Vasya has got n books, numbered from 1 to n, arranged in a stack. The topmost book has number a_1, the next one — a_2, and so on. The book at the bottom of the stack has number a_n. All numbers are distinct.

Vasya wants to move all the books to his backpack in n steps. During i-th step he wants to move the book number b_i into his backpack. If the book with number b_i is in the stack, he takes this book and all the books above the book b_i, and puts them into the backpack; otherwise he does nothing and begins the next step. For example, if books are arranged in the order [1, 2, 3] (book 1 is the topmost), and Vasya moves the books in the order [2, 1, 3], then during the first step he will move two books (1 and 2), during the second step he will do nothing (since book 1 is already in the backpack), and during the third step — one book (the book number 3). Note that b_1, b_2, ..., b_n are distinct.

Help Vasya! Tell him the number of books he will put into his backpack during each step.

Input

The first line contains one integer n~(1 ≤ n ≤ 2 ⋅ 10^5) — the number of books in the stack.

The second line contains n integers a_1, a_2, ..., a_n~(1 ≤ a_i ≤ n) denoting the stack of books.

The third line contains n integers b_1, b_2, ..., b_n~(1 ≤ b_i ≤ n) denoting the steps Vasya is going to perform.

All numbers a_1 ... a_n are distinct, the same goes for b_1 ... b_n.

Output

Print n integers. The i-th of them should be equal to the number of books Vasya moves to his backpack during the i-th step.

Examples

Input

3
1 2 3
2 1 3


Output

2 0 1 


Input

5
3 1 4 2 5
4 5 1 3 2


Output

3 2 0 0 0 


Input

6
6 5 4 3 2 1
6 5 3 4 2 1


Output

1 1 2 0 1 1 

Note

The first example is described in the statement.

In the second example, during the first step Vasya will move the books [3, 1, 4]. After that only books 2 and 5 remain in the stack (2 is above 5). During the second step Vasya will take the books 2 and 5. After that the stack becomes empty, so during next steps Vasya won't move any books.
import java.io.*;
import java.text.DecimalFormat;
import java.util.HashMap;
import java.util.StringTokenizer;

public class Main {
    public void solve() {
        int n = ni();
        int[] a = new int[n];
        HashMap<Integer, Integer> pos = new HashMap<>();
        for (int i = 0; i < n; i++) {
            a[i] = ni();
            pos.put(a[i], i);
        }

        int j = 0, oldJ = -1;
        for (int i = 0; i < n; i++) {
            int b = ni();
            if ((j == n) || (pos.get(b) < j)) {
                write(0 + " ");
                continue;
            }
            while (j < n) {
                if (a[j] == b) {
                    write(j - oldJ + " ");
                    oldJ = j++;
                    break;
                }
                j++;
            }

        }
    }



    public static void main(String[] args){
        Main m = new Main();
        m.solve();
        try {
            m.writer.close();
        } catch (IOException e) {};
    }
    BufferedReader reader;
    BufferedWriter writer;
    StringTokenizer tokenizer;
    public Main() {
        reader = new BufferedReader(new InputStreamReader(System.in));
        writer = new BufferedWriter(new OutputStreamWriter(System.out));
    }
    int ni() {
        return Integer.parseInt(n());
    }
    String n() {
        if (tokenizer == null || !tokenizer.hasMoreTokens()) {
            try {
                tokenizer = new StringTokenizer(reader.readLine());
            } catch (IOException e) {}
        }
        return tokenizer.nextToken();
    }
    void write(String s) {
        try {
            writer.write(s);
        } catch(IOException e) {};
    }
}