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Goodwill and Other Intangible Assets - Schedule of Estimated Future Amortization Expense (Details) - USD ($)
$ in Thousands
Aug. 27, 2022
Aug. 28, 2021
Goodwill and Intangible Assets Disclosure [Abstract]    
2022 $ 13,404  
2023 11,840  
2024 9,400  
2025 9,385  
2026 8,133  
Thereafter 32,811  
Net Carrying Amount $ 84,973 $ 84,638