Consider the sequence $27,56,47,72,20,55,49,90.$

$($a$)$ Illustrate how to compute the number of inversions in the sequence in time O$($n log$($n$)).$

$($b$)$ While the number of inversions can be as large as quadratic in n$,$

the running time to count the inversions is subquadratic. Explain why this is so$.$