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Goodwill and Intangible Assets - Narrative (Details)
$ in Millions
3 Months Ended 9 Months Ended
Jun. 01, 2020
USD ($)
intangible_asset
May 31, 2020
USD ($)
May 31, 2019
USD ($)
May 31, 2020
USD ($)
May 31, 2019
USD ($)
Goodwill and Intangible Assets Disclosure [Abstract]          
Amortization of intangible assets   $ 10.8 $ 7.7 $ 30.8 $ 23.1
Finite-Lived Intangible Assets, Net, Amortization Expense, Fiscal Year Maturity [Abstract]          
Amortization expense in fiscal 2020   41.5   41.5  
Amortization expense in fiscal 2021   40.1   40.1  
Amortization expense in fiscal 2022   40.0   40.0  
Amortization expense in fiscal 2023   38.9   38.9  
Amortization expense in fiscal 2024   $ 38.0   $ 38.0  
Subsequent Event | Trade Names          
Indefinite-lived Intangible Assets [Line Items]          
Number of intangible assets | intangible_asset 13        
Carrying value of trade names $ 174.7        
Impairment charge $ 1.4        
Number of impaired intangible assets | intangible_asset 1        
Number of intangible assets whose fair values exceeded carrying values | intangible_asset 12        
Growth rate | Minimum | Subsequent Event          
Indefinite-lived Intangible Assets [Line Items]          
Intangible asset measurement input (percent) 3.00%        
Royalty rates | Minimum | Subsequent Event          
Indefinite-lived Intangible Assets [Line Items]          
Intangible asset measurement input (percent) 1.00%        
Royalty rates | Maximum | Subsequent Event          
Indefinite-lived Intangible Assets [Line Items]          
Intangible asset measurement input (percent) 4.00%        
Discount rate | Minimum | Subsequent Event          
Indefinite-lived Intangible Assets [Line Items]          
Intangible asset measurement input (percent) 10.00%        
Discount rate | Maximum | Subsequent Event          
Indefinite-lived Intangible Assets [Line Items]          
Intangible asset measurement input (percent) 13.00%