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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.TreeMap;
import java.util.StringTokenizer;
import java.util.Map;
import java.util.Map.Entry;
import java.io.BufferedReader;
import java.util.Comparator;
import java.util.Collections;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskD solver = new TaskD();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskD {
        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int N = in.nextInt();
            ArrayList<long[]> arr = new ArrayList<>();
            for (int i = 0; i < N; i++) {
                arr.add(new long[]{in.nextInt(), 0});
            }
            for (int i = 0; i < N; i++) {
                arr.get(i)[1] += in.nextInt();
            }
            Collections.sort(arr, new Comparator<long[]>() {

                public int compare(long[] ints, long[] t1) {
                    return Long.compare(ints[0], t1[0]);
                }
            });
            Multiset maxCost = new Multiset();
            long res = 0;
            long curSum = 0;
            long cur = arr.get(0)[0];
            for (int i = 0; i < N; i++) {
                while (cur < arr.get(i)[0]) {
                    if (maxCost.isEmpty()) {
                        cur = arr.get(i)[0];
                        break;
                    }
                    curSum -= maxCost.pollFirst();
                    res += curSum;
                    cur++;
                }
                maxCost.add(arr.get(i)[1]);
                curSum += arr.get(i)[1];
            }
            while (!maxCost.isEmpty()) {
                curSum -= maxCost.pollFirst();
                res += curSum;
            }
            out.println(res);
        }

        class Multiset {
            TreeMap<Long, Integer> cnt = new TreeMap<>(new Comparator<Long>() {

                public int compare(Long aLong, Long t1) {
                    return Long.compare(t1, aLong);
                }
            });

            void add(long val) {
                cnt.putIfAbsent(val, 0);
                cnt.replace(val, cnt.get(val) + 1);
            }

            long pollFirst() {
                Map.Entry<Long, Integer> e = cnt.firstEntry();
                if (e.getValue() == 1) {
                    cnt.remove(e.getKey());
                } else {
                    cnt.replace(e.getKey(), e.getValue() - 1);
                }
                return e.getKey();
            }

            boolean isEmpty() {
                return (cnt.size() == 0);
            }

        }

    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

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

    }
}

