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Stock-Based Compensation - Performance-Based Restricted Stock Unit Grants (Details)
9 Months Ended 12 Months Ended
Jun. 30, 2023
Sep. 30, 2022
Disclosure of Compensation Related Costs, Share-based Payments [Abstract]    
Performance-based awards granted, percentage (as a percent) 100.00% 100.00%
Performance-based awards granted, percentage, maximum threshold met (as a percent) 200.00% 200.00%
Performance goal measurement period (in years) 3 years