We said say a directed graph G$=($V$,$E$)$ is well$-$connected if for every pair of distinct vertices u and v in V$,$ there exists a path from u to v OR a path from v to u $($both may exist, but at least one must be present$).$ Design an algorithm that takes as input a directed graph G and determines if it is well$-$connected. Faster $($in asymptotic Big O notation$)$ and correct solutions are worth more credit.