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Revenue Recognition - Narrative (Details) - USD ($)
$ in Millions
3 Months Ended 6 Months Ended
Feb. 27, 2021
Feb. 29, 2020
Feb. 27, 2021
Feb. 29, 2020
Aug. 29, 2020
Revenue From Contract With Customer [Abstract]          
Percentage of revenues derived from route servicing fees 91.10% 90.20% 91.10% 90.90%  
Current assets related to deferred commissions $ 13.8   $ 13.8   $ 13.3
Noncurrent assets related to deferred commissions 58.3   58.3   $ 55.6
Amortization expense related to deferred commissions $ 3.6 $ 3.4 $ 7.1 $ 6.7