Alice and Bob are playing a game on a permutation $$$p$$$ of length $$$n$$$, where $$$p$$$ contains each integer from $$$1$$$ to $$$n$$$ exactly once.

The game is played with a statue that can be placed on any position of the permutation. Initially, the statue is placed at position $$$x$$$. Alice moves first, and the players alternate turns.

On each turn, the current player can move the statue from its current position $$$i$$$ to any position $$$j$$$ (where $$$i \neq j$$$), but only if $$$p_i \geq p_k$$$ for all indices $$$k$$$ such that $$$\min(i, j) \leq k \leq \max(i, j)$$$.

The first player who cannot make any valid move loses the game.

Both Alice and Bob play optimally, meaning that at their turns they perform the best possible move. Due to this, the game becomes quite deterministic if you know the initial permutation $$$p$$$ and the initial position of the statue, $$$x$$$. In fact, for a given permutation $$$p$$$, we can figure out for each initial position $$$x$$$ whether Alice or Bob will win the game.

You are given a string $$$s$$$ of length $$$n$$$ consisting of letters A and B. Your task is to construct a permutation $$$p$$$ of length $$$n$$$ such that, for each position $$$x$$$, if the game starts with the statue at position $$$x$$$, the winner is Alice if the $$$x$$$-th character of the string is A, and Bob if it is B.