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Goodwill and Other Intangible Assets - Schedule of Changes in Carrying Amount of Goodwill (Details) - USD ($)
$ in Thousands
12 Months Ended
Aug. 28, 2021
Aug. 29, 2020
Goodwill And Intangible Assets Disclosure [Abstract]    
Beginning balance $ 424,844 $ 401,178
Goodwill recorded during the period 4,533 23,544
Other 161 122
Ending balance $ 429,538 $ 424,844