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Stock-Based Compensation - Stock-Based Compensation Accounting (Details) - Stock Options - $ / shares
9 Months Ended 12 Months Ended
Jun. 30, 2022
Jun. 30, 2023
Weighted average assumptions    
Weighted average fair value (in dollars per share) $ 71.90 $ 79.02
Risk-free interest rate (as a percent) 3.00% 3.40%
Expected dividend yield (as a percent) 0.00% 0.00%
Expected life (in years) 5 years 2 months 12 days 4 years 9 months 18 days
Expected volatility factor (as a percent) 36.10% 38.20%