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Debt and Lines of Credit - Lines of Credit (Details)
$ in Millions
Jun. 29, 2018
USD ($)
Aug. 31, 2021
USD ($)
Aug. 31, 2020
USD ($)
Line of Credit Facility [Line Items]      
Borrowings outstanding under term loan facility   $ 494.3 $ 401.1
Revolving credit facility borrowings      
Line of Credit Facility [Line Items]      
Outstanding letters of credit   4.1  
Lines of Credit      
Line of Credit Facility [Line Items]      
Minimum interest coverage ratio 2.50    
Maximum leverage ratio 3.50    
Outstanding letters of credit   4.1  
Lines of Credit | Minimum      
Line of Credit Facility [Line Items]      
Commitment fees rate 0.125%    
Lines of Credit | Maximum      
Line of Credit Facility [Line Items]      
Commitment fees rate 0.25%    
Lines of Credit | New Revolving Credit Facility      
Line of Credit Facility [Line Items]      
Revolving credit facility $ 400.0    
Term of facility 5 years    
Lines of Credit | Borrowings under Term Loan Facility      
Line of Credit Facility [Line Items]      
Revolving credit facility $ 400.0    
Lines of Credit | Revolving credit facility borrowings      
Line of Credit Facility [Line Items]      
Additional borrowing capacity under revolving credit facility   395.9  
Unsecured Term Loan | Borrowings under Term Loan Facility      
Line of Credit Facility [Line Items]      
Borrowings outstanding under term loan facility   $ 0.0 $ 395.0
Eurocurrency Rate | Lines of Credit | New Revolving Credit Facility | Minimum      
Line of Credit Facility [Line Items]      
Applicable margins as determined by leverage ratio 1.00%    
Eurocurrency Rate | Lines of Credit | New Revolving Credit Facility | Maximum      
Line of Credit Facility [Line Items]      
Applicable margins as determined by leverage ratio 1.375%    
Base Rate | Lines of Credit | New Revolving Credit Facility | Minimum      
Line of Credit Facility [Line Items]      
Applicable margins as determined by leverage ratio 0.00%    
Base Rate | Lines of Credit | New Revolving Credit Facility | Maximum      
Line of Credit Facility [Line Items]      
Applicable margins as determined by leverage ratio 0.375%