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Fair Value Measurements - Narrative (Details)
$ in Millions
12 Months Ended
Aug. 31, 2023
USD ($)
intangible_asset
Aug. 31, 2021
USD ($)
Jun. 01, 2023
USD ($)
Feb. 28, 2023
USD ($)
Aug. 31, 2022
USD ($)
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]          
Cost basis of investment       $ 2.5  
Credit loss         $ 0.0
Operating lease right-of-use assets $ 84.1       74.9
Operating lease asset group impairment charge 4.3 $ 0.0      
Estimate of Fair Value Measurement | Revolving credit facility borrowings | Credit Facility          
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]          
Short-term debt, fair value 0.0       18.0
Estimate of Fair Value Measurement | Senior Unsecured Notes Payable          
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]          
Carrying and estimated fair value of financial instruments $ 401.4       $ 399.2
Trade Names          
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]          
Number of impaired intangible assets | intangible_asset 6        
Indefinite-lived trade names     $ 46.5    
Intangible asset impairment charge $ 14.0        
Number of unimpaired intangible assets | intangible_asset 7        
Trade Names | Long-term Growth Rate          
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]          
Intangible asset fair value measurement inputs (percent) 0.025        
Trade Names | Discount Rate | Minimum          
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]          
Intangible asset fair value measurement inputs (percent)     0.11    
Trade Names | Discount Rate | Maximum          
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]          
Intangible asset fair value measurement inputs (percent)     0.13    
Trade Names | Royalty Rate | Minimum          
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]          
Intangible asset fair value measurement inputs (percent) 0.01        
Trade Names | Royalty Rate | Maximum          
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]          
Intangible asset fair value measurement inputs (percent) 0.03        
Trade Names No Longer With Indefinite Lives          
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]          
No longer indefinite lives | intangible_asset 5        
Amortization period     15 years    
Fair value measured on nonrecurring basis | Level 3          
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]          
Indefinite-lived trade names $ 46.5        
Operating lease right-of-use assets 3.4        
Operating lease asset group impairment charge $ 4.3