题目描述

Lina is playing with $n$ cubes placed in a row. Each cube has an integer from $1$ to $n$ written on it. Every integer from $1$ to $n$ appears on exactly one cube.

Initially, the numbers on the cubes from left to right are $a_1, a_2, \ldots, a_n$. Lina wants the numbers on the cubes from left to right to be $b_1, b_2, \ldots, b_n$.

Lina can swap any two adjacent cubes, but only if the difference between the numbers on them is at least $2$. This operation can be performed at most $20\,000$ times.

Find any sequence of swaps that transforms the initial configuration of numbers on the cubes into the desired one, or report that it is impossible.

输入格式

The first line contains a single integer $n$ --- the number of cubes ($1 \le n \le 100$).

The second line contains $n$ distinct integers $a_1, a_2, \ldots, a_n$ --- the initial numbers on the cubes from left to right ($1 \le a_i \le n$).

The third line contains $n$ distinct integers $b_1, b_2, \ldots, b_n$ --- the desired numbers on the cubes from left to right ($1 \le b_i \le n$).

输出格式

If it is impossible to obtain the desired configuration of numbers on the cubes from the initial one, print a single integer $-1$.

Otherwise, in the first line, print a single integer $k$ --- the number of swaps in your sequence ($0 \le k \le 20\,000$).

In the second line, print $k$ integers $s_1, s_2, \ldots, s_k$ describing the operations in order ($1 \le s_i \le n - 1$). Integer $s_i$ stands for "swap the $s_i$-th cube from the left with the $(s_i + 1)$-th cube from the left".

You do not have to find the shortest solution. Any solution satisfying the constraints will be accepted.

5
1 3 5 2 4
3 5 1 4 2

3
1 2 4

4
1 2 3 4
4 3 2 1

-1

提示

In the first example test, the configuration of numbers changes as follows:

$1$ $\underline{3\ 5}$ $2$ $4$ $\rightarrow$ $\underline{1\ 5}$ $3$ $2$ $4$ $\rightarrow$ $5$ $\underline{1\ 3}$ $2$ $4$ $\rightarrow$ $5$ $3$ $1$ $\underline{2\ 4}$ $\rightarrow$ $\underline{5\ 3}$ $1$ $4$ $2$ $\rightarrow$ $3$ $5$ $1$ $4$ $2$

In the second example test, making even a single swap in the initial configuration is impossible.