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Stock-Based Compensation Plans - Share Awards Activity (Details) - $ / shares
12 Months Ended
Aug. 28, 2021
Aug. 29, 2020
Aug. 31, 2019
Time-based      
Shares      
Beginning balance (in shares) 302,264    
Granted (in shares) 150,275    
Vested (in shares) (92,942)    
Forfeited/canceled (in shares) (28,778)    
Ending balance (in shares) 330,819 302,264  
Weighted Average Fair Value      
Beginning balance (in dollars per share) $ 44.35 $ 38.27  
Granted (in dollars per share)   54.56  
Vested (in dollars per share)   40.36  
Forfeited/canceled (in dollars per share)   42.13  
Ending balance (in dollars per share)   $ 44.35 $ 38.27
Performance-based      
Shares      
Beginning balance (in shares) 188,992    
Granted (in shares) 97,996    
Vested (in shares) (26,515) 0 0
Forfeited/canceled (in shares) (32,722)    
Ending balance (in shares) 227,751 188,992  
Weighted Average Fair Value      
Beginning balance (in dollars per share) $ 45.81 $ 40.73  
Granted (in dollars per share)   54.49  
Vested (in dollars per share)   45.18  
Forfeited/canceled (in dollars per share)   42.97  
Ending balance (in dollars per share)   $ 45.81 $ 40.73