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 scored 11 points first in four games.

After carefully inspecting how each game was played, Alice realized that she could have won more games than Bob if they had played under a different rule, 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 each game with zero points. 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. If the gym closes during a game and neither player has reached $k$ points, that game has no winner.

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

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