Three girls $$G_1, G_2, G_3,$$ each read four stories $$ S_1, S_2, S_3, S_4 $$ and discuss which ones they like. No story is liked by all the three. For each of the three pairs of the girls, there is at least one story which is liked by the pair and not liked by the third. Let $$n$$ be the number of ways in which this is possible. Find the sum of the squares of the digits of $$n$$.