#include <bits/stdc++.h>
using namespace std;
const long long INF = 0x3f3f3f3f3f3f3f;
const int MAXN = 1e6 + 10;
const int N = 1e5;
const int P = 1e9 + 7;
const double pi = acos(-1);
int n;
int num[MAXN];
set<int> s;
long long ans;
struct node {
  int a;
  long long t;
} p[MAXN];
bool cmp(node x, node y) { return x.a < y.a; }
bool cmp2(node x, node y) { return x.t < y.t; }
int main() {
  scanf("%d", &n);
  for (int i = 1; i <= n; i++) scanf("%d", &p[i].a);
  for (int i = 1; i <= n; i++) scanf("%lld", &p[i].t);
  sort(p + 1, p + n + 1, cmp);
  for (int i = 1; i <= n; i++)
    num[i] = max(num[i - 1] + 1, p[i].a), s.insert(num[i]);
  sort(p + 1, p + n + 1, cmp2);
  for (int i = n; i >= 1; i--) {
    set<int>::iterator it = s.lower_bound(p[i].a);
    ans += (*it - p[i].a) * p[i].t;
    s.erase(*it);
  }
  printf("%lld\n", ans);
  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 INF = 0x3f3f3f3f3f3f3f;
const int MAXN = 1e6 + 10;
const int N = 1e5;
const int P = 1e9 + 7;
const double pi = acos(-1);
int n;
int num[MAXN];
set<int> s;
long long ans;
struct node {
  int a;
  long long t;
} p[MAXN];
bool cmp(node x, node y) { return x.a < y.a; }
bool cmp2(node x, node y) { return x.t < y.t; }
int main() {
  scanf("%d", &n);
  for (int i = 1; i <= n; i++) scanf("%d", &p[i].a);
  for (int i = 1; i <= n; i++) scanf("%lld", &p[i].t);
  sort(p + 1, p + n + 1, cmp);
  for (int i = 1; i <= n; i++)
    num[i] = max(num[i - 1] + 1, p[i].a), s.insert(num[i]);
  sort(p + 1, p + n + 1, cmp2);
  for (int i = n; i >= 1; i--) {
    set<int>::iterator it = s.lower_bound(p[i].a);
    ans += (*it - p[i].a) * p[i].t;
    s.erase(*it);
  }
  printf("%lld\n", ans);
  return 0;
}

```