Given the nine-sided regular polygon A_{1} A_{2} A_{3} A_{4} A_{5} A_{6} A_{7} A_{8} A_{9}, how many distinct equilateral triangles in the plane of the polygon have at least two vertices in the set \left\{A_{1}, A_{2}, \ldots A_{9}\right\} ?
Answer Choices
A. 30
B. 36
C. 63
D. 66
E. 72