onsider an input sequence A :$=($a$1,...,$ an$)$ with n distinct elements.

Suppose we can perform comparisons in a more efficient way using a magic machine A$.$ Instead

of only comparing two elements, this magic machine can tell us the relative relationship among

three given elements in O$(1)$ time.

For example, if we do a powerful comparison among a$2,$ a$6,$ and a$7$ with the machine A$,$ we can

immediately determine which of the six possible orderings holds true: a$2<$ a$6<$ a$7,$ a$2<$ a$7<$ a$6,$

a$6<$ a$2<$ a$7,$ a$6<$ a$7<$ a$2,$ a$7<$ a$2<$ a$6,$ a$7<$ a$6<$ a$2.$

Does the $($n log n$)$ lower bound for the general comparison sort problem still hold for the com$-$

parison sort with the magic machine A described above? Justify your answer