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Goodwill and Other Intangible Assets - Schedule of Estimated Future Amortization Expense (Details) - USD ($)
$ in Thousands
Aug. 26, 2023
Aug. 27, 2022
Goodwill and Intangible Assets Disclosure [Abstract]    
2024 $ 26,507  
2025 24,578  
2026 21,731  
2027 15,106  
2028 13,561  
Thereafter 44,135  
Net Carrying Amount $ 145,618 $ 84,973