Question $1$: Suppose we are given an unsorted array. Let s$($i$)$ be the index of A$[$i$]$ in the sorted array, with the index starting at $1.$ Define distance$($i$)=|$s$($i$)$ i$|.$ Provide an algorithm that sorts the elements, assuming that distance$($i$)<=20$ for every i$.$

Example:

Given the unsorted array $[4,1,3,2,6,5]$: In the sorted array $[1,2,3,4,5,6],$ the index

of $4$ is $4($originally at index $1),$ so s$(1)=4.$ Thus, distance$(1)=|41|=3.$