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Income Taxes - Narrative (Details) - USD ($)
$ in Millions
3 Months Ended 9 Months Ended
May 28, 2022
May 29, 2021
May 28, 2022
Income Tax Disclosure [Abstract]      
Effective income tax rate 25.40% 22.90% 23.60%
Net decrease in unrecognized tax position     $ 0.5