Problem Statement

You are given $2$ strings $S, T$ of length $2N$ consisting of $0$ and $1$. Let $S = s_0 s_1 \cdots s_{2N-1}$.

You can perform the following operation on the string $S$ up to $2N$ times (possibly $0$ times).
(Operation)

Step 1. Choose an integer $x$ satisfying $0 \leq x \leq 2N-1$.
Step 2. For every integer $i$ satisfying $0 \leq i \leq N-1$, replace $s_{(x+i)\,\%\,(2N)}$ with $s_{(x+i)\,\%\,(2N)} \oplus s_{(x+i+N)\,\%\,(2N)}$.

Input

$N$
$S$
$T$

$1 \leq N \leq 500$
$N$ is an integer
$S, T$ are strings of length $2N$, and each character is '0' or '1'.

Output

If it is impossible to make $S$ and $T$ equal within $2N$ operations, output $-1$.
If it is possible to make $S$ and $T$ equal within $2N$ operations, output the number of operations $M\, (0 \leq M \leq 2N)$ on line $1$,
and output the sequence of operations on the $M$ lines from line $2$ to line $M+1$.
Specifically, on line $i+1$, output the $x$ chosen in Step 1 of the $i$-th operation.
If there are multiple answers, any of them will be accepted.
Print a newline at the end.

Sample

4
10101001
10011011

2
6
0

5
1101001100
1000111010

-1