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Revenue Recognition - Narrative (Details) - USD ($)
$ in Millions
3 Months Ended 9 Months Ended
May 25, 2024
May 27, 2023
May 25, 2024
May 27, 2023
Aug. 26, 2023
Revenue from Contract with Customer [Abstract]          
Percentage of revenues derived from route servicing fees 83.80% 84.10% 84.10% 84.20%  
Current assets related to deferred commissions $ 17.7   $ 17.7   $ 16.5
Noncurrent assets related to deferred commissions 77.0   77.0   $ 70.4
Amortization expense related to deferred commissions $ 4.6 $ 4.2 $ 13.4 $ 12.3