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Property, Plant, and Equipment (Details) - USD ($)
$ in Millions
3 Months Ended
Nov. 25, 2023
Nov. 26, 2022
Aug. 26, 2023
Property, Plant and Equipment [Line Items]      
Property, plant, and equipment, gross $ 541.6   $ 530.4
Less: Accumulated depreciation 210.5   203.1
Property, plant, and equipment, net 331.1   327.3
Depreciation 8.1 $ 6.6  
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 248.0   247.3
Machinery and equipment      
Property, Plant and Equipment [Line Items]      
Property, plant, and equipment, gross 163.2   159.3
Software      
Property, Plant and Equipment [Line Items]      
Property, plant, and equipment, gross 52.7   52.7
Transportation      
Property, Plant and Equipment [Line Items]      
Property, plant, and equipment, gross 7.2   7.2
Construction in progress      
Property, Plant and Equipment [Line Items]      
Property, plant, and equipment, gross $ 55.9   $ 49.3