Bulbs and Wires

There are $N$ light bulbs in a row, numbered $1$ through $N$ from left to right. Each bulb can be in one of the states "on" or "off". Initially, all the bulbs are "off". Each bulb is also connected to its (at most two) adjacent bulbs by wires. You should reach a state described by a given a binary string $S$ with length $N$ ― for each valid $i$, if the $i$-th character of $S$ is '1', the $i$-th