#include <bits/stdc++.h>
using namespace std;
const long long inf = 1e15;
const int N = 2e5 + 5;
const int mod = 1e9 + 7;
int n, m, k, t, T, x, y, z;
int a[N], b[N];
struct node {
  int num, v;
  bool operator<(const node p) const {
    if (v != p.v)
      return v > p.v;
    else
      return num < p.num;
  }
} q[N];
map<int, int> mmp;
int f(int x) {
  if (mmp[x] == 0)
    return x;
  else
    return mmp[x] = f(mmp[x]);
}
void solve() {
  scanf("%d", &n);
  for (int i = 1; i <= n; i++) scanf("%d", &q[i].num);
  for (int i = 1; i <= n; i++) scanf("%d", &q[i].v);
  sort(q + 1, q + 1 + n);
  long long ans = 0;
  for (int i = 1; i <= n; i++) {
    t = f(q[i].num);
    if (t != q[i].num) {
      ans += 1LL * (t - q[i].num) * q[i].v;
    }
    mmp[t] = f(t + 1);
  }
  printf("%lld\n", ans);
}
int main() {
  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 inf = 1e15;
const int N = 2e5 + 5;
const int mod = 1e9 + 7;
int n, m, k, t, T, x, y, z;
int a[N], b[N];
struct node {
  int num, v;
  bool operator<(const node p) const {
    if (v != p.v)
      return v > p.v;
    else
      return num < p.num;
  }
} q[N];
map<int, int> mmp;
int f(int x) {
  if (mmp[x] == 0)
    return x;
  else
    return mmp[x] = f(mmp[x]);
}
void solve() {
  scanf("%d", &n);
  for (int i = 1; i <= n; i++) scanf("%d", &q[i].num);
  for (int i = 1; i <= n; i++) scanf("%d", &q[i].v);
  sort(q + 1, q + 1 + n);
  long long ans = 0;
  for (int i = 1; i <= n; i++) {
    t = f(q[i].num);
    if (t != q[i].num) {
      ans += 1LL * (t - q[i].num) * q[i].v;
    }
    mmp[t] = f(t + 1);
  }
  printf("%lld\n", ans);
}
int main() {
  solve();
  return 0;
}

```