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Share-Based Compensation - Stock Option Plan (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 692,652 588,020  
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
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, Total Intrinsic Value $ 700,000 $ 2,100,000 $ 2,600,000