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Stock-Based Compensation Plans - Share Awards Activity (Details) - $ / shares
12 Months Ended
Aug. 29, 2020
Aug. 31, 2019
Aug. 25, 2018
Time-based      
Shares      
Beginning balance (in shares) 215,506    
Granted (in shares) 166,440    
Vested (in shares) (77,550)    
Forfeited/canceled (in shares) (2,132)    
Ending balance (in shares) 302,264 215,506  
Weighted Average Fair Value      
Beginning balance (in dollars per share) $ 38.27 $ 33.40  
Granted (in dollars per share)   42.76  
Vested (in dollars per share)   34.45  
Forfeited/canceled (in dollars per share)   36.08  
Ending balance (in dollars per share)   $ 38.27 $ 33.40
Performance-based      
Shares      
Beginning balance (in shares) 207,433    
Granted (in shares) 64,914    
Vested (in shares) (65,302) 0 0
Forfeited/canceled (in shares) (18,053)    
Ending balance (in shares) 188,992 207,433  
Weighted Average Fair Value      
Beginning balance (in dollars per share) $ 40.73 $ 33.87  
Granted (in dollars per share)   47.93  
Vested (in dollars per share)   28.21  
Forfeited/canceled (in dollars per share)   32.79  
Ending balance (in dollars per share)   $ 40.73 $ 33.87