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Share-based Compensation - Narrative (Details) - USD ($)
12 Months Ended
Oct. 27, 2014
Aug. 28, 2021
Aug. 29, 2020
Aug. 31, 2019
Oct. 30, 2010
Nov. 30, 1996
Stock Appreciation Rights (SARs)            
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]            
Period awards become fully vested or exercisable   5 years        
Expiration period   10 years        
Weighted average fair values of Share-Based Awards granted (in dollars per share)   $ 42.63 $ 46.58 $ 46.20    
Stock Appreciation Rights (SARs) | Tranche One            
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]            
Percentage vested after each anniversary of the grant date   20.00%        
Stock Appreciation Rights (SARs) | Tranche Two            
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]            
Percentage vested after each anniversary of the grant date   60.00%        
Stock Appreciation Rights (SARs) | Tranche Three            
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]            
Percentage vested after each anniversary of the grant date   20.00%        
Stock Appreciation Rights (SARs) | Cliff Vesting            
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]            
Period awards become fully vested or exercisable   5 years        
Share-Based Awards            
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]            
Total compensation cost not yet recognized related to non-vested awards   $ 14,600        
Period for recognition   1 year 10 months 24 days        
Time-Based Restricted Stock Units | Tranche One            
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]            
Percentage vested after each anniversary of the grant date   20.00%        
Period awards become fully vested or exercisable   5 years        
Time-Based Restricted Stock Units | Tranche Two            
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]            
Percentage vested after each anniversary of the grant date   33.00%        
Period awards become fully vested or exercisable   3 years        
Time-Based Restricted Stock Units | Tranche Three            
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]            
Period awards become fully vested or exercisable   5 years        
Time-Based Restricted Stock Units | Cliff Vesting            
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]            
Period awards become fully vested or exercisable   5 years        
Time-Based Restricted Stock Units | Tranche Four            
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]            
Percentage vested after each anniversary of the grant date   60.00%        
Time-Based Restricted Stock Units | Tranche Five            
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]            
Percentage vested after each anniversary of the grant date   20.00%        
Non-Employee Directors | Unrestricted Stock            
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]            
Shares granted (in shares)   0 0 291    
The 1996 Plan            
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]            
Number of shares reserved for issuance (in shares)           1,500,000
The 2010 Plan            
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]            
Number of shares reserved for issuance (in shares)         600,000  
Number of additional shares reserved for issuance (in shares) 750,000          
Shares available for future grants (in shares)   251,713        
The 2010 Plan | Non-Employee Directors | Stock Appreciation Rights (SARs)            
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]            
Shares granted (in shares)   5,000 5,000 5,000