#include <bits/stdc++.h>
using namespace std;
const int maxn = 2e5 + 10;
const int MAX = 1000;
const int inf = 0x3f3f3f3f;
const int mod = 1e9 + 7;
int n, m;
struct re {
  int a, t;
} a[maxn];
map<int, int> fa;
bool cmp(re a, re b) { return a.t > b.t; }
int find(int k) {
  if (fa[k] == 0) fa[k] = k;
  if (fa[k] == k) return k;
  return fa[k] = find(fa[k]);
}
void unite(int x, int y) {
  int fay = find(y), fax = find(x);
  fa[fax] = fa[fay];
}
signed main() {
  int n;
  cin >> n;
  for (int i = (1); i <= (n); ++i) {
    scanf("%d", &a[i].a);
  }
  for (int i = (1); i <= (n); ++i) {
    scanf("%d", &a[i].t);
  }
  sort(a + 1, a + 1 + n, cmp);
  long long ans = 0;
  for (int i = (1); i <= (n); ++i) {
    int now = find(a[i].a);
    ans += 1ll * (now - a[i].a) * a[i].t;
    unite(now, now + 1);
  }
  cout << (ans) << endl;
}

### Prompt

Construct a cpp code solution to the problem outlined:

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 maxn = 2e5 + 10;
const int MAX = 1000;
const int inf = 0x3f3f3f3f;
const int mod = 1e9 + 7;
int n, m;
struct re {
  int a, t;
} a[maxn];
map<int, int> fa;
bool cmp(re a, re b) { return a.t > b.t; }
int find(int k) {
  if (fa[k] == 0) fa[k] = k;
  if (fa[k] == k) return k;
  return fa[k] = find(fa[k]);
}
void unite(int x, int y) {
  int fay = find(y), fax = find(x);
  fa[fax] = fa[fay];
}
signed main() {
  int n;
  cin >> n;
  for (int i = (1); i <= (n); ++i) {
    scanf("%d", &a[i].a);
  }
  for (int i = (1); i <= (n); ++i) {
    scanf("%d", &a[i].t);
  }
  sort(a + 1, a + 1 + n, cmp);
  long long ans = 0;
  for (int i = (1); i <= (n); ++i) {
    int now = find(a[i].a);
    ans += 1ll * (now - a[i].a) * a[i].t;
    unite(now, now + 1);
  }
  cout << (ans) << endl;
}

```