#include <bits/stdc++.h>
using namespace std;
const int maxn = 2e5 + 177;
struct Node {
  long long x, y;
  bool operator<(const Node &a) const {
    if (y == a.y) {
      return x < a.x;
    }
    return y > a.y;
  }
} kk[maxn];
map<long long, long long> fa;
int n;
long long find(long long x) {
  if (fa[x] == 0) {
    return x;
  }
  return fa[x] = find(fa[x]);
}
void bcj(long long x, long long y) {
  long long x1 = find(x);
  long long y1 = find(y);
  if (x1 != y1) {
    fa[x1] = y1;
  }
}
int main() {
  cin >> n;
  for (int i = 0; i < n; i++) {
    scanf("%lld", &kk[i].x);
  }
  for (int i = 0; i < n; i++) {
    scanf("%lld", &kk[i].y);
  }
  sort(kk, kk + n);
  long long ans = 0;
  for (int i = 0; i < n; i++) {
    long long now = find(kk[i].x);
    ans = ans + (now - kk[i].x) * kk[i].y;
    bcj(now, now + 1);
  }
  printf("%lld\n", ans);
}

### Prompt

Please create a solution in CPP 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 int maxn = 2e5 + 177;
struct Node {
  long long x, y;
  bool operator<(const Node &a) const {
    if (y == a.y) {
      return x < a.x;
    }
    return y > a.y;
  }
} kk[maxn];
map<long long, long long> fa;
int n;
long long find(long long x) {
  if (fa[x] == 0) {
    return x;
  }
  return fa[x] = find(fa[x]);
}
void bcj(long long x, long long y) {
  long long x1 = find(x);
  long long y1 = find(y);
  if (x1 != y1) {
    fa[x1] = y1;
  }
}
int main() {
  cin >> n;
  for (int i = 0; i < n; i++) {
    scanf("%lld", &kk[i].x);
  }
  for (int i = 0; i < n; i++) {
    scanf("%lld", &kk[i].y);
  }
  sort(kk, kk + n);
  long long ans = 0;
  for (int i = 0; i < n; i++) {
    long long now = find(kk[i].x);
    ans = ans + (now - kk[i].x) * kk[i].y;
    bcj(now, now + 1);
  }
  printf("%lld\n", ans);
}

```