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.

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Scanner;
import java.util.StringTokenizer;
import java.util.*;
import java.math.*;
public class Simple
{


    static class FastReader
    {
        BufferedReader br;
        StringTokenizer st;

        public FastReader()
        {
            br = new BufferedReader(new
                     InputStreamReader(System.in));
        }

        String next()
        {
            while (st == null || !st.hasMoreElements())
            {
                try
                {
                    st = new StringTokenizer(br.readLine());
                }
                catch (IOException  e)
                {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt()
        {
            return Integer.parseInt(next());
        }

        long nextLong()
        {
            return Long.parseLong(next());
        }

        double nextDouble()
        {
            return Double.parseDouble(next());
        }

        String nextLine()
        {
            String str = "";
            try
            {
                str = br.readLine();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
            return str;
        }
    }


    public static void main(String[] args)
    {
        FastReader sc=new FastReader();


          int n=sc.nextInt();
        long a[]=new long[n];
        long t[]=new long[n];
        PriorityQueue<Pair> pq=new PriorityQueue<>(new cmp());
        for( int i=0;i<n;i++)
        {
          a[i]=sc.nextLong();
                }
for( int i=0;i<n;i++)
{
  t[i]=sc.nextLong();
}
Pair arr[]=new Pair[n];
for( int i=0;i<n;i++)
{
  arr[i]=new Pair(a[i],t[i]);
}
Arrays.sort(arr, new Comparator<Pair>(){
  public int compare(Pair a, Pair b)
  {
    return (int)(a.x-b.x);
  }
});

long val=arr[0].x;
pq.add(arr[0]);
long sum=0;
sum=sum+arr[0].y;
long ans=0;
for( int i=0;i<n;)
{

  if(pq.isEmpty())
  {
    i++;
    if(i==n)
    break;
    pq.add(arr[i]);
    sum+=arr[i].y;
    val=arr[i].x;

  }
  while(i<n-1&&arr[i+1].x==val)
  {
    pq.add(arr[i+1]);
    sum+=arr[i+1].y;
    i++;
  }
  Pair d=pq.remove();
  sum-=d.y;
  ans+=sum;
  val++;
  if(i==n)
  break;
}
System.out.println(ans);
  }
}
class Pair
{
  long x,y;
  Pair(long x, long y)
  {
    this.x=x;
    this.y=y;
  }
}
class cmp implements Comparator<Pair>
{
  public int compare(Pair a, Pair b)
  {
    return Long.compare(b.y, a.y);
  }
}
