Question: Square $ABCD$ has side length $1$. Points $P$, $Q$, $R$, and $S$ each lie on a side of $ABCD$ such that $APQCRS$ is an equilateral convex hexagon with side length $s$. What is $s$?  A) $\frac{\sqrt{2}}{3}$  B) $\frac{1}{2}$  C) $2-\sqrt{2}$  D) $1-\frac{\sqrt{2}}{4}$. Please choose an answer from [A, B, C, D].
Answer: C