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.
#include <bits/stdc++.h>
using namespace std;
void debug_out() { cerr << endl; }
void clock_out() {
  cerr << "\nTime Elapsed : " << 1.0 * clock() / CLOCKS_PER_SEC << " s\n";
}
void fileio() {
  freopen("/home/dwai/Desktop/cp/input.txt", "r", stdin);
  freopen("/home/dwai/Desktop/cp/output.txt", "w", stdout);
  freopen("/home/dwai/Desktop/cp/debug.txt", "w", stderr);
}
void ofileio() {
  freopen("input.txt", "r", stdin);
  freopen("output.txt", "w", stdout);
}
template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
  cerr << " " << H;
  debug_out(T...);
}
int IT_MAX = 1 << 20;
const long long MOD = 1000000007;
const int INF = 0x3f3f3f3f;
const long long LL_INF = 0x3f3f3f3f3f3f3f3f;
const double PI = acos(-1);
const double ERR = 1e-10;
void solve() {
  long long n;
  cin >> n;
  pair<long long, long long> a[n];
  long long i;
  for (i = 0; i < n; i++) cin >> a[i].first;
  for (i = 0; i < n; i++) cin >> a[i].second;
  priority_queue<long long, vector<long long>> p;
  sort(a, a + n);
  i = 0;
  long long sm = 0;
  p.push(a[0].second);
  sm += a[0].second;
  long long idx = a[0].first;
  i++;
  while (i < n && a[i].first == idx) {
    p.push(a[i].second);
    sm += a[i].second;
    i++;
  }
  long long res = 0;
  while (!p.empty()) {
    long long x = p.top();
    p.pop();
    sm -= x;
    res += sm;
    idx++;
    while (i < n && a[i].first == idx) {
      p.push(a[i].second);
      sm += a[i].second;
      i++;
    }
    if (p.empty()) {
      if (i < n) {
        idx = a[i].first;
      }
      while (i < n && a[i].first == idx) {
        p.push(a[i].second);
        sm += a[i].second;
        i++;
      }
    }
  }
  cout << res;
}
int main() {
  42;
  ios_base::sync_with_stdio(false), cin.tie(0), cout.tie(0);
  srand(time(NULL));
  long long t = 1;
  while (t--) {
    solve();
  }
  return 0;
}
