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I know we can augment Red black tree with black depth without affecting its basic operations which is a theorem. But let say I define red depth as number of red ancestors a node has. Can we maintain all basic operations without affecting its asymptotic performance when we augment trees with red depth?

Findings: I think when we change the depth of a parent node, the depth of all nodes in subtree will decrease, so I believe Insert and Delete won't work. Is that so?

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