Friend Groups In A Line

There are $N$ positions in a queue. Given a *binary string* $S$ of length $N$, where $S_i =$ `'$1$'` denotes, there is a person standing in the $i^{th}$ position. The distance between two people standing in the $i^{th}$ and $j^{th}$ positions respectively in the queue is $\mid i - j \mid$, where $\mid x \mid$ denotes the absolute value of $x$. Now, two people are considered to be friends if they