F. Double Sort II
time limit per test
2 seconds
memory limit per test
512 megabytes
input
standard input
output
standard output

You are given two permutations $$$a$$$ and $$$b$$$, both of size $$$n$$$. A permutation of size $$$n$$$ is an array of $$$n$$$ elements, where each integer from $$$1$$$ to $$$n$$$ appears exactly once. The elements in each permutation are indexed from $$$1$$$ to $$$n$$$.

You can perform the following operation any number of times:

  • choose an integer $$$i$$$ from $$$1$$$ to $$$n$$$;
  • let $$$x$$$ be the integer such that $$$a_x = i$$$. Swap $$$a_i$$$ with $$$a_x$$$;
  • let $$$y$$$ be the integer such that $$$b_y = i$$$. Swap $$$b_i$$$ with $$$b_y$$$.

Your goal is to make both permutations sorted in ascending order (i. e. the conditions $$$a_1 < a_2 < \dots < a_n$$$ and $$$b_1 < b_2 < \dots < b_n$$$ must be satisfied) using minimum number of operations. Note that both permutations must be sorted after you perform the sequence of operations you have chosen.

Input

The first line contains one integer $$$n$$$ ($$$2 \le n \le 3000$$$).

The second line contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$1 \le a_i \le n$$$; all $$$a_i$$$ are distinct).

The third line contains $$$n$$$ integers $$$b_1, b_2, \dots, b_n$$$ ($$$1 \le b_i \le n$$$; all $$$b_i$$$ are distinct).

Output

First, print one integer $$$k$$$ ($$$0 \le k \le 2n$$$) — the minimum number of operations required to sort both permutations. Note that it can be shown that $$$2n$$$ operations are always enough.

Then, print $$$k$$$ integers $$$op_1, op_2, \dots, op_k$$$ ($$$1 \le op_j \le n$$$), where $$$op_j$$$ is the value of $$$i$$$ you choose during the $$$j$$$-th operation.

If there are multiple answers, print any of them.

Examples
Input
5
1 3 2 4 5
2 1 3 4 5
Output
1
2
Input
2
1 2
1 2
Output
0
Input
4
1 3 4 2
4 3 2 1
Output
2
3 4