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Stock-Based Compensation - Employee Stock Purchase Plan (Details) - shares
6 Months Ended
Mar. 31, 2022
Mar. 31, 2021
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]    
Shares issued under employee stock purchase plan (in shares) 51,133 58,124
Employee Stock    
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]    
Purchase price of common stock (as a percent) 85.00%