Let $$ABCD^{}_{}$$ be a tetrahedron with $$AB=41^{}_{}, AC=7^{}_{}, AD=18^{}_{}, BC=36^{}_{}, BD=27^{}_{}$$, and $$CD=13^{}_{}$$, as shown in the figure. Let $$d^{}_{}$$ be the distance between the midpoints of edges $$AB^{}_{}$$ and $$CD^{}_{}$$. Find $$d^{2}_{}$$.

(第七届AIME1989 第12题)