Stock-Based Compensation (Details) - USD ($) shares in Millions, $ in Millions	3 Months Ended		9 Months Ended
	May 27, 2023	May 28, 2022	May 27, 2023	May 28, 2022	Dec. 11, 2018
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Stock-based compensation	$ 1.7	$ 5.6	$ 8.2	$ 12.5
Incentive Compensation Plan 2019
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Number of awards issued under the plan (in shares)					4.1