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Stock-Based Compensation (Details) - USD ($)
shares in Millions, $ in Millions
3 Months Ended
Nov. 26, 2022
Nov. 27, 2021
Dec. 11, 2018
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Stock-based compensation $ 3.0 $ 2.7  
Incentive Compensation Plan 2019      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Number of awards issued under the plan (in shares)     4.1