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Goodwill and Intangible Assets (Details) - USD ($)
$ in Millions
3 Months Ended
Nov. 30, 2018
Nov. 30, 2017
Goodwill and Intangible Assets Disclosure [Abstract]    
Amortization of intangible assets $ 7.7 $ 6.6
Finite-Lived Intangible Assets, Net, Amortization Expense, Fiscal Year Maturity [Abstract]    
Amortization expense in fiscal 2019 30.9  
Amortization expense in fiscal 2020 30.9  
Amortization expense in fiscal 2021 28.4  
Amortization expense in fiscal 2022 26.9  
Amortization expense in fiscal 2023 $ 25.6