Maximize coins collected by 3-step pieces

You are given a 1D board of length N. Each cell is in one of three states:

• Empty
• Piece (a movable token)
• Coin (collectible)

In one move, you may choose any one piece and move it exactly 3 cells to the right (from index i to i+3). The move rules are:

1. If the destination cell is empty, the piece moves there.
2. If the destination cell contains a coin, the piece moves there and you collect that coin (the coin is removed).
3. Pieces cannot overlap: a move is not allowed if the destination cell already contains another piece.
4. The piece may “jump over” intervening cells; only the destination cell matters.
5. A move is not allowed if i+3 is outside the board.

You may perform moves in any order, for as many turns as you like, until no piece can legally move.

Return the maximum number of coins you can collect.

Input

• A representation of the board (e.g., a string/array of length N) containing exactly one of {empty, piece, coin} per cell.

Output

• An integer: the maximum number of coins collectible.

Notes / Clarifications

• Multiple pieces may exist.
• Coins are collected at most once (they disappear after collection).
• The result depends on the order in which you choose moves.