#include <bits/stdc++.h>
using namespace std;
using ull = uint64_t;
using ll = int64_t;
using PII = pair<int, int>;
using VI = vector<int>;
string to_string(string s) { return '"' + s + '"'; }
string to_string(const char* s) { return to_string((string)s); }
string to_string(bool b) { return (b ? "true" : "false"); }
template <typename A, typename B>
string to_string(pair<A, B> p) {
  return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
}
template <typename A>
string to_string(A v) {
  bool first = true;
  string res = "{";
  for (const auto& x : v) {
    if (!first) {
      res += ", ";
    }
    first = false;
    res += to_string(x);
  }
  res += "}";
  return res;
}
void debug_out() { cerr << endl; }
template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
  cerr << " " << to_string(H);
  debug_out(T...);
}
const ll mod = 1000000007;
bool cmp(pair<ll, ll> a, pair<ll, ll> b) {
  if (a.first == b.first) {
    return a.second > b.second;
  } else {
    return a.first < b.first;
  }
}
int main() {
  ios::sync_with_stdio(false), cin.tie(0);
  int n;
  cin >> n;
  vector<ll> A(n), T(n);
  for (int _n = n, i = 0; i < _n; ++i) cin >> A[i];
  for (int _n = n, i = 0; i < _n; ++i) cin >> T[i];
  vector<pair<ll, ll>> V;
  for (int _n = n, i = 0; i < _n; ++i) {
    V.push_back({A[i], T[i]});
  }
  sort((V).begin(), (V).end(), cmp);
  multiset<ll> S;
  ll last = 0, ans = 0, sum = 0;
  for (int _n = n, i = 0; i < _n; ++i) {
    ll fst = V[i].first;
    while (last < fst - 1 && !S.empty()) {
      auto it = prev(S.end());
      ans += sum;
      sum -= *it;
      S.erase(it);
      last++;
    }
    if (last == fst - 1 && !S.empty()) {
      ans += sum;
      S.insert(V[i].second);
      sum += V[i].second;
      auto it = prev(S.end());
      sum -= *it;
      S.erase(it);
      last = fst;
    } else if (last == fst) {
      S.insert(V[i].second);
      sum += V[i].second;
    }
    last = fst;
  }
  while (!S.empty()) {
    auto it = prev(S.end());
    ans += sum;
    sum -= *it;
    S.erase(it);
  }
  cout << ans << "\n";
}

### Prompt

Please create a solution in cpp 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;
using ull = uint64_t;
using ll = int64_t;
using PII = pair<int, int>;
using VI = vector<int>;
string to_string(string s) { return '"' + s + '"'; }
string to_string(const char* s) { return to_string((string)s); }
string to_string(bool b) { return (b ? "true" : "false"); }
template <typename A, typename B>
string to_string(pair<A, B> p) {
  return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
}
template <typename A>
string to_string(A v) {
  bool first = true;
  string res = "{";
  for (const auto& x : v) {
    if (!first) {
      res += ", ";
    }
    first = false;
    res += to_string(x);
  }
  res += "}";
  return res;
}
void debug_out() { cerr << endl; }
template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
  cerr << " " << to_string(H);
  debug_out(T...);
}
const ll mod = 1000000007;
bool cmp(pair<ll, ll> a, pair<ll, ll> b) {
  if (a.first == b.first) {
    return a.second > b.second;
  } else {
    return a.first < b.first;
  }
}
int main() {
  ios::sync_with_stdio(false), cin.tie(0);
  int n;
  cin >> n;
  vector<ll> A(n), T(n);
  for (int _n = n, i = 0; i < _n; ++i) cin >> A[i];
  for (int _n = n, i = 0; i < _n; ++i) cin >> T[i];
  vector<pair<ll, ll>> V;
  for (int _n = n, i = 0; i < _n; ++i) {
    V.push_back({A[i], T[i]});
  }
  sort((V).begin(), (V).end(), cmp);
  multiset<ll> S;
  ll last = 0, ans = 0, sum = 0;
  for (int _n = n, i = 0; i < _n; ++i) {
    ll fst = V[i].first;
    while (last < fst - 1 && !S.empty()) {
      auto it = prev(S.end());
      ans += sum;
      sum -= *it;
      S.erase(it);
      last++;
    }
    if (last == fst - 1 && !S.empty()) {
      ans += sum;
      S.insert(V[i].second);
      sum += V[i].second;
      auto it = prev(S.end());
      sum -= *it;
      S.erase(it);
      last = fst;
    } else if (last == fst) {
      S.insert(V[i].second);
      sum += V[i].second;
    }
    last = fst;
  }
  while (!S.empty()) {
    auto it = prev(S.end());
    ans += sum;
    sum -= *it;
    S.erase(it);
  }
  cout << ans << "\n";
}

```