Obtaining the String
Description
You are given two strings $s$ and $t$. Both strings have length $n$ and consist of lowercase Latin letters. The characters in the strings are numbered from $1$ to $n$.
You can successively perform the following move any number of times (possibly, zero):
- swap any two adjacent (neighboring) characters of $s$ (i.e. for any $i = \{1, 2, \dots, n - 1\}$ you can swap $s_i$ and $s_{i + 1})$.
You can't apply a move to the string $t$. The moves are applied to the string $s$ one after another.
Your task is to obtain the string $t$ from the string $s$. Find any way to do it with at most $10^4$ such moves.
You do not have to minimize the number of moves, just find any sequence of moves of length $10^4$ or less to transform $s$ into $t$.
The first line of the input contains one integer $n$ ($1 \le n \le 50$) — the length of strings $s$ and $t$.
The second line of the input contains the string $s$ consisting of $n$ lowercase Latin letters.
The third line of the input contains the string $t$ consisting of $n$ lowercase Latin letters.
If it is impossible to obtain the string $t$ using moves, print "-1".
Otherwise in the first line print one integer $k$ — the number of moves to transform $s$ to $t$. Note that $k$ must be an integer number between $0$ and $10^4$ inclusive.
In the second line print $k$ integers $c_j$ ($1 \le c_j < n$), where $c_j$ means that on the $j$-th move you swap characters $s_{c_j}$ and $s_{c_j + 1}$.
If you do not need to apply any moves, print a single integer $0$ in the first line and either leave the second line empty or do not print it at all.
Input
The first line of the input contains one integer $n$ ($1 \le n \le 50$) — the length of strings $s$ and $t$.
The second line of the input contains the string $s$ consisting of $n$ lowercase Latin letters.
The third line of the input contains the string $t$ consisting of $n$ lowercase Latin letters.
Output
If it is impossible to obtain the string $t$ using moves, print "-1".
Otherwise in the first line print one integer $k$ — the number of moves to transform $s$ to $t$. Note that $k$ must be an integer number between $0$ and $10^4$ inclusive.
In the second line print $k$ integers $c_j$ ($1 \le c_j < n$), where $c_j$ means that on the $j$-th move you swap characters $s_{c_j}$ and $s_{c_j + 1}$.
If you do not need to apply any moves, print a single integer $0$ in the first line and either leave the second line empty or do not print it at all.
Samples
6
abcdef
abdfec
4
3 5 4 5
4
abcd
accd
-1
Note
In the first example the string $s$ changes as follows: "abcdef" $\rightarrow$ "abdcef" $\rightarrow$ "abdcfe" $\rightarrow$ "abdfce" $\rightarrow$ "abdfec".
In the second example there is no way to transform the string $s$ into the string $t$ through any allowed moves.