Byzantine Empresses

Which Byzantine empress did the most damage to the empire, either directly or indirectly: Zoe (11th century) or Anna of Savoy ?
 
Personally I'd say Anna. After Zoe the Empire still had the possibility of recovery. Personally I think that the Byzantine Empire might have been able to survive as a Balkan state (although not as a great power) up till the early 1340s, but then Anna had to start a rather nasty civil war. After that, Byzantium's fall was virtually certain.
 
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