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.