Marching Orders

Let $S$ be a string of length $N$, containing only the characters `'L'` and `'R'`, with the following properties: - $N \ge 3$ - $S_1 = S_2 = \text{R}$ - $S_N = \text{L}$ There is also a strip of $N$ cells, numbered $1$ to $N$ from left to right. Suppose you are standing at position $X$ on the strip. Then, - If $S_X = \text{R}$, you will move one step right. - If $S_X = \text{L}$, you will move