a$)$ rootrleaves must be black $($And N$|$llleaves are not shown in the diagram$).$ Select the correct colors to make this a proper red black tree:

n$1$:

n$3$:

n$4$:

n$6$:

$n7$ :

n$9$:

b$)$ children of red nodes must be black

G$)$ For every node in the tree, the number of black nodes on every path from a node $n$ to a leaf $($not counting $n$ but counting the leaf$)$ must be the same.