Solution: Cherry Pickup

Statement

You are given an $n \times n$ grid representing a field of cherries. Each cell in the grid can have one of three possible values:

• $0$: An empty cell that can be walked through

• $1$: A cell containing a cherry that can be picked and then passed through

• $-1$: A cell containing a thorn, which cannot be crossed

Your task is to find the maximum number of cherries that can be collected while following these rules:

1. Start at the top-left corner $(0,0)$ and reach the bottom-right corner $(n-1,~n-1)$ by only moving right or down through valid cells ($0$ or $1$).

2. After reaching the bottom-right corner, return to the starting point $(0, 0)$ ...