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

• $1 \le n \le 100$

Example 1

Input:

3
AB..BA

Output:

2
ABBA..
A..ABB

Example 2

Input:

3
ABAB..

Output:

-1