Let $$A_1, A_2, A_3, \ldots, A_{12}$$ be the vertices of a regular dodecagon. How many distinct squares in the plane of the dodecagon have at least two vertices in the set $$\{A_1,A_2,A_3,\ldots,A_{12}\}$$?

(第二十届AIME1 2002 第5题)