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Share-based Compensation - Schedule of Weighted Average Assumptions (Details) - Stock Appreciation Rights (SARs)
12 Months Ended
Aug. 27, 2022
Aug. 28, 2021
Aug. 29, 2020
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Risk-free interest rate 1.27% 0.47% 1.69%
Expected dividend yield 0.60% 0.58% 0.50%
Expected life in years 5 years 2 months 1 day 5 years 8 months 12 days 5 years 7 months 6 days
Expected volatility 28.40% 27.50% 22.40%