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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. 31, 2024
Aug. 26, 2023
Goodwill and Intangible Assets Disclosure [Abstract]    
Beginning balance $ 647,900 $ 457,259
Purchase price adjustments recorded during the period 900 190,777
Other 50 (136)
Ending balance $ 648,850 $ 647,900