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Leases - Operating Lease Cost (Details) - USD ($)
$ in Millions
12 Months Ended
Aug. 26, 2023
Aug. 27, 2022
Aug. 28, 2021
Leases [Abstract]      
Operating lease expense $ 10.3 $ 9.6 $ 5.8
Finance lease cost:      
Depreciation of lease assets 1.0 0.8 0.6
Interest on lease liabilities 0.5 0.4 0.3
Total lease cost $ 11.8 $ 10.8 $ 6.7