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Stock-Based Compensation Plans - Stock Option Valuation Assumptions (Details) - $ / shares
12 Months Ended
Aug. 27, 2022
Aug. 28, 2021
Aug. 29, 2020
Share-Based Payment Arrangement [Abstract]      
Expected dividend yield 1.00% 0.80% 0.90%
Risk free interest rate 1.10% 0.30% 1.70%
Expected life of stock options (in years) 5 years 5 years 5 years
Expected stock price volatility 48.50% 48.60% 41.20%
Weighted average fair value of options granted (in dollars per share) $ 30.47 $ 21.65 $ 17.18