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Revenue Recognition - Narrative (Details) - USD ($)
$ in Millions
3 Months Ended
Nov. 25, 2023
Nov. 26, 2022
Aug. 26, 2023
Revenue from Contract with Customer [Abstract]      
Percentage of revenues derived from route servicing fees 84.40% 84.50%  
Current assets related to deferred commissions $ 16.9   $ 16.5
Noncurrent assets related to deferred commissions 73.2   $ 70.4
Amortization expense related to deferred commissions $ 4.3 $ 4.0