Light All

Chefland's jail has $N$ prison cells, all arranged in a row. Above each prison cell is a light. Each light can be made to face either left or right (but not both). The lights aren't very strong, and so can only light up adjacent cells. In particular, - If the light at index $i$ is facing right, it will light up cells $i$ and $i+1$ (the latter only if $i+1 \leq N$). - If the light at index $i$