Property, Plant, and Equipment (Details) - USD ($) $ in Thousands	Aug. 27, 2022	Aug. 28, 2021
Property, Plant and Equipment [Line Items]
Property, plant, and equipment, gross	$ 455,333	$ 351,938
Less: Accumulated depreciation	179,114	160,511
Property, plant, and equipment, net	276,219	191,427
Land
Property, Plant and Equipment [Line Items]
Property, plant, and equipment, gross	14,626	9,111
Buildings and building improvements
Property, Plant and Equipment [Line Items]
Property, plant, and equipment, gross	171,035	147,629
Machinery and equipment
Property, Plant and Equipment [Line Items]
Property, plant, and equipment, gross	142,574	121,911
Software
Property, Plant and Equipment [Line Items]
Property, plant, and equipment, gross	43,792	36,815
Transportation
Property, Plant and Equipment [Line Items]
Property, plant, and equipment, gross	6,509	5,335
Construction in progress
Property, Plant and Equipment [Line Items]
Property, plant, and equipment, gross	$ 76,797	$ 31,137