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.*;
import java.io.*;
import static java.lang.Math.*;

public class Main implements Runnable
{
    boolean multiple = false;
    long MOD;

    @SuppressWarnings("Duplicates")
    void solve() throws Exception
    {
        int n = sc.nextInt();
        long[] count = new long[n];
        for (int I = 0; I < n; I++)
            count[I] = sc.nextInt();
        long[] time = new long[n];
        for (int I = 0; I < n; I++)
            time[I] = sc.nextInt();

        TreeMap<Long, TreeSet<Integer>> map = new TreeMap<>();

        for (int i = 0; i < n; i++)
        {
            if (!map.containsKey(count[i]))
                map.put(count[i], new TreeSet<>());
            map.get(count[i]).add(i);
        }

        long ptr = -1;
        long ans = 0;

        while (map.higherKey(ptr) != null)
        {
            ptr = map.higherKey(ptr);

            PriorityQueue<Long> pq = new PriorityQueue<>();
            long temp = 0;
            for (Integer idx : map.get(ptr))
            {
                pq.add(-time[idx]);
                temp += time[idx];
            }

//            System.out.println(pq);

            while (pq.size() > 1)
            {
                ptr++;

                temp -= -pq.poll();
                ans += temp;

                if (map.containsKey(ptr))
                    for (Integer idx : map.get(ptr))
                    {
                        pq.add(-time[idx]);
                        temp += time[idx];
                    }
            }
        }

        System.out.println(ans);
    }

    class Node implements Comparable<Node>
    {
        long cost;
        int idx;

        Node(long C, int i)
        {
            cost = C;
            idx = i;
        }

        @Override
        public int compareTo(Node o)
        {
            return (int)(o.cost - cost);
        }
    }

    long inv(long a, long b)
    {
        return 1 < a ? b - inv(b % a, a) * b / a : 1;
    }

    long gcd(long a, long b)
    {
        return a == 0 ? b : gcd(b % a, a);
    }

    long lcm(long a, long b) { return (a * b) / gcd(a , b); }

    class SegNode
    {
        int max;
        int L, R;
        SegNode left = null, right = null;

        int query(int queryL, int queryR)
        {
            if (queryL == L && queryR == R)
                return max;

            int leftAns = Integer.MIN_VALUE, rightAns = Integer.MIN_VALUE;
            if (left != null && queryL <= left.R)
                leftAns = left.query(queryL, min(queryR, left.R));
            if (right != null && queryR >= right.L)
                rightAns = right.query(max(queryL, right.L), queryR);

            return max(leftAns, rightAns);
        }

        SegNode(int[] arr, int l, int r)
        {
            L = l;
            R = r;
            max = arr[l];

            if (l == r) return;

            int mid = (l + r) / 2;
            left = new SegNode(arr, l, mid);
            right = new SegNode(arr, mid + 1, r);
            max = max(left.max, right.max);
        }
    }

    void print(long[] arr)
    {
        for (int i = 0; i < arr.length; i++)
            System.out.print(arr[i] + " ");
        System.out.println();
    }

    @Override
    public void run()
    {
        try
        {
            in = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(System.out);
            sc = new FastScanner(in);
            if (multiple)
            {
                int q = sc.nextInt();
                for (int i = 0; i < q; i++)
                    solve();
            }
            else
                solve();
        }
        catch (Throwable uncaught)
        {
            Main.uncaught = uncaught;
        }
        finally
        {
            out.close();
        }
    }

    public static void main(String[] args) throws Throwable
    {
        Thread thread = new Thread(null, new Main(), "", (1 << 26));
        thread.start();
        thread.join();
        if (Main.uncaught != null) {
            throw Main.uncaught;
        }
    }

    static Throwable uncaught; BufferedReader in; FastScanner sc; PrintWriter out;
}

class FastScanner
{
    BufferedReader in;
    StringTokenizer st;

    public FastScanner(BufferedReader in)
    {
        this.in = in;
    }

    public String nextToken() throws Exception {
        while (st == null || !st.hasMoreTokens()) {
            st = new StringTokenizer(in.readLine());
        }
        return st.nextToken();
    }

    public int nextInt() throws Exception {
        return Integer.parseInt(nextToken());
    }

    public long nextLong() throws Exception {
        return Long.parseLong(nextToken());
    }

    public double nextDouble() throws Exception {
        return Double.parseDouble(nextToken());
    }
}