About insertion sort an array $A$ of $n$ integers:

$($a$)$ Prove by induction that insertion sort correctly sorts $n$ integers. $6\%$

$($b$)$ Let $a_i$ be an item in $A,$ and $k_i$ be the rank of $a_i($means that $a_i$ is the

$k_i$ th largest integer among all integers in the array$).$ We don't know

what $k_i$ is$,$ but we do know that $a_i$ stored in $A[I_i]$ and $|k_i-I_i|10.$

What can you conclude about the time required to insertion sort the $n$ integers? $6\%$