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.util.*;


public class Main2 {

	public static void main(String[] args) {
		MyScanner sc = new MyScanner();
	      out = new PrintWriter(new BufferedOutputStream(System.out));
	      int n=sc.nextInt();
	      Set<Integer> a=new LinkedHashSet();
	      //List<Integer> b=new ArrayList<>();
	      List<Integer> array=new ArrayList<>();
	      for (int i = 0; i < n; i++) {
	    	  a.add(sc.nextInt());
		}
	      
	      int gcounter=0;
	      for (int i = 0; i < n; i++) {
	    	  int b=sc.nextInt();
	    	  int counter=0;
	    	  if(a.contains(b)) {
	    		  
	    	  for (Iterator iterator = a.iterator(); iterator.hasNext();) {
	    		  Integer integer = (Integer) iterator.next();
	    		  iterator.remove();
	    		  counter++;
				if(integer==b) {
			    	out.print(counter+" ");
					break;
				}
			}
	    	  
	    	  /*for (int j = gcounter; j < a.size(); j++) {
					if(b!=a.get(j)) {
						counter++;
						
					}
					else {
						counter++;
						gcounter2+=counter;

						break;
					}
					

					}
				if(gcounter==gcounter2)out.print(0+" ");
				else {
					gcounter=gcounter2;
					out.print(counter+" ");
				}*/
	}
	      
    	  else out.print(0+" ");
	      }
	      out.close();
	}
    

	   //-----------PrintWriter for faster output---------------------------------
	   public static PrintWriter out;
	      
	   //-----------MyScanner class for faster input----------
	   public static class MyScanner {
	      BufferedReader br;
	      StringTokenizer st;
	 
	      public MyScanner() {
	         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;
	      }

	   }

}
