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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, 2023
Jun. 30, 2022
Jun. 30, 2023
Jun. 30, 2022
Shares        
Outstanding at beginning of period (in shares)     538,238  
Restricted stocks granted (in shares)     590,066 231,696
Vested (in shares)     (263,777)  
Forfeited (in shares)     (104,220)  
Outstanding at end of period (in shares) 760,307   760,307  
Weighted Average Grant-Date Fair Value        
Outstanding at beginning of period (in dollars per share)     $ 71.99  
Granted (in dollars per share) $ 42.35 $ 80.58 55.10 $ 103.00
Vested (in dollars per share)     55.76  
Forfeited (in dollars per share)     73.62  
Outstanding at end of period (in dollars per share) $ 66.22   $ 66.22