Good Game

Finn is playing a game of Twos and Threes. Twos and Threes is a one-player game played on a one-dimensional board. In the starting position, there are $N$ blocks arranged in a row, with each block labelled either $A$ or $B$. Blocks are numbered from $1$ to $N$ from left to right. Finn is allowed to make moves of the following form:

• Select $2$ or $3$ consecutive blocks that share the same label. Remove them from the board. Connect any remaining blocks together. Re-index the blocks from left to right, starting with index $1$.

Finn wins the game if all blocks are removed from the board. Your task is to help Finn determine a winning sequence of moves, or determine if the game cannot be won.

The first line of input will contain the integer $N$.

The second line of input will contain the string $S$, which is the starting position of the game.

There are $N$ characters in $S$, and each of these characters in $S$ is either A or B.

If there is a winning sequence of moves, output $K$, the number of moves in the winning sequence. On each of the next $K$ lines, print an index $i$, followed by one space, followed by a number $j$, denoting a move that will remove the blocks currently at indices $i$ to $i + j - 1$, inclusive.

If there is no winning sequence of moves, output -1.

If there are multiple winning sequences, then any winning sequence will be accepted. There is no need to minimize or maximize $K$.

The sample output denotes this winning sequence:

\displaystyle \begin{align\*} & ABAAB\underline{BB}AA \\\ & AB\underline{AA}BAA \\\ & A\underline{BB}AA \\\ & \underline{AAA} \end{align\*}