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Stock-Based Compensation - Restricted Stock Unit Activity - Additional Information (Details) - Restricted Stock Units (RSUs) - USD ($)
$ / shares in Units, $ in Millions
3 Months Ended 9 Months Ended
Jun. 30, 2022
Jun. 30, 2021
Jun. 30, 2022
Jun. 30, 2021
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Granted (in dollars per share) $ 80.58 $ 104.54 $ 103.00 $ 71.81
Fair value of restricted stock awards vested $ 0.2 $ 0.3 $ 66.9 $ 28.2
Proceeds from employees to satisfy tax obligation     $ 25.1 $ 9.7