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.BufferedReader;
import java.io.BufferedWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.LinkedList;
import java.util.*;

public class Main {
	static LinkedList<String> wordQueue = new LinkedList<>();
	public static void main(String[] args) {
		FastReader fr = new FastReader();
		PrintWriter pr = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
		int n = fr.nextInt();
		int[] books = new int[n];
		boolean[] backpack = new boolean[n+1];
		for(int count = 0; count < n; count++) {
			books[count] = fr.nextInt();
		}
		int total = 0;
		for(int count = 0; count < n; count++) {
			int next = fr.nextInt();
			int bookCount = 0;
			if(total != n ) {
				if(!backpack[next]) {
					for(int i = total; i < n; i++) {
						backpack[books[i]] = true;
						bookCount++;
						if(books[i] == next) {
							break;
						}
					}
				}
			}
			total +=bookCount;
			pr.print(bookCount + " ");
		}
		pr.close();
	}
	static class FastReader{
	    BufferedReader br;
	    StringTokenizer st;

	    public FastReader(){
	        br = new BufferedReader(new InputStreamReader(System.in));
	    }

	    String next(){
	        while (st == null || !st.hasMoreElements()){
	            try{
	                st = new StringTokenizer(br.readLine());
	            }catch (IOException  e){
	                e.printStackTrace();
	            }
	        }
	        return st.nextToken();
	    }

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

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

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

	    String nextLine(){
	        String str = "";
	        try{
	            str = br.readLine();
	        }catch (IOException e){
	            e.printStackTrace();
	        }
	        return str;
	    }
	}
}
