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Stock-Based Compensation Plans - Stock Option Valuation Assumptions (Details) - $ / shares
12 Months Ended
Aug. 31, 2024
Aug. 26, 2023
Aug. 27, 2022
Share-Based Payment Arrangement [Abstract]      
Expected dividend yield 2.10% 1.90% 1.00%
Risk free interest rate 4.60% 4.10% 1.10%
Expected life of stock options (in years) 5 years 5 years 5 years
Expected stock price volatility 50.80% 50.80% 48.50%
Weighted average fair value of options granted (in dollars per share) $ 25.10 $ 23.94 $ 30.47