Question II $[$B$-$Trees$]$: Consider a B$-$Tree of minimum degree $t=3($meaning each node can have a minimum of $3$ children and a maximum of $6$ children, which is equivalent to saying that the $B-$Tree is of order $6).$ Answer the following questions:

$(5$ points$)$ What is the maximum height of such a B$-$Tree that contains $100$ keys? Clearly justify your answer.

$(5$ points$)$ Suppose you have such a B$-$Tree of height $2.$ What is the minimum number of keys it must contain? Show your calculations and reasoning.