$($B$1).$ Considering fixing up the color, insert node $9$ into the following red$/$black tree, e$.$g$.,$ T$.$ In T$,$ we denote each node

with a positive value as the node with BLACK color and the node with a negative value as the node with RED color. For

simplicity, we consider each node only comes with a positive key value in the RB tree T$,$ here. For example, in the following

tree, node $3,5,7,11,12,13,15,17$ are with BLACK color, and node $4,6,8,10,14$ are with RED color.