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Property, Plant, and Equipment (Details) - USD ($)
$ in Millions
3 Months Ended 6 Months Ended
Feb. 24, 2024
Feb. 25, 2023
Feb. 24, 2024
Feb. 25, 2023
Aug. 26, 2023
Property, Plant and Equipment [Line Items]          
Property, plant, and equipment, gross $ 552.1   $ 552.1   $ 530.4
Less: Accumulated depreciation 218.4   218.4   203.1
Property, plant, and equipment, net 333.7   333.7   327.3
Depreciation 8.5 $ 6.7 16.6 $ 13.3  
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 268.3   268.3   247.3
Machinery and equipment          
Property, Plant and Equipment [Line Items]          
Property, plant, and equipment, gross 167.3   167.3   159.3
Software          
Property, Plant and Equipment [Line Items]          
Property, plant, and equipment, gross 53.4   53.4   52.7
Transportation          
Property, Plant and Equipment [Line Items]          
Property, plant, and equipment, gross 7.4   7.4   7.2
Construction in progress          
Property, Plant and Equipment [Line Items]          
Property, plant, and equipment, gross $ 41.1   $ 41.1   $ 49.3