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Stock-Based Compensation - Additional Information (Details) - USD ($)
$ in Millions
3 Months Ended 9 Months Ended
Jun. 30, 2021
Jun. 30, 2020
Jun. 30, 2021
Jun. 30, 2020
Disclosure Of Compensation Related Costs Sharebased Payments [Abstract]        
Common stock reserved for issuance stock awards (in shares) 4,525,189   4,525,189  
Stock-based compensation expense $ 6.2 $ 7.0 $ 23.5 $ 24.9
Stock-based compensation expense, net of tax $ 5.3 $ 6.1 $ 20.0 $ 21.8