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Stock-Based Compensation Plans - Stock Option Valuation Assumptions (Details) - $ / shares
12 Months Ended
Aug. 28, 2021
Aug. 29, 2020
Aug. 31, 2019
Share-based Payment Arrangement [Abstract]      
Expected dividend yield 0.80% 0.90% 1.30%
Risk free interest rate 0.30% 1.70% 3.00%
Expected life of stock options (in years) 5 years 5 years 5 years
Expected stock price volatility 48.60% 41.20% 39.10%
Weighted average fair value of options granted (in dollars per share) $ 21.65 $ 17.18 $ 11.09