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 Recommendations {
	private static StreamTokenizer st;
	private static int nextInt() throws IOException{
		st.nextToken();
		return (int)st.nval;
	}
	public static void main(String[] args) throws IOException{
		st = new StreamTokenizer(new BufferedReader(new InputStreamReader(System.in)));
		int n = nextInt();
		Cat[] cat = new Cat[n];
		int[] a = new int[n], t = new int[n];
		for(int i = 0; i < n; ++i) a[i] = nextInt();
		for(int i = 0; i < n; ++i) t[i] = nextInt();
		for(int i = 0; i < n; ++i) cat[i] = new Cat(a[i],t[i]);
		Arrays.sort(cat);
		PriorityQueue<Cat> pq = new PriorityQueue<>(new dec());
		long cur = cat[0].a;
		long ans = 0;
		for(int i = 0; i < n; ++i) {
			if(cur==cat[i].a) {
				pq.add(cat[i]);
				continue;
			}
			while(!pq.isEmpty() && cur < cat[i].a) {
				Cat e = pq.poll();
				ans += (cur-e.a)*e.t;
				++cur;
			}
			cur = cat[i].a;
			pq.add(cat[i]);
		}
		while(!pq.isEmpty()) {
			Cat e = pq.poll();
			ans += (cur-e.a)*e.t;
			++cur;
		}
		PrintWriter pw = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
		pw.println(ans);
		pw.close();
	}
	private static class Cat implements Comparable<Cat>{
		int a, t;
		public Cat(int a, int t) {
			this.a = a;
			this.t = t;
		}
		@Override
		public int compareTo(Cat o) {
			return a-o.a;
		}
		
	}
	private static class dec implements Comparator<Cat>{
		@Override
		public int compare(Cat o1, Cat o2) {
			return o2.t-o1.t;
		}
		
	}
}
