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.*;
import java.util.*;

public class Main {
    static PrintWriter out = new PrintWriter(System.out);
    static Scanner sc = new Scanner(System.in);
    static BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
    public static void main(String[] args) throws IOException {
        Main main = new Main();
        main.solve();
        out.flush();
//        System.out.println(main.solve());
    }
    long solve() throws IOException{
        String[] buf = reader.readLine().split(" ");
        int n = Integer.parseInt(buf[0]);
        int[][] at = new int[n][2]; // {quantiy_now, time}
        buf = reader.readLine().split(" ");
        for(int i=0;i<n;i++) at[i][0] = Integer.parseInt(buf[i]);
        buf = reader.readLine().split(" ");
        for(int i=0;i<n;i++) at[i][1] = Integer.parseInt(buf[i]);
        Arrays.sort(at,Comparator.comparingInt(o1->o1[0]));
        // pq, the reverse order of time
        PriorityQueue<int[]> pq =  new PriorityQueue<>(n,(o1,o2)->(o2[1]-o1[1]));
        int cnt = 0; // # categories that already settled
        int idx = 0,next = at[0][0]; // next is the expected value of next category to settle
        long ans = 0;
        while(cnt<n){
            while(idx<n&&at[idx][0]<=next){
                pq.add(at[idx]);
                idx++;
            }
            int[] cur = pq.poll();
            ans += ((long)cur[1])*(next-cur[0]);
            cnt ++;
            if(idx==cnt){
                if(idx<n) next = at[idx][0]; // from previous can be sure that at[idx][0]>next
            } else{
                next++;
            }
        }
        out.println(ans);
        return 0;
    }
}

