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Share-Based Compensation - Share-Based Compensation Table (Details) - USD ($)
12 Months Ended
Sep. 30, 2019
Sep. 30, 2018
Sep. 30, 2017
Disclosure of Compensation Related Costs, Share-based Payments [Abstract]      
Share-based Compensation Arrangement by Share-based Payment Award, Number of Shares Authorized 2,000,000    
Share-based Compensation Arrangement by Share-based Payment Award, Number of Shares Available for Grant 588,020    
Share-based Compensation Arrangement by Share-based Payment Award, Options, Outstanding, Number 835,454    
Share-based Compensation Arrangement by Share-based Payment Award, Options, Grants in Period, Gross (922,000)    
Share-based Compensation Arrangement by Share-based Payment Award, Options, Forfeitures in Period 25,048    
Share-based Compensation Arrangement by Share-based Payment Award, Options, Other Increases (Decreases) in Period (46,444)    
Share-based Compensation Arrangement by Share-based Payment Award, Options, Expirations in Period (1,584)    
Share-based Compensation Arrangement by Share-based Payment Award, Number of Shares Available for Grant 692,652 588,020  
Share-based Compensation Arrangement by Share-based Payment Award, Options, Outstanding, Number 1,684,378 835,454  
Share-based Compensation Arrangement by Share-based Payment Award, Options, Exercisable, Number 472,424    
Share-based Compensation Arrangement by Share-based Payment Award, Options, Outstanding, Weighted Average Exercise Price $ 37.59 $ 29.27  
Share-based Compensation Arrangements by Share-based Payment Award, Options, Grants in Period, Weighted Average Exercise Price 44.31    
Share-based Compensation Arrangements by Share-based Payment Award, Options, Exercises in Period, Weighted Average Exercise Price 25.04    
Share-based Compensation Arrangements by Share-based Payment Award, Options, Forfeitures in Period, Weighted Average Exercise Price 31.31    
Share-based Compensation Arrangements by Share-based Payment Award, Options, Expirations in Period, Weighted Average Exercise Price 33.83    
Share-based Compensation Arrangement by Share-based Payment Award, Options, Exercisable, Weighted Average Exercise Price 28.96    
Share-based Compensation Arrangement by Share-based Payment Award, Options, Outstanding, Weighted Average Grant Date Fair Value 11.32 11.93  
Share-based Compensation Arrangement by Share-based Payment Award, Options, Grants in Period, Weighted Average Grant Date Fair Value 10.47 $ 9.79 $ 8.67
Share-based Compensation Arrangement by Share-based Payment Award, Options, Excrecises in Period, Weighted Average Grant Date Fair Value 5.21    
Share-based Compensation Arrangement by Share-based Payment Award, Options, Forfeited in Period, Weighted Average Grant Date Fair Value 11.91    
Share-based Compensation Arrangement by Share-based Payment Award, Options, Expired in Period, Weighted Average Grant Date Fair Value 7.46    
Share-based Compensation Arrangement by Share-based Payment Award, Options, Excercisable, Weighted Average Grant Date Fair Value $ 12.27    
Share-based Compensation Arrangement by Share-based Payment Award, Options, Outstanding, Weighted Average Remaining Contractual Term 4 years 7 months 13 days 3 years 4 days  
Share-based Compensation Arrangement by Share-based Payment Award, Options, Exercisable, Weighted Average Remaining Contractual Term 2 years 29 days    
Share-based Compensation Arrangement by Share-based Payment Award, Options, Outstanding, Intrinsic Value $ 9,200,000 $ 15,900,000  
Share-based Compensation Arrangement by Share-based Payment Award, Number of Additional Shares Authorized 1,000,000    
Share-based Compensation Arrangement by Share-based Payment Award, Options, Exercisable, Intrinsic Value $ 5,800,000    
Employee Service Share-based Compensation, Nonvested Awards, Total Compensation Cost Not yet Recognized, Stock Options $ 9,900,000    
Employee Service Share-based Compensation, Nonvested Awards, Total Compensation Cost Not yet Recognized, Period for Recognition 5 years 7 months 10 days    
Share-based Compensation Arrangement by Share-based Payment Award, Options, Exercises in Period, Intrinsic Value $ 700,000 $ 2,100,000 $ 2,600,000