B. Obtaining the String
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

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 $t$.

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.

Examples
Input
6abcdefabdfec
Output
43 5 4 5
Input
4abcdaccd
Output
-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.