$5.$ Insert the keys: $5,9,7,2,6,4,8,3,1,10($in order$)$ into an initially empty Binary Search Tree $.($Note: use the Binary Search Tree Insert algorithm to do this.$)$ a$.$ Give the keys in the order printed by a pre$-$order tree walk. b$.$ Give the keys in the order printed by a post$-$order tree walk. Note: the three questions below do not refer in any way to the Red Black Tree Insert algorithm. Instead they ask if it is possible to assign colors in the BST T$,$ which you found above, so as to satisfy the RBT properties. Be sure to include nil children when computing the black$-$height of T$.$ c$.$ Is it possible to assign the colors $\{$Red$,$ Black$\}$ to the vertices of $$ so that the Red$-$Black Tree properties are satisfied, and bh$()=1?$ If it is possible, specify all such colorings by stating, for each coloring, the set of keys belonging to red nodes.