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Share-Based Compensation - Stock Options Activity (Details) - USD ($)
$ / shares in Units, $ in Millions
12 Months Ended
Sep. 30, 2021
Sep. 30, 2020
Sep. 30, 2019
Share-based Payment Arrangement [Abstract]      
Shares available for grant, Beginning (in shares) 724,483    
Number of additional shares authorized (in shares) 1,000,000    
Stock options granted (in shares) 277,700 0  
Stock options forfeited in period (in shares) 122,014    
Stock options expired in period (in shares) (in shares) 1,001    
Shares available for grant, Ending (in shares) 1,569,798 724,483  
Number of Options Outstanding      
Number of options outstanding, Beginning (in shares) 1,408,036    
Number of options outstanding, granted (in shares) 277,700 0  
Number of options outstanding, exercised (in shares) (333,121)    
Number of options outstanding, forfeited (in shares) 122,014    
Number of options outstanding, expired (in shares) 1,001    
Number of options outstanding, Ending (in shares) 1,229,600 1,408,036  
Number of options outstanding, exercisable (in shares) 237,040    
Weighted Average  Exercise Price      
Weighted average  exercise price, Beginning (in dollar per share) $ 45.17 $ 38.79  
Weighted average  exercise price, granted (in dollar per share) 58.64    
Weighted average  exercise price, exercised (in dollar per share) 28.71    
Weighted average  exercise price, forfeited (in dollar per share) 47.13    
Weighted average  exercise price, expired (in dollar per share) 41.83    
Weighted average  exercise price, exercisable (in dollar per share) 31.83    
Weighted Average Grant Date Fair Value      
Weighted average grant date fair value, Beginning (in dollar per share) 11.38    
Weighted average grant date fair value, granted (in dollar per share) 19.83 0.00 $ 10.47
Weighted average grant date fair value, exercised (in dollar per share) 12.74    
Weighted average grant date fair value, forfeited (in dollar per share) 12.22    
Weighted average grant date fair value, expired (in dollar per share) 9.04    
Weighted average grant date fair value, Ending (in dollar per share) 12.82 $ 11.38  
Weighted average grant date fair value, exercisable (in dollar per share) $ 11.94    
Stock Option Activity, Additional Disclosures      
Weighted average remaining term (in years) 4 years 2 months 15 days 4 years 1 month 28 days  
Weighted average remaining term (in years), exercisable 6 months 21 days    
Aggregate intrinsic value $ 25.5 $ 17.4  
Aggregate intrinsic value, exercisable $ 8.1