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Stock-Based Compensation - Restricted Stock Unit Activity - Tabular Disclosure (Details) - Restricted Stock Units (RSUs) - $ / shares
3 Months Ended 9 Months Ended
Jun. 30, 2022
Jun. 30, 2021
Jun. 30, 2022
Jun. 30, 2021
Shares        
Outstanding at beginning of period (in shares)     1,088,652  
Restricted stocks granted (in shares)     231,696 346,172
Vested (in shares)     (555,513)  
Forfeited (in shares)     (223,821)  
Outstanding at end of period (in shares) 541,014   541,014  
Weighted Average Grant-Date Fair Value        
Outstanding at beginning of period (in dollars per share)     $ 47.35  
Granted (in dollars per share) $ 80.58 $ 104.54 103.00 $ 71.81
Vested (in dollars per share)     41.50  
Forfeited (in dollars per share)     39.51  
Outstanding at end of period (in dollars per share) $ 93.96   $ 93.96