Stock-Based Compensation (Details) - USD ($) shares in Millions, $ in Millions	3 Months Ended		9 Months Ended
	May 25, 2024	May 27, 2023	May 25, 2024	May 27, 2023	Dec. 14, 2023
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Stock-based compensation	$ 3.4	$ 1.7	$ 11.5	$ 8.2
Incentive Compensation Plan 2019
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Number of awards issued under the plan (in shares)					2.4