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.IOException;
import java.io.InputStreamReader;

public class Main
{

	public static void main(String[] args) throws IOException
	{
		BufferedReader bi = new BufferedReader(new InputStreamReader(System.in));
		String lineOne = bi.readLine();
		String lineTwo = bi.readLine();
		String lineThree = bi.readLine();
		bi.close();

		int n = Integer.parseInt(lineOne);

		int[] indexN = new int[n +1];
		int r=0;
		for (String numStr: lineTwo.split("\\s"))
		{
			int bn = Integer.parseInt(numStr);
			indexN[bn] = r;
			r++;
		}

		boolean printZeros = false;
		int countOfPrinted = 0;
		int c = 0;
		int biggestIndex =0;
		int sum = 0;
		int previous = -1;
		int i=0;
		for (String numStr: lineThree.split("\\s"))
		{
			int a = Integer.parseInt(numStr);

			int indexOfNumber = indexN[a] + 1;
			if(indexOfNumber > biggestIndex)
			{
				biggestIndex = indexOfNumber;
				int current;
				sum = indexOfNumber;
				if(previous == -1)
				{
					previous = sum;
					current = sum;
				}
				else
				{
					current = sum - previous;
					previous = sum;
				}
				c = current;
			}
			else
			{
				c = 0;
			}
			System.out.print(c + " ");
			
			if(indexN[a] == n -1)
			{
				printZeros = true;
				countOfPrinted = i +1;
				break;
			}
			i++;
		}

		if (printZeros)
		{
			while (n > countOfPrinted)
			{
				countOfPrinted++;
				System.out.print("0 ");
			}
		}

	}

}
