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.math.BigInteger;
import java.util.*;
                                 
public class Main {
                             
    static Scanner in;
    static long gcd(long a, long c) {
        BigInteger q = BigInteger.valueOf(a);
        BigInteger w = BigInteger.valueOf(c);
        q = q.gcd(w);
        return q.longValue();
    }

    public static void main(String args[]) throws IOException {
    	
//      in = new StreamTokenizer(new BufferedReader(new InputStreamReader(System.in)));
        in = new Scanner(System.in);         
        PrintWriter out = new PrintWriter(System.out);
        
	    int n = in.nextInt();
	    int[] a = new int[n];
	    int[] ind = new int[n];
//	    int[] b = new int[n];
	    for(int i = 0;i<n;i++) {
	    	a[i] = in.nextInt();
	    	ind[a[i]-1] = i;
	    }
	    int now = -1;
	    for(int i = 0;i<n;i++) {
	    	int b =in.nextInt();
	    	if(ind[b -1 ] > now) {  		
	    		out.print(ind[b-1] - now +" ");
	    		now = ind[b-1];
	    	}else
	    		out.print("0 ");
	    }
	    out.close();
	    
    }
}
                                 
class Pair implements Comparable{
	int a;
    int b;
    public Pair() {
        this.a = 0;
        this.b = 0;
    }
    public Pair(int a, int b) {
        this.a = a;
        this.b = b;
    }
    public int compareTo(Object arg0) {
        if(Integer.compare(this.a, ((Pair) arg0).a) == 0) return Integer.compare(this.b, ((Pair) arg0).b);
            return Integer.compare(this.a, ((Pair) arg0).a);
    }
}