# Problem D

I Could Have Won

“We will be closing in about 5 minutes. Thank you for visiting the ICPC gym today.”

With this announcement, Alice and Bob stopped playing their
rock-paper-scissors marathon in the middle of the $10$th game. Each player scores a
point if their throw beats the other player’s throw. Each game
was played by the *first-to-11* rule, meaning that
whoever scores $11$ points
first wins the game. Today, Bob narrowly defeated Alice by a
single game; he scored 11 points first in five games, while
Alice only scored 11 points first in four games.

After carefully inspecting how each game was played,
however, Alice realized that she could have won more games than
Bob if they played under slightly different rules, such as
*first-to-5* or *first-to-8*, instead of the
regular *first-to-11*.

Given the sequence of points scored by Alice and Bob,
determine all values of $k$ such that Alice would have won
more games than Bob under the *first-to-*$k$ rule.

Both Alice and Bob start with zero points at the beginning of a game. As soon as one player reaches $k$ points, that player wins the game, and a new game starts. Alice wins a game if she scores $k$ points before Bob does. Neither player wins the game if it’s interrupted by the gym closing before either player reaches $k$ points.

## Input

The single line of input consists of a string of uppercase
letters “`A`” or “`B`”, denoting who scored each point from the
beginning of the rock-paper-scissors marathon. The length of
the string is between $1$
and $2\, 000$ letters,
inclusive. “`A`” means Alice scored the
point, “`B`” means Bob scored the
point.

## Output

On the first line, output the number of positive integers
$k$ for which a
*first-to-*$k$ rule
would have made Alice win more games than Bob. If this number
isn’t zero, on the next line output all such values of
$k$ in increasing order,
separated by spaces.

Sample Input 1 | Sample Output 1 |
---|---|

BBAAABABBAAABB |
3 3 6 7 |

Sample Input 2 | Sample Output 2 |
---|---|

AABBBAAB |
2 2 4 |