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B. Vasya and Books

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputVasya 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 $$$b_1, b_2, \dots, b_n$$$ 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 $$$n~(1 \le n \le 2 \cdot 10^5)$$$ — the number of books in the stack.

The second line contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n~(1 \le a_i \le n)$$$ denoting the stack of books.

The third line contains $$$n$$$ integers $$$b_1, b_2, \dots, b_n~(1 \le b_i \le n)$$$ denoting the steps Vasya is going to perform.

All numbers $$$a_1 \dots a_n$$$ are distinct, the same goes for $$$b_1 \dots b_n$$$.

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.

Codeforces (c) Copyright 2010-2022 Mike Mirzayanov

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