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Goodwill and Intangible Assets - (Details) - USD ($)
$ in Millions
12 Months Ended
Sep. 30, 2022
Sep. 30, 2021
Sep. 30, 2020
Indefinite and Finite Lived Intangible Assets by Major Class      
Amortization expense $ 4.1 $ 6.6 $ 9.0
Minimum      
Indefinite and Finite Lived Intangible Assets by Major Class      
Definite-lived intangible assets, useful life 3 years    
Maximum      
Indefinite and Finite Lived Intangible Assets by Major Class      
Definite-lived intangible assets, useful life 10 years