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Property, Plant, and Equipment (Details) - USD ($)
$ in Thousands
3 Months Ended
Nov. 27, 2021
Nov. 28, 2020
Aug. 28, 2021
Property, Plant and Equipment [Line Items]      
Property, plant, and equipment, gross $ 388,736   $ 351,938
Less: Accumulated depreciation 164,607   160,511
Property, plant, and equipment, net 224,129   191,427
Depreciation 5,306 $ 4,160  
Land      
Property, Plant and Equipment [Line Items]      
Property, plant, and equipment, gross 10,697   9,111
Buildings and building improvements      
Property, Plant and Equipment [Line Items]      
Property, plant, and equipment, gross 163,731   147,629
Machinery and equipment      
Property, Plant and Equipment [Line Items]      
Property, plant, and equipment, gross 126,093   121,911
Software      
Property, Plant and Equipment [Line Items]      
Property, plant, and equipment, gross 36,099   36,815
Transportation      
Property, Plant and Equipment [Line Items]      
Property, plant, and equipment, gross 5,972   5,335
Construction in progress      
Property, Plant and Equipment [Line Items]      
Property, plant, and equipment, gross $ 46,144   $ 31,137