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Property, Plant, and Equipment (Details) - USD ($)
$ in Millions
3 Months Ended
Nov. 26, 2022
Nov. 27, 2021
Aug. 27, 2022
Property, Plant and Equipment [Line Items]      
Property, plant, and equipment, gross $ 480.1   $ 455.3
Less: Accumulated depreciation 185.3   179.1
Property, plant, and equipment, net 294.8   276.2
Depreciation 6.6 $ 5.3  
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 197.8   171.0
Machinery and equipment      
Property, Plant and Equipment [Line Items]      
Property, plant, and equipment, gross 145.1   142.6
Software      
Property, Plant and Equipment [Line Items]      
Property, plant, and equipment, gross 43.8   43.8
Transportation      
Property, Plant and Equipment [Line Items]      
Property, plant, and equipment, gross 6.5   6.5
Construction in progress      
Property, Plant and Equipment [Line Items]      
Property, plant, and equipment, gross $ 72.3   $ 76.8