];
    }
    while (pt < n && a[ord[pt]] == c) {
      sum += b[ord[pt]];
      ts.insert(b[ord[pt++]]);
    }
    sum -= *(--ts.end());
    ts.erase(--ts.end());
    ans += sum;
  }
  cout << ans;
}

```