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Stock-Based Compensation - Time-Based Restricted Stock Unit Grants (Details) - Restricted Stock, Time Based Shares
6 Months Ended
Mar. 31, 2023
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]  
Award vesting period (in years) 3 years
Share-Based Payment Arrangement, Tranche One  
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]  
Award vesting percentage (as a percent) 33.33%
Share-Based Payment Arrangement, Tranche Two  
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]  
Award vesting percentage (as a percent) 33.33%
Share-Based Payment Arrangement, Tranche Three  
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]  
Award vesting percentage (as a percent) 33.33%