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.util.*;
import java.io.*;
public class second{
public static void main(String[] args)throws IOException {
    FastReader in=new FastReader(System.in);
    int i,j;
        int n=in.nextInt();
        StringBuilder sb=new StringBuilder();
        int k=1,x,y;
        int arr[]=new int[n];
        int freq[]=new int[n+1];
        int val[]=new int[n];
        for(i=0;i<n;i++)
        {
            arr[i]=in.nextInt();
            freq[arr[i]]=k;
            k++;
        }
        val[0]=in.nextInt();
        sb.append(freq[val[0]]+" ");
        y=freq[val[0]];
        for(i=1;i<n;i++)
        {
            val[i]=in.nextInt();
            x=freq[val[i]];
            if(x<y)
            sb.append("0"+" ");
            else
            {
                sb.append((x-y)+" ");
                y=x;
            }
        }
        System.out.println(sb);
}
}
class FastReader {
 
    byte[] buf = new byte[2048];
    int index, total;
    InputStream in;
 
    FastReader(InputStream is) {
        in = is;
    }
 
    int scan() throws IOException {
        if (index >= total) {
            index = 0;
            total = in.read(buf);
            if (total <= 0) {
                return -1;
            }
        }
        return buf[index++];
    }
 
    String next() throws IOException {
        int c;
        for (c = scan(); c <= 32; c = scan());
        StringBuilder sb = new StringBuilder();
        for (; c > 32; c = scan()) {
            sb.append((char) c);
        }
        return sb.toString();
    }
    String nextLine() throws IOException {
        int c;
        for (c = scan(); c <= 32; c = scan());
        StringBuilder sb = new StringBuilder();
        for (; c !=10 && c!=13; c = scan()) {
            sb.append((char) c);
        }
        return sb.toString();
    }
    char nextChar() throws IOException{
        int c;
         for (c = scan(); c <= 32; c = scan());
         return (char)c;
        }
 
    int nextInt() throws IOException {
        int c, val = 0;
        for (c = scan(); c <= 32; c = scan());
        boolean neg = c == '-';
        if (c == '-' || c == '+') {
            c = scan();
        }
        for (; c >= '0' && c <= '9'; c = scan()) {
            val = (val << 3) + (val << 1) + (c & 15);
        }
        return neg ? -val : val;
    }
 
    long nextLong() throws IOException {
        int c;
        long val = 0;
        for (c = scan(); c <= 32; c = scan());
        boolean neg = c == '-';
        if (c == '-' || c == '+') {
            c = scan();
        }
        for (; c >= '0' && c <= '9'; c = scan()) {
            val = (val << 3) + (val << 1) + (c & 15);
        }
        return neg ? -val : val;
    }
}