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Summary of Significant Accounting Policies - Capitalized Direct Costs (Details) - USD ($)
$ in Millions
12 Months Ended
Sep. 30, 2022
Sep. 30, 2021
Property, Plant and Equipment, Gross [Abstract]    
Capitalized computer software, gross $ 26.9 $ 22.7
Software Development    
Property, Plant and Equipment, Gross [Abstract]    
Capitalized computer software, gross 8.6  
Capitalized computer software costs $ 4.2