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}