Sequence under Rotation $($marks$=3,3,4).$ There is a sequence S of n elements $$a$1,$ a$2,...,$ an$.$ You need to build a data structure for S that can perform the following operations.

$$Report$($S$,$i$)$: Report ith element of the sequence.

$$Rotate$($S$,$i$,$j$)$: Rotate the sequence from element ai to aj for any given i$$j$.$ In other words, this will lead to swapping ai with aj$,$ swapping ai$+1$ with aj$1,$ and so on$.$ The data structure must take O$($n$)$ space and each operation must be executed in worst case O$($log n$)$ time. Note: To solve this problem, you may directly use any algorithm or any data structure or any result stated in the lectures as a black box without provide any details.

$($a$)$Describe the data structure completely and precisely.