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;
import java.util.StringTokenizer;

public class VasyaAndBooks {
    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        int n = Integer.parseInt(br.readLine());
        StringTokenizer st = new StringTokenizer(br.readLine());
        int[] aIndex = new int[n];

        for(int i=0; i<n; i++){
            //store the index of the book number, i.e. a, at the book number index
            //So fetching value a is O(1)
            int a = Integer.parseInt(st.nextToken()) - 1; //-1 to start at 0
            aIndex[a] = i;
        }

        st = new StringTokenizer(br.readLine());
        int h=-1; //since we are starting index from 0, book at 0 should be count 1 when count = 0 - (-1)
        for(int i=0; i<n; i++){
            int book = Integer.parseInt(st.nextToken()) -1;
            int nextIndex = aIndex[book];
            //if the index of book to keep is less than current index h, then it is already kept
            if(nextIndex < h){
                System.out.print(0 + " ");
                continue;
            }

            //total books kept when you keep this book is book_index - current_index in the stack
            int count = nextIndex - h;
            h = nextIndex;
            System.out.print(count + " ");
        }
    }
}


/*
// Time limit exceeded with boolean lookup map

import java.util.Scanner;

public class VasyaAndBooks {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int[] a = new int[n];
        int[] b = new int[n];
        boolean[] kept = new boolean[n+1];

        for(int i=0; i<n; i++){
            a[i] = sc.nextInt();
        }

        for(int i=0; i<n; i++){
            b[i] = sc.nextInt();
        }

        int h=0;
        for(int i=0; i<n; i++){
            int keep = b[i];
            if(kept[keep]){
                System.out.print(0 + " ");
                continue;
            }
            int count=0;
            while(a[h] != keep && h<n){
                kept[a[h]] = true;
                count++;
                h++;
            }
            if(a[h] == keep){
                kept[a[h]] = true;
                count++;
                h++;
                System.out.print(count + " ");
            }
        }
    }
}
 */