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.util.*;

public class D_623 {
    public static long sum = 0;
    public static void add_t_val(TreeMap<Integer, Integer> t_val, int t){
        sum += t;
        if(t_val.containsKey(t)){
            t_val.put(t, t_val.get(t) + 1);
        }
        else {
            t_val.put(t, 1);
        }
    }
    public static void rem_t_val(TreeMap<Integer, Integer> t_val, int t){
        sum -= t;
        int cnt = t_val.get(t);
        if(cnt==1){
            t_val.remove(t);
        }
        else{
            t_val.put(t, cnt - 1);
        }
    }
    public static void main(String[] args){
        Scanner in = new Scanner(System.in);
        int n=in.nextInt();
        int[] a = new int[n];
        int[] t = new int[n];
        TreeMap<Integer, ArrayList<Integer>> map = new TreeMap<Integer, ArrayList<Integer>>();
        for(int i=0;i<n;i++){
            a[i] = in.nextInt();
            if(map.containsKey(a[i])){
                map.get(a[i]).add(i);
            }
            else {
                ArrayList<Integer> l = new ArrayList<>();
                l.add(i);
                map.put(a[i], l);
            }
        }
        for(int i=0;i<n;i++){
            t[i] = in.nextInt();
        }
        TreeMap<Integer, Integer> t_val = new TreeMap<Integer, Integer>();
        long ans = 0;
        for (Map.Entry<Integer, ArrayList<Integer>> entry : map.entrySet()){
            //System.out.println( "[" + entry.getKey() + ", " + entry.getValue() + "]");
            int cnt = entry.getKey();
            ArrayList<Integer> indxes = entry.getValue();
            for(Integer indx: indxes){
                add_t_val(t_val, t[indx]);
            }
            do{
                int max_t = t_val.floorKey(100005);
                rem_t_val(t_val, max_t);
                ans += sum;
                cnt++;
            }
            while (!t_val.isEmpty() && !map.containsKey(cnt));
        }
        System.out.println(ans);
    }
}