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Share-Based Compensation - Share-based Compensation Expense (Details) - USD ($)
$ in Millions
12 Months Ended
Sep. 30, 2018
Sep. 30, 2017
Sep. 30, 2016
Disclosure of Compensation Related Costs, Share-based Payments [Abstract]      
Allocated Share-based Compensation Expense $ 6.6 $ 6.3 $ 5.1