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Summary of Significant Accounting Policies - Valuation Assumptions for Employee Stock Purchase Plan (Details) - Employee Stock
12 Months Ended
Sep. 30, 2022
Sep. 30, 2021
Sep. 30, 2020
Share-based Compensation Arrangement by Share-based Payment Award, Fair Value Assumptions and Methodology [Abstract]      
Risk-free interest rate (as a percent) 1.70% 0.30% 0.90%
Volatility (as a percent) 49.00% 53.00% 58.00%
Expected life 6 months 6 months 6 months
Dividend yield (as a percent)   0.60% 1.10%