#include <bits/stdc++.h>
using namespace std;
const long long N = 2e5 + 5;
struct elem {
  long long x, t;
} a[N];
bool sortfun(elem a, elem b) {
  if (a.x == b.x) {
    return a.t > b.t;
  }
  return a.x < b.x;
}
void solve() {
  long long n;
  cin >> n;
  for (long long i = 0; i < n; i++) {
    cin >> a[i].x;
  }
  for (long long i = 0; i < n; i++) {
    cin >> a[i].t;
  }
  sort(a, a + n, sortfun);
  long long nxt = 0, v = a[0].x, j = 0, sm = 0, tmp, ans = 0;
  priority_queue<long long> q;
  while (j < n) {
    while (nxt < n && a[nxt].x == v) q.push(a[nxt].t), sm += a[nxt].t, nxt++;
    tmp = q.top();
    ans += (sm - tmp);
    sm -= tmp;
    q.pop();
    if (q.empty())
      j = nxt, v = a[j].x;
    else
      j++, v++;
  }
  cout << ans << endl;
}
int32_t main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  ;
  solve();
  return 0;
}

### Prompt

Please formulate 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 long long N = 2e5 + 5;
struct elem {
  long long x, t;
} a[N];
bool sortfun(elem a, elem b) {
  if (a.x == b.x) {
    return a.t > b.t;
  }
  return a.x < b.x;
}
void solve() {
  long long n;
  cin >> n;
  for (long long i = 0; i < n; i++) {
    cin >> a[i].x;
  }
  for (long long i = 0; i < n; i++) {
    cin >> a[i].t;
  }
  sort(a, a + n, sortfun);
  long long nxt = 0, v = a[0].x, j = 0, sm = 0, tmp, ans = 0;
  priority_queue<long long> q;
  while (j < n) {
    while (nxt < n && a[nxt].x == v) q.push(a[nxt].t), sm += a[nxt].t, nxt++;
    tmp = q.top();
    ans += (sm - tmp);
    sm -= tmp;
    q.pop();
    if (q.empty())
      j = nxt, v = a[j].x;
    else
      j++, v++;
  }
  cout << ans << endl;
}
int32_t main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  ;
  solve();
  return 0;
}

```