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.nio.CharBuffer;
import java.util.ArrayList;
import java.util.Comparator;
import java.util.NoSuchElementException;
import java.util.PriorityQueue;

public class P1315D {

    public static void main(String[] args) {
        SimpleScanner scanner = new SimpleScanner(System.in);
        PrintWriter writer = new PrintWriter(System.out);

        int n = scanner.nextInt();
        ArrayList<int[]> x = new ArrayList<>(n);
        for (int i = 0; i < n; ++i)
            x.add(new int[]{scanner.nextInt(), -1});
        for (int i = 0; i < n; ++i)
            x.get(i)[1] = scanner.nextInt();
        x.sort(Comparator.comparingInt(o -> o[0]));
        PriorityQueue<Integer> heap = new PriorityQueue<>(n, Comparator.reverseOrder());
        long heapSum = 0;
        long ans = 0;
        int pre = 0;
        for (int i = 0; i < n; ) {
            while (!heap.isEmpty() && pre != x.get(i)[0] - 1) {
                int v = heap.poll();
                heapSum -= v;
                ans += heapSum;
                ++pre;
            }
            int j = i;
            while (j < n && x.get(j)[0] == x.get(i)[0]) {
                heap.offer(x.get(j)[1]);
                heapSum += x.get(j)[1];
                ++j;
            }
            int v = heap.poll();
            heapSum -= v;
            ans += heapSum;
            pre = x.get(i)[0];
            i = j;
        }
        while (!heap.isEmpty()) {
            int v = heap.poll();
            heapSum -= v;
            ans += heapSum;
        }
        writer.println(ans);

        writer.close();
    }

    private static class SimpleScanner {

        private static final int BUFFER_SIZE = 10240;

        private Readable in;
        private CharBuffer buffer;
        private boolean eof;

        private SimpleScanner(InputStream in) {
            this.in = new BufferedReader(new InputStreamReader(in));
            buffer = CharBuffer.allocate(BUFFER_SIZE);
            buffer.limit(0);
            eof = false;
        }


        private char read() {
            if (!buffer.hasRemaining()) {
                buffer.clear();
                int n;
                try {
                    n = in.read(buffer);
                } catch (IOException e) {
                    n = -1;
                }
                if (n <= 0) {
                    eof = true;
                    return '\0';
                }
                buffer.flip();
            }
            return buffer.get();
        }

        private void checkEof() {
            if (eof)
                throw new NoSuchElementException();
        }

        private char nextChar() {
            checkEof();
            char b = read();
            checkEof();
            return b;
        }

        private String next() {
            char b;
            do {
                b = read();
                checkEof();
            } while (Character.isWhitespace(b));
            StringBuilder sb = new StringBuilder();
            do {
                sb.append(b);
                b = read();
            } while (!eof && !Character.isWhitespace(b));
            return sb.toString();
        }

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

        private long nextLong() {
            return Long.parseLong(next());
        }

        private double nextDouble() {
            return Double.parseDouble(next());
        }
    }
}
