Letter Pair Move Game

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

Input

3
AB..BA

Output

2
ABBA..
A..ABB
```Example 2
## Input

3 ABAB..

## Output

-1