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Stock-Based Employee Benefit Plans - Assumptions Used to Estimate Fair Value of Stock Options (Details) - Equity Option [Member]
 12 Months Ended
Sep. 30, 2023
Sep. 30, 2022
Sep. 30, 2021
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Weighted average expected term (years) 5 years 2 months 23 days 4 years 5 months 4 days 4 years 5 months 19 days
Expected volatility (range), minimum 33.40% 32.90% 33.60%
Expected volatility (range), maximum 35.50% 34.10% 34.40%
Weighted average volatility 33.50% 33.20% 33.90%
Risk free interest rate, minimum 3.40% 1.18% 0.29%
Risk free interest rate, maximum 4.49% 2.85% 0.73%
Weighted average expected dividend yield 0.00% 0.00% 0.00%