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Basis of Presentation (Details) - USD ($)
shares in Millions, $ in Millions
 3 Months Ended 9 Months Ended
May 27, 2023
May 28, 2022
May 27, 2023
May 28, 2022
Nov. 26, 2022
Aug. 27, 2022
New Accounting Pronouncements or Change in Accounting Principle [Line Items]            
Decrease in additional paid-in capital $ (195.5)   $ (195.5)     $ (256.3)
Long-term debt, net 591.7   591.7     545.9
Decrease in deferred income tax liability 0.0   0.0     (6.1)
Increase in retained earnings $ 1,713.4   1,713.4     $ 1,537.5
Reduction of non-cash interest expense   $ (3.9) $ 0.0 $ (11.2)    
Dilutive impact of convertible notes (in shares) 4.7 0.0 4.7 0.2    
Accounting Standards Update 2020-06            
New Accounting Pronouncements or Change in Accounting Principle [Line Items]            
Decrease in additional paid-in capital         $ 62.0  
Long-term debt, net         43.8  
Decrease in deferred income tax liability         10.8  
Increase in retained earnings         $ 29.0  
Reduction of non-cash interest expense $ (3.9)   $ (11.2)      
Dilutive impact of convertible notes (in shares)     4.7