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Share-Based Compensation - Stock Options Activity (Details) - USD ($)
$ / shares in Units, $ in Millions
12 Months Ended
Sep. 30, 2022
Sep. 30, 2021
Sep. 30, 2020
Shares Available for Grant      
Shares available for grant, beginning (in shares) 1,569,798    
Shares available for grant, Additional shares authorized by shareholders (in shares)    
Shares available for grant, Stock options granted (in shares) (240,500)   0
Shares available for grant, stock options forfeited in period (in shares) 43,389    
Shares available for grant, stock options expired in period (in shares) 15,010    
Shares available for grant, ending (in shares) 1,387,697 1,569,798  
Number of Options Outstanding      
Number of options outstanding, beginning (in shares) 1,229,600    
Number of options outstanding, granted (in shares) 240,500   0
Number of options outstanding, exercised (in shares) (212,356)    
Number of options outstanding, forfeited (in shares) (43,389)    
Number of options outstanding, expired (in shares) (15,010)    
Number of options outstanding, ending (in shares) 1,199,345 1,229,600  
Number of options outstanding, exercisable (in shares) 233,655    
Weighted Average  Exercise Price      
Weighted average exercise price, beginning (in dollar per share) $ 45.17    
Weighted average  exercise price, granted (in dollar per share) 62.04    
Weighted average  exercise price, exercised (in dollar per share) 31.31    
Weighted average  exercise price, forfeited (in dollar per share) 59.89    
Weighted average  exercise price, expired (in dollar per share) 46.39    
Weighted average exercise price, ending (in dollar per share) 50.46 $ 45.17  
Weighted average  exercise price, exercisable (in dollar per share) 46.14    
Weighted Average Grant Date Fair Value      
Weighted average grant date fair value, beginning (in dollar per share) 12.82    
Weighted average grant date fair value, granted (in dollar per share) 22.82 19.83 $ 0.00
Weighted average grant date fair value, exercised (in dollar per share) 12.72    
Weighted average grant date fair value, forfeited (in dollar per share) 21.65    
Weighted average grant date fair value, expired (in dollar per share) 10.69    
Weighted average grant date fair value, ending (in dollar per share) 14.57 $ 12.82  
Weighted average grant date fair value, exercisable (in dollar per share) $ 11.78    
Stock Option Activity, Additional Disclosures      
Weighted average remaining term (in years) 4 years 6 months 14 days 4 years 2 months 15 days  
Weighted average remaining term (in years), exercisable 3 years 3 months 29 days    
Aggregate intrinsic value $ 39.0 $ 25.5  
Aggregate intrinsic value, exercisable $ 8.6