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Revenue Recognition - Narrative (Details) - USD ($)
$ in Millions
3 Months Ended 6 Months Ended
Feb. 26, 2022
Feb. 27, 2021
Feb. 26, 2022
Feb. 27, 2021
Aug. 28, 2021
Revenue From Contract With Customer [Abstract]          
Percentage of revenues derived from route servicing fees 91.50% 91.10% 91.40% 91.10%  
Current assets related to deferred commissions $ 14.7   $ 14.7   $ 14.2
Noncurrent assets related to deferred commissions 63.4   63.4   $ 60.6
Amortization expense related to deferred commissions $ 3.8 $ 3.6 $ 7.6 $ 7.1