Square String

The *sqing* value for a binary string $S$ of length $N$ is calculated as follows: - Let $X = 0$ be the initial sqing value. - For each $i$ from $1$ to $N$, let $j$ be the **largest** index such that $1 \leq j \lt i$ and $S_j \neq S_i$. If such an index $j$ exists, add $(i-j)^2$ to $X$, otherwise do nothing. For example, consider $S = \texttt{000110}$. - For $i = 1, 2, 3$, there is no $j \lt i$