#include <bits/stdc++.h>
using namespace std;
const int inf = 1 << 30;
const long long int INF = 1e18;
const int MOD = 1e9 + 7;
const int MAXN = 300005;
bool Compare(const pair<int, int> &x, const pair<int, int> &y) {
  if (x.first == y.first) {
    return x.second > y.second;
  }
  return x.first < y.first;
}
int dx[] = {-1, 1, 0, 0, 0, 0};
int dy[] = {0, 0, 1, -1, 0, 0};
int dz[] = {0, 0, 0, 0, 1, -1};
long long int a[200002];
map<long long int, multiset<long long int> > mp;
map<long long int, long long int> mq;
long long int GetMid(int lo, int hi, long long int val) {
  int pos = 0;
  while (lo <= hi) {
    int mid = (lo + hi) / 2;
    if (a[mid] > val) {
      pos = mid;
      hi = mid - 1;
    } else
      lo = mid + 1;
  }
  return a[pos];
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  int n;
  cin >> n;
  long long int p[n];
  long long int sum = 0;
  for (int i = 0; i < n; i++) {
    cin >> a[i];
  }
  for (int i = 0; i < n; i++) {
    cin >> p[i];
    mq[a[i]] += p[i];
    mp[a[i]].insert(p[i]);
  }
  sort(a, a + n);
  long long int crt = -1;
  int pos = 0;
  while (pos < n) {
    crt = GetMid(0, n - 1, crt);
    while (pos < n) {
      if (mp[crt].size() == 1) {
        pos++;
        break;
      }
      long long int nxt = crt + 1;
      multiset<long long int>::iterator it = mp[crt].end();
      --it;
      mq[crt] -= *it;
      mp[crt].erase(it);
      sum += mq[crt];
      if (mp[nxt].size() < mp[crt].size()) {
        swap(mp[nxt], mp[crt]);
        swap(mq[nxt], mq[crt]);
      }
      for (auto v : mp[crt]) mp[nxt].insert(v);
      mq[nxt] += mq[crt];
      crt = nxt;
      pos++;
    }
  }
  cout << sum << '\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;
const int inf = 1 << 30;
const long long int INF = 1e18;
const int MOD = 1e9 + 7;
const int MAXN = 300005;
bool Compare(const pair<int, int> &x, const pair<int, int> &y) {
  if (x.first == y.first) {
    return x.second > y.second;
  }
  return x.first < y.first;
}
int dx[] = {-1, 1, 0, 0, 0, 0};
int dy[] = {0, 0, 1, -1, 0, 0};
int dz[] = {0, 0, 0, 0, 1, -1};
long long int a[200002];
map<long long int, multiset<long long int> > mp;
map<long long int, long long int> mq;
long long int GetMid(int lo, int hi, long long int val) {
  int pos = 0;
  while (lo <= hi) {
    int mid = (lo + hi) / 2;
    if (a[mid] > val) {
      pos = mid;
      hi = mid - 1;
    } else
      lo = mid + 1;
  }
  return a[pos];
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  int n;
  cin >> n;
  long long int p[n];
  long long int sum = 0;
  for (int i = 0; i < n; i++) {
    cin >> a[i];
  }
  for (int i = 0; i < n; i++) {
    cin >> p[i];
    mq[a[i]] += p[i];
    mp[a[i]].insert(p[i]);
  }
  sort(a, a + n);
  long long int crt = -1;
  int pos = 0;
  while (pos < n) {
    crt = GetMid(0, n - 1, crt);
    while (pos < n) {
      if (mp[crt].size() == 1) {
        pos++;
        break;
      }
      long long int nxt = crt + 1;
      multiset<long long int>::iterator it = mp[crt].end();
      --it;
      mq[crt] -= *it;
      mp[crt].erase(it);
      sum += mq[crt];
      if (mp[nxt].size() < mp[crt].size()) {
        swap(mp[nxt], mp[crt]);
        swap(mq[nxt], mq[crt]);
      }
      for (auto v : mp[crt]) mp[nxt].insert(v);
      mq[nxt] += mq[crt];
      crt = nxt;
      pos++;
    }
  }
  cout << sum << '\n';
  return 0;
}

```