Permutation Representation 

Time-Limit: 5 second(s)

A permutation is a bijection from a set $X$ onto itself. If $X$ is finite, the elements of $X$ are often numbered 1,2,3,...n. A permutation of a set with five elements is often denoted by

$$\left( \begin{array}{c c c c c} 1 & 2 & 3 & 4 & 5 \\ 3 & 2 & 5 & 1 & 4 \end{array}\right)$$

meaning the element 1 is mapped to the element 3 of the set, the element 2 is mapped to the element 2 and so on and so forth. Another way of denoting permutations is to use cycle notation. Cycle notation is not necessarily unique. The following cycle

$$(2 4 7)$$

means that the element 2 is mapped to the element 4, the element 4 is mapped to the element 7 and the element 7 is mapped to the element 2. The cycle above could also be written

$$(7 2 4)$$

The product of several cycles is evaluated from right to left. The above permutation can be written as

$$(5 3) (5 1) (5 4)$$

$$(1 3 5 4) (1)$$

$$(1) (1 3 5 4)$$

A permutation can be written uniquely as the product of cylces

$$\left( \begin{array}{c c c c} 1 & 2 & \ldots & n \\ b_1 & b... ...)^{a_2} (1 2 3)^{a_3} (1 2 3 4)^{a_4}\ldots (1 \ldots n)^{a_n}$$

if $0 \leq a_i \leq i - 1$ holds for each exponent a_i. The example permutation can be uniquely written as

$$\left( \begin{array}{c c c c c} 1 & 2 & 3 & 4 & 5 \\ 3 & 2 &... ...array}\right) = (1)^0(1 2)^1(1 2 3)^2(1 2 3 4)^2(1 2 3 4 5)^2$$

Your task is to compute the a_i's of a given permutation.

Input
The input consists of several test cases. Each test case consists of three lines. The first line contains the number n, 1 ≤ n ≤ 200000. The second line contains the elements from $1$ to $n$. The third line contains a mapping for every element from the second line.

Output
For each test case there should be one line of output. Print all the a_i's on a single line separated by one space in the order a₁...a_n

Sample Input

5
1 2 3 4 5
3 2 5 1 4
4
1 2 3 4
3 4 1 2

 

Sample Output

0 1 2 2 2
0 0 0 2