Question: Define the red depth of a node in a red-black tree as the number of red ancestors that the node has. Can the red depths

Define the red depth of a node in a red-black tree as the number of red ancestors that the node has. Can the red depths of nodes in a red-black tree be maintained as fields in the nodes of the tree without affecting the asymptotic performance of any of the red-black tree operations? Show how, or argue why not.

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