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Revenue Recognition - Narrative (Details) - USD ($)
$ in Millions
3 Months Ended
Nov. 26, 2022
Nov. 27, 2021
Aug. 27, 2022
Revenue from Contract with Customer [Abstract]      
Percentage of revenues derived from route servicing fees 88.20% 91.20%  
Current assets related to deferred commissions $ 15.6   $ 15.2
Noncurrent assets related to deferred commissions 67.2   $ 65.1
Amortization expense related to deferred commissions $ 4.0 $ 3.8