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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. 27, 2022
Aug. 28, 2021
Goodwill and Intangible Assets Disclosure [Abstract]    
Beginning balance $ 429,538 $ 424,844
Goodwill recorded during the period 27,964 4,533
Other (243) 161
Ending balance $ 457,259 $ 429,538