EDIT: Embarrassingly, on the last paragraph I got the number of possible input pairs wrong: > only three possible input pairs, (a,b), (a,c), or (b,c) (within e

EDIT: Embarrassingly, on the last paragraph I got the number of possible input pairs wrong: > only three possible input pairs, (a,b), (a,c), or (b,c) (within each pair, order doesn't matter) The correct number, ignoring order, is six pairs, because we have to include (a,a), (b,b), and (c,c).