A regular 12-gon is inscribed in a circle of radius 12. The sum of the lengths of all sides and diagonals of the 12-gon can be written in the form $$a + b \sqrt{2} + c \sqrt{3} + d \sqrt{6},$$ where $$a^{}_{}$$, $$b^{}_{}$$, $$c^{}_{}$$, and $$d^{}_{}$$ are positive integers. Find $$a + b + c + d^{}_{}$$.

(第八届AIME1990 第12题)