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Revenue Recognition - Narrative (Details) - USD ($)
$ in Millions
3 Months Ended 6 Months Ended
Feb. 24, 2024
Feb. 25, 2023
Feb. 24, 2024
Feb. 25, 2023
Aug. 26, 2023
Revenue from Contract with Customer [Abstract]          
Percentage of revenues derived from route servicing fees 84.00% 84.10% 84.20% 84.30%  
Current assets related to deferred commissions $ 17.3   $ 17.3   $ 16.5
Noncurrent assets related to deferred commissions 75.0   75.0   $ 70.4
Amortization expense related to deferred commissions $ 4.5 $ 4.1 $ 8.8 $ 8.1