\begin{problem}{Limited Swaps}{standard input}{standard output}{2 seconds}{512 megabytes}

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.

\InputFile
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 ($1 \le b_i \le n$).


\OutputFile
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. 

\Examples

\begin{example}
\exmpfile{example.01}{example.01.a}%
\exmpfile{example.02}{example.02.a}%
\end{example}

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

\begin{center}
$1$ \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{$5$ $3$} $1$ $4$ $2$ \, $\rightarrow$ \, $3$ $5$ $1$ $4$ $2$
\end{center}

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

\end{problem}

