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Property, Plant, and Equipment (Details) - USD ($)
$ in Millions
Aug. 31, 2024
Aug. 26, 2023
Property, Plant and Equipment [Line Items]    
Property, plant, and equipment, gross $ 570.0 $ 530.4
Less: Accumulated depreciation 231.1 203.1
Property, plant, and equipment, net 338.9 327.3
Land    
Property, Plant and Equipment [Line Items]    
Property, plant, and equipment, gross 14.6 14.6
Buildings and building improvements    
Property, Plant and Equipment [Line Items]    
Property, plant, and equipment, gross 279.3 247.3
Machinery and equipment    
Property, Plant and Equipment [Line Items]    
Property, plant, and equipment, gross 171.8 159.3
Software    
Property, Plant and Equipment [Line Items]    
Property, plant, and equipment, gross 72.0 52.7
Transportation    
Property, Plant and Equipment [Line Items]    
Property, plant, and equipment, gross 7.8 7.2
Construction in progress    
Property, Plant and Equipment [Line Items]    
Property, plant, and equipment, gross $ 24.5 $ 49.3