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Revenue Recognition - Narrative (Details) - USD ($)
$ in Millions
3 Months Ended 9 Months Ended
May 29, 2021
May 30, 2020
May 29, 2021
May 30, 2020
Revenue From Contract With Customer [Abstract]        
Percentage of revenues derived from route servicing fees 90.90% 85.70% 91.00% 89.20%
Current assets related to deferred commissions $ 13.9 $ 13.3 $ 13.9 $ 13.3
Noncurrent assets related to deferred commissions 59.1 55.6 59.1 55.6
Amortization expense related to deferred commissions $ 3.6 $ 3.4 $ 10.8 $ 10.2