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Acquisitions - Schedule of Acquisition of Business (Details)
$ in Thousands
12 Months Ended
Aug. 28, 2021
USD ($)
Business
Aug. 29, 2020
USD ($)
Business
Aug. 31, 2019
USD ($)
Business
Business Acquisition [Line Items]      
Goodwill $ 429,538 $ 424,844 $ 401,178
Aggregate Information Relating to Acquisition of Businesses      
Business Acquisition [Line Items]      
Number of businesses acquired | Business 8 8 6
Tangible assets acquired $ 812 $ 6,370 $ 322
Goodwill 4,533 23,544 3,929
Customer contracts 3,219 12,697 1,344
Other intangible assets 179 594 118
Liabilities assumed   (1,872)  
Acquisition of businesses $ 8,743 $ 41,333 $ 5,713