There are $2n$ boxes in a line. Two adjacent boxes are empty, and all other boxes have a letter "A" or "B". Both letters appear in exactly $n-1$ boxes.
Your task is to move the letters so that all letters "A" appear before any letter "B". On each turn you can choose any two adjacent boxes that have a letter and move the letters to the two adjacent empty boxes, preserving their order.
It can be proven that either there is a solution that consists of at most $10n$ turns or there are no solutions.
Input
The first line has an integer $n$: there are $2n$ boxes.
The second line has a string of $2n$ characters which describes the starting position. Each character is "A", "B" or "." (empty box).
Output
First print an integer $k$: the number of turns. After this, print $k$ lines that describe the moves. You can print any solution, as long as $k \le 1000$.
If there are no solutions, print only "-1".
Constraints
Example 1
Input:
3
AB..BA
Output:
2
ABBA..
A..ABB
Example 2
Input:
3
ABAB..
Output:
-1