Square A B C D has side length 1. Points P, Q, R, and S each lie on a side of A B C D such that A P Q C R S is an equilateral convex hexagon with side length s. What is s ?
Answer Choices
A. \dfrac{\sqrt{2}}{3}
B. \dfrac{1}{2}
C. 2-\sqrt{2}
D. 1-\dfrac{\sqrt{2}}{4}
E. \dfrac{2}{3}