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Property, Plant, and Equipment (Details) - USD ($)
$ in Millions
3 Months Ended 9 Months Ended
May 25, 2024
May 27, 2023
May 25, 2024
May 27, 2023
Aug. 26, 2023
Property, Plant and Equipment [Line Items]          
Property, plant, and equipment, gross $ 560.6   $ 560.6   $ 530.4
Less: Accumulated depreciation 225.1   225.1   203.1
Property, plant, and equipment, net 335.5   335.5   327.3
Depreciation 8.9 $ 7.6 25.5 $ 20.9  
Land          
Property, Plant and Equipment [Line Items]          
Property, plant, and equipment, gross 14.6   14.6   14.6
Buildings and building improvements          
Property, Plant and Equipment [Line Items]          
Property, plant, and equipment, gross 277.5   277.5   247.3
Machinery and equipment          
Property, Plant and Equipment [Line Items]          
Property, plant, and equipment, gross 168.7   168.7   159.3
Software          
Property, Plant and Equipment [Line Items]          
Property, plant, and equipment, gross 72.0   72.0   52.7
Transportation          
Property, Plant and Equipment [Line Items]          
Property, plant, and equipment, gross 7.8   7.8   7.2
Construction in progress          
Property, Plant and Equipment [Line Items]          
Property, plant, and equipment, gross $ 20.0   $ 20.0   $ 49.3