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Revenue Recognition - Narrative (Details) - USD ($)
$ in Millions
3 Months Ended
Nov. 27, 2021
Nov. 28, 2020
Revenue From Contract With Customer [Abstract]    
Percentage of revenues derived from route servicing fees 91.20% 91.00%
Current assets related to deferred commissions $ 14.6 $ 14.2
Noncurrent assets related to deferred commissions 62.6 60.6
Amortization expense related to deferred commissions $ 3.8 $ 3.5