#include <bits/stdc++.h>
using namespace std;
long long GCD(long long a, long long b) { return b ? GCD(b, a % b) : a; }
long long LCM(long long a, long long b) { return a * b / GCD(a, b); }
const long long N = 2e5 + 7;
const int mod = 998244353;
const long long inf = 8e18 + 7;
long long n, a[N];
struct node {
  long long val, t;
  bool operator<(const node& a) const {
    return t == a.t ? val > a.val : t < a.t;
  }
};
int main() {
  cin >> n;
  priority_queue<node> q;
  for (int i = 1; i <= n; i++) cin >> a[i];
  for (long long i = 1, x = 1; i <= n; i++) cin >> x, q.push({a[i], x});
  long long ans = 0;
  unordered_set<long long> et;
  unordered_map<long long, long long> mp;
  while (!q.empty()) {
    long long val = q.top().val;
    long long t = q.top().t;
    long long pos = val, tmp = pos;
    q.pop();
    while (et.count(val)) val = mp[val];
    while (et.count(tmp)) {
      long long k = tmp;
      tmp = mp[tmp];
      mp[k] = val + 1;
    }
    et.insert(val);
    mp[val] = val + 1;
    ans += (val - pos) * t;
  }
  cout << ans << "\n";
  return 0;
}

### Prompt

Generate 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>
using namespace std;
long long GCD(long long a, long long b) { return b ? GCD(b, a % b) : a; }
long long LCM(long long a, long long b) { return a * b / GCD(a, b); }
const long long N = 2e5 + 7;
const int mod = 998244353;
const long long inf = 8e18 + 7;
long long n, a[N];
struct node {
  long long val, t;
  bool operator<(const node& a) const {
    return t == a.t ? val > a.val : t < a.t;
  }
};
int main() {
  cin >> n;
  priority_queue<node> q;
  for (int i = 1; i <= n; i++) cin >> a[i];
  for (long long i = 1, x = 1; i <= n; i++) cin >> x, q.push({a[i], x});
  long long ans = 0;
  unordered_set<long long> et;
  unordered_map<long long, long long> mp;
  while (!q.empty()) {
    long long val = q.top().val;
    long long t = q.top().t;
    long long pos = val, tmp = pos;
    q.pop();
    while (et.count(val)) val = mp[val];
    while (et.count(tmp)) {
      long long k = tmp;
      tmp = mp[tmp];
      mp[k] = val + 1;
    }
    et.insert(val);
    mp[val] = val + 1;
    ans += (val - pos) * t;
  }
  cout << ans << "\n";
  return 0;
}

```