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.


line = raw_input()
line = raw_input()
a = line.strip().split()
line = raw_input()
b = line.strip().split()

n = len(a)

output = []

a_set = set()

i = 0

for j in xrange(n):
    if b[j] in a_set:
        output.append("0")
        continue
        
    for k in xrange(i, n):
        a_set.add(a[k])
        if a[k] == b[j]:
            output.append(str(k - i + 1))
            i = k + 1
            break
print ' '.join(output)
    

#n, l, r, k = (int(i) for i in line.split())

# b = n
# e = 2 * n

# gap_l = ((n + r - l) % n + 1)
# gap_r = gap_l * 2

# if k <= 2 * n:
#     flag = True
#         for i in xrange(k / 2):
#             if gap_l <= k / 2 - i and k / 2 - i <= gap_r:
#                 print n - (k - (k / 2 - i))
#                 flag = False
#                 break
#         if not flag:
#             print -1
# else:
    
        

# while b < e:
#     m = (b + e) // 2
    
#     left = k % m
#     if left <= gap:
        

# line = raw_input()

# print ''.join(sorted(list(line.strip())))



# line = raw_input()
# t = int(line.strip())

# for i in xrange(t):
#     line = raw_input()
#     a = int(line.strip())
    
#     num_one = 0
#     while a > 0:
#         num_one += (a % 2)
#         a /= 2

#     print 2**num_one
# for i in xrange(t):
    
# t = [int(i) for i in line.split()]
# #n, k = (int(i) for i in line.split())


# a = [int(i) for i in line.split()]



# a = sorted(a)

# if a[0] + a[1] > a[2]:
#     print 0
# else:
#     print a[2] - (a[0] + a[1]) + 1