#include <bits/stdc++.h>
using namespace std;
long long n, a[200009], t[200009], ans;
multiset<pair<long long, long long> > s;
set<pair<long long, long long> > ranges;
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  cin >> n;
  for (int i = 1; i <= n; i++) cin >> a[i];
  for (int i = 1; i <= n; i++) {
    cin >> t[i];
    s.insert({t[i], a[i]});
  }
  for (auto it = s.rbegin(); it != s.rend(); it++) {
    long long time = it->first;
    long long val = it->second;
    auto rit = ranges.lower_bound({val, 0});
    if (rit == ranges.end()) {
      auto ritestrit = ranges.rbegin();
      if (ritestrit == ranges.rend() || ritestrit->first != val - 1) {
        ranges.insert({val, val});
        continue;
      }
      long long l = ritestrit->second;
      ranges.erase({ritestrit->first, ritestrit->second});
      ranges.insert({val, l});
      continue;
    }
    long long l = rit->second, r = rit->first;
    if (l <= val) {
      ans += (r - val + 1) * time;
      long long le = l, ri = r + 1;
      rit++;
      if (rit != ranges.end()) {
        long long l2 = rit->second, r2 = rit->first;
        if (l2 == ri + 1) {
          ri = r2;
          ranges.erase({r2, l2});
        }
      }
      ranges.erase({r, l});
      ranges.insert({ri, le});
      continue;
    }
    long long le = val, ri = val;
    bool erasel = 0;
    if (l == val + 1) {
      ri = r;
      erasel = 1;
    }
    if (rit != ranges.begin()) {
      rit--;
      if (rit != ranges.end()) {
        if (rit->first == val - 1) {
          le = rit->second;
          ranges.erase({rit->first, rit->second});
        }
      }
    }
    if (erasel) ranges.erase({r, l});
    ranges.insert({ri, le});
  }
  cout << ans << endl;
}

### Prompt

In cpp, your task is to solve 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 n, a[200009], t[200009], ans;
multiset<pair<long long, long long> > s;
set<pair<long long, long long> > ranges;
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  cin >> n;
  for (int i = 1; i <= n; i++) cin >> a[i];
  for (int i = 1; i <= n; i++) {
    cin >> t[i];
    s.insert({t[i], a[i]});
  }
  for (auto it = s.rbegin(); it != s.rend(); it++) {
    long long time = it->first;
    long long val = it->second;
    auto rit = ranges.lower_bound({val, 0});
    if (rit == ranges.end()) {
      auto ritestrit = ranges.rbegin();
      if (ritestrit == ranges.rend() || ritestrit->first != val - 1) {
        ranges.insert({val, val});
        continue;
      }
      long long l = ritestrit->second;
      ranges.erase({ritestrit->first, ritestrit->second});
      ranges.insert({val, l});
      continue;
    }
    long long l = rit->second, r = rit->first;
    if (l <= val) {
      ans += (r - val + 1) * time;
      long long le = l, ri = r + 1;
      rit++;
      if (rit != ranges.end()) {
        long long l2 = rit->second, r2 = rit->first;
        if (l2 == ri + 1) {
          ri = r2;
          ranges.erase({r2, l2});
        }
      }
      ranges.erase({r, l});
      ranges.insert({ri, le});
      continue;
    }
    long long le = val, ri = val;
    bool erasel = 0;
    if (l == val + 1) {
      ri = r;
      erasel = 1;
    }
    if (rit != ranges.begin()) {
      rit--;
      if (rit != ranges.end()) {
        if (rit->first == val - 1) {
          le = rit->second;
          ranges.erase({rit->first, rit->second});
        }
      }
    }
    if (erasel) ranges.erase({r, l});
    ranges.insert({ri, le});
  }
  cout << ans << endl;
}

```