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Stock-Based Compensation Plans - Stock Option Valuation Assumptions (Details) - $ / shares
12 Months Ended
Aug. 26, 2023
Aug. 27, 2022
Aug. 28, 2021
Share-Based Payment Arrangement [Abstract]      
Expected dividend yield 1.90% 1.00% 0.80%
Risk free interest rate 4.10% 1.10% 0.30%
Expected life of stock options (in years) 5 years 5 years 5 years
Expected stock price volatility 50.80% 48.50% 48.60%
Weighted average fair value of options granted (in dollars per share) $ 23.94 $ 30.47 $ 21.65