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.
// package com.company;
import org.omg.PortableInterceptor.INACTIVE;

import java.util.*;
import java.lang.*;
import java.io.*;
//****Use Integer Wrapper Class for Arrays.sort()****
public class BV4 {
    public static void main(String[] Args){
        FastReader scan=new FastReader();
        int n=scan.nextInt();
        cat[] arr=new cat[n];
        for(int i=0;i<n;i++){
            arr[i]=new cat(scan.nextInt());
        }
        for(int i=0;i<n;i++){
            arr[i].t=scan.nextInt();
        }
        Arrays.sort(arr);
        PriorityQueue<Integer> pq=new PriorityQueue<>(Collections.reverseOrder());
        long sum=0;
        long ans=0;
        int rep=arr[0].np;
        for(int i=1;i<n;i++){
            if(arr[i].np==rep){
                pq.add(arr[i].t);
                sum+=arr[i].t;
            }
            else {
                while (rep < arr[i].np - 1 && pq.size() > 0) {
                    rep++;
                    ans += sum;
                    sum -= pq.remove();
                }
                if (pq.size() > 0) {
                    rep++;
                    ans += sum;
                    pq.add(arr[i].t);
                    sum += arr[i].t;
                    sum -= pq.remove();
                } else {
                    rep=arr[i].np;
                }
            }
        }
        while(pq.size()>0){
            ans+=sum;
            sum-=pq.remove();
        }
        System.out.println(ans);
    }
    static class cat implements Comparable<cat>{
        int np;
        int t;
        cat(int np){
            this.np=np;
        }

        @Override
        public int compareTo(cat o) {
            if(this.np!=o.np) {
              return  this.np - o.np;
            }
            else{
                return -(this.t-o.t);
            }
        }
    }
    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;
        }
    }

}
