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Revenue Recognition - Narrative (Details) - USD ($)
$ in Millions
3 Months Ended 6 Months Ended
Feb. 25, 2023
Feb. 26, 2022
Feb. 25, 2023
Feb. 26, 2022
Aug. 27, 2022
Revenue from Contract with Customer [Abstract]          
Percentage of revenues derived from route servicing fees 88.40% 91.50% 88.30% 91.40%  
Current assets related to deferred commissions $ 15.9   $ 15.9   $ 15.2
Noncurrent assets related to deferred commissions 68.0   68.0   $ 65.1
Amortization expense related to deferred commissions $ 4.1 $ 3.8 $ 8.1 $ 7.6