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Business Combinations - Schedule of Preliminary Fair Values Assigned (Details) - USD ($)
$ in Millions
Aug. 26, 2023
Aug. 27, 2022
Aug. 31, 2021
Aug. 28, 2021
Business Acquisition [Line Items]        
Goodwill $ 514.5 $ 484.2   $ 348.1
Barletta        
Business Acquisition [Line Items]        
Cash     $ 11.9  
Other current assets     24.6  
Property, plant, and equipment     17.3  
Goodwill     136.1  
Other intangible assets     111.4  
Total assets acquired     301.3  
Accounts payable     7.2  
Product warranties     4.7  
Other current liabilities     3.1  
Total liabilities assumed     15.0  
Total purchase price     $ 286.3