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.HashSet;
import java.util.Set;
import java.util.StringTokenizer;

/**
 * Created by Anton Berezin on 2/18/2017.
 */
public class Books {

	public static void main(String[] args) throws Exception {
		try (FastScanner fastScanner = new FastScanner();
		     PrintWriter writer = new PrintWriter(new BufferedOutputStream(System.out))) {
			int n = fastScanner.nextInt();
			int[] a = new int[n];
			int[] b = new int[n];
			for (int i = 0; i < n; i++) {
				a[i] = fastScanner.nextInt();
			}
			for (int i = 0; i < n; i++) {
				b[i] = fastScanner.nextInt();
			}
			int j = 0;
			Set<Integer> removed = new HashSet<>();
			for (int i = 0; i < n; i++) {
				int cnt = 0;
				if (!removed.contains(b[i])) {
					while (a[j] != b[i]) {
						removed.add(a[j]);
						j++;
						cnt++;
					}
					cnt++;
					removed.add(a[j]);
					j++;
				}
				writer.print(cnt + " ");
			}
			writer.println();

		}
	}

	public static class FastScanner implements AutoCloseable {
		BufferedReader bufferedReader;
		StringTokenizer tokenizer;

		public FastScanner() {
			bufferedReader = new BufferedReader(new InputStreamReader(System.in));
		}

		String next() {
			while (tokenizer == null || !tokenizer.hasMoreElements()) {
				try {
					tokenizer = new StringTokenizer(bufferedReader.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			}
			return tokenizer.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 = bufferedReader.readLine();
			} catch (IOException e) {
				e.printStackTrace();
			}
			return str;
		}

		@Override
		public void close() throws IOException {
			bufferedReader.close();
		}
	}
}
